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 | 91.27 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.30 |
$q$-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 | ||||||||
\(7\) | 3.80775i | 0.543964i | 0.962302 | + | 0.271982i | \(0.0876791\pi\) | ||||
−0.962302 | + | 0.271982i | \(0.912321\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | − | 16.1827i | − | 1.47115i | −0.677442 | − | 0.735576i | \(-0.736912\pi\) | ||
0.677442 | − | 0.735576i | \(-0.263088\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 12.9618 | 0.997064 | 0.498532 | − | 0.866871i | \(-0.333873\pi\) | ||||
0.498532 | + | 0.866871i | \(0.333873\pi\) | |||||||
\(14\) | 5.38497i | 0.384641i | ||||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 10.8189i | − | 0.636408i | −0.948022 | − | 0.318204i | \(-0.896920\pi\) | ||
0.948022 | − | 0.318204i | \(-0.103080\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 17.1074i | 0.900390i | 0.892930 | + | 0.450195i | \(0.148646\pi\) | ||||
−0.892930 | + | 0.450195i | \(0.851354\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 6.59521i | 0.314058i | ||||||||
\(22\) | − | 22.8858i | − | 1.04026i | ||||||
\(23\) | 11.6478 | − | 19.8325i | 0.506424 | − | 0.862285i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 18.3308 | 0.705031 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 7.61550i | 0.271982i | ||||||||
\(29\) | −10.1177 | −0.348887 | −0.174443 | − | 0.984667i | \(-0.555813\pi\) | ||||
−0.174443 | + | 0.984667i | \(0.555813\pi\) | |||||||
\(30\) | − | 5.47723i | − | 0.182574i | ||||||
\(31\) | 29.2531 | 0.943650 | 0.471825 | − | 0.881692i | \(-0.343595\pi\) | ||||
0.471825 | + | 0.881692i | \(0.343595\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 28.0292i | − | 0.849370i | ||||||
\(34\) | − | 15.3003i | − | 0.450008i | ||||||
\(35\) | 8.51438 | 0.243268 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 3.06540i | 0.0828486i | 0.999142 | + | 0.0414243i | \(0.0131895\pi\) | ||||
−0.999142 | + | 0.0414243i | \(0.986810\pi\) | |||||||
\(38\) | 24.1935i | 0.636672i | ||||||||
\(39\) | 22.4505 | 0.575655 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | 55.3042 | 1.34888 | 0.674441 | − | 0.738328i | \(-0.264384\pi\) | ||||
0.674441 | + | 0.738328i | \(0.264384\pi\) | |||||||
\(42\) | 9.32704i | 0.222072i | ||||||||
\(43\) | 34.1448i | 0.794065i | 0.917804 | + | 0.397033i | \(0.129960\pi\) | ||||
−0.917804 | + | 0.397033i | \(0.870040\pi\) | |||||||
\(44\) | − | 32.3653i | − | 0.735576i | ||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 16.4724 | − | 28.0475i | 0.358096 | − | 0.609727i | ||||
\(47\) | −49.2975 | −1.04888 | −0.524442 | − | 0.851446i | \(-0.675726\pi\) | ||||
−0.524442 | + | 0.851446i | \(0.675726\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 34.5011 | 0.704103 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | − | 18.7389i | − | 0.367430i | ||||||
\(52\) | 25.9237 | 0.498532 | ||||||||
\(53\) | 28.6856i | 0.541238i | 0.962687 | + | 0.270619i | \(0.0872283\pi\) | ||||
−0.962687 | + | 0.270619i | \(0.912772\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | −36.1856 | −0.657919 | ||||||||
\(56\) | 10.7699i | 0.192320i | ||||||||
\(57\) | 29.6309i | 0.519840i | ||||||||
\(58\) | −14.3086 | −0.246700 | ||||||||
\(59\) | 24.2529 | 0.411066 | 0.205533 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205533 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | − | 52.9773i | − | 0.868481i | −0.900797 | − | 0.434240i | \(-0.857017\pi\) | ||
0.900797 | − | 0.434240i | \(-0.142983\pi\) | |||||||
\(62\) | 41.3702 | 0.667261 | ||||||||
\(63\) | 11.4232i | 0.181321i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 28.9835i | − | 0.445900i | ||||||
\(66\) | − | 39.6393i | − | 0.600595i | ||||||
\(67\) | − | 7.48607i | − | 0.111732i | −0.998438 | − | 0.0558662i | \(-0.982208\pi\) | ||
0.998438 | − | 0.0558662i | \(-0.0177920\pi\) | |||||||
\(68\) | − | 21.6379i | − | 0.318204i | ||||||
\(69\) | 20.1745 | − | 34.3510i | 0.292384 | − | 0.497840i | ||||
\(70\) | 12.0412 | 0.172017 | ||||||||
\(71\) | −121.879 | −1.71661 | −0.858305 | − | 0.513140i | \(-0.828482\pi\) | ||||
−0.858305 | + | 0.513140i | \(0.828482\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | −132.268 | −1.81189 | −0.905947 | − | 0.423391i | \(-0.860840\pi\) | ||||
−0.905947 | + | 0.423391i | \(0.860840\pi\) | |||||||
\(74\) | 4.33513i | 0.0585828i | ||||||||
\(75\) | −8.66025 | −0.115470 | ||||||||
\(76\) | 34.2148i | 0.450195i | ||||||||
\(77\) | 61.6195 | 0.800254 | ||||||||
\(78\) | 31.7499 | 0.407050 | ||||||||
\(79\) | 18.6463i | 0.236030i | 0.993012 | + | 0.118015i | \(0.0376530\pi\) | ||||
−0.993012 | + | 0.118015i | \(0.962347\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 78.2120 | 0.953804 | ||||||||
\(83\) | − | 46.3088i | − | 0.557938i | −0.960300 | − | 0.278969i | \(-0.910007\pi\) | ||
0.960300 | − | 0.278969i | \(-0.0899926\pi\) | |||||||
\(84\) | 13.1904i | 0.157029i | ||||||||
\(85\) | −24.1919 | −0.284610 | ||||||||
\(86\) | 48.2881i | 0.561489i | ||||||||
\(87\) | −17.5244 | −0.201430 | ||||||||
\(88\) | − | 45.7715i | − | 0.520131i | ||||||
\(89\) | − | 17.2346i | − | 0.193647i | −0.995302 | − | 0.0968234i | \(-0.969132\pi\) | ||
0.995302 | − | 0.0968234i | \(-0.0308682\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | 49.3554i | 0.542367i | ||||||||
\(92\) | 23.2955 | − | 39.6651i | 0.253212 | − | 0.431142i | ||||
\(93\) | 50.6679 | 0.544817 | ||||||||
\(94\) | −69.7172 | −0.741672 | ||||||||
\(95\) | 38.2533 | 0.402667 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 31.4987i | 0.324728i | 0.986731 | + | 0.162364i | \(0.0519120\pi\) | ||||
−0.986731 | + | 0.162364i | \(0.948088\pi\) | |||||||
\(98\) | 48.7919 | 0.497876 | ||||||||
\(99\) | − | 48.5480i | − | 0.490384i | ||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 11.8823 | 0.117646 | 0.0588232 | − | 0.998268i | \(-0.481265\pi\) | ||||
0.0588232 | + | 0.998268i | \(0.481265\pi\) | |||||||
\(102\) | − | 26.5009i | − | 0.259812i | ||||||
\(103\) | − | 61.0381i | − | 0.592603i | −0.955094 | − | 0.296301i | \(-0.904247\pi\) | ||
0.955094 | − | 0.296301i | \(-0.0957533\pi\) | |||||||
\(104\) | 36.6616 | 0.352515 | ||||||||
\(105\) | 14.7473 | 0.140451 | ||||||||
\(106\) | 40.5676i | 0.382713i | ||||||||
\(107\) | 144.705i | 1.35238i | 0.736728 | + | 0.676190i | \(0.236370\pi\) | ||||
−0.736728 | + | 0.676190i | \(0.763630\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 162.558i | 1.49135i | 0.666308 | + | 0.745677i | \(0.267874\pi\) | ||||
−0.666308 | + | 0.745677i | \(0.732126\pi\) | |||||||
\(110\) | −51.1741 | −0.465219 | ||||||||
\(111\) | 5.30942i | 0.0478326i | ||||||||
\(112\) | 15.2310i | 0.135991i | ||||||||
\(113\) | 141.903i | 1.25578i | 0.778304 | + | 0.627888i | \(0.216080\pi\) | ||||
−0.778304 | + | 0.627888i | \(0.783920\pi\) | |||||||
\(114\) | 41.9044i | 0.367583i | ||||||||
\(115\) | −44.3469 | − | 26.0452i | −0.385625 | − | 0.226480i | ||||
\(116\) | −20.2354 | −0.174443 | ||||||||
\(117\) | 38.8855 | 0.332355 | ||||||||
\(118\) | 34.2988 | 0.290668 | ||||||||
\(119\) | 41.1958 | 0.346183 | ||||||||
\(120\) | − | 10.9545i | − | 0.0912871i | ||||||
\(121\) | −140.879 | −1.16429 | ||||||||
\(122\) | − | 74.9213i | − | 0.614109i | ||||||
\(123\) | 95.7897 | 0.778778 | ||||||||
\(124\) | 58.5063 | 0.471825 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 16.1549i | 0.128214i | ||||||||
\(127\) | 36.2207 | 0.285202 | 0.142601 | − | 0.989780i | \(-0.454453\pi\) | ||||
0.142601 | + | 0.989780i | \(0.454453\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 59.1405i | 0.458454i | ||||||||
\(130\) | − | 40.9889i | − | 0.315299i | ||||||
\(131\) | −0.512699 | −0.00391373 | −0.00195687 | − | 0.999998i | \(-0.500623\pi\) | ||||
−0.00195687 | + | 0.999998i | \(0.500623\pi\) | |||||||
\(132\) | − | 56.0584i | − | 0.424685i | ||||||
\(133\) | −65.1407 | −0.489780 | ||||||||
\(134\) | − | 10.5869i | − | 0.0790067i | ||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | − | 30.6006i | − | 0.225004i | ||||||
\(137\) | 64.7952i | 0.472958i | 0.971637 | + | 0.236479i | \(0.0759934\pi\) | ||||
−0.971637 | + | 0.236479i | \(0.924007\pi\) | |||||||
\(138\) | 28.5311 | − | 48.5796i | 0.206747 | − | 0.352026i | ||||
\(139\) | −170.051 | −1.22339 | −0.611693 | − | 0.791095i | \(-0.709511\pi\) | ||||
−0.611693 | + | 0.791095i | \(0.709511\pi\) | |||||||
\(140\) | 17.0288 | 0.121634 | ||||||||
\(141\) | −85.3858 | −0.605573 | ||||||||
\(142\) | −172.363 | −1.21383 | ||||||||
\(143\) | − | 209.757i | − | 1.46683i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 22.6239i | 0.156027i | ||||||||
\(146\) | −187.056 | −1.28120 | ||||||||
\(147\) | 59.7576 | 0.406514 | ||||||||
\(148\) | 6.13079i | 0.0414243i | ||||||||
\(149\) | − | 54.6548i | − | 0.366810i | −0.983037 | − | 0.183405i | \(-0.941288\pi\) | ||
0.983037 | − | 0.183405i | \(-0.0587120\pi\) | |||||||
\(150\) | −12.2474 | −0.0816497 | ||||||||
\(151\) | 131.579 | 0.871382 | 0.435691 | − | 0.900096i | \(-0.356504\pi\) | ||||
0.435691 | + | 0.900096i | \(0.356504\pi\) | |||||||
\(152\) | 48.3871i | 0.318336i | ||||||||
\(153\) | − | 32.4568i | − | 0.212136i | ||||||
\(154\) | 87.1432 | 0.565865 | ||||||||
\(155\) | − | 65.4120i | − | 0.422013i | ||||||
\(156\) | 44.9011 | 0.287828 | ||||||||
\(157\) | 62.7071i | 0.399409i | 0.979856 | + | 0.199704i | \(0.0639982\pi\) | ||||
−0.979856 | + | 0.199704i | \(0.936002\pi\) | |||||||
\(158\) | 26.3699i | 0.166898i | ||||||||
\(159\) | 49.6849i | 0.312484i | ||||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | 75.5173 | + | 44.3517i | 0.469052 | + | 0.275477i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 65.2642 | 0.400394 | 0.200197 | − | 0.979756i | \(-0.435842\pi\) | ||||
0.200197 | + | 0.979756i | \(0.435842\pi\) | |||||||
\(164\) | 110.608 | 0.674441 | ||||||||
\(165\) | −62.6752 | −0.379850 | ||||||||
\(166\) | − | 65.4906i | − | 0.394521i | ||||||
\(167\) | −89.9666 | −0.538722 | −0.269361 | − | 0.963039i | \(-0.586813\pi\) | ||||
−0.269361 | + | 0.963039i | \(0.586813\pi\) | |||||||
\(168\) | 18.6541i | 0.111036i | ||||||||
\(169\) | −0.991006 | −0.00586394 | ||||||||
\(170\) | −34.2125 | −0.201250 | ||||||||
\(171\) | 51.3222i | 0.300130i | ||||||||
\(172\) | 68.2896i | 0.397033i | ||||||||
\(173\) | −177.669 | −1.02699 | −0.513494 | − | 0.858093i | \(-0.671649\pi\) | ||||
−0.513494 | + | 0.858093i | \(0.671649\pi\) | |||||||
\(174\) | −24.7832 | −0.142432 | ||||||||
\(175\) | − | 19.0387i | − | 0.108793i | ||||||
\(176\) | − | 64.7307i | − | 0.367788i | ||||||
\(177\) | 42.0073 | 0.237329 | ||||||||
\(178\) | − | 24.3734i | − | 0.136929i | ||||||
\(179\) | −193.456 | −1.08076 | −0.540379 | − | 0.841421i | \(-0.681719\pi\) | ||||
−0.540379 | + | 0.841421i | \(0.681719\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | − | 186.354i | − | 1.02958i | −0.857316 | − | 0.514790i | \(-0.827870\pi\) | ||
0.857316 | − | 0.514790i | \(-0.172130\pi\) | |||||||
\(182\) | 69.7991i | 0.383511i | ||||||||
\(183\) | − | 91.7594i | − | 0.501418i | ||||||
\(184\) | 32.9448 | − | 56.0949i | 0.179048 | − | 0.304864i | ||||
\(185\) | 6.85443 | 0.0370510 | ||||||||
\(186\) | 71.6553 | 0.385243 | ||||||||
\(187\) | −175.079 | −0.936253 | ||||||||
\(188\) | −98.5950 | −0.524442 | ||||||||
\(189\) | 19.7856i | 0.104686i | ||||||||
\(190\) | 54.0984 | 0.284728 | ||||||||
\(191\) | 18.7678i | 0.0982605i | 0.998792 | + | 0.0491303i | \(0.0156449\pi\) | ||||
−0.998792 | + | 0.0491303i | \(0.984355\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | −161.771 | −0.838193 | −0.419097 | − | 0.907942i | \(-0.637653\pi\) | ||||
−0.419097 | + | 0.907942i | \(0.637653\pi\) | |||||||
\(194\) | 44.5458i | 0.229618i | ||||||||
\(195\) | − | 50.2009i | − | 0.257441i | ||||||
\(196\) | 69.0021 | 0.352052 | ||||||||
\(197\) | 62.3846 | 0.316673 | 0.158337 | − | 0.987385i | \(-0.449387\pi\) | ||||
0.158337 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(198\) | − | 68.6573i | − | 0.346754i | ||||||
\(199\) | 280.675i | 1.41043i | 0.708994 | + | 0.705214i | \(0.249149\pi\) | ||||
−0.708994 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | − | 12.9663i | − | 0.0645087i | ||||||
\(202\) | 16.8041 | 0.0831885 | ||||||||
\(203\) | − | 38.5257i | − | 0.189782i | ||||||
\(204\) | − | 37.4779i | − | 0.183715i | ||||||
\(205\) | − | 123.664i | − | 0.603239i | ||||||
\(206\) | − | 86.3209i | − | 0.419033i | ||||||
\(207\) | 34.9433 | − | 59.4976i | 0.168808 | − | 0.287428i | ||||
\(208\) | 51.8473 | 0.249266 | ||||||||
\(209\) | 276.844 | 1.32461 | ||||||||
\(210\) | 20.8559 | 0.0993138 | ||||||||
\(211\) | −252.159 | −1.19507 | −0.597533 | − | 0.801844i | \(-0.703852\pi\) | ||||
−0.597533 | + | 0.801844i | \(0.703852\pi\) | |||||||
\(212\) | 57.3712i | 0.270619i | ||||||||
\(213\) | −211.101 | −0.991085 | ||||||||
\(214\) | 204.643i | 0.956276i | ||||||||
\(215\) | 76.3501 | 0.355117 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 111.389i | 0.513312i | ||||||||
\(218\) | 229.891i | 1.05455i | ||||||||
\(219\) | −229.095 | −1.04610 | ||||||||
\(220\) | −72.3711 | −0.328960 | ||||||||
\(221\) | − | 140.233i | − | 0.634539i | ||||||
\(222\) | 7.50866i | 0.0338228i | ||||||||
\(223\) | −225.671 | −1.01198 | −0.505989 | − | 0.862540i | \(-0.668872\pi\) | ||||
−0.505989 | + | 0.862540i | \(0.668872\pi\) | |||||||
\(224\) | 21.5399i | 0.0961602i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 200.681i | 0.887967i | ||||||||
\(227\) | 397.011i | 1.74895i | 0.485074 | + | 0.874473i | \(0.338793\pi\) | ||||
−0.485074 | + | 0.874473i | \(0.661207\pi\) | |||||||
\(228\) | 59.2618i | 0.259920i | ||||||||
\(229\) | 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 | ||||
\(231\) | 106.728 | 0.462027 | ||||||||
\(232\) | −28.6172 | −0.123350 | ||||||||
\(233\) | 350.279 | 1.50334 | 0.751672 | − | 0.659537i | \(-0.229248\pi\) | ||||
0.751672 | + | 0.659537i | \(0.229248\pi\) | |||||||
\(234\) | 54.9924 | 0.235010 | ||||||||
\(235\) | 110.233i | 0.469075i | ||||||||
\(236\) | 48.5058 | 0.205533 | ||||||||
\(237\) | 32.2964i | 0.136272i | ||||||||
\(238\) | 58.2596 | 0.244788 | ||||||||
\(239\) | 34.7609 | 0.145443 | 0.0727215 | − | 0.997352i | \(-0.476832\pi\) | ||||
0.0727215 | + | 0.997352i | \(0.476832\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | 343.644i | 1.42591i | 0.701211 | + | 0.712954i | \(0.252643\pi\) | ||||
−0.701211 | + | 0.712954i | \(0.747357\pi\) | |||||||
\(242\) | −199.233 | −0.823276 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 105.955i | − | 0.434240i | ||||||
\(245\) | − | 77.1467i | − | 0.314884i | ||||||
\(246\) | 135.467 | 0.550679 | ||||||||
\(247\) | 221.743i | 0.897746i | ||||||||
\(248\) | 82.7404 | 0.333631 | ||||||||
\(249\) | − | 80.2092i | − | 0.322125i | ||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | − | 442.427i | − | 1.76266i | −0.472505 | − | 0.881328i | \(-0.656650\pi\) | ||
0.472505 | − | 0.881328i | \(-0.343350\pi\) | |||||||
\(252\) | 22.8465i | 0.0906607i | ||||||||
\(253\) | −320.944 | − | 188.492i | −1.26855 | − | 0.745027i | ||||
\(254\) | 51.2238 | 0.201669 | ||||||||
\(255\) | −41.9016 | −0.164320 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 377.957 | 1.47065 | 0.735325 | − | 0.677715i | \(-0.237029\pi\) | ||||
0.735325 | + | 0.677715i | \(0.237029\pi\) | |||||||
\(258\) | 83.6374i | 0.324176i | ||||||||
\(259\) | −11.6723 | −0.0450666 | ||||||||
\(260\) | − | 57.9671i | − | 0.222950i | ||||||
\(261\) | −30.3531 | −0.116296 | ||||||||
\(262\) | −0.725066 | −0.00276743 | ||||||||
\(263\) | 233.084i | 0.886251i | 0.896459 | + | 0.443126i | \(0.146130\pi\) | ||||
−0.896459 | + | 0.443126i | \(0.853870\pi\) | |||||||
\(264\) | − | 79.2786i | − | 0.300298i | ||||||
\(265\) | 64.1430 | 0.242049 | ||||||||
\(266\) | −92.1229 | −0.346327 | ||||||||
\(267\) | − | 29.8512i | − | 0.111802i | ||||||
\(268\) | − | 14.9721i | − | 0.0558662i | ||||||
\(269\) | −278.353 | −1.03477 | −0.517385 | − | 0.855753i | \(-0.673094\pi\) | ||||
−0.517385 | + | 0.855753i | \(0.673094\pi\) | |||||||
\(270\) | − | 16.4317i | − | 0.0608581i | ||||||
\(271\) | −508.787 | −1.87744 | −0.938722 | − | 0.344676i | \(-0.887989\pi\) | ||||
−0.938722 | + | 0.344676i | \(0.887989\pi\) | |||||||
\(272\) | − | 43.2757i | − | 0.159102i | ||||||
\(273\) | 85.4860i | 0.313136i | ||||||||
\(274\) | 91.6343i | 0.334432i | ||||||||
\(275\) | 80.9134i | 0.294230i | ||||||||
\(276\) | 40.3490 | − | 68.7019i | 0.146192 | − | 0.248920i | ||||
\(277\) | −19.7229 | −0.0712019 | −0.0356009 | − | 0.999366i | \(-0.511335\pi\) | ||||
−0.0356009 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(278\) | −240.488 | −0.865065 | ||||||||
\(279\) | 87.7594 | 0.314550 | ||||||||
\(280\) | 24.0823 | 0.0860083 | ||||||||
\(281\) | − | 343.453i | − | 1.22225i | −0.791533 | − | 0.611126i | \(-0.790717\pi\) | ||
0.791533 | − | 0.611126i | \(-0.209283\pi\) | |||||||
\(282\) | −120.754 | −0.428205 | ||||||||
\(283\) | − | 149.531i | − | 0.528378i | −0.964471 | − | 0.264189i | \(-0.914896\pi\) | ||
0.964471 | − | 0.264189i | \(-0.0851043\pi\) | |||||||
\(284\) | −243.759 | −0.858305 | ||||||||
\(285\) | 66.2567 | 0.232480 | ||||||||
\(286\) | − | 296.641i | − | 1.03721i | ||||||
\(287\) | 210.584i | 0.733744i | ||||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 171.951 | 0.594985 | ||||||||
\(290\) | 31.9950i | 0.110328i | ||||||||
\(291\) | 54.5573i | 0.187482i | ||||||||
\(292\) | −264.537 | −0.905947 | ||||||||
\(293\) | − | 80.2344i | − | 0.273838i | −0.990582 | − | 0.136919i | \(-0.956280\pi\) | ||
0.990582 | − | 0.136919i | \(-0.0437199\pi\) | |||||||
\(294\) | 84.5100 | 0.287449 | ||||||||
\(295\) | − | 54.2312i | − | 0.183834i | ||||||
\(296\) | 8.67025i | 0.0292914i | ||||||||
\(297\) | − | 84.0876i | − | 0.283123i | ||||||
\(298\) | − | 77.2935i | − | 0.259374i | ||||||
\(299\) | 150.976 | − | 257.066i | 0.504937 | − | 0.859753i | ||||
\(300\) | −17.3205 | −0.0577350 | ||||||||
\(301\) | −130.015 | −0.431943 | ||||||||
\(302\) | 186.080 | 0.616160 | ||||||||
\(303\) | 20.5807 | 0.0679232 | ||||||||
\(304\) | 68.4296i | 0.225097i | ||||||||
\(305\) | −118.461 | −0.388396 | ||||||||
\(306\) | − | 45.9009i | − | 0.150003i | ||||||
\(307\) | 153.780 | 0.500911 | 0.250456 | − | 0.968128i | \(-0.419420\pi\) | ||||
0.250456 | + | 0.968128i | \(0.419420\pi\) | |||||||
\(308\) | 123.239 | 0.400127 | ||||||||
\(309\) | − | 105.721i | − | 0.342139i | ||||||
\(310\) | − | 92.5066i | − | 0.298408i | ||||||
\(311\) | −124.567 | −0.400536 | −0.200268 | − | 0.979741i | \(-0.564181\pi\) | ||||
−0.200268 | + | 0.979741i | \(0.564181\pi\) | |||||||
\(312\) | 63.4997 | 0.203525 | ||||||||
\(313\) | − | 222.424i | − | 0.710619i | −0.934749 | − | 0.355310i | \(-0.884375\pi\) | ||
0.934749 | − | 0.355310i | \(-0.115625\pi\) | |||||||
\(314\) | 88.6813i | 0.282425i | ||||||||
\(315\) | 25.5432 | 0.0810894 | ||||||||
\(316\) | 37.2927i | 0.118015i | ||||||||
\(317\) | 303.301 | 0.956785 | 0.478393 | − | 0.878146i | \(-0.341220\pi\) | ||||
0.478393 | + | 0.878146i | \(0.341220\pi\) | |||||||
\(318\) | 70.2651i | 0.220959i | ||||||||
\(319\) | 163.732i | 0.513265i | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 250.636i | 0.780796i | ||||||||
\(322\) | 106.798 | + | 62.7228i | 0.331670 | + | 0.194791i | ||||
\(323\) | 185.084 | 0.573015 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −64.8091 | −0.199413 | ||||||||
\(326\) | 92.2975 | 0.283121 | ||||||||
\(327\) | 281.558i | 0.861034i | ||||||||
\(328\) | 156.424 | 0.476902 | ||||||||
\(329\) | − | 187.713i | − | 0.570555i | ||||||
\(330\) | −88.6361 | −0.268594 | ||||||||
\(331\) | −281.157 | −0.849416 | −0.424708 | − | 0.905330i | \(-0.639623\pi\) | ||||
−0.424708 | + | 0.905330i | \(0.639623\pi\) | |||||||
\(332\) | − | 92.6176i | − | 0.278969i | ||||||
\(333\) | 9.19619i | 0.0276162i | ||||||||
\(334\) | −127.232 | −0.380934 | ||||||||
\(335\) | −16.7394 | −0.0499683 | ||||||||
\(336\) | 26.3809i | 0.0785145i | ||||||||
\(337\) | 258.510i | 0.767091i | 0.923522 | + | 0.383546i | \(0.125297\pi\) | ||||
−0.923522 | + | 0.383546i | \(0.874703\pi\) | |||||||
\(338\) | −1.40149 | −0.00414643 | ||||||||
\(339\) | 245.783i | 0.725022i | ||||||||
\(340\) | −48.3837 | −0.142305 | ||||||||
\(341\) | − | 473.394i | − | 1.38825i | ||||||
\(342\) | 72.5806i | 0.212224i | ||||||||
\(343\) | 317.951i | 0.926971i | ||||||||
\(344\) | 96.5761i | 0.280744i | ||||||||
\(345\) | −76.8111 | − | 45.1116i | −0.222641 | − | 0.130758i | ||||
\(346\) | −251.262 | −0.726191 | ||||||||
\(347\) | 613.312 | 1.76747 | 0.883735 | − | 0.467988i | \(-0.155021\pi\) | ||||
0.883735 | + | 0.467988i | \(0.155021\pi\) | |||||||
\(348\) | −35.0488 | −0.100715 | ||||||||
\(349\) | −75.5131 | −0.216370 | −0.108185 | − | 0.994131i | \(-0.534504\pi\) | ||||
−0.108185 | + | 0.994131i | \(0.534504\pi\) | |||||||
\(350\) | − | 26.9248i | − | 0.0769281i | ||||||
\(351\) | 67.3516 | 0.191885 | ||||||||
\(352\) | − | 91.5430i | − | 0.260065i | ||||||
\(353\) | −31.5279 | −0.0893142 | −0.0446571 | − | 0.999002i | \(-0.514220\pi\) | ||||
−0.0446571 | + | 0.999002i | \(0.514220\pi\) | |||||||
\(354\) | 59.4073 | 0.167817 | ||||||||
\(355\) | 272.530i | 0.767691i | ||||||||
\(356\) | − | 34.4691i | − | 0.0968234i | ||||||
\(357\) | 71.3532 | 0.199869 | ||||||||
\(358\) | −273.588 | −0.764212 | ||||||||
\(359\) | 192.855i | 0.537199i | 0.963252 | + | 0.268600i | \(0.0865608\pi\) | ||||
−0.963252 | + | 0.268600i | \(0.913439\pi\) | |||||||
\(360\) | − | 18.9737i | − | 0.0527046i | ||||||
\(361\) | 68.3365 | 0.189298 | ||||||||
\(362\) | − | 263.544i | − | 0.728023i | ||||||
\(363\) | −244.009 | −0.672202 | ||||||||
\(364\) | 98.7108i | 0.271183i | ||||||||
\(365\) | 295.761i | 0.810304i | ||||||||
\(366\) | − | 129.767i | − | 0.354556i | ||||||
\(367\) | 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 | ||||
\(369\) | 165.913 | 0.449628 | ||||||||
\(370\) | 9.69363 | 0.0261990 | ||||||||
\(371\) | −109.228 | −0.294414 | ||||||||
\(372\) | 101.336 | 0.272408 | ||||||||
\(373\) | − | 308.198i | − | 0.826267i | −0.910670 | − | 0.413134i | \(-0.864434\pi\) | ||
0.910670 | − | 0.413134i | \(-0.135566\pi\) | |||||||
\(374\) | −247.599 | −0.662031 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | −139.434 | −0.370836 | ||||||||
\(377\) | −131.144 | −0.347862 | ||||||||
\(378\) | 27.9811i | 0.0740241i | ||||||||
\(379\) | − | 274.002i | − | 0.722959i | −0.932380 | − | 0.361480i | \(-0.882272\pi\) | ||
0.932380 | − | 0.361480i | \(-0.117728\pi\) | |||||||
\(380\) | 76.5067 | 0.201333 | ||||||||
\(381\) | 62.7361 | 0.164662 | ||||||||
\(382\) | 26.5416i | 0.0694807i | ||||||||
\(383\) | − | 184.563i | − | 0.481889i | −0.970539 | − | 0.240944i | \(-0.922543\pi\) | ||
0.970539 | − | 0.240944i | \(-0.0774571\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | − | 137.785i | − | 0.357884i | ||||||
\(386\) | −228.779 | −0.592692 | ||||||||
\(387\) | 102.434i | 0.264688i | ||||||||
\(388\) | 62.9973i | 0.162364i | ||||||||
\(389\) | − | 384.497i | − | 0.988425i | −0.869341 | − | 0.494212i | \(-0.835457\pi\) | ||
0.869341 | − | 0.494212i | \(-0.164543\pi\) | |||||||
\(390\) | − | 70.9949i | − | 0.182038i | ||||||
\(391\) | −214.567 | − | 126.016i | −0.548765 | − | 0.322292i | ||||
\(392\) | 97.5837 | 0.248938 | ||||||||
\(393\) | −0.888020 | −0.00225959 | ||||||||
\(394\) | 88.2252 | 0.223922 | ||||||||
\(395\) | 41.6945 | 0.105556 | ||||||||
\(396\) | − | 97.0960i | − | 0.245192i | ||||||
\(397\) | 340.530 | 0.857757 | 0.428879 | − | 0.903362i | \(-0.358909\pi\) | ||||
0.428879 | + | 0.903362i | \(0.358909\pi\) | |||||||
\(398\) | 396.935i | 0.997324i | ||||||||
\(399\) | −112.827 | −0.282775 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 742.537i | − | 1.85171i | −0.377875 | − | 0.925857i | \(-0.623345\pi\) | ||
0.377875 | − | 0.925857i | \(-0.376655\pi\) | |||||||
\(402\) | − | 18.3371i | − | 0.0456146i | ||||||
\(403\) | 379.174 | 0.940879 | ||||||||
\(404\) | 23.7646 | 0.0588232 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | − | 54.4836i | − | 0.134196i | ||||||
\(407\) | 49.6063 | 0.121883 | ||||||||
\(408\) | − | 53.0017i | − | 0.129906i | ||||||
\(409\) | 757.373 | 1.85177 | 0.925884 | − | 0.377807i | \(-0.123322\pi\) | ||||
0.925884 | + | 0.377807i | \(0.123322\pi\) | |||||||
\(410\) | − | 174.887i | − | 0.426554i | ||||||
\(411\) | 112.229i | 0.273062i | ||||||||
\(412\) | − | 122.076i | − | 0.296301i | ||||||
\(413\) | 92.3490i | 0.223605i | ||||||||
\(414\) | 49.4172 | − | 84.1424i | 0.119365 | − | 0.203242i | ||||
\(415\) | −103.550 | −0.249517 | ||||||||
\(416\) | 73.3232 | 0.176258 | ||||||||
\(417\) | −294.537 | −0.706323 | ||||||||
\(418\) | 391.516 | 0.936641 | ||||||||
\(419\) | 213.737i | 0.510113i | 0.966926 | + | 0.255056i | \(0.0820940\pi\) | ||||
−0.966926 | + | 0.255056i | \(0.917906\pi\) | |||||||
\(420\) | 29.4947 | 0.0702255 | ||||||||
\(421\) | − | 675.986i | − | 1.60567i | −0.596202 | − | 0.802834i | \(-0.703324\pi\) | ||
0.596202 | − | 0.802834i | \(-0.296676\pi\) | |||||||
\(422\) | −356.607 | −0.845040 | ||||||||
\(423\) | −147.893 | −0.349628 | ||||||||
\(424\) | 81.1351i | 0.191356i | ||||||||
\(425\) | 54.0947i | 0.127282i | ||||||||
\(426\) | −298.542 | −0.700803 | ||||||||
\(427\) | 201.724 | 0.472422 | ||||||||
\(428\) | 289.409i | 0.676190i | ||||||||
\(429\) | − | 363.310i | − | 0.846876i | ||||||
\(430\) | 107.975 | 0.251105 | ||||||||
\(431\) | − | 8.04660i | − | 0.0186696i | −0.999956 | − | 0.00933480i | \(-0.997029\pi\) | ||
0.999956 | − | 0.00933480i | \(-0.00297140\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | − | 369.369i | − | 0.853046i | −0.904477 | − | 0.426523i | \(-0.859738\pi\) | ||
0.904477 | − | 0.426523i | \(-0.140262\pi\) | |||||||
\(434\) | 157.527i | 0.362966i | ||||||||
\(435\) | 39.1857i | 0.0900821i | ||||||||
\(436\) | 325.115i | 0.745677i | ||||||||
\(437\) | 339.283 | + | 199.263i | 0.776392 | + | 0.455979i | ||||
\(438\) | −323.990 | −0.739703 | ||||||||
\(439\) | −54.3077 | −0.123708 | −0.0618539 | − | 0.998085i | \(-0.519701\pi\) | ||||
−0.0618539 | + | 0.998085i | \(0.519701\pi\) | |||||||
\(440\) | −102.348 | −0.232610 | ||||||||
\(441\) | 103.503 | 0.234701 | ||||||||
\(442\) | − | 198.320i | − | 0.448687i | ||||||
\(443\) | 263.570 | 0.594966 | 0.297483 | − | 0.954727i | \(-0.403853\pi\) | ||||
0.297483 | + | 0.954727i | \(0.403853\pi\) | |||||||
\(444\) | 10.6188i | 0.0239163i | ||||||||
\(445\) | −38.5377 | −0.0866015 | ||||||||
\(446\) | −319.147 | −0.715576 | ||||||||
\(447\) | − | 94.6648i | − | 0.211778i | ||||||
\(448\) | 30.4620i | 0.0679955i | ||||||||
\(449\) | 578.427 | 1.28826 | 0.644128 | − | 0.764917i | \(-0.277220\pi\) | ||||
0.644128 | + | 0.764917i | \(0.277220\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | − | 894.970i | − | 1.98441i | ||||||
\(452\) | 283.805i | 0.627888i | ||||||||
\(453\) | 227.901 | 0.503092 | ||||||||
\(454\) | 561.458i | 1.23669i | ||||||||
\(455\) | 110.362 | 0.242554 | ||||||||
\(456\) | 83.8088i | 0.183791i | ||||||||
\(457\) | 514.251i | 1.12528i | 0.826703 | + | 0.562638i | \(0.190214\pi\) | ||||
−0.826703 | + | 0.562638i | \(0.809786\pi\) | |||||||
\(458\) | 380.972i | 0.831816i | ||||||||
\(459\) | − | 56.2168i | − | 0.122477i | ||||||
\(460\) | −88.6938 | − | 52.0903i | −0.192813 | − | 0.113240i | ||||
\(461\) | 545.697 | 1.18372 | 0.591862 | − | 0.806039i | \(-0.298393\pi\) | ||||
0.591862 | + | 0.806039i | \(0.298393\pi\) | |||||||
\(462\) | 150.936 | 0.326702 | ||||||||
\(463\) | −481.885 | −1.04079 | −0.520395 | − | 0.853926i | \(-0.674215\pi\) | ||||
−0.520395 | + | 0.853926i | \(0.674215\pi\) | |||||||
\(464\) | −40.4708 | −0.0872217 | ||||||||
\(465\) | − | 113.297i | − | 0.243649i | ||||||
\(466\) | 495.370 | 1.06302 | ||||||||
\(467\) | 6.72759i | 0.0144060i | 0.999974 | + | 0.00720299i | \(0.00229280\pi\) | ||||
−0.999974 | + | 0.00720299i | \(0.997707\pi\) | |||||||
\(468\) | 77.7710 | 0.166177 | ||||||||
\(469\) | 28.5051 | 0.0607784 | ||||||||
\(470\) | 155.892i | 0.331686i | ||||||||
\(471\) | 108.612i | 0.230599i | ||||||||
\(472\) | 68.5976 | 0.145334 | ||||||||
\(473\) | 552.554 | 1.16819 | ||||||||
\(474\) | 45.6740i | 0.0963587i | ||||||||
\(475\) | − | 85.5370i | − | 0.180078i | ||||||
\(476\) | 82.3916 | 0.173092 | ||||||||
\(477\) | 86.0568i | 0.180413i | ||||||||
\(478\) | 49.1593 | 0.102844 | ||||||||
\(479\) | − | 366.353i | − | 0.764828i | −0.923991 | − | 0.382414i | \(-0.875093\pi\) | ||
0.923991 | − | 0.382414i | \(-0.124907\pi\) | |||||||
\(480\) | − | 21.9089i | − | 0.0456435i | ||||||
\(481\) | 39.7331i | 0.0826053i | ||||||||
\(482\) | 485.985i | 1.00827i | ||||||||
\(483\) | 130.800 | + | 76.8194i | 0.270807 | + | 0.159046i | ||||
\(484\) | −281.758 | −0.582144 | ||||||||
\(485\) | 70.4331 | 0.145223 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 212.080 | 0.435483 | 0.217742 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217742 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(488\) | − | 149.843i | − | 0.307054i | ||||||
\(489\) | 113.041 | 0.231167 | ||||||||
\(490\) | − | 109.102i | − | 0.222657i | ||||||
\(491\) | −323.833 | −0.659537 | −0.329768 | − | 0.944062i | \(-0.606971\pi\) | ||||
−0.329768 | + | 0.944062i | \(0.606971\pi\) | |||||||
\(492\) | 191.579 | 0.389389 | ||||||||
\(493\) | 109.463i | 0.222034i | ||||||||
\(494\) | 313.592i | 0.634802i | ||||||||
\(495\) | −108.557 | −0.219306 | ||||||||
\(496\) | 117.013 | 0.235912 | ||||||||
\(497\) | − | 464.086i | − | 0.933774i | ||||||
\(498\) | − | 113.433i | − | 0.227777i | ||||||
\(499\) | 113.014 | 0.226481 | 0.113241 | − | 0.993568i | \(-0.463877\pi\) | ||||
0.113241 | + | 0.993568i | \(0.463877\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −155.827 | −0.311032 | ||||||||
\(502\) | − | 625.686i | − | 1.24639i | ||||||
\(503\) | 841.141i | 1.67225i | 0.548541 | + | 0.836124i | \(0.315184\pi\) | ||||
−0.548541 | + | 0.836124i | \(0.684816\pi\) | |||||||
\(504\) | 32.3098i | 0.0641068i | ||||||||
\(505\) | − | 26.5696i | − | 0.0526131i | ||||||
\(506\) | −453.883 | − | 266.568i | −0.897001 | − | 0.526813i | ||||
\(507\) | −1.71647 | −0.00338555 | ||||||||
\(508\) | 72.4414 | 0.142601 | ||||||||
\(509\) | −570.869 | −1.12155 | −0.560775 | − | 0.827968i | \(-0.689497\pi\) | ||||
−0.560775 | + | 0.827968i | \(0.689497\pi\) | |||||||
\(510\) | −59.2577 | −0.116192 | ||||||||
\(511\) | − | 503.644i | − | 0.985605i | ||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 88.8927i | 0.173280i | ||||||||
\(514\) | 534.512 | 1.03991 | ||||||||
\(515\) | −136.485 | −0.265020 | ||||||||
\(516\) | 118.281i | 0.229227i | ||||||||
\(517\) | 797.765i | 1.54307i | ||||||||
\(518\) | −16.5071 | −0.0318669 | ||||||||
\(519\) | −307.732 | −0.592932 | ||||||||
\(520\) | − | 81.9778i | − | 0.157650i | ||||||
\(521\) | 823.426i | 1.58047i | 0.612802 | + | 0.790236i | \(0.290042\pi\) | ||||
−0.612802 | + | 0.790236i | \(0.709958\pi\) | |||||||
\(522\) | −42.9258 | −0.0822334 | ||||||||
\(523\) | − | 692.210i | − | 1.32354i | −0.749709 | − | 0.661768i | \(-0.769806\pi\) | ||
0.749709 | − | 0.661768i | \(-0.230194\pi\) | |||||||
\(524\) | −1.02540 | −0.00195687 | ||||||||
\(525\) | − | 32.9761i | − | 0.0628116i | ||||||
\(526\) | 329.631i | 0.626674i | ||||||||
\(527\) | − | 316.488i | − | 0.600546i | ||||||
\(528\) | − | 112.117i | − | 0.212342i | ||||||
\(529\) | −257.660 | − | 462.009i | −0.487069 | − | 0.873363i | ||||
\(530\) | 90.7118 | 0.171154 | ||||||||
\(531\) | 72.7587 | 0.137022 | ||||||||
\(532\) | −130.281 | −0.244890 | ||||||||
\(533\) | 716.844 | 1.34492 | ||||||||
\(534\) | − | 42.2159i | − | 0.0790560i | ||||||
\(535\) | 323.569 | 0.604802 | ||||||||
\(536\) | − | 21.1738i | − | 0.0395034i | ||||||
\(537\) | −335.075 | −0.623976 | ||||||||
\(538\) | −393.650 | −0.731692 | ||||||||
\(539\) | − | 558.319i | − | 1.03584i | ||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | 915.849 | 1.69288 | 0.846440 | − | 0.532483i | \(-0.178741\pi\) | ||||
0.846440 | + | 0.532483i | \(0.178741\pi\) | |||||||
\(542\) | −719.534 | −1.32755 | ||||||||
\(543\) | − | 322.775i | − | 0.594428i | ||||||
\(544\) | − | 61.2011i | − | 0.112502i | ||||||
\(545\) | 363.490 | 0.666954 | ||||||||
\(546\) | 120.896i | 0.221420i | ||||||||
\(547\) | 203.592 | 0.372197 | 0.186099 | − | 0.982531i | \(-0.440416\pi\) | ||||
0.186099 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(548\) | 129.590i | 0.236479i | ||||||||
\(549\) | − | 158.932i | − | 0.289494i | ||||||
\(550\) | 114.429i | 0.208052i | ||||||||
\(551\) | − | 173.088i | − | 0.314134i | ||||||
\(552\) | 57.0621 | − | 97.1592i | 0.103373 | − | 0.176013i | ||||
\(553\) | −71.0006 | −0.128392 | ||||||||
\(554\) | −27.8924 | −0.0503473 | ||||||||
\(555\) | 11.8722 | 0.0213914 | ||||||||
\(556\) | −340.102 | −0.611693 | ||||||||
\(557\) | − | 624.298i | − | 1.12082i | −0.828215 | − | 0.560411i | \(-0.810643\pi\) | ||
0.828215 | − | 0.560411i | \(-0.189357\pi\) | |||||||
\(558\) | 124.111 | 0.222420 | ||||||||
\(559\) | 442.579i | 0.791734i | ||||||||
\(560\) | 34.0575 | 0.0608170 | ||||||||
\(561\) | −303.246 | −0.540546 | ||||||||
\(562\) | − | 485.716i | − | 0.864263i | ||||||
\(563\) | 961.054i | 1.70702i | 0.521074 | + | 0.853511i | \(0.325531\pi\) | ||||
−0.521074 | + | 0.853511i | \(0.674469\pi\) | |||||||
\(564\) | −170.772 | −0.302786 | ||||||||
\(565\) | 317.304 | 0.561600 | ||||||||
\(566\) | − | 211.469i | − | 0.373620i | ||||||
\(567\) | 34.2697i | 0.0604405i | ||||||||
\(568\) | −344.727 | −0.606913 | ||||||||
\(569\) | − | 576.159i | − | 1.01258i | −0.862363 | − | 0.506290i | \(-0.831016\pi\) | ||
0.862363 | − | 0.506290i | \(-0.168984\pi\) | |||||||
\(570\) | 93.7011 | 0.164388 | ||||||||
\(571\) | − | 346.570i | − | 0.606952i | −0.952839 | − | 0.303476i | \(-0.901853\pi\) | ||
0.952839 | − | 0.303476i | \(-0.0981472\pi\) | |||||||
\(572\) | − | 419.514i | − | 0.733416i | ||||||
\(573\) | 32.5067i | 0.0567307i | ||||||||
\(574\) | 297.811i | 0.518835i | ||||||||
\(575\) | −58.2388 | + | 99.1627i | −0.101285 | + | 0.172457i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 675.477 | 1.17067 | 0.585335 | − | 0.810791i | \(-0.300963\pi\) | ||||
0.585335 | + | 0.810791i | \(0.300963\pi\) | |||||||
\(578\) | 243.175 | 0.420718 | ||||||||
\(579\) | −280.196 | −0.483931 | ||||||||
\(580\) | 45.2478i | 0.0780134i | ||||||||
\(581\) | 176.332 | 0.303498 | ||||||||
\(582\) | 77.1556i | 0.132570i | ||||||||
\(583\) | 464.210 | 0.796243 | ||||||||
\(584\) | −374.111 | −0.640601 | ||||||||
\(585\) | − | 86.9506i | − | 0.148633i | ||||||
\(586\) | − | 113.469i | − | 0.193632i | ||||||
\(587\) | −820.083 | −1.39708 | −0.698538 | − | 0.715573i | \(-0.746165\pi\) | ||||
−0.698538 | + | 0.715573i | \(0.746165\pi\) | |||||||
\(588\) | 119.515 | 0.203257 | ||||||||
\(589\) | 500.446i | 0.849653i | ||||||||
\(590\) | − | 76.6944i | − | 0.129991i | ||||||
\(591\) | 108.053 | 0.182831 | ||||||||
\(592\) | 12.2616i | 0.0207121i | ||||||||
\(593\) | 768.200 | 1.29545 | 0.647723 | − | 0.761876i | \(-0.275721\pi\) | ||||
0.647723 | + | 0.761876i | \(0.275721\pi\) | |||||||
\(594\) | − | 118.918i | − | 0.200198i | ||||||
\(595\) | − | 92.1166i | − | 0.154818i | ||||||
\(596\) | − | 109.310i | − | 0.183405i | ||||||
\(597\) | 486.144i | 0.814311i | ||||||||
\(598\) | 213.513 | − | 363.546i | 0.357044 | − | 0.607937i | ||||
\(599\) | −192.340 | −0.321102 | −0.160551 | − | 0.987028i | \(-0.551327\pi\) | ||||
−0.160551 | + | 0.987028i | \(0.551327\pi\) | |||||||
\(600\) | −24.4949 | −0.0408248 | ||||||||
\(601\) | 829.949 | 1.38095 | 0.690474 | − | 0.723358i | \(-0.257402\pi\) | ||||
0.690474 | + | 0.723358i | \(0.257402\pi\) | |||||||
\(602\) | −183.869 | −0.305430 | ||||||||
\(603\) | − | 22.4582i | − | 0.0372441i | ||||||
\(604\) | 263.157 | 0.435691 | ||||||||
\(605\) | 315.015i | 0.520685i | ||||||||
\(606\) | 29.1055 | 0.0480289 | ||||||||
\(607\) | 503.567 | 0.829600 | 0.414800 | − | 0.909913i | \(-0.363851\pi\) | ||||
0.414800 | + | 0.909913i | \(0.363851\pi\) | |||||||
\(608\) | 96.7741i | 0.159168i | ||||||||
\(609\) | − | 66.7285i | − | 0.109571i | ||||||
\(610\) | −167.529 | −0.274638 | ||||||||
\(611\) | −638.986 | −1.04580 | ||||||||
\(612\) | − | 64.9136i | − | 0.106068i | ||||||
\(613\) | − | 117.049i | − | 0.190944i | −0.995432 | − | 0.0954721i | \(-0.969564\pi\) | ||
0.995432 | − | 0.0954721i | \(-0.0304361\pi\) | |||||||
\(614\) | 217.477 | 0.354198 | ||||||||
\(615\) | − | 214.192i | − | 0.348280i | ||||||
\(616\) | 174.286 | 0.282932 | ||||||||
\(617\) | 13.5947i | 0.0220336i | 0.999939 | + | 0.0110168i | \(0.00350682\pi\) | ||||
−0.999939 | + | 0.0110168i | \(0.996493\pi\) | |||||||
\(618\) | − | 149.512i | − | 0.241929i | ||||||
\(619\) | − | 351.787i | − | 0.568315i | −0.958778 | − | 0.284158i | \(-0.908286\pi\) | ||
0.958778 | − | 0.284158i | \(-0.0917139\pi\) | |||||||
\(620\) | − | 130.824i | − | 0.211007i | ||||||
\(621\) | 60.5235 | − | 103.053i | 0.0974614 | − | 0.165947i | ||||
\(622\) | −176.164 | −0.283222 | ||||||||
\(623\) | 65.6249 | 0.105337 | ||||||||
\(624\) | 89.8022 | 0.143914 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 314.555i | − | 0.502484i | ||||||
\(627\) | 479.507 | 0.764764 | ||||||||
\(628\) | 125.414i | 0.199704i | ||||||||
\(629\) | 33.1643 | 0.0527255 | ||||||||
\(630\) | 36.1235 | 0.0573389 | ||||||||
\(631\) | − | 719.196i | − | 1.13977i | −0.821724 | − | 0.569886i | \(-0.806987\pi\) | ||
0.821724 | − | 0.569886i | \(-0.193013\pi\) | |||||||
\(632\) | 52.7398i | 0.0834491i | ||||||||
\(633\) | −436.752 | −0.689972 | ||||||||
\(634\) | 428.932 | 0.676549 | ||||||||
\(635\) | − | 80.9920i | − | 0.127546i | ||||||
\(636\) | 99.3698i | 0.156242i | ||||||||
\(637\) | 447.197 | 0.702036 | ||||||||
\(638\) | 231.551i | 0.362933i | ||||||||
\(639\) | −365.638 | −0.572203 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | − | 745.251i | − | 1.16264i | −0.813676 | − | 0.581319i | \(-0.802537\pi\) | ||
0.813676 | − | 0.581319i | \(-0.197463\pi\) | |||||||
\(642\) | 354.452i | 0.552106i | ||||||||
\(643\) | 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 | ||||
\(645\) | 132.242 | 0.205027 | ||||||||
\(646\) | 261.748 | 0.405183 | ||||||||
\(647\) | −772.723 | −1.19432 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − | 392.477i | − | 0.604741i | ||||||
\(650\) | −91.6540 | −0.141006 | ||||||||
\(651\) | 192.931i | 0.296361i | ||||||||
\(652\) | 130.528 | 0.200197 | ||||||||
\(653\) | 42.1242 | 0.0645088 | 0.0322544 | − | 0.999480i | \(-0.489731\pi\) | ||||
0.0322544 | + | 0.999480i | \(0.489731\pi\) | |||||||
\(654\) | 398.183i | 0.608843i | ||||||||
\(655\) | 1.14643i | 0.00175027i | ||||||||
\(656\) | 221.217 | 0.337221 | ||||||||
\(657\) | −396.805 | −0.603965 | ||||||||
\(658\) | − | 265.466i | − | 0.403443i | ||||||
\(659\) | − | 1033.80i | − | 1.56873i | −0.620297 | − | 0.784367i | \(-0.712988\pi\) | ||
0.620297 | − | 0.784367i | \(-0.287012\pi\) | |||||||
\(660\) | −125.350 | −0.189925 | ||||||||
\(661\) | 512.065i | 0.774683i | 0.921936 | + | 0.387341i | \(0.126607\pi\) | ||||
−0.921936 | + | 0.387341i | \(0.873393\pi\) | |||||||
\(662\) | −397.615 | −0.600628 | ||||||||
\(663\) | − | 242.891i | − | 0.366351i | ||||||
\(664\) | − | 130.981i | − | 0.197261i | ||||||
\(665\) | 145.659i | 0.219036i | ||||||||
\(666\) | 13.0054i | 0.0195276i | ||||||||
\(667\) | −117.849 | + | 200.660i | −0.176685 | + | 0.300840i | ||||
\(668\) | −179.933 | −0.269361 | ||||||||
\(669\) | −390.874 | −0.584265 | ||||||||
\(670\) | −23.6730 | −0.0353329 | ||||||||
\(671\) | −857.315 | −1.27767 | ||||||||
\(672\) | 37.3082i | 0.0555181i | ||||||||
\(673\) | 611.507 | 0.908628 | 0.454314 | − | 0.890842i | \(-0.349884\pi\) | ||||
0.454314 | + | 0.890842i | \(0.349884\pi\) | |||||||
\(674\) | 365.588i | 0.542415i | ||||||||
\(675\) | −25.9808 | −0.0384900 | ||||||||
\(676\) | −1.98201 | −0.00293197 | ||||||||
\(677\) | 109.122i | 0.161184i | 0.996747 | + | 0.0805920i | \(0.0256811\pi\) | ||||
−0.996747 | + | 0.0805920i | \(0.974319\pi\) | |||||||
\(678\) | 347.589i | 0.512668i | ||||||||
\(679\) | −119.939 | −0.176641 | ||||||||
\(680\) | −68.4250 | −0.100625 | ||||||||
\(681\) | 687.643i | 1.00975i | ||||||||
\(682\) | − | 669.480i | − | 0.981643i | ||||||
\(683\) | −426.220 | −0.624042 | −0.312021 | − | 0.950075i | \(-0.601006\pi\) | ||||
−0.312021 | + | 0.950075i | \(0.601006\pi\) | |||||||
\(684\) | 102.644i | 0.150065i | ||||||||
\(685\) | 144.886 | 0.211513 | ||||||||
\(686\) | 449.651i | 0.655467i | ||||||||
\(687\) | 466.593i | 0.679175i | ||||||||
\(688\) | 136.579i | 0.198516i | ||||||||
\(689\) | 371.818i | 0.539649i | ||||||||
\(690\) | −108.627 | − | 63.7974i | −0.157431 | − | 0.0924600i | ||||
\(691\) | 152.559 | 0.220780 | 0.110390 | − | 0.993888i | \(-0.464790\pi\) | ||||
0.110390 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(692\) | −355.338 | −0.513494 | ||||||||
\(693\) | 184.859 | 0.266751 | ||||||||
\(694\) | 867.354 | 1.24979 | ||||||||
\(695\) | 380.245i | 0.547115i | ||||||||
\(696\) | −49.5665 | −0.0712162 | ||||||||
\(697\) | − | 598.333i | − | 0.858440i | ||||||
\(698\) | −106.792 | −0.152997 | ||||||||
\(699\) | 606.701 | 0.867956 | ||||||||
\(700\) | − | 38.0775i | − | 0.0543964i | ||||||
\(701\) | 828.197i | 1.18145i | 0.806873 | + | 0.590725i | \(0.201158\pi\) | ||||
−0.806873 | + | 0.590725i | \(0.798842\pi\) | |||||||
\(702\) | 95.2496 | 0.135683 | ||||||||
\(703\) | −52.4410 | −0.0745960 | ||||||||
\(704\) | − | 129.461i | − | 0.183894i | ||||||
\(705\) | 190.928i | 0.270820i | ||||||||
\(706\) | −44.5872 | −0.0631547 | ||||||||
\(707\) | 45.2447i | 0.0639954i | ||||||||
\(708\) | 84.0145 | 0.118665 | ||||||||
\(709\) | − | 319.241i | − | 0.450269i | −0.974328 | − | 0.225134i | \(-0.927718\pi\) | ||
0.974328 | − | 0.225134i | \(-0.0722821\pi\) | |||||||
\(710\) | 385.416i | 0.542840i | ||||||||
\(711\) | 55.9390i | 0.0786765i | ||||||||
\(712\) | − | 48.7467i | − | 0.0684645i | ||||||
\(713\) | 340.734 | − | 580.164i | 0.477887 | − | 0.813695i | ||||
\(714\) | 100.909 | 0.141329 | ||||||||
\(715\) | −469.031 | −0.655987 | ||||||||
\(716\) | −386.912 | −0.540379 | ||||||||
\(717\) | 60.2076 | 0.0839716 | ||||||||
\(718\) | 272.737i | 0.379857i | ||||||||
\(719\) | −894.454 | −1.24402 | −0.622012 | − | 0.783008i | \(-0.713685\pi\) | ||||
−0.622012 | + | 0.783008i | \(0.713685\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | 232.418 | 0.322355 | ||||||||
\(722\) | 96.6425 | 0.133854 | ||||||||
\(723\) | 595.208i | 0.823248i | ||||||||
\(724\) | − | 372.708i | − | 0.514790i | ||||||
\(725\) | 50.5886 | 0.0697773 | ||||||||
\(726\) | −345.081 | −0.475319 | ||||||||
\(727\) | 1349.88i | 1.85679i | 0.371601 | + | 0.928393i | \(0.378809\pi\) | ||||
−0.371601 | + | 0.928393i | \(0.621191\pi\) | |||||||
\(728\) | 139.598i | 0.191756i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 418.269i | 0.572971i | ||||||||
\(731\) | 369.410 | 0.505349 | ||||||||
\(732\) | − | 183.519i | − | 0.250709i | ||||||
\(733\) | 584.473i | 0.797371i | 0.917088 | + | 0.398686i | \(0.130534\pi\) | ||||
−0.917088 | + | 0.398686i | \(0.869466\pi\) | |||||||
\(734\) | 724.522i | 0.987087i | ||||||||
\(735\) | − | 133.622i | − | 0.181799i | ||||||
\(736\) | 65.8896 | − | 112.190i | 0.0895240 | − | 0.152432i | ||||
\(737\) | −121.145 | −0.164375 | ||||||||
\(738\) | 234.636 | 0.317935 | ||||||||
\(739\) | 100.840 | 0.136454 | 0.0682272 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682272 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(740\) | 13.7089 | 0.0185255 | ||||||||
\(741\) | 384.071i | 0.518314i | ||||||||
\(742\) | −154.471 | −0.208182 | ||||||||
\(743\) | 1214.22i | 1.63422i | 0.576482 | + | 0.817110i | \(0.304425\pi\) | ||||
−0.576482 | + | 0.817110i | \(0.695575\pi\) | |||||||
\(744\) | 143.311 | 0.192622 | ||||||||
\(745\) | −122.212 | −0.164043 | ||||||||
\(746\) | − | 435.857i | − | 0.584259i | ||||||
\(747\) | − | 138.926i | − | 0.185979i | ||||||
\(748\) | −350.159 | −0.468126 | ||||||||
\(749\) | −550.999 | −0.735646 | ||||||||
\(750\) | 27.3861i | 0.0365148i | ||||||||
\(751\) | 209.572i | 0.279057i | 0.990218 | + | 0.139529i | \(0.0445587\pi\) | ||||
−0.990218 | + | 0.139529i | \(0.955441\pi\) | |||||||
\(752\) | −197.190 | −0.262221 | ||||||||
\(753\) | − | 766.305i | − | 1.01767i | ||||||
\(754\) | −185.466 | −0.245976 | ||||||||
\(755\) | − | 294.219i | − | 0.389694i | ||||||
\(756\) | 39.5713i | 0.0523430i | ||||||||
\(757\) | − | 1291.76i | − | 1.70643i | −0.521563 | − | 0.853213i | \(-0.674651\pi\) | ||
0.521563 | − | 0.853213i | \(-0.325349\pi\) | |||||||
\(758\) | − | 387.497i | − | 0.511209i | ||||||
\(759\) | −555.891 | − | 326.477i | −0.732399 | − | 0.430141i | ||||
\(760\) | 108.197 | 0.142364 | ||||||||
\(761\) | −1137.06 | −1.49417 | −0.747083 | − | 0.664731i | \(-0.768546\pi\) | ||||
−0.747083 | + | 0.664731i | \(0.768546\pi\) | |||||||
\(762\) | 88.7223 | 0.116433 | ||||||||
\(763\) | −618.978 | −0.811243 | ||||||||
\(764\) | 37.5355i | 0.0491303i | ||||||||
\(765\) | −72.5756 | −0.0948701 | ||||||||
\(766\) | − | 261.012i | − | 0.340747i | ||||||
\(767\) | 314.362 | 0.409859 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | − | 1211.18i | − | 1.57501i | −0.616310 | − | 0.787504i | \(-0.711373\pi\) | ||
0.616310 | − | 0.787504i | \(-0.288627\pi\) | |||||||
\(770\) | − | 194.858i | − | 0.253062i | ||||||
\(771\) | 654.641 | 0.849080 | ||||||||
\(772\) | −323.543 | −0.419097 | ||||||||
\(773\) | 1006.14i | 1.30160i | 0.759247 | + | 0.650802i | \(0.225567\pi\) | ||||
−0.759247 | + | 0.650802i | \(0.774433\pi\) | |||||||
\(774\) | 144.864i | 0.187163i | ||||||||
\(775\) | −146.266 | −0.188730 | ||||||||
\(776\) | 89.0917i | 0.114809i | ||||||||
\(777\) | −20.2169 | −0.0260192 | ||||||||
\(778\) | − | 543.761i | − | 0.698922i | ||||||
\(779\) | 946.112i | 1.21452i | ||||||||
\(780\) | − | 100.402i | − | 0.128720i | ||||||
\(781\) | 1972.33i | 2.52539i | ||||||||
\(782\) | −303.444 | − | 178.214i | −0.388035 | − | 0.227895i | ||||
\(783\) | −52.5732 | −0.0671433 | ||||||||
\(784\) | 138.004 | 0.176026 | ||||||||
\(785\) | 140.217 | 0.178621 | ||||||||
\(786\) | −1.25585 | −0.00159777 | ||||||||
\(787\) | − | 837.892i | − | 1.06467i | −0.846535 | − | 0.532333i | \(-0.821315\pi\) | ||
0.846535 | − | 0.532333i | \(-0.178685\pi\) | |||||||
\(788\) | 124.769 | 0.158337 | ||||||||
\(789\) | 403.714i | 0.511677i | ||||||||
\(790\) | 58.9649 | 0.0746391 | ||||||||
\(791\) | −540.330 | −0.683097 | ||||||||
\(792\) | − | 137.315i | − | 0.173377i | ||||||
\(793\) | − | 686.683i | − | 0.865931i | ||||||
\(794\) | 481.582 | 0.606526 | ||||||||
\(795\) | 111.099 | 0.139747 | ||||||||
\(796\) | 561.351i | 0.705214i | ||||||||
\(797\) | − | 866.601i | − | 1.08733i | −0.839303 | − | 0.543665i | \(-0.817036\pi\) | ||
0.839303 | − | 0.543665i | \(-0.182964\pi\) | |||||||
\(798\) | −159.562 | −0.199952 | ||||||||
\(799\) | 533.346i | 0.667518i | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | − | 51.7037i | − | 0.0645490i | ||||||
\(802\) | − | 1050.11i | − | 1.30936i | ||||||
\(803\) | 2140.45i | 2.66557i | ||||||||
\(804\) | − | 25.9325i | − | 0.0322544i | ||||||
\(805\) | 99.1735 | − | 168.862i | 0.123197 | − | 0.209766i | ||||
\(806\) | 536.233 | 0.665302 | ||||||||
\(807\) | −482.121 | −0.597424 | ||||||||
\(808\) | 33.6082 | 0.0415943 | ||||||||
\(809\) | −1290.76 | −1.59550 | −0.797749 | − | 0.602990i | \(-0.793976\pi\) | ||||
−0.797749 | + | 0.602990i | \(0.793976\pi\) | |||||||
\(810\) | − | 28.4605i | − | 0.0351364i | ||||||
\(811\) | −526.205 | −0.648835 | −0.324418 | − | 0.945914i | \(-0.605168\pi\) | ||||
−0.324418 | + | 0.945914i | \(0.605168\pi\) | |||||||
\(812\) | − | 77.0514i | − | 0.0948909i | ||||||
\(813\) | −881.245 | −1.08394 | ||||||||
\(814\) | 70.1539 | 0.0861842 | ||||||||
\(815\) | − | 145.935i | − | 0.179061i | ||||||
\(816\) | − | 74.9558i | − | 0.0918576i | ||||||
\(817\) | −584.129 | −0.714968 | ||||||||
\(818\) | 1071.09 | 1.30940 | ||||||||
\(819\) | 148.066i | 0.180789i | ||||||||
\(820\) | − | 247.328i | − | 0.301619i | ||||||
\(821\) | −445.751 | −0.542937 | −0.271468 | − | 0.962447i | \(-0.587509\pi\) | ||||
−0.271468 | + | 0.962447i | \(0.587509\pi\) | |||||||
\(822\) | 158.715i | 0.193084i | ||||||||
\(823\) | −1114.24 | −1.35388 | −0.676938 | − | 0.736040i | \(-0.736693\pi\) | ||||
−0.676938 | + | 0.736040i | \(0.736693\pi\) | |||||||
\(824\) | − | 172.642i | − | 0.209517i | ||||||
\(825\) | 140.146i | 0.169874i | ||||||||
\(826\) | 130.601i | 0.158113i | ||||||||
\(827\) | 426.354i | 0.515543i | 0.966206 | + | 0.257771i | \(0.0829882\pi\) | ||||
−0.966206 | + | 0.257771i | \(0.917012\pi\) | |||||||
\(828\) | 69.8865 | − | 118.995i | 0.0844040 | − | 0.143714i | ||||
\(829\) | 413.046 | 0.498246 | 0.249123 | − | 0.968472i | \(-0.419858\pi\) | ||||
0.249123 | + | 0.968472i | \(0.419858\pi\) | |||||||
\(830\) | −146.441 | −0.176435 | ||||||||
\(831\) | −34.1611 | −0.0411084 | ||||||||
\(832\) | 103.695 | 0.124633 | ||||||||
\(833\) | − | 373.265i | − | 0.448097i | ||||||
\(834\) | −416.538 | −0.499446 | ||||||||
\(835\) | 201.172i | 0.240924i | ||||||||
\(836\) | 553.687 | 0.662305 | ||||||||
\(837\) | 152.004 | 0.181606 | ||||||||
\(838\) | 302.270i | 0.360704i | ||||||||
\(839\) | 1356.51i | 1.61682i | 0.588619 | + | 0.808411i | \(0.299672\pi\) | ||||
−0.588619 | + | 0.808411i | \(0.700328\pi\) | |||||||
\(840\) | 41.7118 | 0.0496569 | ||||||||
\(841\) | −738.632 | −0.878278 | ||||||||
\(842\) | − | 955.989i | − | 1.13538i | ||||||
\(843\) | − | 594.878i | − | 0.705668i | ||||||
\(844\) | −504.318 | −0.597533 | ||||||||
\(845\) | 2.21596i | 0.00262243i | ||||||||
\(846\) | −209.152 | −0.247224 | ||||||||
\(847\) | − | 536.431i | − | 0.633331i | ||||||
\(848\) | 114.742i | 0.135309i | ||||||||
\(849\) | − | 258.995i | − | 0.305059i | ||||||
\(850\) | 76.5014i | 0.0900017i | ||||||||
\(851\) | 60.7946 | + | 35.7050i | 0.0714390 | + | 0.0419565i | ||||
\(852\) | −422.202 | −0.495543 | ||||||||
\(853\) | −1215.79 | −1.42531 | −0.712657 | − | 0.701512i | \(-0.752509\pi\) | ||||
−0.712657 | + | 0.701512i | \(0.752509\pi\) | |||||||
\(854\) | 285.281 | 0.334053 | ||||||||
\(855\) | 114.760 | 0.134222 | ||||||||
\(856\) | 409.286i | 0.478138i | ||||||||
\(857\) | −321.853 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(858\) | − | 513.798i | − | 0.598832i | ||||||
\(859\) | 217.358 | 0.253036 | 0.126518 | − | 0.991964i | \(-0.459620\pi\) | ||||
0.126518 | + | 0.991964i | \(0.459620\pi\) | |||||||
\(860\) | 152.700 | 0.177558 | ||||||||
\(861\) | 364.743i | 0.423627i | ||||||||
\(862\) | − | 11.3796i | − | 0.0132014i | ||||||
\(863\) | −1162.38 | −1.34690 | −0.673451 | − | 0.739232i | \(-0.735189\pi\) | ||||
−0.673451 | + | 0.739232i | \(0.735189\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | 397.280i | 0.459283i | ||||||||
\(866\) | − | 522.366i | − | 0.603194i | ||||||
\(867\) | 297.827 | 0.343515 | ||||||||
\(868\) | 222.777i | 0.256656i | ||||||||
\(869\) | 301.748 | 0.347235 | ||||||||
\(870\) | 55.4170i | 0.0636977i | ||||||||
\(871\) | − | 97.0332i | − | 0.111404i | ||||||
\(872\) | 459.782i | 0.527273i | ||||||||
\(873\) | 94.4960i | 0.108243i | ||||||||
\(874\) | 479.819 | + | 281.800i | 0.548992 | + | 0.322426i | ||||
\(875\) | −42.5719 | −0.0486536 | ||||||||
\(876\) | −458.191 | −0.523049 | ||||||||
\(877\) | −143.677 | −0.163828 | −0.0819139 | − | 0.996639i | \(-0.526103\pi\) | ||||
−0.0819139 | + | 0.996639i | \(0.526103\pi\) | |||||||
\(878\) | −76.8027 | −0.0874746 | ||||||||
\(879\) | − | 138.970i | − | 0.158100i | ||||||
\(880\) | −144.742 | −0.164480 | ||||||||
\(881\) | 26.5389i | 0.0301237i | 0.999887 | + | 0.0150618i | \(0.00479451\pi\) | ||||
−0.999887 | + | 0.0150618i | \(0.995205\pi\) | |||||||
\(882\) | 146.376 | 0.165959 | ||||||||
\(883\) | 1442.75 | 1.63391 | 0.816957 | − | 0.576698i | \(-0.195659\pi\) | ||||
0.816957 | + | 0.576698i | \(0.195659\pi\) | |||||||
\(884\) | − | 280.466i | − | 0.317270i | ||||||
\(885\) | − | 93.9311i | − | 0.106137i | ||||||
\(886\) | 372.744 | 0.420704 | ||||||||
\(887\) | −373.153 | −0.420691 | −0.210345 | − | 0.977627i | \(-0.567459\pi\) | ||||
−0.210345 | + | 0.977627i | \(0.567459\pi\) | |||||||
\(888\) | 15.0173i | 0.0169114i | ||||||||
\(889\) | 137.919i | 0.155140i | ||||||||
\(890\) | −54.5005 | −0.0612365 | ||||||||
\(891\) | − | 145.644i | − | 0.163461i | ||||||
\(892\) | −451.342 | −0.505989 | ||||||||
\(893\) | − | 843.353i | − | 0.944404i | ||||||
\(894\) | − | 133.876i | − | 0.149750i | ||||||
\(895\) | 432.580i | 0.483330i | ||||||||
\(896\) | 43.0798i | 0.0480801i | ||||||||
\(897\) | 261.498 | − | 445.251i | 0.291526 | − | 0.496378i | ||||
\(898\) | 818.020 | 0.910935 | ||||||||
\(899\) | −295.975 | −0.329227 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 310.348 | 0.344448 | ||||||||
\(902\) | − | 1265.68i | − | 1.40319i | ||||||
\(903\) | −225.192 | −0.249382 | ||||||||
\(904\) | 401.361i | 0.443984i | ||||||||
\(905\) | −416.700 | −0.460442 | ||||||||
\(906\) | 322.300 | 0.355740 | ||||||||
\(907\) | 488.681i | 0.538788i | 0.963030 | + | 0.269394i | \(0.0868234\pi\) | ||||
−0.963030 | + | 0.269394i | \(0.913177\pi\) | |||||||
\(908\) | 794.022i | 0.874473i | ||||||||
\(909\) | 35.6468 | 0.0392155 | ||||||||
\(910\) | 156.075 | 0.171511 | ||||||||
\(911\) | 978.988i | 1.07463i | 0.843382 | + | 0.537315i | \(0.180561\pi\) | ||||
−0.843382 | + | 0.537315i | \(0.819439\pi\) | |||||||
\(912\) | 118.524i | 0.129960i | ||||||||
\(913\) | −749.400 | −0.820811 | ||||||||
\(914\) | 727.261i | 0.795690i | ||||||||
\(915\) | −205.180 | −0.224241 | ||||||||
\(916\) | 538.775i | 0.588183i | ||||||||
\(917\) | − | 1.95223i | − | 0.00212893i | ||||||
\(918\) | − | 79.5026i | − | 0.0866041i | ||||||
\(919\) | 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 | ||||
\(921\) | 266.354 | 0.289201 | ||||||||
\(922\) | 771.732 | 0.837019 | ||||||||
\(923\) | −1579.78 | −1.71157 | ||||||||
\(924\) | 213.456 | 0.231013 | ||||||||
\(925\) | − | 15.3270i | − | 0.0165697i | ||||||
\(926\) | −681.489 | −0.735949 | ||||||||
\(927\) | − | 183.114i | − | 0.197534i | ||||||
\(928\) | −57.2344 | −0.0616750 | ||||||||
\(929\) | 700.599 | 0.754143 | 0.377072 | − | 0.926184i | \(-0.376931\pi\) | ||||
0.377072 | + | 0.926184i | \(0.376931\pi\) | |||||||
\(930\) | − | 160.226i | − | 0.172286i | ||||||
\(931\) | 590.224i | 0.633967i | ||||||||
\(932\) | 700.558 | 0.751672 | ||||||||
\(933\) | −215.756 | −0.231249 | ||||||||
\(934\) | 9.51426i | 0.0101866i | ||||||||
\(935\) | 391.489i | 0.418705i | ||||||||
\(936\) | 109.985 | 0.117505 | ||||||||
\(937\) | 1140.57i | 1.21726i | 0.793455 | + | 0.608628i | \(0.208280\pi\) | ||||
−0.793455 | + | 0.608628i | \(0.791720\pi\) | |||||||
\(938\) | 40.3123 | 0.0429768 | ||||||||
\(939\) | − | 385.249i | − | 0.410276i | ||||||
\(940\) | 220.465i | 0.234537i | ||||||||
\(941\) | 561.160i | 0.596344i | 0.954512 | + | 0.298172i | \(0.0963769\pi\) | ||||
−0.954512 | + | 0.298172i | \(0.903623\pi\) | |||||||
\(942\) | 153.601i | 0.163058i | ||||||||
\(943\) | 644.170 | − | 1096.82i | 0.683107 | − | 1.16312i | ||||
\(944\) | 97.0116 | 0.102767 | ||||||||
\(945\) | 44.2420 | 0.0468170 | ||||||||
\(946\) | 781.430 | 0.826036 | ||||||||
\(947\) | −974.501 | −1.02904 | −0.514520 | − | 0.857478i | \(-0.672030\pi\) | ||||
−0.514520 | + | 0.857478i | \(0.672030\pi\) | |||||||
\(948\) | 64.5928i | 0.0681359i | ||||||||
\(949\) | −1714.44 | −1.80657 | ||||||||
\(950\) | − | 120.968i | − | 0.127334i | ||||||
\(951\) | 525.333 | 0.552400 | ||||||||
\(952\) | 116.519 | 0.122394 | ||||||||
\(953\) | 245.849i | 0.257974i | 0.991646 | + | 0.128987i | \(0.0411725\pi\) | ||||
−0.991646 | + | 0.128987i | \(0.958827\pi\) | |||||||
\(954\) | 121.703i | 0.127571i | ||||||||
\(955\) | 41.9660 | 0.0439434 | ||||||||
\(956\) | 69.5218 | 0.0727215 | ||||||||
\(957\) | 283.591i | 0.296334i | ||||||||
\(958\) | − | 518.101i | − | 0.540815i | ||||||
\(959\) | −246.724 | −0.257272 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | −105.253 | −0.109525 | ||||||||
\(962\) | 56.1911i | 0.0584108i | ||||||||
\(963\) | 434.114i | 0.450793i | ||||||||
\(964\) | 687.287i | 0.712954i | ||||||||
\(965\) | 361.732i | 0.374852i | ||||||||
\(966\) | 184.979 | + | 108.639i | 0.191490 | + | 0.112463i | ||||
\(967\) | −958.537 | −0.991248 | −0.495624 | − | 0.868537i | \(-0.665061\pi\) | ||||
−0.495624 | + | 0.868537i | \(0.665061\pi\) | |||||||
\(968\) | −398.465 | −0.411638 | ||||||||
\(969\) | 320.575 | 0.330831 | ||||||||
\(970\) | 99.6075 | 0.102688 | ||||||||
\(971\) | − | 797.683i | − | 0.821506i | −0.911747 | − | 0.410753i | \(-0.865266\pi\) | ||
0.911747 | − | 0.410753i | \(-0.134734\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | − | 647.511i | − | 0.665479i | ||||||
\(974\) | 299.927 | 0.307933 | ||||||||
\(975\) | −112.253 | −0.115131 | ||||||||
\(976\) | − | 211.909i | − | 0.217120i | ||||||
\(977\) | − | 968.304i | − | 0.991099i | −0.868580 | − | 0.495550i | \(-0.834967\pi\) | ||
0.868580 | − | 0.495550i | \(-0.165033\pi\) | |||||||
\(978\) | 159.864 | 0.163460 | ||||||||
\(979\) | −278.901 | −0.284884 | ||||||||
\(980\) | − | 154.293i | − | 0.157442i | ||||||
\(981\) | 487.673i | 0.497118i | ||||||||
\(982\) | −457.968 | −0.466363 | ||||||||
\(983\) | − | 242.603i | − | 0.246799i | −0.992357 | − | 0.123399i | \(-0.960620\pi\) | ||
0.992357 | − | 0.123399i | \(-0.0393796\pi\) | |||||||
\(984\) | 270.934 | 0.275340 | ||||||||
\(985\) | − | 139.496i | − | 0.141621i | ||||||
\(986\) | 154.804i | 0.157002i | ||||||||
\(987\) | − | 325.128i | − | 0.329410i | ||||||
\(988\) | 443.487i | 0.448873i | ||||||||
\(989\) | 677.178 | + | 397.710i | 0.684710 | + | 0.402134i | ||||
\(990\) | −153.522 | −0.155073 | ||||||||
\(991\) | 1231.78 | 1.24297 | 0.621483 | − | 0.783428i | \(-0.286530\pi\) | ||||
0.621483 | + | 0.783428i | \(0.286530\pi\) | |||||||
\(992\) | 165.481 | 0.166815 | ||||||||
\(993\) | −486.978 | −0.490410 | ||||||||
\(994\) | − | 656.316i | − | 0.660278i | ||||||
\(995\) | 627.609 | 0.630763 | ||||||||
\(996\) | − | 160.418i | − | 0.161063i | ||||||
\(997\) | −689.979 | −0.692055 | −0.346027 | − | 0.938224i | \(-0.612470\pi\) | ||||
−0.346027 | + | 0.938224i | \(0.612470\pi\) | |||||||
\(998\) | 159.826 | 0.160146 | ||||||||
\(999\) | 15.9283i | 0.0159442i |
(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.91.27 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.14 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.30 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.27 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.30 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.3 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.14 | 32 | 3.2 | odd | 2 |