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lfunc_lfunctions • Show schema
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{'Lhash': '617139224552142591499481468840', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [3.622660633047949, 3.44620515027249], 'a6': [0, 0], 'a7': [5.873670062235365, 3.391164991562634], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.1418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.622660633047949, -3.44620515027249]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.269', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '2103103088167344068051290745176', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.622660633047949, -3.44620515027249]], [[1.0, 0], [-5.873670062235365, -3.391164991562634], [24.5, 42.4352447854375]], [[1.0, 0], [-8.573214099741124, -4.949747468305833], [60.5, 104.78907385791707]], [[1.0, 0], 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[-5041.0, 0]], [[1.0, 0], [0, 13.564659966250536], [-5329.0, 0]], [[1.0, 0], [15.0, -25.98076211353316], [-3120.5, -5404.864545018681]], [[1.0, 0], [67.14164132637808, -116.29273408085305], [-3444.5, -5966.049006670998]], [[1.0, 0], [0, 32.526911934581186], [-7921.0, 0]], [[1.0, 0], [-82.23138087129512, -47.47630988187688], [4704.5, 8148.433024207783]], [[1.0, 0], [-68.58571279792899, -39.59797974644666], [5100.5, 8834.325144005059]], [[1.0, 0], [76.35771080905975, -44.08514489031424], [5304.5, -9187.66350874911]], [[1.0, 0], [57.54997827975264, 0], [11449.0, 0]], [[1.0, 0], [-74.0, 0], [11881.0, 0]], [[1.0, 0], [-86.32496741962895, -149.51922953252534], [-6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1620-45.29-c2-0-15', 'leading_term': '1.932979926356325592937310851417150757228317129769788849', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 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1.7264957962466159, 2.1725397569931566, 2.5968042040981913, 2.978187618998288, 3.2975720254502616, 3.5387390373950653, 3.6891504367693293, 3.7405543322222425, 3.6893861015715115, 3.536943092493016, 3.2893229872402965, 2.957127302439117, 2.5549431280074657, 2.1006273309316366, 1.6144274968461434, 1.117982336548276, 0.6332506986871927, 0.1814223522899121, -0.21813490311531977, -0.5488385838010598, -0.7977161569061179, -0.9560483841871596], 'positive_zeros': ['0.48683700732759647862798945680911', '1.60989358505051742037958348956712', '2.63854890995332164458987902074101', '4.01734229861403811879319084846052', '4.89815206241994338836946246986786', '5.43694041597542558896548099162263', '6.55977537931332354370886616133707', '7.30294277597402127371010993392192', '8.352286345764549994246514734913638', '8.766889458580715893500065882199869'], 'prelabel': '2-1620-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.7023885566080253, 'root_number': '-0.5938394067493051893711578039392236605191205874261193984 - 0.8045835935386908361991556224347727602425472487737900972*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3511942783040127', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48683700732759647862798945681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60989358505051742037958348957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63854890995332164458987902074', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.1418028263681, 'bad_primes': [2, 3, 5], 'central_character': '45.29', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/t/c/269/4'], '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': '2-1620-45.29-c2-0-15', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1620-45.29-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.643929772835358, 'root_angle': -0.3511942783040127, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48683700732759647862798945681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '617139224552142591499481468840', 'Lhash_array': ['617139224552142591499481468840'], 'label': '2-1620-45.29-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/t/c/269/4'}