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  • lfunc_lfunctions • Show schema
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-29.40815862514205, -31.907145405937413, -32.10004950915365, -30.095930841328578, -26.09863310196733, -20.392854093875265, -13.327085436492041, -5.294217969174228, 3.290144759793758, 12.009379017823168, 20.465441457626163, 28.29644040625701, 35.19154275192179, 40.90270643906704, 45.25662323714975, 48.1606109321196, 49.59709182204373, 49.61716399945179, 48.33217138385945, 45.90335393023718, 42.52910739568786, 38.42552446472403, 33.821167239615335, 28.95109599483709, 24.044395764285483, 19.310461034012796, 14.927969028661064, 11.039100205807072, 7.745614873351068, 5.092496624474943, 3.072964907686531, 1.6396832983796923, 0.7163635148171275], 'positive_zeros': ['1.10876524187700719941787450513128', '1.30165720220255559326268160221964', '1.30711384512383907495092731926621', '1.31429040404889462024778991618173', '1.37130446486533707872307212185038', '1.51786059131022507392827202115746', '1.58796233473676478163332758977815', '1.74892997219920836412079456263344', '2.16216206319439227930244226121199', '2.18854117088884262207869100009488', '2.25152758590992857517398808092254', '2.27101028384090827778624545519031', '2.44490057383513629653025831134069', '2.45511936349161204277270975531951', '2.50723317184675712955960883712264', '2.68272697089408182477276556648921', '2.97354129892694325771752549498909', '3.07181088960356476542134712123371', '3.13014410442255156776337085301445', '3.14921108605357625637670752411656', '3.18271994820844461338509969160206', '3.21785953698397577767453393549860', '3.30637861791742570564466997033209', '3.57717846435173523668317316652609', '3.64908404039973833116864310984879', '3.73669877873818628130307949533013', '3.73800427022498362912151208332001', '3.88283315977825044954707993410078', '3.93900759978050976529184851272298', '4.02307101179898369841047661742060', '4.32305016713534525488353940147968', '4.46548036511044007825389248739264', '4.46869822230647887559082466083643', '4.50812845642373898447123501107431', '4.61605482287040643833994158933704', '4.69204877859155270589114695378014', '4.80788541256896991304466185101579', '4.88037041986040021126743802681692', '5.01968853561658824124018697947225', '5.04931121865230538063658831193677', '5.11367587379466360006425926997163', '5.11798267976408743413823941681275', '5.18100291698845877721640015522506', '5.38172693456445509367492235406559', '5.39446685717346912903096924572955', '5.45822428230126870289516610786129', '5.48910715906507259249367708580320', '5.66675248532786947376673843839325', '5.77726324969414723680670211670057', '5.96814731353195676712401891900647', '5.97383736932478545043547740408993', '6.04640519542522629685266209810184', '6.05943060986303666536945600474868', '6.19929017210344234246728067530275', '6.20668096508086571044011233962414', '6.24043135284843538645577170544888', '6.35646535959355193427353809197245', '6.43510235217485926020714851615321', '6.56771822123084925812717756591968', '6.61985344061175024125072469959983', '6.67840009003950417240961464304199', '6.79373671221296397744102179595251', '6.83845956278950973140272764215043', '6.93696197731091478433089396240758', '6.99851688869603039275354439047769', '7.05905163726895448807439076282876', '7.22767116754033881422697506673207', '7.27536586290370128731205338206636', '7.53276455301191751625686664569603', '7.57907192303562074215398212236241', '7.61581159607999819856800477503194', '7.66708383849422604202789008503034'], 'prelabel': '16-7942e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e8-0', 'trace_hash': 488776419326682673, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10876524187700719941787450513', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.30165720220255559326268160222', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.30711384512383907495092731927', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 261610950031859.22, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 15828474533481853782019206390016, 'conductor_radical': 418, 'degree': 16, 'dirichlet_coefficients': [1, 8, -5, 36, 1, -40, -4, 120, 8, 8, -8, -180, -3, -32, -5, 330, -6, 64, 0, 36, 20, -64, 9, -600, -19, -24, 2, -144, -4, -40, -11, 792, 40, -48, -4, 288, 10, 0, 15, 120, -29, 160, 2, -288, 8, 72, 0, -1650, -24, -152, 30, -108, -59, 16, -8, -480, 0, -32, -23, -180, -2, -88, -32, 1716, -3, 320, 3, -216, -45, -32, -1, 960, -6, 80, 95, 0, 32, 120, 0, 330, -21, -232, 15, 720, -6, 16, 20, -960, -4, 64, 12, 324, 55, 0, 0, -3960, -62, -192, -64, -684], 'euler11': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 3, 32, 32, 458, -644, 2607, -29023, -625, -377299, 440583, -1414868, 13080938, 11881376, 154457888, 188245551, 815730721], 'euler17': [1, 6, 116, 587, 6153, 26305, 195117, 699036, 4050559, 11883612, 56388813, 129236465, 513904713, 833456059, 2799958004, 2462032038, 6975757441], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -9, 122, -736, 5373, -26844, 144595, -725377, 3403722, -16683671, 76490755, -326610948, 1503585693, -4737148448, 18060378458, -30643429023, 78310985281], 'euler29': [1, 4, 132, 149, 7210, -8455, 261495, -702233, 7976455, -20364757, 219917295, -206208995, 5099496010, 3056161201, 78516678372, 68999505236, 500246412961], 'euler3': [1, 5, 17, 43, 90, 182, 378, 760, 1420, 2280, 3402, 4914, 7290, 10449, 12393, 10935, 6561], 'euler31': [1, 11, 222, 1765, 20656, 130021, 1137593, 5928155, 42218816, 183772805, 1093226873, 3873455611, 19076249776, 50530451515, 197025817182, 302638755221, 852891037441], 'euler37': [1, -10, 221, -1934, 23831, -175415, 1590889, -9764443, 71129081, -361284391, 2177927041, -8885295995, 44663130791, -134111212838, 567025536389, -949318771330, 3512479453921], 'euler41': [1, 29, 591, 8870, 109589, 1132509, 10137134, 78739477, 538618569, 3228318557, 17040522254, 78053652789, 309672322229, 1027644502870, 2807311606431, 5647873942549, 7984925229121], 'euler43': [1, -2, 236, -465, 27460, -51575, 2034075, -3419244, 104089696, -147027492, 3761004675, -4100573525, 93880275460, -68358925995, 1491841679564, -543637222214, 11688200277601], 'euler47': [1, 0, 117, 136, 7238, 18338, 426984, 1406698, 22678952, 66114806, 943207656, 1903906174, 35319131078, 31190920952, 1261168193493, 0, 23811286661761], 'euler5': [1, -1, 20, -12, 174, -56, 953, -141, 4561, -705, 23825, -7000, 108750, -37500, 312500, -78125, 390625], 'euler53': [1, 59, 1773, 35994, 555641, 6950535, 73081626, 659060411, 5148041929, 34930201783, 205286287434, 1034774799195, 4384274753321, 15052528575042, 39297412281717, 69307957250383, 62259690411361], 'euler59': [1, 23, 391, 5027, 56886, 553890, 5066388, 41897990, 333030964, 2471981410, 17636096628, 113757374310, 689308197846, 3593924451073, 16492588653631, 57238984150837, 146830437604321], 'euler61': [1, 2, 59, 36, 8639, 3895, 529997, -186683, 37362403, -11387663, 1972118837, 884090995, 119614220399, 30405466836, 3039702087299, 6285485672042, 191707312997281], 'euler67': [1, -3, 339, -841, 56502, -122764, 6176868, -11961514, 484321692, -801421438, 27727960452, -36922868932, 1138578638742, -1135455214987, 30665391555291, -18182134815969, 406067677556641], 'euler7': [1, 4, 40, 141, 746, 2383, 8841, 25082, 73288, 175574, 433209, 817369, 1791146, 2369787, 4705960, 3294172, 5764801], 'euler71': [1, 1, 200, 642, 22644, 133805, 1838211, 14593132, 133386112, 1036112372, 9266421651, 47890281355, 575422104564, 1158315243342, 25620056784200, 9095120158391, 645753531245761], 'euler73': [1, 6, 155, 1840, 23849, 267699, 2403405, 25891991, 218901495, 1890115343, 12807745245, 104139461883, 677269649609, 3814451731120, 23456805074795, 66284391114582, 806460091894081], 'euler79': [1, 0, 222, -1008, 23865, -199880, 2046977, -22369928, 157302126, -1767224312, 12775183457, -98548635320, 929543683065, -3101672850192, 53965415125662, 0, 1517108809906561], 'euler83': [1, -15, 425, -5251, 90501, -941833, 12398464, -111235053, 1207619210, -9232509399, 85413018496, -538527865571, 4295025508821, -20683902416393, 138949658681825, -407040764844405, 2252292232139041], 'euler89': [1, 4, 615, 2228, 173044, 549813, 29004737, 78354964, 3163082895, 6973591796, 229746521777, 387601120797, 10857168351604, 12441284452372, 305643493941015, 176925339582116, 3936588805702081], 'euler97': [1, 62, 2150, 52739, 1017422, 16273323, 222841507, 2658362297, 27886183171, 257861142809, 2096715739363, 14852222522379, 90071638133582, 452887737813923, 1790889810597350, 5009493637643006, 7837433594376961], 'euler_factors': [[1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 17, 43, 90, 182, 378, 760, 1420, 2280, 3402, 4914, 7290, 10449, 12393, 10935, 6561], [1, -1, 20, -12, 174, -56, 953, -141, 4561, -705, 23825, -7000, 108750, -37500, 312500, -78125, 390625], [1, 4, 40, 141, 746, 2383, 8841, 25082, 73288, 175574, 433209, 817369, 1791146, 2369787, 4705960, 3294172, 5764801], [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 32, 32, 458, -644, 2607, -29023, -625, -377299, 440583, -1414868, 13080938, 11881376, 154457888, 188245551, 815730721], [1, 6, 116, 587, 6153, 26305, 195117, 699036, 4050559, 11883612, 56388813, 129236465, 513904713, 833456059, 2799958004, 2462032038, 6975757441], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -9, 122, -736, 5373, -26844, 144595, -725377, 3403722, -16683671, 76490755, -326610948, 1503585693, -4737148448, 18060378458, -30643429023, 78310985281], [1, 4, 132, 149, 7210, -8455, 261495, -702233, 7976455, -20364757, 219917295, -206208995, 5099496010, 3056161201, 78516678372, 68999505236, 500246412961], [1, 11, 222, 1765, 20656, 130021, 1137593, 5928155, 42218816, 183772805, 1093226873, 3873455611, 19076249776, 50530451515, 197025817182, 302638755221, 852891037441], [1, -10, 221, -1934, 23831, -175415, 1590889, -9764443, 71129081, -361284391, 2177927041, -8885295995, 44663130791, -134111212838, 567025536389, -949318771330, 3512479453921], [1, 29, 591, 8870, 109589, 1132509, 10137134, 78739477, 538618569, 3228318557, 17040522254, 78053652789, 309672322229, 1027644502870, 2807311606431, 5647873942549, 7984925229121], [1, -2, 236, -465, 27460, -51575, 2034075, -3419244, 104089696, -147027492, 3761004675, -4100573525, 93880275460, -68358925995, 1491841679564, -543637222214, 11688200277601], [1, 0, 117, 136, 7238, 18338, 426984, 1406698, 22678952, 66114806, 943207656, 1903906174, 35319131078, 31190920952, 1261168193493, 0, 23811286661761], [1, 59, 1773, 35994, 555641, 6950535, 73081626, 659060411, 5148041929, 34930201783, 205286287434, 1034774799195, 4384274753321, 15052528575042, 39297412281717, 69307957250383, 62259690411361], [1, 23, 391, 5027, 56886, 553890, 5066388, 41897990, 333030964, 2471981410, 17636096628, 113757374310, 689308197846, 3593924451073, 16492588653631, 57238984150837, 146830437604321], [1, 2, 59, 36, 8639, 3895, 529997, -186683, 37362403, -11387663, 1972118837, 884090995, 119614220399, 30405466836, 3039702087299, 6285485672042, 191707312997281], [1, -3, 339, -841, 56502, -122764, 6176868, -11961514, 484321692, -801421438, 27727960452, -36922868932, 1138578638742, -1135455214987, 30665391555291, -18182134815969, 406067677556641], [1, 1, 200, 642, 22644, 133805, 1838211, 14593132, 133386112, 1036112372, 9266421651, 47890281355, 575422104564, 1158315243342, 25620056784200, 9095120158391, 645753531245761], [1, 6, 155, 1840, 23849, 267699, 2403405, 25891991, 218901495, 1890115343, 12807745245, 104139461883, 677269649609, 3814451731120, 23456805074795, 66284391114582, 806460091894081], [1, 0, 222, -1008, 23865, -199880, 2046977, -22369928, 157302126, -1767224312, 12775183457, -98548635320, 929543683065, -3101672850192, 53965415125662, 0, 1517108809906561], [1, -15, 425, -5251, 90501, -941833, 12398464, -111235053, 1207619210, -9232509399, 85413018496, -538527865571, 4295025508821, -20683902416393, 138949658681825, -407040764844405, 2252292232139041], [1, 4, 615, 2228, 173044, 549813, 29004737, 78354964, 3163082895, 6973591796, 229746521777, 387601120797, 10857168351604, 12441284452372, 305643493941015, 176925339582116, 3936588805702081], [1, 62, 2150, 52739, 1017422, 16273323, 222841507, 2658362297, 27886183171, 257861142809, 2096715739363, 14852222522379, 90071638133582, 452887737813923, 1790889810597350, 5009493637643006, 7837433594376961]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/bp'], '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': '16-7942e8-1.1-c1e8-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 8, 'prelabel': '16-7942e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 488776419326682673, 'z1': {'__RealLiteral__': 0, 'data': '1.10876524187700719941787450513', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1405526924377586130100324985600,1650046533663467363545356739017,1656963650337863488225656186385,1666061019566783407002822486299,1738334927982195464331522359492,1924116889637182015410383079399,2012981406768880410752635999649,2217032129015467043117414800586', 'Lhash_array': ['1405526924377586130100324985600', '1650046533663467363545356739017', '1656963650337863488225656186385', '1666061019566783407002822486299', '1738334927982195464331522359492', '1924116889637182015410383079399', '2012981406768880410752635999649', '2217032129015467043117414800586'], 'factors': ['2-7942-1.1-c1-0-164', '2-7942-1.1-c1-0-196', '2-7942-1.1-c1-0-198', '2-7942-1.1-c1-0-200', '2-7942-1.1-c1-0-218', '2-7942-1.1-c1-0-245', '2-7942-1.1-c1-0-259', '2-7942-1.1-c1-0-274'], 'label': '16-7942e8-1.1-c1e8-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/bp'}