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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 97 }(T)\)
2-110-1.1-c1-0-3 Elliptic curve 110.b Modular form 110.2.a.b Modular form 110.2.a.b.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 - T$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-123-1.1-c1-0-5 Elliptic curve 123.a Modular form 123.2.a.a Modular form 123.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-139-1.1-c1-0-6 Elliptic curve 139.a Modular form 139.2.a.a Modular form 139.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-201-1.1-c1-0-9 Elliptic curve 201.b Modular form 201.2.a.b Modular form 201.2.a.b.1.1 $1 + T + 2 T^{2}$ $1 - T$ $1 + T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-214-1.1-c1-0-4 Elliptic curve 214.a Modular form 214.2.a.a Modular form 214.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-285-1.1-c1-0-8 Elliptic curve 285.a Modular form 285.2.a.a Modular form 285.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 - T$ $1 + T$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-296-1.1-c1-0-8 Elliptic curve 296.b Modular form 296.2.a.b Modular form 296.2.a.b.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-338-1.1-c1-0-11 Elliptic curve 338.d Modular form 338.2.a.d Modular form 338.2.a.d.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-354-1.1-c1-0-9 Elliptic curve 354.a Modular form 354.2.a.a Modular form 354.2.a.a.1.1 $1 + T$ $1 + T$ $1 + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-357-1.1-c1-0-10 Elliptic curve 357.d Modular form 357.2.a.d Modular form 357.2.a.d.1.1 $1 - 2 T + 2 T^{2}$ $1 - T$ $1 - T + 5 T^{2}$ $1 + T$ $1 + 12 T + 97 T^{2}$
2-369-1.1-c1-0-11 Elliptic curve 369.b Modular form 369.2.a.b Modular form 369.2.a.b.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-399-1.1-c1-0-8 Elliptic curve 399.b Modular form 399.2.a.b Modular form 399.2.a.b.1.1 $1 + T + 2 T^{2}$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 + T$ $1 + 12 T + 97 T^{2}$
2-422-1.1-c1-0-13 Elliptic curve 422.a Modular form 422.2.a.a Modular form 422.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-428-1.1-c1-0-7 Elliptic curve 428.a Modular form 428.2.a.a Modular form 428.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 - 2 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-433-1.1-c1-0-33 Elliptic curve 433.a Modular form 433.2.a.a Modular form 433.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-522-1.1-c1-0-10 Elliptic curve 522.f Modular form 522.2.a.f Modular form 522.2.a.f.1.1 $1 + T$ $1$ $1 - 3 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-522-1.1-c1-0-11 Elliptic curve 522.g Modular form 522.2.a.g Modular form 522.2.a.g.1.1 $1 - T$ $1$ $1 + 3 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-532-1.1-c1-0-2 Elliptic curve 532.a Modular form 532.2.a.a Modular form 532.2.a.a.1.1 $1$ $1 + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 - T$ $1 + 12 T + 97 T^{2}$
2-537-1.1-c1-0-4 Elliptic curve 537.a Modular form 537.2.a.a Modular form 537.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 - T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-550-1.1-c1-0-4 Elliptic curve 550.j Modular form 550.2.a.j Modular form 550.2.a.j.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-550-1.1-c1-0-7 Elliptic curve 550.k Modular form 550.2.a.k Modular form 550.2.a.k.1.1 $1 - T$ $1 - 2 T + 3 T^{2}$ $1$ $1 + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-570-1.1-c1-0-8 Elliptic curve 570.l Modular form 570.2.a.l Modular form 570.2.a.l.1.1 $1 - T$ $1 - T$ $1 - T$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-580-1.1-c1-0-7 Elliptic curve 580.b Modular form 580.2.a.b Modular form 580.2.a.b.1.1 $1$ $1 + 3 T^{2}$ $1 - T$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-590-1.1-c1-0-17 Elliptic curve 590.b Modular form 590.2.a.b Modular form 590.2.a.b.1.1 $1 + T$ $1 + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-592-1.1-c1-0-5 Elliptic curve 592.d Modular form 592.2.a.d Modular form 592.2.a.d.1.1 $1$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-598-1.1-c1-0-7 Elliptic curve 598.d Modular form 598.2.a.d Modular form 598.2.a.d.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-603-1.1-c1-0-24 Elliptic curve 603.e Modular form 603.2.a.e Modular form 603.2.a.e.1.1 $1 - T + 2 T^{2}$ $1$ $1 - T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-608-1.1-c1-0-14 Elliptic curve 608.b Modular form 608.2.a.b Modular form 608.2.a.b.1.1 $1$ $1 + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-608-1.1-c1-0-15 Elliptic curve 608.c Modular form 608.2.a.c Modular form 608.2.a.c.1.1 $1$ $1 + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-608-1.1-c1-0-17 Elliptic curve 608.d Modular form 608.2.a.d Modular form 608.2.a.d.1.1 $1$ $1 + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-608-1.1-c1-0-7 Elliptic curve 608.e Modular form 608.2.a.e Modular form 608.2.a.e.1.1 $1$ $1 + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - 5 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-610-1.1-c1-0-2 Elliptic curve 610.a Modular form 610.2.a.a Modular form 610.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + T$ $1 + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-628-1.1-c1-0-8 Elliptic curve 628.a Modular form 628.2.a.a Modular form 628.2.a.a.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-659-1.1-c1-0-53 Elliptic curve 659.a Modular form 659.2.a.a Modular form 659.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-664-1.1-c1-0-15 Elliptic curve 664.b Modular form 664.2.a.b Modular form 664.2.a.b.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-666-1.1-c1-0-1 Elliptic curve 666.c Modular form 666.2.a.c Modular form 666.2.a.c.1.1 $1 + T$ $1$ $1 - 2 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-666-1.1-c1-0-14 Elliptic curve 666.e Modular form 666.2.a.e Modular form 666.2.a.e.1.1 $1 - T$ $1$ $1 + 2 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-700-1.1-c1-0-2 Elliptic curve 700.h Modular form 700.2.a.h Modular form 700.2.a.h.1.1 $1$ $1 + 3 T^{2}$ $1$ $1 - T$ $1 + 12 T + 97 T^{2}$
2-722-1.1-c1-0-11 Elliptic curve 722.a Modular form 722.2.a.a Modular form 722.2.a.a.1.1 $1 + T$ $1 + 3 T + 3 T^{2}$ $1 - 2 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-753-1.1-c1-0-17 Elliptic curve 753.c Modular form 753.2.a.c Modular form 753.2.a.c.1.1 $1 - 2 T + 2 T^{2}$ $1 + T$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-760-1.1-c1-0-3 Elliptic curve 760.b Modular form 760.2.a.b Modular form 760.2.a.b.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 - T$ $1 - 4 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-762-1.1-c1-0-3 Elliptic curve 762.b Modular form 762.2.a.b Modular form 762.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-798-1.1-c1-0-13 Elliptic curve 798.b Modular form 798.2.a.b Modular form 798.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 2 T + 5 T^{2}$ $1 + T$ $1 + 12 T + 97 T^{2}$
2-806-1.1-c1-0-9 Elliptic curve 806.d Modular form 806.2.a.d Modular form 806.2.a.d.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-834-1.1-c1-0-22 Elliptic curve 834.g Modular form 834.2.a.g Modular form 834.2.a.g.1.1 $1 - T$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-855-1.1-c1-0-11 Elliptic curve 855.c Modular form 855.2.a.c Modular form 855.2.a.c.1.1 $1 - T + 2 T^{2}$ $1$ $1 - T$ $1 + 2 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-880-1.1-c1-0-19 Elliptic curve 880.i Modular form 880.2.a.i Modular form 880.2.a.i.1.1 $1$ $1 - T + 3 T^{2}$ $1 - T$ $1 + 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-892-1.1-c1-0-11 Elliptic curve 892.c Modular form 892.2.a.c Modular form 892.2.a.c.1.1 $1$ $1 - 3 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - 4 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
2-924-1.1-c1-0-4 Elliptic curve 924.b Modular form 924.2.a.b Modular form 924.2.a.b.1.1 $1$ $1 + T$ $1 + T + 5 T^{2}$ $1 + T$ $1 + 12 T + 97 T^{2}$
2-935-1.1-c1-0-33 Elliptic curve 935.a Modular form 935.2.a.a Modular form 935.2.a.a.1.1 $1 + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + T$ $1 - 3 T + 7 T^{2}$ $1 + 12 T + 97 T^{2}$
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