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lfunc_lfunctions • Show schema
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{'Lhash': '813386107529168155330961427205,1088002043862922219138772563665', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2530.668812404866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, 0, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6300.1', 'coefficient_field': '1.1.1.1', 'conductor': 39690000, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1], [1], [1], [1, 0, 1], [1, -4, 26, -44, 121], [1, 0, -10, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -30, 0, 529], [1, -12, 94, -348, 841], [1, 4, 66, 124, 961], [1, 0, 26, 0, 1369], [1, -20, 182, -820, 1681], [1, 0, 58, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -106, 0, 2809], [1, 16, 182, 944, 3481], [1, 4, 126, 244, 3721], [1, 0, 10, 0, 4489], [1, -20, 242, -1420, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -22, 0, 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0.7214233174074138, 0.351591015142174, 0.10836795909779295, -0.008693241550693625], 'positive_zeros': ['0.64164850107965483703340264521718', '0.858282277204015813740215577932828', '1.74391184899707157466825444562114', '1.89907005178994095225488619317568', '2.75739453643418687511031109826113', '2.81508504838901768470439952618855', '3.42244125722796490654879978995328', '4.00647991642999781317710018219605', '4.20668315968916506154938187359010', '4.44478499298663224056762754506515', '5.11542120668297631948622964551168', '5.17571917677945202904205026066734', '5.93598055542009928829687955892002', '6.23077888690775140778736351497376', '6.46028655286727064212423854705189', '6.55453481382828141098344411268351', '7.35056163543842104933475572534847', '7.39064780084228608815784087944237', '7.937671080429113715282872728934604', '8.091172535600355663489655844032136'], 'prelabel': '4-6300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.092654881876508, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 523273306793094617, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64164850107965483703340264522', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.858282277204015813740215577933', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.74391184899707157466825444562', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2530.668812404866, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 39690000, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, 4, 42, 76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, 66, 124, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, -20, 182, -820, 1681], 'euler43': [1, 0, 58, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -106, 0, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, -20, 242, -1420, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, -4, 182, -356, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, -4, 26, -44, 121], [1, 0, -10, 0, 169], [1, 0, -30, 0, 289], [1, 4, 42, 76, 361], [1, 0, -30, 0, 529], [1, -12, 94, -348, 841], [1, 4, 66, 124, 961], [1, 0, 26, 0, 1369], [1, -20, 182, -820, 1681], [1, 0, 58, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -106, 0, 2809], [1, 16, 182, 944, 3481], [1, 4, 126, 244, 3721], [1, 0, 10, 0, 4489], [1, -20, 242, -1420, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -22, 0, 6889], [1, -4, 182, -356, 7921], [1, 0, -130, 0, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6300/2/k/m'], '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': '4-6300e2-1.1-c1e2-0-14', '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': 0, 'prelabel': '4-6300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.092654881876508, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 523273306793094617, 'z1': {'__RealLiteral__': 0, 'data': '0.64164850107965483703340264522', 'prec': 103}}
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{'Lhash': '813386107529168155330961427205,1088002043862922219138772563665', 'Lhash_array': ['813386107529168155330961427205', '1088002043862922219138772563665'], 'label': '4-6300e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6300/2/k/m'}