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lfunc_lfunctions • Show schema
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{'Lhash': '2059613726883201386980113103128', 'a10': [0.0, 0.0], 'a2': [0.3696803841210112, 0.0], 'a3': [-1.2768396985835726, 0.0], 'a4': [-1.8633364135961417, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.4720225902333313, 0.0], 'a7': [1.4936560294751304, 0.0], 'a8': [-1.4281996893669113, 0.0], 'a9': [-1.3696803841210112, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.583918217287646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 43], 'central_character': '1075.1', 'coefficient_field': 'CDF', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3696803841210112, 0], [2.0, 0]], [[1.0, 0], [1.2768396985835726, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4936560294751304, 0], [7.0, 0]], [[1.0, 0], [-3.686918474484541, 0], [11.0, 0]], [[1.0, 0], [-3.616267250571723, 0], [13.0, 0]], [[1.0, 0], [5.000644039072215, 0], 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'6.14602241258999256371964122774180', '6.50601006398646804262922770885408', '8.026238170011618857088958812206069', '8.804195996087228114691402666230388', '9.201494522786011758492437889933389'], 'prelabel': '2-1075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.929832455497694, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.62474874899470402365962240706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40759582315194519582462784292', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36349535666295560606446320470', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.583918217287646, 'bad_primes': [5, 43], 'central_character': '1.1', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1075/2/a/n/1/3'], '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': '2-1075-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.929832455497694, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.62474874899470402365962240706', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2059613726883201386980113103128', 'Lhash_array': ['2059613726883201386980113103128'], 'label': '2-1075-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1075/2/a/n/1/3'}