Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,3,Mod(269,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.35696713773\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 269.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.269 |
Dual form | 270.3.b.c.269.3 |
$q$-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 \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(217\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 3.53553 | + | 3.53553i | 0.707107 | + | 0.707107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000i | 0.714286i | 0.934050 | + | 0.357143i | \(0.116249\pi\) | ||||
−0.934050 | + | 0.357143i | \(0.883751\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | + | 5.00000i | 0.500000 | + | 0.500000i | ||||
\(11\) | − | 1.41421i | − | 0.128565i | −0.997932 | − | 0.0642824i | \(-0.979524\pi\) | ||
0.997932 | − | 0.0642824i | \(-0.0204759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.00000i | 0.692308i | 0.938178 | + | 0.346154i | \(0.112512\pi\) | ||||
−0.938178 | + | 0.346154i | \(0.887488\pi\) | |||||||
\(14\) | 7.07107i | 0.505076i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −11.3137 | −0.665512 | −0.332756 | − | 0.943013i | \(-0.607979\pi\) | ||||
−0.332756 | + | 0.943013i | \(0.607979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.0000 | 1.10526 | 0.552632 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552632 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(20\) | 7.07107 | + | 7.07107i | 0.353553 | + | 0.353553i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.0909091i | ||||||
\(23\) | −1.41421 | −0.0614875 | −0.0307438 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307438 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000i | 1.00000i | ||||||||
\(26\) | 12.7279i | 0.489535i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.0000i | 0.357143i | ||||||||
\(29\) | − | 38.1838i | − | 1.31668i | −0.752720 | − | 0.658341i | \(-0.771259\pi\) | ||
0.752720 | − | 0.658341i | \(-0.228741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.0000 | 1.29032 | 0.645161 | − | 0.764046i | \(-0.276790\pi\) | ||||
0.645161 | + | 0.764046i | \(0.276790\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.0000 | −0.470588 | ||||||||
\(35\) | −17.6777 | + | 17.6777i | −0.505076 | + | 0.505076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 25.0000i | − | 0.675676i | −0.941204 | − | 0.337838i | \(-0.890304\pi\) | ||
0.941204 | − | 0.337838i | \(-0.109696\pi\) | |||||||
\(38\) | 29.6985 | 0.781539 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.0000 | + | 10.0000i | 0.250000 | + | 0.250000i | ||||
\(41\) | − | 52.3259i | − | 1.27624i | −0.769936 | − | 0.638121i | \(-0.779712\pi\) | ||
0.769936 | − | 0.638121i | \(-0.220288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.0000i | 1.48837i | 0.667972 | + | 0.744186i | \(0.267162\pi\) | ||||
−0.667972 | + | 0.744186i | \(0.732838\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.0642824i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.0434783 | ||||||||
\(47\) | −22.6274 | −0.481434 | −0.240717 | − | 0.970595i | \(-0.577383\pi\) | ||||
−0.240717 | + | 0.970595i | \(0.577383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 24.0000 | 0.489796 | ||||||||
\(50\) | 35.3553i | 0.707107i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18.0000i | 0.346154i | ||||||||
\(53\) | −72.1249 | −1.36085 | −0.680424 | − | 0.732819i | \(-0.738204\pi\) | ||||
−0.680424 | + | 0.732819i | \(0.738204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | − | 5.00000i | 0.0909091 | − | 0.0909091i | ||||
\(56\) | 14.1421i | 0.252538i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 54.0000i | − | 0.931034i | ||||||
\(59\) | − | 90.5097i | − | 1.53406i | −0.641610 | − | 0.767031i | \(-0.721733\pi\) | ||
0.641610 | − | 0.767031i | \(-0.278267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −97.0000 | −1.59016 | −0.795082 | − | 0.606502i | \(-0.792572\pi\) | ||||
−0.795082 | + | 0.606502i | \(0.792572\pi\) | |||||||
\(62\) | 56.5685 | 0.912396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −31.8198 | + | 31.8198i | −0.489535 | + | 0.489535i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 131.000i | − | 1.95522i | −0.210416 | − | 0.977612i | \(-0.567482\pi\) | ||
0.210416 | − | 0.977612i | \(-0.432518\pi\) | |||||||
\(68\) | −22.6274 | −0.332756 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −25.0000 | + | 25.0000i | −0.357143 | + | 0.357143i | ||||
\(71\) | 89.0955i | 1.25487i | 0.778671 | + | 0.627433i | \(0.215894\pi\) | ||||
−0.778671 | + | 0.627433i | \(0.784106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 17.0000i | − | 0.232877i | −0.993198 | − | 0.116438i | \(-0.962852\pi\) | ||
0.993198 | − | 0.116438i | \(-0.0371477\pi\) | |||||||
\(74\) | − | 35.3553i | − | 0.477775i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 42.0000 | 0.552632 | ||||||||
\(77\) | 7.07107 | 0.0918320 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −117.000 | −1.48101 | −0.740506 | − | 0.672049i | \(-0.765414\pi\) | ||||
−0.740506 | + | 0.672049i | \(0.765414\pi\) | |||||||
\(80\) | 14.1421 | + | 14.1421i | 0.176777 | + | 0.176777i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 74.0000i | − | 0.902439i | ||||||
\(83\) | 57.9828 | 0.698587 | 0.349294 | − | 0.937013i | \(-0.386422\pi\) | ||||
0.349294 | + | 0.937013i | \(0.386422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −40.0000 | − | 40.0000i | −0.470588 | − | 0.470588i | ||||
\(86\) | 90.5097i | 1.05244i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.00000i | − | 0.0454545i | ||||||
\(89\) | − | 147.078i | − | 1.65256i | −0.563257 | − | 0.826282i | \(-0.690452\pi\) | ||
0.563257 | − | 0.826282i | \(-0.309548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −45.0000 | −0.494505 | ||||||||
\(92\) | −2.82843 | −0.0307438 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −32.0000 | −0.340426 | ||||||||
\(95\) | 74.2462 | + | 74.2462i | 0.781539 | + | 0.781539i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 41.0000i | − | 0.422680i | −0.977413 | − | 0.211340i | \(-0.932217\pi\) | ||
0.977413 | − | 0.211340i | \(-0.0677828\pi\) | |||||||
\(98\) | 33.9411 | 0.346338 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 50.0000i | 0.500000i | ||||||||
\(101\) | 90.5097i | 0.896135i | 0.894000 | + | 0.448068i | \(0.147888\pi\) | ||||
−0.894000 | + | 0.448068i | \(0.852112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.0000i | − | 0.126214i | −0.998007 | − | 0.0631068i | \(-0.979899\pi\) | ||
0.998007 | − | 0.0631068i | \(-0.0201009\pi\) | |||||||
\(104\) | 25.4558i | 0.244768i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −102.000 | −0.962264 | ||||||||
\(107\) | 123.037 | 1.14987 | 0.574937 | − | 0.818197i | \(-0.305026\pi\) | ||||
0.574937 | + | 0.818197i | \(0.305026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.0733945 | 0.0366972 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366972 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(110\) | 7.07107 | − | 7.07107i | 0.0642824 | − | 0.0642824i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 20.0000i | 0.178571i | ||||||||
\(113\) | 38.1838 | 0.337909 | 0.168955 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168955 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.00000 | − | 5.00000i | −0.0434783 | − | 0.0434783i | ||||
\(116\) | − | 76.3675i | − | 0.658341i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 128.000i | − | 1.08475i | ||||||
\(119\) | − | 56.5685i | − | 0.475366i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.000 | 0.983471 | ||||||||
\(122\) | −137.179 | −1.12442 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 80.0000 | 0.645161 | ||||||||
\(125\) | −88.3883 | + | 88.3883i | −0.707107 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.0629921i | 0.999504 | + | 0.0314961i | \(0.0100272\pi\) | ||||
−0.999504 | + | 0.0314961i | \(0.989973\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −45.0000 | + | 45.0000i | −0.346154 | + | 0.346154i | ||||
\(131\) | 135.765i | 1.03637i | 0.855268 | + | 0.518185i | \(0.173392\pi\) | ||||
−0.855268 | + | 0.518185i | \(0.826608\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 105.000i | 0.789474i | ||||||||
\(134\) | − | 185.262i | − | 1.38255i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.0000 | −0.235294 | ||||||||
\(137\) | −267.286 | −1.95100 | −0.975498 | − | 0.220010i | \(-0.929391\pi\) | ||||
−0.975498 | + | 0.220010i | \(0.929391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −37.0000 | −0.266187 | −0.133094 | − | 0.991103i | \(-0.542491\pi\) | ||||
−0.133094 | + | 0.991103i | \(0.542491\pi\) | |||||||
\(140\) | −35.3553 | + | 35.3553i | −0.252538 | + | 0.252538i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 126.000i | 0.887324i | ||||||||
\(143\) | 12.7279 | 0.0890064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 135.000 | − | 135.000i | 0.931034 | − | 0.931034i | ||||
\(146\) | − | 24.0416i | − | 0.164669i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 50.0000i | − | 0.337838i | ||||||
\(149\) | − | 260.215i | − | 1.74641i | −0.487352 | − | 0.873206i | \(-0.662037\pi\) | ||
0.487352 | − | 0.873206i | \(-0.337963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 109.000 | 0.721854 | 0.360927 | − | 0.932594i | \(-0.382460\pi\) | ||||
0.360927 | + | 0.932594i | \(0.382460\pi\) | |||||||
\(152\) | 59.3970 | 0.390770 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | 0.0649351 | ||||||||
\(155\) | 141.421 | + | 141.421i | 0.912396 | + | 0.912396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 118.000i | 0.751592i | 0.926702 | + | 0.375796i | \(0.122631\pi\) | ||||
−0.926702 | + | 0.375796i | \(0.877369\pi\) | |||||||
\(158\) | −165.463 | −1.04723 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.0000 | + | 20.0000i | 0.125000 | + | 0.125000i | ||||
\(161\) | − | 7.07107i | − | 0.0439197i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 203.000i | 1.24540i | 0.782461 | + | 0.622699i | \(0.213964\pi\) | ||||
−0.782461 | + | 0.622699i | \(0.786036\pi\) | |||||||
\(164\) | − | 104.652i | − | 0.638121i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 82.0000 | 0.493976 | ||||||||
\(167\) | 101.823 | 0.609721 | 0.304860 | − | 0.952397i | \(-0.401390\pi\) | ||||
0.304860 | + | 0.952397i | \(0.401390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.0000 | 0.520710 | ||||||||
\(170\) | −56.5685 | − | 56.5685i | −0.332756 | − | 0.332756i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 128.000i | 0.744186i | ||||||||
\(173\) | −11.3137 | −0.0653972 | −0.0326986 | − | 0.999465i | \(-0.510410\pi\) | ||||
−0.0326986 | + | 0.999465i | \(0.510410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −125.000 | −0.714286 | ||||||||
\(176\) | − | 5.65685i | − | 0.0321412i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 208.000i | − | 1.16854i | ||||||
\(179\) | 125.865i | 0.703156i | 0.936159 | + | 0.351578i | \(0.114355\pi\) | ||||
−0.936159 | + | 0.351578i | \(0.885645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −127.000 | −0.701657 | −0.350829 | − | 0.936440i | \(-0.614100\pi\) | ||||
−0.350829 | + | 0.936440i | \(0.614100\pi\) | |||||||
\(182\) | −63.6396 | −0.349668 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.0217391 | ||||||||
\(185\) | 88.3883 | − | 88.3883i | 0.477775 | − | 0.477775i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000i | 0.0855615i | ||||||||
\(188\) | −45.2548 | −0.240717 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 105.000 | + | 105.000i | 0.552632 | + | 0.552632i | ||||
\(191\) | 101.823i | 0.533107i | 0.963820 | + | 0.266553i | \(0.0858849\pi\) | ||||
−0.963820 | + | 0.266553i | \(0.914115\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 271.000i | 1.40415i | 0.712105 | + | 0.702073i | \(0.247742\pi\) | ||||
−0.712105 | + | 0.702073i | \(0.752258\pi\) | |||||||
\(194\) | − | 57.9828i | − | 0.298880i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 48.0000 | 0.244898 | ||||||||
\(197\) | 316.784 | 1.60804 | 0.804020 | − | 0.594602i | \(-0.202691\pi\) | ||||
0.804020 | + | 0.594602i | \(0.202691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 147.000 | 0.738693 | 0.369347 | − | 0.929292i | \(-0.379581\pi\) | ||||
0.369347 | + | 0.929292i | \(0.379581\pi\) | |||||||
\(200\) | 70.7107i | 0.353553i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 128.000i | 0.633663i | ||||||||
\(203\) | 190.919 | 0.940487 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 185.000 | − | 185.000i | 0.902439 | − | 0.902439i | ||||
\(206\) | − | 18.3848i | − | 0.0892465i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 36.0000i | 0.173077i | ||||||||
\(209\) | − | 29.6985i | − | 0.142098i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 141.000 | 0.668246 | 0.334123 | − | 0.942529i | \(-0.391560\pi\) | ||||
0.334123 | + | 0.942529i | \(0.391560\pi\) | |||||||
\(212\) | −144.250 | −0.680424 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 174.000 | 0.813084 | ||||||||
\(215\) | −226.274 | + | 226.274i | −1.05244 | + | 1.05244i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 200.000i | 0.921659i | ||||||||
\(218\) | 11.3137 | 0.0518977 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.0000 | − | 10.0000i | 0.0454545 | − | 0.0454545i | ||||
\(221\) | − | 101.823i | − | 0.460739i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.0358744i | −0.999839 | − | 0.0179372i | \(-0.994290\pi\) | ||
0.999839 | − | 0.0179372i | \(-0.00570990\pi\) | |||||||
\(224\) | 28.2843i | 0.126269i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.0000 | 0.238938 | ||||||||
\(227\) | 69.2965 | 0.305271 | 0.152635 | − | 0.988283i | \(-0.451224\pi\) | ||||
0.152635 | + | 0.988283i | \(0.451224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | −0.0349345 | −0.0174672 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174672 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(230\) | −7.07107 | − | 7.07107i | −0.0307438 | − | 0.0307438i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 108.000i | − | 0.465517i | ||||||
\(233\) | −316.784 | −1.35959 | −0.679794 | − | 0.733403i | \(-0.737931\pi\) | ||||
−0.679794 | + | 0.733403i | \(0.737931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80.0000 | − | 80.0000i | −0.340426 | − | 0.340426i | ||||
\(236\) | − | 181.019i | − | 0.767031i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 80.0000i | − | 0.336134i | ||||||
\(239\) | 205.061i | 0.857996i | 0.903306 | + | 0.428998i | \(0.141133\pi\) | ||||
−0.903306 | + | 0.428998i | \(0.858867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 79.0000 | 0.327801 | 0.163900 | − | 0.986477i | \(-0.447592\pi\) | ||||
0.163900 | + | 0.986477i | \(0.447592\pi\) | |||||||
\(242\) | 168.291 | 0.695419 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −194.000 | −0.795082 | ||||||||
\(245\) | 84.8528 | + | 84.8528i | 0.346338 | + | 0.346338i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 189.000i | 0.765182i | ||||||||
\(248\) | 113.137 | 0.456198 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −125.000 | + | 125.000i | −0.500000 | + | 0.500000i | ||||
\(251\) | 46.6690i | 0.185932i | 0.995669 | + | 0.0929662i | \(0.0296349\pi\) | ||||
−0.995669 | + | 0.0929662i | \(0.970365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000i | 0.00790514i | ||||||||
\(254\) | 11.3137i | 0.0445422i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −169.706 | −0.660333 | −0.330167 | − | 0.943923i | \(-0.607105\pi\) | ||||
−0.330167 | + | 0.943923i | \(0.607105\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 125.000 | 0.482625 | ||||||||
\(260\) | −63.6396 | + | 63.6396i | −0.244768 | + | 0.244768i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 192.000i | 0.732824i | ||||||||
\(263\) | 282.843 | 1.07545 | 0.537724 | − | 0.843121i | \(-0.319284\pi\) | ||||
0.537724 | + | 0.843121i | \(0.319284\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −255.000 | − | 255.000i | −0.962264 | − | 0.962264i | ||||
\(266\) | 148.492i | 0.558242i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 262.000i | − | 0.977612i | ||||||
\(269\) | 101.823i | 0.378526i | 0.981926 | + | 0.189263i | \(0.0606098\pi\) | ||||
−0.981926 | + | 0.189263i | \(0.939390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −221.000 | −0.815498 | −0.407749 | − | 0.913094i | \(-0.633686\pi\) | ||||
−0.407749 | + | 0.913094i | \(0.633686\pi\) | |||||||
\(272\) | −45.2548 | −0.166378 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −378.000 | −1.37956 | ||||||||
\(275\) | 35.3553 | 0.128565 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 88.0000i | − | 0.317690i | −0.987304 | − | 0.158845i | \(-0.949223\pi\) | ||
0.987304 | − | 0.158845i | \(-0.0507769\pi\) | |||||||
\(278\) | −52.3259 | −0.188223 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −50.0000 | + | 50.0000i | −0.178571 | + | 0.178571i | ||||
\(281\) | − | 203.647i | − | 0.724722i | −0.932038 | − | 0.362361i | \(-0.881971\pi\) | ||
0.932038 | − | 0.362361i | \(-0.118029\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.0000i | 0.113074i | 0.998400 | + | 0.0565371i | \(0.0180059\pi\) | ||||
−0.998400 | + | 0.0565371i | \(0.981994\pi\) | |||||||
\(284\) | 178.191i | 0.627433i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 0.0629371 | ||||||||
\(287\) | 261.630 | 0.911601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | 190.919 | − | 190.919i | 0.658341 | − | 0.658341i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 34.0000i | − | 0.116438i | ||||||
\(293\) | 173.948 | 0.593680 | 0.296840 | − | 0.954927i | \(-0.404067\pi\) | ||||
0.296840 | + | 0.954927i | \(0.404067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 320.000 | − | 320.000i | 1.08475 | − | 1.08475i | ||||
\(296\) | − | 70.7107i | − | 0.238887i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 368.000i | − | 1.23490i | ||||||
\(299\) | − | 12.7279i | − | 0.0425683i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −320.000 | −1.06312 | ||||||||
\(302\) | 154.149 | 0.510428 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 84.0000 | 0.276316 | ||||||||
\(305\) | −342.947 | − | 342.947i | −1.12442 | − | 1.12442i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 486.000i | − | 1.58306i | −0.611129 | − | 0.791531i | \(-0.709284\pi\) | ||
0.611129 | − | 0.791531i | \(-0.290716\pi\) | |||||||
\(308\) | 14.1421 | 0.0459160 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 200.000 | + | 200.000i | 0.645161 | + | 0.645161i | ||||
\(311\) | − | 67.8823i | − | 0.218271i | −0.994027 | − | 0.109135i | \(-0.965192\pi\) | ||
0.994027 | − | 0.109135i | \(-0.0348082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 281.000i | − | 0.897764i | −0.893591 | − | 0.448882i | \(-0.851822\pi\) | ||
0.893591 | − | 0.448882i | \(-0.148178\pi\) | |||||||
\(314\) | 166.877i | 0.531456i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −234.000 | −0.740506 | ||||||||
\(317\) | −520.431 | −1.64174 | −0.820868 | − | 0.571117i | \(-0.806510\pi\) | ||||
−0.820868 | + | 0.571117i | \(0.806510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.0000 | −0.169279 | ||||||||
\(320\) | 28.2843 | + | 28.2843i | 0.0883883 | + | 0.0883883i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 10.0000i | − | 0.0310559i | ||||||
\(323\) | −237.588 | −0.735566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −225.000 | −0.692308 | ||||||||
\(326\) | 287.085i | 0.880630i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 148.000i | − | 0.451220i | ||||||
\(329\) | − | 113.137i | − | 0.343882i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −59.0000 | −0.178248 | −0.0891239 | − | 0.996021i | \(-0.528407\pi\) | ||||
−0.0891239 | + | 0.996021i | \(0.528407\pi\) | |||||||
\(332\) | 115.966 | 0.349294 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 144.000 | 0.431138 | ||||||||
\(335\) | 463.155 | − | 463.155i | 1.38255 | − | 1.38255i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 55.0000i | − | 0.163205i | −0.996665 | − | 0.0816024i | \(-0.973996\pi\) | ||
0.996665 | − | 0.0816024i | \(-0.0260038\pi\) | |||||||
\(338\) | 124.451 | 0.368198 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −80.0000 | − | 80.0000i | −0.235294 | − | 0.235294i | ||||
\(341\) | − | 56.5685i | − | 0.165890i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 365.000i | 1.06414i | ||||||||
\(344\) | 181.019i | 0.526219i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.0462428 | ||||||||
\(347\) | −598.212 | −1.72395 | −0.861977 | − | 0.506947i | \(-0.830774\pi\) | ||||
−0.861977 | + | 0.506947i | \(0.830774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −439.000 | −1.25788 | −0.628940 | − | 0.777454i | \(-0.716511\pi\) | ||||
−0.628940 | + | 0.777454i | \(0.716511\pi\) | |||||||
\(350\) | −176.777 | −0.505076 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 8.00000i | − | 0.0227273i | ||||||
\(353\) | −520.431 | −1.47431 | −0.737154 | − | 0.675725i | \(-0.763831\pi\) | ||||
−0.737154 | + | 0.675725i | \(0.763831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −315.000 | + | 315.000i | −0.887324 | + | 0.887324i | ||||
\(356\) | − | 294.156i | − | 0.826282i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 178.000i | 0.497207i | ||||||||
\(359\) | 55.1543i | 0.153633i | 0.997045 | + | 0.0768166i | \(0.0244756\pi\) | ||||
−0.997045 | + | 0.0768166i | \(0.975524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 80.0000 | 0.221607 | ||||||||
\(362\) | −179.605 | −0.496147 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −90.0000 | −0.247253 | ||||||||
\(365\) | 60.1041 | − | 60.1041i | 0.164669 | − | 0.164669i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 589.000i | − | 1.60490i | −0.596716 | − | 0.802452i | \(-0.703528\pi\) | ||
0.596716 | − | 0.802452i | \(-0.296472\pi\) | |||||||
\(368\) | −5.65685 | −0.0153719 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 125.000 | − | 125.000i | 0.337838 | − | 0.337838i | ||||
\(371\) | − | 360.624i | − | 0.972034i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.00000i | 0.0241287i | 0.999927 | + | 0.0120643i | \(0.00384029\pi\) | ||||
−0.999927 | + | 0.0120643i | \(0.996160\pi\) | |||||||
\(374\) | 22.6274i | 0.0605011i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −64.0000 | −0.170213 | ||||||||
\(377\) | 343.654 | 0.911549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.000 | 0.414248 | 0.207124 | − | 0.978315i | \(-0.433590\pi\) | ||||
0.207124 | + | 0.978315i | \(0.433590\pi\) | |||||||
\(380\) | 148.492 | + | 148.492i | 0.390770 | + | 0.390770i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 144.000i | 0.376963i | ||||||||
\(383\) | −282.843 | −0.738493 | −0.369246 | − | 0.929332i | \(-0.620384\pi\) | ||||
−0.369246 | + | 0.929332i | \(0.620384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.0000 | + | 25.0000i | 0.0649351 | + | 0.0649351i | ||||
\(386\) | 383.252i | 0.992881i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 82.0000i | − | 0.211340i | ||||||
\(389\) | 599.627i | 1.54146i | 0.637164 | + | 0.770728i | \(0.280107\pi\) | ||||
−0.637164 | + | 0.770728i | \(0.719893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.0409207 | ||||||||
\(392\) | 67.8823 | 0.173169 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 448.000 | 1.13706 | ||||||||
\(395\) | −413.657 | − | 413.657i | −1.04723 | − | 1.04723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 296.000i | 0.745592i | 0.927913 | + | 0.372796i | \(0.121601\pi\) | ||||
−0.927913 | + | 0.372796i | \(0.878399\pi\) | |||||||
\(398\) | 207.889 | 0.522335 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 100.000i | 0.250000i | ||||||||
\(401\) | − | 388.909i | − | 0.969847i | −0.874557 | − | 0.484924i | \(-0.838847\pi\) | ||
0.874557 | − | 0.484924i | \(-0.161153\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 360.000i | 0.893300i | ||||||||
\(404\) | 181.019i | 0.448068i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 270.000 | 0.665025 | ||||||||
\(407\) | −35.3553 | −0.0868682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 145.000 | 0.354523 | 0.177262 | − | 0.984164i | \(-0.443276\pi\) | ||||
0.177262 | + | 0.984164i | \(0.443276\pi\) | |||||||
\(410\) | 261.630 | − | 261.630i | 0.638121 | − | 0.638121i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 26.0000i | − | 0.0631068i | ||||||
\(413\) | 452.548 | 1.09576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 205.000 | + | 205.000i | 0.493976 | + | 0.493976i | ||||
\(416\) | 50.9117i | 0.122384i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 42.0000i | − | 0.100478i | ||||||
\(419\) | 701.450i | 1.67410i | 0.547123 | + | 0.837052i | \(0.315723\pi\) | ||||
−0.547123 | + | 0.837052i | \(0.684277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 505.000 | 1.19952 | 0.599762 | − | 0.800178i | \(-0.295262\pi\) | ||||
0.599762 | + | 0.800178i | \(0.295262\pi\) | |||||||
\(422\) | 199.404 | 0.472522 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −204.000 | −0.481132 | ||||||||
\(425\) | − | 282.843i | − | 0.665512i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 485.000i | − | 1.13583i | ||||||
\(428\) | 246.073 | 0.574937 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −320.000 | + | 320.000i | −0.744186 | + | 0.744186i | ||||
\(431\) | − | 43.8406i | − | 0.101718i | −0.998706 | − | 0.0508592i | \(-0.983804\pi\) | ||
0.998706 | − | 0.0508592i | \(-0.0161960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.0000i | − | 0.0739030i | −0.999317 | − | 0.0369515i | \(-0.988235\pi\) | ||
0.999317 | − | 0.0369515i | \(-0.0117647\pi\) | |||||||
\(434\) | 282.843i | 0.651711i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | 0.0366972 | ||||||||
\(437\) | −29.6985 | −0.0679599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −504.000 | −1.14806 | −0.574032 | − | 0.818833i | \(-0.694621\pi\) | ||||
−0.574032 | + | 0.818833i | \(0.694621\pi\) | |||||||
\(440\) | 14.1421 | − | 14.1421i | 0.0321412 | − | 0.0321412i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 144.000i | − | 0.325792i | ||||||
\(443\) | 237.588 | 0.536316 | 0.268158 | − | 0.963375i | \(-0.413585\pi\) | ||||
0.268158 | + | 0.963375i | \(0.413585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 520.000 | − | 520.000i | 1.16854 | − | 1.16854i | ||||
\(446\) | − | 11.3137i | − | 0.0253671i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 40.0000i | 0.0892857i | ||||||||
\(449\) | 67.8823i | 0.151185i | 0.997139 | + | 0.0755927i | \(0.0240849\pi\) | ||||
−0.997139 | + | 0.0755927i | \(0.975915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74.0000 | −0.164080 | ||||||||
\(452\) | 76.3675 | 0.168955 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 98.0000 | 0.215859 | ||||||||
\(455\) | −159.099 | − | 159.099i | −0.349668 | − | 0.349668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 752.000i | 1.64551i | 0.568393 | + | 0.822757i | \(0.307565\pi\) | ||||
−0.568393 | + | 0.822757i | \(0.692435\pi\) | |||||||
\(458\) | −11.3137 | −0.0247024 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0000 | − | 10.0000i | −0.0217391 | − | 0.0217391i | ||||
\(461\) | 610.940i | 1.32525i | 0.748951 | + | 0.662625i | \(0.230558\pi\) | ||||
−0.748951 | + | 0.662625i | \(0.769442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 597.000i | 1.28942i | 0.764429 | + | 0.644708i | \(0.223021\pi\) | ||||
−0.764429 | + | 0.644708i | \(0.776979\pi\) | |||||||
\(464\) | − | 152.735i | − | 0.329170i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −448.000 | −0.961373 | ||||||||
\(467\) | 848.528 | 1.81698 | 0.908488 | − | 0.417910i | \(-0.137237\pi\) | ||||
0.908488 | + | 0.417910i | \(0.137237\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 655.000 | 1.39659 | ||||||||
\(470\) | −113.137 | − | 113.137i | −0.240717 | − | 0.240717i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 256.000i | − | 0.542373i | ||||||
\(473\) | 90.5097 | 0.191352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 525.000i | 1.10526i | ||||||||
\(476\) | − | 113.137i | − | 0.237683i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 290.000i | 0.606695i | ||||||||
\(479\) | − | 168.291i | − | 0.351339i | −0.984449 | − | 0.175670i | \(-0.943791\pi\) | ||
0.984449 | − | 0.175670i | \(-0.0562090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 225.000 | 0.467775 | ||||||||
\(482\) | 111.723 | 0.231790 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 238.000 | 0.491736 | ||||||||
\(485\) | 144.957 | − | 144.957i | 0.298880 | − | 0.298880i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 507.000i | − | 1.04107i | −0.853841 | − | 0.520534i | \(-0.825733\pi\) | ||
0.853841 | − | 0.520534i | \(-0.174267\pi\) | |||||||
\(488\) | −274.357 | −0.562208 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 120.000 | + | 120.000i | 0.244898 | + | 0.244898i | ||||
\(491\) | 428.507i | 0.872722i | 0.899772 | + | 0.436361i | \(0.143733\pi\) | ||||
−0.899772 | + | 0.436361i | \(0.856267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 432.000i | 0.876268i | ||||||||
\(494\) | 267.286i | 0.541066i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 160.000 | 0.322581 | ||||||||
\(497\) | −445.477 | −0.896333 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 870.000 | 1.74349 | 0.871743 | − | 0.489963i | \(-0.162990\pi\) | ||||
0.871743 | + | 0.489963i | \(0.162990\pi\) | |||||||
\(500\) | −176.777 | + | 176.777i | −0.353553 | + | 0.353553i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 66.0000i | 0.131474i | ||||||||
\(503\) | −462.448 | −0.919379 | −0.459690 | − | 0.888080i | \(-0.652039\pi\) | ||||
−0.459690 | + | 0.888080i | \(0.652039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −320.000 | + | 320.000i | −0.633663 | + | 0.633663i | ||||
\(506\) | 2.82843i | 0.00558978i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000i | 0.0314961i | ||||||||
\(509\) | 818.830i | 1.60870i | 0.594154 | + | 0.804351i | \(0.297487\pi\) | ||||
−0.594154 | + | 0.804351i | \(0.702513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 85.0000 | 0.166341 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −240.000 | −0.466926 | ||||||||
\(515\) | 45.9619 | − | 45.9619i | 0.0892465 | − | 0.0892465i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.0000i | 0.0618956i | ||||||||
\(518\) | 176.777 | 0.341268 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −90.0000 | + | 90.0000i | −0.173077 | + | 0.173077i | ||||
\(521\) | − | 864.084i | − | 1.65851i | −0.558869 | − | 0.829256i | \(-0.688765\pi\) | ||
0.558869 | − | 0.829256i | \(-0.311235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 163.000i | − | 0.311663i | −0.987784 | − | 0.155832i | \(-0.950194\pi\) | ||
0.987784 | − | 0.155832i | \(-0.0498058\pi\) | |||||||
\(524\) | 271.529i | 0.518185i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 400.000 | 0.760456 | ||||||||
\(527\) | −452.548 | −0.858726 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −527.000 | −0.996219 | ||||||||
\(530\) | −360.624 | − | 360.624i | −0.680424 | − | 0.680424i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 210.000i | 0.394737i | ||||||||
\(533\) | 470.933 | 0.883552 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 435.000 | + | 435.000i | 0.813084 | + | 0.813084i | ||||
\(536\) | − | 370.524i | − | 0.691276i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 144.000i | 0.267658i | ||||||||
\(539\) | − | 33.9411i | − | 0.0629705i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 697.000 | 1.28835 | 0.644177 | − | 0.764876i | \(-0.277200\pi\) | ||||
0.644177 | + | 0.764876i | \(0.277200\pi\) | |||||||
\(542\) | −312.541 | −0.576644 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −64.0000 | −0.117647 | ||||||||
\(545\) | 28.2843 | + | 28.2843i | 0.0518977 | + | 0.0518977i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 389.000i | 0.711152i | 0.934647 | + | 0.355576i | \(0.115715\pi\) | ||||
−0.934647 | + | 0.355576i | \(0.884285\pi\) | |||||||
\(548\) | −534.573 | −0.975498 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.0000 | 0.0909091 | ||||||||
\(551\) | − | 801.859i | − | 1.45528i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 585.000i | − | 1.05787i | ||||||
\(554\) | − | 124.451i | − | 0.224640i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −74.0000 | −0.133094 | ||||||||
\(557\) | 1086.12 | 1.94994 | 0.974969 | − | 0.222339i | \(-0.0713691\pi\) | ||||
0.974969 | + | 0.222339i | \(0.0713691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −576.000 | −1.03041 | ||||||||
\(560\) | −70.7107 | + | 70.7107i | −0.126269 | + | 0.126269i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 288.000i | − | 0.512456i | ||||||
\(563\) | −622.254 | −1.10525 | −0.552623 | − | 0.833431i | \(-0.686373\pi\) | ||||
−0.552623 | + | 0.833431i | \(0.686373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 135.000 | + | 135.000i | 0.238938 | + | 0.238938i | ||||
\(566\) | 45.2548i | 0.0799555i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 252.000i | 0.443662i | ||||||||
\(569\) | 463.862i | 0.815223i | 0.913155 | + | 0.407612i | \(0.133638\pi\) | ||||
−0.913155 | + | 0.407612i | \(0.866362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −923.000 | −1.61646 | −0.808231 | − | 0.588865i | \(-0.799575\pi\) | ||||
−0.808231 | + | 0.588865i | \(0.799575\pi\) | |||||||
\(572\) | 25.4558 | 0.0445032 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 370.000 | 0.644599 | ||||||||
\(575\) | − | 35.3553i | − | 0.0614875i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 247.000i | − | 0.428076i | −0.976825 | − | 0.214038i | \(-0.931338\pi\) | ||
0.976825 | − | 0.214038i | \(-0.0686617\pi\) | |||||||
\(578\) | −227.688 | −0.393925 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 270.000 | − | 270.000i | 0.465517 | − | 0.465517i | ||||
\(581\) | 289.914i | 0.498991i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 102.000i | 0.174957i | ||||||||
\(584\) | − | 48.0833i | − | 0.0823344i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 246.000 | 0.419795 | ||||||||
\(587\) | −453.963 | −0.773360 | −0.386680 | − | 0.922214i | \(-0.626378\pi\) | ||||
−0.386680 | + | 0.922214i | \(0.626378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 840.000 | 1.42615 | ||||||||
\(590\) | 452.548 | − | 452.548i | 0.767031 | − | 0.767031i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 100.000i | − | 0.168919i | ||||||
\(593\) | −4.24264 | −0.00715454 | −0.00357727 | − | 0.999994i | \(-0.501139\pi\) | ||||
−0.00357727 | + | 0.999994i | \(0.501139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 200.000 | − | 200.000i | 0.336134 | − | 0.336134i | ||||
\(596\) | − | 520.431i | − | 0.873206i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 18.0000i | − | 0.0301003i | ||||||
\(599\) | 224.860i | 0.375392i | 0.982227 | + | 0.187696i | \(0.0601020\pi\) | ||||
−0.982227 | + | 0.187696i | \(0.939898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −736.000 | −1.22463 | −0.612313 | − | 0.790616i | \(-0.709761\pi\) | ||||
−0.612313 | + | 0.790616i | \(0.709761\pi\) | |||||||
\(602\) | −452.548 | −0.751741 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 218.000 | 0.360927 | ||||||||
\(605\) | 420.729 | + | 420.729i | 0.695419 | + | 0.695419i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 437.000i | − | 0.719934i | −0.932965 | − | 0.359967i | \(-0.882788\pi\) | ||
0.932965 | − | 0.359967i | \(-0.117212\pi\) | |||||||
\(608\) | 118.794 | 0.195385 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −485.000 | − | 485.000i | −0.795082 | − | 0.795082i | ||||
\(611\) | − | 203.647i | − | 0.333301i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 335.000i | − | 0.546493i | −0.961944 | − | 0.273246i | \(-0.911903\pi\) | ||
0.961944 | − | 0.273246i | \(-0.0880974\pi\) | |||||||
\(614\) | − | 687.308i | − | 1.11939i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.0000 | 0.0324675 | ||||||||
\(617\) | 255.973 | 0.414867 | 0.207433 | − | 0.978249i | \(-0.433489\pi\) | ||||
0.207433 | + | 0.978249i | \(0.433489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −965.000 | −1.55897 | −0.779483 | − | 0.626423i | \(-0.784518\pi\) | ||||
−0.779483 | + | 0.626423i | \(0.784518\pi\) | |||||||
\(620\) | 282.843 | + | 282.843i | 0.456198 | + | 0.456198i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 96.0000i | − | 0.154341i | ||||||
\(623\) | 735.391 | 1.18040 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −625.000 | −1.00000 | ||||||||
\(626\) | − | 397.394i | − | 0.634815i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 236.000i | 0.375796i | ||||||||
\(629\) | 282.843i | 0.449670i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 275.000 | 0.435816 | 0.217908 | − | 0.975969i | \(-0.430077\pi\) | ||||
0.217908 | + | 0.975969i | \(0.430077\pi\) | |||||||
\(632\) | −330.926 | −0.523617 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −736.000 | −1.16088 | ||||||||
\(635\) | −28.2843 | + | 28.2843i | −0.0445422 | + | 0.0445422i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 216.000i | 0.339089i | ||||||||
\(638\) | −76.3675 | −0.119698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.0000 | + | 40.0000i | 0.0625000 | + | 0.0625000i | ||||
\(641\) | 486.489i | 0.758954i | 0.925201 | + | 0.379477i | \(0.123896\pi\) | ||||
−0.925201 | + | 0.379477i | \(0.876104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1152.00i | − | 1.79160i | −0.444455 | − | 0.895801i | \(-0.646603\pi\) | ||
0.444455 | − | 0.895801i | \(-0.353397\pi\) | |||||||
\(644\) | − | 14.1421i | − | 0.0219598i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −336.000 | −0.520124 | ||||||||
\(647\) | −691.550 | −1.06886 | −0.534428 | − | 0.845214i | \(-0.679473\pi\) | ||||
−0.534428 | + | 0.845214i | \(0.679473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −128.000 | −0.197227 | ||||||||
\(650\) | −318.198 | −0.489535 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 406.000i | 0.622699i | ||||||||
\(653\) | 350.725 | 0.537098 | 0.268549 | − | 0.963266i | \(-0.413456\pi\) | ||||
0.268549 | + | 0.963266i | \(0.413456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −480.000 | + | 480.000i | −0.732824 | + | 0.732824i | ||||
\(656\) | − | 209.304i | − | 0.319060i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 160.000i | − | 0.243161i | ||||||
\(659\) | − | 497.803i | − | 0.755392i | −0.925930 | − | 0.377696i | \(-0.876716\pi\) | ||
0.925930 | − | 0.377696i | \(-0.123284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −577.000 | −0.872920 | −0.436460 | − | 0.899724i | \(-0.643768\pi\) | ||||
−0.436460 | + | 0.899724i | \(0.643768\pi\) | |||||||
\(662\) | −83.4386 | −0.126040 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 164.000 | 0.246988 | ||||||||
\(665\) | −371.231 | + | 371.231i | −0.558242 | + | 0.558242i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000i | 0.0809595i | ||||||||
\(668\) | 203.647 | 0.304860 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 655.000 | − | 655.000i | 0.977612 | − | 0.977612i | ||||
\(671\) | 137.179i | 0.204439i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 489.000i | − | 0.726597i | −0.931673 | − | 0.363299i | \(-0.881650\pi\) | ||
0.931673 | − | 0.363299i | \(-0.118350\pi\) | |||||||
\(674\) | − | 77.7817i | − | 0.115403i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 176.000 | 0.260355 | ||||||||
\(677\) | 599.627 | 0.885711 | 0.442856 | − | 0.896593i | \(-0.353965\pi\) | ||||
0.442856 | + | 0.896593i | \(0.353965\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 205.000 | 0.301915 | ||||||||
\(680\) | −113.137 | − | 113.137i | −0.166378 | − | 0.166378i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 80.0000i | − | 0.117302i | ||||||
\(683\) | 236.174 | 0.345789 | 0.172894 | − | 0.984940i | \(-0.444688\pi\) | ||||
0.172894 | + | 0.984940i | \(0.444688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −945.000 | − | 945.000i | −1.37956 | − | 1.37956i | ||||
\(686\) | 516.188i | 0.752461i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 256.000i | 0.372093i | ||||||||
\(689\) | − | 649.124i | − | 0.942125i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 640.000 | 0.926194 | 0.463097 | − | 0.886308i | \(-0.346738\pi\) | ||||
0.463097 | + | 0.886308i | \(0.346738\pi\) | |||||||
\(692\) | −22.6274 | −0.0326986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −846.000 | −1.21902 | ||||||||
\(695\) | −130.815 | − | 130.815i | −0.188223 | − | 0.188223i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 592.000i | 0.849354i | ||||||||
\(698\) | −620.840 | −0.889455 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −250.000 | −0.357143 | ||||||||
\(701\) | 1093.19i | 1.55947i | 0.626111 | + | 0.779734i | \(0.284646\pi\) | ||||
−0.626111 | + | 0.779734i | \(0.715354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 525.000i | − | 0.746799i | ||||||
\(704\) | − | 11.3137i | − | 0.0160706i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −736.000 | −1.04249 | ||||||||
\(707\) | −452.548 | −0.640097 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −489.000 | −0.689704 | −0.344852 | − | 0.938657i | \(-0.612071\pi\) | ||||
−0.344852 | + | 0.938657i | \(0.612071\pi\) | |||||||
\(710\) | −445.477 | + | 445.477i | −0.627433 | + | 0.627433i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 416.000i | − | 0.584270i | ||||||
\(713\) | −56.5685 | −0.0793388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.0000 | + | 45.0000i | 0.0629371 | + | 0.0629371i | ||||
\(716\) | 251.730i | 0.351578i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 78.0000i | 0.108635i | ||||||||
\(719\) | 620.840i | 0.863477i | 0.901999 | + | 0.431738i | \(0.142100\pi\) | ||||
−0.901999 | + | 0.431738i | \(0.857900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.0000 | 0.0901526 | ||||||||
\(722\) | 113.137 | 0.156700 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −254.000 | −0.350829 | ||||||||
\(725\) | 954.594 | 1.31668 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1080.00i | − | 1.48556i | −0.669537 | − | 0.742779i | \(-0.733508\pi\) | ||
0.669537 | − | 0.742779i | \(-0.266492\pi\) | |||||||
\(728\) | −127.279 | −0.174834 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 85.0000 | − | 85.0000i | 0.116438 | − | 0.116438i | ||||
\(731\) | − | 724.077i | − | 0.990530i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 248.000i | 0.338336i | 0.985587 | + | 0.169168i | \(0.0541080\pi\) | ||||
−0.985587 | + | 0.169168i | \(0.945892\pi\) | |||||||
\(734\) | − | 832.972i | − | 1.13484i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.0108696 | ||||||||
\(737\) | −185.262 | −0.251373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 848.000 | 1.14750 | 0.573748 | − | 0.819032i | \(-0.305489\pi\) | ||||
0.573748 | + | 0.819032i | \(0.305489\pi\) | |||||||
\(740\) | 176.777 | − | 176.777i | 0.238887 | − | 0.238887i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 510.000i | − | 0.687332i | ||||||
\(743\) | 33.9411 | 0.0456812 | 0.0228406 | − | 0.999739i | \(-0.492729\pi\) | ||||
0.0228406 | + | 0.999739i | \(0.492729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 920.000 | − | 920.000i | 1.23490 | − | 1.23490i | ||||
\(746\) | 12.7279i | 0.0170616i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 32.0000i | 0.0427807i | ||||||||
\(749\) | 615.183i | 0.821339i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −133.000 | −0.177097 | −0.0885486 | − | 0.996072i | \(-0.528223\pi\) | ||||
−0.0885486 | + | 0.996072i | \(0.528223\pi\) | |||||||
\(752\) | −90.5097 | −0.120359 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 486.000 | 0.644562 | ||||||||
\(755\) | 385.373 | + | 385.373i | 0.510428 | + | 0.510428i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1271.00i | 1.67900i | 0.543363 | + | 0.839498i | \(0.317151\pi\) | ||||
−0.543363 | + | 0.839498i | \(0.682849\pi\) | |||||||
\(758\) | 222.032 | 0.292918 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 210.000 | + | 210.000i | 0.276316 | + | 0.276316i | ||||
\(761\) | 538.815i | 0.708036i | 0.935239 | + | 0.354018i | \(0.115185\pi\) | ||||
−0.935239 | + | 0.354018i | \(0.884815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.0000i | 0.0524246i | ||||||||
\(764\) | 203.647i | 0.266553i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −400.000 | −0.522193 | ||||||||
\(767\) | 814.587 | 1.06204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −81.0000 | −0.105332 | −0.0526658 | − | 0.998612i | \(-0.516772\pi\) | ||||
−0.0526658 | + | 0.998612i | \(0.516772\pi\) | |||||||
\(770\) | 35.3553 | + | 35.3553i | 0.0459160 | + | 0.0459160i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 542.000i | 0.702073i | ||||||||
\(773\) | 445.477 | 0.576297 | 0.288148 | − | 0.957586i | \(-0.406960\pi\) | ||||
0.288148 | + | 0.957586i | \(0.406960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1000.00i | 1.29032i | ||||||||
\(776\) | − | 115.966i | − | 0.149440i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 848.000i | 1.08997i | ||||||||
\(779\) | − | 1098.84i | − | 1.41058i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 126.000 | 0.161332 | ||||||||
\(782\) | 22.6274 | 0.0289353 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 96.0000 | 0.122449 | ||||||||
\(785\) | −417.193 | + | 417.193i | −0.531456 | + | 0.531456i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 395.000i | 0.501906i | 0.967999 | + | 0.250953i | \(0.0807440\pi\) | ||||
−0.967999 | + | 0.250953i | \(0.919256\pi\) | |||||||
\(788\) | 633.568 | 0.804020 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −585.000 | − | 585.000i | −0.740506 | − | 0.740506i | ||||
\(791\) | 190.919i | 0.241364i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 873.000i | − | 1.10088i | ||||||
\(794\) | 418.607i | 0.527213i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 294.000 | 0.369347 | ||||||||
\(797\) | 1074.80 | 1.34856 | 0.674280 | − | 0.738476i | \(-0.264454\pi\) | ||||
0.674280 | + | 0.738476i | \(0.264454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 256.000 | 0.320401 | ||||||||
\(800\) | 141.421i | 0.176777i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 550.000i | − | 0.685786i | ||||||
\(803\) | −24.0416 | −0.0299398 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.0000 | − | 25.0000i | 0.0310559 | − | 0.0310559i | ||||
\(806\) | 509.117i | 0.631659i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 256.000i | 0.316832i | ||||||||
\(809\) | − | 1255.82i | − | 1.55231i | −0.630540 | − | 0.776157i | \(-0.717167\pi\) | ||
0.630540 | − | 0.776157i | \(-0.282833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −752.000 | −0.927250 | −0.463625 | − | 0.886031i | \(-0.653452\pi\) | ||||
−0.463625 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(812\) | 381.838 | 0.470243 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −50.0000 | −0.0614251 | ||||||||
\(815\) | −717.713 | + | 717.713i | −0.880630 | + | 0.880630i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1344.00i | 1.64504i | ||||||||
\(818\) | 205.061 | 0.250686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 370.000 | − | 370.000i | 0.451220 | − | 0.451220i | ||||
\(821\) | 497.803i | 0.606338i | 0.952937 | + | 0.303169i | \(0.0980446\pi\) | ||||
−0.952937 | + | 0.303169i | \(0.901955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 531.000i | − | 0.645200i | −0.946535 | − | 0.322600i | \(-0.895443\pi\) | ||
0.946535 | − | 0.322600i | \(-0.104557\pi\) | |||||||
\(824\) | − | 36.7696i | − | 0.0446232i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 640.000 | 0.774818 | ||||||||
\(827\) | −350.725 | −0.424093 | −0.212047 | − | 0.977260i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977260i | \(0.568013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −705.000 | −0.850422 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(830\) | 289.914 | + | 289.914i | 0.349294 | + | 0.349294i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 72.0000i | 0.0865385i | ||||||||
\(833\) | −271.529 | −0.325965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 360.000 | + | 360.000i | 0.431138 | + | 0.431138i | ||||
\(836\) | − | 59.3970i | − | 0.0710490i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 992.000i | 1.18377i | ||||||||
\(839\) | − | 1617.86i | − | 1.92832i | −0.265322 | − | 0.964160i | \(-0.585478\pi\) | ||
0.265322 | − | 0.964160i | \(-0.414522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −617.000 | −0.733650 | ||||||||
\(842\) | 714.178 | 0.848192 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 282.000 | 0.334123 | ||||||||
\(845\) | 311.127 | + | 311.127i | 0.368198 | + | 0.368198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 595.000i | 0.702479i | ||||||||
\(848\) | −288.500 | −0.340212 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 400.000i | − | 0.470588i | ||||||
\(851\) | 35.3553i | 0.0415456i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1639.00i | − | 1.92145i | −0.277496 | − | 0.960727i | \(-0.589504\pi\) | ||
0.277496 | − | 0.960727i | \(-0.410496\pi\) | |||||||
\(854\) | − | 685.894i | − | 0.803154i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 348.000 | 0.406542 | ||||||||
\(857\) | −988.535 | −1.15348 | −0.576742 | − | 0.816927i | \(-0.695676\pi\) | ||||
−0.576742 | + | 0.816927i | \(0.695676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 355.000 | 0.413271 | 0.206636 | − | 0.978418i | \(-0.433749\pi\) | ||||
0.206636 | + | 0.978418i | \(0.433749\pi\) | |||||||
\(860\) | −452.548 | + | 452.548i | −0.526219 | + | 0.526219i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 62.0000i | − | 0.0719258i | ||||||
\(863\) | −1459.47 | −1.69116 | −0.845578 | − | 0.533851i | \(-0.820744\pi\) | ||||
−0.845578 | + | 0.533851i | \(0.820744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | − | 40.0000i | −0.0462428 | − | 0.0462428i | ||||
\(866\) | − | 45.2548i | − | 0.0522573i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 400.000i | 0.460829i | ||||||||
\(869\) | 165.463i | 0.190406i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1179.00 | 1.35362 | ||||||||
\(872\) | 22.6274 | 0.0259489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.0000 | −0.0480549 | ||||||||
\(875\) | −441.942 | − | 441.942i | −0.505076 | − | 0.505076i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1129.00i | 1.28734i | 0.765302 | + | 0.643672i | \(0.222590\pi\) | ||||
−0.765302 | + | 0.643672i | \(0.777410\pi\) | |||||||
\(878\) | −712.764 | −0.811804 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.0000 | − | 20.0000i | 0.0227273 | − | 0.0227273i | ||||
\(881\) | 165.463i | 0.187813i | 0.995581 | + | 0.0939063i | \(0.0299354\pi\) | ||||
−0.995581 | + | 0.0939063i | \(0.970065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1227.00i | 1.38958i | 0.719212 | + | 0.694790i | \(0.244503\pi\) | ||||
−0.719212 | + | 0.694790i | \(0.755497\pi\) | |||||||
\(884\) | − | 203.647i | − | 0.230370i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 336.000 | 0.379233 | ||||||||
\(887\) | 237.588 | 0.267856 | 0.133928 | − | 0.990991i | \(-0.457241\pi\) | ||||
0.133928 | + | 0.990991i | \(0.457241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0000 | −0.0449944 | ||||||||
\(890\) | 735.391 | − | 735.391i | 0.826282 | − | 0.826282i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.0000i | − | 0.0179372i | ||||||
\(893\) | −475.176 | −0.532112 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −445.000 | + | 445.000i | −0.497207 | + | 0.497207i | ||||
\(896\) | 56.5685i | 0.0631345i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 96.0000i | 0.106904i | ||||||||
\(899\) | − | 1527.35i | − | 1.69894i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 816.000 | 0.905660 | ||||||||
\(902\) | −104.652 | −0.116022 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 108.000 | 0.119469 | ||||||||
\(905\) | −449.013 | − | 449.013i | −0.496147 | − | 0.496147i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1005.00i | − | 1.10805i | −0.832501 | − | 0.554024i | \(-0.813091\pi\) | ||
0.832501 | − | 0.554024i | \(-0.186909\pi\) | |||||||
\(908\) | 138.593 | 0.152635 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −225.000 | − | 225.000i | −0.247253 | − | 0.247253i | ||||
\(911\) | 780.646i | 0.856911i | 0.903563 | + | 0.428455i | \(0.140942\pi\) | ||||
−0.903563 | + | 0.428455i | \(0.859058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 82.0000i | − | 0.0898138i | ||||||
\(914\) | 1063.49i | 1.16355i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0000 | −0.0174672 | ||||||||
\(917\) | −678.823 | −0.740264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 600.000 | 0.652884 | 0.326442 | − | 0.945217i | \(-0.394150\pi\) | ||||
0.326442 | + | 0.945217i | \(0.394150\pi\) | |||||||
\(920\) | −14.1421 | − | 14.1421i | −0.0153719 | − | 0.0153719i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 864.000i | 0.937093i | ||||||||
\(923\) | −801.859 | −0.868753 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 625.000 | 0.675676 | ||||||||
\(926\) | 844.285i | 0.911755i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 216.000i | − | 0.232759i | ||||||
\(929\) | − | 1260.06i | − | 1.35637i | −0.734893 | − | 0.678183i | \(-0.762768\pi\) | ||
0.734893 | − | 0.678183i | \(-0.237232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 504.000 | 0.541353 | ||||||||
\(932\) | −633.568 | −0.679794 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1200.00 | 1.28480 | ||||||||
\(935\) | −56.5685 | + | 56.5685i | −0.0605011 | + | 0.0605011i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1465.00i | 1.56350i | 0.623592 | + | 0.781750i | \(0.285673\pi\) | ||||
−0.623592 | + | 0.781750i | \(0.714327\pi\) | |||||||
\(938\) | 926.310 | 0.987537 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −160.000 | − | 160.000i | −0.170213 | − | 0.170213i | ||||
\(941\) | − | 255.973i | − | 0.272022i | −0.990707 | − | 0.136011i | \(-0.956572\pi\) | ||
0.990707 | − | 0.136011i | \(-0.0434282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.0000i | 0.0784730i | ||||||||
\(944\) | − | 362.039i | − | 0.383516i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 128.000 | 0.135307 | ||||||||
\(947\) | 407.294 | 0.430088 | 0.215044 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215044 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 153.000 | 0.161222 | ||||||||
\(950\) | 742.462i | 0.781539i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 160.000i | − | 0.168067i | ||||||
\(953\) | 497.803 | 0.522354 | 0.261177 | − | 0.965291i | \(-0.415889\pi\) | ||||
0.261177 | + | 0.965291i | \(0.415889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −360.000 | + | 360.000i | −0.376963 | + | 0.376963i | ||||
\(956\) | 410.122i | 0.428998i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 238.000i | − | 0.248434i | ||||||
\(959\) | − | 1336.43i | − | 1.39357i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 639.000 | 0.664932 | ||||||||
\(962\) | 318.198 | 0.330767 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 158.000 | 0.163900 | ||||||||
\(965\) | −958.130 | + | 958.130i | −0.992881 | + | 0.992881i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 491.000i | − | 0.507756i | −0.967236 | − | 0.253878i | \(-0.918294\pi\) | ||
0.967236 | − | 0.253878i | \(-0.0817062\pi\) | |||||||
\(968\) | 336.583 | 0.347710 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 205.000 | − | 205.000i | 0.211340 | − | 0.211340i | ||||
\(971\) | − | 509.117i | − | 0.524322i | −0.965024 | − | 0.262161i | \(-0.915565\pi\) | ||
0.965024 | − | 0.262161i | \(-0.0844352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 185.000i | − | 0.190134i | ||||||
\(974\) | − | 717.006i | − | 0.736146i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −388.000 | −0.397541 | ||||||||
\(977\) | −470.933 | −0.482020 | −0.241010 | − | 0.970523i | \(-0.577479\pi\) | ||||
−0.241010 | + | 0.970523i | \(0.577479\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −208.000 | −0.212462 | ||||||||
\(980\) | 169.706 | + | 169.706i | 0.173169 | + | 0.173169i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 606.000i | 0.617108i | ||||||||
\(983\) | −601.041 | −0.611435 | −0.305718 | − | 0.952122i | \(-0.598896\pi\) | ||||
−0.305718 | + | 0.952122i | \(0.598896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1120.00 | + | 1120.00i | 1.13706 | + | 1.13706i | ||||
\(986\) | 610.940i | 0.619615i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 378.000i | 0.382591i | ||||||||
\(989\) | − | 90.5097i | − | 0.0915163i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −755.000 | −0.761857 | −0.380928 | − | 0.924605i | \(-0.624396\pi\) | ||||
−0.380928 | + | 0.924605i | \(0.624396\pi\) | |||||||
\(992\) | 226.274 | 0.228099 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −630.000 | −0.633803 | ||||||||
\(995\) | 519.723 | + | 519.723i | 0.522335 | + | 0.522335i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.0000i | 0.0240722i | 0.999928 | + | 0.0120361i | \(0.00383130\pi\) | ||||
−0.999928 | + | 0.0120361i | \(0.996169\pi\) | |||||||
\(998\) | 1230.37 | 1.23283 | ||||||||
\(999\) | 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 | 270.3.b.c.269.4 | yes | 4 | |
3.2 | odd | 2 | inner | 270.3.b.c.269.1 | ✓ | 4 | |
4.3 | odd | 2 | 2160.3.c.i.1889.4 | 4 | |||
5.2 | odd | 4 | 1350.3.d.f.701.2 | 2 | |||
5.3 | odd | 4 | 1350.3.d.g.701.1 | 2 | |||
5.4 | even | 2 | inner | 270.3.b.c.269.2 | yes | 4 | |
9.2 | odd | 6 | 810.3.j.e.539.4 | 8 | |||
9.4 | even | 3 | 810.3.j.e.269.2 | 8 | |||
9.5 | odd | 6 | 810.3.j.e.269.3 | 8 | |||
9.7 | even | 3 | 810.3.j.e.539.1 | 8 | |||
12.11 | even | 2 | 2160.3.c.i.1889.1 | 4 | |||
15.2 | even | 4 | 1350.3.d.f.701.1 | 2 | |||
15.8 | even | 4 | 1350.3.d.g.701.2 | 2 | |||
15.14 | odd | 2 | inner | 270.3.b.c.269.3 | yes | 4 | |
20.19 | odd | 2 | 2160.3.c.i.1889.2 | 4 | |||
45.4 | even | 6 | 810.3.j.e.269.4 | 8 | |||
45.14 | odd | 6 | 810.3.j.e.269.1 | 8 | |||
45.29 | odd | 6 | 810.3.j.e.539.2 | 8 | |||
45.34 | even | 6 | 810.3.j.e.539.3 | 8 | |||
60.59 | even | 2 | 2160.3.c.i.1889.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.3.b.c.269.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
270.3.b.c.269.2 | yes | 4 | 5.4 | even | 2 | inner | |
270.3.b.c.269.3 | yes | 4 | 15.14 | odd | 2 | inner | |
270.3.b.c.269.4 | yes | 4 | 1.1 | even | 1 | trivial | |
810.3.j.e.269.1 | 8 | 45.14 | odd | 6 | |||
810.3.j.e.269.2 | 8 | 9.4 | even | 3 | |||
810.3.j.e.269.3 | 8 | 9.5 | odd | 6 | |||
810.3.j.e.269.4 | 8 | 45.4 | even | 6 | |||
810.3.j.e.539.1 | 8 | 9.7 | even | 3 | |||
810.3.j.e.539.2 | 8 | 45.29 | odd | 6 | |||
810.3.j.e.539.3 | 8 | 45.34 | even | 6 | |||
810.3.j.e.539.4 | 8 | 9.2 | odd | 6 | |||
1350.3.d.f.701.1 | 2 | 15.2 | even | 4 | |||
1350.3.d.f.701.2 | 2 | 5.2 | odd | 4 | |||
1350.3.d.g.701.1 | 2 | 5.3 | odd | 4 | |||
1350.3.d.g.701.2 | 2 | 15.8 | even | 4 | |||
2160.3.c.i.1889.1 | 4 | 12.11 | even | 2 | |||
2160.3.c.i.1889.2 | 4 | 20.19 | odd | 2 | |||
2160.3.c.i.1889.3 | 4 | 60.59 | even | 2 | |||
2160.3.c.i.1889.4 | 4 | 4.3 | odd | 2 |