Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(353,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.t (of order \(4\), degree \(2\), 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: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.7 | ||
Character | \(\chi\) | \(=\) | 640.353 |
Dual form | 640.3.t.b.417.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.77329 | −0.924429 | −0.462215 | − | 0.886768i | \(-0.652945\pi\) | ||||
−0.462215 | + | 0.886768i | \(0.652945\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.05735 | − | 4.55712i | 0.411470 | − | 0.911424i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.39242 | + | 5.39242i | 0.770346 | + | 0.770346i | 0.978167 | − | 0.207821i | \(-0.0666370\pi\) |
−0.207821 | + | 0.978167i | \(0.566637\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30888 | −0.145431 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.98007 | − | 2.98007i | −0.270915 | − | 0.270915i | 0.558553 | − | 0.829469i | \(-0.311357\pi\) |
−0.829469 | + | 0.558553i | \(0.811357\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.2000 | −1.63077 | −0.815383 | − | 0.578921i | \(-0.803474\pi\) | ||||
−0.815383 | + | 0.578921i | \(0.803474\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.70562 | + | 12.6382i | −0.380374 | + | 0.842546i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.66924 | − | 6.66924i | 0.392308 | − | 0.392308i | −0.483201 | − | 0.875509i | \(-0.660526\pi\) |
0.875509 | + | 0.483201i | \(0.160526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.3102 | + | 14.3102i | 0.753169 | + | 0.753169i | 0.975069 | − | 0.221901i | \(-0.0712261\pi\) |
−0.221901 | + | 0.975069i | \(0.571226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.9547 | − | 14.9547i | −0.712131 | − | 0.712131i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.07267 | + | 2.07267i | −0.0901163 | + | 0.0901163i | −0.750728 | − | 0.660612i | \(-0.770297\pi\) |
0.660612 | + | 0.750728i | \(0.270297\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.5346 | − | 18.7512i | −0.661386 | − | 0.750046i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.5895 | 1.05887 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.5413 | + | 17.5413i | 0.604872 | + | 0.604872i | 0.941601 | − | 0.336730i | \(-0.109321\pi\) |
−0.336730 | + | 0.941601i | \(0.609321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.6474 | −0.762819 | −0.381410 | − | 0.924406i | \(-0.624561\pi\) | ||||
−0.381410 | + | 0.924406i | \(0.624561\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.26459 | + | 8.26459i | 0.250442 | + | 0.250442i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.6680 | − | 13.4798i | 1.01909 | − | 0.385138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −65.3234 | −1.76550 | −0.882749 | − | 0.469845i | \(-0.844310\pi\) | ||||
−0.882749 | + | 0.469845i | \(0.844310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 58.7936 | 1.50753 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.18249i | 0.0288413i | 0.999896 | + | 0.0144207i | \(0.00459040\pi\) | ||||
−0.999896 | + | 0.0144207i | \(0.995410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.57434i | − | 0.222659i | −0.993784 | − | 0.111330i | \(-0.964489\pi\) | ||
0.993784 | − | 0.111330i | \(-0.0355109\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.69282 | + | 5.96472i | −0.0598404 | + | 0.132549i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −47.2286 | + | 47.2286i | −1.00486 | + | 1.00486i | −0.00487524 | + | 0.999988i | \(0.501552\pi\) |
−0.999988 | + | 0.00487524i | \(0.998448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.15649i | 0.186867i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.4957 | + | 18.4957i | −0.362661 | + | 0.362661i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 99.2178i | 1.87203i | 0.351955 | + | 0.936017i | \(0.385517\pi\) | ||||
−0.351955 | + | 0.936017i | \(0.614483\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.7116 | + | 7.44949i | −0.358392 | + | 0.135445i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −39.6863 | − | 39.6863i | −0.696251 | − | 0.696251i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −54.7400 | + | 54.7400i | −0.927796 | + | 0.927796i | −0.997563 | − | 0.0697673i | \(-0.977774\pi\) |
0.0697673 | + | 0.997563i | \(0.477774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1054 | − | 12.1054i | 0.198449 | − | 0.198449i | −0.600886 | − | 0.799335i | \(-0.705185\pi\) |
0.799335 | + | 0.600886i | \(0.205185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.05803 | − | 7.05803i | −0.112032 | − | 0.112032i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −43.6157 | + | 96.6108i | −0.671011 | + | 1.48632i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.074i | 1.62798i | 0.580882 | + | 0.813988i | \(0.302708\pi\) | ||||
−0.580882 | + | 0.813988i | \(0.697292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.74812 | − | 5.74812i | 0.0833061 | − | 0.0833061i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 73.1674i | 1.03053i | 0.857032 | + | 0.515263i | \(0.172306\pi\) | ||||
−0.857032 | + | 0.515263i | \(0.827694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.0166 | + | 17.0166i | −0.233103 | + | 0.233103i | −0.813987 | − | 0.580883i | \(-0.802707\pi\) |
0.580883 | + | 0.813987i | \(0.302707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 45.8553 | + | 52.0023i | 0.611404 | + | 0.693364i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 32.1396i | − | 0.417397i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.15129i | − | 0.0272315i | −0.999907 | − | 0.0136157i | \(-0.995666\pi\) | ||
0.999907 | − | 0.0136157i | \(-0.00433416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −67.5069 | −0.833419 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −76.4850 | −0.921506 | −0.460753 | − | 0.887528i | \(-0.652421\pi\) | ||||
−0.460753 | + | 0.887528i | \(0.652421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.6716 | − | 44.1134i | −0.196136 | − | 0.518982i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −48.6470 | − | 48.6470i | −0.559161 | − | 0.559161i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 38.7296 | 0.435164 | 0.217582 | − | 0.976042i | \(-0.430183\pi\) | ||||
0.217582 | + | 0.976042i | \(0.430183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −114.319 | − | 114.319i | −1.25626 | − | 1.25626i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 65.5810 | 0.705172 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 94.6543 | − | 35.7722i | 0.996361 | − | 0.376550i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.53929 | − | 8.53929i | 0.0880339 | − | 0.0880339i | −0.661718 | − | 0.749752i | \(-0.730173\pi\) |
0.749752 | + | 0.661718i | \(0.230173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.90055 | + | 3.90055i | 0.0393995 | + | 0.0393995i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −65.0118 | − | 65.0118i | −0.643681 | − | 0.643681i | 0.307777 | − | 0.951458i | \(-0.400415\pi\) |
−0.951458 | + | 0.307777i | \(0.900415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32.9039 | + | 32.9039i | −0.319456 | + | 0.319456i | −0.848558 | − | 0.529102i | \(-0.822529\pi\) |
0.529102 | + | 0.848558i | \(0.322529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −98.9176 | + | 37.3834i | −0.942073 | + | 0.356033i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.9537 | 0.186484 | 0.0932418 | − | 0.995643i | \(-0.470277\pi\) | ||||
0.0932418 | + | 0.995643i | \(0.470277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −31.4162 | − | 31.4162i | −0.288222 | − | 0.288222i | 0.548155 | − | 0.836377i | \(-0.315330\pi\) |
−0.836377 | + | 0.548155i | \(0.815330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 181.161 | 1.63208 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −48.1807 | − | 48.1807i | −0.426378 | − | 0.426378i | 0.461014 | − | 0.887393i | \(-0.347486\pi\) |
−0.887393 | + | 0.461014i | \(0.847486\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.18121 | + | 13.7096i | 0.0450540 | + | 0.119214i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.7482 | 0.237164 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 71.9267 | 0.604426 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 103.238i | − | 0.853210i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.27939i | − | 0.0266617i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −119.469 | + | 36.7727i | −0.955750 | + | 0.294181i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −165.164 | + | 165.164i | −1.30051 | + | 1.30051i | −0.372456 | + | 0.928050i | \(0.621484\pi\) |
−0.928050 | + | 0.372456i | \(0.878516\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.5524i | 0.205832i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9705 | + | 10.9705i | −0.0837444 | + | 0.0837444i | −0.747738 | − | 0.663994i | \(-0.768860\pi\) |
0.663994 | + | 0.747738i | \(0.268860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 154.333i | 1.16040i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 58.8185 | − | 130.286i | 0.435693 | − | 0.965079i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 122.401 | + | 122.401i | 0.893436 | + | 0.893436i | 0.994845 | − | 0.101408i | \(-0.0323349\pi\) |
−0.101408 | + | 0.994845i | \(0.532335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 163.514 | − | 163.514i | 1.17636 | − | 1.17636i | 0.195693 | − | 0.980665i | \(-0.437305\pi\) |
0.980665 | − | 0.195693i | \(-0.0626955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 130.978 | − | 130.978i | 0.928925 | − | 0.928925i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 63.1774 | + | 63.1774i | 0.441800 | + | 0.441800i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 116.026 | − | 43.8492i | 0.800181 | − | 0.302408i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 25.3936i | − | 0.172745i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 182.956 | − | 182.956i | 1.22789 | − | 1.22789i | 0.263134 | − | 0.964759i | \(-0.415244\pi\) |
0.964759 | − | 0.263134i | \(-0.0847562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 100.104i | − | 0.662938i | −0.943466 | − | 0.331469i | \(-0.892456\pi\) | ||
0.943466 | − | 0.331469i | \(-0.107544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.72923 | + | 8.72923i | −0.0570538 | + | 0.0570538i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −48.6509 | + | 107.764i | −0.313877 | + | 0.695251i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27.8875i | 0.177627i | 0.996048 | + | 0.0888136i | \(0.0283076\pi\) | ||||
−0.996048 | + | 0.0888136i | \(0.971692\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 275.159i | − | 1.73056i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.3535 | −0.138841 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 122.177 | 0.749552 | 0.374776 | − | 0.927115i | \(-0.377720\pi\) | ||||
0.374776 | + | 0.927115i | \(0.377720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 54.6658 | − | 20.6596i | 0.331308 | − | 0.125209i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 102.217 | + | 102.217i | 0.612078 | + | 0.612078i | 0.943487 | − | 0.331409i | \(-0.107524\pi\) |
−0.331409 | + | 0.943487i | \(0.607524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 280.439 | 1.65940 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.7303 | − | 18.7303i | −0.109534 | − | 0.109534i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −144.968 | −0.837968 | −0.418984 | − | 0.907994i | \(-0.637614\pi\) | ||||
−0.418984 | + | 0.907994i | \(0.637614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.9524 | − | 190.276i | 0.0682992 | − | 1.08729i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 151.810 | − | 151.810i | 0.857682 | − | 0.857682i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −71.1438 | − | 71.1438i | −0.397451 | − | 0.397451i | 0.479882 | − | 0.877333i | \(-0.340680\pi\) |
−0.877333 | + | 0.479882i | \(0.840680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 192.954 | + | 192.954i | 1.06604 | + | 1.06604i | 0.997659 | + | 0.0683832i | \(0.0217841\pi\) |
0.0683832 | + | 0.997659i | \(0.478216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.5717 | + | 33.5717i | −0.183452 | + | 0.183452i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −134.393 | + | 297.687i | −0.726449 | + | 1.60912i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.7496 | −0.212565 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 154.167 | + | 154.167i | 0.815696 | + | 0.815696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −209.558 | −1.09716 | −0.548581 | − | 0.836097i | \(-0.684832\pi\) | ||||
−0.548581 | + | 0.836097i | \(0.684832\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −90.2693 | − | 90.2693i | −0.467717 | − | 0.467717i | 0.433457 | − | 0.901174i | \(-0.357293\pi\) |
−0.901174 | + | 0.433457i | \(0.857293\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 120.959 | − | 267.929i | 0.620302 | − | 1.37400i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −67.8338 | −0.344334 | −0.172167 | − | 0.985068i | \(-0.555077\pi\) | ||||
−0.172167 | + | 0.985068i | \(0.555077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −278.771 | −1.40086 | −0.700430 | − | 0.713721i | \(-0.747009\pi\) | ||||
−0.700430 | + | 0.713721i | \(0.747009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 302.495i | − | 1.50495i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 189.180i | 0.931922i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.38876 | + | 2.43280i | 0.0262866 | + | 0.0118673i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.71288 | − | 2.71288i | 0.0131057 | − | 0.0131057i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 85.2908i | − | 0.408090i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.5489 | − | 26.5489i | 0.125824 | − | 0.125824i | −0.641391 | − | 0.767215i | \(-0.721642\pi\) |
0.767215 | + | 0.641391i | \(0.221642\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 202.914i | − | 0.952648i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −43.6314 | − | 19.6977i | −0.202937 | − | 0.0916174i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −127.517 | − | 127.517i | −0.587635 | − | 0.587635i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 47.1918 | − | 47.1918i | 0.215488 | − | 0.215488i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −141.388 | + | 141.388i | −0.639763 | + | 0.639763i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 90.1705 | + | 90.1705i | 0.404352 | + | 0.404352i | 0.879764 | − | 0.475412i | \(-0.157701\pi\) |
−0.475412 | + | 0.879764i | \(0.657701\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.6418 | + | 24.5430i | 0.0961860 | + | 0.109080i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 346.057i | − | 1.52448i | −0.647294 | − | 0.762240i | \(-0.724100\pi\) | ||
0.647294 | − | 0.762240i | \(-0.275900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73.4761 | − | 73.4761i | 0.320856 | − | 0.320856i | −0.528239 | − | 0.849096i | \(-0.677148\pi\) |
0.849096 | + | 0.528239i | \(0.177148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 89.1323i | 0.385854i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −86.7985 | + | 86.7985i | −0.372526 | + | 0.372526i | −0.868396 | − | 0.495871i | \(-0.834849\pi\) |
0.495871 | + | 0.868396i | \(0.334849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 118.061 | + | 312.392i | 0.502385 | + | 1.32933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.96613i | 0.0251736i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 204.791i | − | 0.856868i | −0.903573 | − | 0.428434i | \(-0.859065\pi\) | ||
0.903573 | − | 0.428434i | \(-0.140935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 98.8804 | 0.410292 | 0.205146 | − | 0.978731i | \(-0.434233\pi\) | ||||
0.205146 | + | 0.978731i | \(0.434233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −70.0893 | −0.288433 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 41.7272 | + | 18.8381i | 0.170315 | + | 0.0768902i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −303.376 | − | 303.376i | −1.22824 | − | 1.22824i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 212.115 | 0.851867 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 38.3371 | + | 38.3371i | 0.152737 | + | 0.152737i | 0.779339 | − | 0.626602i | \(-0.215555\pi\) |
−0.626602 | + | 0.779339i | \(0.715555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3534 | 0.0488277 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 46.2350 | + | 122.339i | 0.181314 | + | 0.479762i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 166.481 | − | 166.481i | 0.647785 | − | 0.647785i | −0.304672 | − | 0.952457i | \(-0.598547\pi\) |
0.952457 | + | 0.304672i | \(0.0985468\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −352.252 | − | 352.252i | −1.36005 | − | 1.36005i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.9594 | − | 22.9594i | −0.0879671 | − | 0.0879671i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −78.7097 | + | 78.7097i | −0.299276 | + | 0.299276i | −0.840730 | − | 0.541454i | \(-0.817874\pi\) |
0.541454 | + | 0.840730i | \(0.317874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 452.147 | + | 204.126i | 1.70622 | + | 0.770285i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −107.408 | −0.402279 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 98.2650 | + | 98.2650i | 0.365297 | + | 0.365297i | 0.865759 | − | 0.500461i | \(-0.166836\pi\) |
−0.500461 | + | 0.865759i | \(0.666836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −115.967 | −0.427922 | −0.213961 | − | 0.976842i | \(-0.568637\pi\) | ||||
−0.213961 | + | 0.976842i | \(0.568637\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 317.040 | + | 317.040i | 1.16132 | + | 1.16132i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.60535 | + | 105.154i | −0.0240195 | + | 0.382378i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −340.610 | −1.22964 | −0.614819 | − | 0.788668i | \(-0.710771\pi\) | ||||
−0.614819 | + | 0.788668i | \(0.710771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.9516 | 0.110938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 103.541i | 0.368474i | 0.982882 | + | 0.184237i | \(0.0589814\pi\) | ||||
−0.982882 | + | 0.184237i | \(0.941019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 561.986i | − | 1.98582i | −0.118887 | − | 0.992908i | \(-0.537932\pi\) | ||
0.118887 | − | 0.992908i | \(-0.462068\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −262.504 | + | 99.2066i | −0.921065 | + | 0.348093i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.37651 | + | 6.37651i | −0.0222178 | + | 0.0222178i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 200.043i | 0.692189i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.6819 | + | 23.6819i | −0.0813811 | + | 0.0813811i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.90920i | − | 0.00651604i | −0.999995 | − | 0.00325802i | \(-0.998963\pi\) | ||
0.999995 | − | 0.00325802i | \(-0.00103706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 136.837 | + | 362.076i | 0.463855 | + | 1.22737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −85.1986 | − | 85.1986i | −0.286864 | − | 0.286864i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43.9406 | − | 43.9406i | 0.146959 | − | 0.146959i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 51.6289 | − | 51.6289i | 0.171525 | − | 0.171525i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 180.296 | + | 180.296i | 0.595037 | + | 0.595037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.2607 | − | 80.0707i | −0.0992154 | − | 0.262527i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 465.516i | 1.51634i | 0.652058 | + | 0.758169i | \(0.273906\pi\) | ||||
−0.652058 | + | 0.758169i | \(0.726094\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 91.2520 | − | 91.2520i | 0.295314 | − | 0.295314i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 212.375i | − | 0.682879i | −0.939904 | − | 0.341439i | \(-0.889086\pi\) | ||
0.939904 | − | 0.341439i | \(-0.110914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −46.0307 | + | 46.0307i | −0.147063 | + | 0.147063i | −0.776805 | − | 0.629742i | \(-0.783161\pi\) |
0.629742 | + | 0.776805i | \(0.283161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −46.6851 | + | 17.6435i | −0.148207 | + | 0.0560110i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 430.649i | − | 1.35851i | −0.733901 | − | 0.679257i | \(-0.762302\pi\) | ||
0.733901 | − | 0.679257i | \(-0.237698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 104.548i | − | 0.327738i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.3375 | −0.172391 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 190.876 | 0.590948 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 350.534 | + | 397.524i | 1.07857 | + | 1.22315i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 87.1261 | + | 87.1261i | 0.266441 | + | 0.266441i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −509.353 | −1.54819 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.70469 | − | 3.70469i | −0.0111924 | − | 0.0111924i | 0.701488 | − | 0.712681i | \(-0.252519\pi\) |
−0.712681 | + | 0.701488i | \(0.752519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 85.5005 | 0.256758 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 497.065 | + | 224.404i | 1.48378 | + | 0.669862i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −226.237 | + | 226.237i | −0.671327 | + | 0.671327i | −0.958022 | − | 0.286695i | \(-0.907443\pi\) |
0.286695 | + | 0.958022i | \(0.407443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 133.619 | + | 133.619i | 0.394156 | + | 0.394156i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 70.4709 | + | 70.4709i | 0.206659 | + | 0.206659i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 214.853 | − | 214.853i | 0.626394 | − | 0.626394i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.3690 | − | 38.0207i | −0.0416492 | − | 0.110205i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −231.886 | −0.668259 | −0.334130 | − | 0.942527i | \(-0.608442\pi\) | ||||
−0.334130 | + | 0.942527i | \(0.608442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 205.898 | + | 205.898i | 0.589965 | + | 0.589965i | 0.937622 | − | 0.347657i | \(-0.113022\pi\) |
−0.347657 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −606.096 | −1.72677 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −299.539 | − | 299.539i | −0.848551 | − | 0.848551i | 0.141401 | − | 0.989952i | \(-0.454839\pi\) |
−0.989952 | + | 0.141401i | \(0.954839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 333.432 | + | 150.531i | 0.939246 | + | 0.424030i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −199.473 | −0.558749 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 108.844 | 0.303187 | 0.151593 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151593 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.5638i | 0.134526i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 286.310i | 0.788732i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.5375 | + | 112.555i | 0.116541 | + | 0.308371i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 271.565 | − | 271.565i | 0.739960 | − | 0.739960i | −0.232610 | − | 0.972570i | \(-0.574726\pi\) |
0.972570 | + | 0.232610i | \(0.0747265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.54774i | − | 0.00419442i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −535.025 | + | 535.025i | −1.44211 | + | 1.44211i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 205.735i | − | 0.551569i | −0.961220 | − | 0.275784i | \(-0.911062\pi\) | ||
0.961220 | − | 0.275784i | \(-0.0889376\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 331.321 | − | 101.981i | 0.883523 | − | 0.271950i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −371.875 | − | 371.875i | −0.986405 | − | 0.986405i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146.474 | − | 146.474i | 0.386475 | − | 0.386475i | −0.486953 | − | 0.873428i | \(-0.661892\pi\) |
0.873428 | + | 0.486953i | \(0.161892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 458.048 | − | 458.048i | 1.20223 | − | 1.20223i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 77.8502 | + | 77.8502i | 0.203264 | + | 0.203264i | 0.801397 | − | 0.598133i | \(-0.204090\pi\) |
−0.598133 | + | 0.801397i | \(0.704090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −146.464 | − | 66.1223i | −0.380426 | − | 0.171746i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5317i | 0.0323815i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 91.3251 | − | 91.3251i | 0.234769 | − | 0.234769i | −0.579911 | − | 0.814680i | \(-0.696913\pi\) |
0.814680 | + | 0.579911i | \(0.196913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.6463i | 0.0707067i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.4244 | − | 30.4244i | 0.0774158 | − | 0.0774158i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.80366 | − | 4.42594i | −0.0248194 | − | 0.0112049i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 181.720i | − | 0.457732i | −0.973458 | − | 0.228866i | \(-0.926498\pi\) | ||
0.973458 | − | 0.228866i | \(-0.0735017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 428.011i | − | 1.07271i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −559.201 | −1.39452 | −0.697258 | − | 0.716821i | \(-0.745597\pi\) | ||||
−0.697258 | + | 0.716821i | \(0.745597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 501.324 | 1.24398 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −138.885 | + | 307.637i | −0.342926 | + | 0.759597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 194.668 | + | 194.668i | 0.478301 | + | 0.478301i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 724.291 | 1.77088 | 0.885441 | − | 0.464752i | \(-0.153856\pi\) | ||||
0.885441 | + | 0.464752i | \(0.153856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −339.453 | − | 339.453i | −0.825919 | − | 0.825919i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −590.362 | −1.42945 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −157.356 | + | 348.551i | −0.379172 | + | 0.839882i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −453.471 | + | 453.471i | −1.08746 | + | 1.08746i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 76.4657 | + | 76.4657i | 0.182496 | + | 0.182496i | 0.792442 | − | 0.609947i | \(-0.208809\pi\) |
−0.609947 | + | 0.792442i | \(0.708809\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −470.702 | − | 470.702i | −1.11806 | − | 1.11806i | −0.992026 | − | 0.126030i | \(-0.959776\pi\) |
−0.126030 | − | 0.992026i | \(-0.540224\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 61.8165 | − | 61.8165i | 0.146138 | − | 0.146138i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −235.329 | − | 14.7824i | −0.553716 | − | 0.0347822i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 130.555 | 0.305749 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −175.209 | − | 175.209i | −0.408413 | − | 0.408413i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 185.108 | 0.429485 | 0.214742 | − | 0.976671i | \(-0.431109\pi\) | ||||
0.214742 | + | 0.976671i | \(0.431109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −354.954 | − | 354.954i | −0.819756 | − | 0.819756i | 0.166317 | − | 0.986072i | \(-0.446813\pi\) |
−0.986072 | + | 0.166317i | \(0.946813\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −321.774 | + | 121.606i | −0.739710 | + | 0.279555i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −59.3208 | −0.135745 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 155.719 | 0.354714 | 0.177357 | − | 0.984147i | \(-0.443245\pi\) | ||||
0.177357 | + | 0.984147i | \(0.443245\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 11.9847i | − | 0.0271763i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 728.951i | 1.64549i | 0.568412 | + | 0.822744i | \(0.307558\pi\) | ||||
−0.568412 | + | 0.822744i | \(0.692442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 79.6803 | − | 176.496i | 0.179057 | − | 0.396619i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −507.390 | + | 507.390i | −1.13510 | + | 1.13510i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 46.9465i | 0.104558i | 0.998633 | + | 0.0522790i | \(0.0166485\pi\) | ||||
−0.998633 | + | 0.0522790i | \(0.983351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52391 | − | 3.52391i | 0.00781355 | − | 0.00781355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 277.616i | 0.612839i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −756.161 | + | 285.772i | −1.66189 | + | 0.628070i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −227.434 | − | 227.434i | −0.497667 | − | 0.497667i | 0.413044 | − | 0.910711i | \(-0.364466\pi\) |
−0.910711 | + | 0.413044i | \(0.864466\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 190.670 | − | 190.670i | 0.415403 | − | 0.415403i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −265.869 | + | 265.869i | −0.576722 | + | 0.576722i | −0.933999 | − | 0.357277i | \(-0.883705\pi\) |
0.357277 | + | 0.933999i | \(0.383705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.16661 | + | 1.16661i | 0.00251968 | + | 0.00251968i | 0.708366 | − | 0.705846i | \(-0.249433\pi\) |
−0.705846 | + | 0.708366i | \(0.749433\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 134.923 | − | 298.860i | 0.290157 | − | 0.642711i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 632.343i | 1.35405i | 0.735958 | + | 0.677027i | \(0.236732\pi\) | ||||
−0.735958 | + | 0.677027i | \(0.763268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −588.175 | + | 588.175i | −1.25411 | + | 1.25411i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 77.3400i | − | 0.164204i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.5322 | + | 28.5322i | −0.0603217 | + | 0.0603217i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7187 | − | 504.947i | 0.0667762 | − | 1.06305i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 129.864i | − | 0.272252i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 552.415i | 1.15327i | 0.817003 | + | 0.576633i | \(0.195634\pi\) | ||||
−0.817003 | + | 0.576633i | \(0.804366\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1384.85 | 2.87912 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 61.9926 | 0.128349 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.3463 | − | 56.4828i | −0.0440129 | − | 0.116459i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 285.326 | + | 285.326i | 0.585886 | + | 0.585886i | 0.936515 | − | 0.350629i | \(-0.114032\pi\) |
−0.350629 | + | 0.936515i | \(0.614032\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −338.832 | −0.692908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 617.833 | + | 617.833i | 1.25831 | + | 1.25831i | 0.951897 | + | 0.306418i | \(0.0991305\pi\) |
0.306418 | + | 0.951897i | \(0.400870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 233.974 | 0.474592 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 25.8001 | − | 9.75048i | 0.0521213 | − | 0.0196979i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −394.550 | + | 394.550i | −0.793862 | + | 0.793862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −430.585 | − | 430.585i | −0.862895 | − | 0.862895i | 0.128778 | − | 0.991673i | \(-0.458894\pi\) |
−0.991673 | + | 0.128778i | \(0.958894\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −283.477 | − | 283.477i | −0.565823 | − | 0.565823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −102.108 | + | 102.108i | −0.202998 | + | 0.202998i | −0.801283 | − | 0.598285i | \(-0.795849\pi\) |
0.598285 | + | 0.801283i | \(0.295849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −430.018 | + | 162.514i | −0.851521 | + | 0.321811i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −777.737 | −1.53400 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 350.381 | + | 350.381i | 0.688372 | + | 0.688372i | 0.961872 | − | 0.273500i | \(-0.0881813\pi\) |
−0.273500 | + | 0.961872i | \(0.588181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −183.521 | −0.359141 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 409.121 | + | 409.121i | 0.797507 | + | 0.797507i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 82.2523 | + | 217.642i | 0.159713 | + | 0.422606i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 281.489 | 0.544466 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 402.039 | 0.774642 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 89.0292i | − | 0.170881i | −0.996343 | − | 0.0854407i | \(-0.972770\pi\) | ||
0.996343 | − | 0.0854407i | \(-0.0272298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 399.222i | 0.763331i | 0.924300 | + | 0.381666i | \(0.124649\pi\) | ||||
−0.924300 | + | 0.381666i | \(0.875351\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −33.1473 | + | 527.690i | −0.0631378 | + | 1.00512i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −157.710 | + | 157.710i | −0.299260 | + | 0.299260i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 520.408i | 0.983758i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 71.6480 | − | 71.6480i | 0.134930 | − | 0.134930i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 25.0688i | − | 0.0470334i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.0518 | − | 90.9316i | 0.0767323 | − | 0.169966i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 197.302 | + | 197.302i | 0.367415 | + | 0.367415i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.2870 | − | 27.2870i | 0.0506252 | − | 0.0506252i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −151.552 | + | 151.552i | −0.280133 | + | 0.280133i | −0.833162 | − | 0.553029i | \(-0.813472\pi\) |
0.553029 | + | 0.833162i | \(0.313472\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −535.116 | − | 535.116i | −0.985480 | − | 0.985480i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −207.801 | + | 78.5333i | −0.381287 | + | 0.144098i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 327.523i | − | 0.598762i | −0.954134 | − | 0.299381i | \(-0.903220\pi\) | ||
0.954134 | − | 0.299381i | \(-0.0967802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.8445 | + | 15.8445i | −0.0288607 | + | 0.0288607i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 502.039i | 0.911141i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6006 | − | 11.6006i | 0.0209777 | − | 0.0209777i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 372.710 | − | 825.570i | 0.671550 | − | 1.48751i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 609.704i | 1.09462i | 0.836930 | + | 0.547311i | \(0.184348\pi\) | ||||
−0.836930 | + | 0.547311i | \(0.815652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 202.976i | 0.363105i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 110.237 | 0.196501 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −104.576 | −0.185748 | −0.0928738 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928738 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −318.690 | + | 120.441i | −0.564053 | + | 0.213169i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −364.026 | − | 364.026i | −0.642021 | − | 0.642021i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 153.954 | 0.270569 | 0.135284 | − | 0.990807i | \(-0.456805\pi\) | ||||
0.135284 | + | 0.990807i | \(0.456805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −475.501 | − | 475.501i | −0.832751 | − | 0.832751i | 0.155141 | − | 0.987892i | \(-0.450417\pi\) |
−0.987892 | + | 0.155141i | \(0.950417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 581.164 | 1.01425 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 73.1359 | + | 4.59410i | 0.127193 | + | 0.00798974i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 430.563 | − | 430.563i | 0.746210 | − | 0.746210i | −0.227555 | − | 0.973765i | \(-0.573073\pi\) |
0.973765 | + | 0.227555i | \(0.0730731\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 250.343 | + | 250.343i | 0.432371 | + | 0.432371i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −412.440 | − | 412.440i | −0.709879 | − | 0.709879i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 295.676 | − | 295.676i | 0.507163 | − | 0.507163i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 57.0877 | − | 126.452i | 0.0975858 | − | 0.216157i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8014 | 0.0422512 | 0.0211256 | − | 0.999777i | \(-0.493275\pi\) | ||||
0.0211256 | + | 0.999777i | \(0.493275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −338.399 | − | 338.399i | −0.574531 | − | 0.574531i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 188.123 | 0.318312 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 714.962 | + | 714.962i | 1.20567 | + | 1.20567i | 0.972416 | + | 0.233255i | \(0.0749375\pi\) |
0.233255 | + | 0.972416i | \(0.425062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 147.978 | − | 327.779i | 0.248703 | − | 0.550888i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 773.113 | 1.29500 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −898.559 | −1.50010 | −0.750049 | − | 0.661382i | \(-0.769970\pi\) | ||||
−0.750049 | + | 0.661382i | \(0.769970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 498.405i | − | 0.829293i | −0.909983 | − | 0.414646i | \(-0.863905\pi\) | ||
0.909983 | − | 0.414646i | \(-0.136095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 142.765i | − | 0.236758i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −470.469 | − | 212.397i | −0.777635 | − | 0.351070i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 476.327 | − | 476.327i | 0.784723 | − | 0.784723i | −0.195900 | − | 0.980624i | \(-0.562763\pi\) |
0.980624 | + | 0.195900i | \(0.0627629\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 524.651i | − | 0.861495i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1001.24 | − | 1001.24i | 1.63870 | − | 1.63870i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 294.722i | − | 0.480787i | −0.970676 | − | 0.240393i | \(-0.922724\pi\) | ||
0.970676 | − | 0.240393i | \(-0.0772764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.9446 | − | 6.74685i | −0.0243001 | − | 0.0109705i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −248.885 | − | 248.885i | −0.403379 | − | 0.403379i | 0.476043 | − | 0.879422i | \(-0.342071\pi\) |
−0.879422 | + | 0.476043i | \(0.842071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −320.358 | + | 320.358i | −0.517541 | + | 0.517541i | −0.916826 | − | 0.399286i | \(-0.869258\pi\) |
0.399286 | + | 0.916826i | \(0.369258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −59.2567 | + | 59.2567i | −0.0954214 | + | 0.0954214i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 208.847 | + | 208.847i | 0.335227 | + | 0.335227i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −78.2113 | + | 620.087i | −0.125138 | + | 0.992139i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 236.536i | 0.377250i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −435.658 | + | 435.658i | −0.692619 | + | 0.692619i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 110.857i | 0.175685i | 0.996134 | + | 0.0878423i | \(0.0279972\pi\) | ||||
−0.996134 | + | 0.0878423i | \(0.972003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −73.6276 | + | 73.6276i | −0.116315 | + | 0.116315i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 412.873 | + | 1092.47i | 0.650193 | + | 1.72043i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 194.117i | − | 0.304737i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 95.7673i | − | 0.149871i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −370.450 | −0.577926 | −0.288963 | − | 0.957340i | \(-0.593310\pi\) | ||||
−0.288963 | + | 0.957340i | \(0.593310\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −686.295 | −1.06733 | −0.533667 | − | 0.845695i | \(-0.679186\pi\) | ||||
−0.533667 | + | 0.845695i | \(0.679186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 121.002 | + | 54.6275i | 0.187601 | + | 0.0846938i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 499.985 | + | 499.985i | 0.772774 | + | 0.772774i | 0.978591 | − | 0.205817i | \(-0.0659851\pi\) |
−0.205817 | + | 0.978591i | \(0.565985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 326.258 | 0.502708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 353.641 | + | 353.641i | 0.543227 | + | 0.543227i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −599.129 | −0.917502 | −0.458751 | − | 0.888565i | \(-0.651703\pi\) | ||||
−0.458751 | + | 0.888565i | \(0.651703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.4238 | + | 72.5641i | 0.0418684 | + | 0.110785i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.2726 | − | 22.2726i | 0.0339005 | − | 0.0339005i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −55.5691 | − | 55.5691i | −0.0843233 | − | 0.0843233i | 0.663687 | − | 0.748010i | \(-0.268991\pi\) |
−0.748010 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3517 | − | 24.3517i | −0.0368407 | − | 0.0368407i | 0.688446 | − | 0.725287i | \(-0.258293\pi\) |
−0.725287 | + | 0.688446i | \(0.758293\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 392.109 | − | 392.109i | 0.591416 | − | 0.591416i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 703.315 | + | 317.517i | 1.05762 | + | 0.477470i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −72.7147 | −0.109018 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −250.069 | − | 250.069i | −0.373795 | − | 0.373795i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.1498 | −0.107526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −348.271 | − | 348.271i | −0.517490 | − | 0.517490i | 0.399321 | − | 0.916811i | \(-0.369246\pi\) |
−0.916811 | + | 0.399321i | \(0.869246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −472.717 | − | 536.086i | −0.700321 | − | 0.794201i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 780.155 | 1.15237 | 0.576185 | − | 0.817319i | \(-0.304541\pi\) | ||||
0.576185 | + | 0.817319i | \(0.304541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 92.0950 | 0.135633 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 959.715i | 1.40927i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 170.375i | − | 0.249451i | −0.992191 | − | 0.124725i | \(-0.960195\pi\) | ||
0.992191 | − | 0.124725i | \(-0.0398050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 809.616 | − | 305.974i | 1.18192 | − | 0.446677i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −203.770 | + | 203.770i | −0.296609 | + | 0.296609i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2103.41i | − | 3.05285i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.2626 | − | 51.2626i | 0.0741861 | − | 0.0741861i | −0.669040 | − | 0.743226i | \(-0.733295\pi\) |
0.743226 | + | 0.669040i | \(0.233295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.0668i | 0.0607025i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −408.747 | − | 1081.56i | −0.588125 | − | 1.55620i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.88633 | + | 7.88633i | 0.0113147 | + | 0.0113147i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 240.717 | − | 240.717i | 0.344374 | − | 0.344374i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −68.3903 | + | 68.3903i | −0.0975610 | + | 0.0975610i | −0.754203 | − | 0.656642i | \(-0.771976\pi\) |
0.656642 | + | 0.754203i | \(0.271976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −934.792 | − | 934.792i | −1.32972 | − | 1.32972i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −327.416 | − | 866.352i | −0.464420 | − | 1.22887i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 701.142i | − | 0.991714i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 815.622 | − | 815.622i | 1.15038 | − | 1.15038i | 0.163908 | − | 0.986476i | \(-0.447590\pi\) |
0.986476 | − | 0.163908i | \(-0.0524101\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.81577i | 0.00396030i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49.0133 | − | 49.0133i | 0.0687424 | − | 0.0687424i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 417.885 | − | 157.929i | 0.584454 | − | 0.220880i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 567.946i | 0.792114i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 125.050i | − | 0.173922i | −0.996212 | − | 0.0869612i | \(-0.972284\pi\) | ||
0.996212 | − | 0.0869612i | \(-0.0277156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −354.864 | −0.492183 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −274.224 | −0.379286 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.8804 | − | 618.958i | 0.0536282 | − | 0.853735i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −307.763 | − | 307.763i | −0.423333 | − | 0.423333i | 0.463016 | − | 0.886350i | \(-0.346767\pi\) |
−0.886350 | + | 0.463016i | \(0.846767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 801.940 | 1.10005 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −63.8535 | − | 63.8535i | −0.0873510 | − | 0.0873510i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 94.8581 | 0.129411 | 0.0647054 | − | 0.997904i | \(-0.479389\pi\) | ||||
0.0647054 | + | 0.997904i | \(0.479389\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −115.722 | − | 52.2434i | −0.157444 | − | 0.0710795i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 325.049 | − | 325.049i | 0.441044 | − | 0.441044i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 761.284 | + | 761.284i | 1.03015 | + | 1.03015i | 0.999531 | + | 0.0306228i | \(0.00974907\pi\) |
0.0306228 | + | 0.999531i | \(0.490251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 841.348 | + | 841.348i | 1.13542 | + | 1.13542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −700.467 | + | 700.467i | −0.942754 | + | 0.942754i | −0.998448 | − | 0.0556935i | \(-0.982263\pi\) |
0.0556935 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −457.348 | − | 1210.16i | −0.613890 | − | 1.62437i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 100.110 | 0.134016 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 107.599 | + | 107.599i | 0.143657 | + | 0.143657i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 268.325 | 0.357291 | 0.178645 | − | 0.983914i | \(-0.442829\pi\) | ||||
0.178645 | + | 0.983914i | \(0.442829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −106.320 | − | 106.320i | −0.141195 | − | 0.141195i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −456.184 | − | 205.948i | −0.604217 | − | 0.272779i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 777.969 | 1.02770 | 0.513850 | − | 0.857880i | \(-0.328219\pi\) | ||||
0.513850 | + | 0.857880i | \(0.328219\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.2596 | −0.0451378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1058.98i | 1.39156i | 0.718254 | + | 0.695781i | \(0.244942\pi\) | ||||
−0.718254 | + | 0.695781i | \(0.755058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 338.819i | − | 0.444062i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.8211 | + | 57.7392i | 0.0285243 | + | 0.0754760i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1160.49 | − | 1160.49i | 1.51302 | − | 1.51302i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 262.583i | 0.341461i | 0.985318 | + | 0.170730i | \(0.0546127\pi\) | ||||
−0.985318 | + | 0.170730i | \(0.945387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −461.699 | + | 461.699i | −0.598832 | + | 0.598832i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 405.962i | 0.525177i | 0.964908 | + | 0.262588i | \(0.0845761\pi\) | ||||
−0.964908 | + | 0.262588i | \(0.915424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 391.001 | + | 443.416i | 0.504518 | + | 0.572150i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 976.895 | + | 976.895i | 1.25727 | + | 1.25727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.9217 | + | 16.9217i | −0.0217224 | + | 0.0217224i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 218.044 | − | 218.044i | 0.279185 | − | 0.279185i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 501.496 | + | 501.496i | 0.640480 | + | 0.640480i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 127.087 | + | 57.3742i | 0.161894 | + | 0.0730882i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 107.060i | 0.136036i | 0.997684 | + | 0.0680181i | \(0.0216676\pi\) | ||||
−0.997684 | + | 0.0680181i | \(0.978332\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 218.285 | − | 218.285i | 0.276660 | − | 0.276660i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 519.622i | − | 0.656918i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −256.634 | + | 256.634i | −0.323624 | + | 0.323624i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1253.93 | − | 566.099i | −1.57728 | − | 0.712074i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 615.958i | − | 0.772846i | −0.922322 | − | 0.386423i | \(-0.873711\pi\) | ||
0.922322 | − | 0.386423i | \(-0.126289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 629.957i | 0.788432i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −50.6924 | −0.0632864 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 101.421 | 0.126303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.9889 | + | 101.867i | −0.0571290 | + | 0.126543i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −272.517 | − | 272.517i | −0.337692 | − | 0.337692i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −304.293 | −0.376135 | −0.188067 | − | 0.982156i | \(-0.560222\pi\) | ||||
−0.188067 | + | 0.982156i | \(0.560222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2059 | + | 20.2059i | 0.0249148 | + | 0.0249148i | 0.719454 | − | 0.694540i | \(-0.244392\pi\) |
−0.694540 | + | 0.719454i | \(0.744392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 321.610 | 0.395584 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 251.360 | − | 556.775i | 0.308418 | − | 0.683159i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 137.011 | − | 137.011i | 0.167700 | − | 0.167700i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 149.630 | + | 149.630i | 0.182699 | + | 0.182699i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 381.316 | + | 381.316i | 0.464453 | + | 0.464453i | 0.900112 | − | 0.435659i | \(-0.143485\pi\) |
−0.435659 | + | 0.900112i | \(0.643485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −420.324 | + | 420.324i | −0.510721 | + | 0.510721i | −0.914747 | − | 0.404026i | \(-0.867610\pi\) |
0.404026 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.3185 | − | 291.622i | 0.0222043 | − | 0.353482i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 844.006 | 1.02056 | 0.510281 | − | 0.860007i | \(-0.329541\pi\) | ||||
0.510281 | + | 0.860007i | \(0.329541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −222.833 | − | 222.833i | −0.268798 | − | 0.268798i | 0.559818 | − | 0.828616i | \(-0.310871\pi\) |
−0.828616 | + | 0.559818i | \(0.810871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 944.609 | 1.13671 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 61.0668 | + | 61.0668i | 0.0733095 | + | 0.0733095i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 676.111 | − | 255.519i | 0.809714 | − | 0.306011i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −676.067 | −0.807726 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 554.445 | 0.660841 | 0.330420 | − | 0.943834i | \(-0.392809\pi\) | ||||
0.330420 | + | 0.943834i | \(0.392809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 225.607i | − | 0.268260i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 287.150i | − | 0.340628i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 576.960 | − | 1277.99i | 0.682793 | − | 1.51242i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 556.705 | − | 556.705i | 0.657267 | − | 0.657267i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1558.55i | 1.83575i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 135.394 | − | 135.394i | 0.159100 | − | 0.159100i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 431.993i | − | 0.506440i | −0.967409 | − | 0.253220i | \(-0.918510\pi\) | ||
0.967409 | − | 0.253220i | \(-0.0814896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −123.891 | + | 46.8215i | −0.144902 | + | 0.0547620i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 457.844 | + | 457.844i | 0.534241 | + | 0.534241i | 0.921831 | − | 0.387591i | \(-0.126693\pi\) |
−0.387591 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −822.277 | + | 822.277i | −0.957249 | + | 0.957249i | −0.999123 | − | 0.0418737i | \(-0.986667\pi\) |
0.0418737 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.6839 | − | 17.6839i | 0.0205388 | − | 0.0205388i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 132.089 | + | 132.089i | 0.153058 | + | 0.153058i | 0.779482 | − | 0.626424i | \(-0.215482\pi\) |
−0.626424 | + | 0.779482i | \(0.715482\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −298.251 | + | 660.638i | −0.344798 | + | 0.763744i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 554.775i | − | 0.639879i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.41098 | + | 6.41098i | −0.00737742 | + | 0.00737742i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2312.37i | − | 2.65485i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.1769 | + | 11.1769i | −0.0128029 | + | 0.0128029i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −842.520 | − | 445.932i | −0.962880 | − | 0.509637i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 363.488i | 0.414468i | 0.978291 | + | 0.207234i | \(0.0664461\pi\) | ||||
−0.978291 | + | 0.207234i | \(0.933554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.29476i | 0.00602362i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −242.827 | −0.275627 | −0.137813 | − | 0.990458i | \(-0.544007\pi\) | ||||
−0.137813 | + | 0.990458i | \(0.544007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1629.94 | −1.84592 | −0.922959 | − | 0.384899i | \(-0.874236\pi\) | ||||
−0.922959 | + | 0.384899i | \(0.874236\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −379.489 | − | 1004.14i | −0.428801 | − | 1.13462i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 196.533 | + | 196.533i | 0.221570 | + | 0.221570i | 0.809160 | − | 0.587589i | \(-0.199923\pi\) |
−0.587589 | + | 0.809160i | \(0.699923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1781.27 | −2.00368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 201.175 | + | 201.175i | 0.225786 | + | 0.225786i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1351.70 | −1.51366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −470.578 | + | 177.843i | −0.525786 | + | 0.198707i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −121.860 | + | 121.860i | −0.135853 | + | 0.135853i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −414.806 | − | 414.806i | −0.461408 | − | 0.461408i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 661.707 | + | 661.707i | 0.734414 | + | 0.734414i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −143.182 | + | 143.182i | −0.158562 | + | 0.158562i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1276.29 | − | 482.340i | 1.41026 | − | 0.532972i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 188.488 | 0.207814 | 0.103907 | − | 0.994587i | \(-0.466866\pi\) | ||||
0.103907 | + | 0.994587i | \(0.466866\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 85.0925 | + | 85.0925i | 0.0936112 | + | 0.0936112i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1051.06 | 1.15374 | 0.576870 | − | 0.816836i | \(-0.304274\pi\) | ||||
0.576870 | + | 0.816836i | \(0.304274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 227.930 | + | 227.930i | 0.249650 | + | 0.249650i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 83.9216 | + | 222.059i | 0.0917176 | + | 0.242687i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −118.315 | −0.129024 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 158.471 | 0.172439 | 0.0862195 | − | 0.996276i | \(-0.472521\pi\) | ||||
0.0862195 | + | 0.996276i | \(0.472521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1291.01i | − | 1.40175i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1551.15i | − | 1.68055i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1080.10 | + | 1224.89i | 1.16768 | + | 1.32420i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.0673 | − | 43.0673i | 0.0464588 | − | 0.0464588i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1081.59i | 1.16425i | 0.813100 | + | 0.582124i | \(0.197778\pi\) | ||||
−0.813100 | + | 0.582124i | \(0.802222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −131.031 | + | 131.031i | −0.140743 | + | 0.140743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 588.978i | 0.631273i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −81.7787 | + | 181.144i | −0.0874639 | + | 0.193736i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 484.345 | + | 484.345i | 0.516910 | + | 0.516910i | 0.916635 | − | 0.399725i | \(-0.130894\pi\) |
−0.399725 | + | 0.916635i | \(0.630894\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 127.656 | − | 127.656i | 0.135949 | − | 0.135949i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −555.577 | + | 555.577i | −0.590411 | + | 0.590411i | −0.937742 | − | 0.347331i | \(-0.887088\pi\) |
0.347331 | + | 0.937742i | \(0.387088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.45092 | − | 2.45092i | −0.00259907 | − | 0.00259907i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1019.73 | − | 385.381i | 1.07908 | − | 0.407811i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 476.289i | − | 0.502945i | −0.967864 | − | 0.251473i | \(-0.919085\pi\) | ||
0.967864 | − | 0.251473i | \(-0.0809149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 360.750 | − | 360.750i | 0.380137 | − | 0.380137i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1194.31i | 1.25585i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −80.9782 | + | 80.9782i | −0.0849719 | + | 0.0849719i | −0.748315 | − | 0.663343i | \(-0.769137\pi\) |
0.663343 | + | 0.748315i | \(0.269137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −431.134 | + | 954.980i | −0.451449 | + | 0.999979i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 289.943i | 0.302971i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1320.07i | 1.37651i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −401.801 | −0.418107 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.1170 | −0.0271205 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −597.083 | + | 225.652i | −0.618739 | + | 0.233837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 226.347 | + | 226.347i | 0.234072 | + | 0.234072i | 0.814390 | − | 0.580318i | \(-0.197072\pi\) |
−0.580318 | + | 0.814390i | \(0.697072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −529.355 | −0.546290 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 375.576 | + | 375.576i | 0.386793 | + | 0.386793i | 0.873542 | − | 0.486749i | \(-0.161817\pi\) |
−0.486749 | + | 0.873542i | \(0.661817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1763.47 | 1.81241 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −972.131 | − | 1102.45i | −0.997058 | − | 1.13072i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 201.023 | − | 201.023i | 0.205756 | − | 0.205756i | −0.596705 | − | 0.802461i | \(-0.703524\pi\) |
0.802461 | + | 0.596705i | \(0.203524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −115.417 | − | 115.417i | −0.117893 | − | 0.117893i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.1200 | + | 41.1200i | 0.0419164 | + | 0.0419164i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −536.933 | + | 536.933i | −0.546218 | + | 0.546218i | −0.925345 | − | 0.379126i | \(-0.876225\pi\) |
0.379126 | + | 0.925345i | \(0.376225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −139.558 | + | 309.126i | −0.141683 | + | 0.313834i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1412.58 | 1.43119 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.8445 | + | 19.8445i | 0.0200652 | + | 0.0200652i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1164.95 | −1.17553 | −0.587764 | − | 0.809032i | \(-0.699992\pi\) | ||||
−0.587764 | + | 0.809032i | \(0.699992\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.2742 | + | 10.2742i | 0.0103466 | + | 0.0103466i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −573.530 | + | 1270.39i | −0.576412 | + | 1.27678i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1493.41 | −1.49790 | −0.748950 | − | 0.662627i | \(-0.769442\pi\) | ||||
−0.748950 | + | 0.662627i | \(0.769442\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1867.56 | −1.86943 |
(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 | 640.3.t.b.353.7 | 44 | ||
4.3 | odd | 2 | 640.3.t.a.353.16 | 44 | |||
5.2 | odd | 4 | 640.3.i.b.97.16 | 44 | |||
8.3 | odd | 2 | 320.3.t.a.113.7 | 44 | |||
8.5 | even | 2 | 80.3.t.a.53.4 | yes | 44 | ||
16.3 | odd | 4 | 640.3.i.a.33.16 | 44 | |||
16.5 | even | 4 | 80.3.i.a.13.14 | ✓ | 44 | ||
16.11 | odd | 4 | 320.3.i.a.273.7 | 44 | |||
16.13 | even | 4 | 640.3.i.b.33.7 | 44 | |||
20.7 | even | 4 | 640.3.i.a.97.7 | 44 | |||
40.13 | odd | 4 | 400.3.i.b.357.9 | 44 | |||
40.27 | even | 4 | 320.3.i.a.177.16 | 44 | |||
40.29 | even | 2 | 400.3.t.b.293.19 | 44 | |||
40.37 | odd | 4 | 80.3.i.a.37.14 | yes | 44 | ||
80.27 | even | 4 | 320.3.t.a.17.7 | 44 | |||
80.37 | odd | 4 | 80.3.t.a.77.4 | yes | 44 | ||
80.53 | odd | 4 | 400.3.t.b.157.19 | 44 | |||
80.67 | even | 4 | 640.3.t.a.417.16 | 44 | |||
80.69 | even | 4 | 400.3.i.b.93.9 | 44 | |||
80.77 | odd | 4 | inner | 640.3.t.b.417.7 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.i.a.13.14 | ✓ | 44 | 16.5 | even | 4 | ||
80.3.i.a.37.14 | yes | 44 | 40.37 | odd | 4 | ||
80.3.t.a.53.4 | yes | 44 | 8.5 | even | 2 | ||
80.3.t.a.77.4 | yes | 44 | 80.37 | odd | 4 | ||
320.3.i.a.177.16 | 44 | 40.27 | even | 4 | |||
320.3.i.a.273.7 | 44 | 16.11 | odd | 4 | |||
320.3.t.a.17.7 | 44 | 80.27 | even | 4 | |||
320.3.t.a.113.7 | 44 | 8.3 | odd | 2 | |||
400.3.i.b.93.9 | 44 | 80.69 | even | 4 | |||
400.3.i.b.357.9 | 44 | 40.13 | odd | 4 | |||
400.3.t.b.157.19 | 44 | 80.53 | odd | 4 | |||
400.3.t.b.293.19 | 44 | 40.29 | even | 2 | |||
640.3.i.a.33.16 | 44 | 16.3 | odd | 4 | |||
640.3.i.a.97.7 | 44 | 20.7 | even | 4 | |||
640.3.i.b.33.7 | 44 | 16.13 | even | 4 | |||
640.3.i.b.97.16 | 44 | 5.2 | odd | 4 | |||
640.3.t.a.353.16 | 44 | 4.3 | odd | 2 | |||
640.3.t.a.417.16 | 44 | 80.67 | even | 4 | |||
640.3.t.b.353.7 | 44 | 1.1 | even | 1 | trivial | ||
640.3.t.b.417.7 | 44 | 80.77 | odd | 4 | inner |