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lfunc_lfunctions • Show schema
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{'Lhash': '3955685475384399020154181879783', 'a10': [-1.6177975625866372, 2.1178772279375004], 'a2': [1.1200958013199653, -0.8633570500467257], 'a3': [0.05307730234741501, -0.19808718908924766], 'a4': [0.509229208269231, -1.9340852135946576], 'a5': [-1.8202862465561118, 0.4877442297581897], 'a6': [-0.11156830771941093, -0.26770129197324277], 'a7': [1.849331264304137, -1.8920818890490079], 'a8': [-1.099420606456219, -2.6060073541913575], 'a9': [2.5616548768965153, 1.4789721327471208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8943245026383407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1200958013199653, 0.8633570500467257]]], [7, [[1.0, 0], [-1.849331264304137, 1.8920818890490079]]]], 'bad_primes': [2, 7], 'central_character': '112.19', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '2600393204638689251391166424223', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'5.63401278626575310731307788332406', '7.22672805012713971212345456291422', '8.103467150338102257625282879953181', '9.222129193356392619708358978782825', '11.13270326246337693014841603291680', '11.86253712968622592959569089518811', '12.81735526537097257427838068448459', '13.85188508094204150808743927565621'], 'prelabel': '2-112-112.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9456873175835344, 'root_angle': 0.32560617077102205, 'root_number': '0.5208739001028329 + 0.8536336334702752*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.162803085386', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.12048562488134542247559895899', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.58846511821549714061640895171', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.63401278626575310731307788332', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8943245026383407, 'bad_primes': [2, 7], 'central_character': '112.19', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/2/v/a/19/11'], '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': '2-112-112.19-c1-0-11', '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': '2-112-112.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9456873175835344, 'root_angle': 0.16280308538551103, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.12048562488134542247559895899', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3955685475384399020154181879783', 'Lhash_array': ['3955685475384399020154181879783'], 'label': '2-112-112.19-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/2/v/a/19/11'}