{'Lhash': '1244945325280298843974544137953,1837322665914669819436519170852', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': -1, 'a7': 4, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.29635590013517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1, 1, 1]], [5, [1]], [7, [1, -4, 7]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.1', 'coefficient_field': '1.1.1.1', 'conductor': 1102500, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 1, 1], [1], [1, -4, 7], [1, -5, 14, -55, 121], [1, -10, 51, -130, 169], [1, 4, -1, 68, 289], [1, -7, 30, -133, 361], [1, -1, -22, -23, 529], [1, 0, 58, 0, 841], [1, -2, -27, -62, 961], [1, -1, -36, -37, 1369], [1, -10, 107, -410, 1681], [1, 24, 230, 1032, 1849], [1, 11, 74, 517, 2209], [1, 9, 28, 477, 2809], [1, 4, -43, 236, 3481], [1, 4, -45, 244, 3721], [1, 12, 77, 804, 4489], [1, -4, 146, -284, 5041], [1, -10, 27, -730, 5329], [1, -12, 65, -948, 6241], [1, -24, 310, -1992, 6889], [1, 14, 107, 1246, 7921], [1, -16, 258, -1552, 9409], [1, 0, -101, 0, 10201], [1, -8, -39, -824, 10609], [1, 2, -103, 214, 11449], [1, -2, -105, -218, 11881], [1, -28, 422, -3164, 12769]], 'euler_factors_factorization': [[[[1, -1, 1], 1]], [[[1, 1, 1], 1]], [1], [[[1, -4, 7], 1]], [[[1, -5, 14, -55, 121], 1]], [[[1, -5, 13], 2]], [[[1, 4, -1, 68, 289], 1]], [[[1, -8, 19], 1], [[1, 1, 19], 1]], [[[1, -1, -22, -23, 529], 1]], [[[1, 0, 29], 2]], [[[1, -2, -27, -62, 961], 1]], [[[1, -11, 37], 1], [[1, 10, 37], 1]], [[[1, -5, 41], 2]], [[[1, 12, 43], 2]], [[[1, 11, 74, 517, 2209], 1]], [[[1, 9, 28, 477, 2809], 1]], [[[1, 4, -43, 236, 3481], 1]], [[[1, 4, -45, 244, 3721], 1]], [[[1, 12, 77, 804, 4489], 1]], [[[1, -2, 71], 2]], [[[1, -17, 73], 1], [[1, 7, 73], 1]], [[[1, -12, 65, -948, 6241], 1]], [[[1, -12, 83], 2]], [[[1, 14, 107, 1246, 7921], 1]], [[[1, -8, 97], 2]], [[[1, 0, -101, 0, 10201], 1]], [[[1, -8, -39, -824, 10609], 1]], [[[1, 2, -103, 214, 11449], 1]], [[[1, -19, 109], 1], [[1, 17, 109], 1]], [[[1, -14, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'id': 23579475, 'index': 28, 'label': '4-1050e2-1.1-c1e2-0-28', 'leading_term': '3.92395861892654489390052244749483528774550460725295833279158646748532234696985090824492687', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/2/i/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [3.9239586189265454, 3.919553564634885, 3.9086653767264794, 3.889509415216945, 3.862132578412566, 3.826749899156412, 3.783014828067526, 3.730539391428464, 3.6690231513827416, 3.598173858192119, 3.517664070627367, 3.4272109355615967, 3.326571818659015, 3.215584912405696, 3.094158058897052, 2.9623211990693754, 2.820213254618215, 2.6681310114356367, 2.5065135245321586, 2.3359846307014625, 2.157337496530319, 1.9715631049321647, 1.7798376051117428, 1.5835312013992864, 1.384199283831742, 1.1835687947436866, 0.9835317959305175, 0.7861100158373833, 0.5934472464551616, 0.4077562919095444, 0.23130523366269218, 0.06635365793829708, -0.08487196065702565, -0.22024481354989167, -0.337775719025537, -0.43567550710249486, -0.5124046270942922, -0.566726639594121, -0.5977636929867949, -0.6050379783883357, -0.5885249257592031, -0.5486797319345513, -0.4864799418087928, -0.4034332748104998, -0.30160301097899406, -0.18359210703631212, -0.05254760588557107, 0.08788423287999494, 0.23357589099251289, 0.37999547469438805, 0.5222477937460335, 0.6551809525369372, 0.7734522679039849, 0.8716553058041754, 0.9444132337714464, 0.9865107807459607, 0.9930167042353497, 0.9594017854001757, 0.8816880980732233, 0.7565353370216003, 0.5814070613644319, 0.35461398748133655, 0.0754772521409229, -0.2556726071274578, -0.6373644723335626, -1.0670245458428933, -1.5409076231036478, -2.0541622675510203, -2.6008469746498433, -3.1740157499475177, -3.7658275157979717, -4.3676500108271705, -4.970254287618735, -5.56393861648852, -6.138785427176503, -6.684806334214605, -7.192230924854042, -7.651666529298165, -8.05439006917292, -8.392501788797073, -8.65920144161838, -8.848900431439219, -8.95747444630334, -8.982291953381216, -8.92244094927803, -8.778637458537268, -8.553423047195768, -8.250934382138848, -7.877061998441039, -7.439087460060469, -6.9457860691337485, -6.406965744016354, -5.833491658452009, -5.236782737785086, -4.628741005087277, -4.0212678394367405, -3.4261008681263725, -2.8544004587405563, -2.3165231373168296, -1.821710575529948, -1.377848477728182, -0.9912730710931773, -0.6665720948768644, -0.4065106875453347, -0.21192499229142991, -0.08176077102413172, -0.013092559792925198, -0.001262386291790126, -0.040033873666310504, -0.1218118643665974, -0.23791837513948522, -0.3788640425259855, -0.5347167691045928, -0.6953838772856875, -0.8510352749854685, -0.9923464420364012, -1.1109333701354502, -1.1995066061799424, -1.2522729708691471, -1.2649624061812628, -1.2351514512397552, -1.1621459835674457, -1.0471857598583176, -0.893191620066659, -0.7048228782735767, -0.48811892671747237, -0.25040464768139975, 0.00013162893475251547, 0.2546600456124482, 0.5041484468563353, 0.7396604800255289, 0.952765323014879, 1.135845313592282, 1.2824312202973427, 1.3874528837001108, 1.4474585139810952, 1.4607572272276108, 1.4274883849212872, 1.3496296606421407, 1.230898771549996, 1.0766248921225676, 0.8934939120882389, 0.6892978748672719, 0.47257007481465524, 0.2522387636234266, 0.03722812355154932, -0.16394747155721998, -0.34352700080031573, -0.49492079716345166, -0.6129178201051498, -0.6940574610781771, -0.7366504871353518, -0.7410387186990749, -0.7094237043297763, -0.6459534325277186, -0.5563932378416256, -0.44800752867407534, -0.3291297991951133, -0.20885483796453952, -0.09657122981509067, -0.0015294838602231658, 0.06760302647612079, 0.10319572613118345, 0.09902579779727257, 0.05063870633242772, -0.044396376336763875, -0.186318926282873, -0.3730658750236535, -0.6003588103054559, -0.8617467380710283, -1.1489624952410882, -1.4520996335035854, -1.7602088618449658, -2.061552130605934, -2.3443765374172916, -2.597156349883794, -2.8094581112350077, -2.972067726510525, -3.0778452569778474, -3.121647928807021, -3.1010671773162177, -3.0160991276752775, -2.869663603161011, -2.667030885944588, -2.416048860545855, -2.1263900810234007, -1.809463996016493, -1.4775855989319677, -1.1436148197462945, -0.8201652026773989, -0.5190724464274866, -0.2507609103917812, -0.023680145282687037, 0.1560691002410544, 0.28518805598147856, 0.36322328705945806, 0.3927972008731708, 0.3792946281693005, 0.33081179138027367, 0.25751819438417256, 0.17132743924127947, 0.0850309313749959, 0.011753001564137484, -0.03599309040249352, -0.04695265510765988, -0.011976632985386398, 0.07537906375886987, 0.21826121202585355, 0.4161354860563129, 0.6645521826189916, 0.9551287198690539, 1.2757033179213308, 1.6107724341784342, 1.9419963873787927, 2.249071936480203, 2.5105103602017835, 2.7047998990099504, 2.811348367417875, 2.811690020318579, 2.6904629196689522, 2.4363740629654225, 2.0430635042717573, 1.5095770687003827, 0.8409595802824976, 0.04808839112398539, -0.852148451464387, -1.8376648767568116, -2.8815016807470077, -3.9531660155438053, -5.019432525786588, -6.046022803348392, -6.9986957194405575, -7.845072418887828, -8.555693021415657, -9.105803014045097, -9.476007565982737, -9.653841383348613, -9.633719884060739, -9.418116034304749, -9.016674124542062, -8.446828847313377, -7.732163526196164, -6.902352350870113, -5.991040333319416, -5.035094186231029, -4.072382501722329, -3.1404906387905798, -2.2747622484698438, -1.5068015640670316, -0.8630508538581915, -0.3634909089747279, -0.0209162962915293, 0.15978443019574548, 0.1816088377164508, 0.055336827554295476, -0.20117174985018585, -0.5639468776907625, -1.0041268211016716, -1.4896351359865696, -1.9866490563464607, -2.4616813720028707, -2.8829542658545866, -3.222521047920143, -3.457183391446751, -3.570294838053958, -3.551934200970408, -3.4000922882250704, -3.119978258948856, -2.7243926043177242, -2.2322565579028986, -1.6681122477777954, -1.0601656000647124, -0.4390195841422287, 0.16435298850431612, 0.7203672206558382, 1.2024895856501814, 1.5890804222555794, 1.8643398354621956, 2.019794236228106, 2.0543107566035665, 1.9748732062941052, 1.795621185723274, 1.5377446964539065, 1.2276835852695582, 0.8961954328708004, 0.5760206535216182, 0.3003790524176568, 0.10053972880303909, 0.004128860051528567, 0.033102924700549194, 0.20229070678222374, 0.5182104000206766, 0.9782377829148053, 1.5705191964274985, 2.2740687976679776, 3.059751327824033, 3.891465143289146, 4.727884666634368, 5.52468294638366, 6.23652742877763, 6.820051860615253, 7.235557746775182, 7.45020483992324, 7.438990660645415, 7.187476879342455, 6.6918211220351065, 5.960406756511605, 5.012883548530317, 3.8803294900559875, 2.603403507318635, 1.2310479458635775, -0.18202093710104897, -1.577687371250475, -2.8972708256137243, -4.0843449734740735, -5.087460033172177, -5.862719392528077, -6.375886959864467, -6.6041706089817485, -6.5372388564616575, -6.1778983635723606, -5.54173317543643, -4.656591161559028, -3.5608944724846068, -2.302030059998098, -0.9337486692317803, 0.4862997487166982, 1.8993954834746751, 3.2487012002304505, 4.481571645789146, 5.552522276352955, 6.424428593933932, 7.0709930695556595, 7.47655936374317, 7.637623748592862, 7.561332548304407, 7.265805924813807, 6.7776373454711765, 6.13112772329366, 5.365236377345949, 4.5221379385836515, 3.6441084828910464, 2.7719968250328546, 1.942498211639408, 1.1871123372573866, 0.5301788151315786, -0.011309206008770572, -0.42865820490404405, -0.7207377096740853, -0.893856892209176, -0.960309246076286, -0.9373549781260979, -0.8454028818489419, -0.7065130153115001, -0.5426117033824608, -0.37404225706934524, -0.2181681699590996, -0.08844373461158254, 0.006337455288234809, 0.06218504115609243, 0.07990175242432718, 0.06444830593891024, 0.024227032328224783, -0.030074981779930635, -0.08667395599189476, -0.13397359601025138, -0.16185143491930679, -0.16266802618257972, -0.13224159828371324, -0.07027531930706597, 0.01929035619032701, 0.12858145219433342, 0.2461605947134214, 0.35802543419219435, 0.44855484213651653, 0.50198183776996, 0.503577904663873, 0.4412311710989928, 0.3064584619814564, 0.09565169294855193, -0.18944390865967434, -0.5411823820629234, -0.946309913773519, -1.38627011870492, -1.8383413845662793, -2.27665841626346, -2.674085192841625, -3.003556489096135, -3.2403966914522817, -3.3634563128682813, -3.3574370240102556, -3.2133509115854757, -2.9303397272579317, -2.5151921674997166, -1.983207754126161, -1.3567733246790592, -0.665054861988906, 0.05814147429871473, 0.7757210621133269, 1.4497817697859579, 2.0435536762339335, 2.5237749628307466, 2.862582794620965, 3.039331758028176, 3.0418314764059065, 2.8672231480523536, 2.522184507310149, 2.0226399604493617, 1.3928679361612668, 0.6640871509355063, -0.12732761981474572, -0.9420030668406549, -1.7398810749165496, -2.4824605408481903, -3.1352198771815374, -3.6691979707566325, -4.063112456336398, -4.3037003899088875, -4.387177662926623, -4.318132206779052, -4.110082814372256, -3.7831659258121175, -3.363730542629997, -2.881416225925862, -2.3679647497907594, -1.8544130400577699, -1.3695670585314448, -0.9379135272280251, -0.5783475394020466, -0.3031564846792566, -0.11751840587721817, -0.019629266873609292, -0.0012128667366857935, -0.048607933937688, -0.1441635135306897, -0.2679053465435005, -0.39938045553296797, -0.5193995271782563, -0.6117583510291451, -0.6645273086625976, -0.6711463076184395, -0.6308420386398256, -0.5488070328284068, -0.4355784554136764, -0.30628339839235175, -0.17914512645783312, -0.07403609560162727, -0.010570301809112476, -0.006404718951478277, -0.07551329260152788, -0.22678044669859063, -0.4629759787406297, -0.7801581935390303, -1.1676131462025294, -1.6084043324709314, -2.080216238255531, -2.5570610044738715, -3.010698592047234, -3.413125957068017, -3.73809971523334, -3.963735089246154, -4.073641410470274, -4.058874480975609, -3.918292691637829, -3.6592852015985997, -3.2971385809945915, -2.8543501357743595, -2.3590418290069657, -1.8431089252643826, -1.3399832178572673, -0.8822408799738086, -0.4992724857741651, -0.21501743617628408, -0.04623986626698182, -0.001200427033742015, -0.07882336148381675, -0.2689162655422654, -0.55309330853416, -0.9039668348136383, -1.287767158292041], 'positive_zeros': ['0.982088696251283538707303216707445', '1.44939202141652908605457048113944', '1.94506973807200219791793877029545', '3.32940374808960685605755158847991', '3.34044381846113541302232537787063', '3.96873437673761699233149625099713', '4.53683789271397133296162415601323', '5.00057552894100604437023974582603', '5.14352390995270661629306157374839', '6.00367422045603836064956133651351', '6.31862866342823298207153928086722', '6.41198847974206336309067270988938', '7.00176297916936316813590296574265', '7.84631061255104328484130762315244', '7.945666662056008116658145563784320', '8.522554300842937996223940444422910', '9.004742155934751503145198306489294', '9.013140524327360030490668952503988', '9.714730648138680166752435378692333', '10.17684586192007170472353280803142'], 'prelabel': '4-1050e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.895564230376257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2281497277329873736, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.982088696251283538707303216707', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.44939202141652908605457048114', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.94506973807200219791793877030', 'prec': 103}}
