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lfunc_lfunctions • Show schema
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{'Lhash': '1617399490186238807734649996083', 'a10': -92, 'a2': -2, 'a3': -9, 'a4': -28, 'a5': 46, 'a6': 18, 'a7': 148, 'a8': 120, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.292666053828362, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 9]], [11, [1, -121]]], 'bad_primes': [3, 11], 'central_character': '33.1', 'coefficient_field': '1.1.1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[1, 2, 32], [1, 9], [1, -46, 3125], [1, -148, 16807], [1, -121], [1, -574, 371293], [1, 722, 1419857], [1, -2160, 2476099], [1, 2536, 6436343], [1, -4650, 20511149], [1, -5032, 28629151], [1, -8118, 69343957], [1, 5138, 115856201], [1, -8304, 147008443], [1, -24728, 229345007], [1, 28746, 418195493], [1, 5860, 714924299], [1, 53658, 844596301], [1, -30908, 1350125107], [1, 69648, 1804229351], [1, 18446, 2073071593], [1, 25300, 3077056399], [1, 17556, 3939040643], [1, -132570, 5584059449], [1, 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15386239549], 1]], [[[1, 42726, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-33-1.1-c5-0-1', '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/33/6/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.176604191873816, 1.1651227831042377, 1.1306778661884647, 1.0732745852365584, 0.9929452977621075, 0.8897843113923358, 0.7639946457209306, 0.615944969975673, 0.44623436622252016, 0.25576208669414435, 0.04579901893289632, -0.18194284586545043, -0.42524701167266704, -0.6813395045806678, -0.946850874950283, -1.2177977682731558, -1.489588526180818, -1.7570569287615994, -2.0145275841846635, -2.255915582057448, -2.474861835050072, -2.664904037198837, -2.8196813850630256, -2.933169181023795, -2.9999372336105363, -3.015423681526771, 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'11.85003592538449612068029697552944', '13.52218881054187531776200162044089', '14.15947957636882431597188319922154', '15.90030767269105705842286664248656'], 'prelabel': '2-33-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.300579503913821, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 2161186570862999517, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27590322593231934581374699241', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.52220299211329893679080348766', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.91031575310589564754799983038', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.292666053828362, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'dirichlet_coefficients': [1, -2, -9, -28, 46, 18, 148, 120, 81, -92, 121, 252, 574, -296, -414, 656, -722, -162, 2160, -1288, -1332, -242, -2536, -1080, -1009, -1148, -729, -4144, 4650, 828, 5032, -5152, -1089, 1444, 6808, -2268, 8118, -4320, -5166, 5520, -5138, 2664, 8304, -3388, 3726, 5072, 24728, -5904, 5097, 2018, 6498, -16072, -28746, 1458, 5566, 17760, -19440, -9300, -5860, 11592, -53658, -10064, 11988, -10688, 26404, 2178, 30908, 20216, 22824, -13616, -69648, 9720, -18446, -16236, 9081, -60480, 17908, 10332, -25300, 30176, 6561, 10276, -17556, 37296, -33212, -16608, -41850, 14520, 132570, -7452, 84952, 71008, -45288, -49456, 99360, 46368, 70658, -10194, 9801, 28252], 'euler11': [1, -121, 0], 'euler13': [1, -574, 371293], 'euler17': [1, 722, 1419857], 'euler19': [1, -2160, 2476099], 'euler2': [1, 2, 32], 'euler23': [1, 2536, 6436343], 'euler29': [1, -4650, 20511149], 'euler3': [1, 9, 0], 'euler31': [1, -5032, 28629151], 'euler37': [1, -8118, 69343957], 'euler41': [1, 5138, 115856201], 'euler43': [1, -8304, 147008443], 'euler47': [1, -24728, 229345007], 'euler5': [1, -46, 3125], 'euler53': [1, 28746, 418195493], 'euler59': [1, 5860, 714924299], 'euler61': [1, 53658, 844596301], 'euler67': [1, -30908, 1350125107], 'euler7': [1, -148, 16807], 'euler71': [1, 69648, 1804229351], 'euler73': [1, 18446, 2073071593], 'euler79': [1, 25300, 3077056399], 'euler83': [1, 17556, 3939040643], 'euler89': [1, -132570, 5584059449], 'euler97': [1, -70658, 8587340257], 'euler_factors': [[1, 2, 32], [1, 9, 0], [1, -46, 3125], [1, -148, 16807], [1, -121, 0], [1, -574, 371293], [1, 722, 1419857], [1, -2160, 2476099], [1, 2536, 6436343], [1, -4650, 20511149], [1, -5032, 28629151], [1, -8118, 69343957], [1, 5138, 115856201], [1, -8304, 147008443], [1, -24728, 229345007], [1, 28746, 418195493], [1, 5860, 714924299], [1, 53658, 844596301], [1, -30908, 1350125107], [1, 69648, 1804229351], [1, 18446, 2073071593], [1, 25300, 3077056399], [1, 17556, 3939040643], [1, -132570, 5584059449], [1, -70658, 8587340257]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/6/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/33/6/a/a'], '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': '2-33-1.1-c5-0-1', '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': '2-33-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.300579503913821, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 2161186570862999517, 'z1': {'__RealLiteral__': 0, 'data': '1.27590322593231934581374699241', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10205579
{'Lhash': '1617399490186238807734649996083', 'Lhash_array': ['1617399490186238807734649996083'], 'label': '2-33-1.1-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/6/a/a'}
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id: 24550094
{'Lhash': '1617399490186238807734649996083', 'Lhash_array': ['1617399490186238807734649996083'], 'label': '2-33-1.1-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/6/a/a/1/1'}