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lfunc_lfunctions • Show schema
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{'Lhash': '1104119318012036266753712830408', 'a10': [-6.73758518507848, 0.0], 'a2': [1.555828568469336, 0.0], 'a3': [-0.9106198928906833, 0.0], 'a4': [0.4206025344653434, 0.0], 'a5': [-4.33054471528768, 0.0], 'a6': [-1.416768444375812, 0.0], 'a7': [-1.628147989398963, 0.0], 'a8': [-2.457271697846882, 0.0], 'a9': [-2.1707714106717604, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.555828568469336, 0], [2.0, 0]], [[1.0, 0], [0.9106198928906833, 0], [3.0, 0]], [[1.0, 0], [4.33054471528768, 0], [5.0, 0]], [[1.0, 0], [1.628147989398963, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.0352193671427896, 0], [13.0, 0]], [[1.0, 0], 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'3.93428909392475790900937934002517', '4.45856977979095604832625255955106', '5.21707820473077496394866557120484', '5.86834544594476659098840359049764', '6.62708784823067516366956438837768', '7.11221102425309028063579524114731'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, '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': '0.870996564678981134147961925253', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.81617544885669414562835550851', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25678175326646662160184693030', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 330, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/31'], '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': '2-9251-1.1-c1-0-330', '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': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.870996564678981134147961925253', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1104119318012036266753712830408', 'Lhash_array': ['1104119318012036266753712830408'], 'label': '2-9251-1.1-c1-0-330', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/31'}