Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(97,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.f (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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 17x^{2} + 16x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(-1.76556 - 3.05805i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.97 |
Dual form | 2352.3.f.f.97.2 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 4.38404i | − 0.876809i | −0.898778 | − | 0.438404i | \(-0.855544\pi\) | ||||
0.898778 | − | 0.438404i | \(-0.144456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.5934 | 1.78122 | 0.890608 | − | 0.454771i | \(-0.150279\pi\) | ||||
0.890608 | + | 0.454771i | \(0.150279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.11609i | − 0.470469i | −0.971939 | − | 0.235234i | \(-0.924414\pi\) | ||||
0.971939 | − | 0.235234i | \(-0.0755858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.59339 | 0.506226 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.76809i | 0.515770i | 0.966176 | + | 0.257885i | \(0.0830255\pi\) | ||||
−0.966176 | + | 0.257885i | \(0.916974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 30.3648i | − 1.59815i | −0.601233 | − | 0.799074i | \(-0.705324\pi\) | ||||
0.601233 | − | 0.799074i | \(-0.294676\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0000 | 1.04348 | 0.521739 | − | 0.853105i | \(-0.325283\pi\) | ||||
0.521739 | + | 0.853105i | \(0.325283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.78016 | 0.231206 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.5934 | 0.468737 | 0.234369 | − | 0.972148i | \(-0.424698\pi\) | ||||
0.234369 | + | 0.972148i | \(0.424698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.0363i | 0.904397i | 0.891917 | + | 0.452199i | \(0.149360\pi\) | ||||
−0.891917 | + | 0.452199i | \(0.850640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 33.9367i | 1.02839i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.5934 | −1.31333 | −0.656667 | − | 0.754180i | \(-0.728034\pi\) | ||||
−0.656667 | + | 0.754180i | \(0.728034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.5934 | 0.271625 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.14387i | 0.174241i | 0.996198 | + | 0.0871204i | \(0.0277665\pi\) | ||||
−0.996198 | + | 0.0871204i | \(0.972234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −53.7802 | −1.25070 | −0.625351 | − | 0.780344i | \(-0.715044\pi\) | ||||
−0.625351 | + | 0.780344i | \(0.715044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.1521i | 0.292270i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 39.9450i | − 0.849894i | −0.905218 | − | 0.424947i | \(-0.860293\pi\) | ||||
0.905218 | − | 0.424947i | \(-0.139707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.1868 | −0.297780 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −61.5934 | −1.16214 | −0.581070 | − | 0.813854i | \(-0.697366\pi\) | ||||
−0.581070 | + | 0.813854i | \(0.697366\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 85.8983i | − 1.56179i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 52.5934 | 0.922691 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 77.1302i | − 1.30729i | −0.756801 | − | 0.653646i | \(-0.773239\pi\) | ||||
0.756801 | − | 0.653646i | \(-0.226761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.431334i | − 0.00707105i | −0.999994 | − | 0.00353553i | \(-0.998875\pi\) | ||||
0.999994 | − | 0.00353553i | \(-0.00112540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26.8132 | −0.412511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 56.9669 | 0.850253 | 0.425126 | − | 0.905134i | \(-0.360230\pi\) | ||||
0.425126 | + | 0.905134i | \(0.360230\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41.5692i | 0.602452i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 123.560 | 1.74029 | 0.870143 | − | 0.492799i | \(-0.164026\pi\) | ||||
0.870143 | + | 0.492799i | \(0.164026\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.8845i | 0.491568i | 0.969325 | + | 0.245784i | \(0.0790454\pi\) | ||||
−0.969325 | + | 0.245784i | \(0.920955\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.0115i | 0.133487i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.1868 | 0.660592 | 0.330296 | − | 0.943877i | \(-0.392851\pi\) | ||||
0.330296 | + | 0.943877i | \(0.392851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 136.883i | 1.64919i | 0.565725 | + | 0.824594i | \(0.308596\pi\) | ||||
−0.565725 | + | 0.824594i | \(0.691404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 38.4397 | 0.452232 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.5444i | 0.270626i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 15.2650i | − 0.171516i | −0.996316 | − | 0.0857582i | \(-0.972669\pi\) | ||||
0.996316 | − | 0.0857582i | \(-0.0273312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −48.5603 | −0.522154 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −133.121 | −1.40127 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 34.1524i | − 0.352087i | −0.984382 | − | 0.176043i | \(-0.943670\pi\) | ||||
0.984382 | − | 0.176043i | \(-0.0563299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −58.7802 | −0.593739 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 130.874i | − 1.29579i | −0.761732 | − | 0.647893i | \(-0.775651\pi\) | ||||
0.761732 | − | 0.647893i | \(-0.224349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 162.648i | − 1.57910i | −0.613684 | − | 0.789552i | \(-0.710313\pi\) | ||||
0.613684 | − | 0.789552i | \(-0.289687\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 103.967 | 0.971654 | 0.485827 | − | 0.874055i | \(-0.338519\pi\) | ||||
0.485827 | + | 0.874055i | \(0.338519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7802 | −0.144772 | −0.0723861 | − | 0.997377i | \(-0.523061\pi\) | ||||
−0.0723861 | + | 0.997377i | \(0.523061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 84.1662i | − 0.758254i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −59.6265 | −0.527668 | −0.263834 | − | 0.964568i | \(-0.584987\pi\) | ||||
−0.263834 | + | 0.964568i | \(0.584987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 105.217i | − 0.914931i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.3483i | 0.156823i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 262.901 | 2.17273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.3735 | −0.100598 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 134.942i | − 1.07953i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.0000 | 0.196850 | 0.0984252 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984252 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 93.1500i | − 0.722093i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 226.518i | 1.72914i | 0.502509 | + | 0.864572i | \(0.332410\pi\) | ||||
−0.502509 | + | 0.864572i | \(0.667590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.7802 | −0.168742 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −247.121 | −1.80380 | −0.901900 | − | 0.431945i | \(-0.857828\pi\) | ||||
−0.901900 | + | 0.431945i | \(0.857828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 147.383i | − 1.06031i | −0.847902 | − | 0.530154i | \(-0.822134\pi\) | ||||
0.847902 | − | 0.530154i | \(-0.177866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 69.1868 | 0.490686 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 119.835i | − 0.838007i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 59.5940i | − 0.410993i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.813 | 0.864518 | 0.432259 | − | 0.901749i | \(-0.357717\pi\) | ||||
0.432259 | + | 0.901749i | \(0.357717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −62.0331 | −0.410815 | −0.205408 | − | 0.978677i | \(-0.565852\pi\) | ||||
−0.205408 | + | 0.978677i | \(0.565852\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 26.3043i | − 0.171923i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 122.912 | 0.792983 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 250.709i | − 1.59687i | −0.602078 | − | 0.798437i | \(-0.705660\pi\) | ||||
0.602078 | − | 0.798437i | \(-0.294340\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 106.683i | − 0.670961i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 97.9339 | 0.600821 | 0.300411 | − | 0.953810i | \(-0.402876\pi\) | ||||
0.300411 | + | 0.953810i | \(0.402876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 148.780 | 0.901698 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 71.7689i | − 0.429754i | −0.976641 | − | 0.214877i | \(-0.931065\pi\) | ||||
0.976641 | − | 0.214877i | \(-0.0689351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131.593 | 0.778659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.0944i | 0.532716i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 302.024i | − 1.74580i | −0.487897 | − | 0.872901i | \(-0.662236\pi\) | ||||
0.487897 | − | 0.872901i | \(-0.337764\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 133.593 | 0.754765 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −138.000 | −0.770950 | −0.385475 | − | 0.922718i | \(-0.625962\pi\) | ||||
−0.385475 | + | 0.922718i | \(0.625962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 82.9733i | − 0.458416i | −0.973377 | − | 0.229208i | \(-0.926386\pi\) | ||||
0.973377 | − | 0.229208i | \(-0.0736136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.747093 | 0.00408248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 213.036i | 1.15154i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 171.797i | 0.918698i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −172.307 | −0.902133 | −0.451067 | − | 0.892490i | \(-0.648956\pi\) | ||||
−0.451067 | + | 0.892490i | \(0.648956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 275.307 | 1.42646 | 0.713232 | − | 0.700928i | \(-0.247231\pi\) | ||||
0.713232 | + | 0.700928i | \(0.247231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 46.4419i | − 0.238163i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −154.307 | −0.783286 | −0.391643 | − | 0.920117i | \(-0.628093\pi\) | ||||
−0.391643 | + | 0.920117i | \(0.628093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 187.924i | 0.944342i | 0.881507 | + | 0.472171i | \(0.156530\pi\) | ||||
−0.881507 | + | 0.472171i | \(0.843470\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 98.6696i | 0.490894i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.3190 | 0.152776 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −72.0000 | −0.347826 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 594.949i | − 2.84665i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 348.307 | 1.65075 | 0.825373 | − | 0.564588i | \(-0.190965\pi\) | ||||
0.825373 | + | 0.564588i | \(0.190965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 214.013i | 1.00475i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 235.775i | 1.09663i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −62.1537 | −0.283807 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53.6265 | 0.242654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 30.3581i | 0.136135i | 0.997681 | + | 0.0680675i | \(0.0216833\pi\) | ||||
−0.997681 | + | 0.0680675i | \(0.978317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.3405 | −0.0770688 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 64.4667i | − 0.283994i | −0.989867 | − | 0.141997i | \(-0.954648\pi\) | ||||
0.989867 | − | 0.141997i | \(-0.0453523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.0115i | − 0.0437185i | −0.999761 | − | 0.0218592i | \(-0.993041\pi\) | ||||
0.999761 | − | 0.0218592i | \(-0.00695857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.5058 | 0.122343 | 0.0611713 | − | 0.998127i | \(-0.480516\pi\) | ||||
0.0611713 | + | 0.998127i | \(0.480516\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −175.121 | −0.745194 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 90.3901i | 0.381393i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 256.307 | 1.07242 | 0.536208 | − | 0.844086i | \(-0.319856\pi\) | ||||
0.536208 | + | 0.844086i | \(0.319856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 215.694i | 0.894997i | 0.894285 | + | 0.447498i | \(0.147685\pi\) | ||||
−0.894285 | + | 0.447498i | \(0.852315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −185.714 | −0.751879 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −237.088 | −0.952159 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 371.680i | − 1.48080i | −0.672168 | − | 0.740398i | \(-0.734637\pi\) | ||||
0.672168 | − | 0.740398i | \(-0.265363\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 470.241 | 1.85866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 66.5795i | 0.261096i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 74.0401i | 0.288094i | 0.989571 | + | 0.144047i | \(0.0460116\pi\) | ||||
−0.989571 | + | 0.144047i | \(0.953988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −40.7802 | −0.156246 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.3190 | −0.0734564 | −0.0367282 | − | 0.999325i | \(-0.511694\pi\) | ||||
−0.0367282 | + | 0.999325i | \(0.511694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 270.028i | 1.01897i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.4397 | 0.0990250 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 208.982i | − 0.776884i | −0.921473 | − | 0.388442i | \(-0.873013\pi\) | ||||
0.921473 | − | 0.388442i | \(-0.126987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 122.811i | 0.453175i | 0.973991 | + | 0.226588i | \(0.0727570\pi\) | ||||
−0.973991 | + | 0.226588i | \(0.927243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 113.253 | 0.411829 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7802 | 0.100289 | 0.0501447 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501447 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 84.1089i | − 0.301466i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 61.4942 | 0.218841 | 0.109420 | − | 0.993996i | \(-0.465101\pi\) | ||||
0.109420 | + | 0.993996i | \(0.465101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 43.8910i | 0.155092i | 0.996989 | + | 0.0775459i | \(0.0247084\pi\) | ||||
−0.996989 | + | 0.0775459i | \(0.975292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 230.572i | − 0.809024i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 212.121 | 0.733981 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 59.1537 | 0.203277 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 223.600i | − 0.763139i | −0.924340 | − | 0.381569i | \(-0.875384\pi\) | ||||
0.924340 | − | 0.381569i | \(-0.124616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −338.142 | −1.14624 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 101.810i | − 0.342795i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 146.786i | − 0.490924i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 226.681 | 0.748122 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.89099 | −0.00619996 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 66.8457i | 0.217738i | 0.994056 | + | 0.108869i | \(0.0347230\pi\) | ||||
−0.994056 | + | 0.108869i | \(0.965277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 281.714 | 0.911696 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.2225i | 0.0939630i | 0.998896 | + | 0.0469815i | \(0.0149602\pi\) | ||||
−0.998896 | + | 0.0469815i | \(0.985040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 248.115i | 0.792698i | 0.918100 | + | 0.396349i | \(0.129723\pi\) | ||||
−0.918100 | + | 0.396349i | \(0.870277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6479 | 0.0398987 | 0.0199494 | − | 0.999801i | \(-0.493650\pi\) | ||||
0.0199494 | + | 0.999801i | \(0.493650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 266.340 | 0.834923 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 180.076i | 0.560984i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 266.241 | 0.824276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 35.3520i | − 0.108775i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 27.3320i | − 0.0835842i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 502.901 | 1.51934 | 0.759669 | − | 0.650310i | \(-0.225361\pi\) | ||||
0.759669 | + | 0.650310i | \(0.225361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 145.780 | 0.437778 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 249.746i | − 0.745509i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −123.681 | −0.367006 | −0.183503 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183503 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 103.276i | − 0.304649i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 549.326i | 1.61093i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 182.241 | 0.528236 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 226.307 | 0.652183 | 0.326091 | − | 0.945338i | \(-0.394268\pi\) | ||||
0.326091 | + | 0.945338i | \(0.394268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 155.669i | − 0.446043i | −0.974814 | − | 0.223021i | \(-0.928408\pi\) | ||||
0.974814 | − | 0.223021i | \(-0.0715920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.7802 | −0.0905418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 63.9780i | − 0.181241i | −0.995886 | − | 0.0906205i | \(-0.971115\pi\) | ||||
0.995886 | − | 0.0906205i | \(-0.0288850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 541.694i | − 1.52590i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 302.988 | 0.843979 | 0.421989 | − | 0.906601i | \(-0.361332\pi\) | ||||
0.421989 | + | 0.906601i | \(0.361332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −561.021 | −1.55408 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 455.358i | 1.25443i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 157.319 | 0.431011 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.00671348i | 0 1.82929e-5i | 1.00000 | 9.14643e-6i | \(2.91140e-6\pi\) | |||||
−1.00000 | 9.14643e-6i | \(0.999997\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 21.4316i | − 0.0580802i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −125.780 | −0.337212 | −0.168606 | − | 0.985684i | \(-0.553927\pi\) | ||||
−0.168606 | + | 0.985684i | \(0.553927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 233.726 | 0.623268 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 83.1384i | − 0.220526i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 485.076 | 1.27988 | 0.639942 | − | 0.768423i | \(-0.278958\pi\) | ||||
0.639942 | + | 0.768423i | \(0.278958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 43.3013i | 0.113652i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 260.138i | − 0.679211i | −0.940568 | − | 0.339606i | \(-0.889706\pi\) | ||||
0.940568 | − | 0.339606i | \(-0.110294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 161.340 | 0.416900 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 85.8677 | 0.220740 | 0.110370 | − | 0.993891i | \(-0.464796\pi\) | ||||
0.110370 | + | 0.993891i | \(0.464796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 210.434i | 0.538195i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −392.340 | −0.998322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 228.789i | − 0.579213i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 463.809i | − 1.16828i | −0.811651 | − | 0.584142i | \(-0.801431\pi\) | ||||
0.811651 | − | 0.584142i | \(-0.198569\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −463.868 | −1.15678 | −0.578389 | − | 0.815761i | \(-0.696318\pi\) | ||||
−0.578389 | + | 0.815761i | \(0.696318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 171.473 | 0.425491 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 39.4564i | − 0.0974232i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −952.109 | −2.33933 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 466.137i | 1.13970i | 0.821749 | + | 0.569850i | \(0.192999\pi\) | ||||
−0.821749 | + | 0.569850i | \(0.807001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 428.026i | − 1.04142i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 600.099 | 1.44602 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 255.274 | 0.612169 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 89.9655i | − 0.214715i | −0.994220 | − | 0.107357i | \(-0.965761\pi\) | ||||
0.994220 | − | 0.107357i | \(-0.0342389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −413.582 | −0.982379 | −0.491190 | − | 0.871053i | \(-0.663438\pi\) | ||||
−0.491190 | + | 0.871053i | \(0.663438\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 119.835i | 0.283298i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 50.6809i | 0.119249i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 207.560 | 0.483824 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −70.1323 | −0.162720 | −0.0813599 | − | 0.996685i | \(-0.525926\pi\) | ||||
−0.0813599 | + | 0.996685i | \(0.525926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 431.223i | 0.995897i | 0.867207 | + | 0.497948i | \(0.165913\pi\) | ||||
−0.867207 | + | 0.497948i | \(0.834087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 103.220 | 0.237287 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 728.755i | − 1.66763i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 94.3496i | − 0.214919i | −0.994209 | − | 0.107460i | \(-0.965728\pi\) | ||||
0.994209 | − | 0.107460i | \(-0.0342716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −412.582 | −0.931336 | −0.465668 | − | 0.884960i | \(-0.654186\pi\) | ||||
−0.465668 | + | 0.884960i | \(0.654186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.9222 | −0.150387 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 223.111i | 0.499130i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 617.802 | 1.37595 | 0.687975 | − | 0.725734i | \(-0.258500\pi\) | ||||
0.687975 | + | 0.725734i | \(0.258500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 139.973i | 0.310361i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 107.444i | − 0.237184i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.0240700 | −0.0120350 | − | 0.999928i | \(-0.503831\pi\) | ||||
−0.0120350 | + | 0.999928i | \(0.503831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 45.5603 | 0.0992600 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 859.960i | 1.86542i | 0.360624 | + | 0.932711i | \(0.382564\pi\) | ||||
−0.360624 | + | 0.932711i | \(0.617436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −397.340 | −0.858187 | −0.429093 | − | 0.903260i | \(-0.641167\pi\) | ||||
−0.429093 | + | 0.903260i | \(0.641167\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 212.891i | 0.457829i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 297.151i | 0.636298i | 0.948041 | + | 0.318149i | \(0.103061\pi\) | ||||
−0.948041 | + | 0.318149i | \(0.896939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 434.241 | 0.921956 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1053.74 | −2.22777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 175.513i | − 0.369502i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 184.780 | 0.387380 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 804.420i | − 1.67937i | −0.543071 | − | 0.839687i | \(-0.682739\pi\) | ||||
0.543071 | − | 0.839687i | \(-0.317261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 297.202i | 0.617883i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −149.726 | −0.308713 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −60.8016 | −0.124849 | −0.0624246 | − | 0.998050i | \(-0.519883\pi\) | ||||
−0.0624246 | + | 0.998050i | \(0.519883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 169.626i | 0.346884i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −514.955 | −1.04879 | −0.524394 | − | 0.851475i | \(-0.675708\pi\) | ||||
−0.524394 | + | 0.851475i | \(0.675708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 119.188i | 0.241761i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 257.695i | 0.520596i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −888.901 | −1.78136 | −0.890682 | − | 0.454627i | \(-0.849773\pi\) | ||||
−0.890682 | + | 0.454627i | \(0.849773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 124.307 | 0.248119 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 822.920i | − 1.63602i | −0.575202 | − | 0.818012i | \(-0.695076\pi\) | ||||
0.575202 | − | 0.818012i | \(-0.304924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −573.759 | −1.13616 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 227.926i | 0.449559i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 568.157i | 1.11622i | 0.829767 | + | 0.558111i | \(0.188473\pi\) | ||||
−0.829767 | + | 0.558111i | \(0.811527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −157.780 | −0.307564 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −713.055 | −1.38457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 782.658i | − 1.51385i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 523.121 | 1.00794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 136.724i | 0.262426i | 0.991354 | + | 0.131213i | \(0.0418873\pi\) | ||||
−0.991354 | + | 0.131213i | \(0.958113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5674i | 0.0278535i | 0.999903 | + | 0.0139268i | \(0.00443317\pi\) | ||||
−0.999903 | + | 0.0139268i | \(0.995567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −245.825 | −0.466461 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.0000 | 0.0888469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 231.391i | 0.435764i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.6926 | 0.0819748 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 455.796i | − 0.851954i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 239.023i | − 0.445108i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −924.901 | −1.70961 | −0.854807 | − | 0.518947i | \(-0.826324\pi\) | ||||
−0.854807 | + | 0.518947i | \(0.826324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 143.714 | 0.264667 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 69.1809i | 0.126937i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −103.626 | −0.189445 | −0.0947225 | − | 0.995504i | \(-0.530196\pi\) | ||||
−0.0947225 | + | 0.995504i | \(0.530196\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.29400i | 0.00235702i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 412.761i | − 0.749112i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −368.988 | −0.664844 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 412.407 | 0.740407 | 0.370203 | − | 0.928951i | \(-0.379288\pi\) | ||||
0.370203 | + | 0.928951i | \(0.379288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 328.925i | 0.588416i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −297.560 | −0.530411 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 686.367i | 1.21912i | 0.792738 | + | 0.609562i | \(0.208655\pi\) | ||||
−0.792738 | + | 0.609562i | \(0.791345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 261.405i | 0.462664i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −146.615 | −0.257671 | −0.128836 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128836 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −356.263 | −0.623928 | −0.311964 | − | 0.950094i | \(-0.600987\pi\) | ||||
−0.311964 | + | 0.950094i | \(0.600987\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 298.445i | − 0.520847i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 138.724 | 0.241259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 171.028i | − 0.296409i | −0.988957 | − | 0.148205i | \(-0.952651\pi\) | ||||
0.988957 | − | 0.148205i | \(-0.0473495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 476.846i | 0.823569i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1206.82 | −2.07002 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 80.4397 | 0.137504 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8384i | 0.0423142i | 0.999776 | + | 0.0211571i | \(0.00673502\pi\) | ||||
−0.999776 | + | 0.0211571i | \(0.993265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 851.317 | 1.44536 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 267.268i | − 0.452231i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 136.077i | 0.229472i | 0.993396 | + | 0.114736i | \(0.0366023\pi\) | ||||
−0.993396 | + | 0.114736i | \(0.963398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −325.494 | −0.545216 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −989.230 | −1.65147 | −0.825734 | − | 0.564059i | \(-0.809239\pi\) | ||||
−0.825734 | + | 0.564059i | \(0.809239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 78.8184i | 0.131145i | 0.997848 | + | 0.0655727i | \(0.0208874\pi\) | ||||
−0.997848 | + | 0.0655727i | \(0.979113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −170.901 | −0.283418 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1152.57i | − 1.90507i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 840.449i | 1.38459i | 0.721612 | + | 0.692297i | \(0.243401\pi\) | ||||
−0.721612 | + | 0.692297i | \(0.756599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −244.307 | −0.399848 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 847.428 | 1.38243 | 0.691214 | − | 0.722650i | \(-0.257076\pi\) | ||||
0.691214 | + | 0.722650i | \(0.257076\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 54.2462i | 0.0882052i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −649.669 | −1.05295 | −0.526474 | − | 0.850191i | \(-0.676486\pi\) | ||||
−0.526474 | + | 0.850191i | \(0.676486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 488.044i | 0.788440i | 0.919016 | + | 0.394220i | \(0.128985\pi\) | ||||
−0.919016 | + | 0.394220i | \(0.871015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 124.708i | − 0.200817i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −447.086 | −0.715337 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1030.48 | 1.64351 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 426.071i | − 0.677378i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 820.473 | 1.30027 | 0.650137 | − | 0.759817i | \(-0.274712\pi\) | ||||
0.650137 | + | 0.759817i | \(0.274712\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 603.286i | 0.953059i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 109.601i | − 0.172600i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −370.681 | −0.580095 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.8677 | −0.0309949 | −0.0154975 | − | 0.999880i | \(-0.504933\pi\) | ||||
−0.0154975 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1013.95i | 1.57691i | 0.615092 | + | 0.788456i | \(0.289119\pi\) | ||||
−0.615092 | + | 0.788456i | \(0.710881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −408.374 | −0.633137 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 133.462i | − 0.206279i | −0.994667 | − | 0.103139i | \(-0.967111\pi\) | ||||
0.994667 | − | 0.103139i | \(-0.0328888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 1511.24i | − 2.32857i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 604.757 | 0.926121 | 0.463060 | − | 0.886327i | \(-0.346751\pi\) | ||||
0.463060 | + | 0.886327i | \(0.346751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 993.064 | 1.51613 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 107.653i | − 0.163856i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −335.451 | −0.509031 | −0.254515 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254515 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 702.273i | 1.06244i | 0.847234 | + | 0.531220i | \(0.178266\pi\) | ||||
−0.847234 | + | 0.531220i | \(0.821734\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 92.8837i | 0.140096i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 326.241 | 0.489117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.5818 | −0.0785975 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 8.45130i | − 0.0125951i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1119.48 | −1.66342 | −0.831711 | − | 0.555209i | \(-0.812638\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 30.0346i | − 0.0444957i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 260.626i | − 0.384973i | −0.981300 | − | 0.192486i | \(-0.938345\pi\) | ||||
0.981300 | − | 0.192486i | \(-0.0616551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 111.660 | 0.163964 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 200.516 | 0.293581 | 0.146790 | − | 0.989168i | \(-0.453106\pi\) | ||||
0.146790 | + | 0.989168i | \(0.453106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1083.39i | 1.58159i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.3405 | 0.0252409 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 376.711i | 0.546750i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 994.120i | 1.43867i | 0.694664 | + | 0.719334i | \(0.255553\pi\) | ||||
−0.694664 | + | 0.719334i | \(0.744447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −646.132 | −0.929687 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.6381 | −0.0898681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 49.3735i | 0.0706345i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −148.231 | −0.211457 | −0.105729 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105729 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1475.53i | 2.09890i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 303.318i | − 0.430238i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 711.977 | 1.00420 | 0.502099 | − | 0.864810i | \(-0.332561\pi\) | ||||
0.502099 | + | 0.864810i | \(0.332561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −156.560 | −0.220197 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 672.872i | 0.943719i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −525.362 | −0.734772 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 443.937i | 0.619160i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 749.527i | − 1.04246i | −0.853417 | − | 0.521228i | \(-0.825474\pi\) | ||||
0.853417 | − | 0.521228i | \(-0.174526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −373.593 | −0.516727 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 78.5719 | 0.108375 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 865.702i | 1.19079i | 0.803434 | + | 0.595393i | \(0.203004\pi\) | ||||
−0.803434 | + | 0.595393i | \(0.796996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 471.549i | − 0.645074i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 96.4995i | − 0.131650i | −0.997831 | − | 0.0658251i | \(-0.979032\pi\) | ||||
0.997831 | − | 0.0658251i | \(-0.0209679\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1116.18 | 1.51448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 420.901 | 0.569555 | 0.284777 | − | 0.958594i | \(-0.408080\pi\) | ||||
0.284777 | + | 0.958594i | \(0.408080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 321.666i | − 0.434097i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −920.043 | −1.23828 | −0.619141 | − | 0.785280i | \(-0.712519\pi\) | ||||
−0.619141 | + | 0.785280i | \(0.712519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 564.723i | − 0.758017i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 410.648i | − 0.549729i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 320.362 | 0.426580 | 0.213290 | − | 0.976989i | \(-0.431582\pi\) | ||||
0.213290 | + | 0.976989i | \(0.431582\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 643.769 | 0.854938 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 271.956i | 0.360206i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 330.813 | 0.437006 | 0.218503 | − | 0.975836i | \(-0.429883\pi\) | ||||
0.218503 | + | 0.975836i | \(0.429883\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 814.482i | 1.07310i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 266.291i | − 0.349923i | −0.984575 | − | 0.174961i | \(-0.944020\pi\) | ||||
0.984575 | − | 0.174961i | \(-0.0559800\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −115.319 | −0.150744 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −471.735 | −0.615040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 241.301i | − 0.313785i | −0.987616 | − | 0.156893i | \(-0.949852\pi\) | ||||
0.987616 | − | 0.156893i | \(-0.0501477\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −128.241 | −0.166331 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 929.774i | − 1.20281i | −0.798943 | − | 0.601406i | \(-0.794607\pi\) | ||||
0.798943 | − | 0.601406i | \(-0.205393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 162.054i | 0.209102i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 216.922 | 0.278462 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2420.97 | 3.09983 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 70.6333i | − 0.0902086i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1099.12 | −1.40015 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1109.78i | − 1.41014i | −0.709138 | − | 0.705070i | \(-0.750916\pi\) | ||||
0.709138 | − | 0.705070i | \(-0.249084\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 33.4616i | − 0.0424101i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.63808 | −0.00332671 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −467.702 | −0.588305 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 231.047i | 0.289896i | 0.989439 | + | 0.144948i | \(0.0463014\pi\) | ||||
−0.989439 | + | 0.144948i | \(0.953699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 350.241 | 0.438350 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.7949i | 0.0571721i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 703.098i | 0.875589i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 361.967 | 0.448534 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −318.945 | −0.394247 | −0.197123 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197123 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 196.807i | − 0.242672i | −0.992612 | − | 0.121336i | \(-0.961282\pi\) | ||||
0.992612 | − | 0.121336i | \(-0.0387178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −212.714 | −0.261641 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 429.346i | − 0.526805i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1633.02i | 1.99881i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1384.01 | −1.68576 | −0.842881 | − | 0.538101i | \(-0.819142\pi\) | ||||
−0.842881 | + | 0.538101i | \(0.819142\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −276.506 | −0.335973 | −0.167987 | − | 0.985789i | \(-0.553727\pi\) | ||||
−0.167987 | + | 0.985789i | \(0.553727\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 196.160i | 0.237769i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1467.81 | −1.77486 | −0.887431 | − | 0.460940i | \(-0.847512\pi\) | ||||
−0.887431 | + | 0.460940i | \(0.847512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 78.7343i | 0.0949750i | 0.998872 | + | 0.0474875i | \(0.0151214\pi\) | ||||
−0.998872 | + | 0.0474875i | \(0.984879\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.1166i | 0.0579021i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −314.638 | −0.376812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 145.681 | 0.174051 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 591.398i | 0.704884i | 0.935834 | + | 0.352442i | \(0.114649\pi\) | ||||
−0.935834 | + | 0.352442i | \(0.885351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −656.220 | −0.780285 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 106.511i | 0.126348i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 576.911i | − 0.682735i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −76.0214 | −0.0895423 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1166.24 | −1.37044 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1048.80i | 1.22954i | 0.788707 | + | 0.614770i | \(0.210751\pi\) | ||||
−0.788707 | + | 0.614770i | \(0.789249\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 399.362 | 0.467090 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 107.171i | 0.125054i | 0.998043 | + | 0.0625271i | \(0.0199160\pi\) | ||||
−0.998043 | + | 0.0625271i | \(0.980084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1506.32i | − 1.75358i | −0.480874 | − | 0.876790i | \(-0.659680\pi\) | ||||
0.480874 | − | 0.876790i | \(-0.340320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −375.362 | −0.434950 | −0.217475 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217475 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1324.09 | −1.53073 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 367.404i | 0.423764i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1022.52 | 1.17666 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 348.415i | − 0.400017i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 102.457i | 0.117362i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1408.79 | 1.60637 | 0.803187 | − | 0.595727i | \(-0.203136\pi\) | ||||
0.803187 | + | 0.595727i | \(0.203136\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 387.286 | 0.440598 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1236.04i | 1.40299i | 0.712673 | + | 0.701497i | \(0.247485\pi\) | ||||
−0.712673 | + | 0.701497i | \(0.752515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 72.9437 | 0.0826089 | 0.0413045 | − | 0.999147i | \(-0.486849\pi\) | ||||
0.0413045 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 585.679i | − 0.661784i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1442.23i | 1.62597i | 0.582287 | + | 0.812983i | \(0.302158\pi\) | ||||
−0.582287 | + | 0.812983i | \(0.697842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 176.340 | 0.197913 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1212.92 | −1.35826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 604.998i | 0.675975i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 254.241 | 0.283435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 381.108i | 0.423925i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 540.056i | − 0.599396i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −363.759 | −0.401943 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1209.76 | 1.33380 | 0.666900 | − | 0.745147i | \(-0.267621\pi\) | ||||
0.666900 | + | 0.745147i | \(0.267621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 392.623i | 0.431928i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1328.22 | 1.45798 | 0.728989 | − | 0.684525i | \(-0.239991\pi\) | ||||
0.728989 | + | 0.684525i | \(0.239991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2681.99i | 2.93756i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3.27529i | − 0.00357955i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 488.858 | 0.531946 | 0.265973 | − | 0.963981i | \(-0.414307\pi\) | ||||
0.265973 | + | 0.963981i | \(0.414307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −115.780 | −0.125711 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 755.707i | − 0.818750i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −280.878 | −0.303651 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 487.943i | 0.526368i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 951.536i | 1.02426i | 0.858908 | + | 0.512129i | \(0.171143\pi\) | ||||
−0.858908 | + | 0.512129i | \(0.828857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.6148 | −0.0542495 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 753.164 | 0.805522 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 309.707i | − 0.330530i | −0.986249 | − | 0.165265i | \(-0.947152\pi\) | ||||
0.986249 | − | 0.165265i | \(-0.0528480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −429.747 | −0.457665 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1172.51i | 1.24602i | 0.782213 | + | 0.623011i | \(0.214091\pi\) | ||||
−0.782213 | + | 0.623011i | \(0.785909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 171.453i | 0.181816i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 724.856 | 0.765424 | 0.382712 | − | 0.923868i | \(-0.374990\pi\) | ||||
0.382712 | + | 0.923868i | \(0.374990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 219.473 | 0.231267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9068i | 0.0230355i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5371 | 0.0288951 | 0.0144476 | − | 0.999896i | \(-0.495401\pi\) | ||||
0.0144476 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 755.403i | 0.790998i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 461.315i | 0.482043i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 174.965 | 0.182066 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −311.901 | −0.323885 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1206.96i | − 1.25074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1279.81 | −1.32349 | −0.661744 | − | 0.749730i | \(-0.730183\pi\) | ||||
−0.661744 | + | 0.749730i | \(0.730183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 461.143i | 0.475896i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1112.77i | 1.14600i | 0.819554 | + | 0.573001i | \(0.194221\pi\) | ||||
−0.819554 | + | 0.573001i | \(0.805779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61.2315 | 0.0628015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −435.759 | −0.446017 | −0.223009 | − | 0.974816i | \(-0.571588\pi\) | ||||
−0.223009 | + | 0.974816i | \(0.571588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 299.092i | − 0.305508i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.3405 | 0.0482574 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 281.556i | 0.286425i | 0.989692 | + | 0.143213i | \(0.0457433\pi\) | ||||
−0.989692 | + | 0.143213i | \(0.954257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 676.490i | 0.686792i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1290.72 | −1.30508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 617.572 | 0.623181 | 0.311590 | − | 0.950217i | \(-0.399138\pi\) | ||||
0.311590 | + | 0.950217i | \(0.399138\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 871.050i | 0.877190i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 823.868 | 0.828008 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1505.63i | − 1.51016i | −0.655634 | − | 0.755079i | \(-0.727599\pi\) | ||||
0.655634 | − | 0.755079i | \(-0.272401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 252.499i | 0.252751i |
(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 | 2352.3.f.f.97.3 | 4 | ||
4.3 | odd | 2 | 588.3.d.b.97.1 | 4 | |||
7.4 | even | 3 | 336.3.bh.f.145.2 | 4 | |||
7.5 | odd | 6 | 336.3.bh.f.241.2 | 4 | |||
7.6 | odd | 2 | inner | 2352.3.f.f.97.2 | 4 | ||
12.11 | even | 2 | 1764.3.d.f.685.3 | 4 | |||
21.5 | even | 6 | 1008.3.cg.m.577.1 | 4 | |||
21.11 | odd | 6 | 1008.3.cg.m.145.1 | 4 | |||
28.3 | even | 6 | 588.3.m.d.313.1 | 4 | |||
28.11 | odd | 6 | 84.3.m.b.61.2 | ✓ | 4 | ||
28.19 | even | 6 | 84.3.m.b.73.2 | yes | 4 | ||
28.23 | odd | 6 | 588.3.m.d.325.1 | 4 | |||
28.27 | even | 2 | 588.3.d.b.97.4 | 4 | |||
84.11 | even | 6 | 252.3.z.e.145.1 | 4 | |||
84.23 | even | 6 | 1764.3.z.h.325.2 | 4 | |||
84.47 | odd | 6 | 252.3.z.e.73.1 | 4 | |||
84.59 | odd | 6 | 1764.3.z.h.901.2 | 4 | |||
84.83 | odd | 2 | 1764.3.d.f.685.2 | 4 | |||
140.19 | even | 6 | 2100.3.bd.f.1501.2 | 4 | |||
140.39 | odd | 6 | 2100.3.bd.f.901.1 | 4 | |||
140.47 | odd | 12 | 2100.3.be.d.1249.2 | 8 | |||
140.67 | even | 12 | 2100.3.be.d.649.3 | 8 | |||
140.103 | odd | 12 | 2100.3.be.d.1249.3 | 8 | |||
140.123 | even | 12 | 2100.3.be.d.649.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.m.b.61.2 | ✓ | 4 | 28.11 | odd | 6 | ||
84.3.m.b.73.2 | yes | 4 | 28.19 | even | 6 | ||
252.3.z.e.73.1 | 4 | 84.47 | odd | 6 | |||
252.3.z.e.145.1 | 4 | 84.11 | even | 6 | |||
336.3.bh.f.145.2 | 4 | 7.4 | even | 3 | |||
336.3.bh.f.241.2 | 4 | 7.5 | odd | 6 | |||
588.3.d.b.97.1 | 4 | 4.3 | odd | 2 | |||
588.3.d.b.97.4 | 4 | 28.27 | even | 2 | |||
588.3.m.d.313.1 | 4 | 28.3 | even | 6 | |||
588.3.m.d.325.1 | 4 | 28.23 | odd | 6 | |||
1008.3.cg.m.145.1 | 4 | 21.11 | odd | 6 | |||
1008.3.cg.m.577.1 | 4 | 21.5 | even | 6 | |||
1764.3.d.f.685.2 | 4 | 84.83 | odd | 2 | |||
1764.3.d.f.685.3 | 4 | 12.11 | even | 2 | |||
1764.3.z.h.325.2 | 4 | 84.23 | even | 6 | |||
1764.3.z.h.901.2 | 4 | 84.59 | odd | 6 | |||
2100.3.bd.f.901.1 | 4 | 140.39 | odd | 6 | |||
2100.3.bd.f.1501.2 | 4 | 140.19 | even | 6 | |||
2100.3.be.d.649.2 | 8 | 140.123 | even | 12 | |||
2100.3.be.d.649.3 | 8 | 140.67 | even | 12 | |||
2100.3.be.d.1249.2 | 8 | 140.47 | odd | 12 | |||
2100.3.be.d.1249.3 | 8 | 140.103 | odd | 12 | |||
2352.3.f.f.97.2 | 4 | 7.6 | odd | 2 | inner | ||
2352.3.f.f.97.3 | 4 | 1.1 | even | 1 | trivial |