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lfunc_lfunctions • Show schema
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{'Lhash': '2255109746407392280588540759042', 'a10': [1.5950258064192895, 1.567128800340449], 'a2': [-0.7557495743542583, 0.6548607339452851], 'a3': [-1.3709565816902722, 2.1332500811406505], 'a4': [0.14231483827328514, -0.9898214418809327], 'a5': [-0.179188957907695, -2.228876694069], 'a6': [-0.36088186075401335, -2.5099884741060445], 'a7': [1.234419741249226, -4.204047560205459], 'a8': [0.5406408174555976, 0.8412535328311812], 'a9': [-1.4249889208010578, -3.120290492198609], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7557495743542583, -0.6548607339452851]]], [5, [[1.0, 0], [0.179188957907695, 2.228876694069]]], [23, [[1.0, 0], [-3.6749625833440565, -3.0813389964463793]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.59', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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'root_angle': 0.1473657462269041, 'root_number': '0.8947330827380402 + 0.44660128823603207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0736828731135', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77896791592366184961017332953', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96063184762259701357609174505', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.30973631515818804015160443739', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.59', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/j/a/59/1'], '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': '2-230-115.59-c1-0-4', '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': '2-230-115.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.07368287311345205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77896791592366184961017332953', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2255109746407392280588540759042', 'Lhash_array': ['2255109746407392280588540759042'], 'label': '2-230-115.59-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/j/a/59/1'}