Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,7,Mod(127,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.127");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.o (of order \(6\), 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: | \(99.3833641238\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 415.1 | ||
Character | \(\chi\) | \(=\) | 432.415 |
Dual form | 432.7.o.c.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −119.170 | + | 206.408i | −0.953359 | + | 1.65127i | −0.215281 | + | 0.976552i | \(0.569067\pi\) |
−0.738079 | + | 0.674715i | \(0.764267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 297.697 | − | 171.875i | 0.867921 | − | 0.501095i | 0.00126437 | − | 0.999999i | \(-0.499598\pi\) |
0.866657 | + | 0.498905i | \(0.166264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1236.99 | + | 714.175i | −0.929367 | + | 0.536570i | −0.886611 | − | 0.462516i | \(-0.846947\pi\) |
−0.0427554 | + | 0.999086i | \(0.513614\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 473.058 | − | 819.360i | 0.215320 | − | 0.372945i | −0.738052 | − | 0.674744i | \(-0.764254\pi\) |
0.953371 | + | 0.301799i | \(0.0975873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6404.62 | 1.30361 | 0.651804 | − | 0.758388i | \(-0.274013\pi\) | ||||
0.651804 | + | 0.758388i | \(0.274013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2546.17i | − | 0.371216i | −0.982624 | − | 0.185608i | \(-0.940575\pi\) | ||
0.982624 | − | 0.185608i | \(-0.0594255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17689.0 | + | 10212.7i | 1.45385 | + | 0.839380i | 0.998697 | − | 0.0510336i | \(-0.0162515\pi\) |
0.455152 | + | 0.890414i | \(0.349585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20590.4 | − | 35663.7i | −1.31779 | − | 2.28248i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1735.29 | − | 3005.61i | −0.0711505 | − | 0.123236i | 0.828255 | − | 0.560351i | \(-0.189334\pi\) |
−0.899406 | + | 0.437115i | \(0.856000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21927.8 | + | 12660.0i | 0.736056 | + | 0.424962i | 0.820634 | − | 0.571455i | \(-0.193621\pi\) |
−0.0845776 | + | 0.996417i | \(0.526954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 81929.5i | 1.91089i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66492.6 | 1.31271 | 0.656355 | − | 0.754453i | \(-0.272098\pi\) | ||||
0.656355 | + | 0.754453i | \(0.272098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 58777.3 | − | 101805.i | 0.852822 | − | 1.47713i | −0.0258291 | − | 0.999666i | \(-0.508223\pi\) |
0.878651 | − | 0.477465i | \(-0.158444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50903.9 | − | 29389.4i | 0.640244 | − | 0.369645i | −0.144464 | − | 0.989510i | \(-0.546146\pi\) |
0.784709 | + | 0.619865i | \(0.212813\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −43680.1 | + | 25218.7i | −0.420717 | + | 0.242901i | −0.695384 | − | 0.718638i | \(-0.744766\pi\) |
0.274667 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 257.833 | − | 446.580i | 0.00219155 | − | 0.00379587i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −110518. | −0.742347 | −0.371173 | − | 0.928564i | \(-0.621044\pi\) | ||||
−0.371173 | + | 0.928564i | \(0.621044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 340433.i | − | 2.04618i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27925.3 | + | 16122.7i | 0.135969 | + | 0.0785020i | 0.566442 | − | 0.824102i | \(-0.308320\pi\) |
−0.430472 | + | 0.902604i | \(0.641653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 77336.7 | + | 133951.i | 0.340719 | + | 0.590142i | 0.984566 | − | 0.175012i | \(-0.0559963\pi\) |
−0.643848 | + | 0.765154i | \(0.722663\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 112748. | + | 195286.i | 0.410554 | + | 0.711101i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −138114. | − | 79740.3i | −0.459213 | − | 0.265127i | 0.252500 | − | 0.967597i | \(-0.418747\pi\) |
−0.711713 | + | 0.702470i | \(0.752080\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 52596.8i | − | 0.146955i | −0.997297 | − | 0.0734775i | \(-0.976590\pi\) | ||
0.997297 | − | 0.0734775i | \(-0.0234097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 494799. | 1.27192 | 0.635961 | − | 0.771721i | \(-0.280604\pi\) | ||||
0.635961 | + | 0.771721i | \(0.280604\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −245498. | + | 425215.i | −0.537745 | + | 0.931401i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −532196. | + | 307264.i | −1.07942 | + | 0.623203i | −0.930740 | − | 0.365682i | \(-0.880836\pi\) |
−0.148680 | + | 0.988885i | \(0.547502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −929041. | + | 536382.i | −1.62480 | + | 0.938080i | −0.639192 | + | 0.769047i | \(0.720731\pi\) |
−0.985610 | + | 0.169033i | \(0.945936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −763238. | + | 1.32197e6i | −1.24281 | + | 2.15260i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −626436. | −0.888601 | −0.444301 | − | 0.895878i | \(-0.646548\pi\) | ||||
−0.444301 | + | 0.895878i | \(0.646548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 325228.i | − | 0.431582i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 525551. | + | 303427.i | 0.612977 | + | 0.353902i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 286108. | + | 495554.i | 0.313484 | + | 0.542970i | 0.979114 | − | 0.203312i | \(-0.0651705\pi\) |
−0.665630 | + | 0.746282i | \(0.731837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 440747. | + | 763396.i | 0.427784 | + | 0.740944i | 0.996676 | − | 0.0814682i | \(-0.0259609\pi\) |
−0.568891 | + | 0.822413i | \(0.692628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21906e6 | + | 703824.i | 1.11561 | + | 0.644098i | 0.940277 | − | 0.340411i | \(-0.110566\pi\) |
0.175334 | + | 0.984509i | \(0.443899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 182957.i | 0.149347i | 0.997208 | + | 0.0746735i | \(0.0237915\pi\) | ||||
−0.997208 | + | 0.0746735i | \(0.976209\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −244357. | −0.188688 | −0.0943441 | − | 0.995540i | \(-0.530075\pi\) | ||||
−0.0943441 | + | 0.995540i | \(0.530075\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 733410. | − | 1.27030e6i | 0.508290 | − | 0.880384i | −0.491664 | − | 0.870785i | \(-0.663611\pi\) |
0.999954 | − | 0.00959925i | \(-0.00305558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.21599e6 | + | 2.43410e6i | −2.77208 | + | 1.60046i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.90664e6 | − | 1.10080e6i | 1.13143 | − | 0.653231i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 134311. | − | 232633.i | 0.0758148 | − | 0.131315i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.09098e6 | 3.11858 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.90681e6i | − | 1.41908i | −0.704667 | − | 0.709538i | \(-0.748904\pi\) | ||
0.704667 | − | 0.709538i | \(-0.251096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.30910e6 | − | 755809.i | −0.582316 | − | 0.336200i | 0.179737 | − | 0.983715i | \(-0.442475\pi\) |
−0.762053 | + | 0.647514i | \(0.775809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −437624. | − | 757987.i | −0.186014 | − | 0.322186i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.52718e6 | + | 2.64515e6i | 0.593921 | + | 1.02870i | 0.993698 | + | 0.112089i | \(0.0357542\pi\) |
−0.399777 | + | 0.916612i | \(0.630912\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16098e6 | + | 1.82499e6i | 1.17700 | + | 0.679542i | 0.955319 | − | 0.295577i | \(-0.0955120\pi\) |
0.221682 | + | 0.975119i | \(0.428845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.35138e6i | 0.462137i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 827177. | 0.271328 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.53836e6 | − | 2.66452e6i | 0.465049 | − | 0.805489i | −0.534154 | − | 0.845387i | \(-0.679370\pi\) |
0.999204 | + | 0.0398977i | \(0.0127032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.37059e6 | − | 1.36866e6i | 0.688533 | − | 0.397525i | −0.114529 | − | 0.993420i | \(-0.536536\pi\) |
0.803062 | + | 0.595895i | \(0.203203\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.22628e6 | + | 3.01739e6i | −1.40345 | + | 0.810283i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.32390e6 | + | 5.75716e6i | −0.858913 | + | 1.48768i | 0.0140546 | + | 0.999901i | \(0.495526\pi\) |
−0.872967 | + | 0.487779i | \(0.837807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.02128e6 | 1.68244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.64679e6i | 1.53479i | 0.641174 | + | 0.767396i | \(0.278448\pi\) | ||||
−0.641174 | + | 0.767396i | \(0.721552\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.16723e6 | + | 1.25125e6i | 0.465325 | + | 0.268656i | 0.714281 | − | 0.699859i | \(-0.246754\pi\) |
−0.248956 | + | 0.968515i | \(0.580087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.96584e6 | + | 3.40493e6i | 0.407275 | + | 0.705421i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 713118. | + | 1.23516e6i | 0.137728 | + | 0.238552i | 0.926636 | − | 0.375959i | \(-0.122687\pi\) |
−0.788908 | + | 0.614511i | \(0.789353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.22594e7 | − | 7.07798e6i | −2.28747 | − | 1.32067i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.21323e6i | 0.211536i | 0.994391 | + | 0.105768i | \(0.0337301\pi\) | ||||
−0.994391 | + | 0.105768i | \(0.966270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 296213. | 0.0499539 | 0.0249769 | − | 0.999688i | \(-0.492049\pi\) | ||||
0.0249769 | + | 0.999688i | \(0.492049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.92392e6 | + | 1.37246e7i | −1.25148 | + | 2.16763i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.92244e6 | + | 4.57402e6i | −1.21153 | + | 0.699477i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 548352. | − | 316591.i | 0.0786972 | − | 0.0454358i | −0.460135 | − | 0.887849i | \(-0.652199\pi\) |
0.538832 | + | 0.842413i | \(0.318866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.66007e6 | + | 9.80353e6i | −0.787317 | + | 1.36367i | 0.140288 | + | 0.990111i | \(0.455197\pi\) |
−0.927605 | + | 0.373563i | \(0.878136\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.97684e6 | −0.258566 | −0.129283 | − | 0.991608i | \(-0.541268\pi\) | ||||
−0.129283 | + | 0.991608i | \(0.541268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.80885e6i | 0.483320i | 0.970361 | + | 0.241660i | \(0.0776919\pi\) | ||||
−0.970361 | + | 0.241660i | \(0.922308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.03318e6 | − | 596507.i | −0.123506 | − | 0.0713062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.40090e7 | + | 2.42643e7i | 1.62609 | + | 2.81647i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.81841e6 | + | 3.14958e6i | 0.199183 | + | 0.344996i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.04522e7 | − | 6.03456e6i | −1.11265 | − | 0.642389i | −0.173136 | − | 0.984898i | \(-0.555390\pi\) |
−0.939515 | + | 0.342509i | \(0.888723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.40093e7i | 1.40962i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.70380e6 | 0.851785 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.02976e6 | − | 5.24769e6i | 0.280692 | − | 0.486174i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.91395e6 | − | 5.72382e6i | 0.893989 | − | 0.516145i | 0.0187436 | − | 0.999824i | \(-0.494033\pi\) |
0.875245 | + | 0.483680i | \(0.160700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.05785e7 | + | 6.10752e6i | −0.904374 | + | 0.522141i | −0.878617 | − | 0.477528i | \(-0.841533\pi\) |
−0.0257573 | + | 0.999668i | \(0.508200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.55787e6 | − | 4.43037e6i | 0.212996 | − | 0.368921i | −0.739654 | − | 0.672987i | \(-0.765011\pi\) |
0.952651 | + | 0.304066i | \(0.0983444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.13676e6 | 0.327034 | 0.163517 | − | 0.986541i | \(-0.447716\pi\) | ||||
0.163517 | + | 0.986541i | \(0.447716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.20213e7i | − | 0.926288i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −207614. | − | 119866.i | −0.0152077 | − | 0.00878016i | 0.492377 | − | 0.870382i | \(-0.336128\pi\) |
−0.507585 | + | 0.861602i | \(0.669462\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.05216e6 | − | 3.55444e6i | −0.146609 | − | 0.253934i | 0.783363 | − | 0.621564i | \(-0.213502\pi\) |
−0.929972 | + | 0.367630i | \(0.880169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 61451.9 | + | 106438.i | 0.00417866 | + | 0.00723765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.08623e6 | − | 1.20449e6i | −0.138443 | − | 0.0799301i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.62075e6i | − | 0.165731i | −0.996561 | − | 0.0828655i | \(-0.973593\pi\) | ||
0.996561 | − | 0.0828655i | \(-0.0264072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91747e7 | −1.80154 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.38542e6 | − | 4.13166e6i | 0.140529 | − | 0.243403i | −0.787167 | − | 0.616740i | \(-0.788453\pi\) |
0.927696 | + | 0.373337i | \(0.121786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.97947e7 | − | 1.14285e7i | 1.13933 | − | 0.657791i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.85537e7 | + | 1.64855e7i | −1.56962 | + | 0.906222i | −0.573409 | + | 0.819269i | \(0.694380\pi\) |
−0.996212 | + | 0.0869525i | \(0.972287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.31705e7 | − | 2.28119e7i | 0.707723 | − | 1.22581i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.67419e7 | 1.88758 | 0.943789 | − | 0.330548i | \(-0.107234\pi\) | ||||
0.943789 | + | 0.330548i | \(0.107234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.68695e7i | 0.847605i | 0.905755 | + | 0.423803i | \(0.139305\pi\) | ||||
−0.905755 | + | 0.423803i | \(0.860695\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.09402e7 | + | 2.94103e7i | 2.44942 | + | 1.41417i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.56226e6 | + | 4.43797e6i | 0.120555 | + | 0.208807i | 0.919987 | − | 0.391950i | \(-0.128199\pi\) |
−0.799432 | + | 0.600757i | \(0.794866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.49551e6 | + | 9.51850e6i | 0.247679 | + | 0.428993i | 0.962881 | − | 0.269925i | \(-0.0869988\pi\) |
−0.715202 | + | 0.698917i | \(0.753666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.21732e6 | + | 1.28017e6i | 0.0978294 | + | 0.0564818i | 0.548117 | − | 0.836402i | \(-0.315345\pi\) |
−0.450287 | + | 0.892884i | \(0.648678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.04095e7i | − | 1.70938i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.68816e7 | 0.699392 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.33423e7 | − | 2.31095e7i | 0.530428 | − | 0.918728i | −0.468942 | − | 0.883229i | \(-0.655365\pi\) |
0.999370 | − | 0.0354991i | \(-0.0113021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.65570e6 | + | 3.84267e6i | −0.259255 | + | 0.149681i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.67358e7 | − | 9.66243e6i | 0.626085 | − | 0.361470i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.01026e7 | − | 1.74983e7i | 0.370454 | − | 0.641646i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.68648e7 | −1.29931 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80526e7i | 0.623912i | 0.950096 | + | 0.311956i | \(0.100984\pi\) | ||||
−0.950096 | + | 0.311956i | \(0.899016\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.62362e7 | − | 2.09210e7i | −1.20465 | − | 0.695506i | −0.243066 | − | 0.970010i | \(-0.578153\pi\) |
−0.961586 | + | 0.274503i | \(0.911487\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.93993e7 | − | 3.36005e7i | −0.632633 | − | 1.09575i | −0.987011 | − | 0.160651i | \(-0.948641\pi\) |
0.354378 | − | 0.935102i | \(-0.384693\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.69786e7 | − | 2.94079e7i | −0.532997 | − | 0.923178i | −0.999257 | − | 0.0385306i | \(-0.987732\pi\) |
0.466260 | − | 0.884648i | \(-0.345601\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.29306e6 | + | 2.47860e6i | 0.132250 | + | 0.0763544i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.63073e7i | − | 0.483920i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.89618e7 | −1.13498 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.66896e6 | + | 1.50151e7i | −0.243433 | + | 0.421638i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.05366e6 | + | 1.76303e6i | −0.0842047 | + | 0.0486156i | −0.541511 | − | 0.840694i | \(-0.682148\pi\) |
0.457306 | + | 0.889309i | \(0.348814\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.29181e7 | − | 1.90053e7i | 0.875590 | − | 0.505522i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.81383e7 | + | 4.87370e7i | −0.735205 | + | 1.27341i | 0.219429 | + | 0.975629i | \(0.429581\pi\) |
−0.954633 | + | 0.297784i | \(0.903753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.61659e7 | −0.912088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.02647e7i | 0.997796i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.15843e7 | + | 1.24617e7i | 0.516594 | + | 0.298255i | 0.735540 | − | 0.677481i | \(-0.236929\pi\) |
−0.218946 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.85248e6 | + | 8.40475e6i | 0.114153 | + | 0.197719i | 0.917441 | − | 0.397872i | \(-0.130251\pi\) |
−0.803288 | + | 0.595591i | \(0.796918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.39254e6 | − | 5.87605e6i | −0.0771259 | − | 0.133586i | 0.824883 | − | 0.565304i | \(-0.191241\pi\) |
−0.902009 | + | 0.431718i | \(0.857908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.08564e7 | + | 6.26796e6i | 0.242662 | + | 0.140101i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.77924e7i | − | 1.24907i | −0.780996 | − | 0.624536i | \(-0.785288\pi\) | ||
0.780996 | − | 0.624536i | \(-0.214712\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.05629e7 | 0.862199 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.89652e7 | + | 1.02131e8i | −1.21260 | + | 2.10028i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.91261e7 | + | 3.41365e7i | −1.19614 | + | 0.690591i | −0.959692 | − | 0.281054i | \(-0.909316\pi\) |
−0.236446 | + | 0.971645i | \(0.575983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.29010e7 | + | 1.89954e7i | −0.644299 | + | 0.371986i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.29579e7 | − | 2.24437e7i | 0.249693 | − | 0.432481i | −0.713748 | − | 0.700403i | \(-0.753004\pi\) |
0.963441 | + | 0.267922i | \(0.0863369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.28357e6 | −0.0612804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.83783e7i | − | 1.07234i | −0.844109 | − | 0.536171i | \(-0.819870\pi\) | ||
0.844109 | − | 0.536171i | \(-0.180130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.77446e7 | − | 1.60184e7i | −0.493836 | − | 0.285116i | 0.232328 | − | 0.972637i | \(-0.425366\pi\) |
−0.726165 | + | 0.687521i | \(0.758699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.85120e7 | − | 1.01346e8i | −1.02533 | − | 1.77592i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.10417e7 | − | 5.37658e7i | −0.527347 | − | 0.913393i | −0.999492 | − | 0.0318714i | \(-0.989853\pi\) |
0.472145 | − | 0.881521i | \(-0.343480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.13291e8 | + | 6.54087e7i | 1.89525 | + | 1.09422i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.46466e8i | − | 2.37655i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.04878e7 | 0.167615 | 0.0838075 | − | 0.996482i | \(-0.473292\pi\) | ||||
0.0838075 | + | 0.996482i | \(0.473292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.96212e6 | + | 8.59464e6i | −0.0769545 | + | 0.133289i | −0.901935 | − | 0.431873i | \(-0.857853\pi\) |
0.824980 | + | 0.565162i | \(0.191186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.07463e7 | − | 1.19779e7i | 0.316975 | − | 0.183005i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.22505e7 | + | 4.74874e7i | −1.21999 | + | 0.704360i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.87888e6 | + | 1.01825e7i | −0.0859260 | + | 0.148828i | −0.905785 | − | 0.423737i | \(-0.860718\pi\) |
0.819859 | + | 0.572565i | \(0.194052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.10844e7 | 0.157348 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.55682e8i | − | 3.57731i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.26782e8 | + | 7.31976e7i | 1.72352 | + | 0.995073i | 0.911331 | + | 0.411674i | \(0.135056\pi\) |
0.812186 | + | 0.583399i | \(0.198278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.11860e7 | − | 5.40158e7i | −0.417940 | − | 0.723894i | 0.577792 | − | 0.816184i | \(-0.303914\pi\) |
−0.995732 | + | 0.0922905i | \(0.970581\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.31874e8 | − | 2.28412e8i | −1.71788 | − | 2.97545i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.60458e7 | + | 2.65845e7i | 0.591434 | + | 0.341465i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.02542e7i | 0.252978i | 0.991968 | + | 0.126489i | \(0.0403709\pi\) | ||||
−0.991968 | + | 0.126489i | \(0.959629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.42026e8 | 1.74946 | 0.874732 | − | 0.484607i | \(-0.161037\pi\) | ||||
0.874732 | + | 0.484607i | \(0.161037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.60034e7 | − | 4.50392e7i | 0.311591 | − | 0.539692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.21442e8 | − | 7.01145e7i | 1.43541 | − | 0.828732i | 0.437881 | − | 0.899033i | \(-0.355729\pi\) |
0.997526 | + | 0.0703005i | \(0.0223958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.69677e7 | − | 2.13433e7i | 0.425217 | − | 0.245499i | −0.272090 | − | 0.962272i | \(-0.587715\pi\) |
0.697307 | + | 0.716773i | \(0.254381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.46524e7 | − | 1.29302e8i | 0.847157 | − | 1.46732i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.63226e7 | 0.843168 | 0.421584 | − | 0.906789i | \(-0.361474\pi\) | ||||
0.421584 | + | 0.906789i | \(0.361474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67909e8i | 1.83039i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.71297e7 | + | 3.87574e7i | 0.712657 | + | 0.411453i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.36449e7 | − | 9.29157e7i | −0.562056 | − | 0.973510i | −0.997317 | − | 0.0732054i | \(-0.976677\pi\) |
0.435261 | − | 0.900304i | \(-0.356656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.75328e7 | + | 3.03678e7i | 0.178957 | + | 0.309963i | 0.941524 | − | 0.336947i | \(-0.109394\pi\) |
−0.762566 | + | 0.646910i | \(0.776061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.99139e7 | − | 2.88178e7i | −0.502897 | − | 0.290348i | 0.227012 | − | 0.973892i | \(-0.427104\pi\) |
−0.729909 | + | 0.683544i | \(0.760438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.29340e8i | 1.26994i | 0.772536 | + | 0.634970i | \(0.218988\pi\) | ||||
−0.772536 | + | 0.634970i | \(0.781012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.48216e7 | −0.531414 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.19783e7 | + | 7.27085e7i | −0.396681 | + | 0.687072i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.08058e7 | + | 5.24268e7i | −0.847292 | + | 0.489184i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.36830e7 | − | 1.94469e7i | 0.306482 | − | 0.176947i | −0.338869 | − | 0.940833i | \(-0.610044\pi\) |
0.645351 | + | 0.763886i | \(0.276711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.14548e7 | − | 5.44814e7i | 0.282652 | − | 0.489568i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.36382e8 | −1.19545 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.04552e7i | − | 0.696574i | −0.937388 | − | 0.348287i | \(-0.886763\pi\) | ||
0.937388 | − | 0.348287i | \(-0.113237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.14375e7 | + | 1.81504e7i | 0.265585 | + | 0.153336i | 0.626880 | − | 0.779116i | \(-0.284332\pi\) |
−0.361295 | + | 0.932452i | \(0.617665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.11139e7 | − | 1.92498e7i | −0.0927523 | − | 0.160652i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.04010e6 | − | 1.56579e7i | −0.0736384 | − | 0.127545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.95533e7 | + | 4.01566e7i | 0.559779 | + | 0.323188i | 0.753057 | − | 0.657956i | \(-0.228579\pi\) |
−0.193278 | + | 0.981144i | \(0.561912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.38884e8i | − | 1.09131i | −0.838009 | − | 0.545656i | \(-0.816281\pi\) | ||
0.838009 | − | 0.545656i | \(-0.183719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.10095e8 | −1.63133 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.47554e7 | + | 7.75187e7i | −0.339385 | + | 0.587832i | −0.984317 | − | 0.176408i | \(-0.943552\pi\) |
0.644932 | + | 0.764240i | \(0.276886\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.47300e8 | − | 8.50438e7i | 1.10393 | − | 0.637353i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.90550e8 | + | 1.67749e8i | −2.12716 | + | 1.22811i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60211e7 | − | 6.23905e7i | 0.260667 | − | 0.451488i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93181e7 | 0.631577 | 0.315789 | − | 0.948830i | \(-0.397731\pi\) | ||||
0.315789 | + | 0.948830i | \(0.397731\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.96143e7i | 0.696333i | 0.937433 | + | 0.348166i | \(0.113196\pi\) | ||||
−0.937433 | + | 0.348166i | \(0.886804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.40440e8 | + | 8.10828e7i | 0.959528 | + | 0.553984i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.34582e8 | + | 2.33103e8i | 0.909118 | + | 1.57464i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.56101e7 | − | 9.63196e7i | −0.367259 | − | 0.636111i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.77638e7 | − | 2.18029e7i | −0.246612 | − | 0.142381i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 736552.i | 0.00470367i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.95037e6 | −0.0502106 | −0.0251053 | − | 0.999685i | \(-0.507992\pi\) | ||||
−0.0251053 | + | 0.999685i | \(0.507992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.91200e7 | − | 5.04373e7i | 0.179888 | − | 0.311575i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.55761e8 | + | 8.99286e7i | −0.951692 | + | 0.549460i | −0.893606 | − | 0.448852i | \(-0.851833\pi\) |
−0.0580857 | + | 0.998312i | \(0.518500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.65279e6 | + | 4.41834e6i | −0.0457473 | + | 0.0264122i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.05622e8 | + | 1.82943e8i | −0.624568 | + | 1.08178i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.76720e7 | 0.507335 | 0.253668 | − | 0.967291i | \(-0.418363\pi\) | ||||
0.253668 | + | 0.967291i | \(0.418363\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.56115e7i | − | 0.318368i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.14612e7 | − | 5.28051e7i | −0.512521 | − | 0.295904i | 0.221348 | − | 0.975195i | \(-0.428954\pi\) |
−0.733869 | + | 0.679291i | \(0.762288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.74801e8 | + | 3.02764e8i | 0.969166 | + | 1.67865i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.44922e8 | + | 2.51013e8i | 0.786681 | + | 1.36257i | 0.927990 | + | 0.372606i | \(0.121536\pi\) |
−0.141308 | + | 0.989966i | \(0.545131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.91357e8 | − | 1.68215e8i | −1.56501 | − | 0.903558i | −0.996737 | − | 0.0807168i | \(-0.974279\pi\) |
−0.568271 | − | 0.822841i | \(-0.692388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.41139e8i | − | 4.42450i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.90800e7 | −0.151379 | −0.0756897 | − | 0.997131i | \(-0.524116\pi\) | ||||
−0.0756897 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.84382e8 | + | 3.19359e8i | −0.940134 | + | 1.62836i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.36710e8 | − | 7.89294e7i | 0.689912 | − | 0.398321i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.96478e7 | + | 5.75317e7i | −0.492667 | + | 0.284441i | −0.725680 | − | 0.688032i | \(-0.758475\pi\) |
0.233013 | + | 0.972474i | \(0.425141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22346e7 | − | 5.58320e7i | 0.157753 | − | 0.273236i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.96643e7 | 0.382032 | 0.191016 | − | 0.981587i | \(-0.438822\pi\) | ||||
0.191016 | + | 0.981587i | \(0.438822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.24728e8i | 2.49105i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.07735e7 | − | 1.77671e7i | −0.143185 | − | 0.0826677i | 0.426696 | − | 0.904395i | \(-0.359677\pi\) |
−0.569881 | + | 0.821727i | \(0.693011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.91559e7 | − | 1.02461e8i | −0.272505 | − | 0.471993i | 0.696997 | − | 0.717074i | \(-0.254519\pi\) |
−0.969503 | + | 0.245081i | \(0.921186\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.20116e7 | + | 5.54456e7i | 0.144557 | + | 0.250381i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.33321e8 | − | 1.92443e8i | −1.49038 | − | 0.860471i | −0.490441 | − | 0.871475i | \(-0.663164\pi\) |
−0.999939 | + | 0.0110032i | \(0.996497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.77196e7i | 0.209206i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.68018e8 | 1.16354 | 0.581772 | − | 0.813352i | \(-0.302359\pi\) | ||||
0.581772 | + | 0.813352i | \(0.302359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.46408e8 | − | 2.53587e8i | 0.623319 | − | 1.07962i | −0.365545 | − | 0.930794i | \(-0.619117\pi\) |
0.988863 | − | 0.148826i | \(-0.0475494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.72469e8 | + | 1.57310e8i | −1.14880 | + | 0.663260i | −0.948595 | − | 0.316493i | \(-0.897494\pi\) |
−0.200206 | + | 0.979754i | \(0.564161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.86488e8 | + | 1.07669e8i | −0.771236 | + | 0.445273i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.04136e8 | + | 6.99985e8i | −1.65534 | + | 2.86714i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.25860e8 | 1.71126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.28584e8i | 0.909823i | 0.890537 | + | 0.454912i | \(0.150329\pi\) | ||||
−0.890537 | + | 0.454912i | \(0.849671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.99990e8 | + | 3.46404e8i | 2.34327 | + | 1.35289i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −243940. | − | 422516.i | −0.000943766 | − | 0.00163465i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.91187e7 | + | 6.77556e7i | 0.148529 | + | 0.257259i | 0.930684 | − | 0.365824i | \(-0.119213\pi\) |
−0.782155 | + | 0.623084i | \(0.785880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.81207e8 | + | 1.04620e8i | 0.681620 | + | 0.393533i | 0.800465 | − | 0.599379i | \(-0.204586\pi\) |
−0.118845 | + | 0.992913i | \(0.537919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.71445e8i | 1.74068i | 0.492454 | + | 0.870338i | \(0.336100\pi\) | ||||
−0.492454 | + | 0.870338i | \(0.663900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.60576e7 | −0.168487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.27587e8 | − | 2.20987e8i | 0.458211 | − | 0.793645i | −0.540655 | − | 0.841244i | \(-0.681824\pi\) |
0.998867 | + | 0.0475991i | \(0.0151570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12010e8 | − | 1.80139e8i | 1.11031 | − | 0.641039i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.80068e7 | − | 2.19433e7i | 0.132802 | − | 0.0766734i | −0.432127 | − | 0.901813i | \(-0.642237\pi\) |
0.564929 | + | 0.825139i | \(0.308903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.51278e8 | − | 2.62022e8i | 0.523808 | − | 0.907263i | −0.475808 | − | 0.879549i | \(-0.657844\pi\) |
0.999616 | − | 0.0277132i | \(-0.00882251\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.08607e8 | 0.709354 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.08882e7i | − | 0.238889i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.91329e8 | − | 1.10464e8i | −0.633305 | − | 0.365639i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.62925e6 | + | 6.28605e6i | 0.0119062 | + | 0.0206221i | 0.871917 | − | 0.489654i | \(-0.162877\pi\) |
−0.860011 | + | 0.510276i | \(0.829543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.92116e7 | − | 1.19878e8i | −0.223056 | − | 0.386344i | 0.732679 | − | 0.680575i | \(-0.238270\pi\) |
−0.955734 | + | 0.294231i | \(0.904936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.70347e8 | + | 9.83499e7i | 0.544158 | + | 0.314170i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.48842e8i | 1.09488i | 0.836844 | + | 0.547441i | \(0.184398\pi\) | ||||
−0.836844 | + | 0.547441i | \(0.815602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.27976e8 | −2.26488 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.22815e7 | + | 9.05543e7i | −0.159842 | + | 0.276854i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.12929e7 | − | 1.80670e7i | 0.0948443 | − | 0.0547584i | −0.451828 | − | 0.892105i | \(-0.649228\pi\) |
0.546672 | + | 0.837347i | \(0.315894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.53386e8 | + | 4.34968e8i | −2.24421 | + | 1.29569i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.76447e8 | − | 6.52025e8i | 1.11175 | − | 1.92560i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.82722e8 | 1.40134 | 0.700670 | − | 0.713486i | \(-0.252885\pi\) | ||||
0.700670 | + | 0.713486i | \(0.252885\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.69302e8i | − | 0.487299i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.62418e8 | + | 1.51507e8i | 0.742566 | + | 0.428721i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.94025e7 | + | 1.37529e8i | 0.222790 | + | 0.385883i | 0.955654 | − | 0.294492i | \(-0.0951503\pi\) |
−0.732864 | + | 0.680375i | \(0.761817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.58587e8 | + | 4.47887e8i | 0.713410 | + | 1.23566i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.78937e8 | − | 1.61044e8i | −0.763111 | − | 0.440582i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.75480e8i | − | 1.01018i | −0.863066 | − | 0.505091i | \(-0.831459\pi\) | ||
0.863066 | − | 0.505091i | \(-0.168541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.83880e8 | 1.29102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.14607e7 | + | 1.23774e8i | −0.187523 | + | 0.324799i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.63797e8 | + | 2.10038e8i | −0.946795 | + | 0.546632i | −0.892084 | − | 0.451870i | \(-0.850757\pi\) |
−0.0547113 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.26020e8 | − | 1.88228e8i | 0.834627 | − | 0.481872i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.20496e8 | + | 3.81910e8i | −0.559872 | + | 0.969726i | 0.437635 | + | 0.899153i | \(0.355816\pi\) |
−0.997507 | + | 0.0705732i | \(0.977517\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.27794e8 | 0.569036 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.18237e8i | − | 0.540749i | −0.962755 | − | 0.270374i | \(-0.912853\pi\) | ||
0.962755 | − | 0.270374i | \(-0.0871475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.89192e8 | + | 2.24700e8i | 0.948850 | + | 0.547819i | 0.892724 | − | 0.450605i | \(-0.148792\pi\) |
0.0561268 | + | 0.998424i | \(0.482125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.66652e8 | + | 6.35061e8i | 0.886718 | + | 1.53584i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.14457e7 | + | 5.44656e7i | 0.0748370 | + | 0.129621i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.43189e8 | − | 1.40405e8i | −0.574148 | − | 0.331484i | 0.184656 | − | 0.982803i | \(-0.440883\pi\) |
−0.758804 | + | 0.651319i | \(0.774216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.52412e8i | 1.51594i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.32455e8 | 0.766382 | 0.383191 | − | 0.923669i | \(-0.374825\pi\) | ||||
0.383191 | + | 0.923669i | \(0.374825\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.14007e8 | + | 3.70670e8i | −0.485594 | + | 0.841073i | −0.999863 | − | 0.0165555i | \(-0.994730\pi\) |
0.514269 | + | 0.857629i | \(0.328063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.27443e7 | + | 4.19989e7i | −0.163767 | + | 0.0945507i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.64205e7 | − | 1.52539e7i | 0.0585538 | − | 0.0338060i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.54555e7 | + | 1.30693e8i | −0.165925 | + | 0.287391i | −0.936983 | − | 0.349374i | \(-0.886394\pi\) |
0.771058 | + | 0.636764i | \(0.219728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.61066e8 | 0.565212 | 0.282606 | − | 0.959236i | \(-0.408801\pi\) | ||||
0.282606 | + | 0.959236i | \(0.408801\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.04270e9i | − | 2.24004i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.59214e8 | − | 1.49657e8i | −0.548335 | − | 0.316581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.75633e7 | + | 6.50616e7i | 0.0788517 | + | 0.136575i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.92218e8 | − | 1.37216e9i | −1.63770 | − | 2.83659i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.56186e8 | + | 1.47909e8i | 0.525572 | + | 0.303439i | 0.739211 | − | 0.673474i | \(-0.235199\pi\) |
−0.213640 | + | 0.976913i | \(0.568532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.04221e8i | − | 1.01881i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.46339e8 | 0.293454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.45926e8 | + | 5.99161e8i | −0.683294 | + | 1.18350i | 0.290675 | + | 0.956822i | \(0.406120\pi\) |
−0.973970 | + | 0.226679i | \(0.927213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.79755e8 | + | 1.61516e8i | −0.548450 | + | 0.316648i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.12060e8 | + | 3.53373e8i | −1.18208 | + | 0.682475i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.36725e8 | + | 1.44925e9i | −1.60397 | + | 2.77815i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.30305e8 | −1.56817 | −0.784083 | − | 0.620656i | \(-0.786867\pi\) | ||||
−0.784083 | + | 0.620656i | \(0.786867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.46518e8i | − | 0.462154i | −0.972935 | − | 0.231077i | \(-0.925775\pi\) | ||
0.972935 | − | 0.231077i | \(-0.0742249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.37195e9 | − | 7.92098e8i | −2.53435 | − | 1.46321i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.48304e7 | − | 1.29610e8i | −0.137218 | − | 0.237669i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.60349e8 | + | 2.77733e8i | 0.289759 | + | 0.501878i | 0.973752 | − | 0.227611i | \(-0.0730913\pi\) |
−0.683993 | + | 0.729489i | \(0.739758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.94858e8 | + | 2.85706e8i | 0.887731 | + | 0.512532i | 0.873200 | − | 0.487363i | \(-0.162041\pi\) |
0.0145312 | + | 0.999894i | \(0.495374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.13199e8i | − | 0.553737i | −0.960908 | − | 0.276868i | \(-0.910703\pi\) | ||
0.960908 | − | 0.276868i | \(-0.0892966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.66387e8 | 1.69624 | 0.848120 | − | 0.529804i | \(-0.177735\pi\) | ||||
0.848120 | + | 0.529804i | \(0.177735\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.65132e6 | − | 2.86018e6i | 0.00285692 | − | 0.00494832i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.16538e8 | + | 2.98223e8i | −0.887244 | + | 0.512251i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.93011e7 | + | 5.15580e7i | −0.151207 | + | 0.0872992i | −0.573694 | − | 0.819069i | \(-0.694490\pi\) |
0.422488 | + | 0.906369i | \(0.361157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.91389e8 | − | 5.04701e8i | 0.489875 | − | 0.848489i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.37075e8 | −1.55312 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.23387e7i | − | 0.151962i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17619e9 | + | 6.79072e8i | 1.90848 | + | 1.10186i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.78379e7 | − | 4.82167e7i | −0.0448528 | − | 0.0776874i | 0.842727 | − | 0.538341i | \(-0.180949\pi\) |
−0.887580 | + | 0.460653i | \(0.847615\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.54438e8 | + | 7.87110e8i | 0.721992 | + | 1.25053i | 0.960200 | + | 0.279313i | \(0.0901067\pi\) |
−0.238208 | + | 0.971214i | \(0.576560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.03338e8 | + | 4.63807e8i | 1.26741 | + | 0.731742i | 0.974498 | − | 0.224396i | \(-0.0720408\pi\) |
0.292917 | + | 0.956138i | \(0.405374\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.55042e8i | 1.33032i | 0.746703 | + | 0.665158i | \(0.231636\pi\) | ||||
−0.746703 | + | 0.665158i | \(0.768364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.39929e8 | −0.525218 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.38880e8 | − | 7.60162e8i | 0.668784 | − | 1.15837i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.30672e8 | + | 7.54435e7i | −0.197755 | + | 0.114174i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.81327e9 | − | 1.04689e9i | 2.70668 | − | 1.56271i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.61167e7 | − | 2.79149e7i | 0.0238933 | − | 0.0413844i | −0.853832 | − | 0.520549i | \(-0.825727\pi\) |
0.877725 | + | 0.479165i | \(0.159060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.65989e8 | 0.827714 | 0.413857 | − | 0.910342i | \(-0.364181\pi\) | ||||
0.413857 | + | 0.910342i | \(0.364181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.04660e8i | 0.587772i | 0.955841 | + | 0.293886i | \(0.0949485\pi\) | ||||
−0.955841 | + | 0.293886i | \(0.905051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.11050e8 | − | 2.37320e8i | −0.589012 | − | 0.340066i | 0.175695 | − | 0.984445i | \(-0.443783\pi\) |
−0.764707 | + | 0.644379i | \(0.777116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.99609e8 | − | 8.65349e8i | −0.711091 | − | 1.23165i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.42112e7 | + | 1.11217e8i | 0.0901688 | + | 0.156177i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.50421e8 | − | 1.44580e8i | −0.349302 | − | 0.201670i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 8.78754e7i | − | 0.120945i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.07829e8 | −0.967729 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.52997e7 | + | 6.11409e7i | −0.0476240 | + | 0.0824872i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.47026e8 | + | 3.73561e8i | −0.867162 | + | 0.500656i | −0.866404 | − | 0.499344i | \(-0.833574\pi\) |
−0.000757622 | 1.00000i | \(0.500241\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.93280e8 | + | 1.69325e8i | −0.387907 | + | 0.223958i | −0.681253 | − | 0.732048i | \(-0.738565\pi\) |
0.293346 | + | 0.956006i | \(0.405231\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.66141e8 | − | 1.32700e9i | 1.00669 | − | 1.74364i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.19620e8 | −0.673872 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.27845e8i | 0.680080i | 0.940411 | + | 0.340040i | \(0.110441\pi\) | ||||
−0.940411 | + | 0.340040i | \(0.889559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.30957e7 | − | 2.48813e7i | −0.0548061 | − | 0.0316423i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.36911e9 | − | 2.37137e9i | −1.72987 | − | 2.99623i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.14026e8 | + | 3.70703e8i | 0.266943 | + | 0.462359i | 0.968071 | − | 0.250677i | \(-0.0806531\pi\) |
−0.701128 | + | 0.713036i | \(0.747320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.13707e6 | − | 656487.i | −0.00140909 | − | 0.000813537i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.18034e9i | − | 2.66741i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.26186e9 | −1.53389 | −0.766945 | − | 0.641713i | \(-0.778224\pi\) | ||||
−0.766945 | + | 0.641713i | \(0.778224\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.21493e8 | − | 7.30047e8i | 0.505850 | − | 0.876158i | −0.494127 | − | 0.869390i | \(-0.664512\pi\) |
0.999977 | − | 0.00676797i | \(-0.00215433\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.07942e9 | − | 1.20056e9i | 2.47975 | − | 1.43168i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.87771e7 | + | 5.70290e7i | −0.116307 | + | 0.0671500i | −0.557025 | − | 0.830496i | \(-0.688057\pi\) |
0.440718 | + | 0.897646i | \(0.354724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.34068e8 | − | 4.05419e8i | 0.273870 | − | 0.474357i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.92357e8 | 0.337781 | 0.168890 | − | 0.985635i | \(-0.445982\pi\) | ||||
0.168890 | + | 0.985635i | \(0.445982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50913e8i | 0.173267i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.09274e8 | + | 5.24970e8i | 1.03095 | + | 0.595221i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.23198e8 | − | 2.13386e8i | −0.138814 | − | 0.240434i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.34902e9 | − | 2.33657e9i | −1.50119 | − | 2.60014i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.26838e8 | + | 3.61905e8i | 0.693227 | + | 0.400235i | 0.804820 | − | 0.593519i | \(-0.202262\pi\) |
−0.111593 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.27074e8i | 0.684954i | 0.939526 | + | 0.342477i | \(0.111266\pi\) | ||||
−0.939526 | + | 0.342477i | \(0.888734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.25468e9 | 1.36206 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.56152e7 | − | 1.13649e8i | 0.0703592 | − | 0.121866i | −0.828700 | − | 0.559694i | \(-0.810919\pi\) |
0.899059 | + | 0.437828i | \(0.144252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.74894e8 | − | 4.47385e8i | 0.825836 | − | 0.476797i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.40095e9 | − | 8.08836e8i | 1.47489 | − | 0.851530i | 0.475294 | − | 0.879827i | \(-0.342342\pi\) |
0.999600 | + | 0.0282964i | \(0.00900821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.35580e8 | − | 4.08036e8i | 0.246507 | − | 0.426962i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.20058e9 | 1.24109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.35082e9i | 1.38796i | 0.719993 | + | 0.693981i | \(0.244145\pi\) | ||||
−0.719993 | + | 0.693981i | \(0.755855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.86179e8 | − | 4.53901e8i | −0.798090 | − | 0.460778i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.05565e8 | + | 7.02459e8i | 0.409237 | + | 0.708819i | 0.994804 | − | 0.101805i | \(-0.0324617\pi\) |
−0.585568 | + | 0.810624i | \(0.699128\pi\) | |||||||
\(998\) | 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 | 432.7.o.c.415.1 | 24 | ||
3.2 | odd | 2 | 144.7.o.a.31.11 | ✓ | 24 | ||
4.3 | odd | 2 | 432.7.o.b.415.1 | 24 | |||
9.2 | odd | 6 | 144.7.o.c.79.2 | yes | 24 | ||
9.7 | even | 3 | 432.7.o.b.127.1 | 24 | |||
12.11 | even | 2 | 144.7.o.c.31.2 | yes | 24 | ||
36.7 | odd | 6 | inner | 432.7.o.c.127.1 | 24 | ||
36.11 | even | 6 | 144.7.o.a.79.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.7.o.a.31.11 | ✓ | 24 | 3.2 | odd | 2 | ||
144.7.o.a.79.11 | yes | 24 | 36.11 | even | 6 | ||
144.7.o.c.31.2 | yes | 24 | 12.11 | even | 2 | ||
144.7.o.c.79.2 | yes | 24 | 9.2 | odd | 6 | ||
432.7.o.b.127.1 | 24 | 9.7 | even | 3 | |||
432.7.o.b.415.1 | 24 | 4.3 | odd | 2 | |||
432.7.o.c.127.1 | 24 | 36.7 | odd | 6 | inner | ||
432.7.o.c.415.1 | 24 | 1.1 | even | 1 | trivial |