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lfunc_lfunctions • Show schema
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{'Lhash': '608938056675567788882617979266', 'a10': -22, 'a2': 2, 'a3': 0, 'a4': -28, 'a5': -11, 'a6': 0, 'a7': 0, 'a8': -120, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, -2, 32], [1], [1, 11, 3125], [1], [1, 269, 161051], [1, 308, 371293], [1, 1896, 1419857], [1, 164, 2476099], [1, -3264, 6436343], [1, 2417, 20511149], [1, -2841, 28629151], [1, 11328, 69343957], [1, -16856, 115856201], [1, 7894, 147008443], [1, 21102, 229345007], [1, -29691, 418195493], [1, -8163, 714924299], [1, -15166, 844596301], [1, 32078, 1350125107], [1, -38274, 1804229351], [1, -34866, 2073071593], [1, -13529, 3077056399], [1, -68103, 3939040643], [1, -114922, 5584059449], [1, -154959, 8587340257], 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1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-21e2-1.1-c5-0-9', 'leading_term': '1.025185959476971258410614076475100000000000000000000000000000000000000000000000000000000000', '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/441/6/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0251859594769712, 1.0063754383724373, 0.9502515403485837, 0.8577335445447153, 0.7303411911298499, 0.5701760867924017, 0.3798956667342486, 0.1626797260979122, -0.07781043689529943, -0.3374801768480055, -0.6118568001089181, -0.8961517628859584, -1.1853294156962753, -1.474181811978583, -1.7574089511348723, -2.029703663651424, -2.285840172524799, -2.5207651862245046, -2.729690199960721, -2.9081835108989873, -3.052260296497164, -3.1584689709558034, 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'5.29621828875002232903808259837126', '6.51056653555152851260743999808861', '7.61514901050822142364310534052858', '8.611192527019822928221568068930289', '9.312523009832640561866485308560798', '10.29273593753359442714264281834491'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'trace_hash': 1376984577340290105, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48036742661261219661656768673', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27315949575493103006232454174', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53379589401821721882330478726', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, -28, -11, 0, 0, -120, 0, -22, -269, 0, -308, 0, 0, 656, -1896, 0, -164, 308, 0, -538, 3264, 0, -3004, -616, 0, 0, -2417, 0, 2841, 5152, 0, -3792, 0, 0, -11328, -328, 0, 1320, 16856, 0, -7894, 7532, 0, 6528, -21102, 0, 0, -6008, 0, 8624, 29691, 0, 2959, 0, 0, -4834, 8163, 0, 15166, 5682, 0, -10688, 3388, 0, -32078, 53088, 0, 0, 38274, 0, 34866, -22656, 0, 4592, 0, 0, 13529, -7216, 0, 33712, 68103, 0, 20856, -15788, 0, 32280, 114922, 0, 0, -91392, 0, -42204, 1804, 0, 154959, 0, 0, 84112], 'euler11': [1, 269, 161051], 'euler13': [1, 308, 371293], 'euler17': [1, 1896, 1419857], 'euler19': [1, 164, 2476099], 'euler2': [1, -2, 32], 'euler23': [1, -3264, 6436343], 'euler29': [1, 2417, 20511149], 'euler3': [1, 0, 0], 'euler31': [1, -2841, 28629151], 'euler37': [1, 11328, 69343957], 'euler41': [1, -16856, 115856201], 'euler43': [1, 7894, 147008443], 'euler47': [1, 21102, 229345007], 'euler5': [1, 11, 3125], 'euler53': [1, -29691, 418195493], 'euler59': [1, -8163, 714924299], 'euler61': [1, -15166, 844596301], 'euler67': [1, 32078, 1350125107], 'euler7': [1, 0, 0], 'euler71': [1, -38274, 1804229351], 'euler73': [1, -34866, 2073071593], 'euler79': [1, -13529, 3077056399], 'euler83': [1, -68103, 3939040643], 'euler89': [1, -114922, 5584059449], 'euler97': [1, -154959, 8587340257], 'euler_factors': [[1, -2, 32], [1, 0, 0], [1, 11, 3125], [1, 0, 0], [1, 269, 161051], [1, 308, 371293], [1, 1896, 1419857], [1, 164, 2476099], [1, -3264, 6436343], [1, 2417, 20511149], [1, -2841, 28629151], [1, 11328, 69343957], [1, -16856, 115856201], [1, 7894, 147008443], [1, 21102, 229345007], [1, -29691, 418195493], [1, -8163, 714924299], [1, -15166, 844596301], [1, 32078, 1350125107], [1, -38274, 1804229351], [1, -34866, 2073071593], [1, -13529, 3077056399], [1, -68103, 3939040643], [1, -114922, 5584059449], [1, -154959, 8587340257]], 'index': 9, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/441/6/a/g'], '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': '2-21e2-1.1-c5-0-9', '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': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1376984577340290105, 'z1': {'__RealLiteral__': 0, 'data': '0.48036742661261219661656768673', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20357636
{'Lhash': '608938056675567788882617979266', 'Lhash_array': ['608938056675567788882617979266'], 'label': '2-21e2-1.1-c5-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/g'}
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id: 24585926
{'Lhash': '608938056675567788882617979266', 'Lhash_array': ['608938056675567788882617979266'], 'label': '2-21e2-1.1-c5-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/g/1/1'}