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lfunc_lfunctions • Show schema
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{'Lhash': '3548809835239577021693887777289', 'a10': [259.34156641149696, 5.848381506096407e-60], 'a2': [-2.0, 3.4641016151377544], 'a3': [-10.004477497086198, -17.32826332813281], 'a4': [-8.0, -13.856406460551018], 'a5': [-32.41769580143712, -56.149096192401366], 'a6': [80.03581997668958, 2.513645161398086e-60], 'a7': [-55.24519204647913, -95.6874794984019], 'a8': [64.0, 0.0], 'a9': [-78.67913997940823, 136.27626794015876], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.86840266616057, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, -3.4641016151377544]]], [37, [[1.0, 0], [-5049.997801369323, -6621.289844597124]]]], 'bad_primes': [2, 37], 'central_character': '74.47', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '157177382822277748478849259863', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -3.4641016151377544]], [[1.0, 0], [10.004477497086198, 17.32826332813281], 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'7.32076540765396416480474548497329', '8.979409036877657443458782878016906', '10.03044547699907980521512914729730', '10.96821285336812155671855901545011', '11.58553057197758769588795341497303', '12.86234258287702069152625734832620', '14.49598189091387853097855838139755'], 'prelabel': '2-74-37.10-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4450548132302004, 'root_angle': -0.7542264996201024, 'root_number': '-0.7164330949772414 - 0.697655803689277*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.37711324981', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.79951733908432248989984285189', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.09370747887354007950207875047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.67178888809866258136168536703', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.86840266616057, 'bad_primes': [2, 37], 'central_character': '37.10', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/6/c/a/47/2'], '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': '2-74-37.10-c5-0-12', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-74-37.10-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4450548132302004, 'root_angle': -0.3771132498100512, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.79951733908432248989984285189', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3548809835239577021693887777289', 'Lhash_array': ['3548809835239577021693887777289'], 'label': '2-74-37.10-c5-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/6/c/a/47/2'}