Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (of order \(2\), degree \(1\), 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.15 | ||
Root | \(0.0964469 - 1.72936i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.k.881.16 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72936 | − | 0.0964469i | 0.998448 | − | 0.0556837i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.208829 | + | 2.63750i | −0.0789298 | + | 0.996880i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98140 | − | 0.333584i | 0.993799 | − | 0.111195i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.71212i | 0.516224i | 0.966115 | + | 0.258112i | \(0.0831004\pi\) | ||||
−0.966115 | + | 0.258112i | \(0.916900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.11462i | 0.863839i | 0.901912 | + | 0.431920i | \(0.142164\pi\) | ||||
−0.901912 | + | 0.431920i | \(0.857836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.72936 | + | 0.0964469i | −0.446520 | + | 0.0249025i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.59399 | −0.871671 | −0.435836 | − | 0.900026i | \(-0.643547\pi\) | ||||
−0.435836 | + | 0.900026i | \(0.643547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.04495i | − | 0.239729i | −0.992790 | − | 0.119865i | \(-0.961754\pi\) | ||
0.992790 | − | 0.119865i | \(-0.0382460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.106762 | + | 4.58133i | −0.0232974 | + | 0.999729i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.587015i | − | 0.122401i | −0.998125 | − | 0.0612006i | \(-0.980507\pi\) | ||
0.998125 | − | 0.0612006i | \(-0.0194929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.12374 | − | 0.864434i | 0.986065 | − | 0.166360i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47468i | 0.830928i | 0.909610 | + | 0.415464i | \(0.136381\pi\) | ||||
−0.909610 | + | 0.415464i | \(0.863619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.51183i | 1.52877i | 0.644760 | + | 0.764385i | \(0.276957\pi\) | ||||
−0.644760 | + | 0.764385i | \(0.723043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.165129 | + | 2.96088i | 0.0287452 | + | 0.515423i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.208829 | − | 2.63750i | 0.0352985 | − | 0.445818i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.99549 | −1.31445 | −0.657225 | − | 0.753694i | \(-0.728270\pi\) | ||||
−0.657225 | + | 0.753694i | \(0.728270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.300395 | + | 5.38630i | 0.0481017 | + | 0.862499i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.74927 | −1.21023 | −0.605116 | − | 0.796137i | \(-0.706873\pi\) | ||||
−0.605116 | + | 0.796137i | \(0.706873\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.05272 | 0.770533 | 0.385266 | − | 0.922805i | \(-0.374110\pi\) | ||||
0.385266 | + | 0.922805i | \(0.374110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.98140 | + | 0.333584i | −0.444440 | + | 0.0497277i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.90809 | 1.44524 | 0.722622 | − | 0.691244i | \(-0.242937\pi\) | ||||
0.722622 | + | 0.691244i | \(0.242937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91278 | − | 1.10157i | −0.987540 | − | 0.157367i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.21532 | + | 0.346630i | −0.870319 | + | 0.0485378i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.63566i | − | 0.636757i | −0.947964 | − | 0.318379i | \(-0.896862\pi\) | ||
0.947964 | − | 0.318379i | \(-0.103138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.71212i | − | 0.230862i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.100783 | − | 1.80711i | −0.0133490 | − | 0.239357i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.11673 | −0.275575 | −0.137788 | − | 0.990462i | \(-0.543999\pi\) | ||||
−0.137788 | + | 0.990462i | \(0.543999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.11222i | 1.03866i | 0.854573 | + | 0.519332i | \(0.173819\pi\) | ||||
−0.854573 | + | 0.519332i | \(0.826181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.257225 | + | 7.93308i | 0.0324072 | + | 0.999475i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.11462i | − | 0.386321i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.80626 | 1.07586 | 0.537928 | − | 0.842991i | \(-0.319207\pi\) | ||||
0.537928 | + | 0.842991i | \(0.319207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0566158 | − | 1.01516i | −0.00681574 | − | 0.122211i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.57259i | 0.305311i | 0.988279 | + | 0.152655i | \(0.0487825\pi\) | ||||
−0.988279 | + | 0.152655i | \(0.951218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.88336i | 0.805637i | 0.915280 | + | 0.402818i | \(0.131969\pi\) | ||||
−0.915280 | + | 0.402818i | \(0.868031\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.72936 | − | 0.0964469i | 0.199690 | − | 0.0111367i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.51572 | − | 0.357540i | −0.514614 | − | 0.0407455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.01425 | 0.789164 | 0.394582 | − | 0.918861i | \(-0.370889\pi\) | ||||
0.394582 | + | 0.918861i | \(0.370889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.77744 | − | 1.98909i | 0.975272 | − | 0.221010i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.21838 | −0.572791 | −0.286396 | − | 0.958111i | \(-0.592457\pi\) | ||||
−0.286396 | + | 0.958111i | \(0.592457\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.59399 | 0.389823 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.431570 | + | 7.73836i | 0.0462691 | + | 0.829639i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.17632 | 0.866688 | 0.433344 | − | 0.901229i | \(-0.357334\pi\) | ||||
0.433344 | + | 0.901229i | \(0.357334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.21479 | − | 0.650421i | −0.861144 | − | 0.0681827i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.820940 | + | 14.7200i | 0.0851275 | + | 1.52640i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.04495i | 0.107210i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5934i | 1.38020i | 0.723715 | + | 0.690099i | \(0.242433\pi\) | ||||
−0.723715 | + | 0.690099i | \(0.757567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.571136 | + | 5.10451i | 0.0574013 | + | 0.513023i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.28370 | 0.426245 | 0.213122 | − | 0.977026i | \(-0.431637\pi\) | ||||
0.213122 | + | 0.977026i | \(0.431637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0227i | 1.38170i | 0.722998 | + | 0.690850i | \(0.242764\pi\) | ||||
−0.722998 | + | 0.690850i | \(0.757236\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.106762 | − | 4.58133i | 0.0104189 | − | 0.447092i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19.4771i | − | 1.88292i | −0.337118 | − | 0.941462i | \(-0.609452\pi\) | ||
0.337118 | − | 0.941462i | \(-0.390548\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7331 | −1.02804 | −0.514021 | − | 0.857778i | \(-0.671845\pi\) | ||||
−0.514021 | + | 0.857778i | \(0.671845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.8271 | + | 0.771140i | −1.31241 | + | 0.0731934i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.81346i | − | 0.829100i | −0.910026 | − | 0.414550i | \(-0.863939\pi\) | ||
0.910026 | − | 0.414550i | \(-0.136061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.587015i | 0.0547395i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.03898 | + | 9.28590i | 0.0960542 | + | 0.858482i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.750529 | − | 9.47915i | 0.0688009 | − | 0.868952i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.06864 | 0.733513 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.4013 | + | 0.747393i | −1.20835 | + | 0.0673902i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2398 | 1.52978 | 0.764890 | − | 0.644160i | \(-0.222793\pi\) | ||||
0.764890 | + | 0.644160i | \(0.222793\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.73799 | − | 0.487319i | 0.769337 | − | 0.0429061i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.92330 | 0.604891 | 0.302446 | − | 0.953167i | \(-0.402197\pi\) | ||||
0.302446 | + | 0.953167i | \(0.402197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.75606 | + | 0.218217i | 0.238981 | + | 0.0189218i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.12374 | + | 0.864434i | −0.440982 | + | 0.0743986i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 21.5200i | − | 1.83858i | −0.393584 | − | 0.919289i | \(-0.628765\pi\) | ||
0.393584 | − | 0.919289i | \(-0.371235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.37425i | − | 0.455838i | −0.973680 | − | 0.227919i | \(-0.926808\pi\) | ||
0.973680 | − | 0.227919i | \(-0.0731921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.1347 | − | 0.955605i | 1.44300 | − | 0.0804764i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.33260 | −0.445935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.47468i | − | 0.371602i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0610 | − | 1.23830i | −0.994771 | − | 0.102133i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.35482i | 0.110992i | 0.998459 | + | 0.0554958i | \(0.0176739\pi\) | ||||
−0.998459 | + | 0.0554958i | \(0.982326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4778 | −1.17819 | −0.589093 | − | 0.808065i | \(-0.700515\pi\) | ||||
−0.589093 | + | 0.808065i | \(0.700515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.7151 | + | 1.19890i | −0.866266 | + | 0.0969251i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.51183i | − | 0.683687i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.6973i | − | 1.41239i | −0.708015 | − | 0.706197i | \(-0.750409\pi\) | ||
0.708015 | − | 0.706197i | \(-0.249591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.447095 | − | 8.01675i | −0.0354570 | − | 0.635769i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.54825 | + | 0.122586i | 0.122019 | + | 0.00966110i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1348 | 1.10713 | 0.553563 | − | 0.832807i | \(-0.313268\pi\) | ||||
0.553563 | + | 0.832807i | \(0.313268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.165129 | − | 2.96088i | −0.0128553 | − | 0.230504i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5005 | −0.812554 | −0.406277 | − | 0.913750i | \(-0.633173\pi\) | ||||
−0.406277 | + | 0.913750i | \(0.633173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.29917 | 0.253782 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.348580 | − | 3.11542i | −0.0266566 | − | 0.238242i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.6775 | 1.49605 | 0.748025 | − | 0.663671i | \(-0.231002\pi\) | ||||
0.748025 | + | 0.663671i | \(0.231002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.208829 | + | 2.63750i | −0.0157860 | + | 0.199376i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.66060 | + | 0.204152i | −0.275148 | + | 0.0153450i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.2730i | 1.59002i | 0.606599 | + | 0.795008i | \(0.292534\pi\) | ||||
−0.606599 | + | 0.795008i | \(0.707466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.52329i | 0.707861i | 0.935272 | + | 0.353930i | \(0.115155\pi\) | ||||
−0.935272 | + | 0.353930i | \(0.884845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.782399 | + | 14.0290i | 0.0578366 | + | 1.03705i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.99549 | 0.587840 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.15335i | − | 0.449978i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.20996 | + | 13.6944i | 0.0880114 | + | 0.996119i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 22.1742i | − | 1.60447i | −0.597007 | − | 0.802236i | \(-0.703644\pi\) | ||
0.597007 | − | 0.802236i | \(-0.296356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1540 | −0.946846 | −0.473423 | − | 0.880835i | \(-0.656982\pi\) | ||||
−0.473423 | + | 0.880835i | \(0.656982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.300395 | − | 5.38630i | −0.0215117 | − | 0.385721i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.8493i | − | 0.986721i | −0.869825 | − | 0.493361i | \(-0.835768\pi\) | ||
0.869825 | − | 0.493361i | \(-0.164232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.51305i | − | 0.107257i | −0.998561 | − | 0.0536285i | \(-0.982921\pi\) | ||
0.998561 | − | 0.0536285i | \(-0.0170787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2292 | − | 0.849336i | 1.07419 | − | 0.0599076i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.8020 | − | 0.934443i | −0.828336 | − | 0.0655850i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.74927 | 0.541232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.195819 | − | 1.75012i | −0.0136103 | − | 0.121642i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.78909 | 0.123754 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.10496 | −0.213754 | −0.106877 | − | 0.994272i | \(-0.534085\pi\) | ||||
−0.106877 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.248119 | + | 4.44895i | 0.0170008 | + | 0.304837i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.05272 | −0.344593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.4499 | − | 1.77751i | −1.52400 | − | 0.120666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.663879 | + | 11.9038i | 0.0448608 | + | 0.804387i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.1939i | − | 0.752984i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.39251i | 0.428074i | 0.976826 | + | 0.214037i | \(0.0686614\pi\) | ||||
−0.976826 | + | 0.214037i | \(0.931339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.98140 | − | 0.333584i | 0.198760 | − | 0.0222389i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.2462 | −0.879181 | −0.439591 | − | 0.898198i | \(-0.644876\pi\) | ||||
−0.439591 | + | 0.898198i | \(0.644876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.4689i | − | 1.02221i | −0.859517 | − | 0.511107i | \(-0.829236\pi\) | ||
0.859517 | − | 0.511107i | \(-0.170764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.84380 | − | 0.182790i | −0.516084 | − | 0.0120267i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.5413i | 1.86980i | 0.354907 | + | 0.934901i | \(0.384512\pi\) | ||||
−0.354907 | + | 0.934901i | \(0.615488\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.90809 | −0.646332 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.1302 | − | 0.676502i | 0.787940 | − | 0.0439436i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.61686i | − | 0.298640i | −0.988789 | − | 0.149320i | \(-0.952292\pi\) | ||
0.988789 | − | 0.149320i | \(-0.0477084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.3604i | − | 0.667375i | −0.942684 | − | 0.333687i | \(-0.891707\pi\) | ||
0.942684 | − | 0.333687i | \(-0.108293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9875 | − | 4.28642i | 0.961452 | − | 0.274974i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.91278 | + | 1.10157i | 0.441641 | + | 0.0703767i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.25463 | 0.207087 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.02447 | + | 0.503297i | −0.571903 | + | 0.0318951i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.0748113 | 0.00472205 | 0.00236102 | − | 0.999997i | \(-0.499248\pi\) | ||||
0.00236102 | + | 0.999997i | \(0.499248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00504 | 0.0631864 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.21532 | − | 0.346630i | 0.389218 | − | 0.0217068i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.49720 | 0.467663 | 0.233831 | − | 0.972277i | \(-0.424874\pi\) | ||||
0.233831 | + | 0.972277i | \(0.424874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66969 | − | 21.0881i | 0.103749 | − | 1.31035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.49268 | + | 13.3408i | 0.0923947 | + | 0.825775i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.0579i | 1.23682i | 0.785855 | + | 0.618410i | \(0.212223\pi\) | ||||
−0.785855 | + | 0.618410i | \(0.787777\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.63566i | 0.284766i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.1398 | − | 0.788581i | 0.865343 | − | 0.0482603i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.2069 | −1.53689 | −0.768447 | − | 0.639914i | \(-0.778970\pi\) | ||||
−0.768447 | + | 0.639914i | \(0.778970\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0716i | 1.09777i | 0.835896 | + | 0.548887i | \(0.184948\pi\) | ||||
−0.835896 | + | 0.548887i | \(0.815052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.2691 | − | 0.332524i | −0.863605 | − | 0.0201252i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.71212i | 0.103245i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7938 | −0.828786 | −0.414393 | − | 0.910098i | \(-0.636006\pi\) | ||||
−0.414393 | + | 0.910098i | \(0.636006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.83941 | + | 25.3771i | 0.169991 | + | 1.51929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.315357i | 0.0188126i | 0.999956 | + | 0.00940632i | \(0.00299417\pi\) | ||||
−0.999956 | + | 0.00940632i | \(0.997006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.6408i | − | 1.22697i | −0.789707 | − | 0.613484i | \(-0.789767\pi\) | ||
0.789707 | − | 0.613484i | \(-0.210233\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.100783 | + | 1.80711i | 0.00596985 | + | 0.107044i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.61827 | − | 20.4387i | 0.0955234 | − | 1.20646i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.08321 | −0.240189 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.31104 | + | 23.5079i | 0.0768544 | + | 1.37806i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.75188 | 0.219187 | 0.109594 | − | 0.993976i | \(-0.465045\pi\) | ||||
0.109594 | + | 0.993976i | \(0.465045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11673 | 0.123241 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.48002 | + | 8.77247i | 0.0858792 | + | 0.509031i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.82833 | 0.105735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05515 | + | 13.3265i | −0.0608180 | + | 0.768129i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.40808 | − | 0.413150i | 0.425583 | − | 0.0237349i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.11222i | − | 0.464504i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.9301i | − | 1.70820i | −0.520108 | − | 0.854101i | \(-0.674108\pi\) | ||
0.520108 | − | 0.854101i | \(-0.325892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.35245 | + | 24.2504i | 0.0769381 | + | 1.37956i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.0310 | 1.19256 | 0.596280 | − | 0.802777i | \(-0.296645\pi\) | ||||
0.596280 | + | 0.802777i | \(0.296645\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.74984i | − | 0.551094i | −0.961288 | − | 0.275547i | \(-0.911141\pi\) | ||
0.961288 | − | 0.275547i | \(-0.0888589\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.257225 | − | 7.93308i | −0.0144930 | − | 0.446979i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.2388i | − | 0.912064i | −0.889963 | − | 0.456032i | \(-0.849270\pi\) | ||
0.889963 | − | 0.456032i | \(-0.150730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.66120 | −0.428945 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.87851 | − | 33.6830i | −0.104848 | − | 1.88000i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.75556i | 0.208965i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.11462i | 0.172768i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5614 | + | 1.03517i | −1.02645 | + | 0.0572451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.06909 | + | 26.1326i | −0.114073 | + | 1.44073i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3877 | −0.570957 | −0.285479 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285479 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.8377 | + | 2.66716i | −1.30630 | + | 0.146160i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.80626 | −0.481137 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3020 | 0.779080 | 0.389540 | − | 0.921010i | \(-0.372634\pi\) | ||||
0.389540 | + | 0.921010i | \(0.372634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.850031 | − | 15.2417i | −0.0461673 | − | 0.827814i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.5733 | −0.789188 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.34898 | − | 18.0024i | 0.234823 | − | 0.972038i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0566158 | + | 1.01516i | 0.00304809 | + | 0.0546545i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.55313i | − | 0.190742i | −0.995442 | − | 0.0953711i | \(-0.969596\pi\) | ||
0.995442 | − | 0.0953711i | \(-0.0304038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 33.8742i | − | 1.81324i | −0.421943 | − | 0.906622i | \(-0.638652\pi\) | ||
0.421943 | − | 0.906622i | \(-0.361348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.69238 | + | 15.9585i | 0.143709 | + | 0.851802i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.702991 | 0.0374165 | 0.0187082 | − | 0.999825i | \(-0.494045\pi\) | ||||
0.0187082 | + | 0.999825i | \(0.494045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.57259i | − | 0.136539i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.383703 | − | 16.4653i | 0.0203077 | − | 0.871435i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.0033i | 1.74185i | 0.491420 | + | 0.870923i | \(0.336478\pi\) | ||||
−0.491420 | + | 0.870923i | \(0.663522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9081 | 0.942530 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.9536 | − | 0.778195i | 0.732375 | − | 0.0408447i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.88336i | − | 0.360292i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.88379i | 0.359331i | 0.983728 | + | 0.179666i | \(0.0575015\pi\) | ||||
−0.983728 | + | 0.179666i | \(0.942498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.1036 | + | 2.58503i | −1.20273 | + | 0.134571i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2265 | + | 0.968060i | 0.634771 | + | 0.0502591i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.1278 | 1.40462 | 0.702311 | − | 0.711870i | \(-0.252152\pi\) | ||||
0.702311 | + | 0.711870i | \(0.252152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.72936 | + | 0.0964469i | −0.0893039 | + | 0.00498050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.9369 | −0.717788 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2240 | 1.29567 | 0.647836 | − | 0.761780i | \(-0.275674\pi\) | ||||
0.647836 | + | 0.761780i | \(0.275674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.8138 | − | 1.66272i | 1.52741 | − | 0.0851838i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8647 | 0.555163 | 0.277581 | − | 0.960702i | \(-0.410467\pi\) | ||||
0.277581 | + | 0.960702i | \(0.410467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.51572 | + | 0.357540i | 0.230142 | + | 0.0182219i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.0642 | − | 1.68550i | 0.765754 | − | 0.0856790i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 24.7623i | − | 1.25550i | −0.778415 | − | 0.627750i | \(-0.783976\pi\) | ||
0.778415 | − | 0.627750i | \(-0.216024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.10973i | 0.106694i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9729 | − | 0.667731i | 0.603953 | − | 0.0336826i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.01425 | −0.352925 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.9258i | − | 1.20080i | −0.799699 | − | 0.600401i | \(-0.795008\pi\) | ||
0.799699 | − | 0.600401i | \(-0.204992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.78728 | + | 0.111562i | 0.239664 | + | 0.00558507i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5963i | 0.678966i | 0.940612 | + | 0.339483i | \(0.110252\pi\) | ||||
−0.940612 | + | 0.339483i | \(0.889748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.5111 | −1.32061 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.77744 | + | 1.98909i | −0.436155 | + | 0.0988386i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 13.6892i | − | 0.678551i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6024i | 1.36485i | 0.730954 | + | 0.682426i | \(0.239075\pi\) | ||||
−0.730954 | + | 0.682426i | \(0.760925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.07554 | − | 37.2159i | −0.102379 | − | 1.83573i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.442035 | − | 5.58288i | 0.0217511 | − | 0.274715i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.21838 | 0.256160 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.518330 | − | 9.29403i | −0.0253827 | − | 0.455130i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.2886 | 1.43084 | 0.715421 | − | 0.698694i | \(-0.246235\pi\) | ||||
0.715421 | + | 0.698694i | \(0.246235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8900 | 1.11559 | 0.557794 | − | 0.829979i | \(-0.311648\pi\) | ||||
0.557794 | + | 0.829979i | \(0.311648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.5399 | − | 3.30518i | 1.43628 | − | 0.160703i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.59399 | −0.174334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.3960 | − | 1.69407i | −1.03542 | − | 0.0819816i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.22201 | + | 0.514313i | −0.445243 | + | 0.0248313i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 14.1215i | − | 0.680208i | −0.940388 | − | 0.340104i | \(-0.889538\pi\) | ||
0.940388 | − | 0.340104i | \(-0.110462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.5976i | − | 1.23014i | −0.788471 | − | 0.615072i | \(-0.789127\pi\) | ||
0.788471 | − | 0.615072i | \(-0.210873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.431570 | − | 7.73836i | −0.0206922 | − | 0.371026i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.613404 | −0.0293431 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.5553i | 0.933322i | 0.884436 | + | 0.466661i | \(0.154543\pi\) | ||||
−0.884436 | + | 0.466661i | \(0.845457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9772 | − | 0.978227i | −0.998914 | − | 0.0465822i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 35.7251i | − | 1.69735i | −0.528916 | − | 0.848674i | \(-0.677401\pi\) | ||
0.528916 | − | 0.848674i | \(-0.322599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.17632 | −0.387595 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.130669 | + | 2.34298i | 0.00618042 | + | 0.110819i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.1071i | 0.948912i | 0.880279 | + | 0.474456i | \(0.157355\pi\) | ||||
−0.880279 | + | 0.474456i | \(0.842645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.2677i | − | 0.624751i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.0374 | + | 1.39634i | −1.17636 | + | 0.0656057i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.21479 | + | 0.650421i | 0.385115 | + | 0.0304922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.65005 | 0.311076 | 0.155538 | − | 0.987830i | \(-0.450289\pi\) | ||||
0.155538 | + | 0.987830i | \(0.450289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.4147 | + | 3.10677i | −0.859525 | + | 0.145012i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7531 | −1.10629 | −0.553146 | − | 0.833084i | \(-0.686573\pi\) | ||||
−0.553146 | + | 0.833084i | \(0.686573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.26150 | −0.430418 | −0.215209 | − | 0.976568i | \(-0.569043\pi\) | ||||
−0.215209 | + | 0.976568i | \(0.569043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.820940 | − | 14.7200i | −0.0380702 | − | 0.682626i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.2641 | 0.845161 | 0.422580 | − | 0.906325i | \(-0.361124\pi\) | ||||
0.422580 | + | 0.906325i | \(0.361124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.83900 | + | 23.2265i | −0.0849171 | + | 1.07250i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.70685 | − | 30.6050i | −0.0786473 | − | 1.41020i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.65087i | 0.397767i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.04495i | − | 0.0479458i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.54638 | − | 13.8207i | −0.0708039 | − | 0.632808i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.944391 | 0.0431503 | 0.0215752 | − | 0.999767i | \(-0.493132\pi\) | ||||
0.0215752 | + | 0.999767i | \(0.493132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 24.9029i | − | 1.13547i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.68931 | + | 0.0626711i | 0.122368 | + | 0.00285163i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13.5934i | − | 0.617243i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.11446 | −0.367701 | −0.183851 | − | 0.982954i | \(-0.558856\pi\) | ||||
−0.183851 | + | 0.982954i | \(0.558856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.4443 | − | 1.36326i | 1.10541 | − | 0.0616488i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9773i | 0.856432i | 0.903676 | + | 0.428216i | \(0.140858\pi\) | ||||
−0.903676 | + | 0.428216i | \(0.859142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.0820i | − | 0.724296i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.571136 | − | 5.10451i | −0.0256706 | − | 0.229431i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.78521 | − | 0.537232i | −0.304358 | − | 0.0240981i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.1764 | −0.903220 | −0.451610 | − | 0.892215i | \(-0.649150\pi\) | ||||
−0.451610 | + | 0.892215i | \(0.649150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.1592 | + | 1.01274i | −0.811293 | + | 0.0452460i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.6527 | −1.50050 | −0.750249 | − | 0.661155i | \(-0.770066\pi\) | ||||
−0.750249 | + | 0.661155i | \(0.770066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.28370 | −0.190622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.70546 | − | 0.318194i | 0.253388 | − | 0.0141315i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.4818 | −0.641896 | −0.320948 | − | 0.947097i | \(-0.604001\pi\) | ||||
−0.320948 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1548 | − | 1.43744i | −0.803123 | − | 0.0635888i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.903294 | − | 5.35408i | −0.0398814 | − | 0.236388i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 14.0227i | − | 0.617915i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.9639i | 0.746069i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.0295 | − | 1.89783i | 1.49373 | − | 0.0833055i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.7476 | −1.39089 | −0.695445 | − | 0.718580i | \(-0.744793\pi\) | ||||
−0.695445 | + | 0.718580i | \(0.744793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.24913i | − | 0.142074i | −0.997474 | − | 0.0710372i | \(-0.977369\pi\) | ||
0.997474 | − | 0.0710372i | \(-0.0226309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.106762 | + | 4.58133i | −0.00465949 | + | 0.199946i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 30.5915i | − | 1.33259i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.6554 | 0.985018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.31082 | + | 0.706107i | −0.273866 | + | 0.0306424i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.1360i | − | 1.04545i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4771i | 0.842070i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.05171 | + | 36.7887i | 0.0885379 | + | 1.58755i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.88602 | − | 11.8355i | 0.0812367 | − | 0.509792i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9697 | −0.772578 | −0.386289 | − | 0.922378i | \(-0.626243\pi\) | ||||
−0.386289 | + | 0.922378i | \(0.626243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.918492 | + | 16.4692i | 0.0394163 | + | 0.706763i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.7331 | 0.459754 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.3387 | −0.784107 | −0.392054 | − | 0.919942i | \(-0.628235\pi\) | ||||
−0.392054 | + | 0.919942i | \(0.628235\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.70610 | + | 24.1857i | 0.115494 | + | 1.03222i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.67584 | 0.199198 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.46478 | + | 18.5001i | −0.0622886 | + | 0.786702i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8271 | − | 0.771140i | 0.586928 | − | 0.0327331i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 28.3017i | − | 1.19918i | −0.800306 | − | 0.599591i | \(-0.795330\pi\) | ||
0.800306 | − | 0.599591i | \(-0.204670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7373i | 0.665616i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.593472 | − | 10.6414i | −0.0250564 | − | 0.449280i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.8742 | −0.753308 | −0.376654 | − | 0.926354i | \(-0.622925\pi\) | ||||
−0.376654 | + | 0.926354i | \(0.622925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.81346i | 0.370785i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.41323 | + | 23.5659i | 0.143342 | + | 0.989673i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.42862i | − | 0.101813i | −0.998703 | − | 0.0509066i | \(-0.983789\pi\) | ||
0.998703 | − | 0.0509066i | \(-0.0162111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.8480 | 0.998008 | 0.499004 | − | 0.866600i | \(-0.333699\pi\) | ||||
0.499004 | + | 0.866600i | \(0.333699\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.13864 | − | 38.3473i | −0.0893429 | − | 1.60198i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.587015i | − | 0.0244802i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.1298i | − | 1.12943i | −0.825287 | − | 0.564714i | \(-0.808987\pi\) | ||
0.825287 | − | 0.564714i | \(-0.191013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.7481 | + | 1.26866i | −0.945377 | + | 0.0527239i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.08975 | − | 13.7635i | 0.0452103 | − | 0.571004i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.93682 | 0.328709 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.03898 | − | 9.28590i | −0.0429567 | − | 0.383925i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.5360 | 1.59055 | 0.795275 | − | 0.606249i | \(-0.207327\pi\) | ||||
0.795275 | + | 0.606249i | \(0.207327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.89448 | 0.366490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.33572 | − | 23.9505i | −0.0549442 | − | 0.985190i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.2739 | 1.48959 | 0.744796 | − | 0.667293i | \(-0.232547\pi\) | ||||
0.744796 | + | 0.667293i | \(0.232547\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.750529 | + | 9.47915i | −0.0307687 | + | 0.388607i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.145929 | − | 2.61661i | −0.00597246 | − | 0.107091i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4627i | 0.550072i | 0.961434 | + | 0.275036i | \(0.0886898\pi\) | ||||
−0.961434 | + | 0.275036i | \(0.911310\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0055i | 0.612088i | 0.952017 | + | 0.306044i | \(0.0990054\pi\) | ||||
−0.952017 | + | 0.306044i | \(0.900995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.2549 | − | 2.93762i | 1.06918 | − | 0.119629i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.06864 | −0.328037 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.84471i | − | 0.399585i | −0.979838 | − | 0.199792i | \(-0.935973\pi\) | ||
0.979838 | − | 0.199792i | \(-0.0640267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.5000 | − | 0.477728i | −0.830703 | − | 0.0193585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.8599i | 1.24846i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.8700 | −1.44878 | −0.724388 | − | 0.689392i | \(-0.757878\pi\) | ||||
−0.724388 | + | 0.689392i | \(0.757878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.4013 | − | 0.747393i | 0.540393 | − | 0.0301378i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.01170i | 0.161505i | 0.996734 | + | 0.0807524i | \(0.0257323\pi\) | ||||
−0.996734 | + | 0.0807524i | \(0.974268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.91495i | − | 0.237742i | −0.992910 | − | 0.118871i | \(-0.962073\pi\) | ||
0.992910 | − | 0.118871i | \(-0.0379275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.507436 | − | 3.00772i | −0.0203627 | − | 0.120695i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.70745 | + | 21.5650i | −0.0684075 | + | 0.863984i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.09399 | − | 0.172552i | 0.123562 | − | 0.00689107i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.7357 | 1.14577 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.3710 | 1.76638 | 0.883191 | − | 0.469014i | \(-0.155391\pi\) | ||||
0.883191 | + | 0.469014i | \(0.155391\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.36960 | + | 0.299464i | −0.213423 | + | 0.0119026i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.2398 | −0.684139 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.43097 | − | 21.5307i | 0.135940 | − | 0.853076i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.858175 | + | 7.66992i | 0.0339489 | + | 0.303417i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.2004i | 1.27184i | 0.771756 | + | 0.635919i | \(0.219379\pi\) | ||||
−0.771756 | + | 0.635919i | \(0.780621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9089i | 0.430204i | 0.976592 | + | 0.215102i | \(0.0690084\pi\) | ||||
−0.976592 | + | 0.215102i | \(0.930992\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.73799 | + | 0.487319i | −0.344058 | + | 0.0191882i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.60683 | 0.220427 | 0.110214 | − | 0.993908i | \(-0.464847\pi\) | ||||
0.110214 | + | 0.993908i | \(0.464847\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.62410i | − | 0.142259i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.9955 | − | 0.908743i | −1.52835 | − | 0.0356164i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.1436i | 0.827414i | 0.910410 | + | 0.413707i | \(0.135766\pi\) | ||||
−0.910410 | + | 0.413707i | \(0.864234\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.92330 | −0.270516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.29618 | + | 20.5220i | 0.0895824 | + | 0.800641i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.88542i | 0.229264i | 0.993408 | + | 0.114632i | \(0.0365688\pi\) | ||||
−0.993408 | + | 0.114632i | \(0.963431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.9175i | 1.94157i | 0.239956 | + | 0.970784i | \(0.422867\pi\) | ||||
−0.239956 | + | 0.970784i | \(0.577133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.07962 | − | 19.3583i | −0.0419289 | − | 0.751816i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.75606 | − | 0.218217i | −0.106876 | − | 0.00846207i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.62671 | 0.101707 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.616538 | + | 11.0550i | 0.0238367 | + | 0.427410i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8891 | −0.536183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.1364 | 1.27732 | 0.638658 | − | 0.769491i | \(-0.279490\pi\) | ||||
0.638658 | + | 0.769491i | \(0.279490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.12374 | − | 0.864434i | 0.197213 | − | 0.0332721i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.16011 | −0.236752 | −0.118376 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118376 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.8525 | − | 2.83869i | −1.37589 | − | 0.108939i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.9075 | + | 1.27756i | −0.877817 | + | 0.0489560i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 28.6145i | − | 1.09490i | −0.836837 | − | 0.547451i | \(-0.815598\pi\) | ||
0.836837 | − | 0.547451i | \(-0.184402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5200i | 0.822237i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.49193 | − | 26.7513i | −0.0569206 | − | 1.02063i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4383 | 0.550056 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4683i | 1.23515i | 0.786511 | + | 0.617576i | \(0.211885\pi\) | ||||
−0.786511 | + | 0.617576i | \(0.788115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.5824 | + | 0.440400i | −0.515953 | + | 0.0167294i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.37425i | 0.203857i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.8508 | 1.05492 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.75272 | + | 49.3583i | 0.104117 | + | 1.86690i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.46493i | 0.0930990i | 0.998916 | + | 0.0465495i | \(0.0148225\pi\) | ||||
−0.998916 | + | 0.0465495i | \(0.985177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.35492i | 0.315112i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.1347 | + | 0.955605i | −0.645330 | + | 0.0359902i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.894561 | + | 11.2983i | −0.0336434 | + | 0.424915i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.7646 | 1.00517 | 0.502584 | − | 0.864529i | \(-0.332383\pi\) | ||||
0.502584 | + | 0.864529i | \(0.332383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9122 | − | 2.33984i | 0.784270 | − | 0.0877507i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.99657 | 0.187123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.33260 | 0.199428 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.445281 | − | 7.98422i | −0.0166293 | − | 0.298176i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.2186 | −1.08967 | −0.544835 | − | 0.838543i | \(-0.683408\pi\) | ||||
−0.544835 | + | 0.838543i | \(0.683408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.9849 | − | 2.92835i | −1.37739 | − | 0.109057i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.999233 | − | 17.9170i | −0.0371619 | − | 0.666339i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.47468i | 0.166186i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 49.9735i | − | 1.85341i | −0.375784 | − | 0.926707i | \(-0.622627\pi\) | ||
0.375784 | − | 0.926707i | \(-0.377373\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5055 | − | 8.85827i | 0.944648 | − | 0.328084i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1594 | −0.671651 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.25200i | − | 0.304795i | −0.988319 | − | 0.152397i | \(-0.951301\pi\) | ||
0.988319 | − | 0.152397i | \(-0.0486993\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0610 | + | 1.23830i | 0.444875 | + | 0.0456753i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0774i | 0.555382i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.17080 | 0.337353 | 0.168677 | − | 0.985671i | \(-0.446051\pi\) | ||||
0.168677 | + | 0.985671i | \(0.446051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.62844 | − | 0.313899i | 0.206766 | − | 0.0115314i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.3646i | 1.66427i | 0.554575 | + | 0.832133i | \(0.312881\pi\) | ||||
−0.554575 | + | 0.832133i | \(0.687119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.35482i | − | 0.0496369i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.5581 | + | 1.74077i | −0.569239 | + | 0.0636913i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.3709 | + | 4.06738i | 1.87705 | + | 0.148619i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.19247 | 0.225966 | 0.112983 | − | 0.993597i | \(-0.463959\pi\) | ||||
0.112983 | + | 0.993597i | \(0.463959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.129376 | − | 0.00721532i | 0.00471472 | − | 0.000262941i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.4778 | 0.526901 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.0168 | 1.34540 | 0.672700 | − | 0.739916i | \(-0.265135\pi\) | ||||
0.672700 | + | 0.739916i | \(0.265135\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.73808 | − | 0.0969332i | 0.0630884 | − | 0.00351845i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5683 | 0.455600 | 0.227800 | − | 0.973708i | \(-0.426847\pi\) | ||||
0.227800 | + | 0.973708i | \(0.426847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.24137 | − | 28.3085i | 0.0811432 | − | 1.02483i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.7151 | − | 1.19890i | 0.387406 | − | 0.0433462i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.59281i | − | 0.238053i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.34523i | − | 0.120632i | −0.998179 | − | 0.0603161i | \(-0.980789\pi\) | ||
0.998179 | − | 0.0603161i | \(-0.0192109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9654 | − | 0.723082i | 0.466937 | − | 0.0260412i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.9333 | 1.18453 | 0.592265 | − | 0.805743i | \(-0.298234\pi\) | ||||
0.592265 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.51183i | 0.305754i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.853617 | − | 36.6300i | 0.0306233 | − | 1.31409i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.09763i | 0.290128i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.40459 | −0.157609 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.86807 | + | 22.9271i | 0.138233 | + | 0.819349i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6973i | 0.631642i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.4703i | 1.01486i | 0.861694 | + | 0.507429i | \(0.169404\pi\) | ||||
−0.861694 | + | 0.507429i | \(0.830596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.93452 | + | 34.6873i | 0.0688707 | + | 1.23490i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.2455 | + | 1.84050i | 0.826514 | + | 0.0654408i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.2665 | −0.897238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.447095 | + | 8.01675i | 0.0158568 | + | 0.284325i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.80494 | 0.134778 | 0.0673890 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673890 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.6096 | −1.25978 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.3768 | − | 2.72748i | 0.861313 | − | 0.0963709i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.7852 | −0.415889 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.54825 | − | 0.122586i | −0.0545687 | − | 0.00432058i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.5919 | + | 2.43113i | −1.53451 | + | 0.0855799i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.4444i | 1.45711i | 0.684989 | + | 0.728553i | \(0.259807\pi\) | ||||
−0.684989 | + | 0.728553i | \(0.740193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.7455i | 0.517784i | 0.965906 | + | 0.258892i | \(0.0833574\pi\) | ||||
−0.965906 | + | 0.258892i | \(0.916643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.74295 | + | 31.2524i | 0.0611281 | + | 1.09607i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.1348 | −0.495122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.27986i | − | 0.184719i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.7085 | + | 0.801156i | −0.863385 | + | 0.0279946i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 16.8830i | − | 0.589222i | −0.955617 | − | 0.294611i | \(-0.904810\pi\) | ||
0.955617 | − | 0.294611i | \(-0.0951901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.4749 | −1.79430 | −0.897151 | − | 0.441725i | \(-0.854367\pi\) | ||||
−0.897151 | + | 0.441725i | \(0.854367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.165129 | + | 2.96088i | 0.00574905 | + | 0.103085i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1522i | 0.665988i | 0.942929 | + | 0.332994i | \(0.108059\pi\) | ||||
−0.942929 | + | 0.332994i | \(0.891941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.62424i | − | 0.0564121i | −0.999602 | − | 0.0282060i | \(-0.991021\pi\) | ||
0.999602 | − | 0.0282060i | \(-0.00897946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.8544 | + | 1.33036i | −0.827500 | + | 0.0461499i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.8445 | + | 3.95904i | 0.860811 | + | 0.137172i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5005 | 0.363385 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.35791 | + | 43.6124i | 0.254327 | + | 1.50747i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.8128 | −1.09830 | −0.549150 | − | 0.835724i | \(-0.685048\pi\) | ||||
−0.549150 | + | 0.835724i | \(0.685048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.97719 | 0.309558 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0304152 | + | 0.545367i | 0.00104756 | + | 0.0187835i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.29917 | −0.113495 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.68496 | + | 21.2810i | −0.0578960 | + | 0.731224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.99074 | − | 35.6954i | −0.0683221 | − | 1.22506i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.69347i | 0.160890i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0272i | 1.47322i | 0.676316 | + | 0.736612i | \(0.263575\pi\) | ||||
−0.676316 | + | 0.736612i | \(0.736425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.348580 | + | 3.11542i | 0.0119212 | + | 0.106545i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.7323 | −0.469086 | −0.234543 | − | 0.972106i | \(-0.575359\pi\) | ||||
−0.234543 | + | 0.972106i | \(0.575359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.6976i | 0.842673i | 0.906904 | + | 0.421336i | \(0.138439\pi\) | ||||
−0.906904 | + | 0.421336i | \(0.861561\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.827330 | − | 35.5020i | 0.0281953 | − | 1.20990i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.4217i | 1.68233i | 0.540775 | + | 0.841167i | \(0.318131\pi\) | ||||
−0.540775 | + | 0.841167i | \(0.681869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.6775 | −0.669054 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.06136 | + | 0.393813i | −0.239816 | + | 0.0133746i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0092i | 0.407386i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.4281i | 0.929366i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.53452 | + | 40.5272i | 0.153470 | + | 1.37164i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.208829 | − | 2.63750i | 0.00705970 | − | 0.0891637i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.8346 | 1.58149 | 0.790746 | − | 0.612144i | \(-0.209693\pi\) | ||||
0.790746 | + | 0.612144i | \(0.209693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.48837 | − | 0.361857i | 0.218847 | − | 0.0122051i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2322 | 0.850096 | 0.425048 | − | 0.905171i | \(-0.360257\pi\) | ||||
0.425048 | + | 0.905171i | \(0.360257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.140777 | 0.00473751 | 0.00236876 | − | 0.999997i | \(-0.499246\pi\) | ||||
0.00236876 | + | 0.999997i | \(0.499246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.66060 | − | 0.204152i | 0.123050 | − | 0.00686251i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.336941 | 0.0113134 | 0.00565669 | − | 0.999984i | \(-0.498199\pi\) | ||||
0.00565669 | + | 0.999984i | \(0.498199\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.60016 | + | 45.4698i | −0.120745 | + | 1.52501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.40556 | + | 15.0281i | 0.114091 | + | 0.503459i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.3535i | − | 0.346467i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 21.2730i | − | 0.711077i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.16184 | − | 0.176337i | 0.105571 | − | 0.00588771i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.0878 | −1.27030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6605i | 0.555043i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.539440 | + | 23.1482i | −0.0179514 | + | 0.770323i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.52329i | − | 0.316565i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.5312 | −1.37902 | −0.689511 | − | 0.724275i | \(-0.742175\pi\) | ||||
−0.689511 | + | 0.724275i | \(0.742175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.7714 | − | 1.42897i | 0.423601 | − | 0.0473961i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.7168i | − | 1.51467i | −0.653029 | − | 0.757333i | \(-0.726502\pi\) | ||
0.653029 | − | 0.757333i | \(-0.273498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.93450i | − | 0.295689i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.782399 | − | 14.0290i | −0.0258653 | − | 0.463784i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44578 | + | 18.2602i | −0.0477440 | + | 0.603004i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6957 | 0.385806 | 0.192903 | − | 0.981218i | \(-0.438210\pi\) | ||||
0.192903 | + | 0.981218i | \(0.438210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.88667 | − | 51.7600i | −0.0951189 | − | 1.70555i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.01264 | −0.263739 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.99549 | −0.262890 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.67775 | + | 41.8073i | 0.153637 | + | 1.37313i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.6691 | −1.85925 | −0.929627 | − | 0.368501i | \(-0.879871\pi\) | ||||
−0.929627 | + | 0.368501i | \(0.879871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.15109 | + | 7.22354i | −0.0377255 | + | 0.236742i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.3703 | − | 2.02838i | 1.19071 | − | 0.0664061i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.15335i | 0.201236i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2225i | 1.83671i | 0.395760 | + | 0.918354i | \(0.370481\pi\) | ||||
−0.395760 | + | 0.918354i | \(0.629519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.940342 | − | 16.8610i | −0.0306869 | − | 0.550239i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.1463 | −0.852345 | −0.426172 | − | 0.904642i | \(-0.640138\pi\) | ||||
−0.426172 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.54894i | 0.148134i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.20996 | − | 13.6944i | −0.0393599 | − | 0.445478i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.7126i | 0.965530i | 0.875750 | + | 0.482765i | \(0.160368\pi\) | ||||
−0.875750 | + | 0.482765i | \(0.839632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.4390 | −0.695940 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.56619 | − | 28.0828i | −0.0507870 | − | 0.910648i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6858i | 0.961618i | 0.876825 | + | 0.480809i | \(0.159657\pi\) | ||||
−0.876825 | + | 0.480809i | \(0.840343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.1742i | 0.717542i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.2490 | + | 0.738900i | −0.428280 | + | 0.0238852i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.7589 | + | 4.49399i | 1.83284 | + | 0.145119i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.4513 | −1.33714 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.49725 | − | 58.0690i | −0.209371 | − | 1.87125i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1540 | 0.423443 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0668 | 1.54572 | 0.772862 | − | 0.634574i | \(-0.218824\pi\) | ||||
0.772862 | + | 0.634574i | \(0.218824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.362212 | + | 6.49473i | 0.0116359 | + | 0.208641i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.6857 | 0.856385 | 0.428192 | − | 0.903688i | \(-0.359151\pi\) | ||||
0.428192 | + | 0.903688i | \(0.359151\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1746 | + | 1.12230i | 0.454416 | + | 0.0359792i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.300395 | + | 5.38630i | 0.00962034 | + | 0.172500i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.3351i | 1.03449i | 0.855837 | + | 0.517246i | \(0.173043\pi\) | ||||
−0.855837 | + | 0.517246i | \(0.826957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.9988i | 0.447405i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.9995 | + | 3.58038i | −1.02167 | + | 0.114313i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.7145 | −0.565005 | −0.282502 | − | 0.959267i | \(-0.591165\pi\) | ||||
−0.282502 | + | 0.959267i | \(0.591165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8493i | 0.441275i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.05781 | + | 45.3922i | −0.0336705 | + | 1.44485i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.96602i | − | 0.0943141i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.5895 | 1.67056 | 0.835280 | − | 0.549825i | \(-0.185305\pi\) | ||||
0.835280 | + | 0.549825i | \(0.185305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.9640 | + | 1.00186i | −0.570072 | + | 0.0317930i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.51305i | 0.0479668i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.0605i | − | 1.20539i | −0.797972 | − | 0.602695i | \(-0.794094\pi\) | ||
0.797972 | − | 0.602695i | \(-0.205906\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.9668 | + | 6.91157i | −1.29613 | + | 0.218672i |
(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 | 1680.2.f.k.881.15 | 16 | ||
3.2 | odd | 2 | 1680.2.f.l.881.1 | 16 | |||
4.3 | odd | 2 | 840.2.f.a.41.2 | yes | 16 | ||
7.6 | odd | 2 | 1680.2.f.l.881.2 | 16 | |||
12.11 | even | 2 | 840.2.f.b.41.16 | yes | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.k.881.16 | 16 | ||
28.27 | even | 2 | 840.2.f.b.41.15 | yes | 16 | ||
84.83 | odd | 2 | 840.2.f.a.41.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.1 | ✓ | 16 | 84.83 | odd | 2 | ||
840.2.f.a.41.2 | yes | 16 | 4.3 | odd | 2 | ||
840.2.f.b.41.15 | yes | 16 | 28.27 | even | 2 | ||
840.2.f.b.41.16 | yes | 16 | 12.11 | even | 2 | ||
1680.2.f.k.881.15 | 16 | 1.1 | even | 1 | trivial | ||
1680.2.f.k.881.16 | 16 | 21.20 | even | 2 | inner | ||
1680.2.f.l.881.1 | 16 | 3.2 | odd | 2 | |||
1680.2.f.l.881.2 | 16 | 7.6 | odd | 2 |