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lfunc_lfunctions • Show schema
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{'Lhash': '323988420494105168338863311914', 'a10': [0, 0], 'a2': [0, 0], 'a3': [4.5, -7.794228634059948], 'a4': [0, 0], 'a5': [-43.576358844927405, -75.4764675282677], 'a6': [0, 0], 'a7': [113.23610252712211, -63.1235699597788], 'a8': [0, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.8889634571615, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-4.5, 7.794228634059948]]], [7, [[1.0, 0], [-113.23610252712211, 63.1235699597788]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.193', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1426521939153657706357183661141', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.5, 7.794228634059948]], [[1.0, 0], [43.576358844927405, 75.4764675282677], [-1562.5, 2706.329386826371]], [[1.0, 0], [-113.23610252712211, 63.1235699597788]], [[1.0, 0], 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[-143441.84464702022, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-336-7.4-c5-0-5', 'leading_term': '0.954668837905877233232394410798887077906937521401742977', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/6/q/h/193/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9546688379058772, 0.7570589321043367, 0.5345128241969163, 0.2894213016960655, 0.024520472611520214, -0.25713939260606, -0.5522287139041655, -0.8571770774384431, -1.1682152428408534, -1.4814205559197215, -1.7927655911322804, -2.0981697837858904, -2.393553733841901, -2.6748957731447507, -2.9382902882528845, -3.1800071847798077, -3.3965517697677834, -3.58472422006747, -3.7416777012901106, -3.864974108180053, -3.952636317884874, -4.003195787218481, 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'5.48350579051231646745773935846862', '7.02842537434247408111462609576982', '7.62571789911891943437198164672783', '8.704163854006706908953855721076337', '9.641518876180494197398130189313828', '10.92660192003388049187957194973706'], 'prelabel': '2-336-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.3409102608029135, 'root_angle': -0.3083688331529422, 'root_number': '0.5663143219278929165866913248496233879627892695737789368 - 0.8241893525030221258251465530587103073432555504286609672*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1541844165764711', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25558179867210561600686952156', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54801014024911472429720034308', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08847689588628885930750833384', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.8889634571615, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/6/q/h/193/1'], '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': '2-336-7.4-c5-0-5', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-336-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.3409102608029135, 'root_angle': -0.1541844165764711, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25558179867210561600686952156', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '323988420494105168338863311914', 'Lhash_array': ['323988420494105168338863311914'], 'label': '2-336-7.4-c5-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/6/q/h/193/1'}