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lfunc_lfunctions • Show schema
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{'Lhash': '973120032787846861514174555319', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.48175367410171527, 0.8763066800438636], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.8443279255020151, -0.5358267949789967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.48175367410171527, -0.8763066800438636]]]], 'bad_primes': [2, 5], 'central_character': '4000.2433', 'coefficient_field': 'CDF', 'conductor': 4000, 'conductor_radical': 10, 'conjugate': '1934896552692026529438152915059', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8443279255020151, 0.5358267949789967]], [[1.0, 0], [-0.48175367410171527, -0.8763066800438636]], [[1.0, 0], [0, 0], [-0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0], [0.7289686274214116, 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'4.20768919979889126216358642907926', '4.63529501759760337179274691587022', '5.44801117588648594838314027708148', '6.17967775155053456865133838244388', '7.07929874153631908741597665726251', '7.79645269002367685529669030907647', '8.553809278810817404463997991181090'], 'prelabel': '2-4000-125.58-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.41400000000000003, 'root_number': '0.26690198932037556364523766243676 - 0.96372367829000970778546847255352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.207', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76765634995372156350424394191', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03379530163509663049968379230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75672258975497628142650564088', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'bad_primes': [2, 5], 'central_character': '125.58', 'conductor': 4000, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4000/1/cq/a/2433/1'], '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': '2-4000-125.58-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-4000-125.58-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.20700000000000002, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76765634995372156350424394191', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '973120032787846861514174555319', 'Lhash_array': ['973120032787846861514174555319'], 'label': '2-4000-125.58-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4000/1/cq/a/2433/1'}