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lfunc_lfunctions • Show schema
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{'Lhash': '1812459234414843899645745905979', 'a10': [-1411.1911737095593, 0.0], 'a2': [-8.0, 0.0], 'a3': [27.0, 0.0], 'a4': [64.0, 0.0], 'a5': [176.3988967136949, 0.0], 'a6': [-216.0, 0.0], 'a7': [-148.3616074226206, 0.0], 'a8': [-512.0, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.58429902137915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [8.0, 0]]], [3, [[1.0, 0], [-27.0, 0]]], [59, [[1.0, 0], [205379.0, 0]]]], 'bad_primes': [2, 3, 59], 'central_character': '354.1', 'coefficient_field': 'CDF', 'conductor': 354, 'conductor_radical': 354, 'degree': 2, 'euler_factors': [[[1.0, 0], [8.0, 0]], [[1.0, 0], [-27.0, 0]], [[1.0, 0], [-176.3988967136949, 0], [78125.0, 0]], [[1.0, 0], [148.3616074226206, 0], [823543.0, 0]], [[1.0, 0], [-994.0721323105698, 0], [19487171.0, 0]], [[1.0, 0], [10986.879931226218, 0], [62748517.0, 0]], [[1.0, 0], [-9147.308130017327, 0], [410338673.0, 0]], 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0.1475545344566259], 'positive_zeros': ['1.42977823233667579174145630406374', '2.38951863956471379123836920099966', '3.45059688085521716860597355867849', '4.98049692652732538738593554217256', '6.09515979355996916705850098847160', '7.26183275104742251929163101896176', '7.892446476793421500021777091944498', '9.113595496355845029914584627068801', '9.730456349868614047570747017826323'], 'prelabel': '2-354-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.515906951917136, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42977823233667579174145630406', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38951863956471379123836920100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45059688085521716860597355868', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.58429902137915, 'bad_primes': [2, 3, 59], 'central_character': '1.1', 'conductor': 354, 'conductor_radical': 354, 'degree': 2, 'index': 54, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/354/8/a/c/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': '2-354-1.1-c7-0-54', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-354-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.515906951917136, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42977823233667579174145630406', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1812459234414843899645745905979', 'Lhash_array': ['1812459234414843899645745905979'], 'label': '2-354-1.1-c7-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/354/8/a/c/1/5'}