Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(1349,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.1349");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.b (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: | \(36.7848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1349.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.1349 |
Dual form | 1350.3.b.a.1349.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.242641i | 0.0346630i | 0.999850 | + | 0.0173315i | \(0.00551706\pi\) | ||||
−0.999850 | + | 0.0173315i | \(0.994483\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.00000i | − 0.272727i | −0.990659 | − | 0.136364i | \(-0.956458\pi\) | ||||
0.990659 | − | 0.136364i | \(-0.0435416\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.48528i | 0.268099i | 0.990975 | + | 0.134049i | \(0.0427980\pi\) | ||||
−0.990975 | + | 0.134049i | \(0.957202\pi\) | |||||||
\(14\) | − 0.343146i | − 0.0245104i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −7.75736 | −0.456315 | −0.228158 | − | 0.973624i | \(-0.573270\pi\) | ||||
−0.228158 | + | 0.973624i | \(0.573270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.97056 | 0.472135 | 0.236067 | − | 0.971737i | \(-0.424141\pi\) | ||||
0.236067 | + | 0.971737i | \(0.424141\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264i | 0.192847i | ||||||||
\(23\) | −6.51472 | −0.283249 | −0.141624 | − | 0.989920i | \(-0.545232\pi\) | ||||
−0.141624 | + | 0.989920i | \(0.545232\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 4.92893i | − 0.189574i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.485281i | 0.0173315i | ||||||||
\(29\) | 7.02944i | 0.242394i | 0.992628 | + | 0.121197i | \(0.0386733\pi\) | ||||
−0.992628 | + | 0.121197i | \(0.961327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.2132 | 0.942361 | 0.471181 | − | 0.882037i | \(-0.343828\pi\) | ||||
0.471181 | + | 0.882037i | \(0.343828\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.9706 | 0.322664 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.4558i | 0.985293i | 0.870230 | + | 0.492647i | \(0.163970\pi\) | ||||
−0.870230 | + | 0.492647i | \(0.836030\pi\) | |||||||
\(38\) | −12.6863 | −0.333850 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 57.2132i | − 1.39544i | −0.716369 | − | 0.697722i | \(-0.754197\pi\) | ||||
0.716369 | − | 0.697722i | \(-0.245803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0294i | 0.256499i | 0.991742 | + | 0.128249i | \(0.0409358\pi\) | ||||
−0.991742 | + | 0.128249i | \(0.959064\pi\) | |||||||
\(44\) | − 6.00000i | − 0.136364i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.21320 | 0.200287 | ||||||||
\(47\) | −6.51472 | −0.138611 | −0.0693055 | − | 0.997595i | \(-0.522078\pi\) | ||||
−0.0693055 | + | 0.997595i | \(0.522078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.9411 | 0.998798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.97056i | 0.134049i | ||||||||
\(53\) | −26.9117 | −0.507768 | −0.253884 | − | 0.967235i | \(-0.581708\pi\) | ||||
−0.253884 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 0.686292i | − 0.0122552i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 9.94113i | − 0.171399i | ||||||||
\(59\) | 84.9411i | 1.43968i | 0.694140 | + | 0.719840i | \(0.255785\pi\) | ||||
−0.694140 | + | 0.719840i | \(0.744215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.3675 | 0.940451 | 0.470226 | − | 0.882546i | \(-0.344173\pi\) | ||||
0.470226 | + | 0.882546i | \(0.344173\pi\) | |||||||
\(62\) | −41.3137 | −0.666350 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 97.0955i | 1.44919i | 0.689177 | + | 0.724593i | \(0.257972\pi\) | ||||
−0.689177 | + | 0.724593i | \(0.742028\pi\) | |||||||
\(68\) | −15.5147 | −0.228158 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 72.5147i | − 1.02133i | −0.859779 | − | 0.510667i | \(-0.829398\pi\) | ||||
0.859779 | − | 0.510667i | \(-0.170602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 106.912i | − 1.46454i | −0.681012 | − | 0.732272i | \(-0.738460\pi\) | ||||
0.681012 | − | 0.732272i | \(-0.261540\pi\) | |||||||
\(74\) | − 51.5563i | − 0.696707i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.9411 | 0.236067 | ||||||||
\(77\) | 0.727922 | 0.00945353 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 78.1838 | 0.989668 | 0.494834 | − | 0.868988i | \(-0.335229\pi\) | ||||
0.494834 | + | 0.868988i | \(0.335229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 80.9117i | 0.986728i | ||||||||
\(83\) | 25.8823 | 0.311834 | 0.155917 | − | 0.987770i | \(-0.450167\pi\) | ||||
0.155917 | + | 0.987770i | \(0.450167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 15.5980i | − 0.181372i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.48528i | 0.0964237i | ||||||||
\(89\) | 31.7574i | 0.356824i | 0.983956 | + | 0.178412i | \(0.0570960\pi\) | ||||
−0.983956 | + | 0.178412i | \(0.942904\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.845671 | −0.00929309 | ||||||||
\(92\) | −13.0294 | −0.141624 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.21320 | 0.0980128 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110.765i | 1.14190i | 0.820984 | + | 0.570951i | \(0.193425\pi\) | ||||
−0.820984 | + | 0.570951i | \(0.806575\pi\) | |||||||
\(98\) | −69.2132 | −0.706257 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 75.0366i | 0.742936i | 0.928446 | + | 0.371468i | \(0.121146\pi\) | ||||
−0.928446 | + | 0.371468i | \(0.878854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 61.0955i | − 0.593160i | −0.955008 | − | 0.296580i | \(-0.904154\pi\) | ||||
0.955008 | − | 0.296580i | \(-0.0958461\pi\) | |||||||
\(104\) | − 9.85786i | − 0.0947872i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 38.0589 | 0.359046 | ||||||||
\(107\) | −33.8528 | −0.316381 | −0.158191 | − | 0.987409i | \(-0.550566\pi\) | ||||
−0.158191 | + | 0.987409i | \(0.550566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.1472 | −0.175662 | −0.0878311 | − | 0.996135i | \(-0.527994\pi\) | ||||
−0.0878311 | + | 0.996135i | \(0.527994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.970563i | 0.00866574i | ||||||||
\(113\) | 26.7868 | 0.237051 | 0.118526 | − | 0.992951i | \(-0.462183\pi\) | ||||
0.118526 | + | 0.992951i | \(0.462183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 14.0589i | 0.121197i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 120.125i | − 1.01801i | ||||||||
\(119\) | − 1.88225i | − 0.0158172i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 112.000 | 0.925620 | ||||||||
\(122\) | −81.1299 | −0.665000 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 58.4264 | 0.471181 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 174.919i | 1.37731i | 0.725087 | + | 0.688657i | \(0.241799\pi\) | ||||
−0.725087 | + | 0.688657i | \(0.758201\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 149.735i | − 1.14302i | −0.820597 | − | 0.571508i | \(-0.806359\pi\) | ||||
0.820597 | − | 0.571508i | \(-0.193641\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.17662i | 0.0163656i | ||||||||
\(134\) | − 137.314i | − 1.02473i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.9411 | 0.161332 | ||||||||
\(137\) | 192.853 | 1.40768 | 0.703842 | − | 0.710356i | \(-0.251466\pi\) | ||||
0.703842 | + | 0.710356i | \(0.251466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 117.095 | 0.842413 | 0.421207 | − | 0.906965i | \(-0.361607\pi\) | ||||
0.421207 | + | 0.906965i | \(0.361607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 102.551i | 0.722192i | ||||||||
\(143\) | 10.4558 | 0.0731178 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 151.196i | 1.03559i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 72.9117i | 0.492647i | ||||||||
\(149\) | 140.007i | 0.939645i | 0.882761 | + | 0.469823i | \(0.155682\pi\) | ||||
−0.882761 | + | 0.469823i | \(0.844318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130.912 | 0.866965 | 0.433482 | − | 0.901162i | \(-0.357285\pi\) | ||||
0.433482 | + | 0.901162i | \(0.357285\pi\) | |||||||
\(152\) | −25.3726 | −0.166925 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.02944 | −0.00668466 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.706i | 0.979017i | 0.871999 | + | 0.489508i | \(0.162824\pi\) | ||||
−0.871999 | + | 0.489508i | \(0.837176\pi\) | |||||||
\(158\) | −110.569 | −0.699801 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.58074i | − 0.00981823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 182.302i | − 1.11841i | −0.829028 | − | 0.559207i | \(-0.811106\pi\) | ||||
0.829028 | − | 0.559207i | \(-0.188894\pi\) | |||||||
\(164\) | − 114.426i | − 0.697722i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.6030 | −0.220500 | ||||||||
\(167\) | 31.7208 | 0.189945 | 0.0949724 | − | 0.995480i | \(-0.469724\pi\) | ||||
0.0949724 | + | 0.995480i | \(0.469724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 156.853 | 0.928123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.0589i | 0.128249i | ||||||||
\(173\) | 331.154 | 1.91419 | 0.957093 | − | 0.289779i | \(-0.0935820\pi\) | ||||
0.957093 | + | 0.289779i | \(0.0935820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 12.0000i | − 0.0681818i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 44.9117i | − 0.252313i | ||||||||
\(179\) | 144.088i | 0.804963i | 0.915428 | + | 0.402481i | \(0.131852\pi\) | ||||
−0.915428 | + | 0.402481i | \(0.868148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46.6913 | −0.257963 | −0.128982 | − | 0.991647i | \(-0.541171\pi\) | ||||
−0.128982 | + | 0.991647i | \(0.541171\pi\) | |||||||
\(182\) | 1.19596 | 0.00657121 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.4264 | 0.100144 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.2721i | 0.124450i | ||||||||
\(188\) | −13.0294 | −0.0693055 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 298.441i | 1.56252i | 0.624208 | + | 0.781258i | \(0.285422\pi\) | ||||
−0.624208 | + | 0.781258i | \(0.714578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 66.9117i | 0.346693i | 0.984861 | + | 0.173346i | \(0.0554580\pi\) | ||||
−0.984861 | + | 0.173346i | \(0.944542\pi\) | |||||||
\(194\) | − 156.645i | − 0.807447i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.8823 | 0.499399 | ||||||||
\(197\) | 122.059 | 0.619588 | 0.309794 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309794 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −94.7868 | −0.476316 | −0.238158 | − | 0.971226i | \(-0.576544\pi\) | ||||
−0.238158 | + | 0.971226i | \(0.576544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 106.118i | − 0.525335i | ||||||||
\(203\) | −1.70563 | −0.00840211 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 86.4020i | 0.419427i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.9411i | 0.0670246i | ||||||||
\(209\) | − 26.9117i | − 0.128764i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 165.706 | 0.785335 | 0.392667 | − | 0.919681i | \(-0.371552\pi\) | ||||
0.392667 | + | 0.919681i | \(0.371552\pi\) | |||||||
\(212\) | −53.8234 | −0.253884 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 47.8751 | 0.223715 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.08831i | 0.0326650i | ||||||||
\(218\) | 27.0782 | 0.124212 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 27.0366i | − 0.122337i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 200.971i | 0.901213i | 0.892723 | + | 0.450607i | \(0.148792\pi\) | ||||
−0.892723 | + | 0.450607i | \(0.851208\pi\) | |||||||
\(224\) | − 1.37258i | − 0.00612760i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.8823 | −0.167621 | ||||||||
\(227\) | 349.441 | 1.53939 | 0.769693 | − | 0.638414i | \(-0.220409\pi\) | ||||
0.769693 | + | 0.638414i | \(0.220409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 172.515 | 0.753339 | 0.376670 | − | 0.926348i | \(-0.377069\pi\) | ||||
0.376670 | + | 0.926348i | \(0.377069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 19.8823i | − 0.0856994i | ||||||||
\(233\) | 148.243 | 0.636235 | 0.318117 | − | 0.948051i | \(-0.396949\pi\) | ||||
0.318117 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 169.882i | 0.719840i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.66190i | 0.0111845i | ||||||||
\(239\) | 141.603i | 0.592481i | 0.955113 | + | 0.296241i | \(0.0957330\pi\) | ||||
−0.955113 | + | 0.296241i | \(0.904267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 83.8528 | 0.347937 | 0.173968 | − | 0.984751i | \(-0.444341\pi\) | ||||
0.173968 | + | 0.984751i | \(0.444341\pi\) | |||||||
\(242\) | −158.392 | −0.654512 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 114.735 | 0.470226 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.2649i | 0.126579i | ||||||||
\(248\) | −82.6274 | −0.333175 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 202.529i | − 0.806888i | −0.915004 | − | 0.403444i | \(-0.867813\pi\) | ||||
0.915004 | − | 0.403444i | \(-0.132187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5442i | 0.0772496i | ||||||||
\(254\) | − 247.373i | − 0.973908i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −39.8894 | −0.155212 | −0.0776058 | − | 0.996984i | \(-0.524728\pi\) | ||||
−0.0776058 | + | 0.996984i | \(0.524728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.84567 | −0.0341532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 211.757i | 0.808234i | ||||||||
\(263\) | 295.014 | 1.12173 | 0.560864 | − | 0.827908i | \(-0.310469\pi\) | ||||
0.560864 | + | 0.827908i | \(0.310469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 3.07821i | − 0.0115722i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 194.191i | 0.724593i | ||||||||
\(269\) | 181.706i | 0.675486i | 0.941238 | + | 0.337743i | \(0.109663\pi\) | ||||
−0.941238 | + | 0.337743i | \(0.890337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −261.823 | −0.966138 | −0.483069 | − | 0.875582i | \(-0.660478\pi\) | ||||
−0.483069 | + | 0.875582i | \(0.660478\pi\) | |||||||
\(272\) | −31.0294 | −0.114079 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −272.735 | −0.995383 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 305.882i | − 1.10427i | −0.833755 | − | 0.552134i | \(-0.813814\pi\) | ||||
0.833755 | − | 0.552134i | \(-0.186186\pi\) | |||||||
\(278\) | −165.598 | −0.595676 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 558.323i | 1.98691i | 0.114205 | + | 0.993457i | \(0.463568\pi\) | ||||
−0.114205 | + | 0.993457i | \(0.536432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.97056i | 0.0316981i | 0.999874 | + | 0.0158491i | \(0.00504512\pi\) | ||||
−0.999874 | + | 0.0158491i | \(0.994955\pi\) | |||||||
\(284\) | − 145.029i | − 0.510667i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.7868 | −0.0517021 | ||||||||
\(287\) | 13.8823 | 0.0483702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −228.823 | −0.791776 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 213.823i | − 0.732272i | ||||||||
\(293\) | −146.683 | −0.500626 | −0.250313 | − | 0.968165i | \(-0.580533\pi\) | ||||
−0.250313 | + | 0.968165i | \(0.580533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 103.113i | − 0.348354i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 198.000i | − 0.664430i | ||||||||
\(299\) | − 22.7056i | − 0.0759386i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.67619 | −0.00889100 | ||||||||
\(302\) | −185.137 | −0.613037 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 35.8823 | 0.118034 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 343.640i | − 1.11935i | −0.828713 | − | 0.559674i | \(-0.810926\pi\) | ||||
0.828713 | − | 0.559674i | \(-0.189074\pi\) | |||||||
\(308\) | 1.45584 | 0.00472677 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 512.044i | − 1.64644i | −0.567720 | − | 0.823221i | \(-0.692175\pi\) | ||||
0.567720 | − | 0.823221i | \(-0.307825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 68.6173i | 0.219225i | 0.993974 | + | 0.109612i | \(0.0349609\pi\) | ||||
−0.993974 | + | 0.109612i | \(0.965039\pi\) | |||||||
\(314\) | − 217.373i | − 0.692269i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 156.368 | 0.494834 | ||||||||
\(317\) | 516.500 | 1.62934 | 0.814668 | − | 0.579928i | \(-0.196919\pi\) | ||||
0.814668 | + | 0.579928i | \(0.196919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.0883 | 0.0661076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.23550i | 0.00694254i | ||||||||
\(323\) | −69.5879 | −0.215442 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 257.813i | 0.790838i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 161.823i | 0.493364i | ||||||||
\(329\) | − 1.58074i | − 0.00480467i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −265.110 | −0.800936 | −0.400468 | − | 0.916311i | \(-0.631152\pi\) | ||||
−0.400468 | + | 0.916311i | \(0.631152\pi\) | |||||||
\(332\) | 51.7645 | 0.155917 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −44.8600 | −0.134311 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 72.4710i | 0.215047i | 0.994203 | + | 0.107524i | \(0.0342922\pi\) | ||||
−0.994203 | + | 0.107524i | \(0.965708\pi\) | |||||||
\(338\) | −221.823 | −0.656282 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 87.6396i | − 0.257008i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23.7645i | 0.0692843i | ||||||||
\(344\) | − 31.1960i | − 0.0906859i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −468.323 | −1.35353 | ||||||||
\(347\) | −529.706 | −1.52653 | −0.763265 | − | 0.646086i | \(-0.776405\pi\) | ||||
−0.763265 | + | 0.646086i | \(0.776405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −337.470 | −0.966963 | −0.483482 | − | 0.875355i | \(-0.660628\pi\) | ||||
−0.483482 | + | 0.875355i | \(0.660628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9706i | 0.0482118i | ||||||||
\(353\) | 490.087 | 1.38835 | 0.694175 | − | 0.719806i | \(-0.255769\pi\) | ||||
0.694175 | + | 0.719806i | \(0.255769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 63.5147i | 0.178412i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 203.772i | − 0.569195i | ||||||||
\(359\) | 370.955i | 1.03330i | 0.856196 | + | 0.516651i | \(0.172822\pi\) | ||||
−0.856196 | + | 0.516651i | \(0.827178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −280.529 | −0.777089 | ||||||||
\(362\) | 66.0315 | 0.182408 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.69134 | −0.00464654 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 393.823i | − 1.07309i | −0.843872 | − | 0.536544i | \(-0.819730\pi\) | ||||
0.843872 | − | 0.536544i | \(-0.180270\pi\) | |||||||
\(368\) | −26.0589 | −0.0708122 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.52987i | − 0.0176007i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 90.1177i | − 0.241603i | −0.992677 | − | 0.120801i | \(-0.961454\pi\) | ||||
0.992677 | − | 0.120801i | \(-0.0385464\pi\) | |||||||
\(374\) | − 32.9117i | − 0.0879992i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.4264 | 0.0490064 | ||||||||
\(377\) | −24.4996 | −0.0649856 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −327.051 | −0.862931 | −0.431466 | − | 0.902129i | \(-0.642003\pi\) | ||||
−0.431466 | + | 0.902129i | \(0.642003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 422.059i | − 1.10487i | ||||||||
\(383\) | −468.338 | −1.22281 | −0.611407 | − | 0.791316i | \(-0.709396\pi\) | ||||
−0.611407 | + | 0.791316i | \(0.709396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 94.6274i | − 0.245149i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 221.529i | 0.570951i | ||||||||
\(389\) | − 80.3818i | − 0.206637i | −0.994648 | − | 0.103319i | \(-0.967054\pi\) | ||||
0.994648 | − | 0.103319i | \(-0.0329461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.5370 | 0.129251 | ||||||||
\(392\) | −138.426 | −0.353129 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −172.617 | −0.438115 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 489.632i | − 1.23333i | −0.787226 | − | 0.616664i | \(-0.788484\pi\) | ||||
0.787226 | − | 0.616664i | \(-0.211516\pi\) | |||||||
\(398\) | 134.049 | 0.336806 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 263.418i | − 0.656904i | −0.944521 | − | 0.328452i | \(-0.893473\pi\) | ||||
0.944521 | − | 0.328452i | \(-0.106527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 101.816i | 0.252646i | ||||||||
\(404\) | 150.073i | 0.371468i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.41212 | 0.00594119 | ||||||||
\(407\) | 109.368 | 0.268716 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −170.411 | −0.416653 | −0.208327 | − | 0.978059i | \(-0.566802\pi\) | ||||
−0.208327 | + | 0.978059i | \(0.566802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 122.191i | − 0.296580i | ||||||||
\(413\) | −20.6102 | −0.0499036 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 19.7157i | − 0.0473936i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 38.0589i | 0.0910499i | ||||||||
\(419\) | 353.647i | 0.844026i | 0.906590 | + | 0.422013i | \(0.138676\pi\) | ||||
−0.906590 | + | 0.422013i | \(0.861324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −661.749 | −1.57185 | −0.785926 | − | 0.618321i | \(-0.787813\pi\) | ||||
−0.785926 | + | 0.618321i | \(0.787813\pi\) | |||||||
\(422\) | −234.343 | −0.555316 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 76.1177 | 0.179523 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.9197i | 0.0325988i | ||||||||
\(428\) | −67.7056 | −0.158191 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 757.544i | − 1.75764i | −0.477151 | − | 0.878822i | \(-0.658330\pi\) | ||||
0.477151 | − | 0.878822i | \(-0.341670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 293.294i | 0.677354i | 0.940903 | + | 0.338677i | \(0.109979\pi\) | ||||
−0.940903 | + | 0.338677i | \(0.890021\pi\) | |||||||
\(434\) | − 10.0244i | − 0.0230977i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.2944 | −0.0878311 | ||||||||
\(437\) | −58.4407 | −0.133732 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −441.831 | −1.00645 | −0.503224 | − | 0.864156i | \(-0.667853\pi\) | ||||
−0.503224 | + | 0.864156i | \(0.667853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 38.2355i | 0.0865057i | ||||||||
\(443\) | −46.3827 | −0.104701 | −0.0523507 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523507 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 284.215i | − 0.637254i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.94113i | 0.00433287i | ||||||||
\(449\) | 69.2132i | 0.154150i | 0.997025 | + | 0.0770748i | \(0.0245580\pi\) | ||||
−0.997025 | + | 0.0770748i | \(0.975442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −171.640 | −0.380576 | ||||||||
\(452\) | 53.5736 | 0.118526 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −494.184 | −1.08851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 189.382i | − 0.414402i | −0.978298 | − | 0.207201i | \(-0.933565\pi\) | ||||
0.978298 | − | 0.207201i | \(-0.0664354\pi\) | |||||||
\(458\) | −243.973 | −0.532691 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 615.058i | 1.33418i | 0.744976 | + | 0.667091i | \(0.232461\pi\) | ||||
−0.744976 | + | 0.667091i | \(0.767539\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 137.088i | − 0.296087i | −0.988981 | − | 0.148044i | \(-0.952702\pi\) | ||||
0.988981 | − | 0.148044i | \(-0.0472976\pi\) | |||||||
\(464\) | 28.1177i | 0.0605986i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −209.647 | −0.449886 | ||||||||
\(467\) | −337.118 | −0.721880 | −0.360940 | − | 0.932589i | \(-0.617544\pi\) | ||||
−0.360940 | + | 0.932589i | \(0.617544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.5593 | −0.0502331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 240.250i | − 0.509004i | ||||||||
\(473\) | 33.0883 | 0.0699541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 3.76450i | − 0.00790862i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 200.257i | − 0.418948i | ||||||||
\(479\) | 227.647i | 0.475254i | 0.971356 | + | 0.237627i | \(0.0763696\pi\) | ||||
−0.971356 | + | 0.237627i | \(0.923630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −127.059 | −0.264156 | ||||||||
\(482\) | −118.586 | −0.246029 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 224.000 | 0.462810 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 640.874i | − 1.31596i | −0.753034 | − | 0.657982i | \(-0.771410\pi\) | ||||
0.753034 | − | 0.657982i | \(-0.228590\pi\) | |||||||
\(488\) | −162.260 | −0.332500 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 610.118i | − 1.24260i | −0.783572 | − | 0.621301i | \(-0.786604\pi\) | ||||
0.783572 | − | 0.621301i | \(-0.213396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 54.5299i | − 0.110608i | ||||||||
\(494\) | − 44.2153i | − 0.0895046i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 116.853 | 0.235590 | ||||||||
\(497\) | 17.5950 | 0.0354025 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.2935 | −0.0867605 | −0.0433803 | − | 0.999059i | \(-0.513813\pi\) | ||||
−0.0433803 | + | 0.999059i | \(0.513813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 286.419i | 0.570556i | ||||||||
\(503\) | −303.765 | −0.603906 | −0.301953 | − | 0.953323i | \(-0.597638\pi\) | ||||
−0.301953 | + | 0.953323i | \(0.597638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 27.6396i | − 0.0546237i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 349.838i | 0.688657i | ||||||||
\(509\) | − 40.2426i | − 0.0790622i | −0.999218 | − | 0.0395311i | \(-0.987414\pi\) | ||||
0.999218 | − | 0.0395311i | \(-0.0125864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.9411 | 0.0507654 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 56.4121 | 0.109751 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5442i | 0.0378030i | ||||||||
\(518\) | 12.5097 | 0.0241499 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 88.5959i | 0.170050i | 0.996379 | + | 0.0850248i | \(0.0270970\pi\) | ||||
−0.996379 | + | 0.0850248i | \(0.972903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 711.647i | 1.36070i | 0.732887 | + | 0.680351i | \(0.238172\pi\) | ||||
−0.732887 | + | 0.680351i | \(0.761828\pi\) | |||||||
\(524\) | − 299.470i | − 0.571508i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −417.213 | −0.793181 | ||||||||
\(527\) | −226.617 | −0.430014 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −486.558 | −0.919770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.35325i | 0.00818280i | ||||||||
\(533\) | 199.404 | 0.374117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 274.627i | − 0.512365i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 256.971i | − 0.477640i | ||||||||
\(539\) | − 146.823i | − 0.272400i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 197.426 | 0.364929 | 0.182464 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182464 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(542\) | 370.274 | 0.683163 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 43.8823 | 0.0806659 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 453.470i | − 0.829013i | −0.910046 | − | 0.414507i | \(-0.863954\pi\) | ||||
0.910046 | − | 0.414507i | \(-0.136046\pi\) | |||||||
\(548\) | 385.706 | 0.703842 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 63.0580i | 0.114443i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.9706i | 0.0343048i | ||||||||
\(554\) | 432.583i | 0.780835i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 234.191 | 0.421207 | ||||||||
\(557\) | 156.978 | 0.281827 | 0.140914 | − | 0.990022i | \(-0.454996\pi\) | ||||
0.140914 | + | 0.990022i | \(0.454996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.4407 | −0.0687669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 789.588i | − 1.40496i | ||||||||
\(563\) | −699.323 | −1.24214 | −0.621068 | − | 0.783756i | \(-0.713301\pi\) | ||||
−0.621068 | + | 0.783756i | \(0.713301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 12.6863i | − 0.0224139i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 205.103i | 0.361096i | ||||||||
\(569\) | − 792.978i | − 1.39363i | −0.717249 | − | 0.696817i | \(-0.754599\pi\) | ||||
0.717249 | − | 0.696817i | \(-0.245401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −327.418 | −0.573412 | −0.286706 | − | 0.958019i | \(-0.592560\pi\) | ||||
−0.286706 | + | 0.958019i | \(0.592560\pi\) | |||||||
\(572\) | 20.9117 | 0.0365589 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.6325 | −0.0342029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 844.088i | − 1.46289i | −0.681900 | − | 0.731446i | \(-0.738846\pi\) | ||||
0.681900 | − | 0.731446i | \(-0.261154\pi\) | |||||||
\(578\) | 323.605 | 0.559870 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.28009i | 0.0108091i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 80.7351i | 0.138482i | ||||||||
\(584\) | 302.392i | 0.517794i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 207.442 | 0.353996 | ||||||||
\(587\) | −304.471 | −0.518690 | −0.259345 | − | 0.965785i | \(-0.583507\pi\) | ||||
−0.259345 | + | 0.965785i | \(0.583507\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 262.059 | 0.444922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145.823i | 0.246323i | ||||||||
\(593\) | −403.882 | −0.681083 | −0.340542 | − | 0.940229i | \(-0.610610\pi\) | ||||
−0.340542 | + | 0.940229i | \(0.610610\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 280.014i | 0.469823i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.1106i | 0.0536967i | ||||||||
\(599\) | 133.176i | 0.222330i | 0.993802 | + | 0.111165i | \(0.0354582\pi\) | ||||
−0.993802 | + | 0.111165i | \(0.964542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −263.294 | −0.438094 | −0.219047 | − | 0.975714i | \(-0.570295\pi\) | ||||
−0.219047 | + | 0.975714i | \(0.570295\pi\) | |||||||
\(602\) | 3.78470 | 0.00628688 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 261.823 | 0.433482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 613.449i | 1.01062i | 0.862937 | + | 0.505312i | \(0.168623\pi\) | ||||
−0.862937 | + | 0.505312i | \(0.831377\pi\) | |||||||
\(608\) | −50.7452 | −0.0834624 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 22.7056i | − 0.0371614i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 712.838i | 1.16287i | 0.813594 | + | 0.581434i | \(0.197508\pi\) | ||||
−0.813594 | + | 0.581434i | \(0.802492\pi\) | |||||||
\(614\) | 485.980i | 0.791498i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.05887 | −0.00334233 | ||||||||
\(617\) | 192.728 | 0.312363 | 0.156181 | − | 0.987728i | \(-0.450082\pi\) | ||||
0.156181 | + | 0.987728i | \(0.450082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 660.403 | 1.06689 | 0.533444 | − | 0.845836i | \(-0.320898\pi\) | ||||
0.533444 | + | 0.845836i | \(0.320898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 724.139i | 1.16421i | ||||||||
\(623\) | −7.70563 | −0.0123686 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 97.0395i | − 0.155015i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 307.411i | 0.489508i | ||||||||
\(629\) | − 282.801i | − 0.449604i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −128.971 | −0.204391 | −0.102195 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(632\) | −221.137 | −0.349900 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −730.441 | −1.15211 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 170.574i | 0.267776i | ||||||||
\(638\) | −29.8234 | −0.0467451 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 526.773i | 0.821798i | 0.911681 | + | 0.410899i | \(0.134785\pi\) | ||||
−0.911681 | + | 0.410899i | \(0.865215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 558.169i | − 0.868071i | −0.900896 | − | 0.434035i | \(-0.857089\pi\) | ||||
0.900896 | − | 0.434035i | \(-0.142911\pi\) | |||||||
\(644\) | − 3.16147i | − 0.00490912i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 98.4121 | 0.152341 | ||||||||
\(647\) | −990.131 | −1.53034 | −0.765171 | − | 0.643827i | \(-0.777346\pi\) | ||||
−0.765171 | + | 0.643827i | \(0.777346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 254.823 | 0.392640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 364.603i | − 0.559207i | ||||||||
\(653\) | 832.139 | 1.27433 | 0.637166 | − | 0.770726i | \(-0.280106\pi\) | ||||
0.637166 | + | 0.770726i | \(0.280106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 228.853i | − 0.348861i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.23550i | 0.00339741i | ||||||||
\(659\) | − 239.793i | − 0.363874i | −0.983310 | − | 0.181937i | \(-0.941763\pi\) | ||||
0.983310 | − | 0.181937i | \(-0.0582367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1053.01 | 1.59306 | 0.796531 | − | 0.604597i | \(-0.206666\pi\) | ||||
0.796531 | + | 0.604597i | \(0.206666\pi\) | |||||||
\(662\) | 374.922 | 0.566347 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −73.2061 | −0.110250 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 45.7948i | − 0.0686579i | ||||||||
\(668\) | 63.4416 | 0.0949724 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 172.103i | − 0.256487i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 721.912i | − 1.07268i | −0.844003 | − | 0.536339i | \(-0.819807\pi\) | ||||
0.844003 | − | 0.536339i | \(-0.180193\pi\) | |||||||
\(674\) | − 102.489i | − 0.152062i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 313.706 | 0.464062 | ||||||||
\(677\) | 538.419 | 0.795302 | 0.397651 | − | 0.917537i | \(-0.369826\pi\) | ||||
0.397651 | + | 0.917537i | \(0.369826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.8760 | −0.0395817 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 123.941i | 0.181732i | ||||||||
\(683\) | −335.412 | −0.491087 | −0.245543 | − | 0.969386i | \(-0.578966\pi\) | ||||
−0.245543 | + | 0.969386i | \(0.578966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − 33.6081i | − 0.0489914i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 44.1177i | 0.0641246i | ||||||||
\(689\) | − 93.7948i | − 0.136132i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 225.477 | 0.326306 | 0.163153 | − | 0.986601i | \(-0.447834\pi\) | ||||
0.163153 | + | 0.986601i | \(0.447834\pi\) | |||||||
\(692\) | 662.309 | 0.957093 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 749.117 | 1.07942 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 443.823i | 0.636762i | ||||||||
\(698\) | 477.255 | 0.683746 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 709.684i | 1.01239i | 0.862420 | + | 0.506194i | \(0.168948\pi\) | ||||
−0.862420 | + | 0.506194i | \(0.831052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 327.029i | 0.465191i | ||||||||
\(704\) | − 24.0000i | − 0.0340909i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −693.088 | −0.981711 | ||||||||
\(707\) | −18.2069 | −0.0257524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −663.867 | −0.936343 | −0.468171 | − | 0.883638i | \(-0.655087\pi\) | ||||
−0.468171 | + | 0.883638i | \(0.655087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 89.8234i | − 0.126156i | ||||||||
\(713\) | −190.316 | −0.266923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 288.177i | 0.402481i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 524.610i | − 0.730655i | ||||||||
\(719\) | − 402.161i | − 0.559334i | −0.960097 | − | 0.279667i | \(-0.909776\pi\) | ||||
0.960097 | − | 0.279667i | \(-0.0902241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.8242 | 0.0205607 | ||||||||
\(722\) | 396.728 | 0.549485 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −93.3827 | −0.128982 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 643.294i | 0.884860i | 0.896803 | + | 0.442430i | \(0.145884\pi\) | ||||
−0.896803 | + | 0.442430i | \(0.854116\pi\) | |||||||
\(728\) | 2.39192 | 0.00328560 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 85.5593i | − 0.117044i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 159.191i | − 0.217177i | −0.994087 | − | 0.108589i | \(-0.965367\pi\) | ||||
0.994087 | − | 0.108589i | \(-0.0346331\pi\) | |||||||
\(734\) | 556.950i | 0.758788i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.8528 | 0.0500718 | ||||||||
\(737\) | 291.286 | 0.395233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −115.272 | −0.155984 | −0.0779919 | − | 0.996954i | \(-0.524851\pi\) | ||||
−0.0779919 | + | 0.996954i | \(0.524851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.23463i | 0.0124456i | ||||||||
\(743\) | 93.0732 | 0.125267 | 0.0626334 | − | 0.998037i | \(-0.480050\pi\) | ||||
0.0626334 | + | 0.998037i | \(0.480050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 127.446i | 0.170839i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 46.5442i | 0.0622248i | ||||||||
\(749\) | − 8.21407i | − 0.0109667i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 109.823 | 0.146236 | 0.0731181 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731181 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(752\) | −26.0589 | −0.0346528 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.6476 | 0.0459518 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 305.573i | 0.403663i | 0.979420 | + | 0.201831i | \(0.0646893\pi\) | ||||
−0.979420 | + | 0.201831i | \(0.935311\pi\) | |||||||
\(758\) | 462.520 | 0.610184 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1323.79i | 1.73953i | 0.493462 | + | 0.869767i | \(0.335731\pi\) | ||||
−0.493462 | + | 0.869767i | \(0.664269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.64589i | − 0.00608897i | ||||||||
\(764\) | 596.881i | 0.781258i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 662.330 | 0.864661 | ||||||||
\(767\) | −296.044 | −0.385976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1383.79 | 1.79947 | 0.899735 | − | 0.436436i | \(-0.143759\pi\) | ||||
0.899735 | + | 0.436436i | \(0.143759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 133.823i | 0.173346i | ||||||||
\(773\) | 1058.56 | 1.36942 | 0.684708 | − | 0.728818i | \(-0.259930\pi\) | ||||
0.684708 | + | 0.728818i | \(0.259930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 313.289i | − 0.403723i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 113.677i | 0.146114i | ||||||||
\(779\) | − 513.235i | − 0.658838i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −217.544 | −0.278546 | ||||||||
\(782\) | −71.4701 | −0.0913940 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 195.765 | 0.249700 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1092.76i | 1.38852i | 0.719725 | + | 0.694259i | \(0.244268\pi\) | ||||
−0.719725 | + | 0.694259i | \(0.755732\pi\) | |||||||
\(788\) | 244.118 | 0.309794 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.49957i | 0.00821690i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 199.942i | 0.252134i | ||||||||
\(794\) | 692.444i | 0.872095i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −189.574 | −0.238158 | ||||||||
\(797\) | 464.029 | 0.582219 | 0.291110 | − | 0.956690i | \(-0.405976\pi\) | ||||
0.291110 | + | 0.956690i | \(0.405976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.5370 | 0.0632503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 372.530i | 0.464501i | ||||||||
\(803\) | −320.735 | −0.399421 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 143.990i | − 0.178648i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 212.235i | − 0.262668i | ||||||||
\(809\) | − 1324.26i | − 1.63691i | −0.574567 | − | 0.818457i | \(-0.694830\pi\) | ||||
0.574567 | − | 0.818457i | \(-0.305170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 527.433 | 0.650349 | 0.325174 | − | 0.945654i | \(-0.394577\pi\) | ||||
0.325174 | + | 0.945654i | \(0.394577\pi\) | |||||||
\(812\) | −3.41125 | −0.00420105 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −154.669 | −0.190011 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 98.9403i | 0.121102i | ||||||||
\(818\) | 240.998 | 0.294618 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 718.169i | 0.874750i | 0.899279 | + | 0.437375i | \(0.144092\pi\) | ||||
−0.899279 | + | 0.437375i | \(0.855908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 864.617i | − 1.05057i | −0.850927 | − | 0.525284i | \(-0.823959\pi\) | ||||
0.850927 | − | 0.525284i | \(-0.176041\pi\) | |||||||
\(824\) | 172.804i | 0.209714i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.1472 | 0.0352872 | ||||||||
\(827\) | 555.323 | 0.671491 | 0.335745 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335745 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 347.721 | 0.419446 | 0.209723 | − | 0.977761i | \(-0.432744\pi\) | ||||
0.209723 | + | 0.977761i | \(0.432744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.8823i | 0.0335123i | ||||||||
\(833\) | −379.654 | −0.455767 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 53.8234i | − 0.0643820i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 500.132i | − 0.596816i | ||||||||
\(839\) | − 529.721i | − 0.631372i | −0.948864 | − | 0.315686i | \(-0.897765\pi\) | ||||
0.948864 | − | 0.315686i | \(-0.102235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 791.587 | 0.941245 | ||||||||
\(842\) | 935.855 | 1.11147 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 331.411 | 0.392667 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.1758i | 0.0320847i | ||||||||
\(848\) | −107.647 | −0.126942 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 237.500i | − 0.279083i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 917.043i | − 1.07508i | −0.843238 | − | 0.537540i | \(-0.819354\pi\) | ||||
0.843238 | − | 0.537540i | \(-0.180646\pi\) | |||||||
\(854\) | − 19.6854i | − 0.0230508i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 95.7502 | 0.111858 | ||||||||
\(857\) | −287.294 | −0.335232 | −0.167616 | − | 0.985852i | \(-0.553607\pi\) | ||||
−0.167616 | + | 0.985852i | \(0.553607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −82.5584 | −0.0961099 | −0.0480550 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480550 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1071.33i | 1.24284i | ||||||||
\(863\) | −1214.56 | −1.40737 | −0.703684 | − | 0.710513i | \(-0.748463\pi\) | ||||
−0.703684 | + | 0.710513i | \(0.748463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − 414.781i | − 0.478962i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.1766i | 0.0163325i | ||||||||
\(869\) | − 234.551i | − 0.269909i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −338.405 | −0.388525 | ||||||||
\(872\) | 54.1564 | 0.0621060 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 82.6476 | 0.0945625 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1489.63i | 1.69855i | 0.527948 | + | 0.849277i | \(0.322962\pi\) | ||||
−0.527948 | + | 0.849277i | \(0.677038\pi\) | |||||||
\(878\) | 624.843 | 0.711666 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1438.94i | 1.63330i | 0.577131 | + | 0.816652i | \(0.304172\pi\) | ||||
−0.577131 | + | 0.816652i | \(0.695828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 684.139i | − 0.774790i | −0.921914 | − | 0.387395i | \(-0.873375\pi\) | ||||
0.921914 | − | 0.387395i | \(-0.126625\pi\) | |||||||
\(884\) | − 54.0732i | − 0.0611687i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 65.5950 | 0.0740350 | ||||||||
\(887\) | −1005.57 | −1.13368 | −0.566839 | − | 0.823828i | \(-0.691834\pi\) | ||||
−0.566839 | + | 0.823828i | \(0.691834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.4424 | −0.0477418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 401.941i | 0.450607i | ||||||||
\(893\) | −58.4407 | −0.0654431 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 2.74517i | − 0.00306380i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 97.8823i | − 0.109000i | ||||||||
\(899\) | 205.352i | 0.228423i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 208.764 | 0.231702 | ||||||||
\(902\) | 242.735 | 0.269108 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −75.7645 | −0.0838103 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 73.4416i | − 0.0809720i | −0.999180 | − | 0.0404860i | \(-0.987109\pi\) | ||||
0.999180 | − | 0.0404860i | \(-0.0128906\pi\) | |||||||
\(908\) | 698.881 | 0.769693 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1557.69i | − 1.70987i | −0.518738 | − | 0.854933i | \(-0.673598\pi\) | ||||
0.518738 | − | 0.854933i | \(-0.326402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 77.6468i | − 0.0850457i | ||||||||
\(914\) | 267.826i | 0.293027i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 345.029 | 0.376670 | ||||||||
\(917\) | 36.3318 | 0.0396203 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 635.322 | 0.691319 | 0.345659 | − | 0.938360i | \(-0.387655\pi\) | ||||
0.345659 | + | 0.938360i | \(0.387655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 869.823i | − 0.943409i | ||||||||
\(923\) | 252.734 | 0.273818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 193.872i | 0.209365i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 39.7645i | − 0.0428497i | ||||||||
\(929\) | − 1051.26i | − 1.13160i | −0.824542 | − | 0.565801i | \(-0.808567\pi\) | ||||
0.824542 | − | 0.565801i | \(-0.191433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 439.029 | 0.471568 | ||||||||
\(932\) | 296.485 | 0.318117 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 476.756 | 0.510446 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 782.381i | 0.834985i | 0.908680 | + | 0.417493i | \(0.137091\pi\) | ||||
−0.908680 | + | 0.417493i | \(0.862909\pi\) | |||||||
\(938\) | 33.3179 | 0.0355201 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1085.14i | 1.15318i | 0.817035 | + | 0.576588i | \(0.195616\pi\) | ||||
−0.817035 | + | 0.576588i | \(0.804384\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 372.728i | 0.395258i | ||||||||
\(944\) | 339.765i | 0.359920i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.7939 | −0.0494651 | ||||||||
\(947\) | −1358.56 | −1.43459 | −0.717296 | − | 0.696769i | \(-0.754620\pi\) | ||||
−0.717296 | + | 0.696769i | \(0.754620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 372.617 | 0.392642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.32381i | 0.00559224i | ||||||||
\(953\) | 790.648 | 0.829641 | 0.414820 | − | 0.909903i | \(-0.363844\pi\) | ||||
0.414820 | + | 0.909903i | \(0.363844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 283.206i | 0.296241i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 321.941i | − 0.336055i | ||||||||
\(959\) | 46.7939i | 0.0487945i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −107.589 | −0.111955 | ||||||||
\(962\) | 179.688 | 0.186786 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 167.706 | 0.173968 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1062.23i | 1.09848i | 0.835663 | + | 0.549242i | \(0.185083\pi\) | ||||
−0.835663 | + | 0.549242i | \(0.814917\pi\) | |||||||
\(968\) | −316.784 | −0.327256 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 194.500i | − 0.200309i | −0.994972 | − | 0.100155i | \(-0.968066\pi\) | ||||
0.994972 | − | 0.100155i | \(-0.0319338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.4121i | 0.0292005i | ||||||||
\(974\) | 906.333i | 0.930527i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 229.470 | 0.235113 | ||||||||
\(977\) | 715.882 | 0.732735 | 0.366368 | − | 0.930470i | \(-0.380601\pi\) | ||||
0.366368 | + | 0.930470i | \(0.380601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95.2721 | 0.0973157 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 862.837i | 0.878653i | ||||||||
\(983\) | −1679.98 | −1.70904 | −0.854519 | − | 0.519420i | \(-0.826148\pi\) | ||||
−0.854519 | + | 0.519420i | \(0.826148\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 77.1169i | 0.0782118i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 62.5299i | 0.0632893i | ||||||||
\(989\) | − 71.8537i | − 0.0726529i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 655.294 | 0.661245 | 0.330622 | − | 0.943763i | \(-0.392741\pi\) | ||||
0.330622 | + | 0.943763i | \(0.392741\pi\) | |||||||
\(992\) | −165.255 | −0.166588 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.8831 | −0.0250333 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1169.57i | 1.17309i | 0.809916 | + | 0.586546i | \(0.199513\pi\) | ||||
−0.809916 | + | 0.586546i | \(0.800487\pi\) | |||||||
\(998\) | 61.2263 | 0.0613490 | ||||||||
\(999\) | 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 | 1350.3.b.a.1349.2 | 4 | ||
3.2 | odd | 2 | 1350.3.b.f.1349.4 | 4 | |||
5.2 | odd | 4 | 1350.3.d.n.701.1 | yes | 4 | ||
5.3 | odd | 4 | 1350.3.d.l.701.4 | yes | 4 | ||
5.4 | even | 2 | 1350.3.b.f.1349.3 | 4 | |||
15.2 | even | 4 | 1350.3.d.n.701.3 | yes | 4 | ||
15.8 | even | 4 | 1350.3.d.l.701.2 | ✓ | 4 | ||
15.14 | odd | 2 | inner | 1350.3.b.a.1349.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.3.b.a.1349.1 | 4 | 15.14 | odd | 2 | inner | ||
1350.3.b.a.1349.2 | 4 | 1.1 | even | 1 | trivial | ||
1350.3.b.f.1349.3 | 4 | 5.4 | even | 2 | |||
1350.3.b.f.1349.4 | 4 | 3.2 | odd | 2 | |||
1350.3.d.l.701.2 | ✓ | 4 | 15.8 | even | 4 | ||
1350.3.d.l.701.4 | yes | 4 | 5.3 | odd | 4 | ||
1350.3.d.n.701.1 | yes | 4 | 5.2 | odd | 4 | ||
1350.3.d.n.701.3 | yes | 4 | 15.2 | even | 4 |