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lfunc_lfunctions • Show schema
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{'Lhash': '2356074781675622495961724318001', 'a10': [-9.19985946770019, -15.934624020550295], 'a2': [-1.8399718935400378, 3.186924804110059], 'a3': [-1.5, -2.598076211353316], 'a4': [-2.770993138034625, -4.799500902500689], 'a5': [-2.5, 4.330127018922194], 'a6': [11.039831361240227, 9.830318508431337e-61], 'a7': [5.0817239709109, 17.809437988984087], 'a8': [-9.045352331936526, 0.0], 'a9': [-4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.195200550602768, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, 2.598076211353316]]], [5, [[1.0, 0], [2.5, -4.330127018922194]]], [7, [[1.0, 0], [-5.0817239709109, -17.809437988984087]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.16', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '34334453201751674451878653809', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8399718935400378, -3.186924804110059], [-4.0, 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'9.693309676655131468918219333510940', '10.42681412269498297663526340702004', '11.15127404776035370039605885524426', '12.34326681225941281322042587315505', '13.08654927359734278448260269585097'], 'prelabel': '2-105-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.558018687097541, 'root_number': '-0.18126349867672759 + 0.9834345652088257*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.279009343549', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85861528504102931978589823275', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81407876482468821749707271274', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.08703108310779805543292292588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.195200550602768, 'bad_primes': [3, 5, 7], 'central_character': '7.2', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/4/i/d/16/2'], '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': '2-105-7.2-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-105-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.2790093435487705, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85861528504102931978589823275', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2356074781675622495961724318001', 'Lhash_array': ['2356074781675622495961724318001'], 'label': '2-105-7.2-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/4/i/d/16/2'}