Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.193 |
Dual form | 1200.3.bg.o.1057.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.44949 | − | 7.44949i | 1.06421 | − | 1.06421i | 0.0664211 | − | 0.997792i | \(-0.478842\pi\) |
0.997792 | − | 0.0664211i | \(-0.0211581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 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 | 0.0563023 | − | 0.998414i | \(-0.482069\pi\) |
−0.998414 | + | 0.0563023i | \(0.982069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.55051 | − | 7.55051i | 0.444148 | − | 0.444148i | −0.449256 | − | 0.893403i | \(-0.648311\pi\) |
0.893403 | + | 0.449256i | \(0.148311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 14.4949i | − | 0.762889i | −0.924392 | − | 0.381445i | \(-0.875427\pi\) | ||
0.924392 | − | 0.381445i | \(-0.124573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.2474 | −0.868926 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65153 | − | 2.65153i | −0.115284 | − | 0.115284i | 0.647111 | − | 0.762395i | \(-0.275977\pi\) |
−0.762395 | + | 0.647111i | \(0.775977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 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 | \(-0.392761\pi\) | ||||
0.330563 | + | 0.943784i | \(0.392761\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19.8990 | − | 19.8990i | −0.602999 | − | 0.602999i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | + | 7.34847i | −0.198607 | + | 0.198607i | −0.799403 | − | 0.600795i | \(-0.794851\pi\) |
0.600795 | + | 0.799403i | \(0.294851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0000i | 0.769231i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 25.5051 | 0.622076 | 0.311038 | − | 0.950398i | \(-0.399323\pi\) | ||||
0.311038 | + | 0.950398i | \(0.399323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.1010 | + | 25.1010i | 0.583745 | + | 0.583745i | 0.935930 | − | 0.352186i | \(-0.114561\pi\) |
−0.352186 | + | 0.935930i | \(0.614561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.0454 | − | 22.0454i | 0.469051 | − | 0.469051i | −0.432556 | − | 0.901607i | \(-0.642388\pi\) |
0.901607 | + | 0.432556i | \(0.142388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 61.9898i | − | 1.26510i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.4949 | −0.362645 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.3031 | + | 35.3031i | 0.666096 | + | 0.666096i | 0.956810 | − | 0.290714i | \(-0.0938929\pi\) |
−0.290714 | + | 0.956810i | \(0.593893\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.7526 | + | 17.7526i | −0.311448 | + | 0.311448i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 88.7423i | − | 1.50411i | −0.659102 | − | 0.752054i | \(-0.729063\pi\) | ||
0.659102 | − | 0.752054i | \(-0.270937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.495 | −1.68024 | −0.840122 | − | 0.542397i | \(-0.817517\pi\) | ||||
−0.840122 | + | 0.542397i | \(0.817517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.3485 | + | 22.3485i | 0.354738 | + | 0.354738i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.6969 | + | 24.6969i | −0.368611 | + | 0.368611i | −0.866970 | − | 0.498359i | \(-0.833936\pi\) |
0.498359 | + | 0.866970i | \(0.333936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.49490i | 0.0941289i | ||||||||
\(70\) | 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 | 0.941732 | − | 0.336364i | \(-0.109197\pi\) |
−0.336364 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.641 | − | 101.641i | −1.22459 | − | 1.22459i | −0.965981 | − | 0.258613i | \(-0.916734\pi\) |
−0.258613 | − | 0.965981i | \(-0.583266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 41.9444 | − | 41.9444i | 0.482119 | − | 0.482119i | ||||
\(88\) | 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 | ||||||||
\(93\) | −25.1010 | − | 25.1010i | −0.269903 | − | 0.269903i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −55.4041 | + | 55.4041i | −0.571176 | + | 0.571176i | −0.932457 | − | 0.361281i | \(-0.882340\pi\) |
0.361281 | + | 0.932457i | \(0.382340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 48.7423i | 0.492347i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 45.7526 | 0.452996 | 0.226498 | − | 0.974012i | \(-0.427272\pi\) | ||||
0.226498 | + | 0.974012i | \(0.427272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 23.1566 | + | 23.1566i | 0.224822 | + | 0.224822i | 0.810525 | − | 0.585704i | \(-0.199182\pi\) |
−0.585704 | + | 0.810525i | \(0.699182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3383 | − | 16.3383i | 0.152694 | − | 0.152694i | −0.626626 | − | 0.779320i | \(-0.715565\pi\) |
0.779320 | + | 0.626626i | \(0.215565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 159.485i | − | 1.46316i | −0.681754 | − | 0.731581i | \(-0.738783\pi\) | ||
0.681754 | − | 0.731581i | \(-0.261217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.0000 | 0.162162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0556 | − | 13.0556i | −0.115536 | − | 0.115536i | 0.646975 | − | 0.762511i | \(-0.276034\pi\) |
−0.762511 | + | 0.646975i | \(0.776034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36.7423 | − | 36.7423i | 0.314037 | − | 0.314037i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 112.495i | − | 0.945335i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 142.980 | 1.18165 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31.2372 | − | 31.2372i | −0.253961 | − | 0.253961i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44949 | − | 7.44949i | 0.0586574 | − | 0.0586574i | −0.677170 | − | 0.735827i | \(-0.736794\pi\) |
0.735827 | + | 0.677170i | \(0.236794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 61.4847i | − | 0.476626i | ||||||
\(130\) | 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 | \(-0.574212\pi\) |
0.972945 | + | 0.231037i | \(0.0742120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 24.0204i | 0.172809i | 0.996260 | + | 0.0864044i | \(0.0275377\pi\) | ||||
−0.996260 | + | 0.0864044i | \(0.972462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −54.0000 | −0.382979 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198.990 | − | 198.990i | −1.39154 | − | 1.39154i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −75.9217 | + | 75.9217i | −0.516474 | + | 0.516474i | ||||
\(148\) | 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 | \(-0.323520\pi\) | ||||
0.526456 | + | 0.850202i | \(0.323520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.6515 | + | 22.6515i | 0.148049 | + | 0.148049i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 37.3485 | − | 37.3485i | 0.237888 | − | 0.237888i | −0.578087 | − | 0.815975i | \(-0.696201\pi\) |
0.815975 | + | 0.578087i | \(0.196201\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 86.4745i | − | 0.543865i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39.5051 | −0.245373 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.98979 | + | 8.98979i | 0.0551521 | + | 0.0551521i | 0.734145 | − | 0.678993i | \(-0.237583\pi\) |
−0.678993 | + | 0.734145i | \(0.737583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 88.3587 | − | 88.3587i | 0.529094 | − | 0.529094i | −0.391208 | − | 0.920302i | \(-0.627943\pi\) |
0.920302 | + | 0.391208i | \(0.127943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131.000i | 0.775148i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.4847 | 0.254296 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −170.631 | − | 170.631i | −0.986307 | − | 0.986307i | 0.0136005 | − | 0.999908i | \(-0.495671\pi\) |
−0.999908 | + | 0.0136005i | \(0.995671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −108.687 | + | 108.687i | −0.614049 | + | 0.614049i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 75.7526i | 0.423199i | 0.977357 | + | 0.211599i | \(0.0678672\pi\) | ||||
−0.977357 | + | 0.211599i | \(0.932133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −279.444 | −1.54389 | −0.771944 | − | 0.635690i | \(-0.780716\pi\) | ||||
−0.771944 | + | 0.635690i | \(0.780716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 125.530 | + | 125.530i | 0.685957 | + | 0.685957i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 122.677 | − | 122.677i | 0.656024 | − | 0.656024i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 54.7423i | − | 0.289642i | ||||||
\(190\) | 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 | 0.832169 | − | 0.554523i | \(-0.187099\pi\) |
−0.554523 | + | 0.832169i | \(0.687099\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −260.252 | + | 260.252i | −1.32108 | + | 1.32108i | −0.408171 | + | 0.912906i | \(0.633833\pi\) |
−0.912906 | + | 0.408171i | \(0.866167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 65.0102i | − | 0.326684i | −0.986569 | − | 0.163342i | \(-0.947773\pi\) | ||
0.986569 | − | 0.163342i | \(-0.0522275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 60.4949 | 0.300970 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 255.126 | + | 255.126i | 1.25678 | + | 1.25678i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.95459 | − | 7.95459i | 0.0384280 | − | 0.0384280i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 235.505i | − | 1.12682i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0204 | −0.0569688 | −0.0284844 | − | 0.999594i | \(-0.509068\pi\) | ||||
−0.0284844 | + | 0.999594i | \(0.509068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 95.5051 | + | 95.5051i | 0.448381 | + | 0.448381i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 152.677 | − | 152.677i | 0.703578 | − | 0.703578i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 108.247i | − | 0.494281i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −184.949 | −0.836873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −239.722 | − | 239.722i | −1.07499 | − | 1.07499i | −0.996951 | − | 0.0780357i | \(-0.975135\pi\) |
−0.0780357 | − | 0.996951i | \(-0.524865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.02041 | − | 2.02041i | 0.00890049 | − | 0.00890049i | −0.702643 | − | 0.711543i | \(-0.747997\pi\) |
0.711543 | + | 0.702643i | \(0.247997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 284.969i | 1.24441i | 0.782855 | + | 0.622204i | \(0.213763\pi\) | ||||
−0.782855 | + | 0.622204i | \(0.786237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −296.474 | −1.28344 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −151.237 | − | 151.237i | −0.649087 | − | 0.649087i | 0.303685 | − | 0.952772i | \(-0.401783\pi\) |
−0.952772 | + | 0.303685i | \(0.901783\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −59.3939 | + | 59.3939i | −0.250607 | + | 0.250607i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 50.9694i | − | 0.213261i | −0.994299 | − | 0.106631i | \(-0.965994\pi\) | ||
0.994299 | − | 0.106631i | \(-0.0340062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −32.0000 | −0.132780 | −0.0663900 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663900 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −177.526 | + | 177.526i | −0.718727 | + | 0.718727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 248.969i | 0.999877i | ||||||||
\(250\) | 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 | \(-0.558042\pi\) |
0.983421 | + | 0.181335i | \(0.0580418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 109.485i | 0.422721i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −102.742 | −0.393649 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 210.833 | + | 210.833i | 0.801647 | + | 0.801647i | 0.983353 | − | 0.181706i | \(-0.0581619\pi\) |
−0.181706 | + | 0.983353i | \(0.558162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −192.247 | + | 192.247i | −0.720028 | + | 0.720028i | ||||
\(268\) | 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 | \(-0.461143\pi\) | ||||
0.121771 | + | 0.992558i | \(0.461143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 223.485 | + | 223.485i | 0.818625 | + | 0.818625i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −148.157 | + | 148.157i | −0.534861 | + | 0.534861i | −0.922015 | − | 0.387154i | \(-0.873458\pi\) |
0.387154 | + | 0.922015i | \(0.373458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 61.4847i | 0.220375i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 324.434 | 1.15457 | 0.577284 | − | 0.816543i | \(-0.304113\pi\) | ||||
0.577284 | + | 0.816543i | \(0.304113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 304.747 | + | 304.747i | 1.07684 | + | 1.07684i | 0.996791 | + | 0.0800537i | \(0.0255092\pi\) |
0.0800537 | + | 0.996791i | \(0.474491\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | 135.712 | 0.466363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 145.151 | + | 145.151i | 0.495396 | + | 0.495396i | 0.910001 | − | 0.414605i | \(-0.136080\pi\) |
−0.414605 | + | 0.910001i | \(0.636080\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 59.6969 | − | 59.6969i | 0.201000 | − | 0.201000i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 64.9490i | 0.217221i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 373.980 | 1.24246 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −56.0352 | − | 56.0352i | −0.184935 | − | 0.184935i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 120.606 | − | 120.606i | 0.392854 | − | 0.392854i | −0.482850 | − | 0.875703i | \(-0.660398\pi\) |
0.875703 | + | 0.482850i | \(0.160398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 56.7219i | − | 0.183566i | ||||||
\(310\) | 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 | 0.999408 | + | 0.0344125i | \(0.0109560\pi\) |
0.0344125 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −62.4495 | + | 62.4495i | −0.197002 | + | 0.197002i | −0.798713 | − | 0.601712i | \(-0.794486\pi\) |
0.601712 | + | 0.798713i | \(0.294486\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 556.434i | 1.74431i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.0204 | −0.124674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −109.444 | − | 109.444i | −0.338836 | − | 0.338836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −195.328 | + | 195.328i | −0.597334 | + | 0.597334i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 328.454i | − | 0.998341i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −618.413 | −1.86832 | −0.934159 | − | 0.356857i | \(-0.883848\pi\) | ||||
−0.934159 | + | 0.356857i | \(0.883848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.0454 | − | 22.0454i | −0.0662024 | − | 0.0662024i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 55.4041 | − | 55.4041i | 0.164404 | − | 0.164404i | −0.620111 | − | 0.784514i | \(-0.712912\pi\) |
0.784514 | + | 0.620111i | \(0.212912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.9796i | 0.0943351i | ||||||||
\(340\) | 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 | 0.213488 | − | 0.976946i | \(-0.431517\pi\) |
0.976946 | − | 0.213488i | \(-0.0684826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 258.454i | 0.740556i | 0.928921 | + | 0.370278i | \(0.120738\pi\) | ||||
−0.928921 | + | 0.370278i | \(0.879262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −90.0000 | −0.256410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 83.9138 | + | 83.9138i | 0.237716 | + | 0.237716i | 0.815904 | − | 0.578188i | \(-0.196240\pi\) |
−0.578188 | + | 0.815904i | \(0.696240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −137.778 | + | 137.778i | −0.385932 | + | 0.385932i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 138.515i | − | 0.385837i | −0.981215 | − | 0.192918i | \(-0.938205\pi\) | ||
0.981215 | − | 0.192918i | \(-0.0617952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 150.898 | 0.418000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −175.114 | − | 175.114i | −0.482406 | − | 0.482406i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −408.964 | + | 408.964i | −1.11434 | + | 1.11434i | −0.121786 | + | 0.992556i | \(0.538862\pi\) |
−0.992556 | + | 0.121786i | \(0.961138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 76.5153i | 0.207359i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 525.980 | 1.41773 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 143.106 | + | 143.106i | 0.383661 | + | 0.383661i | 0.872419 | − | 0.488758i | \(-0.162550\pi\) |
−0.488758 | + | 0.872419i | \(0.662550\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | −18.2474 | −0.0478936 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 51.4893 | + | 51.4893i | 0.134437 | + | 0.134437i | 0.771123 | − | 0.636686i | \(-0.219695\pi\) |
−0.636686 | + | 0.771123i | \(0.719695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75.3031 | + | 75.3031i | −0.194582 | + | 0.194582i | ||||
\(388\) | 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 | ||||||||
\(393\) | 24.1918 | + | 24.1918i | 0.0615568 | + | 0.0615568i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −409.267 | + | 409.267i | −1.03090 | + | 1.03090i | −0.0313917 | + | 0.999507i | \(0.509994\pi\) |
−0.999507 | + | 0.0313917i | \(0.990006\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 264.495i | 0.662894i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 375.898 | 0.937401 | 0.468701 | − | 0.883357i | \(-0.344722\pi\) | ||||
0.468701 | + | 0.883357i | \(0.344722\pi\) | |||||||
\(402\) | 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 | \(-0.918178\pi\) | ||
0.967144 | − | 0.254229i | \(-0.0818216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −248.969 | −0.605765 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −661.085 | − | 661.085i | −1.60069 | − | 1.60069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.4189 | − | 29.4189i | 0.0705489 | − | 0.0705489i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 810.186i | 1.93362i | 0.255499 | + | 0.966809i | \(0.417760\pi\) | ||||
−0.255499 | + | 0.966809i | \(0.582240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −505.959 | −1.20180 | −0.600902 | − | 0.799323i | \(-0.705192\pi\) | ||||
−0.600902 | + | 0.799323i | \(0.705192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.1362 | + | 66.1362i | 0.156350 | + | 0.156350i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −763.535 | + | 763.535i | −1.78814 | + | 1.78814i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 487.423i | 1.13619i | ||||||||
\(430\) | 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 | 0.621770 | − | 0.783200i | \(-0.286414\pi\) |
−0.783200 | + | 0.621770i | \(0.786414\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | 185.969 | 0.421699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −335.555 | − | 335.555i | −0.757461 | − | 0.757461i | 0.218399 | − | 0.975860i | \(-0.429917\pi\) |
−0.975860 | + | 0.218399i | \(0.929917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 244.621 | − | 244.621i | 0.547250 | − | 0.547250i | ||||
\(448\) | 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 | ||||||||
\(453\) | −194.722 | − | 194.722i | −0.429850 | − | 0.429850i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −548.939 | + | 548.939i | −1.20118 | + | 1.20118i | −0.227371 | + | 0.973808i | \(0.573013\pi\) |
−0.973808 | + | 0.227371i | \(0.926987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 55.4847i | − | 0.120882i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 142.288 | 0.308651 | 0.154326 | − | 0.988020i | \(-0.450680\pi\) | ||||
0.154326 | + | 0.988020i | \(0.450680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 537.045 | + | 537.045i | 1.15993 | + | 1.15993i | 0.984491 | + | 0.175434i | \(0.0561329\pi\) |
0.175434 | + | 0.984491i | \(0.443867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −367.044 | + | 367.044i | −0.785962 | + | 0.785962i | −0.980830 | − | 0.194867i | \(-0.937572\pi\) |
0.194867 | + | 0.980830i | \(0.437572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 367.959i | 0.784561i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −91.4847 | −0.194235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 407.828 | + | 407.828i | 0.862215 | + | 0.862215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −105.909 | + | 105.909i | −0.222032 | + | 0.222032i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 94.9694i | 0.198266i | 0.995074 | + | 0.0991330i | \(0.0316069\pi\) | ||||
−0.995074 | + | 0.0991330i | \(0.968393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 180.000 | 0.374220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 48.3837 | + | 48.3837i | 0.100173 | + | 0.100173i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 244.621 | − | 244.621i | 0.502302 | − | 0.502302i | −0.409851 | − | 0.912153i | \(-0.634419\pi\) |
0.912153 | + | 0.409851i | \(0.134419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22.0204i | − | 0.0450315i | ||||||
\(490\) | 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 | ||||||||
\(501\) | −216.434 | −0.432003 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 46.5903 | + | 46.5903i | 0.0926249 | + | 0.0926249i | 0.751901 | − | 0.659276i | \(-0.229137\pi\) |
−0.659276 | + | 0.751901i | \(0.729137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 160.442 | − | 160.442i | 0.316453 | − | 0.316453i | ||||
\(508\) | 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 | ||||||||
\(513\) | −53.2577 | − | 53.2577i | −0.103816 | − | 0.103816i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 358.182 | − | 358.182i | 0.692808 | − | 0.692808i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 417.959i | 0.805316i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 252.556 | 0.484753 | 0.242376 | − | 0.970182i | \(-0.422073\pi\) | ||||
0.242376 | + | 0.970182i | \(0.422073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.6867 | − | 33.6867i | −0.0644106 | − | 0.0644106i | 0.674168 | − | 0.738578i | \(-0.264502\pi\) |
−0.738578 | + | 0.674168i | \(0.764502\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 266.227 | 0.501369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −312.372 | − | 312.372i | −0.586065 | − | 0.586065i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 92.7775 | − | 92.7775i | 0.172770 | − | 0.172770i | ||||
\(538\) | 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 | ||||||||
\(543\) | 342.247 | + | 342.247i | 0.630290 | + | 0.630290i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 615.353 | − | 615.353i | 1.12496 | − | 1.12496i | 0.133975 | − | 0.990985i | \(-0.457226\pi\) |
0.990985 | − | 0.133975i | \(-0.0427742\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 307.485i | − | 0.560081i | ||||||
\(550\) | 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 | \(-0.561815\pi\) |
0.981203 | + | 0.192980i | \(0.0618154\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 614.847i | − | 1.09991i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −300.495 | −0.535642 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −52.5765 | − | 52.5765i | −0.0933864 | − | 0.0933864i | 0.658870 | − | 0.752257i | \(-0.271035\pi\) |
−0.752257 | + | 0.658870i | \(0.771035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −67.0454 | + | 67.0454i | −0.118246 | + | 0.118246i | ||||
\(568\) | 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 | \(-0.571536\pi\) | ||||
−0.222850 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −85.1010 | − | 85.1010i | −0.148518 | − | 0.148518i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 279.999 | − | 279.999i | 0.485267 | − | 0.485267i | −0.421542 | − | 0.906809i | \(-0.638511\pi\) |
0.906809 | + | 0.421542i | \(0.138511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 131.258i | − | 0.226697i | ||||||
\(580\) | 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 | −0.389091 | − | 0.921199i | \(-0.627211\pi\) |
0.921199 | + | 0.389091i | \(0.127211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 297.071i | − | 0.504366i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 637.485 | 1.07865 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 424.570 | + | 424.570i | 0.715969 | + | 0.715969i | 0.967777 | − | 0.251808i | \(-0.0810251\pi\) |
−0.251808 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −79.6209 | + | 79.6209i | −0.133368 | + | 0.133368i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 396.536i | − | 0.661996i | −0.943631 | − | 0.330998i | \(-0.892615\pi\) | ||
0.943631 | − | 0.330998i | \(-0.107385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 238.908 | 0.397518 | 0.198759 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198759 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −74.0908 | − | 74.0908i | −0.122870 | − | 0.122870i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 92.8025 | − | 92.8025i | 0.152887 | − | 0.152887i | −0.626519 | − | 0.779406i | \(-0.715521\pi\) |
0.779406 | + | 0.626519i | \(0.215521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 624.929i | − | 1.02616i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −540.000 | −0.883797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −301.943 | − | 301.943i | −0.492567 | − | 0.492567i | 0.416547 | − | 0.909114i | \(-0.363240\pi\) |
−0.909114 | + | 0.416547i | \(0.863240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 372.904 | − | 372.904i | 0.604382 | − | 0.604382i | −0.337090 | − | 0.941472i | \(-0.609443\pi\) |
0.941472 | + | 0.337090i | \(0.109443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 815.939i | − | 1.31816i | −0.752074 | − | 0.659078i | \(-0.770947\pi\) | ||
0.752074 | − | 0.659078i | \(-0.229053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.4847 | −0.0313763 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1169.34 | − | 1169.34i | −1.87695 | − | 1.87695i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −288.434 | + | 288.434i | −0.460022 | + | 0.460022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 110.969i | 0.176422i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −550.434 | −0.872320 | −0.436160 | − | 0.899869i | \(-0.643662\pi\) | ||||
−0.436160 | + | 0.899869i | \(0.643662\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7219 | + | 14.7219i | 0.0232574 | + | 0.0232574i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −759.217 | + | 759.217i | −1.19186 | + | 1.19186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 233.939i | − | 0.366101i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 927.939 | 1.44764 | 0.723821 | − | 0.689988i | \(-0.242384\pi\) | ||||
0.723821 | + | 0.689988i | \(0.242384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 190.960 | + | 190.960i | 0.296983 | + | 0.296983i | 0.839831 | − | 0.542848i | \(-0.182654\pi\) |
−0.542848 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −637.146 | + | 637.146i | −0.984770 | + | 0.984770i | −0.999886 | − | 0.0151154i | \(-0.995188\pi\) |
0.0151154 | + | 0.999886i | \(0.495188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1441.84i | − | 2.22163i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −373.980 | −0.574469 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 404.116 | + | 404.116i | 0.618860 | + | 0.618860i | 0.945239 | − | 0.326379i | \(-0.105828\pi\) |
−0.326379 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −132.576 | + | 132.576i | −0.201789 | + | 0.201789i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 453.196i | 0.687703i | 0.939024 | + | 0.343852i | \(0.111732\pi\) | ||||
−0.939024 | + | 0.343852i | \(0.888268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 717.546 | 1.08555 | 0.542773 | − | 0.839879i | \(-0.317374\pi\) | ||||
0.542773 | + | 0.839879i | \(0.317374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 226.515 | + | 226.515i | 0.341652 | + | 0.341652i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 90.8082 | − | 90.8082i | 0.136144 | − | 0.136144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 587.196i | 0.877723i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1665.28 | −2.48179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 121.413 | + | 121.413i | 0.180406 | + | 0.180406i | 0.791533 | − | 0.611127i | \(-0.209283\pi\) |
−0.611127 | + | 0.791533i | \(0.709283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 671.943 | − | 671.943i | 0.992531 | − | 0.992531i | −0.00744150 | − | 0.999972i | \(-0.502369\pi\) |
0.999972 | + | 0.00744150i | \(0.00236873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 825.464i | 1.21571i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.94897 | −0.00726722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 802.095 | + | 802.095i | 1.17437 | + | 1.17437i | 0.981157 | + | 0.193214i | \(0.0618913\pi\) |
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 349.015 | − | 349.015i | 0.508027 | − | 0.508027i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 864.745i | − | 1.25507i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1146.49 | 1.65918 | 0.829591 | − | 0.558371i | \(-0.188574\pi\) | ||||
0.829591 | + | 0.558371i | \(0.188574\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 363.106 | + | 363.106i | 0.523962 | + | 0.523962i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 192.577 | − | 192.577i | 0.276293 | − | 0.276293i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 370.454i | 0.529977i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −673.217 | −0.960366 | −0.480183 | − | 0.877168i | \(-0.659430\pi\) | ||||
−0.480183 | + | 0.877168i | \(0.659430\pi\) | |||||||
\(702\) | 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 | \(0.235488\pi\) | ||||
−0.738598 | + | 0.674146i | \(0.764512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 145.485 | 0.204620 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54.3429 | − | 54.3429i | −0.0762172 | − | 0.0762172i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −62.4245 | + | 62.4245i | −0.0870634 | + | 0.0870634i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 89.0306i | 0.123826i | 0.998082 | + | 0.0619128i | \(0.0197201\pi\) | ||||
−0.998082 | + | 0.0619128i | \(0.980280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 345.010 | 0.478516 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.1918 | + | 39.1918i | 0.0542072 | + | 0.0542072i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 332.703 | − | 332.703i | 0.457638 | − | 0.457638i | −0.440242 | − | 0.897879i | \(-0.645107\pi\) |
0.897879 | + | 0.440242i | \(0.145107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 379.051 | 0.518538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −229.823 | − | 229.823i | −0.313537 | − | 0.313537i | 0.532741 | − | 0.846278i | \(-0.321162\pi\) |
−0.846278 | + | 0.532741i | \(0.821162\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 434.847 | 0.586838 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −585.782 | − | 585.782i | −0.788401 | − | 0.788401i | 0.192831 | − | 0.981232i | \(-0.438233\pi\) |
−0.981232 | + | 0.192831i | \(0.938233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 304.924 | − | 304.924i | 0.408198 | − | 0.408198i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 243.423i | − | 0.324998i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1354.27 | −1.80329 | −0.901645 | − | 0.432477i | \(-0.857639\pi\) | ||||
−0.901645 | + | 0.432477i | \(0.857639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −457.120 | − | 457.120i | −0.607066 | − | 0.607066i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 985.832 | − | 985.832i | 1.30229 | − | 1.30229i | 0.375442 | − | 0.926846i | \(-0.377491\pi\) |
0.926846 | − | 0.375442i | \(-0.122509\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 105.526i | 0.139032i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 206.495 | 0.271347 | 0.135673 | − | 0.990754i | \(-0.456680\pi\) | ||||
0.135673 | + | 0.990754i | \(0.456680\pi\) | |||||||
\(762\) | 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 | \(0.187127\pi\) | ||||
−0.832119 | + | 0.554596i | \(0.812873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −504.929 | −0.654901 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 491.035 | + | 491.035i | 0.635233 | + | 0.635233i | 0.949376 | − | 0.314143i | \(-0.101717\pi\) |
−0.314143 | + | 0.949376i | \(0.601717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 134.091 | − | 134.091i | 0.172575 | − | 0.172575i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 369.694i | − | 0.474575i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1266.97 | −1.62224 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 125.833 | + | 125.833i | 0.160706 | + | 0.160706i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −958.586 | + | 958.586i | −1.21803 | + | 1.21803i | −0.249702 | + | 0.968323i | \(0.580333\pi\) |
−0.968323 | + | 0.249702i | \(0.919667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 516.434i | − | 0.654542i | ||||||
\(790\) | 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 | \(-0.797926\pi\) |
0.593044 | + | 0.805170i | \(0.297926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 332.908i | − | 0.416656i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 470.908 | 0.587900 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 718.005 | + | 718.005i | 0.894153 | + | 0.894153i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −251.388 | + | 251.388i | −0.311510 | + | 0.311510i | ||||
\(808\) | 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 | \(-0.506463\pi\) | ||||
−0.0203012 | + | 0.999794i | \(0.506463\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −80.8332 | − | 80.8332i | −0.0994258 | − | 0.0994258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 363.837 | − | 363.837i | 0.445333 | − | 0.445333i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 547.423i | − | 0.668405i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 980.064 | 1.19374 | 0.596872 | − | 0.802337i | \(-0.296410\pi\) | ||||
0.596872 | + | 0.802337i | \(0.296410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −503.863 | − | 503.863i | −0.612227 | − | 0.612227i | 0.331299 | − | 0.943526i | \(-0.392513\pi\) |
−0.943526 | + | 0.331299i | \(0.892513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1078.84 | − | 1078.84i | 1.30452 | − | 1.30452i | 0.379208 | − | 0.925311i | \(-0.376196\pi\) |
0.925311 | − | 0.379208i | \(-0.123804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 124.352i | − | 0.150002i | −0.997183 | − | 0.0750012i | \(-0.976104\pi\) | ||
0.997183 | − | 0.0750012i | \(-0.0238961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 362.908 | 0.436713 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −468.055 | − | 468.055i | −0.561890 | − | 0.561890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 75.3031 | − | 75.3031i | 0.0899678 | − | 0.0899678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1125.48i | − | 1.34146i | −0.741702 | − | 0.670730i | \(-0.765981\pi\) | ||
0.741702 | − | 0.670730i | \(-0.234019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −331.888 | −0.394635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −397.348 | − | 397.348i | −0.471350 | − | 0.471350i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1065.12 | − | 1065.12i | 1.25753 | − | 1.25753i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 746.474i | − | 0.879240i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.9694 | 0.0457925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1039.87 | − | 1039.87i | −1.21908 | − | 1.21908i | −0.967955 | − | 0.251122i | \(-0.919201\pi\) |
−0.251122 | − | 0.967955i | \(-0.580799\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −620.177 | + | 620.177i | −0.723660 | + | 0.723660i | −0.969349 | − | 0.245688i | \(-0.920986\pi\) |
0.245688 | + | 0.969349i | \(0.420986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 948.888i | 1.10464i | 0.833631 | + | 0.552321i | \(0.186258\pi\) | ||||
−0.833631 | + | 0.552321i | \(0.813742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −465.403 | −0.540538 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1064.42 | − | 1064.42i | −1.23339 | − | 1.23339i | −0.962652 | − | 0.270740i | \(-0.912732\pi\) |
−0.270740 | − | 0.962652i | \(-0.587268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 214.305 | − | 214.305i | 0.247180 | − | 0.247180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 787.918i | − | 0.906695i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 604.949 | 0.694545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −166.212 | − | 166.212i | −0.190392 | − | 0.190392i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 329.975 | − | 329.975i | 0.376254 | − | 0.376254i | −0.493495 | − | 0.869749i | \(-0.664281\pi\) |
0.869749 | + | 0.493495i | \(0.164281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 355.546i | − | 0.404489i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 135.857 | 0.154208 | 0.0771039 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771039 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.8694 | − | 46.8694i | −0.0530797 | − | 0.0530797i | 0.680069 | − | 0.733148i | \(-0.261950\pi\) |
−0.733148 | + | 0.680069i | \(0.761950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.5097 | + | 43.5097i | −0.0490526 | + | 0.0490526i | −0.731208 | − | 0.682155i | \(-0.761043\pi\) |
0.682155 | + | 0.731208i | \(0.261043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 110.990i | − | 0.124848i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −146.227 | −0.164116 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −319.546 | − | 319.546i | −0.357834 | − | 0.357834i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 79.5459 | − | 79.5459i | 0.0886800 | − | 0.0886800i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 701.898i | 0.780754i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 533.112 | 0.591690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −458.030 | − | 458.030i | −0.507231 | − | 0.507231i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 638.938 | − | 638.938i | 0.704452 | − | 0.704452i | −0.260911 | − | 0.965363i | \(-0.584023\pi\) |
0.965363 | + | 0.260911i | \(0.0840229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 137.258i | 0.150999i | ||||||||
\(910\) | 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 | ||||||||
\(921\) | −295.423 | −0.320764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 955.051 | + | 955.051i | 1.03472 | + | 1.03472i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −69.4699 | + | 69.4699i | −0.0749406 | + | 0.0749406i | ||||
\(928\) | 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 | ||||||||
\(933\) | −22.0704 | − | 22.0704i | −0.0236553 | − | 0.0236553i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −60.5551 | + | 60.5551i | −0.0646266 | + | 0.0646266i | −0.738681 | − | 0.674055i | \(-0.764551\pi\) |
0.674055 | + | 0.738681i | \(0.264551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 792.620i | − | 0.844111i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −264.064 | −0.280620 | −0.140310 | − | 0.990108i | \(-0.544810\pi\) | ||||
−0.140310 | + | 0.990108i | \(0.544810\pi\) | |||||||
\(942\) | 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 | −0.765433 | − | 0.643516i | \(-0.777475\pi\) |
0.643516 | + | 0.765433i | \(0.277475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1082.47i | − | 1.14065i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 152.969 | 0.160851 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 378.359 | + | 378.359i | 0.397019 | + | 0.397019i | 0.877180 | − | 0.480162i | \(-0.159422\pi\) |
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 681.489 | − | 681.489i | 0.712110 | − | 0.712110i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1514.35i | − | 1.57909i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −540.959 | −0.562913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.0148 | + | 49.0148i | 0.0508980 | + | 0.0508980i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.1964 | + | 52.1964i | −0.0539777 | + | 0.0539777i | −0.733580 | − | 0.679603i | \(-0.762152\pi\) |
0.679603 | + | 0.733580i | \(0.262152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 268.082i | 0.276658i | ||||||||
\(970\) | 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 | \(-0.541060\pi\) |
0.991692 | + | 0.128636i | \(0.0410599\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2550.35i | − | 2.60506i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 478.454 | 0.487721 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1241.39 | + | 1241.39i | 1.26286 | + | 1.26286i | 0.949703 | + | 0.313153i | \(0.101385\pi\) |
0.313153 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −402.272 | + | 402.272i | −0.407571 | + | 0.407571i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 133.112i | − | 0.134593i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −219.816 | −0.221813 | −0.110906 | − | 0.993831i | \(-0.535375\pi\) | ||||
−0.110906 | + | 0.993831i | \(0.535375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 757.398 | + | 757.398i | 0.762738 | + | 0.762738i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −599.571 | + | 599.571i | −0.601375 | + | 0.601375i | −0.940677 | − | 0.339302i | \(-0.889809\pi\) |
0.339302 | + | 0.940677i | \(0.389809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.0000i | 0.0540541i |
(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 | 1200.3.bg.o.193.1 | 4 | ||
4.3 | odd | 2 | 300.3.k.a.193.2 | 4 | |||
5.2 | odd | 4 | inner | 1200.3.bg.o.1057.1 | 4 | ||
5.3 | odd | 4 | 240.3.bg.d.97.2 | 4 | |||
5.4 | even | 2 | 240.3.bg.d.193.2 | 4 | |||
12.11 | even | 2 | 900.3.l.b.793.1 | 4 | |||
15.8 | even | 4 | 720.3.bh.f.577.1 | 4 | |||
15.14 | odd | 2 | 720.3.bh.f.433.1 | 4 | |||
20.3 | even | 4 | 60.3.k.a.37.1 | yes | 4 | ||
20.7 | even | 4 | 300.3.k.a.157.2 | 4 | |||
20.19 | odd | 2 | 60.3.k.a.13.1 | ✓ | 4 | ||
40.3 | even | 4 | 960.3.bg.b.577.2 | 4 | |||
40.13 | odd | 4 | 960.3.bg.a.577.1 | 4 | |||
40.19 | odd | 2 | 960.3.bg.b.193.2 | 4 | |||
40.29 | even | 2 | 960.3.bg.a.193.1 | 4 | |||
60.23 | odd | 4 | 180.3.l.b.37.1 | 4 | |||
60.47 | odd | 4 | 900.3.l.b.757.1 | 4 | |||
60.59 | even | 2 | 180.3.l.b.73.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.k.a.13.1 | ✓ | 4 | 20.19 | odd | 2 | ||
60.3.k.a.37.1 | yes | 4 | 20.3 | even | 4 | ||
180.3.l.b.37.1 | 4 | 60.23 | odd | 4 | |||
180.3.l.b.73.1 | 4 | 60.59 | even | 2 | |||
240.3.bg.d.97.2 | 4 | 5.3 | odd | 4 | |||
240.3.bg.d.193.2 | 4 | 5.4 | even | 2 | |||
300.3.k.a.157.2 | 4 | 20.7 | even | 4 | |||
300.3.k.a.193.2 | 4 | 4.3 | odd | 2 | |||
720.3.bh.f.433.1 | 4 | 15.14 | odd | 2 | |||
720.3.bh.f.577.1 | 4 | 15.8 | even | 4 | |||
900.3.l.b.757.1 | 4 | 60.47 | odd | 4 | |||
900.3.l.b.793.1 | 4 | 12.11 | even | 2 | |||
960.3.bg.a.193.1 | 4 | 40.29 | even | 2 | |||
960.3.bg.a.577.1 | 4 | 40.13 | odd | 4 | |||
960.3.bg.b.193.2 | 4 | 40.19 | odd | 2 | |||
960.3.bg.b.577.2 | 4 | 40.3 | even | 4 | |||
1200.3.bg.o.193.1 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.o.1057.1 | 4 | 5.2 | odd | 4 | inner |