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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 \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
2-26-1.1-c1-0-0 Elliptic curve 26.a Modular form 26.2.a.a Modular form 26.2.a.a.1.1 $1 + T$ $1 - T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-44-1.1-c1-0-0 Elliptic curve 44.a Modular form 44.2.a.a Modular form 44.2.a.a.1.1 $1$ $1 - T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-54-1.1-c1-0-1 Elliptic curve 54.b Modular form 54.2.a.b Modular form 54.2.a.b.1.1 $1 - T$ $1$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-57-1.1-c1-0-2 Elliptic curve 57.a Modular form 57.2.a.a Modular form 57.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$
2-58-1.1-c1-0-1 Elliptic curve 58.a Modular form 58.2.a.a Modular form 58.2.a.a.1.1 $1 + T$ $1 + 3 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-61-1.1-c1-0-3 Elliptic curve 61.a Modular form 61.2.a.a Modular form 61.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-79-1.1-c1-0-5 Elliptic curve 79.a Modular form 79.2.a.a Modular form 79.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-88-1.1-c1-0-2 Elliptic curve 88.a Modular form 88.2.a.a Modular form 88.2.a.a.1.1 $1$ $1 + 3 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-91-1.1-c1-0-4 Elliptic curve 91.a Modular form 91.2.a.a Modular form 91.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T$
2-91-1.1-c1-0-6 Elliptic curve 91.b Modular form 91.2.a.b Modular form 91.2.a.b.1.1 $1 + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T$
2-118-1.1-c1-0-3 Elliptic curve 118.a Modular form 118.2.a.a Modular form 118.2.a.a.1.1 $1 + T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-11e2-1.1-c1-0-3 Elliptic curve 121.b Modular form 121.2.a.b Modular form 121.2.a.b.1.1 $1 + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 7 T^{2}$
2-124-1.1-c1-0-1 Elliptic curve 124.a Modular form 124.2.a.a Modular form 124.2.a.a.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-141-1.1-c1-0-4 Elliptic curve 141.a Modular form 141.2.a.a Modular form 141.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-153-1.1-c1-0-5 Elliptic curve 153.b Modular form 153.2.a.b Modular form 153.2.a.b.1.1 $1 + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-158-1.1-c1-0-6 Elliptic curve 158.c Modular form 158.2.a.c Modular form 158.2.a.c.1.1 $1 - T$ $1 + 3 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-162-1.1-c1-0-3 Elliptic curve 162.a Modular form 162.2.a.a Modular form 162.2.a.a.1.1 $1 + T$ $1$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
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 $1 + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-174-1.1-c1-0-1 Elliptic curve 174.b Modular form 174.2.a.b Modular form 174.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 - 5 T + 7 T^{2}$
2-176-1.1-c1-0-2 Elliptic curve 176.c Modular form 176.2.a.c Modular form 176.2.a.c.1.1 $1$ $1 - 3 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-176-1.1-c1-0-4 Elliptic curve 176.a Modular form 176.2.a.a Modular form 176.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-189-1.1-c1-0-7 Elliptic curve 189.b Modular form 189.2.a.b Modular form 189.2.a.b.1.1 $1 + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 - T$
2-14e2-1.1-c1-0-3 Elliptic curve 196.a Modular form 196.2.a.a Modular form 196.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1$
2-201-1.1-c1-0-10 Elliptic curve 201.c Modular form 201.2.a.c Modular form 201.2.a.c.1.1 $1 - T + 2 T^{2}$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
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 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-209-1.1-c1-0-14 Elliptic curve 209.a Modular form 209.2.a.a Modular form 209.2.a.a.1.1 $1 + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-214-1.1-c1-0-7 Elliptic curve 214.c Modular form 214.2.a.c Modular form 214.2.a.c.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-218-1.1-c1-0-9 Elliptic curve 218.a Modular form 218.2.a.a Modular form 218.2.a.a.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-219-1.1-c1-0-12 Elliptic curve 219.b Modular form 219.2.a.b Modular form 219.2.a.b.1.1 $1 + 2 T^{2}$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-228-1.1-c1-0-3 Elliptic curve 228.a Modular form 228.2.a.a Modular form 228.2.a.a.1.1 $1$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-229-1.1-c1-0-12 Elliptic curve 229.a Modular form 229.2.a.a Modular form 229.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-232-1.1-c1-0-5 Elliptic curve 232.a Modular form 232.2.a.a Modular form 232.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-242-1.1-c1-0-0 Elliptic curve 242.a Modular form 242.2.a.a Modular form 242.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-242-1.1-c1-0-9 Elliptic curve 242.b Modular form 242.2.a.b Modular form 242.2.a.b.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-244-1.1-c1-0-4 Elliptic curve 244.a Modular form 244.2.a.a Modular form 244.2.a.a.1.1 $1$ $1 + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-248-1.1-c1-0-7 Elliptic curve 248.c Modular form 248.2.a.c Modular form 248.2.a.c.1.1 $1$ $1 + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-254-1.1-c1-0-10 Elliptic curve 254.b Modular form 254.2.a.b Modular form 254.2.a.b.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-258-1.1-c1-0-6 Elliptic curve 258.c Modular form 258.2.a.c Modular form 258.2.a.c.1.1 $1 + T$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-274-1.1-c1-0-10 Elliptic curve 274.c Modular form 274.2.a.c Modular form 274.2.a.c.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 7 T^{2}$
2-274-1.1-c1-0-8 Elliptic curve 274.a Modular form 274.2.a.a Modular form 274.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-286-1.1-c1-0-8 Elliptic curve 286.c Modular form 286.2.a.c Modular form 286.2.a.c.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$
2-294-1.1-c1-0-0 Elliptic curve 294.a Modular form 294.2.a.a Modular form 294.2.a.a.1.1 $1 + T$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1$
2-303-1.1-c1-0-15 Elliptic curve 303.b Modular form 303.2.a.b Modular form 303.2.a.b.1.1 $1 + 2 T^{2}$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 + 7 T^{2}$
2-318-1.1-c1-0-8 Elliptic curve 318.d Modular form 318.2.a.d Modular form 318.2.a.d.1.1 $1 - T$ $1 + T$ $1 + 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-18e2-1.1-c1-0-0 Elliptic curve 324.b Modular form 324.2.a.b Modular form 324.2.a.b.1.1 $1$ $1$ $1 + 3 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-18e2-1.1-c1-0-3 Elliptic curve 324.a Modular form 324.2.a.a Modular form 324.2.a.a.1.1 $1$ $1$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
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 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$
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 $1 - T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-339-1.1-c1-0-11 Elliptic curve 339.a Modular form 339.2.a.a Modular form 339.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-346-1.1-c1-0-13 Elliptic curve 346.a Modular form 346.2.a.a Modular form 346.2.a.a.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
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