Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,3,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(0.408720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.13 |
Dual form | 15.3.f.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22474 | + | 2.22474i | −1.11237 | + | 1.11237i | −0.119543 | + | 0.992829i | \(0.538143\pi\) |
−0.992829 | + | 0.119543i | \(0.961857\pi\) | |||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 5.89898i | − | 1.47474i | ||||||
\(5\) | 2.67423 | − | 4.22474i | 0.534847 | − | 0.844949i | ||||
\(6\) | −5.44949 | −0.908248 | ||||||||
\(7\) | −1.44949 | + | 1.44949i | −0.207070 | + | 0.207070i | −0.803021 | − | 0.595951i | \(-0.796775\pi\) |
0.595951 | + | 0.803021i | \(0.296775\pi\) | |||||||
\(8\) | 4.22474 | + | 4.22474i | 0.528093 | + | 0.528093i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 3.44949 | + | 15.3485i | 0.344949 | + | 1.53485i | ||||
\(11\) | −3.34847 | −0.304406 | −0.152203 | − | 0.988349i | \(-0.548637\pi\) | ||||
−0.152203 | + | 0.988349i | \(0.548637\pi\) | |||||||
\(12\) | 7.22474 | − | 7.22474i | 0.602062 | − | 0.602062i | ||||
\(13\) | −10.4495 | − | 10.4495i | −0.803807 | − | 0.803807i | 0.179881 | − | 0.983688i | \(-0.442429\pi\) |
−0.983688 | + | 0.179881i | \(0.942429\pi\) | |||||||
\(14\) | − | 6.44949i | − | 0.460678i | ||||||
\(15\) | 8.44949 | − | 1.89898i | 0.563299 | − | 0.126599i | ||||
\(16\) | 4.79796 | 0.299872 | ||||||||
\(17\) | −2.65153 | + | 2.65153i | −0.155972 | + | 0.155972i | −0.780779 | − | 0.624807i | \(-0.785178\pi\) |
0.624807 | + | 0.780779i | \(0.285178\pi\) | |||||||
\(18\) | −6.67423 | − | 6.67423i | −0.370791 | − | 0.370791i | ||||
\(19\) | 20.6969i | 1.08931i | 0.838659 | + | 0.544656i | \(0.183340\pi\) | ||||
−0.838659 | + | 0.544656i | \(0.816660\pi\) | |||||||
\(20\) | −24.9217 | − | 15.7753i | −1.24608 | − | 0.788763i | ||||
\(21\) | −3.55051 | −0.169072 | ||||||||
\(22\) | 7.44949 | − | 7.44949i | 0.338613 | − | 0.338613i | ||||
\(23\) | 16.4495 | + | 16.4495i | 0.715195 | + | 0.715195i | 0.967617 | − | 0.252422i | \(-0.0812271\pi\) |
−0.252422 | + | 0.967617i | \(0.581227\pi\) | |||||||
\(24\) | 10.3485i | 0.431186i | ||||||||
\(25\) | −10.6969 | − | 22.5959i | −0.427878 | − | 0.903837i | ||||
\(26\) | 46.4949 | 1.78827 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 8.55051 | + | 8.55051i | 0.305375 | + | 0.305375i | ||||
\(29\) | − | 0.853572i | − | 0.0294335i | −0.999892 | − | 0.0147168i | \(-0.995315\pi\) | ||
0.999892 | − | 0.0147168i | \(-0.00468466\pi\) | |||||||
\(30\) | −14.5732 | + | 23.0227i | −0.485774 | + | 0.767423i | ||||
\(31\) | −18.6969 | −0.603127 | −0.301564 | − | 0.953446i | \(-0.597509\pi\) | ||||
−0.301564 | + | 0.953446i | \(0.597509\pi\) | |||||||
\(32\) | −27.5732 | + | 27.5732i | −0.861663 | + | 0.861663i | ||||
\(33\) | −4.10102 | − | 4.10102i | −0.124273 | − | 0.124273i | ||||
\(34\) | − | 11.7980i | − | 0.346999i | ||||||
\(35\) | 2.24745 | + | 10.0000i | 0.0642128 | + | 0.285714i | ||||
\(36\) | 17.6969 | 0.491582 | ||||||||
\(37\) | 38.0454 | − | 38.0454i | 1.02825 | − | 1.02825i | 0.0286652 | − | 0.999589i | \(-0.490874\pi\) |
0.999589 | − | 0.0286652i | \(-0.00912566\pi\) | |||||||
\(38\) | −46.0454 | − | 46.0454i | −1.21172 | − | 1.21172i | ||||
\(39\) | − | 25.5959i | − | 0.656306i | ||||||
\(40\) | 29.1464 | − | 6.55051i | 0.728661 | − | 0.163763i | ||||
\(41\) | −28.6969 | −0.699925 | −0.349963 | − | 0.936764i | \(-0.613806\pi\) | ||||
−0.349963 | + | 0.936764i | \(0.613806\pi\) | |||||||
\(42\) | 7.89898 | − | 7.89898i | 0.188071 | − | 0.188071i | ||||
\(43\) | 22.4949 | + | 22.4949i | 0.523137 | + | 0.523137i | 0.918517 | − | 0.395380i | \(-0.129387\pi\) |
−0.395380 | + | 0.918517i | \(0.629387\pi\) | |||||||
\(44\) | 19.7526i | 0.448922i | ||||||||
\(45\) | 12.6742 | + | 8.02270i | 0.281650 | + | 0.178282i | ||||
\(46\) | −73.1918 | −1.59113 | ||||||||
\(47\) | 19.7526 | − | 19.7526i | 0.420267 | − | 0.420267i | −0.465029 | − | 0.885296i | \(-0.653956\pi\) |
0.885296 | + | 0.465029i | \(0.153956\pi\) | |||||||
\(48\) | 5.87628 | + | 5.87628i | 0.122422 | + | 0.122422i | ||||
\(49\) | 44.7980i | 0.914244i | ||||||||
\(50\) | 74.0681 | + | 26.4722i | 1.48136 | + | 0.529444i | ||||
\(51\) | −6.49490 | −0.127351 | ||||||||
\(52\) | −61.6413 | + | 61.6413i | −1.18541 | + | 1.18541i | ||||
\(53\) | 28.6969 | + | 28.6969i | 0.541452 | + | 0.541452i | 0.923954 | − | 0.382503i | \(-0.124938\pi\) |
−0.382503 | + | 0.923954i | \(0.624938\pi\) | |||||||
\(54\) | − | 16.3485i | − | 0.302749i | ||||||
\(55\) | −8.95459 | + | 14.1464i | −0.162811 | + | 0.257208i | ||||
\(56\) | −12.2474 | −0.218704 | ||||||||
\(57\) | −25.3485 | + | 25.3485i | −0.444710 | + | 0.444710i | ||||
\(58\) | 1.89898 | + | 1.89898i | 0.0327410 | + | 0.0327410i | ||||
\(59\) | − | 111.934i | − | 1.89719i | −0.316493 | − | 0.948595i | \(-0.602505\pi\) | ||
0.316493 | − | 0.948595i | \(-0.397495\pi\) | |||||||
\(60\) | −11.2020 | − | 49.8434i | −0.186701 | − | 0.830723i | ||||
\(61\) | 94.0908 | 1.54247 | 0.771236 | − | 0.636549i | \(-0.219639\pi\) | ||||
0.771236 | + | 0.636549i | \(0.219639\pi\) | |||||||
\(62\) | 41.5959 | − | 41.5959i | 0.670902 | − | 0.670902i | ||||
\(63\) | −4.34847 | − | 4.34847i | −0.0690233 | − | 0.0690233i | ||||
\(64\) | − | 103.495i | − | 1.61711i | ||||||
\(65\) | −72.0908 | + | 16.2020i | −1.10909 | + | 0.249262i | ||||
\(66\) | 18.2474 | 0.276476 | ||||||||
\(67\) | −54.8990 | + | 54.8990i | −0.819388 | + | 0.819388i | −0.986019 | − | 0.166631i | \(-0.946711\pi\) |
0.166631 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(68\) | 15.6413 | + | 15.6413i | 0.230019 | + | 0.230019i | ||||
\(69\) | 40.2929i | 0.583954i | ||||||||
\(70\) | −27.2474 | − | 17.2474i | −0.389249 | − | 0.246392i | ||||
\(71\) | −68.0000 | −0.957746 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(72\) | −12.6742 | + | 12.6742i | −0.176031 | + | 0.176031i | ||||
\(73\) | −39.7878 | − | 39.7878i | −0.545038 | − | 0.545038i | 0.379964 | − | 0.925001i | \(-0.375936\pi\) |
−0.925001 | + | 0.379964i | \(0.875936\pi\) | |||||||
\(74\) | 169.283i | 2.28760i | ||||||||
\(75\) | 14.5732 | − | 40.7753i | 0.194310 | − | 0.543670i | ||||
\(76\) | 122.091 | 1.60646 | ||||||||
\(77\) | 4.85357 | − | 4.85357i | 0.0630334 | − | 0.0630334i | ||||
\(78\) | 56.9444 | + | 56.9444i | 0.730056 | + | 0.730056i | ||||
\(79\) | − | 24.4949i | − | 0.310062i | −0.987910 | − | 0.155031i | \(-0.950452\pi\) | ||
0.987910 | − | 0.155031i | \(-0.0495477\pi\) | |||||||
\(80\) | 12.8309 | − | 20.2702i | 0.160386 | − | 0.253377i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 63.8434 | − | 63.8434i | 0.778578 | − | 0.778578i | ||||
\(83\) | −21.1464 | − | 21.1464i | −0.254776 | − | 0.254776i | 0.568149 | − | 0.822926i | \(-0.307660\pi\) |
−0.822926 | + | 0.568149i | \(0.807660\pi\) | |||||||
\(84\) | 20.9444i | 0.249338i | ||||||||
\(85\) | 4.11123 | + | 18.2929i | 0.0483674 | + | 0.215210i | ||||
\(86\) | −100.091 | −1.16385 | ||||||||
\(87\) | 1.04541 | − | 1.04541i | 0.0120162 | − | 0.0120162i | ||||
\(88\) | −14.1464 | − | 14.1464i | −0.160755 | − | 0.160755i | ||||
\(89\) | 94.1816i | 1.05822i | 0.848553 | + | 0.529110i | \(0.177474\pi\) | ||||
−0.848553 | + | 0.529110i | \(0.822526\pi\) | |||||||
\(90\) | −46.0454 | + | 10.3485i | −0.511616 | + | 0.114983i | ||||
\(91\) | 30.2929 | 0.332889 | ||||||||
\(92\) | 97.0352 | − | 97.0352i | 1.05473 | − | 1.05473i | ||||
\(93\) | −22.8990 | − | 22.8990i | −0.246226 | − | 0.246226i | ||||
\(94\) | 87.8888i | 0.934987i | ||||||||
\(95\) | 87.4393 | + | 55.3485i | 0.920414 | + | 0.582615i | ||||
\(96\) | −67.5403 | −0.703545 | ||||||||
\(97\) | 14.5959 | − | 14.5959i | 0.150473 | − | 0.150473i | −0.627856 | − | 0.778329i | \(-0.716067\pi\) |
0.778329 | + | 0.627856i | \(0.216067\pi\) | |||||||
\(98\) | −99.6640 | − | 99.6640i | −1.01698 | − | 1.01698i | ||||
\(99\) | − | 10.0454i | − | 0.101469i | ||||||
\(100\) | −133.293 | + | 63.1010i | −1.33293 | + | 0.631010i | ||||
\(101\) | 173.621 | 1.71902 | 0.859509 | − | 0.511120i | \(-0.170769\pi\) | ||||
0.859509 | + | 0.511120i | \(0.170769\pi\) | |||||||
\(102\) | 14.4495 | − | 14.4495i | 0.141662 | − | 0.141662i | ||||
\(103\) | −64.7526 | − | 64.7526i | −0.628666 | − | 0.628666i | 0.319067 | − | 0.947732i | \(-0.396631\pi\) |
−0.947732 | + | 0.319067i | \(0.896631\pi\) | |||||||
\(104\) | − | 88.2929i | − | 0.848970i | ||||||
\(105\) | −9.49490 | + | 15.0000i | −0.0904276 | + | 0.142857i | ||||
\(106\) | −127.687 | −1.20459 | ||||||||
\(107\) | −4.74235 | + | 4.74235i | −0.0443210 | + | 0.0443210i | −0.728920 | − | 0.684599i | \(-0.759977\pi\) |
0.684599 | + | 0.728920i | \(0.259977\pi\) | |||||||
\(108\) | 21.6742 | + | 21.6742i | 0.200687 | + | 0.200687i | ||||
\(109\) | − | 39.3031i | − | 0.360579i | −0.983614 | − | 0.180289i | \(-0.942297\pi\) | ||
0.983614 | − | 0.180289i | \(-0.0577034\pi\) | |||||||
\(110\) | −11.5505 | − | 51.3939i | −0.105005 | − | 0.467217i | ||||
\(111\) | 93.1918 | 0.839566 | ||||||||
\(112\) | −6.95459 | + | 6.95459i | −0.0620946 | + | 0.0620946i | ||||
\(113\) | 14.3587 | + | 14.3587i | 0.127068 | + | 0.127068i | 0.767781 | − | 0.640713i | \(-0.221361\pi\) |
−0.640713 | + | 0.767781i | \(0.721361\pi\) | |||||||
\(114\) | − | 112.788i | − | 0.989366i | ||||||
\(115\) | 113.485 | − | 25.5051i | 0.986823 | − | 0.221784i | ||||
\(116\) | −5.03520 | −0.0434069 | ||||||||
\(117\) | 31.3485 | − | 31.3485i | 0.267936 | − | 0.267936i | ||||
\(118\) | 249.025 | + | 249.025i | 2.11038 | + | 2.11038i | ||||
\(119\) | − | 7.68673i | − | 0.0645944i | ||||||
\(120\) | 43.7196 | + | 27.6742i | 0.364330 | + | 0.230619i | ||||
\(121\) | −109.788 | −0.907337 | ||||||||
\(122\) | −209.328 | + | 209.328i | −1.71580 | + | 1.71580i | ||||
\(123\) | −35.1464 | − | 35.1464i | −0.285743 | − | 0.285743i | ||||
\(124\) | 110.293i | 0.889459i | ||||||||
\(125\) | −124.068 | − | 15.2350i | −0.992545 | − | 0.121880i | ||||
\(126\) | 19.3485 | 0.153559 | ||||||||
\(127\) | −114.621 | + | 114.621i | −0.902527 | + | 0.902527i | −0.995654 | − | 0.0931273i | \(-0.970314\pi\) |
0.0931273 | + | 0.995654i | \(0.470314\pi\) | |||||||
\(128\) | 119.957 | + | 119.957i | 0.937163 | + | 0.937163i | ||||
\(129\) | 55.1010i | 0.427140i | ||||||||
\(130\) | 124.338 | − | 196.429i | 0.956448 | − | 1.51099i | ||||
\(131\) | −26.1362 | −0.199513 | −0.0997566 | − | 0.995012i | \(-0.531806\pi\) | ||||
−0.0997566 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(132\) | −24.1918 | + | 24.1918i | −0.183271 | + | 0.183271i | ||||
\(133\) | −30.0000 | − | 30.0000i | −0.225564 | − | 0.225564i | ||||
\(134\) | − | 244.272i | − | 1.82293i | ||||||
\(135\) | 5.69694 | + | 25.3485i | 0.0421995 | + | 0.187766i | ||||
\(136\) | −22.4041 | −0.164736 | ||||||||
\(137\) | 14.6311 | − | 14.6311i | 0.106796 | − | 0.106796i | −0.651689 | − | 0.758486i | \(-0.725939\pi\) |
0.758486 | + | 0.651689i | \(0.225939\pi\) | |||||||
\(138\) | −89.6413 | − | 89.6413i | −0.649575 | − | 0.649575i | ||||
\(139\) | − | 83.1714i | − | 0.598356i | −0.954197 | − | 0.299178i | \(-0.903288\pi\) | ||
0.954197 | − | 0.299178i | \(-0.0967124\pi\) | |||||||
\(140\) | 58.9898 | − | 13.2577i | 0.421356 | − | 0.0946975i | ||||
\(141\) | 48.3837 | 0.343147 | ||||||||
\(142\) | 151.283 | − | 151.283i | 1.06537 | − | 1.06537i | ||||
\(143\) | 34.9898 | + | 34.9898i | 0.244684 | + | 0.244684i | ||||
\(144\) | 14.3939i | 0.0999575i | ||||||||
\(145\) | −3.60612 | − | 2.28265i | −0.0248698 | − | 0.0157424i | ||||
\(146\) | 177.035 | 1.21257 | ||||||||
\(147\) | −54.8661 | + | 54.8661i | −0.373239 | + | 0.373239i | ||||
\(148\) | −224.429 | − | 224.429i | −1.51641 | − | 1.51641i | ||||
\(149\) | − | 119.146i | − | 0.799640i | −0.916594 | − | 0.399820i | \(-0.869073\pi\) | ||
0.916594 | − | 0.399820i | \(-0.130927\pi\) | |||||||
\(150\) | 58.2929 | + | 123.136i | 0.388619 | + | 0.820908i | ||||
\(151\) | −144.969 | −0.960062 | −0.480031 | − | 0.877251i | \(-0.659375\pi\) | ||||
−0.480031 | + | 0.877251i | \(0.659375\pi\) | |||||||
\(152\) | −87.4393 | + | 87.4393i | −0.575258 | + | 0.575258i | ||||
\(153\) | −7.95459 | − | 7.95459i | −0.0519908 | − | 0.0519908i | ||||
\(154\) | 21.5959i | 0.140233i | ||||||||
\(155\) | −50.0000 | + | 78.9898i | −0.322581 | + | 0.509612i | ||||
\(156\) | −150.990 | −0.967883 | ||||||||
\(157\) | 51.1464 | − | 51.1464i | 0.325773 | − | 0.325773i | −0.525203 | − | 0.850977i | \(-0.676011\pi\) |
0.850977 | + | 0.525203i | \(0.176011\pi\) | |||||||
\(158\) | 54.4949 | + | 54.4949i | 0.344904 | + | 0.344904i | ||||
\(159\) | 70.2929i | 0.442093i | ||||||||
\(160\) | 42.7526 | + | 190.227i | 0.267203 | + | 1.18892i | ||||
\(161\) | −47.6867 | −0.296191 | ||||||||
\(162\) | 20.0227 | − | 20.0227i | 0.123597 | − | 0.123597i | ||||
\(163\) | 189.394 | + | 189.394i | 1.16193 | + | 1.16193i | 0.984054 | + | 0.177872i | \(0.0569213\pi\) |
0.177872 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(164\) | 169.283i | 1.03221i | ||||||||
\(165\) | −28.2929 | + | 6.35867i | −0.171472 | + | 0.0385374i | ||||
\(166\) | 94.0908 | 0.566812 | ||||||||
\(167\) | 97.0352 | − | 97.0352i | 0.581049 | − | 0.581049i | −0.354142 | − | 0.935192i | \(-0.615227\pi\) |
0.935192 | + | 0.354142i | \(0.115227\pi\) | |||||||
\(168\) | −15.0000 | − | 15.0000i | −0.0892857 | − | 0.0892857i | ||||
\(169\) | 49.3837i | 0.292211i | ||||||||
\(170\) | −49.8434 | − | 31.5505i | −0.293196 | − | 0.185591i | ||||
\(171\) | −62.0908 | −0.363104 | ||||||||
\(172\) | 132.697 | − | 132.697i | 0.771494 | − | 0.771494i | ||||
\(173\) | −34.6311 | − | 34.6311i | −0.200180 | − | 0.200180i | 0.599897 | − | 0.800077i | \(-0.295208\pi\) |
−0.800077 | + | 0.599897i | \(0.795208\pi\) | |||||||
\(174\) | 4.65153i | 0.0267329i | ||||||||
\(175\) | 48.2577 | + | 17.2474i | 0.275758 | + | 0.0985568i | ||||
\(176\) | −16.0658 | −0.0912831 | ||||||||
\(177\) | 137.091 | − | 137.091i | 0.774524 | − | 0.774524i | ||||
\(178\) | −209.530 | − | 209.530i | −1.17714 | − | 1.17714i | ||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 47.3258 | − | 74.7650i | 0.262921 | − | 0.415361i | ||||
\(181\) | −21.7276 | −0.120042 | −0.0600209 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600209 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(182\) | −67.3939 | + | 67.3939i | −0.370296 | + | 0.370296i | ||||
\(183\) | 115.237 | + | 115.237i | 0.629712 | + | 0.629712i | ||||
\(184\) | 138.990i | 0.755379i | ||||||||
\(185\) | −58.9898 | − | 262.474i | −0.318864 | − | 1.41878i | ||||
\(186\) | 101.889 | 0.547789 | ||||||||
\(187\) | 8.87857 | − | 8.87857i | 0.0474790 | − | 0.0474790i | ||||
\(188\) | −116.520 | − | 116.520i | −0.619787 | − | 0.619787i | ||||
\(189\) | − | 10.6515i | − | 0.0563573i | ||||||
\(190\) | −317.666 | + | 71.3939i | −1.67193 | + | 0.375757i | ||||
\(191\) | −40.0908 | −0.209900 | −0.104950 | − | 0.994478i | \(-0.533468\pi\) | ||||
−0.104950 | + | 0.994478i | \(0.533468\pi\) | |||||||
\(192\) | 126.755 | − | 126.755i | 0.660181 | − | 0.660181i | ||||
\(193\) | 77.5653 | + | 77.5653i | 0.401893 | + | 0.401893i | 0.878900 | − | 0.477007i | \(-0.158278\pi\) |
−0.477007 | + | 0.878900i | \(0.658278\pi\) | |||||||
\(194\) | 64.9444i | 0.334765i | ||||||||
\(195\) | −108.136 | − | 68.4495i | −0.554545 | − | 0.351023i | ||||
\(196\) | 264.262 | 1.34828 | ||||||||
\(197\) | −67.3031 | + | 67.3031i | −0.341640 | + | 0.341640i | −0.856984 | − | 0.515344i | \(-0.827664\pi\) |
0.515344 | + | 0.856984i | \(0.327664\pi\) | |||||||
\(198\) | 22.3485 | + | 22.3485i | 0.112871 | + | 0.112871i | ||||
\(199\) | − | 251.394i | − | 1.26329i | −0.775259 | − | 0.631643i | \(-0.782381\pi\) | ||
0.775259 | − | 0.631643i | \(-0.217619\pi\) | |||||||
\(200\) | 50.2702 | − | 140.654i | 0.251351 | − | 0.703269i | ||||
\(201\) | −134.474 | −0.669027 | ||||||||
\(202\) | −386.262 | + | 386.262i | −1.91219 | + | 1.91219i | ||||
\(203\) | 1.23724 | + | 1.23724i | 0.00609480 | + | 0.00609480i | ||||
\(204\) | 38.3133i | 0.187810i | ||||||||
\(205\) | −76.7423 | + | 121.237i | −0.374353 | + | 0.591401i | ||||
\(206\) | 288.116 | 1.39862 | ||||||||
\(207\) | −49.3485 | + | 49.3485i | −0.238398 | + | 0.238398i | ||||
\(208\) | −50.1362 | − | 50.1362i | −0.241040 | − | 0.241040i | ||||
\(209\) | − | 69.3031i | − | 0.331594i | ||||||
\(210\) | −12.2474 | − | 54.4949i | −0.0583212 | − | 0.259500i | ||||
\(211\) | 264.788 | 1.25492 | 0.627459 | − | 0.778649i | \(-0.284095\pi\) | ||||
0.627459 | + | 0.778649i | \(0.284095\pi\) | |||||||
\(212\) | 169.283 | − | 169.283i | 0.798503 | − | 0.798503i | ||||
\(213\) | −83.2827 | − | 83.2827i | −0.390998 | − | 0.390998i | ||||
\(214\) | − | 21.1010i | − | 0.0986029i | ||||||
\(215\) | 155.192 | − | 34.8786i | 0.721822 | − | 0.162226i | ||||
\(216\) | −31.0454 | −0.143729 | ||||||||
\(217\) | 27.1010 | − | 27.1010i | 0.124889 | − | 0.124889i | ||||
\(218\) | 87.4393 | + | 87.4393i | 0.401098 | + | 0.401098i | ||||
\(219\) | − | 97.4597i | − | 0.445021i | ||||||
\(220\) | 83.4495 | + | 52.8230i | 0.379316 | + | 0.240104i | ||||
\(221\) | 55.4143 | 0.250743 | ||||||||
\(222\) | −207.328 | + | 207.328i | −0.933910 | + | 0.933910i | ||||
\(223\) | −33.4291 | − | 33.4291i | −0.149906 | − | 0.149906i | 0.628170 | − | 0.778076i | \(-0.283804\pi\) |
−0.778076 | + | 0.628170i | \(0.783804\pi\) | |||||||
\(224\) | − | 79.9342i | − | 0.356849i | ||||||
\(225\) | 67.7878 | − | 32.0908i | 0.301279 | − | 0.142626i | ||||
\(226\) | −63.8888 | −0.282694 | ||||||||
\(227\) | −21.1714 | + | 21.1714i | −0.0932662 | + | 0.0932662i | −0.752200 | − | 0.658934i | \(-0.771008\pi\) |
0.658934 | + | 0.752200i | \(0.271008\pi\) | |||||||
\(228\) | 149.530 | + | 149.530i | 0.655834 | + | 0.655834i | ||||
\(229\) | 243.798i | 1.06462i | 0.846550 | + | 0.532310i | \(0.178676\pi\) | ||||
−0.846550 | + | 0.532310i | \(0.821324\pi\) | |||||||
\(230\) | −195.732 | + | 309.217i | −0.851009 | + | 1.34442i | ||||
\(231\) | 11.8888 | 0.0514666 | ||||||||
\(232\) | 3.60612 | − | 3.60612i | 0.0155436 | − | 0.0155436i | ||||
\(233\) | 161.712 | + | 161.712i | 0.694042 | + | 0.694042i | 0.963119 | − | 0.269077i | \(-0.0867186\pi\) |
−0.269077 | + | 0.963119i | \(0.586719\pi\) | |||||||
\(234\) | 139.485i | 0.596088i | ||||||||
\(235\) | −30.6265 | − | 136.272i | −0.130326 | − | 0.579883i | ||||
\(236\) | −660.297 | −2.79787 | ||||||||
\(237\) | 30.0000 | − | 30.0000i | 0.126582 | − | 0.126582i | ||||
\(238\) | 17.1010 | + | 17.1010i | 0.0718530 | + | 0.0718530i | ||||
\(239\) | 326.202i | 1.36486i | 0.730950 | + | 0.682431i | \(0.239077\pi\) | ||||
−0.730950 | + | 0.682431i | \(0.760923\pi\) | |||||||
\(240\) | 40.5403 | − | 9.11123i | 0.168918 | − | 0.0379634i | ||||
\(241\) | −133.576 | −0.554255 | −0.277128 | − | 0.960833i | \(-0.589382\pi\) | ||||
−0.277128 | + | 0.960833i | \(0.589382\pi\) | |||||||
\(242\) | 244.250 | − | 244.250i | 1.00930 | − | 1.00930i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 555.040i | − | 2.27475i | ||||||
\(245\) | 189.260 | + | 119.800i | 0.772490 | + | 0.488981i | ||||
\(246\) | 156.384 | 0.635706 | ||||||||
\(247\) | 216.272 | − | 216.272i | 0.875597 | − | 0.875597i | ||||
\(248\) | −78.9898 | − | 78.9898i | −0.318507 | − | 0.318507i | ||||
\(249\) | − | 51.7980i | − | 0.208024i | ||||||
\(250\) | 309.914 | − | 242.126i | 1.23966 | − | 0.968504i | ||||
\(251\) | −404.742 | −1.61252 | −0.806260 | − | 0.591562i | \(-0.798512\pi\) | ||||
−0.806260 | + | 0.591562i | \(0.798512\pi\) | |||||||
\(252\) | −25.6515 | + | 25.6515i | −0.101792 | + | 0.101792i | ||||
\(253\) | −55.0806 | − | 55.0806i | −0.217710 | − | 0.217710i | ||||
\(254\) | − | 510.005i | − | 2.00789i | ||||||
\(255\) | −17.3689 | + | 27.4393i | −0.0681133 | + | 0.107605i | ||||
\(256\) | −119.767 | −0.467841 | ||||||||
\(257\) | −89.2372 | + | 89.2372i | −0.347227 | + | 0.347227i | −0.859076 | − | 0.511849i | \(-0.828961\pi\) |
0.511849 | + | 0.859076i | \(0.328961\pi\) | |||||||
\(258\) | −122.586 | − | 122.586i | −0.475138 | − | 0.475138i | ||||
\(259\) | 110.293i | 0.425841i | ||||||||
\(260\) | 95.5755 | + | 425.262i | 0.367598 | + | 1.63562i | ||||
\(261\) | 2.56072 | 0.00981117 | ||||||||
\(262\) | 58.1464 | − | 58.1464i | 0.221933 | − | 0.221933i | ||||
\(263\) | −341.843 | − | 341.843i | −1.29978 | − | 1.29978i | −0.928532 | − | 0.371253i | \(-0.878928\pi\) |
−0.371253 | − | 0.928532i | \(-0.621072\pi\) | |||||||
\(264\) | − | 34.6515i | − | 0.131256i | ||||||
\(265\) | 197.980 | − | 44.4949i | 0.747093 | − | 0.167905i | ||||
\(266\) | 133.485 | 0.501822 | ||||||||
\(267\) | −115.348 | + | 115.348i | −0.432017 | + | 0.432017i | ||||
\(268\) | 323.848 | + | 323.848i | 1.20839 | + | 1.20839i | ||||
\(269\) | 3.50052i | 0.0130131i | 0.999979 | + | 0.00650653i | \(0.00207111\pi\) | ||||
−0.999979 | + | 0.00650653i | \(0.997929\pi\) | |||||||
\(270\) | −69.0681 | − | 43.7196i | −0.255808 | − | 0.161925i | ||||
\(271\) | −103.576 | −0.382197 | −0.191099 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191099 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(272\) | −12.7219 | + | 12.7219i | −0.0467718 | + | 0.0467718i | ||||
\(273\) | 37.1010 | + | 37.1010i | 0.135901 | + | 0.135901i | ||||
\(274\) | 65.1010i | 0.237595i | ||||||||
\(275\) | 35.8184 | + | 75.6617i | 0.130249 | + | 0.275134i | ||||
\(276\) | 237.687 | 0.861184 | ||||||||
\(277\) | −285.510 | + | 285.510i | −1.03072 | + | 1.03072i | −0.0312080 | + | 0.999513i | \(0.509935\pi\) |
−0.999513 | + | 0.0312080i | \(0.990065\pi\) | |||||||
\(278\) | 185.035 | + | 185.035i | 0.665594 | + | 0.665594i | ||||
\(279\) | − | 56.0908i | − | 0.201042i | ||||||
\(280\) | −32.7526 | + | 51.7423i | −0.116973 | + | 0.184794i | ||||
\(281\) | 372.697 | 1.32632 | 0.663162 | − | 0.748476i | \(-0.269214\pi\) | ||||
0.663162 | + | 0.748476i | \(0.269214\pi\) | |||||||
\(282\) | −107.641 | + | 107.641i | −0.381707 | + | 0.381707i | ||||
\(283\) | −77.1918 | − | 77.1918i | −0.272763 | − | 0.272763i | 0.557449 | − | 0.830211i | \(-0.311780\pi\) |
−0.830211 | + | 0.557449i | \(0.811780\pi\) | |||||||
\(284\) | 401.131i | 1.41243i | ||||||||
\(285\) | 39.3031 | + | 174.879i | 0.137905 | + | 0.613609i | ||||
\(286\) | −155.687 | −0.544359 | ||||||||
\(287\) | 41.5959 | − | 41.5959i | 0.144934 | − | 0.144934i | ||||
\(288\) | −82.7196 | − | 82.7196i | −0.287221 | − | 0.287221i | ||||
\(289\) | 274.939i | 0.951345i | ||||||||
\(290\) | 13.1010 | − | 2.94439i | 0.0451759 | − | 0.0101531i | ||||
\(291\) | 35.7526 | 0.122861 | ||||||||
\(292\) | −234.707 | + | 234.707i | −0.803792 | + | 0.803792i | ||||
\(293\) | −236.565 | − | 236.565i | −0.807390 | − | 0.807390i | 0.176848 | − | 0.984238i | \(-0.443410\pi\) |
−0.984238 | + | 0.176848i | \(0.943410\pi\) | |||||||
\(294\) | − | 244.126i | − | 0.830361i | ||||||
\(295\) | −472.893 | − | 299.338i | −1.60303 | − | 1.01471i | ||||
\(296\) | 321.464 | 1.08603 | ||||||||
\(297\) | 12.3031 | − | 12.3031i | 0.0414244 | − | 0.0414244i | ||||
\(298\) | 265.070 | + | 265.070i | 0.889498 | + | 0.889498i | ||||
\(299\) | − | 343.778i | − | 1.14976i | ||||||
\(300\) | −240.532 | − | 85.9671i | −0.801775 | − | 0.286557i | ||||
\(301\) | −65.2122 | −0.216652 | ||||||||
\(302\) | 322.520 | − | 322.520i | 1.06795 | − | 1.06795i | ||||
\(303\) | 212.641 | + | 212.641i | 0.701787 | + | 0.701787i | ||||
\(304\) | 99.3031i | 0.326655i | ||||||||
\(305\) | 251.621 | − | 397.510i | 0.824987 | − | 1.30331i | ||||
\(306\) | 35.3939 | 0.115666 | ||||||||
\(307\) | 168.969 | − | 168.969i | 0.550389 | − | 0.550389i | −0.376164 | − | 0.926553i | \(-0.622757\pi\) |
0.926553 | + | 0.376164i | \(0.122757\pi\) | |||||||
\(308\) | −28.6311 | − | 28.6311i | −0.0929582 | − | 0.0929582i | ||||
\(309\) | − | 158.611i | − | 0.513303i | ||||||
\(310\) | −64.4949 | − | 286.969i | −0.208048 | − | 0.925708i | ||||
\(311\) | 354.302 | 1.13923 | 0.569617 | − | 0.821910i | \(-0.307091\pi\) | ||||
0.569617 | + | 0.821910i | \(0.307091\pi\) | |||||||
\(312\) | 108.136 | − | 108.136i | 0.346590 | − | 0.346590i | ||||
\(313\) | 152.373 | + | 152.373i | 0.486816 | + | 0.486816i | 0.907300 | − | 0.420484i | \(-0.138140\pi\) |
−0.420484 | + | 0.907300i | \(0.638140\pi\) | |||||||
\(314\) | 227.576i | 0.724763i | ||||||||
\(315\) | −30.0000 | + | 6.74235i | −0.0952381 | + | 0.0214043i | ||||
\(316\) | −144.495 | −0.457262 | ||||||||
\(317\) | −427.217 | + | 427.217i | −1.34769 | + | 1.34769i | −0.459519 | + | 0.888168i | \(0.651978\pi\) |
−0.888168 | + | 0.459519i | \(0.848022\pi\) | |||||||
\(318\) | −156.384 | − | 156.384i | −0.491773 | − | 0.491773i | ||||
\(319\) | 2.85816i | 0.00895975i | ||||||||
\(320\) | −437.240 | − | 276.770i | −1.36637 | − | 0.864905i | ||||
\(321\) | −11.6163 | −0.0361879 | ||||||||
\(322\) | 106.091 | − | 106.091i | 0.329475 | − | 0.329475i | ||||
\(323\) | −54.8786 | − | 54.8786i | −0.169903 | − | 0.169903i | ||||
\(324\) | 53.0908i | 0.163861i | ||||||||
\(325\) | −124.338 | + | 347.893i | −0.382579 | + | 1.07044i | ||||
\(326\) | −842.706 | −2.58499 | ||||||||
\(327\) | 48.1362 | − | 48.1362i | 0.147206 | − | 0.147206i | ||||
\(328\) | −121.237 | − | 121.237i | −0.369626 | − | 0.369626i | ||||
\(329\) | 57.2622i | 0.174049i | ||||||||
\(330\) | 48.7980 | − | 77.0908i | 0.147873 | − | 0.233609i | ||||
\(331\) | 489.423 | 1.47862 | 0.739310 | − | 0.673365i | \(-0.235152\pi\) | ||||
0.739310 | + | 0.673365i | \(0.235152\pi\) | |||||||
\(332\) | −124.742 | + | 124.742i | −0.375730 | + | 0.375730i | ||||
\(333\) | 114.136 | + | 114.136i | 0.342751 | + | 0.342751i | ||||
\(334\) | 431.757i | 1.29269i | ||||||||
\(335\) | 85.1214 | + | 378.747i | 0.254094 | + | 1.13059i | ||||
\(336\) | −17.0352 | −0.0507000 | ||||||||
\(337\) | 292.192 | − | 292.192i | 0.867038 | − | 0.867038i | −0.125105 | − | 0.992143i | \(-0.539927\pi\) |
0.992143 | + | 0.125105i | \(0.0399269\pi\) | |||||||
\(338\) | −109.866 | − | 109.866i | −0.325048 | − | 0.325048i | ||||
\(339\) | 35.1714i | 0.103751i | ||||||||
\(340\) | 107.909 | − | 24.2520i | 0.317380 | − | 0.0713295i | ||||
\(341\) | 62.6061 | 0.183596 | ||||||||
\(342\) | 138.136 | − | 138.136i | 0.403907 | − | 0.403907i | ||||
\(343\) | −135.959 | − | 135.959i | −0.396382 | − | 0.396382i | ||||
\(344\) | 190.070i | 0.552530i | ||||||||
\(345\) | 170.227 | + | 107.753i | 0.493412 | + | 0.312326i | ||||
\(346\) | 154.091 | 0.445349 | ||||||||
\(347\) | 320.050 | − | 320.050i | 0.922334 | − | 0.922334i | −0.0748598 | − | 0.997194i | \(-0.523851\pi\) |
0.997194 | + | 0.0748598i | \(0.0238509\pi\) | |||||||
\(348\) | −6.16684 | − | 6.16684i | −0.0177208 | − | 0.0177208i | ||||
\(349\) | − | 574.009i | − | 1.64473i | −0.568964 | − | 0.822363i | \(-0.692655\pi\) | ||
0.568964 | − | 0.822363i | \(-0.307345\pi\) | |||||||
\(350\) | −145.732 | + | 68.9898i | −0.416378 | + | 0.197114i | ||||
\(351\) | 76.7878 | 0.218769 | ||||||||
\(352\) | 92.3281 | − | 92.3281i | 0.262296 | − | 0.262296i | ||||
\(353\) | 266.520 | + | 266.520i | 0.755014 | + | 0.755014i | 0.975410 | − | 0.220396i | \(-0.0707351\pi\) |
−0.220396 | + | 0.975410i | \(0.570735\pi\) | |||||||
\(354\) | 609.984i | 1.72312i | ||||||||
\(355\) | −181.848 | + | 287.283i | −0.512248 | + | 0.809247i | ||||
\(356\) | 555.576 | 1.56061 | ||||||||
\(357\) | 9.41429 | − | 9.41429i | 0.0263706 | − | 0.0263706i | ||||
\(358\) | −408.712 | − | 408.712i | −1.14165 | − | 1.14165i | ||||
\(359\) | 216.272i | 0.602430i | 0.953556 | + | 0.301215i | \(0.0973922\pi\) | ||||
−0.953556 | + | 0.301215i | \(0.902608\pi\) | |||||||
\(360\) | 19.6515 | + | 87.4393i | 0.0545876 | + | 0.242887i | ||||
\(361\) | −67.3633 | −0.186602 | ||||||||
\(362\) | 48.3383 | − | 48.3383i | 0.133531 | − | 0.133531i | ||||
\(363\) | −134.462 | − | 134.462i | −0.370419 | − | 0.370419i | ||||
\(364\) | − | 178.697i | − | 0.490926i | ||||||
\(365\) | −274.495 | + | 61.6913i | −0.752041 | + | 0.169017i | ||||
\(366\) | −512.747 | −1.40095 | ||||||||
\(367\) | −240.510 | + | 240.510i | −0.655340 | + | 0.655340i | −0.954274 | − | 0.298934i | \(-0.903369\pi\) |
0.298934 | + | 0.954274i | \(0.403369\pi\) | |||||||
\(368\) | 78.9240 | + | 78.9240i | 0.214467 | + | 0.214467i | ||||
\(369\) | − | 86.0908i | − | 0.233308i | ||||||
\(370\) | 715.176 | + | 452.702i | 1.93291 | + | 1.22352i | ||||
\(371\) | −83.1918 | −0.224237 | ||||||||
\(372\) | −135.081 | + | 135.081i | −0.363120 | + | 0.363120i | ||||
\(373\) | −330.207 | − | 330.207i | −0.885272 | − | 0.885272i | 0.108792 | − | 0.994065i | \(-0.465302\pi\) |
−0.994065 | + | 0.108792i | \(0.965302\pi\) | |||||||
\(374\) | 39.5051i | 0.105629i | ||||||||
\(375\) | −133.293 | − | 170.611i | −0.355448 | − | 0.454962i | ||||
\(376\) | 166.899 | 0.443880 | ||||||||
\(377\) | −8.91939 | + | 8.91939i | −0.0236589 | + | 0.0236589i | ||||
\(378\) | 23.6969 | + | 23.6969i | 0.0626903 | + | 0.0626903i | ||||
\(379\) | 210.000i | 0.554090i | 0.960857 | + | 0.277045i | \(0.0893551\pi\) | ||||
−0.960857 | + | 0.277045i | \(0.910645\pi\) | |||||||
\(380\) | 326.499 | − | 515.803i | 0.859209 | − | 1.35738i | ||||
\(381\) | −280.763 | −0.736910 | ||||||||
\(382\) | 89.1918 | − | 89.1918i | 0.233486 | − | 0.233486i | ||||
\(383\) | 170.631 | + | 170.631i | 0.445512 | + | 0.445512i | 0.893859 | − | 0.448347i | \(-0.147987\pi\) |
−0.448347 | + | 0.893859i | \(0.647987\pi\) | |||||||
\(384\) | 293.833i | 0.765191i | ||||||||
\(385\) | −7.52551 | − | 33.4847i | −0.0195468 | − | 0.0869732i | ||||
\(386\) | −345.126 | −0.894109 | ||||||||
\(387\) | −67.4847 | + | 67.4847i | −0.174379 | + | 0.174379i | ||||
\(388\) | −86.1010 | − | 86.1010i | −0.221910 | − | 0.221910i | ||||
\(389\) | − | 547.337i | − | 1.40704i | −0.710677 | − | 0.703518i | \(-0.751611\pi\) | ||
0.710677 | − | 0.703518i | \(-0.248389\pi\) | |||||||
\(390\) | 392.858 | − | 88.2929i | 1.00733 | − | 0.226392i | ||||
\(391\) | −87.2327 | −0.223101 | ||||||||
\(392\) | −189.260 | + | 189.260i | −0.482806 | + | 0.482806i | ||||
\(393\) | −32.0102 | − | 32.0102i | −0.0814509 | − | 0.0814509i | ||||
\(394\) | − | 299.464i | − | 0.760062i | ||||||
\(395\) | −103.485 | − | 65.5051i | −0.261987 | − | 0.165836i | ||||
\(396\) | −59.2577 | −0.149641 | ||||||||
\(397\) | 45.2577 | − | 45.2577i | 0.113999 | − | 0.113999i | −0.647806 | − | 0.761805i | \(-0.724313\pi\) |
0.761805 | + | 0.647806i | \(0.224313\pi\) | |||||||
\(398\) | 559.287 | + | 559.287i | 1.40524 | + | 1.40524i | ||||
\(399\) | − | 73.4847i | − | 0.184172i | ||||||
\(400\) | −51.3235 | − | 108.414i | −0.128309 | − | 0.271036i | ||||
\(401\) | −520.302 | −1.29751 | −0.648756 | − | 0.760997i | \(-0.724710\pi\) | ||||
−0.648756 | + | 0.760997i | \(0.724710\pi\) | |||||||
\(402\) | 299.171 | − | 299.171i | 0.744208 | − | 0.744208i | ||||
\(403\) | 195.373 | + | 195.373i | 0.484798 | + | 0.484798i | ||||
\(404\) | − | 1024.19i | − | 2.53511i | ||||||
\(405\) | −24.0681 | + | 38.0227i | −0.0594274 | + | 0.0938832i | ||||
\(406\) | −5.50510 | −0.0135594 | ||||||||
\(407\) | −127.394 | + | 127.394i | −0.313007 | + | 0.313007i | ||||
\(408\) | −27.4393 | − | 27.4393i | −0.0672531 | − | 0.0672531i | ||||
\(409\) | − | 347.110i | − | 0.848680i | −0.905503 | − | 0.424340i | \(-0.860506\pi\) | ||
0.905503 | − | 0.424340i | \(-0.139494\pi\) | |||||||
\(410\) | −98.9898 | − | 440.454i | −0.241439 | − | 1.07428i | ||||
\(411\) | 35.8388 | 0.0871990 | ||||||||
\(412\) | −381.974 | + | 381.974i | −0.927121 | + | 0.927121i | ||||
\(413\) | 162.247 | + | 162.247i | 0.392851 | + | 0.392851i | ||||
\(414\) | − | 219.576i | − | 0.530376i | ||||||
\(415\) | −145.889 | + | 32.7878i | −0.351539 | + | 0.0790066i | ||||
\(416\) | 576.252 | 1.38522 | ||||||||
\(417\) | 101.864 | − | 101.864i | 0.244278 | − | 0.244278i | ||||
\(418\) | 154.182 | + | 154.182i | 0.368856 | + | 0.368856i | ||||
\(419\) | 583.398i | 1.39236i | 0.717868 | + | 0.696180i | \(0.245118\pi\) | ||||
−0.717868 | + | 0.696180i | \(0.754882\pi\) | |||||||
\(420\) | 88.4847 | + | 56.0102i | 0.210678 | + | 0.133358i | ||||
\(421\) | 213.151 | 0.506297 | 0.253148 | − | 0.967427i | \(-0.418534\pi\) | ||||
0.253148 | + | 0.967427i | \(0.418534\pi\) | |||||||
\(422\) | −589.085 | + | 589.085i | −1.39594 | + | 1.39594i | ||||
\(423\) | 59.2577 | + | 59.2577i | 0.140089 | + | 0.140089i | ||||
\(424\) | 242.474i | 0.571874i | ||||||||
\(425\) | 88.2770 | + | 31.5505i | 0.207711 | + | 0.0742365i | ||||
\(426\) | 370.565 | 0.869872 | ||||||||
\(427\) | −136.384 | + | 136.384i | −0.319400 | + | 0.319400i | ||||
\(428\) | 27.9750 | + | 27.9750i | 0.0653622 | + | 0.0653622i | ||||
\(429\) | 85.7071i | 0.199784i | ||||||||
\(430\) | −267.666 | + | 422.858i | −0.622480 | + | 0.983391i | ||||
\(431\) | 187.364 | 0.434720 | 0.217360 | − | 0.976092i | \(-0.430255\pi\) | ||||
0.217360 | + | 0.976092i | \(0.430255\pi\) | |||||||
\(432\) | −17.6288 | + | 17.6288i | −0.0408075 | + | 0.0408075i | ||||
\(433\) | 154.848 | + | 154.848i | 0.357617 | + | 0.357617i | 0.862934 | − | 0.505317i | \(-0.168624\pi\) |
−0.505317 | + | 0.862934i | \(0.668624\pi\) | |||||||
\(434\) | 120.586i | 0.277847i | ||||||||
\(435\) | −1.62092 | − | 7.21225i | −0.00372624 | − | 0.0165799i | ||||
\(436\) | −231.848 | −0.531761 | ||||||||
\(437\) | −340.454 | + | 340.454i | −0.779071 | + | 0.779071i | ||||
\(438\) | 216.823 | + | 216.823i | 0.495030 | + | 0.495030i | ||||
\(439\) | 252.929i | 0.576147i | 0.957608 | + | 0.288074i | \(0.0930148\pi\) | ||||
−0.957608 | + | 0.288074i | \(0.906985\pi\) | |||||||
\(440\) | −97.5959 | + | 21.9342i | −0.221809 | + | 0.0498504i | ||||
\(441\) | −134.394 | −0.304748 | ||||||||
\(442\) | −123.283 | + | 123.283i | −0.278920 | + | 0.278920i | ||||
\(443\) | −421.131 | − | 421.131i | −0.950633 | − | 0.950633i | 0.0482041 | − | 0.998838i | \(-0.484650\pi\) |
−0.998838 | + | 0.0482041i | \(0.984650\pi\) | |||||||
\(444\) | − | 549.737i | − | 1.23815i | ||||||
\(445\) | 397.893 | + | 251.864i | 0.894142 | + | 0.565986i | ||||
\(446\) | 148.742 | 0.333503 | ||||||||
\(447\) | 145.924 | − | 145.924i | 0.326452 | − | 0.326452i | ||||
\(448\) | 150.015 | + | 150.015i | 0.334854 | + | 0.334854i | ||||
\(449\) | − | 297.909i | − | 0.663495i | −0.943368 | − | 0.331747i | \(-0.892362\pi\) | ||
0.943368 | − | 0.331747i | \(-0.107638\pi\) | |||||||
\(450\) | −79.4166 | + | 222.204i | −0.176481 | + | 0.493787i | ||||
\(451\) | 96.0908 | 0.213062 | ||||||||
\(452\) | 84.7015 | − | 84.7015i | 0.187393 | − | 0.187393i | ||||
\(453\) | −177.551 | − | 177.551i | −0.391944 | − | 0.391944i | ||||
\(454\) | − | 94.2020i | − | 0.207493i | ||||||
\(455\) | 81.0102 | − | 127.980i | 0.178044 | − | 0.281274i | ||||
\(456\) | −214.182 | −0.469697 | ||||||||
\(457\) | 285.747 | − | 285.747i | 0.625267 | − | 0.625267i | −0.321607 | − | 0.946873i | \(-0.604223\pi\) |
0.946873 | + | 0.321607i | \(0.104223\pi\) | |||||||
\(458\) | −542.388 | − | 542.388i | −1.18425 | − | 1.18425i | ||||
\(459\) | − | 19.4847i | − | 0.0424503i | ||||||
\(460\) | −150.454 | − | 669.444i | −0.327074 | − | 1.45531i | ||||
\(461\) | 526.620 | 1.14234 | 0.571171 | − | 0.820831i | \(-0.306489\pi\) | ||||
0.571171 | + | 0.820831i | \(0.306489\pi\) | |||||||
\(462\) | −26.4495 | + | 26.4495i | −0.0572500 | + | 0.0572500i | ||||
\(463\) | 335.702 | + | 335.702i | 0.725057 | + | 0.725057i | 0.969631 | − | 0.244573i | \(-0.0786479\pi\) |
−0.244573 | + | 0.969631i | \(0.578648\pi\) | |||||||
\(464\) | − | 4.09540i | − | 0.00882630i | ||||||
\(465\) | −157.980 | + | 35.5051i | −0.339741 | + | 0.0763551i | ||||
\(466\) | −719.535 | −1.54407 | ||||||||
\(467\) | 488.742 | − | 488.742i | 1.04656 | − | 1.04656i | 0.0476956 | − | 0.998862i | \(-0.484812\pi\) |
0.998862 | − | 0.0476956i | \(-0.0151877\pi\) | |||||||
\(468\) | −184.924 | − | 184.924i | −0.395137 | − | 0.395137i | ||||
\(469\) | − | 159.151i | − | 0.339341i | ||||||
\(470\) | 371.308 | + | 235.035i | 0.790016 | + | 0.500075i | ||||
\(471\) | 125.283 | 0.265993 | ||||||||
\(472\) | 472.893 | − | 472.893i | 1.00189 | − | 1.00189i | ||||
\(473\) | −75.3235 | − | 75.3235i | −0.159246 | − | 0.159246i | ||||
\(474\) | 133.485i | 0.281613i | ||||||||
\(475\) | 467.666 | − | 221.394i | 0.984561 | − | 0.466092i | ||||
\(476\) | −45.3439 | −0.0952603 | ||||||||
\(477\) | −86.0908 | + | 86.0908i | −0.180484 | + | 0.180484i | ||||
\(478\) | −725.716 | − | 725.716i | −1.51823 | − | 1.51823i | ||||
\(479\) | 184.949i | 0.386115i | 0.981187 | + | 0.193057i | \(0.0618404\pi\) | ||||
−0.981187 | + | 0.193057i | \(0.938160\pi\) | |||||||
\(480\) | −180.619 | + | 285.341i | −0.376289 | + | 0.594459i | ||||
\(481\) | −795.110 | −1.65304 | ||||||||
\(482\) | 297.171 | − | 297.171i | 0.616538 | − | 0.616538i | ||||
\(483\) | −58.4041 | − | 58.4041i | −0.120919 | − | 0.120919i | ||||
\(484\) | 647.636i | 1.33809i | ||||||||
\(485\) | −22.6311 | − | 100.697i | −0.0466621 | − | 0.207623i | ||||
\(486\) | 49.0454 | 0.100916 | ||||||||
\(487\) | −120.682 | + | 120.682i | −0.247807 | + | 0.247807i | −0.820070 | − | 0.572263i | \(-0.806066\pi\) |
0.572263 | + | 0.820070i | \(0.306066\pi\) | |||||||
\(488\) | 397.510 | + | 397.510i | 0.814569 | + | 0.814569i | ||||
\(489\) | 463.918i | 0.948708i | ||||||||
\(490\) | −687.580 | + | 154.530i | −1.40322 | + | 0.315368i | ||||
\(491\) | −105.682 | −0.215239 | −0.107619 | − | 0.994192i | \(-0.534323\pi\) | ||||
−0.107619 | + | 0.994192i | \(0.534323\pi\) | |||||||
\(492\) | −207.328 | + | 207.328i | −0.421398 | + | 0.421398i | ||||
\(493\) | 2.26327 | + | 2.26327i | 0.00459082 | + | 0.00459082i | ||||
\(494\) | 962.302i | 1.94798i | ||||||||
\(495\) | −42.4393 | − | 26.8638i | −0.0857359 | − | 0.0542703i | ||||
\(496\) | −89.7071 | −0.180861 | ||||||||
\(497\) | 98.5653 | − | 98.5653i | 0.198321 | − | 0.198321i | ||||
\(498\) | 115.237 | + | 115.237i | 0.231400 | + | 0.231400i | ||||
\(499\) | 739.585i | 1.48213i | 0.671431 | + | 0.741067i | \(0.265680\pi\) | ||||
−0.671431 | + | 0.741067i | \(0.734320\pi\) | |||||||
\(500\) | −89.8707 | + | 731.875i | −0.179741 | + | 1.46375i | ||||
\(501\) | 237.687 | 0.474425 | ||||||||
\(502\) | 900.448 | − | 900.448i | 1.79372 | − | 1.79372i | ||||
\(503\) | −406.409 | − | 406.409i | −0.807970 | − | 0.807970i | 0.176357 | − | 0.984326i | \(-0.443569\pi\) |
−0.984326 | + | 0.176357i | \(0.943569\pi\) | |||||||
\(504\) | − | 36.7423i | − | 0.0729015i | ||||||
\(505\) | 464.303 | − | 733.504i | 0.919412 | − | 1.45248i | ||||
\(506\) | 245.081 | 0.484349 | ||||||||
\(507\) | −60.4824 | + | 60.4824i | −0.119295 | + | 0.119295i | ||||
\(508\) | 676.146 | + | 676.146i | 1.33100 | + | 1.33100i | ||||
\(509\) | − | 194.511i | − | 0.382143i | −0.981576 | − | 0.191071i | \(-0.938804\pi\) | ||
0.981576 | − | 0.191071i | \(-0.0611962\pi\) | |||||||
\(510\) | −22.4041 | − | 99.6867i | −0.0439296 | − | 0.195464i | ||||
\(511\) | 115.344 | 0.225722 | ||||||||
\(512\) | −213.376 | + | 213.376i | −0.416750 | + | 0.416750i | ||||
\(513\) | −76.0454 | − | 76.0454i | −0.148237 | − | 0.148237i | ||||
\(514\) | − | 397.060i | − | 0.772491i | ||||||
\(515\) | −446.727 | + | 100.399i | −0.867430 | + | 0.194950i | ||||
\(516\) | 325.040 | 0.629922 | ||||||||
\(517\) | −66.1408 | + | 66.1408i | −0.127932 | + | 0.127932i | ||||
\(518\) | −245.373 | − | 245.373i | −0.473694 | − | 0.473694i | ||||
\(519\) | − | 84.8286i | − | 0.163446i | ||||||
\(520\) | −373.015 | − | 236.116i | −0.717336 | − | 0.454069i | ||||
\(521\) | −589.605 | −1.13168 | −0.565840 | − | 0.824515i | \(-0.691448\pi\) | ||||
−0.565840 | + | 0.824515i | \(0.691448\pi\) | |||||||
\(522\) | −5.69694 | + | 5.69694i | −0.0109137 | + | 0.0109137i | ||||
\(523\) | −141.546 | − | 141.546i | −0.270642 | − | 0.270642i | 0.558716 | − | 0.829359i | \(-0.311294\pi\) |
−0.829359 | + | 0.558716i | \(0.811294\pi\) | |||||||
\(524\) | 154.177i | 0.294231i | ||||||||
\(525\) | 37.9796 | + | 80.2270i | 0.0723421 | + | 0.152813i | ||||
\(526\) | 1521.03 | 2.89169 | ||||||||
\(527\) | 49.5755 | − | 49.5755i | 0.0940712 | − | 0.0940712i | ||||
\(528\) | −19.6765 | − | 19.6765i | −0.0372662 | − | 0.0372662i | ||||
\(529\) | 12.1714i | 0.0230084i | ||||||||
\(530\) | −341.464 | + | 539.444i | −0.644272 | + | 1.01782i | ||||
\(531\) | 335.803 | 0.632397 | ||||||||
\(532\) | −176.969 | + | 176.969i | −0.332649 | + | 0.332649i | ||||
\(533\) | 299.868 | + | 299.868i | 0.562605 | + | 0.562605i | ||||
\(534\) | − | 513.242i | − | 0.961127i | ||||||
\(535\) | 7.35306 | + | 32.7173i | 0.0137440 | + | 0.0611539i | ||||
\(536\) | −463.868 | −0.865426 | ||||||||
\(537\) | −225.000 | + | 225.000i | −0.418994 | + | 0.418994i | ||||
\(538\) | −7.78775 | − | 7.78775i | −0.0144754 | − | 0.0144754i | ||||
\(539\) | − | 150.005i | − | 0.278302i | ||||||
\(540\) | 149.530 | − | 33.6061i | 0.276908 | − | 0.0622336i | ||||
\(541\) | 431.303 | 0.797233 | 0.398617 | − | 0.917118i | \(-0.369490\pi\) | ||||
0.398617 | + | 0.917118i | \(0.369490\pi\) | |||||||
\(542\) | 230.429 | − | 230.429i | 0.425146 | − | 0.425146i | ||||
\(543\) | −26.6107 | − | 26.6107i | −0.0490068 | − | 0.0490068i | ||||
\(544\) | − | 146.222i | − | 0.268791i | ||||||
\(545\) | −166.045 | − | 105.106i | −0.304670 | − | 0.192854i | ||||
\(546\) | −165.081 | −0.302345 | ||||||||
\(547\) | −446.222 | + | 446.222i | −0.815763 | + | 0.815763i | −0.985491 | − | 0.169728i | \(-0.945711\pi\) |
0.169728 | + | 0.985491i | \(0.445711\pi\) | |||||||
\(548\) | −86.3087 | − | 86.3087i | −0.157498 | − | 0.157498i | ||||
\(549\) | 282.272i | 0.514157i | ||||||||
\(550\) | −248.015 | − | 88.6413i | −0.450936 | − | 0.161166i | ||||
\(551\) | 17.6663 | 0.0320623 | ||||||||
\(552\) | −170.227 | + | 170.227i | −0.308382 | + | 0.308382i | ||||
\(553\) | 35.5051 | + | 35.5051i | 0.0642045 | + | 0.0642045i | ||||
\(554\) | − | 1270.37i | − | 2.29309i | ||||||
\(555\) | 249.217 | − | 393.712i | 0.449039 | − | 0.709391i | ||||
\(556\) | −490.627 | −0.882422 | ||||||||
\(557\) | 214.091 | − | 214.091i | 0.384364 | − | 0.384364i | −0.488308 | − | 0.872672i | \(-0.662386\pi\) |
0.872672 | + | 0.488308i | \(0.162386\pi\) | |||||||
\(558\) | 124.788 | + | 124.788i | 0.223634 | + | 0.223634i | ||||
\(559\) | − | 470.120i | − | 0.841003i | ||||||
\(560\) | 10.7832 | + | 47.9796i | 0.0192557 | + | 0.0856778i | ||||
\(561\) | 21.7480 | 0.0387664 | ||||||||
\(562\) | −829.156 | + | 829.156i | −1.47537 | + | 1.47537i | ||||
\(563\) | 672.009 | + | 672.009i | 1.19362 | + | 1.19362i | 0.976043 | + | 0.217579i | \(0.0698161\pi\) |
0.217579 | + | 0.976043i | \(0.430184\pi\) | |||||||
\(564\) | − | 285.414i | − | 0.506054i | ||||||
\(565\) | 99.0602 | − | 22.2633i | 0.175328 | − | 0.0394040i | ||||
\(566\) | 343.464 | 0.606827 | ||||||||
\(567\) | 13.0454 | − | 13.0454i | 0.0230078 | − | 0.0230078i | ||||
\(568\) | −287.283 | − | 287.283i | −0.505779 | − | 0.505779i | ||||
\(569\) | 972.161i | 1.70854i | 0.519827 | + | 0.854272i | \(0.325997\pi\) | ||||
−0.519827 | + | 0.854272i | \(0.674003\pi\) | |||||||
\(570\) | −476.499 | − | 301.621i | −0.835964 | − | 0.529160i | ||||
\(571\) | −924.030 | −1.61827 | −0.809133 | − | 0.587626i | \(-0.800063\pi\) | ||||
−0.809133 | + | 0.587626i | \(0.800063\pi\) | |||||||
\(572\) | 206.404 | − | 206.404i | 0.360846 | − | 0.360846i | ||||
\(573\) | −49.1010 | − | 49.1010i | −0.0856911 | − | 0.0856911i | ||||
\(574\) | 185.081i | 0.322440i | ||||||||
\(575\) | 195.732 | − | 547.650i | 0.340404 | − | 0.952436i | ||||
\(576\) | 310.485 | 0.539036 | ||||||||
\(577\) | −497.879 | + | 497.879i | −0.862874 | + | 0.862874i | −0.991671 | − | 0.128797i | \(-0.958889\pi\) |
0.128797 | + | 0.991671i | \(0.458889\pi\) | |||||||
\(578\) | −611.669 | − | 611.669i | −1.05825 | − | 1.05825i | ||||
\(579\) | 189.995i | 0.328144i | ||||||||
\(580\) | −13.4653 | + | 21.2724i | −0.0232161 | + | 0.0366766i | ||||
\(581\) | 61.3031 | 0.105513 | ||||||||
\(582\) | −79.5403 | + | 79.5403i | −0.136667 | + | 0.136667i | ||||
\(583\) | −96.0908 | − | 96.0908i | −0.164821 | − | 0.164821i | ||||
\(584\) | − | 336.186i | − | 0.575661i | ||||||
\(585\) | −48.6061 | − | 216.272i | −0.0830874 | − | 0.369696i | ||||
\(586\) | 1052.59 | 1.79624 | ||||||||
\(587\) | 292.783 | − | 292.783i | 0.498779 | − | 0.498779i | −0.412279 | − | 0.911058i | \(-0.635267\pi\) |
0.911058 | + | 0.412279i | \(0.135267\pi\) | |||||||
\(588\) | 323.654 | + | 323.654i | 0.550432 | + | 0.550432i | ||||
\(589\) | − | 386.969i | − | 0.656994i | ||||||
\(590\) | 1718.02 | − | 386.116i | 2.91190 | − | 0.654434i | ||||
\(591\) | −164.858 | −0.278948 | ||||||||
\(592\) | 182.540 | − | 182.540i | 0.308345 | − | 0.308345i | ||||
\(593\) | 451.258 | + | 451.258i | 0.760974 | + | 0.760974i | 0.976498 | − | 0.215524i | \(-0.0691461\pi\) |
−0.215524 | + | 0.976498i | \(0.569146\pi\) | |||||||
\(594\) | 54.7423i | 0.0921588i | ||||||||
\(595\) | −32.4745 | − | 20.5561i | −0.0545790 | − | 0.0345481i | ||||
\(596\) | −702.842 | −1.17927 | ||||||||
\(597\) | 307.893 | − | 307.893i | 0.515734 | − | 0.515734i | ||||
\(598\) | 764.817 | + | 764.817i | 1.27896 | + | 1.27896i | ||||
\(599\) | − | 32.8582i | − | 0.0548550i | −0.999624 | − | 0.0274275i | \(-0.991268\pi\) | ||
0.999624 | − | 0.0274275i | \(-0.00873154\pi\) | |||||||
\(600\) | 233.833 | − | 110.697i | 0.389722 | − | 0.184495i | ||||
\(601\) | −184.484 | −0.306961 | −0.153481 | − | 0.988152i | \(-0.549048\pi\) | ||||
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(602\) | 145.081 | − | 145.081i | 0.240998 | − | 0.240998i | ||||
\(603\) | −164.697 | − | 164.697i | −0.273129 | − | 0.273129i | ||||
\(604\) | 855.171i | 1.41585i | ||||||||
\(605\) | −293.598 | + | 463.825i | −0.485286 | + | 0.766653i | ||||
\(606\) | −946.145 | −1.56130 | ||||||||
\(607\) | 136.389 | − | 136.389i | 0.224694 | − | 0.224694i | −0.585778 | − | 0.810472i | \(-0.699211\pi\) |
0.810472 | + | 0.585778i | \(0.199211\pi\) | |||||||
\(608\) | −570.681 | − | 570.681i | −0.938620 | − | 0.938620i | ||||
\(609\) | 3.03062i | 0.00497638i | ||||||||
\(610\) | 324.565 | + | 1444.15i | 0.532074 | + | 2.36746i | ||||
\(611\) | −412.808 | −0.675627 | ||||||||
\(612\) | −46.9240 | + | 46.9240i | −0.0766732 | + | 0.0766732i | ||||
\(613\) | −12.7128 | − | 12.7128i | −0.0207386 | − | 0.0207386i | 0.696661 | − | 0.717400i | \(-0.254668\pi\) |
−0.717400 | + | 0.696661i | \(0.754668\pi\) | |||||||
\(614\) | 751.828i | 1.22447i | ||||||||
\(615\) | −242.474 | + | 54.4949i | −0.394267 | + | 0.0886096i | ||||
\(616\) | 41.0102 | 0.0665750 | ||||||||
\(617\) | −398.752 | + | 398.752i | −0.646275 | + | 0.646275i | −0.952091 | − | 0.305816i | \(-0.901071\pi\) |
0.305816 | + | 0.952091i | \(0.401071\pi\) | |||||||
\(618\) | 352.868 | + | 352.868i | 0.570984 | + | 0.570984i | ||||
\(619\) | − | 819.131i | − | 1.32331i | −0.749807 | − | 0.661656i | \(-0.769854\pi\) | ||
0.749807 | − | 0.661656i | \(-0.230146\pi\) | |||||||
\(620\) | 465.959 | + | 294.949i | 0.751547 | + | 0.475724i | ||||
\(621\) | −120.879 | −0.194651 | ||||||||
\(622\) | −788.232 | + | 788.232i | −1.26725 | + | 1.26725i | ||||
\(623\) | −136.515 | − | 136.515i | −0.219126 | − | 0.219126i | ||||
\(624\) | − | 122.808i | − | 0.196808i | ||||||
\(625\) | −396.151 | + | 483.414i | −0.633842 | + | 0.773463i | ||||
\(626\) | −677.984 | −1.08304 | ||||||||
\(627\) | 84.8786 | − | 84.8786i | 0.135373 | − | 0.135373i | ||||
\(628\) | −301.712 | − | 301.712i | −0.480433 | − | 0.480433i | ||||
\(629\) | 201.757i | 0.320759i | ||||||||
\(630\) | 51.7423 | − | 81.7423i | 0.0821307 | − | 0.129750i | ||||
\(631\) | 105.485 | 0.167171 | 0.0835853 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835853 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(632\) | 103.485 | − | 103.485i | 0.163742 | − | 0.163742i | ||||
\(633\) | 324.297 | + | 324.297i | 0.512318 | + | 0.512318i | ||||
\(634\) | − | 1900.90i | − | 2.99826i | ||||||
\(635\) | 177.721 | + | 790.767i | 0.279875 | + | 1.24530i | ||||
\(636\) | 414.656 | 0.651975 | ||||||||
\(637\) | 468.116 | − | 468.116i | 0.734876 | − | 0.734876i | ||||
\(638\) | −6.35867 | − | 6.35867i | −0.00996657 | − | 0.00996657i | ||||
\(639\) | − | 204.000i | − | 0.319249i | ||||||
\(640\) | 827.580 | − | 185.994i | 1.29309 | − | 0.290616i | ||||
\(641\) | 164.788 | 0.257079 | 0.128540 | − | 0.991704i | \(-0.458971\pi\) | ||||
0.128540 | + | 0.991704i | \(0.458971\pi\) | |||||||
\(642\) | 25.8434 | − | 25.8434i | 0.0402545 | − | 0.0402545i | ||||
\(643\) | −764.372 | − | 764.372i | −1.18876 | − | 1.18876i | −0.977411 | − | 0.211349i | \(-0.932214\pi\) |
−0.211349 | − | 0.977411i | \(-0.567786\pi\) | |||||||
\(644\) | 281.303i | 0.436806i | ||||||||
\(645\) | 232.788 | + | 147.353i | 0.360911 | + | 0.228454i | ||||
\(646\) | 244.182 | 0.377990 | ||||||||
\(647\) | 321.287 | − | 321.287i | 0.496580 | − | 0.496580i | −0.413792 | − | 0.910372i | \(-0.635796\pi\) |
0.910372 | + | 0.413792i | \(0.135796\pi\) | |||||||
\(648\) | −38.0227 | − | 38.0227i | −0.0586770 | − | 0.0586770i | ||||
\(649\) | 374.808i | 0.577516i | ||||||||
\(650\) | −497.353 | − | 1050.59i | −0.765159 | − | 1.61630i | ||||
\(651\) | 66.3837 | 0.101972 | ||||||||
\(652\) | 1117.23 | − | 1117.23i | 1.71354 | − | 1.71354i | ||||
\(653\) | −169.823 | − | 169.823i | −0.260066 | − | 0.260066i | 0.565015 | − | 0.825081i | \(-0.308870\pi\) |
−0.825081 | + | 0.565015i | \(0.808870\pi\) | |||||||
\(654\) | 214.182i | 0.327495i | ||||||||
\(655\) | −69.8944 | + | 110.419i | −0.106709 | + | 0.168578i | ||||
\(656\) | −137.687 | −0.209888 | ||||||||
\(657\) | 119.363 | − | 119.363i | 0.181679 | − | 0.181679i | ||||
\(658\) | −127.394 | − | 127.394i | −0.193608 | − | 0.193608i | ||||
\(659\) | − | 958.763i | − | 1.45488i | −0.686174 | − | 0.727438i | \(-0.740711\pi\) | ||
0.686174 | − | 0.727438i | \(-0.259289\pi\) | |||||||
\(660\) | 37.5097 | + | 166.899i | 0.0568329 | + | 0.252877i | ||||
\(661\) | 396.393 | 0.599687 | 0.299843 | − | 0.953988i | \(-0.403066\pi\) | ||||
0.299843 | + | 0.953988i | \(0.403066\pi\) | |||||||
\(662\) | −1088.84 | + | 1088.84i | −1.64478 | + | 1.64478i | ||||
\(663\) | 67.8684 | + | 67.8684i | 0.102366 | + | 0.102366i | ||||
\(664\) | − | 178.677i | − | 0.269091i | ||||||
\(665\) | −206.969 | + | 46.5153i | −0.311232 | + | 0.0699478i | ||||
\(666\) | −507.848 | −0.762534 | ||||||||
\(667\) | 14.0408 | − | 14.0408i | 0.0210507 | − | 0.0210507i | ||||
\(668\) | −572.409 | − | 572.409i | −0.856899 | − | 0.856899i | ||||
\(669\) | − | 81.8842i | − | 0.122398i | ||||||
\(670\) | −1031.99 | − | 653.242i | −1.54028 | − | 0.974988i | ||||
\(671\) | −315.060 | −0.469538 | ||||||||
\(672\) | 97.8990 | − | 97.8990i | 0.145683 | − | 0.145683i | ||||
\(673\) | 164.707 | + | 164.707i | 0.244736 | + | 0.244736i | 0.818806 | − | 0.574070i | \(-0.194636\pi\) |
−0.574070 | + | 0.818806i | \(0.694636\pi\) | |||||||
\(674\) | 1300.10i | 1.92894i | ||||||||
\(675\) | 122.326 | + | 43.7196i | 0.181223 | + | 0.0647698i | ||||
\(676\) | 291.313 | 0.430937 | ||||||||
\(677\) | 544.388 | − | 544.388i | 0.804119 | − | 0.804119i | −0.179618 | − | 0.983736i | \(-0.557486\pi\) |
0.983736 | + | 0.179618i | \(0.0574861\pi\) | |||||||
\(678\) | −78.2474 | − | 78.2474i | −0.115409 | − | 0.115409i | ||||
\(679\) | 42.3133i | 0.0623170i | ||||||||
\(680\) | −59.9138 | + | 94.6515i | −0.0881085 | + | 0.139193i | ||||
\(681\) | −51.8592 | −0.0761515 | ||||||||
\(682\) | −139.283 | + | 139.283i | −0.204227 | + | 0.204227i | ||||
\(683\) | 786.590 | + | 786.590i | 1.15167 | + | 1.15167i | 0.986218 | + | 0.165452i | \(0.0529082\pi\) |
0.165452 | + | 0.986218i | \(0.447092\pi\) | |||||||
\(684\) | 366.272i | 0.535486i | ||||||||
\(685\) | −22.6857 | − | 100.940i | −0.0331178 | − | 0.147357i | ||||
\(686\) | 604.949 | 0.881850 | ||||||||
\(687\) | −298.590 | + | 298.590i | −0.434629 | + | 0.434629i | ||||
\(688\) | 107.930 | + | 107.930i | 0.156874 | + | 0.156874i | ||||
\(689\) | − | 599.737i | − | 0.870445i | ||||||
\(690\) | −618.434 | + | 138.990i | −0.896281 | + | 0.201434i | ||||
\(691\) | 356.879 | 0.516467 | 0.258233 | − | 0.966083i | \(-0.416860\pi\) | ||||
0.258233 | + | 0.966083i | \(0.416860\pi\) | |||||||
\(692\) | −204.288 | + | 204.288i | −0.295214 | + | 0.295214i | ||||
\(693\) | 14.5607 | + | 14.5607i | 0.0210111 | + | 0.0210111i | ||||
\(694\) | 1424.06i | 2.05196i | ||||||||
\(695\) | −351.378 | − | 222.420i | −0.505580 | − | 0.320029i | ||||
\(696\) | 8.83316 | 0.0126913 | ||||||||
\(697\) | 76.0908 | − | 76.0908i | 0.109169 | − | 0.109169i | ||||
\(698\) | 1277.02 | + | 1277.02i | 1.82955 | + | 1.82955i | ||||
\(699\) | 396.111i | 0.566683i | ||||||||
\(700\) | 101.742 | − | 284.671i | 0.145346 | − | 0.406673i | ||||
\(701\) | 885.680 | 1.26345 | 0.631726 | − | 0.775192i | \(-0.282347\pi\) | ||||
0.631726 | + | 0.775192i | \(0.282347\pi\) | |||||||
\(702\) | −170.833 | + | 170.833i | −0.243352 | + | 0.243352i | ||||
\(703\) | 787.423 | + | 787.423i | 1.12009 | + | 1.12009i | ||||
\(704\) | 346.549i | 0.492258i | ||||||||
\(705\) | 129.389 | − | 204.409i | 0.183531 | − | 0.289941i | ||||
\(706\) | −1185.88 | −1.67971 | ||||||||
\(707\) | −251.662 | + | 251.662i | −0.355957 | + | 0.355957i | ||||
\(708\) | −808.696 | − | 808.696i | −1.14223 | − | 1.14223i | ||||
\(709\) | 731.049i | 1.03110i | 0.856860 | + | 0.515549i | \(0.172412\pi\) | ||||
−0.856860 | + | 0.515549i | \(0.827588\pi\) | |||||||
\(710\) | −234.565 | − | 1043.70i | −0.330374 | − | 1.46999i | ||||
\(711\) | 73.4847 | 0.103354 | ||||||||
\(712\) | −397.893 | + | 397.893i | −0.558839 | + | 0.558839i | ||||
\(713\) | −307.555 | − | 307.555i | −0.431354 | − | 0.431354i | ||||
\(714\) | 41.8888i | 0.0586678i | ||||||||
\(715\) | 241.394 | − | 54.2520i | 0.337614 | − | 0.0758770i | ||||
\(716\) | 1083.71 | 1.51356 | ||||||||
\(717\) | −399.514 | + | 399.514i | −0.557203 | + | 0.557203i | ||||
\(718\) | −481.151 | − | 481.151i | −0.670127 | − | 0.670127i | ||||
\(719\) | − | 629.271i | − | 0.875204i | −0.899169 | − | 0.437602i | \(-0.855828\pi\) | ||
0.899169 | − | 0.437602i | \(-0.144172\pi\) | |||||||
\(720\) | 60.8105 | + | 38.4926i | 0.0844590 | + | 0.0534619i | ||||
\(721\) | 187.716 | 0.260356 | ||||||||
\(722\) | 149.866 | − | 149.866i | 0.207571 | − | 0.207571i | ||||
\(723\) | −163.596 | − | 163.596i | −0.226274 | − | 0.226274i | ||||
\(724\) | 128.170i | 0.177031i | ||||||||
\(725\) | −19.2872 | + | 9.13061i | −0.0266031 | + | 0.0125939i | ||||
\(726\) | 598.287 | 0.824087 | ||||||||
\(727\) | −15.8740 | + | 15.8740i | −0.0218349 | + | 0.0218349i | −0.717940 | − | 0.696105i | \(-0.754915\pi\) |
0.696105 | + | 0.717940i | \(0.254915\pi\) | |||||||
\(728\) | 127.980 | + | 127.980i | 0.175796 | + | 0.175796i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 473.434 | − | 747.929i | 0.648539 | − | 1.02456i | ||||
\(731\) | −119.292 | −0.163190 | ||||||||
\(732\) | 679.782 | − | 679.782i | 0.928664 | − | 0.928664i | ||||
\(733\) | −393.237 | − | 393.237i | −0.536476 | − | 0.536476i | 0.386016 | − | 0.922492i | \(-0.373851\pi\) |
−0.922492 | + | 0.386016i | \(0.873851\pi\) | |||||||
\(734\) | − | 1070.15i | − | 1.45796i | ||||||
\(735\) | 85.0704 | + | 378.520i | 0.115742 | + | 0.514993i | ||||
\(736\) | −907.131 | −1.23251 | ||||||||
\(737\) | 183.828 | − | 183.828i | 0.249427 | − | 0.249427i | ||||
\(738\) | 191.530 | + | 191.530i | 0.259526 | + | 0.259526i | ||||
\(739\) | 192.334i | 0.260262i | 0.991497 | + | 0.130131i | \(0.0415398\pi\) | ||||
−0.991497 | + | 0.130131i | \(0.958460\pi\) | |||||||
\(740\) | −1548.33 | + | 347.980i | −2.09234 | + | 0.470243i | ||||
\(741\) | 529.757 | 0.714922 | ||||||||
\(742\) | 185.081 | − | 185.081i | 0.249435 | − | 0.249435i | ||||
\(743\) | −44.7015 | − | 44.7015i | −0.0601636 | − | 0.0601636i | 0.676385 | − | 0.736548i | \(-0.263546\pi\) |
−0.736548 | + | 0.676385i | \(0.763546\pi\) | |||||||
\(744\) | − | 193.485i | − | 0.260060i | ||||||
\(745\) | −503.363 | − | 318.626i | −0.675655 | − | 0.427685i | ||||
\(746\) | 1469.25 | 1.96951 | ||||||||
\(747\) | 63.4393 | − | 63.4393i | 0.0849254 | − | 0.0849254i | ||||
\(748\) | −52.3745 | − | 52.3745i | −0.0700194 | − | 0.0700194i | ||||
\(749\) | − | 13.7480i | − | 0.0183551i | ||||||
\(750\) | 676.108 | + | 83.0227i | 0.901477 | + | 0.110697i | ||||
\(751\) | 227.787 | 0.303311 | 0.151656 | − | 0.988433i | \(-0.451540\pi\) | ||||
0.151656 | + | 0.988433i | \(0.451540\pi\) | |||||||
\(752\) | 94.7719 | − | 94.7719i | 0.126027 | − | 0.126027i | ||||
\(753\) | −495.706 | − | 495.706i | −0.658308 | − | 0.658308i | ||||
\(754\) | − | 39.6867i | − | 0.0526349i | ||||||
\(755\) | −387.682 | + | 612.459i | −0.513486 | + | 0.811204i | ||||
\(756\) | −62.8332 | −0.0831126 | ||||||||
\(757\) | −235.925 | + | 235.925i | −0.311658 | + | 0.311658i | −0.845552 | − | 0.533894i | \(-0.820728\pi\) |
0.533894 | + | 0.845552i | \(0.320728\pi\) | |||||||
\(758\) | −467.196 | − | 467.196i | −0.616354 | − | 0.616354i | ||||
\(759\) | − | 134.919i | − | 0.177759i | ||||||
\(760\) | 135.576 | + | 603.242i | 0.178389 | + | 0.793739i | ||||
\(761\) | −881.242 | −1.15801 | −0.579003 | − | 0.815326i | \(-0.696558\pi\) | ||||
−0.579003 | + | 0.815326i | \(0.696558\pi\) | |||||||
\(762\) | 624.626 | − | 624.626i | 0.819719 | − | 0.819719i | ||||
\(763\) | 56.9694 | + | 56.9694i | 0.0746650 | + | 0.0746650i | ||||
\(764\) | 236.495i | 0.309548i | ||||||||
\(765\) | −54.8786 | + | 12.3337i | −0.0717367 | + | 0.0161225i | ||||
\(766\) | −759.221 | −0.991151 | ||||||||
\(767\) | −1169.66 | + | 1169.66i | −1.52497 | + | 1.52497i | ||||
\(768\) | −146.684 | − | 146.684i | −0.190995 | − | 0.190995i | ||||
\(769\) | 1208.40i | 1.57139i | 0.618612 | + | 0.785697i | \(0.287696\pi\) | ||||
−0.618612 | + | 0.785697i | \(0.712304\pi\) | |||||||
\(770\) | 91.2372 | + | 57.7526i | 0.118490 | + | 0.0750033i | ||||
\(771\) | −218.586 | −0.283509 | ||||||||
\(772\) | 457.556 | − | 457.556i | 0.592689 | − | 0.592689i | ||||
\(773\) | −815.226 | − | 815.226i | −1.05463 | − | 1.05463i | −0.998419 | − | 0.0562070i | \(-0.982099\pi\) |
−0.0562070 | − | 0.998419i | \(-0.517901\pi\) | |||||||
\(774\) | − | 300.272i | − | 0.387949i | ||||||
\(775\) | 200.000 | + | 422.474i | 0.258065 | + | 0.545128i | ||||
\(776\) | 123.328 | 0.158928 | ||||||||
\(777\) | −135.081 | + | 135.081i | −0.173849 | + | 0.173849i | ||||
\(778\) | 1217.69 | + | 1217.69i | 1.56515 | + | 1.56515i | ||||
\(779\) | − | 593.939i | − | 0.762437i | ||||||
\(780\) | −403.782 | + | 637.893i | −0.517669 | + | 0.817812i | ||||
\(781\) | 227.696 | 0.291544 | ||||||||
\(782\) | 194.070 | − | 194.070i | 0.248172 | − | 0.248172i | ||||
\(783\) | 3.13622 | + | 3.13622i | 0.00400539 | + | 0.00400539i | ||||
\(784\) | 214.939i | 0.274157i | ||||||||
\(785\) | −79.3031 | − | 352.858i | −0.101023 | − | 0.449501i | ||||
\(786\) | 142.429 | 0.181207 | ||||||||
\(787\) | 813.010 | − | 813.010i | 1.03305 | − | 1.03305i | 0.0336150 | − | 0.999435i | \(-0.489298\pi\) |
0.999435 | − | 0.0336150i | \(-0.0107020\pi\) | |||||||
\(788\) | 397.019 | + | 397.019i | 0.503832 | + | 0.503832i | ||||
\(789\) | − | 837.342i | − | 1.06127i | ||||||
\(790\) | 375.959 | − | 84.4949i | 0.475898 | − | 0.106956i | ||||
\(791\) | −41.6255 | −0.0526239 | ||||||||
\(792\) | 42.4393 | − | 42.4393i | 0.0535850 | − | 0.0535850i | ||||
\(793\) | −983.201 | − | 983.201i | −1.23985 | − | 1.23985i | ||||
\(794\) | 201.373i | 0.253619i | ||||||||
\(795\) | 296.969 | + | 187.980i | 0.373546 | + | 0.236452i | ||||
\(796\) | −1482.97 | −1.86302 | ||||||||
\(797\) | 311.217 | − | 311.217i | 0.390485 | − | 0.390485i | −0.484375 | − | 0.874860i | \(-0.660953\pi\) |
0.874860 | + | 0.484375i | \(0.160953\pi\) | |||||||
\(798\) | 163.485 | + | 163.485i | 0.204868 | + | 0.204868i | ||||
\(799\) | 104.749i | 0.131100i | ||||||||
\(800\) | 917.991 | + | 328.093i | 1.14749 | + | 0.410116i | ||||
\(801\) | −282.545 | −0.352740 | ||||||||
\(802\) | 1157.54 | − | 1157.54i | 1.44332 | − | 1.44332i | ||||
\(803\) | 133.228 | + | 133.228i | 0.165913 | + | 0.165913i | ||||
\(804\) | 793.262i | 0.986645i | ||||||||
\(805\) | −127.526 | + | 201.464i | −0.158417 | + | 0.250266i | ||||
\(806\) | −869.312 | −1.07855 | ||||||||
\(807\) | −4.28724 | + | 4.28724i | −0.00531256 | + | 0.00531256i | ||||
\(808\) | 733.504 | + | 733.504i | 0.907802 | + | 0.907802i | ||||
\(809\) | 150.000i | 0.185414i | 0.995693 | + | 0.0927070i | \(0.0295520\pi\) | ||||
−0.995693 | + | 0.0927070i | \(0.970448\pi\) | |||||||
\(810\) | −31.0454 | − | 138.136i | −0.0383277 | − | 0.170539i | ||||
\(811\) | −132.847 | −0.163806 | −0.0819032 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819032 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(812\) | 7.29847 | − | 7.29847i | 0.00898827 | − | 0.00898827i | ||||
\(813\) | −126.854 | − | 126.854i | −0.156031 | − | 0.156031i | ||||
\(814\) | − | 566.838i | − | 0.696361i | ||||||
\(815\) | 1306.62 | − | 293.657i | 1.60322 | − | 0.360316i | ||||
\(816\) | −31.1623 | −0.0381890 | ||||||||
\(817\) | −465.576 | + | 465.576i | −0.569860 | + | 0.569860i | ||||
\(818\) | 772.232 | + | 772.232i | 0.944048 | + | 0.944048i | ||||
\(819\) | 90.8786i | 0.110963i | ||||||||
\(820\) | 715.176 | + | 452.702i | 0.872166 | + | 0.552075i | ||||
\(821\) | 509.893 | 0.621064 | 0.310532 | − | 0.950563i | \(-0.399493\pi\) | ||||
0.310532 | + | 0.950563i | \(0.399493\pi\) | |||||||
\(822\) | −79.7321 | + | 79.7321i | −0.0969977 | + | 0.0969977i | ||||
\(823\) | 300.369 | + | 300.369i | 0.364968 | + | 0.364968i | 0.865638 | − | 0.500670i | \(-0.166913\pi\) |
−0.500670 | + | 0.865638i | \(0.666913\pi\) | |||||||
\(824\) | − | 547.126i | − | 0.663988i | ||||||
\(825\) | −48.7980 | + | 136.535i | −0.0591490 | + | 0.165497i | ||||
\(826\) | −721.918 | −0.873993 | ||||||||
\(827\) | −1030.76 | + | 1030.76i | −1.24638 | + | 1.24638i | −0.289073 | + | 0.957307i | \(0.593347\pi\) |
−0.957307 | + | 0.289073i | \(0.906653\pi\) | |||||||
\(828\) | 291.106 | + | 291.106i | 0.351577 | + | 0.351577i | ||||
\(829\) | − | 37.4235i | − | 0.0451429i | −0.999745 | − | 0.0225714i | \(-0.992815\pi\) | ||
0.999745 | − | 0.0225714i | \(-0.00718533\pi\) | |||||||
\(830\) | 251.621 | − | 397.510i | 0.303158 | − | 0.478927i | ||||
\(831\) | −699.353 | −0.841580 | ||||||||
\(832\) | −1081.47 | + | 1081.47i | −1.29984 | + | 1.29984i | ||||
\(833\) | −118.783 | − | 118.783i | −0.142597 | − | 0.142597i | ||||
\(834\) | 453.242i | 0.543455i | ||||||||
\(835\) | −150.454 | − | 669.444i | −0.180185 | − | 0.801729i | ||||
\(836\) | −408.817 | −0.489016 | ||||||||
\(837\) | 68.6969 | − | 68.6969i | 0.0820752 | − | 0.0820752i | ||||
\(838\) | −1297.91 | − | 1297.91i | −1.54882 | − | 1.54882i | ||||
\(839\) | 1152.37i | 1.37351i | 0.726890 | + | 0.686754i | \(0.240965\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(840\) | −103.485 | + | 23.2577i | −0.123196 | + | 0.0276877i | ||||
\(841\) | 840.271 | 0.999134 | ||||||||
\(842\) | −474.207 | + | 474.207i | −0.563191 | + | 0.563191i | ||||
\(843\) | 456.459 | + | 456.459i | 0.541469 | + | 0.541469i | ||||
\(844\) | − | 1561.98i | − | 1.85068i | ||||||
\(845\) | 208.633 | + | 132.064i | 0.246903 | + | 0.156288i | ||||
\(846\) | −263.666 | −0.311662 | ||||||||
\(847\) | 159.136 | − | 159.136i | 0.187882 | − | 0.187882i | ||||
\(848\) | 137.687 | + | 137.687i | 0.162366 | + | 0.162366i | ||||
\(849\) | − | 189.081i | − | 0.222710i | ||||||
\(850\) | −266.586 | + | 126.202i | −0.313630 | + | 0.148473i | ||||
\(851\) | 1251.66 | 1.47081 | ||||||||
\(852\) | −491.283 | + | 491.283i | −0.576623 | + | 0.576623i | ||||
\(853\) | 694.570 | + | 694.570i | 0.814267 | + | 0.814267i | 0.985270 | − | 0.171003i | \(-0.0547009\pi\) |
−0.171003 | + | 0.985270i | \(0.554701\pi\) | |||||||
\(854\) | − | 606.838i | − | 0.710583i | ||||||
\(855\) | −166.045 | + | 262.318i | −0.194205 | + | 0.306805i | ||||
\(856\) | −40.0704 | −0.0468112 | ||||||||
\(857\) | 417.176 | − | 417.176i | 0.486786 | − | 0.486786i | −0.420504 | − | 0.907291i | \(-0.638147\pi\) |
0.907291 | + | 0.420504i | \(0.138147\pi\) | |||||||
\(858\) | −190.677 | − | 190.677i | −0.222234 | − | 0.222234i | ||||
\(859\) | − | 486.867i | − | 0.566784i | −0.959004 | − | 0.283392i | \(-0.908540\pi\) | ||
0.959004 | − | 0.283392i | \(-0.0914597\pi\) | |||||||
\(860\) | −205.748 | − | 915.473i | −0.239242 | − | 1.06450i | ||||
\(861\) | 101.889 | 0.118338 | ||||||||
\(862\) | −416.838 | + | 416.838i | −0.483570 | + | 0.483570i | ||||
\(863\) | −411.319 | − | 411.319i | −0.476615 | − | 0.476615i | 0.427432 | − | 0.904047i | \(-0.359418\pi\) |
−0.904047 | + | 0.427432i | \(0.859418\pi\) | |||||||
\(864\) | − | 202.621i | − | 0.234515i | ||||||
\(865\) | −238.919 | + | 53.6959i | −0.276207 | + | 0.0620762i | ||||
\(866\) | −688.994 | −0.795606 | ||||||||
\(867\) | −336.730 | + | 336.730i | −0.388385 | + | 0.388385i | ||||
\(868\) | −159.868 | − | 159.868i | −0.184180 | − | 0.184180i | ||||
\(869\) | 82.0204i | 0.0943848i | ||||||||
\(870\) | 19.6515 | + | 12.4393i | 0.0225880 | + | 0.0142980i | ||||
\(871\) | 1147.33 | 1.31726 | ||||||||
\(872\) | 166.045 | − | 166.045i | 0.190419 | − | 0.190419i | ||||
\(873\) | 43.7878 | + | 43.7878i | 0.0501578 | + | 0.0501578i | ||||
\(874\) | − | 1514.85i | − | 1.73323i | ||||||
\(875\) | 201.918 | − | 157.753i | 0.230764 | − | 0.180289i | ||||
\(876\) | −574.913 | −0.656293 | ||||||||
\(877\) | 332.540 | − | 332.540i | 0.379179 | − | 0.379179i | −0.491627 | − | 0.870806i | \(-0.663598\pi\) |
0.870806 | + | 0.491627i | \(0.163598\pi\) | |||||||
\(878\) | −562.702 | − | 562.702i | −0.640890 | − | 0.640890i | ||||
\(879\) | − | 579.464i | − | 0.659231i | ||||||
\(880\) | −42.9638 | + | 67.8740i | −0.0488225 | + | 0.0771295i | ||||
\(881\) | 533.151 | 0.605166 | 0.302583 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302583 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(882\) | 298.992 | − | 298.992i | 0.338993 | − | 0.338993i | ||||
\(883\) | −745.939 | − | 745.939i | −0.844778 | − | 0.844778i | 0.144698 | − | 0.989476i | \(-0.453779\pi\) |
−0.989476 | + | 0.144698i | \(0.953779\pi\) | |||||||
\(884\) | − | 326.888i | − | 0.369783i | ||||||
\(885\) | −212.561 | − | 945.787i | −0.240182 | − | 1.06869i | ||||
\(886\) | 1873.82 | 2.11492 | ||||||||
\(887\) | −386.207 | + | 386.207i | −0.435408 | + | 0.435408i | −0.890463 | − | 0.455055i | \(-0.849619\pi\) |
0.455055 | + | 0.890463i | \(0.349619\pi\) | |||||||
\(888\) | 393.712 | + | 393.712i | 0.443369 | + | 0.443369i | ||||
\(889\) | − | 332.284i | − | 0.373772i | ||||||
\(890\) | −1445.54 | + | 324.879i | −1.62421 | + | 0.365032i | ||||
\(891\) | 30.1362 | 0.0338229 | ||||||||
\(892\) | −197.197 | + | 197.197i | −0.221073 | + | 0.221073i | ||||
\(893\) | 408.817 | + | 408.817i | 0.457802 | + | 0.457802i | ||||
\(894\) | 649.287i | 0.726272i | ||||||||
\(895\) | 776.135 | + | 491.288i | 0.867190 | + | 0.548925i | ||||
\(896\) | −347.753 | −0.388117 | ||||||||
\(897\) | 421.040 | − | 421.040i | 0.469387 | − | 0.469387i | ||||
\(898\) | 662.772 | + | 662.772i | 0.738053 | + | 0.738053i | ||||
\(899\) | 15.9592i | 0.0177521i | ||||||||
\(900\) | −189.303 | − | 399.879i | −0.210337 | − | 0.444310i | ||||
\(901\) | −152.182 | −0.168903 | ||||||||
\(902\) | −213.778 | + | 213.778i | −0.237004 | + | 0.237004i | ||||
\(903\) | −79.8684 | − | 79.8684i | −0.0884478 | − | 0.0884478i | ||||
\(904\) | 121.323i | 0.134207i | ||||||||
\(905\) | −58.1046 | + | 91.7934i | −0.0642040 | + | 0.101429i | ||||
\(906\) | 790.009 | 0.871975 | ||||||||
\(907\) | −947.342 | + | 947.342i | −1.04448 | + | 1.04448i | −0.0455146 | + | 0.998964i | \(0.514493\pi\) |
−0.998964 | + | 0.0455146i | \(0.985507\pi\) | |||||||
\(908\) | 124.890 | + | 124.890i | 0.137544 | + | 0.137544i | ||||
\(909\) | 520.863i | 0.573006i | ||||||||
\(910\) | 104.495 | + | 464.949i | 0.114830 | + | 0.510933i | ||||
\(911\) | −1149.36 | −1.26165 | −0.630824 | − | 0.775926i | \(-0.717283\pi\) | ||||
−0.630824 | + | 0.775926i | \(0.717283\pi\) | |||||||
\(912\) | −121.621 | + | 121.621i | −0.133356 | + | 0.133356i | ||||
\(913\) | 70.8082 | + | 70.8082i | 0.0775555 | + | 0.0775555i | ||||
\(914\) | 1271.43i | 1.39106i | ||||||||
\(915\) | 795.019 | − | 178.677i | 0.868874 | − | 0.195275i | ||||
\(916\) | 1438.16 | 1.57004 | ||||||||
\(917\) | 37.8842 | − | 37.8842i | 0.0413132 | − | 0.0413132i | ||||
\(918\) | 43.3485 | + | 43.3485i | 0.0472206 | + | 0.0472206i | ||||
\(919\) | − | 412.577i | − | 0.448941i | −0.974481 | − | 0.224470i | \(-0.927935\pi\) | ||
0.974481 | − | 0.224470i | \(-0.0720652\pi\) | |||||||
\(920\) | 587.196 | + | 371.691i | 0.638257 | + | 0.404012i | ||||
\(921\) | 413.889 | 0.449391 | ||||||||
\(922\) | −1171.59 | + | 1171.59i | −1.27071 | + | 1.27071i | ||||
\(923\) | 710.565 | + | 710.565i | 0.769843 | + | 0.769843i | ||||
\(924\) | − | 70.1316i | − | 0.0759000i | ||||||
\(925\) | −1266.64 | − | 452.702i | −1.36934 | − | 0.489407i | ||||
\(926\) | −1493.70 | −1.61307 | ||||||||
\(927\) | 194.258 | − | 194.258i | 0.209555 | − | 0.209555i | ||||
\(928\) | 23.5357 | + | 23.5357i | 0.0253618 | + | 0.0253618i | ||||
\(929\) | 151.707i | 0.163302i | 0.996661 | + | 0.0816508i | \(0.0260192\pi\) | ||||
−0.996661 | + | 0.0816508i | \(0.973981\pi\) | |||||||
\(930\) | 272.474 | − | 430.454i | 0.292983 | − | 0.462854i | ||||
\(931\) | −927.181 | −0.995898 | ||||||||
\(932\) | 953.934 | − | 953.934i | 1.02353 | − | 1.02353i | ||||
\(933\) | 433.930 | + | 433.930i | 0.465091 | + | 0.465091i | ||||
\(934\) | 2174.65i | 2.32832i | ||||||||
\(935\) | −13.7663 | − | 61.2531i | −0.0147233 | − | 0.0655113i | ||||
\(936\) | 264.879 | 0.282990 | ||||||||
\(937\) | 662.090 | − | 662.090i | 0.706606 | − | 0.706606i | −0.259214 | − | 0.965820i | \(-0.583463\pi\) |
0.965820 | + | 0.259214i | \(0.0834635\pi\) | |||||||
\(938\) | 354.070 | + | 354.070i | 0.377474 | + | 0.377474i | ||||
\(939\) | 373.237i | 0.397484i | ||||||||
\(940\) | −803.868 | + | 180.665i | −0.855179 | + | 0.192197i | ||||
\(941\) | −1533.77 | −1.62994 | −0.814969 | − | 0.579505i | \(-0.803246\pi\) | ||||
−0.814969 | + | 0.579505i | \(0.803246\pi\) | |||||||
\(942\) | −278.722 | + | 278.722i | −0.295883 | + | 0.295883i | ||||
\(943\) | −472.050 | − | 472.050i | −0.500583 | − | 0.500583i | ||||
\(944\) | − | 537.056i | − | 0.568915i | ||||||
\(945\) | −45.0000 | − | 28.4847i | −0.0476190 | − | 0.0301425i | ||||
\(946\) | 335.151 | 0.354282 | ||||||||
\(947\) | 1173.19 | − | 1173.19i | 1.23885 | − | 1.23885i | 0.278377 | − | 0.960472i | \(-0.410204\pi\) |
0.960472 | − | 0.278377i | \(-0.0897964\pi\) | |||||||
\(948\) | −176.969 | − | 176.969i | −0.186677 | − | 0.186677i | ||||
\(949\) | 831.523i | 0.876210i | ||||||||
\(950\) | −547.893 | + | 1532.98i | −0.576730 | + | 1.61367i | ||||
\(951\) | −1046.46 | −1.10038 | ||||||||
\(952\) | 32.4745 | − | 32.4745i | 0.0341119 | − | 0.0341119i | ||||
\(953\) | −145.501 | − | 145.501i | −0.152676 | − | 0.152676i | 0.626636 | − | 0.779312i | \(-0.284431\pi\) |
−0.779312 | + | 0.626636i | \(0.784431\pi\) | |||||||
\(954\) | − | 383.060i | − | 0.401531i | ||||||
\(955\) | −107.212 | + | 169.373i | −0.112264 | + | 0.177354i | ||||
\(956\) | 1924.26 | 2.01282 | ||||||||
\(957\) | −3.50052 | + | 3.50052i | −0.00365780 | + | 0.00365780i | ||||
\(958\) | −411.464 | − | 411.464i | −0.429503 | − | 0.429503i | ||||
\(959\) | 42.4153i | 0.0442287i | ||||||||
\(960\) | −196.535 | − | 874.479i | −0.204724 | − | 0.910916i | ||||
\(961\) | −611.424 | −0.636238 | ||||||||
\(962\) | 1768.92 | − | 1768.92i | 1.83879 | − | 1.83879i | ||||
\(963\) | −14.2270 | − | 14.2270i | −0.0147737 | − | 0.0147737i | ||||
\(964\) | 787.959i | 0.817385i | ||||||||
\(965\) | 535.121 | − | 120.266i | 0.554530 | − | 0.124628i | ||||
\(966\) | 259.868 | 0.269015 | ||||||||
\(967\) | 1151.69 | − | 1151.69i | 1.19099 | − | 1.19099i | 0.214204 | − | 0.976789i | \(-0.431284\pi\) |
0.976789 | − | 0.214204i | \(-0.0687158\pi\) | |||||||
\(968\) | −463.825 | − | 463.825i | −0.479158 | − | 0.479158i | ||||
\(969\) | − | 134.424i | − | 0.138725i | ||||||
\(970\) | 274.373 | + | 173.677i | 0.282859 | + | 0.179048i | ||||
\(971\) | 72.4383 | 0.0746017 | 0.0373009 | − | 0.999304i | \(-0.488124\pi\) | ||||
0.0373009 | + | 0.999304i | \(0.488124\pi\) | |||||||
\(972\) | −65.0227 | + | 65.0227i | −0.0668958 | + | 0.0668958i | ||||
\(973\) | 120.556 | + | 120.556i | 0.123901 | + | 0.123901i | ||||
\(974\) | − | 536.974i | − | 0.551308i | ||||||
\(975\) | −578.363 | + | 273.798i | −0.593193 | + | 0.280818i | ||||
\(976\) | 451.444 | 0.462545 | ||||||||
\(977\) | 706.338 | − | 706.338i | 0.722966 | − | 0.722966i | −0.246242 | − | 0.969208i | \(-0.579196\pi\) |
0.969208 | + | 0.246242i | \(0.0791958\pi\) | |||||||
\(978\) | −1032.10 | − | 1032.10i | −1.05532 | − | 1.05532i | ||||
\(979\) | − | 315.364i | − | 0.322129i | ||||||
\(980\) | 706.699 | − | 1116.44i | 0.721122 | − | 1.13923i | ||||
\(981\) | 117.909 | 0.120193 | ||||||||
\(982\) | 235.116 | − | 235.116i | 0.239425 | − | 0.239425i | ||||
\(983\) | −134.663 | − | 134.663i | −0.136992 | − | 0.136992i | 0.635286 | − | 0.772277i | \(-0.280882\pi\) |
−0.772277 | + | 0.635286i | \(0.780882\pi\) | |||||||
\(984\) | − | 296.969i | − | 0.301798i | ||||||
\(985\) | 104.354 | + | 464.322i | 0.105943 | + | 0.471393i | ||||
\(986\) | −10.0704 | −0.0102134 | ||||||||
\(987\) | −70.1316 | + | 70.1316i | −0.0710554 | + | 0.0710554i | ||||
\(988\) | −1275.79 | − | 1275.79i | −1.29128 | − | 1.29128i | ||||
\(989\) | 740.059i | 0.748290i | ||||||||
\(990\) | 154.182 | − | 34.6515i | 0.155739 | − | 0.0350015i | ||||
\(991\) | −1131.94 | −1.14222 | −0.571109 | − | 0.820874i | \(-0.693487\pi\) | ||||
−0.571109 | + | 0.820874i | \(0.693487\pi\) | |||||||
\(992\) | 515.535 | − | 515.535i | 0.519692 | − | 0.519692i | ||||
\(993\) | 599.419 | + | 599.419i | 0.603644 | + | 0.603644i | ||||
\(994\) | 438.565i | 0.441213i | ||||||||
\(995\) | −1062.07 | − | 672.286i | −1.06741 | − | 0.675665i | ||||
\(996\) | −305.555 | −0.306782 | ||||||||
\(997\) | −1115.27 | + | 1115.27i | −1.11862 | + | 1.11862i | −0.126679 | + | 0.991944i | \(0.540432\pi\) |
−0.991944 | + | 0.126679i | \(0.959568\pi\) | |||||||
\(998\) | −1645.39 | − | 1645.39i | −1.64868 | − | 1.64868i | ||||
\(999\) | 279.576i | 0.279855i |
(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 | 15.3.f.a.13.1 | yes | 4 | |
3.2 | odd | 2 | 45.3.g.b.28.2 | 4 | |||
4.3 | odd | 2 | 240.3.bg.a.193.1 | 4 | |||
5.2 | odd | 4 | inner | 15.3.f.a.7.1 | ✓ | 4 | |
5.3 | odd | 4 | 75.3.f.c.7.2 | 4 | |||
5.4 | even | 2 | 75.3.f.c.43.2 | 4 | |||
8.3 | odd | 2 | 960.3.bg.h.193.2 | 4 | |||
8.5 | even | 2 | 960.3.bg.i.193.1 | 4 | |||
9.2 | odd | 6 | 405.3.l.f.28.1 | 8 | |||
9.4 | even | 3 | 405.3.l.h.298.1 | 8 | |||
9.5 | odd | 6 | 405.3.l.f.298.2 | 8 | |||
9.7 | even | 3 | 405.3.l.h.28.2 | 8 | |||
12.11 | even | 2 | 720.3.bh.k.433.1 | 4 | |||
15.2 | even | 4 | 45.3.g.b.37.2 | 4 | |||
15.8 | even | 4 | 225.3.g.a.82.1 | 4 | |||
15.14 | odd | 2 | 225.3.g.a.118.1 | 4 | |||
20.3 | even | 4 | 1200.3.bg.k.1057.2 | 4 | |||
20.7 | even | 4 | 240.3.bg.a.97.1 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.k.193.2 | 4 | |||
40.27 | even | 4 | 960.3.bg.h.577.2 | 4 | |||
40.37 | odd | 4 | 960.3.bg.i.577.1 | 4 | |||
45.2 | even | 12 | 405.3.l.f.352.2 | 8 | |||
45.7 | odd | 12 | 405.3.l.h.352.1 | 8 | |||
45.22 | odd | 12 | 405.3.l.h.217.2 | 8 | |||
45.32 | even | 12 | 405.3.l.f.217.1 | 8 | |||
60.47 | odd | 4 | 720.3.bh.k.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.1 | ✓ | 4 | 5.2 | odd | 4 | inner | |
15.3.f.a.13.1 | yes | 4 | 1.1 | even | 1 | trivial | |
45.3.g.b.28.2 | 4 | 3.2 | odd | 2 | |||
45.3.g.b.37.2 | 4 | 15.2 | even | 4 | |||
75.3.f.c.7.2 | 4 | 5.3 | odd | 4 | |||
75.3.f.c.43.2 | 4 | 5.4 | even | 2 | |||
225.3.g.a.82.1 | 4 | 15.8 | even | 4 | |||
225.3.g.a.118.1 | 4 | 15.14 | odd | 2 | |||
240.3.bg.a.97.1 | 4 | 20.7 | even | 4 | |||
240.3.bg.a.193.1 | 4 | 4.3 | odd | 2 | |||
405.3.l.f.28.1 | 8 | 9.2 | odd | 6 | |||
405.3.l.f.217.1 | 8 | 45.32 | even | 12 | |||
405.3.l.f.298.2 | 8 | 9.5 | odd | 6 | |||
405.3.l.f.352.2 | 8 | 45.2 | even | 12 | |||
405.3.l.h.28.2 | 8 | 9.7 | even | 3 | |||
405.3.l.h.217.2 | 8 | 45.22 | odd | 12 | |||
405.3.l.h.298.1 | 8 | 9.4 | even | 3 | |||
405.3.l.h.352.1 | 8 | 45.7 | odd | 12 | |||
720.3.bh.k.433.1 | 4 | 12.11 | even | 2 | |||
720.3.bh.k.577.1 | 4 | 60.47 | odd | 4 | |||
960.3.bg.h.193.2 | 4 | 8.3 | odd | 2 | |||
960.3.bg.h.577.2 | 4 | 40.27 | even | 4 | |||
960.3.bg.i.193.1 | 4 | 8.5 | even | 2 | |||
960.3.bg.i.577.1 | 4 | 40.37 | odd | 4 | |||
1200.3.bg.k.193.2 | 4 | 20.19 | odd | 2 | |||
1200.3.bg.k.1057.2 | 4 | 20.3 | even | 4 |