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lfunc_lfunctions • Show schema
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{'Lhash': '1385742914185736411482726423778,1936656775924982210324391099686,2242574363800522751908601055651', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 423958.40269502887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '9408.1', 'coefficient_field': '1.1.1.1', 'conductor': 832706445312, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1, 0, 6, 4, 30, 0, 125], [1], [1, 0, 6, -38, 66, 0, 1331], [1, 3, 3, -34, 39, 507, 2197], [1, 6, 27, 108, 459, 1734, 4913], [1, -3, 21, -2, 399, -1083, 6859], [1, 6, 45, 180, 1035, 3174, 12167], [1, 12, 126, 728, 3654, 10092, 24389], [1, 3, 72, 139, 2232, 2883, 29791], [1, 3, 27, -146, 999, 4107, 50653], [1, -6, 27, 20, 1107, -10086, 68921], [1, 15, 177, 1318, 7611, 27735, 79507], [1, 12, 153, 1016, 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[[[1, 3, 72, 139, 2232, 2883, 29791], 1]], [[[1, 3, 27, -146, 999, 4107, 50653], 1]], [[[1, -6, 27, 20, 1107, -10086, 68921], 1]], [[[1, 15, 177, 1318, 7611, 27735, 79507], 1]], [[[1, 12, 153, 1016, 7191, 26508, 103823], 1]], [[[1, 6, 78, 802, 4134, 16854, 148877], 1]], [[[1, -12, 198, -1334, 11682, -41772, 205379], 1]], [[[1, 18, 195, 1644, 11895, 66978, 226981], 1]], [[[1, 9, 189, 1042, 12663, 40401, 300763], 1]], [[[1, 0, 177, -32, 12567, 0, 357911], 1]], [[[1, 33, 555, 5814, 40515, 175857, 389017], 1]], [[[1, 27, 432, 4619, 34128, 168507, 493039], 1]], [[[1, -18, 234, -2040, 19422, -124002, 571787], 1]], [[[1, -12, 279, -2024, 24831, -95052, 704969], 1]], [[[1, 0, 264, -38, 25608, 0, 912673], 1]], [[[1, -18, 315, -3468, 31815, -183618, 1030301], 1]], [[[1, 15, 357, 3042, 36771, 159135, 1092727], 1]], [[[1, 24, 390, 4238, 41730, 274776, 1225043], 1]], [[[1, 9, 135, 2558, 14715, 106929, 1295029], 1]], [[[1, -8, 113], 3]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 3, 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'5.44671339569784654178691637400916', '5.84180859648746657195865322276103', '6.17267145425137821830976439875398', '6.20206591827279172002310625883428', '6.40801437943889114175738642018133', '6.75587048098838539261431354110940', '7.20405945165639230519978538402005', '7.34020726946861713556109191395585', '7.34775950750346559942834608258097', '7.48073371779343684785431177528616'], 'prelabel': '6-9408e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.667367433172577, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 1832664303316525490, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09315840968816290695441560999', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.52775281735858768905543728517', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.76907924265311502645732162474', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 423958.40269502887, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 832706445312, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, 0, 0, -6, 0, 3, 0, 0, 0, -6, 0, -6, 0, 10, 0, -12, 0, -3, 0, 0, 0, 0, 0, -3, 0, -9, 0, 6, 0, -15, 0, 0, 0, -12, 0, 0, 0, -18, 0, -6, 0, 0, 0, 9, 0, 12, 0, -18, 0, 0, 0, 0, 0, -9, 0, -18, 0, 0, 0, -33, 0, -18, 0, 0, 0, -27, 0, 15, 0, 18, 0, 0, 0, -36, 0, 12, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 6, -38, 66, 0, 1331], 'euler13': [1, 3, 3, -34, 39, 507, 2197], 'euler17': [1, 6, 27, 108, 459, 1734, 4913], 'euler19': [1, -3, 21, -2, 399, -1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 6, 45, 180, 1035, 3174, 12167], 'euler29': [1, 12, 126, 728, 3654, 10092, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, 3, 72, 139, 2232, 2883, 29791], 'euler37': [1, 3, 27, -146, 999, 4107, 50653], 'euler41': [1, -6, 27, 20, 1107, -10086, 68921], 'euler43': [1, 15, 177, 1318, 7611, 27735, 79507], 'euler47': [1, 12, 153, 1016, 7191, 26508, 103823], 'euler5': [1, 0, 6, 4, 30, 0, 125], 'euler53': [1, 6, 78, 802, 4134, 16854, 148877], 'euler59': [1, -12, 198, -1334, 11682, -41772, 205379], 'euler61': [1, 18, 195, 1644, 11895, 66978, 226981], 'euler67': [1, 9, 189, 1042, 12663, 40401, 300763], 'euler7': [1, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 177, -32, 12567, 0, 357911], 'euler73': [1, 33, 555, 5814, 40515, 175857, 389017], 'euler79': [1, 27, 432, 4619, 34128, 168507, 493039], 'euler83': [1, -18, 234, -2040, 19422, -124002, 571787], 'euler89': [1, -12, 279, -2024, 24831, -95052, 704969], 'euler97': [1, 0, 264, -38, 25608, 0, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 0, 6, 4, 30, 0, 125], [1, 0, 0, 0, 0, 0, 0], [1, 0, 6, -38, 66, 0, 1331], [1, 3, 3, -34, 39, 507, 2197], [1, 6, 27, 108, 459, 1734, 4913], [1, -3, 21, -2, 399, -1083, 6859], [1, 6, 45, 180, 1035, 3174, 12167], [1, 12, 126, 728, 3654, 10092, 24389], [1, 3, 72, 139, 2232, 2883, 29791], [1, 3, 27, -146, 999, 4107, 50653], [1, -6, 27, 20, 1107, -10086, 68921], [1, 15, 177, 1318, 7611, 27735, 79507], [1, 12, 153, 1016, 7191, 26508, 103823], [1, 6, 78, 802, 4134, 16854, 148877], [1, -12, 198, -1334, 11682, -41772, 205379], [1, 18, 195, 1644, 11895, 66978, 226981], [1, 9, 189, 1042, 12663, 40401, 300763], [1, 0, 177, -32, 12567, 0, 357911], [1, 33, 555, 5814, 40515, 175857, 389017], [1, 27, 432, 4619, 34128, 168507, 493039], [1, -18, 234, -2040, 19422, -124002, 571787], [1, -12, 279, -2024, 24831, -95052, 704969], [1, 0, 264, -38, 25608, 0, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9408/2/a/ei'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-9408e3-1.1-c1e3-0-3', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-9408e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.667367433172577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1832664303316525490, 'z1': {'__RealLiteral__': 0, 'data': '1.09315840968816290695441560999', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1385742914185736411482726423778,1936656775924982210324391099686,2242574363800522751908601055651', 'Lhash_array': ['1385742914185736411482726423778', '1936656775924982210324391099686', '2242574363800522751908601055651'], 'label': '6-9408e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9408/2/a/ei'}