Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,4,Mod(1849,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1849");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.k (of order \(2\), degree \(1\), 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: | \(123.904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1849 |
Dual form | 2100.4.k.g.1849.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 0.109640 | 0.0548202 | − | 0.998496i | \(-0.482541\pi\) | ||||
0.0548202 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 54.0000i | − 1.15207i | −0.817425 | − | 0.576035i | \(-0.804599\pi\) | ||||
0.817425 | − | 0.576035i | \(-0.195401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 14.0000i | − 0.199735i | −0.995001 | − | 0.0998676i | \(-0.968158\pi\) | ||||
0.995001 | − | 0.0998676i | \(-0.0318419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 152.000i | 1.37801i | 0.724757 | + | 0.689004i | \(0.241952\pi\) | ||||
−0.724757 | + | 0.689004i | \(0.758048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 106.000 | 0.678748 | 0.339374 | − | 0.940651i | \(-0.389785\pi\) | ||||
0.339374 | + | 0.940651i | \(0.389785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −144.000 | −0.834296 | −0.417148 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417148 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 12.0000i | − 0.0633010i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 158.000i | 0.702028i | 0.936370 | + | 0.351014i | \(0.114163\pi\) | ||||
−0.936370 | + | 0.351014i | \(0.885837\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −162.000 | −0.665148 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 508.000i | 1.80161i | 0.434223 | + | 0.900806i | \(0.357023\pi\) | ||||
−0.434223 | + | 0.900806i | \(0.642977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 528.000i | − 1.63865i | −0.573327 | − | 0.819327i | \(-0.694347\pi\) | ||||
0.573327 | − | 0.819327i | \(-0.305653\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.0000 | −0.115317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 606.000i | − 1.57058i | −0.619131 | − | 0.785288i | \(-0.712515\pi\) | ||||
0.619131 | − | 0.785288i | \(-0.287485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000i | 0.641353i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 364.000 | 0.803199 | 0.401600 | − | 0.915815i | \(-0.368454\pi\) | ||||
0.401600 | + | 0.915815i | \(0.368454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 678.000 | 1.42310 | 0.711549 | − | 0.702636i | \(-0.247994\pi\) | ||||
0.711549 | + | 0.702636i | \(0.247994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 844.000i | 1.53897i | 0.638665 | + | 0.769485i | \(0.279487\pi\) | ||||
−0.638665 | + | 0.769485i | \(0.720513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 456.000 | 0.795593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.0133722 | −0.00668609 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668609 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 422.000i | 0.676594i | 0.941039 | + | 0.338297i | \(0.109851\pi\) | ||||
−0.941039 | + | 0.338297i | \(0.890149\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 28.0000i | − 0.0414402i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −384.000 | −0.546878 | −0.273439 | − | 0.961889i | \(-0.588161\pi\) | ||||
−0.273439 | + | 0.961889i | \(0.588161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 548.000i | 0.724709i | 0.932040 | + | 0.362354i | \(0.118027\pi\) | ||||
−0.932040 | + | 0.362354i | \(0.881973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 318.000i | − 0.391876i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1194.00 | −1.42206 | −0.711032 | − | 0.703159i | \(-0.751772\pi\) | ||||
−0.711032 | + | 0.703159i | \(0.751772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −378.000 | −0.435441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 432.000i | 0.481681i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1502.00i | − 1.57222i | −0.618089 | − | 0.786108i | \(-0.712093\pi\) | ||||
0.618089 | − | 0.786108i | \(-0.287907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.0000 | −0.0365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 398.000 | 0.392104 | 0.196052 | − | 0.980594i | \(-0.437188\pi\) | ||||
0.196052 | + | 0.980594i | \(0.437188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1160.00i | − 1.10969i | −0.831953 | − | 0.554846i | \(-0.812777\pi\) | ||||
0.831953 | − | 0.554846i | \(-0.187223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 324.000i | 0.292731i | 0.989231 | + | 0.146366i | \(0.0467576\pi\) | ||||
−0.989231 | + | 0.146366i | \(0.953242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 938.000 | 0.824258 | 0.412129 | − | 0.911126i | \(-0.364785\pi\) | ||||
0.412129 | + | 0.911126i | \(0.364785\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 474.000 | 0.405316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 622.000i | 0.517813i | 0.965902 | + | 0.258906i | \(0.0833621\pi\) | ||||
−0.965902 | + | 0.258906i | \(0.916638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 486.000i | 0.384023i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −98.0000 | −0.0754928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1170.00i | 0.857686i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1200.00i | 0.838447i | 0.907883 | + | 0.419224i | \(0.137698\pi\) | ||||
−0.907883 | + | 0.419224i | \(0.862302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1524.00 | 1.04016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1396.00 | −0.931062 | −0.465531 | − | 0.885032i | \(-0.654137\pi\) | ||||
−0.465531 | + | 0.885032i | \(0.654137\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 644.000i | 0.419864i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2810.00i | 1.75237i | 0.481976 | + | 0.876184i | \(0.339919\pi\) | ||||
−0.481976 | + | 0.876184i | \(0.660081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.00244083 | −0.00122042 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00122042 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1584.00 | −0.946077 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 216.000i | − 0.126313i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1374.00 | −0.755453 | −0.377726 | − | 0.925917i | \(-0.623294\pi\) | ||||
−0.377726 | + | 0.925917i | \(0.623294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2104.00 | 1.13391 | 0.566957 | − | 0.823747i | \(-0.308120\pi\) | ||||
0.566957 | + | 0.823747i | \(0.308120\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 126.000i | 0.0665784i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3206.00i | 1.62972i | 0.579655 | + | 0.814862i | \(0.303187\pi\) | ||||
−0.579655 | + | 0.814862i | \(0.696813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1818.00 | −0.906772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1064.00 | 0.520838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 332.000i | − 0.159535i | −0.996813 | − | 0.0797676i | \(-0.974582\pi\) | ||||
0.996813 | − | 0.0797676i | \(-0.0254178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1496.00i | 0.693197i | 0.938014 | + | 0.346599i | \(0.112663\pi\) | ||||
−0.938014 | + | 0.346599i | \(0.887337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −719.000 | −0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 828.000 | 0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3322.00i | 1.45992i | 0.683487 | + | 0.729962i | \(0.260462\pi\) | ||||
−0.683487 | + | 0.729962i | \(0.739538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1092.00i | − 0.463727i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 900.000 | 0.375805 | 0.187903 | − | 0.982188i | \(-0.439831\pi\) | ||||
0.187903 | + | 0.982188i | \(0.439831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1902.00 | 0.781075 | 0.390537 | − | 0.920587i | \(-0.372289\pi\) | ||||
0.390537 | + | 0.920587i | \(0.372289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2034.00i | − 0.821626i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 56.0000i | − 0.0218991i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4128.00 | 1.56383 | 0.781915 | − | 0.623385i | \(-0.214243\pi\) | ||||
0.781915 | + | 0.623385i | \(0.214243\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1342.00i | 0.500514i | 0.968179 | + | 0.250257i | \(0.0805152\pi\) | ||||
−0.968179 | + | 0.250257i | \(0.919485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3506.00i | − 1.26798i | −0.773341 | − | 0.633990i | \(-0.781416\pi\) | ||||
0.773341 | − | 0.633990i | \(-0.218584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −680.000 | −0.242231 | −0.121115 | − | 0.992638i | \(-0.538647\pi\) | ||||
−0.121115 | + | 0.992638i | \(0.538647\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2532.00 | 0.888525 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 742.000i | − 0.256543i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1368.00i | − 0.459336i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −368.000 | −0.121795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5372.00 | 1.75272 | 0.876360 | − | 0.481657i | \(-0.159965\pi\) | ||||
0.876360 | + | 0.481657i | \(0.159965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.0000i | 0.00772044i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1008.00i | 0.315334i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1266.00 | 0.390632 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −756.000 | −0.230109 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1072.00i | 0.321912i | 0.986962 | + | 0.160956i | \(0.0514578\pi\) | ||||
−0.986962 | + | 0.160956i | \(0.948542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2868.00i | − 0.838572i | −0.907854 | − | 0.419286i | \(-0.862280\pi\) | ||||
0.907854 | − | 0.419286i | \(-0.137720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4798.00 | −1.38454 | −0.692272 | − | 0.721636i | \(-0.743390\pi\) | ||||
−0.692272 | + | 0.721636i | \(0.743390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −84.0000 | −0.0239255 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5126.00i | 1.44127i | 0.693316 | + | 0.720634i | \(0.256149\pi\) | ||||
−0.693316 | + | 0.720634i | \(0.743851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1152.00i | 0.315740i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 528.000 | 0.142902 | 0.0714508 | − | 0.997444i | \(-0.477237\pi\) | ||||
0.0714508 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −814.000 | −0.217570 | −0.108785 | − | 0.994065i | \(-0.534696\pi\) | ||||
−0.108785 | + | 0.994065i | \(0.534696\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4968.00i | 1.27978i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1644.00 | 0.418411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1932.00 | −0.485844 | −0.242922 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242922 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 608.000i | 0.151086i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3294.00i | − 0.799510i | −0.916622 | − | 0.399755i | \(-0.869095\pi\) | ||||
0.916622 | − | 0.399755i | \(-0.130905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1106.00 | 0.265342 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −954.000 | −0.226249 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7080.00i | 1.65997i | 0.557787 | + | 0.829984i | \(0.311650\pi\) | ||||
−0.557787 | + | 0.829984i | \(0.688350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3582.00i | 0.821029i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7814.00 | −1.77111 | −0.885554 | − | 0.464537i | \(-0.846221\pi\) | ||||
−0.885554 | + | 0.464537i | \(0.846221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3168.00 | 0.710119 | 0.355060 | − | 0.934844i | \(-0.384461\pi\) | ||||
0.355060 | + | 0.934844i | \(0.384461\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1134.00i | 0.251402i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7858.00i | − 1.70448i | −0.523150 | − | 0.852241i | \(-0.675243\pi\) | ||||
0.523150 | − | 0.852241i | \(-0.324757\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1296.00 | 0.278099 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6730.00 | 1.42875 | 0.714374 | − | 0.699764i | \(-0.246712\pi\) | ||||
0.714374 | + | 0.699764i | \(0.246712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3020.00i | 0.634348i | 0.948367 | + | 0.317174i | \(0.102734\pi\) | ||||
−0.948367 | + | 0.317174i | \(0.897266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2730.00i | 0.561487i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4717.00 | 0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4506.00 | −0.907720 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6834.00i | 1.36262i | 0.731997 | + | 0.681308i | \(0.238589\pi\) | ||||
−0.731997 | + | 0.681308i | \(0.761411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 108.000i | 0.0211003i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8208.00 | 1.58756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3556.00 | 0.680945 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1194.00i | − 0.226381i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2332.00i | 0.433532i | 0.976224 | + | 0.216766i | \(0.0695508\pi\) | ||||
−0.976224 | + | 0.216766i | \(0.930449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3480.00 | −0.640681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8840.00 | 1.61180 | 0.805901 | − | 0.592050i | \(-0.201681\pi\) | ||||
0.805901 | + | 0.592050i | \(0.201681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1046.00i | 0.188893i | 0.995530 | + | 0.0944464i | \(0.0301081\pi\) | ||||
−0.995530 | + | 0.0944464i | \(0.969892\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7542.00i | 1.33628i | 0.744035 | + | 0.668140i | \(0.232909\pi\) | ||||
−0.744035 | + | 0.668140i | \(0.767091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 424.000 | 0.0744183 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 972.000 | 0.169009 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1288.00i | 0.221877i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2814.00i | − 0.475885i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3696.00 | −0.619353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2756.00 | 0.457654 | 0.228827 | − | 0.973467i | \(-0.426511\pi\) | ||||
0.228827 | + | 0.973467i | \(0.426511\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1422.00i | − 0.234009i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3954.00i | 0.639134i | 0.947564 | + | 0.319567i | \(0.103537\pi\) | ||||
−0.947564 | + | 0.319567i | \(0.896463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1866.00 | 0.298959 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576.000 | −0.0914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6900.00i | 1.06747i | 0.845652 | + | 0.533734i | \(0.179212\pi\) | ||||
−0.845652 | + | 0.533734i | \(0.820788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2426.00 | 0.372094 | 0.186047 | − | 0.982541i | \(-0.440432\pi\) | ||||
0.186047 | + | 0.982541i | \(0.440432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1458.00 | 0.221716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1470.00i | 0.221644i | 0.993840 | + | 0.110822i | \(0.0353483\pi\) | ||||
−0.993840 | + | 0.110822i | \(0.964652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 294.000i | 0.0435858i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6872.00 | −1.01028 | −0.505140 | − | 0.863038i | \(-0.668559\pi\) | ||||
−0.505140 | + | 0.863038i | \(0.668559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3945.00i | 0.570410i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7072.00i | − 1.00587i | −0.864323 | − | 0.502937i | \(-0.832253\pi\) | ||||
0.864323 | − | 0.502937i | \(-0.167747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3510.00 | 0.495185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4242.00 | −0.593622 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 818.000i | 0.113551i | 0.998387 | + | 0.0567754i | \(0.0180819\pi\) | ||||
−0.998387 | + | 0.0567754i | \(0.981918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 5724.00i | − 0.781966i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5132.00 | 0.695549 | 0.347775 | − | 0.937578i | \(-0.386937\pi\) | ||||
0.347775 | + | 0.937578i | \(0.386937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3600.00 | 0.484078 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8576.00i | 1.14416i | 0.820198 | + | 0.572080i | \(0.193863\pi\) | ||||
−0.820198 | + | 0.572080i | \(0.806137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4572.00i | − 0.600537i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3730.00 | 0.486166 | 0.243083 | − | 0.970006i | \(-0.421841\pi\) | ||||
0.243083 | + | 0.970006i | \(0.421841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2128.00 | 0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4188.00i | 0.537549i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6678.00i | 0.844230i | 0.906542 | + | 0.422115i | \(0.138712\pi\) | ||||
−0.906542 | + | 0.422115i | \(0.861288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1932.00 | 0.242408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3054.00 | −0.380323 | −0.190161 | − | 0.981753i | \(-0.560901\pi\) | ||||
−0.190161 | + | 0.981753i | \(0.560901\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7776.00i | 0.961167i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 632.000i | 0.0769707i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −266.000 | −0.0321586 | −0.0160793 | − | 0.999871i | \(-0.505118\pi\) | ||||
−0.0160793 | + | 0.999871i | \(0.505118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8430.00 | 1.01173 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2548.00i | − 0.303581i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000i | 0.00140921i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8844.00 | −1.03116 | −0.515582 | − | 0.856840i | \(-0.672424\pi\) | ||||
−0.515582 | + | 0.856840i | \(0.672424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4482.00 | −0.518858 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4752.00i | 0.546218i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4746.00i | − 0.537881i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −648.000 | −0.0729271 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9936.00 | 1.11044 | 0.555221 | − | 0.831703i | \(-0.312634\pi\) | ||||
0.555221 | + | 0.831703i | \(0.312634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11758.0i | 1.30497i | 0.757800 | + | 0.652487i | \(0.226274\pi\) | ||||
−0.757800 | + | 0.652487i | \(0.773726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 13984.0i | − 1.53077i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4104.00 | 0.446180 | 0.223090 | − | 0.974798i | \(-0.428386\pi\) | ||||
0.223090 | + | 0.974798i | \(0.428386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9748.00i | − 1.04547i | −0.852496 | − | 0.522733i | \(-0.824912\pi\) | ||||
0.852496 | − | 0.522733i | \(-0.175088\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4122.00i | 0.436161i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 478.000 | 0.0502410 | 0.0251205 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251205 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1560.00 | −0.162877 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6312.00i | − 0.654666i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 11174.0i | − 1.14376i | −0.820338 | − | 0.571879i | \(-0.806215\pi\) | ||||
0.820338 | − | 0.571879i | \(-0.193785\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 378.000 | 0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11674.0 | −1.17942 | −0.589710 | − | 0.807615i | \(-0.700758\pi\) | ||||
−0.589710 | + | 0.807615i | \(0.700758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 10528.0i | − 1.05676i | −0.849009 | − | 0.528378i | \(-0.822801\pi\) | ||||
0.849009 | − | 0.528378i | \(-0.177199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16604.0i | 1.64527i | 0.568569 | + | 0.822635i | \(0.307497\pi\) | ||||
−0.568569 | + | 0.822635i | \(0.692503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5908.00 | 0.581676 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9618.00 | 0.940922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2032.00i | 0.197530i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5454.00i | 0.523525i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8576.00 | 0.818053 | 0.409027 | − | 0.912522i | \(-0.365868\pi\) | ||||
0.409027 | + | 0.912522i | \(0.365868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8532.00 | 0.808785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3192.00i | − 0.300706i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9704.00i | 0.902937i | 0.892287 | + | 0.451468i | \(0.149100\pi\) | ||||
−0.892287 | + | 0.451468i | \(0.850900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −996.000 | −0.0921077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4092.00 | −0.376109 | −0.188054 | − | 0.982159i | \(-0.560218\pi\) | ||||
−0.188054 | + | 0.982159i | \(0.560218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1484.00i | − 0.135570i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 56.0000i | 0.00505421i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17884.0 | −1.60440 | −0.802202 | − | 0.597052i | \(-0.796338\pi\) | ||||
−0.802202 | + | 0.597052i | \(0.796338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4488.00 | 0.400218 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7704.00i | 0.682911i | 0.939898 | + | 0.341456i | \(0.110920\pi\) | ||||
−0.939898 | + | 0.341456i | \(0.889080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2157.00i | 0.188946i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14358.0 | −1.25031 | −0.625154 | − | 0.780501i | \(-0.714964\pi\) | ||||
−0.625154 | + | 0.780501i | \(0.714964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2954.00 | 0.255729 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 2484.00i | − 0.213784i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2112.00i | − 0.179663i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9966.00 | 0.842888 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5082.00 | 0.427344 | 0.213672 | − | 0.976905i | \(-0.431458\pi\) | ||||
0.213672 | + | 0.976905i | \(0.431458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1756.00i | 0.146816i | 0.997302 | + | 0.0734078i | \(0.0233875\pi\) | ||||
−0.997302 | + | 0.0734078i | \(0.976613\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2016.00i | 0.166638i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10937.0 | −0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3276.00 | −0.267733 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21060.0i | 1.71146i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2700.00i | − 0.216971i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −196.000 | −0.0156629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16230.0 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5706.00i | − 0.450954i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17676.0i | 1.38167i | 0.723014 | + | 0.690833i | \(0.242756\pi\) | ||||
−0.723014 | + | 0.690833i | \(0.757244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6102.00 | −0.474366 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9752.00 | −0.753991 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2688.00i | 0.206701i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 12250.0i | − 0.931866i | −0.884820 | − | 0.465933i | \(-0.845719\pi\) | ||||
0.884820 | − | 0.465933i | \(-0.154281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27432.0 | 2.07558 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −168.000 | −0.0126434 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10052.0i | 0.752471i | 0.926524 | + | 0.376236i | \(0.122782\pi\) | ||||
−0.926524 | + | 0.376236i | \(0.877218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25674.0 | −1.89158 | −0.945791 | − | 0.324776i | \(-0.894711\pi\) | ||||
−0.945791 | + | 0.324776i | \(0.894711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3732.00 | 0.273519 | 0.136759 | − | 0.990604i | \(-0.456331\pi\) | ||||
0.136759 | + | 0.990604i | \(0.456331\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 12384.0i | − 0.902878i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1214.00i | − 0.0875901i | −0.999041 | − | 0.0437950i | \(-0.986055\pi\) | ||||
0.999041 | − | 0.0437950i | \(-0.0139449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4026.00 | 0.288972 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3836.00 | 0.273914 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2424.00i | − 0.172199i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7108.00i | 0.499793i | 0.968273 | + | 0.249897i | \(0.0803966\pi\) | ||||
−0.968273 | + | 0.249897i | \(0.919603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13248.0 | 0.926782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10518.0 | −0.732069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 6162.00i | − 0.426717i | −0.976974 | − | 0.213358i | \(-0.931560\pi\) | ||||
0.976974 | − | 0.213358i | \(-0.0684402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2040.00i | 0.139852i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2472.00 | −0.168620 | −0.0843098 | − | 0.996440i | \(-0.526869\pi\) | ||||
−0.0843098 | + | 0.996440i | \(0.526869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13750.0 | −0.933235 | −0.466617 | − | 0.884459i | \(-0.654528\pi\) | ||||
−0.466617 | + | 0.884459i | \(0.654528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7596.00i | − 0.512990i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 11376.0i | − 0.760688i | −0.924845 | − | 0.380344i | \(-0.875806\pi\) | ||||
0.924845 | − | 0.380344i | \(-0.124194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2226.00 | −0.148115 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28512.0 | −1.88784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20382.0i | − 1.34294i | −0.741032 | − | 0.671469i | \(-0.765664\pi\) | ||||
0.741032 | − | 0.671469i | \(-0.234336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21178.0i | 1.38184i | 0.722932 | + | 0.690919i | \(0.242794\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4700.00 | 0.305184 | 0.152592 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152592 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4104.00 | −0.265198 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8358.00i | 0.537490i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1104.00i | 0.0703182i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2212.00 | 0.140220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21736.0 | −1.37131 | −0.685655 | − | 0.727927i | \(-0.740484\pi\) | ||||
−0.685655 | + | 0.727927i | \(0.740484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 16116.0i | − 1.01193i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2646.00i | 0.164581i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 72.0000 | 0.00445740 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13022.0 | −0.802399 | −0.401200 | − | 0.915991i | \(-0.631407\pi\) | ||||
−0.401200 | + | 0.915991i | \(0.631407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3308.00i | − 0.202885i | −0.994841 | − | 0.101442i | \(-0.967654\pi\) | ||||
0.994841 | − | 0.101442i | \(-0.0323457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 13800.0i | − 0.838538i | −0.907862 | − | 0.419269i | \(-0.862286\pi\) | ||||
0.907862 | − | 0.419269i | \(-0.137714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1456.00 | 0.0880632 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3024.00 | 0.182058 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2682.00i | 0.160727i | 0.996766 | + | 0.0803635i | \(0.0256081\pi\) | ||||
−0.996766 | + | 0.0803635i | \(0.974392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 3798.00i | − 0.225531i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23836.0 | −1.40898 | −0.704491 | − | 0.709713i | \(-0.748825\pi\) | ||||
−0.704491 | + | 0.709713i | \(0.748825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11282.0 | −0.663871 | −0.331936 | − | 0.943302i | \(-0.607702\pi\) | ||||
−0.331936 | + | 0.943302i | \(0.607702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2268.00i | 0.132853i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16112.0i | 0.935321i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3216.00 | 0.185856 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2712.00 | 0.156029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13726.0i | 0.786179i | 0.919500 | + | 0.393089i | \(0.128594\pi\) | ||||
−0.919500 | + | 0.393089i | \(0.871406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4974.00i | 0.282373i | 0.989983 | + | 0.141186i | \(0.0450917\pi\) | ||||
−0.989983 | + | 0.141186i | \(0.954908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10514.0 | −0.594242 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8604.00 | −0.484150 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8988.00i | 0.503538i | 0.967787 | + | 0.251769i | \(0.0810123\pi\) | ||||
−0.967787 | + | 0.251769i | \(0.918988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14394.0i | 0.799367i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32724.0 | −1.80941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10172.0 | 0.560002 | 0.280001 | − | 0.960000i | \(-0.409665\pi\) | ||||
0.280001 | + | 0.960000i | \(0.409665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 252.000i | 0.0138134i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5460.00i | 0.296718i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15378.0 | 0.832116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27446.0 | 1.47877 | 0.739387 | − | 0.673280i | \(-0.235115\pi\) | ||||
0.739387 | + | 0.673280i | \(0.235115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 14536.0i | − 0.779852i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2786.00i | − 0.148201i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3998.00 | −0.211774 | −0.105887 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105887 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3456.00 | 0.182293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 21888.0i | − 1.14967i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1584.00i | − 0.0825043i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25872.0 | −1.34195 | −0.670976 | − | 0.741480i | \(-0.734124\pi\) | ||||
−0.670976 | + | 0.741480i | \(0.734124\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8120.00 | −0.419424 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2442.00i | 0.125614i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12088.0i | 0.616670i | 0.951278 | + | 0.308335i | \(0.0997718\pi\) | ||||
−0.951278 | + | 0.308335i | \(0.900228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7112.00 | 0.359845 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7974.00i | − 0.401810i | −0.979611 | − | 0.200905i | \(-0.935612\pi\) | ||||
0.979611 | − | 0.200905i | \(-0.0643882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3376.00i | 0.168733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31764.0 | 1.58113 | 0.790567 | − | 0.612376i | \(-0.209786\pi\) | ||||
0.790567 | + | 0.612376i | \(0.209786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14904.0 | 0.738883 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 888.000i | − 0.0438460i | −0.999760 | − | 0.0219230i | \(-0.993021\pi\) | ||||
0.999760 | − | 0.0219230i | \(-0.00697886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4932.00i | − 0.241570i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2268.00 | 0.110642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34656.0 | −1.68391 | −0.841954 | − | 0.539549i | \(-0.818595\pi\) | ||||
−0.841954 | + | 0.539549i | \(0.818595\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5796.00i | 0.280502i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22866.0i | − 1.09786i | −0.835869 | − | 0.548929i | \(-0.815036\pi\) | ||||
0.835869 | − | 0.548929i | \(-0.184964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1824.00 | 0.0872293 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22570.0 | 1.07511 | 0.537557 | − | 0.843227i | \(-0.319347\pi\) | ||||
0.537557 | + | 0.843227i | \(0.319347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6566.00i | − 0.311540i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 19656.0i | − 0.925342i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1790.00 | 0.0839389 | 0.0419695 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419695 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9882.00 | −0.461597 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2990.00i | − 0.139124i | −0.997578 | − | 0.0695620i | \(-0.977840\pi\) | ||||
0.997578 | − | 0.0695620i | \(-0.0221602\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3318.00i | − 0.153195i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35880.0 | 1.65024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −0.00146613 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2862.00i | 0.130625i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 30756.0i | − 1.39305i | −0.717531 | − | 0.696527i | \(-0.754728\pi\) | ||||
0.717531 | − | 0.696527i | \(-0.245272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21240.0 | 0.958383 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4354.00 | 0.195715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 36612.0i | − 1.63951i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15126.0i | 0.672259i | 0.941816 | + | 0.336129i | \(0.109118\pi\) | ||||
−0.941816 | + | 0.336129i | \(0.890882\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7392.00 | −0.327297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10746.0 | 0.474022 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1688.00i | 0.0741821i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23442.0i | 1.02255i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6502.00 | 0.282569 | 0.141284 | − | 0.989969i | \(-0.454877\pi\) | ||||
0.141284 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8252.00 | −0.357296 | −0.178648 | − | 0.983913i | \(-0.557172\pi\) | ||||
−0.178648 | + | 0.983913i | \(0.557172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9504.00i | − 0.409987i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 46736.0i | − 2.00133i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3402.00 | 0.145147 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21986.0 | −0.934612 | −0.467306 | − | 0.884096i | \(-0.654775\pi\) | ||||
−0.467306 | + | 0.884096i | \(0.654775\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3736.00i | − 0.158237i | −0.996865 | − | 0.0791183i | \(-0.974790\pi\) | ||||
0.996865 | − | 0.0791183i | \(-0.0252105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 23820.0i | − 1.00158i | −0.865570 | − | 0.500788i | \(-0.833044\pi\) | ||||
0.865570 | − | 0.500788i | \(-0.166956\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7942.00 | −0.332735 | −0.166367 | − | 0.986064i | \(-0.553204\pi\) | ||||
−0.166367 | + | 0.986064i | \(0.553204\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23574.0 | −0.984083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 686.000i | 0.0285336i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3888.00i | − 0.160560i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21016.0 | −0.864783 | −0.432391 | − | 0.901686i | \(-0.642330\pi\) | ||||
−0.432391 | + | 0.901686i | \(0.642330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13153.0 | −0.539301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 20190.0i | − 0.824888i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9205.00i | 0.373421i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9060.00 | 0.366241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24016.0 | −0.967401 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 24878.0i | − 0.998601i | −0.866429 | − | 0.499300i | \(-0.833590\pi\) | ||||
0.866429 | − | 0.499300i | \(-0.166410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 6390.00i | − 0.254700i | −0.991858 | − | 0.127350i | \(-0.959353\pi\) | ||||
0.991858 | − | 0.127350i | \(-0.0406472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46444.0 | 1.84476 | 0.922380 | − | 0.386284i | \(-0.126241\pi\) | ||||
0.922380 | + | 0.386284i | \(0.126241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8190.00 | 0.324175 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25408.0i | 1.00220i | 0.865389 | + | 0.501100i | \(0.167071\pi\) | ||||
−0.865389 | + | 0.501100i | \(0.832929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 14151.0i | − 0.554317i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1536.00 | −0.0599600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45576.0 | 1.77300 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13518.0i | 0.524072i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1078.00i | 0.0415068i | 0.999785 | + | 0.0207534i | \(0.00660649\pi\) | ||||
−0.999785 | + | 0.0207534i | \(0.993394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20502.0 | 0.786707 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45006.0 | −1.72110 | −0.860551 | − | 0.509364i | \(-0.829881\pi\) | ||||
−0.860551 | + | 0.509364i | \(0.829881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4028.00i | − 0.153514i | −0.997050 | − | 0.0767571i | \(-0.975543\pi\) | ||||
0.997050 | − | 0.0767571i | \(-0.0244566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 29304.0i | − 1.10928i | −0.832090 | − | 0.554640i | \(-0.812856\pi\) | ||||
0.832090 | − | 0.554640i | \(-0.187144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8400.00 | 0.316903 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 324.000 | 0.0121823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48576.0i | 1.82031i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 24624.0i | − 0.916579i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15264.0 | −0.566277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8484.00 | −0.313699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 10668.0i | − 0.393144i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50916.0i | 1.86399i | 0.362472 | + | 0.931995i | \(0.381933\pi\) | ||||
−0.362472 | + | 0.931995i | \(0.618067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3582.00 | −0.130701 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24432.0 | −0.888549 | −0.444275 | − | 0.895891i | \(-0.646539\pi\) | ||||
−0.444275 | + | 0.895891i | \(0.646539\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2192.00i | 0.0794574i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9772.00i | 0.351908i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20360.0 | 0.730810 | 0.365405 | − | 0.930849i | \(-0.380930\pi\) | ||||
0.365405 | + | 0.930849i | \(0.380930\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6996.00 | 0.250300 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 432.000i | 0.0154057i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10440.0i | 0.369897i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23202.0 | −0.819411 | −0.409706 | − | 0.912218i | \(-0.634369\pi\) | ||||
−0.409706 | + | 0.912218i | \(0.634369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4508.00 | 0.158694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 26520.0i | − 0.930574i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1990.00i | − 0.0693815i | −0.999398 | − | 0.0346908i | \(-0.988955\pi\) | ||||
0.999398 | − | 0.0346908i | \(-0.0110446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3138.00 | 0.109057 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51130.0 | −1.77130 | −0.885648 | − | 0.464356i | \(-0.846286\pi\) | ||||
−0.885648 | + | 0.464356i | \(0.846286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 59280.0i | − 2.04711i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 47044.0i | − 1.61428i | −0.590359 | − | 0.807141i | \(-0.701014\pi\) | ||||
0.590359 | − | 0.807141i | \(-0.298986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22788.0 | 0.779483 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22626.0 | 0.771502 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 46858.0i | − 1.59274i | −0.604811 | − | 0.796369i | \(-0.706751\pi\) | ||||
0.604811 | − | 0.796369i | \(-0.293249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1272.00i | − 0.0429654i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19670.0 | 0.662333 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9055.00 | −0.303951 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2916.00i | − 0.0975771i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30632.0i | 1.01867i | 0.860567 | + | 0.509337i | \(0.170110\pi\) | ||||
−0.860567 | + | 0.509337i | \(0.829890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3864.00 | 0.128101 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3804.00 | −0.125722 | −0.0628611 | − | 0.998022i | \(-0.520022\pi\) | ||||
−0.0628611 | + | 0.998022i | \(0.520022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.0000i | 0 0.000922548i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 49326.0i | − 1.61523i | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||||
0.589711 | − | 0.807614i | \(-0.299242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4776.00 | −0.155916 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8442.00 | −0.274753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 11112.0i | − 0.360547i | −0.983617 | − | 0.180274i | \(-0.942302\pi\) | ||||
0.983617 | − | 0.180274i | \(-0.0576983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11088.0i | 0.357584i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −77216.0 | −2.48263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13616.0 | 0.436455 | 0.218227 | − | 0.975898i | \(-0.429973\pi\) | ||||
0.218227 | + | 0.975898i | \(0.429973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 8268.00i | − 0.264227i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 56674.0i | − 1.80028i | −0.435596 | − | 0.900142i | \(-0.643462\pi\) | ||||
0.435596 | − | 0.900142i | \(-0.356538\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4266.00 | −0.135105 |
(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 | 2100.4.k.g.1849.1 | 2 | ||
5.2 | odd | 4 | 2100.4.a.g.1.1 | 1 | |||
5.3 | odd | 4 | 84.4.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 2100.4.k.g.1849.2 | 2 | ||
15.8 | even | 4 | 252.4.a.a.1.1 | 1 | |||
20.3 | even | 4 | 336.4.a.e.1.1 | 1 | |||
35.3 | even | 12 | 588.4.i.h.373.1 | 2 | |||
35.13 | even | 4 | 588.4.a.a.1.1 | 1 | |||
35.18 | odd | 12 | 588.4.i.a.373.1 | 2 | |||
35.23 | odd | 12 | 588.4.i.a.361.1 | 2 | |||
35.33 | even | 12 | 588.4.i.h.361.1 | 2 | |||
40.3 | even | 4 | 1344.4.a.p.1.1 | 1 | |||
40.13 | odd | 4 | 1344.4.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 1008.4.a.d.1.1 | 1 | |||
105.23 | even | 12 | 1764.4.k.n.361.1 | 2 | |||
105.38 | odd | 12 | 1764.4.k.c.1549.1 | 2 | |||
105.53 | even | 12 | 1764.4.k.n.1549.1 | 2 | |||
105.68 | odd | 12 | 1764.4.k.c.361.1 | 2 | |||
105.83 | odd | 4 | 1764.4.a.l.1.1 | 1 | |||
140.83 | odd | 4 | 2352.4.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.a.b.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
252.4.a.a.1.1 | 1 | 15.8 | even | 4 | |||
336.4.a.e.1.1 | 1 | 20.3 | even | 4 | |||
588.4.a.a.1.1 | 1 | 35.13 | even | 4 | |||
588.4.i.a.361.1 | 2 | 35.23 | odd | 12 | |||
588.4.i.a.373.1 | 2 | 35.18 | odd | 12 | |||
588.4.i.h.361.1 | 2 | 35.33 | even | 12 | |||
588.4.i.h.373.1 | 2 | 35.3 | even | 12 | |||
1008.4.a.d.1.1 | 1 | 60.23 | odd | 4 | |||
1344.4.a.b.1.1 | 1 | 40.13 | odd | 4 | |||
1344.4.a.p.1.1 | 1 | 40.3 | even | 4 | |||
1764.4.a.l.1.1 | 1 | 105.83 | odd | 4 | |||
1764.4.k.c.361.1 | 2 | 105.68 | odd | 12 | |||
1764.4.k.c.1549.1 | 2 | 105.38 | odd | 12 | |||
1764.4.k.n.361.1 | 2 | 105.23 | even | 12 | |||
1764.4.k.n.1549.1 | 2 | 105.53 | even | 12 | |||
2100.4.a.g.1.1 | 1 | 5.2 | odd | 4 | |||
2100.4.k.g.1849.1 | 2 | 1.1 | even | 1 | trivial | ||
2100.4.k.g.1849.2 | 2 | 5.4 | even | 2 | inner | ||
2352.4.a.v.1.1 | 1 | 140.83 | odd | 4 |