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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-43e2-1.1-c1e2-0-1 Modular form 43.2.c.a $( 1 - T + 2 T^{2} )^{2}$ $1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$ $1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4}$
4-7e4-1.1-c1e2-0-1 Elliptic curve 2.0.7.1-49.1-CMa $( 1 - T + 2 T^{2} )^{2}$ $( 1 + 3 T^{2} )^{2}$ $( 1 + 5 T^{2} )^{2}$ $1$
4-51e2-1.1-c1e2-0-4 Elliptic curve 2.2.17.1-9.1-a Hilbert modular form 2.2.17.1-9.1-a Modular form 51.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $1 + T^{2}$ $( 1 - 5 T^{2} )^{2}$ $1 + 2 T^{2} + 49 T^{4}$
4-63e2-1.1-c1e2-0-4 Modular form 63.2.h.a $( 1 - T + 2 T^{2} )^{2}$ $1 + 3 T^{2}$ $1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$ $1 - 4 T + 7 T^{2}$
4-65e2-1.1-c1e2-0-3 Elliptic curve 2.2.65.1-1.1-a Hilbert modular form 2.2.65.1-1.1-a Modular form 65.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T + 5 T^{2}$ $( 1 + 7 T^{2} )^{2}$
4-65e2-1.1-c1e2-0-5 Modular form 65.2.k.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 10 T^{2} + 49 T^{4}$
4-73e2-1.1-c1e2-0-1 Modular form 73.2.d.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4}$
4-85e2-1.1-c1e2-0-1 Modular form 85.2.j.b $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4}$
4-91e2-1.1-c1e2-0-3 Modular form 91.2.h.a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 - 4 T + 7 T^{2}$
4-113e2-1.1-c1e2-0-1 Modular form 113.2.a.b $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )^{2}$
4-27783-1.1-c1e2-0-2 Bianchi modular form 2.0.7.1-567.1-a Elliptic curve 2.0.7.1-567.1-a $( 1 - T + 2 T^{2} )^{2}$ $1$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + T$
4-33e3-1.1-c1e2-0-1 Elliptic curve 2.2.33.1-33.1-a Hilbert modular form 2.2.33.1-33.1-a $( 1 - T + 2 T^{2} )^{2}$ $1 + T$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-41503-1.1-c1e2-0-5 Bianchi modular form 2.0.7.1-847.2-c Elliptic curve 2.0.7.1-847.2-c $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + T$
4-215e2-1.1-c1e2-0-0 Modular form 215.2.e.a $( 1 - T + 2 T^{2} )^{2}$ $1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$ $1 + T + T^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-219e2-1.1-c1e2-0-1 Elliptic curve 2.2.73.1-9.1-a Hilbert modular form 2.2.73.1-9.1-a Modular form 219.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $( 1 + T )^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $1 - 6 T^{2} + 49 T^{4}$
4-221e2-1.1-c1e2-0-2 Elliptic curve 2.2.17.1-169.1-a Hilbert modular form 2.2.17.1-169.1-a Modular form 221.2.d.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 7 T^{2} )^{2}$
4-227e2-1.1-c1e2-0-0 Modular form 227.2.a.c $( 1 - T + 2 T^{2} )^{2}$ $1 + T - T^{2} + 3 T^{3} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )^{2}$ $1 - 3 T + 9 T^{2} - 21 T^{3} + 49 T^{4}$
4-52577-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-1073.1-a Bianchi modular form 2.0.7.1-1073.4-a Elliptic curve 2.0.7.1-1073.1-a Elliptic curve 2.0.7.1-1073.4-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 2 T + 7 T^{2}$
4-231e2-1.1-c1e2-0-5 Bianchi modular form 2.0.7.1-1089.2-a Elliptic curve 2.0.7.1-1089.2-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 4 T + 7 T^{2}$
4-265e2-1.1-c1e2-0-0 Modular form 265.2.j.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-273e2-1.1-c1e2-0-22 Bianchi modular form 2.0.7.1-1521.1-a Elliptic curve 2.0.7.1-1521.1-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 4 T + 7 T^{2}$
4-277e2-1.1-c1e2-0-0 Modular form 277.2.c.a $( 1 - T + 2 T^{2} )^{2}$ $1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-77175-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-1575.1-a Elliptic curve 2.0.7.1-1575.1-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $( 1 - T )( 1 + T )$ $1 - T$
4-281e2-1.1-c1e2-0-0 Modular form 281.2.c.a $( 1 - T + 2 T^{2} )^{2}$ $1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$ $( 1 - 5 T^{2} )^{2}$ $1 - 10 T^{2} + 49 T^{4}$
4-81675-1.1-c1e2-0-8 Elliptic curve 2.2.33.1-75.1-c Hilbert modular form 2.2.33.1-75.1-c $( 1 - T + 2 T^{2} )^{2}$ $1 + T$ $( 1 - T )( 1 + T )$ $( 1 + 7 T^{2} )^{2}$
4-17e4-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-289.1-a Hilbert modular form 2.2.17.1-289.1-a Modular form 289.2.b.a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 3 T^{2} )^{2}$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + 2 T^{2} + 49 T^{4}$
4-291e2-1.1-c1e2-0-0 Elliptic curve 2.2.97.1-9.1-c Hilbert modular form 2.2.97.1-9.1-c Modular form 291.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $( 1 + T )^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 - 7 T^{2} )^{2}$
4-291e2-1.1-c1e2-0-1 Elliptic curve 2.2.97.1-9.2-b Elliptic curve 2.2.97.1-9.3-b Hilbert modular form 2.2.97.1-9.2-b Hilbert modular form 2.2.97.1-9.3-b $( 1 - T + 2 T^{2} )^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 4 T^{2} + 25 T^{4}$ $1 + 6 T^{2} + 49 T^{4}$
4-291e2-1.1-c1e2-0-8 Elliptic curve 2.2.97.1-9.1-b Hilbert modular form 2.2.97.1-9.1-b Modular form 291.2.d.c $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $1 - 6 T^{2} + 49 T^{4}$
4-87857-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-1793.2-a Bianchi modular form 2.0.7.1-1793.3-a Elliptic curve 2.0.7.1-1793.2-a Elliptic curve 2.0.7.1-1793.3-a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 2 T + 7 T^{2}$
4-315e2-1.1-c1e2-0-6 Bianchi modular form 2.0.7.1-2025.1-a Elliptic curve 2.0.7.1-2025.1-a $( 1 - T + 2 T^{2} )^{2}$ $1$ $( 1 - T )( 1 + T )$ $1 + 7 T^{2}$
4-101277-1.1-c1e2-0-11 Elliptic curve 2.2.33.1-93.1-e Elliptic curve 2.2.33.1-93.2-e Hilbert modular form 2.2.33.1-93.1-e Hilbert modular form 2.2.33.1-93.2-e $( 1 - T + 2 T^{2} )^{2}$ $1 - T$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 6 T^{2} + 49 T^{4}$
4-103243-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-2107.1-a Bianchi modular form 2.0.7.1-2107.2-a Elliptic curve 2.0.7.1-2107.1-a Elliptic curve 2.0.7.1-2107.2-a $( 1 - T + 2 T^{2} )^{2}$ $1 - T^{2} + 9 T^{4}$ $1 - 4 T^{2} + 25 T^{4}$ $1$
4-323e2-1.1-c1e2-0-2 Elliptic curve 2.2.17.1-361.1-a Hilbert modular form 2.2.17.1-361.1-a Modular form 323.2.d.c $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - 5 T^{2} )^{2}$ $( 1 - 7 T^{2} )^{2}$
4-325e2-1.1-c1e2-0-1 Elliptic curve 2.2.65.1-25.1-c Hilbert modular form 2.2.65.1-25.1-c Modular form 325.2.d.c $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1$ $( 1 + 5 T + 7 T^{2} )^{2}$
4-107811-1.1-c1e2-0-0 Elliptic curve 2.2.33.1-99.1-a Hilbert modular form 2.2.33.1-99.1-a $( 1 - T + 2 T^{2} )^{2}$ $1$ $( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-111843-1.1-c1e2-0-1 Elliptic curve 2.2.17.1-387.1-b Elliptic curve 2.2.17.1-387.2-b Hilbert modular form 2.2.17.1-387.1-b Hilbert modular form 2.2.17.1-387.2-b $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 10 T^{2} + 49 T^{4}$
4-337e2-1.1-c1e2-0-1 Elliptic curve 2.2.337.1-1.1-a Hilbert modular form 2.2.337.1-1.1-a Modular form 337.2.b.a $( 1 - T + 2 T^{2} )^{2}$ $( 1 + 3 T^{2} )^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $( 1 - 4 T + 7 T^{2} )^{2}$
4-347e2-1.1-c1e2-0-0 Modular form 347.2.a.b $( 1 - T + 2 T^{2} )^{2}$ $1 + T + 5 T^{2} + 3 T^{3} + 9 T^{4}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 + 2 T + 7 T^{2} )^{2}$
4-122825-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-425.1-a Hilbert modular form 2.2.17.1-425.1-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - 2 T + 3 T^{2} )( 1 + 2 T + 3 T^{2} )$ $( 1 - T )( 1 + T )$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-353e2-1.1-c1e2-0-0 Modular form 353.2.c.a $( 1 - T + 2 T^{2} )^{2}$ $1 + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T + 8 T^{2} - 28 T^{3} + 49 T^{4}$
4-130193-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-2657.1-a Bianchi modular form 2.0.7.1-2657.2-a Elliptic curve 2.0.7.1-2657.1-a Elliptic curve 2.0.7.1-2657.2-a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 4 T + 7 T^{2}$
4-363e2-1.1-c1e2-0-17 Elliptic curve 2.2.33.1-121.1-a Hilbert modular form 2.2.33.1-121.1-a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 3 T^{2}$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-363e2-1.1-c1e2-0-3 Elliptic curve 2.2.33.1-121.1-h Hilbert modular form 2.2.33.1-121.1-h Modular form 363.2.d.b $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 2 T^{2} + 25 T^{4}$ $1 - 12 T^{2} + 49 T^{4}$
4-132741-1.1-c1e2-0-6 Bianchi modular form 2.0.7.1-2709.1-a Bianchi modular form 2.0.7.1-2709.2-a Elliptic curve 2.0.7.1-2709.1-a Elliptic curve 2.0.7.1-2709.2-a $( 1 - T + 2 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $1 + 2 T^{2} + 25 T^{4}$ $1 + T$
4-369e2-1.1-c1e2-0-0 Elliptic curve 2.2.41.1-81.1-b Hilbert modular form 2.2.41.1-81.1-b Modular form 369.2.d.c $( 1 - T + 2 T^{2} )^{2}$ $1$ $( 1 + 2 T + 5 T^{2} )^{2}$ $1 - 6 T^{2} + 49 T^{4}$
4-136367-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-2783.1-a Bianchi modular form 2.0.7.1-2783.6-a Elliptic curve 2.0.7.1-2783.1-a Elliptic curve 2.0.7.1-2783.6-a $( 1 - T + 2 T^{2} )^{2}$ $1 + 4 T^{2} + 9 T^{4}$ $( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 2 T + 7 T^{2}$
4-137275-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-475.1-a Elliptic curve 2.2.17.1-475.2-a Hilbert modular form 2.2.17.1-475.1-a Hilbert modular form 2.2.17.1-475.2-a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T^{2} + 9 T^{4}$ $( 1 - T )( 1 + T )$ $1 - 6 T^{2} + 49 T^{4}$
4-377e2-1.1-c1e2-0-5 Modular form 377.2.k.a $( 1 - T + 2 T^{2} )^{2}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 - 4 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4}$
4-385e2-1.1-c1e2-0-2 Bianchi modular form 2.0.7.1-3025.2-c Elliptic curve 2.0.7.1-3025.2-c $( 1 - T + 2 T^{2} )^{2}$ $( 1 + 3 T^{2} )^{2}$ $( 1 - T )( 1 + T )$ $1 + 7 T^{2}$
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