Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(647,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.c (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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 647.9 | ||
Character | \(\chi\) | \(=\) | 684.647 |
Dual form | 684.2.c.b.647.10 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965364 | − | 1.03348i | −0.682616 | − | 0.730778i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.136143 | + | 1.99536i | −0.0680717 | + | 0.997680i | ||||
\(5\) | − | 0.0590006i | − | 0.0263859i | −0.999913 | − | 0.0131929i | \(-0.995800\pi\) | ||
0.999913 | − | 0.0131929i | \(-0.00419956\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27229i | 0.480879i | 0.970664 | + | 0.240440i | \(0.0772916\pi\) | ||||
−0.970664 | + | 0.240440i | \(0.922708\pi\) | |||||||
\(8\) | 2.19358 | − | 1.78555i | 0.775549 | − | 0.631287i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0609757 | + | 0.0569571i | −0.0192822 | + | 0.0180114i | ||||
\(11\) | −5.27604 | −1.59079 | −0.795394 | − | 0.606093i | \(-0.792736\pi\) | ||||
−0.795394 | + | 0.606093i | \(0.792736\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.40536 | −0.389777 | −0.194888 | − | 0.980825i | \(-0.562434\pi\) | ||||
−0.194888 | + | 0.980825i | \(0.562434\pi\) | |||||||
\(14\) | 1.31488 | − | 1.22822i | 0.351416 | − | 0.328256i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.96293 | − | 0.543311i | −0.990732 | − | 0.135828i | ||||
\(17\) | − | 8.20009i | − | 1.98881i | −0.105618 | − | 0.994407i | \(-0.533682\pi\) | ||
0.105618 | − | 0.994407i | \(-0.466318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0.117728 | + | 0.00803255i | 0.0263247 | + | 0.00179613i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.09330 | + | 5.45266i | 1.08590 | + | 1.16251i | ||||
\(23\) | 7.75602 | 1.61724 | 0.808621 | − | 0.588330i | \(-0.200215\pi\) | ||||
0.808621 | + | 0.588330i | \(0.200215\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99652 | 0.999304 | ||||||||
\(26\) | 1.35668 | + | 1.45241i | 0.266068 | + | 0.284840i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.53867 | − | 0.173214i | −0.479764 | − | 0.0327343i | ||||
\(29\) | − | 6.17369i | − | 1.14643i | −0.819407 | − | 0.573213i | \(-0.805697\pi\) | ||
0.819407 | − | 0.573213i | \(-0.194303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.05893i | − | 1.26782i | −0.773406 | − | 0.633911i | \(-0.781449\pi\) | ||
0.773406 | − | 0.633911i | \(-0.218551\pi\) | |||||||
\(32\) | 3.26417 | + | 4.62008i | 0.577030 | + | 0.816723i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.47459 | + | 7.91607i | −1.45338 | + | 1.35760i | ||||
\(35\) | 0.0750657 | 0.0126884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.75595 | −0.946272 | −0.473136 | − | 0.880989i | \(-0.656878\pi\) | ||||
−0.473136 | + | 0.880989i | \(0.656878\pi\) | |||||||
\(38\) | −1.03348 | + | 0.965364i | −0.167652 | + | 0.156603i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.105349 | − | 0.129423i | −0.0166571 | − | 0.0204636i | ||||
\(41\) | − | 7.99536i | − | 1.24867i | −0.781159 | − | 0.624333i | \(-0.785371\pi\) | ||
0.781159 | − | 0.624333i | \(-0.214629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.49049i | − | 0.684794i | −0.939555 | − | 0.342397i | \(-0.888761\pi\) | ||
0.939555 | − | 0.342397i | \(-0.111239\pi\) | |||||||
\(44\) | 0.718299 | − | 10.5276i | 0.108288 | − | 1.58710i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.48738 | − | 8.01565i | −1.10395 | − | 1.18184i | ||||
\(47\) | −6.31694 | −0.921421 | −0.460710 | − | 0.887551i | \(-0.652405\pi\) | ||||
−0.460710 | + | 0.887551i | \(0.652405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.38129 | 0.768755 | ||||||||
\(50\) | −4.82346 | − | 5.16378i | −0.682140 | − | 0.730269i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.191331 | − | 2.80420i | 0.0265328 | − | 0.388873i | ||||
\(53\) | 10.5521i | 1.44944i | 0.689043 | + | 0.724720i | \(0.258031\pi\) | ||||
−0.689043 | + | 0.724720i | \(0.741969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.311290i | 0.0419743i | ||||||||
\(56\) | 2.27173 | + | 2.79087i | 0.303573 | + | 0.372946i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.38036 | + | 5.95986i | −0.837782 | + | 0.782568i | ||||
\(59\) | −6.05569 | −0.788384 | −0.394192 | − | 0.919028i | \(-0.628975\pi\) | ||||
−0.394192 | + | 0.919028i | \(0.628975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.72327 | 0.860827 | 0.430413 | − | 0.902632i | \(-0.358368\pi\) | ||||
0.430413 | + | 0.902632i | \(0.358368\pi\) | |||||||
\(62\) | −7.29524 | + | 6.81444i | −0.926496 | + | 0.865435i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.62363 | − | 7.83351i | 0.202953 | − | 0.979188i | ||||
\(65\) | 0.0829171i | 0.0102846i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.89516i | − | 0.353701i | −0.984238 | − | 0.176850i | \(-0.943409\pi\) | ||
0.984238 | − | 0.176850i | \(-0.0565908\pi\) | |||||||
\(68\) | 16.3621 | + | 1.11639i | 1.98420 | + | 0.135382i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0724658 | − | 0.0775786i | −0.00866132 | − | 0.00927241i | ||||
\(71\) | −8.96642 | −1.06412 | −0.532059 | − | 0.846707i | \(-0.678582\pi\) | ||||
−0.532059 | + | 0.846707i | \(0.678582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.05558 | −0.357629 | −0.178815 | − | 0.983883i | \(-0.557226\pi\) | ||||
−0.178815 | + | 0.983883i | \(0.557226\pi\) | |||||||
\(74\) | 5.55659 | + | 5.94863i | 0.645940 | + | 0.691515i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.99536 | + | 0.136143i | 0.228884 | + | 0.0156167i | ||||
\(77\) | − | 6.71264i | − | 0.764977i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.67861i | − | 0.301367i | −0.988582 | − | 0.150683i | \(-0.951853\pi\) | ||
0.988582 | − | 0.150683i | \(-0.0481474\pi\) | |||||||
\(80\) | −0.0320557 | + | 0.233815i | −0.00358393 | + | 0.0261413i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.26301 | + | 7.71843i | −0.912497 | + | 0.852359i | ||||
\(83\) | −9.34505 | −1.02575 | −0.512876 | − | 0.858463i | \(-0.671420\pi\) | ||||
−0.512876 | + | 0.858463i | \(0.671420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.483810 | −0.0524766 | ||||||||
\(86\) | −4.64082 | + | 4.33496i | −0.500432 | + | 0.467451i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.5735 | + | 9.42064i | −1.23373 | + | 1.00424i | ||||
\(89\) | 2.25918i | 0.239472i | 0.992806 | + | 0.119736i | \(0.0382049\pi\) | ||||
−0.992806 | + | 0.119736i | \(0.961795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.78802i | − | 0.187436i | ||||||
\(92\) | −1.05593 | + | 15.4761i | −0.110088 | + | 1.61349i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.09815 | + | 6.52840i | 0.628976 | + | 0.673353i | ||||
\(95\) | −0.0590006 | −0.00605334 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2821 | −1.45013 | −0.725065 | − | 0.688681i | \(-0.758190\pi\) | ||||
−0.725065 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(98\) | −5.19490 | − | 5.56143i | −0.524764 | − | 0.561789i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.680243 | + | 9.96986i | −0.0680243 | + | 0.996986i | ||||
\(101\) | 8.91661i | 0.887235i | 0.896216 | + | 0.443618i | \(0.146305\pi\) | ||||
−0.896216 | + | 0.443618i | \(0.853695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.17304i | − | 0.411182i | −0.978638 | − | 0.205591i | \(-0.934088\pi\) | ||
0.978638 | − | 0.205591i | \(-0.0659116\pi\) | |||||||
\(104\) | −3.08278 | + | 2.50934i | −0.302291 | + | 0.246061i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9053 | − | 10.1866i | 1.05922 | − | 0.989411i | ||||
\(107\) | 12.7308 | 1.23073 | 0.615367 | − | 0.788241i | \(-0.289008\pi\) | ||||
0.615367 | + | 0.788241i | \(0.289008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2273 | 1.45852 | 0.729258 | − | 0.684239i | \(-0.239866\pi\) | ||||
0.729258 | + | 0.684239i | \(0.239866\pi\) | |||||||
\(110\) | 0.321710 | − | 0.300508i | 0.0306739 | − | 0.0286523i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.691247 | − | 5.04198i | 0.0653167 | − | 0.476423i | ||||
\(113\) | − | 2.72179i | − | 0.256045i | −0.991771 | − | 0.128022i | \(-0.959137\pi\) | ||
0.991771 | − | 0.128022i | \(-0.0408629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.457610i | − | 0.0426723i | ||||||
\(116\) | 12.3187 | + | 0.840507i | 1.14377 | + | 0.0780392i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.84595 | + | 6.25841i | 0.538163 | + | 0.576133i | ||||
\(119\) | 10.4329 | 0.956379 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.8366 | 1.53060 | ||||||||
\(122\) | −6.49041 | − | 6.94834i | −0.587614 | − | 0.629073i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.0851 | + | 0.961028i | 1.26488 | + | 0.0863028i | ||||
\(125\) | − | 0.589801i | − | 0.0527534i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.9702i | − | 1.59459i | −0.603587 | − | 0.797297i | \(-0.706262\pi\) | ||
0.603587 | − | 0.797297i | \(-0.293738\pi\) | |||||||
\(128\) | −9.66313 | + | 5.88421i | −0.854108 | + | 0.520095i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0856928 | − | 0.0800452i | 0.00751576 | − | 0.00702043i | ||||
\(131\) | −17.1149 | −1.49534 | −0.747669 | − | 0.664072i | \(-0.768827\pi\) | ||||
−0.747669 | + | 0.664072i | \(0.768827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.27229 | 0.110321 | ||||||||
\(134\) | −2.99208 | + | 2.79489i | −0.258476 | + | 0.241442i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.6417 | − | 17.9876i | −1.25551 | − | 1.54242i | ||||
\(137\) | 16.6962i | 1.42645i | 0.700935 | + | 0.713225i | \(0.252766\pi\) | ||||
−0.700935 | + | 0.713225i | \(0.747234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.43783i | 0.800506i | 0.916405 | + | 0.400253i | \(0.131078\pi\) | ||||
−0.916405 | + | 0.400253i | \(0.868922\pi\) | |||||||
\(140\) | −0.0102197 | + | 0.149783i | −0.000863723 | + | 0.0126590i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.65586 | + | 9.26658i | 0.726384 | + | 0.777634i | ||||
\(143\) | 7.41474 | 0.620052 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.364252 | −0.0302494 | ||||||||
\(146\) | 2.94975 | + | 3.15787i | 0.244123 | + | 0.261347i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.783635 | − | 11.4852i | 0.0644144 | − | 0.944077i | ||||
\(149\) | − | 4.82279i | − | 0.395098i | −0.980293 | − | 0.197549i | \(-0.936702\pi\) | ||
0.980293 | − | 0.197549i | \(-0.0632982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.91310i | 0.237065i | 0.992950 | + | 0.118532i | \(0.0378189\pi\) | ||||
−0.992950 | + | 0.118532i | \(0.962181\pi\) | |||||||
\(152\) | −1.78555 | − | 2.19358i | −0.144827 | − | 0.177923i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.93735 | + | 6.48015i | −0.559028 | + | 0.522185i | ||||
\(155\) | −0.416481 | −0.0334526 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5208 | 1.07908 | 0.539540 | − | 0.841960i | \(-0.318598\pi\) | ||||
0.539540 | + | 0.841960i | \(0.318598\pi\) | |||||||
\(158\) | −2.76828 | + | 2.58583i | −0.220232 | + | 0.205718i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.272588 | − | 0.192588i | 0.0215500 | − | 0.0152254i | ||||
\(161\) | 9.86788i | 0.777698i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.626149i | − | 0.0490438i | −0.999699 | − | 0.0245219i | \(-0.992194\pi\) | ||
0.999699 | − | 0.0245219i | \(-0.00780634\pi\) | |||||||
\(164\) | 15.9536 | + | 1.08852i | 1.24577 | + | 0.0849988i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.02138 | + | 9.65788i | 0.700195 | + | 0.749597i | ||||
\(167\) | 6.55967 | 0.507602 | 0.253801 | − | 0.967256i | \(-0.418319\pi\) | ||||
0.253801 | + | 0.967256i | \(0.418319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0250 | −0.848074 | ||||||||
\(170\) | 0.467053 | + | 0.500006i | 0.0358213 | + | 0.0383487i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.96016 | + | 0.611351i | 0.683206 | + | 0.0466151i | ||||
\(173\) | − | 10.2796i | − | 0.781547i | −0.920487 | − | 0.390773i | \(-0.872208\pi\) | ||
0.920487 | − | 0.390773i | \(-0.127792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.35701i | 0.480544i | ||||||||
\(176\) | 20.9086 | + | 2.86653i | 1.57604 | + | 0.216073i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.33480 | − | 2.18093i | 0.175001 | − | 0.163468i | ||||
\(179\) | 18.6314 | 1.39258 | 0.696288 | − | 0.717762i | \(-0.254834\pi\) | ||||
0.696288 | + | 0.717762i | \(0.254834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.58568 | −0.266522 | −0.133261 | − | 0.991081i | \(-0.542545\pi\) | ||||
−0.133261 | + | 0.991081i | \(0.542545\pi\) | |||||||
\(182\) | −1.84788 | + | 1.72609i | −0.136974 | + | 0.127946i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.0135 | − | 13.8487i | 1.25425 | − | 1.02094i | ||||
\(185\) | 0.339605i | 0.0249682i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 43.2640i | 3.16378i | ||||||||
\(188\) | 0.860010 | − | 12.6046i | 0.0627227 | − | 0.919283i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0569571 | + | 0.0609757i | 0.00413210 | + | 0.00442364i | ||||
\(191\) | −3.91466 | −0.283255 | −0.141627 | − | 0.989920i | \(-0.545233\pi\) | ||||
−0.141627 | + | 0.989920i | \(0.545233\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.01999 | 0.505310 | 0.252655 | − | 0.967556i | \(-0.418696\pi\) | ||||
0.252655 | + | 0.967556i | \(0.418696\pi\) | |||||||
\(194\) | 13.7874 | + | 14.7602i | 0.989881 | + | 1.05972i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.732627 | + | 10.7376i | −0.0523305 | + | 0.766972i | ||||
\(197\) | 5.42454i | 0.386483i | 0.981151 | + | 0.193241i | \(0.0619000\pi\) | ||||
−0.981151 | + | 0.193241i | \(0.938100\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.02347i | 0.0725521i | 0.999342 | + | 0.0362761i | \(0.0115496\pi\) | ||||
−0.999342 | + | 0.0362761i | \(0.988450\pi\) | |||||||
\(200\) | 10.9603 | − | 8.92153i | 0.775009 | − | 0.630847i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.21509 | − | 8.60777i | 0.648372 | − | 0.605641i | ||||
\(203\) | 7.85470 | 0.551292 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.471731 | −0.0329471 | ||||||||
\(206\) | −4.31273 | + | 4.02850i | −0.300482 | + | 0.280679i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.56934 | + | 0.763547i | 0.386165 | + | 0.0529425i | ||||
\(209\) | 5.27604i | 0.364952i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6167i | 0.868572i | 0.900775 | + | 0.434286i | \(0.142999\pi\) | ||||
−0.900775 | + | 0.434286i | \(0.857001\pi\) | |||||||
\(212\) | −21.0552 | − | 1.43660i | −1.44608 | − | 0.0986659i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.2899 | − | 13.1570i | −0.840118 | − | 0.899392i | ||||
\(215\) | −0.264942 | −0.0180689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.98099 | 0.609669 | ||||||||
\(218\) | −14.6999 | − | 15.7371i | −0.995605 | − | 1.06585i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.621136 | − | 0.0423801i | −0.0418770 | − | 0.00285726i | ||||
\(221\) | 11.5241i | 0.775193i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 27.0222i | − | 1.80954i | −0.425898 | − | 0.904771i | \(-0.640042\pi\) | ||
0.425898 | − | 0.904771i | \(-0.359958\pi\) | |||||||
\(224\) | −5.87807 | + | 4.15296i | −0.392745 | + | 0.277482i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.81291 | + | 2.62752i | −0.187112 | + | 0.174780i | ||||
\(227\) | −20.2086 | −1.34129 | −0.670645 | − | 0.741778i | \(-0.733983\pi\) | ||||
−0.670645 | + | 0.741778i | \(0.733983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.92551 | 0.655896 | 0.327948 | − | 0.944696i | \(-0.393643\pi\) | ||||
0.327948 | + | 0.944696i | \(0.393643\pi\) | |||||||
\(230\) | −0.472928 | + | 0.441760i | −0.0311840 | + | 0.0291288i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.0234 | − | 13.5425i | −0.723723 | − | 0.889109i | ||||
\(233\) | 1.92511i | 0.126118i | 0.998010 | + | 0.0630591i | \(0.0200857\pi\) | ||||
−0.998010 | + | 0.0630591i | \(0.979914\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.372703i | 0.0243125i | ||||||||
\(236\) | 0.824442 | − | 12.0833i | 0.0536666 | − | 0.786555i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.0715 | − | 10.7821i | −0.652839 | − | 0.698900i | ||||
\(239\) | 20.3148 | 1.31406 | 0.657029 | − | 0.753866i | \(-0.271813\pi\) | ||||
0.657029 | + | 0.753866i | \(0.271813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.879196 | 0.0566340 | 0.0283170 | − | 0.999599i | \(-0.490985\pi\) | ||||
0.0283170 | + | 0.999599i | \(0.490985\pi\) | |||||||
\(242\) | −16.2535 | − | 17.4003i | −1.04481 | − | 1.11853i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.915329 | + | 13.4154i | −0.0585980 | + | 0.858830i | ||||
\(245\) | − | 0.317499i | − | 0.0202843i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.40536i | 0.0894209i | ||||||||
\(248\) | −12.6041 | − | 15.4844i | −0.800359 | − | 0.983258i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.609545 | + | 0.569373i | −0.0385510 | + | 0.0360103i | ||||
\(251\) | 10.2545 | 0.647259 | 0.323630 | − | 0.946184i | \(-0.395097\pi\) | ||||
0.323630 | + | 0.946184i | \(0.395097\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.9211 | −2.57269 | ||||||||
\(254\) | −18.5717 | + | 17.3478i | −1.16529 | + | 1.08850i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4096 | + | 4.30620i | 0.963102 | + | 0.269138i | ||||
\(257\) | 12.9473i | 0.807633i | 0.914840 | + | 0.403816i | \(0.132317\pi\) | ||||
−0.914840 | + | 0.403816i | \(0.867683\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.32322i | − | 0.455043i | ||||||
\(260\) | −0.165450 | − | 0.0112886i | −0.0102607 | − | 0.000700091i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5221 | + | 17.6878i | 1.02074 | + | 1.09276i | ||||
\(263\) | −1.76321 | −0.108724 | −0.0543620 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543620 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.622580 | 0.0382448 | ||||||||
\(266\) | −1.22822 | − | 1.31488i | −0.0753070 | − | 0.0806203i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.77690 | + | 0.394158i | 0.352880 | + | 0.0240770i | ||||
\(269\) | 0.479329i | 0.0292252i | 0.999893 | + | 0.0146126i | \(0.00465150\pi\) | ||||
−0.999893 | + | 0.0146126i | \(0.995349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1638i | 1.04262i | 0.853366 | + | 0.521312i | \(0.174557\pi\) | ||||
−0.853366 | + | 0.521312i | \(0.825443\pi\) | |||||||
\(272\) | −4.45520 | + | 32.4964i | −0.270136 | + | 1.97038i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2551 | − | 16.1179i | 1.04242 | − | 0.973718i | ||||
\(275\) | −26.3619 | −1.58968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0304 | −0.843006 | −0.421503 | − | 0.906827i | \(-0.638497\pi\) | ||||
−0.421503 | + | 0.906827i | \(0.638497\pi\) | |||||||
\(278\) | 9.75377 | − | 9.11094i | 0.584992 | − | 0.546438i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.164663 | − | 0.134034i | 0.00984050 | − | 0.00801004i | ||||
\(281\) | − | 14.7356i | − | 0.879053i | −0.898230 | − | 0.439526i | \(-0.855146\pi\) | ||
0.898230 | − | 0.439526i | \(-0.144854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.8917i | − | 0.885219i | −0.896715 | − | 0.442609i | \(-0.854053\pi\) | ||
0.896715 | − | 0.442609i | \(-0.145947\pi\) | |||||||
\(284\) | 1.22072 | − | 17.8912i | 0.0724364 | − | 1.06165i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.15793 | − | 7.66296i | −0.423257 | − | 0.453120i | ||||
\(287\) | 10.1724 | 0.600457 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −50.2415 | −2.95538 | ||||||||
\(290\) | 0.351635 | + | 0.376445i | 0.0206487 | + | 0.0221056i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.415998 | − | 6.09699i | 0.0243444 | − | 0.356799i | ||||
\(293\) | − | 30.9507i | − | 1.80816i | −0.427362 | − | 0.904081i | \(-0.640557\pi\) | ||
0.427362 | − | 0.904081i | \(-0.359443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.357289i | 0.0208022i | ||||||||
\(296\) | −12.6262 | + | 10.2775i | −0.733881 | + | 0.597369i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.98423 | + | 4.65575i | −0.288729 | + | 0.269700i | ||||
\(299\) | −10.9000 | −0.630363 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.71320 | 0.329303 | ||||||||
\(302\) | 3.01062 | − | 2.81220i | 0.173241 | − | 0.161824i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.543311 | + | 3.96293i | −0.0311610 | + | 0.227290i | ||||
\(305\) | − | 0.396677i | − | 0.0227137i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0882i | 1.43186i | 0.698172 | + | 0.715930i | \(0.253997\pi\) | ||||
−0.698172 | + | 0.715930i | \(0.746003\pi\) | |||||||
\(308\) | 13.3941 | + | 0.913882i | 0.763202 | + | 0.0520733i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.402056 | + | 0.430423i | 0.0228353 | + | 0.0244464i | ||||
\(311\) | 29.1948 | 1.65548 | 0.827742 | − | 0.561108i | \(-0.189625\pi\) | ||||
0.827742 | + | 0.561108i | \(0.189625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6549 | −0.771819 | −0.385909 | − | 0.922537i | \(-0.626112\pi\) | ||||
−0.385909 | + | 0.922537i | \(0.626112\pi\) | |||||||
\(314\) | −13.0525 | − | 13.9735i | −0.736597 | − | 0.788568i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.34479 | + | 0.364675i | 0.300668 | + | 0.0205146i | ||||
\(317\) | 10.3696i | 0.582414i | 0.956660 | + | 0.291207i | \(0.0940568\pi\) | ||||
−0.956660 | + | 0.291207i | \(0.905943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.5727i | 1.82372i | ||||||||
\(320\) | −0.462182 | − | 0.0957950i | −0.0258367 | − | 0.00535511i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.1982 | − | 9.52610i | 0.568324 | − | 0.530869i | ||||
\(323\) | −8.20009 | −0.456265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.02191 | −0.389505 | ||||||||
\(326\) | −0.647110 | + | 0.604462i | −0.0358401 | + | 0.0334780i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.2761 | − | 17.5385i | −0.788266 | − | 0.968402i | ||||
\(329\) | − | 8.03696i | − | 0.443092i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.2153i | − | 1.33099i | −0.746402 | − | 0.665496i | \(-0.768220\pi\) | ||
0.746402 | − | 0.665496i | \(-0.231780\pi\) | |||||||
\(332\) | 1.27227 | − | 18.6467i | 0.0698247 | − | 1.02337i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.33247 | − | 6.77926i | −0.346497 | − | 0.370944i | ||||
\(335\) | −0.170816 | −0.00933270 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8973 | −0.648085 | −0.324043 | − | 0.946042i | \(-0.605042\pi\) | ||||
−0.324043 | + | 0.946042i | \(0.605042\pi\) | |||||||
\(338\) | 10.6431 | + | 11.3940i | 0.578909 | + | 0.619753i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0658676 | − | 0.965376i | 0.00357217 | − | 0.0523549i | ||||
\(341\) | 37.2432i | 2.01683i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7525i | 0.850558i | ||||||||
\(344\) | −8.01800 | − | 9.85028i | −0.432302 | − | 0.531091i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.6238 | + | 9.92360i | −0.571137 | + | 0.533496i | ||||
\(347\) | −3.57698 | −0.192022 | −0.0960112 | − | 0.995380i | \(-0.530608\pi\) | ||||
−0.0960112 | + | 0.995380i | \(0.530608\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.64766 | 0.195255 | 0.0976275 | − | 0.995223i | \(-0.468875\pi\) | ||||
0.0976275 | + | 0.995223i | \(0.468875\pi\) | |||||||
\(350\) | 6.56981 | − | 6.13683i | 0.351171 | − | 0.328027i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.2219 | − | 24.3758i | −0.917931 | − | 1.29923i | ||||
\(353\) | 1.39070i | 0.0740197i | 0.999315 | + | 0.0370098i | \(0.0117833\pi\) | ||||
−0.999315 | + | 0.0370098i | \(0.988217\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.529024i | 0.0280777i | ||||||||
\(356\) | −4.50787 | − | 0.307572i | −0.238917 | − | 0.0163013i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.9861 | − | 19.2551i | −0.950595 | − | 1.01766i | ||||
\(359\) | 31.8137 | 1.67906 | 0.839531 | − | 0.543311i | \(-0.182830\pi\) | ||||
0.839531 | + | 0.543311i | \(0.182830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 3.46149 | + | 3.70572i | 0.181932 | + | 0.194768i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.56775 | + | 0.243427i | 0.187001 | + | 0.0127591i | ||||
\(365\) | 0.180281i | 0.00943636i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.2863i | 0.693537i | 0.937951 | + | 0.346768i | \(0.112721\pi\) | ||||
−0.937951 | + | 0.346768i | \(0.887279\pi\) | |||||||
\(368\) | −30.7365 | − | 4.21393i | −1.60225 | − | 0.219666i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.350973 | − | 0.327842i | 0.0182462 | − | 0.0170437i | ||||
\(371\) | −13.4253 | −0.697006 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1909 | −1.61500 | −0.807502 | − | 0.589865i | \(-0.799181\pi\) | ||||
−0.807502 | + | 0.589865i | \(0.799181\pi\) | |||||||
\(374\) | 44.7123 | − | 41.7656i | 2.31202 | − | 2.15965i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.8567 | + | 11.2792i | −0.714607 | + | 0.581681i | ||||
\(377\) | 8.67626i | 0.446850i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.24887i | − | 0.475083i | −0.971377 | − | 0.237541i | \(-0.923658\pi\) | ||
0.971377 | − | 0.237541i | \(-0.0763415\pi\) | |||||||
\(380\) | 0.00803255 | − | 0.117728i | 0.000412061 | − | 0.00603929i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.77907 | + | 4.04570i | 0.193354 | + | 0.206996i | ||||
\(383\) | −15.5740 | −0.795796 | −0.397898 | − | 0.917430i | \(-0.630260\pi\) | ||||
−0.397898 | + | 0.917430i | \(0.630260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.396050 | −0.0201846 | ||||||||
\(386\) | −6.77685 | − | 7.25499i | −0.344933 | − | 0.369269i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.94442 | − | 28.4980i | 0.0987128 | − | 1.44677i | ||||
\(389\) | − | 19.6827i | − | 0.997951i | −0.866616 | − | 0.498976i | \(-0.833710\pi\) | ||
0.866616 | − | 0.498976i | \(-0.166290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 63.6000i | − | 3.21639i | ||||||
\(392\) | 11.8043 | − | 9.60855i | 0.596208 | − | 0.485305i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.60613 | − | 5.23666i | 0.282433 | − | 0.263819i | ||||
\(395\) | −0.158039 | −0.00795183 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.62956 | 0.433105 | 0.216553 | − | 0.976271i | \(-0.430519\pi\) | ||||
0.216553 | + | 0.976271i | \(0.430519\pi\) | |||||||
\(398\) | 1.05773 | − | 0.988025i | 0.0530195 | − | 0.0495252i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.8009 | − | 2.71466i | −0.990043 | − | 0.135733i | ||||
\(401\) | 20.6012i | 1.02877i | 0.857558 | + | 0.514387i | \(0.171981\pi\) | ||||
−0.857558 | + | 0.514387i | \(0.828019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.92035i | 0.494168i | ||||||||
\(404\) | −17.7918 | − | 1.21394i | −0.885177 | − | 0.0603956i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.58265 | − | 8.11765i | −0.376321 | − | 0.402872i | ||||
\(407\) | 30.3686 | 1.50532 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3613 | 1.64961 | 0.824805 | − | 0.565418i | \(-0.191285\pi\) | ||||
0.824805 | + | 0.565418i | \(0.191285\pi\) | |||||||
\(410\) | 0.455392 | + | 0.487523i | 0.0224902 | + | 0.0240770i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.32672 | + | 0.568132i | 0.410228 | + | 0.0279898i | ||||
\(413\) | − | 7.70457i | − | 0.379117i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.551364i | 0.0270654i | ||||||||
\(416\) | −4.58734 | − | 6.49288i | −0.224913 | − | 0.318340i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.45266 | − | 5.09330i | 0.266698 | − | 0.249122i | ||||
\(419\) | −24.8571 | −1.21435 | −0.607174 | − | 0.794569i | \(-0.707697\pi\) | ||||
−0.607174 | + | 0.794569i | \(0.707697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1678 | 0.885446 | 0.442723 | − | 0.896659i | \(-0.354013\pi\) | ||||
0.442723 | + | 0.896659i | \(0.354013\pi\) | |||||||
\(422\) | 13.0391 | − | 12.1797i | 0.634733 | − | 0.592901i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.8413 | + | 23.1469i | 0.915013 | + | 1.12411i | ||||
\(425\) | − | 40.9719i | − | 1.98743i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.55393i | 0.413954i | ||||||||
\(428\) | −1.73322 | + | 25.4025i | −0.0837781 | + | 1.22788i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.255765 | + | 0.273811i | 0.0123341 | + | 0.0132043i | ||||
\(431\) | 19.1589 | 0.922850 | 0.461425 | − | 0.887179i | \(-0.347338\pi\) | ||||
0.461425 | + | 0.887179i | \(0.347338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.63029 | −0.270575 | −0.135287 | − | 0.990806i | \(-0.543196\pi\) | ||||
−0.135287 | + | 0.990806i | \(0.543196\pi\) | |||||||
\(434\) | −8.66993 | − | 9.28163i | −0.416170 | − | 0.445533i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.07310 | + | 30.3840i | −0.0992836 | + | 1.45513i | ||||
\(437\) | − | 7.75602i | − | 0.371021i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.947873i | − | 0.0452395i | −0.999744 | − | 0.0226198i | \(-0.992799\pi\) | ||
0.999744 | − | 0.0226198i | \(-0.00720071\pi\) | |||||||
\(440\) | 0.555823 | + | 0.682841i | 0.0264978 | + | 0.0325532i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.9099 | − | 11.1249i | 0.566494 | − | 0.529159i | ||||
\(443\) | −14.0866 | −0.669276 | −0.334638 | − | 0.942347i | \(-0.608614\pi\) | ||||
−0.334638 | + | 0.942347i | \(0.608614\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.133293 | 0.00631869 | ||||||||
\(446\) | −27.9268 | + | 26.0863i | −1.32237 | + | 1.23522i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.96647 | + | 2.06572i | 0.470871 | + | 0.0975961i | ||||
\(449\) | − | 9.55838i | − | 0.451088i | −0.974233 | − | 0.225544i | \(-0.927584\pi\) | ||
0.974233 | − | 0.225544i | \(-0.0724159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.1839i | 1.98636i | ||||||||
\(452\) | 5.43096 | + | 0.370554i | 0.255451 | + | 0.0174294i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.5086 | + | 20.8851i | 0.915586 | + | 0.980185i | ||||
\(455\) | −0.105494 | −0.00494565 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0167 | −0.608895 | −0.304448 | − | 0.952529i | \(-0.598472\pi\) | ||||
−0.304448 | + | 0.952529i | \(0.598472\pi\) | |||||||
\(458\) | −9.58173 | − | 10.2578i | −0.447725 | − | 0.479314i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.913097 | + | 0.0623006i | 0.0425733 | + | 0.00290478i | ||||
\(461\) | − | 24.7561i | − | 1.15301i | −0.817095 | − | 0.576503i | \(-0.804417\pi\) | ||
0.817095 | − | 0.576503i | \(-0.195583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0596i | 1.07167i | 0.844322 | + | 0.535836i | \(0.180003\pi\) | ||||
−0.844322 | + | 0.535836i | \(0.819997\pi\) | |||||||
\(464\) | −3.35423 | + | 24.4659i | −0.155716 | + | 1.13580i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.98956 | − | 1.85843i | 0.0921644 | − | 0.0860903i | ||||
\(467\) | 19.2484 | 0.890712 | 0.445356 | − | 0.895354i | \(-0.353077\pi\) | ||||
0.445356 | + | 0.895354i | \(0.353077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.68348 | 0.170087 | ||||||||
\(470\) | 0.385180 | − | 0.359795i | 0.0177670 | − | 0.0165961i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.2837 | + | 10.8127i | −0.611430 | + | 0.497696i | ||||
\(473\) | 23.6920i | 1.08936i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.99652i | − | 0.229256i | ||||||
\(476\) | −1.42037 | + | 20.8173i | −0.0651024 | + | 0.954161i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.6112 | − | 20.9949i | −0.896996 | − | 0.960284i | ||||
\(479\) | 24.6787 | 1.12760 | 0.563799 | − | 0.825912i | \(-0.309339\pi\) | ||||
0.563799 | + | 0.825912i | \(0.309339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.08918 | 0.368835 | ||||||||
\(482\) | −0.848745 | − | 0.908628i | −0.0386593 | − | 0.0413869i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.29220 | + | 33.5952i | −0.104191 | + | 1.52705i | ||||
\(485\) | 0.842654i | 0.0382629i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.2803i | − | 0.918986i | −0.888181 | − | 0.459493i | \(-0.848031\pi\) | ||
0.888181 | − | 0.459493i | \(-0.151969\pi\) | |||||||
\(488\) | 14.7481 | − | 12.0047i | 0.667614 | − | 0.543429i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.328128 | + | 0.306502i | −0.0148233 | + | 0.0138464i | ||||
\(491\) | 21.5002 | 0.970289 | 0.485144 | − | 0.874434i | \(-0.338767\pi\) | ||||
0.485144 | + | 0.874434i | \(0.338767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −50.6248 | −2.28003 | ||||||||
\(494\) | 1.45241 | − | 1.35668i | 0.0653468 | − | 0.0610401i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.83519 | + | 27.9741i | −0.172205 | + | 1.25607i | ||||
\(497\) | − | 11.4079i | − | 0.511712i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8397i | 0.619551i | 0.950810 | + | 0.309776i | \(0.100254\pi\) | ||||
−0.950810 | + | 0.309776i | \(0.899746\pi\) | |||||||
\(500\) | 1.17687 | + | 0.0802975i | 0.0526310 | + | 0.00359101i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.89934 | − | 10.5978i | −0.441829 | − | 0.473002i | ||||
\(503\) | −30.3835 | −1.35473 | −0.677366 | − | 0.735646i | \(-0.736879\pi\) | ||||
−0.677366 | + | 0.735646i | \(0.736879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.526085 | 0.0234105 | ||||||||
\(506\) | 39.5038 | + | 42.2909i | 1.75616 | + | 1.88006i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 35.8570 | + | 2.44652i | 1.59090 | + | 0.108547i | ||||
\(509\) | − | 1.67351i | − | 0.0741769i | −0.999312 | − | 0.0370884i | \(-0.988192\pi\) | ||
0.999312 | − | 0.0370884i | \(-0.0118083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.88758i | − | 0.171976i | ||||||
\(512\) | −10.4255 | − | 20.0825i | −0.460748 | − | 0.887531i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.3808 | − | 12.4989i | 0.590200 | − | 0.551303i | ||||
\(515\) | −0.246212 | −0.0108494 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.3285 | 1.46578 | ||||||||
\(518\) | −7.56837 | + | 7.06958i | −0.332535 | + | 0.310619i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.148053 | + | 0.181886i | 0.00649254 | + | 0.00797622i | ||||
\(521\) | 1.00103i | 0.0438557i | 0.999760 | + | 0.0219279i | \(0.00698042\pi\) | ||||
−0.999760 | + | 0.0219279i | \(0.993020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.5428i | 0.461003i | 0.973072 | + | 0.230502i | \(0.0740367\pi\) | ||||
−0.973072 | + | 0.230502i | \(0.925963\pi\) | |||||||
\(524\) | 2.33008 | − | 34.1504i | 0.101790 | − | 1.49187i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.70214 | + | 1.82223i | 0.0742168 | + | 0.0794531i | ||||
\(527\) | −57.8839 | −2.52146 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.1558 | 1.61547 | ||||||||
\(530\) | −0.601016 | − | 0.643421i | −0.0261065 | − | 0.0279484i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.173214 | + | 2.53867i | −0.00750976 | + | 0.110065i | ||||
\(533\) | 11.2364i | 0.486701i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.751125i | − | 0.0324740i | ||||||
\(536\) | −5.16946 | − | 6.35079i | −0.223287 | − | 0.274312i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.495375 | − | 0.462727i | 0.0213571 | − | 0.0199496i | ||||
\(539\) | −28.3919 | −1.22293 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8721 | 0.553414 | 0.276707 | − | 0.960954i | \(-0.410757\pi\) | ||||
0.276707 | + | 0.960954i | \(0.410757\pi\) | |||||||
\(542\) | 17.7383 | − | 16.5693i | 0.761926 | − | 0.711712i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 37.8851 | − | 26.7665i | 1.62431 | − | 1.14760i | ||||
\(545\) | − | 0.898423i | − | 0.0384842i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.97730i | 0.298328i | 0.988812 | + | 0.149164i | \(0.0476582\pi\) | ||||
−0.988812 | + | 0.149164i | \(0.952342\pi\) | |||||||
\(548\) | −33.3149 | − | 2.27308i | −1.42314 | − | 0.0971010i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.4488 | + | 27.2443i | 1.08514 | + | 1.16170i | ||||
\(551\) | −6.17369 | −0.263008 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.40796 | 0.144921 | ||||||||
\(554\) | 13.5445 | + | 14.5001i | 0.575449 | + | 0.616050i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8319 | − | 1.28490i | −0.798649 | − | 0.0544918i | ||||
\(557\) | 25.0555i | 1.06164i | 0.847485 | + | 0.530819i | \(0.178115\pi\) | ||||
−0.847485 | + | 0.530819i | \(0.821885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.31076i | 0.266917i | ||||||||
\(560\) | −0.297480 | − | 0.0407840i | −0.0125708 | − | 0.00172344i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.2289 | + | 14.2252i | −0.642392 | + | 0.600055i | ||||
\(563\) | 3.47474 | 0.146443 | 0.0732213 | − | 0.997316i | \(-0.476672\pi\) | ||||
0.0732213 | + | 0.997316i | \(0.476672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.160587 | −0.00675596 | ||||||||
\(566\) | −15.3902 | + | 14.3759i | −0.646898 | + | 0.604264i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.6686 | + | 16.0100i | −0.825276 | + | 0.671764i | ||||
\(569\) | 7.33875i | 0.307656i | 0.988098 | + | 0.153828i | \(0.0491602\pi\) | ||||
−0.988098 | + | 0.153828i | \(0.950840\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.2529i | − | 0.470918i | −0.971884 | − | 0.235459i | \(-0.924341\pi\) | ||
0.971884 | − | 0.235459i | \(-0.0756593\pi\) | |||||||
\(572\) | −1.00947 | + | 14.7951i | −0.0422080 | + | 0.618614i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.82006 | − | 10.5129i | −0.409882 | − | 0.438801i | ||||
\(575\) | 38.7531 | 1.61612 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2311 | 1.63321 | 0.816606 | − | 0.577196i | \(-0.195853\pi\) | ||||
0.816606 | + | 0.577196i | \(0.195853\pi\) | |||||||
\(578\) | 48.5013 | + | 51.9233i | 2.01739 | + | 2.15973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0495905 | − | 0.726813i | 0.00205913 | − | 0.0301793i | ||||
\(581\) | − | 11.8896i | − | 0.493263i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 55.6733i | − | 2.30575i | ||||||
\(584\) | −6.70268 | + | 5.45590i | −0.277359 | + | 0.225767i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.9868 | + | 29.8787i | −1.32136 | + | 1.23428i | ||||
\(587\) | −13.3109 | −0.549400 | −0.274700 | − | 0.961530i | \(-0.588579\pi\) | ||||
−0.274700 | + | 0.961530i | \(0.588579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.05893 | −0.290858 | ||||||||
\(590\) | 0.369250 | − | 0.344914i | 0.0152018 | − | 0.0141999i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.8104 | + | 3.12727i | 0.937503 | + | 0.128530i | ||||
\(593\) | − | 16.0593i | − | 0.659475i | −0.944073 | − | 0.329737i | \(-0.893040\pi\) | ||
0.944073 | − | 0.329737i | \(-0.106960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.615546i | − | 0.0252349i | ||||||
\(596\) | 9.62320 | + | 0.656591i | 0.394182 | + | 0.0268950i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.5225 | + | 11.2649i | 0.430296 | + | 0.460655i | ||||
\(599\) | 19.0431 | 0.778081 | 0.389041 | − | 0.921221i | \(-0.372807\pi\) | ||||
0.389041 | + | 0.921221i | \(0.372807\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3126 | 0.787776 | 0.393888 | − | 0.919158i | \(-0.371130\pi\) | ||||
0.393888 | + | 0.919158i | \(0.371130\pi\) | |||||||
\(602\) | −5.51532 | − | 5.90445i | −0.224788 | − | 0.240647i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.81268 | − | 0.396599i | −0.236515 | − | 0.0161374i | ||||
\(605\) | − | 0.993372i | − | 0.0403863i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 47.0591i | − | 1.91007i | −0.296496 | − | 0.955034i | \(-0.595818\pi\) | ||
0.296496 | − | 0.955034i | \(-0.404182\pi\) | |||||||
\(608\) | 4.62008 | − | 3.26417i | 0.187369 | − | 0.132380i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.409956 | + | 0.382938i | −0.0165986 | + | 0.0155047i | ||||
\(611\) | 8.87758 | 0.359148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.2968 | 0.698611 | 0.349305 | − | 0.937009i | \(-0.386418\pi\) | ||||
0.349305 | + | 0.937009i | \(0.386418\pi\) | |||||||
\(614\) | 25.9280 | − | 24.2193i | 1.04637 | − | 0.977410i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.9858 | − | 14.7247i | −0.482920 | − | 0.593277i | ||||
\(617\) | 41.0256i | 1.65163i | 0.563943 | + | 0.825814i | \(0.309284\pi\) | ||||
−0.563943 | + | 0.825814i | \(0.690716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.7560i | 0.753868i | 0.926240 | + | 0.376934i | \(0.123022\pi\) | ||||
−0.926240 | + | 0.376934i | \(0.876978\pi\) | |||||||
\(620\) | 0.0567012 | − | 0.831031i | 0.00227718 | − | 0.0333750i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.1836 | − | 30.1721i | −1.13006 | − | 1.20979i | ||||
\(623\) | −2.87432 | −0.115157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9478 | 0.997912 | ||||||||
\(626\) | 13.1819 | + | 14.1120i | 0.526856 | + | 0.564028i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.84077 | + | 26.9789i | −0.0734549 | + | 1.07658i | ||||
\(629\) | 47.1993i | 1.88196i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.5966i | − | 1.33746i | −0.743506 | − | 0.668729i | \(-0.766839\pi\) | ||
0.743506 | − | 0.668729i | \(-0.233161\pi\) | |||||||
\(632\) | −4.78279 | − | 5.87575i | −0.190249 | − | 0.233725i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.7167 | − | 10.0104i | 0.425615 | − | 0.397565i | ||||
\(635\) | −1.06025 | −0.0420748 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.56265 | −0.299643 | ||||||||
\(638\) | 33.6630 | − | 31.4445i | 1.33273 | − | 1.24490i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.347172 | + | 0.570131i | 0.0137232 | + | 0.0225364i | ||||
\(641\) | − | 13.0330i | − | 0.514774i | −0.966308 | − | 0.257387i | \(-0.917139\pi\) | ||
0.966308 | − | 0.257387i | \(-0.0828614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.7535i | 1.72547i | 0.505656 | + | 0.862735i | \(0.331251\pi\) | ||||
−0.505656 | + | 0.862735i | \(0.668749\pi\) | |||||||
\(644\) | −19.6900 | − | 1.34345i | −0.775894 | − | 0.0529392i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.91607 | + | 8.47459i | 0.311454 | + | 0.333428i | ||||
\(647\) | 13.7984 | 0.542470 | 0.271235 | − | 0.962513i | \(-0.412568\pi\) | ||||
0.271235 | + | 0.962513i | \(0.412568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.9501 | 1.25415 | ||||||||
\(650\) | 6.77870 | + | 7.25697i | 0.265883 | + | 0.284642i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.24939 | + | 0.0852461i | 0.0489300 | + | 0.00333849i | ||||
\(653\) | − | 12.0895i | − | 0.473098i | −0.971620 | − | 0.236549i | \(-0.923984\pi\) | ||
0.971620 | − | 0.236549i | \(-0.0760163\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00979i | 0.0394558i | ||||||||
\(656\) | −4.34396 | + | 31.6850i | −0.169603 | + | 1.23709i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.30600 | + | 7.75860i | −0.323802 | + | 0.302462i | ||||
\(659\) | −11.0743 | −0.431395 | −0.215698 | − | 0.976460i | \(-0.569203\pi\) | ||||
−0.215698 | + | 0.976460i | \(0.569203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6286 | −0.880151 | −0.440075 | − | 0.897961i | \(-0.645048\pi\) | ||||
−0.440075 | + | 0.897961i | \(0.645048\pi\) | |||||||
\(662\) | −25.0259 | + | 23.3766i | −0.972659 | + | 0.908556i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.4992 | + | 16.6860i | −0.795522 | + | 0.647544i | ||||
\(665\) | − | 0.0750657i | − | 0.00291092i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 47.8832i | − | 1.85405i | ||||||
\(668\) | −0.893056 | + | 13.0889i | −0.0345534 | + | 0.506425i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.164900 | + | 0.176535i | 0.00637065 | + | 0.00682013i | ||||
\(671\) | −35.4723 | −1.36939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8668 | 0.418885 | 0.209442 | − | 0.977821i | \(-0.432835\pi\) | ||||
0.209442 | + | 0.977821i | \(0.432835\pi\) | |||||||
\(674\) | 11.4852 | + | 12.2955i | 0.442393 | + | 0.473606i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.50098 | − | 21.9988i | 0.0577299 | − | 0.846107i | ||||
\(677\) | 14.7801i | 0.568044i | 0.958818 | + | 0.284022i | \(0.0916688\pi\) | ||||
−0.958818 | + | 0.284022i | \(0.908331\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 18.1709i | − | 0.697337i | ||||||
\(680\) | −1.06128 | + | 0.863867i | −0.0406982 | + | 0.0331278i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 38.4900 | − | 35.9533i | 1.47386 | − | 1.37672i | ||||
\(683\) | −21.9180 | −0.838669 | −0.419334 | − | 0.907832i | \(-0.637737\pi\) | ||||
−0.419334 | + | 0.907832i | \(0.637737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.985085 | 0.0376382 | ||||||||
\(686\) | 16.2799 | − | 15.2069i | 0.621568 | − | 0.580604i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.43973 | + | 17.7955i | −0.0930140 | + | 0.678448i | ||||
\(689\) | − | 14.8295i | − | 0.564958i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.66773i | 0.215611i | 0.994172 | + | 0.107805i | \(0.0343823\pi\) | ||||
−0.994172 | + | 0.107805i | \(0.965618\pi\) | |||||||
\(692\) | 20.5116 | + | 1.39951i | 0.779734 | + | 0.0532012i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.45309 | + | 3.69672i | 0.131078 | + | 0.140326i | ||||
\(695\) | 0.556838 | 0.0211221 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −65.5627 | −2.48336 | ||||||||
\(698\) | −3.52132 | − | 3.76977i | −0.133284 | − | 0.142688i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.6845 | − | 0.865465i | −0.479430 | − | 0.0327115i | ||||
\(701\) | 23.8905i | 0.902331i | 0.892440 | + | 0.451166i | \(0.148992\pi\) | ||||
−0.892440 | + | 0.451166i | \(0.851008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.75595i | 0.217090i | ||||||||
\(704\) | −8.56633 | + | 41.3299i | −0.322856 | + | 1.55768i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.43726 | − | 1.34254i | 0.0540919 | − | 0.0505270i | ||||
\(707\) | −11.3445 | −0.426653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2727 | 1.51247 | 0.756237 | − | 0.654298i | \(-0.227036\pi\) | ||||
0.756237 | + | 0.654298i | \(0.227036\pi\) | |||||||
\(710\) | 0.546734 | − | 0.510701i | 0.0205186 | − | 0.0191663i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.03387 | + | 4.95570i | 0.151176 | + | 0.185723i | ||||
\(713\) | − | 54.7492i | − | 2.05037i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.437474i | − | 0.0163606i | ||||||
\(716\) | −2.53654 | + | 37.1764i | −0.0947951 | + | 1.38935i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.7118 | − | 32.8787i | −1.14615 | − | 1.22702i | ||||
\(719\) | 11.8037 | 0.440203 | 0.220101 | − | 0.975477i | \(-0.429361\pi\) | ||||
0.220101 | + | 0.975477i | \(0.429361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.30930 | 0.197729 | ||||||||
\(722\) | 0.965364 | + | 1.03348i | 0.0359271 | + | 0.0384620i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.488167 | − | 7.15473i | 0.0181426 | − | 0.265903i | ||||
\(725\) | − | 30.8470i | − | 1.14563i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7659i | 0.621813i | 0.950441 | + | 0.310906i | \(0.100633\pi\) | ||||
−0.950441 | + | 0.310906i | \(0.899367\pi\) | |||||||
\(728\) | −3.19260 | − | 3.92218i | −0.118326 | − | 0.145366i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.186316 | − | 0.174037i | 0.00689588 | − | 0.00644140i | ||||
\(731\) | −36.8224 | −1.36193 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1955 | 0.745936 | 0.372968 | − | 0.927844i | \(-0.378340\pi\) | ||||
0.372968 | + | 0.927844i | \(0.378340\pi\) | |||||||
\(734\) | 13.7310 | − | 12.8261i | 0.506821 | − | 0.473419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.3170 | + | 35.8334i | 0.933196 | + | 1.32084i | ||||
\(737\) | 15.2750i | 0.562662i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 36.9489i | − | 1.35919i | −0.733589 | − | 0.679593i | \(-0.762156\pi\) | ||
0.733589 | − | 0.679593i | \(-0.237844\pi\) | |||||||
\(740\) | −0.677634 | − | 0.0462349i | −0.0249103 | − | 0.00169963i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.9603 | + | 13.8747i | 0.475787 | + | 0.509356i | ||||
\(743\) | 0.783282 | 0.0287358 | 0.0143679 | − | 0.999897i | \(-0.495426\pi\) | ||||
0.0143679 | + | 0.999897i | \(0.495426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.284547 | −0.0104250 | ||||||||
\(746\) | 30.1106 | + | 32.2350i | 1.10243 | + | 1.18021i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −86.3274 | − | 5.89011i | −3.15644 | − | 0.215364i | ||||
\(749\) | 16.1972i | 0.591834i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 30.8590i | − | 1.12606i | −0.826437 | − | 0.563030i | \(-0.809636\pi\) | ||
0.826437 | − | 0.563030i | \(-0.190364\pi\) | |||||||
\(752\) | 25.0336 | + | 3.43206i | 0.912881 | + | 0.125154i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.96670 | − | 8.37575i | 0.326548 | − | 0.305027i | ||||
\(755\) | 0.171875 | 0.00625516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.0549 | 0.765255 | 0.382627 | − | 0.923903i | \(-0.375019\pi\) | ||||
0.382627 | + | 0.923903i | \(0.375019\pi\) | |||||||
\(758\) | −9.55848 | + | 8.92853i | −0.347180 | + | 0.324299i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.129423 | + | 0.105349i | −0.00469466 | + | 0.00382139i | ||||
\(761\) | 2.32164i | 0.0841592i | 0.999114 | + | 0.0420796i | \(0.0133983\pi\) | ||||
−0.999114 | + | 0.0420796i | \(0.986602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3736i | 0.701370i | ||||||||
\(764\) | 0.532955 | − | 7.81115i | 0.0192816 | − | 0.282598i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0346 | + | 16.0954i | 0.543223 | + | 0.581550i | ||||
\(767\) | 8.51042 | 0.307294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.4345 | −1.34992 | −0.674961 | − | 0.737853i | \(-0.735840\pi\) | ||||
−0.674961 | + | 0.737853i | \(0.735840\pi\) | |||||||
\(770\) | 0.382333 | + | 0.409308i | 0.0137783 | + | 0.0147504i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.955726 | + | 14.0074i | −0.0343973 | + | 0.504138i | ||||
\(773\) | − | 7.48535i | − | 0.269229i | −0.990898 | − | 0.134615i | \(-0.957020\pi\) | ||
0.990898 | − | 0.134615i | \(-0.0429797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 35.2701i | − | 1.26694i | ||||||
\(776\) | −31.3290 | + | 25.5014i | −1.12465 | + | 0.915448i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.3416 | + | 19.0010i | −0.729280 | + | 0.681217i | ||||
\(779\) | −7.99536 | −0.286463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.3072 | 1.69279 | ||||||||
\(782\) | −65.7291 | + | 61.3972i | −2.35047 | + | 2.19556i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.3257 | − | 2.92371i | −0.761631 | − | 0.104418i | ||||
\(785\) | − | 0.797738i | − | 0.0284725i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.29084i | − | 0.0816598i | −0.999166 | − | 0.0408299i | \(-0.987000\pi\) | ||
0.999166 | − | 0.0408299i | \(-0.0130002\pi\) | |||||||
\(788\) | −10.8239 | − | 0.738516i | −0.385586 | − | 0.0263085i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.152566 | + | 0.163330i | 0.00542804 | + | 0.00581102i | ||||
\(791\) | 3.46290 | 0.123127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.44862 | −0.335530 | ||||||||
\(794\) | −8.33067 | − | 8.91844i | −0.295644 | − | 0.316504i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.04220 | − | 0.139339i | −0.0723838 | − | 0.00493875i | ||||
\(797\) | 9.49545i | 0.336346i | 0.985757 | + | 0.168173i | \(0.0537868\pi\) | ||||
−0.985757 | + | 0.168173i | \(0.946213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.7995i | 1.83253i | ||||||||
\(800\) | 16.3095 | + | 23.0843i | 0.576628 | + | 0.816155i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.2908 | − | 19.8877i | 0.751805 | − | 0.702258i | ||||
\(803\) | 16.1214 | 0.568912 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.582211 | 0.0205202 | ||||||||
\(806\) | 10.2524 | − | 9.57675i | 0.361127 | − | 0.337327i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.9210 | + | 19.5593i | 0.560100 | + | 0.688095i | ||||
\(809\) | 52.8555i | 1.85830i | 0.369704 | + | 0.929150i | \(0.379459\pi\) | ||||
−0.369704 | + | 0.929150i | \(0.620541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 53.7682i | − | 1.88806i | −0.329863 | − | 0.944029i | \(-0.607002\pi\) | ||
0.329863 | − | 0.944029i | \(-0.392998\pi\) | |||||||
\(812\) | −1.06937 | + | 15.6730i | −0.0375274 | + | 0.550013i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.3168 | − | 31.3853i | −1.02755 | − | 1.10005i | ||||
\(815\) | −0.0369432 | −0.00129406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.49049 | −0.157103 | ||||||||
\(818\) | −32.2058 | − | 34.4781i | −1.12605 | − | 1.20550i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0642231 | − | 0.941274i | 0.00224277 | − | 0.0328707i | ||||
\(821\) | − | 27.3310i | − | 0.953860i | −0.878941 | − | 0.476930i | \(-0.841750\pi\) | ||
0.878941 | − | 0.476930i | \(-0.158250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.84119i | 0.203611i | 0.994804 | + | 0.101805i | \(0.0324619\pi\) | ||||
−0.994804 | + | 0.101805i | \(0.967538\pi\) | |||||||
\(824\) | −7.45116 | − | 9.15391i | −0.259574 | − | 0.318892i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.96249 | + | 7.43772i | −0.277050 | + | 0.258791i | ||||
\(827\) | 42.5549 | 1.47978 | 0.739889 | − | 0.672729i | \(-0.234878\pi\) | ||||
0.739889 | + | 0.672729i | \(0.234878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.5676 | −1.82575 | −0.912874 | − | 0.408240i | \(-0.866143\pi\) | ||||
−0.912874 | + | 0.408240i | \(0.866143\pi\) | |||||||
\(830\) | 0.569821 | − | 0.532267i | 0.0197788 | − | 0.0184753i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.28178 | + | 11.0089i | −0.0791066 | + | 0.381665i | ||||
\(833\) | − | 44.1270i | − | 1.52891i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.387024i | − | 0.0133935i | ||||||
\(836\) | −10.5276 | − | 0.718299i | −0.364105 | − | 0.0248429i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.9961 | + | 25.6892i | 0.828933 | + | 0.887418i | ||||
\(839\) | −5.79622 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.11445 | −0.314291 | ||||||||
\(842\) | −17.5386 | − | 18.7760i | −0.604419 | − | 0.647064i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.1749 | − | 1.71769i | −0.866557 | − | 0.0591252i | ||||
\(845\) | 0.650480i | 0.0223772i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.4210i | 0.736036i | ||||||||
\(848\) | 5.73306 | − | 41.8172i | 0.196874 | − | 1.43601i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −42.3435 | + | 39.5528i | −1.45237 | + | 1.35665i | ||||
\(851\) | −44.6432 | −1.53035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.1964 | −0.931186 | −0.465593 | − | 0.884999i | \(-0.654159\pi\) | ||||
−0.465593 | + | 0.884999i | \(0.654159\pi\) | |||||||
\(854\) | 8.84028 | − | 8.25766i | 0.302508 | − | 0.282571i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.9261 | − | 22.7315i | 0.954494 | − | 0.776946i | ||||
\(857\) | − | 18.1477i | − | 0.619912i | −0.950751 | − | 0.309956i | \(-0.899686\pi\) | ||
0.950751 | − | 0.309956i | \(-0.100314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.4786i | − | 0.766959i | −0.923549 | − | 0.383479i | \(-0.874726\pi\) | ||
0.923549 | − | 0.383479i | \(-0.125274\pi\) | |||||||
\(860\) | 0.0360701 | − | 0.528655i | 0.00122998 | − | 0.0180270i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.4953 | − | 19.8002i | −0.629952 | − | 0.674398i | ||||
\(863\) | 7.67220 | 0.261165 | 0.130582 | − | 0.991437i | \(-0.458315\pi\) | ||||
0.130582 | + | 0.991437i | \(0.458315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.606505 | −0.0206218 | ||||||||
\(866\) | 5.43528 | + | 5.81877i | 0.184698 | + | 0.197730i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.22270 | + | 17.9203i | −0.0415012 | + | 0.608255i | ||||
\(869\) | 14.1325i | 0.479411i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.06875i | 0.137864i | ||||||||
\(872\) | 33.4025 | − | 27.1892i | 1.13115 | − | 0.920742i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.01565 | + | 7.48738i | −0.271134 | + | 0.253264i | ||||
\(875\) | 0.750396 | 0.0253680 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0069 | 0.776888 | 0.388444 | − | 0.921472i | \(-0.373013\pi\) | ||||
0.388444 | + | 0.921472i | \(0.373013\pi\) | |||||||
\(878\) | −0.979604 | + | 0.915043i | −0.0330600 | + | 0.0308812i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.169127 | − | 1.23362i | 0.00570127 | − | 0.0415853i | ||||
\(881\) | − | 10.0755i | − | 0.339452i | −0.985491 | − | 0.169726i | \(-0.945712\pi\) | ||
0.985491 | − | 0.169726i | \(-0.0542883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.12094i | 0.0377225i | 0.999822 | + | 0.0188613i | \(0.00600408\pi\) | ||||
−0.999822 | + | 0.0188613i | \(0.993996\pi\) | |||||||
\(884\) | −22.9947 | − | 1.56893i | −0.773395 | − | 0.0527688i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5987 | + | 14.5582i | 0.456858 | + | 0.489092i | ||||
\(887\) | 28.4631 | 0.955698 | 0.477849 | − | 0.878442i | \(-0.341417\pi\) | ||||
0.477849 | + | 0.878442i | \(0.341417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8632 | 0.766808 | ||||||||
\(890\) | −0.128676 | − | 0.137755i | −0.00431324 | − | 0.00461756i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 53.9191 | + | 3.67890i | 1.80535 | + | 0.123179i | ||||
\(893\) | 6.31694i | 0.211388i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.09926i | − | 0.0367444i | ||||||
\(896\) | −7.48640 | − | 12.2943i | −0.250103 | − | 0.410723i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.87836 | + | 9.22732i | −0.329645 | + | 0.307920i | ||||
\(899\) | −43.5797 | −1.45346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 86.5281 | 2.88267 | ||||||||
\(902\) | 43.5960 | − | 40.7228i | 1.45159 | − | 1.35592i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.85989 | − | 5.97048i | −0.161638 | − | 0.198575i | ||||
\(905\) | 0.211557i | 0.00703241i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6933i | 0.554292i | 0.960828 | + | 0.277146i | \(0.0893886\pi\) | ||||
−0.960828 | + | 0.277146i | \(0.910611\pi\) | |||||||
\(908\) | 2.75127 | − | 40.3234i | 0.0913040 | − | 1.33818i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.101841 | + | 0.109026i | 0.00337598 | + | 0.00361417i | ||||
\(911\) | −40.2610 | −1.33391 | −0.666954 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666954 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.3049 | 1.63175 | ||||||||
\(914\) | 12.5659 | + | 13.4524i | 0.415642 | + | 0.444967i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.35129 | + | 19.8050i | −0.0446480 | + | 0.654375i | ||||
\(917\) | − | 21.7751i | − | 0.719077i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.2655i | 1.72408i | 0.506841 | + | 0.862040i | \(0.330813\pi\) | ||||
−0.506841 | + | 0.862040i | \(0.669187\pi\) | |||||||
\(920\) | −0.817085 | − | 1.00381i | −0.0269385 | − | 0.0330945i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.5848 | + | 23.8986i | −0.842591 | + | 0.787060i | ||||
\(923\) | 12.6011 | 0.414769 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.7597 | −0.945614 | ||||||||
\(926\) | 23.8315 | − | 22.2609i | 0.783153 | − | 0.731539i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 28.5230 | − | 20.1520i | 0.936312 | − | 0.661522i | ||||
\(929\) | − | 3.61665i | − | 0.118658i | −0.998238 | − | 0.0593291i | \(-0.981104\pi\) | ||
0.998238 | − | 0.0593291i | \(-0.0188961\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.38129i | − | 0.176365i | ||||||
\(932\) | −3.84129 | − | 0.262091i | −0.125826 | − | 0.00858509i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.5818 | − | 19.8928i | −0.608014 | − | 0.650912i | ||||
\(935\) | 2.55260 | 0.0834791 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.8905 | −1.40117 | −0.700587 | − | 0.713567i | \(-0.747078\pi\) | ||||
−0.700587 | + | 0.713567i | \(0.747078\pi\) | |||||||
\(938\) | −3.55590 | − | 3.80679i | −0.116104 | − | 0.124296i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.743678 | − | 0.0507411i | −0.0242561 | − | 0.00165499i | ||||
\(941\) | − | 4.99580i | − | 0.162858i | −0.996679 | − | 0.0814292i | \(-0.974052\pi\) | ||
0.996679 | − | 0.0814292i | \(-0.0259484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 62.0121i | − | 2.01939i | ||||||
\(944\) | 23.9983 | + | 3.29012i | 0.781077 | + | 0.107084i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.4852 | − | 22.8715i | 0.796081 | − | 0.743615i | ||||
\(947\) | −37.6577 | −1.22371 | −0.611856 | − | 0.790969i | \(-0.709577\pi\) | ||||
−0.611856 | + | 0.790969i | \(0.709577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.29420 | 0.139396 | ||||||||
\(950\) | −5.16378 | + | 4.82346i | −0.167535 | + | 0.156494i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.8854 | − | 18.6284i | 0.741719 | − | 0.603750i | ||||
\(953\) | 15.6600i | 0.507278i | 0.967299 | + | 0.253639i | \(0.0816274\pi\) | ||||
−0.967299 | + | 0.253639i | \(0.918373\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.230967i | 0.00747392i | ||||||||
\(956\) | −2.76573 | + | 40.5354i | −0.0894501 | + | 1.31101i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.8239 | − | 25.5048i | −0.769716 | − | 0.824024i | ||||
\(959\) | −21.2423 | −0.685951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.8285 | −0.607372 | ||||||||
\(962\) | −7.80901 | − | 8.35997i | −0.251773 | − | 0.269536i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.119697 | + | 1.75431i | −0.00385517 | + | 0.0565026i | ||||
\(965\) | − | 0.414184i | − | 0.0133331i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.2763i | 1.26304i | 0.775360 | + | 0.631520i | \(0.217569\pi\) | ||||
−0.775360 | + | 0.631520i | \(0.782431\pi\) | |||||||
\(968\) | 36.9326 | − | 30.0627i | 1.18706 | − | 0.966250i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.870862 | − | 0.813468i | 0.0279617 | − | 0.0261189i | ||||
\(971\) | −30.1803 | −0.968532 | −0.484266 | − | 0.874921i | \(-0.660913\pi\) | ||||
−0.484266 | + | 0.874921i | \(0.660913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0076 | −0.384947 | ||||||||
\(974\) | −20.9591 | + | 19.5778i | −0.671574 | + | 0.627314i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.6439 | − | 3.65283i | −0.852849 | − | 0.116924i | ||||
\(977\) | 4.23963i | 0.135638i | 0.997698 | + | 0.0678189i | \(0.0216040\pi\) | ||||
−0.997698 | + | 0.0678189i | \(0.978396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.9195i | − | 0.380950i | ||||||
\(980\) | 0.633525 | + | 0.0432254i | 0.0202372 | + | 0.00138079i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.7555 | − | 22.2199i | −0.662334 | − | 0.709065i | ||||
\(983\) | 33.6677 | 1.07383 | 0.536916 | − | 0.843635i | \(-0.319589\pi\) | ||||
0.536916 | + | 0.843635i | \(0.319589\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.320051 | 0.0101977 | ||||||||
\(986\) | 48.8714 | + | 52.3195i | 1.55638 | + | 1.66619i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.80420 | − | 0.191331i | −0.0892135 | − | 0.00608704i | ||||
\(989\) | − | 34.8283i | − | 1.10748i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.37922i | 0.234409i | 0.993108 | + | 0.117204i | \(0.0373932\pi\) | ||||
−0.993108 | + | 0.117204i | \(0.962607\pi\) | |||||||
\(992\) | 32.6129 | − | 23.0416i | 1.03546 | − | 0.731571i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.7897 | + | 11.0127i | −0.373948 | + | 0.349303i | ||||
\(995\) | 0.0603856 | 0.00191435 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.7846 | −0.816607 | −0.408303 | − | 0.912846i | \(-0.633879\pi\) | ||||
−0.408303 | + | 0.912846i | \(0.633879\pi\) | |||||||
\(998\) | 14.3030 | − | 13.3604i | 0.452754 | − | 0.422915i | ||||
\(999\) | 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 | 684.2.c.b.647.9 | ✓ | 32 | |
3.2 | odd | 2 | inner | 684.2.c.b.647.24 | yes | 32 | |
4.3 | odd | 2 | inner | 684.2.c.b.647.23 | yes | 32 | |
12.11 | even | 2 | inner | 684.2.c.b.647.10 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.c.b.647.9 | ✓ | 32 | 1.1 | even | 1 | trivial | |
684.2.c.b.647.10 | yes | 32 | 12.11 | even | 2 | inner | |
684.2.c.b.647.23 | yes | 32 | 4.3 | odd | 2 | inner | |
684.2.c.b.647.24 | yes | 32 | 3.2 | odd | 2 | inner |