Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(87,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.m (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 87.1 | ||
Character | \(\chi\) | \(=\) | 731.87 |
Dual form | 731.2.m.c.689.1 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.95137 | − | 1.95137i | −1.37983 | − | 1.37983i | −0.844899 | − | 0.534926i | \(-0.820339\pi\) |
−0.534926 | − | 0.844899i | \(-0.679661\pi\) | |||||||
\(3\) | 1.54767 | − | 0.641064i | 0.893546 | − | 0.370119i | 0.111811 | − | 0.993730i | \(-0.464335\pi\) |
0.781735 | + | 0.623611i | \(0.214335\pi\) | |||||||
\(4\) | 5.61567i | 2.80783i | ||||||||
\(5\) | 0.779040 | + | 1.88077i | 0.348397 | + | 0.841106i | 0.996810 | + | 0.0798162i | \(0.0254334\pi\) |
−0.648412 | + | 0.761289i | \(0.724567\pi\) | |||||||
\(6\) | −4.27102 | − | 1.76911i | −1.74364 | − | 0.722238i | ||||
\(7\) | −0.326309 | + | 0.787780i | −0.123333 | + | 0.297753i | −0.973472 | − | 0.228806i | \(-0.926518\pi\) |
0.850139 | + | 0.526559i | \(0.176518\pi\) | |||||||
\(8\) | 7.05550 | − | 7.05550i | 2.49450 | − | 2.49450i | ||||
\(9\) | −0.137012 | + | 0.137012i | −0.0456708 | + | 0.0456708i | ||||
\(10\) | 2.14988 | − | 5.19027i | 0.679851 | − | 1.64131i | ||||
\(11\) | 1.25834 | + | 0.521220i | 0.379402 | + | 0.157154i | 0.564231 | − | 0.825617i | \(-0.309173\pi\) |
−0.184828 | + | 0.982771i | \(0.559173\pi\) | |||||||
\(12\) | 3.60001 | + | 8.69118i | 1.03923 | + | 2.50893i | ||||
\(13\) | 3.25478i | 0.902713i | 0.892344 | + | 0.451356i | \(0.149060\pi\) | ||||
−0.892344 | + | 0.451356i | \(0.850940\pi\) | |||||||
\(14\) | 2.17400 | − | 0.900499i | 0.581025 | − | 0.240668i | ||||
\(15\) | 2.41139 | + | 2.41139i | 0.622618 | + | 0.622618i | ||||
\(16\) | −16.3044 | −4.07610 | ||||||||
\(17\) | −3.79776 | + | 1.60530i | −0.921093 | + | 0.389343i | ||||
\(18\) | 0.534723 | 0.126035 | ||||||||
\(19\) | −4.59097 | − | 4.59097i | −1.05324 | − | 1.05324i | −0.998501 | − | 0.0547393i | \(-0.982567\pi\) |
−0.0547393 | − | 0.998501i | \(-0.517433\pi\) | |||||||
\(20\) | −10.5618 | + | 4.37483i | −2.36169 | + | 0.978242i | ||||
\(21\) | 1.42841i | 0.311704i | ||||||||
\(22\) | −1.43838 | − | 3.47257i | −0.306664 | − | 0.740354i | ||||
\(23\) | 1.16789 | + | 0.483757i | 0.243522 | + | 0.100870i | 0.501106 | − | 0.865386i | \(-0.332926\pi\) |
−0.257584 | + | 0.966256i | \(0.582926\pi\) | |||||||
\(24\) | 6.39653 | − | 15.4426i | 1.30569 | − | 3.15221i | ||||
\(25\) | 0.605144 | − | 0.605144i | 0.121029 | − | 0.121029i | ||||
\(26\) | 6.35127 | − | 6.35127i | 1.24559 | − | 1.24559i | ||||
\(27\) | −2.04741 | + | 4.94288i | −0.394024 | + | 0.951258i | ||||
\(28\) | −4.42391 | − | 1.83244i | −0.836040 | − | 0.346299i | ||||
\(29\) | 3.67818 | + | 8.87991i | 0.683021 | + | 1.64896i | 0.758389 | + | 0.651802i | \(0.225987\pi\) |
−0.0753686 | + | 0.997156i | \(0.524013\pi\) | |||||||
\(30\) | − | 9.41101i | − | 1.71821i | ||||||
\(31\) | 0.941198 | − | 0.389857i | 0.169044 | − | 0.0700204i | −0.296556 | − | 0.955015i | \(-0.595838\pi\) |
0.465601 | + | 0.884995i | \(0.345838\pi\) | |||||||
\(32\) | 17.7049 | + | 17.7049i | 3.12981 | + | 3.12981i | ||||
\(33\) | 2.28162 | 0.397179 | ||||||||
\(34\) | 10.5434 | + | 4.27829i | 1.80817 | + | 0.733721i | ||||
\(35\) | −1.73584 | −0.293410 | ||||||||
\(36\) | −0.769416 | − | 0.769416i | −0.128236 | − | 0.128236i | ||||
\(37\) | −9.31588 | + | 3.85876i | −1.53152 | + | 0.634377i | −0.979859 | − | 0.199691i | \(-0.936006\pi\) |
−0.551662 | + | 0.834068i | \(0.686006\pi\) | |||||||
\(38\) | 17.9173i | 2.90657i | ||||||||
\(39\) | 2.08652 | + | 5.03731i | 0.334111 | + | 0.806615i | ||||
\(40\) | 18.7663 | + | 7.77325i | 2.96721 | + | 1.22906i | ||||
\(41\) | −0.940103 | + | 2.26961i | −0.146819 | + | 0.354453i | −0.980131 | − | 0.198350i | \(-0.936442\pi\) |
0.833312 | + | 0.552803i | \(0.186442\pi\) | |||||||
\(42\) | 2.78734 | − | 2.78734i | 0.430096 | − | 0.430096i | ||||
\(43\) | −0.707107 | + | 0.707107i | −0.107833 | + | 0.107833i | ||||
\(44\) | −2.92700 | + | 7.06640i | −0.441261 | + | 1.06530i | ||||
\(45\) | −0.364427 | − | 0.150950i | −0.0543255 | − | 0.0225024i | ||||
\(46\) | −1.33500 | − | 3.22297i | −0.196835 | − | 0.475201i | ||||
\(47\) | 1.19572i | 0.174414i | 0.996190 | + | 0.0872068i | \(0.0277941\pi\) | ||||
−0.996190 | + | 0.0872068i | \(0.972206\pi\) | |||||||
\(48\) | −25.2338 | + | 10.4522i | −3.64218 | + | 1.50864i | ||||
\(49\) | 4.43563 | + | 4.43563i | 0.633661 | + | 0.633661i | ||||
\(50\) | −2.36172 | −0.333997 | ||||||||
\(51\) | −4.84857 | + | 4.91908i | −0.678935 | + | 0.688810i | ||||
\(52\) | −18.2778 | −2.53467 | ||||||||
\(53\) | 8.68181 | + | 8.68181i | 1.19254 | + | 1.19254i | 0.976352 | + | 0.216187i | \(0.0693620\pi\) |
0.216187 | + | 0.976352i | \(0.430638\pi\) | |||||||
\(54\) | 13.6406 | − | 5.65013i | 1.85625 | − | 0.768886i | ||||
\(55\) | 2.77269i | 0.373869i | ||||||||
\(56\) | 3.25591 | + | 7.86045i | 0.435089 | + | 1.05040i | ||||
\(57\) | −10.0484 | − | 4.16218i | −1.33094 | − | 0.551294i | ||||
\(58\) | 10.1505 | − | 24.5054i | 1.33282 | − | 3.21772i | ||||
\(59\) | 7.34629 | − | 7.34629i | 0.956405 | − | 0.956405i | −0.0426833 | − | 0.999089i | \(-0.513591\pi\) |
0.999089 | + | 0.0426833i | \(0.0135906\pi\) | |||||||
\(60\) | −13.5416 | + | 13.5416i | −1.74821 | + | 1.74821i | ||||
\(61\) | 1.30664 | − | 3.15452i | 0.167299 | − | 0.403894i | −0.817889 | − | 0.575376i | \(-0.804856\pi\) |
0.985187 | + | 0.171482i | \(0.0548556\pi\) | |||||||
\(62\) | −2.59738 | − | 1.07587i | −0.329867 | − | 0.136636i | ||||
\(63\) | −0.0632272 | − | 0.152644i | −0.00796587 | − | 0.0192313i | ||||
\(64\) | − | 36.4886i | − | 4.56108i | ||||||
\(65\) | −6.12149 | + | 2.53560i | −0.759277 | + | 0.314503i | ||||
\(66\) | −4.45228 | − | 4.45228i | −0.548037 | − | 0.548037i | ||||
\(67\) | 0.247976 | 0.0302951 | 0.0151476 | − | 0.999885i | \(-0.495178\pi\) | ||||
0.0151476 | + | 0.999885i | \(0.495178\pi\) | |||||||
\(68\) | −9.01485 | − | 21.3270i | −1.09321 | − | 2.58628i | ||||
\(69\) | 2.11763 | 0.254932 | ||||||||
\(70\) | 3.38726 | + | 3.38726i | 0.404855 | + | 0.404855i | ||||
\(71\) | −8.72130 | + | 3.61248i | −1.03503 | + | 0.428723i | −0.834525 | − | 0.550970i | \(-0.814258\pi\) |
−0.200503 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(72\) | 1.93338i | 0.227851i | ||||||||
\(73\) | −0.570430 | − | 1.37714i | −0.0667638 | − | 0.161182i | 0.886976 | − | 0.461816i | \(-0.152802\pi\) |
−0.953740 | + | 0.300634i | \(0.902802\pi\) | |||||||
\(74\) | 25.7086 | + | 10.6488i | 2.98856 | + | 1.23790i | ||||
\(75\) | 0.548625 | − | 1.32450i | 0.0633497 | − | 0.152940i | ||||
\(76\) | 25.7814 | − | 25.7814i | 2.95732 | − | 2.95732i | ||||
\(77\) | −0.821212 | + | 0.821212i | −0.0935858 | + | 0.0935858i | ||||
\(78\) | 5.75807 | − | 13.9012i | 0.651973 | − | 1.57400i | ||||
\(79\) | 1.72313 | + | 0.713744i | 0.193867 | + | 0.0803024i | 0.477505 | − | 0.878629i | \(-0.341541\pi\) |
−0.283638 | + | 0.958932i | \(0.591541\pi\) | |||||||
\(80\) | −12.7018 | − | 30.6648i | −1.42010 | − | 3.42843i | ||||
\(81\) | 8.38116i | 0.931240i | ||||||||
\(82\) | 6.26333 | − | 2.59435i | 0.691669 | − | 0.286499i | ||||
\(83\) | −2.76434 | − | 2.76434i | −0.303426 | − | 0.303426i | 0.538927 | − | 0.842353i | \(-0.318830\pi\) |
−0.842353 | + | 0.538927i | \(0.818830\pi\) | |||||||
\(84\) | −8.02145 | −0.875212 | ||||||||
\(85\) | −5.97782 | − | 5.89212i | −0.648385 | − | 0.639090i | ||||
\(86\) | 2.75965 | 0.297581 | ||||||||
\(87\) | 11.3852 | + | 11.3852i | 1.22062 | + | 1.22062i | ||||
\(88\) | 12.5556 | − | 5.20072i | 1.33844 | − | 0.554399i | ||||
\(89\) | 4.73203i | 0.501595i | 0.968040 | + | 0.250797i | \(0.0806928\pi\) | ||||
−0.968040 | + | 0.250797i | \(0.919307\pi\) | |||||||
\(90\) | 0.416571 | + | 1.00569i | 0.0439104 | + | 0.106009i | ||||
\(91\) | −2.56405 | − | 1.06206i | −0.268785 | − | 0.111334i | ||||
\(92\) | −2.71662 | + | 6.55849i | −0.283227 | + | 0.683770i | ||||
\(93\) | 1.20674 | − | 1.20674i | 0.125133 | − | 0.125133i | ||||
\(94\) | 2.33329 | − | 2.33329i | 0.240660 | − | 0.240660i | ||||
\(95\) | 5.05800 | − | 12.2111i | 0.518940 | − | 1.25283i | ||||
\(96\) | 38.7512 | + | 16.0513i | 3.95503 | + | 1.63823i | ||||
\(97\) | −1.15465 | − | 2.78758i | −0.117237 | − | 0.283036i | 0.854358 | − | 0.519685i | \(-0.173951\pi\) |
−0.971595 | + | 0.236649i | \(0.923951\pi\) | |||||||
\(98\) | − | 17.3111i | − | 1.74868i | ||||||
\(99\) | −0.243821 | + | 0.100994i | −0.0245049 | + | 0.0101503i | ||||
\(100\) | 3.39829 | + | 3.39829i | 0.339829 | + | 0.339829i | ||||
\(101\) | 17.5883 | 1.75010 | 0.875052 | − | 0.484030i | \(-0.160827\pi\) | ||||
0.875052 | + | 0.484030i | \(0.160827\pi\) | |||||||
\(102\) | 19.0603 | − | 0.137606i | 1.88725 | − | 0.0136251i | ||||
\(103\) | −8.13309 | −0.801377 | −0.400689 | − | 0.916214i | \(-0.631229\pi\) | ||||
−0.400689 | + | 0.916214i | \(0.631229\pi\) | |||||||
\(104\) | 22.9641 | + | 22.9641i | 2.25181 | + | 2.25181i | ||||
\(105\) | −2.68650 | + | 1.11279i | −0.262176 | + | 0.108597i | ||||
\(106\) | − | 33.8828i | − | 3.29099i | ||||||
\(107\) | −5.94708 | − | 14.3575i | −0.574926 | − | 1.38799i | −0.897316 | − | 0.441388i | \(-0.854486\pi\) |
0.322390 | − | 0.946607i | \(-0.395514\pi\) | |||||||
\(108\) | −27.7576 | − | 11.4976i | −2.67098 | − | 1.10635i | ||||
\(109\) | 2.72814 | − | 6.58631i | 0.261308 | − | 0.630854i | −0.737712 | − | 0.675116i | \(-0.764094\pi\) |
0.999020 | + | 0.0442620i | \(0.0140936\pi\) | |||||||
\(110\) | 5.41054 | − | 5.41054i | 0.515874 | − | 0.515874i | ||||
\(111\) | −11.9442 | + | 11.9442i | −1.13369 | + | 1.13369i | ||||
\(112\) | 5.32027 | − | 12.8443i | 0.502719 | − | 1.21367i | ||||
\(113\) | −6.10745 | − | 2.52979i | −0.574540 | − | 0.237982i | 0.0764436 | − | 0.997074i | \(-0.475643\pi\) |
−0.650984 | + | 0.759092i | \(0.725643\pi\) | |||||||
\(114\) | 11.4862 | + | 27.7300i | 1.07578 | + | 2.59716i | ||||
\(115\) | 2.57340i | 0.239971i | ||||||||
\(116\) | −49.8666 | + | 20.6554i | −4.63000 | + | 1.91781i | ||||
\(117\) | −0.445945 | − | 0.445945i | −0.0412276 | − | 0.0412276i | ||||
\(118\) | −28.6706 | −2.63934 | ||||||||
\(119\) | −0.0253812 | − | 3.51562i | −0.00232669 | − | 0.322277i | ||||
\(120\) | 34.0271 | 3.10624 | ||||||||
\(121\) | −6.46644 | − | 6.46644i | −0.587858 | − | 0.587858i | ||||
\(122\) | −8.70536 | + | 3.60588i | −0.788146 | + | 0.326461i | ||||
\(123\) | 4.11526i | 0.371061i | ||||||||
\(124\) | 2.18931 | + | 5.28546i | 0.196606 | + | 0.474648i | ||||
\(125\) | 11.0134 | + | 4.56191i | 0.985070 | + | 0.408029i | ||||
\(126\) | −0.174485 | + | 0.421244i | −0.0155443 | + | 0.0375274i | ||||
\(127\) | 10.7753 | − | 10.7753i | 0.956152 | − | 0.956152i | −0.0429260 | − | 0.999078i | \(-0.513668\pi\) |
0.999078 | + | 0.0429260i | \(0.0136680\pi\) | |||||||
\(128\) | −35.7930 | + | 35.7930i | −3.16368 | + | 3.16368i | ||||
\(129\) | −0.641064 | + | 1.54767i | −0.0564426 | + | 0.136264i | ||||
\(130\) | 16.8932 | + | 6.99738i | 1.48163 | + | 0.613711i | ||||
\(131\) | 3.98964 | + | 9.63185i | 0.348577 | + | 0.841539i | 0.996789 | + | 0.0800786i | \(0.0255171\pi\) |
−0.648212 | + | 0.761460i | \(0.724483\pi\) | |||||||
\(132\) | 12.8128i | 1.11521i | ||||||||
\(133\) | 5.11474 | − | 2.11860i | 0.443505 | − | 0.183706i | ||||
\(134\) | −0.483893 | − | 0.483893i | −0.0418020 | − | 0.0418020i | ||||
\(135\) | −10.8914 | −0.937386 | ||||||||
\(136\) | −15.4689 | + | 38.1213i | −1.32645 | + | 3.26888i | ||||
\(137\) | −2.16211 | −0.184722 | −0.0923608 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923608 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(138\) | −4.13227 | − | 4.13227i | −0.351762 | − | 0.351762i | ||||
\(139\) | 16.1123 | − | 6.67394i | 1.36663 | − | 0.566076i | 0.425757 | − | 0.904838i | \(-0.360008\pi\) |
0.940872 | + | 0.338761i | \(0.110008\pi\) | |||||||
\(140\) | − | 9.74790i | − | 0.823848i | ||||||
\(141\) | 0.766533 | + | 1.85057i | 0.0645537 | + | 0.155846i | ||||
\(142\) | 24.0677 | + | 9.96919i | 2.01972 | + | 0.836595i | ||||
\(143\) | −1.69645 | + | 4.09560i | −0.141865 | + | 0.342492i | ||||
\(144\) | 2.23390 | − | 2.23390i | 0.186159 | − | 0.186159i | ||||
\(145\) | −13.8356 | + | 13.8356i | −1.14899 | + | 1.14899i | ||||
\(146\) | −1.57419 | + | 3.80043i | −0.130281 | + | 0.314526i | ||||
\(147\) | 9.70840 | + | 4.02135i | 0.800735 | + | 0.331675i | ||||
\(148\) | −21.6695 | − | 52.3149i | −1.78122 | − | 4.30026i | ||||
\(149\) | 1.65045i | 0.135210i | 0.997712 | + | 0.0676051i | \(0.0215358\pi\) | ||||
−0.997712 | + | 0.0676051i | \(0.978464\pi\) | |||||||
\(150\) | −3.65515 | + | 1.51401i | −0.298442 | + | 0.123619i | ||||
\(151\) | 2.24294 | + | 2.24294i | 0.182528 | + | 0.182528i | 0.792456 | − | 0.609929i | \(-0.208802\pi\) |
−0.609929 | + | 0.792456i | \(0.708802\pi\) | |||||||
\(152\) | −64.7831 | −5.25460 | ||||||||
\(153\) | 0.300394 | − | 0.740287i | 0.0242854 | − | 0.0598486i | ||||
\(154\) | 3.20497 | 0.258264 | ||||||||
\(155\) | 1.46646 | + | 1.46646i | 0.117789 | + | 0.117789i | ||||
\(156\) | −28.2879 | + | 11.7172i | −2.26484 | + | 0.938128i | ||||
\(157\) | 12.3729i | 0.987466i | 0.869614 | + | 0.493733i | \(0.164368\pi\) | ||||
−0.869614 | + | 0.493733i | \(0.835632\pi\) | |||||||
\(158\) | −1.96968 | − | 4.75524i | −0.156700 | − | 0.378306i | ||||
\(159\) | 19.0022 | + | 7.87095i | 1.50697 | + | 0.624207i | ||||
\(160\) | −19.5060 | + | 47.0916i | −1.54208 | + | 3.72292i | ||||
\(161\) | −0.762187 | + | 0.762187i | −0.0600688 | + | 0.0600688i | ||||
\(162\) | 16.3547 | − | 16.3547i | 1.28495 | − | 1.28495i | ||||
\(163\) | −4.73955 | + | 11.4423i | −0.371230 | + | 0.896228i | 0.622313 | + | 0.782769i | \(0.286193\pi\) |
−0.993543 | + | 0.113459i | \(0.963807\pi\) | |||||||
\(164\) | −12.7454 | − | 5.27931i | −0.995246 | − | 0.412245i | ||||
\(165\) | 1.77747 | + | 4.29120i | 0.138376 | + | 0.334069i | ||||
\(166\) | 10.7885i | 0.837349i | ||||||||
\(167\) | 17.4430 | − | 7.22514i | 1.34978 | − | 0.559098i | 0.413550 | − | 0.910481i | \(-0.364289\pi\) |
0.936232 | + | 0.351383i | \(0.114289\pi\) | |||||||
\(168\) | 10.0781 | + | 10.0781i | 0.777543 | + | 0.777543i | ||||
\(169\) | 2.40642 | 0.185109 | ||||||||
\(170\) | 0.167223 | + | 23.1626i | 0.0128254 | + | 1.77649i | ||||
\(171\) | 1.25804 | 0.0962046 | ||||||||
\(172\) | −3.97088 | − | 3.97088i | −0.302777 | − | 0.302777i | ||||
\(173\) | −1.21903 | + | 0.504937i | −0.0926808 | + | 0.0383896i | −0.428542 | − | 0.903522i | \(-0.640973\pi\) |
0.335861 | + | 0.941911i | \(0.390973\pi\) | |||||||
\(174\) | − | 44.4334i | − | 3.36849i | ||||||
\(175\) | 0.279256 | + | 0.674184i | 0.0211098 | + | 0.0509635i | ||||
\(176\) | −20.5164 | − | 8.49817i | −1.54648 | − | 0.640574i | ||||
\(177\) | 6.66016 | − | 16.0791i | 0.500608 | − | 1.20858i | ||||
\(178\) | 9.23394 | − | 9.23394i | 0.692113 | − | 0.692113i | ||||
\(179\) | −0.982287 | + | 0.982287i | −0.0734196 | + | 0.0734196i | −0.742863 | − | 0.669443i | \(-0.766533\pi\) |
0.669443 | + | 0.742863i | \(0.266533\pi\) | |||||||
\(180\) | 0.847688 | − | 2.04650i | 0.0631829 | − | 0.152537i | ||||
\(181\) | −8.00682 | − | 3.31653i | −0.595142 | − | 0.246516i | 0.0647190 | − | 0.997904i | \(-0.479385\pi\) |
−0.659861 | + | 0.751388i | \(0.729385\pi\) | |||||||
\(182\) | 2.93092 | + | 7.07587i | 0.217254 | + | 0.524499i | ||||
\(183\) | − | 5.71978i | − | 0.422818i | ||||||
\(184\) | 11.6532 | − | 4.82691i | 0.859085 | − | 0.355845i | ||||
\(185\) | −14.5149 | − | 14.5149i | −1.06716 | − | 1.06716i | ||||
\(186\) | −4.70958 | −0.345323 | ||||||||
\(187\) | −5.61558 | + | 0.0405418i | −0.410652 | + | 0.00296471i | ||||
\(188\) | −6.71476 | −0.489724 | ||||||||
\(189\) | −3.22581 | − | 3.22581i | −0.234643 | − | 0.234643i | ||||
\(190\) | −33.6984 | + | 13.9583i | −2.44474 | + | 1.01264i | ||||
\(191\) | 12.4129i | 0.898164i | 0.893490 | + | 0.449082i | \(0.148249\pi\) | ||||
−0.893490 | + | 0.449082i | \(0.851751\pi\) | |||||||
\(192\) | −23.3916 | − | 56.4722i | −1.68814 | − | 4.07553i | ||||
\(193\) | 22.3594 | + | 9.26157i | 1.60947 | + | 0.666663i | 0.992714 | − | 0.120495i | \(-0.0384481\pi\) |
0.616752 | + | 0.787157i | \(0.288448\pi\) | |||||||
\(194\) | −3.18644 | + | 7.69275i | −0.228773 | + | 0.552307i | ||||
\(195\) | −7.84854 | + | 7.84854i | −0.562045 | + | 0.562045i | ||||
\(196\) | −24.9090 | + | 24.9090i | −1.77922 | + | 1.77922i | ||||
\(197\) | −2.06791 | + | 4.99239i | −0.147333 | + | 0.355693i | −0.980267 | − | 0.197680i | \(-0.936659\pi\) |
0.832934 | + | 0.553373i | \(0.186659\pi\) | |||||||
\(198\) | 0.672861 | + | 0.278708i | 0.0478181 | + | 0.0198069i | ||||
\(199\) | −0.0293660 | − | 0.0708958i | −0.00208170 | − | 0.00502567i | 0.922835 | − | 0.385195i | \(-0.125866\pi\) |
−0.924917 | + | 0.380169i | \(0.875866\pi\) | |||||||
\(200\) | − | 8.53918i | − | 0.603811i | ||||||
\(201\) | 0.383785 | − | 0.158969i | 0.0270701 | − | 0.0112128i | ||||
\(202\) | −34.3213 | − | 34.3213i | −2.41484 | − | 2.41484i | ||||
\(203\) | −8.19563 | −0.575221 | ||||||||
\(204\) | −27.6240 | − | 27.2279i | −1.93406 | − | 1.90634i | ||||
\(205\) | −5.00099 | −0.349284 | ||||||||
\(206\) | 15.8706 | + | 15.8706i | 1.10576 | + | 1.10576i | ||||
\(207\) | −0.226296 | + | 0.0937349i | −0.0157287 | + | 0.00651503i | ||||
\(208\) | − | 53.0672i | − | 3.67955i | ||||||
\(209\) | −3.38407 | − | 8.16988i | −0.234081 | − | 0.565122i | ||||
\(210\) | 7.41380 | + | 3.07090i | 0.511601 | + | 0.211912i | ||||
\(211\) | 8.87785 | − | 21.4330i | 0.611176 | − | 1.47551i | −0.250533 | − | 0.968108i | \(-0.580606\pi\) |
0.861710 | − | 0.507402i | \(-0.169394\pi\) | |||||||
\(212\) | −48.7542 | + | 48.7542i | −3.34845 | + | 3.34845i | ||||
\(213\) | −11.1818 | + | 11.1818i | −0.766167 | + | 0.766167i | ||||
\(214\) | −16.4119 | + | 39.6218i | −1.12189 | + | 2.70849i | ||||
\(215\) | −1.88077 | − | 0.779040i | −0.128267 | − | 0.0531301i | ||||
\(216\) | 20.4290 | + | 49.3200i | 1.39002 | + | 3.35580i | ||||
\(217\) | 0.868671i | 0.0589692i | ||||||||
\(218\) | −18.1759 | + | 7.52871i | −1.23103 | + | 0.509908i | ||||
\(219\) | −1.76567 | − | 1.76567i | −0.119313 | − | 0.119313i | ||||
\(220\) | −15.5705 | −1.04976 | ||||||||
\(221\) | −5.22491 | − | 12.3609i | −0.351465 | − | 0.831482i | ||||
\(222\) | 46.6149 | 3.12859 | ||||||||
\(223\) | −13.0424 | − | 13.0424i | −0.873381 | − | 0.873381i | 0.119458 | − | 0.992839i | \(-0.461884\pi\) |
−0.992839 | + | 0.119458i | \(0.961884\pi\) | |||||||
\(224\) | −19.7248 | + | 8.17028i | −1.31792 | + | 0.545900i | ||||
\(225\) | 0.165824i | 0.0110550i | ||||||||
\(226\) | 6.98133 | + | 16.8544i | 0.464391 | + | 1.12114i | ||||
\(227\) | −10.7335 | − | 4.44595i | −0.712406 | − | 0.295088i | −0.00310592 | − | 0.999995i | \(-0.500989\pi\) |
−0.709300 | + | 0.704907i | \(0.750989\pi\) | |||||||
\(228\) | 23.3734 | − | 56.4284i | 1.54794 | − | 3.73706i | ||||
\(229\) | −11.6060 | + | 11.6060i | −0.766943 | + | 0.766943i | −0.977567 | − | 0.210624i | \(-0.932450\pi\) |
0.210624 | + | 0.977567i | \(0.432450\pi\) | |||||||
\(230\) | 5.02165 | − | 5.02165i | 0.331118 | − | 0.331118i | ||||
\(231\) | −0.744513 | + | 1.79741i | −0.0489854 | + | 0.118261i | ||||
\(232\) | 88.6036 | + | 36.7008i | 5.81711 | + | 2.40953i | ||||
\(233\) | −5.52181 | − | 13.3308i | −0.361746 | − | 0.873332i | −0.995045 | − | 0.0994249i | \(-0.968300\pi\) |
0.633299 | − | 0.773907i | \(-0.281700\pi\) | |||||||
\(234\) | 1.74040i | 0.113774i | ||||||||
\(235\) | −2.24887 | + | 0.931513i | −0.146700 | + | 0.0607652i | ||||
\(236\) | 41.2543 | + | 41.2543i | 2.68543 | + | 2.68543i | ||||
\(237\) | 3.12439 | 0.202951 | ||||||||
\(238\) | −6.81075 | + | 6.90980i | −0.441475 | + | 0.447896i | ||||
\(239\) | 1.82310 | 0.117926 | 0.0589632 | − | 0.998260i | \(-0.481221\pi\) | ||||
0.0589632 | + | 0.998260i | \(0.481221\pi\) | |||||||
\(240\) | −39.3163 | − | 39.3163i | −2.53785 | − | 2.53785i | ||||
\(241\) | −3.04039 | + | 1.25937i | −0.195849 | + | 0.0811232i | −0.478452 | − | 0.878114i | \(-0.658802\pi\) |
0.282603 | + | 0.959237i | \(0.408802\pi\) | |||||||
\(242\) | 25.2368i | 1.62228i | ||||||||
\(243\) | −0.769363 | − | 1.85741i | −0.0493546 | − | 0.119153i | ||||
\(244\) | 17.7147 | + | 7.33768i | 1.13407 | + | 0.469747i | ||||
\(245\) | −4.88686 | + | 11.7979i | −0.312210 | + | 0.753742i | ||||
\(246\) | 8.03039 | − | 8.03039i | 0.511999 | − | 0.511999i | ||||
\(247\) | 14.9426 | − | 14.9426i | 0.950773 | − | 0.950773i | ||||
\(248\) | 3.88999 | − | 9.39126i | 0.247014 | − | 0.596346i | ||||
\(249\) | −6.05040 | − | 2.50616i | −0.383429 | − | 0.158821i | ||||
\(250\) | −12.5893 | − | 30.3932i | −0.796215 | − | 1.92223i | ||||
\(251\) | 25.6059i | 1.61623i | 0.589025 | + | 0.808115i | \(0.299512\pi\) | ||||
−0.589025 | + | 0.808115i | \(0.700488\pi\) | |||||||
\(252\) | 0.857197 | − | 0.355063i | 0.0539984 | − | 0.0223669i | ||||
\(253\) | 1.21746 | + | 1.21746i | 0.0765408 | + | 0.0765408i | ||||
\(254\) | −42.0531 | −2.63865 | ||||||||
\(255\) | −13.0289 | − | 5.28687i | −0.815901 | − | 0.331077i | ||||
\(256\) | 66.7132 | 4.16958 | ||||||||
\(257\) | 15.0470 | + | 15.0470i | 0.938603 | + | 0.938603i | 0.998221 | − | 0.0596182i | \(-0.0189883\pi\) |
−0.0596182 | + | 0.998221i | \(0.518988\pi\) | |||||||
\(258\) | 4.27102 | − | 1.76911i | 0.265902 | − | 0.110140i | ||||
\(259\) | − | 8.59801i | − | 0.534254i | ||||||
\(260\) | −14.2391 | − | 34.3762i | −0.883072 | − | 2.13192i | ||||
\(261\) | −1.72061 | − | 0.712701i | −0.106503 | − | 0.0441151i | ||||
\(262\) | 11.0100 | − | 26.5805i | 0.680201 | − | 1.64215i | ||||
\(263\) | 14.2682 | − | 14.2682i | 0.879818 | − | 0.879818i | −0.113698 | − | 0.993515i | \(-0.536270\pi\) |
0.993515 | + | 0.113698i | \(0.0362695\pi\) | |||||||
\(264\) | 16.0980 | − | 16.0980i | 0.990761 | − | 0.990761i | ||||
\(265\) | −9.56501 | + | 23.0920i | −0.587574 | + | 1.41853i | ||||
\(266\) | −14.1149 | − | 5.84658i | −0.865440 | − | 0.358477i | ||||
\(267\) | 3.03354 | + | 7.32361i | 0.185650 | + | 0.448198i | ||||
\(268\) | 1.39255i | 0.0850637i | ||||||||
\(269\) | 11.9062 | − | 4.93172i | 0.725936 | − | 0.300692i | 0.0110549 | − | 0.999939i | \(-0.496481\pi\) |
0.714881 | + | 0.699247i | \(0.246481\pi\) | |||||||
\(270\) | 21.2532 | + | 21.2532i | 1.29343 | + | 1.29343i | ||||
\(271\) | 3.90023 | 0.236922 | 0.118461 | − | 0.992959i | \(-0.462204\pi\) | ||||
0.118461 | + | 0.992959i | \(0.462204\pi\) | |||||||
\(272\) | 61.9202 | − | 26.1735i | 3.75447 | − | 1.58700i | ||||
\(273\) | −4.64914 | −0.281379 | ||||||||
\(274\) | 4.21907 | + | 4.21907i | 0.254883 | + | 0.254883i | ||||
\(275\) | 1.07689 | − | 0.446061i | 0.0649387 | − | 0.0268985i | ||||
\(276\) | 11.8919i | 0.715808i | ||||||||
\(277\) | −10.7766 | − | 26.0169i | −0.647501 | − | 1.56321i | −0.816345 | − | 0.577564i | \(-0.804003\pi\) |
0.168844 | − | 0.985643i | \(-0.445997\pi\) | |||||||
\(278\) | −44.4644 | − | 18.4177i | −2.66680 | − | 1.10462i | ||||
\(279\) | −0.0755405 | + | 0.182371i | −0.00452249 | + | 0.0109183i | ||||
\(280\) | −12.2472 | + | 12.2472i | −0.731911 | + | 0.731911i | ||||
\(281\) | 22.0570 | − | 22.0570i | 1.31581 | − | 1.31581i | 0.398753 | − | 0.917058i | \(-0.369443\pi\) |
0.917058 | − | 0.398753i | \(-0.130557\pi\) | |||||||
\(282\) | 2.11536 | − | 5.10694i | 0.125968 | − | 0.304114i | ||||
\(283\) | 9.50148 | + | 3.93564i | 0.564804 | + | 0.233950i | 0.646769 | − | 0.762686i | \(-0.276120\pi\) |
−0.0819652 | + | 0.996635i | \(0.526120\pi\) | |||||||
\(284\) | −20.2865 | − | 48.9759i | −1.20378 | − | 2.90619i | ||||
\(285\) | − | 22.1412i | − | 1.31153i | ||||||
\(286\) | 11.3024 | − | 4.68162i | 0.668327 | − | 0.276830i | ||||
\(287\) | −1.48119 | − | 1.48119i | −0.0874317 | − | 0.0874317i | ||||
\(288\) | −4.85157 | −0.285882 | ||||||||
\(289\) | 11.8460 | − | 12.1931i | 0.696824 | − | 0.717243i | ||||
\(290\) | 53.9967 | 3.17080 | ||||||||
\(291\) | −3.57404 | − | 3.57404i | −0.209514 | − | 0.209514i | ||||
\(292\) | 7.73357 | − | 3.20335i | 0.452573 | − | 0.187462i | ||||
\(293\) | 20.0323i | 1.17030i | 0.810926 | + | 0.585149i | \(0.198964\pi\) | ||||
−0.810926 | + | 0.585149i | \(0.801036\pi\) | |||||||
\(294\) | −11.0975 | − | 26.7918i | −0.647220 | − | 1.56253i | ||||
\(295\) | 19.5397 | + | 8.09362i | 1.13765 | + | 0.471229i | ||||
\(296\) | −38.5027 | + | 92.9537i | −2.23792 | + | 5.40282i | ||||
\(297\) | −5.15266 | + | 5.15266i | −0.298987 | + | 0.298987i | ||||
\(298\) | 3.22063 | − | 3.22063i | 0.186566 | − | 0.186566i | ||||
\(299\) | −1.57452 | + | 3.80123i | −0.0910569 | + | 0.219831i | ||||
\(300\) | 7.43794 | + | 3.08089i | 0.429429 | + | 0.177876i | ||||
\(301\) | −0.326309 | − | 0.787780i | −0.0188081 | − | 0.0454069i | ||||
\(302\) | − | 8.75358i | − | 0.503712i | ||||||
\(303\) | 27.2209 | − | 11.2752i | 1.56380 | − | 0.647746i | ||||
\(304\) | 74.8530 | + | 74.8530i | 4.29311 | + | 4.29311i | ||||
\(305\) | 6.95084 | 0.398004 | ||||||||
\(306\) | −2.03075 | + | 0.858392i | −0.116090 | + | 0.0490710i | ||||
\(307\) | −12.2411 | −0.698634 | −0.349317 | − | 0.937005i | \(-0.613586\pi\) | ||||
−0.349317 | + | 0.937005i | \(0.613586\pi\) | |||||||
\(308\) | −4.61166 | − | 4.61166i | −0.262774 | − | 0.262774i | ||||
\(309\) | −12.5873 | + | 5.21383i | −0.716067 | + | 0.296605i | ||||
\(310\) | − | 5.72322i | − | 0.325057i | ||||||
\(311\) | 7.45681 | + | 18.0023i | 0.422837 | + | 1.02082i | 0.981507 | + | 0.191428i | \(0.0613119\pi\) |
−0.558670 | + | 0.829390i | \(0.688688\pi\) | |||||||
\(312\) | 50.2622 | + | 20.8193i | 2.84554 | + | 1.17866i | ||||
\(313\) | −7.22100 | + | 17.4330i | −0.408155 | + | 0.985374i | 0.577468 | + | 0.816414i | \(0.304041\pi\) |
−0.985623 | + | 0.168960i | \(0.945959\pi\) | |||||||
\(314\) | 24.1441 | − | 24.1441i | 1.36253 | − | 1.36253i | ||||
\(315\) | 0.237831 | − | 0.237831i | 0.0134003 | − | 0.0134003i | ||||
\(316\) | −4.00815 | + | 9.67653i | −0.225476 | + | 0.544347i | ||||
\(317\) | −6.57904 | − | 2.72513i | −0.369516 | − | 0.153058i | 0.190195 | − | 0.981746i | \(-0.439088\pi\) |
−0.559711 | + | 0.828688i | \(0.689088\pi\) | |||||||
\(318\) | −21.7211 | − | 52.4393i | −1.21806 | − | 2.94065i | ||||
\(319\) | 13.0910i | 0.732958i | ||||||||
\(320\) | 68.6267 | − | 28.4261i | 3.83635 | − | 1.58907i | ||||
\(321\) | −18.4082 | − | 18.4082i | −1.02745 | − | 1.02745i | ||||
\(322\) | 2.97461 | 0.165769 | ||||||||
\(323\) | 24.8053 | + | 10.0655i | 1.38020 | + | 0.560060i | ||||
\(324\) | −47.0658 | −2.61477 | ||||||||
\(325\) | 1.96961 | + | 1.96961i | 0.109254 | + | 0.109254i | ||||
\(326\) | 31.5767 | − | 13.0795i | 1.74887 | − | 0.724406i | ||||
\(327\) | − | 11.9423i | − | 0.660412i | ||||||
\(328\) | 9.38033 | + | 22.6461i | 0.517942 | + | 1.25042i | ||||
\(329\) | −0.941963 | − | 0.390174i | −0.0519321 | − | 0.0215110i | ||||
\(330\) | 4.90520 | − | 11.8422i | 0.270023 | − | 0.651892i | ||||
\(331\) | −5.18062 | + | 5.18062i | −0.284752 | + | 0.284752i | −0.835001 | − | 0.550249i | \(-0.814533\pi\) |
0.550249 | + | 0.835001i | \(0.314533\pi\) | |||||||
\(332\) | 15.5236 | − | 15.5236i | 0.851970 | − | 0.851970i | ||||
\(333\) | 0.747692 | − | 1.80509i | 0.0409733 | − | 0.0989182i | ||||
\(334\) | −48.1367 | − | 19.9389i | −2.63392 | − | 1.09101i | ||||
\(335\) | 0.193184 | + | 0.466386i | 0.0105547 | + | 0.0254814i | ||||
\(336\) | − | 23.2893i | − | 1.27053i | ||||||
\(337\) | −26.7596 | + | 11.0842i | −1.45769 | + | 0.603795i | −0.964014 | − | 0.265851i | \(-0.914347\pi\) |
−0.493675 | + | 0.869646i | \(0.664347\pi\) | |||||||
\(338\) | −4.69581 | − | 4.69581i | −0.255418 | − | 0.255418i | ||||
\(339\) | −11.0740 | −0.601460 | ||||||||
\(340\) | 33.0882 | − | 33.5694i | 1.79446 | − | 1.82056i | ||||
\(341\) | 1.38754 | 0.0751398 | ||||||||
\(342\) | −2.45489 | − | 2.45489i | −0.132745 | − | 0.132745i | ||||
\(343\) | −10.4561 | + | 4.33108i | −0.564578 | + | 0.233856i | ||||
\(344\) | 9.97798i | 0.537977i | ||||||||
\(345\) | 1.64972 | + | 3.98277i | 0.0888177 | + | 0.214425i | ||||
\(346\) | 3.36408 | + | 1.39345i | 0.180854 | + | 0.0749123i | ||||
\(347\) | −0.434423 | + | 1.04879i | −0.0233210 | + | 0.0563020i | −0.935111 | − | 0.354355i | \(-0.884701\pi\) |
0.911790 | + | 0.410657i | \(0.134701\pi\) | |||||||
\(348\) | −63.9354 | + | 63.9354i | −3.42730 | + | 3.42730i | ||||
\(349\) | 10.9036 | − | 10.9036i | 0.583658 | − | 0.583658i | −0.352249 | − | 0.935906i | \(-0.614583\pi\) |
0.935906 | + | 0.352249i | \(0.114583\pi\) | |||||||
\(350\) | 0.770649 | − | 1.86051i | 0.0411929 | − | 0.0994485i | ||||
\(351\) | −16.0880 | − | 6.66386i | −0.858713 | − | 0.355691i | ||||
\(352\) | 13.0505 | + | 31.5068i | 0.695597 | + | 1.67932i | ||||
\(353\) | − | 23.2851i | − | 1.23934i | −0.784863 | − | 0.619670i | \(-0.787267\pi\) | ||
0.784863 | − | 0.619670i | \(-0.212733\pi\) | |||||||
\(354\) | −44.3726 | + | 18.3797i | −2.35837 | + | 0.976871i | ||||
\(355\) | −13.5885 | − | 13.5885i | −0.721202 | − | 0.721202i | ||||
\(356\) | −26.5735 | −1.40839 | ||||||||
\(357\) | −2.29302 | − | 5.42474i | −0.121360 | − | 0.287108i | ||||
\(358\) | 3.83361 | 0.202612 | ||||||||
\(359\) | −9.49136 | − | 9.49136i | −0.500935 | − | 0.500935i | 0.410794 | − | 0.911728i | \(-0.365252\pi\) |
−0.911728 | + | 0.410794i | \(0.865252\pi\) | |||||||
\(360\) | −3.63624 | + | 1.50618i | −0.191647 | + | 0.0793827i | ||||
\(361\) | 23.1540i | 1.21863i | ||||||||
\(362\) | 9.15247 | + | 22.0960i | 0.481043 | + | 1.16134i | ||||
\(363\) | −14.1533 | − | 5.86248i | −0.742855 | − | 0.307701i | ||||
\(364\) | 5.96420 | − | 14.3988i | 0.312609 | − | 0.754704i | ||||
\(365\) | 2.14570 | − | 2.14570i | 0.112311 | − | 0.112311i | ||||
\(366\) | −11.1614 | + | 11.1614i | −0.583415 | + | 0.583415i | ||||
\(367\) | 6.54457 | − | 15.8000i | 0.341624 | − | 0.824753i | −0.655928 | − | 0.754824i | \(-0.727722\pi\) |
0.997552 | − | 0.0699298i | \(-0.0222775\pi\) | |||||||
\(368\) | −19.0418 | − | 7.88736i | −0.992621 | − | 0.411157i | ||||
\(369\) | −0.182159 | − | 0.439770i | −0.00948280 | − | 0.0228935i | ||||
\(370\) | 56.6478i | 2.94498i | ||||||||
\(371\) | −9.67231 | + | 4.00640i | −0.502161 | + | 0.208002i | ||||
\(372\) | 6.77664 | + | 6.77664i | 0.351352 | + | 0.351352i | ||||
\(373\) | 2.00560 | 0.103846 | 0.0519230 | − | 0.998651i | \(-0.483465\pi\) | ||||
0.0519230 | + | 0.998651i | \(0.483465\pi\) | |||||||
\(374\) | 11.0372 | + | 10.8789i | 0.570718 | + | 0.562537i | ||||
\(375\) | 19.9696 | 1.03122 | ||||||||
\(376\) | 8.43639 | + | 8.43639i | 0.435074 | + | 0.435074i | ||||
\(377\) | −28.9021 | + | 11.9717i | −1.48854 | + | 0.616572i | ||||
\(378\) | 12.5895i | 0.647534i | ||||||||
\(379\) | −6.01110 | − | 14.5121i | −0.308769 | − | 0.745435i | −0.999746 | − | 0.0225576i | \(-0.992819\pi\) |
0.690976 | − | 0.722877i | \(-0.257181\pi\) | |||||||
\(380\) | 68.5735 | + | 28.4041i | 3.51775 | + | 1.45710i | ||||
\(381\) | 9.76890 | − | 23.5842i | 0.500476 | − | 1.20826i | ||||
\(382\) | 24.2221 | − | 24.2221i | 1.23931 | − | 1.23931i | ||||
\(383\) | 20.0752 | − | 20.0752i | 1.02579 | − | 1.02579i | 0.0261359 | − | 0.999658i | \(-0.491680\pi\) |
0.999658 | − | 0.0261359i | \(-0.00832027\pi\) | |||||||
\(384\) | −32.4500 | + | 78.3412i | −1.65596 | + | 3.99783i | ||||
\(385\) | −2.18427 | − | 0.904754i | −0.111321 | − | 0.0461105i | ||||
\(386\) | −25.5587 | − | 61.7042i | −1.30090 | − | 3.14066i | ||||
\(387\) | − | 0.193765i | − | 0.00984961i | ||||||
\(388\) | 15.6541 | − | 6.48416i | 0.794718 | − | 0.329183i | ||||
\(389\) | 9.30279 | + | 9.30279i | 0.471670 | + | 0.471670i | 0.902455 | − | 0.430784i | \(-0.141763\pi\) |
−0.430784 | + | 0.902455i | \(0.641763\pi\) | |||||||
\(390\) | 30.6308 | 1.55105 | ||||||||
\(391\) | −5.21195 | + | 0.0376278i | −0.263580 | + | 0.00190292i | ||||
\(392\) | 62.5911 | 3.16133 | ||||||||
\(393\) | 12.3493 | + | 12.3493i | 0.622938 | + | 0.622938i | ||||
\(394\) | 13.7772 | − | 5.70672i | 0.694087 | − | 0.287500i | ||||
\(395\) | 3.79684i | 0.191040i | ||||||||
\(396\) | −0.567149 | − | 1.36922i | −0.0285003 | − | 0.0688058i | ||||
\(397\) | −9.74100 | − | 4.03485i | −0.488887 | − | 0.202503i | 0.124602 | − | 0.992207i | \(-0.460234\pi\) |
−0.613489 | + | 0.789703i | \(0.710234\pi\) | |||||||
\(398\) | −0.0810399 | + | 0.195648i | −0.00406216 | + | 0.00980692i | ||||
\(399\) | 6.55776 | − | 6.55776i | 0.328299 | − | 0.328299i | ||||
\(400\) | −9.86651 | + | 9.86651i | −0.493325 | + | 0.493325i | ||||
\(401\) | 13.6813 | − | 33.0297i | 0.683214 | − | 1.64942i | −0.0748109 | − | 0.997198i | \(-0.523835\pi\) |
0.758025 | − | 0.652226i | \(-0.226165\pi\) | |||||||
\(402\) | −1.05911 | − | 0.438698i | −0.0528237 | − | 0.0218803i | ||||
\(403\) | 1.26890 | + | 3.06339i | 0.0632083 | + | 0.152598i | ||||
\(404\) | 98.7702i | 4.91400i | ||||||||
\(405\) | −15.7630 | + | 6.52926i | −0.783271 | + | 0.324442i | ||||
\(406\) | 15.9927 | + | 15.9927i | 0.793704 | + | 0.793704i | ||||
\(407\) | −13.7338 | −0.680757 | ||||||||
\(408\) | 0.497539 | + | 68.9157i | 0.0246318 | + | 3.41183i | ||||
\(409\) | 13.6173 | 0.673332 | 0.336666 | − | 0.941624i | \(-0.390701\pi\) | ||||
0.336666 | + | 0.941624i | \(0.390701\pi\) | |||||||
\(410\) | 9.75877 | + | 9.75877i | 0.481951 | + | 0.481951i | ||||
\(411\) | −3.34623 | + | 1.38605i | −0.165057 | + | 0.0683689i | ||||
\(412\) | − | 45.6727i | − | 2.25013i | ||||||
\(413\) | 3.39010 | + | 8.18442i | 0.166816 | + | 0.402729i | ||||
\(414\) | 0.624498 | + | 0.258676i | 0.0306924 | + | 0.0127132i | ||||
\(415\) | 3.04556 | − | 7.35262i | 0.149500 | − | 0.360926i | ||||
\(416\) | −57.6254 | + | 57.6254i | −2.82532 | + | 2.82532i | ||||
\(417\) | 20.6581 | − | 20.6581i | 1.01163 | − | 1.01163i | ||||
\(418\) | −9.33886 | + | 22.5460i | −0.456779 | + | 1.10276i | ||||
\(419\) | −15.5120 | − | 6.42529i | −0.757812 | − | 0.313896i | −0.0298873 | − | 0.999553i | \(-0.509515\pi\) |
−0.727924 | + | 0.685657i | \(0.759515\pi\) | |||||||
\(420\) | −6.24903 | − | 15.0865i | −0.304922 | − | 0.736146i | ||||
\(421\) | − | 15.1135i | − | 0.736586i | −0.929710 | − | 0.368293i | \(-0.879942\pi\) | ||
0.929710 | − | 0.368293i | \(-0.120058\pi\) | |||||||
\(422\) | −59.1476 | + | 24.4998i | −2.87926 | + | 1.19263i | ||||
\(423\) | −0.163828 | − | 0.163828i | −0.00796560 | − | 0.00796560i | ||||
\(424\) | 122.509 | 5.94957 | ||||||||
\(425\) | −1.32675 | + | 3.26963i | −0.0643570 | + | 0.158600i | ||||
\(426\) | 43.6397 | 2.11435 | ||||||||
\(427\) | 2.05869 | + | 2.05869i | 0.0996272 | + | 0.0996272i | ||||
\(428\) | 80.6271 | − | 33.3968i | 3.89726 | − | 1.61430i | ||||
\(429\) | 7.42616i | 0.358539i | ||||||||
\(430\) | 2.14988 | + | 5.19027i | 0.103676 | + | 0.250297i | ||||
\(431\) | −24.6128 | − | 10.1950i | −1.18556 | − | 0.491074i | −0.299252 | − | 0.954174i | \(-0.596737\pi\) |
−0.886306 | + | 0.463100i | \(0.846737\pi\) | |||||||
\(432\) | 33.3818 | − | 80.5907i | 1.60608 | − | 3.87742i | ||||
\(433\) | −22.2348 | + | 22.2348i | −1.06854 | + | 1.06854i | −0.0710636 | + | 0.997472i | \(0.522639\pi\) |
−0.997472 | + | 0.0710636i | \(0.977361\pi\) | |||||||
\(434\) | 1.69510 | − | 1.69510i | 0.0813672 | − | 0.0813672i | ||||
\(435\) | −12.5434 | + | 30.2824i | −0.601410 | + | 1.45193i | ||||
\(436\) | 36.9865 | + | 15.3203i | 1.77133 | + | 0.733710i | ||||
\(437\) | −3.14084 | − | 7.58266i | −0.150247 | − | 0.362728i | ||||
\(438\) | 6.89095i | 0.329262i | ||||||||
\(439\) | −17.2583 | + | 7.14864i | −0.823696 | + | 0.341186i | −0.754404 | − | 0.656410i | \(-0.772074\pi\) |
−0.0692920 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(440\) | 19.5627 | + | 19.5627i | 0.932616 | + | 0.932616i | ||||
\(441\) | −1.21547 | −0.0578796 | ||||||||
\(442\) | −13.9249 | + | 34.3163i | −0.662340 | + | 1.63226i | ||||
\(443\) | 31.5518 | 1.49907 | 0.749535 | − | 0.661965i | \(-0.230277\pi\) | ||||
0.749535 | + | 0.661965i | \(0.230277\pi\) | |||||||
\(444\) | −67.0744 | − | 67.0744i | −3.18321 | − | 3.18321i | ||||
\(445\) | −8.89987 | + | 3.68645i | −0.421894 | + | 0.174754i | ||||
\(446\) | 50.9009i | 2.41023i | ||||||||
\(447\) | 1.05804 | + | 2.55435i | 0.0500438 | + | 0.120816i | ||||
\(448\) | 28.7450 | + | 11.9066i | 1.35807 | + | 0.562533i | ||||
\(449\) | 2.99236 | − | 7.22419i | 0.141218 | − | 0.340931i | −0.837408 | − | 0.546578i | \(-0.815930\pi\) |
0.978626 | + | 0.205648i | \(0.0659301\pi\) | |||||||
\(450\) | 0.323584 | − | 0.323584i | 0.0152539 | − | 0.0152539i | ||||
\(451\) | −2.36593 | + | 2.36593i | −0.111407 | + | 0.111407i | ||||
\(452\) | 14.2064 | − | 34.2974i | 0.668215 | − | 1.61321i | ||||
\(453\) | 4.90918 | + | 2.03345i | 0.230654 | + | 0.0955398i | ||||
\(454\) | 12.2693 | + | 29.6206i | 0.575825 | + | 1.39016i | ||||
\(455\) | − | 5.64977i | − | 0.264865i | ||||||
\(456\) | −100.263 | + | 41.5302i | −4.69523 | + | 1.94483i | ||||
\(457\) | −20.1678 | − | 20.1678i | −0.943408 | − | 0.943408i | 0.0550746 | − | 0.998482i | \(-0.482460\pi\) |
−0.998482 | + | 0.0550746i | \(0.982460\pi\) | |||||||
\(458\) | 45.2950 | 2.11650 | ||||||||
\(459\) | −0.159253 | − | 22.0586i | −0.00743328 | − | 1.02961i | ||||
\(460\) | −14.4514 | −0.673799 | ||||||||
\(461\) | 8.54921 | + | 8.54921i | 0.398176 | + | 0.398176i | 0.877589 | − | 0.479413i | \(-0.159150\pi\) |
−0.479413 | + | 0.877589i | \(0.659150\pi\) | |||||||
\(462\) | 4.96023 | − | 2.05460i | 0.230771 | − | 0.0955884i | ||||
\(463\) | − | 11.9973i | − | 0.557562i | −0.960355 | − | 0.278781i | \(-0.910070\pi\) | ||
0.960355 | − | 0.278781i | \(-0.0899303\pi\) | |||||||
\(464\) | −59.9705 | − | 144.782i | −2.78406 | − | 6.72132i | ||||
\(465\) | 3.20969 | + | 1.32950i | 0.148846 | + | 0.0616540i | ||||
\(466\) | −15.2383 | + | 36.7884i | −0.705899 | + | 1.70419i | ||||
\(467\) | −17.3237 | + | 17.3237i | −0.801644 | + | 0.801644i | −0.983352 | − | 0.181709i | \(-0.941837\pi\) |
0.181709 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(468\) | 2.50428 | − | 2.50428i | 0.115760 | − | 0.115760i | ||||
\(469\) | −0.0809169 | + | 0.195351i | −0.00373640 | + | 0.00902046i | ||||
\(470\) | 6.20610 | + | 2.57065i | 0.286266 | + | 0.118575i | ||||
\(471\) | 7.93183 | + | 19.1491i | 0.365480 | + | 0.882346i | ||||
\(472\) | − | 103.663i | − | 4.77150i | ||||||
\(473\) | −1.25834 | + | 0.521220i | −0.0578583 | + | 0.0239657i | ||||
\(474\) | −6.09682 | − | 6.09682i | −0.280036 | − | 0.280036i | ||||
\(475\) | −5.55639 | −0.254945 | ||||||||
\(476\) | 19.7426 | − | 0.142532i | 0.904900 | − | 0.00653295i | ||||
\(477\) | −2.37903 | −0.108928 | ||||||||
\(478\) | −3.55754 | − | 3.55754i | −0.162718 | − | 0.162718i | ||||
\(479\) | 8.07082 | − | 3.34304i | 0.368765 | − | 0.152748i | −0.190602 | − | 0.981667i | \(-0.561044\pi\) |
0.559367 | + | 0.828920i | \(0.311044\pi\) | |||||||
\(480\) | 85.3867i | 3.89735i | ||||||||
\(481\) | −12.5594 | − | 30.3211i | −0.572660 | − | 1.38252i | ||||
\(482\) | 8.39041 | + | 3.47542i | 0.382173 | + | 0.158301i | ||||
\(483\) | −0.691000 | + | 1.66822i | −0.0314416 | + | 0.0759068i | ||||
\(484\) | 36.3134 | − | 36.3134i | 1.65061 | − | 1.65061i | ||||
\(485\) | 4.34328 | − | 4.34328i | 0.197218 | − | 0.197218i | ||||
\(486\) | −2.12317 | + | 5.12579i | −0.0963090 | + | 0.232511i | ||||
\(487\) | −6.91374 | − | 2.86376i | −0.313291 | − | 0.129770i | 0.220497 | − | 0.975388i | \(-0.429232\pi\) |
−0.533788 | + | 0.845618i | \(0.679232\pi\) | |||||||
\(488\) | −13.0377 | − | 31.4757i | −0.590187 | − | 1.42484i | ||||
\(489\) | 20.7472i | 0.938220i | ||||||||
\(490\) | 32.5582 | − | 13.4860i | 1.47083 | − | 0.609237i | ||||
\(491\) | 16.4576 | + | 16.4576i | 0.742719 | + | 0.742719i | 0.973100 | − | 0.230381i | \(-0.0739974\pi\) |
−0.230381 | + | 0.973100i | \(0.573997\pi\) | |||||||
\(492\) | −23.1100 | −1.04188 | ||||||||
\(493\) | −28.2238 | − | 27.8192i | −1.27114 | − | 1.25291i | ||||
\(494\) | −58.3169 | −2.62380 | ||||||||
\(495\) | −0.379893 | − | 0.379893i | −0.0170749 | − | 0.0170749i | ||||
\(496\) | −15.3457 | + | 6.35639i | −0.689041 | + | 0.285410i | ||||
\(497\) | − | 8.04925i | − | 0.361058i | ||||||
\(498\) | 6.91612 | + | 16.6970i | 0.309919 | + | 0.748210i | ||||
\(499\) | 22.4507 | + | 9.29937i | 1.00503 | + | 0.416297i | 0.823639 | − | 0.567114i | \(-0.191940\pi\) |
0.181391 | + | 0.983411i | \(0.441940\pi\) | |||||||
\(500\) | −25.6182 | + | 61.8477i | −1.14568 | + | 2.76591i | ||||
\(501\) | 22.3642 | − | 22.3642i | 0.999159 | − | 0.999159i | ||||
\(502\) | 49.9665 | − | 49.9665i | 2.23012 | − | 2.23012i | ||||
\(503\) | 8.39859 | − | 20.2760i | 0.374475 | − | 0.904061i | −0.618506 | − | 0.785780i | \(-0.712262\pi\) |
0.992980 | − | 0.118281i | \(-0.0377384\pi\) | |||||||
\(504\) | −1.52308 | − | 0.630879i | −0.0678433 | − | 0.0281016i | ||||
\(505\) | 13.7020 | + | 33.0796i | 0.609731 | + | 1.47202i | ||||
\(506\) | − | 4.75141i | − | 0.211226i | ||||||
\(507\) | 3.72434 | − | 1.54267i | 0.165404 | − | 0.0685124i | ||||
\(508\) | 60.5105 | + | 60.5105i | 2.68472 | + | 2.68472i | ||||
\(509\) | 39.6020 | 1.75533 | 0.877663 | − | 0.479278i | \(-0.159102\pi\) | ||||
0.877663 | + | 0.479278i | \(0.159102\pi\) | |||||||
\(510\) | 15.1075 | + | 35.7408i | 0.668973 | + | 1.58263i | ||||
\(511\) | 1.27102 | 0.0562266 | ||||||||
\(512\) | −58.5961 | − | 58.5961i | −2.58961 | − | 2.58961i | ||||
\(513\) | 32.0922 | − | 13.2930i | 1.41691 | − | 0.586901i | ||||
\(514\) | − | 58.7243i | − | 2.59022i | ||||||
\(515\) | −6.33600 | − | 15.2965i | −0.279198 | − | 0.674043i | ||||
\(516\) | −8.69118 | − | 3.60001i | −0.382608 | − | 0.158481i | ||||
\(517\) | −0.623232 | + | 1.50462i | −0.0274097 | + | 0.0661729i | ||||
\(518\) | −16.7779 | + | 16.7779i | −0.737177 | + | 0.737177i | ||||
\(519\) | −1.56295 | + | 1.56295i | −0.0686058 | + | 0.0686058i | ||||
\(520\) | −25.3002 | + | 61.0801i | −1.10949 | + | 2.67854i | ||||
\(521\) | −24.3017 | − | 10.0661i | −1.06468 | − | 0.441004i | −0.219568 | − | 0.975597i | \(-0.570465\pi\) |
−0.845109 | + | 0.534593i | \(0.820465\pi\) | |||||||
\(522\) | 1.96681 | + | 4.74829i | 0.0860848 | + | 0.207827i | ||||
\(523\) | 35.8861i | 1.56919i | 0.620009 | + | 0.784595i | \(0.287129\pi\) | ||||
−0.620009 | + | 0.784595i | \(0.712871\pi\) | |||||||
\(524\) | −54.0893 | + | 22.4045i | −2.36290 | + | 0.978746i | ||||
\(525\) | 0.864391 | + | 0.864391i | 0.0377251 | + | 0.0377251i | ||||
\(526\) | −55.6852 | −2.42799 | ||||||||
\(527\) | −2.94861 | + | 2.99149i | −0.128443 | + | 0.130312i | ||||
\(528\) | −37.2004 | −1.61894 | ||||||||
\(529\) | −15.1335 | − | 15.1335i | −0.657978 | − | 0.657978i | ||||
\(530\) | 63.7258 | − | 26.3961i | 2.76807 | − | 1.14657i | ||||
\(531\) | 2.01306i | 0.0873596i | ||||||||
\(532\) | 11.8973 | + | 28.7227i | 0.515815 | + | 1.24529i | ||||
\(533\) | −7.38707 | − | 3.05983i | −0.319970 | − | 0.132536i | ||||
\(534\) | 8.37151 | − | 20.2106i | 0.362271 | − | 0.874598i | ||||
\(535\) | 22.3702 | − | 22.3702i | 0.967147 | − | 0.967147i | ||||
\(536\) | 1.74960 | − | 1.74960i | 0.0755711 | − | 0.0755711i | ||||
\(537\) | −0.890544 | + | 2.14996i | −0.0384298 | + | 0.0927778i | ||||
\(538\) | −32.8570 | − | 13.6098i | −1.41657 | − | 0.586761i | ||||
\(539\) | 3.26957 | + | 7.89345i | 0.140830 | + | 0.339995i | ||||
\(540\) | − | 61.1627i | − | 2.63202i | ||||||
\(541\) | −5.73630 | + | 2.37605i | −0.246623 | + | 0.102154i | −0.502571 | − | 0.864536i | \(-0.667612\pi\) |
0.255948 | + | 0.966691i | \(0.417612\pi\) | |||||||
\(542\) | −7.61079 | − | 7.61079i | −0.326911 | − | 0.326911i | ||||
\(543\) | −14.5180 | −0.623027 | ||||||||
\(544\) | −95.6606 | − | 38.8172i | −4.10142 | − | 1.66427i | ||||
\(545\) | 14.5127 | 0.621654 | ||||||||
\(546\) | 9.07218 | + | 9.07218i | 0.388254 | + | 0.388254i | ||||
\(547\) | −34.8140 | + | 14.4204i | −1.48854 | + | 0.616573i | −0.970998 | − | 0.239087i | \(-0.923152\pi\) |
−0.517540 | + | 0.855659i | \(0.673152\pi\) | |||||||
\(548\) | − | 12.1417i | − | 0.518668i | ||||||
\(549\) | 0.253181 | + | 0.611234i | 0.0108055 | + | 0.0260868i | ||||
\(550\) | −2.97183 | − | 1.23097i | −0.126719 | − | 0.0524888i | ||||
\(551\) | 23.8810 | − | 57.6538i | 1.01736 | − | 2.45613i | ||||
\(552\) | 14.9409 | − | 14.9409i | 0.635927 | − | 0.635927i | ||||
\(553\) | −1.12455 | + | 1.12455i | −0.0478205 | + | 0.0478205i | ||||
\(554\) | −29.7396 | + | 71.7977i | −1.26351 | + | 3.05039i | ||||
\(555\) | −31.7692 | − | 13.1592i | −1.34853 | − | 0.558578i | ||||
\(556\) | 37.4786 | + | 90.4815i | 1.58945 | + | 3.83727i | ||||
\(557\) | − | 15.0954i | − | 0.639611i | −0.947483 | − | 0.319806i | \(-0.896382\pi\) | ||
0.947483 | − | 0.319806i | \(-0.103618\pi\) | |||||||
\(558\) | 0.503280 | − | 0.208465i | 0.0213055 | − | 0.00882505i | ||||
\(559\) | −2.30148 | − | 2.30148i | −0.0973420 | − | 0.0973420i | ||||
\(560\) | 28.3018 | 1.19597 | ||||||||
\(561\) | −8.66505 | + | 3.66269i | −0.365839 | + | 0.154639i | ||||
\(562\) | −86.0827 | −3.63118 | ||||||||
\(563\) | 29.4702 | + | 29.4702i | 1.24202 | + | 1.24202i | 0.959161 | + | 0.282861i | \(0.0912834\pi\) |
0.282861 | + | 0.959161i | \(0.408717\pi\) | |||||||
\(564\) | −10.3922 | + | 4.30460i | −0.437591 | + | 0.181256i | ||||
\(565\) | − | 13.4575i | − | 0.566162i | ||||||
\(566\) | −10.8610 | − | 26.2207i | −0.456521 | − | 1.10214i | ||||
\(567\) | −6.60251 | − | 2.73485i | −0.277279 | − | 0.114853i | ||||
\(568\) | −36.0453 | + | 87.0210i | −1.51243 | + | 3.65132i | ||||
\(569\) | −20.6335 | + | 20.6335i | −0.865002 | + | 0.865002i | −0.991914 | − | 0.126912i | \(-0.959493\pi\) |
0.126912 | + | 0.991914i | \(0.459493\pi\) | |||||||
\(570\) | −43.2056 | + | 43.2056i | −1.80969 | + | 1.80969i | ||||
\(571\) | −6.19180 | + | 14.9483i | −0.259119 | + | 0.625568i | −0.998881 | − | 0.0473005i | \(-0.984938\pi\) |
0.739762 | + | 0.672869i | \(0.234938\pi\) | |||||||
\(572\) | −22.9995 | − | 9.52673i | −0.961659 | − | 0.398332i | ||||
\(573\) | 7.95745 | + | 19.2110i | 0.332427 | + | 0.802551i | ||||
\(574\) | 5.78068i | 0.241281i | ||||||||
\(575\) | 0.999485 | − | 0.414000i | 0.0416814 | − | 0.0172650i | ||||
\(576\) | 4.99939 | + | 4.99939i | 0.208308 | + | 0.208308i | ||||
\(577\) | 18.5841 | 0.773666 | 0.386833 | − | 0.922150i | \(-0.373569\pi\) | ||||
0.386833 | + | 0.922150i | \(0.373569\pi\) | |||||||
\(578\) | −46.9092 | + | 0.677360i | −1.95116 | + | 0.0281744i | ||||
\(579\) | 40.5422 | 1.68488 | ||||||||
\(580\) | −77.6962 | − | 77.6962i | −3.22616 | − | 3.22616i | ||||
\(581\) | 3.07972 | − | 1.27566i | 0.127768 | − | 0.0529234i | ||||
\(582\) | 13.9485i | 0.578185i | ||||||||
\(583\) | 6.39950 | + | 15.4498i | 0.265040 | + | 0.639864i | ||||
\(584\) | −13.7411 | − | 5.69174i | −0.568610 | − | 0.235526i | ||||
\(585\) | 0.491310 | − | 1.18613i | 0.0203132 | − | 0.0490404i | ||||
\(586\) | 39.0903 | − | 39.0903i | 1.61481 | − | 1.61481i | ||||
\(587\) | 32.2970 | − | 32.2970i | 1.33304 | − | 1.33304i | 0.430399 | − | 0.902639i | \(-0.358373\pi\) |
0.902639 | − | 0.430399i | \(-0.141627\pi\) | |||||||
\(588\) | −22.5826 | + | 54.5191i | −0.931289 | + | 2.24833i | ||||
\(589\) | −6.11083 | − | 2.53119i | −0.251792 | − | 0.104296i | ||||
\(590\) | −22.3356 | − | 53.9228i | −0.919541 | − | 2.21997i | ||||
\(591\) | 9.05222i | 0.372358i | ||||||||
\(592\) | 151.890 | − | 62.9148i | 6.24263 | − | 2.58578i | ||||
\(593\) | −26.1923 | − | 26.1923i | −1.07559 | − | 1.07559i | −0.996899 | − | 0.0786906i | \(-0.974926\pi\) |
−0.0786906 | − | 0.996899i | \(-0.525074\pi\) | |||||||
\(594\) | 20.1094 | 0.825101 | ||||||||
\(595\) | 6.59231 | − | 2.78655i | 0.270258 | − | 0.114237i | ||||
\(596\) | −9.26838 | −0.379648 | ||||||||
\(597\) | −0.0908975 | − | 0.0908975i | −0.00372019 | − | 0.00372019i | ||||
\(598\) | 10.4901 | − | 4.34513i | 0.428970 | − | 0.177685i | ||||
\(599\) | − | 15.9949i | − | 0.653534i | −0.945105 | − | 0.326767i | \(-0.894041\pi\) | ||
0.945105 | − | 0.326767i | \(-0.105959\pi\) | |||||||
\(600\) | −5.47417 | − | 13.2158i | −0.223482 | − | 0.539533i | ||||
\(601\) | −29.1125 | − | 12.0588i | −1.18752 | − | 0.491888i | −0.300575 | − | 0.953758i | \(-0.597178\pi\) |
−0.886947 | + | 0.461870i | \(0.847178\pi\) | |||||||
\(602\) | −0.900499 | + | 2.17400i | −0.0367016 | + | 0.0886055i | ||||
\(603\) | −0.0339758 | + | 0.0339758i | −0.00138360 | + | 0.00138360i | ||||
\(604\) | −12.5956 | + | 12.5956i | −0.512507 | + | 0.512507i | ||||
\(605\) | 7.12426 | − | 17.1995i | 0.289642 | − | 0.699259i | ||||
\(606\) | −75.1200 | − | 31.1157i | −3.05154 | − | 1.26399i | ||||
\(607\) | 9.20355 | + | 22.2193i | 0.373560 | + | 0.901855i | 0.993141 | + | 0.116922i | \(0.0373027\pi\) |
−0.619581 | + | 0.784933i | \(0.712697\pi\) | |||||||
\(608\) | − | 162.565i | − | 6.59288i | ||||||
\(609\) | −12.6841 | + | 5.25393i | −0.513986 | + | 0.212900i | ||||
\(610\) | −13.5637 | − | 13.5637i | −0.549176 | − | 0.549176i | ||||
\(611\) | −3.89180 | −0.157445 | ||||||||
\(612\) | 4.15720 | + | 1.68691i | 0.168045 | + | 0.0681894i | ||||
\(613\) | −39.8476 | −1.60943 | −0.804716 | − | 0.593660i | \(-0.797682\pi\) | ||||
−0.804716 | + | 0.593660i | \(0.797682\pi\) | |||||||
\(614\) | 23.8868 | + | 23.8868i | 0.963993 | + | 0.963993i | ||||
\(615\) | −7.73986 | + | 3.20596i | −0.312101 | + | 0.129277i | ||||
\(616\) | 11.5881i | 0.466899i | ||||||||
\(617\) | 11.7168 | + | 28.2867i | 0.471699 | + | 1.13878i | 0.963412 | + | 0.268024i | \(0.0863708\pi\) |
−0.491713 | + | 0.870757i | \(0.663629\pi\) | |||||||
\(618\) | 34.7366 | + | 14.3884i | 1.39731 | + | 0.578785i | ||||
\(619\) | −14.8962 | + | 35.9626i | −0.598729 | + | 1.44546i | 0.276148 | + | 0.961115i | \(0.410942\pi\) |
−0.874877 | + | 0.484344i | \(0.839058\pi\) | |||||||
\(620\) | −8.23517 | + | 8.23517i | −0.330732 | + | 0.330732i | ||||
\(621\) | −4.78230 | + | 4.78230i | −0.191907 | + | 0.191907i | ||||
\(622\) | 20.5782 | − | 49.6801i | 0.825110 | − | 1.99199i | ||||
\(623\) | −3.72780 | − | 1.54411i | −0.149351 | − | 0.0618633i | ||||
\(624\) | −34.0195 | − | 82.1303i | −1.36187 | − | 3.28784i | ||||
\(625\) | 19.9886i | 0.799544i | ||||||||
\(626\) | 48.1091 | − | 19.9274i | 1.92283 | − | 0.796461i | ||||
\(627\) | −10.4748 | − | 10.4748i | −0.418325 | − | 0.418325i | ||||
\(628\) | −69.4822 | −2.77264 | ||||||||
\(629\) | 29.1850 | − | 29.6095i | 1.16368 | − | 1.18061i | ||||
\(630\) | −0.928193 | −0.0369801 | ||||||||
\(631\) | 24.4611 | + | 24.4611i | 0.973779 | + | 0.973779i | 0.999665 | − | 0.0258856i | \(-0.00824055\pi\) |
−0.0258856 | + | 0.999665i | \(0.508241\pi\) | |||||||
\(632\) | 17.1934 | − | 7.12172i | 0.683915 | − | 0.283287i | ||||
\(633\) | − | 38.8624i | − | 1.54464i | ||||||
\(634\) | 7.52040 | + | 18.1559i | 0.298673 | + | 0.721061i | ||||
\(635\) | 28.6602 | + | 11.8715i | 1.13735 | + | 0.471104i | ||||
\(636\) | −44.2007 | + | 106.710i | −1.75267 | + | 4.23132i | ||||
\(637\) | −14.4370 | + | 14.4370i | −0.572014 | + | 0.572014i | ||||
\(638\) | 25.5454 | − | 25.5454i | 1.01135 | − | 1.01135i | ||||
\(639\) | 0.699971 | − | 1.68988i | 0.0276904 | − | 0.0668506i | ||||
\(640\) | −95.2025 | − | 39.4342i | −3.76321 | − | 1.55877i | ||||
\(641\) | 7.38639 | + | 17.8323i | 0.291745 | + | 0.704334i | 0.999999 | − | 0.00162373i | \(-0.000516849\pi\) |
−0.708254 | + | 0.705958i | \(0.750517\pi\) | |||||||
\(642\) | 71.8423i | 2.83539i | ||||||||
\(643\) | 5.87421 | − | 2.43318i | 0.231656 | − | 0.0959552i | −0.263836 | − | 0.964568i | \(-0.584988\pi\) |
0.495492 | + | 0.868612i | \(0.334988\pi\) | |||||||
\(644\) | −4.28019 | − | 4.28019i | −0.168663 | − | 0.168663i | ||||
\(645\) | −3.41022 | −0.134277 | ||||||||
\(646\) | −28.7627 | − | 68.0457i | −1.13166 | − | 2.67722i | ||||
\(647\) | −17.8781 | −0.702860 | −0.351430 | − | 0.936214i | \(-0.614304\pi\) | ||||
−0.351430 | + | 0.936214i | \(0.614304\pi\) | |||||||
\(648\) | 59.1333 | + | 59.1333i | 2.32297 | + | 2.32297i | ||||
\(649\) | 13.0731 | − | 5.41507i | 0.513165 | − | 0.212560i | ||||
\(650\) | − | 7.68686i | − | 0.301503i | ||||||
\(651\) | 0.556874 | + | 1.34441i | 0.0218256 | + | 0.0526917i | ||||
\(652\) | −64.2560 | − | 26.6157i | −2.51646 | − | 1.04235i | ||||
\(653\) | −2.56117 | + | 6.18321i | −0.100226 | + | 0.241968i | −0.966037 | − | 0.258404i | \(-0.916803\pi\) |
0.865811 | + | 0.500372i | \(0.166803\pi\) | |||||||
\(654\) | −23.3039 | + | 23.3039i | −0.911253 | + | 0.911253i | ||||
\(655\) | −15.0072 | + | 15.0072i | −0.586380 | + | 0.586380i | ||||
\(656\) | 15.3278 | − | 37.0046i | 0.598451 | − | 1.44479i | ||||
\(657\) | 0.266841 | + | 0.110529i | 0.0104105 | + | 0.00431216i | ||||
\(658\) | 1.07674 | + | 2.59949i | 0.0419758 | + | 0.101339i | ||||
\(659\) | 28.9866i | 1.12916i | 0.825379 | + | 0.564579i | \(0.190962\pi\) | ||||
−0.825379 | + | 0.564579i | \(0.809038\pi\) | |||||||
\(660\) | −24.0980 | + | 9.98170i | −0.938012 | + | 0.388537i | ||||
\(661\) | 23.0132 | + | 23.0132i | 0.895111 | + | 0.895111i | 0.994999 | − | 0.0998880i | \(-0.0318485\pi\) |
−0.0998880 | + | 0.994999i | \(0.531848\pi\) | |||||||
\(662\) | 20.2186 | 0.785817 | ||||||||
\(663\) | −16.0105 | − | 15.7810i | −0.621797 | − | 0.612884i | ||||
\(664\) | −39.0076 | −1.51379 | ||||||||
\(665\) | 7.96918 | + | 7.96918i | 0.309032 | + | 0.309032i | ||||
\(666\) | −4.98141 | + | 2.06337i | −0.193026 | + | 0.0799539i | ||||
\(667\) | 12.1501i | 0.470454i | ||||||||
\(668\) | 40.5740 | + | 97.9543i | 1.56985 | + | 3.78996i | ||||
\(669\) | −28.5462 | − | 11.8242i | −1.10366 | − | 0.457151i | ||||
\(670\) | 0.533119 | − | 1.28706i | 0.0205962 | − | 0.0497236i | ||||
\(671\) | 3.28839 | − | 3.28839i | 0.126947 | − | 0.126947i | ||||
\(672\) | −25.2897 | + | 25.2897i | −0.975573 | + | 0.975573i | ||||
\(673\) | −15.6355 | + | 37.7475i | −0.602706 | + | 1.45506i | 0.268079 | + | 0.963397i | \(0.413611\pi\) |
−0.870785 | + | 0.491664i | \(0.836389\pi\) | |||||||
\(674\) | 73.8472 | + | 30.5885i | 2.84449 | + | 1.17823i | ||||
\(675\) | 1.75218 | + | 4.23013i | 0.0674414 | + | 0.162818i | ||||
\(676\) | 13.5137i | 0.519756i | ||||||||
\(677\) | 27.4236 | − | 11.3592i | 1.05397 | − | 0.436570i | 0.212665 | − | 0.977125i | \(-0.431786\pi\) |
0.841309 | + | 0.540555i | \(0.181786\pi\) | |||||||
\(678\) | 21.6095 | + | 21.6095i | 0.829909 | + | 0.829909i | ||||
\(679\) | 2.57277 | 0.0987340 | ||||||||
\(680\) | −83.7483 | + | 0.604624i | −3.21160 | + | 0.0231863i | ||||
\(681\) | −19.4620 | −0.745784 | ||||||||
\(682\) | −2.70761 | − | 2.70761i | −0.103680 | − | 0.103680i | ||||
\(683\) | 3.57206 | − | 1.47960i | 0.136681 | − | 0.0566152i | −0.313294 | − | 0.949656i | \(-0.601433\pi\) |
0.449976 | + | 0.893041i | \(0.351433\pi\) | |||||||
\(684\) | 7.06473i | 0.270127i | ||||||||
\(685\) | −1.68437 | − | 4.06643i | −0.0643565 | − | 0.155370i | ||||
\(686\) | 28.8553 | + | 11.9523i | 1.10170 | + | 0.456339i | ||||
\(687\) | −10.5220 | + | 25.4023i | −0.401439 | + | 0.969159i | ||||
\(688\) | 11.5290 | − | 11.5290i | 0.439537 | − | 0.439537i | ||||
\(689\) | −28.2574 | + | 28.2574i | −1.07652 | + | 1.07652i | ||||
\(690\) | 4.55264 | − | 10.9910i | 0.173316 | − | 0.418422i | ||||
\(691\) | 17.7379 | + | 7.34727i | 0.674780 | + | 0.279503i | 0.693643 | − | 0.720319i | \(-0.256005\pi\) |
−0.0188627 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(692\) | −2.83556 | − | 6.84564i | −0.107792 | − | 0.260232i | ||||
\(693\) | − | 0.225032i | − | 0.00854828i | ||||||
\(694\) | 2.89429 | − | 1.19886i | 0.109866 | − | 0.0455079i | ||||
\(695\) | 25.1043 | + | 25.1043i | 0.952260 | + | 0.952260i | ||||
\(696\) | 160.656 | 6.08966 | ||||||||
\(697\) | −0.0731236 | − | 10.1286i | −0.00276976 | − | 0.383648i | ||||
\(698\) | −42.5540 | −1.61069 | ||||||||
\(699\) | −17.0919 | − | 17.0919i | −0.646473 | − | 0.646473i | ||||
\(700\) | −3.78599 | + | 1.56821i | −0.143097 | + | 0.0592728i | ||||
\(701\) | − | 35.1008i | − | 1.32574i | −0.748734 | − | 0.662870i | \(-0.769338\pi\) | ||
0.748734 | − | 0.662870i | \(-0.230662\pi\) | |||||||
\(702\) | 18.3899 | + | 44.3972i | 0.694083 | + | 1.67566i | ||||
\(703\) | 60.4843 | + | 25.0534i | 2.28121 | + | 0.944908i | ||||
\(704\) | 19.0186 | − | 45.9150i | 0.716790 | − | 1.73048i | ||||
\(705\) | −2.88334 | + | 2.88334i | −0.108593 | + | 0.108593i | ||||
\(706\) | −45.4377 | + | 45.4377i | −1.71007 | + | 1.71007i | ||||
\(707\) | −5.73923 | + | 13.8557i | −0.215846 | + | 0.521098i | ||||
\(708\) | 90.2946 | + | 37.4013i | 3.39348 | + | 1.40563i | ||||
\(709\) | 6.02394 | + | 14.5431i | 0.226234 | + | 0.546177i | 0.995713 | − | 0.0924951i | \(-0.0294842\pi\) |
−0.769479 | + | 0.638672i | \(0.779484\pi\) | |||||||
\(710\) | 53.0323i | 1.99027i | ||||||||
\(711\) | −0.333882 | + | 0.138298i | −0.0125215 | + | 0.00518659i | ||||
\(712\) | 33.3869 | + | 33.3869i | 1.25123 | + | 1.25123i | ||||
\(713\) | 1.28781 | 0.0482290 | ||||||||
\(714\) | −6.11114 | + | 15.0602i | −0.228704 | + | 0.563614i | ||||
\(715\) | −9.02449 | −0.337497 | ||||||||
\(716\) | −5.51620 | − | 5.51620i | −0.206150 | − | 0.206150i | ||||
\(717\) | 2.82155 | − | 1.16872i | 0.105373 | − | 0.0436468i | ||||
\(718\) | 37.0423i | 1.38240i | ||||||||
\(719\) | 6.66163 | + | 16.0826i | 0.248437 | + | 0.599780i | 0.998072 | − | 0.0620721i | \(-0.0197709\pi\) |
−0.749635 | + | 0.661852i | \(0.769771\pi\) | |||||||
\(720\) | 5.94176 | + | 2.46116i | 0.221436 | + | 0.0917219i | ||||
\(721\) | 2.65390 | − | 6.40708i | 0.0988364 | − | 0.238612i | ||||
\(722\) | 45.1819 | − | 45.1819i | 1.68149 | − | 1.68149i | ||||
\(723\) | −3.89817 | + | 3.89817i | −0.144975 | + | 0.144975i | ||||
\(724\) | 18.6245 | − | 44.9636i | 0.692176 | − | 1.67106i | ||||
\(725\) | 7.59945 | + | 3.14779i | 0.282236 | + | 0.116906i | ||||
\(726\) | 16.1784 | + | 39.0581i | 0.600437 | + | 1.44958i | ||||
\(727\) | − | 3.29769i | − | 0.122305i | −0.998128 | − | 0.0611523i | \(-0.980522\pi\) | ||
0.998128 | − | 0.0611523i | \(-0.0194775\pi\) | |||||||
\(728\) | −25.5840 | + | 10.5972i | −0.948207 | + | 0.392760i | ||||
\(729\) | −20.1606 | − | 20.1606i | −0.746687 | − | 0.746687i | ||||
\(730\) | −8.37408 | −0.309939 | ||||||||
\(731\) | 1.55030 | − | 3.82054i | 0.0573400 | − | 0.141308i | ||||
\(732\) | 32.1204 | 1.18720 | ||||||||
\(733\) | −7.84996 | − | 7.84996i | −0.289945 | − | 0.289945i | 0.547113 | − | 0.837058i | \(-0.315727\pi\) |
−0.837058 | + | 0.547113i | \(0.815727\pi\) | |||||||
\(734\) | −43.6025 | + | 18.0607i | −1.60940 | + | 0.666634i | ||||
\(735\) | 21.3921i | 0.789058i | ||||||||
\(736\) | 12.1125 | + | 29.2422i | 0.446474 | + | 1.07788i | ||||
\(737\) | 0.312038 | + | 0.129250i | 0.0114941 | + | 0.00476099i | ||||
\(738\) | −0.502694 | + | 1.21361i | −0.0185044 | + | 0.0446737i | ||||
\(739\) | 32.0698 | − | 32.0698i | 1.17971 | − | 1.17971i | 0.199887 | − | 0.979819i | \(-0.435943\pi\) |
0.979819 | − | 0.199887i | \(-0.0640574\pi\) | |||||||
\(740\) | 81.5108 | − | 81.5108i | 2.99640 | − | 2.99640i | ||||
\(741\) | 13.5470 | − | 32.7053i | 0.497660 | − | 1.20146i | ||||
\(742\) | 26.6922 | + | 11.0563i | 0.979901 | + | 0.405888i | ||||
\(743\) | 19.5303 | + | 47.1503i | 0.716497 | + | 1.72978i | 0.683089 | + | 0.730335i | \(0.260636\pi\) |
0.0334077 | + | 0.999442i | \(0.489364\pi\) | |||||||
\(744\) | − | 17.0283i | − | 0.624287i | ||||||
\(745\) | −3.10412 | + | 1.28577i | −0.113726 | + | 0.0471069i | ||||
\(746\) | −3.91366 | − | 3.91366i | −0.143289 | − | 0.143289i | ||||
\(747\) | 0.757498 | 0.0277154 | ||||||||
\(748\) | −0.227669 | − | 31.5352i | −0.00832442 | − | 1.15304i | ||||
\(749\) | 13.2512 | 0.484187 | ||||||||
\(750\) | −38.9680 | − | 38.9680i | −1.42291 | − | 1.42291i | ||||
\(751\) | 45.9853 | − | 19.0477i | 1.67803 | − | 0.695062i | 0.678799 | − | 0.734324i | \(-0.262501\pi\) |
0.999229 | + | 0.0392616i | \(0.0125006\pi\) | |||||||
\(752\) | − | 19.4955i | − | 0.710927i | ||||||
\(753\) | 16.4150 | + | 39.6294i | 0.598197 | + | 1.44418i | ||||
\(754\) | 79.7598 | + | 33.0376i | 2.90468 | + | 1.20316i | ||||
\(755\) | −2.47111 | + | 5.96578i | −0.0899328 | + | 0.217117i | ||||
\(756\) | 18.1151 | − | 18.1151i | 0.658840 | − | 0.658840i | ||||
\(757\) | 14.2444 | − | 14.2444i | 0.517723 | − | 0.517723i | −0.399159 | − | 0.916882i | \(-0.630698\pi\) |
0.916882 | + | 0.399159i | \(0.130698\pi\) | |||||||
\(758\) | −16.5885 | + | 40.0482i | −0.602522 | + | 1.45462i | ||||
\(759\) | 2.66468 | + | 1.10375i | 0.0967219 | + | 0.0400635i | ||||
\(760\) | −50.4687 | − | 121.842i | −1.83069 | − | 4.41968i | ||||
\(761\) | 16.6616i | 0.603983i | 0.953311 | + | 0.301991i | \(0.0976514\pi\) | ||||
−0.953311 | + | 0.301991i | \(0.902349\pi\) | |||||||
\(762\) | −65.0842 | + | 26.9587i | −2.35775 | + | 0.976612i | ||||
\(763\) | 4.29834 | + | 4.29834i | 0.155610 | + | 0.155610i | ||||
\(764\) | −69.7066 | −2.52190 | ||||||||
\(765\) | 1.62633 | − | 0.0117413i | 0.0588000 | − | 0.000424508i | ||||
\(766\) | −78.3481 | −2.83083 | ||||||||
\(767\) | 23.9105 | + | 23.9105i | 0.863360 | + | 0.863360i | ||||
\(768\) | 103.250 | − | 42.7675i | 3.72571 | − | 1.54324i | ||||
\(769\) | − | 7.67329i | − | 0.276706i | −0.990383 | − | 0.138353i | \(-0.955819\pi\) | ||
0.990383 | − | 0.138353i | \(-0.0441808\pi\) | |||||||
\(770\) | 2.49680 | + | 6.02782i | 0.0899786 | + | 0.217227i | ||||
\(771\) | 32.9337 | + | 13.6416i | 1.18608 | + | 0.491290i | ||||
\(772\) | −52.0099 | + | 125.563i | −1.87188 | + | 4.51911i | ||||
\(773\) | −13.6573 | + | 13.6573i | −0.491218 | + | 0.491218i | −0.908690 | − | 0.417472i | \(-0.862916\pi\) |
0.417472 | + | 0.908690i | \(0.362916\pi\) | |||||||
\(774\) | −0.378106 | + | 0.378106i | −0.0135907 | + | 0.0135907i | ||||
\(775\) | 0.333641 | − | 0.805480i | 0.0119847 | − | 0.0289337i | ||||
\(776\) | −27.8144 | − | 11.5211i | −0.998480 | − | 0.413584i | ||||
\(777\) | −5.51188 | − | 13.3068i | −0.197737 | − | 0.477381i | ||||
\(778\) | − | 36.3063i | − | 1.30165i | ||||||
\(779\) | 14.7357 | − | 6.10372i | 0.527961 | − | 0.218688i | ||||
\(780\) | −44.0748 | − | 44.0748i | −1.57813 | − | 1.57813i | ||||
\(781\) | −12.8572 | −0.460068 | ||||||||
\(782\) | 10.2439 | + | 10.0970i | 0.366320 | + | 0.361068i | ||||
\(783\) | −51.4231 | −1.83771 | ||||||||
\(784\) | −72.3203 | − | 72.3203i | −2.58287 | − | 2.58287i | ||||
\(785\) | −23.2706 | + | 9.63900i | −0.830563 | + | 0.344031i | ||||
\(786\) | − | 48.1959i | − | 1.71909i | ||||||
\(787\) | 11.0852 | + | 26.7620i | 0.395145 | + | 0.953963i | 0.988800 | + | 0.149244i | \(0.0476841\pi\) |
−0.593656 | + | 0.804719i | \(0.702316\pi\) | |||||||
\(788\) | −28.0356 | − | 11.6127i | −0.998727 | − | 0.413686i | ||||
\(789\) | 12.9356 | − | 31.2294i | 0.460520 | − | 1.11179i | ||||
\(790\) | 7.40904 | − | 7.40904i | 0.263602 | − | 0.263602i | ||||
\(791\) | 3.98583 | − | 3.98583i | 0.141720 | − | 0.141720i | ||||
\(792\) | −1.00772 | + | 2.43284i | −0.0358076 | + | 0.0864473i | ||||
\(793\) | 10.2672 | + | 4.25283i | 0.364601 | + | 0.151023i | ||||
\(794\) | 11.1348 | + | 26.8817i | 0.395159 | + | 0.953997i | ||||
\(795\) | 41.8705i | 1.48499i | ||||||||
\(796\) | 0.398127 | − | 0.164910i | 0.0141112 | − | 0.00584507i | ||||
\(797\) | −21.0874 | − | 21.0874i | −0.746952 | − | 0.746952i | 0.226953 | − | 0.973906i | \(-0.427124\pi\) |
−0.973906 | + | 0.226953i | \(0.927124\pi\) | |||||||
\(798\) | −25.5932 | −0.905989 | ||||||||
\(799\) | −1.91949 | − | 4.54106i | −0.0679067 | − | 0.160651i | ||||
\(800\) | 21.4280 | 0.757594 | ||||||||
\(801\) | −0.648347 | − | 0.648347i | −0.0229082 | − | 0.0229082i | ||||
\(802\) | −91.1504 | + | 37.7557i | −3.21863 | + | 1.33320i | ||||
\(803\) | − | 2.03022i | − | 0.0716451i | ||||||
\(804\) | 0.892717 | + | 2.15521i | 0.0314837 | + | 0.0760083i | ||||
\(805\) | −2.02727 | − | 0.839724i | −0.0714520 | − | 0.0295964i | ||||
\(806\) | 3.50172 | − | 8.45389i | 0.123343 | − | 0.297776i | ||||
\(807\) | 15.2653 | − | 15.2653i | 0.537365 | − | 0.537365i | ||||
\(808\) | 124.094 | − | 124.094i | 4.36562 | − | 4.36562i | ||||
\(809\) | −15.6171 | + | 37.7030i | −0.549068 | + | 1.32557i | 0.369104 | + | 0.929388i | \(0.379665\pi\) |
−0.918173 | + | 0.396181i | \(0.870335\pi\) | |||||||
\(810\) | 43.5005 | + | 18.0185i | 1.52845 | + | 0.633105i | ||||
\(811\) | −12.8568 | − | 31.0391i | −0.451463 | − | 1.08993i | −0.971766 | − | 0.235947i | \(-0.924181\pi\) |
0.520303 | − | 0.853982i | \(-0.325819\pi\) | |||||||
\(812\) | − | 46.0240i | − | 1.61512i | ||||||
\(813\) | 6.03626 | − | 2.50030i | 0.211701 | − | 0.0876894i | ||||
\(814\) | 26.7996 | + | 26.7996i | 0.939326 | + | 0.939326i | ||||
\(815\) | −25.2126 | −0.883158 | ||||||||
\(816\) | 79.0530 | − | 80.2027i | 2.76741 | − | 2.80766i | ||||
\(817\) | 6.49261 | 0.227148 | ||||||||
\(818\) | −26.5724 | − | 26.5724i | −0.929081 | − | 0.929081i | ||||
\(819\) | 0.496822 | − | 0.205790i | 0.0173604 | − | 0.00719090i | ||||
\(820\) | − | 28.0839i | − | 0.980732i | ||||||
\(821\) | −3.26160 | − | 7.87421i | −0.113831 | − | 0.274812i | 0.856689 | − | 0.515833i | \(-0.172518\pi\) |
−0.970520 | + | 0.241021i | \(0.922518\pi\) | |||||||
\(822\) | 9.23442 | + | 3.82502i | 0.322087 | + | 0.133413i | ||||
\(823\) | 2.25709 | − | 5.44910i | 0.0786773 | − | 0.189944i | −0.879647 | − | 0.475628i | \(-0.842221\pi\) |
0.958324 | + | 0.285684i | \(0.0922209\pi\) | |||||||
\(824\) | −57.3830 | + | 57.3830i | −1.99903 | + | 1.99903i | ||||
\(825\) | 1.38071 | − | 1.38071i | 0.0480701 | − | 0.0480701i | ||||
\(826\) | 9.35548 | − | 22.5861i | 0.325519 | − | 0.785872i | ||||
\(827\) | −8.71508 | − | 3.60991i | −0.303053 | − | 0.125529i | 0.225975 | − | 0.974133i | \(-0.427443\pi\) |
−0.529028 | + | 0.848604i | \(0.677443\pi\) | |||||||
\(828\) | −0.526384 | − | 1.27080i | −0.0182931 | − | 0.0441635i | ||||
\(829\) | − | 37.2243i | − | 1.29286i | −0.762975 | − | 0.646428i | \(-0.776262\pi\) | ||
0.762975 | − | 0.646428i | \(-0.223738\pi\) | |||||||
\(830\) | −20.2907 | + | 8.40467i | −0.704299 | + | 0.291730i | ||||
\(831\) | −33.3571 | − | 33.3571i | −1.15714 | − | 1.15714i | ||||
\(832\) | 118.762 | 4.11735 | ||||||||
\(833\) | −23.9660 | − | 9.72493i | −0.830372 | − | 0.336949i | ||||
\(834\) | −80.6230 | −2.79175 | ||||||||
\(835\) | 27.1776 | + | 27.1776i | 0.940521 | + | 0.940521i | ||||
\(836\) | 45.8793 | − | 19.0038i | 1.58677 | − | 0.657262i | ||||
\(837\) | 5.45043i | 0.188394i | ||||||||
\(838\) | 17.7315 | + | 42.8077i | 0.612526 | + | 1.47877i | ||||
\(839\) | 36.2087 | + | 14.9981i | 1.25006 | + | 0.517793i | 0.906845 | − | 0.421463i | \(-0.138483\pi\) |
0.343217 | + | 0.939256i | \(0.388483\pi\) | |||||||
\(840\) | −11.1033 | + | 26.8059i | −0.383102 | + | 0.924890i | ||||
\(841\) | −44.8177 | + | 44.8177i | −1.54544 | + | 1.54544i | ||||
\(842\) | −29.4919 | + | 29.4919i | −1.01636 | + | 1.01636i | ||||
\(843\) | 19.9969 | − | 48.2769i | 0.688731 | − | 1.66274i | ||||
\(844\) | 120.361 | + | 49.8550i | 4.14299 | + | 1.71608i | ||||
\(845\) | 1.87470 | + | 4.52592i | 0.0644916 | + | 0.155696i | ||||
\(846\) | 0.639378i | 0.0219823i | ||||||||
\(847\) | 7.20418 | − | 2.98407i | 0.247539 | − | 0.102534i | ||||
\(848\) | −141.552 | − | 141.552i | −4.86091 | − | 4.86091i | ||||
\(849\) | 17.2281 | 0.591267 | ||||||||
\(850\) | 8.96924 | − | 3.79127i | 0.307642 | − | 0.130039i | ||||
\(851\) | −12.7466 | −0.436949 | ||||||||
\(852\) | −62.7935 | − | 62.7935i | −2.15127 | − | 2.15127i | ||||
\(853\) | 21.8389 | − | 9.04595i | 0.747748 | − | 0.309727i | 0.0239256 | − | 0.999714i | \(-0.492384\pi\) |
0.723822 | + | 0.689986i | \(0.242384\pi\) | |||||||
\(854\) | − | 8.03453i | − | 0.274936i | ||||||
\(855\) | 0.980062 | + | 2.36608i | 0.0335174 | + | 0.0809182i | ||||
\(856\) | −143.259 | − | 59.3399i | −4.89650 | − | 2.02820i | ||||
\(857\) | 7.80645 | − | 18.8464i | 0.266663 | − | 0.643782i | −0.732659 | − | 0.680596i | \(-0.761721\pi\) |
0.999322 | + | 0.0368140i | \(0.0117209\pi\) | |||||||
\(858\) | 14.4912 | − | 14.4912i | 0.494721 | − | 0.494721i | ||||
\(859\) | 10.7489 | − | 10.7489i | 0.366748 | − | 0.366748i | −0.499542 | − | 0.866290i | \(-0.666498\pi\) |
0.866290 | + | 0.499542i | \(0.166498\pi\) | |||||||
\(860\) | 4.37483 | − | 10.5618i | 0.149181 | − | 0.360154i | ||||
\(861\) | −3.24192 | − | 1.34285i | −0.110484 | − | 0.0457641i | ||||
\(862\) | 28.1345 | + | 67.9227i | 0.958266 | + | 2.31346i | ||||
\(863\) | − | 27.1366i | − | 0.923741i | −0.886947 | − | 0.461870i | \(-0.847179\pi\) | ||
0.886947 | − | 0.461870i | \(-0.152821\pi\) | |||||||
\(864\) | −123.762 | + | 51.2640i | −4.21048 | + | 1.74404i | ||||
\(865\) | −1.89934 | − | 1.89934i | −0.0645795 | − | 0.0645795i | ||||
\(866\) | 86.7765 | 2.94878 | ||||||||
\(867\) | 10.5171 | − | 26.4649i | 0.357179 | − | 0.898796i | ||||
\(868\) | −4.87817 | −0.165576 | ||||||||
\(869\) | 1.79626 | + | 1.79626i | 0.0609339 | + | 0.0609339i | ||||
\(870\) | 83.5689 | − | 34.6154i | 2.83325 | − | 1.17357i | ||||
\(871\) | 0.807108i | 0.0273478i | ||||||||
\(872\) | −27.2213 | − | 65.7181i | −0.921830 | − | 2.22549i | ||||
\(873\) | 0.540135 | + | 0.223731i | 0.0182808 | + | 0.00757215i | ||||
\(874\) | −8.66762 | + | 20.9255i | −0.293187 | + | 0.707815i | ||||
\(875\) | −7.18755 | + | 7.18755i | −0.242984 | + | 0.242984i | ||||
\(876\) | 9.91543 | − | 9.91543i | 0.335011 | − | 0.335011i | ||||
\(877\) | 15.7061 | − | 37.9179i | 0.530357 | − | 1.28040i | −0.400929 | − | 0.916109i | \(-0.631313\pi\) |
0.931287 | − | 0.364287i | \(-0.118687\pi\) | |||||||
\(878\) | 47.6270 | + | 19.7278i | 1.60733 | + | 0.665779i | ||||
\(879\) | 12.8420 | + | 31.0033i | 0.433149 | + | 1.04571i | ||||
\(880\) | − | 45.2071i | − | 1.52393i | ||||||
\(881\) | 49.4867 | − | 20.4981i | 1.66725 | − | 0.690598i | 0.668655 | − | 0.743573i | \(-0.266870\pi\) |
0.998596 | + | 0.0529752i | \(0.0168704\pi\) | |||||||
\(882\) | 2.37183 | + | 2.37183i | 0.0798637 | + | 0.0798637i | ||||
\(883\) | 51.2194 | 1.72367 | 0.861834 | − | 0.507190i | \(-0.169316\pi\) | ||||
0.861834 | + | 0.507190i | \(0.169316\pi\) | |||||||
\(884\) | 69.4146 | − | 29.3413i | 2.33466 | − | 0.986856i | ||||
\(885\) | 35.4295 | 1.19095 | ||||||||
\(886\) | −61.5691 | − | 61.5691i | −2.06845 | − | 2.06845i | ||||
\(887\) | −39.1368 | + | 16.2110i | −1.31408 | + | 0.544311i | −0.926073 | − | 0.377343i | \(-0.876838\pi\) |
−0.388011 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(888\) | 168.544i | 5.65596i | ||||||||
\(889\) | 4.97248 | + | 12.0046i | 0.166772 | + | 0.402622i | ||||
\(890\) | 24.5605 | + | 10.1733i | 0.823270 | + | 0.341010i | ||||
\(891\) | −4.36843 | + | 10.5463i | −0.146348 | + | 0.353315i | ||||
\(892\) | 73.2416 | − | 73.2416i | 2.45231 | − | 2.45231i | ||||
\(893\) | 5.48951 | − | 5.48951i | 0.183699 | − | 0.183699i | ||||
\(894\) | 2.91983 | − | 7.04910i | 0.0976538 | − | 0.235757i | ||||
\(895\) | −2.61270 | − | 1.08221i | −0.0873329 | − | 0.0361745i | ||||
\(896\) | −16.5174 | − | 39.8766i | −0.551808 | − | 1.33218i | ||||
\(897\) | 6.89240i | 0.230131i | ||||||||
\(898\) | −19.9362 | + | 8.25786i | −0.665281 | + | 0.275568i | ||||
\(899\) | 6.92379 | + | 6.92379i | 0.230921 | + | 0.230921i | ||||
\(900\) | −0.931214 | −0.0310405 | ||||||||
\(901\) | −46.9084 | − | 19.0345i | −1.56275 | − | 0.634132i | ||||
\(902\) | 9.23360 | 0.307445 | ||||||||
\(903\) | −1.01004 | − | 1.01004i | −0.0336119 | − | 0.0336119i | ||||
\(904\) | −60.9400 | + | 25.2422i | −2.02683 | + | 0.839542i | ||||
\(905\) | − | 17.6427i | − | 0.586463i | ||||||
\(906\) | −5.61161 | − | 13.5476i | −0.186433 | − | 0.450090i | ||||
\(907\) | −4.41554 | − | 1.82898i | −0.146616 | − | 0.0607302i | 0.308169 | − | 0.951332i | \(-0.400284\pi\) |
−0.454785 | + | 0.890601i | \(0.650284\pi\) | |||||||
\(908\) | 24.9670 | − | 60.2756i | 0.828558 | − | 2.00032i | ||||
\(909\) | −2.40982 | + | 2.40982i | −0.0799286 | + | 0.0799286i | ||||
\(910\) | −11.0248 | + | 11.0248i | −0.365468 | + | 0.365468i | ||||
\(911\) | −7.25856 | + | 17.5237i | −0.240487 | + | 0.580587i | −0.997331 | − | 0.0730083i | \(-0.976740\pi\) |
0.756844 | + | 0.653595i | \(0.226740\pi\) | |||||||
\(912\) | 163.833 | + | 67.8618i | 5.42505 | + | 2.24713i | ||||
\(913\) | −2.03764 | − | 4.91930i | −0.0674360 | − | 0.162805i | ||||
\(914\) | 78.7094i | 2.60348i | ||||||||
\(915\) | 10.7576 | − | 4.45594i | 0.355635 | − | 0.147309i | ||||
\(916\) | −65.1752 | − | 65.1752i | −2.15345 | − | 2.15345i | ||||
\(917\) | −8.88963 | −0.293561 | ||||||||
\(918\) | −42.7337 | + | 43.3552i | −1.41042 | + | 1.43094i | ||||
\(919\) | 52.5201 | 1.73248 | 0.866238 | − | 0.499631i | \(-0.166531\pi\) | ||||
0.866238 | + | 0.499631i | \(0.166531\pi\) | |||||||
\(920\) | 18.1566 | + | 18.1566i | 0.598606 | + | 0.598606i | ||||
\(921\) | −18.9451 | + | 7.84731i | −0.624262 | + | 0.258578i | ||||
\(922\) | − | 33.3653i | − | 1.09883i | ||||||
\(923\) | −11.7578 | − | 28.3859i | −0.387014 | − | 0.934333i | ||||
\(924\) | −10.0937 | − | 4.18094i | −0.332058 | − | 0.137543i | ||||
\(925\) | −3.30234 | + | 7.97255i | −0.108580 | + | 0.262136i | ||||
\(926\) | −23.4111 | + | 23.4111i | −0.769338 | + | 0.769338i | ||||
\(927\) | 1.11433 | − | 1.11433i | 0.0365995 | − | 0.0365995i | ||||
\(928\) | −92.0960 | + | 222.339i | −3.02320 | + | 7.29865i | ||||
\(929\) | −5.08493 | − | 2.10625i | −0.166831 | − | 0.0691037i | 0.297705 | − | 0.954658i | \(-0.403779\pi\) |
−0.464536 | + | 0.885554i | \(0.653779\pi\) | |||||||
\(930\) | −3.66895 | − | 8.85763i | −0.120310 | − | 0.290453i | ||||
\(931\) | − | 40.7276i | − | 1.33479i | ||||||
\(932\) | 74.8616 | − | 31.0087i | 2.45217 | − | 1.01572i | ||||
\(933\) | 23.0813 | + | 23.0813i | 0.755648 | + | 0.755648i | ||||
\(934\) | 67.6097 | 2.21226 | ||||||||
\(935\) | −4.45101 | − | 10.5300i | −0.145564 | − | 0.344368i | ||||
\(936\) | −6.29272 | −0.205684 | ||||||||
\(937\) | 14.3372 | + | 14.3372i | 0.468378 | + | 0.468378i | 0.901389 | − | 0.433011i | \(-0.142549\pi\) |
−0.433011 | + | 0.901389i | \(0.642549\pi\) | |||||||
\(938\) | 0.539100 | − | 0.223302i | 0.0176022 | − | 0.00729108i | ||||
\(939\) | 31.6097i | 1.03154i | ||||||||
\(940\) | −5.23107 | − | 12.6289i | −0.170619 | − | 0.411910i | ||||
\(941\) | −26.4131 | − | 10.9407i | −0.861044 | − | 0.356656i | −0.0919281 | − | 0.995766i | \(-0.529303\pi\) |
−0.769116 | + | 0.639110i | \(0.779303\pi\) | |||||||
\(942\) | 21.8891 | − | 52.8449i | 0.713185 | − | 1.72178i | ||||
\(943\) | −2.19588 | + | 2.19588i | −0.0715076 | + | 0.0715076i | ||||
\(944\) | −119.777 | + | 119.777i | −3.89840 | + | 3.89840i | ||||
\(945\) | 3.55397 | − | 8.58005i | 0.115611 | − | 0.279109i | ||||
\(946\) | 3.47257 | + | 1.43838i | 0.112903 | + | 0.0467659i | ||||
\(947\) | 3.88046 | + | 9.36826i | 0.126098 | + | 0.304428i | 0.974303 | − | 0.225240i | \(-0.0723166\pi\) |
−0.848205 | + | 0.529668i | \(0.822317\pi\) | |||||||
\(948\) | 17.5455i | 0.569852i | ||||||||
\(949\) | 4.48229 | − | 1.85662i | 0.145501 | − | 0.0602686i | ||||
\(950\) | 10.8426 | + | 10.8426i | 0.351779 | + | 0.351779i | ||||
\(951\) | −11.9291 | −0.386829 | ||||||||
\(952\) | −24.9836 | − | 24.6254i | −0.809722 | − | 0.798114i | ||||
\(953\) | 56.4287 | 1.82790 | 0.913952 | − | 0.405822i | \(-0.133015\pi\) | ||||
0.913952 | + | 0.405822i | \(0.133015\pi\) | |||||||
\(954\) | 4.64236 | + | 4.64236i | 0.150302 | + | 0.150302i | ||||
\(955\) | −23.3458 | + | 9.67013i | −0.755451 | + | 0.312918i | ||||
\(956\) | 10.2379i | 0.331118i | ||||||||
\(957\) | 8.39220 | + | 20.2606i | 0.271281 | + | 0.654931i | ||||
\(958\) | −22.2726 | − | 9.22563i | −0.719596 | − | 0.298067i | ||||
\(959\) | 0.705516 | − | 1.70327i | 0.0227823 | − | 0.0550014i | ||||
\(960\) | 87.9883 | − | 87.9883i | 2.83981 | − | 2.83981i | ||||
\(961\) | −21.1864 | + | 21.1864i | −0.683434 | + | 0.683434i | ||||
\(962\) | −34.6596 | + | 83.6757i | −1.11747 | + | 2.69781i | ||||
\(963\) | 2.78198 | + | 1.15233i | 0.0896481 | + | 0.0371335i | ||||
\(964\) | −7.07221 | − | 17.0738i | −0.227780 | − | 0.549911i | ||||
\(965\) | 49.2680i | 1.58599i | ||||||||
\(966\) | 4.60371 | − | 1.90692i | 0.148122 | − | 0.0613541i | ||||
\(967\) | 7.73852 | + | 7.73852i | 0.248854 | + | 0.248854i | 0.820500 | − | 0.571646i | \(-0.193695\pi\) |
−0.571646 | + | 0.820500i | \(0.693695\pi\) | |||||||
\(968\) | −91.2479 | −2.93282 | ||||||||
\(969\) | 44.8430 | − | 0.323745i | 1.44056 | − | 0.0104002i | ||||
\(970\) | −16.9507 | −0.544253 | ||||||||
\(971\) | 11.1490 | + | 11.1490i | 0.357787 | + | 0.357787i | 0.862997 | − | 0.505209i | \(-0.168585\pi\) |
−0.505209 | + | 0.862997i | \(0.668585\pi\) | |||||||
\(972\) | 10.4306 | − | 4.32049i | 0.334561 | − | 0.138580i | ||||
\(973\) | 14.8707i | 0.476734i | ||||||||
\(974\) | 7.90299 | + | 19.0795i | 0.253228 | + | 0.611346i | ||||
\(975\) | 4.31094 | + | 1.78565i | 0.138061 | + | 0.0571866i | ||||
\(976\) | −21.3040 | + | 51.4325i | −0.681925 | + | 1.64631i | ||||
\(977\) | 17.2134 | − | 17.2134i | 0.550706 | − | 0.550706i | −0.375938 | − | 0.926645i | \(-0.622680\pi\) |
0.926645 | + | 0.375938i | \(0.122680\pi\) | |||||||
\(978\) | 40.4854 | − | 40.4854i | 1.29458 | − | 1.29458i | ||||
\(979\) | −2.46643 | + | 5.95449i | −0.0788274 | + | 0.190306i | ||||
\(980\) | −66.2533 | − | 27.4430i | −2.11638 | − | 0.876634i | ||||
\(981\) | 0.528617 | + | 1.27619i | 0.0168774 | + | 0.0407457i | ||||
\(982\) | − | 64.2295i | − | 2.04964i | ||||||
\(983\) | −30.6288 | + | 12.6868i | −0.976906 | + | 0.404648i | −0.813279 | − | 0.581875i | \(-0.802319\pi\) |
−0.163627 | + | 0.986522i | \(0.552319\pi\) | |||||||
\(984\) | 29.0352 | + | 29.0352i | 0.925610 | + | 0.925610i | ||||
\(985\) | −11.0005 | −0.350506 | ||||||||
\(986\) | 0.789531 | + | 109.360i | 0.0251438 | + | 3.48275i | ||||
\(987\) | −1.70797 | −0.0543653 | ||||||||
\(988\) | 83.9126 | + | 83.9126i | 2.66961 | + | 2.66961i | ||||
\(989\) | −1.16789 | + | 0.483757i | −0.0371368 | + | 0.0153826i | ||||
\(990\) | 1.48262i | 0.0471208i | ||||||||
\(991\) | 10.3059 | + | 24.8807i | 0.327379 | + | 0.790362i | 0.998785 | + | 0.0492728i | \(0.0156904\pi\) |
−0.671407 | + | 0.741089i | \(0.734310\pi\) | |||||||
\(992\) | 23.5662 | + | 9.76143i | 0.748227 | + | 0.309926i | ||||
\(993\) | −4.69676 | + | 11.3390i | −0.149047 | + | 0.359831i | ||||
\(994\) | −15.7070 | + | 15.7070i | −0.498197 | + | 0.498197i | ||||
\(995\) | 0.110461 | − | 0.110461i | 0.00350186 | − | 0.00350186i | ||||
\(996\) | 14.0738 | − | 33.9770i | 0.445944 | − | 1.07660i | ||||
\(997\) | 2.19447 | + | 0.908980i | 0.0694996 | + | 0.0287877i | 0.417162 | − | 0.908832i | \(-0.363025\pi\) |
−0.347663 | + | 0.937620i | \(0.613025\pi\) | |||||||
\(998\) | −25.6630 | − | 61.9560i | −0.812349 | − | 1.96118i | ||||
\(999\) | − | 53.9478i | − | 1.70683i |
(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 | 731.2.m.c.87.1 | ✓ | 128 | |
17.9 | even | 8 | inner | 731.2.m.c.689.1 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.m.c.87.1 | ✓ | 128 | 1.1 | even | 1 | trivial | |
731.2.m.c.689.1 | yes | 128 | 17.9 | even | 8 | inner |