Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,2,Mod(77,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.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: | \(2.42745222145\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.18 | ||
Character | \(\chi\) | \(=\) | 304.77 |
Dual form | 304.2.k.b.229.18 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0411449 | − | 1.41361i | 0.0290939 | − | 0.999577i | ||||
\(3\) | 1.66448 | + | 1.66448i | 0.960989 | + | 0.960989i | 0.999267 | − | 0.0382784i | \(-0.0121874\pi\) |
−0.0382784 | + | 0.999267i | \(0.512187\pi\) | |||||||
\(4\) | −1.99661 | − | 0.116326i | −0.998307 | − | 0.0581631i | ||||
\(5\) | −2.15868 | + | 2.15868i | −0.965389 | + | 0.965389i | −0.999421 | − | 0.0340313i | \(-0.989165\pi\) |
0.0340313 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(6\) | 2.42142 | − | 2.28445i | 0.988541 | − | 0.932623i | ||||
\(7\) | 1.65346i | 0.624948i | 0.949926 | + | 0.312474i | \(0.101158\pi\) | ||||
−0.949926 | + | 0.312474i | \(0.898842\pi\) | |||||||
\(8\) | −0.246591 | + | 2.81766i | −0.0871831 | + | 0.996192i | ||||
\(9\) | 2.54100i | 0.846999i | ||||||||
\(10\) | 2.96272 | + | 3.14036i | 0.936894 | + | 0.993068i | ||||
\(11\) | −2.90962 | + | 2.90962i | −0.877282 | + | 0.877282i | −0.993253 | − | 0.115970i | \(-0.963002\pi\) |
0.115970 | + | 0.993253i | \(0.463002\pi\) | |||||||
\(12\) | −3.12970 | − | 3.51695i | −0.903468 | − | 1.01526i | ||||
\(13\) | −1.83379 | − | 1.83379i | −0.508601 | − | 0.508601i | 0.405496 | − | 0.914097i | \(-0.367099\pi\) |
−0.914097 | + | 0.405496i | \(0.867099\pi\) | |||||||
\(14\) | 2.33735 | + | 0.0680314i | 0.624684 | + | 0.0181822i | ||||
\(15\) | −7.18615 | −1.85546 | ||||||||
\(16\) | 3.97294 | + | 0.464517i | 0.993234 | + | 0.116129i | ||||
\(17\) | 6.74010 | 1.63471 | 0.817357 | − | 0.576131i | \(-0.195438\pi\) | ||||
0.817357 | + | 0.576131i | \(0.195438\pi\) | |||||||
\(18\) | 3.59199 | + | 0.104549i | 0.846640 | + | 0.0246425i | ||||
\(19\) | 0.707107 | + | 0.707107i | 0.162221 | + | 0.162221i | ||||
\(20\) | 4.56115 | − | 4.05893i | 1.01991 | − | 0.907605i | ||||
\(21\) | −2.75215 | + | 2.75215i | −0.600568 | + | 0.600568i | ||||
\(22\) | 3.99336 | + | 4.23279i | 0.851387 | + | 0.902434i | ||||
\(23\) | 2.23617i | 0.466274i | 0.972444 | + | 0.233137i | \(0.0748990\pi\) | ||||
−0.972444 | + | 0.233137i | \(0.925101\pi\) | |||||||
\(24\) | −5.10038 | + | 4.27949i | −1.04111 | + | 0.873548i | ||||
\(25\) | − | 4.31977i | − | 0.863954i | ||||||
\(26\) | −2.66772 | + | 2.51682i | −0.523183 | + | 0.493589i | ||||
\(27\) | 0.764004 | − | 0.764004i | 0.147033 | − | 0.147033i | ||||
\(28\) | 0.192340 | − | 3.30132i | 0.0363489 | − | 0.623890i | ||||
\(29\) | −3.73185 | − | 3.73185i | −0.692988 | − | 0.692988i | 0.269900 | − | 0.962888i | \(-0.413009\pi\) |
−0.962888 | + | 0.269900i | \(0.913009\pi\) | |||||||
\(30\) | −0.295674 | + | 10.1585i | −0.0539824 | + | 1.85467i | ||||
\(31\) | 6.94654 | 1.24764 | 0.623818 | − | 0.781570i | \(-0.285581\pi\) | ||||
0.623818 | + | 0.781570i | \(0.285581\pi\) | |||||||
\(32\) | 0.820115 | − | 5.59709i | 0.144977 | − | 0.989435i | ||||
\(33\) | −9.68600 | −1.68612 | ||||||||
\(34\) | 0.277321 | − | 9.52791i | 0.0475602 | − | 1.63402i | ||||
\(35\) | −3.56928 | − | 3.56928i | −0.603318 | − | 0.603318i | ||||
\(36\) | 0.295584 | − | 5.07339i | 0.0492641 | − | 0.845565i | ||||
\(37\) | −1.89479 | + | 1.89479i | −0.311502 | + | 0.311502i | −0.845491 | − | 0.533989i | \(-0.820692\pi\) |
0.533989 | + | 0.845491i | \(0.320692\pi\) | |||||||
\(38\) | 1.02867 | − | 0.970483i | 0.166872 | − | 0.157433i | ||||
\(39\) | − | 6.10461i | − | 0.977520i | ||||||
\(40\) | −5.55010 | − | 6.61472i | −0.877548 | − | 1.04588i | ||||
\(41\) | 6.17447i | 0.964290i | 0.876092 | + | 0.482145i | \(0.160142\pi\) | ||||
−0.876092 | + | 0.482145i | \(0.839858\pi\) | |||||||
\(42\) | 3.77724 | + | 4.00372i | 0.582841 | + | 0.617787i | ||||
\(43\) | 4.55725 | − | 4.55725i | 0.694974 | − | 0.694974i | −0.268348 | − | 0.963322i | \(-0.586478\pi\) |
0.963322 | + | 0.268348i | \(0.0864777\pi\) | |||||||
\(44\) | 6.14784 | − | 5.47092i | 0.926822 | − | 0.824772i | ||||
\(45\) | −5.48519 | − | 5.48519i | −0.817684 | − | 0.817684i | ||||
\(46\) | 3.16108 | + | 0.0920071i | 0.466076 | + | 0.0135657i | ||||
\(47\) | 8.44701 | 1.23212 | 0.616062 | − | 0.787698i | \(-0.288727\pi\) | ||||
0.616062 | + | 0.787698i | \(0.288727\pi\) | |||||||
\(48\) | 5.83970 | + | 7.38606i | 0.842888 | + | 1.06609i | ||||
\(49\) | 4.26608 | 0.609440 | ||||||||
\(50\) | −6.10649 | − | 0.177737i | −0.863588 | − | 0.0251358i | ||||
\(51\) | 11.2188 | + | 11.2188i | 1.57094 | + | 1.57094i | ||||
\(52\) | 3.44805 | + | 3.87469i | 0.478159 | + | 0.537322i | ||||
\(53\) | −4.47968 | + | 4.47968i | −0.615332 | + | 0.615332i | −0.944330 | − | 0.328999i | \(-0.893289\pi\) |
0.328999 | + | 0.944330i | \(0.393289\pi\) | |||||||
\(54\) | −1.04857 | − | 1.11144i | −0.142693 | − | 0.151248i | ||||
\(55\) | − | 12.5618i | − | 1.69384i | ||||||
\(56\) | −4.65888 | − | 0.407728i | −0.622569 | − | 0.0544849i | ||||
\(57\) | 2.35393i | 0.311786i | ||||||||
\(58\) | −5.42895 | + | 5.12186i | −0.712856 | + | 0.672533i | ||||
\(59\) | 1.79258 | − | 1.79258i | 0.233375 | − | 0.233375i | −0.580725 | − | 0.814100i | \(-0.697231\pi\) |
0.814100 | + | 0.580725i | \(0.197231\pi\) | |||||||
\(60\) | 14.3480 | + | 0.835938i | 1.85232 | + | 0.107919i | ||||
\(61\) | −7.56656 | − | 7.56656i | −0.968798 | − | 0.968798i | 0.0307295 | − | 0.999528i | \(-0.490217\pi\) |
−0.999528 | + | 0.0307295i | \(0.990217\pi\) | |||||||
\(62\) | 0.285815 | − | 9.81974i | 0.0362986 | − | 1.24711i | ||||
\(63\) | −4.20143 | −0.529330 | ||||||||
\(64\) | −7.87839 | − | 1.38962i | −0.984798 | − | 0.173702i | ||||
\(65\) | 7.91711 | 0.981997 | ||||||||
\(66\) | −0.398530 | + | 13.6923i | −0.0490557 | + | 1.68540i | ||||
\(67\) | −4.88385 | − | 4.88385i | −0.596657 | − | 0.596657i | 0.342764 | − | 0.939421i | \(-0.388637\pi\) |
−0.939421 | + | 0.342764i | \(0.888637\pi\) | |||||||
\(68\) | −13.4574 | − | 0.784051i | −1.63195 | − | 0.0950801i | ||||
\(69\) | −3.72206 | + | 3.72206i | −0.448084 | + | 0.448084i | ||||
\(70\) | −5.19244 | + | 4.89873i | −0.620616 | + | 0.585510i | ||||
\(71\) | 12.6271i | 1.49856i | 0.662254 | + | 0.749280i | \(0.269600\pi\) | ||||
−0.662254 | + | 0.749280i | \(0.730400\pi\) | |||||||
\(72\) | −7.15966 | − | 0.626587i | −0.843774 | − | 0.0738440i | ||||
\(73\) | − | 4.06266i | − | 0.475498i | −0.971327 | − | 0.237749i | \(-0.923590\pi\) | ||
0.971327 | − | 0.237749i | \(-0.0764096\pi\) | |||||||
\(74\) | 2.60054 | + | 2.75647i | 0.302307 | + | 0.320433i | ||||
\(75\) | 7.19017 | − | 7.19017i | 0.830250 | − | 0.830250i | ||||
\(76\) | −1.32956 | − | 1.49407i | −0.152511 | − | 0.171382i | ||||
\(77\) | −4.81093 | − | 4.81093i | −0.548256 | − | 0.548256i | ||||
\(78\) | −8.62957 | − | 0.251174i | −0.977107 | − | 0.0284399i | ||||
\(79\) | −7.88110 | −0.886693 | −0.443346 | − | 0.896350i | \(-0.646209\pi\) | ||||
−0.443346 | + | 0.896350i | \(0.646209\pi\) | |||||||
\(80\) | −9.57903 | + | 7.57354i | −1.07097 | + | 0.846748i | ||||
\(81\) | 10.1663 | 1.12959 | ||||||||
\(82\) | 8.72832 | + | 0.254048i | 0.963881 | + | 0.0280549i | ||||
\(83\) | 7.61886 | + | 7.61886i | 0.836279 | + | 0.836279i | 0.988367 | − | 0.152088i | \(-0.0485997\pi\) |
−0.152088 | + | 0.988367i | \(0.548600\pi\) | |||||||
\(84\) | 5.81513 | − | 5.17483i | 0.634482 | − | 0.564621i | ||||
\(85\) | −14.5497 | + | 14.5497i | −1.57814 | + | 1.57814i | ||||
\(86\) | −6.25469 | − | 6.62970i | −0.674460 | − | 0.714899i | ||||
\(87\) | − | 12.4232i | − | 1.33191i | ||||||
\(88\) | −7.48082 | − | 8.91579i | −0.797458 | − | 0.950426i | ||||
\(89\) | 9.46463i | 1.00325i | 0.865086 | + | 0.501624i | \(0.167264\pi\) | ||||
−0.865086 | + | 0.501624i | \(0.832736\pi\) | |||||||
\(90\) | −7.97963 | + | 7.52826i | −0.841127 | + | 0.793548i | ||||
\(91\) | 3.03209 | − | 3.03209i | 0.317849 | − | 0.317849i | ||||
\(92\) | 0.260125 | − | 4.46477i | 0.0271199 | − | 0.465484i | ||||
\(93\) | 11.5624 | + | 11.5624i | 1.19896 | + | 1.19896i | ||||
\(94\) | 0.347552 | − | 11.9408i | 0.0358472 | − | 1.23160i | ||||
\(95\) | −3.05283 | −0.313214 | ||||||||
\(96\) | 10.6813 | − | 7.95119i | 1.09016 | − | 0.811514i | ||||
\(97\) | −14.3016 | −1.45211 | −0.726056 | − | 0.687635i | \(-0.758649\pi\) | ||||
−0.726056 | + | 0.687635i | \(0.758649\pi\) | |||||||
\(98\) | 0.175528 | − | 6.03059i | 0.0177310 | − | 0.609182i | ||||
\(99\) | −7.39332 | − | 7.39332i | −0.743057 | − | 0.743057i | ||||
\(100\) | −0.502502 | + | 8.62491i | −0.0502502 | + | 0.862491i | ||||
\(101\) | 0.159188 | − | 0.159188i | 0.0158398 | − | 0.0158398i | −0.699143 | − | 0.714982i | \(-0.746435\pi\) |
0.714982 | + | 0.699143i | \(0.246435\pi\) | |||||||
\(102\) | 16.3206 | − | 15.3974i | 1.61598 | − | 1.52457i | ||||
\(103\) | − | 10.2611i | − | 1.01106i | −0.862810 | − | 0.505528i | \(-0.831298\pi\) | ||
0.862810 | − | 0.505528i | \(-0.168702\pi\) | |||||||
\(104\) | 5.61918 | − | 4.71479i | 0.551006 | − | 0.462323i | ||||
\(105\) | − | 11.8820i | − | 1.15956i | ||||||
\(106\) | 6.14823 | + | 6.51686i | 0.597169 | + | 0.632974i | ||||
\(107\) | 3.76195 | − | 3.76195i | 0.363682 | − | 0.363682i | −0.501485 | − | 0.865166i | \(-0.667213\pi\) |
0.865166 | + | 0.501485i | \(0.167213\pi\) | |||||||
\(108\) | −1.61429 | + | 1.43655i | −0.155336 | + | 0.138232i | ||||
\(109\) | 12.0574 | + | 12.0574i | 1.15489 | + | 1.15489i | 0.985560 | + | 0.169327i | \(0.0541594\pi\) |
0.169327 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(110\) | −17.7576 | − | 0.516856i | −1.69312 | − | 0.0492803i | ||||
\(111\) | −6.30769 | −0.598699 | ||||||||
\(112\) | −0.768059 | + | 6.56908i | −0.0725748 | + | 0.620720i | ||||
\(113\) | −18.0518 | −1.69817 | −0.849084 | − | 0.528258i | \(-0.822846\pi\) | ||||
−0.849084 | + | 0.528258i | \(0.822846\pi\) | |||||||
\(114\) | 3.32755 | + | 0.0968524i | 0.311654 | + | 0.00907106i | ||||
\(115\) | −4.82717 | − | 4.82717i | −0.450136 | − | 0.450136i | ||||
\(116\) | 7.01696 | + | 7.88519i | 0.651508 | + | 0.732121i | ||||
\(117\) | 4.65965 | − | 4.65965i | 0.430785 | − | 0.430785i | ||||
\(118\) | −2.46027 | − | 2.60778i | −0.226486 | − | 0.240066i | ||||
\(119\) | 11.1445i | 1.02161i | ||||||||
\(120\) | 1.77204 | − | 20.2481i | 0.161764 | − | 1.84839i | ||||
\(121\) | − | 5.93173i | − | 0.539248i | ||||||
\(122\) | −11.0075 | + | 10.3849i | −0.996574 | + | 0.940202i | ||||
\(123\) | −10.2773 | + | 10.2773i | −0.926671 | + | 0.926671i | ||||
\(124\) | −13.8696 | − | 0.808065i | −1.24552 | − | 0.0725664i | ||||
\(125\) | −1.46840 | − | 1.46840i | −0.131338 | − | 0.131338i | ||||
\(126\) | −0.172868 | + | 5.93920i | −0.0154003 | + | 0.529106i | ||||
\(127\) | 18.9412 | 1.68076 | 0.840380 | − | 0.541997i | \(-0.182332\pi\) | ||||
0.840380 | + | 0.541997i | \(0.182332\pi\) | |||||||
\(128\) | −2.28854 | + | 11.0798i | −0.202280 | + | 0.979328i | ||||
\(129\) | 15.1709 | 1.33572 | ||||||||
\(130\) | 0.325749 | − | 11.1917i | 0.0285701 | − | 0.981581i | ||||
\(131\) | 6.28136 | + | 6.28136i | 0.548805 | + | 0.548805i | 0.926095 | − | 0.377290i | \(-0.123144\pi\) |
−0.377290 | + | 0.926095i | \(0.623144\pi\) | |||||||
\(132\) | 19.3392 | + | 1.12674i | 1.68326 | + | 0.0980698i | ||||
\(133\) | −1.16917 | + | 1.16917i | −0.101380 | + | 0.101380i | ||||
\(134\) | −7.10483 | + | 6.70294i | −0.613764 | + | 0.579046i | ||||
\(135\) | 3.29847i | 0.283887i | ||||||||
\(136\) | −1.66205 | + | 18.9913i | −0.142520 | + | 1.62849i | ||||
\(137\) | − | 19.5253i | − | 1.66816i | −0.551645 | − | 0.834079i | \(-0.686000\pi\) | ||
0.551645 | − | 0.834079i | \(-0.314000\pi\) | |||||||
\(138\) | 5.10842 | + | 5.41471i | 0.434858 | + | 0.460931i | ||||
\(139\) | 8.73082 | − | 8.73082i | 0.740539 | − | 0.740539i | −0.232143 | − | 0.972682i | \(-0.574574\pi\) |
0.972682 | + | 0.232143i | \(0.0745737\pi\) | |||||||
\(140\) | 6.71127 | + | 7.54168i | 0.567206 | + | 0.637388i | ||||
\(141\) | 14.0599 | + | 14.0599i | 1.18406 | + | 1.18406i | ||||
\(142\) | 17.8498 | + | 0.519541i | 1.49793 | + | 0.0435989i | ||||
\(143\) | 10.6712 | 0.892374 | ||||||||
\(144\) | −1.18034 | + | 10.0952i | −0.0983614 | + | 0.841268i | ||||
\(145\) | 16.1117 | 1.33801 | ||||||||
\(146\) | −5.74303 | − | 0.167158i | −0.475297 | − | 0.0138341i | ||||
\(147\) | 7.10081 | + | 7.10081i | 0.585665 | + | 0.585665i | ||||
\(148\) | 4.00358 | − | 3.56275i | 0.329092 | − | 0.292856i | ||||
\(149\) | 0.282217 | − | 0.282217i | 0.0231201 | − | 0.0231201i | −0.695452 | − | 0.718572i | \(-0.744796\pi\) |
0.718572 | + | 0.695452i | \(0.244796\pi\) | |||||||
\(150\) | −9.86830 | − | 10.4600i | −0.805743 | − | 0.854054i | ||||
\(151\) | − | 20.6379i | − | 1.67949i | −0.542980 | − | 0.839746i | \(-0.682704\pi\) | ||
0.542980 | − | 0.839746i | \(-0.317296\pi\) | |||||||
\(152\) | −2.16675 | + | 1.81802i | −0.175747 | + | 0.147461i | ||||
\(153\) | 17.1266i | 1.38460i | ||||||||
\(154\) | −6.99874 | + | 6.60285i | −0.563975 | + | 0.532073i | ||||
\(155\) | −14.9953 | + | 14.9953i | −1.20445 | + | 1.20445i | ||||
\(156\) | −0.710127 | + | 12.1886i | −0.0568556 | + | 0.975866i | ||||
\(157\) | 7.90285 | + | 7.90285i | 0.630716 | + | 0.630716i | 0.948248 | − | 0.317532i | \(-0.102854\pi\) |
−0.317532 | + | 0.948248i | \(0.602854\pi\) | |||||||
\(158\) | −0.324267 | + | 11.1408i | −0.0257973 | + | 0.886317i | ||||
\(159\) | −14.9127 | −1.18265 | ||||||||
\(160\) | 10.3119 | + | 13.8527i | 0.815231 | + | 1.09515i | ||||
\(161\) | −3.69741 | −0.291397 | ||||||||
\(162\) | 0.418293 | − | 14.3713i | 0.0328642 | − | 1.12911i | ||||
\(163\) | 16.8892 | + | 16.8892i | 1.32287 | + | 1.32287i | 0.911445 | + | 0.411422i | \(0.134968\pi\) |
0.411422 | + | 0.911445i | \(0.365032\pi\) | |||||||
\(164\) | 0.718252 | − | 12.3280i | 0.0560861 | − | 0.962657i | ||||
\(165\) | 20.9089 | − | 20.9089i | 1.62776 | − | 1.62776i | ||||
\(166\) | 11.0836 | − | 10.4567i | 0.860256 | − | 0.811594i | ||||
\(167\) | 6.82763i | 0.528338i | 0.964476 | + | 0.264169i | \(0.0850976\pi\) | ||||
−0.964476 | + | 0.264169i | \(0.914902\pi\) | |||||||
\(168\) | −7.07596 | − | 8.43327i | −0.545922 | − | 0.650641i | ||||
\(169\) | − | 6.27444i | − | 0.482649i | ||||||
\(170\) | 19.9690 | + | 21.1663i | 1.53155 | + | 1.62338i | ||||
\(171\) | −1.79676 | + | 1.79676i | −0.137401 | + | 0.137401i | ||||
\(172\) | −9.62919 | + | 8.56894i | −0.734219 | + | 0.653376i | ||||
\(173\) | 1.70937 | + | 1.70937i | 0.129961 | + | 0.129961i | 0.769095 | − | 0.639134i | \(-0.220707\pi\) |
−0.639134 | + | 0.769095i | \(0.720707\pi\) | |||||||
\(174\) | −17.5616 | − | 0.511152i | −1.33134 | − | 0.0387503i | ||||
\(175\) | 7.14255 | 0.539926 | ||||||||
\(176\) | −12.9113 | + | 10.2082i | −0.973225 | + | 0.769468i | ||||
\(177\) | 5.96745 | 0.448541 | ||||||||
\(178\) | 13.3793 | + | 0.389422i | 1.00282 | + | 0.0291884i | ||||
\(179\) | −3.93881 | − | 3.93881i | −0.294401 | − | 0.294401i | 0.544415 | − | 0.838816i | \(-0.316752\pi\) |
−0.838816 | + | 0.544415i | \(0.816752\pi\) | |||||||
\(180\) | 10.3137 | + | 11.5899i | 0.768740 | + | 0.863858i | ||||
\(181\) | 5.72963 | − | 5.72963i | 0.425880 | − | 0.425880i | −0.461342 | − | 0.887222i | \(-0.652632\pi\) |
0.887222 | + | 0.461342i | \(0.152632\pi\) | |||||||
\(182\) | −4.16145 | − | 4.41096i | −0.308467 | − | 0.326962i | ||||
\(183\) | − | 25.1888i | − | 1.86201i | ||||||
\(184\) | −6.30076 | − | 0.551420i | −0.464498 | − | 0.0406512i | ||||
\(185\) | − | 8.18048i | − | 0.601441i | ||||||
\(186\) | 16.8205 | − | 15.8690i | 1.23334 | − | 1.16357i | ||||
\(187\) | −19.6111 | + | 19.6111i | −1.43411 | + | 1.43411i | ||||
\(188\) | −16.8654 | − | 0.982609i | −1.23004 | − | 0.0716641i | ||||
\(189\) | 1.26325 | + | 1.26325i | 0.0918877 | + | 0.0918877i | ||||
\(190\) | −0.125609 | + | 4.31553i | −0.00911260 | + | 0.313081i | ||||
\(191\) | −2.86264 | −0.207134 | −0.103567 | − | 0.994622i | \(-0.533026\pi\) | ||||
−0.103567 | + | 0.994622i | \(0.533026\pi\) | |||||||
\(192\) | −10.8004 | − | 15.4264i | −0.779454 | − | 1.11331i | ||||
\(193\) | 8.17302 | 0.588307 | 0.294154 | − | 0.955758i | \(-0.404962\pi\) | ||||
0.294154 | + | 0.955758i | \(0.404962\pi\) | |||||||
\(194\) | −0.588441 | + | 20.2170i | −0.0422476 | + | 1.45150i | ||||
\(195\) | 13.1779 | + | 13.1779i | 0.943688 | + | 0.943688i | ||||
\(196\) | −8.51771 | − | 0.496257i | −0.608408 | − | 0.0354469i | ||||
\(197\) | 17.4841 | − | 17.4841i | 1.24569 | − | 1.24569i | 0.288083 | − | 0.957606i | \(-0.406982\pi\) |
0.957606 | − | 0.288083i | \(-0.0930178\pi\) | |||||||
\(198\) | −10.7555 | + | 10.1471i | −0.764361 | + | 0.721124i | ||||
\(199\) | − | 11.4643i | − | 0.812679i | −0.913722 | − | 0.406340i | \(-0.866805\pi\) | ||
0.913722 | − | 0.406340i | \(-0.133195\pi\) | |||||||
\(200\) | 12.1716 | + | 1.06522i | 0.860664 | + | 0.0753222i | ||||
\(201\) | − | 16.2582i | − | 1.14676i | ||||||
\(202\) | −0.218481 | − | 0.231581i | −0.0153723 | − | 0.0162940i | ||||
\(203\) | 6.17046 | − | 6.17046i | 0.433082 | − | 0.433082i | ||||
\(204\) | −21.0945 | − | 23.7046i | −1.47691 | − | 1.65965i | ||||
\(205\) | −13.3287 | − | 13.3287i | −0.930915 | − | 0.930915i | ||||
\(206\) | −14.5052 | − | 0.422192i | −1.01063 | − | 0.0294155i | ||||
\(207\) | −5.68210 | −0.394933 | ||||||||
\(208\) | −6.43370 | − | 8.13735i | −0.446097 | − | 0.564224i | ||||
\(209\) | −4.11482 | −0.284628 | ||||||||
\(210\) | −16.7966 | − | 0.488884i | −1.15907 | − | 0.0337362i | ||||
\(211\) | −7.40651 | − | 7.40651i | −0.509885 | − | 0.509885i | 0.404606 | − | 0.914491i | \(-0.367409\pi\) |
−0.914491 | + | 0.404606i | \(0.867409\pi\) | |||||||
\(212\) | 9.46530 | − | 8.42309i | 0.650080 | − | 0.578500i | ||||
\(213\) | −21.0176 | + | 21.0176i | −1.44010 | + | 1.44010i | ||||
\(214\) | −5.16316 | − | 5.47273i | −0.352947 | − | 0.374108i | ||||
\(215\) | 19.6753i | 1.34184i | ||||||||
\(216\) | 1.96430 | + | 2.34110i | 0.133654 | + | 0.159291i | ||||
\(217\) | 11.4858i | 0.779708i | ||||||||
\(218\) | 17.5406 | − | 16.5484i | 1.18800 | − | 1.12080i | ||||
\(219\) | 6.76222 | − | 6.76222i | 0.456948 | − | 0.456948i | ||||
\(220\) | −1.46127 | + | 25.0811i | −0.0985189 | + | 1.69097i | ||||
\(221\) | −12.3599 | − | 12.3599i | −0.831418 | − | 0.831418i | ||||
\(222\) | −0.259530 | + | 8.91664i | −0.0174185 | + | 0.598446i | ||||
\(223\) | −10.4533 | −0.700005 | −0.350002 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350002 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(224\) | 9.25455 | + | 1.35602i | 0.618346 | + | 0.0906032i | ||||
\(225\) | 10.9765 | 0.731768 | ||||||||
\(226\) | −0.742739 | + | 25.5183i | −0.0494063 | + | 1.69745i | ||||
\(227\) | −5.88958 | − | 5.88958i | −0.390905 | − | 0.390905i | 0.484105 | − | 0.875010i | \(-0.339145\pi\) |
−0.875010 | + | 0.484105i | \(0.839145\pi\) | |||||||
\(228\) | 0.273824 | − | 4.69989i | 0.0181344 | − | 0.311258i | ||||
\(229\) | 1.11702 | − | 1.11702i | 0.0738150 | − | 0.0738150i | −0.669235 | − | 0.743050i | \(-0.733378\pi\) |
0.743050 | + | 0.669235i | \(0.233378\pi\) | |||||||
\(230\) | −7.02237 | + | 6.62514i | −0.463041 | + | 0.436849i | ||||
\(231\) | − | 16.0154i | − | 1.05374i | ||||||
\(232\) | 11.4353 | − | 9.59484i | 0.750766 | − | 0.629932i | ||||
\(233\) | 0.804275i | 0.0526898i | 0.999653 | + | 0.0263449i | \(0.00838681\pi\) | ||||
−0.999653 | + | 0.0263449i | \(0.991613\pi\) | |||||||
\(234\) | −6.39523 | − | 6.77867i | −0.418069 | − | 0.443136i | ||||
\(235\) | −18.2344 | + | 18.2344i | −1.18948 | + | 1.18948i | ||||
\(236\) | −3.78763 | + | 3.37058i | −0.246553 | + | 0.219406i | ||||
\(237\) | −13.1179 | − | 13.1179i | −0.852102 | − | 0.852102i | ||||
\(238\) | 15.7540 | + | 0.458539i | 1.02118 | + | 0.0297227i | ||||
\(239\) | 15.3510 | 0.992973 | 0.496487 | − | 0.868044i | \(-0.334623\pi\) | ||||
0.496487 | + | 0.868044i | \(0.334623\pi\) | |||||||
\(240\) | −28.5501 | − | 3.33809i | −1.84290 | − | 0.215473i | ||||
\(241\) | −15.6408 | −1.00751 | −0.503755 | − | 0.863847i | \(-0.668049\pi\) | ||||
−0.503755 | + | 0.863847i | \(0.668049\pi\) | |||||||
\(242\) | −8.38518 | − | 0.244061i | −0.539020 | − | 0.0156888i | ||||
\(243\) | 14.6297 | + | 14.6297i | 0.938493 | + | 0.938493i | ||||
\(244\) | 14.2273 | + | 15.9877i | 0.910810 | + | 1.02351i | ||||
\(245\) | −9.20908 | + | 9.20908i | −0.588347 | + | 0.588347i | ||||
\(246\) | 14.1053 | + | 14.9510i | 0.899319 | + | 0.953240i | ||||
\(247\) | − | 2.59337i | − | 0.165012i | ||||||
\(248\) | −1.71296 | + | 19.5730i | −0.108773 | + | 1.24289i | ||||
\(249\) | 25.3629i | 1.60731i | ||||||||
\(250\) | −2.13617 | + | 2.01533i | −0.135103 | + | 0.127461i | ||||
\(251\) | −14.6363 | + | 14.6363i | −0.923835 | + | 0.923835i | −0.997298 | − | 0.0734625i | \(-0.976595\pi\) |
0.0734625 | + | 0.997298i | \(0.476595\pi\) | |||||||
\(252\) | 8.38863 | + | 0.488736i | 0.528434 | + | 0.0307875i | ||||
\(253\) | −6.50640 | − | 6.50640i | −0.409054 | − | 0.409054i | ||||
\(254\) | 0.779335 | − | 26.7756i | 0.0488998 | − | 1.68005i | ||||
\(255\) | −48.4354 | −3.03314 | ||||||||
\(256\) | 15.5684 | + | 3.69099i | 0.973028 | + | 0.230687i | ||||
\(257\) | −25.4029 | −1.58459 | −0.792293 | − | 0.610140i | \(-0.791113\pi\) | ||||
−0.792293 | + | 0.610140i | \(0.791113\pi\) | |||||||
\(258\) | 0.624206 | − | 21.4458i | 0.0388614 | − | 1.33516i | ||||
\(259\) | −3.13296 | − | 3.13296i | −0.194672 | − | 0.194672i | ||||
\(260\) | −15.8074 | − | 0.920968i | −0.980334 | − | 0.0571160i | ||||
\(261\) | 9.48263 | − | 9.48263i | 0.586960 | − | 0.586960i | ||||
\(262\) | 9.13788 | − | 8.62098i | 0.564540 | − | 0.532606i | ||||
\(263\) | 16.4692i | 1.01553i | 0.861494 | + | 0.507767i | \(0.169529\pi\) | ||||
−0.861494 | + | 0.507767i | \(0.830471\pi\) | |||||||
\(264\) | 2.38848 | − | 27.2918i | 0.147001 | − | 1.67970i | ||||
\(265\) | − | 19.3404i | − | 1.18807i | ||||||
\(266\) | 1.60465 | + | 1.70086i | 0.0983875 | + | 0.104287i | ||||
\(267\) | −15.7537 | + | 15.7537i | −0.964110 | + | 0.964110i | ||||
\(268\) | 9.18305 | + | 10.3193i | 0.560944 | + | 0.630351i | ||||
\(269\) | 2.53313 | + | 2.53313i | 0.154448 | + | 0.154448i | 0.780101 | − | 0.625653i | \(-0.215168\pi\) |
−0.625653 | + | 0.780101i | \(0.715168\pi\) | |||||||
\(270\) | 4.66277 | + | 0.135716i | 0.283767 | + | 0.00825938i | ||||
\(271\) | 6.26221 | 0.380402 | 0.190201 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190201 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(272\) | 26.7780 | + | 3.13089i | 1.62365 | + | 0.189838i | ||||
\(273\) | 10.0937 | 0.610900 | ||||||||
\(274\) | −27.6012 | − | 0.803367i | −1.66745 | − | 0.0485332i | ||||
\(275\) | 12.5689 | + | 12.5689i | 0.757931 | + | 0.757931i | ||||
\(276\) | 7.86450 | − | 6.99855i | 0.473387 | − | 0.421263i | ||||
\(277\) | −3.69833 | + | 3.69833i | −0.222211 | + | 0.222211i | −0.809429 | − | 0.587218i | \(-0.800223\pi\) |
0.587218 | + | 0.809429i | \(0.300223\pi\) | |||||||
\(278\) | −11.9828 | − | 12.7012i | −0.718680 | − | 0.761770i | ||||
\(279\) | 17.6511i | 1.05675i | ||||||||
\(280\) | 10.9372 | − | 9.17685i | 0.653620 | − | 0.548422i | ||||
\(281\) | − | 29.3927i | − | 1.75342i | −0.481019 | − | 0.876710i | \(-0.659733\pi\) | ||
0.481019 | − | 0.876710i | \(-0.340267\pi\) | |||||||
\(282\) | 20.4538 | − | 19.2968i | 1.21800 | − | 1.14911i | ||||
\(283\) | −4.02760 | + | 4.02760i | −0.239416 | + | 0.239416i | −0.816608 | − | 0.577192i | \(-0.804148\pi\) |
0.577192 | + | 0.816608i | \(0.304148\pi\) | |||||||
\(284\) | 1.46886 | − | 25.2114i | 0.0871609 | − | 1.49602i | ||||
\(285\) | −5.08138 | − | 5.08138i | −0.300995 | − | 0.300995i | ||||
\(286\) | 0.439068 | − | 15.0850i | 0.0259626 | − | 0.891996i | ||||
\(287\) | −10.2092 | −0.602631 | ||||||||
\(288\) | 14.2222 | + | 2.08391i | 0.838050 | + | 0.122795i | ||||
\(289\) | 28.4290 | 1.67229 | ||||||||
\(290\) | 0.662916 | − | 22.7758i | 0.0389278 | − | 1.33744i | ||||
\(291\) | −23.8048 | − | 23.8048i | −1.39546 | − | 1.39546i | ||||
\(292\) | −0.472594 | + | 8.11156i | −0.0276564 | + | 0.474693i | ||||
\(293\) | 6.39444 | − | 6.39444i | 0.373567 | − | 0.373567i | −0.495208 | − | 0.868775i | \(-0.664908\pi\) |
0.868775 | + | 0.495208i | \(0.164908\pi\) | |||||||
\(294\) | 10.3300 | − | 9.74565i | 0.602456 | − | 0.568378i | ||||
\(295\) | 7.73922i | 0.450595i | ||||||||
\(296\) | −4.87163 | − | 5.80611i | −0.283158 | − | 0.337473i | ||||
\(297\) | 4.44591i | 0.257978i | ||||||||
\(298\) | −0.387334 | − | 0.410558i | −0.0224377 | − | 0.0237830i | ||||
\(299\) | 4.10066 | − | 4.10066i | 0.237147 | − | 0.237147i | ||||
\(300\) | −15.1924 | + | 13.5196i | −0.877134 | + | 0.780554i | ||||
\(301\) | 7.53522 | + | 7.53522i | 0.434323 | + | 0.434323i | ||||
\(302\) | −29.1741 | − | 0.849147i | −1.67878 | − | 0.0488629i | ||||
\(303\) | 0.529932 | 0.0304438 | ||||||||
\(304\) | 2.48083 | + | 3.13775i | 0.142285 | + | 0.179963i | ||||
\(305\) | 32.6675 | 1.87054 | ||||||||
\(306\) | 24.2104 | + | 0.704672i | 1.38402 | + | 0.0402834i | ||||
\(307\) | −6.56296 | − | 6.56296i | −0.374568 | − | 0.374568i | 0.494570 | − | 0.869138i | \(-0.335326\pi\) |
−0.869138 | + | 0.494570i | \(0.835326\pi\) | |||||||
\(308\) | 9.04593 | + | 10.1652i | 0.515439 | + | 0.579216i | ||||
\(309\) | 17.0794 | − | 17.0794i | 0.971613 | − | 0.971613i | ||||
\(310\) | 20.5807 | + | 21.8146i | 1.16890 | + | 1.23899i | ||||
\(311\) | − | 22.5153i | − | 1.27673i | −0.769735 | − | 0.638364i | \(-0.779612\pi\) | ||
0.769735 | − | 0.638364i | \(-0.220388\pi\) | |||||||
\(312\) | 17.2007 | + | 1.50534i | 0.973798 | + | 0.0852233i | ||||
\(313\) | 27.5578i | 1.55766i | 0.627235 | + | 0.778830i | \(0.284187\pi\) | ||||
−0.627235 | + | 0.778830i | \(0.715813\pi\) | |||||||
\(314\) | 11.4967 | − | 10.8464i | 0.648799 | − | 0.612099i | ||||
\(315\) | 9.06953 | − | 9.06953i | 0.511010 | − | 0.511010i | ||||
\(316\) | 15.7355 | + | 0.916778i | 0.885192 | + | 0.0515728i | ||||
\(317\) | 4.12845 | + | 4.12845i | 0.231877 | + | 0.231877i | 0.813476 | − | 0.581599i | \(-0.197573\pi\) |
−0.581599 | + | 0.813476i | \(0.697573\pi\) | |||||||
\(318\) | −0.613582 | + | 21.0808i | −0.0344080 | + | 1.18215i | ||||
\(319\) | 21.7165 | 1.21589 | ||||||||
\(320\) | 20.0066 | − | 14.0071i | 1.11840 | − | 0.783023i | ||||
\(321\) | 12.5234 | 0.698988 | ||||||||
\(322\) | −0.152130 | + | 5.22672i | −0.00847786 | + | 0.291274i | ||||
\(323\) | 4.76597 | + | 4.76597i | 0.265186 | + | 0.265186i | ||||
\(324\) | −20.2982 | − | 1.18261i | −1.12768 | − | 0.0657006i | ||||
\(325\) | −7.92154 | + | 7.92154i | −0.439408 | + | 0.439408i | ||||
\(326\) | 24.5698 | − | 23.1800i | 1.36079 | − | 1.28382i | ||||
\(327\) | 40.1385i | 2.21967i | ||||||||
\(328\) | −17.3975 | − | 1.52257i | −0.960618 | − | 0.0840698i | ||||
\(329\) | 13.9668i | 0.770013i | ||||||||
\(330\) | −28.6969 | − | 30.4175i | −1.57971 | − | 1.67443i | ||||
\(331\) | 3.94813 | − | 3.94813i | 0.217009 | − | 0.217009i | −0.590228 | − | 0.807237i | \(-0.700962\pi\) |
0.807237 | + | 0.590228i | \(0.200962\pi\) | |||||||
\(332\) | −14.3257 | − | 16.0982i | −0.786223 | − | 0.883504i | ||||
\(333\) | −4.81466 | − | 4.81466i | −0.263842 | − | 0.263842i | ||||
\(334\) | 9.65164 | + | 0.280922i | 0.528114 | + | 0.0153714i | ||||
\(335\) | 21.0853 | 1.15201 | ||||||||
\(336\) | −12.2125 | + | 9.65569i | −0.666248 | + | 0.526761i | ||||
\(337\) | −32.5626 | −1.77380 | −0.886900 | − | 0.461962i | \(-0.847146\pi\) | ||||
−0.886900 | + | 0.461962i | \(0.847146\pi\) | |||||||
\(338\) | −8.86964 | − | 0.258162i | −0.482445 | − | 0.0140421i | ||||
\(339\) | −30.0468 | − | 30.0468i | −1.63192 | − | 1.63192i | ||||
\(340\) | 30.7427 | − | 27.3576i | 1.66725 | − | 1.48368i | ||||
\(341\) | −20.2118 | + | 20.2118i | −1.09453 | + | 1.09453i | ||||
\(342\) | 2.46599 | + | 2.61385i | 0.133346 | + | 0.141341i | ||||
\(343\) | 18.6280i | 1.00582i | ||||||||
\(344\) | 11.7170 | + | 13.9645i | 0.631738 | + | 0.752918i | ||||
\(345\) | − | 16.0695i | − | 0.865151i | ||||||
\(346\) | 2.48673 | − | 2.34606i | 0.133687 | − | 0.126125i | ||||
\(347\) | −9.28304 | + | 9.28304i | −0.498340 | + | 0.498340i | −0.910921 | − | 0.412581i | \(-0.864627\pi\) |
0.412581 | + | 0.910921i | \(0.364627\pi\) | |||||||
\(348\) | −1.44514 | + | 24.8043i | −0.0774679 | + | 1.32965i | ||||
\(349\) | −1.00511 | − | 1.00511i | −0.0538024 | − | 0.0538024i | 0.679694 | − | 0.733496i | \(-0.262113\pi\) |
−0.733496 | + | 0.679694i | \(0.762113\pi\) | |||||||
\(350\) | 0.293880 | − | 10.0968i | 0.0157085 | − | 0.539698i | ||||
\(351\) | −2.80204 | −0.149562 | ||||||||
\(352\) | 13.8992 | + | 18.6716i | 0.740828 | + | 0.995200i | ||||
\(353\) | −31.7333 | −1.68899 | −0.844496 | − | 0.535562i | \(-0.820100\pi\) | ||||
−0.844496 | + | 0.535562i | \(0.820100\pi\) | |||||||
\(354\) | 0.245530 | − | 8.43567i | 0.0130498 | − | 0.448351i | ||||
\(355\) | −27.2578 | − | 27.2578i | −1.44669 | − | 1.44669i | ||||
\(356\) | 1.10098 | − | 18.8972i | 0.0583521 | − | 1.00155i | ||||
\(357\) | −18.5498 | + | 18.5498i | −0.981758 | + | 0.981758i | ||||
\(358\) | −5.73002 | + | 5.40590i | −0.302841 | + | 0.285711i | ||||
\(359\) | − | 17.1036i | − | 0.902693i | −0.892349 | − | 0.451346i | \(-0.850944\pi\) | ||
0.892349 | − | 0.451346i | \(-0.149056\pi\) | |||||||
\(360\) | 16.8080 | − | 14.1028i | 0.885858 | − | 0.743282i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | −7.86375 | − | 8.33524i | −0.413309 | − | 0.438090i | ||||
\(363\) | 9.87325 | − | 9.87325i | 0.518211 | − | 0.518211i | ||||
\(364\) | −6.40663 | + | 5.70120i | −0.335799 | + | 0.298824i | ||||
\(365\) | 8.76996 | + | 8.76996i | 0.459041 | + | 0.459041i | ||||
\(366\) | −35.6072 | − | 1.03639i | −1.86122 | − | 0.0541730i | ||||
\(367\) | 4.19527 | 0.218991 | 0.109496 | − | 0.993987i | \(-0.465076\pi\) | ||||
0.109496 | + | 0.993987i | \(0.465076\pi\) | |||||||
\(368\) | −1.03874 | + | 8.88416i | −0.0541480 | + | 0.463119i | ||||
\(369\) | −15.6893 | −0.816752 | ||||||||
\(370\) | −11.5641 | − | 0.336586i | −0.601186 | − | 0.0174982i | ||||
\(371\) | −7.40696 | − | 7.40696i | −0.384550 | − | 0.384550i | ||||
\(372\) | −21.7406 | − | 24.4306i | −1.12720 | − | 1.26667i | ||||
\(373\) | 15.1359 | − | 15.1359i | 0.783710 | − | 0.783710i | −0.196745 | − | 0.980455i | \(-0.563037\pi\) |
0.980455 | + | 0.196745i | \(0.0630372\pi\) | |||||||
\(374\) | 26.9157 | + | 28.5295i | 1.39178 | + | 1.47522i | ||||
\(375\) | − | 4.88825i | − | 0.252428i | ||||||
\(376\) | −2.08296 | + | 23.8008i | −0.107420 | + | 1.22743i | ||||
\(377\) | 13.6869i | 0.704909i | ||||||||
\(378\) | 1.83772 | − | 1.73377i | 0.0945222 | − | 0.0891755i | ||||
\(379\) | −6.14466 | + | 6.14466i | −0.315630 | + | 0.315630i | −0.847086 | − | 0.531456i | \(-0.821645\pi\) |
0.531456 | + | 0.847086i | \(0.321645\pi\) | |||||||
\(380\) | 6.09532 | + | 0.355124i | 0.312683 | + | 0.0182175i | ||||
\(381\) | 31.5273 | + | 31.5273i | 1.61519 | + | 1.61519i | ||||
\(382\) | −0.117783 | + | 4.04668i | −0.00602632 | + | 0.207046i | ||||
\(383\) | −8.35520 | −0.426931 | −0.213465 | − | 0.976951i | \(-0.568475\pi\) | ||||
−0.213465 | + | 0.976951i | \(0.568475\pi\) | |||||||
\(384\) | −22.2514 | + | 14.6329i | −1.13551 | + | 0.746734i | ||||
\(385\) | 20.7705 | 1.05856 | ||||||||
\(386\) | 0.336279 | − | 11.5535i | 0.0171161 | − | 0.588058i | ||||
\(387\) | 11.5799 | + | 11.5799i | 0.588642 | + | 0.588642i | ||||
\(388\) | 28.5549 | + | 1.66366i | 1.44965 | + | 0.0844594i | ||||
\(389\) | 1.50516 | − | 1.50516i | 0.0763145 | − | 0.0763145i | −0.667919 | − | 0.744234i | \(-0.732815\pi\) |
0.744234 | + | 0.667919i | \(0.232815\pi\) | |||||||
\(390\) | 19.1707 | − | 18.0863i | 0.970744 | − | 0.915833i | ||||
\(391\) | 15.0720i | 0.762225i | ||||||||
\(392\) | −1.05198 | + | 12.0203i | −0.0531329 | + | 0.607119i | ||||
\(393\) | 20.9104i | 1.05479i | ||||||||
\(394\) | −23.9964 | − | 25.4351i | −1.20892 | − | 1.28140i | ||||
\(395\) | 17.0127 | − | 17.0127i | 0.856004 | − | 0.856004i | ||||
\(396\) | 13.9016 | + | 15.6216i | 0.698580 | + | 0.785017i | ||||
\(397\) | 0.0297571 | + | 0.0297571i | 0.00149347 | + | 0.00149347i | 0.707853 | − | 0.706360i | \(-0.249664\pi\) |
−0.706360 | + | 0.707853i | \(0.749664\pi\) | |||||||
\(398\) | −16.2060 | − | 0.471696i | −0.812335 | − | 0.0236440i | ||||
\(399\) | −3.89213 | −0.194850 | ||||||||
\(400\) | 2.00661 | − | 17.1622i | 0.100330 | − | 0.858108i | ||||
\(401\) | 3.99217 | 0.199359 | 0.0996797 | − | 0.995020i | \(-0.468218\pi\) | ||||
0.0996797 | + | 0.995020i | \(0.468218\pi\) | |||||||
\(402\) | −22.9828 | − | 0.668941i | −1.14628 | − | 0.0333637i | ||||
\(403\) | −12.7385 | − | 12.7385i | −0.634549 | − | 0.634549i | ||||
\(404\) | −0.336355 | + | 0.299320i | −0.0167343 | + | 0.0148917i | ||||
\(405\) | −21.9458 | + | 21.9458i | −1.09050 | + | 1.09050i | ||||
\(406\) | −8.46877 | − | 8.97654i | −0.420298 | − | 0.445498i | ||||
\(407\) | − | 11.0262i | − | 0.546550i | ||||||
\(408\) | −34.3771 | + | 28.8442i | −1.70192 | + | 1.42800i | ||||
\(409\) | 6.24741i | 0.308915i | 0.987999 | + | 0.154457i | \(0.0493629\pi\) | ||||
−0.987999 | + | 0.154457i | \(0.950637\pi\) | |||||||
\(410\) | −19.3900 | + | 18.2932i | −0.957605 | + | 0.903437i | ||||
\(411\) | 32.4995 | − | 32.4995i | 1.60308 | − | 1.60308i | ||||
\(412\) | −1.19363 | + | 20.4874i | −0.0588061 | + | 1.00934i | ||||
\(413\) | 2.96396 | + | 2.96396i | 0.145847 | + | 0.145847i | ||||
\(414\) | −0.233790 | + | 8.03230i | −0.0114901 | + | 0.394766i | ||||
\(415\) | −32.8933 | −1.61467 | ||||||||
\(416\) | −11.7678 | + | 8.75996i | −0.576964 | + | 0.429492i | ||||
\(417\) | 29.0646 | 1.42330 | ||||||||
\(418\) | −0.169304 | + | 5.81677i | −0.00828093 | + | 0.284507i | ||||
\(419\) | −12.3865 | − | 12.3865i | −0.605121 | − | 0.605121i | 0.336546 | − | 0.941667i | \(-0.390741\pi\) |
−0.941667 | + | 0.336546i | \(0.890741\pi\) | |||||||
\(420\) | −1.38219 | + | 23.7238i | −0.0674439 | + | 1.15760i | ||||
\(421\) | 7.38277 | − | 7.38277i | 0.359814 | − | 0.359814i | −0.503930 | − | 0.863744i | \(-0.668113\pi\) |
0.863744 | + | 0.503930i | \(0.168113\pi\) | |||||||
\(422\) | −10.7747 | + | 10.1652i | −0.524504 | + | 0.494835i | ||||
\(423\) | 21.4638i | 1.04361i | ||||||||
\(424\) | −11.5176 | − | 13.7269i | −0.559342 | − | 0.666635i | ||||
\(425\) | − | 29.1157i | − | 1.41232i | ||||||
\(426\) | 28.8460 | + | 30.5755i | 1.39759 | + | 1.48139i | ||||
\(427\) | 12.5110 | − | 12.5110i | 0.605449 | − | 0.605449i | ||||
\(428\) | −7.94878 | + | 7.07355i | −0.384219 | + | 0.341913i | ||||
\(429\) | 17.7621 | + | 17.7621i | 0.857561 | + | 0.857561i | ||||
\(430\) | 27.8132 | + | 0.809537i | 1.34127 | + | 0.0390393i | ||||
\(431\) | −14.7657 | −0.711237 | −0.355619 | − | 0.934631i | \(-0.615730\pi\) | ||||
−0.355619 | + | 0.934631i | \(0.615730\pi\) | |||||||
\(432\) | 3.39023 | − | 2.68045i | 0.163113 | − | 0.128963i | ||||
\(433\) | −22.3572 | −1.07442 | −0.537209 | − | 0.843449i | \(-0.680522\pi\) | ||||
−0.537209 | + | 0.843449i | \(0.680522\pi\) | |||||||
\(434\) | 16.2365 | + | 0.472583i | 0.779378 | + | 0.0226847i | ||||
\(435\) | 26.8177 | + | 26.8177i | 1.28581 | + | 1.28581i | ||||
\(436\) | −22.6713 | − | 25.4765i | −1.08576 | − | 1.22010i | ||||
\(437\) | −1.58121 | + | 1.58121i | −0.0756396 | + | 0.0756396i | ||||
\(438\) | −9.28094 | − | 9.83740i | −0.443460 | − | 0.470049i | ||||
\(439\) | − | 3.02626i | − | 0.144436i | −0.997389 | − | 0.0722179i | \(-0.976992\pi\) | ||
0.997389 | − | 0.0722179i | \(-0.0230077\pi\) | |||||||
\(440\) | 35.3950 | + | 3.09764i | 1.68739 | + | 0.147674i | ||||
\(441\) | 10.8401i | 0.516195i | ||||||||
\(442\) | −17.9807 | + | 16.9636i | −0.855255 | + | 0.806877i | ||||
\(443\) | 19.1035 | − | 19.1035i | 0.907634 | − | 0.907634i | −0.0884471 | − | 0.996081i | \(-0.528190\pi\) |
0.996081 | + | 0.0884471i | \(0.0281904\pi\) | |||||||
\(444\) | 12.5940 | + | 0.733750i | 0.597686 | + | 0.0348222i | ||||
\(445\) | −20.4311 | − | 20.4311i | −0.968526 | − | 0.968526i | ||||
\(446\) | −0.430101 | + | 14.7769i | −0.0203659 | + | 0.699708i | ||||
\(447\) | 0.939489 | 0.0444363 | ||||||||
\(448\) | 2.29767 | − | 13.0266i | 0.108555 | − | 0.615448i | ||||
\(449\) | 20.0661 | 0.946979 | 0.473489 | − | 0.880800i | \(-0.342994\pi\) | ||||
0.473489 | + | 0.880800i | \(0.342994\pi\) | |||||||
\(450\) | 0.451628 | − | 15.5166i | 0.0212900 | − | 0.731458i | ||||
\(451\) | −17.9653 | − | 17.9653i | −0.845954 | − | 0.845954i | ||||
\(452\) | 36.0424 | + | 2.09990i | 1.69529 | + | 0.0987708i | ||||
\(453\) | 34.3515 | − | 34.3515i | 1.61397 | − | 1.61397i | ||||
\(454\) | −8.56792 | + | 8.08327i | −0.402113 | + | 0.379367i | ||||
\(455\) | 13.0906i | 0.613697i | ||||||||
\(456\) | −6.63257 | − | 0.580459i | −0.310599 | − | 0.0271825i | ||||
\(457\) | − | 4.19511i | − | 0.196239i | −0.995175 | − | 0.0981195i | \(-0.968717\pi\) | ||
0.995175 | − | 0.0981195i | \(-0.0312827\pi\) | |||||||
\(458\) | −1.53308 | − | 1.62500i | −0.0716362 | − | 0.0759313i | ||||
\(459\) | 5.14946 | − | 5.14946i | 0.240356 | − | 0.240356i | ||||
\(460\) | 9.07647 | + | 10.1995i | 0.423192 | + | 0.475555i | ||||
\(461\) | −5.08285 | − | 5.08285i | −0.236732 | − | 0.236732i | 0.578764 | − | 0.815495i | \(-0.303535\pi\) |
−0.815495 | + | 0.578764i | \(0.803535\pi\) | |||||||
\(462\) | −22.6396 | − | 0.658952i | −1.05329 | − | 0.0306572i | ||||
\(463\) | −18.4414 | −0.857045 | −0.428522 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428522 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(464\) | −13.0929 | − | 16.5599i | −0.607823 | − | 0.768775i | ||||
\(465\) | −49.9189 | −2.31494 | ||||||||
\(466\) | 1.13694 | + | 0.0330919i | 0.0526675 | + | 0.00153295i | ||||
\(467\) | −2.27417 | − | 2.27417i | −0.105236 | − | 0.105236i | 0.652528 | − | 0.757764i | \(-0.273708\pi\) |
−0.757764 | + | 0.652528i | \(0.773708\pi\) | |||||||
\(468\) | −9.84556 | + | 8.76148i | −0.455111 | + | 0.405000i | ||||
\(469\) | 8.07524 | − | 8.07524i | 0.372880 | − | 0.372880i | ||||
\(470\) | 25.0261 | + | 26.5266i | 1.15437 | + | 1.22358i | ||||
\(471\) | 26.3083i | 1.21222i | ||||||||
\(472\) | 4.60885 | + | 5.49293i | 0.212140 | + | 0.252832i | ||||
\(473\) | 26.5197i | 1.21938i | ||||||||
\(474\) | −19.0834 | + | 18.0040i | −0.876532 | + | 0.826950i | ||||
\(475\) | 3.05454 | − | 3.05454i | 0.140152 | − | 0.140152i | ||||
\(476\) | 1.29639 | − | 22.2512i | 0.0594201 | − | 1.01988i | ||||
\(477\) | −11.3829 | − | 11.3829i | −0.521185 | − | 0.521185i | ||||
\(478\) | 0.631616 | − | 21.7004i | 0.0288894 | − | 0.992553i | ||||
\(479\) | 3.83766 | 0.175347 | 0.0876735 | − | 0.996149i | \(-0.472057\pi\) | ||||
0.0876735 | + | 0.996149i | \(0.472057\pi\) | |||||||
\(480\) | −5.89347 | + | 40.2215i | −0.268999 | + | 1.83585i | ||||
\(481\) | 6.94929 | 0.316860 | ||||||||
\(482\) | −0.643538 | + | 22.1100i | −0.0293124 | + | 1.00708i | ||||
\(483\) | −6.15427 | − | 6.15427i | −0.280029 | − | 0.280029i | ||||
\(484\) | −0.690016 | + | 11.8434i | −0.0313643 | + | 0.538335i | ||||
\(485\) | 30.8726 | − | 30.8726i | 1.40185 | − | 1.40185i | ||||
\(486\) | 21.2826 | − | 20.0788i | 0.965400 | − | 0.910791i | ||||
\(487\) | 36.6808i | 1.66217i | 0.556148 | + | 0.831083i | \(0.312279\pi\) | ||||
−0.556148 | + | 0.831083i | \(0.687721\pi\) | |||||||
\(488\) | 23.1858 | − | 19.4541i | 1.04957 | − | 0.880647i | ||||
\(489\) | 56.2236i | 2.54252i | ||||||||
\(490\) | 12.6392 | + | 13.3970i | 0.570980 | + | 0.605215i | ||||
\(491\) | 8.27309 | − | 8.27309i | 0.373359 | − | 0.373359i | −0.495340 | − | 0.868699i | \(-0.664956\pi\) |
0.868699 | + | 0.495340i | \(0.164956\pi\) | |||||||
\(492\) | 21.7153 | − | 19.3243i | 0.979001 | − | 0.871205i | ||||
\(493\) | −25.1531 | − | 25.1531i | −1.13284 | − | 1.13284i | ||||
\(494\) | −3.66602 | − | 0.106704i | −0.164942 | − | 0.00480084i | ||||
\(495\) | 31.9196 | 1.43468 | ||||||||
\(496\) | 27.5982 | + | 3.22679i | 1.23919 | + | 0.144887i | ||||
\(497\) | −20.8784 | −0.936522 | ||||||||
\(498\) | 35.8534 | + | 1.04356i | 1.60663 | + | 0.0467628i | ||||
\(499\) | 13.3714 | + | 13.3714i | 0.598588 | + | 0.598588i | 0.939937 | − | 0.341349i | \(-0.110884\pi\) |
−0.341349 | + | 0.939937i | \(0.610884\pi\) | |||||||
\(500\) | 2.76101 | + | 3.10264i | 0.123476 | + | 0.138754i | ||||
\(501\) | −11.3645 | + | 11.3645i | −0.507727 | + | 0.507727i | ||||
\(502\) | 20.0879 | + | 21.2923i | 0.896566 | + | 0.950322i | ||||
\(503\) | − | 2.50564i | − | 0.111721i | −0.998439 | − | 0.0558604i | \(-0.982210\pi\) | ||
0.998439 | − | 0.0558604i | \(-0.0177902\pi\) | |||||||
\(504\) | 1.03603 | − | 11.8382i | 0.0461487 | − | 0.527315i | ||||
\(505\) | 0.687272i | 0.0305832i | ||||||||
\(506\) | −9.46524 | + | 8.92983i | −0.420781 | + | 0.396980i | ||||
\(507\) | 10.4437 | − | 10.4437i | 0.463821 | − | 0.463821i | ||||
\(508\) | −37.8183 | − | 2.20336i | −1.67792 | − | 0.0977583i | ||||
\(509\) | −5.50329 | − | 5.50329i | −0.243929 | − | 0.243929i | 0.574544 | − | 0.818473i | \(-0.305179\pi\) |
−0.818473 | + | 0.574544i | \(0.805179\pi\) | |||||||
\(510\) | −1.99287 | + | 68.4690i | −0.0882459 | + | 3.03186i | ||||
\(511\) | 6.71743 | 0.297162 | ||||||||
\(512\) | 5.85821 | − | 21.8559i | 0.258899 | − | 0.965904i | ||||
\(513\) | 1.08046 | 0.0477037 | ||||||||
\(514\) | −1.04520 | + | 35.9099i | −0.0461018 | + | 1.58392i | ||||
\(515\) | 22.1504 | + | 22.1504i | 0.976062 | + | 0.976062i | ||||
\(516\) | −30.2905 | − | 1.76477i | −1.33346 | − | 0.0776899i | ||||
\(517\) | −24.5776 | + | 24.5776i | −1.08092 | + | 1.08092i | ||||
\(518\) | −4.55770 | + | 4.29989i | −0.200254 | + | 0.188926i | ||||
\(519\) | 5.69044i | 0.249782i | ||||||||
\(520\) | −1.95229 | + | 22.3077i | −0.0856135 | + | 0.978258i | ||||
\(521\) | − | 33.0861i | − | 1.44953i | −0.688998 | − | 0.724763i | \(-0.741949\pi\) | ||
0.688998 | − | 0.724763i | \(-0.258051\pi\) | |||||||
\(522\) | −13.0146 | − | 13.7949i | −0.569634 | − | 0.603788i | ||||
\(523\) | −8.01638 | + | 8.01638i | −0.350532 | + | 0.350532i | −0.860307 | − | 0.509776i | \(-0.829728\pi\) |
0.509776 | + | 0.860307i | \(0.329728\pi\) | |||||||
\(524\) | −11.8108 | − | 13.2721i | −0.515956 | − | 0.579797i | ||||
\(525\) | 11.8886 | + | 11.8886i | 0.518863 | + | 0.518863i | ||||
\(526\) | 23.2811 | + | 0.677624i | 1.01510 | + | 0.0295458i | ||||
\(527\) | 46.8204 | 2.03953 | ||||||||
\(528\) | −38.4819 | − | 4.49931i | −1.67471 | − | 0.195808i | ||||
\(529\) | 17.9995 | 0.782589 | ||||||||
\(530\) | −27.3398 | − | 0.795758i | −1.18757 | − | 0.0345655i | ||||
\(531\) | 4.55495 | + | 4.55495i | 0.197668 | + | 0.197668i | ||||
\(532\) | 2.47039 | − | 2.19838i | 0.107105 | − | 0.0953118i | ||||
\(533\) | 11.3227 | − | 11.3227i | 0.490439 | − | 0.490439i | ||||
\(534\) | 21.6215 | + | 22.9178i | 0.935653 | + | 0.991752i | ||||
\(535\) | 16.2417i | 0.702189i | ||||||||
\(536\) | 14.9653 | − | 12.5567i | 0.646404 | − | 0.542367i | ||||
\(537\) | − | 13.1122i | − | 0.565831i | ||||||
\(538\) | 3.68510 | − | 3.47665i | 0.158876 | − | 0.149889i | ||||
\(539\) | −12.4126 | + | 12.4126i | −0.534651 | + | 0.534651i | ||||
\(540\) | 0.383699 | − | 6.58578i | 0.0165118 | − | 0.283407i | ||||
\(541\) | −15.9481 | − | 15.9481i | −0.685661 | − | 0.685661i | 0.275609 | − | 0.961270i | \(-0.411120\pi\) |
−0.961270 | + | 0.275609i | \(0.911120\pi\) | |||||||
\(542\) | 0.257658 | − | 8.85235i | 0.0110674 | − | 0.380241i | ||||
\(543\) | 19.0737 | 0.818532 | ||||||||
\(544\) | 5.52766 | − | 37.7250i | 0.236996 | − | 1.61744i | ||||
\(545\) | −52.0559 | −2.22983 | ||||||||
\(546\) | 0.415305 | − | 14.2686i | 0.0177734 | − | 0.610641i | ||||
\(547\) | 7.85985 | + | 7.85985i | 0.336063 | + | 0.336063i | 0.854883 | − | 0.518820i | \(-0.173629\pi\) |
−0.518820 | + | 0.854883i | \(0.673629\pi\) | |||||||
\(548\) | −2.27130 | + | 38.9845i | −0.0970253 | + | 1.66533i | ||||
\(549\) | 19.2266 | − | 19.2266i | 0.820571 | − | 0.820571i | ||||
\(550\) | 18.2847 | − | 17.2504i | 0.779662 | − | 0.735559i | ||||
\(551\) | − | 5.27764i | − | 0.224835i | ||||||
\(552\) | −9.56967 | − | 11.4053i | −0.407312 | − | 0.485443i | ||||
\(553\) | − | 13.0311i | − | 0.554137i | ||||||
\(554\) | 5.07584 | + | 5.38018i | 0.215652 | + | 0.228582i | ||||
\(555\) | 13.6163 | − | 13.6163i | 0.577978 | − | 0.577978i | ||||
\(556\) | −18.4477 | + | 16.4165i | −0.782357 | + | 0.696213i | ||||
\(557\) | 32.3716 | + | 32.3716i | 1.37163 | + | 1.37163i | 0.858032 | + | 0.513596i | \(0.171687\pi\) |
0.513596 | + | 0.858032i | \(0.328313\pi\) | |||||||
\(558\) | 24.9519 | + | 0.726255i | 1.05630 | + | 0.0307448i | ||||
\(559\) | −16.7141 | −0.706929 | ||||||||
\(560\) | −12.5225 | − | 15.8385i | −0.529173 | − | 0.669299i | ||||
\(561\) | −65.2846 | −2.75632 | ||||||||
\(562\) | −41.5499 | − | 1.20936i | −1.75268 | − | 0.0510138i | ||||
\(563\) | 7.43471 | + | 7.43471i | 0.313335 | + | 0.313335i | 0.846200 | − | 0.532865i | \(-0.178885\pi\) |
−0.532865 | + | 0.846200i | \(0.678885\pi\) | |||||||
\(564\) | −26.4367 | − | 29.7077i | −1.11318 | − | 1.25092i | ||||
\(565\) | 38.9679 | − | 38.9679i | 1.63939 | − | 1.63939i | ||||
\(566\) | 5.52776 | + | 5.85919i | 0.232349 | + | 0.246280i | ||||
\(567\) | 16.8096i | 0.705936i | ||||||||
\(568\) | −35.5788 | − | 3.11373i | −1.49285 | − | 0.130649i | ||||
\(569\) | 1.59708i | 0.0669530i | 0.999440 | + | 0.0334765i | \(0.0106579\pi\) | ||||
−0.999440 | + | 0.0334765i | \(0.989342\pi\) | |||||||
\(570\) | −7.39218 | + | 6.97404i | −0.309625 | + | 0.292110i | ||||
\(571\) | 15.3223 | − | 15.3223i | 0.641219 | − | 0.641219i | −0.309636 | − | 0.950855i | \(-0.600207\pi\) |
0.950855 | + | 0.309636i | \(0.100207\pi\) | |||||||
\(572\) | −21.3063 | − | 1.24134i | −0.890863 | − | 0.0519032i | ||||
\(573\) | −4.76482 | − | 4.76482i | −0.199053 | − | 0.199053i | ||||
\(574\) | −0.420058 | + | 14.4319i | −0.0175329 | + | 0.602376i | ||||
\(575\) | 9.65974 | 0.402839 | ||||||||
\(576\) | 3.53101 | − | 20.0189i | 0.147126 | − | 0.834123i | ||||
\(577\) | −7.28279 | −0.303187 | −0.151593 | − | 0.988443i | \(-0.548440\pi\) | ||||
−0.151593 | + | 0.988443i | \(0.548440\pi\) | |||||||
\(578\) | 1.16971 | − | 40.1876i | 0.0486535 | − | 1.67158i | ||||
\(579\) | 13.6038 | + | 13.6038i | 0.565356 | + | 0.565356i | ||||
\(580\) | −32.1689 | − | 1.87422i | −1.33574 | − | 0.0778226i | ||||
\(581\) | −12.5975 | + | 12.5975i | −0.522631 | + | 0.522631i | ||||
\(582\) | −34.6303 | + | 32.6714i | −1.43547 | + | 1.35427i | ||||
\(583\) | − | 26.0683i | − | 1.07964i | ||||||
\(584\) | 11.4472 | + | 1.00182i | 0.473688 | + | 0.0414554i | ||||
\(585\) | 20.1173i | 0.831750i | ||||||||
\(586\) | −8.77617 | − | 9.30237i | −0.362540 | − | 0.384277i | ||||
\(587\) | 20.7800 | − | 20.7800i | 0.857682 | − | 0.857682i | −0.133383 | − | 0.991065i | \(-0.542584\pi\) |
0.991065 | + | 0.133383i | \(0.0425839\pi\) | |||||||
\(588\) | −13.3516 | − | 15.0036i | −0.550609 | − | 0.618737i | ||||
\(589\) | 4.91195 | + | 4.91195i | 0.202393 | + | 0.202393i | ||||
\(590\) | 10.9403 | + | 0.318430i | 0.450404 | + | 0.0131096i | ||||
\(591\) | 58.2038 | 2.39418 | ||||||||
\(592\) | −8.40805 | + | 6.64772i | −0.345569 | + | 0.273220i | ||||
\(593\) | −3.64515 | −0.149688 | −0.0748442 | − | 0.997195i | \(-0.523846\pi\) | ||||
−0.0748442 | + | 0.997195i | \(0.523846\pi\) | |||||||
\(594\) | 6.28481 | + | 0.182927i | 0.257869 | + | 0.00750558i | ||||
\(595\) | −24.0573 | − | 24.0573i | −0.986254 | − | 0.986254i | ||||
\(596\) | −0.596307 | + | 0.530649i | −0.0244257 | + | 0.0217362i | ||||
\(597\) | 19.0820 | − | 19.0820i | 0.780975 | − | 0.780975i | ||||
\(598\) | −5.62804 | − | 5.96548i | −0.230148 | − | 0.243947i | ||||
\(599\) | 12.4653i | 0.509317i | 0.967031 | + | 0.254659i | \(0.0819631\pi\) | ||||
−0.967031 | + | 0.254659i | \(0.918037\pi\) | |||||||
\(600\) | 18.4864 | + | 22.0325i | 0.754705 | + | 0.899472i | ||||
\(601\) | 2.70490i | 0.110335i | 0.998477 | + | 0.0551676i | \(0.0175693\pi\) | ||||
−0.998477 | + | 0.0551676i | \(0.982431\pi\) | |||||||
\(602\) | 10.9619 | − | 10.3419i | 0.446775 | − | 0.421503i | ||||
\(603\) | 12.4098 | − | 12.4098i | 0.505368 | − | 0.505368i | ||||
\(604\) | −2.40073 | + | 41.2060i | −0.0976844 | + | 1.67665i | ||||
\(605\) | 12.8047 | + | 12.8047i | 0.520584 | + | 0.520584i | ||||
\(606\) | 0.0218040 | − | 0.749120i | 0.000885728 | − | 0.0304309i | ||||
\(607\) | 45.5362 | 1.84826 | 0.924129 | − | 0.382080i | \(-0.124792\pi\) | ||||
0.924129 | + | 0.382080i | \(0.124792\pi\) | |||||||
\(608\) | 4.53765 | − | 3.37783i | 0.184026 | − | 0.136989i | ||||
\(609\) | 20.5412 | 0.832373 | ||||||||
\(610\) | 1.34410 | − | 46.1793i | 0.0544211 | − | 1.86974i | ||||
\(611\) | −15.4900 | − | 15.4900i | −0.626660 | − | 0.626660i | ||||
\(612\) | 1.99227 | − | 34.1952i | 0.0805327 | − | 1.38226i | ||||
\(613\) | −31.0423 | + | 31.0423i | −1.25379 | + | 1.25379i | −0.299776 | + | 0.954010i | \(0.596912\pi\) |
−0.954010 | + | 0.299776i | \(0.903088\pi\) | |||||||
\(614\) | −9.54753 | + | 9.00747i | −0.385307 | + | 0.363512i | ||||
\(615\) | − | 44.3707i | − | 1.78920i | ||||||
\(616\) | 14.7419 | − | 12.3692i | 0.593967 | − | 0.498370i | ||||
\(617\) | − | 40.2158i | − | 1.61903i | −0.587103 | − | 0.809513i | \(-0.699731\pi\) | ||
0.587103 | − | 0.809513i | \(-0.300269\pi\) | |||||||
\(618\) | −23.4409 | − | 24.8464i | −0.942933 | − | 0.999469i | ||||
\(619\) | −18.8734 | + | 18.8734i | −0.758587 | + | 0.758587i | −0.976065 | − | 0.217478i | \(-0.930217\pi\) |
0.217478 | + | 0.976065i | \(0.430217\pi\) | |||||||
\(620\) | 31.6843 | − | 28.1956i | 1.27247 | − | 1.13236i | ||||
\(621\) | 1.70844 | + | 1.70844i | 0.0685574 | + | 0.0685574i | ||||
\(622\) | −31.8280 | − | 0.926392i | −1.27619 | − | 0.0371449i | ||||
\(623\) | −15.6494 | −0.626978 | ||||||||
\(624\) | 2.83570 | − | 24.2532i | 0.113519 | − | 0.970907i | ||||
\(625\) | 27.9384 | 1.11754 | ||||||||
\(626\) | 38.9561 | + | 1.13386i | 1.55700 | + | 0.0453184i | ||||
\(627\) | −6.84904 | − | 6.84904i | −0.273524 | − | 0.273524i | ||||
\(628\) | −14.8596 | − | 16.6982i | −0.592964 | − | 0.666332i | ||||
\(629\) | −12.7711 | + | 12.7711i | −0.509217 | + | 0.509217i | ||||
\(630\) | −12.4477 | − | 13.1940i | −0.495926 | − | 0.525661i | ||||
\(631\) | − | 9.83337i | − | 0.391460i | −0.980658 | − | 0.195730i | \(-0.937292\pi\) | ||
0.980658 | − | 0.195730i | \(-0.0627077\pi\) | |||||||
\(632\) | 1.94341 | − | 22.2062i | 0.0773046 | − | 0.883316i | ||||
\(633\) | − | 24.6560i | − | 0.979988i | ||||||
\(634\) | 6.00591 | − | 5.66618i | 0.238525 | − | 0.225033i | ||||
\(635\) | −40.8879 | + | 40.8879i | −1.62259 | + | 1.62259i | ||||
\(636\) | 29.7749 | + | 1.73474i | 1.18065 | + | 0.0687868i | ||||
\(637\) | −7.82309 | − | 7.82309i | −0.309962 | − | 0.309962i | ||||
\(638\) | 0.893525 | − | 30.6988i | 0.0353750 | − | 1.21538i | ||||
\(639\) | −32.0854 | −1.26928 | ||||||||
\(640\) | −18.9775 | − | 28.8580i | −0.750153 | − | 1.14071i | ||||
\(641\) | 32.2957 | 1.27560 | 0.637801 | − | 0.770201i | \(-0.279844\pi\) | ||||
0.637801 | + | 0.770201i | \(0.279844\pi\) | |||||||
\(642\) | 0.515274 | − | 17.7033i | 0.0203363 | − | 0.698692i | ||||
\(643\) | −21.1614 | − | 21.1614i | −0.834525 | − | 0.834525i | 0.153607 | − | 0.988132i | \(-0.450911\pi\) |
−0.988132 | + | 0.153607i | \(0.950911\pi\) | |||||||
\(644\) | 7.38231 | + | 0.430106i | 0.290904 | + | 0.0169486i | ||||
\(645\) | −32.7491 | + | 32.7491i | −1.28949 | + | 1.28949i | ||||
\(646\) | 6.93334 | − | 6.54115i | 0.272789 | − | 0.257358i | ||||
\(647\) | 35.5368i | 1.39710i | 0.715564 | + | 0.698548i | \(0.246170\pi\) | ||||
−0.715564 | + | 0.698548i | \(0.753830\pi\) | |||||||
\(648\) | −2.50693 | + | 28.6452i | −0.0984813 | + | 1.12529i | ||||
\(649\) | 10.4315i | 0.409471i | ||||||||
\(650\) | 10.8721 | + | 11.5239i | 0.426438 | + | 0.452006i | ||||
\(651\) | −19.1179 | + | 19.1179i | −0.749291 | + | 0.749291i | ||||
\(652\) | −31.7566 | − | 35.6859i | −1.24369 | − | 1.39757i | ||||
\(653\) | −17.2398 | − | 17.2398i | −0.674645 | − | 0.674645i | 0.284138 | − | 0.958783i | \(-0.408293\pi\) |
−0.958783 | + | 0.284138i | \(0.908293\pi\) | |||||||
\(654\) | 56.7404 | + | 1.65150i | 2.21873 | + | 0.0645787i | ||||
\(655\) | −27.1189 | −1.05962 | ||||||||
\(656\) | −2.86815 | + | 24.5308i | −0.111982 | + | 0.957765i | ||||
\(657\) | 10.3232 | 0.402746 | ||||||||
\(658\) | 19.7436 | + | 0.574662i | 0.769687 | + | 0.0224027i | ||||
\(659\) | −3.11267 | − | 3.11267i | −0.121253 | − | 0.121253i | 0.643877 | − | 0.765129i | \(-0.277325\pi\) |
−0.765129 | + | 0.643877i | \(0.777325\pi\) | |||||||
\(660\) | −44.1794 | + | 39.3148i | −1.71968 | + | 1.53033i | ||||
\(661\) | 30.0154 | − | 30.0154i | 1.16746 | − | 1.16746i | 0.184660 | − | 0.982802i | \(-0.440882\pi\) |
0.982802 | − | 0.184660i | \(-0.0591185\pi\) | |||||||
\(662\) | −5.41869 | − | 5.74358i | −0.210603 | − | 0.223231i | ||||
\(663\) | − | 41.1457i | − | 1.59797i | ||||||
\(664\) | −23.3461 | + | 19.5886i | −0.906004 | + | 0.760185i | ||||
\(665\) | − | 5.04772i | − | 0.195742i | ||||||
\(666\) | −7.00417 | + | 6.60797i | −0.271406 | + | 0.256054i | ||||
\(667\) | 8.34506 | − | 8.34506i | 0.323122 | − | 0.323122i | ||||
\(668\) | 0.794232 | − | 13.6321i | 0.0307298 | − | 0.527443i | ||||
\(669\) | −17.3993 | − | 17.3993i | −0.672697 | − | 0.672697i | ||||
\(670\) | 0.867554 | − | 29.8065i | 0.0335165 | − | 1.15153i | ||||
\(671\) | 44.0315 | 1.69982 | ||||||||
\(672\) | 13.1469 | + | 17.6611i | 0.507154 | + | 0.681292i | ||||
\(673\) | 8.01937 | 0.309124 | 0.154562 | − | 0.987983i | \(-0.450603\pi\) | ||||
0.154562 | + | 0.987983i | \(0.450603\pi\) | |||||||
\(674\) | −1.33979 | + | 46.0310i | −0.0516067 | + | 1.77305i | ||||
\(675\) | −3.30032 | − | 3.30032i | −0.127029 | − | 0.127029i | ||||
\(676\) | −0.729882 | + | 12.5276i | −0.0280724 | + | 0.481832i | ||||
\(677\) | −17.7844 | + | 17.7844i | −0.683511 | + | 0.683511i | −0.960790 | − | 0.277278i | \(-0.910568\pi\) |
0.277278 | + | 0.960790i | \(0.410568\pi\) | |||||||
\(678\) | −43.7109 | + | 41.2384i | −1.67871 | + | 1.58375i | ||||
\(679\) | − | 23.6472i | − | 0.907495i | ||||||
\(680\) | −37.4082 | − | 44.5839i | −1.43454 | − | 1.70971i | ||||
\(681\) | − | 19.6062i | − | 0.751311i | ||||||
\(682\) | 27.7401 | + | 29.4033i | 1.06222 | + | 1.12591i | ||||
\(683\) | −19.5322 | + | 19.5322i | −0.747378 | + | 0.747378i | −0.973986 | − | 0.226608i | \(-0.927236\pi\) |
0.226608 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(684\) | 3.79644 | − | 3.37842i | 0.145160 | − | 0.129177i | ||||
\(685\) | 42.1488 | + | 42.1488i | 1.61042 | + | 1.61042i | ||||
\(686\) | 26.3328 | + | 0.766447i | 1.00539 | + | 0.0292631i | ||||
\(687\) | 3.71853 | 0.141871 | ||||||||
\(688\) | 20.2226 | − | 15.9887i | 0.770979 | − | 0.609565i | ||||
\(689\) | 16.4296 | 0.625917 | ||||||||
\(690\) | −22.7160 | − | 0.661177i | −0.864785 | − | 0.0251706i | ||||
\(691\) | 15.7926 | + | 15.7926i | 0.600777 | + | 0.600777i | 0.940519 | − | 0.339742i | \(-0.110340\pi\) |
−0.339742 | + | 0.940519i | \(0.610340\pi\) | |||||||
\(692\) | −3.21411 | − | 3.61180i | −0.122182 | − | 0.137300i | ||||
\(693\) | 12.2245 | − | 12.2245i | 0.464372 | − | 0.464372i | ||||
\(694\) | 12.7407 | + | 13.5046i | 0.483630 | + | 0.512627i | ||||
\(695\) | 37.6940i | 1.42982i | ||||||||
\(696\) | 35.0043 | + | 3.06345i | 1.32684 | + | 0.116120i | ||||
\(697\) | 41.6165i | 1.57634i | ||||||||
\(698\) | −1.46220 | + | 1.37949i | −0.0553450 | + | 0.0522144i | ||||
\(699\) | −1.33870 | + | 1.33870i | −0.0506343 | + | 0.0506343i | ||||
\(700\) | −14.2609 | − | 0.830866i | −0.539012 | − | 0.0314038i | ||||
\(701\) | −17.6581 | − | 17.6581i | −0.666935 | − | 0.666935i | 0.290070 | − | 0.957005i | \(-0.406321\pi\) |
−0.957005 | + | 0.290070i | \(0.906321\pi\) | |||||||
\(702\) | −0.115290 | + | 3.96101i | −0.00435134 | + | 0.149499i | ||||
\(703\) | −2.67964 | −0.101065 | ||||||||
\(704\) | 26.9663 | − | 18.8798i | 1.01633 | − | 0.711560i | ||||
\(705\) | −60.7015 | −2.28615 | ||||||||
\(706\) | −1.30566 | + | 44.8586i | −0.0491393 | + | 1.68828i | ||||
\(707\) | 0.263211 | + | 0.263211i | 0.00989907 | + | 0.00989907i | ||||
\(708\) | −11.9147 | − | 0.694171i | −0.447782 | − | 0.0260885i | ||||
\(709\) | 17.4746 | − | 17.4746i | 0.656272 | − | 0.656272i | −0.298224 | − | 0.954496i | \(-0.596394\pi\) |
0.954496 | + | 0.298224i | \(0.0963942\pi\) | |||||||
\(710\) | −39.6536 | + | 37.4105i | −1.48817 | + | 1.40399i | ||||
\(711\) | − | 20.0258i | − | 0.751027i | ||||||
\(712\) | −26.6681 | − | 2.33389i | −0.999428 | − | 0.0874663i | ||||
\(713\) | 15.5337i | 0.581740i | ||||||||
\(714\) | 25.4590 | + | 26.9855i | 0.952779 | + | 1.00991i | ||||
\(715\) | −23.0358 | + | 23.0358i | −0.861488 | + | 0.861488i | ||||
\(716\) | 7.40610 | + | 8.32247i | 0.276779 | + | 0.311025i | ||||
\(717\) | 25.5514 | + | 25.5514i | 0.954236 | + | 0.954236i | ||||
\(718\) | −24.1779 | − | 0.703726i | −0.902310 | − | 0.0262628i | ||||
\(719\) | −8.66057 | −0.322985 | −0.161492 | − | 0.986874i | \(-0.551631\pi\) | ||||
−0.161492 | + | 0.986874i | \(0.551631\pi\) | |||||||
\(720\) | −19.2443 | − | 24.3403i | −0.717194 | − | 0.907108i | ||||
\(721\) | 16.9663 | 0.631857 | ||||||||
\(722\) | 1.41361 | + | 0.0411449i | 0.0526093 | + | 0.00153126i | ||||
\(723\) | −26.0337 | − | 26.0337i | −0.968206 | − | 0.968206i | ||||
\(724\) | −12.1064 | + | 10.7734i | −0.449930 | + | 0.400389i | ||||
\(725\) | −16.1207 | + | 16.1207i | −0.598710 | + | 0.598710i | ||||
\(726\) | −13.5507 | − | 14.3632i | −0.502915 | − | 0.533069i | ||||
\(727\) | − | 52.1123i | − | 1.93274i | −0.257160 | − | 0.966369i | \(-0.582787\pi\) | ||
0.257160 | − | 0.966369i | \(-0.417213\pi\) | |||||||
\(728\) | 7.79571 | + | 9.29108i | 0.288928 | + | 0.344350i | ||||
\(729\) | 18.2026i | 0.674170i | ||||||||
\(730\) | 12.7582 | − | 12.0365i | 0.472202 | − | 0.445491i | ||||
\(731\) | 30.7163 | − | 30.7163i | 1.13608 | − | 1.13608i | ||||
\(732\) | −2.93012 | + | 50.2923i | −0.108300 | + | 1.85886i | ||||
\(733\) | 23.7514 | + | 23.7514i | 0.877279 | + | 0.877279i | 0.993252 | − | 0.115973i | \(-0.0369986\pi\) |
−0.115973 | + | 0.993252i | \(0.536999\pi\) | |||||||
\(734\) | 0.172614 | − | 5.93049i | 0.00637130 | − | 0.218899i | ||||
\(735\) | −30.6567 | −1.13079 | ||||||||
\(736\) | 12.5160 | + | 1.83392i | 0.461348 | + | 0.0675990i | ||||
\(737\) | 28.4203 | 1.04687 | ||||||||
\(738\) | −0.645535 | + | 22.1786i | −0.0237625 | + | 0.816406i | ||||
\(739\) | 6.82503 | + | 6.82503i | 0.251063 | + | 0.251063i | 0.821406 | − | 0.570344i | \(-0.193190\pi\) |
−0.570344 | + | 0.821406i | \(0.693190\pi\) | |||||||
\(740\) | −0.951605 | + | 16.3333i | −0.0349817 | + | 0.600423i | ||||
\(741\) | 4.31661 | − | 4.31661i | 0.158575 | − | 0.158575i | ||||
\(742\) | −10.7754 | + | 10.1658i | −0.395576 | + | 0.373200i | ||||
\(743\) | 31.3539i | 1.15026i | 0.818062 | + | 0.575131i | \(0.195049\pi\) | ||||
−0.818062 | + | 0.575131i | \(0.804951\pi\) | |||||||
\(744\) | −35.4300 | + | 29.7277i | −1.29893 | + | 1.08987i | ||||
\(745\) | 1.21843i | 0.0446398i | ||||||||
\(746\) | −20.7736 | − | 22.0192i | −0.760577 | − | 0.806179i | ||||
\(747\) | −19.3595 | + | 19.3595i | −0.708327 | + | 0.708327i | ||||
\(748\) | 41.4371 | − | 36.8745i | 1.51509 | − | 1.34827i | ||||
\(749\) | 6.22023 | + | 6.22023i | 0.227282 | + | 0.227282i | ||||
\(750\) | −6.91010 | − | 0.201127i | −0.252321 | − | 0.00734411i | ||||
\(751\) | 42.7968 | 1.56168 | 0.780839 | − | 0.624733i | \(-0.214792\pi\) | ||||
0.780839 | + | 0.624733i | \(0.214792\pi\) | |||||||
\(752\) | 33.5595 | + | 3.92378i | 1.22379 | + | 0.143086i | ||||
\(753\) | −48.7237 | −1.77559 | ||||||||
\(754\) | 19.3480 | + | 0.563145i | 0.704611 | + | 0.0205085i | ||||
\(755\) | 44.5506 | + | 44.5506i | 1.62136 | + | 1.62136i | ||||
\(756\) | −2.37527 | − | 2.66917i | −0.0863877 | − | 0.0970767i | ||||
\(757\) | 7.73140 | − | 7.73140i | 0.281002 | − | 0.281002i | −0.552506 | − | 0.833509i | \(-0.686328\pi\) |
0.833509 | + | 0.552506i | \(0.186328\pi\) | |||||||
\(758\) | 8.43337 | + | 8.93901i | 0.306314 | + | 0.324679i | ||||
\(759\) | − | 21.6596i | − | 0.786192i | ||||||
\(760\) | 0.752801 | − | 8.60183i | 0.0273069 | − | 0.312021i | ||||
\(761\) | − | 38.9433i | − | 1.41169i | −0.708365 | − | 0.705846i | \(-0.750567\pi\) | ||
0.708365 | − | 0.705846i | \(-0.249433\pi\) | |||||||
\(762\) | 45.8646 | − | 43.2703i | 1.66150 | − | 1.56752i | ||||
\(763\) | −19.9364 | + | 19.9364i | −0.721744 | + | 0.721744i | ||||
\(764\) | 5.71560 | + | 0.333001i | 0.206783 | + | 0.0120475i | ||||
\(765\) | −36.9707 | − | 36.9707i | −1.33668 | − | 1.33668i | ||||
\(766\) | −0.343774 | + | 11.8110i | −0.0124211 | + | 0.426750i | ||||
\(767\) | −6.57444 | −0.237389 | ||||||||
\(768\) | 19.7698 | + | 32.0570i | 0.713381 | + | 1.15676i | ||||
\(769\) | −16.2839 | −0.587212 | −0.293606 | − | 0.955926i | \(-0.594855\pi\) | ||||
−0.293606 | + | 0.955926i | \(0.594855\pi\) | |||||||
\(770\) | 0.854600 | − | 29.3614i | 0.0307976 | − | 1.05811i | ||||
\(771\) | −42.2826 | − | 42.2826i | −1.52277 | − | 1.52277i | ||||
\(772\) | −16.3184 | − | 0.950737i | −0.587311 | − | 0.0342178i | ||||
\(773\) | 18.1233 | − | 18.1233i | 0.651851 | − | 0.651851i | −0.301588 | − | 0.953438i | \(-0.597517\pi\) |
0.953438 | + | 0.301588i | \(0.0975166\pi\) | |||||||
\(774\) | 16.8460 | − | 15.8931i | 0.605519 | − | 0.571267i | ||||
\(775\) | − | 30.0075i | − | 1.07790i | ||||||
\(776\) | 3.52666 | − | 40.2971i | 0.126600 | − | 1.44658i | ||||
\(777\) | − | 10.4295i | − | 0.374156i | ||||||
\(778\) | −2.06578 | − | 2.18964i | −0.0740619 | − | 0.0785025i | ||||
\(779\) | −4.36601 | + | 4.36601i | −0.156428 | + | 0.156428i | ||||
\(780\) | −24.7782 | − | 27.8441i | −0.887202 | − | 0.996978i | ||||
\(781\) | −36.7400 | − | 36.7400i | −1.31466 | − | 1.31466i | ||||
\(782\) | 21.3060 | + | 0.620137i | 0.761902 | + | 0.0221761i | ||||
\(783\) | −5.70230 | −0.203784 | ||||||||
\(784\) | 16.9489 | + | 1.98167i | 0.605316 | + | 0.0707738i | ||||
\(785\) | −34.1194 | −1.21777 | ||||||||
\(786\) | 29.5593 | + | 0.860358i | 1.05435 | + | 0.0306880i | ||||
\(787\) | −8.02876 | − | 8.02876i | −0.286195 | − | 0.286195i | 0.549379 | − | 0.835573i | \(-0.314864\pi\) |
−0.835573 | + | 0.549379i | \(0.814864\pi\) | |||||||
\(788\) | −36.9428 | + | 32.8751i | −1.31603 | + | 1.17113i | ||||
\(789\) | −27.4127 | + | 27.4127i | −0.975917 | + | 0.975917i | ||||
\(790\) | −23.3495 | − | 24.7494i | −0.830737 | − | 0.880546i | ||||
\(791\) | − | 29.8478i | − | 1.06127i | ||||||
\(792\) | 22.6550 | − | 19.0087i | 0.805009 | − | 0.675445i | ||||
\(793\) | 27.7509i | 0.985464i | ||||||||
\(794\) | 0.0432895 | − | 0.0408408i | 0.00153629 | − | 0.00144938i | ||||
\(795\) | 32.1917 | − | 32.1917i | 1.14172 | − | 1.14172i | ||||
\(796\) | −1.33359 | + | 22.8897i | −0.0472679 | + | 0.811303i | ||||
\(797\) | 11.0459 | + | 11.0459i | 0.391266 | + | 0.391266i | 0.875138 | − | 0.483873i | \(-0.160770\pi\) |
−0.483873 | + | 0.875138i | \(0.660770\pi\) | |||||||
\(798\) | −0.160141 | + | 5.50197i | −0.00566894 | + | 0.194768i | ||||
\(799\) | 56.9337 | 2.01417 | ||||||||
\(800\) | −24.1781 | − | 3.54271i | −0.854826 | − | 0.125254i | ||||
\(801\) | −24.0496 | −0.849750 | ||||||||
\(802\) | 0.164258 | − | 5.64339i | 0.00580014 | − | 0.199275i | ||||
\(803\) | 11.8208 | + | 11.8208i | 0.417146 | + | 0.417146i | ||||
\(804\) | −1.89125 | + | 32.4613i | −0.0666992 | + | 1.14482i | ||||
\(805\) | 7.98152 | − | 7.98152i | 0.281312 | − | 0.281312i | ||||
\(806\) | −18.5314 | + | 17.4832i | −0.652742 | + | 0.615819i | ||||
\(807\) | 8.43270i | 0.296845i | ||||||||
\(808\) | 0.409284 | + | 0.487793i | 0.0143986 | + | 0.0171605i | ||||
\(809\) | 5.34576i | 0.187947i | 0.995575 | + | 0.0939735i | \(0.0299569\pi\) | ||||
−0.995575 | + | 0.0939735i | \(0.970043\pi\) | |||||||
\(810\) | 30.1200 | + | 31.9259i | 1.05831 | + | 1.12176i | ||||
\(811\) | 8.36280 | − | 8.36280i | 0.293657 | − | 0.293657i | −0.544866 | − | 0.838523i | \(-0.683419\pi\) |
0.838523 | + | 0.544866i | \(0.183419\pi\) | |||||||
\(812\) | −13.0378 | + | 11.6022i | −0.457538 | + | 0.407159i | ||||
\(813\) | 10.4233 | + | 10.4233i | 0.365562 | + | 0.365562i | ||||
\(814\) | −15.5868 | − | 0.453674i | −0.546318 | − | 0.0159013i | ||||
\(815\) | −72.9168 | −2.55416 | ||||||||
\(816\) | 39.3602 | + | 49.7828i | 1.37788 | + | 1.74275i | ||||
\(817\) | 6.44492 | 0.225479 | ||||||||
\(818\) | 8.83144 | + | 0.257050i | 0.308784 | + | 0.00898753i | ||||
\(819\) | 7.70453 | + | 7.70453i | 0.269218 | + | 0.269218i | ||||
\(820\) | 25.0617 | + | 28.1627i | 0.875194 | + | 0.983484i | ||||
\(821\) | −21.9983 | + | 21.9983i | −0.767745 | + | 0.767745i | −0.977709 | − | 0.209964i | \(-0.932665\pi\) |
0.209964 | + | 0.977709i | \(0.432665\pi\) | |||||||
\(822\) | −44.6046 | − | 47.2789i | −1.55576 | − | 1.64904i | ||||
\(823\) | 14.3205i | 0.499180i | 0.968352 | + | 0.249590i | \(0.0802958\pi\) | ||||
−0.968352 | + | 0.249590i | \(0.919704\pi\) | |||||||
\(824\) | 28.9122 | + | 2.53029i | 1.00721 | + | 0.0881469i | ||||
\(825\) | 41.8413i | 1.45673i | ||||||||
\(826\) | 4.31185 | − | 4.06795i | 0.150029 | − | 0.141542i | ||||
\(827\) | 12.6413 | − | 12.6413i | 0.439582 | − | 0.439582i | −0.452289 | − | 0.891871i | \(-0.649392\pi\) |
0.891871 | + | 0.452289i | \(0.149392\pi\) | |||||||
\(828\) | 11.3450 | + | 0.660977i | 0.394265 | + | 0.0229705i | ||||
\(829\) | −8.76539 | − | 8.76539i | −0.304435 | − | 0.304435i | 0.538311 | − | 0.842746i | \(-0.319062\pi\) |
−0.842746 | + | 0.538311i | \(0.819062\pi\) | |||||||
\(830\) | −1.35339 | + | 46.4985i | −0.0469770 | + | 1.61399i | ||||
\(831\) | −12.3116 | −0.427084 | ||||||||
\(832\) | 11.8990 | + | 16.9956i | 0.412525 | + | 0.589215i | ||||
\(833\) | 28.7538 | 0.996260 | ||||||||
\(834\) | 1.19586 | − | 41.0861i | 0.0414093 | − | 1.42270i | ||||
\(835\) | −14.7386 | − | 14.7386i | −0.510052 | − | 0.510052i | ||||
\(836\) | 8.21570 | + | 0.478661i | 0.284146 | + | 0.0165548i | ||||
\(837\) | 5.30719 | − | 5.30719i | 0.183443 | − | 0.183443i | ||||
\(838\) | −18.0194 | + | 17.0001i | −0.622470 | + | 0.587260i | ||||
\(839\) | − | 20.1832i | − | 0.696802i | −0.937346 | − | 0.348401i | \(-0.886725\pi\) | ||
0.937346 | − | 0.348401i | \(-0.113275\pi\) | |||||||
\(840\) | 33.4794 | + | 2.92999i | 1.15515 | + | 0.101094i | ||||
\(841\) | − | 1.14653i | − | 0.0395354i | ||||||
\(842\) | −10.1326 | − | 10.7402i | −0.349194 | − | 0.370130i | ||||
\(843\) | 48.9236 | − | 48.9236i | 1.68502 | − | 1.68502i | ||||
\(844\) | 13.9264 | + | 15.6495i | 0.479365 | + | 0.538678i | ||||
\(845\) | 13.5445 | + | 13.5445i | 0.465945 | + | 0.465945i | ||||
\(846\) | 30.3416 | + | 0.883128i | 1.04317 | + | 0.0303626i | ||||
\(847\) | 9.80786 | 0.337002 | ||||||||
\(848\) | −19.8784 | + | 15.7166i | −0.682626 | + | 0.539710i | ||||
\(849\) | −13.4077 | −0.460152 | ||||||||
\(850\) | −41.1584 | − | 1.19796i | −1.41172 | − | 0.0410898i | ||||
\(851\) | −4.23708 | − | 4.23708i | −0.145245 | − | 0.145245i | ||||
\(852\) | 44.4088 | − | 39.5190i | 1.52142 | − | 1.35390i | ||||
\(853\) | −21.8924 | + | 21.8924i | −0.749583 | + | 0.749583i | −0.974401 | − | 0.224818i | \(-0.927821\pi\) |
0.224818 | + | 0.974401i | \(0.427821\pi\) | |||||||
\(854\) | −17.1709 | − | 18.2005i | −0.587578 | − | 0.622807i | ||||
\(855\) | − | 7.75723i | − | 0.265292i | ||||||
\(856\) | 9.67222 | + | 11.5276i | 0.330590 | + | 0.394004i | ||||
\(857\) | − | 26.5057i | − | 0.905417i | −0.891658 | − | 0.452709i | \(-0.850458\pi\) | ||
0.891658 | − | 0.452709i | \(-0.149542\pi\) | |||||||
\(858\) | 25.8396 | − | 24.3779i | 0.882148 | − | 0.832248i | ||||
\(859\) | −20.1778 | + | 20.1778i | −0.688457 | + | 0.688457i | −0.961891 | − | 0.273434i | \(-0.911841\pi\) |
0.273434 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(860\) | 2.28875 | − | 39.2839i | 0.0780456 | − | 1.33957i | ||||
\(861\) | −16.9931 | − | 16.9931i | −0.579122 | − | 0.579122i | ||||
\(862\) | −0.607533 | + | 20.8730i | −0.0206926 | + | 0.710936i | ||||
\(863\) | −28.4763 | −0.969343 | −0.484672 | − | 0.874696i | \(-0.661061\pi\) | ||||
−0.484672 | + | 0.874696i | \(0.661061\pi\) | |||||||
\(864\) | −3.64963 | − | 4.90277i | −0.124163 | − | 0.166796i | ||||
\(865\) | −7.37996 | −0.250926 | ||||||||
\(866\) | −0.919886 | + | 31.6045i | −0.0312590 | + | 1.07396i | ||||
\(867\) | 47.3195 | + | 47.3195i | 1.60705 | + | 1.60705i | ||||
\(868\) | 1.33610 | − | 22.9327i | 0.0453502 | − | 0.778388i | ||||
\(869\) | 22.9310 | − | 22.9310i | 0.777880 | − | 0.777880i | ||||
\(870\) | 39.0133 | − | 36.8065i | 1.32267 | − | 1.24786i | ||||
\(871\) | 17.9119i | 0.606921i | ||||||||
\(872\) | −36.9468 | + | 31.0003i | −1.25118 | + | 1.04980i | ||||
\(873\) | − | 36.3404i | − | 1.22994i | ||||||
\(874\) | 2.17016 | + | 2.30028i | 0.0734069 | + | 0.0778082i | ||||
\(875\) | 2.42794 | − | 2.42794i | 0.0820792 | − | 0.0820792i | ||||
\(876\) | −14.2882 | + | 12.7149i | −0.482752 | + | 0.429597i | ||||
\(877\) | 2.44906 | + | 2.44906i | 0.0826987 | + | 0.0826987i | 0.747246 | − | 0.664547i | \(-0.231376\pi\) |
−0.664547 | + | 0.747246i | \(0.731376\pi\) | |||||||
\(878\) | −4.27797 | − | 0.124515i | −0.144375 | − | 0.00420219i | ||||
\(879\) | 21.2868 | 0.717987 | ||||||||
\(880\) | 5.83519 | − | 49.9074i | 0.196704 | − | 1.68238i | ||||
\(881\) | 4.91215 | 0.165494 | 0.0827472 | − | 0.996571i | \(-0.473631\pi\) | ||||
0.0827472 | + | 0.996571i | \(0.473631\pi\) | |||||||
\(882\) | 15.3237 | + | 0.446015i | 0.515976 | + | 0.0150181i | ||||
\(883\) | 34.4699 | + | 34.4699i | 1.16000 | + | 1.16000i | 0.984474 | + | 0.175531i | \(0.0561641\pi\) |
0.175531 | + | 0.984474i | \(0.443836\pi\) | |||||||
\(884\) | 23.2402 | + | 26.1158i | 0.781653 | + | 0.878369i | ||||
\(885\) | −12.8818 | + | 12.8818i | −0.433017 | + | 0.433017i | ||||
\(886\) | −26.2190 | − | 27.7910i | −0.880843 | − | 0.933656i | ||||
\(887\) | 34.4251i | 1.15588i | 0.816079 | + | 0.577941i | \(0.196144\pi\) | ||||
−0.816079 | + | 0.577941i | \(0.803856\pi\) | |||||||
\(888\) | 1.55542 | − | 17.7729i | 0.0521965 | − | 0.596420i | ||||
\(889\) | 31.3185i | 1.05039i | ||||||||
\(890\) | −29.7223 | + | 28.0410i | −0.996294 | + | 0.939937i | ||||
\(891\) | −29.5801 | + | 29.5801i | −0.990971 | + | 0.990971i | ||||
\(892\) | 20.8712 | + | 1.21599i | 0.698820 | + | 0.0407145i | ||||
\(893\) | 5.97294 | + | 5.97294i | 0.199877 | + | 0.199877i | ||||
\(894\) | 0.0386552 | − | 1.32808i | 0.00129282 | − | 0.0444175i | ||||
\(895\) | 17.0052 | 0.568422 | ||||||||
\(896\) | −18.3200 | − | 3.78400i | −0.612029 | − | 0.126415i | ||||
\(897\) | 13.6510 | 0.455792 | ||||||||
\(898\) | 0.825619 | − | 28.3658i | 0.0275513 | − | 0.946578i | ||||
\(899\) | −25.9235 | − | 25.9235i | −0.864597 | − | 0.864597i | ||||
\(900\) | −21.9159 | − | 1.27686i | −0.730529 | − | 0.0425619i | ||||
\(901\) | −30.1935 | + | 30.1935i | −1.00589 | + | 1.00589i | ||||
\(902\) | −26.1352 | + | 24.6569i | −0.870208 | + | 0.820984i | ||||
\(903\) | 25.0845i | 0.834758i | ||||||||
\(904\) | 4.45141 | − | 50.8637i | 0.148052 | − | 1.69170i | ||||
\(905\) | 24.7368i | 0.822281i | ||||||||
\(906\) | −47.1463 | − | 49.9731i | −1.56633 | − | 1.66025i | ||||
\(907\) | −13.6078 | + | 13.6078i | −0.451839 | + | 0.451839i | −0.895965 | − | 0.444126i | \(-0.853514\pi\) |
0.444126 | + | 0.895965i | \(0.353514\pi\) | |||||||
\(908\) | 11.0741 | + | 12.4443i | 0.367507 | + | 0.412980i | ||||
\(909\) | 0.404497 | + | 0.404497i | 0.0134163 | + | 0.0134163i | ||||
\(910\) | 18.5051 | + | 0.538612i | 0.613437 | + | 0.0178548i | ||||
\(911\) | −34.7876 | −1.15257 | −0.576283 | − | 0.817250i | \(-0.695497\pi\) | ||||
−0.576283 | + | 0.817250i | \(0.695497\pi\) | |||||||
\(912\) | −1.09344 | + | 9.35202i | −0.0362075 | + | 0.309676i | ||||
\(913\) | −44.3359 | −1.46731 | ||||||||
\(914\) | −5.93027 | − | 0.172608i | −0.196156 | − | 0.00570935i | ||||
\(915\) | 54.3744 | + | 54.3744i | 1.79756 | + | 1.79756i | ||||
\(916\) | −2.36021 | + | 2.10033i | −0.0779834 | + | 0.0693967i | ||||
\(917\) | −10.3860 | + | 10.3860i | −0.342975 | + | 0.342975i | ||||
\(918\) | −7.06748 | − | 7.49123i | −0.233262 | − | 0.247247i | ||||
\(919\) | 25.0906i | 0.827663i | 0.910354 | + | 0.413831i | \(0.135810\pi\) | ||||
−0.910354 | + | 0.413831i | \(0.864190\pi\) | |||||||
\(920\) | 14.7916 | − | 12.4110i | 0.487666 | − | 0.409178i | ||||
\(921\) | − | 21.8479i | − | 0.719911i | ||||||
\(922\) | −7.39432 | + | 6.97605i | −0.243519 | + | 0.229744i | ||||
\(923\) | 23.1554 | − | 23.1554i | 0.762169 | − | 0.762169i | ||||
\(924\) | −1.86301 | + | 31.9766i | −0.0612885 | + | 1.05195i | ||||
\(925\) | 8.18506 | + | 8.18506i | 0.269123 | + | 0.269123i | ||||
\(926\) | −0.758771 | + | 26.0690i | −0.0249347 | + | 0.856682i | ||||
\(927\) | 26.0734 | 0.856362 | ||||||||
\(928\) | −23.9481 | + | 17.8270i | −0.786134 | + | 0.585199i | ||||
\(929\) | 25.0250 | 0.821044 | 0.410522 | − | 0.911851i | \(-0.365347\pi\) | ||||
0.410522 | + | 0.911851i | \(0.365347\pi\) | |||||||
\(930\) | −2.05391 | + | 70.5661i | −0.0673504 | + | 2.31396i | ||||
\(931\) | 3.01657 | + | 3.01657i | 0.0988642 | + | 0.0988642i | ||||
\(932\) | 0.0935583 | − | 1.60583i | 0.00306460 | − | 0.0526006i | ||||
\(933\) | 37.4763 | − | 37.4763i | 1.22692 | − | 1.22692i | ||||
\(934\) | −3.30838 | + | 3.12123i | −0.108253 | + | 0.102130i | ||||
\(935\) | − | 84.6681i | − | 2.76894i | ||||||
\(936\) | 11.9803 | + | 14.2783i | 0.391587 | + | 0.466702i | ||||
\(937\) | 9.64668i | 0.315143i | 0.987508 | + | 0.157572i | \(0.0503665\pi\) | ||||
−0.987508 | + | 0.157572i | \(0.949633\pi\) | |||||||
\(938\) | −11.0830 | − | 11.7475i | −0.361874 | − | 0.383571i | ||||
\(939\) | −45.8695 | + | 45.8695i | −1.49689 | + | 1.49689i | ||||
\(940\) | 38.5281 | − | 34.2859i | 1.25665 | − | 1.11828i | ||||
\(941\) | 16.4584 | + | 16.4584i | 0.536528 | + | 0.536528i | 0.922507 | − | 0.385979i | \(-0.126136\pi\) |
−0.385979 | + | 0.922507i | \(0.626136\pi\) | |||||||
\(942\) | 37.1898 | + | 1.08245i | 1.21171 | + | 0.0352682i | ||||
\(943\) | −13.8072 | −0.449623 | ||||||||
\(944\) | 7.95451 | − | 6.28914i | 0.258897 | − | 0.204694i | ||||
\(945\) | −5.45389 | −0.177415 | ||||||||
\(946\) | 37.4886 | + | 1.09115i | 1.21886 | + | 0.0354764i | ||||
\(947\) | −7.86883 | − | 7.86883i | −0.255703 | − | 0.255703i | 0.567601 | − | 0.823304i | \(-0.307872\pi\) |
−0.823304 | + | 0.567601i | \(0.807872\pi\) | |||||||
\(948\) | 24.6655 | + | 27.7174i | 0.801098 | + | 0.900220i | ||||
\(949\) | −7.45005 | + | 7.45005i | −0.241839 | + | 0.241839i | ||||
\(950\) | −4.19226 | − | 4.44362i | −0.136015 | − | 0.144170i | ||||
\(951\) | 13.7435i | 0.445662i | ||||||||
\(952\) | −31.4013 | − | 2.74813i | −1.01772 | − | 0.0890673i | ||||
\(953\) | − | 25.8987i | − | 0.838940i | −0.907769 | − | 0.419470i | \(-0.862216\pi\) | ||
0.907769 | − | 0.419470i | \(-0.137784\pi\) | |||||||
\(954\) | −16.5593 | + | 15.6226i | −0.536128 | + | 0.505801i | ||||
\(955\) | 6.17952 | − | 6.17952i | 0.199965 | − | 0.199965i | ||||
\(956\) | −30.6500 | − | 1.78572i | −0.991292 | − | 0.0577544i | ||||
\(957\) | 36.1467 | + | 36.1467i | 1.16846 | + | 1.16846i | ||||
\(958\) | 0.157900 | − | 5.42497i | 0.00510152 | − | 0.175273i | ||||
\(959\) | 32.2842 | 1.04251 | ||||||||
\(960\) | 56.6153 | + | 9.98601i | 1.82725 | + | 0.322297i | ||||
\(961\) | 17.2545 | 0.556596 | ||||||||
\(962\) | 0.285928 | − | 9.82362i | 0.00921870 | − | 0.316726i | ||||
\(963\) | 9.55910 | + | 9.55910i | 0.308038 | + | 0.308038i | ||||
\(964\) | 31.2286 | + | 1.81943i | 1.00580 | + | 0.0585999i | ||||
\(965\) | −17.6429 | + | 17.6429i | −0.567945 | + | 0.567945i | ||||
\(966\) | −8.95299 | + | 8.44656i | −0.288058 | + | 0.271763i | ||||
\(967\) | − | 1.14283i | − | 0.0367508i | −0.999831 | − | 0.0183754i | \(-0.994151\pi\) | ||
0.999831 | − | 0.0183754i | \(-0.00584940\pi\) | |||||||
\(968\) | 16.7136 | + | 1.46271i | 0.537195 | + | 0.0470133i | ||||
\(969\) | 15.8657i | 0.509681i | ||||||||
\(970\) | −42.3718 | − | 44.9123i | −1.36048 | − | 1.44205i | ||||
\(971\) | −5.53244 | + | 5.53244i | −0.177544 | + | 0.177544i | −0.790284 | − | 0.612740i | \(-0.790067\pi\) |
0.612740 | + | 0.790284i | \(0.290067\pi\) | |||||||
\(972\) | −27.5080 | − | 30.9116i | −0.882318 | − | 0.991489i | ||||
\(973\) | 14.4360 | + | 14.4360i | 0.462798 | + | 0.462798i | ||||
\(974\) | 51.8525 | + | 1.50923i | 1.66146 | + | 0.0483589i | ||||
\(975\) | −26.3705 | −0.844532 | ||||||||
\(976\) | −26.5467 | − | 33.5762i | −0.849738 | − | 1.07475i | ||||
\(977\) | −40.4617 | −1.29449 | −0.647243 | − | 0.762284i | \(-0.724078\pi\) | ||||
−0.647243 | + | 0.762284i | \(0.724078\pi\) | |||||||
\(978\) | 79.4786 | + | 2.31332i | 2.54144 | + | 0.0739718i | ||||
\(979\) | −27.5384 | − | 27.5384i | −0.880132 | − | 0.880132i | ||||
\(980\) | 19.4582 | − | 17.3157i | 0.621571 | − | 0.553131i | ||||
\(981\) | −30.6377 | + | 30.6377i | −0.978188 | + | 0.978188i | ||||
\(982\) | −11.3546 | − | 12.0354i | −0.362339 | − | 0.384064i | ||||
\(983\) | 30.6417i | 0.977318i | 0.872475 | + | 0.488659i | \(0.162514\pi\) | ||||
−0.872475 | + | 0.488659i | \(0.837486\pi\) | |||||||
\(984\) | −26.4236 | − | 31.4922i | −0.842353 | − | 1.00393i | ||||
\(985\) | 75.4849i | 2.40515i | ||||||||
\(986\) | −36.5917 | + | 34.5218i | −1.16532 | + | 1.09940i | ||||
\(987\) | −23.2474 | + | 23.2474i | −0.739974 | + | 0.739974i | ||||
\(988\) | −0.301677 | + | 5.17796i | −0.00959762 | + | 0.164733i | ||||
\(989\) | 10.1908 | + | 10.1908i | 0.324048 | + | 0.324048i | ||||
\(990\) | 1.31333 | − | 45.1220i | 0.0417404 | − | 1.43407i | ||||
\(991\) | 21.4041 | 0.679924 | 0.339962 | − | 0.940439i | \(-0.389586\pi\) | ||||
0.339962 | + | 0.940439i | \(0.389586\pi\) | |||||||
\(992\) | 5.69696 | − | 38.8804i | 0.180879 | − | 1.23445i | ||||
\(993\) | 13.1432 | 0.417086 | ||||||||
\(994\) | −0.859039 | + | 29.5139i | −0.0272471 | + | 0.936126i | ||||
\(995\) | 24.7476 | + | 24.7476i | 0.784552 | + | 0.784552i | ||||
\(996\) | 2.95037 | − | 50.6399i | 0.0934861 | − | 1.60459i | ||||
\(997\) | 3.29934 | − | 3.29934i | 0.104491 | − | 0.104491i | −0.652928 | − | 0.757420i | \(-0.726460\pi\) |
0.757420 | + | 0.652928i | \(0.226460\pi\) | |||||||
\(998\) | 19.4522 | − | 18.3519i | 0.615750 | − | 0.580919i | ||||
\(999\) | 2.89525i | 0.0916018i |
(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 | 304.2.k.b.77.18 | ✓ | 68 | |
4.3 | odd | 2 | 1216.2.k.b.913.5 | 68 | |||
16.5 | even | 4 | inner | 304.2.k.b.229.18 | yes | 68 | |
16.11 | odd | 4 | 1216.2.k.b.305.5 | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.k.b.77.18 | ✓ | 68 | 1.1 | even | 1 | trivial | |
304.2.k.b.229.18 | yes | 68 | 16.5 | even | 4 | inner | |
1216.2.k.b.305.5 | 68 | 16.11 | odd | 4 | |||
1216.2.k.b.913.5 | 68 | 4.3 | odd | 2 |