Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.8 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.33 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.96663i | − | 1.24166i | −0.783946 | − | 0.620829i | \(-0.786796\pi\) | ||
0.783946 | − | 0.620829i | \(-0.213204\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.66741 | −0.541713 | ||||||||
\(5\) | −41.3974 | −1.65590 | −0.827948 | − | 0.560805i | \(-0.810492\pi\) | ||||
−0.827948 | + | 0.560805i | \(0.810492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.08721 | 0.0221880 | 0.0110940 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110940 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(8\) | − | 36.4182i | − | 0.569035i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 205.606i | 2.05606i | ||||||||
\(11\) | 142.708i | 1.17941i | 0.807620 | + | 0.589704i | \(0.200756\pi\) | ||||
−0.807620 | + | 0.589704i | \(0.799244\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 35.2627i | 0.208655i | 0.994543 | + | 0.104327i | \(0.0332690\pi\) | ||||
−0.994543 | + | 0.104327i | \(0.966731\pi\) | |||||||
\(14\) | − | 5.39978i | − | 0.0275499i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −319.555 | −1.24826 | ||||||||
\(17\) | −527.661 | −1.82581 | −0.912907 | − | 0.408167i | \(-0.866168\pi\) | ||||
−0.912907 | + | 0.408167i | \(0.866168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.0375 | 0.210630 | 0.105315 | − | 0.994439i | \(-0.466415\pi\) | ||||
0.105315 | + | 0.994439i | \(0.466415\pi\) | |||||||
\(20\) | 358.808 | 0.897021 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 708.780 | 1.46442 | ||||||||
\(23\) | − | 138.991i | − | 0.262744i | −0.991333 | − | 0.131372i | \(-0.958062\pi\) | ||
0.991333 | − | 0.131372i | \(-0.0419382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1088.75 | 1.74199 | ||||||||
\(26\) | 175.137 | 0.259078 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.42332 | −0.0120195 | ||||||||
\(29\) | 1044.28 | 1.24171 | 0.620857 | − | 0.783924i | \(-0.286785\pi\) | ||||
0.620857 | + | 0.783924i | \(0.286785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1364.14i | 1.41950i | 0.704454 | + | 0.709749i | \(0.251192\pi\) | ||||
−0.704454 | + | 0.709749i | \(0.748808\pi\) | |||||||
\(32\) | 1004.42i | 0.980876i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2620.69i | 2.26704i | ||||||||
\(35\) | −45.0078 | −0.0367410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2076.33i | − | 1.51668i | −0.651860 | − | 0.758339i | \(-0.726011\pi\) | ||
0.651860 | − | 0.758339i | \(-0.273989\pi\) | |||||||
\(38\) | − | 377.650i | − | 0.261530i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1507.62i | 0.942263i | ||||||||
\(41\) | 1604.49 | 0.954485 | 0.477242 | − | 0.878772i | \(-0.341636\pi\) | ||||
0.477242 | + | 0.878772i | \(0.341636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 746.077i | 0.403503i | 0.979437 | + | 0.201751i | \(0.0646633\pi\) | ||||
−0.979437 | + | 0.201751i | \(0.935337\pi\) | |||||||
\(44\) | − | 1236.91i | − | 0.638901i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −690.318 | −0.326237 | ||||||||
\(47\) | 613.862i | 0.277891i | 0.990300 | + | 0.138946i | \(0.0443713\pi\) | ||||
−0.990300 | + | 0.138946i | \(0.955629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2399.82 | −0.999508 | ||||||||
\(50\) | − | 5407.39i | − | 2.16296i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 305.636i | − | 0.113031i | ||||||
\(53\) | 3306.58 | 1.17714 | 0.588569 | − | 0.808447i | \(-0.299692\pi\) | ||||
0.588569 | + | 0.808447i | \(0.299692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5907.75i | − | 1.95298i | ||||||
\(56\) | − | 39.5944i | − | 0.0126258i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5186.56i | − | 1.54178i | ||||||
\(59\) | −330.884 | − | 3465.24i | −0.0950543 | − | 0.995472i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3021.56i | − | 0.812028i | −0.913867 | − | 0.406014i | \(-0.866918\pi\) | ||
0.913867 | − | 0.406014i | \(-0.133082\pi\) | |||||||
\(62\) | 6775.17 | 1.76253 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −124.304 | −0.0303476 | ||||||||
\(65\) | − | 1459.78i | − | 0.345511i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3679.74i | 0.819724i | 0.912148 | + | 0.409862i | \(0.134423\pi\) | ||||
−0.912148 | + | 0.409862i | \(0.865577\pi\) | |||||||
\(68\) | 4573.45 | 0.989068 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 223.537i | 0.0456198i | ||||||||
\(71\) | −1827.67 | −0.362560 | −0.181280 | − | 0.983431i | \(-0.558024\pi\) | ||||
−0.181280 | + | 0.983431i | \(0.558024\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2692.51i | 0.505256i | 0.967563 | + | 0.252628i | \(0.0812949\pi\) | ||||
−0.967563 | + | 0.252628i | \(0.918705\pi\) | |||||||
\(74\) | −10312.4 | −1.88320 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −659.048 | −0.114101 | ||||||||
\(77\) | 155.154i | 0.0261687i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3087.31 | 0.494682 | 0.247341 | − | 0.968928i | \(-0.420443\pi\) | ||||
0.247341 | + | 0.968928i | \(0.420443\pi\) | |||||||
\(80\) | 13228.7 | 2.06699 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7968.90i | − | 1.18514i | ||||||
\(83\) | − | 7955.09i | − | 1.15475i | −0.816478 | − | 0.577377i | \(-0.804076\pi\) | ||
0.816478 | − | 0.577377i | \(-0.195924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21843.8 | 3.02336 | ||||||||
\(86\) | 3705.49 | 0.501012 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5197.19 | 0.671124 | ||||||||
\(89\) | 5141.10i | 0.649047i | 0.945878 | + | 0.324524i | \(0.105204\pi\) | ||||
−0.945878 | + | 0.324524i | \(0.894796\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.3380i | 0.00462964i | ||||||||
\(92\) | 1204.70i | 0.142332i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3048.82 | 0.345046 | ||||||||
\(95\) | −3147.75 | −0.348782 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13063.6i | − | 1.38842i | −0.719772 | − | 0.694210i | \(-0.755754\pi\) | ||
0.719772 | − | 0.694210i | \(-0.244246\pi\) | |||||||
\(98\) | 11919.0i | 1.24105i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9436.60 | −0.943660 | ||||||||
\(101\) | − | 6212.97i | − | 0.609055i | −0.952504 | − | 0.304527i | \(-0.901502\pi\) | ||
0.952504 | − | 0.304527i | \(-0.0984985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12027.0i | − | 1.13366i | −0.823834 | − | 0.566831i | \(-0.808169\pi\) | ||
0.823834 | − | 0.566831i | \(-0.191831\pi\) | |||||||
\(104\) | 1284.21 | 0.118732 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 16422.6i | − | 1.46160i | ||||||
\(107\) | 5915.89 | 0.516717 | 0.258359 | − | 0.966049i | \(-0.416818\pi\) | ||||
0.258359 | + | 0.966049i | \(0.416818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17887.0i | − | 1.50552i | −0.658298 | − | 0.752758i | \(-0.728723\pi\) | ||
0.658298 | − | 0.752758i | \(-0.271277\pi\) | |||||||
\(110\) | −29341.6 | −2.42493 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −347.424 | −0.0276964 | ||||||||
\(113\) | 24933.1i | 1.95262i | 0.216368 | + | 0.976312i | \(0.430579\pi\) | ||||
−0.216368 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5753.88i | 0.435076i | ||||||||
\(116\) | −9051.23 | −0.672653 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17210.6 | + | 1643.38i | −1.23604 | + | 0.118025i | ||||
\(119\) | −573.679 | −0.0405112 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5724.67 | −0.391003 | ||||||||
\(122\) | −15007.0 | −1.00826 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 11823.6i | − | 0.768962i | ||||||
\(125\) | −19197.8 | −1.22866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22413.1 | 1.38961 | 0.694806 | − | 0.719197i | \(-0.255490\pi\) | ||||
0.694806 | + | 0.719197i | \(0.255490\pi\) | |||||||
\(128\) | 16688.0i | 1.01856i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7250.21 | −0.429006 | ||||||||
\(131\) | − | 17802.3i | − | 1.03737i | −0.854965 | − | 0.518685i | \(-0.826422\pi\) | ||
0.854965 | − | 0.518685i | \(-0.173578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 82.6689 | 0.00467346 | ||||||||
\(134\) | 18275.9 | 1.01782 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19216.5i | 1.03895i | ||||||||
\(137\) | 11891.9 | 0.633595 | 0.316797 | − | 0.948493i | \(-0.397393\pi\) | ||||
0.316797 | + | 0.948493i | \(0.397393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −24841.5 | −1.28572 | −0.642862 | − | 0.765982i | \(-0.722253\pi\) | ||||
−0.642862 | + | 0.765982i | \(0.722253\pi\) | |||||||
\(140\) | 390.101 | 0.0199031 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9077.34i | 0.450176i | ||||||||
\(143\) | −5032.28 | −0.246089 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −43230.6 | −2.05615 | ||||||||
\(146\) | 13372.7 | 0.627355 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17996.4i | 0.821605i | ||||||||
\(149\) | 26032.6i | 1.17259i | 0.810099 | + | 0.586293i | \(0.199413\pi\) | ||||
−0.810099 | + | 0.586293i | \(0.800587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12278.3i | − | 0.538497i | −0.963071 | − | 0.269249i | \(-0.913225\pi\) | ||
0.963071 | − | 0.269249i | \(-0.0867753\pi\) | |||||||
\(152\) | − | 2769.15i | − | 0.119856i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 770.594 | 0.0324926 | ||||||||
\(155\) | − | 56471.8i | − | 2.35054i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21189.6i | 0.859655i | 0.902911 | + | 0.429827i | \(0.141426\pi\) | ||||
−0.902911 | + | 0.429827i | \(0.858574\pi\) | |||||||
\(158\) | − | 15333.5i | − | 0.614226i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 41580.3i | − | 1.62423i | ||||||
\(161\) | − | 151.113i | − | 0.00582976i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22822.0 | 0.858970 | 0.429485 | − | 0.903074i | \(-0.358695\pi\) | ||||
0.429485 | + | 0.903074i | \(0.358695\pi\) | |||||||
\(164\) | −13906.8 | −0.517057 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −39510.0 | −1.43381 | ||||||||
\(167\) | 28368.2 | 1.01718 | 0.508592 | − | 0.861008i | \(-0.330166\pi\) | ||||
0.508592 | + | 0.861008i | \(0.330166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27317.5 | 0.956463 | ||||||||
\(170\) | − | 108490.i | − | 3.75398i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6466.56i | − | 0.218583i | ||||||
\(173\) | − | 7580.94i | − | 0.253297i | −0.991948 | − | 0.126649i | \(-0.959578\pi\) | ||
0.991948 | − | 0.126649i | \(-0.0404221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1183.70 | 0.0386513 | ||||||||
\(176\) | − | 45603.1i | − | 1.47221i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 25533.9 | 0.805894 | ||||||||
\(179\) | 34939.2i | 1.09045i | 0.838289 | + | 0.545226i | \(0.183556\pi\) | ||||
−0.838289 | + | 0.545226i | \(0.816444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 37840.7 | 1.15505 | 0.577527 | − | 0.816372i | \(-0.304018\pi\) | ||||
0.577527 | + | 0.816372i | \(0.304018\pi\) | |||||||
\(182\) | 190.411 | 0.00574843 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5061.82 | −0.149510 | ||||||||
\(185\) | 85954.8i | 2.51146i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 75301.6i | − | 2.15338i | ||||||
\(188\) | − | 5320.59i | − | 0.150537i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15633.7i | 0.433067i | ||||||||
\(191\) | 3569.74i | 0.0978521i | 0.998802 | + | 0.0489261i | \(0.0155799\pi\) | ||||
−0.998802 | + | 0.0489261i | \(0.984420\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24451.4 | 0.656430 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(194\) | −64882.3 | −1.72394 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20800.2 | 0.541447 | ||||||||
\(197\) | 29706.3 | 0.765449 | 0.382724 | − | 0.923863i | \(-0.374986\pi\) | ||||
0.382724 | + | 0.923863i | \(0.374986\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22181.5 | −0.560125 | −0.280062 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280062 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(200\) | − | 39650.2i | − | 0.991255i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30857.5 | −0.756237 | ||||||||
\(203\) | 1135.36 | 0.0275512 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −66421.7 | −1.58053 | ||||||||
\(206\) | −59733.8 | −1.40762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 11268.4i | − | 0.260456i | ||||||
\(209\) | 10851.2i | 0.248419i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 81724.8i | 1.83565i | 0.396989 | + | 0.917824i | \(0.370055\pi\) | ||||
−0.396989 | + | 0.917824i | \(0.629945\pi\) | |||||||
\(212\) | −28659.5 | −0.637671 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 29382.1i | − | 0.641586i | ||||||
\(215\) | − | 30885.6i | − | 0.668159i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1483.11i | 0.0314959i | ||||||||
\(218\) | −88838.3 | −1.86933 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 51205.0i | 1.05795i | ||||||||
\(221\) | − | 18606.7i | − | 0.380965i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −54373.6 | −1.09340 | −0.546699 | − | 0.837329i | \(-0.684116\pi\) | ||||
−0.546699 | + | 0.837329i | \(0.684116\pi\) | |||||||
\(224\) | 1092.02i | 0.0217637i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 123833. | 2.42449 | ||||||||
\(227\) | 55801.8i | 1.08292i | 0.840726 | + | 0.541460i | \(0.182128\pi\) | ||||
−0.840726 | + | 0.541460i | \(0.817872\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 102771.i | 1.95975i | 0.199624 | + | 0.979873i | \(0.436028\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(230\) | 28577.4 | 0.540215 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 38030.9i | − | 0.706579i | ||||||
\(233\) | − | 60636.1i | − | 1.11691i | −0.829534 | − | 0.558457i | \(-0.811394\pi\) | ||
0.829534 | − | 0.558457i | \(-0.188606\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 25412.3i | − | 0.460159i | ||||||
\(236\) | 2867.91 | + | 30034.7i | 0.0514922 | + | 0.539261i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2849.25i | 0.0503010i | ||||||||
\(239\) | −12138.8 | −0.212510 | −0.106255 | − | 0.994339i | \(-0.533886\pi\) | ||||
−0.106255 | + | 0.994339i | \(0.533886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13471.2 | −0.231938 | −0.115969 | − | 0.993253i | \(-0.536997\pi\) | ||||
−0.115969 | + | 0.993253i | \(0.536997\pi\) | |||||||
\(242\) | 28432.3i | 0.485491i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26189.1i | 0.439886i | ||||||||
\(245\) | 99346.2 | 1.65508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2681.29i | 0.0439490i | ||||||||
\(248\) | 49679.5 | 0.807745 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 95348.6i | 1.52558i | ||||||||
\(251\) | 20999.2 | 0.333315 | 0.166657 | − | 0.986015i | \(-0.446703\pi\) | ||||
0.166657 | + | 0.986015i | \(0.446703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19835.2 | 0.309882 | ||||||||
\(254\) | − | 111317.i | − | 1.72542i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 80894.5 | 1.23435 | ||||||||
\(257\) | 39315.0 | 0.595240 | 0.297620 | − | 0.954684i | \(-0.403807\pi\) | ||||
0.297620 | + | 0.954684i | \(0.403807\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2257.42i | − | 0.0336521i | ||||||
\(260\) | 12652.5i | 0.187168i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −88417.5 | −1.28806 | ||||||||
\(263\) | −37861.6 | −0.547378 | −0.273689 | − | 0.961818i | \(-0.588244\pi\) | ||||
−0.273689 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −136884. | −1.94922 | ||||||||
\(266\) | − | 410.586i | − | 0.00580284i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 31893.8i | − | 0.444055i | ||||||
\(269\) | 123756.i | 1.71026i | 0.518413 | + | 0.855130i | \(0.326523\pi\) | ||||
−0.518413 | + | 0.855130i | \(0.673477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4855.26 | 0.0661110 | 0.0330555 | − | 0.999454i | \(-0.489476\pi\) | ||||
0.0330555 | + | 0.999454i | \(0.489476\pi\) | |||||||
\(272\) | 168616. | 2.27909 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 59062.9i | − | 0.786707i | ||||||
\(275\) | 155373.i | 2.05452i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 97089.7 | 1.26536 | 0.632680 | − | 0.774414i | \(-0.281955\pi\) | ||||
0.632680 | + | 0.774414i | \(0.281955\pi\) | |||||||
\(278\) | 123378.i | 1.59643i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1639.10i | 0.0209069i | ||||||||
\(281\) | 108342. | 1.37209 | 0.686045 | − | 0.727559i | \(-0.259345\pi\) | ||||
0.686045 | + | 0.727559i | \(0.259345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 67893.8i | − | 0.847729i | −0.905726 | − | 0.423864i | \(-0.860673\pi\) | ||
0.905726 | − | 0.423864i | \(-0.139327\pi\) | |||||||
\(284\) | 15841.1 | 0.196404 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24993.5i | 0.305559i | ||||||||
\(287\) | 1744.42 | 0.0211781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 194905. | 2.33360 | ||||||||
\(290\) | 214710.i | 2.55304i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 23337.1i | − | 0.273704i | ||||||
\(293\) | −51965.3 | −0.605311 | −0.302655 | − | 0.953100i | \(-0.597873\pi\) | ||||
−0.302655 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13697.7 | + | 143452.i | 0.157400 | + | 1.64840i | ||||
\(296\) | −75616.4 | −0.863043 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 129294. | 1.45595 | ||||||||
\(299\) | 4901.21 | 0.0548227 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 811.144i | 0.00895293i | ||||||||
\(302\) | −60981.7 | −0.668629 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24298.1 | −0.262921 | ||||||||
\(305\) | 125085.i | 1.34463i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 122608. | 1.30089 | 0.650445 | − | 0.759553i | \(-0.274582\pi\) | ||||
0.650445 | + | 0.759553i | \(0.274582\pi\) | |||||||
\(308\) | − | 1344.79i | − | 0.0141759i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −280475. | −2.91857 | ||||||||
\(311\) | 159419. | 1.64823 | 0.824117 | − | 0.566420i | \(-0.191672\pi\) | ||||
0.824117 | + | 0.566420i | \(0.191672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17723.3i | − | 0.180907i | −0.995901 | − | 0.0904534i | \(-0.971168\pi\) | ||
0.995901 | − | 0.0904534i | \(-0.0288316\pi\) | |||||||
\(314\) | 105241. | 1.06740 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26759.0 | −0.267976 | ||||||||
\(317\) | 112577. | 1.12029 | 0.560145 | − | 0.828394i | \(-0.310745\pi\) | ||||
0.560145 | + | 0.828394i | \(0.310745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 149028.i | 1.46449i | ||||||||
\(320\) | 5145.85 | 0.0502524 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −750.523 | −0.00723856 | ||||||||
\(323\) | −40122.0 | −0.384572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38392.1i | 0.363475i | ||||||||
\(326\) | − | 113348.i | − | 1.06655i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 58432.7i | − | 0.543135i | ||||||
\(329\) | 667.398i | 0.00616585i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −126890. | −1.15817 | −0.579083 | − | 0.815268i | \(-0.696589\pi\) | ||||
−0.579083 | + | 0.815268i | \(0.696589\pi\) | |||||||
\(332\) | 68950.1i | 0.625545i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 140895.i | − | 1.26299i | ||||||
\(335\) | − | 152332.i | − | 1.35738i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 145883.i | 1.28454i | 0.766480 | + | 0.642268i | \(0.222006\pi\) | ||||
−0.766480 | + | 0.642268i | \(0.777994\pi\) | |||||||
\(338\) | − | 135676.i | − | 1.18760i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −189329. | −1.63779 | ||||||||
\(341\) | −194674. | −1.67417 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5219.51 | −0.0443651 | ||||||||
\(344\) | 27170.8 | 0.229607 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −37651.7 | −0.314509 | ||||||||
\(347\) | 118230.i | 0.981905i | 0.871186 | + | 0.490953i | \(0.163351\pi\) | ||||
−0.871186 | + | 0.490953i | \(0.836649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24509.0i | 0.201222i | 0.994926 | + | 0.100611i | \(0.0320797\pi\) | ||||
−0.994926 | + | 0.100611i | \(0.967920\pi\) | |||||||
\(350\) | − | 5878.99i | − | 0.0479917i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −143339. | −1.15685 | ||||||||
\(353\) | − | 38007.7i | − | 0.305015i | −0.988302 | − | 0.152508i | \(-0.951265\pi\) | ||
0.988302 | − | 0.152508i | \(-0.0487349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 75660.7 | 0.600362 | ||||||||
\(356\) | − | 44560.1i | − | 0.351597i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 173530. | 1.35397 | ||||||||
\(359\) | −192503. | −1.49365 | −0.746826 | − | 0.665020i | \(-0.768423\pi\) | ||||
−0.746826 | + | 0.665020i | \(0.768423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −124539. | −0.955635 | ||||||||
\(362\) | − | 187941.i | − | 1.43418i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 332.292i | − | 0.00250794i | ||||||
\(365\) | − | 111463.i | − | 0.836652i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18295.0i | 0.135831i | 0.997691 | + | 0.0679157i | \(0.0216349\pi\) | ||||
−0.997691 | + | 0.0679157i | \(0.978365\pi\) | |||||||
\(368\) | 44415.3i | 0.327972i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 426906. | 3.11838 | ||||||||
\(371\) | 3594.96 | 0.0261183 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 57630.7 | 0.414225 | 0.207112 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207112 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(374\) | −373995. | −2.67376 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22355.8 | 0.158130 | ||||||||
\(377\) | 36824.2i | 0.259090i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170818. | 1.18920 | 0.594599 | − | 0.804023i | \(-0.297311\pi\) | ||||
0.594599 | + | 0.804023i | \(0.297311\pi\) | |||||||
\(380\) | 27282.9 | 0.188940 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17729.6 | 0.121499 | ||||||||
\(383\) | 221122. | 1.50742 | 0.753709 | − | 0.657208i | \(-0.228263\pi\) | ||||
0.753709 | + | 0.657208i | \(0.228263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6422.99i | − | 0.0433327i | ||||||
\(386\) | − | 121441.i | − | 0.815061i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 113228.i | 0.752126i | ||||||||
\(389\) | −87151.4 | −0.575937 | −0.287969 | − | 0.957640i | \(-0.592980\pi\) | ||||
−0.287969 | + | 0.957640i | \(0.592980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 73340.2i | 0.479721i | ||||||||
\(392\) | 87397.2i | 0.568755i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 147540.i | − | 0.950425i | ||||||
\(395\) | −127807. | −0.819143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 126155.i | 0.800431i | 0.916421 | + | 0.400216i | \(0.131065\pi\) | ||||
−0.916421 | + | 0.400216i | \(0.868935\pi\) | |||||||
\(398\) | 110167.i | 0.695483i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −347913. | −2.17446 | ||||||||
\(401\) | 27343.9i | 0.170048i | 0.996379 | + | 0.0850242i | \(0.0270967\pi\) | ||||
−0.996379 | + | 0.0850242i | \(0.972903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48103.2 | −0.296185 | ||||||||
\(404\) | 53850.4i | 0.329933i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 5638.90i | − | 0.0342091i | ||||||
\(407\) | 296310. | 1.78878 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 104932.i | − | 0.627282i | −0.949542 | − | 0.313641i | \(-0.898451\pi\) | ||
0.949542 | − | 0.313641i | \(-0.101549\pi\) | |||||||
\(410\) | 329892.i | 1.96247i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 104243.i | 0.614120i | ||||||||
\(413\) | −359.741 | − | 3767.45i | −0.00210907 | − | 0.0220875i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 329320.i | 1.91215i | ||||||||
\(416\) | −35418.5 | −0.204665 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 53893.8 | 0.308451 | ||||||||
\(419\) | − | 203320.i | − | 1.15812i | −0.815286 | − | 0.579058i | \(-0.803420\pi\) | ||
0.815286 | − | 0.579058i | \(-0.196580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7915.89i | − | 0.0446617i | −0.999751 | − | 0.0223309i | \(-0.992891\pi\) | ||
0.999751 | − | 0.0223309i | \(-0.00710872\pi\) | |||||||
\(422\) | 405897. | 2.27924 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 120420.i | − | 0.669833i | ||||||
\(425\) | −574488. | −3.18056 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3285.07i | − | 0.0180173i | ||||||
\(428\) | −51275.5 | −0.279913 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −153398. | −0.829625 | ||||||||
\(431\) | − | 166950.i | − | 0.898734i | −0.893347 | − | 0.449367i | \(-0.851650\pi\) | ||
0.893347 | − | 0.449367i | \(-0.148350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −47184.7 | −0.251666 | −0.125833 | − | 0.992051i | \(-0.540160\pi\) | ||||
−0.125833 | + | 0.992051i | \(0.540160\pi\) | |||||||
\(434\) | 7366.05 | 0.0391071 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 155034.i | 0.815558i | ||||||||
\(437\) | − | 10568.5i | − | 0.0553417i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 168825. | 0.876010 | 0.438005 | − | 0.898973i | \(-0.355685\pi\) | ||||
0.438005 | + | 0.898973i | \(0.355685\pi\) | |||||||
\(440\) | −215150. | −1.11131 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −92412.7 | −0.473028 | ||||||||
\(443\) | − | 307500.i | − | 1.56689i | −0.621462 | − | 0.783444i | \(-0.713461\pi\) | ||
0.621462 | − | 0.783444i | \(-0.286539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 212828.i | − | 1.07475i | ||||||
\(446\) | 270053.i | 1.35763i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −135.145 | −0.000673352 | ||||||||
\(449\) | 243616. | 1.20841 | 0.604203 | − | 0.796830i | \(-0.293491\pi\) | ||||
0.604203 | + | 0.796830i | \(0.293491\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 228974.i | 1.12573i | ||||||||
\(452\) | − | 216105.i | − | 1.05776i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 277147. | 1.34462 | ||||||||
\(455\) | − | 1587.10i | − | 0.00766620i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 240817.i | 1.15307i | 0.817073 | + | 0.576535i | \(0.195595\pi\) | ||||
−0.817073 | + | 0.576535i | \(0.804405\pi\) | |||||||
\(458\) | 510426. | 2.43333 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 49871.3i | − | 0.235686i | ||||||
\(461\) | −105419. | −0.496043 | −0.248021 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248021 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 177261.i | − | 0.826895i | −0.910528 | − | 0.413447i | \(-0.864325\pi\) | ||
0.910528 | − | 0.413447i | \(-0.135675\pi\) | |||||||
\(464\) | −333705. | −1.54998 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −301157. | −1.38682 | ||||||||
\(467\) | − | 387563.i | − | 1.77709i | −0.458792 | − | 0.888544i | \(-0.651718\pi\) | ||
0.458792 | − | 0.888544i | \(-0.348282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4000.66i | 0.0181880i | ||||||||
\(470\) | −126213. | −0.571360 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −126198. | + | 12050.2i | −0.566459 | + | 0.0540892i | ||||
\(473\) | −106471. | −0.475894 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 82785.4 | 0.366916 | ||||||||
\(476\) | 4972.31 | 0.0219455 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 60288.8i | 0.263865i | ||||||||
\(479\) | −346182. | −1.50881 | −0.754404 | − | 0.656411i | \(-0.772074\pi\) | ||||
−0.754404 | + | 0.656411i | \(0.772074\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 73217.1 | 0.316463 | ||||||||
\(482\) | 66906.3i | 0.287987i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 49618.1 | 0.211811 | ||||||||
\(485\) | 540801.i | 2.29908i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −204643. | −0.862855 | −0.431428 | − | 0.902148i | \(-0.641990\pi\) | ||||
−0.431428 | + | 0.902148i | \(0.641990\pi\) | |||||||
\(488\) | −110040. | −0.462072 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 493416.i | − | 2.05504i | ||||||
\(491\) | 124429. | 0.516128 | 0.258064 | − | 0.966128i | \(-0.416915\pi\) | ||||
0.258064 | + | 0.966128i | \(0.416915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −551026. | −2.26714 | ||||||||
\(494\) | 13317.0 | 0.0545696 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 435917.i | − | 1.77190i | ||||||
\(497\) | −1987.06 | −0.00804449 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −410778. | −1.64970 | −0.824851 | − | 0.565350i | \(-0.808741\pi\) | ||||
−0.824851 | + | 0.565350i | \(0.808741\pi\) | |||||||
\(500\) | 166396. | 0.665583 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 104295.i | − | 0.413863i | ||||||
\(503\) | − | 245979.i | − | 0.972213i | −0.873899 | − | 0.486107i | \(-0.838417\pi\) | ||
0.873899 | − | 0.486107i | \(-0.161583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 257201.i | 1.00853i | ||||||||
\(506\) | − | 98514.2i | − | 0.384767i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −194263. | −0.752771 | ||||||||
\(509\) | − | 32679.0i | − | 0.126134i | −0.998009 | − | 0.0630672i | \(-0.979912\pi\) | ||
0.998009 | − | 0.0630672i | \(-0.0200882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2927.33i | 0.0112106i | ||||||||
\(512\) | − | 134764.i | − | 0.514085i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 195263.i | − | 0.739084i | ||||||
\(515\) | 497887.i | 1.87723i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −87603.2 | −0.327747 | ||||||||
\(518\) | −11211.7 | −0.0417844 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −53162.8 | −0.196608 | ||||||||
\(521\) | 113050. | 0.416479 | 0.208240 | − | 0.978078i | \(-0.433227\pi\) | ||||
0.208240 | + | 0.978078i | \(0.433227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 237542. | 0.868435 | 0.434218 | − | 0.900808i | \(-0.357025\pi\) | ||||
0.434218 | + | 0.900808i | \(0.357025\pi\) | |||||||
\(524\) | 154300.i | 0.561957i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 188044.i | 0.679656i | ||||||||
\(527\) | − | 719802.i | − | 2.59174i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 260522. | 0.930966 | ||||||||
\(530\) | 679851.i | 2.42026i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −716.525 | −0.00253168 | ||||||||
\(533\) | 56578.6i | 0.199158i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −244903. | −0.855630 | ||||||||
\(536\) | 134010. | 0.466452 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 614651. | 2.12356 | ||||||||
\(539\) | − | 342474.i | − | 1.17883i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 203519.i | 0.695360i | 0.937613 | + | 0.347680i | \(0.113030\pi\) | ||||
−0.937613 | + | 0.347680i | \(0.886970\pi\) | |||||||
\(542\) | − | 24114.3i | − | 0.0820873i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 529991.i | − | 1.79090i | ||||||
\(545\) | 740477.i | 2.49298i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −388812. | −1.29947 | −0.649733 | − | 0.760163i | \(-0.725119\pi\) | ||||
−0.649733 | + | 0.760163i | \(0.725119\pi\) | |||||||
\(548\) | −103072. | −0.343227 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 771680. | 2.55101 | ||||||||
\(551\) | 79404.6 | 0.261543 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3356.57 | 0.0109760 | ||||||||
\(554\) | − | 482209.i | − | 1.57114i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 215311. | 0.696493 | ||||||||
\(557\) | −307150. | −0.990011 | −0.495006 | − | 0.868890i | \(-0.664834\pi\) | ||||
−0.495006 | + | 0.868890i | \(0.664834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26308.7 | −0.0841929 | ||||||||
\(560\) | 14382.4 | 0.0458624 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 538093.i | − | 1.70367i | ||||||
\(563\) | − | 224936.i | − | 0.709647i | −0.934933 | − | 0.354824i | \(-0.884541\pi\) | ||
0.934933 | − | 0.354824i | \(-0.115459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.03216e6i | − | 3.23334i | ||||||
\(566\) | −337203. | −1.05259 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 66560.4i | 0.206310i | ||||||||
\(569\) | 48390.1i | 0.149463i | 0.997204 | + | 0.0747313i | \(0.0238099\pi\) | ||||
−0.997204 | + | 0.0747313i | \(0.976190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 344185.i | − | 1.05565i | −0.849353 | − | 0.527825i | \(-0.823008\pi\) | ||
0.849353 | − | 0.527825i | \(-0.176992\pi\) | |||||||
\(572\) | 43616.8 | 0.133310 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8663.89i | − | 0.0262960i | ||||||
\(575\) | − | 151326.i | − | 0.457697i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 68280.6 | 0.205091 | 0.102545 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102545 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(578\) | − | 968019.i | − | 2.89753i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 374697. | 1.11384 | ||||||||
\(581\) | − | 8648.88i | − | 0.0256217i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 471876.i | 1.38833i | ||||||||
\(584\) | 98056.5 | 0.287509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 258093.i | 0.751589i | ||||||||
\(587\) | 275118.i | 0.798441i | 0.916855 | + | 0.399220i | \(0.130719\pi\) | ||||
−0.916855 | + | 0.399220i | \(0.869281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 103726.i | 0.298989i | ||||||||
\(590\) | 712472. | − | 68031.6i | 2.04675 | − | 0.195437i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 663502.i | 1.89321i | ||||||||
\(593\) | −84870.1 | −0.241349 | −0.120674 | − | 0.992692i | \(-0.538506\pi\) | ||||
−0.120674 | + | 0.992692i | \(0.538506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23748.8 | 0.0670823 | ||||||||
\(596\) | − | 225635.i | − | 0.635206i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 24342.5i | − | 0.0680711i | ||||||
\(599\) | 75105.1 | 0.209322 | 0.104661 | − | 0.994508i | \(-0.466624\pi\) | ||||
0.104661 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 94230.3i | − | 0.260880i | −0.991456 | − | 0.130440i | \(-0.958361\pi\) | ||
0.991456 | − | 0.130440i | \(-0.0416391\pi\) | |||||||
\(602\) | 4028.65 | 0.0111165 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 106421.i | 0.291711i | ||||||||
\(605\) | 236986. | 0.647460 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 247136. | 0.670747 | 0.335374 | − | 0.942085i | \(-0.391137\pi\) | ||||
0.335374 | + | 0.942085i | \(0.391137\pi\) | |||||||
\(608\) | 76373.4i | 0.206602i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 621249. | 1.66957 | ||||||||
\(611\) | −21646.4 | −0.0579834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 349727.i | − | 0.930696i | −0.885128 | − | 0.465348i | \(-0.845929\pi\) | ||
0.885128 | − | 0.465348i | \(-0.154071\pi\) | |||||||
\(614\) | − | 608947.i | − | 1.61526i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5650.45 | 0.0148909 | ||||||||
\(617\) | 645133. | 1.69465 | 0.847323 | − | 0.531078i | \(-0.178213\pi\) | ||||
0.847323 | + | 0.531078i | \(0.178213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −473269. | −1.23517 | −0.617585 | − | 0.786504i | \(-0.711889\pi\) | ||||
−0.617585 | + | 0.786504i | \(0.711889\pi\) | |||||||
\(620\) | 489464.i | 1.27332i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 791774.i | − | 2.04654i | ||||||
\(623\) | 5589.47i | 0.0144011i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 114275. | 0.292544 | ||||||||
\(626\) | −88024.9 | −0.224624 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 183659.i | − | 0.465687i | ||||||
\(629\) | 1.09560e6i | 2.76917i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 775739. | 1.94831 | 0.974153 | − | 0.225891i | \(-0.0725294\pi\) | ||||
0.974153 | + | 0.225891i | \(0.0725294\pi\) | |||||||
\(632\) | − | 112435.i | − | 0.281492i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 559128.i | − | 1.39102i | ||||||
\(635\) | −927842. | −2.30105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 84624.0i | − | 0.208552i | ||||||
\(638\) | 740166. | 1.81839 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 690842.i | − | 1.68663i | ||||||
\(641\) | −368716. | −0.897380 | −0.448690 | − | 0.893688i | \(-0.648109\pi\) | ||||
−0.448690 | + | 0.893688i | \(0.648109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −81254.3 | −0.196528 | −0.0982640 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982640 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(644\) | 1309.76i | 0.00315806i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 199271.i | 0.477506i | ||||||||
\(647\) | 176909. | 0.422612 | 0.211306 | − | 0.977420i | \(-0.432228\pi\) | ||||
0.211306 | + | 0.977420i | \(0.432228\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 494518. | − | 47219.9i | 1.17407 | − | 0.112108i | ||||
\(650\) | 190679. | 0.451312 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −197807. | −0.465316 | ||||||||
\(653\) | −467222. | −1.09571 | −0.547857 | − | 0.836572i | \(-0.684556\pi\) | ||||
−0.547857 | + | 0.836572i | \(0.684556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 736970.i | 1.71778i | ||||||||
\(656\) | −512722. | −1.19145 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3314.72 | 0.00765588 | ||||||||
\(659\) | 41300.9i | 0.0951018i | 0.998869 | + | 0.0475509i | \(0.0151416\pi\) | ||||
−0.998869 | + | 0.0475509i | \(0.984858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −298921. | −0.684153 | −0.342077 | − | 0.939672i | \(-0.611130\pi\) | ||||
−0.342077 | + | 0.939672i | \(0.611130\pi\) | |||||||
\(662\) | 630215.i | 1.43805i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −289711. | −0.657095 | ||||||||
\(665\) | −3422.28 | −0.00773877 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 145146.i | − | 0.326253i | ||||||
\(668\) | −245879. | −0.551022 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −756575. | −1.68540 | ||||||||
\(671\) | 431201. | 0.957712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 814423.i | − | 1.79812i | −0.437821 | − | 0.899062i | \(-0.644249\pi\) | ||
0.437821 | − | 0.899062i | \(-0.355751\pi\) | |||||||
\(674\) | 724549. | 1.59495 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −236772. | −0.518129 | ||||||||
\(677\) | 345729. | 0.754324 | 0.377162 | − | 0.926147i | \(-0.376900\pi\) | ||||
0.377162 | + | 0.926147i | \(0.376900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 14203.0i | − | 0.0308063i | ||||||
\(680\) | − | 795512.i | − | 1.72040i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 966873.i | 2.07874i | ||||||||
\(683\) | 239945.i | 0.514363i | 0.966363 | + | 0.257181i | \(0.0827938\pi\) | ||||
−0.966363 | + | 0.257181i | \(0.917206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −492295. | −1.04917 | ||||||||
\(686\) | 25923.4i | 0.0550863i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 238412.i | − | 0.503677i | ||||||
\(689\) | 116599.i | 0.245616i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 695558.i | 1.45672i | 0.685193 | + | 0.728362i | \(0.259718\pi\) | ||||
−0.685193 | + | 0.728362i | \(0.740282\pi\) | |||||||
\(692\) | 65707.1i | 0.137215i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 587206. | 1.21919 | ||||||||
\(695\) | 1.02837e6 | 2.12902 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −846626. | −1.74271 | ||||||||
\(698\) | 121727. | 0.249848 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10259.6 | −0.0209379 | ||||||||
\(701\) | 839756.i | 1.70890i | 0.519533 | + | 0.854451i | \(0.326106\pi\) | ||||
−0.519533 | + | 0.854451i | \(0.673894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 157879.i | − | 0.319458i | ||||||
\(704\) | − | 17739.2i | − | 0.0357922i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −188770. | −0.378725 | ||||||||
\(707\) | − | 6754.82i | − | 0.0135137i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 340569. | 0.677505 | 0.338753 | − | 0.940875i | \(-0.389995\pi\) | ||||
0.338753 | + | 0.940875i | \(0.389995\pi\) | |||||||
\(710\) | − | 375778.i | − | 0.745444i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 187230. | 0.369331 | ||||||||
\(713\) | 189603. | 0.372964 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 208323. | 0.407498 | ||||||||
\(716\) | − | 302832.i | − | 0.590712i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 956093.i | 1.85460i | ||||||||
\(719\) | 155487.i | 0.300770i | 0.988627 | + | 0.150385i | \(0.0480514\pi\) | ||||
−0.988627 | + | 0.150385i | \(0.951949\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13075.9i | − | 0.0251537i | ||||||
\(722\) | 618541.i | 1.18657i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −327981. | −0.625708 | ||||||||
\(725\) | 1.13696e6 | 2.16306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −61349.1 | −0.116075 | −0.0580376 | − | 0.998314i | \(-0.518484\pi\) | ||||
−0.0580376 | + | 0.998314i | \(0.518484\pi\) | |||||||
\(728\) | 1396.20 | 0.00263443 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −553595. | −1.03884 | ||||||||
\(731\) | − | 393675.i | − | 0.736722i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39246.3 | 0.0730451 | 0.0365225 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365225 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(734\) | 90864.4 | 0.168656 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 139605. | 0.257719 | ||||||||
\(737\) | −525130. | −0.966789 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 856850.i | 1.56898i | 0.620144 | + | 0.784488i | \(0.287074\pi\) | ||||
−0.620144 | + | 0.784488i | \(0.712926\pi\) | |||||||
\(740\) | − | 745006.i | − | 1.36049i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 17854.8i | − | 0.0324300i | ||||||
\(743\) | −598825. | −1.08473 | −0.542366 | − | 0.840143i | \(-0.682471\pi\) | ||||
−0.542366 | + | 0.840143i | \(0.682471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.07768e6i | − | 1.94168i | ||||||
\(746\) | − | 286230.i | − | 0.514325i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 652670.i | 1.16651i | ||||||||
\(749\) | 6431.83 | 0.0114649 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 332338.i | 0.589250i | 0.955613 | + | 0.294625i | \(0.0951947\pi\) | ||||
−0.955613 | + | 0.294625i | \(0.904805\pi\) | |||||||
\(752\) | − | 196162.i | − | 0.346880i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 182892. | 0.321701 | ||||||||
\(755\) | 508289.i | 0.891696i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 824719. | 1.43918 | 0.719588 | − | 0.694401i | \(-0.244331\pi\) | ||||
0.719588 | + | 0.694401i | \(0.244331\pi\) | |||||||
\(758\) | − | 848387.i | − | 1.47658i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 114636.i | 0.198469i | ||||||||
\(761\) | −1.09768e6 | −1.89542 | −0.947711 | − | 0.319130i | \(-0.896609\pi\) | ||||
−0.947711 | + | 0.319130i | \(0.896609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 19447.0i | − | 0.0334044i | ||||||
\(764\) | − | 30940.4i | − | 0.0530078i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1.09823e6i | − | 1.87170i | ||||||
\(767\) | 122194. | − | 11667.9i | 0.207710 | − | 0.0198336i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 237713.i | 0.401976i | 0.979594 | + | 0.200988i | \(0.0644153\pi\) | ||||
−0.979594 | + | 0.200988i | \(0.935585\pi\) | |||||||
\(770\) | −31900.6 | −0.0538043 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −211930. | −0.355597 | ||||||||
\(773\) | − | 998180.i | − | 1.67051i | −0.549860 | − | 0.835257i | \(-0.685319\pi\) | ||
0.549860 | − | 0.835257i | \(-0.314681\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.48520e6i | 2.47276i | ||||||||
\(776\) | −475755. | −0.790060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 432849.i | 0.715117i | ||||||||
\(779\) | 122001. | 0.201043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 260823.i | − | 0.427606i | ||||||
\(782\) | 364254. | 0.595649 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 766873. | 1.24765 | ||||||||
\(785\) | − | 877196.i | − | 1.42350i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −292759. | −0.472673 | −0.236337 | − | 0.971671i | \(-0.575947\pi\) | ||||
−0.236337 | + | 0.971671i | \(0.575947\pi\) | |||||||
\(788\) | −257477. | −0.414654 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 634769.i | 1.01709i | ||||||||
\(791\) | 27107.5i | 0.0433248i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 106548. | 0.169434 | ||||||||
\(794\) | 626566. | 0.993861 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 192256. | 0.303427 | ||||||||
\(797\) | − | 105074.i | − | 0.165416i | −0.996574 | − | 0.0827079i | \(-0.973643\pi\) | ||
0.996574 | − | 0.0827079i | \(-0.0263569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 323911.i | − | 0.507378i | ||||||
\(800\) | 1.09355e6i | 1.70868i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 135807. | 0.211142 | ||||||||
\(803\) | −384244. | −0.595903 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6255.69i | 0.00965347i | ||||||||
\(806\) | 238911.i | 0.367761i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −226265. | −0.346573 | ||||||||
\(809\) | 526375.i | 0.804263i | 0.915582 | + | 0.402131i | \(0.131731\pi\) | ||||
−0.915582 | + | 0.402131i | \(0.868269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 725298.i | 1.10274i | 0.834260 | + | 0.551372i | \(0.185895\pi\) | ||||
−0.834260 | + | 0.551372i | \(0.814105\pi\) | |||||||
\(812\) | −9840.61 | −0.0149248 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 1.47166e6i | − | 2.22106i | ||||||
\(815\) | −944770. | −1.42237 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56729.8i | 0.0849899i | ||||||||
\(818\) | −521160. | −0.778869 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 575704. | 0.856193 | ||||||||
\(821\) | 299805.i | 0.444787i | 0.974957 | + | 0.222393i | \(0.0713870\pi\) | ||||
−0.974957 | + | 0.222393i | \(0.928613\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 416111.i | 0.614341i | 0.951655 | + | 0.307170i | \(0.0993821\pi\) | ||||
−0.951655 | + | 0.307170i | \(0.900618\pi\) | |||||||
\(824\) | −438003. | −0.645094 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18711.5 | + | 1786.70i | −0.0274252 | + | 0.00261874i | ||||
\(827\) | −1.32953e6 | −1.94396 | −0.971982 | − | 0.235057i | \(-0.924472\pi\) | ||||
−0.971982 | + | 0.235057i | \(0.924472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 212633. | 0.309401 | 0.154700 | − | 0.987961i | \(-0.450559\pi\) | ||||
0.154700 | + | 0.987961i | \(0.450559\pi\) | |||||||
\(830\) | 1.63561e6 | 2.37424 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4383.28i | − | 0.00633217i | ||||||
\(833\) | 1.26629e6 | 1.82492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.17437e6 | −1.68435 | ||||||||
\(836\) | − | 94051.7i | − | 0.134572i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.00982e6 | −1.43798 | ||||||||
\(839\) | 916109.i | 1.30144i | 0.759319 | + | 0.650719i | \(0.225532\pi\) | ||||
−0.759319 | + | 0.650719i | \(0.774468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 383244. | 0.541856 | ||||||||
\(842\) | −39315.3 | −0.0554546 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 708343.i | − | 0.994394i | ||||||
\(845\) | −1.13088e6 | −1.58380 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6223.93 | −0.00867557 | ||||||||
\(848\) | −1.05663e6 | −1.46937 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.85327e6i | 3.94916i | ||||||||
\(851\) | −288592. | −0.398497 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.10136e6 | 1.51367 | 0.756833 | − | 0.653609i | \(-0.226746\pi\) | ||||
0.756833 | + | 0.653609i | \(0.226746\pi\) | |||||||
\(854\) | −16315.7 | −0.0223713 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 215446.i | − | 0.294030i | ||||||
\(857\) | − | 1.13182e6i | − | 1.54105i | −0.637410 | − | 0.770525i | \(-0.719994\pi\) | ||
0.637410 | − | 0.770525i | \(-0.280006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 574395.i | − | 0.778439i | −0.921145 | − | 0.389220i | \(-0.872745\pi\) | ||
0.921145 | − | 0.389220i | \(-0.127255\pi\) | |||||||
\(860\) | 267699.i | 0.361951i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −829178. | −1.11592 | ||||||||
\(863\) | − | 792718.i | − | 1.06438i | −0.846625 | − | 0.532190i | \(-0.821369\pi\) | ||
0.846625 | − | 0.532190i | \(-0.178631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 313831.i | 0.419434i | ||||||||
\(866\) | 234349.i | 0.312483i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 12854.7i | − | 0.0170617i | ||||||
\(869\) | 440585.i | 0.583432i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −129758. | −0.171039 | ||||||||
\(872\) | −651414. | −0.856691 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52490.1 | −0.0687154 | ||||||||
\(875\) | −20872.1 | −0.0272616 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17892.2 | −0.0232629 | −0.0116314 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116314 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(878\) | − | 838494.i | − | 1.08770i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.88785e6i | 2.43782i | ||||||||
\(881\) | − | 1.36036e6i | − | 1.75268i | −0.481697 | − | 0.876338i | \(-0.659979\pi\) | ||
0.481697 | − | 0.876338i | \(-0.340021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 125594. | 0.161082 | 0.0805408 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805408 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(884\) | 161272.i | 0.206374i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.52724e6 | −1.94554 | ||||||||
\(887\) | 1.43325e6i | 1.82169i | 0.412750 | + | 0.910844i | \(0.364568\pi\) | ||||
−0.412750 | + | 0.910844i | \(0.635432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24367.8 | 0.0308327 | ||||||||
\(890\) | −1.05704e6 | −1.33448 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 471278. | 0.592308 | ||||||||
\(893\) | 46676.5i | 0.0585323i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.44639e6i | − | 1.80567i | ||||||
\(896\) | 18143.5i | 0.0225998i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 1.20995e6i | − | 1.50043i | ||||||
\(899\) | 1.42455e6i | 1.76261i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.74475e6 | −2.14924 | ||||||||
\(902\) | 1.13723e6 | 1.39777 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 908018. | 1.11111 | ||||||||
\(905\) | −1.56651e6 | −1.91265 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 780561. | 0.948838 | 0.474419 | − | 0.880299i | \(-0.342658\pi\) | ||||
0.474419 | + | 0.880299i | \(0.342658\pi\) | |||||||
\(908\) | − | 483657.i | − | 0.586633i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7882.51 | −0.00951880 | ||||||||
\(911\) | −414587. | −0.499550 | −0.249775 | − | 0.968304i | \(-0.580357\pi\) | ||||
−0.249775 | + | 0.968304i | \(0.580357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.13526e6 | 1.36192 | ||||||||
\(914\) | 1.19605e6 | 1.43172 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 890759.i | − | 1.06162i | ||||||
\(917\) | − | 19354.9i | − | 0.0230172i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56347.3i | 0.0667179i | 0.999443 | + | 0.0333590i | \(0.0106205\pi\) | ||||
−0.999443 | + | 0.0333590i | \(0.989380\pi\) | |||||||
\(920\) | 209546. | 0.247573 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 523580.i | 0.615915i | ||||||||
\(923\) | − | 64448.4i | − | 0.0756500i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.26060e6i | − | 2.64204i | ||||||
\(926\) | −880388. | −1.02672 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.04890e6i | 1.21797i | ||||||||
\(929\) | − | 1.10326e6i | − | 1.27834i | −0.769067 | − | 0.639168i | \(-0.779279\pi\) | ||
0.769067 | − | 0.639168i | \(-0.220721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −182476. | −0.210526 | ||||||||
\(932\) | 525558.i | 0.605047i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.92488e6 | −2.20653 | ||||||||
\(935\) | 3.11729e6i | 3.56577i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 912935.i | 1.03983i | 0.854219 | + | 0.519913i | \(0.174036\pi\) | ||||
−0.854219 | + | 0.519913i | \(0.825964\pi\) | |||||||
\(938\) | 19869.8 | 0.0225833 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 220259.i | 0.249274i | ||||||||
\(941\) | − | 1.63562e6i | − | 1.84716i | −0.383409 | − | 0.923579i | \(-0.625250\pi\) | ||
0.383409 | − | 0.923579i | \(-0.374750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 223010.i | − | 0.250785i | ||||||
\(944\) | 105735. | + | 1.10733e6i | 0.118652 | + | 1.24261i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 528804.i | 0.590898i | ||||||||
\(947\) | 927647. | 1.03439 | 0.517193 | − | 0.855869i | \(-0.326977\pi\) | ||||
0.517193 | + | 0.855869i | \(0.326977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −94945.2 | −0.105424 | ||||||||
\(950\) | − | 411165.i | − | 0.455584i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20892.4i | 0.0230523i | ||||||||
\(953\) | 1.38318e6 | 1.52297 | 0.761487 | − | 0.648180i | \(-0.224470\pi\) | ||||
0.761487 | + | 0.648180i | \(0.224470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 147778.i | − | 0.162033i | ||||||
\(956\) | 105212. | 0.115119 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.71936e6i | 1.87342i | ||||||||
\(959\) | 12929.1 | 0.0140582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −937353. | −1.01498 | ||||||||
\(962\) | − | 363642.i | − | 0.392938i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 116760. | 0.125644 | ||||||||
\(965\) | −1.01222e6 | −1.08698 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 671415.i | 0.718023i | 0.933333 | + | 0.359011i | \(0.116886\pi\) | ||||
−0.933333 | + | 0.359011i | \(0.883114\pi\) | |||||||
\(968\) | 208482.i | 0.222494i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.68596e6 | 2.85467 | ||||||||
\(971\) | 819673. | 0.869365 | 0.434683 | − | 0.900584i | \(-0.356861\pi\) | ||||
0.434683 | + | 0.900584i | \(0.356861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27007.9 | −0.0285276 | ||||||||
\(974\) | 1.01638e6i | 1.07137i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 965552.i | 1.01362i | ||||||||
\(977\) | − | 209664.i | − | 0.219651i | −0.993951 | − | 0.109826i | \(-0.964971\pi\) | ||
0.993951 | − | 0.109826i | \(-0.0350293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −733678. | −0.765491 | ||||||||
\(980\) | −861075. | −0.896579 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 617991.i | − | 0.640854i | ||||||
\(983\) | 777728.i | 0.804861i | 0.915451 | + | 0.402431i | \(0.131835\pi\) | ||||
−0.915451 | + | 0.402431i | \(0.868165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.22976e6 | −1.26750 | ||||||||
\(986\) | 2.73674e6i | 2.81501i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 23239.8i | − | 0.0238078i | ||||||
\(989\) | 103698. | 0.106018 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.67117e6i | − | 1.70166i | −0.525442 | − | 0.850829i | \(-0.676100\pi\) | ||
0.525442 | − | 0.850829i | \(-0.323900\pi\) | |||||||
\(992\) | −1.37016e6 | −1.39235 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9869.00i | 0.00998850i | ||||||||
\(995\) | 918257. | 0.927509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43262.3 | 0.0435230 | 0.0217615 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217615 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(998\) | 2.04018e6i | 2.04837i | ||||||||
\(999\) | 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 | 531.5.c.d.235.8 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.33 | yes | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.33 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.8 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.8 | ✓ | 40 | 177.176 | even | 2 | ||
177.5.c.a.58.33 | yes | 40 | 3.2 | odd | 2 | ||
531.5.c.d.235.8 | 40 | 1.1 | even | 1 | trivial | ||
531.5.c.d.235.33 | 40 | 59.58 | odd | 2 | inner |