Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.a (trivial) |
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: | yes |
Analytic conductor: | \(130.099211563\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 55x^{6} + 80x^{5} + 969x^{4} - 866x^{3} - 5783x^{2} + 2328x + 9992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 735) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.78988\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.78988 | −0.986373 | −0.493187 | − | 0.869924i | \(-0.664168\pi\) | ||||
−0.493187 | + | 0.869924i | \(0.664168\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.216543 | −0.0270678 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.9232 | 1.01307 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 13.9494 | 0.441120 | ||||||||
\(11\) | −0.731118 | −0.0200400 | −0.0100200 | − | 0.999950i | \(-0.503190\pi\) | ||||
−0.0100200 | + | 0.999950i | \(0.503190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 63.9983 | 1.36538 | 0.682690 | − | 0.730708i | \(-0.260810\pi\) | ||||
0.682690 | + | 0.730708i | \(0.260810\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −62.2208 | −0.972199 | ||||||||
\(17\) | 29.6307 | 0.422735 | 0.211368 | − | 0.977407i | \(-0.432208\pi\) | ||||
0.211368 | + | 0.977407i | \(0.432208\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 43.7843 | 0.528674 | 0.264337 | − | 0.964430i | \(-0.414847\pi\) | ||||
0.264337 | + | 0.964430i | \(0.414847\pi\) | |||||||
\(20\) | 1.08271 | 0.0121051 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.03973 | 0.0197669 | ||||||||
\(23\) | −157.920 | −1.43167 | −0.715837 | − | 0.698268i | \(-0.753955\pi\) | ||||
−0.715837 | + | 0.698268i | \(0.753955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −178.548 | −1.34677 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −192.402 | −1.23201 | −0.616003 | − | 0.787744i | \(-0.711249\pi\) | ||||
−0.616003 | + | 0.787744i | \(0.711249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24.2100 | −0.140266 | −0.0701330 | − | 0.997538i | \(-0.522342\pi\) | ||||
−0.0701330 | + | 0.997538i | \(0.522342\pi\) | |||||||
\(32\) | −9.79689 | −0.0541207 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −82.6662 | −0.416975 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −62.1980 | −0.276359 | −0.138180 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138180 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(38\) | −122.153 | −0.521470 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −114.616 | −0.453060 | ||||||||
\(41\) | 65.8313 | 0.250759 | 0.125380 | − | 0.992109i | \(-0.459985\pi\) | ||||
0.125380 | + | 0.992109i | \(0.459985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 97.8275 | 0.346943 | 0.173472 | − | 0.984839i | \(-0.444502\pi\) | ||||
0.173472 | + | 0.984839i | \(0.444502\pi\) | |||||||
\(44\) | 0.158318 | 0.000542440 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 440.577 | 1.41216 | ||||||||
\(47\) | −432.364 | −1.34184 | −0.670922 | − | 0.741528i | \(-0.734102\pi\) | ||||
−0.670922 | + | 0.741528i | \(0.734102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −69.7471 | −0.197275 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.8584 | −0.0369579 | ||||||||
\(53\) | −301.048 | −0.780228 | −0.390114 | − | 0.920767i | \(-0.627564\pi\) | ||||
−0.390114 | + | 0.920767i | \(0.627564\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.65559 | 0.00896217 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 536.780 | 1.21522 | ||||||||
\(59\) | 350.512 | 0.773438 | 0.386719 | − | 0.922198i | \(-0.373608\pi\) | ||||
0.386719 | + | 0.922198i | \(0.373608\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 405.997 | 0.852173 | 0.426087 | − | 0.904682i | \(-0.359892\pi\) | ||||
0.426087 | + | 0.904682i | \(0.359892\pi\) | |||||||
\(62\) | 67.5432 | 0.138355 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 525.098 | 1.02558 | ||||||||
\(65\) | −319.992 | −0.610616 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 853.677 | 1.55662 | 0.778308 | − | 0.627883i | \(-0.216078\pi\) | ||||
0.778308 | + | 0.627883i | \(0.216078\pi\) | |||||||
\(68\) | −6.41631 | −0.0114425 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 214.879 | 0.359175 | 0.179588 | − | 0.983742i | \(-0.442524\pi\) | ||||
0.179588 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1132.86 | −1.81632 | −0.908162 | − | 0.418618i | \(-0.862515\pi\) | ||||
−0.908162 | + | 0.418618i | \(0.862515\pi\) | |||||||
\(74\) | 173.525 | 0.272593 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.48117 | −0.0143101 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51.4032 | 0.0732064 | 0.0366032 | − | 0.999330i | \(-0.488346\pi\) | ||||
0.0366032 | + | 0.999330i | \(0.488346\pi\) | |||||||
\(80\) | 311.104 | 0.434781 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −183.662 | −0.247342 | ||||||||
\(83\) | 1411.04 | 1.86604 | 0.933022 | − | 0.359820i | \(-0.117162\pi\) | ||||
0.933022 | + | 0.359820i | \(0.117162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −148.153 | −0.189053 | ||||||||
\(86\) | −272.928 | −0.342216 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.7596 | −0.0203020 | ||||||||
\(89\) | 266.685 | 0.317624 | 0.158812 | − | 0.987309i | \(-0.449234\pi\) | ||||
0.158812 | + | 0.987309i | \(0.449234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 34.1963 | 0.0387523 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1206.24 | 1.32356 | ||||||||
\(95\) | −218.921 | −0.236430 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −546.792 | −0.572354 | −0.286177 | − | 0.958177i | \(-0.592385\pi\) | ||||
−0.286177 | + | 0.958177i | \(0.592385\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.41357 | −0.00541357 | ||||||||
\(101\) | −968.034 | −0.953693 | −0.476847 | − | 0.878987i | \(-0.658220\pi\) | ||||
−0.476847 | + | 0.878987i | \(0.658220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 585.116 | 0.559740 | 0.279870 | − | 0.960038i | \(-0.409709\pi\) | ||||
0.279870 | + | 0.960038i | \(0.409709\pi\) | |||||||
\(104\) | 1467.05 | 1.38323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 839.889 | 0.769596 | ||||||||
\(107\) | −1673.12 | −1.51165 | −0.755825 | − | 0.654774i | \(-0.772764\pi\) | ||||
−0.755825 | + | 0.654774i | \(0.772764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1742.46 | 1.53117 | 0.765585 | − | 0.643334i | \(-0.222450\pi\) | ||||
0.765585 | + | 0.643334i | \(0.222450\pi\) | |||||||
\(110\) | −10.1987 | −0.00884005 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1436.28 | 1.19570 | 0.597850 | − | 0.801608i | \(-0.296022\pi\) | ||||
0.597850 | + | 0.801608i | \(0.296022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 789.598 | 0.640264 | ||||||||
\(116\) | 41.6633 | 0.0333478 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −977.889 | −0.762898 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.47 | −0.999598 | ||||||||
\(122\) | −1132.68 | −0.840561 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.24250 | 0.00379670 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −733.011 | −0.512159 | −0.256079 | − | 0.966656i | \(-0.582431\pi\) | ||||
−0.256079 | + | 0.966656i | \(0.582431\pi\) | |||||||
\(128\) | −1386.59 | −0.957487 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 892.740 | 0.602296 | ||||||||
\(131\) | 660.369 | 0.440433 | 0.220217 | − | 0.975451i | \(-0.429324\pi\) | ||||
0.220217 | + | 0.975451i | \(0.429324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2381.66 | −1.53540 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 679.230 | 0.428261 | ||||||||
\(137\) | −1102.19 | −0.687344 | −0.343672 | − | 0.939090i | \(-0.611671\pi\) | ||||
−0.343672 | + | 0.939090i | \(0.611671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −959.854 | −0.585711 | −0.292855 | − | 0.956157i | \(-0.594605\pi\) | ||||
−0.292855 | + | 0.956157i | \(0.594605\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −599.487 | −0.354281 | ||||||||
\(143\) | −46.7903 | −0.0273622 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 962.011 | 0.550970 | ||||||||
\(146\) | 3160.56 | 1.79157 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.4685 | 0.00748045 | ||||||||
\(149\) | 1408.20 | 0.774257 | 0.387129 | − | 0.922026i | \(-0.373467\pi\) | ||||
0.387129 | + | 0.922026i | \(0.373467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −926.239 | −0.499180 | −0.249590 | − | 0.968352i | \(-0.580296\pi\) | ||||
−0.249590 | + | 0.968352i | \(0.580296\pi\) | |||||||
\(152\) | 1003.68 | 0.535585 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 121.050 | 0.0627289 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2579.44 | 1.31122 | 0.655610 | − | 0.755099i | \(-0.272411\pi\) | ||||
0.655610 | + | 0.755099i | \(0.272411\pi\) | |||||||
\(158\) | −143.409 | −0.0722088 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 48.9844 | 0.0242035 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2004.72 | −0.963325 | −0.481662 | − | 0.876357i | \(-0.659967\pi\) | ||||
−0.481662 | + | 0.876357i | \(0.659967\pi\) | |||||||
\(164\) | −14.2553 | −0.00678751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3936.64 | −1.84062 | ||||||||
\(167\) | 895.797 | 0.415083 | 0.207541 | − | 0.978226i | \(-0.433454\pi\) | ||||
0.207541 | + | 0.978226i | \(0.433454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1898.78 | 0.864262 | ||||||||
\(170\) | 413.331 | 0.186477 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21.1838 | −0.00939101 | ||||||||
\(173\) | −1252.14 | −0.550279 | −0.275140 | − | 0.961404i | \(-0.588724\pi\) | ||||
−0.275140 | + | 0.961404i | \(0.588724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 45.4907 | 0.0194829 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −744.020 | −0.313296 | ||||||||
\(179\) | 4175.60 | 1.74357 | 0.871785 | − | 0.489889i | \(-0.162963\pi\) | ||||
0.871785 | + | 0.489889i | \(0.162963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1773.00 | −0.728098 | −0.364049 | − | 0.931380i | \(-0.618606\pi\) | ||||
−0.364049 | + | 0.931380i | \(0.618606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3620.02 | −1.45039 | ||||||||
\(185\) | 310.990 | 0.123592 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.6635 | −0.00847162 | ||||||||
\(188\) | 93.6252 | 0.0363208 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 610.766 | 0.233208 | ||||||||
\(191\) | −2864.67 | −1.08524 | −0.542619 | − | 0.839979i | \(-0.682567\pi\) | ||||
−0.542619 | + | 0.839979i | \(0.682567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1638.56 | 0.611119 | 0.305559 | − | 0.952173i | \(-0.401157\pi\) | ||||
0.305559 | + | 0.952173i | \(0.401157\pi\) | |||||||
\(194\) | 1525.49 | 0.564555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4927.04 | 1.78192 | 0.890958 | − | 0.454086i | \(-0.150034\pi\) | ||||
0.890958 | + | 0.454086i | \(0.150034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4727.29 | −1.68396 | −0.841982 | − | 0.539506i | \(-0.818611\pi\) | ||||
−0.841982 | + | 0.539506i | \(0.818611\pi\) | |||||||
\(200\) | 573.080 | 0.202614 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2700.70 | 0.940697 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −329.157 | −0.112143 | ||||||||
\(206\) | −1632.41 | −0.552113 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3982.02 | −1.32742 | ||||||||
\(209\) | −32.0115 | −0.0105946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4450.18 | −1.45196 | −0.725978 | − | 0.687718i | \(-0.758613\pi\) | ||||
−0.725978 | + | 0.687718i | \(0.758613\pi\) | |||||||
\(212\) | 65.1897 | 0.0211191 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4667.81 | 1.49105 | ||||||||
\(215\) | −489.138 | −0.155158 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4861.27 | −1.51031 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.791591 | −0.000242587 0 | ||||||||
\(221\) | 1896.31 | 0.577194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2400.22 | 0.720766 | 0.360383 | − | 0.932804i | \(-0.382646\pi\) | ||||
0.360383 | + | 0.932804i | \(0.382646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4007.06 | −1.17941 | ||||||||
\(227\) | −4793.00 | −1.40142 | −0.700710 | − | 0.713446i | \(-0.747133\pi\) | ||||
−0.700710 | + | 0.713446i | \(0.747133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2051.56 | 0.592014 | 0.296007 | − | 0.955186i | \(-0.404345\pi\) | ||||
0.296007 | + | 0.955186i | \(0.404345\pi\) | |||||||
\(230\) | −2202.89 | −0.631539 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4410.47 | −1.24811 | ||||||||
\(233\) | −5459.91 | −1.53515 | −0.767576 | − | 0.640958i | \(-0.778537\pi\) | ||||
−0.767576 | + | 0.640958i | \(0.778537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2161.82 | 0.600091 | ||||||||
\(236\) | −75.9009 | −0.0209353 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2381.20 | −0.644465 | −0.322233 | − | 0.946661i | \(-0.604433\pi\) | ||||
−0.322233 | + | 0.946661i | \(0.604433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1653.02 | −0.441828 | −0.220914 | − | 0.975293i | \(-0.570904\pi\) | ||||
−0.220914 | + | 0.975293i | \(0.570904\pi\) | |||||||
\(242\) | 3711.85 | 0.985977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −87.9157 | −0.0230665 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2802.12 | 0.721841 | ||||||||
\(248\) | −554.971 | −0.142100 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 348.736 | 0.0882239 | ||||||||
\(251\) | −1231.36 | −0.309652 | −0.154826 | − | 0.987942i | \(-0.549482\pi\) | ||||
−0.154826 | + | 0.987942i | \(0.549482\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 115.458 | 0.0286908 | ||||||||
\(254\) | 2045.02 | 0.505180 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −332.364 | −0.0811435 | ||||||||
\(257\) | −671.457 | −0.162974 | −0.0814871 | − | 0.996674i | \(-0.525967\pi\) | ||||
−0.0814871 | + | 0.996674i | \(0.525967\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 69.2919 | 0.0165281 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1842.35 | −0.434432 | ||||||||
\(263\) | 2703.80 | 0.633928 | 0.316964 | − | 0.948437i | \(-0.397336\pi\) | ||||
0.316964 | + | 0.948437i | \(0.397336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1505.24 | 0.348929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −184.858 | −0.0421342 | ||||||||
\(269\) | 3301.70 | 0.748358 | 0.374179 | − | 0.927357i | \(-0.377925\pi\) | ||||
0.374179 | + | 0.927357i | \(0.377925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2324.28 | −0.520995 | −0.260498 | − | 0.965474i | \(-0.583887\pi\) | ||||
−0.260498 | + | 0.965474i | \(0.583887\pi\) | |||||||
\(272\) | −1843.64 | −0.410983 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3074.97 | 0.677977 | ||||||||
\(275\) | −18.2779 | −0.00400801 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8571.17 | 1.85918 | 0.929588 | − | 0.368600i | \(-0.120163\pi\) | ||||
0.929588 | + | 0.368600i | \(0.120163\pi\) | |||||||
\(278\) | 2677.88 | 0.577729 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1009.22 | 0.214252 | 0.107126 | − | 0.994245i | \(-0.465835\pi\) | ||||
0.107126 | + | 0.994245i | \(0.465835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9099.63 | −1.91137 | −0.955684 | − | 0.294395i | \(-0.904882\pi\) | ||||
−0.955684 | + | 0.294395i | \(0.904882\pi\) | |||||||
\(284\) | −46.5305 | −0.00972209 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 130.540 | 0.0269894 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4035.02 | −0.821295 | ||||||||
\(290\) | −2683.90 | −0.543462 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 245.313 | 0.0491640 | ||||||||
\(293\) | 1843.00 | 0.367471 | 0.183736 | − | 0.982976i | \(-0.441181\pi\) | ||||
0.183736 | + | 0.982976i | \(0.441181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1752.56 | −0.345892 | ||||||||
\(296\) | −1425.78 | −0.279972 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3928.72 | −0.763707 | ||||||||
\(299\) | −10106.6 | −1.95478 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2584.10 | 0.492378 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2724.29 | −0.513977 | ||||||||
\(305\) | −2029.98 | −0.381103 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3479.16 | 0.646796 | 0.323398 | − | 0.946263i | \(-0.395175\pi\) | ||||
0.323398 | + | 0.946263i | \(0.395175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −337.716 | −0.0618741 | ||||||||
\(311\) | 9352.18 | 1.70519 | 0.852594 | − | 0.522574i | \(-0.175028\pi\) | ||||
0.852594 | + | 0.522574i | \(0.175028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8798.47 | −1.58888 | −0.794439 | − | 0.607343i | \(-0.792235\pi\) | ||||
−0.794439 | + | 0.607343i | \(0.792235\pi\) | |||||||
\(314\) | −7196.34 | −1.29335 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.1310 | −0.00198154 | ||||||||
\(317\) | −4292.39 | −0.760519 | −0.380260 | − | 0.924880i | \(-0.624165\pi\) | ||||
−0.380260 | + | 0.924880i | \(0.624165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 140.669 | 0.0246894 | ||||||||
\(320\) | −2625.49 | −0.458655 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1297.36 | 0.223489 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1599.96 | 0.273076 | ||||||||
\(326\) | 5592.94 | 0.950198 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1509.06 | 0.254037 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2894.70 | 0.480687 | 0.240343 | − | 0.970688i | \(-0.422740\pi\) | ||||
0.240343 | + | 0.970688i | \(0.422740\pi\) | |||||||
\(332\) | −305.550 | −0.0505098 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2499.17 | −0.409427 | ||||||||
\(335\) | −4268.38 | −0.696140 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3578.67 | −0.578464 | −0.289232 | − | 0.957259i | \(-0.593400\pi\) | ||||
−0.289232 | + | 0.957259i | \(0.593400\pi\) | |||||||
\(338\) | −5297.39 | −0.852485 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 32.0816 | 0.00511725 | ||||||||
\(341\) | 17.7004 | 0.00281093 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2242.52 | 0.351479 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3493.32 | 0.542781 | ||||||||
\(347\) | 5633.16 | 0.871481 | 0.435741 | − | 0.900072i | \(-0.356486\pi\) | ||||
0.435741 | + | 0.900072i | \(0.356486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3643.34 | 0.558807 | 0.279404 | − | 0.960174i | \(-0.409863\pi\) | ||||
0.279404 | + | 0.960174i | \(0.409863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.16268 | 0.00108458 | ||||||||
\(353\) | 11996.2 | 1.80877 | 0.904383 | − | 0.426721i | \(-0.140331\pi\) | ||||
0.904383 | + | 0.426721i | \(0.140331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1074.39 | −0.160628 | ||||||||
\(356\) | −57.7486 | −0.00859739 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11649.4 | −1.71981 | ||||||||
\(359\) | 3809.64 | 0.560070 | 0.280035 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280035 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4941.94 | −0.720504 | ||||||||
\(362\) | 4946.46 | 0.718177 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5664.32 | 0.812285 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11373.0 | −1.61761 | −0.808807 | − | 0.588074i | \(-0.799886\pi\) | ||||
−0.808807 | + | 0.588074i | \(0.799886\pi\) | |||||||
\(368\) | 9825.87 | 1.39187 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −867.626 | −0.121907 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11378.1 | 1.57945 | 0.789726 | − | 0.613460i | \(-0.210223\pi\) | ||||
0.789726 | + | 0.613460i | \(0.210223\pi\) | |||||||
\(374\) | 60.4387 | 0.00835618 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9911.16 | −1.35939 | ||||||||
\(377\) | −12313.4 | −1.68216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6703.78 | 0.908575 | 0.454287 | − | 0.890855i | \(-0.349894\pi\) | ||||
0.454287 | + | 0.890855i | \(0.349894\pi\) | |||||||
\(380\) | 47.4059 | 0.00639966 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7992.11 | 1.07045 | ||||||||
\(383\) | −1331.05 | −0.177581 | −0.0887904 | − | 0.996050i | \(-0.528300\pi\) | ||||
−0.0887904 | + | 0.996050i | \(0.528300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4571.39 | −0.602791 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 118.404 | 0.0154924 | ||||||||
\(389\) | −7343.70 | −0.957173 | −0.478586 | − | 0.878040i | \(-0.658851\pi\) | ||||
−0.478586 | + | 0.878040i | \(0.658851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4679.26 | −0.605219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13745.9 | −1.75763 | ||||||||
\(395\) | −257.016 | −0.0327389 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7022.99 | −0.887843 | −0.443921 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443921 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(398\) | 13188.6 | 1.66102 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1555.52 | −0.194440 | ||||||||
\(401\) | −1321.37 | −0.164554 | −0.0822769 | − | 0.996610i | \(-0.526219\pi\) | ||||
−0.0822769 | + | 0.996610i | \(0.526219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1549.40 | −0.191516 | ||||||||
\(404\) | 209.621 | 0.0258144 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.4741 | 0.00553824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7688.44 | −0.929509 | −0.464754 | − | 0.885440i | \(-0.653857\pi\) | ||||
−0.464754 | + | 0.885440i | \(0.653857\pi\) | |||||||
\(410\) | 918.309 | 0.110615 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −126.703 | −0.0151510 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7055.19 | −0.834520 | ||||||||
\(416\) | −626.984 | −0.0738953 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 89.3083 | 0.0104503 | ||||||||
\(419\) | −8557.89 | −0.997805 | −0.498903 | − | 0.866658i | \(-0.666263\pi\) | ||||
−0.498903 | + | 0.866658i | \(0.666263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5035.39 | −0.582922 | −0.291461 | − | 0.956583i | \(-0.594141\pi\) | ||||
−0.291461 | + | 0.956583i | \(0.594141\pi\) | |||||||
\(422\) | 12415.5 | 1.43217 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6900.98 | −0.790428 | ||||||||
\(425\) | 740.767 | 0.0845470 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 362.302 | 0.0409171 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1364.64 | 0.153043 | ||||||||
\(431\) | −12084.9 | −1.35060 | −0.675300 | − | 0.737543i | \(-0.735986\pi\) | ||||
−0.675300 | + | 0.737543i | \(0.735986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17171.7 | −1.90582 | −0.952911 | − | 0.303251i | \(-0.901928\pi\) | ||||
−0.952911 | + | 0.303251i | \(0.901928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −377.318 | −0.0414455 | ||||||||
\(437\) | −6914.39 | −0.756889 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −194.147 | −0.0211074 | −0.0105537 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105537 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(440\) | 83.7978 | 0.00907933 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5290.50 | −0.569329 | ||||||||
\(443\) | 9741.13 | 1.04473 | 0.522365 | − | 0.852722i | \(-0.325050\pi\) | ||||
0.522365 | + | 0.852722i | \(0.325050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1333.42 | −0.142046 | ||||||||
\(446\) | −6696.34 | −0.710944 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11654.8 | −1.22500 | −0.612499 | − | 0.790471i | \(-0.709836\pi\) | ||||
−0.612499 | + | 0.790471i | \(0.709836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.1304 | −0.00502522 | ||||||||
\(452\) | −311.017 | −0.0323650 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13371.9 | 1.38232 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13348.6 | 1.36634 | 0.683172 | − | 0.730258i | \(-0.260600\pi\) | ||||
0.683172 | + | 0.730258i | \(0.260600\pi\) | |||||||
\(458\) | −5723.63 | −0.583947 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −170.982 | −0.0173306 | ||||||||
\(461\) | −14731.8 | −1.48835 | −0.744174 | − | 0.667986i | \(-0.767157\pi\) | ||||
−0.744174 | + | 0.667986i | \(0.767157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6127.24 | −0.615026 | −0.307513 | − | 0.951544i | \(-0.599497\pi\) | ||||
−0.307513 | + | 0.951544i | \(0.599497\pi\) | |||||||
\(464\) | 11971.4 | 1.19776 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15232.5 | 1.51423 | ||||||||
\(467\) | −9314.99 | −0.923012 | −0.461506 | − | 0.887137i | \(-0.652691\pi\) | ||||
−0.461506 | + | 0.887137i | \(0.652691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6031.22 | −0.591914 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8034.87 | 0.783548 | ||||||||
\(473\) | −71.5234 | −0.00695275 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1094.61 | 0.105735 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6643.28 | 0.635683 | ||||||||
\(479\) | −12944.7 | −1.23478 | −0.617388 | − | 0.786659i | \(-0.711809\pi\) | ||||
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3980.57 | −0.377335 | ||||||||
\(482\) | 4611.75 | 0.435808 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 288.103 | 0.0270570 | ||||||||
\(485\) | 2733.96 | 0.255965 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3020.84 | 0.281083 | 0.140542 | − | 0.990075i | \(-0.455116\pi\) | ||||
0.140542 | + | 0.990075i | \(0.455116\pi\) | |||||||
\(488\) | 9306.75 | 0.863313 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1787.34 | −0.164280 | −0.0821400 | − | 0.996621i | \(-0.526175\pi\) | ||||
−0.0821400 | + | 0.996621i | \(0.526175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5701.01 | −0.520812 | ||||||||
\(494\) | −7817.59 | −0.712004 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1506.37 | 0.136367 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4646.59 | −0.416853 | −0.208427 | − | 0.978038i | \(-0.566834\pi\) | ||||
−0.208427 | + | 0.978038i | \(0.566834\pi\) | |||||||
\(500\) | 27.0678 | 0.00242102 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3435.35 | 0.305432 | ||||||||
\(503\) | 3776.03 | 0.334721 | 0.167361 | − | 0.985896i | \(-0.446476\pi\) | ||||
0.167361 | + | 0.985896i | \(0.446476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4840.17 | 0.426505 | ||||||||
\(506\) | −322.114 | −0.0282998 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 158.728 | 0.0138630 | ||||||||
\(509\) | −12236.2 | −1.06554 | −0.532772 | − | 0.846259i | \(-0.678850\pi\) | ||||
−0.532772 | + | 0.846259i | \(0.678850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12020.0 | 1.03752 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1873.29 | 0.160753 | ||||||||
\(515\) | −2925.58 | −0.250323 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 316.109 | 0.0268906 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7335.23 | −0.618599 | ||||||||
\(521\) | −6367.49 | −0.535441 | −0.267721 | − | 0.963497i | \(-0.586270\pi\) | ||||
−0.267721 | + | 0.963497i | \(0.586270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6786.42 | −0.567398 | −0.283699 | − | 0.958913i | \(-0.591562\pi\) | ||||
−0.283699 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(524\) | −142.998 | −0.0119216 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7543.28 | −0.625290 | ||||||||
\(527\) | −717.359 | −0.0592954 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12771.6 | 1.04969 | ||||||||
\(530\) | −4199.44 | −0.344174 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4213.09 | 0.342381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8365.59 | 0.676030 | ||||||||
\(536\) | 19569.0 | 1.57696 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9211.37 | −0.738160 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14729.1 | −1.17052 | −0.585262 | − | 0.810844i | \(-0.699008\pi\) | ||||
−0.585262 | + | 0.810844i | \(0.699008\pi\) | |||||||
\(542\) | 6484.46 | 0.513896 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −290.289 | −0.0228787 | ||||||||
\(545\) | −8712.31 | −0.684760 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12444.4 | 0.972734 | 0.486367 | − | 0.873755i | \(-0.338322\pi\) | ||||
0.486367 | + | 0.873755i | \(0.338322\pi\) | |||||||
\(548\) | 238.670 | 0.0186049 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.9934 | 0.00395339 | ||||||||
\(551\) | −8424.19 | −0.651330 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23912.6 | −1.83384 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 207.849 | 0.0158539 | ||||||||
\(557\) | 11188.3 | 0.851100 | 0.425550 | − | 0.904935i | \(-0.360081\pi\) | ||||
0.425550 | + | 0.904935i | \(0.360081\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6260.80 | 0.473709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2815.60 | −0.211332 | ||||||||
\(563\) | −22723.4 | −1.70103 | −0.850513 | − | 0.525954i | \(-0.823708\pi\) | ||||
−0.850513 | + | 0.525954i | \(0.823708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7181.41 | −0.534733 | ||||||||
\(566\) | 25386.9 | 1.88532 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4925.71 | 0.363870 | ||||||||
\(569\) | 16424.6 | 1.21011 | 0.605057 | − | 0.796182i | \(-0.293150\pi\) | ||||
0.605057 | + | 0.796182i | \(0.293150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24106.3 | −1.76676 | −0.883378 | − | 0.468660i | \(-0.844737\pi\) | ||||
−0.883378 | + | 0.468660i | \(0.844737\pi\) | |||||||
\(572\) | 10.1321 | 0.000740637 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3947.99 | −0.286335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15925.5 | −1.14902 | −0.574512 | − | 0.818496i | \(-0.694808\pi\) | ||||
−0.574512 | + | 0.818496i | \(0.694808\pi\) | |||||||
\(578\) | 11257.2 | 0.810103 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −208.316 | −0.0149136 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 220.101 | 0.0156358 | ||||||||
\(584\) | −25968.9 | −1.84007 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5141.75 | −0.362464 | ||||||||
\(587\) | −8033.03 | −0.564836 | −0.282418 | − | 0.959291i | \(-0.591136\pi\) | ||||
−0.282418 | + | 0.959291i | \(0.591136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1060.02 | −0.0741550 | ||||||||
\(590\) | 4889.45 | 0.341179 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3870.01 | 0.268676 | ||||||||
\(593\) | 5753.12 | 0.398402 | 0.199201 | − | 0.979959i | \(-0.436165\pi\) | ||||
0.199201 | + | 0.979959i | \(0.436165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −304.936 | −0.0209575 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28196.2 | 1.92814 | ||||||||
\(599\) | −17086.5 | −1.16550 | −0.582752 | − | 0.812650i | \(-0.698024\pi\) | ||||
−0.582752 | + | 0.812650i | \(0.698024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27943.6 | −1.89658 | −0.948290 | − | 0.317405i | \(-0.897189\pi\) | ||||
−0.948290 | + | 0.317405i | \(0.897189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 200.570 | 0.0135117 | ||||||||
\(605\) | 6652.33 | 0.447034 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18259.9 | 1.22100 | 0.610500 | − | 0.792016i | \(-0.290969\pi\) | ||||
0.610500 | + | 0.792016i | \(0.290969\pi\) | |||||||
\(608\) | −428.950 | −0.0286122 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5663.42 | 0.375910 | ||||||||
\(611\) | −27670.5 | −1.83213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17268.4 | 1.13779 | 0.568895 | − | 0.822410i | \(-0.307371\pi\) | ||||
0.568895 | + | 0.822410i | \(0.307371\pi\) | |||||||
\(614\) | −9706.46 | −0.637982 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27762.0 | −1.81144 | −0.905719 | − | 0.423878i | \(-0.860669\pi\) | ||||
−0.905719 | + | 0.423878i | \(0.860669\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11829.9 | −0.768147 | −0.384074 | − | 0.923302i | \(-0.625479\pi\) | ||||
−0.384074 | + | 0.923302i | \(0.625479\pi\) | |||||||
\(620\) | −26.2125 | −0.00169794 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26091.5 | −1.68195 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 24546.7 | 1.56723 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −558.559 | −0.0354919 | ||||||||
\(629\) | −1842.97 | −0.116827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1835.49 | 0.115800 | 0.0579000 | − | 0.998322i | \(-0.481560\pi\) | ||||
0.0579000 | + | 0.998322i | \(0.481560\pi\) | |||||||
\(632\) | 1178.33 | 0.0741634 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11975.3 | 0.750156 | ||||||||
\(635\) | 3665.05 | 0.229044 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −392.449 | −0.0243530 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6932.94 | 0.428201 | ||||||||
\(641\) | −21034.5 | −1.29612 | −0.648060 | − | 0.761589i | \(-0.724419\pi\) | ||||
−0.648060 | + | 0.761589i | \(0.724419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27368.9 | −1.67858 | −0.839288 | − | 0.543687i | \(-0.817028\pi\) | ||||
−0.839288 | + | 0.543687i | \(0.817028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3619.48 | −0.220444 | ||||||||
\(647\) | 6272.47 | 0.381138 | 0.190569 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190569 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −256.266 | −0.0154997 | ||||||||
\(650\) | −4463.70 | −0.269355 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 434.108 | 0.0260751 | ||||||||
\(653\) | −14081.2 | −0.843856 | −0.421928 | − | 0.906629i | \(-0.638647\pi\) | ||||
−0.421928 | + | 0.906629i | \(0.638647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3301.85 | −0.196968 | ||||||||
\(656\) | −4096.07 | −0.243788 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3490.76 | −0.206344 | −0.103172 | − | 0.994664i | \(-0.532899\pi\) | ||||
−0.103172 | + | 0.994664i | \(0.532899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30723.5 | 1.80787 | 0.903936 | − | 0.427667i | \(-0.140664\pi\) | ||||
0.903936 | + | 0.427667i | \(0.140664\pi\) | |||||||
\(662\) | −8075.89 | −0.474137 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32345.5 | 1.89044 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30384.1 | 1.76383 | ||||||||
\(668\) | −193.978 | −0.0112354 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11908.3 | 0.686653 | ||||||||
\(671\) | −296.831 | −0.0170776 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3435.85 | −0.196794 | −0.0983968 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983968 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(674\) | 9984.07 | 0.570581 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −411.168 | −0.0233937 | ||||||||
\(677\) | 19600.2 | 1.11270 | 0.556350 | − | 0.830948i | \(-0.312201\pi\) | ||||
0.556350 | + | 0.830948i | \(0.312201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3396.15 | −0.191524 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −49.3820 | −0.00277263 | ||||||||
\(683\) | −28431.7 | −1.59284 | −0.796418 | − | 0.604746i | \(-0.793274\pi\) | ||||
−0.796418 | + | 0.604746i | \(0.793274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5510.93 | 0.307389 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6086.90 | −0.337298 | ||||||||
\(689\) | −19266.6 | −1.06531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −853.786 | −0.0470037 | −0.0235019 | − | 0.999724i | \(-0.507482\pi\) | ||||
−0.0235019 | + | 0.999724i | \(0.507482\pi\) | |||||||
\(692\) | 271.141 | 0.0148949 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15715.9 | −0.859606 | ||||||||
\(695\) | 4799.27 | 0.261938 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1950.63 | 0.106005 | ||||||||
\(698\) | −10164.5 | −0.551192 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6952.79 | 0.374612 | 0.187306 | − | 0.982302i | \(-0.440024\pi\) | ||||
0.187306 | + | 0.982302i | \(0.440024\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2723.30 | −0.146104 | ||||||||
\(704\) | −383.909 | −0.0205527 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33468.1 | −1.78412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22740.2 | 1.20455 | 0.602275 | − | 0.798289i | \(-0.294261\pi\) | ||||
0.602275 | + | 0.798289i | \(0.294261\pi\) | |||||||
\(710\) | 2997.44 | 0.158439 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6113.27 | 0.321776 | ||||||||
\(713\) | 3823.23 | 0.200815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 233.952 | 0.0122368 | ||||||||
\(716\) | −904.196 | −0.0471947 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10628.5 | −0.552438 | ||||||||
\(719\) | −9318.04 | −0.483316 | −0.241658 | − | 0.970361i | \(-0.577691\pi\) | ||||
−0.241658 | + | 0.970361i | \(0.577691\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13787.4 | 0.710686 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 383.930 | 0.0197080 | ||||||||
\(725\) | −4810.05 | −0.246401 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19866.3 | −1.01348 | −0.506740 | − | 0.862099i | \(-0.669150\pi\) | ||||
−0.506740 | + | 0.862099i | \(0.669150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15802.8 | −0.801216 | ||||||||
\(731\) | 2898.70 | 0.146665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2009.24 | −0.101246 | −0.0506228 | − | 0.998718i | \(-0.516121\pi\) | ||||
−0.0506228 | + | 0.998718i | \(0.516121\pi\) | |||||||
\(734\) | 31729.3 | 1.59557 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1547.12 | 0.0774831 | ||||||||
\(737\) | −624.138 | −0.0311946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7608.18 | 0.378716 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(740\) | −67.3426 | −0.00334536 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19382.7 | 0.957040 | 0.478520 | − | 0.878077i | \(-0.341173\pi\) | ||||
0.478520 | + | 0.878077i | \(0.341173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7041.01 | −0.346258 | ||||||||
\(746\) | −31743.6 | −1.55793 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.69108 | 0.000229309 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35182.8 | 1.70951 | 0.854753 | − | 0.519035i | \(-0.173709\pi\) | ||||
0.854753 | + | 0.519035i | \(0.173709\pi\) | |||||||
\(752\) | 26902.0 | 1.30454 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34353.0 | 1.65923 | ||||||||
\(755\) | 4631.19 | 0.223240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32409.1 | 1.55605 | 0.778025 | − | 0.628234i | \(-0.216222\pi\) | ||||
0.778025 | + | 0.628234i | \(0.216222\pi\) | |||||||
\(758\) | −18702.8 | −0.896194 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5018.38 | −0.239521 | ||||||||
\(761\) | 3587.94 | 0.170910 | 0.0854551 | − | 0.996342i | \(-0.472766\pi\) | ||||
0.0854551 | + | 0.996342i | \(0.472766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 620.324 | 0.0293751 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3713.48 | 0.175161 | ||||||||
\(767\) | 22432.2 | 1.05604 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36593.9 | 1.71601 | 0.858003 | − | 0.513644i | \(-0.171705\pi\) | ||||
0.858003 | + | 0.513644i | \(0.171705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −354.818 | −0.0165417 | ||||||||
\(773\) | −3543.13 | −0.164861 | −0.0824306 | − | 0.996597i | \(-0.526268\pi\) | ||||
−0.0824306 | + | 0.996597i | \(0.526268\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −605.250 | −0.0280532 | ||||||||
\(776\) | −12534.2 | −0.579836 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20488.1 | 0.944130 | ||||||||
\(779\) | 2882.38 | 0.132570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −157.102 | −0.00719788 | ||||||||
\(782\) | 13054.6 | 0.596971 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12897.2 | −0.586396 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33793.1 | −1.53061 | −0.765307 | − | 0.643665i | \(-0.777413\pi\) | ||||
−0.765307 | + | 0.643665i | \(0.777413\pi\) | |||||||
\(788\) | −1066.92 | −0.0482326 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 717.044 | 0.0322928 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25983.1 | 1.16354 | ||||||||
\(794\) | 19593.3 | 0.875744 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1023.66 | 0.0455813 | ||||||||
\(797\) | 3931.05 | 0.174711 | 0.0873556 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873556 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12811.2 | −0.567245 | ||||||||
\(800\) | −244.922 | −0.0108241 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3686.47 | 0.162311 | ||||||||
\(803\) | 828.257 | 0.0363992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4322.65 | 0.188907 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22190.5 | −0.966160 | ||||||||
\(809\) | −32120.2 | −1.39590 | −0.697952 | − | 0.716144i | \(-0.745905\pi\) | ||||
−0.697952 | + | 0.716144i | \(0.745905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32260.5 | 1.39682 | 0.698410 | − | 0.715698i | \(-0.253891\pi\) | ||||
0.698410 | + | 0.715698i | \(0.253891\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −126.867 | −0.00546278 | ||||||||
\(815\) | 10023.6 | 0.430812 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4283.31 | 0.183420 | ||||||||
\(818\) | 21449.9 | 0.916843 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 71.2765 | 0.00303547 | ||||||||
\(821\) | −36937.2 | −1.57018 | −0.785090 | − | 0.619382i | \(-0.787383\pi\) | ||||
−0.785090 | + | 0.619382i | \(0.787383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36494.5 | −1.54571 | −0.772854 | − | 0.634584i | \(-0.781172\pi\) | ||||
−0.772854 | + | 0.634584i | \(0.781172\pi\) | |||||||
\(824\) | 13412.7 | 0.567057 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12606.3 | 0.530067 | 0.265034 | − | 0.964239i | \(-0.414617\pi\) | ||||
0.265034 | + | 0.964239i | \(0.414617\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6446.91 | 0.270097 | 0.135048 | − | 0.990839i | \(-0.456881\pi\) | ||||
0.135048 | + | 0.990839i | \(0.456881\pi\) | |||||||
\(830\) | 19683.2 | 0.823148 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33605.4 | 1.40031 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4478.98 | −0.185631 | ||||||||
\(836\) | 6.93185 | 0.000286774 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23875.5 | 0.984208 | ||||||||
\(839\) | 17728.9 | 0.729523 | 0.364762 | − | 0.931101i | \(-0.381150\pi\) | ||||
0.364762 | + | 0.931101i | \(0.381150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12629.6 | 0.517839 | ||||||||
\(842\) | 14048.2 | 0.574978 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 963.653 | 0.0393013 | ||||||||
\(845\) | −9493.92 | −0.386510 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 18731.4 | 0.758538 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2066.65 | −0.0833949 | ||||||||
\(851\) | 9822.28 | 0.395656 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33066.7 | 1.32730 | 0.663648 | − | 0.748045i | \(-0.269007\pi\) | ||||
0.663648 | + | 0.748045i | \(0.269007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38353.2 | −1.53141 | ||||||||
\(857\) | 3084.25 | 0.122936 | 0.0614680 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614680 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41474.0 | 1.64735 | 0.823675 | − | 0.567062i | \(-0.191920\pi\) | ||||
0.823675 | + | 0.567062i | \(0.191920\pi\) | |||||||
\(860\) | 105.919 | 0.00419979 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33715.5 | 1.33220 | ||||||||
\(863\) | −12327.0 | −0.486230 | −0.243115 | − | 0.969998i | \(-0.578169\pi\) | ||||
−0.243115 | + | 0.969998i | \(0.578169\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6260.69 | 0.246092 | ||||||||
\(866\) | 47907.1 | 1.87985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.5818 | −0.00146706 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54633.9 | 2.12537 | ||||||||
\(872\) | 39942.8 | 1.55119 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19290.4 | 0.746575 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6381.94 | 0.245727 | 0.122864 | − | 0.992424i | \(-0.460792\pi\) | ||||
0.122864 | + | 0.992424i | \(0.460792\pi\) | |||||||
\(878\) | 541.649 | 0.0208198 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −227.454 | −0.00871302 | ||||||||
\(881\) | −10276.4 | −0.392985 | −0.196492 | − | 0.980505i | \(-0.562955\pi\) | ||||
−0.196492 | + | 0.980505i | \(0.562955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38805.8 | −1.47896 | −0.739479 | − | 0.673180i | \(-0.764928\pi\) | ||||
−0.739479 | + | 0.673180i | \(0.764928\pi\) | |||||||
\(884\) | −410.633 | −0.0156234 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27176.6 | −1.03049 | ||||||||
\(887\) | 35174.4 | 1.33150 | 0.665750 | − | 0.746175i | \(-0.268112\pi\) | ||||
0.665750 | + | 0.746175i | \(0.268112\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3720.10 | 0.140110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −519.751 | −0.0195096 | ||||||||
\(893\) | −18930.7 | −0.709398 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20878.0 | −0.779748 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32515.6 | 1.20831 | ||||||||
\(899\) | 4658.06 | 0.172809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8920.25 | −0.329830 | ||||||||
\(902\) | 134.278 | 0.00495674 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32924.2 | 1.21133 | ||||||||
\(905\) | 8864.98 | 0.325615 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13194.2 | 0.483028 | 0.241514 | − | 0.970397i | \(-0.422356\pi\) | ||||
0.241514 | + | 0.970397i | \(0.422356\pi\) | |||||||
\(908\) | 1037.89 | 0.0379334 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25551.3 | 0.929255 | 0.464627 | − | 0.885506i | \(-0.346188\pi\) | ||||
0.464627 | + | 0.885506i | \(0.346188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1031.64 | −0.0373956 | ||||||||
\(914\) | −37240.9 | −1.34772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −444.251 | −0.0160245 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11116.4 | −0.399018 | −0.199509 | − | 0.979896i | \(-0.563935\pi\) | ||||
−0.199509 | + | 0.979896i | \(0.563935\pi\) | |||||||
\(920\) | 18100.1 | 0.648634 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41100.0 | 1.46807 | ||||||||
\(923\) | 13751.9 | 0.490410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1554.95 | −0.0552718 | ||||||||
\(926\) | 17094.3 | 0.606645 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1884.94 | 0.0666770 | ||||||||
\(929\) | −18019.7 | −0.636390 | −0.318195 | − | 0.948025i | \(-0.603077\pi\) | ||||
−0.318195 | + | 0.948025i | \(0.603077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1182.30 | 0.0415533 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25987.8 | 0.910434 | ||||||||
\(935\) | 108.318 | 0.00378862 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15659.4 | −0.545968 | −0.272984 | − | 0.962019i | \(-0.588011\pi\) | ||||
−0.272984 | + | 0.962019i | \(0.588011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −468.126 | −0.0162432 | ||||||||
\(941\) | −632.621 | −0.0219159 | −0.0109579 | − | 0.999940i | \(-0.503488\pi\) | ||||
−0.0109579 | + | 0.999940i | \(0.503488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10396.0 | −0.359005 | ||||||||
\(944\) | −21809.2 | −0.751936 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 199.542 | 0.00685801 | ||||||||
\(947\) | 47903.6 | 1.64378 | 0.821888 | − | 0.569649i | \(-0.192921\pi\) | ||||
0.821888 | + | 0.569649i | \(0.192921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −72501.4 | −2.47997 | ||||||||
\(950\) | −3053.83 | −0.104294 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16683.3 | 0.567079 | 0.283539 | − | 0.958961i | \(-0.408491\pi\) | ||||
0.283539 | + | 0.958961i | \(0.408491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14323.4 | 0.485333 | ||||||||
\(956\) | 515.632 | 0.0174443 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36114.2 | 1.21795 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29204.9 | −0.980325 | ||||||||
\(962\) | 11105.3 | 0.372193 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 357.950 | 0.0119593 | ||||||||
\(965\) | −8192.79 | −0.273301 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46024.1 | 1.53054 | 0.765272 | − | 0.643707i | \(-0.222604\pi\) | ||||
0.765272 | + | 0.643707i | \(0.222604\pi\) | |||||||
\(968\) | −30498.5 | −1.01267 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7627.44 | −0.252477 | ||||||||
\(971\) | −44399.5 | −1.46740 | −0.733701 | − | 0.679472i | \(-0.762209\pi\) | ||||
−0.733701 | + | 0.679472i | \(0.762209\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8427.80 | −0.277253 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25261.4 | −0.828482 | ||||||||
\(977\) | 42047.7 | 1.37689 | 0.688447 | − | 0.725287i | \(-0.258293\pi\) | ||||
0.688447 | + | 0.725287i | \(0.258293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −194.978 | −0.00636519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4986.47 | 0.162041 | ||||||||
\(983\) | −6415.09 | −0.208148 | −0.104074 | − | 0.994570i | \(-0.533188\pi\) | ||||
−0.104074 | + | 0.994570i | \(0.533188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24635.2 | −0.796897 | ||||||||
\(986\) | 15905.2 | 0.513715 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −606.779 | −0.0195387 | ||||||||
\(989\) | −15448.9 | −0.496709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46931.6 | −1.50437 | −0.752186 | − | 0.658951i | \(-0.771000\pi\) | ||||
−0.752186 | + | 0.658951i | \(0.771000\pi\) | |||||||
\(992\) | 237.183 | 0.00759129 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23636.4 | 0.753091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28929.1 | −0.918950 | −0.459475 | − | 0.888191i | \(-0.651962\pi\) | ||||
−0.459475 | + | 0.888191i | \(0.651962\pi\) | |||||||
\(998\) | 12963.4 | 0.411173 | ||||||||
\(999\) | 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 | 2205.4.a.cd.1.3 | 8 | ||
3.2 | odd | 2 | 735.4.a.bc.1.6 | yes | 8 | ||
7.6 | odd | 2 | 2205.4.a.ce.1.3 | 8 | |||
21.20 | even | 2 | 735.4.a.bb.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.4.a.bb.1.6 | ✓ | 8 | 21.20 | even | 2 | ||
735.4.a.bc.1.6 | yes | 8 | 3.2 | odd | 2 | ||
2205.4.a.cd.1.3 | 8 | 1.1 | even | 1 | trivial | ||
2205.4.a.ce.1.3 | 8 | 7.6 | odd | 2 |