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{'Lhash': '244504194391313793142289570966,544539608677865528721097706081,1269383158131467544578418808722,1529345299621969406511381224647,1759413748346052456589464235684,2195920873892448225692064266577', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5827983.7536337515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 6, -7, 6, -3, 1]], [5, [1, 3, 6, 7, 6, 3, 1]], [7, [1, -2, 0, 8, 0, -98, 343]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1680.1', 'coefficient_field': '1.1.1.1', 'conductor': 22483074023424000000, 'conductor_radical': 210, 'degree': 12, 'euler_factors': [[1], [1, -3, 6, -7, 6, -3, 1], [1, 3, 6, 7, 6, 3, 1], [1, -2, 0, 8, 0, -98, 343], [1, 1, -10, -61, -36, 275, 2506, 3025, -4356, -81191, -146410, 161051, 1771561], [1, -2, 49, -94, 1246, -2066, 20237, -26858, 210574, -206518, 1399489, -742586, 4826809], 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'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 1576335767674689827, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19287980011786603643037384363', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.42956600863031653648731986488', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.00136674719589625973213668074', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5827983.7536337515, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 22483074023424000000, 'conductor_radical': 210, 'degree': 12, 'dirichlet_coefficients': [1, 0, 3, 0, -3, 0, 2, 0, 3, 0, -1, 0, 2, 0, -9, 0, -8, 0, -1, 0, 6, 0, 9, 0, 3, 0, -2, 0, 0, 0, 4, 0, -3, 0, -6, 0, -15, 0, 6, 0, 10, 0, 4, 0, -9, 0, -11, 0, 4, 0, -24, 0, 1, 0, 3, 0, -3, 0, 12, 0, -4, 0, 6, 0, -6, 0, -10, 0, 27, 0, 4, 0, 0, 0, 9, 0, -2, 0, 18, 0, -9, 0, -8, 0, 24, 0, 0, 0, -22, 0, 4, 0, 12, 0, 3, 0, 16, 0, -3, 0], 'euler11': [1, 1, -10, -61, -36, 275, 2506, 3025, -4356, -81191, -146410, 161051, 1771561], 'euler13': [1, -2, 49, -94, 1246, -2066, 20237, -26858, 210574, -206518, 1399489, -742586, 4826809], 'euler17': [1, 8, 7, -40, 296, 944, -2399, 16048, 85544, -196520, 584647, 11358856, 24137569], 'euler19': [1, 1, 5, -6, 91, 509, 13054, 9671, 32851, -41154, 651605, 2476099, 47045881], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 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122849307878, 496981290961], 'euler97': [1, -16, 566, -6864, 134479, -1254944, 17279668, -121729568, 1265312911, -6264587472, 50107573046, -137397444112, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 6, -7, 6, -3, 1, 0, 0, 0, 0, 0, 0], [1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], [1, -2, 0, 8, 0, -98, 343, 0, 0, 0, 0, 0, 0], [1, 1, -10, -61, -36, 275, 2506, 3025, -4356, -81191, -146410, 161051, 1771561], [1, -2, 49, -94, 1246, -2066, 20237, -26858, 210574, -206518, 1399489, -742586, 4826809], [1, 8, 7, -40, 296, 944, -2399, 16048, 85544, -196520, 584647, 11358856, 24137569], [1, 1, 5, -6, 91, 509, 13054, 9671, 32851, -41154, 651605, 2476099, 47045881], [1, -9, 42, -135, -348, 7173, -41834, 164979, -184092, -1642545, 11753322, -57927087, 148035889], [1, 0, 18, -512, 603, -4608, 119012, -133632, 507123, -12487168, 12731058, 0, 594823321], [1, -4, -58, 132, 2326, -1328, -79754, -41168, 2235286, 3932412, -53564218, -114516604, 887503681], [1, 15, 117, 442, 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'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-1680e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.662631231720593, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1576335767674689827, 'z1': {'__RealLiteral__': 0, 'data': '0.19287980011786603643037384363', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '244504194391313793142289570966,544539608677865528721097706081,1269383158131467544578418808722,1529345299621969406511381224647,1759413748346052456589464235684,2195920873892448225692064266577', 'Lhash_array': ['244504194391313793142289570966', '544539608677865528721097706081', '1269383158131467544578418808722', '1529345299621969406511381224647', '1759413748346052456589464235684', '2195920873892448225692064266577'], 'label': '12-1680e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1680/2/bg/u'}