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lfunc_lfunctions • Show schema
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{'Lhash': '3182319275702005537611321088631', 'a10': [-1.0, 0.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.35932680909576176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.19', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '1438087798723312167057215920775', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], 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'label': '2-720-80.19-c0-0-1', 'leading_term': '1.1725922309209337444185570508035', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/720/1/r/a/19/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.1725922309209338, 1.2359422562111761, 1.3180400314071536, 1.4197387844477998, 1.5408839908911538, 1.6805208698937366, 1.8371259372159696, 2.0087966061967175, 2.1933759574752933, 2.388519432815283, 2.59172163945189, 2.800321391823107, 3.0114987263301884, 3.2222728997660544, 3.4295067235072905, 3.629920117053512, 3.820114198659728, 3.99660624772921, 4.155875232669895, 4.294417144484141, 4.408809020382872, 4.4957802353096055, 4.552289360426779, 4.575604629726057, 4.563385821301509, 4.513765155885785, 4.42542465211791, 4.29766726696333, 4.130479102069768, 3.9245799831387016, 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'10.18655162890125860536696265525898', '10.97317434809376828717867320608340'], 'prelabel': '2-720-80.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738914, 'root_angle': 0.625, 'root_number': '-0.38268343236508977172845998403043 + 0.92387953251128675612818318939698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51040726453255872723452292787', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71103122058905116286250460304', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32768987079081907197032935784', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.35932680909576176, 'bad_primes': [2, 3, 5], 'central_character': '80.19', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/1/r/a/19/2'], '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': '2-720-80.19-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-720-80.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738914, 'root_angle': 0.3125, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.51040726453255872723452292787', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3182319275702005537611321088631', 'Lhash_array': ['3182319275702005537611321088631'], 'label': '2-720-80.19-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/1/r/a/19/2'}