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lfunc_lfunctions • Show schema
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{'Lhash': '1890244222347828272196399483331', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [203.36605146451672, -117.41344455707001], 'a6': [0, 0], 'a7': [1130.3390814554416, 2118.2857599800996], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 102.6594097354041, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1130.3390814554416, -2118.2857599800996]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.73', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '59644566668364446146992945420', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-203.36605146451672, 117.41344455707001], [195312.5, -338291.17335329636]], [[1.0, 0], [-1130.3390814554416, -2118.2857599800996]], [[1.0, 0], [-7474.441563572267, 12946.112546311728], [-107179440.5, 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[-9962813208450960.0, -17256098663355364]], [[1.0, 0], [214139914.1931219, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-252-7.3-c8-0-23', 'leading_term': '0.236417543567188988986754742526331555470238943372261890', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/252/9/z/d/73/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.236417543567189, 0.5484847367749782, 0.8528032677650725, 1.1435408377394427, 1.4151418758004668, 1.6624389200579508, 1.8807569062803586, 2.066008424623772, 2.2147781393287844, 2.324394729371953, 2.3929888987514385, 2.419536221926079, 2.4038838311101207, 2.3467602154490033, 2.249767684919165, 2.115357350981797, 1.9467867879464147, 1.7480608595152307, 1.5238565194169207, 1.2794327182349128, 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'4.54539603837038583108683020031799', '6.59291412315165731128247395408767', '6.75457130848951671569241922598193', '8.255157163326787737841394297366522', '9.150990799271794868321314683742167', '10.22359456078782251580788379448004', '10.98893493711067351344512369005361'], 'prelabel': '2-252-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.13209799278531, 'root_angle': 0.9702938722170695, 'root_number': '-0.99564842362507465887543678460220606978600642042052903466 + 0.0931891438575538898383249473823365180282744242258404493*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.48514693610853477', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49113976833009532383962044013', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38091674890544825921570039176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27272886466162636917379273712', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 102.6594097354041, 'bad_primes': [2, 3, 7], 'central_character': '7.3', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/9/z/d/73/4'], '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': '2-252-7.3-c8-0-23', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-252-7.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.13209799278531, 'root_angle': 0.48514693610853477, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49113976833009532383962044013', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1890244222347828272196399483331', 'Lhash_array': ['1890244222347828272196399483331'], 'label': '2-252-7.3-c8-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/9/z/d/73/4'}