Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.5 | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.d.1277.5 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.474393 | + | 0.821673i | −0.212155 | + | 0.367463i | −0.952389 | − | 0.304886i | \(-0.901381\pi\) |
0.740234 | + | 0.672350i | \(0.234715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41034 | + | 2.23851i | 0.533059 | + | 0.846078i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.821673 | − | 0.474393i | 0.259836 | − | 0.150016i | ||||
\(11\) | 0.866025 | − | 0.500000i | 0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 7.03063i | − | 1.94995i | −0.222322 | − | 0.974973i | \(-0.571364\pi\) | ||
0.222322 | − | 0.974973i | \(-0.428636\pi\) | |||||||
\(14\) | −0.102135 | − | 2.64378i | −0.0272968 | − | 0.706580i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.29971 | − | 3.98321i | −0.557761 | − | 0.966071i | −0.997683 | − | 0.0680349i | \(-0.978327\pi\) |
0.439922 | − | 0.898036i | \(-0.355006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.93280 | + | 1.11590i | 0.443415 | + | 0.256006i | 0.705045 | − | 0.709163i | \(-0.250927\pi\) |
−0.261630 | + | 0.965168i | \(0.584260\pi\) | |||||||
\(20\) | −0.948786 | −0.212155 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.17812 | − | 4.14429i | −1.49674 | − | 0.864144i | −0.496748 | − | 0.867895i | \(-0.665473\pi\) |
−0.999993 | + | 0.00375054i | \(0.998806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.04990 | + | 3.55054i | 0.409981 | + | 0.710107i | ||||
\(26\) | −3.51532 | + | 6.08871i | −0.689410 | + | 1.19409i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.23344 | + | 2.34065i | −0.233098 | + | 0.442341i | ||||
\(29\) | − | 0.930621i | − | 0.172812i | −0.996260 | − | 0.0864060i | \(-0.972462\pi\) | ||
0.996260 | − | 0.0864060i | \(-0.0275382\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.80537 | + | 1.61968i | −0.503859 | + | 0.290903i | −0.730306 | − | 0.683121i | \(-0.760622\pi\) |
0.226447 | + | 0.974023i | \(0.427289\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.59942i | 0.788794i | ||||||||
\(35\) | −2.50838 | + | 0.0969044i | −0.423994 | + | 0.0163798i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.57553 | − | 7.92505i | 0.752213 | − | 1.30287i | −0.194535 | − | 0.980895i | \(-0.562320\pi\) |
0.946748 | − | 0.321975i | \(-0.104347\pi\) | |||||||
\(38\) | −1.11590 | − | 1.93280i | −0.181023 | − | 0.313542i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.821673 | + | 0.474393i | 0.129918 | + | 0.0750081i | ||||
\(41\) | 8.54500 | 1.33450 | 0.667252 | − | 0.744832i | \(-0.267470\pi\) | ||||
0.667252 | + | 0.744832i | \(0.267470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.7269 | 1.94084 | 0.970418 | − | 0.241430i | \(-0.0776164\pi\) | ||||
0.970418 | + | 0.241430i | \(0.0776164\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.14429 | + | 7.17812i | 0.611042 | + | 1.05836i | ||||
\(47\) | 0.251245 | − | 0.435168i | 0.0366478 | − | 0.0634758i | −0.847120 | − | 0.531402i | \(-0.821665\pi\) |
0.883768 | + | 0.467926i | \(0.154999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.02187 | + | 6.31413i | −0.431696 | + | 0.902019i | ||||
\(50\) | − | 4.09981i | − | 0.579800i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.08871 | − | 3.51532i | 0.844352 | − | 0.487487i | ||||
\(53\) | 8.22868 | − | 4.75083i | 1.13030 | − | 0.652577i | 0.186287 | − | 0.982495i | \(-0.440355\pi\) |
0.944009 | + | 0.329919i | \(0.107021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.948786i | 0.127934i | ||||||||
\(56\) | 2.23851 | − | 1.41034i | 0.299134 | − | 0.188465i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.465310 | + | 0.805941i | −0.0610982 | + | 0.105825i | ||||
\(59\) | 3.94585 | + | 6.83441i | 0.513706 | + | 0.889764i | 0.999874 | + | 0.0158990i | \(0.00506102\pi\) |
−0.486168 | + | 0.873865i | \(0.661606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.02250 | − | 1.16769i | −0.258955 | − | 0.149508i | 0.364903 | − | 0.931046i | \(-0.381102\pi\) |
−0.623858 | + | 0.781538i | \(0.714436\pi\) | |||||||
\(62\) | 3.23936 | 0.411399 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.77688 | + | 3.33528i | 0.716533 | + | 0.413691i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.94653 | − | 5.10354i | −0.359976 | − | 0.623497i | 0.627980 | − | 0.778229i | \(-0.283882\pi\) |
−0.987956 | + | 0.154732i | \(0.950548\pi\) | |||||||
\(68\) | 2.29971 | − | 3.98321i | 0.278881 | − | 0.483036i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.22077 | + | 1.17027i | 0.265433 | + | 0.139874i | ||||
\(71\) | − | 12.7563i | − | 1.51390i | −0.653475 | − | 0.756948i | \(-0.726689\pi\) | ||
0.653475 | − | 0.756948i | \(-0.273311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.85471 | − | 2.80287i | 0.568201 | − | 0.328051i | −0.188229 | − | 0.982125i | \(-0.560275\pi\) |
0.756431 | + | 0.654074i | \(0.226942\pi\) | |||||||
\(74\) | −7.92505 | + | 4.57553i | −0.921269 | + | 0.531895i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.23181i | 0.256006i | ||||||||
\(77\) | 2.34065 | + | 1.23344i | 0.266742 | + | 0.140563i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.16723 | + | 7.21785i | −0.468850 | + | 0.812072i | −0.999366 | − | 0.0356031i | \(-0.988665\pi\) |
0.530516 | + | 0.847675i | \(0.321998\pi\) | |||||||
\(80\) | −0.474393 | − | 0.821673i | −0.0530387 | − | 0.0918658i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.40019 | − | 4.27250i | −0.817214 | − | 0.471819i | ||||
\(83\) | −12.0026 | −1.31745 | −0.658727 | − | 0.752382i | \(-0.728905\pi\) | ||||
−0.658727 | + | 0.752382i | \(0.728905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.36386 | 0.473327 | ||||||||
\(86\) | −11.0218 | − | 6.36346i | −1.18851 | − | 0.686189i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −0.441480 | + | 0.764665i | −0.0467968 | + | 0.0810544i | −0.888475 | − | 0.458925i | \(-0.848235\pi\) |
0.841678 | + | 0.539979i | \(0.181568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.7382 | − | 9.91559i | 1.64981 | − | 1.03944i | ||||
\(92\) | − | 8.28858i | − | 0.864144i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.435168 | + | 0.251245i | −0.0448842 | + | 0.0259139i | ||||
\(95\) | −1.83381 | + | 1.05875i | −0.188145 | + | 0.108626i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.6315i | − | 1.28253i | −0.767319 | − | 0.641265i | \(-0.778410\pi\) | ||
0.767319 | − | 0.641265i | \(-0.221590\pi\) | |||||||
\(98\) | 5.77409 | − | 3.95726i | 0.583271 | − | 0.399744i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.04990 | + | 3.55054i | −0.204990 | + | 0.355054i | ||||
\(101\) | −8.03742 | − | 13.9212i | −0.799754 | − | 1.38521i | −0.919776 | − | 0.392443i | \(-0.871630\pi\) |
0.120023 | − | 0.992771i | \(-0.461703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.42570 | + | 4.28723i | 0.731676 | + | 0.422433i | 0.819035 | − | 0.573743i | \(-0.194509\pi\) |
−0.0873588 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(104\) | −7.03063 | −0.689410 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.50166 | −0.922883 | ||||||||
\(107\) | 12.2507 | + | 7.07294i | 1.18432 | + | 0.683767i | 0.957010 | − | 0.290056i | \(-0.0936740\pi\) |
0.227309 | + | 0.973823i | \(0.427007\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.35840 | + | 5.81692i | 0.321676 | + | 0.557160i | 0.980834 | − | 0.194845i | \(-0.0624203\pi\) |
−0.659158 | + | 0.752005i | \(0.729087\pi\) | |||||||
\(110\) | 0.474393 | − | 0.821673i | 0.0452316 | − | 0.0783434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.64378 | + | 0.102135i | −0.249814 | + | 0.00965087i | ||||
\(113\) | 8.39880i | 0.790093i | 0.918661 | + | 0.395046i | \(0.129271\pi\) | ||||
−0.918661 | + | 0.395046i | \(0.870729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.81050 | − | 3.93204i | 0.635082 | − | 0.366665i | ||||
\(116\) | 0.805941 | − | 0.465310i | 0.0748298 | − | 0.0432030i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 7.89170i | − | 0.726490i | ||||||
\(119\) | 5.67310 | − | 10.7656i | 0.520052 | − | 0.986882i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.16769 | + | 2.02250i | 0.105718 | + | 0.183109i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.80537 | − | 1.61968i | −0.251929 | − | 0.145451i | ||||
\(125\) | −8.63377 | −0.772227 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.99819 | −0.709724 | −0.354862 | − | 0.934919i | \(-0.615472\pi\) | ||||
−0.354862 | + | 0.934919i | \(0.615472\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.33528 | − | 5.77688i | −0.292524 | − | 0.506666i | ||||
\(131\) | −4.37253 | + | 7.57344i | −0.382030 | + | 0.661695i | −0.991352 | − | 0.131228i | \(-0.958108\pi\) |
0.609323 | + | 0.792922i | \(0.291441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.227946 | + | 5.90040i | 0.0197654 | + | 0.511630i | ||||
\(134\) | 5.89306i | 0.509083i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.98321 | + | 2.29971i | −0.341558 | + | 0.197198i | ||||
\(137\) | 0.350664 | − | 0.202456i | 0.0299592 | − | 0.0172970i | −0.484946 | − | 0.874544i | \(-0.661161\pi\) |
0.514905 | + | 0.857247i | \(0.327827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.5997i | − | 1.49278i | −0.665506 | − | 0.746392i | \(-0.731784\pi\) | ||
0.665506 | − | 0.746392i | \(-0.268216\pi\) | |||||||
\(140\) | −1.33811 | − | 2.12387i | −0.113091 | − | 0.179500i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.37816 | + | 11.0473i | −0.535243 | + | 0.927069i | ||||
\(143\) | −3.51532 | − | 6.08871i | −0.293966 | − | 0.509163i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.764665 | + | 0.441480i | 0.0635020 | + | 0.0366629i | ||||
\(146\) | −5.60574 | −0.463934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.15106 | 0.752213 | ||||||||
\(149\) | 17.5141 | + | 10.1118i | 1.43481 | + | 0.828390i | 0.997483 | − | 0.0709110i | \(-0.0225906\pi\) |
0.437331 | + | 0.899301i | \(0.355924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.93283 | − | 6.81186i | −0.320049 | − | 0.554341i | 0.660449 | − | 0.750871i | \(-0.270366\pi\) |
−0.980498 | + | 0.196530i | \(0.937033\pi\) | |||||||
\(152\) | 1.11590 | − | 1.93280i | 0.0905117 | − | 0.156771i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.41034 | − | 2.23851i | −0.113649 | − | 0.180384i | ||||
\(155\) | − | 3.07346i | − | 0.246866i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.300234 | + | 0.173340i | −0.0239613 | + | 0.0138340i | −0.511933 | − | 0.859026i | \(-0.671070\pi\) |
0.487972 | + | 0.872860i | \(0.337737\pi\) | |||||||
\(158\) | 7.21785 | − | 4.16723i | 0.574221 | − | 0.331527i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.948786i | 0.0750081i | ||||||||
\(161\) | −0.846556 | − | 21.9132i | −0.0667179 | − | 1.72700i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00467 | + | 6.93629i | −0.313670 | + | 0.543292i | −0.979154 | − | 0.203120i | \(-0.934892\pi\) |
0.665484 | + | 0.746412i | \(0.268225\pi\) | |||||||
\(164\) | 4.27250 | + | 7.40019i | 0.333626 | + | 0.577857i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3945 | + | 6.00129i | 0.806772 | + | 0.465790i | ||||
\(167\) | 23.3784 | 1.80907 | 0.904537 | − | 0.426395i | \(-0.140217\pi\) | ||||
0.904537 | + | 0.426395i | \(0.140217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −36.4298 | −2.80229 | ||||||||
\(170\) | −3.77922 | − | 2.18193i | −0.289853 | − | 0.167346i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.36346 | + | 11.0218i | 0.485209 | + | 0.840407i | ||||
\(173\) | 3.94270 | − | 6.82895i | 0.299758 | − | 0.519196i | −0.676323 | − | 0.736605i | \(-0.736427\pi\) |
0.976080 | + | 0.217410i | \(0.0697608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.05686 | + | 9.59620i | −0.382262 | + | 0.725405i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.764665 | − | 0.441480i | 0.0573141 | − | 0.0330903i | ||||
\(179\) | −3.03581 | + | 1.75273i | −0.226907 | + | 0.131005i | −0.609145 | − | 0.793059i | \(-0.708487\pi\) |
0.382237 | + | 0.924064i | \(0.375154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.4507i | − | 1.37143i | −0.727871 | − | 0.685714i | \(-0.759490\pi\) | ||
0.727871 | − | 0.685714i | \(-0.240510\pi\) | |||||||
\(182\) | −18.5874 | + | 0.718075i | −1.37779 | + | 0.0532273i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.14429 | + | 7.17812i | −0.305521 | + | 0.529178i | ||||
\(185\) | 4.34120 | + | 7.51918i | 0.319171 | + | 0.552821i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.98321 | − | 2.29971i | −0.291281 | − | 0.168171i | ||||
\(188\) | 0.502489 | 0.0366478 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.11750 | 0.153620 | ||||||||
\(191\) | 22.4364 | + | 12.9536i | 1.62344 | + | 0.937293i | 0.985991 | + | 0.166800i | \(0.0533436\pi\) |
0.637449 | + | 0.770493i | \(0.279990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.304714 | − | 0.527780i | −0.0219338 | − | 0.0379904i | 0.854850 | − | 0.518875i | \(-0.173649\pi\) |
−0.876784 | + | 0.480884i | \(0.840316\pi\) | |||||||
\(194\) | −6.31573 | + | 10.9392i | −0.453443 | + | 0.785386i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.97914 | + | 0.540046i | −0.498510 | + | 0.0385747i | ||||
\(197\) | 2.19657i | 0.156499i | 0.996934 | + | 0.0782494i | \(0.0249330\pi\) | ||||
−0.996934 | + | 0.0782494i | \(0.975067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.9865 | − | 13.2713i | 1.62947 | − | 0.940775i | 0.645220 | − | 0.763997i | \(-0.276766\pi\) |
0.984251 | − | 0.176778i | \(-0.0565675\pi\) | |||||||
\(200\) | 3.55054 | − | 2.04990i | 0.251061 | − | 0.144950i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.0748i | 1.13102i | ||||||||
\(203\) | 2.08321 | − | 1.31249i | 0.146212 | − | 0.0921189i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.05369 | + | 7.02119i | −0.283122 | + | 0.490381i | ||||
\(206\) | −4.28723 | − | 7.42570i | −0.298706 | − | 0.517373i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.08871 | + | 3.51532i | 0.422176 | + | 0.243743i | ||||
\(209\) | 2.23181 | 0.154377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.72897 | 0.463242 | 0.231621 | − | 0.972806i | \(-0.425597\pi\) | ||||
0.231621 | + | 0.972806i | \(0.425597\pi\) | |||||||
\(212\) | 8.22868 | + | 4.75083i | 0.565148 | + | 0.326288i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.07294 | − | 12.2507i | −0.483496 | − | 0.837440i | ||||
\(215\) | −6.03756 | + | 10.4574i | −0.411758 | + | 0.713186i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.58219 | − | 3.99555i | −0.514713 | − | 0.271235i | ||||
\(218\) | − | 6.71680i | − | 0.454919i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.821673 | + | 0.474393i | −0.0553971 | + | 0.0319836i | ||||
\(221\) | −28.0045 | + | 16.1684i | −1.88379 | + | 1.08760i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.1105i | − | 1.61456i | −0.590168 | − | 0.807280i | \(-0.700939\pi\) | ||
0.590168 | − | 0.807280i | \(-0.299061\pi\) | |||||||
\(224\) | 2.34065 | + | 1.23344i | 0.156391 | + | 0.0824125i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.19940 | − | 7.27357i | 0.279340 | − | 0.483831i | ||||
\(227\) | 4.95825 | + | 8.58794i | 0.329091 | + | 0.570002i | 0.982332 | − | 0.187148i | \(-0.0599245\pi\) |
−0.653241 | + | 0.757150i | \(0.726591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6700 | − | 11.3565i | −1.29983 | − | 0.750458i | −0.319456 | − | 0.947601i | \(-0.603500\pi\) |
−0.980375 | + | 0.197144i | \(0.936833\pi\) | |||||||
\(230\) | −7.86408 | −0.518542 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.930621 | −0.0610982 | ||||||||
\(233\) | −10.6634 | − | 6.15652i | −0.698583 | − | 0.403327i | 0.108237 | − | 0.994125i | \(-0.465480\pi\) |
−0.806819 | + | 0.590798i | \(0.798813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.238377 | + | 0.412882i | 0.0155500 | + | 0.0269334i | ||||
\(236\) | −3.94585 | + | 6.83441i | −0.256853 | + | 0.444882i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.2959 | + | 6.48675i | −0.667381 | + | 0.420474i | ||||
\(239\) | 0.355903i | 0.0230215i | 0.999934 | + | 0.0115107i | \(0.00366406\pi\) | ||||
−0.999934 | + | 0.0115107i | \(0.996336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3413 | + | 11.1667i | −1.24588 | + | 0.719311i | −0.970286 | − | 0.241962i | \(-0.922209\pi\) |
−0.275597 | + | 0.961273i | \(0.588876\pi\) | |||||||
\(242\) | −0.866025 | + | 0.500000i | −0.0556702 | + | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.33539i | − | 0.149508i | ||||||
\(245\) | −3.75459 | − | 5.47837i | −0.239872 | − | 0.350000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.84550 | − | 13.5888i | 0.499197 | − | 0.864635i | ||||
\(248\) | 1.61968 | + | 2.80537i | 0.102850 | + | 0.178141i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.47706 | + | 4.31688i | 0.472891 | + | 0.273024i | ||||
\(251\) | 10.8938 | 0.687612 | 0.343806 | − | 0.939041i | \(-0.388284\pi\) | ||||
0.343806 | + | 0.939041i | \(0.388284\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.28858 | −0.521098 | ||||||||
\(254\) | 6.92663 | + | 3.99909i | 0.434616 | + | 0.250925i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.48335 | + | 7.76538i | −0.279663 | + | 0.484391i | −0.971301 | − | 0.237853i | \(-0.923556\pi\) |
0.691638 | + | 0.722245i | \(0.256890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.1934 | − | 0.934646i | 1.50330 | − | 0.0580761i | ||||
\(260\) | 6.67056i | 0.413691i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.57344 | − | 4.37253i | 0.467889 | − | 0.270136i | ||||
\(263\) | −7.32723 | + | 4.23038i | −0.451817 | + | 0.260856i | −0.708597 | − | 0.705613i | \(-0.750672\pi\) |
0.256781 | + | 0.966470i | \(0.417338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.01504i | 0.553790i | ||||||||
\(266\) | 2.75279 | − | 5.22387i | 0.168785 | − | 0.320296i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.94653 | − | 5.10354i | 0.179988 | − | 0.311748i | ||||
\(269\) | 1.61227 | + | 2.79253i | 0.0983017 | + | 0.170264i | 0.910982 | − | 0.412447i | \(-0.135326\pi\) |
−0.812680 | + | 0.582710i | \(0.801992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.662223 | + | 0.382335i | 0.0402272 | + | 0.0232252i | 0.519979 | − | 0.854179i | \(-0.325940\pi\) |
−0.479752 | + | 0.877404i | \(0.659273\pi\) | |||||||
\(272\) | 4.59942 | 0.278881 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.404912 | −0.0244616 | ||||||||
\(275\) | 3.55054 | + | 2.04990i | 0.214105 | + | 0.123614i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6448 | + | 23.6334i | 0.819834 | + | 1.41999i | 0.905804 | + | 0.423697i | \(0.139268\pi\) |
−0.0859699 | + | 0.996298i | \(0.527399\pi\) | |||||||
\(278\) | −8.79984 | + | 15.2418i | −0.527779 | + | 0.914140i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0969044 | + | 2.50838i | 0.00579115 | + | 0.149904i | ||||
\(281\) | − | 4.36625i | − | 0.260468i | −0.991483 | − | 0.130234i | \(-0.958427\pi\) | ||
0.991483 | − | 0.130234i | \(-0.0415729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5596 | + | 9.56067i | −0.984364 | + | 0.568323i | −0.903585 | − | 0.428409i | \(-0.859074\pi\) |
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(284\) | 11.0473 | − | 6.37816i | 0.655537 | − | 0.378474i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.03063i | 0.415730i | ||||||||
\(287\) | 12.0514 | + | 19.1281i | 0.711370 | + | 1.12910i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.07732 | + | 3.59803i | −0.122196 | + | 0.211649i | ||||
\(290\) | −0.441480 | − | 0.764665i | −0.0259246 | − | 0.0449027i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.85471 | + | 2.80287i | 0.284101 | + | 0.164026i | ||||
\(293\) | −9.23974 | −0.539791 | −0.269896 | − | 0.962890i | \(-0.586989\pi\) | ||||
−0.269896 | + | 0.962890i | \(0.586989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.48753 | −0.435941 | ||||||||
\(296\) | −7.92505 | − | 4.57553i | −0.460634 | − | 0.265947i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.1118 | − | 17.5141i | −0.585760 | − | 1.01457i | ||||
\(299\) | −29.1370 | + | 50.4667i | −1.68503 | + | 2.91857i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.9493 | + | 28.4894i | 1.03458 | + | 1.64210i | ||||
\(302\) | 7.86566i | 0.452618i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.93280 | + | 1.11590i | −0.110854 | + | 0.0640014i | ||||
\(305\) | 1.91892 | − | 1.10789i | 0.109877 | − | 0.0634377i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.06021i | 0.402947i | 0.979494 | + | 0.201474i | \(0.0645730\pi\) | ||||
−0.979494 | + | 0.201474i | \(0.935427\pi\) | |||||||
\(308\) | 0.102135 | + | 2.64378i | 0.00581969 | + | 0.150643i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.53673 | + | 2.66169i | −0.0872803 | + | 0.151174i | ||||
\(311\) | −4.32056 | − | 7.48343i | −0.244997 | − | 0.424346i | 0.717134 | − | 0.696935i | \(-0.245453\pi\) |
−0.962131 | + | 0.272589i | \(0.912120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6329 | − | 11.9124i | −1.16624 | − | 0.673330i | −0.213450 | − | 0.976954i | \(-0.568470\pi\) |
−0.952792 | + | 0.303624i | \(0.901803\pi\) | |||||||
\(314\) | 0.346680 | 0.0195643 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.33446 | −0.468850 | ||||||||
\(317\) | 21.9545 | + | 12.6754i | 1.23309 | + | 0.711923i | 0.967672 | − | 0.252212i | \(-0.0811579\pi\) |
0.265414 | + | 0.964134i | \(0.414491\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.465310 | − | 0.805941i | −0.0260524 | − | 0.0451240i | ||||
\(320\) | 0.474393 | − | 0.821673i | 0.0265194 | − | 0.0459329i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.2234 | + | 19.4006i | −0.569730 | + | 1.08116i | ||||
\(323\) | − | 10.2650i | − | 0.571160i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.9625 | − | 14.4121i | 1.38467 | − | 0.799440i | ||||
\(326\) | 6.93629 | − | 4.00467i | 0.384166 | − | 0.221798i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.54500i | − | 0.471819i | ||||||
\(329\) | 1.32847 | − | 0.0513218i | 0.0732410 | − | 0.00282946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.86378 | + | 6.69226i | −0.212372 | + | 0.367840i | −0.952457 | − | 0.304674i | \(-0.901452\pi\) |
0.740084 | + | 0.672514i | \(0.234786\pi\) | |||||||
\(332\) | −6.00129 | − | 10.3945i | −0.329363 | − | 0.570474i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.2463 | − | 11.6892i | −1.10783 | − | 0.639604i | ||||
\(335\) | 5.59125 | 0.305483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9208 | 1.35752 | 0.678761 | − | 0.734359i | \(-0.262517\pi\) | ||||
0.678761 | + | 0.734359i | \(0.262517\pi\) | |||||||
\(338\) | 31.5491 | + | 18.2149i | 1.71605 | + | 0.990760i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.18193 | + | 3.77922i | 0.118332 | + | 0.204957i | ||||
\(341\) | −1.61968 | + | 2.80537i | −0.0877105 | + | 0.151919i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3961 | + | 2.14058i | −0.993298 | + | 0.115580i | ||||
\(344\) | − | 12.7269i | − | 0.686189i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.82895 | + | 3.94270i | −0.367127 | + | 0.211961i | ||||
\(347\) | −11.0204 | + | 6.36264i | −0.591607 | + | 0.341564i | −0.765733 | − | 0.643159i | \(-0.777623\pi\) |
0.174126 | + | 0.984723i | \(0.444290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.72324i | 0.359887i | 0.983677 | + | 0.179943i | \(0.0575914\pi\) | ||||
−0.983677 | + | 0.179943i | \(0.942409\pi\) | |||||||
\(350\) | 9.17747 | − | 5.78213i | 0.490556 | − | 0.309068i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | −9.54247 | − | 16.5280i | −0.507895 | − | 0.879699i | −0.999958 | − | 0.00914007i | \(-0.997091\pi\) |
0.492064 | − | 0.870559i | \(-0.336243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4815 | + | 6.05151i | 0.556301 | + | 0.321181i | ||||
\(356\) | −0.882960 | −0.0467968 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.50545 | 0.185269 | ||||||||
\(359\) | 11.1639 | + | 6.44550i | 0.589210 | + | 0.340181i | 0.764785 | − | 0.644285i | \(-0.222845\pi\) |
−0.175575 | + | 0.984466i | \(0.556178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00952 | − | 12.1408i | −0.368922 | − | 0.638992i | ||||
\(362\) | −9.22534 | + | 15.9788i | −0.484873 | + | 0.839825i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.4562 | + | 8.67185i | 0.862541 | + | 0.454528i | ||||
\(365\) | 5.31865i | 0.278391i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.21459 | + | 1.27860i | −0.115601 | + | 0.0667422i | −0.556686 | − | 0.830723i | \(-0.687927\pi\) |
0.441085 | + | 0.897465i | \(0.354594\pi\) | |||||||
\(368\) | 7.17812 | − | 4.14429i | 0.374185 | − | 0.216036i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 8.68240i | − | 0.451376i | ||||||
\(371\) | 22.2400 | + | 11.7197i | 1.15465 | + | 0.608457i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1993 | + | 26.3259i | −0.786989 | + | 1.36310i | 0.140815 | + | 0.990036i | \(0.455028\pi\) |
−0.927804 | + | 0.373069i | \(0.878306\pi\) | |||||||
\(374\) | 2.29971 | + | 3.98321i | 0.118915 | + | 0.205967i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.435168 | − | 0.251245i | −0.0224421 | − | 0.0129570i | ||||
\(377\) | −6.54285 | −0.336974 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.6206 | −0.699642 | −0.349821 | − | 0.936817i | \(-0.613758\pi\) | ||||
−0.349821 | + | 0.936817i | \(0.613758\pi\) | |||||||
\(380\) | −1.83381 | − | 1.05875i | −0.0940726 | − | 0.0543129i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.9536 | − | 22.4364i | −0.662766 | − | 1.14795i | ||||
\(383\) | −11.4051 | + | 19.7542i | −0.582774 | + | 1.00939i | 0.412375 | + | 0.911014i | \(0.364699\pi\) |
−0.995149 | + | 0.0983803i | \(0.968634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.12387 | + | 1.33811i | −0.108242 | + | 0.0681965i | ||||
\(386\) | 0.609428i | 0.0310191i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.9392 | − | 6.31573i | 0.555352 | − | 0.320633i | ||||
\(389\) | −1.46953 | + | 0.848435i | −0.0745083 | + | 0.0430174i | −0.536791 | − | 0.843715i | \(-0.680364\pi\) |
0.462283 | + | 0.886732i | \(0.347030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.1226i | 1.92794i | ||||||||
\(392\) | 6.31413 | + | 3.02187i | 0.318912 | + | 0.152628i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.09828 | − | 1.90228i | 0.0553307 | − | 0.0958356i | ||||
\(395\) | −3.95381 | − | 6.84819i | −0.198938 | − | 0.344570i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.7326 | − | 12.5473i | −1.09073 | − | 0.629733i | −0.156958 | − | 0.987605i | \(-0.550169\pi\) |
−0.933770 | + | 0.357873i | \(0.883502\pi\) | |||||||
\(398\) | −26.5425 | −1.33046 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.09981 | −0.204990 | ||||||||
\(401\) | −18.8176 | − | 10.8643i | −0.939705 | − | 0.542539i | −0.0498372 | − | 0.998757i | \(-0.515870\pi\) |
−0.889868 | + | 0.456218i | \(0.849204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3874 | + | 19.7235i | 0.567245 | + | 0.982497i | ||||
\(404\) | 8.03742 | − | 13.9212i | 0.399877 | − | 0.692607i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.46036 | + | 0.0950491i | −0.122105 | + | 0.00471721i | ||||
\(407\) | − | 9.15106i | − | 0.453601i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.03930 | + | 2.33209i | −0.199730 | + | 0.115314i | −0.596530 | − | 0.802591i | \(-0.703454\pi\) |
0.396799 | + | 0.917905i | \(0.370121\pi\) | |||||||
\(410\) | 7.02119 | − | 4.05369i | 0.346752 | − | 0.200197i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.57446i | 0.422433i | ||||||||
\(413\) | −9.73392 | + | 18.4717i | −0.478975 | + | 0.908932i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.69394 | − | 9.86219i | 0.279504 | − | 0.484116i | ||||
\(416\) | −3.51532 | − | 6.08871i | −0.172353 | − | 0.298523i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.93280 | − | 1.11590i | −0.0945363 | − | 0.0545806i | ||||
\(419\) | −36.6109 | −1.78856 | −0.894281 | − | 0.447506i | \(-0.852312\pi\) | ||||
−0.894281 | + | 0.447506i | \(0.852312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.4576 | −1.48441 | −0.742206 | − | 0.670172i | \(-0.766220\pi\) | ||||
−0.742206 | + | 0.670172i | \(0.766220\pi\) | |||||||
\(422\) | −5.82746 | − | 3.36449i | −0.283676 | − | 0.163781i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.75083 | − | 8.22868i | −0.230721 | − | 0.399620i | ||||
\(425\) | 9.42836 | − | 16.3304i | 0.457343 | − | 0.792141i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.238525 | − | 6.17425i | −0.0115430 | − | 0.298793i | ||||
\(428\) | 14.1459i | 0.683767i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.4574 | − | 6.03756i | 0.504299 | − | 0.291157i | ||||
\(431\) | −16.1392 | + | 9.31798i | −0.777399 | + | 0.448832i | −0.835508 | − | 0.549479i | \(-0.814826\pi\) |
0.0581087 | + | 0.998310i | \(0.481493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.69502i | 0.465913i | 0.972487 | + | 0.232956i | \(0.0748400\pi\) | ||||
−0.972487 | + | 0.232956i | \(0.925160\pi\) | |||||||
\(434\) | 4.56860 | + | 7.25134i | 0.219300 | + | 0.348075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.35840 | + | 5.81692i | −0.160838 | + | 0.278580i | ||||
\(437\) | −9.24925 | − | 16.0202i | −0.442451 | − | 0.766348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.0710 | + | 16.7841i | 1.38748 | + | 0.801063i | 0.993031 | − | 0.117854i | \(-0.0376016\pi\) |
0.394450 | + | 0.918917i | \(0.370935\pi\) | |||||||
\(440\) | 0.948786 | 0.0452316 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 32.3368 | 1.53811 | ||||||||
\(443\) | 2.64582 | + | 1.52756i | 0.125707 | + | 0.0725767i | 0.561535 | − | 0.827453i | \(-0.310211\pi\) |
−0.435828 | + | 0.900030i | \(0.643544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.418870 | − | 0.725504i | −0.0198563 | − | 0.0343922i | ||||
\(446\) | −12.0553 | + | 20.8803i | −0.570833 | + | 0.988713i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.41034 | − | 2.23851i | −0.0666324 | − | 0.105760i | ||||
\(449\) | 0.355204i | 0.0167631i | 0.999965 | + | 0.00838157i | \(0.00266797\pi\) | ||||
−0.999965 | + | 0.00838157i | \(0.997332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.40019 | − | 4.27250i | 0.348461 | − | 0.201184i | ||||
\(452\) | −7.27357 | + | 4.19940i | −0.342120 | + | 0.197523i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 9.91650i | − | 0.465404i | ||||||
\(455\) | 0.681299 | + | 17.6355i | 0.0319398 | + | 0.826765i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.80324 | + | 8.31946i | −0.224686 | + | 0.389168i | −0.956225 | − | 0.292632i | \(-0.905469\pi\) |
0.731539 | + | 0.681800i | \(0.238802\pi\) | |||||||
\(458\) | 11.3565 | + | 19.6700i | 0.530654 | + | 0.919119i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.81050 | + | 3.93204i | 0.317541 | + | 0.183332i | ||||
\(461\) | 38.6120 | 1.79834 | 0.899169 | − | 0.437602i | \(-0.144172\pi\) | ||||
0.899169 | + | 0.437602i | \(0.144172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.61880 | 0.168180 | 0.0840899 | − | 0.996458i | \(-0.473202\pi\) | ||||
0.0840899 | + | 0.996458i | \(0.473202\pi\) | |||||||
\(464\) | 0.805941 | + | 0.465310i | 0.0374149 | + | 0.0216015i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.15652 | + | 10.6634i | 0.285195 | + | 0.493972i | ||||
\(467\) | 4.07804 | − | 7.06337i | 0.188709 | − | 0.326854i | −0.756111 | − | 0.654443i | \(-0.772903\pi\) |
0.944820 | + | 0.327590i | \(0.106236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.26873 | − | 13.7936i | 0.335639 | − | 0.636928i | ||||
\(470\) | − | 0.476755i | − | 0.0219910i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.83441 | − | 3.94585i | 0.314579 | − | 0.181622i | ||||
\(473\) | 11.0218 | − | 6.36346i | 0.506784 | − | 0.292592i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.14997i | 0.419829i | ||||||||
\(476\) | 12.1598 | − | 0.469763i | 0.557346 | − | 0.0215315i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.177951 | − | 0.308221i | 0.00813931 | − | 0.0140977i | ||||
\(479\) | −12.9635 | − | 22.4534i | −0.592316 | − | 1.02592i | −0.993920 | − | 0.110108i | \(-0.964880\pi\) |
0.401604 | − | 0.915814i | \(-0.368453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −55.7181 | − | 32.1689i | −2.54053 | − | 1.46677i | ||||
\(482\) | 22.3334 | 1.01726 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.3789 | + | 5.99227i | 0.471283 | + | 0.272095i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.93103 | − | 3.34464i | −0.0875032 | − | 0.151560i | 0.818952 | − | 0.573862i | \(-0.194555\pi\) |
−0.906455 | + | 0.422302i | \(0.861222\pi\) | |||||||
\(488\) | −1.16769 | + | 2.02250i | −0.0528590 | + | 0.0915545i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.512388 | + | 6.62171i | 0.0231473 | + | 0.299138i | ||||
\(491\) | 13.5459i | 0.611317i | 0.952141 | + | 0.305658i | \(0.0988766\pi\) | ||||
−0.952141 | + | 0.305658i | \(0.901123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.70686 | + | 2.14016i | −0.166949 | + | 0.0963878i | ||||
\(494\) | −13.5888 | + | 7.84550i | −0.611389 | + | 0.352986i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.23936i | − | 0.145451i | ||||||
\(497\) | 28.5552 | − | 17.9908i | 1.28088 | − | 0.806996i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.02599 | + | 8.70526i | −0.224994 | + | 0.389701i | −0.956318 | − | 0.292329i | \(-0.905570\pi\) |
0.731324 | + | 0.682031i | \(0.238903\pi\) | |||||||
\(500\) | −4.31688 | − | 7.47706i | −0.193057 | − | 0.334384i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.43433 | − | 5.44691i | −0.421075 | − | 0.243108i | ||||
\(503\) | −10.4299 | −0.465048 | −0.232524 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232524 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2516 | 0.678687 | ||||||||
\(506\) | 7.17812 | + | 4.14429i | 0.319106 | + | 0.184236i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.99909 | − | 6.92663i | −0.177431 | − | 0.307320i | ||||
\(509\) | 5.46543 | − | 9.46640i | 0.242251 | − | 0.419591i | −0.719104 | − | 0.694902i | \(-0.755448\pi\) |
0.961355 | + | 0.275311i | \(0.0887809\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.1211 | + | 6.91433i | 0.580441 | + | 0.305872i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.76538 | − | 4.48335i | 0.342516 | − | 0.197752i | ||||
\(515\) | −7.04540 | + | 4.06766i | −0.310457 | + | 0.179243i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.502489i | − | 0.0220995i | ||||||
\(518\) | −21.4194 | − | 11.2873i | −0.941115 | − | 0.495934i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.33528 | − | 5.77688i | 0.146262 | − | 0.253333i | ||||
\(521\) | −0.801194 | − | 1.38771i | −0.0351010 | − | 0.0607966i | 0.847941 | − | 0.530090i | \(-0.177842\pi\) |
−0.883042 | + | 0.469294i | \(0.844509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.6963 | + | 10.7943i | 0.817533 | + | 0.472003i | 0.849565 | − | 0.527484i | \(-0.176865\pi\) |
−0.0320322 | + | 0.999487i | \(0.510198\pi\) | |||||||
\(524\) | −8.74506 | −0.382030 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.46076 | 0.368907 | ||||||||
\(527\) | 12.9030 | + | 7.44958i | 0.562066 | + | 0.324509i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8503 | + | 39.5778i | 0.993490 | + | 1.72077i | ||||
\(530\) | 4.50752 | − | 7.80725i | 0.195794 | − | 0.339125i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.99592 | + | 3.14761i | −0.216601 | + | 0.136466i | ||||
\(533\) | − | 60.0767i | − | 2.60221i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6233 | + | 6.71070i | −0.502518 | + | 0.290129i | ||||
\(536\) | −5.10354 | + | 2.94653i | −0.220439 | + | 0.127271i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.22454i | − | 0.139020i | ||||||
\(539\) | 0.540046 | + | 6.97914i | 0.0232614 | + | 0.300613i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.76339 | + | 3.05429i | −0.0758142 | + | 0.131314i | −0.901440 | − | 0.432904i | \(-0.857489\pi\) |
0.825626 | + | 0.564218i | \(0.190822\pi\) | |||||||
\(542\) | −0.382335 | − | 0.662223i | −0.0164227 | − | 0.0284449i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.98321 | − | 2.29971i | −0.170779 | − | 0.0985992i | ||||
\(545\) | −6.37280 | −0.272981 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.548636 | 0.0234580 | 0.0117290 | − | 0.999931i | \(-0.496266\pi\) | ||||
0.0117290 | + | 0.999931i | \(0.496266\pi\) | |||||||
\(548\) | 0.350664 | + | 0.202456i | 0.0149796 | + | 0.00864848i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.04990 | − | 3.55054i | −0.0874082 | − | 0.151395i | ||||
\(551\) | 1.03848 | − | 1.79870i | 0.0442408 | − | 0.0766274i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.0345 | + | 0.851241i | −0.937001 | + | 0.0361985i | ||||
\(554\) | − | 27.2895i | − | 1.15942i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2418 | − | 8.79984i | 0.646395 | − | 0.373196i | ||||
\(557\) | −6.28514 | + | 3.62873i | −0.266310 | + | 0.153754i | −0.627209 | − | 0.778851i | \(-0.715803\pi\) |
0.360900 | + | 0.932605i | \(0.382470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 89.4783i | − | 3.78453i | ||||||
\(560\) | 1.17027 | − | 2.22077i | 0.0494529 | − | 0.0938448i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.18312 | + | 3.78128i | −0.0920895 | + | 0.159504i | ||||
\(563\) | 4.89429 | + | 8.47715i | 0.206270 | + | 0.357269i | 0.950537 | − | 0.310613i | \(-0.100534\pi\) |
−0.744267 | + | 0.667882i | \(0.767201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.90106 | − | 3.98433i | −0.290330 | − | 0.167622i | ||||
\(566\) | 19.1213 | 0.803730 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7563 | −0.535243 | ||||||||
\(569\) | −25.5726 | − | 14.7644i | −1.07206 | − | 0.618954i | −0.143316 | − | 0.989677i | \(-0.545777\pi\) |
−0.928743 | + | 0.370723i | \(0.879110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4562 | + | 28.5031i | 0.688673 | + | 1.19282i | 0.972267 | + | 0.233872i | \(0.0751396\pi\) |
−0.283595 | + | 0.958944i | \(0.591527\pi\) | |||||||
\(572\) | 3.51532 | − | 6.08871i | 0.146983 | − | 0.254582i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.872745 | − | 22.5911i | −0.0364277 | − | 0.942934i | ||||
\(575\) | − | 33.9816i | − | 1.41713i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0259 | − | 8.09787i | 0.583907 | − | 0.337119i | −0.178777 | − | 0.983890i | \(-0.557214\pi\) |
0.762685 | + | 0.646771i | \(0.223881\pi\) | |||||||
\(578\) | 3.59803 | − | 2.07732i | 0.149658 | − | 0.0864053i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.882960i | 0.0366629i | ||||||||
\(581\) | −16.9277 | − | 26.8679i | −0.702281 | − | 1.11467i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.75083 | − | 8.22868i | 0.196759 | − | 0.340797i | ||||
\(584\) | −2.80287 | − | 4.85471i | −0.115984 | − | 0.200889i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.00185 | + | 4.61987i | 0.330553 | + | 0.190845i | ||||
\(587\) | 13.5685 | 0.560031 | 0.280016 | − | 0.959995i | \(-0.409660\pi\) | ||||
0.280016 | + | 0.959995i | \(0.409660\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.22961 | −0.297891 | ||||||||
\(590\) | 6.48439 | + | 3.74376i | 0.266958 | + | 0.154128i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.57553 | + | 7.92505i | 0.188053 | + | 0.325718i | ||||
\(593\) | −12.5012 | + | 21.6528i | −0.513365 | + | 0.889174i | 0.486515 | + | 0.873672i | \(0.338268\pi\) |
−0.999880 | + | 0.0155014i | \(0.995066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.15454 | + | 9.76856i | 0.252311 | + | 0.400472i | ||||
\(596\) | 20.2236i | 0.828390i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 50.4667 | − | 29.1370i | 2.06374 | − | 1.19150i | ||||
\(599\) | −12.1564 | + | 7.01849i | −0.496696 | + | 0.286768i | −0.727348 | − | 0.686269i | \(-0.759247\pi\) |
0.230652 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.3598i | − | 0.626540i | −0.949664 | − | 0.313270i | \(-0.898576\pi\) | ||
0.949664 | − | 0.313270i | \(-0.101424\pi\) | |||||||
\(602\) | −1.29987 | − | 33.6472i | −0.0529786 | − | 1.37136i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.93283 | − | 6.81186i | 0.160025 | − | 0.277171i | ||||
\(605\) | 0.474393 | + | 0.821673i | 0.0192868 | + | 0.0334057i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.15436 | + | 1.82117i | 0.128032 | + | 0.0739190i | 0.562648 | − | 0.826697i | \(-0.309783\pi\) |
−0.434616 | + | 0.900616i | \(0.643116\pi\) | |||||||
\(608\) | 2.23181 | 0.0905117 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.21578 | −0.0897144 | ||||||||
\(611\) | −3.05951 | − | 1.76641i | −0.123774 | − | 0.0714612i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.4436 | − | 37.1414i | −0.866099 | − | 1.50013i | −0.865952 | − | 0.500127i | \(-0.833287\pi\) |
−0.000146529 | − | 1.00000i | \(-0.500047\pi\) | |||||||
\(614\) | 3.53010 | − | 6.11432i | 0.142463 | − | 0.246754i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.23344 | − | 2.34065i | 0.0496966 | − | 0.0943074i | ||||
\(617\) | − | 2.97864i | − | 0.119915i | −0.998201 | − | 0.0599577i | \(-0.980903\pi\) | ||
0.998201 | − | 0.0599577i | \(-0.0190966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.6085 | + | 8.43422i | −0.587165 | + | 0.339000i | −0.763976 | − | 0.645245i | \(-0.776755\pi\) |
0.176810 | + | 0.984245i | \(0.443422\pi\) | |||||||
\(620\) | 2.66169 | − | 1.53673i | 0.106896 | − | 0.0617165i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.64112i | 0.346477i | ||||||||
\(623\) | −2.33435 | + | 0.0901812i | −0.0935238 | + | 0.00361304i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.15372 | + | 10.6586i | −0.246149 | + | 0.426342i | ||||
\(626\) | 11.9124 | + | 20.6329i | 0.476116 | + | 0.824657i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.300234 | − | 0.173340i | −0.0119806 | − | 0.00691702i | ||||
\(629\) | −42.0896 | −1.67822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6847 | 1.06230 | 0.531150 | − | 0.847278i | \(-0.321760\pi\) | ||||
0.531150 | + | 0.847278i | \(0.321760\pi\) | |||||||
\(632\) | 7.21785 | + | 4.16723i | 0.287111 | + | 0.165763i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.6754 | − | 21.9545i | −0.503405 | − | 0.871924i | ||||
\(635\) | 3.79428 | − | 6.57189i | 0.150572 | − | 0.260798i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.3923 | + | 21.2457i | 1.75889 | + | 0.841785i | ||||
\(638\) | 0.930621i | 0.0368436i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.821673 | + | 0.474393i | −0.0324795 | + | 0.0187520i | ||||
\(641\) | −26.1562 | + | 15.1013i | −1.03311 | + | 0.596464i | −0.917873 | − | 0.396874i | \(-0.870095\pi\) |
−0.115234 | + | 0.993338i | \(0.536762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.8154i | − | 0.426517i | −0.976996 | − | 0.213259i | \(-0.931592\pi\) | ||
0.976996 | − | 0.213259i | \(-0.0684077\pi\) | |||||||
\(644\) | 18.5541 | − | 11.6897i | 0.731133 | − | 0.460640i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.13250 | + | 8.88976i | −0.201936 | + | 0.349763i | ||||
\(647\) | −7.24060 | − | 12.5411i | −0.284657 | − | 0.493041i | 0.687869 | − | 0.725835i | \(-0.258547\pi\) |
−0.972526 | + | 0.232794i | \(0.925213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.83441 | + | 3.94585i | 0.268274 | + | 0.154888i | ||||
\(650\) | −28.8242 | −1.13058 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.00934 | −0.313670 | ||||||||
\(653\) | 37.4800 | + | 21.6391i | 1.46671 | + | 0.846804i | 0.999306 | − | 0.0372417i | \(-0.0118571\pi\) |
0.467401 | + | 0.884045i | \(0.345190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.14859 | − | 7.18557i | −0.162099 | − | 0.280764i | ||||
\(656\) | −4.27250 | + | 7.40019i | −0.166813 | + | 0.288929i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.17615 | − | 0.619789i | −0.0458511 | − | 0.0241619i | ||||
\(659\) | 9.95936i | 0.387962i | 0.981005 | + | 0.193981i | \(0.0621400\pi\) | ||||
−0.981005 | + | 0.193981i | \(0.937860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1474 | + | 12.7868i | −0.861434 | + | 0.497349i | −0.864492 | − | 0.502646i | \(-0.832360\pi\) |
0.00305800 | + | 0.999995i | \(0.499027\pi\) | |||||||
\(662\) | 6.69226 | − | 3.86378i | 0.260102 | − | 0.150170i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0026i | 0.465790i | ||||||||
\(665\) | −4.95633 | − | 2.61181i | −0.192198 | − | 0.101282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.85676 | + | 6.68011i | −0.149334 | + | 0.258655i | ||||
\(668\) | 11.6892 | + | 20.2463i | 0.452269 | + | 0.783352i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.84217 | − | 2.79563i | −0.187069 | − | 0.108004i | ||||
\(671\) | −2.33539 | −0.0901566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7065 | 0.875269 | 0.437635 | − | 0.899153i | \(-0.355816\pi\) | ||||
0.437635 | + | 0.899153i | \(0.355816\pi\) | |||||||
\(674\) | −21.5820 | − | 12.4604i | −0.831309 | − | 0.479957i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.2149 | − | 31.5491i | −0.700573 | − | 1.21343i | ||||
\(677\) | 13.1278 | − | 22.7380i | 0.504542 | − | 0.873893i | −0.495444 | − | 0.868640i | \(-0.664995\pi\) |
0.999986 | − | 0.00525286i | \(-0.00167205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.2757 | − | 17.8147i | 1.08512 | − | 0.683664i | ||||
\(680\) | − | 4.36386i | − | 0.167346i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.80537 | − | 1.61968i | 0.107423 | − | 0.0620207i | ||||
\(683\) | 27.1231 | − | 15.6595i | 1.03784 | − | 0.599194i | 0.118616 | − | 0.992940i | \(-0.462154\pi\) |
0.919219 | + | 0.393746i | \(0.128821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.384174i | 0.0146785i | ||||||||
\(686\) | 17.0018 | + | 7.34427i | 0.649132 | + | 0.280406i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.36346 | + | 11.0218i | −0.242605 | + | 0.420203i | ||||
\(689\) | −33.4013 | − | 57.8528i | −1.27249 | − | 2.20402i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.5041 | − | 12.9927i | −0.856096 | − | 0.494267i | 0.00660716 | − | 0.999978i | \(-0.497897\pi\) |
−0.862703 | + | 0.505711i | \(0.831230\pi\) | |||||||
\(692\) | 7.88540 | 0.299758 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.7253 | 0.483045 | ||||||||
\(695\) | 14.4612 | + | 8.34916i | 0.548543 | + | 0.316702i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.6510 | − | 34.0366i | −0.744335 | − | 1.28923i | ||||
\(698\) | 3.36162 | − | 5.82250i | 0.127239 | − | 0.220385i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.8390 | + | 0.418734i | −0.409675 | + | 0.0158267i | ||||
\(701\) | − | 1.46095i | − | 0.0551793i | −0.999619 | − | 0.0275897i | \(-0.991217\pi\) | ||
0.999619 | − | 0.0275897i | \(-0.00878318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.6872 | − | 10.2117i | 0.667084 | − | 0.385141i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.0849i | 0.718271i | ||||||||
\(707\) | 19.8273 | − | 37.6256i | 0.745683 | − | 1.41505i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.35318 | + | 12.7361i | −0.276155 | + | 0.478314i | −0.970426 | − | 0.241400i | \(-0.922394\pi\) |
0.694271 | + | 0.719714i | \(0.255727\pi\) | |||||||
\(710\) | −6.05151 | − | 10.4815i | −0.227109 | − | 0.393364i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.764665 | + | 0.441480i | 0.0286570 | + | 0.0165452i | ||||
\(713\) | 26.8497 | 1.00553 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.67056 | 0.249465 | ||||||||
\(716\) | −3.03581 | − | 1.75273i | −0.113454 | − | 0.0655025i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.44550 | − | 11.1639i | −0.240544 | − | 0.416634i | ||||
\(719\) | 15.2799 | − | 26.4656i | 0.569844 | − | 0.986999i | −0.426737 | − | 0.904376i | \(-0.640337\pi\) |
0.996581 | − | 0.0826233i | \(-0.0263298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.875755 | + | 22.6690i | 0.0326148 | + | 0.844237i | ||||
\(722\) | 14.0190i | 0.521735i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.9788 | − | 9.22534i | 0.593846 | − | 0.342857i | ||||
\(725\) | 3.30420 | − | 1.90768i | 0.122715 | − | 0.0708495i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9985i | 0.890056i | 0.895517 | + | 0.445028i | \(0.146806\pi\) | ||||
−0.895517 | + | 0.445028i | \(0.853194\pi\) | |||||||
\(728\) | −9.91559 | − | 15.7382i | −0.367496 | − | 0.583295i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.65932 | − | 4.60608i | 0.0984259 | − | 0.170479i | ||||
\(731\) | −29.2682 | − | 50.6940i | −1.08252 | − | 1.87499i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1549 | + | 12.2138i | 0.781373 | + | 0.451126i | 0.836917 | − | 0.547330i | \(-0.184356\pi\) |
−0.0555434 | + | 0.998456i | \(0.517689\pi\) | |||||||
\(734\) | 2.55719 | 0.0943877 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.28858 | −0.305521 | ||||||||
\(737\) | −5.10354 | − | 2.94653i | −0.187991 | − | 0.108537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6718 | + | 20.2161i | 0.429354 | + | 0.743663i | 0.996816 | − | 0.0797369i | \(-0.0254080\pi\) |
−0.567462 | + | 0.823399i | \(0.692075\pi\) | |||||||
\(740\) | −4.34120 | + | 7.51918i | −0.159586 | + | 0.276410i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.4006 | − | 21.2696i | −0.491951 | − | 0.780831i | ||||
\(743\) | − | 7.04913i | − | 0.258608i | −0.991605 | − | 0.129304i | \(-0.958726\pi\) | ||
0.991605 | − | 0.129304i | \(-0.0412742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.6172 | + | 9.59392i | −0.608805 | + | 0.351494i | ||||
\(746\) | 26.3259 | − | 15.1993i | 0.963860 | − | 0.556485i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.59942i | − | 0.168171i | ||||||
\(749\) | 1.44479 | + | 37.3986i | 0.0527915 | + | 1.36651i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.999206 | + | 1.73068i | −0.0364615 | + | 0.0631533i | −0.883680 | − | 0.468091i | \(-0.844942\pi\) |
0.847219 | + | 0.531244i | \(0.178275\pi\) | |||||||
\(752\) | 0.251245 | + | 0.435168i | 0.00916195 | + | 0.0158690i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.66628 | + | 3.27143i | 0.206354 | + | 0.119138i | ||||
\(755\) | 7.46283 | 0.271600 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.3860 | −1.43151 | −0.715753 | − | 0.698353i | \(-0.753917\pi\) | ||||
−0.715753 | + | 0.698353i | \(0.753917\pi\) | |||||||
\(758\) | 11.7958 | + | 6.81029i | 0.428442 | + | 0.247361i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.05875 | + | 1.83381i | 0.0384050 | + | 0.0665194i | ||||
\(761\) | −4.01747 | + | 6.95846i | −0.145633 | + | 0.252244i | −0.929609 | − | 0.368547i | \(-0.879855\pi\) |
0.783976 | + | 0.620791i | \(0.213189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.28476 | + | 15.7217i | −0.299928 | + | 0.569162i | ||||
\(764\) | 25.9073i | 0.937293i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7542 | − | 11.4051i | 0.713750 | − | 0.412084i | ||||
\(767\) | 48.0502 | − | 27.7418i | 1.73499 | − | 1.00170i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.71938i | − | 0.0620025i | −0.999519 | − | 0.0310013i | \(-0.990130\pi\) | ||
0.999519 | − | 0.0310013i | \(-0.00986959\pi\) | |||||||
\(770\) | 2.50838 | − | 0.0969044i | 0.0903957 | − | 0.00349219i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.304714 | − | 0.527780i | 0.0109669 | − | 0.0189952i | ||||
\(773\) | 5.05536 | + | 8.75614i | 0.181829 | + | 0.314936i | 0.942503 | − | 0.334197i | \(-0.108465\pi\) |
−0.760675 | + | 0.649133i | \(0.775132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.5015 | − | 6.64037i | −0.413144 | − | 0.238529i | ||||
\(776\) | −12.6315 | −0.453443 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.69687 | 0.0608357 | ||||||||
\(779\) | 16.5158 | + | 9.53539i | 0.591739 | + | 0.341641i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.37816 | − | 11.0473i | −0.228229 | − | 0.395303i | ||||
\(782\) | 19.0613 | − | 33.0152i | 0.681631 | − | 1.18062i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.95726 | − | 5.77409i | −0.141331 | − | 0.206217i | ||||
\(785\) | − | 0.328925i | − | 0.0117398i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.25705 | − | 5.34456i | 0.329978 | − | 0.190513i | −0.325853 | − | 0.945420i | \(-0.605652\pi\) |
0.655831 | + | 0.754907i | \(0.272318\pi\) | |||||||
\(788\) | −1.90228 | + | 1.09828i | −0.0677660 | + | 0.0391247i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.90761i | 0.281340i | ||||||||
\(791\) | −18.8008 | + | 11.8452i | −0.668480 | + | 0.421166i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.20962 | + | 14.2195i | −0.291532 | + | 0.504949i | ||||
\(794\) | 12.5473 | + | 21.7326i | 0.445288 | + | 0.771262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.9865 | + | 13.2713i | 0.814735 | + | 0.470388i | ||||
\(797\) | −8.76241 | −0.310380 | −0.155190 | − | 0.987885i | \(-0.549599\pi\) | ||||
−0.155190 | + | 0.987885i | \(0.549599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.31116 | −0.0817629 | ||||||||
\(800\) | 3.55054 | + | 2.04990i | 0.125530 | + | 0.0724750i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.8643 | + | 18.8176i | 0.383633 | + | 0.664472i | ||||
\(803\) | 2.80287 | − | 4.85471i | 0.0989111 | − | 0.171319i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4071 | + | 9.69986i | 0.648763 | + | 0.341875i | ||||
\(806\) | − | 22.7747i | − | 0.802206i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.9212 | + | 8.03742i | −0.489747 | + | 0.282756i | ||||
\(809\) | −24.4799 | + | 14.1335i | −0.860669 | + | 0.496908i | −0.864236 | − | 0.503086i | \(-0.832198\pi\) |
0.00356720 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6593i | 0.690331i | 0.938542 | + | 0.345166i | \(0.112177\pi\) | ||||
−0.938542 | + | 0.345166i | \(0.887823\pi\) | |||||||
\(812\) | 2.17825 | + | 1.14786i | 0.0764418 | + | 0.0402821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.57553 | + | 7.92505i | −0.160372 | + | 0.277773i | ||||
\(815\) | −3.79957 | − | 6.58105i | −0.133093 | − | 0.230524i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.5986 | + | 14.2020i | 0.860596 | + | 0.496865i | ||||
\(818\) | 4.66418 | 0.163079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.10737 | −0.283122 | ||||||||
\(821\) | −8.92687 | − | 5.15393i | −0.311550 | − | 0.179873i | 0.336070 | − | 0.941837i | \(-0.390902\pi\) |
−0.647620 | + | 0.761964i | \(0.724235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.561944 | − | 0.973316i | −0.0195881 | − | 0.0339277i | 0.856065 | − | 0.516868i | \(-0.172902\pi\) |
−0.875653 | + | 0.482940i | \(0.839569\pi\) | |||||||
\(824\) | 4.28723 | − | 7.42570i | 0.149353 | − | 0.258687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.6657 | − | 11.1300i | 0.614667 | − | 0.387262i | ||||
\(827\) | 23.9832i | 0.833976i | 0.908912 | + | 0.416988i | \(0.136914\pi\) | ||||
−0.908912 | + | 0.416988i | \(0.863086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.07807 | − | 2.93182i | 0.176369 | − | 0.101826i | −0.409217 | − | 0.912437i | \(-0.634198\pi\) |
0.585585 | + | 0.810611i | \(0.300865\pi\) | |||||||
\(830\) | −9.86219 | + | 5.69394i | −0.342322 | + | 0.197639i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.03063i | 0.243743i | ||||||||
\(833\) | 32.1000 | − | 2.48390i | 1.11220 | − | 0.0860619i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.0905 | + | 19.2094i | −0.383804 | + | 0.664768i | ||||
\(836\) | 1.11590 | + | 1.93280i | 0.0385943 | + | 0.0668473i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.7060 | + | 18.3055i | 1.09527 | + | 0.632352i | ||||
\(839\) | 14.4962 | 0.500464 | 0.250232 | − | 0.968186i | \(-0.419493\pi\) | ||||
0.250232 | + | 0.968186i | \(0.419493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1339 | 0.970136 | ||||||||
\(842\) | 26.3771 | + | 15.2288i | 0.909013 | + | 0.524819i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.36449 | + | 5.82746i | 0.115810 | + | 0.200590i | ||||
\(845\) | 17.2820 | − | 29.9334i | 0.594520 | − | 1.02974i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.64378 | − | 0.102135i | 0.0908413 | − | 0.00350941i | ||||
\(848\) | 9.50166i | 0.326288i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.3304 | + | 9.42836i | −0.560128 | + | 0.323390i | ||||
\(851\) | −65.6874 | + | 37.9246i | −2.25174 | + | 1.30004i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.1687i | 0.759042i | 0.925183 | + | 0.379521i | \(0.123911\pi\) | ||||
−0.925183 | + | 0.379521i | \(0.876089\pi\) | |||||||
\(854\) | −2.88056 | + | 5.46632i | −0.0985706 | + | 0.187054i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.07294 | − | 12.2507i | 0.241748 | − | 0.418720i | ||||
\(857\) | −8.89302 | − | 15.4032i | −0.303780 | − | 0.526162i | 0.673209 | − | 0.739452i | \(-0.264915\pi\) |
−0.976989 | + | 0.213290i | \(0.931582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.96846 | − | 3.44589i | −0.203641 | − | 0.117572i | 0.394712 | − | 0.918805i | \(-0.370845\pi\) |
−0.598353 | + | 0.801233i | \(0.704178\pi\) | |||||||
\(860\) | −12.0751 | −0.411758 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.6360 | 0.634744 | ||||||||
\(863\) | 30.7013 | + | 17.7254i | 1.04508 | + | 0.603380i | 0.921269 | − | 0.388926i | \(-0.127154\pi\) |
0.123815 | + | 0.992305i | \(0.460487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.74078 | + | 6.47921i | 0.127190 | + | 0.220300i | ||||
\(866\) | 4.84751 | − | 8.39613i | 0.164725 | − | 0.285312i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.330852 | − | 8.56414i | −0.0112299 | − | 0.290686i | ||||
\(869\) | 8.33446i | 0.282727i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.8811 | + | 20.7160i | −1.21579 | + | 0.701934i | ||||
\(872\) | 5.81692 | − | 3.35840i | 0.196986 | − | 0.113730i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.4985i | 0.625721i | ||||||||
\(875\) | −12.1766 | − | 19.3268i | −0.411643 | − | 0.653365i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5495 | − | 20.0042i | 0.389997 | − | 0.675495i | −0.602451 | − | 0.798156i | \(-0.705809\pi\) |
0.992449 | + | 0.122660i | \(0.0391425\pi\) | |||||||
\(878\) | −16.7841 | − | 29.0710i | −0.566437 | − | 0.981097i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.821673 | − | 0.474393i | −0.0276986 | − | 0.0159918i | ||||
\(881\) | 10.9038 | 0.367360 | 0.183680 | − | 0.982986i | \(-0.441199\pi\) | ||||
0.183680 | + | 0.982986i | \(0.441199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5478 | 1.19628 | 0.598140 | − | 0.801392i | \(-0.295907\pi\) | ||||
0.598140 | + | 0.801392i | \(0.295907\pi\) | |||||||
\(884\) | −28.0045 | − | 16.1684i | −0.941893 | − | 0.543802i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.52756 | − | 2.64582i | −0.0513195 | − | 0.0888880i | ||||
\(887\) | 5.61786 | − | 9.73042i | 0.188629 | − | 0.326716i | −0.756164 | − | 0.654382i | \(-0.772929\pi\) |
0.944793 | + | 0.327666i | \(0.106262\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.2802 | − | 17.9040i | −0.378325 | − | 0.600482i | ||||
\(890\) | 0.837739i | 0.0280811i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.8803 | − | 12.0553i | 0.699125 | − | 0.403640i | ||||
\(893\) | 0.971211 | − | 0.560729i | 0.0325003 | − | 0.0187641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.32593i | − | 0.111173i | ||||||
\(896\) | 0.102135 | + | 2.64378i | 0.00341210 | + | 0.0883225i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.177602 | − | 0.307616i | 0.00592666 | − | 0.0102653i | ||||
\(899\) | 1.50731 | + | 2.61073i | 0.0502715 | + | 0.0870728i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.8471 | − | 21.8511i | −1.26087 | − | 0.727964i | ||||
\(902\) | −8.54500 | −0.284517 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.39880 | 0.279340 | ||||||||
\(905\) | 15.1604 | + | 8.75287i | 0.503949 | + | 0.290955i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.85180 | + | 17.0638i | 0.327124 | + | 0.566595i | 0.981940 | − | 0.189193i | \(-0.0605873\pi\) |
−0.654816 | + | 0.755788i | \(0.727254\pi\) | |||||||
\(908\) | −4.95825 | + | 8.58794i | −0.164545 | + | 0.285001i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.22773 | − | 15.6134i | 0.272746 | − | 0.517580i | ||||
\(911\) | 35.0219i | 1.16033i | 0.814500 | + | 0.580164i | \(0.197011\pi\) | ||||
−0.814500 | + | 0.580164i | \(0.802989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3945 | + | 6.00129i | −0.344009 | + | 0.198614i | ||||
\(914\) | 8.31946 | − | 4.80324i | 0.275183 | − | 0.158877i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 22.7130i | − | 0.750458i | ||||||
\(917\) | −23.1200 | + | 0.893178i | −0.763490 | + | 0.0294953i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8411 | − | 32.6337i | 0.621510 | − | 1.07649i | −0.367694 | − | 0.929947i | \(-0.619853\pi\) |
0.989205 | − | 0.146541i | \(-0.0468139\pi\) | |||||||
\(920\) | −3.93204 | − | 6.81050i | −0.129636 | − | 0.224535i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.4389 | − | 19.3060i | −1.10125 | − | 0.635808i | ||||
\(923\) | −89.6850 | −2.95202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.5176 | 1.23357 | ||||||||
\(926\) | −3.13397 | − | 1.80940i | −0.102989 | − | 0.0594605i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.465310 | − | 0.805941i | −0.0152746 | − | 0.0264563i | ||||
\(929\) | −17.5570 | + | 30.4096i | −0.576027 | + | 0.997707i | 0.419903 | + | 0.907569i | \(0.362064\pi\) |
−0.995929 | + | 0.0901382i | \(0.971269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.8866 | + | 8.83184i | −0.422342 | + | 0.289452i | ||||
\(932\) | − | 12.3130i | − | 0.403327i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.06337 | + | 4.07804i | −0.231120 | + | 0.133437i | ||||
\(935\) | 3.77922 | − | 2.18193i | 0.123594 | − | 0.0713568i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.17435i | − | 0.299713i | −0.988708 | − | 0.149857i | \(-0.952119\pi\) | ||
0.988708 | − | 0.149857i | \(-0.0478812\pi\) | |||||||
\(938\) | −13.1917 | + | 8.31123i | −0.430724 | + | 0.271371i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.238377 | + | 0.412882i | −0.00777501 | + | 0.0134667i | ||||
\(941\) | −13.1537 | − | 22.7828i | −0.428798 | − | 0.742699i | 0.567969 | − | 0.823050i | \(-0.307729\pi\) |
−0.996767 | + | 0.0803507i | \(0.974396\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.3370 | − | 35.4129i | −1.99741 | − | 1.15320i | ||||
\(944\) | −7.89170 | −0.256853 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.7269 | −0.413788 | ||||||||
\(947\) | −29.2145 | − | 16.8670i | −0.949343 | − | 0.548103i | −0.0564662 | − | 0.998405i | \(-0.517983\pi\) |
−0.892877 | + | 0.450301i | \(0.851317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7059 | − | 34.1317i | −0.639682 | − | 1.10796i | ||||
\(950\) | 4.57498 | − | 7.92410i | 0.148432 | − | 0.257092i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.7656 | − | 5.67310i | −0.348916 | − | 0.183866i | ||||
\(953\) | − | 26.6703i | − | 0.863937i | −0.901889 | − | 0.431968i | \(-0.857819\pi\) | ||
0.901889 | − | 0.431968i | \(-0.142181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.2873 | + | 12.2902i | −0.688841 | + | 0.397703i | ||||
\(956\) | −0.308221 | + | 0.177951i | −0.00996858 | + | 0.00575536i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.9269i | 0.837661i | ||||||||
\(959\) | 0.947755 | + | 0.499433i | 0.0306046 | + | 0.0161275i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2533 | + | 17.7592i | −0.330751 | + | 0.572878i | ||||
\(962\) | 32.1689 | + | 55.7181i | 1.03717 | + | 1.79642i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.3413 | − | 11.1667i | −0.622942 | − | 0.359655i | ||||
\(965\) | 0.578217 | 0.0186135 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.1827 | 1.16356 | 0.581779 | − | 0.813347i | \(-0.302357\pi\) | ||||
0.581779 | + | 0.813347i | \(0.302357\pi\) | |||||||
\(968\) | −0.866025 | − | 0.500000i | −0.0278351 | − | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.99227 | − | 10.3789i | −0.192400 | − | 0.333247i | ||||
\(971\) | −14.3469 | + | 24.8495i | −0.460413 | + | 0.797459i | −0.998981 | − | 0.0451229i | \(-0.985632\pi\) |
0.538568 | + | 0.842582i | \(0.318965\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.3971 | − | 24.8215i | 1.26301 | − | 0.795742i | ||||
\(974\) | 3.86205i | 0.123748i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.02250 | − | 1.16769i | 0.0647388 | − | 0.0373770i | ||||
\(977\) | 40.1239 | − | 23.1656i | 1.28368 | − | 0.741132i | 0.306160 | − | 0.951980i | \(-0.400956\pi\) |
0.977519 | + | 0.210848i | \(0.0676226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.882960i | 0.0282195i | ||||||||
\(980\) | 2.86711 | − | 5.99076i | 0.0915865 | − | 0.191368i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.77294 | − | 11.7311i | 0.216133 | − | 0.374354i | ||||
\(983\) | −25.0199 | − | 43.3357i | −0.798009 | − | 1.38219i | −0.920911 | − | 0.389774i | \(-0.872553\pi\) |
0.122901 | − | 0.992419i | \(-0.460780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.80486 | − | 1.04203i | −0.0575075 | − | 0.0332020i | ||||
\(986\) | 4.28031 | 0.136313 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.6910 | 0.499197 | ||||||||
\(989\) | −91.3553 | − | 52.7440i | −2.90493 | − | 1.67716i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.38422 | + | 14.5219i | 0.266334 | + | 0.461303i | 0.967912 | − | 0.251289i | \(-0.0808544\pi\) |
−0.701579 | + | 0.712592i | \(0.747521\pi\) | |||||||
\(992\) | −1.61968 | + | 2.80537i | −0.0514248 | + | 0.0890704i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.7249 | + | 1.30287i | −1.06969 | + | 0.0413245i | ||||
\(995\) | 25.1832i | 0.798360i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.51546 | − | 2.60700i | 0.143006 | − | 0.0825645i | −0.426790 | − | 0.904351i | \(-0.640356\pi\) |
0.569796 | + | 0.821786i | \(0.307022\pi\) | |||||||
\(998\) | 8.70526 | − | 5.02599i | 0.275560 | − | 0.159095i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.r.d.89.5 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1386.2.r.d.89.8 | yes | 24 | |
7.3 | odd | 6 | inner | 1386.2.r.d.1277.8 | yes | 24 | |
21.17 | even | 6 | inner | 1386.2.r.d.1277.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.d.89.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1386.2.r.d.89.8 | yes | 24 | 3.2 | odd | 2 | inner | |
1386.2.r.d.1277.5 | yes | 24 | 21.17 | even | 6 | inner | |
1386.2.r.d.1277.8 | yes | 24 | 7.3 | odd | 6 | inner |