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lfunc_lfunctions • Show schema
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{'Lhash': '1419852201870665054190970690269', 'a10': [-0.6233292740332399, 0.24954339807873602], 'a2': [0.18039566624217274, 0.017225697554462086], 'a3': [-0.690079011482112, 0.7237340381050702], 'a4': [-1.9316115227826938, -0.37228760634717367], 'a5': [-3.2932270552636838, 1.6977765469139643], 'a6': [-0.13695408668632306, 0.11867139164562913], 'a7': [0.6353498001961292, -2.5683322665478348], 'a8': [-0.6897928275589442, -0.20254144881017236], 'a9': [-0.0475819158237423, -0.998867339183008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.690079011482112, -0.7237340381050702]]], [7, [[1.0, 0], [-0.6353498001961292, 2.5683322665478348]]], [23, [[1.0, 0], [4.543389224711459, 1.5354524912141723]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.19', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '748037682842150368997312691945', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.18039566624217274, -0.017225697554462086], [1.9638573945254134, 0.37850248872082043]], [[1.0, 0], [0.690079011482112, -0.7237340381050702]], [[1.0, 0], [3.2932270552636838, -1.6977765469139643], [2.900284547855991, -4.072879760251679]], [[1.0, 0], [-0.6353498001961292, 2.5683322665478348]], [[1.0, 0], [-0.27700296937675345, -2.9009063379750053], [-10.801215669889773, 2.081763687964512]], [[1.0, 0], [-6.10711965251296, -0.8780712448614877], [12.473408656988466, 3.662523238938586]], [[1.0, 0], [-1.7204227973847452, 4.970835222054793], [-13.362902610627387, -10.50870276575029]], [[1.0, 0], [1.7902451842141431, 5.172573759969487], [-14.935008800112962, 11.7450207381915]], [[1.0, 0], [4.543389224711459, 1.5354524912141723]], [[1.0, 0], [-0.9429734156755959, -1.0882493339167838], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-7.09866319966096, 1.722117058535401], [27.553898908302628, 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'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.20189754744119381, 'root_number': '0.8054986633840058 + 0.5925975896732791*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.100948773721', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12006589324773962615421695172', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54991012377640480010858190208', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15191177928636344077003596544', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.19', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/19'], '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': '2-483-161.19-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': '2-483-161.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.10094877372059691, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12006589324773962615421695172', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1419852201870665054190970690269', 'Lhash_array': ['1419852201870665054190970690269'], 'label': '2-483-161.19-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/19'}