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  • lfunc_lfunctions • Show schema
    {'Lhash': '210239449037591815787189639730', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-32.077164466275356, 18.519759539443974], 'a4': [0, 0], 'a5': [-143.56601717798213, -82.88787866419042], 'a6': [0, 0], 'a7': [197.28636328851496, -280.5834828716617], 'a8': [0, 0], 'a9': [321.4629867976521, -556.7902258863767], '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], [-197.28636328851496, 280.5834828716617]]]], 'bad_primes': [2, 7], 'central_character': '112.33', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '1139540988845727996911184261425', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [32.077164466275356, -18.519759539443974], [364.5, -631.3325193588557]], [[1.0, 0], [143.56601717798213, 82.88787866419042], [7812.5, 13531.646934131853]], [[1.0, 0], [-197.28636328851496, 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'5.43860354190689549242123849936069', '6.55403971104233678823628696598988', '7.52514705588714917937222307659328', '8.653299481494355503398906871520030', '10.46993714171426462362528892390364', '11.44131208632531223241362773890480', '11.93952207752930455907050375786470'], 'prelabel': '2-112-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.076027715194561, 'root_angle': -0.2989599309626906, 'root_number': '-0.3027953368218349074410479056383046363226775873151518490 - 0.9530556038337697899033983858736695571195966962595464651*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2989599309626906', 'prec': 54}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16584968208096145902304097338', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.97101918105287149752957402195', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.94479473071691667050746170054', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 25.766057365423315, 'bad_primes': [2, 7], 'central_character': '7.5', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/7/s/b/33/1'], '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': '2-112-7.5-c6-0-2', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-112-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.076027715194561, 'root_angle': -0.2989599309626906, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16584968208096145902304097338', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '210239449037591815787189639730', 'Lhash_array': ['210239449037591815787189639730'], 'factors': ['2-112-7.5-c6-0-2'], 'label': '2-112-7.5-c6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/7/s/b/33/1'}