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lfunc_lfunctions • Show schema
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{'Lhash': '168305971574023809942744769859', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [4.193218966553319, 2.723401310592605], 'a6': [0, 0], 'a7': [0, -3.4385656936812126], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-4.193218966553319, -2.723401310592605]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.809', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1828435603444746481501903398783', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.193218966553319, -2.723401310592605]], [[1.0, 0], [0, 3.4385656936812126], [-49.0, 0]], [[1.0, 0], [0, 12.82172663407183], [-121.0, 0]], [[1.0, 0], [0, 1.7938760847168278], [-169.0, 0]], [[1.0, 0], [30.952337105941012, 0], [289.0, 0]], 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['0.13277000108998630384213170688811', '2.02957862853434421444033065411544', '2.20464028184857417649319981506470', '4.01355328096929777095269066580651', '4.72261186903755967095270622828405', '5.59599839773856257602934502489337', '6.45197438253236502851142082061400', '7.13935296035195453275321395309011', '8.288374776289678286648376935928453', '9.047680296684922697508840568575105'], 'prelabel': '2-1620-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.8166510190398159, 'root_number': '-0.8386437933106637613589260494157441167192425695257675408 - 0.5446802621185209429730057489012366720125406196347997318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.408325509519908', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13277000108998630384213170689', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02957862853434421444033065412', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.20464028184857417649319981506', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/b/a/809/22'], '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': '2-1620-15.14-c2-0-3', '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': '2-1620-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.4083255095199079, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.13277000108998630384213170689', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '168305971574023809942744769859', 'Lhash_array': ['168305971574023809942744769859'], 'label': '2-1620-15.14-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/b/a/809/22'}