Formats: - HTML - YAML - JSON - 2026-09-22T15:33:28.939066
  • lfunc_lfunctions • Show schema
    {'Lhash': '1226330313454369800410332993322', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.5, 4.330127018922194], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.348612101957944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.433', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '1658718680250270021833655423483', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.5, -4.330127018922194], [-3.5, 6.06217782649107]], [[1.0, 0], [0, 0], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.5, 6.06217782649107], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-11.5, 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0], [109.0, 0]], [[1.0, 0], [0, 0], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-6e4-9.4-c1-0-9', 'leading_term': '1.927621296659998131045697788326273059587136561903521417', '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/1296/2/i/j/433/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.9276212966599982, 1.8768385113592836, 1.8191238993608538, 1.754163592318788, 1.6814849645709053, 1.6005138001862864, 1.5106391773973664, 1.4112821692616597, 1.3019646854023248, 1.1823752780266832, 1.0524293558840907, 0.9123218625405086, 0.7625709953188322, 0.6040519329110641, 0.438019807440469, 0.2661213297892136, 0.09039459448740352, -0.0867433091904394, -0.2625211385789902, -0.4338508989811597, -0.5973777124968338, -0.7495418084359782, -0.8866519852974278, 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'4.21506353738067378167055571986196', '5.19990589401770204189990802203191', '6.51812222681218102349888219477206', '7.04087245293201946205076287175338', '7.947006811232314191575044139511340', '8.666624470547837945098700561826628', '9.605601286847581918190700150285008'], 'prelabel': '2-6e4-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': -0.11111111111111113, 'root_number': '0.76604444311897803520239265055541667393583245708039524585 - 0.6427876096865393263226434099072634329075598842056817904*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1111111111111111', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.967404041171581313564045931711', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.04461999123608432021111609236', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.80216600046040162357829510346', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.348612101957944, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/2/i/j/433/1'], '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': '2-6e4-9.4-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6e4-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.216925877597733, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.967404041171581313564045931711', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1226330313454369800410332993322', 'Lhash_array': ['1226330313454369800410332993322'], 'factors': ['2-6e4-9.4-c1-0-9'], 'label': '2-6e4-9.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/2/i/j/433/1'}