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 | 485.1 | ||
Root | \(-3.62039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.i.485.16 |
$q$-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 | \(-0.639797\pi\) | ||||
0.425202 | − | 0.905098i | \(-0.360203\pi\) | |||||||
\(3\) | 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 | \(-0.236885\pi\) | ||||
0.735633 | + | 0.677381i | \(0.236885\pi\) | |||||||
\(8\) | 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 | \(-0.786260\pi\) | ||||
−0.782899 | + | 0.622148i | \(0.786260\pi\) | |||||||
\(14\) | − 37.2859i | − 2.66328i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 30.5130 | 1.90706 | ||||||||
\(17\) | 23.0147i | 1.35381i | 0.736072 | + | 0.676903i | \(0.236679\pi\) | ||||
−0.736072 | + | 0.676903i | \(0.763321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.13897 | −0.217840 | −0.108920 | − | 0.994051i | \(-0.534739\pi\) | ||||
−0.108920 | + | 0.994051i | \(0.534739\pi\) | |||||||
\(20\) | − 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 | \(0.0220604\pi\) | ||||
−0.997599 | + | 0.0692494i | \(0.977940\pi\) | |||||||
\(30\) | 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 | \(0.219017\pi\) | ||||
−0.772478 | + | 0.635042i | \(0.780983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.5698 | 1.45511 | 0.727556 | − | 0.686048i | \(-0.240656\pi\) | ||||
0.727556 | + | 0.686048i | \(0.240656\pi\) | |||||||
\(44\) | 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 | \(-0.516769\pi\) | ||||
−0.0526583 | + | 0.998613i | \(0.516769\pi\) | |||||||
\(62\) | 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 | \(-0.549932\pi\) | ||||
−0.156224 | + | 0.987722i | \(0.549932\pi\) | |||||||
\(74\) | − 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 | \(-0.617820\pi\) | ||||
−0.361748 | + | 0.932276i | \(0.617820\pi\) | |||||||
\(80\) | 5.04069i | 0.0630086i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 188.526 | 2.29910 | ||||||||
\(83\) | − 56.8060i | − 0.684410i | −0.939625 | − | 0.342205i | \(-0.888826\pi\) | ||||
0.939625 | − | 0.342205i | \(-0.111174\pi\) | |||||||
\(84\) | 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 | \(-0.726346\pi\) | ||||
0.652658 | − | 0.757653i | \(-0.273654\pi\) | |||||||
\(102\) | 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 | \(-0.823344\pi\) | ||||
0.849910 | − | 0.526929i | \(-0.176656\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.1530 | −0.882137 | −0.441069 | − | 0.897473i | \(-0.645400\pi\) | ||||
−0.441069 | + | 0.897473i | \(0.645400\pi\) | |||||||
\(110\) | 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 | \(-0.510100\pi\) | ||||
−0.0317251 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(128\) | − 109.388i | − 0.854597i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.1742 | −0.0936477 | ||||||||
\(131\) | 240.588i | 1.83655i | 0.395947 | + | 0.918273i | \(0.370416\pi\) | ||||
−0.395947 | + | 0.918273i | \(0.629584\pi\) | |||||||
\(132\) | 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 | \(-0.538425\pi\) | ||||
−0.120422 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(140\) | − 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 | \(0.112816\pi\) | ||||
−0.937847 | + | 0.347049i | \(0.887184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −286.382 | −1.89657 | −0.948283 | − | 0.317425i | \(-0.897182\pi\) | ||||
−0.948283 | + | 0.317425i | \(0.897182\pi\) | |||||||
\(152\) | − 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 | \(0.217896\pi\) | ||||
−0.774710 | + | 0.632316i | \(0.782104\pi\) | |||||||
\(168\) | 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 | \(0.0969607\pi\) | ||||
−0.953964 | + | 0.299922i | \(0.903039\pi\) | |||||||
\(174\) | 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 | \(-0.282895\pi\) | ||||
0.630391 | + | 0.776278i | \(0.282895\pi\) | |||||||
\(194\) | − 300.248i | − 1.54767i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −519.718 | −2.65162 | ||||||||
\(197\) | 215.588i | 1.09435i | 0.837017 | + | 0.547177i | \(0.184298\pi\) | ||||
−0.837017 | + | 0.547177i | \(0.815702\pi\) | |||||||
\(198\) | 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 | \(-0.715438\pi\) | ||||
−0.626315 | + | 0.779570i | \(0.715438\pi\) | |||||||
\(212\) | − 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 | \(0.0869778\pi\) | ||||
−0.962899 | + | 0.269861i | \(0.913022\pi\) | |||||||
\(228\) | 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 | \(-0.712710\pi\) | ||||
0.619612 | − | 0.784908i | \(-0.287290\pi\) | |||||||
\(234\) | 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 | \(0.0997112\pi\) | ||||
−0.951336 | + | 0.308154i | \(0.900289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 278.601 | 1.15602 | 0.578010 | − | 0.816029i | \(-0.303829\pi\) | ||||
0.578010 | + | 0.816029i | \(0.303829\pi\) | |||||||
\(242\) | 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 | \(-0.957934\pi\) | ||||
0.991280 | − | 0.131769i | \(-0.0420658\pi\) | |||||||
\(264\) | 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 | \(-0.551741\pi\) | ||||
−0.161835 | + | 0.986818i | \(0.551741\pi\) | |||||||
\(272\) | 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 | \(-0.648533\pi\) | ||||
−0.449878 | + | 0.893090i | \(0.648533\pi\) | |||||||
\(278\) | 121.201i | 0.435975i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −31.4584 | −0.112352 | ||||||||
\(281\) | 16.8466i | 0.0599524i | 0.999551 | + | 0.0299762i | \(0.00954314\pi\) | ||||
−0.999551 | + | 0.0299762i | \(0.990457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 47.6126 | 0.168242 | 0.0841212 | − | 0.996456i | \(-0.473192\pi\) | ||||
0.0841212 | + | 0.996456i | \(0.473192\pi\) | |||||||
\(284\) | − 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 | \(0.258360\pi\) | ||||
−0.688293 | + | 0.725433i | \(0.741640\pi\) | |||||||
\(294\) | 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 | \(-0.772284\pi\) | ||||
−0.754836 | + | 0.655914i | \(0.772284\pi\) | |||||||
\(308\) | 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 | \(-0.761741\pi\) | ||||
−0.732702 | + | 0.680550i | \(0.761741\pi\) | |||||||
\(338\) | − 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 | \(-0.774400\pi\) | ||||
0.759181 | − | 0.650880i | \(-0.225600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 177.153 | 0.507603 | 0.253802 | − | 0.967256i | \(-0.418319\pi\) | ||||
0.253802 | + | 0.967256i | \(0.418319\pi\) | |||||||
\(350\) | − 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 | \(-0.691339\pi\) | ||||
0.565558 | − | 0.824709i | \(-0.308661\pi\) | |||||||
\(360\) | 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 | \(-0.532720\pi\) | ||||
−0.102611 | + | 0.994722i | \(0.532720\pi\) | |||||||
\(374\) | 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 | \(-0.273662\pi\) | ||||
0.652639 | + | 0.757669i | \(0.273662\pi\) | |||||||
\(410\) | 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 | \(0.0491944\pi\) | ||||
−0.988081 | + | 0.153934i | \(0.950806\pi\) | |||||||
\(432\) | 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 | \(-0.460264\pi\) | ||||
0.124511 | + | 0.992218i | \(0.460264\pi\) | |||||||
\(440\) | 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 | \(-0.643307\pi\) | ||||
−0.435158 | + | 0.900354i | \(0.643307\pi\) | |||||||
\(458\) | − 14.0967i | − 0.0307789i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20.3251 | 0.0441849 | ||||||||
\(461\) | − 452.581i | − 0.981737i | −0.871234 | − | 0.490869i | \(-0.836680\pi\) | ||||
0.871234 | − | 0.490869i | \(-0.163320\pi\) | |||||||
\(462\) | 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 | \(0.175171\pi\) | ||||
−0.852360 | + | 0.522956i | \(0.824829\pi\) | |||||||
\(480\) | 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 | \(0.118026\pi\) | ||||
−0.932041 | + | 0.362353i | \(0.881974\pi\) | |||||||
\(492\) | 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 | \(0.331881\pi\) | ||||
−0.503947 | + | 0.863734i | \(0.668119\pi\) | |||||||
\(504\) | 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 | \(-0.306587\pi\) | ||||
0.570918 | + | 0.821007i | \(0.306587\pi\) | |||||||
\(524\) | − 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 | \(-0.428288\pi\) | ||||
0.223388 | + | 0.974730i | \(0.428288\pi\) | |||||||
\(542\) | 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 | \(-0.662752\pi\) | ||||
−0.489311 | + | 0.872109i | \(0.662752\pi\) | |||||||
\(548\) | 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 | \(-0.988953\pi\) | ||||
0.999398 | − | 0.0346980i | \(-0.0110469\pi\) | |||||||
\(558\) | 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 | \(-0.897590\pi\) | ||||
0.948690 | − | 0.316209i | \(-0.102410\pi\) | |||||||
\(564\) | 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 | \(0.0276463\pi\) | ||||
−0.996231 | + | 0.0867442i | \(0.972354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.7221 | −0.0660633 | −0.0330316 | − | 0.999454i | \(-0.510516\pi\) | ||||
−0.0330316 | + | 0.999454i | \(0.510516\pi\) | |||||||
\(572\) | 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 | \(0.322731\pi\) | ||||
−0.528563 | + | 0.848894i | \(0.677269\pi\) | |||||||
\(594\) | 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 | \(-0.714761\pi\) | ||||
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(602\) | − 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 | \(-0.453647\pi\) | ||||
0.145109 | + | 0.989416i | \(0.453647\pi\) | |||||||
\(608\) | 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 | \(-0.234365\pi\) | ||||
0.740972 | + | 0.671535i | \(0.234365\pi\) | |||||||
\(614\) | 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 | \(-0.914247\pi\) | ||||
0.963930 | − | 0.266154i | \(-0.0857531\pi\) | |||||||
\(660\) | 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 | \(-0.476036\pi\) | ||||
0.0752128 | + | 0.997168i | \(0.476036\pi\) | |||||||
\(674\) | 1787.90i | 2.65267i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2234.39 | −3.30531 | ||||||||
\(677\) | 399.059i | 0.589453i | 0.955582 | + | 0.294726i | \(0.0952285\pi\) | ||||
−0.955582 | + | 0.294726i | \(0.904772\pi\) | |||||||
\(678\) | 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 | \(-0.924936\pi\) | ||||
0.972323 | − | 0.233640i | \(-0.0750639\pi\) | |||||||
\(702\) | 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 | \(-0.390166\pi\) | ||||
0.338246 | + | 0.941058i | \(0.390166\pi\) | |||||||
\(734\) | − 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 | \(-0.232958\pi\) | ||||
0.743934 | + | 0.668253i | \(0.232958\pi\) | |||||||
\(740\) | − 65.5871i | − 0.0886312i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1319.10 | 1.77777 | ||||||||
\(743\) | − 723.678i | − 0.973994i | −0.873404 | − | 0.486997i | \(-0.838092\pi\) | ||||
0.873404 | − | 0.486997i | \(-0.161908\pi\) | |||||||
\(744\) | 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 | \(-0.823285\pi\) | ||||
0.849813 | − | 0.527084i | \(-0.176715\pi\) | |||||||
\(762\) | 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 | \(-0.886554\pi\) | ||||
−0.937158 | + | 0.348905i | \(0.886554\pi\) | |||||||
\(770\) | 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 | \(-0.590626\pi\) | ||||
−0.280878 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(788\) | − 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 | \(-0.809001\pi\) | ||||
0.825313 | − | 0.564675i | \(-0.190999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 343.061 | 0.423010 | 0.211505 | − | 0.977377i | \(-0.432163\pi\) | ||||
0.211505 | + | 0.977377i | \(0.432163\pi\) | |||||||
\(812\) | − 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 | \(0.00317232\pi\) | ||||
−0.999950 | + | 0.00996596i | \(0.996828\pi\) | |||||||
\(822\) | 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 | \(0.251453\pi\) | ||||
−0.703871 | + | 0.710328i | \(0.748547\pi\) | |||||||
\(828\) | 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 | \(-0.857995\pi\) | ||||
−0.902127 | + | 0.431471i | \(0.857995\pi\) | |||||||
\(854\) | 239.536i | 0.280488i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2085.01 | 2.43576 | ||||||||
\(857\) | 443.512i | 0.517517i | 0.965942 | + | 0.258758i | \(0.0833133\pi\) | ||||
−0.965942 | + | 0.258758i | \(0.916687\pi\) | |||||||
\(858\) | 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 | \(-0.535225\pi\) | ||||
−0.110437 | + | 0.993883i | \(0.535225\pi\) | |||||||
\(878\) | − 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 | \(0.220767\pi\) | ||||
−0.768975 | + | 0.639279i | \(0.779233\pi\) | |||||||
\(888\) | 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 | \(-0.597712\pi\) | ||||
−0.302172 | + | 0.953254i | \(0.597712\pi\) | |||||||
\(920\) | − 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 | \(-0.453941\pi\) | ||||
0.144193 | + | 0.989550i | \(0.453941\pi\) | |||||||
\(938\) | 148.662i | 0.158488i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 58.2321 | 0.0619490 | ||||||||
\(941\) | 1656.43i | 1.76029i | 0.474703 | + | 0.880146i | \(0.342555\pi\) | ||||
−0.474703 | + | 0.880146i | \(0.657445\pi\) | |||||||
\(942\) | 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 | \(-0.950108\pi\) | ||||
0.987741 | − | 0.156099i | \(-0.0498920\pi\) | |||||||
\(954\) | 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 | \(-0.311762\pi\) | ||||
0.557497 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(968\) | 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 | \(-0.203277\pi\) | ||||
0.802923 | + | 0.596083i | \(0.203277\pi\) | |||||||
\(998\) | − 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.i.485.1 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.i.485.16 | 16 | ||
11.3 | even | 5 | 99.3.l.a.53.1 | ✓ | 32 | ||
11.4 | even | 5 | 99.3.l.a.71.8 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.j.485.16 | 16 | |||
33.14 | odd | 10 | 99.3.l.a.53.8 | yes | 32 | ||
33.26 | odd | 10 | 99.3.l.a.71.1 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.j.485.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.53.1 | ✓ | 32 | 11.3 | even | 5 | ||
99.3.l.a.53.8 | yes | 32 | 33.14 | odd | 10 | ||
99.3.l.a.71.1 | yes | 32 | 33.26 | odd | 10 | ||
99.3.l.a.71.8 | yes | 32 | 11.4 | even | 5 | ||
1089.3.b.i.485.1 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.i.485.16 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.b.j.485.1 | 16 | 33.32 | even | 2 | |||
1089.3.b.j.485.16 | 16 | 11.10 | odd | 2 |