Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(46,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.r (of order \(15\), degree \(8\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 46.12 | ||
Character | \(\chi\) | \(=\) | 675.46 |
Dual form | 675.2.r.a.631.12 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.510289 | − | 0.566733i | −0.360829 | − | 0.400741i | 0.535208 | − | 0.844720i | \(-0.320233\pi\) |
−0.896037 | + | 0.443979i | \(0.853566\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.148265 | − | 1.41065i | 0.0741326 | − | 0.705324i | ||||
\(5\) | 0.965605 | + | 2.01683i | 0.431832 | + | 0.901954i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.476660 | + | 0.825599i | −0.180161 | + | 0.312047i | −0.941935 | − | 0.335795i | \(-0.890995\pi\) |
0.761775 | + | 0.647842i | \(0.224328\pi\) | |||||||
\(8\) | −2.10906 | + | 1.53232i | −0.745664 | + | 0.541757i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.650268 | − | 1.57641i | 0.205633 | − | 0.498504i | ||||
\(11\) | −1.93658 | − | 2.15079i | −0.583900 | − | 0.648487i | 0.376728 | − | 0.926324i | \(-0.377049\pi\) |
−0.960628 | + | 0.277837i | \(0.910382\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30724 | − | 1.45184i | 0.362564 | − | 0.402668i | −0.534070 | − | 0.845440i | \(-0.679338\pi\) |
0.896634 | + | 0.442772i | \(0.146005\pi\) | |||||||
\(14\) | 0.711129 | − | 0.151155i | 0.190057 | − | 0.0403979i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.830202 | − | 0.176465i | −0.207551 | − | 0.0441162i | ||||
\(17\) | 5.51944 | − | 4.01011i | 1.33866 | − | 0.972594i | 0.339168 | − | 0.940726i | \(-0.389854\pi\) |
0.999492 | − | 0.0318678i | \(-0.0101456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.77403 | − | 2.74200i | 0.865823 | − | 0.629057i | −0.0636402 | − | 0.997973i | \(-0.520271\pi\) |
0.929463 | + | 0.368916i | \(0.120271\pi\) | |||||||
\(20\) | 2.98821 | − | 1.06310i | 0.668183 | − | 0.237717i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.230709 | + | 2.19505i | −0.0491872 | + | 0.467985i | ||||
\(23\) | 8.61700 | − | 1.83160i | 1.79677 | − | 0.381915i | 0.816149 | − | 0.577841i | \(-0.196105\pi\) |
0.980619 | + | 0.195926i | \(0.0627713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.13521 | + | 3.89492i | −0.627043 | + | 0.778985i | ||||
\(26\) | −1.48988 | −0.292189 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.09396 | + | 0.794807i | 0.206739 | + | 0.150204i | ||||
\(29\) | −0.852862 | + | 0.379719i | −0.158372 | + | 0.0705120i | −0.484392 | − | 0.874851i | \(-0.660959\pi\) |
0.326020 | + | 0.945363i | \(0.394292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.42766 | − | 1.08086i | −0.436021 | − | 0.194129i | 0.176975 | − | 0.984215i | \(-0.443369\pi\) |
−0.612995 | + | 0.790086i | \(0.710036\pi\) | |||||||
\(32\) | 2.93057 | + | 5.07590i | 0.518057 | + | 0.897300i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.08917 | − | 1.08174i | −0.872785 | − | 0.185516i | ||||
\(35\) | −2.12536 | − | 0.164140i | −0.359251 | − | 0.0277447i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.799338 | + | 2.46011i | 0.131410 | + | 0.404439i | 0.995014 | − | 0.0997312i | \(-0.0317983\pi\) |
−0.863604 | + | 0.504171i | \(0.831798\pi\) | |||||||
\(38\) | −3.47983 | − | 0.739660i | −0.564502 | − | 0.119989i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.12694 | − | 2.77400i | −0.810641 | − | 0.438607i | ||||
\(41\) | 3.62683 | − | 4.02800i | 0.566415 | − | 0.629068i | −0.390092 | − | 0.920776i | \(-0.627557\pi\) |
0.956507 | + | 0.291708i | \(0.0942236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.43871 | − | 7.68807i | 0.676897 | − | 1.17242i | −0.299014 | − | 0.954249i | \(-0.596658\pi\) |
0.975911 | − | 0.218171i | \(-0.0700090\pi\) | |||||||
\(44\) | −3.32113 | + | 2.41294i | −0.500679 | + | 0.363765i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.43519 | − | 3.94889i | −0.801374 | − | 0.582233i | ||||
\(47\) | 3.66588 | − | 1.63216i | 0.534724 | − | 0.238074i | −0.121566 | − | 0.992583i | \(-0.538792\pi\) |
0.656290 | + | 0.754509i | \(0.272125\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.04559 | + | 5.27512i | 0.435084 | + | 0.753588i | ||||
\(50\) | 3.80725 | − | 0.210706i | 0.538426 | − | 0.0297983i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.85422 | − | 2.05932i | −0.257134 | − | 0.285576i | ||||
\(53\) | −4.30252 | − | 3.12596i | −0.590996 | − | 0.429384i | 0.251675 | − | 0.967812i | \(-0.419018\pi\) |
−0.842672 | + | 0.538428i | \(0.819018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.46781 | − | 5.98256i | 0.332759 | − | 0.806688i | ||||
\(56\) | −0.259779 | − | 2.47163i | −0.0347144 | − | 0.330285i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.650405 | + | 0.289579i | 0.0854024 | + | 0.0380236i | ||||
\(59\) | −3.21068 | + | 3.56582i | −0.417995 | + | 0.464231i | −0.914963 | − | 0.403539i | \(-0.867780\pi\) |
0.496968 | + | 0.867769i | \(0.334447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.51779 | − | 8.34935i | −0.962554 | − | 1.06902i | −0.997572 | − | 0.0696383i | \(-0.977815\pi\) |
0.0350179 | − | 0.999387i | \(-0.488851\pi\) | |||||||
\(62\) | 0.626247 | + | 1.92739i | 0.0795334 | + | 0.244779i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.856686 | − | 2.63661i | 0.107086 | − | 0.329576i | ||||
\(65\) | 4.19039 | + | 1.23458i | 0.519754 | + | 0.153131i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.38246 | + | 1.50597i | 0.413234 | + | 0.183983i | 0.602814 | − | 0.797882i | \(-0.294046\pi\) |
−0.189580 | + | 0.981865i | \(0.560713\pi\) | |||||||
\(68\) | −4.83851 | − | 8.38055i | −0.586756 | − | 1.01629i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.991523 | + | 1.28827i | 0.118510 | + | 0.153978i | ||||
\(71\) | 0.125408 | + | 0.0911140i | 0.0148832 | + | 0.0108132i | 0.595202 | − | 0.803576i | \(-0.297072\pi\) |
−0.580319 | + | 0.814389i | \(0.697072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.09917 | + | 9.53828i | −0.362731 | + | 1.11637i | 0.588659 | + | 0.808381i | \(0.299656\pi\) |
−0.951390 | + | 0.307989i | \(0.900344\pi\) | |||||||
\(74\) | 0.986332 | − | 1.70838i | 0.114659 | − | 0.198595i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.30843 | − | 5.73038i | −0.379503 | − | 0.657319i | ||||
\(77\) | 2.69878 | − | 0.573643i | 0.307554 | − | 0.0653726i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86470 | − | 1.72068i | 0.434813 | − | 0.193591i | −0.177644 | − | 0.984095i | \(-0.556848\pi\) |
0.612458 | + | 0.790503i | \(0.290181\pi\) | |||||||
\(80\) | −0.445747 | − | 1.84477i | −0.0498361 | − | 0.206252i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.13353 | −0.456472 | ||||||||
\(83\) | −0.344989 | − | 3.28235i | −0.0378675 | − | 0.360285i | −0.997005 | − | 0.0773432i | \(-0.975356\pi\) |
0.959137 | − | 0.282942i | \(-0.0913104\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4173 | + | 7.25960i | 1.45531 | + | 0.787414i | ||||
\(86\) | −6.62211 | + | 1.40757i | −0.714080 | + | 0.151782i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.38004 | + | 1.56868i | 0.786715 | + | 0.167221i | ||||
\(89\) | −5.32122 | + | 16.3770i | −0.564048 | + | 1.73596i | 0.106716 | + | 0.994290i | \(0.465966\pi\) |
−0.670764 | + | 0.741671i | \(0.734034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.575527 | + | 1.77129i | 0.0603317 | + | 0.185682i | ||||
\(92\) | −1.30614 | − | 12.4271i | −0.136175 | − | 1.29562i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.79565 | − | 1.24471i | −0.288350 | − | 0.128382i | ||||
\(95\) | 9.17437 | + | 4.96390i | 0.941270 | + | 0.509286i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.77459 | + | 0.790097i | −0.180182 | + | 0.0802222i | −0.494845 | − | 0.868981i | \(-0.664775\pi\) |
0.314663 | + | 0.949203i | \(0.398108\pi\) | |||||||
\(98\) | 1.43545 | − | 4.41787i | 0.145003 | − | 0.446272i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.02952 | + | 5.00017i | 0.502952 | + | 0.500017i | ||||
\(101\) | −3.61804 | + | 6.26663i | −0.360009 | + | 0.623553i | −0.987962 | − | 0.154698i | \(-0.950560\pi\) |
0.627953 | + | 0.778251i | \(0.283893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.85476 | − | 17.6469i | 0.182755 | − | 1.73880i | −0.391552 | − | 0.920156i | \(-0.628062\pi\) |
0.574307 | − | 0.818640i | \(-0.305272\pi\) | |||||||
\(104\) | −0.532366 | + | 5.06512i | −0.0522027 | + | 0.496676i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.423940 | + | 4.03352i | 0.0411767 | + | 0.391770i | ||||
\(107\) | −1.19151 | −0.115188 | −0.0575940 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575940 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.597453 | + | 1.83877i | 0.0572256 | + | 0.176122i | 0.975584 | − | 0.219628i | \(-0.0704845\pi\) |
−0.918358 | + | 0.395751i | \(0.870484\pi\) | |||||||
\(110\) | −4.64981 | + | 1.65425i | −0.443342 | + | 0.157726i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.541413 | − | 0.601300i | 0.0511588 | − | 0.0568176i | ||||
\(113\) | −5.37736 | + | 5.97216i | −0.505859 | + | 0.561814i | −0.940938 | − | 0.338579i | \(-0.890054\pi\) |
0.435079 | + | 0.900392i | \(0.356721\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0146 | + | 15.6104i | 1.12037 | + | 1.45568i | ||||
\(116\) | 0.409200 | + | 1.25939i | 0.0379932 | + | 0.116931i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.65924 | 0.336861 | ||||||||
\(119\) | 0.679846 | + | 6.46830i | 0.0623214 | + | 0.592948i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.274260 | − | 2.60941i | 0.0249327 | − | 0.237219i | ||||
\(122\) | −0.895610 | + | 8.52116i | −0.0810847 | + | 0.771470i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.88466 | + | 3.26432i | −0.169247 | + | 0.293145i | ||||
\(125\) | −10.8828 | − | 2.56224i | −0.973385 | − | 0.229174i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.50280 | + | 13.8582i | −0.399559 | + | 1.22972i | 0.525794 | + | 0.850612i | \(0.323768\pi\) |
−0.925354 | + | 0.379105i | \(0.876232\pi\) | |||||||
\(128\) | 8.77743 | − | 3.90796i | 0.775822 | − | 0.345418i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.43863 | − | 3.00483i | −0.126176 | − | 0.263541i | ||||
\(131\) | −12.3994 | − | 5.52056i | −1.08334 | − | 0.482334i | −0.214144 | − | 0.976802i | \(-0.568696\pi\) |
−0.869195 | + | 0.494469i | \(0.835363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.464859 | + | 4.42284i | 0.0403084 | + | 0.383509i | ||||
\(134\) | −0.872550 | − | 2.68543i | −0.0753768 | − | 0.231986i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.49604 | + | 16.9151i | −0.471282 | + | 1.45046i | ||||
\(137\) | −8.55444 | − | 1.81830i | −0.730855 | − | 0.155348i | −0.172570 | − | 0.984997i | \(-0.555207\pi\) |
−0.558285 | + | 0.829649i | \(0.688541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.5125 | + | 3.93495i | −1.57021 | + | 0.333758i | −0.909115 | − | 0.416545i | \(-0.863241\pi\) |
−0.661094 | + | 0.750303i | \(0.729908\pi\) | |||||||
\(140\) | −0.546660 | + | 2.97380i | −0.0462012 | + | 0.251332i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.0123568 | − | 0.117567i | −0.00103696 | − | 0.00986602i | ||||
\(143\) | −5.65417 | −0.472825 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.58936 | − | 1.35342i | −0.131989 | − | 0.112395i | ||||
\(146\) | 6.98713 | − | 3.11087i | 0.578259 | − | 0.257458i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.58886 | − | 0.762836i | 0.295003 | − | 0.0627048i | ||||
\(149\) | −3.03989 | − | 5.26524i | −0.249037 | − | 0.431345i | 0.714222 | − | 0.699919i | \(-0.246781\pi\) |
−0.963259 | + | 0.268574i | \(0.913447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.71367 | − | 8.16432i | 0.383593 | − | 0.664403i | −0.607980 | − | 0.793952i | \(-0.708020\pi\) |
0.991573 | + | 0.129550i | \(0.0413532\pi\) | |||||||
\(152\) | −3.75804 | + | 11.5660i | −0.304817 | + | 0.938130i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.70226 | − | 1.23676i | −0.137172 | − | 0.0996612i | ||||
\(155\) | −0.164240 | − | 5.93987i | −0.0131921 | − | 0.477102i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2999 | + | 17.8399i | 0.822020 | + | 1.42378i | 0.904175 | + | 0.427162i | \(0.140486\pi\) |
−0.0821548 | + | 0.996620i | \(0.526180\pi\) | |||||||
\(158\) | −2.94728 | − | 1.31221i | −0.234473 | − | 0.104394i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.40745 | + | 10.8118i | −0.585611 | + | 0.854746i | ||||
\(161\) | −2.59521 | + | 7.98723i | −0.204531 | + | 0.629482i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.22118 | − | 9.91378i | −0.252302 | − | 0.776507i | −0.994349 | − | 0.106159i | \(-0.966145\pi\) |
0.742047 | − | 0.670348i | \(-0.233855\pi\) | |||||||
\(164\) | −5.14436 | − | 5.71339i | −0.401707 | − | 0.446141i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.68418 | + | 1.87047i | −0.130717 | + | 0.145176i | ||||
\(167\) | 14.1271 | + | 6.28980i | 1.09319 | + | 0.486719i | 0.872495 | − | 0.488624i | \(-0.162501\pi\) |
0.220695 | + | 0.975343i | \(0.429168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.959914 | + | 9.13298i | 0.0738396 | + | 0.702537i | ||||
\(170\) | −2.73245 | − | 11.3085i | −0.209569 | − | 0.867324i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.1871 | − | 7.40133i | −0.776756 | − | 0.564346i | ||||
\(173\) | 9.95195 | + | 11.0528i | 0.756633 | + | 0.840326i | 0.991282 | − | 0.131754i | \(-0.0420610\pi\) |
−0.234650 | + | 0.972080i | \(0.575394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.72121 | − | 4.44498i | −0.130112 | − | 0.336009i | ||||
\(176\) | 1.22821 | + | 2.12733i | 0.0925800 | + | 0.160353i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.9968 | − | 5.34130i | 0.899195 | − | 0.400347i | ||||
\(179\) | 21.5801 | + | 15.6788i | 1.61297 | + | 1.17189i | 0.852954 | + | 0.521987i | \(0.174809\pi\) |
0.760016 | + | 0.649904i | \(0.225191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0289 | − | 11.6457i | 1.19142 | − | 0.865617i | 0.198007 | − | 0.980201i | \(-0.436553\pi\) |
0.993414 | + | 0.114583i | \(0.0365533\pi\) | |||||||
\(182\) | 0.710164 | − | 1.23004i | 0.0526409 | − | 0.0911767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.3671 | + | 17.0669i | −1.13288 | + | 1.25819i | ||||
\(185\) | −4.18978 | + | 3.98762i | −0.308039 | + | 0.293176i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.3137 | − | 4.10525i | −1.41236 | − | 0.300206i | ||||
\(188\) | −1.75888 | − | 5.41326i | −0.128279 | − | 0.394803i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.86837 | − | 7.73244i | −0.135546 | − | 0.560970i | ||||
\(191\) | −11.7458 | − | 2.49665i | −0.849896 | − | 0.180651i | −0.237682 | − | 0.971343i | \(-0.576388\pi\) |
−0.612214 | + | 0.790692i | \(0.709721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6897 | + | 21.9792i | 0.913424 | + | 1.58210i | 0.809192 | + | 0.587544i | \(0.199905\pi\) |
0.104232 | + | 0.994553i | \(0.466762\pi\) | |||||||
\(194\) | 1.35333 | + | 0.602539i | 0.0971631 | + | 0.0432598i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.89289 | − | 3.51414i | 0.563778 | − | 0.251010i | ||||
\(197\) | 1.37622 | + | 0.999883i | 0.0980516 | + | 0.0712387i | 0.635731 | − | 0.771911i | \(-0.280699\pi\) |
−0.537679 | + | 0.843150i | \(0.680699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.51877 | −0.462104 | −0.231052 | − | 0.972941i | \(-0.574217\pi\) | ||||
−0.231052 | + | 0.972941i | \(0.574217\pi\) | |||||||
\(200\) | 0.644079 | − | 13.0188i | 0.0455433 | − | 0.920565i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.39776 | − | 1.14733i | 0.379785 | − | 0.0807258i | ||||
\(203\) | 0.0930297 | − | 0.885119i | 0.00652941 | − | 0.0621231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6259 | + | 3.42524i | 0.811986 | + | 0.239229i | ||||
\(206\) | −10.9475 | + | 7.95384i | −0.762750 | + | 0.554170i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.34147 | + | 0.974638i | −0.0930145 | + | 0.0675790i | ||||
\(209\) | −13.2062 | − | 2.80705i | −0.913489 | − | 0.194168i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.80500 | + | 1.65900i | −0.537318 | + | 0.114210i | −0.468575 | − | 0.883424i | \(-0.655232\pi\) |
−0.0687434 | + | 0.997634i | \(0.521899\pi\) | |||||||
\(212\) | −5.04755 | + | 5.60587i | −0.346667 | + | 0.385013i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.608017 | + | 0.675271i | 0.0415632 | + | 0.0461606i | ||||
\(215\) | 19.7916 | + | 1.52849i | 1.34977 | + | 0.104242i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.04953 | − | 1.48907i | 0.139131 | − | 0.101085i | ||||
\(218\) | 0.737219 | − | 1.27690i | 0.0499307 | − | 0.0864826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.07340 | − | 4.36821i | −0.544308 | − | 0.294505i | ||||
\(221\) | 1.39321 | − | 13.2555i | 0.0937175 | − | 0.891662i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.31480 | − | 7.01329i | −0.422870 | − | 0.469645i | 0.493634 | − | 0.869670i | \(-0.335668\pi\) |
−0.916504 | + | 0.400025i | \(0.869002\pi\) | |||||||
\(224\) | −5.58754 | −0.373333 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.12863 | 0.407670 | ||||||||
\(227\) | 15.7939 | + | 17.5409i | 1.04828 | + | 1.16423i | 0.986097 | + | 0.166169i | \(0.0531397\pi\) |
0.0621833 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.64184 | − | 15.6210i | 0.108496 | − | 1.03227i | −0.795858 | − | 0.605484i | \(-0.792980\pi\) |
0.904354 | − | 0.426784i | \(-0.140354\pi\) | |||||||
\(230\) | 2.71601 | − | 14.7749i | 0.179088 | − | 0.974229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.21688 | − | 2.10770i | 0.0798923 | − | 0.138378i | ||||
\(233\) | 1.52687 | − | 1.10933i | 0.100028 | − | 0.0726749i | −0.536647 | − | 0.843807i | \(-0.680309\pi\) |
0.636675 | + | 0.771132i | \(0.280309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.83157 | + | 5.81744i | 0.445643 | + | 0.379488i | ||||
\(236\) | 4.55409 | + | 5.05783i | 0.296446 | + | 0.329237i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.31888 | − | 3.68599i | 0.215131 | − | 0.238927i | ||||
\(239\) | −1.40198 | + | 0.298000i | −0.0906865 | + | 0.0192760i | −0.253031 | − | 0.967458i | \(-0.581428\pi\) |
0.162345 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7140 | − | 2.27733i | −0.690150 | − | 0.146696i | −0.150531 | − | 0.988605i | \(-0.548098\pi\) |
−0.539619 | + | 0.841910i | \(0.681432\pi\) | |||||||
\(242\) | −1.61879 | + | 1.17612i | −0.104060 | + | 0.0756039i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.8926 | + | 9.36704i | −0.825366 | + | 0.599663i | ||||
\(245\) | −7.69818 | + | 11.2361i | −0.491819 | + | 0.717849i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.952637 | − | 9.06374i | 0.0606149 | − | 0.576712i | ||||
\(248\) | 6.77630 | − | 1.44035i | 0.430296 | − | 0.0914621i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.10125 | + | 7.47512i | 0.259386 | + | 0.472768i | ||||
\(251\) | −9.34568 | −0.589894 | −0.294947 | − | 0.955514i | \(-0.595302\pi\) | ||||
−0.294947 | + | 0.955514i | \(0.595302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.6269 | − | 14.9863i | −1.29680 | − | 0.942180i | ||||
\(254\) | 10.1516 | − | 4.51980i | 0.636970 | − | 0.283597i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7590 | − | 5.23546i | −0.734939 | − | 0.327216i | ||||
\(257\) | 3.12162 | + | 5.40681i | 0.194722 | + | 0.337268i | 0.946809 | − | 0.321795i | \(-0.104286\pi\) |
−0.752088 | + | 0.659063i | \(0.770953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.41208 | − | 0.512703i | −0.149879 | − | 0.0318578i | ||||
\(260\) | 2.36285 | − | 5.72813i | 0.146538 | − | 0.355243i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.19858 | + | 9.84422i | 0.197609 | + | 0.608178i | ||||
\(263\) | 1.82124 | + | 0.387117i | 0.112303 | + | 0.0238707i | 0.263720 | − | 0.964599i | \(-0.415050\pi\) |
−0.151418 | + | 0.988470i | \(0.548384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.15001 | − | 11.6959i | 0.132074 | − | 0.718473i | ||||
\(266\) | 2.26936 | − | 2.52038i | 0.139143 | − | 0.154534i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.62589 | − | 4.54818i | 0.160402 | − | 0.277824i | ||||
\(269\) | −3.89397 | + | 2.82914i | −0.237420 | + | 0.172496i | −0.700133 | − | 0.714012i | \(-0.746876\pi\) |
0.462713 | + | 0.886508i | \(0.346876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4402 | + | 13.3976i | 1.12016 | + | 0.813846i | 0.984234 | − | 0.176873i | \(-0.0565982\pi\) |
0.135929 | + | 0.990719i | \(0.456598\pi\) | |||||||
\(272\) | −5.28989 | + | 2.35521i | −0.320747 | + | 0.142806i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.33474 | + | 5.77595i | 0.201459 | + | 0.348938i | ||||
\(275\) | 14.4487 | − | 0.799641i | 0.871292 | − | 0.0482202i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.22689 | + | 5.80505i | 0.314054 | + | 0.348792i | 0.879419 | − | 0.476049i | \(-0.157931\pi\) |
−0.565365 | + | 0.824841i | \(0.691265\pi\) | |||||||
\(278\) | 11.6768 | + | 8.48368i | 0.700327 | + | 0.508817i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.73402 | − | 2.91055i | 0.282912 | − | 0.173938i | ||||
\(281\) | −0.164928 | − | 1.56918i | −0.00983878 | − | 0.0936097i | 0.988501 | − | 0.151218i | \(-0.0483194\pi\) |
−0.998339 | + | 0.0576078i | \(0.981653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.09288 | − | 3.15795i | −0.421628 | − | 0.187721i | 0.184945 | − | 0.982749i | \(-0.440789\pi\) |
−0.606573 | + | 0.795028i | \(0.707456\pi\) | |||||||
\(284\) | 0.147123 | − | 0.163397i | 0.00873017 | − | 0.00969584i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.88526 | + | 3.20441i | 0.170609 | + | 0.189481i | ||||
\(287\) | 1.59675 | + | 4.91429i | 0.0942532 | + | 0.290081i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.12995 | − | 28.0991i | 0.537056 | − | 1.65289i | ||||
\(290\) | 0.0440023 | + | 1.59138i | 0.00258391 | + | 0.0934488i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.9957 | + | 5.78604i | 0.760513 | + | 0.338602i | ||||
\(293\) | −5.25540 | − | 9.10262i | −0.307024 | − | 0.531781i | 0.670686 | − | 0.741741i | \(-0.266000\pi\) |
−0.977710 | + | 0.209961i | \(0.932666\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2919 | − | 3.03223i | −0.599218 | − | 0.176543i | ||||
\(296\) | −5.45552 | − | 3.96367i | −0.317096 | − | 0.230383i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.43276 | + | 4.40960i | −0.0829978 | + | 0.255441i | ||||
\(299\) | 8.60531 | − | 14.9048i | 0.497658 | − | 0.861969i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23151 | + | 7.32919i | 0.243900 | + | 0.422447i | ||||
\(302\) | −7.03232 | + | 1.49477i | −0.404665 | + | 0.0860141i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.61708 | + | 1.61043i | −0.207454 | + | 0.0923643i | ||||
\(305\) | 9.58002 | − | 23.2243i | 0.548550 | − | 1.32982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.00205 | 0.171336 | 0.0856680 | − | 0.996324i | \(-0.472698\pi\) | ||||
0.0856680 | + | 0.996324i | \(0.472698\pi\) | |||||||
\(308\) | −0.409074 | − | 3.89208i | −0.0233091 | − | 0.221772i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.28251 | + | 3.12413i | −0.186434 | + | 0.177439i | ||||
\(311\) | −13.7061 | + | 2.91331i | −0.777199 | + | 0.165199i | −0.579399 | − | 0.815044i | \(-0.696713\pi\) |
−0.197800 | + | 0.980242i | \(0.563380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.43306 | + | 1.15483i | 0.307095 | + | 0.0652751i | 0.358882 | − | 0.933383i | \(-0.383158\pi\) |
−0.0517865 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(314\) | 4.85456 | − | 14.9408i | 0.273959 | − | 0.843158i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.85427 | − | 5.70685i | −0.104311 | − | 0.321036i | ||||
\(317\) | 0.475026 | + | 4.51957i | 0.0266801 | + | 0.253844i | 0.999730 | + | 0.0232485i | \(0.00740090\pi\) |
−0.973050 | + | 0.230596i | \(0.925932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.46833 | + | 1.09897i | 0.138200 | + | 0.0615305i | ||||
\(320\) | 6.14481 | − | 0.818131i | 0.343506 | − | 0.0457349i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.85094 | − | 2.60501i | 0.326060 | − | 0.145171i | ||||
\(323\) | 9.83485 | − | 30.2685i | 0.547226 | − | 1.68419i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.55632 | + | 9.64343i | 0.0863290 | + | 0.534921i | ||||
\(326\) | −3.97473 | + | 6.88444i | −0.220140 | + | 0.381294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.47700 | + | 14.0527i | −0.0815538 | + | 0.775932i | ||||
\(329\) | −0.399872 | + | 3.80453i | −0.0220457 | + | 0.209751i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.606412 | − | 5.76962i | −0.0333314 | − | 0.317127i | −0.998466 | − | 0.0553723i | \(-0.982365\pi\) |
0.965134 | − | 0.261755i | \(-0.0843012\pi\) | |||||||
\(332\) | −4.68140 | −0.256925 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.64427 | − | 11.2159i | −0.199406 | − | 0.613708i | ||||
\(335\) | 0.228836 | + | 8.27603i | 0.0125027 | + | 0.452168i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.28848 | − | 3.65223i | 0.179135 | − | 0.198950i | −0.646890 | − | 0.762584i | \(-0.723931\pi\) |
0.826025 | + | 0.563634i | \(0.190597\pi\) | |||||||
\(338\) | 4.68613 | − | 5.20447i | 0.254892 | − | 0.283086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.2301 | − | 17.8508i | 0.663268 | − | 0.968093i | ||||
\(341\) | 2.37664 | + | 7.31456i | 0.128702 | + | 0.396106i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.4801 | −0.673861 | ||||||||
\(344\) | 2.41909 | + | 23.0161i | 0.130428 | + | 1.24094i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.18560 | − | 11.2802i | 0.0637381 | − | 0.606427i | ||||
\(347\) | 1.04204 | − | 9.91437i | 0.0559398 | − | 0.532231i | −0.930287 | − | 0.366833i | \(-0.880442\pi\) |
0.986227 | − | 0.165399i | \(-0.0528911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.15701 | − | 12.3963i | 0.383106 | − | 0.663559i | −0.608398 | − | 0.793632i | \(-0.708188\pi\) |
0.991504 | + | 0.130073i | \(0.0415210\pi\) | |||||||
\(350\) | −1.64080 | + | 3.24370i | −0.0877046 | + | 0.173383i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.24190 | − | 16.1329i | 0.279394 | − | 0.859887i | ||||
\(353\) | −23.1580 | + | 10.3106i | −1.23257 | + | 0.548778i | −0.916530 | − | 0.399966i | \(-0.869022\pi\) |
−0.316045 | + | 0.948744i | \(0.602355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0626673 | + | 0.340906i | −0.00332604 | + | 0.0180934i | ||||
\(356\) | 22.3133 | + | 9.93451i | 1.18260 | + | 0.526528i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.12635 | − | 20.2309i | −0.112381 | − | 1.06923i | ||||
\(359\) | −6.35182 | − | 19.5489i | −0.335236 | − | 1.03175i | −0.966606 | − | 0.256269i | \(-0.917507\pi\) |
0.631369 | − | 0.775482i | \(-0.282493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.853463 | − | 2.62669i | 0.0449191 | − | 0.138247i | ||||
\(362\) | −14.7794 | − | 3.14145i | −0.776787 | − | 0.165111i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.58400 | − | 0.549246i | 0.135438 | − | 0.0287883i | ||||
\(365\) | −22.2297 | + | 2.95970i | −1.16355 | + | 0.154918i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00921 | − | 28.6307i | −0.157080 | − | 1.49451i | −0.734803 | − | 0.678280i | \(-0.762725\pi\) |
0.577724 | − | 0.816233i | \(-0.303941\pi\) | |||||||
\(368\) | −7.47706 | −0.389769 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.39792 | + | 0.339648i | 0.228637 | + | 0.0176575i | ||||
\(371\) | 4.63163 | − | 2.06213i | 0.240462 | − | 0.107061i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1760 | + | 2.37553i | −0.578671 | + | 0.123000i | −0.487943 | − | 0.872875i | \(-0.662253\pi\) |
−0.0907279 | + | 0.995876i | \(0.528919\pi\) | |||||||
\(374\) | 7.52898 | + | 13.0406i | 0.389314 | + | 0.674312i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.23057 | + | 9.05960i | −0.269746 | + | 0.467213i | ||||
\(377\) | −0.563606 | + | 1.73460i | −0.0290272 | + | 0.0893365i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.90335 | + | 2.10941i | 0.149135 | + | 0.108353i | 0.659851 | − | 0.751397i | \(-0.270620\pi\) |
−0.510716 | + | 0.859750i | \(0.670620\pi\) | |||||||
\(380\) | 8.36256 | − | 12.2058i | 0.428990 | − | 0.626146i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.57882 | + | 7.93074i | 0.234273 | + | 0.405772i | ||||
\(383\) | −4.67766 | − | 2.08263i | −0.239017 | − | 0.106417i | 0.283733 | − | 0.958903i | \(-0.408427\pi\) |
−0.522750 | + | 0.852486i | \(0.675094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.76289 | + | 4.88906i | 0.191775 | + | 0.249170i | ||||
\(386\) | 5.98093 | − | 18.4074i | 0.304421 | − | 0.936912i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.851440 | + | 2.62046i | 0.0432253 | + | 0.133034i | ||||
\(389\) | −20.6772 | − | 22.9643i | −1.04837 | − | 1.16434i | −0.986079 | − | 0.166279i | \(-0.946825\pi\) |
−0.0622946 | − | 0.998058i | \(-0.519842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.2161 | − | 44.6645i | 2.03381 | − | 2.25878i | ||||
\(392\) | −14.5065 | − | 6.45870i | −0.732688 | − | 0.326214i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.135603 | − | 1.29018i | −0.00683159 | − | 0.0649983i | ||||
\(395\) | 7.20209 | + | 6.13296i | 0.362376 | + | 0.308583i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.15821 | − | 3.74766i | −0.258883 | − | 0.188090i | 0.450771 | − | 0.892639i | \(-0.351149\pi\) |
−0.709654 | + | 0.704550i | \(0.751149\pi\) | |||||||
\(398\) | 3.32646 | + | 3.69441i | 0.166740 | + | 0.185184i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.29018 | − | 2.68032i | 0.164509 | − | 0.134016i | ||||
\(401\) | −8.96136 | − | 15.5215i | −0.447509 | − | 0.775108i | 0.550714 | − | 0.834694i | \(-0.314355\pi\) |
−0.998223 | + | 0.0595856i | \(0.981022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.74278 | + | 2.11162i | −0.236255 | + | 0.105187i | ||||
\(404\) | 8.30359 | + | 6.03291i | 0.413119 | + | 0.300149i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.549098 | + | 0.398943i | −0.0272513 | + | 0.0197992i | ||||
\(407\) | 3.74319 | − | 6.48340i | 0.185543 | − | 0.321370i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7159 | + | 28.5604i | −1.27157 | + | 1.41222i | −0.404109 | + | 0.914711i | \(0.632418\pi\) |
−0.867459 | + | 0.497508i | \(0.834248\pi\) | |||||||
\(410\) | −3.99136 | − | 8.33663i | −0.197119 | − | 0.411717i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.6185 | − | 5.23283i | −1.21287 | − | 0.257803i | ||||
\(413\) | −1.41354 | − | 4.35042i | −0.0695556 | − | 0.214070i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.28683 | − | 3.86524i | 0.308608 | − | 0.189737i | ||||
\(416\) | 11.2004 | + | 2.38071i | 0.549142 | + | 0.116724i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.14810 | + | 8.91677i | 0.251802 | + | 0.436134i | ||||
\(419\) | −4.82889 | − | 2.14996i | −0.235907 | − | 0.105033i | 0.285379 | − | 0.958415i | \(-0.407881\pi\) |
−0.521285 | + | 0.853382i | \(0.674547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.7502 | + | 11.0195i | −1.20625 | + | 0.537057i | −0.908620 | − | 0.417625i | \(-0.862863\pi\) |
−0.297629 | + | 0.954681i | \(0.596196\pi\) | |||||||
\(422\) | 4.92301 | + | 3.57678i | 0.239649 | + | 0.174115i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.8642 | 0.673306 | ||||||||
\(425\) | −1.68557 | + | 34.0703i | −0.0817620 | + | 1.65265i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4766 | − | 2.22688i | 0.507000 | − | 0.107766i | ||||
\(428\) | −0.176660 | + | 1.68081i | −0.00853919 | + | 0.0812449i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.23317 | − | 11.9965i | −0.445263 | − | 0.578523i | ||||
\(431\) | 28.0178 | − | 20.3561i | 1.34957 | − | 0.980518i | 0.350535 | − | 0.936550i | \(-0.386000\pi\) |
0.999033 | − | 0.0439685i | \(-0.0140001\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.43160 | + | 5.39937i | −0.357140 | + | 0.259477i | −0.751858 | − | 0.659325i | \(-0.770842\pi\) |
0.394718 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(434\) | −1.88976 | − | 0.401680i | −0.0907113 | − | 0.0192813i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.68244 | − | 0.570170i | 0.128466 | − | 0.0273062i | ||||
\(437\) | 27.4986 | − | 30.5403i | 1.31544 | − | 1.46094i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.80344 | + | 5.33476i | 0.229256 | + | 0.254614i | 0.846787 | − | 0.531932i | \(-0.178534\pi\) |
−0.617531 | + | 0.786546i | \(0.711867\pi\) | |||||||
\(440\) | 3.96245 | + | 16.3990i | 0.188902 | + | 0.781792i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.22328 | + | 5.97456i | −0.391141 | + | 0.284181i | ||||
\(443\) | −12.6804 | + | 21.9630i | −0.602462 | + | 1.04349i | 0.389985 | + | 0.920821i | \(0.372480\pi\) |
−0.992447 | + | 0.122673i | \(0.960853\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.1679 | + | 5.08173i | −1.80933 | + | 0.240897i | ||||
\(446\) | −0.752295 | + | 7.15761i | −0.0356222 | + | 0.338923i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.76843 | + | 1.96404i | 0.0835506 | + | 0.0927924i | ||||
\(449\) | 7.13943 | 0.336930 | 0.168465 | − | 0.985708i | \(-0.446119\pi\) | ||||
0.168465 | + | 0.985708i | \(0.446119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.6870 | −0.738672 | ||||||||
\(452\) | 7.62735 | + | 8.47103i | 0.358760 | + | 0.398444i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.88157 | − | 17.9019i | 0.0883062 | − | 0.840178i | ||||
\(455\) | −3.01666 | + | 2.87111i | −0.141423 | + | 0.134600i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8907 | + | 30.9875i | −0.836890 | + | 1.44954i | 0.0555925 | + | 0.998454i | \(0.482295\pi\) |
−0.892482 | + | 0.451082i | \(0.851038\pi\) | |||||||
\(458\) | −9.69078 | + | 7.04076i | −0.452820 | + | 0.328993i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.8022 | − | 14.6340i | 1.10978 | − | 0.682311i | ||||
\(461\) | 10.1936 | + | 11.3211i | 0.474763 | + | 0.527278i | 0.932190 | − | 0.361969i | \(-0.117895\pi\) |
−0.457427 | + | 0.889247i | \(0.651229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6298 | + | 18.4693i | −0.772852 | + | 0.858339i | −0.993120 | − | 0.117100i | \(-0.962640\pi\) |
0.220268 | + | 0.975439i | \(0.429307\pi\) | |||||||
\(464\) | 0.775055 | − | 0.164743i | 0.0359810 | − | 0.00764800i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.40784 | − | 0.299246i | −0.0652170 | − | 0.0138623i | ||||
\(467\) | 21.1648 | − | 15.3771i | 0.979389 | − | 0.711568i | 0.0218169 | − | 0.999762i | \(-0.493055\pi\) |
0.957572 | + | 0.288194i | \(0.0930549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.85561 | + | 2.07472i | −0.131860 | + | 0.0958018i | ||||
\(470\) | −0.189137 | − | 6.84026i | −0.00872422 | − | 0.315518i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.30753 | − | 12.4403i | 0.0601839 | − | 0.572612i | ||||
\(473\) | −25.1313 | + | 5.34182i | −1.15554 | + | 0.245617i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.15254 | + | 23.2963i | −0.0528823 | + | 1.06891i | ||||
\(476\) | 9.22529 | 0.422841 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.884301 | + | 0.642482i | 0.0404470 | + | 0.0293865i | ||||
\(479\) | 8.78889 | − | 3.91307i | 0.401575 | − | 0.178793i | −0.196004 | − | 0.980603i | \(-0.562796\pi\) |
0.597578 | + | 0.801811i | \(0.296130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.61661 | + | 2.05545i | 0.210499 | + | 0.0937203i | ||||
\(482\) | 4.17660 | + | 7.23408i | 0.190239 | + | 0.329503i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.64030 | − | 0.773769i | −0.165468 | − | 0.0351713i | ||||
\(485\) | −3.30704 | − | 2.81612i | −0.150165 | − | 0.127873i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1864 | + | 37.5059i | 0.552219 | + | 1.69956i | 0.703177 | + | 0.711015i | \(0.251764\pi\) |
−0.150958 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(488\) | 28.6493 | + | 6.08960i | 1.29689 | + | 0.275663i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.2962 | − | 1.37085i | 0.465134 | − | 0.0619287i | ||||
\(491\) | −6.51647 | + | 7.23727i | −0.294084 | + | 0.326614i | −0.872021 | − | 0.489468i | \(-0.837191\pi\) |
0.577937 | + | 0.816081i | \(0.303858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.18461 | + | 5.51590i | −0.143427 | + | 0.248424i | ||||
\(494\) | −5.62284 | + | 4.08523i | −0.252984 | + | 0.183803i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.82471 | + | 1.32573i | 0.0819321 | + | 0.0595272i | ||||
\(497\) | −0.135001 | + | 0.0601061i | −0.00605560 | + | 0.00269613i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.37718 | − | 7.58149i | −0.195949 | − | 0.339394i | 0.751262 | − | 0.660004i | \(-0.229445\pi\) |
−0.947211 | + | 0.320610i | \(0.896112\pi\) | |||||||
\(500\) | −5.22796 | + | 14.9719i | −0.233801 | + | 0.669563i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.76899 | + | 5.29650i | 0.212851 | + | 0.236395i | ||||
\(503\) | 16.1674 | + | 11.7463i | 0.720867 | + | 0.523741i | 0.886661 | − | 0.462420i | \(-0.153019\pi\) |
−0.165794 | + | 0.986160i | \(0.553019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1323 | − | 1.24589i | −0.717880 | − | 0.0554414i | ||||
\(506\) | 2.03243 | + | 19.3373i | 0.0903524 | + | 0.859646i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.8814 | + | 8.40656i | 0.837729 | + | 0.372981i | ||||
\(509\) | 22.3109 | − | 24.7788i | 0.988914 | − | 1.09830i | −0.00624107 | − | 0.999981i | \(-0.501987\pi\) |
0.995155 | − | 0.0983195i | \(-0.0313467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.39754 | − | 7.10519i | −0.283011 | − | 0.314315i | ||||
\(512\) | −2.90473 | − | 8.93985i | −0.128372 | − | 0.395089i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.47129 | − | 4.52816i | 0.0648958 | − | 0.199729i | ||||
\(515\) | 37.3817 | − | 13.2992i | 1.64723 | − | 0.586031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6097 | − | 4.72373i | −0.466613 | − | 0.207750i | ||||
\(518\) | 0.940290 | + | 1.62863i | 0.0413140 | + | 0.0715579i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.7295 | + | 3.81721i | −0.470522 | + | 0.167396i | ||||
\(521\) | 18.9750 | + | 13.7861i | 0.831308 | + | 0.603981i | 0.919929 | − | 0.392085i | \(-0.128246\pi\) |
−0.0886210 | + | 0.996065i | \(0.528246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.59815 | − | 20.3070i | 0.288517 | − | 0.887963i | −0.696806 | − | 0.717260i | \(-0.745396\pi\) |
0.985322 | − | 0.170703i | \(-0.0546040\pi\) | |||||||
\(524\) | −9.62597 | + | 16.6727i | −0.420512 | + | 0.728349i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.709968 | − | 1.22970i | −0.0309561 | − | 0.0536175i | ||||
\(527\) | −17.7337 | + | 3.76941i | −0.772492 | + | 0.164198i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.8863 | − | 22.2108i | 2.16897 | − | 0.965688i | ||||
\(530\) | −7.72558 | + | 4.74981i | −0.335578 | + | 0.206318i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.30799 | 0.273486 | ||||||||
\(533\) | −1.10687 | − | 10.5311i | −0.0479437 | − | 0.456154i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.15053 | − | 2.40308i | −0.0497419 | − | 0.103894i | ||||
\(536\) | −9.44143 | + | 2.00684i | −0.407808 | + | 0.0866822i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.59042 | + | 0.763167i | 0.154794 | + | 0.0329025i | ||||
\(539\) | 5.44763 | − | 16.7661i | 0.234646 | − | 0.722167i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.3808 | + | 31.9488i | 0.446305 | + | 1.37358i | 0.881047 | + | 0.473029i | \(0.156840\pi\) |
−0.434742 | + | 0.900555i | \(0.643160\pi\) | |||||||
\(542\) | −1.81697 | − | 17.2873i | −0.0780455 | − | 0.742554i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 36.5300 | + | 16.2642i | 1.56621 | + | 0.697322i | ||||
\(545\) | −3.13158 | + | 2.98049i | −0.134142 | + | 0.127670i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.3937 | − | 13.5321i | 1.29954 | − | 0.578593i | 0.363864 | − | 0.931452i | \(-0.381457\pi\) |
0.935677 | + | 0.352859i | \(0.114790\pi\) | |||||||
\(548\) | −3.83331 | + | 11.7977i | −0.163751 | + | 0.503974i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.82621 | − | 7.78053i | −0.333711 | − | 0.331763i | ||||
\(551\) | −2.17754 | + | 3.77161i | −0.0927664 | + | 0.160676i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.421560 | + | 4.01087i | −0.0179265 | + | 0.170560i | ||||
\(554\) | 0.622691 | − | 5.92451i | 0.0264556 | − | 0.251708i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.80608 | + | 26.6980i | 0.119004 | + | 1.13225i | ||||
\(557\) | −29.7702 | −1.26140 | −0.630702 | − | 0.776025i | \(-0.717233\pi\) | ||||
−0.630702 | + | 0.776025i | \(0.717233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.35937 | − | 16.4945i | −0.226677 | − | 0.697641i | ||||
\(560\) | 1.73551 | + | 0.511321i | 0.0733388 | + | 0.0216072i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.805148 | + | 0.894208i | −0.0339631 | + | 0.0377199i | ||||
\(563\) | −15.8795 | + | 17.6360i | −0.669243 | + | 0.743270i | −0.978168 | − | 0.207817i | \(-0.933364\pi\) |
0.308925 | + | 0.951086i | \(0.400031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.2372 | − | 5.07848i | −0.725176 | − | 0.213653i | ||||
\(566\) | 1.82970 | + | 5.63124i | 0.0769080 | + | 0.236699i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.404108 | −0.0169560 | ||||||||
\(569\) | 3.04989 | + | 29.0177i | 0.127858 | + | 1.21649i | 0.850767 | + | 0.525543i | \(0.176138\pi\) |
−0.722909 | + | 0.690943i | \(0.757195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.278873 | − | 2.65330i | 0.0116705 | − | 0.111037i | −0.987136 | − | 0.159884i | \(-0.948888\pi\) |
0.998806 | + | 0.0488470i | \(0.0155547\pi\) | |||||||
\(572\) | −0.838316 | + | 7.97605i | −0.0350518 | + | 0.333495i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.97029 | − | 3.41264i | 0.0822382 | − | 0.142441i | ||||
\(575\) | −19.8822 | + | 39.3050i | −0.829145 | + | 1.63913i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1294 | + | 31.1750i | −0.421692 | + | 1.29783i | 0.484435 | + | 0.874827i | \(0.339025\pi\) |
−0.906127 | + | 0.423007i | \(0.860975\pi\) | |||||||
\(578\) | −20.5836 | + | 9.16441i | −0.856165 | + | 0.381189i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.14485 | + | 2.04136i | −0.0890599 | + | 0.0847627i | ||||
\(581\) | 2.87435 | + | 1.27974i | 0.119248 | + | 0.0530927i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.60888 | + | 15.3075i | 0.0666330 | + | 0.633971i | ||||
\(584\) | −8.07935 | − | 24.8657i | −0.334326 | − | 1.02895i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.47698 | + | 7.62337i | −0.102323 | + | 0.314919i | ||||
\(587\) | −4.17376 | − | 0.887160i | −0.172270 | − | 0.0366170i | 0.120969 | − | 0.992656i | \(-0.461400\pi\) |
−0.293239 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.1258 | + | 2.57742i | −0.499635 | + | 0.106201i | ||||
\(590\) | 3.53338 | + | 7.38008i | 0.145467 | + | 0.303833i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.229489 | − | 2.18344i | −0.00943194 | − | 0.0897389i | ||||
\(593\) | 7.81313 | 0.320847 | 0.160423 | − | 0.987048i | \(-0.448714\pi\) | ||||
0.160423 | + | 0.987048i | \(0.448714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.3890 | + | 7.61695i | −0.507900 | + | 0.312265i | ||||
\(596\) | −7.87811 | + | 3.50756i | −0.322700 | + | 0.143675i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.8383 | + | 2.72886i | −0.524995 | + | 0.111591i | ||||
\(599\) | −22.2102 | − | 38.4691i | −0.907483 | − | 1.57181i | −0.817550 | − | 0.575858i | \(-0.804668\pi\) |
−0.0899331 | − | 0.995948i | \(-0.528665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98356 | + | 13.8279i | −0.325656 | + | 0.564053i | −0.981645 | − | 0.190718i | \(-0.938919\pi\) |
0.655989 | + | 0.754771i | \(0.272252\pi\) | |||||||
\(602\) | 1.99440 | − | 6.13814i | 0.0812858 | − | 0.250172i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.8181 | − | 7.85982i | −0.440183 | − | 0.319811i | ||||
\(605\) | 5.52757 | − | 1.96652i | 0.224728 | − | 0.0799506i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.79724 | − | 10.0411i | −0.235303 | − | 0.407557i | 0.724058 | − | 0.689739i | \(-0.242275\pi\) |
−0.959361 | + | 0.282183i | \(0.908942\pi\) | |||||||
\(608\) | 24.9782 | + | 11.1210i | 1.01300 | + | 0.451016i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0506 | + | 6.42178i | −0.730845 | + | 0.260010i | ||||
\(611\) | 2.42257 | − | 7.45589i | 0.0980065 | − | 0.301633i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0509077 | + | 0.156678i | 0.00205614 | + | 0.00632816i | 0.952079 | − | 0.305851i | \(-0.0989410\pi\) |
−0.950023 | + | 0.312179i | \(0.898941\pi\) | |||||||
\(614\) | −1.53191 | − | 1.70136i | −0.0618229 | − | 0.0686613i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.81287 | + | 5.34523i | −0.193916 | + | 0.215365i | ||||
\(617\) | −32.8935 | − | 14.6451i | −1.32424 | − | 0.589591i | −0.381888 | − | 0.924208i | \(-0.624726\pi\) |
−0.942354 | + | 0.334618i | \(0.891393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.99377 | + | 47.5125i | 0.200716 | + | 1.90969i | 0.378469 | + | 0.925614i | \(0.376451\pi\) |
−0.177753 | + | 0.984075i | \(0.556883\pi\) | |||||||
\(620\) | −8.40342 | − | 0.648990i | −0.337489 | − | 0.0260641i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.64512 | + | 6.28105i | 0.346638 | + | 0.251847i | ||||
\(623\) | −10.9844 | − | 12.1995i | −0.440082 | − | 0.488761i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.34086 | − | 24.4228i | −0.213634 | − | 0.976914i | ||||
\(626\) | −2.11795 | − | 3.66840i | −0.0846503 | − | 0.146619i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.6930 | − | 11.8845i | 1.06517 | − | 0.474242i | ||||
\(629\) | 14.2772 | + | 10.3730i | 0.569269 | + | 0.413598i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6855 | + | 9.21654i | −0.505001 | + | 0.366905i | −0.810924 | − | 0.585152i | \(-0.801035\pi\) |
0.305923 | + | 0.952056i | \(0.401035\pi\) | |||||||
\(632\) | −5.51425 | + | 9.55096i | −0.219345 | + | 0.379917i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.31899 | − | 2.57550i | 0.0920989 | − | 0.102286i | ||||
\(635\) | −32.2976 | + | 4.30015i | −1.28169 | + | 0.170646i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.6399 | + | 2.47415i | 0.461191 | + | 0.0980293i | ||||
\(638\) | −0.636737 | − | 1.95967i | −0.0252087 | − | 0.0775843i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.3572 | + | 13.9290i | 0.646576 | + | 0.550594i | ||||
\(641\) | −36.2559 | − | 7.70643i | −1.43202 | − | 0.304386i | −0.574361 | − | 0.818602i | \(-0.694749\pi\) |
−0.857660 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.29095 | + | 5.70009i | 0.129782 | + | 0.224790i | 0.923592 | − | 0.383376i | \(-0.125239\pi\) |
−0.793810 | + | 0.608166i | \(0.791905\pi\) | |||||||
\(644\) | 10.8824 | + | 4.84516i | 0.428827 | + | 0.190926i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.1728 | + | 9.87197i | −0.872377 | + | 0.388407i | ||||
\(647\) | −2.22736 | − | 1.61827i | −0.0875666 | − | 0.0636209i | 0.543141 | − | 0.839642i | \(-0.317235\pi\) |
−0.630707 | + | 0.776021i | \(0.717235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8871 | 0.545115 | ||||||||
\(650\) | 4.67108 | − | 5.80295i | 0.183215 | − | 0.227611i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.4624 | + | 3.07409i | −0.566393 | + | 0.120391i | ||||
\(653\) | 0.676372 | − | 6.43525i | 0.0264685 | − | 0.251831i | −0.973284 | − | 0.229603i | \(-0.926257\pi\) |
0.999753 | − | 0.0222280i | \(-0.00707598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.838865 | − | 30.3381i | −0.0327772 | − | 1.18541i | ||||
\(656\) | −3.72180 | + | 2.70405i | −0.145312 | + | 0.105575i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.36020 | − | 1.71479i | 0.0920103 | − | 0.0668494i | ||||
\(659\) | 9.56798 | + | 2.03374i | 0.372716 | + | 0.0792231i | 0.390461 | − | 0.920619i | \(-0.372316\pi\) |
−0.0177456 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.325445 | − | 0.0691755i | 0.0126583 | − | 0.00269062i | −0.201578 | − | 0.979472i | \(-0.564607\pi\) |
0.214237 | + | 0.976782i | \(0.431274\pi\) | |||||||
\(662\) | −2.96039 | + | 3.28785i | −0.115059 | + | 0.127786i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.75722 | + | 6.39404i | 0.223423 | + | 0.248137i | ||||
\(665\) | −8.47125 | + | 5.20826i | −0.328501 | + | 0.201967i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.65361 | + | 4.83413i | −0.257629 | + | 0.187178i | ||||
\(668\) | 10.9673 | − | 18.9958i | 0.424336 | − | 0.734971i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.57353 | − | 4.35285i | 0.176691 | − | 0.168165i | ||||
\(671\) | −3.39890 | + | 32.3383i | −0.131213 | + | 1.24841i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.12557 | − | 4.58191i | −0.159029 | − | 0.176620i | 0.658365 | − | 0.752699i | \(-0.271249\pi\) |
−0.817394 | + | 0.576079i | \(0.804582\pi\) | |||||||
\(674\) | −3.74792 | −0.144364 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0257 | 0.500990 | ||||||||
\(677\) | 9.77758 | + | 10.8591i | 0.375783 | + | 0.417349i | 0.901137 | − | 0.433535i | \(-0.142734\pi\) |
−0.525354 | + | 0.850884i | \(0.676067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.193571 | − | 1.84170i | 0.00742857 | − | 0.0706781i | ||||
\(680\) | −39.4219 | + | 5.24869i | −1.51176 | + | 0.201278i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.93263 | − | 5.07946i | 0.112296 | − | 0.194503i | ||||
\(683\) | −16.7839 | + | 12.1942i | −0.642217 | + | 0.466598i | −0.860611 | − | 0.509263i | \(-0.829918\pi\) |
0.218394 | + | 0.975861i | \(0.429918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.59300 | − | 19.0086i | −0.175490 | − | 0.726282i | ||||
\(686\) | 6.36845 | + | 7.07288i | 0.243148 | + | 0.270044i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.04170 | + | 5.59938i | −0.192213 | + | 0.213474i | ||||
\(689\) | −10.1628 | + | 2.16018i | −0.387173 | + | 0.0822961i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.5937 | − | 5.44011i | −0.973630 | − | 0.206951i | −0.306482 | − | 0.951876i | \(-0.599152\pi\) |
−0.667148 | + | 0.744925i | \(0.732485\pi\) | |||||||
\(692\) | 17.0671 | − | 12.4000i | 0.648793 | − | 0.471376i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.15055 | + | 4.46863i | −0.233472 | + | 0.169627i | ||||
\(695\) | −25.8119 | − | 33.5370i | −0.979101 | − | 1.27213i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.86534 | − | 36.7762i | 0.146410 | − | 1.39300i | ||||
\(698\) | −10.6775 | + | 2.26958i | −0.404151 | + | 0.0859049i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.52551 | + | 1.76899i | −0.246641 | + | 0.0668616i | ||||
\(701\) | 24.6481 | 0.930945 | 0.465472 | − | 0.885062i | \(-0.345884\pi\) | ||||
0.465472 | + | 0.885062i | \(0.345884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.76234 | + | 7.09275i | 0.368193 | + | 0.267508i | ||||
\(704\) | −7.32982 | + | 3.26345i | −0.276253 | + | 0.122996i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.6606 | + | 7.86301i | 0.664666 | + | 0.295928i | ||||
\(707\) | −3.44915 | − | 5.97411i | −0.129719 | − | 0.224679i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8700 | + | 5.71140i | 1.00912 | + | 0.214496i | 0.682678 | − | 0.730719i | \(-0.260815\pi\) |
0.326447 | + | 0.945216i | \(0.394149\pi\) | |||||||
\(710\) | 0.225181 | − | 0.138445i | 0.00845091 | − | 0.00519575i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8721 | − | 42.6938i | −0.519878 | − | 1.60002i | ||||
\(713\) | −22.8989 | − | 4.86730i | −0.857569 | − | 0.182282i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.45969 | − | 11.4035i | −0.204181 | − | 0.426467i | ||||
\(716\) | 25.3169 | − | 28.1173i | 0.946137 | − | 1.05079i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.83774 | + | 13.5754i | −0.292502 | + | 0.506628i | ||||
\(719\) | −29.6588 | + | 21.5483i | −1.10609 | + | 0.803618i | −0.982043 | − | 0.188659i | \(-0.939586\pi\) |
−0.124042 | + | 0.992277i | \(0.539586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6851 | + | 9.94284i | 0.509661 | + | 0.370291i | ||||
\(722\) | −1.92415 | + | 0.856685i | −0.0716093 | + | 0.0318825i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0514 | − | 24.3378i | −0.522218 | − | 0.904508i | ||||
\(725\) | 1.19493 | − | 4.51233i | 0.0443786 | − | 0.167584i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.36275 | + | 7.06654i | 0.235981 | + | 0.262084i | 0.849491 | − | 0.527604i | \(-0.176909\pi\) |
−0.613509 | + | 0.789687i | \(0.710243\pi\) | |||||||
\(728\) | −3.92800 | − | 2.85386i | −0.145581 | − | 0.105771i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0209 | + | 11.0880i | 0.481925 | + | 0.410385i | ||||
\(731\) | −6.33080 | − | 60.2335i | −0.234153 | − | 2.22782i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.20387 | + | 4.09783i | 0.339953 | + | 0.151357i | 0.569611 | − | 0.821915i | \(-0.307094\pi\) |
−0.229658 | + | 0.973271i | \(0.573761\pi\) | |||||||
\(734\) | −14.6904 | + | 16.3154i | −0.542234 | + | 0.602211i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.5497 | + | 38.3714i | 1.27352 | + | 1.41439i | ||||
\(737\) | −3.31138 | − | 10.1914i | −0.121976 | − | 0.375404i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.85917 | + | 18.0327i | −0.215533 | + | 0.663342i | 0.783582 | + | 0.621288i | \(0.213390\pi\) |
−0.999115 | + | 0.0420544i | \(0.986610\pi\) | |||||||
\(740\) | 5.00394 | + | 6.50153i | 0.183948 | + | 0.239001i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.53215 | − | 1.57261i | −0.129669 | − | 0.0577325i | ||||
\(743\) | 10.9750 | + | 19.0092i | 0.402633 | + | 0.697381i | 0.994043 | − | 0.108990i | \(-0.0347617\pi\) |
−0.591410 | + | 0.806371i | \(0.701428\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.68376 | − | 11.2151i | 0.281511 | − | 0.410888i | ||||
\(746\) | 7.04928 | + | 5.12160i | 0.258092 | + | 0.187515i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.65462 | + | 26.6362i | −0.316444 | + | 0.973915i | ||||
\(749\) | 0.567947 | − | 0.983714i | 0.0207523 | − | 0.0359441i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.43136 | − | 11.1394i | −0.234684 | − | 0.406484i | 0.724497 | − | 0.689278i | \(-0.242072\pi\) |
−0.959181 | + | 0.282794i | \(0.908739\pi\) | |||||||
\(752\) | −3.33144 | + | 0.708119i | −0.121485 | + | 0.0258225i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.27066 | − | 0.565734i | 0.0462747 | − | 0.0206028i | ||||
\(755\) | 21.0176 | + | 1.62317i | 0.764908 | + | 0.0590733i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.01935 | −0.109740 | −0.0548701 | − | 0.998494i | \(-0.517474\pi\) | ||||
−0.0548701 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(758\) | −0.286076 | − | 2.72183i | −0.0103907 | − | 0.0988613i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −26.9555 | + | 3.58890i | −0.977780 | + | 0.130183i | ||||
\(761\) | 40.9454 | − | 8.70321i | 1.48427 | − | 0.315491i | 0.606696 | − | 0.794934i | \(-0.292495\pi\) |
0.877573 | + | 0.479443i | \(0.159161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.80287 | − | 0.383212i | −0.0652682 | − | 0.0138732i | ||||
\(764\) | −5.26338 | + | 16.1990i | −0.190422 | + | 0.586060i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.20666 | + | 3.71373i | 0.0435985 | + | 0.134183i | ||||
\(767\) | 0.979864 | + | 9.32278i | 0.0353808 | + | 0.336626i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.9240 | + | 19.1110i | 1.54788 | + | 0.689160i | 0.990040 | − | 0.140789i | \(-0.0449640\pi\) |
0.557839 | + | 0.829949i | \(0.311631\pi\) | |||||||
\(770\) | 0.850633 | − | 4.62739i | 0.0306547 | − | 0.166760i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.8864 | − | 14.6419i | 1.18361 | − | 0.526975i | ||||
\(773\) | −8.38597 | + | 25.8093i | −0.301622 | + | 0.928298i | 0.679294 | + | 0.733866i | \(0.262286\pi\) |
−0.980916 | + | 0.194431i | \(0.937714\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.8211 | − | 6.06681i | 0.424627 | − | 0.217926i | ||||
\(776\) | 2.53202 | − | 4.38559i | 0.0908943 | − | 0.157434i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.46331 | + | 23.4369i | −0.0883141 | + | 0.840252i | ||||
\(779\) | 2.64301 | − | 25.1465i | 0.0946956 | − | 0.900968i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0468948 | − | 0.446175i | −0.00167803 | − | 0.0159654i | ||||
\(782\) | −45.8346 | −1.63904 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.59758 | − | 4.91685i | −0.0570565 | − | 0.175602i | ||||
\(785\) | −26.0345 | + | 37.9994i | −0.929211 | + | 1.35626i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.95642 | + | 6.61528i | −0.212323 | + | 0.235809i | −0.839894 | − | 0.542751i | \(-0.817383\pi\) |
0.627570 | + | 0.778560i | \(0.284049\pi\) | |||||||
\(788\) | 1.61453 | − | 1.79312i | 0.0575152 | − | 0.0638771i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.199395 | − | 7.21124i | −0.00709414 | − | 0.256565i | ||||
\(791\) | −2.36744 | − | 7.28623i | −0.0841765 | − | 0.259069i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.9495 | −0.779449 | ||||||||
\(794\) | 0.508254 | + | 4.83572i | 0.0180373 | + | 0.171613i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.966507 | + | 9.19570i | −0.0342569 | + | 0.325933i | ||||
\(797\) | 3.95641 | − | 37.6427i | 0.140143 | − | 1.33337i | −0.667900 | − | 0.744251i | \(-0.732807\pi\) |
0.808043 | − | 0.589123i | \(-0.200527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6885 | − | 23.7091i | 0.484264 | − | 0.838769i | ||||
\(800\) | −28.9582 | − | 4.49968i | −1.02383 | − | 0.159088i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.22368 | + | 12.9992i | −0.149143 | + | 0.459016i | ||||
\(803\) | 26.5166 | − | 11.8059i | 0.935750 | − | 0.416623i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.6148 | + | 2.47841i | −0.656087 | + | 0.0873525i | ||||
\(806\) | 3.61691 | + | 1.61035i | 0.127400 | + | 0.0567223i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.97183 | − | 18.7607i | −0.0693686 | − | 0.659998i | ||||
\(809\) | −5.78411 | − | 17.8016i | −0.203358 | − | 0.625873i | −0.999777 | − | 0.0211267i | \(-0.993275\pi\) |
0.796418 | − | 0.604746i | \(-0.206725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.0270 | − | 40.0931i | 0.457441 | − | 1.40786i | −0.410804 | − | 0.911723i | \(-0.634752\pi\) |
0.868245 | − | 0.496135i | \(-0.165248\pi\) | |||||||
\(812\) | −1.23480 | − | 0.262464i | −0.0433329 | − | 0.00921070i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.58446 | + | 1.18701i | −0.195735 | + | 0.0416048i | ||||
\(815\) | 16.8840 | − | 16.0694i | 0.591422 | − | 0.562886i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.32882 | − | 41.1859i | −0.151446 | − | 1.44091i | ||||
\(818\) | 29.3086 | 1.02475 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.55552 | − | 15.8922i | 0.228929 | − | 0.554979i | ||||
\(821\) | 26.4525 | − | 11.7774i | 0.923197 | − | 0.411034i | 0.110603 | − | 0.993865i | \(-0.464722\pi\) |
0.812593 | + | 0.582831i | \(0.198055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.9474 | − | 2.53950i | 0.416461 | − | 0.0885215i | 0.00508458 | − | 0.999987i | \(-0.498382\pi\) |
0.411376 | + | 0.911466i | \(0.365048\pi\) | |||||||
\(824\) | 23.1288 | + | 40.0603i | 0.805731 | + | 1.39557i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.74422 | + | 3.02107i | −0.0606890 | + | 0.105116i | ||||
\(827\) | −5.83473 | + | 17.9575i | −0.202894 | + | 0.624442i | 0.796900 | + | 0.604112i | \(0.206472\pi\) |
−0.999793 | + | 0.0203307i | \(0.993528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.2118 | − | 7.41933i | −0.354672 | − | 0.257684i | 0.396155 | − | 0.918184i | \(-0.370344\pi\) |
−0.750826 | + | 0.660500i | \(0.770344\pi\) | |||||||
\(830\) | −5.39866 | − | 1.59057i | −0.187390 | − | 0.0552093i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.70804 | − | 4.69045i | −0.0938842 | − | 0.162612i | ||||
\(833\) | 37.9637 | + | 16.9025i | 1.31537 | + | 0.585638i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.955752 | + | 34.5655i | 0.0330752 | + | 1.19619i | ||||
\(836\) | −5.91778 | + | 18.2131i | −0.204671 | + | 0.629912i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.24568 | + | 3.83380i | 0.0430312 | + | 0.132436i | ||||
\(839\) | 29.4416 | + | 32.6982i | 1.01644 | + | 1.12887i | 0.991622 | + | 0.129177i | \(0.0412335\pi\) |
0.0248166 | + | 0.999692i | \(0.492100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.8216 | + | 20.9035i | −0.649021 | + | 0.720811i | ||||
\(842\) | 18.8748 | + | 8.40362i | 0.650470 | + | 0.289608i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.18306 | + | 11.2561i | 0.0407227 | + | 0.387450i | ||||
\(845\) | −17.4928 | + | 10.7548i | −0.601770 | + | 0.369977i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.02360 | + | 1.47023i | 0.0695317 | + | 0.0505177i | ||||
\(848\) | 3.02034 | + | 3.35442i | 0.103719 | + | 0.115191i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.1689 | − | 16.4304i | 0.691788 | − | 0.563560i | ||||
\(851\) | 11.3938 | + | 19.7347i | 0.390575 | + | 0.676496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.7951 | + | 19.4988i | −1.49952 | + | 0.667627i | −0.982143 | − | 0.188133i | \(-0.939756\pi\) |
−0.517372 | + | 0.855761i | \(0.673090\pi\) | |||||||
\(854\) | −6.60816 | − | 4.80111i | −0.226127 | − | 0.164291i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.51297 | − | 1.82578i | 0.0858916 | − | 0.0624039i | ||||
\(857\) | 12.6888 | − | 21.9776i | 0.433440 | − | 0.750741i | −0.563727 | − | 0.825961i | \(-0.690633\pi\) |
0.997167 | + | 0.0752208i | \(0.0239662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.62539 | + | 6.24763i | −0.191936 | + | 0.213166i | −0.831430 | − | 0.555630i | \(-0.812477\pi\) |
0.639494 | + | 0.768796i | \(0.279144\pi\) | |||||||
\(860\) | 5.09056 | − | 27.6923i | 0.173587 | − | 0.944301i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.8336 | − | 5.49110i | −0.879897 | − | 0.187028i | ||||
\(863\) | 9.08240 | + | 27.9528i | 0.309168 | + | 0.951523i | 0.978089 | + | 0.208189i | \(0.0667568\pi\) |
−0.668920 | + | 0.743334i | \(0.733243\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.6819 | + | 30.7440i | −0.431197 | + | 1.04533i | ||||
\(866\) | 6.85227 | + | 1.45649i | 0.232850 | + | 0.0494937i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.79668 | − | 3.11194i | −0.0609833 | − | 0.105626i | ||||
\(869\) | −11.1851 | − | 4.97993i | −0.379429 | − | 0.168933i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.60812 | − | 2.94212i | 0.223908 | − | 0.0996901i | ||||
\(872\) | −4.07764 | − | 2.96258i | −0.138086 | − | 0.100326i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −31.3404 | −1.06011 | ||||||||
\(875\) | 7.30277 | − | 7.76350i | 0.246879 | − | 0.262454i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.7629 | − | 9.51464i | 1.51153 | − | 0.321287i | 0.623779 | − | 0.781601i | \(-0.285597\pi\) |
0.887756 | + | 0.460314i | \(0.152263\pi\) | |||||||
\(878\) | 0.572244 | − | 5.44454i | 0.0193123 | − | 0.183744i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.10449 | + | 4.53125i | −0.104652 | + | 0.152748i | ||||
\(881\) | −22.8783 | + | 16.6220i | −0.770789 | + | 0.560011i | −0.902200 | − | 0.431317i | \(-0.858049\pi\) |
0.131412 | + | 0.991328i | \(0.458049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.86953 | − | 7.17063i | 0.332136 | − | 0.241311i | −0.409200 | − | 0.912445i | \(-0.634192\pi\) |
0.741336 | + | 0.671134i | \(0.234192\pi\) | |||||||
\(884\) | −18.4923 | − | 3.93066i | −0.621963 | − | 0.132202i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.9178 | − | 4.02111i | 0.635556 | − | 0.135092i | ||||
\(887\) | −7.43378 | + | 8.25605i | −0.249602 | + | 0.277211i | −0.854906 | − | 0.518784i | \(-0.826385\pi\) |
0.605304 | + | 0.795995i | \(0.293052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.29502 | − | 10.3232i | −0.311745 | − | 0.346228i | ||||
\(890\) | 22.3566 | + | 19.0378i | 0.749396 | + | 0.638150i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.8296 | + | 7.86813i | −0.362600 | + | 0.263445i | ||||
\(893\) | 9.35979 | − | 16.2116i | 0.313214 | − | 0.542502i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7837 | + | 58.6629i | −0.360461 | + | 1.96088i | ||||
\(896\) | −0.957437 | + | 9.10941i | −0.0319857 | + | 0.304324i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.64317 | − | 4.04615i | −0.121574 | − | 0.135022i | ||||
\(899\) | 2.48088 | 0.0827421 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.2829 | −1.20876 | ||||||||
\(902\) | 8.00490 | + | 8.89034i | 0.266534 | + | 0.296016i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.18989 | − | 20.8355i | 0.0728348 | − | 0.692977i | ||||
\(905\) | 38.9650 | + | 21.0825i | 1.29524 | + | 0.700806i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6216 | − | 35.7176i | 0.684728 | − | 1.18598i | −0.288794 | − | 0.957391i | \(-0.593254\pi\) |
0.973522 | − | 0.228593i | \(-0.0734125\pi\) | |||||||
\(908\) | 27.0858 | − | 19.6790i | 0.898874 | − | 0.653070i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.16652 | + | 0.244548i | 0.104969 | + | 0.00810670i | ||||
\(911\) | 8.06488 | + | 8.95695i | 0.267201 | + | 0.296757i | 0.861782 | − | 0.507279i | \(-0.169349\pi\) |
−0.594581 | + | 0.804036i | \(0.702682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.39155 | + | 7.09853i | −0.211529 | + | 0.234927i | ||||
\(914\) | 26.6911 | − | 5.67336i | 0.882862 | − | 0.187658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.7924 | − | 4.63211i | −0.720040 | − | 0.153049i | ||||
\(917\) | 10.4681 | − | 7.60549i | 0.345686 | − | 0.251155i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.2727 | − | 22.7209i | 1.03159 | − | 0.749494i | 0.0629636 | − | 0.998016i | \(-0.479945\pi\) |
0.968626 | + | 0.248522i | \(0.0799448\pi\) | |||||||
\(920\) | −49.2597 | − | 14.5130i | −1.62404 | − | 0.478479i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.21439 | − | 11.5541i | 0.0399937 | − | 0.380514i | ||||
\(923\) | 0.296221 | − | 0.0629637i | 0.00975024 | − | 0.00207248i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0880 | − | 4.59961i | −0.397452 | − | 0.151234i | ||||
\(926\) | 18.9531 | 0.622839 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.42678 | − | 3.21625i | −0.145316 | − | 0.105578i | ||||
\(929\) | 41.6150 | − | 18.5282i | 1.36535 | − | 0.607891i | 0.412391 | − | 0.911007i | \(-0.364694\pi\) |
0.952954 | + | 0.303116i | \(0.0980269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.9585 | + | 11.5575i | 0.850756 | + | 0.378781i | ||||
\(932\) | −1.33850 | − | 2.31835i | −0.0438440 | − | 0.0759401i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.5149 | − | 4.14801i | −0.638546 | − | 0.135727i | ||||
\(935\) | −10.3698 | − | 42.9165i | −0.339129 | − | 1.40352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9573 | − | 33.7230i | −0.357958 | − | 1.10168i | −0.954274 | − | 0.298932i | \(-0.903370\pi\) |
0.596316 | − | 0.802750i | \(-0.296630\pi\) | |||||||
\(938\) | 2.63300 | + | 0.559662i | 0.0859705 | + | 0.0182736i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.21925 | − | 8.77442i | 0.300699 | − | 0.286190i | ||||
\(941\) | −13.4712 | + | 14.9612i | −0.439147 | + | 0.487723i | −0.921568 | − | 0.388217i | \(-0.873091\pi\) |
0.482420 | + | 0.875940i | \(0.339758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.8747 | − | 41.3521i | 0.777466 | − | 1.34661i | ||||
\(944\) | 3.29476 | − | 2.39378i | 0.107235 | − | 0.0779109i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.8516 | + | 11.5169i | 0.515380 | + | 0.374446i | ||||
\(947\) | 22.1124 | − | 9.84509i | 0.718558 | − | 0.319923i | −0.0146824 | − | 0.999892i | \(-0.504674\pi\) |
0.733240 | + | 0.679970i | \(0.238007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.79667 | + | 16.9683i | 0.318013 | + | 0.550815i | ||||
\(950\) | 13.7909 | − | 11.2347i | 0.447437 | − | 0.364501i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.3453 | − | 12.6003i | −0.367704 | − | 0.408377i | ||||
\(953\) | 14.5798 | + | 10.5929i | 0.472287 | + | 0.343137i | 0.798332 | − | 0.602218i | \(-0.205716\pi\) |
−0.326045 | + | 0.945354i | \(0.605716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.30648 | − | 26.1001i | −0.204073 | − | 0.844578i | ||||
\(956\) | 0.212509 | + | 2.02188i | 0.00687302 | + | 0.0653924i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.70254 | − | 2.98416i | −0.216549 | − | 0.0964139i | ||||
\(959\) | 5.57875 | − | 6.19583i | 0.180147 | − | 0.200074i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0178 | − | 17.7895i | −0.516703 | − | 0.573856i | ||||
\(962\) | −1.19091 | − | 3.66526i | −0.0383966 | − | 0.118173i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.80103 | + | 14.7760i | −0.154631 | + | 0.475904i | ||||
\(965\) | −32.0751 | + | 46.8162i | −1.03253 | + | 1.50707i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.2214 | − | 14.7911i | −1.06833 | − | 0.475651i | −0.204204 | − | 0.978928i | \(-0.565461\pi\) |
−0.864125 | + | 0.503277i | \(0.832127\pi\) | |||||||
\(968\) | 3.42002 | + | 5.92365i | 0.109924 | + | 0.190393i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0915576 | + | 3.31124i | 0.00293974 | + | 0.106318i | ||||
\(971\) | −46.1160 | − | 33.5052i | −1.47993 | − | 1.07523i | −0.977578 | − | 0.210572i | \(-0.932467\pi\) |
−0.502354 | − | 0.864662i | \(-0.667533\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.57547 | − | 17.1595i | 0.178741 | − | 0.550109i | ||||
\(974\) | 15.0373 | − | 26.0453i | 0.481825 | − | 0.834545i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.76792 | + | 8.25828i | 0.152617 | + | 0.264341i | ||||
\(977\) | −15.1510 | + | 3.22044i | −0.484722 | + | 0.103031i | −0.443790 | − | 0.896131i | \(-0.646366\pi\) |
−0.0409326 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.5284 | − | 20.2706i | 1.45509 | − | 0.647850i | ||||
\(980\) | 14.7088 | + | 12.5254i | 0.469857 | + | 0.400108i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.42689 | 0.237001 | ||||||||
\(983\) | −1.64381 | − | 15.6398i | −0.0524293 | − | 0.498831i | −0.988953 | − | 0.148228i | \(-0.952643\pi\) |
0.936524 | − | 0.350604i | \(-0.114024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.687709 | + | 3.74109i | −0.0219122 | + | 0.119201i | ||||
\(986\) | 4.75111 | − | 1.00988i | 0.151306 | − | 0.0321611i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.6445 | − | 2.68767i | −0.402275 | − | 0.0855063i | ||||
\(989\) | 24.1669 | − | 74.3780i | 0.768462 | − | 2.36508i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.23054 | + | 19.1756i | 0.197920 | + | 0.609134i | 0.999930 | + | 0.0118242i | \(0.00376384\pi\) |
−0.802010 | + | 0.597310i | \(0.796236\pi\) | |||||||
\(992\) | −1.62808 | − | 15.4901i | −0.0516915 | − | 0.491811i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.102953 | + | 0.0458378i | 0.00326548 | + | 0.00145389i | ||||
\(995\) | −6.29456 | − | 13.1473i | −0.199551 | − | 0.416796i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.2806 | + | 16.5984i | −1.18069 | + | 0.525677i | −0.900749 | − | 0.434341i | \(-0.856981\pi\) |
−0.279940 | + | 0.960017i | \(0.590315\pi\) | |||||||
\(998\) | −2.06306 | + | 6.34944i | −0.0653050 | + | 0.200988i | ||||
\(999\) | 0 | 0 |
(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 | 675.2.r.a.46.12 | 224 | ||
3.2 | odd | 2 | 225.2.q.a.196.17 | yes | 224 | ||
9.4 | even | 3 | inner | 675.2.r.a.496.17 | 224 | ||
9.5 | odd | 6 | 225.2.q.a.121.12 | yes | 224 | ||
25.6 | even | 5 | inner | 675.2.r.a.181.17 | 224 | ||
75.56 | odd | 10 | 225.2.q.a.106.12 | yes | 224 | ||
225.31 | even | 15 | inner | 675.2.r.a.631.12 | 224 | ||
225.131 | odd | 30 | 225.2.q.a.31.17 | ✓ | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.q.a.31.17 | ✓ | 224 | 225.131 | odd | 30 | ||
225.2.q.a.106.12 | yes | 224 | 75.56 | odd | 10 | ||
225.2.q.a.121.12 | yes | 224 | 9.5 | odd | 6 | ||
225.2.q.a.196.17 | yes | 224 | 3.2 | odd | 2 | ||
675.2.r.a.46.12 | 224 | 1.1 | even | 1 | trivial | ||
675.2.r.a.181.17 | 224 | 25.6 | even | 5 | inner | ||
675.2.r.a.496.17 | 224 | 9.4 | even | 3 | inner | ||
675.2.r.a.631.12 | 224 | 225.31 | even | 15 | inner |