Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.30 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.11 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.10319i | 1.02580i | 0.858449 | + | 0.512899i | \(0.171429\pi\) | ||||
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.836195 | −0.0522622 | ||||||||
\(5\) | 39.6276 | 1.58510 | 0.792551 | − | 0.609805i | \(-0.208752\pi\) | ||||
0.792551 | + | 0.609805i | \(0.208752\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −85.8400 | −1.75184 | −0.875918 | − | 0.482459i | \(-0.839744\pi\) | ||||
−0.875918 | + | 0.482459i | \(0.839744\pi\) | |||||||
\(8\) | 62.2200i | 0.972188i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 162.600i | 1.62600i | ||||||||
\(11\) | − | 68.0678i | − | 0.562544i | −0.959628 | − | 0.281272i | \(-0.909244\pi\) | ||
0.959628 | − | 0.281272i | \(-0.0907563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 254.341i | − | 1.50498i | −0.658605 | − | 0.752489i | \(-0.728853\pi\) | ||
0.658605 | − | 0.752489i | \(-0.271147\pi\) | |||||||
\(14\) | − | 352.218i | − | 1.79703i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −268.680 | −1.04953 | ||||||||
\(17\) | −229.593 | −0.794440 | −0.397220 | − | 0.917724i | \(-0.630025\pi\) | ||||
−0.397220 | + | 0.917724i | \(0.630025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 425.861 | 1.17967 | 0.589836 | − | 0.807523i | \(-0.299193\pi\) | ||||
0.589836 | + | 0.807523i | \(0.299193\pi\) | |||||||
\(20\) | −33.1364 | −0.0828409 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 279.295 | 0.577056 | ||||||||
\(23\) | − | 954.505i | − | 1.80436i | −0.431363 | − | 0.902178i | \(-0.641967\pi\) | ||
0.431363 | − | 0.902178i | \(-0.358033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 945.343 | 1.51255 | ||||||||
\(26\) | 1043.61 | 1.54380 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 71.7790 | 0.0915548 | ||||||||
\(29\) | 396.928 | 0.471971 | 0.235986 | − | 0.971757i | \(-0.424168\pi\) | ||||
0.235986 | + | 0.971757i | \(0.424168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1421.82i | 1.47952i | 0.672871 | + | 0.739760i | \(0.265061\pi\) | ||||
−0.672871 | + | 0.739760i | \(0.734939\pi\) | |||||||
\(32\) | − | 106.925i | − | 0.104419i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 942.065i | − | 0.814935i | ||||||
\(35\) | −3401.63 | −2.77684 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 996.969i | − | 0.728246i | −0.931351 | − | 0.364123i | \(-0.881369\pi\) | ||
0.931351 | − | 0.364123i | \(-0.118631\pi\) | |||||||
\(38\) | 1747.39i | 1.21010i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2465.63i | 1.54102i | ||||||||
\(41\) | 1020.06 | 0.606817 | 0.303408 | − | 0.952861i | \(-0.401875\pi\) | ||||
0.303408 | + | 0.952861i | \(0.401875\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2587.59i | − | 1.39945i | −0.714410 | − | 0.699727i | \(-0.753305\pi\) | ||
0.714410 | − | 0.699727i | \(-0.246695\pi\) | |||||||
\(44\) | 56.9180i | 0.0293998i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3916.52 | 1.85091 | ||||||||
\(47\) | − | 1477.61i | − | 0.668905i | −0.942413 | − | 0.334452i | \(-0.891449\pi\) | ||
0.942413 | − | 0.334452i | \(-0.108551\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4967.50 | 2.06893 | ||||||||
\(50\) | 3878.93i | 1.55157i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 212.679i | 0.0786535i | ||||||||
\(53\) | 3156.03 | 1.12354 | 0.561770 | − | 0.827293i | \(-0.310120\pi\) | ||||
0.561770 | + | 0.827293i | \(0.310120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2697.36i | − | 0.891689i | ||||||
\(56\) | − | 5340.97i | − | 1.70311i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1628.67i | 0.484147i | ||||||||
\(59\) | −3480.96 | + | 16.5981i | −0.999989 | + | 0.00476820i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2170.20i | − | 0.583230i | −0.956536 | − | 0.291615i | \(-0.905807\pi\) | ||
0.956536 | − | 0.291615i | \(-0.0941927\pi\) | |||||||
\(62\) | −5834.00 | −1.51769 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3860.14 | −0.942418 | ||||||||
\(65\) | − | 10078.9i | − | 2.38554i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 667.653i | − | 0.148731i | −0.997231 | − | 0.0743655i | \(-0.976307\pi\) | ||
0.997231 | − | 0.0743655i | \(-0.0236931\pi\) | |||||||
\(68\) | 191.985 | 0.0415192 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 13957.5i | − | 2.84848i | ||||||
\(71\) | 2586.30 | 0.513054 | 0.256527 | − | 0.966537i | \(-0.417422\pi\) | ||||
0.256527 | + | 0.966537i | \(0.417422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1200.66i | − | 0.225306i | −0.993634 | − | 0.112653i | \(-0.964065\pi\) | ||
0.993634 | − | 0.112653i | \(-0.0359349\pi\) | |||||||
\(74\) | 4090.76 | 0.747034 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −356.103 | −0.0616522 | ||||||||
\(77\) | 5842.94i | 0.985485i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1243.99 | −0.199325 | −0.0996626 | − | 0.995021i | \(-0.531776\pi\) | ||||
−0.0996626 | + | 0.995021i | \(0.531776\pi\) | |||||||
\(80\) | −10647.1 | −1.66361 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4185.50i | 0.622471i | ||||||||
\(83\) | − | 6111.54i | − | 0.887145i | −0.896239 | − | 0.443572i | \(-0.853711\pi\) | ||
0.896239 | − | 0.443572i | \(-0.146289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9098.21 | −1.25927 | ||||||||
\(86\) | 10617.4 | 1.43556 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4235.18 | 0.546898 | ||||||||
\(89\) | − | 12034.3i | − | 1.51929i | −0.650340 | − | 0.759643i | \(-0.725374\pi\) | ||
0.650340 | − | 0.759643i | \(-0.274626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21832.7i | 2.63648i | ||||||||
\(92\) | 798.152i | 0.0942997i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6062.92 | 0.686161 | ||||||||
\(95\) | 16875.8 | 1.86990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16943.5i | 1.80078i | 0.435085 | + | 0.900389i | \(0.356718\pi\) | ||||
−0.435085 | + | 0.900389i | \(0.643282\pi\) | |||||||
\(98\) | 20382.6i | 2.12231i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −790.492 | −0.0790492 | ||||||||
\(101\) | − | 8659.11i | − | 0.848849i | −0.905463 | − | 0.424424i | \(-0.860476\pi\) | ||
0.905463 | − | 0.424424i | \(-0.139524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1183.70i | − | 0.111575i | −0.998443 | − | 0.0557873i | \(-0.982233\pi\) | ||
0.998443 | − | 0.0557873i | \(-0.0177669\pi\) | |||||||
\(104\) | 15825.1 | 1.46312 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12949.8i | 1.15253i | ||||||||
\(107\) | −11910.3 | −1.04029 | −0.520145 | − | 0.854078i | \(-0.674122\pi\) | ||||
−0.520145 | + | 0.854078i | \(0.674122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5882.90i | 0.495152i | 0.968868 | + | 0.247576i | \(0.0796340\pi\) | ||||
−0.968868 | + | 0.247576i | \(0.920366\pi\) | |||||||
\(110\) | 11067.8 | 0.914693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 23063.5 | 1.83861 | ||||||||
\(113\) | 21194.2i | 1.65982i | 0.557900 | + | 0.829908i | \(0.311607\pi\) | ||||
−0.557900 | + | 0.829908i | \(0.688393\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 37824.7i | − | 2.86009i | ||||||
\(116\) | −331.909 | −0.0246663 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −68.1052 | − | 14283.1i | −0.00489121 | − | 1.02579i | ||||
\(119\) | 19708.3 | 1.39173 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10007.8 | 0.683545 | ||||||||
\(122\) | 8904.75 | 0.598277 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1188.92i | − | 0.0773230i | ||||||
\(125\) | 12694.4 | 0.812443 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26800.6 | 1.66164 | 0.830820 | − | 0.556541i | \(-0.187872\pi\) | ||||
0.830820 | + | 0.556541i | \(0.187872\pi\) | |||||||
\(128\) | − | 17549.7i | − | 1.07115i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 41355.8 | 2.44709 | ||||||||
\(131\) | − | 1959.64i | − | 0.114192i | −0.998369 | − | 0.0570958i | \(-0.981816\pi\) | ||
0.998369 | − | 0.0570958i | \(-0.0181840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36555.9 | −2.06659 | ||||||||
\(134\) | 2739.51 | 0.152568 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 14285.3i | − | 0.772345i | ||||||
\(137\) | 3510.97 | 0.187062 | 0.0935310 | − | 0.995616i | \(-0.470185\pi\) | ||||
0.0935310 | + | 0.995616i | \(0.470185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8435.85 | −0.436616 | −0.218308 | − | 0.975880i | \(-0.570054\pi\) | ||||
−0.218308 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(140\) | 2844.43 | 0.145124 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10612.1i | 0.526290i | ||||||||
\(143\) | −17312.4 | −0.846616 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15729.3 | 0.748123 | ||||||||
\(146\) | 4926.52 | 0.231119 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 833.661i | 0.0380597i | ||||||||
\(149\) | − | 25735.7i | − | 1.15921i | −0.814896 | − | 0.579607i | \(-0.803206\pi\) | ||
0.814896 | − | 0.579607i | \(-0.196794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13763.3i | 0.603628i | 0.953367 | + | 0.301814i | \(0.0975921\pi\) | ||||
−0.953367 | + | 0.301814i | \(0.902408\pi\) | |||||||
\(152\) | 26497.1i | 1.14686i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −23974.7 | −1.01091 | ||||||||
\(155\) | 56343.2i | 2.34519i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5484.96i | 0.222523i | 0.993791 | + | 0.111261i | \(0.0354891\pi\) | ||||
−0.993791 | + | 0.111261i | \(0.964511\pi\) | |||||||
\(158\) | − | 5104.33i | − | 0.204467i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 4237.19i | − | 0.165515i | ||||||
\(161\) | 81934.7i | 3.16094i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 137.440 | 0.00517295 | 0.00258648 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258648 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(164\) | −852.968 | −0.0317136 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25076.8 | 0.910032 | ||||||||
\(167\) | 4707.17 | 0.168782 | 0.0843911 | − | 0.996433i | \(-0.473105\pi\) | ||||
0.0843911 | + | 0.996433i | \(0.473105\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −36128.5 | −1.26496 | ||||||||
\(170\) | − | 37331.7i | − | 1.29176i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2163.73i | 0.0731386i | ||||||||
\(173\) | − | 25132.5i | − | 0.839737i | −0.907585 | − | 0.419869i | \(-0.862076\pi\) | ||
0.907585 | − | 0.419869i | \(-0.137924\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −81148.3 | −2.64974 | ||||||||
\(176\) | 18288.4i | 0.590407i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 49378.9 | 1.55848 | ||||||||
\(179\) | − | 16585.2i | − | 0.517623i | −0.965928 | − | 0.258811i | \(-0.916669\pi\) | ||
0.965928 | − | 0.258811i | \(-0.0833308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 51985.4 | 1.58681 | 0.793404 | − | 0.608695i | \(-0.208307\pi\) | ||||
0.793404 | + | 0.608695i | \(0.208307\pi\) | |||||||
\(182\) | −89583.6 | −2.70449 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 59389.3 | 1.75417 | ||||||||
\(185\) | − | 39507.4i | − | 1.15434i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15627.9i | 0.446907i | ||||||||
\(188\) | 1235.57i | 0.0349584i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 69244.8i | 1.91814i | ||||||||
\(191\) | 39194.8i | 1.07439i | 0.843458 | + | 0.537195i | \(0.180516\pi\) | ||||
−0.843458 | + | 0.537195i | \(0.819484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 36220.3 | 0.972384 | 0.486192 | − | 0.873852i | \(-0.338386\pi\) | ||||
0.486192 | + | 0.873852i | \(0.338386\pi\) | |||||||
\(194\) | −69522.6 | −1.84724 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4153.80 | −0.108127 | ||||||||
\(197\) | −37466.1 | −0.965396 | −0.482698 | − | 0.875787i | \(-0.660343\pi\) | ||||
−0.482698 | + | 0.875787i | \(0.660343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −76403.0 | −1.92932 | −0.964660 | − | 0.263497i | \(-0.915124\pi\) | ||||
−0.964660 | + | 0.263497i | \(0.915124\pi\) | |||||||
\(200\) | 58819.3i | 1.47048i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 35530.0 | 0.870748 | ||||||||
\(203\) | −34072.3 | −0.826817 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40422.4 | 0.961866 | ||||||||
\(206\) | 4856.93 | 0.114453 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 68336.4i | 1.57952i | ||||||||
\(209\) | − | 28987.4i | − | 0.663616i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24399.1i | − | 0.548036i | −0.961725 | − | 0.274018i | \(-0.911647\pi\) | ||
0.961725 | − | 0.274018i | \(-0.0883527\pi\) | |||||||
\(212\) | −2639.05 | −0.0587187 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 48870.2i | − | 1.06713i | ||||||
\(215\) | − | 102540.i | − | 2.21828i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 122049.i | − | 2.59188i | ||||||
\(218\) | −24138.7 | −0.507926 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2255.52i | 0.0466016i | ||||||||
\(221\) | 58395.0i | 1.19561i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26520.0 | −0.533290 | −0.266645 | − | 0.963795i | \(-0.585915\pi\) | ||||
−0.266645 | + | 0.963795i | \(0.585915\pi\) | |||||||
\(224\) | 9178.46i | 0.182925i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −86963.9 | −1.70264 | ||||||||
\(227\) | − | 71618.1i | − | 1.38986i | −0.719077 | − | 0.694930i | \(-0.755435\pi\) | ||
0.719077 | − | 0.694930i | \(-0.244565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 42669.2i | 0.813660i | 0.913504 | + | 0.406830i | \(0.133366\pi\) | ||||
−0.913504 | + | 0.406830i | \(0.866634\pi\) | |||||||
\(230\) | 155202. | 2.93388 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24696.9i | 0.458845i | ||||||||
\(233\) | − | 68586.1i | − | 1.26335i | −0.775233 | − | 0.631676i | \(-0.782367\pi\) | ||
0.775233 | − | 0.631676i | \(-0.217633\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 58554.1i | − | 1.06028i | ||||||
\(236\) | 2910.76 | − | 13.8793i | 0.0522616 | − | 0.000249197i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 80866.8i | 1.42763i | ||||||||
\(239\) | −963.908 | −0.0168749 | −0.00843743 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843743 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16329.4 | 0.281149 | 0.140574 | − | 0.990070i | \(-0.455105\pi\) | ||||
0.140574 | + | 0.990070i | \(0.455105\pi\) | |||||||
\(242\) | 41063.8i | 0.701179i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1814.71i | 0.0304809i | ||||||||
\(245\) | 196850. | 3.27947 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 108314.i | − | 1.77538i | ||||||
\(248\) | −88465.6 | −1.43837 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 52087.7i | 0.833403i | ||||||||
\(251\) | −57856.7 | −0.918346 | −0.459173 | − | 0.888347i | \(-0.651854\pi\) | ||||
−0.459173 | + | 0.888347i | \(0.651854\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −64971.0 | −1.01503 | ||||||||
\(254\) | 109968.i | 1.70451i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10247.6 | 0.156366 | ||||||||
\(257\) | 94257.4 | 1.42708 | 0.713542 | − | 0.700613i | \(-0.247090\pi\) | ||||
0.713542 | + | 0.700613i | \(0.247090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 85579.8i | 1.27577i | ||||||||
\(260\) | 8427.95i | 0.124674i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8040.79 | 0.117137 | ||||||||
\(263\) | −6388.77 | −0.0923646 | −0.0461823 | − | 0.998933i | \(-0.514706\pi\) | ||||
−0.0461823 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 125066. | 1.78093 | ||||||||
\(266\) | − | 149996.i | − | 2.11991i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 558.288i | 0.00777301i | ||||||||
\(269\) | 50975.4i | 0.704460i | 0.935914 | + | 0.352230i | \(0.114576\pi\) | ||||
−0.935914 | + | 0.352230i | \(0.885424\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 103419. | 1.40820 | 0.704098 | − | 0.710103i | \(-0.251352\pi\) | ||||
0.704098 | + | 0.710103i | \(0.251352\pi\) | |||||||
\(272\) | 61687.0 | 0.833789 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14406.2i | 0.191888i | ||||||||
\(275\) | − | 64347.4i | − | 0.850875i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −118682. | −1.54676 | −0.773381 | − | 0.633941i | \(-0.781436\pi\) | ||||
−0.773381 | + | 0.633941i | \(0.781436\pi\) | |||||||
\(278\) | − | 34613.9i | − | 0.447879i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 211649.i | − | 2.69961i | ||||||
\(281\) | 63690.0 | 0.806600 | 0.403300 | − | 0.915068i | \(-0.367863\pi\) | ||||
0.403300 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7522.96i | 0.0939325i | 0.998896 | + | 0.0469662i | \(0.0149553\pi\) | ||||
−0.998896 | + | 0.0469662i | \(0.985045\pi\) | |||||||
\(284\) | −2162.66 | −0.0268133 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 71036.3i | − | 0.868457i | ||||||
\(287\) | −87561.8 | −1.06304 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30808.0 | −0.368866 | ||||||||
\(290\) | 64540.3i | 0.767423i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1003.98i | 0.0117750i | ||||||||
\(293\) | 32964.4 | 0.383981 | 0.191990 | − | 0.981397i | \(-0.438506\pi\) | ||||
0.191990 | + | 0.981397i | \(0.438506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −137942. | + | 657.742i | −1.58508 | + | 0.00755809i | ||||
\(296\) | 62031.4 | 0.707992 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 105599. | 1.18912 | ||||||||
\(299\) | −242770. | −2.71552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 222119.i | 2.45162i | ||||||||
\(302\) | −56473.5 | −0.619200 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −114420. | −1.23810 | ||||||||
\(305\) | − | 85999.7i | − | 0.924480i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −85864.5 | −0.911039 | −0.455520 | − | 0.890226i | \(-0.650547\pi\) | ||||
−0.455520 | + | 0.890226i | \(0.650547\pi\) | |||||||
\(308\) | − | 4885.84i | − | 0.0515036i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −231187. | −2.40569 | ||||||||
\(311\) | 20927.4 | 0.216368 | 0.108184 | − | 0.994131i | \(-0.465496\pi\) | ||||
0.108184 | + | 0.994131i | \(0.465496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 132516.i | − | 1.35264i | −0.736610 | − | 0.676318i | \(-0.763575\pi\) | ||
0.736610 | − | 0.676318i | \(-0.236425\pi\) | |||||||
\(314\) | −22505.9 | −0.228263 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1040.22 | 0.0104172 | ||||||||
\(317\) | 108659. | 1.08130 | 0.540649 | − | 0.841248i | \(-0.318179\pi\) | ||||
0.540649 | + | 0.841248i | \(0.318179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27018.0i | − | 0.265504i | ||||||
\(320\) | −152968. | −1.49383 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −336194. | −3.24249 | ||||||||
\(323\) | −97774.8 | −0.937177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 240440.i | − | 2.27635i | ||||||
\(326\) | 563.944i | 0.00530641i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 63468.1i | 0.589940i | ||||||||
\(329\) | 126838.i | 1.17181i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −101850. | −0.929619 | −0.464809 | − | 0.885411i | \(-0.653877\pi\) | ||||
−0.464809 | + | 0.885411i | \(0.653877\pi\) | |||||||
\(332\) | 5110.44i | 0.0463641i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19314.4i | 0.173137i | ||||||||
\(335\) | − | 26457.5i | − | 0.235754i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 74871.2i | − | 0.659258i | −0.944111 | − | 0.329629i | \(-0.893076\pi\) | ||
0.944111 | − | 0.329629i | \(-0.106924\pi\) | |||||||
\(338\) | − | 148242.i | − | 1.29759i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7607.88 | 0.0658121 | ||||||||
\(341\) | 96780.0 | 0.832294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −220309. | −1.87259 | ||||||||
\(344\) | 161000. | 1.36053 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 103123. | 0.861401 | ||||||||
\(347\) | 90583.5i | 0.752298i | 0.926559 | + | 0.376149i | \(0.122752\pi\) | ||||
−0.926559 | + | 0.376149i | \(0.877248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 134492.i | 1.10420i | 0.833779 | + | 0.552098i | \(0.186172\pi\) | ||||
−0.833779 | + | 0.552098i | \(0.813828\pi\) | |||||||
\(350\) | − | 332967.i | − | 2.71810i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7278.16 | −0.0587403 | ||||||||
\(353\) | − | 81414.3i | − | 0.653358i | −0.945135 | − | 0.326679i | \(-0.894070\pi\) | ||
0.945135 | − | 0.326679i | \(-0.105930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 102489. | 0.813243 | ||||||||
\(356\) | 10063.0i | 0.0794013i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 68052.1 | 0.530977 | ||||||||
\(359\) | −64385.0 | −0.499570 | −0.249785 | − | 0.968301i | \(-0.580360\pi\) | ||||
−0.249785 | + | 0.968301i | \(0.580360\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51036.8 | 0.391624 | ||||||||
\(362\) | 213306.i | 1.62775i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 18256.4i | − | 0.137788i | ||||||
\(365\) | − | 47579.1i | − | 0.357133i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 129178.i | 0.959083i | 0.877519 | + | 0.479541i | \(0.159197\pi\) | ||||
−0.877519 | + | 0.479541i | \(0.840803\pi\) | |||||||
\(368\) | 256456.i | 1.89373i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 162107. | 1.18412 | ||||||||
\(371\) | −270913. | −1.96826 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −71866.8 | −0.516548 | −0.258274 | − | 0.966072i | \(-0.583154\pi\) | ||||
−0.258274 | + | 0.966072i | \(0.583154\pi\) | |||||||
\(374\) | −64124.3 | −0.458436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 91936.9 | 0.650301 | ||||||||
\(377\) | − | 100955.i | − | 0.710306i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 85467.7 | 0.595009 | 0.297504 | − | 0.954720i | \(-0.403846\pi\) | ||||
0.297504 | + | 0.954720i | \(0.403846\pi\) | |||||||
\(380\) | −14111.5 | −0.0977251 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −160824. | −1.10211 | ||||||||
\(383\) | −278371. | −1.89769 | −0.948846 | − | 0.315739i | \(-0.897747\pi\) | ||||
−0.948846 | + | 0.315739i | \(0.897747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 231541.i | 1.56209i | ||||||||
\(386\) | 148619.i | 0.997470i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 14168.1i | − | 0.0941127i | ||||||
\(389\) | 21226.2 | 0.140273 | 0.0701364 | − | 0.997537i | \(-0.477657\pi\) | ||||
0.0701364 | + | 0.997537i | \(0.477657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 219148.i | 1.43345i | ||||||||
\(392\) | 309078.i | 2.01139i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 153731.i | − | 0.990302i | ||||||
\(395\) | −49296.2 | −0.315951 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45611.1i | 0.289394i | 0.989476 | + | 0.144697i | \(0.0462208\pi\) | ||||
−0.989476 | + | 0.144697i | \(0.953779\pi\) | |||||||
\(398\) | − | 313496.i | − | 1.97909i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −253995. | −1.58747 | ||||||||
\(401\) | − | 56817.4i | − | 0.353340i | −0.984270 | − | 0.176670i | \(-0.943468\pi\) | ||
0.984270 | − | 0.176670i | \(-0.0565325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 361627. | 2.22664 | ||||||||
\(404\) | 7240.70i | 0.0443627i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 139805.i | − | 0.848147i | ||||||
\(407\) | −67861.5 | −0.409670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 152246.i | 0.910123i | 0.890460 | + | 0.455061i | \(0.150383\pi\) | ||||
−0.890460 | + | 0.455061i | \(0.849617\pi\) | |||||||
\(410\) | 165861.i | 0.986681i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 989.801i | 0.00583114i | ||||||||
\(413\) | 298806. | − | 1424.78i | 1.75182 | − | 0.00835311i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 242185.i | − | 1.40622i | ||||||
\(416\) | −27195.5 | −0.157149 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 118941. | 0.680737 | ||||||||
\(419\) | − | 14956.8i | − | 0.0851945i | −0.999092 | − | 0.0425972i | \(-0.986437\pi\) | ||
0.999092 | − | 0.0425972i | \(-0.0135632\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 192146.i | 1.08410i | 0.840347 | + | 0.542048i | \(0.182351\pi\) | ||||
−0.840347 | + | 0.542048i | \(0.817649\pi\) | |||||||
\(422\) | 100114. | 0.562174 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 196368.i | 1.09229i | ||||||||
\(425\) | −217044. | −1.20163 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186290.i | 1.02172i | ||||||||
\(428\) | 9959.31 | 0.0543678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 420741. | 2.27551 | ||||||||
\(431\) | − | 134989.i | − | 0.726679i | −0.931657 | − | 0.363340i | \(-0.881636\pi\) | ||
0.931657 | − | 0.363340i | \(-0.118364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27732.6 | −0.147916 | −0.0739580 | − | 0.997261i | \(-0.523563\pi\) | ||||
−0.0739580 | + | 0.997261i | \(0.523563\pi\) | |||||||
\(434\) | 500790. | 2.65874 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4919.25i | − | 0.0258777i | ||||||
\(437\) | − | 406487.i | − | 2.12855i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −256732. | −1.33215 | −0.666073 | − | 0.745887i | \(-0.732026\pi\) | ||||
−0.666073 | + | 0.745887i | \(0.732026\pi\) | |||||||
\(440\) | 167830. | 0.866889 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −239606. | −1.22646 | ||||||||
\(443\) | − | 104213.i | − | 0.531022i | −0.964108 | − | 0.265511i | \(-0.914459\pi\) | ||
0.964108 | − | 0.265511i | \(-0.0855407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 476889.i | − | 2.40822i | ||||||
\(446\) | − | 108817.i | − | 0.547048i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 331355. | 1.65096 | ||||||||
\(449\) | −15237.3 | −0.0755814 | −0.0377907 | − | 0.999286i | \(-0.512032\pi\) | ||||
−0.0377907 | + | 0.999286i | \(0.512032\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 69433.1i | − | 0.341361i | ||||||
\(452\) | − | 17722.5i | − | 0.0867457i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 293863. | 1.42572 | ||||||||
\(455\) | 865175.i | 4.17908i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 351744.i | − | 1.68420i | −0.539318 | − | 0.842102i | \(-0.681318\pi\) | ||
0.539318 | − | 0.842102i | \(-0.318682\pi\) | |||||||
\(458\) | −175080. | −0.834651 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 31628.8i | 0.149475i | ||||||||
\(461\) | 91900.9 | 0.432432 | 0.216216 | − | 0.976346i | \(-0.430628\pi\) | ||||
0.216216 | + | 0.976346i | \(0.430628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 284633.i | 1.32777i | 0.747835 | + | 0.663885i | \(0.231093\pi\) | ||||
−0.747835 | + | 0.663885i | \(0.768907\pi\) | |||||||
\(464\) | −106647. | −0.495348 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 281422. | 1.29594 | ||||||||
\(467\) | 304437.i | 1.39593i | 0.716132 | + | 0.697965i | \(0.245911\pi\) | ||||
−0.716132 | + | 0.697965i | \(0.754089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 57311.3i | 0.260552i | ||||||||
\(470\) | 240259. | 1.08764 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1032.73 | − | 216585.i | −0.00463559 | − | 0.972177i | ||||
\(473\) | −176132. | −0.787254 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 402585. | 1.78431 | ||||||||
\(476\) | −16480.0 | −0.0727348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 3955.10i | − | 0.0173102i | ||||||
\(479\) | −397464. | −1.73231 | −0.866157 | − | 0.499772i | \(-0.833417\pi\) | ||||
−0.866157 | + | 0.499772i | \(0.833417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −253570. | −1.09599 | ||||||||
\(482\) | 67002.7i | 0.288402i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8368.46 | −0.0357235 | ||||||||
\(485\) | 671431.i | 2.85442i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −157762. | −0.665187 | −0.332593 | − | 0.943070i | \(-0.607924\pi\) | ||||
−0.332593 | + | 0.943070i | \(0.607924\pi\) | |||||||
\(488\) | 135030. | 0.567010 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 807714.i | 3.36407i | ||||||||
\(491\) | −76943.9 | −0.319162 | −0.159581 | − | 0.987185i | \(-0.551014\pi\) | ||||
−0.159581 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −91131.9 | −0.374953 | ||||||||
\(494\) | 444434. | 1.82118 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 382014.i | − | 1.55280i | ||||||
\(497\) | −222008. | −0.898787 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1118.26 | 0.00449100 | 0.00224550 | − | 0.999997i | \(-0.499285\pi\) | ||||
0.00224550 | + | 0.999997i | \(0.499285\pi\) | |||||||
\(500\) | −10615.0 | −0.0424601 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 237397.i | − | 0.942038i | ||||||
\(503\) | 143292.i | 0.566351i | 0.959068 | + | 0.283176i | \(0.0913879\pi\) | ||||
−0.959068 | + | 0.283176i | \(0.908612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 343139.i | − | 1.34551i | ||||||
\(506\) | − | 266589.i | − | 1.04122i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22410.5 | −0.0868410 | ||||||||
\(509\) | − | 39802.5i | − | 0.153630i | −0.997045 | − | 0.0768148i | \(-0.975525\pi\) | ||
0.997045 | − | 0.0768148i | \(-0.0244750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 103064.i | 0.394699i | ||||||||
\(512\) | − | 238748.i | − | 0.910750i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 386756.i | 1.46390i | ||||||||
\(515\) | − | 46907.0i | − | 0.176857i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −100578. | −0.376288 | ||||||||
\(518\) | −351150. | −1.30868 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 627111. | 2.31920 | ||||||||
\(521\) | 228531. | 0.841917 | 0.420958 | − | 0.907080i | \(-0.361694\pi\) | ||||
0.420958 | + | 0.907080i | \(0.361694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 508793. | 1.86011 | 0.930054 | − | 0.367423i | \(-0.119760\pi\) | ||||
0.930054 | + | 0.367423i | \(0.119760\pi\) | |||||||
\(524\) | 1638.64i | 0.00596790i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 26214.4i | − | 0.0947475i | ||||||
\(527\) | − | 326440.i | − | 1.17539i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −631238. | −2.25570 | ||||||||
\(530\) | 513168.i | 1.82687i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30567.9 | 0.108005 | ||||||||
\(533\) | − | 259443.i | − | 0.913246i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −471975. | −1.64897 | ||||||||
\(536\) | 41541.4 | 0.144594 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −209162. | −0.722634 | ||||||||
\(539\) | − | 338127.i | − | 1.16386i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 560174.i | − | 1.91394i | −0.290187 | − | 0.956970i | \(-0.593718\pi\) | ||
0.290187 | − | 0.956970i | \(-0.406282\pi\) | |||||||
\(542\) | 424349.i | 1.44452i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24549.3i | 0.0829547i | ||||||||
\(545\) | 233125.i | 0.784867i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −273979. | −0.915679 | −0.457839 | − | 0.889035i | \(-0.651377\pi\) | ||||
−0.457839 | + | 0.889035i | \(0.651377\pi\) | |||||||
\(548\) | −2935.85 | −0.00977627 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 264030. | 0.872826 | ||||||||
\(551\) | 169036. | 0.556771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 106784. | 0.349185 | ||||||||
\(554\) | − | 486973.i | − | 1.58667i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7054.02 | 0.0228185 | ||||||||
\(557\) | −339532. | −1.09439 | −0.547193 | − | 0.837006i | \(-0.684304\pi\) | ||||
−0.547193 | + | 0.837006i | \(0.684304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −658131. | −2.10615 | ||||||||
\(560\) | 913949. | 2.91438 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 261332.i | 0.827409i | ||||||||
\(563\) | − | 92097.7i | − | 0.290558i | −0.989391 | − | 0.145279i | \(-0.953592\pi\) | ||
0.989391 | − | 0.145279i | \(-0.0464079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 839874.i | 2.63098i | ||||||||
\(566\) | −30868.1 | −0.0963558 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 160920.i | 0.498785i | ||||||||
\(569\) | 443913.i | 1.37111i | 0.728019 | + | 0.685557i | \(0.240441\pi\) | ||||
−0.728019 | + | 0.685557i | \(0.759559\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 254417.i | − | 0.780321i | −0.920747 | − | 0.390161i | \(-0.872419\pi\) | ||
0.920747 | − | 0.390161i | \(-0.127581\pi\) | |||||||
\(572\) | 14476.6 | 0.0442460 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 359283.i | − | 1.09047i | ||||||
\(575\) | − | 902335.i | − | 2.72918i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 311437. | 0.935445 | 0.467723 | − | 0.883875i | \(-0.345075\pi\) | ||||
0.467723 | + | 0.883875i | \(0.345075\pi\) | |||||||
\(578\) | − | 126411.i | − | 0.378382i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13152.8 | −0.0390985 | ||||||||
\(581\) | 524615.i | 1.55413i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 214824.i | − | 0.632041i | ||||||
\(584\) | 74704.8 | 0.219040 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 135259.i | 0.393887i | ||||||||
\(587\) | − | 581088.i | − | 1.68642i | −0.537584 | − | 0.843210i | \(-0.680663\pi\) | ||
0.537584 | − | 0.843210i | \(-0.319337\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 605497.i | 1.74535i | ||||||||
\(590\) | −2698.84 | − | 566003.i | −0.00775307 | − | 1.62598i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 267866.i | 0.764317i | ||||||||
\(593\) | 218284. | 0.620743 | 0.310371 | − | 0.950615i | \(-0.399547\pi\) | ||||
0.310371 | + | 0.950615i | \(0.399547\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 780990. | 2.20603 | ||||||||
\(596\) | 21520.1i | 0.0605830i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 996132.i | − | 2.78557i | ||||||
\(599\) | 549532. | 1.53158 | 0.765789 | − | 0.643091i | \(-0.222349\pi\) | ||||
0.765789 | + | 0.643091i | \(0.222349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 611697.i | 1.69351i | 0.531984 | + | 0.846755i | \(0.321447\pi\) | ||||
−0.531984 | + | 0.846755i | \(0.678553\pi\) | |||||||
\(602\) | −911397. | −2.51486 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 11508.8i | − | 0.0315469i | ||||||
\(605\) | 396584. | 1.08349 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1086.59 | 0.00294908 | 0.00147454 | − | 0.999999i | \(-0.499531\pi\) | ||||
0.00147454 | + | 0.999999i | \(0.499531\pi\) | |||||||
\(608\) | − | 45535.3i | − | 0.123180i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 352874. | 0.948330 | ||||||||
\(611\) | −375817. | −1.00669 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 331052.i | 0.880999i | 0.897753 | + | 0.440500i | \(0.145199\pi\) | ||||
−0.897753 | + | 0.440500i | \(0.854801\pi\) | |||||||
\(614\) | − | 352319.i | − | 0.934543i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −363548. | −0.958076 | ||||||||
\(617\) | 247255. | 0.649492 | 0.324746 | − | 0.945801i | \(-0.394721\pi\) | ||||
0.324746 | + | 0.945801i | \(0.394721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 307344. | 0.802127 | 0.401064 | − | 0.916050i | \(-0.368641\pi\) | ||||
0.401064 | + | 0.916050i | \(0.368641\pi\) | |||||||
\(620\) | − | 47113.9i | − | 0.122565i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 85869.1i | 0.221950i | ||||||||
\(623\) | 1.03302e6i | 2.66154i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −87790.4 | −0.224744 | ||||||||
\(626\) | 543740. | 1.38753 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4586.50i | − | 0.0116295i | ||||||
\(629\) | 228897.i | 0.578548i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 469556. | 1.17931 | 0.589657 | − | 0.807654i | \(-0.299263\pi\) | ||||
0.589657 | + | 0.807654i | \(0.299263\pi\) | |||||||
\(632\) | − | 77401.0i | − | 0.193782i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 445847.i | 1.10919i | ||||||||
\(635\) | 1.06204e6 | 2.63387 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.26344e6i | − | 3.11370i | ||||||
\(638\) | 110860. | 0.272354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 695453.i | − | 1.69788i | ||||||
\(641\) | −244837. | −0.595882 | −0.297941 | − | 0.954584i | \(-0.596300\pi\) | ||||
−0.297941 | + | 0.954584i | \(0.596300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −199751. | −0.483133 | −0.241567 | − | 0.970384i | \(-0.577661\pi\) | ||||
−0.241567 | + | 0.970384i | \(0.577661\pi\) | |||||||
\(644\) | − | 68513.4i | − | 0.165198i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 401189.i | − | 0.961355i | ||||||
\(647\) | −406276. | −0.970538 | −0.485269 | − | 0.874365i | \(-0.661278\pi\) | ||||
−0.485269 | + | 0.874365i | \(0.661278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1129.80 | + | 236941.i | 0.00268232 | + | 0.562537i | ||||
\(650\) | 986571. | 2.33508 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −114.927 | −0.000270350 | ||||||||
\(653\) | −334544. | −0.784562 | −0.392281 | − | 0.919845i | \(-0.628314\pi\) | ||||
−0.392281 | + | 0.919845i | \(0.628314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 77655.8i | − | 0.181005i | ||||||
\(656\) | −274069. | −0.636873 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −520441. | −1.20204 | ||||||||
\(659\) | − | 286185.i | − | 0.658986i | −0.944158 | − | 0.329493i | \(-0.893122\pi\) | ||
0.944158 | − | 0.329493i | \(-0.106878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 759053. | 1.73728 | 0.868639 | − | 0.495446i | \(-0.164995\pi\) | ||||
0.868639 | + | 0.495446i | \(0.164995\pi\) | |||||||
\(662\) | − | 417910.i | − | 0.953601i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 380260. | 0.862471 | ||||||||
\(665\) | −1.44862e6 | −3.27576 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 378870.i | − | 0.851605i | ||||||
\(668\) | −3936.11 | −0.00882093 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 108560. | 0.241836 | ||||||||
\(671\) | −147721. | −0.328093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 664503.i | 1.46712i | 0.679622 | + | 0.733562i | \(0.262144\pi\) | ||||
−0.679622 | + | 0.733562i | \(0.737856\pi\) | |||||||
\(674\) | 307211. | 0.676265 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30210.5 | 0.0661095 | ||||||||
\(677\) | 252653. | 0.551249 | 0.275624 | − | 0.961265i | \(-0.411115\pi\) | ||||
0.275624 | + | 0.961265i | \(0.411115\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.45443e6i | − | 3.15467i | ||||||
\(680\) | − | 566091.i | − | 1.22425i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 397107.i | 0.853766i | ||||||||
\(683\) | 506823.i | 1.08646i | 0.839583 | + | 0.543232i | \(0.182800\pi\) | ||||
−0.839583 | + | 0.543232i | \(0.817200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 139131. | 0.296512 | ||||||||
\(686\) | − | 903969.i | − | 1.92090i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 695234.i | 1.46877i | ||||||||
\(689\) | − | 802708.i | − | 1.69090i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 789140.i | 1.65271i | 0.563146 | + | 0.826357i | \(0.309591\pi\) | ||||
−0.563146 | + | 0.826357i | \(0.690409\pi\) | |||||||
\(692\) | 21015.7i | 0.0438865i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −371682. | −0.771706 | ||||||||
\(695\) | −334292. | −0.692080 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −234198. | −0.482079 | ||||||||
\(698\) | −551847. | −1.13268 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 67855.8 | 0.138481 | ||||||||
\(701\) | 259759.i | 0.528608i | 0.964439 | + | 0.264304i | \(0.0851423\pi\) | ||||
−0.964439 | + | 0.264304i | \(0.914858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 424570.i | − | 0.859091i | ||||||
\(704\) | 262751.i | 0.530151i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 334059. | 0.670213 | ||||||||
\(707\) | 743298.i | 1.48704i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 171973. | 0.342112 | 0.171056 | − | 0.985261i | \(-0.445282\pi\) | ||||
0.171056 | + | 0.985261i | \(0.445282\pi\) | |||||||
\(710\) | 420532.i | 0.834223i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 748772. | 1.47703 | ||||||||
\(713\) | 1.35713e6 | 2.66958 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −686050. | −1.34197 | ||||||||
\(716\) | 13868.4i | 0.0270521i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 264184.i | − | 0.512458i | ||||||
\(719\) | − | 823365.i | − | 1.59270i | −0.604835 | − | 0.796351i | \(-0.706761\pi\) | ||
0.604835 | − | 0.796351i | \(-0.293239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 101608.i | 0.195461i | ||||||||
\(722\) | 209414.i | 0.401727i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43470.0 | −0.0829301 | ||||||||
\(725\) | 375233. | 0.713880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −403704. | −0.763825 | −0.381912 | − | 0.924198i | \(-0.624734\pi\) | ||||
−0.381912 | + | 0.924198i | \(0.624734\pi\) | |||||||
\(728\) | −1.35843e6 | −2.56315 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 195226. | 0.366347 | ||||||||
\(731\) | 594093.i | 1.11178i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −472977. | −0.880302 | −0.440151 | − | 0.897924i | \(-0.645075\pi\) | ||||
−0.440151 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(734\) | −530042. | −0.983825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −102061. | −0.188409 | ||||||||
\(737\) | −45445.7 | −0.0836676 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 107013.i | − | 0.195951i | −0.995189 | − | 0.0979757i | \(-0.968763\pi\) | ||
0.995189 | − | 0.0979757i | \(-0.0312368\pi\) | |||||||
\(740\) | 33035.9i | 0.0603286i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 1.11161e6i | − | 2.01904i | ||||||
\(743\) | 915468. | 1.65831 | 0.829155 | − | 0.559019i | \(-0.188822\pi\) | ||||
0.829155 | + | 0.559019i | \(0.188822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.01984e6i | − | 1.83747i | ||||||
\(746\) | − | 294883.i | − | 0.529874i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 13068.0i | − | 0.0233563i | ||||||
\(749\) | 1.02238e6 | 1.82242 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 832564.i | 1.47617i | 0.674705 | + | 0.738087i | \(0.264271\pi\) | ||||
−0.674705 | + | 0.738087i | \(0.735729\pi\) | |||||||
\(752\) | 397004.i | 0.702036i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 414238. | 0.728631 | ||||||||
\(755\) | 545406.i | 0.956811i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 247540. | 0.431970 | 0.215985 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215985 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(758\) | 350690.i | 0.610359i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.05002e6i | 1.81789i | ||||||||
\(761\) | 539545. | 0.931662 | 0.465831 | − | 0.884874i | \(-0.345756\pi\) | ||||
0.465831 | + | 0.884874i | \(0.345756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 504988.i | − | 0.867425i | ||||||
\(764\) | − | 32774.5i | − | 0.0561500i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1.14221e6i | − | 1.94665i | ||||||
\(767\) | 4221.58 | + | 885352.i | 0.00717604 | + | 1.50496i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 97270.6i | − | 0.164486i | −0.996612 | − | 0.0822430i | \(-0.973792\pi\) | ||
0.996612 | − | 0.0822430i | \(-0.0262084\pi\) | |||||||
\(770\) | −950059. | −1.60239 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30287.3 | −0.0508189 | ||||||||
\(773\) | − | 234313.i | − | 0.392136i | −0.980590 | − | 0.196068i | \(-0.937183\pi\) | ||
0.980590 | − | 0.196068i | \(-0.0628173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.34411e6i | 2.23785i | ||||||||
\(776\) | −1.05423e6 | −1.75069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 87095.3i | 0.143892i | ||||||||
\(779\) | 434403. | 0.715844 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 176044.i | − | 0.288615i | ||||||
\(782\) | −899205. | −1.47043 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.33467e6 | −2.17141 | ||||||||
\(785\) | 217356.i | 0.352721i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 773520. | 1.24888 | 0.624442 | − | 0.781071i | \(-0.285327\pi\) | ||||
0.624442 | + | 0.781071i | \(0.285327\pi\) | |||||||
\(788\) | 31328.9 | 0.0504537 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 202272.i | − | 0.324102i | ||||||
\(791\) | − | 1.81931e6i | − | 2.90773i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −551972. | −0.877749 | ||||||||
\(794\) | −187151. | −0.296860 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 63887.8 | 0.100831 | ||||||||
\(797\) | − | 254532.i | − | 0.400705i | −0.979724 | − | 0.200353i | \(-0.935791\pi\) | ||
0.979724 | − | 0.200353i | \(-0.0642088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 339249.i | 0.531404i | ||||||||
\(800\) | − | 101081.i | − | 0.157939i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 233133. | 0.362455 | ||||||||
\(803\) | −81726.0 | −0.126744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.24687e6i | 5.01041i | ||||||||
\(806\) | 1.48383e6i | 2.28409i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 538770. | 0.825240 | ||||||||
\(809\) | − | 3663.27i | − | 0.00559721i | −0.999996 | − | 0.00279861i | \(-0.999109\pi\) | ||
0.999996 | − | 0.00279861i | \(-0.000890825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 137551.i | − | 0.209133i | −0.994518 | − | 0.104567i | \(-0.966654\pi\) | ||
0.994518 | − | 0.104567i | \(-0.0333456\pi\) | |||||||
\(812\) | 28491.1 | 0.0432113 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 278449.i | − | 0.420239i | ||||||
\(815\) | 5446.42 | 0.00819966 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.10196e6i | − | 1.65090i | ||||||
\(818\) | −624696. | −0.933602 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33801.0 | −0.0502693 | ||||||||
\(821\) | 336436.i | 0.499132i | 0.968358 | + | 0.249566i | \(0.0802880\pi\) | ||||
−0.968358 | + | 0.249566i | \(0.919712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 197126.i | 0.291035i | 0.989356 | + | 0.145517i | \(0.0464847\pi\) | ||||
−0.989356 | + | 0.145517i | \(0.953515\pi\) | |||||||
\(824\) | 73649.6 | 0.108472 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5846.15 | + | 1.22606e6i | 0.00856860 | + | 1.79701i | ||||
\(827\) | 1.17052e6 | 1.71146 | 0.855730 | − | 0.517422i | \(-0.173108\pi\) | ||||
0.855730 | + | 0.517422i | \(0.173108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −596609. | −0.868122 | −0.434061 | − | 0.900884i | \(-0.642920\pi\) | ||||
−0.434061 | + | 0.900884i | \(0.642920\pi\) | |||||||
\(830\) | 993734. | 1.44249 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 981794.i | 1.41832i | ||||||||
\(833\) | −1.14050e6 | −1.64364 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 186534. | 0.267537 | ||||||||
\(836\) | 24239.2i | 0.0346821i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61370.7 | 0.0873923 | ||||||||
\(839\) | 763822.i | 1.08510i | 0.840025 | + | 0.542548i | \(0.182540\pi\) | ||||
−0.840025 | + | 0.542548i | \(0.817460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −549729. | −0.777243 | ||||||||
\(842\) | −788414. | −1.11206 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20402.4i | 0.0286416i | ||||||||
\(845\) | −1.43168e6 | −2.00509 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −859068. | −1.19746 | ||||||||
\(848\) | −847961. | −1.17919 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 890575.i | − | 1.23263i | ||||||
\(851\) | −951612. | −1.31402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 262734. | 0.361092 | 0.180546 | − | 0.983567i | \(-0.442214\pi\) | ||||
0.180546 | + | 0.983567i | \(0.442214\pi\) | |||||||
\(854\) | −764384. | −1.04808 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 741057.i | − | 1.01136i | ||||||
\(857\) | − | 1.18773e6i | − | 1.61717i | −0.588382 | − | 0.808583i | \(-0.700235\pi\) | ||
0.588382 | − | 0.808583i | \(-0.299765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 403204.i | 0.546435i | 0.961952 | + | 0.273217i | \(0.0880878\pi\) | ||||
−0.961952 | + | 0.273217i | \(0.911912\pi\) | |||||||
\(860\) | 85743.4i | 0.115932i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 553885. | 0.745426 | ||||||||
\(863\) | − | 709539.i | − | 0.952697i | −0.879257 | − | 0.476348i | \(-0.841960\pi\) | ||
0.879257 | − | 0.476348i | \(-0.158040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 995939.i | − | 1.33107i | ||||||
\(866\) | − | 113792.i | − | 0.151732i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 102057.i | 0.135457i | ||||||||
\(869\) | 84675.5i | 0.112129i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −169812. | −0.223837 | ||||||||
\(872\) | −366034. | −0.481381 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.66789e6 | 2.18346 | ||||||||
\(875\) | −1.08969e6 | −1.42327 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 557208. | 0.724466 | 0.362233 | − | 0.932087i | \(-0.382014\pi\) | ||||
0.362233 | + | 0.932087i | \(0.382014\pi\) | |||||||
\(878\) | − | 1.05342e6i | − | 1.36651i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 724726.i | 0.935855i | ||||||||
\(881\) | 511735.i | 0.659316i | 0.944101 | + | 0.329658i | \(0.106933\pi\) | ||||
−0.944101 | + | 0.329658i | \(0.893067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.39799e6 | 1.79301 | 0.896507 | − | 0.443029i | \(-0.146096\pi\) | ||||
0.896507 | + | 0.443029i | \(0.146096\pi\) | |||||||
\(884\) | − | 48829.6i | − | 0.0624854i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 427605. | 0.544722 | ||||||||
\(887\) | − | 526850.i | − | 0.669638i | −0.942282 | − | 0.334819i | \(-0.891325\pi\) | ||
0.942282 | − | 0.334819i | \(-0.108675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.30056e6 | −2.91092 | ||||||||
\(890\) | 1.95677e6 | 2.47035 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22175.9 | 0.0278709 | ||||||||
\(893\) | − | 629257.i | − | 0.789087i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 657229.i | − | 0.820485i | ||||||
\(896\) | 1.50647e6i | 1.87648i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 62521.5i | − | 0.0775313i | ||||||
\(899\) | 564359.i | 0.698291i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −724602. | −0.892585 | ||||||||
\(902\) | 284898. | 0.350167 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.31870e6 | −1.61365 | ||||||||
\(905\) | 2.06006e6 | 2.51525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −836151. | −1.01641 | −0.508206 | − | 0.861235i | \(-0.669691\pi\) | ||||
−0.508206 | + | 0.861235i | \(0.669691\pi\) | |||||||
\(908\) | 59886.7i | 0.0726371i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.54998e6 | −4.28690 | ||||||||
\(911\) | −527285. | −0.635343 | −0.317672 | − | 0.948201i | \(-0.602901\pi\) | ||||
−0.317672 | + | 0.948201i | \(0.602901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −415999. | −0.499058 | ||||||||
\(914\) | 1.44328e6 | 1.72765 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 35679.7i | − | 0.0425237i | ||||||
\(917\) | 168216.i | 0.200045i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 156081.i | − | 0.184807i | −0.995722 | − | 0.0924036i | \(-0.970545\pi\) | ||
0.995722 | − | 0.0924036i | \(-0.0294550\pi\) | |||||||
\(920\) | 2.35345e6 | 2.78055 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 377087.i | 0.443588i | ||||||||
\(923\) | − | 657804.i | − | 0.772135i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 942478.i | − | 1.10151i | ||||||
\(926\) | −1.16790e6 | −1.36202 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 42441.6i | − | 0.0492828i | ||||||
\(929\) | − | 443250.i | − | 0.513591i | −0.966466 | − | 0.256795i | \(-0.917333\pi\) | ||
0.966466 | − | 0.256795i | \(-0.0826667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.11547e6 | 2.44066 | ||||||||
\(932\) | 57351.3i | 0.0660255i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.24916e6 | −1.43194 | ||||||||
\(935\) | 619295.i | 0.708393i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 176637.i | − | 0.201188i | −0.994928 | − | 0.100594i | \(-0.967926\pi\) | ||
0.994928 | − | 0.100594i | \(-0.0320743\pi\) | |||||||
\(938\) | −235160. | −0.267274 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48962.6i | 0.0554127i | ||||||||
\(941\) | 1.41132e6i | 1.59385i | 0.604078 | + | 0.796925i | \(0.293542\pi\) | ||||
−0.604078 | + | 0.796925i | \(0.706458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 973651.i | − | 1.09491i | ||||||
\(944\) | 935264. | − | 4459.58i | 1.04952 | − | 0.00500437i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 722702.i | − | 0.807564i | ||||||
\(947\) | −774655. | −0.863791 | −0.431895 | − | 0.901924i | \(-0.642155\pi\) | ||||
−0.431895 | + | 0.901924i | \(0.642155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −305376. | −0.339081 | ||||||||
\(950\) | 1.65188e6i | 1.83034i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.22625e6i | 1.35302i | ||||||||
\(953\) | −443289. | −0.488091 | −0.244046 | − | 0.969764i | \(-0.578475\pi\) | ||||
−0.244046 | + | 0.969764i | \(0.578475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.55320e6i | 1.70302i | ||||||||
\(956\) | 806.016 | 0.000881917 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.63087e6i | − | 1.77701i | ||||||
\(959\) | −301381. | −0.327702 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.09805e6 | −1.18898 | ||||||||
\(962\) | − | 1.04045e6i | − | 1.12427i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13654.6 | −0.0146934 | ||||||||
\(965\) | 1.43532e6 | 1.54133 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 376709.i | 0.402859i | 0.979503 | + | 0.201429i | \(0.0645587\pi\) | ||||
−0.979503 | + | 0.201429i | \(0.935441\pi\) | |||||||
\(968\) | 622684.i | 0.664534i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.75501e6 | −2.92806 | ||||||||
\(971\) | −563582. | −0.597749 | −0.298875 | − | 0.954292i | \(-0.596611\pi\) | ||||
−0.298875 | + | 0.954292i | \(0.596611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 724133. | 0.764879 | ||||||||
\(974\) | − | 647327.i | − | 0.682347i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 583089.i | 0.612118i | ||||||||
\(977\) | 242271.i | 0.253812i | 0.991915 | + | 0.126906i | \(0.0405046\pi\) | ||||
−0.991915 | + | 0.126906i | \(0.959495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −819146. | −0.854665 | ||||||||
\(980\) | −164605. | −0.171392 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 315716.i | − | 0.327396i | ||||||
\(983\) | 1.65719e6i | 1.71501i | 0.514478 | + | 0.857504i | \(0.327986\pi\) | ||||
−0.514478 | + | 0.857504i | \(0.672014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.48469e6 | −1.53025 | ||||||||
\(986\) | − | 373932.i | − | 0.384626i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 90571.7i | 0.0927852i | ||||||||
\(989\) | −2.46987e6 | −2.52512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.43312e6i | 1.45927i | 0.683835 | + | 0.729636i | \(0.260311\pi\) | ||||
−0.683835 | + | 0.729636i | \(0.739689\pi\) | |||||||
\(992\) | 152028. | 0.154490 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 910943.i | − | 0.921974i | ||||||
\(995\) | −3.02766e6 | −3.05817 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.54766e6 | 1.55699 | 0.778495 | − | 0.627650i | \(-0.215983\pi\) | ||||
0.778495 | + | 0.627650i | \(0.215983\pi\) | |||||||
\(998\) | 4588.45i | 0.00460686i | ||||||||
\(999\) | 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 | 531.5.c.d.235.30 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.11 | ✓ | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.11 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.30 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.11 | ✓ | 40 | 3.2 | odd | 2 | ||
177.5.c.a.58.30 | yes | 40 | 177.176 | even | 2 | ||
531.5.c.d.235.11 | 40 | 59.58 | odd | 2 | inner | ||
531.5.c.d.235.30 | 40 | 1.1 | even | 1 | trivial |