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lfunc_lfunctions • Show schema
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{'Lhash': '2299667676375474695500606522181', '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': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [337.28636328851496, -62.3450811179832]]]], 'bad_primes': [2, 7], 'central_character': '112.33', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '622255951413927034139680271728', '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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[-838550055420.5, 1452411300678.004]], [[1.0, 0], [-1290314.3903935791, 0], [2081951752609.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-112-7.5-c6-0-20', 'leading_term': '1.771185484057121195887301511242513311648282097156731971', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/112/7/s/b/33/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [1.7711854840571213, 1.9971564970618558, 2.2034433973572884, 2.387471275517606, 2.546919792713392, 2.6797512030941215, 2.7842366998938703, 2.858980901857039, 2.902944234513764, 2.9154628971819117, 2.896266044621349, 2.8454897554016876, 2.7636873106616, 2.6518352703493, 2.5113348123777115, 2.3440077962730475, 2.152087029347551, 1.9382002522362154, 1.7053474233092907, 1.456870968884567, 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'4.47907937095541515671987117117795', '6.07441783587326367378917466750195', '7.34461844518095105775780072303800', '8.802566347918525457521613770006932', '9.603923133059841262866175046345128', '10.22040050340151340922823575657469', '11.93142185759661481438563575562819', '12.97003425906311513817313367301489'], 'prelabel': '2-112-7.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.076027715194561, 'root_angle': 0.6488318525034688, 'root_number': '-0.4507175953823599943548702223466179195947670421800622707 + 0.8926665946548818966251408585158929805978479411907044117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3244159262517344', 'prec': 60}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81411792489305779309994628234', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25478405085986605148147764197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47907937095541515671987117118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.766057365423315, 'bad_primes': [2, 7], 'central_character': '7.5', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/7/s/b/33/2'], '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': '2-112-7.5-c6-0-20', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], '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': 0.3244159262517344, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81411792489305779309994628234', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2299667676375474695500606522181', 'Lhash_array': ['2299667676375474695500606522181'], 'label': '2-112-7.5-c6-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/7/s/b/33/2'}