Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.30 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.11 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(0.828571\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −0.836195 | −0.0522622 | ||||||||
\(5\) | −39.6276 | −1.58510 | −0.792551 | − | 0.609805i | \(-0.791248\pi\) | ||||
−0.792551 | + | 0.609805i | \(0.791248\pi\) | |||||||
\(6\) | − | 21.3208i | − | 0.592245i | ||||||
\(7\) | −85.8400 | −1.75184 | −0.875918 | − | 0.482459i | \(-0.839744\pi\) | ||||
−0.875918 | + | 0.482459i | \(0.839744\pi\) | |||||||
\(8\) | 62.2200i | 0.972188i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 162.600i | − | 1.62600i | ||||||
\(11\) | − | 68.0678i | − | 0.562544i | −0.959628 | − | 0.281272i | \(-0.909244\pi\) | ||
0.959628 | − | 0.281272i | \(-0.0907563\pi\) | |||||||
\(12\) | 4.34500 | 0.0301736 | ||||||||
\(13\) | 254.341i | 1.50498i | 0.658605 | + | 0.752489i | \(0.271147\pi\) | ||||
−0.658605 | + | 0.752489i | \(0.728853\pi\) | |||||||
\(14\) | − | 352.218i | − | 1.79703i | ||||||
\(15\) | 205.911 | 0.915159 | ||||||||
\(16\) | −268.680 | −1.04953 | ||||||||
\(17\) | 229.593 | 0.794440 | 0.397220 | − | 0.917724i | \(-0.369975\pi\) | ||||
0.397220 | + | 0.917724i | \(0.369975\pi\) | |||||||
\(18\) | 110.786i | 0.341933i | ||||||||
\(19\) | 425.861 | 1.17967 | 0.589836 | − | 0.807523i | \(-0.299193\pi\) | ||||
0.589836 | + | 0.807523i | \(0.299193\pi\) | |||||||
\(20\) | 33.1364 | 0.0828409 | ||||||||
\(21\) | 446.038 | 1.01142 | ||||||||
\(22\) | 279.295 | 0.577056 | ||||||||
\(23\) | − | 954.505i | − | 1.80436i | −0.431363 | − | 0.902178i | \(-0.641967\pi\) | ||
0.431363 | − | 0.902178i | \(-0.358033\pi\) | |||||||
\(24\) | − | 323.305i | − | 0.561293i | ||||||
\(25\) | 945.343 | 1.51255 | ||||||||
\(26\) | −1043.61 | −1.54380 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 71.7790 | 0.0915548 | ||||||||
\(29\) | −396.928 | −0.471971 | −0.235986 | − | 0.971757i | \(-0.575832\pi\) | ||||
−0.235986 | + | 0.971757i | \(0.575832\pi\) | |||||||
\(30\) | 844.892i | 0.938769i | ||||||||
\(31\) | − | 1421.82i | − | 1.47952i | −0.672871 | − | 0.739760i | \(-0.734939\pi\) | ||
0.672871 | − | 0.739760i | \(-0.265061\pi\) | |||||||
\(32\) | − | 106.925i | − | 0.104419i | ||||||
\(33\) | 353.691i | 0.324785i | ||||||||
\(34\) | 942.065i | 0.814935i | ||||||||
\(35\) | 3401.63 | 2.77684 | ||||||||
\(36\) | −22.5773 | −0.0174207 | ||||||||
\(37\) | 996.969i | 0.728246i | 0.931351 | + | 0.364123i | \(0.118631\pi\) | ||||
−0.931351 | + | 0.364123i | \(0.881369\pi\) | |||||||
\(38\) | 1747.39i | 1.21010i | ||||||||
\(39\) | − | 1321.60i | − | 0.868899i | ||||||
\(40\) | − | 2465.63i | − | 1.54102i | ||||||
\(41\) | −1020.06 | −0.606817 | −0.303408 | − | 0.952861i | \(-0.598125\pi\) | ||||
−0.303408 | + | 0.952861i | \(0.598125\pi\) | |||||||
\(42\) | 1830.18i | 1.03752i | ||||||||
\(43\) | 2587.59i | 1.39945i | 0.714410 | + | 0.699727i | \(0.246695\pi\) | ||||
−0.714410 | + | 0.699727i | \(0.753305\pi\) | |||||||
\(44\) | 56.9180i | 0.0293998i | ||||||||
\(45\) | −1069.94 | −0.528367 | ||||||||
\(46\) | 3916.52 | 1.85091 | ||||||||
\(47\) | − | 1477.61i | − | 0.668905i | −0.942413 | − | 0.334452i | \(-0.891449\pi\) | ||
0.942413 | − | 0.334452i | \(-0.108551\pi\) | |||||||
\(48\) | 1396.10 | 0.605947 | ||||||||
\(49\) | 4967.50 | 2.06893 | ||||||||
\(50\) | 3878.93i | 1.55157i | ||||||||
\(51\) | −1193.00 | −0.458670 | ||||||||
\(52\) | − | 212.679i | − | 0.0786535i | ||||||
\(53\) | −3156.03 | −1.12354 | −0.561770 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561770 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(54\) | − | 575.662i | − | 0.197415i | ||||||
\(55\) | 2697.36i | 0.891689i | ||||||||
\(56\) | − | 5340.97i | − | 1.70311i | ||||||
\(57\) | −2212.84 | −0.681083 | ||||||||
\(58\) | − | 1628.67i | − | 0.484147i | ||||||
\(59\) | 3480.96 | + | 16.5981i | 0.999989 | + | 0.00476820i | ||||
\(60\) | −172.182 | −0.0478282 | ||||||||
\(61\) | 2170.20i | 0.583230i | 0.956536 | + | 0.291615i | \(0.0941927\pi\) | ||||
−0.956536 | + | 0.291615i | \(0.905807\pi\) | |||||||
\(62\) | 5834.00 | 1.51769 | ||||||||
\(63\) | −2317.68 | −0.583946 | ||||||||
\(64\) | −3860.14 | −0.942418 | ||||||||
\(65\) | − | 10078.9i | − | 2.38554i | ||||||
\(66\) | −1451.26 | −0.333164 | ||||||||
\(67\) | 667.653i | 0.148731i | 0.997231 | + | 0.0743655i | \(0.0236931\pi\) | ||||
−0.997231 | + | 0.0743655i | \(0.976307\pi\) | |||||||
\(68\) | −191.985 | −0.0415192 | ||||||||
\(69\) | 4959.75i | 1.04175i | ||||||||
\(70\) | 13957.5i | 2.84848i | ||||||||
\(71\) | −2586.30 | −0.513054 | −0.256527 | − | 0.966537i | \(-0.582578\pi\) | ||||
−0.256527 | + | 0.966537i | \(0.582578\pi\) | |||||||
\(72\) | 1679.94i | 0.324063i | ||||||||
\(73\) | 1200.66i | 0.225306i | 0.993634 | + | 0.112653i | \(0.0359349\pi\) | ||||
−0.993634 | + | 0.112653i | \(0.964065\pi\) | |||||||
\(74\) | −4090.76 | −0.747034 | ||||||||
\(75\) | −4912.15 | −0.873271 | ||||||||
\(76\) | −356.103 | −0.0616522 | ||||||||
\(77\) | 5842.94i | 0.985485i | ||||||||
\(78\) | 5422.76 | 0.891316 | ||||||||
\(79\) | −1243.99 | −0.199325 | −0.0996626 | − | 0.995021i | \(-0.531776\pi\) | ||||
−0.0996626 | + | 0.995021i | \(0.531776\pi\) | |||||||
\(80\) | 10647.1 | 1.66361 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 4185.50i | − | 0.622471i | ||||||
\(83\) | − | 6111.54i | − | 0.887145i | −0.896239 | − | 0.443572i | \(-0.853711\pi\) | ||
0.896239 | − | 0.443572i | \(-0.146289\pi\) | |||||||
\(84\) | −372.975 | −0.0528592 | ||||||||
\(85\) | −9098.21 | −1.25927 | ||||||||
\(86\) | −10617.4 | −1.43556 | ||||||||
\(87\) | 2062.50 | 0.272493 | ||||||||
\(88\) | 4235.18 | 0.546898 | ||||||||
\(89\) | − | 12034.3i | − | 1.51929i | −0.650340 | − | 0.759643i | \(-0.725374\pi\) | ||
0.650340 | − | 0.759643i | \(-0.274626\pi\) | |||||||
\(90\) | − | 4390.19i | − | 0.541998i | ||||||
\(91\) | − | 21832.7i | − | 2.63648i | ||||||
\(92\) | 798.152i | 0.0942997i | ||||||||
\(93\) | 7387.98i | 0.854201i | ||||||||
\(94\) | 6062.92 | 0.686161 | ||||||||
\(95\) | −16875.8 | −1.86990 | ||||||||
\(96\) | 555.600i | 0.0602864i | ||||||||
\(97\) | − | 16943.5i | − | 1.80078i | −0.435085 | − | 0.900389i | \(-0.643282\pi\) | ||
0.435085 | − | 0.900389i | \(-0.356718\pi\) | |||||||
\(98\) | 20382.6i | 2.12231i | ||||||||
\(99\) | − | 1837.83i | − | 0.187515i | ||||||
\(100\) | −790.492 | −0.0790492 | ||||||||
\(101\) | − | 8659.11i | − | 0.848849i | −0.905463 | − | 0.424424i | \(-0.860476\pi\) | ||
0.905463 | − | 0.424424i | \(-0.139524\pi\) | |||||||
\(102\) | − | 4895.11i | − | 0.470503i | ||||||
\(103\) | 1183.70i | 0.111575i | 0.998443 | + | 0.0557873i | \(0.0177669\pi\) | ||||
−0.998443 | + | 0.0557873i | \(0.982233\pi\) | |||||||
\(104\) | −15825.1 | −1.46312 | ||||||||
\(105\) | −17675.4 | −1.60321 | ||||||||
\(106\) | − | 12949.8i | − | 1.15253i | ||||||
\(107\) | 11910.3 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(108\) | 117.315 | 0.0100579 | ||||||||
\(109\) | − | 5882.90i | − | 0.495152i | −0.968868 | − | 0.247576i | \(-0.920366\pi\) | ||
0.968868 | − | 0.247576i | \(-0.0796340\pi\) | |||||||
\(110\) | −11067.8 | −0.914693 | ||||||||
\(111\) | − | 5180.40i | − | 0.420453i | ||||||
\(112\) | 23063.5 | 1.83861 | ||||||||
\(113\) | 21194.2i | 1.65982i | 0.557900 | + | 0.829908i | \(0.311607\pi\) | ||||
−0.557900 | + | 0.829908i | \(0.688393\pi\) | |||||||
\(114\) | − | 9079.71i | − | 0.698654i | ||||||
\(115\) | 37824.7i | 2.86009i | ||||||||
\(116\) | 331.909 | 0.0246663 | ||||||||
\(117\) | 6867.21i | 0.501659i | ||||||||
\(118\) | −68.1052 | + | 14283.1i | −0.00489121 | + | 1.02579i | ||||
\(119\) | −19708.3 | −1.39173 | ||||||||
\(120\) | 12811.8i | 0.889707i | ||||||||
\(121\) | 10007.8 | 0.683545 | ||||||||
\(122\) | −8904.75 | −0.598277 | ||||||||
\(123\) | 5300.38 | 0.350346 | ||||||||
\(124\) | 1188.92i | 0.0773230i | ||||||||
\(125\) | −12694.4 | −0.812443 | ||||||||
\(126\) | − | 9509.89i | − | 0.599010i | ||||||
\(127\) | 26800.6 | 1.66164 | 0.830820 | − | 0.556541i | \(-0.187872\pi\) | ||||
0.830820 | + | 0.556541i | \(0.187872\pi\) | |||||||
\(128\) | − | 17549.7i | − | 1.07115i | ||||||
\(129\) | − | 13445.5i | − | 0.807976i | ||||||
\(130\) | 41355.8 | 2.44709 | ||||||||
\(131\) | − | 1959.64i | − | 0.114192i | −0.998369 | − | 0.0570958i | \(-0.981816\pi\) | ||
0.998369 | − | 0.0570958i | \(-0.0181840\pi\) | |||||||
\(132\) | − | 295.754i | − | 0.0169740i | ||||||
\(133\) | −36555.9 | −2.06659 | ||||||||
\(134\) | −2739.51 | −0.152568 | ||||||||
\(135\) | 5559.59 | 0.305053 | ||||||||
\(136\) | 14285.3i | 0.772345i | ||||||||
\(137\) | −3510.97 | −0.187062 | −0.0935310 | − | 0.995616i | \(-0.529815\pi\) | ||||
−0.0935310 | + | 0.995616i | \(0.529815\pi\) | |||||||
\(138\) | −20350.8 | −1.06862 | ||||||||
\(139\) | −8435.85 | −0.436616 | −0.218308 | − | 0.975880i | \(-0.570054\pi\) | ||||
−0.218308 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(140\) | −2844.43 | −0.145124 | ||||||||
\(141\) | 7677.89i | 0.386192i | ||||||||
\(142\) | − | 10612.1i | − | 0.526290i | ||||||
\(143\) | 17312.4 | 0.846616 | ||||||||
\(144\) | −7254.36 | −0.349844 | ||||||||
\(145\) | 15729.3 | 0.748123 | ||||||||
\(146\) | −4926.52 | −0.231119 | ||||||||
\(147\) | −25811.9 | −1.19450 | ||||||||
\(148\) | − | 833.661i | − | 0.0380597i | ||||||
\(149\) | − | 25735.7i | − | 1.15921i | −0.814896 | − | 0.579607i | \(-0.803206\pi\) | ||
0.814896 | − | 0.579607i | \(-0.196794\pi\) | |||||||
\(150\) | − | 20155.5i | − | 0.895800i | ||||||
\(151\) | − | 13763.3i | − | 0.603628i | −0.953367 | − | 0.301814i | \(-0.902408\pi\) | ||
0.953367 | − | 0.301814i | \(-0.0975921\pi\) | |||||||
\(152\) | 26497.1i | 1.14686i | ||||||||
\(153\) | 6199.01 | 0.264813 | ||||||||
\(154\) | −23974.7 | −1.01091 | ||||||||
\(155\) | 56343.2i | 2.34519i | ||||||||
\(156\) | 1105.11i | 0.0454106i | ||||||||
\(157\) | − | 5484.96i | − | 0.222523i | −0.993791 | − | 0.111261i | \(-0.964511\pi\) | ||
0.993791 | − | 0.111261i | \(-0.0354891\pi\) | |||||||
\(158\) | − | 5104.33i | − | 0.204467i | ||||||
\(159\) | 16399.2 | 0.648676 | ||||||||
\(160\) | 4237.19i | 0.165515i | ||||||||
\(161\) | 81934.7i | 3.16094i | ||||||||
\(162\) | 2991.23i | 0.113978i | ||||||||
\(163\) | 137.440 | 0.00517295 | 0.00258648 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258648 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(164\) | 852.968 | 0.0317136 | ||||||||
\(165\) | − | 14015.9i | − | 0.514817i | ||||||
\(166\) | 25076.8 | 0.910032 | ||||||||
\(167\) | −4707.17 | −0.168782 | −0.0843911 | − | 0.996433i | \(-0.526895\pi\) | ||||
−0.0843911 | + | 0.996433i | \(0.526895\pi\) | |||||||
\(168\) | 27752.5i | 0.983293i | ||||||||
\(169\) | −36128.5 | −1.26496 | ||||||||
\(170\) | − | 37331.7i | − | 1.29176i | ||||||
\(171\) | 11498.3 | 0.393224 | ||||||||
\(172\) | − | 2163.73i | − | 0.0731386i | ||||||
\(173\) | − | 25132.5i | − | 0.839737i | −0.907585 | − | 0.419869i | \(-0.862076\pi\) | ||
0.907585 | − | 0.419869i | \(-0.137924\pi\) | |||||||
\(174\) | 8462.83i | 0.279523i | ||||||||
\(175\) | −81148.3 | −2.64974 | ||||||||
\(176\) | 18288.4i | 0.590407i | ||||||||
\(177\) | −18087.6 | − | 86.2463i | −0.577344 | − | 0.00275292i | ||||
\(178\) | 49378.9 | 1.55848 | ||||||||
\(179\) | − | 16585.2i | − | 0.517623i | −0.965928 | − | 0.258811i | \(-0.916669\pi\) | ||
0.965928 | − | 0.258811i | \(-0.0833308\pi\) | |||||||
\(180\) | 894.682 | 0.0276136 | ||||||||
\(181\) | 51985.4 | 1.58681 | 0.793404 | − | 0.608695i | \(-0.208307\pi\) | ||||
0.793404 | + | 0.608695i | \(0.208307\pi\) | |||||||
\(182\) | 89583.6 | 2.70449 | ||||||||
\(183\) | − | 11276.7i | − | 0.336728i | ||||||
\(184\) | 59389.3 | 1.75417 | ||||||||
\(185\) | − | 39507.4i | − | 1.15434i | ||||||
\(186\) | −30314.3 | −0.876238 | ||||||||
\(187\) | − | 15627.9i | − | 0.446907i | ||||||
\(188\) | 1235.57i | 0.0349584i | ||||||||
\(189\) | 12043.0 | 0.337141 | ||||||||
\(190\) | − | 69244.8i | − | 1.91814i | ||||||
\(191\) | 39194.8i | 1.07439i | 0.843458 | + | 0.537195i | \(0.180516\pi\) | ||||
−0.843458 | + | 0.537195i | \(0.819484\pi\) | |||||||
\(192\) | 20057.9 | 0.544105 | ||||||||
\(193\) | 36220.3 | 0.972384 | 0.486192 | − | 0.873852i | \(-0.338386\pi\) | ||||
0.486192 | + | 0.873852i | \(0.338386\pi\) | |||||||
\(194\) | 69522.6 | 1.84724 | ||||||||
\(195\) | 52371.6i | 1.37729i | ||||||||
\(196\) | −4153.80 | −0.108127 | ||||||||
\(197\) | 37466.1 | 0.965396 | 0.482698 | − | 0.875787i | \(-0.339657\pi\) | ||||
0.482698 | + | 0.875787i | \(0.339657\pi\) | |||||||
\(198\) | 7540.97 | 0.192352 | ||||||||
\(199\) | −76403.0 | −1.92932 | −0.964660 | − | 0.263497i | \(-0.915124\pi\) | ||||
−0.964660 | + | 0.263497i | \(0.915124\pi\) | |||||||
\(200\) | 58819.3i | 1.47048i | ||||||||
\(201\) | − | 3469.23i | − | 0.0858698i | ||||||
\(202\) | 35530.0 | 0.870748 | ||||||||
\(203\) | 34072.3 | 0.826817 | ||||||||
\(204\) | 997.581 | 0.0239711 | ||||||||
\(205\) | 40422.4 | 0.961866 | ||||||||
\(206\) | −4856.93 | −0.114453 | ||||||||
\(207\) | − | 25771.6i | − | 0.601452i | ||||||
\(208\) | − | 68336.4i | − | 1.57952i | ||||||
\(209\) | − | 28987.4i | − | 0.663616i | ||||||
\(210\) | − | 72525.5i | − | 1.64457i | ||||||
\(211\) | 24399.1i | 0.548036i | 0.961725 | + | 0.274018i | \(0.0883527\pi\) | ||||
−0.961725 | + | 0.274018i | \(0.911647\pi\) | |||||||
\(212\) | 2639.05 | 0.0587187 | ||||||||
\(213\) | 13438.8 | 0.296212 | ||||||||
\(214\) | 48870.2i | 1.06713i | ||||||||
\(215\) | − | 102540.i | − | 2.21828i | ||||||
\(216\) | − | 8729.23i | − | 0.187098i | ||||||
\(217\) | 122049.i | 2.59188i | ||||||||
\(218\) | 24138.7 | 0.507926 | ||||||||
\(219\) | − | 6238.79i | − | 0.130081i | ||||||
\(220\) | − | 2255.52i | − | 0.0466016i | ||||||
\(221\) | 58395.0i | 1.19561i | ||||||||
\(222\) | 21256.2 | 0.431300 | ||||||||
\(223\) | −26520.0 | −0.533290 | −0.266645 | − | 0.963795i | \(-0.585915\pi\) | ||||
−0.266645 | + | 0.963795i | \(0.585915\pi\) | |||||||
\(224\) | 9178.46i | 0.182925i | ||||||||
\(225\) | 25524.3 | 0.504183 | ||||||||
\(226\) | −86963.9 | −1.70264 | ||||||||
\(227\) | − | 71618.1i | − | 1.38986i | −0.719077 | − | 0.694930i | \(-0.755435\pi\) | ||
0.719077 | − | 0.694930i | \(-0.244565\pi\) | |||||||
\(228\) | 1850.37 | 0.0355949 | ||||||||
\(229\) | − | 42669.2i | − | 0.813660i | −0.913504 | − | 0.406830i | \(-0.866634\pi\) | ||
0.913504 | − | 0.406830i | \(-0.133366\pi\) | |||||||
\(230\) | −155202. | −2.93388 | ||||||||
\(231\) | − | 30360.8i | − | 0.568970i | ||||||
\(232\) | − | 24696.9i | − | 0.458845i | ||||||
\(233\) | − | 68586.1i | − | 1.26335i | −0.775233 | − | 0.631676i | \(-0.782367\pi\) | ||
0.775233 | − | 0.631676i | \(-0.217633\pi\) | |||||||
\(234\) | −28177.5 | −0.514601 | ||||||||
\(235\) | 58554.1i | 1.06028i | ||||||||
\(236\) | −2910.76 | − | 13.8793i | −0.0522616 | − | 0.000249197i | ||||
\(237\) | 6463.95 | 0.115080 | ||||||||
\(238\) | − | 80866.8i | − | 1.42763i | ||||||
\(239\) | 963.908 | 0.0168749 | 0.00843743 | − | 0.999964i | \(-0.497314\pi\) | ||||
0.00843743 | + | 0.999964i | \(0.497314\pi\) | |||||||
\(240\) | −55324.1 | −0.960488 | ||||||||
\(241\) | 16329.4 | 0.281149 | 0.140574 | − | 0.990070i | \(-0.455105\pi\) | ||||
0.140574 | + | 0.990070i | \(0.455105\pi\) | |||||||
\(242\) | 41063.8i | 0.701179i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 1814.71i | − | 0.0304809i | ||||||
\(245\) | −196850. | −3.27947 | ||||||||
\(246\) | 21748.5i | 0.359384i | ||||||||
\(247\) | 108314.i | 1.77538i | ||||||||
\(248\) | 88465.6 | 1.43837 | ||||||||
\(249\) | 31756.5i | 0.512193i | ||||||||
\(250\) | − | 52087.7i | − | 0.833403i | ||||||
\(251\) | 57856.7 | 0.918346 | 0.459173 | − | 0.888347i | \(-0.348146\pi\) | ||||
0.459173 | + | 0.888347i | \(0.348146\pi\) | |||||||
\(252\) | 1938.03 | 0.0305183 | ||||||||
\(253\) | −64971.0 | −1.01503 | ||||||||
\(254\) | 109968.i | 1.70451i | ||||||||
\(255\) | 47275.7 | 0.727039 | ||||||||
\(256\) | 10247.6 | 0.156366 | ||||||||
\(257\) | −94257.4 | −1.42708 | −0.713542 | − | 0.700613i | \(-0.752910\pi\) | ||||
−0.713542 | + | 0.700613i | \(0.752910\pi\) | |||||||
\(258\) | 55169.6 | 0.828820 | ||||||||
\(259\) | − | 85579.8i | − | 1.27577i | ||||||
\(260\) | 8427.95i | 0.124674i | ||||||||
\(261\) | −10717.1 | −0.157324 | ||||||||
\(262\) | 8040.79 | 0.117137 | ||||||||
\(263\) | 6388.77 | 0.0923646 | 0.0461823 | − | 0.998933i | \(-0.485294\pi\) | ||||
0.0461823 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(264\) | −22006.6 | −0.315752 | ||||||||
\(265\) | 125066. | 1.78093 | ||||||||
\(266\) | − | 149996.i | − | 2.11991i | ||||||
\(267\) | 62531.9i | 0.877160i | ||||||||
\(268\) | − | 558.288i | − | 0.00777301i | ||||||
\(269\) | 50975.4i | 0.704460i | 0.935914 | + | 0.352230i | \(0.114576\pi\) | ||||
−0.935914 | + | 0.352230i | \(0.885424\pi\) | |||||||
\(270\) | 22812.1i | 0.312923i | ||||||||
\(271\) | 103419. | 1.40820 | 0.704098 | − | 0.710103i | \(-0.251352\pi\) | ||||
0.704098 | + | 0.710103i | \(0.251352\pi\) | |||||||
\(272\) | −61687.0 | −0.833789 | ||||||||
\(273\) | 113446.i | 1.52217i | ||||||||
\(274\) | − | 14406.2i | − | 0.191888i | ||||||
\(275\) | − | 64347.4i | − | 0.850875i | ||||||
\(276\) | − | 4147.32i | − | 0.0544439i | ||||||
\(277\) | −118682. | −1.54676 | −0.773381 | − | 0.633941i | \(-0.781436\pi\) | ||||
−0.773381 | + | 0.633941i | \(0.781436\pi\) | |||||||
\(278\) | − | 34613.9i | − | 0.447879i | ||||||
\(279\) | − | 38389.1i | − | 0.493173i | ||||||
\(280\) | 211649.i | 2.69961i | ||||||||
\(281\) | −63690.0 | −0.806600 | −0.403300 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403300 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(282\) | −31503.9 | −0.396155 | ||||||||
\(283\) | − | 7522.96i | − | 0.0939325i | −0.998896 | − | 0.0469662i | \(-0.985045\pi\) | ||
0.998896 | − | 0.0469662i | \(-0.0149553\pi\) | |||||||
\(284\) | 2162.66 | 0.0268133 | ||||||||
\(285\) | 87689.4 | 1.07959 | ||||||||
\(286\) | 71036.3i | 0.868457i | ||||||||
\(287\) | 87561.8 | 1.06304 | ||||||||
\(288\) | − | 2886.98i | − | 0.0348064i | ||||||
\(289\) | −30808.0 | −0.368866 | ||||||||
\(290\) | 64540.3i | 0.767423i | ||||||||
\(291\) | 88041.1i | 1.03968i | ||||||||
\(292\) | − | 1003.98i | − | 0.0117750i | ||||||
\(293\) | −32964.4 | −0.383981 | −0.191990 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191990 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(294\) | − | 105911.i | − | 1.22531i | ||||||
\(295\) | −137942. | − | 657.742i | −1.58508 | − | 0.00755809i | ||||
\(296\) | −62031.4 | −0.707992 | ||||||||
\(297\) | 9549.65i | 0.108262i | ||||||||
\(298\) | 105599. | 1.18912 | ||||||||
\(299\) | 242770. | 2.71552 | ||||||||
\(300\) | 4107.52 | 0.0456391 | ||||||||
\(301\) | − | 222119.i | − | 2.45162i | ||||||
\(302\) | 56473.5 | 0.619200 | ||||||||
\(303\) | 44994.0i | 0.490083i | ||||||||
\(304\) | −114420. | −1.23810 | ||||||||
\(305\) | − | 85999.7i | − | 0.924480i | ||||||
\(306\) | 25435.7i | 0.271645i | ||||||||
\(307\) | −85864.5 | −0.911039 | −0.455520 | − | 0.890226i | \(-0.650547\pi\) | ||||
−0.455520 | + | 0.890226i | \(0.650547\pi\) | |||||||
\(308\) | − | 4885.84i | − | 0.0515036i | ||||||
\(309\) | − | 6150.66i | − | 0.0644177i | ||||||
\(310\) | −231187. | −2.40569 | ||||||||
\(311\) | −20927.4 | −0.216368 | −0.108184 | − | 0.994131i | \(-0.534504\pi\) | ||||
−0.108184 | + | 0.994131i | \(0.534504\pi\) | |||||||
\(312\) | 82229.7 | 0.844733 | ||||||||
\(313\) | 132516.i | 1.35264i | 0.736610 | + | 0.676318i | \(0.236425\pi\) | ||||
−0.736610 | + | 0.676318i | \(0.763575\pi\) | |||||||
\(314\) | 22505.9 | 0.228263 | ||||||||
\(315\) | 91844.0 | 0.925613 | ||||||||
\(316\) | 1040.22 | 0.0104172 | ||||||||
\(317\) | −108659. | −1.08130 | −0.540649 | − | 0.841248i | \(-0.681821\pi\) | ||||
−0.540649 | + | 0.841248i | \(0.681821\pi\) | |||||||
\(318\) | 67289.0i | 0.665411i | ||||||||
\(319\) | 27018.0i | 0.265504i | ||||||||
\(320\) | 152968. | 1.49383 | ||||||||
\(321\) | −61887.6 | −0.600611 | ||||||||
\(322\) | −336194. | −3.24249 | ||||||||
\(323\) | 97774.8 | 0.937177 | ||||||||
\(324\) | −609.586 | −0.00580691 | ||||||||
\(325\) | 240440.i | 2.27635i | ||||||||
\(326\) | 563.944i | 0.00530641i | ||||||||
\(327\) | 30568.5i | 0.285876i | ||||||||
\(328\) | − | 63468.1i | − | 0.589940i | ||||||
\(329\) | 126838.i | 1.17181i | ||||||||
\(330\) | 57509.9 | 0.528098 | ||||||||
\(331\) | −101850. | −0.929619 | −0.464809 | − | 0.885411i | \(-0.653877\pi\) | ||||
−0.464809 | + | 0.885411i | \(0.653877\pi\) | |||||||
\(332\) | 5110.44i | 0.0463641i | ||||||||
\(333\) | 26918.2i | 0.242749i | ||||||||
\(334\) | − | 19314.4i | − | 0.173137i | ||||||
\(335\) | − | 26457.5i | − | 0.235754i | ||||||
\(336\) | −119841. | −1.06152 | ||||||||
\(337\) | 74871.2i | 0.659258i | 0.944111 | + | 0.329629i | \(0.106924\pi\) | ||||
−0.944111 | + | 0.329629i | \(0.893076\pi\) | |||||||
\(338\) | − | 148242.i | − | 1.29759i | ||||||
\(339\) | − | 110128.i | − | 0.958295i | ||||||
\(340\) | 7607.88 | 0.0658121 | ||||||||
\(341\) | −96780.0 | −0.832294 | ||||||||
\(342\) | 47179.6i | 0.403368i | ||||||||
\(343\) | −220309. | −1.87259 | ||||||||
\(344\) | −161000. | −1.36053 | ||||||||
\(345\) | − | 196543.i | − | 1.65127i | ||||||
\(346\) | 103123. | 0.861401 | ||||||||
\(347\) | 90583.5i | 0.752298i | 0.926559 | + | 0.376149i | \(0.122752\pi\) | ||||
−0.926559 | + | 0.376149i | \(0.877248\pi\) | |||||||
\(348\) | −1724.65 | −0.0142411 | ||||||||
\(349\) | − | 134492.i | − | 1.10420i | −0.833779 | − | 0.552098i | \(-0.813828\pi\) | ||
0.833779 | − | 0.552098i | \(-0.186172\pi\) | |||||||
\(350\) | − | 332967.i | − | 2.71810i | ||||||
\(351\) | − | 35683.1i | − | 0.289633i | ||||||
\(352\) | −7278.16 | −0.0587403 | ||||||||
\(353\) | − | 81414.3i | − | 0.653358i | −0.945135 | − | 0.326679i | \(-0.894070\pi\) | ||
0.945135 | − | 0.326679i | \(-0.105930\pi\) | |||||||
\(354\) | 353.885 | − | 74216.9i | 0.00282394 | − | 0.592238i | ||||
\(355\) | 102489. | 0.813243 | ||||||||
\(356\) | 10063.0i | 0.0794013i | ||||||||
\(357\) | 102407. | 0.803515 | ||||||||
\(358\) | 68052.1 | 0.530977 | ||||||||
\(359\) | 64385.0 | 0.499570 | 0.249785 | − | 0.968301i | \(-0.419640\pi\) | ||||
0.249785 | + | 0.968301i | \(0.419640\pi\) | |||||||
\(360\) | − | 66571.9i | − | 0.513672i | ||||||
\(361\) | 51036.8 | 0.391624 | ||||||||
\(362\) | 213306.i | 1.62775i | ||||||||
\(363\) | −52001.9 | −0.394645 | ||||||||
\(364\) | 18256.4i | 0.137788i | ||||||||
\(365\) | − | 47579.1i | − | 0.357133i | ||||||
\(366\) | 46270.4 | 0.345415 | ||||||||
\(367\) | − | 129178.i | − | 0.959083i | −0.877519 | − | 0.479541i | \(-0.840803\pi\) | ||
0.877519 | − | 0.479541i | \(-0.159197\pi\) | |||||||
\(368\) | 256456.i | 1.89373i | ||||||||
\(369\) | −27541.6 | −0.202272 | ||||||||
\(370\) | 162107. | 1.18412 | ||||||||
\(371\) | 270913. | 1.96826 | ||||||||
\(372\) | − | 6177.80i | − | 0.0446424i | ||||||
\(373\) | −71866.8 | −0.516548 | −0.258274 | − | 0.966072i | \(-0.583154\pi\) | ||||
−0.258274 | + | 0.966072i | \(0.583154\pi\) | |||||||
\(374\) | 64124.3 | 0.458436 | ||||||||
\(375\) | 65962.2 | 0.469064 | ||||||||
\(376\) | 91936.9 | 0.650301 | ||||||||
\(377\) | − | 100955.i | − | 0.710306i | ||||||
\(378\) | 49414.8i | 0.345839i | ||||||||
\(379\) | 85467.7 | 0.595009 | 0.297504 | − | 0.954720i | \(-0.403846\pi\) | ||||
0.297504 | + | 0.954720i | \(0.403846\pi\) | |||||||
\(380\) | 14111.5 | 0.0977251 | ||||||||
\(381\) | −139260. | −0.959349 | ||||||||
\(382\) | −160824. | −1.10211 | ||||||||
\(383\) | 278371. | 1.89769 | 0.948846 | − | 0.315739i | \(-0.102253\pi\) | ||||
0.948846 | + | 0.315739i | \(0.102253\pi\) | |||||||
\(384\) | 91191.0i | 0.618429i | ||||||||
\(385\) | − | 231541.i | − | 1.56209i | ||||||
\(386\) | 148619.i | 0.997470i | ||||||||
\(387\) | 69865.0i | 0.466485i | ||||||||
\(388\) | 14168.1i | 0.0941127i | ||||||||
\(389\) | −21226.2 | −0.140273 | −0.0701364 | − | 0.997537i | \(-0.522343\pi\) | ||||
−0.0701364 | + | 0.997537i | \(0.522343\pi\) | |||||||
\(390\) | −214891. | −1.41283 | ||||||||
\(391\) | − | 219148.i | − | 1.43345i | ||||||
\(392\) | 309078.i | 2.01139i | ||||||||
\(393\) | 10182.6i | 0.0659285i | ||||||||
\(394\) | 153731.i | 0.990302i | ||||||||
\(395\) | 49296.2 | 0.315951 | ||||||||
\(396\) | 1536.78i | 0.00979992i | ||||||||
\(397\) | − | 45611.1i | − | 0.289394i | −0.989476 | − | 0.144697i | \(-0.953779\pi\) | ||
0.989476 | − | 0.144697i | \(-0.0462208\pi\) | |||||||
\(398\) | − | 313496.i | − | 1.97909i | ||||||
\(399\) | 189950. | 1.19315 | ||||||||
\(400\) | −253995. | −1.58747 | ||||||||
\(401\) | − | 56817.4i | − | 0.353340i | −0.984270 | − | 0.176670i | \(-0.943468\pi\) | ||
0.984270 | − | 0.176670i | \(-0.0565325\pi\) | |||||||
\(402\) | 14234.9 | 0.0880851 | ||||||||
\(403\) | 361627. | 2.22664 | ||||||||
\(404\) | 7240.70i | 0.0443627i | ||||||||
\(405\) | −28888.5 | −0.176122 | ||||||||
\(406\) | 139805.i | 0.848147i | ||||||||
\(407\) | 67861.5 | 0.409670 | ||||||||
\(408\) | − | 74228.5i | − | 0.445913i | ||||||
\(409\) | − | 152246.i | − | 0.910123i | −0.890460 | − | 0.455061i | \(-0.849617\pi\) | ||
0.890460 | − | 0.455061i | \(-0.150383\pi\) | |||||||
\(410\) | 165861.i | 0.986681i | ||||||||
\(411\) | 18243.5 | 0.108000 | ||||||||
\(412\) | − | 989.801i | − | 0.00583114i | ||||||
\(413\) | −298806. | − | 1424.78i | −1.75182 | − | 0.00835311i | ||||
\(414\) | 105746. | 0.616969 | ||||||||
\(415\) | 242185.i | 1.40622i | ||||||||
\(416\) | 27195.5 | 0.157149 | ||||||||
\(417\) | 43834.0 | 0.252080 | ||||||||
\(418\) | 118941. | 0.680737 | ||||||||
\(419\) | − | 14956.8i | − | 0.0851945i | −0.999092 | − | 0.0425972i | \(-0.986437\pi\) | ||
0.999092 | − | 0.0425972i | \(-0.0135632\pi\) | |||||||
\(420\) | 14780.1 | 0.0837873 | ||||||||
\(421\) | − | 192146.i | − | 1.08410i | −0.840347 | − | 0.542048i | \(-0.817649\pi\) | ||
0.840347 | − | 0.542048i | \(-0.182351\pi\) | |||||||
\(422\) | −100114. | −0.562174 | ||||||||
\(423\) | − | 39895.5i | − | 0.222968i | ||||||
\(424\) | − | 196368.i | − | 1.09229i | ||||||
\(425\) | 217044. | 1.20163 | ||||||||
\(426\) | 55142.1i | 0.303854i | ||||||||
\(427\) | − | 186290.i | − | 1.02172i | ||||||
\(428\) | −9959.31 | −0.0543678 | ||||||||
\(429\) | −89958.1 | −0.488794 | ||||||||
\(430\) | 420741. | 2.27551 | ||||||||
\(431\) | − | 134989.i | − | 0.726679i | −0.931657 | − | 0.363340i | \(-0.881636\pi\) | ||
0.931657 | − | 0.363340i | \(-0.118364\pi\) | |||||||
\(432\) | 37694.7 | 0.201982 | ||||||||
\(433\) | −27732.6 | −0.147916 | −0.0739580 | − | 0.997261i | \(-0.523563\pi\) | ||||
−0.0739580 | + | 0.997261i | \(0.523563\pi\) | |||||||
\(434\) | −500790. | −2.65874 | ||||||||
\(435\) | −81731.7 | −0.431929 | ||||||||
\(436\) | 4919.25i | 0.0258777i | ||||||||
\(437\) | − | 406487.i | − | 2.12855i | ||||||
\(438\) | 25599.0 | 0.133436 | ||||||||
\(439\) | −256732. | −1.33215 | −0.666073 | − | 0.745887i | \(-0.732026\pi\) | ||||
−0.666073 | + | 0.745887i | \(0.732026\pi\) | |||||||
\(440\) | −167830. | −0.866889 | ||||||||
\(441\) | 134123. | 0.689644 | ||||||||
\(442\) | −239606. | −1.22646 | ||||||||
\(443\) | − | 104213.i | − | 0.531022i | −0.964108 | − | 0.265511i | \(-0.914459\pi\) | ||
0.964108 | − | 0.265511i | \(-0.0855407\pi\) | |||||||
\(444\) | 4331.83i | 0.0219738i | ||||||||
\(445\) | 476889.i | 2.40822i | ||||||||
\(446\) | − | 108817.i | − | 0.547048i | ||||||
\(447\) | 133727.i | 0.669272i | ||||||||
\(448\) | 331355. | 1.65096 | ||||||||
\(449\) | 15237.3 | 0.0755814 | 0.0377907 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377907 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(450\) | 104731.i | 0.517190i | ||||||||
\(451\) | 69433.1i | 0.341361i | ||||||||
\(452\) | − | 17722.5i | − | 0.0867457i | ||||||
\(453\) | 71516.3i | 0.348505i | ||||||||
\(454\) | 293863. | 1.42572 | ||||||||
\(455\) | 865175.i | 4.17908i | ||||||||
\(456\) | − | 137683.i | − | 0.662141i | ||||||
\(457\) | 351744.i | 1.68420i | 0.539318 | + | 0.842102i | \(0.318682\pi\) | ||||
−0.539318 | + | 0.842102i | \(0.681318\pi\) | |||||||
\(458\) | 175080. | 0.834651 | ||||||||
\(459\) | −32211.0 | −0.152890 | ||||||||
\(460\) | − | 31628.8i | − | 0.149475i | ||||||
\(461\) | −91900.9 | −0.432432 | −0.216216 | − | 0.976346i | \(-0.569372\pi\) | ||||
−0.216216 | + | 0.976346i | \(0.569372\pi\) | |||||||
\(462\) | 124576. | 0.583648 | ||||||||
\(463\) | − | 284633.i | − | 1.32777i | −0.747835 | − | 0.663885i | \(-0.768907\pi\) | ||
0.747835 | − | 0.663885i | \(-0.231093\pi\) | |||||||
\(464\) | 106647. | 0.495348 | ||||||||
\(465\) | − | 292768.i | − | 1.35400i | ||||||
\(466\) | 281422. | 1.29594 | ||||||||
\(467\) | 304437.i | 1.39593i | 0.716132 | + | 0.697965i | \(0.245911\pi\) | ||||
−0.716132 | + | 0.697965i | \(0.754089\pi\) | |||||||
\(468\) | − | 5742.33i | − | 0.0262178i | ||||||
\(469\) | − | 57311.3i | − | 0.260552i | ||||||
\(470\) | −240259. | −1.08764 | ||||||||
\(471\) | 28500.7i | 0.128474i | ||||||||
\(472\) | −1032.73 | + | 216585.i | −0.00463559 | + | 0.972177i | ||||
\(473\) | 176132. | 0.787254 | ||||||||
\(474\) | 26522.9i | 0.118049i | ||||||||
\(475\) | 402585. | 1.78431 | ||||||||
\(476\) | 16480.0 | 0.0727348 | ||||||||
\(477\) | −85212.7 | −0.374514 | ||||||||
\(478\) | 3955.10i | 0.0173102i | ||||||||
\(479\) | 397464. | 1.73231 | 0.866157 | − | 0.499772i | \(-0.166583\pi\) | ||||
0.866157 | + | 0.499772i | \(0.166583\pi\) | |||||||
\(480\) | − | 22017.1i | − | 0.0955602i | ||||||
\(481\) | −253570. | −1.09599 | ||||||||
\(482\) | 67002.7i | 0.288402i | ||||||||
\(483\) | − | 425745.i | − | 1.82497i | ||||||
\(484\) | −8368.46 | −0.0357235 | ||||||||
\(485\) | 671431.i | 2.85442i | ||||||||
\(486\) | − | 15542.9i | − | 0.0658050i | ||||||
\(487\) | −157762. | −0.665187 | −0.332593 | − | 0.943070i | \(-0.607924\pi\) | ||||
−0.332593 | + | 0.943070i | \(0.607924\pi\) | |||||||
\(488\) | −135030. | −0.567010 | ||||||||
\(489\) | −714.160 | −0.00298660 | ||||||||
\(490\) | − | 807714.i | − | 3.36407i | ||||||
\(491\) | 76943.9 | 0.319162 | 0.159581 | − | 0.987185i | \(-0.448986\pi\) | ||||
0.159581 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(492\) | −4432.15 | −0.0183098 | ||||||||
\(493\) | −91131.9 | −0.374953 | ||||||||
\(494\) | −444434. | −1.82118 | ||||||||
\(495\) | 72828.7i | 0.297230i | ||||||||
\(496\) | 382014.i | 1.55280i | ||||||||
\(497\) | 222008. | 0.898787 | ||||||||
\(498\) | −130303. | −0.525407 | ||||||||
\(499\) | 1118.26 | 0.00449100 | 0.00224550 | − | 0.999997i | \(-0.499285\pi\) | ||||
0.00224550 | + | 0.999997i | \(0.499285\pi\) | |||||||
\(500\) | 10615.0 | 0.0424601 | ||||||||
\(501\) | 24459.2 | 0.0974465 | ||||||||
\(502\) | 237397.i | 0.942038i | ||||||||
\(503\) | 143292.i | 0.566351i | 0.959068 | + | 0.283176i | \(0.0913879\pi\) | ||||
−0.959068 | + | 0.283176i | \(0.908612\pi\) | |||||||
\(504\) | − | 144206.i | − | 0.567705i | ||||||
\(505\) | 343139.i | 1.34551i | ||||||||
\(506\) | − | 266589.i | − | 1.04122i | ||||||
\(507\) | 187729. | 0.730324 | ||||||||
\(508\) | −22410.5 | −0.0868410 | ||||||||
\(509\) | − | 39802.5i | − | 0.153630i | −0.997045 | − | 0.0768148i | \(-0.975525\pi\) | ||
0.997045 | − | 0.0768148i | \(-0.0244750\pi\) | |||||||
\(510\) | 193981.i | 0.745795i | ||||||||
\(511\) | − | 103064.i | − | 0.394699i | ||||||
\(512\) | − | 238748.i | − | 0.910750i | ||||||
\(513\) | −59746.7 | −0.227028 | ||||||||
\(514\) | − | 386756.i | − | 1.46390i | ||||||
\(515\) | − | 46907.0i | − | 0.176857i | ||||||
\(516\) | 11243.1i | 0.0422266i | ||||||||
\(517\) | −100578. | −0.376288 | ||||||||
\(518\) | 351150. | 1.30868 | ||||||||
\(519\) | 130592.i | 0.484823i | ||||||||
\(520\) | 627111. | 2.31920 | ||||||||
\(521\) | −228531. | −0.841917 | −0.420958 | − | 0.907080i | \(-0.638306\pi\) | ||||
−0.420958 | + | 0.907080i | \(0.638306\pi\) | |||||||
\(522\) | − | 43974.1i | − | 0.161382i | ||||||
\(523\) | 508793. | 1.86011 | 0.930054 | − | 0.367423i | \(-0.119760\pi\) | ||||
0.930054 | + | 0.367423i | \(0.119760\pi\) | |||||||
\(524\) | 1638.64i | 0.00596790i | ||||||||
\(525\) | 421659. | 1.52983 | ||||||||
\(526\) | 26214.4i | 0.0947475i | ||||||||
\(527\) | − | 326440.i | − | 1.17539i | ||||||
\(528\) | − | 95029.5i | − | 0.340872i | ||||||
\(529\) | −631238. | −2.25570 | ||||||||
\(530\) | 513168.i | 1.82687i | ||||||||
\(531\) | 93985.9 | + | 448.149i | 0.333330 | + | 0.00158940i | ||||
\(532\) | 30567.9 | 0.108005 | ||||||||
\(533\) | − | 259443.i | − | 0.913246i | ||||||
\(534\) | −256580. | −0.899790 | ||||||||
\(535\) | −471975. | −1.64897 | ||||||||
\(536\) | −41541.4 | −0.144594 | ||||||||
\(537\) | 86179.0i | 0.298850i | ||||||||
\(538\) | −209162. | −0.722634 | ||||||||
\(539\) | − | 338127.i | − | 1.16386i | ||||||
\(540\) | −4648.90 | −0.0159427 | ||||||||
\(541\) | 560174.i | 1.91394i | 0.290187 | + | 0.956970i | \(0.406282\pi\) | ||||
−0.290187 | + | 0.956970i | \(0.593718\pi\) | |||||||
\(542\) | 424349.i | 1.44452i | ||||||||
\(543\) | −270124. | −0.916144 | ||||||||
\(544\) | − | 24549.3i | − | 0.0829547i | ||||||
\(545\) | 233125.i | 0.784867i | ||||||||
\(546\) | −465490. | −1.56144 | ||||||||
\(547\) | −273979. | −0.915679 | −0.457839 | − | 0.889035i | \(-0.651377\pi\) | ||||
−0.457839 | + | 0.889035i | \(0.651377\pi\) | |||||||
\(548\) | 2935.85 | 0.00977627 | ||||||||
\(549\) | 58595.4i | 0.194410i | ||||||||
\(550\) | 264030. | 0.872826 | ||||||||
\(551\) | −169036. | −0.556771 | ||||||||
\(552\) | −308596. | −1.01277 | ||||||||
\(553\) | 106784. | 0.349185 | ||||||||
\(554\) | − | 486973.i | − | 1.58667i | ||||||
\(555\) | 205287.i | 0.666461i | ||||||||
\(556\) | 7054.02 | 0.0228185 | ||||||||
\(557\) | 339532. | 1.09439 | 0.547193 | − | 0.837006i | \(-0.315696\pi\) | ||||
0.547193 | + | 0.837006i | \(0.315696\pi\) | |||||||
\(558\) | 157518. | 0.505896 | ||||||||
\(559\) | −658131. | −2.10615 | ||||||||
\(560\) | −913949. | −2.91438 | ||||||||
\(561\) | 81204.9i | 0.258022i | ||||||||
\(562\) | − | 261332.i | − | 0.827409i | ||||||
\(563\) | − | 92097.7i | − | 0.290558i | −0.989391 | − | 0.145279i | \(-0.953592\pi\) | ||
0.989391 | − | 0.145279i | \(-0.0464079\pi\) | |||||||
\(564\) | − | 6420.21i | − | 0.0201833i | ||||||
\(565\) | − | 839874.i | − | 2.63098i | ||||||
\(566\) | 30868.1 | 0.0963558 | ||||||||
\(567\) | −62577.4 | −0.194649 | ||||||||
\(568\) | − | 160920.i | − | 0.498785i | ||||||
\(569\) | 443913.i | 1.37111i | 0.728019 | + | 0.685557i | \(0.240441\pi\) | ||||
−0.728019 | + | 0.685557i | \(0.759559\pi\) | |||||||
\(570\) | 359807.i | 1.10744i | ||||||||
\(571\) | 254417.i | 0.780321i | 0.920747 | + | 0.390161i | \(0.127581\pi\) | ||||
−0.920747 | + | 0.390161i | \(0.872419\pi\) | |||||||
\(572\) | −14476.6 | −0.0442460 | ||||||||
\(573\) | − | 203662.i | − | 0.620299i | ||||||
\(574\) | 359283.i | 1.09047i | ||||||||
\(575\) | − | 902335.i | − | 2.72918i | ||||||
\(576\) | −104224. | −0.314139 | ||||||||
\(577\) | 311437. | 0.935445 | 0.467723 | − | 0.883875i | \(-0.345075\pi\) | ||||
0.467723 | + | 0.883875i | \(0.345075\pi\) | |||||||
\(578\) | − | 126411.i | − | 0.378382i | ||||||
\(579\) | −188206. | −0.561406 | ||||||||
\(580\) | −13152.8 | −0.0390985 | ||||||||
\(581\) | 524615.i | 1.55413i | ||||||||
\(582\) | −361250. | −1.06650 | ||||||||
\(583\) | 214824.i | 0.632041i | ||||||||
\(584\) | −74704.8 | −0.219040 | ||||||||
\(585\) | − | 272131.i | − | 0.795181i | ||||||
\(586\) | − | 135259.i | − | 0.393887i | ||||||
\(587\) | − | 581088.i | − | 1.68642i | −0.537584 | − | 0.843210i | \(-0.680663\pi\) | ||
0.537584 | − | 0.843210i | \(-0.319337\pi\) | |||||||
\(588\) | 21583.8 | 0.0624271 | ||||||||
\(589\) | − | 605497.i | − | 1.74535i | ||||||
\(590\) | 2698.84 | − | 566003.i | 0.00775307 | − | 1.62598i | ||||
\(591\) | −194679. | −0.557372 | ||||||||
\(592\) | − | 267866.i | − | 0.764317i | ||||||
\(593\) | −218284. | −0.620743 | −0.310371 | − | 0.950615i | \(-0.600453\pi\) | ||||
−0.310371 | + | 0.950615i | \(0.600453\pi\) | |||||||
\(594\) | −39184.0 | −0.111055 | ||||||||
\(595\) | 780990. | 2.20603 | ||||||||
\(596\) | 21520.1i | 0.0605830i | ||||||||
\(597\) | 397002. | 1.11389 | ||||||||
\(598\) | 996132.i | 2.78557i | ||||||||
\(599\) | −549532. | −1.53158 | −0.765789 | − | 0.643091i | \(-0.777651\pi\) | ||||
−0.765789 | + | 0.643091i | \(0.777651\pi\) | |||||||
\(600\) | − | 305634.i | − | 0.848983i | ||||||
\(601\) | − | 611697.i | − | 1.69351i | −0.531984 | − | 0.846755i | \(-0.678553\pi\) | ||
0.531984 | − | 0.846755i | \(-0.321447\pi\) | |||||||
\(602\) | 911397. | 2.51486 | ||||||||
\(603\) | 18026.6i | 0.0495770i | ||||||||
\(604\) | 11508.8i | 0.0315469i | ||||||||
\(605\) | −396584. | −1.08349 | ||||||||
\(606\) | −184619. | −0.502726 | ||||||||
\(607\) | 1086.59 | 0.00294908 | 0.00147454 | − | 0.999999i | \(-0.499531\pi\) | ||||
0.00147454 | + | 0.999999i | \(0.499531\pi\) | |||||||
\(608\) | − | 45535.3i | − | 0.123180i | ||||||
\(609\) | −177045. | −0.477363 | ||||||||
\(610\) | 352874. | 0.948330 | ||||||||
\(611\) | 375817. | 1.00669 | ||||||||
\(612\) | −5183.58 | −0.0138397 | ||||||||
\(613\) | − | 331052.i | − | 0.880999i | −0.897753 | − | 0.440500i | \(-0.854801\pi\) | ||
0.897753 | − | 0.440500i | \(-0.145199\pi\) | |||||||
\(614\) | − | 352319.i | − | 0.934543i | ||||||
\(615\) | −210041. | −0.555334 | ||||||||
\(616\) | −363548. | −0.958076 | ||||||||
\(617\) | −247255. | −0.649492 | −0.324746 | − | 0.945801i | \(-0.605279\pi\) | ||||
−0.324746 | + | 0.945801i | \(0.605279\pi\) | |||||||
\(618\) | 25237.4 | 0.0660795 | ||||||||
\(619\) | 307344. | 0.802127 | 0.401064 | − | 0.916050i | \(-0.368641\pi\) | ||||
0.401064 | + | 0.916050i | \(0.368641\pi\) | |||||||
\(620\) | − | 47113.9i | − | 0.122565i | ||||||
\(621\) | 133913.i | 0.347249i | ||||||||
\(622\) | − | 85869.1i | − | 0.221950i | ||||||
\(623\) | 1.03302e6i | 2.66154i | ||||||||
\(624\) | 355086.i | 0.911937i | ||||||||
\(625\) | −87790.4 | −0.224744 | ||||||||
\(626\) | −543740. | −1.38753 | ||||||||
\(627\) | 150623.i | 0.383139i | ||||||||
\(628\) | 4586.50i | 0.0116295i | ||||||||
\(629\) | 228897.i | 0.578548i | ||||||||
\(630\) | 376854.i | 0.949493i | ||||||||
\(631\) | 469556. | 1.17931 | 0.589657 | − | 0.807654i | \(-0.299263\pi\) | ||||
0.589657 | + | 0.807654i | \(0.299263\pi\) | |||||||
\(632\) | − | 77401.0i | − | 0.193782i | ||||||
\(633\) | − | 126781.i | − | 0.316409i | ||||||
\(634\) | − | 445847.i | − | 1.10919i | ||||||
\(635\) | −1.06204e6 | −2.63387 | ||||||||
\(636\) | −13712.9 | −0.0339013 | ||||||||
\(637\) | 1.26344e6i | 3.11370i | ||||||||
\(638\) | −110860. | −0.272354 | ||||||||
\(639\) | −69830.2 | −0.171018 | ||||||||
\(640\) | 695453.i | 1.69788i | ||||||||
\(641\) | 244837. | 0.595882 | 0.297941 | − | 0.954584i | \(-0.403700\pi\) | ||||
0.297941 | + | 0.954584i | \(0.403700\pi\) | |||||||
\(642\) | − | 253937.i | − | 0.616106i | ||||||
\(643\) | −199751. | −0.483133 | −0.241567 | − | 0.970384i | \(-0.577661\pi\) | ||||
−0.241567 | + | 0.970384i | \(0.577661\pi\) | |||||||
\(644\) | − | 68513.4i | − | 0.165198i | ||||||
\(645\) | 532813.i | 1.28072i | ||||||||
\(646\) | 401189.i | 0.961355i | ||||||||
\(647\) | 406276. | 0.970538 | 0.485269 | − | 0.874365i | \(-0.338722\pi\) | ||||
0.485269 | + | 0.874365i | \(0.338722\pi\) | |||||||
\(648\) | 45358.4i | 0.108021i | ||||||||
\(649\) | 1129.80 | − | 236941.i | 0.00268232 | − | 0.562537i | ||||
\(650\) | −986571. | −2.33508 | ||||||||
\(651\) | − | 634185.i | − | 1.49642i | ||||||
\(652\) | −114.927 | −0.000270350 | ||||||||
\(653\) | 334544. | 0.784562 | 0.392281 | − | 0.919845i | \(-0.371686\pi\) | ||||
0.392281 | + | 0.919845i | \(0.371686\pi\) | |||||||
\(654\) | −125428. | −0.293251 | ||||||||
\(655\) | 77655.8i | 0.181005i | ||||||||
\(656\) | 274069. | 0.636873 | ||||||||
\(657\) | 32417.7i | 0.0751020i | ||||||||
\(658\) | −520441. | −1.20204 | ||||||||
\(659\) | − | 286185.i | − | 0.658986i | −0.944158 | − | 0.329493i | \(-0.893122\pi\) | ||
0.944158 | − | 0.329493i | \(-0.106878\pi\) | |||||||
\(660\) | 11720.0i | 0.0269055i | ||||||||
\(661\) | 759053. | 1.73728 | 0.868639 | − | 0.495446i | \(-0.164995\pi\) | ||||
0.868639 | + | 0.495446i | \(0.164995\pi\) | |||||||
\(662\) | − | 417910.i | − | 0.953601i | ||||||
\(663\) | − | 303429.i | − | 0.690288i | ||||||
\(664\) | 380260. | 0.862471 | ||||||||
\(665\) | 1.44862e6 | 3.27576 | ||||||||
\(666\) | −110450. | −0.249011 | ||||||||
\(667\) | 378870.i | 0.851605i | ||||||||
\(668\) | 3936.11 | 0.00882093 | ||||||||
\(669\) | 137802. | 0.307895 | ||||||||
\(670\) | 108560. | 0.241836 | ||||||||
\(671\) | 147721. | 0.328093 | ||||||||
\(672\) | − | 47692.7i | − | 0.105612i | ||||||
\(673\) | − | 664503.i | − | 1.46712i | −0.679622 | − | 0.733562i | \(-0.737856\pi\) | ||
0.679622 | − | 0.733562i | \(-0.262144\pi\) | |||||||
\(674\) | −307211. | −0.676265 | ||||||||
\(675\) | −132628. | −0.291090 | ||||||||
\(676\) | 30210.5 | 0.0661095 | ||||||||
\(677\) | −252653. | −0.551249 | −0.275624 | − | 0.961265i | \(-0.588885\pi\) | ||||
−0.275624 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(678\) | 451878. | 0.983018 | ||||||||
\(679\) | 1.45443e6i | 3.15467i | ||||||||
\(680\) | − | 566091.i | − | 1.22425i | ||||||
\(681\) | 372139.i | 0.802436i | ||||||||
\(682\) | − | 397107.i | − | 0.853766i | ||||||
\(683\) | 506823.i | 1.08646i | 0.839583 | + | 0.543232i | \(0.182800\pi\) | ||||
−0.839583 | + | 0.543232i | \(0.817200\pi\) | |||||||
\(684\) | −9614.79 | −0.0205507 | ||||||||
\(685\) | 139131. | 0.296512 | ||||||||
\(686\) | − | 903969.i | − | 1.92090i | ||||||
\(687\) | 221715.i | 0.469767i | ||||||||
\(688\) | − | 695234.i | − | 1.46877i | ||||||
\(689\) | − | 802708.i | − | 1.69090i | ||||||
\(690\) | 806453. | 1.69387 | ||||||||
\(691\) | − | 789140.i | − | 1.65271i | −0.563146 | − | 0.826357i | \(-0.690409\pi\) | ||
0.563146 | − | 0.826357i | \(-0.309591\pi\) | |||||||
\(692\) | 21015.7i | 0.0438865i | ||||||||
\(693\) | 157759.i | 0.328495i | ||||||||
\(694\) | −371682. | −0.771706 | ||||||||
\(695\) | 334292. | 0.692080 | ||||||||
\(696\) | 128329.i | 0.264914i | ||||||||
\(697\) | −234198. | −0.482079 | ||||||||
\(698\) | 551847. | 1.13268 | ||||||||
\(699\) | 356384.i | 0.729396i | ||||||||
\(700\) | 67855.8 | 0.138481 | ||||||||
\(701\) | 259759.i | 0.528608i | 0.964439 | + | 0.264304i | \(0.0851423\pi\) | ||||
−0.964439 | + | 0.264304i | \(0.914858\pi\) | |||||||
\(702\) | 146415. | 0.297105 | ||||||||
\(703\) | 424570.i | 0.859091i | ||||||||
\(704\) | 262751.i | 0.530151i | ||||||||
\(705\) | − | 304256.i | − | 0.612154i | ||||||
\(706\) | 334059. | 0.670213 | ||||||||
\(707\) | 743298.i | 1.48704i | ||||||||
\(708\) | 15124.8 | + | 72.1187i | 0.0301733 | + | 0.000143874i | ||||
\(709\) | 171973. | 0.342112 | 0.171056 | − | 0.985261i | \(-0.445282\pi\) | ||||
0.171056 | + | 0.985261i | \(0.445282\pi\) | |||||||
\(710\) | 420532.i | 0.834223i | ||||||||
\(711\) | −33587.7 | −0.0664417 | ||||||||
\(712\) | 748772. | 1.47703 | ||||||||
\(713\) | −1.35713e6 | −2.66958 | ||||||||
\(714\) | 420196.i | 0.824244i | ||||||||
\(715\) | −686050. | −1.34197 | ||||||||
\(716\) | 13868.4i | 0.0270521i | ||||||||
\(717\) | −5008.62 | −0.00974270 | ||||||||
\(718\) | 264184.i | 0.512458i | ||||||||
\(719\) | − | 823365.i | − | 1.59270i | −0.604835 | − | 0.796351i | \(-0.706761\pi\) | ||
0.604835 | − | 0.796351i | \(-0.293239\pi\) | |||||||
\(720\) | 287472. | 0.554538 | ||||||||
\(721\) | − | 101608.i | − | 0.195461i | ||||||
\(722\) | 209414.i | 0.401727i | ||||||||
\(723\) | −84850.0 | −0.162321 | ||||||||
\(724\) | −43470.0 | −0.0829301 | ||||||||
\(725\) | −375233. | −0.713880 | ||||||||
\(726\) | − | 213374.i | − | 0.404826i | ||||||
\(727\) | −403704. | −0.763825 | −0.381912 | − | 0.924198i | \(-0.624734\pi\) | ||||
−0.381912 | + | 0.924198i | \(0.624734\pi\) | |||||||
\(728\) | 1.35843e6 | 2.56315 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 195226. | 0.366347 | ||||||||
\(731\) | 594093.i | 1.11178i | ||||||||
\(732\) | 9429.52i | 0.0175982i | ||||||||
\(733\) | −472977. | −0.880302 | −0.440151 | − | 0.897924i | \(-0.645075\pi\) | ||||
−0.440151 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(734\) | 530042. | 0.983825 | ||||||||
\(735\) | 1.02286e6 | 1.89340 | ||||||||
\(736\) | −102061. | −0.188409 | ||||||||
\(737\) | 45445.7 | 0.0836676 | ||||||||
\(738\) | − | 113008.i | − | 0.207490i | ||||||
\(739\) | 107013.i | 0.195951i | 0.995189 | + | 0.0979757i | \(0.0312368\pi\) | ||||
−0.995189 | + | 0.0979757i | \(0.968763\pi\) | |||||||
\(740\) | 33035.9i | 0.0603286i | ||||||||
\(741\) | − | 562817.i | − | 1.02502i | ||||||
\(742\) | 1.11161e6i | 2.01904i | ||||||||
\(743\) | −915468. | −1.65831 | −0.829155 | − | 0.559019i | \(-0.811178\pi\) | ||||
−0.829155 | + | 0.559019i | \(0.811178\pi\) | |||||||
\(744\) | −459681. | −0.830444 | ||||||||
\(745\) | 1.01984e6i | 1.83747i | ||||||||
\(746\) | − | 294883.i | − | 0.529874i | ||||||
\(747\) | − | 165012.i | − | 0.295715i | ||||||
\(748\) | 13068.0i | 0.0233563i | ||||||||
\(749\) | −1.02238e6 | −1.82242 | ||||||||
\(750\) | 270656.i | 0.481165i | ||||||||
\(751\) | − | 832564.i | − | 1.47617i | −0.674705 | − | 0.738087i | \(-0.735729\pi\) | ||
0.674705 | − | 0.738087i | \(-0.264271\pi\) | |||||||
\(752\) | 397004.i | 0.702036i | ||||||||
\(753\) | −300632. | −0.530208 | ||||||||
\(754\) | 414238. | 0.728631 | ||||||||
\(755\) | 545406.i | 0.956811i | ||||||||
\(756\) | −10070.3 | −0.0176197 | ||||||||
\(757\) | 247540. | 0.431970 | 0.215985 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215985 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(758\) | 350690.i | 0.610359i | ||||||||
\(759\) | 337599. | 0.586028 | ||||||||
\(760\) | − | 1.05002e6i | − | 1.81789i | ||||||
\(761\) | −539545. | −0.931662 | −0.465831 | − | 0.884874i | \(-0.654244\pi\) | ||||
−0.465831 | + | 0.884874i | \(0.654244\pi\) | |||||||
\(762\) | − | 571411.i | − | 0.984098i | ||||||
\(763\) | 504988.i | 0.867425i | ||||||||
\(764\) | − | 32774.5i | − | 0.0561500i | ||||||
\(765\) | −245652. | −0.419756 | ||||||||
\(766\) | 1.14221e6i | 1.94665i | ||||||||
\(767\) | −4221.58 | + | 885352.i | −0.00717604 | + | 1.50496i | ||||
\(768\) | −53248.0 | −0.0902779 | ||||||||
\(769\) | 97270.6i | 0.164486i | 0.996612 | + | 0.0822430i | \(0.0262084\pi\) | ||||
−0.996612 | + | 0.0822430i | \(0.973792\pi\) | |||||||
\(770\) | 950059. | 1.60239 | ||||||||
\(771\) | 489776. | 0.823927 | ||||||||
\(772\) | −30287.3 | −0.0508189 | ||||||||
\(773\) | − | 234313.i | − | 0.392136i | −0.980590 | − | 0.196068i | \(-0.937183\pi\) | ||
0.980590 | − | 0.196068i | \(-0.0628173\pi\) | |||||||
\(774\) | −286670. | −0.478520 | ||||||||
\(775\) | − | 1.34411e6i | − | 2.23785i | ||||||
\(776\) | 1.05423e6 | 1.75069 | ||||||||
\(777\) | 444686.i | 0.736565i | ||||||||
\(778\) | − | 87095.3i | − | 0.143892i | ||||||
\(779\) | −434403. | −0.715844 | ||||||||
\(780\) | − | 43792.9i | − | 0.0719804i | ||||||
\(781\) | 176044.i | 0.288615i | ||||||||
\(782\) | 899205. | 1.47043 | ||||||||
\(783\) | 55687.4 | 0.0908309 | ||||||||
\(784\) | −1.33467e6 | −2.17141 | ||||||||
\(785\) | 217356.i | 0.352721i | ||||||||
\(786\) | −41781.1 | −0.0676294 | ||||||||
\(787\) | 773520. | 1.24888 | 0.624442 | − | 0.781071i | \(-0.285327\pi\) | ||||
0.624442 | + | 0.781071i | \(0.285327\pi\) | |||||||
\(788\) | −31328.9 | −0.0504537 | ||||||||
\(789\) | −33197.0 | −0.0533267 | ||||||||
\(790\) | 202272.i | 0.324102i | ||||||||
\(791\) | − | 1.81931e6i | − | 2.90773i | ||||||
\(792\) | 114350. | 0.182299 | ||||||||
\(793\) | −551972. | −0.877749 | ||||||||
\(794\) | 187151. | 0.296860 | ||||||||
\(795\) | −649860. | −1.02822 | ||||||||
\(796\) | 63887.8 | 0.100831 | ||||||||
\(797\) | − | 254532.i | − | 0.400705i | −0.979724 | − | 0.200353i | \(-0.935791\pi\) | ||
0.979724 | − | 0.200353i | \(-0.0642088\pi\) | |||||||
\(798\) | 779402.i | 1.22393i | ||||||||
\(799\) | − | 339249.i | − | 0.531404i | ||||||
\(800\) | − | 101081.i | − | 0.157939i | ||||||
\(801\) | − | 324925.i | − | 0.506429i | ||||||
\(802\) | 233133. | 0.362455 | ||||||||
\(803\) | 81726.0 | 0.126744 | ||||||||
\(804\) | 2900.95i | 0.00448775i | ||||||||
\(805\) | − | 3.24687e6i | − | 5.01041i | ||||||
\(806\) | 1.48383e6i | 2.28409i | ||||||||
\(807\) | − | 264876.i | − | 0.406720i | ||||||
\(808\) | 538770. | 0.825240 | ||||||||
\(809\) | − | 3663.27i | − | 0.00559721i | −0.999996 | − | 0.00279861i | \(-0.999109\pi\) | ||
0.999996 | − | 0.00279861i | \(-0.000890825\pi\) | |||||||
\(810\) | − | 118535.i | − | 0.180666i | ||||||
\(811\) | 137551.i | 0.209133i | 0.994518 | + | 0.104567i | \(0.0333456\pi\) | ||||
−0.994518 | + | 0.104567i | \(0.966654\pi\) | |||||||
\(812\) | −28491.1 | −0.0432113 | ||||||||
\(813\) | −537383. | −0.813022 | ||||||||
\(814\) | 278449.i | 0.420239i | ||||||||
\(815\) | −5446.42 | −0.00819966 | ||||||||
\(816\) | 320535. | 0.481388 | ||||||||
\(817\) | 1.10196e6i | 1.65090i | ||||||||
\(818\) | 624696. | 0.933602 | ||||||||
\(819\) | − | 589482.i | − | 0.878825i | ||||||
\(820\) | −33801.0 | −0.0502693 | ||||||||
\(821\) | 336436.i | 0.499132i | 0.968358 | + | 0.249566i | \(0.0802880\pi\) | ||||
−0.968358 | + | 0.249566i | \(0.919712\pi\) | |||||||
\(822\) | 74856.7i | 0.110787i | ||||||||
\(823\) | − | 197126.i | − | 0.291035i | −0.989356 | − | 0.145517i | \(-0.953515\pi\) | ||
0.989356 | − | 0.145517i | \(-0.0464847\pi\) | |||||||
\(824\) | −73649.6 | −0.108472 | ||||||||
\(825\) | 334359.i | 0.491253i | ||||||||
\(826\) | 5846.15 | − | 1.22606e6i | 0.00856860 | − | 1.79701i | ||||
\(827\) | −1.17052e6 | −1.71146 | −0.855730 | − | 0.517422i | \(-0.826892\pi\) | ||||
−0.855730 | + | 0.517422i | \(0.826892\pi\) | |||||||
\(828\) | 21550.1i | 0.0314332i | ||||||||
\(829\) | −596609. | −0.868122 | −0.434061 | − | 0.900884i | \(-0.642920\pi\) | ||||
−0.434061 | + | 0.900884i | \(0.642920\pi\) | |||||||
\(830\) | −993734. | −1.44249 | ||||||||
\(831\) | 616688. | 0.893024 | ||||||||
\(832\) | − | 981794.i | − | 1.41832i | ||||||
\(833\) | 1.14050e6 | 1.64364 | ||||||||
\(834\) | 179859.i | 0.258583i | ||||||||
\(835\) | 186534. | 0.267537 | ||||||||
\(836\) | 24239.2i | 0.0346821i | ||||||||
\(837\) | 199476.i | 0.284734i | ||||||||
\(838\) | 61370.7 | 0.0873923 | ||||||||
\(839\) | 763822.i | 1.08510i | 0.840025 | + | 0.542548i | \(0.182540\pi\) | ||||
−0.840025 | + | 0.542548i | \(0.817460\pi\) | |||||||
\(840\) | − | 1.09976e6i | − | 1.55862i | ||||||
\(841\) | −549729. | −0.777243 | ||||||||
\(842\) | 788414. | 1.11206 | ||||||||
\(843\) | 330943. | 0.465691 | ||||||||
\(844\) | − | 20402.4i | − | 0.0286416i | ||||||
\(845\) | 1.43168e6 | 2.00509 | ||||||||
\(846\) | 163699. | 0.228720 | ||||||||
\(847\) | −859068. | −1.19746 | ||||||||
\(848\) | 847961. | 1.17919 | ||||||||
\(849\) | 39090.4i | 0.0542319i | ||||||||
\(850\) | 890575.i | 1.23263i | ||||||||
\(851\) | 951612. | 1.31402 | ||||||||
\(852\) | −11237.5 | −0.0154807 | ||||||||
\(853\) | 262734. | 0.361092 | 0.180546 | − | 0.983567i | \(-0.442214\pi\) | ||||
0.180546 | + | 0.983567i | \(0.442214\pi\) | |||||||
\(854\) | 764384. | 1.04808 | ||||||||
\(855\) | −455648. | −0.623300 | ||||||||
\(856\) | 741057.i | 1.01136i | ||||||||
\(857\) | − | 1.18773e6i | − | 1.61717i | −0.588382 | − | 0.808583i | \(-0.700235\pi\) | ||
0.588382 | − | 0.808583i | \(-0.299765\pi\) | |||||||
\(858\) | − | 369116.i | − | 0.501404i | ||||||
\(859\) | − | 403204.i | − | 0.546435i | −0.961952 | − | 0.273217i | \(-0.911912\pi\) | ||
0.961952 | − | 0.273217i | \(-0.0880878\pi\) | |||||||
\(860\) | 85743.4i | 0.115932i | ||||||||
\(861\) | −454985. | −0.613748 | ||||||||
\(862\) | 553885. | 0.745426 | ||||||||
\(863\) | − | 709539.i | − | 0.952697i | −0.879257 | − | 0.476348i | \(-0.841960\pi\) | ||
0.879257 | − | 0.476348i | \(-0.158040\pi\) | |||||||
\(864\) | 15001.2i | 0.0200955i | ||||||||
\(865\) | 995939.i | 1.33107i | ||||||||
\(866\) | − | 113792.i | − | 0.151732i | ||||||
\(867\) | 160083. | 0.212965 | ||||||||
\(868\) | − | 102057.i | − | 0.135457i | ||||||
\(869\) | 84675.5i | 0.112129i | ||||||||
\(870\) | − | 335361.i | − | 0.443072i | ||||||
\(871\) | −169812. | −0.223837 | ||||||||
\(872\) | 366034. | 0.481381 | ||||||||
\(873\) | − | 457475.i | − | 0.600259i | ||||||
\(874\) | 1.66789e6 | 2.18346 | ||||||||
\(875\) | 1.08969e6 | 1.42327 | ||||||||
\(876\) | 5216.85i | 0.00679829i | ||||||||
\(877\) | 557208. | 0.724466 | 0.362233 | − | 0.932087i | \(-0.382014\pi\) | ||||
0.362233 | + | 0.932087i | \(0.382014\pi\) | |||||||
\(878\) | − | 1.05342e6i | − | 1.36651i | ||||||
\(879\) | 171288. | 0.221691 | ||||||||
\(880\) | − | 724726.i | − | 0.935855i | ||||||
\(881\) | 511735.i | 0.659316i | 0.944101 | + | 0.329658i | \(0.106933\pi\) | ||||
−0.944101 | + | 0.329658i | \(0.893067\pi\) | |||||||
\(882\) | 550331.i | 0.707436i | ||||||||
\(883\) | 1.39799e6 | 1.79301 | 0.896507 | − | 0.443029i | \(-0.146096\pi\) | ||||
0.896507 | + | 0.443029i | \(0.146096\pi\) | |||||||
\(884\) | − | 48829.6i | − | 0.0624854i | ||||||
\(885\) | 716767. | + | 3417.73i | 0.915149 | + | 0.00436366i | ||||
\(886\) | 427605. | 0.544722 | ||||||||
\(887\) | − | 526850.i | − | 0.669638i | −0.942282 | − | 0.334819i | \(-0.891325\pi\) | ||
0.942282 | − | 0.334819i | \(-0.108675\pi\) | |||||||
\(888\) | 322325. | 0.408759 | ||||||||
\(889\) | −2.30056e6 | −2.91092 | ||||||||
\(890\) | −1.95677e6 | −2.47035 | ||||||||
\(891\) | − | 49621.4i | − | 0.0625048i | ||||||
\(892\) | 22175.9 | 0.0278709 | ||||||||
\(893\) | − | 629257.i | − | 0.789087i | ||||||
\(894\) | −548706. | −0.686538 | ||||||||
\(895\) | 657229.i | 0.820485i | ||||||||
\(896\) | 1.50647e6i | 1.87648i | ||||||||
\(897\) | −1.26147e6 | −1.56780 | ||||||||
\(898\) | 62521.5i | 0.0775313i | ||||||||
\(899\) | 564359.i | 0.698291i | ||||||||
\(900\) | −21343.3 | −0.0263497 | ||||||||
\(901\) | −724602. | −0.892585 | ||||||||
\(902\) | −284898. | −0.350167 | ||||||||
\(903\) | 1.15416e6i | 1.41544i | ||||||||
\(904\) | −1.31870e6 | −1.61365 | ||||||||
\(905\) | −2.06006e6 | −2.51525 | ||||||||
\(906\) | −293445. | −0.357495 | ||||||||
\(907\) | −836151. | −1.01641 | −0.508206 | − | 0.861235i | \(-0.669691\pi\) | ||||
−0.508206 | + | 0.861235i | \(0.669691\pi\) | |||||||
\(908\) | 59886.7i | 0.0726371i | ||||||||
\(909\) | − | 233796.i | − | 0.282950i | ||||||
\(910\) | −3.54998e6 | −4.28690 | ||||||||
\(911\) | 527285. | 0.635343 | 0.317672 | − | 0.948201i | \(-0.397099\pi\) | ||||
0.317672 | + | 0.948201i | \(0.397099\pi\) | |||||||
\(912\) | 594546. | 0.714818 | ||||||||
\(913\) | −415999. | −0.499058 | ||||||||
\(914\) | −1.44328e6 | −1.72765 | ||||||||
\(915\) | 446868.i | 0.533749i | ||||||||
\(916\) | 35679.7i | 0.0425237i | ||||||||
\(917\) | 168216.i | 0.200045i | ||||||||
\(918\) | − | 132168.i | − | 0.156834i | ||||||
\(919\) | 156081.i | 0.184807i | 0.995722 | + | 0.0924036i | \(0.0294550\pi\) | ||||
−0.995722 | + | 0.0924036i | \(0.970545\pi\) | |||||||
\(920\) | −2.35345e6 | −2.78055 | ||||||||
\(921\) | 446165. | 0.525989 | ||||||||
\(922\) | − | 377087.i | − | 0.443588i | ||||||
\(923\) | − | 657804.i | − | 0.772135i | ||||||
\(924\) | 25387.6i | 0.0297356i | ||||||||
\(925\) | 942478.i | 1.10151i | ||||||||
\(926\) | 1.16790e6 | 1.36202 | ||||||||
\(927\) | 31959.8i | 0.0371916i | ||||||||
\(928\) | 42441.6i | 0.0492828i | ||||||||
\(929\) | − | 443250.i | − | 0.513591i | −0.966466 | − | 0.256795i | \(-0.917333\pi\) | ||
0.966466 | − | 0.256795i | \(-0.0826667\pi\) | |||||||
\(930\) | 1.20128e6 | 1.38893 | ||||||||
\(931\) | 2.11547e6 | 2.44066 | ||||||||
\(932\) | 57351.3i | 0.0660255i | ||||||||
\(933\) | 108742. | 0.124920 | ||||||||
\(934\) | −1.24916e6 | −1.43194 | ||||||||
\(935\) | 619295.i | 0.708393i | ||||||||
\(936\) | −427278. | −0.487707 | ||||||||
\(937\) | 176637.i | 0.201188i | 0.994928 | + | 0.100594i | \(0.0320743\pi\) | ||||
−0.994928 | + | 0.100594i | \(0.967926\pi\) | |||||||
\(938\) | 235160. | 0.267274 | ||||||||
\(939\) | − | 688575.i | − | 0.780944i | ||||||
\(940\) | − | 48962.6i | − | 0.0554127i | ||||||
\(941\) | 1.41132e6i | 1.59385i | 0.604078 | + | 0.796925i | \(0.293542\pi\) | ||||
−0.604078 | + | 0.796925i | \(0.706458\pi\) | |||||||
\(942\) | −116944. | −0.131788 | ||||||||
\(943\) | 973651.i | 1.09491i | ||||||||
\(944\) | −935264. | − | 4459.58i | −1.04952 | − | 0.00500437i | ||||
\(945\) | −477235. | −0.534403 | ||||||||
\(946\) | 722702.i | 0.807564i | ||||||||
\(947\) | 774655. | 0.863791 | 0.431895 | − | 0.901924i | \(-0.357845\pi\) | ||||
0.431895 | + | 0.901924i | \(0.357845\pi\) | |||||||
\(948\) | −5405.13 | −0.00601436 | ||||||||
\(949\) | −305376. | −0.339081 | ||||||||
\(950\) | 1.65188e6i | 1.83034i | ||||||||
\(951\) | 564606. | 0.624288 | ||||||||
\(952\) | − | 1.22625e6i | − | 1.35302i | ||||||
\(953\) | 443289. | 0.488091 | 0.244046 | − | 0.969764i | \(-0.421525\pi\) | ||||
0.244046 | + | 0.969764i | \(0.421525\pi\) | |||||||
\(954\) | − | 349644.i | − | 0.384175i | ||||||
\(955\) | − | 1.55320e6i | − | 1.70302i | ||||||
\(956\) | −806.016 | −0.000881917 | ||||||||
\(957\) | − | 140390.i | − | 0.153289i | ||||||
\(958\) | 1.63087e6i | 1.77701i | ||||||||
\(959\) | 301381. | 0.327702 | ||||||||
\(960\) | −794845. | −0.862462 | ||||||||
\(961\) | −1.09805e6 | −1.18898 | ||||||||
\(962\) | − | 1.04045e6i | − | 1.12427i | ||||||
\(963\) | 321577. | 0.346763 | ||||||||
\(964\) | −13654.6 | −0.0146934 | ||||||||
\(965\) | −1.43532e6 | −1.54133 | ||||||||
\(966\) | 1.74691e6 | 1.87205 | ||||||||
\(967\) | − | 376709.i | − | 0.402859i | −0.979503 | − | 0.201429i | \(-0.935441\pi\) | ||
0.979503 | − | 0.201429i | \(-0.0645587\pi\) | |||||||
\(968\) | 622684.i | 0.664534i | ||||||||
\(969\) | −508053. | −0.541080 | ||||||||
\(970\) | −2.75501e6 | −2.92806 | ||||||||
\(971\) | 563582. | 0.597749 | 0.298875 | − | 0.954292i | \(-0.403389\pi\) | ||||
0.298875 | + | 0.954292i | \(0.403389\pi\) | |||||||
\(972\) | 3167.50 | 0.00335262 | ||||||||
\(973\) | 724133. | 0.764879 | ||||||||
\(974\) | − | 647327.i | − | 0.682347i | ||||||
\(975\) | − | 1.24936e6i | − | 1.31425i | ||||||
\(976\) | − | 583089.i | − | 0.612118i | ||||||
\(977\) | 242271.i | 0.253812i | 0.991915 | + | 0.126906i | \(0.0405046\pi\) | ||||
−0.991915 | + | 0.126906i | \(0.959495\pi\) | |||||||
\(978\) | − | 2930.34i | − | 0.00306365i | ||||||
\(979\) | −819146. | −0.854665 | ||||||||
\(980\) | 164605. | 0.171392 | ||||||||
\(981\) | − | 158838.i | − | 0.165051i | ||||||
\(982\) | 315716.i | 0.327396i | ||||||||
\(983\) | 1.65719e6i | 1.71501i | 0.514478 | + | 0.857504i | \(0.327986\pi\) | ||||
−0.514478 | + | 0.857504i | \(0.672014\pi\) | |||||||
\(984\) | 329790.i | 0.340602i | ||||||||
\(985\) | −1.48469e6 | −1.53025 | ||||||||
\(986\) | − | 373932.i | − | 0.384626i | ||||||
\(987\) | − | 659070.i | − | 0.676546i | ||||||
\(988\) | − | 90571.7i | − | 0.0927852i | ||||||
\(989\) | 2.46987e6 | 2.52512 | ||||||||
\(990\) | −298830. | −0.304898 | ||||||||
\(991\) | − | 1.43312e6i | − | 1.45927i | −0.683835 | − | 0.729636i | \(-0.739689\pi\) | ||
0.683835 | − | 0.729636i | \(-0.260311\pi\) | |||||||
\(992\) | −152028. | −0.154490 | ||||||||
\(993\) | 529228. | 0.536716 | ||||||||
\(994\) | 910943.i | 0.921974i | ||||||||
\(995\) | 3.02766e6 | 3.05817 | ||||||||
\(996\) | − | 26554.6i | − | 0.0267683i | ||||||
\(997\) | 1.54766e6 | 1.55699 | 0.778495 | − | 0.627650i | \(-0.215983\pi\) | ||||
0.778495 | + | 0.627650i | \(0.215983\pi\) | |||||||
\(998\) | 4588.45i | 0.00460686i | ||||||||
\(999\) | − | 139871.i | − | 0.140151i |
(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 | 177.5.c.a.58.30 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.11 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.11 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.30 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.11 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.30 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.11 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.30 | 40 | 177.176 | even | 2 |