Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(107,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.u (of order \(30\), degree \(8\), not 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 107.4 | ||
Character | \(\chi\) | \(=\) | 891.107 |
Dual form | 891.2.u.c.458.4 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.254665 | + | 2.42297i | 0.180075 | + | 1.71330i | 0.595235 | + | 0.803552i | \(0.297059\pi\) |
−0.415160 | + | 0.909748i | \(0.636274\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.84965 | + | 0.818267i | −1.92482 | + | 0.409134i | ||||
\(5\) | 3.77497 | + | 0.396765i | 1.68822 | + | 0.177439i | 0.899381 | − | 0.437166i | \(-0.144018\pi\) |
0.788835 | + | 0.614605i | \(0.210685\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.273322 | − | 0.246100i | 0.103306 | − | 0.0930172i | −0.615859 | − | 0.787856i | \(-0.711191\pi\) |
0.719165 | + | 0.694839i | \(0.244524\pi\) | |||||||
\(8\) | −1.45728 | − | 4.48505i | −0.515226 | − | 1.58570i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.24768i | 2.92437i | ||||||||
\(11\) | 2.75393 | − | 1.84821i | 0.830340 | − | 0.557257i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.385693 | + | 0.866281i | −0.106972 | + | 0.240263i | −0.959098 | − | 0.283073i | \(-0.908646\pi\) |
0.852126 | + | 0.523336i | \(0.175313\pi\) | |||||||
\(14\) | 0.665900 | + | 0.599579i | 0.177969 | + | 0.160244i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.30524 | − | 1.47159i | 0.826310 | − | 0.367897i | ||||
\(17\) | 2.77873 | + | 2.01886i | 0.673940 | + | 0.489646i | 0.871342 | − | 0.490676i | \(-0.163250\pi\) |
−0.197402 | + | 0.980323i | \(0.563250\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.05368 | − | 1.31712i | 0.929979 | − | 0.302168i | 0.195425 | − | 0.980719i | \(-0.437391\pi\) |
0.734554 | + | 0.678550i | \(0.237391\pi\) | |||||||
\(20\) | −14.8569 | + | 1.56153i | −3.32211 | + | 0.349168i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.17950 | + | 6.20201i | 1.10427 | + | 1.32227i | ||||
\(23\) | −4.30242 | + | 2.48400i | −0.897116 | + | 0.517950i | −0.876263 | − | 0.481832i | \(-0.839971\pi\) |
−0.0208527 | + | 0.999783i | \(0.506638\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.20220 | + | 1.95599i | 1.84044 | + | 0.391198i | ||||
\(26\) | −2.19720 | − | 0.713913i | −0.430906 | − | 0.140010i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.850818 | + | 1.17105i | −0.160789 | + | 0.221308i | ||||
\(29\) | −1.66173 | − | 1.84554i | −0.308576 | − | 0.342708i | 0.568832 | − | 0.822454i | \(-0.307396\pi\) |
−0.877408 | + | 0.479746i | \(0.840729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.21012 | + | 1.42924i | 0.576554 | + | 0.256698i | 0.674232 | − | 0.738520i | \(-0.264475\pi\) |
−0.0976778 | + | 0.995218i | \(0.531141\pi\) | |||||||
\(32\) | −0.308515 | − | 0.534364i | −0.0545383 | − | 0.0944632i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.18401 | + | 7.24691i | −0.717551 | + | 1.24284i | ||||
\(35\) | 1.12943 | − | 0.820576i | 0.190908 | − | 0.138703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21947 | + | 6.83082i | −0.364878 | + | 1.12298i | 0.585179 | + | 0.810904i | \(0.301024\pi\) |
−0.950057 | + | 0.312075i | \(0.898976\pi\) | |||||||
\(38\) | 4.22368 | + | 9.48654i | 0.685171 | + | 1.53892i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.72167 | − | 17.5091i | −0.588448 | − | 2.76843i | ||||
\(41\) | −1.81944 | + | 2.02069i | −0.284148 | + | 0.315578i | −0.868274 | − | 0.496084i | \(-0.834771\pi\) |
0.584126 | + | 0.811663i | \(0.301437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63461 | − | 0.943743i | −0.249276 | − | 0.143919i | 0.370157 | − | 0.928969i | \(-0.379304\pi\) |
−0.619433 | + | 0.785050i | \(0.712637\pi\) | |||||||
\(44\) | −9.08931 | + | 9.36841i | −1.37026 | + | 1.41234i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.11434 | − | 9.79205i | −1.04895 | − | 1.44376i | ||||
\(47\) | −0.00428458 | + | 0.0201574i | −0.000624971 | + | 0.00294026i | −0.978459 | − | 0.206441i | \(-0.933812\pi\) |
0.977834 | + | 0.209382i | \(0.0671451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.717560 | + | 6.82712i | −0.102509 | + | 0.975303i | ||||
\(50\) | −2.39583 | + | 22.7948i | −0.338822 | + | 3.22367i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.775933 | − | 3.65048i | 0.107602 | − | 0.506230i | ||||
\(53\) | −3.25941 | − | 4.48619i | −0.447714 | − | 0.616226i | 0.524190 | − | 0.851601i | \(-0.324368\pi\) |
−0.971905 | + | 0.235375i | \(0.924368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.1293 | − | 5.88428i | 1.50067 | − | 0.793436i | ||||
\(56\) | −1.50208 | − | 0.867226i | −0.200724 | − | 0.115888i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.04851 | − | 4.49632i | 0.531595 | − | 0.590396i | ||||
\(59\) | −1.37725 | − | 6.47943i | −0.179302 | − | 0.843550i | −0.972192 | − | 0.234185i | \(-0.924758\pi\) |
0.792890 | − | 0.609365i | \(-0.208576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.96670 | − | 8.90935i | −0.507884 | − | 1.14073i | −0.967561 | − | 0.252639i | \(-0.918701\pi\) |
0.459677 | − | 0.888086i | \(-0.347965\pi\) | |||||||
\(62\) | −2.64550 | + | 8.14200i | −0.335978 | + | 1.03404i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.07028 | − | 5.13686i | 0.883786 | − | 0.642108i | ||||
\(65\) | −1.79969 | + | 3.11715i | −0.223224 | + | 0.386635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.23176 | − | 3.86552i | −0.272652 | − | 0.472248i | 0.696888 | − | 0.717180i | \(-0.254568\pi\) |
−0.969540 | + | 0.244932i | \(0.921234\pi\) | |||||||
\(68\) | −12.3491 | − | 5.49817i | −1.49755 | − | 0.666751i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.27586 | + | 2.52760i | 0.272017 | + | 0.302106i | ||||
\(71\) | 6.06985 | − | 8.35443i | 0.720359 | − | 0.991489i | −0.279153 | − | 0.960247i | \(-0.590054\pi\) |
0.999512 | − | 0.0312420i | \(-0.00994626\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.18072 | − | 1.35840i | −0.489317 | − | 0.158989i | 0.0539588 | − | 0.998543i | \(-0.482816\pi\) |
−0.543275 | + | 0.839555i | \(0.682816\pi\) | |||||||
\(74\) | −17.1161 | − | 3.63814i | −1.98971 | − | 0.422925i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.5275 | + | 8.38745i | −1.66642 | + | 0.962106i | ||||
\(77\) | 0.297863 | − | 1.18290i | 0.0339447 | − | 0.134804i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8772 | + | 1.14324i | −1.22378 | + | 0.128624i | −0.694292 | − | 0.719693i | \(-0.744283\pi\) |
−0.529488 | + | 0.848318i | \(0.677616\pi\) | |||||||
\(80\) | 13.0610 | − | 4.24379i | 1.46027 | − | 0.474470i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.35942 | − | 3.89384i | −0.591848 | − | 0.430003i | ||||
\(83\) | −8.38931 | + | 3.73516i | −0.920847 | + | 0.409987i | −0.811724 | − | 0.584041i | \(-0.801471\pi\) |
−0.109122 | + | 0.994028i | \(0.534804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.68858 | + | 8.72364i | 1.05087 | + | 0.946212i | ||||
\(86\) | 1.87039 | − | 4.20095i | 0.201689 | − | 0.453000i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.3026 | − | 9.65812i | −1.31146 | − | 1.02956i | ||||
\(89\) | 3.04837i | 0.323127i | 0.986862 | + | 0.161563i | \(0.0516536\pi\) | ||||
−0.986862 | + | 0.161563i | \(0.948346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.107774 | + | 0.331693i | 0.0112978 | + | 0.0347709i | ||||
\(92\) | 14.5302 | − | 13.0831i | 1.51488 | − | 1.36400i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0499319 | − | 0.00524806i | −0.00515008 | − | 0.000541296i | ||||
\(95\) | 15.8251 | − | 3.36373i | 1.62362 | − | 0.345111i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.57700 | + | 15.0042i | 0.160121 | + | 1.52345i | 0.719476 | + | 0.694517i | \(0.244382\pi\) |
−0.559355 | + | 0.828928i | \(0.688951\pi\) | |||||||
\(98\) | −16.7247 | −1.68945 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −37.0257 | −3.70257 | ||||||||
\(101\) | −1.82505 | − | 17.3642i | −0.181599 | − | 1.72780i | −0.583498 | − | 0.812114i | \(-0.698317\pi\) |
0.401899 | − | 0.915684i | \(-0.368350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.11204 | − | 1.93682i | 0.897836 | − | 0.190841i | 0.264196 | − | 0.964469i | \(-0.414893\pi\) |
0.633640 | + | 0.773628i | \(0.281560\pi\) | |||||||
\(104\) | 4.44738 | + | 0.467438i | 0.436101 | + | 0.0458361i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0399 | − | 9.03994i | 0.975158 | − | 0.878036i | ||||
\(107\) | −4.76675 | − | 14.6705i | −0.460819 | − | 1.41825i | −0.864166 | − | 0.503207i | \(-0.832153\pi\) |
0.403347 | − | 0.915047i | \(-0.367847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6286i | 1.01803i | 0.860757 | + | 0.509016i | \(0.169991\pi\) | ||||
−0.860757 | + | 0.509016i | \(0.830009\pi\) | |||||||
\(110\) | 17.0917 | + | 25.4674i | 1.62963 | + | 2.42822i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.541237 | − | 1.21564i | 0.0511421 | − | 0.114867i | ||||
\(113\) | 0.778087 | + | 0.700592i | 0.0731962 | + | 0.0659062i | 0.704917 | − | 0.709290i | \(-0.250984\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.2270 | + | 7.66997i | −1.60643 | + | 0.715229i | ||||
\(116\) | 7.90722 | + | 5.74493i | 0.734167 | + | 0.533404i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.3487 | − | 4.98711i | 1.41297 | − | 0.459101i | ||||
\(119\) | 1.25633 | − | 0.132046i | 0.115168 | − | 0.0121046i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16822 | − | 10.1797i | 0.378929 | − | 0.925426i | ||||
\(122\) | 20.5769 | − | 11.8801i | 1.86295 | − | 1.07557i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.5273 | − | 2.87532i | −1.21479 | − | 0.258211i | ||||
\(125\) | 15.9120 | + | 5.17013i | 1.42321 | + | 0.462430i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3127 | − | 14.1942i | 0.915101 | − | 1.25953i | −0.0502930 | − | 0.998735i | \(-0.516016\pi\) |
0.965394 | − | 0.260794i | \(-0.0839845\pi\) | |||||||
\(128\) | 13.4213 | + | 14.9058i | 1.18628 | + | 1.31750i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.01109 | − | 3.56677i | −0.702619 | − | 0.312826i | ||||
\(131\) | 6.94451 | + | 12.0282i | 0.606744 | + | 1.05091i | 0.991773 | + | 0.128008i | \(0.0408582\pi\) |
−0.385029 | + | 0.922905i | \(0.625808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.783818 | − | 1.35761i | 0.0679656 | − | 0.117720i | ||||
\(134\) | 8.79769 | − | 6.39189i | 0.760004 | − | 0.552176i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.00531 | − | 15.4048i | 0.429202 | − | 1.32095i | ||||
\(137\) | −0.422083 | − | 0.948014i | −0.0360610 | − | 0.0809943i | 0.894617 | − | 0.446834i | \(-0.147449\pi\) |
−0.930678 | + | 0.365840i | \(0.880782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.12394 | + | 19.4016i | 0.349788 | + | 1.64563i | 0.703810 | + | 0.710388i | \(0.251481\pi\) |
−0.354022 | + | 0.935237i | \(0.615186\pi\) | |||||||
\(140\) | −3.67644 | + | 4.08310i | −0.310716 | + | 0.345085i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.7883 | + | 12.5795i | 1.82844 | + | 1.05565i | ||||
\(143\) | 0.538902 | + | 3.09852i | 0.0450652 | + | 0.259111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.54073 | − | 7.62616i | −0.460133 | − | 0.633318i | ||||
\(146\) | 2.22668 | − | 10.4757i | 0.184281 | − | 0.866976i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.95473 | − | 28.1123i | 0.242877 | − | 2.31082i | ||||
\(149\) | 0.839990 | − | 7.99197i | 0.0688146 | − | 0.654727i | −0.904692 | − | 0.426067i | \(-0.859899\pi\) |
0.973506 | − | 0.228660i | \(-0.0734346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.09441 | − | 9.85341i | 0.170440 | − | 0.801859i | −0.806984 | − | 0.590573i | \(-0.798902\pi\) |
0.977424 | − | 0.211286i | \(-0.0677650\pi\) | |||||||
\(152\) | −11.8147 | − | 16.2615i | −0.958299 | − | 1.31899i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.94199 | + | 0.420471i | 0.237072 | + | 0.0338826i | ||||
\(155\) | 11.5510 | + | 6.66898i | 0.927800 | + | 0.535665i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8281 | + | 12.0258i | −0.864177 | + | 0.959765i | −0.999518 | − | 0.0310336i | \(-0.990120\pi\) |
0.135342 | + | 0.990799i | \(0.456787\pi\) | |||||||
\(158\) | −5.54007 | − | 26.0640i | −0.440745 | − | 2.07354i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.952618 | − | 2.13962i | −0.0753111 | − | 0.169151i | ||||
\(161\) | −0.564633 | + | 1.73776i | −0.0444993 | + | 0.136955i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.45923 | + | 2.51328i | −0.270948 | + | 0.196855i | −0.714959 | − | 0.699166i | \(-0.753555\pi\) |
0.444012 | + | 0.896021i | \(0.353555\pi\) | |||||||
\(164\) | 5.35072 | − | 9.26772i | 0.417821 | − | 0.723687i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1867 | − | 19.3759i | −0.868253 | − | 1.50386i | ||||
\(167\) | −16.7662 | − | 7.46478i | −1.29741 | − | 0.577642i | −0.362316 | − | 0.932055i | \(-0.618014\pi\) |
−0.935089 | + | 0.354413i | \(0.884681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.09701 | + | 8.99265i | 0.622847 | + | 0.691742i | ||||
\(170\) | −18.6698 | + | 25.6968i | −1.43191 | + | 1.97085i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.06490 | + | 2.29553i | 0.538694 | + | 0.175032i | ||||
\(173\) | −6.04729 | − | 1.28539i | −0.459767 | − | 0.0977264i | −0.0277951 | − | 0.999614i | \(-0.508849\pi\) |
−0.431972 | + | 0.901887i | \(0.642182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.99654 | − | 1.73005i | 0.226517 | − | 0.130780i | ||||
\(176\) | 6.38258 | − | 10.1614i | 0.481105 | − | 0.765946i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.38612 | + | 0.776312i | −0.553613 | + | 0.0581871i | ||||
\(179\) | 8.77414 | − | 2.85089i | 0.655810 | − | 0.213086i | 0.0378357 | − | 0.999284i | \(-0.487954\pi\) |
0.617974 | + | 0.786198i | \(0.287954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.38790 | + | 2.46145i | 0.251821 | + | 0.182958i | 0.706533 | − | 0.707680i | \(-0.250258\pi\) |
−0.454713 | + | 0.890638i | \(0.650258\pi\) | |||||||
\(182\) | −0.776237 | + | 0.345603i | −0.0575386 | + | 0.0256178i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.4107 | + | 15.6767i | 1.28353 | + | 1.15570i | ||||
\(185\) | −11.0886 | + | 24.9055i | −0.815253 | + | 1.83109i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3837 | + | 0.424121i | 0.832459 | + | 0.0310148i | ||||
\(188\) | − | 0.0811047i | − | 0.00591517i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.1803 | + | 37.4872i | 0.883653 | + | 2.71960i | ||||
\(191\) | 14.9989 | − | 13.5050i | 1.08528 | − | 0.977190i | 0.0854633 | − | 0.996341i | \(-0.472763\pi\) |
0.999817 | + | 0.0191509i | \(0.00609630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.97006 | − | 0.837687i | −0.573697 | − | 0.0602980i | −0.186762 | − | 0.982405i | \(-0.559799\pi\) |
−0.386935 | + | 0.922107i | \(0.626466\pi\) | |||||||
\(194\) | −35.9531 | + | 7.64208i | −2.58129 | + | 0.548669i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.82406 | − | 26.8692i | −0.201719 | − | 1.91923i | ||||
\(197\) | 21.1710 | 1.50837 | 0.754187 | − | 0.656659i | \(-0.228031\pi\) | ||||
0.754187 | + | 0.656659i | \(0.228031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5160 | −0.745457 | −0.372729 | − | 0.927940i | \(-0.621578\pi\) | ||||
−0.372729 | + | 0.927940i | \(0.621578\pi\) | |||||||
\(200\) | −4.63749 | − | 44.1227i | −0.327920 | − | 3.11995i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 41.6081 | − | 8.84407i | 2.92754 | − | 0.622267i | ||||
\(203\) | −0.908376 | − | 0.0954742i | −0.0637555 | − | 0.00670098i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.67004 | + | 6.90614i | −0.535699 | + | 0.482346i | ||||
\(206\) | 7.01339 | + | 21.5850i | 0.488646 | + | 1.50390i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.43085i | 0.237886i | ||||||||
\(209\) | 8.72922 | − | 11.1193i | 0.603813 | − | 0.769140i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.50420 | + | 3.37850i | −0.103554 | + | 0.232585i | −0.957890 | − | 0.287135i | \(-0.907297\pi\) |
0.854336 | + | 0.519720i | \(0.173964\pi\) | |||||||
\(212\) | 16.2185 | + | 14.6032i | 1.11389 | + | 1.00295i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.3324 | − | 15.2858i | 2.34691 | − | 1.04491i | ||||
\(215\) | −5.79615 | − | 4.21115i | −0.395294 | − | 0.287198i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22913 | − | 0.399369i | 0.0834390 | − | 0.0271110i | ||||
\(218\) | −25.7527 | + | 2.70672i | −1.74419 | + | 0.183322i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −38.0289 | + | 31.7591i | −2.56391 | + | 2.14120i | ||||
\(221\) | −2.82064 | + | 1.62850i | −0.189737 | + | 0.109545i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5060 | + | 3.72102i | 1.17229 | + | 0.249178i | 0.752593 | − | 0.658486i | \(-0.228803\pi\) |
0.419697 | + | 0.907664i | \(0.362136\pi\) | |||||||
\(224\) | −0.215832 | − | 0.0701279i | −0.0144209 | − | 0.00468562i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.49936 | + | 2.06370i | −0.0997363 | + | 0.137275i | ||||
\(227\) | −11.6284 | − | 12.9147i | −0.771805 | − | 0.857176i | 0.221203 | − | 0.975228i | \(-0.429002\pi\) |
−0.993007 | + | 0.118052i | \(0.962335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.90692 | + | 1.73947i | 0.258176 | + | 0.114948i | 0.531744 | − | 0.846905i | \(-0.321537\pi\) |
−0.273567 | + | 0.961853i | \(0.588204\pi\) | |||||||
\(230\) | −22.9713 | − | 39.7874i | −1.51468 | − | 2.62350i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.85572 | + | 10.1424i | −0.384447 | + | 0.665882i | ||||
\(233\) | −18.9171 | + | 13.7441i | −1.23930 | + | 0.900404i | −0.997552 | − | 0.0699355i | \(-0.977721\pi\) |
−0.241748 | + | 0.970339i | \(0.577721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0241719 | + | 0.0743935i | −0.00157680 | + | 0.00485289i | ||||
\(236\) | 10.6038 | + | 23.8166i | 0.690250 | + | 1.55033i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.639886 | + | 3.01043i | 0.0414777 | + | 0.195137i | ||||
\(239\) | 13.3797 | − | 14.8597i | 0.865464 | − | 0.961195i | −0.134093 | − | 0.990969i | \(-0.542812\pi\) |
0.999557 | + | 0.0297740i | \(0.00947875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.01411 | − | 1.16285i | −0.129740 | − | 0.0749057i | 0.433725 | − | 0.901045i | \(-0.357199\pi\) |
−0.563466 | + | 0.826140i | \(0.690532\pi\) | |||||||
\(242\) | 25.7266 | + | 7.50707i | 1.65377 | + | 0.482573i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.5606 | + | 31.0520i | 1.44430 | + | 1.98790i | ||||
\(245\) | −5.41753 | + | 25.4875i | −0.346113 | + | 1.62833i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.422481 | + | 4.01963i | −0.0268818 | + | 0.255763i | ||||
\(248\) | 1.73215 | − | 16.4803i | 0.109992 | − | 1.04650i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.47485 | + | 39.8710i | −0.535997 | + | 2.52167i | ||||
\(251\) | 1.88681 | + | 2.59698i | 0.119095 | + | 0.163920i | 0.864402 | − | 0.502801i | \(-0.167697\pi\) |
−0.745307 | + | 0.666721i | \(0.767697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.25758 | + | 14.7925i | −0.456280 | + | 0.929999i | ||||
\(254\) | 37.0184 | + | 21.3726i | 2.32274 | + | 1.34103i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.0030 | + | 23.3262i | −1.31269 | + | 1.45789i | ||||
\(257\) | 3.75130 | + | 17.6485i | 0.234000 | + | 1.10088i | 0.925571 | + | 0.378574i | \(0.123586\pi\) |
−0.691571 | + | 0.722309i | \(0.743081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.07444 | + | 2.41323i | 0.0667623 | + | 0.149951i | ||||
\(260\) | 4.37750 | − | 13.4726i | 0.271481 | − | 0.835533i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −27.3756 | + | 19.8895i | −1.69127 | + | 1.22878i | ||||
\(263\) | −1.02983 | + | 1.78372i | −0.0635019 | + | 0.109989i | −0.896028 | − | 0.443997i | \(-0.853560\pi\) |
0.832527 | + | 0.553985i | \(0.186894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5242 | − | 18.2284i | −0.646496 | − | 1.11976i | ||||
\(266\) | 3.48907 | + | 1.55343i | 0.213928 | + | 0.0952471i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.7545 | + | 13.0547i | 0.718020 | + | 0.797442i | ||||
\(269\) | 1.69280 | − | 2.32994i | 0.103212 | − | 0.142059i | −0.754287 | − | 0.656545i | \(-0.772017\pi\) |
0.857499 | + | 0.514486i | \(0.172017\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.67272 | + | 3.14286i | 0.587576 | + | 0.190915i | 0.587692 | − | 0.809085i | \(-0.300037\pi\) |
−0.000115761 | 1.00000i | \(0.500037\pi\) | ||||||||
\(272\) | 12.1553 | + | 2.58369i | 0.737023 | + | 0.156659i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.18952 | − | 1.26412i | 0.132274 | − | 0.0763683i | ||||
\(275\) | 28.9573 | − | 11.6210i | 1.74619 | − | 0.700772i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.27067 | + | 0.764179i | −0.436852 | + | 0.0459150i | −0.320402 | − | 0.947282i | \(-0.603818\pi\) |
−0.116450 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(278\) | −45.9594 | + | 14.9331i | −2.75646 | + | 0.895629i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.32621 | − | 3.86972i | −0.318302 | − | 0.231260i | ||||
\(281\) | 2.10612 | − | 0.937703i | 0.125640 | − | 0.0559387i | −0.342954 | − | 0.939352i | \(-0.611427\pi\) |
0.468594 | + | 0.883414i | \(0.344761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1571 | − | 16.3487i | −1.07933 | − | 0.971832i | −0.0796411 | − | 0.996824i | \(-0.525377\pi\) |
−0.999688 | + | 0.0249916i | \(0.992044\pi\) | |||||||
\(284\) | −16.5306 | + | 37.1284i | −0.980911 | + | 2.20316i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.37038 | + | 2.09483i | −0.435820 | + | 0.123870i | ||||
\(287\) | 1.00006i | 0.0590318i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.60777 | − | 4.94822i | −0.0945749 | − | 0.291072i | ||||
\(290\) | 17.0670 | − | 15.3672i | 1.00221 | − | 0.902390i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.2058 | + | 1.80841i | 1.00690 | + | 0.105829i | ||||
\(293\) | −10.4284 | + | 2.21663i | −0.609236 | + | 0.129497i | −0.502190 | − | 0.864757i | \(-0.667472\pi\) |
−0.107045 | + | 0.994254i | \(0.534139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.62824 | − | 25.0061i | −0.153022 | − | 1.45591i | ||||
\(296\) | 33.8709 | 1.96871 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.5782 | 1.13414 | ||||||||
\(299\) | −0.492431 | − | 4.68517i | −0.0284780 | − | 0.270950i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.679031 | + | 0.144332i | −0.0391387 | + | 0.00831919i | ||||
\(302\) | 24.4079 | + | 2.56537i | 1.40452 | + | 0.147621i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.4601 | − | 10.3187i | 0.657284 | − | 0.591821i | ||||
\(305\) | −11.4392 | − | 35.2063i | −0.655009 | − | 2.01591i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.56848i | 0.260737i | 0.991466 | + | 0.130369i | \(0.0416160\pi\) | ||||
−0.991466 | + | 0.130369i | \(0.958384\pi\) | |||||||
\(308\) | −0.178739 | + | 4.79748i | −0.0101846 | + | 0.273362i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.2171 | + | 29.6861i | −0.750682 | + | 1.68606i | ||||
\(311\) | 6.97234 | + | 6.27793i | 0.395365 | + | 0.355989i | 0.842705 | − | 0.538376i | \(-0.180962\pi\) |
−0.447340 | + | 0.894364i | \(0.647628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.58235 | + | 2.04019i | −0.259010 | + | 0.115319i | −0.532134 | − | 0.846660i | \(-0.678610\pi\) |
0.273124 | + | 0.961979i | \(0.411943\pi\) | |||||||
\(314\) | −31.8958 | − | 23.1736i | −1.79998 | − | 1.30776i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.9379 | − | 13.3015i | 2.30294 | − | 0.748269i | ||||
\(317\) | −11.6122 | + | 1.22050i | −0.652208 | + | 0.0685498i | −0.424853 | − | 0.905262i | \(-0.639674\pi\) |
−0.227355 | + | 0.973812i | \(0.573008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.98724 | − | 2.01125i | −0.447199 | − | 0.112608i | ||||
\(320\) | 28.7282 | − | 16.5862i | 1.60596 | − | 0.927199i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.35434 | − | 0.925543i | −0.242658 | − | 0.0515785i | ||||
\(323\) | 13.9232 | + | 4.52391i | 0.774706 | + | 0.251717i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.24366 | + | 7.21728i | −0.290866 | + | 0.400343i | ||||
\(326\) | −6.97054 | − | 7.74157i | −0.386062 | − | 0.428766i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.7143 | + | 5.21554i | 0.646814 | + | 0.287980i | ||||
\(329\) | 0.00378967 | + | 0.00656390i | 0.000208931 | + | 0.000361880i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5258 | − | 25.1595i | 0.798411 | − | 1.38289i | −0.122239 | − | 0.992501i | \(-0.539007\pi\) |
0.920650 | − | 0.390388i | \(-0.127659\pi\) | |||||||
\(332\) | 29.2395 | − | 21.2438i | 1.60473 | − | 1.16590i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.8172 | − | 42.5250i | 0.756044 | − | 2.32686i | ||||
\(335\) | −6.89110 | − | 15.4777i | −0.376501 | − | 0.845635i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00455 | − | 28.2492i | −0.327089 | − | 1.53883i | −0.767508 | − | 0.641040i | \(-0.778503\pi\) |
0.440419 | − | 0.897792i | \(-0.354830\pi\) | |||||||
\(338\) | −19.7269 | + | 21.9089i | −1.07300 | + | 1.19169i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −44.4359 | − | 25.6551i | −2.40987 | − | 1.39134i | ||||
\(341\) | 11.4820 | − | 1.99697i | 0.621783 | − | 0.108142i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.99731 | + | 4.12544i | 0.161840 | + | 0.222753i | ||||
\(344\) | −1.85065 | + | 8.70660i | −0.0997801 | + | 0.469429i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.57444 | − | 14.9798i | 0.0846422 | − | 0.805316i | ||||
\(347\) | 2.31457 | − | 22.0217i | 0.124253 | − | 1.18219i | −0.737675 | − | 0.675156i | \(-0.764076\pi\) |
0.861928 | − | 0.507031i | \(-0.169257\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25641 | − | 15.3202i | 0.174312 | − | 0.820072i | −0.800900 | − | 0.598798i | \(-0.795645\pi\) |
0.975212 | − | 0.221274i | \(-0.0710215\pi\) | |||||||
\(350\) | 4.95498 | + | 6.81994i | 0.264855 | + | 0.364541i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.83725 | − | 0.901398i | −0.0979257 | − | 0.0480447i | ||||
\(353\) | −9.66798 | − | 5.58181i | −0.514575 | − | 0.297090i | 0.220137 | − | 0.975469i | \(-0.429349\pi\) |
−0.734712 | + | 0.678379i | \(0.762683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.2282 | − | 29.1294i | 1.39205 | − | 1.54603i | ||||
\(356\) | −2.49438 | − | 11.7351i | −0.132202 | − | 0.621961i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.14209 | + | 20.5335i | 0.483175 | + | 1.08523i | ||||
\(359\) | 5.11867 | − | 15.7536i | 0.270153 | − | 0.831445i | −0.720308 | − | 0.693654i | \(-0.756000\pi\) |
0.990461 | − | 0.137791i | \(-0.0440002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.673787 | + | 0.489535i | −0.0354625 | + | 0.0257650i | ||||
\(362\) | −5.10125 | + | 8.83563i | −0.268116 | + | 0.464390i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.686304 | − | 1.18871i | −0.0359721 | − | 0.0623055i | ||||
\(365\) | −15.2431 | − | 6.78667i | −0.797861 | − | 0.355231i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.56435 | + | 7.29045i | 0.342656 | + | 0.380559i | 0.889700 | − | 0.456546i | \(-0.150913\pi\) |
−0.547044 | + | 0.837104i | \(0.684247\pi\) | |||||||
\(368\) | −10.5651 | + | 14.5416i | −0.550743 | + | 0.758033i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −63.1692 | − | 20.5249i | −3.28401 | − | 1.06704i | ||||
\(371\) | −1.99492 | − | 0.424034i | −0.103571 | − | 0.0220148i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9422 | + | 6.31750i | −0.566567 | + | 0.327108i | −0.755777 | − | 0.654829i | \(-0.772741\pi\) |
0.189210 | + | 0.981937i | \(0.439407\pi\) | |||||||
\(374\) | 1.87139 | + | 27.6904i | 0.0967674 | + | 1.43184i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0966507 | − | 0.0101584i | 0.00498438 | − | 0.000523879i | ||||
\(377\) | 2.23967 | − | 0.727714i | 0.115349 | − | 0.0374792i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3981 | − | 20.6325i | −1.45871 | − | 1.05982i | −0.983695 | − | 0.179843i | \(-0.942441\pi\) |
−0.475019 | − | 0.879975i | \(-0.657559\pi\) | |||||||
\(380\) | −58.1686 | + | 25.8983i | −2.98399 | + | 1.32856i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 36.5420 | + | 32.9026i | 1.86965 | + | 1.68344i | ||||
\(383\) | 9.18677 | − | 20.6338i | 0.469422 | − | 1.05434i | −0.511384 | − | 0.859352i | \(-0.670867\pi\) |
0.980806 | − | 0.194987i | \(-0.0624664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.59376 | − | 4.34723i | 0.0812254 | − | 0.221555i | ||||
\(386\) | − | 19.5246i | − | 0.993774i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.3484 | − | 56.4704i | −0.931497 | − | 2.86685i | ||||
\(389\) | −5.46868 | + | 4.92402i | −0.277273 | + | 0.249658i | −0.796020 | − | 0.605270i | \(-0.793065\pi\) |
0.518747 | + | 0.854928i | \(0.326399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9701 | − | 1.78363i | −0.858215 | − | 0.0902020i | ||||
\(392\) | 31.6657 | − | 6.73074i | 1.59936 | − | 0.339954i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.39152 | + | 51.2969i | 0.271621 | + | 2.58430i | ||||
\(395\) | −41.5146 | −2.08883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7327 | 0.839790 | 0.419895 | − | 0.907573i | \(-0.362067\pi\) | ||||
0.419895 | + | 0.907573i | \(0.362067\pi\) | |||||||
\(398\) | −2.67804 | − | 25.4799i | −0.134238 | − | 1.27719i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 33.2939 | − | 7.07683i | 1.66469 | − | 0.353842i | ||||
\(401\) | 5.04563 | + | 0.530318i | 0.251967 | + | 0.0264828i | 0.229670 | − | 0.973269i | \(-0.426235\pi\) |
0.0222971 | + | 0.999751i | \(0.492902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.47624 | + | 2.22962i | −0.123350 | + | 0.111065i | ||||
\(404\) | 21.2343 | + | 65.3525i | 1.05645 | + | 3.25141i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 2.22528i | − | 0.110439i | ||||||
\(407\) | 6.51256 | + | 22.9136i | 0.322815 | + | 1.13579i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1570 | − | 29.5511i | 0.650571 | − | 1.46121i | −0.223152 | − | 0.974784i | \(-0.571635\pi\) |
0.873723 | − | 0.486423i | \(-0.161699\pi\) | |||||||
\(410\) | −18.6867 | − | 16.8256i | −0.922869 | − | 0.830955i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −33.4933 | + | 14.9122i | −1.65010 | + | 0.734670i | ||||
\(413\) | −1.97102 | − | 1.43203i | −0.0969877 | − | 0.0704657i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.1513 | + | 10.7715i | −1.62734 | + | 0.528753i | ||||
\(416\) | 0.581902 | − | 0.0611604i | 0.0285301 | − | 0.00299864i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.1648 | + | 18.3190i | 1.42650 | + | 0.896010i | ||||
\(419\) | −24.1686 | + | 13.9538i | −1.18071 | + | 0.681686i | −0.956180 | − | 0.292781i | \(-0.905419\pi\) |
−0.224534 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1446 | − | 5.55720i | −1.27421 | − | 0.270841i | −0.479343 | − | 0.877628i | \(-0.659125\pi\) |
−0.794865 | + | 0.606786i | \(0.792458\pi\) | |||||||
\(422\) | −8.56907 | − | 2.78426i | −0.417136 | − | 0.135536i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.3709 | + | 21.1562i | −0.746478 | + | 1.02744i | ||||
\(425\) | 21.6215 | + | 24.0131i | 1.04880 | + | 1.16481i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27678 | − | 1.45892i | −0.158575 | − | 0.0706020i | ||||
\(428\) | 30.3547 | + | 52.5759i | 1.46725 | + | 2.54135i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.72743 | − | 15.1164i | 0.420874 | − | 0.728975i | ||||
\(431\) | −0.579760 | + | 0.421220i | −0.0279260 | + | 0.0202895i | −0.601661 | − | 0.798752i | \(-0.705494\pi\) |
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.53281 | − | 10.8729i | 0.169776 | − | 0.522517i | −0.829580 | − | 0.558387i | \(-0.811420\pi\) |
0.999356 | + | 0.0358703i | \(0.0114203\pi\) | |||||||
\(434\) | 1.28068 | + | 2.87645i | 0.0614745 | + | 0.138074i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.69701 | − | 40.9162i | −0.416511 | − | 1.95953i | ||||
\(437\) | −14.1689 | + | 15.7362i | −0.677791 | + | 0.752763i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.42639 | − | 4.28763i | −0.354442 | − | 0.204637i | 0.312198 | − | 0.950017i | \(-0.398935\pi\) |
−0.666640 | + | 0.745380i | \(0.732268\pi\) | |||||||
\(440\) | −42.6097 | − | 41.3403i | −2.03134 | − | 1.97082i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.66412 | − | 6.41961i | −0.221850 | − | 0.305350i | ||||
\(443\) | −2.90596 | + | 13.6715i | −0.138066 | + | 0.649551i | 0.853622 | + | 0.520892i | \(0.174401\pi\) |
−0.991689 | + | 0.128659i | \(0.958933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.20949 | + | 11.5075i | −0.0573351 | + | 0.545507i | ||||
\(446\) | −4.55776 | + | 43.3642i | −0.215816 | + | 2.05336i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.668282 | − | 3.14402i | 0.0315734 | − | 0.148541i | ||||
\(449\) | 12.7008 | + | 17.4811i | 0.599388 | + | 0.824986i | 0.995652 | − | 0.0931501i | \(-0.0296936\pi\) |
−0.396264 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.27593 | + | 8.92753i | −0.0600811 | + | 0.420381i | ||||
\(452\) | −3.56863 | − | 2.06035i | −0.167854 | − | 0.0969107i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.3305 | − | 31.4642i | 1.32962 | − | 1.47669i | ||||
\(455\) | 0.275238 | + | 1.29489i | 0.0129033 | + | 0.0607054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.98808 | + | 8.95737i | 0.186554 | + | 0.419008i | 0.982475 | − | 0.186392i | \(-0.0596796\pi\) |
−0.795921 | + | 0.605401i | \(0.793013\pi\) | |||||||
\(458\) | −3.21974 | + | 9.90934i | −0.150449 | + | 0.463033i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 60.0419 | − | 43.6230i | 2.79947 | − | 2.03393i | ||||
\(461\) | 6.17927 | − | 10.7028i | 0.287797 | − | 0.498479i | −0.685486 | − | 0.728085i | \(-0.740410\pi\) |
0.973284 | + | 0.229606i | \(0.0737437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9359 | + | 29.3338i | 0.787076 | + | 1.36326i | 0.927751 | + | 0.373200i | \(0.121739\pi\) |
−0.140675 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(464\) | −8.20829 | − | 3.65457i | −0.381060 | − | 0.169659i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −38.1190 | − | 42.3354i | −1.76583 | − | 1.96115i | ||||
\(467\) | 9.24994 | − | 12.7315i | 0.428036 | − | 0.589142i | −0.539465 | − | 0.842008i | \(-0.681373\pi\) |
0.967501 | + | 0.252867i | \(0.0813734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56129 | − | 0.507295i | −0.0720939 | − | 0.0234247i | ||||
\(470\) | −0.186409 | − | 0.0396225i | −0.00859841 | − | 0.00182765i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.0535 | + | 15.6194i | −1.24524 | + | 0.718939i | ||||
\(473\) | −6.24583 | + | 0.422111i | −0.287184 | + | 0.0194087i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.8791 | − | 4.19146i | 1.82978 | − | 0.192317i | ||||
\(476\) | −4.72838 | + | 1.53634i | −0.216725 | + | 0.0704182i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 39.4120 | + | 28.6345i | 1.80266 | + | 1.30971i | ||||
\(479\) | −11.3911 | + | 5.07162i | −0.520471 | + | 0.231728i | −0.650120 | − | 0.759831i | \(-0.725281\pi\) |
0.129650 | + | 0.991560i | \(0.458615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.06137 | − | 4.55728i | −0.230779 | − | 0.207794i | ||||
\(482\) | 2.30463 | − | 5.17628i | 0.104973 | − | 0.235773i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.71645 | + | 42.5989i | −0.350748 | + | 1.93631i | ||||
\(485\) | 57.2660i | 2.60032i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.14955 | − | 6.61563i | −0.0974054 | − | 0.299783i | 0.890468 | − | 0.455046i | \(-0.150377\pi\) |
−0.987873 | + | 0.155263i | \(0.950377\pi\) | |||||||
\(488\) | −34.1783 | + | 30.7743i | −1.54718 | + | 1.39309i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −63.1350 | − | 6.63576i | −2.85215 | − | 0.299773i | ||||
\(491\) | −0.295322 | + | 0.0627727i | −0.0133277 | + | 0.00283289i | −0.214571 | − | 0.976708i | \(-0.568835\pi\) |
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.891605 | − | 8.48306i | −0.0401559 | − | 0.382058i | ||||
\(494\) | −9.84705 | −0.443040 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.7135 | 0.570851 | ||||||||
\(497\) | −0.397004 | − | 3.77725i | −0.0178081 | − | 0.169433i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.47212 | + | 1.37569i | −0.289732 | + | 0.0615844i | −0.350485 | − | 0.936568i | \(-0.613983\pi\) |
0.0607529 | + | 0.998153i | \(0.480650\pi\) | |||||||
\(500\) | −65.4862 | − | 6.88288i | −2.92863 | − | 0.307812i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.81190 | + | 5.23305i | −0.259398 | + | 0.233563i | ||||
\(503\) | −3.19188 | − | 9.82361i | −0.142319 | − | 0.438013i | 0.854337 | − | 0.519719i | \(-0.173963\pi\) |
−0.996657 | + | 0.0817056i | \(0.973963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 66.2732i | − | 2.94912i | ||||||
\(506\) | −37.6902 | − | 13.8178i | −1.67553 | − | 0.614275i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.0855 | + | 63.0810i | −1.24609 | + | 2.79877i | ||||
\(509\) | −15.1044 | − | 13.6001i | −0.669492 | − | 0.602813i | 0.262656 | − | 0.964889i | \(-0.415401\pi\) |
−0.932149 | + | 0.362076i | \(0.882068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.47699 | + | 0.657597i | −0.0653381 | + | 0.0290904i | ||||
\(512\) | −29.4132 | − | 21.3699i | −1.29989 | − | 0.944427i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.8065 | + | 13.5838i | −1.84401 | + | 0.599154i | ||||
\(515\) | 35.1661 | − | 3.69611i | 1.54960 | − | 0.162870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0254557 | + | 0.0634308i | 0.00111954 | + | 0.00278968i | ||||
\(518\) | −5.57356 | + | 3.21790i | −0.244888 | + | 0.141386i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.6032 | + | 3.52912i | 0.728100 | + | 0.154762i | ||||
\(521\) | 11.4110 | + | 3.70764i | 0.499923 | + | 0.162435i | 0.548115 | − | 0.836403i | \(-0.315346\pi\) |
−0.0481915 | + | 0.998838i | \(0.515346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2395 | + | 30.6101i | −0.972466 | + | 1.33848i | −0.0316743 | + | 0.999498i | \(0.510084\pi\) |
−0.940791 | + | 0.338986i | \(0.889916\pi\) | |||||||
\(524\) | −36.5762 | − | 40.6220i | −1.59784 | − | 1.77458i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.58415 | − | 2.04100i | −0.199879 | − | 0.0889917i | ||||
\(527\) | 6.03461 | + | 10.4522i | 0.262872 | + | 0.455307i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.840532 | − | 1.45584i | 0.0365449 | − | 0.0632976i | ||||
\(530\) | 41.4869 | − | 30.1420i | 1.80207 | − | 1.30928i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.90653 | + | 5.86770i | −0.0826586 | + | 0.254397i | ||||
\(533\) | −1.04874 | − | 2.35551i | −0.0454260 | − | 0.102028i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.1735 | − | 57.2720i | −0.526308 | − | 2.47609i | ||||
\(536\) | −14.0847 | + | 15.6427i | −0.608367 | + | 0.675660i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.07649 | + | 3.50826i | 0.261976 | + | 0.151252i | ||||
\(539\) | 10.6419 | + | 20.1276i | 0.458378 | + | 0.866957i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6491 | + | 29.7975i | 0.930769 | + | 1.28109i | 0.959559 | + | 0.281508i | \(0.0908345\pi\) |
−0.0287904 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(542\) | −5.15176 | + | 24.2371i | −0.221287 | + | 1.04107i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.221529 | − | 2.10770i | 0.00949796 | − | 0.0903671i | ||||
\(545\) | −4.21704 | + | 40.1225i | −0.180638 | + | 1.71866i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.62505 | + | 35.8730i | −0.326023 | + | 1.53382i | 0.444131 | + | 0.895962i | \(0.353513\pi\) |
−0.770154 | + | 0.637858i | \(0.779821\pi\) | |||||||
\(548\) | 2.40060 | + | 3.30414i | 0.102548 | + | 0.141146i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 35.5317 | + | 67.2032i | 1.51508 | + | 2.86555i | ||||
\(551\) | −9.16693 | − | 5.29253i | −0.390524 | − | 0.225469i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.69163 | + | 2.98936i | −0.114460 | + | 0.127120i | ||||
\(554\) | −3.70317 | − | 17.4220i | −0.157333 | − | 0.740191i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.7514 | − | 71.3149i | −1.34656 | − | 3.02443i | ||||
\(557\) | −2.30765 | + | 7.10223i | −0.0977784 | + | 0.300931i | −0.987968 | − | 0.154660i | \(-0.950572\pi\) |
0.890189 | + | 0.455591i | \(0.150572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.44800 | − | 1.05204i | 0.0612441 | − | 0.0444964i | ||||
\(560\) | 2.52547 | − | 4.37425i | 0.106721 | − | 0.184846i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.80838 | + | 4.86426i | 0.118464 | + | 0.205186i | ||||
\(563\) | −3.57636 | − | 1.59230i | −0.150725 | − | 0.0671073i | 0.329988 | − | 0.943985i | \(-0.392955\pi\) |
−0.480713 | + | 0.876878i | \(0.659622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.65928 | + | 2.95343i | 0.111877 | + | 0.124252i | ||||
\(566\) | 34.9886 | − | 48.1576i | 1.47068 | − | 2.02422i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −46.3155 | − | 15.0488i | −1.94335 | − | 0.631434i | ||||
\(569\) | −36.8479 | − | 7.83227i | −1.54475 | − | 0.328346i | −0.644802 | − | 0.764350i | \(-0.723060\pi\) |
−0.899945 | + | 0.436004i | \(0.856393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.2762 | + | 15.1706i | −1.09962 | + | 0.634868i | −0.936122 | − | 0.351675i | \(-0.885612\pi\) |
−0.163502 | + | 0.986543i | \(0.552279\pi\) | |||||||
\(572\) | −4.61000 | − | 11.4872i | −0.192754 | − | 0.480305i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.42312 | + | 0.254681i | −0.101139 | + | 0.0106302i | ||||
\(575\) | −44.4504 | + | 14.4428i | −1.85371 | + | 0.602307i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.68563 | + | 1.95122i | 0.111804 | + | 0.0812305i | 0.642282 | − | 0.766468i | \(-0.277988\pi\) |
−0.530478 | + | 0.847699i | \(0.677988\pi\) | |||||||
\(578\) | 11.5800 | − | 5.15573i | 0.481663 | − | 0.214450i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 27.5701 | + | 24.8242i | 1.14479 | + | 1.03077i | ||||
\(581\) | −1.37376 | + | 3.08552i | −0.0569932 | + | 0.128009i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2676 | − | 6.33056i | −0.715152 | − | 0.262185i | ||||
\(584\) | 20.7303i | 0.857826i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.02659 | − | 24.7033i | −0.331576 | − | 1.02048i | ||||
\(587\) | 30.4002 | − | 27.3724i | 1.25475 | − | 1.12978i | 0.268718 | − | 0.963219i | \(-0.413400\pi\) |
0.986031 | − | 0.166562i | \(-0.0532667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8953 | + | 1.56556i | 0.613749 | + | 0.0645076i | ||||
\(590\) | 59.9197 | − | 12.7363i | 2.46685 | − | 0.524346i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.71627 | + | 25.8436i | 0.111638 | + | 1.06217i | ||||
\(593\) | 4.62924 | 0.190100 | 0.0950500 | − | 0.995472i | \(-0.469699\pi\) | ||||
0.0950500 | + | 0.995472i | \(0.469699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.79500 | 0.196576 | ||||||||
\(596\) | 3.30590 | + | 31.4536i | 0.135415 | + | 1.28839i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.2266 | − | 2.38629i | 0.459091 | − | 0.0975828i | ||||
\(599\) | 30.4113 | + | 3.19636i | 1.24257 | + | 0.130600i | 0.702909 | − | 0.711280i | \(-0.251884\pi\) |
0.539665 | + | 0.841880i | \(0.318551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2084 | − | 20.8970i | 0.946692 | − | 0.852405i | −0.0424903 | − | 0.999097i | \(-0.513529\pi\) |
0.989182 | + | 0.146692i | \(0.0468625\pi\) | |||||||
\(602\) | −0.522639 | − | 1.60852i | −0.0213012 | − | 0.0655583i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39.6459i | 1.61317i | ||||||||
\(605\) | 19.7738 | − | 36.7742i | 0.803920 | − | 1.49508i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5139 | + | 28.1068i | −0.507925 | + | 1.14082i | 0.459619 | + | 0.888116i | \(0.347986\pi\) |
−0.967544 | + | 0.252703i | \(0.918681\pi\) | |||||||
\(608\) | −1.95445 | − | 1.75979i | −0.0792633 | − | 0.0713690i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 82.3908 | − | 36.6828i | 3.33591 | − | 1.48524i | ||||
\(611\) | −0.0158094 | − | 0.0114862i | −0.000639581 | − | 0.000464683i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.2244 | − | 7.87097i | 0.978413 | − | 0.317906i | 0.224205 | − | 0.974542i | \(-0.428021\pi\) |
0.754207 | + | 0.656636i | \(0.228021\pi\) | |||||||
\(614\) | −11.0693 | + | 1.16343i | −0.446721 | + | 0.0469523i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.73943 | + | 0.387887i | −0.231248 | + | 0.0156284i | ||||
\(617\) | −3.64536 | + | 2.10465i | −0.146757 | + | 0.0847300i | −0.571580 | − | 0.820546i | \(-0.693669\pi\) |
0.424824 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.6618 | − | 8.00527i | −1.51376 | − | 0.321759i | −0.625177 | − | 0.780483i | \(-0.714973\pi\) |
−0.888579 | + | 0.458724i | \(0.848307\pi\) | |||||||
\(620\) | −49.9243 | − | 16.2214i | −2.00501 | − | 0.651467i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.4356 | + | 18.4926i | −0.538720 | + | 0.741484i | ||||
\(623\) | 0.750205 | + | 0.833188i | 0.0300563 | + | 0.0333810i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0438 | + | 6.69793i | 0.601752 | + | 0.267917i | ||||
\(626\) | −6.11030 | − | 10.5833i | −0.244217 | − | 0.422995i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 31.8440 | − | 55.1554i | 1.27071 | − | 2.20094i | ||||
\(629\) | −19.9578 | + | 14.5002i | −0.795769 | + | 0.578160i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.65655 | + | 11.2537i | −0.145565 | + | 0.448003i | −0.997083 | − | 0.0763220i | \(-0.975682\pi\) |
0.851518 | + | 0.524325i | \(0.175682\pi\) | |||||||
\(632\) | 20.9786 | + | 47.1187i | 0.834484 | + | 1.87428i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.91445 | − | 27.8253i | −0.234893 | − | 1.10508i | ||||
\(635\) | 44.5617 | − | 49.4908i | 1.76838 | − | 1.96398i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.63745 | − | 3.25478i | −0.223364 | − | 0.128959i | ||||
\(638\) | 2.83913 | − | 19.8650i | 0.112402 | − | 0.786465i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 44.7507 | + | 61.5941i | 1.76893 | + | 2.43472i | ||||
\(641\) | −7.47236 | + | 35.1547i | −0.295140 | + | 1.38853i | 0.541466 | + | 0.840723i | \(0.317869\pi\) |
−0.836607 | + | 0.547804i | \(0.815464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.340268 | + | 3.23744i | −0.0134189 | + | 0.127672i | −0.999180 | − | 0.0404769i | \(-0.987112\pi\) |
0.985762 | + | 0.168149i | \(0.0537789\pi\) | |||||||
\(644\) | 0.751682 | − | 7.15178i | 0.0296204 | − | 0.281820i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.41557 | + | 34.8875i | −0.291762 | + | 1.37263i | ||||
\(647\) | 7.14454 | + | 9.83361i | 0.280881 | + | 0.386599i | 0.926025 | − | 0.377461i | \(-0.123203\pi\) |
−0.645145 | + | 0.764060i | \(0.723203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7682 | − | 15.2984i | −0.618956 | − | 0.600516i | ||||
\(650\) | −18.8227 | − | 10.8673i | −0.738285 | − | 0.426249i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.2603 | − | 12.5058i | 0.440986 | − | 0.489765i | ||||
\(653\) | 5.30599 | + | 24.9627i | 0.207639 | + | 0.976866i | 0.951290 | + | 0.308298i | \(0.0997593\pi\) |
−0.743651 | + | 0.668568i | \(0.766907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.4429 | + | 48.1615i | 0.837843 | + | 1.88183i | ||||
\(656\) | −3.04005 | + | 9.35631i | −0.118694 | + | 0.365303i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0149391 | + | 0.0108539i | −0.000582385 | + | 0.000423127i | ||||
\(659\) | −13.9720 | + | 24.2003i | −0.544273 | + | 0.942708i | 0.454379 | + | 0.890808i | \(0.349861\pi\) |
−0.998652 | + | 0.0519000i | \(0.983472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6899 | + | 23.7116i | 0.532475 | + | 0.922274i | 0.999281 | + | 0.0379144i | \(0.0120714\pi\) |
−0.466806 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(662\) | 64.6599 | + | 28.7884i | 2.51308 | + | 1.11889i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.9780 | + | 32.1833i | 1.12456 | + | 1.24895i | ||||
\(665\) | 3.49754 | − | 4.81395i | 0.135629 | − | 0.186677i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7338 | + | 3.81254i | 0.454334 | + | 0.147622i | ||||
\(668\) | 70.6520 | + | 15.0175i | 2.73361 | + | 0.581046i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.7470 | − | 20.6386i | 1.38103 | − | 0.797337i | ||||
\(671\) | −27.3904 | − | 17.2044i | −1.05739 | − | 0.664168i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4746 | − | 1.41623i | 0.519406 | − | 0.0545918i | 0.158801 | − | 0.987311i | \(-0.449237\pi\) |
0.360605 | + | 0.932719i | \(0.382570\pi\) | |||||||
\(674\) | 66.9179 | − | 21.7429i | 2.57758 | − | 0.837507i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −38.5290 | − | 27.9930i | −1.48189 | − | 1.07665i | ||||
\(677\) | 33.5244 | − | 14.9260i | 1.28845 | − | 0.573653i | 0.355840 | − | 0.934547i | \(-0.384195\pi\) |
0.932607 | + | 0.360894i | \(0.117528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.12357 | + | 3.71288i | 0.158248 | + | 0.142487i | ||||
\(680\) | 25.0070 | − | 56.1665i | 0.958973 | − | 2.15389i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.76265 | + | 27.3119i | 0.297247 | + | 1.04583i | ||||
\(683\) | − | 30.8347i | − | 1.17986i | −0.807455 | − | 0.589929i | \(-0.799156\pi\) | ||
0.807455 | − | 0.589929i | \(-0.200844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21721 | − | 3.74619i | −0.0465072 | − | 0.143134i | ||||
\(686\) | −9.23253 | + | 8.31300i | −0.352499 | + | 0.317392i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.79158 | − | 0.713823i | −0.258926 | − | 0.0272143i | ||||
\(689\) | 5.14344 | − | 1.09327i | 0.195949 | − | 0.0416503i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.98809 | + | 47.4585i | 0.189756 | + | 1.80541i | 0.512251 | + | 0.858836i | \(0.328812\pi\) |
−0.322495 | + | 0.946571i | \(0.604521\pi\) | |||||||
\(692\) | 24.3317 | 0.924953 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53.9474 | 2.04782 | ||||||||
\(695\) | 7.86986 | + | 74.8767i | 0.298521 | + | 2.84024i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.13521 | + | 1.94175i | −0.346021 | + | 0.0735490i | ||||
\(698\) | 37.9498 | + | 3.98868i | 1.43642 | + | 0.150974i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.1200 | + | 9.11205i | −0.382499 | + | 0.344403i | ||||
\(701\) | −4.34678 | − | 13.3780i | −0.164176 | − | 0.505281i | 0.834799 | − | 0.550555i | \(-0.185584\pi\) |
−0.998975 | + | 0.0452742i | \(0.985584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6133i | 1.15460i | ||||||||
\(704\) | 9.97702 | − | 27.2139i | 0.376023 | − | 1.02566i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.0625 | − | 24.8467i | 0.416342 | − | 0.935119i | ||||
\(707\) | −4.77215 | − | 4.29687i | −0.179475 | − | 0.161600i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.28966 | + | 3.69079i | −0.311325 | + | 0.138611i | −0.556451 | − | 0.830880i | \(-0.687837\pi\) |
0.245126 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(710\) | 77.2591 | + | 56.1320i | 2.89948 | + | 2.10660i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.6721 | − | 4.44233i | 0.512383 | − | 0.166483i | ||||
\(713\) | −17.3615 | + | 1.82477i | −0.650193 | + | 0.0683380i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.804952 | + | 11.9106i | 0.0301035 | + | 0.445432i | ||||
\(716\) | −31.4445 | + | 18.1545i | −1.17514 | + | 0.678466i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.4742 | + | 8.39049i | 1.47316 | + | 0.313130i | ||||
\(719\) | −32.2802 | − | 10.4885i | −1.20385 | − | 0.391155i | −0.362674 | − | 0.931916i | \(-0.618136\pi\) |
−0.841176 | + | 0.540761i | \(0.818136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.01387 | − | 2.77186i | 0.0750005 | − | 0.103229i | ||||
\(722\) | −1.35772 | − | 1.50790i | −0.0505291 | − | 0.0561183i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.0563 | − | 6.70351i | −0.559564 | − | 0.249134i | ||||
\(725\) | −11.6817 | − | 20.2334i | −0.433849 | − | 0.751448i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.4496 | + | 26.7595i | −0.572993 | + | 0.992454i | 0.423263 | + | 0.906007i | \(0.360885\pi\) |
−0.996256 | + | 0.0864469i | \(0.972449\pi\) | |||||||
\(728\) | 1.33060 | − | 0.966740i | 0.0493154 | − | 0.0358298i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.5620 | − | 38.6620i | 0.464942 | − | 1.43094i | ||||
\(731\) | −2.63685 | − | 5.92246i | −0.0975274 | − | 0.219050i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.64932 | + | 40.6919i | 0.319470 | + | 1.50299i | 0.785857 | + | 0.618408i | \(0.212222\pi\) |
−0.466387 | + | 0.884581i | \(0.654445\pi\) | |||||||
\(734\) | −15.9929 | + | 17.7619i | −0.590307 | + | 0.655602i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.65472 | + | 1.53271i | 0.0978545 | + | 0.0564963i | ||||
\(737\) | −13.2904 | − | 6.52058i | −0.489558 | − | 0.240189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.44687 | − | 11.6261i | −0.310723 | − | 0.427674i | 0.624883 | − | 0.780718i | \(-0.285146\pi\) |
−0.935607 | + | 0.353044i | \(0.885146\pi\) | |||||||
\(740\) | 22.3080 | − | 104.951i | 0.820057 | − | 3.85807i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.519386 | − | 4.94163i | 0.0190673 | − | 0.181413i | ||||
\(743\) | 1.40380 | − | 13.3562i | 0.0515003 | − | 0.489993i | −0.938123 | − | 0.346303i | \(-0.887437\pi\) |
0.989623 | − | 0.143689i | \(-0.0458966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.34186 | − | 29.8361i | 0.232348 | − | 1.09311i | ||||
\(746\) | −18.0937 | − | 24.9039i | −0.662459 | − | 0.911796i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −44.1703 | + | 7.68220i | −1.61502 | + | 0.280889i | ||||
\(749\) | −4.91328 | − | 2.83669i | −0.179528 | − | 0.103650i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3326 | + | 27.0241i | −0.887911 | + | 0.986125i | −0.999971 | − | 0.00757678i | \(-0.997588\pi\) |
0.112061 | + | 0.993701i | \(0.464255\pi\) | |||||||
\(752\) | 0.0155018 | + | 0.0729301i | 0.000565291 | + | 0.00265949i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.33360 | + | 5.24135i | 0.0849846 | + | 0.190879i | ||||
\(755\) | 11.8158 | − | 36.3653i | 0.430021 | − | 1.32347i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2811 | + | 23.4536i | −1.17328 | + | 0.852435i | −0.991397 | − | 0.130887i | \(-0.958218\pi\) |
−0.181878 | + | 0.983321i | \(0.558218\pi\) | |||||||
\(758\) | 42.7599 | − | 74.0623i | 1.55311 | − | 2.69006i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −38.1481 | − | 66.0744i | −1.38378 | − | 2.39677i | ||||
\(761\) | −3.11533 | − | 1.38703i | −0.112930 | − | 0.0502799i | 0.349494 | − | 0.936939i | \(-0.386354\pi\) |
−0.462424 | + | 0.886659i | \(0.653020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.61570 | + | 2.90502i | 0.0946945 | + | 0.105169i | ||||
\(764\) | −46.6896 | + | 64.2627i | −1.68917 | + | 2.32494i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 52.3347 | + | 17.0046i | 1.89093 | + | 0.614401i | ||||
\(767\) | 6.14420 | + | 1.30599i | 0.221854 | + | 0.0471566i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5463 | − | 10.7077i | 0.668796 | − | 0.386130i | −0.126824 | − | 0.991925i | \(-0.540478\pi\) |
0.795620 | + | 0.605795i | \(0.207145\pi\) | |||||||
\(770\) | 10.9391 | + | 2.75454i | 0.394217 | + | 0.0992668i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.3673 | − | 3.29684i | 1.12894 | − | 0.118656i | ||||
\(773\) | −34.1302 | + | 11.0896i | −1.22758 | + | 0.398864i | −0.849836 | − | 0.527048i | \(-0.823299\pi\) |
−0.377741 | + | 0.925911i | \(0.623299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.7446 | + | 19.4311i | 0.960694 | + | 0.697985i | ||||
\(776\) | 64.9964 | − | 28.9383i | 2.33323 | − | 1.03882i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.3235 | − | 11.9965i | −0.477669 | − | 0.430095i | ||||
\(779\) | −4.71392 | + | 10.5876i | −0.168894 | + | 0.379342i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.27515 | − | 34.2259i | 0.0456284 | − | 1.22470i | ||||
\(782\) | − | 41.5723i | − | 1.48662i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.67500 | + | 23.6212i | 0.274107 | + | 0.843615i | ||||
\(785\) | −45.6471 | + | 41.1009i | −1.62922 | + | 1.46695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.8002 | + | 5.02400i | 1.70389 | + | 0.179086i | 0.905874 | − | 0.423548i | \(-0.139215\pi\) |
0.798018 | + | 0.602634i | \(0.205882\pi\) | |||||||
\(788\) | −81.5010 | + | 17.3236i | −2.90335 | + | 0.617127i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.5723 | − | 100.589i | −0.376146 | − | 3.57879i | ||||
\(791\) | 0.385085 | 0.0136920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.24793 | 0.328404 | ||||||||
\(794\) | 4.26123 | + | 40.5429i | 0.151225 | + | 1.43881i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 40.4827 | − | 8.60487i | 1.43487 | − | 0.304992i | ||||
\(797\) | −6.01268 | − | 0.631958i | −0.212980 | − | 0.0223851i | −0.00256245 | − | 0.999997i | \(-0.500816\pi\) |
−0.210417 | + | 0.977612i | \(0.567482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0526007 | + | 0.0473619i | −0.00186088 | + | 0.00167554i | ||||
\(800\) | −1.79381 | − | 5.52078i | −0.0634208 | − | 0.195189i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.3605i | 0.436464i | ||||||||
\(803\) | −14.0240 | + | 3.98594i | −0.494897 | + | 0.140661i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.82095 | + | 6.33596i | −0.0994254 | + | 0.223313i | ||||
\(806\) | −6.03291 | − | 5.43206i | −0.212500 | − | 0.191336i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −75.2195 | + | 33.4899i | −2.64621 | + | 1.17817i | ||||
\(809\) | −6.01444 | − | 4.36974i | −0.211456 | − | 0.153632i | 0.477016 | − | 0.878895i | \(-0.341718\pi\) |
−0.688472 | + | 0.725263i | \(0.741718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7357 | − | 9.01188i | 0.973933 | − | 0.316450i | 0.221530 | − | 0.975154i | \(-0.428895\pi\) |
0.752402 | + | 0.658704i | \(0.228895\pi\) | |||||||
\(812\) | 3.57505 | − | 0.375753i | 0.125460 | − | 0.0131863i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −53.8605 | + | 21.6150i | −1.88781 | + | 0.757606i | ||||
\(815\) | −14.0556 | + | 8.11503i | −0.492348 | + | 0.284257i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.86922 | − | 1.67265i | −0.275309 | − | 0.0585187i | ||||
\(818\) | 74.9521 | + | 24.3534i | 2.62064 | + | 0.851497i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.8759 | − | 32.8623i | 0.833782 | − | 1.14760i | ||||
\(821\) | −0.717575 | − | 0.796947i | −0.0250435 | − | 0.0278137i | 0.730493 | − | 0.682920i | \(-0.239290\pi\) |
−0.755536 | + | 0.655107i | \(0.772624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.17276 | − | 3.63875i | −0.284884 | − | 0.126839i | 0.259320 | − | 0.965792i | \(-0.416502\pi\) |
−0.544204 | + | 0.838953i | \(0.683168\pi\) | |||||||
\(824\) | −21.9655 | − | 38.0454i | −0.765206 | − | 1.32538i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.96782 | − | 5.14042i | 0.103264 | − | 0.178858i | ||||
\(827\) | −28.5608 | + | 20.7507i | −0.993157 | + | 0.721571i | −0.960610 | − | 0.277899i | \(-0.910362\pi\) |
−0.0325471 | + | 0.999470i | \(0.510362\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.36614 | − | 25.7483i | 0.290568 | − | 0.894276i | −0.694106 | − | 0.719873i | \(-0.744200\pi\) |
0.984674 | − | 0.174404i | \(-0.0557998\pi\) | |||||||
\(830\) | −34.5416 | − | 77.5817i | −1.19896 | − | 2.69290i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.72301 | + | 8.10611i | 0.0597345 | + | 0.281029i | ||||
\(833\) | −15.7769 | + | 17.5221i | −0.546638 | + | 0.607103i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −60.3300 | − | 34.8315i | −2.08780 | − | 1.20539i | ||||
\(836\) | −24.5058 | + | 49.9483i | −0.847552 | + | 1.72750i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −39.9645 | − | 55.0064i | −1.38055 | − | 1.90016i | ||||
\(839\) | 7.74116 | − | 36.4193i | 0.267255 | − | 1.25733i | −0.615739 | − | 0.787950i | \(-0.711143\pi\) |
0.882994 | − | 0.469384i | \(-0.155524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.38666 | − | 22.7076i | 0.0822986 | − | 0.783019i | ||||
\(842\) | 6.80684 | − | 64.7628i | 0.234579 | − | 2.23187i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.02614 | − | 14.2369i | 0.104164 | − | 0.490053i | ||||
\(845\) | 26.9980 | + | 37.1595i | 0.928759 | + | 1.27833i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.36596 | − | 3.80813i | −0.0469349 | − | 0.130849i | ||||
\(848\) | −17.3750 | − | 10.0314i | −0.596658 | − | 0.344481i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −52.6770 | + | 58.5037i | −1.80680 | + | 2.00666i | ||||
\(851\) | −7.41869 | − | 34.9022i | −0.254309 | − | 1.19643i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2842 | + | 32.0828i | 0.489080 | + | 1.09849i | 0.974536 | + | 0.224231i | \(0.0719871\pi\) |
−0.485455 | + | 0.874261i | \(0.661346\pi\) | |||||||
\(854\) | 2.70044 | − | 8.31109i | 0.0924070 | − | 0.284400i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −58.8516 | + | 42.7582i | −2.01151 | + | 1.46144i | ||||
\(857\) | −14.9819 | + | 25.9493i | −0.511770 | + | 0.886412i | 0.488137 | + | 0.872767i | \(0.337677\pi\) |
−0.999907 | + | 0.0136449i | \(0.995657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.63419 | − | 14.9548i | −0.294595 | − | 0.510253i | 0.680296 | − | 0.732938i | \(-0.261851\pi\) |
−0.974891 | + | 0.222685i | \(0.928518\pi\) | |||||||
\(860\) | 25.7590 | + | 11.4686i | 0.878374 | + | 0.391077i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.16825 | − | 1.29747i | −0.0397907 | − | 0.0441921i | ||||
\(863\) | 20.4637 | − | 28.1659i | 0.696593 | − | 0.958778i | −0.303389 | − | 0.952867i | \(-0.598118\pi\) |
0.999983 | − | 0.00591175i | \(-0.00188178\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.3183 | − | 7.25166i | −0.758845 | − | 0.246564i | ||||
\(866\) | 27.2444 | + | 5.79097i | 0.925801 | + | 0.196785i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.40493 | + | 2.54319i | −0.149513 | + | 0.0863215i | ||||
\(869\) | −27.8420 | + | 23.2518i | −0.944477 | + | 0.788762i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.20940 | − | 0.442425i | 0.142630 | − | 0.0149910i | ||||
\(872\) | 47.6696 | − | 15.4888i | 1.61430 | − | 0.524517i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.7366 | − | 30.3234i | −1.41176 | − | 1.02570i | ||||
\(875\) | 5.62148 | − | 2.50284i | 0.190041 | − | 0.0846116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.47358 | + | 1.32682i | 0.0497592 | + | 0.0448034i | 0.693635 | − | 0.720327i | \(-0.256008\pi\) |
−0.643876 | + | 0.765130i | \(0.722675\pi\) | |||||||
\(878\) | 8.49756 | − | 19.0858i | 0.286779 | − | 0.644116i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28.1257 | − | 35.8267i | 0.948117 | − | 1.20772i | ||||
\(881\) | 48.9571i | 1.64941i | 0.565566 | + | 0.824703i | \(0.308658\pi\) | ||||
−0.565566 | + | 0.824703i | \(0.691342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.7400 | + | 33.0542i | 0.361429 | + | 1.11236i | 0.952187 | + | 0.305515i | \(0.0988286\pi\) |
−0.590758 | + | 0.806848i | \(0.701171\pi\) | |||||||
\(884\) | 9.52592 | − | 8.57718i | 0.320391 | − | 0.288482i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.8657 | − | 3.55942i | −1.13774 | − | 0.119581i | ||||
\(887\) | −14.1763 | + | 3.01328i | −0.475995 | + | 0.101176i | −0.439661 | − | 0.898164i | \(-0.644901\pi\) |
−0.0363341 | + | 0.999340i | \(0.511568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.674510 | − | 6.41754i | −0.0226223 | − | 0.215237i | ||||
\(890\) | −28.1903 | −0.944943 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −70.4368 | −2.35840 | ||||||||
\(893\) | 0.00918138 | + | 0.0873550i | 0.000307243 | + | 0.00292322i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.2532 | − | 7.28074i | 1.14496 | − | 0.243368i | ||||
\(896\) | 7.33667 | + | 0.771115i | 0.245101 | + | 0.0257611i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.1219 | + | 35.2255i | −1.30551 | + | 1.17549i | ||||
\(899\) | −2.69664 | − | 8.29941i | −0.0899380 | − | 0.276801i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.0462i | − | 0.634521i | ||||||
\(902\) | −21.9561 | − | 0.818015i | −0.731058 | − | 0.0272369i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.00830 | − | 4.51072i | 0.0667951 | − | 0.150024i | ||||
\(905\) | 11.8126 | + | 10.6361i | 0.392664 | + | 0.353556i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8007 | − | 9.26105i | 0.690674 | − | 0.307508i | −0.0312188 | − | 0.999513i | \(-0.509939\pi\) |
0.721893 | + | 0.692005i | \(0.243272\pi\) | |||||||
\(908\) | 55.3329 | + | 40.2017i | 1.83629 | + | 1.33414i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.06739 | + | 0.996656i | −0.101683 | + | 0.0330388i | ||||
\(911\) | 22.5701 | − | 2.37221i | 0.747781 | − | 0.0785950i | 0.277030 | − | 0.960861i | \(-0.410650\pi\) |
0.470751 | + | 0.882266i | \(0.343983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.2002 | + | 25.7916i | −0.536147 | + | 0.853577i | ||||
\(914\) | −20.6878 | + | 11.9441i | −0.684293 | + | 0.395077i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.4636 | − | 3.49945i | −0.543973 | − | 0.115625i | ||||
\(917\) | 4.85824 | + | 1.57854i | 0.160433 | + | 0.0521280i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.737746 | + | 1.01542i | −0.0243360 | + | 0.0334956i | −0.821012 | − | 0.570911i | \(-0.806590\pi\) |
0.796676 | + | 0.604407i | \(0.206590\pi\) | |||||||
\(920\) | 59.5048 | + | 66.0868i | 1.96182 | + | 2.17882i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.5062 | + | 12.2466i | 0.905870 | + | 0.403319i | ||||
\(923\) | 4.89619 | + | 8.48045i | 0.161160 | + | 0.279137i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.7850 | + | 58.5173i | −1.11084 | + | 1.92404i | ||||
\(926\) | −66.7619 | + | 48.5054i | −2.19393 | + | 1.59399i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.473521 | + | 1.45735i | −0.0155441 | + | 0.0478398i | ||||
\(929\) | −1.16942 | − | 2.62655i | −0.0383673 | − | 0.0861744i | 0.893345 | − | 0.449371i | \(-0.148352\pi\) |
−0.931712 | + | 0.363197i | \(0.881685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.08339 | + | 28.6201i | 0.199375 | + | 0.937986i | ||||
\(932\) | 61.5777 | − | 68.3890i | 2.01705 | − | 2.24016i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.2036 | + | 19.1701i | 1.08645 | + | 0.627265i | ||||
\(935\) | 42.8048 | + | 6.11769i | 1.39987 | + | 0.200070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1303 | + | 24.9542i | 0.592291 | + | 0.815219i | 0.994975 | − | 0.100120i | \(-0.0319227\pi\) |
−0.402684 | + | 0.915339i | \(0.631923\pi\) | |||||||
\(938\) | 0.831556 | − | 3.91216i | 0.0271513 | − | 0.127737i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0321795 | − | 0.306168i | 0.00104958 | − | 0.00998608i | ||||
\(941\) | 0.683706 | − | 6.50503i | 0.0222882 | − | 0.212058i | −0.977710 | − | 0.209962i | \(-0.932666\pi\) |
0.999998 | − | 0.00209621i | \(-0.000667244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.80858 | − | 13.2133i | 0.0914599 | − | 0.430285i | ||||
\(944\) | −14.0872 | − | 19.3893i | −0.458498 | − | 0.631069i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.61336 | − | 15.0260i | −0.0849675 | − | 0.488537i | ||||
\(947\) | 28.8021 | + | 16.6289i | 0.935944 | + | 0.540368i | 0.888687 | − | 0.458515i | \(-0.151619\pi\) |
0.0472574 | + | 0.998883i | \(0.484952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.78923 | − | 3.09776i | 0.0905423 | − | 0.100557i | ||||
\(950\) | 20.3116 | + | 95.5585i | 0.658995 | + | 3.10033i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.42306 | − | 5.44228i | −0.0785318 | − | 0.176385i | ||||
\(953\) | −16.9820 | + | 52.2651i | −0.550100 | + | 1.69303i | 0.158445 | + | 0.987368i | \(0.449352\pi\) |
−0.708545 | + | 0.705666i | \(0.750648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.9785 | − | 45.0300i | 2.00558 | − | 1.45714i | ||||
\(956\) | −39.3481 | + | 68.1528i | −1.27261 | + | 2.20422i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.1893 | − | 26.3086i | −0.490744 | − | 0.849994i | ||||
\(959\) | −0.348671 | − | 0.155238i | −0.0112592 | − | 0.00501291i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.4809 | − | 13.8615i | −0.402610 | − | 0.447144i | ||||
\(962\) | 9.75321 | − | 13.4241i | 0.314456 | − | 0.432812i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.70515 | + | 2.82847i | 0.280374 | + | 0.0910990i | ||||
\(965\) | −29.7543 | − | 6.32448i | −0.957825 | − | 0.203592i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.4790 | − | 17.0197i | 0.947982 | − | 0.547318i | 0.0555286 | − | 0.998457i | \(-0.482316\pi\) |
0.892454 | + | 0.451139i | \(0.148982\pi\) | |||||||
\(968\) | −51.7306 | − | 3.86000i | −1.66269 | − | 0.124065i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −138.754 | + | 14.5836i | −4.45512 | + | 0.468252i | ||||
\(971\) | −36.2008 | + | 11.7624i | −1.16174 | + | 0.377472i | −0.825554 | − | 0.564323i | \(-0.809137\pi\) |
−0.336186 | + | 0.941796i | \(0.609137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.90192 | + | 4.28799i | 0.189207 | + | 0.137467i | ||||
\(974\) | 15.4821 | − | 6.89307i | 0.496078 | − | 0.220868i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.2218 | − | 23.6102i | −0.839339 | − | 0.755744i | ||||
\(977\) | 13.0565 | − | 29.3253i | 0.417713 | − | 0.938199i | −0.575051 | − | 0.818118i | \(-0.695018\pi\) |
0.992764 | − | 0.120081i | \(-0.0383156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.63404 | + | 8.39499i | 0.180065 | + | 0.268305i | ||||
\(980\) | − | 102.551i | − | 3.27586i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.227305 | − | 0.699572i | −0.00725358 | − | 0.0223242i | ||||
\(983\) | 15.9259 | − | 14.3398i | 0.507958 | − | 0.457368i | −0.374861 | − | 0.927081i | \(-0.622309\pi\) |
0.882819 | + | 0.469713i | \(0.155643\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 79.9200 | + | 8.39993i | 2.54646 | + | 0.267644i | ||||
\(986\) | 20.3272 | − | 4.32067i | 0.647349 | − | 0.137598i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.66274 | − | 15.8199i | −0.0528987 | − | 0.503297i | ||||
\(989\) | 9.37704 | 0.298172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.3068 | −0.930962 | −0.465481 | − | 0.885058i | \(-0.654119\pi\) | ||||
−0.465481 | + | 0.885058i | \(0.654119\pi\) | |||||||
\(992\) | −0.226638 | − | 2.15631i | −0.00719576 | − | 0.0684631i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.05106 | − | 1.92386i | 0.287082 | − | 0.0610212i | ||||
\(995\) | −39.6974 | − | 4.17237i | −1.25849 | − | 0.132273i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3471 | − | 21.9222i | 0.771080 | − | 0.694283i | −0.186499 | − | 0.982455i | \(-0.559714\pi\) |
0.957579 | + | 0.288172i | \(0.0930475\pi\) | |||||||
\(998\) | −4.98148 | − | 15.3314i | −0.157686 | − | 0.485308i | ||||
\(999\) | 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 | 891.2.u.c.107.4 | 32 | ||
3.2 | odd | 2 | inner | 891.2.u.c.107.1 | 32 | ||
9.2 | odd | 6 | 99.2.j.a.8.1 | ✓ | 16 | ||
9.4 | even | 3 | inner | 891.2.u.c.701.1 | 32 | ||
9.5 | odd | 6 | inner | 891.2.u.c.701.4 | 32 | ||
9.7 | even | 3 | 99.2.j.a.8.4 | yes | 16 | ||
11.7 | odd | 10 | inner | 891.2.u.c.755.4 | 32 | ||
33.29 | even | 10 | inner | 891.2.u.c.755.1 | 32 | ||
36.7 | odd | 6 | 1584.2.cd.c.305.1 | 16 | |||
36.11 | even | 6 | 1584.2.cd.c.305.4 | 16 | |||
99.2 | even | 30 | 1089.2.d.g.1088.2 | 16 | |||
99.7 | odd | 30 | 99.2.j.a.62.1 | yes | 16 | ||
99.20 | odd | 30 | 1089.2.d.g.1088.16 | 16 | |||
99.29 | even | 30 | 99.2.j.a.62.4 | yes | 16 | ||
99.40 | odd | 30 | inner | 891.2.u.c.458.1 | 32 | ||
99.79 | odd | 30 | 1089.2.d.g.1088.15 | 16 | |||
99.95 | even | 30 | inner | 891.2.u.c.458.4 | 32 | ||
99.97 | even | 15 | 1089.2.d.g.1088.1 | 16 | |||
396.7 | even | 30 | 1584.2.cd.c.161.4 | 16 | |||
396.227 | odd | 30 | 1584.2.cd.c.161.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.8.1 | ✓ | 16 | 9.2 | odd | 6 | ||
99.2.j.a.8.4 | yes | 16 | 9.7 | even | 3 | ||
99.2.j.a.62.1 | yes | 16 | 99.7 | odd | 30 | ||
99.2.j.a.62.4 | yes | 16 | 99.29 | even | 30 | ||
891.2.u.c.107.1 | 32 | 3.2 | odd | 2 | inner | ||
891.2.u.c.107.4 | 32 | 1.1 | even | 1 | trivial | ||
891.2.u.c.458.1 | 32 | 99.40 | odd | 30 | inner | ||
891.2.u.c.458.4 | 32 | 99.95 | even | 30 | inner | ||
891.2.u.c.701.1 | 32 | 9.4 | even | 3 | inner | ||
891.2.u.c.701.4 | 32 | 9.5 | odd | 6 | inner | ||
891.2.u.c.755.1 | 32 | 33.29 | even | 10 | inner | ||
891.2.u.c.755.4 | 32 | 11.7 | odd | 10 | inner | ||
1089.2.d.g.1088.1 | 16 | 99.97 | even | 15 | |||
1089.2.d.g.1088.2 | 16 | 99.2 | even | 30 | |||
1089.2.d.g.1088.15 | 16 | 99.79 | odd | 30 | |||
1089.2.d.g.1088.16 | 16 | 99.20 | odd | 30 | |||
1584.2.cd.c.161.1 | 16 | 396.227 | odd | 30 | |||
1584.2.cd.c.161.4 | 16 | 396.7 | even | 30 | |||
1584.2.cd.c.305.1 | 16 | 36.7 | odd | 6 | |||
1584.2.cd.c.305.4 | 16 | 36.11 | even | 6 |