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  • lfunc_lfunctions • Show schema
    {'Lhash': '622255951413927034139680271728', 'a10': [0, 0], 'a2': [0, 0], 'a3': [23.077164466275352, 13.323607116737342], 'a4': [0, 0], 'a5': [68.56601717798213, -39.586608474968486], 'a6': [0, 0], 'a7': [-337.28636328851496, -62.3450811179832], 'a8': [0, 0], 'a9': [-9.462986797652121, -16.39037392488698], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.766057365423315, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [337.28636328851496, 62.3450811179832]]]], 'bad_primes': [2, 7], 'central_character': '112.17', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '2299667676375474695500606522181', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-23.077164466275352, -13.323607116737342], [364.5, 631.3325193588557]], [[1.0, 0], [-68.56601717798213, 39.586608474968486], [7812.5, -13531.646934131853]], [[1.0, 0], [337.28636328851496, 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'3.15711655263472753712434670872211', '5.43454254135255849745393840017003', '6.51474967867912190750957976307188', '7.897347289652044007150628569620632', '8.702294360468436277244579191963968', '10.00926054901400828862033691811635', '10.84432894596921965529662677368162', '12.53384648233157699112857343855124'], 'prelabel': '2-112-7.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.076027715194561, 'root_angle': -0.3244159262517344, 'root_number': '-0.4507175953823599943548702223466179195947670421800622707 - 0.8926665946548818966251408585158929805978479411907044117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3244159262517344', 'prec': 54}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49087339311155242100557894163', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.55983643745444356410719377616', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.15711655263472753712434670872', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 25.766057365423315, 'bad_primes': [2, 7], 'central_character': '7.3', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/7/s/b/17/2'], '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': '2-112-7.3-c6-0-4', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-112-7.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.076027715194561, 'root_angle': -0.3244159262517344, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49087339311155242100557894163', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '622255951413927034139680271728', 'Lhash_array': ['622255951413927034139680271728'], 'factors': ['2-112-7.3-c6-0-4'], 'label': '2-112-7.3-c6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/7/s/b/17/2'}