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lfunc_lfunctions • Show schema
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{'Lhash': '882887525954457392311347096966', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -49, 'a8': 0, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.30974346156227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 49]]], 'bad_primes': [2, 7], 'central_character': '448.321', 'coefficient_field': '1.1.1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 0, -81], [1, 0, -625], [1, 49], [1, 206, 14641], [1, 0, -28561], [1, 0, -83521], [1, 0, -130321], [1, -734, 279841], [1, 1234, 707281], [1, 0, -923521], [1, -1294, 1874161], [1, 0, -2825761], [1, 334, 3418801], [1, 0, -4879681], [1, -5582, 7890481], [1, 0, -12117361], [1, 0, -13845841], [1, -4946, 20151121], [1, 2914, 25411681], [1, 0, -28398241], [1, -3646, 38950081], [1, 0, -47458321], [1, 0, -62742241], [1, 0, -88529281], [1, 0, -104060401], [1, 0, -112550881], [1, -11698, 131079601], [1, -12526, 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[0]], 'group': 'GL2', 'index': 22, 'label': '2-448-7.6-c4-0-22', 'leading_term': '1.576279695417874974436009066370588777262403321328320239200000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/448/5/c/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.576279695417875, 1.561786126826376, 1.5184844567646785, 1.4469109820074664, 1.3479567737479488, 1.2228633508497393, 1.0732162492913773, 0.9009361378897293, 0.7082670626401868, 0.4977613568865816, 0.2722607354198672, 0.03487310000836142, -0.21105537667016358, -0.4619732516578232, -0.7141621597048391, -0.9637806426829797, -1.2069134397417003, -1.4396260402786878, -1.658024106490939, -1.858317164186794, -2.036885745705166, -2.1903509538804897, -2.315645208200664, -2.4100827411859065, 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'6.94672474132811524374364967915842', '7.53174631305035294399807229534602', '8.761704619550267261495116396397978', '9.713555352646143021945384394051905', '10.40400159871017845817282482463996'], 'prelabel': '2-448-7.6-c4-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.805126263454799, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c4-0', 'trace_hash': 1503627153716355377, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69647545293277281336935830312', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39148155442852206233792784718', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44217921918032755984935478283', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.30974346156227, 'bad_primes': [2, 7], 'central_character': '7.6', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -49, 0, 81, 0, -206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 734, 0, 625, 0, 0, 0, -1234, 0, 0, 0, 0, 0, 0, 0, 1294, 0, 0, 0, 0, 0, -334, 0, 0, 0, 0, 0, 2401, 0, 0, 0, 5582, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3969, 0, 0, 0, 4946, 0, 0, 0, -2914, 0, 0, 0, 0, 0, 10094, 0, 3646, 0, 6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16686, 0], 'euler11': [1, 206, 14641], 'euler13': [1, 0, -28561], 'euler17': [1, 0, -83521], 'euler19': [1, 0, -130321], 'euler2': [1, 0, 0], 'euler23': [1, -734, 279841], 'euler29': [1, 1234, 707281], 'euler3': [1, 0, -81], 'euler31': [1, 0, -923521], 'euler37': [1, -1294, 1874161], 'euler41': [1, 0, -2825761], 'euler43': [1, 334, 3418801], 'euler47': [1, 0, -4879681], 'euler5': [1, 0, -625], 'euler53': [1, -5582, 7890481], 'euler59': [1, 0, -12117361], 'euler61': [1, 0, -13845841], 'euler67': [1, -4946, 20151121], 'euler7': [1, 49, 0], 'euler71': [1, 2914, 25411681], 'euler73': [1, 0, -28398241], 'euler79': [1, -3646, 38950081], 'euler83': [1, 0, -47458321], 'euler89': [1, 0, -62742241], 'euler97': [1, 0, -88529281], 'euler_factors': [[1, 0, 0], [1, 0, -81], [1, 0, -625], [1, 49, 0], [1, 206, 14641], [1, 0, -28561], [1, 0, -83521], [1, 0, -130321], [1, -734, 279841], [1, 1234, 707281], [1, 0, -923521], [1, -1294, 1874161], [1, 0, -2825761], [1, 334, 3418801], [1, 0, -4879681], [1, -5582, 7890481], [1, 0, -12117361], [1, 0, -13845841], [1, -4946, 20151121], [1, 2914, 25411681], [1, 0, -28398241], [1, -3646, 38950081], [1, 0, -47458321], [1, 0, -62742241], [1, 0, -88529281]], 'index': 22, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/5/c/a', 'ModularForm/GL2/Q/holomorphic/448/5/c/a/321/1'], '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': '2-448-7.6-c4-0-22', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-448-7.6-c4-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.805126263454799, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4-0', 'trace_hash': 1503627153716355377, 'z1': {'__RealLiteral__': 0, 'data': '0.69647545293277281336935830312', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24572007
{'Lhash': '882887525954457392311347096966', 'Lhash_array': ['882887525954457392311347096966'], 'factors': ['2-448-7.6-c4-0-22'], 'label': '2-448-7.6-c4-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/5/c/a/321/1'}
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id: 24282321
{'Lhash': '882887525954457392311347096966', 'Lhash_array': ['882887525954457392311347096966'], 'factors': ['2-448-7.6-c4-0-22'], 'label': '2-448-7.6-c4-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/5/c/a'}