Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(757,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.757");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.l (of order \(4\), degree \(2\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 757.1 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.757 |
Dual form | 900.3.l.b.793.1 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.44949 | − | 7.44949i | −1.06421 | − | 1.06421i | −0.997792 | − | 0.0664211i | \(-0.978842\pi\) |
−0.0664211 | − | 0.997792i | \(-0.521158\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.2474 | 1.47704 | 0.738520 | − | 0.674231i | \(-0.235525\pi\) | ||||
0.738520 | + | 0.674231i | \(0.235525\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.2474 | + | 12.2474i | −0.942111 | + | 0.942111i | −0.998414 | − | 0.0563023i | \(-0.982069\pi\) |
0.0563023 | + | 0.998414i | \(0.482069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.55051 | − | 7.55051i | −0.444148 | − | 0.444148i | 0.449256 | − | 0.893403i | \(-0.351689\pi\) |
−0.893403 | + | 0.449256i | \(0.851689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 14.4949i | − | 0.762889i | −0.924392 | − | 0.381445i | \(-0.875427\pi\) | ||
0.924392 | − | 0.381445i | \(-0.124573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65153 | + | 2.65153i | −0.115284 | + | 0.115284i | −0.762395 | − | 0.647111i | \(-0.775977\pi\) |
0.647111 | + | 0.762395i | \(0.275977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.2474i | 1.18095i | 0.807057 | + | 0.590473i | \(0.201059\pi\) | ||||
−0.807057 | + | 0.590473i | \(0.798941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.4949 | −0.661126 | −0.330563 | − | 0.943784i | \(-0.607239\pi\) | ||||
−0.330563 | + | 0.943784i | \(0.607239\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | − | 7.34847i | −0.198607 | − | 0.198607i | 0.600795 | − | 0.799403i | \(-0.294851\pi\) |
−0.799403 | + | 0.600795i | \(0.794851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −25.5051 | −0.622076 | −0.311038 | − | 0.950398i | \(-0.600677\pi\) | ||||
−0.311038 | + | 0.950398i | \(0.600677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −25.1010 | + | 25.1010i | −0.583745 | + | 0.583745i | −0.935930 | − | 0.352186i | \(-0.885439\pi\) |
0.352186 | + | 0.935930i | \(0.385439\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.0454 | + | 22.0454i | 0.469051 | + | 0.469051i | 0.901607 | − | 0.432556i | \(-0.142388\pi\) |
−0.432556 | + | 0.901607i | \(0.642388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 61.9898i | 1.26510i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.3031 | + | 35.3031i | −0.666096 | + | 0.666096i | −0.956810 | − | 0.290714i | \(-0.906107\pi\) |
0.290714 | + | 0.956810i | \(0.406107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 88.7423i | 1.50411i | 0.659102 | + | 0.752054i | \(0.270937\pi\) | ||||
−0.659102 | + | 0.752054i | \(0.729063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.495 | −1.68024 | −0.840122 | − | 0.542397i | \(-0.817517\pi\) | ||||
−0.840122 | + | 0.542397i | \(0.817517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.6969 | + | 24.6969i | 0.368611 | + | 0.368611i | 0.866970 | − | 0.498359i | \(-0.166064\pi\) |
−0.498359 | + | 0.866970i | \(0.666064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −77.9796 | −1.09830 | −0.549152 | − | 0.835722i | \(-0.685049\pi\) | ||||
−0.549152 | + | 0.835722i | \(0.685049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 44.1918 | − | 44.1918i | 0.605368 | − | 0.605368i | −0.336364 | − | 0.941732i | \(-0.609197\pi\) |
0.941732 | + | 0.336364i | \(0.109197\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −121.035 | − | 121.035i | −1.57189 | − | 1.57189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 48.4949i | − | 0.613859i | −0.951732 | − | 0.306930i | \(-0.900698\pi\) | ||
0.951732 | − | 0.306930i | \(-0.0993017\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.641 | + | 101.641i | −1.22459 | + | 1.22459i | −0.258613 | + | 0.965981i | \(0.583266\pi\) |
−0.965981 | + | 0.258613i | \(0.916734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 156.969i | − | 1.76370i | −0.471529 | − | 0.881850i | \(-0.656298\pi\) | ||
0.471529 | − | 0.881850i | \(-0.343702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 182.474 | 2.00521 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −55.4041 | − | 55.4041i | −0.571176 | − | 0.571176i | 0.361281 | − | 0.932457i | \(-0.382340\pi\) |
−0.932457 | + | 0.361281i | \(0.882340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −45.7526 | −0.452996 | −0.226498 | − | 0.974012i | \(-0.572728\pi\) | ||||
−0.226498 | + | 0.974012i | \(0.572728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −23.1566 | + | 23.1566i | −0.224822 | + | 0.224822i | −0.810525 | − | 0.585704i | \(-0.800818\pi\) |
0.585704 | + | 0.810525i | \(0.300818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3383 | + | 16.3383i | 0.152694 | + | 0.152694i | 0.779320 | − | 0.626626i | \(-0.215565\pi\) |
−0.626626 | + | 0.779320i | \(0.715565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 159.485i | 1.46316i | 0.681754 | + | 0.731581i | \(0.261217\pi\) | ||||
−0.681754 | + | 0.731581i | \(0.738783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0556 | − | 13.0556i | 0.115536 | − | 0.115536i | −0.646975 | − | 0.762511i | \(-0.723966\pi\) |
0.762511 | + | 0.646975i | \(0.223966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.495i | 0.945335i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 142.980 | 1.18165 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.44949 | − | 7.44949i | −0.0586574 | − | 0.0586574i | 0.677170 | − | 0.735827i | \(-0.263206\pi\) |
−0.735827 | + | 0.677170i | \(0.763206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.7526 | −0.150783 | −0.0753914 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753914 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −107.980 | + | 107.980i | −0.811877 | + | 0.811877i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −101.641 | − | 101.641i | −0.741907 | − | 0.741907i | 0.231037 | − | 0.972945i | \(-0.425788\pi\) |
−0.972945 | + | 0.231037i | \(0.925788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24.0204i | 0.172809i | 0.996260 | + | 0.0864044i | \(0.0275377\pi\) | ||||
−0.996260 | + | 0.0864044i | \(0.972462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198.990 | + | 198.990i | −1.39154 | + | 1.39154i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 199.732i | 1.34048i | 0.742143 | + | 0.670242i | \(0.233810\pi\) | ||||
−0.742143 | + | 0.670242i | \(0.766190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −158.990 | −1.05291 | −0.526456 | − | 0.850202i | \(-0.676480\pi\) | ||||
−0.526456 | + | 0.850202i | \(0.676480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 37.3485 | + | 37.3485i | 0.237888 | + | 0.237888i | 0.815975 | − | 0.578087i | \(-0.196201\pi\) |
−0.578087 | + | 0.815975i | \(0.696201\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 39.5051 | 0.245373 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.98979 | + | 8.98979i | −0.0551521 | + | 0.0551521i | −0.734145 | − | 0.678993i | \(-0.762417\pi\) |
0.678993 | + | 0.734145i | \(0.262417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 88.3587 | + | 88.3587i | 0.529094 | + | 0.529094i | 0.920302 | − | 0.391208i | \(-0.127943\pi\) |
−0.391208 | + | 0.920302i | \(0.627943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 131.000i | − | 0.775148i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 170.631 | − | 170.631i | 0.986307 | − | 0.986307i | −0.0136005 | − | 0.999908i | \(-0.504329\pi\) |
0.999908 | + | 0.0136005i | \(0.00432929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 75.7526i | − | 0.423199i | −0.977357 | − | 0.211599i | \(-0.932133\pi\) | ||
0.977357 | − | 0.211599i | \(-0.0678672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −279.444 | −1.54389 | −0.771944 | − | 0.635690i | \(-0.780716\pi\) | ||||
−0.771944 | + | 0.635690i | \(0.780716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −122.677 | − | 122.677i | −0.656024 | − | 0.656024i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 69.4847 | 0.363794 | 0.181897 | − | 0.983318i | \(-0.441776\pi\) | ||||
0.181897 | + | 0.983318i | \(0.441776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 53.5857 | − | 53.5857i | 0.277646 | − | 0.277646i | −0.554523 | − | 0.832169i | \(-0.687099\pi\) |
0.832169 | + | 0.554523i | \(0.187099\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 260.252 | + | 260.252i | 1.32108 | + | 1.32108i | 0.912906 | + | 0.408171i | \(0.133833\pi\) |
0.408171 | + | 0.912906i | \(0.366167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 65.0102i | − | 0.326684i | −0.986569 | − | 0.163342i | \(-0.947773\pi\) | ||
0.986569 | − | 0.163342i | \(-0.0522275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 255.126 | − | 255.126i | 1.25678 | − | 1.25678i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 235.505i | − | 1.12682i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0204 | 0.0569688 | 0.0284844 | − | 0.999594i | \(-0.490932\pi\) | ||||
0.0284844 | + | 0.999594i | \(0.490932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 152.677 | + | 152.677i | 0.703578 | + | 0.703578i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 184.949 | 0.836873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 239.722 | − | 239.722i | 1.07499 | − | 1.07499i | 0.0780357 | − | 0.996951i | \(-0.475135\pi\) |
0.996951 | − | 0.0780357i | \(-0.0248648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.02041 | + | 2.02041i | 0.00890049 | + | 0.00890049i | 0.711543 | − | 0.702643i | \(-0.247997\pi\) |
−0.702643 | + | 0.711543i | \(0.747997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 284.969i | − | 1.24441i | −0.782855 | − | 0.622204i | \(-0.786237\pi\) | ||
0.782855 | − | 0.622204i | \(-0.213763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 151.237 | − | 151.237i | 0.649087 | − | 0.649087i | −0.303685 | − | 0.952772i | \(-0.598217\pi\) |
0.952772 | + | 0.303685i | \(0.0982172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 50.9694i | 0.213261i | 0.994299 | + | 0.106631i | \(0.0340062\pi\) | ||||
−0.994299 | + | 0.106631i | \(0.965994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −32.0000 | −0.132780 | −0.0663900 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663900 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 177.526 | + | 177.526i | 0.718727 | + | 0.718727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 373.237 | 1.48700 | 0.743500 | − | 0.668735i | \(-0.233164\pi\) | ||||
0.743500 | + | 0.668735i | \(0.233164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −43.0806 | + | 43.0806i | −0.170279 | + | 0.170279i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −206.136 | − | 206.136i | −0.802086 | − | 0.802086i | 0.181335 | − | 0.983421i | \(-0.441958\pi\) |
−0.983421 | + | 0.181335i | \(0.941958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 109.485i | 0.422721i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 210.833 | − | 210.833i | 0.801647 | − | 0.801647i | −0.181706 | − | 0.983353i | \(-0.558162\pi\) |
0.983353 | + | 0.181706i | \(0.0581619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 205.258i | − | 0.763040i | −0.924361 | − | 0.381520i | \(-0.875401\pi\) | ||
0.924361 | − | 0.381520i | \(-0.124599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −66.0000 | −0.243542 | −0.121771 | − | 0.992558i | \(-0.538857\pi\) | ||||
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −148.157 | − | 148.157i | −0.534861 | − | 0.534861i | 0.387154 | − | 0.922015i | \(-0.373458\pi\) |
−0.922015 | + | 0.387154i | \(0.873458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −324.434 | −1.15457 | −0.577284 | − | 0.816543i | \(-0.695887\pi\) | ||||
−0.577284 | + | 0.816543i | \(0.695887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −304.747 | + | 304.747i | −1.07684 | + | 1.07684i | −0.0800537 | + | 0.996791i | \(0.525509\pi\) |
−0.996791 | + | 0.0800537i | \(0.974491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 190.000 | + | 190.000i | 0.662021 | + | 0.662021i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 174.980i | − | 0.605466i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −145.151 | + | 145.151i | −0.495396 | + | 0.495396i | −0.910001 | − | 0.414605i | \(-0.863920\pi\) |
0.414605 | + | 0.910001i | \(0.363920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 64.9490i | − | 0.217221i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 373.980 | 1.24246 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −120.606 | − | 120.606i | −0.392854 | − | 0.392854i | 0.482850 | − | 0.875703i | \(-0.339602\pi\) |
−0.875703 | + | 0.482850i | \(0.839602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0204 | 0.0579434 | 0.0289717 | − | 0.999580i | \(-0.490777\pi\) | ||||
0.0289717 | + | 0.999580i | \(0.490777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 323.586 | − | 323.586i | 1.03382 | − | 1.03382i | 0.0344125 | − | 0.999408i | \(-0.489044\pi\) |
0.999408 | − | 0.0344125i | \(-0.0109560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 62.4495 | + | 62.4495i | 0.197002 | + | 0.197002i | 0.798713 | − | 0.601712i | \(-0.205514\pi\) |
−0.601712 | + | 0.798713i | \(0.705514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 556.434i | 1.74431i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −109.444 | + | 109.444i | −0.338836 | + | 0.338836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 328.454i | − | 0.998341i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 618.413 | 1.86832 | 0.934159 | − | 0.356857i | \(-0.116152\pi\) | ||||
0.934159 | + | 0.356857i | \(0.116152\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 55.4041 | + | 55.4041i | 0.164404 | + | 0.164404i | 0.784514 | − | 0.620111i | \(-0.212912\pi\) |
−0.620111 | + | 0.784514i | \(0.712912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −332.990 | −0.976510 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 96.7673 | − | 96.7673i | 0.282121 | − | 0.282121i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 413.081 | + | 413.081i | 1.19043 | + | 1.19043i | 0.976946 | + | 0.213488i | \(0.0684826\pi\) |
0.213488 | + | 0.976946i | \(0.431517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 258.454i | − | 0.740556i | −0.928921 | − | 0.370278i | \(-0.879262\pi\) | ||
0.928921 | − | 0.370278i | \(-0.120738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −83.9138 | + | 83.9138i | −0.237716 | + | 0.237716i | −0.815904 | − | 0.578188i | \(-0.803760\pi\) |
0.578188 | + | 0.815904i | \(0.303760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 138.515i | 0.385837i | 0.981215 | + | 0.192918i | \(0.0617952\pi\) | ||||
−0.981215 | + | 0.192918i | \(0.938205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 150.898 | 0.418000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 408.964 | + | 408.964i | 1.11434 | + | 1.11434i | 0.992556 | + | 0.121786i | \(0.0388623\pi\) |
0.121786 | + | 0.992556i | \(0.461138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 525.980 | 1.41773 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 143.106 | − | 143.106i | 0.383661 | − | 0.383661i | −0.488758 | − | 0.872419i | \(-0.662550\pi\) |
0.872419 | + | 0.488758i | \(0.162550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −419.444 | − | 419.444i | −1.11258 | − | 1.11258i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 194.000i | − | 0.511873i | −0.966694 | − | 0.255937i | \(-0.917616\pi\) | ||
0.966694 | − | 0.255937i | \(-0.0823839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 51.4893 | − | 51.4893i | 0.134437 | − | 0.134437i | −0.636686 | − | 0.771123i | \(-0.719695\pi\) |
0.771123 | + | 0.636686i | \(0.219695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.1964i | 0.0904792i | 0.998976 | + | 0.0452396i | \(0.0144051\pi\) | ||||
−0.998976 | + | 0.0452396i | \(0.985595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.0408 | 0.102406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −409.267 | − | 409.267i | −1.03090 | − | 1.03090i | −0.999507 | − | 0.0313917i | \(-0.990006\pi\) |
−0.0313917 | − | 0.999507i | \(-0.509994\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −375.898 | −0.937401 | −0.468701 | − | 0.883357i | \(-0.655278\pi\) | ||||
−0.468701 | + | 0.883357i | \(0.655278\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 251.010 | − | 251.010i | 0.622854 | − | 0.622854i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −119.394 | − | 119.394i | −0.293351 | − | 0.293351i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 207.959i | 0.508458i | 0.967144 | + | 0.254229i | \(0.0818216\pi\) | ||||
−0.967144 | + | 0.254229i | \(0.918178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 661.085 | − | 661.085i | 1.60069 | − | 1.60069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 810.186i | − | 1.93362i | −0.255499 | − | 0.966809i | \(-0.582240\pi\) | ||
0.255499 | − | 0.966809i | \(-0.417760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −505.959 | −1.20180 | −0.600902 | − | 0.799323i | \(-0.705192\pi\) | ||||
−0.600902 | + | 0.799323i | \(0.705192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 763.535 | + | 763.535i | 1.78814 | + | 1.78814i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 92.4541 | 0.214511 | 0.107255 | − | 0.994232i | \(-0.465794\pi\) | ||||
0.107255 | + | 0.994232i | \(0.465794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −69.8990 | + | 69.8990i | −0.161430 | + | 0.161430i | −0.783200 | − | 0.621770i | \(-0.786414\pi\) |
0.621770 | + | 0.783200i | \(0.286414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.4337 | + | 38.4337i | 0.0879489 | + | 0.0879489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 128.929i | 0.293687i | 0.989160 | + | 0.146843i | \(0.0469114\pi\) | ||||
−0.989160 | + | 0.146843i | \(0.953089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −335.555 | + | 335.555i | −0.757461 | + | 0.757461i | −0.975860 | − | 0.218399i | \(-0.929917\pi\) |
0.218399 | + | 0.975860i | \(0.429917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 521.423i | 1.16130i | 0.814153 | + | 0.580650i | \(0.197201\pi\) | ||||
−0.814153 | + | 0.580650i | \(0.802799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −414.393 | −0.918831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −548.939 | − | 548.939i | −1.20118 | − | 1.20118i | −0.973808 | − | 0.227371i | \(-0.926987\pi\) |
−0.227371 | − | 0.973808i | \(-0.573013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −142.288 | −0.308651 | −0.154326 | − | 0.988020i | \(-0.549320\pi\) | ||||
−0.154326 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −537.045 | + | 537.045i | −1.15993 | + | 1.15993i | −0.175434 | + | 0.984491i | \(0.556133\pi\) |
−0.984491 | + | 0.175434i | \(0.943867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −367.044 | − | 367.044i | −0.785962 | − | 0.785962i | 0.194867 | − | 0.980830i | \(-0.437572\pi\) |
−0.980830 | + | 0.194867i | \(0.937572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 367.959i | − | 0.784561i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −407.828 | + | 407.828i | −0.862215 | + | 0.862215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 94.9694i | − | 0.198266i | −0.995074 | − | 0.0991330i | \(-0.968393\pi\) | ||
0.995074 | − | 0.0991330i | \(-0.0316069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 180.000 | 0.374220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −244.621 | − | 244.621i | −0.502302 | − | 0.502302i | 0.409851 | − | 0.912153i | \(-0.365581\pi\) |
−0.912153 | + | 0.409851i | \(0.865581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −163.217 | −0.332417 | −0.166209 | − | 0.986091i | \(-0.553153\pi\) | ||||
−0.166209 | + | 0.986091i | \(0.553153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 258.586 | − | 258.586i | 0.524515 | − | 0.524515i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 580.908 | + | 580.908i | 1.16883 | + | 1.16883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.55613i | 0.0171465i | 0.999963 | + | 0.00857327i | \(0.00272899\pi\) | ||||
−0.999963 | + | 0.00857327i | \(0.997271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 46.5903 | − | 46.5903i | 0.0926249 | − | 0.0926249i | −0.659276 | − | 0.751901i | \(-0.729137\pi\) |
0.751901 | + | 0.659276i | \(0.229137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 336.227i | 0.660564i | 0.943882 | + | 0.330282i | \(0.107144\pi\) | ||||
−0.943882 | + | 0.330282i | \(0.892856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −658.413 | −1.28848 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 358.182 | + | 358.182i | 0.692808 | + | 0.692808i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −252.556 | −0.484753 | −0.242376 | − | 0.970182i | \(-0.577927\pi\) | ||||
−0.242376 | + | 0.970182i | \(0.577927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.6867 | − | 33.6867i | 0.0644106 | − | 0.0644106i | −0.674168 | − | 0.738578i | \(-0.735498\pi\) |
0.738578 | + | 0.674168i | \(0.235498\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 154.747 | + | 154.747i | 0.293637 | + | 0.293637i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 514.939i | 0.973419i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 312.372 | − | 312.372i | 0.586065 | − | 0.586065i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1007.18i | 1.86860i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −604.474 | −1.11733 | −0.558664 | − | 0.829394i | \(-0.688686\pi\) | ||||
−0.558664 | + | 0.829394i | \(0.688686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −615.353 | − | 615.353i | −1.12496 | − | 1.12496i | −0.990985 | − | 0.133975i | \(-0.957226\pi\) |
−0.133975 | − | 0.990985i | \(-0.542774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 496.413 | 0.900931 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −361.262 | + | 361.262i | −0.653277 | + | 0.653277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −439.040 | − | 439.040i | −0.788222 | − | 0.788222i | 0.192980 | − | 0.981203i | \(-0.438185\pi\) |
−0.981203 | + | 0.192980i | \(0.938185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 614.847i | − | 1.09991i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −52.5765 | + | 52.5765i | −0.0933864 | + | 0.0933864i | −0.752257 | − | 0.658870i | \(-0.771035\pi\) |
0.658870 | + | 0.752257i | \(0.271035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 680.929i | 1.19671i | 0.801231 | + | 0.598356i | \(0.204179\pi\) | ||||
−0.801231 | + | 0.598356i | \(0.795821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 254.495 | 0.445700 | 0.222850 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222850 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 279.999 | + | 279.999i | 0.485267 | + | 0.485267i | 0.906809 | − | 0.421542i | \(-0.138511\pi\) |
−0.421542 | + | 0.906809i | \(0.638511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1514.35 | 2.60646 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −573.585 | + | 573.585i | −0.983850 | + | 0.983850i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 312.347 | + | 312.347i | 0.532108 | + | 0.532108i | 0.921199 | − | 0.389091i | \(-0.127211\pi\) |
−0.389091 | + | 0.921199i | \(0.627211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 297.071i | 0.504366i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −424.570 | + | 424.570i | −0.715969 | + | 0.715969i | −0.967777 | − | 0.251808i | \(-0.918975\pi\) |
0.251808 | + | 0.967777i | \(0.418975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 396.536i | 0.661996i | 0.943631 | + | 0.330998i | \(0.107385\pi\) | ||||
−0.943631 | + | 0.330998i | \(0.892615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 238.908 | 0.397518 | 0.198759 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198759 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −92.8025 | − | 92.8025i | −0.152887 | − | 0.152887i | 0.626519 | − | 0.779406i | \(-0.284479\pi\) |
−0.779406 | + | 0.626519i | \(0.784479\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −540.000 | −0.883797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −301.943 | + | 301.943i | −0.492567 | + | 0.492567i | −0.909114 | − | 0.416547i | \(-0.863240\pi\) |
0.416547 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −372.904 | − | 372.904i | −0.604382 | − | 0.604382i | 0.337090 | − | 0.941472i | \(-0.390557\pi\) |
−0.941472 | + | 0.337090i | \(0.890557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 815.939i | − | 1.31816i | −0.752074 | − | 0.659078i | \(-0.770947\pi\) | ||
0.752074 | − | 0.659078i | \(-0.229053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1169.34 | + | 1169.34i | −1.87695 | + | 1.87695i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 110.969i | 0.176422i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 550.434 | 0.872320 | 0.436160 | − | 0.899869i | \(-0.356338\pi\) | ||||
0.436160 | + | 0.899869i | \(0.356338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −759.217 | − | 759.217i | −1.19186 | − | 1.19186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −927.939 | −1.44764 | −0.723821 | − | 0.689988i | \(-0.757616\pi\) | ||||
−0.723821 | + | 0.689988i | \(0.757616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −190.960 | + | 190.960i | −0.296983 | + | 0.296983i | −0.839831 | − | 0.542848i | \(-0.817346\pi\) |
0.542848 | + | 0.839831i | \(0.317346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −637.146 | − | 637.146i | −0.984770 | − | 0.984770i | 0.0151154 | − | 0.999886i | \(-0.495188\pi\) |
−0.999886 | + | 0.0151154i | \(0.995188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1441.84i | 2.22163i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −404.116 | + | 404.116i | −0.618860 | + | 0.618860i | −0.945239 | − | 0.326379i | \(-0.894172\pi\) |
0.326379 | + | 0.945239i | \(0.394172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 453.196i | − | 0.687703i | −0.939024 | − | 0.343852i | \(-0.888268\pi\) | ||
0.939024 | − | 0.343852i | \(-0.111732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 717.546 | 1.08555 | 0.542773 | − | 0.839879i | \(-0.317374\pi\) | ||||
0.542773 | + | 0.839879i | \(0.317374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −90.8082 | − | 90.8082i | −0.136144 | − | 0.136144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1665.28 | −2.48179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 121.413 | − | 121.413i | 0.180406 | − | 0.180406i | −0.611127 | − | 0.791533i | \(-0.709283\pi\) |
0.791533 | + | 0.611127i | \(0.209283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −671.943 | − | 671.943i | −0.992531 | − | 0.992531i | 0.00744150 | − | 0.999972i | \(-0.497631\pi\) |
−0.999972 | + | 0.00744150i | \(0.997631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 825.464i | 1.21571i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 802.095 | − | 802.095i | 1.17437 | − | 1.17437i | 0.193214 | − | 0.981157i | \(-0.438109\pi\) |
0.981157 | − | 0.193214i | \(-0.0618913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 864.745i | − | 1.25507i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1146.49 | −1.65918 | −0.829591 | − | 0.558371i | \(-0.811426\pi\) | ||||
−0.829591 | + | 0.558371i | \(0.811426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 192.577 | + | 192.577i | 0.276293 | + | 0.276293i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 673.217 | 0.960366 | 0.480183 | − | 0.877168i | \(-0.340570\pi\) | ||||
0.480183 | + | 0.877168i | \(0.340570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −106.515 | + | 106.515i | −0.151515 | + | 0.151515i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 340.833 | + | 340.833i | 0.482084 | + | 0.482084i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 955.939i | − | 1.34829i | −0.738598 | − | 0.674146i | \(-0.764512\pi\) | ||
0.738598 | − | 0.674146i | \(-0.235488\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 54.3429 | − | 54.3429i | 0.0762172 | − | 0.0762172i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 89.0306i | − | 0.123826i | −0.998082 | − | 0.0619128i | \(-0.980280\pi\) | ||
0.998082 | − | 0.0619128i | \(-0.0197201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 345.010 | 0.478516 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −332.703 | − | 332.703i | −0.457638 | − | 0.457638i | 0.440242 | − | 0.897879i | \(-0.354893\pi\) |
−0.897879 | + | 0.440242i | \(0.854893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 379.051 | 0.518538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −229.823 | + | 229.823i | −0.313537 | + | 0.313537i | −0.846278 | − | 0.532741i | \(-0.821162\pi\) |
0.532741 | + | 0.846278i | \(0.321162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 401.262 | + | 401.262i | 0.544454 | + | 0.544454i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 923.281i | 1.24936i | 0.780879 | + | 0.624682i | \(0.214772\pi\) | ||||
−0.780879 | + | 0.624682i | \(0.785228\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −585.782 | + | 585.782i | −0.788401 | + | 0.788401i | −0.981232 | − | 0.192831i | \(-0.938233\pi\) |
0.192831 | + | 0.981232i | \(0.438233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 243.423i | − | 0.324998i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1354.27 | 1.80329 | 0.901645 | − | 0.432477i | \(-0.142361\pi\) | ||||
0.901645 | + | 0.432477i | \(0.142361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 985.832 | + | 985.832i | 1.30229 | + | 1.30229i | 0.926846 | + | 0.375442i | \(0.122509\pi\) |
0.375442 | + | 0.926846i | \(0.377491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −206.495 | −0.271347 | −0.135673 | − | 0.990754i | \(-0.543320\pi\) | ||||
−0.135673 | + | 0.990754i | \(0.543320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1188.08 | − | 1188.08i | 1.55712 | − | 1.55712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1086.87 | − | 1086.87i | −1.41704 | − | 1.41704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 852.969i | − | 1.10919i | −0.832119 | − | 0.554596i | \(-0.812873\pi\) | ||
0.832119 | − | 0.554596i | \(-0.187127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −491.035 | + | 491.035i | −0.635233 | + | 0.635233i | −0.949376 | − | 0.314143i | \(-0.898283\pi\) |
0.314143 | + | 0.949376i | \(0.398283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 369.694i | 0.474575i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1266.97 | −1.62224 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 958.586 | + | 958.586i | 1.21803 | + | 1.21803i | 0.968323 | + | 0.249702i | \(0.0803328\pi\) |
0.249702 | + | 0.968323i | \(0.419667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −194.515 | −0.245911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1255.30 | − | 1255.30i | 1.58298 | − | 1.58298i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 169.065 | + | 169.065i | 0.212126 | + | 0.212126i | 0.805170 | − | 0.593044i | \(-0.202074\pi\) |
−0.593044 | + | 0.805170i | \(0.702074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 332.908i | − | 0.416656i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 718.005 | − | 718.005i | 0.894153 | − | 0.894153i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 126.082i | 0.155849i | 0.996959 | + | 0.0779244i | \(0.0248293\pi\) | ||||
−0.996959 | + | 0.0779244i | \(0.975171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.9286 | 0.0406024 | 0.0203012 | − | 0.999794i | \(-0.493537\pi\) | ||||
0.0203012 | + | 0.999794i | \(0.493537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 363.837 | + | 363.837i | 0.445333 | + | 0.445333i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −980.064 | −1.19374 | −0.596872 | − | 0.802337i | \(-0.703590\pi\) | ||||
−0.596872 | + | 0.802337i | \(0.703590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 503.863 | − | 503.863i | 0.612227 | − | 0.612227i | −0.331299 | − | 0.943526i | \(-0.607487\pi\) |
0.943526 | + | 0.331299i | \(0.107487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1078.84 | + | 1078.84i | 1.30452 | + | 1.30452i | 0.925311 | + | 0.379208i | \(0.123804\pi\) |
0.379208 | + | 0.925311i | \(0.376196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 124.352i | 0.150002i | 0.997183 | + | 0.0750012i | \(0.0238961\pi\) | ||||
−0.997183 | + | 0.0750012i | \(0.976104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 468.055 | − | 468.055i | 0.561890 | − | 0.561890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1125.48i | 1.34146i | 0.741702 | + | 0.670730i | \(0.234019\pi\) | ||||
−0.741702 | + | 0.670730i | \(0.765981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −331.888 | −0.394635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1065.12 | − | 1065.12i | −1.25753 | − | 1.25753i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.9694 | 0.0457925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1039.87 | + | 1039.87i | −1.21908 | + | 1.21908i | −0.251122 | + | 0.967955i | \(0.580799\pi\) |
−0.967955 | + | 0.251122i | \(0.919201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 620.177 | + | 620.177i | 0.723660 | + | 0.723660i | 0.969349 | − | 0.245688i | \(-0.0790140\pi\) |
−0.245688 | + | 0.969349i | \(0.579014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 948.888i | 1.10464i | 0.833631 | + | 0.552321i | \(0.186258\pi\) | ||||
−0.833631 | + | 0.552321i | \(0.813742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1064.42 | + | 1064.42i | −1.23339 | + | 1.23339i | −0.270740 | + | 0.962652i | \(0.587268\pi\) |
−0.962652 | + | 0.270740i | \(0.912732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 787.918i | − | 0.906695i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −604.949 | −0.694545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 329.975 | + | 329.975i | 0.376254 | + | 0.376254i | 0.869749 | − | 0.493495i | \(-0.164281\pi\) |
−0.493495 | + | 0.869749i | \(0.664281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −135.857 | −0.154208 | −0.0771039 | − | 0.997023i | \(-0.524567\pi\) | ||||
−0.0771039 | + | 0.997023i | \(0.524567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.8694 | − | 46.8694i | 0.0530797 | − | 0.0530797i | −0.680069 | − | 0.733148i | \(-0.738050\pi\) |
0.733148 | + | 0.680069i | \(0.238050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.5097 | − | 43.5097i | −0.0490526 | − | 0.0490526i | 0.682155 | − | 0.731208i | \(-0.261043\pi\) |
−0.731208 | + | 0.682155i | \(0.761043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 110.990i | 0.124848i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 319.546 | − | 319.546i | 0.357834 | − | 0.357834i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 701.898i | − | 0.780754i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 533.112 | 0.591690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −638.938 | − | 638.938i | −0.704452 | − | 0.704452i | 0.260911 | − | 0.965363i | \(-0.415977\pi\) |
−0.965363 | + | 0.260911i | \(0.915977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −347.546 | −0.381499 | −0.190750 | − | 0.981639i | \(-0.561092\pi\) | ||||
−0.190750 | + | 0.981639i | \(0.561092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1651.41 | + | 1651.41i | −1.80878 | + | 1.80878i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 147.146 | + | 147.146i | 0.160465 | + | 0.160465i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.6684i | 0.0301071i | 0.999887 | + | 0.0150535i | \(0.00479187\pi\) | ||||
−0.999887 | + | 0.0150535i | \(0.995208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 955.051 | − | 955.051i | 1.03472 | − | 1.03472i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1070.49i | − | 1.15231i | −0.817341 | − | 0.576154i | \(-0.804553\pi\) | ||
0.817341 | − | 0.576154i | \(-0.195447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 898.536 | 0.965130 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −60.5551 | − | 60.5551i | −0.0646266 | − | 0.0646266i | 0.674055 | − | 0.738681i | \(-0.264551\pi\) |
−0.738681 | + | 0.674055i | \(0.764551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 264.064 | 0.280620 | 0.140310 | − | 0.990108i | \(-0.455190\pi\) | ||||
0.140310 | + | 0.990108i | \(0.455190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.6276 | − | 67.6276i | 0.0717153 | − | 0.0717153i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −115.455 | − | 115.455i | −0.121917 | − | 0.121917i | 0.643516 | − | 0.765433i | \(-0.277475\pi\) |
−0.765433 | + | 0.643516i | \(0.777475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1082.47i | 1.14065i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −378.359 | + | 378.359i | −0.397019 | + | 0.397019i | −0.877180 | − | 0.480162i | \(-0.840578\pi\) |
0.480162 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1514.35i | 1.57909i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −540.959 | −0.562913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1964 | + | 52.1964i | 0.0539777 | + | 0.0539777i | 0.733580 | − | 0.679603i | \(-0.237848\pi\) |
−0.679603 | + | 0.733580i | \(0.737848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1545.61 | 1.59177 | 0.795886 | − | 0.605447i | \(-0.207006\pi\) | ||||
0.795886 | + | 0.605447i | \(0.207006\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 178.940 | − | 178.940i | 0.183905 | − | 0.183905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −843.206 | − | 843.206i | −0.863056 | − | 0.863056i | 0.128636 | − | 0.991692i | \(-0.458940\pi\) |
−0.991692 | + | 0.128636i | \(0.958940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2550.35i | − | 2.60506i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1241.39 | − | 1241.39i | 1.26286 | − | 1.26286i | 0.313153 | − | 0.949703i | \(-0.398615\pi\) |
0.949703 | − | 0.313153i | \(-0.101385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 133.112i | − | 0.134593i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 219.816 | 0.221813 | 0.110906 | − | 0.993831i | \(-0.464625\pi\) | ||||
0.110906 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −599.571 | − | 599.571i | −0.601375 | − | 0.601375i | 0.339302 | − | 0.940677i | \(-0.389809\pi\) |
−0.940677 | + | 0.339302i | \(0.889809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 900.3.l.b.757.1 | 4 | ||
3.2 | odd | 2 | 300.3.k.a.157.2 | 4 | |||
5.2 | odd | 4 | 180.3.l.b.73.1 | 4 | |||
5.3 | odd | 4 | inner | 900.3.l.b.793.1 | 4 | ||
5.4 | even | 2 | 180.3.l.b.37.1 | 4 | |||
12.11 | even | 2 | 1200.3.bg.o.1057.1 | 4 | |||
15.2 | even | 4 | 60.3.k.a.13.1 | ✓ | 4 | ||
15.8 | even | 4 | 300.3.k.a.193.2 | 4 | |||
15.14 | odd | 2 | 60.3.k.a.37.1 | yes | 4 | ||
20.7 | even | 4 | 720.3.bh.f.433.1 | 4 | |||
20.19 | odd | 2 | 720.3.bh.f.577.1 | 4 | |||
60.23 | odd | 4 | 1200.3.bg.o.193.1 | 4 | |||
60.47 | odd | 4 | 240.3.bg.d.193.2 | 4 | |||
60.59 | even | 2 | 240.3.bg.d.97.2 | 4 | |||
120.29 | odd | 2 | 960.3.bg.b.577.2 | 4 | |||
120.59 | even | 2 | 960.3.bg.a.577.1 | 4 | |||
120.77 | even | 4 | 960.3.bg.b.193.2 | 4 | |||
120.107 | odd | 4 | 960.3.bg.a.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.k.a.13.1 | ✓ | 4 | 15.2 | even | 4 | ||
60.3.k.a.37.1 | yes | 4 | 15.14 | odd | 2 | ||
180.3.l.b.37.1 | 4 | 5.4 | even | 2 | |||
180.3.l.b.73.1 | 4 | 5.2 | odd | 4 | |||
240.3.bg.d.97.2 | 4 | 60.59 | even | 2 | |||
240.3.bg.d.193.2 | 4 | 60.47 | odd | 4 | |||
300.3.k.a.157.2 | 4 | 3.2 | odd | 2 | |||
300.3.k.a.193.2 | 4 | 15.8 | even | 4 | |||
720.3.bh.f.433.1 | 4 | 20.7 | even | 4 | |||
720.3.bh.f.577.1 | 4 | 20.19 | odd | 2 | |||
900.3.l.b.757.1 | 4 | 1.1 | even | 1 | trivial | ||
900.3.l.b.793.1 | 4 | 5.3 | odd | 4 | inner | ||
960.3.bg.a.193.1 | 4 | 120.107 | odd | 4 | |||
960.3.bg.a.577.1 | 4 | 120.59 | even | 2 | |||
960.3.bg.b.193.2 | 4 | 120.77 | even | 4 | |||
960.3.bg.b.577.2 | 4 | 120.29 | odd | 2 | |||
1200.3.bg.o.193.1 | 4 | 60.23 | odd | 4 | |||
1200.3.bg.o.1057.1 | 4 | 12.11 | even | 2 |