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lfunc_lfunctions • Show schema
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{'Lhash': '1774036498421433547010069132224', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 5.30218681787435], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0.20662459801748023], 'a8': [0, 0], 'a9': [-19.11318505164053, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.798421148823756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '800.351', 'coefficient_field': 'CDF', 'conductor': 800, 'conductor_radical': 10, 'conjugate': '362523181206679149216291247618', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.30218681787435], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.20662459801748023], [-49.0, 0]], [[1.0, 0], [0, 15.017622831783662], [-121.0, 0]], [[1.0, 0], [11.699935855605572, 0], [169.0, 0]], [[1.0, 0], [-18.19112443971374, 0], [289.0, 0]], [[1.0, 0], [0, 19.399871711211144], [-361.0, 0]], [[1.0, 0], [0, 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'3.46868957315388694714585776217306', '5.07120599242926733142273387453524', '5.92231434120680956082472172114006', '6.96889489303890563426014459686243', '7.55600871711364804729649121282580', '8.009247094928790964246259837808081', '9.346389061779468604801147616784847', '10.03797439772891393557691478609765'], 'prelabel': '2-800-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.668877932525518, 'root_angle': 0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39946803803984614867414536093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14888236591819552324899314748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46868957315388694714585776217', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.798421148823756, 'bad_primes': [2, 5], 'central_character': '4.3', 'conductor': 800, 'conductor_radical': 10, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/800/3/b/i/351/6'], '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': '2-800-4.3-c2-0-27', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-800-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.668877932525518, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39946803803984614867414536093', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1774036498421433547010069132224', 'Lhash_array': ['1774036498421433547010069132224'], 'label': '2-800-4.3-c2-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/800/3/b/i/351/6'}