Formats: - HTML - YAML - JSON - 2026-08-26T19:38:43.851291
  • lfunc_lfunctions • Show schema
    {'Lhash': '1303793662768240016998262487565,1561326371339596239446166956486', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2611.645113532459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '6400.1', 'coefficient_field': '1.1.1.1', 'conductor': 40960000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 2, 7, 6, 9], [1], [1, 0, 2, 0, 49], [1, 6, 31, 66, 121], [1, 0, 14, 0, 169], [1, -6, 43, -102, 289], [1, -2, 39, -38, 361], [1, 0, 46, 0, 529], [1, 0, -50, 0, 841], [1, 0, 14, 0, 961], [1, 0, -34, 0, 1369], [1, -18, 163, -738, 1681], [1, 8, 102, 344, 1849], [1, 0, -14, 0, 2209], [1, 0, 106, 0, 2809], [1, -24, 262, -1416, 3481], [1, 0, 110, 0, 3721], [1, 22, 255, 1474, 4489], [1, 0, 34, 0, 5041], [1, 14, 195, 1022, 5329], [1, 0, 50, 0, 6241], [1, 30, 391, 2490, 6889], 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'4.29540563998387000260642623835159', '4.90624736158526718878273568930999', '5.04318839647285545666921392296007', '5.52626339177379673315659638159507', '5.62920368284516816425504237222877', '5.98413333545002015693438473382219', '6.17662238146902434575253380161590', '6.83242231925202286569576968900653', '7.12801620229096879882879342161289', '7.59730464086360264715983843332128', '7.78780378961370343832532905981497'], 'prelabel': '4-80e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.148724172439406, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 984265648828175478, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02851184903277241635924384639', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.23166933464039151195080706374', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.34186024121928306578464351097', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2611.645113532459, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 40960000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 18, 0, -8, 0, 0, 0, 0, 0, -2, 0, -12, 0, 0, 0, 0, 0, -4, 0, 24, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -4, 0, -30, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 28, 0, 18, 0], 'euler11': [1, 6, 31, 66, 121], 'euler13': [1, 0, 14, 0, 169], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, -2, 39, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, -50, 0, 841], 'euler3': [1, 2, 7, 6, 9], 'euler31': [1, 0, 14, 0, 961], 'euler37': [1, 0, -34, 0, 1369], 'euler41': [1, -18, 163, -738, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, 0, 110, 0, 3721], 'euler67': [1, 22, 255, 1474, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, 34, 0, 5041], 'euler73': [1, 14, 195, 1022, 5329], 'euler79': [1, 0, 50, 0, 6241], 'euler83': [1, 30, 391, 2490, 6889], 'euler89': [1, -6, 187, -534, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 7, 6, 9], [1, 0, 0, 0, 0], [1, 0, 2, 0, 49], [1, 6, 31, 66, 121], [1, 0, 14, 0, 169], [1, -6, 43, -102, 289], [1, -2, 39, -38, 361], [1, 0, 46, 0, 529], [1, 0, -50, 0, 841], [1, 0, 14, 0, 961], [1, 0, -34, 0, 1369], [1, -18, 163, -738, 1681], [1, 8, 102, 344, 1849], [1, 0, -14, 0, 2209], [1, 0, 106, 0, 2809], [1, -24, 262, -1416, 3481], [1, 0, 110, 0, 3721], [1, 22, 255, 1474, 4489], [1, 0, 34, 0, 5041], [1, 14, 195, 1022, 5329], [1, 0, 50, 0, 6241], [1, 30, 391, 2490, 6889], [1, -6, 187, -534, 7921], [1, -28, 390, -2716, 9409]], 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6400/2/a/ba'], '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': '4-80e4-1.1-c1e2-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-80e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.148724172439406, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 984265648828175478, 'z1': {'__RealLiteral__': 0, 'data': '1.02851184903277241635924384639', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1303793662768240016998262487565,1561326371339596239446166956486', 'Lhash_array': ['1303793662768240016998262487565', '1561326371339596239446166956486'], 'factors': ['2-80e2-1.1-c1-0-72', '2-80e2-1.1-c1-0-96'], 'label': '4-80e4-1.1-c1e2-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6400/2/a/ba'}