Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (of order \(4\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.10 | ||
Character | \(\chi\) | \(=\) | 2100.1457 |
Dual form | 2100.2.s.c.1793.10 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.369667 | − | 1.69214i | 0.213428 | − | 0.976959i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72669 | − | 1.25106i | −0.908897 | − | 0.417020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.03821i | − | 1.21756i | −0.793337 | − | 0.608782i | \(-0.791658\pi\) | ||
0.793337 | − | 0.608782i | \(-0.208342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.70112 | + | 3.70112i | −1.02651 | + | 1.02651i | −0.0268663 | + | 0.999639i | \(0.508553\pi\) |
−0.999639 | + | 0.0268663i | \(0.991447\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.26756 | − | 5.26756i | 1.27757 | − | 1.27757i | 0.335549 | − | 0.942023i | \(-0.391078\pi\) |
0.942023 | − | 0.335549i | \(-0.108922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.18379i | 0.500995i | 0.968117 | + | 0.250498i | \(0.0805943\pi\) | ||||
−0.968117 | + | 0.250498i | \(0.919406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.45792 | + | 0.935131i | −0.318144 | + | 0.204062i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.73460 | − | 3.73460i | −0.778717 | − | 0.778717i | 0.200895 | − | 0.979613i | \(-0.435615\pi\) |
−0.979613 | + | 0.200895i | \(0.935615\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.12494 | + | 4.15147i | −0.601395 | + | 0.798952i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.12019 | 1.32219 | 0.661093 | − | 0.750304i | \(-0.270093\pi\) | ||||
0.661093 | + | 0.750304i | \(0.270093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41796 | −0.613884 | −0.306942 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306942 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.83322 | − | 1.49279i | −1.18951 | − | 0.259862i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.40822 | − | 4.40822i | −0.724708 | − | 0.724708i | 0.244853 | − | 0.969560i | \(-0.421260\pi\) |
−0.969560 | + | 0.244853i | \(0.921260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.89464 | + | 7.63100i | 0.783769 | + | 1.22194i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.501135i | 0.0782642i | 0.999234 | + | 0.0391321i | \(0.0124593\pi\) | ||||
−0.999234 | + | 0.0391321i | \(0.987541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.62698 | + | 8.62698i | −1.31560 | + | 1.31560i | −0.398383 | + | 0.917219i | \(0.630429\pi\) |
−0.917219 | + | 0.398383i | \(0.869571\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.51062 | + | 5.51062i | −0.803807 | + | 0.803807i | −0.983688 | − | 0.179882i | \(-0.942429\pi\) |
0.179882 | + | 0.983688i | \(0.442429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.96622 | − | 10.8607i | −0.975466 | − | 1.52080i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.79236 | − | 5.79236i | −0.795642 | − | 0.795642i | 0.186763 | − | 0.982405i | \(-0.440200\pi\) |
−0.982405 | + | 0.186763i | \(0.940200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.69528 | + | 0.807276i | 0.489452 | + | 0.106926i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0602 | −1.70030 | −0.850150 | − | 0.526541i | \(-0.823489\pi\) | ||||
−0.850150 | + | 0.526541i | \(0.823489\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3462 | 1.58076 | 0.790382 | − | 0.612614i | \(-0.209882\pi\) | ||||
0.790382 | + | 0.612614i | \(0.209882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.04343 | + | 2.81270i | 0.131460 | + | 0.354366i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.56252 | − | 5.56252i | −0.679570 | − | 0.679570i | 0.280333 | − | 0.959903i | \(-0.409555\pi\) |
−0.959903 | + | 0.280333i | \(0.909555\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.70003 | + | 4.93891i | −0.926974 | + | 0.594575i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2044i | 1.32972i | 0.746966 | + | 0.664862i | \(0.231510\pi\) | ||||
−0.746966 | + | 0.664862i | \(0.768490\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.731795 | + | 0.731795i | −0.0856501 | + | 0.0856501i | −0.748634 | − | 0.662984i | \(-0.769290\pi\) |
0.662984 | + | 0.748634i | \(0.269290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.85544 | + | 2.85544i | −0.325408 | + | 0.325408i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.73515i | 0.420238i | 0.977676 | + | 0.210119i | \(0.0673851\pi\) | ||||
−0.977676 | + | 0.210119i | \(0.932615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.86970 | + | 6.82251i | 0.652189 | + | 0.758057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.07942 | − | 1.07942i | −0.118482 | − | 0.118482i | 0.645380 | − | 0.763862i | \(-0.276699\pi\) |
−0.763862 | + | 0.645380i | \(0.776699\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.63210 | − | 12.0484i | 0.282191 | − | 1.29172i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.06582 | −0.854975 | −0.427488 | − | 0.904021i | \(-0.640601\pi\) | ||||
−0.427488 | + | 0.904021i | \(0.640601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.23417 | 0.548690 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.26351 | + | 5.78367i | −0.131020 | + | 0.599739i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.14555 | − | 1.14555i | −0.116313 | − | 0.116313i | 0.646554 | − | 0.762868i | \(-0.276209\pi\) |
−0.762868 | + | 0.646554i | \(0.776209\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.05204 | + | 11.0109i | −0.507749 | + | 1.10664i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.93078i | − | 0.192120i | −0.995376 | − | 0.0960598i | \(-0.969376\pi\) | ||
0.995376 | − | 0.0960598i | \(-0.0306240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.19442 | − | 3.19442i | 0.314755 | − | 0.314755i | −0.531993 | − | 0.846749i | \(-0.678557\pi\) |
0.846749 | + | 0.531993i | \(0.178557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4714 | − | 12.4714i | 1.20565 | − | 1.20565i | 0.233231 | − | 0.972421i | \(-0.425070\pi\) |
0.972421 | − | 0.233231i | \(-0.0749299\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.36758i | 0.130990i | 0.997853 | + | 0.0654951i | \(0.0208627\pi\) | ||||
−0.997853 | + | 0.0654951i | \(0.979137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.08892 | + | 5.82977i | −0.862682 | + | 0.553337i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.20243 | − | 9.20243i | −0.865691 | − | 0.865691i | 0.126301 | − | 0.991992i | \(-0.459690\pi\) |
−0.991992 | + | 0.126301i | \(0.959690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.7221 | − | 5.46149i | 1.36106 | − | 0.504915i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.44946 | −0.682891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.30710 | −0.482464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.847992 | + | 0.185253i | 0.0764609 | + | 0.0167037i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.728797 | − | 0.728797i | −0.0646703 | − | 0.0646703i | 0.674032 | − | 0.738702i | \(-0.264561\pi\) |
−0.738702 | + | 0.674032i | \(0.764561\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4090 | + | 17.7872i | 1.00450 | + | 1.56608i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.42407i | − | 0.561273i | −0.959814 | − | 0.280637i | \(-0.909454\pi\) | ||
0.959814 | − | 0.280637i | \(-0.0905456\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.54417 | − | 1.54417i | 0.133897 | − | 0.133897i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.82288 | + | 2.82288i | −0.241175 | + | 0.241175i | −0.817336 | − | 0.576161i | \(-0.804550\pi\) |
0.576161 | + | 0.817336i | \(0.304550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.96312i | − | 0.845061i | −0.906349 | − | 0.422530i | \(-0.861142\pi\) | ||
0.906349 | − | 0.422530i | \(-0.138858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.28766 | + | 11.3619i | 0.613731 | + | 0.956840i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.9459 | + | 14.9459i | 1.24984 | + | 1.24984i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.69214 | + | 0.369667i | 0.139566 | + | 0.0304897i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.15343 | 0.340262 | 0.170131 | − | 0.985421i | \(-0.445581\pi\) | ||||
0.170131 | + | 0.985421i | \(0.445581\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0670 | 0.900619 | 0.450309 | − | 0.892873i | \(-0.351314\pi\) | ||||
0.450309 | + | 0.892873i | \(0.351314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.9531 | + | 7.77299i | −1.69395 | + | 0.628409i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8476 | − | 13.8476i | −1.10516 | − | 1.10516i | −0.993778 | − | 0.111379i | \(-0.964473\pi\) |
−0.111379 | − | 0.993778i | \(-0.535527\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.9428 | + | 7.66025i | −0.947122 | + | 0.607498i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28152i | 0.416242i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.3889 | + | 17.3889i | −1.36200 | + | 1.36200i | −0.490636 | + | 0.871365i | \(0.663236\pi\) |
−0.871365 | + | 0.490636i | \(0.836764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.879154 | − | 0.879154i | 0.0680310 | − | 0.0680310i | −0.672273 | − | 0.740304i | \(-0.734682\pi\) |
0.740304 | + | 0.672273i | \(0.234682\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 14.3965i | − | 1.10743i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.73205 | − | 5.95452i | 0.208925 | − | 0.455353i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8678 | + | 15.8678i | 1.20641 | + | 1.20641i | 0.972182 | + | 0.234226i | \(0.0752555\pi\) |
0.234226 | + | 0.972182i | \(0.424745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.82795 | + | 22.0998i | −0.362891 | + | 1.66112i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.9266 | −1.26515 | −0.632576 | − | 0.774498i | \(-0.718002\pi\) | ||||
−0.632576 | + | 0.774498i | \(0.718002\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7292 | 1.09481 | 0.547407 | − | 0.836867i | \(-0.315615\pi\) | ||||
0.547407 | + | 0.836867i | \(0.315615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.56397 | − | 20.8915i | 0.337379 | − | 1.54434i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.2715 | − | 21.2715i | −1.55553 | − | 1.55553i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.14520 | − | 0.725869i | 0.374258 | − | 0.0527992i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.3345i | − | 0.747780i | −0.927473 | − | 0.373890i | \(-0.878024\pi\) | ||
0.927473 | − | 0.373890i | \(-0.121976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.01859 | + | 1.01859i | −0.0733200 | + | 0.0733200i | −0.742816 | − | 0.669496i | \(-0.766510\pi\) |
0.669496 | + | 0.742816i | \(0.266510\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.76865 | + | 7.76865i | −0.553493 | + | 0.553493i | −0.927447 | − | 0.373954i | \(-0.878002\pi\) |
0.373954 | + | 0.927447i | \(0.378002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.12642i | 0.221626i | 0.993841 | + | 0.110813i | \(0.0353455\pi\) | ||||
−0.993841 | + | 0.110813i | \(0.964655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.4689 | + | 7.35630i | −0.808951 | + | 0.518873i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.03474 | − | 5.03474i | −0.353369 | − | 0.353369i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.51089 | + | 14.8553i | 0.383033 | + | 1.03251i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.81859 | 0.609994 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2620 | −1.18837 | −0.594183 | − | 0.804330i | \(-0.702524\pi\) | ||||
−0.594183 | + | 0.804330i | \(0.702524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.9595 | + | 4.14192i | 1.29909 | + | 0.283800i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.41686 | + | 2.41686i | 0.164067 | + | 0.164067i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.967781 | + | 1.50882i | 0.0653966 | + | 0.101957i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.9918i | 2.62287i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2046 | − | 10.2046i | 0.683349 | − | 0.683349i | −0.277404 | − | 0.960753i | \(-0.589474\pi\) |
0.960753 | + | 0.277404i | \(0.0894740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.84739 | − | 7.84739i | 0.520849 | − | 0.520849i | −0.396979 | − | 0.917828i | \(-0.629941\pi\) |
0.917828 | + | 0.396979i | \(0.129941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0085i | 1.05787i | 0.848662 | + | 0.528935i | \(0.177409\pi\) | ||||
−0.848662 | + | 0.528935i | \(0.822591\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.77625 | + | 5.88738i | 0.248459 | + | 0.387361i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.99044 | − | 4.99044i | −0.326935 | − | 0.326935i | 0.524485 | − | 0.851420i | \(-0.324258\pi\) |
−0.851420 | + | 0.524485i | \(0.824258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.32041 | + | 1.38077i | 0.410555 | + | 0.0896903i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.710589 | −0.0459642 | −0.0229821 | − | 0.999736i | \(-0.507316\pi\) | ||||
−0.0229821 | + | 0.999736i | \(0.507316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6008 | 1.45585 | 0.727923 | − | 0.685658i | \(-0.240486\pi\) | ||||
0.727923 | + | 0.685658i | \(0.240486\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7145 | − | 7.41030i | 0.879785 | − | 0.475371i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.08246 | − | 8.08246i | −0.514275 | − | 0.514275i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.22556 | + | 1.42750i | −0.141039 | + | 0.0904644i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.31088i | − | 0.145862i | −0.997337 | − | 0.0729308i | \(-0.976765\pi\) | ||
0.997337 | − | 0.0729308i | \(-0.0232352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.0811 | + | 15.0811i | −0.948139 | + | 0.948139i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3424 | − | 10.3424i | 0.645138 | − | 0.645138i | −0.306676 | − | 0.951814i | \(-0.599217\pi\) |
0.951814 | + | 0.306676i | \(0.0992168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.23417i | 0.387373i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.4146 | − | 8.90779i | −1.20173 | − | 0.551378i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.31716 | − | 4.31716i | −0.266208 | − | 0.266208i | 0.561362 | − | 0.827570i | \(-0.310277\pi\) |
−0.827570 | + | 0.561362i | \(0.810277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.98167 | + | 13.6485i | −0.182475 | + | 0.835276i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.58085 | −0.157357 | −0.0786786 | − | 0.996900i | \(-0.525070\pi\) | ||||
−0.0786786 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.667337 | 0.0405378 | 0.0202689 | − | 0.999795i | \(-0.493548\pi\) | ||||
0.0202689 | + | 0.999795i | \(0.493548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.93490 | − | 8.85696i | 0.117106 | − | 0.536048i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9874 | + | 12.9874i | 0.780339 | + | 0.780339i | 0.979888 | − | 0.199549i | \(-0.0639476\pi\) |
−0.199549 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.31972 | + | 4.27607i | 0.557957 | + | 0.256002i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.9016i | − | 1.24689i | −0.781869 | − | 0.623443i | \(-0.785733\pi\) | ||
0.781869 | − | 0.623443i | \(-0.214267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4774 | − | 13.4774i | 0.801147 | − | 0.801147i | −0.182127 | − | 0.983275i | \(-0.558298\pi\) |
0.983275 | + | 0.182127i | \(0.0582983\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.354356 | − | 0.354356i | 0.0209170 | − | 0.0209170i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 38.4945i | − | 2.26438i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.36192 | + | 1.51497i | −0.138458 | + | 0.0888090i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.0132 | − | 20.0132i | −1.16918 | − | 1.16918i | −0.982402 | − | 0.186780i | \(-0.940195\pi\) |
−0.186780 | − | 0.982402i | \(-0.559805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.7645 | + | 12.6192i | 0.972775 | + | 0.732238i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.6444 | 1.59871 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2004 | 0.703219 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.26715 | − | 0.713746i | −0.187693 | − | 0.0410036i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.81548 | + | 2.81548i | 0.160688 | + | 0.160688i | 0.782871 | − | 0.622184i | \(-0.213754\pi\) |
−0.622184 | + | 0.782871i | \(0.713754\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.22454 | − | 6.58628i | −0.240325 | − | 0.374680i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.0658i | − | 1.47805i | −0.673675 | − | 0.739027i | \(-0.735285\pi\) | ||
0.673675 | − | 0.739027i | \(-0.264715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.9696 | − | 10.9696i | 0.620038 | − | 0.620038i | −0.325503 | − | 0.945541i | \(-0.605534\pi\) |
0.945541 | + | 0.325503i | \(0.105534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.36184 | + | 2.36184i | −0.132654 | + | 0.132654i | −0.770316 | − | 0.637662i | \(-0.779902\pi\) |
0.637662 | + | 0.770316i | \(0.279902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.7528i | − | 1.60985i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4931 | − | 25.7136i | −0.920553 | − | 1.43519i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.5032 | + | 11.5032i | 0.640058 | + | 0.640058i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.31414 | + | 0.505549i | 0.127972 | + | 0.0279569i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.79319 | 0.429653 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.5396 | −1.67861 | −0.839303 | − | 0.543664i | \(-0.817037\pi\) | ||||
−0.839303 | + | 0.543664i | \(0.817037\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.50492 | + | 17.5348i | 0.356467 | + | 0.960902i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.43131 | − | 4.43131i | −0.241389 | − | 0.241389i | 0.576036 | − | 0.817424i | \(-0.304599\pi\) |
−0.817424 | + | 0.576036i | \(0.804599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.9737 | + | 12.1700i | −1.03051 | + | 0.660982i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8024i | 0.747443i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.86429 | + | 4.86429i | −0.261129 | + | 0.261129i | −0.825513 | − | 0.564384i | \(-0.809114\pi\) |
0.564384 | + | 0.825513i | \(0.309114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.0155i | − | 1.28552i | −0.766068 | − | 0.642759i | \(-0.777790\pi\) | ||
0.766068 | − | 0.642759i | \(-0.222210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.79932 | − | 26.9309i | −0.202793 | − | 1.43746i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.05518 | − | 9.05518i | −0.481959 | − | 0.481959i | 0.423798 | − | 0.905757i | \(-0.360697\pi\) |
−0.905757 | + | 0.423798i | \(0.860697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.75382 | + | 12.6055i | −0.145748 | + | 0.667156i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6520 | 0.878860 | 0.439430 | − | 0.898277i | \(-0.355180\pi\) | ||||
0.439430 | + | 0.898277i | \(0.355180\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2311 | 0.749004 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.96186 | + | 8.98038i | −0.102971 | + | 0.471347i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.82498 | − | 4.82498i | −0.251862 | − | 0.251862i | 0.569872 | − | 0.821734i | \(-0.306993\pi\) |
−0.821734 | + | 0.569872i | \(0.806993\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.626950 | − | 1.36644i | 0.0326377 | − | 0.0711341i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.19164i | 0.425289i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8256 | + | 13.8256i | −0.715864 | + | 0.715864i | −0.967756 | − | 0.251891i | \(-0.918948\pi\) |
0.251891 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.3527 | + | 26.3527i | −1.35723 | + | 1.35723i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.35853i | − | 0.0697828i | −0.999391 | − | 0.0348914i | \(-0.988891\pi\) | ||
0.999391 | − | 0.0348914i | \(-0.0111085\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50264 | + | 0.963815i | −0.0769826 | + | 0.0493778i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.5094 | + | 15.5094i | 0.792491 | + | 0.792491i | 0.981899 | − | 0.189407i | \(-0.0606567\pi\) |
−0.189407 | + | 0.981899i | \(0.560657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.3160 | − | 12.7302i | 1.74438 | − | 0.647115i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.2676 | 0.571291 | 0.285646 | − | 0.958335i | \(-0.407792\pi\) | ||||
0.285646 | + | 0.958335i | \(0.407792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.3445 | −1.98973 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8704 | − | 2.37477i | −0.548341 | − | 0.119791i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.97144 | + | 7.97144i | 0.400075 | + | 0.400075i | 0.878260 | − | 0.478184i | \(-0.158705\pi\) |
−0.478184 | + | 0.878260i | \(0.658705\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.04213 | − | 3.18379i | −0.102234 | − | 0.159389i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 38.3735i | − | 1.91628i | −0.286302 | − | 0.958140i | \(-0.592426\pi\) | ||
0.286302 | − | 0.958140i | \(-0.407574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6503 | − | 12.6503i | 0.630155 | − | 0.630155i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.8013 | + | 17.8013i | −0.882379 | + | 0.882379i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.7754i | − | 1.02727i | −0.858007 | − | 0.513637i | \(-0.828298\pi\) | ||
0.858007 | − | 0.513637i | \(-0.171702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.73319 | + | 5.82024i | 0.184145 | + | 0.287091i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.23499 | + | 9.23499i | 0.454424 | + | 0.454424i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.8590 | − | 3.68304i | −0.825589 | − | 0.180359i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4419 | 1.58489 | 0.792445 | − | 0.609944i | \(-0.208808\pi\) | ||||
0.792445 | + | 0.609944i | \(0.208808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.6205 | 1.58983 | 0.794914 | − | 0.606723i | \(-0.207516\pi\) | ||||
0.794914 | + | 0.606723i | \(0.207516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.9199 | − | 8.13165i | 1.06578 | − | 0.395374i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.73006 | − | 8.73006i | −0.422477 | − | 0.422477i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.8156 | − | 19.7655i | 1.48779 | − | 0.954289i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.42014i | − | 0.405584i | −0.979222 | − | 0.202792i | \(-0.934998\pi\) | ||
0.979222 | − | 0.202792i | \(-0.0650015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.03089 | − | 1.03089i | 0.0495412 | − | 0.0495412i | −0.681902 | − | 0.731443i | \(-0.738847\pi\) |
0.731443 | + | 0.681902i | \(0.238847\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.15557 | − | 8.15557i | 0.390134 | − | 0.390134i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.3968i | − | 1.59394i | −0.604017 | − | 0.796971i | \(-0.706434\pi\) | ||
0.604017 | − | 0.796971i | \(-0.293566\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.25106 | − | 2.72669i | 0.0595743 | − | 0.129842i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.0348 | − | 23.0348i | −1.09442 | − | 1.09442i | −0.995051 | − | 0.0993662i | \(-0.968318\pi\) |
−0.0993662 | − | 0.995051i | \(-0.531682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.53539 | − | 7.02820i | 0.0726214 | − | 0.332422i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.12450 | 0.194647 | 0.0973237 | − | 0.995253i | \(-0.468972\pi\) | ||||
0.0973237 | + | 0.995253i | \(0.468972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.02369 | 0.0952917 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.09110 | − | 18.7269i | 0.192217 | − | 0.879867i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0345 | + | 18.0345i | 0.843619 | + | 0.843619i | 0.989328 | − | 0.145709i | \(-0.0465462\pi\) |
−0.145709 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.40733 | + | 38.3290i | 0.252393 | + | 1.78904i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2611i | 0.524481i | 0.965003 | + | 0.262241i | \(0.0844614\pi\) | ||||
−0.965003 | + | 0.262241i | \(0.915539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.56932 | − | 5.56932i | 0.258828 | − | 0.258828i | −0.565749 | − | 0.824577i | \(-0.691413\pi\) |
0.824577 | + | 0.565749i | \(0.191413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8229 | − | 10.8229i | 0.500822 | − | 0.500822i | −0.410871 | − | 0.911693i | \(-0.634775\pi\) |
0.911693 | + | 0.410871i | \(0.134775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.86659i | 0.363246i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.5511 | + | 18.3131i | −1.31556 | + | 0.843822i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.8375 | + | 34.8375i | 1.60183 | + | 1.60183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.54739 | + | 23.0406i | 0.391358 | + | 1.05496i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.06355 | −0.322742 | −0.161371 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161371 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.6307 | 1.48783 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.93708 | + | 1.95241i | 0.406651 | + | 0.0888375i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2597 | − | 10.2597i | −0.464913 | − | 0.464913i | 0.435349 | − | 0.900262i | \(-0.356625\pi\) |
−0.900262 | + | 0.435349i | \(0.856625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.9963 | + | 35.8525i | 1.03993 | + | 1.62131i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.60260i | 0.388230i | 0.980979 | + | 0.194115i | \(0.0621835\pi\) | ||||
−0.980979 | + | 0.194115i | \(0.937817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.5061 | − | 37.5061i | 1.68919 | − | 1.68919i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.92274 | − | 7.92274i | 0.355384 | − | 0.355384i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.7241i | − | 0.793441i | −0.917939 | − | 0.396721i | \(-0.870148\pi\) | ||
0.917939 | − | 0.396721i | \(-0.129852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.16266 | − | 1.81265i | −0.0519438 | − | 0.0809832i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.5869 | + | 16.5869i | 0.739573 | + | 0.739573i | 0.972495 | − | 0.232922i | \(-0.0748287\pi\) |
−0.232922 | + | 0.972495i | \(0.574829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.3610 | − | 5.32193i | −1.08191 | − | 0.236355i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.8614 | −1.63385 | −0.816926 | − | 0.576742i | \(-0.804324\pi\) | ||||
−0.816926 | + | 0.576742i | \(0.804324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.03491 | 0.0457819 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.06594 | − | 6.82421i | −0.400271 | − | 0.301296i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2530 | + | 22.2530i | 0.978687 | + | 0.978687i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.7164 | − | 20.9848i | 1.43609 | − | 0.921130i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7823i | 0.910491i | 0.890366 | + | 0.455245i | \(0.150448\pi\) | ||||
−0.890366 | + | 0.455245i | \(0.849552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.13422 | − | 8.13422i | 0.355684 | − | 0.355684i | −0.506535 | − | 0.862219i | \(-0.669074\pi\) |
0.862219 | + | 0.506535i | \(0.169074\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0043 | + | 18.0043i | −0.784281 | + | 0.784281i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.89442i | 0.212801i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.6113 | + | 16.3392i | 1.54540 | + | 0.709059i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.85476 | − | 1.85476i | −0.0803386 | − | 0.0803386i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.25721 | + | 28.6422i | −0.270018 | + | 1.23600i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.03821 | 0.173938 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6052 | −1.01486 | −0.507432 | − | 0.861692i | \(-0.669405\pi\) | ||||
−0.507432 | + | 0.861692i | \(0.669405\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.44491 | − | 24.9239i | 0.233663 | − | 1.06959i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.421111 | − | 0.421111i | −0.0180054 | − | 0.0180054i | 0.698047 | − | 0.716052i | \(-0.254053\pi\) |
−0.716052 | + | 0.698047i | \(0.754053\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.6642 | − | 15.4458i | −1.43675 | − | 0.659210i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5490i | 0.662409i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.64115 | − | 2.64115i | 0.112313 | − | 0.112313i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.7063 | + | 11.7063i | −0.496010 | + | 0.496010i | −0.910193 | − | 0.414184i | \(-0.864067\pi\) |
0.414184 | + | 0.910193i | \(0.364067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 63.8589i | − | 2.70095i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −43.8578 | + | 28.1310i | −1.85168 | + | 1.18769i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.0035 | + | 15.0035i | 0.632323 | + | 0.632323i | 0.948650 | − | 0.316327i | \(-0.102450\pi\) |
−0.316327 | + | 0.948650i | \(0.602450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.673741 | − | 8.97475i | 0.0282944 | − | 0.376904i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.77215 | −0.409670 | −0.204835 | − | 0.978797i | \(-0.565666\pi\) | ||||
−0.204835 | + | 0.978797i | \(0.565666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0880438 | −0.00368452 | −0.00184226 | − | 0.999998i | \(-0.500586\pi\) | ||||
−0.00184226 | + | 0.999998i | \(0.500586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.4875 | − | 3.82034i | −0.730551 | − | 0.159597i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.88795 | + | 5.88795i | 0.245118 | + | 0.245118i | 0.818964 | − | 0.573845i | \(-0.194549\pi\) |
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.34707 | + | 2.10015i | 0.0559821 | + | 0.0872792i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.52653i | 0.0633311i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.3907 | + | 23.3907i | −0.968746 | + | 0.968746i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1279 | − | 21.1279i | 0.872042 | − | 0.872042i | −0.120653 | − | 0.992695i | \(-0.538499\pi\) |
0.992695 | + | 0.120653i | \(0.0384989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.46410i | − | 0.307553i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.2738 | + | 16.0175i | 0.422610 | + | 0.658871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0929 | − | 26.0929i | −1.07151 | − | 1.07151i | −0.997238 | − | 0.0742681i | \(-0.976338\pi\) |
−0.0742681 | − | 0.997238i | \(-0.523662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.29035 | + | 1.15574i | 0.216519 | + | 0.0473011i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.53040 | −0.0625306 | −0.0312653 | − | 0.999511i | \(-0.509954\pi\) | ||||
−0.0312653 | + | 0.999511i | \(0.509954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.0845 | −0.819265 | −0.409632 | − | 0.912251i | \(-0.634343\pi\) | ||||
−0.409632 | + | 0.912251i | \(0.634343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.20823 | + | 22.1263i | 0.334265 | + | 0.901054i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1386 | + | 12.1386i | 0.492692 | + | 0.492692i | 0.909153 | − | 0.416462i | \(-0.136730\pi\) |
−0.416462 | + | 0.909153i | \(0.636730\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3807 | + | 6.65831i | −0.420646 | + | 0.269808i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 40.7909i | − | 1.65022i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.2937 | − | 32.2937i | 1.30433 | − | 1.30433i | 0.378885 | − | 0.925444i | \(-0.376308\pi\) |
0.925444 | − | 0.378885i | \(-0.123692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.62124 | − | 4.62124i | 0.186044 | − | 0.186044i | −0.607939 | − | 0.793983i | \(-0.708004\pi\) |
0.793983 | + | 0.607939i | \(0.208004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8998i | 0.840034i | 0.907516 | + | 0.420017i | \(0.137976\pi\) | ||||
−0.907516 | + | 0.420017i | \(0.862024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.1745 | − | 3.83369i | 1.09047 | − | 0.153841i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.70340 | + | 5.70340i | 0.228502 | + | 0.228502i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.25995 | − | 14.9223i | 0.130190 | − | 0.595940i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.4412 | −1.85173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4621 | −0.615538 | −0.307769 | − | 0.951461i | \(-0.599582\pi\) | ||||
−0.307769 | + | 0.951461i | \(0.599582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.38120 | + | 29.2098i | −0.253630 | + | 1.16098i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.70112 | − | 3.70112i | −0.146644 | − | 0.146644i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0174 | − | 30.5511i | 0.554521 | − | 1.20858i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22.2245i | − | 0.877815i | −0.898532 | − | 0.438907i | \(-0.855366\pi\) | ||
0.898532 | − | 0.438907i | \(-0.144634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.6685 | + | 19.6685i | −0.775649 | + | 0.775649i | −0.979088 | − | 0.203439i | \(-0.934788\pi\) |
0.203439 | + | 0.979088i | \(0.434788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.31036 | − | 5.31036i | 0.208772 | − | 0.208772i | −0.594974 | − | 0.803745i | \(-0.702838\pi\) |
0.803745 | + | 0.594974i | \(0.202838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.7400i | 2.07022i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.98311 | − | 3.19624i | 0.195304 | − | 0.125271i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5932 | + | 21.5932i | 0.845006 | + | 0.845006i | 0.989505 | − | 0.144499i | \(-0.0461570\pi\) |
−0.144499 | + | 0.989505i | \(0.546157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.91090 | − | 1.07986i | 0.113565 | − | 0.0421294i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2414 | −0.671629 | −0.335815 | − | 0.941928i | \(-0.609012\pi\) | ||||
−0.335815 | + | 0.941928i | \(0.609012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0262 | 0.778930 | 0.389465 | − | 0.921041i | \(-0.372660\pi\) | ||||
0.389465 | + | 0.921041i | \(0.372660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 65.9796 | + | 14.4140i | 2.56244 | + | 0.559793i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.5910 | − | 26.5910i | −1.02961 | − | 1.02961i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.4953 | − | 21.0399i | −0.521759 | − | 0.813450i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 49.8563i | − | 1.92468i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.75909 | − | 3.75909i | 0.144902 | − | 0.144902i | −0.630934 | − | 0.775836i | \(-0.717328\pi\) |
0.775836 | + | 0.630934i | \(0.217328\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.7768 | + | 16.7768i | −0.644785 | + | 0.644785i | −0.951728 | − | 0.306943i | \(-0.900694\pi\) |
0.306943 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.62006i | 0.0621722i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.3780 | − | 16.1798i | −0.397685 | − | 0.620012i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7708 | − | 12.7708i | −0.488662 | − | 0.488662i | 0.419222 | − | 0.907884i | \(-0.362303\pi\) |
−0.907884 | + | 0.419222i | \(0.862303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.0886 | + | 5.91781i | 1.03350 | + | 0.225779i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.8764 | 1.63346 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.8477 | 1.70609 | 0.853044 | − | 0.521839i | \(-0.174754\pi\) | ||||
0.853044 | + | 0.521839i | \(0.174754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.3582 | − | 4.21358i | 0.431464 | − | 0.160061i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.63976 | + | 2.63976i | 0.0999881 | + | 0.0999881i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2893 | + | 6.59974i | −0.389179 | + | 0.249625i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.5197i | 0.623940i | 0.950092 | + | 0.311970i | \(0.100989\pi\) | ||||
−0.950092 | + | 0.311970i | \(0.899011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.62663 | − | 9.62663i | 0.363075 | − | 0.363075i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.36527 | + | 1.36527i | −0.0513461 | + | 0.0513461i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.1113i | 1.73175i | 0.500263 | + | 0.865874i | \(0.333237\pi\) | ||||
−0.500263 | + | 0.865874i | \(0.666763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.67290 | − | 10.1846i | 0.175248 | − | 0.381953i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.7647 | + | 12.7647i | 0.478042 | + | 0.478042i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.262682 | + | 1.20242i | −0.00981003 | + | 0.0449051i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.2823 | 1.20393 | 0.601964 | − | 0.798523i | \(-0.294385\pi\) | ||||
0.601964 | + | 0.798523i | \(0.294385\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.51759 | −0.168244 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.35479 | − | 38.2438i | 0.310718 | − | 1.42230i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.89414 | + | 3.89414i | 0.144426 | + | 0.144426i | 0.775623 | − | 0.631197i | \(-0.217436\pi\) |
−0.631197 | + | 0.775623i | \(0.717436\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.46949 | − | 25.9462i | −0.276648 | − | 0.960971i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 90.8863i | 3.36155i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.4310 | + | 20.4310i | −0.754638 | + | 0.754638i | −0.975341 | − | 0.220703i | \(-0.929165\pi\) |
0.220703 | + | 0.975341i | \(0.429165\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.4626 | + | 22.4626i | −0.827421 | + | 0.827421i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.2705i | 0.598519i | 0.954172 | + | 0.299260i | \(0.0967397\pi\) | ||||
−0.954172 | + | 0.299260i | \(0.903260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.6645 | + | 10.6888i | −0.612185 | + | 0.392665i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.98855 | − | 8.98855i | −0.329758 | − | 0.329758i | 0.522736 | − | 0.852494i | \(-0.324911\pi\) |
−0.852494 | + | 0.522736i | \(0.824911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.59283 | + | 4.29366i | 0.0582784 | + | 0.157097i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.6372 | −0.644448 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.9439 | −1.42108 | −0.710541 | − | 0.703656i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703656i | \(0.751550\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.91034 | − | 0.854258i | −0.142501 | − | 0.0311309i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.1204 | − | 27.1204i | −0.985706 | − | 0.985706i | 0.0141931 | − | 0.999899i | \(-0.495482\pi\) |
−0.999899 | + | 0.0141931i | \(0.995482\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.9443 | + | 31.0943i | 0.723934 | + | 1.12865i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1968i | 1.38463i | 0.721594 | + | 0.692317i | \(0.243410\pi\) | ||||
−0.721594 | + | 0.692317i | \(0.756590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.967023 | − | 0.967023i | 0.0350086 | − | 0.0350086i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48.3375 | − | 48.3375i | 1.74537 | − | 1.74537i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.8103i | − | 1.21923i | −0.792698 | − | 0.609615i | \(-0.791324\pi\) | ||
0.792698 | − | 0.609615i | \(-0.208676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.6775 | − | 21.3240i | −0.492583 | − | 0.767964i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.9284 | + | 31.9284i | 1.14839 | + | 1.14839i | 0.986870 | + | 0.161515i | \(0.0516380\pi\) |
0.161515 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5491 | + | 2.30457i | 0.378447 | + | 0.0826760i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.09437 | −0.0392100 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.2459 | 1.61902 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.2502 | + | 29.5593i | −0.795157 | + | 1.05636i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.9530 | + | 15.9530i | 0.568661 | + | 0.568661i | 0.931753 | − | 0.363092i | \(-0.118279\pi\) |
−0.363092 | + | 0.931753i | \(0.618279\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.90116 | + | 5.70934i | −0.316890 | + | 0.203258i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.0142i | 0.462732i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.6946 | + | 45.6946i | −1.62266 | + | 1.62266i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.55804 | + | 1.55804i | −0.0551887 | + | 0.0551887i | −0.734163 | − | 0.678974i | \(-0.762425\pi\) |
0.678974 | + | 0.734163i | \(0.262425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.0551i | 2.05384i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.9930 | + | 10.0908i | 0.777085 | + | 0.356542i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.95514 | + | 2.95514i | 0.104285 | + | 0.104285i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.954057 | + | 4.36717i | −0.0335844 | + | 0.153732i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.5723 | 1.42644 | 0.713222 | − | 0.700938i | \(-0.247235\pi\) | ||||
0.713222 | + | 0.700938i | \(0.247235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.3205 | −1.17004 | −0.585021 | − | 0.811018i | \(-0.698914\pi\) | ||||
−0.585021 | + | 0.811018i | \(0.698914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.246693 | − | 1.12923i | 0.00865189 | − | 0.0396038i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.8395 | − | 18.8395i | −0.659111 | − | 0.659111i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.2720 | − | 6.54826i | −0.498703 | − | 0.228815i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.00023i | 0.174509i | 0.996186 | + | 0.0872546i | \(0.0278094\pi\) | ||||
−0.996186 | + | 0.0872546i | \(0.972191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.3054 | − | 13.3054i | 0.463797 | − | 0.463797i | −0.436101 | − | 0.899898i | \(-0.643641\pi\) |
0.899898 | + | 0.436101i | \(0.143641\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0487 | − | 28.0487i | 0.975349 | − | 0.975349i | −0.0243539 | − | 0.999703i | \(-0.507753\pi\) |
0.999703 | + | 0.0243539i | \(0.00775285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.4634i | 1.33589i | 0.744210 | + | 0.667945i | \(0.232826\pi\) | ||||
−0.744210 | + | 0.667945i | \(0.767174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.7776 | − | 17.1756i | 0.928905 | − | 0.595813i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.26756 | + | 5.26756i | 0.182510 | + | 0.182510i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.6809 | − | 14.1896i | 0.369187 | − | 0.490463i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.2844 | −0.562201 | −0.281101 | − | 0.959678i | \(-0.590699\pi\) | ||||
−0.281101 | + | 0.959678i | \(0.590699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.6971 | 0.748177 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.3685 | − | 7.72665i | −1.21816 | − | 0.266120i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.75269 | + | 3.75269i | 0.128944 | + | 0.128944i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.8235 | − | 27.7878i | −0.611701 | − | 0.953675i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.9259i | 1.12868i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.2526 | − | 32.2526i | 1.10431 | − | 1.10431i | 0.110423 | − | 0.993885i | \(-0.464779\pi\) |
0.993885 | − | 0.110423i | \(-0.0352205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.3551 | + | 36.3551i | −1.24187 | + | 1.24187i | −0.282642 | + | 0.959225i | \(0.591211\pi\) |
−0.959225 | + | 0.282642i | \(0.908789\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.01075i | − | 0.0686060i | −0.999411 | − | 0.0343030i | \(-0.989079\pi\) | ||
0.999411 | − | 0.0343030i | \(-0.0109211\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.468627 | − | 0.730615i | −0.0159708 | − | 0.0248993i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.6710 | − | 25.6710i | −0.873852 | − | 0.873852i | 0.119037 | − | 0.992890i | \(-0.462019\pi\) |
−0.992890 | + | 0.119037i | \(0.962019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −65.1381 | − | 14.2302i | −2.21221 | − | 0.483281i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.0833 | 0.511667 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.1751 | 1.39516 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.69042 | + | 4.55673i | 0.0572119 | + | 0.154222i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8267 | + | 15.8267i | 0.534428 | + | 0.534428i | 0.921887 | − | 0.387459i | \(-0.126647\pi\) |
−0.387459 | + | 0.921887i | \(0.626647\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.2634 | + | 26.4669i | −1.39178 | + | 0.892707i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.5440i | − | 0.355236i | −0.984100 | − | 0.177618i | \(-0.943161\pi\) | ||
0.984100 | − | 0.177618i | \(-0.0568391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.7596 | + | 13.7596i | −0.463048 | + | 0.463048i | −0.899653 | − | 0.436605i | \(-0.856181\pi\) |
0.436605 | + | 0.899653i | \(0.356181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.01621 | − | 2.01621i | 0.0676978 | − | 0.0676978i | −0.672447 | − | 0.740145i | \(-0.734757\pi\) |
0.740145 | + | 0.672447i | \(0.234757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.03067i | 0.0345677i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5507 | − | 23.7030i | 0.922983 | − | 0.794082i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0340 | − | 12.0340i | −0.402703 | − | 0.402703i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.2192 | − | 46.7782i | 0.341210 | − | 1.56188i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.3365 | −0.811669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61.0233 | −2.03298 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.51009 | − | 20.6448i | 0.150086 | − | 0.687016i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.39044 | − | 6.39044i | −0.212191 | − | 0.212191i | 0.593007 | − | 0.805198i | \(-0.297941\pi\) |
−0.805198 | + | 0.593007i | \(0.797941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.41552 | + | 5.26464i | −0.0801177 | + | 0.174617i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 43.0010i | − | 1.42469i | −0.701831 | − | 0.712344i | \(-0.747634\pi\) | ||
0.701831 | − | 0.712344i | \(-0.252366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.35892 | + | 4.35892i | −0.144259 | + | 0.144259i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.54250 | + | 4.54250i | −0.150007 | + | 0.150007i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 52.2248i | − | 1.72274i | −0.507980 | − | 0.861369i | \(-0.669608\pi\) | ||
0.507980 | − | 0.861369i | \(-0.330392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.80498 | − | 3.72340i | 0.191281 | − | 0.122690i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −41.4690 | − | 41.4690i | −1.36497 | − | 1.36497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.7066 | + | 4.71378i | −0.417339 | + | 0.154821i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.2248 | −1.87749 | −0.938743 | − | 0.344619i | \(-0.888008\pi\) | ||||
−0.938743 | + | 0.344619i | \(0.888008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.18379 | −0.0715708 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.1070 | − | 9.63567i | −1.44400 | − | 0.315458i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.78270 | + | 4.78270i | 0.156244 | + | 0.156244i | 0.780900 | − | 0.624656i | \(-0.214761\pi\) |
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.5070 | − | 22.6172i | −0.473418 | − | 0.738085i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.54340i | − | 0.148110i | −0.997254 | − | 0.0740552i | \(-0.976406\pi\) | ||
0.997254 | − | 0.0740552i | \(-0.0235941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.87154 | − | 1.87154i | 0.0609457 | − | 0.0609457i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.9836 | + | 32.9836i | −1.07182 | + | 1.07182i | −0.0746109 | + | 0.997213i | \(0.523771\pi\) |
−0.997213 | + | 0.0746109i | \(0.976229\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.41692i | − | 0.175841i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.12348 | + | 4.86967i | 0.101286 | + | 0.157910i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.1748 | − | 36.1748i | −1.17182 | − | 1.17182i | −0.981776 | − | 0.190042i | \(-0.939138\pi\) |
−0.190042 | − | 0.981776i | \(-0.560862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.6538 | − | 10.6290i | −1.57276 | − | 0.343586i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.99215 | 0.128913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3176 | −0.623147 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −49.6080 | + | 18.4031i | −1.59860 | + | 0.593033i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4059 | + | 32.4059i | 1.04210 | + | 1.04210i | 0.999074 | + | 0.0430291i | \(0.0137008\pi\) |
0.0430291 | + | 0.999074i | \(0.486299\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.7175 | − | 15.2128i | 0.761916 | − | 0.488704i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 21.3519i | − | 0.685216i | −0.939479 | − | 0.342608i | \(-0.888690\pi\) | ||
0.939479 | − | 0.342608i | \(-0.111310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.04499 | + | 7.04499i | −0.225852 | + | 0.225852i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.42366 | − | 7.42366i | 0.237504 | − | 0.237504i | −0.578312 | − | 0.815816i | \(-0.696288\pi\) |
0.815816 | + | 0.578312i | \(0.196288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.5714i | 1.04099i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.71092 | − | 3.72896i | 0.0546255 | − | 0.119057i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.5911 | − | 22.5911i | −0.720545 | − | 0.720545i | 0.248171 | − | 0.968716i | \(-0.420170\pi\) |
−0.968716 | + | 0.248171i | \(0.920170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.88089 | − | 13.1872i | 0.0916997 | − | 0.419753i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.4366 | 2.04896 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.9966 | −1.23877 | −0.619384 | − | 0.785088i | \(-0.712617\pi\) | ||||
−0.619384 | + | 0.785088i | \(0.712617\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.2895 | + | 51.6773i | −0.358261 | + | 1.63993i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.0775 | − | 19.0775i | −0.604192 | − | 0.604192i | 0.337230 | − | 0.941422i | \(-0.390510\pi\) |
−0.941422 | + | 0.337230i | \(0.890510\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.0761 | − | 4.52519i | 1.01484 | − | 0.143171i |
(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 | 2100.2.s.c.1457.10 | yes | 32 | |
3.2 | odd | 2 | inner | 2100.2.s.c.1457.15 | yes | 32 | |
5.2 | odd | 4 | inner | 2100.2.s.c.1793.2 | yes | 32 | |
5.3 | odd | 4 | inner | 2100.2.s.c.1793.15 | yes | 32 | |
5.4 | even | 2 | inner | 2100.2.s.c.1457.7 | yes | 32 | |
15.2 | even | 4 | inner | 2100.2.s.c.1793.7 | yes | 32 | |
15.8 | even | 4 | inner | 2100.2.s.c.1793.10 | yes | 32 | |
15.14 | odd | 2 | inner | 2100.2.s.c.1457.2 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.s.c.1457.2 | ✓ | 32 | 15.14 | odd | 2 | inner | |
2100.2.s.c.1457.7 | yes | 32 | 5.4 | even | 2 | inner | |
2100.2.s.c.1457.10 | yes | 32 | 1.1 | even | 1 | trivial | |
2100.2.s.c.1457.15 | yes | 32 | 3.2 | odd | 2 | inner | |
2100.2.s.c.1793.2 | yes | 32 | 5.2 | odd | 4 | inner | |
2100.2.s.c.1793.7 | yes | 32 | 15.2 | even | 4 | inner | |
2100.2.s.c.1793.10 | yes | 32 | 15.8 | even | 4 | inner | |
2100.2.s.c.1793.15 | yes | 32 | 5.3 | odd | 4 | inner |