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lfunc_lfunctions • Show schema
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{'Lhash': '643784947141818965823190642346,964582044254292928913794810967', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3725.5943885377233, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '7644.1', 'coefficient_field': '1.1.1.1', 'conductor': 58430736, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 1, 2, 5, 25], [1], [1, -4, 26, -44, 121], [1, -2, 1], [1, 0, 34, 0, 289], [1, 7, 42, 133, 361], [1, -3, 40, -69, 529], [1, 3, 52, 87, 841], [1, -1, 54, -31, 961], [1, -2, 42, -74, 1369], [1, 6, 58, 246, 1681], [1, -5, 18, -215, 1849], [1, -7, 98, -329, 2209], [1, -5, 104, -265, 2809], [1, -16, 182, -944, 3481], [1, 12, 158, 732, 3721], [1, -14, 150, -938, 4489], [1, 6, 118, 426, 5041], [1, 1, -60, 73, 5329], [1, -5, 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['0.50785677616995654619015389336577', '0.76092106459037558910641398196006', '1.54989730858972343540937227116108', '1.79461396008775756194560689390896', '2.45659779218722649991064154283212', '2.87873491698267737217202065508336', '3.67961576420719775120124934790156', '3.74456166261019688731733419534999', '4.23794332031473584731802141805419', '4.33948800390894330558888376112488', '4.93447468015548704998185027680296', '5.25697696782888812571226921187531', '5.80124821209625027960061926441377', '5.83439717668421762673464716386753', '6.45196946005752336279303381948907', '6.58621968710743022131789556476646', '6.91374354999532100307991331989196', '7.17339974202224055847078632512972', '7.80646403650249034745819303763283', '7.83422983549892817206374131692144'], 'prelabel': '4-7644e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.812659425897609, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3725.5943885377233, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 58430736, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -1, 0, 0, 0, 3, 0, 4, 0, 2, 0, 2, 0, 0, 0, -7, 0, 0, 0, 3, 0, -1, 0, -4, 0, -3, 0, 1, 0, -8, 0, 0, 0, 2, 0, -4, 0, -6, 0, 5, 0, -3, 0, 7, 0, 0, 0, 0, 0, 5, 0, -4, 0, 14, 0, 16, 0, -12, 0, 0, 0, -2, 0, 14, 0, -6, 0, -6, 0, -1, 0, 2, 0, 0, 0, 5, 0, 5, 0, -5, 0, 0, 0, 6, 0, 9, 0, 0, 0, -2, 0, 7, 0, -29, 0, 12, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 7, 42, 133, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -3, 40, -69, 529], 'euler29': [1, 3, 52, 87, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -1, 54, -31, 961], 'euler37': [1, -2, 42, -74, 1369], 'euler41': [1, 6, 58, 246, 1681], 'euler43': [1, -5, 18, -215, 1849], 'euler47': [1, -7, 98, -329, 2209], 'euler5': [1, 1, 2, 5, 25], 'euler53': [1, -5, 104, -265, 2809], 'euler59': [1, -16, 182, -944, 3481], 'euler61': [1, 12, 158, 732, 3721], 'euler67': [1, -14, 150, -938, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 6, 118, 426, 5041], 'euler73': [1, 1, -60, 73, 5329], 'euler79': [1, -5, 90, -395, 6241], 'euler83': [1, 5, 98, 415, 6889], 'euler89': [1, -9, 190, -801, 7921], 'euler97': [1, 29, 396, 2813, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 1, 2, 5, 25], [1, 0, 0, 0, 0], [1, -4, 26, -44, 121], [1, -2, 1, 0, 0], [1, 0, 34, 0, 289], [1, 7, 42, 133, 361], [1, -3, 40, -69, 529], [1, 3, 52, 87, 841], [1, -1, 54, -31, 961], [1, -2, 42, -74, 1369], [1, 6, 58, 246, 1681], [1, -5, 18, -215, 1849], [1, -7, 98, -329, 2209], [1, -5, 104, -265, 2809], [1, -16, 182, -944, 3481], [1, 12, 158, 732, 3721], [1, -14, 150, -938, 4489], [1, 6, 118, 426, 5041], [1, 1, -60, 73, 5329], [1, -5, 90, -395, 6241], [1, 5, 98, 415, 6889], [1, -9, 190, -801, 7921], [1, 29, 396, 2813, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7644/2/a/n'], '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': '4-7644e2-1.1-c1e2-0-7', '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': '4-7644e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.812659425897609, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 543317451463511821, 'z1': {'__RealLiteral__': 0, 'data': '0.50785677616995654619015389337', 'prec': 103}}
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{'Lhash': '643784947141818965823190642346,964582044254292928913794810967', 'Lhash_array': ['643784947141818965823190642346', '964582044254292928913794810967'], 'label': '4-7644e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7644/2/a/n'}