Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 619.5 | ||
Character | \(\chi\) | \(=\) | 784.619 |
Dual form | 784.2.w.e.19.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.757684 | + | 1.19412i | 0.535763 | + | 0.844368i | ||||
\(3\) | −0.817885 | − | 3.05239i | −0.472206 | − | 1.76230i | −0.631816 | − | 0.775118i | \(-0.717690\pi\) |
0.159610 | − | 0.987180i | \(-0.448976\pi\) | |||||||
\(4\) | −0.851831 | + | 1.80953i | −0.425915 | + | 0.904763i | ||||
\(5\) | 0.797811 | + | 0.213773i | 0.356792 | + | 0.0956021i | 0.432763 | − | 0.901508i | \(-0.357539\pi\) |
−0.0759706 | + | 0.997110i | \(0.524205\pi\) | |||||||
\(6\) | 3.02521 | − | 3.28940i | 1.23504 | − | 1.34289i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.80620 | + | 0.353863i | −0.992143 | + | 0.125109i | ||||
\(9\) | −6.05007 | + | 3.49301i | −2.01669 | + | 1.16434i | ||||
\(10\) | 0.349219 | + | 1.11465i | 0.110433 | + | 0.352484i | ||||
\(11\) | −0.732051 | − | 2.73205i | −0.220722 | − | 0.823744i | −0.984074 | − | 0.177762i | \(-0.943114\pi\) |
0.763352 | − | 0.645983i | \(-0.223552\pi\) | |||||||
\(12\) | 6.22008 | + | 1.12013i | 1.79558 | + | 0.323355i | ||||
\(13\) | −2.91203 | − | 2.91203i | −0.807651 | − | 0.807651i | 0.176627 | − | 0.984278i | \(-0.443481\pi\) |
−0.984278 | + | 0.176627i | \(0.943481\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.61007i | − | 0.673918i | ||||||
\(16\) | −2.54877 | − | 3.08282i | −0.637192 | − | 0.770705i | ||||
\(17\) | −2.30469 | − | 1.33061i | −0.558969 | − | 0.322721i | 0.193763 | − | 0.981048i | \(-0.437931\pi\) |
−0.752732 | + | 0.658328i | \(0.771264\pi\) | |||||||
\(18\) | −8.75510 | − | 4.57790i | −2.06360 | − | 1.07902i | ||||
\(19\) | 0.436928 | + | 0.117075i | 0.100238 | + | 0.0268587i | 0.308590 | − | 0.951195i | \(-0.400143\pi\) |
−0.208351 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(20\) | −1.06643 | + | 1.26156i | −0.238461 | + | 0.282094i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.70773 | − | 2.94418i | 0.577289 | − | 0.627702i | ||||
\(23\) | 1.63915 | + | 2.83909i | 0.341786 | + | 0.591991i | 0.984764 | − | 0.173894i | \(-0.0556349\pi\) |
−0.642978 | + | 0.765884i | \(0.722302\pi\) | |||||||
\(24\) | 3.37528 | + | 8.27621i | 0.688976 | + | 1.68937i | ||||
\(25\) | −3.73932 | − | 2.15890i | −0.747865 | − | 0.431780i | ||||
\(26\) | 1.27091 | − | 5.68370i | 0.249245 | − | 1.11466i | ||||
\(27\) | 8.90678 | + | 8.90678i | 1.71411 | + | 1.71411i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.04184 | + | 2.04184i | −0.379160 | + | 0.379160i | −0.870799 | − | 0.491639i | \(-0.836398\pi\) |
0.491639 | + | 0.870799i | \(0.336398\pi\) | |||||||
\(30\) | 3.11673 | − | 1.97761i | 0.569035 | − | 0.361060i | ||||
\(31\) | 1.26156 | − | 2.18509i | 0.226583 | − | 0.392454i | −0.730210 | − | 0.683223i | \(-0.760578\pi\) |
0.956793 | + | 0.290769i | \(0.0939111\pi\) | |||||||
\(32\) | 1.75009 | − | 5.37933i | 0.309375 | − | 0.950940i | ||||
\(33\) | −7.74055 | + | 4.46901i | −1.34746 | + | 0.777955i | ||||
\(34\) | −0.157318 | − | 3.76025i | −0.0269798 | − | 0.644878i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.16706 | − | 13.9232i | −0.194509 | − | 2.32054i | ||||
\(37\) | 0.625071 | − | 2.33280i | 0.102761 | − | 0.383509i | −0.895321 | − | 0.445422i | \(-0.853054\pi\) |
0.998082 | + | 0.0619131i | \(0.0197202\pi\) | |||||||
\(38\) | 0.191253 | + | 0.610449i | 0.0310253 | + | 0.0990279i | ||||
\(39\) | −6.50694 | + | 11.2704i | −1.04194 | + | 1.80470i | ||||
\(40\) | −2.31447 | − | 0.317575i | −0.365949 | − | 0.0502130i | ||||
\(41\) | −11.9895 | −1.87245 | −0.936224 | − | 0.351405i | \(-0.885704\pi\) | ||||
−0.936224 | + | 0.351405i | \(0.885704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.27830 | + | 3.27830i | −0.499936 | + | 0.499936i | −0.911418 | − | 0.411482i | \(-0.865011\pi\) |
0.411482 | + | 0.911418i | \(0.365011\pi\) | |||||||
\(44\) | 5.56730 | + | 1.00258i | 0.839302 | + | 0.151145i | ||||
\(45\) | −5.57353 | + | 1.49342i | −0.830852 | + | 0.222626i | ||||
\(46\) | −2.14825 | + | 4.10847i | −0.316742 | + | 0.605760i | ||||
\(47\) | −4.98400 | − | 8.63254i | −0.726991 | − | 1.25918i | −0.958149 | − | 0.286269i | \(-0.907585\pi\) |
0.231159 | − | 0.972916i | \(-0.425748\pi\) | |||||||
\(48\) | −7.32537 | + | 10.3012i | −1.05733 | + | 1.48685i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.255246 | − | 6.10095i | −0.0360972 | − | 0.862805i | ||||
\(51\) | −2.17658 | + | 8.12310i | −0.304782 | + | 1.13746i | ||||
\(52\) | 7.74995 | − | 2.78884i | 1.07472 | − | 0.386742i | ||||
\(53\) | 3.24561 | − | 0.869658i | 0.445818 | − | 0.119457i | −0.0289238 | − | 0.999582i | \(-0.509208\pi\) |
0.474742 | + | 0.880125i | \(0.342541\pi\) | |||||||
\(54\) | −3.88722 | + | 17.3843i | −0.528983 | + | 2.36570i | ||||
\(55\) | − | 2.33615i | − | 0.315007i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.42943i | − | 0.189332i | ||||||
\(58\) | −3.98526 | − | 0.891126i | −0.523290 | − | 0.117011i | ||||
\(59\) | 5.66785 | − | 1.51870i | 0.737891 | − | 0.197717i | 0.129751 | − | 0.991547i | \(-0.458582\pi\) |
0.608141 | + | 0.793829i | \(0.291916\pi\) | |||||||
\(60\) | 4.72299 | + | 2.22334i | 0.609736 | + | 0.287032i | ||||
\(61\) | 1.65615 | − | 6.18083i | 0.212048 | − | 0.791374i | −0.775137 | − | 0.631793i | \(-0.782319\pi\) |
0.987185 | − | 0.159580i | \(-0.0510141\pi\) | |||||||
\(62\) | 3.56512 | − | 0.149154i | 0.452770 | − | 0.0189426i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.74956 | − | 1.98602i | 0.968695 | − | 0.248253i | ||||
\(65\) | −1.70074 | − | 2.94576i | −0.210950 | − | 0.365377i | ||||
\(66\) | −11.2014 | − | 5.85703i | −1.37880 | − | 0.720950i | ||||
\(67\) | 5.97447 | − | 1.60085i | 0.729897 | − | 0.195575i | 0.125314 | − | 0.992117i | \(-0.460006\pi\) |
0.604584 | + | 0.796542i | \(0.293340\pi\) | |||||||
\(68\) | 4.37098 | − | 3.03694i | 0.530060 | − | 0.368283i | ||||
\(69\) | 7.32537 | − | 7.32537i | 0.881871 | − | 0.881871i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.14114 | 0.610141 | 0.305071 | − | 0.952330i | \(-0.401320\pi\) | ||||
0.305071 | + | 0.952330i | \(0.401320\pi\) | |||||||
\(72\) | 15.7417 | − | 11.9430i | 1.85518 | − | 1.40750i | ||||
\(73\) | −3.49607 | + | 6.05536i | −0.409184 | + | 0.708727i | −0.994798 | − | 0.101863i | \(-0.967520\pi\) |
0.585615 | + | 0.810589i | \(0.300853\pi\) | |||||||
\(74\) | 3.25924 | − | 1.02111i | 0.378879 | − | 0.118702i | ||||
\(75\) | −3.53146 | + | 13.1796i | −0.407778 | + | 1.52185i | ||||
\(76\) | −0.584038 | + | 0.690905i | −0.0669938 | + | 0.0792523i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.3883 | + | 0.769313i | −2.08207 | + | 0.0871076i | ||||
\(79\) | −9.72098 | + | 5.61241i | −1.09370 | + | 0.631445i | −0.934558 | − | 0.355811i | \(-0.884205\pi\) |
−0.159137 | + | 0.987256i | \(0.550871\pi\) | |||||||
\(80\) | −1.37441 | − | 3.00437i | −0.153664 | − | 0.335898i | ||||
\(81\) | 9.42322 | − | 16.3215i | 1.04702 | − | 1.81350i | ||||
\(82\) | −9.08426 | − | 14.3169i | −1.00319 | − | 1.58103i | ||||
\(83\) | 5.39734 | − | 5.39734i | 0.592435 | − | 0.592435i | −0.345854 | − | 0.938288i | \(-0.612411\pi\) |
0.938288 | + | 0.345854i | \(0.112411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.55426 | − | 1.55426i | −0.168583 | − | 0.168583i | ||||
\(86\) | −6.39858 | − | 1.43076i | −0.689977 | − | 0.154283i | ||||
\(87\) | 7.90247 | + | 4.56249i | 0.847234 | + | 0.489151i | ||||
\(88\) | 3.02105 | + | 7.40765i | 0.322046 | + | 0.789658i | ||||
\(89\) | −0.528369 | − | 0.915163i | −0.0560071 | − | 0.0970071i | 0.836663 | − | 0.547719i | \(-0.184504\pi\) |
−0.892670 | + | 0.450712i | \(0.851170\pi\) | |||||||
\(90\) | −6.00629 | − | 5.52390i | −0.633119 | − | 0.582270i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.53368 | + | 0.547659i | −0.681183 | + | 0.0570974i | ||||
\(93\) | −7.70156 | − | 2.06363i | −0.798614 | − | 0.213988i | ||||
\(94\) | 6.53196 | − | 12.4922i | 0.673721 | − | 1.28847i | ||||
\(95\) | 0.323559 | + | 0.186807i | 0.0331964 | + | 0.0191660i | ||||
\(96\) | −17.8512 | − | 0.942273i | −1.82193 | − | 0.0961704i | ||||
\(97\) | 13.2689i | 1.34726i | 0.739071 | + | 0.673628i | \(0.235265\pi\) | ||||
−0.739071 | + | 0.673628i | \(0.764735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.9720 | + | 13.9720i | 1.40424 | + | 1.40424i | ||||
\(100\) | 7.09185 | − | 4.92739i | 0.709185 | − | 0.492739i | ||||
\(101\) | −0.0918003 | − | 0.342603i | −0.00913447 | − | 0.0340903i | 0.961208 | − | 0.275824i | \(-0.0889507\pi\) |
−0.970343 | + | 0.241734i | \(0.922284\pi\) | |||||||
\(102\) | −11.3491 | + | 3.55565i | −1.12373 | + | 0.352062i | ||||
\(103\) | 10.8408 | − | 6.25894i | 1.06818 | − | 0.616712i | 0.140494 | − | 0.990082i | \(-0.455131\pi\) |
0.927683 | + | 0.373370i | \(0.121798\pi\) | |||||||
\(104\) | 9.20220 | + | 7.14129i | 0.902350 | + | 0.700261i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.49762 | + | 3.21671i | 0.339718 | + | 0.312434i | ||||
\(107\) | 5.31161 | + | 1.42324i | 0.513493 | + | 0.137590i | 0.506255 | − | 0.862384i | \(-0.331029\pi\) |
0.00723781 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(108\) | −23.7041 | + | 8.52998i | −2.28093 | + | 0.820798i | ||||
\(109\) | −1.56085 | − | 5.82517i | −0.149502 | − | 0.557950i | −0.999514 | − | 0.0311855i | \(-0.990072\pi\) |
0.850011 | − | 0.526764i | \(-0.176595\pi\) | |||||||
\(110\) | 2.78964 | − | 1.77007i | 0.265982 | − | 0.168769i | ||||
\(111\) | −7.63184 | −0.724382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.79072 | 0.732889 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(114\) | 1.70691 | − | 1.08306i | 0.159866 | − | 0.101437i | ||||
\(115\) | 0.700811 | + | 2.61546i | 0.0653510 | + | 0.243893i | ||||
\(116\) | −1.95546 | − | 5.43406i | −0.181560 | − | 0.504540i | ||||
\(117\) | 27.7897 | + | 7.44623i | 2.56916 | + | 0.688405i | ||||
\(118\) | 6.10794 | + | 5.61739i | 0.562281 | + | 0.517122i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.923607 | + | 7.32440i | 0.0843134 | + | 0.668623i | ||||
\(121\) | 2.59808 | − | 1.50000i | 0.236189 | − | 0.136364i | ||||
\(122\) | 8.63546 | − | 2.70548i | 0.781818 | − | 0.244942i | ||||
\(123\) | 9.80605 | + | 36.5967i | 0.884182 | + | 3.29981i | ||||
\(124\) | 2.87934 | + | 4.14416i | 0.258572 | + | 0.372156i | ||||
\(125\) | −5.44195 | − | 5.44195i | −0.486743 | − | 0.486743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.02552i | − | 0.712150i | −0.934457 | − | 0.356075i | \(-0.884115\pi\) | ||
0.934457 | − | 0.356075i | \(-0.115885\pi\) | |||||||
\(128\) | 8.24326 | + | 7.74911i | 0.728608 | + | 0.684931i | ||||
\(129\) | 12.6879 | + | 7.32537i | 1.11711 | + | 0.644963i | ||||
\(130\) | 2.22896 | − | 4.26283i | 0.195493 | − | 0.373875i | ||||
\(131\) | 12.6038 | + | 3.37718i | 1.10120 | + | 0.295066i | 0.763254 | − | 0.646099i | \(-0.223601\pi\) |
0.337947 | + | 0.941165i | \(0.390267\pi\) | |||||||
\(132\) | −1.49315 | − | 17.8136i | −0.129962 | − | 1.55047i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.43836 | + | 5.92127i | 0.556190 | + | 0.511520i | ||||
\(135\) | 5.20190 | + | 9.00996i | 0.447709 | + | 0.775454i | ||||
\(136\) | 6.93828 | + | 2.91843i | 0.594953 | + | 0.250253i | ||||
\(137\) | 7.81979 | + | 4.51476i | 0.668089 | + | 0.385722i | 0.795352 | − | 0.606147i | \(-0.207286\pi\) |
−0.127263 | + | 0.991869i | \(0.540619\pi\) | |||||||
\(138\) | 14.2977 | + | 3.19703i | 1.21710 | + | 0.272150i | ||||
\(139\) | −4.33613 | − | 4.33613i | −0.367785 | − | 0.367785i | 0.498884 | − | 0.866669i | \(-0.333744\pi\) |
−0.866669 | + | 0.498884i | \(0.833744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.2735 | + | 22.2735i | −1.87577 | + | 1.87577i | ||||
\(142\) | 3.89536 | + | 6.13913i | 0.326891 | + | 0.515184i | ||||
\(143\) | −5.82406 | + | 10.0876i | −0.487032 | + | 0.843564i | ||||
\(144\) | 26.1886 | + | 9.74841i | 2.18238 | + | 0.812367i | ||||
\(145\) | −2.06549 | + | 1.19251i | −0.171530 | + | 0.0990327i | ||||
\(146\) | −9.87973 | + | 0.413339i | −0.817652 | + | 0.0342082i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.68880 | + | 3.11823i | 0.303218 | + | 0.256317i | ||||
\(149\) | −4.85422 | + | 18.1162i | −0.397673 | + | 1.48414i | 0.419505 | + | 0.907753i | \(0.362204\pi\) |
−0.817179 | + | 0.576384i | \(0.804463\pi\) | |||||||
\(150\) | −18.4137 | + | 5.76899i | −1.50347 | + | 0.471036i | ||||
\(151\) | 5.87561 | − | 10.1769i | 0.478150 | − | 0.828180i | −0.521536 | − | 0.853229i | \(-0.674641\pi\) |
0.999686 | + | 0.0250489i | \(0.00797414\pi\) | |||||||
\(152\) | −1.26754 | − | 0.173923i | −0.102811 | − | 0.0141070i | ||||
\(153\) | 18.5914 | 1.50302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.47360 | − | 1.47360i | 0.118362 | − | 0.118362i | ||||
\(156\) | −14.8512 | − | 21.3749i | −1.18905 | − | 1.71136i | ||||
\(157\) | 10.8045 | − | 2.89504i | 0.862289 | − | 0.231050i | 0.199539 | − | 0.979890i | \(-0.436056\pi\) |
0.662750 | + | 0.748840i | \(0.269389\pi\) | |||||||
\(158\) | −14.0673 | − | 7.35555i | −1.11913 | − | 0.585176i | ||||
\(159\) | −5.30907 | − | 9.19558i | −0.421037 | − | 0.729257i | ||||
\(160\) | 2.54619 | − | 3.91757i | 0.201294 | − | 0.309711i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 26.6296 | − | 1.11410i | 2.09222 | − | 0.0875323i | ||||
\(163\) | 3.53284 | − | 13.1848i | 0.276714 | − | 1.03271i | −0.677971 | − | 0.735089i | \(-0.737140\pi\) |
0.954684 | − | 0.297621i | \(-0.0961930\pi\) | |||||||
\(164\) | 10.2130 | − | 21.6953i | 0.797504 | − | 1.69412i | ||||
\(165\) | −7.13085 | + | 1.91071i | −0.555136 | + | 0.148748i | ||||
\(166\) | 10.5345 | + | 2.35558i | 0.817638 | + | 0.182828i | ||||
\(167\) | − | 7.84557i | − | 0.607109i | −0.952814 | − | 0.303554i | \(-0.901827\pi\) | ||
0.952814 | − | 0.303554i | \(-0.0981734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.95982i | 0.304601i | ||||||||
\(170\) | 0.678330 | − | 3.03360i | 0.0520255 | − | 0.232667i | ||||
\(171\) | −3.05239 | + | 0.817885i | −0.233422 | + | 0.0625453i | ||||
\(172\) | −3.13961 | − | 8.72472i | −0.239393 | − | 0.665253i | ||||
\(173\) | −0.804044 | + | 3.00073i | −0.0611303 | + | 0.228141i | −0.989732 | − | 0.142937i | \(-0.954345\pi\) |
0.928601 | + | 0.371079i | \(0.121012\pi\) | |||||||
\(174\) | 0.539422 | + | 12.8934i | 0.0408935 | + | 0.977446i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.55659 | + | 9.22015i | −0.494222 | + | 0.694995i | ||||
\(177\) | −9.27131 | − | 16.0584i | −0.696874 | − | 1.20702i | ||||
\(178\) | 0.692474 | − | 1.32434i | 0.0519032 | − | 0.0992634i | ||||
\(179\) | −13.7015 | + | 3.67131i | −1.02410 | + | 0.274406i | −0.731509 | − | 0.681832i | \(-0.761184\pi\) |
−0.292589 | + | 0.956238i | \(0.594517\pi\) | |||||||
\(180\) | 2.04532 | − | 11.3576i | 0.152449 | − | 0.846544i | ||||
\(181\) | 3.03153 | − | 3.03153i | 0.225332 | − | 0.225332i | −0.585407 | − | 0.810739i | \(-0.699065\pi\) |
0.810739 | + | 0.585407i | \(0.199065\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.2208 | −1.49477 | ||||||||
\(184\) | −5.60443 | − | 7.38703i | −0.413164 | − | 0.544579i | ||||
\(185\) | 0.997377 | − | 1.72751i | 0.0733286 | − | 0.127009i | ||||
\(186\) | −3.37113 | − | 10.7601i | −0.247184 | − | 0.788972i | ||||
\(187\) | −1.94815 | + | 7.27060i | −0.142463 | + | 0.531679i | ||||
\(188\) | 19.8663 | − | 1.66521i | 1.44890 | − | 0.121448i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0220861 | + | 0.527908i | 0.00160229 | + | 0.0382984i | ||||
\(191\) | 12.3049 | − | 7.10425i | 0.890353 | − | 0.514046i | 0.0162951 | − | 0.999867i | \(-0.494813\pi\) |
0.874058 | + | 0.485822i | \(0.161480\pi\) | |||||||
\(192\) | −12.4004 | − | 22.0303i | −0.894919 | − | 1.58990i | ||||
\(193\) | 9.64726 | − | 16.7095i | 0.694425 | − | 1.20278i | −0.275950 | − | 0.961172i | \(-0.588992\pi\) |
0.970374 | − | 0.241607i | \(-0.0776744\pi\) | |||||||
\(194\) | −15.8447 | + | 10.0536i | −1.13758 | + | 0.721810i | ||||
\(195\) | −7.60061 | + | 7.60061i | −0.544291 | + | 0.544291i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.454953 | + | 0.454953i | 0.0324140 | + | 0.0324140i | 0.723128 | − | 0.690714i | \(-0.242704\pi\) |
−0.690714 | + | 0.723128i | \(0.742704\pi\) | |||||||
\(198\) | −6.09787 | + | 27.2706i | −0.433356 | + | 1.93804i | ||||
\(199\) | −21.3063 | − | 12.3012i | −1.51036 | − | 0.872009i | −0.999927 | − | 0.0120940i | \(-0.996150\pi\) |
−0.510437 | − | 0.859915i | \(-0.670516\pi\) | |||||||
\(200\) | 11.2573 | + | 4.73510i | 0.796008 | + | 0.334822i | ||||
\(201\) | −9.77286 | − | 16.9271i | −0.689324 | − | 1.19394i | ||||
\(202\) | 0.339553 | − | 0.369205i | 0.0238909 | − | 0.0259772i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.8449 | − | 10.8581i | −0.899321 | − | 0.760217i | ||||
\(205\) | −9.56537 | − | 2.56303i | −0.668074 | − | 0.179010i | ||||
\(206\) | 15.6878 | + | 8.20289i | 1.09302 | + | 0.571522i | ||||
\(207\) | −19.8339 | − | 11.4511i | −1.37855 | − | 0.795908i | ||||
\(208\) | −1.55517 | + | 16.3993i | −0.107832 | + | 1.13709i | ||||
\(209\) | − | 1.27941i | − | 0.0884990i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1092 | + | 10.1092i | 0.695946 | + | 0.695946i | 0.963534 | − | 0.267588i | \(-0.0862265\pi\) |
−0.267588 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(212\) | −1.19104 | + | 6.61381i | −0.0818009 | + | 0.454238i | ||||
\(213\) | −4.20487 | − | 15.6928i | −0.288113 | − | 1.07525i | ||||
\(214\) | 2.32500 | + | 7.42105i | 0.158934 | + | 0.507293i | ||||
\(215\) | −3.31627 | + | 1.91465i | −0.226168 | + | 0.130578i | ||||
\(216\) | −28.1460 | − | 21.8425i | −1.91509 | − | 1.48619i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.77330 | − | 6.27747i | 0.391017 | − | 0.425164i | ||||
\(219\) | 21.3427 | + | 5.71876i | 1.44221 | + | 0.386438i | ||||
\(220\) | 4.22733 | + | 1.99001i | 0.285007 | + | 0.134166i | ||||
\(221\) | 2.83654 | + | 10.5861i | 0.190806 | + | 0.712098i | ||||
\(222\) | −5.78252 | − | 9.11331i | −0.388097 | − | 0.611645i | ||||
\(223\) | −15.1035 | −1.01140 | −0.505702 | − | 0.862708i | \(-0.668766\pi\) | ||||
−0.505702 | + | 0.862708i | \(0.668766\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 30.1642 | 2.01095 | ||||||||
\(226\) | 5.90290 | + | 9.30303i | 0.392655 | + | 0.618828i | ||||
\(227\) | 2.60794 | + | 9.73295i | 0.173095 | + | 0.645999i | 0.996868 | + | 0.0790797i | \(0.0251981\pi\) |
−0.823773 | + | 0.566919i | \(0.808135\pi\) | |||||||
\(228\) | 2.58659 | + | 1.21763i | 0.171301 | + | 0.0806396i | ||||
\(229\) | −25.6721 | − | 6.87883i | −1.69646 | − | 0.454566i | −0.724418 | − | 0.689361i | \(-0.757891\pi\) |
−0.972045 | + | 0.234795i | \(0.924558\pi\) | |||||||
\(230\) | −2.59217 | + | 2.81854i | −0.170923 | + | 0.185849i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00728 | − | 6.45234i | 0.328744 | − | 0.423617i | ||||
\(233\) | 3.87771 | − | 2.23879i | 0.254037 | − | 0.146668i | −0.367574 | − | 0.929994i | \(-0.619812\pi\) |
0.621611 | + | 0.783326i | \(0.286478\pi\) | |||||||
\(234\) | 12.1641 | + | 38.8261i | 0.795195 | + | 2.53814i | ||||
\(235\) | −2.13089 | − | 7.95258i | −0.139004 | − | 0.518769i | ||||
\(236\) | −2.07993 | + | 11.5498i | −0.135392 | + | 0.751828i | ||||
\(237\) | 25.0819 | + | 25.0819i | 1.62924 | + | 1.62924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.13871i | − | 0.591134i | −0.955322 | − | 0.295567i | \(-0.904491\pi\) | ||
0.955322 | − | 0.295567i | \(-0.0955086\pi\) | |||||||
\(240\) | −8.04639 | + | 6.65247i | −0.519392 | + | 0.429415i | ||||
\(241\) | −8.37419 | − | 4.83484i | −0.539429 | − | 0.311440i | 0.205418 | − | 0.978674i | \(-0.434144\pi\) |
−0.744848 | + | 0.667235i | \(0.767478\pi\) | |||||||
\(242\) | 3.75970 | + | 1.96588i | 0.241682 | + | 0.126372i | ||||
\(243\) | −21.0260 | − | 5.63390i | −1.34882 | − | 0.361415i | ||||
\(244\) | 9.77361 | + | 8.26186i | 0.625691 | + | 0.528911i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −36.2708 | + | 39.4383i | −2.31254 | + | 2.51449i | ||||
\(247\) | −0.931423 | − | 1.61327i | −0.0592650 | − | 0.102650i | ||||
\(248\) | −2.76698 | + | 6.57823i | −0.175703 | + | 0.417718i | ||||
\(249\) | −20.8892 | − | 12.0604i | −1.32380 | − | 0.764295i | ||||
\(250\) | 2.37505 | − | 10.6216i | 0.150211 | − | 0.671769i | ||||
\(251\) | −10.9231 | − | 10.9231i | −0.689459 | − | 0.689459i | 0.272653 | − | 0.962112i | \(-0.412099\pi\) |
−0.962112 | + | 0.272653i | \(0.912099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.55659 | − | 6.55659i | 0.412209 | − | 0.412209i | ||||
\(254\) | 9.58341 | − | 6.08081i | 0.601317 | − | 0.381544i | ||||
\(255\) | −3.47300 | + | 6.01541i | −0.217487 | + | 0.376699i | ||||
\(256\) | −3.00756 | + | 15.7148i | −0.187972 | + | 0.982174i | ||||
\(257\) | −20.4285 | + | 11.7944i | −1.27429 | + | 0.735713i | −0.975793 | − | 0.218697i | \(-0.929819\pi\) |
−0.298500 | + | 0.954410i | \(0.596486\pi\) | |||||||
\(258\) | 0.866076 | + | 20.7012i | 0.0539195 | + | 1.28880i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.77917 | − | 0.568236i | 0.420426 | − | 0.0352405i | ||||
\(261\) | 5.22110 | − | 19.4854i | 0.323178 | − | 1.20612i | ||||
\(262\) | 5.51696 | + | 17.6093i | 0.340839 | + | 1.08790i | ||||
\(263\) | −12.6798 | + | 21.9620i | −0.781868 | + | 1.35424i | 0.148984 | + | 0.988840i | \(0.452400\pi\) |
−0.930852 | + | 0.365396i | \(0.880934\pi\) | |||||||
\(264\) | 20.1402 | − | 15.2800i | 1.23954 | − | 0.940422i | ||||
\(265\) | 2.77529 | 0.170485 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.36129 | + | 2.36129i | −0.144508 | + | 0.144508i | ||||
\(268\) | −2.19245 | + | 12.1746i | −0.133925 | + | 0.743683i | ||||
\(269\) | 7.85436 | − | 2.10457i | 0.478889 | − | 0.128318i | −0.0112965 | − | 0.999936i | \(-0.503596\pi\) |
0.490185 | + | 0.871618i | \(0.336929\pi\) | |||||||
\(270\) | −6.81755 | + | 13.0384i | −0.414903 | + | 0.793491i | ||||
\(271\) | 8.37841 | + | 14.5118i | 0.508952 | + | 0.881531i | 0.999946 | + | 0.0103684i | \(0.00330043\pi\) |
−0.490994 | + | 0.871163i | \(0.663366\pi\) | |||||||
\(272\) | 1.77208 | + | 10.4964i | 0.107448 | + | 0.636436i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.533778 | + | 12.7585i | 0.0322467 | + | 0.770769i | ||||
\(275\) | −3.16085 | + | 11.7964i | −0.190606 | + | 0.711352i | ||||
\(276\) | 7.01547 | + | 19.4954i | 0.422282 | + | 1.17349i | ||||
\(277\) | 7.45479 | − | 1.99751i | 0.447915 | − | 0.120019i | −0.0278086 | − | 0.999613i | \(-0.508853\pi\) |
0.475724 | + | 0.879595i | \(0.342186\pi\) | |||||||
\(278\) | 1.89243 | − | 8.46325i | 0.113500 | − | 0.507592i | ||||
\(279\) | 17.6266i | 1.05528i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.11163i | − | 0.364589i | −0.983244 | − | 0.182295i | \(-0.941648\pi\) | ||
0.983244 | − | 0.182295i | \(-0.0583525\pi\) | |||||||
\(282\) | −43.4735 | − | 9.72091i | −2.58881 | − | 0.578872i | ||||
\(283\) | −6.87634 | + | 1.84251i | −0.408756 | + | 0.109526i | −0.457337 | − | 0.889293i | \(-0.651197\pi\) |
0.0485811 | + | 0.998819i | \(0.484530\pi\) | |||||||
\(284\) | −4.37938 | + | 9.30303i | −0.259869 | + | 0.552033i | ||||
\(285\) | 0.305573 | − | 1.14041i | 0.0181006 | − | 0.0675523i | ||||
\(286\) | −16.4585 | + | 0.688576i | −0.973213 | + | 0.0407164i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.20190 | + | 38.6584i | 0.483302 | + | 2.27797i | ||||
\(289\) | −4.95894 | − | 8.58914i | −0.291702 | − | 0.505243i | ||||
\(290\) | −2.98899 | − | 1.56289i | −0.175519 | − | 0.0917761i | ||||
\(291\) | 40.5019 | − | 10.8525i | 2.37427 | − | 0.636183i | ||||
\(292\) | −7.97928 | − | 11.4844i | −0.466952 | − | 0.672072i | ||||
\(293\) | −19.6200 | + | 19.6200i | −1.14621 | + | 1.14621i | −0.158921 | + | 0.987291i | \(0.550801\pi\) |
−0.987291 | + | 0.158921i | \(0.949199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.84653 | 0.282176 | ||||||||
\(296\) | −0.928587 | + | 6.76749i | −0.0539730 | + | 0.393352i | ||||
\(297\) | 17.8136 | − | 30.8540i | 1.03365 | − | 1.79033i | ||||
\(298\) | −25.3108 | + | 7.92984i | −1.46622 | + | 0.459364i | ||||
\(299\) | 3.49426 | − | 13.0407i | 0.202078 | − | 0.754166i | ||||
\(300\) | −20.8406 | − | 17.6171i | −1.20323 | − | 1.01712i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 16.6042 | − | 0.694671i | 0.955464 | − | 0.0399738i | ||||
\(303\) | −0.970677 | + | 0.560420i | −0.0557639 | + | 0.0321953i | ||||
\(304\) | −0.752709 | − | 1.64537i | −0.0431708 | − | 0.0943683i | ||||
\(305\) | 2.64259 | − | 4.57709i | 0.151314 | − | 0.262084i | ||||
\(306\) | 14.0864 | + | 22.2003i | 0.805265 | + | 1.26911i | ||||
\(307\) | 3.08795 | − | 3.08795i | 0.176238 | − | 0.176238i | −0.613475 | − | 0.789714i | \(-0.710229\pi\) |
0.789714 | + | 0.613475i | \(0.210229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.9713 | − | 27.9713i | −1.59123 | − | 1.59123i | ||||
\(310\) | 2.87618 | + | 0.643129i | 0.163356 | + | 0.0365273i | ||||
\(311\) | −17.5043 | − | 10.1061i | −0.992576 | − | 0.573064i | −0.0865328 | − | 0.996249i | \(-0.527579\pi\) |
−0.906043 | + | 0.423185i | \(0.860912\pi\) | |||||||
\(312\) | 14.2716 | − | 33.9295i | 0.807973 | − | 1.92088i | ||||
\(313\) | 7.61557 | + | 13.1906i | 0.430457 | + | 0.745574i | 0.996913 | − | 0.0785183i | \(-0.0250189\pi\) |
−0.566455 | + | 0.824093i | \(0.691686\pi\) | |||||||
\(314\) | 11.6434 | + | 10.7083i | 0.657074 | + | 0.604302i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.87517 | − | 22.3712i | −0.105487 | − | 1.25848i | ||||
\(317\) | 27.7959 | + | 7.44788i | 1.56117 | + | 0.418315i | 0.933034 | − | 0.359788i | \(-0.117151\pi\) |
0.628138 | + | 0.778102i | \(0.283817\pi\) | |||||||
\(318\) | 6.95800 | − | 13.3070i | 0.390185 | − | 0.746219i | ||||
\(319\) | 7.07313 | + | 4.08367i | 0.396019 | + | 0.228642i | ||||
\(320\) | 6.60725 | + | 0.0721758i | 0.369356 | + | 0.00403475i | ||||
\(321\) | − | 17.3772i | − | 0.969898i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.851203 | − | 0.851203i | −0.0473622 | − | 0.0473622i | ||||
\(324\) | 21.5072 | + | 30.9547i | 1.19484 | + | 1.71971i | ||||
\(325\) | 4.60224 | + | 17.1758i | 0.255286 | + | 0.952741i | ||||
\(326\) | 18.4209 | − | 5.77124i | 1.02024 | − | 0.319640i | ||||
\(327\) | −16.5041 | + | 9.52864i | −0.912678 | + | 0.526935i | ||||
\(328\) | 33.6450 | − | 4.24264i | 1.85774 | − | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.68454 | − | 7.06736i | −0.423020 | − | 0.389045i | ||||
\(331\) | −28.4387 | − | 7.62013i | −1.56313 | − | 0.418840i | −0.629479 | − | 0.777018i | \(-0.716732\pi\) |
−0.933654 | + | 0.358177i | \(0.883398\pi\) | |||||||
\(332\) | 5.16900 | + | 14.3642i | 0.283686 | + | 0.788340i | ||||
\(333\) | 4.36676 | + | 16.2970i | 0.239297 | + | 0.893068i | ||||
\(334\) | 9.36853 | − | 5.94446i | 0.512623 | − | 0.325267i | ||||
\(335\) | 5.10872 | 0.279119 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7954 | −0.751483 | −0.375741 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375741 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(338\) | −4.72848 | + | 3.00029i | −0.257196 | + | 0.163194i | ||||
\(339\) | −6.37191 | − | 23.7803i | −0.346075 | − | 1.29157i | ||||
\(340\) | 4.13643 | − | 1.48851i | 0.224330 | − | 0.0807255i | ||||
\(341\) | −6.89330 | − | 1.84705i | −0.373293 | − | 0.100024i | ||||
\(342\) | −3.28940 | − | 3.02521i | −0.177870 | − | 0.163585i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.03950 | − | 10.3596i | 0.433461 | − | 0.558554i | ||||
\(345\) | 7.41023 | − | 4.27830i | 0.398953 | − | 0.230336i | ||||
\(346\) | −4.19244 | + | 1.31348i | −0.225387 | + | 0.0706133i | ||||
\(347\) | −1.34603 | − | 5.02347i | −0.0722589 | − | 0.269674i | 0.920339 | − | 0.391122i | \(-0.127913\pi\) |
−0.992598 | + | 0.121448i | \(0.961246\pi\) | |||||||
\(348\) | −14.9875 | + | 10.4133i | −0.803415 | + | 0.558209i | ||||
\(349\) | −17.8960 | − | 17.8960i | −0.957951 | − | 0.957951i | 0.0412000 | − | 0.999151i | \(-0.486882\pi\) |
−0.999151 | + | 0.0412000i | \(0.986882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 51.8736i | − | 2.76881i | ||||||
\(352\) | −15.9778 | − | 0.843385i | −0.851617 | − | 0.0449526i | ||||
\(353\) | −3.79300 | − | 2.18989i | −0.201881 | − | 0.116556i | 0.395652 | − | 0.918401i | \(-0.370519\pi\) |
−0.597533 | + | 0.801845i | \(0.703852\pi\) | |||||||
\(354\) | 12.1509 | − | 23.2382i | 0.645811 | − | 1.23510i | ||||
\(355\) | 4.10166 | + | 1.09904i | 0.217694 | + | 0.0583308i | ||||
\(356\) | 2.10609 | − | 0.176534i | 0.111623 | − | 0.00935631i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.7654 | − | 13.5795i | −0.780374 | − | 0.717699i | ||||
\(359\) | 7.66467 | + | 13.2756i | 0.404526 | + | 0.700659i | 0.994266 | − | 0.106934i | \(-0.0341032\pi\) |
−0.589740 | + | 0.807593i | \(0.700770\pi\) | |||||||
\(360\) | 15.1120 | − | 6.16311i | 0.796472 | − | 0.324824i | ||||
\(361\) | −16.2773 | − | 9.39769i | −0.856699 | − | 0.494615i | ||||
\(362\) | 5.91694 | + | 1.32306i | 0.310988 | + | 0.0695385i | ||||
\(363\) | −6.70351 | − | 6.70351i | −0.351843 | − | 0.351843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.08367 | + | 4.08367i | −0.213749 | + | 0.213749i | ||||
\(366\) | −15.3210 | − | 24.1460i | −0.800841 | − | 1.26213i | ||||
\(367\) | 13.1576 | − | 22.7896i | 0.686821 | − | 1.18961i | −0.286040 | − | 0.958218i | \(-0.592339\pi\) |
0.972861 | − | 0.231391i | \(-0.0743275\pi\) | |||||||
\(368\) | 4.57459 | − | 12.2894i | 0.238467 | − | 0.640628i | ||||
\(369\) | 72.5374 | − | 41.8795i | 3.77615 | − | 2.18016i | ||||
\(370\) | 2.81854 | − | 0.117920i | 0.146529 | − | 0.00613035i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.2946 | − | 12.1783i | 0.533751 | − | 0.631416i | ||||
\(373\) | 9.03428 | − | 33.7164i | 0.467777 | − | 1.74577i | −0.179737 | − | 0.983715i | \(-0.557525\pi\) |
0.647514 | − | 0.762053i | \(-0.275809\pi\) | |||||||
\(374\) | −10.1580 | + | 3.18250i | −0.525259 | + | 0.164563i | ||||
\(375\) | −12.1601 | + | 21.0619i | −0.627943 | + | 1.08763i | ||||
\(376\) | 17.0408 | + | 22.4610i | 0.878814 | + | 1.15834i | ||||
\(377\) | 11.8918 | 0.612458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8512 | + | 14.8512i | −0.762855 | + | 0.762855i | −0.976838 | − | 0.213982i | \(-0.931356\pi\) |
0.213982 | + | 0.976838i | \(0.431356\pi\) | |||||||
\(380\) | −0.613649 | + | 0.426360i | −0.0314795 | + | 0.0218718i | ||||
\(381\) | −24.4970 | + | 6.56396i | −1.25502 | + | 0.336282i | ||||
\(382\) | 17.8065 | + | 9.31074i | 0.911062 | + | 0.476379i | ||||
\(383\) | 12.7227 | + | 22.0364i | 0.650100 | + | 1.12601i | 0.983098 | + | 0.183079i | \(0.0586063\pi\) |
−0.332998 | + | 0.942927i | \(0.608060\pi\) | |||||||
\(384\) | 16.9113 | − | 31.4995i | 0.862999 | − | 1.60745i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.2627 | − | 1.14059i | 1.38764 | − | 0.0580546i | ||||
\(387\) | 8.38281 | − | 31.2851i | 0.426122 | − | 1.59031i | ||||
\(388\) | −24.0105 | − | 11.3029i | −1.21895 | − | 0.573817i | ||||
\(389\) | −1.15957 | + | 0.310707i | −0.0587928 | + | 0.0157535i | −0.288096 | − | 0.957602i | \(-0.593022\pi\) |
0.229303 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(390\) | −14.8349 | − | 3.31716i | −0.751193 | − | 0.167971i | ||||
\(391\) | − | 8.72428i | − | 0.441206i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 41.2339i | − | 2.07998i | ||||||
\(394\) | −0.198556 | + | 0.887977i | −0.0100031 | + | 0.0447356i | ||||
\(395\) | −8.95529 | + | 2.39956i | −0.450589 | + | 0.120735i | ||||
\(396\) | −37.1846 | + | 13.3810i | −1.86860 | + | 0.672418i | ||||
\(397\) | −5.65782 | + | 21.1153i | −0.283958 | + | 1.05975i | 0.665640 | + | 0.746273i | \(0.268159\pi\) |
−0.949598 | + | 0.313472i | \(0.898508\pi\) | |||||||
\(398\) | −1.45437 | − | 34.7626i | −0.0729008 | − | 1.74249i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.87517 | + | 17.0302i | 0.143759 | + | 0.851510i | ||||
\(401\) | 10.8674 | + | 18.8229i | 0.542692 | + | 0.939970i | 0.998748 | + | 0.0500194i | \(0.0159283\pi\) |
−0.456056 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(402\) | 12.8082 | − | 24.4953i | 0.638814 | − | 1.22172i | ||||
\(403\) | −10.0367 | + | 2.68934i | −0.499966 | + | 0.133965i | ||||
\(404\) | 0.698148 | + | 0.125725i | 0.0347342 | + | 0.00625505i | ||||
\(405\) | 11.0070 | − | 11.0070i | 0.546944 | − | 0.546944i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.83090 | −0.338595 | ||||||||
\(408\) | 3.23346 | − | 23.5653i | 0.160080 | − | 1.16666i | ||||
\(409\) | −13.5071 | + | 23.3950i | −0.667883 | + | 1.15681i | 0.310612 | + | 0.950537i | \(0.399466\pi\) |
−0.978495 | + | 0.206270i | \(0.933867\pi\) | |||||||
\(410\) | −4.18696 | − | 13.3641i | −0.206779 | − | 0.660008i | ||||
\(411\) | 7.38511 | − | 27.5616i | 0.364280 | − | 1.35951i | ||||
\(412\) | 2.09119 | + | 24.9483i | 0.103025 | + | 1.22911i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.35386 | − | 32.3604i | −0.0665387 | − | 1.59043i | ||||
\(415\) | 5.45986 | − | 3.15225i | 0.268014 | − | 0.154738i | ||||
\(416\) | −20.7611 | + | 10.5685i | −1.01789 | + | 0.518161i | ||||
\(417\) | −9.68909 | + | 16.7820i | −0.474477 | + | 0.821818i | ||||
\(418\) | 1.52777 | − | 0.969392i | 0.0747257 | − | 0.0474145i | ||||
\(419\) | 1.31859 | − | 1.31859i | 0.0644176 | − | 0.0644176i | −0.674164 | − | 0.738582i | \(-0.735496\pi\) |
0.738582 | + | 0.674164i | \(0.235496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.73490 | − | 9.73490i | −0.474450 | − | 0.474450i | 0.428901 | − | 0.903351i | \(-0.358901\pi\) |
−0.903351 | + | 0.428901i | \(0.858901\pi\) | |||||||
\(422\) | −4.41199 | + | 19.7311i | −0.214772 | + | 0.960497i | ||||
\(423\) | 60.3071 | + | 34.8183i | 2.93223 | + | 1.69292i | ||||
\(424\) | −8.80009 | + | 3.58894i | −0.427370 | + | 0.174294i | ||||
\(425\) | 5.74532 | + | 9.95118i | 0.278689 | + | 0.482703i | ||||
\(426\) | 15.5530 | − | 16.9113i | 0.753548 | − | 0.819353i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.09999 | + | 8.39914i | −0.343191 | + | 0.405988i | ||||
\(429\) | 35.5546 | + | 9.52682i | 1.71659 | + | 0.459959i | ||||
\(430\) | −4.79900 | − | 2.50932i | −0.231428 | − | 0.121010i | ||||
\(431\) | −19.5083 | − | 11.2631i | −0.939680 | − | 0.542525i | −0.0498200 | − | 0.998758i | \(-0.515865\pi\) |
−0.889860 | + | 0.456234i | \(0.849198\pi\) | |||||||
\(432\) | 4.75668 | − | 50.1593i | 0.228856 | − | 2.41329i | ||||
\(433\) | − | 7.16594i | − | 0.344373i | −0.985064 | − | 0.172187i | \(-0.944917\pi\) | ||
0.985064 | − | 0.172187i | \(-0.0550832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.32934 | + | 5.32934i | 0.255522 | + | 0.255522i | ||||
\(436\) | 11.8704 | + | 2.13766i | 0.568488 | + | 0.102375i | ||||
\(437\) | 0.383805 | + | 1.43238i | 0.0183599 | + | 0.0685200i | ||||
\(438\) | 9.34216 | + | 29.8187i | 0.446385 | + | 1.42479i | ||||
\(439\) | −12.5170 | + | 7.22667i | −0.597402 | + | 0.344910i | −0.768019 | − | 0.640427i | \(-0.778757\pi\) |
0.170617 | + | 0.985337i | \(0.445424\pi\) | |||||||
\(440\) | 0.826678 | + | 6.55572i | 0.0394103 | + | 0.312532i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4918 | + | 11.4081i | −0.499046 | + | 0.542627i | ||||
\(443\) | 18.4615 | + | 4.94674i | 0.877132 | + | 0.235027i | 0.669169 | − | 0.743110i | \(-0.266650\pi\) |
0.207963 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(444\) | 6.50104 | − | 13.8100i | 0.308526 | − | 0.655394i | ||||
\(445\) | −0.225902 | − | 0.843078i | −0.0107088 | − | 0.0399657i | ||||
\(446\) | −11.4437 | − | 18.0353i | −0.541873 | − | 0.853997i | ||||
\(447\) | 59.2679 | 2.80328 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2712 | 0.626306 | 0.313153 | − | 0.949703i | \(-0.398615\pi\) | ||||
0.313153 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(450\) | 22.8549 | + | 36.0196i | 1.07739 | + | 1.69798i | ||||
\(451\) | 8.77693 | + | 32.7560i | 0.413290 | + | 1.54242i | ||||
\(452\) | −6.63637 | + | 14.0975i | −0.312149 | + | 0.663091i | ||||
\(453\) | −35.8693 | − | 9.61115i | −1.68529 | − | 0.451571i | ||||
\(454\) | −9.64629 | + | 10.4887i | −0.452723 | + | 0.492258i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.505822 | + | 4.01127i | 0.0236873 | + | 0.187845i | ||||
\(457\) | −30.3726 | + | 17.5356i | −1.42077 | + | 0.820282i | −0.996365 | − | 0.0851904i | \(-0.972850\pi\) |
−0.424405 | + | 0.905472i | \(0.639517\pi\) | |||||||
\(458\) | −11.2372 | − | 35.8675i | −0.525082 | − | 1.67598i | ||||
\(459\) | −8.67588 | − | 32.3788i | −0.404956 | − | 1.51131i | ||||
\(460\) | −5.32972 | − | 0.959795i | −0.248499 | − | 0.0447507i | ||||
\(461\) | 16.3005 | + | 16.3005i | 0.759188 | + | 0.759188i | 0.976175 | − | 0.216987i | \(-0.0696228\pi\) |
−0.216987 | + | 0.976175i | \(0.569623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.09532i | − | 0.0509037i | −0.999676 | − | 0.0254519i | \(-0.991898\pi\) | ||
0.999676 | − | 0.0254519i | \(-0.00810245\pi\) | |||||||
\(464\) | 11.4988 | + | 1.09045i | 0.533818 | + | 0.0506227i | ||||
\(465\) | −5.70324 | − | 3.29277i | −0.264482 | − | 0.152698i | ||||
\(466\) | 5.61146 | + | 2.93414i | 0.259946 | + | 0.135921i | ||||
\(467\) | 23.9334 | + | 6.41294i | 1.10751 | + | 0.296755i | 0.765818 | − | 0.643058i | \(-0.222334\pi\) |
0.341689 | + | 0.939813i | \(0.389001\pi\) | |||||||
\(468\) | −37.1463 | + | 43.9433i | −1.71709 | + | 2.03128i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.88177 | − | 8.57007i | 0.363559 | − | 0.395308i | ||||
\(471\) | −17.6736 | − | 30.6116i | −0.814357 | − | 1.41051i | ||||
\(472\) | −15.3677 | + | 6.26741i | −0.707358 | + | 0.288481i | ||||
\(473\) | 11.3564 | + | 6.55659i | 0.522166 | + | 0.301472i | ||||
\(474\) | −10.9466 | + | 48.9549i | −0.502793 | + | 2.24857i | ||||
\(475\) | −1.38106 | − | 1.38106i | −0.0633675 | − | 0.0633675i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.5984 | + | 16.5984i | −0.759990 | + | 0.759990i | ||||
\(478\) | 10.9127 | − | 6.92425i | 0.499135 | − | 0.316708i | ||||
\(479\) | 3.89155 | − | 6.74037i | 0.177810 | − | 0.307975i | −0.763320 | − | 0.646020i | \(-0.776432\pi\) |
0.941130 | + | 0.338045i | \(0.109766\pi\) | |||||||
\(480\) | −14.0404 | − | 4.56786i | −0.640856 | − | 0.208493i | ||||
\(481\) | −8.61339 | + | 4.97294i | −0.392737 | + | 0.226747i | ||||
\(482\) | −0.571622 | − | 13.6630i | −0.0260367 | − | 0.622335i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.501168 | + | 5.97903i | 0.0227803 | + | 0.271774i | ||||
\(485\) | −2.83654 | + | 10.5861i | −0.128800 | + | 0.480690i | ||||
\(486\) | −9.20352 | − | 29.3762i | −0.417480 | − | 1.33253i | ||||
\(487\) | 13.8477 | − | 23.9848i | 0.627497 | − | 1.08686i | −0.360555 | − | 0.932738i | \(-0.617413\pi\) |
0.988052 | − | 0.154119i | \(-0.0492539\pi\) | |||||||
\(488\) | −2.46032 | + | 17.9307i | −0.111374 | + | 0.811685i | ||||
\(489\) | −43.1345 | −1.95061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2667 | − | 20.2667i | 0.914621 | − | 0.914621i | −0.0820102 | − | 0.996631i | \(-0.526134\pi\) |
0.996631 | + | 0.0820102i | \(0.0261340\pi\) | |||||||
\(492\) | −74.5757 | − | 13.4299i | −3.36213 | − | 0.605465i | ||||
\(493\) | 7.42269 | − | 1.98890i | 0.334301 | − | 0.0895758i | ||||
\(494\) | 1.22071 | − | 2.33458i | 0.0549224 | − | 0.105038i | ||||
\(495\) | 8.16021 | + | 14.1339i | 0.366774 | + | 0.635271i | ||||
\(496\) | −9.95167 | + | 1.68012i | −0.446843 | + | 0.0754396i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.42589 | − | 34.0821i | −0.0638958 | − | 1.52725i | ||||
\(499\) | 7.31511 | − | 27.3003i | 0.327469 | − | 1.22213i | −0.584337 | − | 0.811511i | \(-0.698645\pi\) |
0.911806 | − | 0.410620i | \(-0.134688\pi\) | |||||||
\(500\) | 14.4830 | − | 5.21173i | 0.647698 | − | 0.233076i | ||||
\(501\) | −23.9478 | + | 6.41678i | −1.06991 | + | 0.286681i | ||||
\(502\) | 4.76720 | − | 21.3197i | 0.212770 | − | 0.951544i | ||||
\(503\) | − | 3.04877i | − | 0.135938i | −0.997687 | − | 0.0679689i | \(-0.978348\pi\) | ||
0.997687 | − | 0.0679689i | \(-0.0216519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.292957i | − | 0.0130364i | ||||||
\(506\) | 12.7972 | + | 2.86152i | 0.568903 | + | 0.127210i | ||||
\(507\) | 12.0869 | − | 3.23868i | 0.536798 | − | 0.143835i | ||||
\(508\) | 14.5224 | + | 6.83639i | 0.644327 | + | 0.303316i | ||||
\(509\) | 6.02673 | − | 22.4920i | 0.267130 | − | 0.996942i | −0.693804 | − | 0.720164i | \(-0.744067\pi\) |
0.960934 | − | 0.276778i | \(-0.0892668\pi\) | |||||||
\(510\) | −9.81453 | + | 0.410611i | −0.434595 | + | 0.0181822i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.0441 | + | 8.31546i | −0.930025 | + | 0.367495i | ||||
\(513\) | 2.84887 | + | 4.93438i | 0.125781 | + | 0.217858i | ||||
\(514\) | −29.5622 | − | 15.4576i | −1.30393 | − | 0.681804i | ||||
\(515\) | 9.98691 | − | 2.67598i | 0.440076 | − | 0.117918i | ||||
\(516\) | −24.0634 | + | 16.7191i | −1.05933 | + | 0.736019i | ||||
\(517\) | −19.9360 | + | 19.9360i | −0.876784 | + | 0.876784i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.81702 | 0.430919 | ||||||||
\(520\) | 5.81501 | + | 7.66458i | 0.255005 | + | 0.336114i | ||||
\(521\) | −17.4291 | + | 30.1881i | −0.763584 | + | 1.32257i | 0.177408 | + | 0.984137i | \(0.443229\pi\) |
−0.940992 | + | 0.338429i | \(0.890104\pi\) | |||||||
\(522\) | 27.2238 | − | 8.52918i | 1.19155 | − | 0.373312i | ||||
\(523\) | 11.6875 | − | 43.6182i | 0.511057 | − | 1.90729i | 0.101989 | − | 0.994786i | \(-0.467479\pi\) |
0.409068 | − | 0.912504i | \(-0.365854\pi\) | |||||||
\(524\) | −16.8474 | + | 19.9302i | −0.735983 | + | 0.870653i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.8325 | + | 1.49912i | −1.56237 | + | 0.0653649i | ||||
\(527\) | −5.81501 | + | 3.35730i | −0.253306 | + | 0.146246i | ||||
\(528\) | 33.5060 | + | 12.4723i | 1.45816 | + | 0.542785i | ||||
\(529\) | 6.12639 | − | 10.6112i | 0.266365 | − | 0.461357i | ||||
\(530\) | 2.10279 | + | 3.31402i | 0.0913395 | + | 0.143952i | ||||
\(531\) | −28.9861 | + | 28.9861i | −1.25789 | + | 1.25789i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.9138 | + | 34.9138i | 1.51228 | + | 1.51228i | ||||
\(534\) | −4.60876 | − | 1.03054i | −0.199441 | − | 0.0445960i | ||||
\(535\) | 3.93341 | + | 2.27096i | 0.170056 | + | 0.0981820i | ||||
\(536\) | −16.1991 | + | 6.60646i | −0.699694 | + | 0.285356i | ||||
\(537\) | 22.4125 | + | 38.8196i | 0.967171 | + | 1.67519i | ||||
\(538\) | 8.46422 | + | 7.78442i | 0.364918 | + | 0.335610i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −20.7349 | + | 1.73802i | −0.892288 | + | 0.0747923i | ||||
\(541\) | −39.0280 | − | 10.4575i | −1.67794 | − | 0.449604i | −0.710709 | − | 0.703486i | \(-0.751626\pi\) |
−0.967235 | + | 0.253882i | \(0.918293\pi\) | |||||||
\(542\) | −10.9806 | + | 21.0002i | −0.471659 | + | 0.902035i | ||||
\(543\) | −11.7329 | − | 6.77397i | −0.503505 | − | 0.290699i | ||||
\(544\) | −11.1912 | + | 10.0690i | −0.479819 | + | 0.431704i | ||||
\(545\) | − | 4.98105i | − | 0.213365i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.86041 | − | 7.86041i | −0.336087 | − | 0.336087i | 0.518805 | − | 0.854892i | \(-0.326377\pi\) |
−0.854892 | + | 0.518805i | \(0.826377\pi\) | |||||||
\(548\) | −14.8307 | + | 10.3043i | −0.633536 | + | 0.440178i | ||||
\(549\) | 11.5699 | + | 43.1794i | 0.493790 | + | 1.84285i | ||||
\(550\) | −16.4813 | + | 5.16355i | −0.702763 | + | 0.220175i | ||||
\(551\) | −1.13118 | + | 0.653089i | −0.0481900 | + | 0.0278225i | ||||
\(552\) | −17.9643 | + | 23.1487i | −0.764612 | + | 0.985272i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.03363 | + | 7.38842i | 0.341316 | + | 0.313904i | ||||
\(555\) | −6.08877 | − | 1.63148i | −0.258454 | − | 0.0692525i | ||||
\(556\) | 11.5400 | − | 4.15269i | 0.489404 | − | 0.176113i | ||||
\(557\) | 2.05002 | + | 7.65079i | 0.0868622 | + | 0.324174i | 0.995660 | − | 0.0930619i | \(-0.0296655\pi\) |
−0.908798 | + | 0.417236i | \(0.862999\pi\) | |||||||
\(558\) | −21.0482 | + | 13.3554i | −0.891042 | + | 0.565379i | ||||
\(559\) | 19.0930 | 0.807547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.7861 | 1.00425 | ||||||||
\(562\) | 7.29800 | − | 4.63068i | 0.307848 | − | 0.195334i | ||||
\(563\) | 0.975986 | + | 3.64243i | 0.0411329 | + | 0.153510i | 0.983438 | − | 0.181246i | \(-0.0580129\pi\) |
−0.942305 | + | 0.334756i | \(0.891346\pi\) | |||||||
\(564\) | −21.3313 | − | 59.2778i | −0.898208 | − | 2.49605i | ||||
\(565\) | 6.21552 | + | 1.66544i | 0.261489 | + | 0.0700658i | ||||
\(566\) | −7.41026 | − | 6.81512i | −0.311477 | − | 0.286461i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.4271 | + | 1.81926i | −0.605347 | + | 0.0763344i | ||||
\(569\) | 24.5695 | − | 14.1852i | 1.03001 | − | 0.594675i | 0.113020 | − | 0.993593i | \(-0.463948\pi\) |
0.916987 | + | 0.398918i | \(0.130614\pi\) | |||||||
\(570\) | 1.59332 | − | 0.499183i | 0.0667367 | − | 0.0209085i | ||||
\(571\) | 0.0484925 | + | 0.180977i | 0.00202935 | + | 0.00757363i | 0.966933 | − | 0.255030i | \(-0.0820854\pi\) |
−0.964904 | + | 0.262604i | \(0.915419\pi\) | |||||||
\(572\) | −13.2926 | − | 19.1317i | −0.555791 | − | 0.799936i | ||||
\(573\) | −31.7490 | − | 31.7490i | −1.32633 | − | 1.32633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.1550i | − | 0.590305i | ||||||
\(576\) | −39.9482 | + | 39.0849i | −1.66451 | + | 1.62854i | ||||
\(577\) | 0.530825 | + | 0.306472i | 0.0220985 | + | 0.0127586i | 0.511009 | − | 0.859576i | \(-0.329272\pi\) |
−0.488910 | + | 0.872334i | \(0.662605\pi\) | |||||||
\(578\) | 6.49913 | − | 12.4294i | 0.270328 | − | 0.516995i | ||||
\(579\) | −58.8944 | − | 15.7807i | −2.44757 | − | 0.655824i | ||||
\(580\) | −0.398432 | − | 4.75338i | −0.0165440 | − | 0.197373i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 43.6468 | + | 40.1413i | 1.80922 | + | 1.66391i | ||||
\(583\) | −4.75190 | − | 8.23053i | −0.196803 | − | 0.340874i | ||||
\(584\) | 7.66791 | − | 18.2297i | 0.317300 | − | 0.754351i | ||||
\(585\) | 20.5792 | + | 11.8814i | 0.850843 | + | 0.491235i | ||||
\(586\) | −38.2943 | − | 8.56282i | −1.58192 | − | 0.353727i | ||||
\(587\) | 21.1197 | + | 21.1197i | 0.871704 | + | 0.871704i | 0.992658 | − | 0.120954i | \(-0.0385954\pi\) |
−0.120954 | + | 0.992658i | \(0.538595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.807030 | − | 0.807030i | 0.0332531 | − | 0.0332531i | ||||
\(590\) | 3.67214 | + | 5.78733i | 0.151180 | + | 0.238260i | ||||
\(591\) | 1.01659 | − | 1.76079i | 0.0418171 | − | 0.0724293i | ||||
\(592\) | −8.78475 | + | 4.01878i | −0.361051 | + | 0.165171i | ||||
\(593\) | 3.03239 | − | 1.75075i | 0.124525 | − | 0.0718947i | −0.436443 | − | 0.899732i | \(-0.643762\pi\) |
0.560969 | + | 0.827837i | \(0.310429\pi\) | |||||||
\(594\) | 50.3403 | − | 2.10609i | 2.06549 | − | 0.0864140i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.6468 | − | 24.2158i | −1.17342 | − | 0.991917i | ||||
\(597\) | −20.1219 | + | 75.0961i | −0.823536 | + | 3.07348i | ||||
\(598\) | 18.2197 | − | 5.70821i | 0.745060 | − | 0.233426i | ||||
\(599\) | 7.18793 | − | 12.4499i | 0.293691 | − | 0.508687i | −0.680989 | − | 0.732294i | \(-0.738450\pi\) |
0.974679 | + | 0.223607i | \(0.0717831\pi\) | |||||||
\(600\) | 5.24624 | − | 38.2343i | 0.214177 | − | 1.56091i | ||||
\(601\) | 4.26571 | 0.174002 | 0.0870010 | − | 0.996208i | \(-0.472272\pi\) | ||||
0.0870010 | + | 0.996208i | \(0.472272\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.5542 | + | 30.5542i | −1.24426 | + | 1.24426i | ||||
\(604\) | 13.4103 | + | 19.3010i | 0.545655 | + | 0.785347i | ||||
\(605\) | 2.39343 | − | 0.641319i | 0.0973069 | − | 0.0260733i | ||||
\(606\) | −1.40467 | − | 0.734480i | −0.0570610 | − | 0.0298362i | ||||
\(607\) | 6.52176 | + | 11.2960i | 0.264710 | + | 0.458491i | 0.967488 | − | 0.252918i | \(-0.0813904\pi\) |
−0.702778 | + | 0.711410i | \(0.748057\pi\) | |||||||
\(608\) | 1.39445 | − | 2.14549i | 0.0565522 | − | 0.0870111i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.46783 | − | 0.312432i | 0.302364 | − | 0.0126500i | ||||
\(611\) | −10.6246 | + | 39.6517i | −0.429827 | + | 1.60414i | ||||
\(612\) | −15.8367 | + | 33.6416i | −0.640161 | + | 1.35988i | ||||
\(613\) | −40.0487 | + | 10.7310i | −1.61755 | + | 0.433422i | −0.950281 | − | 0.311393i | \(-0.899205\pi\) |
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(614\) | 6.02705 | + | 1.34768i | 0.243232 | + | 0.0543880i | ||||
\(615\) | 31.2935i | 1.26188i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2992i | 0.776956i | 0.921458 | + | 0.388478i | \(0.126999\pi\) | ||||
−0.921458 | + | 0.388478i | \(0.873001\pi\) | |||||||
\(618\) | 12.2076 | − | 54.5943i | 0.491061 | − | 2.19611i | ||||
\(619\) | −2.16428 | + | 0.579917i | −0.0869897 | + | 0.0233088i | −0.302051 | − | 0.953292i | \(-0.597671\pi\) |
0.215062 | + | 0.976600i | \(0.431005\pi\) | |||||||
\(620\) | 1.41126 | + | 3.92178i | 0.0566776 | + | 0.157502i | ||||
\(621\) | −10.6876 | + | 39.8867i | −0.428879 | + | 1.60060i | ||||
\(622\) | −1.19484 | − | 28.5594i | −0.0479087 | − | 1.14513i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 51.3291 | − | 8.66579i | 2.05481 | − | 0.346909i | ||||
\(625\) | 7.61619 | + | 13.1916i | 0.304647 | + | 0.527665i | ||||
\(626\) | −9.98087 | + | 19.0881i | −0.398916 | + | 0.762916i | ||||
\(627\) | −3.90527 | + | 1.04641i | −0.155962 | + | 0.0417898i | ||||
\(628\) | −3.96491 | + | 22.0170i | −0.158217 | + | 0.878575i | ||||
\(629\) | −4.54464 | + | 4.54464i | −0.181207 | + | 0.181207i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7915 | −0.549031 | −0.274515 | − | 0.961583i | \(-0.588517\pi\) | ||||
−0.274515 | + | 0.961583i | \(0.588517\pi\) | |||||||
\(632\) | 25.2930 | − | 19.1895i | 1.00610 | − | 0.763315i | ||||
\(633\) | 22.5890 | − | 39.1254i | 0.897834 | − | 1.55509i | ||||
\(634\) | 12.1668 | + | 38.8347i | 0.483207 | + | 1.54232i | ||||
\(635\) | 1.71564 | − | 6.40285i | 0.0680831 | − | 0.254089i | ||||
\(636\) | 21.1621 | − | 1.77382i | 0.839130 | − | 0.0703366i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.482811 | + | 11.5403i | 0.0191147 | + | 0.456884i | ||||
\(639\) | −31.1043 | + | 17.9581i | −1.23047 | + | 0.710410i | ||||
\(640\) | 4.92002 | + | 7.94451i | 0.194481 | + | 0.314034i | ||||
\(641\) | −3.41080 | + | 5.90767i | −0.134718 | + | 0.233339i | −0.925490 | − | 0.378772i | \(-0.876346\pi\) |
0.790771 | + | 0.612111i | \(0.209680\pi\) | |||||||
\(642\) | 20.7504 | − | 13.1664i | 0.818951 | − | 0.519636i | ||||
\(643\) | 32.9875 | − | 32.9875i | 1.30090 | − | 1.30090i | 0.373112 | − | 0.927786i | \(-0.378291\pi\) |
0.927786 | − | 0.373112i | \(-0.121709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.55659 | + | 8.55659i | 0.336916 | + | 0.336916i | ||||
\(646\) | 0.371493 | − | 1.66138i | 0.0146162 | − | 0.0653660i | ||||
\(647\) | −17.7203 | − | 10.2308i | −0.696657 | − | 0.402215i | 0.109444 | − | 0.993993i | \(-0.465093\pi\) |
−0.806101 | + | 0.591778i | \(0.798426\pi\) | |||||||
\(648\) | −20.6679 | + | 49.1360i | −0.811912 | + | 1.93024i | ||||
\(649\) | −8.29831 | − | 14.3731i | −0.325737 | − | 0.564193i | ||||
\(650\) | −17.0229 | + | 18.5094i | −0.667692 | + | 0.725999i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.8488 | + | 17.6240i | 0.816501 | + | 0.690207i | ||||
\(653\) | −4.60844 | − | 1.23483i | −0.180342 | − | 0.0483226i | 0.167518 | − | 0.985869i | \(-0.446425\pi\) |
−0.347860 | + | 0.937547i | \(0.613092\pi\) | |||||||
\(654\) | −23.8832 | − | 12.4881i | −0.933906 | − | 0.488324i | ||||
\(655\) | 9.33352 | + | 5.38871i | 0.364691 | + | 0.210554i | ||||
\(656\) | 30.5585 | + | 36.9615i | 1.19311 | + | 1.44310i | ||||
\(657\) | − | 48.8472i | − | 1.90571i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8983 | − | 17.8983i | −0.697217 | − | 0.697217i | 0.266592 | − | 0.963809i | \(-0.414102\pi\) |
−0.963809 | + | 0.266592i | \(0.914102\pi\) | |||||||
\(660\) | 2.61681 | − | 14.5311i | 0.101859 | − | 0.565621i | ||||
\(661\) | −5.61408 | − | 20.9520i | −0.218362 | − | 0.814939i | −0.984956 | − | 0.172807i | \(-0.944716\pi\) |
0.766593 | − | 0.642133i | \(-0.221950\pi\) | |||||||
\(662\) | −12.4482 | − | 39.7328i | −0.483814 | − | 1.54426i | ||||
\(663\) | 29.9929 | − | 17.3164i | 1.16483 | − | 0.672515i | ||||
\(664\) | −13.2361 | + | 17.0559i | −0.513661 | + | 0.661899i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.1519 | + | 17.5624i | −0.625872 | + | 0.680528i | ||||
\(667\) | −9.14383 | − | 2.45008i | −0.354050 | − | 0.0948675i | ||||
\(668\) | 14.1968 | + | 6.68310i | 0.549290 | + | 0.258577i | ||||
\(669\) | 12.3529 | + | 46.1017i | 0.477591 | + | 1.78239i | ||||
\(670\) | 3.87079 | + | 6.10041i | 0.149542 | + | 0.235679i | ||||
\(671\) | −18.0987 | −0.698693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.74723 | −0.260086 | −0.130043 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130043 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(674\) | −10.4525 | − | 16.4733i | −0.402617 | − | 0.634528i | ||||
\(675\) | −14.0765 | − | 52.5342i | −0.541805 | − | 2.02204i | ||||
\(676\) | −7.16539 | − | 3.37309i | −0.275592 | − | 0.129734i | ||||
\(677\) | −37.4932 | − | 10.0463i | −1.44098 | − | 0.386110i | −0.548105 | − | 0.836410i | \(-0.684651\pi\) |
−0.892878 | + | 0.450299i | \(0.851317\pi\) | |||||||
\(678\) | 23.5686 | − | 25.6268i | 0.905146 | − | 0.984190i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.91156 | + | 3.81157i | 0.188350 | + | 0.146167i | ||||
\(681\) | 27.5758 | − | 15.9209i | 1.05671 | − | 0.610090i | ||||
\(682\) | −3.01734 | − | 9.63089i | −0.115540 | − | 0.368786i | ||||
\(683\) | 6.26215 | + | 23.3707i | 0.239615 | + | 0.894254i | 0.976014 | + | 0.217707i | \(0.0698577\pi\) |
−0.736400 | + | 0.676547i | \(0.763476\pi\) | |||||||
\(684\) | 1.12013 | − | 6.22008i | 0.0428294 | − | 0.237831i | ||||
\(685\) | 5.27358 | + | 5.27358i | 0.201493 | + | 0.201493i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 83.9875i | 3.20432i | ||||||||
\(688\) | 18.4620 | + | 1.75078i | 0.703858 | + | 0.0667478i | ||||
\(689\) | −11.9838 | − | 6.91883i | −0.456545 | − | 0.263586i | ||||
\(690\) | 10.7234 | + | 5.60708i | 0.408233 | + | 0.213458i | ||||
\(691\) | 15.1401 | + | 4.05677i | 0.575955 | + | 0.154327i | 0.535026 | − | 0.844835i | \(-0.320302\pi\) |
0.0409286 | + | 0.999162i | \(0.486968\pi\) | |||||||
\(692\) | −4.74499 | − | 4.01105i | −0.180378 | − | 0.152477i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.97874 | − | 5.41352i | 0.188990 | − | 0.205494i | ||||
\(695\) | −2.53246 | − | 4.38636i | −0.0960618 | − | 0.166384i | ||||
\(696\) | −23.7904 | − | 10.0069i | −0.901775 | − | 0.379311i | ||||
\(697\) | 27.6321 | + | 15.9534i | 1.04664 | + | 0.604278i | ||||
\(698\) | 7.81041 | − | 34.9294i | 0.295628 | − | 1.32210i | ||||
\(699\) | −10.0052 | − | 10.0052i | −0.378431 | − | 0.378431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.821691 | − | 0.821691i | 0.0310348 | − | 0.0310348i | −0.691419 | − | 0.722454i | \(-0.743014\pi\) |
0.722454 | + | 0.691419i | \(0.243014\pi\) | |||||||
\(702\) | 61.9432 | − | 39.3038i | 2.33789 | − | 1.48343i | ||||
\(703\) | 0.546222 | − | 0.946085i | 0.0206012 | − | 0.0356823i | ||||
\(704\) | −11.0990 | − | 19.7183i | −0.418309 | − | 0.743163i | ||||
\(705\) | −22.5315 | + | 13.0086i | −0.848587 | + | 0.489932i | ||||
\(706\) | −0.258910 | − | 6.18853i | −0.00974420 | − | 0.232908i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 36.9556 | − | 3.09765i | 1.38888 | − | 0.116417i | ||||
\(709\) | 3.15427 | − | 11.7719i | 0.118461 | − | 0.442103i | −0.881061 | − | 0.473002i | \(-0.843170\pi\) |
0.999523 | + | 0.0308989i | \(0.00983700\pi\) | |||||||
\(710\) | 1.79538 | + | 5.73059i | 0.0673795 | + | 0.215065i | ||||
\(711\) | 39.2084 | − | 67.9109i | 1.47043 | − | 2.54686i | ||||
\(712\) | 1.80655 | + | 2.38116i | 0.0677035 | + | 0.0892379i | ||||
\(713\) | 8.27155 | 0.309772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.80294 | + | 6.80294i | −0.254416 | + | 0.254416i | ||||
\(716\) | 5.02804 | − | 27.9206i | 0.187907 | − | 1.04344i | ||||
\(717\) | −27.8949 | + | 7.47442i | −1.04175 | + | 0.279137i | ||||
\(718\) | −10.0452 | + | 19.2112i | −0.374884 | + | 0.716956i | ||||
\(719\) | −11.4433 | − | 19.8204i | −0.426763 | − | 0.739175i | 0.569821 | − | 0.821769i | \(-0.307013\pi\) |
−0.996583 | + | 0.0825945i | \(0.973679\pi\) | |||||||
\(720\) | 18.8096 | + | 13.3758i | 0.700992 | + | 0.498486i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.11109 | − | 26.5575i | −0.0413503 | − | 0.988366i | ||||
\(723\) | −7.90870 | + | 29.5157i | −0.294128 | + | 1.09770i | ||||
\(724\) | 2.90328 | + | 8.06798i | 0.107900 | + | 0.299844i | ||||
\(725\) | 12.0432 | − | 3.22697i | 0.447274 | − | 0.119847i | ||||
\(726\) | 2.92564 | − | 13.0839i | 0.108581 | − | 0.485590i | ||||
\(727\) | 12.6428i | 0.468896i | 0.972129 | + | 0.234448i | \(0.0753283\pi\) | ||||
−0.972129 | + | 0.234448i | \(0.924672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.2481i | 0.453633i | ||||||||
\(730\) | −7.97052 | − | 1.78225i | −0.295002 | − | 0.0659641i | ||||
\(731\) | 11.9176 | − | 3.19331i | 0.440788 | − | 0.118109i | ||||
\(732\) | 17.2247 | − | 36.5901i | 0.636644 | − | 1.35241i | ||||
\(733\) | 6.18646 | − | 23.0882i | 0.228502 | − | 0.852782i | −0.752469 | − | 0.658628i | \(-0.771137\pi\) |
0.980971 | − | 0.194154i | \(-0.0621962\pi\) | |||||||
\(734\) | 37.1828 | − | 1.55562i | 1.37244 | − | 0.0574189i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.1410 | − | 3.84887i | 0.668688 | − | 0.141871i | ||||
\(737\) | −8.74723 | − | 15.1506i | −0.322208 | − | 0.558081i | ||||
\(738\) | 104.969 | + | 54.8867i | 3.86398 | + | 2.02041i | ||||
\(739\) | 20.1695 | − | 5.40440i | 0.741947 | − | 0.198804i | 0.132004 | − | 0.991249i | \(-0.457859\pi\) |
0.609943 | + | 0.792445i | \(0.291192\pi\) | |||||||
\(740\) | 2.27637 | + | 3.27632i | 0.0836812 | + | 0.120440i | ||||
\(741\) | −4.16254 | + | 4.16254i | −0.152915 | + | 0.152915i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6332 | −0.390093 | −0.195046 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195046 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(744\) | 22.3424 | + | 3.06566i | 0.819112 | + | 0.112393i | ||||
\(745\) | −7.74551 | + | 13.4156i | −0.283773 | + | 0.491510i | ||||
\(746\) | 47.1064 | − | 14.7584i | 1.72469 | − | 0.540342i | ||||
\(747\) | −13.8013 | + | 51.5072i | −0.504964 | + | 1.88455i | ||||
\(748\) | −11.4968 | − | 9.71855i | −0.420366 | − | 0.355346i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −34.3638 | + | 1.43768i | −1.25479 | + | 0.0524967i | ||||
\(751\) | 9.49457 | − | 5.48169i | 0.346462 | − | 0.200030i | −0.316664 | − | 0.948538i | \(-0.602563\pi\) |
0.663126 | + | 0.748508i | \(0.269229\pi\) | |||||||
\(752\) | −13.9095 | + | 37.3671i | −0.507227 | + | 1.36264i | ||||
\(753\) | −24.4077 | + | 42.2753i | −0.889465 | + | 1.54060i | ||||
\(754\) | 9.01020 | + | 14.2002i | 0.328132 | + | 0.517140i | ||||
\(755\) | 6.86316 | − | 6.86316i | 0.249776 | − | 0.249776i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.8153 | − | 21.8153i | −0.792889 | − | 0.792889i | 0.189073 | − | 0.981963i | \(-0.439452\pi\) |
−0.981963 | + | 0.189073i | \(0.939452\pi\) | |||||||
\(758\) | −28.9866 | − | 6.48156i | −1.05284 | − | 0.235421i | ||||
\(759\) | −25.3758 | − | 14.6507i | −0.921084 | − | 0.531788i | ||||
\(760\) | −0.974076 | − | 0.409723i | −0.0353335 | − | 0.0148622i | ||||
\(761\) | 4.75921 | + | 8.24319i | 0.172521 | + | 0.298816i | 0.939301 | − | 0.343095i | \(-0.111475\pi\) |
−0.766779 | + | 0.641911i | \(0.778142\pi\) | |||||||
\(762\) | −26.3991 | − | 24.2789i | −0.956340 | − | 0.879532i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.37361 | + | 28.3177i | 0.0858743 | + | 1.02450i | ||||
\(765\) | 14.8324 | + | 3.97433i | 0.536267 | + | 0.143692i | ||||
\(766\) | −16.6742 | + | 31.8890i | −0.602464 | + | 1.15220i | ||||
\(767\) | −20.9274 | − | 12.0825i | −0.755646 | − | 0.436272i | ||||
\(768\) | 50.4275 | − | 3.67266i | 1.81965 | − | 0.132526i | ||||
\(769\) | 36.0771i | 1.30098i | 0.759517 | + | 0.650488i | \(0.225435\pi\) | ||||
−0.759517 | + | 0.650488i | \(0.774565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.7092 | + | 52.7092i | 1.89827 | + | 1.89827i | ||||
\(772\) | 22.0185 | + | 31.6907i | 0.792464 | + | 1.14057i | ||||
\(773\) | −8.82499 | − | 32.9353i | −0.317413 | − | 1.18460i | −0.921722 | − | 0.387851i | \(-0.873217\pi\) |
0.604309 | − | 0.796750i | \(-0.293449\pi\) | |||||||
\(774\) | 43.7095 | − | 13.6941i | 1.57111 | − | 0.492225i | ||||
\(775\) | −9.43477 | + | 5.44717i | −0.338907 | + | 0.195668i | ||||
\(776\) | −4.69538 | − | 37.2353i | −0.168554 | − | 1.33667i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.24961 | − | 1.14925i | −0.0448007 | − | 0.0412026i | ||||
\(779\) | −5.23856 | − | 1.40367i | −0.187691 | − | 0.0502916i | ||||
\(780\) | −7.27906 | − | 20.2279i | −0.260632 | − | 0.724276i | ||||
\(781\) | −3.76358 | − | 14.0459i | −0.134671 | − | 0.502600i | ||||
\(782\) | 10.4178 | − | 6.61025i | 0.372540 | − | 0.236382i | ||||
\(783\) | −36.3724 | −1.29984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.23879 | 0.329747 | ||||||||
\(786\) | 49.2381 | − | 31.2423i | 1.75627 | − | 1.11438i | ||||
\(787\) | 1.33937 | + | 4.99859i | 0.0477433 | + | 0.178180i | 0.985680 | − | 0.168626i | \(-0.0539329\pi\) |
−0.937937 | + | 0.346806i | \(0.887266\pi\) | |||||||
\(788\) | −1.21079 | + | 0.435706i | −0.0431327 | + | 0.0155214i | ||||
\(789\) | 77.4072 | + | 20.7412i | 2.75577 | + | 0.738406i | ||||
\(790\) | −9.65063 | − | 8.87555i | −0.343354 | − | 0.315778i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −44.1526 | − | 34.2642i | −1.56889 | − | 1.21753i | ||||
\(793\) | −22.8215 | + | 13.1760i | −0.810415 | + | 0.467893i | ||||
\(794\) | −29.5009 | + | 9.24260i | −1.04695 | + | 0.328008i | ||||
\(795\) | −2.26987 | − | 8.47127i | −0.0805040 | − | 0.300445i | ||||
\(796\) | 40.4087 | − | 28.0758i | 1.43225 | − | 0.995119i | ||||
\(797\) | 8.56228 | + | 8.56228i | 0.303291 | + | 0.303291i | 0.842300 | − | 0.539009i | \(-0.181201\pi\) |
−0.539009 | + | 0.842300i | \(0.681201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.5271i | 0.938460i | ||||||||
\(800\) | −18.1576 | + | 16.3368i | −0.641967 | + | 0.577593i | ||||
\(801\) | 6.39335 | + | 3.69120i | 0.225898 | + | 0.130422i | ||||
\(802\) | −14.2427 | + | 27.2387i | −0.502927 | + | 0.961834i | ||||
\(803\) | 19.1029 | + | 5.11860i | 0.674125 | + | 0.180631i | ||||
\(804\) | 38.9548 | − | 3.26523i | 1.37383 | − | 0.115156i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.8161 | − | 9.94738i | −0.380980 | − | 0.350382i | ||||
\(807\) | −12.8479 | − | 22.2533i | −0.452268 | − | 0.783352i | ||||
\(808\) | 0.378845 | + | 0.928930i | 0.0133277 | + | 0.0326796i | ||||
\(809\) | 8.21438 | + | 4.74257i | 0.288802 | + | 0.166740i | 0.637402 | − | 0.770532i | \(-0.280009\pi\) |
−0.348599 | + | 0.937272i | \(0.613343\pi\) | |||||||
\(810\) | 21.4836 | + | 4.80384i | 0.754855 | + | 0.168790i | ||||
\(811\) | 8.37320 | + | 8.37320i | 0.294023 | + | 0.294023i | 0.838667 | − | 0.544644i | \(-0.183335\pi\) |
−0.544644 | + | 0.838667i | \(0.683335\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.4432 | − | 37.4432i | 1.31319 | − | 1.31319i | ||||
\(814\) | −5.17566 | − | 8.15690i | −0.181407 | − | 0.285899i | ||||
\(815\) | 5.63709 | − | 9.76372i | 0.197459 | − | 0.342008i | ||||
\(816\) | 30.5896 | − | 13.9939i | 1.07085 | − | 0.489884i | ||||
\(817\) | −1.81619 | + | 1.04858i | −0.0635403 | + | 0.0366850i | ||||
\(818\) | −38.1704 | + | 1.59694i | −1.33460 | + | 0.0558357i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.7859 | − | 15.1255i | 0.446505 | − | 0.528206i | ||||
\(821\) | 10.9739 | − | 40.9552i | 0.382992 | − | 1.42934i | −0.458316 | − | 0.888789i | \(-0.651547\pi\) |
0.841308 | − | 0.540556i | \(-0.181786\pi\) | |||||||
\(822\) | 38.5073 | − | 12.0643i | 1.34310 | − | 0.420790i | ||||
\(823\) | 4.62629 | − | 8.01297i | 0.161262 | − | 0.279314i | −0.774059 | − | 0.633113i | \(-0.781777\pi\) |
0.935322 | + | 0.353799i | \(0.115110\pi\) | |||||||
\(824\) | −28.2067 | + | 21.4000i | −0.982627 | + | 0.745505i | ||||
\(825\) | 38.5926 | 1.34362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2363 | − | 18.2363i | 0.634137 | − | 0.634137i | −0.314966 | − | 0.949103i | \(-0.601993\pi\) |
0.949103 | + | 0.314966i | \(0.101993\pi\) | |||||||
\(828\) | 37.6163 | − | 26.1356i | 1.30726 | − | 0.908275i | ||||
\(829\) | 44.7008 | − | 11.9775i | 1.55252 | − | 0.415997i | 0.622236 | − | 0.782829i | \(-0.286224\pi\) |
0.930287 | + | 0.366832i | \(0.119558\pi\) | |||||||
\(830\) | 7.90100 | + | 4.13130i | 0.274248 | + | 0.143400i | ||||
\(831\) | −12.1943 | − | 21.1212i | −0.423017 | − | 0.732687i | ||||
\(832\) | −28.3503 | − | 16.7836i | −0.982870 | − | 0.581866i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −27.3809 | + | 1.14554i | −0.948124 | + | 0.0396667i | ||||
\(835\) | 1.67717 | − | 6.25929i | 0.0580409 | − | 0.216612i | ||||
\(836\) | 2.31513 | + | 1.08984i | 0.0800706 | + | 0.0376931i | ||||
\(837\) | 30.6986 | − | 8.22566i | 1.06110 | − | 0.284320i | ||||
\(838\) | 2.57363 | + | 0.575479i | 0.0889047 | + | 0.0198796i | ||||
\(839\) | − | 14.1360i | − | 0.488028i | −0.969772 | − | 0.244014i | \(-0.921536\pi\) | ||
0.969772 | − | 0.244014i | \(-0.0784643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6618i | 0.712476i | ||||||||
\(842\) | 4.24864 | − | 19.0006i | 0.146418 | − | 0.654804i | ||||
\(843\) | −18.6551 | + | 4.99861i | −0.642515 | + | 0.172161i | ||||
\(844\) | −26.9042 | + | 9.68153i | −0.926080 | + | 0.333252i | ||||
\(845\) | −0.846501 | + | 3.15919i | −0.0291205 | + | 0.108679i | ||||
\(846\) | 4.11656 | + | 98.3950i | 0.141530 | + | 3.38289i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.9533 | − | 7.78906i | −0.376138 | − | 0.267478i | ||||
\(849\) | 11.2481 | + | 19.4823i | 0.386034 | + | 0.668631i | ||||
\(850\) | −7.52974 | + | 14.4004i | −0.258268 | + | 0.493931i | ||||
\(851\) | 7.64760 | − | 2.04917i | 0.262156 | − | 0.0702446i | ||||
\(852\) | 31.9783 | + | 5.75877i | 1.09556 | + | 0.197292i | ||||
\(853\) | 11.3648 | − | 11.3648i | 0.389122 | − | 0.389122i | −0.485252 | − | 0.874374i | \(-0.661272\pi\) |
0.874374 | + | 0.485252i | \(0.161272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61007 | −0.0892626 | ||||||||
\(856\) | −15.4091 | − | 2.11433i | −0.526672 | − | 0.0722662i | ||||
\(857\) | −7.66444 | + | 13.2752i | −0.261812 | + | 0.453472i | −0.966724 | − | 0.255823i | \(-0.917653\pi\) |
0.704911 | + | 0.709295i | \(0.250987\pi\) | |||||||
\(858\) | 15.5630 | + | 49.6746i | 0.531312 | + | 1.69586i | ||||
\(859\) | −4.74614 | + | 17.7129i | −0.161936 | + | 0.604355i | 0.836475 | + | 0.548005i | \(0.184613\pi\) |
−0.998411 | + | 0.0563492i | \(0.982054\pi\) | |||||||
\(860\) | −0.639707 | − | 7.63184i | −0.0218138 | − | 0.260244i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.33163 | − | 31.8290i | −0.0453556 | − | 1.08410i | ||||
\(863\) | −37.0810 | + | 21.4088i | −1.26225 | + | 0.728762i | −0.973510 | − | 0.228644i | \(-0.926571\pi\) |
−0.288744 | + | 0.957406i | \(0.593237\pi\) | |||||||
\(864\) | 63.5002 | − | 32.3249i | 2.16032 | − | 1.09971i | ||||
\(865\) | −1.28295 | + | 2.22214i | −0.0436216 | + | 0.0755549i | ||||
\(866\) | 8.55697 | − | 5.42952i | 0.290778 | − | 0.184502i | ||||
\(867\) | −22.1616 | + | 22.1616i | −0.752646 | + | 0.752646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.4496 | + | 22.4496i | 0.761552 | + | 0.761552i | ||||
\(870\) | −2.32590 | + | 10.4018i | −0.0788555 | + | 0.352655i | ||||
\(871\) | −22.0595 | − | 12.7361i | −0.747459 | − | 0.431546i | ||||
\(872\) | 6.44137 | + | 15.7943i | 0.218132 | + | 0.534862i | ||||
\(873\) | −46.3485 | − | 80.2780i | −1.56866 | − | 2.71700i | ||||
\(874\) | −1.41963 | + | 1.54360i | −0.0480196 | + | 0.0522130i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28.5286 | + | 33.7488i | −0.963893 | + | 1.14027i | ||||
\(877\) | 39.0969 | + | 10.4760i | 1.32021 | + | 0.353749i | 0.849056 | − | 0.528302i | \(-0.177171\pi\) |
0.471153 | + | 0.882051i | \(0.343838\pi\) | |||||||
\(878\) | −18.1134 | − | 9.47118i | −0.611297 | − | 0.319637i | ||||
\(879\) | 75.9348 | + | 43.8410i | 2.56122 | + | 1.47872i | ||||
\(880\) | −7.20194 | + | 5.95431i | −0.242777 | + | 0.200720i | ||||
\(881\) | 5.93539i | 0.199969i | 0.994989 | + | 0.0999843i | \(0.0318792\pi\) | ||||
−0.994989 | + | 0.0999843i | \(0.968121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.96040 | + | 2.96040i | 0.0996254 | + | 0.0996254i | 0.755163 | − | 0.655537i | \(-0.227558\pi\) |
−0.655537 | + | 0.755163i | \(0.727558\pi\) | |||||||
\(884\) | −21.5721 | − | 3.88478i | −0.725547 | − | 0.130659i | ||||
\(885\) | −3.96391 | − | 14.7935i | −0.133245 | − | 0.497278i | ||||
\(886\) | 8.08099 | + | 25.7933i | 0.271486 | + | 0.866541i | ||||
\(887\) | −10.4423 | + | 6.02888i | −0.350619 | + | 0.202430i | −0.664958 | − | 0.746881i | \(-0.731551\pi\) |
0.314339 | + | 0.949311i | \(0.398217\pi\) | |||||||
\(888\) | 21.4165 | − | 2.70062i | 0.718691 | − | 0.0906270i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.835572 | − | 0.908540i | 0.0280084 | − | 0.0304543i | ||||
\(891\) | −51.4894 | − | 13.7965i | −1.72496 | − | 0.462202i | ||||
\(892\) | 12.8656 | − | 27.3301i | 0.430772 | − | 0.915080i | ||||
\(893\) | −1.16700 | − | 4.35530i | −0.0390521 | − | 0.145744i | ||||
\(894\) | 44.9063 | + | 70.7728i | 1.50189 | + | 2.36700i | ||||
\(895\) | −11.7160 | −0.391624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.6634 | −1.42449 | ||||||||
\(898\) | 10.0554 | + | 15.8474i | 0.335552 | + | 0.528833i | ||||
\(899\) | 1.88569 | + | 7.03750i | 0.0628914 | + | 0.234714i | ||||
\(900\) | −25.6948 | + | 54.5830i | −0.856494 | + | 1.81943i | ||||
\(901\) | −8.63729 | − | 2.31435i | −0.287750 | − | 0.0771023i | ||||
\(902\) | −32.4643 | + | 35.2993i | −1.08094 | + | 1.17534i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.8623 | + | 2.75684i | −0.727131 | + | 0.0916913i | ||||
\(905\) | 3.06665 | − | 1.77053i | 0.101939 | − | 0.0588544i | ||||
\(906\) | −15.7007 | − | 50.1143i | −0.521622 | − | 1.66494i | ||||
\(907\) | −2.27648 | − | 8.49595i | −0.0755893 | − | 0.282103i | 0.917777 | − | 0.397096i | \(-0.129982\pi\) |
−0.993366 | + | 0.114993i | \(0.963315\pi\) | |||||||
\(908\) | −19.8336 | − | 3.57170i | −0.658200 | − | 0.118531i | ||||
\(909\) | 1.75212 | + | 1.75212i | 0.0581140 | + | 0.0581140i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.3682i | − | 0.873617i | −0.899554 | − | 0.436809i | \(-0.856109\pi\) | ||
0.899554 | − | 0.436809i | \(-0.143891\pi\) | |||||||
\(912\) | −4.40667 | + | 3.64328i | −0.145919 | + | 0.120641i | ||||
\(913\) | −18.6969 | − | 10.7947i | −0.618778 | − | 0.357251i | ||||
\(914\) | −43.9524 | − | 22.9820i | −1.45382 | − | 0.760176i | ||||
\(915\) | −16.1324 | − | 4.32266i | −0.533321 | − | 0.142903i | ||||
\(916\) | 34.3157 | − | 40.5948i | 1.13382 | − | 1.34129i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 32.0905 | − | 34.8929i | 1.05915 | − | 1.15164i | ||||
\(919\) | 30.0247 | + | 52.0044i | 0.990425 | + | 1.71547i | 0.614770 | + | 0.788707i | \(0.289249\pi\) |
0.375655 | + | 0.926759i | \(0.377418\pi\) | |||||||
\(920\) | −2.89213 | − | 7.09153i | −0.0953508 | − | 0.233801i | ||||
\(921\) | −11.9512 | − | 6.90003i | −0.393805 | − | 0.227364i | ||||
\(922\) | −7.11406 | + | 31.8152i | −0.234289 | + | 1.04778i | ||||
\(923\) | −14.9712 | − | 14.9712i | −0.492781 | − | 0.492781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.37361 | + | 7.37361i | −0.242443 | + | 0.242443i | ||||
\(926\) | 1.30794 | − | 0.829904i | 0.0429815 | − | 0.0272723i | ||||
\(927\) | −43.7251 | + | 75.7341i | −1.43612 | + | 2.48743i | ||||
\(928\) | 7.41032 | + | 14.5571i | 0.243256 | + | 0.477861i | ||||
\(929\) | −33.0418 | + | 19.0767i | −1.08407 | + | 0.625887i | −0.931991 | − | 0.362482i | \(-0.881929\pi\) |
−0.152077 | + | 0.988369i | \(0.548596\pi\) | |||||||
\(930\) | −0.389303 | − | 9.30522i | −0.0127657 | − | 0.305130i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.748007 | + | 8.92388i | 0.0245018 | + | 0.292312i | ||||
\(933\) | −16.5313 | + | 61.6955i | −0.541209 | + | 2.01982i | ||||
\(934\) | 10.4762 | + | 33.4383i | 0.342790 | + | 1.09413i | ||||
\(935\) | −3.10852 | + | 5.38411i | −0.101659 | + | 0.176079i | ||||
\(936\) | −80.6186 | − | 11.0619i | −2.63510 | − | 0.361570i | ||||
\(937\) | −15.2637 | −0.498643 | −0.249321 | − | 0.968421i | \(-0.580208\pi\) | ||||
−0.249321 | + | 0.968421i | \(0.580208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.0341 | − | 34.0341i | 1.11066 | − | 1.11066i | ||||
\(940\) | 16.2056 | + | 2.91836i | 0.528567 | + | 0.0951863i | ||||
\(941\) | 48.7913 | − | 13.0736i | 1.59055 | − | 0.426187i | 0.648380 | − | 0.761317i | \(-0.275447\pi\) |
0.942172 | + | 0.335130i | \(0.108780\pi\) | |||||||
\(942\) | 23.1628 | − | 44.2983i | 0.754685 | − | 1.44332i | ||||
\(943\) | −19.6526 | − | 34.0393i | −0.639976 | − | 1.10847i | ||||
\(944\) | −19.1279 | − | 13.6022i | −0.622560 | − | 0.442713i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.775184 | + | 18.5286i | 0.0252034 | + | 0.602418i | ||||
\(947\) | 9.67121 | − | 36.0934i | 0.314272 | − | 1.17288i | −0.610393 | − | 0.792098i | \(-0.708989\pi\) |
0.924665 | − | 0.380781i | \(-0.124345\pi\) | |||||||
\(948\) | −66.7519 | + | 24.0208i | −2.16800 | + | 0.780160i | ||||
\(949\) | 27.8140 | − | 7.45275i | 0.902882 | − | 0.241926i | ||||
\(950\) | 0.602742 | − | 2.69556i | 0.0195555 | − | 0.0874555i | ||||
\(951\) | − | 90.9354i | − | 2.94878i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.2788i | 1.69348i | 0.532010 | + | 0.846738i | \(0.321437\pi\) | ||||
−0.532010 | + | 0.846738i | \(0.678563\pi\) | |||||||
\(954\) | −32.3968 | − | 7.24411i | −1.04889 | − | 0.234537i | ||||
\(955\) | 11.3357 | − | 3.03739i | 0.366815 | − | 0.0982877i | ||||
\(956\) | 16.5367 | + | 7.78463i | 0.534836 | + | 0.251773i | ||||
\(957\) | 6.67996 | − | 24.9299i | 0.215932 | − | 0.805870i | ||||
\(958\) | 10.9974 | − | 0.460097i | 0.355308 | − | 0.0148651i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.18366 | − | 20.2269i | −0.167302 | − | 0.652821i | ||||
\(961\) | 12.3169 | + | 21.3335i | 0.397320 | + | 0.688179i | ||||
\(962\) | −12.4645 | − | 6.51748i | −0.401872 | − | 0.210132i | ||||
\(963\) | −37.1070 | + | 9.94280i | −1.19576 | + | 0.320402i | ||||
\(964\) | 15.8822 | − | 11.0349i | 0.511530 | − | 0.355409i | ||||
\(965\) | 11.2687 | − | 11.2687i | 0.362753 | − | 0.362753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6054 | 0.919888 | 0.459944 | − | 0.887948i | \(-0.347870\pi\) | ||||
0.459944 | + | 0.887948i | \(0.347870\pi\) | |||||||
\(968\) | −6.75994 | + | 5.12867i | −0.217273 | + | 0.164842i | ||||
\(969\) | −1.90202 | + | 3.29439i | −0.0611016 | + | 0.105831i | ||||
\(970\) | −14.7902 | + | 4.63376i | −0.474886 | + | 0.148781i | ||||
\(971\) | −11.9998 | + | 44.7840i | −0.385093 | + | 1.43719i | 0.452927 | + | 0.891548i | \(0.350380\pi\) |
−0.838020 | + | 0.545639i | \(0.816287\pi\) | |||||||
\(972\) | 28.1053 | − | 33.2479i | 0.901477 | − | 1.06643i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 39.1328 | − | 1.63720i | 1.25390 | − | 0.0524594i | ||||
\(975\) | 48.6631 | − | 28.0957i | 1.55847 | − | 0.899781i | ||||
\(976\) | −23.2755 | + | 10.6479i | −0.745031 | + | 0.340831i | ||||
\(977\) | −16.6403 | + | 28.8218i | −0.532369 | + | 0.922091i | 0.466916 | + | 0.884301i | \(0.345365\pi\) |
−0.999286 | + | 0.0377892i | \(0.987968\pi\) | |||||||
\(978\) | −32.6823 | − | 51.5076i | −1.04506 | − | 1.64703i | ||||
\(979\) | −2.11348 | + | 2.11348i | −0.0675470 | + | 0.0675470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.7906 | + | 29.7906i | 0.951141 | + | 0.951141i | ||||
\(982\) | 39.5565 | + | 8.84504i | 1.26230 | + | 0.282257i | ||||
\(983\) | 23.5506 | + | 13.5969i | 0.751147 | + | 0.433675i | 0.826108 | − | 0.563511i | \(-0.190550\pi\) |
−0.0749609 | + | 0.997186i | \(0.523883\pi\) | |||||||
\(984\) | −40.4680 | − | 99.2277i | −1.29007 | − | 3.16326i | ||||
\(985\) | 0.265710 | + | 0.460223i | 0.00846622 | + | 0.0146639i | ||||
\(986\) | 7.99904 | + | 7.35660i | 0.254741 | + | 0.234282i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.71267 | − | 0.311199i | 0.118116 | − | 0.00990057i | ||||
\(989\) | −14.6810 | − | 3.93376i | −0.466828 | − | 0.125086i | ||||
\(990\) | −10.6947 | + | 20.4533i | −0.339899 | + | 0.650048i | ||||
\(991\) | −36.7867 | − | 21.2388i | −1.16857 | − | 0.674673i | −0.215225 | − | 0.976564i | \(-0.569048\pi\) |
−0.953342 | + | 0.301892i | \(0.902382\pi\) | |||||||
\(992\) | −9.54647 | − | 10.6105i | −0.303101 | − | 0.336882i | ||||
\(993\) | 93.0384i | 2.95248i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3687 | − | 14.3687i | −0.455520 | − | 0.455520i | ||||
\(996\) | 39.6176 | − | 27.5261i | 1.25533 | − | 0.872198i | ||||
\(997\) | −11.3289 | − | 42.2801i | −0.358791 | − | 1.33902i | −0.875647 | − | 0.482952i | \(-0.839564\pi\) |
0.516856 | − | 0.856072i | \(-0.327102\pi\) | |||||||
\(998\) | 38.1423 | − | 11.9499i | 1.20737 | − | 0.378269i | ||||
\(999\) | 26.3451 | − | 15.2103i | 0.833522 | − | 0.481234i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 784.2.w.e.619.5 | 32 | ||
7.2 | even | 3 | inner | 784.2.w.e.411.6 | 32 | ||
7.3 | odd | 6 | 112.2.j.d.27.2 | yes | 16 | ||
7.4 | even | 3 | 112.2.j.d.27.1 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 784.2.w.e.411.5 | 32 | ||
7.6 | odd | 2 | inner | 784.2.w.e.619.6 | 32 | ||
16.3 | odd | 4 | inner | 784.2.w.e.227.5 | 32 | ||
28.3 | even | 6 | 448.2.j.d.335.1 | 16 | |||
28.11 | odd | 6 | 448.2.j.d.335.8 | 16 | |||
56.3 | even | 6 | 896.2.j.g.671.8 | 16 | |||
56.11 | odd | 6 | 896.2.j.g.671.1 | 16 | |||
56.45 | odd | 6 | 896.2.j.h.671.1 | 16 | |||
56.53 | even | 6 | 896.2.j.h.671.8 | 16 | |||
112.3 | even | 12 | 112.2.j.d.83.1 | yes | 16 | ||
112.11 | odd | 12 | 896.2.j.h.223.1 | 16 | |||
112.19 | even | 12 | inner | 784.2.w.e.19.5 | 32 | ||
112.45 | odd | 12 | 448.2.j.d.111.8 | 16 | |||
112.51 | odd | 12 | inner | 784.2.w.e.19.6 | 32 | ||
112.53 | even | 12 | 896.2.j.g.223.8 | 16 | |||
112.59 | even | 12 | 896.2.j.h.223.8 | 16 | |||
112.67 | odd | 12 | 112.2.j.d.83.2 | yes | 16 | ||
112.83 | even | 4 | inner | 784.2.w.e.227.6 | 32 | ||
112.101 | odd | 12 | 896.2.j.g.223.1 | 16 | |||
112.109 | even | 12 | 448.2.j.d.111.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.1 | ✓ | 16 | 7.4 | even | 3 | ||
112.2.j.d.27.2 | yes | 16 | 7.3 | odd | 6 | ||
112.2.j.d.83.1 | yes | 16 | 112.3 | even | 12 | ||
112.2.j.d.83.2 | yes | 16 | 112.67 | odd | 12 | ||
448.2.j.d.111.1 | 16 | 112.109 | even | 12 | |||
448.2.j.d.111.8 | 16 | 112.45 | odd | 12 | |||
448.2.j.d.335.1 | 16 | 28.3 | even | 6 | |||
448.2.j.d.335.8 | 16 | 28.11 | odd | 6 | |||
784.2.w.e.19.5 | 32 | 112.19 | even | 12 | inner | ||
784.2.w.e.19.6 | 32 | 112.51 | odd | 12 | inner | ||
784.2.w.e.227.5 | 32 | 16.3 | odd | 4 | inner | ||
784.2.w.e.227.6 | 32 | 112.83 | even | 4 | inner | ||
784.2.w.e.411.5 | 32 | 7.5 | odd | 6 | inner | ||
784.2.w.e.411.6 | 32 | 7.2 | even | 3 | inner | ||
784.2.w.e.619.5 | 32 | 1.1 | even | 1 | trivial | ||
784.2.w.e.619.6 | 32 | 7.6 | odd | 2 | inner | ||
896.2.j.g.223.1 | 16 | 112.101 | odd | 12 | |||
896.2.j.g.223.8 | 16 | 112.53 | even | 12 | |||
896.2.j.g.671.1 | 16 | 56.11 | odd | 6 | |||
896.2.j.g.671.8 | 16 | 56.3 | even | 6 | |||
896.2.j.h.223.1 | 16 | 112.11 | odd | 12 | |||
896.2.j.h.223.8 | 16 | 112.59 | even | 12 | |||
896.2.j.h.671.1 | 16 | 56.45 | odd | 6 | |||
896.2.j.h.671.8 | 16 | 56.53 | even | 6 |