Download Class Field Theory by Emil Artin and John Tate PDF

By Emil Artin and John Tate

This vintage e-book, initially released in 1968, is predicated on notes of a year-long seminar the authors ran at Princeton college. the first target of the e-book used to be to offer a slightly entire presentation of algebraic facets of world classification box idea, and the authors finished this aim spectacularly: for greater than forty years given that its first booklet, the publication has served as an final resource for lots of generations of mathematicians. during this revised variation, mathematical additions complementing the exposition within the unique textual content are made. the recent version additionally comprises numerous new footnotes, extra references, and historic reviews.

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LEVEL AUTOS 39 48 39 48 117 48 117 12 117 16 117 12 39 24 39 8 117 8 117 8 MASS 1/24 0= 120 GENUS. 1 1 1 2 2 2 2 3 3 3 3 4 4 4 F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 10 1 0 0 0 0 0 1 1 3 3 0 1 1 0 0 0 2 2 2 2 1 1 1 2 2 0 1 1 1 15 1 1 0 0 0 0 1 1 2 4 0 0 0 0 1 0 1 1 2 6 1 1 0 0 0 0 1 2 2 2 2 1 3 0 0 0 1 1 1 8 0 0 0 0 1 1 1 1 2 5 1 0 0 0 0 0 0 0 0 1 0 1 2 2 2 0 1 2 2 1 0 2 0 0 0 3 1 1 1 1 2 5 0 0 0 0 1 1 1 1 0 0 3 3 0 0 1 1 4 1 0 0 1 1 2 3 HASSE SYM 1-1-1 1-1-1 1-1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 111 111 111 LEVEL AUTOS 120 48 120 32 120 8 120 96 120 16 120 24 120 16 120 32 120 48 120 16 120 16 120 32 120 16 120 12 MASS 17/96 1/24 1/24 1/3 1/3 1/8 1/24 1/8 5/32 5/32 1/4 1/6 1/4 17/96 17/96 17/96 30 Quaternary Quadratic Forms D= 121 GENUS' 1 1 1 D= 124 GENUS' 1 1 1 1 1 1 2 2 2 D= 125 GENUS' 1 1 1 1 1 2 3 4 D= 128 GENUSt 1 1 1 1 2 2 3 4 5 5 6 6 7 8 9 10 11 12 13 14 D= 129 GENUS' 1 1 1 1 2 2 2 2 D= 132 GENUS' 1 1 1 1 1 1 2 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 3 3 0 1 0 0 1 0 4 1 1 1 1 4 1 1 4 0 1 2 2 2 2 2 1 0 1 2 HASSE SYM F11 F22 F33 F44 Fl2 F13 F23 F14 F24 F34 1 1 16 1 1 1 1 0 0 0 1 1 1 1 8 0 0 0 0 0 1 2 4 0 1 1 0 0 0 0 1 2 1 0 2 1 5 0 0 0 1 1 1 1 3 4 0 0 0 3 2 1 1 2 1 2 3 0 0 0 1 2 1 1 2 1 6 0 0 0 1 2 2 3 1 0 1 0 2 0 2 2 0 2 1 1 1 1 3 0 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 11 1 0 0 1 0 1 1 1 0 1 1 1 1 16 0 0 1 2 1 1 1 1 5 0 0 0 1 1 3 4 1 1 0 0 0 1 1 2 2 1 0 1 1 2 0 3 1 2 7 1 1 1 1 2 1 0 2 2 2 2 1 1 -1 -1 1 1 4 1 1 1 1 1 3 0 0 3 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 11 1 0 1 0 0 1 0 0 1 1 1 1 3 3 0 0 0 1 1 1 1 1 4 4 0 0 3 1 2 2 1 1 0 1 0 0 3 1 1 1 16 1 1 0 0 0 0 1 1 2 1 1 2 5 0 0 0 1 1 1 8 0 0 0 0 0 0 1 2 4 1 0 0 0 0 0 0 1 1 2 6 0 1 1 1 1 0 2 2 2 2 1 2 2 0 0 0 7 1 1 2 1 1 0 0 1 1 2 2 1 1 2 1 3 0 0 0 1 1 3 4 1 1 0 0 0 0 1 5 1 1 0 1 1 3 1 3 1 2 2 2 0 0 0 0 0 0 2 4 1 2 2 1 2 0 0 0 1 3 0 0 0 0 0 2 1 3 1 2 2 3 1 1 0 0 1 1 1 2 2 3 0 0 0 0 2 2 2 2 2 2 2 2 3 0 0 0 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 11 1 1 1 0 0 0 0 2 1 1 1 1 1 5 0 0 0 1 2 2 1 1 1 1 3 0 0 2 1 1 1 1 2 2 2 2 2 1 1 2 6 0 1 1 1 0 2 1 1 4 0 1 0 0 1 3 3 4 1 1 1 1 3 0 0 0 1 1 2 2 3 1 0 0 1 2 1 HASSE SYM Fll F22 F33 F44 F12 Fl3 F23 F14 F24 F34 1 0 0 0 0 0 1 1 1 11 7 1 1 1 1 1 2 0 0 0 1 1 1 3 3 0 0 v 0 0 1 1 4 1 0 0 0 0 2 3 1 1 1 4 1 0 0 0 0 3 2 2 3 0 0 1 0 2 2 1 1 0 1 0 0 1 1 1 17 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 111 LEVEL AUTOS 11 11 11 32 72 24 LEVEL AUTOS 124 124 124 124 124 124 124 124 124 96 32 16 8 16 8 24 4 8 LEVEL AUTOS 125 125 125 125 125 25 5 25 24 48 8 12 4 24 240 16 LEVEL AUTOS 128 128 128 128 64 64 32 16 64 64 128 128 32 64 8 64 32 32 32 32 24 8 24 8 96 32 96 32 16 16 12 4 24 24 96 8 32 8 32 96 LEVEL AUTOS 129 129 129 129 129 129 129 129 48 8 8 4 16 8 12 4 LEVEL AUTOS 132 132 132 132 132 132 66 MASS 25/288 48 12 16 24 24 8 96 MASS 5/12 5/12 MASS 25/48 1/24 1/240 1/16 MASS 1/3 1/24 1/96 1/32 1/8 1/3 1/24 1/24 1/96 1/8 1/32 1/8 1/32 1/96 MASS 25/48 25/48 MASS 3/8 1/32 Tables 31 2 3 3 4 4 5 5 5 6 6 6 0= 133 GENUSt 1 1 1 2 2 2 2 0= 136 GENUSt 1 1 1 1 1 2 2 2 2 2 0= 137 GENUSt 1 1 1 1 1 1 0= 140 GENUSt 1 1 1 1 2 2 2 3 3 3 3 4 4 4 0= 141 GENUS' 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 3 2 2 6 9 3 5 3 6 4 2 4 3 3 1 0 0 0 1 0 1 2 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 2 0 1 1 2 -1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 -1 1 2 1 0 0 1 1 2 1 3 1 2 111 1-1-1 1-1-1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 66 66 66 132 132 66 66 66 66 66 66 48 96 48 8 4 32 8 8 32 8 8 1/32 3/8 9/32 9/32 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 17 1 1 0 0 1 0 1 1 1 5 1 0 0 1 2 3 1 2 2 3 0 0 1 1 0 2 1 1 2 1 5 0 0 0 1 0 1 1 2 6 1 0 1 1 0 0 1 1 2 7 1 1 0 0 1 0 1 2 1 3 3 0 2 1 1 3 HASSE SYM -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 LEVEL AUTOS 133 48 133 12 133 4 133 16 133 12 133 12 133 8 MASS 17/48 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 17 1 1 0 0 0 0 1 1 1 9 0 0 0 0 1 1 0 0 1 2 5 1 1 2 0 0 2 2 1 1 3 0 0 0 1 2 3 1 1 1 1 1 2 2 0 1 2 5 0 1 0 1 1 1 0 0 1 1 2 6 1 0 0 1 0 0 4 1 1 3 0 1 1 1 1 0 1 2 2 3 0 0 2 0 1 0 1 2 2 3 1 0 0 0 2 0 HASSE SYM 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 136 96 136 32 136 16 136 8 136 4 136 8 136 24 136 16 136 8 136 8 MASS 23/48 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 1 0 0 0 1 1 1 2 6 0 1 1 1 0 0 1 1 2 7 1 1 1 0 0 0 2 2 1 1 3 0 1 0 -1 1 1 2 2 3 1 1 1 0 0 0 1 2 2 4 1 0 2 0 2 1 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 137 24 137 8 137 12 137 4 137 4 137 4 MASS 1/1 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 0 0 1 0 0 1 1 2 5 1 0 0 0 0 0 1 1 3 3 0 0 0 0 0 1 2 2 4 1 2 1 0 0 1 2 1 1 1 18 1 1 0 1 0 0 1 1 2 1 1 5 0 0 0 1 2 2 2 2 1 1 -1 2 0 0 1 1 2 1 1 1 6 0 0 0 1 1 2 7 1 1 0 0 0 0 1 1 4 1 1 1 1 1 3 0 1 2 2 3 1 0 0 0 0 2 1 1 1 1 9 0 0 0 0 0 1 1 3 4 0 1 0 0 0 3 1 1 4 4 1 1 1 1 0 3 HASSE SYM -1-1 1 -1-1 1 -1-1 1 -1-1 1 1-1-1 1-1-1 1-1-1 111 111 111 111 -1 1-1 -1 1-1 -1 1-1 LEVEL AUTOS 140 24 140 16 140 32 140 16 140 96 140 16 140 8 140 16 140 24 140 32 140 16 140 32 140 8 140 24 MASS 19/96 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 0 0 1 1 1 1 12 0 0 1 1 1 18 1 1 0 0 1 0 1 1 2 1 0 1 6 0 0 0 1 1 4 1 0 0 0 0 1 3 1 1 0 0 0 3 1 1 3 5 1 1 0 1 1 2 1 1 3 5 2 1 0 2 0 0 3 1 3 3 1 1 1 4 0 1 0 1 2 3 2 2 1 0 1 1 0 0 1 3 HASSE SYM -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1-1 1 -1-1 1 LEVEL AUTOS 141 48 141 48 141 24 141 24 141 24 141 12 141 8 141 8 141 4 MASS 3/8 17/48 23/48 19/96 19/96 19/96 3/8 32 Quaternary Quadratic Forms D= 144 GENUS' 1 1 2 2 2 3 3 4 5 6 7 8 8 9 9 10 10 11 11 12 D= 145 GENUSt 1 1 1 1 2 2 2 2 2 D= 148 GENUSt 1 1 1 1 2 2 2 2 3 3 3 3 3 3 D= 149 GENUSt 1 1 1 1 1 1 1 D= 152 GENUSt 1 1 1 1 1 1 2 2 F11 F22 F"-, F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 0 0 0 0 0 1 1 3 4 0 0 0 0 1 3 1 1 1 18 1 1 0 0 0 0 1 1 2 5 0 0 0 1 1 0 1 1 3 5 1 1 1 0 0 1 1 1 1 9 0 0 0 0 0 0 2 2 2 2 3 2 0 2 0 0 1 1 3 3 0 0 0 0 0 0 1 1 4 4 1 0 0 0 0 4 1 2 2 4 1 1 1 2 0 2 1 1 2 5 0 0 0 0 0 2 1 1 2 6 0 1 1 0 0 0 2 2 2 2 2 1 -1 0 0 0 1 1 2 6 1 0 0 0 0 0 2 1 3 3 1 2 0 1 2 0 1 1 4 3 1 0 0 0 0 0 1 2 2 1 1 3 0 0 0 0 1 1 4 3 0 1 1 2 0 0 1 2 2 3 1 0 0 0 2 0 1 2 2 3 0 2 0 0 0 0 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 2 1 6 0 1 0 2 0 1 2 1 8 1 1 1 1 0 2 1 2 2 3 1 1 0 0 1 1 2 2 2 2 2 1 0 -1 -1 1 1 1 4 3 0 1 1 1 2 0 4 1 1 1 4 1 1 0 0 2 1 2 2 3 1 1 0 0 0 1 1 2 2 3 0 0 1 1 -1 1 1 2 2 4 1 0 2 1 1 1 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 0 0 0 1 1 1 1 10 1 2 2 4 0 0 2 1 2 0 1 2 2 4 1 0 2 1 0 0 2 2 2 2 2 3 0 2 0 1 1 1 1 19 1 1 1 0 0 0 1 1 2 7 1 1 0 0 0 2 1 1 3 1 5 1 0 1 0 0 2 1 3 3 0 2 1 0 0 3 1 1 2 5 0 0 0 1 1 0 1 1 2 8 1 1 0 0 1 1 1 1 3 5 1 1 0 0 2 0 1 2 2 3 1 0 1 0 1 0 1 2 2 3 0 1 0 0 2 0 1 2 3 3 1 0 2 1 0 2 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 13 1 0 0 1 0 1 1 1 1 19 1 1 0 0 1 0 1 1 4 3 0 1 1 1 0 0 1 1 3 4 0 1 0 0 1 2 1 1 3 5 1 1 0 0 1 0 1 1 4 4 1 1 0 0 0 3 1 2 2 3 1 0 1 0 1 0 HASSE SYM LEVEL AUTOS F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 13 1 0 0 1 0 0 1 1 1 19 1 1 0 0 0 0 1 1 2 5 0 0 0 1 0 0 1 1 3 4 0 0 0 1 1 2 1 2 2 3 1 0 1 0 0 0 1 2 2 4 1 0 2 0 1 0 1 1 1 10 0 0 0 1 1 0 1 1 2 6 0 1 0 0 0 2 HASSE SYM LEVEL AUTOS -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 1 1 -1-1 -1-1 1 1 1 1 -1-1 -1-1 1 1 1 1 1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 LEVEL AUTOS 48 48 72 72 72 36 36 12 12 12 36 24 24 24 24 48 48 72 72 12 48 16 96 32 12 96 48 64 144 16 32 32 32 48 16 48 16 16 16 48 LEVEL AUTOS 145 145 145 145 145 145 145 145 145 8 24 4 4 8 24 4 8 8 LEVEL AUTOS 74 74 74 74 74 74 74 74 148 148 148 148 148 148 149 149 149 149 149 149 149 152 152 152 152 152 152 152 152 96 24 8 12 96 24 12 8 8 12 12 4 4 4 24 48 8 8 12 12 4 24 96 16 16 8 8 32 8 MASS 1/12 1/8 1/32 1/64 1/144 1/16 1/32 1/16 1/12 1/12 1/8 1/48 MASS 2/3 2/3 MASS 25/96 25/96 25/24 MASS 35/48 MASS 41/96 41/96 Tables 33 2: 2: 2: 1 1 1 1 1 2 2 2 2 7 8 3 0 1 0 1 1 0 1 0 0 1 0 2 0: -1-1 0: -1-1 1 : -1-1 152 152 152 16 12 8 D= 153 GENUSi!

LEVEL AUTOS 39 48 39 48 117 48 117 12 117 16 117 12 39 24 39 8 117 8 117 8 MASS 1/24 0= 120 GENUS. 1 1 1 2 2 2 2 3 3 3 3 4 4 4 F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 10 1 0 0 0 0 0 1 1 3 3 0 1 1 0 0 0 2 2 2 2 1 1 1 2 2 0 1 1 1 15 1 1 0 0 0 0 1 1 2 4 0 0 0 0 1 0 1 1 2 6 1 1 0 0 0 0 1 2 2 2 2 1 3 0 0 0 1 1 1 8 0 0 0 0 1 1 1 1 2 5 1 0 0 0 0 0 0 0 0 1 0 1 2 2 2 0 1 2 2 1 0 2 0 0 0 3 1 1 1 1 2 5 0 0 0 0 1 1 1 1 0 0 3 3 0 0 1 1 4 1 0 0 1 1 2 3 HASSE SYM 1-1-1 1-1-1 1-1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 111 111 111 LEVEL AUTOS 120 48 120 32 120 8 120 96 120 16 120 24 120 16 120 32 120 48 120 16 120 16 120 32 120 16 120 12 MASS 17/96 1/24 1/24 1/3 1/3 1/8 1/24 1/8 5/32 5/32 1/4 1/6 1/4 17/96 17/96 17/96 30 Quaternary Quadratic Forms D= 121 GENUS' 1 1 1 D= 124 GENUS' 1 1 1 1 1 1 2 2 2 D= 125 GENUS' 1 1 1 1 1 2 3 4 D= 128 GENUSt 1 1 1 1 2 2 3 4 5 5 6 6 7 8 9 10 11 12 13 14 D= 129 GENUS' 1 1 1 1 2 2 2 2 D= 132 GENUS' 1 1 1 1 1 1 2 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 3 3 0 1 0 0 1 0 4 1 1 1 1 4 1 1 4 0 1 2 2 2 2 2 1 0 1 2 HASSE SYM F11 F22 F33 F44 Fl2 F13 F23 F14 F24 F34 1 1 16 1 1 1 1 0 0 0 1 1 1 1 8 0 0 0 0 0 1 2 4 0 1 1 0 0 0 0 1 2 1 0 2 1 5 0 0 0 1 1 1 1 3 4 0 0 0 3 2 1 1 2 1 2 3 0 0 0 1 2 1 1 2 1 6 0 0 0 1 2 2 3 1 0 1 0 2 0 2 2 0 2 1 1 1 1 3 0 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 11 1 0 0 1 0 1 1 1 0 1 1 1 1 16 0 0 1 2 1 1 1 1 5 0 0 0 1 1 3 4 1 1 0 0 0 1 1 2 2 1 0 1 1 2 0 3 1 2 7 1 1 1 1 2 1 0 2 2 2 2 1 1 -1 -1 1 1 4 1 1 1 1 1 3 0 0 3 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 11 1 0 1 0 0 1 0 0 1 1 1 1 3 3 0 0 0 1 1 1 1 1 4 4 0 0 3 1 2 2 1 1 0 1 0 0 3 1 1 1 16 1 1 0 0 0 0 1 1 2 1 1 2 5 0 0 0 1 1 1 8 0 0 0 0 0 0 1 2 4 1 0 0 0 0 0 0 1 1 2 6 0 1 1 1 1 0 2 2 2 2 1 2 2 0 0 0 7 1 1 2 1 1 0 0 1 1 2 2 1 1 2 1 3 0 0 0 1 1 3 4 1 1 0 0 0 0 1 5 1 1 0 1 1 3 1 3 1 2 2 2 0 0 0 0 0 0 2 4 1 2 2 1 2 0 0 0 1 3 0 0 0 0 0 2 1 3 1 2 2 3 1 1 0 0 1 1 1 2 2 3 0 0 0 0 2 2 2 2 2 2 2 2 3 0 0 0 HASSE SYM Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 11 1 1 1 0 0 0 0 2 1 1 1 1 1 5 0 0 0 1 2 2 1 1 1 1 3 0 0 2 1 1 1 1 2 2 2 2 2 1 1 2 6 0 1 1 1 0 2 1 1 4 0 1 0 0 1 3 3 4 1 1 1 1 3 0 0 0 1 1 2 2 3 1 0 0 1 2 1 HASSE SYM Fll F22 F33 F44 F12 Fl3 F23 F14 F24 F34 1 0 0 0 0 0 1 1 1 11 7 1 1 1 1 1 2 0 0 0 1 1 1 3 3 0 0 v 0 0 1 1 4 1 0 0 0 0 2 3 1 1 1 4 1 0 0 0 0 3 2 2 3 0 0 1 0 2 2 1 1 0 1 0 0 1 1 1 17 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 111 LEVEL AUTOS 11 11 11 32 72 24 LEVEL AUTOS 124 124 124 124 124 124 124 124 124 96 32 16 8 16 8 24 4 8 LEVEL AUTOS 125 125 125 125 125 25 5 25 24 48 8 12 4 24 240 16 LEVEL AUTOS 128 128 128 128 64 64 32 16 64 64 128 128 32 64 8 64 32 32 32 32 24 8 24 8 96 32 96 32 16 16 12 4 24 24 96 8 32 8 32 96 LEVEL AUTOS 129 129 129 129 129 129 129 129 48 8 8 4 16 8 12 4 LEVEL AUTOS 132 132 132 132 132 132 66 MASS 25/288 48 12 16 24 24 8 96 MASS 5/12 5/12 MASS 25/48 1/24 1/240 1/16 MASS 1/3 1/24 1/96 1/32 1/8 1/3 1/24 1/24 1/96 1/8 1/32 1/8 1/32 1/96 MASS 25/48 25/48 MASS 3/8 1/32 Tables 31 2 3 3 4 4 5 5 5 6 6 6 0= 133 GENUSt 1 1 1 2 2 2 2 0= 136 GENUSt 1 1 1 1 1 2 2 2 2 2 0= 137 GENUSt 1 1 1 1 1 1 0= 140 GENUSt 1 1 1 1 2 2 2 3 3 3 3 4 4 4 0= 141 GENUS' 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 3 2 2 6 9 3 5 3 6 4 2 4 3 3 1 0 0 0 1 0 1 2 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 2 0 1 1 2 -1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 -1 1 2 1 0 0 1 1 2 1 3 1 2 111 1-1-1 1-1-1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 66 66 66 132 132 66 66 66 66 66 66 48 96 48 8 4 32 8 8 32 8 8 1/32 3/8 9/32 9/32 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 17 1 1 0 0 1 0 1 1 1 5 1 0 0 1 2 3 1 2 2 3 0 0 1 1 0 2 1 1 2 1 5 0 0 0 1 0 1 1 2 6 1 0 1 1 0 0 1 1 2 7 1 1 0 0 1 0 1 2 1 3 3 0 2 1 1 3 HASSE SYM -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 LEVEL AUTOS 133 48 133 12 133 4 133 16 133 12 133 12 133 8 MASS 17/48 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 17 1 1 0 0 0 0 1 1 1 9 0 0 0 0 1 1 0 0 1 2 5 1 1 2 0 0 2 2 1 1 3 0 0 0 1 2 3 1 1 1 1 1 2 2 0 1 2 5 0 1 0 1 1 1 0 0 1 1 2 6 1 0 0 1 0 0 4 1 1 3 0 1 1 1 1 0 1 2 2 3 0 0 2 0 1 0 1 2 2 3 1 0 0 0 2 0 HASSE SYM 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 136 96 136 32 136 16 136 8 136 4 136 8 136 24 136 16 136 8 136 8 MASS 23/48 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 1 0 0 0 1 1 1 2 6 0 1 1 1 0 0 1 1 2 7 1 1 1 0 0 0 2 2 1 1 3 0 1 0 -1 1 1 2 2 3 1 1 1 0 0 0 1 2 2 4 1 0 2 0 2 1 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 137 24 137 8 137 12 137 4 137 4 137 4 MASS 1/1 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 0 0 1 0 0 1 1 2 5 1 0 0 0 0 0 1 1 3 3 0 0 0 0 0 1 2 2 4 1 2 1 0 0 1 2 1 1 1 18 1 1 0 1 0 0 1 1 2 1 1 5 0 0 0 1 2 2 2 2 1 1 -1 2 0 0 1 1 2 1 1 1 6 0 0 0 1 1 2 7 1 1 0 0 0 0 1 1 4 1 1 1 1 1 3 0 1 2 2 3 1 0 0 0 0 2 1 1 1 1 9 0 0 0 0 0 1 1 3 4 0 1 0 0 0 3 1 1 4 4 1 1 1 1 0 3 HASSE SYM -1-1 1 -1-1 1 -1-1 1 -1-1 1 1-1-1 1-1-1 1-1-1 111 111 111 111 -1 1-1 -1 1-1 -1 1-1 LEVEL AUTOS 140 24 140 16 140 32 140 16 140 96 140 16 140 8 140 16 140 24 140 32 140 16 140 32 140 8 140 24 MASS 19/96 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 0 0 1 1 1 1 12 0 0 1 1 1 18 1 1 0 0 1 0 1 1 2 1 0 1 6 0 0 0 1 1 4 1 0 0 0 0 1 3 1 1 0 0 0 3 1 1 3 5 1 1 0 1 1 2 1 1 3 5 2 1 0 2 0 0 3 1 3 3 1 1 1 4 0 1 0 1 2 3 2 2 1 0 1 1 0 0 1 3 HASSE SYM -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1-1 1 -1-1 1 LEVEL AUTOS 141 48 141 48 141 24 141 24 141 24 141 12 141 8 141 8 141 4 MASS 3/8 17/48 23/48 19/96 19/96 19/96 3/8 32 Quaternary Quadratic Forms D= 144 GENUS' 1 1 2 2 2 3 3 4 5 6 7 8 8 9 9 10 10 11 11 12 D= 145 GENUSt 1 1 1 1 2 2 2 2 2 D= 148 GENUSt 1 1 1 1 2 2 2 2 3 3 3 3 3 3 D= 149 GENUSt 1 1 1 1 1 1 1 D= 152 GENUSt 1 1 1 1 1 1 2 2 F11 F22 F"-, F44 F12 F13 F23 F14 F24 F34 1 1 1 12 1 0 0 0 0 0 1 1 3 4 0 0 0 0 1 3 1 1 1 18 1 1 0 0 0 0 1 1 2 5 0 0 0 1 1 0 1 1 3 5 1 1 1 0 0 1 1 1 1 9 0 0 0 0 0 0 2 2 2 2 3 2 0 2 0 0 1 1 3 3 0 0 0 0 0 0 1 1 4 4 1 0 0 0 0 4 1 2 2 4 1 1 1 2 0 2 1 1 2 5 0 0 0 0 0 2 1 1 2 6 0 1 1 0 0 0 2 2 2 2 2 1 -1 0 0 0 1 1 2 6 1 0 0 0 0 0 2 1 3 3 1 2 0 1 2 0 1 1 4 3 1 0 0 0 0 0 1 2 2 1 1 3 0 0 0 0 1 1 4 3 0 1 1 2 0 0 1 2 2 3 1 0 0 0 2 0 1 2 2 3 0 2 0 0 0 0 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 2 1 6 0 1 0 2 0 1 2 1 8 1 1 1 1 0 2 1 2 2 3 1 1 0 0 1 1 2 2 2 2 2 1 0 -1 -1 1 1 1 4 3 0 1 1 1 2 0 4 1 1 1 4 1 1 0 0 2 1 2 2 3 1 1 0 0 0 1 1 2 2 3 0 0 1 1 -1 1 1 2 2 4 1 0 2 1 1 1 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 0 0 0 1 1 1 1 10 1 2 2 4 0 0 2 1 2 0 1 2 2 4 1 0 2 1 0 0 2 2 2 2 2 3 0 2 0 1 1 1 1 19 1 1 1 0 0 0 1 1 2 7 1 1 0 0 0 2 1 1 3 1 5 1 0 1 0 0 2 1 3 3 0 2 1 0 0 3 1 1 2 5 0 0 0 1 1 0 1 1 2 8 1 1 0 0 1 1 1 1 3 5 1 1 0 0 2 0 1 2 2 3 1 0 1 0 1 0 1 2 2 3 0 1 0 0 2 0 1 2 3 3 1 0 2 1 0 2 HASSE SYM F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 13 1 0 0 1 0 1 1 1 1 19 1 1 0 0 1 0 1 1 4 3 0 1 1 1 0 0 1 1 3 4 0 1 0 0 1 2 1 1 3 5 1 1 0 0 1 0 1 1 4 4 1 1 0 0 0 3 1 2 2 3 1 0 1 0 1 0 HASSE SYM LEVEL AUTOS F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 13 1 0 0 1 0 0 1 1 1 19 1 1 0 0 0 0 1 1 2 5 0 0 0 1 0 0 1 1 3 4 0 0 0 1 1 2 1 2 2 3 1 0 1 0 0 0 1 2 2 4 1 0 2 0 1 0 1 1 1 10 0 0 0 1 1 0 1 1 2 6 0 1 0 0 0 2 HASSE SYM LEVEL AUTOS -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 1 1 -1-1 -1-1 1 1 1 1 -1-1 -1-1 1 1 1 1 1 1 -1-1 1 -1-1 1 -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 1 1 1 1 1 1 -1-1 -1-1 LEVEL AUTOS 48 48 72 72 72 36 36 12 12 12 36 24 24 24 24 48 48 72 72 12 48 16 96 32 12 96 48 64 144 16 32 32 32 48 16 48 16 16 16 48 LEVEL AUTOS 145 145 145 145 145 145 145 145 145 8 24 4 4 8 24 4 8 8 LEVEL AUTOS 74 74 74 74 74 74 74 74 148 148 148 148 148 148 149 149 149 149 149 149 149 152 152 152 152 152 152 152 152 96 24 8 12 96 24 12 8 8 12 12 4 4 4 24 48 8 8 12 12 4 24 96 16 16 8 8 32 8 MASS 1/12 1/8 1/32 1/64 1/144 1/16 1/32 1/16 1/12 1/12 1/8 1/48 MASS 2/3 2/3 MASS 25/96 25/96 25/24 MASS 35/48 MASS 41/96 41/96 Tables 33 2: 2: 2: 1 1 1 1 1 2 2 2 2 7 8 3 0 1 0 1 1 0 1 0 0 1 0 2 0: -1-1 0: -1-1 1 : -1-1 152 152 152 16 12 8 D= 153 GENUSi!

1 1 1 1 2 2 2 2 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 13 1 1 0 0 0 0 2 4 0 1 2 1 1 0 0 0 2 4 1 0 1 0 1 1 0 0 2 1 1 1 1 5 0 1 1 0 1 7 0 1 1 1 1 0 0 0 1 1 1 1 9 1 0 0 0 0 2 1 3 3 0 1 1 0 0 1 2 2 0 1 1 1 2 0 0 0 HASSE SYM -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 1 1 LEVEL AUTOS 104 96 104 16 104 8 104 16 104 32 104 24 104 16 104 8 MASS 25/96 D= 105 GENUSt 1 1 1 2 2 3 3 4 4 4 4 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 0 0 1 1 1 9 0 0 1 1 2 1 1 2 6 1 0 1 1 2 2 1 1 0 0 2 1 3 1 1 2 4 0 1 0 0 1 0 1 2 2 2 2 2 2 0 0 1 1 1 2 1 1 1 0 2 5 0 2 2 1 1 1 1 2 3 1 0 1 3 1 0 0 0 1 1 3 0 1 0 0 1 2 1 1 3 3 0 4 1 1 1 3 1 0 0 0 3 2 2 2 1 0 0 0 1 1 0 HASSE SYM -1 1-1 1 -1 1-1 1 -1 1-1 1 -1-1-1-1 -1-1-1-1 -1-1 1 1 -1-1 1 1 -1 1 1-1 -1 1 1-1 -1 1 1-1 -1 1 1-1 LEVEL AUTOS 105 48 105 24 105 8 105 16 105 8 105 16 105 8 105 48 105 16 105 24 105 16 MASS 3/16 D= 108 GENUSt 1 1 1 1 2 2 3 3 4 4 4 5 6 7 8 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 14 1 1 0 1 0 0 1 1 1 1 2 4 0 0 0 1 1 1 2 1 1 0 0 1 1 6 1 2 2 1 0 0 0 2 2 3 1 1 1 1 0 0 0 0 0 9 1 1 3 3 0 0 0 0 0 3 2 1 0 2 1 1 5 0 0 0 1 2 2 2 0 1 0 1 1 0 1 7 1 1 0 0 0 0 1 0 1 1 2 4 1 0 0 0 1 0 1 2 2 3 1 0 2 1 0 0 1 2 1 1 1 1 1 5 0 1 1 1 1 0 3 3 0 0 0 0 1 2 2 3 0 0 2 -1 1 -1 1 -1 2 2 2 1 -1 -1 2 2 HASSE SYM 1 1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 -1-1 LEVEL AUTOS 108 96 108 16 108 12 108 8 36 48 36 96 36 48 36 24 108 32 108 8 108 8 36 32 12 96 16 36 12 96 MASS 9/32 D= 109 GENUS # 1 1 1 1 1 Fll F22 F33 F44 F12 F13 F23 F14 F24 F34 1 14 1 0 1 0 1 1 1 0 1 2 0 1 1 1 5 1 0 0 1 1 1 1 1 3 3 0 0 0 1 2 1 1 3 4 1 0 1 1 2 1 2 2 1 0 1 1 0 3 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 109 48 109 12 109 8 109 12 109 4 MASS 9/16 5/96 1/64 1/12 1/16 25/96 3/16 3/16 3/16 1/32 1/16 9/32 1/32 1/96 1/16 1/96 Tables 29 0= 112 GENUS' 1 1 2 2 3 4 4 5 5 5 5 6 6 6 7 8 F11 F22 1"33 F44 F12 F13 F23 F14 F24 F34 1 1 1 14 1 1 0 0 0 0 1 2 2 3 0 0 0 1 2 2 1 1 1 7 0 0 0 0 0 0 1 1 2 4 0 0 0 0 0 2 1 1 2 1 5 0 0 1 0 0 1 1 2 1 6 1 0 1 0 0 1 2 2 1 3 0 1 2 2 0 1 1 2 4 0 1 0 0 0 0 1 1 3 3 0 1 0 1 2 0 1 1 3 4 1 1 0 0 1 1 1 2 2 2 0 0 1 1 0 0 1 1 2 4 1 0 0 0 1 0 1 2 2 2 0 0 0 1 0 0 2 2 2 2 2 1 2 0 0 0 1 2 2 3 0 0 2 0 2 0 1 2 2 3 1 0 2 1 0 0 HASSE SYM -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 LEVEL AUTOS 56 96 56 32 28 96 28 32 56 24 112 12 112 4 112 16 112 16 112 12 112 8 56 32 56 32 56 16 28 24 56 8 MASS 1/24 0= 113 GENUS' 1 1 1 1 1 F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 10 1 0 0 1 0 1 1 1 2 5 0 1 1 0 1 0 1 1 2 6 1 1 0 0 1 0 1 2 2 1 1 3 0 1 2 1 1 2 2 3 1 0 2 0 1 1 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 LEVEL AUTOS 113 24 113 8 113 12 113 4 113 4 MASS 3/4 0= 116 GENUS' 1 1 1 1 1 2 2 2 3 3 3 F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 10 1 1 0 0 0 0 1 2 4 1 0 0 0 0 1 1 1 1 3 3 0 1 0 0 0 2 1 1 4 1 1 3 0 1 0 0 1 2 2 3 1 1 0 2 0 0 1 1 1 15 1 1 1 0 0 0 1 1 3 3 0 0 0 1 1 1 1 1 3 4 1 1 2 0 0 0 1 1 1 8 0 0 0 1 1 1 1 1 2 1 5 0 1 0 0 1 2 2 2 2 2 1 2 0 0 0 HASSE SYM -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 -1-1 1 1 1 1 1 1 LEVEL AUTOS 116 24 116 8 116 8 116 12 116 4 58 96 58 16 58 12 58 96 16 58 58 12 MASS 5/8 0= 117 GENUS' 1 1 2 2 2 2 3 3 4 4 F11 F22 F33 F44 F12 F13 F23 F14 F24 F34 1 1 1 10 1 0 0 0 0 1 1 1 4 1 3 0 0 0 0 3 1 1 1 15 1 1 0 0 1 0 1 1 2 1 1 6 0 0 0 1 1 1 3 3 0 1 0 0 1 1 1 1 3 4 1 1 1 0 0 0 1 1 2 5 1 0 0 0 0 1 1 2 2 0 1 1 2 2 3 0 1 1 2 5 0 1 0 0 1 2 1 2 2 1 0 1 1 1 2 3 HASSE SYM -1-1 1 -1-1 1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1 -1 1-1.

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