Formats: - HTML - YAML - JSON - 2026-08-24T20:07:04.192284
  • lfunc_lfunctions • Show schema
    {'Lhash': '1379883225086088635621773382711', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.8740320488976422], 'a4': [0, 0], 'a5': [2.23606797749979, 0], 'a6': [0, 0], 'a7': [0, 2.8284271247461903], 'a8': [0, 0], 'a9': [2.23606797749979, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.23606797749979, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.609', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '1614093010091566583718266095890', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.8740320488976422], [-3.0, 0]], [[1.0, 0], [-2.23606797749979, 0]], [[1.0, 0], [0, -2.8284271247461903], [-7.0, 0]], [[1.0, 0], [-0.7639320225002103, 0], [11.0, 0]], [[1.0, 0], [0, 5.450523271439116], [-13.0, 0]], [[1.0, 0], [0, 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[[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [0, 16.35156981431735], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1520-5.4-c1-0-27', 'leading_term': '2.2561272272123696010788989086507035771713065358517508113', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/d/f/609/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [2.2561272272123696, 2.2389969437970887, 2.2134206661006384, 2.178906650798455, 2.134743582584637, 2.080050047492616, 2.0138372061418677, 1.9350806317807117, 1.8427971821102844, 1.7361230560823517, 1.6143896944482485, 1.4771947648423487, 1.3244660146018121, 1.1565162140800187, 0.9740877335120997, 0.7783855145771663, 0.5710973486239778, 0.35440049704425824, 0.1309538219014422, -0.09612523494703434, -0.32329925945169646, -0.5466652022628431, 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'4.60092908589301462952784790210559', '4.98178539175047273138265417362869', '6.59405542835070585831169088580680', '6.73338720964366953546835899140926', '7.76494788730919408381344375564958', '9.077632763134642413390577396687622', '9.471766248116396315255224588331414'], 'prelabel': '2-1520-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08853593004070106684044245866', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.26374560378313040173124509091', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.57236117439916879968614843310', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '5.4', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/d/f/609/2'], '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': '2-1520-5.4-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1520-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08853593004070106684044245866', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1379883225086088635621773382711', 'Lhash_array': ['1379883225086088635621773382711'], 'factors': ['2-1520-5.4-c1-0-27'], 'label': '2-1520-5.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/d/f/609/2'}