Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.1 | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.c.235.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05353 | + | 1.49197i | −1.45206 | + | 1.05499i | −0.466718 | + | 0.884406i | \(0.654564\pi\) |
−0.985344 | + | 0.170579i | \(0.945436\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 1.37295 | − | 4.22550i | 0.686475 | − | 2.11275i | ||||
\(5\) | −3.43019 | − | 2.49218i | −1.53403 | − | 1.11454i | −0.953946 | − | 0.299978i | \(-0.903021\pi\) |
−0.580082 | − | 0.814558i | \(-0.696979\pi\) | |||||||
\(6\) | 2.05353 | + | 1.49197i | 0.838349 | + | 0.609096i | ||||
\(7\) | 0.899200 | − | 2.76745i | 0.339866 | − | 1.04600i | −0.624410 | − | 0.781097i | \(-0.714660\pi\) |
0.964275 | − | 0.264902i | \(-0.0853396\pi\) | |||||||
\(8\) | 1.91620 | + | 5.89746i | 0.677479 | + | 2.08507i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 10.7623 | 3.40332 | ||||||||
\(11\) | 3.13933 | − | 1.06986i | 0.946544 | − | 0.322576i | ||||
\(12\) | −4.44296 | −1.28257 | ||||||||
\(13\) | −0.809017 | + | 0.587785i | −0.224381 | + | 0.163022i | ||||
\(14\) | 2.28244 | + | 7.02462i | 0.610007 | + | 1.87741i | ||||
\(15\) | −1.31022 | + | 4.03243i | −0.338296 | + | 1.04117i | ||||
\(16\) | −5.54497 | − | 4.02866i | −1.38624 | − | 1.00716i | ||||
\(17\) | −0.626709 | − | 0.455331i | −0.151999 | − | 0.110434i | 0.509186 | − | 0.860656i | \(-0.329946\pi\) |
−0.661186 | + | 0.750222i | \(0.729946\pi\) | |||||||
\(18\) | 0.784377 | − | 2.41407i | 0.184879 | − | 0.569001i | ||||
\(19\) | −2.41669 | − | 7.43781i | −0.554427 | − | 1.70635i | −0.697452 | − | 0.716632i | \(-0.745683\pi\) |
0.143025 | − | 0.989719i | \(-0.454317\pi\) | |||||||
\(20\) | −15.2402 | + | 11.0726i | −3.40781 | + | 2.47592i | ||||
\(21\) | −2.90987 | −0.634986 | ||||||||
\(22\) | −4.85049 | + | 6.88079i | −1.03413 | + | 1.46699i | ||||
\(23\) | −3.36268 | −0.701168 | −0.350584 | − | 0.936531i | \(-0.614017\pi\) | ||||
−0.350584 | + | 0.936531i | \(0.614017\pi\) | |||||||
\(24\) | 5.01668 | − | 3.64483i | 1.02403 | − | 0.743998i | ||||
\(25\) | 4.01016 | + | 12.3420i | 0.802033 | + | 2.46840i | ||||
\(26\) | 0.784377 | − | 2.41407i | 0.153829 | − | 0.473437i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −10.4593 | − | 7.59915i | −1.97663 | − | 1.43610i | ||||
\(29\) | −0.289444 | + | 0.890816i | −0.0537483 | + | 0.165420i | −0.974327 | − | 0.225136i | \(-0.927717\pi\) |
0.920579 | + | 0.390556i | \(0.127717\pi\) | |||||||
\(30\) | −3.32572 | − | 10.2355i | −0.607191 | − | 1.86874i | ||||
\(31\) | −3.28474 | + | 2.38651i | −0.589957 | + | 0.428629i | −0.842300 | − | 0.539009i | \(-0.818799\pi\) |
0.252343 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(32\) | 4.99548 | 0.883084 | ||||||||
\(33\) | −1.98761 | − | 2.65507i | −0.345998 | − | 0.462189i | ||||
\(34\) | 1.96631 | 0.337219 | ||||||||
\(35\) | −9.98142 | + | 7.25192i | −1.68717 | + | 1.22580i | ||||
\(36\) | 1.37295 | + | 4.22550i | 0.228825 | + | 0.704251i | ||||
\(37\) | −1.44029 | + | 4.43274i | −0.236781 | + | 0.728738i | 0.760099 | + | 0.649808i | \(0.225151\pi\) |
−0.996880 | + | 0.0789307i | \(0.974849\pi\) | |||||||
\(38\) | 16.0598 | + | 11.6681i | 2.60524 | + | 1.89282i | ||||
\(39\) | 0.809017 | + | 0.587785i | 0.129546 | + | 0.0941210i | ||||
\(40\) | 8.12459 | − | 25.0049i | 1.28461 | − | 3.95363i | ||||
\(41\) | −0.615421 | − | 1.89407i | −0.0961126 | − | 0.295804i | 0.891429 | − | 0.453160i | \(-0.149703\pi\) |
−0.987542 | + | 0.157355i | \(0.949703\pi\) | |||||||
\(42\) | 5.97550 | − | 4.34145i | 0.922040 | − | 0.669901i | ||||
\(43\) | 3.54317 | 0.540328 | 0.270164 | − | 0.962814i | \(-0.412922\pi\) | ||||
0.270164 | + | 0.962814i | \(0.412922\pi\) | |||||||
\(44\) | −0.210571 | − | 14.7341i | −0.0317448 | − | 2.22125i | ||||
\(45\) | 4.23995 | 0.632054 | ||||||||
\(46\) | 6.90536 | − | 5.01703i | 1.01814 | − | 0.739721i | ||||
\(47\) | −1.43367 | − | 4.41239i | −0.209123 | − | 0.643613i | −0.999519 | − | 0.0310171i | \(-0.990125\pi\) |
0.790396 | − | 0.612596i | \(-0.209875\pi\) | |||||||
\(48\) | −2.11799 | + | 6.51850i | −0.305705 | + | 0.940865i | ||||
\(49\) | −1.18712 | − | 0.862491i | −0.169588 | − | 0.123213i | ||||
\(50\) | −26.6490 | − | 19.3616i | −3.76873 | − | 2.73814i | ||||
\(51\) | −0.239382 | + | 0.736741i | −0.0335201 | + | 0.103164i | ||||
\(52\) | 1.37295 | + | 4.22550i | 0.190394 | + | 0.585972i | ||||
\(53\) | −6.46262 | + | 4.69537i | −0.887710 | + | 0.644959i | −0.935280 | − | 0.353909i | \(-0.884852\pi\) |
0.0475702 | + | 0.998868i | \(0.484852\pi\) | |||||||
\(54\) | −2.53830 | −0.345419 | ||||||||
\(55\) | −13.4348 | − | 4.15394i | −1.81155 | − | 0.560117i | ||||
\(56\) | 18.0440 | 2.41123 | ||||||||
\(57\) | −6.32698 | + | 4.59682i | −0.838029 | + | 0.608864i | ||||
\(58\) | −0.734694 | − | 2.26116i | −0.0964700 | − | 0.296904i | ||||
\(59\) | 2.90367 | − | 8.93657i | 0.378025 | − | 1.16344i | −0.563389 | − | 0.826192i | \(-0.690503\pi\) |
0.941415 | − | 0.337251i | \(-0.109497\pi\) | |||||||
\(60\) | 15.2402 | + | 11.0726i | 1.96750 | + | 1.42947i | ||||
\(61\) | 4.52572 | + | 3.28813i | 0.579459 | + | 0.421001i | 0.838529 | − | 0.544857i | \(-0.183416\pi\) |
−0.259070 | + | 0.965858i | \(0.583416\pi\) | |||||||
\(62\) | 3.18470 | − | 9.80150i | 0.404458 | − | 1.24479i | ||||
\(63\) | 0.899200 | + | 2.76745i | 0.113289 | + | 0.348666i | ||||
\(64\) | 0.831591 | − | 0.604186i | 0.103949 | − | 0.0755233i | ||||
\(65\) | 4.23995 | 0.525901 | ||||||||
\(66\) | 8.04291 | + | 2.48681i | 0.990013 | + | 0.306105i | ||||
\(67\) | −13.2680 | −1.62095 | −0.810474 | − | 0.585775i | \(-0.800790\pi\) | ||||
−0.810474 | + | 0.585775i | \(0.800790\pi\) | |||||||
\(68\) | −2.78444 | + | 2.02302i | −0.337663 | + | 0.245327i | ||||
\(69\) | 1.03913 | + | 3.19810i | 0.125096 | + | 0.385006i | ||||
\(70\) | 9.67742 | − | 29.7840i | 1.15667 | − | 3.55987i | ||||
\(71\) | 8.27322 | + | 6.01084i | 0.981850 | + | 0.713356i | 0.958121 | − | 0.286362i | \(-0.0924461\pi\) |
0.0237289 | + | 0.999718i | \(0.492446\pi\) | |||||||
\(72\) | −5.01668 | − | 3.64483i | −0.591221 | − | 0.429547i | ||||
\(73\) | −0.616317 | + | 1.89683i | −0.0721345 | + | 0.222007i | −0.980624 | − | 0.195901i | \(-0.937237\pi\) |
0.908489 | + | 0.417908i | \(0.137237\pi\) | |||||||
\(74\) | −3.65587 | − | 11.2516i | −0.424987 | − | 1.30797i | ||||
\(75\) | 10.4987 | − | 7.62779i | 1.21229 | − | 0.880781i | ||||
\(76\) | −34.7465 | −3.98570 | ||||||||
\(77\) | −0.137912 | − | 9.64997i | −0.0157165 | − | 1.09972i | ||||
\(78\) | −2.53830 | −0.287406 | ||||||||
\(79\) | −5.01552 | + | 3.64399i | −0.564290 | + | 0.409981i | −0.833027 | − | 0.553233i | \(-0.813394\pi\) |
0.268736 | + | 0.963214i | \(0.413394\pi\) | |||||||
\(80\) | 8.98017 | + | 27.6381i | 1.00401 | + | 3.09003i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 4.08969 | + | 2.97133i | 0.451631 | + | 0.328129i | ||||
\(83\) | 13.9807 | + | 10.1576i | 1.53459 | + | 1.11494i | 0.953620 | + | 0.301013i | \(0.0973247\pi\) |
0.580965 | + | 0.813929i | \(0.302675\pi\) | |||||||
\(84\) | −3.99511 | + | 12.2957i | −0.435902 | + | 1.34157i | ||||
\(85\) | 1.01497 | + | 3.12374i | 0.110089 | + | 0.338818i | ||||
\(86\) | −7.27598 | + | 5.28631i | −0.784589 | + | 0.570038i | ||||
\(87\) | 0.936659 | 0.100420 | ||||||||
\(88\) | 12.3251 | + | 16.4640i | 1.31386 | + | 1.75507i | ||||
\(89\) | 1.56195 | 0.165566 | 0.0827831 | − | 0.996568i | \(-0.473619\pi\) | ||||
0.0827831 | + | 0.996568i | \(0.473619\pi\) | |||||||
\(90\) | −8.70685 | + | 6.32589i | −0.917782 | + | 0.666808i | ||||
\(91\) | 0.899200 | + | 2.76745i | 0.0942618 | + | 0.290108i | ||||
\(92\) | −4.61679 | + | 14.2090i | −0.481334 | + | 1.48139i | ||||
\(93\) | 3.28474 | + | 2.38651i | 0.340612 | + | 0.247469i | ||||
\(94\) | 9.52725 | + | 6.92195i | 0.982661 | + | 0.713945i | ||||
\(95\) | −10.2466 | + | 31.5359i | −1.05128 | + | 3.23552i | ||||
\(96\) | −1.54369 | − | 4.75098i | −0.157552 | − | 0.484895i | ||||
\(97\) | −7.32906 | + | 5.32487i | −0.744153 | + | 0.540659i | −0.894009 | − | 0.448049i | \(-0.852119\pi\) |
0.149856 | + | 0.988708i | \(0.452119\pi\) | |||||||
\(98\) | 3.72459 | 0.376241 | ||||||||
\(99\) | −1.91092 | + | 2.71079i | −0.192055 | + | 0.272445i | ||||
\(100\) | 57.6570 | 5.76570 | ||||||||
\(101\) | 2.49382 | − | 1.81187i | 0.248144 | − | 0.180287i | −0.456760 | − | 0.889590i | \(-0.650990\pi\) |
0.704904 | + | 0.709303i | \(0.250990\pi\) | |||||||
\(102\) | −0.607622 | − | 1.87007i | −0.0601635 | − | 0.185164i | ||||
\(103\) | −2.54026 | + | 7.81813i | −0.250300 | + | 0.770343i | 0.744420 | + | 0.667712i | \(0.232726\pi\) |
−0.994719 | + | 0.102631i | \(0.967274\pi\) | |||||||
\(104\) | −5.01668 | − | 3.64483i | −0.491926 | − | 0.357405i | ||||
\(105\) | 9.98142 | + | 7.25192i | 0.974087 | + | 0.707715i | ||||
\(106\) | 6.26580 | − | 19.2841i | 0.608588 | − | 1.87304i | ||||
\(107\) | −5.82809 | − | 17.9370i | −0.563423 | − | 1.73404i | −0.672592 | − | 0.740013i | \(-0.734819\pi\) |
0.109169 | − | 0.994023i | \(-0.465181\pi\) | |||||||
\(108\) | 3.59443 | − | 2.61150i | 0.345874 | − | 0.251292i | ||||
\(109\) | −10.7130 | −1.02612 | −0.513061 | − | 0.858352i | \(-0.671488\pi\) | ||||
−0.513061 | + | 0.858352i | \(0.671488\pi\) | |||||||
\(110\) | 33.7863 | − | 11.5141i | 3.22139 | − | 1.09783i | ||||
\(111\) | 4.66086 | 0.442389 | ||||||||
\(112\) | −16.1351 | + | 11.7229i | −1.52463 | + | 1.10771i | ||||
\(113\) | 1.34981 | + | 4.15430i | 0.126980 | + | 0.390804i | 0.994257 | − | 0.107023i | \(-0.0341317\pi\) |
−0.867277 | + | 0.497826i | \(0.834132\pi\) | |||||||
\(114\) | 6.13428 | − | 18.8794i | 0.574528 | − | 1.76822i | ||||
\(115\) | 11.5346 | + | 8.38041i | 1.07561 | + | 0.781477i | ||||
\(116\) | 3.36675 | + | 2.44609i | 0.312595 | + | 0.227114i | ||||
\(117\) | 0.309017 | − | 0.951057i | 0.0285686 | − | 0.0879252i | ||||
\(118\) | 7.37038 | + | 22.6837i | 0.678498 | + | 2.08820i | ||||
\(119\) | −1.82364 | + | 1.32495i | −0.167173 | + | 0.121458i | ||||
\(120\) | −26.2917 | −2.40010 | ||||||||
\(121\) | 8.71078 | − | 6.71731i | 0.791889 | − | 0.610664i | ||||
\(122\) | −14.1995 | −1.28556 | ||||||||
\(123\) | −1.61119 | + | 1.17060i | −0.145276 | + | 0.105550i | ||||
\(124\) | 5.57440 | + | 17.1562i | 0.500596 | + | 1.54068i | ||||
\(125\) | 10.4518 | − | 32.1674i | 0.934838 | − | 2.87714i | ||||
\(126\) | −5.97550 | − | 4.34145i | −0.532340 | − | 0.386768i | ||||
\(127\) | 0.116965 | + | 0.0849802i | 0.0103790 | + | 0.00754078i | 0.592963 | − | 0.805230i | \(-0.297958\pi\) |
−0.582584 | + | 0.812771i | \(0.697958\pi\) | |||||||
\(128\) | −3.89364 | + | 11.9834i | −0.344152 | + | 1.05919i | ||||
\(129\) | −1.09490 | − | 3.36975i | −0.0964004 | − | 0.296690i | ||||
\(130\) | −8.70685 | + | 6.32589i | −0.763641 | + | 0.554818i | ||||
\(131\) | 4.28002 | 0.373947 | 0.186974 | − | 0.982365i | \(-0.440132\pi\) | ||||
0.186974 | + | 0.982365i | \(0.440132\pi\) | |||||||
\(132\) | −13.9479 | + | 4.75336i | −1.21401 | + | 0.413727i | ||||
\(133\) | −22.7569 | −1.97327 | ||||||||
\(134\) | 27.2462 | − | 19.7956i | 2.35372 | − | 1.71008i | ||||
\(135\) | −1.31022 | − | 4.03243i | −0.112765 | − | 0.347056i | ||||
\(136\) | 1.48439 | − | 4.56850i | 0.127286 | − | 0.391745i | ||||
\(137\) | −9.44724 | − | 6.86382i | −0.807132 | − | 0.586416i | 0.105866 | − | 0.994380i | \(-0.466239\pi\) |
−0.912998 | + | 0.407965i | \(0.866239\pi\) | |||||||
\(138\) | −6.90536 | − | 5.01703i | −0.587823 | − | 0.427078i | ||||
\(139\) | 7.07374 | − | 21.7707i | 0.599987 | − | 1.84657i | 0.0718412 | − | 0.997416i | \(-0.477113\pi\) |
0.528146 | − | 0.849154i | \(-0.322887\pi\) | |||||||
\(140\) | 16.9391 | + | 52.1330i | 1.43161 | + | 4.40605i | ||||
\(141\) | −3.75340 | + | 2.72701i | −0.316093 | + | 0.229655i | ||||
\(142\) | −25.9573 | −2.17829 | ||||||||
\(143\) | −1.91092 | + | 2.71079i | −0.159799 | + | 0.226688i | ||||
\(144\) | 6.85396 | 0.571163 | ||||||||
\(145\) | 3.21292 | − | 2.33432i | 0.266818 | − | 0.193855i | ||||
\(146\) | −1.56440 | − | 4.81472i | −0.129470 | − | 0.398469i | ||||
\(147\) | −0.453438 | + | 1.39554i | −0.0373990 | + | 0.115102i | ||||
\(148\) | 16.7531 | + | 12.1719i | 1.37710 | + | 1.00052i | ||||
\(149\) | −7.61950 | − | 5.53589i | −0.624214 | − | 0.453518i | 0.230177 | − | 0.973149i | \(-0.426070\pi\) |
−0.854391 | + | 0.519631i | \(0.826070\pi\) | |||||||
\(150\) | −10.1790 | + | 31.3277i | −0.831111 | + | 2.55790i | ||||
\(151\) | −0.881867 | − | 2.71411i | −0.0717653 | − | 0.220871i | 0.908740 | − | 0.417362i | \(-0.137045\pi\) |
−0.980506 | + | 0.196491i | \(0.937045\pi\) | |||||||
\(152\) | 39.2333 | − | 28.5047i | 3.18224 | − | 2.31203i | ||||
\(153\) | 0.774655 | 0.0626272 | ||||||||
\(154\) | 14.6807 | + | 19.6107i | 1.18301 | + | 1.58028i | ||||
\(155\) | 17.2149 | 1.38273 | ||||||||
\(156\) | 3.59443 | − | 2.61150i | 0.287785 | − | 0.209088i | ||||
\(157\) | 1.20738 | + | 3.71595i | 0.0963597 | + | 0.296565i | 0.987606 | − | 0.156956i | \(-0.0501680\pi\) |
−0.891246 | + | 0.453520i | \(0.850168\pi\) | |||||||
\(158\) | 4.86277 | − | 14.9661i | 0.386861 | − | 1.19064i | ||||
\(159\) | 6.46262 | + | 4.69537i | 0.512519 | + | 0.372367i | ||||
\(160\) | −17.1354 | − | 12.4496i | −1.35468 | − | 0.984229i | ||||
\(161\) | −3.02372 | + | 9.30606i | −0.238303 | + | 0.733421i | ||||
\(162\) | 0.784377 | + | 2.41407i | 0.0616265 | + | 0.189667i | ||||
\(163\) | 3.63845 | − | 2.64349i | 0.284985 | − | 0.207054i | −0.436104 | − | 0.899896i | \(-0.643642\pi\) |
0.721089 | + | 0.692842i | \(0.243642\pi\) | |||||||
\(164\) | −8.84835 | −0.690940 | ||||||||
\(165\) | 0.200950 | + | 14.0609i | 0.0156439 | + | 1.09464i | ||||
\(166\) | −43.8647 | −3.40456 | ||||||||
\(167\) | −11.4583 | + | 8.32495i | −0.886670 | + | 0.644204i | −0.935008 | − | 0.354627i | \(-0.884608\pi\) |
0.0483375 | + | 0.998831i | \(0.484608\pi\) | |||||||
\(168\) | −5.57590 | − | 17.1609i | −0.430190 | − | 1.32399i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | −6.74480 | − | 4.90039i | −0.517303 | − | 0.375843i | ||||
\(171\) | 6.32698 | + | 4.59682i | 0.483836 | + | 0.351528i | ||||
\(172\) | 4.86459 | − | 14.9717i | 0.370921 | − | 1.14158i | ||||
\(173\) | −5.76564 | − | 17.7448i | −0.438353 | − | 1.34911i | −0.889611 | − | 0.456719i | \(-0.849025\pi\) |
0.451258 | − | 0.892394i | \(-0.350975\pi\) | |||||||
\(174\) | −1.92345 | + | 1.39747i | −0.145817 | + | 0.105942i | ||||
\(175\) | 37.7619 | 2.85453 | ||||||||
\(176\) | −21.7176 | − | 6.71492i | −1.63703 | − | 0.506156i | ||||
\(177\) | −9.39647 | −0.706282 | ||||||||
\(178\) | −3.20750 | + | 2.33039i | −0.240413 | + | 0.174670i | ||||
\(179\) | 4.58270 | + | 14.1041i | 0.342527 | + | 1.05419i | 0.962895 | + | 0.269878i | \(0.0869834\pi\) |
−0.620368 | + | 0.784311i | \(0.713017\pi\) | |||||||
\(180\) | 5.82124 | − | 17.9159i | 0.433889 | − | 1.33537i | ||||
\(181\) | −10.3293 | − | 7.50464i | −0.767767 | − | 0.557816i | 0.133515 | − | 0.991047i | \(-0.457373\pi\) |
−0.901283 | + | 0.433231i | \(0.857373\pi\) | |||||||
\(182\) | −5.97550 | − | 4.34145i | −0.442934 | − | 0.321810i | ||||
\(183\) | 1.72867 | − | 5.32030i | 0.127787 | − | 0.393288i | ||||
\(184\) | −6.44357 | − | 19.8313i | −0.475026 | − | 1.46198i | ||||
\(185\) | 15.9876 | − | 11.6157i | 1.17543 | − | 0.854003i | ||||
\(186\) | −10.3059 | −0.755666 | ||||||||
\(187\) | −2.45459 | − | 0.758941i | −0.179497 | − | 0.0554992i | ||||
\(188\) | −20.6129 | −1.50335 | ||||||||
\(189\) | 2.35414 | − | 1.71038i | 0.171238 | − | 0.124412i | ||||
\(190\) | −26.0090 | − | 80.0476i | −1.88689 | − | 5.80726i | ||||
\(191\) | −1.03127 | + | 3.17391i | −0.0746199 | + | 0.229656i | −0.981409 | − | 0.191928i | \(-0.938526\pi\) |
0.906789 | + | 0.421585i | \(0.138526\pi\) | |||||||
\(192\) | −0.831591 | − | 0.604186i | −0.0600149 | − | 0.0436034i | ||||
\(193\) | −15.2261 | − | 11.0624i | −1.09600 | − | 0.796291i | −0.115598 | − | 0.993296i | \(-0.536879\pi\) |
−0.980403 | + | 0.197005i | \(0.936879\pi\) | |||||||
\(194\) | 7.10584 | − | 21.8695i | 0.510170 | − | 1.57014i | ||||
\(195\) | −1.31022 | − | 4.03243i | −0.0938265 | − | 0.288768i | ||||
\(196\) | −5.27431 | + | 3.83201i | −0.376737 | + | 0.273715i | ||||
\(197\) | 7.88673 | 0.561907 | 0.280953 | − | 0.959721i | \(-0.409349\pi\) | ||||
0.280953 | + | 0.959721i | \(0.409349\pi\) | |||||||
\(198\) | −0.120301 | − | 8.41772i | −0.00854942 | − | 0.598222i | ||||
\(199\) | 6.64393 | 0.470976 | 0.235488 | − | 0.971877i | \(-0.424331\pi\) | ||||
0.235488 | + | 0.971877i | \(0.424331\pi\) | |||||||
\(200\) | −65.1023 | + | 47.2996i | −4.60342 | + | 3.34458i | ||||
\(201\) | 4.10005 | + | 12.6186i | 0.289195 | + | 0.890050i | ||||
\(202\) | −2.41787 | + | 7.44143i | −0.170121 | + | 0.523577i | ||||
\(203\) | 2.20502 | + | 1.60204i | 0.154762 | + | 0.112441i | ||||
\(204\) | 2.78444 | + | 2.02302i | 0.194950 | + | 0.141639i | ||||
\(205\) | −2.60935 | + | 8.03077i | −0.182245 | + | 0.560893i | ||||
\(206\) | −6.44794 | − | 19.8447i | −0.449250 | − | 1.38265i | ||||
\(207\) | 2.72047 | − | 1.97653i | 0.189085 | − | 0.137379i | ||||
\(208\) | 6.85396 | 0.475236 | ||||||||
\(209\) | −15.5442 | − | 20.7642i | −1.07522 | − | 1.43629i | ||||
\(210\) | −31.3168 | −2.16106 | ||||||||
\(211\) | 7.65263 | − | 5.55996i | 0.526829 | − | 0.382764i | −0.292341 | − | 0.956314i | \(-0.594434\pi\) |
0.819170 | + | 0.573550i | \(0.194434\pi\) | |||||||
\(212\) | 10.9675 | + | 33.7543i | 0.753248 | + | 2.31826i | ||||
\(213\) | 3.16009 | − | 9.72575i | 0.216526 | − | 0.666397i | ||||
\(214\) | 38.7297 | + | 28.1388i | 2.64751 | + | 1.92353i | ||||
\(215\) | −12.1537 | − | 8.83020i | −0.828878 | − | 0.602215i | ||||
\(216\) | −1.91620 | + | 5.89746i | −0.130381 | + | 0.401271i | ||||
\(217\) | 3.65090 | + | 11.2363i | 0.247839 | + | 0.762771i | ||||
\(218\) | 21.9995 | − | 15.9836i | 1.48999 | − | 1.08254i | ||||
\(219\) | 1.99444 | 0.134772 | ||||||||
\(220\) | −35.9978 | + | 51.0656i | −2.42697 | + | 3.44284i | ||||
\(221\) | 0.774655 | 0.0521089 | ||||||||
\(222\) | −9.57120 | + | 6.95388i | −0.642377 | + | 0.466714i | ||||
\(223\) | 4.18676 | + | 12.8855i | 0.280366 | + | 0.862878i | 0.987749 | + | 0.156048i | \(0.0498755\pi\) |
−0.707383 | + | 0.706830i | \(0.750125\pi\) | |||||||
\(224\) | 4.49193 | − | 13.8248i | 0.300130 | − | 0.923705i | ||||
\(225\) | −10.4987 | − | 7.62779i | −0.699916 | − | 0.508519i | ||||
\(226\) | −8.96998 | − | 6.51707i | −0.596674 | − | 0.433509i | ||||
\(227\) | 8.05283 | − | 24.7840i | 0.534485 | − | 1.64498i | −0.210275 | − | 0.977642i | \(-0.567436\pi\) |
0.744760 | − | 0.667333i | \(-0.232564\pi\) | |||||||
\(228\) | 10.7373 | + | 33.0459i | 0.711092 | + | 2.18852i | ||||
\(229\) | 22.2301 | − | 16.1511i | 1.46901 | − | 1.06730i | 0.488110 | − | 0.872782i | \(-0.337687\pi\) |
0.980899 | − | 0.194515i | \(-0.0623134\pi\) | |||||||
\(230\) | −36.1900 | −2.38630 | ||||||||
\(231\) | −9.13505 | + | 3.11317i | −0.601042 | + | 0.204831i | ||||
\(232\) | −5.80818 | −0.381326 | ||||||||
\(233\) | 4.19683 | − | 3.04918i | 0.274944 | − | 0.199758i | −0.441765 | − | 0.897131i | \(-0.645648\pi\) |
0.716709 | + | 0.697372i | \(0.245648\pi\) | |||||||
\(234\) | 0.784377 | + | 2.41407i | 0.0512763 | + | 0.157812i | ||||
\(235\) | −6.07870 | + | 18.7083i | −0.396530 | + | 1.22039i | ||||
\(236\) | −33.7749 | − | 24.5389i | −2.19856 | − | 1.59735i | ||||
\(237\) | 5.01552 | + | 3.64399i | 0.325793 | + | 0.236702i | ||||
\(238\) | 1.76810 | − | 5.44166i | 0.114609 | − | 0.352730i | ||||
\(239\) | −0.644556 | − | 1.98374i | −0.0416929 | − | 0.128317i | 0.928044 | − | 0.372472i | \(-0.121490\pi\) |
−0.969736 | + | 0.244154i | \(0.921490\pi\) | |||||||
\(240\) | 23.5104 | − | 17.0813i | 1.51759 | − | 1.10259i | ||||
\(241\) | −7.72932 | −0.497889 | −0.248945 | − | 0.968518i | \(-0.580084\pi\) | ||||
−0.248945 | + | 0.968518i | \(0.580084\pi\) | |||||||
\(242\) | −7.86577 | + | 26.7904i | −0.505631 | + | 1.72215i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 20.1076 | − | 14.6090i | 1.28726 | − | 0.935246i | ||||
\(245\) | 1.92256 | + | 5.91702i | 0.122828 | + | 0.378024i | ||||
\(246\) | 1.56212 | − | 4.80772i | 0.0995973 | − | 0.306529i | ||||
\(247\) | 6.32698 | + | 4.59682i | 0.402576 | + | 0.292489i | ||||
\(248\) | −20.3685 | − | 14.7986i | −1.29340 | − | 0.939713i | ||||
\(249\) | 5.34017 | − | 16.4353i | 0.338419 | − | 1.04155i | ||||
\(250\) | 26.5298 | + | 81.6504i | 1.67789 | + | 5.16402i | ||||
\(251\) | −16.5162 | + | 11.9997i | −1.04249 | + | 0.757415i | −0.970770 | − | 0.240010i | \(-0.922849\pi\) |
−0.0717218 | + | 0.997425i | \(0.522849\pi\) | |||||||
\(252\) | 12.9284 | 0.814415 | ||||||||
\(253\) | −10.5566 | + | 3.59761i | −0.663686 | + | 0.226180i | ||||
\(254\) | −0.366980 | −0.0230263 | ||||||||
\(255\) | 2.65722 | − | 1.93058i | 0.166401 | − | 0.120898i | ||||
\(256\) | −9.24794 | − | 28.4622i | −0.577996 | − | 1.77889i | ||||
\(257\) | 3.06767 | − | 9.44131i | 0.191356 | − | 0.588932i | −0.808644 | − | 0.588298i | \(-0.799798\pi\) |
1.00000 | 0.000634216i | \(-0.000201877\pi\) | ||||||||
\(258\) | 7.27598 | + | 5.28631i | 0.452983 | + | 0.329111i | ||||
\(259\) | 10.9723 | + | 7.97184i | 0.681786 | + | 0.495346i | ||||
\(260\) | 5.82124 | − | 17.9159i | 0.361018 | − | 1.11110i | ||||
\(261\) | −0.289444 | − | 0.890816i | −0.0179161 | − | 0.0551401i | ||||
\(262\) | −8.78914 | + | 6.38568i | −0.542995 | + | 0.394509i | ||||
\(263\) | −11.0697 | −0.682588 | −0.341294 | − | 0.939957i | \(-0.610865\pi\) | ||||
−0.341294 | + | 0.939957i | \(0.610865\pi\) | |||||||
\(264\) | 11.8495 | − | 16.8095i | 0.729289 | − | 1.03455i | ||||
\(265\) | 33.8697 | 2.08060 | ||||||||
\(266\) | 46.7319 | − | 33.9527i | 2.86531 | − | 2.08177i | ||||
\(267\) | −0.482669 | − | 1.48550i | −0.0295388 | − | 0.0909112i | ||||
\(268\) | −18.2163 | + | 56.0641i | −1.11274 | + | 3.42466i | ||||
\(269\) | 1.26350 | + | 0.917984i | 0.0770367 | + | 0.0559705i | 0.625637 | − | 0.780114i | \(-0.284839\pi\) |
−0.548600 | + | 0.836085i | \(0.684839\pi\) | |||||||
\(270\) | 8.70685 | + | 6.32589i | 0.529882 | + | 0.384982i | ||||
\(271\) | −0.622397 | + | 1.91554i | −0.0378079 | + | 0.116361i | −0.968179 | − | 0.250258i | \(-0.919485\pi\) |
0.930371 | + | 0.366619i | \(0.119485\pi\) | |||||||
\(272\) | 1.64071 | + | 5.04959i | 0.0994827 | + | 0.306176i | ||||
\(273\) | 2.35414 | − | 1.71038i | 0.142479 | − | 0.103517i | ||||
\(274\) | 29.6408 | 1.79067 | ||||||||
\(275\) | 25.7935 | + | 34.4553i | 1.55541 | + | 2.07773i | ||||
\(276\) | 14.9403 | 0.899297 | ||||||||
\(277\) | 7.73303 | − | 5.61837i | 0.464633 | − | 0.337575i | −0.330713 | − | 0.943731i | \(-0.607289\pi\) |
0.795346 | + | 0.606156i | \(0.207289\pi\) | |||||||
\(278\) | 17.9553 | + | 55.2606i | 1.07689 | + | 3.31431i | ||||
\(279\) | 1.25466 | − | 3.86145i | 0.0751145 | − | 0.231179i | ||||
\(280\) | −61.8943 | − | 44.9689i | −3.69889 | − | 2.68740i | ||||
\(281\) | −3.18700 | − | 2.31549i | −0.190120 | − | 0.138130i | 0.488653 | − | 0.872478i | \(-0.337488\pi\) |
−0.678774 | + | 0.734348i | \(0.737488\pi\) | |||||||
\(282\) | 3.63909 | − | 11.2000i | 0.216704 | − | 0.666948i | ||||
\(283\) | −2.65674 | − | 8.17662i | −0.157927 | − | 0.486050i | 0.840519 | − | 0.541783i | \(-0.182250\pi\) |
−0.998446 | + | 0.0557331i | \(0.982250\pi\) | |||||||
\(284\) | 36.7576 | − | 26.7059i | 2.18116 | − | 1.58471i | ||||
\(285\) | 33.1588 | 1.96416 | ||||||||
\(286\) | −0.120301 | − | 8.41772i | −0.00711355 | − | 0.497750i | ||||
\(287\) | −5.79514 | −0.342076 | ||||||||
\(288\) | −4.04143 | + | 2.93627i | −0.238143 | + | 0.173021i | ||||
\(289\) | −5.06785 | − | 15.5972i | −0.298109 | − | 0.917485i | ||||
\(290\) | −3.11506 | + | 9.58718i | −0.182923 | + | 0.562979i | ||||
\(291\) | 7.32906 | + | 5.32487i | 0.429637 | + | 0.312150i | ||||
\(292\) | 7.16889 | + | 5.20850i | 0.419527 | + | 0.304804i | ||||
\(293\) | −8.27637 | + | 25.4721i | −0.483511 | + | 1.48809i | 0.350615 | + | 0.936520i | \(0.385973\pi\) |
−0.834126 | + | 0.551574i | \(0.814027\pi\) | |||||||
\(294\) | −1.15096 | − | 3.54230i | −0.0671255 | − | 0.206591i | ||||
\(295\) | −32.2317 | + | 23.4177i | −1.87660 | + | 1.36343i | ||||
\(296\) | −28.9018 | −1.67988 | ||||||||
\(297\) | 3.16862 | + | 0.979714i | 0.183862 | + | 0.0568488i | ||||
\(298\) | 23.9063 | 1.38485 | ||||||||
\(299\) | 2.72047 | − | 1.97653i | 0.157329 | − | 0.114306i | ||||
\(300\) | −17.8170 | − | 54.8351i | −1.02866 | − | 3.16590i | ||||
\(301\) | 3.18601 | − | 9.80554i | 0.183639 | − | 0.565182i | ||||
\(302\) | 5.86032 | + | 4.25777i | 0.337223 | + | 0.245007i | ||||
\(303\) | −2.49382 | − | 1.81187i | −0.143266 | − | 0.104089i | ||||
\(304\) | −16.5639 | + | 50.9784i | −0.950005 | + | 2.92381i | ||||
\(305\) | −7.32947 | − | 22.5578i | −0.419684 | − | 1.29166i | ||||
\(306\) | −1.59077 | + | 1.15577i | −0.0909385 | + | 0.0660707i | ||||
\(307\) | 17.0080 | 0.970700 | 0.485350 | − | 0.874320i | \(-0.338692\pi\) | ||||
0.485350 | + | 0.874320i | \(0.338692\pi\) | |||||||
\(308\) | −40.9653 | − | 12.6662i | −2.33422 | − | 0.721722i | ||||
\(309\) | 8.22046 | 0.467646 | ||||||||
\(310\) | −35.3512 | + | 25.6842i | −2.00782 | + | 1.45876i | ||||
\(311\) | −7.58929 | − | 23.3574i | −0.430349 | − | 1.32448i | −0.897778 | − | 0.440448i | \(-0.854820\pi\) |
0.467429 | − | 0.884031i | \(-0.345180\pi\) | |||||||
\(312\) | −1.91620 | + | 5.89746i | −0.108483 | + | 0.333878i | ||||
\(313\) | −18.9782 | − | 13.7885i | −1.07271 | − | 0.779372i | −0.0963159 | − | 0.995351i | \(-0.530706\pi\) |
−0.976398 | + | 0.215978i | \(0.930706\pi\) | |||||||
\(314\) | −8.02349 | − | 5.82941i | −0.452792 | − | 0.328972i | ||||
\(315\) | 3.81256 | − | 11.7339i | 0.214814 | − | 0.661128i | ||||
\(316\) | 8.51163 | + | 26.1961i | 0.478817 | + | 1.47365i | ||||
\(317\) | −24.3500 | + | 17.6913i | −1.36763 | + | 0.993643i | −0.369714 | + | 0.929146i | \(0.620544\pi\) |
−0.997918 | + | 0.0644969i | \(0.979456\pi\) | |||||||
\(318\) | −20.2765 | −1.13705 | ||||||||
\(319\) | 0.0443924 | + | 3.10623i | 0.00248550 | + | 0.173915i | ||||
\(320\) | −4.35826 | −0.243634 | ||||||||
\(321\) | −15.2581 | + | 11.0857i | −0.851626 | + | 0.618743i | ||||
\(322\) | −7.67511 | − | 23.6216i | −0.427717 | − | 1.31638i | ||||
\(323\) | −1.87210 | + | 5.76174i | −0.104167 | + | 0.320592i | ||||
\(324\) | −3.59443 | − | 2.61150i | −0.199690 | − | 0.145084i | ||||
\(325\) | −10.4987 | − | 7.62779i | −0.582366 | − | 0.423113i | ||||
\(326\) | −3.52764 | + | 10.8569i | −0.195378 | + | 0.601311i | ||||
\(327\) | 3.31051 | + | 10.1887i | 0.183071 | + | 0.563436i | ||||
\(328\) | 9.99094 | − | 7.25884i | 0.551657 | − | 0.400802i | ||||
\(329\) | −13.5002 | −0.744292 | ||||||||
\(330\) | −21.3911 | − | 28.5746i | −1.17754 | − | 1.57298i | ||||
\(331\) | 11.2054 | 0.615907 | 0.307953 | − | 0.951401i | \(-0.400356\pi\) | ||||
0.307953 | + | 0.951401i | \(0.400356\pi\) | |||||||
\(332\) | 62.1158 | − | 45.1298i | 3.40905 | − | 2.47682i | ||||
\(333\) | −1.44029 | − | 4.43274i | −0.0789271 | − | 0.242913i | ||||
\(334\) | 11.1093 | − | 34.1910i | 0.607875 | − | 1.87085i | ||||
\(335\) | 45.5119 | + | 33.0663i | 2.48658 | + | 1.80660i | ||||
\(336\) | 16.1351 | + | 11.7229i | 0.880245 | + | 0.639535i | ||||
\(337\) | 7.73245 | − | 23.7980i | 0.421213 | − | 1.29636i | −0.485360 | − | 0.874314i | \(-0.661312\pi\) |
0.906574 | − | 0.422047i | \(-0.138688\pi\) | |||||||
\(338\) | 0.784377 | + | 2.41407i | 0.0426645 | + | 0.131308i | ||||
\(339\) | 3.53386 | − | 2.56750i | 0.191933 | − | 0.139447i | ||||
\(340\) | 14.5929 | 0.791410 | ||||||||
\(341\) | −7.75866 | + | 11.0063i | −0.420155 | + | 0.596022i | ||||
\(342\) | −19.8510 | −1.07342 | ||||||||
\(343\) | 13.0246 | − | 9.46292i | 0.703262 | − | 0.510950i | ||||
\(344\) | 6.78941 | + | 20.8957i | 0.366061 | + | 1.12662i | ||||
\(345\) | 4.40584 | − | 13.5598i | 0.237202 | − | 0.730034i | ||||
\(346\) | 38.3147 | + | 27.8372i | 2.05981 | + | 1.49654i | ||||
\(347\) | 18.9220 | + | 13.7476i | 1.01579 | + | 0.738011i | 0.965415 | − | 0.260719i | \(-0.0839597\pi\) |
0.0503706 | + | 0.998731i | \(0.483960\pi\) | |||||||
\(348\) | 1.28599 | − | 3.95786i | 0.0689360 | − | 0.212163i | ||||
\(349\) | 3.33327 | + | 10.2587i | 0.178426 | + | 0.549138i | 0.999773 | − | 0.0212900i | \(-0.00677732\pi\) |
−0.821348 | + | 0.570428i | \(0.806777\pi\) | |||||||
\(350\) | −77.5450 | + | 56.3398i | −4.14496 | + | 3.01149i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 15.6825 | − | 5.34448i | 0.835877 | − | 0.284862i | ||||
\(353\) | 1.10779 | 0.0589615 | 0.0294807 | − | 0.999565i | \(-0.490615\pi\) | ||||
0.0294807 | + | 0.999565i | \(0.490615\pi\) | |||||||
\(354\) | 19.2959 | − | 14.0193i | 1.02557 | − | 0.745117i | ||||
\(355\) | −13.3986 | − | 41.2367i | −0.711124 | − | 2.18862i | ||||
\(356\) | 2.14448 | − | 6.60002i | 0.113657 | − | 0.349800i | ||||
\(357\) | 1.82364 | + | 1.32495i | 0.0965175 | + | 0.0701240i | ||||
\(358\) | −30.4536 | − | 22.1259i | −1.60952 | − | 1.16939i | ||||
\(359\) | 1.70698 | − | 5.25353i | 0.0900907 | − | 0.277271i | −0.895852 | − | 0.444352i | \(-0.853434\pi\) |
0.985943 | + | 0.167081i | \(0.0534341\pi\) | |||||||
\(360\) | 8.12459 | + | 25.0049i | 0.428204 | + | 1.31788i | ||||
\(361\) | −34.1093 | + | 24.7819i | −1.79523 | + | 1.30431i | ||||
\(362\) | 32.4081 | 1.70333 | ||||||||
\(363\) | −9.08032 | − | 6.20869i | −0.476593 | − | 0.325871i | ||||
\(364\) | 12.9284 | 0.677634 | ||||||||
\(365\) | 6.84132 | − | 4.97051i | 0.358091 | − | 0.260168i | ||||
\(366\) | 4.38788 | + | 13.5045i | 0.229358 | + | 0.705892i | ||||
\(367\) | −5.87475 | + | 18.0806i | −0.306659 | + | 0.943801i | 0.672393 | + | 0.740194i | \(0.265266\pi\) |
−0.979053 | + | 0.203607i | \(0.934734\pi\) | |||||||
\(368\) | 18.6460 | + | 13.5471i | 0.971988 | + | 0.706191i | ||||
\(369\) | 1.61119 | + | 1.17060i | 0.0838754 | + | 0.0609390i | ||||
\(370\) | −15.5007 | + | 47.7063i | −0.805844 | + | 2.48013i | ||||
\(371\) | 7.18303 | + | 22.1071i | 0.372924 | + | 1.14774i | ||||
\(372\) | 14.5940 | − | 10.6031i | 0.756662 | − | 0.549747i | ||||
\(373\) | 8.71301 | 0.451143 | 0.225571 | − | 0.974227i | \(-0.427575\pi\) | ||||
0.225571 | + | 0.974227i | \(0.427575\pi\) | |||||||
\(374\) | 6.17288 | − | 2.10368i | 0.319192 | − | 0.108779i | ||||
\(375\) | −33.8228 | −1.74660 | ||||||||
\(376\) | 23.2747 | − | 16.9100i | 1.20030 | − | 0.872069i | ||||
\(377\) | −0.289444 | − | 0.890816i | −0.0149071 | − | 0.0458793i | ||||
\(378\) | −2.28244 | + | 7.02462i | −0.117396 | + | 0.361308i | ||||
\(379\) | −26.4936 | − | 19.2487i | −1.36088 | − | 0.988740i | −0.998388 | − | 0.0567553i | \(-0.981925\pi\) |
−0.362496 | − | 0.931985i | \(-0.618075\pi\) | |||||||
\(380\) | 119.187 | + | 86.5945i | 6.11417 | + | 4.44220i | ||||
\(381\) | 0.0446768 | − | 0.137501i | 0.00228886 | − | 0.00704438i | ||||
\(382\) | −2.61766 | − | 8.05634i | −0.133931 | − | 0.412198i | ||||
\(383\) | −9.13555 | + | 6.63737i | −0.466805 | + | 0.339154i | −0.796195 | − | 0.605040i | \(-0.793157\pi\) |
0.329390 | + | 0.944194i | \(0.393157\pi\) | |||||||
\(384\) | 12.6001 | 0.642995 | ||||||||
\(385\) | −23.5764 | + | 33.4449i | −1.20156 | + | 1.70451i | ||||
\(386\) | 47.7721 | 2.43154 | ||||||||
\(387\) | −2.86648 | + | 2.08262i | −0.145711 | + | 0.105866i | ||||
\(388\) | 12.4378 | + | 38.2797i | 0.631436 | + | 1.94336i | ||||
\(389\) | 2.58841 | − | 7.96630i | 0.131238 | − | 0.403908i | −0.863748 | − | 0.503924i | \(-0.831889\pi\) |
0.994986 | + | 0.100016i | \(0.0318893\pi\) | |||||||
\(390\) | 8.70685 | + | 6.32589i | 0.440888 | + | 0.320324i | ||||
\(391\) | 2.10742 | + | 1.53113i | 0.106577 | + | 0.0774327i | ||||
\(392\) | 2.81175 | − | 8.65368i | 0.142015 | − | 0.437077i | ||||
\(393\) | −1.32260 | − | 4.07054i | −0.0667163 | − | 0.205332i | ||||
\(394\) | −16.1956 | + | 11.7668i | −0.815923 | + | 0.592803i | ||||
\(395\) | 26.2857 | 1.32258 | ||||||||
\(396\) | 8.83085 | + | 11.7964i | 0.443767 | + | 0.592790i | ||||
\(397\) | −9.15050 | −0.459250 | −0.229625 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229625 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(398\) | −13.6435 | + | 9.91258i | −0.683886 | + | 0.496873i | ||||
\(399\) | 7.03226 | + | 21.6431i | 0.352054 | + | 1.08351i | ||||
\(400\) | 27.4855 | − | 84.5917i | 1.37427 | − | 4.22958i | ||||
\(401\) | 8.53273 | + | 6.19939i | 0.426104 | + | 0.309583i | 0.780089 | − | 0.625668i | \(-0.215174\pi\) |
−0.353985 | + | 0.935251i | \(0.615174\pi\) | |||||||
\(402\) | −27.2462 | − | 19.7956i | −1.35892 | − | 0.987312i | ||||
\(403\) | 1.25466 | − | 3.86145i | 0.0624991 | − | 0.192352i | ||||
\(404\) | −4.23216 | − | 13.0252i | −0.210558 | − | 0.648030i | ||||
\(405\) | −3.43019 | + | 2.49218i | −0.170448 | + | 0.123837i | ||||
\(406\) | −6.91828 | −0.343348 | ||||||||
\(407\) | 0.220899 | + | 15.4567i | 0.0109495 | + | 0.766163i | ||||
\(408\) | −4.80360 | −0.237814 | ||||||||
\(409\) | −18.0486 | + | 13.1131i | −0.892447 | + | 0.648401i | −0.936515 | − | 0.350628i | \(-0.885968\pi\) |
0.0440681 | + | 0.999029i | \(0.485968\pi\) | |||||||
\(410\) | −6.62332 | − | 20.3845i | −0.327102 | − | 1.00672i | ||||
\(411\) | −3.60852 | + | 11.1059i | −0.177995 | + | 0.547813i | ||||
\(412\) | 29.5479 | + | 21.4678i | 1.45572 | + | 1.05764i | ||||
\(413\) | −22.1206 | − | 16.0715i | −1.08848 | − | 0.790828i | ||||
\(414\) | −2.63761 | + | 8.11773i | −0.129632 | + | 0.398965i | ||||
\(415\) | −22.6420 | − | 69.6850i | −1.11145 | − | 3.42070i | ||||
\(416\) | −4.04143 | + | 2.93627i | −0.198147 | + | 0.143962i | ||||
\(417\) | −22.8911 | −1.12098 | ||||||||
\(418\) | 62.9002 | + | 19.4483i | 3.07655 | + | 0.951246i | ||||
\(419\) | −14.9132 | −0.728556 | −0.364278 | − | 0.931290i | \(-0.618684\pi\) | ||||
−0.364278 | + | 0.931290i | \(0.618684\pi\) | |||||||
\(420\) | 44.3470 | − | 32.2200i | 2.16391 | − | 1.57217i | ||||
\(421\) | −3.79331 | − | 11.6746i | −0.184875 | − | 0.568986i | 0.815072 | − | 0.579360i | \(-0.196698\pi\) |
−0.999946 | + | 0.0103746i | \(0.996698\pi\) | |||||||
\(422\) | −7.41956 | + | 22.8351i | −0.361179 | + | 1.11159i | ||||
\(423\) | 3.75340 | + | 2.72701i | 0.182497 | + | 0.132592i | ||||
\(424\) | −40.0744 | − | 29.1158i | −1.94619 | − | 1.41399i | ||||
\(425\) | 3.10649 | − | 9.56081i | 0.150687 | − | 0.463767i | ||||
\(426\) | 8.02125 | + | 24.6869i | 0.388631 | + | 1.19608i | ||||
\(427\) | 13.1693 | − | 9.56803i | 0.637305 | − | 0.463029i | ||||
\(428\) | −83.7946 | −4.05036 | ||||||||
\(429\) | 3.16862 | + | 0.979714i | 0.152982 | + | 0.0473010i | ||||
\(430\) | 38.1324 | 1.83891 | ||||||||
\(431\) | 4.68595 | − | 3.40455i | 0.225714 | − | 0.163991i | −0.469181 | − | 0.883102i | \(-0.655451\pi\) |
0.694895 | + | 0.719111i | \(0.255451\pi\) | |||||||
\(432\) | −2.11799 | − | 6.51850i | −0.101902 | − | 0.313622i | ||||
\(433\) | 4.77298 | − | 14.6897i | 0.229375 | − | 0.705943i | −0.768443 | − | 0.639918i | \(-0.778968\pi\) |
0.997818 | − | 0.0660250i | \(-0.0210317\pi\) | |||||||
\(434\) | −24.2615 | − | 17.6270i | −1.16459 | − | 0.846124i | ||||
\(435\) | −3.21292 | − | 2.33432i | −0.154048 | − | 0.111922i | ||||
\(436\) | −14.7084 | + | 45.2679i | −0.704407 | + | 2.16794i | ||||
\(437\) | 8.12656 | + | 25.0110i | 0.388746 | + | 1.19644i | ||||
\(438\) | −4.09564 | + | 2.97566i | −0.195697 | + | 0.142182i | ||||
\(439\) | −25.9386 | −1.23798 | −0.618990 | − | 0.785399i | \(-0.712458\pi\) | ||||
−0.618990 | + | 0.785399i | \(0.712458\pi\) | |||||||
\(440\) | −1.24608 | − | 87.1909i | −0.0594045 | − | 4.15666i | ||||
\(441\) | 1.46736 | 0.0698742 | ||||||||
\(442\) | −1.59077 | + | 1.15577i | −0.0756654 | + | 0.0549742i | ||||
\(443\) | 2.00121 | + | 6.15911i | 0.0950806 | + | 0.292628i | 0.987275 | − | 0.159024i | \(-0.0508348\pi\) |
−0.892194 | + | 0.451652i | \(0.850835\pi\) | |||||||
\(444\) | 6.39913 | − | 19.6945i | 0.303689 | − | 0.934659i | ||||
\(445\) | −5.35778 | − | 3.89266i | −0.253983 | − | 0.184530i | ||||
\(446\) | −27.8225 | − | 20.2142i | −1.31743 | − | 0.957171i | ||||
\(447\) | −2.91039 | + | 8.95726i | −0.137657 | + | 0.423664i | ||||
\(448\) | −0.924291 | − | 2.84467i | −0.0436686 | − | 0.134398i | ||||
\(449\) | −20.3046 | + | 14.7522i | −0.958235 | + | 0.696199i | −0.952740 | − | 0.303786i | \(-0.901749\pi\) |
−0.00549499 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(450\) | 32.9399 | 1.55280 | ||||||||
\(451\) | −3.95841 | − | 5.28770i | −0.186394 | − | 0.248988i | ||||
\(452\) | 19.4072 | 0.912839 | ||||||||
\(453\) | −2.30876 | + | 1.67741i | −0.108475 | + | 0.0788117i | ||||
\(454\) | 20.4405 | + | 62.9093i | 0.959319 | + | 2.95248i | ||||
\(455\) | 3.81256 | − | 11.7339i | 0.178736 | − | 0.550092i | ||||
\(456\) | −39.2333 | − | 28.5047i | −1.83727 | − | 1.33485i | ||||
\(457\) | −4.61687 | − | 3.35435i | −0.215968 | − | 0.156910i | 0.474542 | − | 0.880233i | \(-0.342614\pi\) |
−0.690510 | + | 0.723323i | \(0.742614\pi\) | |||||||
\(458\) | −21.5531 | + | 66.3336i | −1.00711 | + | 3.09957i | ||||
\(459\) | −0.239382 | − | 0.736741i | −0.0111734 | − | 0.0343881i | ||||
\(460\) | 51.2479 | − | 37.2338i | 2.38945 | − | 1.73603i | ||||
\(461\) | −10.0596 | −0.468520 | −0.234260 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234260 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(462\) | 14.1143 | − | 20.0222i | 0.656657 | − | 0.931518i | ||||
\(463\) | 19.6675 | 0.914024 | 0.457012 | − | 0.889461i | \(-0.348920\pi\) | ||||
0.457012 | + | 0.889461i | \(0.348920\pi\) | |||||||
\(464\) | 5.19374 | − | 3.77348i | 0.241113 | − | 0.175179i | ||||
\(465\) | −5.31970 | − | 16.3723i | −0.246695 | − | 0.759249i | ||||
\(466\) | −4.06901 | + | 12.5231i | −0.188493 | + | 0.580123i | ||||
\(467\) | −18.8337 | − | 13.6835i | −0.871522 | − | 0.633198i | 0.0594731 | − | 0.998230i | \(-0.481058\pi\) |
−0.930995 | + | 0.365032i | \(0.881058\pi\) | |||||||
\(468\) | −3.59443 | − | 2.61150i | −0.166153 | − | 0.120717i | ||||
\(469\) | −11.9306 | + | 36.7186i | −0.550904 | + | 1.69551i | ||||
\(470\) | −15.4295 | − | 47.4872i | −0.711712 | − | 2.19042i | ||||
\(471\) | 3.16097 | − | 2.29658i | 0.145650 | − | 0.105821i | ||||
\(472\) | 58.2671 | 2.68196 | ||||||||
\(473\) | 11.1232 | − | 3.79070i | 0.511444 | − | 0.174297i | ||||
\(474\) | −15.7362 | −0.722789 | ||||||||
\(475\) | 82.1063 | − | 59.6537i | 3.76729 | − | 2.73710i | ||||
\(476\) | 3.09483 | + | 9.52491i | 0.141851 | + | 0.436574i | ||||
\(477\) | 2.46850 | − | 7.59727i | 0.113025 | − | 0.347855i | ||||
\(478\) | 4.28330 | + | 3.11200i | 0.195914 | + | 0.142340i | ||||
\(479\) | −1.58621 | − | 1.15245i | −0.0724759 | − | 0.0526568i | 0.550957 | − | 0.834533i | \(-0.314263\pi\) |
−0.623433 | + | 0.781877i | \(0.714263\pi\) | |||||||
\(480\) | −6.54516 | + | 20.1439i | −0.298744 | + | 0.919440i | ||||
\(481\) | −1.44029 | − | 4.43274i | −0.0656714 | − | 0.202116i | ||||
\(482\) | 15.8724 | − | 11.5319i | 0.722966 | − | 0.525266i | ||||
\(483\) | 9.78497 | 0.445232 | ||||||||
\(484\) | −16.4245 | − | 46.0300i | −0.746570 | − | 2.09227i | ||||
\(485\) | 38.4106 | 1.74414 | ||||||||
\(486\) | 2.05353 | − | 1.49197i | 0.0931498 | − | 0.0676773i | ||||
\(487\) | 0.511393 | + | 1.57391i | 0.0231734 | + | 0.0713205i | 0.961974 | − | 0.273139i | \(-0.0880620\pi\) |
−0.938801 | + | 0.344460i | \(0.888062\pi\) | |||||||
\(488\) | −10.7194 | + | 32.9909i | −0.485245 | + | 1.49343i | ||||
\(489\) | −3.63845 | − | 2.64349i | −0.164536 | − | 0.119543i | ||||
\(490\) | −12.7761 | − | 9.28235i | −0.577163 | − | 0.419334i | ||||
\(491\) | −6.40416 | + | 19.7100i | −0.289016 | + | 0.889499i | 0.696150 | + | 0.717896i | \(0.254895\pi\) |
−0.985166 | + | 0.171603i | \(0.945105\pi\) | |||||||
\(492\) | 2.73429 | + | 8.41528i | 0.123271 | + | 0.379390i | ||||
\(493\) | 0.587013 | − | 0.426490i | 0.0264377 | − | 0.0192081i | ||||
\(494\) | −19.8510 | −0.893137 | ||||||||
\(495\) | 13.3106 | − | 4.53617i | 0.598267 | − | 0.203886i | ||||
\(496\) | 27.8282 | 1.24952 | ||||||||
\(497\) | 24.0740 | − | 17.4908i | 1.07987 | − | 0.784569i | ||||
\(498\) | 13.5549 | + | 41.7178i | 0.607411 | + | 1.86942i | ||||
\(499\) | −4.11783 | + | 12.6734i | −0.184339 | + | 0.567338i | −0.999936 | − | 0.0112821i | \(-0.996409\pi\) |
0.815597 | + | 0.578620i | \(0.196409\pi\) | |||||||
\(500\) | −121.574 | − | 88.3283i | −5.43693 | − | 3.95016i | ||||
\(501\) | 11.4583 | + | 8.32495i | 0.511919 | + | 0.371931i | ||||
\(502\) | 16.0132 | − | 49.2834i | 0.714702 | − | 2.19963i | ||||
\(503\) | −3.09643 | − | 9.52983i | −0.138063 | − | 0.424914i | 0.857991 | − | 0.513665i | \(-0.171713\pi\) |
−0.996054 | + | 0.0887508i | \(0.971713\pi\) | |||||||
\(504\) | −14.5979 | + | 10.6060i | −0.650242 | + | 0.472428i | ||||
\(505\) | −13.0698 | −0.581597 | ||||||||
\(506\) | 16.3106 | − | 23.1379i | 0.725097 | − | 1.02861i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0.519672 | − | 0.377564i | 0.0230567 | − | 0.0167517i | ||||
\(509\) | −9.48804 | − | 29.2012i | −0.420550 | − | 1.29432i | −0.907192 | − | 0.420718i | \(-0.861778\pi\) |
0.486642 | − | 0.873602i | \(-0.338222\pi\) | |||||||
\(510\) | −2.57629 | + | 7.92899i | −0.114080 | + | 0.351102i | ||||
\(511\) | 4.69519 | + | 3.41126i | 0.207703 | + | 0.150905i | ||||
\(512\) | 41.0684 | + | 29.8380i | 1.81499 | + | 1.31866i | ||||
\(513\) | 2.41669 | − | 7.43781i | 0.106700 | − | 0.328387i | ||||
\(514\) | 7.78665 | + | 23.9648i | 0.343454 | + | 1.05704i | ||||
\(515\) | 28.1978 | − | 20.4869i | 1.24254 | − | 0.902759i | ||||
\(516\) | −15.7421 | −0.693009 | ||||||||
\(517\) | −9.22142 | − | 12.3181i | −0.405558 | − | 0.541750i | ||||
\(518\) | −34.4257 | −1.51258 | ||||||||
\(519\) | −15.0946 | + | 10.9669i | −0.662581 | + | 0.481393i | ||||
\(520\) | 8.12459 | + | 25.0049i | 0.356287 | + | 1.09654i | ||||
\(521\) | −4.81093 | + | 14.8065i | −0.210771 | + | 0.648686i | 0.788656 | + | 0.614835i | \(0.210777\pi\) |
−0.999427 | + | 0.0338512i | \(0.989223\pi\) | |||||||
\(522\) | 1.92345 | + | 1.39747i | 0.0841873 | + | 0.0611656i | ||||
\(523\) | −5.04532 | − | 3.66564i | −0.220616 | − | 0.160287i | 0.471988 | − | 0.881605i | \(-0.343537\pi\) |
−0.692604 | + | 0.721318i | \(0.743537\pi\) | |||||||
\(524\) | 5.87625 | − | 18.0853i | 0.256705 | − | 0.790058i | ||||
\(525\) | −11.6691 | − | 35.9137i | −0.509280 | − | 1.56740i | ||||
\(526\) | 22.7320 | − | 16.5157i | 0.991160 | − | 0.720120i | ||||
\(527\) | 3.14523 | 0.137008 | ||||||||
\(528\) | 0.324839 | + | 22.7297i | 0.0141368 | + | 0.989183i | ||||
\(529\) | −11.6924 | −0.508364 | ||||||||
\(530\) | −69.5524 | + | 50.5328i | −3.02116 | + | 2.19500i | ||||
\(531\) | 2.90367 | + | 8.93657i | 0.126008 | + | 0.387814i | ||||
\(532\) | −31.2440 | + | 96.1593i | −1.35460 | + | 4.16903i | ||||
\(533\) | 1.61119 | + | 1.17060i | 0.0697885 | + | 0.0507043i | ||||
\(534\) | 3.20750 | + | 2.33039i | 0.138802 | + | 0.100846i | ||||
\(535\) | −24.7108 | + | 76.0520i | −1.06834 | + | 3.28802i | ||||
\(536\) | −25.4242 | − | 78.2476i | −1.09816 | − | 3.37978i | ||||
\(537\) | 11.9977 | − | 8.71681i | 0.517737 | − | 0.376158i | ||||
\(538\) | −3.96423 | −0.170910 | ||||||||
\(539\) | −4.64950 | − | 1.43759i | −0.200268 | − | 0.0619214i | ||||
\(540\) | −18.8379 | −0.810655 | ||||||||
\(541\) | 11.0803 | − | 8.05029i | 0.476378 | − | 0.346109i | −0.323544 | − | 0.946213i | \(-0.604874\pi\) |
0.799922 | + | 0.600104i | \(0.204874\pi\) | |||||||
\(542\) | −1.57983 | − | 4.86222i | −0.0678595 | − | 0.208850i | ||||
\(543\) | −3.94542 | + | 12.1428i | −0.169314 | + | 0.521096i | ||||
\(544\) | −3.13071 | − | 2.27460i | −0.134228 | − | 0.0975225i | ||||
\(545\) | 36.7477 | + | 26.6988i | 1.57410 | + | 1.14365i | ||||
\(546\) | −2.28244 | + | 7.02462i | −0.0976793 | + | 0.300626i | ||||
\(547\) | −10.8993 | − | 33.5447i | −0.466022 | − | 1.43427i | −0.857692 | − | 0.514164i | \(-0.828102\pi\) |
0.391670 | − | 0.920106i | \(-0.371898\pi\) | |||||||
\(548\) | −41.9737 | + | 30.4957i | −1.79303 | + | 1.30271i | ||||
\(549\) | −5.59409 | −0.238750 | ||||||||
\(550\) | −104.374 | − | 32.2717i | −4.45053 | − | 1.37607i | ||||
\(551\) | 7.32521 | 0.312065 | ||||||||
\(552\) | −16.8695 | + | 12.2564i | −0.718013 | + | 0.521667i | ||||
\(553\) | 5.57461 | + | 17.1569i | 0.237057 | + | 0.729585i | ||||
\(554\) | −7.49751 | + | 23.0750i | −0.318539 | + | 0.980361i | ||||
\(555\) | −15.9876 | − | 11.6157i | −0.678638 | − | 0.493059i | ||||
\(556\) | −82.2804 | − | 59.7802i | −3.48947 | − | 2.53525i | ||||
\(557\) | 0.118885 | − | 0.365889i | 0.00503730 | − | 0.0155032i | −0.948506 | − | 0.316758i | \(-0.897406\pi\) |
0.953544 | + | 0.301255i | \(0.0974056\pi\) | |||||||
\(558\) | 3.18470 | + | 9.80150i | 0.134819 | + | 0.414931i | ||||
\(559\) | −2.86648 | + | 2.08262i | −0.121239 | + | 0.0880854i | ||||
\(560\) | 84.5621 | 3.57340 | ||||||||
\(561\) | 0.0367143 | + | 2.56898i | 0.00155008 | + | 0.108462i | ||||
\(562\) | 9.99923 | 0.421792 | ||||||||
\(563\) | 7.47112 | − | 5.42809i | 0.314870 | − | 0.228767i | −0.419113 | − | 0.907934i | \(-0.637659\pi\) |
0.733983 | + | 0.679167i | \(0.237659\pi\) | |||||||
\(564\) | 6.36974 | + | 19.6041i | 0.268215 | + | 0.825480i | ||||
\(565\) | 5.72314 | − | 17.6140i | 0.240774 | − | 0.741027i | ||||
\(566\) | 17.6550 | + | 12.8271i | 0.742095 | + | 0.539164i | ||||
\(567\) | −2.35414 | − | 1.71038i | −0.0988644 | − | 0.0718292i | ||||
\(568\) | −19.5956 | + | 60.3089i | −0.822212 | + | 2.53051i | ||||
\(569\) | −2.91295 | − | 8.96514i | −0.122117 | − | 0.375838i | 0.871248 | − | 0.490844i | \(-0.163311\pi\) |
−0.993365 | + | 0.115005i | \(0.963311\pi\) | |||||||
\(570\) | −68.0926 | + | 49.4721i | −2.85208 | + | 2.07216i | ||||
\(571\) | 9.23726 | 0.386567 | 0.193284 | − | 0.981143i | \(-0.438086\pi\) | ||||
0.193284 | + | 0.981143i | \(0.438086\pi\) | |||||||
\(572\) | 8.83085 | + | 11.7964i | 0.369237 | + | 0.493232i | ||||
\(573\) | 3.33725 | 0.139416 | ||||||||
\(574\) | 11.9005 | − | 8.64620i | 0.496716 | − | 0.360885i | ||||
\(575\) | −13.4849 | − | 41.5023i | −0.562359 | − | 1.73076i | ||||
\(576\) | −0.317640 | + | 0.977594i | −0.0132350 | + | 0.0407331i | ||||
\(577\) | −6.16974 | − | 4.48258i | −0.256850 | − | 0.186612i | 0.451907 | − | 0.892065i | \(-0.350744\pi\) |
−0.708757 | + | 0.705453i | \(0.750744\pi\) | |||||||
\(578\) | 33.6776 | + | 24.4682i | 1.40081 | + | 1.01774i | ||||
\(579\) | −5.81586 | + | 17.8994i | −0.241699 | + | 0.743873i | ||||
\(580\) | −5.45251 | − | 16.7811i | −0.226403 | − | 0.696797i | ||||
\(581\) | 40.6822 | − | 29.5573i | 1.68778 | − | 1.22624i | ||||
\(582\) | −22.9950 | −0.953173 | ||||||||
\(583\) | −15.2649 | + | 21.6544i | −0.632208 | + | 0.896835i | ||||
\(584\) | −12.3675 | −0.511769 | ||||||||
\(585\) | −3.43019 | + | 2.49218i | −0.141821 | + | 0.103039i | ||||
\(586\) | −21.0079 | − | 64.6557i | −0.867828 | − | 2.67090i | ||||
\(587\) | −7.96326 | + | 24.5084i | −0.328679 | + | 1.01157i | 0.641074 | + | 0.767479i | \(0.278489\pi\) |
−0.969753 | + | 0.244090i | \(0.921511\pi\) | |||||||
\(588\) | 5.27431 | + | 3.83201i | 0.217509 | + | 0.158030i | ||||
\(589\) | 25.6886 | + | 18.6639i | 1.05848 | + | 0.769031i | ||||
\(590\) | 31.2500 | − | 96.1777i | 1.28654 | − | 3.95957i | ||||
\(591\) | −2.43714 | − | 7.50073i | −0.100250 | − | 0.308539i | ||||
\(592\) | 25.8443 | − | 18.7770i | 1.06220 | − | 0.771730i | ||||
\(593\) | 23.7206 | 0.974088 | 0.487044 | − | 0.873377i | \(-0.338075\pi\) | ||||
0.487044 | + | 0.873377i | \(0.338075\pi\) | |||||||
\(594\) | −7.96856 | + | 2.71563i | −0.326954 | + | 0.111424i | ||||
\(595\) | 9.55747 | 0.391818 | ||||||||
\(596\) | −33.8531 | + | 24.5957i | −1.38668 | + | 1.00748i | ||||
\(597\) | −2.05309 | − | 6.31876i | −0.0840273 | − | 0.258609i | ||||
\(598\) | −2.63761 | + | 8.11773i | −0.107860 | + | 0.331959i | ||||
\(599\) | 5.28929 | + | 3.84289i | 0.216114 | + | 0.157016i | 0.690576 | − | 0.723260i | \(-0.257357\pi\) |
−0.474461 | + | 0.880276i | \(0.657357\pi\) | |||||||
\(600\) | 65.1023 | + | 47.2996i | 2.65779 | + | 1.93100i | ||||
\(601\) | −1.92550 | + | 5.92609i | −0.0785430 | + | 0.241730i | −0.982617 | − | 0.185646i | \(-0.940562\pi\) |
0.904074 | + | 0.427377i | \(0.140562\pi\) | |||||||
\(602\) | 8.08705 | + | 24.8894i | 0.329604 | + | 1.01442i | ||||
\(603\) | 10.7341 | − | 7.79875i | 0.437125 | − | 0.317590i | ||||
\(604\) | −12.6792 | −0.515911 | ||||||||
\(605\) | −46.6204 | + | 1.33281i | −1.89539 | + | 0.0541866i | ||||
\(606\) | 7.82438 | 0.317844 | ||||||||
\(607\) | −23.4618 | + | 17.0460i | −0.952287 | + | 0.691877i | −0.951347 | − | 0.308122i | \(-0.900299\pi\) |
−0.000940390 | 1.00000i | \(0.500299\pi\) | ||||||||
\(608\) | −12.0725 | − | 37.1554i | −0.489606 | − | 1.50685i | ||||
\(609\) | 0.842244 | − | 2.59216i | 0.0341294 | − | 0.105040i | ||||
\(610\) | 48.7069 | + | 35.3876i | 1.97209 | + | 1.43280i | ||||
\(611\) | 3.75340 | + | 2.72701i | 0.151846 | + | 0.110323i | ||||
\(612\) | 1.06356 | − | 3.27331i | 0.0429920 | − | 0.132316i | ||||
\(613\) | −3.60379 | − | 11.0913i | −0.145556 | − | 0.447975i | 0.851526 | − | 0.524312i | \(-0.175677\pi\) |
−0.997082 | + | 0.0763372i | \(0.975677\pi\) | |||||||
\(614\) | −34.9265 | + | 25.3756i | −1.40952 | + | 1.02407i | ||||
\(615\) | 8.44405 | 0.340497 | ||||||||
\(616\) | 56.6460 | − | 19.3046i | 2.28233 | − | 0.777805i | ||||
\(617\) | 35.3625 | 1.42364 | 0.711820 | − | 0.702362i | \(-0.247871\pi\) | ||||
0.711820 | + | 0.702362i | \(0.247871\pi\) | |||||||
\(618\) | −16.8809 | + | 12.2647i | −0.679051 | + | 0.493359i | ||||
\(619\) | 7.03025 | + | 21.6369i | 0.282570 | + | 0.869660i | 0.987117 | + | 0.160003i | \(0.0511503\pi\) |
−0.704547 | + | 0.709657i | \(0.748850\pi\) | |||||||
\(620\) | 23.6352 | − | 72.7416i | 0.949212 | − | 2.92137i | ||||
\(621\) | −2.72047 | − | 1.97653i | −0.109169 | − | 0.0793156i | ||||
\(622\) | 50.4335 | + | 36.6421i | 2.02220 | + | 1.46921i | ||||
\(623\) | 1.40450 | − | 4.32262i | 0.0562703 | − | 0.173182i | ||||
\(624\) | −2.11799 | − | 6.51850i | −0.0847874 | − | 0.260949i | ||||
\(625\) | −63.5248 | + | 46.1535i | −2.54099 | + | 1.84614i | ||||
\(626\) | 59.5444 | 2.37987 | ||||||||
\(627\) | −14.9445 | + | 21.1999i | −0.596826 | + | 0.846644i | ||||
\(628\) | 17.3594 | 0.692716 | ||||||||
\(629\) | 2.92100 | − | 2.12223i | 0.116468 | − | 0.0846190i | ||||
\(630\) | 9.67742 | + | 29.7840i | 0.385558 | + | 1.18662i | ||||
\(631\) | −10.3091 | + | 31.7283i | −0.410400 | + | 1.26308i | 0.505901 | + | 0.862592i | \(0.331160\pi\) |
−0.916301 | + | 0.400491i | \(0.868840\pi\) | |||||||
\(632\) | −31.1010 | − | 22.5962i | −1.23713 | − | 0.898829i | ||||
\(633\) | −7.65263 | − | 5.55996i | −0.304165 | − | 0.220989i | ||||
\(634\) | 23.6084 | − | 72.6591i | 0.937608 | − | 2.88566i | ||||
\(635\) | −0.189427 | − | 0.582997i | −0.00751719 | − | 0.0231355i | ||||
\(636\) | 28.7132 | − | 20.8613i | 1.13855 | − | 0.827206i | ||||
\(637\) | 1.46736 | 0.0581388 | ||||||||
\(638\) | −4.72557 | − | 6.31249i | −0.187087 | − | 0.249914i | ||||
\(639\) | −10.2263 | −0.404545 | ||||||||
\(640\) | 43.2207 | − | 31.4017i | 1.70845 | − | 1.24126i | ||||
\(641\) | 14.3083 | + | 44.0364i | 0.565144 | + | 1.73933i | 0.667523 | + | 0.744589i | \(0.267355\pi\) |
−0.102379 | + | 0.994745i | \(0.532645\pi\) | |||||||
\(642\) | 14.7934 | − | 45.5295i | 0.583850 | − | 1.79691i | ||||
\(643\) | −32.1592 | − | 23.3650i | −1.26824 | − | 0.921427i | −0.269105 | − | 0.963111i | \(-0.586728\pi\) |
−0.999131 | + | 0.0416837i | \(0.986728\pi\) | |||||||
\(644\) | 35.1714 | + | 25.5535i | 1.38595 | + | 1.00695i | ||||
\(645\) | −4.64231 | + | 14.2876i | −0.182791 | + | 0.562572i | ||||
\(646\) | −4.75195 | − | 14.6250i | −0.186963 | − | 0.575413i | ||||
\(647\) | 13.5189 | − | 9.82207i | 0.531484 | − | 0.386146i | −0.289429 | − | 0.957200i | \(-0.593465\pi\) |
0.820913 | + | 0.571054i | \(0.193465\pi\) | |||||||
\(648\) | 6.20095 | 0.243597 | ||||||||
\(649\) | −0.445340 | − | 31.1614i | −0.0174811 | − | 1.22319i | ||||
\(650\) | 32.9399 | 1.29201 | ||||||||
\(651\) | 9.55818 | − | 6.94443i | 0.374615 | − | 0.272174i | ||||
\(652\) | −6.17466 | − | 19.0037i | −0.241818 | − | 0.744241i | ||||
\(653\) | 9.29381 | − | 28.6034i | 0.363695 | − | 1.11934i | −0.587099 | − | 0.809515i | \(-0.699730\pi\) |
0.950794 | − | 0.309823i | \(-0.100270\pi\) | |||||||
\(654\) | −21.9995 | − | 15.9836i | −0.860248 | − | 0.625007i | ||||
\(655\) | −14.6813 | − | 10.6666i | −0.573646 | − | 0.416778i | ||||
\(656\) | −4.21807 | + | 12.9819i | −0.164688 | + | 0.506858i | ||||
\(657\) | −0.616317 | − | 1.89683i | −0.0240448 | − | 0.0740023i | ||||
\(658\) | 27.7231 | − | 20.1420i | 1.08076 | − | 0.785217i | ||||
\(659\) | −8.53745 | −0.332572 | −0.166286 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166286 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(660\) | 59.6902 | + | 18.4558i | 2.32344 | + | 0.718390i | ||||
\(661\) | −7.46076 | −0.290190 | −0.145095 | − | 0.989418i | \(-0.546349\pi\) | ||||
−0.145095 | + | 0.989418i | \(0.546349\pi\) | |||||||
\(662\) | −23.0107 | + | 16.7182i | −0.894335 | + | 0.649772i | ||||
\(663\) | −0.239382 | − | 0.736741i | −0.00929681 | − | 0.0286126i | ||||
\(664\) | −33.1141 | + | 101.915i | −1.28508 | + | 3.95506i | ||||
\(665\) | 78.0604 | + | 56.7142i | 3.02705 | + | 2.19928i | ||||
\(666\) | 9.57120 | + | 6.95388i | 0.370876 | + | 0.269458i | ||||
\(667\) | 0.973306 | − | 2.99553i | 0.0376866 | − | 0.115987i | ||||
\(668\) | 19.4454 | + | 59.8468i | 0.752366 | + | 2.31554i | ||||
\(669\) | 10.9611 | − | 7.96369i | 0.423780 | − | 0.307894i | ||||
\(670\) | −142.794 | −5.51661 | ||||||||
\(671\) | 17.7256 | + | 5.48061i | 0.684288 | + | 0.211577i | ||||
\(672\) | −14.5362 | −0.560746 | ||||||||
\(673\) | 18.8649 | − | 13.7062i | 0.727190 | − | 0.528334i | −0.161483 | − | 0.986875i | \(-0.551628\pi\) |
0.888673 | + | 0.458541i | \(0.151628\pi\) | |||||||
\(674\) | 19.6273 | + | 60.4065i | 0.756014 | + | 2.32677i | ||||
\(675\) | −4.01016 | + | 12.3420i | −0.154351 | + | 0.475044i | ||||
\(676\) | −3.59443 | − | 2.61150i | −0.138247 | − | 0.100442i | ||||
\(677\) | 22.9295 | + | 16.6592i | 0.881251 | + | 0.640266i | 0.933582 | − | 0.358364i | \(-0.116665\pi\) |
−0.0523313 | + | 0.998630i | \(0.516665\pi\) | |||||||
\(678\) | −3.42623 | + | 10.5448i | −0.131584 | + | 0.404972i | ||||
\(679\) | 8.14604 | + | 25.0709i | 0.312617 | + | 0.962135i | ||||
\(680\) | −16.4773 | + | 11.9714i | −0.631874 | + | 0.459084i | ||||
\(681\) | −26.0595 | −0.998602 | ||||||||
\(682\) | −0.488442 | − | 34.1774i | −0.0187034 | − | 1.30872i | ||||
\(683\) | 7.36889 | 0.281963 | 0.140981 | − | 0.990012i | \(-0.454974\pi\) | ||||
0.140981 | + | 0.990012i | \(0.454974\pi\) | |||||||
\(684\) | 28.1105 | − | 20.4235i | 1.07483 | − | 0.780911i | ||||
\(685\) | 15.3000 | + | 47.0884i | 0.584581 | + | 1.79916i | ||||
\(686\) | −12.6279 | + | 38.8647i | −0.482136 | + | 1.48386i | ||||
\(687\) | −22.2301 | − | 16.1511i | −0.848133 | − | 0.616205i | ||||
\(688\) | −19.6467 | − | 14.2742i | −0.749025 | − | 0.544198i | ||||
\(689\) | 2.46850 | − | 7.59727i | 0.0940425 | − | 0.289433i | ||||
\(690\) | 11.1833 | + | 34.4188i | 0.425742 | + | 1.31030i | ||||
\(691\) | 11.2321 | − | 8.16063i | 0.427291 | − | 0.310445i | −0.353274 | − | 0.935520i | \(-0.614932\pi\) |
0.780565 | + | 0.625075i | \(0.214932\pi\) | |||||||
\(692\) | −82.8967 | −3.15126 | ||||||||
\(693\) | 5.78368 | + | 7.72593i | 0.219704 | + | 0.293484i | ||||
\(694\) | −59.3679 | −2.25357 | ||||||||
\(695\) | −78.5209 | + | 57.0487i | −2.97847 | + | 2.16398i | ||||
\(696\) | 1.79483 | + | 5.52391i | 0.0680327 | + | 0.209383i | ||||
\(697\) | −0.476739 | + | 1.46725i | −0.0180578 | + | 0.0555762i | ||||
\(698\) | −22.1507 | − | 16.0935i | −0.838418 | − | 0.609146i | ||||
\(699\) | −4.19683 | − | 3.04918i | −0.158739 | − | 0.115330i | ||||
\(700\) | 51.8452 | − | 159.563i | 1.95956 | − | 6.03092i | ||||
\(701\) | −5.29491 | − | 16.2961i | −0.199986 | − | 0.615494i | −0.999882 | − | 0.0153553i | \(-0.995112\pi\) |
0.799896 | − | 0.600139i | \(-0.204888\pi\) | |||||||
\(702\) | 2.05353 | − | 1.49197i | 0.0775054 | − | 0.0563109i | ||||
\(703\) | 36.4506 | 1.37476 | ||||||||
\(704\) | 1.96424 | − | 2.78643i | 0.0740302 | − | 0.105018i | ||||
\(705\) | 19.6711 | 0.740855 | ||||||||
\(706\) | −2.27487 | + | 1.65279i | −0.0856157 | + | 0.0622035i | ||||
\(707\) | −2.77181 | − | 8.53076i | −0.104245 | − | 0.320832i | ||||
\(708\) | −12.9009 | + | 39.7048i | −0.484845 | + | 1.49220i | ||||
\(709\) | −8.06019 | − | 5.85607i | −0.302707 | − | 0.219929i | 0.426054 | − | 0.904698i | \(-0.359903\pi\) |
−0.728761 | + | 0.684768i | \(0.759903\pi\) | |||||||
\(710\) | 89.0385 | + | 64.6902i | 3.34155 | + | 2.42778i | ||||
\(711\) | 1.91576 | − | 5.89610i | 0.0718465 | − | 0.221121i | ||||
\(712\) | 2.99301 | + | 9.21153i | 0.112168 | + | 0.345217i | ||||
\(713\) | 11.0455 | − | 8.02506i | 0.413659 | − | 0.300541i | ||||
\(714\) | −5.72170 | −0.214129 | ||||||||
\(715\) | 13.3106 | − | 4.53617i | 0.497788 | − | 0.169643i | ||||
\(716\) | 65.8887 | 2.46238 | ||||||||
\(717\) | −1.68747 | + | 1.22602i | −0.0630197 | + | 0.0457865i | ||||
\(718\) | 4.33281 | + | 13.3350i | 0.161699 | + | 0.497659i | ||||
\(719\) | −8.97751 | + | 27.6299i | −0.334805 | + | 1.03042i | 0.632013 | + | 0.774957i | \(0.282229\pi\) |
−0.966818 | + | 0.255466i | \(0.917771\pi\) | |||||||
\(720\) | −23.5104 | − | 17.0813i | −0.876180 | − | 0.636582i | ||||
\(721\) | 19.3521 | + | 14.0601i | 0.720710 | + | 0.523626i | ||||
\(722\) | 33.0705 | − | 101.780i | 1.23076 | − | 3.78788i | ||||
\(723\) | 2.38849 | + | 7.35102i | 0.0888290 | + | 0.273387i | ||||
\(724\) | −45.8924 | + | 33.3428i | −1.70558 | + | 1.23918i | ||||
\(725\) | −12.1552 | −0.451432 | ||||||||
\(726\) | 27.9099 | − | 0.797906i | 1.03583 | − | 0.0296131i | ||||
\(727\) | −8.86626 | −0.328831 | −0.164416 | − | 0.986391i | \(-0.552574\pi\) | ||||
−0.164416 | + | 0.986391i | \(0.552574\pi\) | |||||||
\(728\) | −14.5979 | + | 10.6060i | −0.541034 | + | 0.393084i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −6.63296 | + | 20.4142i | −0.245497 | + | 0.755562i | ||||
\(731\) | −2.22053 | − | 1.61331i | −0.0821294 | − | 0.0596705i | ||||
\(732\) | −20.1076 | − | 14.6090i | −0.743197 | − | 0.539964i | ||||
\(733\) | 7.21724 | − | 22.2124i | 0.266575 | − | 0.820433i | −0.724752 | − | 0.689010i | \(-0.758045\pi\) |
0.991326 | − | 0.131423i | \(-0.0419545\pi\) | |||||||
\(734\) | −14.9119 | − | 45.8940i | −0.550407 | − | 1.69398i | ||||
\(735\) | 5.03332 | − | 3.65692i | 0.185657 | − | 0.134887i | ||||
\(736\) | −16.7982 | −0.619190 | ||||||||
\(737\) | −41.6527 | + | 14.1950i | −1.53430 | + | 0.522879i | ||||
\(738\) | −5.05513 | −0.186082 | ||||||||
\(739\) | −6.32918 | + | 4.59842i | −0.232823 | + | 0.169156i | −0.698080 | − | 0.716020i | \(-0.745962\pi\) |
0.465257 | + | 0.885176i | \(0.345962\pi\) | |||||||
\(740\) | −27.1320 | − | 83.5036i | −0.997391 | − | 3.06965i | ||||
\(741\) | 2.41669 | − | 7.43781i | 0.0887794 | − | 0.273235i | ||||
\(742\) | −47.7337 | − | 34.6806i | −1.75236 | − | 1.27316i | ||||
\(743\) | −28.7485 | − | 20.8870i | −1.05468 | − | 0.766269i | −0.0815823 | − | 0.996667i | \(-0.525997\pi\) |
−0.973097 | + | 0.230398i | \(0.925997\pi\) | |||||||
\(744\) | −7.78009 | + | 23.9447i | −0.285232 | + | 0.877854i | ||||
\(745\) | 12.3399 | + | 37.9783i | 0.452099 | + | 1.39142i | ||||
\(746\) | −17.8924 | + | 12.9996i | −0.655087 | + | 0.475949i | ||||
\(747\) | −17.2811 | −0.632284 | ||||||||
\(748\) | −6.57693 | + | 9.32989i | −0.240476 | + | 0.341134i | ||||
\(749\) | −54.8805 | −2.00529 | ||||||||
\(750\) | 69.4560 | − | 50.4627i | 2.53617 | − | 1.84264i | ||||
\(751\) | 10.7353 | + | 33.0399i | 0.391738 | + | 1.20564i | 0.931473 | + | 0.363810i | \(0.118524\pi\) |
−0.539735 | + | 0.841835i | \(0.681476\pi\) | |||||||
\(752\) | −9.82633 | + | 30.2423i | −0.358329 | + | 1.10282i | ||||
\(753\) | 16.5162 | + | 11.9997i | 0.601883 | + | 0.437294i | ||||
\(754\) | 1.92345 | + | 1.39747i | 0.0700481 | + | 0.0508929i | ||||
\(755\) | −3.73907 | + | 11.5077i | −0.136079 | + | 0.418807i | ||||
\(756\) | −3.99511 | − | 12.2957i | −0.145301 | − | 0.447189i | ||||
\(757\) | 26.0420 | − | 18.9206i | 0.946514 | − | 0.687683i | −0.00346582 | − | 0.999994i | \(-0.501103\pi\) |
0.949980 | + | 0.312311i | \(0.101103\pi\) | |||||||
\(758\) | 83.1239 | 3.01920 | ||||||||
\(759\) | 6.68369 | + | 8.92817i | 0.242603 | + | 0.324072i | ||||
\(760\) | −205.617 | −7.45849 | ||||||||
\(761\) | −19.4476 | + | 14.1295i | −0.704974 | + | 0.512194i | −0.881548 | − | 0.472094i | \(-0.843498\pi\) |
0.176574 | + | 0.984287i | \(0.443498\pi\) | |||||||
\(762\) | 0.113403 | + | 0.349018i | 0.00410815 | + | 0.0126436i | ||||
\(763\) | −9.63315 | + | 29.6478i | −0.348744 | + | 1.07332i | ||||
\(764\) | 11.9955 | + | 8.71525i | 0.433982 | + | 0.315307i | ||||
\(765\) | −2.65722 | − | 1.93058i | −0.0960718 | − | 0.0698003i | ||||
\(766\) | 8.85732 | − | 27.2600i | 0.320028 | − | 0.984944i | ||||
\(767\) | 2.90367 | + | 8.93657i | 0.104845 | + | 0.322681i | ||||
\(768\) | −24.2114 | + | 17.5906i | −0.873654 | + | 0.634747i | ||||
\(769\) | 17.7925 | 0.641613 | 0.320807 | − | 0.947145i | \(-0.396046\pi\) | ||||
0.320807 | + | 0.947145i | \(0.396046\pi\) | |||||||
\(770\) | −1.48424 | − | 103.855i | −0.0534883 | − | 3.74269i | ||||
\(771\) | −9.92718 | −0.357519 | ||||||||
\(772\) | −67.6491 | + | 49.1499i | −2.43474 | + | 1.76894i | ||||
\(773\) | −4.33107 | − | 13.3297i | −0.155778 | − | 0.479435i | 0.842461 | − | 0.538757i | \(-0.181106\pi\) |
−0.998239 | + | 0.0593223i | \(0.981106\pi\) | |||||||
\(774\) | 2.77918 | − | 8.55343i | 0.0998955 | − | 0.307447i | ||||
\(775\) | −42.6267 | − | 30.9701i | −1.53119 | − | 1.11248i | ||||
\(776\) | −45.4472 | − | 33.0193i | −1.63146 | − | 1.18532i | ||||
\(777\) | 4.19105 | − | 12.8987i | 0.150353 | − | 0.462739i | ||||
\(778\) | 6.57015 | + | 20.2209i | 0.235551 | + | 0.724953i | ||||
\(779\) | −12.6005 | + | 9.15477i | −0.451458 | + | 0.328004i | ||||
\(780\) | −18.8379 | −0.674505 | ||||||||
\(781\) | 32.4031 | + | 10.0188i | 1.15948 | + | 0.358501i | ||||
\(782\) | −6.61206 | −0.236447 | ||||||||
\(783\) | −0.757773 | + | 0.550554i | −0.0270806 | + | 0.0196752i | ||||
\(784\) | 3.10785 | + | 9.56497i | 0.110995 | + | 0.341606i | ||||
\(785\) | 5.11925 | − | 15.7554i | 0.182714 | − | 0.562335i | ||||
\(786\) | 8.78914 | + | 6.38568i | 0.313498 | + | 0.227770i | ||||
\(787\) | 28.7442 | + | 20.8839i | 1.02462 | + | 0.744431i | 0.967225 | − | 0.253920i | \(-0.0817201\pi\) |
0.0573965 | + | 0.998351i | \(0.481720\pi\) | |||||||
\(788\) | 10.8281 | − | 33.3254i | 0.385735 | − | 1.18717i | ||||
\(789\) | 3.42073 | + | 10.5279i | 0.121781 | + | 0.374804i | ||||
\(790\) | −53.9783 | + | 39.2175i | −1.92046 | + | 1.39530i | ||||
\(791\) | 12.7106 | 0.451936 | ||||||||
\(792\) | −19.6485 | − | 6.07516i | −0.698178 | − | 0.215872i | ||||
\(793\) | −5.59409 | −0.198652 | ||||||||
\(794\) | 18.7908 | − | 13.6523i | 0.666860 | − | 0.484502i | ||||
\(795\) | −10.4663 | − | 32.2120i | −0.371202 | − | 1.14244i | ||||
\(796\) | 9.12178 | − | 28.0740i | 0.323313 | − | 0.995055i | ||||
\(797\) | −30.5386 | − | 22.1876i | −1.08173 | − | 0.785926i | −0.103750 | − | 0.994603i | \(-0.533084\pi\) |
−0.977984 | + | 0.208678i | \(0.933084\pi\) | |||||||
\(798\) | −46.7319 | − | 33.9527i | −1.65429 | − | 1.20191i | ||||
\(799\) | −1.11060 | + | 3.41808i | −0.0392903 | + | 0.120923i | ||||
\(800\) | 20.0327 | + | 61.6543i | 0.708262 | + | 2.17981i | ||||
\(801\) | −1.26364 | + | 0.918091i | −0.0446486 | + | 0.0324391i | ||||
\(802\) | −26.7715 | −0.945335 | ||||||||
\(803\) | 0.0945254 | + | 6.61415i | 0.00333573 | + | 0.233408i | ||||
\(804\) | 58.9493 | 2.07898 | ||||||||
\(805\) | 33.5643 | − | 24.3859i | 1.18299 | − | 0.859490i | ||||
\(806\) | 3.18470 | + | 9.80150i | 0.112176 | + | 0.345243i | ||||
\(807\) | 0.482613 | − | 1.48533i | 0.0169888 | − | 0.0522861i | ||||
\(808\) | 15.4641 | + | 11.2353i | 0.544024 | + | 0.395256i | ||||
\(809\) | 8.96242 | + | 6.51158i | 0.315102 | + | 0.228935i | 0.734083 | − | 0.679060i | \(-0.237612\pi\) |
−0.418981 | + | 0.907995i | \(0.637612\pi\) | |||||||
\(810\) | 3.32572 | − | 10.2355i | 0.116854 | − | 0.359639i | ||||
\(811\) | −3.48859 | − | 10.7368i | −0.122501 | − | 0.377019i | 0.870937 | − | 0.491395i | \(-0.163513\pi\) |
−0.993437 | + | 0.114376i | \(0.963513\pi\) | |||||||
\(812\) | 9.79682 | − | 7.11781i | 0.343801 | − | 0.249786i | ||||
\(813\) | 2.01412 | 0.0706383 | ||||||||
\(814\) | −23.5147 | − | 31.4113i | −0.824190 | − | 1.10096i | ||||
\(815\) | −19.0686 | −0.667945 | ||||||||
\(816\) | 4.29544 | − | 3.12082i | 0.150370 | − | 0.109251i | ||||
\(817\) | −8.56274 | − | 26.3534i | −0.299572 | − | 0.921988i | ||||
\(818\) | 17.4989 | − | 53.8561i | 0.611836 | − | 1.88304i | ||||
\(819\) | −2.35414 | − | 1.71038i | −0.0822602 | − | 0.0597655i | ||||
\(820\) | 30.3515 | + | 22.0517i | 1.05992 | + | 0.770078i | ||||
\(821\) | −7.03946 | + | 21.6652i | −0.245679 | + | 0.756121i | 0.749845 | + | 0.661613i | \(0.230128\pi\) |
−0.995524 | + | 0.0945082i | \(0.969872\pi\) | |||||||
\(822\) | −9.15951 | − | 28.1901i | −0.319475 | − | 0.983242i | ||||
\(823\) | 37.1408 | − | 26.9844i | 1.29465 | − | 0.940616i | 0.294758 | − | 0.955572i | \(-0.404761\pi\) |
0.999888 | + | 0.0149563i | \(0.00476092\pi\) | |||||||
\(824\) | −50.9747 | −1.77579 | ||||||||
\(825\) | 24.7983 | − | 35.1784i | 0.863367 | − | 1.22475i | ||||
\(826\) | 69.4035 | 2.41486 | ||||||||
\(827\) | 31.2959 | − | 22.7378i | 1.08826 | − | 0.790671i | 0.109160 | − | 0.994024i | \(-0.465184\pi\) |
0.979105 | + | 0.203353i | \(0.0651841\pi\) | |||||||
\(828\) | −4.61679 | − | 14.2090i | −0.160445 | − | 0.493798i | ||||
\(829\) | 15.3511 | − | 47.2458i | 0.533166 | − | 1.64092i | −0.214413 | − | 0.976743i | \(-0.568784\pi\) |
0.747579 | − | 0.664173i | \(-0.231216\pi\) | |||||||
\(830\) | 150.464 | + | 109.319i | 5.22269 | + | 3.79451i | ||||
\(831\) | −7.73303 | − | 5.61837i | −0.268256 | − | 0.194899i | ||||
\(832\) | −0.317640 | + | 0.977594i | −0.0110122 | + | 0.0338920i | ||||
\(833\) | 0.351258 | + | 1.08106i | 0.0121704 | + | 0.0374566i | ||||
\(834\) | 47.0075 | − | 34.1529i | 1.62774 | − | 1.18262i | ||||
\(835\) | 60.0514 | 2.07817 | ||||||||
\(836\) | −109.081 | + | 37.1740i | −3.77264 | + | 1.28569i | ||||
\(837\) | −4.06017 | −0.140340 | ||||||||
\(838\) | 30.6246 | − | 22.2501i | 1.05791 | − | 0.768616i | ||||
\(839\) | −16.3528 | − | 50.3288i | −0.564561 | − | 1.73754i | −0.669251 | − | 0.743037i | \(-0.733385\pi\) |
0.104689 | − | 0.994505i | \(-0.466615\pi\) | |||||||
\(840\) | −23.6415 | + | 72.7611i | −0.815710 | + | 2.51050i | ||||
\(841\) | 22.7517 | + | 16.5301i | 0.784542 | + | 0.570003i | ||||
\(842\) | 25.2079 | + | 18.3146i | 0.868721 | + | 0.631163i | ||||
\(843\) | −1.21732 | + | 3.74654i | −0.0419269 | + | 0.129038i | ||||
\(844\) | −12.9870 | − | 39.9698i | −0.447030 | − | 1.37582i | ||||
\(845\) | −3.43019 | + | 2.49218i | −0.118002 | + | 0.0857336i | ||||
\(846\) | −11.7763 | −0.404879 | ||||||||
\(847\) | −10.7571 | − | 30.1469i | −0.369618 | − | 1.03586i | ||||
\(848\) | 54.7511 | 1.88016 | ||||||||
\(849\) | −6.95545 | + | 5.05343i | −0.238710 | + | 0.173433i | ||||
\(850\) | 7.88521 | + | 24.2682i | 0.270460 | + | 0.832392i | ||||
\(851\) | 4.84322 | − | 14.9059i | 0.166023 | − | 0.510968i | ||||
\(852\) | −36.7576 | − | 26.7059i | −1.25929 | − | 0.914930i | ||||
\(853\) | −21.5047 | − | 15.6241i | −0.736306 | − | 0.534958i | 0.155246 | − | 0.987876i | \(-0.450383\pi\) |
−0.891552 | + | 0.452918i | \(0.850383\pi\) | |||||||
\(854\) | −12.7682 | + | 39.2964i | −0.436918 | + | 1.34469i | ||||
\(855\) | −10.2466 | − | 31.5359i | −0.350428 | − | 1.07851i | ||||
\(856\) | 94.6150 | − | 68.7418i | 3.23387 | − | 2.34955i | ||||
\(857\) | 0.463785 | 0.0158426 | 0.00792130 | − | 0.999969i | \(-0.497479\pi\) | ||||
0.00792130 | + | 0.999969i | \(0.497479\pi\) | |||||||
\(858\) | −7.96856 | + | 2.71563i | −0.272042 | + | 0.0927102i | ||||
\(859\) | 35.7585 | 1.22006 | 0.610032 | − | 0.792376i | \(-0.291156\pi\) | ||||
0.610032 | + | 0.792376i | \(0.291156\pi\) | |||||||
\(860\) | −53.9985 | + | 39.2322i | −1.84133 | + | 1.33781i | ||||
\(861\) | 1.79080 | + | 5.51151i | 0.0610302 | + | 0.187832i | ||||
\(862\) | −4.54324 | + | 13.9826i | −0.154743 | + | 0.476251i | ||||
\(863\) | −3.78032 | − | 2.74656i | −0.128684 | − | 0.0934941i | 0.521582 | − | 0.853201i | \(-0.325342\pi\) |
−0.650265 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(864\) | 4.04143 | + | 2.93627i | 0.137492 | + | 0.0998939i | ||||
\(865\) | −24.4460 | + | 75.2371i | −0.831189 | + | 2.55814i | ||||
\(866\) | 12.1152 | + | 37.2869i | 0.411693 | + | 1.26706i | ||||
\(867\) | −13.2678 | + | 9.63962i | −0.450598 | + | 0.327379i | ||||
\(868\) | 52.4916 | 1.78168 | ||||||||
\(869\) | −11.8468 | + | 16.8056i | −0.401875 | + | 0.570091i | ||||
\(870\) | 10.0806 | 0.341763 | ||||||||
\(871\) | 10.7341 | − | 7.79875i | 0.363710 | − | 0.264251i | ||||
\(872\) | −20.5283 | − | 63.1796i | −0.695176 | − | 2.13953i | ||||
\(873\) | 2.79945 | − | 8.61582i | 0.0947471 | − | 0.291601i | ||||
\(874\) | −54.0039 | − | 39.2361i | −1.82671 | − | 1.32718i | ||||
\(875\) | −79.6234 | − | 57.8498i | −2.69176 | − | 1.95568i | ||||
\(876\) | 2.73827 | − | 8.42753i | 0.0925176 | − | 0.284740i | ||||
\(877\) | −14.7163 | − | 45.2921i | −0.496934 | − | 1.52941i | −0.813920 | − | 0.580976i | \(-0.802671\pi\) |
0.316986 | − | 0.948430i | \(-0.397329\pi\) | |||||||
\(878\) | 53.2655 | − | 38.6997i | 1.79763 | − | 1.30605i | ||||
\(879\) | 26.7829 | 0.903365 | ||||||||
\(880\) | 57.7607 | + | 77.1576i | 1.94711 | + | 2.60098i | ||||
\(881\) | 33.2974 | 1.12182 | 0.560909 | − | 0.827877i | \(-0.310452\pi\) | ||||
0.560909 | + | 0.827877i | \(0.310452\pi\) | |||||||
\(882\) | −3.01326 | + | 2.18926i | −0.101462 | + | 0.0737162i | ||||
\(883\) | 7.72739 | + | 23.7825i | 0.260047 | + | 0.800344i | 0.992793 | + | 0.119841i | \(0.0382385\pi\) |
−0.732746 | + | 0.680503i | \(0.761762\pi\) | |||||||
\(884\) | 1.06356 | − | 3.27331i | 0.0357715 | − | 0.110093i | ||||
\(885\) | 32.2317 | + | 23.4177i | 1.08346 | + | 0.787177i | ||||
\(886\) | −13.2988 | − | 9.66212i | −0.446781 | − | 0.324605i | ||||
\(887\) | 9.68079 | − | 29.7944i | 0.325049 | − | 1.00040i | −0.646369 | − | 0.763025i | \(-0.723713\pi\) |
0.971418 | − | 0.237374i | \(-0.0762865\pi\) | |||||||
\(888\) | 8.93114 | + | 27.4872i | 0.299710 | + | 0.922411i | ||||
\(889\) | 0.340354 | − | 0.247282i | 0.0114151 | − | 0.00829356i | ||||
\(890\) | 16.8101 | 0.563476 | ||||||||
\(891\) | −0.0473944 | − | 3.31629i | −0.00158777 | − | 0.111100i | ||||
\(892\) | 60.1960 | 2.01551 | ||||||||
\(893\) | −29.3538 | + | 21.3268i | −0.982286 | + | 0.713673i | ||||
\(894\) | −7.38744 | − | 22.7362i | −0.247073 | − | 0.760413i | ||||
\(895\) | 19.4304 | − | 59.8006i | 0.649487 | − | 1.99891i | ||||
\(896\) | 29.6623 | + | 21.5509i | 0.990948 | + | 0.719966i | ||||
\(897\) | −2.72047 | − | 1.97653i | −0.0908337 | − | 0.0659946i | ||||
\(898\) | 19.6862 | − | 60.5880i | 0.656938 | − | 2.02185i | ||||
\(899\) | −1.17519 | − | 3.61686i | −0.0391947 | − | 0.120629i | ||||
\(900\) | −46.6455 | + | 33.8899i | −1.55485 | + | 1.12966i | ||||
\(901\) | 6.18813 | 0.206157 | ||||||||
\(902\) | 16.0178 | + | 4.95259i | 0.533335 | + | 0.164903i | ||||
\(903\) | −10.3102 | −0.343101 | ||||||||
\(904\) | −21.9133 | + | 15.9209i | −0.728825 | + | 0.529522i | ||||
\(905\) | 16.7284 | + | 51.4847i | 0.556071 | + | 1.71141i | ||||
\(906\) | 2.23844 | − | 6.88922i | 0.0743673 | − | 0.228879i | ||||
\(907\) | 39.9052 | + | 28.9928i | 1.32503 | + | 0.962692i | 0.999855 | + | 0.0170385i | \(0.00542379\pi\) |
0.325177 | + | 0.945653i | \(0.394576\pi\) | |||||||
\(908\) | −93.6690 | − | 68.0545i | −3.10851 | − | 2.25847i | ||||
\(909\) | −0.952554 | + | 2.93166i | −0.0315942 | + | 0.0972370i | ||||
\(910\) | 9.67742 | + | 29.7840i | 0.320803 | + | 0.987331i | ||||
\(911\) | 5.09260 | − | 3.69999i | 0.168726 | − | 0.122586i | −0.500218 | − | 0.865900i | \(-0.666747\pi\) |
0.668944 | + | 0.743313i | \(0.266747\pi\) | |||||||
\(912\) | 53.6019 | 1.77494 | ||||||||
\(913\) | 54.7574 | + | 16.9306i | 1.81220 | + | 0.560320i | ||||
\(914\) | 14.4855 | 0.479137 | ||||||||
\(915\) | −19.1888 | + | 13.9415i | −0.634362 | + | 0.460891i | ||||
\(916\) | −37.7259 | − | 116.108i | −1.24650 | − | 3.83632i | ||||
\(917\) | 3.84860 | − | 11.8448i | 0.127092 | − | 0.391149i | ||||
\(918\) | 1.59077 | + | 1.15577i | 0.0525034 | + | 0.0381459i | ||||
\(919\) | −5.87612 | − | 4.26925i | −0.193835 | − | 0.140830i | 0.486635 | − | 0.873606i | \(-0.338224\pi\) |
−0.680470 | + | 0.732776i | \(0.738224\pi\) | |||||||
\(920\) | −27.3204 | + | 84.0836i | −0.900727 | + | 2.77215i | ||||
\(921\) | −5.25577 | − | 16.1756i | −0.173184 | − | 0.533004i | ||||
\(922\) | 20.6576 | − | 15.0086i | 0.680320 | − | 0.494282i | ||||
\(923\) | −10.2263 | −0.336601 | ||||||||
\(924\) | 0.612735 | + | 42.8744i | 0.0201575 | + | 1.41046i | ||||
\(925\) | −60.4848 | −1.98873 | ||||||||
\(926\) | −40.3876 | + | 29.3433i | −1.32722 | + | 0.964282i | ||||
\(927\) | −2.54026 | − | 7.81813i | −0.0834332 | − | 0.256781i | ||||
\(928\) | −1.44591 | + | 4.45005i | −0.0474643 | + | 0.146080i | ||||
\(929\) | 8.07166 | + | 5.86440i | 0.264822 | + | 0.192405i | 0.712270 | − | 0.701905i | \(-0.247667\pi\) |
−0.447448 | + | 0.894310i | \(0.647667\pi\) | |||||||
\(930\) | 35.3512 | + | 25.6842i | 1.15921 | + | 0.842217i | ||||
\(931\) | −3.54615 | + | 10.9139i | −0.116220 | + | 0.357690i | ||||
\(932\) | −7.12227 | − | 21.9201i | −0.233298 | − | 0.718017i | ||||
\(933\) | −19.8690 | + | 14.4357i | −0.650483 | + | 0.472603i | ||||
\(934\) | 59.0910 | 1.93352 | ||||||||
\(935\) | 6.52829 | + | 8.72059i | 0.213498 | + | 0.285194i | ||||
\(936\) | 6.20095 | 0.202685 | ||||||||
\(937\) | 24.2072 | − | 17.5876i | 0.790815 | − | 0.574561i | −0.117390 | − | 0.993086i | \(-0.537453\pi\) |
0.908205 | + | 0.418525i | \(0.137453\pi\) | |||||||
\(938\) | −30.2834 | − | 93.2029i | −0.988790 | − | 3.04318i | ||||
\(939\) | −7.24905 | + | 22.3103i | −0.236564 | + | 0.728068i | ||||
\(940\) | 70.7063 | + | 51.3711i | 2.30618 | + | 1.67554i | ||||
\(941\) | −5.50383 | − | 3.99877i | −0.179420 | − | 0.130356i | 0.494450 | − | 0.869206i | \(-0.335369\pi\) |
−0.673870 | + | 0.738850i | \(0.735369\pi\) | |||||||
\(942\) | −3.06470 | + | 9.43218i | −0.0998533 | + | 0.307317i | ||||
\(943\) | 2.06947 | + | 6.36916i | 0.0673911 | + | 0.207408i | ||||
\(944\) | −52.1031 | + | 37.8551i | −1.69581 | + | 1.23208i | ||||
\(945\) | −12.3377 | −0.401346 | ||||||||
\(946\) | −17.1861 | + | 24.3798i | −0.558768 | + | 0.792655i | ||||
\(947\) | −25.6645 | −0.833985 | −0.416993 | − | 0.908910i | \(-0.636916\pi\) | ||||
−0.416993 | + | 0.908910i | \(0.636916\pi\) | |||||||
\(948\) | 22.2837 | − | 16.1901i | 0.723742 | − | 0.525830i | ||||
\(949\) | −0.616317 | − | 1.89683i | −0.0200065 | − | 0.0615737i | ||||
\(950\) | −79.6056 | + | 245.001i | −2.58275 | + | 7.94888i | ||||
\(951\) | 24.3500 | + | 17.6913i | 0.789603 | + | 0.573680i | ||||
\(952\) | −11.3083 | − | 8.21599i | −0.366505 | − | 0.266282i | ||||
\(953\) | 1.19456 | − | 3.67647i | 0.0386955 | − | 0.119093i | −0.929843 | − | 0.367957i | \(-0.880057\pi\) |
0.968538 | + | 0.248864i | \(0.0800574\pi\) | |||||||
\(954\) | 6.26580 | + | 19.2841i | 0.202863 | + | 0.624347i | ||||
\(955\) | 11.4474 | − | 8.31703i | 0.370429 | − | 0.269133i | ||||
\(956\) | −9.26725 | −0.299724 | ||||||||
\(957\) | 2.94048 | − | 1.00210i | 0.0950523 | − | 0.0323932i | ||||
\(958\) | 4.97675 | 0.160792 | ||||||||
\(959\) | −27.4903 | + | 19.9728i | −0.887707 | + | 0.644957i | ||||
\(960\) | 1.34678 | + | 4.14495i | 0.0434670 | + | 0.133778i | ||||
\(961\) | −4.48540 | + | 13.8046i | −0.144690 | + | 0.445311i | ||||
\(962\) | 9.57120 | + | 6.95388i | 0.308588 | + | 0.224202i | ||||
\(963\) | 15.2581 | + | 11.0857i | 0.491687 | + | 0.357231i | ||||
\(964\) | −10.6120 | + | 32.6603i | −0.341788 | + | 1.05192i | ||||
\(965\) | 24.6590 | + | 75.8925i | 0.793800 | + | 2.44307i | ||||
\(966\) | −20.0937 | + | 14.5989i | −0.646504 | + | 0.469713i | ||||
\(967\) | −12.4272 | −0.399632 | −0.199816 | − | 0.979833i | \(-0.564034\pi\) | ||||
−0.199816 | + | 0.979833i | \(0.564034\pi\) | |||||||
\(968\) | 56.3067 | + | 38.4998i | 1.80976 | + | 1.23743i | ||||
\(969\) | 6.05825 | 0.194619 | ||||||||
\(970\) | −78.8772 | + | 57.3076i | −2.53259 | + | 1.84004i | ||||
\(971\) | 12.8549 | + | 39.5632i | 0.412532 | + | 1.26964i | 0.914440 | + | 0.404722i | \(0.132632\pi\) |
−0.501908 | + | 0.864921i | \(0.667368\pi\) | |||||||
\(972\) | −1.37295 | + | 4.22550i | −0.0440374 | + | 0.135533i | ||||
\(973\) | −53.8888 | − | 39.1525i | −1.72760 | − | 1.25517i | ||||
\(974\) | −3.39839 | − | 2.46907i | −0.108891 | − | 0.0791142i | ||||
\(975\) | −4.01016 | + | 12.3420i | −0.128428 | + | 0.395261i | ||||
\(976\) | −11.8482 | − | 36.4651i | −0.379253 | − | 1.16722i | ||||
\(977\) | 22.4162 | − | 16.2863i | 0.717157 | − | 0.521045i | −0.168317 | − | 0.985733i | \(-0.553833\pi\) |
0.885475 | + | 0.464688i | \(0.153833\pi\) | |||||||
\(978\) | 11.4157 | 0.365033 | ||||||||
\(979\) | 4.90347 | − | 1.67107i | 0.156716 | − | 0.0534077i | ||||
\(980\) | 27.6420 | 0.882990 | ||||||||
\(981\) | 8.66702 | − | 6.29696i | 0.276717 | − | 0.201046i | ||||
\(982\) | −16.2557 | − | 50.0298i | −0.518739 | − | 1.59652i | ||||
\(983\) | 13.8777 | − | 42.7113i | 0.442631 | − | 1.36228i | −0.442429 | − | 0.896803i | \(-0.645883\pi\) |
0.885061 | − | 0.465476i | \(-0.154117\pi\) | |||||||
\(984\) | −9.99094 | − | 7.25884i | −0.318499 | − | 0.231403i | ||||
\(985\) | −27.0530 | − | 19.6552i | −0.861980 | − | 0.626265i | ||||
\(986\) | −0.569135 | + | 1.75162i | −0.0181249 | + | 0.0557828i | ||||
\(987\) | 4.17180 | + | 12.8395i | 0.132790 | + | 0.408685i | ||||
\(988\) | 28.1105 | − | 20.4235i | 0.894314 | − | 0.649757i | ||||
\(989\) | −11.9145 | −0.378860 | ||||||||
\(990\) | −20.5658 | + | 29.1742i | −0.653625 | + | 0.927217i | ||||
\(991\) | −27.2762 | −0.866456 | −0.433228 | − | 0.901284i | \(-0.642626\pi\) | ||||
−0.433228 | + | 0.901284i | \(0.642626\pi\) | |||||||
\(992\) | −16.4089 | + | 11.9217i | −0.520982 | + | 0.378515i | ||||
\(993\) | −3.46267 | − | 10.6570i | −0.109885 | − | 0.338190i | ||||
\(994\) | −23.3408 | + | 71.8356i | −0.740325 | + | 2.27849i | ||||
\(995\) | −22.7900 | − | 16.5579i | −0.722490 | − | 0.524920i | ||||
\(996\) | −62.1158 | − | 45.1298i | −1.96821 | − | 1.42999i | ||||
\(997\) | −12.0855 | + | 37.1952i | −0.382750 | + | 1.17798i | 0.555349 | + | 0.831618i | \(0.312585\pi\) |
−0.938099 | + | 0.346367i | \(0.887415\pi\) | |||||||
\(998\) | −10.4523 | − | 32.1688i | −0.330861 | − | 1.01829i | ||||
\(999\) | −3.77072 | + | 2.73959i | −0.119300 | + | 0.0866766i |
(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 | 429.2.n.c.157.1 | ✓ | 28 | |
11.2 | odd | 10 | 4719.2.a.bo.1.2 | 14 | |||
11.4 | even | 5 | inner | 429.2.n.c.235.1 | yes | 28 | |
11.9 | even | 5 | 4719.2.a.bp.1.13 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.c.157.1 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.n.c.235.1 | yes | 28 | 11.4 | even | 5 | inner | |
4719.2.a.bo.1.2 | 14 | 11.2 | odd | 10 | |||
4719.2.a.bp.1.13 | 14 | 11.9 | even | 5 |