Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [140,2,Mod(17,140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("140.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.u (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.11790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(0.500000 - 2.27536i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 140.17 |
Dual form | 140.2.u.a.33.4 |
$q$-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 \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.42519 | − | 0.649827i | 1.40018 | − | 0.375178i | 0.521773 | − | 0.853085i | \(-0.325271\pi\) |
0.878411 | + | 0.477907i | \(0.158604\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.19862 | − | 0.407542i | −0.983251 | − | 0.182258i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59537 | − | 0.513853i | 0.980958 | − | 0.194218i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.86119 | − | 1.65191i | 0.953729 | − | 0.550636i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.86346 | + | 3.22761i | −0.561855 | + | 0.973161i | 0.435480 | + | 0.900199i | \(0.356579\pi\) |
−0.997335 | + | 0.0729628i | \(0.976755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.90450 | − | 2.90450i | −0.805563 | − | 0.805563i | 0.178396 | − | 0.983959i | \(-0.442909\pi\) |
−0.983959 | + | 0.178396i | \(0.942909\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.59689 | + | 0.440354i | −1.44511 | + | 0.113699i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.78788 | + | 6.67247i | 0.433625 | + | 1.61831i | 0.744335 | + | 0.667806i | \(0.232767\pi\) |
−0.310710 | + | 0.950505i | \(0.600567\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.65698 | − | 2.86997i | −0.380136 | − | 0.658415i | 0.610945 | − | 0.791673i | \(-0.290790\pi\) |
−0.991081 | + | 0.133258i | \(0.957456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.96035 | − | 2.93273i | 1.30066 | − | 0.639975i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.84153 | − | 0.493436i | −0.383985 | − | 0.102889i | 0.0616623 | − | 0.998097i | \(-0.480360\pi\) |
−0.445647 | + | 0.895209i | \(0.647026\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.66782 | + | 1.79206i | 0.933564 | + | 0.358411i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.539383 | − | 0.539383i | 0.103804 | − | 0.103804i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.563886i | 0.104711i | 0.998629 | + | 0.0523555i | \(0.0166729\pi\) | ||||
−0.998629 | + | 0.0523555i | \(0.983327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.20505 | − | 1.85044i | −0.575644 | − | 0.332348i | 0.183756 | − | 0.982972i | \(-0.441174\pi\) |
−0.759400 | + | 0.650624i | \(0.774508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.42186 | + | 9.03849i | −0.421591 | + | 1.57340i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.91564 | + | 0.0720411i | −0.999926 | + | 0.0121772i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.268453 | + | 1.00188i | −0.0441334 | + | 0.164708i | −0.984475 | − | 0.175523i | \(-0.943838\pi\) |
0.940342 | + | 0.340231i | \(0.110505\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.93138 | − | 5.15654i | −1.43017 | − | 0.825706i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.88697i | − | 1.23174i | −0.787849 | − | 0.615869i | \(-0.788805\pi\) | ||
0.787849 | − | 0.615869i | \(-0.211195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.53537 | + | 7.53537i | −1.14913 | + | 1.14913i | −0.162409 | + | 0.986723i | \(0.551926\pi\) |
−0.986723 | + | 0.162409i | \(0.948074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.96387 | + | 2.46586i | −1.03811 | + | 0.367588i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.543934 | − | 0.145747i | −0.0793410 | − | 0.0212593i | 0.218930 | − | 0.975741i | \(-0.429743\pi\) |
−0.298271 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.47191 | − | 2.66728i | 0.924559 | − | 0.381040i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.67191 | + | 15.0202i | 1.21431 | + | 2.10325i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.479610 | + | 1.78993i | 0.0658795 | + | 0.245866i | 0.991011 | − | 0.133782i | \(-0.0427120\pi\) |
−0.925131 | + | 0.379647i | \(0.876045\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.41242 | − | 6.33684i | 0.729811 | − | 0.854459i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.88346 | − | 5.88346i | −0.779283 | − | 0.779283i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.38015 | − | 11.0507i | 0.830624 | − | 1.43868i | −0.0669197 | − | 0.997758i | \(-0.521317\pi\) |
0.897544 | − | 0.440925i | \(-0.145350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00463 | − | 4.62147i | 1.02489 | − | 0.591719i | 0.109372 | − | 0.994001i | \(-0.465116\pi\) |
0.915516 | + | 0.402282i | \(0.131783\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.57701 | − | 5.75754i | 0.828625 | − | 0.725382i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.20217 | + | 7.56958i | 0.645250 | + | 0.938891i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.56658 | − | 1.49156i | 0.680065 | − | 0.182223i | 0.0977808 | − | 0.995208i | \(-0.468826\pi\) |
0.582285 | + | 0.812985i | \(0.302159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.78670 | −0.576251 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.683178 | 0.0810783 | 0.0405391 | − | 0.999178i | \(-0.487092\pi\) | ||||
0.0405391 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6096 | − | 3.11079i | 1.35880 | − | 0.364091i | 0.495427 | − | 0.868649i | \(-0.335012\pi\) |
0.863377 | + | 0.504559i | \(0.168345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.4849 | + | 1.31280i | 1.44163 | + | 0.151589i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.17786 | + | 9.33440i | −0.362151 | + | 1.06375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.76589 | + | 1.59689i | −0.311187 | + | 0.179664i | −0.647458 | − | 0.762101i | \(-0.724168\pi\) |
0.336270 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.99812 | + | 6.92495i | −0.444236 | + | 0.769439i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.44070 | + | 1.44070i | 0.158138 | + | 0.158138i | 0.781741 | − | 0.623603i | \(-0.214332\pi\) |
−0.623603 | + | 0.781741i | \(0.714332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21155 | − | 15.3988i | −0.131411 | − | 1.67024i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.366428 | + | 1.36753i | 0.0392852 | + | 0.146614i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.26421 | − | 2.18968i | −0.134006 | − | 0.232106i | 0.791211 | − | 0.611543i | \(-0.209451\pi\) |
−0.925217 | + | 0.379437i | \(0.876118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.03074 | − | 6.04577i | −0.946679 | − | 0.633769i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.97532 | − | 2.40493i | −0.930697 | − | 0.249380i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.47342 | + | 6.98524i | 0.253767 | + | 0.716670i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.99033 | − | 3.99033i | 0.405156 | − | 0.405156i | −0.474889 | − | 0.880046i | \(-0.657512\pi\) |
0.880046 | + | 0.474889i | \(0.157512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.3131i | 1.23751i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5093 | − | 6.64487i | −1.14521 | − | 0.661189i | −0.197497 | − | 0.980303i | \(-0.563281\pi\) |
−0.947716 | + | 0.319114i | \(0.896615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.243935 | + | 0.910379i | −0.0240357 | + | 0.0897023i | −0.976902 | − | 0.213689i | \(-0.931452\pi\) |
0.952866 | + | 0.303391i | \(0.0981188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.2997 | + | 4.01886i | −1.39551 | + | 0.392200i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.06874 | − | 7.72065i | 0.199993 | − | 0.746383i | −0.790925 | − | 0.611913i | \(-0.790400\pi\) |
0.990918 | − | 0.134470i | \(-0.0429332\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1969 | + | 7.04187i | 1.16825 | + | 0.674489i | 0.953267 | − | 0.302129i | \(-0.0976974\pi\) |
0.214982 | + | 0.976618i | \(0.431031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.60420i | 0.247179i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.16304 | − | 3.16304i | 0.297554 | − | 0.297554i | −0.542501 | − | 0.840055i | \(-0.682523\pi\) |
0.840055 | + | 0.542501i | \(0.182523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.84772 | + | 1.83538i | 0.358801 | + | 0.171150i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.1083 | − | 3.51235i | −1.21186 | − | 0.324717i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.06889 | + | 16.3988i | 0.739674 | + | 1.50328i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.44498 | − | 2.50278i | −0.131362 | − | 0.227526i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.12517 | − | 19.1274i | −0.462121 | − | 1.72466i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.53240 | − | 5.84238i | −0.852604 | − | 0.522558i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.75766 | + | 7.75766i | 0.688381 | + | 0.688381i | 0.961874 | − | 0.273493i | \(-0.0881789\pi\) |
−0.273493 | + | 0.961874i | \(0.588179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.3780 | + | 23.1714i | −1.17787 | + | 2.04013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.80420 | + | 2.19636i | −0.332375 | + | 0.191897i | −0.656895 | − | 0.753982i | \(-0.728131\pi\) |
0.324520 | + | 0.945879i | \(0.394797\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.77521 | − | 6.59719i | −0.500774 | − | 0.572049i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.40572 | + | 0.966074i | −0.120985 | + | 0.0831464i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.83901 | + | 1.83251i | −0.584296 | + | 0.156562i | −0.538845 | − | 0.842405i | \(-0.681139\pi\) |
−0.0454510 | + | 0.998967i | \(0.514473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.68255 | −0.821263 | −0.410632 | − | 0.911801i | \(-0.634692\pi\) | ||||
−0.410632 | + | 0.911801i | \(0.634692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41385 | −0.119068 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.7870 | − | 3.96217i | 1.23655 | − | 0.331333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.229807 | − | 1.23977i | 0.0190844 | − | 0.102957i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.9623 | − | 10.6743i | 1.15159 | − | 0.880400i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.21464 | − | 3.58802i | 0.509123 | − | 0.293942i | −0.223350 | − | 0.974738i | \(-0.571699\pi\) |
0.732473 | + | 0.680796i | \(0.238366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.52187 | + | 6.10006i | −0.286606 | + | 0.496416i | −0.972997 | − | 0.230816i | \(-0.925860\pi\) |
0.686391 | + | 0.727232i | \(0.259194\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.1378 | + | 16.1378i | 1.30466 | + | 1.30466i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.29254 | + | 5.37459i | 0.505429 | + | 0.431698i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0907875 | − | 0.338824i | −0.00724563 | − | 0.0270411i | 0.962208 | − | 0.272314i | \(-0.0877890\pi\) |
−0.969454 | + | 0.245273i | \(0.921122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.32629 | + | 4.02925i | 0.184487 | + | 0.319540i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.03300 | − | 0.334376i | −0.396656 | − | 0.0263525i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.8709 | − | 6.12825i | −1.79139 | − | 0.480001i | −0.798808 | − | 0.601586i | \(-0.794536\pi\) |
−0.992581 | + | 0.121584i | \(0.961203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.00830 | − | 18.8852i | 0.701295 | − | 1.47021i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2886 | + | 12.2886i | −0.950924 | + | 0.950924i | −0.998851 | − | 0.0479272i | \(-0.984738\pi\) |
0.0479272 | + | 0.998851i | \(0.484738\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.87223i | 0.297864i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.48184 | − | 5.47434i | −0.725094 | − | 0.418633i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.34733 | + | 12.4924i | −0.254492 | + | 0.949779i | 0.713880 | + | 0.700268i | \(0.246936\pi\) |
−0.968372 | + | 0.249510i | \(0.919730\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.0356 | + | 2.25248i | 0.985397 | + | 0.170272i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.29199 | − | 30.9461i | 0.623264 | − | 2.32605i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5351 | − | 8.96922i | −1.16115 | − | 0.670391i | −0.209571 | − | 0.977793i | \(-0.567207\pi\) |
−0.951580 | + | 0.307403i | \(0.900540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8442i | 1.84666i | 0.384013 | + | 0.923328i | \(0.374542\pi\) | ||||
−0.384013 | + | 0.923328i | \(0.625458\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.4096 | − | 16.4096i | 1.21303 | − | 1.21303i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.998533 | − | 2.09334i | 0.0734136 | − | 0.153906i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.8678 | − | 6.66330i | −1.81851 | − | 0.487269i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.12274 | − | 1.67706i | 0.0816670 | − | 0.121988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3611 | − | 17.9459i | −0.749700 | − | 1.29852i | −0.947967 | − | 0.318370i | \(-0.896865\pi\) |
0.198267 | − | 0.980148i | \(-0.436469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.77723 | + | 14.0968i | 0.271891 | + | 1.01471i | 0.957896 | + | 0.287114i | \(0.0926958\pi\) |
−0.686006 | + | 0.727596i | \(0.740638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.5352 | + | 14.9772i | 1.25572 | + | 1.07254i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.55541 | + | 4.55541i | 0.324559 | + | 0.324559i | 0.850513 | − | 0.525954i | \(-0.176292\pi\) |
−0.525954 | + | 0.850513i | \(0.676292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.64840 | + | 11.5154i | −0.471293 | + | 0.816303i | −0.999461 | − | 0.0328370i | \(-0.989546\pi\) |
0.528168 | + | 0.849140i | \(0.322879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.5307 | − | 7.23463i | 0.883850 | − | 0.510291i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.289754 | + | 1.46349i | 0.0203368 | + | 0.102717i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.21427 | + | 17.3404i | −0.224495 | + | 1.21111i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.08407 | + | 1.63022i | −0.422872 | + | 0.113308i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.3508 | 0.854326 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2245 | 0.979256 | 0.489628 | − | 0.871931i | \(-0.337133\pi\) | ||||
0.489628 | + | 0.871931i | \(0.337133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.65684 | − | 0.443948i | 0.113524 | − | 0.0304188i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.6384 | − | 13.4964i | 1.33932 | − | 0.920446i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.26915 | − | 3.15565i | −0.629231 | − | 0.214219i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.1341 | − | 15.0885i | 1.76598 | − | 1.01959i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.1873 | − | 24.5731i | 0.954339 | − | 1.65296i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.14150 | − | 2.14150i | −0.143406 | − | 0.143406i | 0.631759 | − | 0.775165i | \(-0.282333\pi\) |
−0.775165 | + | 0.631759i | \(0.782333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.3158 | − | 2.58339i | 1.08772 | − | 0.172226i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.41341 | + | 9.00695i | 0.160183 | + | 0.597812i | 0.998606 | + | 0.0527911i | \(0.0168117\pi\) |
−0.838422 | + | 0.545021i | \(0.816522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6863 | − | 23.7054i | −0.904417 | − | 1.56650i | −0.821698 | − | 0.569924i | \(-0.806973\pi\) |
−0.0827198 | − | 0.996573i | \(-0.526361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.64117 | + | 24.7027i | −0.107981 | + | 1.62532i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.53462 | + | 1.21505i | 0.297073 | + | 0.0796005i | 0.404277 | − | 0.914637i | \(-0.367523\pi\) |
−0.107204 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.13650 | + | 0.542117i | 0.0741374 | + | 0.0353638i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.67011 | + | 5.67011i | −0.368313 | + | 0.368313i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3001i | − | 0.666256i | −0.942882 | − | 0.333128i | \(-0.891896\pi\) | ||
0.942882 | − | 0.333128i | \(-0.108104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2358 | + | 6.48699i | 0.723761 | + | 0.417864i | 0.816135 | − | 0.577861i | \(-0.196112\pi\) |
−0.0923744 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.78846 | + | 21.6028i | −0.371330 | + | 1.38582i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3163 | + | 3.22674i | −0.978521 | + | 0.206149i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.52313 | + | 13.1485i | −0.224171 | + | 0.836619i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.43019 | + | 2.55777i | 0.280752 | + | 0.162092i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.5640i | − | 0.793030i | −0.918028 | − | 0.396515i | \(-0.870219\pi\) | ||
0.918028 | − | 0.396515i | \(-0.129781\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.02424 | − | 5.02424i | 0.315871 | − | 0.315871i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.9448 | − | 36.5578i | −0.810637 | − | 2.28934i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3713 | + | 5.19052i | 1.20835 | + | 0.323776i | 0.806114 | − | 0.591761i | \(-0.201567\pi\) |
0.402235 | + | 0.915537i | \(0.368234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.181916 | + | 2.73820i | −0.0113037 | + | 0.170143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.931487 | + | 1.61338i | 0.0576576 | + | 0.0998659i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.52433 | + | 20.6171i | 0.340645 | + | 1.27130i | 0.897618 | + | 0.440773i | \(0.145296\pi\) |
−0.556974 | + | 0.830530i | \(0.688038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.325007 | − | 4.13083i | −0.0199650 | − | 0.253755i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.48887 | − | 4.48887i | −0.274714 | − | 0.274714i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.60824 | − | 2.78555i | 0.0980561 | − | 0.169838i | −0.812824 | − | 0.582510i | \(-0.802071\pi\) |
0.910880 | + | 0.412671i | \(0.135404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.87194 | + | 3.96752i | −0.417441 | + | 0.241009i | −0.693982 | − | 0.719993i | \(-0.744145\pi\) |
0.276541 | + | 0.961002i | \(0.410812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.8300 | − | 8.79371i | −1.56330 | − | 0.532220i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4824 | + | 11.7265i | −0.873319 | + | 0.707133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.67281 | − | 2.59182i | 0.581183 | − | 0.155727i | 0.0437625 | − | 0.999042i | \(-0.486066\pi\) |
0.537420 | + | 0.843314i | \(0.319399\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.2270 | −0.732012 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.6924 | −0.936132 | −0.468066 | − | 0.883693i | \(-0.655049\pi\) | ||||
−0.468066 | + | 0.883693i | \(0.655049\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.15682 | + | 2.45356i | −0.544316 | + | 0.145849i | −0.520491 | − | 0.853867i | \(-0.674251\pi\) |
−0.0238252 | + | 0.999716i | \(0.507585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5377 | + | 15.3332i | 0.624200 | + | 0.908262i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.05274 | − | 20.4696i | −0.239226 | − | 1.20828i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.6029 | + | 15.3592i | −1.56488 | + | 0.903481i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.08427 | − | 12.2703i | 0.415287 | − | 0.719299i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.18750 | + | 7.18750i | 0.419898 | + | 0.419898i | 0.885169 | − | 0.465270i | \(-0.154043\pi\) |
−0.465270 | + | 0.885169i | \(0.654043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.5311 | + | 21.6961i | −1.07892 | + | 1.26320i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.735799 | + | 2.74604i | 0.0426954 | + | 0.159341i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.91553 | + | 6.78190i | 0.226441 | + | 0.392207i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.6850 | + | 23.4291i | −0.904069 | + | 1.35043i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.2301 | − | 8.63604i | −1.85157 | − | 0.496127i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.4825 | + | 6.89862i | −1.11557 | + | 0.395014i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.61456 | + | 5.61456i | −0.320440 | + | 0.320440i | −0.848936 | − | 0.528496i | \(-0.822756\pi\) |
0.528496 | + | 0.848936i | \(0.322756\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.36636i | 0.134617i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.000487840 | 0 | 0.000281654i | 2.76628e−5 | 0 | 1.59712e-5i | 0.500014 | − | 0.866017i | \(-0.333328\pi\) |
−0.499986 | + | 0.866033i | \(0.666662\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.60863 | − | 20.9317i | 0.317019 | − | 1.18313i | −0.605077 | − | 0.796167i | \(-0.706858\pi\) |
0.922095 | − | 0.386963i | \(-0.126476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.8068 | + | 9.97822i | −0.946954 | + | 0.562209i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.97785 | − | 7.38145i | 0.111087 | − | 0.414584i | −0.887877 | − | 0.460081i | \(-0.847820\pi\) |
0.998964 | + | 0.0454970i | \(0.0144871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.82000 | − | 1.05078i | −0.101901 | − | 0.0588323i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.0684i | − | 1.12011i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.1873 | − | 16.1873i | 0.900684 | − | 0.900684i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.35265 | − | 18.7627i | −0.463322 | − | 1.04077i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 34.1557 | + | 9.15200i | 1.88882 | + | 0.506107i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.48660 | − | 0.0987649i | −0.0819591 | − | 0.00544509i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5834 | + | 23.5271i | 0.746609 | + | 1.29316i | 0.949439 | + | 0.313950i | \(0.101653\pi\) |
−0.202831 | + | 0.979214i | \(0.565014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.886919 | + | 3.31003i | 0.0486029 | + | 0.181388i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8466 | + | 1.01075i | −0.701886 | + | 0.0552233i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3001 | + | 17.3001i | 0.942395 | + | 0.942395i | 0.998429 | − | 0.0560343i | \(-0.0178456\pi\) |
−0.0560343 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.61554 | − | 9.72639i | 0.304994 | − | 0.528265i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.9450 | − | 6.89644i | 0.646857 | − | 0.373463i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4264 | − | 10.2482i | 0.832949 | − | 0.553350i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5241 | + | 1.95078i | 0.566599 | + | 0.105027i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.504852 | + | 0.135275i | −0.0271019 | + | 0.00726192i | −0.272345 | − | 0.962200i | \(-0.587799\pi\) |
0.245243 | + | 0.969462i | \(0.421132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.3880 | 1.09134 | 0.545671 | − | 0.837999i | \(-0.316275\pi\) | ||||
0.545671 | + | 0.837999i | \(0.316275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.13327 | −0.167242 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6519 | + | 3.39007i | −0.673393 | + | 0.180435i | −0.579283 | − | 0.815127i | \(-0.696667\pi\) |
−0.0941102 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50205 | − | 0.278424i | −0.0797203 | − | 0.0147772i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.2250 | + | 34.5269i | 1.59968 | + | 1.82736i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.9508 | − | 14.4053i | 1.31685 | − | 0.760284i | 0.333630 | − | 0.942704i | \(-0.391726\pi\) |
0.983221 | + | 0.182420i | \(0.0583929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00887 | − | 6.94356i | 0.210993 | − | 0.365451i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.13073 | − | 5.13073i | −0.269293 | − | 0.269293i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.7929 | + | 2.10802i | −1.40240 | + | 0.110339i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.86273 | − | 10.6839i | −0.149433 | − | 0.557693i | −0.999518 | − | 0.0310469i | \(-0.990116\pi\) |
0.850084 | − | 0.526646i | \(-0.176551\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.0285 | − | 22.5661i | −0.678239 | − | 1.17474i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.16453 | + | 4.39908i | 0.112377 | + | 0.228389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.05366 | + | 1.08617i | 0.209891 | + | 0.0562400i | 0.362232 | − | 0.932088i | \(-0.382015\pi\) |
−0.152342 | + | 0.988328i | \(0.548681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.9144 | − | 7.97445i | −1.38985 | − | 0.411799i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.63781 | − | 1.63781i | 0.0843513 | − | 0.0843513i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.8555i | − | 0.711708i | −0.934542 | − | 0.355854i | \(-0.884190\pi\) | ||
0.934542 | − | 0.355854i | \(-0.115810\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.8549 | + | 13.7727i | 1.22213 | + | 0.705595i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.28064 | + | 12.2435i | −0.167633 | + | 0.625614i | 0.830057 | + | 0.557678i | \(0.188308\pi\) |
−0.997690 | + | 0.0679352i | \(0.978359\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.7911 | − | 19.2276i | 0.549963 | − | 0.979931i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.11237 | + | 34.0078i | −0.463208 | + | 1.72872i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.9033 | + | 16.1100i | 1.41476 | + | 0.816809i | 0.995831 | − | 0.0912123i | \(-0.0290742\pi\) |
0.418924 | + | 0.908022i | \(0.362408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.1697i | − | 0.666023i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.79866 | + | 7.79866i | −0.393390 | + | 0.393390i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.73193 | − | 2.38373i | 0.338720 | − | 0.119938i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8785 | − | 6.93413i | −1.29881 | − | 0.348014i | −0.457807 | − | 0.889052i | \(-0.651365\pi\) |
−0.840998 | + | 0.541038i | \(0.818032\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2930 | − | 12.2465i | −0.915795 | − | 0.613094i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.93447 | + | 14.6837i | 0.195990 | + | 0.731445i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.6125 | − | 13.5959i | 0.577032 | − | 0.675586i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.73343 | − | 2.73343i | −0.135491 | − | 0.135491i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.8208 | + | 20.4742i | −0.584501 | + | 1.01239i | 0.410436 | + | 0.911889i | \(0.365376\pi\) |
−0.994937 | + | 0.100496i | \(0.967957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3951 | + | 8.88835i | −0.759383 | + | 0.438430i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.8804 | − | 31.9592i | 0.535390 | − | 1.57261i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.58041 | − | 3.75470i | −0.126667 | − | 0.184311i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.4820 | + | 6.29199i | −1.14992 | + | 0.308120i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.35275 | −0.0660862 | −0.0330431 | − | 0.999454i | \(-0.510520\pi\) | ||||
−0.0330431 | + | 0.999454i | \(0.510520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3346 | −0.552412 | −0.276206 | − | 0.961098i | \(-0.589077\pi\) | ||||
−0.276206 | + | 0.961098i | \(0.589077\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.79706 | + | 0.481520i | −0.0873760 | + | 0.0234123i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.61193 | + | 34.3499i | −0.175204 | + | 1.66621i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4002 | − | 16.1076i | 0.890449 | − | 0.779503i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.2866 | − | 19.2180i | 1.60709 | − | 0.927855i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8635 | − | 18.8161i | 0.523275 | − | 0.906338i | −0.476359 | − | 0.879251i | \(-0.658044\pi\) |
0.999633 | − | 0.0270870i | \(-0.00862311\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.74688 | + | 8.74688i | 0.420348 | + | 0.420348i | 0.885324 | − | 0.464976i | \(-0.153937\pi\) |
−0.464976 | + | 0.885324i | \(0.653937\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.248309 | − | 3.15601i | −0.0119055 | − | 0.151319i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63522 | + | 6.10273i | 0.0782233 | + | 0.291933i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5117 | − | 18.2067i | −0.501695 | − | 0.868960i | −0.999998 | − | 0.00195777i | \(-0.999377\pi\) |
0.498304 | − | 0.867003i | \(-0.333957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.1113 | − | 18.3226i | 0.671965 | − | 0.872504i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.9894 | + | 10.1792i | 1.80493 | + | 0.483629i | 0.994730 | − | 0.102527i | \(-0.0326927\pi\) |
0.810198 | + | 0.586156i | \(0.199359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.88713 | + | 5.32949i | 0.0894586 | + | 0.252642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7401 | − | 12.7401i | 0.602585 | − | 0.602585i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 40.8069i | − | 1.92580i | −0.269863 | − | 0.962899i | \(-0.586979\pi\) | ||
0.269863 | − | 0.962899i | \(-0.413021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.4561 | + | 14.6971i | 1.19868 | + | 0.692058i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.57722 | + | 17.0824i | −0.215057 | + | 0.802602i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.3912 | + | 16.9727i | 0.815313 | + | 0.795694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.49326 | − | 16.7691i | 0.210186 | − | 0.784425i | −0.777620 | − | 0.628735i | \(-0.783573\pi\) |
0.987806 | − | 0.155690i | \(-0.0497602\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.56337 | + | 2.63466i | 0.213000 | + | 0.122976i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.6505i | 1.47411i | 0.675833 | + | 0.737054i | \(0.263784\pi\) | ||||
−0.675833 | + | 0.737054i | \(0.736216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4868 | + | 20.4868i | −0.952103 | + | 0.952103i | −0.998904 | − | 0.0468014i | \(-0.985097\pi\) |
0.0468014 | + | 0.998904i | \(0.485097\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7532 | + | 8.94533i | 0.869657 | + | 0.414830i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0233 | − | 2.95367i | −0.510095 | − | 0.136680i | −0.00541398 | − | 0.999985i | \(-0.501723\pi\) |
−0.504681 | + | 0.863306i | \(0.668390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6809 | − | 6.73155i | 0.631725 | − | 0.310834i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.440354 | − | 0.762715i | −0.0202904 | − | 0.0351441i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2794 | − | 38.3631i | −0.472646 | − | 1.76394i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.59132 | − | 16.3659i | −0.118898 | − | 0.750918i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.32905 | + | 4.32905i | 0.198214 | + | 0.198214i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0791 | + | 17.4576i | −0.460527 | + | 0.797656i | −0.998987 | − | 0.0449948i | \(-0.985673\pi\) |
0.538460 | + | 0.842651i | \(0.319006\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.68968 | − | 2.13024i | 0.168235 | − | 0.0971305i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.4233 | + | 2.45966i | −0.565278 | + | 0.111918i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.3994 | + | 7.14697i | −0.472213 | + | 0.324527i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.57376 | − | 2.02938i | 0.343200 | − | 0.0919601i | −0.0831022 | − | 0.996541i | \(-0.526483\pi\) |
0.426302 | + | 0.904581i | \(0.359816\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −59.4486 | −2.68836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.08749 | −0.184466 | −0.0922330 | − | 0.995737i | \(-0.529400\pi\) | ||||
−0.0922330 | + | 0.995737i | \(0.529400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.76251 | + | 1.00816i | −0.169455 | + | 0.0454053i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.01809 | − | 27.0717i | 0.225547 | − | 1.21678i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.77310 | − | 0.351053i | 0.0795344 | − | 0.0157469i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.6472 | + | 7.87922i | −0.610933 | + | 0.352722i | −0.773331 | − | 0.634003i | \(-0.781411\pi\) |
0.162398 | + | 0.986725i | \(0.448077\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.8168 | + | 37.7878i | −0.974702 | + | 1.68823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.80892 | + | 2.80892i | 0.125244 | + | 0.125244i | 0.766950 | − | 0.641707i | \(-0.221773\pi\) |
−0.641707 | + | 0.766950i | \(0.721773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.5964 | + | 19.3000i | 1.00552 | + | 0.858840i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.51628 | + | 9.39089i | 0.111752 | + | 0.417064i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.79044 | + | 3.10113i | 0.0793597 | + | 0.137455i | 0.902974 | − | 0.429695i | \(-0.141379\pi\) |
−0.823614 | + | 0.567151i | \(0.808046\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.5328 | − | 14.0393i | 1.26222 | − | 0.621062i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.44175 | − | 0.654266i | −0.107806 | − | 0.0288866i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.907337 | − | 1.90216i | 0.0399821 | − | 0.0838191i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.48401 | − | 1.48401i | 0.0652669 | − | 0.0652669i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.4716i | 1.42534i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.7064 | − | 7.33604i | −0.556677 | − | 0.321398i | 0.195133 | − | 0.980777i | \(-0.437486\pi\) |
−0.751811 | + | 0.659379i | \(0.770819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.38220 | + | 5.15843i | −0.0604392 | + | 0.225562i | −0.989539 | − | 0.144268i | \(-0.953917\pi\) |
0.929099 | + | 0.369830i | \(0.120584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.0775 | − | 3.00818i | 1.44362 | − | 0.131288i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.61673 | − | 24.6940i | 0.288229 | − | 1.07569i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7708 | − | 9.68265i | −0.729167 | − | 0.420985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 42.1577i | − | 1.82949i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.9077 | + | 22.9077i | −0.992242 | + | 0.992242i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.69486 | + | 16.1316i | −0.332678 | + | 0.697432i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −43.5041 | − | 11.6569i | −1.87734 | − | 0.503032i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.45122 | + | 25.8592i | −0.148655 | + | 1.11383i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.91010 | − | 8.50455i | −0.211102 | − | 0.365639i | 0.740958 | − | 0.671552i | \(-0.234372\pi\) |
−0.952060 | + | 0.305913i | \(0.901038\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1444 | + | 60.2519i | 0.692824 | + | 2.58566i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.9464 | − | 20.4531i | −1.02575 | − | 0.876115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.51763 | − | 7.51763i | −0.321431 | − | 0.321431i | 0.527885 | − | 0.849316i | \(-0.322985\pi\) |
−0.849316 | + | 0.527885i | \(0.822985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.2685 | − | 26.4458i | 0.651644 | − | 1.12868i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61833 | − | 0.934344i | 0.0689433 | − | 0.0398044i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.35796 | + | 5.56578i | −0.270368 | + | 0.236681i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.06132 | − | 5.72563i | 0.0450505 | − | 0.243039i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.3925 | + | 9.75133i | −1.54200 | + | 0.413177i | −0.926911 | − | 0.375282i | \(-0.877546\pi\) |
−0.615087 | + | 0.788459i | \(0.710879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.7729 | 1.85140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64.6391 | −2.72906 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.37876 | − | 1.70918i | 0.268832 | − | 0.0720334i | −0.121885 | − | 0.992544i | \(-0.538894\pi\) |
0.390717 | + | 0.920511i | \(0.372227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.24338 | + | 5.66523i | −0.346801 | + | 0.238338i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.81821 | + | 20.0273i | −0.286338 | + | 0.841067i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.6304 | + | 14.7977i | −1.07448 | + | 0.620352i | −0.929402 | − | 0.369068i | \(-0.879677\pi\) |
−0.145079 | + | 0.989420i | \(0.546344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.35180 | − | 5.80549i | 0.140269 | − | 0.242952i | −0.787329 | − | 0.616533i | \(-0.788537\pi\) |
0.927598 | + | 0.373581i | \(0.121870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.7892 | − | 36.7892i | −1.53689 | − | 1.53689i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.71165 | − | 5.60339i | −0.321598 | − | 0.233678i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.32878 | − | 27.3514i | −0.305101 | − | 1.13865i | −0.932858 | − | 0.360243i | \(-0.882694\pi\) |
0.627757 | − | 0.778409i | \(-0.283973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3210 | + | 31.7329i | 0.761394 | + | 1.31877i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.47947 | + | 2.99885i | 0.185840 | + | 0.124413i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.67093 | − | 1.78747i | −0.276282 | − | 0.0740294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.3886 | + | 13.0645i | 1.13238 | + | 0.540150i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.913148 | − | 0.913148i | 0.0376897 | − | 0.0376897i | −0.688011 | − | 0.725700i | \(-0.741516\pi\) |
0.725700 | + | 0.688011i | \(0.241516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2645i | 0.505350i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0079 | + | 8.08749i | 0.576210 | + | 0.332675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.642069 | − | 2.39623i | 0.0263666 | − | 0.0984015i | −0.951489 | − | 0.307684i | \(-0.900446\pi\) |
0.977855 | + | 0.209282i | \(0.0671128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0572 | − | 39.3431i | −0.453300 | − | 1.61291i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.64063 | + | 32.2473i | −0.353637 | + | 1.31979i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.27210 | − | 4.19855i | −0.297130 | − | 0.171548i | 0.344023 | − | 0.938961i | \(-0.388210\pi\) |
−0.641153 | + | 0.767413i | \(0.721544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.6555i | − | 1.00572i | −0.864368 | − | 0.502859i | \(-0.832281\pi\) | ||
0.864368 | − | 0.502859i | \(-0.167719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.4631 | − | 13.4631i | 0.548260 | − | 0.548260i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.15697 | + | 6.09154i | 0.0876933 | + | 0.247656i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5365 | + | 3.62709i | 0.549429 | + | 0.147219i | 0.522845 | − | 0.852428i | \(-0.324871\pi\) |
0.0265835 | + | 0.999647i | \(0.491537\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.65373 | + | 3.36096i | 0.0670124 | + | 0.136193i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.15654 | + | 2.00318i | 0.0467884 | + | 0.0810399i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.69654 | − | 10.0636i | −0.108912 | − | 0.406465i | 0.889848 | − | 0.456258i | \(-0.150811\pi\) |
−0.998760 | + | 0.0497928i | \(0.984144\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.47306 | + | 44.1425i | 0.140047 | + | 1.78000i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.40085 | + | 3.40085i | 0.136913 | + | 0.136913i | 0.772242 | − | 0.635329i | \(-0.219135\pi\) |
−0.635329 | + | 0.772242i | \(0.719135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.43441 | + | 7.68063i | −0.178234 | + | 0.308711i | −0.941276 | − | 0.337639i | \(-0.890372\pi\) |
0.763042 | + | 0.646349i | \(0.223705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.25944 | + | 0.727138i | −0.0505396 | + | 0.0291790i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.40628 | − | 5.03342i | −0.176534 | − | 0.201660i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5771 | + | 16.7300i | 0.743083 | + | 0.669200i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.9531 | − | 8.02591i | 1.19621 | − | 0.320524i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.16498 | −0.285686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.858162 | −0.0341629 | −0.0170815 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170815 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.4971 | − | 9.24348i | 1.37114 | − | 0.367395i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.8945 | − | 20.2177i | −0.551388 | − | 0.802315i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.5448 | − | 11.0506i | −1.05174 | − | 0.437839i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.95470 | − | 1.12855i | 0.0773268 | − | 0.0446446i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.0661 | + | 17.4350i | −0.397587 | + | 0.688641i | −0.993428 | − | 0.114461i | \(-0.963486\pi\) |
0.595840 | + | 0.803103i | \(0.296819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.68541 | − | 3.68541i | −0.145338 | − | 0.145338i | 0.630694 | − | 0.776032i | \(-0.282770\pi\) |
−0.776032 | + | 0.630694i | \(0.782770\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.8564 | − | 45.4928i | 1.52997 | − | 1.79128i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.09978 | + | 22.7647i | 0.239807 | + | 0.894973i | 0.975923 | + | 0.218117i | \(0.0699913\pi\) |
−0.736116 | + | 0.676856i | \(0.763342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.7783 | + | 41.1853i | 0.933381 | + | 1.61666i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.5301 | − | 1.62969i | −0.961409 | − | 0.0638727i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.6764 | + | 9.82740i | 1.43526 | + | 0.384576i | 0.890870 | − | 0.454258i | \(-0.150096\pi\) |
0.544387 | + | 0.838834i | \(0.316762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.25909 | − | 3.27857i | 0.361783 | − | 0.128104i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.0786 | − | 28.0786i | 1.09545 | − | 1.09545i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.0353i | 0.897327i | 0.893701 | + | 0.448663i | \(0.148100\pi\) | ||||
−0.893701 | + | 0.448663i | \(0.851900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5377 | − | 13.0121i | −0.876614 | − | 0.506114i | −0.00707383 | − | 0.999975i | \(-0.502252\pi\) |
−0.869541 | + | 0.493861i | \(0.835585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.4386 | − | 68.8136i | 0.716094 | − | 2.67250i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0088 | + | 16.8583i | 0.388126 | + | 0.653737i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.278241 | − | 1.03841i | 0.0107736 | − | 0.0402074i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.58515 | − | 3.80194i | −0.254597 | − | 0.146991i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4478i | 1.32984i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1667 | − | 27.1667i | 1.04720 | − | 1.04720i | 0.0483701 | − | 0.998829i | \(-0.484597\pi\) |
0.998829 | − | 0.0483701i | \(-0.0154027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.48435 | − | 1.55114i | 0.134113 | − | 0.0597033i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.8245 | + | 12.2786i | 1.76118 | + | 0.471907i | 0.986954 | − | 0.161003i | \(-0.0514729\pi\) |
0.774226 | + | 0.632910i | \(0.218140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.30594 | − | 12.4068i | 0.318753 | − | 0.476130i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.7059 | + | 20.2753i | 0.448572 | + | 0.776950i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.45542 | − | 35.2881i | −0.361801 | − | 1.35026i | −0.871705 | − | 0.490030i | \(-0.836986\pi\) |
0.509904 | − | 0.860231i | \(-0.329681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.7832 | − | 1.24179i | 0.603044 | − | 0.0474465i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.5963 | − | 48.5963i | −1.85407 | − | 1.85407i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.80582 | − | 6.59187i | 0.144990 | − | 0.251130i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6519 | + | 7.30456i | −0.481300 | + | 0.277878i | −0.720958 | − | 0.692979i | \(-0.756298\pi\) |
0.239658 | + | 0.970857i | \(0.422965\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.32710 | + | 31.9570i | 0.240347 | + | 1.21395i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.2882 | + | 3.94605i | 0.807508 | + | 0.149682i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.6256 | − | 14.1010i | 1.99334 | − | 0.534113i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.7869 | 0.445821 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.3885 | 1.56322 | 0.781612 | − | 0.623765i | \(-0.214398\pi\) | ||||
0.781612 | + | 0.623765i | \(0.214398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.32018 | − | 0.889640i | 0.125223 | − | 0.0335534i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.10852 | + | 0.576205i | 0.117074 | + | 0.0217011i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.2853 | − | 11.3319i | −1.25182 | − | 0.426178i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2236 | + | 16.2949i | −1.05996 | + | 0.611968i | −0.925421 | − | 0.378940i | \(-0.876289\pi\) |
−0.134539 | + | 0.990908i | \(0.542955\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.27583 | + | 9.13800i | −0.197859 | + | 0.342702i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.98912 | + | 4.98912i | 0.186844 | + | 0.186844i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.1257 | + | 2.68495i | −1.27623 | + | 0.100412i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.69326 | − | 24.9796i | −0.249965 | − | 0.932880i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.555682 | − | 0.962469i | −0.0207234 | − | 0.0358940i | 0.855478 | − | 0.517840i | \(-0.173264\pi\) |
−0.876201 | + | 0.481946i | \(0.839930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.165302 | + | 2.48812i | −0.00615617 | + | 0.0926624i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.4643 | + | 8.43084i | 1.17017 | + | 0.313546i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.01051 | + | 2.63212i | −0.0375296 | + | 0.0977543i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4058 | + | 17.4058i | −0.645545 | + | 0.645545i | −0.951913 | − | 0.306368i | \(-0.900886\pi\) |
0.306368 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.1637i | 1.19125i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −63.7519 | − | 36.8071i | −2.35795 | − | 1.36136i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.55744 | − | 20.7406i | 0.205269 | − | 0.766073i | −0.784099 | − | 0.620636i | \(-0.786874\pi\) |
0.989367 | − | 0.145437i | \(-0.0464589\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.0480 | + | 17.7784i | −1.29277 | + | 0.655766i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.55893 | + | 20.7462i | −0.204766 | + | 0.764196i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.1855 | + | 11.0767i | 0.705750 | + | 0.407465i | 0.809485 | − | 0.587140i | \(-0.199746\pi\) |
−0.103736 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.1770i | 1.25552i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3901 | + | 15.3901i | −0.564607 | + | 0.564607i | −0.930613 | − | 0.366006i | \(-0.880725\pi\) |
0.366006 | + | 0.930613i | \(0.380725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1259 | + | 5.35595i | −0.554169 | + | 0.196227i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.50204 | + | 1.74222i | 0.237897 | + | 0.0637443i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.40188 | − | 21.1010i | 0.0512235 | − | 0.771013i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.68491 | − | 15.0427i | −0.316917 | − | 0.548916i | 0.662926 | − | 0.748685i | \(-0.269314\pi\) |
−0.979843 | + | 0.199769i | \(0.935981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.16440 | − | 30.4700i | −0.297527 | − | 1.11039i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2293 | − | 11.9764i | 0.372281 | − | 0.435865i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.00848 | − | 4.00848i | −0.145691 | − | 0.145691i | 0.630499 | − | 0.776190i | \(-0.282850\pi\) |
−0.776190 | + | 0.630499i | \(0.782850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.91984 | − | 15.4496i | 0.323770 | − | 0.560785i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8872 | + | 8.59511i | −0.539659 | + | 0.311573i | −0.744941 | − | 0.667130i | \(-0.767522\pi\) |
0.205281 | + | 0.978703i | \(0.434189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.2739 | + | 12.0089i | 1.27700 | + | 0.434750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.9039 | − | 42.0576i | −1.04502 | − | 1.52059i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.6280 | + | 13.5657i | −1.82807 | + | 0.489830i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.2755 | 0.622969 | 0.311484 | − | 0.950251i | \(-0.399174\pi\) | ||||
0.311484 | + | 0.950251i | \(0.399174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.3520 | 1.81338 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.64124 | + | 2.04746i | −0.274836 | + | 0.0736422i | −0.393605 | − | 0.919280i | \(-0.628772\pi\) |
0.118768 | + | 0.992922i | \(0.462105\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.6445 | − | 14.3811i | −0.418283 | − | 0.516586i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.33817 | + | 6.75886i | 0.0480067 | + | 0.242473i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6353 | + | 13.0685i | −0.810995 | + | 0.468228i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.27308 | + | 2.20503i | −0.0455542 | + | 0.0789023i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.304150 | + | 0.304150i | 0.0108694 | + | 0.0108694i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0615219 | + | 0.781943i | 0.00219581 | + | 0.0279087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.25353 | + | 15.8744i | 0.151622 | + | 0.565861i | 0.999371 | + | 0.0354635i | \(0.0112907\pi\) |
−0.847749 | + | 0.530398i | \(0.822043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.7951 | + | 46.4104i | 0.953930 | + | 1.65226i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.58393 | − | 9.83460i | 0.234097 | − | 0.349678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.6725 | − | 9.82637i | −1.30228 | − | 0.348944i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.47253 | − | 9.80684i | −0.123158 | − | 0.347813i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.0830 | − | 32.0830i | 1.13644 | − | 1.13644i | 0.147354 | − | 0.989084i | \(-0.452924\pi\) |
0.989084 | − | 0.147354i | \(-0.0470758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.88996i | − | 0.137617i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.23430 | − | 4.17673i | −0.255612 | − | 0.147577i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.5937 | + | 43.2682i | −0.409132 | + | 1.52690i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.9294 | + | 2.78632i | 0.385210 | + | 0.0982050i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.09016 | − | 7.80057i | 0.0735770 | − | 0.274593i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.4551 | − | 14.6965i | −0.894955 | − | 0.516702i | −0.0193950 | − | 0.999812i | \(-0.506174\pi\) |
−0.875560 | + | 0.483109i | \(0.839507\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.63576i | − | 0.197898i | −0.995092 | − | 0.0989491i | \(-0.968452\pi\) | ||
0.995092 | − | 0.0989491i | \(-0.0315481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.0876 | + | 14.0876i | −0.494072 | + | 0.494072i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.7869 | + | 22.7945i | 1.67390 | + | 0.798457i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1122 | + | 9.14032i | 1.19343 | + | 0.319779i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.8257 | − | 2.38014i | −1.25185 | − | 0.0831687i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.70640 | + | 8.15172i | 0.164254 | + | 0.284497i | 0.936390 | − | 0.350961i | \(-0.114145\pi\) |
−0.772136 | + | 0.635457i | \(0.780812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.68634 | − | 13.7576i | −0.128498 | − | 0.479560i | 0.871442 | − | 0.490498i | \(-0.163185\pi\) |
−0.999940 | + | 0.0109378i | \(0.996518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.5023 | + | 37.8499i | −0.957507 | + | 1.31777i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.3153 | + | 13.3153i | 0.463018 | + | 0.463018i | 0.899643 | − | 0.436625i | \(-0.143826\pi\) |
−0.436625 | + | 0.899643i | \(0.643826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.93159 | − | 10.2738i | 0.206013 | − | 0.356824i | −0.744442 | − | 0.667687i | \(-0.767285\pi\) |
0.950455 | + | 0.310863i | \(0.100618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.7742 | − | 12.5713i | 0.755337 | − | 0.436094i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.3683 | + | 38.4148i | 1.01755 | + | 1.33100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0261 | − | 22.0099i | 1.10831 | − | 0.761683i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.72684 | + | 0.730656i | −0.0942535 | + | 0.0252552i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.5847 | 0.883281 | 0.441641 | − | 0.897192i | \(-0.354397\pi\) | ||||
0.441641 | + | 0.897192i | \(0.354397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6820 | 0.989036 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.0571 | + | 10.1974i | −1.31076 | + | 0.351216i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.57810 | − | 8.51354i | 0.0542882 | − | 0.292875i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.03632 | − | 5.75314i | −0.173050 | − | 0.197680i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.6126 | + | 11.9007i | −0.707423 | + | 0.408431i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.988727 | − | 1.71253i | 0.0338931 | − | 0.0587046i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.77628 | − | 1.77628i | −0.0608187 | − | 0.0608187i | 0.676043 | − | 0.736862i | \(-0.263693\pi\) |
−0.736862 | + | 0.676043i | \(0.763693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.6159 | + | 15.9002i | 0.636650 | + | 0.543776i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.37730 | − | 31.2645i | −0.286163 | − | 1.06798i | −0.947985 | − | 0.318314i | \(-0.896883\pi\) |
0.661822 | − | 0.749661i | \(-0.269783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2878 | − | 48.9959i | −0.965168 | − | 1.67172i | −0.709164 | − | 0.705043i | \(-0.750928\pi\) |
−0.256003 | − | 0.966676i | \(-0.582406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.1304 | − | 47.0091i | −0.788281 | − | 1.60207i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.3027 | − | 13.4786i | −1.71232 | − | 0.458816i | −0.736331 | − | 0.676622i | \(-0.763443\pi\) |
−0.975992 | + | 0.217806i | \(0.930110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4507 | − | 26.1018i | 0.423335 | − | 0.887487i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −54.5362 | + | 54.5362i | −1.85215 | + | 1.85215i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.9030i | − | 0.403781i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.5003 | − | 11.8359i | −0.694628 | − | 0.401043i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.82542 | − | 18.0087i | 0.163316 | − | 0.609503i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.7422 | − | 10.2649i | −0.937859 | − | 0.347017i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.02787 | + | 3.83607i | −0.0347088 | + | 0.129535i | −0.981106 | − | 0.193469i | \(-0.938026\pi\) |
0.946398 | + | 0.323004i | \(0.104693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1017 | + | 12.7604i | 0.745471 | + | 0.430398i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.7339i | 0.833307i | 0.909065 | + | 0.416654i | \(0.136797\pi\) | ||||
−0.909065 | + | 0.416654i | \(0.863203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.69618 | + | 3.69618i | −0.124387 | + | 0.124387i | −0.766560 | − | 0.642173i | \(-0.778033\pi\) |
0.642173 | + | 0.766560i | \(0.278033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.8427 | + | 64.6593i | −1.03677 | + | 2.17350i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7690 | − | 5.02913i | −0.630200 | − | 0.168862i | −0.0704398 | − | 0.997516i | \(-0.522440\pi\) |
−0.559761 | + | 0.828654i | \(0.689107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.1203 | + | 16.1477i | 0.808970 | + | 0.541577i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9007 | − | 25.8088i | −0.499192 | − | 0.864627i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.482997 | + | 1.80257i | 0.0161629 | + | 0.0603207i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5005 | + | 26.0511i | 1.01952 | + | 0.870792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.9030 | + | 13.9030i | 0.464207 | + | 0.464207i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.04343 | − | 1.80728i | 0.0348005 | − | 0.0602762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0858 | + | 6.40037i | −0.369320 | + | 0.213227i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.8142 | + | 67.0127i | −0.759209 | + | 2.23004i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.1251 | − | 54.6229i | 0.336568 | − | 1.81573i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.1505 | − | 12.0980i | 1.49920 | − | 0.401709i | 0.586367 | − | 0.810046i | \(-0.300558\pi\) |
0.912831 | + | 0.408337i | \(0.133891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.9069 | −1.45630 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.4768 | 1.44045 | 0.720225 | − | 0.693740i | \(-0.244038\pi\) | ||||
0.720225 | + | 0.693740i | \(0.244038\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.33473 | + | 1.96533i | −0.242744 | + | 0.0650431i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.7659 | + | 29.3907i | −1.41380 | + | 0.971628i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.74472 | + | 7.65517i | −0.288776 | + | 0.252796i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.80127 | − | 3.92672i | 0.224353 | − | 0.129530i | −0.383611 | − | 0.923495i | \(-0.625320\pi\) |
0.607964 | + | 0.793964i | \(0.291986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.96787 | + | 17.2649i | −0.328453 | + | 0.568897i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.98429 | − | 1.98429i | −0.0653137 | − | 0.0653137i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.04852 | + | 4.19551i | −0.100235 | + | 0.137948i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.805917 | + | 3.00772i | 0.0264698 | + | 0.0987866i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.2493 | − | 22.9485i | −0.434696 | − | 0.752916i | 0.562575 | − | 0.826747i | \(-0.309811\pi\) |
−0.997271 | + | 0.0738305i | \(0.976478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.3788 | − | 14.1545i | −0.602341 | − | 0.463896i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.00136613 | 0.000366053i | 4.47251e−5 | 1.19841e-5i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.9591 | + | 24.7847i | 1.69924 | + | 0.810547i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0373 | + | 37.0373i | −1.20995 | + | 1.20995i | −0.238914 | + | 0.971041i | \(0.576792\pi\) |
−0.971041 | + | 0.238914i | \(0.923208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 54.4080i | − | 1.77554i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.0947 | + | 21.9940i | 1.24185 | + | 0.716984i | 0.969471 | − | 0.245205i | \(-0.0788554\pi\) |
0.272382 | + | 0.962189i | \(0.412189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.89171 | + | 14.5241i | −0.126732 | + | 0.472969i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.15194 | + | 3.22965i | −0.102533 | + | 0.105061i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.07076 | − | 22.6564i | 0.197273 | − | 0.736233i | −0.794394 | − | 0.607403i | \(-0.792211\pi\) |
0.991667 | − | 0.128830i | \(-0.0411221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.7554 | − | 24.6849i | −1.38790 | − | 0.801305i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 19.1867i | − | 0.622171i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.9160 | + | 15.9160i | −0.515569 | + | 0.515569i | −0.916227 | − | 0.400658i | \(-0.868781\pi\) |
0.400658 | + | 0.916227i | \(0.368781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4663 | + | 43.6786i | 0.500477 | + | 1.41341i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.09668 | − | 1.36565i | −0.164752 | − | 0.0441452i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.8081 | + | 8.27028i | −0.542763 | + | 0.267061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.65177 | − | 14.9853i | −0.279089 | − | 0.483397i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.83474 | − | 25.5076i | −0.220246 | − | 0.821971i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.55963 | − | 32.5328i | −0.0823973 | − | 1.04727i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.3556 | − | 20.3556i | −0.654591 | − | 0.654591i | 0.299504 | − | 0.954095i | \(-0.403179\pi\) |
−0.954095 | + | 0.299504i | \(0.903179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.7383 | − | 49.7761i | 0.923206 | − | 1.59904i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3848 | + | 6.57304i | −0.365357 | + | 0.210939i | −0.671428 | − | 0.741070i | \(-0.734319\pi\) |
0.306071 | + | 0.952009i | \(0.400985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.1298 | + | 4.97541i | −0.805625 | + | 0.159504i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.4493 | − | 40.0753i | −1.03921 | − | 1.28344i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.1240 | − | 4.58835i | 0.547844 | − | 0.146794i | 0.0257283 | − | 0.999669i | \(-0.491810\pi\) |
0.522116 | + | 0.852875i | \(0.325143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.42325 | 0.301168 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.5301 | 1.48559 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.3603 | + | 10.5466i | −1.25540 | + | 0.336383i | −0.824420 | − | 0.565979i | \(-0.808498\pi\) |
−0.430979 | + | 0.902362i | \(0.641832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.15907 | − | 11.8721i | −0.259969 | − | 0.378277i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.66948 | + | 0.726512i | −0.116801 | + | 0.0231251i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.5948 | − | 10.1584i | 0.559482 | − | 0.323017i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.8834 | + | 51.7596i | −0.949278 | + | 1.64420i | −0.202328 | + | 0.979318i | \(0.564851\pi\) |
−0.746950 | + | 0.664880i | \(0.768483\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.2307 | + | 48.2307i | 1.53056 | + | 1.53056i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3103 | − | 22.6084i | 0.612177 | − | 0.716733i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.39130 | + | 23.8526i | 0.202414 | + | 0.755421i | 0.990222 | + | 0.139500i | \(0.0445494\pi\) |
−0.787808 | + | 0.615921i | \(0.788784\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.395598 | + | 0.685196i | 0.0125162 | + | 0.0216786i |
(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 | 140.2.u.a.17.4 | ✓ | 16 | |
3.2 | odd | 2 | 1260.2.dq.a.577.4 | 16 | |||
4.3 | odd | 2 | 560.2.ci.d.17.1 | 16 | |||
5.2 | odd | 4 | 700.2.bc.b.493.1 | 16 | |||
5.3 | odd | 4 | inner | 140.2.u.a.73.4 | yes | 16 | |
5.4 | even | 2 | 700.2.bc.b.157.1 | 16 | |||
7.2 | even | 3 | 980.2.v.a.117.1 | 16 | |||
7.3 | odd | 6 | 980.2.m.a.97.7 | 16 | |||
7.4 | even | 3 | 980.2.m.a.97.2 | 16 | |||
7.5 | odd | 6 | inner | 140.2.u.a.117.4 | yes | 16 | |
7.6 | odd | 2 | 980.2.v.a.717.1 | 16 | |||
15.8 | even | 4 | 1260.2.dq.a.73.3 | 16 | |||
20.3 | even | 4 | 560.2.ci.d.353.1 | 16 | |||
21.5 | even | 6 | 1260.2.dq.a.397.3 | 16 | |||
28.19 | even | 6 | 560.2.ci.d.257.1 | 16 | |||
35.3 | even | 12 | 980.2.m.a.293.2 | 16 | |||
35.12 | even | 12 | 700.2.bc.b.593.1 | 16 | |||
35.13 | even | 4 | 980.2.v.a.913.1 | 16 | |||
35.18 | odd | 12 | 980.2.m.a.293.7 | 16 | |||
35.19 | odd | 6 | 700.2.bc.b.257.1 | 16 | |||
35.23 | odd | 12 | 980.2.v.a.313.1 | 16 | |||
35.33 | even | 12 | inner | 140.2.u.a.33.4 | yes | 16 | |
105.68 | odd | 12 | 1260.2.dq.a.1153.4 | 16 | |||
140.103 | odd | 12 | 560.2.ci.d.33.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.u.a.17.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
140.2.u.a.33.4 | yes | 16 | 35.33 | even | 12 | inner | |
140.2.u.a.73.4 | yes | 16 | 5.3 | odd | 4 | inner | |
140.2.u.a.117.4 | yes | 16 | 7.5 | odd | 6 | inner | |
560.2.ci.d.17.1 | 16 | 4.3 | odd | 2 | |||
560.2.ci.d.33.1 | 16 | 140.103 | odd | 12 | |||
560.2.ci.d.257.1 | 16 | 28.19 | even | 6 | |||
560.2.ci.d.353.1 | 16 | 20.3 | even | 4 | |||
700.2.bc.b.157.1 | 16 | 5.4 | even | 2 | |||
700.2.bc.b.257.1 | 16 | 35.19 | odd | 6 | |||
700.2.bc.b.493.1 | 16 | 5.2 | odd | 4 | |||
700.2.bc.b.593.1 | 16 | 35.12 | even | 12 | |||
980.2.m.a.97.2 | 16 | 7.4 | even | 3 | |||
980.2.m.a.97.7 | 16 | 7.3 | odd | 6 | |||
980.2.m.a.293.2 | 16 | 35.3 | even | 12 | |||
980.2.m.a.293.7 | 16 | 35.18 | odd | 12 | |||
980.2.v.a.117.1 | 16 | 7.2 | even | 3 | |||
980.2.v.a.313.1 | 16 | 35.23 | odd | 12 | |||
980.2.v.a.717.1 | 16 | 7.6 | odd | 2 | |||
980.2.v.a.913.1 | 16 | 35.13 | even | 4 | |||
1260.2.dq.a.73.3 | 16 | 15.8 | even | 4 | |||
1260.2.dq.a.397.3 | 16 | 21.5 | even | 6 | |||
1260.2.dq.a.577.4 | 16 | 3.2 | odd | 2 | |||
1260.2.dq.a.1153.4 | 16 | 105.68 | odd | 12 |