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  • lfunc_lfunctions • Show schema
    {'Lhash': '909144350424940242971267841029', 'a10': [-31622.776601683792, 0], 'a2': [-19.595917942265423, -11.313708498984761], 'a3': [239.5002190603248, 41.09312679824233], 'a4': [256.0, 443.40500673763256], 'a5': [1210.3072956898177, -698.7712429686843], 'a6': [-4228.310981953587, -3514.893204620974], 'a7': [-5111.914022341152, 8854.09481061866], 'a8': [0, -11585.237502960395], 'a9': [55671.70985988715, 19683.625740105486], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.1821527406352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [19.595917942265423, 11.313708498984761]]], [3, [[1.0, 0], [-239.5002190603248, -41.09312679824233]]], [5, [[1.0, 0], [-1210.3072956898177, 698.7712429686843]]]], 'bad_primes': [2, 3, 5], 'central_character': '90.11', 'coefficient_field': 'CDF', 'conductor': 90, 'conductor_radical': 30, 'conjugate': '1430930717980878867485625603884', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-1.6288554508688546, -0.9531551554633393, 0.07627821621993859, 1.234549438950472, 2.272519748158735], 'positive_zeros': ['0.71718843525278712890852349722316', '2.10494136892572125953902891585622', '3.31637919779456287646410844574358', '5.05248754297130104722446274751586', '6.81432326437866300901655711754419', '7.43579882356989441040952971449130', '8.713484334015986120436924214662988', '9.690781446585444505615985007913271', '10.43185493527937240734466825589408', '12.00375113604477052475651374088580'], 'prelabel': '2-90-9.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.561888172978704, 'root_angle': -0.084800376034527, 'root_number': '0.8613798273745685 - 0.5079614089595376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08480037603452702', 'prec': 54}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71718843525278712890852349722316', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.10494136892572125953902891585622', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '3.31637919779456287646410844574358', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 57.1821527406352, 'bad_primes': [2, 3, 5], 'central_character': '9.2', 'conductor': 90, 'conductor_radical': 30, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/90/11/h/a/11/20'], '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': '2-90-9.2-c10-0-17', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-90-9.2-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.561888172978704, 'root_angle': -0.084800376034527, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71718843525278712890852349722316', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '909144350424940242971267841029', 'Lhash_array': ['909144350424940242971267841029'], 'factors': ['2-90-9.2-c10-0-17'], 'label': '2-90-9.2-c10-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/90/11/h/a/11/20'}