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lfunc_lfunctions • Show schema
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{'Lhash': '816358947112661065828737257445', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [7.231742271384567, 0], 'a6': [0, 0], 'a7': [-93.12375826453062, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.70505474934954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [361.0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.37', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.231742271384567, 0], [625.0, 0]], [[1.0, 0], [93.12375826453062, 0], [2401.0, 0]], [[1.0, 0], [-169.09217700521916, 0], [14641.0, 0]], [[1.0, 0], [0, 0], [-28561.0, 0]], [[1.0, 0], [-534.5491620717922, 0], [83521.0, 0]], [[1.0, 0], [361.0, 0]], [[1.0, 0], [1046.1357464497617, 0], [279841.0, 0]], [[1.0, 0], [0, 0], [-707281.0, 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'9.313091242272222981563338649979417', '9.831354033228673322601474955841174'], 'prelabel': '2-684-19.18-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.408629778349713, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64399365800456591011330930648', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10567316538357749232164367897', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48099822564587284079115598994', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.70505474934954, 'bad_primes': [2, 3, 19], 'central_character': '19.18', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/5/h/d/37/3'], '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': '2-684-19.18-c4-0-17', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-684-19.18-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.408629778349713, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64399365800456591011330930648', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '816358947112661065828737257445', 'Lhash_array': ['816358947112661065828737257445'], 'label': '2-684-19.18-c4-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/5/h/d/37/3'}