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lfunc_lfunctions • Show schema
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{'Lhash': '227905480352950152257242920523', 'a10': [4.291502622129181, 7.433100582342803], 'a2': [-1.224744871391589, -0.7071067811865476], 'a3': [0, 0], 'a4': [1.0, 1.7320508075688772], 'a5': [-5.255995827016271, -3.034550605587394], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, -2.8284271247461903], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03275931657819, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.224744871391589, 0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.863', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '1274988552186501500316262733995', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.255995827016271, 3.034550605587394], [12.5, 21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[[1.0, 0], [-66.33202097703345, -114.8904305009465], [-2244.5, 3887.5880375883453]], [[1.0, 0], [0, -12.138202422349575], [-5041.0, 0]], [[1.0, 0], [-38.457513110645905, -66.61036664038492], [-2664.5, 4615.049376767273]], [[1.0, 0], [16.833989511483274, -29.157325127970616], [-3120.5, -5404.864545018681]], [[1.0, 0], [0, -60.576408897686555], [-6889.0, 0]], [[1.0, 0], [4.135322155300299, 2.3875293595484512], [3960.5, 6859.787223376538]], [[1.0, 0], [188.413057686842, 0], [9409.0, 0]], [[1.0, 0], [92.41620219022717, -53.35651921201053], [5100.5, -8834.325144005059]], [[1.0, 0], [65.74901573277509, -113.8806357968119], [-5304.5, -9187.66350874911]], [[1.0, 0], [-71.34259423479585, -41.18966598614563], [5724.5, 9915.124847928038]], [[1.0, 0], [16.91502622129181, 29.297684826637216], [-5940.5, 10289.247822362915]], [[1.0, 0], [0, -28.519045531818435], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-882-21.2-c2-0-4', 'leading_term': '0.368109754192620491829979167949086793375407629449068935', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/3/s/e/863/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.3681097541926205, 0.2585920077003048, 0.13863523855026055, 0.00917023532155347, -0.12879235157251184, -0.2741449899994573, -0.4256657868864386, -0.5820018516431005, -0.7416548005913135, -0.9029696445223323, -1.0641281993833671, -1.2231480200656022, -1.377887687363251, -1.5260590856519756, -1.6652470996810858, -1.792936937700961, -1.9065490583979823, -2.0034814434562778, -2.081158718395111, -2.1370873842139826, -2.1689161844582654, -2.1745004005778616, -2.151968647837948, -2.0997905404654875, -2.0168434149335046, -1.902476151682605, -1.7565680258838225, -1.5795804547882004, -1.37259950014379, 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'8.981616921572864649106338210681888', '9.597845333395858164695457752128852'], 'prelabel': '2-882-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.43040748454347083, 'root_number': '0.2168937427126198451204379472713968874232571735022005397 - 0.9761952183718745637671305469550791571164894409176918445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21520374227173542', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17978572353605777820556918976', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92855990831688585391888783216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29408018365350200546128548804', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.03275931657819, 'bad_primes': [2, 3, 7], 'central_character': '21.2', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/s/e/863/1'], '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': '2-882-21.2-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-882-21.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.21520374227173542, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17978572353605777820556918976', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '227905480352950152257242920523', 'Lhash_array': ['227905480352950152257242920523'], 'label': '2-882-21.2-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/s/e/863/1'}