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 | 91.15 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.10 |
$q$-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 | \(0.0804109\pi\) | ||||
−0.968261 | + | 0.249940i | \(0.919589\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | − | 11.9699i | − | 1.08817i | −0.839030 | − | 0.544086i | \(-0.816877\pi\) | ||
0.839030 | − | 0.544086i | \(-0.183123\pi\) | |||||||
\(12\) | 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 | \(0.280477\pi\) | ||||
−0.636269 | + | 0.771467i | \(0.719523\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | − | 0.0297478i | − | 0.00156568i | −1.00000 | 0.000782838i | \(-0.999751\pi\) | |||
1.00000 | 0.000782838i | \(-0.000249185\pi\) | ||||||||
\(20\) | 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 | \(-0.755889\pi\) | ||
0.720067 | − | 0.693905i | \(-0.244111\pi\) | |||||||
\(38\) | 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 | \(0.205747\pi\) | ||||
−0.798274 | + | 0.602294i | \(0.794253\pi\) | |||||||
\(44\) | − | 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 | \(0.0452963\pi\) | ||||
−0.989892 | + | 0.141823i | \(0.954704\pi\) | |||||||
\(54\) | −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 | \(0.0337871\pi\) | ||||
−0.994372 | + | 0.105946i | \(0.966213\pi\) | |||||||
\(62\) | −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 | \(-0.932294\pi\) | ||
0.977464 | − | 0.211103i | \(-0.0677055\pi\) | |||||||
\(68\) | 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 | \(0.170311\pi\) | ||||
−0.860245 | + | 0.509882i | \(0.829689\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.572 | 1.28746 | ||||||||
\(83\) | − | 55.8397i | − | 0.672767i | −0.941725 | − | 0.336384i | \(-0.890796\pi\) | ||
0.941725 | − | 0.336384i | \(-0.109204\pi\) | |||||||
\(84\) | 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 | \(0.152290\pi\) | ||||
−0.887718 | + | 0.460387i | \(0.847710\pi\) | |||||||
\(90\) | − | 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 | \(-0.993387\pi\) | ||
0.999784 | − | 0.0207752i | \(-0.00661343\pi\) | |||||||
\(98\) | −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 | \(0.232711\pi\) | ||||
−0.744453 | + | 0.667675i | \(0.767289\pi\) | |||||||
\(104\) | 56.4664 | 0.542946 | ||||||||
\(105\) | −13.5522 | −0.129068 | ||||||||
\(106\) | − | 21.2602i | − | 0.200567i | ||||||
\(107\) | − | 66.5945i | − | 0.622379i | −0.950348 | − | 0.311189i | \(-0.899273\pi\) | ||
0.950348 | − | 0.311189i | \(-0.100727\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | − | 95.0049i | − | 0.871605i | −0.900042 | − | 0.435802i | \(-0.856465\pi\) | ||
0.900042 | − | 0.435802i | \(-0.143535\pi\) | |||||||
\(110\) | −37.8521 | −0.344110 | ||||||||
\(111\) | − | 88.9390i | − | 0.801252i | ||||||
\(112\) | 13.9966i | 0.124970i | ||||||||
\(113\) | 194.493i | 1.72118i | 0.509300 | + | 0.860589i | \(0.329904\pi\) | ||||
−0.509300 | + | 0.860589i | \(0.670096\pi\) | |||||||
\(114\) | 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 | \(0.230302\pi\) | ||||
−0.749484 | + | 0.662023i | \(0.769698\pi\) | |||||||
\(138\) | 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 | \(-0.938991\pi\) | ||
0.981688 | − | 0.190495i | \(-0.0610094\pi\) | |||||||
\(150\) | 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 | \(-0.951454\pi\) | ||
0.988392 | − | 0.151922i | \(-0.0485463\pi\) | |||||||
\(158\) | − | 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 | \(-0.792875\pi\) | ||
0.795659 | − | 0.605745i | \(-0.207125\pi\) | |||||||
\(182\) | 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 | \(-0.783756\pi\) | ||
0.777981 | − | 0.628288i | \(-0.216244\pi\) | |||||||
\(192\) | 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 | \(0.0453428\pi\) | ||||
−0.989871 | + | 0.141967i | \(0.954657\pi\) | |||||||
\(200\) | 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 | \(0.0536688\pi\) | ||||
−0.985820 | + | 0.167808i | \(0.946331\pi\) | |||||||
\(228\) | − | 0.103050i | − | 0.000451972i | ||||||
\(229\) | 81.3519i | 0.355248i | 0.984098 | + | 0.177624i | \(0.0568411\pi\) | ||||
−0.984098 | + | 0.177624i | \(0.943159\pi\) | |||||||
\(230\) | 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 | \(-0.870244\pi\) | ||
0.918059 | − | 0.396444i | \(-0.129756\pi\) | |||||||
\(242\) | 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 | \(0.364008\pi\) | ||||
−0.414354 | + | 0.910116i | \(0.635992\pi\) | |||||||
\(252\) | 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 | \(-0.636706\pi\) | ||
0.416392 | − | 0.909185i | \(-0.363294\pi\) | |||||||
\(264\) | 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 | \(-0.890670\pi\) | ||
0.941592 | − | 0.336755i | \(-0.109330\pi\) | |||||||
\(282\) | 67.4685 | 0.239250 | ||||||||
\(283\) | 157.312i | 0.555872i | 0.960600 | + | 0.277936i | \(0.0896503\pi\) | ||||
−0.960600 | + | 0.277936i | \(0.910350\pi\) | |||||||
\(284\) | −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 | \(0.290578\pi\) | ||||
−0.611472 | + | 0.791266i | \(0.709422\pi\) | |||||||
\(294\) | −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 | \(-0.975757\pi\) | ||
0.997101 | − | 0.0760884i | \(-0.0242431\pi\) | |||||||
\(314\) | 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 | \(0.238051\pi\) | ||||
−0.733146 | + | 0.680071i | \(0.761949\pi\) | |||||||
\(338\) | −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 | \(0.271003\pi\) | ||||
−0.658945 | + | 0.752192i | \(0.728997\pi\) | |||||||
\(360\) | − | 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 | \(-0.814186\pi\) | ||
0.834401 | − | 0.551158i | \(-0.185814\pi\) | |||||||
\(368\) | −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 | \(-0.916951\pi\) | ||
0.966157 | − | 0.257955i | \(-0.0830487\pi\) | |||||||
\(374\) | −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 | \(-0.612429\pi\) | ||
0.345908 | − | 0.938269i | \(-0.387571\pi\) | |||||||
\(380\) | 0.133036 | 0.000350096 | ||||||||
\(381\) | −241.195 | −0.633058 | ||||||||
\(382\) | 339.420i | 0.888533i | ||||||||
\(383\) | 308.566i | 0.805655i | 0.915276 | + | 0.402827i | \(0.131973\pi\) | ||||
−0.915276 | + | 0.402827i | \(0.868027\pi\) | |||||||
\(384\) | −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 | \(0.0819022\pi\) | ||||
−0.967080 | + | 0.254474i | \(0.918098\pi\) | |||||||
\(390\) | 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 | \(-0.615415\pi\) | ||
0.354694 | − | 0.934983i | \(-0.384585\pi\) | |||||||
\(402\) | 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 | \(0.130569\pi\) | ||||
−0.917044 | + | 0.398787i | \(0.869431\pi\) | |||||||
\(420\) | −27.1044 | −0.0645342 | ||||||||
\(421\) | 414.441i | 0.984422i | 0.870476 | + | 0.492211i | \(0.163811\pi\) | ||||
−0.870476 | + | 0.492211i | \(0.836189\pi\) | |||||||
\(422\) | 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 | \(-0.684477\pi\) | ||
0.547649 | − | 0.836708i | \(-0.315523\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | − | 231.360i | − | 0.534319i | −0.963652 | − | 0.267160i | \(-0.913915\pi\) | ||
0.963652 | − | 0.267160i | \(-0.0860851\pi\) | |||||||
\(434\) | − | 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 | \(0.163087\pi\) | ||||
−0.871593 | + | 0.490230i | \(0.836913\pi\) | |||||||
\(458\) | − | 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 | \(0.117096\pi\) | ||||
−0.933096 | + | 0.359627i | \(0.882904\pi\) | |||||||
\(468\) | −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 | \(0.206196\pi\) | ||||
−0.797422 | + | 0.603422i | \(0.793804\pi\) | |||||||
\(480\) | − | 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 | \(0.0128225\pi\) | ||||
−0.999189 | + | 0.0402722i | \(0.987178\pi\) | |||||||
\(504\) | − | 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 | \(-0.871566\pi\) | ||
0.919698 | − | 0.392628i | \(-0.128434\pi\) | |||||||
\(522\) | 174.114 | 0.333552 | ||||||||
\(523\) | 88.2598i | 0.168757i | 0.996434 | + | 0.0843784i | \(0.0268904\pi\) | ||||
−0.996434 | + | 0.0843784i | \(0.973110\pi\) | |||||||
\(524\) | 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 | \(-0.810413\pi\) | ||
0.827809 | − | 0.561010i | \(-0.189587\pi\) | |||||||
\(558\) | −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 | \(0.212534\pi\) | ||||
−0.785251 | + | 0.619177i | \(0.787466\pi\) | |||||||
\(564\) | −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 | \(0.311278\pi\) | ||||
−0.558759 | + | 0.829330i | \(0.688722\pi\) | |||||||
\(570\) | −0.162936 | −0.000285852 | ||||||||
\(571\) | − | 159.659i | − | 0.279613i | −0.990179 | − | 0.139806i | \(-0.955352\pi\) | ||
0.990179 | − | 0.139806i | \(-0.0446480\pi\) | |||||||
\(572\) | 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 | \(0.278088\pi\) | ||||
−0.642040 | + | 0.766671i | \(0.721912\pi\) | |||||||
\(614\) | −495.485 | −0.806979 | ||||||||
\(615\) | − | 289.120i | − | 0.470114i | ||||||
\(616\) | −118.467 | −0.192317 | ||||||||
\(617\) | − | 571.784i | − | 0.926717i | −0.886171 | − | 0.463359i | \(-0.846644\pi\) | ||
0.886171 | − | 0.463359i | \(-0.153356\pi\) | |||||||
\(618\) | − | 336.906i | − | 0.545155i | ||||||
\(619\) | 944.586i | 1.52599i | 0.646406 | + | 0.762994i | \(0.276271\pi\) | ||||
−0.646406 | + | 0.762994i | \(0.723729\pi\) | |||||||
\(620\) | 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 | \(0.306496\pi\) | ||||
−0.571154 | + | 0.820843i | \(0.693504\pi\) | |||||||
\(632\) | − | 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 | \(-0.927061\pi\) | ||
0.973861 | − | 0.227144i | \(-0.0729389\pi\) | |||||||
\(642\) | 163.123i | 0.254085i | ||||||||
\(643\) | 183.214i | 0.284936i | 0.989799 | + | 0.142468i | \(0.0455038\pi\) | ||||
−0.989799 | + | 0.142468i | \(0.954496\pi\) | |||||||
\(644\) | −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 | \(0.0349344\pi\) | ||||
−0.993984 | + | 0.109529i | \(0.965066\pi\) | |||||||
\(660\) | 92.7183 | 0.140482 | ||||||||
\(661\) | − | 639.386i | − | 0.967301i | −0.875261 | − | 0.483650i | \(-0.839311\pi\) | ||
0.875261 | − | 0.483650i | \(-0.160689\pi\) | |||||||
\(662\) | 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 | \(-0.875995\pi\) | ||
0.925071 | − | 0.379795i | \(-0.124005\pi\) | |||||||
\(678\) | − | 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 | \(0.0437861\pi\) | ||||
−0.990554 | + | 0.137125i | \(0.956214\pi\) | |||||||
\(702\) | 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 | \(0.371230\pi\) | ||||
−0.393599 | + | 0.919282i | \(0.628770\pi\) | |||||||
\(710\) | 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 | \(0.251742\pi\) | ||||
−0.703227 | + | 0.710966i | \(0.748258\pi\) | |||||||
\(728\) | 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 | \(0.0193117\pi\) | ||||
−0.998160 | + | 0.0606324i | \(0.980688\pi\) | |||||||
\(734\) | 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 | \(-0.772865\pi\) | ||
0.756033 | − | 0.654534i | \(-0.227135\pi\) | |||||||
\(744\) | −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 | \(0.0182046\pi\) | ||||
−0.998365 | + | 0.0571604i | \(0.981795\pi\) | |||||||
\(752\) | −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 | \(0.0274219\pi\) | ||||
−0.996292 | + | 0.0860419i | \(0.972578\pi\) | |||||||
\(758\) | 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 | \(-0.947102\pi\) | ||
0.986223 | − | 0.165421i | \(-0.0528984\pi\) | |||||||
\(770\) | − | 132.451i | − | 0.172014i | ||||||
\(771\) | 368.062 | 0.477383 | ||||||||
\(772\) | 736.038 | 0.953417 | ||||||||
\(773\) | 849.508i | 1.09898i | 0.835502 | + | 0.549488i | \(0.185177\pi\) | ||||
−0.835502 | + | 0.549488i | \(0.814823\pi\) | |||||||
\(774\) | − | 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 | \(0.196665\pi\) | ||||
−0.815130 | + | 0.579278i | \(0.803335\pi\) | |||||||
\(788\) | −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 | \(-0.747170\pi\) | ||
0.700791 | − | 0.713366i | \(-0.252830\pi\) | |||||||
\(798\) | −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 | \(-0.823435\pi\) | ||
0.850062 | − | 0.526683i | \(-0.176565\pi\) | |||||||
\(828\) | −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 | \(0.201982\pi\) | ||||
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(840\) | 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 | \(-0.835593\pi\) | ||
0.869553 | − | 0.493840i | \(-0.164407\pi\) | |||||||
\(882\) | −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 | \(-0.904931\pi\) | ||
0.955729 | − | 0.294247i | \(-0.0950689\pi\) | |||||||
\(908\) | 152.370i | 0.167808i | ||||||||
\(909\) | −488.921 | −0.537867 | ||||||||
\(910\) | −220.907 | −0.242754 | ||||||||
\(911\) | 953.921i | 1.04711i | 0.851991 | + | 0.523557i | \(0.175395\pi\) | ||||
−0.851991 | + | 0.523557i | \(0.824605\pi\) | |||||||
\(912\) | − | 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 | \(0.233353\pi\) | ||||
−0.743104 | + | 0.669176i | \(0.766647\pi\) | |||||||
\(920\) | 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 | \(-0.794601\pi\) | ||
0.798931 | − | 0.601423i | \(-0.205399\pi\) | |||||||
\(938\) | −139.984 | −0.149236 | ||||||||
\(939\) | − | 82.4999i | − | 0.0878593i | ||||||
\(940\) | − | 123.180i | − | 0.131043i | ||||||
\(941\) | − | 117.572i | − | 0.124943i | −0.998047 | − | 0.0624717i | \(-0.980102\pi\) | ||
0.998047 | − | 0.0624717i | \(-0.0198983\pi\) | |||||||
\(942\) | 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 | \(-0.712347\pi\) | ||
0.618716 | − | 0.785615i | \(-0.287653\pi\) | |||||||
\(954\) | − | 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 | \(0.0657320\pi\) | ||||
−0.978754 | + | 0.205039i | \(0.934268\pi\) | |||||||
\(972\) | 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 | \(-0.665041\pi\) | ||
0.495570 | − | 0.868568i | \(-0.334959\pi\) | |||||||
\(978\) | −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 | \(0.0583234\pi\) | ||||
−0.983261 | + | 0.182205i | \(0.941677\pi\) | |||||||
\(984\) | 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.91.15 | yes | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.21 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.10 | ✓ | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.28 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.10 | ✓ | 32 | 23.22 | odd | 2 | inner | |
690.3.c.a.91.15 | yes | 32 | 1.1 | even | 1 | trivial | |
2070.3.c.b.91.21 | 32 | 3.2 | odd | 2 | |||
2070.3.c.b.91.28 | 32 | 69.68 | even | 2 |