Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, 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("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.16 | ||
Root | \(3.62039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.1 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62039i | 1.81020i | 0.425202 | + | 0.905098i | \(0.360203\pi\) | ||||
−0.425202 | + | 0.905098i | \(0.639797\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.10725 | −2.27681 | ||||||||
\(5\) | 0.165198i | 0.0330396i | 0.999864 | + | 0.0165198i | \(0.00525866\pi\) | ||||
−0.999864 | + | 0.0165198i | \(0.994741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2989 | −1.47127 | −0.735633 | − | 0.677381i | \(-0.763115\pi\) | ||||
−0.735633 | + | 0.677381i | \(0.763115\pi\) | |||||||
\(8\) | − 18.4903i | − 2.31128i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.598083 | −0.0598083 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.3554 | 1.56580 | 0.782899 | − | 0.622148i | \(-0.213740\pi\) | ||||
0.782899 | + | 0.622148i | \(0.213740\pi\) | |||||||
\(14\) | − 37.2859i | − 2.66328i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 30.5130 | 1.90706 | ||||||||
\(17\) | − 23.0147i | − 1.35381i | −0.736072 | − | 0.676903i | \(-0.763321\pi\) | ||||
0.736072 | − | 0.676903i | \(-0.236679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.13897 | 0.217840 | 0.108920 | − | 0.994051i | \(-0.465261\pi\) | ||||
0.108920 | + | 0.994051i | \(0.465261\pi\) | |||||||
\(20\) | − 1.50450i | − 0.0752251i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.5095i | 0.587369i | 0.955902 | + | 0.293685i | \(0.0948816\pi\) | ||||
−0.955902 | + | 0.293685i | \(0.905118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9727 | 0.998908 | ||||||||
\(26\) | 73.6945i | 2.83440i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 93.7943 | 3.34979 | ||||||||
\(29\) | − 4.01646i | − 0.138499i | −0.997599 | − | 0.0692494i | \(-0.977940\pi\) | ||||
0.997599 | − | 0.0692494i | \(-0.0220604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.5033 | −0.661397 | −0.330699 | − | 0.943736i | \(-0.607284\pi\) | ||||
−0.330699 | + | 0.943736i | \(0.607284\pi\) | |||||||
\(32\) | 36.5080i | 1.14088i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 83.3223 | 2.45066 | ||||||||
\(35\) | − 1.70135i | − 0.0486101i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 43.5939 | 1.17821 | 0.589107 | − | 0.808055i | \(-0.299480\pi\) | ||||
0.589107 | + | 0.808055i | \(0.299480\pi\) | |||||||
\(38\) | 14.9847i | 0.394334i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.05456 | 0.0763639 | ||||||||
\(41\) | − 52.0734i | − 1.27008i | −0.772478 | − | 0.635042i | \(-0.780983\pi\) | ||||
0.772478 | − | 0.635042i | \(-0.219017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −62.5698 | −1.45511 | −0.727556 | − | 0.686048i | \(-0.759344\pi\) | ||||
−0.727556 | + | 0.686048i | \(0.759344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.9097 | −1.06325 | ||||||||
\(47\) | 38.7052i | 0.823515i | 0.911293 | + | 0.411758i | \(0.135085\pi\) | ||||
−0.911293 | + | 0.411758i | \(0.864915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0665 | 1.16462 | ||||||||
\(50\) | 90.4110i | 1.80822i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −185.382 | −3.56503 | ||||||||
\(53\) | 35.3780i | 0.667510i | 0.942660 | + | 0.333755i | \(0.108316\pi\) | ||||
−0.942660 | + | 0.333755i | \(0.891684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 190.428i | 3.40051i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.5412 | 0.250710 | ||||||||
\(59\) | 19.6883i | 0.333699i | 0.985982 | + | 0.166850i | \(0.0533594\pi\) | ||||
−0.985982 | + | 0.166850i | \(0.946641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.42431 | 0.105317 | 0.0526583 | − | 0.998613i | \(-0.483231\pi\) | ||||
0.0526583 | + | 0.998613i | \(0.483231\pi\) | |||||||
\(62\) | − 74.2301i | − 1.19726i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.1214 | −0.158147 | ||||||||
\(65\) | 3.36267i | 0.0517334i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.98708 | −0.0595087 | −0.0297543 | − | 0.999557i | \(-0.509472\pi\) | ||||
−0.0297543 | + | 0.999557i | \(0.509472\pi\) | |||||||
\(68\) | 209.601i | 3.08236i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.15957 | 0.0879938 | ||||||||
\(71\) | 54.7712i | 0.771426i | 0.922619 | + | 0.385713i | \(0.126044\pi\) | ||||
−0.922619 | + | 0.385713i | \(0.873956\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22.8087 | 0.312448 | 0.156224 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156224 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(74\) | 157.827i | 2.13280i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −37.6946 | −0.495981 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 57.1563 | 0.723497 | 0.361748 | − | 0.932276i | \(-0.382180\pi\) | ||||
0.361748 | + | 0.932276i | \(0.382180\pi\) | |||||||
\(80\) | 5.04069i | 0.0630086i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 188.526 | 2.29910 | ||||||||
\(83\) | 56.8060i | 0.684410i | 0.939625 | + | 0.342205i | \(0.111174\pi\) | ||||
−0.939625 | + | 0.342205i | \(0.888826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.80199 | 0.0447293 | ||||||||
\(86\) | − 226.527i | − 2.63404i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 28.1602i | 0.316407i | 0.987407 | + | 0.158203i | \(0.0505701\pi\) | ||||
−0.987407 | + | 0.158203i | \(0.949430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −209.637 | −2.30370 | ||||||||
\(92\) | − 123.034i | − 1.33733i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −140.128 | −1.49073 | ||||||||
\(95\) | 0.683750i | 0.00719737i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82.9323 | 0.854972 | 0.427486 | − | 0.904022i | \(-0.359399\pi\) | ||||
0.427486 | + | 0.904022i | \(0.359399\pi\) | |||||||
\(98\) | 206.603i | 2.10819i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −227.433 | −2.27433 | ||||||||
\(101\) | 153.046i | 1.51531i | 0.652658 | + | 0.757653i | \(0.273654\pi\) | ||||
−0.652658 | + | 0.757653i | \(0.726346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 105.119 | 1.02057 | 0.510287 | − | 0.860004i | \(-0.329539\pi\) | ||||
0.510287 | + | 0.860004i | \(0.329539\pi\) | |||||||
\(104\) | − 376.376i | − 3.61900i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −128.082 | −1.20832 | ||||||||
\(107\) | 112.763i | 1.05386i | 0.849910 | + | 0.526929i | \(0.176656\pi\) | ||||
−0.849910 | + | 0.526929i | \(0.823344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96.1530 | 0.882137 | 0.441069 | − | 0.897473i | \(-0.354600\pi\) | ||||
0.441069 | + | 0.897473i | \(0.354600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −314.249 | −2.80579 | ||||||||
\(113\) | − 104.101i | − 0.921249i | −0.887595 | − | 0.460625i | \(-0.847625\pi\) | ||||
0.887595 | − | 0.460625i | \(-0.152375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.23175 | −0.0194065 | ||||||||
\(116\) | 36.5789i | 0.315336i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −71.2792 | −0.604061 | ||||||||
\(119\) | 237.025i | 1.99181i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 23.2585i | 0.190644i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 186.729 | 1.50588 | ||||||||
\(125\) | 8.25540i | 0.0660432i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.05817 | 0.0634502 | 0.0317251 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317251 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(128\) | 109.388i | 0.854597i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.1742 | −0.0936477 | ||||||||
\(131\) | − 240.588i | − 1.83655i | −0.395947 | − | 0.918273i | \(-0.629584\pi\) | ||||
0.395947 | − | 0.918273i | \(-0.370416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −42.6266 | −0.320501 | ||||||||
\(134\) | − 14.4348i | − 0.107722i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −425.548 | −3.12903 | ||||||||
\(137\) | − 18.8680i | − 0.137723i | −0.997626 | − | 0.0688614i | \(-0.978063\pi\) | ||||
0.997626 | − | 0.0688614i | \(-0.0219366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 33.4773 | 0.240844 | 0.120422 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120422 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(140\) | 15.4946i | 0.110676i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −198.293 | −1.39643 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.663513 | 0.00457595 | ||||||||
\(146\) | 82.5765i | 0.565593i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −397.020 | −2.68257 | ||||||||
\(149\) | − 103.421i | − 0.694098i | −0.937847 | − | 0.347049i | \(-0.887184\pi\) | ||||
0.937847 | − | 0.347049i | \(-0.112816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 286.382 | 1.89657 | 0.948283 | − | 0.317425i | \(-0.102818\pi\) | ||||
0.948283 | + | 0.317425i | \(0.102818\pi\) | |||||||
\(152\) | − 76.5305i | − 0.503490i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3.38711i | − 0.0218523i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 261.304 | 1.66436 | 0.832179 | − | 0.554508i | \(-0.187093\pi\) | ||||
0.832179 | + | 0.554508i | \(0.187093\pi\) | |||||||
\(158\) | 206.928i | 1.30967i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.03106 | −0.0376941 | ||||||||
\(161\) | − 139.132i | − 0.864176i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 192.496 | 1.18096 | 0.590480 | − | 0.807052i | \(-0.298938\pi\) | ||||
0.590480 | + | 0.807052i | \(0.298938\pi\) | |||||||
\(164\) | 474.246i | 2.89174i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −205.660 | −1.23892 | ||||||||
\(167\) | − 211.194i | − 1.26463i | −0.774710 | − | 0.632316i | \(-0.782104\pi\) | ||||
0.774710 | − | 0.632316i | \(-0.217896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 245.342 | 1.45173 | ||||||||
\(170\) | 13.7647i | 0.0809688i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 569.839 | 3.31302 | ||||||||
\(173\) | − 103.773i | − 0.599844i | −0.953964 | − | 0.299922i | \(-0.903039\pi\) | ||||
0.953964 | − | 0.299922i | \(-0.0969607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −257.190 | −1.46966 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −101.951 | −0.572758 | ||||||||
\(179\) | 11.0578i | 0.0617755i | 0.999523 | + | 0.0308877i | \(0.00983344\pi\) | ||||
−0.999523 | + | 0.0308877i | \(0.990167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 124.377 | 0.687164 | 0.343582 | − | 0.939123i | \(-0.388360\pi\) | ||||
0.343582 | + | 0.939123i | \(0.388360\pi\) | |||||||
\(182\) | − 758.969i | − 4.17016i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 249.794 | 1.35758 | ||||||||
\(185\) | 7.20163i | 0.0389278i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 352.498i | − 1.87499i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.47544 | −0.0130286 | ||||||||
\(191\) | 177.560i | 0.929634i | 0.885407 | + | 0.464817i | \(0.153880\pi\) | ||||
−0.885407 | + | 0.464817i | \(0.846120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −243.331 | −1.26078 | −0.630391 | − | 0.776278i | \(-0.717105\pi\) | ||||
−0.630391 | + | 0.776278i | \(0.717105\pi\) | |||||||
\(194\) | 300.248i | 1.54767i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −519.718 | −2.65162 | ||||||||
\(197\) | − 215.588i | − 1.09435i | −0.837017 | − | 0.547177i | \(-0.815702\pi\) | ||||
0.837017 | − | 0.547177i | \(-0.184298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −44.0830 | −0.221523 | −0.110761 | − | 0.993847i | \(-0.535329\pi\) | ||||
−0.110761 | + | 0.993847i | \(0.535329\pi\) | |||||||
\(200\) | − 461.752i | − 2.30876i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −554.086 | −2.74300 | ||||||||
\(203\) | 41.3650i | 0.203768i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.60244 | 0.0419631 | ||||||||
\(206\) | 380.573i | 1.84744i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 621.103 | 2.98607 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 264.305 | 1.25263 | 0.626315 | − | 0.779570i | \(-0.284562\pi\) | ||||
0.626315 | + | 0.779570i | \(0.284562\pi\) | |||||||
\(212\) | − 322.197i | − 1.51980i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −408.245 | −1.90769 | ||||||||
\(215\) | − 10.3364i | − 0.0480764i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 211.161 | 0.973091 | ||||||||
\(218\) | 348.112i | 1.59684i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 468.473i | − 2.11979i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5149 | 0.0650890 | 0.0325445 | − | 0.999470i | \(-0.489639\pi\) | ||||
0.0325445 | + | 0.999470i | \(0.489639\pi\) | |||||||
\(224\) | − 375.991i | − 1.67853i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 376.887 | 1.66764 | ||||||||
\(227\) | − 122.517i | − 0.539722i | −0.962899 | − | 0.269861i | \(-0.913022\pi\) | ||||
0.962899 | − | 0.269861i | \(-0.0869778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.89370 | 0.0170030 | 0.00850152 | − | 0.999964i | \(-0.497294\pi\) | ||||
0.00850152 | + | 0.999964i | \(0.497294\pi\) | |||||||
\(230\) | − 8.07980i | − 0.0351295i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −74.2654 | −0.320110 | ||||||||
\(233\) | 365.767i | 1.56982i | 0.619612 | + | 0.784908i | \(0.287290\pi\) | ||||
−0.619612 | + | 0.784908i | \(0.712710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.39404 | −0.0272087 | ||||||||
\(236\) | − 179.306i | − 0.759770i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −858.125 | −3.60557 | ||||||||
\(239\) | − 147.298i | − 0.616308i | −0.951336 | − | 0.308154i | \(-0.900289\pi\) | ||||
0.951336 | − | 0.308154i | \(-0.0997112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −278.601 | −1.15602 | −0.578010 | − | 0.816029i | \(-0.696171\pi\) | ||||
−0.578010 | + | 0.816029i | \(0.696171\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −58.5078 | −0.239786 | ||||||||
\(245\) | 9.42728i | 0.0384787i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 84.2502 | 0.341094 | ||||||||
\(248\) | 379.112i | 1.52868i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.8878 | −0.119551 | ||||||||
\(251\) | − 48.3215i | − 0.192516i | −0.995356 | − | 0.0962580i | \(-0.969313\pi\) | ||||
0.995356 | − | 0.0962580i | \(-0.0306874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 29.1737i | 0.114857i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −436.515 | −1.70514 | ||||||||
\(257\) | − 199.225i | − 0.775195i | −0.921829 | − | 0.387597i | \(-0.873305\pi\) | ||||
0.921829 | − | 0.387597i | \(-0.126695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −448.967 | −1.73346 | ||||||||
\(260\) | − 30.6247i | − 0.117787i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 871.022 | 3.32451 | ||||||||
\(263\) | 69.3106i | 0.263538i | 0.991280 | + | 0.131769i | \(0.0420658\pi\) | ||||
−0.991280 | + | 0.131769i | \(0.957934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.84439 | −0.0220543 | ||||||||
\(266\) | − 154.325i | − 0.580170i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 36.3113 | 0.135490 | ||||||||
\(269\) | − 184.094i | − 0.684363i | −0.939634 | − | 0.342181i | \(-0.888834\pi\) | ||||
0.939634 | − | 0.342181i | \(-0.111166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 87.7148 | 0.323671 | 0.161835 | − | 0.986818i | \(-0.448259\pi\) | ||||
0.161835 | + | 0.986818i | \(0.448259\pi\) | |||||||
\(272\) | − 702.248i | − 2.58179i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 68.3096 | 0.249305 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 249.233 | 0.899757 | 0.449878 | − | 0.893090i | \(-0.351467\pi\) | ||||
0.449878 | + | 0.893090i | \(0.351467\pi\) | |||||||
\(278\) | 121.201i | 0.435975i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −31.4584 | −0.112352 | ||||||||
\(281\) | − 16.8466i | − 0.0599524i | −0.999551 | − | 0.0299762i | \(-0.990457\pi\) | ||||
0.999551 | − | 0.0299762i | \(-0.00954314\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −47.6126 | −0.168242 | −0.0841212 | − | 0.996456i | \(-0.526808\pi\) | ||||
−0.0841212 | + | 0.996456i | \(0.526808\pi\) | |||||||
\(284\) | − 498.815i | − 1.75639i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 536.297i | 1.86863i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −240.677 | −0.832793 | ||||||||
\(290\) | 2.40218i | 0.00828337i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −207.725 | −0.711386 | ||||||||
\(293\) | − 425.104i | − 1.45087i | −0.688293 | − | 0.725433i | \(-0.741640\pi\) | ||||
0.688293 | − | 0.725433i | \(-0.258360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.25246 | −0.0110253 | ||||||||
\(296\) | − 806.062i | − 2.72318i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 374.423 | 1.25645 | ||||||||
\(299\) | 274.991i | 0.919702i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 644.398 | 2.14086 | ||||||||
\(302\) | 1036.81i | 3.43316i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 126.292 | 0.415435 | ||||||||
\(305\) | 1.06129i | 0.00347962i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 463.469 | 1.50967 | 0.754836 | − | 0.655914i | \(-0.227716\pi\) | ||||
0.754836 | + | 0.655914i | \(0.227716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.2627 | 0.0395570 | ||||||||
\(311\) | 143.144i | 0.460269i | 0.973159 | + | 0.230135i | \(0.0739166\pi\) | ||||
−0.973159 | + | 0.230135i | \(0.926083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 237.744 | 0.759565 | 0.379783 | − | 0.925076i | \(-0.375999\pi\) | ||||
0.379783 | + | 0.925076i | \(0.375999\pi\) | |||||||
\(314\) | 946.024i | 3.01281i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −520.536 | −1.64727 | ||||||||
\(317\) | 313.909i | 0.990249i | 0.868822 | + | 0.495125i | \(0.164878\pi\) | ||||
−0.868822 | + | 0.495125i | \(0.835122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 1.67204i | − 0.00522514i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 503.714 | 1.56433 | ||||||||
\(323\) | − 95.2571i | − 0.294914i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 508.329 | 1.56409 | ||||||||
\(326\) | 696.913i | 2.13777i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −962.851 | −2.93552 | ||||||||
\(329\) | − 398.620i | − 1.21161i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −52.4920 | −0.158586 | −0.0792931 | − | 0.996851i | \(-0.525266\pi\) | ||||
−0.0792931 | + | 0.996851i | \(0.525266\pi\) | |||||||
\(332\) | − 517.347i | − 1.55827i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 764.604 | 2.28923 | ||||||||
\(335\) | − 0.658659i | − 0.00196615i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 493.841 | 1.46540 | 0.732702 | − | 0.680550i | \(-0.238259\pi\) | ||||
0.732702 | + | 0.680550i | \(0.238259\pi\) | |||||||
\(338\) | 888.233i | 2.62791i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.6257 | −0.101840 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −83.0752 | −0.242202 | ||||||||
\(344\) | 1156.93i | 3.36317i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 375.699 | 1.08584 | ||||||||
\(347\) | 451.711i | 1.30176i | 0.759181 | + | 0.650880i | \(0.225600\pi\) | ||||
−0.759181 | + | 0.650880i | \(0.774400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −177.153 | −0.507603 | −0.253802 | − | 0.967256i | \(-0.581681\pi\) | ||||
−0.253802 | + | 0.967256i | \(0.581681\pi\) | |||||||
\(350\) | − 931.130i | − 2.66037i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 590.460i | 1.67269i | 0.548203 | + | 0.836346i | \(0.315312\pi\) | ||||
−0.548203 | + | 0.836346i | \(0.684688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.04811 | −0.0254876 | ||||||||
\(356\) | − 256.462i | − 0.720399i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −40.0336 | −0.111826 | ||||||||
\(359\) | 592.141i | 1.64942i | 0.565558 | + | 0.824709i | \(0.308661\pi\) | ||||
−0.565558 | + | 0.824709i | \(0.691339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −343.869 | −0.952546 | ||||||||
\(362\) | 450.292i | 1.24390i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1909.22 | 5.24510 | ||||||||
\(365\) | 3.76796i | 0.0103232i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 226.762 | 0.617880 | 0.308940 | − | 0.951082i | \(-0.400026\pi\) | ||||
0.308940 | + | 0.951082i | \(0.400026\pi\) | |||||||
\(368\) | 412.215i | 1.12015i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.0727 | −0.0704669 | ||||||||
\(371\) | − 364.353i | − 0.982084i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 76.5478 | 0.205222 | 0.102611 | − | 0.994722i | \(-0.467280\pi\) | ||||
0.102611 | + | 0.994722i | \(0.467280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 715.669 | 1.90338 | ||||||||
\(377\) | − 81.7566i | − 0.216861i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 351.579 | 0.927649 | 0.463825 | − | 0.885927i | \(-0.346477\pi\) | ||||
0.463825 | + | 0.885927i | \(0.346477\pi\) | |||||||
\(380\) | − 6.22708i | − 0.0163871i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −642.837 | −1.68282 | ||||||||
\(383\) | 572.874i | 1.49575i | 0.663837 | + | 0.747877i | \(0.268927\pi\) | ||||
−0.663837 | + | 0.747877i | \(0.731073\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 880.953i | − 2.28226i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −755.285 | −1.94661 | ||||||||
\(389\) | − 196.178i | − 0.504313i | −0.967687 | − | 0.252156i | \(-0.918860\pi\) | ||||
0.967687 | − | 0.252156i | \(-0.0811397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 310.917 | 0.795185 | ||||||||
\(392\) | − 1055.17i | − 2.69177i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 780.512 | 1.98100 | ||||||||
\(395\) | 9.44211i | 0.0239041i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −105.240 | −0.265089 | −0.132544 | − | 0.991177i | \(-0.542315\pi\) | ||||
−0.132544 | + | 0.991177i | \(0.542315\pi\) | |||||||
\(398\) | − 159.598i | − 0.401000i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 761.992 | 1.90498 | ||||||||
\(401\) | 490.021i | 1.22200i | 0.791631 | + | 0.610999i | \(0.209232\pi\) | ||||
−0.791631 | + | 0.610999i | \(0.790768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −417.353 | −1.03562 | ||||||||
\(404\) | − 1393.83i | − 3.45007i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −149.757 | −0.368861 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −533.858 | −1.30528 | −0.652639 | − | 0.757669i | \(-0.726338\pi\) | ||||
−0.652639 | + | 0.757669i | \(0.726338\pi\) | |||||||
\(410\) | 31.1442i | 0.0759615i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −957.346 | −2.32366 | ||||||||
\(413\) | − 202.767i | − 0.490960i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.38426 | −0.0226127 | ||||||||
\(416\) | 743.135i | 1.78638i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 344.904i | − 0.823160i | −0.911374 | − | 0.411580i | \(-0.864977\pi\) | ||||
0.911374 | − | 0.411580i | \(-0.135023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −403.467 | −0.958355 | −0.479177 | − | 0.877718i | \(-0.659065\pi\) | ||||
−0.479177 | + | 0.877718i | \(0.659065\pi\) | |||||||
\(422\) | 956.888i | 2.26751i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 654.149 | 1.54280 | ||||||||
\(425\) | − 574.740i | − 1.35233i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −66.1631 | −0.154949 | ||||||||
\(428\) | − 1026.96i | − 2.39943i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 37.4219 | 0.0870277 | ||||||||
\(431\) | − 132.691i | − 0.307868i | −0.988081 | − | 0.153934i | \(-0.950806\pi\) | ||||
0.988081 | − | 0.153934i | \(-0.0491944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −823.887 | −1.90274 | −0.951370 | − | 0.308049i | \(-0.900324\pi\) | ||||
−0.951370 | + | 0.308049i | \(0.900324\pi\) | |||||||
\(434\) | 764.485i | 1.76149i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −875.689 | −2.00846 | ||||||||
\(437\) | 55.9154i | 0.127953i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −109.320 | −0.249021 | −0.124511 | − | 0.992218i | \(-0.539736\pi\) | ||||
−0.124511 | + | 0.992218i | \(0.539736\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1696.06 | 3.83723 | ||||||||
\(443\) | − 375.738i | − 0.848167i | −0.905623 | − | 0.424083i | \(-0.860596\pi\) | ||||
0.905623 | − | 0.424083i | \(-0.139404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.65201 | −0.0104540 | ||||||||
\(446\) | 52.5495i | 0.117824i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 104.239 | 0.232677 | ||||||||
\(449\) | 377.057i | 0.839770i | 0.907577 | + | 0.419885i | \(0.137930\pi\) | ||||
−0.907577 | + | 0.419885i | \(0.862070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 948.075i | 2.09751i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 443.560 | 0.977004 | ||||||||
\(455\) | − 34.6317i | − 0.0761136i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 397.734 | 0.870316 | 0.435158 | − | 0.900354i | \(-0.356693\pi\) | ||||
0.435158 | + | 0.900354i | \(0.356693\pi\) | |||||||
\(458\) | 14.0967i | 0.0307789i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.3251 | 0.0441849 | ||||||||
\(461\) | 452.581i | 0.981737i | 0.871234 | + | 0.490869i | \(0.163320\pi\) | ||||
−0.871234 | + | 0.490869i | \(0.836680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −125.818 | −0.271745 | −0.135873 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135873 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(464\) | − 122.554i | − 0.264126i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1324.22 | −2.84168 | ||||||||
\(467\) | − 277.000i | − 0.593147i | −0.955010 | − | 0.296574i | \(-0.904156\pi\) | ||||
0.955010 | − | 0.296574i | \(-0.0958440\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.0624 | 0.0875530 | ||||||||
\(470\) | − 23.1489i | − 0.0492530i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 364.041 | 0.771273 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 103.361 | 0.217603 | ||||||||
\(476\) | − 2158.65i | − 4.53497i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 533.275 | 1.11564 | ||||||||
\(479\) | − 500.992i | − 1.04591i | −0.852360 | − | 0.522956i | \(-0.824829\pi\) | ||||
0.852360 | − | 0.522956i | \(-0.175171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 887.370 | 1.84484 | ||||||||
\(482\) | − 1008.65i | − 2.09263i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.7003i | 0.0282480i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 690.163 | 1.41717 | 0.708586 | − | 0.705624i | \(-0.249333\pi\) | ||||
0.708586 | + | 0.705624i | \(0.249333\pi\) | |||||||
\(488\) | − 118.787i | − 0.243416i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −34.1305 | −0.0696540 | ||||||||
\(491\) | − 355.830i | − 0.724705i | −0.932041 | − | 0.362353i | \(-0.881974\pi\) | ||||
0.932041 | − | 0.362353i | \(-0.118026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −92.4378 | −0.187501 | ||||||||
\(494\) | 305.019i | 0.617447i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −625.618 | −1.26133 | ||||||||
\(497\) | − 564.081i | − 1.13497i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 145.012 | 0.290604 | 0.145302 | − | 0.989387i | \(-0.453585\pi\) | ||||
0.145302 | + | 0.989387i | \(0.453585\pi\) | |||||||
\(500\) | − 75.1840i | − 0.150368i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 174.943 | 0.348492 | ||||||||
\(503\) | − 868.917i | − 1.72747i | −0.503947 | − | 0.863734i | \(-0.668119\pi\) | ||||
0.503947 | − | 0.863734i | \(-0.331881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.2829 | −0.0500651 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −73.3878 | −0.144464 | ||||||||
\(509\) | 504.109i | 0.990391i | 0.868782 | + | 0.495195i | \(0.164904\pi\) | ||||
−0.868782 | + | 0.495195i | \(0.835096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −234.904 | −0.459694 | ||||||||
\(512\) | − 1142.80i | − 2.23204i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 721.273 | 1.40325 | ||||||||
\(515\) | 17.3655i | 0.0337194i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 1625.44i | − 3.13791i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 62.1767 | 0.119571 | ||||||||
\(521\) | 258.912i | 0.496951i | 0.968638 | + | 0.248476i | \(0.0799296\pi\) | ||||
−0.968638 | + | 0.248476i | \(0.920070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −597.180 | −1.14184 | −0.570918 | − | 0.821007i | \(-0.693413\pi\) | ||||
−0.570918 | + | 0.821007i | \(0.693413\pi\) | |||||||
\(524\) | 2191.09i | 4.18147i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −250.932 | −0.477056 | ||||||||
\(527\) | 471.878i | 0.895404i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 346.493 | 0.654997 | ||||||||
\(530\) | − 21.1590i | − 0.0399226i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 388.211 | 0.729720 | ||||||||
\(533\) | − 1059.97i | − 1.98870i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.6282 | −0.0348191 | ||||||||
\(536\) | 73.7221i | 0.137541i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 666.491 | 1.23883 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −241.706 | −0.446776 | −0.223388 | − | 0.974730i | \(-0.571712\pi\) | ||||
−0.223388 | + | 0.974730i | \(0.571712\pi\) | |||||||
\(542\) | 317.562i | 0.585908i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 840.222 | 1.54453 | ||||||||
\(545\) | 15.8843i | 0.0291455i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 535.306 | 0.978622 | 0.489311 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489311 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(548\) | 171.836i | 0.313569i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 16.6240i | − 0.0301706i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −588.644 | −1.06446 | ||||||||
\(554\) | 902.320i | 1.62874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −304.886 | −0.548356 | ||||||||
\(557\) | 38.6536i | 0.0693961i | 0.999398 | + | 0.0346980i | \(0.0110469\pi\) | ||||
−0.999398 | + | 0.0346980i | \(0.988953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1273.63 | −2.27841 | ||||||||
\(560\) | − 51.9134i | − 0.0927024i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.9914 | 0.108526 | ||||||||
\(563\) | 356.051i | 0.632418i | 0.948690 | + | 0.316209i | \(0.102410\pi\) | ||||
−0.948690 | + | 0.316209i | \(0.897590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1973 | 0.0304378 | ||||||||
\(566\) | − 172.376i | − 0.304552i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1012.73 | 1.78298 | ||||||||
\(569\) | − 98.7149i | − 0.173488i | −0.996231 | − | 0.0867442i | \(-0.972354\pi\) | ||||
0.996231 | − | 0.0867442i | \(-0.0276463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.7221 | 0.0660633 | 0.0330316 | − | 0.999454i | \(-0.489484\pi\) | ||||
0.0330316 | + | 0.999454i | \(0.489484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1941.61 | −3.38259 | ||||||||
\(575\) | 337.369i | 0.586728i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −978.346 | −1.69557 | −0.847787 | − | 0.530337i | \(-0.822065\pi\) | ||||
−0.847787 | + | 0.530337i | \(0.822065\pi\) | |||||||
\(578\) | − 871.346i | − 1.50752i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.04277 | −0.0104186 | ||||||||
\(581\) | − 585.037i | − 1.00695i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 421.739i | − 0.722156i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1539.04 | 2.62635 | ||||||||
\(587\) | − 1115.33i | − 1.90006i | −0.312162 | − | 0.950029i | \(-0.601053\pi\) | ||||
0.312162 | − | 0.950029i | \(-0.398947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −84.8625 | −0.144079 | ||||||||
\(590\) | − 11.7752i | − 0.0199580i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1330.18 | 2.24693 | ||||||||
\(593\) | − 1006.79i | − 1.69779i | −0.528563 | − | 0.848894i | \(-0.677269\pi\) | ||||
0.528563 | − | 0.848894i | \(-0.322731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.1562 | −0.0658087 | ||||||||
\(596\) | 941.877i | 1.58033i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −995.576 | −1.66484 | ||||||||
\(599\) | − 590.141i | − 0.985210i | −0.870253 | − | 0.492605i | \(-0.836045\pi\) | ||||
0.870253 | − | 0.492605i | \(-0.163955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 750.837 | 1.24931 | 0.624656 | − | 0.780900i | \(-0.285239\pi\) | ||||
0.624656 | + | 0.780900i | \(0.285239\pi\) | |||||||
\(602\) | 2332.97i | 3.87537i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2608.15 | −4.31813 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −176.162 | −0.290218 | −0.145109 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145109 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(608\) | 151.105i | 0.248529i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.84227 | −0.00629880 | ||||||||
\(611\) | 787.860i | 1.28946i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −908.432 | −1.48194 | −0.740972 | − | 0.671535i | \(-0.765635\pi\) | ||||
−0.740972 | + | 0.671535i | \(0.765635\pi\) | |||||||
\(614\) | 1677.94i | 2.73280i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 836.440i | 1.35566i | 0.735220 | + | 0.677828i | \(0.237079\pi\) | ||||
−0.735220 | + | 0.677828i | \(0.762921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 960.477 | 1.55166 | 0.775830 | − | 0.630942i | \(-0.217332\pi\) | ||||
0.775830 | + | 0.630942i | \(0.217332\pi\) | |||||||
\(620\) | 30.8473i | 0.0497537i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −518.237 | −0.833178 | ||||||||
\(623\) | − 290.018i | − 0.465518i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 622.954 | 0.996726 | ||||||||
\(626\) | 860.727i | 1.37496i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2379.76 | −3.78943 | ||||||||
\(629\) | − 1003.30i | − 1.59507i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 230.308 | 0.364988 | 0.182494 | − | 0.983207i | \(-0.441583\pi\) | ||||
0.182494 | + | 0.983207i | \(0.441583\pi\) | |||||||
\(632\) | − 1056.83i | − 1.67220i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1136.47 | −1.79255 | ||||||||
\(635\) | 1.33120i | 0.00209637i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1161.61 | 1.82356 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.0708 | −0.0282356 | ||||||||
\(641\) | 478.911i | 0.747131i | 0.927604 | + | 0.373565i | \(0.121865\pi\) | ||||
−0.927604 | + | 0.373565i | \(0.878135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −716.383 | −1.11413 | −0.557063 | − | 0.830470i | \(-0.688072\pi\) | ||||
−0.557063 | + | 0.830470i | \(0.688072\pi\) | |||||||
\(644\) | 1267.11i | 1.96757i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 344.868 | 0.533852 | ||||||||
\(647\) | − 977.171i | − 1.51031i | −0.655546 | − | 0.755155i | \(-0.727562\pi\) | ||||
0.655546 | − | 0.755155i | \(-0.272438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1840.35i | 2.83131i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1753.11 | −2.68882 | ||||||||
\(653\) | − 892.901i | − 1.36738i | −0.729771 | − | 0.683692i | \(-0.760373\pi\) | ||||
0.729771 | − | 0.683692i | \(-0.239627\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.7446 | 0.0606788 | ||||||||
\(656\) | − 1588.92i | − 2.42213i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1443.16 | 2.19325 | ||||||||
\(659\) | 350.792i | 0.532309i | 0.963930 | + | 0.266154i | \(0.0857531\pi\) | ||||
−0.963930 | + | 0.266154i | \(0.914247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −285.033 | −0.431215 | −0.215607 | − | 0.976480i | \(-0.569173\pi\) | ||||
−0.215607 | + | 0.976480i | \(0.569173\pi\) | |||||||
\(662\) | − 190.042i | − 0.287072i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1050.36 | 1.58186 | ||||||||
\(665\) | − 7.04184i | − 0.0105892i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.2604 | 0.0813499 | ||||||||
\(668\) | 1923.39i | 2.87933i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.38460 | 0.00355911 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −101.236 | −0.150426 | −0.0752128 | − | 0.997168i | \(-0.523964\pi\) | ||||
−0.0752128 | + | 0.997168i | \(0.523964\pi\) | |||||||
\(674\) | 1787.90i | 2.65267i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2234.39 | −3.30531 | ||||||||
\(677\) | − 399.059i | − 0.589453i | −0.955582 | − | 0.294726i | \(-0.904772\pi\) | ||||
0.955582 | − | 0.294726i | \(-0.0952285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −854.108 | −1.25789 | ||||||||
\(680\) | − 70.2998i | − 0.103382i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 781.537i | − 1.14427i | −0.820159 | − | 0.572135i | \(-0.806115\pi\) | ||||
0.820159 | − | 0.572135i | \(-0.193885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.11696 | 0.00455031 | ||||||||
\(686\) | − 300.765i | − 0.438433i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1909.19 | −2.77499 | ||||||||
\(689\) | 720.133i | 1.04519i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −551.762 | −0.798497 | −0.399249 | − | 0.916843i | \(-0.630729\pi\) | ||||
−0.399249 | + | 0.916843i | \(0.630729\pi\) | |||||||
\(692\) | 945.087i | 1.36573i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1635.37 | −2.35644 | ||||||||
\(695\) | 5.53039i | 0.00795740i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1198.46 | −1.71945 | ||||||||
\(698\) | − 641.365i | − 0.918861i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2342.30 | 3.34614 | ||||||||
\(701\) | 327.564i | 0.467281i | 0.972323 | + | 0.233640i | \(0.0750639\pi\) | ||||
−0.972323 | + | 0.233640i | \(0.924936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 180.434 | 0.256662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2137.70 | −3.02790 | ||||||||
\(707\) | − 1576.20i | − 2.22942i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1039.76 | 1.46652 | 0.733260 | − | 0.679949i | \(-0.237998\pi\) | ||||
0.733260 | + | 0.679949i | \(0.237998\pi\) | |||||||
\(710\) | − 32.7577i | − 0.0461376i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 520.689 | 0.731305 | ||||||||
\(713\) | − 276.990i | − 0.388485i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 100.706i | − 0.140651i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2143.78 | −2.98577 | ||||||||
\(719\) | − 909.087i | − 1.26438i | −0.774815 | − | 0.632188i | \(-0.782157\pi\) | ||||
0.774815 | − | 0.632188i | \(-0.217843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1082.61 | −1.50153 | ||||||||
\(722\) | − 1244.94i | − 1.72429i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1132.73 | −1.56454 | ||||||||
\(725\) | − 100.302i | − 0.138348i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −709.728 | −0.976242 | −0.488121 | − | 0.872776i | \(-0.662318\pi\) | ||||
−0.488121 | + | 0.872776i | \(0.662318\pi\) | |||||||
\(728\) | 3876.24i | 5.32451i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.6415 | −0.0186870 | ||||||||
\(731\) | 1440.03i | 1.96994i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −495.869 | −0.676493 | −0.338246 | − | 0.941058i | \(-0.609834\pi\) | ||||
−0.338246 | + | 0.941058i | \(0.609834\pi\) | |||||||
\(734\) | 820.967i | 1.11848i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −493.205 | −0.670115 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1099.53 | −1.48787 | −0.743934 | − | 0.668253i | \(-0.767042\pi\) | ||||
−0.743934 | + | 0.668253i | \(0.767042\pi\) | |||||||
\(740\) | − 65.5871i | − 0.0886312i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1319.10 | 1.77777 | ||||||||
\(743\) | 723.678i | 0.973994i | 0.873404 | + | 0.486997i | \(0.161908\pi\) | ||||
−0.873404 | + | 0.486997i | \(0.838092\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0849 | 0.0229328 | ||||||||
\(746\) | 277.133i | 0.371492i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1161.33i | − 1.55050i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −543.282 | −0.723412 | −0.361706 | − | 0.932292i | \(-0.617806\pi\) | ||||
−0.361706 | + | 0.932292i | \(0.617806\pi\) | |||||||
\(752\) | 1181.01i | 1.57049i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 295.991 | 0.392561 | ||||||||
\(755\) | 47.3097i | 0.0626619i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −347.247 | −0.458715 | −0.229357 | − | 0.973342i | \(-0.573662\pi\) | ||||
−0.229357 | + | 0.973342i | \(0.573662\pi\) | |||||||
\(758\) | 1272.85i | 1.67923i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.6427 | 0.0166351 | ||||||||
\(761\) | 802.222i | 1.05417i | 0.849813 | + | 0.527084i | \(0.176715\pi\) | ||||
−0.849813 | + | 0.527084i | \(0.823285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −990.266 | −1.29786 | ||||||||
\(764\) | − 1617.08i | − 2.11660i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2074.03 | −2.70761 | ||||||||
\(767\) | 400.762i | 0.522506i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1441.35 | 1.87432 | 0.937158 | − | 0.348905i | \(-0.113446\pi\) | ||||
0.937158 | + | 0.348905i | \(0.113446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2216.07 | 2.87056 | ||||||||
\(773\) | 1333.16i | 1.72466i | 0.506348 | + | 0.862329i | \(0.330995\pi\) | ||||
−0.506348 | + | 0.862329i | \(0.669005\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −512.023 | −0.660675 | ||||||||
\(776\) | − 1533.44i | − 1.97608i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 710.240 | 0.912905 | ||||||||
\(779\) | − 215.530i | − 0.276675i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1125.64i | 1.43944i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1741.27 | 2.22100 | ||||||||
\(785\) | 43.1670i | 0.0549898i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 442.103 | 0.561757 | 0.280878 | − | 0.959743i | \(-0.409374\pi\) | ||||
0.280878 | + | 0.959743i | \(0.409374\pi\) | |||||||
\(788\) | 1963.41i | 2.49164i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −34.1842 | −0.0432711 | ||||||||
\(791\) | 1072.12i | 1.35540i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 130.769 | 0.164905 | ||||||||
\(794\) | − 381.011i | − 0.479863i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 401.475 | 0.504365 | ||||||||
\(797\) | − 1298.24i | − 1.62891i | −0.580225 | − | 0.814456i | \(-0.697035\pi\) | ||||
0.580225 | − | 0.814456i | \(-0.302965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 890.790 | 1.11488 | ||||||||
\(800\) | 911.704i | 1.13963i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1774.07 | −2.21206 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.9844 | 0.0285521 | ||||||||
\(806\) | − 1510.98i | − 1.87467i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2829.86 | 3.50230 | ||||||||
\(809\) | 913.645i | 1.12935i | 0.825313 | + | 0.564675i | \(0.190999\pi\) | ||||
−0.825313 | + | 0.564675i | \(0.809001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −343.061 | −0.423010 | −0.211505 | − | 0.977377i | \(-0.567837\pi\) | ||||
−0.211505 | + | 0.977377i | \(0.567837\pi\) | |||||||
\(812\) | − 376.721i | − 0.463942i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.8001i | 0.0390185i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −258.974 | −0.316982 | ||||||||
\(818\) | − 1932.78i | − 2.36281i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −78.3445 | −0.0955421 | ||||||||
\(821\) | − 16.3641i | − 0.0199319i | −0.999950 | − | 0.00996596i | \(-0.996828\pi\) | ||||
0.999950 | − | 0.00996596i | \(-0.00317232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −63.5873 | −0.0772628 | −0.0386314 | − | 0.999254i | \(-0.512300\pi\) | ||||
−0.0386314 | + | 0.999254i | \(0.512300\pi\) | |||||||
\(824\) | − 1943.68i | − 2.35883i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 734.095 | 0.888734 | ||||||||
\(827\) | − 1174.88i | − 1.42066i | −0.703871 | − | 0.710328i | \(-0.748547\pi\) | ||||
0.703871 | − | 0.710328i | \(-0.251453\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −277.361 | −0.334573 | −0.167287 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167287 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(830\) | − 33.9747i | − 0.0409334i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −206.026 | −0.247627 | ||||||||
\(833\) | − 1313.37i | − 1.57667i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.8888 | 0.0417830 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1248.69 | 1.49008 | ||||||||
\(839\) | − 932.487i | − 1.11143i | −0.831374 | − | 0.555713i | \(-0.812445\pi\) | ||||
0.831374 | − | 0.555713i | \(-0.187555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 824.868 | 0.980818 | ||||||||
\(842\) | − 1460.71i | − 1.73481i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2407.09 | −2.85200 | ||||||||
\(845\) | 40.5300i | 0.0479645i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1079.49i | 1.27298i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2080.78 | 2.44798 | ||||||||
\(851\) | 588.932i | 0.692047i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1539.03 | 1.80425 | 0.902127 | − | 0.431471i | \(-0.142005\pi\) | ||||
0.902127 | + | 0.431471i | \(0.142005\pi\) | |||||||
\(854\) | − 239.536i | − 0.280488i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2085.01 | 2.43576 | ||||||||
\(857\) | − 443.512i | − 0.517517i | −0.965942 | − | 0.258758i | \(-0.916687\pi\) | ||||
0.965942 | − | 0.258758i | \(-0.0833133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1399.85 | 1.62962 | 0.814812 | − | 0.579725i | \(-0.196840\pi\) | ||||
0.814812 | + | 0.579725i | \(0.196840\pi\) | |||||||
\(860\) | 94.1364i | 0.109461i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 480.395 | 0.557302 | ||||||||
\(863\) | 1447.63i | 1.67744i | 0.544566 | + | 0.838718i | \(0.316694\pi\) | ||||
−0.544566 | + | 0.838718i | \(0.683306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1431 | 0.0198186 | ||||||||
\(866\) | − 2982.79i | − 3.44433i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1923.09 | −2.21555 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −81.1586 | −0.0931786 | ||||||||
\(872\) | − 1777.89i | − 2.03887i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −202.436 | −0.231620 | ||||||||
\(875\) | − 85.0212i | − 0.0971671i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 193.706 | 0.220874 | 0.110437 | − | 0.993883i | \(-0.464775\pi\) | ||||
0.110437 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(878\) | − 395.782i | − 0.450777i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1111.18i | 1.26127i | 0.776079 | + | 0.630636i | \(0.217206\pi\) | ||||
−0.776079 | + | 0.630636i | \(0.782794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 710.379 | 0.804507 | 0.402253 | − | 0.915528i | \(-0.368227\pi\) | ||||
0.402253 | + | 0.915528i | \(0.368227\pi\) | |||||||
\(884\) | 4266.50i | 4.82636i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1360.32 | 1.53535 | ||||||||
\(887\) | − 1134.08i | − 1.27856i | −0.768975 | − | 0.639279i | \(-0.779233\pi\) | ||||
0.768975 | − | 0.639279i | \(-0.220767\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.9899 | −0.0933520 | ||||||||
\(890\) | − 16.8421i | − 0.0189237i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −132.190 | −0.148196 | ||||||||
\(893\) | 160.200i | 0.179395i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.82673 | −0.00204104 | ||||||||
\(896\) | − 1126.58i | − 1.25734i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1365.09 | −1.52015 | ||||||||
\(899\) | 82.3508i | 0.0916027i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 814.215 | 0.903680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1924.86 | −2.12927 | ||||||||
\(905\) | 20.5468i | 0.0227036i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −987.303 | −1.08854 | −0.544268 | − | 0.838911i | \(-0.683193\pi\) | ||||
−0.544268 | + | 0.838911i | \(0.683193\pi\) | |||||||
\(908\) | 1115.79i | 1.22885i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 125.380 | 0.137781 | ||||||||
\(911\) | 1029.67i | 1.13026i | 0.825002 | + | 0.565130i | \(0.191174\pi\) | ||||
−0.825002 | + | 0.565130i | \(0.808826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1439.95i | 1.57544i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.4609 | −0.0387127 | ||||||||
\(917\) | 2477.78i | 2.70205i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 555.392 | 0.604343 | 0.302172 | − | 0.953254i | \(-0.402288\pi\) | ||||
0.302172 | + | 0.953254i | \(0.402288\pi\) | |||||||
\(920\) | 41.2655i | 0.0448538i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1638.52 | −1.77714 | ||||||||
\(923\) | 1114.89i | 1.20790i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1088.66 | 1.17693 | ||||||||
\(926\) | − 455.511i | − 0.491913i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 146.633 | 0.158010 | ||||||||
\(929\) | − 624.021i | − 0.671713i | −0.941913 | − | 0.335856i | \(-0.890974\pi\) | ||||
0.941913 | − | 0.335856i | \(-0.109026\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 236.196 | 0.253701 | ||||||||
\(932\) | − 3331.13i | − 3.57418i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1002.85 | 1.07371 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −270.217 | −0.288386 | −0.144193 | − | 0.989550i | \(-0.546059\pi\) | ||||
−0.144193 | + | 0.989550i | \(0.546059\pi\) | |||||||
\(938\) | 148.662i | 0.158488i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 58.2321 | 0.0619490 | ||||||||
\(941\) | − 1656.43i | − 1.76029i | −0.474703 | − | 0.880146i | \(-0.657445\pi\) | ||||
0.474703 | − | 0.880146i | \(-0.342555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 703.486 | 0.746008 | ||||||||
\(944\) | 600.747i | 0.636385i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 771.207i | − 0.814368i | −0.913346 | − | 0.407184i | \(-0.866511\pi\) | ||||
0.913346 | − | 0.407184i | \(-0.133489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 464.280 | 0.489231 | ||||||||
\(950\) | 374.208i | 0.393903i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4382.66 | 4.60363 | ||||||||
\(953\) | 297.525i | 0.312199i | 0.987741 | + | 0.156099i | \(0.0498920\pi\) | ||||
−0.987741 | + | 0.156099i | \(0.950108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.3326 | −0.0307148 | ||||||||
\(956\) | 1341.48i | 1.40322i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1813.79 | 1.89331 | ||||||||
\(959\) | 194.319i | 0.202627i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −540.614 | −0.562553 | ||||||||
\(962\) | 3212.63i | 3.33953i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2537.29 | 2.63204 | ||||||||
\(965\) | − 40.1978i | − 0.0416558i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1078.20 | −1.11499 | −0.557497 | − | 0.830179i | \(-0.688238\pi\) | ||||
−0.557497 | + | 0.830179i | \(0.688238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −49.6004 | −0.0511344 | ||||||||
\(971\) | 687.460i | 0.707992i | 0.935247 | + | 0.353996i | \(0.115177\pi\) | ||||
−0.935247 | + | 0.353996i | \(0.884823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −344.778 | −0.354345 | ||||||||
\(974\) | 2498.66i | 2.56536i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 196.025 | 0.200845 | ||||||||
\(977\) | − 1597.66i | − 1.63527i | −0.575738 | − | 0.817634i | \(-0.695285\pi\) | ||||
0.575738 | − | 0.817634i | \(-0.304715\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 85.8566i | − 0.0876087i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1288.25 | 1.31186 | ||||||||
\(983\) | − 1254.84i | − 1.27654i | −0.769811 | − | 0.638272i | \(-0.779650\pi\) | ||||
0.769811 | − | 0.638272i | \(-0.220350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.6147 | 0.0361571 | ||||||||
\(986\) | − 334.661i | − 0.339413i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −767.288 | −0.776607 | ||||||||
\(989\) | − 845.287i | − 0.854689i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 973.882 | 0.982727 | 0.491363 | − | 0.870955i | \(-0.336499\pi\) | ||||
0.491363 | + | 0.870955i | \(0.336499\pi\) | |||||||
\(992\) | − 748.536i | − 0.754572i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2042.20 | 2.05452 | ||||||||
\(995\) | − 7.28243i | − 0.00731903i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1601.03 | −1.60585 | −0.802923 | − | 0.596083i | \(-0.796723\pi\) | ||||
−0.802923 | + | 0.596083i | \(0.796723\pi\) | |||||||
\(998\) | 524.999i | 0.526051i | ||||||||
\(999\) | 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 | 1089.3.b.j.485.16 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.1 | 16 | ||
11.7 | odd | 10 | 99.3.l.a.71.8 | yes | 32 | ||
11.8 | odd | 10 | 99.3.l.a.53.1 | ✓ | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.1 | 16 | |||
33.8 | even | 10 | 99.3.l.a.53.8 | yes | 32 | ||
33.29 | even | 10 | 99.3.l.a.71.1 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.53.1 | ✓ | 32 | 11.8 | odd | 10 | ||
99.3.l.a.53.8 | yes | 32 | 33.8 | even | 10 | ||
99.3.l.a.71.1 | yes | 32 | 33.29 | even | 10 | ||
99.3.l.a.71.8 | yes | 32 | 11.7 | odd | 10 | ||
1089.3.b.i.485.1 | 16 | 11.10 | odd | 2 | |||
1089.3.b.i.485.16 | 16 | 33.32 | even | 2 | |||
1089.3.b.j.485.1 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.b.j.485.16 | 16 | 1.1 | even | 1 | trivial |