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lfunc_lfunctions • Show schema
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{'Lhash': '1611558699627777625477388208219', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -173.9482681718907], 'a6': [0, 0], 'a7': [484.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.12778804125855, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '144.17', 'coefficient_field': 'CDF', 'conductor': 144, 'conductor_radical': 6, 'conjugate': '1161174052837253137902871838275', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 173.9482681718907], [-15625.0, 0]], [[1.0, 0], [-484.0, 0], [117649.0, 0]], [[1.0, 0], [0, -1340.674457129694], [-1771561.0, 0]], [[1.0, 0], [-3368.0, 0], [4826809.0, 0]], [[1.0, 0], [0, 12.727922061357855], [-24137569.0, 0]], [[1.0, 0], [5744.0, 0], [47045881.0, 0]], [[1.0, 0], [0, 3377.141986946951], [-148035889.0, 0]], 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'2.80971070822736746315287972799123', '4.07536074456574609125939238882816', '5.70754577173580074259172128053071', '6.70100945721013363536436576812781', '7.982442961510968947010264665720710', '8.772853546570716716963485991315629', '10.58971707827712798579318381849925', '10.94325142230083535338597538768553', '11.75658301839717524534462347246319'], 'prelabel': '2-12e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.755674421061232, 'root_angle': 0.3040867239846964, 'root_number': '0.5773502691896257645091487805019574556476017512701268761 + 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1520433619923482', 'prec': 60}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27129565460516531850455623138', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80971070822736746315287972799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07536074456574609125939238883', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.12778804125855, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/7/e/d/17/1'], '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': '2-12e2-3.2-c6-0-8', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-12e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.755674421061232, 'root_angle': 0.1520433619923482, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27129565460516531850455623138', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1611558699627777625477388208219', 'Lhash_array': ['1611558699627777625477388208219'], 'label': '2-12e2-3.2-c6-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/7/e/d/17/1'}