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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e4-0', 'trace_hash': 1972092481477132722, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.896128000723338810231908931665', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.30769029412786992155024163499', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.75806075413476988627121443342', 'prec': 103}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 449.66286821639795, 'bad_primes': [13], 'central_character': '1.1', 'conductor': 815730721, 'conductor_radical': 13, 'degree': 8, 'dirichlet_coefficients': [1, -4, -2, 11, 14, 8, 20, -18, 16, -56, -28, -22, 0, -80, -28, 24, 12, -64, 14, 154, -40, 112, -18, 36, 98, 0, -52, 220, 2, 112, 20, -40, 56, -48, 280, 176, 38, -56, 0, -252, 62, 160, -180, -308, 224, 72, 68, -48, 236, -392, -24, 0, 128, 208, -392, -360, -28, -8, 32, -308, -124, -80, 320, 97, 0, -224, 170, 132, 36, -1120, -106, -288, -58, -152, -196, 154, -560, 0, -40, 336, 149, -248, 188, -440, 168, 720, -4, 504, -190, -896, 0, -198, -40, -272, 196, 80, 146, -944, -448, 1078], 'euler11': [1, 28, 200, -3456, -75457, -418176, 2928200, 49603708, 214358881], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, -12, 413, -4380, 63576, -1265820, 34494173, -289650828, 6975757441], 'euler19': [1, -14, 74, 1224, -131281, 441864, 9643754, -658642334, 16983563041], 'euler2': [1, 4, 5, -6, -31, -24, 80, 256, 256], 'euler23': [1, 18, 968, 15480, 516891, 8188920, 270886088, 2664646002, 78310985281], 'euler29': [1, -2, -1571, 214, 1769980, 179974, -1111138451, -1189646642, 500246412961], 'euler3': [1, 2, -12, -4, 139, -36, -972, 1458, 6561], 'euler31': [1, -20, 200, -18300, 1672334, -17586300, 184704200, -17750073620, 852891037441], 'euler37': [1, -38, 1517, 52158, -1571608, 71404302, 2843102237, -97497603542, 3512479453921], 'euler41': [1, -62, 3461, -155178, 6251432, -260854218, 9779958821, -294506462942, 7984925229121], 'euler43': [1, 180, 17198, 1151640, 57484803, 2129382360, 58796539598, 1137845348820, 11688200277601], 'euler47': [1, -68, 2312, -148716, 9565454, -328513644, 11281822472, -732986642372, 23811286661761], 'euler5': [1, -14, 98, -672, 4079, -16800, 61250, -218750, 390625], 'euler53': [1, -128, 13006, -929792, 58639315, -2611785728, 102623595886, -2837038224512, 62259690411361], 'euler59': [1, -32, 6980, 13812, 21149519, 48079572, 84579179780, -1349777076512, 146830437604321], 'euler61': [1, 124, 5413, 312604, 28201432, 1163199484, 74947537333, 6388526420764, 191707312997281], 'euler67': [1, -170, 10706, -134496, -16049425, -603752544, 215737901426, -15377924968730, 406067677556641], 'euler7': [1, -20, 164, -636, 1871, -31164, 393764, -2352980, 5764801], 'euler71': [1, 106, 4658, 26976, -17900353, 135986016, 118367610098, 13578630095626, 645753531245761], 'euler73': [1, 58, 1682, 201144, 20590727, 1071896376, 47765841362, 8777385124762, 806460091894081], 'euler79': [1, 40, 14980, 541240, 136037062, 3377878840, 583472213380, 9723498220840, 1517108809906561], 'euler83': [1, -188, 17672, -1935084, 200304482, -13330793676, 838683448712, -61464790193372, 2252292232139041], 'euler89': [1, 190, 12050, -309180, -102357841, -2449014780, 756044004050, 94426445282590, 3936588805702081], 'euler97': [1, -146, 13250, -1056876, 58176719, -9944146284, 1173012973250, -121613912719634, 7837433594376961], 'euler_factors': [[1, 4, 5, -6, -31, -24, 80, 256, 256], [1, 2, -12, -4, 139, -36, -972, 1458, 6561], [1, -14, 98, -672, 4079, -16800, 61250, -218750, 390625], [1, -20, 164, -636, 1871, -31164, 393764, -2352980, 5764801], [1, 28, 200, -3456, -75457, -418176, 2928200, 49603708, 214358881], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -12, 413, -4380, 63576, -1265820, 34494173, -289650828, 6975757441], [1, -14, 74, 1224, -131281, 441864, 9643754, -658642334, 16983563041], [1, 18, 968, 15480, 516891, 8188920, 270886088, 2664646002, 78310985281], [1, -2, -1571, 214, 1769980, 179974, -1111138451, -1189646642, 500246412961], [1, -20, 200, -18300, 1672334, -17586300, 184704200, -17750073620, 852891037441], [1, -38, 1517, 52158, -1571608, 71404302, 2843102237, -97497603542, 3512479453921], [1, -62, 3461, -155178, 6251432, -260854218, 9779958821, -294506462942, 7984925229121], [1, 180, 17198, 1151640, 57484803, 2129382360, 58796539598, 1137845348820, 11688200277601], [1, -68, 2312, -148716, 9565454, -328513644, 11281822472, -732986642372, 23811286661761], [1, -128, 13006, -929792, 58639315, -2611785728, 102623595886, -2837038224512, 62259690411361], [1, -32, 6980, 13812, 21149519, 48079572, 84579179780, -1349777076512, 146830437604321], [1, 124, 5413, 312604, 28201432, 1163199484, 74947537333, 6388526420764, 191707312997281], [1, -170, 10706, -134496, -16049425, -603752544, 215737901426, -15377924968730, 406067677556641], [1, 106, 4658, 26976, -17900353, 135986016, 118367610098, 13578630095626, 645753531245761], [1, 58, 1682, 201144, 20590727, 1071896376, 47765841362, 8777385124762, 806460091894081], [1, 40, 14980, 541240, 136037062, 3377878840, 583472213380, 9723498220840, 1517108809906561], [1, -188, 17672, -1935084, 200304482, -13330793676, 838683448712, -61464790193372, 2252292232139041], [1, 190, 12050, -309180, -102357841, -2449014780, 756044004050, 94426445282590, 3936588805702081], [1, -146, 13250, -1056876, 58176719, -9944146284, 1173012973250, -121613912719634, 7837433594376961]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/3/f/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': '8-13e8-1.1-c2e4-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '8-13e8-1.1-c2e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.145906910303664, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e4-0', 'trace_hash': 1972092481477132722, 'z1': {'__RealLiteral__': 0, 'data': '0.896128000723338810231908931665', 'prec': 107}}
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{'Lhash': '1135977197998263634063290330136,1657694386263824155946968269074,2501300085457669098488427847688,2885239473672233178917074111809', 'Lhash_array': ['1135977197998263634063290330136', '1657694386263824155946968269074', '2501300085457669098488427847688', '2885239473672233178917074111809'], 'label': '8-13e8-1.1-c2e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/3/f/a'}