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  • lfunc_lfunctions • Show schema
    {'Lhash': '1821349323348530663217017233461', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.625452505516817, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [2.625452505516817, 0.0], 'a7': [-1.832267089819811, 0.0], 'a8': [1.0, 0.0], 'a9': [3.8930008587245326, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': 'CDF', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.625452505516817, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.832267089819811, 0], [7.0, 0]], [[1.0, 0], [-4.190171242128913, 0], [11.0, 0]], [[1.0, 0], [0.36945396858088286, 0], [13.0, 0]], [[1.0, 0], [5.083172100853445, 0], [17.0, 0]], [[1.0, 0], [-3.5596252107097954, 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[[1.0, 0], [0.6529843633678407, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-1850-1.1-c1-0-34', 'leading_term': '4.60284358384579490098810980121', '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/1850/2/a/be/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [4.602843583845795, 4.598708750719137, 4.58606453106154, 4.564207068146864, 4.532013012981946, 4.488009921376907, 4.430467085120655, 4.357500538820169, 4.267185839589731, 4.15767270523178, 4.027296468804537, 3.874682312335443, 3.698839186501573, 3.4992410954131468, 3.2758939927559383, 3.029386920017282, 2.760926272433274, 2.4723522659073525, 2.166136855601897, 1.8453625687549347, 1.5136819900485234, 1.1752579925829494, 0.8346852436725308, 0.496894024561191, 0.1670379710944657, -0.14963205328704351, 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1.9489171234590341, 1.620334024626238, 1.2615112260814425, 0.8992116219605911, 0.558698830568973, 0.26193441681649143, 0.02607517925363248, -0.137624455716928, -0.22443075090018394, -0.2362317157158651, -0.1811218614069809, -0.07251040501550755, 0.07217153623299942, 0.23305910403659136, 0.3896093968483275, 0.5223844008214816, 0.6147190347975108, 0.6541412758241494, 0.6334307213851299, 0.5512302585030391, 0.4121606739782756, 0.22642743006136232, 0.008949459963873549, -0.22192142040448445, -0.4459880701798324, -0.6429739537520632, -0.7943224720539673, -0.8848796157427241, -0.9043166362680666, -0.8481677979190118, -0.7183870361942506, -0.5233644737386376, -0.2773865047857173, 0.0004316824019918047, 0.2876682214220812, 0.5604589564438338, 0.7955601506257138], 'positive_zeros': ['1.43679127594039923164431537594514', '2.67121695803865695587107361898660', '3.23518045657027919867410381212504', '4.09363201413085186110958710718207', '4.88412689989903802429346644502537', '6.31233989340225536201941060684590', '6.78098513328263379983282590622946', '7.64417047746911667206271298515815', '8.575952082750777824426924662200030', '9.197722515630436105611758493531902'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43679127594039923164431537595', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.67121695803865695587107361899', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.23518045657027919867410381213', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/a/be/1/5'], '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': '2-1850-1.1-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43679127594039923164431537595', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1821349323348530663217017233461', 'Lhash_array': ['1821349323348530663217017233461'], 'factors': ['2-1850-1.1-c1-0-34'], 'label': '2-1850-1.1-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/be/1/5'}