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lfunc_lfunctions • Show schema
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{'Lhash': '155438605780784633314881049997', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.8228854223083655, 0.7563898692331154], 'a4': [0.0, 0.0], 'a5': [1.259430976621454, 1.8476562491779498], 'a6': [0.0, 0.0], 'a7': [-2.7870617411614576, 1.6091108465076747], 'a8': [0.0, 0.0], 'a9': [4.7984802618492735, -2.7704038708797842], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.152220905106582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.259430976621454, -1.8476562491779498]]], [13, [[1.0, 0], [3.602396981999055, -0.15078456182282118]]]], 'bad_primes': [2, 5, 13], 'central_character': '520.33', 'coefficient_field': 'CDF', 'conductor': 520, 'conductor_radical': 130, 'conjugate': '2928718857043434955904299663801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.8228854223083655, -0.7563898692331154], [2.598076211353316, -1.5]], [[1.0, 0], [-1.259430976621454, 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[-97.86087062764156, -56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-520-65.33-c1-0-0', '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/520/2/cw/c/33/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.16901177965622993, -0.0031631857262368634, -0.16355288882160463, -0.3126794095197323, -0.44808419004440514, -0.5639667990033072, -0.6513533752545629, -0.6987054077144629, -0.6928812696787832, -0.620386362516754, -0.46885665834695933, -0.22870507349850236, 0.10517298024581616, 0.5317777760899848, 1.0426443746817502, 1.620939790960032, 2.2412136045580553, 2.869968760951946, 3.4671614853824315, 3.988653459059297, 4.389531108552176, 4.628085839485404, 4.670129103882014, 4.493214017985196, 4.0902686053920885, 3.4721310382003883, 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'6.56915378247798785586605306770235', '7.22226375852163122061463191448070', '8.624453926817090107279802573861304', '9.768720219642199160190302836585603', '10.34094302114888379385428541516393'], 'prelabel': '2-520-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, 'root_angle': 0.7975733595629714, 'root_number': '-0.8045125385310042 + 0.5939356659996093*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.398786679781', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12261943926252176434116337534', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46423490364281461224806345476', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58665877507938517261495533484', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.152220905106582, 'bad_primes': [2, 5, 13], 'central_character': '65.33', 'conductor': 520, 'conductor_radical': 130, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/520/2/cw/c/33/1'], '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': '2-520-65.33-c1-0-0', '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': '2-520-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, 'root_angle': 0.3987866797814857, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12261943926252176434116337534', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '155438605780784633314881049997', 'Lhash_array': ['155438605780784633314881049997'], 'label': '2-520-65.33-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/520/2/cw/c/33/1'}