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lfunc_lfunctions • Show schema
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{'Lhash': '1606480779898071985202711140038', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.158105378588505, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '960.449', 'coefficient_field': '1.1.1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -3], [1, -5], [1, 0, -49], [1, 0, -121], [1, 0, -169], [1, -14, 289], [1, 22, 361], [1, -34, 529], [1, 0, -841], [1, 2, 961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, 14, 2209], [1, 86, 2809], [1, 0, -3481], [1, -118, 3721], [1, 0, -4489], [1, 0, -5041], [1, 0, -5329], [1, 98, 6241], [1, 154, 6889], [1, 0, -7921], [1, 0, -9409], [1, 0, -10201], [1, 0, -10609], [1, 106, 11449], [1, -22, 11881], [1, -206, 12769]], 'euler_factors_factorization': [[1], [[[1, -3], 1]], [[[1, -5], 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'primitive': True, 'rational': True, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2-0', 'trace_hash': 796474705216398623, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26728988225055009152667195052', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36054040198612594023373609551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26369749967234816523191262033', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.158105378588505, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 5, 0, 0, 0, 9, 0, 0, 0, 0, 0, 15, 0, 14, 0, -22, 0, 0, 0, 34, 0, 25, 0, 27, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, -14, 0, 49, 0, 42, 0, -86, 0, 0, 0, -66, 0, 0, 0, 118, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 75, 0, 0, 0, -98, 0, 81, 0, -154, 0, 70, 0, 0, 0, 0, 0, 0, 0, -6, 0, -110, 0, 0, 0, 0, 0], 'euler11': [1, 0, -121], 'euler13': [1, 0, -169], 'euler17': [1, -14, 289], 'euler19': [1, 22, 361], 'euler2': [1, 0, 0], 'euler23': [1, -34, 529], 'euler29': [1, 0, -841], 'euler3': [1, -3, 0], 'euler31': [1, 2, 961], 'euler37': [1, 0, -1369], 'euler41': [1, 0, -1681], 'euler43': [1, 0, -1849], 'euler47': [1, 14, 2209], 'euler5': [1, -5, 0], 'euler53': [1, 86, 2809], 'euler59': [1, 0, -3481], 'euler61': [1, -118, 3721], 'euler67': [1, 0, -4489], 'euler7': [1, 0, -49], 'euler71': [1, 0, -5041], 'euler73': [1, 0, -5329], 'euler79': [1, 98, 6241], 'euler83': [1, 154, 6889], 'euler89': [1, 0, -7921], 'euler97': [1, 0, -9409], 'euler_factors': [[1, 0, 0], [1, -3, 0], [1, -5, 0], [1, 0, -49], [1, 0, -121], [1, 0, -169], [1, -14, 289], [1, 22, 361], [1, -34, 529], [1, 0, -841], [1, 2, 961], [1, 0, -1369], [1, 0, -1681], [1, 0, -1849], [1, 14, 2209], [1, 86, 2809], [1, 0, -3481], [1, -118, 3721], [1, 0, -4489], [1, 0, -5041], [1, 0, -5329], [1, 98, 6241], [1, 154, 6889], [1, 0, -7921], [1, 0, -9409]], 'index': 65, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/3/c/d', 'ModularForm/GL2/Q/holomorphic/960/3/c/d/449/1'], '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': '2-960-15.14-c2-0-65', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-960-15.14-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.114499523764618, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2-0', 'trace_hash': 796474705216398623, 'z1': {'__RealLiteral__': 0, 'data': '1.26728988225055009152667195052', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24560868
{'Lhash': '1606480779898071985202711140038', 'Lhash_array': ['1606480779898071985202711140038'], 'label': '2-960-15.14-c2-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/3/c/d/449/1'}
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id: 24374114
{'Lhash': '1606480779898071985202711140038', 'Lhash_array': ['1606480779898071985202711140038'], 'label': '2-960-15.14-c2-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/3/c/d'}