Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.2 | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.d.749.2 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.70777 | + | 1.29149i | −0.902591 | + | 0.430498i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00081 | − | 1.73252i | 0.428686 | − | 0.247502i | −0.270100 | − | 0.962832i | \(-0.587057\pi\) |
0.698787 | + | 0.715330i | \(0.253724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.66408 | − | 6.99415i | 0.629342 | − | 0.777128i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.3770 | + | 7.14587i | −1.12518 | + | 0.649624i | −0.942719 | − | 0.333588i | \(-0.891741\pi\) |
−0.182464 | + | 0.983213i | \(0.558407\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.28062 | + | 3.04877i | 0.406202 | + | 0.234521i | 0.689156 | − | 0.724613i | \(-0.257981\pi\) |
−0.282955 | + | 0.959133i | \(0.591315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.7361 | 0.690360 | 0.345180 | − | 0.938536i | \(-0.387818\pi\) | ||||
0.345180 | + | 0.938536i | \(0.387818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.4795 | −1.23576 | −0.617882 | − | 0.786271i | \(-0.712009\pi\) | ||||
−0.617882 | + | 0.786271i | \(0.712009\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.88797 | + | 8.56679i | −0.280379 | + | 0.407942i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.3544 | − | 24.8625i | 0.624103 | − | 1.08098i | −0.364611 | − | 0.931160i | \(-0.618798\pi\) |
0.988714 | − | 0.149818i | \(-0.0478687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.30414 | + | 26.2537i | −0.233487 | + | 0.972360i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.3136 | − | 7.68660i | 0.459089 | − | 0.265055i | −0.252572 | − | 0.967578i | \(-0.581277\pi\) |
0.711661 | + | 0.702523i | \(0.247943\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.4920 | + | 32.0291i | −0.596517 | + | 1.03320i | 0.396814 | + | 0.917899i | \(0.370116\pi\) |
−0.993331 | + | 0.115298i | \(0.963218\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.2853 | − | 35.3342i | 0.735918 | − | 1.07073i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 46.7299i | 1.26297i | 0.775388 | + | 0.631485i | \(0.217554\pi\) | ||||
−0.775388 | + | 0.631485i | \(0.782446\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.2362 | − | 1.43548i | −0.467595 | − | 0.0368072i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17.1469 | − | 9.89974i | −0.418216 | − | 0.241457i | 0.276098 | − | 0.961130i | \(-0.410959\pi\) |
−0.694314 | + | 0.719672i | \(0.744292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.76655 | − | 2.75197i | 0.110850 | − | 0.0639992i | −0.443550 | − | 0.896250i | \(-0.646281\pi\) |
0.554400 | + | 0.832250i | \(0.312948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.15814 | − | 8.93416i | −0.109748 | − | 0.190089i | 0.805920 | − | 0.592024i | \(-0.201671\pi\) |
−0.915668 | + | 0.401935i | \(0.868338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.4968 | + | 32.0374i | −0.377485 | + | 0.653824i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.7788 | + | 15.1571i | −0.623113 | + | 0.297199i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −41.5607 | −0.784164 | −0.392082 | − | 0.919930i | \(-0.628245\pi\) | ||||
−0.392082 | + | 0.919930i | \(0.628245\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 63.5772 | − | 30.3237i | 1.11539 | − | 0.531994i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −58.5202 | − | 33.7866i | −0.991867 | − | 0.572655i | −0.0860352 | − | 0.996292i | \(-0.527420\pi\) |
−0.905832 | + | 0.423637i | \(0.860753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.5253 | − | 45.9431i | −0.434841 | − | 0.753166i | 0.562442 | − | 0.826837i | \(-0.309862\pi\) |
−0.997283 | + | 0.0736707i | \(0.976529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.87932 | − | 30.8012i | 0.0774496 | − | 0.488908i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.5426 | − | 15.9017i | −0.411084 | − | 0.237339i | 0.280172 | − | 0.959950i | \(-0.409609\pi\) |
−0.691255 | + | 0.722611i | \(0.742942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.75860 | + | 85.8606i | −0.0979507 | + | 1.24436i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.28568i | − | 0.0321927i | −0.999870 | − | 0.0160964i | \(-0.994876\pi\) | ||
0.999870 | − | 0.0160964i | \(-0.00512385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 86.2854i | − | 1.18199i | −0.806675 | − | 0.590996i | \(-0.798735\pi\) | ||
0.806675 | − | 0.590996i | \(-0.201265\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.7607 | + | 42.8867i | −0.321567 | + | 0.556970i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −58.4264 | − | 101.198i | −0.739575 | − | 1.28098i | −0.952687 | − | 0.303953i | \(-0.901693\pi\) |
0.213112 | − | 0.977028i | \(-0.431640\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16.8364 | − | 79.2309i | −0.207856 | − | 0.978159i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −65.2494 | − | 113.015i | −0.786137 | − | 1.36163i | −0.928317 | − | 0.371789i | \(-0.878744\pi\) |
0.142180 | − | 0.989841i | \(-0.454589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −26.1230 | + | 38.0080i | −0.300264 | + | 0.436873i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 75.3347i | − | 0.846457i | −0.906023 | − | 0.423229i | \(-0.860897\pi\) | ||
0.906023 | − | 0.423229i | \(-0.139103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.1282 | 0.232178 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.70677 | − | 110.610i | 0.0936212 | − | 1.18935i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.4829 | + | 14.1352i | −0.252401 | + | 0.145724i | −0.620863 | − | 0.783919i | \(-0.713218\pi\) |
0.368462 | + | 0.929643i | \(0.379884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.1251 | + | 127.041i | −0.203284 | + | 1.28325i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −110.083 | + | 63.5564i | −1.08993 | + | 0.629272i | −0.933558 | − | 0.358426i | \(-0.883313\pi\) |
−0.156373 | + | 0.987698i | \(0.549980\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −43.5261 | − | 25.1298i | −0.422583 | − | 0.243978i | 0.273599 | − | 0.961844i | \(-0.411786\pi\) |
−0.696182 | + | 0.717865i | \(0.745119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −151.704 | −1.41779 | −0.708897 | − | 0.705312i | \(-0.750807\pi\) | ||||
−0.708897 | + | 0.705312i | \(0.750807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −131.449 | −1.20595 | −0.602976 | − | 0.797759i | \(-0.706018\pi\) | ||||
−0.602976 | + | 0.797759i | \(0.706018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −60.3515 | − | 126.534i | −0.543707 | − | 1.13995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 45.7257 | − | 79.1993i | 0.404652 | − | 0.700878i | −0.589629 | − | 0.807674i | \(-0.700726\pi\) |
0.994281 | + | 0.106796i | \(0.0340592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 51.2335 | − | 19.6650i | 0.437893 | − | 0.168077i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.2178 | − | 20.3330i | 0.295948 | − | 0.170866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 41.6269 | − | 72.0999i | 0.344024 | − | 0.595867i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 59.2153 | + | 4.66119i | 0.481425 | + | 0.0378958i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 152.636i | 1.20186i | 0.799301 | + | 0.600931i | \(0.205203\pi\) | ||||
−0.799301 | + | 0.600931i | \(0.794797\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.35258 | + | 13.6077i | −0.0725006 | + | 0.105486i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 69.2312 | + | 39.9706i | 0.528482 | + | 0.305119i | 0.740398 | − | 0.672169i | \(-0.234637\pi\) |
−0.211916 | + | 0.977288i | \(0.567970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −70.4574 | + | 40.6786i | −0.529755 | + | 0.305854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −54.9029 | − | 95.0945i | −0.400751 | − | 0.694121i | 0.593066 | − | 0.805154i | \(-0.297917\pi\) |
−0.993817 | + | 0.111033i | \(0.964584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −96.4057 | + | 166.980i | −0.693566 | + | 1.20129i | 0.277096 | + | 0.960842i | \(0.410628\pi\) |
−0.970662 | + | 0.240449i | \(0.922705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.5055 | + | 17.5300i | 0.180890 | + | 0.124326i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −87.1444 | −0.609402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.70901 | − | 110.638i | 0.0592450 | − | 0.752642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 153.314 | + | 88.5160i | 1.02895 | + | 0.594067i | 0.916685 | − | 0.399610i | \(-0.130855\pi\) |
0.112270 | + | 0.993678i | \(0.464188\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 61.7618 | + | 106.975i | 0.409018 | + | 0.708441i | 0.994780 | − | 0.102043i | \(-0.0325379\pi\) |
−0.585762 | + | 0.810483i | \(0.699205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 66.4744 | − | 82.0843i | 0.434473 | − | 0.536499i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 204.764 | + | 118.221i | 1.30423 | + | 0.752997i | 0.981127 | − | 0.193366i | \(-0.0619406\pi\) |
0.323103 | + | 0.946364i | \(0.395274\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 112.537 | − | 53.6754i | 0.707779 | − | 0.337581i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 99.4766i | − | 0.617867i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 286.295i | 1.75641i | 0.478284 | + | 0.878205i | \(0.341259\pi\) | ||||
−0.478284 | + | 0.878205i | \(0.658741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9445 | − | 31.0808i | 0.107452 | − | 0.186113i | −0.807285 | − | 0.590161i | \(-0.799064\pi\) |
0.914737 | + | 0.404049i | \(0.132397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −65.9100 | − | 114.159i | −0.390000 | − | 0.675500i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −132.990 | + | 164.219i | −0.777719 | + | 0.960347i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −49.1670 | − | 85.1597i | −0.284202 | − | 0.492253i | 0.688213 | − | 0.725509i | \(-0.258395\pi\) |
−0.972415 | + | 0.233256i | \(0.925062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 202.095 | + | 15.9081i | 1.14178 | + | 0.0898761i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 312.477i | − | 1.74568i | −0.488004 | − | 0.872841i | \(-0.662275\pi\) | ||
0.488004 | − | 0.872841i | \(-0.337725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5133 | 0.0801838 | 0.0400919 | − | 0.999196i | \(-0.487235\pi\) | ||||
0.0400919 | + | 0.999196i | \(0.487235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 131.160 | + | 90.1463i | 0.716720 | + | 0.492603i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −145.258 | + | 83.8648i | −0.776782 | + | 0.448475i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.5675 | + | 89.7043i | 0.140569 | + | 0.474626i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −224.881 | + | 129.835i | −1.17739 | + | 0.679766i | −0.955409 | − | 0.295285i | \(-0.904585\pi\) |
−0.221980 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 205.486 | + | 118.638i | 1.06470 | + | 0.614703i | 0.926728 | − | 0.375734i | \(-0.122609\pi\) |
0.137969 | + | 0.990437i | \(0.455943\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 152.304 | 0.773117 | 0.386558 | − | 0.922265i | \(-0.373664\pi\) | ||||
0.386558 | + | 0.922265i | \(0.373664\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −382.914 | −1.92419 | −0.962096 | − | 0.272711i | \(-0.912080\pi\) | ||||
−0.962096 | + | 0.272711i | \(0.912080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 95.1162 | + | 7.48716i | 0.473215 | + | 0.0372495i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.6343 | − | 46.1320i | 0.131203 | − | 0.227251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −92.5878 | − | 241.220i | −0.447284 | − | 1.16531i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 290.606 | − | 167.782i | 1.39046 | − | 0.802782i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31.8015 | − | 55.0818i | 0.150718 | − | 0.261051i | −0.780774 | − | 0.624814i | \(-0.785175\pi\) |
0.931492 | + | 0.363763i | \(0.118508\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.95195 | + | 6.18912i | 0.0138589 | + | 0.0290569i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 128.151i | 0.590557i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 111.437 | + | 233.641i | 0.508846 | + | 1.06686i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 61.9741 | + | 35.7807i | 0.280426 | + | 0.161904i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.39692 | − | 0.806511i | 0.00626421 | − | 0.00361664i | −0.496865 | − | 0.867828i | \(-0.665515\pi\) |
0.503129 | + | 0.864211i | \(0.332182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −194.272 | − | 336.488i | −0.855822 | − | 1.48233i | −0.875880 | − | 0.482529i | \(-0.839718\pi\) |
0.0200581 | − | 0.999799i | \(-0.493615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 136.247 | − | 235.987i | 0.594965 | − | 1.03051i | −0.398586 | − | 0.917131i | \(-0.630499\pi\) |
0.993552 | − | 0.113380i | \(-0.0361676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.6583 | − | 148.106i | 0.0504688 | − | 0.641151i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −264.865 | −1.13676 | −0.568380 | − | 0.822766i | \(-0.692430\pi\) | ||||
−0.568380 | + | 0.822766i | \(0.692430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 288.902 | + | 198.563i | 1.21899 | + | 0.837817i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 155.390 | + | 89.7143i | 0.650166 | + | 0.375374i | 0.788520 | − | 0.615009i | \(-0.210848\pi\) |
−0.138354 | + | 0.990383i | \(0.544181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 141.807 | + | 245.617i | 0.588412 | + | 1.01916i | 0.994441 | + | 0.105299i | \(0.0335800\pi\) |
−0.406029 | + | 0.913860i | \(0.633087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 147.915 | + | 192.795i | 0.608705 | + | 0.793396i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −123.986 | − | 71.5836i | −0.501970 | − | 0.289812i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 322.639 | + | 221.751i | 1.29574 | + | 0.890565i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 429.903i | 1.71276i | 0.516345 | + | 0.856381i | \(0.327292\pi\) | ||||
−0.516345 | + | 0.856381i | \(0.672708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 410.298i | 1.62173i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −95.1538 | + | 164.811i | −0.370248 | + | 0.641289i | −0.989604 | − | 0.143822i | \(-0.954061\pi\) |
0.619355 | + | 0.785111i | \(0.287394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 80.9603 | + | 140.227i | 0.312588 | + | 0.541418i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.6479 | − | 136.655i | 0.0829423 | − | 0.523581i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 199.902 | + | 346.240i | 0.760083 | + | 1.31650i | 0.942807 | + | 0.333338i | \(0.108175\pi\) |
−0.182725 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 97.2944 | + | 203.989i | 0.364399 | + | 0.764005i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 488.409i | − | 1.81565i | −0.419353 | − | 0.907823i | \(-0.637743\pi\) | ||
0.419353 | − | 0.907823i | \(-0.362257\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 302.576 | 1.11652 | 0.558258 | − | 0.829667i | \(-0.311470\pi\) | ||||
0.558258 | + | 0.829667i | \(0.311470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −57.2103 | + | 27.2869i | −0.209562 | + | 0.0999521i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0638 | + | 12.7386i | −0.0796528 | + | 0.0459876i | −0.539297 | − | 0.842115i | \(-0.681310\pi\) |
0.459645 | + | 0.888103i | \(0.347977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 119.276 | + | 310.752i | 0.427514 | + | 1.11381i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 284.675 | − | 164.357i | 1.01308 | − | 0.584901i | 0.100986 | − | 0.994888i | \(-0.467800\pi\) |
0.912091 | + | 0.409987i | \(0.134467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −70.8265 | − | 40.8917i | −0.250270 | − | 0.144494i | 0.369618 | − | 0.929184i | \(-0.379489\pi\) |
−0.619888 | + | 0.784690i | \(0.712822\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −68.6058 | −0.239045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −151.263 | −0.523403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48.0386 | − | 69.8945i | 0.165081 | − | 0.240187i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −236.472 | + | 409.582i | −0.807072 | + | 1.39789i | 0.107811 | + | 0.994171i | \(0.465616\pi\) |
−0.914883 | + | 0.403719i | \(0.867717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −109.579 | − | 369.991i | −0.368954 | − | 1.24576i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 151.600 | − | 87.5263i | 0.507023 | − | 0.292730i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.53565 | − | 16.5162i | 0.0316799 | − | 0.0548712i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 215.997 | − | 314.268i | 0.712862 | − | 1.03719i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 447.529i | − | 1.45775i | −0.684647 | − | 0.728875i | \(-0.740043\pi\) | ||
0.684647 | − | 0.728875i | \(-0.259957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 150.314 | + | 11.8321i | 0.486452 | + | 0.0382915i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 78.3670 | + | 45.2452i | 0.251984 | + | 0.145483i | 0.620672 | − | 0.784070i | \(-0.286860\pi\) |
−0.368688 | + | 0.929553i | \(0.620193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −311.354 | + | 179.760i | −0.994742 | + | 0.574314i | −0.906688 | − | 0.421801i | \(-0.861398\pi\) |
−0.0880535 | + | 0.996116i | \(0.528065\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −209.399 | − | 362.689i | −0.660563 | − | 1.14413i | −0.980468 | − | 0.196679i | \(-0.936984\pi\) |
0.319905 | − | 0.947450i | \(-0.396349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −109.855 | + | 190.274i | −0.344373 | + | 0.596471i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 410.780 | − | 195.925i | 1.27969 | − | 0.610358i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −275.559 | −0.853122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 355.933 | − | 169.765i | 1.08848 | − | 0.519160i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.9572 | − | 17.8731i | −0.0940947 | − | 0.0543256i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −135.615 | − | 234.891i | −0.409712 | − | 0.709641i | 0.585146 | − | 0.810928i | \(-0.301037\pi\) |
−0.994857 | + | 0.101287i | \(0.967704\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 326.836 | + | 264.682i | 0.981490 | + | 0.794841i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 246.800 | + | 142.490i | 0.732345 | + | 0.422819i | 0.819279 | − | 0.573395i | \(-0.194374\pi\) |
−0.0869346 | + | 0.996214i | \(0.527707\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.5295 | + | 273.508i | −0.0635087 | + | 0.806809i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 528.566i | − | 1.55005i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 297.970i | 0.868718i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.2479 | + | 43.7306i | −0.0727604 | + | 0.126025i | −0.900110 | − | 0.435662i | \(-0.856514\pi\) |
0.827350 | + | 0.561687i | \(0.189848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −122.113 | − | 211.507i | −0.349895 | − | 0.606036i | 0.636335 | − | 0.771413i | \(-0.280449\pi\) |
−0.986231 | + | 0.165376i | \(0.947116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −113.331 | + | 119.416i | −0.322881 | + | 0.340217i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −219.922 | − | 380.917i | −0.623009 | − | 1.07908i | −0.988922 | − | 0.148435i | \(-0.952577\pi\) |
0.365913 | − | 0.930649i | \(-0.380757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −69.1019 | + | 100.541i | −0.193563 | + | 0.281627i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.2266i | 0.0925532i | 0.998929 | + | 0.0462766i | \(0.0147356\pi\) | ||||
−0.998929 | + | 0.0462766i | \(0.985264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 190.288 | 0.527112 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.5996 | + | 248.991i | −0.0539933 | + | 0.685926i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −439.356 | + | 253.662i | −1.19715 | + | 0.691178i | −0.959920 | − | 0.280275i | \(-0.909574\pi\) |
−0.237235 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −166.362 | + | 63.8548i | −0.450844 | + | 0.173048i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −124.715 | + | 72.0045i | −0.336160 | + | 0.194082i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 229.322 | + | 132.399i | 0.614804 | + | 0.354957i | 0.774843 | − | 0.632153i | \(-0.217829\pi\) |
−0.160039 | + | 0.987111i | \(0.551162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 93.7387 | 0.248644 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 88.5410 | 0.233617 | 0.116809 | − | 0.993154i | \(-0.462734\pi\) | ||||
0.116809 | + | 0.993154i | \(0.462734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −197.129 | − | 413.305i | −0.517399 | − | 1.08479i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 279.465 | − | 484.048i | 0.729674 | − | 1.26383i | −0.227347 | − | 0.973814i | \(-0.573005\pi\) |
0.957021 | − | 0.290018i | \(-0.0936614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.75043 | − | 48.9253i | 0.0200269 | − | 0.126422i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 97.7241 | − | 56.4211i | 0.251219 | − | 0.145041i | −0.369103 | − | 0.929388i | \(-0.620335\pi\) |
0.620322 | + | 0.784347i | \(0.287002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 168.465 | − | 291.789i | 0.430856 | − | 0.746264i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −239.084 | − | 18.8197i | −0.608357 | − | 0.0478874i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 687.758i | 1.73239i | 0.499707 | + | 0.866195i | \(0.333441\pi\) | ||||
−0.499707 | + | 0.866195i | \(0.666559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 138.247 | − | 201.144i | 0.346483 | − | 0.504120i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 155.762 | + | 89.9295i | 0.388435 | + | 0.224263i | 0.681482 | − | 0.731835i | \(-0.261336\pi\) |
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −195.299 | + | 112.756i | −0.484613 | + | 0.279791i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −333.926 | − | 578.377i | −0.820457 | − | 1.42107i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −112.950 | + | 195.635i | −0.276162 | + | 0.478326i | −0.970428 | − | 0.241393i | \(-0.922396\pi\) |
0.694266 | + | 0.719719i | \(0.255729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 271.479 | + | 186.588i | 0.660532 | + | 0.453985i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −234.143 | −0.566933 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 45.3916 | − | 576.650i | 0.108853 | − | 1.38285i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 509.790 | + | 294.327i | 1.21668 | + | 0.702452i | 0.964207 | − | 0.265152i | \(-0.0854221\pi\) |
0.252475 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 154.778 | + | 268.083i | 0.367643 | + | 0.636776i | 0.989197 | − | 0.146595i | \(-0.0468316\pi\) |
−0.621554 | + | 0.783372i | \(0.713498\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −91.7030 | − | 14.5270i | −0.216792 | − | 0.0343428i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −159.194 | − | 91.9109i | −0.372821 | − | 0.215248i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 235.967 | − | 112.547i | 0.550041 | − | 0.262346i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 73.7566i | 0.171129i | 0.996333 | + | 0.0855645i | \(0.0272694\pi\) | ||||
−0.996333 | + | 0.0855645i | \(0.972731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 153.697i | − | 0.354958i | −0.984125 | − | 0.177479i | \(-0.943206\pi\) | ||
0.984125 | − | 0.177479i | \(-0.0567941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −337.033 | + | 583.759i | −0.771244 | + | 1.33583i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −117.866 | − | 204.149i | −0.268487 | − | 0.465033i | 0.699985 | − | 0.714158i | \(-0.253190\pi\) |
−0.968471 | + | 0.249125i | \(0.919857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 119.307 | + | 310.832i | 0.270537 | + | 0.704833i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 121.716 | + | 210.818i | 0.274753 | + | 0.475887i | 0.970073 | − | 0.242814i | \(-0.0780705\pi\) |
−0.695319 | + | 0.718701i | \(0.744737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −529.458 | − | 41.6768i | −1.18447 | − | 0.0932367i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 286.103i | − | 0.637201i | −0.947889 | − | 0.318600i | \(-0.896787\pi\) | ||
0.947889 | − | 0.318600i | \(-0.103213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 282.969 | 0.627426 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −305.394 | − | 209.898i | −0.674159 | − | 0.463351i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 619.606 | − | 357.730i | 1.35581 | − | 0.782778i | 0.366755 | − | 0.930317i | \(-0.380469\pi\) |
0.989056 | + | 0.147539i | \(0.0471353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −73.9862 | + | 308.117i | −0.161190 | + | 0.671279i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −643.206 | + | 371.355i | −1.39524 | + | 0.805543i | −0.993889 | − | 0.110381i | \(-0.964793\pi\) |
−0.401352 | + | 0.915924i | \(0.631460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 174.430 | + | 100.707i | 0.376738 | + | 0.217510i | 0.676398 | − | 0.736536i | \(-0.263540\pi\) |
−0.299660 | + | 0.954046i | \(0.596873\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 870.009 | 1.86298 | 0.931488 | − | 0.363773i | \(-0.118512\pi\) | ||||
0.931488 | + | 0.363773i | \(0.118512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −110.200 | −0.234968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −707.136 | − | 55.6629i | −1.50135 | − | 0.118180i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.3304 | + | 68.1222i | −0.0831509 | + | 0.144022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −235.403 | + | 290.682i | −0.493507 | + | 0.609396i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −372.537 | + | 215.085i | −0.777740 | + | 0.449028i | −0.835629 | − | 0.549295i | \(-0.814896\pi\) |
0.0578889 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −142.469 | + | 246.763i | −0.296193 | + | 0.513021i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 128.474 | + | 269.360i | 0.265991 | + | 0.557682i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 128.924i | 0.264732i | 0.991201 | + | 0.132366i | \(0.0422574\pi\) | ||||
−0.991201 | + | 0.132366i | \(0.957743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −369.748 | − | 775.222i | −0.756132 | − | 1.58532i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 412.034 | + | 237.888i | 0.839173 | + | 0.484497i | 0.856983 | − | 0.515344i | \(-0.172336\pi\) |
−0.0178098 | + | 0.999841i | \(0.505669\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 156.250 | − | 90.2109i | 0.316937 | − | 0.182984i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.95998 | − | 6.85889i | −0.00796777 | − | 0.0138006i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −191.161 | + | 331.101i | −0.383088 | + | 0.663528i | −0.991502 | − | 0.130092i | \(-0.958473\pi\) |
0.608414 | + | 0.793620i | \(0.291806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.44898 | + | 107.335i | −0.0168642 | + | 0.214242i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 787.756 | 1.56612 | 0.783058 | − | 0.621949i | \(-0.213659\pi\) | ||||
0.783058 | + | 0.621949i | \(0.213659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 325.906 | + | 223.996i | 0.642812 | + | 0.441806i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 416.243 | + | 240.318i | 0.817766 | + | 0.472137i | 0.849645 | − | 0.527354i | \(-0.176816\pi\) |
−0.0318795 | + | 0.999492i | \(0.510149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −149.491 | − | 258.926i | −0.292546 | − | 0.506704i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 148.018 | − | 616.425i | 0.288534 | − | 1.20161i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 127.685 | + | 73.7188i | 0.246972 | + | 0.142590i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 243.117 | + | 167.094i | 0.468433 | + | 0.321955i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 241.071i | − | 0.462709i | −0.972870 | − | 0.231354i | \(-0.925684\pi\) | ||
0.972870 | − | 0.231354i | \(-0.0743157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 779.301i | − | 1.49006i | −0.667032 | − | 0.745029i | \(-0.732435\pi\) | ||
0.667032 | − | 0.745029i | \(-0.267565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −217.025 | + | 375.898i | −0.411812 | + | 0.713279i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −147.596 | − | 255.643i | −0.279009 | − | 0.483257i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −567.772 | + | 217.929i | −1.06925 | + | 0.410412i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.3641 | − | 104.554i | −0.113253 | − | 0.196161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 403.563 | + | 846.117i | 0.751513 | + | 1.57564i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 528.702i | − | 0.980895i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −811.510 | −1.50002 | −0.750009 | − | 0.661428i | \(-0.769951\pi\) | ||||
−0.750009 | + | 0.661428i | \(0.769951\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.2986 | + | 18.7438i | −0.0723732 | + | 0.0345190i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 354.493 | − | 204.667i | 0.648069 | − | 0.374163i | −0.139647 | − | 0.990201i | \(-0.544597\pi\) |
0.787716 | + | 0.616039i | \(0.211264\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −471.575 | − | 74.7038i | −0.858970 | − | 0.136072i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −312.596 | + | 180.478i | −0.567326 | + | 0.327546i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −350.653 | − | 202.449i | −0.634091 | − | 0.366093i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 72.8356 | 0.130764 | 0.0653820 | − | 0.997860i | \(-0.479173\pi\) | ||||
0.0653820 | + | 0.997860i | \(0.479173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.5605 | 0.0600366 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 285.015 | − | 414.687i | 0.508049 | − | 0.739193i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.9255 | − | 70.8850i | 0.0726918 | − | 0.125906i | −0.827388 | − | 0.561630i | \(-0.810174\pi\) |
0.900080 | + | 0.435724i | \(0.143508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −187.791 | − | 208.587i | −0.331202 | − | 0.367879i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −880.986 | + | 508.637i | −1.54831 | + | 0.893914i | −0.550034 | + | 0.835142i | \(0.685385\pi\) |
−0.998271 | + | 0.0587719i | \(0.981282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −243.972 | + | 422.572i | −0.427271 | + | 0.740056i | −0.996630 | − | 0.0820339i | \(-0.973858\pi\) |
0.569358 | + | 0.822090i | \(0.307192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 441.246 | − | 641.998i | 0.770063 | − | 1.12042i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 328.037i | 0.568522i | 0.958747 | + | 0.284261i | \(0.0917482\pi\) | ||||
−0.958747 | + | 0.284261i | \(0.908252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −709.631 | − | 55.8592i | −1.22561 | − | 0.0964754i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −391.601 | − | 226.091i | −0.674013 | − | 0.389142i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 514.397 | − | 296.987i | 0.882327 | − | 0.509412i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −46.5708 | − | 80.6629i | −0.0793369 | − | 0.137416i | 0.823627 | − | 0.567132i | \(-0.191947\pi\) |
−0.902964 | + | 0.429716i | \(0.858614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 434.184 | − | 752.028i | 0.737154 | − | 1.27679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −412.405 | + | 196.700i | −0.697808 | + | 0.332825i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −61.3791 | −0.103506 | −0.0517530 | − | 0.998660i | \(-0.516481\pi\) | ||||
−0.0517530 | + | 0.998660i | \(0.516481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1036.85 | − | 494.532i | 1.73676 | − | 0.828362i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −720.881 | − | 416.201i | −1.20347 | − | 0.694826i | −0.242148 | − | 0.970239i | \(-0.577852\pi\) |
−0.961326 | + | 0.275413i | \(0.911185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −192.246 | − | 332.980i | −0.319877 | − | 0.554043i | 0.660585 | − | 0.750751i | \(-0.270308\pi\) |
−0.980462 | + | 0.196708i | \(0.936975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −267.223 | + | 102.569i | −0.443155 | + | 0.170097i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −628.428 | − | 362.823i | −1.03530 | − | 0.597732i | −0.116803 | − | 0.993155i | \(-0.537265\pi\) |
−0.918499 | + | 0.395423i | \(0.870598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.5405 | + | 159.313i | −0.0205919 | + | 0.261598i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 62.9039i | − | 0.102952i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.61994i | − | 0.00590529i | −0.999996 | − | 0.00295265i | \(-0.999060\pi\) | ||
0.999996 | − | 0.00295265i | \(-0.000939858\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −239.072 | + | 414.084i | −0.387474 | + | 0.671125i | −0.992109 | − | 0.125378i | \(-0.959986\pi\) |
0.604635 | + | 0.796503i | \(0.293319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 160.807 | + | 278.525i | 0.259784 | + | 0.449960i | 0.966184 | − | 0.257853i | \(-0.0830151\pi\) |
−0.706400 | + | 0.707813i | \(0.749682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 562.241 | + | 533.592i | 0.905380 | + | 0.859246i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −130.519 | − | 226.065i | −0.209500 | − | 0.362865i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −570.207 | + | 829.631i | −0.909421 | + | 1.32318i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 548.428i | 0.871905i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −457.380 | −0.724850 | −0.362425 | − | 0.932013i | \(-0.618051\pi\) | ||||
−0.362425 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9734 | + | 190.221i | −0.0236547 | + | 0.300507i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −195.349 | + | 112.785i | −0.306670 | + | 0.177056i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.9864 | − | 12.9463i | −0.0250179 | − | 0.0202603i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.11287 | − | 4.68397i | 0.0126566 | − | 0.00730728i | −0.493658 | − | 0.869656i | \(-0.664341\pi\) |
0.506315 | + | 0.862349i | \(0.331007\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −461.736 | − | 266.583i | −0.718096 | − | 0.414593i | 0.0959557 | − | 0.995386i | \(-0.469409\pi\) |
−0.814051 | + | 0.580793i | \(0.802743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 792.544 | 1.22495 | 0.612476 | − | 0.790489i | \(-0.290174\pi\) | ||||
0.612476 | + | 0.790489i | \(0.290174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 965.739 | 1.48804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −165.506 | − | 347.004i | −0.254234 | − | 0.533032i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 367.827 | − | 637.096i | 0.563288 | − | 0.975644i | −0.433918 | − | 0.900952i | \(-0.642869\pi\) |
0.997207 | − | 0.0746918i | \(-0.0237973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −603.493 | − | 488.728i | −0.918559 | − | 0.743878i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −859.395 | + | 496.172i | −1.30409 | + | 0.752917i | −0.981103 | − | 0.193487i | \(-0.938020\pi\) |
−0.322987 | + | 0.946403i | \(0.604687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −336.164 | + | 582.252i | −0.508568 | + | 0.880866i | 0.491383 | + | 0.870944i | \(0.336492\pi\) |
−0.999951 | + | 0.00992217i | \(0.996842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −214.022 | − | 16.8470i | −0.322809 | − | 0.0254102i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 441.345i | − | 0.661687i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.74093 | + | 3.98796i | −0.00409706 | + | 0.00596108i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 656.607 | + | 379.092i | 0.978550 | + | 0.564966i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 642.106 | − | 370.720i | 0.954095 | − | 0.550847i | 0.0597446 | − | 0.998214i | \(-0.480971\pi\) |
0.894351 | + | 0.447366i | \(0.147638\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 330.560 | + | 572.547i | 0.488272 | + | 0.845711i | 0.999909 | − | 0.0134901i | \(-0.00429415\pi\) |
−0.511637 | + | 0.859202i | \(0.670961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.9789 | + | 84.8340i | −0.0721339 | + | 0.124940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 960.617 | + | 660.234i | 1.41060 | + | 0.969506i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1179.82 | −1.72741 | −0.863704 | − | 0.503999i | \(-0.831862\pi\) | ||||
−0.863704 | + | 0.503999i | \(0.831862\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −64.1505 | + | 814.962i | −0.0933777 | + | 1.18626i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −219.466 | − | 126.709i | −0.318529 | − | 0.183903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.3297 | − | 40.4083i | −0.0337623 | − | 0.0584780i | 0.848651 | − | 0.528954i | \(-0.177416\pi\) |
−0.882413 | + | 0.470476i | \(0.844082\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 159.710 | + | 416.094i | 0.230462 | + | 0.600424i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −201.238 | − | 116.185i | −0.288720 | − | 0.166692i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 717.194 | − | 342.072i | 1.02603 | − | 0.489373i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1384.15i | − | 1.97453i | −0.159078 | − | 0.987266i | \(-0.550852\pi\) | ||
0.159078 | − | 0.987266i | \(-0.449148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1097.20i | − | 1.56073i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −220.225 | + | 381.441i | −0.311492 | + | 0.539521i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 563.387 | + | 975.815i | 0.794622 | + | 1.37633i | 0.923079 | + | 0.384610i | \(0.125664\pi\) |
−0.128457 | + | 0.991715i | \(0.541002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1038.72 | − | 164.548i | −1.46093 | − | 0.231431i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 530.882 | + | 919.515i | 0.744576 | + | 1.28964i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −536.626 | − | 42.2410i | −0.748432 | − | 0.0589135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 205.596i | − | 0.285947i | −0.989726 | − | 0.142974i | \(-0.954334\pi\) | ||
0.989726 | − | 0.142974i | \(-0.0456664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −174.151 | −0.241541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −701.196 | − | 481.933i | −0.969842 | − | 0.666574i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −157.186 | + | 90.7513i | −0.216212 | + | 0.124830i | −0.604195 | − | 0.796837i | \(-0.706505\pi\) |
0.387983 | + | 0.921666i | \(0.373172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −649.516 | − | 331.014i | −0.890968 | − | 0.454066i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55.9408 | − | 32.2974i | 0.0765264 | − | 0.0441825i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −424.253 | − | 244.943i | −0.578790 | − | 0.334165i | 0.181862 | − | 0.983324i | \(-0.441787\pi\) |
−0.760652 | + | 0.649159i | \(0.775121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 454.527 | 0.616726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −312.730 | −0.423180 | −0.211590 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211590 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 428.177 | + | 33.7044i | 0.577837 | + | 0.0454850i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 660.954 | − | 1144.81i | 0.889574 | − | 1.54079i | 0.0491945 | − | 0.998789i | \(-0.484335\pi\) |
0.840380 | − | 0.541998i | \(-0.182332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1160.02 | − | 183.763i | −1.55291 | − | 0.246002i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −455.234 | + | 262.829i | −0.607789 | + | 0.350907i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 637.535 | − | 1104.24i | 0.848914 | − | 1.47036i | −0.0332638 | − | 0.999447i | \(-0.510590\pi\) |
0.882178 | − | 0.470916i | \(-0.156077\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −555.218 | − | 1164.08i | −0.737341 | − | 1.54592i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1371.91i | − | 1.81230i | −0.422959 | − | 0.906149i | \(-0.639009\pi\) | ||
0.422959 | − | 0.906149i | \(-0.360991\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −529.897 | − | 1110.99i | −0.698152 | − | 1.46376i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −733.212 | − | 423.320i | −0.963485 | − | 0.556269i | −0.0662413 | − | 0.997804i | \(-0.521101\pi\) |
−0.897244 | + | 0.441535i | \(0.854434\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −394.452 | + | 227.737i | −0.516975 | + | 0.298476i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −206.015 | − | 356.829i | −0.268599 | − | 0.465227i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −155.867 | + | 269.969i | −0.202688 | + | 0.351066i | −0.949394 | − | 0.314089i | \(-0.898301\pi\) |
0.746706 | + | 0.665154i | \(0.231634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.8021 | − | 569.162i | 0.0581091 | − | 0.738213i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 140.050 | 0.181178 | 0.0905889 | − | 0.995888i | \(-0.471125\pi\) | ||||
0.0905889 | + | 0.995888i | \(0.471125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −400.325 | − | 275.144i | −0.515219 | − | 0.354111i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 402.600 | + | 232.441i | 0.516816 | + | 0.298384i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3332 | + | 28.2899i | 0.0209132 | + | 0.0362227i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 117.871 | + | 397.988i | 0.150538 | + | 0.508287i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 321.229 | + | 185.462i | 0.408169 | + | 0.235657i | 0.690003 | − | 0.723807i | \(-0.257609\pi\) |
−0.281833 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −988.456 | − | 679.368i | −1.25280 | − | 0.861049i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 316.882i | − | 0.400609i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 323.478i | − | 0.407917i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.56272 | − | 13.0990i | 0.00948898 | − | 0.0164354i | −0.861242 | − | 0.508195i | \(-0.830313\pi\) |
0.870731 | + | 0.491760i | \(0.163646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.5366 | − | 104.852i | −0.0757655 | − | 0.131230i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −526.903 | − | 426.702i | −0.657806 | − | 0.532712i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 616.584 | + | 1067.96i | 0.767851 | + | 1.32996i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 630.778 | + | 1322.50i | 0.781633 | + | 1.63879i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1123.71i | 1.38901i | 0.719488 | + | 0.694505i | \(0.244377\pi\) | ||||
−0.719488 | + | 0.694505i | \(0.755623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 181.717 | 0.224065 | 0.112033 | − | 0.993705i | \(-0.464264\pi\) | ||||
0.112033 | + | 0.993705i | \(0.464264\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −819.307 | + | 390.775i | −1.00776 | + | 0.480658i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −111.916 | + | 64.6148i | −0.136984 | + | 0.0790879i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 119.672 | − | 147.774i | 0.146119 | − | 0.180432i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −532.274 | + | 307.308i | −0.648323 | + | 0.374310i | −0.787814 | − | 0.615914i | \(-0.788787\pi\) |
0.139490 | + | 0.990223i | \(0.455454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −382.649 | − | 220.922i | −0.464944 | − | 0.268436i | 0.249177 | − | 0.968458i | \(-0.419840\pi\) |
−0.714121 | + | 0.700022i | \(0.753173\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1400.26 | 1.69318 | 0.846589 | − | 0.532247i | \(-0.178652\pi\) | ||||
0.846589 | + | 0.532247i | \(0.178652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 166.752 | 0.201149 | 0.100574 | − | 0.994930i | \(-0.467932\pi\) | ||||
0.100574 | + | 0.994930i | \(0.467932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.2921 | − | 62.9885i | 0.0520964 | − | 0.0757984i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −217.081 | + | 375.995i | −0.260601 | + | 0.451374i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −724.307 | − | 687.400i | −0.865361 | − | 0.821267i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −682.428 | + | 394.000i | −0.813382 | + | 0.469607i | −0.848129 | − | 0.529790i | \(-0.822271\pi\) |
0.0347467 | + | 0.999396i | \(0.488938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −302.332 | + | 523.655i | −0.359492 | + | 0.622658i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −558.569 | + | 812.698i | −0.662596 | + | 0.964055i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 288.477i | − | 0.340587i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 244.593 | + | 19.2534i | 0.288096 | + | 0.0226777i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1161.82 | + | 670.778i | 1.36524 | + | 0.788224i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 385.927 | − | 222.815i | 0.452435 | − | 0.261213i | −0.256423 | − | 0.966565i | \(-0.582544\pi\) |
0.708858 | + | 0.705351i | \(0.249211\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −451.485 | − | 781.995i | −0.526820 | − | 0.912479i | −0.999512 | − | 0.0312512i | \(-0.990051\pi\) |
0.472691 | − | 0.881228i | \(-0.343283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 376.214 | − | 651.622i | 0.437967 | − | 0.758582i | −0.559565 | − | 0.828786i | \(-0.689032\pi\) |
0.997533 | + | 0.0702046i | \(0.0223652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 185.769 | − | 88.6041i | 0.215760 | − | 0.102908i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 900.969 | 1.04400 | 0.521998 | − | 0.852946i | \(-0.325187\pi\) | ||||
0.521998 | + | 0.852946i | \(0.325187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 409.587 | − | 195.356i | 0.472419 | − | 0.225324i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1446.29 | + | 835.015i | 1.66431 | + | 0.960892i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −96.9614 | − | 167.942i | −0.111322 | − | 0.192815i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.8093 | + | 251.300i | −0.0456006 | + | 0.287858i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 719.863 | + | 415.613i | 0.820824 | + | 0.473903i | 0.850701 | − | 0.525651i | \(-0.176178\pi\) |
−0.0298765 | + | 0.999554i | \(0.509511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 111.340 | − | 1414.46i | 0.126667 | − | 1.60917i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1140.44i | − | 1.29448i | −0.762286 | − | 0.647240i | \(-0.775923\pi\) | ||
0.762286 | − | 0.647240i | \(-0.224077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 137.466i | 0.155680i | 0.996966 | + | 0.0778401i | \(0.0248024\pi\) | ||||
−0.996966 | + | 0.0778401i | \(0.975198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −168.286 | + | 291.479i | −0.189724 | + | 0.328612i | −0.945158 | − | 0.326613i | \(-0.894093\pi\) |
0.755434 | + | 0.655225i | \(0.227426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 264.445 | + | 458.032i | 0.297463 | + | 0.515222i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 774.558 | + | 860.331i | 0.869313 | + | 0.965579i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 121.111 | + | 209.770i | 0.135622 | + | 0.234905i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −297.459 | + | 432.792i | −0.331615 | + | 0.482488i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 568.563i | 0.632439i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −487.761 | −0.541355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.48976 | + | 57.0375i | −0.00497205 | + | 0.0631644i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 343.242 | − | 198.171i | 0.378437 | − | 0.218490i | −0.298701 | − | 0.954347i | \(-0.596553\pi\) |
0.677138 | + | 0.735856i | \(0.263220\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −178.996 | + | 1129.93i | −0.196915 | + | 1.24304i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 738.564 | − | 426.410i | 0.810718 | − | 0.468068i | −0.0364874 | − | 0.999334i | \(-0.511617\pi\) |
0.847205 | + | 0.531266i | \(0.178284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1615.18 | + | 932.527i | 1.76910 | + | 1.02139i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 276.999 | 0.302071 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1499.67 | 1.63185 | 0.815924 | − | 0.578160i | \(-0.196229\pi\) | ||||
0.815924 | + | 0.578160i | \(0.196229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 577.982 | + | 1211.81i | 0.627559 | + | 1.31575i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.96852 | − | 12.0698i | 0.00754986 | − | 0.0130767i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −422.297 | + | 162.091i | −0.455552 | + | 0.174855i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −949.861 | + | 548.402i | −1.02246 | + | 0.590315i | −0.914814 | − | 0.403875i | \(-0.867663\pi\) |
−0.107641 | + | 0.994190i | \(0.534330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 434.295 | − | 752.222i | 0.466483 | − | 0.807972i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −270.634 | − | 21.3032i | −0.290069 | − | 0.0228330i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 950.251i | − | 1.01414i | −0.861904 | − | 0.507071i | \(-0.830728\pi\) | ||
0.861904 | − | 0.507071i | \(-0.169272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 610.917 | − | 888.863i | 0.650604 | − | 0.946606i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1163.08 | + | 671.503i | 1.23600 | + | 0.713606i | 0.968274 | − | 0.249889i | \(-0.0803941\pi\) |
0.267727 | + | 0.963495i | \(0.413727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −492.264 | + | 284.209i | −0.522020 | + | 0.301388i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 294.370 | + | 509.863i | 0.310844 | + | 0.538398i | 0.978545 | − | 0.206031i | \(-0.0660549\pi\) |
−0.667701 | + | 0.744430i | \(0.732722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 263.064 | − | 455.641i | 0.277202 | − | 0.480127i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1035.42 | + | 711.643i | 1.08876 | + | 0.748310i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −80.5286 | −0.0845001 | −0.0422501 | − | 0.999107i | \(-0.513453\pi\) | ||||
−0.0422501 | + | 0.999107i | \(0.513453\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 51.7240 | − | 657.097i | 0.0540480 | − | 0.686621i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −329.506 | − | 190.240i | −0.343593 | − | 0.198373i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −203.410 | − | 352.316i | −0.211665 | − | 0.366614i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −859.263 | + | 1061.04i | −0.892277 | + | 1.10181i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −249.502 | − | 144.050i | −0.258017 | − | 0.148966i | 0.365413 | − | 0.930846i | \(-0.380928\pi\) |
−0.623429 | + | 0.781880i | \(0.714261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 746.150 | − | 355.882i | 0.770021 | − | 0.367268i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1036.38i | 1.06733i | 0.845696 | + | 0.533665i | \(0.179186\pi\) | ||||
−0.845696 | + | 0.533665i | \(0.820814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 668.097i | 0.686636i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −793.878 | + | 1375.04i | −0.812567 | + | 1.40741i | 0.0984946 | + | 0.995138i | \(0.468597\pi\) |
−0.911062 | + | 0.412270i | \(0.864736\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 538.332 | + | 932.418i | 0.549879 | + | 0.952419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −744.536 | + | 919.373i | −0.758956 | + | 0.937179i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 602.511 | + | 1043.58i | 0.612931 | + | 1.06163i | 0.990744 | + | 0.135745i | \(0.0433429\pi\) |
−0.377813 | + | 0.925882i | \(0.623324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 106.908 | + | 8.41537i | 0.108316 | + | 0.00852621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 158.011i | − | 0.159768i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −326.691 | −0.329658 | −0.164829 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164829 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 670.574 | + | 460.887i | 0.675301 | + | 0.464136i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −239.663 | + | 138.370i | −0.240384 | + | 0.138786i | −0.615353 | − | 0.788251i | \(-0.710987\pi\) |
0.374969 | + | 0.927037i | \(0.377653\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1226.83 | − | 294.592i | −1.22806 | − | 0.294887i |
(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 | 900.3.u.d.149.2 | 32 | ||
3.2 | odd | 2 | 2700.3.u.d.449.10 | 32 | |||
5.2 | odd | 4 | 900.3.p.d.401.6 | yes | 16 | ||
5.3 | odd | 4 | 900.3.p.e.401.3 | yes | 16 | ||
5.4 | even | 2 | inner | 900.3.u.d.149.15 | 32 | ||
9.2 | odd | 6 | inner | 900.3.u.d.749.15 | 32 | ||
9.7 | even | 3 | 2700.3.u.d.2249.7 | 32 | |||
15.2 | even | 4 | 2700.3.p.e.2501.5 | 16 | |||
15.8 | even | 4 | 2700.3.p.d.2501.4 | 16 | |||
15.14 | odd | 2 | 2700.3.u.d.449.7 | 32 | |||
45.2 | even | 12 | 900.3.p.d.101.6 | ✓ | 16 | ||
45.7 | odd | 12 | 2700.3.p.e.1601.5 | 16 | |||
45.29 | odd | 6 | inner | 900.3.u.d.749.2 | 32 | ||
45.34 | even | 6 | 2700.3.u.d.2249.10 | 32 | |||
45.38 | even | 12 | 900.3.p.e.101.3 | yes | 16 | ||
45.43 | odd | 12 | 2700.3.p.d.1601.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.6 | ✓ | 16 | 45.2 | even | 12 | ||
900.3.p.d.401.6 | yes | 16 | 5.2 | odd | 4 | ||
900.3.p.e.101.3 | yes | 16 | 45.38 | even | 12 | ||
900.3.p.e.401.3 | yes | 16 | 5.3 | odd | 4 | ||
900.3.u.d.149.2 | 32 | 1.1 | even | 1 | trivial | ||
900.3.u.d.149.15 | 32 | 5.4 | even | 2 | inner | ||
900.3.u.d.749.2 | 32 | 45.29 | odd | 6 | inner | ||
900.3.u.d.749.15 | 32 | 9.2 | odd | 6 | inner | ||
2700.3.p.d.1601.4 | 16 | 45.43 | odd | 12 | |||
2700.3.p.d.2501.4 | 16 | 15.8 | even | 4 | |||
2700.3.p.e.1601.5 | 16 | 45.7 | odd | 12 | |||
2700.3.p.e.2501.5 | 16 | 15.2 | even | 4 | |||
2700.3.u.d.449.7 | 32 | 15.14 | odd | 2 | |||
2700.3.u.d.449.10 | 32 | 3.2 | odd | 2 | |||
2700.3.u.d.2249.7 | 32 | 9.7 | even | 3 | |||
2700.3.u.d.2249.10 | 32 | 45.34 | even | 6 |