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lfunc_lfunctions • Show schema
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{'Lhash': '1406228253846465755553905178979', 'a10': [0.8412535328311812, -0.5406408174555976], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [-0.41541501300188644, -0.9096319953545183], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [-0.6548607339452851, -0.7557495743542583], 'a6': [0.9594929736144974, -0.28173255684142967], 'a7': [1.9997267251065136, 1.2851463312265787], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.14231483827328514, -0.9898214418809327]]], [3, [[1.0, 0], [0.41541501300188644, 0.9096319953545183]]], [5, [[1.0, 0], [0.6548607339452851, 0.7557495743542583]]], [23, [[1.0, 0], [0.24062168650942511, 4.789791352865108]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.31', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '1271583692516336555387297257917', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.14231483827328514, -0.9898214418809327]], [[1.0, 0], [0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [0.6548607339452851, 0.7557495743542583]], [[1.0, 0], [-1.9997267251065136, -1.2851463312265787], [2.907905091013205, 6.367423967481629]], [[1.0, 0], [0.04820850563696413, 0.3352975216039882], [-10.554422709759471, 3.0990581252557265]], [[1.0, 0], [3.0088595720246545, -1.9336766327196508], [5.400395169024524, -11.82521593960874]], [[1.0, 0], [-5.917017531376176, 1.7373931063928187], [14.30131005813008, -9.190893896745159]], [[1.0, 0], [-3.666888542922979, -1.076695622854352], [15.983817123792441, 10.272175531656353]], [[1.0, 0], [0.24062168650942511, 4.789791352865108]], [[1.0, 0], [-8.33098330391855, 2.446197410257691], [24.396352452104253, -15.67858370621233]], [[1.0, 0], [-2.083337465736321, 4.561872721595523], [-20.300682752303835, 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[32.817786027149026, -71.86092763300695]], [[1.0, 0], [3.143699498482488, -3.6280226233175594], [-11.812131576682667, -82.15517967611741]], [[1.0, 0], [5.325723592811038, 11.6617079951642], [-58.28260532113037, 67.26171211752899]], [[1.0, 0], [-2.502996468673574, -2.8886119105261785], [-13.804539312508659, 96.01267986245047]], [[1.0, 0], [0.7838690484689272, -0.9046331059748135], [-14.373798665601798, -99.9719656299742]], [[1.0, 0], [-0.6189613630080643, -4.3049708395462245], [-98.82777628229323, 29.01845335466726]], [[1.0, 0], [7.741082806925493, -16.950606933977653], [-70.07009853214551, -80.86520445590564]], [[1.0, 0], [-3.650165168821953, 1.0717851971669714], [91.69663507859875, -58.929849102660135]], [[1.0, 0], [-2.5454646402446413, 17.704095448048886], [-108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-690-23.8-c1-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.07313812626709451, 'root_number': '0.973718758490569 - 0.22775376915341042*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0365690631335', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10931849327668575218135234670', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84238517762667612600727183322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77928825643567378643198332498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.8', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/c/31/2'], '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': '2-690-23.8-c1-0-10', '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': '2-690-23.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.036569063133547255, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10931849327668575218135234670', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1406228253846465755553905178979', 'Lhash_array': ['1406228253846465755553905178979'], 'label': '2-690-23.8-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/c/31/2'}