Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.3.f.b.93.3 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −2.98637 | + | 2.98637i | −0.995456 | + | 0.995456i | −0.999990 | − | 0.00453331i | \(-0.998557\pi\) |
0.00453331 | + | 0.999990i | \(0.498557\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.91488 | + | 3.11026i | −0.782975 | + | 0.622053i | ||||
\(6\) | −5.97274 | −0.995456 | ||||||||
\(7\) | −3.94695 | − | 3.94695i | −0.563849 | − | 0.563849i | 0.366549 | − | 0.930399i | \(-0.380539\pi\) |
−0.930399 | + | 0.366549i | \(0.880539\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 8.83680i | − | 0.981867i | ||||||
\(10\) | −7.02514 | − | 0.804611i | −0.702514 | − | 0.0804611i | ||||
\(11\) | 8.59939 | 0.781763 | 0.390881 | − | 0.920441i | \(-0.372170\pi\) | ||||
0.390881 | + | 0.920441i | \(0.372170\pi\) | |||||||
\(12\) | −5.97274 | − | 5.97274i | −0.497728 | − | 0.497728i | ||||
\(13\) | 2.89951 | − | 2.89951i | 0.223039 | − | 0.223039i | −0.586738 | − | 0.809777i | \(-0.699588\pi\) |
0.809777 | + | 0.586738i | \(0.199588\pi\) | |||||||
\(14\) | − | 7.89389i | − | 0.563849i | ||||||
\(15\) | 2.40286 | − | 20.9797i | 0.160191 | − | 1.39864i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −15.7131 | − | 15.7131i | −0.924302 | − | 0.924302i | 0.0730280 | − | 0.997330i | \(-0.476734\pi\) |
−0.997330 | + | 0.0730280i | \(0.976734\pi\) | |||||||
\(18\) | 8.83680 | − | 8.83680i | 0.490933 | − | 0.490933i | ||||
\(19\) | 12.0018i | 0.631674i | 0.948814 | + | 0.315837i | \(0.102285\pi\) | ||||
−0.948814 | + | 0.315837i | \(0.897715\pi\) | |||||||
\(20\) | −6.22053 | − | 7.82975i | −0.311026 | − | 0.391488i | ||||
\(21\) | 23.5741 | 1.12257 | ||||||||
\(22\) | 8.59939 | + | 8.59939i | 0.390881 | + | 0.390881i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 11.9455i | − | 0.497728i | ||||||
\(25\) | 5.65250 | − | 24.3526i | 0.226100 | − | 0.974104i | ||||
\(26\) | 5.79903 | 0.223039 | ||||||||
\(27\) | −0.487368 | − | 0.487368i | −0.0180507 | − | 0.0180507i | ||||
\(28\) | 7.89389 | − | 7.89389i | 0.281925 | − | 0.281925i | ||||
\(29\) | 41.1195i | 1.41791i | 0.705253 | + | 0.708956i | \(0.250834\pi\) | ||||
−0.705253 | + | 0.708956i | \(0.749166\pi\) | |||||||
\(30\) | 23.3825 | − | 18.5768i | 0.779418 | − | 0.619227i | ||||
\(31\) | −19.8906 | −0.641633 | −0.320817 | − | 0.947141i | \(-0.603957\pi\) | ||||
−0.320817 | + | 0.947141i | \(0.603957\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −25.6809 | + | 25.6809i | −0.778211 | + | 0.778211i | ||||
\(34\) | − | 31.4263i | − | 0.924302i | ||||||
\(35\) | 27.7278 | + | 3.17576i | 0.792224 | + | 0.0907359i | ||||
\(36\) | 17.6736 | 0.490933 | ||||||||
\(37\) | −40.5371 | − | 40.5371i | −1.09560 | − | 1.09560i | −0.994919 | − | 0.100680i | \(-0.967898\pi\) |
−0.100680 | − | 0.994919i | \(-0.532102\pi\) | |||||||
\(38\) | −12.0018 | + | 12.0018i | −0.315837 | + | 0.315837i | ||||
\(39\) | 17.3180i | 0.444052i | ||||||||
\(40\) | 1.60922 | − | 14.0503i | 0.0402305 | − | 0.351257i | ||||
\(41\) | −48.8398 | −1.19121 | −0.595607 | − | 0.803276i | \(-0.703088\pi\) | ||||
−0.595607 | + | 0.803276i | \(0.703088\pi\) | |||||||
\(42\) | 23.5741 | + | 23.5741i | 0.561287 | + | 0.561287i | ||||
\(43\) | −29.7297 | + | 29.7297i | −0.691388 | + | 0.691388i | −0.962537 | − | 0.271149i | \(-0.912596\pi\) |
0.271149 | + | 0.962537i | \(0.412596\pi\) | |||||||
\(44\) | 17.1988i | 0.390881i | ||||||||
\(45\) | 27.4848 | + | 34.5950i | 0.610773 | + | 0.768777i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 5.79882 | + | 5.79882i | 0.123379 | + | 0.123379i | 0.766100 | − | 0.642721i | \(-0.222195\pi\) |
−0.642721 | + | 0.766100i | \(0.722195\pi\) | |||||||
\(48\) | 11.9455 | − | 11.9455i | 0.248864 | − | 0.248864i | ||||
\(49\) | − | 17.8432i | − | 0.364148i | ||||||
\(50\) | 30.0051 | − | 18.7001i | 0.600102 | − | 0.374002i | ||||
\(51\) | 93.8504 | 1.84020 | ||||||||
\(52\) | 5.79903 | + | 5.79903i | 0.111520 | + | 0.111520i | ||||
\(53\) | −8.37708 | + | 8.37708i | −0.158058 | + | 0.158058i | −0.781706 | − | 0.623648i | \(-0.785650\pi\) |
0.623648 | + | 0.781706i | \(0.285650\pi\) | |||||||
\(54\) | − | 0.974735i | − | 0.0180507i | ||||||
\(55\) | −33.6655 | + | 26.7464i | −0.612101 | + | 0.486298i | ||||
\(56\) | 15.7878 | 0.281925 | ||||||||
\(57\) | −35.8418 | − | 35.8418i | −0.628804 | − | 0.628804i | ||||
\(58\) | −41.1195 | + | 41.1195i | −0.708956 | + | 0.708956i | ||||
\(59\) | 91.8342i | 1.55651i | 0.627947 | + | 0.778256i | \(0.283895\pi\) | ||||
−0.627947 | + | 0.778256i | \(0.716105\pi\) | |||||||
\(60\) | 41.9593 | + | 4.80573i | 0.699322 | + | 0.0800955i | ||||
\(61\) | −6.02932 | −0.0988413 | −0.0494206 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494206 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(62\) | −19.8906 | − | 19.8906i | −0.320817 | − | 0.320817i | ||||
\(63\) | −34.8784 | + | 34.8784i | −0.553625 | + | 0.553625i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −2.33298 | + | 20.3695i | −0.0358920 | + | 0.313377i | ||||
\(66\) | −51.3619 | −0.778211 | ||||||||
\(67\) | 21.2877 | + | 21.2877i | 0.317727 | + | 0.317727i | 0.847893 | − | 0.530167i | \(-0.177871\pi\) |
−0.530167 | + | 0.847893i | \(0.677871\pi\) | |||||||
\(68\) | 31.4263 | − | 31.4263i | 0.462151 | − | 0.462151i | ||||
\(69\) | − | 20.2545i | − | 0.293544i | ||||||
\(70\) | 24.5521 | + | 30.9036i | 0.350744 | + | 0.441480i | ||||
\(71\) | 89.1373 | 1.25545 | 0.627727 | − | 0.778433i | \(-0.283985\pi\) | ||||
0.627727 | + | 0.778433i | \(0.283985\pi\) | |||||||
\(72\) | 17.6736 | + | 17.6736i | 0.245467 | + | 0.245467i | ||||
\(73\) | −80.4250 | + | 80.4250i | −1.10171 | + | 1.10171i | −0.107509 | + | 0.994204i | \(0.534287\pi\) |
−0.994204 | + | 0.107509i | \(0.965713\pi\) | |||||||
\(74\) | − | 81.0743i | − | 1.09560i | ||||||
\(75\) | 55.8454 | + | 89.6063i | 0.744605 | + | 1.19475i | ||||
\(76\) | −24.0036 | −0.315837 | ||||||||
\(77\) | −33.9413 | − | 33.9413i | −0.440796 | − | 0.440796i | ||||
\(78\) | −17.3180 | + | 17.3180i | −0.222026 | + | 0.222026i | ||||
\(79\) | 66.7607i | 0.845072i | 0.906346 | + | 0.422536i | \(0.138860\pi\) | ||||
−0.906346 | + | 0.422536i | \(0.861140\pi\) | |||||||
\(80\) | 15.6595 | − | 12.4411i | 0.195744 | − | 0.155513i | ||||
\(81\) | 82.4421 | 1.01780 | ||||||||
\(82\) | −48.8398 | − | 48.8398i | −0.595607 | − | 0.595607i | ||||
\(83\) | 30.2065 | − | 30.2065i | 0.363934 | − | 0.363934i | −0.501325 | − | 0.865259i | \(-0.667154\pi\) |
0.865259 | + | 0.501325i | \(0.167154\pi\) | |||||||
\(84\) | 47.1481i | 0.561287i | ||||||||
\(85\) | 110.387 | + | 12.6430i | 1.29867 | + | 0.148741i | ||||
\(86\) | −59.4594 | −0.691388 | ||||||||
\(87\) | −122.798 | − | 122.798i | −1.41147 | − | 1.41147i | ||||
\(88\) | −17.1988 | + | 17.1988i | −0.195441 | + | 0.195441i | ||||
\(89\) | − | 48.7863i | − | 0.548161i | −0.961707 | − | 0.274081i | \(-0.911627\pi\) | ||
0.961707 | − | 0.274081i | \(-0.0883735\pi\) | |||||||
\(90\) | −7.11019 | + | 62.0798i | −0.0790021 | + | 0.689775i | ||||
\(91\) | −22.8884 | −0.251521 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 59.4008 | − | 59.4008i | 0.638718 | − | 0.638718i | ||||
\(94\) | 11.5976i | 0.123379i | ||||||||
\(95\) | −37.3288 | − | 46.9855i | −0.392934 | − | 0.494585i | ||||
\(96\) | 23.8910 | 0.248864 | ||||||||
\(97\) | −40.6035 | − | 40.6035i | −0.418593 | − | 0.418593i | 0.466126 | − | 0.884718i | \(-0.345649\pi\) |
−0.884718 | + | 0.466126i | \(0.845649\pi\) | |||||||
\(98\) | 17.8432 | − | 17.8432i | 0.182074 | − | 0.182074i | ||||
\(99\) | − | 75.9911i | − | 0.767587i | ||||||
\(100\) | 48.7052 | + | 11.3050i | 0.487052 | + | 0.113050i | ||||
\(101\) | −58.6599 | −0.580791 | −0.290396 | − | 0.956907i | \(-0.593787\pi\) | ||||
−0.290396 | + | 0.956907i | \(0.593787\pi\) | |||||||
\(102\) | 93.8504 | + | 93.8504i | 0.920102 | + | 0.920102i | ||||
\(103\) | −31.9173 | + | 31.9173i | −0.309876 | + | 0.309876i | −0.844861 | − | 0.534985i | \(-0.820317\pi\) |
0.534985 | + | 0.844861i | \(0.320317\pi\) | |||||||
\(104\) | 11.5981i | 0.111520i | ||||||||
\(105\) | −92.2896 | + | 73.3216i | −0.878948 | + | 0.698301i | ||||
\(106\) | −16.7542 | −0.158058 | ||||||||
\(107\) | 69.1476 | + | 69.1476i | 0.646239 | + | 0.646239i | 0.952082 | − | 0.305843i | \(-0.0989382\pi\) |
−0.305843 | + | 0.952082i | \(0.598938\pi\) | |||||||
\(108\) | 0.974735 | − | 0.974735i | 0.00902533 | − | 0.00902533i | ||||
\(109\) | − | 209.433i | − | 1.92141i | −0.277577 | − | 0.960703i | \(-0.589531\pi\) | ||
0.277577 | − | 0.960703i | \(-0.410469\pi\) | |||||||
\(110\) | −60.4119 | − | 6.91916i | −0.549199 | − | 0.0629015i | ||||
\(111\) | 242.118 | 2.18124 | ||||||||
\(112\) | 15.7878 | + | 15.7878i | 0.140962 | + | 0.140962i | ||||
\(113\) | −49.5439 | + | 49.5439i | −0.438441 | + | 0.438441i | −0.891487 | − | 0.453046i | \(-0.850337\pi\) |
0.453046 | + | 0.891487i | \(0.350337\pi\) | |||||||
\(114\) | − | 71.6836i | − | 0.628804i | ||||||
\(115\) | 2.72857 | − | 23.8234i | 0.0237267 | − | 0.207160i | ||||
\(116\) | −82.2389 | −0.708956 | ||||||||
\(117\) | −25.6224 | − | 25.6224i | −0.218995 | − | 0.218995i | ||||
\(118\) | −91.8342 | + | 91.8342i | −0.778256 | + | 0.778256i | ||||
\(119\) | 124.038i | 1.04233i | ||||||||
\(120\) | 37.1536 | + | 46.7651i | 0.309613 | + | 0.389709i | ||||
\(121\) | −47.0505 | −0.388847 | ||||||||
\(122\) | −6.02932 | − | 6.02932i | −0.0494206 | − | 0.0494206i | ||||
\(123\) | 145.854 | − | 145.854i | 1.18580 | − | 1.18580i | ||||
\(124\) | − | 39.7813i | − | 0.320817i | ||||||
\(125\) | 53.6142 | + | 112.918i | 0.428914 | + | 0.903346i | ||||
\(126\) | −69.7568 | −0.553625 | ||||||||
\(127\) | 50.2129 | + | 50.2129i | 0.395377 | + | 0.395377i | 0.876599 | − | 0.481222i | \(-0.159807\pi\) |
−0.481222 | + | 0.876599i | \(0.659807\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 177.568i | − | 1.37649i | ||||||
\(130\) | −22.7025 | + | 18.0365i | −0.174634 | + | 0.138742i | ||||
\(131\) | −76.6729 | −0.585289 | −0.292645 | − | 0.956221i | \(-0.594535\pi\) | ||||
−0.292645 | + | 0.956221i | \(0.594535\pi\) | |||||||
\(132\) | −51.3619 | − | 51.3619i | −0.389105 | − | 0.389105i | ||||
\(133\) | 47.3704 | − | 47.3704i | 0.356169 | − | 0.356169i | ||||
\(134\) | 42.5754i | 0.317727i | ||||||||
\(135\) | 3.42383 | + | 0.392141i | 0.0253617 | + | 0.00290475i | ||||
\(136\) | 62.8525 | 0.462151 | ||||||||
\(137\) | 188.464 | + | 188.464i | 1.37565 | + | 1.37565i | 0.851831 | + | 0.523817i | \(0.175492\pi\) |
0.523817 | + | 0.851831i | \(0.324508\pi\) | |||||||
\(138\) | 20.2545 | − | 20.2545i | 0.146772 | − | 0.146772i | ||||
\(139\) | 182.679i | 1.31424i | 0.753786 | + | 0.657120i | \(0.228226\pi\) | ||||
−0.753786 | + | 0.657120i | \(0.771774\pi\) | |||||||
\(140\) | −6.35151 | + | 55.4557i | −0.0453679 | + | 0.396112i | ||||
\(141\) | −34.6348 | −0.245637 | ||||||||
\(142\) | 89.1373 | + | 89.1373i | 0.627727 | + | 0.627727i | ||||
\(143\) | 24.9340 | − | 24.9340i | 0.174364 | − | 0.174364i | ||||
\(144\) | 35.3472i | 0.245467i | ||||||||
\(145\) | −127.892 | − | 160.978i | −0.882016 | − | 1.11019i | ||||
\(146\) | −160.850 | −1.10171 | ||||||||
\(147\) | 53.2865 | + | 53.2865i | 0.362493 | + | 0.362493i | ||||
\(148\) | 81.0743 | − | 81.0743i | 0.547799 | − | 0.547799i | ||||
\(149\) | − | 228.292i | − | 1.53216i | −0.642744 | − | 0.766081i | \(-0.722204\pi\) | ||
0.642744 | − | 0.766081i | \(-0.277796\pi\) | |||||||
\(150\) | −33.7609 | + | 145.452i | −0.225073 | + | 0.969678i | ||||
\(151\) | −87.2770 | −0.577994 | −0.288997 | − | 0.957330i | \(-0.593322\pi\) | ||||
−0.288997 | + | 0.957330i | \(0.593322\pi\) | |||||||
\(152\) | −24.0036 | − | 24.0036i | −0.157918 | − | 0.157918i | ||||
\(153\) | −138.854 | + | 138.854i | −0.907541 | + | 0.907541i | ||||
\(154\) | − | 67.8826i | − | 0.440796i | ||||||
\(155\) | 77.8693 | − | 61.8651i | 0.502383 | − | 0.399130i | ||||
\(156\) | −34.6361 | −0.222026 | ||||||||
\(157\) | −179.098 | − | 179.098i | −1.14075 | − | 1.14075i | −0.988313 | − | 0.152440i | \(-0.951287\pi\) |
−0.152440 | − | 0.988313i | \(-0.548713\pi\) | |||||||
\(158\) | −66.7607 | + | 66.7607i | −0.422536 | + | 0.422536i | ||||
\(159\) | − | 50.0341i | − | 0.314680i | ||||||
\(160\) | 28.1006 | + | 3.21844i | 0.175629 | + | 0.0201153i | ||||
\(161\) | 26.7695 | 0.166270 | ||||||||
\(162\) | 82.4421 | + | 82.4421i | 0.508902 | + | 0.508902i | ||||
\(163\) | −2.08145 | + | 2.08145i | −0.0127697 | + | 0.0127697i | −0.713463 | − | 0.700693i | \(-0.752874\pi\) |
0.700693 | + | 0.713463i | \(0.252874\pi\) | |||||||
\(164\) | − | 97.6796i | − | 0.595607i | ||||||
\(165\) | 20.6632 | − | 180.412i | 0.125231 | − | 1.09341i | ||||
\(166\) | 60.4131 | 0.363934 | ||||||||
\(167\) | −19.6858 | − | 19.6858i | −0.117879 | − | 0.117879i | 0.645707 | − | 0.763586i | \(-0.276563\pi\) |
−0.763586 | + | 0.645707i | \(0.776563\pi\) | |||||||
\(168\) | −47.1481 | + | 47.1481i | −0.280644 | + | 0.280644i | ||||
\(169\) | 152.186i | 0.900507i | ||||||||
\(170\) | 97.7440 | + | 123.030i | 0.574965 | + | 0.723705i | ||||
\(171\) | 106.058 | 0.620219 | ||||||||
\(172\) | −59.4594 | − | 59.4594i | −0.345694 | − | 0.345694i | ||||
\(173\) | 14.1760 | − | 14.1760i | 0.0819422 | − | 0.0819422i | −0.664948 | − | 0.746890i | \(-0.731546\pi\) |
0.746890 | + | 0.664948i | \(0.231546\pi\) | |||||||
\(174\) | − | 245.596i | − | 1.41147i | ||||||
\(175\) | −118.429 | + | 73.8083i | −0.676734 | + | 0.421762i | ||||
\(176\) | −34.3976 | −0.195441 | ||||||||
\(177\) | −274.251 | − | 274.251i | −1.54944 | − | 1.54944i | ||||
\(178\) | 48.7863 | − | 48.7863i | 0.274081 | − | 0.274081i | ||||
\(179\) | − | 292.614i | − | 1.63472i | −0.576130 | − | 0.817358i | \(-0.695438\pi\) | ||
0.576130 | − | 0.817358i | \(-0.304562\pi\) | |||||||
\(180\) | −69.1900 | + | 54.9696i | −0.384389 | + | 0.305387i | ||||
\(181\) | 78.0441 | 0.431183 | 0.215591 | − | 0.976484i | \(-0.430832\pi\) | ||||
0.215591 | + | 0.976484i | \(0.430832\pi\) | |||||||
\(182\) | −22.8884 | − | 22.8884i | −0.125761 | − | 0.125761i | ||||
\(183\) | 18.0058 | − | 18.0058i | 0.0983922 | − | 0.0983922i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 284.779 | + | 32.6166i | 1.53935 | + | 0.176306i | ||||
\(186\) | 118.802 | 0.638718 | ||||||||
\(187\) | −135.123 | − | 135.123i | −0.722585 | − | 0.722585i | ||||
\(188\) | −11.5976 | + | 11.5976i | −0.0616896 | + | 0.0616896i | ||||
\(189\) | 3.84723i | 0.0203557i | ||||||||
\(190\) | 9.65678 | − | 84.3143i | 0.0508251 | − | 0.443760i | ||||
\(191\) | −69.6705 | −0.364767 | −0.182384 | − | 0.983227i | \(-0.558381\pi\) | ||||
−0.182384 | + | 0.983227i | \(0.558381\pi\) | |||||||
\(192\) | 23.8910 | + | 23.8910i | 0.124432 | + | 0.124432i | ||||
\(193\) | −235.374 | + | 235.374i | −1.21956 | + | 1.21956i | −0.251769 | + | 0.967787i | \(0.581012\pi\) |
−0.967787 | + | 0.251769i | \(0.918988\pi\) | |||||||
\(194\) | − | 81.2070i | − | 0.418593i | ||||||
\(195\) | −53.8637 | − | 67.7980i | −0.276224 | − | 0.347682i | ||||
\(196\) | 35.6865 | 0.182074 | ||||||||
\(197\) | 137.287 | + | 137.287i | 0.696887 | + | 0.696887i | 0.963738 | − | 0.266851i | \(-0.0859832\pi\) |
−0.266851 | + | 0.963738i | \(0.585983\pi\) | |||||||
\(198\) | 75.9911 | − | 75.9911i | 0.383793 | − | 0.383793i | ||||
\(199\) | − | 221.293i | − | 1.11202i | −0.831174 | − | 0.556012i | \(-0.812331\pi\) | ||
0.831174 | − | 0.556012i | \(-0.187669\pi\) | |||||||
\(200\) | 37.4002 | + | 60.0102i | 0.187001 | + | 0.300051i | ||||
\(201\) | −127.146 | −0.632566 | ||||||||
\(202\) | −58.6599 | − | 58.6599i | −0.290396 | − | 0.290396i | ||||
\(203\) | 162.296 | − | 162.296i | 0.799489 | − | 0.799489i | ||||
\(204\) | 187.701i | 0.920102i | ||||||||
\(205\) | 191.202 | − | 151.905i | 0.932691 | − | 0.740998i | ||||
\(206\) | −63.8345 | −0.309876 | ||||||||
\(207\) | 29.9671 | + | 29.9671i | 0.144768 | + | 0.144768i | ||||
\(208\) | −11.5981 | + | 11.5981i | −0.0557599 | + | 0.0557599i | ||||
\(209\) | 103.208i | 0.493819i | ||||||||
\(210\) | −165.611 | − | 18.9680i | −0.788625 | − | 0.0903236i | ||||
\(211\) | 206.938 | 0.980749 | 0.490374 | − | 0.871512i | \(-0.336860\pi\) | ||||
0.490374 | + | 0.871512i | \(0.336860\pi\) | |||||||
\(212\) | −16.7542 | − | 16.7542i | −0.0790290 | − | 0.0790290i | ||||
\(213\) | −266.197 | + | 266.197i | −1.24975 | + | 1.24975i | ||||
\(214\) | 138.295i | 0.646239i | ||||||||
\(215\) | 23.9208 | − | 208.855i | 0.111260 | − | 0.971420i | ||||
\(216\) | 1.94947 | 0.00902533 | ||||||||
\(217\) | 78.5072 | + | 78.5072i | 0.361784 | + | 0.361784i | ||||
\(218\) | 209.433 | − | 209.433i | 0.960703 | − | 0.960703i | ||||
\(219\) | − | 480.358i | − | 2.19341i | ||||||
\(220\) | −53.4928 | − | 67.3311i | −0.243149 | − | 0.306050i | ||||
\(221\) | −91.1209 | −0.412312 | ||||||||
\(222\) | 242.118 | + | 242.118i | 1.09062 | + | 1.09062i | ||||
\(223\) | −146.489 | + | 146.489i | −0.656901 | + | 0.656901i | −0.954646 | − | 0.297745i | \(-0.903766\pi\) |
0.297745 | + | 0.954646i | \(0.403766\pi\) | |||||||
\(224\) | 31.5756i | 0.140962i | ||||||||
\(225\) | −215.199 | − | 49.9501i | −0.956441 | − | 0.222000i | ||||
\(226\) | −99.0877 | −0.438441 | ||||||||
\(227\) | 116.497 | + | 116.497i | 0.513202 | + | 0.513202i | 0.915506 | − | 0.402304i | \(-0.131791\pi\) |
−0.402304 | + | 0.915506i | \(0.631791\pi\) | |||||||
\(228\) | 71.6836 | − | 71.6836i | 0.314402 | − | 0.314402i | ||||
\(229\) | 398.498i | 1.74017i | 0.492905 | + | 0.870083i | \(0.335935\pi\) | ||||
−0.492905 | + | 0.870083i | \(0.664065\pi\) | |||||||
\(230\) | 26.5520 | − | 21.0948i | 0.115443 | − | 0.0917167i | ||||
\(231\) | 202.723 | 0.877587 | ||||||||
\(232\) | −82.2389 | − | 82.2389i | −0.354478 | − | 0.354478i | ||||
\(233\) | −133.851 | + | 133.851i | −0.574470 | + | 0.574470i | −0.933374 | − | 0.358904i | \(-0.883150\pi\) |
0.358904 | + | 0.933374i | \(0.383150\pi\) | |||||||
\(234\) | − | 51.2449i | − | 0.218995i | ||||||
\(235\) | −40.7375 | − | 4.66579i | −0.173351 | − | 0.0198544i | ||||
\(236\) | −183.668 | −0.778256 | ||||||||
\(237\) | −199.372 | − | 199.372i | −0.841233 | − | 0.841233i | ||||
\(238\) | −124.038 | + | 124.038i | −0.521167 | + | 0.521167i | ||||
\(239\) | 206.404i | 0.863615i | 0.901966 | + | 0.431808i | \(0.142124\pi\) | ||||
−0.901966 | + | 0.431808i | \(0.857876\pi\) | |||||||
\(240\) | −9.61146 | + | 83.9187i | −0.0400477 | + | 0.349661i | ||||
\(241\) | −92.8472 | −0.385258 | −0.192629 | − | 0.981272i | \(-0.561701\pi\) | ||||
−0.192629 | + | 0.981272i | \(0.561701\pi\) | |||||||
\(242\) | −47.0505 | − | 47.0505i | −0.194424 | − | 0.194424i | ||||
\(243\) | −241.816 | + | 241.816i | −0.995129 | + | 0.995129i | ||||
\(244\) | − | 12.0586i | − | 0.0494206i | ||||||
\(245\) | 55.4972 | + | 69.8541i | 0.226519 | + | 0.285119i | ||||
\(246\) | 291.707 | 1.18580 | ||||||||
\(247\) | 34.7994 | + | 34.7994i | 0.140888 | + | 0.140888i | ||||
\(248\) | 39.7813 | − | 39.7813i | 0.160408 | − | 0.160408i | ||||
\(249\) | 180.416i | 0.724561i | ||||||||
\(250\) | −59.3040 | + | 166.532i | −0.237216 | + | 0.666130i | ||||
\(251\) | 427.161 | 1.70184 | 0.850918 | − | 0.525298i | \(-0.176046\pi\) | ||||
0.850918 | + | 0.525298i | \(0.176046\pi\) | |||||||
\(252\) | −69.7568 | − | 69.7568i | −0.276813 | − | 0.276813i | ||||
\(253\) | −29.1619 | + | 29.1619i | −0.115265 | + | 0.115265i | ||||
\(254\) | 100.426i | 0.395377i | ||||||||
\(255\) | −367.413 | + | 291.900i | −1.44083 | + | 1.14470i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 209.203 | + | 209.203i | 0.814019 | + | 0.814019i | 0.985234 | − | 0.171214i | \(-0.0547691\pi\) |
−0.171214 | + | 0.985234i | \(0.554769\pi\) | |||||||
\(258\) | 177.568 | − | 177.568i | 0.688247 | − | 0.688247i | ||||
\(259\) | 319.996i | 1.23551i | ||||||||
\(260\) | −40.7390 | − | 4.66596i | −0.156688 | − | 0.0179460i | ||||
\(261\) | 363.364 | 1.39220 | ||||||||
\(262\) | −76.6729 | − | 76.6729i | −0.292645 | − | 0.292645i | ||||
\(263\) | 86.9091 | − | 86.9091i | 0.330453 | − | 0.330453i | −0.522305 | − | 0.852758i | \(-0.674928\pi\) |
0.852758 | + | 0.522305i | \(0.174928\pi\) | |||||||
\(264\) | − | 102.724i | − | 0.389105i | ||||||
\(265\) | 6.74029 | − | 58.8501i | 0.0254350 | − | 0.222076i | ||||
\(266\) | 94.7409 | 0.356169 | ||||||||
\(267\) | 145.694 | + | 145.694i | 0.545670 | + | 0.545670i | ||||
\(268\) | −42.5754 | + | 42.5754i | −0.158863 | + | 0.158863i | ||||
\(269\) | 324.191i | 1.20517i | 0.798054 | + | 0.602586i | \(0.205863\pi\) | ||||
−0.798054 | + | 0.602586i | \(0.794137\pi\) | |||||||
\(270\) | 3.03168 | + | 3.81597i | 0.0112285 | + | 0.0141332i | ||||
\(271\) | −374.518 | −1.38199 | −0.690993 | − | 0.722862i | \(-0.742826\pi\) | ||||
−0.690993 | + | 0.722862i | \(0.742826\pi\) | |||||||
\(272\) | 62.8525 | + | 62.8525i | 0.231075 | + | 0.231075i | ||||
\(273\) | 68.3533 | − | 68.3533i | 0.250379 | − | 0.250379i | ||||
\(274\) | 376.928i | 1.37565i | ||||||||
\(275\) | 48.6081 | − | 209.417i | 0.176757 | − | 0.761518i | ||||
\(276\) | 40.5091 | 0.146772 | ||||||||
\(277\) | 51.1306 | + | 51.1306i | 0.184587 | + | 0.184587i | 0.793351 | − | 0.608764i | \(-0.208334\pi\) |
−0.608764 | + | 0.793351i | \(0.708334\pi\) | |||||||
\(278\) | −182.679 | + | 182.679i | −0.657120 | + | 0.657120i | ||||
\(279\) | 175.770i | 0.629998i | ||||||||
\(280\) | −61.8072 | + | 49.1042i | −0.220740 | + | 0.175372i | ||||
\(281\) | 398.890 | 1.41954 | 0.709769 | − | 0.704434i | \(-0.248799\pi\) | ||||
0.709769 | + | 0.704434i | \(0.248799\pi\) | |||||||
\(282\) | −34.6348 | − | 34.6348i | −0.122819 | − | 0.122819i | ||||
\(283\) | −23.1698 | + | 23.1698i | −0.0818720 | + | 0.0818720i | −0.746857 | − | 0.664985i | \(-0.768438\pi\) |
0.664985 | + | 0.746857i | \(0.268438\pi\) | |||||||
\(284\) | 178.275i | 0.627727i | ||||||||
\(285\) | 251.794 | + | 28.8387i | 0.883487 | + | 0.101188i | ||||
\(286\) | 49.8681 | 0.174364 | ||||||||
\(287\) | 192.768 | + | 192.768i | 0.671665 | + | 0.671665i | ||||
\(288\) | −35.3472 | + | 35.3472i | −0.122733 | + | 0.122733i | ||||
\(289\) | 204.805i | 0.708668i | ||||||||
\(290\) | 33.0852 | − | 288.870i | 0.114087 | − | 0.996103i | ||||
\(291\) | 242.514 | 0.833381 | ||||||||
\(292\) | −160.850 | − | 160.850i | −0.550856 | − | 0.550856i | ||||
\(293\) | −60.7766 | + | 60.7766i | −0.207429 | + | 0.207429i | −0.803174 | − | 0.595745i | \(-0.796857\pi\) |
0.595745 | + | 0.803174i | \(0.296857\pi\) | |||||||
\(294\) | 106.573i | 0.362493i | ||||||||
\(295\) | −285.629 | − | 359.520i | −0.968233 | − | 1.21871i | ||||
\(296\) | 162.149 | 0.547799 | ||||||||
\(297\) | −4.19106 | − | 4.19106i | −0.0141113 | − | 0.0141113i | ||||
\(298\) | 228.292 | − | 228.292i | 0.766081 | − | 0.766081i | ||||
\(299\) | 19.6655i | 0.0657708i | ||||||||
\(300\) | −179.213 | + | 111.691i | −0.597375 | + | 0.372303i | ||||
\(301\) | 234.683 | 0.779678 | ||||||||
\(302\) | −87.2770 | − | 87.2770i | −0.288997 | − | 0.288997i | ||||
\(303\) | 175.180 | − | 175.180i | 0.578152 | − | 0.578152i | ||||
\(304\) | − | 48.0072i | − | 0.157918i | ||||||
\(305\) | 23.6040 | − | 18.7528i | 0.0773903 | − | 0.0614845i | ||||
\(306\) | −277.708 | −0.907541 | ||||||||
\(307\) | 265.540 | + | 265.540i | 0.864951 | + | 0.864951i | 0.991908 | − | 0.126957i | \(-0.0405210\pi\) |
−0.126957 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(308\) | 67.8826 | − | 67.8826i | 0.220398 | − | 0.220398i | ||||
\(309\) | − | 190.633i | − | 0.616937i | ||||||
\(310\) | 139.734 | + | 16.0042i | 0.450756 | + | 0.0516265i | ||||
\(311\) | −421.810 | −1.35630 | −0.678150 | − | 0.734923i | \(-0.737218\pi\) | ||||
−0.678150 | + | 0.734923i | \(0.737218\pi\) | |||||||
\(312\) | −34.6361 | − | 34.6361i | −0.111013 | − | 0.111013i | ||||
\(313\) | 129.271 | − | 129.271i | 0.413008 | − | 0.413008i | −0.469777 | − | 0.882785i | \(-0.655666\pi\) |
0.882785 | + | 0.469777i | \(0.155666\pi\) | |||||||
\(314\) | − | 358.196i | − | 1.14075i | ||||||
\(315\) | 28.0635 | − | 245.026i | 0.0890905 | − | 0.777859i | ||||
\(316\) | −133.521 | −0.422536 | ||||||||
\(317\) | −268.224 | − | 268.224i | −0.846131 | − | 0.846131i | 0.143517 | − | 0.989648i | \(-0.454159\pi\) |
−0.989648 | + | 0.143517i | \(0.954159\pi\) | |||||||
\(318\) | 50.0341 | − | 50.0341i | 0.157340 | − | 0.157340i | ||||
\(319\) | 353.602i | 1.10847i | ||||||||
\(320\) | 24.8821 | + | 31.3190i | 0.0777566 | + | 0.0978719i | ||||
\(321\) | −413.001 | −1.28661 | ||||||||
\(322\) | 26.7695 | + | 26.7695i | 0.0831351 | + | 0.0831351i | ||||
\(323\) | 188.586 | − | 188.586i | 0.583857 | − | 0.583857i | ||||
\(324\) | 164.884i | 0.508902i | ||||||||
\(325\) | −54.2212 | − | 87.0002i | −0.166834 | − | 0.267693i | ||||
\(326\) | −4.16291 | −0.0127697 | ||||||||
\(327\) | 625.445 | + | 625.445i | 1.91268 | + | 1.91268i | ||||
\(328\) | 97.6796 | − | 97.6796i | 0.297804 | − | 0.297804i | ||||
\(329\) | − | 45.7752i | − | 0.139134i | ||||||
\(330\) | 201.075 | − | 159.749i | 0.609320 | − | 0.484088i | ||||
\(331\) | −234.830 | −0.709455 | −0.354727 | − | 0.934970i | \(-0.615426\pi\) | ||||
−0.354727 | + | 0.934970i | \(0.615426\pi\) | |||||||
\(332\) | 60.4131 | + | 60.4131i | 0.181967 | + | 0.181967i | ||||
\(333\) | −358.219 | + | 358.219i | −1.07573 | + | 1.07573i | ||||
\(334\) | − | 39.3716i | − | 0.117879i | ||||||
\(335\) | −149.549 | − | 17.1283i | −0.446415 | − | 0.0511292i | ||||
\(336\) | −94.2963 | −0.280644 | ||||||||
\(337\) | 183.913 | + | 183.913i | 0.545737 | + | 0.545737i | 0.925205 | − | 0.379468i | \(-0.123893\pi\) |
−0.379468 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(338\) | −152.186 | + | 152.186i | −0.450253 | + | 0.450253i | ||||
\(339\) | − | 295.912i | − | 0.872898i | ||||||
\(340\) | −25.2859 | + | 220.774i | −0.0743703 | + | 0.649335i | ||||
\(341\) | −171.047 | −0.501605 | ||||||||
\(342\) | 106.058 | + | 106.058i | 0.310110 | + | 0.310110i | ||||
\(343\) | −263.827 | + | 263.827i | −0.769174 | + | 0.769174i | ||||
\(344\) | − | 118.919i | − | 0.345694i | ||||||
\(345\) | 62.9970 | + | 79.2940i | 0.182600 | + | 0.229838i | ||||
\(346\) | 28.3520 | 0.0819422 | ||||||||
\(347\) | −50.3871 | − | 50.3871i | −0.145208 | − | 0.145208i | 0.630766 | − | 0.775973i | \(-0.282741\pi\) |
−0.775973 | + | 0.630766i | \(0.782741\pi\) | |||||||
\(348\) | 245.596 | − | 245.596i | 0.705735 | − | 0.705735i | ||||
\(349\) | − | 344.711i | − | 0.987711i | −0.869544 | − | 0.493855i | \(-0.835587\pi\) | ||
0.869544 | − | 0.493855i | \(-0.164413\pi\) | |||||||
\(350\) | −192.237 | − | 44.6203i | −0.549248 | − | 0.127486i | ||||
\(351\) | −2.82626 | −0.00805202 | ||||||||
\(352\) | −34.3976 | − | 34.3976i | −0.0977203 | − | 0.0977203i | ||||
\(353\) | 462.680 | − | 462.680i | 1.31071 | − | 1.31071i | 0.389814 | − | 0.920894i | \(-0.372539\pi\) |
0.920894 | − | 0.389814i | \(-0.127461\pi\) | |||||||
\(354\) | − | 548.502i | − | 1.54944i | ||||||
\(355\) | −348.961 | + | 277.241i | −0.982990 | + | 0.780959i | ||||
\(356\) | 97.5727 | 0.274081 | ||||||||
\(357\) | −370.423 | − | 370.423i | −1.03760 | − | 1.03760i | ||||
\(358\) | 292.614 | − | 292.614i | 0.817358 | − | 0.817358i | ||||
\(359\) | 408.460i | 1.13777i | 0.822417 | + | 0.568886i | \(0.192625\pi\) | ||||
−0.822417 | + | 0.568886i | \(0.807375\pi\) | |||||||
\(360\) | −124.160 | − | 14.2204i | −0.344888 | − | 0.0395010i | ||||
\(361\) | 216.957 | 0.600988 | ||||||||
\(362\) | 78.0441 | + | 78.0441i | 0.215591 | + | 0.215591i | ||||
\(363\) | 140.510 | − | 140.510i | 0.387081 | − | 0.387081i | ||||
\(364\) | − | 45.7769i | − | 0.125761i | ||||||
\(365\) | 64.7109 | − | 564.997i | 0.177290 | − | 1.54794i | ||||
\(366\) | 36.0115 | 0.0983922 | ||||||||
\(367\) | −460.907 | − | 460.907i | −1.25588 | − | 1.25588i | −0.953043 | − | 0.302836i | \(-0.902067\pi\) |
−0.302836 | − | 0.953043i | \(-0.597933\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 431.588i | 1.16961i | ||||||||
\(370\) | 252.163 | + | 317.396i | 0.681520 | + | 0.857826i | ||||
\(371\) | 66.1277 | 0.178242 | ||||||||
\(372\) | 118.802 | + | 118.802i | 0.319359 | + | 0.319359i | ||||
\(373\) | 267.027 | − | 267.027i | 0.715889 | − | 0.715889i | −0.251871 | − | 0.967761i | \(-0.581046\pi\) |
0.967761 | + | 0.251871i | \(0.0810460\pi\) | |||||||
\(374\) | − | 270.247i | − | 0.722585i | ||||||
\(375\) | −497.327 | − | 177.104i | −1.32621 | − | 0.472276i | ||||
\(376\) | −23.1953 | −0.0616896 | ||||||||
\(377\) | 119.226 | + | 119.226i | 0.316250 | + | 0.316250i | ||||
\(378\) | −3.84723 | + | 3.84723i | −0.0101778 | + | 0.0101778i | ||||
\(379\) | 257.246i | 0.678749i | 0.940651 | + | 0.339374i | \(0.110215\pi\) | ||||
−0.940651 | + | 0.339374i | \(0.889785\pi\) | |||||||
\(380\) | 93.9711 | − | 74.6575i | 0.247292 | − | 0.196467i | ||||
\(381\) | −299.909 | −0.787161 | ||||||||
\(382\) | −69.6705 | − | 69.6705i | −0.182384 | − | 0.182384i | ||||
\(383\) | 102.313 | − | 102.313i | 0.267136 | − | 0.267136i | −0.560809 | − | 0.827945i | \(-0.689510\pi\) |
0.827945 | + | 0.560809i | \(0.189510\pi\) | |||||||
\(384\) | 47.7819i | 0.124432i | ||||||||
\(385\) | 238.443 | + | 27.3096i | 0.619331 | + | 0.0709339i | ||||
\(386\) | −470.749 | −1.21956 | ||||||||
\(387\) | 262.715 | + | 262.715i | 0.678851 | + | 0.678851i | ||||
\(388\) | 81.2070 | − | 81.2070i | 0.209296 | − | 0.209296i | ||||
\(389\) | 13.5885i | 0.0349319i | 0.999847 | + | 0.0174660i | \(0.00555987\pi\) | ||||
−0.999847 | + | 0.0174660i | \(0.994440\pi\) | |||||||
\(390\) | 13.9343 | − | 121.662i | 0.0357289 | − | 0.311953i | ||||
\(391\) | 106.572 | 0.272562 | ||||||||
\(392\) | 35.6865 | + | 35.6865i | 0.0910369 | + | 0.0910369i | ||||
\(393\) | 228.974 | − | 228.974i | 0.582630 | − | 0.582630i | ||||
\(394\) | 274.573i | 0.696887i | ||||||||
\(395\) | −207.644 | − | 261.360i | −0.525680 | − | 0.661671i | ||||
\(396\) | 151.982 | 0.383793 | ||||||||
\(397\) | −444.867 | − | 444.867i | −1.12057 | − | 1.12057i | −0.991655 | − | 0.128918i | \(-0.958850\pi\) |
−0.128918 | − | 0.991655i | \(-0.541150\pi\) | |||||||
\(398\) | 221.293 | − | 221.293i | 0.556012 | − | 0.556012i | ||||
\(399\) | 282.931i | 0.709101i | ||||||||
\(400\) | −22.6100 | + | 97.4104i | −0.0565250 | + | 0.243526i | ||||
\(401\) | −496.549 | −1.23828 | −0.619139 | − | 0.785281i | \(-0.712518\pi\) | ||||
−0.619139 | + | 0.785281i | \(0.712518\pi\) | |||||||
\(402\) | −127.146 | − | 127.146i | −0.316283 | − | 0.316283i | ||||
\(403\) | −57.6731 | + | 57.6731i | −0.143110 | + | 0.143110i | ||||
\(404\) | − | 117.320i | − | 0.290396i | ||||||
\(405\) | −322.751 | + | 256.417i | −0.796915 | + | 0.633128i | ||||
\(406\) | 324.592 | 0.799489 | ||||||||
\(407\) | −348.595 | − | 348.595i | −0.856498 | − | 0.856498i | ||||
\(408\) | −187.701 | + | 187.701i | −0.460051 | + | 0.460051i | ||||
\(409\) | 504.901i | 1.23448i | 0.786776 | + | 0.617238i | \(0.211748\pi\) | ||||
−0.786776 | + | 0.617238i | \(0.788252\pi\) | |||||||
\(410\) | 343.106 | + | 39.2970i | 0.836845 | + | 0.0958464i | ||||
\(411\) | −1125.64 | −2.73880 | ||||||||
\(412\) | −63.8345 | − | 63.8345i | −0.154938 | − | 0.154938i | ||||
\(413\) | 362.465 | − | 362.465i | 0.877638 | − | 0.877638i | ||||
\(414\) | 59.9341i | 0.144768i | ||||||||
\(415\) | −24.3045 | + | 212.205i | −0.0585651 | + | 0.511338i | ||||
\(416\) | −23.1961 | −0.0557599 | ||||||||
\(417\) | −545.548 | − | 545.548i | −1.30827 | − | 1.30827i | ||||
\(418\) | −103.208 | + | 103.208i | −0.246909 | + | 0.246909i | ||||
\(419\) | 496.330i | 1.18456i | 0.805733 | + | 0.592280i | \(0.201772\pi\) | ||||
−0.805733 | + | 0.592280i | \(0.798228\pi\) | |||||||
\(420\) | −146.643 | − | 184.579i | −0.349151 | − | 0.439474i | ||||
\(421\) | −217.991 | −0.517793 | −0.258897 | − | 0.965905i | \(-0.583359\pi\) | ||||
−0.258897 | + | 0.965905i | \(0.583359\pi\) | |||||||
\(422\) | 206.938 | + | 206.938i | 0.490374 | + | 0.490374i | ||||
\(423\) | 51.2430 | − | 51.2430i | 0.121142 | − | 0.121142i | ||||
\(424\) | − | 33.5083i | − | 0.0790290i | ||||||
\(425\) | −471.474 | + | 293.837i | −1.10935 | + | 0.691381i | ||||
\(426\) | −532.394 | −1.24975 | ||||||||
\(427\) | 23.7974 | + | 23.7974i | 0.0557316 | + | 0.0557316i | ||||
\(428\) | −138.295 | + | 138.295i | −0.323120 | + | 0.323120i | ||||
\(429\) | 148.925i | 0.347143i | ||||||||
\(430\) | 232.776 | − | 184.934i | 0.541340 | − | 0.430080i | ||||
\(431\) | −194.670 | −0.451670 | −0.225835 | − | 0.974166i | \(-0.572511\pi\) | ||||
−0.225835 | + | 0.974166i | \(0.572511\pi\) | |||||||
\(432\) | 1.94947 | + | 1.94947i | 0.00451266 | + | 0.00451266i | ||||
\(433\) | −83.0439 | + | 83.0439i | −0.191787 | + | 0.191787i | −0.796468 | − | 0.604681i | \(-0.793301\pi\) |
0.604681 | + | 0.796468i | \(0.293301\pi\) | |||||||
\(434\) | 157.014i | 0.361784i | ||||||||
\(435\) | 862.672 | + | 98.8045i | 1.98315 | + | 0.227137i | ||||
\(436\) | 418.867 | 0.960703 | ||||||||
\(437\) | −40.7001 | − | 40.7001i | −0.0931352 | − | 0.0931352i | ||||
\(438\) | 480.358 | − | 480.358i | 1.09671 | − | 1.09671i | ||||
\(439\) | − | 651.478i | − | 1.48400i | −0.670397 | − | 0.742002i | \(-0.733876\pi\) | ||
0.670397 | − | 0.742002i | \(-0.266124\pi\) | |||||||
\(440\) | 13.8383 | − | 120.824i | 0.0314507 | − | 0.274600i | ||||
\(441\) | −157.677 | −0.357545 | ||||||||
\(442\) | −91.1209 | − | 91.1209i | −0.206156 | − | 0.206156i | ||||
\(443\) | 32.9886 | − | 32.9886i | 0.0744663 | − | 0.0744663i | −0.668893 | − | 0.743359i | \(-0.733231\pi\) |
0.743359 | + | 0.668893i | \(0.233231\pi\) | |||||||
\(444\) | 484.236i | 1.09062i | ||||||||
\(445\) | 151.738 | + | 190.992i | 0.340985 | + | 0.429196i | ||||
\(446\) | −292.978 | −0.656901 | ||||||||
\(447\) | 681.765 | + | 681.765i | 1.52520 | + | 1.52520i | ||||
\(448\) | −31.5756 | + | 31.5756i | −0.0704812 | + | 0.0704812i | ||||
\(449\) | − | 528.035i | − | 1.17603i | −0.808852 | − | 0.588013i | \(-0.799911\pi\) | ||
0.808852 | − | 0.588013i | \(-0.200089\pi\) | |||||||
\(450\) | −165.249 | − | 265.149i | −0.367220 | − | 0.589220i | ||||
\(451\) | −419.992 | −0.931247 | ||||||||
\(452\) | −99.0877 | − | 99.0877i | −0.219221 | − | 0.219221i | ||||
\(453\) | 260.641 | − | 260.641i | 0.575368 | − | 0.575368i | ||||
\(454\) | 232.994i | 0.513202i | ||||||||
\(455\) | 89.6054 | − | 71.1891i | 0.196935 | − | 0.156460i | ||||
\(456\) | 143.367 | 0.314402 | ||||||||
\(457\) | −299.231 | − | 299.231i | −0.654773 | − | 0.654773i | 0.299365 | − | 0.954139i | \(-0.403225\pi\) |
−0.954139 | + | 0.299365i | \(0.903225\pi\) | |||||||
\(458\) | −398.498 | + | 398.498i | −0.870083 | + | 0.870083i | ||||
\(459\) | 15.3161i | 0.0333685i | ||||||||
\(460\) | 47.6468 | + | 5.45714i | 0.103580 | + | 0.0118633i | ||||
\(461\) | 482.726 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(462\) | 202.723 | + | 202.723i | 0.438794 | + | 0.438794i | ||||
\(463\) | 342.679 | − | 342.679i | 0.740128 | − | 0.740128i | −0.232474 | − | 0.972603i | \(-0.574682\pi\) |
0.972603 | + | 0.232474i | \(0.0746821\pi\) | |||||||
\(464\) | − | 164.478i | − | 0.354478i | ||||||
\(465\) | −47.7945 | + | 417.299i | −0.102784 | + | 0.897417i | ||||
\(466\) | −267.703 | −0.574470 | ||||||||
\(467\) | 513.486 | + | 513.486i | 1.09954 | + | 1.09954i | 0.994464 | + | 0.105077i | \(0.0335088\pi\) |
0.105077 | + | 0.994464i | \(0.466491\pi\) | |||||||
\(468\) | 51.2449 | − | 51.2449i | 0.109498 | − | 0.109498i | ||||
\(469\) | − | 168.043i | − | 0.358300i | ||||||
\(470\) | −36.0717 | − | 45.4033i | −0.0767483 | − | 0.0966028i | ||||
\(471\) | 1069.71 | 2.27114 | ||||||||
\(472\) | −183.668 | − | 183.668i | −0.389128 | − | 0.389128i | ||||
\(473\) | −255.657 | + | 255.657i | −0.540501 | + | 0.540501i | ||||
\(474\) | − | 398.744i | − | 0.841233i | ||||||
\(475\) | 292.275 | + | 67.8402i | 0.615316 | + | 0.142822i | ||||
\(476\) | −248.076 | −0.521167 | ||||||||
\(477\) | 74.0266 | + | 74.0266i | 0.155192 | + | 0.155192i | ||||
\(478\) | −206.404 | + | 206.404i | −0.431808 | + | 0.431808i | ||||
\(479\) | − | 303.049i | − | 0.632671i | −0.948647 | − | 0.316335i | \(-0.897548\pi\) | ||
0.948647 | − | 0.316335i | \(-0.102452\pi\) | |||||||
\(480\) | −93.5301 | + | 74.3072i | −0.194854 | + | 0.154807i | ||||
\(481\) | −235.076 | −0.488723 | ||||||||
\(482\) | −92.8472 | − | 92.8472i | −0.192629 | − | 0.192629i | ||||
\(483\) | −79.9436 | + | 79.9436i | −0.165515 | + | 0.165515i | ||||
\(484\) | − | 94.1010i | − | 0.194424i | ||||||
\(485\) | 285.245 | + | 32.6700i | 0.588134 | + | 0.0673608i | ||||
\(486\) | −483.633 | −0.995129 | ||||||||
\(487\) | −269.987 | − | 269.987i | −0.554388 | − | 0.554388i | 0.373316 | − | 0.927704i | \(-0.378221\pi\) |
−0.927704 | + | 0.373316i | \(0.878221\pi\) | |||||||
\(488\) | 12.0586 | − | 12.0586i | 0.0247103 | − | 0.0247103i | ||||
\(489\) | − | 12.4320i | − | 0.0254233i | ||||||
\(490\) | −14.3569 | + | 125.351i | −0.0292997 | + | 0.255819i | ||||
\(491\) | −788.957 | −1.60684 | −0.803418 | − | 0.595415i | \(-0.796988\pi\) | ||||
−0.803418 | + | 0.595415i | \(0.796988\pi\) | |||||||
\(492\) | 291.707 | + | 291.707i | 0.592901 | + | 0.592901i | ||||
\(493\) | 646.115 | − | 646.115i | 1.31058 | − | 1.31058i | ||||
\(494\) | 69.5988i | 0.140888i | ||||||||
\(495\) | 236.352 | + | 297.496i | 0.477480 | + | 0.601001i | ||||
\(496\) | 79.5625 | 0.160408 | ||||||||
\(497\) | −351.820 | − | 351.820i | −0.707887 | − | 0.707887i | ||||
\(498\) | −180.416 | + | 180.416i | −0.362281 | + | 0.362281i | ||||
\(499\) | − | 811.329i | − | 1.62591i | −0.582326 | − | 0.812955i | \(-0.697857\pi\) | ||
0.582326 | − | 0.812955i | \(-0.302143\pi\) | |||||||
\(500\) | −225.836 | + | 107.228i | −0.451673 | + | 0.214457i | ||||
\(501\) | 117.578 | 0.234687 | ||||||||
\(502\) | 427.161 | + | 427.161i | 0.850918 | + | 0.850918i | ||||
\(503\) | 690.146 | − | 690.146i | 1.37206 | − | 1.37206i | 0.514675 | − | 0.857385i | \(-0.327912\pi\) |
0.857385 | − | 0.514675i | \(-0.172088\pi\) | |||||||
\(504\) | − | 139.514i | − | 0.276813i | ||||||
\(505\) | 229.646 | − | 182.448i | 0.454745 | − | 0.361283i | ||||
\(506\) | −58.3239 | −0.115265 | ||||||||
\(507\) | −454.483 | − | 454.483i | −0.896415 | − | 0.896415i | ||||
\(508\) | −100.426 | + | 100.426i | −0.197689 | + | 0.197689i | ||||
\(509\) | 282.285i | 0.554588i | 0.960785 | + | 0.277294i | \(0.0894377\pi\) | ||||
−0.960785 | + | 0.277294i | \(0.910562\pi\) | |||||||
\(510\) | −659.312 | − | 75.5131i | −1.29277 | − | 0.148065i | ||||
\(511\) | 634.867 | 1.24240 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.84929 | − | 5.84929i | 0.0114021 | − | 0.0114021i | ||||
\(514\) | 418.406i | 0.814019i | ||||||||
\(515\) | 25.6810 | − | 224.223i | 0.0498660 | − | 0.435385i | ||||
\(516\) | 355.135 | 0.688247 | ||||||||
\(517\) | 49.8663 | + | 49.8663i | 0.0964532 | + | 0.0964532i | ||||
\(518\) | −319.996 | + | 319.996i | −0.617753 | + | 0.617753i | ||||
\(519\) | 84.6695i | 0.163140i | ||||||||
\(520\) | −36.0730 | − | 45.4049i | −0.0693712 | − | 0.0873172i | ||||
\(521\) | 89.0529 | 0.170927 | 0.0854634 | − | 0.996341i | \(-0.472763\pi\) | ||||
0.0854634 | + | 0.996341i | \(0.472763\pi\) | |||||||
\(522\) | 363.364 | + | 363.364i | 0.696101 | + | 0.696101i | ||||
\(523\) | 126.934 | − | 126.934i | 0.242703 | − | 0.242703i | −0.575265 | − | 0.817967i | \(-0.695101\pi\) |
0.817967 | + | 0.575265i | \(0.195101\pi\) | |||||||
\(524\) | − | 153.346i | − | 0.292645i | ||||||
\(525\) | 133.253 | − | 574.090i | 0.253814 | − | 1.09350i | ||||
\(526\) | 173.818 | 0.330453 | ||||||||
\(527\) | 312.544 | + | 312.544i | 0.593063 | + | 0.593063i | ||||
\(528\) | 102.724 | − | 102.724i | 0.194553 | − | 0.194553i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 65.5904 | − | 52.1099i | 0.123756 | − | 0.0983205i | ||||
\(531\) | 811.521 | 1.52829 | ||||||||
\(532\) | 94.7409 | + | 94.7409i | 0.178084 | + | 0.178084i | ||||
\(533\) | −141.612 | + | 141.612i | −0.265688 | + | 0.265688i | ||||
\(534\) | 291.388i | 0.545670i | ||||||||
\(535\) | −485.772 | − | 55.6369i | −0.907984 | − | 0.103994i | ||||
\(536\) | −85.1507 | −0.158863 | ||||||||
\(537\) | 873.854 | + | 873.854i | 1.62729 | + | 1.62729i | ||||
\(538\) | −324.191 | + | 324.191i | −0.602586 | + | 0.602586i | ||||
\(539\) | − | 153.441i | − | 0.284677i | ||||||
\(540\) | −0.784282 | + | 6.84765i | −0.00145237 | + | 0.0126808i | ||||
\(541\) | 190.762 | 0.352609 | 0.176305 | − | 0.984336i | \(-0.443586\pi\) | ||||
0.176305 | + | 0.984336i | \(0.443586\pi\) | |||||||
\(542\) | −374.518 | − | 374.518i | −0.690993 | − | 0.690993i | ||||
\(543\) | −233.068 | + | 233.068i | −0.429224 | + | 0.429224i | ||||
\(544\) | 125.705i | 0.231075i | ||||||||
\(545\) | 651.393 | + | 819.906i | 1.19522 | + | 1.50441i | ||||
\(546\) | 136.707 | 0.250379 | ||||||||
\(547\) | 409.164 | + | 409.164i | 0.748015 | + | 0.748015i | 0.974106 | − | 0.226091i | \(-0.0725947\pi\) |
−0.226091 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(548\) | −376.928 | + | 376.928i | −0.687824 | + | 0.687824i | ||||
\(549\) | 53.2799i | 0.0970490i | ||||||||
\(550\) | 258.026 | − | 160.809i | 0.469137 | − | 0.292381i | ||||
\(551\) | −493.507 | −0.895658 | ||||||||
\(552\) | 40.5091 | + | 40.5091i | 0.0733860 | + | 0.0733860i | ||||
\(553\) | 263.501 | − | 263.501i | 0.476494 | − | 0.476494i | ||||
\(554\) | 102.261i | 0.184587i | ||||||||
\(555\) | −947.861 | + | 753.050i | −1.70786 | + | 1.35685i | ||||
\(556\) | −365.359 | −0.657120 | ||||||||
\(557\) | 490.274 | + | 490.274i | 0.880205 | + | 0.880205i | 0.993555 | − | 0.113351i | \(-0.0361583\pi\) |
−0.113351 | + | 0.993555i | \(0.536158\pi\) | |||||||
\(558\) | −175.770 | + | 175.770i | −0.314999 | + | 0.314999i | ||||
\(559\) | 172.403i | 0.308414i | ||||||||
\(560\) | −110.911 | − | 12.7030i | −0.198056 | − | 0.0226840i | ||||
\(561\) | 807.056 | 1.43860 | ||||||||
\(562\) | 398.890 | + | 398.890i | 0.709769 | + | 0.709769i | ||||
\(563\) | −624.598 | + | 624.598i | −1.10941 | + | 1.10941i | −0.116182 | + | 0.993228i | \(0.537066\pi\) |
−0.993228 | + | 0.116182i | \(0.962934\pi\) | |||||||
\(564\) | − | 69.2696i | − | 0.122819i | ||||||
\(565\) | 39.8635 | − | 348.053i | 0.0705549 | − | 0.616022i | ||||
\(566\) | −46.3395 | −0.0818720 | ||||||||
\(567\) | −325.395 | − | 325.395i | −0.573888 | − | 0.573888i | ||||
\(568\) | −178.275 | + | 178.275i | −0.313864 | + | 0.313864i | ||||
\(569\) | − | 646.904i | − | 1.13691i | −0.822713 | − | 0.568457i | \(-0.807541\pi\) | ||
0.822713 | − | 0.568457i | \(-0.192459\pi\) | |||||||
\(570\) | 222.955 | + | 280.632i | 0.391149 | + | 0.492338i | ||||
\(571\) | −320.656 | −0.561569 | −0.280785 | − | 0.959771i | \(-0.590595\pi\) | ||||
−0.280785 | + | 0.959771i | \(0.590595\pi\) | |||||||
\(572\) | 49.8681 | + | 49.8681i | 0.0871820 | + | 0.0871820i | ||||
\(573\) | 208.062 | − | 208.062i | 0.363110 | − | 0.363110i | ||||
\(574\) | 385.536i | 0.671665i | ||||||||
\(575\) | 63.4151 | + | 101.752i | 0.110287 | + | 0.176960i | ||||
\(576\) | −70.6944 | −0.122733 | ||||||||
\(577\) | −45.0178 | − | 45.0178i | −0.0780204 | − | 0.0780204i | 0.667020 | − | 0.745040i | \(-0.267570\pi\) |
−0.745040 | + | 0.667020i | \(0.767570\pi\) | |||||||
\(578\) | −204.805 | + | 204.805i | −0.354334 | + | 0.354334i | ||||
\(579\) | − | 1405.83i | − | 2.42803i | ||||||
\(580\) | 321.955 | − | 255.785i | 0.555095 | − | 0.441008i | ||||
\(581\) | −238.447 | −0.410408 | ||||||||
\(582\) | 242.514 | + | 242.514i | 0.416691 | + | 0.416691i | ||||
\(583\) | −72.0377 | + | 72.0377i | −0.123564 | + | 0.123564i | ||||
\(584\) | − | 321.700i | − | 0.550856i | ||||||
\(585\) | 180.001 | + | 20.6161i | 0.307694 | + | 0.0352412i | ||||
\(586\) | −121.553 | −0.207429 | ||||||||
\(587\) | −154.614 | − | 154.614i | −0.263397 | − | 0.263397i | 0.563036 | − | 0.826433i | \(-0.309633\pi\) |
−0.826433 | + | 0.563036i | \(0.809633\pi\) | |||||||
\(588\) | −106.573 | + | 106.573i | −0.181247 | + | 0.181247i | ||||
\(589\) | − | 238.723i | − | 0.405303i | ||||||
\(590\) | 73.8908 | − | 645.148i | 0.125239 | − | 1.09347i | ||||
\(591\) | −819.978 | −1.38744 | ||||||||
\(592\) | 162.149 | + | 162.149i | 0.273900 | + | 0.273900i | ||||
\(593\) | −488.246 | + | 488.246i | −0.823349 | + | 0.823349i | −0.986587 | − | 0.163238i | \(-0.947806\pi\) |
0.163238 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(594\) | − | 8.38213i | − | 0.0141113i | ||||||
\(595\) | −385.790 | − | 485.592i | −0.648387 | − | 0.816122i | ||||
\(596\) | 456.585 | 0.766081 | ||||||||
\(597\) | 660.862 | + | 660.862i | 1.10697 | + | 1.10697i | ||||
\(598\) | −19.6655 | + | 19.6655i | −0.0328854 | + | 0.0328854i | ||||
\(599\) | 313.455i | 0.523297i | 0.965163 | + | 0.261649i | \(0.0842661\pi\) | ||||
−0.965163 | + | 0.261649i | \(0.915734\pi\) | |||||||
\(600\) | −290.903 | − | 67.5219i | −0.484839 | − | 0.112536i | ||||
\(601\) | 785.232 | 1.30654 | 0.653271 | − | 0.757124i | \(-0.273396\pi\) | ||||
0.653271 | + | 0.757124i | \(0.273396\pi\) | |||||||
\(602\) | 234.683 | + | 234.683i | 0.389839 | + | 0.389839i | ||||
\(603\) | 188.115 | − | 188.115i | 0.311965 | − | 0.311965i | ||||
\(604\) | − | 174.554i | − | 0.288997i | ||||||
\(605\) | 184.197 | − | 146.340i | 0.304458 | − | 0.241884i | ||||
\(606\) | 350.360 | 0.578152 | ||||||||
\(607\) | −586.527 | − | 586.527i | −0.966271 | − | 0.966271i | 0.0331784 | − | 0.999449i | \(-0.489437\pi\) |
−0.999449 | + | 0.0331784i | \(0.989437\pi\) | |||||||
\(608\) | 48.0072 | − | 48.0072i | 0.0789592 | − | 0.0789592i | ||||
\(609\) | 969.353i | 1.59171i | ||||||||
\(610\) | 42.3568 | + | 4.85126i | 0.0694374 | + | 0.00795288i | ||||
\(611\) | 33.6275 | 0.0550368 | ||||||||
\(612\) | −277.708 | − | 277.708i | −0.453771 | − | 0.453771i | ||||
\(613\) | 67.0740 | − | 67.0740i | 0.109419 | − | 0.109419i | −0.650277 | − | 0.759697i | \(-0.725347\pi\) |
0.759697 | + | 0.650277i | \(0.225347\pi\) | |||||||
\(614\) | 531.080i | 0.864951i | ||||||||
\(615\) | −117.355 | + | 1024.64i | −0.190822 | + | 1.66608i | ||||
\(616\) | 135.765 | 0.220398 | ||||||||
\(617\) | −264.729 | − | 264.729i | −0.429058 | − | 0.429058i | 0.459250 | − | 0.888307i | \(-0.348118\pi\) |
−0.888307 | + | 0.459250i | \(0.848118\pi\) | |||||||
\(618\) | 190.633 | − | 190.633i | 0.308468 | − | 0.308468i | ||||
\(619\) | 116.113i | 0.187581i | 0.995592 | + | 0.0937907i | \(0.0298985\pi\) | ||||
−0.995592 | + | 0.0937907i | \(0.970102\pi\) | |||||||
\(620\) | 123.730 | + | 155.739i | 0.199565 | + | 0.251191i | ||||
\(621\) | 3.30549 | 0.00532285 | ||||||||
\(622\) | −421.810 | − | 421.810i | −0.678150 | − | 0.678150i | ||||
\(623\) | −192.557 | + | 192.557i | −0.309080 | + | 0.309080i | ||||
\(624\) | − | 69.2721i | − | 0.111013i | ||||||
\(625\) | −561.098 | − | 275.306i | −0.897757 | − | 0.440490i | ||||
\(626\) | 258.543 | 0.413008 | ||||||||
\(627\) | −308.218 | − | 308.218i | −0.491575 | − | 0.491575i | ||||
\(628\) | 358.196 | − | 358.196i | 0.570376 | − | 0.570376i | ||||
\(629\) | 1273.93i | 2.02533i | ||||||||
\(630\) | 273.089 | − | 216.962i | 0.433475 | − | 0.344384i | ||||
\(631\) | 1195.53 | 1.89466 | 0.947331 | − | 0.320255i | \(-0.103769\pi\) | ||||
0.947331 | + | 0.320255i | \(0.103769\pi\) | |||||||
\(632\) | −133.521 | − | 133.521i | −0.211268 | − | 0.211268i | ||||
\(633\) | −617.993 | + | 617.993i | −0.976293 | + | 0.976293i | ||||
\(634\) | − | 536.447i | − | 0.846131i | ||||||
\(635\) | −352.753 | − | 40.4018i | −0.555516 | − | 0.0636249i | ||||
\(636\) | 100.068 | 0.157340 | ||||||||
\(637\) | −51.7367 | − | 51.7367i | −0.0812193 | − | 0.0812193i | ||||
\(638\) | −353.602 | + | 353.602i | −0.554235 | + | 0.554235i | ||||
\(639\) | − | 787.689i | − | 1.23269i | ||||||
\(640\) | −6.43689 | + | 56.2011i | −0.0100576 | + | 0.0878143i | ||||
\(641\) | −799.813 | −1.24776 | −0.623879 | − | 0.781521i | \(-0.714444\pi\) | ||||
−0.623879 | + | 0.781521i | \(0.714444\pi\) | |||||||
\(642\) | −413.001 | − | 413.001i | −0.643303 | − | 0.643303i | ||||
\(643\) | −873.735 | + | 873.735i | −1.35884 | + | 1.35884i | −0.483495 | + | 0.875347i | \(0.660633\pi\) |
−0.875347 | + | 0.483495i | \(0.839367\pi\) | |||||||
\(644\) | 53.5390i | 0.0831351i | ||||||||
\(645\) | 552.283 | + | 695.155i | 0.856252 | + | 1.07776i | ||||
\(646\) | 377.172 | 0.583857 | ||||||||
\(647\) | −332.571 | − | 332.571i | −0.514019 | − | 0.514019i | 0.401736 | − | 0.915756i | \(-0.368407\pi\) |
−0.915756 | + | 0.401736i | \(0.868407\pi\) | |||||||
\(648\) | −164.884 | + | 164.884i | −0.254451 | + | 0.254451i | ||||
\(649\) | 789.718i | 1.21682i | ||||||||
\(650\) | 32.7790 | − | 141.221i | 0.0504293 | − | 0.217264i | ||||
\(651\) | −468.903 | −0.720281 | ||||||||
\(652\) | −4.16291 | − | 4.16291i | −0.00638483 | − | 0.00638483i | ||||
\(653\) | −372.410 | + | 372.410i | −0.570307 | + | 0.570307i | −0.932214 | − | 0.361907i | \(-0.882126\pi\) |
0.361907 | + | 0.932214i | \(0.382126\pi\) | |||||||
\(654\) | 1250.89i | 1.91268i | ||||||||
\(655\) | 300.165 | − | 238.473i | 0.458267 | − | 0.364081i | ||||
\(656\) | 195.359 | 0.297804 | ||||||||
\(657\) | 710.700 | + | 710.700i | 1.08174 | + | 1.08174i | ||||
\(658\) | 45.7752 | − | 45.7752i | 0.0695672 | − | 0.0695672i | ||||
\(659\) | 348.049i | 0.528147i | 0.964503 | + | 0.264074i | \(0.0850662\pi\) | ||||
−0.964503 | + | 0.264074i | \(0.914934\pi\) | |||||||
\(660\) | 360.825 | + | 41.3263i | 0.546704 | + | 0.0626157i | ||||
\(661\) | 577.080 | 0.873040 | 0.436520 | − | 0.899694i | \(-0.356211\pi\) | ||||
0.436520 | + | 0.899694i | \(0.356211\pi\) | |||||||
\(662\) | −234.830 | − | 234.830i | −0.354727 | − | 0.354727i | ||||
\(663\) | 272.121 | − | 272.121i | 0.410438 | − | 0.410438i | ||||
\(664\) | 120.826i | 0.181967i | ||||||||
\(665\) | −38.1148 | + | 332.784i | −0.0573154 | + | 0.500427i | ||||
\(666\) | −716.438 | −1.07573 | ||||||||
\(667\) | −139.443 | − | 139.443i | −0.209060 | − | 0.209060i | ||||
\(668\) | 39.3716 | − | 39.3716i | 0.0589395 | − | 0.0589395i | ||||
\(669\) | − | 874.940i | − | 1.30783i | ||||||
\(670\) | −132.421 | − | 166.677i | −0.197643 | − | 0.248772i | ||||
\(671\) | −51.8485 | −0.0772704 | ||||||||
\(672\) | −94.2963 | − | 94.2963i | −0.140322 | − | 0.140322i | ||||
\(673\) | 766.103 | − | 766.103i | 1.13834 | − | 1.13834i | 0.149593 | − | 0.988748i | \(-0.452204\pi\) |
0.988748 | − | 0.149593i | \(-0.0477964\pi\) | |||||||
\(674\) | 367.827i | 0.545737i | ||||||||
\(675\) | −14.6235 | + | 9.11382i | −0.0216645 | + | 0.0135020i | ||||
\(676\) | −304.371 | −0.450253 | ||||||||
\(677\) | −85.8895 | − | 85.8895i | −0.126868 | − | 0.126868i | 0.640822 | − | 0.767690i | \(-0.278594\pi\) |
−0.767690 | + | 0.640822i | \(0.778594\pi\) | |||||||
\(678\) | 295.912 | − | 295.912i | 0.436449 | − | 0.436449i | ||||
\(679\) | 320.519i | 0.472046i | ||||||||
\(680\) | −246.060 | + | 195.488i | −0.361853 | + | 0.287482i | ||||
\(681\) | −695.805 | −1.02174 | ||||||||
\(682\) | −171.047 | − | 171.047i | −0.250802 | − | 0.250802i | ||||
\(683\) | −789.547 | + | 789.547i | −1.15600 | + | 1.15600i | −0.170671 | + | 0.985328i | \(0.554594\pi\) |
−0.985328 | + | 0.170671i | \(0.945406\pi\) | |||||||
\(684\) | 212.115i | 0.310110i | ||||||||
\(685\) | −1323.98 | − | 151.640i | −1.93282 | − | 0.221372i | ||||
\(686\) | −527.653 | −0.769174 | ||||||||
\(687\) | −1190.06 | − | 1190.06i | −1.73226 | − | 1.73226i | ||||
\(688\) | 118.919 | − | 118.919i | 0.172847 | − | 0.172847i | ||||
\(689\) | 48.5789i | 0.0705064i | ||||||||
\(690\) | −16.2970 | + | 142.291i | −0.0236189 | + | 0.206219i | ||||
\(691\) | −61.5184 | −0.0890281 | −0.0445140 | − | 0.999009i | \(-0.514174\pi\) | ||||
−0.0445140 | + | 0.999009i | \(0.514174\pi\) | |||||||
\(692\) | 28.3520 | + | 28.3520i | 0.0409711 | + | 0.0409711i | ||||
\(693\) | −299.933 | + | 299.933i | −0.432803 | + | 0.432803i | ||||
\(694\) | − | 100.774i | − | 0.145208i | ||||||
\(695\) | −568.181 | − | 715.167i | −0.817527 | − | 1.02902i | ||||
\(696\) | 491.191 | 0.705735 | ||||||||
\(697\) | 767.426 | + | 767.426i | 1.10104 | + | 1.10104i | ||||
\(698\) | 344.711 | − | 344.711i | 0.493855 | − | 0.493855i | ||||
\(699\) | − | 799.460i | − | 1.14372i | ||||||
\(700\) | −147.617 | − | 236.857i | −0.210881 | − | 0.338367i | ||||
\(701\) | 304.128 | 0.433849 | 0.216925 | − | 0.976188i | \(-0.430397\pi\) | ||||
0.216925 | + | 0.976188i | \(0.430397\pi\) | |||||||
\(702\) | −2.82626 | − | 2.82626i | −0.00402601 | − | 0.00402601i | ||||
\(703\) | 486.519 | − | 486.519i | 0.692061 | − | 0.692061i | ||||
\(704\) | − | 68.7951i | − | 0.0977203i | ||||||
\(705\) | 135.591 | − | 107.723i | 0.192328 | − | 0.152799i | ||||
\(706\) | 925.359 | 1.31071 | ||||||||
\(707\) | 231.527 | + | 231.527i | 0.327479 | + | 0.327479i | ||||
\(708\) | 548.502 | − | 548.502i | 0.774720 | − | 0.774720i | ||||
\(709\) | 548.324i | 0.773376i | 0.922210 | + | 0.386688i | \(0.126381\pi\) | ||||
−0.922210 | + | 0.386688i | \(0.873619\pi\) | |||||||
\(710\) | −626.202 | − | 71.7208i | −0.881975 | − | 0.101015i | ||||
\(711\) | 589.951 | 0.829749 | ||||||||
\(712\) | 97.5727 | + | 97.5727i | 0.137040 | + | 0.137040i | ||||
\(713\) | 67.4524 | − | 67.4524i | 0.0946037 | − | 0.0946037i | ||||
\(714\) | − | 740.845i | − | 1.03760i | ||||||
\(715\) | −20.0622 | + | 175.165i | −0.0280590 | + | 0.244986i | ||||
\(716\) | 585.228 | 0.817358 | ||||||||
\(717\) | −616.399 | − | 616.399i | −0.859691 | − | 0.859691i | ||||
\(718\) | −408.460 | + | 408.460i | −0.568886 | + | 0.568886i | ||||
\(719\) | − | 235.548i | − | 0.327605i | −0.986493 | − | 0.163802i | \(-0.947624\pi\) | ||
0.986493 | − | 0.163802i | \(-0.0523759\pi\) | |||||||
\(720\) | −109.939 | − | 138.380i | −0.152693 | − | 0.192194i | ||||
\(721\) | 251.951 | 0.349447 | ||||||||
\(722\) | 216.957 | + | 216.957i | 0.300494 | + | 0.300494i | ||||
\(723\) | 277.276 | − | 277.276i | 0.383508 | − | 0.383508i | ||||
\(724\) | 156.088i | 0.215591i | ||||||||
\(725\) | 1001.37 | + | 232.428i | 1.38119 | + | 0.320590i | ||||
\(726\) | 281.020 | 0.387081 | ||||||||
\(727\) | −125.017 | − | 125.017i | −0.171963 | − | 0.171963i | 0.615878 | − | 0.787841i | \(-0.288801\pi\) |
−0.787841 | + | 0.615878i | \(0.788801\pi\) | |||||||
\(728\) | 45.7769 | − | 45.7769i | 0.0628803 | − | 0.0628803i | ||||
\(729\) | − | 702.327i | − | 0.963411i | ||||||
\(730\) | 629.708 | − | 500.286i | 0.862614 | − | 0.685324i | ||||
\(731\) | 934.293 | 1.27810 | ||||||||
\(732\) | 36.0115 | + | 36.0115i | 0.0491961 | + | 0.0491961i | ||||
\(733\) | 644.938 | − | 644.938i | 0.879861 | − | 0.879861i | −0.113659 | − | 0.993520i | \(-0.536257\pi\) |
0.993520 | + | 0.113659i | \(0.0362570\pi\) | |||||||
\(734\) | − | 921.815i | − | 1.25588i | ||||||
\(735\) | −374.345 | − | 42.8749i | −0.509313 | − | 0.0583332i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 183.061 | + | 183.061i | 0.248387 | + | 0.248387i | ||||
\(738\) | −431.588 | + | 431.588i | −0.584807 | + | 0.584807i | ||||
\(739\) | − | 1162.01i | − | 1.57241i | −0.617966 | − | 0.786205i | \(-0.712043\pi\) | ||
0.617966 | − | 0.786205i | \(-0.287957\pi\) | |||||||
\(740\) | −65.2332 | + | 569.558i | −0.0881530 | + | 0.769673i | ||||
\(741\) | −207.848 | −0.280496 | ||||||||
\(742\) | 66.1277 | + | 66.1277i | 0.0891209 | + | 0.0891209i | ||||
\(743\) | 736.103 | − | 736.103i | 0.990718 | − | 0.990718i | −0.00923932 | − | 0.999957i | \(-0.502941\pi\) |
0.999957 | + | 0.00923932i | \(0.00294101\pi\) | |||||||
\(744\) | 237.603i | 0.319359i | ||||||||
\(745\) | 710.049 | + | 893.736i | 0.953086 | + | 1.19965i | ||||
\(746\) | 534.053 | 0.715889 | ||||||||
\(747\) | −266.929 | − | 266.929i | −0.357335 | − | 0.357335i | ||||
\(748\) | 270.247 | − | 270.247i | 0.361292 | − | 0.361292i | ||||
\(749\) | − | 545.844i | − | 0.728763i | ||||||
\(750\) | −320.224 | − | 674.431i | −0.426965 | − | 0.899241i | ||||
\(751\) | 793.620 | 1.05675 | 0.528375 | − | 0.849011i | \(-0.322801\pi\) | ||||
0.528375 | + | 0.849011i | \(0.322801\pi\) | |||||||
\(752\) | −23.1953 | − | 23.1953i | −0.0308448 | − | 0.0308448i | ||||
\(753\) | −1275.66 | + | 1275.66i | −1.69410 | + | 1.69410i | ||||
\(754\) | 238.453i | 0.316250i | ||||||||
\(755\) | 341.679 | − | 271.455i | 0.452555 | − | 0.359543i | ||||
\(756\) | −7.69445 | −0.0101778 | ||||||||
\(757\) | −472.738 | − | 472.738i | −0.624489 | − | 0.624489i | 0.322187 | − | 0.946676i | \(-0.395582\pi\) |
−0.946676 | + | 0.322187i | \(0.895582\pi\) | |||||||
\(758\) | −257.246 | + | 257.246i | −0.339374 | + | 0.339374i | ||||
\(759\) | − | 174.177i | − | 0.229482i | ||||||
\(760\) | 168.629 | + | 19.3136i | 0.221880 | + | 0.0254126i | ||||
\(761\) | 17.0753 | 0.0224379 | 0.0112190 | − | 0.999937i | \(-0.496429\pi\) | ||||
0.0112190 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(762\) | −299.909 | − | 299.909i | −0.393581 | − | 0.393581i | ||||
\(763\) | −826.622 | + | 826.622i | −1.08338 | + | 1.08338i | ||||
\(764\) | − | 139.341i | − | 0.182384i | ||||||
\(765\) | 111.723 | − | 975.468i | 0.146044 | − | 1.27512i | ||||
\(766\) | 204.626 | 0.267136 | ||||||||
\(767\) | 266.275 | + | 266.275i | 0.347164 | + | 0.347164i | ||||
\(768\) | −47.7819 | + | 47.7819i | −0.0622160 | + | 0.0622160i | ||||
\(769\) | − | 1084.43i | − | 1.41019i | −0.709114 | − | 0.705094i | \(-0.750905\pi\) | ||
0.709114 | − | 0.705094i | \(-0.249095\pi\) | |||||||
\(770\) | 211.133 | + | 265.752i | 0.274199 | + | 0.345133i | ||||
\(771\) | −1249.51 | −1.62064 | ||||||||
\(772\) | −470.749 | − | 470.749i | −0.609778 | − | 0.609778i | ||||
\(773\) | 352.889 | − | 352.889i | 0.456519 | − | 0.456519i | −0.440992 | − | 0.897511i | \(-0.645373\pi\) |
0.897511 | + | 0.440992i | \(0.145373\pi\) | |||||||
\(774\) | 525.431i | 0.678851i | ||||||||
\(775\) | −112.432 | + | 484.389i | −0.145073 | + | 0.625017i | ||||
\(776\) | 162.414 | 0.209296 | ||||||||
\(777\) | −955.626 | − | 955.626i | −1.22989 | − | 1.22989i | ||||
\(778\) | −13.5885 | + | 13.5885i | −0.0174660 | + | 0.0174660i | ||||
\(779\) | − | 586.165i | − | 0.752459i | ||||||
\(780\) | 135.596 | − | 107.727i | 0.173841 | − | 0.138112i | ||||
\(781\) | 766.526 | 0.981467 | ||||||||
\(782\) | 106.572 | + | 106.572i | 0.136281 | + | 0.136281i | ||||
\(783\) | 20.0403 | − | 20.0403i | 0.0255942 | − | 0.0255942i | ||||
\(784\) | 71.3730i | 0.0910369i | ||||||||
\(785\) | 1258.19 | + | 144.104i | 1.60279 | + | 0.183572i | ||||
\(786\) | 457.947 | 0.582630 | ||||||||
\(787\) | 958.735 | + | 958.735i | 1.21822 | + | 1.21822i | 0.968256 | + | 0.249959i | \(0.0804171\pi\) |
0.249959 | + | 0.968256i | \(0.419583\pi\) | |||||||
\(788\) | −274.573 | + | 274.573i | −0.348443 | + | 0.348443i | ||||
\(789\) | 519.085i | 0.657903i | ||||||||
\(790\) | 53.7164 | − | 469.003i | 0.0679954 | − | 0.593675i | ||||
\(791\) | 391.094 | 0.494430 | ||||||||
\(792\) | 151.982 | + | 151.982i | 0.191897 | + | 0.191897i | ||||
\(793\) | −17.4821 | + | 17.4821i | −0.0220455 | + | 0.0220455i | ||||
\(794\) | − | 889.735i | − | 1.12057i | ||||||
\(795\) | 155.619 | + | 195.877i | 0.195748 | + | 0.246386i | ||||
\(796\) | 442.586 | 0.556012 | ||||||||
\(797\) | 575.899 | + | 575.899i | 0.722583 | + | 0.722583i | 0.969131 | − | 0.246547i | \(-0.0792961\pi\) |
−0.246547 | + | 0.969131i | \(0.579296\pi\) | |||||||
\(798\) | −282.931 | + | 282.931i | −0.354550 | + | 0.354550i | ||||
\(799\) | − | 182.235i | − | 0.228079i | ||||||
\(800\) | −120.020 | + | 74.8004i | −0.150026 | + | 0.0935005i | ||||
\(801\) | −431.115 | −0.538221 | ||||||||
\(802\) | −496.549 | − | 496.549i | −0.619139 | − | 0.619139i | ||||
\(803\) | −691.606 | + | 691.606i | −0.861278 | + | 0.861278i | ||||
\(804\) | − | 254.291i | − | 0.316283i | ||||||
\(805\) | −104.799 | + | 83.2602i | −0.130185 | + | 0.103429i | ||||
\(806\) | −115.346 | −0.143110 | ||||||||
\(807\) | −968.155 | − | 968.155i | −1.19970 | − | 1.19970i | ||||
\(808\) | 117.320 | − | 117.320i | 0.145198 | − | 0.145198i | ||||
\(809\) | 694.940i | 0.859011i | 0.903064 | + | 0.429505i | \(0.141312\pi\) | ||||
−0.903064 | + | 0.429505i | \(0.858688\pi\) | |||||||
\(810\) | −579.168 | − | 66.3338i | −0.715022 | − | 0.0818936i | ||||
\(811\) | 700.473 | 0.863715 | 0.431857 | − | 0.901942i | \(-0.357858\pi\) | ||||
0.431857 | + | 0.901942i | \(0.357858\pi\) | |||||||
\(812\) | 324.592 | + | 324.592i | 0.399744 | + | 0.399744i | ||||
\(813\) | 1118.45 | − | 1118.45i | 1.37571 | − | 1.37571i | ||||
\(814\) | − | 697.189i | − | 0.856498i | ||||||
\(815\) | 1.67476 | − | 14.6225i | 0.00205492 | − | 0.0179417i | ||||
\(816\) | −375.402 | −0.460051 | ||||||||
\(817\) | −356.810 | − | 356.810i | −0.436732 | − | 0.436732i | ||||
\(818\) | −504.901 | + | 504.901i | −0.617238 | + | 0.617238i | ||||
\(819\) | 202.261i | 0.246961i | ||||||||
\(820\) | 303.809 | + | 382.403i | 0.370499 | + | 0.466346i | ||||
\(821\) | −803.333 | −0.978481 | −0.489240 | − | 0.872149i | \(-0.662726\pi\) | ||||
−0.489240 | + | 0.872149i | \(0.662726\pi\) | |||||||
\(822\) | −1125.64 | − | 1125.64i | −1.36940 | − | 1.36940i | ||||
\(823\) | −112.109 | + | 112.109i | −0.136220 | + | 0.136220i | −0.771929 | − | 0.635709i | \(-0.780708\pi\) |
0.635709 | + | 0.771929i | \(0.280708\pi\) | |||||||
\(824\) | − | 127.669i | − | 0.154938i | ||||||
\(825\) | 480.236 | + | 770.560i | 0.582105 | + | 0.934012i | ||||
\(826\) | 724.929 | 0.877638 | ||||||||
\(827\) | 132.725 | + | 132.725i | 0.160490 | + | 0.160490i | 0.782784 | − | 0.622294i | \(-0.213799\pi\) |
−0.622294 | + | 0.782784i | \(0.713799\pi\) | |||||||
\(828\) | −59.9341 | + | 59.9341i | −0.0723842 | + | 0.0723842i | ||||
\(829\) | 901.283i | 1.08719i | 0.839347 | + | 0.543597i | \(0.182938\pi\) | ||||
−0.839347 | + | 0.543597i | \(0.817062\pi\) | |||||||
\(830\) | −236.510 | + | 187.901i | −0.284951 | + | 0.226386i | ||||
\(831\) | −305.390 | −0.367497 | ||||||||
\(832\) | −23.1961 | − | 23.1961i | −0.0278799 | − | 0.0278799i | ||||
\(833\) | −280.373 | + | 280.373i | −0.336582 | + | 0.336582i | ||||
\(834\) | − | 1091.10i | − | 1.30827i | ||||||
\(835\) | 138.296 | + | 15.8394i | 0.165623 | + | 0.0189694i | ||||
\(836\) | −206.416 | −0.246909 | ||||||||
\(837\) | 9.69405 | + | 9.69405i | 0.0115819 | + | 0.0115819i | ||||
\(838\) | −496.330 | + | 496.330i | −0.592280 | + | 0.592280i | ||||
\(839\) | − | 590.121i | − | 0.703363i | −0.936120 | − | 0.351681i | \(-0.885610\pi\) | ||
0.936120 | − | 0.351681i | \(-0.114390\pi\) | |||||||
\(840\) | 37.9359 | − | 331.222i | 0.0451618 | − | 0.394312i | ||||
\(841\) | −849.809 | −1.01047 | ||||||||
\(842\) | −217.991 | − | 217.991i | −0.258897 | − | 0.258897i | ||||
\(843\) | −1191.23 | + | 1191.23i | −1.41309 | + | 1.41309i | ||||
\(844\) | 413.876i | 0.490374i | ||||||||
\(845\) | −473.338 | − | 595.788i | −0.560163 | − | 0.705074i | ||||
\(846\) | 102.486 | 0.121142 | ||||||||
\(847\) | 185.706 | + | 185.706i | 0.219251 | + | 0.219251i | ||||
\(848\) | 33.5083 | − | 33.5083i | 0.0395145 | − | 0.0395145i | ||||
\(849\) | − | 138.387i | − | 0.163000i | ||||||
\(850\) | −765.311 | − | 177.637i | −0.900366 | − | 0.208985i | ||||
\(851\) | 274.936 | 0.323074 | ||||||||
\(852\) | −532.394 | − | 532.394i | −0.624875 | − | 0.624875i | ||||
\(853\) | 250.343 | − | 250.343i | 0.293485 | − | 0.293485i | −0.544970 | − | 0.838455i | \(-0.683459\pi\) |
0.838455 | + | 0.544970i | \(0.183459\pi\) | |||||||
\(854\) | 47.5948i | 0.0557316i | ||||||||
\(855\) | −415.202 | + | 329.867i | −0.485616 | + | 0.385809i | ||||
\(856\) | −276.590 | −0.323120 | ||||||||
\(857\) | 728.387 | + | 728.387i | 0.849926 | + | 0.849926i | 0.990124 | − | 0.140197i | \(-0.0447737\pi\) |
−0.140197 | + | 0.990124i | \(0.544774\pi\) | |||||||
\(858\) | −148.925 | + | 148.925i | −0.173572 | + | 0.173572i | ||||
\(859\) | − | 285.323i | − | 0.332157i | −0.986113 | − | 0.166078i | \(-0.946889\pi\) | ||
0.986113 | − | 0.166078i | \(-0.0531105\pi\) | |||||||
\(860\) | 417.711 | + | 47.8417i | 0.485710 | + | 0.0556298i | ||||
\(861\) | −1151.35 | −1.33723 | ||||||||
\(862\) | −194.670 | − | 194.670i | −0.225835 | − | 0.225835i | ||||
\(863\) | −804.770 | + | 804.770i | −0.932526 | + | 0.932526i | −0.997863 | − | 0.0653374i | \(-0.979188\pi\) |
0.0653374 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(864\) | 3.89894i | 0.00451266i | ||||||||
\(865\) | −11.4062 | + | 99.5884i | −0.0131863 | + | 0.115131i | ||||
\(866\) | −166.088 | −0.191787 | ||||||||
\(867\) | −611.623 | − | 611.623i | −0.705448 | − | 0.705448i | ||||
\(868\) | −157.014 | + | 157.014i | −0.180892 | + | 0.180892i | ||||
\(869\) | 574.101i | 0.660646i | ||||||||
\(870\) | 763.868 | + | 961.477i | 0.878009 | + | 1.10515i | ||||
\(871\) | 123.448 | 0.141731 | ||||||||
\(872\) | 418.867 | + | 418.867i | 0.480352 | + | 0.480352i | ||||
\(873\) | −358.805 | + | 358.805i | −0.411002 | + | 0.411002i | ||||
\(874\) | − | 81.4002i | − | 0.0931352i | ||||||
\(875\) | 234.070 | − | 657.294i | 0.267508 | − | 0.751193i | ||||
\(876\) | 960.715 | 1.09671 | ||||||||
\(877\) | 469.300 | + | 469.300i | 0.535120 | + | 0.535120i | 0.922091 | − | 0.386972i | \(-0.126479\pi\) |
−0.386972 | + | 0.922091i | \(0.626479\pi\) | |||||||
\(878\) | 651.478 | − | 651.478i | 0.742002 | − | 0.742002i | ||||
\(879\) | − | 363.003i | − | 0.412973i | ||||||
\(880\) | 134.662 | − | 106.986i | 0.153025 | − | 0.121574i | ||||
\(881\) | −1625.01 | −1.84451 | −0.922254 | − | 0.386584i | \(-0.873655\pi\) | ||||
−0.922254 | + | 0.386584i | \(0.873655\pi\) | |||||||
\(882\) | −157.677 | − | 157.677i | −0.178772 | − | 0.178772i | ||||
\(883\) | −931.471 | + | 931.471i | −1.05489 | + | 1.05489i | −0.0564909 | + | 0.998403i | \(0.517991\pi\) |
−0.998403 | + | 0.0564909i | \(0.982009\pi\) | |||||||
\(884\) | − | 182.242i | − | 0.206156i | ||||||
\(885\) | 1926.65 | + | 220.665i | 2.17701 | + | 0.249339i | ||||
\(886\) | 65.9772 | 0.0744663 | ||||||||
\(887\) | 1221.10 | + | 1221.10i | 1.37666 | + | 1.37666i | 0.850193 | + | 0.526471i | \(0.176485\pi\) |
0.526471 | + | 0.850193i | \(0.323515\pi\) | |||||||
\(888\) | −484.236 | + | 484.236i | −0.545310 | + | 0.545310i | ||||
\(889\) | − | 396.375i | − | 0.445866i | ||||||
\(890\) | −39.2540 | + | 342.731i | −0.0441056 | + | 0.385091i | ||||
\(891\) | 708.952 | 0.795681 | ||||||||
\(892\) | −292.978 | − | 292.978i | −0.328451 | − | 0.328451i | ||||
\(893\) | −69.5962 | + | 69.5962i | −0.0779353 | + | 0.0779353i | ||||
\(894\) | 1363.53i | 1.52520i | ||||||||
\(895\) | 910.107 | + | 1145.55i | 1.01688 | + | 1.27994i | ||||
\(896\) | −63.1511 | −0.0704812 | ||||||||
\(897\) | −58.7283 | − | 58.7283i | −0.0654719 | − | 0.0654719i | ||||
\(898\) | 528.035 | − | 528.035i | 0.588013 | − | 0.588013i | ||||
\(899\) | − | 817.892i | − | 0.909779i | ||||||
\(900\) | 99.9001 | − | 430.398i | 0.111000 | − | 0.478220i | ||||
\(901\) | 263.260 | 0.292187 | ||||||||
\(902\) | −419.992 | − | 419.992i | −0.465623 | − | 0.465623i | ||||
\(903\) | −700.850 | + | 700.850i | −0.776135 | + | 0.776135i | ||||
\(904\) | − | 198.175i | − | 0.219221i | ||||||
\(905\) | −305.533 | + | 242.738i | −0.337605 | + | 0.268219i | ||||
\(906\) | 521.283 | 0.575368 | ||||||||
\(907\) | 8.51812 | + | 8.51812i | 0.00939153 | + | 0.00939153i | 0.711787 | − | 0.702395i | \(-0.247886\pi\) |
−0.702395 | + | 0.711787i | \(0.747886\pi\) | |||||||
\(908\) | −232.994 | + | 232.994i | −0.256601 | + | 0.256601i | ||||
\(909\) | 518.366i | 0.570260i | ||||||||
\(910\) | 160.795 | + | 18.4163i | 0.176697 | + | 0.0202377i | ||||
\(911\) | −1480.85 | −1.62552 | −0.812760 | − | 0.582599i | \(-0.802036\pi\) | ||||
−0.812760 | + | 0.582599i | \(0.802036\pi\) | |||||||
\(912\) | 143.367 | + | 143.367i | 0.157201 | + | 0.157201i | ||||
\(913\) | 259.758 | − | 259.758i | 0.284510 | − | 0.284510i | ||||
\(914\) | − | 598.463i | − | 0.654773i | ||||||
\(915\) | −14.4876 | + | 126.493i | −0.0158335 | + | 0.138244i | ||||
\(916\) | −796.996 | −0.870083 | ||||||||
\(917\) | 302.624 | + | 302.624i | 0.330015 | + | 0.330015i | ||||
\(918\) | −15.3161 | + | 15.3161i | −0.0166843 | + | 0.0166843i | ||||
\(919\) | − | 886.832i | − | 0.964996i | −0.875897 | − | 0.482498i | \(-0.839729\pi\) | ||
0.875897 | − | 0.482498i | \(-0.160271\pi\) | |||||||
\(920\) | 42.1897 | + | 53.1040i | 0.0458584 | + | 0.0577217i | ||||
\(921\) | −1586.00 | −1.72204 | ||||||||
\(922\) | 482.726 | + | 482.726i | 0.523564 | + | 0.523564i | ||||
\(923\) | 258.455 | − | 258.455i | 0.280016 | − | 0.280016i | ||||
\(924\) | 405.445i | 0.438794i | ||||||||
\(925\) | −1216.32 | + | 758.049i | −1.31494 | + | 0.819512i | ||||
\(926\) | 685.359 | 0.740128 | ||||||||
\(927\) | 282.047 | + | 282.047i | 0.304257 | + | 0.304257i | ||||
\(928\) | 164.478 | − | 164.478i | 0.177239 | − | 0.177239i | ||||
\(929\) | − | 435.730i | − | 0.469031i | −0.972112 | − | 0.234516i | \(-0.924650\pi\) | ||
0.972112 | − | 0.234516i | \(-0.0753504\pi\) | |||||||
\(930\) | −465.093 | + | 369.504i | −0.500100 | + | 0.397316i | ||||
\(931\) | 214.151 | 0.230023 | ||||||||
\(932\) | −267.703 | − | 267.703i | −0.287235 | − | 0.287235i | ||||
\(933\) | 1259.68 | − | 1259.68i | 1.35014 | − | 1.35014i | ||||
\(934\) | 1026.97i | 1.09954i | ||||||||
\(935\) | 949.260 | + | 108.722i | 1.01525 | + | 0.116280i | ||||
\(936\) | 102.490 | 0.109498 | ||||||||
\(937\) | 642.646 | + | 642.646i | 0.685854 | + | 0.685854i | 0.961313 | − | 0.275459i | \(-0.0888297\pi\) |
−0.275459 | + | 0.961313i | \(0.588830\pi\) | |||||||
\(938\) | 168.043 | − | 168.043i | 0.179150 | − | 0.179150i | ||||
\(939\) | 772.105i | 0.822263i | ||||||||
\(940\) | 9.33158 | − | 81.4750i | 0.00992722 | − | 0.0866756i | ||||
\(941\) | −615.461 | −0.654050 | −0.327025 | − | 0.945016i | \(-0.606046\pi\) | ||||
−0.327025 | + | 0.945016i | \(0.606046\pi\) | |||||||
\(942\) | 1069.71 | + | 1069.71i | 1.13557 | + | 1.13557i | ||||
\(943\) | 165.624 | − | 165.624i | 0.175635 | − | 0.175635i | ||||
\(944\) | − | 367.337i | − | 0.389128i | ||||||
\(945\) | −11.9659 | − | 15.0614i | −0.0126623 | − | 0.0159380i | ||||
\(946\) | −511.314 | −0.540501 | ||||||||
\(947\) | 870.854 | + | 870.854i | 0.919593 | + | 0.919593i | 0.997000 | − | 0.0774070i | \(-0.0246641\pi\) |
−0.0774070 | + | 0.997000i | \(0.524664\pi\) | |||||||
\(948\) | 398.744 | − | 398.744i | 0.420616 | − | 0.420616i | ||||
\(949\) | 466.387i | 0.491451i | ||||||||
\(950\) | 224.435 | + | 360.115i | 0.236247 | + | 0.379069i | ||||
\(951\) | 1602.03 | 1.68457 | ||||||||
\(952\) | −248.076 | − | 248.076i | −0.260584 | − | 0.260584i | ||||
\(953\) | −45.2805 | + | 45.2805i | −0.0475137 | + | 0.0475137i | −0.730464 | − | 0.682951i | \(-0.760696\pi\) |
0.682951 | + | 0.730464i | \(0.260696\pi\) | |||||||
\(954\) | 148.053i | 0.155192i | ||||||||
\(955\) | 272.751 | − | 216.694i | 0.285604 | − | 0.226904i | ||||
\(956\) | −412.808 | −0.431808 | ||||||||
\(957\) | −1055.99 | − | 1055.99i | −1.10343 | − | 1.10343i | ||||
\(958\) | 303.049 | − | 303.049i | 0.316335 | − | 0.316335i | ||||
\(959\) | − | 1487.71i | − | 1.55132i | ||||||
\(960\) | −167.837 | − | 19.2229i | −0.174831 | − | 0.0200239i | ||||
\(961\) | −565.363 | −0.588307 | ||||||||
\(962\) | −235.076 | − | 235.076i | −0.244362 | − | 0.244362i | ||||
\(963\) | 611.044 | − | 611.044i | 0.634521 | − | 0.634521i | ||||
\(964\) | − | 185.694i | − | 0.192629i | ||||||
\(965\) | 189.385 | − | 1653.54i | 0.196254 | − | 1.71351i | ||||
\(966\) | −159.887 | −0.165515 | ||||||||
\(967\) | −16.9436 | − | 16.9436i | −0.0175218 | − | 0.0175218i | 0.698292 | − | 0.715813i | \(-0.253944\pi\) |
−0.715813 | + | 0.698292i | \(0.753944\pi\) | |||||||
\(968\) | 94.1010 | − | 94.1010i | 0.0972118 | − | 0.0972118i | ||||
\(969\) | 1126.37i | 1.16241i | ||||||||
\(970\) | 252.575 | + | 317.915i | 0.260387 | + | 0.327748i | ||||
\(971\) | −477.035 | −0.491282 | −0.245641 | − | 0.969361i | \(-0.578999\pi\) | ||||
−0.245641 | + | 0.969361i | \(0.578999\pi\) | |||||||
\(972\) | −483.633 | − | 483.633i | −0.497565 | − | 0.497565i | ||||
\(973\) | 721.026 | − | 721.026i | 0.741033 | − | 0.741033i | ||||
\(974\) | − | 539.974i | − | 0.554388i | ||||||
\(975\) | 421.739 | + | 97.8903i | 0.432553 | + | 0.100400i | ||||
\(976\) | 24.1173 | 0.0247103 | ||||||||
\(977\) | −1000.38 | − | 1000.38i | −1.02393 | − | 1.02393i | −0.999706 | − | 0.0242270i | \(-0.992288\pi\) |
−0.0242270 | − | 0.999706i | \(-0.507712\pi\) | |||||||
\(978\) | 12.4320 | − | 12.4320i | 0.0127116 | − | 0.0127116i | ||||
\(979\) | − | 419.533i | − | 0.428532i | ||||||
\(980\) | −139.708 | + | 110.994i | −0.142559 | + | 0.113260i | ||||
\(981\) | −1850.72 | −1.88657 | ||||||||
\(982\) | −788.957 | − | 788.957i | −0.803418 | − | 0.803418i | ||||
\(983\) | −58.1099 | + | 58.1099i | −0.0591149 | + | 0.0591149i | −0.736046 | − | 0.676931i | \(-0.763309\pi\) |
0.676931 | + | 0.736046i | \(0.263309\pi\) | |||||||
\(984\) | 583.414i | 0.592901i | ||||||||
\(985\) | −964.458 | − | 110.462i | −0.979146 | − | 0.112145i | ||||
\(986\) | 1292.23 | 1.31058 | ||||||||
\(987\) | 136.702 | + | 136.702i | 0.138502 | + | 0.138502i | ||||
\(988\) | −69.5988 | + | 69.5988i | −0.0704441 | + | 0.0704441i | ||||
\(989\) | − | 201.637i | − | 0.203879i | ||||||
\(990\) | −61.1433 | + | 533.848i | −0.0617609 | + | 0.539241i | ||||
\(991\) | −637.010 | −0.642795 | −0.321398 | − | 0.946944i | \(-0.604153\pi\) | ||||
−0.321398 | + | 0.946944i | \(0.604153\pi\) | |||||||
\(992\) | 79.5625 | + | 79.5625i | 0.0802041 | + | 0.0802041i | ||||
\(993\) | 701.288 | − | 701.288i | 0.706231 | − | 0.706231i | ||||
\(994\) | − | 703.640i | − | 0.707887i | ||||||
\(995\) | 688.280 | + | 866.334i | 0.691738 | + | 0.870688i | ||||
\(996\) | −360.832 | −0.362281 | ||||||||
\(997\) | 192.918 | + | 192.918i | 0.193498 | + | 0.193498i | 0.797206 | − | 0.603708i | \(-0.206311\pi\) |
−0.603708 | + | 0.797206i | \(0.706311\pi\) | |||||||
\(998\) | 811.329 | − | 811.329i | 0.812955 | − | 0.812955i | ||||
\(999\) | 39.5130i | 0.0395525i |
(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 | 230.3.f.b.47.3 | ✓ | 24 | |
5.3 | odd | 4 | inner | 230.3.f.b.93.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.b.47.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.f.b.93.3 | yes | 24 | 5.3 | odd | 4 | inner |