Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.5 | ||
Root | \(1.96139 + 0.391068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.d.161.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.164573 | − | 2.99548i | 0.0548575 | − | 0.998494i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.61305 | − | 3.61305i | 0.722609 | − | 0.722609i | −0.246527 | − | 0.969136i | \(-0.579289\pi\) |
0.969136 | + | 0.246527i | \(0.0792893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 12.2792i | − | 1.75417i | −0.480338 | − | 0.877083i | \(-0.659486\pi\) | ||
0.480338 | − | 0.877083i | \(-0.340514\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.94583 | − | 0.985948i | −0.993981 | − | 0.109550i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.76932 | + | 1.76932i | −0.160847 | + | 0.160847i | −0.782942 | − | 0.622095i | \(-0.786282\pi\) |
0.622095 | + | 0.782942i | \(0.286282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38826 | − | 2.38826i | 0.183713 | − | 0.183713i | −0.609259 | − | 0.792971i | \(-0.708533\pi\) |
0.792971 | + | 0.609259i | \(0.208533\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.2282 | − | 11.4174i | −0.681881 | − | 0.761162i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 20.0754i | 1.18091i | 0.807072 | + | 0.590453i | \(0.201051\pi\) | ||||
−0.807072 | + | 0.590453i | \(0.798949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.77090 | − | 8.77090i | 0.461626 | − | 0.461626i | −0.437562 | − | 0.899188i | \(-0.644158\pi\) |
0.899188 | + | 0.437562i | \(0.144158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −36.7820 | − | 2.02081i | −1.75153 | − | 0.0962292i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.1821 | −0.573134 | −0.286567 | − | 0.958060i | \(-0.592514\pi\) | ||||
−0.286567 | + | 0.958060i | \(0.592514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.10820i | − | 0.0443281i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.42563 | + | 26.6348i | −0.163912 | + | 0.986475i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.51544 | + | 6.51544i | 0.224670 | + | 0.224670i | 0.810462 | − | 0.585792i | \(-0.199216\pi\) |
−0.585792 | + | 0.810462i | \(0.699216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 37.5922 | 1.21265 | 0.606326 | − | 0.795216i | \(-0.292643\pi\) | ||||
0.606326 | + | 0.795216i | \(0.292643\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.00877 | + | 5.59113i | 0.151781 | + | 0.169428i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −44.3652 | − | 44.3652i | −1.26758 | − | 1.26758i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0057 | − | 10.0057i | −0.270423 | − | 0.270423i | 0.558847 | − | 0.829271i | \(-0.311244\pi\) |
−0.829271 | + | 0.558847i | \(0.811244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.76096 | − | 7.54704i | −0.173358 | − | 0.193514i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.57407 | −0.111563 | −0.0557814 | − | 0.998443i | \(-0.517765\pi\) | ||||
−0.0557814 | + | 0.998443i | \(0.517765\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.2835 | − | 21.2835i | −0.494966 | − | 0.494966i | 0.414901 | − | 0.909867i | \(-0.363816\pi\) |
−0.909867 | + | 0.414901i | \(0.863816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −35.8840 | + | 28.7594i | −0.797422 | + | 0.639098i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 54.8366i | − | 1.16674i | −0.812208 | − | 0.583368i | \(-0.801734\pi\) | ||
0.812208 | − | 0.583368i | \(-0.198266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −101.778 | −2.07710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 60.1356 | + | 3.30386i | 1.17913 | + | 0.0647816i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −21.5215 | + | 21.5215i | −0.406065 | + | 0.406065i | −0.880364 | − | 0.474299i | \(-0.842702\pi\) |
0.474299 | + | 0.880364i | \(0.342702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.7852i | 0.232459i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.8296 | − | 27.7165i | −0.435607 | − | 0.486255i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 53.6617 | − | 53.6617i | 0.909520 | − | 0.909520i | −0.0867132 | − | 0.996233i | \(-0.527636\pi\) |
0.996233 | + | 0.0867132i | \(0.0276364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.2186 | − | 19.2186i | 0.315059 | − | 0.315059i | −0.531807 | − | 0.846866i | \(-0.678487\pi\) |
0.846866 | + | 0.531807i | \(0.178487\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.1066 | + | 109.847i | −0.192169 | + | 1.74361i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 17.2578i | − | 0.265505i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.5603 | + | 31.5603i | −0.471049 | + | 0.471049i | −0.902254 | − | 0.431205i | \(-0.858089\pi\) |
0.431205 | + | 0.902254i | \(0.358089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.16941 | + | 39.4867i | −0.0314407 | + | 0.572271i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −65.1220 | −0.917211 | −0.458606 | − | 0.888640i | \(-0.651651\pi\) | ||||
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 50.2451i | − | 0.688290i | −0.938917 | − | 0.344145i | \(-0.888169\pi\) | ||
0.938917 | − | 0.344145i | \(-0.111831\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.31960 | − | 0.182380i | −0.0442614 | − | 0.00243173i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.7257 | + | 21.7257i | 0.282152 | + | 0.282152i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 20.9299 | 0.264935 | 0.132468 | − | 0.991187i | \(-0.457710\pi\) | ||||
0.132468 | + | 0.991187i | \(0.457710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.0558 | + | 17.6403i | 0.975998 | + | 0.217781i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.35791 | + | 6.35791i | 0.0766013 | + | 0.0766013i | 0.744369 | − | 0.667768i | \(-0.232750\pi\) |
−0.667768 | + | 0.744369i | \(0.732750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.5334 | + | 72.5334i | 0.853334 | + | 0.853334i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.5891 | − | 18.4446i | 0.236657 | − | 0.212007i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 166.399 | 1.86966 | 0.934828 | − | 0.355102i | \(-0.115554\pi\) | ||||
0.934828 | + | 0.355102i | \(0.115554\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.3259 | − | 29.3259i | −0.322262 | − | 0.322262i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.18664 | − | 112.607i | 0.0665231 | − | 1.21083i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 63.3793i | − | 0.667151i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 139.213 | 1.43519 | 0.717593 | − | 0.696463i | \(-0.245244\pi\) | ||||
0.717593 | + | 0.696463i | \(0.245244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.5725 | − | 14.0835i | 0.177500 | − | 0.142258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 125.879 | − | 125.879i | 1.24632 | − | 1.24632i | 0.288994 | − | 0.957331i | \(-0.406679\pi\) |
0.957331 | − | 0.288994i | \(-0.0933207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26.3937i | 0.256250i | 0.991758 | + | 0.128125i | \(0.0408958\pi\) | ||||
−0.991758 | + | 0.128125i | \(0.959104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −140.196 | + | 125.594i | −1.33520 | + | 1.19613i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −83.9534 | + | 83.9534i | −0.784611 | + | 0.784611i | −0.980605 | − | 0.195994i | \(-0.937207\pi\) |
0.195994 | + | 0.980605i | \(0.437207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.29518 | + | 2.29518i | −0.0210567 | + | 0.0210567i | −0.717557 | − | 0.696500i | \(-0.754740\pi\) |
0.696500 | + | 0.717557i | \(0.254740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.6184 | + | 28.3251i | −0.284851 | + | 0.255181i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 177.630i | − | 1.57195i | −0.618260 | − | 0.785974i | \(-0.712162\pi\) | ||
0.618260 | − | 0.785974i | \(-0.287838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −47.6275 | + | 47.6275i | −0.414152 | + | 0.414152i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23.7197 | + | 19.0103i | −0.202733 | + | 0.162481i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 246.509 | 2.07151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.739i | 0.948257i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.752766 | + | 13.7016i | −0.00612005 | + | 0.111395i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 86.3222 | + | 86.3222i | 0.690577 | + | 0.690577i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −152.167 | −1.19816 | −0.599082 | − | 0.800687i | \(-0.704468\pi\) | ||||
−0.599082 | + | 0.800687i | \(0.704468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −67.2571 | + | 60.2517i | −0.521373 | + | 0.467068i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 65.6955 | + | 65.6955i | 0.501492 | + | 0.501492i | 0.911901 | − | 0.410409i | \(-0.134614\pi\) |
−0.410409 | + | 0.911901i | \(0.634614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −107.699 | − | 107.699i | −0.809769 | − | 0.809769i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 80.2428 | + | 112.223i | 0.594391 | + | 0.831280i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 53.1509 | 0.387963 | 0.193982 | − | 0.981005i | \(-0.437860\pi\) | ||||
0.193982 | + | 0.981005i | \(0.437860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 161.324 | + | 161.324i | 1.16060 | + | 1.16060i | 0.984343 | + | 0.176261i | \(0.0564004\pi\) |
0.176261 | + | 0.984343i | \(0.443600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −164.262 | − | 9.02460i | −1.16498 | − | 0.0640043i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.45118i | 0.0590992i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 47.0811 | 0.324698 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.7498 | + | 304.874i | −0.113945 | + | 2.07397i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 116.911 | − | 116.911i | 0.784638 | − | 0.784638i | −0.195971 | − | 0.980610i | \(-0.562786\pi\) |
0.980610 | + | 0.195971i | \(0.0627859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9723i | 0.0726643i | 0.999340 | + | 0.0363321i | \(0.0115674\pi\) | ||||
−0.999340 | + | 0.0363321i | \(0.988433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.7933 | − | 179.591i | 0.129368 | − | 1.17380i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 135.822 | − | 135.822i | 0.876273 | − | 0.876273i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −49.8246 | + | 49.8246i | −0.317354 | + | 0.317354i | −0.847750 | − | 0.530396i | \(-0.822043\pi\) |
0.530396 | + | 0.847750i | \(0.322043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 60.9253 | + | 68.0090i | 0.383178 | + | 0.427730i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 161.865i | 1.00537i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66.4240 | − | 66.4240i | 0.407509 | − | 0.407509i | −0.473360 | − | 0.880869i | \(-0.656959\pi\) |
0.880869 | + | 0.473360i | \(0.156959\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 38.2980 | + | 2.10410i | 0.232109 | + | 0.0127521i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −182.851 | −1.09492 | −0.547459 | − | 0.836832i | \(-0.684405\pi\) | ||||
−0.547459 | + | 0.836832i | \(0.684405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 157.592i | 0.932499i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −87.1106 | + | 69.8153i | −0.509419 | + | 0.408277i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −123.809 | − | 123.809i | −0.715661 | − | 0.715661i | 0.252052 | − | 0.967714i | \(-0.418894\pi\) |
−0.967714 | + | 0.252052i | \(0.918894\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.6078 | −0.0777589 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −151.911 | − | 169.574i | −0.858257 | − | 0.958045i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −168.642 | − | 168.642i | −0.942134 | − | 0.942134i | 0.0562807 | − | 0.998415i | \(-0.482076\pi\) |
−0.998415 | + | 0.0562807i | \(0.982076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 162.162 | + | 162.162i | 0.895920 | + | 0.895920i | 0.995072 | − | 0.0991520i | \(-0.0316130\pi\) |
−0.0991520 | + | 0.995072i | \(0.531613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −54.4061 | − | 60.7318i | −0.297301 | − | 0.331868i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −72.3018 | −0.390821 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −35.5198 | − | 35.5198i | −0.189945 | − | 0.189945i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 327.053 | + | 54.3430i | 1.73044 | + | 0.287529i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 60.8777i | − | 0.318731i | −0.987220 | − | 0.159366i | \(-0.949055\pi\) | ||
0.987220 | − | 0.159366i | \(-0.0509449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 177.871 | 0.921611 | 0.460806 | − | 0.887501i | \(-0.347561\pi\) | ||||
0.460806 | + | 0.887501i | \(0.347561\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −51.6955 | − | 2.84016i | −0.265105 | − | 0.0145649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −66.9411 | + | 66.9411i | −0.339803 | + | 0.339803i | −0.856293 | − | 0.516490i | \(-0.827238\pi\) |
0.516490 | + | 0.856293i | \(0.327238\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.826328i | 0.00415240i | 0.999998 | + | 0.00207620i | \(0.000660875\pi\) | ||||
−0.999998 | + | 0.00207620i | \(0.999339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 89.3443 | + | 99.7322i | 0.444499 | + | 0.496180i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 80.0041 | − | 80.0041i | 0.394109 | − | 0.394109i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.5263 | + | 16.5263i | −0.0806162 | + | 0.0806162i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 117.925 | + | 12.9969i | 0.569685 | + | 0.0627868i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.0370i | 0.148502i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 181.344 | − | 181.344i | 0.859448 | − | 0.859448i | −0.131825 | − | 0.991273i | \(-0.542084\pi\) |
0.991273 | + | 0.131825i | \(0.0420837\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.7173 | + | 195.072i | −0.0503159 | + | 0.915830i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −153.797 | −0.715333 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 461.601i | − | 2.12719i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −150.508 | − | 8.26897i | −0.687253 | − | 0.0377579i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 47.9454 | + | 47.9454i | 0.216947 | + | 0.216947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7339 | −0.0795241 | −0.0397621 | − | 0.999209i | \(-0.512660\pi\) | ||||
−0.0397621 | + | 0.999209i | \(0.512660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.09263 | + | 9.91380i | −0.00485614 | + | 0.0440613i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.53766 | − | 7.53766i | −0.0332055 | − | 0.0332055i | 0.690309 | − | 0.723515i | \(-0.257475\pi\) |
−0.723515 | + | 0.690309i | \(0.757475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −223.748 | − | 223.748i | −0.977063 | − | 0.977063i | 0.0226794 | − | 0.999743i | \(-0.492780\pi\) |
−0.999743 | + | 0.0226794i | \(0.992780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 68.6545 | − | 61.5036i | 0.297205 | − | 0.266249i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −123.585 | −0.530406 | −0.265203 | − | 0.964193i | \(-0.585439\pi\) | ||||
−0.265203 | + | 0.964193i | \(0.585439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −198.127 | − | 198.127i | −0.843095 | − | 0.843095i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.44448 | − | 62.6951i | 0.0145337 | − | 0.264536i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 118.501i | 0.495820i | 0.968783 | + | 0.247910i | \(0.0797437\pi\) | ||||
−0.968783 | + | 0.247910i | \(0.920256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −264.162 | −1.09611 | −0.548053 | − | 0.836443i | \(-0.684631\pi\) | ||||
−0.548053 | + | 0.836443i | \(0.684631\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 65.8515 | − | 233.907i | 0.270994 | − | 0.962581i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −367.728 | + | 367.728i | −1.50093 | + | 1.50093i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 41.8944i | − | 0.169613i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.0913 | − | 17.9987i | 0.0806881 | − | 0.0722838i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −152.477 | + | 152.477i | −0.607478 | + | 0.607478i | −0.942286 | − | 0.334808i | \(-0.891328\pi\) |
0.334808 | + | 0.942286i | \(0.391328\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.3233 | − | 23.3233i | 0.0921869 | − | 0.0921869i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 229.210 | − | 205.336i | 0.898861 | − | 0.805238i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 113.118i | 0.440147i | 0.975483 | + | 0.220074i | \(0.0706298\pi\) | ||||
−0.975483 | + | 0.220074i | \(0.929370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −122.861 | + | 122.861i | −0.474367 | + | 0.474367i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −51.8621 | − | 64.7099i | −0.198705 | − | 0.247931i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 129.324 | 0.491727 | 0.245864 | − | 0.969304i | \(-0.420928\pi\) | ||||
0.245864 | + | 0.969304i | \(0.420928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 155.516i | 0.586853i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.3848 | − | 498.446i | 0.102565 | − | 1.86684i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −129.457 | − | 129.457i | −0.481253 | − | 0.481253i | 0.424278 | − | 0.905532i | \(-0.360528\pi\) |
−0.905532 | + | 0.424278i | \(0.860528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 170.727 | 0.629990 | 0.314995 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314995 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −92.6714 | + | 83.0189i | −0.339456 | + | 0.304099i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.96076 | + | 1.96076i | 0.00713004 | + | 0.00713004i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −114.051 | − | 114.051i | −0.411737 | − | 0.411737i | 0.470606 | − | 0.882343i | \(-0.344035\pi\) |
−0.882343 | + | 0.470606i | \(0.844035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −336.294 | − | 37.0640i | −1.20535 | − | 0.132846i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 136.468 | 0.485650 | 0.242825 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242825 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 132.657 | + | 132.657i | 0.468752 | + | 0.468752i | 0.901510 | − | 0.432758i | \(-0.142460\pi\) |
−0.432758 | + | 0.901510i | \(0.642460\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −189.852 | − | 10.4305i | −0.666146 | − | 0.0365982i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 56.1658i | 0.195700i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −114.022 | −0.394541 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.9106 | − | 417.010i | 0.0787307 | − | 1.43303i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 143.968 | − | 143.968i | 0.491360 | − | 0.491360i | −0.417375 | − | 0.908735i | \(-0.637050\pi\) |
0.908735 | + | 0.417375i | \(0.137050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 387.764i | − | 1.31446i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −39.2951 | − | 54.9557i | −0.132307 | − | 0.185036i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.4823 | + | 31.4823i | −0.105292 | + | 0.105292i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −261.344 | + | 261.344i | −0.868252 | + | 0.868252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −356.352 | − | 397.784i | −1.17608 | − | 1.31282i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 138.875i | − | 0.455328i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 89.3258 | − | 89.3258i | 0.290964 | − | 0.290964i | −0.546497 | − | 0.837461i | \(-0.684039\pi\) |
0.837461 | + | 0.546497i | \(0.184039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 79.0619 | + | 4.34368i | 0.255864 | + | 0.0140572i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −314.507 | −1.01128 | −0.505638 | − | 0.862746i | \(-0.668743\pi\) | ||||
−0.505638 | + | 0.862746i | \(0.668743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 103.874i | − | 0.331867i | −0.986137 | − | 0.165934i | \(-0.946936\pi\) | ||
0.986137 | − | 0.165934i | \(-0.0530638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 353.142 | + | 440.625i | 1.12108 | + | 1.39881i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 321.109 | + | 321.109i | 1.01296 | + | 1.01296i | 0.999915 | + | 0.0130482i | \(0.00415349\pi\) |
0.0130482 | + | 0.999915i | \(0.495847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.0557 | −0.0722750 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 237.665 | + | 265.297i | 0.740388 | + | 0.826472i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 176.079 | + | 176.079i | 0.545138 | + | 0.545138i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.64668 | − | 2.64668i | −0.00814363 | − | 0.00814363i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.49746 | + | 7.25291i | 0.0198699 | + | 0.0221801i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −673.348 | −2.04665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 313.858 | + | 313.858i | 0.948213 | + | 0.948213i | 0.998724 | − | 0.0505107i | \(-0.0160849\pi\) |
−0.0505107 | + | 0.998724i | \(0.516085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 79.6439 | + | 99.3740i | 0.239171 | + | 0.298420i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 228.057i | 0.680768i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −236.028 | −0.700380 | −0.350190 | − | 0.936679i | \(-0.613883\pi\) | ||||
−0.350190 | + | 0.936679i | \(0.613883\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −532.088 | − | 29.2330i | −1.56958 | − | 0.0862331i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −66.5125 | + | 66.5125i | −0.195051 | + | 0.195051i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 648.069i | 1.88941i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 134.829 | + | 150.506i | 0.390809 | + | 0.436248i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −441.946 | + | 441.946i | −1.27362 | + | 1.27362i | −0.329445 | + | 0.944175i | \(0.606862\pi\) |
−0.944175 | + | 0.329445i | \(0.893138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 476.643 | − | 476.643i | 1.36574 | − | 1.36574i | 0.499321 | − | 0.866417i | \(-0.333583\pi\) |
0.866417 | − | 0.499321i | \(-0.166417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53.0414 | + | 74.1805i | 0.151115 | + | 0.211341i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 452.246i | 1.28115i | 0.767895 | + | 0.640575i | \(0.221304\pi\) | ||||
−0.767895 | + | 0.640575i | \(0.778696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −235.289 | + | 235.289i | −0.662785 | + | 0.662785i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 40.5687 | − | 738.415i | 0.113638 | − | 2.06839i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 617.295 | 1.71948 | 0.859742 | − | 0.510728i | \(-0.170624\pi\) | ||||
0.859742 | + | 0.510728i | \(0.170624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 207.143i | 0.573803i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 343.699 | + | 18.8829i | 0.946829 | + | 0.0520190i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −181.538 | − | 181.538i | −0.497364 | − | 0.497364i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3588 | −0.0309505 | −0.0154753 | − | 0.999880i | \(-0.504926\pi\) | ||||
−0.0154753 | + | 0.999880i | \(0.504926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40.9189 | + | 4.50980i | 0.110891 | + | 0.0122217i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 264.266 | + | 264.266i | 0.712306 | + | 0.712306i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 59.4092 | + | 59.4092i | 0.159274 | + | 0.159274i | 0.782245 | − | 0.622971i | \(-0.214075\pi\) |
−0.622971 | + | 0.782245i | \(0.714075\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 272.783 | − | 244.370i | 0.727421 | − | 0.651654i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.1212 | 0.0825495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −435.432 | − | 435.432i | −1.14890 | − | 1.14890i | −0.986770 | − | 0.162129i | \(-0.948164\pi\) |
−0.162129 | − | 0.986770i | \(-0.551836\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.0425 | + | 455.813i | −0.0657283 | + | 1.19636i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 272.117i | − | 0.710488i | −0.934774 | − | 0.355244i | \(-0.884398\pi\) | ||
0.934774 | − | 0.355244i | \(-0.115602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 156.992 | 0.407772 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 169.414 | + | 211.383i | 0.437763 | + | 0.546210i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −260.985 | + | 260.985i | −0.670913 | + | 0.670913i | −0.957927 | − | 0.287013i | \(-0.907338\pi\) |
0.287013 | + | 0.957927i | \(0.407338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 264.636i | − | 0.676818i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 207.601 | − | 185.978i | 0.528248 | − | 0.473226i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 75.6206 | − | 75.6206i | 0.191445 | − | 0.191445i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −258.248 | + | 258.248i | −0.650500 | + | 0.650500i | −0.953113 | − | 0.302614i | \(-0.902141\pi\) |
0.302614 | + | 0.953113i | \(0.402141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −340.336 | + | 304.887i | −0.852972 | + | 0.764128i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 430.073i | − | 1.07250i | −0.844059 | − | 0.536250i | \(-0.819840\pi\) | ||
0.844059 | − | 0.536250i | \(-0.180160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 89.7801 | − | 89.7801i | 0.222779 | − | 0.222779i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 349.367 | − | 221.897i | 0.862635 | − | 0.547894i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.4063 | 0.0869935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 207.501i | 0.507337i | 0.967291 | + | 0.253668i | \(0.0816372\pi\) | ||||
−0.967291 | + | 0.253668i | \(0.918363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.74718 | − | 159.213i | 0.0212827 | − | 0.387379i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −658.921 | − | 658.921i | −1.59545 | − | 1.59545i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.9428 | 0.110706 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 509.793 | − | 456.694i | 1.22253 | − | 1.09519i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 108.717 | + | 108.717i | 0.259467 | + | 0.259467i | 0.824837 | − | 0.565370i | \(-0.191267\pi\) |
−0.565370 | + | 0.824837i | \(0.691267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 484.985 | + | 484.985i | 1.15198 | + | 1.15198i | 0.986155 | + | 0.165829i | \(0.0530300\pi\) |
0.165829 | + | 0.986155i | \(0.446970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −54.0661 | + | 490.559i | −0.127816 | + | 1.15971i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.2476 | 0.0523474 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −235.988 | − | 235.988i | −0.552665 | − | 0.552665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.3154 | + | 1.39083i | 0.0590102 | + | 0.00324203i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 213.570i | 0.495522i | 0.968821 | + | 0.247761i | \(0.0796947\pi\) | ||||
−0.968821 | + | 0.247761i | \(0.920305\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 440.669 | 1.01771 | 0.508856 | − | 0.860852i | \(-0.330069\pi\) | ||||
0.508856 | + | 0.860852i | \(0.330069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.74826 | − | 141.031i | 0.0178121 | − | 0.324209i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −115.619 | + | 115.619i | −0.264574 | + | 0.264574i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 400.367i | − | 0.911998i | −0.889980 | − | 0.455999i | \(-0.849282\pi\) | ||
0.889980 | − | 0.455999i | \(-0.150718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 910.488 | + | 100.348i | 2.06460 | + | 0.227546i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 324.076 | − | 324.076i | 0.731549 | − | 0.731549i | −0.239378 | − | 0.970926i | \(-0.576943\pi\) |
0.970926 | + | 0.239378i | \(0.0769435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 601.208 | − | 601.208i | 1.35103 | − | 1.35103i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −330.965 | − | 369.446i | −0.740414 | − | 0.826500i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 691.918i | − | 1.54102i | −0.637427 | − | 0.770510i | \(-0.720001\pi\) | ||
0.637427 | − | 0.770510i | \(-0.279999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.09298 | − | 8.09298i | 0.0179445 | − | 0.0179445i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.8674 | + | 1.80574i | 0.0725549 | + | 0.00398618i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −211.912 | −0.465740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 385.436i | 0.843404i | 0.906734 | + | 0.421702i | \(0.138567\pi\) | ||||
−0.906734 | + | 0.421702i | \(0.861433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −534.705 | − | 88.8463i | −1.16494 | − | 0.193565i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 312.070 | + | 312.070i | 0.676942 | + | 0.676942i | 0.959307 | − | 0.282365i | \(-0.0911190\pi\) |
−0.282365 | + | 0.959307i | \(0.591119\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 718.961 | 1.55283 | 0.776416 | − | 0.630220i | \(-0.217035\pi\) | ||||
0.776416 | + | 0.630220i | \(0.217035\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −384.501 | − | 429.206i | −0.826884 | − | 0.923024i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 82.7894 | + | 82.7894i | 0.177279 | + | 0.177279i | 0.790169 | − | 0.612889i | \(-0.209993\pi\) |
−0.612889 | + | 0.790169i | \(0.709993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 387.534 | + | 387.534i | 0.826298 | + | 0.826298i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 141.049 | + | 157.448i | 0.299467 | + | 0.334285i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 75.3145 | 0.159227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.71993 | − | 9.71993i | −0.0204630 | − | 0.0204630i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 213.746 | − | 171.308i | 0.448106 | − | 0.359137i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 749.099i | 1.56388i | 0.623353 | + | 0.781941i | \(0.285770\pi\) | ||||
−0.623353 | + | 0.781941i | \(0.714230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −47.7923 | −0.0993603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 484.864 | + | 26.6385i | 1.00386 | + | 0.0551523i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 502.983 | − | 502.983i | 1.03708 | − | 1.03708i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 533.210i | 1.09489i | 0.836843 | + | 0.547443i | \(0.184399\pi\) | ||||
−0.836843 | + | 0.547443i | \(0.815601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −188.040 | − | 209.904i | −0.384541 | − | 0.429251i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.75013 | − | 6.75013i | 0.0137477 | − | 0.0137477i | −0.700200 | − | 0.713947i | \(-0.746906\pi\) |
0.713947 | + | 0.700200i | \(0.246906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −130.800 | + | 130.800i | −0.265315 | + | 0.265315i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.6056 | − | 114.375i | 0.0254658 | − | 0.231060i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 799.644i | 1.60894i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −556.347 | + | 556.347i | −1.11492 | + | 1.11492i | −0.122448 | + | 0.992475i | \(0.539075\pi\) |
−0.992475 | + | 0.122448i | \(0.960925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.0923 | + | 547.728i | −0.0600645 | + | 1.09327i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 304.892 | 0.606147 | 0.303074 | − | 0.952967i | \(-0.401987\pi\) | ||||
0.303074 | + | 0.952967i | \(0.401987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 909.612i | − | 1.80121i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 472.065 | + | 25.9354i | 0.931095 | + | 0.0511546i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 118.591 | + | 118.591i | 0.232988 | + | 0.232988i | 0.813939 | − | 0.580951i | \(-0.197319\pi\) |
−0.580951 | + | 0.813939i | \(0.697319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −616.968 | −1.20737 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 194.795 | + | 272.428i | 0.379716 | + | 0.531049i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 95.3617 | + | 95.3617i | 0.185168 | + | 0.185168i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 97.0233 | + | 97.0233i | 0.187666 | + | 0.187666i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −391.244 | + | 350.493i | −0.753843 | + | 0.675324i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −105.077 | −0.201683 | −0.100842 | − | 0.994902i | \(-0.532154\pi\) | ||||
−0.100842 | + | 0.994902i | \(0.532154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 479.455 | + | 479.455i | 0.916740 | + | 0.916740i | 0.996791 | − | 0.0800507i | \(-0.0255082\pi\) |
−0.0800507 | + | 0.996791i | \(0.525508\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.23947 | + | 40.7619i | −0.00426566 | + | 0.0776418i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 754.679i | 1.43203i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −355.232 | −0.671517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −532.956 | + | 427.141i | −1.00368 | + | 0.804408i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9241 | + | 10.9241i | −0.0204955 | + | 0.0204955i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 606.655i | 1.13393i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −532.918 | + | 477.410i | −0.992399 | + | 0.889032i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 180.077 | − | 180.077i | 0.334095 | − | 0.334095i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −726.230 | + | 726.230i | −1.34238 | + | 1.34238i | −0.448704 | + | 0.893680i | \(0.648114\pi\) |
−0.893680 | + | 0.448704i | \(0.851886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 512.439 | − | 459.065i | 0.943719 | − | 0.845423i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.5852i | 0.0304316i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −314.507 | + | 314.507i | −0.574966 | + | 0.574966i | −0.933512 | − | 0.358546i | \(-0.883273\pi\) |
0.358546 | + | 0.933512i | \(0.383273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −190.875 | + | 152.978i | −0.347677 | + | 0.278648i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 114.292 | 0.207427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 257.002i | − | 0.464741i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.8989 | + | 216.579i | −0.0214394 | + | 0.390232i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −134.274 | − | 134.274i | −0.241066 | − | 0.241066i | 0.576225 | − | 0.817291i | \(-0.304525\pi\) |
−0.817291 | + | 0.576225i | \(0.804525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −101.661 | −0.181863 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −112.244 | + | 100.553i | −0.200079 | + | 0.179239i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −102.810 | − | 102.810i | −0.182612 | − | 0.182612i | 0.609881 | − | 0.792493i | \(-0.291217\pi\) |
−0.792493 | + | 0.609881i | \(0.791217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −641.785 | − | 641.785i | −1.13590 | − | 1.13590i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 216.608 | − | 970.739i | 0.382024 | − | 1.71206i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 78.4572 | 0.137886 | 0.0689430 | − | 0.997621i | \(-0.478037\pi\) | ||||
0.0689430 | + | 0.997621i | \(0.478037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −363.164 | − | 363.164i | −0.636013 | − | 0.636013i | 0.313556 | − | 0.949570i | \(-0.398480\pi\) |
−0.949570 | + | 0.313556i | \(0.898480\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −182.358 | − | 10.0188i | −0.318251 | − | 0.0174848i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.6084i | 0.0254060i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −566.880 | −0.982460 | −0.491230 | − | 0.871030i | \(-0.663453\pi\) | ||||
−0.491230 | + | 0.871030i | \(0.663453\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.2727 | − | 532.809i | 0.0505573 | − | 0.920223i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 78.0698 | − | 78.0698i | 0.134371 | − | 0.134371i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 76.1565i | − | 0.130629i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.0153 | + | 154.385i | −0.0290860 | + | 0.263907i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −73.3693 | + | 73.3693i | −0.124990 | + | 0.124990i | −0.766835 | − | 0.641845i | \(-0.778169\pi\) |
0.641845 | + | 0.766835i | \(0.278169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 329.717 | − | 329.717i | 0.559792 | − | 0.559792i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 189.504 | + | 211.538i | 0.320650 | + | 0.357932i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 458.708i | − | 0.773538i | −0.922177 | − | 0.386769i | \(-0.873591\pi\) | ||
0.922177 | − | 0.386769i | \(-0.126409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 890.650 | − | 890.650i | 1.49689 | − | 1.49689i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.47525 | + | 0.135991i | 0.00414615 | + | 0.000227790i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −423.611 | −0.707197 | −0.353599 | − | 0.935397i | \(-0.615042\pi\) | ||||
−0.353599 | + | 0.935397i | \(0.615042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 795.376i | 1.32342i | 0.749759 | + | 0.661711i | \(0.230169\pi\) | ||||
−0.749759 | + | 0.661711i | \(0.769831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 313.450 | − | 251.216i | 0.519817 | − | 0.416610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 414.557 | + | 414.557i | 0.685219 | + | 0.685219i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −631.699 | −1.04069 | −0.520345 | − | 0.853956i | \(-0.674197\pi\) | ||||
−0.520345 | + | 0.853956i | \(0.674197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −226.484 | − | 252.817i | −0.371896 | − | 0.415135i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −130.964 | − | 130.964i | −0.214344 | − | 0.214344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −385.264 | − | 385.264i | −0.628490 | − | 0.628490i | 0.319198 | − | 0.947688i | \(-0.396586\pi\) |
−0.947688 | + | 0.319198i | \(0.896586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 46.7846 | + | 52.2241i | 0.0760724 | + | 0.0849173i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 953.333 | 1.54511 | 0.772555 | − | 0.634947i | \(-0.218978\pi\) | ||||
0.772555 | + | 0.634947i | \(0.218978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 574.046 | + | 574.046i | 0.927377 | + | 0.927377i | 0.997536 | − | 0.0701591i | \(-0.0223507\pi\) |
−0.0701591 | + | 0.997536i | \(0.522351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 58.3390 | − | 351.103i | 0.0939437 | − | 0.565383i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2043.24i | − | 3.27969i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 651.477 | 1.04236 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 92.9707 | + | 5.10783i | 0.148279 | + | 0.00814646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 200.868 | − | 200.868i | 0.319345 | − | 0.319345i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 138.048i | − | 0.218777i | −0.993999 | − | 0.109389i | \(-0.965111\pi\) | ||
0.993999 | − | 0.109389i | \(-0.0348893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −513.367 | − | 573.056i | −0.811007 | − | 0.905301i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −549.786 | + | 549.786i | −0.865805 | + | 0.865805i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −243.072 | + | 243.072i | −0.381589 | + | 0.381589i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 582.570 | + | 64.2069i | 0.911691 | + | 0.100480i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 784.889i | 1.22448i | 0.790673 | + | 0.612238i | \(0.209731\pi\) | ||||
−0.790673 | + | 0.612238i | \(0.790269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 238.456 | − | 238.456i | 0.370850 | − | 0.370850i | −0.496937 | − | 0.867787i | \(-0.665542\pi\) |
0.867787 | + | 0.496937i | \(0.165542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.3107 | + | 460.695i | −0.0392414 | + | 0.714256i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −681.751 | −1.05371 | −0.526855 | − | 0.849955i | \(-0.676629\pi\) | ||||
−0.526855 | + | 0.849955i | \(0.676629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 189.889i | 0.292587i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1382.72 | − | 75.9668i | −2.12399 | − | 0.116693i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −636.071 | − | 636.071i | −0.974075 | − | 0.974075i | 0.0255977 | − | 0.999672i | \(-0.491851\pi\) |
−0.999672 | + | 0.0255977i | \(0.991851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 474.721 | 0.724766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49.5391 | + | 449.485i | −0.0754020 | + | 0.684147i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 91.6052 | + | 91.6052i | 0.139006 | + | 0.139006i | 0.773186 | − | 0.634179i | \(-0.218662\pi\) |
−0.634179 | + | 0.773186i | \(0.718662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −721.715 | − | 721.715i | −1.09185 | − | 1.09185i | −0.995331 | − | 0.0965216i | \(-0.969228\pi\) |
−0.0965216 | − | 0.995331i | \(-0.530772\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 151.510 | − | 135.729i | 0.228522 | − | 0.204720i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −778.245 | −1.17029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −85.8871 | − | 85.8871i | −0.128766 | − | 0.128766i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.91851 | + | 53.1215i | −0.00436250 | + | 0.0794044i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.0074i | 0.101352i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 417.305 | 0.620067 | 0.310033 | − | 0.950726i | \(-0.399660\pi\) | ||||
0.310033 | + | 0.950726i | \(0.399660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 29.5168 | + | 4.90449i | 0.0437286 | + | 0.00726592i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −585.326 | + | 585.326i | −0.864587 | + | 0.864587i | −0.991867 | − | 0.127280i | \(-0.959375\pi\) |
0.127280 | + | 0.991867i | \(0.459375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1709.42i | − | 2.51756i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.8194 | + | 21.3384i | −0.0349771 | + | 0.0313340i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 104.261 | − | 104.261i | 0.152651 | − | 0.152651i | −0.626650 | − | 0.779301i | \(-0.715574\pi\) |
0.779301 | + | 0.626650i | \(0.215574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 192.037 | − | 192.037i | 0.280346 | − | 0.280346i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −707.054 | + | 633.409i | −1.02919 | + | 0.921993i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 102.798i | 0.149199i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 335.701 | − | 335.701i | 0.485818 | − | 0.485818i | −0.421165 | − | 0.906984i | \(-0.638379\pi\) |
0.906984 | + | 0.421165i | \(0.138379\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −172.934 | − | 215.775i | −0.249544 | − | 0.311364i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1165.74 | 1.67733 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 91.8264i | − | 0.131745i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3386 | + | 370.196i | −0.0290968 | + | 0.529608i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 490.458 | + | 490.458i | 0.699655 | + | 0.699655i | 0.964336 | − | 0.264681i | \(-0.0852666\pi\) |
−0.264681 | + | 0.964336i | \(0.585267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −175.517 | −0.249669 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −626.093 | + | 560.881i | −0.888075 | + | 0.795575i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1545.69 | − | 1545.69i | −2.18626 | − | 2.18626i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −435.817 | − | 435.817i | −0.614692 | − | 0.614692i | 0.329473 | − | 0.944165i | \(-0.393129\pi\) |
−0.944165 | + | 0.329473i | \(0.893129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −187.235 | − | 20.6358i | −0.263341 | − | 0.0290236i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −495.544 | −0.695012 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.5345 | + | 30.5345i | 0.0427056 | + | 0.0427056i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 354.968 | + | 19.5020i | 0.495073 | + | 0.0271994i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1083.05i | − | 1.50633i | −0.657831 | − | 0.753166i | \(-0.728526\pi\) | ||
0.657831 | − | 0.753166i | \(-0.271474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 324.093 | 0.449505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.4738 | + | 791.292i | −0.0601297 | + | 1.09446i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.22042 | − | 7.22042i | 0.00995921 | − | 0.00995921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 513.215i | 0.705935i | 0.935636 | + | 0.352968i | \(0.114827\pi\) | ||||
−0.935636 | + | 0.352968i | \(0.885173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −689.828 | − | 235.752i | −0.946266 | − | 0.323390i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 427.276 | − | 427.276i | 0.584508 | − | 0.584508i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −73.6001 | + | 73.6001i | −0.100409 | + | 0.100409i | −0.755527 | − | 0.655118i | \(-0.772619\pi\) |
0.655118 | + | 0.755527i | \(0.272619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1041.01 | + | 1162.04i | 1.41633 | + | 1.58101i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 111.680i | − | 0.151533i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −152.386 | + | 152.386i | −0.206206 | + | 0.206206i | −0.802653 | − | 0.596447i | \(-0.796579\pi\) |
0.596447 | + | 0.802653i | \(0.296579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −125.494 | − | 6.89467i | −0.169358 | − | 0.00930455i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −574.044 | −0.772603 | −0.386302 | − | 0.922373i | \(-0.626248\pi\) | ||||
−0.386302 | + | 0.922373i | \(0.626248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 844.811i | − | 1.13397i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.6082 | − | 63.1454i | −0.0677486 | − | 0.0845319i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1030.88 | + | 1030.88i | 1.37634 | + | 1.37634i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1014.28 | −1.35058 | −0.675289 | − | 0.737553i | \(-0.735981\pi\) | ||||
−0.675289 | + | 0.737553i | \(0.735981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 431.649 | + | 481.836i | 0.573239 | + | 0.639888i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.6435 | + | 39.6435i | 0.0525079 | + | 0.0525079i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1003.73 | + | 1003.73i | 1.32594 | + | 1.32594i | 0.908880 | + | 0.417057i | \(0.136938\pi\) |
0.417057 | + | 0.908880i | \(0.363062\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −66.0261 | − | 73.7028i | −0.0869909 | − | 0.0971052i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.1069 | 0.0710997 | 0.0355499 | − | 0.999368i | \(-0.488682\pi\) | ||||
0.0355499 | + | 0.999368i | \(0.488682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.1829 | + | 28.1829i | 0.0369370 | + | 0.0369370i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −577.358 | − | 720.386i | −0.754716 | − | 0.941681i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 256.316i | − | 0.334181i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 143.904 | 0.187132 | 0.0935659 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935659 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 338.843 | + | 18.6161i | 0.439485 | + | 0.0241454i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −339.143 | + | 339.143i | −0.438736 | + | 0.438736i | −0.891586 | − | 0.452850i | \(-0.850407\pi\) |
0.452850 | + | 0.891586i | \(0.350407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 41.6598i | − | 0.0537546i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 347.809 | + | 388.248i | 0.447630 | + | 0.499676i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.1187 | + | 40.1187i | −0.0515003 | + | 0.0515003i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 115.221 | − | 115.221i | 0.147531 | − | 0.147531i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −202.372 | + | 144.703i | −0.258458 | + | 0.184805i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 360.037i | 0.458646i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 924.878 | − | 924.878i | 1.17519 | − | 1.17519i | 0.194241 | − | 0.980954i | \(-0.437776\pi\) |
0.980954 | − | 0.194241i | \(-0.0622243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.2832 | − | 387.389i | 0.0269749 | − | 0.490987i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2181.15 | −2.75746 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 91.7980i | − | 0.115760i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 465.846 | + | 25.5937i | 0.585970 | + | 0.0321933i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −707.837 | − | 707.837i | −0.888127 | − | 0.888127i | 0.106216 | − | 0.994343i | \(-0.466127\pi\) |
−0.994343 | + | 0.106216i | \(0.966127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1100.87 | 1.37781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1488.58 | − | 164.061i | −1.85840 | − | 0.204820i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 88.8995 | + | 88.8995i | 0.110709 | + | 0.110709i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 584.826 | + | 584.826i | 0.726492 | + | 0.726492i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −409.092 | + | 366.482i | −0.506929 | + | 0.454128i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1107.83 | 1.36938 | 0.684689 | − | 0.728836i | \(-0.259938\pi\) | ||||
0.684689 | + | 0.728836i | \(0.259938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −217.697 | − | 217.697i | −0.268431 | − | 0.268431i | 0.560037 | − | 0.828468i | \(-0.310787\pi\) |
−0.828468 | + | 0.560037i | \(0.810787\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.0970 | − | 511.411i | 0.0345597 | − | 0.629042i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 479.986i | − | 0.588940i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −373.351 | −0.456978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 233.431 | + | 291.258i | 0.285019 | + | 0.355627i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 761.374 | − | 761.374i | 0.927374 | − | 0.927374i | −0.0701619 | − | 0.997536i | \(-0.522352\pi\) |
0.997536 | + | 0.0701619i | \(0.0223516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 46.9015i | − | 0.0569884i | −0.999594 | − | 0.0284942i | \(-0.990929\pi\) | ||
0.999594 | − | 0.0284942i | \(-0.00907122\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.19611 | − | 5.55074i | 0.00751044 | − | 0.00672817i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 116.383 | − | 116.383i | 0.140729 | − | 0.140729i | −0.633232 | − | 0.773962i | \(-0.718272\pi\) |
0.773962 | + | 0.633232i | \(0.218272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −821.995 | + | 821.995i | −0.991550 | + | 0.991550i | −0.999965 | − | 0.00841482i | \(-0.997321\pi\) |
0.00841482 | + | 0.999965i | \(0.497321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −360.408 | + | 322.868i | −0.433704 | + | 0.388530i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2043.23i | − | 2.45286i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −660.650 | + | 660.650i | −0.791198 | + | 0.791198i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −166.369 | + | 1001.26i | −0.198768 | + | 1.19625i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1328.92 | 1.58393 | 0.791966 | − | 0.610565i | \(-0.209058\pi\) | ||||
0.791966 | + | 0.610565i | \(0.209058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 756.098i | − | 0.899047i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.4588 | − | 408.786i | 0.0266415 | − | 0.484919i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 569.389 | + | 569.389i | 0.673833 | + | 0.673833i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1408.90 | 1.66340 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 419.203 | − | 375.540i | 0.493761 | − | 0.442332i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 131.896 | + | 131.896i | 0.154989 | + | 0.154989i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 74.3835 | + | 74.3835i | 0.0872022 | + | 0.0872022i | 0.749362 | − | 0.662160i | \(-0.230360\pi\) |
−0.662160 | + | 0.749362i | \(0.730360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −62.4887 | + | 566.981i | −0.0730862 | + | 0.663135i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1113.91 | 1.29977 | 0.649887 | − | 0.760030i | \(-0.274816\pi\) | ||||
0.649887 | + | 0.760030i | \(0.274816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 78.5892 | + | 78.5892i | 0.0914891 | + | 0.0914891i | 0.751370 | − | 0.659881i | \(-0.229393\pi\) |
−0.659881 | + | 0.751370i | \(0.729393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 168.244 | + | 9.24334i | 0.195405 | + | 0.0107356i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 814.226i | 0.943483i | 0.881737 | + | 0.471741i | \(0.156374\pi\) | ||||
−0.881737 | + | 0.471741i | \(0.843626\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −894.658 | −1.03429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.7650 | + | 341.552i | −0.0216436 | + | 0.393947i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.0316 | + | 37.0316i | −0.0426140 | + | 0.0426140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 150.748i | 0.173075i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1245.38 | − | 137.257i | −1.42655 | − | 0.157224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1059.96 | − | 1059.96i | 1.21139 | − | 1.21139i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.8840 | − | 36.8840i | 0.0420571 | − | 0.0420571i | −0.685765 | − | 0.727823i | \(-0.740532\pi\) |
0.727823 | + | 0.685765i | \(0.240532\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −407.562 | − | 454.948i | −0.463665 | − | 0.517575i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 69.7752i | 0.0792000i | 0.999216 | + | 0.0396000i | \(0.0126084\pi\) | ||||
−0.999216 | + | 0.0396000i | \(0.987392\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −410.405 | + | 410.405i | −0.464785 | + | 0.464785i | −0.900220 | − | 0.435435i | \(-0.856594\pi\) |
0.435435 | + | 0.900220i | \(0.356594\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1161.54 | − | 63.8153i | −1.31248 | − | 0.0721077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1290.54 | 1.45495 | 0.727475 | − | 0.686135i | \(-0.240694\pi\) | ||||
0.727475 | + | 0.686135i | \(0.240694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1868.48i | 2.10178i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −171.086 | + | 108.664i | −0.192016 | + | 0.121957i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −480.966 | − | 480.966i | −0.538596 | − | 0.538596i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1218.62 | −1.36159 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 89.1236 | + | 99.4858i | 0.0993574 | + | 0.110909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 244.930 | + | 244.930i | 0.272447 | + | 0.272447i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −432.052 | − | 432.052i | −0.479525 | − | 0.479525i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 739.841 | + | 825.861i | 0.819315 | + | 0.914575i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1171.79 | 1.29480 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −395.420 | − | 395.420i | −0.435964 | − | 0.435964i | 0.454687 | − | 0.890651i | \(-0.349751\pi\) |
−0.890651 | + | 0.454687i | \(0.849751\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1250.20 | + | 1001.98i | −1.37536 | + | 1.10229i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1451.84i | 1.59367i | 0.604195 | + | 0.796837i | \(0.293495\pi\) | ||||
−0.604195 | + | 0.796837i | \(0.706505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.4983 | −0.0246422 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −415.998 | − | 22.8550i | −0.454643 | − | 0.0249782i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 806.686 | − | 806.686i | 0.879701 | − | 0.879701i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1626.08i | 1.76940i | 0.466161 | + | 0.884700i | \(0.345637\pi\) | ||||
−0.466161 | + | 0.884700i | \(0.654363\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −252.873 | − | 282.275i | −0.274564 | − | 0.306487i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −155.528 | + | 155.528i | −0.168503 | + | 0.168503i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0883 | + | 11.0883i | −0.0119874 | + | 0.0119874i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.0228 | − | 236.114i | 0.0280721 | − | 0.254707i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 864.883i | 0.930983i | 0.885052 | + | 0.465491i | \(0.154122\pi\) | ||||
−0.885052 | + | 0.465491i | \(0.845878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −892.684 | + | 892.684i | −0.958844 | + | 0.958844i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −51.7592 | + | 942.100i | −0.0554761 | + | 1.00975i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −256.669 | −0.274512 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 177.635i | 0.189579i | 0.995497 | + | 0.0947893i | \(0.0302177\pi\) | ||||
−0.995497 | + | 0.0947893i | \(0.969782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −311.154 | − | 17.0949i | −0.331368 | − | 0.0182054i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.5787 | − | 49.5787i | −0.0526872 | − | 0.0526872i | 0.680272 | − | 0.732959i | \(-0.261862\pi\) |
−0.732959 | + | 0.680272i | \(0.761862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.2958 | 0.0639404 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1378.00 | − | 985.315i | 1.45820 | − | 1.04266i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 801.785 | + | 801.785i | 0.846658 | + | 0.846658i | 0.989714 | − | 0.143057i | \(-0.0456931\pi\) |
−0.143057 | + | 0.989714i | \(0.545693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −119.999 | − | 119.999i | −0.126447 | − | 0.126447i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1014.72 | − | 909.032i | 1.06701 | − | 0.955869i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −633.331 | −0.664565 | −0.332283 | − | 0.943180i | \(-0.607819\pi\) | ||||
−0.332283 | + | 0.943180i | \(0.607819\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −219.954 | − | 219.954i | −0.230318 | − | 0.230318i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.79434 | + | 69.0630i | −0.00396483 | + | 0.0721662i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 652.649i | − | 0.680552i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 452.174 | 0.470525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 833.807 | − | 668.259i | 0.865843 | − | 0.693935i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 642.656 | − | 642.656i | 0.665965 | − | 0.665965i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 734.798i | 0.759873i | 0.925013 | + | 0.379937i | \(0.124054\pi\) | ||||
−0.925013 | + | 0.379937i | \(0.875946\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 556.421 | − | 498.465i | 0.574222 | − | 0.514412i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1255.23 | + | 1255.23i | −1.29272 | + | 1.29272i | −0.359625 | + | 0.933097i | \(0.617095\pi\) |
−0.933097 | + | 0.359625i | \(0.882905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1980.93 | − | 1980.93i | 2.03589 | − | 2.03589i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.36365 | + | 7.49251i | −0.00857811 | + | 0.00768463i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 75.9504i | 0.0777384i | 0.999244 | + | 0.0388692i | \(0.0123756\pi\) | ||||
−0.999244 | + | 0.0388692i | \(0.987624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −294.413 | + | 294.413i | −0.300728 | + | 0.300728i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.7953 | − | 18.2694i | 0.0232368 | − | 0.0186232i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 211.646 | 0.215306 | 0.107653 | − | 0.994189i | \(-0.465666\pi\) | ||||
0.107653 | + | 0.994189i | \(0.465666\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 483.723i | 0.491089i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −110.815 | + | 2017.00i | −0.112274 | + | 2.04357i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 280.561 | + | 280.561i | 0.283682 | + | 0.283682i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −728.452 | −0.735067 | −0.367534 | − | 0.930010i | \(-0.619798\pi\) | ||||
−0.367534 | + | 0.930010i | \(0.619798\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 991.810 | − | 888.505i | 0.998802 | − | 0.894768i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.98556 | + | 2.98556i | 0.00300056 | + | 0.00300056i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 955.300 | + | 955.300i | 0.958175 | + | 0.958175i | 0.999160 | − | 0.0409850i | \(-0.0130496\pi\) |
−0.0409850 | + | 0.999160i | \(0.513050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 310.780 | − | 222.218i | 0.311091 | − | 0.222440i |
(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 | 384.3.i.d.353.5 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.d.353.10 | 20 | ||
4.3 | odd | 2 | 384.3.i.c.353.6 | 20 | |||
8.3 | odd | 2 | 192.3.i.b.113.5 | 20 | |||
8.5 | even | 2 | 48.3.i.b.5.10 | yes | 20 | ||
12.11 | even | 2 | 384.3.i.c.353.1 | 20 | |||
16.3 | odd | 4 | 384.3.i.c.161.1 | 20 | |||
16.5 | even | 4 | 48.3.i.b.29.1 | yes | 20 | ||
16.11 | odd | 4 | 192.3.i.b.17.10 | 20 | |||
16.13 | even | 4 | inner | 384.3.i.d.161.10 | 20 | ||
24.5 | odd | 2 | 48.3.i.b.5.1 | ✓ | 20 | ||
24.11 | even | 2 | 192.3.i.b.113.10 | 20 | |||
48.5 | odd | 4 | 48.3.i.b.29.10 | yes | 20 | ||
48.11 | even | 4 | 192.3.i.b.17.5 | 20 | |||
48.29 | odd | 4 | inner | 384.3.i.d.161.5 | 20 | ||
48.35 | even | 4 | 384.3.i.c.161.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.1 | ✓ | 20 | 24.5 | odd | 2 | ||
48.3.i.b.5.10 | yes | 20 | 8.5 | even | 2 | ||
48.3.i.b.29.1 | yes | 20 | 16.5 | even | 4 | ||
48.3.i.b.29.10 | yes | 20 | 48.5 | odd | 4 | ||
192.3.i.b.17.5 | 20 | 48.11 | even | 4 | |||
192.3.i.b.17.10 | 20 | 16.11 | odd | 4 | |||
192.3.i.b.113.5 | 20 | 8.3 | odd | 2 | |||
192.3.i.b.113.10 | 20 | 24.11 | even | 2 | |||
384.3.i.c.161.1 | 20 | 16.3 | odd | 4 | |||
384.3.i.c.161.6 | 20 | 48.35 | even | 4 | |||
384.3.i.c.353.1 | 20 | 12.11 | even | 2 | |||
384.3.i.c.353.6 | 20 | 4.3 | odd | 2 | |||
384.3.i.d.161.5 | 20 | 48.29 | odd | 4 | inner | ||
384.3.i.d.161.10 | 20 | 16.13 | even | 4 | inner | ||
384.3.i.d.353.5 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.d.353.10 | 20 | 3.2 | odd | 2 | inner |