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  • lfunc_lfunctions • Show schema
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'4.34386226779509351156400204614827', '4.47293814114098997955554837725059', '4.77389846871387830475818770869464', '5.19233035991046395444126014430170', '5.22061096574823682298447574405823', '5.42119087663726254201007447649569', '5.49672253798160849947206373928669', '5.50161858650883499758728825204414', '5.98399594974280293387008692650288', '6.00083453941299709470696651655735', '6.12214569637732916425932733371858', '6.16646798842223823711460349217301', '6.39834600009049416597851441737658', '6.62165584669153511463230716148960', '6.75258424623485185070456172580491', '6.81640709496995942122297468157920', '6.92206813233682959022221625954639', '6.93881223837962596258912995061167', '7.24188732254505740092564111774110', '7.36371667233005678310950643472018', '7.63271793364741959849528881290492', '7.66404779175231043964932941437298', '7.82081141380022946289323497595279', '8.305364435361646081959876699223223', '8.318229365740873942860938157247018', '8.396959140388180474020591550573378', '8.482842592740911072921092933040447', '8.487993400323692998078976581643577'], 'prelabel': '10-2960e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.861658050325939, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e5-0', 'trace_hash': 26486939106359502, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01719091867096492065771285146', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.02909451604647836276138012946', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.37286047707614436608066097285', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7376393.735953809, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 227226278297600000, 'conductor_radical': 370, 'degree': 10, 'dirichlet_coefficients': [1, 0, -3, 0, -5, 0, -11, 0, 0, 0, 5, 0, 4, 0, 15, 0, 0, 0, 4, 0, 33, 0, -4, 0, 15, 0, 11, 0, -4, 0, -8, 0, -15, 0, 55, 0, 5, 0, -12, 0, -5, 0, -10, 0, 0, 0, -7, 0, 54, 0, 0, 0, -1, 0, -25, 0, -12, 0, 30, 0, -14, 0, 0, 0, -20, 0, -24, 0, 12, 0, 7, 0, 5, 0, -45, 0, -55, 0, -28, 0, -25, 0, -27, 0, 0, 0, 12, 0, 6, 0, -44, 0, 24, 0, -20, 0, -26, 0, 0, 0], 'euler11': [1, -5, 47, -172, 962, -2670, 10582, -20812, 62557, -73205, 161051], 'euler13': [1, -4, 37, -148, 746, -2752, 9698, -25012, 81289, -114244, 371293], 'euler17': [1, 0, 33, 12, 594, 600, 10098, 3468, 162129, 0, 1419857], 'euler19': [1, -4, 57, -238, 1522, -6148, 28918, -85918, 390963, -521284, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 4, 43, 160, 1106, 2936, 25438, 84640, 523181, 1119364, 6436343], 'euler29': [1, 4, 113, 416, 5930, 17208, 171970, 349856, 2755957, 2829124, 20511149], 'euler3': [1, 3, 9, 16, 40, 64, 120, 144, 243, 243, 243], 'euler31': [1, 8, 125, 650, 6118, 24600, 189658, 624650, 3723875, 7388168, 28629151], 'euler37': [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], 'euler41': [1, 5, 197, 772, 15842, 46590, 649522, 1297732, 13577437, 14128805, 115856201], 'euler43': [1, 10, 135, 968, 8506, 48796, 365758, 1789832, 10733445, 34188010, 147008443], 'euler47': [1, 7, 143, 724, 8598, 38108, 404106, 1599316, 14846689, 34157767, 229345007], 'euler5': [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], 'euler53': [1, 1, 121, 172, 10010, 13142, 530530, 483148, 18014117, 7890481, 418195493], 'euler59': [1, -30, 597, -8214, 89262, -759816, 5266458, -28592934, 122611263, -363520830, 714924299], 'euler61': [1, 14, 297, 2984, 35634, 263156, 2173674, 11103464, 67413357, 193841774, 844596301], 'euler67': [1, 24, 429, 5118, 54298, 459388, 3637966, 22974702, 129027327, 483626904, 1350125107], 'euler7': [1, 11, 67, 276, 894, 2484, 6258, 13524, 22981, 26411, 16807], 'euler71': [1, -7, 223, -356, 16278, 27126, 1155738, -1794596, 79814153, -177881767, 1804229351], 'euler73': [1, -5, 173, -1660, 13834, -188702, 1009882, -8846140, 67299941, -141991205, 2073071593], 'euler79': [1, 28, 529, 7286, 85626, 821200, 6764454, 45471926, 260817631, 1090602268, 3077056399], 'euler83': [1, 27, 593, 8588, 108392, 1048784, 8996536, 59162732, 339069691, 1281374667, 3939040643], 'euler89': [1, -6, 197, -1608, 29394, -168228, 2616066, -12736968, 138878893, -376453446, 5584059449], 'euler97': [1, 26, 397, 2904, 4802, -92868, 465794, 27323736, 362331181, 2301761306, 8587340257], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 9, 16, 40, 64, 120, 144, 243, 243, 243], [1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0], [1, 11, 67, 276, 894, 2484, 6258, 13524, 22981, 26411, 16807], [1, -5, 47, -172, 962, -2670, 10582, -20812, 62557, -73205, 161051], [1, -4, 37, -148, 746, -2752, 9698, -25012, 81289, -114244, 371293], [1, 0, 33, 12, 594, 600, 10098, 3468, 162129, 0, 1419857], [1, -4, 57, -238, 1522, -6148, 28918, -85918, 390963, -521284, 2476099], [1, 4, 43, 160, 1106, 2936, 25438, 84640, 523181, 1119364, 6436343], [1, 4, 113, 416, 5930, 17208, 171970, 349856, 2755957, 2829124, 20511149], [1, 8, 125, 650, 6118, 24600, 189658, 624650, 3723875, 7388168, 28629151], [1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0], [1, 5, 197, 772, 15842, 46590, 649522, 1297732, 13577437, 14128805, 115856201], [1, 10, 135, 968, 8506, 48796, 365758, 1789832, 10733445, 34188010, 147008443], [1, 7, 143, 724, 8598, 38108, 404106, 1599316, 14846689, 34157767, 229345007], [1, 1, 121, 172, 10010, 13142, 530530, 483148, 18014117, 7890481, 418195493], [1, -30, 597, -8214, 89262, -759816, 5266458, -28592934, 122611263, -363520830, 714924299], [1, 14, 297, 2984, 35634, 263156, 2173674, 11103464, 67413357, 193841774, 844596301], [1, 24, 429, 5118, 54298, 459388, 3637966, 22974702, 129027327, 483626904, 1350125107], [1, -7, 223, -356, 16278, 27126, 1155738, -1794596, 79814153, -177881767, 1804229351], [1, -5, 173, -1660, 13834, -188702, 1009882, -8846140, 67299941, -141991205, 2073071593], [1, 28, 529, 7286, 85626, 821200, 6764454, 45471926, 260817631, 1090602268, 3077056399], [1, 27, 593, 8588, 108392, 1048784, 8996536, 59162732, 339069691, 1281374667, 3939040643], [1, -6, 197, -1608, 29394, -168228, 2616066, -12736968, 138878893, -376453446, 5584059449], [1, 26, 397, 2904, 4802, -92868, 465794, 27323736, 362331181, 2301761306, 8587340257]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2960/2/a/w'], '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': '10-2960e5-1.1-c1e5-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 5, 'prelabel': '10-2960e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.861658050325939, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 26486939106359502, 'z1': {'__RealLiteral__': 0, 'data': '1.01719091867096492065771285146', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1289442678599952758826858120493,1304532280957897549922308367590,1740307407795187776370336390189,1952628232337892348485945382634,2220537826426187506917759012143', 'Lhash_array': ['1289442678599952758826858120493', '1304532280957897549922308367590', '1740307407795187776370336390189', '1952628232337892348485945382634', '2220537826426187506917759012143'], 'factors': ['2-2960-1.1-c1-0-32', '2-2960-1.1-c1-0-33', '2-2960-1.1-c1-0-55', '2-2960-1.1-c1-0-59', '2-2960-1.1-c1-0-65'], 'label': '10-2960e5-1.1-c1e5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/w'}