Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), degree \(2\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.15 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.15 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.08861 | − | 1.34719i | 0.628511 | − | 0.777801i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.539236 | + | 2.17007i | 0.241153 | + | 0.970487i | ||||
\(6\) | −0.182842 | − | 1.72237i | −0.0746447 | − | 0.703156i | ||||
\(7\) | 2.86820 | + | 2.86820i | 1.08408 | + | 1.08408i | 0.996125 | + | 0.0879519i | \(0.0280322\pi\) |
0.0879519 | + | 0.996125i | \(0.471968\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −0.629843 | − | 2.93314i | −0.209948 | − | 0.977713i | ||||
\(10\) | 1.91577 | + | 1.15318i | 0.605820 | + | 0.364667i | ||||
\(11\) | 4.60223i | 1.38763i | 0.720156 | + | 0.693813i | \(0.244070\pi\) | ||||
−0.720156 | + | 0.693813i | \(0.755930\pi\) | |||||||
\(12\) | −1.34719 | − | 1.08861i | −0.388900 | − | 0.314256i | ||||
\(13\) | 1.32932 | − | 1.32932i | 0.368687 | − | 0.368687i | −0.498311 | − | 0.866998i | \(-0.666046\pi\) |
0.866998 | + | 0.498311i | \(0.166046\pi\) | |||||||
\(14\) | 4.05624 | 1.08408 | ||||||||
\(15\) | 3.51052 | + | 1.63592i | 0.906413 | + | 0.422393i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.40435 | − | 3.40435i | 0.825677 | − | 0.825677i | −0.161239 | − | 0.986915i | \(-0.551549\pi\) |
0.986915 | + | 0.161239i | \(0.0515489\pi\) | |||||||
\(18\) | −2.51941 | − | 1.62868i | −0.593830 | − | 0.383883i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 2.17007 | − | 0.539236i | 0.485243 | − | 0.120577i | ||||
\(21\) | 6.98636 | − | 0.741650i | 1.52455 | − | 0.161841i | ||||
\(22\) | 3.25427 | + | 3.25427i | 0.693813 | + | 0.693813i | ||||
\(23\) | −2.00597 | − | 2.00597i | −0.418274 | − | 0.418274i | 0.466334 | − | 0.884609i | \(-0.345574\pi\) |
−0.884609 | + | 0.466334i | \(0.845574\pi\) | |||||||
\(24\) | −1.72237 | + | 0.182842i | −0.351578 | + | 0.0373224i | ||||
\(25\) | −4.41845 | + | 2.34036i | −0.883690 | + | 0.468073i | ||||
\(26\) | − | 1.87994i | − | 0.368687i | ||||||
\(27\) | −4.63715 | − | 2.34453i | −0.892420 | − | 0.451206i | ||||
\(28\) | 2.86820 | − | 2.86820i | 0.542038 | − | 0.542038i | ||||
\(29\) | −6.21092 | −1.15334 | −0.576670 | − | 0.816978i | \(-0.695648\pi\) | ||||
−0.576670 | + | 0.816978i | \(0.695648\pi\) | |||||||
\(30\) | 3.63908 | − | 1.32554i | 0.664403 | − | 0.242010i | ||||
\(31\) | −3.91496 | −0.703148 | −0.351574 | − | 0.936160i | \(-0.614353\pi\) | ||||
−0.351574 | + | 0.936160i | \(0.614353\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 6.20008 | + | 5.01005i | 1.07930 | + | 0.872138i | ||||
\(34\) | − | 4.81448i | − | 0.825677i | ||||||
\(35\) | −4.67757 | + | 7.77084i | −0.790653 | + | 1.31351i | ||||
\(36\) | −2.93314 | + | 0.629843i | −0.488856 | + | 0.104974i | ||||
\(37\) | −4.28573 | − | 4.28573i | −0.704570 | − | 0.704570i | 0.260818 | − | 0.965388i | \(-0.416008\pi\) |
−0.965388 | + | 0.260818i | \(0.916008\pi\) | |||||||
\(38\) | −0.707107 | − | 0.707107i | −0.114708 | − | 0.114708i | ||||
\(39\) | −0.343732 | − | 3.23796i | −0.0550411 | − | 0.518489i | ||||
\(40\) | 1.15318 | − | 1.91577i | 0.182333 | − | 0.302910i | ||||
\(41\) | 1.74242i | 0.272120i | 0.990701 | + | 0.136060i | \(0.0434440\pi\) | ||||
−0.990701 | + | 0.136060i | \(0.956556\pi\) | |||||||
\(42\) | 4.41568 | − | 5.46453i | 0.681354 | − | 0.843195i | ||||
\(43\) | 8.19327 | − | 8.19327i | 1.24946 | − | 1.24946i | 0.293504 | − | 0.955958i | \(-0.405178\pi\) |
0.955958 | − | 0.293504i | \(-0.0948215\pi\) | |||||||
\(44\) | 4.60223 | 0.693813 | ||||||||
\(45\) | 6.02550 | − | 2.94846i | 0.898228 | − | 0.439530i | ||||
\(46\) | −2.83687 | −0.418274 | ||||||||
\(47\) | −5.22236 | + | 5.22236i | −0.761759 | + | 0.761759i | −0.976640 | − | 0.214881i | \(-0.931064\pi\) |
0.214881 | + | 0.976640i | \(0.431064\pi\) | |||||||
\(48\) | −1.08861 | + | 1.34719i | −0.157128 | + | 0.194450i | ||||
\(49\) | 9.45311i | 1.35044i | ||||||||
\(50\) | −1.46943 | + | 4.77920i | −0.207809 | + | 0.675881i | ||||
\(51\) | −0.880287 | − | 8.29233i | −0.123265 | − | 1.16116i | ||||
\(52\) | −1.32932 | − | 1.32932i | −0.184344 | − | 0.184344i | ||||
\(53\) | −4.96160 | − | 4.96160i | −0.681527 | − | 0.681527i | 0.278817 | − | 0.960344i | \(-0.410058\pi\) |
−0.960344 | + | 0.278817i | \(0.910058\pi\) | |||||||
\(54\) | −4.93680 | + | 1.62112i | −0.671813 | + | 0.220607i | ||||
\(55\) | −9.98719 | + | 2.48169i | −1.34667 | + | 0.334631i | ||||
\(56\) | − | 4.05624i | − | 0.542038i | ||||||
\(57\) | −1.34719 | − | 1.08861i | −0.178440 | − | 0.144190i | ||||
\(58\) | −4.39178 | + | 4.39178i | −0.576670 | + | 0.576670i | ||||
\(59\) | 5.08697 | 0.662268 | 0.331134 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331134 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(60\) | 1.63592 | − | 3.51052i | 0.211196 | − | 0.453207i | ||||
\(61\) | −0.446018 | −0.0571067 | −0.0285534 | − | 0.999592i | \(-0.509090\pi\) | ||||
−0.0285534 | + | 0.999592i | \(0.509090\pi\) | |||||||
\(62\) | −2.76830 | + | 2.76830i | −0.351574 | + | 0.351574i | ||||
\(63\) | 6.60631 | − | 10.2193i | 0.832316 | − | 1.28751i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 3.60154 | + | 2.16791i | 0.446716 | + | 0.268896i | ||||
\(66\) | 7.92676 | − | 0.841479i | 0.975717 | − | 0.103579i | ||||
\(67\) | 6.27966 | + | 6.27966i | 0.767183 | + | 0.767183i | 0.977610 | − | 0.210427i | \(-0.0674854\pi\) |
−0.210427 | + | 0.977610i | \(0.567485\pi\) | |||||||
\(68\) | −3.40435 | − | 3.40435i | −0.412838 | − | 0.412838i | ||||
\(69\) | −4.88616 | + | 0.518698i | −0.588224 | + | 0.0624440i | ||||
\(70\) | 2.18727 | + | 8.80235i | 0.261429 | + | 1.05208i | ||||
\(71\) | − | 15.5294i | − | 1.84300i | −0.388380 | − | 0.921499i | \(-0.626965\pi\) | ||
0.388380 | − | 0.921499i | \(-0.373035\pi\) | |||||||
\(72\) | −1.62868 | + | 2.51941i | −0.191941 | + | 0.296915i | ||||
\(73\) | −6.36719 | + | 6.36719i | −0.745223 | + | 0.745223i | −0.973578 | − | 0.228355i | \(-0.926665\pi\) |
0.228355 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(74\) | −6.06094 | −0.704570 | ||||||||
\(75\) | −1.65707 | + | 8.50024i | −0.191342 | + | 0.981523i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −13.2001 | + | 13.2001i | −1.50429 | + | 1.50429i | ||||
\(78\) | −2.53264 | − | 2.04653i | −0.286765 | − | 0.231724i | ||||
\(79\) | − | 10.4449i | − | 1.17514i | −0.809173 | − | 0.587571i | \(-0.800084\pi\) | ||
0.809173 | − | 0.587571i | \(-0.199916\pi\) | |||||||
\(80\) | −0.539236 | − | 2.17007i | −0.0602884 | − | 0.242622i | ||||
\(81\) | −8.20660 | + | 3.69483i | −0.911844 | + | 0.410537i | ||||
\(82\) | 1.23207 | + | 1.23207i | 0.136060 | + | 0.136060i | ||||
\(83\) | 3.87813 | + | 3.87813i | 0.425680 | + | 0.425680i | 0.887154 | − | 0.461474i | \(-0.152679\pi\) |
−0.461474 | + | 0.887154i | \(0.652679\pi\) | |||||||
\(84\) | −0.741650 | − | 6.98636i | −0.0809206 | − | 0.762275i | ||||
\(85\) | 9.22345 | + | 5.55195i | 1.00042 | + | 0.602194i | ||||
\(86\) | − | 11.5870i | − | 1.24946i | ||||||
\(87\) | −6.76129 | + | 8.36729i | −0.724886 | + | 0.897068i | ||||
\(88\) | 3.25427 | − | 3.25427i | 0.346906 | − | 0.346906i | ||||
\(89\) | 2.07373 | 0.219814 | 0.109907 | − | 0.993942i | \(-0.464945\pi\) | ||||
0.109907 | + | 0.993942i | \(0.464945\pi\) | |||||||
\(90\) | 2.17579 | − | 6.34554i | 0.229349 | − | 0.668879i | ||||
\(91\) | 7.62551 | 0.799370 | ||||||||
\(92\) | −2.00597 | + | 2.00597i | −0.209137 | + | 0.209137i | ||||
\(93\) | −4.26188 | + | 5.27420i | −0.441936 | + | 0.546909i | ||||
\(94\) | 7.38553i | 0.761759i | ||||||||
\(95\) | 2.17007 | − | 0.539236i | 0.222645 | − | 0.0553244i | ||||
\(96\) | 0.182842 | + | 1.72237i | 0.0186612 | + | 0.175789i | ||||
\(97\) | 12.5075 | + | 12.5075i | 1.26994 | + | 1.26994i | 0.946116 | + | 0.323828i | \(0.104970\pi\) |
0.323828 | + | 0.946116i | \(0.395030\pi\) | |||||||
\(98\) | 6.68436 | + | 6.68436i | 0.675222 | + | 0.675222i | ||||
\(99\) | 13.4990 | − | 2.89868i | 1.35670 | − | 0.291328i | ||||
\(100\) | 2.34036 | + | 4.41845i | 0.234036 | + | 0.441845i | ||||
\(101\) | − | 1.85435i | − | 0.184514i | −0.995735 | − | 0.0922571i | \(-0.970592\pi\) | ||
0.995735 | − | 0.0922571i | \(-0.0294082\pi\) | |||||||
\(102\) | −6.48602 | − | 5.24111i | −0.642212 | − | 0.518947i | ||||
\(103\) | −11.4600 | + | 11.4600i | −1.12919 | + | 1.12919i | −0.138882 | + | 0.990309i | \(0.544351\pi\) |
−0.990309 | + | 0.138882i | \(0.955649\pi\) | |||||||
\(104\) | −1.87994 | −0.184344 | ||||||||
\(105\) | 5.37673 | + | 14.7610i | 0.524715 | + | 1.44053i | ||||
\(106\) | −7.01675 | −0.681527 | ||||||||
\(107\) | 8.61306 | − | 8.61306i | 0.832656 | − | 0.832656i | −0.155223 | − | 0.987879i | \(-0.549610\pi\) |
0.987879 | + | 0.155223i | \(0.0496097\pi\) | |||||||
\(108\) | −2.34453 | + | 4.63715i | −0.225603 | + | 0.446210i | ||||
\(109\) | 6.32736i | 0.606051i | 0.952982 | + | 0.303025i | \(0.0979967\pi\) | ||||
−0.952982 | + | 0.303025i | \(0.902003\pi\) | |||||||
\(110\) | −5.30719 | + | 8.81683i | −0.506021 | + | 0.840651i | ||||
\(111\) | −10.4392 | + | 1.10819i | −0.990845 | + | 0.105185i | ||||
\(112\) | −2.86820 | − | 2.86820i | −0.271019 | − | 0.271019i | ||||
\(113\) | −0.984759 | − | 0.984759i | −0.0926383 | − | 0.0926383i | 0.659269 | − | 0.751907i | \(-0.270866\pi\) |
−0.751907 | + | 0.659269i | \(0.770866\pi\) | |||||||
\(114\) | −1.72237 | + | 0.182842i | −0.161315 | + | 0.0171247i | ||||
\(115\) | 3.27142 | − | 5.43480i | 0.305061 | − | 0.506798i | ||||
\(116\) | 6.21092i | 0.576670i | ||||||||
\(117\) | −4.73634 | − | 3.06182i | −0.437875 | − | 0.283065i | ||||
\(118\) | 3.59703 | − | 3.59703i | 0.331134 | − | 0.331134i | ||||
\(119\) | 19.5287 | 1.79019 | ||||||||
\(120\) | −1.32554 | − | 3.63908i | −0.121005 | − | 0.332201i | ||||
\(121\) | −10.1805 | −0.925503 | ||||||||
\(122\) | −0.315382 | + | 0.315382i | −0.0285534 | + | 0.0285534i | ||||
\(123\) | 2.34737 | + | 1.89682i | 0.211655 | + | 0.171030i | ||||
\(124\) | 3.91496i | 0.351574i | ||||||||
\(125\) | −7.46135 | − | 8.32636i | −0.667363 | − | 0.744732i | ||||
\(126\) | −2.55479 | − | 11.8975i | −0.227599 | − | 1.05992i | ||||
\(127\) | 8.32109 | + | 8.32109i | 0.738378 | + | 0.738378i | 0.972264 | − | 0.233886i | \(-0.0751443\pi\) |
−0.233886 | + | 0.972264i | \(0.575144\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −2.11859 | − | 19.9572i | −0.186532 | − | 1.75713i | ||||
\(130\) | 4.07962 | − | 1.01373i | 0.357806 | − | 0.0889102i | ||||
\(131\) | − | 18.6781i | − | 1.63191i | −0.578115 | − | 0.815955i | \(-0.696211\pi\) | ||
0.578115 | − | 0.815955i | \(-0.303789\pi\) | |||||||
\(132\) | 5.01005 | − | 6.20008i | 0.436069 | − | 0.539648i | ||||
\(133\) | 2.86820 | − | 2.86820i | 0.248704 | − | 0.248704i | ||||
\(134\) | 8.88078 | 0.767183 | ||||||||
\(135\) | 2.58730 | − | 11.3272i | 0.222679 | − | 0.974892i | ||||
\(136\) | −4.81448 | −0.412838 | ||||||||
\(137\) | −14.3208 | + | 14.3208i | −1.22351 | + | 1.22351i | −0.257137 | + | 0.966375i | \(0.582779\pi\) |
−0.966375 | + | 0.257137i | \(0.917221\pi\) | |||||||
\(138\) | −3.08826 | + | 3.82181i | −0.262890 | + | 0.325334i | ||||
\(139\) | 11.2626i | 0.955283i | 0.878555 | + | 0.477642i | \(0.158508\pi\) | ||||
−0.878555 | + | 0.477642i | \(0.841492\pi\) | |||||||
\(140\) | 7.77084 | + | 4.67757i | 0.656756 | + | 0.395327i | ||||
\(141\) | 1.35038 | + | 12.7206i | 0.113723 | + | 1.07127i | ||||
\(142\) | −10.9809 | − | 10.9809i | −0.921499 | − | 0.921499i | ||||
\(143\) | 6.11784 | + | 6.11784i | 0.511600 | + | 0.511600i | ||||
\(144\) | 0.629843 | + | 2.93314i | 0.0524869 | + | 0.244428i | ||||
\(145\) | −3.34915 | − | 13.4782i | −0.278132 | − | 1.11930i | ||||
\(146\) | 9.00456i | 0.745223i | ||||||||
\(147\) | 12.7351 | + | 10.2908i | 1.05038 | + | 0.848769i | ||||
\(148\) | −4.28573 | + | 4.28573i | −0.352285 | + | 0.352285i | ||||
\(149\) | 5.59268 | 0.458170 | 0.229085 | − | 0.973406i | \(-0.426427\pi\) | ||||
0.229085 | + | 0.973406i | \(0.426427\pi\) | |||||||
\(150\) | 4.83885 | + | 7.18230i | 0.395091 | + | 0.586433i | ||||
\(151\) | −4.62138 | −0.376083 | −0.188041 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188041 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(152\) | −0.707107 | + | 0.707107i | −0.0573539 | + | 0.0573539i | ||||
\(153\) | −12.1296 | − | 7.84123i | −0.980623 | − | 0.633926i | ||||
\(154\) | 18.6678i | 1.50429i | ||||||||
\(155\) | −2.11109 | − | 8.49576i | −0.169567 | − | 0.682396i | ||||
\(156\) | −3.23796 | + | 0.343732i | −0.259245 | + | 0.0275206i | ||||
\(157\) | −10.3075 | − | 10.3075i | −0.822626 | − | 0.822626i | 0.163858 | − | 0.986484i | \(-0.447606\pi\) |
−0.986484 | + | 0.163858i | \(0.947606\pi\) | |||||||
\(158\) | −7.38565 | − | 7.38565i | −0.587571 | − | 0.587571i | ||||
\(159\) | −12.0855 | + | 1.28295i | −0.958440 | + | 0.101745i | ||||
\(160\) | −1.91577 | − | 1.15318i | −0.151455 | − | 0.0911667i | ||||
\(161\) | − | 11.5071i | − | 0.906883i | ||||||
\(162\) | −3.19030 | + | 8.41558i | −0.250654 | + | 0.661190i | ||||
\(163\) | −11.0783 | + | 11.0783i | −0.867718 | + | 0.867718i | −0.992219 | − | 0.124502i | \(-0.960267\pi\) |
0.124502 | + | 0.992219i | \(0.460267\pi\) | |||||||
\(164\) | 1.74242 | 0.136060 | ||||||||
\(165\) | −7.52888 | + | 16.1562i | −0.586122 | + | 1.25776i | ||||
\(166\) | 5.48450 | 0.425680 | ||||||||
\(167\) | −4.00388 | + | 4.00388i | −0.309830 | + | 0.309830i | −0.844843 | − | 0.535014i | \(-0.820306\pi\) |
0.535014 | + | 0.844843i | \(0.320306\pi\) | |||||||
\(168\) | −5.46453 | − | 4.41568i | −0.421598 | − | 0.340677i | ||||
\(169\) | 9.46581i | 0.728140i | ||||||||
\(170\) | 10.4478 | − | 2.59614i | 0.801308 | − | 0.199115i | ||||
\(171\) | −2.93314 | + | 0.629843i | −0.224303 | + | 0.0481653i | ||||
\(172\) | −8.19327 | − | 8.19327i | −0.624731 | − | 0.624731i | ||||
\(173\) | −8.19231 | − | 8.19231i | −0.622850 | − | 0.622850i | 0.323409 | − | 0.946259i | \(-0.395171\pi\) |
−0.946259 | + | 0.323409i | \(0.895171\pi\) | |||||||
\(174\) | 1.13561 | + | 10.6975i | 0.0860907 | + | 0.810977i | ||||
\(175\) | −19.3856 | − | 5.96036i | −1.46541 | − | 0.450561i | ||||
\(176\) | − | 4.60223i | − | 0.346906i | ||||||
\(177\) | 5.53775 | − | 6.85312i | 0.416243 | − | 0.515112i | ||||
\(178\) | 1.46635 | − | 1.46635i | 0.109907 | − | 0.109907i | ||||
\(179\) | 5.97757 | 0.446784 | 0.223392 | − | 0.974729i | \(-0.428287\pi\) | ||||
0.223392 | + | 0.974729i | \(0.428287\pi\) | |||||||
\(180\) | −2.94846 | − | 6.02550i | −0.219765 | − | 0.449114i | ||||
\(181\) | 8.47586 | 0.630006 | 0.315003 | − | 0.949091i | \(-0.397994\pi\) | ||||
0.315003 | + | 0.949091i | \(0.397994\pi\) | |||||||
\(182\) | 5.39205 | − | 5.39205i | 0.399685 | − | 0.399685i | ||||
\(183\) | −0.485541 | + | 0.600871i | −0.0358922 | + | 0.0444177i | ||||
\(184\) | 2.83687i | 0.209137i | ||||||||
\(185\) | 6.98934 | − | 11.6114i | 0.513866 | − | 0.853685i | ||||
\(186\) | 0.715817 | + | 6.74302i | 0.0524863 | + | 0.494422i | ||||
\(187\) | 15.6676 | + | 15.6676i | 1.14573 | + | 1.14573i | ||||
\(188\) | 5.22236 | + | 5.22236i | 0.380879 | + | 0.380879i | ||||
\(189\) | −6.57567 | − | 20.0248i | −0.478310 | − | 1.45659i | ||||
\(190\) | 1.15318 | − | 1.91577i | 0.0836603 | − | 0.138985i | ||||
\(191\) | 6.45739i | 0.467240i | 0.972328 | + | 0.233620i | \(0.0750572\pi\) | ||||
−0.972328 | + | 0.233620i | \(0.924943\pi\) | |||||||
\(192\) | 1.34719 | + | 1.08861i | 0.0972251 | + | 0.0785639i | ||||
\(193\) | 4.32749 | − | 4.32749i | 0.311500 | − | 0.311500i | −0.533991 | − | 0.845490i | \(-0.679308\pi\) |
0.845490 | + | 0.533991i | \(0.179308\pi\) | |||||||
\(194\) | 17.6883 | 1.26994 | ||||||||
\(195\) | 6.84127 | − | 2.49195i | 0.489914 | − | 0.178452i | ||||
\(196\) | 9.45311 | 0.675222 | ||||||||
\(197\) | −14.8702 | + | 14.8702i | −1.05946 | + | 1.05946i | −0.0613383 | + | 0.998117i | \(0.519537\pi\) |
−0.998117 | + | 0.0613383i | \(0.980463\pi\) | |||||||
\(198\) | 7.49554 | − | 11.5949i | 0.532685 | − | 0.824014i | ||||
\(199\) | − | 0.789726i | − | 0.0559822i | −0.999608 | − | 0.0279911i | \(-0.991089\pi\) | ||
0.999608 | − | 0.0279911i | \(-0.00891101\pi\) | |||||||
\(200\) | 4.77920 | + | 1.46943i | 0.337941 | + | 0.103904i | ||||
\(201\) | 15.2960 | − | 1.62378i | 1.07890 | − | 0.114532i | ||||
\(202\) | −1.31122 | − | 1.31122i | −0.0922571 | − | 0.0922571i | ||||
\(203\) | −17.8141 | − | 17.8141i | −1.25031 | − | 1.25031i | ||||
\(204\) | −8.29233 | + | 0.880287i | −0.580579 | + | 0.0616324i | ||||
\(205\) | −3.78118 | + | 0.939573i | −0.264089 | + | 0.0656226i | ||||
\(206\) | 16.2069i | 1.12919i | ||||||||
\(207\) | −4.62035 | + | 7.14724i | −0.321136 | + | 0.496768i | ||||
\(208\) | −1.32932 | + | 1.32932i | −0.0921718 | + | 0.0921718i | ||||
\(209\) | 4.60223 | 0.318343 | ||||||||
\(210\) | 14.2395 | + | 6.63569i | 0.982621 | + | 0.457906i | ||||
\(211\) | −19.8686 | −1.36781 | −0.683905 | − | 0.729571i | \(-0.739720\pi\) | ||||
−0.683905 | + | 0.729571i | \(0.739720\pi\) | |||||||
\(212\) | −4.96160 | + | 4.96160i | −0.340764 | + | 0.340764i | ||||
\(213\) | −20.9210 | − | 16.9055i | −1.43349 | − | 1.15834i | ||||
\(214\) | − | 12.1807i | − | 0.832656i | ||||||
\(215\) | 22.1981 | + | 13.3619i | 1.51390 | + | 0.911275i | ||||
\(216\) | 1.62112 | + | 4.93680i | 0.110303 | + | 0.335906i | ||||
\(217\) | −11.2289 | − | 11.2289i | −0.762266 | − | 0.762266i | ||||
\(218\) | 4.47412 | + | 4.47412i | 0.303025 | + | 0.303025i | ||||
\(219\) | 1.64641 | + | 15.5092i | 0.111254 | + | 1.04802i | ||||
\(220\) | 2.48169 | + | 9.98719i | 0.167315 | + | 0.673336i | ||||
\(221\) | − | 9.05095i | − | 0.608833i | ||||||
\(222\) | −6.59802 | + | 8.16524i | −0.442830 | + | 0.548015i | ||||
\(223\) | 10.1226 | − | 10.1226i | 0.677856 | − | 0.677856i | −0.281659 | − | 0.959515i | \(-0.590885\pi\) |
0.959515 | + | 0.281659i | \(0.0908845\pi\) | |||||||
\(224\) | −4.05624 | −0.271019 | ||||||||
\(225\) | 9.64754 | + | 11.4859i | 0.643169 | + | 0.765724i | ||||
\(226\) | −1.39266 | −0.0926383 | ||||||||
\(227\) | 13.7553 | − | 13.7553i | 0.912969 | − | 0.912969i | −0.0835359 | − | 0.996505i | \(-0.526621\pi\) |
0.996505 | + | 0.0835359i | \(0.0266213\pi\) | |||||||
\(228\) | −1.08861 | + | 1.34719i | −0.0720952 | + | 0.0892198i | ||||
\(229\) | − | 6.47050i | − | 0.427583i | −0.976879 | − | 0.213791i | \(-0.931419\pi\) | ||
0.976879 | − | 0.213791i | \(-0.0685813\pi\) | |||||||
\(230\) | −1.52974 | − | 6.15623i | −0.100868 | − | 0.405930i | ||||
\(231\) | 3.41324 | + | 32.1529i | 0.224575 | + | 2.11550i | ||||
\(232\) | 4.39178 | + | 4.39178i | 0.288335 | + | 0.288335i | ||||
\(233\) | −4.00499 | − | 4.00499i | −0.262376 | − | 0.262376i | 0.563643 | − | 0.826019i | \(-0.309399\pi\) |
−0.826019 | + | 0.563643i | \(0.809399\pi\) | |||||||
\(234\) | −5.51413 | + | 1.18407i | −0.360470 | + | 0.0774050i | ||||
\(235\) | −14.1490 | − | 8.51682i | −0.922978 | − | 0.555576i | ||||
\(236\) | − | 5.08697i | − | 0.331134i | ||||||
\(237\) | −14.0713 | − | 11.3704i | −0.914026 | − | 0.738590i | ||||
\(238\) | 13.8089 | − | 13.8089i | 0.895097 | − | 0.895097i | ||||
\(239\) | 1.96845 | 0.127329 | 0.0636643 | − | 0.997971i | \(-0.479721\pi\) | ||||
0.0636643 | + | 0.997971i | \(0.479721\pi\) | |||||||
\(240\) | −3.51052 | − | 1.63592i | −0.226603 | − | 0.105598i | ||||
\(241\) | 23.9008 | 1.53959 | 0.769794 | − | 0.638292i | \(-0.220359\pi\) | ||||
0.769794 | + | 0.638292i | \(0.220359\pi\) | |||||||
\(242\) | −7.19873 | + | 7.19873i | −0.462752 | + | 0.462752i | ||||
\(243\) | −3.95617 | + | 15.0781i | −0.253788 | + | 0.967260i | ||||
\(244\) | 0.446018i | 0.0285534i | ||||||||
\(245\) | −20.5140 | + | 5.09745i | −1.31059 | + | 0.325664i | ||||
\(246\) | 3.00109 | − | 0.318586i | 0.191343 | − | 0.0203123i | ||||
\(247\) | −1.32932 | − | 1.32932i | −0.0845826 | − | 0.0845826i | ||||
\(248\) | 2.76830 | + | 2.76830i | 0.175787 | + | 0.175787i | ||||
\(249\) | 9.44635 | − | 1.00279i | 0.598638 | − | 0.0635495i | ||||
\(250\) | −11.1636 | − | 0.611655i | −0.706048 | − | 0.0386845i | ||||
\(251\) | 6.34592i | 0.400551i | 0.979740 | + | 0.200275i | \(0.0641837\pi\) | ||||
−0.979740 | + | 0.200275i | \(0.935816\pi\) | |||||||
\(252\) | −10.2193 | − | 6.60631i | −0.643757 | − | 0.416158i | ||||
\(253\) | 9.23195 | − | 9.23195i | 0.580408 | − | 0.580408i | ||||
\(254\) | 11.7678 | 0.738378 | ||||||||
\(255\) | 17.5203 | − | 6.38181i | 1.09716 | − | 0.399644i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.25382 | − | 3.25382i | 0.202968 | − | 0.202968i | −0.598302 | − | 0.801270i | \(-0.704158\pi\) |
0.801270 | + | 0.598302i | \(0.204158\pi\) | |||||||
\(258\) | −15.6099 | − | 12.6138i | −0.971832 | − | 0.785301i | ||||
\(259\) | − | 24.5846i | − | 1.52762i | ||||||
\(260\) | 2.16791 | − | 3.60154i | 0.134448 | − | 0.223358i | ||||
\(261\) | 3.91190 | + | 18.2175i | 0.242141 | + | 1.12763i | ||||
\(262\) | −13.2074 | − | 13.2074i | −0.815955 | − | 0.815955i | ||||
\(263\) | 20.2705 | + | 20.2705i | 1.24993 | + | 1.24993i | 0.955749 | + | 0.294183i | \(0.0950475\pi\) |
0.294183 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(264\) | −0.841479 | − | 7.92676i | −0.0517895 | − | 0.487858i | ||||
\(265\) | 8.09156 | − | 13.4425i | 0.497061 | − | 0.825766i | ||||
\(266\) | − | 4.05624i | − | 0.248704i | ||||||
\(267\) | 2.25748 | − | 2.79370i | 0.138156 | − | 0.170972i | ||||
\(268\) | 6.27966 | − | 6.27966i | 0.383591 | − | 0.383591i | ||||
\(269\) | −16.9049 | −1.03071 | −0.515354 | − | 0.856977i | \(-0.672340\pi\) | ||||
−0.515354 | + | 0.856977i | \(0.672340\pi\) | |||||||
\(270\) | −6.18006 | − | 9.83905i | −0.376106 | − | 0.598786i | ||||
\(271\) | −2.93733 | −0.178430 | −0.0892149 | − | 0.996012i | \(-0.528436\pi\) | ||||
−0.0892149 | + | 0.996012i | \(0.528436\pi\) | |||||||
\(272\) | −3.40435 | + | 3.40435i | −0.206419 | + | 0.206419i | ||||
\(273\) | 8.30123 | − | 10.2730i | 0.502413 | − | 0.621751i | ||||
\(274\) | 20.2527i | 1.22351i | ||||||||
\(275\) | −10.7709 | − | 20.3347i | −0.649509 | − | 1.22623i | ||||
\(276\) | 0.518698 | + | 4.88616i | 0.0312220 | + | 0.294112i | ||||
\(277\) | −4.03864 | − | 4.03864i | −0.242659 | − | 0.242659i | 0.575291 | − | 0.817949i | \(-0.304889\pi\) |
−0.817949 | + | 0.575291i | \(0.804889\pi\) | |||||||
\(278\) | 7.96388 | + | 7.96388i | 0.477642 | + | 0.477642i | ||||
\(279\) | 2.46581 | + | 11.4831i | 0.147624 | + | 0.687476i | ||||
\(280\) | 8.80235 | − | 2.18727i | 0.526041 | − | 0.130714i | ||||
\(281\) | − | 14.0877i | − | 0.840400i | −0.907431 | − | 0.420200i | \(-0.861960\pi\) | ||
0.907431 | − | 0.420200i | \(-0.138040\pi\) | |||||||
\(282\) | 9.94971 | + | 8.03998i | 0.592496 | + | 0.478774i | ||||
\(283\) | 15.0689 | − | 15.0689i | 0.895756 | − | 0.895756i | −0.0993018 | − | 0.995057i | \(-0.531661\pi\) |
0.995057 | + | 0.0993018i | \(0.0316609\pi\) | |||||||
\(284\) | −15.5294 | −0.921499 | ||||||||
\(285\) | 1.63592 | − | 3.51052i | 0.0969035 | − | 0.207945i | ||||
\(286\) | 8.65193 | 0.511600 | ||||||||
\(287\) | −4.99760 | + | 4.99760i | −0.294999 | + | 0.294999i | ||||
\(288\) | 2.51941 | + | 1.62868i | 0.148458 | + | 0.0959706i | ||||
\(289\) | − | 6.17923i | − | 0.363484i | ||||||
\(290\) | −11.8987 | − | 7.16229i | −0.698716 | − | 0.420584i | ||||
\(291\) | 30.4658 | − | 3.23415i | 1.78594 | − | 0.189589i | ||||
\(292\) | 6.36719 | + | 6.36719i | 0.372611 | + | 0.372611i | ||||
\(293\) | 4.92404 | + | 4.92404i | 0.287665 | + | 0.287665i | 0.836156 | − | 0.548491i | \(-0.184798\pi\) |
−0.548491 | + | 0.836156i | \(0.684798\pi\) | |||||||
\(294\) | 16.2818 | − | 1.72842i | 0.949573 | − | 0.100804i | ||||
\(295\) | 2.74308 | + | 11.0391i | 0.159708 | + | 0.642722i | ||||
\(296\) | 6.06094i | 0.352285i | ||||||||
\(297\) | 10.7901 | − | 21.3412i | 0.626105 | − | 1.23834i | ||||
\(298\) | 3.95462 | − | 3.95462i | 0.229085 | − | 0.229085i | ||||
\(299\) | −5.33316 | −0.308425 | ||||||||
\(300\) | 8.50024 | + | 1.65707i | 0.490762 | + | 0.0956709i | ||||
\(301\) | 46.9998 | 2.70903 | ||||||||
\(302\) | −3.26781 | + | 3.26781i | −0.188041 | + | 0.188041i | ||||
\(303\) | −2.49816 | − | 2.01866i | −0.143515 | − | 0.115969i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | −0.240509 | − | 0.967892i | −0.0137715 | − | 0.0554214i | ||||
\(306\) | −14.1215 | + | 3.03237i | −0.807275 | + | 0.173349i | ||||
\(307\) | −7.41152 | − | 7.41152i | −0.422998 | − | 0.422998i | 0.463237 | − | 0.886235i | \(-0.346688\pi\) |
−0.886235 | + | 0.463237i | \(0.846688\pi\) | |||||||
\(308\) | 13.2001 | + | 13.2001i | 0.752146 | + | 0.752146i | ||||
\(309\) | 2.96330 | + | 27.9144i | 0.168576 | + | 1.58799i | ||||
\(310\) | −7.50017 | − | 4.51465i | −0.425981 | − | 0.256415i | ||||
\(311\) | − | 22.6059i | − | 1.28186i | −0.767598 | − | 0.640931i | \(-0.778548\pi\) | ||
0.767598 | − | 0.640931i | \(-0.221452\pi\) | |||||||
\(312\) | −2.04653 | + | 2.53264i | −0.115862 | + | 0.143383i | ||||
\(313\) | −17.6638 | + | 17.6638i | −0.998419 | + | 0.998419i | −0.999999 | − | 0.00158010i | \(-0.999497\pi\) |
0.00158010 | + | 0.999999i | \(0.499497\pi\) | |||||||
\(314\) | −14.5770 | −0.822626 | ||||||||
\(315\) | 25.7391 | + | 8.82555i | 1.45023 | + | 0.497263i | ||||
\(316\) | −10.4449 | −0.587571 | ||||||||
\(317\) | 0.617852 | − | 0.617852i | 0.0347020 | − | 0.0347020i | −0.689543 | − | 0.724245i | \(-0.742189\pi\) |
0.724245 | + | 0.689543i | \(0.242189\pi\) | |||||||
\(318\) | −7.63853 | + | 9.45290i | −0.428348 | + | 0.530092i | ||||
\(319\) | − | 28.5841i | − | 1.60040i | ||||||
\(320\) | −2.17007 | + | 0.539236i | −0.121311 | + | 0.0301442i | ||||
\(321\) | −2.22714 | − | 20.9797i | −0.124307 | − | 1.17097i | ||||
\(322\) | −8.13672 | − | 8.13672i | −0.453441 | − | 0.453441i | ||||
\(323\) | −3.40435 | − | 3.40435i | −0.189423 | − | 0.189423i | ||||
\(324\) | 3.69483 | + | 8.20660i | 0.205268 | + | 0.455922i | ||||
\(325\) | −2.76244 | + | 8.98463i | −0.153233 | + | 0.498377i | ||||
\(326\) | 15.6671i | 0.867718i | ||||||||
\(327\) | 8.52415 | + | 6.88804i | 0.471387 | + | 0.380910i | ||||
\(328\) | 1.23207 | − | 1.23207i | 0.0680300 | − | 0.0680300i | ||||
\(329\) | −29.9575 | −1.65161 | ||||||||
\(330\) | 6.10046 | + | 16.7479i | 0.335819 | + | 0.921942i | ||||
\(331\) | 16.7769 | 0.922142 | 0.461071 | − | 0.887363i | \(-0.347465\pi\) | ||||
0.461071 | + | 0.887363i | \(0.347465\pi\) | |||||||
\(332\) | 3.87813 | − | 3.87813i | 0.212840 | − | 0.212840i | ||||
\(333\) | −9.87131 | + | 15.2700i | −0.540944 | + | 0.836790i | ||||
\(334\) | 5.66235i | 0.309830i | ||||||||
\(335\) | −10.2411 | + | 17.0135i | −0.559532 | + | 0.929550i | ||||
\(336\) | −6.98636 | + | 0.741650i | −0.381137 | + | 0.0404603i | ||||
\(337\) | 19.3140 | + | 19.3140i | 1.05210 | + | 1.05210i | 0.998566 | + | 0.0535356i | \(0.0170491\pi\) |
0.0535356 | + | 0.998566i | \(0.482951\pi\) | |||||||
\(338\) | 6.69334 | + | 6.69334i | 0.364070 | + | 0.364070i | ||||
\(339\) | −2.39868 | + | 0.254636i | −0.130278 | + | 0.0138299i | ||||
\(340\) | 5.55195 | − | 9.22345i | 0.301097 | − | 0.500212i | ||||
\(341\) | − | 18.0176i | − | 0.975706i | ||||||
\(342\) | −1.62868 | + | 2.51941i | −0.0880687 | + | 0.136234i | ||||
\(343\) | −7.03600 | + | 7.03600i | −0.379908 | + | 0.379908i | ||||
\(344\) | −11.5870 | −0.624731 | ||||||||
\(345\) | −3.76040 | − | 10.3236i | −0.202453 | − | 0.555805i | ||||
\(346\) | −11.5857 | −0.622850 | ||||||||
\(347\) | −20.8770 | + | 20.8770i | −1.12074 | + | 1.12074i | −0.129107 | + | 0.991631i | \(0.541211\pi\) |
−0.991631 | + | 0.129107i | \(0.958789\pi\) | |||||||
\(348\) | 8.36729 | + | 6.76129i | 0.448534 | + | 0.362443i | ||||
\(349\) | − | 11.2937i | − | 0.604537i | −0.953223 | − | 0.302269i | \(-0.902256\pi\) | ||
0.953223 | − | 0.302269i | \(-0.0977440\pi\) | |||||||
\(350\) | −17.9223 | + | 9.49308i | −0.957988 | + | 0.507427i | ||||
\(351\) | −9.28090 | + | 3.04762i | −0.495378 | + | 0.162670i | ||||
\(352\) | −3.25427 | − | 3.25427i | −0.173453 | − | 0.173453i | ||||
\(353\) | −0.723576 | − | 0.723576i | −0.0385121 | − | 0.0385121i | 0.687589 | − | 0.726101i | \(-0.258669\pi\) |
−0.726101 | + | 0.687589i | \(0.758669\pi\) | |||||||
\(354\) | −0.930110 | − | 8.76167i | −0.0494348 | − | 0.465677i | ||||
\(355\) | 33.6999 | − | 8.37399i | 1.78861 | − | 0.444445i | ||||
\(356\) | − | 2.07373i | − | 0.109907i | ||||||
\(357\) | 21.2592 | − | 26.3089i | 1.12516 | − | 1.39241i | ||||
\(358\) | 4.22678 | − | 4.22678i | 0.223392 | − | 0.223392i | ||||
\(359\) | 25.4403 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(360\) | −6.34554 | − | 2.17579i | −0.334439 | − | 0.114674i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 5.99334 | − | 5.99334i | 0.315003 | − | 0.315003i | ||||
\(363\) | −11.0827 | + | 13.7151i | −0.581689 | + | 0.719857i | ||||
\(364\) | − | 7.62551i | − | 0.399685i | ||||||
\(365\) | −17.2507 | − | 10.3839i | −0.902942 | − | 0.543516i | ||||
\(366\) | 0.0815506 | + | 0.768209i | 0.00426272 | + | 0.0401549i | ||||
\(367\) | 14.0536 | + | 14.0536i | 0.733593 | + | 0.733593i | 0.971330 | − | 0.237737i | \(-0.0764055\pi\) |
−0.237737 | + | 0.971330i | \(0.576406\pi\) | |||||||
\(368\) | 2.00597 | + | 2.00597i | 0.104569 | + | 0.104569i | ||||
\(369\) | 5.11075 | − | 1.09745i | 0.266055 | − | 0.0571309i | ||||
\(370\) | −3.26827 | − | 13.1527i | −0.169910 | − | 0.683776i | ||||
\(371\) | − | 28.4617i | − | 1.47766i | ||||||
\(372\) | 5.27420 | + | 4.26188i | 0.273454 | + | 0.220968i | ||||
\(373\) | 5.52563 | − | 5.52563i | 0.286106 | − | 0.286106i | −0.549432 | − | 0.835538i | \(-0.685156\pi\) |
0.835538 | + | 0.549432i | \(0.185156\pi\) | |||||||
\(374\) | 22.1574 | 1.14573 | ||||||||
\(375\) | −19.3397 | + | 0.987670i | −0.998698 | + | 0.0510031i | ||||
\(376\) | 7.38553 | 0.380879 | ||||||||
\(377\) | −8.25630 | + | 8.25630i | −0.425221 | + | 0.425221i | ||||
\(378\) | −18.8094 | − | 9.51000i | −0.967452 | − | 0.489142i | ||||
\(379\) | − | 8.19606i | − | 0.421003i | −0.977593 | − | 0.210502i | \(-0.932490\pi\) | ||
0.977593 | − | 0.210502i | \(-0.0675098\pi\) | |||||||
\(380\) | −0.539236 | − | 2.17007i | −0.0276622 | − | 0.111322i | ||||
\(381\) | 20.2685 | − | 2.15164i | 1.03839 | − | 0.110232i | ||||
\(382\) | 4.56606 | + | 4.56606i | 0.233620 | + | 0.233620i | ||||
\(383\) | −11.6617 | − | 11.6617i | −0.595886 | − | 0.595886i | 0.343329 | − | 0.939215i | \(-0.388445\pi\) |
−0.939215 | + | 0.343329i | \(0.888445\pi\) | |||||||
\(384\) | 1.72237 | − | 0.182842i | 0.0878945 | − | 0.00933059i | ||||
\(385\) | −35.7632 | − | 21.5273i | −1.82266 | − | 1.09713i | ||||
\(386\) | − | 6.12000i | − | 0.311500i | ||||||
\(387\) | −29.1925 | − | 18.8715i | −1.48394 | − | 0.959293i | ||||
\(388\) | 12.5075 | − | 12.5075i | 0.634972 | − | 0.634972i | ||||
\(389\) | 15.6133 | 0.791625 | 0.395813 | − | 0.918331i | \(-0.370463\pi\) | ||||
0.395813 | + | 0.918331i | \(0.370463\pi\) | |||||||
\(390\) | 3.07543 | − | 6.59958i | 0.155731 | − | 0.334183i | ||||
\(391\) | −13.6581 | −0.690719 | ||||||||
\(392\) | 6.68436 | − | 6.68436i | 0.337611 | − | 0.337611i | ||||
\(393\) | −25.1629 | − | 20.3332i | −1.26930 | − | 1.02567i | ||||
\(394\) | 21.0296i | 1.05946i | ||||||||
\(395\) | 22.6662 | − | 5.63226i | 1.14046 | − | 0.283390i | ||||
\(396\) | −2.89868 | − | 13.4990i | −0.145664 | − | 0.678349i | ||||
\(397\) | −23.3976 | − | 23.3976i | −1.17429 | − | 1.17429i | −0.981176 | − | 0.193114i | \(-0.938141\pi\) |
−0.193114 | − | 0.981176i | \(-0.561859\pi\) | |||||||
\(398\) | −0.558421 | − | 0.558421i | −0.0279911 | − | 0.0279911i | ||||
\(399\) | −0.741650 | − | 6.98636i | −0.0371289 | − | 0.349756i | ||||
\(400\) | 4.41845 | − | 2.34036i | 0.220922 | − | 0.117018i | ||||
\(401\) | 4.91777i | 0.245582i | 0.992433 | + | 0.122791i | \(0.0391844\pi\) | ||||
−0.992433 | + | 0.122791i | \(0.960816\pi\) | |||||||
\(402\) | 9.66774 | − | 11.9641i | 0.482183 | − | 0.596715i | ||||
\(403\) | −5.20424 | + | 5.20424i | −0.259242 | + | 0.259242i | ||||
\(404\) | −1.85435 | −0.0922571 | ||||||||
\(405\) | −12.4433 | − | 15.8165i | −0.618315 | − | 0.785930i | ||||
\(406\) | −25.1930 | −1.25031 | ||||||||
\(407\) | 19.7239 | − | 19.7239i | 0.977679 | − | 0.977679i | ||||
\(408\) | −5.24111 | + | 6.48602i | −0.259473 | + | 0.321106i | ||||
\(409\) | 3.39494i | 0.167869i | 0.996471 | + | 0.0839345i | \(0.0267487\pi\) | ||||
−0.996471 | + | 0.0839345i | \(0.973251\pi\) | |||||||
\(410\) | −2.00932 | + | 3.33807i | −0.0992331 | + | 0.164856i | ||||
\(411\) | 3.70304 | + | 34.8828i | 0.182657 | + | 1.72064i | ||||
\(412\) | 11.4600 | + | 11.4600i | 0.564596 | + | 0.564596i | ||||
\(413\) | 14.5904 | + | 14.5904i | 0.717949 | + | 0.717949i | ||||
\(414\) | 1.78678 | + | 8.32094i | 0.0878157 | + | 0.408952i | ||||
\(415\) | −6.32460 | + | 10.5070i | −0.310462 | + | 0.515771i | ||||
\(416\) | 1.87994i | 0.0921718i | ||||||||
\(417\) | 15.1729 | + | 12.2606i | 0.743020 | + | 0.600406i | ||||
\(418\) | 3.25427 | − | 3.25427i | 0.159172 | − | 0.159172i | ||||
\(419\) | 12.5500 | 0.613105 | 0.306553 | − | 0.951854i | \(-0.400824\pi\) | ||||
0.306553 | + | 0.951854i | \(0.400824\pi\) | |||||||
\(420\) | 14.7610 | − | 5.37673i | 0.720264 | − | 0.262358i | ||||
\(421\) | −14.3230 | −0.698060 | −0.349030 | − | 0.937112i | \(-0.613489\pi\) | ||||
−0.349030 | + | 0.937112i | \(0.613489\pi\) | |||||||
\(422\) | −14.0492 | + | 14.0492i | −0.683905 | + | 0.683905i | ||||
\(423\) | 18.6072 | + | 12.0286i | 0.904711 | + | 0.584852i | ||||
\(424\) | 7.01675i | 0.340764i | ||||||||
\(425\) | −7.07454 | + | 23.0094i | −0.343166 | + | 1.11612i | ||||
\(426\) | −26.7474 | + | 2.83942i | −1.29591 | + | 0.137570i | ||||
\(427\) | −1.27927 | − | 1.27927i | −0.0619081 | − | 0.0619081i | ||||
\(428\) | −8.61306 | − | 8.61306i | −0.416328 | − | 0.416328i | ||||
\(429\) | 14.9019 | − | 1.58193i | 0.719468 | − | 0.0763764i | ||||
\(430\) | 25.1447 | − | 6.24814i | 1.21259 | − | 0.301312i | ||||
\(431\) | 8.30157i | 0.399873i | 0.979809 | + | 0.199936i | \(0.0640735\pi\) | ||||
−0.979809 | + | 0.199936i | \(0.935926\pi\) | |||||||
\(432\) | 4.63715 | + | 2.34453i | 0.223105 | + | 0.112801i | ||||
\(433\) | −10.8163 | + | 10.8163i | −0.519799 | + | 0.519799i | −0.917510 | − | 0.397712i | \(-0.869804\pi\) |
0.397712 | + | 0.917510i | \(0.369804\pi\) | |||||||
\(434\) | −15.8800 | −0.762266 | ||||||||
\(435\) | −21.8036 | − | 10.1606i | −1.04540 | − | 0.487162i | ||||
\(436\) | 6.32736 | 0.303025 | ||||||||
\(437\) | −2.00597 | + | 2.00597i | −0.0959587 | + | 0.0959587i | ||||
\(438\) | 12.1309 | + | 9.80248i | 0.579635 | + | 0.468381i | ||||
\(439\) | − | 17.0396i | − | 0.813258i | −0.913593 | − | 0.406629i | \(-0.866704\pi\) | ||
0.913593 | − | 0.406629i | \(-0.133296\pi\) | |||||||
\(440\) | 8.81683 | + | 5.30719i | 0.420326 | + | 0.253010i | ||||
\(441\) | 27.7273 | − | 5.95397i | 1.32035 | − | 0.283522i | ||||
\(442\) | −6.39999 | − | 6.39999i | −0.304416 | − | 0.304416i | ||||
\(443\) | 25.4820 | + | 25.4820i | 1.21069 | + | 1.21069i | 0.970802 | + | 0.239884i | \(0.0771094\pi\) |
0.239884 | + | 0.970802i | \(0.422891\pi\) | |||||||
\(444\) | 1.10819 | + | 10.4392i | 0.0525924 | + | 0.495422i | ||||
\(445\) | 1.11823 | + | 4.50014i | 0.0530090 | + | 0.213327i | ||||
\(446\) | − | 14.3154i | − | 0.677856i | ||||||
\(447\) | 6.08827 | − | 7.53441i | 0.287965 | − | 0.356365i | ||||
\(448\) | −2.86820 | + | 2.86820i | −0.135510 | + | 0.135510i | ||||
\(449\) | −7.40137 | −0.349292 | −0.174646 | − | 0.984631i | \(-0.555878\pi\) | ||||
−0.174646 | + | 0.984631i | \(0.555878\pi\) | |||||||
\(450\) | 14.9436 | + | 1.29989i | 0.704447 | + | 0.0612776i | ||||
\(451\) | −8.01901 | −0.377600 | ||||||||
\(452\) | −0.984759 | + | 0.984759i | −0.0463192 | + | 0.0463192i | ||||
\(453\) | −5.03090 | + | 6.22588i | −0.236372 | + | 0.292517i | ||||
\(454\) | − | 19.4529i | − | 0.912969i | ||||||
\(455\) | 4.11194 | + | 16.5479i | 0.192771 | + | 0.775778i | ||||
\(456\) | 0.182842 | + | 1.72237i | 0.00856234 | + | 0.0806575i | ||||
\(457\) | 14.6959 | + | 14.6959i | 0.687447 | + | 0.687447i | 0.961667 | − | 0.274220i | \(-0.0884196\pi\) |
−0.274220 | + | 0.961667i | \(0.588420\pi\) | |||||||
\(458\) | −4.57533 | − | 4.57533i | −0.213791 | − | 0.213791i | ||||
\(459\) | −23.7681 | + | 7.80487i | −1.10940 | + | 0.364300i | ||||
\(460\) | −5.43480 | − | 3.27142i | −0.253399 | − | 0.152531i | ||||
\(461\) | 37.8041i | 1.76071i | 0.474314 | + | 0.880356i | \(0.342696\pi\) | ||||
−0.474314 | + | 0.880356i | \(0.657304\pi\) | |||||||
\(462\) | 25.1490 | + | 20.3220i | 1.17004 | + | 0.945464i | ||||
\(463\) | −0.789669 | + | 0.789669i | −0.0366990 | + | 0.0366990i | −0.725218 | − | 0.688519i | \(-0.758261\pi\) |
0.688519 | + | 0.725218i | \(0.258261\pi\) | |||||||
\(464\) | 6.21092 | 0.288335 | ||||||||
\(465\) | −13.7436 | − | 6.40456i | −0.637342 | − | 0.297004i | ||||
\(466\) | −5.66392 | −0.262376 | ||||||||
\(467\) | 28.1504 | − | 28.1504i | 1.30265 | − | 1.30265i | 0.376045 | − | 0.926601i | \(-0.377284\pi\) |
0.926601 | − | 0.376045i | \(-0.122716\pi\) | |||||||
\(468\) | −3.06182 | + | 4.73634i | −0.141533 | + | 0.218938i | ||||
\(469\) | 36.0226i | 1.66337i | ||||||||
\(470\) | −16.0271 | + | 3.98254i | −0.739277 | + | 0.183701i | ||||
\(471\) | −25.1070 | + | 2.66528i | −1.15687 | + | 0.122809i | ||||
\(472\) | −3.59703 | − | 3.59703i | −0.165567 | − | 0.165567i | ||||
\(473\) | 37.7073 | + | 37.7073i | 1.73378 | + | 1.73378i | ||||
\(474\) | −17.9900 | + | 1.90976i | −0.826308 | + | 0.0877182i | ||||
\(475\) | 2.34036 | + | 4.41845i | 0.107383 | + | 0.202732i | ||||
\(476\) | − | 19.5287i | − | 0.895097i | ||||||
\(477\) | −11.4280 | + | 17.6781i | −0.523253 | + | 0.809423i | ||||
\(478\) | 1.39191 | − | 1.39191i | 0.0636643 | − | 0.0636643i | ||||
\(479\) | 23.0077 | 1.05125 | 0.525624 | − | 0.850717i | \(-0.323832\pi\) | ||||
0.525624 | + | 0.850717i | \(0.323832\pi\) | |||||||
\(480\) | −3.63908 | + | 1.32554i | −0.166101 | + | 0.0605026i | ||||
\(481\) | −11.3942 | −0.519532 | ||||||||
\(482\) | 16.9005 | − | 16.9005i | 0.769794 | − | 0.769794i | ||||
\(483\) | −15.5022 | − | 12.5267i | −0.705374 | − | 0.569986i | ||||
\(484\) | 10.1805i | 0.462752i | ||||||||
\(485\) | −20.3977 | + | 33.8867i | −0.926213 | + | 1.53872i | ||||
\(486\) | 7.86438 | + | 13.4593i | 0.356736 | + | 0.610524i | ||||
\(487\) | 20.5042 | + | 20.5042i | 0.929134 | + | 0.929134i | 0.997650 | − | 0.0685156i | \(-0.0218263\pi\) |
−0.0685156 | + | 0.997650i | \(0.521826\pi\) | |||||||
\(488\) | 0.315382 | + | 0.315382i | 0.0142767 | + | 0.0142767i | ||||
\(489\) | 2.86459 | + | 26.9845i | 0.129541 | + | 1.22028i | ||||
\(490\) | −10.9011 | + | 18.1100i | −0.492462 | + | 0.818126i | ||||
\(491\) | 16.9198i | 0.763581i | 0.924249 | + | 0.381791i | \(0.124692\pi\) | ||||
−0.924249 | + | 0.381791i | \(0.875308\pi\) | |||||||
\(492\) | 1.89682 | − | 2.34737i | 0.0855152 | − | 0.105827i | ||||
\(493\) | −21.1442 | + | 21.1442i | −0.952285 | + | 0.952285i | ||||
\(494\) | −1.87994 | −0.0845826 | ||||||||
\(495\) | 13.5695 | + | 27.7307i | 0.609903 | + | 1.24640i | ||||
\(496\) | 3.91496 | 0.175787 | ||||||||
\(497\) | 44.5413 | − | 44.5413i | 1.99795 | − | 1.99795i | ||||
\(498\) | 5.97050 | − | 7.38866i | 0.267544 | − | 0.331094i | ||||
\(499\) | − | 26.0020i | − | 1.16401i | −0.813185 | − | 0.582005i | \(-0.802268\pi\) | ||
0.813185 | − | 0.582005i | \(-0.197732\pi\) | |||||||
\(500\) | −8.32636 | + | 7.46135i | −0.372366 | + | 0.333682i | ||||
\(501\) | 1.03531 | + | 9.75267i | 0.0462543 | + | 0.435717i | ||||
\(502\) | 4.48724 | + | 4.48724i | 0.200275 | + | 0.200275i | ||||
\(503\) | −3.80551 | − | 3.80551i | −0.169679 | − | 0.169679i | 0.617159 | − | 0.786838i | \(-0.288284\pi\) |
−0.786838 | + | 0.617159i | \(0.788284\pi\) | |||||||
\(504\) | −11.8975 | + | 2.55479i | −0.529958 | + | 0.113800i | ||||
\(505\) | 4.02407 | − | 0.999929i | 0.179069 | − | 0.0444963i | ||||
\(506\) | − | 13.0560i | − | 0.580408i | ||||||
\(507\) | 12.7523 | + | 10.3046i | 0.566347 | + | 0.457644i | ||||
\(508\) | 8.32109 | − | 8.32109i | 0.369189 | − | 0.369189i | ||||
\(509\) | 7.97379 | 0.353432 | 0.176716 | − | 0.984262i | \(-0.443453\pi\) | ||||
0.176716 | + | 0.984262i | \(0.443453\pi\) | |||||||
\(510\) | 7.87610 | − | 16.9013i | 0.348760 | − | 0.748404i | ||||
\(511\) | −36.5247 | −1.61576 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.34453 | + | 4.63715i | −0.103514 | + | 0.204735i | ||||
\(514\) | − | 4.60160i | − | 0.202968i | ||||||
\(515\) | −31.0488 | − | 18.6895i | −1.36817 | − | 0.823557i | ||||
\(516\) | −19.9572 | + | 2.11859i | −0.878567 | + | 0.0932658i | ||||
\(517\) | −24.0345 | − | 24.0345i | −1.05704 | − | 1.05704i | ||||
\(518\) | −17.3840 | − | 17.3840i | −0.763808 | − | 0.763808i | ||||
\(519\) | −19.9549 | + | 2.11834i | −0.875921 | + | 0.0929849i | ||||
\(520\) | −1.01373 | − | 4.07962i | −0.0444551 | − | 0.178903i | ||||
\(521\) | 21.6995i | 0.950673i | 0.879804 | + | 0.475336i | \(0.157674\pi\) | ||||
−0.879804 | + | 0.475336i | \(0.842326\pi\) | |||||||
\(522\) | 15.6478 | + | 10.1156i | 0.684887 | + | 0.442747i | ||||
\(523\) | −24.3202 | + | 24.3202i | −1.06345 | + | 1.06345i | −0.0656023 | + | 0.997846i | \(0.520897\pi\) |
−0.997846 | + | 0.0656023i | \(0.979103\pi\) | |||||||
\(524\) | −18.6781 | −0.815955 | ||||||||
\(525\) | −29.1332 | + | 19.6276i | −1.27148 | + | 0.856617i | ||||
\(526\) | 28.6668 | 1.24993 | ||||||||
\(527\) | −13.3279 | + | 13.3279i | −0.580573 | + | 0.580573i | ||||
\(528\) | −6.20008 | − | 5.01005i | −0.269824 | − | 0.218034i | ||||
\(529\) | − | 14.9521i | − | 0.650093i | ||||||
\(530\) | −3.78368 | − | 15.2269i | −0.164353 | − | 0.661414i | ||||
\(531\) | −3.20399 | − | 14.9208i | −0.139041 | − | 0.647507i | ||||
\(532\) | −2.86820 | − | 2.86820i | −0.124352 | − | 0.124352i | ||||
\(533\) | 2.31623 | + | 2.31623i | 0.100327 | + | 0.100327i | ||||
\(534\) | −0.379163 | − | 3.57173i | −0.0164080 | − | 0.154564i | ||||
\(535\) | 23.3355 | + | 14.0465i | 1.00888 | + | 0.607284i | ||||
\(536\) | − | 8.88078i | − | 0.383591i | ||||||
\(537\) | 6.50726 | − | 8.05292i | 0.280809 | − | 0.347509i | ||||
\(538\) | −11.9535 | + | 11.9535i | −0.515354 | + | 0.515354i | ||||
\(539\) | −43.5054 | −1.87391 | ||||||||
\(540\) | −11.3272 | − | 2.58730i | −0.487446 | − | 0.111340i | ||||
\(541\) | −14.0695 | −0.604893 | −0.302447 | − | 0.953166i | \(-0.597803\pi\) | ||||
−0.302447 | + | 0.953166i | \(0.597803\pi\) | |||||||
\(542\) | −2.07700 | + | 2.07700i | −0.0892149 | + | 0.0892149i | ||||
\(543\) | 9.22694 | − | 11.4186i | 0.395966 | − | 0.490019i | ||||
\(544\) | 4.81448i | 0.206419i | ||||||||
\(545\) | −13.7308 | + | 3.41194i | −0.588164 | + | 0.146151i | ||||
\(546\) | −1.39426 | − | 13.1340i | −0.0596688 | − | 0.562082i | ||||
\(547\) | 13.8517 | + | 13.8517i | 0.592256 | + | 0.592256i | 0.938240 | − | 0.345984i | \(-0.112455\pi\) |
−0.345984 | + | 0.938240i | \(0.612455\pi\) | |||||||
\(548\) | 14.3208 | + | 14.3208i | 0.611756 | + | 0.611756i | ||||
\(549\) | 0.280921 | + | 1.30823i | 0.0119894 | + | 0.0558340i | ||||
\(550\) | −21.9950 | − | 6.76265i | −0.937870 | − | 0.288361i | ||||
\(551\) | 6.21092i | 0.264594i | ||||||||
\(552\) | 3.82181 | + | 3.08826i | 0.162667 | + | 0.131445i | ||||
\(553\) | 29.9580 | − | 29.9580i | 1.27394 | − | 1.27394i | ||||
\(554\) | −5.71150 | −0.242659 | ||||||||
\(555\) | −8.03405 | − | 22.0563i | −0.341026 | − | 0.936236i | ||||
\(556\) | 11.2626 | 0.477642 | ||||||||
\(557\) | −15.4865 | + | 15.4865i | −0.656182 | + | 0.656182i | −0.954475 | − | 0.298292i | \(-0.903583\pi\) |
0.298292 | + | 0.954475i | \(0.403583\pi\) | |||||||
\(558\) | 9.86338 | + | 6.37620i | 0.417550 | + | 0.269926i | ||||
\(559\) | − | 21.7830i | − | 0.921321i | ||||||
\(560\) | 4.67757 | − | 7.77084i | 0.197663 | − | 0.328378i | ||||
\(561\) | 38.1632 | − | 4.05129i | 1.61125 | − | 0.171045i | ||||
\(562\) | −9.96149 | − | 9.96149i | −0.420200 | − | 0.420200i | ||||
\(563\) | −21.7376 | − | 21.7376i | −0.916131 | − | 0.916131i | 0.0806140 | − | 0.996745i | \(-0.474312\pi\) |
−0.996745 | + | 0.0806140i | \(0.974312\pi\) | |||||||
\(564\) | 12.7206 | − | 1.35038i | 0.535635 | − | 0.0568613i | ||||
\(565\) | 1.60598 | − | 2.66802i | 0.0675642 | − | 0.112244i | ||||
\(566\) | − | 21.3107i | − | 0.895756i | ||||||
\(567\) | −34.1356 | − | 12.9406i | −1.43356 | − | 0.543456i | ||||
\(568\) | −10.9809 | + | 10.9809i | −0.460750 | + | 0.460750i | ||||
\(569\) | −33.8572 | −1.41937 | −0.709684 | − | 0.704520i | \(-0.751162\pi\) | ||||
−0.709684 | + | 0.704520i | \(0.751162\pi\) | |||||||
\(570\) | −1.32554 | − | 3.63908i | −0.0555210 | − | 0.152424i | ||||
\(571\) | −10.2627 | −0.429480 | −0.214740 | − | 0.976671i | \(-0.568890\pi\) | ||||
−0.214740 | + | 0.976671i | \(0.568890\pi\) | |||||||
\(572\) | 6.11784 | − | 6.11784i | 0.255800 | − | 0.255800i | ||||
\(573\) | 8.69933 | + | 7.02960i | 0.363420 | + | 0.293666i | ||||
\(574\) | 7.06767i | 0.294999i | ||||||||
\(575\) | 13.5580 | + | 4.16859i | 0.565408 | + | 0.173842i | ||||
\(576\) | 2.93314 | − | 0.629843i | 0.122214 | − | 0.0262434i | ||||
\(577\) | −13.9733 | − | 13.9733i | −0.581717 | − | 0.581717i | 0.353658 | − | 0.935375i | \(-0.384938\pi\) |
−0.935375 | + | 0.353658i | \(0.884938\pi\) | |||||||
\(578\) | −4.36937 | − | 4.36937i | −0.181742 | − | 0.181742i | ||||
\(579\) | −1.11899 | − | 10.5409i | −0.0465036 | − | 0.438066i | ||||
\(580\) | −13.4782 | + | 3.34915i | −0.559650 | + | 0.139066i | ||||
\(581\) | 22.2465i | 0.922939i | ||||||||
\(582\) | 19.2557 | − | 23.8295i | 0.798174 | − | 0.987763i | ||||
\(583\) | 22.8344 | − | 22.8344i | 0.945705 | − | 0.945705i | ||||
\(584\) | 9.00456 | 0.372611 | ||||||||
\(585\) | 4.09037 | − | 11.9293i | 0.169116 | − | 0.493214i | ||||
\(586\) | 6.96364 | 0.287665 | ||||||||
\(587\) | 22.9650 | − | 22.9650i | 0.947869 | − | 0.947869i | −0.0508382 | − | 0.998707i | \(-0.516189\pi\) |
0.998707 | + | 0.0508382i | \(0.0161893\pi\) | |||||||
\(588\) | 10.2908 | − | 12.7351i | 0.424385 | − | 0.525188i | ||||
\(589\) | 3.91496i | 0.161313i | ||||||||
\(590\) | 9.74548 | + | 5.86618i | 0.401215 | + | 0.241507i | ||||
\(591\) | 3.84508 | + | 36.2208i | 0.158166 | + | 1.48992i | ||||
\(592\) | 4.28573 | + | 4.28573i | 0.176142 | + | 0.176142i | ||||
\(593\) | 2.14305 | + | 2.14305i | 0.0880044 | + | 0.0880044i | 0.749739 | − | 0.661734i | \(-0.230179\pi\) |
−0.661734 | + | 0.749739i | \(0.730179\pi\) | |||||||
\(594\) | −7.46079 | − | 22.7203i | −0.306120 | − | 0.932224i | ||||
\(595\) | 10.5306 | + | 42.3788i | 0.431711 | + | 1.73736i | ||||
\(596\) | − | 5.59268i | − | 0.229085i | ||||||
\(597\) | −1.06391 | − | 0.859707i | −0.0435430 | − | 0.0351855i | ||||
\(598\) | −3.77111 | + | 3.77111i | −0.154212 | + | 0.154212i | ||||
\(599\) | 28.0055 | 1.14427 | 0.572137 | − | 0.820158i | \(-0.306115\pi\) | ||||
0.572137 | + | 0.820158i | \(0.306115\pi\) | |||||||
\(600\) | 7.18230 | − | 4.83885i | 0.293216 | − | 0.197545i | ||||
\(601\) | −10.4827 | −0.427599 | −0.213800 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213800 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(602\) | 33.2339 | − | 33.2339i | 1.35451 | − | 1.35451i | ||||
\(603\) | 14.4639 | − | 22.3743i | 0.589016 | − | 0.911152i | ||||
\(604\) | 4.62138i | 0.188041i | ||||||||
\(605\) | −5.48971 | − | 22.0925i | −0.223188 | − | 0.898189i | ||||
\(606\) | −3.19387 | + | 0.339051i | −0.129742 | + | 0.0137730i | ||||
\(607\) | −25.3869 | − | 25.3869i | −1.03042 | − | 1.03042i | −0.999522 | − | 0.0308996i | \(-0.990163\pi\) |
−0.0308996 | − | 0.999522i | \(-0.509837\pi\) | |||||||
\(608\) | 0.707107 | + | 0.707107i | 0.0286770 | + | 0.0286770i | ||||
\(609\) | −43.3918 | + | 4.60633i | −1.75832 | + | 0.186658i | ||||
\(610\) | −0.854469 | − | 0.514338i | −0.0345964 | − | 0.0208249i | ||||
\(611\) | 13.8844i | 0.561701i | ||||||||
\(612\) | −7.84123 | + | 12.1296i | −0.316963 | + | 0.490312i | ||||
\(613\) | −3.65006 | + | 3.65006i | −0.147425 | + | 0.147425i | −0.776967 | − | 0.629542i | \(-0.783243\pi\) |
0.629542 | + | 0.776967i | \(0.283243\pi\) | |||||||
\(614\) | −10.4815 | −0.422998 | ||||||||
\(615\) | −2.85045 | + | 6.11679i | −0.114941 | + | 0.246653i | ||||
\(616\) | 18.6678 | 0.752146 | ||||||||
\(617\) | −25.7417 | + | 25.7417i | −1.03632 | + | 1.03632i | −0.0370077 | + | 0.999315i | \(0.511783\pi\) |
−0.999315 | + | 0.0370077i | \(0.988217\pi\) | |||||||
\(618\) | 21.8338 | + | 17.6431i | 0.878286 | + | 0.709709i | ||||
\(619\) | − | 26.4712i | − | 1.06397i | −0.846755 | − | 0.531984i | \(-0.821447\pi\) | ||
0.846755 | − | 0.531984i | \(-0.178553\pi\) | |||||||
\(620\) | −8.49576 | + | 2.11109i | −0.341198 | + | 0.0847833i | ||||
\(621\) | 4.59892 | + | 14.0051i | 0.184548 | + | 0.562004i | ||||
\(622\) | −15.9848 | − | 15.9848i | −0.640931 | − | 0.640931i | ||||
\(623\) | 5.94785 | + | 5.94785i | 0.238296 | + | 0.238296i | ||||
\(624\) | 0.343732 | + | 3.23796i | 0.0137603 | + | 0.129622i | ||||
\(625\) | 14.0454 | − | 20.6816i | 0.561816 | − | 0.827262i | ||||
\(626\) | 24.9804i | 0.998419i | ||||||||
\(627\) | 5.01005 | − | 6.20008i | 0.200082 | − | 0.247607i | ||||
\(628\) | −10.3075 | + | 10.3075i | −0.411313 | + | 0.411313i | ||||
\(629\) | −29.1803 | −1.16349 | ||||||||
\(630\) | 24.4409 | − | 11.9597i | 0.973748 | − | 0.476484i | ||||
\(631\) | −0.953154 | −0.0379445 | −0.0189722 | − | 0.999820i | \(-0.506039\pi\) | ||||
−0.0189722 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(632\) | −7.38565 | + | 7.38565i | −0.293786 | + | 0.293786i | ||||
\(633\) | −21.6292 | + | 26.7668i | −0.859683 | + | 1.06388i | ||||
\(634\) | − | 0.873774i | − | 0.0347020i | ||||||
\(635\) | −13.5704 | + | 22.5444i | −0.538524 | + | 0.894648i | ||||
\(636\) | 1.28295 | + | 12.0855i | 0.0508724 | + | 0.479220i | ||||
\(637\) | 12.5662 | + | 12.5662i | 0.497891 | + | 0.497891i | ||||
\(638\) | −20.2120 | − | 20.2120i | −0.800201 | − | 0.800201i | ||||
\(639\) | −45.5498 | + | 9.78106i | −1.80192 | + | 0.386933i | ||||
\(640\) | −1.15318 | + | 1.91577i | −0.0455833 | + | 0.0757275i | ||||
\(641\) | − | 9.36570i | − | 0.369923i | −0.982746 | − | 0.184961i | \(-0.940784\pi\) | ||
0.982746 | − | 0.184961i | \(-0.0592160\pi\) | |||||||
\(642\) | −16.4097 | − | 13.2601i | −0.647640 | − | 0.523334i | ||||
\(643\) | −21.9899 | + | 21.9899i | −0.867197 | + | 0.867197i | −0.992161 | − | 0.124964i | \(-0.960118\pi\) |
0.124964 | + | 0.992161i | \(0.460118\pi\) | |||||||
\(644\) | −11.5071 | −0.453441 | ||||||||
\(645\) | 42.1662 | − | 15.3591i | 1.66029 | − | 0.604765i | ||||
\(646\) | −4.81448 | −0.189423 | ||||||||
\(647\) | 6.75416 | − | 6.75416i | 0.265533 | − | 0.265533i | −0.561764 | − | 0.827297i | \(-0.689877\pi\) |
0.827297 | + | 0.561764i | \(0.189877\pi\) | |||||||
\(648\) | 8.41558 | + | 3.19030i | 0.330595 | + | 0.125327i | ||||
\(649\) | 23.4114i | 0.918979i | ||||||||
\(650\) | 4.39975 | + | 8.30643i | 0.172572 | + | 0.325805i | ||||
\(651\) | −27.3513 | + | 2.90353i | −1.07198 | + | 0.113798i | ||||
\(652\) | 11.0783 | + | 11.0783i | 0.433859 | + | 0.433859i | ||||
\(653\) | −13.6366 | − | 13.6366i | −0.533643 | − | 0.533643i | 0.388011 | − | 0.921655i | \(-0.373162\pi\) |
−0.921655 | + | 0.388011i | \(0.873162\pi\) | |||||||
\(654\) | 10.8981 | − | 1.15690i | 0.426148 | − | 0.0452385i | ||||
\(655\) | 40.5328 | − | 10.0719i | 1.58375 | − | 0.393541i | ||||
\(656\) | − | 1.74242i | − | 0.0680300i | ||||||
\(657\) | 22.6862 | + | 14.6655i | 0.885071 | + | 0.572156i | ||||
\(658\) | −21.1831 | + | 21.1831i | −0.825805 | + | 0.825805i | ||||
\(659\) | −10.2941 | −0.401002 | −0.200501 | − | 0.979694i | \(-0.564257\pi\) | ||||
−0.200501 | + | 0.979694i | \(0.564257\pi\) | |||||||
\(660\) | 16.1562 | + | 7.52888i | 0.628881 | + | 0.293061i | ||||
\(661\) | 3.04994 | 0.118629 | 0.0593145 | − | 0.998239i | \(-0.481109\pi\) | ||||
0.0593145 | + | 0.998239i | \(0.481109\pi\) | |||||||
\(662\) | 11.8631 | − | 11.8631i | 0.461071 | − | 0.461071i | ||||
\(663\) | −12.1933 | − | 9.85298i | −0.473550 | − | 0.382658i | ||||
\(664\) | − | 5.48450i | − | 0.212840i | ||||||
\(665\) | 7.77084 | + | 4.67757i | 0.301340 | + | 0.181388i | ||||
\(666\) | 3.81744 | + | 17.7776i | 0.147923 | + | 0.688867i | ||||
\(667\) | 12.4589 | + | 12.4589i | 0.482412 | + | 0.482412i | ||||
\(668\) | 4.00388 | + | 4.00388i | 0.154915 | + | 0.154915i | ||||
\(669\) | −2.61746 | − | 24.6565i | −0.101197 | − | 0.953277i | ||||
\(670\) | 4.78883 | + | 19.2720i | 0.185009 | + | 0.744541i | ||||
\(671\) | − | 2.05268i | − | 0.0792427i | ||||||
\(672\) | −4.41568 | + | 5.46453i | −0.170339 | + | 0.210799i | ||||
\(673\) | 2.16629 | − | 2.16629i | 0.0835045 | − | 0.0835045i | −0.664121 | − | 0.747625i | \(-0.731194\pi\) |
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(674\) | 27.3141 | 1.05210 | ||||||||
\(675\) | 25.9761 | − | 0.493404i | 0.999820 | − | 0.0189911i | ||||
\(676\) | 9.46581 | 0.364070 | ||||||||
\(677\) | −6.41647 | + | 6.41647i | −0.246605 | + | 0.246605i | −0.819576 | − | 0.572971i | \(-0.805791\pi\) |
0.572971 | + | 0.819576i | \(0.305791\pi\) | |||||||
\(678\) | −1.51607 | + | 1.87618i | −0.0582242 | + | 0.0720541i | ||||
\(679\) | 71.7479i | 2.75343i | ||||||||
\(680\) | −2.59614 | − | 10.4478i | −0.0995574 | − | 0.400654i | ||||
\(681\) | −3.55679 | − | 33.5051i | −0.136297 | − | 1.28392i | ||||
\(682\) | −12.7403 | − | 12.7403i | −0.487853 | − | 0.487853i | ||||
\(683\) | 19.7954 | + | 19.7954i | 0.757448 | + | 0.757448i | 0.975857 | − | 0.218409i | \(-0.0700867\pi\) |
−0.218409 | + | 0.975857i | \(0.570087\pi\) | |||||||
\(684\) | 0.629843 | + | 2.93314i | 0.0240826 | + | 0.112151i | ||||
\(685\) | −38.7996 | − | 23.3550i | −1.48246 | − | 0.892348i | ||||
\(686\) | 9.95041i | 0.379908i | ||||||||
\(687\) | −8.71699 | − | 7.04387i | −0.332574 | − | 0.268740i | ||||
\(688\) | −8.19327 | + | 8.19327i | −0.312366 | + | 0.312366i | ||||
\(689\) | −13.1911 | −0.502541 | ||||||||
\(690\) | −9.95891 | − | 4.64090i | −0.379129 | − | 0.176676i | ||||
\(691\) | 7.17293 | 0.272871 | 0.136436 | − | 0.990649i | \(-0.456435\pi\) | ||||
0.136436 | + | 0.990649i | \(0.456435\pi\) | |||||||
\(692\) | −8.19231 | + | 8.19231i | −0.311425 | + | 0.311425i | ||||
\(693\) | 47.0317 | + | 30.4037i | 1.78659 | + | 1.15494i | ||||
\(694\) | 29.5246i | 1.12074i | ||||||||
\(695\) | −24.4407 | + | 6.07321i | −0.927090 | + | 0.230370i | ||||
\(696\) | 10.6975 | − | 1.13561i | 0.405489 | − | 0.0430453i | ||||
\(697\) | 5.93180 | + | 5.93180i | 0.224683 | + | 0.224683i | ||||
\(698\) | −7.98584 | − | 7.98584i | −0.302269 | − | 0.302269i | ||||
\(699\) | −9.75538 | + | 1.03560i | −0.368982 | + | 0.0391700i | ||||
\(700\) | −5.96036 | + | 19.3856i | −0.225281 | + | 0.732707i | ||||
\(701\) | 28.7624i | 1.08634i | 0.839623 | + | 0.543170i | \(0.182776\pi\) | ||||
−0.839623 | + | 0.543170i | \(0.817224\pi\) | |||||||
\(702\) | −4.40759 | + | 8.71758i | −0.166354 | + | 0.329024i | ||||
\(703\) | −4.28573 | + | 4.28573i | −0.161639 | + | 0.161639i | ||||
\(704\) | −4.60223 | −0.173453 | ||||||||
\(705\) | −26.8765 | + | 9.78984i | −1.01223 | + | 0.368707i | ||||
\(706\) | −1.02329 | −0.0385121 | ||||||||
\(707\) | 5.31863 | − | 5.31863i | 0.200028 | − | 0.200028i | ||||
\(708\) | −6.85312 | − | 5.53775i | −0.257556 | − | 0.208121i | ||||
\(709\) | − | 15.0208i | − | 0.564119i | −0.959397 | − | 0.282060i | \(-0.908982\pi\) | ||
0.959397 | − | 0.282060i | \(-0.0910176\pi\) | |||||||
\(710\) | 17.9081 | − | 29.7507i | 0.672080 | − | 1.11653i | ||||
\(711\) | −30.6363 | + | 6.57864i | −1.14895 | + | 0.246718i | ||||
\(712\) | −1.46635 | − | 1.46635i | −0.0549536 | − | 0.0549536i | ||||
\(713\) | 7.85331 | + | 7.85331i | 0.294109 | + | 0.294109i | ||||
\(714\) | −3.57066 | − | 33.6357i | −0.133629 | − | 1.25879i | ||||
\(715\) | −9.97721 | + | 16.5751i | −0.373127 | + | 0.619875i | ||||
\(716\) | − | 5.97757i | − | 0.223392i | ||||||
\(717\) | 2.14288 | − | 2.65188i | 0.0800274 | − | 0.0990362i | ||||
\(718\) | 17.9890 | − | 17.9890i | 0.671345 | − | 0.671345i | ||||
\(719\) | 0.237709 | 0.00886505 | 0.00443253 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443253 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(720\) | −6.02550 | + | 2.94846i | −0.224557 | + | 0.109883i | ||||
\(721\) | −65.7393 | −2.44826 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | 26.0188 | − | 32.1990i | 0.967649 | − | 1.19749i | ||||
\(724\) | − | 8.47586i | − | 0.315003i | ||||||
\(725\) | 27.4426 | − | 14.5358i | 1.01919 | − | 0.539846i | ||||
\(726\) | 1.86143 | + | 17.5347i | 0.0690840 | + | 0.650773i | ||||
\(727\) | 29.5991 | + | 29.5991i | 1.09777 | + | 1.09777i | 0.994671 | + | 0.103098i | \(0.0328754\pi\) |
0.103098 | + | 0.994671i | \(0.467125\pi\) | |||||||
\(728\) | −5.39205 | − | 5.39205i | −0.199843 | − | 0.199843i | ||||
\(729\) | 16.0063 | + | 21.7439i | 0.592826 | + | 0.805330i | ||||
\(730\) | −19.5406 | + | 4.85558i | −0.723229 | + | 0.179713i | ||||
\(731\) | − | 55.7856i | − | 2.06330i | ||||||
\(732\) | 0.600871 | + | 0.485541i | 0.0222088 | + | 0.0179461i | ||||
\(733\) | 20.2570 | − | 20.2570i | 0.748209 | − | 0.748209i | −0.225933 | − | 0.974143i | \(-0.572543\pi\) |
0.974143 | + | 0.225933i | \(0.0725432\pi\) | |||||||
\(734\) | 19.8748 | 0.733593 | ||||||||
\(735\) | −15.4645 | + | 33.1854i | −0.570418 | + | 1.22406i | ||||
\(736\) | 2.83687 | 0.104569 | ||||||||
\(737\) | −28.9005 | + | 28.9005i | −1.06456 | + | 1.06456i | ||||
\(738\) | 2.83783 | − | 4.38986i | 0.104462 | − | 0.161593i | ||||
\(739\) | − | 48.1026i | − | 1.76948i | −0.466081 | − | 0.884742i | \(-0.654334\pi\) | ||
0.466081 | − | 0.884742i | \(-0.345666\pi\) | |||||||
\(740\) | −11.6114 | − | 6.98934i | −0.426843 | − | 0.256933i | ||||
\(741\) | −3.23796 | + | 0.343732i | −0.118950 | + | 0.0126273i | ||||
\(742\) | −20.1254 | − | 20.1254i | −0.738828 | − | 0.738828i | ||||
\(743\) | 32.7093 | + | 32.7093i | 1.19999 | + | 1.19999i | 0.974170 | + | 0.225817i | \(0.0725052\pi\) |
0.225817 | + | 0.974170i | \(0.427495\pi\) | |||||||
\(744\) | 6.74302 | − | 0.715817i | 0.247211 | − | 0.0262431i | ||||
\(745\) | 3.01577 | + | 12.1365i | 0.110489 | + | 0.444648i | ||||
\(746\) | − | 7.81442i | − | 0.286106i | ||||||
\(747\) | 8.93247 | − | 13.8177i | 0.326822 | − | 0.505563i | ||||
\(748\) | 15.6676 | − | 15.6676i | 0.572865 | − | 0.572865i | ||||
\(749\) | 49.4079 | 1.80533 | ||||||||
\(750\) | −12.9769 | + | 14.3736i | −0.473848 | + | 0.524851i | ||||
\(751\) | 20.7531 | 0.757292 | 0.378646 | − | 0.925542i | \(-0.376390\pi\) | ||||
0.378646 | + | 0.925542i | \(0.376390\pi\) | |||||||
\(752\) | 5.22236 | − | 5.22236i | 0.190440 | − | 0.190440i | ||||
\(753\) | 8.54916 | + | 6.90825i | 0.311549 | + | 0.251751i | ||||
\(754\) | 11.6762i | 0.425221i | ||||||||
\(755\) | −2.49201 | − | 10.0287i | −0.0906937 | − | 0.364983i | ||||
\(756\) | −20.0248 | + | 6.57567i | −0.728297 | + | 0.239155i | ||||
\(757\) | 36.1673 | + | 36.1673i | 1.31452 | + | 1.31452i | 0.918045 | + | 0.396477i | \(0.129767\pi\) |
0.396477 | + | 0.918045i | \(0.370233\pi\) | |||||||
\(758\) | −5.79549 | − | 5.79549i | −0.210502 | − | 0.210502i | ||||
\(759\) | −2.38717 | − | 22.4872i | −0.0866488 | − | 0.816234i | ||||
\(760\) | −1.91577 | − | 1.15318i | −0.0694923 | − | 0.0418301i | ||||
\(761\) | 20.2602i | 0.734432i | 0.930136 | + | 0.367216i | \(0.119689\pi\) | ||||
−0.930136 | + | 0.367216i | \(0.880311\pi\) | |||||||
\(762\) | 12.8106 | − | 15.8535i | 0.464079 | − | 0.574311i | ||||
\(763\) | −18.1481 | + | 18.1481i | −0.657006 | + | 0.657006i | ||||
\(764\) | 6.45739 | 0.233620 | ||||||||
\(765\) | 10.4753 | − | 30.5505i | 0.378736 | − | 1.10456i | ||||
\(766\) | −16.4922 | −0.595886 | ||||||||
\(767\) | 6.76222 | − | 6.76222i | 0.244170 | − | 0.244170i | ||||
\(768\) | 1.08861 | − | 1.34719i | 0.0392819 | − | 0.0486125i | ||||
\(769\) | − | 10.8266i | − | 0.390416i | −0.980762 | − | 0.195208i | \(-0.937462\pi\) | ||
0.980762 | − | 0.195208i | \(-0.0625382\pi\) | |||||||
\(770\) | −40.5105 | + | 10.0663i | −1.45990 | + | 0.362765i | ||||
\(771\) | −0.841363 | − | 7.92567i | −0.0303010 | − | 0.285436i | ||||
\(772\) | −4.32749 | − | 4.32749i | −0.155750 | − | 0.155750i | ||||
\(773\) | 15.4031 | + | 15.4031i | 0.554011 | + | 0.554011i | 0.927596 | − | 0.373585i | \(-0.121872\pi\) |
−0.373585 | + | 0.927596i | \(0.621872\pi\) | |||||||
\(774\) | −33.9864 | + | 7.29801i | −1.22161 | + | 0.262321i | ||||
\(775\) | 17.2981 | − | 9.16243i | 0.621365 | − | 0.329124i | ||||
\(776\) | − | 17.6883i | − | 0.634972i | ||||||
\(777\) | −33.1202 | − | 26.7632i | −1.18818 | − | 0.960123i | ||||
\(778\) | 11.0403 | − | 11.0403i | 0.395813 | − | 0.395813i | ||||
\(779\) | 1.74242 | 0.0624286 | ||||||||
\(780\) | −2.49195 | − | 6.84127i | −0.0892261 | − | 0.244957i | ||||
\(781\) | 71.4698 | 2.55739 | ||||||||
\(782\) | −9.65772 | + | 9.65772i | −0.345359 | + | 0.345359i | ||||
\(783\) | 28.8010 | + | 14.5617i | 1.02926 | + | 0.520393i | ||||
\(784\) | − | 9.45311i | − | 0.337611i | ||||||
\(785\) | 16.8098 | − | 27.9262i | 0.599969 | − | 0.996727i | ||||
\(786\) | −32.1706 | + | 3.41513i | −1.14749 | + | 0.121814i | ||||
\(787\) | 23.9171 | + | 23.9171i | 0.852552 | + | 0.852552i | 0.990447 | − | 0.137895i | \(-0.0440337\pi\) |
−0.137895 | + | 0.990447i | \(0.544034\pi\) | |||||||
\(788\) | 14.8702 | + | 14.8702i | 0.529728 | + | 0.529728i | ||||
\(789\) | 49.3749 | − | 5.24148i | 1.75779 | − | 0.186602i | ||||
\(790\) | 12.0448 | − | 20.0100i | 0.428535 | − | 0.711925i | ||||
\(791\) | − | 5.64896i | − | 0.200854i | ||||||
\(792\) | −11.5949 | − | 7.49554i | −0.412007 | − | 0.266343i | ||||
\(793\) | −0.592901 | + | 0.592901i | −0.0210545 | + | 0.0210545i | ||||
\(794\) | −33.0892 | −1.17429 | ||||||||
\(795\) | −9.30102 | − | 25.5346i | −0.329873 | − | 0.905618i | ||||
\(796\) | −0.789726 | −0.0279911 | ||||||||
\(797\) | 21.0294 | − | 21.0294i | 0.744901 | − | 0.744901i | −0.228616 | − | 0.973517i | \(-0.573420\pi\) |
0.973517 | + | 0.228616i | \(0.0734199\pi\) | |||||||
\(798\) | −5.46453 | − | 4.41568i | −0.193442 | − | 0.156313i | ||||
\(799\) | 35.5575i | 1.25793i | ||||||||
\(800\) | 1.46943 | − | 4.77920i | 0.0519522 | − | 0.168970i | ||||
\(801\) | −1.30612 | − | 6.08252i | −0.0461495 | − | 0.214915i | ||||
\(802\) | 3.47739 | + | 3.47739i | 0.122791 | + | 0.122791i | ||||
\(803\) | −29.3033 | − | 29.3033i | −1.03409 | − | 1.03409i | ||||
\(804\) | −1.62378 | − | 15.2960i | −0.0572661 | − | 0.539449i | ||||
\(805\) | 24.9712 | − | 6.20501i | 0.880118 | − | 0.218698i | ||||
\(806\) | 7.35990i | 0.259242i | ||||||||
\(807\) | −18.4029 | + | 22.7741i | −0.647811 | + | 0.801685i | ||||
\(808\) | −1.31122 | + | 1.31122i | −0.0461286 | + | 0.0461286i | ||||
\(809\) | 55.3606 | 1.94637 | 0.973187 | − | 0.230016i | \(-0.0738780\pi\) | ||||
0.973187 | + | 0.230016i | \(0.0738780\pi\) | |||||||
\(810\) | −19.9828 | − | 2.38521i | −0.702123 | − | 0.0838078i | ||||
\(811\) | −48.8943 | −1.71691 | −0.858455 | − | 0.512889i | \(-0.828575\pi\) | ||||
−0.858455 | + | 0.512889i | \(0.828575\pi\) | |||||||
\(812\) | −17.8141 | + | 17.8141i | −0.625154 | + | 0.625154i | ||||
\(813\) | −3.19761 | + | 3.95714i | −0.112145 | + | 0.138783i | ||||
\(814\) | − | 27.8939i | − | 0.977679i | ||||||
\(815\) | −30.0145 | − | 18.0669i | −1.05136 | − | 0.632856i | ||||
\(816\) | 0.880287 | + | 8.29233i | 0.0308162 | + | 0.290290i | ||||
\(817\) | −8.19327 | − | 8.19327i | −0.286646 | − | 0.286646i | ||||
\(818\) | 2.40059 | + | 2.40059i | 0.0839345 | + | 0.0839345i | ||||
\(819\) | −4.80287 | − | 22.3667i | −0.167826 | − | 0.781554i | ||||
\(820\) | 0.939573 | + | 3.78118i | 0.0328113 | + | 0.132044i | ||||
\(821\) | − | 25.1748i | − | 0.878606i | −0.898339 | − | 0.439303i | \(-0.855225\pi\) | ||
0.898339 | − | 0.439303i | \(-0.144775\pi\) | |||||||
\(822\) | 27.2843 | + | 22.0474i | 0.951648 | + | 0.768991i | ||||
\(823\) | −8.56588 | + | 8.56588i | −0.298588 | + | 0.298588i | −0.840460 | − | 0.541873i | \(-0.817715\pi\) |
0.541873 | + | 0.840460i | \(0.317715\pi\) | |||||||
\(824\) | 16.2069 | 0.564596 | ||||||||
\(825\) | −39.1201 | − | 7.62621i | −1.36199 | − | 0.265511i | ||||
\(826\) | 20.6340 | 0.717949 | ||||||||
\(827\) | 11.7327 | − | 11.7327i | 0.407986 | − | 0.407986i | −0.473050 | − | 0.881036i | \(-0.656847\pi\) |
0.881036 | + | 0.473050i | \(0.156847\pi\) | |||||||
\(828\) | 7.14724 | + | 4.62035i | 0.248384 | + | 0.160568i | ||||
\(829\) | 2.19216i | 0.0761369i | 0.999275 | + | 0.0380684i | \(0.0121205\pi\) | ||||
−0.999275 | + | 0.0380684i | \(0.987880\pi\) | |||||||
\(830\) | 2.95744 | + | 11.9018i | 0.102654 | + | 0.413117i | ||||
\(831\) | −9.83734 | + | 1.04430i | −0.341254 | + | 0.0362264i | ||||
\(832\) | 1.32932 | + | 1.32932i | 0.0460859 | + | 0.0460859i | ||||
\(833\) | 32.1817 | + | 32.1817i | 1.11503 | + | 1.11503i | ||||
\(834\) | 19.3984 | − | 2.05927i | 0.671713 | − | 0.0713069i | ||||
\(835\) | −10.8478 | − | 6.52969i | −0.375402 | − | 0.225969i | ||||
\(836\) | − | 4.60223i | − | 0.159172i | ||||||
\(837\) | 18.1543 | + | 9.17876i | 0.627503 | + | 0.317264i | ||||
\(838\) | 8.87416 | − | 8.87416i | 0.306553 | − | 0.306553i | ||||
\(839\) | −23.1579 | −0.799501 | −0.399750 | − | 0.916624i | \(-0.630903\pi\) | ||||
−0.399750 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(840\) | 6.63569 | − | 14.2395i | 0.228953 | − | 0.491311i | ||||
\(841\) | 9.57554 | 0.330191 | ||||||||
\(842\) | −10.1279 | + | 10.1279i | −0.349030 | + | 0.349030i | ||||
\(843\) | −18.9788 | − | 15.3360i | −0.653664 | − | 0.528201i | ||||
\(844\) | 19.8686i | 0.683905i | ||||||||
\(845\) | −20.5415 | + | 5.10430i | −0.706650 | + | 0.175593i | ||||
\(846\) | 21.6628 | − | 4.65172i | 0.744781 | − | 0.159929i | ||||
\(847\) | −29.1998 | − | 29.1998i | −1.00332 | − | 1.00332i | ||||
\(848\) | 4.96160 | + | 4.96160i | 0.170382 | + | 0.170382i | ||||
\(849\) | −3.89648 | − | 36.7050i | −0.133727 | − | 1.25971i | ||||
\(850\) | 11.2676 | + | 21.2725i | 0.386477 | + | 0.729642i | ||||
\(851\) | 17.1941i | 0.589407i | ||||||||
\(852\) | −16.9055 | + | 20.9210i | −0.579172 | + | 0.716743i | ||||
\(853\) | 28.3401 | − | 28.3401i | 0.970346 | − | 0.970346i | −0.0292268 | − | 0.999573i | \(-0.509305\pi\) |
0.999573 | + | 0.0292268i | \(0.00930451\pi\) | |||||||
\(854\) | −1.80916 | −0.0619081 | ||||||||
\(855\) | −2.94846 | − | 6.02550i | −0.100835 | − | 0.206068i | ||||
\(856\) | −12.1807 | −0.416328 | ||||||||
\(857\) | 37.5618 | − | 37.5618i | 1.28309 | − | 1.28309i | 0.344182 | − | 0.938903i | \(-0.388156\pi\) |
0.938903 | − | 0.344182i | \(-0.111844\pi\) | |||||||
\(858\) | 9.41861 | − | 11.6558i | 0.321546 | − | 0.397922i | ||||
\(859\) | − | 21.0474i | − | 0.718128i | −0.933313 | − | 0.359064i | \(-0.883096\pi\) | ||
0.933313 | − | 0.359064i | \(-0.116904\pi\) | |||||||
\(860\) | 13.3619 | − | 22.1981i | 0.455637 | − | 0.756949i | ||||
\(861\) | 1.29226 | + | 12.1732i | 0.0440402 | + | 0.414860i | ||||
\(862\) | 5.87010 | + | 5.87010i | 0.199936 | + | 0.199936i | ||||
\(863\) | −16.8012 | − | 16.8012i | −0.571918 | − | 0.571918i | 0.360746 | − | 0.932664i | \(-0.382522\pi\) |
−0.932664 | + | 0.360746i | \(0.882522\pi\) | |||||||
\(864\) | 4.93680 | − | 1.62112i | 0.167953 | − | 0.0551517i | ||||
\(865\) | 13.3603 | − | 22.1955i | 0.454265 | − | 0.754670i | ||||
\(866\) | 15.2966i | 0.519799i | ||||||||
\(867\) | −8.32460 | − | 6.72679i | −0.282718 | − | 0.228454i | ||||
\(868\) | −11.2289 | + | 11.2289i | −0.381133 | + | 0.381133i | ||||
\(869\) | 48.0698 | 1.63066 | ||||||||
\(870\) | −22.6021 | + | 8.23285i | −0.766282 | + | 0.279120i | ||||
\(871\) | 16.6954 | 0.565701 | ||||||||
\(872\) | 4.47412 | − | 4.47412i | 0.151513 | − | 0.151513i | ||||
\(873\) | 28.8085 | − | 44.5640i | 0.975019 | − | 1.50826i | ||||
\(874\) | 2.83687i | 0.0959587i | ||||||||
\(875\) | 2.48102 | − | 45.2823i | 0.0838739 | − | 1.53082i | ||||
\(876\) | 15.5092 | − | 1.64641i | 0.524008 | − | 0.0556270i | ||||
\(877\) | −17.3922 | − | 17.3922i | −0.587291 | − | 0.587291i | 0.349606 | − | 0.936897i | \(-0.386316\pi\) |
−0.936897 | + | 0.349606i | \(0.886316\pi\) | |||||||
\(878\) | −12.0488 | − | 12.0488i | −0.406629 | − | 0.406629i | ||||
\(879\) | 11.9940 | − | 1.27324i | 0.404547 | − | 0.0429454i | ||||
\(880\) | 9.98719 | − | 2.48169i | 0.336668 | − | 0.0836577i | ||||
\(881\) | 1.61838i | 0.0545246i | 0.999628 | + | 0.0272623i | \(0.00867894\pi\) | ||||
−0.999628 | + | 0.0272623i | \(0.991321\pi\) | |||||||
\(882\) | 15.3961 | − | 23.8162i | 0.518412 | − | 0.801934i | ||||
\(883\) | 9.09541 | − | 9.09541i | 0.306085 | − | 0.306085i | −0.537304 | − | 0.843389i | \(-0.680557\pi\) |
0.843389 | + | 0.537304i | \(0.180557\pi\) | |||||||
\(884\) | −9.05095 | −0.304416 | ||||||||
\(885\) | 17.8579 | + | 8.32188i | 0.600288 | + | 0.279737i | ||||
\(886\) | 36.0370 | 1.21069 | ||||||||
\(887\) | −31.1947 | + | 31.1947i | −1.04742 | + | 1.04742i | −0.0485966 | + | 0.998818i | \(0.515475\pi\) |
−0.998818 | + | 0.0485966i | \(0.984525\pi\) | |||||||
\(888\) | 8.16524 | + | 6.59802i | 0.274007 | + | 0.221415i | ||||
\(889\) | 47.7331i | 1.60092i | ||||||||
\(890\) | 3.97278 | + | 2.39137i | 0.133168 | + | 0.0801590i | ||||
\(891\) | −17.0045 | − | 37.7687i | −0.569671 | − | 1.26530i | ||||
\(892\) | −10.1226 | − | 10.1226i | −0.338928 | − | 0.338928i | ||||
\(893\) | 5.22236 | + | 5.22236i | 0.174759 | + | 0.174759i | ||||
\(894\) | −1.02257 | − | 9.63269i | −0.0342000 | − | 0.322165i | ||||
\(895\) | 3.22332 | + | 12.9718i | 0.107744 | + | 0.433598i | ||||
\(896\) | 4.05624i | 0.135510i | ||||||||
\(897\) | −5.80575 | + | 7.18478i | −0.193848 | + | 0.239893i | ||||
\(898\) | −5.23356 | + | 5.23356i | −0.174646 | + | 0.174646i | ||||
\(899\) | 24.3155 | 0.810968 | ||||||||
\(900\) | 11.4859 | − | 9.64754i | 0.382862 | − | 0.321585i | ||||
\(901\) | −33.7820 | −1.12544 | ||||||||
\(902\) | −5.67029 | + | 5.67029i | −0.188800 | + | 0.188800i | ||||
\(903\) | 51.1646 | − | 63.3177i | 1.70265 | − | 2.10708i | ||||
\(904\) | 1.39266i | 0.0463192i | ||||||||
\(905\) | 4.57049 | + | 18.3933i | 0.151928 | + | 0.611413i | ||||
\(906\) | 0.844980 | + | 7.95974i | 0.0280726 | + | 0.264445i | ||||
\(907\) | −13.0460 | − | 13.0460i | −0.433187 | − | 0.433187i | 0.456524 | − | 0.889711i | \(-0.349094\pi\) |
−0.889711 | + | 0.456524i | \(0.849094\pi\) | |||||||
\(908\) | −13.7553 | − | 13.7553i | −0.456484 | − | 0.456484i | ||||
\(909\) | −5.43905 | + | 1.16795i | −0.180402 | + | 0.0387383i | ||||
\(910\) | 14.6087 | + | 8.79356i | 0.484275 | + | 0.291504i | ||||
\(911\) | 50.7130i | 1.68020i | 0.542434 | + | 0.840098i | \(0.317503\pi\) | ||||
−0.542434 | + | 0.840098i | \(0.682497\pi\) | |||||||
\(912\) | 1.34719 | + | 1.08861i | 0.0446099 | + | 0.0360476i | ||||
\(913\) | −17.8480 | + | 17.8480i | −0.590684 | + | 0.590684i | ||||
\(914\) | 20.7832 | 0.687447 | ||||||||
\(915\) | −1.56576 | − | 0.729649i | −0.0517623 | − | 0.0241215i | ||||
\(916\) | −6.47050 | −0.213791 | ||||||||
\(917\) | 53.5724 | − | 53.5724i | 1.76912 | − | 1.76912i | ||||
\(918\) | −11.2877 | + | 22.3255i | −0.372550 | + | 0.736850i | ||||
\(919\) | − | 20.6702i | − | 0.681847i | −0.940091 | − | 0.340924i | \(-0.889260\pi\) | ||
0.940091 | − | 0.340924i | \(-0.110740\pi\) | |||||||
\(920\) | −6.15623 | + | 1.52974i | −0.202965 | + | 0.0504342i | ||||
\(921\) | −18.0530 | + | 1.91645i | −0.594867 | + | 0.0631491i | ||||
\(922\) | 26.7315 | + | 26.7315i | 0.880356 | + | 0.880356i | ||||
\(923\) | −20.6435 | − | 20.6435i | −0.679490 | − | 0.679490i | ||||
\(924\) | 32.1529 | − | 3.41324i | 1.05775 | − | 0.112287i | ||||
\(925\) | 28.9665 | + | 8.90612i | 0.952411 | + | 0.292831i | ||||
\(926\) | 1.11676i | 0.0366990i | ||||||||
\(927\) | 40.8319 | + | 26.3959i | 1.34110 | + | 0.866954i | ||||
\(928\) | 4.39178 | − | 4.39178i | 0.144167 | − | 0.144167i | ||||
\(929\) | 24.9065 | 0.817156 | 0.408578 | − | 0.912723i | \(-0.366025\pi\) | ||||
0.408578 | + | 0.912723i | \(0.366025\pi\) | |||||||
\(930\) | −14.2469 | + | 5.18946i | −0.467173 | + | 0.170169i | ||||
\(931\) | 9.45311 | 0.309813 | ||||||||
\(932\) | −4.00499 | + | 4.00499i | −0.131188 | + | 0.131188i | ||||
\(933\) | −30.4544 | − | 24.6091i | −0.997034 | − | 0.805665i | ||||
\(934\) | − | 39.8107i | − | 1.30265i | ||||||
\(935\) | −25.5514 | + | 42.4484i | −0.835619 | + | 1.38821i | ||||
\(936\) | 1.18407 | + | 5.51413i | 0.0387025 | + | 0.180235i | ||||
\(937\) | 33.4021 | + | 33.4021i | 1.09120 | + | 1.09120i | 0.995401 | + | 0.0957973i | \(0.0305401\pi\) |
0.0957973 | + | 0.995401i | \(0.469460\pi\) | |||||||
\(938\) | 25.4718 | + | 25.4718i | 0.831685 | + | 0.831685i | ||||
\(939\) | 4.56746 | + | 43.0256i | 0.149053 | + | 1.40409i | ||||
\(940\) | −8.51682 | + | 14.1490i | −0.277788 | + | 0.461489i | ||||
\(941\) | 2.02241i | 0.0659288i | 0.999457 | + | 0.0329644i | \(0.0104948\pi\) | ||||
−0.999457 | + | 0.0329644i | \(0.989505\pi\) | |||||||
\(942\) | −15.8687 | + | 19.6380i | −0.517030 | + | 0.639839i | ||||
\(943\) | 3.49524 | − | 3.49524i | 0.113821 | − | 0.113821i | ||||
\(944\) | −5.08697 | −0.165567 | ||||||||
\(945\) | 39.9096 | − | 25.0678i | 1.29826 | − | 0.815456i | ||||
\(946\) | 53.3262 | 1.73378 | ||||||||
\(947\) | −7.33043 | + | 7.33043i | −0.238207 | + | 0.238207i | −0.816107 | − | 0.577900i | \(-0.803872\pi\) |
0.577900 | + | 0.816107i | \(0.303872\pi\) | |||||||
\(948\) | −11.3704 | + | 14.0713i | −0.369295 | + | 0.457013i | ||||
\(949\) | 16.9281i | 0.549508i | ||||||||
\(950\) | 4.77920 | + | 1.46943i | 0.155058 | + | 0.0476746i | ||||
\(951\) | −0.159762 | − | 1.50497i | −0.00518064 | − | 0.0488018i | ||||
\(952\) | −13.8089 | − | 13.8089i | −0.447548 | − | 0.447548i | ||||
\(953\) | −17.9338 | − | 17.9338i | −0.580934 | − | 0.580934i | 0.354226 | − | 0.935160i | \(-0.384744\pi\) |
−0.935160 | + | 0.354226i | \(0.884744\pi\) | |||||||
\(954\) | 4.41945 | + | 20.5811i | 0.143085 | + | 0.666338i | ||||
\(955\) | −14.0130 | + | 3.48205i | −0.453451 | + | 0.112677i | ||||
\(956\) | − | 1.96845i | − | 0.0636643i | ||||||
\(957\) | −38.5082 | − | 31.1170i | −1.24479 | − | 1.00587i | ||||
\(958\) | 16.2689 | − | 16.2689i | 0.525624 | − | 0.525624i | ||||
\(959\) | −82.1500 | −2.65276 | ||||||||
\(960\) | −1.63592 | + | 3.51052i | −0.0527991 | + | 0.113302i | ||||
\(961\) | −15.6731 | −0.505583 | ||||||||
\(962\) | −8.05693 | + | 8.05693i | −0.259766 | + | 0.259766i | ||||
\(963\) | −30.6882 | − | 19.8384i | −0.988913 | − | 0.639284i | ||||
\(964\) | − | 23.9008i | − | 0.769794i | ||||||
\(965\) | 11.7245 | + | 7.05744i | 0.377426 | + | 0.227187i | ||||
\(966\) | −19.8194 | + | 2.10397i | −0.637680 | + | 0.0676940i | ||||
\(967\) | −7.13685 | − | 7.13685i | −0.229506 | − | 0.229506i | 0.582980 | − | 0.812486i | \(-0.301886\pi\) |
−0.812486 | + | 0.582980i | \(0.801886\pi\) | |||||||
\(968\) | 7.19873 | + | 7.19873i | 0.231376 | + | 0.231376i | ||||
\(969\) | −8.29233 | + | 0.880287i | −0.266388 | + | 0.0282789i | ||||
\(970\) | 9.53815 | + | 38.3849i | 0.306251 | + | 1.23246i | ||||
\(971\) | 0.247821i | 0.00795295i | 0.999992 | + | 0.00397648i | \(0.00126576\pi\) | ||||
−0.999992 | + | 0.00397648i | \(0.998734\pi\) | |||||||
\(972\) | 15.0781 | + | 3.95617i | 0.483630 | + | 0.126894i | ||||
\(973\) | −32.3034 | + | 32.3034i | −1.03560 | + | 1.03560i | ||||
\(974\) | 28.9973 | 0.929134 | ||||||||
\(975\) | 9.09677 | + | 13.5023i | 0.291330 | + | 0.432420i | ||||
\(976\) | 0.446018 | 0.0142767 | ||||||||
\(977\) | 14.2133 | − | 14.2133i | 0.454724 | − | 0.454724i | −0.442195 | − | 0.896919i | \(-0.645800\pi\) |
0.896919 | + | 0.442195i | \(0.145800\pi\) | |||||||
\(978\) | 21.1065 | + | 17.0554i | 0.674911 | + | 0.545370i | ||||
\(979\) | 9.54376i | 0.305020i | ||||||||
\(980\) | 5.09745 | + | 20.5140i | 0.162832 | + | 0.655294i | ||||
\(981\) | 18.5590 | − | 3.98524i | 0.592544 | − | 0.127239i | ||||
\(982\) | 11.9641 | + | 11.9641i | 0.381791 | + | 0.381791i | ||||
\(983\) | 36.3201 | + | 36.3201i | 1.15843 | + | 1.15843i | 0.984813 | + | 0.173617i | \(0.0555454\pi\) |
0.173617 | + | 0.984813i | \(0.444455\pi\) | |||||||
\(984\) | −0.318586 | − | 3.00109i | −0.0101562 | − | 0.0956713i | ||||
\(985\) | −40.2879 | − | 24.2508i | −1.28368 | − | 0.772696i | ||||
\(986\) | 29.9024i | 0.952285i | ||||||||
\(987\) | −32.6121 | + | 40.3584i | −1.03806 | + | 1.28462i | ||||
\(988\) | −1.32932 | + | 1.32932i | −0.0422913 | + | 0.0422913i | ||||
\(989\) | −32.8710 | −1.04524 | ||||||||
\(990\) | 29.2037 | + | 10.0135i | 0.928153 | + | 0.318250i | ||||
\(991\) | −10.0851 | −0.320364 | −0.160182 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160182 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(992\) | 2.76830 | − | 2.76830i | 0.0878935 | − | 0.0878935i | ||||
\(993\) | 18.2636 | − | 22.6017i | 0.579577 | − | 0.717243i | ||||
\(994\) | − | 62.9909i | − | 1.99795i | ||||||
\(995\) | 1.71377 | − | 0.425849i | 0.0543300 | − | 0.0135003i | ||||
\(996\) | −1.00279 | − | 9.44635i | −0.0317747 | − | 0.299319i | ||||
\(997\) | 8.34108 | + | 8.34108i | 0.264165 | + | 0.264165i | 0.826744 | − | 0.562579i | \(-0.190191\pi\) |
−0.562579 | + | 0.826744i | \(0.690191\pi\) | |||||||
\(998\) | −18.3862 | − | 18.3862i | −0.582005 | − | 0.582005i | ||||
\(999\) | 9.82553 | + | 29.9216i | 0.310866 | + | 0.946678i |
(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 | 570.2.k.b.77.15 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.8 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.8 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.15 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.8 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.77.15 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.533.8 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.b.533.15 | yes | 36 | 15.8 | even | 4 | inner |