Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.10 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.15 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | − | 3.49916i | − | 0.499880i | −0.968261 | − | 0.249940i | \(-0.919589\pi\) | ||
0.968261 | − | 0.249940i | \(-0.0804109\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | 11.9699i | 1.08817i | 0.839030 | + | 0.544086i | \(0.183123\pi\) | ||||
−0.839030 | + | 0.544086i | \(0.816877\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | −19.9639 | −1.53568 | −0.767842 | − | 0.640640i | \(-0.778669\pi\) | ||||
−0.767842 | + | 0.640640i | \(0.778669\pi\) | |||||||
\(14\) | 4.94856i | 0.353468i | ||||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 26.2299i | − | 1.54293i | −0.636269 | − | 0.771467i | \(-0.719523\pi\) | ||
0.636269 | − | 0.771467i | \(-0.280477\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 0.0297478i | 0.00156568i | 1.00000 | 0.000782838i | \(0.000249185\pi\) | |||||
−1.00000 | 0.000782838i | \(0.999751\pi\) | ||||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | − | 6.06072i | − | 0.288606i | ||||||
\(22\) | − | 16.9280i | − | 0.769453i | ||||||
\(23\) | −9.54233 | − | 20.9271i | −0.414884 | − | 0.909874i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 28.2332 | 1.08589 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 6.99832i | − | 0.249940i | ||||||
\(29\) | −41.0391 | −1.41514 | −0.707571 | − | 0.706642i | \(-0.750209\pi\) | ||||
−0.707571 | + | 0.706642i | \(0.750209\pi\) | |||||||
\(30\) | 5.47723i | 0.182574i | ||||||||
\(31\) | 29.7926 | 0.961050 | 0.480525 | − | 0.876981i | \(-0.340446\pi\) | ||||
0.480525 | + | 0.876981i | \(0.340446\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 20.7325i | 0.628256i | ||||||||
\(34\) | 37.0947i | 1.09102i | ||||||||
\(35\) | −7.82436 | −0.223553 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 51.3489i | 1.38781i | 0.720067 | + | 0.693905i | \(0.244111\pi\) | ||||
−0.720067 | + | 0.693905i | \(0.755889\pi\) | |||||||
\(38\) | − | 0.0420698i | − | 0.00110710i | ||||||
\(39\) | −34.5785 | −0.886627 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | −74.6506 | −1.82075 | −0.910373 | − | 0.413789i | \(-0.864205\pi\) | ||||
−0.910373 | + | 0.413789i | \(0.864205\pi\) | |||||||
\(42\) | 8.57115i | 0.204075i | ||||||||
\(43\) | − | 51.7973i | − | 1.20459i | −0.798274 | − | 0.602294i | \(-0.794253\pi\) | ||
0.798274 | − | 0.602294i | \(-0.205747\pi\) | |||||||
\(44\) | 23.9398i | 0.544086i | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 13.4949 | + | 29.5954i | 0.293367 | + | 0.643378i | ||||
\(47\) | −27.5439 | −0.586040 | −0.293020 | − | 0.956106i | \(-0.594660\pi\) | ||||
−0.293020 | + | 0.956106i | \(0.594660\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 36.7559 | 0.750120 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | − | 45.4315i | − | 0.890814i | ||||||
\(52\) | −39.9278 | −0.767842 | ||||||||
\(53\) | − | 15.0332i | − | 0.283645i | −0.989892 | − | 0.141823i | \(-0.954704\pi\) | ||
0.989892 | − | 0.141823i | \(-0.0452963\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | 26.7655 | 0.486645 | ||||||||
\(56\) | 9.89712i | 0.176734i | ||||||||
\(57\) | 0.0515248i | 0.000903943i | ||||||||
\(58\) | 58.0381 | 1.00066 | ||||||||
\(59\) | 1.55359 | 0.0263320 | 0.0131660 | − | 0.999913i | \(-0.495809\pi\) | ||||
0.0131660 | + | 0.999913i | \(0.495809\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | − | 12.9254i | − | 0.211892i | −0.994372 | − | 0.105946i | \(-0.966213\pi\) | ||
0.994372 | − | 0.105946i | \(-0.0337871\pi\) | |||||||
\(62\) | −42.1330 | −0.679565 | ||||||||
\(63\) | − | 10.4975i | − | 0.166627i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 44.6406i | 0.686778i | ||||||||
\(66\) | − | 29.3201i | − | 0.444244i | ||||||
\(67\) | 28.2878i | 0.422206i | 0.977464 | + | 0.211103i | \(0.0677055\pi\) | ||||
−0.977464 | + | 0.211103i | \(0.932294\pi\) | |||||||
\(68\) | − | 52.4598i | − | 0.771467i | ||||||
\(69\) | −16.5278 | − | 36.2468i | −0.239533 | − | 0.525316i | ||||
\(70\) | 11.0653 | 0.158076 | ||||||||
\(71\) | −94.7727 | −1.33483 | −0.667413 | − | 0.744688i | \(-0.732599\pi\) | ||||
−0.667413 | + | 0.744688i | \(0.732599\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | −25.3868 | −0.347764 | −0.173882 | − | 0.984766i | \(-0.555631\pi\) | ||||
−0.173882 | + | 0.984766i | \(0.555631\pi\) | |||||||
\(74\) | − | 72.6184i | − | 0.981329i | ||||||
\(75\) | −8.66025 | −0.115470 | ||||||||
\(76\) | 0.0594957i | 0.000782838i | ||||||||
\(77\) | 41.8845 | 0.543955 | ||||||||
\(78\) | 48.9013 | 0.626940 | ||||||||
\(79\) | − | 80.5613i | − | 1.01976i | −0.860245 | − | 0.509882i | \(-0.829689\pi\) | ||
0.860245 | − | 0.509882i | \(-0.170311\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.572 | 1.28746 | ||||||||
\(83\) | 55.8397i | 0.672767i | 0.941725 | + | 0.336384i | \(0.109204\pi\) | ||||
−0.941725 | + | 0.336384i | \(0.890796\pi\) | |||||||
\(84\) | − | 12.1214i | − | 0.144303i | ||||||
\(85\) | −58.6518 | −0.690021 | ||||||||
\(86\) | 73.2525i | 0.851773i | ||||||||
\(87\) | −71.0818 | −0.817032 | ||||||||
\(88\) | − | 33.8559i | − | 0.384727i | ||||||
\(89\) | − | 81.9490i | − | 0.920775i | −0.887718 | − | 0.460387i | \(-0.847710\pi\) | ||
0.887718 | − | 0.460387i | \(-0.152290\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | 69.8568i | 0.767657i | ||||||||
\(92\) | −19.0847 | − | 41.8542i | −0.207442 | − | 0.454937i | ||||
\(93\) | 51.6022 | 0.554863 | ||||||||
\(94\) | 38.9530 | 0.414393 | ||||||||
\(95\) | 0.0665182 | 0.000700191 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 4.03039i | 0.0415504i | 0.999784 | + | 0.0207752i | \(0.00661343\pi\) | ||||
−0.999784 | + | 0.0207752i | \(0.993387\pi\) | |||||||
\(98\) | −51.9807 | −0.530415 | ||||||||
\(99\) | 35.9097i | 0.362724i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −162.974 | −1.61360 | −0.806801 | − | 0.590823i | \(-0.798803\pi\) | ||||
−0.806801 | + | 0.590823i | \(0.798803\pi\) | |||||||
\(102\) | 64.2498i | 0.629900i | ||||||||
\(103\) | − | 137.541i | − | 1.33535i | −0.744453 | − | 0.667675i | \(-0.767289\pi\) | ||
0.744453 | − | 0.667675i | \(-0.232711\pi\) | |||||||
\(104\) | 56.4664 | 0.542946 | ||||||||
\(105\) | −13.5522 | −0.129068 | ||||||||
\(106\) | 21.2602i | 0.200567i | ||||||||
\(107\) | 66.5945i | 0.622379i | 0.950348 | + | 0.311189i | \(0.100727\pi\) | ||||
−0.950348 | + | 0.311189i | \(0.899273\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 95.0049i | 0.871605i | 0.900042 | + | 0.435802i | \(0.143535\pi\) | ||||
−0.900042 | + | 0.435802i | \(0.856465\pi\) | |||||||
\(110\) | −37.8521 | −0.344110 | ||||||||
\(111\) | 88.9390i | 0.801252i | ||||||||
\(112\) | − | 13.9966i | − | 0.124970i | ||||||
\(113\) | − | 194.493i | − | 1.72118i | −0.509300 | − | 0.860589i | \(-0.670096\pi\) | ||
0.509300 | − | 0.860589i | \(-0.329904\pi\) | |||||||
\(114\) | − | 0.0728670i | − | 0.000639184i | ||||||
\(115\) | −46.7944 | + | 21.3373i | −0.406908 | + | 0.185542i | ||||
\(116\) | −82.0782 | −0.707571 | ||||||||
\(117\) | −59.8916 | −0.511894 | ||||||||
\(118\) | −2.19711 | −0.0186195 | ||||||||
\(119\) | −91.7825 | −0.771282 | ||||||||
\(120\) | 10.9545i | 0.0912871i | ||||||||
\(121\) | −22.2782 | −0.184117 | ||||||||
\(122\) | 18.2793i | 0.149830i | ||||||||
\(123\) | −129.299 | −1.05121 | ||||||||
\(124\) | 59.5851 | 0.480525 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 14.8457i | 0.117823i | ||||||||
\(127\) | −139.254 | −1.09649 | −0.548244 | − | 0.836318i | \(-0.684704\pi\) | ||||
−0.548244 | + | 0.836318i | \(0.684704\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − | 89.7156i | − | 0.695470i | ||||||
\(130\) | − | 63.1313i | − | 0.485626i | ||||||
\(131\) | 87.8593 | 0.670682 | 0.335341 | − | 0.942097i | \(-0.391149\pi\) | ||||
0.335341 | + | 0.942097i | \(0.391149\pi\) | |||||||
\(132\) | 41.4649i | 0.314128i | ||||||||
\(133\) | 0.104092 | 0.000782650 | ||||||||
\(134\) | − | 40.0050i | − | 0.298545i | ||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | 74.1893i | 0.545510i | ||||||||
\(137\) | − | 181.394i | − | 1.32405i | −0.749484 | − | 0.662023i | \(-0.769698\pi\) | ||
0.749484 | − | 0.662023i | \(-0.230302\pi\) | |||||||
\(138\) | 23.3738 | + | 51.2607i | 0.169376 | + | 0.371455i | ||||
\(139\) | −135.089 | −0.971860 | −0.485930 | − | 0.873998i | \(-0.661519\pi\) | ||||
−0.485930 | + | 0.873998i | \(0.661519\pi\) | |||||||
\(140\) | −15.6487 | −0.111777 | ||||||||
\(141\) | −47.7074 | −0.338351 | ||||||||
\(142\) | 134.029 | 0.943865 | ||||||||
\(143\) | − | 238.965i | − | 1.67109i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 91.7662i | 0.632871i | ||||||||
\(146\) | 35.9023 | 0.245906 | ||||||||
\(147\) | 63.6631 | 0.433082 | ||||||||
\(148\) | 102.698i | 0.693905i | ||||||||
\(149\) | 56.7676i | 0.380991i | 0.981688 | + | 0.190495i | \(0.0610094\pi\) | ||||
−0.981688 | + | 0.190495i | \(0.938991\pi\) | |||||||
\(150\) | 12.2474 | 0.0816497 | ||||||||
\(151\) | 36.4693 | 0.241519 | 0.120759 | − | 0.992682i | \(-0.461467\pi\) | ||||
0.120759 | + | 0.992682i | \(0.461467\pi\) | |||||||
\(152\) | − | 0.0841396i | − | 0.000553550i | ||||||
\(153\) | − | 78.6897i | − | 0.514312i | ||||||
\(154\) | −59.2337 | −0.384634 | ||||||||
\(155\) | − | 66.6182i | − | 0.429795i | ||||||
\(156\) | −69.1569 | −0.443314 | ||||||||
\(157\) | 47.7035i | 0.303844i | 0.988392 | + | 0.151922i | \(0.0485463\pi\) | ||||
−0.988392 | + | 0.151922i | \(0.951454\pi\) | |||||||
\(158\) | 113.931i | 0.721081i | ||||||||
\(159\) | − | 26.0383i | − | 0.163763i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −73.2273 | + | 33.3901i | −0.454828 | + | 0.207392i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 118.851 | 0.729148 | 0.364574 | − | 0.931174i | \(-0.381215\pi\) | ||||
0.364574 | + | 0.931174i | \(0.381215\pi\) | |||||||
\(164\) | −149.301 | −0.910373 | ||||||||
\(165\) | 46.3592 | 0.280965 | ||||||||
\(166\) | − | 78.9692i | − | 0.475718i | ||||||
\(167\) | −108.318 | −0.648610 | −0.324305 | − | 0.945952i | \(-0.605130\pi\) | ||||
−0.324305 | + | 0.945952i | \(0.605130\pi\) | |||||||
\(168\) | 17.1423i | 0.102038i | ||||||||
\(169\) | 229.557 | 1.35832 | ||||||||
\(170\) | 82.9462 | 0.487919 | ||||||||
\(171\) | 0.0892435i | 0.000521892i | ||||||||
\(172\) | − | 103.595i | − | 0.602294i | ||||||
\(173\) | 78.7417 | 0.455154 | 0.227577 | − | 0.973760i | \(-0.426920\pi\) | ||||
0.227577 | + | 0.973760i | \(0.426920\pi\) | |||||||
\(174\) | 100.525 | 0.577729 | ||||||||
\(175\) | 17.4958i | 0.0999760i | ||||||||
\(176\) | 47.8795i | 0.272043i | ||||||||
\(177\) | 2.69089 | 0.0152028 | ||||||||
\(178\) | 115.893i | 0.651086i | ||||||||
\(179\) | 225.677 | 1.26077 | 0.630383 | − | 0.776285i | \(-0.282898\pi\) | ||||
0.630383 | + | 0.776285i | \(0.282898\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | 219.280i | 1.21149i | 0.795659 | + | 0.605745i | \(0.207125\pi\) | ||||
−0.795659 | + | 0.605745i | \(0.792875\pi\) | |||||||
\(182\) | − | 98.7924i | − | 0.542816i | ||||||
\(183\) | − | 22.3875i | − | 0.122336i | ||||||
\(184\) | 26.9898 | + | 59.1908i | 0.146684 | + | 0.321689i | ||||
\(185\) | 114.820 | 0.620647 | ||||||||
\(186\) | −72.9766 | −0.392347 | ||||||||
\(187\) | 313.969 | 1.67898 | ||||||||
\(188\) | −55.0878 | −0.293020 | ||||||||
\(189\) | − | 18.1822i | − | 0.0962019i | ||||||
\(190\) | −0.0940709 | −0.000495110 | ||||||||
\(191\) | 240.006i | 1.25658i | 0.777981 | + | 0.628288i | \(0.216244\pi\) | ||||
−0.777981 | + | 0.628288i | \(0.783756\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 368.019 | 1.90683 | 0.953417 | − | 0.301654i | \(-0.0975388\pi\) | ||||
0.953417 | + | 0.301654i | \(0.0975388\pi\) | |||||||
\(194\) | − | 5.69984i | − | 0.0293806i | ||||||
\(195\) | 77.3198i | 0.396512i | ||||||||
\(196\) | 73.5118 | 0.375060 | ||||||||
\(197\) | −1.84737 | −0.00937754 | −0.00468877 | − | 0.999989i | \(-0.501492\pi\) | ||||
−0.00468877 | + | 0.999989i | \(0.501492\pi\) | |||||||
\(198\) | − | 50.7839i | − | 0.256484i | ||||||
\(199\) | − | 56.5030i | − | 0.283934i | −0.989871 | − | 0.141967i | \(-0.954657\pi\) | ||
0.989871 | − | 0.141967i | \(-0.0453428\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 48.9959i | 0.243761i | ||||||||
\(202\) | 230.480 | 1.14099 | ||||||||
\(203\) | 143.602i | 0.707401i | ||||||||
\(204\) | − | 90.8630i | − | 0.445407i | ||||||
\(205\) | 166.924i | 0.814262i | ||||||||
\(206\) | 194.513i | 0.944236i | ||||||||
\(207\) | −28.6270 | − | 62.7813i | −0.138295 | − | 0.303291i | ||||
\(208\) | −79.8555 | −0.383921 | ||||||||
\(209\) | −0.356078 | −0.00170372 | ||||||||
\(210\) | 19.1657 | 0.0912652 | ||||||||
\(211\) | −88.2861 | −0.418418 | −0.209209 | − | 0.977871i | \(-0.567089\pi\) | ||||
−0.209209 | + | 0.977871i | \(0.567089\pi\) | |||||||
\(212\) | − | 30.0664i | − | 0.141823i | ||||||
\(213\) | −164.151 | −0.770662 | ||||||||
\(214\) | − | 94.1788i | − | 0.440088i | ||||||
\(215\) | −115.822 | −0.538708 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | − | 104.249i | − | 0.480410i | ||||||
\(218\) | − | 134.357i | − | 0.616317i | ||||||
\(219\) | −43.9712 | −0.200782 | ||||||||
\(220\) | 53.5310 | 0.243323 | ||||||||
\(221\) | 523.650i | 2.36946i | ||||||||
\(222\) | − | 125.779i | − | 0.566571i | ||||||
\(223\) | 129.548 | 0.580934 | 0.290467 | − | 0.956885i | \(-0.406189\pi\) | ||||
0.290467 | + | 0.956885i | \(0.406189\pi\) | |||||||
\(224\) | 19.7942i | 0.0883671i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 275.055i | 1.21706i | ||||||||
\(227\) | − | 76.1848i | − | 0.335616i | −0.985820 | − | 0.167808i | \(-0.946331\pi\) | ||
0.985820 | − | 0.167808i | \(-0.0536688\pi\) | |||||||
\(228\) | 0.103050i | 0.000451972i | ||||||||
\(229\) | − | 81.3519i | − | 0.355248i | −0.984098 | − | 0.177624i | \(-0.943159\pi\) | ||
0.984098 | − | 0.177624i | \(-0.0568411\pi\) | |||||||
\(230\) | 66.1773 | − | 30.1755i | 0.287728 | − | 0.131198i | ||||
\(231\) | 72.5461 | 0.314053 | ||||||||
\(232\) | 116.076 | 0.500328 | ||||||||
\(233\) | 229.590 | 0.985366 | 0.492683 | − | 0.870209i | \(-0.336016\pi\) | ||||
0.492683 | + | 0.870209i | \(0.336016\pi\) | |||||||
\(234\) | 84.6996 | 0.361964 | ||||||||
\(235\) | 61.5900i | 0.262085i | ||||||||
\(236\) | 3.10718 | 0.0131660 | ||||||||
\(237\) | − | 139.536i | − | 0.588761i | ||||||
\(238\) | 129.800 | 0.545379 | ||||||||
\(239\) | −156.740 | −0.655818 | −0.327909 | − | 0.944709i | \(-0.606344\pi\) | ||||
−0.327909 | + | 0.944709i | \(0.606344\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | 191.086i | 0.792887i | 0.918059 | + | 0.396444i | \(0.129756\pi\) | ||||
−0.918059 | + | 0.396444i | \(0.870244\pi\) | |||||||
\(242\) | 31.5061 | 0.130190 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 25.8508i | − | 0.105946i | ||||||
\(245\) | − | 82.1887i | − | 0.335464i | ||||||
\(246\) | 182.856 | 0.743316 | ||||||||
\(247\) | − | 0.593882i | − | 0.00240438i | ||||||
\(248\) | −84.2661 | −0.339783 | ||||||||
\(249\) | 96.7172i | 0.388422i | ||||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | − | 456.878i | − | 1.82023i | −0.414354 | − | 0.910116i | \(-0.635992\pi\) | ||
0.414354 | − | 0.910116i | \(-0.364008\pi\) | |||||||
\(252\) | − | 20.9950i | − | 0.0833133i | ||||||
\(253\) | 250.495 | − | 114.221i | 0.990099 | − | 0.451465i | ||||
\(254\) | 196.935 | 0.775335 | ||||||||
\(255\) | −101.588 | −0.398384 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 212.501 | 0.826851 | 0.413425 | − | 0.910538i | \(-0.364332\pi\) | ||||
0.413425 | + | 0.910538i | \(0.364332\pi\) | |||||||
\(258\) | 126.877i | 0.491771i | ||||||||
\(259\) | 179.678 | 0.693738 | ||||||||
\(260\) | 89.2812i | 0.343389i | ||||||||
\(261\) | −123.117 | −0.471714 | ||||||||
\(262\) | −124.252 | −0.474243 | ||||||||
\(263\) | 478.231i | 1.81837i | 0.416392 | + | 0.909185i | \(0.363294\pi\) | ||||
−0.416392 | + | 0.909185i | \(0.636706\pi\) | |||||||
\(264\) | − | 58.6402i | − | 0.222122i | ||||||
\(265\) | −33.6153 | −0.126850 | ||||||||
\(266\) | −0.147209 | −0.000553417 | ||||||||
\(267\) | − | 141.940i | − | 0.531610i | ||||||
\(268\) | 56.5756i | 0.211103i | ||||||||
\(269\) | 525.346 | 1.95296 | 0.976479 | − | 0.215613i | \(-0.0691750\pi\) | ||||
0.976479 | + | 0.215613i | \(0.0691750\pi\) | |||||||
\(270\) | 16.4317i | 0.0608581i | ||||||||
\(271\) | 374.732 | 1.38278 | 0.691388 | − | 0.722484i | \(-0.257000\pi\) | ||||
0.691388 | + | 0.722484i | \(0.257000\pi\) | |||||||
\(272\) | − | 104.920i | − | 0.385734i | ||||||
\(273\) | 120.996i | 0.443207i | ||||||||
\(274\) | 256.530i | 0.936241i | ||||||||
\(275\) | − | 59.8494i | − | 0.217634i | ||||||
\(276\) | −33.0556 | − | 72.4936i | −0.119767 | − | 0.262658i | ||||
\(277\) | −406.934 | −1.46907 | −0.734537 | − | 0.678569i | \(-0.762601\pi\) | ||||
−0.734537 | + | 0.678569i | \(0.762601\pi\) | |||||||
\(278\) | 191.044 | 0.687209 | ||||||||
\(279\) | 89.3777 | 0.320350 | ||||||||
\(280\) | 22.1306 | 0.0790379 | ||||||||
\(281\) | 189.257i | 0.673511i | 0.941592 | + | 0.336755i | \(0.109330\pi\) | ||||
−0.941592 | + | 0.336755i | \(0.890670\pi\) | |||||||
\(282\) | 67.4685 | 0.239250 | ||||||||
\(283\) | − | 157.312i | − | 0.555872i | −0.960600 | − | 0.277936i | \(-0.910350\pi\) | ||
0.960600 | − | 0.277936i | \(-0.0896503\pi\) | |||||||
\(284\) | −189.545 | −0.667413 | ||||||||
\(285\) | 0.115213 | 0.000404256 | ||||||||
\(286\) | 337.948i | 1.18164i | ||||||||
\(287\) | 261.214i | 0.910154i | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −399.007 | −1.38065 | ||||||||
\(290\) | − | 129.777i | − | 0.447507i | ||||||
\(291\) | 6.98085i | 0.0239892i | ||||||||
\(292\) | −50.7736 | −0.173882 | ||||||||
\(293\) | − | 463.682i | − | 1.58253i | −0.611472 | − | 0.791266i | \(-0.709422\pi\) | ||
0.611472 | − | 0.791266i | \(-0.290578\pi\) | |||||||
\(294\) | −90.0332 | −0.306235 | ||||||||
\(295\) | − | 3.47393i | − | 0.0117760i | ||||||
\(296\) | − | 145.237i | − | 0.490665i | ||||||
\(297\) | 62.1974i | 0.209419i | ||||||||
\(298\) | − | 80.2815i | − | 0.269401i | ||||||
\(299\) | 190.502 | + | 417.786i | 0.637130 | + | 1.39728i | ||||
\(300\) | −17.3205 | −0.0577350 | ||||||||
\(301\) | −181.247 | −0.602150 | ||||||||
\(302\) | −51.5754 | −0.170780 | ||||||||
\(303\) | −282.279 | −0.931614 | ||||||||
\(304\) | 0.118991i | 0.000391419i | ||||||||
\(305\) | −28.9021 | −0.0947609 | ||||||||
\(306\) | 111.284i | 0.363673i | ||||||||
\(307\) | 350.361 | 1.14124 | 0.570620 | − | 0.821214i | \(-0.306703\pi\) | ||||
0.570620 | + | 0.821214i | \(0.306703\pi\) | |||||||
\(308\) | 83.7691 | 0.271977 | ||||||||
\(309\) | − | 238.228i | − | 0.770965i | ||||||
\(310\) | 94.2123i | 0.303911i | ||||||||
\(311\) | 152.396 | 0.490018 | 0.245009 | − | 0.969521i | \(-0.421209\pi\) | ||||
0.245009 | + | 0.969521i | \(0.421209\pi\) | |||||||
\(312\) | 97.8027 | 0.313470 | ||||||||
\(313\) | 47.6313i | 0.152177i | 0.997101 | + | 0.0760884i | \(0.0242431\pi\) | ||||
−0.997101 | + | 0.0760884i | \(0.975757\pi\) | |||||||
\(314\) | − | 67.4629i | − | 0.214850i | ||||||
\(315\) | −23.4731 | −0.0745177 | ||||||||
\(316\) | − | 161.123i | − | 0.509882i | ||||||
\(317\) | 410.929 | 1.29631 | 0.648153 | − | 0.761511i | \(-0.275542\pi\) | ||||
0.648153 | + | 0.761511i | \(0.275542\pi\) | |||||||
\(318\) | 36.8237i | 0.115798i | ||||||||
\(319\) | − | 491.233i | − | 1.53992i | ||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 115.345i | 0.359330i | ||||||||
\(322\) | 103.559 | − | 47.2208i | 0.321612 | − | 0.146648i | ||||
\(323\) | 0.780282 | 0.00241573 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 99.8194 | 0.307137 | ||||||||
\(326\) | −168.081 | −0.515585 | ||||||||
\(327\) | 164.553i | 0.503221i | ||||||||
\(328\) | 211.144 | 0.643731 | ||||||||
\(329\) | 96.3805i | 0.292950i | ||||||||
\(330\) | −65.5618 | −0.198672 | ||||||||
\(331\) | −392.356 | −1.18537 | −0.592683 | − | 0.805436i | \(-0.701931\pi\) | ||||
−0.592683 | + | 0.805436i | \(0.701931\pi\) | |||||||
\(332\) | 111.679i | 0.336384i | ||||||||
\(333\) | 154.047i | 0.462603i | ||||||||
\(334\) | 153.185 | 0.458637 | ||||||||
\(335\) | 63.2534 | 0.188816 | ||||||||
\(336\) | − | 24.2429i | − | 0.0721514i | ||||||
\(337\) | − | 458.368i | − | 1.36014i | −0.733146 | − | 0.680071i | \(-0.761949\pi\) | ||
0.733146 | − | 0.680071i | \(-0.238051\pi\) | |||||||
\(338\) | −324.642 | −0.960480 | ||||||||
\(339\) | − | 336.872i | − | 0.993722i | ||||||
\(340\) | −117.304 | −0.345011 | ||||||||
\(341\) | 356.614i | 1.04579i | ||||||||
\(342\) | − | 0.126209i | − | 0.000369033i | ||||||
\(343\) | − | 300.073i | − | 0.874850i | ||||||
\(344\) | 146.505i | 0.425886i | ||||||||
\(345\) | −81.0503 | + | 36.9573i | −0.234929 | + | 0.107123i | ||||
\(346\) | −111.358 | −0.321843 | ||||||||
\(347\) | −178.744 | −0.515112 | −0.257556 | − | 0.966263i | \(-0.582917\pi\) | ||||
−0.257556 | + | 0.966263i | \(0.582917\pi\) | |||||||
\(348\) | −142.164 | −0.408516 | ||||||||
\(349\) | −24.0318 | −0.0688591 | −0.0344295 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344295 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(350\) | − | 24.7428i | − | 0.0706937i | ||||||
\(351\) | −103.735 | −0.295542 | ||||||||
\(352\) | − | 67.7119i | − | 0.192363i | ||||||
\(353\) | −568.260 | −1.60980 | −0.804901 | − | 0.593409i | \(-0.797782\pi\) | ||||
−0.804901 | + | 0.593409i | \(0.797782\pi\) | |||||||
\(354\) | −3.80550 | −0.0107500 | ||||||||
\(355\) | 211.918i | 0.596953i | ||||||||
\(356\) | − | 163.898i | − | 0.460387i | ||||||
\(357\) | −158.972 | −0.445300 | ||||||||
\(358\) | −319.155 | −0.891496 | ||||||||
\(359\) | − | 540.074i | − | 1.50438i | −0.658945 | − | 0.752192i | \(-0.728997\pi\) | ||
0.658945 | − | 0.752192i | \(-0.271003\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | 360.999 | 0.999998 | ||||||||
\(362\) | − | 310.108i | − | 0.856653i | ||||||
\(363\) | −38.5869 | −0.106300 | ||||||||
\(364\) | 139.714i | 0.383829i | ||||||||
\(365\) | 56.7666i | 0.155525i | ||||||||
\(366\) | 31.6607i | 0.0865045i | ||||||||
\(367\) | 404.550i | 1.10232i | 0.834401 | + | 0.551158i | \(0.185814\pi\) | ||||
−0.834401 | + | 0.551158i | \(0.814186\pi\) | |||||||
\(368\) | −38.1693 | − | 83.7084i | −0.103721 | − | 0.227469i | ||||
\(369\) | −223.952 | −0.606915 | ||||||||
\(370\) | −162.380 | −0.438864 | ||||||||
\(371\) | −52.6035 | −0.141789 | ||||||||
\(372\) | 103.204 | 0.277431 | ||||||||
\(373\) | 192.435i | 0.515911i | 0.966157 | + | 0.257955i | \(0.0830487\pi\) | ||||
−0.966157 | + | 0.257955i | \(0.916951\pi\) | |||||||
\(374\) | −444.019 | −1.18722 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | 77.9059 | 0.207197 | ||||||||
\(377\) | 819.300 | 2.17321 | ||||||||
\(378\) | 25.7135i | 0.0680250i | ||||||||
\(379\) | 711.208i | 1.87654i | 0.345908 | + | 0.938269i | \(0.387571\pi\) | ||||
−0.345908 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(380\) | 0.133036 | 0.000350096 | ||||||||
\(381\) | −241.195 | −0.633058 | ||||||||
\(382\) | − | 339.420i | − | 0.888533i | ||||||
\(383\) | − | 308.566i | − | 0.805655i | −0.915276 | − | 0.402827i | \(-0.868027\pi\) | ||
0.915276 | − | 0.402827i | \(-0.131973\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | − | 93.6567i | − | 0.243264i | ||||||
\(386\) | −520.458 | −1.34834 | ||||||||
\(387\) | − | 155.392i | − | 0.401530i | ||||||
\(388\) | 8.06079i | 0.0207752i | ||||||||
\(389\) | − | 197.980i | − | 0.508947i | −0.967080 | − | 0.254474i | \(-0.918098\pi\) | ||
0.967080 | − | 0.254474i | \(-0.0819022\pi\) | |||||||
\(390\) | − | 109.347i | − | 0.280376i | ||||||
\(391\) | −548.916 | + | 250.294i | −1.40388 | + | 0.640139i | ||||
\(392\) | −103.961 | −0.265208 | ||||||||
\(393\) | 152.177 | 0.387218 | ||||||||
\(394\) | 2.61258 | 0.00663092 | ||||||||
\(395\) | −180.141 | −0.456052 | ||||||||
\(396\) | 71.8193i | 0.181362i | ||||||||
\(397\) | 267.667 | 0.674224 | 0.337112 | − | 0.941465i | \(-0.390550\pi\) | ||||
0.337112 | + | 0.941465i | \(0.390550\pi\) | |||||||
\(398\) | 79.9073i | 0.200772i | ||||||||
\(399\) | 0.180293 | 0.000451863 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 749.856i | 1.86997i | 0.354694 | + | 0.934983i | \(0.384585\pi\) | ||||
−0.354694 | + | 0.934983i | \(0.615415\pi\) | |||||||
\(402\) | − | 69.2906i | − | 0.172365i | ||||||
\(403\) | −594.775 | −1.47587 | ||||||||
\(404\) | −325.948 | −0.806801 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | − | 203.084i | − | 0.500208i | ||||||
\(407\) | −614.641 | −1.51017 | ||||||||
\(408\) | 128.500i | 0.314950i | ||||||||
\(409\) | 291.243 | 0.712086 | 0.356043 | − | 0.934469i | \(-0.384126\pi\) | ||||
0.356043 | + | 0.934469i | \(0.384126\pi\) | |||||||
\(410\) | − | 236.066i | − | 0.575770i | ||||||
\(411\) | − | 314.184i | − | 0.764438i | ||||||
\(412\) | − | 275.082i | − | 0.667675i | ||||||
\(413\) | − | 5.43625i | − | 0.0131628i | ||||||
\(414\) | 40.4847 | + | 88.7862i | 0.0977891 | + | 0.214459i | ||||
\(415\) | 124.861 | 0.300871 | ||||||||
\(416\) | 112.933 | 0.271473 | ||||||||
\(417\) | −233.980 | −0.561104 | ||||||||
\(418\) | 0.503571 | 0.00120471 | ||||||||
\(419\) | − | 334.184i | − | 0.797574i | −0.917044 | − | 0.398787i | \(-0.869431\pi\) | ||
0.917044 | − | 0.398787i | \(-0.130569\pi\) | |||||||
\(420\) | −27.1044 | −0.0645342 | ||||||||
\(421\) | − | 414.441i | − | 0.984422i | −0.870476 | − | 0.492211i | \(-0.836189\pi\) | ||
0.870476 | − | 0.492211i | \(-0.163811\pi\) | |||||||
\(422\) | 124.855 | 0.295866 | ||||||||
\(423\) | −82.6317 | −0.195347 | ||||||||
\(424\) | 42.5203i | 0.100284i | ||||||||
\(425\) | 131.149i | 0.308587i | ||||||||
\(426\) | 232.145 | 0.544941 | ||||||||
\(427\) | −45.2280 | −0.105920 | ||||||||
\(428\) | 133.189i | 0.311189i | ||||||||
\(429\) | − | 413.900i | − | 0.964802i | ||||||
\(430\) | 163.797 | 0.380924 | ||||||||
\(431\) | 721.242i | 1.67342i | 0.547649 | + | 0.836708i | \(0.315523\pi\) | ||||
−0.547649 | + | 0.836708i | \(0.684477\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 231.360i | 0.534319i | 0.963652 | + | 0.267160i | \(0.0860851\pi\) | ||||
−0.963652 | + | 0.267160i | \(0.913915\pi\) | |||||||
\(434\) | 147.430i | 0.339701i | ||||||||
\(435\) | 158.944i | 0.365388i | ||||||||
\(436\) | 190.010i | 0.435802i | ||||||||
\(437\) | 0.622536 | − | 0.283864i | 0.00142457 | − | 0.000649574i | ||||
\(438\) | 62.1847 | 0.141974 | ||||||||
\(439\) | 110.160 | 0.250935 | 0.125468 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125468 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(440\) | −75.7042 | −0.172055 | ||||||||
\(441\) | 110.268 | 0.250040 | ||||||||
\(442\) | − | 740.553i | − | 1.67546i | ||||||
\(443\) | 140.713 | 0.317636 | 0.158818 | − | 0.987308i | \(-0.449232\pi\) | ||||
0.158818 | + | 0.987308i | \(0.449232\pi\) | |||||||
\(444\) | 177.878i | 0.400626i | ||||||||
\(445\) | −183.243 | −0.411783 | ||||||||
\(446\) | −183.209 | −0.410782 | ||||||||
\(447\) | 98.3244i | 0.219965i | ||||||||
\(448\) | − | 27.9933i | − | 0.0624850i | ||||||
\(449\) | 222.010 | 0.494455 | 0.247227 | − | 0.968958i | \(-0.420481\pi\) | ||||
0.247227 | + | 0.968958i | \(0.420481\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | − | 893.559i | − | 1.98128i | ||||||
\(452\) | − | 388.986i | − | 0.860589i | ||||||
\(453\) | 63.1668 | 0.139441 | ||||||||
\(454\) | 107.742i | 0.237316i | ||||||||
\(455\) | 156.205 | 0.343307 | ||||||||
\(456\) | − | 0.145734i | − | 0.000319592i | ||||||
\(457\) | − | 448.070i | − | 0.980460i | −0.871593 | − | 0.490230i | \(-0.836913\pi\) | ||
0.871593 | − | 0.490230i | \(-0.163087\pi\) | |||||||
\(458\) | 115.049i | 0.251199i | ||||||||
\(459\) | − | 136.294i | − | 0.296938i | ||||||
\(460\) | −93.5889 | + | 42.6746i | −0.203454 | + | 0.0927709i | ||||
\(461\) | 819.214 | 1.77704 | 0.888519 | − | 0.458841i | \(-0.151735\pi\) | ||||
0.888519 | + | 0.458841i | \(0.151735\pi\) | |||||||
\(462\) | −102.596 | −0.222069 | ||||||||
\(463\) | −793.838 | −1.71455 | −0.857276 | − | 0.514857i | \(-0.827845\pi\) | ||||
−0.857276 | + | 0.514857i | \(0.827845\pi\) | |||||||
\(464\) | −164.156 | −0.353785 | ||||||||
\(465\) | − | 115.386i | − | 0.248142i | ||||||
\(466\) | −324.690 | −0.696759 | ||||||||
\(467\) | − | 335.892i | − | 0.719254i | −0.933096 | − | 0.359627i | \(-0.882904\pi\) | ||
0.933096 | − | 0.359627i | \(-0.117096\pi\) | |||||||
\(468\) | −119.783 | −0.255947 | ||||||||
\(469\) | 98.9835 | 0.211052 | ||||||||
\(470\) | − | 87.1015i | − | 0.185322i | ||||||
\(471\) | 82.6249i | 0.175424i | ||||||||
\(472\) | −4.39421 | −0.00930977 | ||||||||
\(473\) | 620.008 | 1.31080 | ||||||||
\(474\) | 197.334i | 0.416317i | ||||||||
\(475\) | − | 0.148739i | − | 0.000313135i | ||||||
\(476\) | −183.565 | −0.385641 | ||||||||
\(477\) | − | 45.0996i | − | 0.0945484i | ||||||
\(478\) | 221.664 | 0.463733 | ||||||||
\(479\) | − | 578.078i | − | 1.20684i | −0.797422 | − | 0.603422i | \(-0.793804\pi\) | ||
0.797422 | − | 0.603422i | \(-0.206196\pi\) | |||||||
\(480\) | 21.9089i | 0.0456435i | ||||||||
\(481\) | − | 1025.12i | − | 2.13124i | ||||||
\(482\) | − | 270.236i | − | 0.560656i | ||||||
\(483\) | −126.833 | + | 57.8334i | −0.262595 | + | 0.119738i | ||||
\(484\) | −44.5563 | −0.0920585 | ||||||||
\(485\) | 9.01223 | 0.0185819 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −921.262 | −1.89171 | −0.945854 | − | 0.324591i | \(-0.894773\pi\) | ||||
−0.945854 | + | 0.324591i | \(0.894773\pi\) | |||||||
\(488\) | 36.5586i | 0.0749151i | ||||||||
\(489\) | 205.856 | 0.420974 | ||||||||
\(490\) | 116.232i | 0.237209i | ||||||||
\(491\) | −830.923 | −1.69231 | −0.846153 | − | 0.532940i | \(-0.821087\pi\) | ||||
−0.846153 | + | 0.532940i | \(0.821087\pi\) | |||||||
\(492\) | −258.597 | −0.525604 | ||||||||
\(493\) | 1076.45i | 2.18347i | ||||||||
\(494\) | 0.839876i | 0.00170015i | ||||||||
\(495\) | 80.2964 | 0.162215 | ||||||||
\(496\) | 119.170 | 0.240263 | ||||||||
\(497\) | 331.625i | 0.667253i | ||||||||
\(498\) | − | 136.779i | − | 0.274656i | ||||||
\(499\) | −547.907 | −1.09801 | −0.549005 | − | 0.835819i | \(-0.684993\pi\) | ||||
−0.549005 | + | 0.835819i | \(0.684993\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −187.612 | −0.374475 | ||||||||
\(502\) | 646.123i | 1.28710i | ||||||||
\(503\) | − | 40.5138i | − | 0.0805443i | −0.999189 | − | 0.0402722i | \(-0.987178\pi\) | ||
0.999189 | − | 0.0402722i | \(-0.0128225\pi\) | |||||||
\(504\) | 29.6913i | 0.0589114i | ||||||||
\(505\) | 364.420i | 0.721625i | ||||||||
\(506\) | −354.254 | + | 161.532i | −0.700106 | + | 0.319234i | ||||
\(507\) | 397.604 | 0.784228 | ||||||||
\(508\) | −278.508 | −0.548244 | ||||||||
\(509\) | −943.330 | −1.85330 | −0.926650 | − | 0.375925i | \(-0.877325\pi\) | ||||
−0.926650 | + | 0.375925i | \(0.877325\pi\) | |||||||
\(510\) | 143.667 | 0.281700 | ||||||||
\(511\) | 88.8324i | 0.173840i | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0.154574i | 0.000301314i | ||||||||
\(514\) | −300.521 | −0.584672 | ||||||||
\(515\) | −307.551 | −0.597187 | ||||||||
\(516\) | − | 179.431i | − | 0.347735i | ||||||
\(517\) | − | 329.697i | − | 0.637712i | ||||||
\(518\) | −254.103 | −0.490547 | ||||||||
\(519\) | 136.385 | 0.262783 | ||||||||
\(520\) | − | 126.263i | − | 0.242813i | ||||||
\(521\) | 409.118i | 0.785255i | 0.919698 | + | 0.392628i | \(0.128434\pi\) | ||||
−0.919698 | + | 0.392628i | \(0.871566\pi\) | |||||||
\(522\) | 174.114 | 0.333552 | ||||||||
\(523\) | − | 88.2598i | − | 0.168757i | −0.996434 | − | 0.0843784i | \(-0.973110\pi\) | ||
0.996434 | − | 0.0843784i | \(-0.0268904\pi\) | |||||||
\(524\) | 175.719 | 0.335341 | ||||||||
\(525\) | 30.3036i | 0.0577211i | ||||||||
\(526\) | − | 676.321i | − | 1.28578i | ||||||
\(527\) | − | 781.455i | − | 1.48284i | ||||||
\(528\) | 82.9298i | 0.157064i | ||||||||
\(529\) | −346.888 | + | 399.387i | −0.655742 | + | 0.754985i | ||||
\(530\) | 47.5391 | 0.0896965 | ||||||||
\(531\) | 4.66076 | 0.00877733 | ||||||||
\(532\) | 0.208185 | 0.000391325 | ||||||||
\(533\) | 1490.31 | 2.79609 | ||||||||
\(534\) | 200.733i | 0.375905i | ||||||||
\(535\) | 148.910 | 0.278336 | ||||||||
\(536\) | − | 80.0099i | − | 0.149272i | ||||||
\(537\) | 390.884 | 0.727903 | ||||||||
\(538\) | −742.951 | −1.38095 | ||||||||
\(539\) | 439.964i | 0.816259i | ||||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | 383.774 | 0.709380 | 0.354690 | − | 0.934984i | \(-0.384586\pi\) | ||||
0.354690 | + | 0.934984i | \(0.384586\pi\) | |||||||
\(542\) | −529.951 | −0.977770 | ||||||||
\(543\) | 379.804i | 0.699454i | ||||||||
\(544\) | 148.379i | 0.272755i | ||||||||
\(545\) | 212.437 | 0.389793 | ||||||||
\(546\) | − | 171.114i | − | 0.313395i | ||||||
\(547\) | −143.193 | −0.261780 | −0.130890 | − | 0.991397i | \(-0.541783\pi\) | ||||
−0.130890 | + | 0.991397i | \(0.541783\pi\) | |||||||
\(548\) | − | 362.788i | − | 0.662023i | ||||||
\(549\) | − | 38.7762i | − | 0.0706306i | ||||||
\(550\) | 84.6399i | 0.153891i | ||||||||
\(551\) | − | 1.22082i | − | 0.00221565i | ||||||
\(552\) | 46.7477 | + | 102.521i | 0.0846878 | + | 0.185727i | ||||
\(553\) | −281.897 | −0.509759 | ||||||||
\(554\) | 575.491 | 1.03879 | ||||||||
\(555\) | 198.874 | 0.358331 | ||||||||
\(556\) | −270.177 | −0.485930 | ||||||||
\(557\) | 624.965i | 1.12202i | 0.827809 | + | 0.561010i | \(0.189587\pi\) | ||||
−0.827809 | + | 0.561010i | \(0.810413\pi\) | |||||||
\(558\) | −126.399 | −0.226522 | ||||||||
\(559\) | 1034.08i | 1.84987i | ||||||||
\(560\) | −31.2974 | −0.0558883 | ||||||||
\(561\) | 543.810 | 0.969358 | ||||||||
\(562\) | − | 267.649i | − | 0.476244i | ||||||
\(563\) | − | 697.193i | − | 1.23835i | −0.785251 | − | 0.619177i | \(-0.787466\pi\) | ||
0.785251 | − | 0.619177i | \(-0.212534\pi\) | |||||||
\(564\) | −95.4149 | −0.169175 | ||||||||
\(565\) | −434.900 | −0.769734 | ||||||||
\(566\) | 222.472i | 0.393061i | ||||||||
\(567\) | − | 31.4924i | − | 0.0555422i | ||||||
\(568\) | 268.058 | 0.471932 | ||||||||
\(569\) | − | 943.778i | − | 1.65866i | −0.558759 | − | 0.829330i | \(-0.688722\pi\) | ||
0.558759 | − | 0.829330i | \(-0.311278\pi\) | |||||||
\(570\) | −0.162936 | −0.000285852 | ||||||||
\(571\) | 159.659i | 0.279613i | 0.990179 | + | 0.139806i | \(0.0446480\pi\) | ||||
−0.990179 | + | 0.139806i | \(0.955352\pi\) | |||||||
\(572\) | − | 477.931i | − | 0.835543i | ||||||
\(573\) | 415.703i | 0.725485i | ||||||||
\(574\) | − | 369.413i | − | 0.643576i | ||||||
\(575\) | 47.7117 | + | 104.636i | 0.0829768 | + | 0.181975i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 689.947 | 1.19575 | 0.597874 | − | 0.801590i | \(-0.296012\pi\) | ||||
0.597874 | + | 0.801590i | \(0.296012\pi\) | |||||||
\(578\) | 564.281 | 0.976265 | ||||||||
\(579\) | 637.428 | 1.10091 | ||||||||
\(580\) | 183.532i | 0.316435i | ||||||||
\(581\) | 195.392 | 0.336303 | ||||||||
\(582\) | − | 9.87241i | − | 0.0169629i | ||||||
\(583\) | 179.946 | 0.308655 | ||||||||
\(584\) | 71.8047 | 0.122953 | ||||||||
\(585\) | 133.922i | 0.228926i | ||||||||
\(586\) | 655.745i | 1.11902i | ||||||||
\(587\) | 46.9308 | 0.0799502 | 0.0399751 | − | 0.999201i | \(-0.487272\pi\) | ||||
0.0399751 | + | 0.999201i | \(0.487272\pi\) | |||||||
\(588\) | 127.326 | 0.216541 | ||||||||
\(589\) | 0.886264i | 0.00150469i | ||||||||
\(590\) | 4.91288i | 0.00832691i | ||||||||
\(591\) | −3.19975 | −0.00541412 | ||||||||
\(592\) | 205.396i | 0.346952i | ||||||||
\(593\) | 52.6508 | 0.0887871 | 0.0443936 | − | 0.999014i | \(-0.485864\pi\) | ||||
0.0443936 | + | 0.999014i | \(0.485864\pi\) | |||||||
\(594\) | − | 87.9603i | − | 0.148081i | ||||||
\(595\) | 205.232i | 0.344928i | ||||||||
\(596\) | 113.535i | 0.190495i | ||||||||
\(597\) | − | 97.8660i | − | 0.163930i | ||||||
\(598\) | −269.411 | − | 590.839i | −0.450519 | − | 0.988025i | ||||
\(599\) | −208.189 | −0.347560 | −0.173780 | − | 0.984784i | \(-0.555598\pi\) | ||||
−0.173780 | + | 0.984784i | \(0.555598\pi\) | |||||||
\(600\) | 24.4949 | 0.0408248 | ||||||||
\(601\) | 116.243 | 0.193417 | 0.0967083 | − | 0.995313i | \(-0.469169\pi\) | ||||
0.0967083 | + | 0.995313i | \(0.469169\pi\) | |||||||
\(602\) | 256.322 | 0.425784 | ||||||||
\(603\) | 84.8634i | 0.140735i | ||||||||
\(604\) | 72.9387 | 0.120759 | ||||||||
\(605\) | 49.8155i | 0.0823396i | ||||||||
\(606\) | 399.203 | 0.658750 | ||||||||
\(607\) | −211.295 | −0.348097 | −0.174048 | − | 0.984737i | \(-0.555685\pi\) | ||||
−0.174048 | + | 0.984737i | \(0.555685\pi\) | |||||||
\(608\) | − | 0.168279i | − | 0.000276775i | ||||||
\(609\) | 248.727i | 0.408418i | ||||||||
\(610\) | 40.8737 | 0.0670061 | ||||||||
\(611\) | 549.883 | 0.899973 | ||||||||
\(612\) | − | 157.379i | − | 0.257156i | ||||||
\(613\) | − | 939.938i | − | 1.53334i | −0.642040 | − | 0.766671i | \(-0.721912\pi\) | ||
0.642040 | − | 0.766671i | \(-0.278088\pi\) | |||||||
\(614\) | −495.485 | −0.806979 | ||||||||
\(615\) | 289.120i | 0.470114i | ||||||||
\(616\) | −118.467 | −0.192317 | ||||||||
\(617\) | 571.784i | 0.926717i | 0.886171 | + | 0.463359i | \(0.153356\pi\) | ||||
−0.886171 | + | 0.463359i | \(0.846644\pi\) | |||||||
\(618\) | 336.906i | 0.545155i | ||||||||
\(619\) | − | 944.586i | − | 1.52599i | −0.646406 | − | 0.762994i | \(-0.723729\pi\) | ||
0.646406 | − | 0.762994i | \(-0.276271\pi\) | |||||||
\(620\) | − | 133.236i | − | 0.214897i | ||||||
\(621\) | −49.5834 | − | 108.740i | −0.0798445 | − | 0.175105i | ||||
\(622\) | −215.520 | −0.346495 | ||||||||
\(623\) | −286.752 | −0.460277 | ||||||||
\(624\) | −138.314 | −0.221657 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 67.3608i | − | 0.107605i | ||||||
\(627\) | −0.616745 | −0.000983645 | ||||||||
\(628\) | 95.4070i | 0.151922i | ||||||||
\(629\) | 1346.88 | 2.14130 | ||||||||
\(630\) | 33.1959 | 0.0526920 | ||||||||
\(631\) | − | 1035.90i | − | 1.64169i | −0.571154 | − | 0.820843i | \(-0.693504\pi\) | ||
0.571154 | − | 0.820843i | \(-0.306496\pi\) | |||||||
\(632\) | 227.862i | 0.360541i | ||||||||
\(633\) | −152.916 | −0.241574 | ||||||||
\(634\) | −581.141 | −0.916626 | ||||||||
\(635\) | 311.382i | 0.490365i | ||||||||
\(636\) | − | 52.0765i | − | 0.0818813i | ||||||
\(637\) | −733.790 | −1.15195 | ||||||||
\(638\) | 694.709i | 1.08889i | ||||||||
\(639\) | −284.318 | −0.444942 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | 291.199i | 0.454289i | 0.973861 | + | 0.227144i | \(0.0729389\pi\) | ||||
−0.973861 | + | 0.227144i | \(0.927061\pi\) | |||||||
\(642\) | − | 163.123i | − | 0.254085i | ||||||
\(643\) | − | 183.214i | − | 0.284936i | −0.989799 | − | 0.142468i | \(-0.954496\pi\) | ||
0.989799 | − | 0.142468i | \(-0.0455038\pi\) | |||||||
\(644\) | −146.455 | + | 66.7803i | −0.227414 | + | 0.103696i | ||||
\(645\) | −200.610 | −0.311023 | ||||||||
\(646\) | −1.10349 | −0.00170818 | ||||||||
\(647\) | −196.253 | −0.303328 | −0.151664 | − | 0.988432i | \(-0.548463\pi\) | ||||
−0.151664 | + | 0.988432i | \(0.548463\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | 18.5963i | 0.0286537i | ||||||||
\(650\) | −141.166 | −0.217178 | ||||||||
\(651\) | − | 180.564i | − | 0.277365i | ||||||
\(652\) | 237.702 | 0.364574 | ||||||||
\(653\) | −215.371 | −0.329818 | −0.164909 | − | 0.986309i | \(-0.552733\pi\) | ||||
−0.164909 | + | 0.986309i | \(0.552733\pi\) | |||||||
\(654\) | − | 232.714i | − | 0.355831i | ||||||
\(655\) | − | 196.459i | − | 0.299938i | ||||||
\(656\) | −298.602 | −0.455186 | ||||||||
\(657\) | −76.1604 | −0.115921 | ||||||||
\(658\) | − | 136.303i | − | 0.207147i | ||||||
\(659\) | − | 144.360i | − | 0.219059i | −0.993984 | − | 0.109529i | \(-0.965066\pi\) | ||
0.993984 | − | 0.109529i | \(-0.0349344\pi\) | |||||||
\(660\) | 92.7183 | 0.140482 | ||||||||
\(661\) | 639.386i | 0.967301i | 0.875261 | + | 0.483650i | \(0.160689\pi\) | ||||
−0.875261 | + | 0.483650i | \(0.839311\pi\) | |||||||
\(662\) | 554.876 | 0.838181 | ||||||||
\(663\) | 906.989i | 1.36801i | ||||||||
\(664\) | − | 157.938i | − | 0.237859i | ||||||
\(665\) | − | 0.232758i | − | 0.000350012i | ||||||
\(666\) | − | 217.855i | − | 0.327110i | ||||||
\(667\) | 391.609 | + | 858.830i | 0.587120 | + | 1.28760i | ||||
\(668\) | −216.636 | −0.324305 | ||||||||
\(669\) | 224.384 | 0.335402 | ||||||||
\(670\) | −89.4538 | −0.133513 | ||||||||
\(671\) | 154.716 | 0.230575 | ||||||||
\(672\) | 34.2846i | 0.0510188i | ||||||||
\(673\) | 594.376 | 0.883174 | 0.441587 | − | 0.897218i | \(-0.354416\pi\) | ||||
0.441587 | + | 0.897218i | \(0.354416\pi\) | |||||||
\(674\) | 648.230i | 0.961766i | ||||||||
\(675\) | −25.9808 | −0.0384900 | ||||||||
\(676\) | 459.113 | 0.679162 | ||||||||
\(677\) | 514.242i | 0.759590i | 0.925071 | + | 0.379795i | \(0.124005\pi\) | ||||
−0.925071 | + | 0.379795i | \(0.875995\pi\) | |||||||
\(678\) | 476.409i | 0.702668i | ||||||||
\(679\) | 14.1030 | 0.0207702 | ||||||||
\(680\) | 165.892 | 0.243959 | ||||||||
\(681\) | − | 131.956i | − | 0.193768i | ||||||
\(682\) | − | 504.328i | − | 0.739483i | ||||||
\(683\) | 304.332 | 0.445581 | 0.222790 | − | 0.974866i | \(-0.428483\pi\) | ||||
0.222790 | + | 0.974866i | \(0.428483\pi\) | |||||||
\(684\) | 0.178487i | 0.000260946i | ||||||||
\(685\) | −405.610 | −0.592131 | ||||||||
\(686\) | 424.368i | 0.618612i | ||||||||
\(687\) | − | 140.906i | − | 0.205103i | ||||||
\(688\) | − | 207.189i | − | 0.301147i | ||||||
\(689\) | 300.121i | 0.435589i | ||||||||
\(690\) | 114.622 | − | 52.2655i | 0.166120 | − | 0.0757471i | ||||
\(691\) | 845.096 | 1.22300 | 0.611502 | − | 0.791243i | \(-0.290566\pi\) | ||||
0.611502 | + | 0.791243i | \(0.290566\pi\) | |||||||
\(692\) | 157.483 | 0.227577 | ||||||||
\(693\) | 125.654 | 0.181318 | ||||||||
\(694\) | 252.782 | 0.364239 | ||||||||
\(695\) | 302.067i | 0.434629i | ||||||||
\(696\) | 201.050 | 0.288865 | ||||||||
\(697\) | 1958.08i | 2.80929i | ||||||||
\(698\) | 33.9861 | 0.0486907 | ||||||||
\(699\) | 397.662 | 0.568901 | ||||||||
\(700\) | 34.9916i | 0.0499880i | ||||||||
\(701\) | − | 192.249i | − | 0.274250i | −0.990554 | − | 0.137125i | \(-0.956214\pi\) | ||
0.990554 | − | 0.137125i | \(-0.0437861\pi\) | |||||||
\(702\) | 146.704 | 0.208980 | ||||||||
\(703\) | −1.52752 | −0.00217286 | ||||||||
\(704\) | 95.7591i | 0.136021i | ||||||||
\(705\) | 106.677i | 0.151315i | ||||||||
\(706\) | 803.641 | 1.13830 | ||||||||
\(707\) | 570.271i | 0.806607i | ||||||||
\(708\) | 5.38179 | 0.00760139 | ||||||||
\(709\) | − | 1303.54i | − | 1.83856i | −0.393599 | − | 0.919282i | \(-0.628770\pi\) | ||
0.393599 | − | 0.919282i | \(-0.371230\pi\) | |||||||
\(710\) | − | 299.698i | − | 0.422109i | ||||||
\(711\) | − | 241.684i | − | 0.339921i | ||||||
\(712\) | 231.787i | 0.325543i | ||||||||
\(713\) | −284.291 | − | 623.472i | −0.398724 | − | 0.874435i | ||||
\(714\) | 224.820 | 0.314874 | ||||||||
\(715\) | −534.343 | −0.747333 | ||||||||
\(716\) | 451.354 | 0.630383 | ||||||||
\(717\) | −271.482 | −0.378637 | ||||||||
\(718\) | 763.779i | 1.06376i | ||||||||
\(719\) | 359.296 | 0.499717 | 0.249858 | − | 0.968282i | \(-0.419616\pi\) | ||||
0.249858 | + | 0.968282i | \(0.419616\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | −481.278 | −0.667515 | ||||||||
\(722\) | −510.530 | −0.707105 | ||||||||
\(723\) | 330.970i | 0.457774i | ||||||||
\(724\) | 438.560i | 0.605745i | ||||||||
\(725\) | 205.196 | 0.283028 | ||||||||
\(726\) | 54.5701 | 0.0751655 | ||||||||
\(727\) | − | 1033.74i | − | 1.42193i | −0.703227 | − | 0.710966i | \(-0.748258\pi\) | ||
0.703227 | − | 0.710966i | \(-0.251742\pi\) | |||||||
\(728\) | − | 197.585i | − | 0.271408i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 80.2801i | − | 0.109973i | ||||||
\(731\) | −1358.64 | −1.85860 | ||||||||
\(732\) | − | 44.7749i | − | 0.0611679i | ||||||
\(733\) | − | 88.8871i | − | 0.121265i | −0.998160 | − | 0.0606324i | \(-0.980688\pi\) | ||
0.998160 | − | 0.0606324i | \(-0.0193117\pi\) | |||||||
\(734\) | − | 572.120i | − | 0.779455i | ||||||
\(735\) | − | 142.355i | − | 0.193680i | ||||||
\(736\) | 53.9796 | + | 118.382i | 0.0733418 | + | 0.160845i | ||||
\(737\) | −338.602 | −0.459432 | ||||||||
\(738\) | 316.715 | 0.429154 | ||||||||
\(739\) | 284.091 | 0.384426 | 0.192213 | − | 0.981353i | \(-0.438434\pi\) | ||||
0.192213 | + | 0.981353i | \(0.438434\pi\) | |||||||
\(740\) | 229.639 | 0.310324 | ||||||||
\(741\) | − | 1.02863i | − | 0.00138817i | ||||||
\(742\) | 74.3927 | 0.100260 | ||||||||
\(743\) | 972.637i | 1.30907i | 0.756033 | + | 0.654534i | \(0.227135\pi\) | ||||
−0.756033 | + | 0.654534i | \(0.772865\pi\) | |||||||
\(744\) | −145.953 | −0.196174 | ||||||||
\(745\) | 126.936 | 0.170384 | ||||||||
\(746\) | − | 272.144i | − | 0.364804i | ||||||
\(747\) | 167.519i | 0.224256i | ||||||||
\(748\) | 627.937 | 0.839489 | ||||||||
\(749\) | 233.025 | 0.311114 | ||||||||
\(750\) | − | 27.3861i | − | 0.0365148i | ||||||
\(751\) | − | 85.8549i | − | 0.114321i | −0.998365 | − | 0.0571604i | \(-0.981795\pi\) | ||
0.998365 | − | 0.0571604i | \(-0.0182046\pi\) | |||||||
\(752\) | −110.176 | −0.146510 | ||||||||
\(753\) | − | 791.336i | − | 1.05091i | ||||||
\(754\) | −1158.67 | −1.53669 | ||||||||
\(755\) | − | 81.5479i | − | 0.108010i | ||||||
\(756\) | − | 36.3643i | − | 0.0481010i | ||||||
\(757\) | − | 130.267i | − | 0.172084i | −0.996292 | − | 0.0860419i | \(-0.972578\pi\) | ||
0.996292 | − | 0.0860419i | \(-0.0274219\pi\) | |||||||
\(758\) | − | 1005.80i | − | 1.32691i | ||||||
\(759\) | 433.870 | − | 197.836i | 0.571634 | − | 0.260653i | ||||
\(760\) | −0.188142 | −0.000247555 | ||||||||
\(761\) | −255.675 | −0.335973 | −0.167987 | − | 0.985789i | \(-0.553727\pi\) | ||||
−0.167987 | + | 0.985789i | \(0.553727\pi\) | |||||||
\(762\) | 341.101 | 0.447640 | ||||||||
\(763\) | 332.437 | 0.435698 | ||||||||
\(764\) | 480.012i | 0.628288i | ||||||||
\(765\) | −175.955 | −0.230007 | ||||||||
\(766\) | 436.378i | 0.569684i | ||||||||
\(767\) | −31.0156 | −0.0404376 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | 254.418i | 0.330843i | 0.986223 | + | 0.165421i | \(0.0528984\pi\) | ||||
−0.986223 | + | 0.165421i | \(0.947102\pi\) | |||||||
\(770\) | 132.451i | 0.172014i | ||||||||
\(771\) | 368.062 | 0.477383 | ||||||||
\(772\) | 736.038 | 0.953417 | ||||||||
\(773\) | − | 849.508i | − | 1.09898i | −0.835502 | − | 0.549488i | \(-0.814823\pi\) | ||
0.835502 | − | 0.549488i | \(-0.185177\pi\) | |||||||
\(774\) | 219.757i | 0.283924i | ||||||||
\(775\) | −148.963 | −0.192210 | ||||||||
\(776\) | − | 11.3997i | − | 0.0146903i | ||||||
\(777\) | 311.212 | 0.400530 | ||||||||
\(778\) | 279.987i | 0.359880i | ||||||||
\(779\) | − | 2.22069i | − | 0.00285070i | ||||||
\(780\) | 154.640i | 0.198256i | ||||||||
\(781\) | − | 1134.42i | − | 1.45252i | ||||||
\(782\) | 776.284 | − | 353.970i | 0.992691 | − | 0.452647i | ||||
\(783\) | −213.245 | −0.272344 | ||||||||
\(784\) | 147.024 | 0.187530 | ||||||||
\(785\) | 106.668 | 0.135883 | ||||||||
\(786\) | −215.210 | −0.273805 | ||||||||
\(787\) | − | 911.783i | − | 1.15856i | −0.815130 | − | 0.579278i | \(-0.803335\pi\) | ||
0.815130 | − | 0.579278i | \(-0.196665\pi\) | |||||||
\(788\) | −3.69475 | −0.00468877 | ||||||||
\(789\) | 828.321i | 1.04984i | ||||||||
\(790\) | 254.757 | 0.322477 | ||||||||
\(791\) | −680.562 | −0.860382 | ||||||||
\(792\) | − | 101.568i | − | 0.128242i | ||||||
\(793\) | 258.041i | 0.325399i | ||||||||
\(794\) | −378.538 | −0.476748 | ||||||||
\(795\) | −58.2233 | −0.0732369 | ||||||||
\(796\) | − | 113.006i | − | 0.141967i | ||||||
\(797\) | 1137.11i | 1.42673i | 0.700791 | + | 0.713366i | \(0.252830\pi\) | ||||
−0.700791 | + | 0.713366i | \(0.747170\pi\) | |||||||
\(798\) | −0.254973 | −0.000319515 | ||||||||
\(799\) | 722.473i | 0.904222i | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − | 245.847i | − | 0.306925i | ||||||
\(802\) | − | 1060.46i | − | 1.32226i | ||||||
\(803\) | − | 303.877i | − | 0.378427i | ||||||
\(804\) | 97.9918i | 0.121880i | ||||||||
\(805\) | 74.6626 | + | 163.741i | 0.0927486 | + | 0.203405i | ||||
\(806\) | 841.139 | 1.04360 | ||||||||
\(807\) | 909.925 | 1.12754 | ||||||||
\(808\) | 460.960 | 0.570494 | ||||||||
\(809\) | 946.247 | 1.16965 | 0.584825 | − | 0.811160i | \(-0.301163\pi\) | ||||
0.584825 | + | 0.811160i | \(0.301163\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | −499.192 | −0.615526 | −0.307763 | − | 0.951463i | \(-0.599580\pi\) | ||||
−0.307763 | + | 0.951463i | \(0.599580\pi\) | |||||||
\(812\) | 287.205i | 0.353700i | ||||||||
\(813\) | 649.055 | 0.798346 | ||||||||
\(814\) | 869.234 | 1.06785 | ||||||||
\(815\) | − | 265.759i | − | 0.326085i | ||||||
\(816\) | − | 181.726i | − | 0.222703i | ||||||
\(817\) | 1.54086 | 0.00188600 | ||||||||
\(818\) | −411.880 | −0.503521 | ||||||||
\(819\) | 209.570i | 0.255886i | ||||||||
\(820\) | 333.847i | 0.407131i | ||||||||
\(821\) | −495.979 | −0.604116 | −0.302058 | − | 0.953290i | \(-0.597674\pi\) | ||||
−0.302058 | + | 0.953290i | \(0.597674\pi\) | |||||||
\(822\) | 444.323i | 0.540539i | ||||||||
\(823\) | −527.562 | −0.641023 | −0.320512 | − | 0.947245i | \(-0.603855\pi\) | ||||
−0.320512 | + | 0.947245i | \(0.603855\pi\) | |||||||
\(824\) | 389.025i | 0.472118i | ||||||||
\(825\) | − | 103.662i | − | 0.125651i | ||||||
\(826\) | 7.68802i | 0.00930753i | ||||||||
\(827\) | 871.134i | 1.05337i | 0.850062 | + | 0.526683i | \(0.176565\pi\) | ||||
−0.850062 | + | 0.526683i | \(0.823435\pi\) | |||||||
\(828\) | −57.2540 | − | 125.563i | −0.0691473 | − | 0.151646i | ||||
\(829\) | −406.931 | −0.490869 | −0.245435 | − | 0.969413i | \(-0.578931\pi\) | ||||
−0.245435 | + | 0.969413i | \(0.578931\pi\) | |||||||
\(830\) | −176.581 | −0.212748 | ||||||||
\(831\) | −704.830 | −0.848170 | ||||||||
\(832\) | −159.711 | −0.191960 | ||||||||
\(833\) | − | 964.103i | − | 1.15739i | ||||||
\(834\) | 330.898 | 0.396760 | ||||||||
\(835\) | 242.206i | 0.290067i | ||||||||
\(836\) | −0.712156 | −0.000851862 | ||||||||
\(837\) | 154.807 | 0.184954 | ||||||||
\(838\) | 472.607i | 0.563970i | ||||||||
\(839\) | − | 994.738i | − | 1.18562i | −0.805341 | − | 0.592812i | \(-0.798018\pi\) | ||
0.805341 | − | 0.592812i | \(-0.201982\pi\) | |||||||
\(840\) | 38.3314 | 0.0456326 | ||||||||
\(841\) | 843.208 | 1.00263 | ||||||||
\(842\) | 586.109i | 0.696091i | ||||||||
\(843\) | 327.802i | 0.388852i | ||||||||
\(844\) | −176.572 | −0.209209 | ||||||||
\(845\) | − | 513.304i | − | 0.607461i | ||||||
\(846\) | 116.859 | 0.138131 | ||||||||
\(847\) | 77.9548i | 0.0920364i | ||||||||
\(848\) | − | 60.1328i | − | 0.0709113i | ||||||
\(849\) | − | 272.472i | − | 0.320933i | ||||||
\(850\) | − | 185.473i | − | 0.218204i | ||||||
\(851\) | 1074.58 | − | 489.989i | 1.26273 | − | 0.575780i | ||||
\(852\) | −328.302 | −0.385331 | ||||||||
\(853\) | −1043.88 | −1.22378 | −0.611888 | − | 0.790945i | \(-0.709590\pi\) | ||||
−0.611888 | + | 0.790945i | \(0.709590\pi\) | |||||||
\(854\) | 63.9621 | 0.0748971 | ||||||||
\(855\) | 0.199555 | 0.000233397 | ||||||||
\(856\) | − | 188.358i | − | 0.220044i | ||||||
\(857\) | −1226.75 | −1.43144 | −0.715722 | − | 0.698385i | \(-0.753902\pi\) | ||||
−0.715722 | + | 0.698385i | \(0.753902\pi\) | |||||||
\(858\) | 585.343i | 0.682218i | ||||||||
\(859\) | −1008.87 | −1.17448 | −0.587238 | − | 0.809414i | \(-0.699785\pi\) | ||||
−0.587238 | + | 0.809414i | \(0.699785\pi\) | |||||||
\(860\) | −231.645 | −0.269354 | ||||||||
\(861\) | 452.436i | 0.525478i | ||||||||
\(862\) | − | 1019.99i | − | 1.18328i | ||||||
\(863\) | −232.004 | −0.268834 | −0.134417 | − | 0.990925i | \(-0.542916\pi\) | ||||
−0.134417 | + | 0.990925i | \(0.542916\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | − | 176.072i | − | 0.203551i | ||||||
\(866\) | − | 327.193i | − | 0.377821i | ||||||
\(867\) | −691.100 | −0.797117 | ||||||||
\(868\) | − | 208.498i | − | 0.240205i | ||||||
\(869\) | 964.309 | 1.10968 | ||||||||
\(870\) | − | 224.780i | − | 0.258368i | ||||||
\(871\) | − | 564.734i | − | 0.648374i | ||||||
\(872\) | − | 268.714i | − | 0.308159i | ||||||
\(873\) | 12.0912i | 0.0138501i | ||||||||
\(874\) | −0.880399 | + | 0.401444i | −0.00100732 | + | 0.000459318i | ||||
\(875\) | 39.1218 | 0.0447106 | ||||||||
\(876\) | −87.9424 | −0.100391 | ||||||||
\(877\) | −90.6500 | −0.103364 | −0.0516819 | − | 0.998664i | \(-0.516458\pi\) | ||||
−0.0516819 | + | 0.998664i | \(0.516458\pi\) | |||||||
\(878\) | −155.790 | −0.177438 | ||||||||
\(879\) | − | 803.121i | − | 0.913675i | ||||||
\(880\) | 107.062 | 0.121661 | ||||||||
\(881\) | 870.146i | 0.987680i | 0.869553 | + | 0.493840i | \(0.164407\pi\) | ||||
−0.869553 | + | 0.493840i | \(0.835593\pi\) | |||||||
\(882\) | −155.942 | −0.176805 | ||||||||
\(883\) | −841.486 | −0.952986 | −0.476493 | − | 0.879178i | \(-0.658092\pi\) | ||||
−0.476493 | + | 0.879178i | \(0.658092\pi\) | |||||||
\(884\) | 1047.30i | 1.18473i | ||||||||
\(885\) | − | 6.01702i | − | 0.00679889i | ||||||
\(886\) | −198.998 | −0.224602 | ||||||||
\(887\) | −138.461 | −0.156100 | −0.0780500 | − | 0.996949i | \(-0.524869\pi\) | ||||
−0.0780500 | + | 0.996949i | \(0.524869\pi\) | |||||||
\(888\) | − | 251.557i | − | 0.283285i | ||||||
\(889\) | 487.272i | 0.548113i | ||||||||
\(890\) | 259.145 | 0.291175 | ||||||||
\(891\) | 107.729i | 0.120908i | ||||||||
\(892\) | 259.097 | 0.290467 | ||||||||
\(893\) | − | 0.819371i | − | 0.000917549i | ||||||
\(894\) | − | 139.052i | − | 0.155539i | ||||||
\(895\) | − | 504.629i | − | 0.563831i | ||||||
\(896\) | 39.5885i | 0.0441836i | ||||||||
\(897\) | 329.959 | + | 723.627i | 0.367847 | + | 0.806719i | ||||
\(898\) | −313.970 | −0.349632 | ||||||||
\(899\) | −1222.66 | −1.36002 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | −394.319 | −0.437646 | ||||||||
\(902\) | 1263.68i | 1.40098i | ||||||||
\(903\) | −313.929 | −0.347651 | ||||||||
\(904\) | 550.110i | 0.608528i | ||||||||
\(905\) | 490.325 | 0.541795 | ||||||||
\(906\) | −89.3313 | −0.0985996 | ||||||||
\(907\) | 533.764i | 0.588494i | 0.955729 | + | 0.294247i | \(0.0950689\pi\) | ||||
−0.955729 | + | 0.294247i | \(0.904931\pi\) | |||||||
\(908\) | − | 152.370i | − | 0.167808i | ||||||
\(909\) | −488.921 | −0.537867 | ||||||||
\(910\) | −220.907 | −0.242754 | ||||||||
\(911\) | − | 953.921i | − | 1.04711i | −0.851991 | − | 0.523557i | \(-0.824605\pi\) | ||
0.851991 | − | 0.523557i | \(-0.175395\pi\) | |||||||
\(912\) | 0.206099i | 0.000225986i | ||||||||
\(913\) | −668.395 | −0.732086 | ||||||||
\(914\) | 633.667i | 0.693290i | ||||||||
\(915\) | −50.0599 | −0.0547103 | ||||||||
\(916\) | − | 162.704i | − | 0.177624i | ||||||
\(917\) | − | 307.434i | − | 0.335260i | ||||||
\(918\) | 192.750i | 0.209967i | ||||||||
\(919\) | − | 1229.95i | − | 1.33835i | −0.743104 | − | 0.669176i | \(-0.766647\pi\) | ||
0.743104 | − | 0.669176i | \(-0.233353\pi\) | |||||||
\(920\) | 132.355 | − | 60.3510i | 0.143864 | − | 0.0655989i | ||||
\(921\) | 606.843 | 0.658896 | ||||||||
\(922\) | −1158.54 | −1.25655 | ||||||||
\(923\) | 1892.03 | 2.04987 | ||||||||
\(924\) | 145.092 | 0.157026 | ||||||||
\(925\) | − | 256.745i | − | 0.277562i | ||||||
\(926\) | 1122.66 | 1.21237 | ||||||||
\(927\) | − | 412.623i | − | 0.445117i | ||||||
\(928\) | 232.152 | 0.250164 | ||||||||
\(929\) | 212.171 | 0.228387 | 0.114193 | − | 0.993459i | \(-0.463572\pi\) | ||||
0.114193 | + | 0.993459i | \(0.463572\pi\) | |||||||
\(930\) | 163.181i | 0.175463i | ||||||||
\(931\) | 1.09341i | 0.00117444i | ||||||||
\(932\) | 459.180 | 0.492683 | ||||||||
\(933\) | 263.957 | 0.282912 | ||||||||
\(934\) | 475.022i | 0.508589i | ||||||||
\(935\) | − | 702.055i | − | 0.750861i | ||||||
\(936\) | 169.399 | 0.180982 | ||||||||
\(937\) | 1127.07i | 1.20285i | 0.798931 | + | 0.601423i | \(0.205399\pi\) | ||||
−0.798931 | + | 0.601423i | \(0.794601\pi\) | |||||||
\(938\) | −139.984 | −0.149236 | ||||||||
\(939\) | 82.4999i | 0.0878593i | ||||||||
\(940\) | 123.180i | 0.131043i | ||||||||
\(941\) | 117.572i | 0.124943i | 0.998047 | + | 0.0624717i | \(0.0198983\pi\) | ||||
−0.998047 | + | 0.0624717i | \(0.980102\pi\) | |||||||
\(942\) | − | 116.849i | − | 0.124044i | ||||||
\(943\) | 712.340 | + | 1562.22i | 0.755398 | + | 1.65665i | ||||
\(944\) | 6.21435 | 0.00658300 | ||||||||
\(945\) | −40.6566 | −0.0430228 | ||||||||
\(946\) | −876.824 | −0.926875 | ||||||||
\(947\) | −1763.85 | −1.86257 | −0.931283 | − | 0.364297i | \(-0.881309\pi\) | ||||
−0.931283 | + | 0.364297i | \(0.881309\pi\) | |||||||
\(948\) | − | 279.072i | − | 0.294380i | ||||||
\(949\) | 506.819 | 0.534056 | ||||||||
\(950\) | 0.210349i | 0.000221420i | ||||||||
\(951\) | 711.749 | 0.748422 | ||||||||
\(952\) | 259.600 | 0.272689 | ||||||||
\(953\) | 1497.38i | 1.57123i | 0.618716 | + | 0.785615i | \(0.287653\pi\) | ||||
−0.618716 | + | 0.785615i | \(0.712347\pi\) | |||||||
\(954\) | 63.7805i | 0.0668558i | ||||||||
\(955\) | 536.670 | 0.561958 | ||||||||
\(956\) | −313.481 | −0.327909 | ||||||||
\(957\) | − | 850.841i | − | 0.889071i | ||||||
\(958\) | 817.526i | 0.853367i | ||||||||
\(959\) | −634.727 | −0.661863 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | −73.4034 | −0.0763823 | ||||||||
\(962\) | 1449.74i | 1.50701i | ||||||||
\(963\) | 199.784i | 0.207460i | ||||||||
\(964\) | 382.172i | 0.396444i | ||||||||
\(965\) | − | 822.916i | − | 0.852762i | ||||||
\(966\) | 179.369 | − | 81.7888i | 0.185683 | − | 0.0846675i | ||||
\(967\) | 355.699 | 0.367837 | 0.183919 | − | 0.982941i | \(-0.441122\pi\) | ||||
0.183919 | + | 0.982941i | \(0.441122\pi\) | |||||||
\(968\) | 63.0122 | 0.0650952 | ||||||||
\(969\) | 1.35149 | 0.00139473 | ||||||||
\(970\) | −12.7452 | −0.0131394 | ||||||||
\(971\) | − | 398.185i | − | 0.410077i | −0.978754 | − | 0.205039i | \(-0.934268\pi\) | ||
0.978754 | − | 0.205039i | \(-0.0657320\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | 472.696i | 0.485813i | ||||||||
\(974\) | 1302.86 | 1.33764 | ||||||||
\(975\) | 172.892 | 0.177325 | ||||||||
\(976\) | − | 51.7016i | − | 0.0529730i | ||||||
\(977\) | 1697.18i | 1.73714i | 0.495570 | + | 0.868568i | \(0.334959\pi\) | ||||
−0.495570 | + | 0.868568i | \(0.665041\pi\) | |||||||
\(978\) | −291.125 | −0.297673 | ||||||||
\(979\) | 980.920 | 1.00196 | ||||||||
\(980\) | − | 164.377i | − | 0.167732i | ||||||
\(981\) | 285.015i | 0.290535i | ||||||||
\(982\) | 1175.10 | 1.19664 | ||||||||
\(983\) | − | 358.215i | − | 0.364410i | −0.983261 | − | 0.182205i | \(-0.941677\pi\) | ||
0.983261 | − | 0.182205i | \(-0.0583234\pi\) | |||||||
\(984\) | 365.712 | 0.371658 | ||||||||
\(985\) | 4.13086i | 0.00419376i | ||||||||
\(986\) | − | 1522.33i | − | 1.54395i | ||||||
\(987\) | 166.936i | 0.169135i | ||||||||
\(988\) | − | 1.18776i | − | 0.00120219i | ||||||
\(989\) | −1083.97 | + | 494.267i | −1.09602 | + | 0.499765i | ||||
\(990\) | −113.556 | −0.114703 | ||||||||
\(991\) | 786.854 | 0.794000 | 0.397000 | − | 0.917819i | \(-0.370051\pi\) | ||||
0.397000 | + | 0.917819i | \(0.370051\pi\) | |||||||
\(992\) | −168.532 | −0.169891 | ||||||||
\(993\) | −679.581 | −0.684372 | ||||||||
\(994\) | − | 468.988i | − | 0.471819i | ||||||
\(995\) | −126.344 | −0.126979 | ||||||||
\(996\) | 193.434i | 0.194211i | ||||||||
\(997\) | −436.962 | −0.438277 | −0.219139 | − | 0.975694i | \(-0.570325\pi\) | ||||
−0.219139 | + | 0.975694i | \(0.570325\pi\) | |||||||
\(998\) | 774.858 | 0.776411 | ||||||||
\(999\) | 266.817i | 0.267084i |
(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 | 690.3.c.a.91.10 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.28 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.15 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.21 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.10 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.15 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.21 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.28 | 32 | 3.2 | odd | 2 |