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lfunc_lfunctions • Show schema
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{'Lhash': '2538038984147755757714131783711', 'a10': [0.3807389401575679, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.3807389401575679, 0.0], 'a6': [1.0, 0.0], 'a7': [1.688724773789342, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.05397193640656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [59, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 17, 59], 'central_character': '6018.1', 'coefficient_field': 'CDF', 'conductor': 6018, 'conductor_radical': 6018, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.3807389401575679, 0], [5.0, 0]], [[1.0, 0], [-1.688724773789342, 0], [7.0, 0]], [[1.0, 0], [3.7786442106463753, 0], [11.0, 0]], [[1.0, 0], [5.191618855947186, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.3566426749719216, 0], 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[[1.0, 0], [-8.694041164649054, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 152, 'label': '2-6018-1.1-c1-0-152', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6018/2/a/r/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [7.645679219801858e-60, 0.3267402235466741, 0.6527742402868083, 0.9773361491256971, 1.2995442770155314, 1.6183520738784198, 1.932508849541301, 2.2405325714546906, 2.540696202864364, 2.8310283085713563, 3.1093279517170114, 3.373193292485488, 3.6200627989530525, 3.847267593566375, 4.052093174801901, 4.231848554463274, 4.383940717408727, 4.505952225317507, 4.595719737050917, 4.651411198126818, 4.67159945852186, 4.655330112963865, 4.602181425132581, 4.512314302070769, 4.386510433077374, 4.2261969030858015, 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'5.34752543822995999404865448887003', '6.16169837584311852770101435619517', '7.27025748174133492803088904658221', '7.61622329753582728748726080644060'], 'prelabel': '2-6018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.932097224967821, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00215973052101583884117576647', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13512025491712521838839710011', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28425707247060373880870941913', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.05397193640656, 'bad_primes': [2, 3, 17, 59], 'central_character': '1.1', 'conductor': 6018, 'conductor_radical': 6018, 'degree': 2, 'index': 152, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6018/2/a/r/1/4'], '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': '2-6018-1.1-c1-0-152', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.932097224967821, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00215973052101583884117576647', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2538038984147755757714131783711', 'Lhash_array': ['2538038984147755757714131783711'], 'label': '2-6018-1.1-c1-0-152', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6018/2/a/r/1/4'}