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lfunc_lfunctions • Show schema
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{'Lhash': '724719665901770843591417919938', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1.4142135623730951, -2.23606797749979], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.152876636703333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.4142135623730951, 2.23606797749979]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3150.251', 'coefficient_field': 'CDF', 'conductor': 3150, 'conductor_radical': 210, 'conjugate': '1078273520755620474353966755402', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 2.23606797749979]], [[1.0, 0], [0, -1.4142135623730951], [-11.0, 0]], [[1.0, 0], [0, 0.9262096826685896], [-13.0, 0]], [[1.0, 0], [2.23606797749979, 0], [17.0, 0]], [[1.0, 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'4.21604127660646282515941997583573', '5.01922632638506484168355111732076', '5.78461380436361397365085703112338', '6.53730279075216729875404632203661', '7.04597913649600945161109375264878', '8.015143563879628099208558773440437', '8.871726537057206116902411316571137'], 'prelabel': '2-3150-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015264363590751, 'root_angle': 0.12457820599900832, 'root_number': '0.9243858169462513522093872889512889985097117055709893684 + 0.3814588594181703972739379390991321459730918365571726923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06228910299950416', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57170301167474019055647450567', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28104005597174552675915997213', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09798031129740401547725106931', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.152876636703333, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.20', 'conductor': 3150, 'conductor_radical': 210, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3150/2/b/d/251/1'], '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': '2-3150-21.20-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3150-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015264363590751, 'root_angle': 0.06228910299950416, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57170301167474019055647450567', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '724719665901770843591417919938', 'Lhash_array': ['724719665901770843591417919938'], 'label': '2-3150-21.20-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3150/2/b/d/251/1'}