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lfunc_lfunctions • Show schema
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{'Lhash': '1375279123199280686169732722069', 'a10': [0.446192741465762, 0.7728284981871444], 'a2': [0.3280919624019473, -0.5682719484351506], 'a3': [-0.10237666626965668, -0.17732158748856827], 'a4': [0.7847113284144783, 1.3591598900887438], 'a5': [-0.6799812134975876, 1.1777620099701616], 'a6': [-0.13435584536232362, 1.2898723766774303e-61], 'a7': [0.0, 0.0], 'a8': [2.34219776824197, 0.0], 'a9': [1.4790380364070226, -2.56176902538387], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.79', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2044441350727822497013710838101', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3280919624019473, 0.5682719484351506], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.10237666626965668, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-637-7.2-c1-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/e/o/79/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8552889650498656, 1.7653475422384604, 1.6596045815001854, 1.5304971910527785, 1.3688354851980509, 1.1657578836573668, 0.9146140359793432, 0.6125833212576083, 0.26194453194702394, -0.1290548249232616, -0.545795084046884, -0.9674322640320184, -1.367682594427477, -1.7162994449428355, -1.9812396971424706, -2.1314352710452376, -2.1399914696550995, -1.9875396730745805, -1.6653922534858667, -1.1780975908524525, -0.54498674419947, 0.19964879035104227, 1.0080020108397678, 1.8219092352681647, 2.577607927719835, 3.2117504269336092, 3.66810934208232, 3.9042302006074676, 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'8.634761165294135347277855764750986', '9.930994250228488608046393541556429', '10.32250938931194410387575492852436'], 'prelabel': '2-637-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.14354881026837107, 'root_number': '0.9000239394702093 - 0.43584046207359534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0717744051342', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08490393405854397940420843815', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59286359570185568096281982255', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32866479282705145328007303837', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '7.2', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/e/o/79/4'], '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': '2-637-7.2-c1-0-14', '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': '2-637-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.07177440513418554, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08490393405854397940420843815', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1375279123199280686169732722069', 'Lhash_array': ['1375279123199280686169732722069'], 'label': '2-637-7.2-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/e/o/79/4'}