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lfunc_lfunctions • Show schema
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{'Lhash': '1402867681443166020451370551810', 'a10': [-2.767242422680514, -1.5304801122906753], 'a2': [-1.374913889377152, 0.3310767234309782], 'a3': [0.0, 0.0], 'a4': [1.7807764064044151, -0.9104039709894599], 'a5': [1.6490068506818232, 1.5102239590221098], 'a6': [0.0, 0.0], 'a7': [0.9364263849242712, 0.0], 'a8': [-2.1470006513268207, 1.841300682453088], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8746144727660954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.374913889377152, -0.3310767234309782]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.6490068506818232, -1.5102239590221098]]]], 'bad_primes': [2, 3, 5], 'central_character': '360.179', 'coefficient_field': 'CDF', 'conductor': 360, 'conductor_radical': 30, 'conjugate': '2061793039765901299688476418576', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.374913889377152, -0.3310767234309782]], [[1.0, 0], [0, 0]], [[1.0, 0], 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1.8121652365021315, -0.4240645386528502], 'positive_zeros': ['1.10666746908855797198803650684799', '2.49001092251217997144707563880172', '4.12552380598186158490468204218032', '5.72379553783218024242215926162845', '6.49581414082637806121756328409545', '7.925360457674972738311337989530800', '8.632195492127046384920777036025979', '9.344844670648950130854113286643125', '10.35224192307352974266320962455969', '11.13517502896787436159661703666958'], 'prelabel': '2-360-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6954688061908114, 'root_angle': -0.2937103051717364, 'root_number': '0.603655367117131 - 0.7972453811410147*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.146855152586', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10666746908855797198803650685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49001092251217997144707563880', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12552380598186158490468204218', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8746144727660954, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 360, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/360/2/m/c/179/4'], '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': '2-360-120.59-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-360-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6954688061908114, 'root_angle': -0.1468551525858682, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10666746908855797198803650685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1402867681443166020451370551810', 'Lhash_array': ['1402867681443166020451370551810'], 'label': '2-360-120.59-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/360/2/m/c/179/4'}