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lfunc_lfunctions • Show schema
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{'Lhash': '1547866255245457964802223097542', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.848257833028395], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 1.7448354690360532], 'a8': [0, 0], 'a9': [2.2804586487059715, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.34315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.3649', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '961871988445819066393954981969', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.848257833028395], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.7448354690360532], [-7.0, 0]], [[1.0, 0], [-5.924253124549462, 0], [11.0, 0]], [[1.0, 0], [0, 6.785823120403602], [-13.0, 0]], [[1.0, 0], [0, -1.8602397879446746], [-17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'4.58887128385372017041781616547880', '5.60095463038775083830483832420408', '6.80304683040596534375394544574238', '6.87712206170750253262522843812154', '7.74511386516323201435774703776532', '9.014812229529090606949252830805572'], 'prelabel': '2-3800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22105117527398968286102999411', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91303258702036406006892527806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60018044465088418457920987096', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.34315276808656, 'bad_primes': [2, 5, 19], 'central_character': '5.4', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 60, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/d/q/3649/5'], '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': '2-3800-5.4-c1-0-60', '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': '2-3800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22105117527398968286102999411', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1547866255245457964802223097542', 'Lhash_array': ['1547866255245457964802223097542'], 'label': '2-3800-5.4-c1-0-60', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/d/q/3649/5'}