Formats: - HTML - YAML - JSON - 2026-10-17T02:10:48.183114
  • lfunc_lfunctions • Show schema
    {'Lhash': '1692757804155981879076226600319', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -7.364352513263748], 'a4': [0, 0], 'a5': [0, 10.105963411921067], 'a6': [0, 0], 'a7': [0, 17.470315925184817], 'a8': [0, 0], 'a9': [-27.233687939614086, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.048519521561456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [12.2119385257662, 69.02078351803105]]]], 'bad_primes': [2, 17], 'central_character': '272.33', 'coefficient_field': 'CDF', 'conductor': 272, 'conductor_radical': 34, 'conjugate': '1046974026014288677583404279958', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.364352513263748], [-27.0, 0]], [[1.0, 0], [0, -10.105963411921067], [-125.0, 0]], [[1.0, 0], [0, -17.470315925184817], [-343.0, 0]], [[1.0, 0], [0, 51.55046759284624], [-1331.0, 0]], [[1.0, 0], [-75.2119385257662, 0], [2197.0, 0]], [[1.0, 0], 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['1.33535045370642008471297947863103', '3.65007862120171194154545927916275', '4.34436821062144865713286689473901', '5.20914196008849948466424555206907', '6.64697839752185359816785720402871', '8.068657600064180299092164716480150', '8.985242380651871381151096285060550', '9.877006483350696237000692639239514', '10.53892914289100836038892412714587', '11.41486727848072677056344823432075'], 'prelabel': '2-272-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.006060349216105, 'root_angle': 0.22212894815107798, 'root_number': '0.1742253025442341241214494235836753333941704886651501631 + 0.9847058159437112243242355191245761531710006085797621256*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22212894815107798', 'prec': 57}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33535045370642008471297947863', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.65007862120171194154545927916', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.34436821062144865713286689474', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 16.048519521561456, 'bad_primes': [2, 17], 'central_character': '17.16', 'conductor': 272, 'conductor_radical': 34, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/272/4/b/d/33/1'], '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': '2-272-17.16-c3-0-15', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-272-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.006060349216105, 'root_angle': 0.22212894815107798, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33535045370642008471297947863', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1692757804155981879076226600319', 'Lhash_array': ['1692757804155981879076226600319'], 'factors': ['2-272-17.16-c3-0-15'], 'label': '2-272-17.16-c3-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/272/4/b/d/33/1'}