Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.3 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.b.487.3 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.26431 | − | 1.84432i | 0.565416 | − | 0.824806i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 1.64144 | − | 1.64144i | 0.620405 | − | 0.620405i | −0.325230 | − | 0.945635i | \(-0.605442\pi\) |
0.945635 | + | 0.325230i | \(0.105442\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.26431 | − | 1.84432i | 0.399809 | − | 0.583226i | ||||
\(11\) | − | 4.17593i | − | 1.25909i | −0.776964 | − | 0.629545i | \(-0.783241\pi\) | ||
0.776964 | − | 0.629545i | \(-0.216759\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −1.20051 | −0.332963 | −0.166481 | − | 0.986045i | \(-0.553241\pi\) | ||||
−0.166481 | + | 0.986045i | \(0.553241\pi\) | |||||||
\(14\) | 1.64144 | − | 1.64144i | 0.438693 | − | 0.438693i | ||||
\(15\) | 0.410132 | + | 2.19813i | 0.105896 | + | 0.567556i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.221929i | 0.0538257i | 0.999638 | + | 0.0269128i | \(0.00856766\pi\) | ||||
−0.999638 | + | 0.0269128i | \(0.991432\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.73909 | − | 3.73909i | −0.857805 | − | 0.857805i | 0.133274 | − | 0.991079i | \(-0.457451\pi\) |
−0.991079 | + | 0.133274i | \(0.957451\pi\) | |||||||
\(20\) | 1.26431 | − | 1.84432i | 0.282708 | − | 0.412403i | ||||
\(21\) | 2.32134i | 0.506559i | ||||||||
\(22\) | − | 4.17593i | − | 0.890311i | ||||||
\(23\) | −4.24635 | −0.885425 | −0.442713 | − | 0.896664i | \(-0.645984\pi\) | ||||
−0.442713 | + | 0.896664i | \(0.645984\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | −1.80305 | − | 4.66358i | −0.360610 | − | 0.932717i | ||||
\(26\) | −1.20051 | −0.235440 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.64144 | − | 1.64144i | 0.310203 | − | 0.310203i | ||||
\(29\) | −5.45356 | + | 5.45356i | −1.01270 | + | 1.01270i | −0.0127828 | + | 0.999918i | \(0.504069\pi\) |
−0.999918 | + | 0.0127828i | \(0.995931\pi\) | |||||||
\(30\) | 0.410132 | + | 2.19813i | 0.0748795 | + | 0.401322i | ||||
\(31\) | 1.77644 | + | 1.77644i | 0.319058 | + | 0.319058i | 0.848405 | − | 0.529347i | \(-0.177563\pi\) |
−0.529347 | + | 0.848405i | \(0.677563\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.95283 | + | 2.95283i | 0.514021 | + | 0.514021i | ||||
\(34\) | 0.221929i | 0.0380605i | ||||||||
\(35\) | −0.952057 | − | 5.10263i | −0.160927 | − | 0.862501i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 6.07033 | + | 0.388773i | 0.997955 | + | 0.0639139i | ||||
\(38\) | −3.73909 | − | 3.73909i | −0.606560 | − | 0.606560i | ||||
\(39\) | 0.848892 | − | 0.848892i | 0.135932 | − | 0.135932i | ||||
\(40\) | 1.26431 | − | 1.84432i | 0.199905 | − | 0.291613i | ||||
\(41\) | − | 2.58213i | − | 0.403261i | −0.979462 | − | 0.201631i | \(-0.935376\pi\) | ||
0.979462 | − | 0.201631i | \(-0.0646240\pi\) | |||||||
\(42\) | 2.32134i | 0.358191i | ||||||||
\(43\) | 7.69386 | 1.17330 | 0.586651 | − | 0.809840i | \(-0.300446\pi\) | ||||
0.586651 | + | 0.809840i | \(0.300446\pi\) | |||||||
\(44\) | − | 4.17593i | − | 0.629545i | ||||||
\(45\) | −1.84432 | − | 1.26431i | −0.274935 | − | 0.188472i | ||||
\(46\) | −4.24635 | −0.626090 | ||||||||
\(47\) | 5.62938 | − | 5.62938i | 0.821129 | − | 0.821129i | −0.165141 | − | 0.986270i | \(-0.552808\pi\) |
0.986270 | + | 0.165141i | \(0.0528079\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 1.61136i | 0.230194i | ||||||||
\(50\) | −1.80305 | − | 4.66358i | −0.254990 | − | 0.659530i | ||||
\(51\) | −0.156927 | − | 0.156927i | −0.0219742 | − | 0.0219742i | ||||
\(52\) | −1.20051 | −0.166481 | ||||||||
\(53\) | −4.45920 | − | 4.45920i | −0.612518 | − | 0.612518i | 0.331084 | − | 0.943601i | \(-0.392586\pi\) |
−0.943601 | + | 0.331084i | \(0.892586\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −7.70175 | − | 5.27966i | −1.03850 | − | 0.711909i | ||||
\(56\) | 1.64144 | − | 1.64144i | 0.219346 | − | 0.219346i | ||||
\(57\) | 5.28787 | 0.700395 | ||||||||
\(58\) | −5.45356 | + | 5.45356i | −0.716088 | + | 0.716088i | ||||
\(59\) | 3.90868 | + | 3.90868i | 0.508866 | + | 0.508866i | 0.914178 | − | 0.405312i | \(-0.132837\pi\) |
−0.405312 | + | 0.914178i | \(0.632837\pi\) | |||||||
\(60\) | 0.410132 | + | 2.19813i | 0.0529478 | + | 0.283778i | ||||
\(61\) | 0.901511 | + | 0.901511i | 0.115427 | + | 0.115427i | 0.762461 | − | 0.647034i | \(-0.223991\pi\) |
−0.647034 | + | 0.762461i | \(0.723991\pi\) | |||||||
\(62\) | 1.77644 | + | 1.77644i | 0.225608 | + | 0.225608i | ||||
\(63\) | −1.64144 | − | 1.64144i | −0.206802 | − | 0.206802i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.51782 | + | 2.21414i | −0.188262 | + | 0.274630i | ||||
\(66\) | 2.95283 | + | 2.95283i | 0.363468 | + | 0.363468i | ||||
\(67\) | 10.3479 | + | 10.3479i | 1.26420 | + | 1.26420i | 0.949038 | + | 0.315162i | \(0.102059\pi\) |
0.315162 | + | 0.949038i | \(0.397941\pi\) | |||||||
\(68\) | 0.221929i | 0.0269128i | ||||||||
\(69\) | 3.00262 | − | 3.00262i | 0.361473 | − | 0.361473i | ||||
\(70\) | −0.952057 | − | 5.10263i | −0.113793 | − | 0.609880i | ||||
\(71\) | 9.11658 | 1.08194 | 0.540969 | − | 0.841042i | \(-0.318058\pi\) | ||||
0.540969 | + | 0.841042i | \(0.318058\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −3.76725 | + | 3.76725i | −0.440923 | + | 0.440923i | −0.892322 | − | 0.451399i | \(-0.850925\pi\) |
0.451399 | + | 0.892322i | \(0.350925\pi\) | |||||||
\(74\) | 6.07033 | + | 0.388773i | 0.705661 | + | 0.0451939i | ||||
\(75\) | 4.57260 | + | 2.02270i | 0.527998 | + | 0.233562i | ||||
\(76\) | −3.73909 | − | 3.73909i | −0.428903 | − | 0.428903i | ||||
\(77\) | −6.85453 | − | 6.85453i | −0.781146 | − | 0.781146i | ||||
\(78\) | 0.848892 | − | 0.848892i | 0.0961181 | − | 0.0961181i | ||||
\(79\) | 0.571724 | + | 0.571724i | 0.0643239 | + | 0.0643239i | 0.738537 | − | 0.674213i | \(-0.235517\pi\) |
−0.674213 | + | 0.738537i | \(0.735517\pi\) | |||||||
\(80\) | 1.26431 | − | 1.84432i | 0.141354 | − | 0.206201i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 2.58213i | − | 0.285149i | ||||||
\(83\) | 7.69554 | + | 7.69554i | 0.844695 | + | 0.844695i | 0.989465 | − | 0.144770i | \(-0.0462443\pi\) |
−0.144770 | + | 0.989465i | \(0.546244\pi\) | |||||||
\(84\) | 2.32134i | 0.253279i | ||||||||
\(85\) | 0.409308 | + | 0.280587i | 0.0443957 | + | 0.0304339i | ||||
\(86\) | 7.69386 | 0.829650 | ||||||||
\(87\) | − | 7.71250i | − | 0.826867i | ||||||
\(88\) | − | 4.17593i | − | 0.445155i | ||||||
\(89\) | 4.28275 | − | 4.28275i | 0.453971 | − | 0.453971i | −0.442699 | − | 0.896670i | \(-0.645979\pi\) |
0.896670 | + | 0.442699i | \(0.145979\pi\) | |||||||
\(90\) | −1.84432 | − | 1.26431i | −0.194409 | − | 0.133270i | ||||
\(91\) | −1.97057 | + | 1.97057i | −0.206572 | + | 0.206572i | ||||
\(92\) | −4.24635 | −0.442713 | ||||||||
\(93\) | −2.51226 | −0.260509 | ||||||||
\(94\) | 5.62938 | − | 5.62938i | 0.580626 | − | 0.580626i | ||||
\(95\) | −11.6234 | + | 2.16872i | −1.19254 | + | 0.222506i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | 8.59029i | 0.872212i | 0.899895 | + | 0.436106i | \(0.143643\pi\) | ||||
−0.899895 | + | 0.436106i | \(0.856357\pi\) | |||||||
\(98\) | 1.61136i | 0.162772i | ||||||||
\(99\) | −4.17593 | −0.419696 | ||||||||
\(100\) | −1.80305 | − | 4.66358i | −0.180305 | − | 0.466358i | ||||
\(101\) | 9.72766i | 0.967938i | 0.875085 | + | 0.483969i | \(0.160805\pi\) | ||||
−0.875085 | + | 0.483969i | \(0.839195\pi\) | |||||||
\(102\) | −0.156927 | − | 0.156927i | −0.0155381 | − | 0.0155381i | ||||
\(103\) | − | 15.6866i | − | 1.54565i | −0.634621 | − | 0.772824i | \(-0.718844\pi\) | ||
0.634621 | − | 0.772824i | \(-0.281156\pi\) | |||||||
\(104\) | −1.20051 | −0.117720 | ||||||||
\(105\) | 4.28131 | + | 2.93490i | 0.417813 | + | 0.286416i | ||||
\(106\) | −4.45920 | − | 4.45920i | −0.433115 | − | 0.433115i | ||||
\(107\) | 1.59584 | − | 1.59584i | 0.154275 | − | 0.154275i | −0.625749 | − | 0.780024i | \(-0.715207\pi\) |
0.780024 | + | 0.625749i | \(0.215207\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 6.35309 | + | 6.35309i | 0.608516 | + | 0.608516i | 0.942558 | − | 0.334042i | \(-0.108413\pi\) |
−0.334042 | + | 0.942558i | \(0.608413\pi\) | |||||||
\(110\) | −7.70175 | − | 5.27966i | −0.734333 | − | 0.503396i | ||||
\(111\) | −4.56727 | + | 4.01746i | −0.433506 | + | 0.381321i | ||||
\(112\) | 1.64144 | − | 1.64144i | 0.155101 | − | 0.155101i | ||||
\(113\) | − | 11.7528i | − | 1.10561i | −0.833311 | − | 0.552805i | \(-0.813558\pi\) | ||
0.833311 | − | 0.552805i | \(-0.186442\pi\) | |||||||
\(114\) | 5.28787 | 0.495254 | ||||||||
\(115\) | −5.36870 | + | 7.83164i | −0.500633 | + | 0.730304i | ||||
\(116\) | −5.45356 | + | 5.45356i | −0.506351 | + | 0.506351i | ||||
\(117\) | 1.20051i | 0.110988i | ||||||||
\(118\) | 3.90868 | + | 3.90868i | 0.359823 | + | 0.359823i | ||||
\(119\) | 0.364283 | + | 0.364283i | 0.0333937 | + | 0.0333937i | ||||
\(120\) | 0.410132 | + | 2.19813i | 0.0374397 | + | 0.200661i | ||||
\(121\) | −6.43836 | −0.585306 | ||||||||
\(122\) | 0.901511 | + | 0.901511i | 0.0816189 | + | 0.0816189i | ||||
\(123\) | 1.82584 | + | 1.82584i | 0.164631 | + | 0.164631i | ||||
\(124\) | 1.77644 | + | 1.77644i | 0.159529 | + | 0.159529i | ||||
\(125\) | −10.8808 | − | 2.57081i | −0.973205 | − | 0.229940i | ||||
\(126\) | −1.64144 | − | 1.64144i | −0.146231 | − | 0.146231i | ||||
\(127\) | 9.18790 | − | 9.18790i | 0.815295 | − | 0.815295i | −0.170127 | − | 0.985422i | \(-0.554418\pi\) |
0.985422 | + | 0.170127i | \(0.0544179\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.44038 | + | 5.44038i | −0.478999 | + | 0.478999i | ||||
\(130\) | −1.51782 | + | 2.21414i | −0.133122 | + | 0.194193i | ||||
\(131\) | −10.7012 | − | 10.7012i | −0.934966 | − | 0.934966i | 0.0630449 | − | 0.998011i | \(-0.479919\pi\) |
−0.998011 | + | 0.0630449i | \(0.979919\pi\) | |||||||
\(132\) | 2.95283 | + | 2.95283i | 0.257011 | + | 0.257011i | ||||
\(133\) | −12.2750 | −1.06437 | ||||||||
\(134\) | 10.3479 | + | 10.3479i | 0.893924 | + | 0.893924i | ||||
\(135\) | 2.19813 | − | 0.410132i | 0.189185 | − | 0.0352985i | ||||
\(136\) | 0.221929i | 0.0190303i | ||||||||
\(137\) | −4.35277 | + | 4.35277i | −0.371882 | + | 0.371882i | −0.868162 | − | 0.496280i | \(-0.834699\pi\) |
0.496280 | + | 0.868162i | \(0.334699\pi\) | |||||||
\(138\) | 3.00262 | − | 3.00262i | 0.255600 | − | 0.255600i | ||||
\(139\) | 18.3422 | 1.55577 | 0.777883 | − | 0.628409i | \(-0.216293\pi\) | ||||
0.777883 | + | 0.628409i | \(0.216293\pi\) | |||||||
\(140\) | −0.952057 | − | 5.10263i | −0.0804635 | − | 0.431251i | ||||
\(141\) | 7.96114i | 0.670449i | ||||||||
\(142\) | 9.11658 | 0.765046 | ||||||||
\(143\) | 5.01326i | 0.419230i | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 3.16314 | + | 16.9531i | 0.262685 | + | 1.40788i | ||||
\(146\) | −3.76725 | + | 3.76725i | −0.311780 | + | 0.311780i | ||||
\(147\) | −1.13940 | − | 1.13940i | −0.0939764 | − | 0.0939764i | ||||
\(148\) | 6.07033 | + | 0.388773i | 0.498978 | + | 0.0319569i | ||||
\(149\) | 9.29218i | 0.761245i | 0.924731 | + | 0.380622i | \(0.124290\pi\) | ||||
−0.924731 | + | 0.380622i | \(0.875710\pi\) | |||||||
\(150\) | 4.57260 | + | 2.02270i | 0.373351 | + | 0.165153i | ||||
\(151\) | 10.0875i | 0.820910i | 0.911881 | + | 0.410455i | \(0.134630\pi\) | ||||
−0.911881 | + | 0.410455i | \(0.865370\pi\) | |||||||
\(152\) | −3.73909 | − | 3.73909i | −0.303280 | − | 0.303280i | ||||
\(153\) | 0.221929 | 0.0179419 | ||||||||
\(154\) | −6.85453 | − | 6.85453i | −0.552353 | − | 0.552353i | ||||
\(155\) | 5.52229 | − | 1.03036i | 0.443561 | − | 0.0827604i | ||||
\(156\) | 0.848892 | − | 0.848892i | 0.0679658 | − | 0.0679658i | ||||
\(157\) | −15.8215 | + | 15.8215i | −1.26269 | + | 1.26269i | −0.312906 | + | 0.949784i | \(0.601302\pi\) |
−0.949784 | + | 0.312906i | \(0.898698\pi\) | |||||||
\(158\) | 0.571724 | + | 0.571724i | 0.0454839 | + | 0.0454839i | ||||
\(159\) | 6.30625 | 0.500119 | ||||||||
\(160\) | 1.26431 | − | 1.84432i | 0.0999524 | − | 0.145806i | ||||
\(161\) | −6.97012 | + | 6.97012i | −0.549323 | + | 0.549323i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 18.7947i | 1.47212i | 0.676918 | + | 0.736058i | \(0.263315\pi\) | ||||
−0.676918 | + | 0.736058i | \(0.736685\pi\) | |||||||
\(164\) | − | 2.58213i | − | 0.201631i | ||||||
\(165\) | 9.17925 | − | 1.71268i | 0.714603 | − | 0.133332i | ||||
\(166\) | 7.69554 | + | 7.69554i | 0.597290 | + | 0.597290i | ||||
\(167\) | − | 14.4189i | − | 1.11577i | −0.829920 | − | 0.557883i | \(-0.811614\pi\) | ||
0.829920 | − | 0.557883i | \(-0.188386\pi\) | |||||||
\(168\) | 2.32134i | 0.179096i | ||||||||
\(169\) | −11.5588 | −0.889136 | ||||||||
\(170\) | 0.409308 | + | 0.280587i | 0.0313925 | + | 0.0215200i | ||||
\(171\) | −3.73909 | + | 3.73909i | −0.285935 | + | 0.285935i | ||||
\(172\) | 7.69386 | 0.586651 | ||||||||
\(173\) | 13.9023 | − | 13.9023i | 1.05697 | − | 1.05697i | 0.0586938 | − | 0.998276i | \(-0.481306\pi\) |
0.998276 | − | 0.0586938i | \(-0.0186935\pi\) | |||||||
\(174\) | − | 7.71250i | − | 0.584683i | ||||||
\(175\) | −10.6146 | − | 4.69539i | −0.802387 | − | 0.354938i | ||||
\(176\) | − | 4.17593i | − | 0.314772i | ||||||
\(177\) | −5.52770 | −0.415487 | ||||||||
\(178\) | 4.28275 | − | 4.28275i | 0.321006 | − | 0.321006i | ||||
\(179\) | −11.4245 | + | 11.4245i | −0.853906 | + | 0.853906i | −0.990612 | − | 0.136705i | \(-0.956349\pi\) |
0.136705 | + | 0.990612i | \(0.456349\pi\) | |||||||
\(180\) | −1.84432 | − | 1.26431i | −0.137468 | − | 0.0942360i | ||||
\(181\) | −18.4010 | −1.36774 | −0.683869 | − | 0.729605i | \(-0.739704\pi\) | ||||
−0.683869 | + | 0.729605i | \(0.739704\pi\) | |||||||
\(182\) | −1.97057 | + | 1.97057i | −0.146068 | + | 0.146068i | ||||
\(183\) | −1.27493 | −0.0942454 | ||||||||
\(184\) | −4.24635 | −0.313045 | ||||||||
\(185\) | 8.39179 | − | 10.7041i | 0.616976 | − | 0.786982i | ||||
\(186\) | −2.51226 | −0.184208 | ||||||||
\(187\) | 0.926759 | 0.0677713 | ||||||||
\(188\) | 5.62938 | − | 5.62938i | 0.410565 | − | 0.410565i | ||||
\(189\) | 2.32134 | 0.168853 | ||||||||
\(190\) | −11.6234 | + | 2.16872i | −0.843253 | + | 0.157336i | ||||
\(191\) | −3.52951 | + | 3.52951i | −0.255386 | + | 0.255386i | −0.823175 | − | 0.567788i | \(-0.807799\pi\) |
0.567788 | + | 0.823175i | \(0.307799\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 9.24953 | 0.665796 | 0.332898 | − | 0.942963i | \(-0.391974\pi\) | ||||
0.332898 | + | 0.942963i | \(0.391974\pi\) | |||||||
\(194\) | 8.59029i | 0.616747i | ||||||||
\(195\) | −0.492369 | − | 2.63889i | −0.0352593 | − | 0.188975i | ||||
\(196\) | 1.61136i | 0.115097i | ||||||||
\(197\) | −1.75235 | + | 1.75235i | −0.124850 | + | 0.124850i | −0.766771 | − | 0.641921i | \(-0.778138\pi\) |
0.641921 | + | 0.766771i | \(0.278138\pi\) | |||||||
\(198\) | −4.17593 | −0.296770 | ||||||||
\(199\) | −1.94022 | + | 1.94022i | −0.137538 | + | 0.137538i | −0.772524 | − | 0.634986i | \(-0.781006\pi\) |
0.634986 | + | 0.772524i | \(0.281006\pi\) | |||||||
\(200\) | −1.80305 | − | 4.66358i | −0.127495 | − | 0.329765i | ||||
\(201\) | −14.6342 | −1.03222 | ||||||||
\(202\) | 9.72766i | 0.684436i | ||||||||
\(203\) | 17.9034i | 1.25657i | ||||||||
\(204\) | −0.156927 | − | 0.156927i | −0.0109871 | − | 0.0109871i | ||||
\(205\) | −4.76228 | − | 3.26461i | −0.332612 | − | 0.228010i | ||||
\(206\) | − | 15.6866i | − | 1.09294i | ||||||
\(207\) | 4.24635i | 0.295142i | ||||||||
\(208\) | −1.20051 | −0.0832407 | ||||||||
\(209\) | −15.6141 | + | 15.6141i | −1.08005 | + | 1.08005i | ||||
\(210\) | 4.28131 | + | 2.93490i | 0.295438 | + | 0.202527i | ||||
\(211\) | −4.88849 | −0.336538 | −0.168269 | − | 0.985741i | \(-0.553818\pi\) | ||||
−0.168269 | + | 0.985741i | \(0.553818\pi\) | |||||||
\(212\) | −4.45920 | − | 4.45920i | −0.306259 | − | 0.306259i | ||||
\(213\) | −6.44639 | + | 6.44639i | −0.441700 | + | 0.441700i | ||||
\(214\) | 1.59584 | − | 1.59584i | 0.109089 | − | 0.109089i | ||||
\(215\) | 9.72741 | − | 14.1899i | 0.663404 | − | 0.967746i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | 5.83183 | 0.395890 | ||||||||
\(218\) | 6.35309 | + | 6.35309i | 0.430285 | + | 0.430285i | ||||
\(219\) | − | 5.32769i | − | 0.360012i | ||||||
\(220\) | −7.70175 | − | 5.27966i | −0.519252 | − | 0.355955i | ||||
\(221\) | − | 0.266429i | − | 0.0179219i | ||||||
\(222\) | −4.56727 | + | 4.01746i | −0.306535 | + | 0.269635i | ||||
\(223\) | 16.9445 | + | 16.9445i | 1.13469 | + | 1.13469i | 0.989388 | + | 0.145300i | \(0.0464147\pi\) |
0.145300 | + | 0.989388i | \(0.453585\pi\) | |||||||
\(224\) | 1.64144 | − | 1.64144i | 0.109673 | − | 0.109673i | ||||
\(225\) | −4.66358 | + | 1.80305i | −0.310906 | + | 0.120203i | ||||
\(226\) | − | 11.7528i | − | 0.781784i | ||||||
\(227\) | − | 22.8426i | − | 1.51612i | −0.652187 | − | 0.758058i | \(-0.726148\pi\) | ||
0.652187 | − | 0.758058i | \(-0.273852\pi\) | |||||||
\(228\) | 5.28787 | 0.350197 | ||||||||
\(229\) | 16.1156i | 1.06495i | 0.846446 | + | 0.532474i | \(0.178738\pi\) | ||||
−0.846446 | + | 0.532474i | \(0.821262\pi\) | |||||||
\(230\) | −5.36870 | + | 7.83164i | −0.354001 | + | 0.516403i | ||||
\(231\) | 9.69376 | 0.637803 | ||||||||
\(232\) | −5.45356 | + | 5.45356i | −0.358044 | + | 0.358044i | ||||
\(233\) | −3.66171 | + | 3.66171i | −0.239886 | + | 0.239886i | −0.816803 | − | 0.576917i | \(-0.804256\pi\) |
0.576917 | + | 0.816803i | \(0.304256\pi\) | |||||||
\(234\) | 1.20051i | 0.0784801i | ||||||||
\(235\) | −3.26512 | − | 17.4997i | −0.212993 | − | 1.14155i | ||||
\(236\) | 3.90868 | + | 3.90868i | 0.254433 | + | 0.254433i | ||||
\(237\) | −0.808539 | −0.0525203 | ||||||||
\(238\) | 0.364283 | + | 0.364283i | 0.0236129 | + | 0.0236129i | ||||
\(239\) | −2.75228 | − | 2.75228i | −0.178030 | − | 0.178030i | 0.612467 | − | 0.790497i | \(-0.290177\pi\) |
−0.790497 | + | 0.612467i | \(0.790177\pi\) | |||||||
\(240\) | 0.410132 | + | 2.19813i | 0.0264739 | + | 0.141889i | ||||
\(241\) | −19.9398 | + | 19.9398i | −1.28444 | + | 1.28444i | −0.346319 | + | 0.938117i | \(0.612569\pi\) |
−0.938117 | + | 0.346319i | \(0.887431\pi\) | |||||||
\(242\) | −6.43836 | −0.413874 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0.901511 | + | 0.901511i | 0.0577133 | + | 0.0577133i | ||||
\(245\) | 2.97187 | + | 2.03726i | 0.189866 | + | 0.130156i | ||||
\(246\) | 1.82584 | + | 1.82584i | 0.116411 | + | 0.116411i | ||||
\(247\) | 4.48883 | + | 4.48883i | 0.285617 | + | 0.285617i | ||||
\(248\) | 1.77644 | + | 1.77644i | 0.112804 | + | 0.112804i | ||||
\(249\) | −10.8831 | −0.689691 | ||||||||
\(250\) | −10.8808 | − | 2.57081i | −0.688160 | − | 0.162592i | ||||
\(251\) | −12.4982 | − | 12.4982i | −0.788880 | − | 0.788880i | 0.192430 | − | 0.981311i | \(-0.438363\pi\) |
−0.981311 | + | 0.192430i | \(0.938363\pi\) | |||||||
\(252\) | −1.64144 | − | 1.64144i | −0.103401 | − | 0.103401i | ||||
\(253\) | 17.7324i | 1.11483i | ||||||||
\(254\) | 9.18790 | − | 9.18790i | 0.576500 | − | 0.576500i | ||||
\(255\) | −0.487830 | + | 0.0910201i | −0.0305491 | + | 0.00569990i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 23.1067i | − | 1.44136i | −0.693269 | − | 0.720679i | \(-0.743830\pi\) | ||
0.693269 | − | 0.720679i | \(-0.256170\pi\) | |||||||
\(258\) | −5.44038 | + | 5.44038i | −0.338703 | + | 0.338703i | ||||
\(259\) | 10.6022 | − | 9.32592i | 0.658789 | − | 0.579484i | ||||
\(260\) | −1.51782 | + | 2.21414i | −0.0941312 | + | 0.137315i | ||||
\(261\) | 5.45356 | + | 5.45356i | 0.337567 | + | 0.337567i | ||||
\(262\) | −10.7012 | − | 10.7012i | −0.661121 | − | 0.661121i | ||||
\(263\) | 8.68658 | − | 8.68658i | 0.535638 | − | 0.535638i | −0.386607 | − | 0.922245i | \(-0.626353\pi\) |
0.922245 | + | 0.386607i | \(0.126353\pi\) | |||||||
\(264\) | 2.95283 | + | 2.95283i | 0.181734 | + | 0.181734i | ||||
\(265\) | −13.8620 | + | 2.58639i | −0.851535 | + | 0.158881i | ||||
\(266\) | −12.2750 | −0.752626 | ||||||||
\(267\) | 6.05673i | 0.370666i | ||||||||
\(268\) | 10.3479 | + | 10.3479i | 0.632100 | + | 0.632100i | ||||
\(269\) | 30.1717i | 1.83960i | 0.392388 | + | 0.919800i | \(0.371649\pi\) | ||||
−0.392388 | + | 0.919800i | \(0.628351\pi\) | |||||||
\(270\) | 2.19813 | − | 0.410132i | 0.133774 | − | 0.0249598i | ||||
\(271\) | −7.28060 | −0.442265 | −0.221133 | − | 0.975244i | \(-0.570975\pi\) | ||||
−0.221133 | + | 0.975244i | \(0.570975\pi\) | |||||||
\(272\) | 0.221929i | 0.0134564i | ||||||||
\(273\) | − | 2.78681i | − | 0.168665i | ||||||
\(274\) | −4.35277 | + | 4.35277i | −0.262960 | + | 0.262960i | ||||
\(275\) | −19.4748 | + | 7.52940i | −1.17437 | + | 0.454040i | ||||
\(276\) | 3.00262 | − | 3.00262i | 0.180737 | − | 0.180737i | ||||
\(277\) | 20.3131 | 1.22050 | 0.610249 | − | 0.792210i | \(-0.291069\pi\) | ||||
0.610249 | + | 0.792210i | \(0.291069\pi\) | |||||||
\(278\) | 18.3422 | 1.10009 | ||||||||
\(279\) | 1.77644 | − | 1.77644i | 0.106353 | − | 0.106353i | ||||
\(280\) | −0.952057 | − | 5.10263i | −0.0568963 | − | 0.304940i | ||||
\(281\) | −5.88467 | + | 5.88467i | −0.351050 | + | 0.351050i | −0.860500 | − | 0.509450i | \(-0.829849\pi\) |
0.509450 | + | 0.860500i | \(0.329849\pi\) | |||||||
\(282\) | 7.96114i | 0.474079i | ||||||||
\(283\) | 3.93264i | 0.233771i | 0.993145 | + | 0.116886i | \(0.0372911\pi\) | ||||
−0.993145 | + | 0.116886i | \(0.962709\pi\) | |||||||
\(284\) | 9.11658 | 0.540969 | ||||||||
\(285\) | 6.68549 | − | 9.75253i | 0.396014 | − | 0.577690i | ||||
\(286\) | 5.01326i | 0.296440i | ||||||||
\(287\) | −4.23841 | − | 4.23841i | −0.250185 | − | 0.250185i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 16.9507 | 0.997103 | ||||||||
\(290\) | 3.16314 | + | 16.9531i | 0.185746 | + | 0.995521i | ||||
\(291\) | −6.07425 | − | 6.07425i | −0.356079 | − | 0.356079i | ||||
\(292\) | −3.76725 | + | 3.76725i | −0.220461 | + | 0.220461i | ||||
\(293\) | −3.68251 | − | 3.68251i | −0.215135 | − | 0.215135i | 0.591310 | − | 0.806444i | \(-0.298611\pi\) |
−0.806444 | + | 0.591310i | \(0.798611\pi\) | |||||||
\(294\) | −1.13940 | − | 1.13940i | −0.0664514 | − | 0.0664514i | ||||
\(295\) | 12.1506 | − | 2.26709i | 0.707437 | − | 0.131995i | ||||
\(296\) | 6.07033 | + | 0.388773i | 0.352831 | + | 0.0225970i | ||||
\(297\) | 2.95283 | − | 2.95283i | 0.171340 | − | 0.171340i | ||||
\(298\) | 9.29218i | 0.538281i | ||||||||
\(299\) | 5.09780 | 0.294814 | ||||||||
\(300\) | 4.57260 | + | 2.02270i | 0.263999 | + | 0.116781i | ||||
\(301\) | 12.6290 | − | 12.6290i | 0.727923 | − | 0.727923i | ||||
\(302\) | 10.0875i | 0.580471i | ||||||||
\(303\) | −6.87849 | − | 6.87849i | −0.395159 | − | 0.395159i | ||||
\(304\) | −3.73909 | − | 3.73909i | −0.214451 | − | 0.214451i | ||||
\(305\) | 2.80246 | − | 0.522889i | 0.160469 | − | 0.0299405i | ||||
\(306\) | 0.221929 | 0.0126868 | ||||||||
\(307\) | −16.3345 | − | 16.3345i | −0.932257 | − | 0.932257i | 0.0655896 | − | 0.997847i | \(-0.479107\pi\) |
−0.997847 | + | 0.0655896i | \(0.979107\pi\) | |||||||
\(308\) | −6.85453 | − | 6.85453i | −0.390573 | − | 0.390573i | ||||
\(309\) | 11.0921 | + | 11.0921i | 0.631008 | + | 0.631008i | ||||
\(310\) | 5.52229 | − | 1.03036i | 0.313645 | − | 0.0585204i | ||||
\(311\) | −0.811220 | − | 0.811220i | −0.0460001 | − | 0.0460001i | 0.683733 | − | 0.729733i | \(-0.260355\pi\) |
−0.729733 | + | 0.683733i | \(0.760355\pi\) | |||||||
\(312\) | 0.848892 | − | 0.848892i | 0.0480590 | − | 0.0480590i | ||||
\(313\) | −3.61149 | −0.204133 | −0.102067 | − | 0.994778i | \(-0.532546\pi\) | ||||
−0.102067 | + | 0.994778i | \(0.532546\pi\) | |||||||
\(314\) | −15.8215 | + | 15.8215i | −0.892857 | + | 0.892857i | ||||
\(315\) | −5.10263 | + | 0.952057i | −0.287500 | + | 0.0536423i | ||||
\(316\) | 0.571724 | + | 0.571724i | 0.0321620 | + | 0.0321620i | ||||
\(317\) | 9.01704 | + | 9.01704i | 0.506447 | + | 0.506447i | 0.913434 | − | 0.406987i | \(-0.133420\pi\) |
−0.406987 | + | 0.913434i | \(0.633420\pi\) | |||||||
\(318\) | 6.30625 | 0.353637 | ||||||||
\(319\) | 22.7737 | + | 22.7737i | 1.27508 | + | 1.27508i | ||||
\(320\) | 1.26431 | − | 1.84432i | 0.0706770 | − | 0.103101i | ||||
\(321\) | 2.25685i | 0.125965i | ||||||||
\(322\) | −6.97012 | + | 6.97012i | −0.388430 | + | 0.388430i | ||||
\(323\) | 0.829811 | − | 0.829811i | 0.0461719 | − | 0.0461719i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 2.16459 | + | 5.59870i | 0.120070 | + | 0.310560i | ||||
\(326\) | 18.7947i | 1.04094i | ||||||||
\(327\) | −8.98462 | −0.496851 | ||||||||
\(328\) | − | 2.58213i | − | 0.142574i | ||||||
\(329\) | − | 18.4806i | − | 1.01887i | ||||||
\(330\) | 9.17925 | − | 1.71268i | 0.505301 | − | 0.0942799i | ||||
\(331\) | 2.86838 | − | 2.86838i | 0.157660 | − | 0.157660i | −0.623869 | − | 0.781529i | \(-0.714440\pi\) |
0.781529 | + | 0.623869i | \(0.214440\pi\) | |||||||
\(332\) | 7.69554 | + | 7.69554i | 0.422347 | + | 0.422347i | ||||
\(333\) | 0.388773 | − | 6.07033i | 0.0213046 | − | 0.332652i | ||||
\(334\) | − | 14.4189i | − | 0.788966i | ||||||
\(335\) | 32.1679 | − | 6.00194i | 1.75752 | − | 0.327921i | ||||
\(336\) | 2.32134i | 0.126640i | ||||||||
\(337\) | 2.56826 | + | 2.56826i | 0.139902 | + | 0.139902i | 0.773589 | − | 0.633687i | \(-0.218459\pi\) |
−0.633687 | + | 0.773589i | \(0.718459\pi\) | |||||||
\(338\) | −11.5588 | −0.628714 | ||||||||
\(339\) | 8.31048 | + | 8.31048i | 0.451363 | + | 0.451363i | ||||
\(340\) | 0.409308 | + | 0.280587i | 0.0221979 | + | 0.0152169i | ||||
\(341\) | 7.41827 | − | 7.41827i | 0.401722 | − | 0.401722i | ||||
\(342\) | −3.73909 | + | 3.73909i | −0.202187 | + | 0.202187i | ||||
\(343\) | 14.1350 | + | 14.1350i | 0.763219 | + | 0.763219i | ||||
\(344\) | 7.69386 | 0.414825 | ||||||||
\(345\) | −1.74156 | − | 9.33405i | −0.0937626 | − | 0.502528i | ||||
\(346\) | 13.9023 | − | 13.9023i | 0.747391 | − | 0.747391i | ||||
\(347\) | −6.67064 | −0.358099 | −0.179049 | − | 0.983840i | \(-0.557302\pi\) | ||||
−0.179049 | + | 0.983840i | \(0.557302\pi\) | |||||||
\(348\) | − | 7.71250i | − | 0.413433i | ||||||
\(349\) | − | 15.3388i | − | 0.821066i | −0.911846 | − | 0.410533i | \(-0.865343\pi\) | ||
0.911846 | − | 0.410533i | \(-0.134657\pi\) | |||||||
\(350\) | −10.6146 | − | 4.69539i | −0.567373 | − | 0.250979i | ||||
\(351\) | −0.848892 | − | 0.848892i | −0.0453105 | − | 0.0453105i | ||||
\(352\) | − | 4.17593i | − | 0.222578i | ||||||
\(353\) | − | 29.7766i | − | 1.58485i | −0.609971 | − | 0.792423i | \(-0.708819\pi\) | ||
0.609971 | − | 0.792423i | \(-0.291181\pi\) | |||||||
\(354\) | −5.52770 | −0.293794 | ||||||||
\(355\) | 11.5262 | − | 16.8139i | 0.611745 | − | 0.892389i | ||||
\(356\) | 4.28275 | − | 4.28275i | 0.226985 | − | 0.226985i | ||||
\(357\) | −0.515174 | −0.0272659 | ||||||||
\(358\) | −11.4245 | + | 11.4245i | −0.603803 | + | 0.603803i | ||||
\(359\) | − | 13.0032i | − | 0.686284i | −0.939284 | − | 0.343142i | \(-0.888509\pi\) | ||
0.939284 | − | 0.343142i | \(-0.111491\pi\) | |||||||
\(360\) | −1.84432 | − | 1.26431i | −0.0972043 | − | 0.0666349i | ||||
\(361\) | 8.96152i | 0.471659i | ||||||||
\(362\) | −18.4010 | −0.967136 | ||||||||
\(363\) | 4.55261 | − | 4.55261i | 0.238950 | − | 0.238950i | ||||
\(364\) | −1.97057 | + | 1.97057i | −0.103286 | + | 0.103286i | ||||
\(365\) | 2.18506 | + | 11.7110i | 0.114371 | + | 0.612981i | ||||
\(366\) | −1.27493 | −0.0666416 | ||||||||
\(367\) | −11.3147 | + | 11.3147i | −0.590624 | + | 0.590624i | −0.937800 | − | 0.347176i | \(-0.887141\pi\) |
0.347176 | + | 0.937800i | \(0.387141\pi\) | |||||||
\(368\) | −4.24635 | −0.221356 | ||||||||
\(369\) | −2.58213 | −0.134420 | ||||||||
\(370\) | 8.39179 | − | 10.7041i | 0.436268 | − | 0.556480i | ||||
\(371\) | −14.6390 | −0.760018 | ||||||||
\(372\) | −2.51226 | −0.130255 | ||||||||
\(373\) | 15.2041 | − | 15.2041i | 0.787238 | − | 0.787238i | −0.193803 | − | 0.981041i | \(-0.562082\pi\) |
0.981041 | + | 0.193803i | \(0.0620821\pi\) | |||||||
\(374\) | 0.926759 | 0.0479216 | ||||||||
\(375\) | 9.51169 | − | 5.87603i | 0.491182 | − | 0.303437i | ||||
\(376\) | 5.62938 | − | 5.62938i | 0.290313 | − | 0.290313i | ||||
\(377\) | 6.54708 | − | 6.54708i | 0.337192 | − | 0.337192i | ||||
\(378\) | 2.32134 | 0.119397 | ||||||||
\(379\) | 1.94256i | 0.0997828i | 0.998755 | + | 0.0498914i | \(0.0158875\pi\) | ||||
−0.998755 | + | 0.0498914i | \(0.984112\pi\) | |||||||
\(380\) | −11.6234 | + | 2.16872i | −0.596270 | + | 0.111253i | ||||
\(381\) | 12.9937i | 0.665685i | ||||||||
\(382\) | −3.52951 | + | 3.52951i | −0.180585 | + | 0.180585i | ||||
\(383\) | −14.7331 | −0.752827 | −0.376413 | − | 0.926452i | \(-0.622843\pi\) | ||||
−0.376413 | + | 0.926452i | \(0.622843\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −21.3082 | + | 3.97572i | −1.08597 | + | 0.202621i | ||||
\(386\) | 9.24953 | 0.470789 | ||||||||
\(387\) | − | 7.69386i | − | 0.391101i | ||||||
\(388\) | 8.59029i | 0.436106i | ||||||||
\(389\) | −11.3037 | − | 11.3037i | −0.573121 | − | 0.573121i | 0.359879 | − | 0.932999i | \(-0.382818\pi\) |
−0.932999 | + | 0.359879i | \(0.882818\pi\) | |||||||
\(390\) | −0.492369 | − | 2.63889i | −0.0249321 | − | 0.133625i | ||||
\(391\) | − | 0.942388i | − | 0.0476586i | ||||||
\(392\) | 1.61136i | 0.0813860i | ||||||||
\(393\) | 15.1337 | 0.763396 | ||||||||
\(394\) | −1.75235 | + | 1.75235i | −0.0882823 | + | 0.0882823i | ||||
\(395\) | 1.77728 | − | 0.331608i | 0.0894245 | − | 0.0166850i | ||||
\(396\) | −4.17593 | −0.209848 | ||||||||
\(397\) | 5.54983 | + | 5.54983i | 0.278538 | + | 0.278538i | 0.832525 | − | 0.553987i | \(-0.186894\pi\) |
−0.553987 | + | 0.832525i | \(0.686894\pi\) | |||||||
\(398\) | −1.94022 | + | 1.94022i | −0.0972542 | + | 0.0972542i | ||||
\(399\) | 8.67970 | − | 8.67970i | 0.434529 | − | 0.434529i | ||||
\(400\) | −1.80305 | − | 4.66358i | −0.0901524 | − | 0.233179i | ||||
\(401\) | 10.5726 | + | 10.5726i | 0.527970 | + | 0.527970i | 0.919967 | − | 0.391996i | \(-0.128215\pi\) |
−0.391996 | + | 0.919967i | \(0.628215\pi\) | |||||||
\(402\) | −14.6342 | −0.729886 | ||||||||
\(403\) | −2.13264 | − | 2.13264i | −0.106234 | − | 0.106234i | ||||
\(404\) | 9.72766i | 0.483969i | ||||||||
\(405\) | −1.26431 | + | 1.84432i | −0.0628240 | + | 0.0916451i | ||||
\(406\) | 17.9034i | 0.888529i | ||||||||
\(407\) | 1.62349 | − | 25.3492i | 0.0804732 | − | 1.25651i | ||||
\(408\) | −0.156927 | − | 0.156927i | −0.00776907 | − | 0.00776907i | ||||
\(409\) | 25.5820 | − | 25.5820i | 1.26495 | − | 1.26495i | 0.316284 | − | 0.948665i | \(-0.397565\pi\) |
0.948665 | − | 0.316284i | \(-0.102435\pi\) | |||||||
\(410\) | −4.76228 | − | 3.26461i | −0.235192 | − | 0.161228i | ||||
\(411\) | − | 6.15574i | − | 0.303640i | ||||||
\(412\) | − | 15.6866i | − | 0.772824i | ||||||
\(413\) | 12.8317 | 0.631407 | ||||||||
\(414\) | 4.24635i | 0.208697i | ||||||||
\(415\) | 23.9226 | − | 4.46352i | 1.17431 | − | 0.219105i | ||||
\(416\) | −1.20051 | −0.0588601 | ||||||||
\(417\) | −12.9699 | + | 12.9699i | −0.635139 | + | 0.635139i | ||||
\(418\) | −15.6141 | + | 15.6141i | −0.763713 | + | 0.763713i | ||||
\(419\) | 3.51437i | 0.171688i | 0.996309 | + | 0.0858441i | \(0.0273587\pi\) | ||||
−0.996309 | + | 0.0858441i | \(0.972641\pi\) | |||||||
\(420\) | 4.28131 | + | 2.93490i | 0.208906 | + | 0.143208i | ||||
\(421\) | −0.351376 | − | 0.351376i | −0.0171250 | − | 0.0171250i | 0.698492 | − | 0.715617i | \(-0.253855\pi\) |
−0.715617 | + | 0.698492i | \(0.753855\pi\) | |||||||
\(422\) | −4.88849 | −0.237968 | ||||||||
\(423\) | −5.62938 | − | 5.62938i | −0.273710 | − | 0.273710i | ||||
\(424\) | −4.45920 | − | 4.45920i | −0.216558 | − | 0.216558i | ||||
\(425\) | 1.03498 | − | 0.400149i | 0.0502041 | − | 0.0194101i | ||||
\(426\) | −6.44639 | + | 6.44639i | −0.312329 | + | 0.312329i | ||||
\(427\) | 2.95955 | 0.143223 | ||||||||
\(428\) | 1.59584 | − | 1.59584i | 0.0771377 | − | 0.0771377i | ||||
\(429\) | −3.54491 | − | 3.54491i | −0.171150 | − | 0.171150i | ||||
\(430\) | 9.72741 | − | 14.1899i | 0.469097 | − | 0.684300i | ||||
\(431\) | −11.7580 | − | 11.7580i | −0.566362 | − | 0.566362i | 0.364745 | − | 0.931107i | \(-0.381156\pi\) |
−0.931107 | + | 0.364745i | \(0.881156\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 12.6439 | + | 12.6439i | 0.607628 | + | 0.607628i | 0.942326 | − | 0.334697i | \(-0.108634\pi\) |
−0.334697 | + | 0.942326i | \(0.608634\pi\) | |||||||
\(434\) | 5.83183 | 0.279937 | ||||||||
\(435\) | −14.2243 | − | 9.75098i | −0.682005 | − | 0.467524i | ||||
\(436\) | 6.35309 | + | 6.35309i | 0.304258 | + | 0.304258i | ||||
\(437\) | 15.8775 | + | 15.8775i | 0.759522 | + | 0.759522i | ||||
\(438\) | − | 5.32769i | − | 0.254567i | ||||||
\(439\) | −2.75100 | + | 2.75100i | −0.131298 | + | 0.131298i | −0.769702 | − | 0.638404i | \(-0.779595\pi\) |
0.638404 | + | 0.769702i | \(0.279595\pi\) | |||||||
\(440\) | −7.70175 | − | 5.27966i | −0.367167 | − | 0.251698i | ||||
\(441\) | 1.61136 | 0.0767314 | ||||||||
\(442\) | − | 0.266429i | − | 0.0126727i | ||||||
\(443\) | 8.68051 | − | 8.68051i | 0.412423 | − | 0.412423i | −0.470158 | − | 0.882582i | \(-0.655803\pi\) |
0.882582 | + | 0.470158i | \(0.155803\pi\) | |||||||
\(444\) | −4.56727 | + | 4.01746i | −0.216753 | + | 0.190660i | ||||
\(445\) | −2.48406 | − | 13.3135i | −0.117756 | − | 0.631120i | ||||
\(446\) | 16.9445 | + | 16.9445i | 0.802345 | + | 0.802345i | ||||
\(447\) | −6.57056 | − | 6.57056i | −0.310777 | − | 0.310777i | ||||
\(448\) | 1.64144 | − | 1.64144i | 0.0775507 | − | 0.0775507i | ||||
\(449\) | 11.3699 | + | 11.3699i | 0.536577 | + | 0.536577i | 0.922522 | − | 0.385945i | \(-0.126124\pi\) |
−0.385945 | + | 0.922522i | \(0.626124\pi\) | |||||||
\(450\) | −4.66358 | + | 1.80305i | −0.219843 | + | 0.0849965i | ||||
\(451\) | −10.7828 | −0.507742 | ||||||||
\(452\) | − | 11.7528i | − | 0.552805i | ||||||
\(453\) | −7.13295 | − | 7.13295i | −0.335135 | − | 0.335135i | ||||
\(454\) | − | 22.8426i | − | 1.07206i | ||||||
\(455\) | 1.14296 | + | 6.12578i | 0.0535827 | + | 0.287181i | ||||
\(456\) | 5.28787 | 0.247627 | ||||||||
\(457\) | 19.6985i | 0.921456i | 0.887541 | + | 0.460728i | \(0.152412\pi\) | ||||
−0.887541 | + | 0.460728i | \(0.847588\pi\) | |||||||
\(458\) | 16.1156i | 0.753032i | ||||||||
\(459\) | −0.156927 | + | 0.156927i | −0.00732475 | + | 0.00732475i | ||||
\(460\) | −5.36870 | + | 7.83164i | −0.250317 | + | 0.365152i | ||||
\(461\) | −19.2408 | + | 19.2408i | −0.896135 | + | 0.896135i | −0.995092 | − | 0.0989566i | \(-0.968449\pi\) |
0.0989566 | + | 0.995092i | \(0.468449\pi\) | |||||||
\(462\) | 9.69376 | 0.450995 | ||||||||
\(463\) | 1.97887 | 0.0919658 | 0.0459829 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459829 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(464\) | −5.45356 | + | 5.45356i | −0.253175 | + | 0.253175i | ||||
\(465\) | −3.17627 | + | 4.63342i | −0.147296 | + | 0.214870i | ||||
\(466\) | −3.66171 | + | 3.66171i | −0.169625 | + | 0.169625i | ||||
\(467\) | 24.0229i | 1.11165i | 0.831300 | + | 0.555824i | \(0.187597\pi\) | ||||
−0.831300 | + | 0.555824i | \(0.812403\pi\) | |||||||
\(468\) | 1.20051i | 0.0554938i | ||||||||
\(469\) | 33.9710 | 1.56863 | ||||||||
\(470\) | −3.26512 | − | 17.4997i | −0.150609 | − | 0.807199i | ||||
\(471\) | − | 22.3749i | − | 1.03098i | ||||||
\(472\) | 3.90868 | + | 3.90868i | 0.179911 | + | 0.179911i | ||||
\(473\) | − | 32.1290i | − | 1.47729i | ||||||
\(474\) | −0.808539 | −0.0371374 | ||||||||
\(475\) | −10.6958 | + | 24.1793i | −0.490756 | + | 1.10942i | ||||
\(476\) | 0.364283 | + | 0.364283i | 0.0166969 | + | 0.0166969i | ||||
\(477\) | −4.45920 | + | 4.45920i | −0.204173 | + | 0.204173i | ||||
\(478\) | −2.75228 | − | 2.75228i | −0.125886 | − | 0.125886i | ||||
\(479\) | 2.92694 | + | 2.92694i | 0.133735 | + | 0.133735i | 0.770806 | − | 0.637070i | \(-0.219854\pi\) |
−0.637070 | + | 0.770806i | \(0.719854\pi\) | |||||||
\(480\) | 0.410132 | + | 2.19813i | 0.0187199 | + | 0.100331i | ||||
\(481\) | −7.28751 | − | 0.466727i | −0.332282 | − | 0.0212809i | ||||
\(482\) | −19.9398 | + | 19.9398i | −0.908233 | + | 0.908233i | ||||
\(483\) | − | 9.85724i | − | 0.448520i | ||||||
\(484\) | −6.43836 | −0.292653 | ||||||||
\(485\) | 15.8433 | + | 10.8608i | 0.719406 | + | 0.493163i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | − | 20.3915i | − | 0.924029i | −0.886872 | − | 0.462014i | \(-0.847127\pi\) | ||
0.886872 | − | 0.462014i | \(-0.152873\pi\) | |||||||
\(488\) | 0.901511 | + | 0.901511i | 0.0408095 | + | 0.0408095i | ||||
\(489\) | −13.2899 | − | 13.2899i | −0.600989 | − | 0.600989i | ||||
\(490\) | 2.97187 | + | 2.03726i | 0.134255 | + | 0.0920338i | ||||
\(491\) | 19.2062 | 0.866762 | 0.433381 | − | 0.901211i | \(-0.357320\pi\) | ||||
0.433381 | + | 0.901211i | \(0.357320\pi\) | |||||||
\(492\) | 1.82584 | + | 1.82584i | 0.0823153 | + | 0.0823153i | ||||
\(493\) | −1.21030 | − | 1.21030i | −0.0545093 | − | 0.0545093i | ||||
\(494\) | 4.48883 | + | 4.48883i | 0.201962 | + | 0.201962i | ||||
\(495\) | −5.27966 | + | 7.70175i | −0.237303 | + | 0.346168i | ||||
\(496\) | 1.77644 | + | 1.77644i | 0.0797644 | + | 0.0797644i | ||||
\(497\) | 14.9643 | − | 14.9643i | 0.671240 | − | 0.671240i | ||||
\(498\) | −10.8831 | −0.487685 | ||||||||
\(499\) | 3.71349 | − | 3.71349i | 0.166238 | − | 0.166238i | −0.619085 | − | 0.785324i | \(-0.712496\pi\) |
0.785324 | + | 0.619085i | \(0.212496\pi\) | |||||||
\(500\) | −10.8808 | − | 2.57081i | −0.486602 | − | 0.114970i | ||||
\(501\) | 10.1957 | + | 10.1957i | 0.455510 | + | 0.455510i | ||||
\(502\) | −12.4982 | − | 12.4982i | −0.557823 | − | 0.557823i | ||||
\(503\) | −16.4264 | −0.732415 | −0.366207 | − | 0.930533i | \(-0.619344\pi\) | ||||
−0.366207 | + | 0.930533i | \(0.619344\pi\) | |||||||
\(504\) | −1.64144 | − | 1.64144i | −0.0731155 | − | 0.0731155i | ||||
\(505\) | 17.9409 | + | 12.2988i | 0.798361 | + | 0.547288i | ||||
\(506\) | 17.7324i | 0.788303i | ||||||||
\(507\) | 8.17328 | − | 8.17328i | 0.362988 | − | 0.362988i | ||||
\(508\) | 9.18790 | − | 9.18790i | 0.407647 | − | 0.407647i | ||||
\(509\) | −37.6361 | −1.66819 | −0.834096 | − | 0.551619i | \(-0.814010\pi\) | ||||
−0.834096 | + | 0.551619i | \(0.814010\pi\) | |||||||
\(510\) | −0.487830 | + | 0.0910201i | −0.0216015 | + | 0.00403044i | ||||
\(511\) | 12.3674i | 0.547102i | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 5.28787i | − | 0.233465i | ||||||
\(514\) | − | 23.1067i | − | 1.01919i | ||||||
\(515\) | −28.9312 | − | 19.8327i | −1.27486 | − | 0.873934i | ||||
\(516\) | −5.44038 | + | 5.44038i | −0.239499 | + | 0.239499i | ||||
\(517\) | −23.5079 | − | 23.5079i | −1.03387 | − | 1.03387i | ||||
\(518\) | 10.6022 | − | 9.32592i | 0.465834 | − | 0.409757i | ||||
\(519\) | 19.6608i | 0.863012i | ||||||||
\(520\) | −1.51782 | + | 2.21414i | −0.0665608 | + | 0.0970963i | ||||
\(521\) | 4.55515i | 0.199565i | 0.995009 | + | 0.0997823i | \(0.0318146\pi\) | ||||
−0.995009 | + | 0.0997823i | \(0.968185\pi\) | |||||||
\(522\) | 5.45356 | + | 5.45356i | 0.238696 | + | 0.238696i | ||||
\(523\) | −25.6939 | −1.12352 | −0.561759 | − | 0.827301i | \(-0.689875\pi\) | ||||
−0.561759 | + | 0.827301i | \(0.689875\pi\) | |||||||
\(524\) | −10.7012 | − | 10.7012i | −0.467483 | − | 0.467483i | ||||
\(525\) | 10.8258 | − | 4.18550i | 0.472476 | − | 0.182670i | ||||
\(526\) | 8.68658 | − | 8.68658i | 0.378753 | − | 0.378753i | ||||
\(527\) | −0.394243 | + | 0.394243i | −0.0171735 | + | 0.0171735i | ||||
\(528\) | 2.95283 | + | 2.95283i | 0.128505 | + | 0.128505i | ||||
\(529\) | −4.96851 | −0.216022 | ||||||||
\(530\) | −13.8620 | + | 2.58639i | −0.602126 | + | 0.112346i | ||||
\(531\) | 3.90868 | − | 3.90868i | 0.169622 | − | 0.169622i | ||||
\(532\) | −12.2750 | −0.532187 | ||||||||
\(533\) | 3.09989i | 0.134271i | ||||||||
\(534\) | 6.05673i | 0.262100i | ||||||||
\(535\) | −0.925607 | − | 4.96087i | −0.0400175 | − | 0.214477i | ||||
\(536\) | 10.3479 | + | 10.3479i | 0.446962 | + | 0.446962i | ||||
\(537\) | − | 16.1567i | − | 0.697212i | ||||||
\(538\) | 30.1717i | 1.30079i | ||||||||
\(539\) | 6.72892 | 0.289835 | ||||||||
\(540\) | 2.19813 | − | 0.410132i | 0.0945926 | − | 0.0176493i | ||||
\(541\) | −5.59059 | + | 5.59059i | −0.240358 | + | 0.240358i | −0.816998 | − | 0.576640i | \(-0.804363\pi\) |
0.576640 | + | 0.816998i | \(0.304363\pi\) | |||||||
\(542\) | −7.28060 | −0.312729 | ||||||||
\(543\) | 13.0115 | − | 13.0115i | 0.558376 | − | 0.558376i | ||||
\(544\) | 0.221929i | 0.00951513i | ||||||||
\(545\) | 19.7494 | − | 3.68488i | 0.845972 | − | 0.157843i | ||||
\(546\) | − | 2.78681i | − | 0.119264i | ||||||
\(547\) | 24.5372 | 1.04913 | 0.524567 | − | 0.851369i | \(-0.324227\pi\) | ||||
0.524567 | + | 0.851369i | \(0.324227\pi\) | |||||||
\(548\) | −4.35277 | + | 4.35277i | −0.185941 | + | 0.185941i | ||||
\(549\) | 0.901511 | − | 0.901511i | 0.0384755 | − | 0.0384755i | ||||
\(550\) | −19.4748 | + | 7.52940i | −0.830408 | + | 0.321055i | ||||
\(551\) | 40.7827 | 1.73740 | ||||||||
\(552\) | 3.00262 | − | 3.00262i | 0.127800 | − | 0.127800i | ||||
\(553\) | 1.87690 | 0.0798138 | ||||||||
\(554\) | 20.3131 | 0.863022 | ||||||||
\(555\) | 1.63506 | + | 13.5028i | 0.0694044 | + | 0.573163i | ||||
\(556\) | 18.3422 | 0.777883 | ||||||||
\(557\) | −11.2422 | −0.476345 | −0.238173 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238173 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(558\) | 1.77644 | − | 1.77644i | 0.0752026 | − | 0.0752026i | ||||
\(559\) | −9.23659 | −0.390666 | ||||||||
\(560\) | −0.952057 | − | 5.10263i | −0.0402317 | − | 0.215625i | ||||
\(561\) | −0.655318 | + | 0.655318i | −0.0276675 | + | 0.0276675i | ||||
\(562\) | −5.88467 | + | 5.88467i | −0.248230 | + | 0.248230i | ||||
\(563\) | −27.5300 | −1.16025 | −0.580125 | − | 0.814528i | \(-0.696996\pi\) | ||||
−0.580125 | + | 0.814528i | \(0.696996\pi\) | |||||||
\(564\) | 7.96114i | 0.335225i | ||||||||
\(565\) | −21.6759 | − | 14.8592i | −0.911913 | − | 0.625129i | ||||
\(566\) | 3.93264i | 0.165301i | ||||||||
\(567\) | −1.64144 | + | 1.64144i | −0.0689339 | + | 0.0689339i | ||||
\(568\) | 9.11658 | 0.382523 | ||||||||
\(569\) | 2.67462 | − | 2.67462i | 0.112126 | − | 0.112126i | −0.648818 | − | 0.760944i | \(-0.724736\pi\) |
0.760944 | + | 0.648818i | \(0.224736\pi\) | |||||||
\(570\) | 6.68549 | − | 9.75253i | 0.280024 | − | 0.408488i | ||||
\(571\) | −39.5492 | −1.65508 | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(572\) | 5.01326i | 0.209615i | ||||||||
\(573\) | − | 4.99148i | − | 0.208522i | ||||||
\(574\) | −4.23841 | − | 4.23841i | −0.176908 | − | 0.176908i | ||||
\(575\) | 7.65637 | + | 19.8032i | 0.319293 | + | 0.825851i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 22.0030i | − | 0.915996i | −0.888953 | − | 0.457998i | \(-0.848567\pi\) | ||
0.888953 | − | 0.457998i | \(-0.151433\pi\) | |||||||
\(578\) | 16.9507 | 0.705058 | ||||||||
\(579\) | −6.54040 | + | 6.54040i | −0.271810 | + | 0.271810i | ||||
\(580\) | 3.16314 | + | 16.9531i | 0.131342 | + | 0.703940i | ||||
\(581\) | 25.2635 | 1.04811 | ||||||||
\(582\) | −6.07425 | − | 6.07425i | −0.251786 | − | 0.251786i | ||||
\(583\) | −18.6213 | + | 18.6213i | −0.771214 | + | 0.771214i | ||||
\(584\) | −3.76725 | + | 3.76725i | −0.155890 | + | 0.155890i | ||||
\(585\) | 2.21414 | + | 1.51782i | 0.0915432 | + | 0.0627542i | ||||
\(586\) | −3.68251 | − | 3.68251i | −0.152123 | − | 0.152123i | ||||
\(587\) | 20.8362 | 0.860000 | 0.430000 | − | 0.902829i | \(-0.358514\pi\) | ||||
0.430000 | + | 0.902829i | \(0.358514\pi\) | |||||||
\(588\) | −1.13940 | − | 1.13940i | −0.0469882 | − | 0.0469882i | ||||
\(589\) | − | 13.2845i | − | 0.547379i | ||||||
\(590\) | 12.1506 | − | 2.26709i | 0.500233 | − | 0.0933344i | ||||
\(591\) | − | 2.47820i | − | 0.101940i | ||||||
\(592\) | 6.07033 | + | 0.388773i | 0.249489 | + | 0.0159785i | ||||
\(593\) | −4.26861 | − | 4.26861i | −0.175291 | − | 0.175291i | 0.614009 | − | 0.789299i | \(-0.289556\pi\) |
−0.789299 | + | 0.614009i | \(0.789556\pi\) | |||||||
\(594\) | 2.95283 | − | 2.95283i | 0.121156 | − | 0.121156i | ||||
\(595\) | 1.13242 | − | 0.211289i | 0.0464247 | − | 0.00866200i | ||||
\(596\) | 9.29218i | 0.380622i | ||||||||
\(597\) | − | 2.74388i | − | 0.112300i | ||||||
\(598\) | 5.09780 | 0.208465 | ||||||||
\(599\) | − | 12.4209i | − | 0.507503i | −0.967269 | − | 0.253752i | \(-0.918335\pi\) | ||
0.967269 | − | 0.253752i | \(-0.0816646\pi\) | |||||||
\(600\) | 4.57260 | + | 2.02270i | 0.186676 | + | 0.0825765i | ||||
\(601\) | −26.7404 | −1.09076 | −0.545382 | − | 0.838187i | \(-0.683615\pi\) | ||||
−0.545382 | + | 0.838187i | \(0.683615\pi\) | |||||||
\(602\) | 12.6290 | − | 12.6290i | 0.514719 | − | 0.514719i | ||||
\(603\) | 10.3479 | − | 10.3479i | 0.421400 | − | 0.421400i | ||||
\(604\) | 10.0875i | 0.410455i | ||||||||
\(605\) | −8.14008 | + | 11.8744i | −0.330941 | + | 0.482764i | ||||
\(606\) | −6.87849 | − | 6.87849i | −0.279420 | − | 0.279420i | ||||
\(607\) | 21.5222 | 0.873559 | 0.436780 | − | 0.899569i | \(-0.356119\pi\) | ||||
0.436780 | + | 0.899569i | \(0.356119\pi\) | |||||||
\(608\) | −3.73909 | − | 3.73909i | −0.151640 | − | 0.151640i | ||||
\(609\) | −12.6596 | − | 12.6596i | −0.512993 | − | 0.512993i | ||||
\(610\) | 2.80246 | − | 0.522889i | 0.113468 | − | 0.0211711i | ||||
\(611\) | −6.75815 | + | 6.75815i | −0.273405 | + | 0.273405i | ||||
\(612\) | 0.221929 | 0.00897095 | ||||||||
\(613\) | 12.0786 | − | 12.0786i | 0.487851 | − | 0.487851i | −0.419777 | − | 0.907627i | \(-0.637892\pi\) |
0.907627 | + | 0.419777i | \(0.137892\pi\) | |||||||
\(614\) | −16.3345 | − | 16.3345i | −0.659205 | − | 0.659205i | ||||
\(615\) | 5.67587 | − | 1.05901i | 0.228873 | − | 0.0427035i | ||||
\(616\) | −6.85453 | − | 6.85453i | −0.276177 | − | 0.276177i | ||||
\(617\) | 19.9970 | + | 19.9970i | 0.805049 | + | 0.805049i | 0.983880 | − | 0.178831i | \(-0.0572315\pi\) |
−0.178831 | + | 0.983880i | \(0.557231\pi\) | |||||||
\(618\) | 11.0921 | + | 11.0921i | 0.446190 | + | 0.446190i | ||||
\(619\) | −43.2741 | −1.73933 | −0.869666 | − | 0.493640i | \(-0.835666\pi\) | ||||
−0.869666 | + | 0.493640i | \(0.835666\pi\) | |||||||
\(620\) | 5.52229 | − | 1.03036i | 0.221780 | − | 0.0413802i | ||||
\(621\) | −3.00262 | − | 3.00262i | −0.120491 | − | 0.120491i | ||||
\(622\) | −0.811220 | − | 0.811220i | −0.0325270 | − | 0.0325270i | ||||
\(623\) | − | 14.0598i | − | 0.563292i | ||||||
\(624\) | 0.848892 | − | 0.848892i | 0.0339829 | − | 0.0339829i | ||||
\(625\) | −18.4980 | + | 16.8173i | −0.739921 | + | 0.672693i | ||||
\(626\) | −3.61149 | −0.144344 | ||||||||
\(627\) | − | 22.0817i | − | 0.881860i | ||||||
\(628\) | −15.8215 | + | 15.8215i | −0.631345 | + | 0.631345i | ||||
\(629\) | −0.0862799 | + | 1.34718i | −0.00344021 | + | 0.0537156i | ||||
\(630\) | −5.10263 | + | 0.952057i | −0.203293 | + | 0.0379309i | ||||
\(631\) | 23.4422 | + | 23.4422i | 0.933219 | + | 0.933219i | 0.997906 | − | 0.0646863i | \(-0.0206047\pi\) |
−0.0646863 | + | 0.997906i | \(0.520605\pi\) | |||||||
\(632\) | 0.571724 | + | 0.571724i | 0.0227419 | + | 0.0227419i | ||||
\(633\) | 3.45668 | − | 3.45668i | 0.137391 | − | 0.137391i | ||||
\(634\) | 9.01704 | + | 9.01704i | 0.358112 | + | 0.358112i | ||||
\(635\) | −5.32911 | − | 28.5618i | −0.211479 | − | 1.13344i | ||||
\(636\) | 6.30625 | 0.250059 | ||||||||
\(637\) | − | 1.93446i | − | 0.0766461i | ||||||
\(638\) | 22.7737 | + | 22.7737i | 0.901618 | + | 0.901618i | ||||
\(639\) | − | 9.11658i | − | 0.360646i | ||||||
\(640\) | 1.26431 | − | 1.84432i | 0.0499762 | − | 0.0729032i | ||||
\(641\) | 12.8649 | 0.508132 | 0.254066 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254066 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(642\) | 2.25685i | 0.0890709i | ||||||||
\(643\) | − | 6.91522i | − | 0.272709i | −0.990660 | − | 0.136355i | \(-0.956461\pi\) | ||
0.990660 | − | 0.136355i | \(-0.0435387\pi\) | |||||||
\(644\) | −6.97012 | + | 6.97012i | −0.274661 | + | 0.274661i | ||||
\(645\) | 3.15549 | + | 16.9121i | 0.124247 | + | 0.665914i | ||||
\(646\) | 0.829811 | − | 0.829811i | 0.0326485 | − | 0.0326485i | ||||
\(647\) | −28.0603 | −1.10317 | −0.551583 | − | 0.834120i | \(-0.685976\pi\) | ||||
−0.551583 | + | 0.834120i | \(0.685976\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 16.3223 | − | 16.3223i | 0.640708 | − | 0.640708i | ||||
\(650\) | 2.16459 | + | 5.59870i | 0.0849020 | + | 0.219599i | ||||
\(651\) | −4.12372 | + | 4.12372i | −0.161621 | + | 0.161621i | ||||
\(652\) | 18.7947i | 0.736058i | ||||||||
\(653\) | 18.1283i | 0.709417i | 0.934977 | + | 0.354708i | \(0.115420\pi\) | ||||
−0.934977 | + | 0.354708i | \(0.884580\pi\) | |||||||
\(654\) | −8.98462 | −0.351327 | ||||||||
\(655\) | −33.2660 | + | 6.20683i | −1.29981 | + | 0.242521i | ||||
\(656\) | − | 2.58213i | − | 0.100815i | ||||||
\(657\) | 3.76725 | + | 3.76725i | 0.146974 | + | 0.146974i | ||||
\(658\) | − | 18.4806i | − | 0.720447i | ||||||
\(659\) | −3.13030 | −0.121939 | −0.0609695 | − | 0.998140i | \(-0.519419\pi\) | ||||
−0.0609695 | + | 0.998140i | \(0.519419\pi\) | |||||||
\(660\) | 9.17925 | − | 1.71268i | 0.357302 | − | 0.0666660i | ||||
\(661\) | −0.420561 | − | 0.420561i | −0.0163579 | − | 0.0163579i | 0.698881 | − | 0.715238i | \(-0.253682\pi\) |
−0.715238 | + | 0.698881i | \(0.753682\pi\) | |||||||
\(662\) | 2.86838 | − | 2.86838i | 0.111483 | − | 0.111483i | ||||
\(663\) | 0.188394 | + | 0.188394i | 0.00731661 | + | 0.00731661i | ||||
\(664\) | 7.69554 | + | 7.69554i | 0.298645 | + | 0.298645i | ||||
\(665\) | −15.5193 | + | 22.6390i | −0.601814 | + | 0.877902i | ||||
\(666\) | 0.388773 | − | 6.07033i | 0.0150646 | − | 0.235220i | ||||
\(667\) | 23.1577 | − | 23.1577i | 0.896671 | − | 0.896671i | ||||
\(668\) | − | 14.4189i | − | 0.557883i | ||||||
\(669\) | −23.9631 | −0.926469 | ||||||||
\(670\) | 32.1679 | − | 6.00194i | 1.24275 | − | 0.231875i | ||||
\(671\) | 3.76464 | − | 3.76464i | 0.145332 | − | 0.145332i | ||||
\(672\) | 2.32134i | 0.0895478i | ||||||||
\(673\) | −11.5151 | − | 11.5151i | −0.443875 | − | 0.443875i | 0.449437 | − | 0.893312i | \(-0.351625\pi\) |
−0.893312 | + | 0.449437i | \(0.851625\pi\) | |||||||
\(674\) | 2.56826 | + | 2.56826i | 0.0989258 | + | 0.0989258i | ||||
\(675\) | 2.02270 | − | 4.57260i | 0.0778539 | − | 0.175999i | ||||
\(676\) | −11.5588 | −0.444568 | ||||||||
\(677\) | 10.6365 | + | 10.6365i | 0.408794 | + | 0.408794i | 0.881318 | − | 0.472524i | \(-0.156657\pi\) |
−0.472524 | + | 0.881318i | \(0.656657\pi\) | |||||||
\(678\) | 8.31048 | + | 8.31048i | 0.319162 | + | 0.319162i | ||||
\(679\) | 14.1004 | + | 14.1004i | 0.541125 | + | 0.541125i | ||||
\(680\) | 0.409308 | + | 0.280587i | 0.0156963 | + | 0.0107600i | ||||
\(681\) | 16.1521 | + | 16.1521i | 0.618952 | + | 0.618952i | ||||
\(682\) | 7.41827 | − | 7.41827i | 0.284060 | − | 0.284060i | ||||
\(683\) | −21.3995 | −0.818828 | −0.409414 | − | 0.912349i | \(-0.634267\pi\) | ||||
−0.409414 | + | 0.912349i | \(0.634267\pi\) | |||||||
\(684\) | −3.73909 | + | 3.73909i | −0.142968 | + | 0.142968i | ||||
\(685\) | 2.52467 | + | 13.5311i | 0.0964625 | + | 0.516999i | ||||
\(686\) | 14.1350 | + | 14.1350i | 0.539677 | + | 0.539677i | ||||
\(687\) | −11.3954 | − | 11.3954i | −0.434763 | − | 0.434763i | ||||
\(688\) | 7.69386 | 0.293325 | ||||||||
\(689\) | 5.35333 | + | 5.35333i | 0.203946 | + | 0.203946i | ||||
\(690\) | −1.74156 | − | 9.33405i | −0.0663002 | − | 0.355341i | ||||
\(691\) | − | 15.8189i | − | 0.601778i | −0.953659 | − | 0.300889i | \(-0.902717\pi\) | ||
0.953659 | − | 0.300889i | \(-0.0972834\pi\) | |||||||
\(692\) | 13.9023 | − | 13.9023i | 0.528485 | − | 0.528485i | ||||
\(693\) | −6.85453 | + | 6.85453i | −0.260382 | + | 0.260382i | ||||
\(694\) | −6.67064 | −0.253214 | ||||||||
\(695\) | 23.1902 | − | 33.8290i | 0.879655 | − | 1.28321i | ||||
\(696\) | − | 7.71250i | − | 0.292342i | ||||||
\(697\) | 0.573050 | 0.0217058 | ||||||||
\(698\) | − | 15.3388i | − | 0.580582i | ||||||
\(699\) | − | 5.17843i | − | 0.195866i | ||||||
\(700\) | −10.6146 | − | 4.69539i | −0.401193 | − | 0.177469i | ||||
\(701\) | −23.5884 | + | 23.5884i | −0.890921 | + | 0.890921i | −0.994610 | − | 0.103688i | \(-0.966935\pi\) |
0.103688 | + | 0.994610i | \(0.466935\pi\) | |||||||
\(702\) | −0.848892 | − | 0.848892i | −0.0320394 | − | 0.0320394i | ||||
\(703\) | −21.2438 | − | 24.1511i | −0.801226 | − | 0.910877i | ||||
\(704\) | − | 4.17593i | − | 0.157386i | ||||||
\(705\) | 14.6829 | + | 10.0653i | 0.552990 | + | 0.379083i | ||||
\(706\) | − | 29.7766i | − | 1.12066i | ||||||
\(707\) | 15.9674 | + | 15.9674i | 0.600514 | + | 0.600514i | ||||
\(708\) | −5.52770 | −0.207744 | ||||||||
\(709\) | −20.0563 | − | 20.0563i | −0.753229 | − | 0.753229i | 0.221851 | − | 0.975080i | \(-0.428790\pi\) |
−0.975080 | + | 0.221851i | \(0.928790\pi\) | |||||||
\(710\) | 11.5262 | − | 16.8139i | 0.432569 | − | 0.631015i | ||||
\(711\) | 0.571724 | − | 0.571724i | 0.0214413 | − | 0.0214413i | ||||
\(712\) | 4.28275 | − | 4.28275i | 0.160503 | − | 0.160503i | ||||
\(713\) | −7.54338 | − | 7.54338i | −0.282502 | − | 0.282502i | ||||
\(714\) | −0.515174 | −0.0192799 | ||||||||
\(715\) | 9.24607 | + | 6.33831i | 0.345783 | + | 0.237039i | ||||
\(716\) | −11.4245 | + | 11.4245i | −0.426953 | + | 0.426953i | ||||
\(717\) | 3.89231 | 0.145361 | ||||||||
\(718\) | − | 13.0032i | − | 0.485276i | ||||||
\(719\) | 26.6689i | 0.994583i | 0.867584 | + | 0.497291i | \(0.165672\pi\) | ||||
−0.867584 | + | 0.497291i | \(0.834328\pi\) | |||||||
\(720\) | −1.84432 | − | 1.26431i | −0.0687338 | − | 0.0471180i | ||||
\(721\) | −25.7486 | − | 25.7486i | −0.958928 | − | 0.958928i | ||||
\(722\) | 8.96152i | 0.333513i | ||||||||
\(723\) | − | 28.1991i | − | 1.04874i | ||||||
\(724\) | −18.4010 | −0.683869 | ||||||||
\(725\) | 35.2662 | + | 15.6001i | 1.30975 | + | 0.579373i | ||||
\(726\) | 4.55261 | − | 4.55261i | 0.168963 | − | 0.168963i | ||||
\(727\) | 36.3257 | 1.34725 | 0.673623 | − | 0.739075i | \(-0.264737\pi\) | ||||
0.673623 | + | 0.739075i | \(0.264737\pi\) | |||||||
\(728\) | −1.97057 | + | 1.97057i | −0.0730342 | + | 0.0730342i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 2.18506 | + | 11.7110i | 0.0808725 | + | 0.433443i | ||||
\(731\) | 1.70749i | 0.0631538i | ||||||||
\(732\) | −1.27493 | −0.0471227 | ||||||||
\(733\) | 3.69185 | − | 3.69185i | 0.136362 | − | 0.136362i | −0.635631 | − | 0.771993i | \(-0.719260\pi\) |
0.771993 | + | 0.635631i | \(0.219260\pi\) | |||||||
\(734\) | −11.3147 | + | 11.3147i | −0.417634 | + | 0.417634i | ||||
\(735\) | −3.54198 | + | 0.660870i | −0.130648 | + | 0.0243765i | ||||
\(736\) | −4.24635 | −0.156523 | ||||||||
\(737\) | 43.2122 | − | 43.2122i | 1.59174 | − | 1.59174i | ||||
\(738\) | −2.58213 | −0.0950495 | ||||||||
\(739\) | 32.1208 | 1.18158 | 0.590792 | − | 0.806824i | \(-0.298815\pi\) | ||||
0.590792 | + | 0.806824i | \(0.298815\pi\) | |||||||
\(740\) | 8.39179 | − | 10.7041i | 0.308488 | − | 0.393491i | ||||
\(741\) | −6.34816 | −0.233205 | ||||||||
\(742\) | −14.6390 | −0.537414 | ||||||||
\(743\) | 14.6516 | − | 14.6516i | 0.537516 | − | 0.537516i | −0.385283 | − | 0.922799i | \(-0.625896\pi\) |
0.922799 | + | 0.385283i | \(0.125896\pi\) | |||||||
\(744\) | −2.51226 | −0.0921040 | ||||||||
\(745\) | 17.1378 | + | 11.7482i | 0.627879 | + | 0.430420i | ||||
\(746\) | 15.2041 | − | 15.2041i | 0.556661 | − | 0.556661i | ||||
\(747\) | 7.69554 | − | 7.69554i | 0.281565 | − | 0.281565i | ||||
\(748\) | 0.926759 | 0.0338857 | ||||||||
\(749\) | − | 5.23894i | − | 0.191427i | ||||||
\(750\) | 9.51169 | − | 5.87603i | 0.347318 | − | 0.214562i | ||||
\(751\) | − | 23.7777i | − | 0.867660i | −0.900995 | − | 0.433830i | \(-0.857162\pi\) | ||
0.900995 | − | 0.433830i | \(-0.142838\pi\) | |||||||
\(752\) | 5.62938 | − | 5.62938i | 0.205282 | − | 0.205282i | ||||
\(753\) | 17.6751 | 0.644118 | ||||||||
\(754\) | 6.54708 | − | 6.54708i | 0.238431 | − | 0.238431i | ||||
\(755\) | 18.6046 | + | 12.7537i | 0.677092 | + | 0.464156i | ||||
\(756\) | 2.32134 | 0.0844265 | ||||||||
\(757\) | − | 11.8515i | − | 0.430750i | −0.976531 | − | 0.215375i | \(-0.930903\pi\) | ||
0.976531 | − | 0.215375i | \(-0.0690974\pi\) | |||||||
\(758\) | 1.94256i | 0.0705571i | ||||||||
\(759\) | −12.5387 | − | 12.5387i | −0.455127 | − | 0.455127i | ||||
\(760\) | −11.6234 | + | 2.16872i | −0.421626 | + | 0.0786678i | ||||
\(761\) | 0.483135i | 0.0175136i | 0.999962 | + | 0.00875681i | \(0.00278741\pi\) | ||||
−0.999962 | + | 0.00875681i | \(0.997213\pi\) | |||||||
\(762\) | 12.9937i | 0.470711i | ||||||||
\(763\) | 20.8564 | 0.755053 | ||||||||
\(764\) | −3.52951 | + | 3.52951i | −0.127693 | + | 0.127693i | ||||
\(765\) | 0.280587 | − | 0.409308i | 0.0101446 | − | 0.0147986i | ||||
\(766\) | −14.7331 | −0.532329 | ||||||||
\(767\) | −4.69242 | − | 4.69242i | −0.169434 | − | 0.169434i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 13.0162 | − | 13.0162i | 0.469377 | − | 0.469377i | −0.432336 | − | 0.901713i | \(-0.642310\pi\) |
0.901713 | + | 0.432336i | \(0.142310\pi\) | |||||||
\(770\) | −21.3082 | + | 3.97572i | −0.767894 | + | 0.143275i | ||||
\(771\) | 16.3389 | + | 16.3389i | 0.588432 | + | 0.588432i | ||||
\(772\) | 9.24953 | 0.332898 | ||||||||
\(773\) | 5.46633 | + | 5.46633i | 0.196610 | + | 0.196610i | 0.798545 | − | 0.601935i | \(-0.205603\pi\) |
−0.601935 | + | 0.798545i | \(0.705603\pi\) | |||||||
\(774\) | − | 7.69386i | − | 0.276550i | ||||||
\(775\) | 5.08156 | − | 11.4876i | 0.182535 | − | 0.412646i | ||||
\(776\) | 8.59029i | 0.308374i | ||||||||
\(777\) | −0.902476 | + | 14.0913i | −0.0323761 | + | 0.505523i | ||||
\(778\) | −11.3037 | − | 11.3037i | −0.405257 | − | 0.405257i | ||||
\(779\) | −9.65481 | + | 9.65481i | −0.345919 | + | 0.345919i | ||||
\(780\) | −0.492369 | − | 2.63889i | −0.0176296 | − | 0.0944875i | ||||
\(781\) | − | 38.0701i | − | 1.36226i | ||||||
\(782\) | − | 0.942388i | − | 0.0336997i | ||||||
\(783\) | −7.71250 | −0.275622 | ||||||||
\(784\) | 1.61136i | 0.0575486i | ||||||||
\(785\) | 9.17666 | + | 49.1831i | 0.327529 | + | 1.75542i | ||||
\(786\) | 15.1337 | 0.539803 | ||||||||
\(787\) | 29.3423 | − | 29.3423i | 1.04594 | − | 1.04594i | 0.0470485 | − | 0.998893i | \(-0.485018\pi\) |
0.998893 | − | 0.0470485i | \(-0.0149815\pi\) | |||||||
\(788\) | −1.75235 | + | 1.75235i | −0.0624250 | + | 0.0624250i | ||||
\(789\) | 12.2847i | 0.437346i | ||||||||
\(790\) | 1.77728 | − | 0.331608i | 0.0632327 | − | 0.0117981i | ||||
\(791\) | −19.2915 | − | 19.2915i | −0.685926 | − | 0.685926i | ||||
\(792\) | −4.17593 | −0.148385 | ||||||||
\(793\) | −1.08228 | − | 1.08228i | −0.0384328 | − | 0.0384328i | ||||
\(794\) | 5.54983 | + | 5.54983i | 0.196956 | + | 0.196956i | ||||
\(795\) | 7.97305 | − | 11.6308i | 0.282775 | − | 0.412501i | ||||
\(796\) | −1.94022 | + | 1.94022i | −0.0687691 | + | 0.0687691i | ||||
\(797\) | −16.4749 | −0.583569 | −0.291785 | − | 0.956484i | \(-0.594249\pi\) | ||||
−0.291785 | + | 0.956484i | \(0.594249\pi\) | |||||||
\(798\) | 8.67970 | − | 8.67970i | 0.307258 | − | 0.307258i | ||||
\(799\) | 1.24932 | + | 1.24932i | 0.0441978 | + | 0.0441978i | ||||
\(800\) | −1.80305 | − | 4.66358i | −0.0637474 | − | 0.164883i | ||||
\(801\) | −4.28275 | − | 4.28275i | −0.151324 | − | 0.151324i | ||||
\(802\) | 10.5726 | + | 10.5726i | 0.373331 | + | 0.373331i | ||||
\(803\) | 15.7317 | + | 15.7317i | 0.555161 | + | 0.555161i | ||||
\(804\) | −14.6342 | −0.516108 | ||||||||
\(805\) | 4.04277 | + | 21.6675i | 0.142489 | + | 0.763680i | ||||
\(806\) | −2.13264 | − | 2.13264i | −0.0751190 | − | 0.0751190i | ||||
\(807\) | −21.3346 | − | 21.3346i | −0.751013 | − | 0.751013i | ||||
\(808\) | 9.72766i | 0.342218i | ||||||||
\(809\) | −36.4616 | + | 36.4616i | −1.28192 | + | 1.28192i | −0.342347 | + | 0.939574i | \(0.611222\pi\) |
−0.939574 | + | 0.342347i | \(0.888778\pi\) | |||||||
\(810\) | −1.26431 | + | 1.84432i | −0.0444233 | + | 0.0648029i | ||||
\(811\) | 17.4891 | 0.614126 | 0.307063 | − | 0.951689i | \(-0.400654\pi\) | ||||
0.307063 | + | 0.951689i | \(0.400654\pi\) | |||||||
\(812\) | 17.9034i | 0.628285i | ||||||||
\(813\) | 5.14816 | − | 5.14816i | 0.180554 | − | 0.180554i | ||||
\(814\) | 1.62349 | − | 25.3492i | 0.0569032 | − | 0.888490i | ||||
\(815\) | 34.6635 | + | 23.7623i | 1.21421 | + | 0.832358i | ||||
\(816\) | −0.156927 | − | 0.156927i | −0.00549356 | − | 0.00549356i | ||||
\(817\) | −28.7680 | − | 28.7680i | −1.00646 | − | 1.00646i | ||||
\(818\) | 25.5820 | − | 25.5820i | 0.894454 | − | 0.894454i | ||||
\(819\) | 1.97057 | + | 1.97057i | 0.0688573 | + | 0.0688573i | ||||
\(820\) | −4.76228 | − | 3.26461i | −0.166306 | − | 0.114005i | ||||
\(821\) | 55.0645 | 1.92176 | 0.960882 | − | 0.276959i | \(-0.0893267\pi\) | ||||
0.960882 | + | 0.276959i | \(0.0893267\pi\) | |||||||
\(822\) | − | 6.15574i | − | 0.214706i | ||||||
\(823\) | 39.8287 | + | 39.8287i | 1.38834 | + | 1.38834i | 0.828808 | + | 0.559533i | \(0.189019\pi\) |
0.559533 | + | 0.828808i | \(0.310981\pi\) | |||||||
\(824\) | − | 15.6866i | − | 0.546469i | ||||||
\(825\) | 8.44666 | − | 19.0948i | 0.294075 | − | 0.664797i | ||||
\(826\) | 12.8317 | 0.446472 | ||||||||
\(827\) | 47.2289i | 1.64231i | 0.570705 | + | 0.821155i | \(0.306670\pi\) | ||||
−0.570705 | + | 0.821155i | \(0.693330\pi\) | |||||||
\(828\) | 4.24635i | 0.147571i | ||||||||
\(829\) | −13.9841 | + | 13.9841i | −0.485688 | + | 0.485688i | −0.906943 | − | 0.421254i | \(-0.861590\pi\) |
0.421254 | + | 0.906943i | \(0.361590\pi\) | |||||||
\(830\) | 23.9226 | − | 4.46352i | 0.830365 | − | 0.154931i | ||||
\(831\) | −14.3636 | + | 14.3636i | −0.498266 | + | 0.498266i | ||||
\(832\) | −1.20051 | −0.0416204 | ||||||||
\(833\) | −0.357607 | −0.0123904 | ||||||||
\(834\) | −12.9699 | + | 12.9699i | −0.449111 | + | 0.449111i | ||||
\(835\) | −26.5930 | − | 18.2299i | −0.920290 | − | 0.630872i | ||||
\(836\) | −15.6141 | + | 15.6141i | −0.540027 | + | 0.540027i | ||||
\(837\) | 2.51226i | 0.0868365i | ||||||||
\(838\) | 3.51437i | 0.121402i | ||||||||
\(839\) | 33.7851 | 1.16639 | 0.583196 | − | 0.812332i | \(-0.301802\pi\) | ||||
0.583196 | + | 0.812332i | \(0.301802\pi\) | |||||||
\(840\) | 4.28131 | + | 2.93490i | 0.147719 | + | 0.101264i | ||||
\(841\) | − | 30.4827i | − | 1.05113i | ||||||
\(842\) | −0.351376 | − | 0.351376i | −0.0121092 | − | 0.0121092i | ||||
\(843\) | − | 8.32219i | − | 0.286631i | ||||||
\(844\) | −4.88849 | −0.168269 | ||||||||
\(845\) | −14.6138 | + | 21.3181i | −0.502732 | + | 0.733364i | ||||
\(846\) | −5.62938 | − | 5.62938i | −0.193542 | − | 0.193542i | ||||
\(847\) | −10.5682 | + | 10.5682i | −0.363127 | + | 0.363127i | ||||
\(848\) | −4.45920 | − | 4.45920i | −0.153129 | − | 0.153129i | ||||
\(849\) | −2.78079 | − | 2.78079i | −0.0954366 | − | 0.0954366i | ||||
\(850\) | 1.03498 | − | 0.400149i | 0.0354997 | − | 0.0137250i | ||||
\(851\) | −25.7767 | − | 1.65087i | −0.883615 | − | 0.0565909i | ||||
\(852\) | −6.44639 | + | 6.44639i | −0.220850 | + | 0.220850i | ||||
\(853\) | 30.3087i | 1.03775i | 0.854850 | + | 0.518875i | \(0.173649\pi\) | ||||
−0.854850 | + | 0.518875i | \(0.826351\pi\) | |||||||
\(854\) | 2.95955 | 0.101274 | ||||||||
\(855\) | 2.16872 | + | 11.6234i | 0.0741687 | + | 0.397513i | ||||
\(856\) | 1.59584 | − | 1.59584i | 0.0545446 | − | 0.0545446i | ||||
\(857\) | 4.58564i | 0.156642i | 0.996928 | + | 0.0783212i | \(0.0249560\pi\) | ||||
−0.996928 | + | 0.0783212i | \(0.975044\pi\) | |||||||
\(858\) | −3.54491 | − | 3.54491i | −0.121021 | − | 0.121021i | ||||
\(859\) | −39.7203 | − | 39.7203i | −1.35524 | − | 1.35524i | −0.879689 | − | 0.475549i | \(-0.842249\pi\) |
−0.475549 | − | 0.879689i | \(-0.657751\pi\) | |||||||
\(860\) | 9.72741 | − | 14.1899i | 0.331702 | − | 0.483873i | ||||
\(861\) | 5.99401 | 0.204275 | ||||||||
\(862\) | −11.7580 | − | 11.7580i | −0.400478 | − | 0.400478i | ||||
\(863\) | −12.7595 | − | 12.7595i | −0.434339 | − | 0.434339i | 0.455762 | − | 0.890101i | \(-0.349367\pi\) |
−0.890101 | + | 0.455762i | \(0.849367\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −8.06351 | − | 43.2170i | −0.274167 | − | 1.46942i | ||||
\(866\) | 12.6439 | + | 12.6439i | 0.429658 | + | 0.429658i | ||||
\(867\) | −11.9860 | + | 11.9860i | −0.407066 | + | 0.407066i | ||||
\(868\) | 5.83183 | 0.197945 | ||||||||
\(869\) | 2.38748 | − | 2.38748i | 0.0809896 | − | 0.0809896i | ||||
\(870\) | −14.2243 | − | 9.75098i | −0.482250 | − | 0.330589i | ||||
\(871\) | −12.4228 | − | 12.4228i | −0.420932 | − | 0.420932i | ||||
\(872\) | 6.35309 | + | 6.35309i | 0.215143 | + | 0.215143i | ||||
\(873\) | 8.59029 | 0.290737 | ||||||||
\(874\) | 15.8775 | + | 15.8775i | 0.537063 | + | 0.537063i | ||||
\(875\) | −22.0799 | + | 13.6403i | −0.746437 | + | 0.461126i | ||||
\(876\) | − | 5.32769i | − | 0.180006i | ||||||
\(877\) | −25.2001 | + | 25.2001i | −0.850947 | + | 0.850947i | −0.990250 | − | 0.139303i | \(-0.955514\pi\) |
0.139303 | + | 0.990250i | \(0.455514\pi\) | |||||||
\(878\) | −2.75100 | + | 2.75100i | −0.0928416 | + | 0.0928416i | ||||
\(879\) | 5.20786 | 0.175657 | ||||||||
\(880\) | −7.70175 | − | 5.27966i | −0.259626 | − | 0.177977i | ||||
\(881\) | − | 24.1141i | − | 0.812426i | −0.913778 | − | 0.406213i | \(-0.866849\pi\) | ||
0.913778 | − | 0.406213i | \(-0.133151\pi\) | |||||||
\(882\) | 1.61136 | 0.0542573 | ||||||||
\(883\) | 39.4787i | 1.32856i | 0.747482 | + | 0.664282i | \(0.231263\pi\) | ||||
−0.747482 | + | 0.664282i | \(0.768737\pi\) | |||||||
\(884\) | − | 0.266429i | − | 0.00896097i | ||||||
\(885\) | −6.98872 | + | 10.1949i | −0.234923 | + | 0.342697i | ||||
\(886\) | 8.68051 | − | 8.68051i | 0.291627 | − | 0.291627i | ||||
\(887\) | −15.0650 | − | 15.0650i | −0.505834 | − | 0.505834i | 0.407411 | − | 0.913245i | \(-0.366432\pi\) |
−0.913245 | + | 0.407411i | \(0.866432\pi\) | |||||||
\(888\) | −4.56727 | + | 4.01746i | −0.153268 | + | 0.134817i | ||||
\(889\) | − | 30.1628i | − | 1.01163i | ||||||
\(890\) | −2.48406 | − | 13.3135i | −0.0832657 | − | 0.446269i | ||||
\(891\) | 4.17593i | 0.139899i | ||||||||
\(892\) | 16.9445 | + | 16.9445i | 0.567344 | + | 0.567344i | ||||
\(893\) | −42.0974 | −1.40874 | ||||||||
\(894\) | −6.57056 | − | 6.57056i | −0.219752 | − | 0.219752i | ||||
\(895\) | 6.62636 | + | 35.5145i | 0.221495 | + | 1.18712i | ||||
\(896\) | 1.64144 | − | 1.64144i | 0.0548366 | − | 0.0548366i | ||||
\(897\) | −3.60469 | + | 3.60469i | −0.120357 | + | 0.120357i | ||||
\(898\) | 11.3699 | + | 11.3699i | 0.379418 | + | 0.379418i | ||||
\(899\) | −19.3758 | −0.646220 | ||||||||
\(900\) | −4.66358 | + | 1.80305i | −0.155453 | + | 0.0601016i | ||||
\(901\) | 0.989625 | − | 0.989625i | 0.0329692 | − | 0.0329692i | ||||
\(902\) | −10.7828 | −0.359028 | ||||||||
\(903\) | 17.8601i | 0.594347i | ||||||||
\(904\) | − | 11.7528i | − | 0.390892i | ||||||
\(905\) | −23.2646 | + | 33.9374i | −0.773340 | + | 1.12812i | ||||
\(906\) | −7.13295 | − | 7.13295i | −0.236976 | − | 0.236976i | ||||
\(907\) | − | 14.7767i | − | 0.490653i | −0.969441 | − | 0.245326i | \(-0.921105\pi\) | ||
0.969441 | − | 0.245326i | \(-0.0788951\pi\) | |||||||
\(908\) | − | 22.8426i | − | 0.758058i | ||||||
\(909\) | 9.72766 | 0.322646 | ||||||||
\(910\) | 1.14296 | + | 6.12578i | 0.0378887 | + | 0.203067i | ||||
\(911\) | 24.5510 | − | 24.5510i | 0.813410 | − | 0.813410i | −0.171734 | − | 0.985143i | \(-0.554937\pi\) |
0.985143 | + | 0.171734i | \(0.0549369\pi\) | |||||||
\(912\) | 5.28787 | 0.175099 | ||||||||
\(913\) | 32.1360 | − | 32.1360i | 1.06355 | − | 1.06355i | ||||
\(914\) | 19.6985i | 0.651568i | ||||||||
\(915\) | −1.61190 | + | 2.35138i | −0.0532879 | + | 0.0777342i | ||||
\(916\) | 16.1156i | 0.532474i | ||||||||
\(917\) | −35.1306 | −1.16012 | ||||||||
\(918\) | −0.156927 | + | 0.156927i | −0.00517938 | + | 0.00517938i | ||||
\(919\) | −34.9734 | + | 34.9734i | −1.15367 | + | 1.15367i | −0.167855 | + | 0.985812i | \(0.553684\pi\) |
−0.985812 | + | 0.167855i | \(0.946316\pi\) | |||||||
\(920\) | −5.36870 | + | 7.83164i | −0.177001 | + | 0.258201i | ||||
\(921\) | 23.1004 | 0.761185 | ||||||||
\(922\) | −19.2408 | + | 19.2408i | −0.633663 | + | 0.633663i | ||||
\(923\) | −10.9446 | −0.360245 | ||||||||
\(924\) | 9.69376 | 0.318901 | ||||||||
\(925\) | −9.13202 | − | 29.0105i | −0.300259 | − | 0.953858i | ||||
\(926\) | 1.97887 | 0.0650296 | ||||||||
\(927\) | −15.6866 | −0.515216 | ||||||||
\(928\) | −5.45356 | + | 5.45356i | −0.179022 | + | 0.179022i | ||||
\(929\) | 51.4784 | 1.68895 | 0.844476 | − | 0.535593i | \(-0.179912\pi\) | ||||
0.844476 | + | 0.535593i | \(0.179912\pi\) | |||||||
\(930\) | −3.17627 | + | 4.63342i | −0.104154 | + | 0.151936i | ||||
\(931\) | 6.02501 | − | 6.02501i | 0.197462 | − | 0.197462i | ||||
\(932\) | −3.66171 | + | 3.66171i | −0.119943 | + | 0.119943i | ||||
\(933\) | 1.14724 | 0.0375589 | ||||||||
\(934\) | 24.0229i | 0.786054i | ||||||||
\(935\) | 1.17171 | − | 1.70924i | 0.0383190 | − | 0.0558982i | ||||
\(936\) | 1.20051i | 0.0392400i | ||||||||
\(937\) | −12.8685 | + | 12.8685i | −0.420395 | + | 0.420395i | −0.885340 | − | 0.464945i | \(-0.846074\pi\) |
0.464945 | + | 0.885340i | \(0.346074\pi\) | |||||||
\(938\) | 33.9710 | 1.10919 | ||||||||
\(939\) | 2.55371 | − | 2.55371i | 0.0833371 | − | 0.0833371i | ||||
\(940\) | −3.26512 | − | 17.4997i | −0.106496 | − | 0.570776i | ||||
\(941\) | −18.7889 | −0.612499 | −0.306250 | − | 0.951951i | \(-0.599074\pi\) | ||||
−0.306250 | + | 0.951951i | \(0.599074\pi\) | |||||||
\(942\) | − | 22.3749i | − | 0.729014i | ||||||
\(943\) | 10.9646i | 0.357057i | ||||||||
\(944\) | 3.90868 | + | 3.90868i | 0.127217 | + | 0.127217i | ||||
\(945\) | 2.93490 | − | 4.28131i | 0.0954722 | − | 0.139271i | ||||
\(946\) | − | 32.1290i | − | 1.04460i | ||||||
\(947\) | 44.6439i | 1.45073i | 0.688363 | + | 0.725366i | \(0.258329\pi\) | ||||
−0.688363 | + | 0.725366i | \(0.741671\pi\) | |||||||
\(948\) | −0.808539 | −0.0262601 | ||||||||
\(949\) | 4.52263 | − | 4.52263i | 0.146811 | − | 0.146811i | ||||
\(950\) | −10.6958 | + | 24.1793i | −0.347017 | + | 0.784480i | ||||
\(951\) | −12.7520 | −0.413513 | ||||||||
\(952\) | 0.364283 | + | 0.364283i | 0.0118065 | + | 0.0118065i | ||||
\(953\) | −30.4910 | + | 30.4910i | −0.987700 | + | 0.987700i | −0.999925 | − | 0.0122255i | \(-0.996108\pi\) |
0.0122255 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(954\) | −4.45920 | + | 4.45920i | −0.144372 | + | 0.144372i | ||||
\(955\) | 2.04716 | + | 10.9719i | 0.0662446 | + | 0.355043i | ||||
\(956\) | −2.75228 | − | 2.75228i | −0.0890150 | − | 0.0890150i | ||||
\(957\) | −32.2068 | −1.04110 | ||||||||
\(958\) | 2.92694 | + | 2.92694i | 0.0945651 | + | 0.0945651i | ||||
\(959\) | 14.2896i | 0.461435i | ||||||||
\(960\) | 0.410132 | + | 2.19813i | 0.0132369 | + | 0.0709445i | ||||
\(961\) | − | 24.6885i | − | 0.796404i | ||||||
\(962\) | −7.28751 | − | 0.466727i | −0.234959 | − | 0.0150479i | ||||
\(963\) | −1.59584 | − | 1.59584i | −0.0514251 | − | 0.0514251i | ||||
\(964\) | −19.9398 | + | 19.9398i | −0.642218 | + | 0.642218i | ||||
\(965\) | 11.6943 | − | 17.0591i | 0.376451 | − | 0.549152i | ||||
\(966\) | − | 9.85724i | − | 0.317152i | ||||||
\(967\) | 25.9848i | 0.835614i | 0.908536 | + | 0.417807i | \(0.137201\pi\) | ||||
−0.908536 | + | 0.417807i | \(0.862799\pi\) | |||||||
\(968\) | −6.43836 | −0.206937 | ||||||||
\(969\) | 1.17353i | 0.0376992i | ||||||||
\(970\) | 15.8433 | + | 10.8608i | 0.508697 | + | 0.348719i | ||||
\(971\) | −29.3865 | −0.943058 | −0.471529 | − | 0.881851i | \(-0.656298\pi\) | ||||
−0.471529 | + | 0.881851i | \(0.656298\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 30.1076 | − | 30.1076i | 0.965206 | − | 0.965206i | ||||
\(974\) | − | 20.3915i | − | 0.653387i | ||||||
\(975\) | −5.48947 | − | 2.42829i | −0.175804 | − | 0.0777674i | ||||
\(976\) | 0.901511 | + | 0.901511i | 0.0288567 | + | 0.0288567i | ||||
\(977\) | −20.9434 | −0.670037 | −0.335019 | − | 0.942211i | \(-0.608743\pi\) | ||||
−0.335019 | + | 0.942211i | \(0.608743\pi\) | |||||||
\(978\) | −13.2899 | − | 13.2899i | −0.424963 | − | 0.424963i | ||||
\(979\) | −17.8845 | − | 17.8845i | −0.571590 | − | 0.571590i | ||||
\(980\) | 2.97187 | + | 2.03726i | 0.0949328 | + | 0.0650778i | ||||
\(981\) | 6.35309 | − | 6.35309i | 0.202839 | − | 0.202839i | ||||
\(982\) | 19.2062 | 0.612893 | ||||||||
\(983\) | −29.6368 | + | 29.6368i | −0.945266 | + | 0.945266i | −0.998578 | − | 0.0533119i | \(-0.983022\pi\) |
0.0533119 | + | 0.998578i | \(0.483022\pi\) | |||||||
\(984\) | 1.82584 | + | 1.82584i | 0.0582057 | + | 0.0582057i | ||||
\(985\) | 1.01639 | + | 5.44742i | 0.0323849 | + | 0.173569i | ||||
\(986\) | −1.21030 | − | 1.21030i | −0.0385439 | − | 0.0385439i | ||||
\(987\) | 13.0677 | + | 13.0677i | 0.415950 | + | 0.415950i | ||||
\(988\) | 4.48883 | + | 4.48883i | 0.142809 | + | 0.142809i | ||||
\(989\) | −32.6708 | −1.03887 | ||||||||
\(990\) | −5.27966 | + | 7.70175i | −0.167799 | + | 0.244778i | ||||
\(991\) | 1.54828 | + | 1.54828i | 0.0491828 | + | 0.0491828i | 0.731270 | − | 0.682088i | \(-0.238928\pi\) |
−0.682088 | + | 0.731270i | \(0.738928\pi\) | |||||||
\(992\) | 1.77644 | + | 1.77644i | 0.0564020 | + | 0.0564020i | ||||
\(993\) | 4.05650i | 0.128729i | ||||||||
\(994\) | 14.9643 | − | 14.9643i | 0.474639 | − | 0.474639i | ||||
\(995\) | 1.12535 | + | 6.03141i | 0.0356761 | + | 0.191209i | ||||
\(996\) | −10.8831 | −0.344845 | ||||||||
\(997\) | − | 39.3599i | − | 1.24654i | −0.782007 | − | 0.623270i | \(-0.785804\pi\) | ||
0.782007 | − | 0.623270i | \(-0.214196\pi\) | |||||||
\(998\) | 3.71349 | − | 3.71349i | 0.117548 | − | 0.117548i | ||||
\(999\) | 4.01746 | + | 4.56727i | 0.127107 | + | 0.144502i |
(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 | 1110.2.o.b.253.3 | yes | 40 | |
5.2 | odd | 4 | 1110.2.l.b.697.18 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.l.b.43.18 | ✓ | 40 | ||
185.117 | even | 4 | inner | 1110.2.o.b.487.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.18 | ✓ | 40 | 37.6 | odd | 4 | ||
1110.2.l.b.697.18 | yes | 40 | 5.2 | odd | 4 | ||
1110.2.o.b.253.3 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.487.3 | yes | 40 | 185.117 | even | 4 | inner |