Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), not 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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 33x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(4.53113i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.h.274.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53113i | 1.60200i | 0.598667 | + | 0.800998i | \(0.295697\pi\) | ||||
−0.598667 | + | 0.800998i | \(0.704303\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −12.5311 | −1.56639 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 13.5934 | 0.924913 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | − 20.5311i | − 0.907356i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.0623 | −0.522499 | −0.261249 | − | 0.965271i | \(-0.584135\pi\) | ||||
−0.261249 | + | 0.965271i | \(0.584135\pi\) | |||||||
\(12\) | 37.5934i | 0.904356i | ||||||||
\(13\) | 2.93774i | 0.0626756i | 0.999509 | + | 0.0313378i | \(0.00997677\pi\) | ||||
−0.999509 | + | 0.0313378i | \(0.990023\pi\) | |||||||
\(14\) | 31.7179 | 0.605498 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.21984 | −0.112810 | ||||||||
\(17\) | − 6.49806i | − 0.0927066i | −0.998925 | − | 0.0463533i | \(-0.985240\pi\) | ||||
0.998925 | − | 0.0463533i | \(-0.0147600\pi\) | |||||||
\(18\) | − 40.7802i | − 0.533999i | ||||||||
\(19\) | 5.43580 | 0.0656347 | 0.0328173 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328173 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − 86.3735i | − 0.837041i | ||||||||
\(23\) | − 49.3774i | − 0.447648i | −0.974630 | − | 0.223824i | \(-0.928146\pi\) | ||||
0.974630 | − | 0.223824i | \(-0.0718541\pi\) | |||||||
\(24\) | −61.5934 | −0.523862 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.3113 | −0.100406 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 87.7179i | 0.592040i | ||||||||
\(29\) | 291.494 | 1.86652 | 0.933261 | − | 0.359200i | \(-0.116950\pi\) | ||||
0.933261 | + | 0.359200i | \(0.116950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 244.307 | 1.41545 | 0.707724 | − | 0.706489i | \(-0.249722\pi\) | ||||
0.707724 | + | 0.706489i | \(0.249722\pi\) | |||||||
\(32\) | − 196.963i | − 1.08808i | ||||||||
\(33\) | 57.1868i | 0.301665i | ||||||||
\(34\) | 29.4436 | 0.148516 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 112.780 | 0.522130 | ||||||||
\(37\) | − 193.121i | − 0.858077i | −0.903286 | − | 0.429038i | \(-0.858853\pi\) | ||||
0.903286 | − | 0.429038i | \(-0.141147\pi\) | |||||||
\(38\) | 24.6303i | 0.105147i | ||||||||
\(39\) | 8.81323 | 0.0361858 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 315.113 | 1.20030 | 0.600151 | − | 0.799887i | \(-0.295107\pi\) | ||||
0.600151 | + | 0.799887i | \(0.295107\pi\) | |||||||
\(42\) | − 95.1537i | − 0.349584i | ||||||||
\(43\) | 300.996i | 1.06748i | 0.845650 | + | 0.533738i | \(0.179213\pi\) | ||||
−0.845650 | + | 0.533738i | \(0.820787\pi\) | |||||||
\(44\) | 238.872 | 0.818437 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 223.735 | 0.717130 | ||||||||
\(47\) | 86.5058i | 0.268472i | 0.990949 | + | 0.134236i | \(0.0428580\pi\) | ||||
−0.990949 | + | 0.134236i | \(0.957142\pi\) | |||||||
\(48\) | 21.6595i | 0.0651309i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.4942 | −0.0535242 | ||||||||
\(52\) | − 36.8132i | − 0.0981745i | ||||||||
\(53\) | − 509.677i | − 1.32093i | −0.750855 | − | 0.660467i | \(-0.770358\pi\) | ||||
0.750855 | − | 0.660467i | \(-0.229642\pi\) | |||||||
\(54\) | −122.340 | −0.308304 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −143.718 | −0.342948 | ||||||||
\(57\) | − 16.3074i | − 0.0378942i | ||||||||
\(58\) | 1320.80i | 2.99016i | ||||||||
\(59\) | 83.3852 | 0.183997 | 0.0919985 | − | 0.995759i | \(-0.470674\pi\) | ||||
0.0919985 | + | 0.995759i | \(0.470674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.25291 | −0.0110257 | −0.00551283 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551283 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(62\) | 1106.99i | 2.26754i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 834.706 | 1.63029 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −259.121 | −0.483266 | ||||||||
\(67\) | 205.992i | 0.375611i | 0.982206 | + | 0.187806i | \(0.0601375\pi\) | ||||
−0.982206 | + | 0.187806i | \(0.939862\pi\) | |||||||
\(68\) | 81.4281i | 0.145215i | ||||||||
\(69\) | −148.132 | −0.258450 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1004.31 | 1.67872 | 0.839362 | − | 0.543573i | \(-0.182929\pi\) | ||||
0.839362 | + | 0.543573i | \(0.182929\pi\) | |||||||
\(72\) | 184.780i | 0.302452i | ||||||||
\(73\) | 1007.29i | 1.61499i | 0.589876 | + | 0.807494i | \(0.299177\pi\) | ||||
−0.589876 | + | 0.807494i | \(0.700823\pi\) | |||||||
\(74\) | 875.055 | 1.37464 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −68.1168 | −0.102810 | ||||||||
\(77\) | 133.436i | 0.197486i | ||||||||
\(78\) | 39.9339i | 0.0579695i | ||||||||
\(79\) | 863.237 | 1.22939 | 0.614695 | − | 0.788765i | \(-0.289279\pi\) | ||||
0.614695 | + | 0.788765i | \(0.289279\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1427.82i | 1.92288i | ||||||||
\(83\) | − 1334.72i | − 1.76512i | −0.470200 | − | 0.882560i | \(-0.655818\pi\) | ||||
0.470200 | − | 0.882560i | \(-0.344182\pi\) | |||||||
\(84\) | 263.154 | 0.341815 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1363.85 | −1.71009 | ||||||||
\(87\) | − 874.483i | − 1.07764i | ||||||||
\(88\) | 391.370i | 0.474093i | ||||||||
\(89\) | −326.249 | −0.388565 | −0.194283 | − | 0.980946i | \(-0.562238\pi\) | ||||
−0.194283 | + | 0.980946i | \(0.562238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.5642 | 0.0236892 | ||||||||
\(92\) | 618.755i | 0.701192i | ||||||||
\(93\) | − 732.922i | − 0.817210i | ||||||||
\(94\) | −391.969 | −0.430091 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −590.889 | −0.628202 | ||||||||
\(97\) | 1526.77i | 1.59815i | 0.601232 | + | 0.799075i | \(0.294677\pi\) | ||||
−0.601232 | + | 0.799075i | \(0.705323\pi\) | |||||||
\(98\) | − 222.025i | − 0.228857i | ||||||||
\(99\) | 171.560 | 0.174166 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 96.8716 | 0.0954365 | 0.0477182 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477182 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(102\) | − 88.3307i | − 0.0857455i | ||||||||
\(103\) | − 1321.99i | − 1.26466i | −0.774700 | − | 0.632329i | \(-0.782099\pi\) | ||||
0.774700 | − | 0.632329i | \(-0.217901\pi\) | |||||||
\(104\) | 60.3152 | 0.0568691 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2309.41 | 2.11613 | ||||||||
\(107\) | 1745.71i | 1.57724i | 0.614883 | + | 0.788619i | \(0.289203\pi\) | ||||
−0.614883 | + | 0.788619i | \(0.710797\pi\) | |||||||
\(108\) | − 338.340i | − 0.301452i | ||||||||
\(109\) | −476.856 | −0.419032 | −0.209516 | − | 0.977805i | \(-0.567189\pi\) | ||||
−0.209516 | + | 0.977805i | \(0.567189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −579.362 | −0.495411 | ||||||||
\(112\) | 50.5389i | 0.0426382i | ||||||||
\(113\) | − 1641.65i | − 1.36666i | −0.730108 | − | 0.683332i | \(-0.760530\pi\) | ||||
0.730108 | − | 0.683332i | \(-0.239470\pi\) | |||||||
\(114\) | 73.8910 | 0.0607064 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3652.75 | −2.92370 | ||||||||
\(117\) | − 26.4397i | − 0.0208919i | ||||||||
\(118\) | 377.829i | 0.294763i | ||||||||
\(119\) | −45.4864 | −0.0350398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −967.630 | −0.726995 | ||||||||
\(122\) | − 23.8016i | − 0.0176631i | ||||||||
\(123\) | − 945.339i | − 0.692994i | ||||||||
\(124\) | −3061.45 | −2.21715 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −285.461 | −0.201833 | ||||||||
\(127\) | − 844.016i | − 0.589719i | −0.955541 | − | 0.294859i | \(-0.904727\pi\) | ||||
0.955541 | − | 0.294859i | \(-0.0952728\pi\) | |||||||
\(128\) | 2206.46i | 1.52363i | ||||||||
\(129\) | 902.988 | 0.616308 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2796.20 | −1.86493 | −0.932463 | − | 0.361265i | \(-0.882345\pi\) | ||||
−0.932463 | + | 0.361265i | \(0.882345\pi\) | |||||||
\(132\) | − 716.615i | − 0.472525i | ||||||||
\(133\) | − 38.0506i | − 0.0248076i | ||||||||
\(134\) | −933.377 | −0.601728 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −133.413 | −0.0841179 | ||||||||
\(137\) | − 2057.13i | − 1.28287i | −0.767179 | − | 0.641433i | \(-0.778340\pi\) | ||||
0.767179 | − | 0.641433i | \(-0.221660\pi\) | |||||||
\(138\) | − 671.206i | − 0.414035i | ||||||||
\(139\) | 1745.12 | 1.06489 | 0.532444 | − | 0.846465i | \(-0.321274\pi\) | ||||
0.532444 | + | 0.846465i | \(0.321274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 259.517 | 0.155002 | ||||||||
\(142\) | 4550.65i | 2.68931i | ||||||||
\(143\) | − 56.0000i | − 0.0327479i | ||||||||
\(144\) | 64.9786 | 0.0376033 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4564.15 | −2.58720 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 2420.02i | 1.34408i | ||||||||
\(149\) | 1173.57 | 0.645254 | 0.322627 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322627 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1540.07 | 0.829994 | 0.414997 | − | 0.909823i | \(-0.363783\pi\) | ||||
0.414997 | + | 0.909823i | \(0.363783\pi\) | |||||||
\(152\) | − 111.603i | − 0.0595540i | ||||||||
\(153\) | 58.4826i | 0.0309022i | ||||||||
\(154\) | −604.615 | −0.316372 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −110.440 | −0.0566811 | ||||||||
\(157\) | − 2544.53i | − 1.29348i | −0.762712 | − | 0.646738i | \(-0.776133\pi\) | ||||
0.762712 | − | 0.646738i | \(-0.223867\pi\) | |||||||
\(158\) | 3911.44i | 1.96948i | ||||||||
\(159\) | −1529.03 | −0.762642 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −345.642 | −0.169195 | ||||||||
\(162\) | 367.021i | 0.178000i | ||||||||
\(163\) | 594.708i | 0.285774i | 0.989739 | + | 0.142887i | \(0.0456385\pi\) | ||||
−0.989739 | + | 0.142887i | \(0.954361\pi\) | |||||||
\(164\) | −3948.72 | −1.88014 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6047.81 | 2.82772 | ||||||||
\(167\) | 928.498i | 0.430236i | 0.976588 | + | 0.215118i | \(0.0690135\pi\) | ||||
−0.976588 | + | 0.215118i | \(0.930986\pi\) | |||||||
\(168\) | 431.154i | 0.198001i | ||||||||
\(169\) | 2188.37 | 0.996072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −48.9222 | −0.0218782 | ||||||||
\(172\) | − 3771.82i | − 1.67209i | ||||||||
\(173\) | 315.642i | 0.138716i | 0.997592 | + | 0.0693578i | \(0.0220950\pi\) | ||||
−0.997592 | + | 0.0693578i | \(0.977905\pi\) | |||||||
\(174\) | 3962.39 | 1.72637 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 137.626 | 0.0589431 | ||||||||
\(177\) | − 250.156i | − 0.106231i | ||||||||
\(178\) | − 1478.28i | − 0.622480i | ||||||||
\(179\) | 1445.49 | 0.603581 | 0.301791 | − | 0.953374i | \(-0.402416\pi\) | ||||
0.301791 | + | 0.953374i | \(0.402416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1843.81 | −0.757180 | −0.378590 | − | 0.925564i | \(-0.623591\pi\) | ||||
−0.378590 | + | 0.925564i | \(0.623591\pi\) | |||||||
\(182\) | 93.1790i | 0.0379499i | ||||||||
\(183\) | 15.7587i | 0.00636567i | ||||||||
\(184\) | −1013.77 | −0.406176 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3320.97 | 1.30917 | ||||||||
\(187\) | 123.868i | 0.0484391i | ||||||||
\(188\) | − 1084.02i | − 0.420532i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −244.074 | −0.0924637 | −0.0462318 | − | 0.998931i | \(-0.514721\pi\) | ||||
−0.0462318 | + | 0.998931i | \(0.514721\pi\) | |||||||
\(192\) | − 2504.12i | − 0.941246i | ||||||||
\(193\) | 1733.03i | 0.646355i | 0.946338 | + | 0.323178i | \(0.104751\pi\) | ||||
−0.946338 | + | 0.323178i | \(0.895249\pi\) | |||||||
\(194\) | −6918.01 | −2.56023 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 614.025 | 0.223770 | ||||||||
\(197\) | 358.230i | 0.129557i | 0.997900 | + | 0.0647787i | \(0.0206342\pi\) | ||||
−0.997900 | + | 0.0647787i | \(0.979366\pi\) | |||||||
\(198\) | 777.362i | 0.279014i | ||||||||
\(199\) | 3203.63 | 1.14120 | 0.570601 | − | 0.821227i | \(-0.306710\pi\) | ||||
0.570601 | + | 0.821227i | \(0.306710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 617.977 | 0.216859 | ||||||||
\(202\) | 438.938i | 0.152889i | ||||||||
\(203\) | − 2040.46i | − 0.705479i | ||||||||
\(204\) | 244.284 | 0.0838398 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5990.12 | 2.02598 | ||||||||
\(207\) | 444.397i | 0.149216i | ||||||||
\(208\) | − 21.2100i | − 0.00707044i | ||||||||
\(209\) | −103.619 | −0.0342940 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4943.16 | 1.61280 | 0.806401 | − | 0.591369i | \(-0.201412\pi\) | ||||
0.806401 | + | 0.591369i | \(0.201412\pi\) | |||||||
\(212\) | 6386.83i | 2.06910i | ||||||||
\(213\) | − 3012.92i | − 0.969211i | ||||||||
\(214\) | −7910.05 | −2.52673 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 554.340 | 0.174621 | ||||||||
\(217\) | − 1710.15i | − 0.534989i | ||||||||
\(218\) | − 2160.70i | − 0.671288i | ||||||||
\(219\) | 3021.86 | 0.932414 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.0896 | 0.00581044 | ||||||||
\(222\) | − 2625.16i | − 0.793646i | ||||||||
\(223\) | − 3160.15i | − 0.948965i | −0.880265 | − | 0.474482i | \(-0.842635\pi\) | ||||
0.880265 | − | 0.474482i | \(-0.157365\pi\) | |||||||
\(224\) | −1378.74 | −0.411255 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7438.51 | 2.18939 | ||||||||
\(227\) | − 3651.11i | − 1.06755i | −0.845628 | − | 0.533773i | \(-0.820774\pi\) | ||||
0.845628 | − | 0.533773i | \(-0.179226\pi\) | |||||||
\(228\) | 204.350i | 0.0593571i | ||||||||
\(229\) | 4083.70 | 1.17842 | 0.589210 | − | 0.807980i | \(-0.299439\pi\) | ||||
0.589210 | + | 0.807980i | \(0.299439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 400.307 | 0.114019 | ||||||||
\(232\) | − 5984.70i | − 1.69360i | ||||||||
\(233\) | 3682.51i | 1.03540i | 0.855561 | + | 0.517702i | \(0.173212\pi\) | ||||
−0.855561 | + | 0.517702i | \(0.826788\pi\) | |||||||
\(234\) | 119.802 | 0.0334687 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1044.91 | −0.288211 | ||||||||
\(237\) | − 2589.71i | − 0.709789i | ||||||||
\(238\) | − 206.105i | − 0.0561336i | ||||||||
\(239\) | −2658.78 | −0.719591 | −0.359796 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359796 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4820.39 | −1.28842 | −0.644209 | − | 0.764850i | \(-0.722813\pi\) | ||||
−0.644209 | + | 0.764850i | \(0.722813\pi\) | |||||||
\(242\) | − 4384.46i | − 1.16464i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 65.8249 | 0.0172705 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4283.45 | 1.11017 | ||||||||
\(247\) | 15.9690i | 0.00411369i | ||||||||
\(248\) | − 5015.91i | − 1.28432i | ||||||||
\(249\) | −4004.17 | −1.01909 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1672.27 | 0.420530 | 0.210265 | − | 0.977644i | \(-0.432567\pi\) | ||||
0.210265 | + | 0.977644i | \(0.432567\pi\) | |||||||
\(252\) | − 789.461i | − 0.197347i | ||||||||
\(253\) | 941.245i | 0.233896i | ||||||||
\(254\) | 3824.34 | 0.944727 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3320.09 | −0.810569 | ||||||||
\(257\) | − 3697.74i | − 0.897506i | −0.893656 | − | 0.448753i | \(-0.851868\pi\) | ||||
0.893656 | − | 0.448753i | \(-0.148132\pi\) | |||||||
\(258\) | 4091.56i | 0.987322i | ||||||||
\(259\) | −1351.84 | −0.324323 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2623.45 | −0.622174 | ||||||||
\(262\) | − 12670.0i | − 2.98760i | ||||||||
\(263\) | − 7319.00i | − 1.71600i | −0.513646 | − | 0.858002i | \(-0.671706\pi\) | ||||
0.513646 | − | 0.858002i | \(-0.328294\pi\) | |||||||
\(264\) | 1174.11 | 0.273717 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 172.412 | 0.0397416 | ||||||||
\(267\) | 978.747i | 0.224338i | ||||||||
\(268\) | − 2581.32i | − 0.588354i | ||||||||
\(269\) | 815.097 | 0.184749 | 0.0923743 | − | 0.995724i | \(-0.470554\pi\) | ||||
0.0923743 | + | 0.995724i | \(0.470554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5106.02 | −1.14453 | −0.572267 | − | 0.820068i | \(-0.693936\pi\) | ||||
−0.572267 | + | 0.820068i | \(0.693936\pi\) | |||||||
\(272\) | 46.9150i | 0.0104582i | ||||||||
\(273\) | − 61.6926i | − 0.0136769i | ||||||||
\(274\) | 9321.13 | 2.05515 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1856.26 | 0.404833 | ||||||||
\(277\) | 1398.72i | 0.303398i | 0.988427 | + | 0.151699i | \(0.0484744\pi\) | ||||
−0.988427 | + | 0.151699i | \(0.951526\pi\) | |||||||
\(278\) | 7907.39i | 1.70595i | ||||||||
\(279\) | −2198.77 | −0.471816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7102.38 | −1.50780 | −0.753901 | − | 0.656988i | \(-0.771830\pi\) | ||||
−0.753901 | + | 0.656988i | \(0.771830\pi\) | |||||||
\(282\) | 1175.91i | 0.248313i | ||||||||
\(283\) | − 4465.18i | − 0.937907i | −0.883223 | − | 0.468953i | \(-0.844631\pi\) | ||||
0.883223 | − | 0.468953i | \(-0.155369\pi\) | |||||||
\(284\) | −12585.1 | −2.62954 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 253.743 | 0.0524621 | ||||||||
\(287\) | − 2205.79i | − 0.453671i | ||||||||
\(288\) | 1772.67i | 0.362692i | ||||||||
\(289\) | 4870.78 | 0.991405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4580.32 | 0.922692 | ||||||||
\(292\) | − 12622.5i | − 2.52970i | ||||||||
\(293\) | − 7590.61i | − 1.51348i | −0.653718 | − | 0.756738i | \(-0.726792\pi\) | ||||
0.653718 | − | 0.756738i | \(-0.273208\pi\) | |||||||
\(294\) | −666.076 | −0.132130 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3964.98 | −0.778581 | ||||||||
\(297\) | − 514.681i | − 0.100555i | ||||||||
\(298\) | 5317.61i | 1.03369i | ||||||||
\(299\) | 145.058 | 0.0280566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2106.97 | 0.403468 | ||||||||
\(302\) | 6978.26i | 1.32965i | ||||||||
\(303\) | − 290.615i | − 0.0551003i | ||||||||
\(304\) | −39.2456 | −0.00740425 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −264.992 | −0.0495052 | ||||||||
\(307\) | 9480.12i | 1.76241i | 0.472737 | + | 0.881203i | \(0.343266\pi\) | ||||
−0.472737 | + | 0.881203i | \(0.656734\pi\) | |||||||
\(308\) | − 1672.10i | − 0.309340i | ||||||||
\(309\) | −3965.98 | −0.730151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7078.01 | 1.29054 | 0.645268 | − | 0.763956i | \(-0.276746\pi\) | ||||
0.645268 | + | 0.763956i | \(0.276746\pi\) | |||||||
\(312\) | − 180.945i | − 0.0328334i | ||||||||
\(313\) | − 5593.84i | − 1.01017i | −0.863070 | − | 0.505084i | \(-0.831461\pi\) | ||||
0.863070 | − | 0.505084i | \(-0.168539\pi\) | |||||||
\(314\) | 11529.6 | 2.07214 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10817.3 | −1.92571 | ||||||||
\(317\) | 3567.81i | 0.632139i | 0.948736 | + | 0.316070i | \(0.102363\pi\) | ||||
−0.948736 | + | 0.316070i | \(0.897637\pi\) | |||||||
\(318\) | − 6928.24i | − 1.22175i | ||||||||
\(319\) | −5556.54 | −0.975255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5237.14 | 0.910618 | ||||||||
\(322\) | − 1566.15i | − 0.271050i | ||||||||
\(323\) | − 35.3222i | − 0.00608477i | ||||||||
\(324\) | −1015.02 | −0.174043 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2694.70 | −0.457809 | ||||||||
\(327\) | 1430.57i | 0.241928i | ||||||||
\(328\) | − 6469.62i | − 1.08910i | ||||||||
\(329\) | 605.541 | 0.101473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4389.67 | −0.728936 | −0.364468 | − | 0.931216i | \(-0.618749\pi\) | ||||
−0.364468 | + | 0.931216i | \(0.618749\pi\) | |||||||
\(332\) | 16725.6i | 2.76487i | ||||||||
\(333\) | 1738.09i | 0.286026i | ||||||||
\(334\) | −4207.14 | −0.689236 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 151.617 | 0.0246172 | ||||||||
\(337\) | 2348.83i | 0.379671i | 0.981816 | + | 0.189835i | \(0.0607955\pi\) | ||||
−0.981816 | + | 0.189835i | \(0.939205\pi\) | |||||||
\(338\) | 9915.79i | 1.59570i | ||||||||
\(339\) | −4924.94 | −0.789044 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4657.05 | −0.739570 | ||||||||
\(342\) | − 221.673i | − 0.0350488i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 6179.79 | 0.968581 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1430.21 | −0.222222 | ||||||||
\(347\) | 558.436i | 0.0863931i | 0.999067 | + | 0.0431965i | \(0.0137542\pi\) | ||||
−0.999067 | + | 0.0431965i | \(0.986246\pi\) | |||||||
\(348\) | 10958.3i | 1.68800i | ||||||||
\(349\) | −3233.89 | −0.496006 | −0.248003 | − | 0.968759i | \(-0.579774\pi\) | ||||
−0.248003 | + | 0.968759i | \(0.579774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −79.3190 | −0.0120619 | ||||||||
\(352\) | 3754.56i | 0.568519i | ||||||||
\(353\) | 7516.35i | 1.13330i | 0.823959 | + | 0.566650i | \(0.191761\pi\) | ||||
−0.823959 | + | 0.566650i | \(0.808239\pi\) | |||||||
\(354\) | 1133.49 | 0.170181 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4088.27 | 0.608646 | ||||||||
\(357\) | 136.459i | 0.0202302i | ||||||||
\(358\) | 6549.70i | 0.966935i | ||||||||
\(359\) | 6577.76 | 0.967021 | 0.483511 | − | 0.875338i | \(-0.339361\pi\) | ||||
0.483511 | + | 0.875338i | \(0.339361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6829.45 | −0.995692 | ||||||||
\(362\) | − 8354.56i | − 1.21300i | ||||||||
\(363\) | 2902.89i | 0.419731i | ||||||||
\(364\) | −257.693 | −0.0371065 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −71.4048 | −0.0101978 | ||||||||
\(367\) | 8307.17i | 1.18155i | 0.806835 | + | 0.590777i | \(0.201179\pi\) | ||||
−0.806835 | + | 0.590777i | \(0.798821\pi\) | |||||||
\(368\) | 356.497i | 0.0504992i | ||||||||
\(369\) | −2836.02 | −0.400101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3567.74 | −0.499266 | ||||||||
\(372\) | 9184.34i | 1.28007i | ||||||||
\(373\) | 4551.09i | 0.631760i | 0.948799 | + | 0.315880i | \(0.102300\pi\) | ||||
−0.948799 | + | 0.315880i | \(0.897700\pi\) | |||||||
\(374\) | −561.261 | −0.0775992 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1776.06 | 0.243599 | ||||||||
\(377\) | 856.335i | 0.116985i | ||||||||
\(378\) | 856.383i | 0.116528i | ||||||||
\(379\) | 1788.29 | 0.242370 | 0.121185 | − | 0.992630i | \(-0.461331\pi\) | ||||
0.121185 | + | 0.992630i | \(0.461331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2532.05 | −0.340474 | ||||||||
\(382\) | − 1105.93i | − 0.148126i | ||||||||
\(383\) | 1358.47i | 0.181240i | 0.995886 | + | 0.0906199i | \(0.0288848\pi\) | ||||
−0.995886 | + | 0.0906199i | \(0.971115\pi\) | |||||||
\(384\) | 6619.37 | 0.879670 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7852.60 | −1.03546 | ||||||||
\(387\) | − 2708.97i | − 0.355825i | ||||||||
\(388\) | − 19132.2i | − 2.50333i | ||||||||
\(389\) | −9722.54 | −1.26723 | −0.633615 | − | 0.773649i | \(-0.718430\pi\) | ||||
−0.633615 | + | 0.773649i | \(0.718430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −320.858 | −0.0414999 | ||||||||
\(392\) | 1006.03i | 0.129622i | ||||||||
\(393\) | 8388.61i | 1.07672i | ||||||||
\(394\) | −1623.19 | −0.207551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2149.84 | −0.272812 | ||||||||
\(397\) | − 4788.04i | − 0.605302i | −0.953101 | − | 0.302651i | \(-0.902128\pi\) | ||||
0.953101 | − | 0.302651i | \(-0.0978717\pi\) | |||||||
\(398\) | 14516.1i | 1.82820i | ||||||||
\(399\) | −114.152 | −0.0143227 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9681.41 | 1.20565 | 0.602826 | − | 0.797873i | \(-0.294041\pi\) | ||||
0.602826 | + | 0.797873i | \(0.294041\pi\) | |||||||
\(402\) | 2800.13i | 0.347408i | ||||||||
\(403\) | 717.712i | 0.0887141i | ||||||||
\(404\) | −1213.91 | −0.149491 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9245.58 | 1.13017 | ||||||||
\(407\) | 3681.32i | 0.448344i | ||||||||
\(408\) | 400.238i | 0.0485655i | ||||||||
\(409\) | −11113.1 | −1.34353 | −0.671767 | − | 0.740763i | \(-0.734464\pi\) | ||||
−0.671767 | + | 0.740763i | \(0.734464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6171.40 | −0.740663 | ||||||||
\(412\) | 16566.1i | 1.98095i | ||||||||
\(413\) | − 583.696i | − 0.0695443i | ||||||||
\(414\) | −2013.62 | −0.239043 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 578.627 | 0.0681959 | ||||||||
\(417\) | − 5235.37i | − 0.614814i | ||||||||
\(418\) | − 469.510i | − 0.0549389i | ||||||||
\(419\) | 1230.09 | 0.143421 | 0.0717107 | − | 0.997425i | \(-0.477154\pi\) | ||||
0.0717107 | + | 0.997425i | \(0.477154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12356.5 | −1.43044 | −0.715222 | − | 0.698897i | \(-0.753674\pi\) | ||||
−0.715222 | + | 0.698897i | \(0.753674\pi\) | |||||||
\(422\) | 22398.1i | 2.58370i | ||||||||
\(423\) | − 778.552i | − 0.0894906i | ||||||||
\(424\) | −10464.2 | −1.19856 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 13651.9 | 1.55267 | ||||||||
\(427\) | 36.7703i | 0.00416731i | ||||||||
\(428\) | − 21875.7i | − 2.47057i | ||||||||
\(429\) | −168.000 | −0.0189070 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7375.27 | −0.824256 | −0.412128 | − | 0.911126i | \(-0.635214\pi\) | ||||
−0.412128 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(432\) | − 194.936i | − 0.0217103i | ||||||||
\(433\) | 690.067i | 0.0765877i | 0.999267 | + | 0.0382939i | \(0.0121923\pi\) | ||||
−0.999267 | + | 0.0382939i | \(0.987808\pi\) | |||||||
\(434\) | 7748.92 | 0.857051 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5975.55 | 0.656369 | ||||||||
\(437\) | − 268.406i | − 0.0293812i | ||||||||
\(438\) | 13692.5i | 1.49372i | ||||||||
\(439\) | −8408.79 | −0.914191 | −0.457095 | − | 0.889418i | \(-0.651110\pi\) | ||||
−0.457095 | + | 0.889418i | \(0.651110\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 86.4976i | 0.00930830i | ||||||||
\(443\) | − 6568.55i | − 0.704473i | −0.935911 | − | 0.352236i | \(-0.885421\pi\) | ||||
0.935911 | − | 0.352236i | \(-0.114579\pi\) | |||||||
\(444\) | 7260.06 | 0.776007 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14319.0 | 1.52024 | ||||||||
\(447\) | − 3520.72i | − 0.372537i | ||||||||
\(448\) | − 5842.94i | − 0.616190i | ||||||||
\(449\) | −2954.55 | −0.310543 | −0.155271 | − | 0.987872i | \(-0.549625\pi\) | ||||
−0.155271 | + | 0.987872i | \(0.549625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6006.76 | −0.627156 | ||||||||
\(452\) | 20571.7i | 2.14073i | ||||||||
\(453\) | − 4620.21i | − 0.479197i | ||||||||
\(454\) | 16543.7 | 1.71020 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −334.810 | −0.0343835 | ||||||||
\(457\) | − 8144.84i | − 0.833697i | −0.908976 | − | 0.416849i | \(-0.863135\pi\) | ||||
0.908976 | − | 0.416849i | \(-0.136865\pi\) | |||||||
\(458\) | 18503.8i | 1.88782i | ||||||||
\(459\) | 175.448 | 0.0178414 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2495.26 | 0.252095 | 0.126048 | − | 0.992024i | \(-0.459771\pi\) | ||||
0.126048 | + | 0.992024i | \(0.459771\pi\) | |||||||
\(462\) | 1813.84i | 0.182657i | ||||||||
\(463\) | 5755.66i | 0.577728i | 0.957370 | + | 0.288864i | \(0.0932776\pi\) | ||||
−0.957370 | + | 0.288864i | \(0.906722\pi\) | |||||||
\(464\) | −2104.54 | −0.210562 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16685.9 | −1.65871 | ||||||||
\(467\) | − 4143.73i | − 0.410598i | −0.978699 | − | 0.205299i | \(-0.934183\pi\) | ||||
0.978699 | − | 0.205299i | \(-0.0658166\pi\) | |||||||
\(468\) | 331.319i | 0.0327248i | ||||||||
\(469\) | 1441.95 | 0.141968 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7633.60 | −0.746789 | ||||||||
\(472\) | − 1711.99i | − 0.166951i | ||||||||
\(473\) | − 5737.67i | − 0.557755i | ||||||||
\(474\) | 11734.3 | 1.13708 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 569.996 | 0.0548860 | ||||||||
\(477\) | 4587.09i | 0.440312i | ||||||||
\(478\) | − 12047.3i | − 1.15278i | ||||||||
\(479\) | 6765.96 | 0.645396 | 0.322698 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322698 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 567.339 | 0.0537805 | ||||||||
\(482\) | − 21841.8i | − 2.06404i | ||||||||
\(483\) | 1036.93i | 0.0976848i | ||||||||
\(484\) | 12125.5 | 1.13876 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1101.06 | 0.102768 | ||||||||
\(487\) | 6360.42i | 0.591824i | 0.955215 | + | 0.295912i | \(0.0956235\pi\) | ||||
−0.955215 | + | 0.295912i | \(0.904377\pi\) | |||||||
\(488\) | 107.848i | 0.0100042i | ||||||||
\(489\) | 1784.12 | 0.164992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7072.54 | −0.650060 | −0.325030 | − | 0.945704i | \(-0.605374\pi\) | ||||
−0.325030 | + | 0.945704i | \(0.605374\pi\) | |||||||
\(492\) | 11846.2i | 1.08550i | ||||||||
\(493\) | − 1894.15i | − 0.173039i | ||||||||
\(494\) | −72.3576 | −0.00659012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1763.86 | −0.159677 | ||||||||
\(497\) | − 7030.15i | − 0.634498i | ||||||||
\(498\) | − 18143.4i | − 1.63258i | ||||||||
\(499\) | 18473.9 | 1.65732 | 0.828661 | − | 0.559751i | \(-0.189103\pi\) | ||||
0.828661 | + | 0.559751i | \(0.189103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2785.49 | 0.248397 | ||||||||
\(502\) | 7577.28i | 0.673687i | ||||||||
\(503\) | − 11379.2i | − 1.00869i | −0.863501 | − | 0.504347i | \(-0.831733\pi\) | ||||
0.863501 | − | 0.504347i | \(-0.168267\pi\) | |||||||
\(504\) | 1293.46 | 0.114316 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4264.90 | −0.374700 | ||||||||
\(507\) | − 6565.11i | − 0.575082i | ||||||||
\(508\) | 10576.5i | 0.923730i | ||||||||
\(509\) | −6064.48 | −0.528101 | −0.264051 | − | 0.964509i | \(-0.585059\pi\) | ||||
−0.264051 | + | 0.964509i | \(0.585059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7051.02 | 0.610408 | ||||||||
\(512\) | 2607.89i | 0.225105i | ||||||||
\(513\) | 146.767i | 0.0126314i | ||||||||
\(514\) | 16755.0 | 1.43780 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11315.5 | −0.965379 | ||||||||
\(517\) | − 1649.00i | − 0.140276i | ||||||||
\(518\) | − 6125.38i | − 0.519563i | ||||||||
\(519\) | 946.926 | 0.0800875 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2682.88 | 0.225603 | 0.112801 | − | 0.993618i | \(-0.464018\pi\) | ||||
0.112801 | + | 0.993618i | \(0.464018\pi\) | |||||||
\(522\) | − 11887.2i | − 0.996720i | ||||||||
\(523\) | 4309.02i | 0.360268i | 0.983642 | + | 0.180134i | \(0.0576532\pi\) | ||||
−0.983642 | + | 0.180134i | \(0.942347\pi\) | |||||||
\(524\) | 35039.6 | 2.92120 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33163.3 | 2.74903 | ||||||||
\(527\) | − 1587.52i | − 0.131221i | ||||||||
\(528\) | − 412.879i | − 0.0340308i | ||||||||
\(529\) | 9728.87 | 0.799611 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −750.467 | −0.0613323 | ||||||||
\(532\) | 476.817i | 0.0388584i | ||||||||
\(533\) | 925.720i | 0.0752296i | ||||||||
\(534\) | −4434.83 | −0.359389 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4229.25 | 0.340813 | ||||||||
\(537\) | − 4336.47i | − 0.348478i | ||||||||
\(538\) | 3693.31i | 0.295966i | ||||||||
\(539\) | 934.051 | 0.0746427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4081.47 | 0.324355 | 0.162178 | − | 0.986762i | \(-0.448148\pi\) | ||||
0.162178 | + | 0.986762i | \(0.448148\pi\) | |||||||
\(542\) | − 23136.0i | − 1.83354i | ||||||||
\(543\) | 5531.44i | 0.437158i | ||||||||
\(544\) | −1279.88 | −0.100872 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 279.537 | 0.0219104 | ||||||||
\(547\) | 8844.82i | 0.691366i | 0.938351 | + | 0.345683i | \(0.112353\pi\) | ||||
−0.938351 | + | 0.345683i | \(0.887647\pi\) | |||||||
\(548\) | 25778.2i | 2.00947i | ||||||||
\(549\) | 47.2762 | 0.00367522 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1584.51 | 0.122509 | ||||||||
\(552\) | 3041.32i | 0.234506i | ||||||||
\(553\) | − 6042.66i | − 0.464666i | ||||||||
\(554\) | −6337.80 | −0.486042 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21868.4 | −1.66803 | ||||||||
\(557\) | − 11144.7i | − 0.847787i | −0.905712 | − | 0.423894i | \(-0.860663\pi\) | ||||
0.905712 | − | 0.423894i | \(-0.139337\pi\) | |||||||
\(558\) | − 9962.90i | − 0.755848i | ||||||||
\(559\) | −884.249 | −0.0669047 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 371.603 | 0.0279663 | ||||||||
\(562\) | − 32181.8i | − 2.41549i | ||||||||
\(563\) | 21857.5i | 1.63621i | 0.575071 | + | 0.818104i | \(0.304975\pi\) | ||||
−0.575071 | + | 0.818104i | \(0.695025\pi\) | |||||||
\(564\) | −3252.05 | −0.242794 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20232.3 | 1.50252 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | − 20619.6i | − 1.52320i | ||||||||
\(569\) | −23496.4 | −1.73115 | −0.865573 | − | 0.500783i | \(-0.833046\pi\) | ||||
−0.865573 | + | 0.500783i | \(0.833046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11067.8 | 0.811164 | 0.405582 | − | 0.914059i | \(-0.367069\pi\) | ||||
0.405582 | + | 0.914059i | \(0.367069\pi\) | |||||||
\(572\) | 701.743i | 0.0512961i | ||||||||
\(573\) | 732.222i | 0.0533839i | ||||||||
\(574\) | 9994.72 | 0.726780 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7512.36 | −0.543429 | ||||||||
\(577\) | 20482.9i | 1.47784i | 0.673791 | + | 0.738922i | \(0.264665\pi\) | ||||
−0.673791 | + | 0.738922i | \(0.735335\pi\) | |||||||
\(578\) | 22070.1i | 1.58823i | ||||||||
\(579\) | 5199.10 | 0.373173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9343.07 | −0.667153 | ||||||||
\(582\) | 20754.0i | 1.47815i | ||||||||
\(583\) | 9715.60i | 0.690187i | ||||||||
\(584\) | 20680.8 | 1.46537 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34394.1 | 2.42458 | ||||||||
\(587\) | − 23444.3i | − 1.64847i | −0.566248 | − | 0.824235i | \(-0.691606\pi\) | ||||
0.566248 | − | 0.824235i | \(-0.308394\pi\) | |||||||
\(588\) | − 1842.08i | − 0.129194i | ||||||||
\(589\) | 1328.01 | 0.0929025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1074.69 | 0.0748000 | ||||||||
\(592\) | 1394.30i | 0.0967996i | ||||||||
\(593\) | − 4404.69i | − 0.305024i | −0.988302 | − | 0.152512i | \(-0.951264\pi\) | ||||
0.988302 | − | 0.152512i | \(-0.0487362\pi\) | |||||||
\(594\) | 2332.09 | 0.161089 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14706.2 | −1.01072 | ||||||||
\(597\) | − 9610.89i | − 0.658874i | ||||||||
\(598\) | 657.277i | 0.0449466i | ||||||||
\(599\) | −3327.05 | −0.226945 | −0.113472 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113472 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14244.8 | −0.966818 | −0.483409 | − | 0.875395i | \(-0.660602\pi\) | ||||
−0.483409 | + | 0.875395i | \(0.660602\pi\) | |||||||
\(602\) | 9546.97i | 0.646354i | ||||||||
\(603\) | − 1853.93i | − 0.125204i | ||||||||
\(604\) | −19298.8 | −1.30010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1316.81 | 0.0882704 | ||||||||
\(607\) | 11446.5i | 0.765402i | 0.923872 | + | 0.382701i | \(0.125006\pi\) | ||||
−0.923872 | + | 0.382701i | \(0.874994\pi\) | |||||||
\(608\) | − 1070.65i | − 0.0714156i | ||||||||
\(609\) | −6121.38 | −0.407308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −254.132 | −0.0168266 | ||||||||
\(612\) | − 732.852i | − 0.0484049i | ||||||||
\(613\) | 19436.4i | 1.28063i | 0.768111 | + | 0.640316i | \(0.221197\pi\) | ||||
−0.768111 | + | 0.640316i | \(0.778803\pi\) | |||||||
\(614\) | −42955.6 | −2.82337 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2739.59 | 0.179190 | ||||||||
\(617\) | − 20530.1i | − 1.33956i | −0.742558 | − | 0.669781i | \(-0.766388\pi\) | ||||
0.742558 | − | 0.669781i | \(-0.233612\pi\) | |||||||
\(618\) | − 17970.4i | − 1.16970i | ||||||||
\(619\) | −5833.35 | −0.378776 | −0.189388 | − | 0.981902i | \(-0.560650\pi\) | ||||
−0.189388 | + | 0.981902i | \(0.560650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1333.19 | 0.0861499 | ||||||||
\(622\) | 32071.4i | 2.06744i | ||||||||
\(623\) | 2283.74i | 0.146864i | ||||||||
\(624\) | −63.6301 | −0.00408212 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25346.4 | 1.61829 | ||||||||
\(627\) | 310.856i | 0.0197997i | ||||||||
\(628\) | 31885.9i | 2.02609i | ||||||||
\(629\) | −1254.91 | −0.0795493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24776.6 | 1.56314 | 0.781568 | − | 0.623820i | \(-0.214420\pi\) | ||||
0.781568 | + | 0.623820i | \(0.214420\pi\) | |||||||
\(632\) | − 17723.2i | − 1.11549i | ||||||||
\(633\) | − 14829.5i | − 0.931152i | ||||||||
\(634\) | −16166.2 | −1.01268 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19160.5 | 1.19460 | ||||||||
\(637\) | − 143.949i | − 0.00895366i | ||||||||
\(638\) | − 25177.4i | − 1.56235i | ||||||||
\(639\) | −9038.77 | −0.559574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27219.4 | 1.67723 | 0.838613 | − | 0.544728i | \(-0.183367\pi\) | ||||
0.838613 | + | 0.544728i | \(0.183367\pi\) | |||||||
\(642\) | 23730.1i | 1.45881i | ||||||||
\(643\) | − 7091.79i | − 0.434950i | −0.976066 | − | 0.217475i | \(-0.930218\pi\) | ||||
0.976066 | − | 0.217475i | \(-0.0697821\pi\) | |||||||
\(644\) | 4331.28 | 0.265026 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 160.049 | 0.00974777 | ||||||||
\(647\) | 27773.0i | 1.68758i | 0.536670 | + | 0.843792i | \(0.319682\pi\) | ||||
−0.536670 | + | 0.843792i | \(0.680318\pi\) | |||||||
\(648\) | − 1663.02i | − 0.100817i | ||||||||
\(649\) | −1589.51 | −0.0961382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5130.46 | −0.308876 | ||||||||
\(652\) | − 7452.37i | − 0.447634i | ||||||||
\(653\) | − 21380.4i | − 1.28129i | −0.767839 | − | 0.640643i | \(-0.778668\pi\) | ||||
0.767839 | − | 0.640643i | \(-0.221332\pi\) | |||||||
\(654\) | −6482.09 | −0.387568 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2275.06 | −0.135406 | ||||||||
\(657\) | − 9065.59i | − 0.538329i | ||||||||
\(658\) | 2743.78i | 0.162559i | ||||||||
\(659\) | 17232.3 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26577.7 | 1.56392 | 0.781962 | − | 0.623326i | \(-0.214219\pi\) | ||||
0.781962 | + | 0.623326i | \(0.214219\pi\) | |||||||
\(662\) | − 19890.1i | − 1.16775i | ||||||||
\(663\) | − 57.2689i | − 0.00335466i | ||||||||
\(664\) | −27403.4 | −1.60159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7875.49 | −0.458212 | ||||||||
\(667\) | − 14393.2i | − 0.835544i | ||||||||
\(668\) | − 11635.1i | − 0.673917i | ||||||||
\(669\) | −9480.44 | −0.547885 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 100.132 | 0.00576090 | ||||||||
\(672\) | 4136.22i | 0.237438i | ||||||||
\(673\) | 31695.2i | 1.81540i | 0.419624 | + | 0.907698i | \(0.362162\pi\) | ||||
−0.419624 | + | 0.907698i | \(0.637838\pi\) | |||||||
\(674\) | −10642.9 | −0.608231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27422.7 | −1.56024 | ||||||||
\(677\) | 20440.3i | 1.16039i | 0.814477 | + | 0.580195i | \(0.197024\pi\) | ||||
−0.814477 | + | 0.580195i | \(0.802976\pi\) | |||||||
\(678\) | − 22315.5i | − 1.26405i | ||||||||
\(679\) | 10687.4 | 0.604044 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10953.3 | −0.616348 | ||||||||
\(682\) | − 21101.7i | − 1.18479i | ||||||||
\(683\) | 22896.9i | 1.28276i | 0.767223 | + | 0.641381i | \(0.221638\pi\) | ||||
−0.767223 | + | 0.641381i | \(0.778362\pi\) | |||||||
\(684\) | 613.051 | 0.0342699 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1554.18 | −0.0864997 | ||||||||
\(687\) | − 12251.1i | − 0.680361i | ||||||||
\(688\) | − 2173.14i | − 0.120422i | ||||||||
\(689\) | 1497.30 | 0.0827904 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23764.0 | −1.30829 | −0.654143 | − | 0.756371i | \(-0.726971\pi\) | ||||
−0.654143 | + | 0.756371i | \(0.726971\pi\) | |||||||
\(692\) | − 3955.35i | − 0.217283i | ||||||||
\(693\) | − 1200.92i | − 0.0658287i | ||||||||
\(694\) | −2530.34 | −0.138401 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17954.1 | −0.977800 | ||||||||
\(697\) | − 2047.62i | − 0.111276i | ||||||||
\(698\) | − 14653.2i | − 0.794600i | ||||||||
\(699\) | 11047.5 | 0.597791 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26259.5 | 1.41485 | 0.707423 | − | 0.706791i | \(-0.249858\pi\) | ||||
0.707423 | + | 0.706791i | \(0.249858\pi\) | |||||||
\(702\) | − 359.405i | − 0.0193232i | ||||||||
\(703\) | − 1049.77i | − 0.0563196i | ||||||||
\(704\) | −15911.4 | −0.851822 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34057.6 | −1.81554 | ||||||||
\(707\) | − 678.101i | − 0.0360716i | ||||||||
\(708\) | 3134.73i | 0.166399i | ||||||||
\(709\) | −12783.0 | −0.677116 | −0.338558 | − | 0.940945i | \(-0.609939\pi\) | ||||
−0.338558 | + | 0.940945i | \(0.609939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7769.14 | −0.409797 | ||||||||
\(712\) | 6698.26i | 0.352567i | ||||||||
\(713\) | − 12063.3i | − 0.633623i | ||||||||
\(714\) | −618.315 | −0.0324087 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18113.6 | −0.945444 | ||||||||
\(717\) | 7976.35i | 0.415456i | ||||||||
\(718\) | 29804.7i | 1.54916i | ||||||||
\(719\) | 27609.0 | 1.43205 | 0.716025 | − | 0.698075i | \(-0.245960\pi\) | ||||
0.716025 | + | 0.698075i | \(0.245960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9253.95 | −0.477996 | ||||||||
\(722\) | − 30945.1i | − 1.59509i | ||||||||
\(723\) | 14461.2i | 0.743868i | ||||||||
\(724\) | 23105.1 | 1.18604 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13153.4 | −0.672407 | ||||||||
\(727\) | 31306.2i | 1.59709i | 0.601937 | + | 0.798544i | \(0.294396\pi\) | ||||
−0.601937 | + | 0.798544i | \(0.705604\pi\) | |||||||
\(728\) | − 422.206i | − 0.0214945i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1955.89 | 0.0989621 | ||||||||
\(732\) | − 197.475i | − 0.00997113i | ||||||||
\(733\) | 15765.8i | 0.794441i | 0.917723 | + | 0.397220i | \(0.130025\pi\) | ||||
−0.917723 | + | 0.397220i | \(0.869975\pi\) | |||||||
\(734\) | −37640.8 | −1.89285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9725.53 | −0.487076 | ||||||||
\(737\) | − 3926.68i | − 0.196256i | ||||||||
\(738\) | − 12850.4i | − 0.640959i | ||||||||
\(739\) | −3966.51 | −0.197443 | −0.0987216 | − | 0.995115i | \(-0.531475\pi\) | ||||
−0.0987216 | + | 0.995115i | \(0.531475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 47.9070 | 0.00237504 | ||||||||
\(742\) | − 16165.9i | − 0.799823i | ||||||||
\(743\) | − 8224.50i | − 0.406094i | −0.979169 | − | 0.203047i | \(-0.934916\pi\) | ||||
0.979169 | − | 0.203047i | \(-0.0650844\pi\) | |||||||
\(744\) | −15047.7 | −0.741500 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20621.6 | −1.01208 | ||||||||
\(747\) | 12012.5i | 0.588373i | ||||||||
\(748\) | − 1552.20i | − 0.0758745i | ||||||||
\(749\) | 12220.0 | 0.596140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18929.2 | 0.919754 | 0.459877 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459877 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(752\) | − 624.558i | − 0.0302863i | ||||||||
\(753\) | − 5016.82i | − 0.242793i | ||||||||
\(754\) | −3880.16 | −0.187410 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2368.38 | −0.113938 | ||||||||
\(757\) | − 34906.8i | − 1.67597i | −0.545695 | − | 0.837984i | \(-0.683734\pi\) | ||||
0.545695 | − | 0.837984i | \(-0.316266\pi\) | |||||||
\(758\) | 8102.96i | 0.388276i | ||||||||
\(759\) | 2823.74 | 0.135040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13683.4 | −0.651803 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(762\) | − 11473.0i | − 0.545438i | ||||||||
\(763\) | 3337.99i | 0.158379i | ||||||||
\(764\) | 3058.52 | 0.144834 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6155.42 | −0.290345 | ||||||||
\(767\) | 244.964i | 0.0115321i | ||||||||
\(768\) | 9960.28i | 0.467982i | ||||||||
\(769\) | −41837.3 | −1.96189 | −0.980943 | − | 0.194294i | \(-0.937758\pi\) | ||||
−0.980943 | + | 0.194294i | \(0.937758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11093.2 | −0.518175 | ||||||||
\(772\) | − 21716.9i | − 1.01245i | ||||||||
\(773\) | − 19640.0i | − 0.913843i | −0.889507 | − | 0.456921i | \(-0.848952\pi\) | ||||
0.889507 | − | 0.456921i | \(-0.151048\pi\) | |||||||
\(774\) | 12274.7 | 0.570031 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 31346.4 | 1.45009 | ||||||||
\(777\) | 4055.53i | 0.187248i | ||||||||
\(778\) | − 44054.1i | − 2.03010i | ||||||||
\(779\) | 1712.89 | 0.0787814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19144.4 | −0.877131 | ||||||||
\(782\) | − 1453.85i | − 0.0664827i | ||||||||
\(783\) | 7870.34i | 0.359212i | ||||||||
\(784\) | 353.772 | 0.0161157 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −38009.9 | −1.72489 | ||||||||
\(787\) | 24935.3i | 1.12941i | 0.825293 | + | 0.564705i | \(0.191010\pi\) | ||||
−0.825293 | + | 0.564705i | \(0.808990\pi\) | |||||||
\(788\) | − 4489.02i | − 0.202938i | ||||||||
\(789\) | −21957.0 | −0.990736 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11491.5 | −0.516551 | ||||||||
\(792\) | − 3522.33i | − 0.158031i | ||||||||
\(793\) | − 15.4317i | 0 0.000691041i | ||||||||
\(794\) | 21695.2 | 0.969692 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40145.1 | −1.78757 | ||||||||
\(797\) | − 1168.33i | − 0.0519251i | −0.999663 | − | 0.0259625i | \(-0.991735\pi\) | ||||
0.999663 | − | 0.0259625i | \(-0.00826506\pi\) | |||||||
\(798\) | − 517.237i | − 0.0229448i | ||||||||
\(799\) | 562.120 | 0.0248891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2936.24 | 0.129522 | ||||||||
\(802\) | 43867.7i | 1.93145i | ||||||||
\(803\) | − 19201.2i | − 0.843829i | ||||||||
\(804\) | −7743.95 | −0.339686 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3252.05 | −0.142120 | ||||||||
\(807\) | − 2445.29i | − 0.106665i | ||||||||
\(808\) | − 1988.88i | − 0.0865949i | ||||||||
\(809\) | 35175.7 | 1.52869 | 0.764345 | − | 0.644807i | \(-0.223062\pi\) | ||||
0.764345 | + | 0.644807i | \(0.223062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15256.5 | −0.660577 | −0.330288 | − | 0.943880i | \(-0.607146\pi\) | ||||
−0.330288 | + | 0.943880i | \(0.607146\pi\) | |||||||
\(812\) | 25569.3i | 1.10506i | ||||||||
\(813\) | 15318.1i | 0.660797i | ||||||||
\(814\) | −16680.5 | −0.718245 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 140.745 | 0.00603806 | ||||||||
\(817\) | 1636.16i | 0.0700635i | ||||||||
\(818\) | − 50354.7i | − 2.15233i | ||||||||
\(819\) | −185.078 | −0.00789639 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15971.9 | −0.678956 | −0.339478 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339478 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(822\) | − 27963.4i | − 1.18654i | ||||||||
\(823\) | − 2312.41i | − 0.0979409i | −0.998800 | − | 0.0489705i | \(-0.984406\pi\) | ||||
0.998800 | − | 0.0489705i | \(-0.0155940\pi\) | |||||||
\(824\) | −27142.0 | −1.14750 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2644.80 | 0.111410 | ||||||||
\(827\) | 10422.4i | 0.438238i | 0.975698 | + | 0.219119i | \(0.0703183\pi\) | ||||
−0.975698 | + | 0.219119i | \(0.929682\pi\) | |||||||
\(828\) | − 5568.79i | − 0.233731i | ||||||||
\(829\) | 13213.4 | 0.553584 | 0.276792 | − | 0.960930i | \(-0.410729\pi\) | ||||
0.276792 | + | 0.960930i | \(0.410729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4196.17 | 0.175167 | ||||||||
\(832\) | 2452.15i | 0.102179i | ||||||||
\(833\) | 318.405i | 0.0132438i | ||||||||
\(834\) | 23722.2 | 0.984929 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1298.46 | 0.0537179 | ||||||||
\(837\) | 6596.30i | 0.272403i | ||||||||
\(838\) | 5573.67i | 0.229761i | ||||||||
\(839\) | 10119.6 | 0.416409 | 0.208205 | − | 0.978085i | \(-0.433238\pi\) | ||||
0.208205 | + | 0.978085i | \(0.433238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60579.9 | 2.48390 | ||||||||
\(842\) | − 55988.7i | − 2.29157i | ||||||||
\(843\) | 21307.1i | 0.870530i | ||||||||
\(844\) | −61943.4 | −2.52628 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3527.72 | 0.143364 | ||||||||
\(847\) | 6773.41i | 0.274778i | ||||||||
\(848\) | 3679.79i | 0.149015i | ||||||||
\(849\) | −13395.5 | −0.541501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9535.80 | −0.384116 | ||||||||
\(852\) | 37755.3i | 1.51816i | ||||||||
\(853\) | − 35378.1i | − 1.42007i | −0.704165 | − | 0.710037i | \(-0.748678\pi\) | ||||
0.704165 | − | 0.710037i | \(-0.251322\pi\) | |||||||
\(854\) | −166.611 | −0.00667602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35841.4 | 1.43112 | ||||||||
\(857\) | 6697.57i | 0.266960i | 0.991052 | + | 0.133480i | \(0.0426152\pi\) | ||||
−0.991052 | + | 0.133480i | \(0.957385\pi\) | |||||||
\(858\) | − 761.230i | − 0.0302890i | ||||||||
\(859\) | 24298.4 | 0.965135 | 0.482568 | − | 0.875859i | \(-0.339704\pi\) | ||||
0.482568 | + | 0.875859i | \(0.339704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6617.37 | −0.261927 | ||||||||
\(862\) | − 33418.3i | − 1.32045i | ||||||||
\(863\) | − 24942.9i | − 0.983853i | −0.870637 | − | 0.491926i | \(-0.836293\pi\) | ||||
0.870637 | − | 0.491926i | \(-0.163707\pi\) | |||||||
\(864\) | 5318.00 | 0.209401 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3126.78 | −0.122693 | ||||||||
\(867\) | − 14612.3i | − 0.572388i | ||||||||
\(868\) | 21430.1i | 0.838002i | ||||||||
\(869\) | −16455.3 | −0.642355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −605.152 | −0.0235417 | ||||||||
\(872\) | 9790.39i | 0.380212i | ||||||||
\(873\) | − 13741.0i | − 0.532716i | ||||||||
\(874\) | 1216.18 | 0.0470686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −37867.4 | −1.46052 | ||||||||
\(877\) | − 16276.6i | − 0.626705i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) | ||||
0.949637 | − | 0.313353i | \(-0.101452\pi\) | |||||||
\(878\) | − 38101.3i | − 1.46453i | ||||||||
\(879\) | −22771.8 | −0.873806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26636.5 | 1.01862 | 0.509311 | − | 0.860582i | \(-0.329900\pi\) | ||||
0.509311 | + | 0.860582i | \(0.329900\pi\) | |||||||
\(882\) | 1998.23i | 0.0762855i | ||||||||
\(883\) | 21788.3i | 0.830392i | 0.909732 | + | 0.415196i | \(0.136287\pi\) | ||||
−0.909732 | + | 0.415196i | \(0.863713\pi\) | |||||||
\(884\) | −239.215 | −0.00910142 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29763.0 | 1.12856 | ||||||||
\(887\) | − 26813.2i | − 1.01499i | −0.861654 | − | 0.507496i | \(-0.830571\pi\) | ||||
0.861654 | − | 0.507496i | \(-0.169429\pi\) | |||||||
\(888\) | 11895.0i | 0.449514i | ||||||||
\(889\) | −5908.11 | −0.222893 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1544.04 | −0.0580554 | ||||||||
\(892\) | 39600.2i | 1.48645i | ||||||||
\(893\) | 470.229i | 0.0176211i | ||||||||
\(894\) | 15952.8 | 0.596803 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15445.2 | 0.575879 | ||||||||
\(897\) | − 435.174i | − 0.0161985i | ||||||||
\(898\) | − 13387.4i | − 0.497488i | ||||||||
\(899\) | 71214.2 | 2.64196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3311.91 | −0.122459 | ||||||||
\(902\) | − 27217.4i | − 1.00470i | ||||||||
\(903\) | − 6320.92i | − 0.232942i | ||||||||
\(904\) | −33704.8 | −1.24005 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20934.8 | 0.767672 | ||||||||
\(907\) | 15543.0i | 0.569014i | 0.958674 | + | 0.284507i | \(0.0918300\pi\) | ||||
−0.958674 | + | 0.284507i | \(0.908170\pi\) | |||||||
\(908\) | 45752.6i | 1.67219i | ||||||||
\(909\) | −871.844 | −0.0318122 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48711.1 | 1.77154 | 0.885768 | − | 0.464128i | \(-0.153632\pi\) | ||||
0.885768 | + | 0.464128i | \(0.153632\pi\) | |||||||
\(912\) | 117.737i | 0.00427485i | ||||||||
\(913\) | 25442.8i | 0.922273i | ||||||||
\(914\) | 36905.3 | 1.33558 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51173.3 | −1.84587 | ||||||||
\(917\) | 19573.4i | 0.704876i | ||||||||
\(918\) | 794.976i | 0.0285818i | ||||||||
\(919\) | −1030.47 | −0.0369883 | −0.0184941 | − | 0.999829i | \(-0.505887\pi\) | ||||
−0.0184941 | + | 0.999829i | \(0.505887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28440.4 | 1.01753 | ||||||||
\(922\) | 11306.3i | 0.403855i | ||||||||
\(923\) | 2950.40i | 0.105215i | ||||||||
\(924\) | −5016.30 | −0.178598 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26079.6 | −0.925518 | ||||||||
\(927\) | 11897.9i | 0.421553i | ||||||||
\(928\) | − 57413.6i | − 2.03092i | ||||||||
\(929\) | −879.756 | −0.0310698 | −0.0155349 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155349 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −266.354 | −0.00937638 | ||||||||
\(932\) | − 46146.0i | − 1.62185i | ||||||||
\(933\) | − 21234.0i | − 0.745092i | ||||||||
\(934\) | 18775.8 | 0.657776 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −542.836 | −0.0189564 | ||||||||
\(937\) | − 18668.1i | − 0.650864i | −0.945565 | − | 0.325432i | \(-0.894490\pi\) | ||||
0.945565 | − | 0.325432i | \(-0.105510\pi\) | |||||||
\(938\) | 6533.64i | 0.227432i | ||||||||
\(939\) | −16781.5 | −0.583221 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29613.4 | 1.02590 | 0.512948 | − | 0.858420i | \(-0.328553\pi\) | ||||
0.512948 | + | 0.858420i | \(0.328553\pi\) | |||||||
\(942\) | − 34588.8i | − 1.19635i | ||||||||
\(943\) | − 15559.5i | − 0.537313i | ||||||||
\(944\) | −602.028 | −0.0207567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25998.1 | 0.893521 | ||||||||
\(947\) | 20738.9i | 0.711640i | 0.934554 | + | 0.355820i | \(0.115798\pi\) | ||||
−0.934554 | + | 0.355820i | \(0.884202\pi\) | |||||||
\(948\) | 32452.0i | 1.11181i | ||||||||
\(949\) | −2959.15 | −0.101220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10703.4 | 0.364966 | ||||||||
\(952\) | 933.888i | 0.0317936i | ||||||||
\(953\) | 45776.5i | 1.55598i | 0.628279 | + | 0.777988i | \(0.283760\pi\) | ||||
−0.628279 | + | 0.777988i | \(0.716240\pi\) | |||||||
\(954\) | −20784.7 | −0.705377 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33317.5 | 1.12716 | ||||||||
\(957\) | 16669.6i | 0.563064i | ||||||||
\(958\) | 30657.4i | 1.03392i | ||||||||
\(959\) | −14399.9 | −0.484878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29895.1 | 1.00349 | ||||||||
\(962\) | 2570.68i | 0.0861561i | ||||||||
\(963\) | − 15711.4i | − 0.525746i | ||||||||
\(964\) | 60404.9 | 2.01817 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4698.44 | −0.156491 | ||||||||
\(967\) | 34461.0i | 1.14601i | 0.819552 | + | 0.573005i | \(0.194222\pi\) | ||||
−0.819552 | + | 0.573005i | \(0.805778\pi\) | |||||||
\(968\) | 19866.5i | 0.659643i | ||||||||
\(969\) | −105.967 | −0.00351304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22762.8 | −0.752309 | −0.376154 | − | 0.926557i | \(-0.622754\pi\) | ||||
−0.376154 | + | 0.926557i | \(0.622754\pi\) | |||||||
\(972\) | 3045.06i | 0.100484i | ||||||||
\(973\) | − 12215.9i | − 0.402490i | ||||||||
\(974\) | −28819.9 | −0.948099 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37.9251 | 0.00124381 | ||||||||
\(977\) | 4809.57i | 0.157494i | 0.996895 | + | 0.0787470i | \(0.0250919\pi\) | ||||
−0.996895 | + | 0.0787470i | \(0.974908\pi\) | |||||||
\(978\) | 8084.10i | 0.264316i | ||||||||
\(979\) | 6219.04 | 0.203025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4291.70 | 0.139677 | ||||||||
\(982\) | − 32046.6i | − 1.04139i | ||||||||
\(983\) | 27591.6i | 0.895256i | 0.894220 | + | 0.447628i | \(0.147731\pi\) | ||||
−0.894220 | + | 0.447628i | \(0.852269\pi\) | |||||||
\(984\) | −19408.9 | −0.628793 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8582.63 | 0.277207 | ||||||||
\(987\) | − 1816.62i | − 0.0585853i | ||||||||
\(988\) | − 200.109i | − 0.00644365i | ||||||||
\(989\) | 14862.4 | 0.477854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22263.4 | −0.713643 | −0.356822 | − | 0.934173i | \(-0.616140\pi\) | ||||
−0.356822 | + | 0.934173i | \(0.616140\pi\) | |||||||
\(992\) | − 48119.5i | − 1.54012i | ||||||||
\(993\) | 13169.0i | 0.420851i | ||||||||
\(994\) | 31854.5 | 1.01646 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 50176.8 | 1.59630 | ||||||||
\(997\) | 30378.2i | 0.964983i | 0.875901 | + | 0.482491i | \(0.160268\pi\) | ||||
−0.875901 | + | 0.482491i | \(0.839732\pi\) | |||||||
\(998\) | 83707.4i | 2.65502i | ||||||||
\(999\) | 5214.26 | 0.165137 |
(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 | 525.4.d.h.274.4 | 4 | ||
5.2 | odd | 4 | 525.4.a.k.1.1 | 2 | |||
5.3 | odd | 4 | 105.4.a.f.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 525.4.d.h.274.1 | 4 | ||
15.2 | even | 4 | 1575.4.a.w.1.2 | 2 | |||
15.8 | even | 4 | 315.4.a.i.1.1 | 2 | |||
20.3 | even | 4 | 1680.4.a.bg.1.2 | 2 | |||
35.13 | even | 4 | 735.4.a.p.1.2 | 2 | |||
105.83 | odd | 4 | 2205.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
315.4.a.i.1.1 | 2 | 15.8 | even | 4 | |||
525.4.a.k.1.1 | 2 | 5.2 | odd | 4 | |||
525.4.d.h.274.1 | 4 | 5.4 | even | 2 | inner | ||
525.4.d.h.274.4 | 4 | 1.1 | even | 1 | trivial | ||
735.4.a.p.1.2 | 2 | 35.13 | even | 4 | |||
1575.4.a.w.1.2 | 2 | 15.2 | even | 4 | |||
1680.4.a.bg.1.2 | 2 | 20.3 | even | 4 | |||
2205.4.a.z.1.1 | 2 | 105.83 | odd | 4 |