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lfunc_lfunctions • Show schema
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{'Lhash': '3478403015856828128153941509138', 'a10': [-6.472912178926085, 0.0], 'a2': [1.759376246814866, 0.0], 'a3': [-1.6741407118633922, 0.0], 'a4': [1.0954047778563643, 0.0], 'a5': [-3.679094901186994, 0.0], 'a6': [-2.945443402278183, 0.0], 'a7': [4.14977469882292, 0.0], 'a8': [-1.5915233468217296, 0.0], 'a9': [-0.19725287688153462, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '403.1', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '3478403015856828128153941509138', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.759376246814866, 0], [2.0, 0]], [[1.0, 0], [1.6741407118633922, 0], [3.0, 0]], [[1.0, 0], [3.679094901186994, 0], [5.0, 0]], [[1.0, 0], [-4.14977469882292, 0], [7.0, 0]], [[1.0, 0], [5.077389634250575, 0], 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'4.74933227691358777173825891207370', '5.55919912917070163629223264068013', '6.83378888526320230706891417558571', '8.050450980546888272970793017149954', '8.478525156994768361649623652473797', '10.65070621310986879700617733031005', '11.08375532002677465931053240060233'], 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, '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': '2.74397615181231491808909336759', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.31367599863913343511589802024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74933227691358777173825891207', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/a/d/1/8'], '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': '2-403-1.1-c1-0-26', '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': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.74397615181231491808909336759', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3478403015856828128153941509138', 'Lhash_array': ['3478403015856828128153941509138'], 'label': '2-403-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/a/d/1/8'}