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lfunc_lfunctions • Show schema
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{'Lhash': '1350828578706440566375347060976,1477161462923137919755849027005', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.612674220014505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 1]], [5, [1]], [13, [1, 0, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '975.1', 'coefficient_field': '1.1.1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 1], [1], [1, 0, -13, 0, 49], [1, -10, 47, -110, 121], [1, 0, 1], [1, 0, 15, 0, 289], [1, -12, 74, -228, 361], [1, 0, -37, 0, 529], [1, 4, 62, 116, 841], [1, -4, 66, -124, 961], [1, 0, -25, 0, 1369], [1, -18, 163, -738, 1681], [1, 0, -22, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, -81, 0, 2809], [1, 0, 118, 0, 3481], [1, -10, 147, -610, 3721], [1, 0, -118, 0, 4489], [1, -18, 223, -1278, 5041], [1, 0, -110, 0, 5329], [1, -6, 167, -474, 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'1.16527492879914064662368930021608', '2.32357140714888001353167288909256', '2.79294761687251196328087093583850', '3.73116461641501034639507186577011', '3.86281532014586325850132885485430', '4.25303219057324838174535968170724', '5.16828518296412863150588415303230', '5.32632479725822535632326487500380', '6.18490496518153754585792650510734', '6.25274741289702926900474348398221', '6.84709493670711635863691803817692', '7.39288382163713073087305494813367', '7.42827363512632460370386271466824', '8.187482288672853866644552945812628', '8.740472855889520499932547426010707', '9.217628409188435316700700330816219', '9.243254900933984545463546409235531', '9.633176476545315607029227176635287', '9.996394008838985257822741622651004'], 'prelabel': '4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, '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': 907032545297132249, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06561585539677549750123855956', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.16527492879914064662368930022', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.32357140714888001353167288909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.612674220014505, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 950625, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 0, 0, 0, -4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0], 'euler11': [1, -10, 47, -110, 121], 'euler13': [1, 0, 1, 0, 0], 'euler17': [1, 0, 15, 0, 289], 'euler19': [1, -12, 74, -228, 361], 'euler2': [1, 0, 0, 0, 4], 'euler23': [1, 0, -37, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 0, -25, 0, 1369], 'euler41': [1, -18, 163, -738, 1681], 'euler43': [1, 0, -22, 0, 1849], 'euler47': [1, 0, 6, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -81, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, -10, 147, -610, 3721], 'euler67': [1, 0, -118, 0, 4489], 'euler7': [1, 0, -13, 0, 49], 'euler71': [1, -18, 223, -1278, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, -6, 167, -474, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 22, 299, 1958, 7921], 'euler97': [1, 0, -73, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 4], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -13, 0, 49], [1, -10, 47, -110, 121], [1, 0, 1, 0, 0], [1, 0, 15, 0, 289], [1, -12, 74, -228, 361], [1, 0, -37, 0, 529], [1, 4, 62, 116, 841], [1, -4, 66, -124, 961], [1, 0, -25, 0, 1369], [1, -18, 163, -738, 1681], [1, 0, -22, 0, 1849], [1, 0, 6, 0, 2209], [1, 0, -81, 0, 2809], [1, 0, 118, 0, 3481], [1, -10, 147, -610, 3721], [1, 0, -118, 0, 4489], [1, -18, 223, -1278, 5041], [1, 0, -110, 0, 5329], [1, -6, 167, -474, 6241], [1, 0, -150, 0, 6889], [1, 22, 299, 1958, 7921], [1, 0, -73, 0, 9409]], 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/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': '4-975e2-1.1-c1e2-0-28', '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': '4-975e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 907032545297132249, 'z1': {'__RealLiteral__': 0, 'data': '1.06561585539677549750123855956', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1350828578706440566375347060976,1477161462923137919755849027005', 'Lhash_array': ['1350828578706440566375347060976', '1477161462923137919755849027005'], 'label': '4-975e2-1.1-c1e2-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/c'}