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lfunc_lfunctions • Show schema
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{'Lhash': '789680333803111612766598605194,1315506135378361027643402767223', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 281.1854236005407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3, 3]], [5, [1]], [7, [1, -4, 7]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.1', 'coefficient_field': '1.1.1.1', 'conductor': 4410000, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1], [1, 3, 3], [1], [1, -4, 7], [1, 0, 11, 0, 121], [1, 0, 22, 0, 169], [1, 0, -17, 0, 289], [1, 6, 31, 114, 361], [1, 0, 23, 0, 529], [1, 0, -58, 0, 841], [1, -3, 34, -93, 961], [1, 1, -36, 37, 1369], [1, 0, 82, 0, 1681], [1, -26, 255, -1118, 1849], [1, 0, -47, 0, 2209], [1, 0, 53, 0, 2809], [1, 0, -59, 0, 3481], [1, -15, 136, -915, 3721], [1, -16, 189, -1072, 4489], [1, 0, -142, 0, 5041], [1, 27, 316, 1971, 5329], [1, -13, 90, -1027, 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'3.92834276564558943061618955118765', '4.26911537494912470828863027768203', '4.33014817758926294166073565446633', '5.10209548304628542923316006719406', '5.23401023591918113429761458279663', '5.69616787640139480810198475648100', '6.13518142396848928272515074892425', '6.45702835026315145294990548188164', '6.83972005759554605461724286702942', '7.48464045462097554541141435737181', '7.58962573124906349133260680891060', '7.997227417527295131417847081264861', '8.668899675287672089802939023409530', '8.786153947070021355750039809156629', '9.243487826523598058905383169705402'], 'prelabel': '4-2100e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 762873803928710318, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62294794295915339493503069249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 281.1854236005407, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 4410000, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -12, 0, 0, 0, 0, 0, -9, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 15, 0, 24, 0, 0, 0, 16, 0, 0, 0, 0, 0, -27, 0, 0, 0, 0, 0, 13, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 11, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, 6, 31, 114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 0, -58, 0, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, -3, 34, -93, 961], 'euler37': [1, 1, -36, 37, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -26, 255, -1118, 1849], 'euler47': [1, 0, -47, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 53, 0, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, -15, 136, -915, 3721], 'euler67': [1, -16, 189, -1072, 4489], 'euler7': [1, -4, 7, 0, 0], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 27, 316, 1971, 5329], 'euler79': [1, -13, 90, -1027, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, -89, 0, 7921], 'euler97': [1, 0, 169, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 3, 0, 0], [1, 0, 0, 0, 0], [1, -4, 7, 0, 0], [1, 0, 11, 0, 121], [1, 0, 22, 0, 169], [1, 0, -17, 0, 289], [1, 6, 31, 114, 361], [1, 0, 23, 0, 529], [1, 0, -58, 0, 841], [1, -3, 34, -93, 961], [1, 1, -36, 37, 1369], [1, 0, 82, 0, 1681], [1, -26, 255, -1118, 1849], [1, 0, -47, 0, 2209], [1, 0, 53, 0, 2809], [1, 0, -59, 0, 3481], [1, -15, 136, -915, 3721], [1, -16, 189, -1072, 4489], [1, 0, -142, 0, 5041], [1, 27, 316, 1971, 5329], [1, -13, 90, -1027, 6241], [1, 0, 166, 0, 6889], [1, 0, -89, 0, 7921], [1, 0, 169, 0, 9409]], 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/bi/c'], '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': '4-2100e2-1.1-c1e2-0-17', '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': '4-2100e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 762873803928710318, 'z1': {'__RealLiteral__': 0, 'data': '0.62294794295915339493503069249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '789680333803111612766598605194,1315506135378361027643402767223', 'Lhash_array': ['789680333803111612766598605194', '1315506135378361027643402767223'], 'factors': ['2-2100-21.5-c1-0-16', '2-2100-21.17-c1-0-26'], 'label': '4-2100e2-1.1-c1e2-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/bi/c'}