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  • lfunc_lfunctions • Show schema
    {'Lhash': '2660619473407263306808246865593', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.0], 'a4': [0, 0], 'a5': [0, -3.414213562373095], 'a6': [0, 0], 'a7': [-0.585786437626905, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3], 'central_character': '1536.769', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '134298267050977830545468988097', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 3.414213562373095], [-5.0, 0]], [[1.0, 0], [0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [0, 2.0], [-11.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-13.0, 0]], [[1.0, 0], [7.656854249492381, 0], [17.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-19.0, 0]], [[1.0, 0], [6.82842712474619, 0], [23.0, 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'group': 'GL2', 'index': 31, 'label': '2-1536-8.5-c1-0-31', 'leading_term': '0.2886256635639975679923652143719187689160923561405566395', '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/1536/2/d/a/769/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.28862566356399755, 0.4508140489569304, 0.6148593941249407, 0.7807210685965114, 0.9482205115198237, 1.1169810590760387, 1.2863801921482112, 1.4555164527514108, 1.6231921461918646, 1.7879119682809745, 1.9478969584802992, 2.101112692455413, 2.2453103493640287, 2.3780791522557556, 2.4969086141670624, 2.5992589713926186, 2.6826381126706678, 2.744683202307183, 2.7832450465173655, 2.796473076790435, 2.7828986399917306, 2.7415141134886687, 2.6718452266882706, 2.57401388869857, 2.4487888137478535, 2.2976213167890966, 2.12266383299663, 1.9267690041408585, 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'8.145022381874293686001303433512844', '9.073554141244365841250157506085557', '9.935127265165520561833333282594895'], 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09885868624070547911338808595', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.59062824636754290046267531710', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.85982861771932665568151632930', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 12.265021750468673, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 1536, 'conductor_radical': 6, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1536/2/d/a/769/3'], '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': '2-1536-8.5-c1-0-31', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09885868624070547911338808595', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2660619473407263306808246865593', 'Lhash_array': ['2660619473407263306808246865593'], 'factors': ['2-1536-8.5-c1-0-31'], 'label': '2-1536-8.5-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1536/2/d/a/769/3'}