Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.9643576194\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 11x^{2} + 10x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-1.35078 + 2.33962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.109 |
Dual form | 324.6.e.f.217.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 28.8141 | − | 49.9074i | 0.515442 | − | 0.892771i | −0.484398 | − | 0.874848i | \(-0.660961\pi\) |
0.999839 | − | 0.0179231i | \(-0.00570541\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 94.4422 | + | 163.579i | 0.728485 | + | 1.26177i | 0.957523 | + | 0.288356i | \(0.0931087\pi\) |
−0.229038 | + | 0.973418i | \(0.573558\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −352.012 | − | 609.703i | −0.877155 | − | 1.51928i | −0.854449 | − | 0.519535i | \(-0.826105\pi\) |
−0.0227057 | − | 0.999742i | \(-0.507228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −397.769 | + | 688.956i | −0.652788 | + | 1.13066i | 0.329655 | + | 0.944101i | \(0.393067\pi\) |
−0.982443 | + | 0.186561i | \(0.940266\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −180.562 | −0.151532 | −0.0757661 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757661 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −661.769 | −0.420554 | −0.210277 | − | 0.977642i | \(-0.567437\pi\) | ||||
−0.210277 | + | 0.977642i | \(0.567437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1816.26 | + | 3145.85i | −0.715909 | + | 1.23999i | 0.246700 | + | 0.969092i | \(0.420654\pi\) |
−0.962608 | + | 0.270898i | \(0.912679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.0000 | − | 169.741i | −0.0313600 | − | 0.0543171i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4010.93 | − | 6947.14i | −0.885626 | − | 1.53395i | −0.844994 | − | 0.534776i | \(-0.820396\pi\) |
−0.0406324 | − | 0.999174i | \(-0.512937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1501.94 | − | 2601.43i | 0.280704 | − | 0.486193i | −0.690855 | − | 0.722994i | \(-0.742766\pi\) |
0.971558 | + | 0.236801i | \(0.0760989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10885.0 | 1.50197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1520.31 | −0.182570 | −0.0912848 | − | 0.995825i | \(-0.529097\pi\) | ||||
−0.0912848 | + | 0.995825i | \(0.529097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1730.78 | + | 2997.81i | −0.160799 | + | 0.278512i | −0.935155 | − | 0.354238i | \(-0.884740\pi\) |
0.774356 | + | 0.632750i | \(0.218074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5907.88 | − | 10232.7i | −0.487260 | − | 0.843958i | 0.512633 | − | 0.858608i | \(-0.328670\pi\) |
−0.999893 | + | 0.0146495i | \(0.995337\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2989.91 | + | 5178.68i | 0.197430 | + | 0.341959i | 0.947694 | − | 0.319179i | \(-0.103407\pi\) |
−0.750264 | + | 0.661138i | \(0.770074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9435.15 | + | 16342.2i | −0.561382 | + | 0.972342i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13819.2 | 0.675761 | 0.337880 | − | 0.941189i | \(-0.390290\pi\) | ||||
0.337880 | + | 0.941189i | \(0.390290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40571.6 | −1.80849 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11320.1 | + | 19607.0i | −0.423370 | + | 0.733298i | −0.996267 | − | 0.0863297i | \(-0.972486\pi\) |
0.572897 | + | 0.819627i | \(0.305820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18702.1 | + | 32393.0i | 0.643526 | + | 1.11462i | 0.984640 | + | 0.174598i | \(0.0558626\pi\) |
−0.341113 | + | 0.940022i | \(0.610804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22922.7 | + | 39703.2i | 0.672948 | + | 1.16558i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −35482.3 | + | 61457.2i | −0.965662 | + | 1.67258i | −0.257836 | + | 0.966189i | \(0.583009\pi\) |
−0.707826 | + | 0.706387i | \(0.750324\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −67767.0 | −1.59541 | −0.797705 | − | 0.603048i | \(-0.793953\pi\) | ||||
−0.797705 | + | 0.603048i | \(0.793953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −31562.4 | −0.693208 | −0.346604 | − | 0.938012i | \(-0.612665\pi\) | ||||
−0.346604 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 66489.6 | − | 115163.i | 1.27799 | − | 2.21354i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31395.8 | − | 54379.1i | −0.565984 | − | 0.980313i | −0.996957 | − | 0.0779481i | \(-0.975163\pi\) |
0.430974 | − | 0.902365i | \(-0.358170\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −46715.7 | − | 80914.0i | −0.744334 | − | 1.28922i | −0.950505 | − | 0.310709i | \(-0.899434\pi\) |
0.206171 | − | 0.978516i | \(-0.433900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5202.73 | + | 9011.40i | −0.0781060 | + | 0.135284i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −68793.1 | −0.920598 | −0.460299 | − | 0.887764i | \(-0.652258\pi\) | ||||
−0.460299 | + | 0.887764i | \(0.652258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −150265. | −1.90219 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19068.2 | + | 33027.2i | −0.216771 | + | 0.375459i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −58887.0 | − | 101995.i | −0.635463 | − | 1.10065i | −0.986417 | − | 0.164261i | \(-0.947476\pi\) |
0.350954 | − | 0.936393i | \(-0.385857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 80942.8 | + | 140197.i | 0.789542 | + | 1.36753i | 0.926248 | + | 0.376914i | \(0.123015\pi\) |
−0.136707 | + | 0.990612i | \(0.543652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −29662.3 | + | 51376.6i | −0.275494 | + | 0.477169i | −0.970260 | − | 0.242067i | \(-0.922175\pi\) |
0.694766 | + | 0.719236i | \(0.255508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21124.1 | 0.178369 | 0.0891845 | − | 0.996015i | \(-0.471574\pi\) | ||||
0.0891845 | + | 0.996015i | \(0.471574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −168898. | −1.36162 | −0.680812 | − | 0.732458i | \(-0.738373\pi\) | ||||
−0.680812 | + | 0.732458i | \(0.738373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −30637.0 | + | 53064.8i | −0.225710 | + | 0.390940i | −0.956532 | − | 0.291627i | \(-0.905803\pi\) |
0.730823 | + | 0.682567i | \(0.239137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 104667. | + | 181289.i | 0.738018 | + | 1.27828i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17052.7 | − | 29536.1i | −0.110389 | − | 0.191199i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −167300. | + | 289772.i | −1.03880 | + | 1.79926i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 168793. | 0.966226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23607.7 | 0.129881 | 0.0649404 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649404 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −103425. | + | 179137.i | −0.526557 | + | 0.912023i | 0.472964 | + | 0.881082i | \(0.343184\pi\) |
−0.999521 | + | 0.0309416i | \(0.990149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −62498.9 | − | 108251.i | −0.306368 | − | 0.530645i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −95747.5 | − | 165839.i | −0.435839 | − | 0.754895i | 0.561525 | − | 0.827460i | \(-0.310215\pi\) |
−0.997364 | + | 0.0725649i | \(0.976882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −125209. | + | 216869.i | −0.549666 | + | 0.952049i | 0.448631 | + | 0.893717i | \(0.351912\pi\) |
−0.998297 | + | 0.0583324i | \(0.981422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 560078. | 2.29039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −462285. | −1.82595 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 100429. | − | 173948.i | 0.370588 | − | 0.641878i | −0.619068 | − | 0.785338i | \(-0.712489\pi\) |
0.989656 | + | 0.143460i | \(0.0458227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11631.6 | + | 20146.5i | 0.0415141 | + | 0.0719046i | 0.886036 | − | 0.463617i | \(-0.153449\pi\) |
−0.844522 | + | 0.535521i | \(0.820115\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −86553.9 | − | 149916.i | −0.289373 | − | 0.501208i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 261993. | − | 453785.i | 0.848281 | − | 1.46927i | −0.0344595 | − | 0.999406i | \(-0.510971\pi\) |
0.882741 | − | 0.469860i | \(-0.155696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −686125. | −2.08612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 194530. | 0.573479 | 0.286739 | − | 0.958009i | \(-0.407429\pi\) | ||||
0.286739 | + | 0.958009i | \(0.407429\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −231379. | + | 400759.i | −0.641995 | + | 1.11197i | 0.342991 | + | 0.939339i | \(0.388560\pi\) |
−0.984987 | + | 0.172630i | \(0.944774\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −130793. | − | 226541.i | −0.352265 | − | 0.610140i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19945.9 | + | 34547.3i | 0.0506685 | + | 0.0877604i | 0.890247 | − | 0.455478i | \(-0.150531\pi\) |
−0.839579 | + | 0.543238i | \(0.817198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18510.7 | − | 32061.4i | 0.0456906 | − | 0.0791385i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 221514. | 0.516736 | 0.258368 | − | 0.966047i | \(-0.416815\pi\) | ||||
0.258368 | + | 0.966047i | \(0.416815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 800588. | 1.81640 | 0.908202 | − | 0.418532i | \(-0.137455\pi\) | ||||
0.908202 | + | 0.418532i | \(0.137455\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −43806.4 | + | 75874.9i | −0.0941040 | + | 0.162993i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 63560.2 | + | 110090.i | 0.132917 | + | 0.230219i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −35275.3 | − | 61098.6i | −0.0699661 | − | 0.121185i | 0.828920 | − | 0.559367i | \(-0.188956\pi\) |
−0.898886 | + | 0.438182i | \(0.855622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 229098. | − | 396809.i | 0.442719 | − | 0.766811i | −0.555171 | − | 0.831736i | \(-0.687347\pi\) |
0.997890 | + | 0.0649247i | \(0.0206807\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −605955. | −1.11244 | −0.556218 | − | 0.831037i | \(-0.687748\pi\) | ||||
−0.556218 | + | 0.831037i | \(0.687748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −108129. | −0.193557 | −0.0967783 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967783 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 757603. | − | 1.31221e6i | 1.29033 | − | 2.23492i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 99741.9 | + | 172758.i | 0.165765 | + | 0.287113i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 232951. | + | 403483.i | 0.368891 | + | 0.638939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −137461. | + | 238090.i | −0.212556 | + | 0.368158i | −0.952514 | − | 0.304495i | \(-0.901512\pi\) |
0.739958 | + | 0.672654i | \(0.234846\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −680920. | −1.00462 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 567385. | 0.817954 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 71822.1 | − | 124399.i | 0.0989184 | − | 0.171332i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 251923. | + | 436343.i | 0.339239 | + | 0.587579i | 0.984290 | − | 0.176561i | \(-0.0564972\pi\) |
−0.645051 | + | 0.764140i | \(0.723164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 194863. | + | 337512.i | 0.250994 | + | 0.434735i | 0.963800 | − | 0.266627i | \(-0.0859091\pi\) |
−0.712805 | + | 0.701362i | \(0.752576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 465752. | − | 806707.i | 0.586903 | − | 1.01655i | −0.407732 | − | 0.913102i | \(-0.633680\pi\) |
0.994635 | − | 0.103444i | \(-0.0329864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 967962. | 1.16807 | 0.584034 | − | 0.811729i | \(-0.301473\pi\) | ||||
0.584034 | + | 0.811729i | \(0.301473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 344606. | 0.407055 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −167948. | + | 290894.i | −0.190187 | + | 0.329413i | −0.945312 | − | 0.326168i | \(-0.894243\pi\) |
0.755125 | + | 0.655580i | \(0.227576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273571. | + | 473839.i | 0.303408 | + | 0.525519i | 0.976906 | − | 0.213671i | \(-0.0685420\pi\) |
−0.673497 | + | 0.739190i | \(0.735209\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 543730. | + | 941768.i | 0.578719 | + | 1.00237i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 263231. | − | 455929.i | 0.274533 | − | 0.475505i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 36479.6 | 0.0365482 | 0.0182741 | − | 0.999833i | \(-0.494183\pi\) | ||||
0.0182741 | + | 0.999833i | \(0.494183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.55738e6 | 2.51185 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −599841. | + | 1.03896e6i | −0.566505 | + | 0.981215i | 0.430403 | + | 0.902637i | \(0.358371\pi\) |
−0.996908 | + | 0.0785784i | \(0.974962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −143582. | − | 248691.i | −0.132999 | − | 0.230362i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 439254. | + | 760810.i | 0.391585 | + | 0.678246i | 0.992659 | − | 0.120948i | \(-0.0385935\pi\) |
−0.601074 | + | 0.799194i | \(0.705260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 398187. | − | 689680.i | 0.348315 | − | 0.603299i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 434159. | 0.365820 | 0.182910 | − | 0.983130i | \(-0.441448\pi\) | ||||
0.182910 | + | 0.983130i | \(0.441448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 799583. | 0.661364 | 0.330682 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330682 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68994.4 | + | 119502.i | −0.0550152 | + | 0.0952891i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −815212. | − | 1.41199e6i | −0.638368 | − | 1.10569i | −0.985791 | − | 0.167977i | \(-0.946277\pi\) |
0.347423 | − | 0.937708i | \(-0.387057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26849e6 | − | 2.19709e6i | −0.958344 | − | 1.65990i | −0.726523 | − | 0.687142i | \(-0.758865\pi\) |
−0.231821 | − | 0.972759i | \(-0.574468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.03662e6 | − | 1.79548e6i | 0.769402 | − | 1.33264i | −0.168486 | − | 0.985704i | \(-0.553888\pi\) |
0.937888 | − | 0.346939i | \(-0.112779\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −653836. | −0.468559 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.38725e6 | −0.977038 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 333384. | − | 577438.i | 0.226869 | − | 0.392949i | −0.730009 | − | 0.683437i | \(-0.760484\pi\) |
0.956879 | + | 0.290488i | \(0.0938176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 652355. | + | 1.12991e6i | 0.436445 | + | 0.755944i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.44490e6 | − | 2.50264e6i | −0.934673 | − | 1.61890i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11591e6 | − | 1.93281e6i | 0.709923 | − | 1.22962i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.15554e6 | 1.32680 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 811069. | 0.491148 | 0.245574 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245574 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −492519. | + | 853067.i | −0.288750 | + | 0.500129i | −0.973512 | − | 0.228638i | \(-0.926573\pi\) |
0.684762 | + | 0.728767i | \(0.259906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −391592. | − | 678257.i | −0.225929 | − | 0.391321i | 0.730668 | − | 0.682732i | \(-0.239209\pi\) |
−0.956598 | + | 0.291411i | \(0.905875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.33259e6 | − | 2.30812e6i | −0.744817 | − | 1.29006i | −0.950280 | − | 0.311396i | \(-0.899203\pi\) |
0.205463 | − | 0.978665i | \(-0.434130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.82380e6 | + | 4.89096e6i | −1.55366 | + | 2.69102i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 119491. | 0.0637275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 155925. | 0.0818857 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −564748. | + | 978171.i | −0.287650 | + | 0.498225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.17076e6 | + | 2.02782e6i | 0.587353 | + | 1.01733i | 0.994578 | + | 0.103998i | \(0.0331635\pi\) |
−0.407224 | + | 0.913328i | \(0.633503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.04478e6 | + | 3.54166e6i | 0.995485 | + | 1.72423i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 355371. | − | 615521.i | 0.170454 | − | 0.295235i | −0.768125 | − | 0.640300i | \(-0.778810\pi\) |
0.938579 | + | 0.345065i | \(0.112143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.11480e6 | −0.984882 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −389725. | −0.178864 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 351093. | − | 608112.i | 0.156531 | − | 0.271119i | −0.777085 | − | 0.629396i | \(-0.783302\pi\) |
0.933615 | + | 0.358277i | \(0.116636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 69349.7 | + | 120117.i | 0.0304776 | + | 0.0527888i | 0.880862 | − | 0.473373i | \(-0.156964\pi\) |
−0.850384 | + | 0.526162i | \(0.823630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27547.1 | + | 47712.9i | 0.0117663 | + | 0.0203798i | 0.871849 | − | 0.489776i | \(-0.162921\pi\) |
−0.860082 | + | 0.510155i | \(0.829588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.95264e6 | + | 3.38207e6i | −0.822340 | + | 1.42434i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.94311e6 | −0.795722 | −0.397861 | − | 0.917446i | \(-0.630247\pi\) | ||||
−0.397861 | + | 0.917446i | \(0.630247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03816e6 | −0.823134 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −909442. | + | 1.57520e6i | −0.357308 | + | 0.618876i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 747966. | + | 1.29551e6i | 0.289879 | + | 0.502085i | 0.973781 | − | 0.227489i | \(-0.0730517\pi\) |
−0.683902 | + | 0.729574i | \(0.739718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30511e6 | + | 2.26052e6i | 0.492282 | + | 0.852657i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 858481. | − | 1.48693e6i | 0.319491 | − | 0.553375i | −0.660891 | − | 0.750482i | \(-0.729821\pi\) |
0.980382 | + | 0.197107i | \(0.0631548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.38170e6 | 2.31251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.54794e6 | −1.26876 | −0.634378 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634378 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.37651e6 | − | 2.38419e6i | 0.479493 | − | 0.830507i | −0.520230 | − | 0.854026i | \(-0.674154\pi\) |
0.999723 | + | 0.0235192i | \(0.00748709\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.83167e6 | − | 6.63665e6i | −1.31746 | − | 2.28190i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.47686e6 | + | 2.55799e6i | 0.494839 | + | 0.857087i | 0.999982 | − | 0.00594868i | \(-0.00189353\pi\) |
−0.505143 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 327948. | − | 568022.i | 0.108483 | − | 0.187898i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.61856e6 | −1.16693 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.21949e6 | −0.706767 | −0.353383 | − | 0.935479i | \(-0.614969\pi\) | ||||
−0.353383 | + | 0.935479i | \(0.614969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.21911e6 | − | 3.84361e6i | 0.689157 | − | 1.19365i | −0.282954 | − | 0.959133i | \(-0.591315\pi\) |
0.972111 | − | 0.234521i | \(-0.0753521\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.19485e6 | + | 2.06954e6i | 0.366480 | + | 0.634762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 535169. | + | 926940.i | 0.160142 | + | 0.277374i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 165800. | − | 287175.i | 0.0490092 | − | 0.0848864i | −0.840480 | − | 0.541842i | \(-0.817727\pi\) |
0.889489 | + | 0.456956i | \(0.151060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.27637e6 | −1.23367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.38428e6 | −1.53464 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.24743e6 | − | 2.16061e6i | 0.347121 | − | 0.601232i | −0.638616 | − | 0.769526i | \(-0.720493\pi\) |
0.985737 | + | 0.168294i | \(0.0538259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.27578e6 | − | 3.94176e6i | −0.625784 | − | 1.08389i | −0.988389 | − | 0.151946i | \(-0.951446\pi\) |
0.362605 | − | 0.931943i | \(-0.381887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17695.1 | + | 30648.8i | 0.00475205 | + | 0.00823079i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.53254e6 | + | 6.11854e6i | −0.937599 | + | 1.62397i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −614314. | −0.159293 | −0.0796466 | − | 0.996823i | \(-0.525379\pi\) | ||||
−0.0796466 | + | 0.996823i | \(0.525379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.42759e6 | 0.622236 | 0.311118 | − | 0.950371i | \(-0.399297\pi\) | ||||
0.311118 | + | 0.950371i | \(0.399297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.20194e6 | − | 2.08182e6i | 0.301079 | − | 0.521483i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.15900e6 | + | 2.00745e6i | 0.287027 | + | 0.497145i | 0.973099 | − | 0.230389i | \(-0.0739998\pi\) |
−0.686072 | + | 0.727534i | \(0.740666\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.61824e6 | − | 4.53493e6i | −0.633870 | − | 1.09790i | −0.986753 | − | 0.162228i | \(-0.948132\pi\) |
0.352883 | − | 0.935667i | \(-0.385201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.98221e6 | + | 3.43329e6i | −0.474515 | + | 0.821883i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 985716. | 0.230747 | 0.115373 | − | 0.993322i | \(-0.463194\pi\) | ||||
0.115373 | + | 0.993322i | \(0.463194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.43703e6 | 0.564183 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.32973e6 | + | 7.49932e6i | −0.980466 | + | 1.69822i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.54748e6 | + | 4.41237e6i | 0.570585 | + | 0.988283i | 0.996506 | + | 0.0835223i | \(0.0266170\pi\) |
−0.425920 | + | 0.904761i | \(0.640050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.44756e6 | + | 7.70340e6i | 0.974697 | + | 1.68822i | 0.680932 | + | 0.732347i | \(0.261575\pi\) |
0.293765 | + | 0.955878i | \(0.405092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.63133e6 | + | 2.82555e6i | −0.353664 | + | 0.612563i | −0.986888 | − | 0.161405i | \(-0.948398\pi\) |
0.633225 | + | 0.773968i | \(0.281731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.63482e6 | 0.346879 | 0.173439 | − | 0.984845i | \(-0.444512\pi\) | ||||
0.173439 | + | 0.984845i | \(0.444512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34041e7 | −2.81388 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.15929e6 | + | 7.20411e6i | −0.854804 | + | 1.48056i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 64853.3 | + | 112329.i | 0.0131886 | + | 0.0228433i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.28557e6 | − | 7.42282e6i | −0.853433 | − | 1.47819i | −0.878091 | − | 0.478493i | \(-0.841183\pi\) |
0.0246586 | − | 0.999696i | \(-0.492150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 604733. | − | 1.04743e6i | 0.119179 | − | 0.206425i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.78709e6 | −1.31018 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12742e6 | −0.979662 | −0.489831 | − | 0.871817i | \(-0.662942\pi\) | ||||
−0.489831 | + | 0.871817i | \(0.662942\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.66995e6 | − | 6.35654e6i | 0.687000 | − | 1.18992i | −0.285804 | − | 0.958288i | \(-0.592261\pi\) |
0.972804 | − | 0.231630i | \(-0.0744060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 724224. | + | 1.25439e6i | 0.134201 | + | 0.232443i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.40006e6 | − | 1.10852e7i | −1.16223 | − | 2.01305i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.04443e6 | + | 5.27310e6i | −0.547336 | + | 0.948015i | 0.451119 | + | 0.892464i | \(0.351025\pi\) |
−0.998456 | + | 0.0555509i | \(0.982308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.11508e6 | 1.60635 | 0.803175 | − | 0.595743i | \(-0.203142\pi\) | ||||
0.803175 | + | 0.595743i | \(0.203142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32917e6 | 1.62785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.59082e6 | − | 2.75538e6i | 0.272162 | − | 0.471398i | −0.697253 | − | 0.716825i | \(-0.745595\pi\) |
0.969415 | + | 0.245427i | \(0.0789281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.98082e6 | − | 5.16294e6i | −0.504992 | − | 0.874671i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.70938e6 | + | 2.96074e6i | 0.284002 | + | 0.491905i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.10497e6 | − | 3.64592e6i | 0.346354 | − | 0.599902i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27154.5 | −0.00438276 | −0.00219138 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219138 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.93041e6 | −0.628324 | −0.314162 | − | 0.949369i | \(-0.601724\pi\) | ||||
−0.314162 | + | 0.949369i | \(0.601724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −271194. | + | 469721.i | −0.0425356 | + | 0.0736739i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.37940e6 | − | 5.85330e6i | −0.525050 | − | 0.909413i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.37690e6 | − | 2.38487e6i | −0.209935 | − | 0.363619i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 608672. | − | 1.05425e6i | 0.0919388 | − | 0.159243i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.32852e7 | 1.96968 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.38180e6 | 1.23124 | 0.615622 | − | 0.788042i | \(-0.288905\pi\) | ||||
0.615622 | + | 0.788042i | \(0.288905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.86662e6 | + | 8.42924e6i | −0.701837 | + | 1.21562i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.75274e6 | + | 6.49994e6i | 0.536266 | + | 0.928840i | 0.999101 | + | 0.0423954i | \(0.0134989\pi\) |
−0.462835 | + | 0.886444i | \(0.653168\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.65431e6 | + | 4.59740e6i | 0.372454 | + | 0.645109i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.93018e6 | − | 1.02714e7i | 0.824622 | − | 1.42829i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.03110e6 | 0.140820 | 0.0704099 | − | 0.997518i | \(-0.477569\pi\) | ||||
0.0704099 | + | 0.997518i | \(0.477569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.39988e6 | 1.27231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.59812e6 | + | 1.14283e7i | −0.877303 | + | 1.51953i | −0.0230137 | + | 0.999735i | \(0.507326\pi\) |
−0.854289 | + | 0.519798i | \(0.826007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.76555e6 | + | 3.05802e6i | 0.232680 | + | 0.403014i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.74578e6 | + | 3.02377e6i | 0.226052 | + | 0.391533i | 0.956634 | − | 0.291291i | \(-0.0940848\pi\) |
−0.730583 | + | 0.682824i | \(0.760752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74727e6 | − | 8.22252e6i | 0.609332 | − | 1.05539i | −0.382019 | − | 0.924155i | \(-0.624771\pi\) |
0.991351 | − | 0.131239i | \(-0.0418957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 711972. | 0.0898036 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.60369e6 | 0.325574 | 0.162787 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162787 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.82387e6 | − | 1.52834e7i | 1.08447 | − | 1.87836i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.86453e6 | − | 8.42561e6i | −0.592747 | − | 1.02667i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.52049e6 | + | 4.36562e6i | 0.301919 | + | 0.522939i | 0.976571 | − | 0.215197i | \(-0.0690394\pi\) |
−0.674652 | + | 0.738136i | \(0.735706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −993936. | + | 1.72155e6i | −0.118051 | + | 0.204471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.35192e7 | −1.57875 | −0.789374 | − | 0.613912i | \(-0.789595\pi\) | ||||
−0.789374 | + | 0.613912i | \(0.789595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.96543e6 | −0.227596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −407892. | + | 706490.i | −0.0464492 | + | 0.0804524i | −0.888315 | − | 0.459234i | \(-0.848124\pi\) |
0.841866 | + | 0.539687i | \(0.181457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.26529e6 | + | 5.65565e6i | 0.368753 | + | 0.638699i | 0.989371 | − | 0.145414i | \(-0.0464514\pi\) |
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.64119e6 | + | 1.66990e7i | 1.07088 | + | 1.85482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 550482. | − | 953464.i | 0.0606418 | − | 0.105035i | −0.834111 | − | 0.551597i | \(-0.814019\pi\) |
0.894752 | + | 0.446562i | \(0.147352\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.75717e6 | −0.515520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.09992e6 | 0.655651 | 0.327825 | − | 0.944738i | \(-0.393684\pi\) | ||||
0.327825 | + | 0.944738i | \(0.393684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 282912. | − | 490019.i | 0.0299184 | − | 0.0518203i | −0.850678 | − | 0.525686i | \(-0.823809\pi\) |
0.880597 | + | 0.473866i | \(0.157142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.87546e6 | + | 1.19086e7i | 0.721232 | + | 1.24921i | 0.960506 | + | 0.278259i | \(0.0897573\pi\) |
−0.239274 | + | 0.970952i | \(0.576909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.49697e6 | − | 1.12531e7i | −0.670642 | − | 1.16159i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.16985e6 | − | 8.95445e6i | 0.529393 | − | 0.916936i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 274511. | 0.0276652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 420973. | 0.0420902 | 0.0210451 | − | 0.999779i | \(-0.493301\pi\) | ||||
0.0210451 | + | 0.999779i | \(0.493301\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 680234. | − | 1.17820e6i | 0.0669459 | − | 0.115954i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.50601e6 | − | 1.30008e7i | −0.732927 | − | 1.26947i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −157211. | − | 272297.i | −0.0151125 | − | 0.0261757i | 0.858370 | − | 0.513031i | \(-0.171477\pi\) |
−0.873483 | + | 0.486855i | \(0.838144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.90197e6 | + | 1.19546e7i | −0.658333 | + | 1.14027i | 0.322714 | + | 0.946496i | \(0.395405\pi\) |
−0.981047 | + | 0.193770i | \(0.937929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.43225e6 | −0.322343 | −0.161172 | − | 0.986926i | \(-0.551527\pi\) | ||||
−0.161172 | + | 0.986926i | \(0.551527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.59392e7 | 1.48544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.74805e6 | − | 1.51521e7i | 0.802839 | − | 1.39056i | −0.114902 | − | 0.993377i | \(-0.536655\pi\) |
0.917741 | − | 0.397181i | \(-0.130011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.96016e6 | + | 1.03233e7i | 0.542819 | + | 0.940189i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.03433e6 | − | 1.04518e7i | −0.541272 | − | 0.937510i | −0.998831 | − | 0.0483313i | \(-0.984610\pi\) |
0.457560 | − | 0.889179i | \(-0.348724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 90936.0 | − | 157506.i | 0.00809529 | − | 0.0140215i | −0.861949 | − | 0.506994i | \(-0.830756\pi\) |
0.870045 | + | 0.492973i | \(0.164090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.20339e6 | −0.631659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.91395e7 | 2.53611 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.31668e7 | − | 2.28055e7i | 1.12894 | − | 1.95539i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.31915e6 | + | 9.21304e6i | 0.452694 | + | 0.784089i | 0.998552 | − | 0.0537884i | \(-0.0171296\pi\) |
−0.545858 | + | 0.837878i | \(0.683796\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.33956e6 | − | 7.51633e6i | −0.363893 | − | 0.630281i | 0.624705 | − | 0.780861i | \(-0.285219\pi\) |
−0.988598 | + | 0.150580i | \(0.951886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.11228e7 | − | 1.92653e7i | 0.925850 | − | 1.60362i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.67179e7 | −1.37129 | −0.685647 | − | 0.727934i | \(-0.740481\pi\) | ||||
−0.685647 | + | 0.727934i | \(0.740481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.10355e7 | −0.898598 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.49684e6 | + | 9.52081e6i | −0.441128 | + | 0.764057i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.92775e6 | + | 3.33897e6i | 0.153588 | + | 0.266022i | 0.932544 | − | 0.361057i | \(-0.117584\pi\) |
−0.778956 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.21556e6 | + | 1.24977e7i | 0.566641 | + | 0.981452i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 312515. | − | 541291.i | 0.0243662 | − | 0.0422035i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.86020e6 | −0.142976 | −0.0714882 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714882 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00610e6 | 0.0767805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.52888e7 | + | 2.64810e7i | −1.15034 | + | 1.99245i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.78040e6 | − | 1.34760e7i | −0.581281 | − | 1.00681i | −0.995328 | − | 0.0965531i | \(-0.969218\pi\) |
0.414046 | − | 0.910256i | \(-0.364115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.45581e6 | + | 9.44974e6i | 0.401916 | + | 0.696139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.61381e7 | − | 2.79521e7i | 1.18056 | − | 2.04479i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.35632e6 | −0.314266 | −0.157133 | − | 0.987577i | \(-0.550225\pi\) | ||||
−0.157133 | + | 0.987577i | \(0.550225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.12055e7 | −0.802772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −786143. | + | 1.36164e6i | −0.0555465 | + | 0.0962093i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.48078e6 | − | 2.56478e6i | −0.103909 | − | 0.179976i | 0.809383 | − | 0.587281i | \(-0.199802\pi\) |
−0.913292 | + | 0.407305i | \(0.866468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.06674e6 | + | 1.84765e6i | 0.0738355 | + | 0.127887i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 480426. | − | 832122.i | 0.0330268 | − | 0.0572041i | −0.849040 | − | 0.528329i | \(-0.822819\pi\) |
0.882066 | + | 0.471125i | \(0.156152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.99609e7 | 3.38814 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.36123e7 | 0.916898 | 0.458449 | − | 0.888721i | \(-0.348405\pi\) | ||||
0.458449 | + | 0.888721i | \(0.348405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.86858e6 | + | 4.96853e6i | −0.190632 | + | 0.330184i | −0.945460 | − | 0.325739i | \(-0.894387\pi\) |
0.754828 | + | 0.655923i | \(0.227720\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.78751e6 | − | 1.00243e7i | −0.382033 | − | 0.661701i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.99501e6 | + | 3.45546e6i | 0.129939 | + | 0.225061i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.22046e7 | + | 2.11390e7i | −0.789631 | + | 1.36768i | 0.136562 | + | 0.990632i | \(0.456395\pi\) |
−0.926193 | + | 0.377049i | \(0.876939\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.34061e6 | 0.0855924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.16979e6 | 0.327894 | 0.163947 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.42163e6 | + | 9.39054e6i | −0.339366 | + | 0.587799i | −0.984314 | − | 0.176428i | \(-0.943546\pi\) |
0.644948 | + | 0.764227i | \(0.276879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.59510e7 | − | 2.76280e7i | −0.991923 | − | 1.71806i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.00555e6 | − | 1.55981e7i | −0.552741 | − | 0.957376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.63905e6 | − | 8.03507e6i | 0.282887 | − | 0.489975i | −0.689208 | − | 0.724564i | \(-0.742041\pi\) |
0.972095 | + | 0.234589i | \(0.0753745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.33311e7 | 0.802450 | 0.401225 | − | 0.915980i | \(-0.368585\pi\) | ||||
0.401225 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −588760. | −0.0352115 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.14538e6 | − | 1.98385e6i | 0.0676247 | − | 0.117129i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.38548e7 | + | 4.13178e7i | 1.39942 | + | 2.42387i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.50981e7 | − | 2.61507e7i | −0.874479 | − | 1.51464i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.17909e6 | + | 5.50634e6i | −0.182964 | + | 0.316903i | −0.942889 | − | 0.333108i | \(-0.891903\pi\) |
0.759925 | + | 0.650011i | \(0.225236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.15737e7 | −0.657704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.97565e7 | −1.68035 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.29576e6 | + | 3.97638e6i | −0.128021 | + | 0.221739i | −0.922910 | − | 0.385016i | \(-0.874196\pi\) |
0.794889 | + | 0.606755i | \(0.207529\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −539866. | − | 935074.i | −0.0299170 | − | 0.0518178i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.11104e7 | + | 1.92437e7i | 0.608050 | + | 1.05317i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.97700e7 | + | 3.42427e7i | −1.07527 | + | 1.86242i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.91492e6 | 0.478901 | 0.239451 | − | 0.970909i | \(-0.423033\pi\) | ||||
0.239451 | + | 0.970909i | \(0.423033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.29527e6 | −0.175930 | −0.0879648 | − | 0.996124i | \(-0.528036\pi\) | ||||
−0.0879648 | + | 0.996124i | \(0.528036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.60520e6 | − | 9.70849e6i | 0.295595 | − | 0.511985i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.90965e6 | + | 6.77171e6i | 0.204919 | + | 0.354930i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.20912e6 | + | 3.82631e6i | 0.114383 | + | 0.198117i | 0.917533 | − | 0.397660i | \(-0.130178\pi\) |
−0.803150 | + | 0.595777i | \(0.796844\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.79130e6 | − | 4.83467e6i | 0.143650 | − | 0.248809i | −0.785218 | − | 0.619219i | \(-0.787449\pi\) |
0.928869 | + | 0.370410i | \(0.120783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.18571e7 | 1.11130 | 0.555648 | − | 0.831418i | \(-0.312470\pi\) | ||||
0.555648 | + | 0.831418i | \(0.312470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.89089e7 | 0.955608 | 0.477804 | − | 0.878466i | \(-0.341433\pi\) | ||||
0.477804 | + | 0.878466i | \(0.341433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.70363e6 | − | 2.95078e6i | 0.0850675 | − | 0.147341i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.33339e7 | + | 2.30950e7i | 0.661822 | + | 1.14631i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.27488e6 | − | 9.13636e6i | −0.258707 | − | 0.448093i | 0.707189 | − | 0.707025i | \(-0.249963\pi\) |
−0.965896 | + | 0.258931i | \(0.916630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.19196e7 | + | 3.79659e7i | −1.06867 | + | 1.85099i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50748e7 | −0.726287 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.32007e7 | −3.02701 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76128e6 | − | 4.78267e6i | 0.130703 | − | 0.226385i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 320767. | + | 555585.i | 0.0150945 | + | 0.0261444i | 0.873474 | − | 0.486871i | \(-0.161862\pi\) |
−0.858380 | + | 0.513015i | \(0.828528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.60855e7 | − | 2.78610e7i | −0.748141 | − | 1.29582i | −0.948713 | − | 0.316139i | \(-0.897613\pi\) |
0.200572 | − | 0.979679i | \(-0.435720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −723696. | + | 1.25348e6i | −0.0334637 | + | 0.0579608i | −0.882272 | − | 0.470740i | \(-0.843987\pi\) |
0.848809 | + | 0.528700i | \(0.177320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.16338e6 | 0.418821 | 0.209411 | − | 0.977828i | \(-0.432845\pi\) | ||||
0.209411 | + | 0.977828i | \(0.432845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.29889e6 | 0.104467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.21034e7 | + | 3.82843e7i | −0.992911 | + | 1.71977i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82275e7 | − | 4.88915e7i | −1.26075 | − | 2.18367i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.59412e7 | + | 2.76109e7i | 0.703882 | + | 1.21916i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.07618e7 | − | 1.86400e7i | 0.472483 | − | 0.818365i | −0.527021 | − | 0.849852i | \(-0.676691\pi\) |
0.999504 | + | 0.0314872i | \(0.0100243\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.58447e7 | −1.98998 | −0.994991 | − | 0.0999625i | \(-0.968128\pi\) | ||||
−0.994991 | + | 0.0999625i | \(0.968128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.10719e7 | −1.34111 | −0.670557 | − | 0.741858i | \(-0.733945\pi\) | ||||
−0.670557 | + | 0.741858i | \(0.733945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.41068e6 | + | 9.37158e6i | −0.230910 | + | 0.399948i | −0.958076 | − | 0.286513i | \(-0.907504\pi\) |
0.727166 | + | 0.686462i | \(0.240837\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.22956e6 | + | 3.86172e6i | 0.0946162 | + | 0.163880i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.97863e6 | − | 3.42709e6i | −0.0830302 | − | 0.143812i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.38272e6 | − | 1.10552e7i | 0.266347 | − | 0.461327i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.40967e7 | −0.994394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.49523e6 | −0.102399 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.30682e7 | − | 3.99553e7i | 0.936250 | − | 1.62163i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.85893e7 | − | 3.21976e7i | −0.750316 | − | 1.29959i | −0.947670 | − | 0.319253i | \(-0.896568\pi\) |
0.197354 | − | 0.980332i | \(-0.436765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.38254e7 | + | 2.39464e7i | 0.551929 | + | 0.955969i | 0.998135 | + | 0.0610389i | \(0.0194414\pi\) |
−0.446206 | + | 0.894930i | \(0.647225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.28890e7 | + | 5.69655e7i | −1.30579 | + | 2.26170i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.90705e7 | −1.53436 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.24727e6 | 0.0877743 | 0.0438872 | − | 0.999036i | \(-0.486026\pi\) | ||||
0.0438872 | + | 0.999036i | \(0.486026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.69556e7 | − | 4.66884e7i | 1.04146 | − | 1.80387i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 148991. | + | 258059.i | 0.00572539 | + | 0.00991666i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −395902. | − | 685723.i | −0.0150504 | − | 0.0260681i | 0.858402 | − | 0.512977i | \(-0.171458\pi\) |
−0.873453 | + | 0.486909i | \(0.838124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.24389e6 | − | 1.08147e7i | 0.236092 | − | 0.408923i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.32571e6 | 0.274044 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.61458e6 | −0.357751 | −0.178876 | − | 0.983872i | \(-0.557246\pi\) | ||||
−0.178876 | + | 0.983872i | \(0.557246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.51978e6 | + | 1.30246e7i | −0.276842 | + | 0.479504i | −0.970598 | − | 0.240706i | \(-0.922621\pi\) |
0.693757 | + | 0.720210i | \(0.255954\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.28710e6 | − | 1.08896e7i | −0.230235 | − | 0.398778i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.75767e6 | + | 1.34367e7i | 0.281097 | + | 0.486874i | 0.971655 | − | 0.236402i | \(-0.0759684\pi\) |
−0.690558 | + | 0.723277i | \(0.742635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.25545e7 | − | 2.17451e7i | 0.452518 | − | 0.783784i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.16599e7 | 1.84256 | 0.921280 | − | 0.388899i | \(-0.127145\pi\) | ||||
0.921280 | + | 0.388899i | \(0.127145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.06570e6 | −0.144254 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.80852e7 | − | 3.13245e7i | 0.635005 | − | 1.09986i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.80294e6 | + | 1.69792e7i | 0.342411 | + | 0.593073i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.32025e7 | − | 2.28674e7i | −0.456391 | − | 0.790493i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.09797e6 | + | 5.36585e6i | −0.106540 | + | 0.184532i | −0.914366 | − | 0.404888i | \(-0.867310\pi\) |
0.807827 | + | 0.589420i | \(0.200644\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.67480e7 | −1.59116 | −0.795582 | − | 0.605846i | \(-0.792835\pi\) | ||||
−0.795582 | + | 0.605846i | \(0.792835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.73001e7 | −1.60169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.31953e6 | + | 4.01755e6i | −0.0777435 | + | 0.134656i | −0.902276 | − | 0.431159i | \(-0.858105\pi\) |
0.824533 | + | 0.565815i | \(0.191438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.42160e7 | + | 4.19434e7i | 0.807507 | + | 1.39864i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.37725e7 | − | 2.38546e7i | −0.454598 | − | 0.787387i | 0.544067 | − | 0.839042i | \(-0.316884\pi\) |
−0.998665 | + | 0.0516545i | \(0.983551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.74600e7 | + | 3.02416e7i | −0.573395 | + | 0.993150i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.29209e7 | 1.39533 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.83035e7 | 0.592038 | 0.296019 | − | 0.955182i | \(-0.404341\pi\) | ||||
0.296019 | + | 0.955182i | \(0.404341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.11563e6 | + | 5.39642e6i | −0.0997672 | + | 0.172802i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.22445e7 | + | 3.85286e7i | 0.708736 | + | 1.22757i | 0.965326 | + | 0.261047i | \(0.0840677\pi\) |
−0.256590 | + | 0.966520i | \(0.582599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 324.6.e.f.109.2 | 4 | ||
3.2 | odd | 2 | 324.6.e.g.109.1 | 4 | |||
9.2 | odd | 6 | 324.6.e.g.217.1 | 4 | |||
9.4 | even | 3 | 108.6.a.c.1.1 | yes | 2 | ||
9.5 | odd | 6 | 108.6.a.b.1.2 | ✓ | 2 | ||
9.7 | even | 3 | inner | 324.6.e.f.217.2 | 4 | ||
36.23 | even | 6 | 432.6.a.r.1.2 | 2 | |||
36.31 | odd | 6 | 432.6.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.b.1.2 | ✓ | 2 | 9.5 | odd | 6 | ||
108.6.a.c.1.1 | yes | 2 | 9.4 | even | 3 | ||
324.6.e.f.109.2 | 4 | 1.1 | even | 1 | trivial | ||
324.6.e.f.217.2 | 4 | 9.7 | even | 3 | inner | ||
324.6.e.g.109.1 | 4 | 3.2 | odd | 2 | |||
324.6.e.g.217.1 | 4 | 9.2 | odd | 6 | |||
432.6.a.q.1.1 | 2 | 36.31 | odd | 6 | |||
432.6.a.r.1.2 | 2 | 36.23 | even | 6 |