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lfunc_lfunctions • Show schema
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{'Lhash': '97397258535572598682748319469', 'a10': [0, 0], 'a2': [0, 1.82842712474619], 'a3': [0, 3.0], 'a4': [4.656854249492381, 0], 'a5': [0, 0], 'a6': [-5.48528137423857, 0], 'a7': [0, -7.0], 'a8': [0, 23.14213562373095], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.976002753013837, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -3.0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 7.0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.274', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '2687525104310120358788390382272', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.82842712474619], [-8.0, 0]], [[1.0, 0], [0, -3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.0]], [[1.0, 0], [64.5685424949238, 0], [1331.0, 0]], [[1.0, 0], [0, -32.34314575050762], [-2197.0, 0]], [[1.0, 0], [0, 56.34314575050762], [-4913.0, 0]], [[1.0, 0], [-2.7451660040609585, 0], 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['0.07683288953441671884117443744629', '1.68404896701510478572898027532768', '2.60844670117902808385764646680396', '3.58594363017692517235905469043058', '5.34928425951295273483486321232748', '6.01219921610400689026852646202369', '7.38587612940060796665089327719805', '7.79597686974351444912605466568971', '9.016646242383752223955638437341260', '10.19447266995388962490466429261957'], 'prelabel': '2-525-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07683288953441671884117443745', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68404896701510478572898027533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60844670117902808385764646680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.976002753013837, 'bad_primes': [3, 5, 7], 'central_character': '5.4', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/4/d/l/274/3'], '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': '2-525-5.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-525-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07683288953441671884117443745', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '97397258535572598682748319469', 'Lhash_array': ['97397258535572598682748319469'], 'label': '2-525-5.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/4/d/l/274/3'}