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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} + \cdots + 88804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 93.7 | ||
Root | \(1.21198 + 1.21198i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.93 |
Dual form | 230.3.f.a.47.7 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.21198 | + | 1.21198i | 0.403994 | + | 0.403994i | 0.879638 | − | 0.475644i | \(-0.157785\pi\) |
−0.475644 | + | 0.879638i | \(0.657785\pi\) | |||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | −0.802406 | − | 4.93519i | −0.160481 | − | 0.987039i | ||||
\(6\) | −2.42397 | −0.403994 | ||||||||
\(7\) | −5.44701 | + | 5.44701i | −0.778144 | + | 0.778144i | −0.979515 | − | 0.201371i | \(-0.935460\pi\) |
0.201371 | + | 0.979515i | \(0.435460\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 6.06220i | − | 0.673577i | ||||||
\(10\) | 5.73760 | + | 4.13279i | 0.573760 | + | 0.413279i | ||||
\(11\) | −4.57608 | −0.416008 | −0.208004 | − | 0.978128i | \(-0.566697\pi\) | ||||
−0.208004 | + | 0.978128i | \(0.566697\pi\) | |||||||
\(12\) | 2.42397 | − | 2.42397i | 0.201997 | − | 0.201997i | ||||
\(13\) | −14.3294 | − | 14.3294i | −1.10227 | − | 1.10227i | −0.994137 | − | 0.108128i | \(-0.965514\pi\) |
−0.108128 | − | 0.994137i | \(-0.534486\pi\) | |||||||
\(14\) | − | 10.8940i | − | 0.778144i | ||||||
\(15\) | 5.00887 | − | 6.95387i | 0.333925 | − | 0.463591i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −19.9013 | + | 19.9013i | −1.17066 | + | 1.17066i | −0.188610 | + | 0.982052i | \(0.560398\pi\) |
−0.982052 | + | 0.188610i | \(0.939602\pi\) | |||||||
\(18\) | 6.06220 | + | 6.06220i | 0.336789 | + | 0.336789i | ||||
\(19\) | − | 11.0420i | − | 0.581156i | −0.956851 | − | 0.290578i | \(-0.906152\pi\) | ||
0.956851 | − | 0.290578i | \(-0.0938475\pi\) | |||||||
\(20\) | −9.87039 | + | 1.60481i | −0.493519 | + | 0.0802406i | ||||
\(21\) | −13.2034 | −0.628731 | ||||||||
\(22\) | 4.57608 | − | 4.57608i | 0.208004 | − | 0.208004i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | 4.84793i | 0.201997i | ||||||||
\(25\) | −23.7123 | + | 7.92006i | −0.948492 | + | 0.316802i | ||||
\(26\) | 28.6589 | 1.10227 | ||||||||
\(27\) | 18.2551 | − | 18.2551i | 0.676116 | − | 0.676116i | ||||
\(28\) | 10.8940 | + | 10.8940i | 0.389072 | + | 0.389072i | ||||
\(29\) | − | 41.2003i | − | 1.42070i | −0.703848 | − | 0.710351i | \(-0.748536\pi\) | ||
0.703848 | − | 0.710351i | \(-0.251464\pi\) | |||||||
\(30\) | 1.94500 | + | 11.9627i | 0.0648334 | + | 0.398758i | ||||
\(31\) | 36.2151 | 1.16823 | 0.584114 | − | 0.811671i | \(-0.301442\pi\) | ||||
0.584114 | + | 0.811671i | \(0.301442\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | −5.54614 | − | 5.54614i | −0.168065 | − | 0.168065i | ||||
\(34\) | − | 39.8025i | − | 1.17066i | ||||||
\(35\) | 31.2527 | + | 22.5113i | 0.892935 | + | 0.643181i | ||||
\(36\) | −12.1244 | −0.336789 | ||||||||
\(37\) | 11.5853 | − | 11.5853i | 0.313115 | − | 0.313115i | −0.533000 | − | 0.846115i | \(-0.678935\pi\) |
0.846115 | + | 0.533000i | \(0.178935\pi\) | |||||||
\(38\) | 11.0420 | + | 11.0420i | 0.290578 | + | 0.290578i | ||||
\(39\) | − | 34.7341i | − | 0.890618i | ||||||
\(40\) | 8.26558 | − | 11.4752i | 0.206639 | − | 0.286880i | ||||
\(41\) | −44.4257 | −1.08355 | −0.541777 | − | 0.840522i | \(-0.682248\pi\) | ||||
−0.541777 | + | 0.840522i | \(0.682248\pi\) | |||||||
\(42\) | 13.2034 | − | 13.2034i | 0.314366 | − | 0.314366i | ||||
\(43\) | −20.7536 | − | 20.7536i | −0.482642 | − | 0.482642i | 0.423332 | − | 0.905975i | \(-0.360860\pi\) |
−0.905975 | + | 0.423332i | \(0.860860\pi\) | |||||||
\(44\) | 9.15217i | 0.208004i | ||||||||
\(45\) | −29.9181 | + | 4.86434i | −0.664847 | + | 0.108096i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −10.9836 | + | 10.9836i | −0.233694 | + | 0.233694i | −0.814232 | − | 0.580539i | \(-0.802842\pi\) |
0.580539 | + | 0.814232i | \(0.302842\pi\) | |||||||
\(48\) | −4.84793 | − | 4.84793i | −0.100999 | − | 0.100999i | ||||
\(49\) | − | 10.3397i | − | 0.211015i | ||||||
\(50\) | 15.7922 | − | 31.6323i | 0.315845 | − | 0.632647i | ||||
\(51\) | −48.2399 | −0.945881 | ||||||||
\(52\) | −28.6589 | + | 28.6589i | −0.551133 | + | 0.551133i | ||||
\(53\) | 29.6479 | + | 29.6479i | 0.559395 | + | 0.559395i | 0.929135 | − | 0.369740i | \(-0.120553\pi\) |
−0.369740 | + | 0.929135i | \(0.620553\pi\) | |||||||
\(54\) | 36.5102i | 0.676116i | ||||||||
\(55\) | 3.67188 | + | 22.5839i | 0.0667614 | + | 0.410616i | ||||
\(56\) | −21.7880 | −0.389072 | ||||||||
\(57\) | 13.3827 | − | 13.3827i | 0.234784 | − | 0.234784i | ||||
\(58\) | 41.2003 | + | 41.2003i | 0.710351 | + | 0.710351i | ||||
\(59\) | 0.711008i | 0.0120510i | 0.999982 | + | 0.00602549i | \(0.00191799\pi\) | ||||
−0.999982 | + | 0.00602549i | \(0.998082\pi\) | |||||||
\(60\) | −13.9077 | − | 10.0177i | −0.231796 | − | 0.166962i | ||||
\(61\) | 48.9711 | 0.802805 | 0.401402 | − | 0.915902i | \(-0.368523\pi\) | ||||
0.401402 | + | 0.915902i | \(0.368523\pi\) | |||||||
\(62\) | −36.2151 | + | 36.2151i | −0.584114 | + | 0.584114i | ||||
\(63\) | 33.0208 | + | 33.0208i | 0.524140 | + | 0.524140i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −59.2206 | + | 82.2166i | −0.911086 | + | 1.26487i | ||||
\(66\) | 11.0923 | 0.168065 | ||||||||
\(67\) | 10.3968 | − | 10.3968i | 0.155175 | − | 0.155175i | −0.625249 | − | 0.780425i | \(-0.715003\pi\) |
0.780425 | + | 0.625249i | \(0.215003\pi\) | |||||||
\(68\) | 39.8025 | + | 39.8025i | 0.585331 | + | 0.585331i | ||||
\(69\) | − | 8.22007i | − | 0.119131i | ||||||
\(70\) | −53.7641 | + | 8.74142i | −0.768058 | + | 0.124877i | ||||
\(71\) | −98.2605 | −1.38395 | −0.691975 | − | 0.721921i | \(-0.743259\pi\) | ||||
−0.691975 | + | 0.721921i | \(0.743259\pi\) | |||||||
\(72\) | 12.1244 | − | 12.1244i | 0.168394 | − | 0.168394i | ||||
\(73\) | 73.7196 | + | 73.7196i | 1.00986 | + | 1.00986i | 0.999951 | + | 0.00990633i | \(0.00315333\pi\) |
0.00990633 | + | 0.999951i | \(0.496847\pi\) | |||||||
\(74\) | 23.1705i | 0.313115i | ||||||||
\(75\) | −38.3379 | − | 19.1399i | −0.511171 | − | 0.255199i | ||||
\(76\) | −22.0839 | −0.290578 | ||||||||
\(77\) | 24.9260 | − | 24.9260i | 0.323714 | − | 0.323714i | ||||
\(78\) | 34.7341 | + | 34.7341i | 0.445309 | + | 0.445309i | ||||
\(79\) | 94.5365i | 1.19666i | 0.801248 | + | 0.598332i | \(0.204170\pi\) | ||||
−0.801248 | + | 0.598332i | \(0.795830\pi\) | |||||||
\(80\) | 3.20962 | + | 19.7408i | 0.0401203 | + | 0.246760i | ||||
\(81\) | −10.3100 | −0.127284 | ||||||||
\(82\) | 44.4257 | − | 44.4257i | 0.541777 | − | 0.541777i | ||||
\(83\) | −49.2784 | − | 49.2784i | −0.593715 | − | 0.593715i | 0.344918 | − | 0.938633i | \(-0.387907\pi\) |
−0.938633 | + | 0.344918i | \(0.887907\pi\) | |||||||
\(84\) | 26.4067i | 0.314366i | ||||||||
\(85\) | 114.185 | + | 82.2477i | 1.34336 | + | 0.967620i | ||||
\(86\) | 41.5073 | 0.482642 | ||||||||
\(87\) | 49.9341 | − | 49.9341i | 0.573955 | − | 0.573955i | ||||
\(88\) | −9.15217 | − | 9.15217i | −0.104002 | − | 0.104002i | ||||
\(89\) | − | 112.584i | − | 1.26499i | −0.774565 | − | 0.632494i | \(-0.782031\pi\) | ||
0.774565 | − | 0.632494i | \(-0.217969\pi\) | |||||||
\(90\) | 25.0538 | − | 34.7825i | 0.278375 | − | 0.386472i | ||||
\(91\) | 156.105 | 1.71544 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 43.8921 | + | 43.8921i | 0.471958 | + | 0.471958i | ||||
\(94\) | − | 21.9672i | − | 0.233694i | ||||||
\(95\) | −54.4942 | + | 8.86013i | −0.573623 | + | 0.0932645i | ||||
\(96\) | 9.69586 | 0.100999 | ||||||||
\(97\) | −20.4455 | + | 20.4455i | −0.210778 | + | 0.210778i | −0.804598 | − | 0.593820i | \(-0.797619\pi\) |
0.593820 | + | 0.804598i | \(0.297619\pi\) | |||||||
\(98\) | 10.3397 | + | 10.3397i | 0.105508 | + | 0.105508i | ||||
\(99\) | 27.7411i | 0.280213i | ||||||||
\(100\) | 15.8401 | + | 47.4246i | 0.158401 | + | 0.474246i | ||||
\(101\) | −132.674 | −1.31361 | −0.656804 | − | 0.754062i | \(-0.728092\pi\) | ||||
−0.656804 | + | 0.754062i | \(0.728092\pi\) | |||||||
\(102\) | 48.2399 | − | 48.2399i | 0.472941 | − | 0.472941i | ||||
\(103\) | 98.6862 | + | 98.6862i | 0.958119 | + | 0.958119i | 0.999158 | − | 0.0410388i | \(-0.0130667\pi\) |
−0.0410388 | + | 0.999158i | \(0.513067\pi\) | |||||||
\(104\) | − | 57.3178i | − | 0.551133i | ||||||
\(105\) | 10.5944 | + | 65.1611i | 0.100899 | + | 0.620582i | ||||
\(106\) | −59.2959 | −0.559395 | ||||||||
\(107\) | −131.190 | + | 131.190i | −1.22608 | + | 1.22608i | −0.260643 | + | 0.965435i | \(0.583935\pi\) |
−0.965435 | + | 0.260643i | \(0.916065\pi\) | |||||||
\(108\) | −36.5102 | − | 36.5102i | −0.338058 | − | 0.338058i | ||||
\(109\) | − | 1.77307i | − | 0.0162667i | −0.999967 | − | 0.00813334i | \(-0.997411\pi\) | ||
0.999967 | − | 0.00813334i | \(-0.00258895\pi\) | |||||||
\(110\) | −26.2557 | − | 18.9120i | −0.238689 | − | 0.171927i | ||||
\(111\) | 28.0823 | 0.252993 | ||||||||
\(112\) | 21.7880 | − | 21.7880i | 0.194536 | − | 0.194536i | ||||
\(113\) | −13.6157 | − | 13.6157i | −0.120493 | − | 0.120493i | 0.644289 | − | 0.764782i | \(-0.277153\pi\) |
−0.764782 | + | 0.644289i | \(0.777153\pi\) | |||||||
\(114\) | 26.7653i | 0.234784i | ||||||||
\(115\) | −14.0150 | + | 19.4571i | −0.121869 | + | 0.169193i | ||||
\(116\) | −82.4007 | −0.710351 | ||||||||
\(117\) | −86.8679 | + | 86.8679i | −0.742461 | + | 0.742461i | ||||
\(118\) | −0.711008 | − | 0.711008i | −0.00602549 | − | 0.00602549i | ||||
\(119\) | − | 216.804i | − | 1.82189i | ||||||
\(120\) | 23.9255 | − | 3.89001i | 0.199379 | − | 0.0324167i | ||||
\(121\) | −100.059 | −0.826938 | ||||||||
\(122\) | −48.9711 | + | 48.9711i | −0.401402 | + | 0.401402i | ||||
\(123\) | −53.8432 | − | 53.8432i | −0.437749 | − | 0.437749i | ||||
\(124\) | − | 72.4302i | − | 0.584114i | ||||||
\(125\) | 58.1139 | + | 110.670i | 0.464911 | + | 0.885357i | ||||
\(126\) | −66.0416 | −0.524140 | ||||||||
\(127\) | 166.174 | − | 166.174i | 1.30846 | − | 1.30846i | 0.385930 | − | 0.922528i | \(-0.373881\pi\) |
0.922528 | − | 0.385930i | \(-0.126119\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 50.3061i | − | 0.389970i | ||||||
\(130\) | −22.9961 | − | 141.437i | −0.176893 | − | 1.08798i | ||||
\(131\) | 159.952 | 1.22101 | 0.610505 | − | 0.792012i | \(-0.290966\pi\) | ||||
0.610505 | + | 0.792012i | \(0.290966\pi\) | |||||||
\(132\) | −11.0923 | + | 11.0923i | −0.0840324 | + | 0.0840324i | ||||
\(133\) | 60.1456 | + | 60.1456i | 0.452223 | + | 0.452223i | ||||
\(134\) | 20.7935i | 0.155175i | ||||||||
\(135\) | −104.741 | − | 75.4446i | −0.775856 | − | 0.558849i | ||||
\(136\) | −79.6050 | −0.585331 | ||||||||
\(137\) | 80.8498 | − | 80.8498i | 0.590144 | − | 0.590144i | −0.347526 | − | 0.937670i | \(-0.612978\pi\) |
0.937670 | + | 0.347526i | \(0.112978\pi\) | |||||||
\(138\) | 8.22007 | + | 8.22007i | 0.0595657 | + | 0.0595657i | ||||
\(139\) | − | 222.118i | − | 1.59797i | −0.601350 | − | 0.798986i | \(-0.705370\pi\) | ||
0.601350 | − | 0.798986i | \(-0.294630\pi\) | |||||||
\(140\) | 45.0227 | − | 62.5055i | 0.321590 | − | 0.446468i | ||||
\(141\) | −26.6239 | −0.188822 | ||||||||
\(142\) | 98.2605 | − | 98.2605i | 0.691975 | − | 0.691975i | ||||
\(143\) | 65.5728 | + | 65.5728i | 0.458551 | + | 0.458551i | ||||
\(144\) | 24.2488i | 0.168394i | ||||||||
\(145\) | −203.332 | + | 33.0594i | −1.40229 | + | 0.227996i | ||||
\(146\) | −147.439 | −1.00986 | ||||||||
\(147\) | 12.5316 | − | 12.5316i | 0.0852490 | − | 0.0852490i | ||||
\(148\) | −23.1705 | − | 23.1705i | −0.156558 | − | 0.156558i | ||||
\(149\) | 70.4124i | 0.472567i | 0.971684 | + | 0.236283i | \(0.0759294\pi\) | ||||
−0.971684 | + | 0.236283i | \(0.924071\pi\) | |||||||
\(150\) | 57.4778 | − | 19.1979i | 0.383185 | − | 0.127986i | ||||
\(151\) | −2.52184 | −0.0167009 | −0.00835045 | − | 0.999965i | \(-0.502658\pi\) | ||||
−0.00835045 | + | 0.999965i | \(0.502658\pi\) | |||||||
\(152\) | 22.0839 | − | 22.0839i | 0.145289 | − | 0.145289i | ||||
\(153\) | 120.645 | + | 120.645i | 0.788531 | + | 0.788531i | ||||
\(154\) | 49.8519i | 0.323714i | ||||||||
\(155\) | −29.0592 | − | 178.729i | −0.187479 | − | 1.15309i | ||||
\(156\) | −69.4682 | −0.445309 | ||||||||
\(157\) | 216.807 | − | 216.807i | 1.38094 | − | 1.38094i | 0.537984 | − | 0.842955i | \(-0.319186\pi\) |
0.842955 | − | 0.537984i | \(-0.180814\pi\) | |||||||
\(158\) | −94.5365 | − | 94.5365i | −0.598332 | − | 0.598332i | ||||
\(159\) | 71.8656i | 0.451985i | ||||||||
\(160\) | −22.9504 | − | 16.5312i | −0.143440 | − | 0.103320i | ||||
\(161\) | 36.9434 | 0.229462 | ||||||||
\(162\) | 10.3100 | − | 10.3100i | 0.0636419 | − | 0.0636419i | ||||
\(163\) | −163.632 | − | 163.632i | −1.00388 | − | 1.00388i | −0.999992 | − | 0.00388720i | \(-0.998763\pi\) |
−0.00388720 | − | 0.999992i | \(-0.501237\pi\) | |||||||
\(164\) | 88.8514i | 0.541777i | ||||||||
\(165\) | −22.9210 | + | 31.8215i | −0.138915 | + | 0.192858i | ||||
\(166\) | 98.5567 | 0.593715 | ||||||||
\(167\) | 86.4343 | − | 86.4343i | 0.517571 | − | 0.517571i | −0.399265 | − | 0.916836i | \(-0.630735\pi\) |
0.916836 | + | 0.399265i | \(0.130735\pi\) | |||||||
\(168\) | −26.4067 | − | 26.4067i | −0.157183 | − | 0.157183i | ||||
\(169\) | 241.666i | 1.42998i | ||||||||
\(170\) | −196.433 | + | 31.9377i | −1.15549 | + | 0.187869i | ||||
\(171\) | −66.9385 | −0.391453 | ||||||||
\(172\) | −41.5073 | + | 41.5073i | −0.241321 | + | 0.241321i | ||||
\(173\) | −231.547 | − | 231.547i | −1.33842 | − | 1.33842i | −0.897591 | − | 0.440830i | \(-0.854684\pi\) |
−0.440830 | − | 0.897591i | \(-0.645316\pi\) | |||||||
\(174\) | 99.8682i | 0.573955i | ||||||||
\(175\) | 86.0204 | − | 172.302i | 0.491545 | − | 0.984580i | ||||
\(176\) | 18.3043 | 0.104002 | ||||||||
\(177\) | −0.861730 | + | 0.861730i | −0.00486853 | + | 0.00486853i | ||||
\(178\) | 112.584 | + | 112.584i | 0.632494 | + | 0.632494i | ||||
\(179\) | − | 166.689i | − | 0.931225i | −0.884989 | − | 0.465613i | \(-0.845834\pi\) | ||
0.884989 | − | 0.465613i | \(-0.154166\pi\) | |||||||
\(180\) | 9.72868 | + | 59.8362i | 0.0540482 | + | 0.332424i | ||||
\(181\) | 105.385 | 0.582237 | 0.291119 | − | 0.956687i | \(-0.405973\pi\) | ||||
0.291119 | + | 0.956687i | \(0.405973\pi\) | |||||||
\(182\) | −156.105 | + | 156.105i | −0.857721 | + | 0.857721i | ||||
\(183\) | 59.3521 | + | 59.3521i | 0.324328 | + | 0.324328i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | −66.4716 | − | 47.8794i | −0.359306 | − | 0.258808i | ||||
\(186\) | −87.7841 | −0.471958 | ||||||||
\(187\) | 91.0698 | − | 91.0698i | 0.487004 | − | 0.487004i | ||||
\(188\) | 21.9672 | + | 21.9672i | 0.116847 | + | 0.116847i | ||||
\(189\) | 198.872i | 1.05223i | ||||||||
\(190\) | 45.6341 | − | 63.3544i | 0.240179 | − | 0.333444i | ||||
\(191\) | 263.782 | 1.38106 | 0.690528 | − | 0.723306i | \(-0.257378\pi\) | ||||
0.690528 | + | 0.723306i | \(0.257378\pi\) | |||||||
\(192\) | −9.69586 | + | 9.69586i | −0.0504993 | + | 0.0504993i | ||||
\(193\) | 40.7072 | + | 40.7072i | 0.210918 | + | 0.210918i | 0.804657 | − | 0.593739i | \(-0.202349\pi\) |
−0.593739 | + | 0.804657i | \(0.702349\pi\) | |||||||
\(194\) | − | 40.8910i | − | 0.210778i | ||||||
\(195\) | −171.419 | + | 27.8708i | −0.879074 | + | 0.142927i | ||||
\(196\) | −20.6795 | −0.105508 | ||||||||
\(197\) | −116.608 | + | 116.608i | −0.591916 | + | 0.591916i | −0.938149 | − | 0.346232i | \(-0.887461\pi\) |
0.346232 | + | 0.938149i | \(0.387461\pi\) | |||||||
\(198\) | −27.7411 | − | 27.7411i | −0.140107 | − | 0.140107i | ||||
\(199\) | 6.54168i | 0.0328728i | 0.999865 | + | 0.0164364i | \(0.00523210\pi\) | ||||
−0.999865 | + | 0.0164364i | \(0.994768\pi\) | |||||||
\(200\) | −63.2647 | − | 31.5845i | −0.316323 | − | 0.157922i | ||||
\(201\) | 25.2014 | 0.125380 | ||||||||
\(202\) | 132.674 | − | 132.674i | 0.656804 | − | 0.656804i | ||||
\(203\) | 224.419 | + | 224.419i | 1.10551 | + | 1.10551i | ||||
\(204\) | 96.4799i | 0.472941i | ||||||||
\(205\) | 35.6474 | + | 219.249i | 0.173890 | + | 1.06951i | ||||
\(206\) | −197.372 | −0.958119 | ||||||||
\(207\) | −20.5579 | + | 20.5579i | −0.0993136 | + | 0.0993136i | ||||
\(208\) | 57.3178 | + | 57.3178i | 0.275566 | + | 0.275566i | ||||
\(209\) | 50.5289i | 0.241765i | ||||||||
\(210\) | −75.7556 | − | 54.5667i | −0.360741 | − | 0.259841i | ||||
\(211\) | 63.3270 | 0.300128 | 0.150064 | − | 0.988676i | \(-0.452052\pi\) | ||||
0.150064 | + | 0.988676i | \(0.452052\pi\) | |||||||
\(212\) | 59.2959 | − | 59.2959i | 0.279698 | − | 0.279698i | ||||
\(213\) | −119.090 | − | 119.090i | −0.559108 | − | 0.559108i | ||||
\(214\) | − | 262.381i | − | 1.22608i | ||||||
\(215\) | −85.7704 | + | 119.076i | −0.398932 | + | 0.553842i | ||||
\(216\) | 73.0205 | 0.338058 | ||||||||
\(217\) | −197.264 | + | 197.264i | −0.909050 | + | 0.909050i | ||||
\(218\) | 1.77307 | + | 1.77307i | 0.00813334 | + | 0.00813334i | ||||
\(219\) | 178.694i | 0.815953i | ||||||||
\(220\) | 45.1677 | − | 7.34375i | 0.205308 | − | 0.0333807i | ||||
\(221\) | 570.348 | 2.58076 | ||||||||
\(222\) | −28.0823 | + | 28.0823i | −0.126497 | + | 0.126497i | ||||
\(223\) | −173.536 | − | 173.536i | −0.778190 | − | 0.778190i | 0.201333 | − | 0.979523i | \(-0.435473\pi\) |
−0.979523 | + | 0.201333i | \(0.935473\pi\) | |||||||
\(224\) | 43.5760i | 0.194536i | ||||||||
\(225\) | 48.0129 | + | 143.749i | 0.213391 | + | 0.638882i | ||||
\(226\) | 27.2315 | 0.120493 | ||||||||
\(227\) | −142.825 | + | 142.825i | −0.629183 | + | 0.629183i | −0.947863 | − | 0.318680i | \(-0.896761\pi\) |
0.318680 | + | 0.947863i | \(0.396761\pi\) | |||||||
\(228\) | −26.7653 | − | 26.7653i | −0.117392 | − | 0.117392i | ||||
\(229\) | − | 216.004i | − | 0.943247i | −0.881800 | − | 0.471624i | \(-0.843668\pi\) | ||
0.881800 | − | 0.471624i | \(-0.156332\pi\) | |||||||
\(230\) | −5.44218 | − | 33.4721i | −0.0236616 | − | 0.145531i | ||||
\(231\) | 60.4197 | 0.261557 | ||||||||
\(232\) | 82.4007 | − | 82.4007i | 0.355175 | − | 0.355175i | ||||
\(233\) | −95.5641 | − | 95.5641i | −0.410146 | − | 0.410146i | 0.471643 | − | 0.881789i | \(-0.343661\pi\) |
−0.881789 | + | 0.471643i | \(0.843661\pi\) | |||||||
\(234\) | − | 173.736i | − | 0.742461i | ||||||
\(235\) | 63.0195 | + | 45.3929i | 0.268168 | + | 0.193161i | ||||
\(236\) | 1.42202 | 0.00602549 | ||||||||
\(237\) | −114.577 | + | 114.577i | −0.483446 | + | 0.483446i | ||||
\(238\) | 216.804 | + | 216.804i | 0.910943 | + | 0.910943i | ||||
\(239\) | 38.4925i | 0.161057i | 0.996752 | + | 0.0805283i | \(0.0256607\pi\) | ||||
−0.996752 | + | 0.0805283i | \(0.974339\pi\) | |||||||
\(240\) | −20.0355 | + | 27.8155i | −0.0834811 | + | 0.115898i | ||||
\(241\) | −189.881 | −0.787887 | −0.393943 | − | 0.919135i | \(-0.628889\pi\) | ||||
−0.393943 | + | 0.919135i | \(0.628889\pi\) | |||||||
\(242\) | 100.059 | − | 100.059i | 0.413469 | − | 0.413469i | ||||
\(243\) | −176.792 | − | 176.792i | −0.727537 | − | 0.727537i | ||||
\(244\) | − | 97.9422i | − | 0.401402i | ||||||
\(245\) | −51.0287 | + | 8.29667i | −0.208280 | + | 0.0338640i | ||||
\(246\) | 107.686 | 0.437749 | ||||||||
\(247\) | −158.225 | + | 158.225i | −0.640588 | + | 0.640588i | ||||
\(248\) | 72.4302 | + | 72.4302i | 0.292057 | + | 0.292057i | ||||
\(249\) | − | 119.449i | − | 0.479715i | ||||||
\(250\) | −168.784 | − | 52.5558i | −0.675134 | − | 0.210223i | ||||
\(251\) | 171.563 | 0.683519 | 0.341759 | − | 0.939787i | \(-0.388977\pi\) | ||||
0.341759 | + | 0.939787i | \(0.388977\pi\) | |||||||
\(252\) | 66.0416 | − | 66.0416i | 0.262070 | − | 0.262070i | ||||
\(253\) | 15.5183 | + | 15.5183i | 0.0613370 | + | 0.0613370i | ||||
\(254\) | 332.348i | 1.30846i | ||||||||
\(255\) | 38.7080 | + | 238.074i | 0.151796 | + | 0.933622i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −273.227 | + | 273.227i | −1.06314 | + | 1.06314i | −0.0652746 | + | 0.997867i | \(0.520792\pi\) |
−0.997867 | + | 0.0652746i | \(0.979208\pi\) | |||||||
\(258\) | 50.3061 | + | 50.3061i | 0.194985 | + | 0.194985i | ||||
\(259\) | 126.210i | 0.487297i | ||||||||
\(260\) | 164.433 | + | 118.441i | 0.632436 | + | 0.455543i | ||||
\(261\) | −249.765 | −0.956952 | ||||||||
\(262\) | −159.952 | + | 159.952i | −0.610505 | + | 0.610505i | ||||
\(263\) | −83.6219 | − | 83.6219i | −0.317954 | − | 0.317954i | 0.530027 | − | 0.847981i | \(-0.322182\pi\) |
−0.847981 | + | 0.530027i | \(0.822182\pi\) | |||||||
\(264\) | − | 22.1845i | − | 0.0840324i | ||||||
\(265\) | 122.529 | − | 170.108i | 0.462372 | − | 0.641917i | ||||
\(266\) | −120.291 | −0.452223 | ||||||||
\(267\) | 136.450 | − | 136.450i | 0.511048 | − | 0.511048i | ||||
\(268\) | −20.7935 | − | 20.7935i | −0.0775877 | − | 0.0775877i | ||||
\(269\) | 238.961i | 0.888331i | 0.895945 | + | 0.444166i | \(0.146500\pi\) | ||||
−0.895945 | + | 0.444166i | \(0.853500\pi\) | |||||||
\(270\) | 180.185 | − | 29.2960i | 0.667352 | − | 0.108504i | ||||
\(271\) | 189.960 | 0.700960 | 0.350480 | − | 0.936570i | \(-0.386018\pi\) | ||||
0.350480 | + | 0.936570i | \(0.386018\pi\) | |||||||
\(272\) | 79.6050 | − | 79.6050i | 0.292665 | − | 0.292665i | ||||
\(273\) | 189.197 | + | 189.197i | 0.693028 | + | 0.693028i | ||||
\(274\) | 161.700i | 0.590144i | ||||||||
\(275\) | 108.509 | − | 36.2428i | 0.394580 | − | 0.131792i | ||||
\(276\) | −16.4401 | −0.0595657 | ||||||||
\(277\) | −12.8005 | + | 12.8005i | −0.0462112 | + | 0.0462112i | −0.729835 | − | 0.683624i | \(-0.760403\pi\) |
0.683624 | + | 0.729835i | \(0.260403\pi\) | |||||||
\(278\) | 222.118 | + | 222.118i | 0.798986 | + | 0.798986i | ||||
\(279\) | − | 219.543i | − | 0.786892i | ||||||
\(280\) | 17.4828 | + | 107.528i | 0.0624387 | + | 0.384029i | ||||
\(281\) | −36.9842 | −0.131617 | −0.0658083 | − | 0.997832i | \(-0.520963\pi\) | ||||
−0.0658083 | + | 0.997832i | \(0.520963\pi\) | |||||||
\(282\) | 26.6239 | − | 26.6239i | 0.0944108 | − | 0.0944108i | ||||
\(283\) | −130.175 | − | 130.175i | −0.459982 | − | 0.459982i | 0.438667 | − | 0.898649i | \(-0.355451\pi\) |
−0.898649 | + | 0.438667i | \(0.855451\pi\) | |||||||
\(284\) | 196.521i | 0.691975i | ||||||||
\(285\) | −76.7844 | − | 55.3077i | −0.269419 | − | 0.194062i | ||||
\(286\) | −131.146 | −0.458551 | ||||||||
\(287\) | 241.987 | − | 241.987i | 0.843160 | − | 0.843160i | ||||
\(288\) | −24.2488 | − | 24.2488i | −0.0841972 | − | 0.0841972i | ||||
\(289\) | − | 503.120i | − | 1.74090i | ||||||
\(290\) | 170.272 | − | 236.391i | 0.587146 | − | 0.815142i | ||||
\(291\) | −49.5592 | −0.170306 | ||||||||
\(292\) | 147.439 | − | 147.439i | 0.504929 | − | 0.504929i | ||||
\(293\) | −88.7345 | − | 88.7345i | −0.302848 | − | 0.302848i | 0.539279 | − | 0.842127i | \(-0.318697\pi\) |
−0.842127 | + | 0.539279i | \(0.818697\pi\) | |||||||
\(294\) | 25.0632i | 0.0852490i | ||||||||
\(295\) | 3.50896 | − | 0.570517i | 0.0118948 | − | 0.00193396i | ||||
\(296\) | 46.3410 | 0.156558 | ||||||||
\(297\) | −83.5370 | + | 83.5370i | −0.281269 | + | 0.281269i | ||||
\(298\) | −70.4124 | − | 70.4124i | −0.236283 | − | 0.236283i | ||||
\(299\) | 97.1870i | 0.325040i | ||||||||
\(300\) | −38.2798 | + | 76.6757i | −0.127599 | + | 0.255586i | ||||
\(301\) | 226.090 | 0.751130 | ||||||||
\(302\) | 2.52184 | − | 2.52184i | 0.00835045 | − | 0.00835045i | ||||
\(303\) | −160.799 | − | 160.799i | −0.530690 | − | 0.530690i | ||||
\(304\) | 44.1678i | 0.145289i | ||||||||
\(305\) | −39.2947 | − | 241.682i | −0.128835 | − | 0.792400i | ||||
\(306\) | −241.291 | −0.788531 | ||||||||
\(307\) | −386.644 | + | 386.644i | −1.25943 | + | 1.25943i | −0.308062 | + | 0.951366i | \(0.599680\pi\) |
−0.951366 | + | 0.308062i | \(0.900320\pi\) | |||||||
\(308\) | −49.8519 | − | 49.8519i | −0.161857 | − | 0.161857i | ||||
\(309\) | 239.212i | 0.774149i | ||||||||
\(310\) | 207.788 | + | 149.669i | 0.670283 | + | 0.482804i | ||||
\(311\) | 234.994 | 0.755607 | 0.377803 | − | 0.925886i | \(-0.376680\pi\) | ||||
0.377803 | + | 0.925886i | \(0.376680\pi\) | |||||||
\(312\) | 69.4682 | − | 69.4682i | 0.222654 | − | 0.222654i | ||||
\(313\) | 20.5782 | + | 20.5782i | 0.0657449 | + | 0.0657449i | 0.739215 | − | 0.673470i | \(-0.235197\pi\) |
−0.673470 | + | 0.739215i | \(0.735197\pi\) | |||||||
\(314\) | 433.615i | 1.38094i | ||||||||
\(315\) | 136.468 | − | 189.460i | 0.433232 | − | 0.601461i | ||||
\(316\) | 189.073 | 0.598332 | ||||||||
\(317\) | −2.05991 | + | 2.05991i | −0.00649813 | + | 0.00649813i | −0.710348 | − | 0.703850i | \(-0.751463\pi\) |
0.703850 | + | 0.710348i | \(0.251463\pi\) | |||||||
\(318\) | −71.8656 | − | 71.8656i | −0.225992 | − | 0.225992i | ||||
\(319\) | 188.536i | 0.591023i | ||||||||
\(320\) | 39.4816 | − | 6.41924i | 0.123380 | − | 0.0200601i | ||||
\(321\) | −318.001 | −0.990657 | ||||||||
\(322\) | −36.9434 | + | 36.9434i | −0.114731 | + | 0.114731i | ||||
\(323\) | 219.749 | + | 219.749i | 0.680337 | + | 0.680337i | ||||
\(324\) | 20.6200i | 0.0636419i | ||||||||
\(325\) | 453.274 | + | 226.294i | 1.39469 | + | 0.696289i | ||||
\(326\) | 327.265 | 1.00388 | ||||||||
\(327\) | 2.14893 | − | 2.14893i | 0.00657164 | − | 0.00657164i | ||||
\(328\) | −88.8514 | − | 88.8514i | −0.270888 | − | 0.270888i | ||||
\(329\) | − | 119.655i | − | 0.363694i | ||||||
\(330\) | −8.90050 | − | 54.7425i | −0.0269712 | − | 0.165886i | ||||
\(331\) | 3.99957 | 0.0120833 | 0.00604165 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00604165 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(332\) | −98.5567 | + | 98.5567i | −0.296858 | + | 0.296858i | ||||
\(333\) | −70.2321 | − | 70.2321i | −0.210907 | − | 0.210907i | ||||
\(334\) | 172.869i | 0.517571i | ||||||||
\(335\) | −59.6524 | − | 42.9676i | −0.178067 | − | 0.128261i | ||||
\(336\) | 52.8134 | 0.157183 | ||||||||
\(337\) | −140.199 | + | 140.199i | −0.416021 | + | 0.416021i | −0.883830 | − | 0.467809i | \(-0.845044\pi\) |
0.467809 | + | 0.883830i | \(0.345044\pi\) | |||||||
\(338\) | −241.666 | − | 241.666i | −0.714989 | − | 0.714989i | ||||
\(339\) | − | 33.0041i | − | 0.0973572i | ||||||
\(340\) | 164.495 | − | 228.371i | 0.483810 | − | 0.671679i | ||||
\(341\) | −165.723 | −0.485992 | ||||||||
\(342\) | 66.9385 | − | 66.9385i | 0.195727 | − | 0.195727i | ||||
\(343\) | −210.583 | − | 210.583i | −0.613943 | − | 0.613943i | ||||
\(344\) | − | 83.0145i | − | 0.241321i | ||||||
\(345\) | −40.5676 | + | 6.59583i | −0.117587 | + | 0.0191183i | ||||
\(346\) | 463.093 | 1.33842 | ||||||||
\(347\) | −100.859 | + | 100.859i | −0.290660 | + | 0.290660i | −0.837341 | − | 0.546681i | \(-0.815891\pi\) |
0.546681 | + | 0.837341i | \(0.315891\pi\) | |||||||
\(348\) | −99.8682 | − | 99.8682i | −0.286978 | − | 0.286978i | ||||
\(349\) | − | 501.448i | − | 1.43681i | −0.695623 | − | 0.718407i | \(-0.744872\pi\) | ||
0.695623 | − | 0.718407i | \(-0.255128\pi\) | |||||||
\(350\) | 86.2812 | + | 258.322i | 0.246518 | + | 0.738063i | ||||
\(351\) | −523.172 | −1.49052 | ||||||||
\(352\) | −18.3043 | + | 18.3043i | −0.0520010 | + | 0.0520010i | ||||
\(353\) | 9.48375 | + | 9.48375i | 0.0268661 | + | 0.0268661i | 0.720412 | − | 0.693546i | \(-0.243953\pi\) |
−0.693546 | + | 0.720412i | \(0.743953\pi\) | |||||||
\(354\) | − | 1.72346i | − | 0.00486853i | ||||||
\(355\) | 78.8447 | + | 484.934i | 0.222098 | + | 1.36601i | ||||
\(356\) | −225.168 | −0.632494 | ||||||||
\(357\) | 262.763 | − | 262.763i | 0.736032 | − | 0.736032i | ||||
\(358\) | 166.689 | + | 166.689i | 0.465613 | + | 0.465613i | ||||
\(359\) | − | 398.005i | − | 1.10865i | −0.832301 | − | 0.554324i | \(-0.812977\pi\) | ||
0.832301 | − | 0.554324i | \(-0.187023\pi\) | |||||||
\(360\) | −69.5649 | − | 50.1076i | −0.193236 | − | 0.139188i | ||||
\(361\) | 239.075 | 0.662258 | ||||||||
\(362\) | −105.385 | + | 105.385i | −0.291119 | + | 0.291119i | ||||
\(363\) | −121.270 | − | 121.270i | −0.334078 | − | 0.334078i | ||||
\(364\) | − | 312.210i | − | 0.857721i | ||||||
\(365\) | 304.667 | − | 422.973i | 0.834705 | − | 1.15883i | ||||
\(366\) | −118.704 | −0.324328 | ||||||||
\(367\) | 357.545 | − | 357.545i | 0.974238 | − | 0.974238i | −0.0254389 | − | 0.999676i | \(-0.508098\pi\) |
0.999676 | + | 0.0254389i | \(0.00809832\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 269.317i | 0.729857i | ||||||||
\(370\) | 114.351 | − | 18.5922i | 0.309057 | − | 0.0502491i | ||||
\(371\) | −322.985 | −0.870580 | ||||||||
\(372\) | 87.7841 | − | 87.7841i | 0.235979 | − | 0.235979i | ||||
\(373\) | 126.123 | + | 126.123i | 0.338131 | + | 0.338131i | 0.855664 | − | 0.517532i | \(-0.173149\pi\) |
−0.517532 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(374\) | 182.140i | 0.487004i | ||||||||
\(375\) | −63.6967 | + | 204.563i | −0.169858 | + | 0.545501i | ||||
\(376\) | −43.9344 | −0.116847 | ||||||||
\(377\) | −590.378 | + | 590.378i | −1.56599 | + | 1.56599i | ||||
\(378\) | −198.872 | − | 198.872i | −0.526115 | − | 0.526115i | ||||
\(379\) | 551.551i | 1.45528i | 0.685959 | + | 0.727640i | \(0.259383\pi\) | ||||
−0.685959 | + | 0.727640i | \(0.740617\pi\) | |||||||
\(380\) | 17.7203 | + | 108.988i | 0.0466323 | + | 0.286812i | ||||
\(381\) | 402.801 | 1.05722 | ||||||||
\(382\) | −263.782 | + | 263.782i | −0.690528 | + | 0.690528i | ||||
\(383\) | −350.165 | − | 350.165i | −0.914270 | − | 0.914270i | 0.0823352 | − | 0.996605i | \(-0.473762\pi\) |
−0.996605 | + | 0.0823352i | \(0.973762\pi\) | |||||||
\(384\) | − | 19.3917i | − | 0.0504993i | ||||||
\(385\) | −143.015 | − | 103.014i | −0.371468 | − | 0.267568i | ||||
\(386\) | −81.4144 | −0.210918 | ||||||||
\(387\) | −125.813 | + | 125.813i | −0.325097 | + | 0.325097i | ||||
\(388\) | 40.8910 | + | 40.8910i | 0.105389 | + | 0.105389i | ||||
\(389\) | 386.345i | 0.993175i | 0.867987 | + | 0.496587i | \(0.165414\pi\) | ||||
−0.867987 | + | 0.496587i | \(0.834586\pi\) | |||||||
\(390\) | 143.549 | − | 199.290i | 0.368073 | − | 0.511001i | ||||
\(391\) | 134.977 | 0.345209 | ||||||||
\(392\) | 20.6795 | − | 20.6795i | 0.0527538 | − | 0.0527538i | ||||
\(393\) | 193.860 | + | 193.860i | 0.493281 | + | 0.493281i | ||||
\(394\) | − | 233.215i | − | 0.591916i | ||||||
\(395\) | 466.556 | − | 75.8566i | 1.18115 | − | 0.192042i | ||||
\(396\) | 55.4822 | 0.140107 | ||||||||
\(397\) | 208.587 | − | 208.587i | 0.525409 | − | 0.525409i | −0.393791 | − | 0.919200i | \(-0.628837\pi\) |
0.919200 | + | 0.393791i | \(0.128837\pi\) | |||||||
\(398\) | −6.54168 | − | 6.54168i | −0.0164364 | − | 0.0164364i | ||||
\(399\) | 145.791i | 0.365391i | ||||||||
\(400\) | 94.8492 | − | 31.6802i | 0.237123 | − | 0.0792006i | ||||
\(401\) | −549.142 | −1.36943 | −0.684716 | − | 0.728810i | \(-0.740074\pi\) | ||||
−0.684716 | + | 0.728810i | \(0.740074\pi\) | |||||||
\(402\) | −25.2014 | + | 25.2014i | −0.0626900 | + | 0.0626900i | ||||
\(403\) | −518.942 | − | 518.942i | −1.28770 | − | 1.28770i | ||||
\(404\) | 265.349i | 0.656804i | ||||||||
\(405\) | 8.27279 | + | 50.8818i | 0.0204266 | + | 0.125634i | ||||
\(406\) | −448.837 | −1.10551 | ||||||||
\(407\) | −53.0151 | + | 53.0151i | −0.130258 | + | 0.130258i | ||||
\(408\) | −96.4799 | − | 96.4799i | −0.236470 | − | 0.236470i | ||||
\(409\) | − | 622.797i | − | 1.52273i | −0.648322 | − | 0.761366i | \(-0.724529\pi\) | ||
0.648322 | − | 0.761366i | \(-0.275471\pi\) | |||||||
\(410\) | −254.897 | − | 183.602i | −0.621700 | − | 0.447810i | ||||
\(411\) | 195.977 | 0.476830 | ||||||||
\(412\) | 197.372 | − | 197.372i | 0.479059 | − | 0.479059i | ||||
\(413\) | −3.87287 | − | 3.87287i | −0.00937740 | − | 0.00937740i | ||||
\(414\) | − | 41.1158i | − | 0.0993136i | ||||||
\(415\) | −203.657 | + | 282.740i | −0.490740 | + | 0.681300i | ||||
\(416\) | −114.636 | −0.275566 | ||||||||
\(417\) | 269.203 | − | 269.203i | 0.645571 | − | 0.645571i | ||||
\(418\) | −50.5289 | − | 50.5289i | −0.120883 | − | 0.120883i | ||||
\(419\) | − | 217.540i | − | 0.519187i | −0.965718 | − | 0.259594i | \(-0.916411\pi\) | ||
0.965718 | − | 0.259594i | \(-0.0835887\pi\) | |||||||
\(420\) | 130.322 | − | 21.1889i | 0.310291 | − | 0.0504497i | ||||
\(421\) | −172.844 | −0.410557 | −0.205278 | − | 0.978704i | \(-0.565810\pi\) | ||||
−0.205278 | + | 0.978704i | \(0.565810\pi\) | |||||||
\(422\) | −63.3270 | + | 63.3270i | −0.150064 | + | 0.150064i | ||||
\(423\) | 66.5847 | + | 66.5847i | 0.157411 | + | 0.157411i | ||||
\(424\) | 118.592i | 0.279698i | ||||||||
\(425\) | 314.285 | − | 629.523i | 0.739495 | − | 1.48123i | ||||
\(426\) | 238.180 | 0.559108 | ||||||||
\(427\) | −266.746 | + | 266.746i | −0.624697 | + | 0.624697i | ||||
\(428\) | 262.381 | + | 262.381i | 0.613039 | + | 0.613039i | ||||
\(429\) | 158.946i | 0.370504i | ||||||||
\(430\) | −33.3057 | − | 204.846i | −0.0774550 | − | 0.476387i | ||||
\(431\) | −23.1272 | −0.0536595 | −0.0268297 | − | 0.999640i | \(-0.508541\pi\) | ||||
−0.0268297 | + | 0.999640i | \(0.508541\pi\) | |||||||
\(432\) | −73.0205 | + | 73.0205i | −0.169029 | + | 0.169029i | ||||
\(433\) | −401.473 | − | 401.473i | −0.927190 | − | 0.927190i | 0.0703332 | − | 0.997524i | \(-0.477594\pi\) |
−0.997524 | + | 0.0703332i | \(0.977594\pi\) | |||||||
\(434\) | − | 394.528i | − | 0.909050i | ||||||
\(435\) | −286.502 | − | 206.367i | −0.658625 | − | 0.474407i | ||||
\(436\) | −3.54613 | −0.00813334 | ||||||||
\(437\) | −37.4451 | + | 37.4451i | −0.0856867 | + | 0.0856867i | ||||
\(438\) | −178.694 | − | 178.694i | −0.407977 | − | 0.407977i | ||||
\(439\) | 437.828i | 0.997331i | 0.866794 | + | 0.498666i | \(0.166176\pi\) | ||||
−0.866794 | + | 0.498666i | \(0.833824\pi\) | |||||||
\(440\) | −37.8240 | + | 52.5115i | −0.0859636 | + | 0.119344i | ||||
\(441\) | −62.6816 | −0.142135 | ||||||||
\(442\) | −570.348 | + | 570.348i | −1.29038 | + | 1.29038i | ||||
\(443\) | 25.3106 | + | 25.3106i | 0.0571345 | + | 0.0571345i | 0.735097 | − | 0.677962i | \(-0.237137\pi\) |
−0.677962 | + | 0.735097i | \(0.737137\pi\) | |||||||
\(444\) | − | 56.1645i | − | 0.126497i | ||||||
\(445\) | −555.623 | + | 90.3379i | −1.24859 | + | 0.203007i | ||||
\(446\) | 347.073 | 0.778190 | ||||||||
\(447\) | −85.3387 | + | 85.3387i | −0.190914 | + | 0.190914i | ||||
\(448\) | −43.5760 | − | 43.5760i | −0.0972680 | − | 0.0972680i | ||||
\(449\) | − | 856.476i | − | 1.90752i | −0.300571 | − | 0.953759i | \(-0.597177\pi\) | ||
0.300571 | − | 0.953759i | \(-0.402823\pi\) | |||||||
\(450\) | −191.761 | − | 95.7356i | −0.426137 | − | 0.212746i | ||||
\(451\) | 203.296 | 0.450767 | ||||||||
\(452\) | −27.2315 | + | 27.2315i | −0.0602466 | + | 0.0602466i | ||||
\(453\) | −3.05642 | − | 3.05642i | −0.00674707 | − | 0.00674707i | ||||
\(454\) | − | 285.649i | − | 0.629183i | ||||||
\(455\) | −125.260 | − | 770.409i | −0.275296 | − | 1.69321i | ||||
\(456\) | 53.5307 | 0.117392 | ||||||||
\(457\) | −253.911 | + | 253.911i | −0.555604 | + | 0.555604i | −0.928053 | − | 0.372449i | \(-0.878518\pi\) |
0.372449 | + | 0.928053i | \(0.378518\pi\) | |||||||
\(458\) | 216.004 | + | 216.004i | 0.471624 | + | 0.471624i | ||||
\(459\) | 726.599i | 1.58301i | ||||||||
\(460\) | 38.9143 | + | 28.0299i | 0.0845963 | + | 0.0609346i | ||||
\(461\) | −316.325 | −0.686172 | −0.343086 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343086 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(462\) | −60.4197 | + | 60.4197i | −0.130779 | + | 0.130779i | ||||
\(463\) | −373.150 | − | 373.150i | −0.805940 | − | 0.805940i | 0.178077 | − | 0.984017i | \(-0.443013\pi\) |
−0.984017 | + | 0.178077i | \(0.943013\pi\) | |||||||
\(464\) | 164.801i | 0.355175i | ||||||||
\(465\) | 181.397 | − | 251.835i | 0.390100 | − | 0.541581i | ||||
\(466\) | 191.128 | 0.410146 | ||||||||
\(467\) | 638.354 | − | 638.354i | 1.36693 | − | 1.36693i | 0.502138 | − | 0.864787i | \(-0.332547\pi\) |
0.864787 | − | 0.502138i | \(-0.167453\pi\) | |||||||
\(468\) | 173.736 | + | 173.736i | 0.371230 | + | 0.371230i | ||||
\(469\) | 113.262i | 0.241498i | ||||||||
\(470\) | −108.412 | + | 17.6266i | −0.230665 | + | 0.0375034i | ||||
\(471\) | 525.534 | 1.11578 | ||||||||
\(472\) | −1.42202 | + | 1.42202i | −0.00301275 | + | 0.00301275i | ||||
\(473\) | 94.9704 | + | 94.9704i | 0.200783 | + | 0.200783i | ||||
\(474\) | − | 229.153i | − | 0.483446i | ||||||
\(475\) | 87.4529 | + | 261.830i | 0.184111 | + | 0.551221i | ||||
\(476\) | −433.609 | −0.910943 | ||||||||
\(477\) | 179.732 | − | 179.732i | 0.376796 | − | 0.376796i | ||||
\(478\) | −38.4925 | − | 38.4925i | −0.0805283 | − | 0.0805283i | ||||
\(479\) | 664.201i | 1.38664i | 0.720629 | + | 0.693320i | \(0.243853\pi\) | ||||
−0.720629 | + | 0.693320i | \(0.756147\pi\) | |||||||
\(480\) | −7.78001 | − | 47.8510i | −0.0162084 | − | 0.0996895i | ||||
\(481\) | −332.021 | −0.690272 | ||||||||
\(482\) | 189.881 | − | 189.881i | 0.393943 | − | 0.393943i | ||||
\(483\) | 44.7748 | + | 44.7748i | 0.0927014 | + | 0.0927014i | ||||
\(484\) | 200.119i | 0.413469i | ||||||||
\(485\) | 117.308 | + | 84.4969i | 0.241872 | + | 0.174220i | ||||
\(486\) | 353.583 | 0.727537 | ||||||||
\(487\) | 297.098 | − | 297.098i | 0.610057 | − | 0.610057i | −0.332904 | − | 0.942961i | \(-0.608029\pi\) |
0.942961 | + | 0.332904i | \(0.108029\pi\) | |||||||
\(488\) | 97.9422 | + | 97.9422i | 0.200701 | + | 0.200701i | ||||
\(489\) | − | 396.639i | − | 0.811123i | ||||||
\(490\) | 42.7320 | − | 59.3253i | 0.0872082 | − | 0.121072i | ||||
\(491\) | 707.506 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(492\) | −107.686 | + | 107.686i | −0.218875 | + | 0.218875i | ||||
\(493\) | 819.938 | + | 819.938i | 1.66316 | + | 1.66316i | ||||
\(494\) | − | 316.450i | − | 0.640588i | ||||||
\(495\) | 136.908 | − | 22.2596i | 0.276581 | − | 0.0449690i | ||||
\(496\) | −144.860 | −0.292057 | ||||||||
\(497\) | 535.225 | − | 535.225i | 1.07691 | − | 1.07691i | ||||
\(498\) | 119.449 | + | 119.449i | 0.239858 | + | 0.239858i | ||||
\(499\) | 626.773i | 1.25606i | 0.778190 | + | 0.628029i | \(0.216138\pi\) | ||||
−0.778190 | + | 0.628029i | \(0.783862\pi\) | |||||||
\(500\) | 221.339 | − | 116.228i | 0.442679 | − | 0.232456i | ||||
\(501\) | 209.514 | 0.418191 | ||||||||
\(502\) | −171.563 | + | 171.563i | −0.341759 | + | 0.341759i | ||||
\(503\) | 676.425 | + | 676.425i | 1.34478 | + | 1.34478i | 0.891231 | + | 0.453550i | \(0.149843\pi\) |
0.453550 | + | 0.891231i | \(0.350157\pi\) | |||||||
\(504\) | 132.083i | 0.262070i | ||||||||
\(505\) | 106.459 | + | 654.774i | 0.210809 | + | 1.29658i | ||||
\(506\) | −31.0365 | −0.0613370 | ||||||||
\(507\) | −292.895 | + | 292.895i | −0.577703 | + | 0.577703i | ||||
\(508\) | −332.348 | − | 332.348i | −0.654229 | − | 0.654229i | ||||
\(509\) | − | 156.217i | − | 0.306909i | −0.988156 | − | 0.153455i | \(-0.950960\pi\) | ||
0.988156 | − | 0.153455i | \(-0.0490399\pi\) | |||||||
\(510\) | −276.782 | − | 199.366i | −0.542709 | − | 0.390913i | ||||
\(511\) | −803.102 | −1.57163 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −201.572 | − | 201.572i | −0.392928 | − | 0.392928i | ||||
\(514\) | − | 546.455i | − | 1.06314i | ||||||
\(515\) | 407.849 | − | 566.222i | 0.791941 | − | 1.09946i | ||||
\(516\) | −100.612 | −0.194985 | ||||||||
\(517\) | 50.2619 | − | 50.2619i | 0.0972183 | − | 0.0972183i | ||||
\(518\) | −126.210 | − | 126.210i | −0.243649 | − | 0.243649i | ||||
\(519\) | − | 561.261i | − | 1.08143i | ||||||
\(520\) | −282.874 | + | 45.9921i | −0.543989 | + | 0.0884464i | ||||
\(521\) | −114.920 | −0.220575 | −0.110288 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110288 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(522\) | 249.765 | − | 249.765i | 0.478476 | − | 0.478476i | ||||
\(523\) | −163.639 | − | 163.639i | −0.312885 | − | 0.312885i | 0.533141 | − | 0.846026i | \(-0.321011\pi\) |
−0.846026 | + | 0.533141i | \(0.821011\pi\) | |||||||
\(524\) | − | 319.905i | − | 0.610505i | ||||||
\(525\) | 313.082 | − | 104.571i | 0.596346 | − | 0.199183i | ||||
\(526\) | 167.244 | 0.317954 | ||||||||
\(527\) | −720.726 | + | 720.726i | −1.36760 | + | 1.36760i | ||||
\(528\) | 22.1845 | + | 22.1845i | 0.0420162 | + | 0.0420162i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 47.5793 | + | 292.637i | 0.0897724 | + | 0.552145i | ||||
\(531\) | 4.31027 | 0.00811727 | ||||||||
\(532\) | 120.291 | − | 120.291i | 0.226111 | − | 0.226111i | ||||
\(533\) | 636.596 | + | 636.596i | 1.19436 | + | 1.19436i | ||||
\(534\) | 272.899i | 0.511048i | ||||||||
\(535\) | 752.718 | + | 542.182i | 1.40695 | + | 1.01342i | ||||
\(536\) | 41.5870 | 0.0775877 | ||||||||
\(537\) | 202.025 | − | 202.025i | 0.376210 | − | 0.376210i | ||||
\(538\) | −238.961 | − | 238.961i | −0.444166 | − | 0.444166i | ||||
\(539\) | 47.3156i | 0.0877840i | ||||||||
\(540\) | −150.889 | + | 209.481i | −0.279424 | + | 0.387928i | ||||
\(541\) | 329.018 | 0.608166 | 0.304083 | − | 0.952646i | \(-0.401650\pi\) | ||||
0.304083 | + | 0.952646i | \(0.401650\pi\) | |||||||
\(542\) | −189.960 | + | 189.960i | −0.350480 | + | 0.350480i | ||||
\(543\) | 127.725 | + | 127.725i | 0.235220 | + | 0.235220i | ||||
\(544\) | 159.210i | 0.292665i | ||||||||
\(545\) | −8.75043 | + | 1.42272i | −0.0160558 | + | 0.00261049i | ||||
\(546\) | −378.394 | −0.693028 | ||||||||
\(547\) | 441.884 | − | 441.884i | 0.807832 | − | 0.807832i | −0.176474 | − | 0.984305i | \(-0.556469\pi\) |
0.984305 | + | 0.176474i | \(0.0564691\pi\) | |||||||
\(548\) | −161.700 | − | 161.700i | −0.295072 | − | 0.295072i | ||||
\(549\) | − | 296.872i | − | 0.540751i | ||||||
\(550\) | −72.2666 | + | 144.752i | −0.131394 | + | 0.263186i | ||||
\(551\) | −454.933 | −0.825649 | ||||||||
\(552\) | 16.4401 | − | 16.4401i | 0.0297829 | − | 0.0297829i | ||||
\(553\) | −514.941 | − | 514.941i | −0.931177 | − | 0.931177i | ||||
\(554\) | − | 25.6010i | − | 0.0462112i | ||||||
\(555\) | −22.5334 | − | 138.591i | −0.0406007 | − | 0.249714i | ||||
\(556\) | −444.236 | −0.798986 | ||||||||
\(557\) | −669.503 | + | 669.503i | −1.20198 | + | 1.20198i | −0.228416 | + | 0.973564i | \(0.573355\pi\) |
−0.973564 | + | 0.228416i | \(0.926645\pi\) | |||||||
\(558\) | 219.543 | + | 219.543i | 0.393446 | + | 0.393446i | ||||
\(559\) | 594.776i | 1.06400i | ||||||||
\(560\) | −125.011 | − | 90.0453i | −0.223234 | − | 0.160795i | ||||
\(561\) | 220.750 | 0.393494 | ||||||||
\(562\) | 36.9842 | − | 36.9842i | 0.0658083 | − | 0.0658083i | ||||
\(563\) | 52.7348 | + | 52.7348i | 0.0936675 | + | 0.0936675i | 0.752388 | − | 0.658720i | \(-0.228902\pi\) |
−0.658720 | + | 0.752388i | \(0.728902\pi\) | |||||||
\(564\) | 53.2477i | 0.0944108i | ||||||||
\(565\) | −56.2710 | + | 78.1217i | −0.0995946 | + | 0.138268i | ||||
\(566\) | 260.350 | 0.459982 | ||||||||
\(567\) | 56.1585 | − | 56.1585i | 0.0990450 | − | 0.0990450i | ||||
\(568\) | −196.521 | − | 196.521i | −0.345988 | − | 0.345988i | ||||
\(569\) | − | 610.597i | − | 1.07311i | −0.843867 | − | 0.536553i | \(-0.819726\pi\) | ||
0.843867 | − | 0.536553i | \(-0.180274\pi\) | |||||||
\(570\) | 132.092 | − | 21.4766i | 0.231741 | − | 0.0376783i | ||||
\(571\) | −77.9436 | −0.136504 | −0.0682519 | − | 0.997668i | \(-0.521742\pi\) | ||||
−0.0682519 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(572\) | 131.146 | − | 131.146i | 0.229275 | − | 0.229275i | ||||
\(573\) | 319.699 | + | 319.699i | 0.557939 | + | 0.557939i | ||||
\(574\) | 483.974i | 0.843160i | ||||||||
\(575\) | 107.271 | + | 53.5541i | 0.186557 | + | 0.0931375i | ||||
\(576\) | 48.4976 | 0.0841972 | ||||||||
\(577\) | −507.604 | + | 507.604i | −0.879730 | + | 0.879730i | −0.993506 | − | 0.113776i | \(-0.963705\pi\) |
0.113776 | + | 0.993506i | \(0.463705\pi\) | |||||||
\(578\) | 503.120 | + | 503.120i | 0.870449 | + | 0.870449i | ||||
\(579\) | 98.6729i | 0.170419i | ||||||||
\(580\) | 66.1188 | + | 406.663i | 0.113998 | + | 0.701144i | ||||
\(581\) | 536.839 | 0.923992 | ||||||||
\(582\) | 49.5592 | − | 49.5592i | 0.0851532 | − | 0.0851532i | ||||
\(583\) | −135.671 | − | 135.671i | −0.232713 | − | 0.232713i | ||||
\(584\) | 294.878i | 0.504929i | ||||||||
\(585\) | 498.413 | + | 359.007i | 0.851989 | + | 0.613687i | ||||
\(586\) | 177.469 | 0.302848 | ||||||||
\(587\) | −105.920 | + | 105.920i | −0.180443 | + | 0.180443i | −0.791549 | − | 0.611106i | \(-0.790725\pi\) |
0.611106 | + | 0.791549i | \(0.290725\pi\) | |||||||
\(588\) | −25.0632 | − | 25.0632i | −0.0426245 | − | 0.0426245i | ||||
\(589\) | − | 399.886i | − | 0.678923i | ||||||
\(590\) | −2.93845 | + | 4.07948i | −0.00498042 | + | 0.00691437i | ||||
\(591\) | −282.653 | −0.478262 | ||||||||
\(592\) | −46.3410 | + | 46.3410i | −0.0782788 | + | 0.0782788i | ||||
\(593\) | −434.460 | − | 434.460i | −0.732648 | − | 0.732648i | 0.238496 | − | 0.971144i | \(-0.423346\pi\) |
−0.971144 | + | 0.238496i | \(0.923346\pi\) | |||||||
\(594\) | − | 167.074i | − | 0.281269i | ||||||
\(595\) | −1069.97 | + | 173.965i | −1.79827 | + | 0.292378i | ||||
\(596\) | 140.825 | 0.236283 | ||||||||
\(597\) | −7.92841 | + | 7.92841i | −0.0132804 | + | 0.0132804i | ||||
\(598\) | −97.1870 | − | 97.1870i | −0.162520 | − | 0.162520i | ||||
\(599\) | 894.980i | 1.49412i | 0.664754 | + | 0.747062i | \(0.268536\pi\) | ||||
−0.664754 | + | 0.747062i | \(0.731464\pi\) | |||||||
\(600\) | −38.3959 | − | 114.956i | −0.0639931 | − | 0.191593i | ||||
\(601\) | 213.837 | 0.355803 | 0.177901 | − | 0.984048i | \(-0.443069\pi\) | ||||
0.177901 | + | 0.984048i | \(0.443069\pi\) | |||||||
\(602\) | −226.090 | + | 226.090i | −0.375565 | + | 0.375565i | ||||
\(603\) | −63.0272 | − | 63.0272i | −0.104523 | − | 0.104523i | ||||
\(604\) | 5.04367i | 0.00835045i | ||||||||
\(605\) | 80.2883 | + | 493.813i | 0.132708 | + | 0.816220i | ||||
\(606\) | 321.598 | 0.530690 | ||||||||
\(607\) | 18.6303 | − | 18.6303i | 0.0306924 | − | 0.0306924i | −0.691594 | − | 0.722286i | \(-0.743091\pi\) |
0.722286 | + | 0.691594i | \(0.243091\pi\) | |||||||
\(608\) | −44.1678 | − | 44.1678i | −0.0726445 | − | 0.0726445i | ||||
\(609\) | 543.983i | 0.893239i | ||||||||
\(610\) | 280.977 | + | 202.387i | 0.460617 | + | 0.331782i | ||||
\(611\) | 314.778 | 0.515184 | ||||||||
\(612\) | 241.291 | − | 241.291i | 0.394266 | − | 0.394266i | ||||
\(613\) | 546.325 | + | 546.325i | 0.891232 | + | 0.891232i | 0.994639 | − | 0.103407i | \(-0.0329744\pi\) |
−0.103407 | + | 0.994639i | \(0.532974\pi\) | |||||||
\(614\) | − | 773.289i | − | 1.25943i | ||||||
\(615\) | −222.522 | + | 308.931i | −0.361825 | + | 0.502326i | ||||
\(616\) | 99.7038 | 0.161857 | ||||||||
\(617\) | −10.8633 | + | 10.8633i | −0.0176066 | + | 0.0176066i | −0.715855 | − | 0.698249i | \(-0.753963\pi\) |
0.698249 | + | 0.715855i | \(0.253963\pi\) | |||||||
\(618\) | −239.212 | − | 239.212i | −0.387074 | − | 0.387074i | ||||
\(619\) | 1082.29i | 1.74845i | 0.485517 | + | 0.874227i | \(0.338631\pi\) | ||||
−0.485517 | + | 0.874227i | \(0.661369\pi\) | |||||||
\(620\) | −357.457 | + | 58.1184i | −0.576544 | + | 0.0937393i | ||||
\(621\) | −123.812 | −0.199376 | ||||||||
\(622\) | −234.994 | + | 234.994i | −0.377803 | + | 0.377803i | ||||
\(623\) | 613.245 | + | 613.245i | 0.984342 | + | 0.984342i | ||||
\(624\) | 138.936i | 0.222654i | ||||||||
\(625\) | 499.545 | − | 375.605i | 0.799273 | − | 0.600968i | ||||
\(626\) | −41.1563 | −0.0657449 | ||||||||
\(627\) | −61.2402 | + | 61.2402i | −0.0976718 | + | 0.0976718i | ||||
\(628\) | −433.615 | − | 433.615i | −0.690470 | − | 0.690470i | ||||
\(629\) | 461.122i | 0.733104i | ||||||||
\(630\) | 52.9922 | + | 325.928i | 0.0841146 | + | 0.517347i | ||||
\(631\) | −55.4217 | −0.0878316 | −0.0439158 | − | 0.999035i | \(-0.513983\pi\) | ||||
−0.0439158 | + | 0.999035i | \(0.513983\pi\) | |||||||
\(632\) | −189.073 | + | 189.073i | −0.299166 | + | 0.299166i | ||||
\(633\) | 76.7513 | + | 76.7513i | 0.121250 | + | 0.121250i | ||||
\(634\) | − | 4.11981i | − | 0.00649813i | ||||||
\(635\) | −953.441 | − | 686.763i | −1.50148 | − | 1.08152i | ||||
\(636\) | 143.731 | 0.225992 | ||||||||
\(637\) | −148.163 | + | 148.163i | −0.232595 | + | 0.232595i | ||||
\(638\) | −188.536 | − | 188.536i | −0.295511 | − | 0.295511i | ||||
\(639\) | 595.674i | 0.932197i | ||||||||
\(640\) | −33.0623 | + | 45.9008i | −0.0516599 | + | 0.0717200i | ||||
\(641\) | 278.912 | 0.435120 | 0.217560 | − | 0.976047i | \(-0.430190\pi\) | ||||
0.217560 | + | 0.976047i | \(0.430190\pi\) | |||||||
\(642\) | 318.001 | − | 318.001i | 0.495329 | − | 0.495329i | ||||
\(643\) | −159.124 | − | 159.124i | −0.247472 | − | 0.247472i | 0.572460 | − | 0.819932i | \(-0.305989\pi\) |
−0.819932 | + | 0.572460i | \(0.805989\pi\) | |||||||
\(644\) | − | 73.8868i | − | 0.114731i | ||||||
\(645\) | −248.270 | + | 40.3659i | −0.384915 | + | 0.0625828i | ||||
\(646\) | −439.498 | −0.680337 | ||||||||
\(647\) | 533.430 | − | 533.430i | 0.824466 | − | 0.824466i | −0.162279 | − | 0.986745i | \(-0.551884\pi\) |
0.986745 | + | 0.162279i | \(0.0518843\pi\) | |||||||
\(648\) | −20.6200 | − | 20.6200i | −0.0318209 | − | 0.0318209i | ||||
\(649\) | − | 3.25363i | − | 0.00501330i | ||||||
\(650\) | −679.568 | + | 226.980i | −1.04549 | + | 0.349200i | ||||
\(651\) | −478.161 | −0.734502 | ||||||||
\(652\) | −327.265 | + | 327.265i | −0.501940 | + | 0.501940i | ||||
\(653\) | −542.883 | − | 542.883i | −0.831367 | − | 0.831367i | 0.156337 | − | 0.987704i | \(-0.450032\pi\) |
−0.987704 | + | 0.156337i | \(0.950032\pi\) | |||||||
\(654\) | 4.29785i | 0.00657164i | ||||||||
\(655\) | −128.347 | − | 789.396i | −0.195949 | − | 1.20519i | ||||
\(656\) | 177.703 | 0.270888 | ||||||||
\(657\) | 446.903 | − | 446.903i | 0.680217 | − | 0.680217i | ||||
\(658\) | 119.655 | + | 119.655i | 0.181847 | + | 0.181847i | ||||
\(659\) | − | 237.009i | − | 0.359650i | −0.983699 | − | 0.179825i | \(-0.942447\pi\) | ||
0.983699 | − | 0.179825i | \(-0.0575531\pi\) | |||||||
\(660\) | 63.6430 | + | 45.8420i | 0.0964288 | + | 0.0694576i | ||||
\(661\) | 143.004 | 0.216346 | 0.108173 | − | 0.994132i | \(-0.465500\pi\) | ||||
0.108173 | + | 0.994132i | \(0.465500\pi\) | |||||||
\(662\) | −3.99957 | + | 3.99957i | −0.00604165 | + | 0.00604165i | ||||
\(663\) | 691.252 | + | 691.252i | 1.04261 | + | 1.04261i | ||||
\(664\) | − | 197.113i | − | 0.296858i | ||||||
\(665\) | 248.569 | − | 345.092i | 0.373788 | − | 0.518935i | ||||
\(666\) | 140.464 | 0.210907 | ||||||||
\(667\) | −139.717 | + | 139.717i | −0.209471 | + | 0.209471i | ||||
\(668\) | −172.869 | − | 172.869i | −0.258785 | − | 0.258785i | ||||
\(669\) | − | 420.646i | − | 0.628769i | ||||||
\(670\) | 102.620 | − | 16.6848i | 0.153164 | − | 0.0249027i | ||||
\(671\) | −224.096 | −0.333973 | ||||||||
\(672\) | −52.8134 | + | 52.8134i | −0.0785914 | + | 0.0785914i | ||||
\(673\) | 2.30268 | + | 2.30268i | 0.00342152 | + | 0.00342152i | 0.708815 | − | 0.705394i | \(-0.249230\pi\) |
−0.705394 | + | 0.708815i | \(0.749230\pi\) | |||||||
\(674\) | − | 280.398i | − | 0.416021i | ||||||
\(675\) | −288.289 | + | 577.452i | −0.427095 | + | 0.855485i | ||||
\(676\) | 483.332 | 0.714989 | ||||||||
\(677\) | 308.359 | − | 308.359i | 0.455479 | − | 0.455479i | −0.441689 | − | 0.897168i | \(-0.645621\pi\) |
0.897168 | + | 0.441689i | \(0.145621\pi\) | |||||||
\(678\) | 33.0041 | + | 33.0041i | 0.0486786 | + | 0.0486786i | ||||
\(679\) | − | 222.733i | − | 0.328032i | ||||||
\(680\) | 63.8755 | + | 392.866i | 0.0939346 | + | 0.577744i | ||||
\(681\) | −346.202 | −0.508373 | ||||||||
\(682\) | 165.723 | − | 165.723i | 0.242996 | − | 0.242996i | ||||
\(683\) | 599.924 | + | 599.924i | 0.878366 | + | 0.878366i | 0.993366 | − | 0.114999i | \(-0.0366866\pi\) |
−0.114999 | + | 0.993366i | \(0.536687\pi\) | |||||||
\(684\) | 133.877i | 0.195727i | ||||||||
\(685\) | −463.884 | − | 334.135i | −0.677202 | − | 0.487788i | ||||
\(686\) | 421.165 | 0.613943 | ||||||||
\(687\) | 261.793 | − | 261.793i | 0.381066 | − | 0.381066i | ||||
\(688\) | 83.0145 | + | 83.0145i | 0.120661 | + | 0.120661i | ||||
\(689\) | − | 849.677i | − | 1.23320i | ||||||
\(690\) | 33.9718 | − | 47.1635i | 0.0492345 | − | 0.0683528i | ||||
\(691\) | 726.534 | 1.05142 | 0.525712 | − | 0.850663i | \(-0.323799\pi\) | ||||
0.525712 | + | 0.850663i | \(0.323799\pi\) | |||||||
\(692\) | −463.093 | + | 463.093i | −0.669210 | + | 0.669210i | ||||
\(693\) | −151.106 | − | 151.106i | −0.218046 | − | 0.218046i | ||||
\(694\) | − | 201.718i | − | 0.290660i | ||||||
\(695\) | −1096.20 | + | 178.229i | −1.57726 | + | 0.256444i | ||||
\(696\) | 199.736 | 0.286978 | ||||||||
\(697\) | 884.127 | − | 884.127i | 1.26847 | − | 1.26847i | ||||
\(698\) | 501.448 | + | 501.448i | 0.718407 | + | 0.718407i | ||||
\(699\) | − | 231.644i | − | 0.331393i | ||||||
\(700\) | −344.603 | − | 172.041i | −0.492290 | − | 0.245773i | ||||
\(701\) | −498.607 | −0.711280 | −0.355640 | − | 0.934623i | \(-0.615737\pi\) | ||||
−0.355640 | + | 0.934623i | \(0.615737\pi\) | |||||||
\(702\) | 523.172 | − | 523.172i | 0.745259 | − | 0.745259i | ||||
\(703\) | −127.924 | − | 127.924i | −0.181969 | − | 0.181969i | ||||
\(704\) | − | 36.6087i | − | 0.0520010i | ||||||
\(705\) | 21.3631 | + | 131.394i | 0.0303023 | + | 0.186374i | ||||
\(706\) | −18.9675 | −0.0268661 | ||||||||
\(707\) | 722.678 | − | 722.678i | 1.02218 | − | 1.02218i | ||||
\(708\) | 1.72346 | + | 1.72346i | 0.00243426 | + | 0.00243426i | ||||
\(709\) | 976.562i | 1.37738i | 0.725056 | + | 0.688690i | \(0.241814\pi\) | ||||
−0.725056 | + | 0.688690i | \(0.758186\pi\) | |||||||
\(710\) | −563.779 | − | 406.090i | −0.794055 | − | 0.571957i | ||||
\(711\) | 573.099 | 0.806046 | ||||||||
\(712\) | 225.168 | − | 225.168i | 0.316247 | − | 0.316247i | ||||
\(713\) | −122.811 | − | 122.811i | −0.172246 | − | 0.172246i | ||||
\(714\) | 525.527i | 0.736032i | ||||||||
\(715\) | 270.998 | − | 376.230i | 0.379019 | − | 0.526196i | ||||
\(716\) | −333.379 | −0.465613 | ||||||||
\(717\) | −46.6523 | + | 46.6523i | −0.0650660 | + | 0.0650660i | ||||
\(718\) | 398.005 | + | 398.005i | 0.554324 | + | 0.554324i | ||||
\(719\) | − | 100.914i | − | 0.140354i | −0.997535 | − | 0.0701769i | \(-0.977644\pi\) | ||
0.997535 | − | 0.0701769i | \(-0.0223564\pi\) | |||||||
\(720\) | 119.672 | − | 19.4574i | 0.166212 | − | 0.0270241i | ||||
\(721\) | −1075.09 | −1.49111 | ||||||||
\(722\) | −239.075 | + | 239.075i | −0.331129 | + | 0.331129i | ||||
\(723\) | −230.132 | − | 230.132i | −0.318302 | − | 0.318302i | ||||
\(724\) | − | 210.770i | − | 0.291119i | ||||||
\(725\) | 326.309 | + | 976.955i | 0.450081 | + | 1.34752i | ||||
\(726\) | 242.541 | 0.334078 | ||||||||
\(727\) | −141.746 | + | 141.746i | −0.194974 | + | 0.194974i | −0.797842 | − | 0.602867i | \(-0.794025\pi\) |
0.602867 | + | 0.797842i | \(0.294025\pi\) | |||||||
\(728\) | 312.210 | + | 312.210i | 0.428860 | + | 0.428860i | ||||
\(729\) | − | 335.747i | − | 0.460558i | ||||||
\(730\) | 118.306 | + | 727.641i | 0.162063 | + | 0.996768i | ||||
\(731\) | 826.046 | 1.13002 | ||||||||
\(732\) | 118.704 | − | 118.704i | 0.162164 | − | 0.162164i | ||||
\(733\) | 88.5143 | + | 88.5143i | 0.120756 | + | 0.120756i | 0.764902 | − | 0.644146i | \(-0.222787\pi\) |
−0.644146 | + | 0.764902i | \(0.722787\pi\) | |||||||
\(734\) | 715.090i | 0.974238i | ||||||||
\(735\) | −71.9013 | − | 51.7904i | −0.0978249 | − | 0.0704632i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −47.5764 | + | 47.5764i | −0.0645542 | + | 0.0645542i | ||||
\(738\) | −269.317 | − | 269.317i | −0.364928 | − | 0.364928i | ||||
\(739\) | − | 408.910i | − | 0.553329i | −0.960967 | − | 0.276665i | \(-0.910771\pi\) | ||
0.960967 | − | 0.276665i | \(-0.0892291\pi\) | |||||||
\(740\) | −95.7589 | + | 132.943i | −0.129404 | + | 0.179653i | ||||
\(741\) | −383.532 | −0.517588 | ||||||||
\(742\) | 322.985 | − | 322.985i | 0.435290 | − | 0.435290i | ||||
\(743\) | 579.264 | + | 579.264i | 0.779629 | + | 0.779629i | 0.979768 | − | 0.200139i | \(-0.0641394\pi\) |
−0.200139 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(744\) | 175.568i | 0.235979i | ||||||||
\(745\) | 347.499 | − | 56.4993i | 0.466442 | − | 0.0758380i | ||||
\(746\) | −252.246 | −0.338131 | ||||||||
\(747\) | −298.735 | + | 298.735i | −0.399913 | + | 0.399913i | ||||
\(748\) | −182.140 | − | 182.140i | −0.243502 | − | 0.243502i | ||||
\(749\) | − | 1429.19i | − | 1.90813i | ||||||
\(750\) | −140.866 | − | 268.259i | −0.187821 | − | 0.357679i | ||||
\(751\) | −833.492 | −1.10984 | −0.554921 | − | 0.831903i | \(-0.687252\pi\) | ||||
−0.554921 | + | 0.831903i | \(0.687252\pi\) | |||||||
\(752\) | 43.9344 | − | 43.9344i | 0.0584234 | − | 0.0584234i | ||||
\(753\) | 207.932 | + | 207.932i | 0.276138 | + | 0.276138i | ||||
\(754\) | − | 1180.76i | − | 1.56599i | ||||||
\(755\) | 2.02354 | + | 12.4458i | 0.00268018 | + | 0.0164844i | ||||
\(756\) | 397.743 | 0.526115 | ||||||||
\(757\) | 383.684 | − | 383.684i | 0.506847 | − | 0.506847i | −0.406710 | − | 0.913557i | \(-0.633324\pi\) |
0.913557 | + | 0.406710i | \(0.133324\pi\) | |||||||
\(758\) | −551.551 | − | 551.551i | −0.727640 | − | 0.727640i | ||||
\(759\) | 37.6157i | 0.0495596i | ||||||||
\(760\) | −126.709 | − | 91.2682i | −0.166722 | − | 0.120090i | ||||
\(761\) | −870.019 | −1.14326 | −0.571629 | − | 0.820512i | \(-0.693688\pi\) | ||||
−0.571629 | + | 0.820512i | \(0.693688\pi\) | |||||||
\(762\) | −402.801 | + | 402.801i | −0.528610 | + | 0.528610i | ||||
\(763\) | 9.65791 | + | 9.65791i | 0.0126578 | + | 0.0126578i | ||||
\(764\) | − | 527.564i | − | 0.690528i | ||||||
\(765\) | 498.601 | − | 692.214i | 0.651767 | − | 0.904855i | ||||
\(766\) | 700.330 | 0.914270 | ||||||||
\(767\) | 10.1884 | − | 10.1884i | 0.0132834 | − | 0.0132834i | ||||
\(768\) | 19.3917 | + | 19.3917i | 0.0252496 | + | 0.0252496i | ||||
\(769\) | 763.597i | 0.992973i | 0.868044 | + | 0.496487i | \(0.165377\pi\) | ||||
−0.868044 | + | 0.496487i | \(0.834623\pi\) | |||||||
\(770\) | 246.029 | − | 40.0015i | 0.319518 | − | 0.0519499i | ||||
\(771\) | −662.294 | −0.859006 | ||||||||
\(772\) | 81.4144 | − | 81.4144i | 0.105459 | − | 0.105459i | ||||
\(773\) | −682.434 | − | 682.434i | −0.882838 | − | 0.882838i | 0.110984 | − | 0.993822i | \(-0.464600\pi\) |
−0.993822 | + | 0.110984i | \(0.964600\pi\) | |||||||
\(774\) | − | 251.625i | − | 0.325097i | ||||||
\(775\) | −858.743 | + | 286.825i | −1.10806 | + | 0.370097i | ||||
\(776\) | −81.7820 | −0.105389 | ||||||||
\(777\) | −152.964 | + | 152.964i | −0.196865 | + | 0.196865i | ||||
\(778\) | −386.345 | − | 386.345i | −0.496587 | − | 0.496587i | ||||
\(779\) | 490.547i | 0.629713i | ||||||||
\(780\) | 55.7416 | + | 342.839i | 0.0714637 | + | 0.439537i | ||||
\(781\) | 449.648 | 0.575734 | ||||||||
\(782\) | −134.977 | + | 134.977i | −0.172605 | + | 0.172605i | ||||
\(783\) | −752.117 | − | 752.117i | −0.960558 | − | 0.960558i | ||||
\(784\) | 41.3590i | 0.0527538i | ||||||||
\(785\) | −1243.95 | − | 896.019i | −1.58466 | − | 1.14143i | ||||
\(786\) | −387.719 | −0.493281 | ||||||||
\(787\) | 715.957 | − | 715.957i | 0.909729 | − | 0.909729i | −0.0865212 | − | 0.996250i | \(-0.527575\pi\) |
0.996250 | + | 0.0865212i | \(0.0275750\pi\) | |||||||
\(788\) | 233.215 | + | 233.215i | 0.295958 | + | 0.295958i | ||||
\(789\) | − | 202.697i | − | 0.256903i | ||||||
\(790\) | −390.699 | + | 542.413i | −0.494556 | + | 0.686598i | ||||
\(791\) | 148.330 | 0.187522 | ||||||||
\(792\) | −55.4822 | + | 55.4822i | −0.0700533 | + | 0.0700533i | ||||
\(793\) | −701.729 | − | 701.729i | −0.884904 | − | 0.884904i | ||||
\(794\) | 417.174i | 0.525409i | ||||||||
\(795\) | 354.671 | − | 57.6653i | 0.446127 | − | 0.0725350i | ||||
\(796\) | 13.0834 | 0.0164364 | ||||||||
\(797\) | 114.511 | − | 114.511i | 0.143677 | − | 0.143677i | −0.631609 | − | 0.775287i | \(-0.717605\pi\) |
0.775287 | + | 0.631609i | \(0.217605\pi\) | |||||||
\(798\) | −145.791 | − | 145.791i | −0.182695 | − | 0.182695i | ||||
\(799\) | − | 437.175i | − | 0.547152i | ||||||
\(800\) | −63.1689 | + | 126.529i | −0.0789612 | + | 0.158162i | ||||
\(801\) | −682.506 | −0.852067 | ||||||||
\(802\) | 549.142 | − | 549.142i | 0.684716 | − | 0.684716i | ||||
\(803\) | −337.347 | − | 337.347i | −0.420108 | − | 0.420108i | ||||
\(804\) | − | 50.4028i | − | 0.0626900i | ||||||
\(805\) | −29.6436 | − | 182.323i | −0.0368243 | − | 0.226488i | ||||
\(806\) | 1037.88 | 1.28770 | ||||||||
\(807\) | −289.617 | + | 289.617i | −0.358881 | + | 0.358881i | ||||
\(808\) | −265.349 | − | 265.349i | −0.328402 | − | 0.328402i | ||||
\(809\) | 612.311i | 0.756874i | 0.925627 | + | 0.378437i | \(0.123538\pi\) | ||||
−0.925627 | + | 0.378437i | \(0.876462\pi\) | |||||||
\(810\) | −59.1546 | − | 42.6090i | −0.0730303 | − | 0.0526037i | ||||
\(811\) | −1080.99 | −1.33291 | −0.666455 | − | 0.745545i | \(-0.732189\pi\) | ||||
−0.666455 | + | 0.745545i | \(0.732189\pi\) | |||||||
\(812\) | 448.837 | − | 448.837i | 0.552755 | − | 0.552755i | ||||
\(813\) | 230.228 | + | 230.228i | 0.283184 | + | 0.283184i | ||||
\(814\) | − | 106.030i | − | 0.130258i | ||||||
\(815\) | −676.258 | + | 938.857i | −0.829765 | + | 1.15197i | ||||
\(816\) | 192.960 | 0.236470 | ||||||||
\(817\) | −229.161 | + | 229.161i | −0.280490 | + | 0.280490i | ||||
\(818\) | 622.797 | + | 622.797i | 0.761366 | + | 0.761366i | ||||
\(819\) | − | 946.340i | − | 1.15548i | ||||||
\(820\) | 438.499 | − | 71.2948i | 0.534755 | − | 0.0869449i | ||||
\(821\) | 542.078 | 0.660266 | 0.330133 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330133 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(822\) | −195.977 | + | 195.977i | −0.238415 | + | 0.238415i | ||||
\(823\) | 353.910 | + | 353.910i | 0.430024 | + | 0.430024i | 0.888637 | − | 0.458612i | \(-0.151653\pi\) |
−0.458612 | + | 0.888637i | \(0.651653\pi\) | |||||||
\(824\) | 394.745i | 0.479059i | ||||||||
\(825\) | 175.437 | + | 87.5859i | 0.212651 | + | 0.106165i | ||||
\(826\) | 7.74573 | 0.00937740 | ||||||||
\(827\) | −137.486 | + | 137.486i | −0.166247 | + | 0.166247i | −0.785327 | − | 0.619081i | \(-0.787505\pi\) |
0.619081 | + | 0.785327i | \(0.287505\pi\) | |||||||
\(828\) | 41.1158 | + | 41.1158i | 0.0496568 | + | 0.0496568i | ||||
\(829\) | − | 1219.64i | − | 1.47122i | −0.677403 | − | 0.735612i | \(-0.736895\pi\) | ||
0.677403 | − | 0.735612i | \(-0.263105\pi\) | |||||||
\(830\) | −79.0825 | − | 486.397i | −0.0952801 | − | 0.586020i | ||||
\(831\) | −31.0280 | −0.0373381 | ||||||||
\(832\) | 114.636 | − | 114.636i | 0.137783 | − | 0.137783i | ||||
\(833\) | 205.774 | + | 205.774i | 0.247028 | + | 0.247028i | ||||
\(834\) | 538.406i | 0.645571i | ||||||||
\(835\) | −495.926 | − | 357.215i | −0.593923 | − | 0.427802i | ||||
\(836\) | 101.058 | 0.120883 | ||||||||
\(837\) | 661.111 | − | 661.111i | 0.789858 | − | 0.789858i | ||||
\(838\) | 217.540 | + | 217.540i | 0.259594 | + | 0.259594i | ||||
\(839\) | − | 1047.03i | − | 1.24795i | −0.781442 | − | 0.623977i | \(-0.785516\pi\) | ||
0.781442 | − | 0.623977i | \(-0.214484\pi\) | |||||||
\(840\) | −109.133 | + | 151.511i | −0.129921 | + | 0.180370i | ||||
\(841\) | −856.469 | −1.01839 | ||||||||
\(842\) | 172.844 | − | 172.844i | 0.205278 | − | 0.205278i | ||||
\(843\) | −44.8243 | − | 44.8243i | −0.0531723 | − | 0.0531723i | ||||
\(844\) | − | 126.654i | − | 0.150064i | ||||||
\(845\) | 1192.67 | − | 193.914i | 1.41144 | − | 0.229484i | ||||
\(846\) | −133.169 | −0.157411 | ||||||||
\(847\) | 545.024 | − | 545.024i | 0.643476 | − | 0.643476i | ||||
\(848\) | −118.592 | − | 118.592i | −0.139849 | − | 0.139849i | ||||
\(849\) | − | 315.540i | − | 0.371660i | ||||||
\(850\) | 315.238 | + | 943.808i | 0.370868 | + | 1.11036i | ||||
\(851\) | −78.5750 | −0.0923326 | ||||||||
\(852\) | −238.180 | + | 238.180i | −0.279554 | + | 0.279554i | ||||
\(853\) | 692.971 | + | 692.971i | 0.812393 | + | 0.812393i | 0.984992 | − | 0.172599i | \(-0.0552165\pi\) |
−0.172599 | + | 0.984992i | \(0.555216\pi\) | |||||||
\(854\) | − | 533.492i | − | 0.624697i | ||||||
\(855\) | 53.7118 | + | 330.355i | 0.0628209 | + | 0.386380i | ||||
\(856\) | −524.762 | −0.613039 | ||||||||
\(857\) | 494.859 | − | 494.859i | 0.577432 | − | 0.577432i | −0.356763 | − | 0.934195i | \(-0.616120\pi\) |
0.934195 | + | 0.356763i | \(0.116120\pi\) | |||||||
\(858\) | −158.946 | − | 158.946i | −0.185252 | − | 0.185252i | ||||
\(859\) | − | 67.9105i | − | 0.0790576i | −0.999218 | − | 0.0395288i | \(-0.987414\pi\) | ||
0.999218 | − | 0.0395288i | \(-0.0125857\pi\) | |||||||
\(860\) | 238.152 | + | 171.541i | 0.276921 | + | 0.199466i | ||||
\(861\) | 586.568 | 0.681264 | ||||||||
\(862\) | 23.1272 | − | 23.1272i | 0.0268297 | − | 0.0268297i | ||||
\(863\) | −172.718 | − | 172.718i | −0.200137 | − | 0.200137i | 0.599922 | − | 0.800059i | \(-0.295198\pi\) |
−0.800059 | + | 0.599922i | \(0.795198\pi\) | |||||||
\(864\) | − | 146.041i | − | 0.169029i | ||||||
\(865\) | −956.934 | + | 1328.52i | −1.10628 | + | 1.53586i | ||||
\(866\) | 802.947 | 0.927190 | ||||||||
\(867\) | 609.772 | − | 609.772i | 0.703313 | − | 0.703313i | ||||
\(868\) | 394.528 | + | 394.528i | 0.454525 | + | 0.454525i | ||||
\(869\) | − | 432.607i | − | 0.497822i | ||||||
\(870\) | 492.869 | − | 80.1348i | 0.566516 | − | 0.0921090i | ||||
\(871\) | −297.960 | −0.342089 | ||||||||
\(872\) | 3.54613 | − | 3.54613i | 0.00406667 | − | 0.00406667i | ||||
\(873\) | 123.945 | + | 123.945i | 0.141975 | + | 0.141975i | ||||
\(874\) | − | 74.8902i | − | 0.0856867i | ||||||
\(875\) | −919.365 | − | 286.272i | −1.05070 | − | 0.327168i | ||||
\(876\) | 357.387 | 0.407977 | ||||||||
\(877\) | −488.190 | + | 488.190i | −0.556659 | + | 0.556659i | −0.928355 | − | 0.371696i | \(-0.878776\pi\) |
0.371696 | + | 0.928355i | \(0.378776\pi\) | |||||||
\(878\) | −437.828 | − | 437.828i | −0.498666 | − | 0.498666i | ||||
\(879\) | − | 215.089i | − | 0.244698i | ||||||
\(880\) | −14.6875 | − | 90.3355i | −0.0166903 | − | 0.102654i | ||||
\(881\) | 166.359 | 0.188829 | 0.0944146 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944146 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(882\) | 62.6816 | − | 62.6816i | 0.0710676 | − | 0.0710676i | ||||
\(883\) | 289.480 | + | 289.480i | 0.327837 | + | 0.327837i | 0.851763 | − | 0.523927i | \(-0.175533\pi\) |
−0.523927 | + | 0.851763i | \(0.675533\pi\) | |||||||
\(884\) | − | 1140.70i | − | 1.29038i | ||||||
\(885\) | 4.94426 | + | 3.56135i | 0.00558673 | + | 0.00402412i | ||||
\(886\) | −50.6212 | −0.0571345 | ||||||||
\(887\) | 463.997 | − | 463.997i | 0.523108 | − | 0.523108i | −0.395400 | − | 0.918509i | \(-0.629394\pi\) |
0.918509 | + | 0.395400i | \(0.129394\pi\) | |||||||
\(888\) | 56.1645 | + | 56.1645i | 0.0632483 | + | 0.0632483i | ||||
\(889\) | 1810.30i | 2.03634i | ||||||||
\(890\) | 465.285 | − | 645.961i | 0.522793 | − | 0.725799i | ||||
\(891\) | 47.1793 | 0.0529510 | ||||||||
\(892\) | −347.073 | + | 347.073i | −0.389095 | + | 0.389095i | ||||
\(893\) | 121.280 | + | 121.280i | 0.135812 | + | 0.135812i | ||||
\(894\) | − | 170.677i | − | 0.190914i | ||||||
\(895\) | −822.644 | + | 133.752i | −0.919156 | + | 0.149444i | ||||
\(896\) | 87.1521 | 0.0972680 | ||||||||
\(897\) | −117.789 | + | 117.789i | −0.131314 | + | 0.131314i | ||||
\(898\) | 856.476 | + | 856.476i | 0.953759 | + | 0.953759i | ||||
\(899\) | − | 1492.07i | − | 1.65970i | ||||||
\(900\) | 287.497 | − | 96.0259i | 0.319441 | − | 0.106695i | ||||
\(901\) | −1180.06 | −1.30972 | ||||||||
\(902\) | −203.296 | + | 203.296i | −0.225383 | + | 0.225383i | ||||
\(903\) | 274.017 | + | 274.017i | 0.303452 | + | 0.303452i | ||||
\(904\) | − | 54.4630i | − | 0.0602466i | ||||||
\(905\) | −84.5614 | − | 520.095i | −0.0934380 | − | 0.574691i | ||||
\(906\) | 6.11284 | 0.00674707 | ||||||||
\(907\) | −1048.61 | + | 1048.61i | −1.15613 | + | 1.15613i | −0.170829 | + | 0.985301i | \(0.554645\pi\) |
−0.985301 | + | 0.170829i | \(0.945355\pi\) | |||||||
\(908\) | 285.649 | + | 285.649i | 0.314591 | + | 0.314591i | ||||
\(909\) | 804.298i | 0.884816i | ||||||||
\(910\) | 895.669 | + | 645.150i | 0.984252 | + | 0.708956i | ||||
\(911\) | −621.762 | −0.682505 | −0.341252 | − | 0.939972i | \(-0.610851\pi\) | ||||
−0.341252 | + | 0.939972i | \(0.610851\pi\) | |||||||
\(912\) | −53.5307 | + | 53.5307i | −0.0586959 | + | 0.0586959i | ||||
\(913\) | 225.502 | + | 225.502i | 0.246990 | + | 0.246990i | ||||
\(914\) | − | 507.822i | − | 0.555604i | ||||||
\(915\) | 245.290 | − | 340.539i | 0.268076 | − | 0.372173i | ||||
\(916\) | −432.007 | −0.471624 | ||||||||
\(917\) | −871.262 | + | 871.262i | −0.950122 | + | 0.950122i | ||||
\(918\) | −726.599 | − | 726.599i | −0.791503 | − | 0.791503i | ||||
\(919\) | 766.157i | 0.833686i | 0.908978 | + | 0.416843i | \(0.136864\pi\) | ||||
−0.908978 | + | 0.416843i | \(0.863136\pi\) | |||||||
\(920\) | −66.9442 | + | 10.8844i | −0.0727655 | + | 0.0118308i | ||||
\(921\) | −937.213 | −1.01760 | ||||||||
\(922\) | 316.325 | − | 316.325i | 0.343086 | − | 0.343086i | ||||
\(923\) | 1408.02 | + | 1408.02i | 1.52548 | + | 1.52548i | ||||
\(924\) | − | 120.839i | − | 0.130779i | ||||||
\(925\) | −182.957 | + | 366.469i | −0.197791 | + | 0.396183i | ||||
\(926\) | 746.301 | 0.805940 | ||||||||
\(927\) | 598.255 | − | 598.255i | 0.645367 | − | 0.645367i | ||||
\(928\) | −164.801 | − | 164.801i | −0.177588 | − | 0.177588i | ||||
\(929\) | 854.661i | 0.919980i | 0.887924 | + | 0.459990i | \(0.152147\pi\) | ||||
−0.887924 | + | 0.459990i | \(0.847853\pi\) | |||||||
\(930\) | 70.4385 | + | 433.232i | 0.0757403 | + | 0.465841i | ||||
\(931\) | −114.171 | −0.122633 | ||||||||
\(932\) | −191.128 | + | 191.128i | −0.205073 | + | 0.205073i | ||||
\(933\) | 284.808 | + | 284.808i | 0.305261 | + | 0.305261i | ||||
\(934\) | 1276.71i | 1.36693i | ||||||||
\(935\) | −522.522 | − | 376.372i | −0.558847 | − | 0.402537i | ||||
\(936\) | −347.472 | −0.371230 | ||||||||
\(937\) | −1054.10 | + | 1054.10i | −1.12497 | + | 1.12497i | −0.133988 | + | 0.990983i | \(0.542778\pi\) |
−0.990983 | + | 0.133988i | \(0.957222\pi\) | |||||||
\(938\) | −113.262 | − | 113.262i | −0.120749 | − | 0.120749i | ||||
\(939\) | 49.8807i | 0.0531211i | ||||||||
\(940\) | 90.7858 | − | 126.039i | 0.0965806 | − | 0.134084i | ||||
\(941\) | −333.543 | −0.354456 | −0.177228 | − | 0.984170i | \(-0.556713\pi\) | ||||
−0.177228 | + | 0.984170i | \(0.556713\pi\) | |||||||
\(942\) | −525.534 | + | 525.534i | −0.557891 | + | 0.557891i | ||||
\(943\) | 150.655 | + | 150.655i | 0.159761 | + | 0.159761i | ||||
\(944\) | − | 2.84403i | − | 0.00301275i | ||||||
\(945\) | 981.470 | − | 159.576i | 1.03859 | − | 0.168863i | ||||
\(946\) | −189.941 | −0.200783 | ||||||||
\(947\) | −1143.97 | + | 1143.97i | −1.20799 | + | 1.20799i | −0.236312 | + | 0.971677i | \(0.575939\pi\) |
−0.971677 | + | 0.236312i | \(0.924061\pi\) | |||||||
\(948\) | 229.153 | + | 229.153i | 0.241723 | + | 0.241723i | ||||
\(949\) | − | 2112.72i | − | 2.22626i | ||||||
\(950\) | −349.283 | − | 174.377i | −0.367666 | − | 0.183555i | ||||
\(951\) | −4.99314 | −0.00525041 | ||||||||
\(952\) | 433.609 | − | 433.609i | 0.455472 | − | 0.455472i | ||||
\(953\) | 714.632 | + | 714.632i | 0.749877 | + | 0.749877i | 0.974456 | − | 0.224579i | \(-0.0721008\pi\) |
−0.224579 | + | 0.974456i | \(0.572101\pi\) | |||||||
\(954\) | 359.463i | 0.376796i | ||||||||
\(955\) | −211.660 | − | 1301.81i | −0.221633 | − | 1.36316i | ||||
\(956\) | 76.9851 | 0.0805283 | ||||||||
\(957\) | −228.503 | + | 228.503i | −0.238770 | + | 0.238770i | ||||
\(958\) | −664.201 | − | 664.201i | −0.693320 | − | 0.693320i | ||||
\(959\) | 880.778i | 0.918434i | ||||||||
\(960\) | 55.6310 | + | 40.0710i | 0.0579489 | + | 0.0417406i | ||||
\(961\) | 350.533 | 0.364758 | ||||||||
\(962\) | 332.021 | − | 332.021i | 0.345136 | − | 0.345136i | ||||
\(963\) | 795.302 | + | 795.302i | 0.825859 | + | 0.825859i | ||||
\(964\) | 379.761i | 0.393943i | ||||||||
\(965\) | 168.234 | − | 233.562i | 0.174336 | − | 0.242033i | ||||
\(966\) | −89.5495 | −0.0927014 | ||||||||
\(967\) | −623.196 | + | 623.196i | −0.644464 | + | 0.644464i | −0.951650 | − | 0.307186i | \(-0.900613\pi\) |
0.307186 | + | 0.951650i | \(0.400613\pi\) | |||||||
\(968\) | −200.119 | − | 200.119i | −0.206734 | − | 0.206734i | ||||
\(969\) | 532.664i | 0.549704i | ||||||||
\(970\) | −201.805 | + | 32.8112i | −0.208046 | + | 0.0338259i | ||||
\(971\) | 795.980 | 0.819753 | 0.409877 | − | 0.912141i | \(-0.365572\pi\) | ||||
0.409877 | + | 0.912141i | \(0.365572\pi\) | |||||||
\(972\) | −353.583 | + | 353.583i | −0.363769 | + | 0.363769i | ||||
\(973\) | 1209.88 | + | 1209.88i | 1.24345 | + | 1.24345i | ||||
\(974\) | 594.195i | 0.610057i | ||||||||
\(975\) | 275.096 | + | 823.625i | 0.282150 | + | 0.844743i | ||||
\(976\) | −195.884 | −0.200701 | ||||||||
\(977\) | −1167.31 | + | 1167.31i | −1.19479 | + | 1.19479i | −0.219088 | + | 0.975705i | \(0.570308\pi\) |
−0.975705 | + | 0.219088i | \(0.929692\pi\) | |||||||
\(978\) | 396.639 | + | 396.639i | 0.405562 | + | 0.405562i | ||||
\(979\) | 515.193i | 0.526245i | ||||||||
\(980\) | 16.5933 | + | 102.057i | 0.0169320 | + | 0.104140i | ||||
\(981\) | −10.7487 | −0.0109569 | ||||||||
\(982\) | −707.506 | + | 707.506i | −0.720475 | + | 0.720475i | ||||
\(983\) | −192.953 | − | 192.953i | −0.196290 | − | 0.196290i | 0.602118 | − | 0.798407i | \(-0.294324\pi\) |
−0.798407 | + | 0.602118i | \(0.794324\pi\) | |||||||
\(984\) | − | 215.373i | − | 0.218875i | ||||||
\(985\) | 669.047 | + | 481.914i | 0.679236 | + | 0.489253i | ||||
\(986\) | −1639.88 | −1.66316 | ||||||||
\(987\) | 145.020 | − | 145.020i | 0.146930 | − | 0.146930i | ||||
\(988\) | 316.450 | + | 316.450i | 0.320294 | + | 0.320294i | ||||
\(989\) | 140.758i | 0.142324i | ||||||||
\(990\) | −114.648 | + | 159.167i | −0.115806 | + | 0.160775i | ||||
\(991\) | 1151.44 | 1.16190 | 0.580948 | − | 0.813940i | \(-0.302682\pi\) | ||||
0.580948 | + | 0.813940i | \(0.302682\pi\) | |||||||
\(992\) | 144.860 | − | 144.860i | 0.146029 | − | 0.146029i | ||||
\(993\) | 4.84742 | + | 4.84742i | 0.00488159 | + | 0.00488159i | ||||
\(994\) | 1070.45i | 1.07691i | ||||||||
\(995\) | 32.2845 | − | 5.24908i | 0.0324467 | − | 0.00527546i | ||||
\(996\) | −238.898 | −0.239858 | ||||||||
\(997\) | 1216.07 | − | 1216.07i | 1.21973 | − | 1.21973i | 0.252003 | − | 0.967726i | \(-0.418911\pi\) |
0.967726 | − | 0.252003i | \(-0.0810892\pi\) | |||||||
\(998\) | −626.773 | − | 626.773i | −0.628029 | − | 0.628029i | ||||
\(999\) | − | 422.981i | − | 0.423404i |
(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.a.93.7 | yes | 20 | |
5.2 | odd | 4 | inner | 230.3.f.a.47.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.a.47.7 | ✓ | 20 | 5.2 | odd | 4 | inner | |
230.3.f.a.93.7 | yes | 20 | 1.1 | even | 1 | trivial |