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lfunc_lfunctions • Show schema
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{'Lhash': '535348239807463356732073864199,2162672729285133416464281045370', 'a10': -3, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -3, 'a6': 0, 'a7': 3, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.5070039818273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': '1.1.1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -1, 0, -2, 4], [1], [1, 3, 8, 15, 25], [1, -3, 12, -21, 49], [1, 4, 26, 44, 121], [1], [1, 1, 30, 17, 289], [1, 6, 30, 114, 361], [1, 4, 50, 92, 529], [1, 1, 20, 29, 841], [1, 1, 58, 31, 961], [1, 11, 100, 407, 1369], [1, -1, 78, -41, 1681], [1, -5, 88, -215, 1849], [1, 0, 26, 0, 2209], [1, 11, 98, 583, 2809], [1, 14, 150, 826, 3481], [1, -16, 169, -976, 3721], [1, 5, 136, 335, 4489], [1, -28, 338, -1988, 5041], [1, -12, 165, -876, 5329], [1, -15, 210, -1185, 6241], [1, 10, 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'9.657833910237604544020920023975992'], 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1153947930314178233, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42231529706299085034984012268', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70604796692066655437177248167', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.06902170765143710046164267312', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.5070039818273, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 2313441, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, -3, 0, 3, 3, 0, -3, -4, 0, 0, 3, 0, 1, -1, 0, -6, -3, 0, -4, -4, 0, 1, 0, 0, 3, -1, 0, -1, -1, 0, -1, -9, 0, -11, -6, 0, -9, 1, 0, 5, -4, 0, -4, 0, 0, -3, 1, 0, 0, -11, 0, 12, 9, 0, -1, -14, 0, 16, -1, 0, 1, 0, 0, -5, -1, 0, -9, 28, 0, 12, -11, 0, -6, -12, 0, 15, -3, 0, 1, -10, 0, 3, 5, 0, -12, 18, 0, 0, -4, 0, 0, 18, 0, 13, -3, 0, 1], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, 1, 30, 17, 289], 'euler19': [1, 6, 30, 114, 361], 'euler2': [1, -1, 0, -2, 4], 'euler23': [1, 4, 50, 92, 529], 'euler29': [1, 1, 20, 29, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 1, 58, 31, 961], 'euler37': [1, 11, 100, 407, 1369], 'euler41': [1, -1, 78, -41, 1681], 'euler43': [1, -5, 88, -215, 1849], 'euler47': [1, 0, 26, 0, 2209], 'euler5': [1, 3, 8, 15, 25], 'euler53': [1, 11, 98, 583, 2809], 'euler59': [1, 14, 150, 826, 3481], 'euler61': [1, -16, 169, -976, 3721], 'euler67': [1, 5, 136, 335, 4489], 'euler7': [1, -3, 12, -21, 49], 'euler71': [1, -28, 338, -1988, 5041], 'euler73': [1, -12, 165, -876, 5329], 'euler79': [1, -15, 210, -1185, 6241], 'euler83': [1, 10, 174, 830, 6889], 'euler89': [1, -18, 242, -1602, 7921], 'euler97': [1, -13, 232, -1261, 9409], 'euler_factors': [[1, -1, 0, -2, 4], [1, 0, 0, 0, 0], [1, 3, 8, 15, 25], [1, -3, 12, -21, 49], [1, 4, 26, 44, 121], [1, 0, 0, 0, 0], [1, 1, 30, 17, 289], [1, 6, 30, 114, 361], [1, 4, 50, 92, 529], [1, 1, 20, 29, 841], [1, 1, 58, 31, 961], [1, 11, 100, 407, 1369], [1, -1, 78, -41, 1681], [1, -5, 88, -215, 1849], [1, 0, 26, 0, 2209], [1, 11, 98, 583, 2809], [1, 14, 150, 826, 3481], [1, -16, 169, -976, 3721], [1, 5, 136, 335, 4489], [1, -28, 338, -1988, 5041], [1, -12, 165, -876, 5329], [1, -15, 210, -1185, 6241], [1, 10, 174, 830, 6889], [1, -18, 242, -1602, 7921], [1, -13, 232, -1261, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/2/a/m'], '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': '4-39e4-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-39e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4850030340642104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1153947930314178233, 'z1': {'__RealLiteral__': 0, 'data': '0.42231529706299085034984012268', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '535348239807463356732073864199,2162672729285133416464281045370', 'Lhash_array': ['535348239807463356732073864199', '2162672729285133416464281045370'], 'label': '4-39e4-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/2/a/m'}