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 | 77.8 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.8 |
$q$-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 | ||||
\(3\) | 1.34719 | − | 1.08861i | 0.777801 | − | 0.628511i | ||||
\(4\) | − | 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 | \(-0.755930\pi\) | ||
0.720156 | − | 0.693813i | \(-0.244070\pi\) | |||||||
\(12\) | −1.08861 | − | 1.34719i | −0.314256 | − | 0.388900i | ||||
\(13\) | 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 | ||||||||
\(15\) | −3.08883 | − | 2.33648i | −0.797531 | − | 0.603278i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.40435 | + | 3.40435i | −0.825677 | + | 0.825677i | −0.986915 | − | 0.161239i | \(-0.948451\pi\) |
0.161239 | + | 0.986915i | \(0.448451\pi\) | |||||||
\(18\) | 1.62868 | + | 2.51941i | 0.383883 | + | 0.593830i | ||||
\(19\) | − | 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 | 0.884609 | − | 0.466334i | \(-0.154426\pi\) |
−0.466334 | + | 0.884609i | \(0.654426\pi\) | |||||||
\(24\) | 1.72237 | + | 0.182842i | 0.351578 | + | 0.0373224i | ||||
\(25\) | −4.41845 | + | 2.34036i | −0.883690 | + | 0.468073i | ||||
\(26\) | 1.87994i | 0.368687i | ||||||||
\(27\) | −2.34453 | − | 4.63715i | −0.451206 | − | 0.892420i | ||||
\(28\) | 2.86820 | − | 2.86820i | 0.542038 | − | 0.542038i | ||||
\(29\) | 6.21092 | 1.15334 | 0.576670 | − | 0.816978i | \(-0.304352\pi\) | ||||
0.576670 | + | 0.816978i | \(0.304352\pi\) | |||||||
\(30\) | 3.83627 | − | 0.531985i | 0.700404 | − | 0.0971267i | ||||
\(31\) | −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 | ||||
\(33\) | −5.01005 | − | 6.20008i | −0.872138 | − | 1.07930i | ||||
\(34\) | − | 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 | \(-0.956556\pi\) | ||
0.990701 | − | 0.136060i | \(-0.0434440\pi\) | |||||||
\(42\) | −5.46453 | + | 4.41568i | −0.843195 | + | 0.681354i | ||||
\(43\) | 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 | ||||||||
\(45\) | −6.70476 | + | 0.214847i | −0.999487 | + | 0.0320275i | ||||
\(46\) | −2.83687 | −0.418274 | ||||||||
\(47\) | 5.22236 | − | 5.22236i | 0.761759 | − | 0.761759i | −0.214881 | − | 0.976640i | \(-0.568936\pi\) |
0.976640 | + | 0.214881i | \(0.0689365\pi\) | |||||||
\(48\) | −1.34719 | + | 1.08861i | −0.194450 | + | 0.157128i | ||||
\(49\) | 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 | 0.960344 | − | 0.278817i | \(-0.0899422\pi\) |
−0.278817 | + | 0.960344i | \(0.589942\pi\) | |||||||
\(54\) | 4.93680 | + | 1.62112i | 0.671813 | + | 0.220607i | ||||
\(55\) | −9.98719 | + | 2.48169i | −1.34667 | + | 0.334631i | ||||
\(56\) | 4.05624i | 0.542038i | ||||||||
\(57\) | −1.08861 | − | 1.34719i | −0.144190 | − | 0.178440i | ||||
\(58\) | −4.39178 | + | 4.39178i | −0.576670 | + | 0.576670i | ||||
\(59\) | −5.08697 | −0.662268 | −0.331134 | − | 0.943584i | \(-0.607431\pi\) | ||||
−0.331134 | + | 0.943584i | \(0.607431\pi\) | |||||||
\(60\) | −2.33648 | + | 3.08883i | −0.301639 | + | 0.398766i | ||||
\(61\) | −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 | ||||
\(63\) | 10.2193 | − | 6.60631i | 1.28751 | − | 0.832316i | ||||
\(64\) | 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 | \(0.373035\pi\) | ||||
−0.388380 | + | 0.921499i | \(0.626965\pi\) | |||||||
\(72\) | 2.51941 | − | 1.62868i | 0.296915 | − | 0.191941i | ||||
\(73\) | −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 | ||||||||
\(75\) | −3.40474 | + | 7.96290i | −0.393146 | + | 0.919476i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 13.2001 | − | 13.2001i | 1.50429 | − | 1.50429i | ||||
\(78\) | 2.04653 | + | 2.53264i | 0.231724 | + | 0.286765i | ||||
\(79\) | − | 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 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) |
−0.887154 | + | 0.461474i | \(0.847321\pi\) | |||||||
\(84\) | 0.741650 | − | 6.98636i | 0.0809206 | − | 0.762275i | ||||
\(85\) | 9.22345 | + | 5.55195i | 1.00042 | + | 0.602194i | ||||
\(86\) | 11.5870i | 1.24946i | ||||||||
\(87\) | 8.36729 | − | 6.76129i | 0.897068 | − | 0.724886i | ||||
\(88\) | 3.25427 | − | 3.25427i | 0.346906 | − | 0.346906i | ||||
\(89\) | −2.07373 | −0.219814 | −0.109907 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109907 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(90\) | 4.58906 | − | 4.89290i | 0.483730 | − | 0.515757i | ||||
\(91\) | 7.62551 | 0.799370 | ||||||||
\(92\) | 2.00597 | − | 2.00597i | 0.209137 | − | 0.209137i | ||||
\(93\) | −5.27420 | + | 4.26188i | −0.546909 | + | 0.441936i | ||||
\(94\) | 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 | \(0.0294082\pi\) | ||||
−0.995735 | + | 0.0922571i | \(0.970592\pi\) | |||||||
\(102\) | −5.24111 | − | 6.48602i | −0.518947 | − | 0.642212i | ||||
\(103\) | −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 | ||||||||
\(105\) | −2.15786 | − | 15.5609i | −0.210586 | − | 1.51858i | ||||
\(106\) | −7.01675 | −0.681527 | ||||||||
\(107\) | −8.61306 | + | 8.61306i | −0.832656 | + | 0.832656i | −0.987879 | − | 0.155223i | \(-0.950390\pi\) |
0.155223 | + | 0.987879i | \(0.450390\pi\) | |||||||
\(108\) | −4.63715 | + | 2.34453i | −0.446210 | + | 0.225603i | ||||
\(109\) | 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 | 0.751907 | − | 0.659269i | \(-0.229134\pi\) |
−0.659269 | + | 0.751907i | \(0.729134\pi\) | |||||||
\(114\) | 1.72237 | + | 0.182842i | 0.161315 | + | 0.0171247i | ||||
\(115\) | 3.27142 | − | 5.43480i | 0.305061 | − | 0.506798i | ||||
\(116\) | − | 6.21092i | − | 0.576670i | ||||||
\(117\) | −3.06182 | − | 4.73634i | −0.283065 | − | 0.437875i | ||||
\(118\) | 3.59703 | − | 3.59703i | 0.331134 | − | 0.331134i | ||||
\(119\) | −19.5287 | −1.79019 | ||||||||
\(120\) | −0.531985 | − | 3.83627i | −0.0485634 | − | 0.350202i | ||||
\(121\) | −10.1805 | −0.925503 | ||||||||
\(122\) | 0.315382 | − | 0.315382i | 0.0285534 | − | 0.0285534i | ||||
\(123\) | −1.89682 | − | 2.34737i | −0.171030 | − | 0.211655i | ||||
\(124\) | 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 | \(0.303789\pi\) | ||||
−0.578115 | + | 0.815955i | \(0.696211\pi\) | |||||||
\(132\) | −6.20008 | + | 5.01005i | −0.539648 | + | 0.436069i | ||||
\(133\) | 2.86820 | − | 2.86820i | 0.248704 | − | 0.248704i | ||||
\(134\) | −8.88078 | −0.767183 | ||||||||
\(135\) | −8.79871 | + | 7.58833i | −0.757272 | + | 0.653100i | ||||
\(136\) | −4.81448 | −0.412838 | ||||||||
\(137\) | 14.3208 | − | 14.3208i | 1.22351 | − | 1.22351i | 0.257137 | − | 0.966375i | \(-0.417221\pi\) |
0.966375 | − | 0.257137i | \(-0.0827792\pi\) | |||||||
\(138\) | −3.82181 | + | 3.08826i | −0.325334 | + | 0.262890i | ||||
\(139\) | 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 | ||||||
\(147\) | 10.2908 | + | 12.7351i | 0.848769 | + | 1.05038i | ||||
\(148\) | −4.28573 | + | 4.28573i | −0.352285 | + | 0.352285i | ||||
\(149\) | −5.59268 | −0.458170 | −0.229085 | − | 0.973406i | \(-0.573573\pi\) | ||||
−0.229085 | + | 0.973406i | \(0.573573\pi\) | |||||||
\(150\) | −3.22310 | − | 8.03813i | −0.263165 | − | 0.656311i | ||||
\(151\) | −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 | ||||
\(153\) | 7.84123 | + | 12.1296i | 0.633926 | + | 0.980623i | ||||
\(154\) | 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 | ||||||||
\(162\) | 8.41558 | − | 3.19030i | 0.661190 | − | 0.250654i | ||||
\(163\) | −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 | ||||||||
\(165\) | −10.7530 | + | 14.2155i | −0.837123 | + | 1.10667i | ||||
\(166\) | 5.48450 | 0.425680 | ||||||||
\(167\) | 4.00388 | − | 4.00388i | 0.309830 | − | 0.309830i | −0.535014 | − | 0.844843i | \(-0.679694\pi\) |
0.844843 | + | 0.535014i | \(0.179694\pi\) | |||||||
\(168\) | 4.41568 | + | 5.46453i | 0.340677 | + | 0.421598i | ||||
\(169\) | 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 | 0.946259 | − | 0.323409i | \(-0.104829\pi\) |
−0.323409 | + | 0.946259i | \(0.604829\pi\) | |||||||
\(174\) | −1.13561 | + | 10.6975i | −0.0860907 | + | 0.810977i | ||||
\(175\) | −19.3856 | − | 5.96036i | −1.46541 | − | 0.450561i | ||||
\(176\) | 4.60223i | 0.346906i | ||||||||
\(177\) | −6.85312 | + | 5.53775i | −0.515112 | + | 0.416243i | ||||
\(178\) | 1.46635 | − | 1.46635i | 0.109907 | − | 0.109907i | ||||
\(179\) | −5.97757 | −0.446784 | −0.223392 | − | 0.974729i | \(-0.571713\pi\) | ||||
−0.223392 | + | 0.974729i | \(0.571713\pi\) | |||||||
\(180\) | 0.214847 | + | 6.70476i | 0.0160137 | + | 0.499743i | ||||
\(181\) | 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 | ||||
\(183\) | −0.600871 | + | 0.485541i | −0.0444177 | + | 0.0358922i | ||||
\(184\) | 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 | \(-0.924943\pi\) | ||
0.972328 | − | 0.233620i | \(-0.0750572\pi\) | |||||||
\(192\) | 1.08861 | + | 1.34719i | 0.0785639 | + | 0.0972251i | ||||
\(193\) | 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 | ||||||||
\(195\) | −7.21197 | + | 1.00010i | −0.516460 | + | 0.0716188i | ||||
\(196\) | 9.45311 | 0.675222 | ||||||||
\(197\) | 14.8702 | − | 14.8702i | 1.05946 | − | 1.05946i | 0.0613383 | − | 0.998117i | \(-0.480463\pi\) |
0.998117 | − | 0.0613383i | \(-0.0195368\pi\) | |||||||
\(198\) | 11.5949 | − | 7.49554i | 0.824014 | − | 0.532685i | ||||
\(199\) | − | 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 | ||||||
\(207\) | 7.14724 | − | 4.62035i | 0.496768 | − | 0.321136i | ||||
\(208\) | −1.32932 | + | 1.32932i | −0.0921718 | + | 0.0921718i | ||||
\(209\) | −4.60223 | −0.318343 | ||||||||
\(210\) | 12.5290 | + | 9.47735i | 0.864585 | + | 0.653999i | ||||
\(211\) | −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 | ||||
\(213\) | 16.9055 | + | 20.9210i | 1.15834 | + | 1.43349i | ||||
\(214\) | − | 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 | ||||||||
\(222\) | 8.16524 | − | 6.59802i | 0.548015 | − | 0.442830i | ||||
\(223\) | 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 | ||||||||
\(225\) | 4.08168 | + | 14.4340i | 0.272112 | + | 0.962266i | ||||
\(226\) | −1.39266 | −0.0926383 | ||||||||
\(227\) | −13.7553 | + | 13.7553i | −0.912969 | + | 0.912969i | −0.996505 | − | 0.0835359i | \(-0.973379\pi\) |
0.0835359 | + | 0.996505i | \(0.473379\pi\) | |||||||
\(228\) | −1.34719 | + | 1.08861i | −0.0892198 | + | 0.0720952i | ||||
\(229\) | − | 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 | 0.826019 | − | 0.563643i | \(-0.190601\pi\) |
−0.563643 | + | 0.826019i | \(0.690601\pi\) | |||||||
\(234\) | 5.51413 | + | 1.18407i | 0.360470 | + | 0.0774050i | ||||
\(235\) | −14.1490 | − | 8.51682i | −0.922978 | − | 0.555576i | ||||
\(236\) | 5.08697i | 0.331134i | ||||||||
\(237\) | −11.3704 | − | 14.0713i | −0.738590 | − | 0.914026i | ||||
\(238\) | 13.8089 | − | 13.8089i | 0.895097 | − | 0.895097i | ||||
\(239\) | −1.96845 | −0.127329 | −0.0636643 | − | 0.997971i | \(-0.520279\pi\) | ||||
−0.0636643 | + | 0.997971i | \(0.520279\pi\) | |||||||
\(240\) | 3.08883 | + | 2.33648i | 0.199383 | + | 0.150819i | ||||
\(241\) | 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 | ||||
\(243\) | −15.0781 | + | 3.95617i | −0.967260 | + | 0.253788i | ||||
\(244\) | 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 | \(-0.935816\pi\) | ||
0.979740 | − | 0.200275i | \(-0.0641837\pi\) | |||||||
\(252\) | −6.60631 | − | 10.2193i | −0.416158 | − | 0.643757i | ||||
\(253\) | 9.23195 | − | 9.23195i | 0.580408 | − | 0.580408i | ||||
\(254\) | −11.7678 | −0.738378 | ||||||||
\(255\) | 18.4697 | − | 2.56123i | 1.15662 | − | 0.160391i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.25382 | + | 3.25382i | −0.202968 | + | 0.202968i | −0.801270 | − | 0.598302i | \(-0.795842\pi\) |
0.598302 | + | 0.801270i | \(0.295842\pi\) | |||||||
\(258\) | 12.6138 | + | 15.6099i | 0.785301 | + | 0.971832i | ||||
\(259\) | − | 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 | \(-0.904952\pi\) |
−0.294183 | − | 0.955749i | \(-0.595048\pi\) | |||||||
\(264\) | 0.841479 | − | 7.92676i | 0.0517895 | − | 0.487858i | ||||
\(265\) | 8.09156 | − | 13.4425i | 0.497061 | − | 0.825766i | ||||
\(266\) | 4.05624i | 0.248704i | ||||||||
\(267\) | −2.79370 | + | 2.25748i | −0.170972 | + | 0.138156i | ||||
\(268\) | 6.27966 | − | 6.27966i | 0.383591 | − | 0.383591i | ||||
\(269\) | 16.9049 | 1.03071 | 0.515354 | − | 0.856977i | \(-0.327660\pi\) | ||||
0.515354 | + | 0.856977i | \(0.327660\pi\) | |||||||
\(270\) | 0.855863 | − | 11.5874i | 0.0520861 | − | 0.705186i | ||||
\(271\) | −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 | ||||
\(273\) | 10.2730 | − | 8.30123i | 0.621751 | − | 0.502413i | ||||
\(274\) | 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 | \(0.138040\pi\) | ||||
−0.907431 | + | 0.420200i | \(0.861960\pi\) | |||||||
\(282\) | 8.03998 | + | 9.94971i | 0.478774 | + | 0.592496i | ||||
\(283\) | 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 | ||||||||
\(285\) | −2.33648 | + | 3.08883i | −0.138401 | + | 0.182966i | ||||
\(286\) | 8.65193 | 0.511600 | ||||||||
\(287\) | 4.99760 | − | 4.99760i | 0.294999 | − | 0.294999i | ||||
\(288\) | −1.62868 | − | 2.51941i | −0.0959706 | − | 0.148458i | ||||
\(289\) | − | 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 | 0.548491 | − | 0.836156i | \(-0.315202\pi\) |
−0.836156 | + | 0.548491i | \(0.815202\pi\) | |||||||
\(294\) | −16.2818 | − | 1.72842i | −0.949573 | − | 0.100804i | ||||
\(295\) | 2.74308 | + | 11.0391i | 0.159708 | + | 0.642722i | ||||
\(296\) | − | 6.06094i | − | 0.352285i | ||||||
\(297\) | −21.3412 | + | 10.7901i | −1.23834 | + | 0.626105i | ||||
\(298\) | 3.95462 | − | 3.95462i | 0.229085 | − | 0.229085i | ||||
\(299\) | 5.33316 | 0.308425 | ||||||||
\(300\) | 7.96290 | + | 3.40474i | 0.459738 | + | 0.196573i | ||||
\(301\) | 46.9998 | 2.70903 | ||||||||
\(302\) | 3.26781 | − | 3.26781i | 0.188041 | − | 0.188041i | ||||
\(303\) | 2.01866 | + | 2.49816i | 0.115969 | + | 0.143515i | ||||
\(304\) | 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 | \(0.221452\pi\) | ||||
−0.767598 | + | 0.640931i | \(0.778548\pi\) | |||||||
\(312\) | 2.53264 | − | 2.04653i | 0.143383 | − | 0.115862i | ||||
\(313\) | −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 | ||||||||
\(315\) | −19.8468 | − | 18.6144i | −1.11824 | − | 1.04880i | ||||
\(316\) | −10.4449 | −0.587571 | ||||||||
\(317\) | −0.617852 | + | 0.617852i | −0.0347020 | + | 0.0347020i | −0.724245 | − | 0.689543i | \(-0.757811\pi\) |
0.689543 | + | 0.724245i | \(0.257811\pi\) | |||||||
\(318\) | −9.45290 | + | 7.63853i | −0.530092 | + | 0.428348i | ||||
\(319\) | − | 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 | ||||||
\(327\) | 6.88804 | + | 8.52415i | 0.380910 | + | 0.471387i | ||||
\(328\) | 1.23207 | − | 1.23207i | 0.0680300 | − | 0.0680300i | ||||
\(329\) | 29.9575 | 1.65161 | ||||||||
\(330\) | −2.44832 | − | 17.6554i | −0.134776 | − | 0.971899i | ||||
\(331\) | 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 | ||||
\(333\) | −15.2700 | + | 9.87131i | −0.836790 | + | 0.540944i | ||||
\(334\) | 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 | ||||||||
\(342\) | 2.51941 | − | 1.62868i | 0.136234 | − | 0.0880687i | ||||
\(343\) | −7.03600 | + | 7.03600i | −0.379908 | + | 0.379908i | ||||
\(344\) | 11.5870 | 0.624731 | ||||||||
\(345\) | −1.50917 | − | 10.8830i | −0.0812512 | − | 0.585922i | ||||
\(346\) | −11.5857 | −0.622850 | ||||||||
\(347\) | 20.8770 | − | 20.8770i | 1.12074 | − | 1.12074i | 0.129107 | − | 0.991631i | \(-0.458789\pi\) |
0.991631 | − | 0.129107i | \(-0.0412109\pi\) | |||||||
\(348\) | −6.76129 | − | 8.36729i | −0.362443 | − | 0.448534i | ||||
\(349\) | − | 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 | 0.726101 | − | 0.687589i | \(-0.241331\pi\) |
−0.687589 | + | 0.726101i | \(0.741331\pi\) | |||||||
\(354\) | 0.930110 | − | 8.76167i | 0.0494348 | − | 0.465677i | ||||
\(355\) | 33.6999 | − | 8.37399i | 1.78861 | − | 0.444445i | ||||
\(356\) | 2.07373i | 0.109907i | ||||||||
\(357\) | −26.3089 | + | 21.2592i | −1.39241 | + | 1.12516i | ||||
\(358\) | 4.22678 | − | 4.22678i | 0.223392 | − | 0.223392i | ||||
\(359\) | −25.4403 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(360\) | −4.89290 | − | 4.58906i | −0.257879 | − | 0.241865i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −5.99334 | + | 5.99334i | −0.315003 | + | 0.315003i | ||||
\(363\) | −13.7151 | + | 11.0827i | −0.719857 | + | 0.581689i | ||||
\(364\) | − | 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 | ||||||||
\(372\) | 4.26188 | + | 5.27420i | 0.220968 | + | 0.273454i | ||||
\(373\) | 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 | ||||||||
\(375\) | 19.1160 | + | 3.09467i | 0.987148 | + | 0.159808i | ||||
\(376\) | 7.38553 | 0.380879 | ||||||||
\(377\) | 8.25630 | − | 8.25630i | 0.425221 | − | 0.425221i | ||||
\(378\) | 9.51000 | + | 18.8094i | 0.489142 | + | 0.967452i | ||||
\(379\) | − | 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 | 0.939215 | − | 0.343329i | \(-0.111555\pi\) |
−0.343329 | + | 0.939215i | \(0.611555\pi\) | |||||||
\(384\) | −1.72237 | − | 0.182842i | −0.0878945 | − | 0.00933059i | ||||
\(385\) | −35.7632 | − | 21.5273i | −1.82266 | − | 1.09713i | ||||
\(386\) | 6.12000i | 0.311500i | ||||||||
\(387\) | −18.8715 | − | 29.1925i | −0.959293 | − | 1.48394i | ||||
\(388\) | 12.5075 | − | 12.5075i | 0.634972 | − | 0.634972i | ||||
\(389\) | −15.6133 | −0.791625 | −0.395813 | − | 0.918331i | \(-0.629537\pi\) | ||||
−0.395813 | + | 0.918331i | \(0.629537\pi\) | |||||||
\(390\) | 4.39246 | − | 5.80681i | 0.222421 | − | 0.294039i | ||||
\(391\) | −13.6581 | −0.690719 | ||||||||
\(392\) | −6.68436 | + | 6.68436i | −0.337611 | + | 0.337611i | ||||
\(393\) | 20.3332 | + | 25.1629i | 1.02567 | + | 1.26930i | ||||
\(394\) | 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 | \(-0.960816\pi\) | ||
0.992433 | − | 0.122791i | \(-0.0391844\pi\) | |||||||
\(402\) | −11.9641 | + | 9.66774i | −0.596715 | + | 0.482183i | ||||
\(403\) | −5.20424 | + | 5.20424i | −0.259242 | + | 0.259242i | ||||
\(404\) | 1.85435 | 0.0922571 | ||||||||
\(405\) | −3.59277 | + | 19.8013i | −0.178526 | + | 0.983935i | ||||
\(406\) | −25.1930 | −1.25031 | ||||||||
\(407\) | −19.7239 | + | 19.7239i | −0.977679 | + | 0.977679i | ||||
\(408\) | −6.48602 | + | 5.24111i | −0.321106 | + | 0.259473i | ||||
\(409\) | 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 | ||||||
\(417\) | 12.2606 | + | 15.1729i | 0.600406 | + | 0.743020i | ||||
\(418\) | 3.25427 | − | 3.25427i | 0.159172 | − | 0.159172i | ||||
\(419\) | −12.5500 | −0.613105 | −0.306553 | − | 0.951854i | \(-0.599176\pi\) | ||||
−0.306553 | + | 0.951854i | \(0.599176\pi\) | |||||||
\(420\) | −15.5609 | + | 2.15786i | −0.759292 | + | 0.105293i | ||||
\(421\) | −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 | ||||
\(423\) | −12.0286 | − | 18.6072i | −0.584852 | − | 0.904711i | ||||
\(424\) | 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 | \(-0.935926\pi\) | ||
0.979809 | − | 0.199936i | \(-0.0640735\pi\) | |||||||
\(432\) | 2.34453 | + | 4.63715i | 0.112801 | + | 0.223105i | ||||
\(433\) | −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 | ||||||||
\(435\) | −19.1844 | − | 14.5117i | −0.919824 | − | 0.695784i | ||||
\(436\) | 6.32736 | 0.303025 | ||||||||
\(437\) | 2.00597 | − | 2.00597i | 0.0959587 | − | 0.0959587i | ||||
\(438\) | −9.80248 | − | 12.1309i | −0.468381 | − | 0.579635i | ||||
\(439\) | − | 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 | \(-0.922891\pi\) |
−0.239884 | − | 0.970802i | \(-0.577109\pi\) | |||||||
\(444\) | −1.10819 | + | 10.4392i | −0.0525924 | + | 0.495422i | ||||
\(445\) | 1.11823 | + | 4.50014i | 0.0530090 | + | 0.213327i | ||||
\(446\) | 14.3154i | 0.677856i | ||||||||
\(447\) | −7.53441 | + | 6.08827i | −0.356365 | + | 0.287965i | ||||
\(448\) | −2.86820 | + | 2.86820i | −0.135510 | + | 0.135510i | ||||
\(449\) | 7.40137 | 0.349292 | 0.174646 | − | 0.984631i | \(-0.444122\pi\) | ||||
0.174646 | + | 0.984631i | \(0.444122\pi\) | |||||||
\(450\) | −13.0926 | − | 7.32018i | −0.617189 | − | 0.345077i | ||||
\(451\) | −8.01901 | −0.377600 | ||||||||
\(452\) | 0.984759 | − | 0.984759i | 0.0463192 | − | 0.0463192i | ||||
\(453\) | −6.22588 | + | 5.03090i | −0.292517 | + | 0.236372i | ||||
\(454\) | − | 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 | \(-0.657304\pi\) | ||
0.474314 | − | 0.880356i | \(-0.342696\pi\) | |||||||
\(462\) | 20.3220 | + | 25.1490i | 0.945464 | + | 1.17004i | ||||
\(463\) | −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 | ||||||||
\(465\) | 12.0926 | + | 9.14725i | 0.560782 | + | 0.424193i | ||||
\(466\) | −5.66392 | −0.262376 | ||||||||
\(467\) | −28.1504 | + | 28.1504i | −1.30265 | + | 1.30265i | −0.376045 | + | 0.926601i | \(0.622716\pi\) |
−0.926601 | + | 0.376045i | \(0.877284\pi\) | |||||||
\(468\) | −4.73634 | + | 3.06182i | −0.218938 | + | 0.141533i | ||||
\(469\) | 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 | ||||||||
\(477\) | 17.6781 | − | 11.4280i | 0.809423 | − | 0.523253i | ||||
\(478\) | 1.39191 | − | 1.39191i | 0.0636643 | − | 0.0636643i | ||||
\(479\) | −23.0077 | −1.05125 | −0.525624 | − | 0.850717i | \(-0.676168\pi\) | ||||
−0.525624 | + | 0.850717i | \(0.676168\pi\) | |||||||
\(480\) | −3.83627 | + | 0.531985i | −0.175101 | + | 0.0242817i | ||||
\(481\) | −11.3942 | −0.519532 | ||||||||
\(482\) | −16.9005 | + | 16.9005i | −0.769794 | + | 0.769794i | ||||
\(483\) | 12.5267 | + | 15.5022i | 0.569986 | + | 0.705374i | ||||
\(484\) | 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 | \(-0.875308\pi\) | ||
0.924249 | − | 0.381791i | \(-0.124692\pi\) | |||||||
\(492\) | −2.34737 | + | 1.89682i | −0.105827 | + | 0.0855152i | ||||
\(493\) | −21.1442 | + | 21.1442i | −0.952285 | + | 0.952285i | ||||
\(494\) | 1.87994 | 0.0845826 | ||||||||
\(495\) | 0.988774 | + | 30.8569i | 0.0444421 | + | 1.38691i | ||||
\(496\) | 3.91496 | 0.175787 | ||||||||
\(497\) | −44.5413 | + | 44.5413i | −1.99795 | + | 1.99795i | ||||
\(498\) | 7.38866 | − | 5.97050i | 0.331094 | − | 0.267544i | ||||
\(499\) | − | 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 | 0.786838 | − | 0.617159i | \(-0.211716\pi\) |
−0.617159 | + | 0.786838i | \(0.711716\pi\) | |||||||
\(504\) | 11.8975 | + | 2.55479i | 0.529958 | + | 0.113800i | ||||
\(505\) | 4.02407 | − | 0.999929i | 0.179069 | − | 0.0444963i | ||||
\(506\) | 13.0560i | 0.580408i | ||||||||
\(507\) | 10.3046 | + | 12.7523i | 0.457644 | + | 0.566347i | ||||
\(508\) | 8.32109 | − | 8.32109i | 0.369189 | − | 0.369189i | ||||
\(509\) | −7.97379 | −0.353432 | −0.176716 | − | 0.984262i | \(-0.556547\pi\) | ||||
−0.176716 | + | 0.984262i | \(0.556547\pi\) | |||||||
\(510\) | −11.2490 | + | 14.8711i | −0.498112 | + | 0.658503i | ||||
\(511\) | −36.5247 | −1.61576 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.63715 | + | 2.34453i | −0.204735 | + | 0.103514i | ||||
\(514\) | − | 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 | \(-0.842326\pi\) | ||
0.879804 | − | 0.475336i | \(-0.157674\pi\) | |||||||
\(522\) | 10.1156 | + | 15.6478i | 0.442747 | + | 0.684887i | ||||
\(523\) | −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 | ||||||||
\(525\) | −32.6046 | + | 13.0737i | −1.42298 | + | 0.570583i | ||||
\(526\) | 28.6668 | 1.24993 | ||||||||
\(527\) | 13.3279 | − | 13.3279i | 0.580573 | − | 0.580573i | ||||
\(528\) | 5.01005 | + | 6.20008i | 0.218034 | + | 0.269824i | ||||
\(529\) | − | 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 | ||||||||
\(537\) | −8.05292 | + | 6.50726i | −0.347509 | + | 0.280809i | ||||
\(538\) | −11.9535 | + | 11.9535i | −0.515354 | + | 0.515354i | ||||
\(539\) | 43.5054 | 1.87391 | ||||||||
\(540\) | 7.58833 | + | 8.79871i | 0.326550 | + | 0.378636i | ||||
\(541\) | −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 | ||||
\(543\) | 11.4186 | − | 9.22694i | 0.490019 | − | 0.395966i | ||||
\(544\) | 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 | ||||||
\(552\) | 3.08826 | + | 3.82181i | 0.131445 | + | 0.162667i | ||||
\(553\) | 29.9580 | − | 29.9580i | 1.27394 | − | 1.27394i | ||||
\(554\) | 5.71150 | 0.242659 | ||||||||
\(555\) | 3.22433 | + | 23.2514i | 0.136865 | + | 0.986968i | ||||
\(556\) | 11.2626 | 0.477642 | ||||||||
\(557\) | 15.4865 | − | 15.4865i | 0.656182 | − | 0.656182i | −0.298292 | − | 0.954475i | \(-0.596417\pi\) |
0.954475 | + | 0.298292i | \(0.0964170\pi\) | |||||||
\(558\) | −6.37620 | − | 9.86338i | −0.269926 | − | 0.417550i | ||||
\(559\) | − | 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 | 0.996745 | − | 0.0806140i | \(-0.0256881\pi\) |
−0.0806140 | + | 0.996745i | \(0.525688\pi\) | |||||||
\(564\) | −12.7206 | − | 1.35038i | −0.535635 | − | 0.0568613i | ||||
\(565\) | 1.60598 | − | 2.66802i | 0.0675642 | − | 0.112244i | ||||
\(566\) | 21.3107i | 0.895756i | ||||||||
\(567\) | −12.9406 | − | 34.1356i | −0.543456 | − | 1.43356i | ||||
\(568\) | −10.9809 | + | 10.9809i | −0.460750 | + | 0.460750i | ||||
\(569\) | 33.8572 | 1.41937 | 0.709684 | − | 0.704520i | \(-0.248838\pi\) | ||||
0.709684 | + | 0.704520i | \(0.248838\pi\) | |||||||
\(570\) | −0.531985 | − | 3.83627i | −0.0222824 | − | 0.160684i | ||||
\(571\) | −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 | ||||
\(573\) | −7.02960 | − | 8.69933i | −0.293666 | − | 0.363420i | ||||
\(574\) | 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 | ||||||
\(582\) | −23.8295 | + | 19.2557i | −0.987763 | + | 0.798174i | ||||
\(583\) | 22.8344 | − | 22.8344i | 0.945705 | − | 0.945705i | ||||
\(584\) | −9.00456 | −0.372611 | ||||||||
\(585\) | −8.62718 | + | 9.19838i | −0.356690 | + | 0.380306i | ||||
\(586\) | 6.96364 | 0.287665 | ||||||||
\(587\) | −22.9650 | + | 22.9650i | −0.947869 | + | 0.947869i | −0.998707 | − | 0.0508382i | \(-0.983811\pi\) |
0.0508382 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(588\) | 12.7351 | − | 10.2908i | 0.525188 | − | 0.424385i | ||||
\(589\) | 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 | 0.661734 | − | 0.749739i | \(-0.269821\pi\) |
−0.749739 | + | 0.661734i | \(0.769821\pi\) | |||||||
\(594\) | 7.46079 | − | 22.7203i | 0.306120 | − | 0.932224i | ||||
\(595\) | 10.5306 | + | 42.3788i | 0.431711 | + | 1.73736i | ||||
\(596\) | 5.59268i | 0.229085i | ||||||||
\(597\) | −0.859707 | − | 1.06391i | −0.0351855 | − | 0.0435430i | ||||
\(598\) | −3.77111 | + | 3.77111i | −0.154212 | + | 0.154212i | ||||
\(599\) | −28.0055 | −1.14427 | −0.572137 | − | 0.820158i | \(-0.693885\pi\) | ||||
−0.572137 | + | 0.820158i | \(0.693885\pi\) | |||||||
\(600\) | −8.03813 | + | 3.22310i | −0.328155 | + | 0.131583i | ||||
\(601\) | −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 | ||||
\(603\) | 22.3743 | − | 14.4639i | 0.911152 | − | 0.589016i | ||||
\(604\) | 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 | ||||||
\(612\) | 12.1296 | − | 7.84123i | 0.490312 | − | 0.316963i | ||||
\(613\) | −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 | ||||||||
\(615\) | −4.07113 | + | 5.38202i | −0.164164 | + | 0.217024i | ||||
\(616\) | 18.6678 | 0.752146 | ||||||||
\(617\) | 25.7417 | − | 25.7417i | 1.03632 | − | 1.03632i | 0.0370077 | − | 0.999315i | \(-0.488217\pi\) |
0.999315 | − | 0.0370077i | \(-0.0117826\pi\) | |||||||
\(618\) | −17.6431 | − | 21.8338i | −0.709709 | − | 0.878286i | ||||
\(619\) | − | 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 | ||||||
\(627\) | −6.20008 | + | 5.01005i | −0.247607 | + | 0.200082i | ||||
\(628\) | −10.3075 | + | 10.3075i | −0.411313 | + | 0.411313i | ||||
\(629\) | 29.1803 | 1.16349 | ||||||||
\(630\) | 27.1961 | − | 0.871471i | 1.08352 | − | 0.0347202i | ||||
\(631\) | −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 | ||||
\(633\) | −26.7668 | + | 21.6292i | −1.06388 | + | 0.859683i | ||||
\(634\) | − | 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 | \(0.0592160\pi\) | ||||
−0.982746 | + | 0.184961i | \(0.940784\pi\) | |||||||
\(642\) | −13.2601 | − | 16.4097i | −0.523334 | − | 0.647640i | ||||
\(643\) | −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 | ||||||||
\(645\) | −44.4510 | + | 6.16413i | −1.75026 | + | 0.242712i | ||||
\(646\) | −4.81448 | −0.189423 | ||||||||
\(647\) | −6.75416 | + | 6.75416i | −0.265533 | + | 0.265533i | −0.827297 | − | 0.561764i | \(-0.810123\pi\) |
0.561764 | + | 0.827297i | \(0.310123\pi\) | |||||||
\(648\) | −3.19030 | − | 8.41558i | −0.125327 | − | 0.330595i | ||||
\(649\) | 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 | 0.921655 | − | 0.388011i | \(-0.126838\pi\) |
−0.388011 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(654\) | −10.8981 | − | 1.15690i | −0.426148 | − | 0.0452385i | ||||
\(655\) | 40.5328 | − | 10.0719i | 1.58375 | − | 0.393541i | ||||
\(656\) | 1.74242i | 0.0680300i | ||||||||
\(657\) | 14.6655 | + | 22.6862i | 0.572156 | + | 0.885071i | ||||
\(658\) | −21.1831 | + | 21.1831i | −0.825805 | + | 0.825805i | ||||
\(659\) | 10.2941 | 0.401002 | 0.200501 | − | 0.979694i | \(-0.435743\pi\) | ||||
0.200501 | + | 0.979694i | \(0.435743\pi\) | |||||||
\(660\) | 14.2155 | + | 10.7530i | 0.553337 | + | 0.418562i | ||||
\(661\) | 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 | ||||
\(663\) | 9.85298 | + | 12.1933i | 0.382658 | + | 0.473550i | ||||
\(664\) | − | 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 | ||||||||
\(672\) | 5.46453 | − | 4.41568i | 0.210799 | − | 0.170339i | ||||
\(673\) | 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 | ||||||||
\(675\) | 21.2118 | + | 15.0020i | 0.816444 | + | 0.577425i | ||||
\(676\) | 9.46581 | 0.364070 | ||||||||
\(677\) | 6.41647 | − | 6.41647i | 0.246605 | − | 0.246605i | −0.572971 | − | 0.819576i | \(-0.694209\pi\) |
0.819576 | + | 0.572971i | \(0.194209\pi\) | |||||||
\(678\) | −1.87618 | + | 1.51607i | −0.0720541 | + | 0.0582242i | ||||
\(679\) | 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 | 0.218409 | − | 0.975857i | \(-0.429913\pi\) |
−0.975857 | + | 0.218409i | \(0.929913\pi\) | |||||||
\(684\) | −0.629843 | + | 2.93314i | −0.0240826 | + | 0.112151i | ||||
\(685\) | −38.7996 | − | 23.3550i | −1.48246 | − | 0.892348i | ||||
\(686\) | − | 9.95041i | − | 0.379908i | ||||||
\(687\) | −7.04387 | − | 8.71699i | −0.268740 | − | 0.332574i | ||||
\(688\) | −8.19327 | + | 8.19327i | −0.312366 | + | 0.312366i | ||||
\(689\) | 13.1911 | 0.502541 | ||||||||
\(690\) | 8.76261 | + | 6.62831i | 0.333587 | + | 0.252336i | ||||
\(691\) | 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 | ||||
\(693\) | −30.4037 | − | 47.0317i | −1.15494 | − | 1.78659i | ||||
\(694\) | 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 | \(-0.817224\pi\) | ||
0.839623 | − | 0.543170i | \(-0.182776\pi\) | |||||||
\(702\) | 8.71758 | − | 4.40759i | 0.329024 | − | 0.166354i | ||||
\(703\) | −4.28573 | + | 4.28573i | −0.161639 | + | 0.161639i | ||||
\(704\) | 4.60223 | 0.173453 | ||||||||
\(705\) | −28.3329 | + | 3.92899i | −1.06708 | + | 0.147974i | ||||
\(706\) | −1.02329 | −0.0385121 | ||||||||
\(707\) | −5.31863 | + | 5.31863i | −0.200028 | + | 0.200028i | ||||
\(708\) | 5.53775 | + | 6.85312i | 0.208121 | + | 0.257556i | ||||
\(709\) | − | 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 | ||||||||
\(717\) | −2.65188 | + | 2.14288i | −0.0990362 | + | 0.0800274i | ||||
\(718\) | 17.9890 | − | 17.9890i | 0.671345 | − | 0.671345i | ||||
\(719\) | −0.237709 | −0.00886505 | −0.00443253 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443253 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(720\) | 6.70476 | − | 0.214847i | 0.249872 | − | 0.00800686i | ||||
\(721\) | −65.7393 | −2.44826 | ||||||||
\(722\) | 0.707107 | − | 0.707107i | 0.0263158 | − | 0.0263158i | ||||
\(723\) | 32.1990 | − | 26.0188i | 1.19749 | − | 0.967649i | ||||
\(724\) | − | 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 | ||||||||
\(732\) | 0.485541 | + | 0.600871i | 0.0179461 | + | 0.0222088i | ||||
\(733\) | 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 | ||||||||
\(735\) | 22.0870 | − | 29.1990i | 0.814693 | − | 1.07702i | ||||
\(736\) | 2.83687 | 0.104569 | ||||||||
\(737\) | 28.9005 | − | 28.9005i | 1.06456 | − | 1.06456i | ||||
\(738\) | 4.38986 | − | 2.83783i | 0.161593 | − | 0.104462i | ||||
\(739\) | − | 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 | \(-0.927495\pi\) |
−0.225817 | − | 0.974170i | \(-0.572505\pi\) | |||||||
\(744\) | −6.74302 | − | 0.715817i | −0.247211 | − | 0.0262431i | ||||
\(745\) | 3.01577 | + | 12.1365i | 0.110489 | + | 0.444648i | ||||
\(746\) | 7.81442i | 0.286106i | ||||||||
\(747\) | −13.8177 | + | 8.93247i | −0.505563 | + | 0.326822i | ||||
\(748\) | 15.6676 | − | 15.6676i | 0.572865 | − | 0.572865i | ||||
\(749\) | −49.4079 | −1.80533 | ||||||||
\(750\) | −15.7053 | + | 11.3288i | −0.573478 | + | 0.413670i | ||||
\(751\) | 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 | ||||
\(753\) | −6.90825 | − | 8.54916i | −0.251751 | − | 0.311549i | ||||
\(754\) | 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 | \(-0.880311\pi\) | ||
0.930136 | − | 0.367216i | \(-0.119689\pi\) | |||||||
\(762\) | −15.8535 | + | 12.8106i | −0.574311 | + | 0.464079i | ||||
\(763\) | −18.1481 | + | 18.1481i | −0.657006 | + | 0.657006i | ||||
\(764\) | −6.45739 | −0.233620 | ||||||||
\(765\) | 22.0940 | − | 23.5568i | 0.798809 | − | 0.851697i | ||||
\(766\) | −16.4922 | −0.595886 | ||||||||
\(767\) | −6.76222 | + | 6.76222i | −0.244170 | + | 0.244170i | ||||
\(768\) | 1.34719 | − | 1.08861i | 0.0486125 | − | 0.0392819i | ||||
\(769\) | − | 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 | 0.373585 | − | 0.927596i | \(-0.378128\pi\) |
−0.927596 | + | 0.373585i | \(0.878128\pi\) | |||||||
\(774\) | 33.9864 | + | 7.29801i | 1.22161 | + | 0.262321i | ||||
\(775\) | 17.2981 | − | 9.16243i | 0.621365 | − | 0.329124i | ||||
\(776\) | 17.6883i | 0.634972i | ||||||||
\(777\) | −26.7632 | − | 33.1202i | −0.960123 | − | 1.18818i | ||||
\(778\) | 11.0403 | − | 11.0403i | 0.395813 | − | 0.395813i | ||||
\(779\) | −1.74242 | −0.0624286 | ||||||||
\(780\) | 1.00010 | + | 7.21197i | 0.0358094 | + | 0.258230i | ||||
\(781\) | 71.4698 | 2.55739 | ||||||||
\(782\) | 9.65772 | − | 9.65772i | 0.345359 | − | 0.345359i | ||||
\(783\) | −14.5617 | − | 28.8010i | −0.520393 | − | 1.02926i | ||||
\(784\) | − | 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 | ||||||||
\(792\) | −7.49554 | − | 11.5949i | −0.266343 | − | 0.412007i | ||||
\(793\) | −0.592901 | + | 0.592901i | −0.0210545 | + | 0.0210545i | ||||
\(794\) | 33.0892 | 1.17429 | ||||||||
\(795\) | −3.73281 | − | 26.9182i | −0.132389 | − | 0.954690i | ||||
\(796\) | −0.789726 | −0.0279911 | ||||||||
\(797\) | −21.0294 | + | 21.0294i | −0.744901 | + | 0.744901i | −0.973517 | − | 0.228616i | \(-0.926580\pi\) |
0.228616 | + | 0.973517i | \(0.426580\pi\) | |||||||
\(798\) | 4.41568 | + | 5.46453i | 0.156313 | + | 0.193442i | ||||
\(799\) | 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 | ||||||
\(807\) | 22.7741 | − | 18.4029i | 0.801685 | − | 0.647811i | ||||
\(808\) | −1.31122 | + | 1.31122i | −0.0461286 | + | 0.0461286i | ||||
\(809\) | −55.3606 | −1.94637 | −0.973187 | − | 0.230016i | \(-0.926122\pi\) | ||||
−0.973187 | + | 0.230016i | \(0.926122\pi\) | |||||||
\(810\) | −11.4612 | − | 16.5421i | −0.402704 | − | 0.581231i | ||||
\(811\) | −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 | ||||
\(813\) | −3.95714 | + | 3.19761i | −0.138783 | + | 0.112145i | ||||
\(814\) | − | 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 | \(0.144775\pi\) | ||||
−0.898339 | + | 0.439303i | \(0.855225\pi\) | |||||||
\(822\) | 22.0474 | + | 27.2843i | 0.768991 | + | 0.951648i | ||||
\(823\) | −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 | ||||||||
\(825\) | 36.6471 | + | 15.6694i | 1.27589 | + | 0.545539i | ||||
\(826\) | 20.6340 | 0.717949 | ||||||||
\(827\) | −11.7327 | + | 11.7327i | −0.407986 | + | 0.407986i | −0.881036 | − | 0.473050i | \(-0.843153\pi\) |
0.473050 | + | 0.881036i | \(0.343153\pi\) | |||||||
\(828\) | −4.62035 | − | 7.14724i | −0.160568 | − | 0.248384i | ||||
\(829\) | 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 | ||||||||
\(837\) | 9.17876 | + | 18.1543i | 0.317264 | + | 0.627503i | ||||
\(838\) | 8.87416 | − | 8.87416i | 0.306553 | − | 0.306553i | ||||
\(839\) | 23.1579 | 0.799501 | 0.399750 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399750 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(840\) | 9.47735 | − | 12.5290i | 0.327000 | − | 0.432292i | ||||
\(841\) | 9.57554 | 0.330191 | ||||||||
\(842\) | 10.1279 | − | 10.1279i | 0.349030 | − | 0.349030i | ||||
\(843\) | 15.3360 | + | 18.9788i | 0.528201 | + | 0.653664i | ||||
\(844\) | 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 | ||||||
\(852\) | 20.9210 | − | 16.9055i | 0.716743 | − | 0.579172i | ||||
\(853\) | 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 | ||||||||
\(855\) | 0.214847 | + | 6.70476i | 0.00734760 | + | 0.229298i | ||||
\(856\) | −12.1807 | −0.416328 | ||||||||
\(857\) | −37.5618 | + | 37.5618i | −1.28309 | + | 1.28309i | −0.344182 | + | 0.938903i | \(0.611844\pi\) |
−0.938903 | + | 0.344182i | \(0.888156\pi\) | |||||||
\(858\) | 11.6558 | − | 9.41861i | 0.397922 | − | 0.321546i | ||||
\(859\) | − | 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 | 0.932664 | − | 0.360746i | \(-0.117478\pi\) |
−0.360746 | + | 0.932664i | \(0.617478\pi\) | |||||||
\(864\) | −4.93680 | − | 1.62112i | −0.167953 | − | 0.0551517i | ||||
\(865\) | 13.3603 | − | 22.1955i | 0.454265 | − | 0.754670i | ||||
\(866\) | − | 15.2966i | − | 0.519799i | ||||||
\(867\) | −6.72679 | − | 8.32460i | −0.228454 | − | 0.282718i | ||||
\(868\) | −11.2289 | + | 11.2289i | −0.381133 | + | 0.381133i | ||||
\(869\) | −48.0698 | −1.63066 | ||||||||
\(870\) | 23.8268 | − | 3.30412i | 0.807804 | − | 0.112020i | ||||
\(871\) | 16.6954 | 0.565701 | ||||||||
\(872\) | −4.47412 | + | 4.47412i | −0.151513 | + | 0.151513i | ||||
\(873\) | 44.5640 | − | 28.8085i | 1.50826 | − | 0.975019i | ||||
\(874\) | 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 | \(-0.991321\pi\) | ||
0.999628 | − | 0.0272623i | \(-0.00867894\pi\) | |||||||
\(882\) | −23.8162 | + | 15.3961i | −0.801934 | + | 0.518412i | ||||
\(883\) | 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 | ||||||||
\(885\) | 15.7128 | + | 11.8856i | 0.528179 | + | 0.399531i | ||||
\(886\) | 36.0370 | 1.21069 | ||||||||
\(887\) | 31.1947 | − | 31.1947i | 1.04742 | − | 1.04742i | 0.0485966 | − | 0.998818i | \(-0.484525\pi\) |
0.998818 | − | 0.0485966i | \(-0.0154749\pi\) | |||||||
\(888\) | −6.59802 | − | 8.16524i | −0.221415 | − | 0.274007i | ||||
\(889\) | 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 | ||||||
\(897\) | 7.18478 | − | 5.80575i | 0.239893 | − | 0.193848i | ||||
\(898\) | −5.23356 | + | 5.23356i | −0.174646 | + | 0.174646i | ||||
\(899\) | −24.3155 | −0.810968 | ||||||||
\(900\) | 14.4340 | − | 4.08168i | 0.481133 | − | 0.136056i | ||||
\(901\) | −33.7820 | −1.12544 | ||||||||
\(902\) | 5.67029 | − | 5.67029i | 0.188800 | − | 0.188800i | ||||
\(903\) | 63.3177 | − | 51.1646i | 2.10708 | − | 1.70265i | ||||
\(904\) | 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 | \(-0.682497\pi\) | ||
0.542434 | − | 0.840098i | \(-0.317503\pi\) | |||||||
\(912\) | 1.08861 | + | 1.34719i | 0.0360476 | + | 0.0446099i | ||||
\(913\) | −17.8480 | + | 17.8480i | −0.590684 | + | 0.590684i | ||||
\(914\) | −20.7832 | −0.687447 | ||||||||
\(915\) | 1.37767 | + | 1.04211i | 0.0455444 | + | 0.0344512i | ||||
\(916\) | −6.47050 | −0.213791 | ||||||||
\(917\) | −53.5724 | + | 53.5724i | −1.76912 | + | 1.76912i | ||||
\(918\) | −22.3255 | + | 11.2877i | −0.736850 | + | 0.372550i | ||||
\(919\) | − | 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 | ||||||
\(927\) | 26.3959 | + | 40.8319i | 0.866954 | + | 1.34110i | ||||
\(928\) | 4.39178 | − | 4.39178i | 0.144167 | − | 0.144167i | ||||
\(929\) | −24.9065 | −0.817156 | −0.408578 | − | 0.912723i | \(-0.633975\pi\) | ||||
−0.408578 | + | 0.912723i | \(0.633975\pi\) | |||||||
\(930\) | −15.0189 | + | 2.08270i | −0.492488 | + | 0.0682945i | ||||
\(931\) | 9.45311 | 0.309813 | ||||||||
\(932\) | 4.00499 | − | 4.00499i | 0.131188 | − | 0.131188i | ||||
\(933\) | 24.6091 | + | 30.4544i | 0.805665 | + | 0.997034i | ||||
\(934\) | − | 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 | \(-0.989505\pi\) | ||
0.999457 | − | 0.0329644i | \(-0.0104948\pi\) | |||||||
\(942\) | 19.6380 | − | 15.8687i | 0.639839 | − | 0.517030i | ||||
\(943\) | 3.49524 | − | 3.49524i | 0.113821 | − | 0.113821i | ||||
\(944\) | 5.08697 | 0.165567 | ||||||||
\(945\) | −47.0013 | − | 3.47159i | −1.52895 | − | 0.112931i | ||||
\(946\) | 53.3262 | 1.73378 | ||||||||
\(947\) | 7.33043 | − | 7.33043i | 0.238207 | − | 0.238207i | −0.577900 | − | 0.816107i | \(-0.696128\pi\) |
0.816107 | + | 0.577900i | \(0.196128\pi\) | |||||||
\(948\) | −14.0713 | + | 11.3704i | −0.457013 | + | 0.369295i | ||||
\(949\) | 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 | 0.935160 | − | 0.354226i | \(-0.115256\pi\) |
−0.354226 | + | 0.935160i | \(0.615256\pi\) | |||||||
\(954\) | −4.41945 | + | 20.5811i | −0.143085 | + | 0.666338i | ||||
\(955\) | −14.0130 | + | 3.48205i | −0.453451 | + | 0.112677i | ||||
\(956\) | 1.96845i | 0.0636643i | ||||||||
\(957\) | −31.1170 | − | 38.5082i | −1.00587 | − | 1.24479i | ||||
\(958\) | 16.2689 | − | 16.2689i | 0.525624 | − | 0.525624i | ||||
\(959\) | 82.1500 | 2.65276 | ||||||||
\(960\) | 2.33648 | − | 3.08883i | 0.0754097 | − | 0.0996914i | ||||
\(961\) | −15.6731 | −0.505583 | ||||||||
\(962\) | 8.05693 | − | 8.05693i | 0.259766 | − | 0.259766i | ||||
\(963\) | 19.8384 | + | 30.6882i | 0.639284 | + | 0.988913i | ||||
\(964\) | − | 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 | \(-0.998734\pi\) | ||
0.999992 | − | 0.00397648i | \(-0.00126576\pi\) | |||||||
\(972\) | 3.95617 | + | 15.0781i | 0.126894 | + | 0.483630i | ||||
\(973\) | −32.3034 | + | 32.3034i | −1.03560 | + | 1.03560i | ||||
\(974\) | −28.9973 | −0.929134 | ||||||||
\(975\) | 6.05925 | + | 15.1112i | 0.194051 | + | 0.483947i | ||||
\(976\) | 0.446018 | 0.0142767 | ||||||||
\(977\) | −14.2133 | + | 14.2133i | −0.454724 | + | 0.454724i | −0.896919 | − | 0.442195i | \(-0.854200\pi\) |
0.442195 | + | 0.896919i | \(0.354200\pi\) | |||||||
\(978\) | −17.0554 | − | 21.1065i | −0.545370 | − | 0.674911i | ||||
\(979\) | 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 | \(-0.944455\pi\) |
−0.173617 | − | 0.984813i | \(-0.555545\pi\) | |||||||
\(984\) | 0.318586 | − | 3.00109i | 0.0101562 | − | 0.0956713i | ||||
\(985\) | −40.2879 | − | 24.2508i | −1.28368 | − | 0.772696i | ||||
\(986\) | − | 29.9024i | − | 0.952285i | ||||||
\(987\) | 40.3584 | − | 32.6121i | 1.28462 | − | 1.03806i | ||||
\(988\) | −1.32932 | + | 1.32932i | −0.0422913 | + | 0.0422913i | ||||
\(989\) | 32.8710 | 1.04524 | ||||||||
\(990\) | −22.5183 | − | 21.1199i | −0.715678 | − | 0.671236i | ||||
\(991\) | −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 | ||||
\(993\) | 22.6017 | − | 18.2636i | 0.717243 | − | 0.579577i | ||||
\(994\) | − | 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.77.8 | ✓ | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.15 | yes | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.15 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.8 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.8 | ✓ | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.77.15 | yes | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.533.8 | yes | 36 | 15.8 | even | 4 | inner | |
570.2.k.b.533.15 | yes | 36 | 5.3 | odd | 4 | inner |