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lfunc_lfunctions • Show schema
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{'Lhash': '681072449748676656177242410973,1188795930907803567957543156001', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1325.8179646667124, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [5, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': '1.1.1.1', 'conductor': 20793600, 'conductor_radical': 570, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, 2, 1], [1, -4, 16, -28, 49], [1, 0, 20, 0, 121], [1, 0, 8, 0, 169], [1, 0, 26, 0, 289], [1, -2, 1], [1, -4, 42, -92, 529], [1, 4, 44, 116, 841], [1, -12, 90, -372, 961], [1, 0, 24, 0, 1369], [1, 4, 68, 164, 1681], [1, -12, 104, -516, 1849], [1, 4, 90, 188, 2209], [1, 8, 50, 424, 2809], [1, 0, 110, 0, 3481], [1, 16, 186, 976, 3721], [1, 0, 6, 0, 4489], [1, -16, 198, -1136, 5041], [1, -4, 118, -292, 5329], [1, 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0.051490817704732225, 0.49872996968008476, 1.1147497906726627], 'positive_zeros': ['0.53727142922983314127949709545629', '0.937794634178985329137266693805926', '1.58748057196747311901682976966904', '1.94355958571798899954313066482224', '2.83864412546053812854048244950584', '3.01785667320687823454346050223461', '3.89446926439897743578843011575446', '3.95329200373950509739396774568766', '4.69661079306401521636875259251395', '4.73638373518931480150586112572313', '5.23025417682103031654133567099855', '5.27235523143529734396562364262913', '6.15199153696383977971176696766952', '6.19425871892741556483277878447157', '6.80101487378957457616175655600419', '6.91076218640348467049664668993649', '7.66953936516252925853522840146401', '7.73372965530860845693000267229165', '8.051770561901685873738901575429953', '8.232734835395951866786952815297494'], 'prelabel': '4-4560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.034217705859135, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2187143838711068217, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53727142922983314127949709546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.937794634178985329137266693806', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.58748057196747311901682976967', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1325.8179646667124, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 20793600, 'conductor_radical': 570, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, -2, 0, 4, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, -8, 0, 4, 0, 3, 0, -4, 0, -4, 0, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, 12, 0, -6, 0, -4, 0, 0, 0, 0, 0, -8, 0, 0, 0, -4, 0, 0, 0, -16, 0, 12, 0, 0, 0, 0, 0, -8, 0, 16, 0, 4, 0, -6, 0, 0, 0, 16, 0, 5, 0, 12, 0, 0, 0, 8, 0, 4, 0, 0, 0, -24, 0, -4, 0, 0, 0, 0, 0], 'euler11': [1, 0, 20, 0, 121], 'euler13': [1, 0, 8, 0, 169], 'euler17': [1, 0, 26, 0, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 42, -92, 529], 'euler29': [1, 4, 44, 116, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -12, 90, -372, 961], 'euler37': [1, 0, 24, 0, 1369], 'euler41': [1, 4, 68, 164, 1681], 'euler43': [1, -12, 104, -516, 1849], 'euler47': [1, 4, 90, 188, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 8, 50, 424, 2809], 'euler59': [1, 0, 110, 0, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, 6, 0, 4489], 'euler7': [1, -4, 16, -28, 49], 'euler71': [1, -16, 198, -1136, 5041], 'euler73': [1, -4, 118, -292, 5329], 'euler79': [1, -16, 190, -1264, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, -4, -60, -356, 7921], 'euler97': [1, 0, 96, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -4, 16, -28, 49], [1, 0, 20, 0, 121], [1, 0, 8, 0, 169], [1, 0, 26, 0, 289], [1, -2, 1, 0, 0], [1, -4, 42, -92, 529], [1, 4, 44, 116, 841], [1, -12, 90, -372, 961], [1, 0, 24, 0, 1369], [1, 4, 68, 164, 1681], [1, -12, 104, -516, 1849], [1, 4, 90, 188, 2209], [1, 8, 50, 424, 2809], [1, 0, 110, 0, 3481], [1, 16, 186, 976, 3721], [1, 0, 6, 0, 4489], [1, -16, 198, -1136, 5041], [1, -4, 118, -292, 5329], [1, -16, 190, -1264, 6241], [1, -12, 202, -996, 6889], [1, -4, -60, -356, 7921], [1, 0, 96, 0, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4560/2/a/bg'], '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': '4-4560e2-1.1-c1e2-0-2', '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': '4-4560e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.034217705859135, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2187143838711068217, 'z1': {'__RealLiteral__': 0, 'data': '0.53727142922983314127949709546', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '681072449748676656177242410973,1188795930907803567957543156001', 'Lhash_array': ['681072449748676656177242410973', '1188795930907803567957543156001'], 'label': '4-4560e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bg'}