Formats: - HTML - YAML - JSON - 2026-10-07T19:34:12.285828
  • lfunc_lfunctions • Show schema
    {'Lhash': '2477727052949745759897031688719', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.79128784747792], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.79128784747792], 'a8': [0, 0], 'a9': [-0.20871215252208, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.783544222340847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '1100.749', 'coefficient_field': 'CDF', 'conductor': 1100, 'conductor_radical': 110, 'conjugate': '792298179463486131813960406794', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.79128784747792], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.79128784747792], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0], [-13.0, 0]], [[1.0, 0], [0, 3.79128784747792], [-17.0, 0]], [[1.0, 0], [-2.58257569495584, 0], [19.0, 0]], [[1.0, 0], [0, 0.79128784747792], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1100-5.4-c1-0-12', 'leading_term': '1.3902133499139845675187452281436489647858140053293372558', '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/1100/2/b/d/749/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [1.3902133499139846, 1.5334415151374166, 1.6782032008701318, 1.8244504948129179, 1.9718516707825426, 2.119742931964484, 2.2670988440738484, 2.4125219562754645, 2.5542508483286737, 2.690185031644346, 2.817924755424427, 2.934823717862425, 3.0380528117496324, 3.124673211083668, 3.191717235994914, 3.236275467298216, 3.2555885065928467, 3.2471416064152594, 3.208760155603765, 3.138703732086675, 3.0357561637916572, 2.899308800976405, 2.729434028859332, 2.5269459624189574, 2.2934452854053595, 2.031345337922984, 1.7438768313412156, 1.435068980422921, 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'8.740041136030264167055978697141564', '9.402893901059134096184535663763827', '10.08141520383487296141256445795363'], 'prelabel': '2-1100-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9637044762156783, 'root_angle': 0.42620819117478337, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95458200588052628896219001414', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.09275382058044285948534933225', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.04929585101012358080694340617', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.783544222340847, 'bad_primes': [2, 5, 11], 'central_character': '5.4', 'conductor': 1100, 'conductor_radical': 110, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1100/2/b/d/749/2'], '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': '2-1100-5.4-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1100-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9637044762156783, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95458200588052628896219001414', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2477727052949745759897031688719', 'Lhash_array': ['2477727052949745759897031688719'], 'factors': ['2-1100-5.4-c1-0-12'], 'label': '2-1100-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1100/2/b/d/749/2'}