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e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 59 }(T)\)
2-51-1.1-c1-0-1 Elliptic curve 51.a Modular form 51.2.a.a Modular form 51.2.a.a.1.1 $1 + 2 T^{2}$ $1 - T$ $1 - 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-56-1.1-c1-0-1 Elliptic curve 56.b Modular form 56.2.a.b Modular form 56.2.a.b.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - T$ $1 - 6 T + 59 T^{2}$
2-65-1.1-c1-0-4 Elliptic curve 65.a Modular form 65.2.a.a Modular form 65.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + T$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-76-1.1-c1-0-0 Elliptic curve 76.a Modular form 76.2.a.a Modular form 76.2.a.a.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-90-1.1-c1-0-0 Elliptic curve 90.a Modular form 90.2.a.a Modular form 90.2.a.a.1.1 $1 + T$ $1$ $1 - T$ $1 - 2 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-98-1.1-c1-0-0 Elliptic curve 98.a Modular form 98.2.a.a Modular form 98.2.a.a.1.1 $1 + T$ $1 - 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1$ $1 - 6 T + 59 T^{2}$
2-104-1.1-c1-0-1 Elliptic curve 104.a Modular form 104.2.a.a Modular form 104.2.a.a.1.1 $1$ $1 - T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - 5 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-106-1.1-c1-0-2 Elliptic curve 106.d Modular form 106.2.a.d Modular form 106.2.a.d.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-110-1.1-c1-0-4 Elliptic curve 110.c Modular form 110.2.a.c Modular form 110.2.a.c.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + T$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-112-1.1-c1-0-1 Elliptic curve 112.c Modular form 112.2.a.c Modular form 112.2.a.c.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + T$ $1 - 6 T + 59 T^{2}$
2-113-1.1-c1-0-2 Elliptic curve 113.a Modular form 113.2.a.a Modular form 113.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 2 T + 5 T^{2}$ $1 + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-116-1.1-c1-0-1 Elliptic curve 116.b Modular form 116.2.a.b Modular form 116.2.a.b.1.1 $1$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-126-1.1-c1-0-1 Elliptic curve 126.b Modular form 126.2.a.b Modular form 126.2.a.b.1.1 $1 - T$ $1$ $1 + 5 T^{2}$ $1 - T$ $1 - 6 T + 59 T^{2}$
2-130-1.1-c1-0-1 Elliptic curve 130.a Modular form 130.2.a.a Modular form 130.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 - T$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
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 $1 - T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-142-1.1-c1-0-2 Elliptic curve 142.e Modular form 142.2.a.e Modular form 142.2.a.e.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-153-1.1-c1-0-2 Elliptic curve 153.a Modular form 153.2.a.a Modular form 153.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-171-1.1-c1-0-7 Elliptic curve 171.b Modular form 171.2.a.b Modular form 171.2.a.b.1.1 $1 + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-182-1.1-c1-0-3 Elliptic curve 182.d Modular form 182.2.a.d Modular form 182.2.a.d.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T$ $1 - 6 T + 59 T^{2}$
2-186-1.1-c1-0-0 Elliptic curve 186.a Modular form 186.2.a.a Modular form 186.2.a.a.1.1 $1 + T$ $1 + T$ $1 + T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-194-1.1-c1-0-6 Elliptic curve 194.a Modular form 194.2.a.a Modular form 194.2.a.a.1.1 $1 - T$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-204-1.1-c1-0-1 Elliptic curve 204.b Modular form 204.2.a.b Modular form 204.2.a.b.1.1 $1$ $1 - T$ $1 - T + 5 T^{2}$ $1 + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-208-1.1-c1-0-4 Elliptic curve 208.a Modular form 208.2.a.a Modular form 208.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-214-1.1-c1-0-3 Elliptic curve 214.d Modular form 214.2.a.d Modular form 214.2.a.d.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - 2 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-234-1.1-c1-0-3 Elliptic curve 234.e Modular form 234.2.a.e Modular form 234.2.a.e.1.1 $1 - T$ $1$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-235-1.1-c1-0-8 Elliptic curve 235.b Modular form 235.2.a.b Modular form 235.2.a.b.1.1 $1 + T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-245-1.1-c1-0-4 Elliptic curve 245.a Modular form 245.2.a.a Modular form 245.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + 3 T + 3 T^{2}$ $1 - T$ $1$ $1 - 6 T + 59 T^{2}$
2-2e8-1.1-c1-0-2 Elliptic curve 256.d Modular form 256.2.a.d Modular form 256.2.a.d.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-262-1.1-c1-0-9 Elliptic curve 262.b Modular form 262.2.a.b Modular form 262.2.a.b.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-278-1.1-c1-0-1 Elliptic curve 278.a Modular form 278.2.a.a Modular form 278.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-304-1.1-c1-0-5 Elliptic curve 304.f Modular form 304.2.a.f Modular form 304.2.a.f.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-307-1.1-c1-0-11 Elliptic curve 307.b Modular form 307.2.a.b Modular form 307.2.a.b.1.1 $1 - T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-325-1.1-c1-0-8 Elliptic curve 325.d Modular form 325.2.a.d Modular form 325.2.a.d.1.1 $1 - T + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1$ $1 - 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-326-1.1-c1-0-0 Elliptic curve 326.a Modular form 326.2.a.a Modular form 326.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
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 $1 - T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-338-1.1-c1-0-9 Elliptic curve 338.f Modular form 338.2.a.f Modular form 338.2.a.f.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-348-1.1-c1-0-0 Elliptic curve 348.a Modular form 348.2.a.a Modular form 348.2.a.a.1.1 $1$ $1 + T$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-19e2-1.1-c1-0-7 Elliptic curve 361.b Modular form 361.2.a.b Modular form 361.2.a.b.1.1 $1 + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-378-1.1-c1-0-4 Elliptic curve 378.g Modular form 378.2.a.g Modular form 378.2.a.g.1.1 $1 - T$ $1$ $1 - 3 T + 5 T^{2}$ $1 - T$ $1 - 6 T + 59 T^{2}$
2-416-1.1-c1-0-4 Elliptic curve 416.b Modular form 416.2.a.b Modular form 416.2.a.b.1.1 $1$ $1 - T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-423-1.1-c1-0-7 Elliptic curve 423.a Modular form 423.2.a.a Modular form 423.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-434-1.1-c1-0-13 Elliptic curve 434.a Modular form 434.2.a.a Modular form 434.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + 5 T^{2}$ $1 + T$ $1 - 6 T + 59 T^{2}$
2-437-1.1-c1-0-29 Elliptic curve 437.a Modular form 437.2.a.a Modular form 437.2.a.a.1.1 $1 + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-438-1.1-c1-0-9 Elliptic curve 438.c Modular form 438.2.a.c Modular form 438.2.a.c.1.1 $1 + T$ $1 - T$ $1 + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-443-1.1-c1-0-16 Elliptic curve 443.a Modular form 443.2.a.a Modular form 443.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-448-1.1-c1-0-4 Elliptic curve 448.g Modular form 448.2.a.g Modular form 448.2.a.g.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + 5 T^{2}$ $1 - T$ $1 - 6 T + 59 T^{2}$
2-448-1.1-c1-0-6 Elliptic curve 448.h Modular form 448.2.a.h Modular form 448.2.a.h.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + T$ $1 - 6 T + 59 T^{2}$
2-450-1.1-c1-0-2 Elliptic curve 450.e Modular form 450.2.a.e Modular form 450.2.a.e.1.1 $1 - T$ $1$ $1$ $1 + 2 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-459-1.1-c1-0-17 Elliptic curve 459.h Modular form 459.2.a.h Modular form 459.2.a.h.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
2-470-1.1-c1-0-16 Elliptic curve 470.e Modular form 470.2.a.e Modular form 470.2.a.e.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + T$ $1 + 3 T + 7 T^{2}$ $1 - 6 T + 59 T^{2}$
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