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lfunc_lfunctions • Show schema
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{'Lhash': '1426608073310889403435074097232,2020087128582345224070182198622', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2677.34431091976, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '6480.1', 'coefficient_field': '1.1.1.1', 'conductor': 41990400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, 1], [1, 1, 0, 7, 49], [1, -5, 14, -55, 121], [1, -5, 18, -65, 169], [1, 4, 38, 68, 289], [1, 2, 39, 38, 361], [1, 7, 44, 161, 529], [1, 5, 50, 145, 841], [1, 5, 54, 155, 961], [1, 6, 26, 222, 1369], [1, 0, 25, 0, 1681], [1, 8, 102, 344, 1849], [1, -5, 86, -235, 2209], [1, 9, 112, 477, 2809], [1, 26, 287, 1534, 3481], [1, -2, 66, -122, 3721], [1, -14, 126, -938, 4489], [1, 9, 148, 639, 5041], [1, 0, -82, 0, 5329], [1, 6, 110, 474, 6241], [1, 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['1.12539533610763178704608994953818', '1.59356776087878332385941049702215', '1.91306684777512295504685932626770', '2.51501938728600943585675844108094', '3.27710965840970815592660045721535', '3.47446982358748978578412285007066', '3.86293974064445782655480772003910', '3.99134488736222242159192807722442', '4.64395894262850131818030697995164', '4.69385241076572364459532301059477', '5.46205575217073485525597760758168', '5.80956872165828048441611625270788', '6.27881928045225106749717240484740', '6.34459203935677027531652839907491', '6.78539329163521561807921330971083', '7.02622982415089490577114519858288', '7.63648193930740373867045325443790', '7.72531370044496940801523440607863'], 'prelabel': '4-6480e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.193264940886698, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 883181041617619711, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12539533610763178704608994954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59356776087878332385941049702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.91306684777512295504685932627', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2677.34431091976, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 41990400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 5, 0, 5, 0, 0, 0, -4, 0, -2, 0, 0, 0, -7, 0, 3, 0, 0, 0, -5, 0, -5, 0, 0, 0, 2, 0, -6, 0, 0, 0, 0, 0, -8, 0, 0, 0, 5, 0, 1, 0, 0, 0, -9, 0, -10, 0, 0, 0, -26, 0, 2, 0, 0, 0, -10, 0, 14, 0, 0, 0, -9, 0, 0, 0, 0, 0, -5, 0, -6, 0, 0, 0, 10, 0, 8, 0, 0, 0, -3, 0, -5, 0, 0, 0, 4, 0, 32, 0, 0, 0], 'euler11': [1, -5, 14, -55, 121], 'euler13': [1, -5, 18, -65, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 7, 44, 161, 529], 'euler29': [1, 5, 50, 145, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 5, 54, 155, 961], 'euler37': [1, 6, 26, 222, 1369], 'euler41': [1, 0, 25, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, -5, 86, -235, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 9, 112, 477, 2809], 'euler59': [1, 26, 287, 1534, 3481], 'euler61': [1, -2, 66, -122, 3721], 'euler67': [1, -14, 126, -938, 4489], 'euler7': [1, 1, 0, 7, 49], 'euler71': [1, 9, 148, 639, 5041], 'euler73': [1, 0, -82, 0, 5329], 'euler79': [1, 6, 110, 474, 6241], 'euler83': [1, -10, 134, -830, 6889], 'euler89': [1, 3, 52, 267, 7921], 'euler97': [1, -32, 450, -3104, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 1, 0, 7, 49], [1, -5, 14, -55, 121], [1, -5, 18, -65, 169], [1, 4, 38, 68, 289], [1, 2, 39, 38, 361], [1, 7, 44, 161, 529], [1, 5, 50, 145, 841], [1, 5, 54, 155, 961], [1, 6, 26, 222, 1369], [1, 0, 25, 0, 1681], [1, 8, 102, 344, 1849], [1, -5, 86, -235, 2209], [1, 9, 112, 477, 2809], [1, 26, 287, 1534, 3481], [1, -2, 66, -122, 3721], [1, -14, 126, -938, 4489], [1, 9, 148, 639, 5041], [1, 0, -82, 0, 5329], [1, 6, 110, 474, 6241], [1, -10, 134, -830, 6889], [1, 3, 52, 267, 7921], [1, -32, 450, -3104, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6480/2/a/bf'], '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': '4-6480e2-1.1-c1e2-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-6480e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.193264940886698, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 883181041617619711, 'z1': {'__RealLiteral__': 0, 'data': '1.12539533610763178704608994954', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1426608073310889403435074097232,2020087128582345224070182198622', 'Lhash_array': ['1426608073310889403435074097232', '2020087128582345224070182198622'], 'label': '4-6480e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6480/2/a/bf'}