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lfunc_lfunctions • Show schema
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{'Lhash': '290148602786793705474079294590', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.7025010097512567, 1.5831905543232832], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [1.0198327341999023, -1.3999789977904495], 'a7': [-2.5623816969241155, -0.6589385701780474], 'a8': [1.0, 0.0], 'a9': [-2.0129846625969297, 2.2243859260815166], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.7025010097512567, -1.5831905543232832]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [2.5623816969241155, 0.6589385701780474]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.331', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '2884184705280387328168258373637', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], 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'5.06435722564729813411055883045566', '5.91891844008547399405538196092685', '6.78841224989512433951597535058173', '7.51606759046608451753149162632924', '8.483664471663689166475900796073596', '9.091984544680371729014878943291477', '10.16382806853957870056867574460714'], 'prelabel': '2-630-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': -0.8170311859803542, 'root_number': '-0.8392937228219013 - 0.5436782567215224*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.40851559299', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22888688944300187108818542133', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21694483529210823960069661927', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15260748959110185665882821794', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.16', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/l/g/331/4'], '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': '2-630-63.16-c1-0-2', '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': '2-630-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': -0.4085155929901771, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.22888688944300187108818542133', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '290148602786793705474079294590', 'Lhash_array': ['290148602786793705474079294590'], 'label': '2-630-63.16-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/l/g/331/4'}