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lfunc_lfunctions • Show schema
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{'Lhash': '215443120620529753248532975567,1653140090389715052131572885444', 'a10': 0, 'a2': 0, 'a3': -20, 'a4': 0, 'a5': 74, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3952.694409496587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '392.1', 'coefficient_field': '1.1.1.1', 'conductor': 153664, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 20, 157, 4860, 59049], [1, -74, 2351, -231250, 9765625], [1], [1, 124, -145675, 19970324, 25937424601], [1, -956, 971070, -354956108, 137858491849], [1, -1198, 15347, -1700988686, 2015993900449], [1, 3044, 6789837, 7537245356, 6131066257801], [1, 184, -6402487, 1184287112, 41426511213649], [1, 6564, 51793822, 134635182036, 420707233300201], [1, -5728, 4180833, -163987776928, 819628286980801], [1, 10326, 37282319, 716045699982, 4808584372417849], [1, 17772, 310673398, 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{'algebraic': True, 'analytic_conductor': 3952.694409496587, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 153664, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, -20, 0, 74, 0, 0, 0, 243, 0, -124, 0, 956, 0, -1480, 0, 1198, 0, -3044, 0, 0, 0, -184, 0, 3125, 0, -6580, 0, -6564, 0, 5728, 0, 2480, 0, 0, 0, -10326, 0, -19120, 0, -17772, 0, -18376, 0, 17982, 0, -23664, 0, 0, 0, -23960, 0, -11686, 0, -9176, 0, 60880, 0, -16876, 0, 18482, 0, 0, 0, 70744, 0, 15532, 0, 3680, 0, -63920, 0, 4886, 0, -62500, 0, 0, 0, -44560, 0, 131600, 0, 134728, 0, 88652, 0, 131280, 0, -71994, 0, 0, 0, -114560, 0, -225256, 0, 97732, 0, -30132, 0], 'euler11': [1, 124, -145675, 19970324, 25937424601], 'euler13': [1, -956, 971070, -354956108, 137858491849], 'euler17': [1, -1198, 15347, -1700988686, 2015993900449], 'euler19': [1, 3044, 6789837, 7537245356, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 184, -6402487, 1184287112, 41426511213649], 'euler29': [1, 6564, 51793822, 134635182036, 420707233300201], 'euler3': [1, 20, 157, 4860, 59049], 'euler31': [1, -5728, 4180833, -163987776928, 819628286980801], 'euler37': [1, 10326, 37282319, 716045699982, 4808584372417849], 'euler41': [1, 17772, 310673398, 2058996404172, 13422659310152401], 'euler43': [1, 18376, 378436230, 2701427148568, 21611482313284249], 'euler47': [1, 23664, 330639889, 5427220245648, 52599132235830049], 'euler5': [1, -74, 2351, -231250, 9765625], 'euler53': [1, 11686, -281632897, 4887032531198, 174887470365513049], 'euler59': [1, 16876, -430124923, 12065062469924, 511116753300641401], 'euler61': [1, -18482, -503011977, -15609828835082, 713342911662882601], 'euler67': [1, -15532, -1108882083, -20970143161924, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 63920, 4629900302, 115326340115920, 3255243551009881201], 'euler73': [1, -4886, -2049198597, -10129027803398, 4297625829703557649], 'euler79': [1, 44560, -1091462799, 137113633139440, 9468276082626847201], 'euler83': [1, -134728, 12415989782, -530699067750104, 15516041187205853449], 'euler89': [1, 71994, -400923413, 402018775971306, 31181719929966183601], 'euler97': [1, -97732, 19562566470, -839257937997124, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 20, 157, 4860, 59049], [1, -74, 2351, -231250, 9765625], [1, 0, 0, 0, 0], [1, 124, -145675, 19970324, 25937424601], [1, -956, 971070, -354956108, 137858491849], [1, -1198, 15347, -1700988686, 2015993900449], [1, 3044, 6789837, 7537245356, 6131066257801], [1, 184, -6402487, 1184287112, 41426511213649], [1, 6564, 51793822, 134635182036, 420707233300201], [1, -5728, 4180833, -163987776928, 819628286980801], [1, 10326, 37282319, 716045699982, 4808584372417849], [1, 17772, 310673398, 2058996404172, 13422659310152401], [1, 18376, 378436230, 2701427148568, 21611482313284249], [1, 23664, 330639889, 5427220245648, 52599132235830049], [1, 11686, -281632897, 4887032531198, 174887470365513049], [1, 16876, -430124923, 12065062469924, 511116753300641401], [1, -18482, -503011977, -15609828835082, 713342911662882601], [1, -15532, -1108882083, -20970143161924, 1822837804551761449], [1, 63920, 4629900302, 115326340115920, 3255243551009881201], [1, -4886, -2049198597, -10129027803398, 4297625829703557649], [1, 44560, -1091462799, 137113633139440, 9468276082626847201], [1, -134728, 12415989782, -530699067750104, 15516041187205853449], [1, 71994, -400923413, 402018775971306, 31181719929966183601], [1, -97732, 19562566470, -839257937997124, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/i/b'], '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': '4-392e2-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-392e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.929089315090884, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1982036944169623900, 'z1': {'__RealLiteral__': 0, 'data': '0.16995465515635073577894450080', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '215443120620529753248532975567,1653140090389715052131572885444', 'Lhash_array': ['215443120620529753248532975567', '1653140090389715052131572885444'], 'label': '4-392e2-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/i/b'}