Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.66 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.19 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47320i | 1.23660i | 0.785943 | + | 0.618300i | \(0.212178\pi\) | ||||
−0.785943 | + | 0.618300i | \(0.787822\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.11671 | −0.529177 | ||||||||
\(5\) | 7.47527i | 1.49505i | 0.664232 | + | 0.747527i | \(0.268759\pi\) | ||||
−0.664232 | + | 0.747527i | \(0.731241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.57682 | −0.510974 | −0.255487 | − | 0.966813i | \(-0.582236\pi\) | ||||
−0.255487 | + | 0.966813i | \(0.582236\pi\) | |||||||
\(8\) | 4.65775i | 0.582219i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.4878 | −1.84878 | ||||||||
\(11\) | − 1.28153i | − 0.116503i | −0.998302 | − | 0.0582513i | \(-0.981448\pi\) | ||||
0.998302 | − | 0.0582513i | \(-0.0185525\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.4150 | −1.10885 | −0.554424 | − | 0.832235i | \(-0.687061\pi\) | ||||
−0.554424 | + | 0.832235i | \(0.687061\pi\) | |||||||
\(14\) | − 8.84618i | − 0.631870i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.9864 | −1.24915 | ||||||||
\(17\) | − 10.3912i | − 0.611247i | −0.952152 | − | 0.305623i | \(-0.901135\pi\) | ||||
0.952152 | − | 0.305623i | \(-0.0988648\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.18314 | −0.167534 | −0.0837668 | − | 0.996485i | \(-0.526695\pi\) | ||||
−0.0837668 | + | 0.996485i | \(0.526695\pi\) | |||||||
\(20\) | − 15.8230i | − 0.791148i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.16948 | 0.144067 | ||||||||
\(23\) | − 24.2785i | − 1.05559i | −0.849373 | − | 0.527794i | \(-0.823019\pi\) | ||||
0.849373 | − | 0.527794i | \(-0.176981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −30.8796 | −1.23519 | ||||||||
\(26\) | − 35.6512i | − 1.37120i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.57108 | 0.270396 | ||||||||
\(29\) | 17.6691i | 0.609280i | 0.952468 | + | 0.304640i | \(0.0985361\pi\) | ||||
−0.952468 | + | 0.304640i | \(0.901464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.6017 | 1.05167 | 0.525833 | − | 0.850588i | \(-0.323754\pi\) | ||||
0.525833 | + | 0.850588i | \(0.323754\pi\) | |||||||
\(32\) | − 30.7993i | − 0.962477i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 25.6995 | 0.755867 | ||||||||
\(35\) | − 26.7377i | − 0.763933i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −49.9752 | −1.35068 | −0.675340 | − | 0.737506i | \(-0.736003\pi\) | ||||
−0.675340 | + | 0.737506i | \(0.736003\pi\) | |||||||
\(38\) | − 7.87253i | − 0.207172i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −34.8180 | −0.870449 | ||||||||
\(41\) | − 10.5982i | − 0.258493i | −0.991613 | − | 0.129246i | \(-0.958744\pi\) | ||||
0.991613 | − | 0.129246i | \(-0.0412558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.4537 | 0.894273 | 0.447136 | − | 0.894466i | \(-0.352444\pi\) | ||||
0.447136 | + | 0.894466i | \(0.352444\pi\) | |||||||
\(44\) | 2.71262i | 0.0616505i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 60.0455 | 1.30534 | ||||||||
\(47\) | − 10.6464i | − 0.226518i | −0.993565 | − | 0.113259i | \(-0.963871\pi\) | ||||
0.993565 | − | 0.113259i | \(-0.0361290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −36.2064 | −0.738906 | ||||||||
\(50\) | − 76.3715i | − 1.52743i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 30.5124 | 0.586777 | ||||||||
\(53\) | 63.3509i | 1.19530i | 0.801757 | + | 0.597650i | \(0.203899\pi\) | ||||
−0.801757 | + | 0.597650i | \(0.796101\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.57977 | 0.174178 | ||||||||
\(56\) | − 16.6599i | − 0.297499i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −43.6992 | −0.753435 | ||||||||
\(59\) | − 1.85123i | − 0.0313768i | −0.999877 | − | 0.0156884i | \(-0.995006\pi\) | ||||
0.999877 | − | 0.0156884i | \(-0.00499398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.8709 | 0.309358 | 0.154679 | − | 0.987965i | \(-0.450566\pi\) | ||||
0.154679 | + | 0.987965i | \(0.450566\pi\) | |||||||
\(62\) | 80.6304i | 1.30049i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.77284 | −0.0589506 | ||||||||
\(65\) | − 107.756i | − 1.65779i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −40.7181 | −0.607733 | −0.303867 | − | 0.952715i | \(-0.598278\pi\) | ||||
−0.303867 | + | 0.952715i | \(0.598278\pi\) | |||||||
\(68\) | 21.9951i | 0.323458i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 66.1275 | 0.944679 | ||||||||
\(71\) | 5.52989i | 0.0778857i | 0.999241 | + | 0.0389429i | \(0.0123990\pi\) | ||||
−0.999241 | + | 0.0389429i | \(0.987601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27.0768 | −0.370915 | −0.185458 | − | 0.982652i | \(-0.559377\pi\) | ||||
−0.185458 | + | 0.982652i | \(0.559377\pi\) | |||||||
\(74\) | − 123.599i | − 1.67025i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.73777 | 0.0886549 | ||||||||
\(77\) | 4.58380i | 0.0595298i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.6548 | 0.514618 | 0.257309 | − | 0.966329i | \(-0.417164\pi\) | ||||
0.257309 | + | 0.966329i | \(0.417164\pi\) | |||||||
\(80\) | − 149.404i | − 1.86754i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.2115 | 0.319652 | ||||||||
\(83\) | 45.3514i | 0.546403i | 0.961957 | + | 0.273201i | \(0.0880826\pi\) | ||||
−0.961957 | + | 0.273201i | \(0.911917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 77.6770 | 0.913847 | ||||||||
\(86\) | 95.1037i | 1.10586i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.96905 | 0.0678301 | ||||||||
\(89\) | 77.0121i | 0.865305i | 0.901561 | + | 0.432652i | \(0.142422\pi\) | ||||
−0.901561 | + | 0.432652i | \(0.857578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 51.5599 | 0.566592 | ||||||||
\(92\) | 51.3905i | 0.558593i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 26.3305 | 0.280112 | ||||||||
\(95\) | − 23.7948i | − 0.250472i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −112.360 | −1.15835 | −0.579174 | − | 0.815204i | \(-0.696625\pi\) | ||||
−0.579174 | + | 0.815204i | \(0.696625\pi\) | |||||||
\(98\) | − 89.5455i | − 0.913730i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 65.3632 | 0.653632 | ||||||||
\(101\) | − 85.3813i | − 0.845359i | −0.906279 | − | 0.422680i | \(-0.861090\pi\) | ||||
0.906279 | − | 0.422680i | \(-0.138910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 32.7075 | 0.317549 | 0.158774 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158774 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(104\) | − 67.1416i | − 0.645592i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −156.679 | −1.47811 | ||||||||
\(107\) | − 200.409i | − 1.87298i | −0.350694 | − | 0.936490i | \(-0.614054\pi\) | ||||
0.350694 | − | 0.936490i | \(-0.385946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38.9278 | −0.357136 | −0.178568 | − | 0.983928i | \(-0.557146\pi\) | ||||
−0.178568 | + | 0.983928i | \(0.557146\pi\) | |||||||
\(110\) | 23.6927i | 0.215388i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 71.4876 | 0.638282 | ||||||||
\(113\) | 24.1549i | 0.213760i | 0.994272 | + | 0.106880i | \(0.0340860\pi\) | ||||
−0.994272 | + | 0.106880i | \(0.965914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 181.488 | 1.57816 | ||||||||
\(116\) | − 37.4004i | − 0.322417i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.57846 | 0.0388005 | ||||||||
\(119\) | 37.1674i | 0.312331i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.358 | 0.986427 | ||||||||
\(122\) | 46.6714i | 0.382552i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −69.0082 | −0.556518 | ||||||||
\(125\) | − 43.9519i | − 0.351615i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2694 | 0.0887357 | ||||||||
\(128\) | − 132.528i | − 1.03538i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 266.502 | 2.05002 | ||||||||
\(131\) | 26.7909i | 0.204511i | 0.994758 | + | 0.102255i | \(0.0326059\pi\) | ||||
−0.994758 | + | 0.102255i | \(0.967394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3855 | 0.0856053 | ||||||||
\(134\) | − 100.704i | − 0.751522i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48.3996 | 0.355880 | ||||||||
\(137\) | − 205.936i | − 1.50318i | −0.659629 | − | 0.751592i | \(-0.729286\pi\) | ||||
0.659629 | − | 0.751592i | \(-0.270714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −159.715 | −1.14903 | −0.574513 | − | 0.818495i | \(-0.694809\pi\) | ||||
−0.574513 | + | 0.818495i | \(0.694809\pi\) | |||||||
\(140\) | 56.5959i | 0.404256i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.6765 | −0.0963134 | ||||||||
\(143\) | 18.4733i | 0.129184i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −132.081 | −0.910906 | ||||||||
\(146\) | − 66.9663i | − 0.458674i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 105.783 | 0.714749 | ||||||||
\(149\) | − 43.3666i | − 0.291051i | −0.989355 | − | 0.145526i | \(-0.953513\pi\) | ||||
0.989355 | − | 0.145526i | \(-0.0464873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −227.463 | −1.50638 | −0.753189 | − | 0.657804i | \(-0.771486\pi\) | ||||
−0.753189 | + | 0.657804i | \(0.771486\pi\) | |||||||
\(152\) | − 14.8263i | − 0.0975412i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.3366 | −0.0736145 | ||||||||
\(155\) | 243.706i | 1.57230i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 59.8855 | 0.381437 | 0.190718 | − | 0.981645i | \(-0.438918\pi\) | ||||
0.190718 | + | 0.981645i | \(0.438918\pi\) | |||||||
\(158\) | 100.547i | 0.636376i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 230.233 | 1.43895 | ||||||||
\(161\) | 86.8398i | 0.539377i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 143.932 | 0.883017 | 0.441508 | − | 0.897257i | \(-0.354444\pi\) | ||||
0.441508 | + | 0.897257i | \(0.354444\pi\) | |||||||
\(164\) | 22.4333i | 0.136788i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −112.163 | −0.675681 | ||||||||
\(167\) | 18.5191i | 0.110893i | 0.998462 | + | 0.0554463i | \(0.0176582\pi\) | ||||
−0.998462 | + | 0.0554463i | \(0.982342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.7927 | 0.229543 | ||||||||
\(170\) | 192.111i | 1.13006i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −81.3954 | −0.473229 | ||||||||
\(173\) | − 8.77175i | − 0.0507038i | −0.999679 | − | 0.0253519i | \(-0.991929\pi\) | ||||
0.999679 | − | 0.0253519i | \(-0.00807062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 110.451 | 0.631148 | ||||||||
\(176\) | 25.6131i | 0.145529i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −190.466 | −1.07004 | ||||||||
\(179\) | 82.8360i | 0.462771i | 0.972862 | + | 0.231385i | \(0.0743258\pi\) | ||||
−0.972862 | + | 0.231385i | \(0.925674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 219.331 | 1.21178 | 0.605888 | − | 0.795550i | \(-0.292818\pi\) | ||||
0.605888 | + | 0.795550i | \(0.292818\pi\) | |||||||
\(182\) | 127.518i | 0.700647i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 113.083 | 0.614583 | ||||||||
\(185\) | − 373.578i | − 2.01934i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3166 | −0.0712119 | ||||||||
\(188\) | 22.5352i | 0.119868i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 58.8493 | 0.309733 | ||||||||
\(191\) | 44.5096i | 0.233034i | 0.993189 | + | 0.116517i | \(0.0371730\pi\) | ||||
−0.993189 | + | 0.116517i | \(0.962827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −73.5363 | −0.381017 | −0.190508 | − | 0.981686i | \(-0.561014\pi\) | ||||
−0.190508 | + | 0.981686i | \(0.561014\pi\) | |||||||
\(194\) | − 277.888i | − 1.43241i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 76.6384 | 0.391012 | ||||||||
\(197\) | 267.608i | 1.35842i | 0.733945 | + | 0.679209i | \(0.237677\pi\) | ||||
−0.733945 | + | 0.679209i | \(0.762323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −173.678 | −0.872753 | −0.436376 | − | 0.899764i | \(-0.643738\pi\) | ||||
−0.436376 | + | 0.899764i | \(0.643738\pi\) | |||||||
\(200\) | − 143.830i | − 0.719149i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 211.165 | 1.04537 | ||||||||
\(203\) | − 63.1992i | − 0.311326i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 79.2244 | 0.386461 | ||||||||
\(206\) | 80.8921i | 0.392680i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 288.104 | 1.38512 | ||||||||
\(209\) | 4.07928i | 0.0195181i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −384.984 | −1.82457 | −0.912284 | − | 0.409559i | \(-0.865683\pi\) | ||||
−0.912284 | + | 0.409559i | \(0.865683\pi\) | |||||||
\(212\) | − 134.095i | − 0.632526i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 495.651 | 2.31613 | ||||||||
\(215\) | 287.452i | 1.33699i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −116.610 | −0.537374 | ||||||||
\(218\) | − 96.2762i | − 0.441634i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −20.2776 | −0.0921709 | ||||||||
\(221\) | 149.789i | 0.677779i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −391.016 | −1.75344 | −0.876719 | − | 0.481004i | \(-0.840272\pi\) | ||||
−0.876719 | + | 0.481004i | \(0.840272\pi\) | |||||||
\(224\) | 110.163i | 0.491801i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −59.7398 | −0.264335 | ||||||||
\(227\) | − 118.447i | − 0.521792i | −0.965367 | − | 0.260896i | \(-0.915982\pi\) | ||||
0.965367 | − | 0.260896i | \(-0.0840180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0828 | −0.0571299 | −0.0285650 | − | 0.999592i | \(-0.509094\pi\) | ||||
−0.0285650 | + | 0.999592i | \(0.509094\pi\) | |||||||
\(230\) | 448.857i | 1.95155i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −82.2984 | −0.354734 | ||||||||
\(233\) | − 31.3816i | − 0.134685i | −0.997730 | − | 0.0673425i | \(-0.978548\pi\) | ||||
0.997730 | − | 0.0673425i | \(-0.0214520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.5844 | 0.338657 | ||||||||
\(236\) | 3.91852i | 0.0166039i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −91.9223 | −0.386228 | ||||||||
\(239\) | 151.225i | 0.632741i | 0.948636 | + | 0.316370i | \(0.102464\pi\) | ||||
−0.948636 | + | 0.316370i | \(0.897536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −138.477 | −0.574593 | −0.287297 | − | 0.957842i | \(-0.592757\pi\) | ||||
−0.287297 | + | 0.957842i | \(0.592757\pi\) | |||||||
\(242\) | 295.195i | 1.21981i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −39.9441 | −0.163705 | ||||||||
\(245\) | − 270.652i | − 1.10470i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 45.8850 | 0.185769 | ||||||||
\(248\) | 151.850i | 0.612300i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 108.702 | 0.434807 | ||||||||
\(251\) | 243.313i | 0.969376i | 0.874687 | + | 0.484688i | \(0.161067\pi\) | ||||
−0.874687 | + | 0.484688i | \(0.838933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.1136 | −0.122979 | ||||||||
\(254\) | 27.8715i | 0.109730i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 312.677 | 1.22139 | ||||||||
\(257\) | 158.311i | 0.615996i | 0.951387 | + | 0.307998i | \(0.0996590\pi\) | ||||
−0.951387 | + | 0.307998i | \(0.900341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 178.752 | 0.690163 | ||||||||
\(260\) | 228.088i | 0.877263i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −66.2593 | −0.252898 | ||||||||
\(263\) | 85.3123i | 0.324381i | 0.986759 | + | 0.162191i | \(0.0518559\pi\) | ||||
−0.986759 | + | 0.162191i | \(0.948144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −473.565 | −1.78704 | ||||||||
\(266\) | 28.1586i | 0.105859i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 86.1884 | 0.321598 | ||||||||
\(269\) | 118.069i | 0.438920i | 0.975622 | + | 0.219460i | \(0.0704295\pi\) | ||||
−0.975622 | + | 0.219460i | \(0.929570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 334.758 | 1.23527 | 0.617634 | − | 0.786466i | \(-0.288091\pi\) | ||||
0.617634 | + | 0.786466i | \(0.288091\pi\) | |||||||
\(272\) | 207.682i | 0.763538i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 509.321 | 1.85884 | ||||||||
\(275\) | 39.5732i | 0.143902i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6223 | −0.110550 | −0.0552750 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552750 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(278\) | − 395.006i | − 1.42089i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 124.537 | 0.444777 | ||||||||
\(281\) | 4.97564i | 0.0177069i | 0.999961 | + | 0.00885345i | \(0.00281818\pi\) | ||||
−0.999961 | + | 0.00885345i | \(0.997182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −230.905 | −0.815918 | −0.407959 | − | 0.913000i | \(-0.633759\pi\) | ||||
−0.407959 | + | 0.913000i | \(0.633759\pi\) | |||||||
\(284\) | − 11.7052i | − 0.0412153i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −45.6880 | −0.159748 | ||||||||
\(287\) | 37.9078i | 0.132083i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 181.023 | 0.626377 | ||||||||
\(290\) | − 326.663i | − 1.12643i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 57.3137 | 0.196280 | ||||||||
\(293\) | − 420.765i | − 1.43606i | −0.696014 | − | 0.718028i | \(-0.745045\pi\) | ||||
0.696014 | − | 0.718028i | \(-0.254955\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8384 | 0.0469100 | ||||||||
\(296\) | − 232.772i | − 0.786392i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 107.254 | 0.359913 | ||||||||
\(299\) | 349.975i | 1.17049i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −137.542 | −0.456950 | ||||||||
\(302\) | − 562.562i | − 1.86279i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 63.6194 | 0.209274 | ||||||||
\(305\) | 141.065i | 0.462507i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 176.646 | 0.575393 | 0.287697 | − | 0.957722i | \(-0.407111\pi\) | ||||
0.287697 | + | 0.957722i | \(0.407111\pi\) | |||||||
\(308\) | − 9.70256i | − 0.0315018i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −602.734 | −1.94430 | ||||||||
\(311\) | − 10.4719i | − 0.0336717i | −0.999858 | − | 0.0168359i | \(-0.994641\pi\) | ||||
0.999858 | − | 0.0168359i | \(-0.00535927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −569.849 | −1.82060 | −0.910302 | − | 0.413946i | \(-0.864150\pi\) | ||||
−0.910302 | + | 0.413946i | \(0.864150\pi\) | |||||||
\(314\) | 148.109i | 0.471684i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −86.0543 | −0.272324 | ||||||||
\(317\) | 68.0365i | 0.214626i | 0.994225 | + | 0.107313i | \(0.0342247\pi\) | ||||
−0.994225 | + | 0.107313i | \(0.965775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.6435 | 0.0709827 | ||||||||
\(320\) | − 28.2030i | − 0.0881343i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −214.772 | −0.666994 | ||||||||
\(323\) | 33.0766i | 0.102404i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 445.131 | 1.36963 | ||||||||
\(326\) | 355.972i | 1.09194i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 49.3638 | 0.150499 | ||||||||
\(329\) | 38.0801i | 0.115745i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 80.7152 | 0.243853 | 0.121926 | − | 0.992539i | \(-0.461093\pi\) | ||||
0.121926 | + | 0.992539i | \(0.461093\pi\) | |||||||
\(332\) | − 95.9958i | − 0.289144i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −45.8013 | −0.137130 | ||||||||
\(335\) | − 304.379i | − 0.908594i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −652.457 | −1.93607 | −0.968037 | − | 0.250806i | \(-0.919304\pi\) | ||||
−0.968037 | + | 0.250806i | \(0.919304\pi\) | |||||||
\(338\) | 95.9421i | 0.283852i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −164.420 | −0.483587 | ||||||||
\(341\) | − 41.7800i | − 0.122522i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 304.768 | 0.888535 | ||||||||
\(344\) | 179.108i | 0.520663i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.6943 | 0.0627002 | ||||||||
\(347\) | 409.886i | 1.18123i | 0.806955 | + | 0.590613i | \(0.201114\pi\) | ||||
−0.806955 | + | 0.590613i | \(0.798886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −415.021 | −1.18917 | −0.594586 | − | 0.804032i | \(-0.702684\pi\) | ||||
−0.594586 | + | 0.804032i | \(0.702684\pi\) | |||||||
\(350\) | 273.167i | 0.780476i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39.4702 | −0.112131 | ||||||||
\(353\) | − 145.012i | − 0.410799i | −0.978678 | − | 0.205400i | \(-0.934151\pi\) | ||||
0.978678 | − | 0.205400i | \(-0.0658494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −41.3374 | −0.116443 | ||||||||
\(356\) | − 163.012i | − 0.457899i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −204.870 | −0.572262 | ||||||||
\(359\) | 188.574i | 0.525277i | 0.964894 | + | 0.262638i | \(0.0845926\pi\) | ||||
−0.964894 | + | 0.262638i | \(0.915407\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −350.868 | −0.971933 | ||||||||
\(362\) | 542.450i | 1.49848i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −109.137 | −0.299828 | ||||||||
\(365\) | − 202.406i | − 0.554538i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −693.878 | −1.89068 | −0.945338 | − | 0.326093i | \(-0.894268\pi\) | ||||
−0.945338 | + | 0.326093i | \(0.894268\pi\) | |||||||
\(368\) | 485.239i | 1.31859i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 923.932 | 2.49711 | ||||||||
\(371\) | − 226.595i | − 0.610767i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −698.882 | −1.87368 | −0.936839 | − | 0.349760i | \(-0.886263\pi\) | ||||
−0.936839 | + | 0.349760i | \(0.886263\pi\) | |||||||
\(374\) | − 32.9346i | − 0.0880605i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 49.5881 | 0.131883 | ||||||||
\(377\) | − 254.701i | − 0.675598i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −117.384 | −0.309721 | −0.154861 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154861 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(380\) | 50.3667i | 0.132544i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −110.081 | −0.288170 | ||||||||
\(383\) | − 565.781i | − 1.47724i | −0.674124 | − | 0.738618i | \(-0.735479\pi\) | ||||
0.674124 | − | 0.738618i | \(-0.264521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.2651 | −0.0890003 | ||||||||
\(386\) | − 181.870i | − 0.471165i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 237.833 | 0.612971 | ||||||||
\(389\) | 293.432i | 0.754325i | 0.926147 | + | 0.377163i | \(0.123100\pi\) | ||||
−0.926147 | + | 0.377163i | \(0.876900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −252.283 | −0.645224 | ||||||||
\(392\) | − 168.640i | − 0.430205i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −661.848 | −1.67982 | ||||||||
\(395\) | 303.905i | 0.769381i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −156.374 | −0.393890 | −0.196945 | − | 0.980415i | \(-0.563102\pi\) | ||||
−0.196945 | + | 0.980415i | \(0.563102\pi\) | |||||||
\(398\) | − 429.539i | − 1.07924i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 617.172 | 1.54293 | ||||||||
\(401\) | − 547.372i | − 1.36502i | −0.730878 | − | 0.682508i | \(-0.760889\pi\) | ||||
0.730878 | − | 0.682508i | \(-0.239111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −469.953 | −1.16614 | ||||||||
\(404\) | 180.727i | 0.447345i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 156.304 | 0.384985 | ||||||||
\(407\) | 64.0447i | 0.157358i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −256.309 | −0.626674 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(410\) | 195.938i | 0.477897i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −69.2323 | −0.168039 | ||||||||
\(413\) | 6.62152i | 0.0160327i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −339.014 | −0.816902 | ||||||||
\(416\) | 443.972i | 1.06724i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.0889 | −0.0241361 | ||||||||
\(419\) | 6.95844i | 0.0166072i | 0.999966 | + | 0.00830362i | \(0.00264316\pi\) | ||||
−0.999966 | + | 0.00830362i | \(0.997357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 164.509 | 0.390757 | 0.195378 | − | 0.980728i | \(-0.437407\pi\) | ||||
0.195378 | + | 0.980728i | \(0.437407\pi\) | |||||||
\(422\) | − 952.141i | − 2.25626i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −295.073 | −0.695927 | ||||||||
\(425\) | 320.876i | 0.755003i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −67.4976 | −0.158074 | ||||||||
\(428\) | 424.207i | 0.991138i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −710.926 | −1.65332 | ||||||||
\(431\) | 436.670i | 1.01316i | 0.862194 | + | 0.506578i | \(0.169090\pi\) | ||||
−0.862194 | + | 0.506578i | \(0.830910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 64.1886 | 0.148242 | 0.0741208 | − | 0.997249i | \(-0.476385\pi\) | ||||
0.0741208 | + | 0.997249i | \(0.476385\pi\) | |||||||
\(434\) | − 288.400i | − 0.664516i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 82.3989 | 0.188988 | ||||||||
\(437\) | 77.2818i | 0.176846i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −258.306 | −0.588397 | −0.294199 | − | 0.955744i | \(-0.595053\pi\) | ||||
−0.294199 | + | 0.955744i | \(0.595053\pi\) | |||||||
\(440\) | 44.6202i | 0.101410i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −370.459 | −0.838141 | ||||||||
\(443\) | − 276.205i | − 0.623487i | −0.950166 | − | 0.311744i | \(-0.899087\pi\) | ||||
0.950166 | − | 0.311744i | \(-0.100913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −575.686 | −1.29368 | ||||||||
\(446\) | − 967.061i | − 2.16830i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.4948 | 0.0301222 | ||||||||
\(449\) | 555.627i | 1.23748i | 0.785597 | + | 0.618738i | \(0.212356\pi\) | ||||
−0.785597 | + | 0.618738i | \(0.787644\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5819 | −0.0301151 | ||||||||
\(452\) | − 51.1288i | − 0.113117i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 292.943 | 0.645248 | ||||||||
\(455\) | 385.424i | 0.847086i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 67.3557 | 0.147387 | 0.0736934 | − | 0.997281i | \(-0.476521\pi\) | ||||
0.0736934 | + | 0.997281i | \(0.476521\pi\) | |||||||
\(458\) | − 32.3562i | − 0.0706468i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −384.158 | −0.835126 | ||||||||
\(461\) | − 799.216i | − 1.73366i | −0.498605 | − | 0.866829i | \(-0.666154\pi\) | ||||
0.498605 | − | 0.866829i | \(-0.333846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −469.674 | −1.01441 | −0.507207 | − | 0.861824i | \(-0.669322\pi\) | ||||
−0.507207 | + | 0.861824i | \(0.669322\pi\) | |||||||
\(464\) | − 353.142i | − 0.761081i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 77.6130 | 0.166551 | ||||||||
\(467\) | 584.567i | 1.25175i | 0.779923 | + | 0.625875i | \(0.215258\pi\) | ||||
−0.779923 | + | 0.625875i | \(0.784742\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 145.641 | 0.310536 | ||||||||
\(470\) | 196.828i | 0.418783i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.62258 | 0.0182682 | ||||||||
\(473\) | − 49.2796i | − 0.104185i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 98.2941 | 0.206935 | ||||||||
\(476\) | − 78.6726i | − 0.165278i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −374.010 | −0.782447 | ||||||||
\(479\) | 442.649i | 0.924111i | 0.886851 | + | 0.462055i | \(0.152888\pi\) | ||||
−0.886851 | + | 0.462055i | \(0.847112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 720.393 | 1.49770 | ||||||||
\(482\) | − 342.481i | − 0.710541i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −252.645 | −0.521995 | ||||||||
\(485\) | − 839.919i | − 1.73179i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 730.873 | 1.50077 | 0.750383 | − | 0.661004i | \(-0.229869\pi\) | ||||
0.750383 | + | 0.661004i | \(0.229869\pi\) | |||||||
\(488\) | 87.8958i | 0.180114i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 669.377 | 1.36608 | ||||||||
\(491\) | 275.276i | 0.560644i | 0.959906 | + | 0.280322i | \(0.0904412\pi\) | ||||
−0.959906 | + | 0.280322i | \(0.909559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 183.603 | 0.372420 | ||||||||
\(494\) | 113.483i | 0.229722i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −651.589 | −1.31369 | ||||||||
\(497\) | − 19.7794i | − 0.0397976i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −185.214 | −0.371170 | −0.185585 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185585 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(500\) | 93.0333i | 0.186067i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −601.762 | −1.19873 | ||||||||
\(503\) | 634.099i | 1.26064i | 0.776337 | + | 0.630318i | \(0.217075\pi\) | ||||
−0.776337 | + | 0.630318i | \(0.782925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 638.248 | 1.26386 | ||||||||
\(506\) | − 76.9501i | − 0.152075i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.8541 | −0.0469569 | ||||||||
\(509\) | − 492.444i | − 0.967473i | −0.875214 | − | 0.483736i | \(-0.839279\pi\) | ||||
0.875214 | − | 0.483736i | \(-0.160721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 96.8488 | 0.189528 | ||||||||
\(512\) | 243.199i | 0.474999i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −391.534 | −0.761740 | ||||||||
\(515\) | 244.497i | 0.474752i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.6436 | −0.0263900 | ||||||||
\(518\) | 442.089i | 0.853454i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 501.901 | 0.965195 | ||||||||
\(521\) | 861.089i | 1.65276i | 0.563111 | + | 0.826381i | \(0.309604\pi\) | ||||
−0.563111 | + | 0.826381i | \(0.690396\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 58.5594 | 0.111968 | 0.0559842 | − | 0.998432i | \(-0.482170\pi\) | ||||
0.0559842 | + | 0.998432i | \(0.482170\pi\) | |||||||
\(524\) | − 56.7086i | − 0.108223i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −210.994 | −0.401129 | ||||||||
\(527\) | − 338.770i | − 0.642828i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −60.4458 | −0.114264 | ||||||||
\(530\) | − 1171.22i | − 2.20985i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.0998 | −0.0453003 | ||||||||
\(533\) | 152.773i | 0.286629i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1498.11 | 2.80021 | ||||||||
\(536\) | − 189.655i | − 0.353834i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −292.009 | −0.542768 | ||||||||
\(539\) | 46.3995i | 0.0860845i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 794.836 | 1.46920 | 0.734599 | − | 0.678501i | \(-0.237370\pi\) | ||||
0.734599 | + | 0.678501i | \(0.237370\pi\) | |||||||
\(542\) | 827.922i | 1.52753i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −320.041 | −0.588311 | ||||||||
\(545\) | − 290.996i | − 0.533938i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −164.077 | −0.299957 | −0.149979 | − | 0.988689i | \(-0.547921\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(548\) | 435.907i | 0.795450i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −97.8723 | −0.177950 | ||||||||
\(551\) | − 56.2432i | − 0.102075i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −145.415 | −0.262956 | ||||||||
\(554\) | − 75.7351i | − 0.136706i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 338.069 | 0.608039 | ||||||||
\(557\) | 806.590i | 1.44810i | 0.689749 | + | 0.724048i | \(0.257721\pi\) | ||||
−0.689749 | + | 0.724048i | \(0.742279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −554.311 | −0.991612 | ||||||||
\(560\) | 534.389i | 0.954266i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.3057 | −0.0218963 | ||||||||
\(563\) | 136.258i | 0.242022i | 0.992651 | + | 0.121011i | \(0.0386136\pi\) | ||||
−0.992651 | + | 0.121011i | \(0.961386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −180.564 | −0.319582 | ||||||||
\(566\) | − 571.073i | − 1.00896i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.7568 | −0.0453465 | ||||||||
\(569\) | 438.619i | 0.770860i | 0.922737 | + | 0.385430i | \(0.125947\pi\) | ||||
−0.922737 | + | 0.385430i | \(0.874053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 279.001 | 0.488618 | 0.244309 | − | 0.969697i | \(-0.421439\pi\) | ||||
0.244309 | + | 0.969697i | \(0.421439\pi\) | |||||||
\(572\) | − 39.1025i | − 0.0683610i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −93.7536 | −0.163334 | ||||||||
\(575\) | 749.711i | 1.30385i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −193.520 | −0.335391 | −0.167695 | − | 0.985839i | \(-0.553633\pi\) | ||||
−0.167695 | + | 0.985839i | \(0.553633\pi\) | |||||||
\(578\) | 447.706i | 0.774578i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 279.578 | 0.482031 | ||||||||
\(581\) | − 162.214i | − 0.279198i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 81.1861 | 0.139256 | ||||||||
\(584\) | − 126.117i | − 0.215954i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1040.63 | 1.77583 | ||||||||
\(587\) | − 159.092i | − 0.271025i | −0.990776 | − | 0.135512i | \(-0.956732\pi\) | ||||
0.990776 | − | 0.135512i | \(-0.0432681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −103.776 | −0.176189 | ||||||||
\(590\) | 34.2252i | 0.0580089i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 998.823 | 1.68720 | ||||||||
\(593\) | − 502.148i | − 0.846793i | −0.905945 | − | 0.423396i | \(-0.860838\pi\) | ||||
0.905945 | − | 0.423396i | \(-0.139162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −277.836 | −0.466952 | ||||||||
\(596\) | 91.7945i | 0.154018i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −865.558 | −1.44742 | ||||||||
\(599\) | 190.124i | 0.317403i | 0.987327 | + | 0.158701i | \(0.0507307\pi\) | ||||
−0.987327 | + | 0.158701i | \(0.949269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 199.419 | 0.331811 | 0.165906 | − | 0.986142i | \(-0.446945\pi\) | ||||
0.165906 | + | 0.986142i | \(0.446945\pi\) | |||||||
\(602\) | − 340.169i | − 0.565064i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 481.473 | 0.797141 | ||||||||
\(605\) | 892.231i | 1.47476i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 748.425 | 1.23299 | 0.616495 | − | 0.787359i | \(-0.288552\pi\) | ||||
0.616495 | + | 0.787359i | \(0.288552\pi\) | |||||||
\(608\) | 98.0383i | 0.161247i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −348.881 | −0.571936 | ||||||||
\(611\) | 153.467i | 0.251174i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 458.107 | 0.747319 | 0.373660 | − | 0.927566i | \(-0.378103\pi\) | ||||
0.373660 | + | 0.927566i | \(0.378103\pi\) | |||||||
\(614\) | 436.880i | 0.711530i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.3502 | −0.0346594 | ||||||||
\(617\) | − 783.814i | − 1.27036i | −0.772363 | − | 0.635182i | \(-0.780925\pi\) | ||||
0.772363 | − | 0.635182i | \(-0.219075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1123.39 | 1.81484 | 0.907421 | − | 0.420223i | \(-0.138048\pi\) | ||||
0.907421 | + | 0.420223i | \(0.138048\pi\) | |||||||
\(620\) | − 515.855i | − 0.832024i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.8991 | 0.0416384 | ||||||||
\(623\) | − 275.458i | − 0.442148i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −443.439 | −0.709502 | ||||||||
\(626\) | − 1409.35i | − 2.25136i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −126.760 | −0.201848 | ||||||||
\(629\) | 519.302i | 0.825599i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 367.570 | 0.582520 | 0.291260 | − | 0.956644i | \(-0.405925\pi\) | ||||
0.291260 | + | 0.956644i | \(0.405925\pi\) | |||||||
\(632\) | 189.360i | 0.299620i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −168.268 | −0.265407 | ||||||||
\(635\) | 84.2420i | 0.132665i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 521.916 | 0.819334 | ||||||||
\(638\) | 56.0018i | 0.0877771i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 990.683 | 1.54794 | ||||||||
\(641\) | 165.990i | 0.258955i | 0.991582 | + | 0.129477i | \(0.0413300\pi\) | ||||
−0.991582 | + | 0.129477i | \(0.958670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −225.814 | −0.351188 | −0.175594 | − | 0.984463i | \(-0.556185\pi\) | ||||
−0.175594 | + | 0.984463i | \(0.556185\pi\) | |||||||
\(644\) | − 183.814i | − 0.285426i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −81.8050 | −0.126633 | ||||||||
\(647\) | 727.421i | 1.12430i | 0.827036 | + | 0.562149i | \(0.190025\pi\) | ||||
−0.827036 | + | 0.562149i | \(0.809975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.37241 | −0.00365548 | ||||||||
\(650\) | 1100.90i | 1.69369i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −304.662 | −0.467272 | ||||||||
\(653\) | 445.966i | 0.682949i | 0.939891 | + | 0.341475i | \(0.110926\pi\) | ||||
−0.939891 | + | 0.341475i | \(0.889074\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −200.269 | −0.305755 | ||||||||
\(656\) | 211.820i | 0.322896i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −94.1796 | −0.143130 | ||||||||
\(659\) | 1167.70i | 1.77192i | 0.463760 | + | 0.885961i | \(0.346500\pi\) | ||||
−0.463760 | + | 0.885961i | \(0.653500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1018.80 | 1.54130 | 0.770652 | − | 0.637256i | \(-0.219931\pi\) | ||||
0.770652 | + | 0.637256i | \(0.219931\pi\) | |||||||
\(662\) | 199.625i | 0.301548i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −211.236 | −0.318126 | ||||||||
\(665\) | 85.1097i | 0.127984i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 428.980 | 0.643148 | ||||||||
\(668\) | − 39.1995i | − 0.0586818i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 752.789 | 1.12357 | ||||||||
\(671\) | − 24.1836i | − 0.0360411i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 547.102 | 0.812930 | 0.406465 | − | 0.913666i | \(-0.366761\pi\) | ||||
0.406465 | + | 0.913666i | \(0.366761\pi\) | |||||||
\(674\) | − 1613.66i | − 2.39415i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −82.1129 | −0.121469 | ||||||||
\(677\) | − 619.136i | − 0.914529i | −0.889331 | − | 0.457264i | \(-0.848829\pi\) | ||||
0.889331 | − | 0.457264i | \(-0.151171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 401.890 | 0.591885 | ||||||||
\(680\) | 361.800i | 0.532059i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 103.330 | 0.151510 | ||||||||
\(683\) | 667.806i | 0.977754i | 0.872353 | + | 0.488877i | \(0.162593\pi\) | ||||
−0.872353 | + | 0.488877i | \(0.837407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1539.43 | 2.24734 | ||||||||
\(686\) | 753.751i | 1.09876i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −768.551 | −1.11708 | ||||||||
\(689\) | − 913.205i | − 1.32541i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 624.648 | 0.903977 | 0.451988 | − | 0.892024i | \(-0.350715\pi\) | ||||
0.451988 | + | 0.892024i | \(0.350715\pi\) | |||||||
\(692\) | 18.5672i | 0.0268313i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1013.73 | −1.46070 | ||||||||
\(695\) | − 1193.91i | − 1.71786i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −110.128 | −0.158003 | ||||||||
\(698\) | − 1026.43i | − 1.47053i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −233.792 | −0.333989 | ||||||||
\(701\) | 714.318i | 1.01900i | 0.860471 | + | 0.509499i | \(0.170169\pi\) | ||||
−0.860471 | + | 0.509499i | \(0.829831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 159.078 | 0.226284 | ||||||||
\(704\) | 4.83500i | 0.00686790i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 358.644 | 0.507994 | ||||||||
\(707\) | 305.393i | 0.431956i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 483.391 | 0.681792 | 0.340896 | − | 0.940101i | \(-0.389270\pi\) | ||||
0.340896 | + | 0.940101i | \(0.389270\pi\) | |||||||
\(710\) | − 102.236i | − 0.143994i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −358.703 | −0.503797 | ||||||||
\(713\) | − 791.519i | − 1.11013i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −138.093 | −0.193137 | ||||||||
\(716\) | − 175.340i | − 0.244888i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −466.382 | −0.649556 | ||||||||
\(719\) | 1146.34i | 1.59436i | 0.603745 | + | 0.797178i | \(0.293675\pi\) | ||||
−0.603745 | + | 0.797178i | \(0.706325\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −116.989 | −0.162259 | ||||||||
\(722\) | − 867.765i | − 1.20189i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −464.260 | −0.641244 | ||||||||
\(725\) | − 545.616i | − 0.752574i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −396.069 | −0.544799 | −0.272400 | − | 0.962184i | \(-0.587817\pi\) | ||||
−0.272400 | + | 0.962184i | \(0.587817\pi\) | |||||||
\(728\) | 240.153i | 0.329881i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 500.591 | 0.685742 | ||||||||
\(731\) | − 399.580i | − 0.546621i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1143.30 | 1.55975 | 0.779876 | − | 0.625934i | \(-0.215282\pi\) | ||||
0.779876 | + | 0.625934i | \(0.215282\pi\) | |||||||
\(734\) | − 1716.10i | − 2.33801i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −747.760 | −1.01598 | ||||||||
\(737\) | 52.1815i | 0.0708025i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −940.492 | −1.27265 | −0.636327 | − | 0.771419i | \(-0.719547\pi\) | ||||
−0.636327 | + | 0.771419i | \(0.719547\pi\) | |||||||
\(740\) | 790.756i | 1.06859i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 560.414 | 0.755274 | ||||||||
\(743\) | − 1295.75i | − 1.74394i | −0.489555 | − | 0.871972i | \(-0.662841\pi\) | ||||
0.489555 | − | 0.871972i | \(-0.337159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 324.177 | 0.435137 | ||||||||
\(746\) | − 1728.47i | − 2.31699i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.1874 | 0.0376837 | ||||||||
\(749\) | 716.826i | 0.957044i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −245.217 | −0.326521 | −0.163260 | − | 0.986583i | \(-0.552201\pi\) | ||||
−0.163260 | + | 0.986583i | \(0.552201\pi\) | |||||||
\(752\) | 212.782i | 0.282955i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 629.925 | 0.835444 | ||||||||
\(755\) | − 1700.35i | − 2.25212i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −210.908 | −0.278610 | −0.139305 | − | 0.990250i | \(-0.544487\pi\) | ||||
−0.139305 | + | 0.990250i | \(0.544487\pi\) | |||||||
\(758\) | − 290.315i | − 0.383001i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 110.830 | 0.145829 | ||||||||
\(761\) | − 237.328i | − 0.311863i | −0.987768 | − | 0.155932i | \(-0.950162\pi\) | ||||
0.987768 | − | 0.155932i | \(-0.0498379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 139.238 | 0.182487 | ||||||||
\(764\) | − 94.2138i | − 0.123316i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1399.29 | 1.82675 | ||||||||
\(767\) | 26.6855i | 0.0347921i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −231.536 | −0.301087 | −0.150543 | − | 0.988603i | \(-0.548102\pi\) | ||||
−0.150543 | + | 0.988603i | \(0.548102\pi\) | |||||||
\(770\) | − 84.7444i | − 0.110058i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 155.655 | 0.201625 | ||||||||
\(773\) | − 1365.28i | − 1.76621i | −0.469171 | − | 0.883107i | \(-0.655447\pi\) | ||||
0.469171 | − | 0.883107i | \(-0.344553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1006.73 | −1.29900 | ||||||||
\(776\) | − 523.344i | − 0.674412i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −725.717 | −0.932798 | ||||||||
\(779\) | 33.7355i | 0.0433062i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.08671 | 0.00907389 | ||||||||
\(782\) | − 623.945i | − 0.797884i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 723.634 | 0.923003 | ||||||||
\(785\) | 447.660i | 0.570268i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 690.289 | 0.877114 | 0.438557 | − | 0.898703i | \(-0.355490\pi\) | ||||
0.438557 | + | 0.898703i | \(0.355490\pi\) | |||||||
\(788\) | − 566.449i | − 0.718844i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −751.618 | −0.951416 | ||||||||
\(791\) | − 86.3975i | − 0.109226i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −272.024 | −0.343031 | ||||||||
\(794\) | − 386.744i | − 0.487083i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 367.625 | 0.461841 | ||||||||
\(797\) | 877.407i | 1.10089i | 0.834873 | + | 0.550443i | \(0.185541\pi\) | ||||
−0.834873 | + | 0.550443i | \(0.814459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −110.628 | −0.138459 | ||||||||
\(800\) | 951.070i | 1.18884i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1353.76 | 1.68798 | ||||||||
\(803\) | 34.6997i | 0.0432126i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −649.151 | −0.806398 | ||||||||
\(806\) | − 1162.29i | − 1.44204i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 397.685 | 0.492184 | ||||||||
\(809\) | 271.708i | 0.335857i | 0.985799 | + | 0.167928i | \(0.0537077\pi\) | ||||
−0.985799 | + | 0.167928i | \(0.946292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 590.185 | 0.727725 | 0.363862 | − | 0.931453i | \(-0.381458\pi\) | ||||
0.363862 | + | 0.931453i | \(0.381458\pi\) | |||||||
\(812\) | 133.774i | 0.164747i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −158.395 | −0.194589 | ||||||||
\(815\) | 1075.93i | 1.32016i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −122.404 | −0.149821 | ||||||||
\(818\) | − 633.904i | − 0.774944i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −167.695 | −0.204506 | ||||||||
\(821\) | 1133.04i | 1.38007i | 0.723774 | + | 0.690037i | \(0.242406\pi\) | ||||
−0.723774 | + | 0.690037i | \(0.757594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −839.497 | −1.02004 | −0.510022 | − | 0.860161i | \(-0.670363\pi\) | ||||
−0.510022 | + | 0.860161i | \(0.670363\pi\) | |||||||
\(824\) | 152.343i | 0.184883i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3763 | −0.0198261 | ||||||||
\(827\) | 104.942i | 0.126895i | 0.997985 | + | 0.0634477i | \(0.0202096\pi\) | ||||
−0.997985 | + | 0.0634477i | \(0.979790\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −361.576 | −0.436159 | −0.218079 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218079 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(830\) | − 838.449i | − 1.01018i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 54.3855 | 0.0653672 | ||||||||
\(833\) | 376.228i | 0.451654i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −138.435 | −0.165790 | ||||||||
\(836\) | − 8.63465i | − 0.0103285i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.2096 | −0.0205365 | ||||||||
\(839\) | − 1033.20i | − 1.23146i | −0.787957 | − | 0.615730i | \(-0.788861\pi\) | ||||
0.787957 | − | 0.615730i | \(-0.211139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 528.802 | 0.628778 | ||||||||
\(842\) | 406.862i | 0.483209i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 814.898 | 0.965519 | ||||||||
\(845\) | 289.986i | 0.343179i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −426.921 | −0.504038 | ||||||||
\(848\) | − 1266.16i | − 1.49311i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −793.591 | −0.933636 | ||||||||
\(851\) | 1213.32i | 1.42576i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1162.20 | 1.36249 | 0.681245 | − | 0.732056i | \(-0.261439\pi\) | ||||
0.681245 | + | 0.732056i | \(0.261439\pi\) | |||||||
\(854\) | − 166.935i | − 0.195474i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 933.455 | 1.09048 | ||||||||
\(857\) | − 172.029i | − 0.200735i | −0.994950 | − | 0.100367i | \(-0.967998\pi\) | ||||
0.994950 | − | 0.100367i | \(-0.0320018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1205.40 | −1.40326 | −0.701631 | − | 0.712540i | \(-0.747545\pi\) | ||||
−0.701631 | + | 0.712540i | \(0.747545\pi\) | |||||||
\(860\) | − 608.452i | − 0.707503i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1079.97 | −1.25287 | ||||||||
\(863\) | − 1547.43i | − 1.79308i | −0.442965 | − | 0.896539i | \(-0.646073\pi\) | ||||
0.442965 | − | 0.896539i | \(-0.353927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.5712 | 0.0758049 | ||||||||
\(866\) | 158.751i | 0.183315i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 246.830 | 0.284366 | ||||||||
\(869\) | − 52.1003i | − 0.0599543i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 586.952 | 0.673883 | ||||||||
\(872\) | − 181.316i | − 0.207931i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −191.133 | −0.218688 | ||||||||
\(875\) | 157.208i | 0.179666i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1072.48 | −1.22289 | −0.611445 | − | 0.791287i | \(-0.709412\pi\) | ||||
−0.611445 | + | 0.791287i | \(0.709412\pi\) | |||||||
\(878\) | − 638.843i | − 0.727611i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −191.465 | −0.217574 | ||||||||
\(881\) | 363.670i | 0.412793i | 0.978468 | + | 0.206396i | \(0.0661736\pi\) | ||||
−0.978468 | + | 0.206396i | \(0.933826\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −910.225 | −1.03083 | −0.515416 | − | 0.856940i | \(-0.672363\pi\) | ||||
−0.515416 | + | 0.856940i | \(0.672363\pi\) | |||||||
\(884\) | − 317.060i | − 0.358665i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 683.109 | 0.771004 | ||||||||
\(887\) | 425.744i | 0.479982i | 0.970775 | + | 0.239991i | \(0.0771446\pi\) | ||||
−0.970775 | + | 0.239991i | \(0.922855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.3087 | −0.0453416 | ||||||||
\(890\) | − 1423.79i | − 1.59976i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 827.668 | 0.927879 | ||||||||
\(893\) | 33.8888i | 0.0379494i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −619.221 | −0.691867 | ||||||||
\(896\) | 474.029i | 0.529050i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1374.17 | −1.53026 | ||||||||
\(899\) | 576.042i | 0.640759i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 658.292 | 0.730624 | ||||||||
\(902\) | − 33.5907i | − 0.0372403i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −112.507 | −0.124455 | ||||||||
\(905\) | 1639.56i | 1.81167i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −735.774 | −0.811218 | −0.405609 | − | 0.914047i | \(-0.632940\pi\) | ||||
−0.405609 | + | 0.914047i | \(0.632940\pi\) | |||||||
\(908\) | 250.717i | 0.276121i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −953.230 | −1.04751 | ||||||||
\(911\) | 791.514i | 0.868841i | 0.900710 | + | 0.434420i | \(0.143047\pi\) | ||||
−0.900710 | + | 0.434420i | \(0.856953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58.1192 | 0.0636574 | ||||||||
\(914\) | 166.584i | 0.182258i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.6924 | 0.0302319 | ||||||||
\(917\) | − 95.8263i | − 0.104500i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −264.051 | −0.287324 | −0.143662 | − | 0.989627i | \(-0.545888\pi\) | ||||
−0.143662 | + | 0.989627i | \(0.545888\pi\) | |||||||
\(920\) | 845.328i | 0.918835i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1976.62 | 2.14384 | ||||||||
\(923\) | − 79.7134i | − 0.0863634i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1543.22 | 1.66834 | ||||||||
\(926\) | − 1161.60i | − 1.25442i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 544.196 | 0.586418 | ||||||||
\(929\) | 197.077i | 0.212139i | 0.994359 | + | 0.106070i | \(0.0338266\pi\) | ||||
−0.994359 | + | 0.106070i | \(0.966173\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 115.250 | 0.123791 | ||||||||
\(932\) | 66.4257i | 0.0712722i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1445.75 | −1.54791 | ||||||||
\(935\) | − 99.5453i | − 0.106466i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1280.61 | −1.36671 | −0.683354 | − | 0.730087i | \(-0.739479\pi\) | ||||
−0.683354 | + | 0.730087i | \(0.739479\pi\) | |||||||
\(938\) | 360.200i | 0.384008i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −168.457 | −0.179209 | ||||||||
\(941\) | 571.596i | 0.607434i | 0.952762 | + | 0.303717i | \(0.0982278\pi\) | ||||
−0.952762 | + | 0.303717i | \(0.901772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −257.309 | −0.272862 | ||||||||
\(944\) | 36.9994i | 0.0391943i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 121.878 | 0.128835 | ||||||||
\(947\) | 135.984i | 0.143594i | 0.997419 | + | 0.0717971i | \(0.0228734\pi\) | ||||
−0.997419 | + | 0.0717971i | \(0.977127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 390.313 | 0.411289 | ||||||||
\(950\) | 243.101i | 0.255896i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −173.117 | −0.181845 | ||||||||
\(953\) | 360.322i | 0.378092i | 0.981968 | + | 0.189046i | \(0.0605395\pi\) | ||||
−0.981968 | + | 0.189046i | \(0.939460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −332.721 | −0.348399 | ||||||||
\(956\) | − 320.099i | − 0.334832i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1094.76 | −1.14275 | ||||||||
\(959\) | 736.596i | 0.768088i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 101.868 | 0.106002 | ||||||||
\(962\) | 1781.68i | 1.85205i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 293.115 | 0.304062 | ||||||||
\(965\) | − 549.703i | − 0.569641i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1222.22 | 1.26393 | 0.631963 | − | 0.774999i | \(-0.282250\pi\) | ||||
0.631963 | + | 0.774999i | \(0.282250\pi\) | |||||||
\(968\) | 555.939i | 0.574317i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2077.29 | 2.14153 | ||||||||
\(971\) | − 286.990i | − 0.295561i | −0.989020 | − | 0.147781i | \(-0.952787\pi\) | ||||
0.989020 | − | 0.147781i | \(-0.0472130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 571.270 | 0.587123 | ||||||||
\(974\) | 1807.59i | 1.85585i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −377.160 | −0.386435 | ||||||||
\(977\) | − 1714.15i | − 1.75451i | −0.480028 | − | 0.877253i | \(-0.659373\pi\) | ||||
0.480028 | − | 0.877253i | \(-0.340627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 98.6933 | 0.100810 | ||||||||
\(980\) | 572.892i | 0.584584i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −680.812 | −0.693292 | ||||||||
\(983\) | − 807.305i | − 0.821267i | −0.911801 | − | 0.410633i | \(-0.865308\pi\) | ||||
0.911801 | − | 0.410633i | \(-0.134692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2000.44 | −2.03091 | ||||||||
\(986\) | 454.087i | 0.460535i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −97.1251 | −0.0983048 | ||||||||
\(989\) | − 933.599i | − 0.943983i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 167.284 | 0.168804 | 0.0844019 | − | 0.996432i | \(-0.473102\pi\) | ||||
0.0844019 | + | 0.996432i | \(0.473102\pi\) | |||||||
\(992\) | − 1004.11i | − 1.01220i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 48.9183 | 0.0492136 | ||||||||
\(995\) | − 1298.29i | − 1.30481i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1733.30 | 1.73851 | 0.869257 | − | 0.494360i | \(-0.164598\pi\) | ||||
0.869257 | + | 0.494360i | \(0.164598\pi\) | |||||||
\(998\) | − 458.071i | − 0.458989i | ||||||||
\(999\) | 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 | 1143.3.b.a.890.66 | yes | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.19 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.19 | ✓ | 84 | 3.2 | odd | 2 | inner | |
1143.3.b.a.890.66 | yes | 84 | 1.1 | even | 1 | trivial |