Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(307,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6679465984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 88x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.8 | ||
Root | \(2.20392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.307 |
Dual form | 1386.2.e.e.307.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.06118i | 1.36900i | 0.729012 | + | 0.684501i | \(0.239980\pi\) | ||||
−0.729012 | + | 0.684501i | \(0.760020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37330 | − | 1.16938i | 0.897023 | − | 0.441984i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.06118 | −0.968031 | ||||||||
\(11\) | 3.20392 | + | 0.857262i | 0.966018 | + | 0.258474i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.338760 | 0.0939550 | 0.0469775 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469775 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(14\) | 1.16938 | + | 2.37330i | 0.312530 | + | 0.634291i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.314583 | 0.0762975 | 0.0381488 | − | 0.999272i | \(-0.487854\pi\) | ||||
0.0381488 | + | 0.999272i | \(0.487854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.09326 | 1.39789 | 0.698944 | − | 0.715176i | \(-0.253653\pi\) | ||||
0.698944 | + | 0.715176i | \(0.253653\pi\) | |||||||
\(20\) | − | 3.06118i | − | 0.684501i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.857262 | + | 3.20392i | −0.182769 | + | 0.683078i | ||||
\(23\) | 3.37576 | 0.703896 | 0.351948 | − | 0.936020i | \(-0.385519\pi\) | ||||
0.351948 | + | 0.936020i | \(0.385519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.37083 | −0.874167 | ||||||||
\(26\) | 0.338760i | 0.0664362i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.37330 | + | 1.16938i | −0.448511 | + | 0.220992i | ||||
\(29\) | − | 4.40784i | − | 0.818515i | −0.912419 | − | 0.409258i | \(-0.865788\pi\) | ||
0.912419 | − | 0.409258i | \(-0.134212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.722422i | − | 0.129751i | −0.997893 | − | 0.0648754i | \(-0.979335\pi\) | ||
0.997893 | − | 0.0648754i | \(-0.0206650\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.314583i | 0.0539505i | ||||||||
\(35\) | 3.57968 | + | 7.26510i | 0.605077 | + | 1.22803i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.49320 | −1.23187 | −0.615937 | − | 0.787795i | \(-0.711222\pi\) | ||||
−0.615937 | + | 0.787795i | \(0.711222\pi\) | |||||||
\(38\) | 6.09326i | 0.988457i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.06118 | 0.484015 | ||||||||
\(41\) | 8.09326 | 1.26395 | 0.631977 | − | 0.774987i | \(-0.282244\pi\) | ||||
0.631977 | + | 0.774987i | \(0.282244\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.12236i | 0.628655i | 0.949315 | + | 0.314327i | \(0.101779\pi\) | ||||
−0.949315 | + | 0.314327i | \(0.898221\pi\) | |||||||
\(44\) | −3.20392 | − | 0.857262i | −0.483009 | − | 0.129237i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.37576i | 0.497729i | ||||||||
\(47\) | 8.77571i | 1.28007i | 0.768346 | + | 0.640034i | \(0.221080\pi\) | ||||
−0.768346 | + | 0.640034i | \(0.778920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.26510 | − | 5.55058i | 0.609300 | − | 0.792940i | ||||
\(50\) | − | 4.37083i | − | 0.618129i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.338760 | −0.0469775 | ||||||||
\(53\) | −13.5623 | −1.86292 | −0.931461 | − | 0.363841i | \(-0.881465\pi\) | ||||
−0.931461 | + | 0.363841i | \(0.881465\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.62424 | + | 9.80778i | −0.353852 | + | 1.32248i | ||||
\(56\) | −1.16938 | − | 2.37330i | −0.156265 | − | 0.317145i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.40784 | 0.578778 | ||||||||
\(59\) | 4.67752i | 0.608961i | 0.952519 | + | 0.304481i | \(0.0984829\pi\) | ||||
−0.952519 | + | 0.304481i | \(0.901517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7836 | 1.76481 | 0.882405 | − | 0.470491i | \(-0.155923\pi\) | ||||
0.882405 | + | 0.470491i | \(0.155923\pi\) | |||||||
\(62\) | 0.722422 | 0.0917477 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.03700i | 0.128625i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73032 | −0.211392 | −0.105696 | − | 0.994398i | \(-0.533707\pi\) | ||||
−0.105696 | + | 0.994398i | \(0.533707\pi\) | |||||||
\(68\) | −0.314583 | −0.0381488 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.26510 | + | 3.57968i | −0.868346 | + | 0.427854i | ||||
\(71\) | −13.5465 | −1.60767 | −0.803836 | − | 0.594851i | \(-0.797211\pi\) | ||||
−0.803836 | + | 0.594851i | \(0.797211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.68542 | −0.197263 | −0.0986316 | − | 0.995124i | \(-0.531447\pi\) | ||||
−0.0986316 | + | 0.995124i | \(0.531447\pi\) | |||||||
\(74\) | − | 7.49320i | − | 0.871067i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.09326 | −0.698944 | ||||||||
\(77\) | 8.60633 | − | 1.71206i | 0.980782 | − | 0.195107i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.86896i | − | 0.772819i | −0.922327 | − | 0.386409i | \(-0.873715\pi\) | ||
0.922327 | − | 0.386409i | \(-0.126285\pi\) | |||||||
\(80\) | 3.06118i | 0.342251i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.09326i | 0.893751i | ||||||||
\(83\) | −7.11447 | −0.780914 | −0.390457 | − | 0.920621i | \(-0.627683\pi\) | ||||
−0.390457 | + | 0.920621i | \(0.627683\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.962995i | 0.104451i | ||||||||
\(86\) | −4.12236 | −0.444526 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.857262 | − | 3.20392i | 0.0913845 | − | 0.341539i | ||||
\(89\) | − | 2.28548i | − | 0.242260i | −0.992637 | − | 0.121130i | \(-0.961348\pi\) | ||
0.992637 | − | 0.121130i | \(-0.0386518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.803978 | − | 0.396139i | 0.0842798 | − | 0.0415266i | ||||
\(92\) | −3.37576 | −0.351948 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.77571 | −0.905145 | ||||||||
\(95\) | 18.6526i | 1.91371i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.08536i | 0.516340i | 0.966100 | + | 0.258170i | \(0.0831195\pi\) | ||||
−0.966100 | + | 0.258170i | \(0.916881\pi\) | |||||||
\(98\) | 5.55058 | + | 4.26510i | 0.560693 | + | 0.430840i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.37083 | 0.437083 | ||||||||
\(101\) | −9.71452 | −0.966631 | −0.483316 | − | 0.875446i | \(-0.660568\pi\) | ||||
−0.483316 | + | 0.875446i | \(0.660568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.70663i | − | 0.660824i | −0.943837 | − | 0.330412i | \(-0.892812\pi\) | ||
0.943837 | − | 0.330412i | \(-0.107188\pi\) | |||||||
\(104\) | − | 0.338760i | − | 0.0332181i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 13.5623i | − | 1.31728i | ||||||
\(107\) | 9.71452i | 0.939139i | 0.882896 | + | 0.469569i | \(0.155591\pi\) | ||||
−0.882896 | + | 0.469569i | \(0.844409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9913i | 1.81904i | 0.415661 | + | 0.909520i | \(0.363550\pi\) | ||||
−0.415661 | + | 0.909520i | \(0.636450\pi\) | |||||||
\(110\) | −9.80778 | − | 2.62424i | −0.935135 | − | 0.250211i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.37330 | − | 1.16938i | 0.224256 | − | 0.110496i | ||||
\(113\) | 11.1012 | 1.04431 | 0.522154 | − | 0.852851i | \(-0.325128\pi\) | ||||
0.522154 | + | 0.852851i | \(0.325128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3338i | 0.963635i | ||||||||
\(116\) | 4.40784i | 0.409258i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.67752 | −0.430601 | ||||||||
\(119\) | 0.746599 | − | 0.367867i | 0.0684406 | − | 0.0337223i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.53020 | + | 5.49320i | 0.866382 | + | 0.499382i | ||||
\(122\) | 13.7836i | 1.24791i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.722422i | 0.0648754i | ||||||||
\(125\) | 1.92599i | 0.172266i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.6106i | − | 1.91763i | −0.284025 | − | 0.958817i | \(-0.591670\pi\) | ||
0.284025 | − | 0.958817i | \(-0.408330\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.03700 | −0.0909514 | ||||||||
\(131\) | −13.9459 | −1.21846 | −0.609231 | − | 0.792993i | \(-0.708522\pi\) | ||||
−0.609231 | + | 0.792993i | \(0.708522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4611 | − | 7.12533i | 1.25394 | − | 0.617845i | ||||
\(134\) | − | 1.73032i | − | 0.149477i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.314583i | − | 0.0269752i | ||||||
\(137\) | −11.7787 | −1.00632 | −0.503160 | − | 0.864193i | \(-0.667829\pi\) | ||||
−0.503160 | + | 0.864193i | \(0.667829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.53810 | −0.639373 | −0.319687 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319687 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(140\) | −3.57968 | − | 7.26510i | −0.302539 | − | 0.614013i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 13.5465i | − | 1.13680i | ||||||
\(143\) | 1.08536 | + | 0.290406i | 0.0907623 | + | 0.0242850i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.4932 | 1.12055 | ||||||||
\(146\) | − | 1.68542i | − | 0.139486i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.49320 | 0.615937 | ||||||||
\(149\) | − | 9.42905i | − | 0.772458i | −0.922403 | − | 0.386229i | \(-0.873777\pi\) | ||
0.922403 | − | 0.386229i | \(-0.126223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.09029i | 0.739757i | 0.929080 | + | 0.369879i | \(0.120601\pi\) | ||||
−0.929080 | + | 0.369879i | \(0.879399\pi\) | |||||||
\(152\) | − | 6.09326i | − | 0.494228i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.71206 | + | 8.60633i | 0.137962 | + | 0.693518i | ||||
\(155\) | 2.21147 | 0.177629 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.45274i | 0.674602i | 0.941397 | + | 0.337301i | \(0.109514\pi\) | ||||
−0.941397 | + | 0.337301i | \(0.890486\pi\) | |||||||
\(158\) | 6.86896 | 0.546465 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.06118 | −0.242008 | ||||||||
\(161\) | 8.01170 | − | 3.94755i | 0.631410 | − | 0.311111i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2077 | 0.877857 | 0.438928 | − | 0.898522i | \(-0.355358\pi\) | ||||
0.438928 | + | 0.898522i | \(0.355358\pi\) | |||||||
\(164\) | −8.09326 | −0.631977 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.11447i | − | 0.552190i | ||||||
\(167\) | 14.6933 | 1.13700 | 0.568501 | − | 0.822682i | \(-0.307523\pi\) | ||||
0.568501 | + | 0.822682i | \(0.307523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8852 | −0.991172 | ||||||||
\(170\) | −0.962995 | −0.0738583 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 4.12236i | − | 0.314327i | ||||||
\(173\) | 11.2077 | 0.852107 | 0.426054 | − | 0.904698i | \(-0.359903\pi\) | ||||
0.426054 | + | 0.904698i | \(0.359903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.3733 | + | 5.11117i | −0.784148 | + | 0.386368i | ||||
\(176\) | 3.20392 | + | 0.857262i | 0.241505 | + | 0.0646186i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.28548 | 0.171304 | ||||||||
\(179\) | 19.0446 | 1.42346 | 0.711731 | − | 0.702453i | \(-0.247912\pi\) | ||||
0.711731 | + | 0.702453i | \(0.247912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5435i | 1.08101i | 0.841341 | + | 0.540505i | \(0.181767\pi\) | ||||
−0.841341 | + | 0.540505i | \(0.818233\pi\) | |||||||
\(182\) | 0.396139 | + | 0.803978i | 0.0293638 | + | 0.0595948i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 3.37576i | − | 0.248865i | ||||||
\(185\) | − | 22.9380i | − | 1.68644i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00790 | + | 0.269680i | 0.0737048 | + | 0.0197209i | ||||
\(188\) | − | 8.77571i | − | 0.640034i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.6526 | −1.35320 | ||||||||
\(191\) | 6.11743 | 0.442642 | 0.221321 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221321 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.7515i | − | 0.773912i | −0.922098 | − | 0.386956i | \(-0.873527\pi\) | ||
0.922098 | − | 0.386956i | \(-0.126473\pi\) | |||||||
\(194\) | −5.08536 | −0.365107 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.26510 | + | 5.55058i | −0.304650 | + | 0.396470i | ||||
\(197\) | − | 25.9010i | − | 1.84537i | −0.385552 | − | 0.922686i | \(-0.625989\pi\) | ||
0.385552 | − | 0.922686i | \(-0.374011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.5707i | − | 1.38733i | −0.720299 | − | 0.693664i | \(-0.755995\pi\) | ||
0.720299 | − | 0.693664i | \(-0.244005\pi\) | |||||||
\(200\) | 4.37083i | 0.309065i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 9.71452i | − | 0.683512i | ||||||
\(203\) | −5.15444 | − | 10.4611i | −0.361771 | − | 0.734227i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.7749i | 1.73036i | ||||||||
\(206\) | 6.70663 | 0.467273 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.338760 | 0.0234888 | ||||||||
\(209\) | 19.5223 | + | 5.22352i | 1.35039 | + | 0.361318i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.95165i | − | 0.409728i | −0.978790 | − | 0.204864i | \(-0.934325\pi\) | ||
0.978790 | − | 0.204864i | \(-0.0656752\pi\) | |||||||
\(212\) | 13.5623 | 0.931461 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.71452 | −0.664071 | ||||||||
\(215\) | −12.6193 | −0.860629 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.844786 | − | 1.71452i | −0.0573478 | − | 0.116389i | ||||
\(218\) | −18.9913 | −1.28625 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.62424 | − | 9.80778i | 0.176926 | − | 0.661240i | ||||
\(221\) | 0.106568 | 0.00716854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.04490i | 0.538727i | 0.963039 | + | 0.269363i | \(0.0868132\pi\) | ||||
−0.963039 | + | 0.269363i | \(0.913187\pi\) | |||||||
\(224\) | 1.16938 | + | 2.37330i | 0.0781325 | + | 0.158573i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1012i | 0.738438i | ||||||||
\(227\) | −17.0155 | −1.12936 | −0.564679 | − | 0.825310i | \(-0.691000\pi\) | ||||
−0.564679 | + | 0.825310i | \(0.691000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.7942i | − | 1.63845i | −0.573476 | − | 0.819223i | \(-0.694405\pi\) | ||
0.573476 | − | 0.819223i | \(-0.305595\pi\) | |||||||
\(230\) | −10.3338 | −0.681393 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.40784 | −0.289389 | ||||||||
\(233\) | 0.170718i | 0.0111841i | 0.999984 | + | 0.00559204i | \(0.00178001\pi\) | ||||
−0.999984 | + | 0.00559204i | \(0.998220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.8640 | −1.75242 | ||||||||
\(236\) | − | 4.67752i | − | 0.304481i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.367867 | + | 0.746599i | 0.0238453 | + | 0.0483948i | ||||
\(239\) | − | 18.8897i | − | 1.22187i | −0.791680 | − | 0.610936i | \(-0.790793\pi\) | ||
0.791680 | − | 0.610936i | \(-0.209207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.436947 | 0.0281462 | 0.0140731 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140731 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(242\) | −5.49320 | + | 9.53020i | −0.353116 | + | 0.612625i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.7836 | −0.882405 | ||||||||
\(245\) | 16.9913 | + | 13.0563i | 1.08554 | + | 0.834133i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.06415 | 0.131339 | ||||||||
\(248\) | −0.722422 | −0.0458739 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.92599 | −0.121810 | ||||||||
\(251\) | 6.69332i | 0.422478i | 0.977434 | + | 0.211239i | \(0.0677499\pi\) | ||||
−0.977434 | + | 0.211239i | \(0.932250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8157 | + | 2.89392i | 0.679976 | + | 0.181939i | ||||
\(254\) | 21.6106 | 1.35597 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.08536i | 0.566729i | 0.959012 | + | 0.283365i | \(0.0914506\pi\) | ||||
−0.959012 | + | 0.283365i | \(0.908549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.7836 | + | 8.76239i | −1.10502 | + | 0.544469i | ||||
\(260\) | − | 1.03700i | − | 0.0643123i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 13.9459i | − | 0.861583i | ||||||
\(263\) | − | 14.7591i | − | 0.910087i | −0.890469 | − | 0.455044i | \(-0.849624\pi\) | ||
0.890469 | − | 0.455044i | \(-0.150376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 41.5166i | − | 2.55034i | ||||||
\(266\) | 7.12533 | + | 14.4611i | 0.436882 | + | 0.886668i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.73032 | 0.105696 | ||||||||
\(269\) | − | 29.1835i | − | 1.77935i | −0.456592 | − | 0.889676i | \(-0.650930\pi\) | ||
0.456592 | − | 0.889676i | \(-0.349070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8048 | −0.777837 | −0.388919 | − | 0.921272i | \(-0.627151\pi\) | ||||
−0.388919 | + | 0.921272i | \(0.627151\pi\) | |||||||
\(272\) | 0.314583 | 0.0190744 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.7787i | − | 0.711576i | ||||||
\(275\) | −14.0038 | − | 3.74695i | −0.844461 | − | 0.225950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9272i | 0.776719i | 0.921508 | + | 0.388359i | \(0.126958\pi\) | ||||
−0.921508 | + | 0.388359i | \(0.873042\pi\) | |||||||
\(278\) | − | 7.53810i | − | 0.452105i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.26510 | − | 3.57968i | 0.434173 | − | 0.213927i | ||||
\(281\) | − | 13.7787i | − | 0.821967i | −0.911643 | − | 0.410983i | \(-0.865185\pi\) | ||
0.911643 | − | 0.410983i | \(-0.134815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1998 | 0.844092 | 0.422046 | − | 0.906574i | \(-0.361312\pi\) | ||||
0.422046 | + | 0.906574i | \(0.361312\pi\) | |||||||
\(284\) | 13.5465 | 0.803836 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.290406 | + | 1.08536i | −0.0171721 | + | 0.0641786i | ||||
\(287\) | 19.2077 | − | 9.46409i | 1.13380 | − | 0.558648i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9010 | −0.994179 | ||||||||
\(290\) | 13.4932i | 0.792348i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.68542 | 0.0986316 | ||||||||
\(293\) | −7.05280 | −0.412029 | −0.206015 | − | 0.978549i | \(-0.566049\pi\) | ||||
−0.206015 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3187 | −0.833669 | ||||||||
\(296\) | 7.49320i | 0.435533i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.42905 | 0.546210 | ||||||||
\(299\) | 1.14357 | 0.0661345 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.82061 | + | 9.78360i | 0.277855 | + | 0.563918i | ||||
\(302\) | −9.09029 | −0.523087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.09326 | 0.349472 | ||||||||
\(305\) | 42.1941i | 2.41603i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.5381 | 1.11510 | 0.557549 | − | 0.830144i | \(-0.311742\pi\) | ||||
0.557549 | + | 0.830144i | \(0.311742\pi\) | |||||||
\(308\) | −8.60633 | + | 1.71206i | −0.490391 | + | 0.0975536i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.21147i | 0.125603i | ||||||||
\(311\) | − | 7.85346i | − | 0.445329i | −0.974895 | − | 0.222664i | \(-0.928525\pi\) | ||
0.974895 | − | 0.222664i | \(-0.0714754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7281i | 1.00205i | 0.865433 | + | 0.501025i | \(0.167043\pi\) | ||||
−0.865433 | + | 0.501025i | \(0.832957\pi\) | |||||||
\(314\) | −8.45274 | −0.477016 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.86896i | 0.386409i | ||||||||
\(317\) | −0.746599 | −0.0419332 | −0.0209666 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209666 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.77867 | − | 14.1224i | 0.211565 | − | 0.790701i | ||||
\(320\) | − | 3.06118i | − | 0.171125i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.94755 | + | 8.01170i | 0.219988 | + | 0.446475i | ||||
\(323\) | 1.91683 | 0.106655 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.48066 | −0.0821324 | ||||||||
\(326\) | 11.2077i | 0.620738i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.09326i | − | 0.446875i | ||||||
\(329\) | 10.2621 | + | 20.8274i | 0.565770 | + | 1.14825i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50899 | −0.0829418 | −0.0414709 | − | 0.999140i | \(-0.513204\pi\) | ||||
−0.0414709 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(332\) | 7.11447 | 0.390457 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.6933i | 0.803982i | ||||||||
\(335\) | − | 5.29682i | − | 0.289396i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.38663i | 0.293428i | 0.989179 | + | 0.146714i | \(0.0468698\pi\) | ||||
−0.989179 | + | 0.146714i | \(0.953130\pi\) | |||||||
\(338\) | − | 12.8852i | − | 0.700865i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 0.962995i | − | 0.0522257i | ||||||
\(341\) | 0.619305 | − | 2.31458i | 0.0335373 | − | 0.125342i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.63163 | − | 18.1607i | 0.196090 | − | 0.980586i | ||||
\(344\) | 4.12236 | 0.222263 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.2077i | 0.602531i | ||||||||
\(347\) | 21.8761i | 1.17437i | 0.809453 | + | 0.587185i | \(0.199764\pi\) | ||||
−0.809453 | + | 0.587185i | \(0.800236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.73525 | −0.0928858 | −0.0464429 | − | 0.998921i | \(-0.514789\pi\) | ||||
−0.0464429 | + | 0.998921i | \(0.514789\pi\) | |||||||
\(350\) | −5.11117 | − | 10.3733i | −0.273203 | − | 0.554476i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.857262 | + | 3.20392i | −0.0456922 | + | 0.170769i | ||||
\(353\) | − | 20.8874i | − | 1.11173i | −0.831274 | − | 0.555863i | \(-0.812388\pi\) | ||
0.831274 | − | 0.555863i | \(-0.187612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 41.4682i | − | 2.20091i | ||||||
\(356\) | 2.28548i | 0.121130i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0446i | 1.00654i | ||||||||
\(359\) | − | 28.5786i | − | 1.50832i | −0.656692 | − | 0.754159i | \(-0.728045\pi\) | ||
0.656692 | − | 0.754159i | \(-0.271955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1278 | 0.954094 | ||||||||
\(362\) | −14.5435 | −0.764390 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.803978 | + | 0.396139i | −0.0421399 | + | 0.0207633i | ||||
\(365\) | − | 5.15937i | − | 0.270054i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.0759i | 1.56995i | 0.619528 | + | 0.784975i | \(0.287324\pi\) | ||||
−0.619528 | + | 0.784975i | \(0.712676\pi\) | |||||||
\(368\) | 3.37576 | 0.175974 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.9380 | 1.19249 | ||||||||
\(371\) | −32.1873 | + | 15.8595i | −1.67108 | + | 0.823382i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.3508i | − | 1.72684i | −0.504486 | − | 0.863420i | \(-0.668318\pi\) | ||
0.504486 | − | 0.863420i | \(-0.331682\pi\) | |||||||
\(374\) | −0.269680 | + | 1.00790i | −0.0139448 | + | 0.0521172i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.77571 | 0.452572 | ||||||||
\(377\) | − | 1.49320i | − | 0.0769036i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.42364 | 0.329960 | 0.164980 | − | 0.986297i | \(-0.447244\pi\) | ||||
0.164980 | + | 0.986297i | \(0.447244\pi\) | |||||||
\(380\) | − | 18.6526i | − | 0.956856i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.11743i | 0.312995i | ||||||||
\(383\) | − | 12.1949i | − | 0.623130i | −0.950225 | − | 0.311565i | \(-0.899147\pi\) | ||
0.950225 | − | 0.311565i | \(-0.100853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.24092 | + | 26.3455i | 0.267102 | + | 1.34269i | ||||
\(386\) | 10.7515 | 0.547238 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 5.08536i | − | 0.258170i | ||||||
\(389\) | 12.7466 | 0.646278 | 0.323139 | − | 0.946351i | \(-0.395262\pi\) | ||||
0.323139 | + | 0.946351i | \(0.395262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06196 | 0.0537055 | ||||||||
\(392\) | −5.55058 | − | 4.26510i | −0.280346 | − | 0.215420i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.9010 | 1.30488 | ||||||||
\(395\) | 21.0271 | 1.05799 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3146i | 1.01956i | 0.860305 | + | 0.509780i | \(0.170273\pi\) | ||||
−0.860305 | + | 0.509780i | \(0.829727\pi\) | |||||||
\(398\) | 19.5707 | 0.980989 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.37083 | −0.218542 | ||||||||
\(401\) | 0.792277 | 0.0395644 | 0.0197822 | − | 0.999804i | \(-0.493703\pi\) | ||||
0.0197822 | + | 0.999804i | \(0.493703\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.244728i | − | 0.0121907i | ||||||
\(404\) | 9.71452 | 0.483316 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.4611 | − | 5.15444i | 0.519177 | − | 0.255810i | ||||
\(407\) | −24.0076 | − | 6.42364i | −1.19001 | − | 0.318408i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.6077 | 1.31566 | 0.657832 | − | 0.753165i | \(-0.271474\pi\) | ||||
0.657832 | + | 0.753165i | \(0.271474\pi\) | |||||||
\(410\) | −24.7749 | −1.22355 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.70663i | 0.330412i | ||||||||
\(413\) | 5.46980 | + | 11.1012i | 0.269151 | + | 0.546252i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 21.7787i | − | 1.06907i | ||||||
\(416\) | 0.338760i | 0.0166091i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.22352 | + | 19.5223i | −0.255491 | + | 0.954867i | ||||
\(419\) | − | 10.9380i | − | 0.534358i | −0.963647 | − | 0.267179i | \(-0.913908\pi\) | ||
0.963647 | − | 0.267179i | \(-0.0860916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3829 | 1.48077 | 0.740386 | − | 0.672182i | \(-0.234643\pi\) | ||||
0.740386 | + | 0.672182i | \(0.234643\pi\) | |||||||
\(422\) | 5.95165 | 0.289722 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.5623i | 0.658642i | ||||||||
\(425\) | −1.37499 | −0.0666968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.7126 | − | 16.1183i | 1.58307 | − | 0.780018i | ||||
\(428\) | − | 9.71452i | − | 0.469569i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 12.6193i | − | 0.608557i | ||||||
\(431\) | − | 24.1458i | − | 1.16306i | −0.813525 | − | 0.581530i | \(-0.802454\pi\) | ||
0.813525 | − | 0.581530i | \(-0.197546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.5031i | − | 0.648916i | −0.945900 | − | 0.324458i | \(-0.894818\pi\) | ||
0.945900 | − | 0.324458i | \(-0.105182\pi\) | |||||||
\(434\) | 1.71452 | − | 0.844786i | 0.0822998 | − | 0.0405510i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 18.9913i | − | 0.909520i | ||||||
\(437\) | 20.5694 | 0.983968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.5911 | −1.46003 | −0.730017 | − | 0.683429i | \(-0.760488\pi\) | ||||
−0.730017 | + | 0.683429i | \(0.760488\pi\) | |||||||
\(440\) | 9.80778 | + | 2.62424i | 0.467568 | + | 0.125106i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.106568i | 0.00506892i | ||||||||
\(443\) | −28.8739 | −1.37184 | −0.685920 | − | 0.727677i | \(-0.740600\pi\) | ||||
−0.685920 | + | 0.727677i | \(0.740600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.99626 | 0.331654 | ||||||||
\(446\) | −8.04490 | −0.380937 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.37330 | + | 1.16938i | −0.112128 | + | 0.0552480i | ||||
\(449\) | 20.5944 | 0.971908 | 0.485954 | − | 0.873984i | \(-0.338472\pi\) | ||||
0.485954 | + | 0.873984i | \(0.338472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.9301 | + | 6.93804i | 1.22100 | + | 0.326700i | ||||
\(452\) | −11.1012 | −0.522154 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 17.0155i | − | 0.798577i | ||||||
\(455\) | 1.21265 | + | 2.46112i | 0.0568500 | + | 0.115379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.87983i | − | 0.321825i | −0.986969 | − | 0.160912i | \(-0.948556\pi\) | ||
0.986969 | − | 0.160912i | \(-0.0514437\pi\) | |||||||
\(458\) | 24.7942 | 1.15856 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10.3338i | − | 0.481817i | ||||||
\(461\) | 16.2681 | 0.757682 | 0.378841 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378841 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5899 | 0.817472 | 0.408736 | − | 0.912653i | \(-0.365970\pi\) | ||||
0.408736 | + | 0.912653i | \(0.365970\pi\) | |||||||
\(464\) | − | 4.40784i | − | 0.204629i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.170718 | −0.00790834 | ||||||||
\(467\) | 41.0022i | 1.89736i | 0.316245 | + | 0.948678i | \(0.397578\pi\) | ||||
−0.316245 | + | 0.948678i | \(0.602422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.10657 | + | 2.02340i | −0.189624 | + | 0.0934320i | ||||
\(470\) | − | 26.8640i | − | 1.23915i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.67752 | 0.215300 | ||||||||
\(473\) | −3.53395 | + | 13.2077i | −0.162491 | + | 0.607292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.6326 | −1.22199 | ||||||||
\(476\) | −0.746599 | + | 0.367867i | −0.0342203 | + | 0.0168611i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8897 | 0.863994 | ||||||||
\(479\) | −4.29308 | −0.196156 | −0.0980779 | − | 0.995179i | \(-0.531269\pi\) | ||||
−0.0980779 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.53839 | −0.115741 | ||||||||
\(482\) | 0.436947i | 0.0199024i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.53020 | − | 5.49320i | −0.433191 | − | 0.249691i | ||||
\(485\) | −15.5672 | −0.706871 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.8897 | −0.674716 | −0.337358 | − | 0.941376i | \(-0.609533\pi\) | ||||
−0.337358 | + | 0.941376i | \(0.609533\pi\) | |||||||
\(488\) | − | 13.7836i | − | 0.623954i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.0563 | + | 16.9913i | −0.589821 | + | 0.767590i | ||||
\(491\) | 4.35949i | 0.196741i | 0.995150 | + | 0.0983704i | \(0.0313630\pi\) | ||||
−0.995150 | + | 0.0983704i | \(0.968637\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.38663i | − | 0.0624507i | ||||||
\(494\) | 2.06415i | 0.0928705i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.722422i | − | 0.0324377i | ||||||
\(497\) | −32.1499 | + | 15.8410i | −1.44212 | + | 0.710565i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.73573 | −0.301533 | −0.150766 | − | 0.988569i | \(-0.548174\pi\) | ||||
−0.150766 | + | 0.988569i | \(0.548174\pi\) | |||||||
\(500\) | − | 1.92599i | − | 0.0861329i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.69332 | −0.298737 | ||||||||
\(503\) | −43.4275 | −1.93634 | −0.968168 | − | 0.250300i | \(-0.919471\pi\) | ||||
−0.968168 | + | 0.250300i | \(0.919471\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 29.7379i | − | 1.32332i | ||||||
\(506\) | −2.89392 | + | 10.8157i | −0.128650 | + | 0.480816i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.6106i | 0.958817i | ||||||||
\(509\) | 6.18729i | 0.274247i | 0.990554 | + | 0.137123i | \(0.0437857\pi\) | ||||
−0.990554 | + | 0.137123i | \(0.956214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | + | 1.97089i | −0.176950 | + | 0.0871872i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.08536 | −0.400738 | ||||||||
\(515\) | 20.5302 | 0.904669 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.52308 | + | 28.1167i | −0.330865 | + | 1.23657i | ||||
\(518\) | −8.76239 | − | 17.7836i | −0.384998 | − | 0.781367i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.03700 | 0.0454757 | ||||||||
\(521\) | 15.2659i | 0.668813i | 0.942429 | + | 0.334406i | \(0.108536\pi\) | ||||
−0.942429 | + | 0.334406i | \(0.891464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.4021 | −0.542307 | −0.271154 | − | 0.962536i | \(-0.587405\pi\) | ||||
−0.271154 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(524\) | 13.9459 | 0.609231 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.7591 | 0.643529 | ||||||||
\(527\) | − | 0.227262i | − | 0.00989967i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6042 | −0.504531 | ||||||||
\(530\) | 41.5166 | 1.80337 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.4611 | + | 7.12533i | −0.626969 | + | 0.308922i | ||||
\(533\) | 2.74167 | 0.118755 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.7379 | −1.28568 | ||||||||
\(536\) | 1.73032i | 0.0747384i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.1835 | 1.25819 | ||||||||
\(539\) | 18.4233 | − | 14.1273i | 0.793550 | − | 0.608506i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.2768i | 1.34469i | 0.740236 | + | 0.672347i | \(0.234714\pi\) | ||||
−0.740236 | + | 0.672347i | \(0.765286\pi\) | |||||||
\(542\) | − | 12.8048i | − | 0.550014i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.314583i | 0.0134876i | ||||||||
\(545\) | −58.1359 | −2.49027 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.1729i | − | 0.905288i | −0.891691 | − | 0.452644i | \(-0.850481\pi\) | ||
0.891691 | − | 0.452644i | \(-0.149519\pi\) | |||||||
\(548\) | 11.7787 | 0.503160 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.74695 | − | 14.0038i | 0.159771 | − | 0.597124i | ||||
\(551\) | − | 26.8581i | − | 1.14419i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.03243 | − | 16.3021i | −0.341574 | − | 0.693236i | ||||
\(554\) | −12.9272 | −0.549223 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.53810 | 0.319687 | ||||||||
\(557\) | − | 8.50455i | − | 0.360349i | −0.983635 | − | 0.180175i | \(-0.942334\pi\) | ||
0.983635 | − | 0.180175i | \(-0.0576663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.39649i | 0.0590653i | ||||||||
\(560\) | 3.57968 | + | 7.26510i | 0.151269 | + | 0.307007i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.7787 | 0.581218 | ||||||||
\(563\) | 4.14161 | 0.174548 | 0.0872740 | − | 0.996184i | \(-0.472184\pi\) | ||||
0.0872740 | + | 0.996184i | \(0.472184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.9827i | 1.42966i | ||||||||
\(566\) | 14.1998i | 0.596863i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.5465i | 0.568398i | ||||||||
\(569\) | 32.7335i | 1.37226i | 0.727480 | + | 0.686129i | \(0.240692\pi\) | ||||
−0.727480 | + | 0.686129i | \(0.759308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.8603i | 1.91919i | 0.281379 | + | 0.959597i | \(0.409208\pi\) | ||||
−0.281379 | + | 0.959597i | \(0.590792\pi\) | |||||||
\(572\) | −1.08536 | − | 0.290406i | −0.0453811 | − | 0.0121425i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.46409 | + | 19.2077i | 0.395024 | + | 0.801715i | ||||
\(575\) | −14.7549 | −0.615322 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.33009i | − | 0.388417i | −0.980960 | − | 0.194208i | \(-0.937786\pi\) | ||
0.980960 | − | 0.194208i | \(-0.0622138\pi\) | |||||||
\(578\) | − | 16.9010i | − | 0.702990i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.4932 | −0.560275 | ||||||||
\(581\) | −16.8848 | + | 8.31951i | −0.700498 | + | 0.345152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.4525 | − | 11.6264i | −1.79962 | − | 0.481517i | ||||
\(584\) | 1.68542i | 0.0697431i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 7.05280i | − | 0.291349i | ||||||
\(587\) | 0.922247i | 0.0380652i | 0.999819 | + | 0.0190326i | \(0.00605863\pi\) | ||||
−0.999819 | + | 0.0190326i | \(0.993941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.40190i | − | 0.181377i | ||||||
\(590\) | − | 14.3187i | − | 0.589493i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.49320 | −0.307969 | ||||||||
\(593\) | −41.7746 | −1.71548 | −0.857739 | − | 0.514085i | \(-0.828132\pi\) | ||||
−0.857739 | + | 0.514085i | \(0.828132\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12611 | + | 2.28548i | 0.0461659 | + | 0.0936954i | ||||
\(596\) | 9.42905i | 0.386229i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.14357i | 0.0467642i | ||||||||
\(599\) | −7.13104 | −0.291366 | −0.145683 | − | 0.989331i | \(-0.546538\pi\) | ||||
−0.145683 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.3908 | 1.03571 | 0.517856 | − | 0.855468i | \(-0.326730\pi\) | ||||
0.517856 | + | 0.855468i | \(0.326730\pi\) | |||||||
\(602\) | −9.78360 | + | 4.82061i | −0.398750 | + | 0.196473i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 9.09029i | − | 0.369879i | ||||||
\(605\) | −16.8157 | + | 29.1737i | −0.683655 | + | 1.18608i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.0397 | −1.82810 | −0.914052 | − | 0.405597i | \(-0.867064\pi\) | ||||
−0.914052 | + | 0.405597i | \(0.867064\pi\) | |||||||
\(608\) | 6.09326i | 0.247114i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −42.1941 | −1.70839 | ||||||||
\(611\) | 2.97286i | 0.120269i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1061i | 0.852467i | 0.904613 | + | 0.426233i | \(0.140160\pi\) | ||||
−0.904613 | + | 0.426233i | \(0.859840\pi\) | |||||||
\(614\) | 19.5381i | 0.788494i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.71206 | − | 8.60633i | −0.0689808 | − | 0.346759i | ||||
\(617\) | 1.21591 | 0.0489508 | 0.0244754 | − | 0.999700i | \(-0.492208\pi\) | ||||
0.0244754 | + | 0.999700i | \(0.492208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.2817i | 1.49848i | 0.662299 | + | 0.749240i | \(0.269581\pi\) | ||||
−0.662299 | + | 0.749240i | \(0.730419\pi\) | |||||||
\(620\) | −2.21147 | −0.0888146 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.85346 | 0.314895 | ||||||||
\(623\) | −2.67259 | − | 5.42412i | −0.107075 | − | 0.217313i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7500 | −1.11000 | ||||||||
\(626\) | −17.7281 | −0.708556 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 8.45274i | − | 0.337301i | ||||||
\(629\) | −2.35723 | −0.0939890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.5356 | −0.936938 | −0.468469 | − | 0.883480i | \(-0.655194\pi\) | ||||
−0.468469 | + | 0.883480i | \(0.655194\pi\) | |||||||
\(632\) | −6.86896 | −0.273233 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 0.746599i | − | 0.0296512i | ||||||
\(635\) | 66.1541 | 2.62524 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44484 | − | 1.88031i | 0.0572468 | − | 0.0745007i | ||||
\(638\) | 14.1224 | + | 3.77867i | 0.559110 | + | 0.149599i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.06118 | 0.121004 | ||||||||
\(641\) | −7.49320 | −0.295964 | −0.147982 | − | 0.988990i | \(-0.547278\pi\) | ||||
−0.147982 | + | 0.988990i | \(0.547278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6101i | 0.576168i | 0.957605 | + | 0.288084i | \(0.0930182\pi\) | ||||
−0.957605 | + | 0.288084i | \(0.906982\pi\) | |||||||
\(644\) | −8.01170 | + | 3.94755i | −0.315705 | + | 0.155555i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.91683i | 0.0754168i | ||||||||
\(647\) | 42.6518i | 1.67681i | 0.545044 | + | 0.838407i | \(0.316513\pi\) | ||||
−0.545044 | + | 0.838407i | \(0.683487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00986 | + | 14.9864i | −0.157401 | + | 0.588268i | ||||
\(650\) | − | 1.48066i | − | 0.0580764i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.2077 | −0.438928 | ||||||||
\(653\) | 11.3916 | 0.445786 | 0.222893 | − | 0.974843i | \(-0.428450\pi\) | ||||
0.222893 | + | 0.974843i | \(0.428450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 42.6911i | − | 1.66808i | ||||||
\(656\) | 8.09326 | 0.315989 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.8274 | + | 10.2621i | −0.811936 | + | 0.400060i | ||||
\(659\) | − | 28.1616i | − | 1.09702i | −0.836144 | − | 0.548509i | \(-0.815196\pi\) | ||
0.836144 | − | 0.548509i | \(-0.184804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.4233i | − | 1.30002i | −0.759927 | − | 0.650009i | \(-0.774765\pi\) | ||
0.759927 | − | 0.650009i | \(-0.225235\pi\) | |||||||
\(662\) | − | 1.50899i | − | 0.0586487i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.11447i | 0.276095i | ||||||||
\(665\) | 21.8119 | + | 44.2681i | 0.845831 | + | 1.71664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.8798i | − | 0.576149i | ||||||
\(668\) | −14.6933 | −0.568501 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.29682 | 0.204634 | ||||||||
\(671\) | 44.1616 | + | 11.8162i | 1.70484 | + | 0.456158i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.2033i | − | 1.39553i | −0.716325 | − | 0.697767i | \(-0.754177\pi\) | ||
0.716325 | − | 0.697767i | \(-0.245823\pi\) | |||||||
\(674\) | −5.38663 | −0.207485 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.8852 | 0.495586 | ||||||||
\(677\) | 38.4221 | 1.47668 | 0.738340 | − | 0.674428i | \(-0.235610\pi\) | ||||
0.738340 | + | 0.674428i | \(0.235610\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.94672 | + | 12.0691i | 0.228214 | + | 0.463169i | ||||
\(680\) | 0.962995 | 0.0369292 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.31458 | + | 0.619305i | 0.0886300 | + | 0.0237144i | ||||
\(683\) | −5.44484 | −0.208341 | −0.104171 | − | 0.994559i | \(-0.533219\pi\) | ||||
−0.104171 | + | 0.994559i | \(0.533219\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.0567i | − | 1.37765i | ||||||
\(686\) | 18.1607 | + | 3.63163i | 0.693379 | + | 0.138656i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.12236i | 0.157164i | ||||||||
\(689\) | −4.59435 | −0.175031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.850492i | 0.0323542i | 0.999869 | + | 0.0161771i | \(0.00514956\pi\) | ||||
−0.999869 | + | 0.0161771i | \(0.994850\pi\) | |||||||
\(692\) | −11.2077 | −0.426054 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.8761 | −0.830405 | ||||||||
\(695\) | − | 23.0755i | − | 0.875304i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.54600 | 0.0964366 | ||||||||
\(698\) | − | 1.73525i | − | 0.0656802i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.3733 | − | 5.11117i | 0.392074 | − | 0.193184i | ||||
\(701\) | 18.9222i | 0.714683i | 0.933974 | + | 0.357342i | \(0.116317\pi\) | ||||
−0.933974 | + | 0.357342i | \(0.883683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.6580 | −1.72202 | ||||||||
\(704\) | −3.20392 | − | 0.857262i | −0.120752 | − | 0.0323093i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.8874 | 0.786109 | ||||||||
\(707\) | −23.0555 | + | 11.3600i | −0.867090 | + | 0.427236i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.8021 | −1.41969 | −0.709843 | − | 0.704360i | \(-0.751234\pi\) | ||||
−0.709843 | + | 0.704360i | \(0.751234\pi\) | |||||||
\(710\) | 41.4682 | 1.55628 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.28548 | −0.0856518 | ||||||||
\(713\) | − | 2.43873i | − | 0.0913311i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.888985 | + | 3.32248i | −0.0332462 | + | 0.124254i | ||||
\(716\) | −19.0446 | −0.711731 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.5786 | 1.06654 | ||||||||
\(719\) | 36.6094i | 1.36530i | 0.730746 | + | 0.682650i | \(0.239172\pi\) | ||||
−0.730746 | + | 0.682650i | \(0.760828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.84259 | − | 15.9168i | −0.292073 | − | 0.592774i | ||||
\(722\) | 18.1278i | 0.674646i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 14.5435i | − | 0.540505i | ||||||
\(725\) | 19.2659i | 0.715519i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0449029i | 0.00166536i | 1.00000 | 0.000832678i | \(0.000265050\pi\) | |||||
−1.00000 | 0.000832678i | \(0.999735\pi\) | ||||||||
\(728\) | −0.396139 | − | 0.803978i | −0.0146819 | − | 0.0297974i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.15937 | 0.190957 | ||||||||
\(731\) | 1.29682i | 0.0479648i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.7601 | −1.35777 | −0.678883 | − | 0.734246i | \(-0.737536\pi\) | ||||
−0.678883 | + | 0.734246i | \(0.737536\pi\) | |||||||
\(734\) | −30.0759 | −1.11012 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.37576i | 0.124432i | ||||||||
\(737\) | −5.54381 | − | 1.48334i | −0.204209 | − | 0.0546395i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.07995i | 0.223654i | 0.993728 | + | 0.111827i | \(0.0356703\pi\) | ||||
−0.993728 | + | 0.111827i | \(0.964330\pi\) | |||||||
\(740\) | 22.9380i | 0.843219i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.8595 | − | 32.1873i | −0.582219 | − | 1.18163i | ||||
\(743\) | − | 1.93585i | − | 0.0710195i | −0.999369 | − | 0.0355097i | \(-0.988695\pi\) | ||
0.999369 | − | 0.0355097i | \(-0.0113055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.8640 | 1.05750 | ||||||||
\(746\) | 33.3508 | 1.22106 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.00790 | − | 0.269680i | −0.0368524 | − | 0.00986047i | ||||
\(749\) | 11.3600 | + | 23.0555i | 0.415084 | + | 0.842429i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.58081 | −0.313118 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(752\) | 8.77571i | 0.320017i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.49320 | 0.0543791 | ||||||||
\(755\) | −27.8270 | −1.01273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6955 | 1.22468 | 0.612342 | − | 0.790593i | \(-0.290228\pi\) | ||||
0.612342 | + | 0.790593i | \(0.290228\pi\) | |||||||
\(758\) | 6.42364i | 0.233317i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.6526 | 0.676600 | ||||||||
\(761\) | 14.2722 | 0.517366 | 0.258683 | − | 0.965962i | \(-0.416712\pi\) | ||||
0.258683 | + | 0.965962i | \(0.416712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.2081 | + | 45.0721i | 0.803986 | + | 1.63172i | ||||
\(764\) | −6.11743 | −0.221321 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.1949 | 0.440619 | ||||||||
\(767\) | 1.58455i | 0.0572150i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.9785 | 1.51378 | 0.756892 | − | 0.653540i | \(-0.226717\pi\) | ||||
0.756892 | + | 0.653540i | \(0.226717\pi\) | |||||||
\(770\) | −26.3455 | + | 5.24092i | −0.949427 | + | 0.188870i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.7515i | 0.386956i | ||||||||
\(773\) | − | 33.9094i | − | 1.21964i | −0.792541 | − | 0.609819i | \(-0.791242\pi\) | ||
0.792541 | − | 0.609819i | \(-0.208758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.15759i | 0.113424i | ||||||||
\(776\) | 5.08536 | 0.182554 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.7466i | 0.456988i | ||||||||
\(779\) | 49.3143 | 1.76687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.4018 | − | 11.6129i | −1.55304 | − | 0.415542i | ||||
\(782\) | 1.06196i | 0.0379755i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.26510 | − | 5.55058i | 0.152325 | − | 0.198235i | ||||
\(785\) | −25.8754 | −0.923532 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.3342 | −1.75858 | −0.879288 | − | 0.476291i | \(-0.841981\pi\) | ||||
−0.879288 | + | 0.476291i | \(0.841981\pi\) | |||||||
\(788\) | 25.9010i | 0.922686i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.0271i | 0.748112i | ||||||||
\(791\) | 26.3464 | − | 12.9815i | 0.936769 | − | 0.461568i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.66933 | 0.165813 | ||||||||
\(794\) | −20.3146 | −0.720938 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.5707i | 0.693664i | ||||||||
\(797\) | 13.9578i | 0.494410i | 0.968963 | + | 0.247205i | \(0.0795121\pi\) | ||||
−0.968963 | + | 0.247205i | \(0.920488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.76069i | 0.0976660i | ||||||||
\(800\) | − | 4.37083i | − | 0.154532i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.792277i | 0.0279763i | ||||||||
\(803\) | −5.39994 | − | 1.44484i | −0.190560 | − | 0.0509875i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0842 | + | 24.5253i | 0.425911 | + | 0.864402i | ||||
\(806\) | 0.244728 | 0.00862016 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.71452i | 0.341756i | ||||||||
\(809\) | − | 36.9864i | − | 1.30037i | −0.759775 | − | 0.650186i | \(-0.774691\pi\) | ||
0.759775 | − | 0.650186i | \(-0.225309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.6023 | −0.758558 | −0.379279 | − | 0.925282i | \(-0.623828\pi\) | ||||
−0.379279 | + | 0.925282i | \(0.623828\pi\) | |||||||
\(812\) | 5.15444 | + | 10.4611i | 0.180885 | + | 0.367113i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.42364 | − | 24.0076i | 0.225148 | − | 0.841466i | ||||
\(815\) | 34.3089i | 1.20179i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.1186i | 0.878789i | ||||||||
\(818\) | 26.6077i | 0.930315i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 24.7749i | − | 0.865178i | ||||||
\(821\) | − | 40.9864i | − | 1.43044i | −0.698902 | − | 0.715218i | \(-0.746328\pi\) | ||
0.698902 | − | 0.715218i | \(-0.253672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.6178 | 1.69471 | 0.847354 | − | 0.531028i | \(-0.178194\pi\) | ||||
0.847354 | + | 0.531028i | \(0.178194\pi\) | |||||||
\(824\) | −6.70663 | −0.233636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1012 | + | 5.46980i | −0.386259 | + | 0.190319i | ||||
\(827\) | − | 47.8988i | − | 1.66560i | −0.553571 | − | 0.832802i | \(-0.686735\pi\) | ||
0.553571 | − | 0.832802i | \(-0.313265\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.45964i | 0.293816i | 0.989150 | + | 0.146908i | \(0.0469321\pi\) | ||||
−0.989150 | + | 0.146908i | \(0.953068\pi\) | |||||||
\(830\) | 21.7787 | 0.755949 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.338760 | −0.0117444 | ||||||||
\(833\) | 1.34173 | − | 1.74612i | 0.0464881 | − | 0.0604993i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.9789i | 1.55656i | ||||||||
\(836\) | −19.5223 | − | 5.22352i | −0.675193 | − | 0.180659i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.9380 | 0.377848 | ||||||||
\(839\) | − | 45.7295i | − | 1.57876i | −0.613905 | − | 0.789380i | \(-0.710402\pi\) | ||
0.613905 | − | 0.789380i | \(-0.289598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.57095 | 0.330033 | ||||||||
\(842\) | 30.3829i | 1.04706i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.95165i | 0.204864i | ||||||||
\(845\) | − | 39.4441i | − | 1.35692i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.0417 | + | 1.89258i | 0.997883 | + | 0.0650297i | ||||
\(848\) | −13.5623 | −0.465731 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 1.37499i | − | 0.0471617i | ||||||
\(851\) | −25.2953 | −0.867111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.7994 | 1.36271 | 0.681353 | − | 0.731955i | \(-0.261392\pi\) | ||||
0.681353 | + | 0.731955i | \(0.261392\pi\) | |||||||
\(854\) | 16.1183 | + | 32.7126i | 0.551556 | + | 1.11940i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.71452 | 0.332036 | ||||||||
\(857\) | 9.92254 | 0.338947 | 0.169474 | − | 0.985535i | \(-0.445793\pi\) | ||||
0.169474 | + | 0.985535i | \(0.445793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.3594i | − | 1.06997i | −0.844862 | − | 0.534985i | \(-0.820317\pi\) | ||
0.844862 | − | 0.534985i | \(-0.179683\pi\) | |||||||
\(860\) | 12.6193 | 0.430315 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.1458 | 0.822408 | ||||||||
\(863\) | −4.06314 | −0.138311 | −0.0691555 | − | 0.997606i | \(-0.522030\pi\) | ||||
−0.0691555 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.3089i | 1.16654i | ||||||||
\(866\) | 13.5031 | 0.458853 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.844786 | + | 1.71452i | 0.0286739 | + | 0.0581947i | ||||
\(869\) | 5.88850 | − | 22.0076i | 0.199754 | − | 0.746557i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.586163 | −0.0198614 | ||||||||
\(872\) | 18.9913 | 0.643127 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.5694i | 0.695770i | ||||||||
\(875\) | 2.25221 | + | 4.57095i | 0.0761387 | + | 0.154526i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 28.8423i | − | 0.973937i | −0.873420 | − | 0.486968i | \(-0.838103\pi\) | ||
0.873420 | − | 0.486968i | \(-0.161897\pi\) | |||||||
\(878\) | − | 30.5911i | − | 1.03240i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.62424 | + | 9.80778i | −0.0884630 | + | 0.330620i | ||||
\(881\) | 19.4856i | 0.656486i | 0.944593 | + | 0.328243i | \(0.106457\pi\) | ||||
−0.944593 | + | 0.328243i | \(0.893543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.11031 | 0.0373649 | 0.0186825 | − | 0.999825i | \(-0.494053\pi\) | ||||
0.0186825 | + | 0.999825i | \(0.494053\pi\) | |||||||
\(884\) | −0.106568 | −0.00358427 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 28.8739i | − | 0.970037i | ||||||
\(887\) | −3.24254 | −0.108874 | −0.0544368 | − | 0.998517i | \(-0.517336\pi\) | ||||
−0.0544368 | + | 0.998517i | \(0.517336\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.2710 | − | 51.2885i | −0.847563 | − | 1.72016i | ||||
\(890\) | 6.99626i | 0.234515i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.04490i | − | 0.269363i | ||||||
\(893\) | 53.4726i | 1.78939i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.2990i | 1.94872i | ||||||||
\(896\) | −1.16938 | − | 2.37330i | −0.0390662 | − | 0.0792864i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.5944i | 0.687242i | ||||||||
\(899\) | −3.18432 | −0.106203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26646 | −0.142136 | ||||||||
\(902\) | −6.93804 | + | 25.9301i | −0.231012 | + | 0.863379i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 11.1012i | − | 0.369219i | ||||||
\(905\) | −44.5203 | −1.47991 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5748 | −0.649971 | −0.324986 | − | 0.945719i | \(-0.605359\pi\) | ||||
−0.324986 | + | 0.945719i | \(0.605359\pi\) | |||||||
\(908\) | 17.0155 | 0.564679 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.46112 | + | 1.21265i | −0.0815854 | + | 0.0401990i | ||||
\(911\) | −10.4535 | −0.346340 | −0.173170 | − | 0.984892i | \(-0.555401\pi\) | ||||
−0.173170 | + | 0.984892i | \(0.555401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.7942 | − | 6.09896i | −0.754377 | − | 0.201846i | ||||
\(914\) | 6.87983 | 0.227565 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.7942i | 0.819223i | ||||||||
\(917\) | −33.0979 | + | 16.3081i | −1.09299 | + | 0.538541i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.5373i | 1.83201i | 0.401170 | + | 0.916004i | \(0.368604\pi\) | ||||
−0.401170 | + | 0.916004i | \(0.631396\pi\) | |||||||
\(920\) | 10.3338 | 0.340696 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.2681i | 0.535762i | ||||||||
\(923\) | −4.58900 | −0.151049 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.7515 | 1.07686 | ||||||||
\(926\) | 17.5899i | 0.578040i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.40784 | 0.144694 | ||||||||
\(929\) | − | 1.16530i | − | 0.0382324i | −0.999817 | − | 0.0191162i | \(-0.993915\pi\) | ||
0.999817 | − | 0.0191162i | \(-0.00608524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.9884 | − | 33.8211i | 0.851734 | − | 1.10844i | ||||
\(932\) | − | 0.170718i | − | 0.00559204i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41.0022 | −1.34163 | ||||||||
\(935\) | −0.825539 | + | 3.08536i | −0.0269980 | + | 0.100902i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.4875 | −1.74736 | −0.873680 | − | 0.486501i | \(-0.838273\pi\) | ||||
−0.873680 | + | 0.486501i | \(0.838273\pi\) | |||||||
\(938\) | −2.02340 | − | 4.10657i | −0.0660664 | − | 0.134084i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 26.8640 | 0.876208 | ||||||||
\(941\) | 33.2985 | 1.08550 | 0.542750 | − | 0.839894i | \(-0.317383\pi\) | ||||
0.542750 | + | 0.839894i | \(0.317383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.3209 | 0.889692 | ||||||||
\(944\) | 4.67752i | 0.152240i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.2077 | − | 3.53395i | −0.429420 | − | 0.114899i | ||||
\(947\) | −47.5965 | −1.54668 | −0.773340 | − | 0.633992i | \(-0.781415\pi\) | ||||
−0.773340 | + | 0.633992i | \(0.781415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.570951 | −0.0185339 | ||||||||
\(950\) | − | 26.6326i | − | 0.864076i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.367867 | − | 0.746599i | −0.0119226 | − | 0.0241974i | ||||
\(953\) | − | 14.4895i | − | 0.469359i | −0.972073 | − | 0.234680i | \(-0.924596\pi\) | ||
0.972073 | − | 0.234680i | \(-0.0754041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.7266i | 0.605978i | ||||||||
\(956\) | 18.8897i | 0.610936i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 4.29308i | − | 0.138703i | ||||||
\(959\) | −27.9543 | + | 13.7737i | −0.902692 | + | 0.444777i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4781 | 0.983165 | ||||||||
\(962\) | − | 2.53839i | − | 0.0818411i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.436947 | −0.0140731 | ||||||||
\(965\) | 32.9124 | 1.05949 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.5600i | 1.07922i | 0.841916 | + | 0.539609i | \(0.181428\pi\) | ||||
−0.841916 | + | 0.539609i | \(0.818572\pi\) | |||||||
\(968\) | 5.49320 | − | 9.53020i | 0.176558 | − | 0.306312i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 15.5672i | − | 0.499833i | ||||||
\(971\) | − | 43.5824i | − | 1.39863i | −0.714815 | − | 0.699313i | \(-0.753489\pi\) | ||
0.714815 | − | 0.699313i | \(-0.246511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.8902 | + | 8.81490i | −0.573533 | + | 0.282593i | ||||
\(974\) | − | 14.8897i | − | 0.477096i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.7836 | 0.441202 | ||||||||
\(977\) | 11.2169 | 0.358860 | 0.179430 | − | 0.983771i | \(-0.442575\pi\) | ||||
0.179430 | + | 0.983771i | \(0.442575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.95925 | − | 7.32248i | 0.0626180 | − | 0.234027i | ||||
\(980\) | −16.9913 | − | 13.0563i | −0.542768 | − | 0.417067i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.35949 | −0.139117 | ||||||||
\(983\) | 53.1221i | 1.69433i | 0.531328 | + | 0.847166i | \(0.321693\pi\) | ||||
−0.531328 | + | 0.847166i | \(0.678307\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 79.2878 | 2.52632 | ||||||||
\(986\) | 1.38663 | 0.0441593 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.06415 | −0.0656693 | ||||||||
\(989\) | 13.9161i | 0.442507i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9827 | 1.20656 | 0.603279 | − | 0.797530i | \(-0.293860\pi\) | ||||
0.603279 | + | 0.797530i | \(0.293860\pi\) | |||||||
\(992\) | 0.722422 | 0.0229369 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.8410 | − | 32.1499i | −0.502445 | − | 1.01973i | ||||
\(995\) | 59.9093 | 1.89925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8939 | −0.345014 | −0.172507 | − | 0.985008i | \(-0.555187\pi\) | ||||
−0.172507 | + | 0.985008i | \(0.555187\pi\) | |||||||
\(998\) | − | 6.73573i | − | 0.213216i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.e.e.307.8 | 8 | ||
3.2 | odd | 2 | 462.2.e.a.307.1 | ✓ | 8 | ||
7.6 | odd | 2 | 1386.2.e.a.307.5 | 8 | |||
11.10 | odd | 2 | 1386.2.e.a.307.4 | 8 | |||
12.11 | even | 2 | 3696.2.q.b.769.5 | 8 | |||
21.20 | even | 2 | 462.2.e.b.307.4 | yes | 8 | ||
33.32 | even | 2 | 462.2.e.b.307.5 | yes | 8 | ||
77.76 | even | 2 | inner | 1386.2.e.e.307.1 | 8 | ||
84.83 | odd | 2 | 3696.2.q.c.769.4 | 8 | |||
132.131 | odd | 2 | 3696.2.q.c.769.5 | 8 | |||
231.230 | odd | 2 | 462.2.e.a.307.8 | yes | 8 | ||
924.923 | even | 2 | 3696.2.q.b.769.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.e.a.307.1 | ✓ | 8 | 3.2 | odd | 2 | ||
462.2.e.a.307.8 | yes | 8 | 231.230 | odd | 2 | ||
462.2.e.b.307.4 | yes | 8 | 21.20 | even | 2 | ||
462.2.e.b.307.5 | yes | 8 | 33.32 | even | 2 | ||
1386.2.e.a.307.4 | 8 | 11.10 | odd | 2 | |||
1386.2.e.a.307.5 | 8 | 7.6 | odd | 2 | |||
1386.2.e.e.307.1 | 8 | 77.76 | even | 2 | inner | ||
1386.2.e.e.307.8 | 8 | 1.1 | even | 1 | trivial | ||
3696.2.q.b.769.4 | 8 | 924.923 | even | 2 | |||
3696.2.q.b.769.5 | 8 | 12.11 | even | 2 | |||
3696.2.q.c.769.4 | 8 | 84.83 | odd | 2 | |||
3696.2.q.c.769.5 | 8 | 132.131 | odd | 2 |