Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,3,Mod(91,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(56.4034147226\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 690) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.14 | ||
Character | \(\chi\) | \(=\) | 2070.91 |
Dual form | 2070.3.c.b.91.3 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.80775i | 0.543964i | 0.962302 | + | 0.271982i | \(0.0876791\pi\) | ||||
−0.962302 | + | 0.271982i | \(0.912321\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | 16.1827i | 1.47115i | 0.677442 | + | 0.735576i | \(0.263088\pi\) | ||||
−0.677442 | + | 0.735576i | \(0.736912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.9618 | 0.997064 | 0.498532 | − | 0.866871i | \(-0.333873\pi\) | ||||
0.498532 | + | 0.866871i | \(0.333873\pi\) | |||||||
\(14\) | − | 5.38497i | − | 0.384641i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 10.8189i | 0.636408i | 0.948022 | + | 0.318204i | \(0.103080\pi\) | ||||
−0.948022 | + | 0.318204i | \(0.896920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.1074i | 0.900390i | 0.892930 | + | 0.450195i | \(0.148646\pi\) | ||||
−0.892930 | + | 0.450195i | \(0.851354\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 22.8858i | − | 1.04026i | ||||||
\(23\) | −11.6478 | + | 19.8325i | −0.506424 | + | 0.862285i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −18.3308 | −0.705031 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.61550i | 0.271982i | ||||||||
\(29\) | 10.1177 | 0.348887 | 0.174443 | − | 0.984667i | \(-0.444187\pi\) | ||||
0.174443 | + | 0.984667i | \(0.444187\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.2531 | 0.943650 | 0.471825 | − | 0.881692i | \(-0.343595\pi\) | ||||
0.471825 | + | 0.881692i | \(0.343595\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 15.3003i | − | 0.450008i | ||||||
\(35\) | −8.51438 | −0.243268 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.06540i | 0.0828486i | 0.999142 | + | 0.0414243i | \(0.0131895\pi\) | ||||
−0.999142 | + | 0.0414243i | \(0.986810\pi\) | |||||||
\(38\) | − | 24.1935i | − | 0.636672i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | −55.3042 | −1.34888 | −0.674441 | − | 0.738328i | \(-0.735616\pi\) | ||||
−0.674441 | + | 0.738328i | \(0.735616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.1448i | 0.794065i | 0.917804 | + | 0.397033i | \(0.129960\pi\) | ||||
−0.917804 | + | 0.397033i | \(0.870040\pi\) | |||||||
\(44\) | 32.3653i | 0.735576i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.4724 | − | 28.0475i | 0.358096 | − | 0.609727i | ||||
\(47\) | 49.2975 | 1.04888 | 0.524442 | − | 0.851446i | \(-0.324274\pi\) | ||||
0.524442 | + | 0.851446i | \(0.324274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34.5011 | 0.704103 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.9237 | 0.498532 | ||||||||
\(53\) | − | 28.6856i | − | 0.541238i | −0.962687 | − | 0.270619i | \(-0.912772\pi\) | ||
0.962687 | − | 0.270619i | \(-0.0872283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36.1856 | −0.657919 | ||||||||
\(56\) | − | 10.7699i | − | 0.192320i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.3086 | −0.246700 | ||||||||
\(59\) | −24.2529 | −0.411066 | −0.205533 | − | 0.978650i | \(-0.565893\pi\) | ||||
−0.205533 | + | 0.978650i | \(0.565893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 52.9773i | − | 0.868481i | −0.900797 | − | 0.434240i | \(-0.857017\pi\) | ||
0.900797 | − | 0.434240i | \(-0.142983\pi\) | |||||||
\(62\) | −41.3702 | −0.667261 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 28.9835i | 0.445900i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.48607i | − | 0.111732i | −0.998438 | − | 0.0558662i | \(-0.982208\pi\) | ||
0.998438 | − | 0.0558662i | \(-0.0177920\pi\) | |||||||
\(68\) | 21.6379i | 0.318204i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.0412 | 0.172017 | ||||||||
\(71\) | 121.879 | 1.71661 | 0.858305 | − | 0.513140i | \(-0.171518\pi\) | ||||
0.858305 | + | 0.513140i | \(0.171518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −132.268 | −1.81189 | −0.905947 | − | 0.423391i | \(-0.860840\pi\) | ||||
−0.905947 | + | 0.423391i | \(0.860840\pi\) | |||||||
\(74\) | − | 4.33513i | − | 0.0585828i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.2148i | 0.450195i | ||||||||
\(77\) | −61.6195 | −0.800254 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 18.6463i | 0.236030i | 0.993012 | + | 0.118015i | \(0.0376530\pi\) | ||||
−0.993012 | + | 0.118015i | \(0.962347\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 78.2120 | 0.953804 | ||||||||
\(83\) | 46.3088i | 0.557938i | 0.960300 | + | 0.278969i | \(0.0899926\pi\) | ||||
−0.960300 | + | 0.278969i | \(0.910007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.1919 | −0.284610 | ||||||||
\(86\) | − | 48.2881i | − | 0.561489i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 45.7715i | − | 0.520131i | ||||||
\(89\) | 17.2346i | 0.193647i | 0.995302 | + | 0.0968234i | \(0.0308682\pi\) | ||||
−0.995302 | + | 0.0968234i | \(0.969132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.3554i | 0.542367i | ||||||||
\(92\) | −23.2955 | + | 39.6651i | −0.253212 | + | 0.431142i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −69.7172 | −0.741672 | ||||||||
\(95\) | −38.2533 | −0.402667 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31.4987i | 0.324728i | 0.986731 | + | 0.162364i | \(0.0519120\pi\) | ||||
−0.986731 | + | 0.162364i | \(0.948088\pi\) | |||||||
\(98\) | −48.7919 | −0.497876 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −11.8823 | −0.117646 | −0.0588232 | − | 0.998268i | \(-0.518735\pi\) | ||||
−0.0588232 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 61.0381i | − | 0.592603i | −0.955094 | − | 0.296301i | \(-0.904247\pi\) | ||
0.955094 | − | 0.296301i | \(-0.0957533\pi\) | |||||||
\(104\) | −36.6616 | −0.352515 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 40.5676i | 0.382713i | ||||||||
\(107\) | − | 144.705i | − | 1.35238i | −0.736728 | − | 0.676190i | \(-0.763630\pi\) | ||
0.736728 | − | 0.676190i | \(-0.236370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 162.558i | 1.49135i | 0.666308 | + | 0.745677i | \(0.267874\pi\) | ||||
−0.666308 | + | 0.745677i | \(0.732126\pi\) | |||||||
\(110\) | 51.1741 | 0.465219 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.2310i | 0.135991i | ||||||||
\(113\) | − | 141.903i | − | 1.25578i | −0.778304 | − | 0.627888i | \(-0.783920\pi\) | ||
0.778304 | − | 0.627888i | \(-0.216080\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −44.3469 | − | 26.0452i | −0.385625 | − | 0.226480i | ||||
\(116\) | 20.2354 | 0.174443 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 34.2988 | 0.290668 | ||||||||
\(119\) | −41.1958 | −0.346183 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140.879 | −1.16429 | ||||||||
\(122\) | 74.9213i | 0.614109i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 58.5063 | 0.471825 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.2207 | 0.285202 | 0.142601 | − | 0.989780i | \(-0.454453\pi\) | ||||
0.142601 | + | 0.989780i | \(0.454453\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | − | 40.9889i | − | 0.315299i | ||||||
\(131\) | 0.512699 | 0.00391373 | 0.00195687 | − | 0.999998i | \(-0.499377\pi\) | ||||
0.00195687 | + | 0.999998i | \(0.499377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −65.1407 | −0.489780 | ||||||||
\(134\) | 10.5869i | 0.0790067i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 30.6006i | − | 0.225004i | ||||||
\(137\) | − | 64.7952i | − | 0.472958i | −0.971637 | − | 0.236479i | \(-0.924007\pi\) | ||
0.971637 | − | 0.236479i | \(-0.0759934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −170.051 | −1.22339 | −0.611693 | − | 0.791095i | \(-0.709511\pi\) | ||||
−0.611693 | + | 0.791095i | \(0.709511\pi\) | |||||||
\(140\) | −17.0288 | −0.121634 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −172.363 | −1.21383 | ||||||||
\(143\) | 209.757i | 1.46683i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.6239i | 0.156027i | ||||||||
\(146\) | 187.056 | 1.28120 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.13079i | 0.0414243i | ||||||||
\(149\) | 54.6548i | 0.366810i | 0.983037 | + | 0.183405i | \(0.0587120\pi\) | ||||
−0.983037 | + | 0.183405i | \(0.941288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 131.579 | 0.871382 | 0.435691 | − | 0.900096i | \(-0.356504\pi\) | ||||
0.435691 | + | 0.900096i | \(0.356504\pi\) | |||||||
\(152\) | − | 48.3871i | − | 0.318336i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 87.1432 | 0.565865 | ||||||||
\(155\) | 65.4120i | 0.422013i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 62.7071i | 0.399409i | 0.979856 | + | 0.199704i | \(0.0639982\pi\) | ||||
−0.979856 | + | 0.199704i | \(0.936002\pi\) | |||||||
\(158\) | − | 26.3699i | − | 0.166898i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | −75.5173 | − | 44.3517i | −0.469052 | − | 0.275477i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 65.2642 | 0.400394 | 0.200197 | − | 0.979756i | \(-0.435842\pi\) | ||||
0.200197 | + | 0.979756i | \(0.435842\pi\) | |||||||
\(164\) | −110.608 | −0.674441 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 65.4906i | − | 0.394521i | ||||||
\(167\) | 89.9666 | 0.538722 | 0.269361 | − | 0.963039i | \(-0.413187\pi\) | ||||
0.269361 | + | 0.963039i | \(0.413187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.991006 | −0.00586394 | ||||||||
\(170\) | 34.2125 | 0.201250 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 68.2896i | 0.397033i | ||||||||
\(173\) | 177.669 | 1.02699 | 0.513494 | − | 0.858093i | \(-0.328351\pi\) | ||||
0.513494 | + | 0.858093i | \(0.328351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 19.0387i | − | 0.108793i | ||||||
\(176\) | 64.7307i | 0.367788i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 24.3734i | − | 0.136929i | ||||||
\(179\) | 193.456 | 1.08076 | 0.540379 | − | 0.841421i | \(-0.318281\pi\) | ||||
0.540379 | + | 0.841421i | \(0.318281\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 186.354i | − | 1.02958i | −0.857316 | − | 0.514790i | \(-0.827870\pi\) | ||
0.857316 | − | 0.514790i | \(-0.172130\pi\) | |||||||
\(182\) | − | 69.7991i | − | 0.383511i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 32.9448 | − | 56.0949i | 0.179048 | − | 0.304864i | ||||
\(185\) | −6.85443 | −0.0370510 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −175.079 | −0.936253 | ||||||||
\(188\) | 98.5950 | 0.524442 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 54.0984 | 0.284728 | ||||||||
\(191\) | − | 18.7678i | − | 0.0982605i | −0.998792 | − | 0.0491303i | \(-0.984355\pi\) | ||
0.998792 | − | 0.0491303i | \(-0.0156449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −161.771 | −0.838193 | −0.419097 | − | 0.907942i | \(-0.637653\pi\) | ||||
−0.419097 | + | 0.907942i | \(0.637653\pi\) | |||||||
\(194\) | − | 44.5458i | − | 0.229618i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 69.0021 | 0.352052 | ||||||||
\(197\) | −62.3846 | −0.316673 | −0.158337 | − | 0.987385i | \(-0.550613\pi\) | ||||
−0.158337 | + | 0.987385i | \(0.550613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 280.675i | 1.41043i | 0.708994 | + | 0.705214i | \(0.249149\pi\) | ||||
−0.708994 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.8041 | 0.0831885 | ||||||||
\(203\) | 38.5257i | 0.189782i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 123.664i | − | 0.603239i | ||||||
\(206\) | 86.3209i | 0.419033i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 51.8473 | 0.249266 | ||||||||
\(209\) | −276.844 | −1.32461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −252.159 | −1.19507 | −0.597533 | − | 0.801844i | \(-0.703852\pi\) | ||||
−0.597533 | + | 0.801844i | \(0.703852\pi\) | |||||||
\(212\) | − | 57.3712i | − | 0.270619i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 204.643i | 0.956276i | ||||||||
\(215\) | −76.3501 | −0.355117 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111.389i | 0.513312i | ||||||||
\(218\) | − | 229.891i | − | 1.05455i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −72.3711 | −0.328960 | ||||||||
\(221\) | 140.233i | 0.634539i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −225.671 | −1.01198 | −0.505989 | − | 0.862540i | \(-0.668872\pi\) | ||||
−0.505989 | + | 0.862540i | \(0.668872\pi\) | |||||||
\(224\) | − | 21.5399i | − | 0.0961602i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 200.681i | 0.887967i | ||||||||
\(227\) | − | 397.011i | − | 1.74895i | −0.485074 | − | 0.874473i | \(-0.661207\pi\) | ||
0.485074 | − | 0.874473i | \(-0.338793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 269.388i | 1.17637i | 0.808728 | + | 0.588183i | \(0.200156\pi\) | ||||
−0.808728 | + | 0.588183i | \(0.799844\pi\) | |||||||
\(230\) | 62.7160 | + | 36.8334i | 0.272678 | + | 0.160145i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −28.6172 | −0.123350 | ||||||||
\(233\) | −350.279 | −1.50334 | −0.751672 | − | 0.659537i | \(-0.770752\pi\) | ||||
−0.751672 | + | 0.659537i | \(0.770752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 110.233i | 0.469075i | ||||||||
\(236\) | −48.5058 | −0.205533 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 58.2596 | 0.244788 | ||||||||
\(239\) | −34.7609 | −0.145443 | −0.0727215 | − | 0.997352i | \(-0.523168\pi\) | ||||
−0.0727215 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 343.644i | 1.42591i | 0.701211 | + | 0.712954i | \(0.252643\pi\) | ||||
−0.701211 | + | 0.712954i | \(0.747357\pi\) | |||||||
\(242\) | 199.233 | 0.823276 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 105.955i | − | 0.434240i | ||||||
\(245\) | 77.1467i | 0.314884i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 221.743i | 0.897746i | ||||||||
\(248\) | −82.7404 | −0.333631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | 442.427i | 1.76266i | 0.472505 | + | 0.881328i | \(0.343350\pi\) | ||||
−0.472505 | + | 0.881328i | \(0.656650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −320.944 | − | 188.492i | −1.26855 | − | 0.745027i | ||||
\(254\) | −51.2238 | −0.201669 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −377.957 | −1.47065 | −0.735325 | − | 0.677715i | \(-0.762971\pi\) | ||||
−0.735325 | + | 0.677715i | \(0.762971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6723 | −0.0450666 | ||||||||
\(260\) | 57.9671i | 0.222950i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.725066 | −0.00276743 | ||||||||
\(263\) | − | 233.084i | − | 0.886251i | −0.896459 | − | 0.443126i | \(-0.853870\pi\) | ||
0.896459 | − | 0.443126i | \(-0.146130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 64.1430 | 0.242049 | ||||||||
\(266\) | 92.1229 | 0.346327 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 14.9721i | − | 0.0558662i | ||||||
\(269\) | 278.353 | 1.03477 | 0.517385 | − | 0.855753i | \(-0.326906\pi\) | ||||
0.517385 | + | 0.855753i | \(0.326906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −508.787 | −1.87744 | −0.938722 | − | 0.344676i | \(-0.887989\pi\) | ||||
−0.938722 | + | 0.344676i | \(0.887989\pi\) | |||||||
\(272\) | 43.2757i | 0.159102i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 91.6343i | 0.334432i | ||||||||
\(275\) | − | 80.9134i | − | 0.294230i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.7229 | −0.0712019 | −0.0356009 | − | 0.999366i | \(-0.511335\pi\) | ||||
−0.0356009 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(278\) | 240.488 | 0.865065 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 24.0823 | 0.0860083 | ||||||||
\(281\) | 343.453i | 1.22225i | 0.791533 | + | 0.611126i | \(0.209283\pi\) | ||||
−0.791533 | + | 0.611126i | \(0.790717\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 149.531i | − | 0.528378i | −0.964471 | − | 0.264189i | \(-0.914896\pi\) | ||
0.964471 | − | 0.264189i | \(-0.0851043\pi\) | |||||||
\(284\) | 243.759 | 0.858305 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 296.641i | − | 1.03721i | ||||||
\(287\) | − | 210.584i | − | 0.733744i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 171.951 | 0.594985 | ||||||||
\(290\) | − | 31.9950i | − | 0.110328i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −264.537 | −0.905947 | ||||||||
\(293\) | 80.2344i | 0.273838i | 0.990582 | + | 0.136919i | \(0.0437199\pi\) | ||||
−0.990582 | + | 0.136919i | \(0.956280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 54.2312i | − | 0.183834i | ||||||
\(296\) | − | 8.67025i | − | 0.0292914i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 77.2935i | − | 0.259374i | ||||||
\(299\) | −150.976 | + | 257.066i | −0.504937 | + | 0.859753i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −130.015 | −0.431943 | ||||||||
\(302\) | −186.080 | −0.616160 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 68.4296i | 0.225097i | ||||||||
\(305\) | 118.461 | 0.388396 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 153.780 | 0.500911 | 0.250456 | − | 0.968128i | \(-0.419420\pi\) | ||||
0.250456 | + | 0.968128i | \(0.419420\pi\) | |||||||
\(308\) | −123.239 | −0.400127 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 92.5066i | − | 0.298408i | ||||||
\(311\) | 124.567 | 0.400536 | 0.200268 | − | 0.979741i | \(-0.435819\pi\) | ||||
0.200268 | + | 0.979741i | \(0.435819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 222.424i | − | 0.710619i | −0.934749 | − | 0.355310i | \(-0.884375\pi\) | ||
0.934749 | − | 0.355310i | \(-0.115625\pi\) | |||||||
\(314\) | − | 88.6813i | − | 0.282425i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 37.2927i | 0.118015i | ||||||||
\(317\) | −303.301 | −0.956785 | −0.478393 | − | 0.878146i | \(-0.658780\pi\) | ||||
−0.478393 | + | 0.878146i | \(0.658780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 163.732i | 0.513265i | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 106.798 | + | 62.7228i | 0.331670 | + | 0.194791i | ||||
\(323\) | −185.084 | −0.573015 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −64.8091 | −0.199413 | ||||||||
\(326\) | −92.2975 | −0.283121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 156.424 | 0.476902 | ||||||||
\(329\) | 187.713i | 0.570555i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −281.157 | −0.849416 | −0.424708 | − | 0.905330i | \(-0.639623\pi\) | ||||
−0.424708 | + | 0.905330i | \(0.639623\pi\) | |||||||
\(332\) | 92.6176i | 0.278969i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −127.232 | −0.380934 | ||||||||
\(335\) | 16.7394 | 0.0499683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 258.510i | 0.767091i | 0.923522 | + | 0.383546i | \(0.125297\pi\) | ||||
−0.923522 | + | 0.383546i | \(0.874703\pi\) | |||||||
\(338\) | 1.40149 | 0.00414643 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −48.3837 | −0.142305 | ||||||||
\(341\) | 473.394i | 1.38825i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 317.951i | 0.926971i | ||||||||
\(344\) | − | 96.5761i | − | 0.280744i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −251.262 | −0.726191 | ||||||||
\(347\) | −613.312 | −1.76747 | −0.883735 | − | 0.467988i | \(-0.844979\pi\) | ||||
−0.883735 | + | 0.467988i | \(0.844979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −75.5131 | −0.216370 | −0.108185 | − | 0.994131i | \(-0.534504\pi\) | ||||
−0.108185 | + | 0.994131i | \(0.534504\pi\) | |||||||
\(350\) | 26.9248i | 0.0769281i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 91.5430i | − | 0.260065i | ||||||
\(353\) | 31.5279 | 0.0893142 | 0.0446571 | − | 0.999002i | \(-0.485780\pi\) | ||||
0.0446571 | + | 0.999002i | \(0.485780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 272.530i | 0.767691i | ||||||||
\(356\) | 34.4691i | 0.0968234i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −273.588 | −0.764212 | ||||||||
\(359\) | − | 192.855i | − | 0.537199i | −0.963252 | − | 0.268600i | \(-0.913439\pi\) | ||
0.963252 | − | 0.268600i | \(-0.0865608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 68.3365 | 0.189298 | ||||||||
\(362\) | 263.544i | 0.728023i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 98.7108i | 0.271183i | ||||||||
\(365\) | − | 295.761i | − | 0.810304i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 512.314i | 1.39595i | 0.716121 | + | 0.697976i | \(0.245916\pi\) | ||||
−0.716121 | + | 0.697976i | \(0.754084\pi\) | |||||||
\(368\) | −46.5910 | + | 79.3302i | −0.126606 | + | 0.215571i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.69363 | 0.0261990 | ||||||||
\(371\) | 109.228 | 0.294414 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 308.198i | − | 0.826267i | −0.910670 | − | 0.413134i | \(-0.864434\pi\) | ||
0.910670 | − | 0.413134i | \(-0.135566\pi\) | |||||||
\(374\) | 247.599 | 0.662031 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −139.434 | −0.370836 | ||||||||
\(377\) | 131.144 | 0.347862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 274.002i | − | 0.722959i | −0.932380 | − | 0.361480i | \(-0.882272\pi\) | ||
0.932380 | − | 0.361480i | \(-0.117728\pi\) | |||||||
\(380\) | −76.5067 | −0.201333 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.5416i | 0.0694807i | ||||||||
\(383\) | 184.563i | 0.481889i | 0.970539 | + | 0.240944i | \(0.0774571\pi\) | ||||
−0.970539 | + | 0.240944i | \(0.922543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 137.785i | − | 0.357884i | ||||||
\(386\) | 228.779 | 0.592692 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 62.9973i | 0.162364i | ||||||||
\(389\) | 384.497i | 0.988425i | 0.869341 | + | 0.494212i | \(0.164543\pi\) | ||||
−0.869341 | + | 0.494212i | \(0.835457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −214.567 | − | 126.016i | −0.548765 | − | 0.322292i | ||||
\(392\) | −97.5837 | −0.248938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 88.2252 | 0.223922 | ||||||||
\(395\) | −41.6945 | −0.105556 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 340.530 | 0.857757 | 0.428879 | − | 0.903362i | \(-0.358909\pi\) | ||||
0.428879 | + | 0.903362i | \(0.358909\pi\) | |||||||
\(398\) | − | 396.935i | − | 0.997324i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 742.537i | 1.85171i | 0.377875 | + | 0.925857i | \(0.376655\pi\) | ||||
−0.377875 | + | 0.925857i | \(0.623345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 379.174 | 0.940879 | ||||||||
\(404\) | −23.7646 | −0.0588232 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 54.4836i | − | 0.134196i | ||||||
\(407\) | −49.6063 | −0.121883 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 757.373 | 1.85177 | 0.925884 | − | 0.377807i | \(-0.123322\pi\) | ||||
0.925884 | + | 0.377807i | \(0.123322\pi\) | |||||||
\(410\) | 174.887i | 0.426554i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 122.076i | − | 0.296301i | ||||||
\(413\) | − | 92.3490i | − | 0.223605i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −103.550 | −0.249517 | ||||||||
\(416\) | −73.3232 | −0.176258 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 391.516 | 0.936641 | ||||||||
\(419\) | − | 213.737i | − | 0.510113i | −0.966926 | − | 0.255056i | \(-0.917906\pi\) | ||
0.966926 | − | 0.255056i | \(-0.0820940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 675.986i | − | 1.60567i | −0.596202 | − | 0.802834i | \(-0.703324\pi\) | ||
0.596202 | − | 0.802834i | \(-0.296676\pi\) | |||||||
\(422\) | 356.607 | 0.845040 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 81.1351i | 0.191356i | ||||||||
\(425\) | − | 54.0947i | − | 0.127282i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 201.724 | 0.472422 | ||||||||
\(428\) | − | 289.409i | − | 0.676190i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 107.975 | 0.251105 | ||||||||
\(431\) | 8.04660i | 0.0186696i | 0.999956 | + | 0.00933480i | \(0.00297140\pi\) | ||||
−0.999956 | + | 0.00933480i | \(0.997029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 369.369i | − | 0.853046i | −0.904477 | − | 0.426523i | \(-0.859738\pi\) | ||
0.904477 | − | 0.426523i | \(-0.140262\pi\) | |||||||
\(434\) | − | 157.527i | − | 0.362966i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 325.115i | 0.745677i | ||||||||
\(437\) | −339.283 | − | 199.263i | −0.776392 | − | 0.455979i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −54.3077 | −0.123708 | −0.0618539 | − | 0.998085i | \(-0.519701\pi\) | ||||
−0.0618539 | + | 0.998085i | \(0.519701\pi\) | |||||||
\(440\) | 102.348 | 0.232610 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 198.320i | − | 0.448687i | ||||||
\(443\) | −263.570 | −0.594966 | −0.297483 | − | 0.954727i | \(-0.596147\pi\) | ||||
−0.297483 | + | 0.954727i | \(0.596147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.5377 | −0.0866015 | ||||||||
\(446\) | 319.147 | 0.715576 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 30.4620i | 0.0679955i | ||||||||
\(449\) | −578.427 | −1.28826 | −0.644128 | − | 0.764917i | \(-0.722780\pi\) | ||||
−0.644128 | + | 0.764917i | \(0.722780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 894.970i | − | 1.98441i | ||||||
\(452\) | − | 283.805i | − | 0.627888i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 561.458i | 1.23669i | ||||||||
\(455\) | −110.362 | −0.242554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 514.251i | 1.12528i | 0.826703 | + | 0.562638i | \(0.190214\pi\) | ||||
−0.826703 | + | 0.562638i | \(0.809786\pi\) | |||||||
\(458\) | − | 380.972i | − | 0.831816i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −88.6938 | − | 52.0903i | −0.192813 | − | 0.113240i | ||||
\(461\) | −545.697 | −1.18372 | −0.591862 | − | 0.806039i | \(-0.701607\pi\) | ||||
−0.591862 | + | 0.806039i | \(0.701607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −481.885 | −1.04079 | −0.520395 | − | 0.853926i | \(-0.674215\pi\) | ||||
−0.520395 | + | 0.853926i | \(0.674215\pi\) | |||||||
\(464\) | 40.4708 | 0.0872217 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 495.370 | 1.06302 | ||||||||
\(467\) | − | 6.72759i | − | 0.0144060i | −0.999974 | − | 0.00720299i | \(-0.997707\pi\) | ||
0.999974 | − | 0.00720299i | \(-0.00229280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.5051 | 0.0607784 | ||||||||
\(470\) | − | 155.892i | − | 0.331686i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 68.5976 | 0.145334 | ||||||||
\(473\) | −552.554 | −1.16819 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 85.5370i | − | 0.180078i | ||||||
\(476\) | −82.3916 | −0.173092 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 49.1593 | 0.102844 | ||||||||
\(479\) | 366.353i | 0.764828i | 0.923991 | + | 0.382414i | \(0.124907\pi\) | ||||
−0.923991 | + | 0.382414i | \(0.875093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.7331i | 0.0826053i | ||||||||
\(482\) | − | 485.985i | − | 1.00827i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −281.758 | −0.582144 | ||||||||
\(485\) | −70.4331 | −0.145223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 212.080 | 0.435483 | 0.217742 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217742 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(488\) | 149.843i | 0.307054i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 109.102i | − | 0.222657i | ||||||
\(491\) | 323.833 | 0.659537 | 0.329768 | − | 0.944062i | \(-0.393029\pi\) | ||||
0.329768 | + | 0.944062i | \(0.393029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 109.463i | 0.222034i | ||||||||
\(494\) | − | 313.592i | − | 0.634802i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 117.013 | 0.235912 | ||||||||
\(497\) | 464.086i | 0.933774i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 113.014 | 0.226481 | 0.113241 | − | 0.993568i | \(-0.463877\pi\) | ||||
0.113241 | + | 0.993568i | \(0.463877\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 625.686i | − | 1.24639i | ||||||
\(503\) | − | 841.141i | − | 1.67225i | −0.548541 | − | 0.836124i | \(-0.684816\pi\) | ||
0.548541 | − | 0.836124i | \(-0.315184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.5696i | − | 0.0526131i | ||||||
\(506\) | 453.883 | + | 266.568i | 0.897001 | + | 0.526813i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 72.4414 | 0.142601 | ||||||||
\(509\) | 570.869 | 1.12155 | 0.560775 | − | 0.827968i | \(-0.310503\pi\) | ||||
0.560775 | + | 0.827968i | \(0.310503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 503.644i | − | 0.985605i | ||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 534.512 | 1.03991 | ||||||||
\(515\) | 136.485 | 0.265020 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 797.765i | 1.54307i | ||||||||
\(518\) | 16.5071 | 0.0318669 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 81.9778i | − | 0.157650i | ||||||
\(521\) | − | 823.426i | − | 1.58047i | −0.612802 | − | 0.790236i | \(-0.709958\pi\) | ||
0.612802 | − | 0.790236i | \(-0.290042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 692.210i | − | 1.32354i | −0.749709 | − | 0.661768i | \(-0.769806\pi\) | ||
0.749709 | − | 0.661768i | \(-0.230194\pi\) | |||||||
\(524\) | 1.02540 | 0.00195687 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 329.631i | 0.626674i | ||||||||
\(527\) | 316.488i | 0.600546i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −257.660 | − | 462.009i | −0.487069 | − | 0.873363i | ||||
\(530\) | −90.7118 | −0.171154 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −130.281 | −0.244890 | ||||||||
\(533\) | −716.844 | −1.34492 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 323.569 | 0.604802 | ||||||||
\(536\) | 21.1738i | 0.0395034i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −393.650 | −0.731692 | ||||||||
\(539\) | 558.319i | 1.03584i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 915.849 | 1.69288 | 0.846440 | − | 0.532483i | \(-0.178741\pi\) | ||||
0.846440 | + | 0.532483i | \(0.178741\pi\) | |||||||
\(542\) | 719.534 | 1.32755 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 61.2011i | − | 0.112502i | ||||||
\(545\) | −363.490 | −0.666954 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 203.592 | 0.372197 | 0.186099 | − | 0.982531i | \(-0.440416\pi\) | ||||
0.186099 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(548\) | − | 129.590i | − | 0.236479i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 114.429i | 0.208052i | ||||||||
\(551\) | 173.088i | 0.314134i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −71.0006 | −0.128392 | ||||||||
\(554\) | 27.8924 | 0.0503473 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −340.102 | −0.611693 | ||||||||
\(557\) | 624.298i | 1.12082i | 0.828215 | + | 0.560411i | \(0.189357\pi\) | ||||
−0.828215 | + | 0.560411i | \(0.810643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 442.579i | 0.791734i | ||||||||
\(560\) | −34.0575 | −0.0608170 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 485.716i | − | 0.864263i | ||||||
\(563\) | − | 961.054i | − | 1.70702i | −0.521074 | − | 0.853511i | \(-0.674469\pi\) | ||
0.521074 | − | 0.853511i | \(-0.325531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 317.304 | 0.561600 | ||||||||
\(566\) | 211.469i | 0.373620i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −344.727 | −0.606913 | ||||||||
\(569\) | 576.159i | 1.01258i | 0.862363 | + | 0.506290i | \(0.168984\pi\) | ||||
−0.862363 | + | 0.506290i | \(0.831016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 346.570i | − | 0.606952i | −0.952839 | − | 0.303476i | \(-0.901853\pi\) | ||
0.952839 | − | 0.303476i | \(-0.0981472\pi\) | |||||||
\(572\) | 419.514i | 0.733416i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 297.811i | 0.518835i | ||||||||
\(575\) | 58.2388 | − | 99.1627i | 0.101285 | − | 0.172457i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 675.477 | 1.17067 | 0.585335 | − | 0.810791i | \(-0.300963\pi\) | ||||
0.585335 | + | 0.810791i | \(0.300963\pi\) | |||||||
\(578\) | −243.175 | −0.420718 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 45.2478i | 0.0780134i | ||||||||
\(581\) | −176.332 | −0.303498 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 464.210 | 0.796243 | ||||||||
\(584\) | 374.111 | 0.640601 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 113.469i | − | 0.193632i | ||||||
\(587\) | 820.083 | 1.39708 | 0.698538 | − | 0.715573i | \(-0.253835\pi\) | ||||
0.698538 | + | 0.715573i | \(0.253835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 500.446i | 0.849653i | ||||||||
\(590\) | 76.6944i | 0.129991i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.2616i | 0.0207121i | ||||||||
\(593\) | −768.200 | −1.29545 | −0.647723 | − | 0.761876i | \(-0.724279\pi\) | ||||
−0.647723 | + | 0.761876i | \(0.724279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 92.1166i | − | 0.154818i | ||||||
\(596\) | 109.310i | 0.183405i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 213.513 | − | 363.546i | 0.357044 | − | 0.607937i | ||||
\(599\) | 192.340 | 0.321102 | 0.160551 | − | 0.987028i | \(-0.448673\pi\) | ||||
0.160551 | + | 0.987028i | \(0.448673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 829.949 | 1.38095 | 0.690474 | − | 0.723358i | \(-0.257402\pi\) | ||||
0.690474 | + | 0.723358i | \(0.257402\pi\) | |||||||
\(602\) | 183.869 | 0.305430 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 263.157 | 0.435691 | ||||||||
\(605\) | − | 315.015i | − | 0.520685i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 503.567 | 0.829600 | 0.414800 | − | 0.909913i | \(-0.363851\pi\) | ||||
0.414800 | + | 0.909913i | \(0.363851\pi\) | |||||||
\(608\) | − | 96.7741i | − | 0.159168i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −167.529 | −0.274638 | ||||||||
\(611\) | 638.986 | 1.04580 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 117.049i | − | 0.190944i | −0.995432 | − | 0.0954721i | \(-0.969564\pi\) | ||
0.995432 | − | 0.0954721i | \(-0.0304361\pi\) | |||||||
\(614\) | −217.477 | −0.354198 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 174.286 | 0.282932 | ||||||||
\(617\) | − | 13.5947i | − | 0.0220336i | −0.999939 | − | 0.0110168i | \(-0.996493\pi\) | ||
0.999939 | − | 0.0110168i | \(-0.00350682\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 351.787i | − | 0.568315i | −0.958778 | − | 0.284158i | \(-0.908286\pi\) | ||
0.958778 | − | 0.284158i | \(-0.0917139\pi\) | |||||||
\(620\) | 130.824i | 0.211007i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −176.164 | −0.283222 | ||||||||
\(623\) | −65.6249 | −0.105337 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 314.555i | 0.502484i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 125.414i | 0.199704i | ||||||||
\(629\) | −33.1643 | −0.0527255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 719.196i | − | 1.13977i | −0.821724 | − | 0.569886i | \(-0.806987\pi\) | ||
0.821724 | − | 0.569886i | \(-0.193013\pi\) | |||||||
\(632\) | − | 52.7398i | − | 0.0834491i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 428.932 | 0.676549 | ||||||||
\(635\) | 80.9920i | 0.127546i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 447.197 | 0.702036 | ||||||||
\(638\) | − | 231.551i | − | 0.362933i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | 745.251i | 1.16264i | 0.813676 | + | 0.581319i | \(0.197463\pi\) | ||||
−0.813676 | + | 0.581319i | \(0.802537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 371.944i | 0.578450i | 0.957261 | + | 0.289225i | \(0.0933976\pi\) | ||||
−0.957261 | + | 0.289225i | \(0.906602\pi\) | |||||||
\(644\) | −151.035 | − | 88.7034i | −0.234526 | − | 0.137738i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 261.748 | 0.405183 | ||||||||
\(647\) | 772.723 | 1.19432 | 0.597159 | − | 0.802123i | \(-0.296296\pi\) | ||||
0.597159 | + | 0.802123i | \(0.296296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 392.477i | − | 0.604741i | ||||||
\(650\) | 91.6540 | 0.141006 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 130.528 | 0.200197 | ||||||||
\(653\) | −42.1242 | −0.0645088 | −0.0322544 | − | 0.999480i | \(-0.510269\pi\) | ||||
−0.0322544 | + | 0.999480i | \(0.510269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.14643i | 0.00175027i | ||||||||
\(656\) | −221.217 | −0.337221 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 265.466i | − | 0.403443i | ||||||
\(659\) | 1033.80i | 1.56873i | 0.620297 | + | 0.784367i | \(0.287012\pi\) | ||||
−0.620297 | + | 0.784367i | \(0.712988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 512.065i | 0.774683i | 0.921936 | + | 0.387341i | \(0.126607\pi\) | ||||
−0.921936 | + | 0.387341i | \(0.873393\pi\) | |||||||
\(662\) | 397.615 | 0.600628 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 130.981i | − | 0.197261i | ||||||
\(665\) | − | 145.659i | − | 0.219036i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −117.849 | + | 200.660i | −0.176685 | + | 0.300840i | ||||
\(668\) | 179.933 | 0.269361 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.6730 | −0.0353329 | ||||||||
\(671\) | 857.315 | 1.27767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 611.507 | 0.908628 | 0.454314 | − | 0.890842i | \(-0.349884\pi\) | ||||
0.454314 | + | 0.890842i | \(0.349884\pi\) | |||||||
\(674\) | − | 365.588i | − | 0.542415i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.98201 | −0.00293197 | ||||||||
\(677\) | − | 109.122i | − | 0.161184i | −0.996747 | − | 0.0805920i | \(-0.974319\pi\) | ||
0.996747 | − | 0.0805920i | \(-0.0256811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −119.939 | −0.176641 | ||||||||
\(680\) | 68.4250 | 0.100625 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 669.480i | − | 0.981643i | ||||||
\(683\) | 426.220 | 0.624042 | 0.312021 | − | 0.950075i | \(-0.398994\pi\) | ||||
0.312021 | + | 0.950075i | \(0.398994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 144.886 | 0.211513 | ||||||||
\(686\) | − | 449.651i | − | 0.655467i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 136.579i | 0.198516i | ||||||||
\(689\) | − | 371.818i | − | 0.539649i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 152.559 | 0.220780 | 0.110390 | − | 0.993888i | \(-0.464790\pi\) | ||||
0.110390 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(692\) | 355.338 | 0.513494 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 867.354 | 1.24979 | ||||||||
\(695\) | − | 380.245i | − | 0.547115i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 598.333i | − | 0.858440i | ||||||
\(698\) | 106.792 | 0.152997 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 38.0775i | − | 0.0543964i | ||||||
\(701\) | − | 828.197i | − | 1.18145i | −0.806873 | − | 0.590725i | \(-0.798842\pi\) | ||
0.806873 | − | 0.590725i | \(-0.201158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.4410 | −0.0745960 | ||||||||
\(704\) | 129.461i | 0.183894i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −44.5872 | −0.0631547 | ||||||||
\(707\) | − | 45.2447i | − | 0.0639954i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 319.241i | − | 0.450269i | −0.974328 | − | 0.225134i | \(-0.927718\pi\) | ||
0.974328 | − | 0.225134i | \(-0.0722821\pi\) | |||||||
\(710\) | − | 385.416i | − | 0.542840i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 48.7467i | − | 0.0684645i | ||||||
\(713\) | −340.734 | + | 580.164i | −0.477887 | + | 0.813695i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −469.031 | −0.655987 | ||||||||
\(716\) | 386.912 | 0.540379 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 272.737i | 0.379857i | ||||||||
\(719\) | 894.454 | 1.24402 | 0.622012 | − | 0.783008i | \(-0.286315\pi\) | ||||
0.622012 | + | 0.783008i | \(0.286315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 232.418 | 0.322355 | ||||||||
\(722\) | −96.6425 | −0.133854 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 372.708i | − | 0.514790i | ||||||
\(725\) | −50.5886 | −0.0697773 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1349.88i | 1.85679i | 0.371601 | + | 0.928393i | \(0.378809\pi\) | ||||
−0.371601 | + | 0.928393i | \(0.621191\pi\) | |||||||
\(728\) | − | 139.598i | − | 0.191756i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 418.269i | 0.572971i | ||||||||
\(731\) | −369.410 | −0.505349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 584.473i | 0.797371i | 0.917088 | + | 0.398686i | \(0.130534\pi\) | ||||
−0.917088 | + | 0.398686i | \(0.869466\pi\) | |||||||
\(734\) | − | 724.522i | − | 0.987087i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 65.8896 | − | 112.190i | 0.0895240 | − | 0.152432i | ||||
\(737\) | 121.145 | 0.164375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 100.840 | 0.136454 | 0.0682272 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682272 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(740\) | −13.7089 | −0.0185255 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −154.471 | −0.208182 | ||||||||
\(743\) | − | 1214.22i | − | 1.63422i | −0.576482 | − | 0.817110i | \(-0.695575\pi\) | ||
0.576482 | − | 0.817110i | \(-0.304425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −122.212 | −0.164043 | ||||||||
\(746\) | 435.857i | 0.584259i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −350.159 | −0.468126 | ||||||||
\(749\) | 550.999 | 0.735646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 209.572i | 0.279057i | 0.990218 | + | 0.139529i | \(0.0445587\pi\) | ||||
−0.990218 | + | 0.139529i | \(0.955441\pi\) | |||||||
\(752\) | 197.190 | 0.262221 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −185.466 | −0.245976 | ||||||||
\(755\) | 294.219i | 0.389694i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1291.76i | − | 1.70643i | −0.521563 | − | 0.853213i | \(-0.674651\pi\) | ||
0.521563 | − | 0.853213i | \(-0.325349\pi\) | |||||||
\(758\) | 387.497i | 0.511209i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 108.197 | 0.142364 | ||||||||
\(761\) | 1137.06 | 1.49417 | 0.747083 | − | 0.664731i | \(-0.231454\pi\) | ||||
0.747083 | + | 0.664731i | \(0.231454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −618.978 | −0.811243 | ||||||||
\(764\) | − | 37.5355i | − | 0.0491303i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 261.012i | − | 0.340747i | ||||||
\(767\) | −314.362 | −0.409859 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1211.18i | − | 1.57501i | −0.616310 | − | 0.787504i | \(-0.711373\pi\) | ||
0.616310 | − | 0.787504i | \(-0.288627\pi\) | |||||||
\(770\) | 194.858i | 0.253062i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −323.543 | −0.419097 | ||||||||
\(773\) | − | 1006.14i | − | 1.30160i | −0.759247 | − | 0.650802i | \(-0.774433\pi\) | ||
0.759247 | − | 0.650802i | \(-0.225567\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −146.266 | −0.188730 | ||||||||
\(776\) | − | 89.0917i | − | 0.114809i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 543.761i | − | 0.698922i | ||||||
\(779\) | − | 946.112i | − | 1.21452i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1972.33i | 2.52539i | ||||||||
\(782\) | 303.444 | + | 178.214i | 0.388035 | + | 0.227895i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 138.004 | 0.176026 | ||||||||
\(785\) | −140.217 | −0.178621 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 837.892i | − | 1.06467i | −0.846535 | − | 0.532333i | \(-0.821315\pi\) | ||
0.846535 | − | 0.532333i | \(-0.178685\pi\) | |||||||
\(788\) | −124.769 | −0.158337 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 58.9649 | 0.0746391 | ||||||||
\(791\) | 540.330 | 0.683097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 686.683i | − | 0.865931i | ||||||
\(794\) | −481.582 | −0.606526 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 561.351i | 0.705214i | ||||||||
\(797\) | 866.601i | 1.08733i | 0.839303 | + | 0.543665i | \(0.182964\pi\) | ||||
−0.839303 | + | 0.543665i | \(0.817036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 533.346i | 0.667518i | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1050.11i | − | 1.30936i | ||||||
\(803\) | − | 2140.45i | − | 2.66557i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 99.1735 | − | 168.862i | 0.123197 | − | 0.209766i | ||||
\(806\) | −536.233 | −0.665302 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.6082 | 0.0415943 | ||||||||
\(809\) | 1290.76 | 1.59550 | 0.797749 | − | 0.602990i | \(-0.206024\pi\) | ||||
0.797749 | + | 0.602990i | \(0.206024\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −526.205 | −0.648835 | −0.324418 | − | 0.945914i | \(-0.605168\pi\) | ||||
−0.324418 | + | 0.945914i | \(0.605168\pi\) | |||||||
\(812\) | 77.0514i | 0.0948909i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 70.1539 | 0.0861842 | ||||||||
\(815\) | 145.935i | 0.179061i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −584.129 | −0.714968 | ||||||||
\(818\) | −1071.09 | −1.30940 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 247.328i | − | 0.301619i | ||||||
\(821\) | 445.751 | 0.542937 | 0.271468 | − | 0.962447i | \(-0.412491\pi\) | ||||
0.271468 | + | 0.962447i | \(0.412491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1114.24 | −1.35388 | −0.676938 | − | 0.736040i | \(-0.736693\pi\) | ||||
−0.676938 | + | 0.736040i | \(0.736693\pi\) | |||||||
\(824\) | 172.642i | 0.209517i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 130.601i | 0.158113i | ||||||||
\(827\) | − | 426.354i | − | 0.515543i | −0.966206 | − | 0.257771i | \(-0.917012\pi\) | ||
0.966206 | − | 0.257771i | \(-0.0829882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 413.046 | 0.498246 | 0.249123 | − | 0.968472i | \(-0.419858\pi\) | ||||
0.249123 | + | 0.968472i | \(0.419858\pi\) | |||||||
\(830\) | 146.441 | 0.176435 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 103.695 | 0.124633 | ||||||||
\(833\) | 373.265i | 0.448097i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 201.172i | 0.240924i | ||||||||
\(836\) | −553.687 | −0.662305 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 302.270i | 0.360704i | ||||||||
\(839\) | − | 1356.51i | − | 1.61682i | −0.588619 | − | 0.808411i | \(-0.700328\pi\) | ||
0.588619 | − | 0.808411i | \(-0.299672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −738.632 | −0.878278 | ||||||||
\(842\) | 955.989i | 1.13538i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −504.318 | −0.597533 | ||||||||
\(845\) | − | 2.21596i | − | 0.00262243i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 536.431i | − | 0.633331i | ||||||
\(848\) | − | 114.742i | − | 0.135309i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 76.5014i | 0.0900017i | ||||||||
\(851\) | −60.7946 | − | 35.7050i | −0.0714390 | − | 0.0419565i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1215.79 | −1.42531 | −0.712657 | − | 0.701512i | \(-0.752509\pi\) | ||||
−0.712657 | + | 0.701512i | \(0.752509\pi\) | |||||||
\(854\) | −285.281 | −0.334053 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 409.286i | 0.478138i | ||||||||
\(857\) | 321.853 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 217.358 | 0.253036 | 0.126518 | − | 0.991964i | \(-0.459620\pi\) | ||||
0.126518 | + | 0.991964i | \(0.459620\pi\) | |||||||
\(860\) | −152.700 | −0.177558 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 11.3796i | − | 0.0132014i | ||||||
\(863\) | 1162.38 | 1.34690 | 0.673451 | − | 0.739232i | \(-0.264811\pi\) | ||||
0.673451 | + | 0.739232i | \(0.264811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 397.280i | 0.459283i | ||||||||
\(866\) | 522.366i | 0.603194i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 222.777i | 0.256656i | ||||||||
\(869\) | −301.748 | −0.347235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 97.0332i | − | 0.111404i | ||||||
\(872\) | − | 459.782i | − | 0.527273i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 479.819 | + | 281.800i | 0.548992 | + | 0.322426i | ||||
\(875\) | 42.5719 | 0.0486536 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −143.677 | −0.163828 | −0.0819139 | − | 0.996639i | \(-0.526103\pi\) | ||||
−0.0819139 | + | 0.996639i | \(0.526103\pi\) | |||||||
\(878\) | 76.8027 | 0.0874746 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −144.742 | −0.164480 | ||||||||
\(881\) | − | 26.5389i | − | 0.0301237i | −0.999887 | − | 0.0150618i | \(-0.995205\pi\) | ||
0.999887 | − | 0.0150618i | \(-0.00479451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1442.75 | 1.63391 | 0.816957 | − | 0.576698i | \(-0.195659\pi\) | ||||
0.816957 | + | 0.576698i | \(0.195659\pi\) | |||||||
\(884\) | 280.466i | 0.317270i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 372.744 | 0.420704 | ||||||||
\(887\) | 373.153 | 0.420691 | 0.210345 | − | 0.977627i | \(-0.432541\pi\) | ||||
0.210345 | + | 0.977627i | \(0.432541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 137.919i | 0.155140i | ||||||||
\(890\) | 54.5005 | 0.0612365 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −451.342 | −0.505989 | ||||||||
\(893\) | 843.353i | 0.944404i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 432.580i | 0.483330i | ||||||||
\(896\) | − | 43.0798i | − | 0.0480801i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 818.020 | 0.910935 | ||||||||
\(899\) | 295.975 | 0.329227 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 310.348 | 0.344448 | ||||||||
\(902\) | 1265.68i | 1.40319i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 401.361i | 0.443984i | ||||||||
\(905\) | 416.700 | 0.460442 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 488.681i | 0.538788i | 0.963030 | + | 0.269394i | \(0.0868234\pi\) | ||||
−0.963030 | + | 0.269394i | \(0.913177\pi\) | |||||||
\(908\) | − | 794.022i | − | 0.874473i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 156.075 | 0.171511 | ||||||||
\(911\) | − | 978.988i | − | 1.07463i | −0.843382 | − | 0.537315i | \(-0.819439\pi\) | ||
0.843382 | − | 0.537315i | \(-0.180561\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −749.400 | −0.820811 | ||||||||
\(914\) | − | 727.261i | − | 0.795690i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 538.775i | 0.588183i | ||||||||
\(917\) | 1.95223i | 0.00212893i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 346.891i | 0.377466i | 0.982028 | + | 0.188733i | \(0.0604381\pi\) | ||||
−0.982028 | + | 0.188733i | \(0.939562\pi\) | |||||||
\(920\) | 125.432 | + | 73.6669i | 0.136339 | + | 0.0800727i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 771.732 | 0.837019 | ||||||||
\(923\) | 1579.78 | 1.71157 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 15.3270i | − | 0.0165697i | ||||||
\(926\) | 681.489 | 0.735949 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −57.2344 | −0.0616750 | ||||||||
\(929\) | −700.599 | −0.754143 | −0.377072 | − | 0.926184i | \(-0.623069\pi\) | ||||
−0.377072 | + | 0.926184i | \(0.623069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 590.224i | 0.633967i | ||||||||
\(932\) | −700.558 | −0.751672 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.51426i | 0.0101866i | ||||||||
\(935\) | − | 391.489i | − | 0.418705i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1140.57i | 1.21726i | 0.793455 | + | 0.608628i | \(0.208280\pi\) | ||||
−0.793455 | + | 0.608628i | \(0.791720\pi\) | |||||||
\(938\) | −40.3123 | −0.0429768 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 220.465i | 0.234537i | ||||||||
\(941\) | − | 561.160i | − | 0.596344i | −0.954512 | − | 0.298172i | \(-0.903623\pi\) | ||
0.954512 | − | 0.298172i | \(-0.0963769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 644.170 | − | 1096.82i | 0.683107 | − | 1.16312i | ||||
\(944\) | −97.0116 | −0.102767 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 781.430 | 0.826036 | ||||||||
\(947\) | 974.501 | 1.02904 | 0.514520 | − | 0.857478i | \(-0.327970\pi\) | ||||
0.514520 | + | 0.857478i | \(0.327970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1714.44 | −1.80657 | ||||||||
\(950\) | 120.968i | 0.127334i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 116.519 | 0.122394 | ||||||||
\(953\) | − | 245.849i | − | 0.257974i | −0.991646 | − | 0.128987i | \(-0.958827\pi\) | ||
0.991646 | − | 0.128987i | \(-0.0411725\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.9660 | 0.0439434 | ||||||||
\(956\) | −69.5218 | −0.0727215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 518.101i | − | 0.540815i | ||||||
\(959\) | 246.724 | 0.257272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −105.253 | −0.109525 | ||||||||
\(962\) | − | 56.1911i | − | 0.0584108i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 687.287i | 0.712954i | ||||||||
\(965\) | − | 361.732i | − | 0.374852i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −958.537 | −0.991248 | −0.495624 | − | 0.868537i | \(-0.665061\pi\) | ||||
−0.495624 | + | 0.868537i | \(0.665061\pi\) | |||||||
\(968\) | 398.465 | 0.411638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 99.6075 | 0.102688 | ||||||||
\(971\) | 797.683i | 0.821506i | 0.911747 | + | 0.410753i | \(0.134734\pi\) | ||||
−0.911747 | + | 0.410753i | \(0.865266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 647.511i | − | 0.665479i | ||||||
\(974\) | −299.927 | −0.307933 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 211.909i | − | 0.217120i | ||||||
\(977\) | 968.304i | 0.991099i | 0.868580 | + | 0.495550i | \(0.165033\pi\) | ||||
−0.868580 | + | 0.495550i | \(0.834967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −278.901 | −0.284884 | ||||||||
\(980\) | 154.293i | 0.157442i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −457.968 | −0.466363 | ||||||||
\(983\) | 242.603i | 0.246799i | 0.992357 | + | 0.123399i | \(0.0393796\pi\) | ||||
−0.992357 | + | 0.123399i | \(0.960620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 139.496i | − | 0.141621i | ||||||
\(986\) | − | 154.804i | − | 0.157002i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 443.487i | 0.448873i | ||||||||
\(989\) | −677.178 | − | 397.710i | −0.684710 | − | 0.402134i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1231.78 | 1.24297 | 0.621483 | − | 0.783428i | \(-0.286530\pi\) | ||||
0.621483 | + | 0.783428i | \(0.286530\pi\) | |||||||
\(992\) | −165.481 | −0.166815 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 656.316i | − | 0.660278i | ||||||
\(995\) | −627.609 | −0.630763 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −689.979 | −0.692055 | −0.346027 | − | 0.938224i | \(-0.612470\pi\) | ||||
−0.346027 | + | 0.938224i | \(0.612470\pi\) | |||||||
\(998\) | −159.826 | −0.160146 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.3.c.b.91.14 | 32 | ||
3.2 | odd | 2 | 690.3.c.a.91.27 | ✓ | 32 | ||
23.22 | odd | 2 | inner | 2070.3.c.b.91.3 | 32 | ||
69.68 | even | 2 | 690.3.c.a.91.30 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.27 | ✓ | 32 | 3.2 | odd | 2 | ||
690.3.c.a.91.30 | yes | 32 | 69.68 | even | 2 | ||
2070.3.c.b.91.3 | 32 | 23.22 | odd | 2 | inner | ||
2070.3.c.b.91.14 | 32 | 1.1 | even | 1 | trivial |