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lfunc_lfunctions • Show schema
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{'Lhash': '3161019990053540145376846609404', 'a10': [0.0, 0.0], 'a2': [0.24697960371746705, 0.0], 'a3': [0.8019377358048383, 0.0], 'a4': [-1.9390010753475628, 0.0], 'a5': [0.0, 0.0], 'a6': [0.19806226419516174, 0.0], 'a7': [-1.6920214716300959, 0.0], 'a8': [-0.9728529246320177, 0.0], 'a9': [-2.3568958678922094, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '3161019990053540145376846609404', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.24697960371746705, 0], [2.0, 0]], [[1.0, 0], [-0.8019377358048383, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6920214716300959, 0], [7.0, 0]], [[1.0, 0], [0.9118539999795806, 0], [11.0, 0]], [[1.0, 0], [1.554958132087371, 0], [13.0, 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'6.80098234552011968694517866111826', '8.178843731293774651268875315309202', '8.699501878265709242751964599774926', '9.592976761335609728551788366749462', '10.33942094150731785763303667945756'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, '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': '2.49360509077534941248010796185', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.62132915979255091333277020305', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69087455650447651896649455709', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/d/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': '2-475-1.1-c1-0-24', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49360509077534941248010796185', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3161019990053540145376846609404', 'Lhash_array': ['3161019990053540145376846609404'], 'label': '2-475-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/d/1/3'}