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 | 161.1 | ||
Root | \(-1.96139 + 0.391068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.161 |
Dual form | 384.3.i.c.353.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.99548 | − | 0.164573i | −0.998494 | − | 0.0548575i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.61305 | − | 3.61305i | −0.722609 | − | 0.722609i | 0.246527 | − | 0.969136i | \(-0.420711\pi\) |
−0.969136 | + | 0.246527i | \(0.920711\pi\) | |||||||
\(6\) | 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 | 0.622095 | − | 0.782942i | \(-0.286282\pi\) |
−0.782942 | + | 0.622095i | \(0.786282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38826 | + | 2.38826i | 0.183713 | + | 0.183713i | 0.792971 | − | 0.609259i | \(-0.208533\pi\) |
−0.609259 | + | 0.792971i | \(0.708533\pi\) | |||||||
\(14\) | 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 | \(-0.355842\pi\) |
−0.899188 | + | 0.437562i | \(0.855842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.02081 | + | 36.7820i | −0.0962292 | + | 1.75153i | ||||
\(22\) | 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 | ||||||||
\(27\) | −26.6348 | − | 4.42563i | −0.986475 | − | 0.163912i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.51544 | + | 6.51544i | −0.224670 | + | 0.224670i | −0.810462 | − | 0.585792i | \(-0.800784\pi\) |
0.585792 | + | 0.810462i | \(0.300784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −37.5922 | −1.21265 | −0.606326 | − | 0.795216i | \(-0.707357\pi\) | ||||
−0.606326 | + | 0.795216i | \(0.707357\pi\) | |||||||
\(32\) | 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 | −0.829271 | − | 0.558847i | \(-0.811244\pi\) |
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.76096 | − | 7.54704i | −0.173358 | − | 0.193514i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.57407 | 0.111563 | 0.0557814 | − | 0.998443i | \(-0.482235\pi\) | ||||
0.0557814 | + | 0.998443i | \(0.482235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.2835 | − | 21.2835i | 0.494966 | − | 0.494966i | −0.414901 | − | 0.909867i | \(-0.636184\pi\) |
0.909867 | + | 0.414901i | \(0.136184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −28.7594 | − | 35.8840i | −0.639098 | − | 0.797422i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 54.8366i | 1.16674i | 0.812208 | + | 0.583368i | \(0.198266\pi\) | ||||
−0.812208 | + | 0.583368i | \(0.801734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −101.778 | −2.07710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30386 | − | 60.1356i | 0.0647816 | − | 1.17913i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 21.5215 | + | 21.5215i | 0.406065 | + | 0.406065i | 0.880364 | − | 0.474299i | \(-0.157298\pi\) |
−0.474299 | + | 0.880364i | \(0.657298\pi\) | |||||||
\(54\) | 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 | 0.996233 | − | 0.0867132i | \(-0.0276364\pi\) |
−0.0867132 | + | 0.996233i | \(0.527636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.2186 | + | 19.2186i | 0.315059 | + | 0.315059i | 0.846866 | − | 0.531807i | \(-0.178487\pi\) |
−0.531807 | + | 0.846866i | \(0.678487\pi\) | |||||||
\(62\) | 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 | \(-0.141911\pi\) |
−0.431205 | + | 0.902254i | \(0.641911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 39.4867 | + | 2.16941i | 0.572271 | + | 0.0314407i | ||||
\(70\) | 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 | \(0.111831\pi\) | ||||
−0.938917 | + | 0.344145i | \(0.888169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.182380 | − | 3.31960i | 0.00243173 | − | 0.0442614i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.7257 | + | 21.7257i | −0.282152 | + | 0.282152i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20.9299 | −0.264935 | −0.132468 | − | 0.991187i | \(-0.542290\pi\) | ||||
−0.132468 | + | 0.991187i | \(0.542290\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.0558 | + | 17.6403i | 0.975998 | + | 0.217781i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.35791 | − | 6.35791i | 0.0766013 | − | 0.0766013i | −0.667768 | − | 0.744369i | \(-0.732750\pi\) |
0.744369 | + | 0.667768i | \(0.232750\pi\) | |||||||
\(84\) | 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 | \(-0.884446\pi\) | ||||
−0.934828 | + | 0.355102i | \(0.884446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.3259 | − | 29.3259i | 0.322262 | − | 0.322262i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 112.607 | + | 6.18664i | 1.21083 | + | 0.0665231i | ||||
\(94\) | 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 | ||||||||
\(99\) | −14.0835 | − | 17.5725i | −0.142258 | − | 0.177500i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −125.879 | − | 125.879i | −1.24632 | − | 1.24632i | −0.957331 | − | 0.288994i | \(-0.906679\pi\) |
−0.288994 | − | 0.957331i | \(-0.593321\pi\) | |||||||
\(102\) | 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 | 0.195994 | − | 0.980605i | \(-0.437207\pi\) |
−0.980605 | + | 0.195994i | \(0.937207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.29518 | − | 2.29518i | −0.0210567 | − | 0.0210567i | 0.696500 | − | 0.717557i | \(-0.254740\pi\) |
−0.717557 | + | 0.696500i | \(0.754740\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | 19.0103 | + | 23.7197i | 0.162481 | + | 0.202733i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 246.509 | 2.07151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 114.739i | − | 0.948257i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.7016 | − | 0.752766i | −0.111395 | − | 0.00612005i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −86.3222 | + | 86.3222i | −0.690577 | + | 0.690577i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 152.167 | 1.19816 | 0.599082 | − | 0.800687i | \(-0.295532\pi\) | ||||
0.599082 | + | 0.800687i | \(0.295532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −67.2571 | + | 60.2517i | −0.521373 | + | 0.467068i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 65.6955 | − | 65.6955i | 0.501492 | − | 0.501492i | −0.410409 | − | 0.911901i | \(-0.634614\pi\) |
0.911901 | + | 0.410409i | \(0.134614\pi\) | |||||||
\(132\) | 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 | \(-0.562140\pi\) | ||||
−0.193982 | + | 0.981005i | \(0.562140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −161.324 | + | 161.324i | −1.16060 | + | 1.16060i | −0.176261 | + | 0.984343i | \(0.556400\pi\) |
−0.984343 | + | 0.176261i | \(0.943600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.02460 | − | 164.262i | 0.0640043 | − | 1.16498i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.45118i | − | 0.0590992i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 47.0811 | 0.324698 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 304.874 | + | 16.7498i | 2.07397 | + | 0.113945i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −116.911 | − | 116.911i | −0.784638 | − | 0.784638i | 0.195971 | − | 0.980610i | \(-0.437214\pi\) |
−0.980610 | + | 0.195971i | \(0.937214\pi\) | |||||||
\(150\) | 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 | 0.530396 | − | 0.847750i | \(-0.322043\pi\) |
−0.847750 | + | 0.530396i | \(0.822043\pi\) | |||||||
\(158\) | 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 | \(-0.343041\pi\) |
−0.880869 | + | 0.473360i | \(0.843041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.10410 | − | 38.2980i | 0.0127521 | − | 0.232109i | ||||
\(166\) | 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 | ||||||||
\(171\) | −69.8153 | − | 87.1106i | −0.408277 | − | 0.509419i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 123.809 | − | 123.809i | 0.715661 | − | 0.715661i | −0.252052 | − | 0.967714i | \(-0.581106\pi\) |
0.967714 | + | 0.252052i | \(0.0811056\pi\) | |||||||
\(174\) | 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 | −0.998415 | − | 0.0562807i | \(-0.982076\pi\) |
0.0562807 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 162.162 | − | 162.162i | 0.895920 | − | 0.895920i | −0.0991520 | − | 0.995072i | \(-0.531613\pi\) |
0.995072 | + | 0.0991520i | \(0.0316130\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | −54.3430 | + | 327.053i | −0.287529 | + | 1.73044i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 60.8777i | 0.318731i | 0.987220 | + | 0.159366i | \(0.0509449\pi\) | ||||
−0.987220 | + | 0.159366i | \(0.949055\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 177.871 | 0.921611 | 0.460806 | − | 0.887501i | \(-0.347561\pi\) | ||||
0.460806 | + | 0.887501i | \(0.347561\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.84016 | + | 51.6955i | −0.0145649 | + | 0.265105i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 66.9411 | + | 66.9411i | 0.339803 | + | 0.339803i | 0.856293 | − | 0.516490i | \(-0.172762\pi\) |
−0.516490 | + | 0.856293i | \(0.672762\pi\) | |||||||
\(198\) | 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 | \(-0.457916\pi\) |
−0.991273 | + | 0.131825i | \(0.957916\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 195.072 | + | 10.7173i | 0.915830 | + | 0.0503159i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −153.797 | −0.715333 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 461.601i | 2.12719i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.26897 | − | 150.508i | 0.0377579 | − | 0.687253i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −47.9454 | + | 47.9454i | −0.216947 | + | 0.216947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.7339 | 0.0795241 | 0.0397621 | − | 0.999209i | \(-0.487340\pi\) | ||||
0.0397621 | + | 0.999209i | \(0.487340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.09263 | + | 9.91380i | −0.00485614 | + | 0.0440613i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.53766 | + | 7.53766i | −0.0332055 | + | 0.0332055i | −0.723515 | − | 0.690309i | \(-0.757475\pi\) |
0.690309 | + | 0.723515i | \(0.257475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −223.748 | + | 223.748i | −0.977063 | + | 0.977063i | −0.999743 | − | 0.0226794i | \(-0.992780\pi\) |
0.0226794 | + | 0.999743i | \(0.492780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 68.6545 | − | 61.5036i | 0.297205 | − | 0.266249i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 123.585 | 0.530406 | 0.265203 | − | 0.964193i | \(-0.414561\pi\) | ||||
0.265203 | + | 0.964193i | \(0.414561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 198.127 | − | 198.127i | 0.843095 | − | 0.843095i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 62.6951 | + | 3.44448i | 0.264536 | + | 0.0145337i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 118.501i | − | 0.495820i | −0.968783 | − | 0.247910i | \(-0.920256\pi\) | ||
0.968783 | − | 0.247910i | \(-0.0797437\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −264.162 | −1.09611 | −0.548053 | − | 0.836443i | \(-0.684631\pi\) | ||||
−0.548053 | + | 0.836443i | \(0.684631\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −233.907 | − | 65.8515i | −0.962581 | − | 0.270994i | ||||
\(244\) | 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 | 0.334808 | − | 0.942286i | \(-0.391328\pi\) |
−0.942286 | + | 0.334808i | \(0.891328\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | −64.7099 | + | 51.8621i | −0.247931 | + | 0.198705i | ||||
\(262\) | 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 | ||||||||
\(267\) | 498.446 | + | 27.3848i | 1.86684 | + | 0.102565i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 129.457 | − | 129.457i | 0.481253 | − | 0.481253i | −0.424278 | − | 0.905532i | \(-0.639472\pi\) |
0.905532 | + | 0.424278i | \(0.139472\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −170.727 | −0.629990 | −0.314995 | − | 0.949093i | \(-0.602003\pi\) | ||||
−0.314995 | + | 0.949093i | \(0.602003\pi\) | |||||||
\(272\) | 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 | −0.882343 | − | 0.470606i | \(-0.844035\pi\) |
0.470606 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −336.294 | − | 37.0640i | −1.20535 | − | 0.132846i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −136.468 | −0.485650 | −0.242825 | − | 0.970070i | \(-0.578074\pi\) | ||||
−0.242825 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −132.657 | + | 132.657i | −0.468752 | + | 0.468752i | −0.901510 | − | 0.432758i | \(-0.857540\pi\) |
0.432758 | + | 0.901510i | \(0.357540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4305 | − | 189.852i | 0.0365982 | − | 0.666146i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 56.1658i | − | 0.195700i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −114.022 | −0.394541 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −417.010 | − | 22.9106i | −1.43303 | − | 0.0787307i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −143.968 | − | 143.968i | −0.491360 | − | 0.491360i | 0.417375 | − | 0.908735i | \(-0.362950\pi\) |
−0.908735 | + | 0.417375i | \(0.862950\pi\) | |||||||
\(294\) | 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 | \(-0.315961\pi\) |
−0.837461 | + | 0.546497i | \(0.815961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.34368 | − | 79.0619i | 0.0140572 | − | 0.255864i | ||||
\(310\) | 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 | \(0.0530638\pi\) | ||||
−0.986137 | + | 0.165934i | \(0.946936\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −440.625 | + | 353.142i | −1.39881 | + | 1.12108i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −321.109 | + | 321.109i | −1.01296 | + | 1.01296i | −0.0130482 | + | 0.999915i | \(0.504153\pi\) |
−0.999915 | + | 0.0130482i | \(0.995847\pi\) | |||||||
\(318\) | 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 | \(-0.983915\pi\) |
0.0505107 | + | 0.998724i | \(0.483915\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −99.3740 | + | 79.6439i | −0.298420 | + | 0.239171i | ||||
\(334\) | 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 | ||||||||
\(339\) | −29.2330 | + | 532.088i | −0.0862331 | + | 1.56958i | ||||
\(340\) | 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 | −0.944175 | − | 0.329445i | \(-0.893138\pi\) |
−0.329445 | − | 0.944175i | \(-0.606862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 476.643 | + | 476.643i | 1.36574 | + | 1.36574i | 0.866417 | + | 0.499321i | \(0.166417\pi\) |
0.499321 | + | 0.866417i | \(0.333583\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | −738.415 | − | 40.5687i | −2.06839 | − | 0.113638i | ||||
\(358\) | 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 | ||||||||
\(363\) | −18.8829 | + | 343.699i | −0.0520190 | + | 0.946829i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 181.538 | − | 181.538i | 0.497364 | − | 0.497364i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3588 | 0.0309505 | 0.0154753 | − | 0.999880i | \(-0.495074\pi\) | ||||
0.0154753 | + | 0.999880i | \(0.495074\pi\) | |||||||
\(368\) | 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 | −0.622971 | − | 0.782245i | \(-0.714075\pi\) |
0.782245 | + | 0.622971i | \(0.214075\pi\) | |||||||
\(374\) | 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 | 0.162129 | − | 0.986770i | \(-0.448164\pi\) |
0.986770 | − | 0.162129i | \(-0.0518359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −455.813 | − | 25.0425i | −1.19636 | − | 0.0657283i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 272.117i | 0.710488i | 0.934774 | + | 0.355244i | \(0.115602\pi\) | ||||
−0.934774 | + | 0.355244i | \(0.884398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 156.992 | 0.407772 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 211.383 | − | 169.414i | 0.546210 | − | 0.437763i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 260.985 | + | 260.985i | 0.670913 | + | 0.670913i | 0.957927 | − | 0.287013i | \(-0.0926623\pi\) |
−0.287013 | + | 0.957927i | \(0.592662\pi\) | |||||||
\(390\) | 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 | 0.302614 | − | 0.953113i | \(-0.402141\pi\) |
−0.953113 | + | 0.302614i | \(0.902141\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | −221.897 | − | 349.367i | −0.547894 | − | 0.862635i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.4063 | 0.0869935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 207.501i | − | 0.507337i | −0.967291 | − | 0.253668i | \(-0.918363\pi\) | ||
0.967291 | − | 0.253668i | \(-0.0816372\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 159.213 | + | 8.74718i | 0.387379 | + | 0.0212827i | ||||
\(412\) | 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 | −0.565370 | − | 0.824837i | \(-0.691267\pi\) |
0.824837 | + | 0.565370i | \(0.191267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 484.985 | − | 484.985i | 1.15198 | − | 1.15198i | 0.165829 | − | 0.986155i | \(-0.446970\pi\) |
0.986155 | − | 0.165829i | \(-0.0530300\pi\) | |||||||
\(422\) | 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 | ||||||||
\(429\) | −1.39083 | + | 25.3154i | −0.00324203 | + | 0.0590102i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 213.570i | − | 0.495522i | −0.968821 | − | 0.247761i | \(-0.920305\pi\) | ||
0.968821 | − | 0.247761i | \(-0.0796947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 440.669 | 1.01771 | 0.508856 | − | 0.860852i | \(-0.330069\pi\) | ||||
0.508856 | + | 0.860852i | \(0.330069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −141.031 | − | 7.74826i | −0.324209 | − | 0.0178121i | ||||
\(436\) | 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 | 0.970926 | − | 0.239378i | \(-0.0769435\pi\) |
−0.239378 | + | 0.970926i | \(0.576943\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | 1.80574 | − | 32.8674i | 0.00398618 | − | 0.0725549i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −211.912 | −0.465740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 385.436i | − | 0.843404i | −0.906734 | − | 0.421702i | \(-0.861433\pi\) | ||
0.906734 | − | 0.421702i | \(-0.138567\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 88.8463 | − | 534.705i | 0.193565 | − | 1.16494i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −312.070 | + | 312.070i | −0.676942 | + | 0.676942i | −0.959307 | − | 0.282365i | \(-0.908881\pi\) |
0.282365 | + | 0.959307i | \(0.408881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −718.961 | −1.55283 | −0.776416 | − | 0.630220i | \(-0.782965\pi\) | ||||
−0.776416 | + | 0.630220i | \(0.782965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −384.501 | − | 429.206i | −0.826884 | − | 0.923024i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 82.7894 | − | 82.7894i | 0.177279 | − | 0.177279i | −0.612889 | − | 0.790169i | \(-0.709993\pi\) |
0.790169 | + | 0.612889i | \(0.209993\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 171.308 | + | 213.746i | 0.359137 | + | 0.448106i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 749.099i | − | 1.56388i | −0.623353 | − | 0.781941i | \(-0.714230\pi\) | ||
0.623353 | − | 0.781941i | \(-0.285770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −47.7923 | −0.0993603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.6385 | − | 484.864i | 0.0551523 | − | 1.00386i | ||||
\(484\) | 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 | 0.713947 | − | 0.700200i | \(-0.246906\pi\) |
−0.700200 | + | 0.713947i | \(0.746906\pi\) | |||||||
\(492\) | 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 | 0.992475 | + | 0.122448i | \(0.0390746\pi\) |
0.122448 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 547.728 | + | 30.0923i | 1.09327 | + | 0.0600645i | ||||
\(502\) | 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 | ||||||||
\(507\) | −25.9354 | + | 472.065i | −0.0511546 | + | 0.931095i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −118.591 | + | 118.591i | −0.232988 | + | 0.232988i | −0.813939 | − | 0.580951i | \(-0.802681\pi\) |
0.580951 | + | 0.813939i | \(0.302681\pi\) | |||||||
\(510\) | 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 | \(-0.467846\pi\) | ||||
0.100842 | + | 0.994902i | \(0.467846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −479.455 | + | 479.455i | −0.916740 | + | 0.916740i | −0.996791 | − | 0.0800507i | \(-0.974492\pi\) |
0.0800507 | + | 0.996791i | \(0.474492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −40.7619 | − | 2.23947i | −0.0776418 | − | 0.00426566i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 754.679i | − | 1.43203i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −355.232 | −0.671517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 427.141 | + | 532.956i | 0.804408 | + | 1.00368i | ||||
\(532\) | 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 | −0.893680 | − | 0.448704i | \(-0.851886\pi\) |
−0.448704 | − | 0.893680i | \(-0.648114\pi\) | |||||||
\(542\) | 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 | \(-0.116727\pi\) |
−0.358546 | + | 0.933512i | \(0.616727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 152.978 | + | 190.875i | 0.278648 | + | 0.347677i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 114.292 | 0.207427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 257.002i | 0.464741i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −216.579 | − | 11.8989i | −0.390232 | − | 0.0214394i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 134.274 | − | 134.274i | 0.241066 | − | 0.241066i | −0.576225 | − | 0.817291i | \(-0.695475\pi\) |
0.817291 | + | 0.576225i | \(0.195475\pi\) | |||||||
\(558\) | 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 | −0.792493 | − | 0.609881i | \(-0.791217\pi\) |
0.609881 | + | 0.792493i | \(0.291217\pi\) | |||||||
\(564\) | 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 | \(-0.521963\pi\) | ||||
−0.0689430 | + | 0.997621i | \(0.521963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 363.164 | − | 363.164i | 0.636013 | − | 0.636013i | −0.313556 | − | 0.949570i | \(-0.601520\pi\) |
0.949570 | + | 0.313556i | \(0.101520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0188 | − | 182.358i | 0.0174848 | − | 0.318251i | ||||
\(574\) | 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 | ||||||||
\(579\) | −532.809 | − | 29.2727i | −0.920223 | − | 0.0505573i | ||||
\(580\) | 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 | 0.641845 | − | 0.766835i | \(-0.278169\pi\) |
−0.766835 | + | 0.641845i | \(0.778169\pi\) | |||||||
\(588\) | 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 | ||||||||
\(597\) | 0.135991 | − | 2.47525i | 0.000227790 | − | 0.00414615i | ||||
\(598\) | 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 | \(-0.769831\pi\) | ||
0.749759 | − | 0.661711i | \(-0.230169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 251.216 | + | 313.450i | 0.416610 | + | 0.519817i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −414.557 | + | 414.557i | −0.685219 | + | 0.685219i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 631.699 | 1.04069 | 0.520345 | − | 0.853956i | \(-0.325803\pi\) | ||||
0.520345 | + | 0.853956i | \(0.325803\pi\) | |||||||
\(608\) | 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 | −0.947688 | − | 0.319198i | \(-0.896586\pi\) |
0.319198 | + | 0.947688i | \(0.396586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 46.7846 | + | 52.2241i | 0.0760724 | + | 0.0849173i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −953.333 | −1.54511 | −0.772555 | − | 0.634947i | \(-0.781022\pi\) | ||||
−0.772555 | + | 0.634947i | \(0.781022\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −574.046 | + | 574.046i | −0.927377 | + | 0.927377i | −0.997536 | − | 0.0701591i | \(-0.977649\pi\) |
0.0701591 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 351.103 | + | 58.3390i | 0.565383 | + | 0.0939437i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2043.24i | 3.27969i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 651.477 | 1.04236 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.10783 | − | 92.9707i | 0.00814646 | − | 0.148279i | ||||
\(628\) | 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 | \(-0.334458\pi\) |
−0.867787 | + | 0.496937i | \(0.834458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 460.695 | + | 25.3107i | 0.714256 | + | 0.0392414i | ||||
\(646\) | 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 | ||||||||
\(651\) | 75.9668 | − | 1382.72i | 0.116693 | − | 2.12399i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 636.071 | − | 636.071i | 0.974075 | − | 0.974075i | −0.0255977 | − | 0.999672i | \(-0.508149\pi\) |
0.999672 | + | 0.0255977i | \(0.00814890\pi\) | |||||||
\(654\) | 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 | −0.634179 | − | 0.773186i | \(-0.718662\pi\) |
0.773186 | + | 0.634179i | \(0.218662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −721.715 | + | 721.715i | −1.09185 | + | 1.09185i | −0.0965216 | + | 0.995331i | \(0.530772\pi\) |
−0.995331 | + | 0.0965216i | \(0.969228\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | −53.1215 | − | 2.91851i | −0.0794044 | − | 0.00436250i | ||||
\(670\) | 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 | ||||||||
\(675\) | 4.90449 | − | 29.5168i | 0.00726592 | − | 0.0437286i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 585.326 | + | 585.326i | 0.864587 | + | 0.864587i | 0.991867 | − | 0.127280i | \(-0.0406246\pi\) |
−0.127280 | + | 0.991867i | \(0.540625\pi\) | |||||||
\(678\) | 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 | 0.779301 | − | 0.626650i | \(-0.215574\pi\) |
−0.626650 | + | 0.779301i | \(0.715574\pi\) | |||||||
\(684\) | 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 | \(-0.361621\pi\) |
−0.906984 | + | 0.421165i | \(0.861621\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −215.775 | + | 172.934i | −0.311364 | + | 0.249544i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1165.74 | 1.67733 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 91.8264i | 0.131745i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −370.196 | − | 20.3386i | −0.529608 | − | 0.0290968i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −490.458 | + | 490.458i | −0.699655 | + | 0.699655i | −0.964336 | − | 0.264681i | \(-0.914733\pi\) |
0.264681 | + | 0.964336i | \(0.414733\pi\) | |||||||
\(702\) | 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 | −0.944165 | − | 0.329473i | \(-0.893129\pi\) |
0.329473 | + | 0.944165i | \(0.393129\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | −19.5020 | + | 354.968i | −0.0271994 | + | 0.495073i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1083.05i | 1.50633i | 0.657831 | + | 0.753166i | \(0.271474\pi\) | ||||
−0.657831 | + | 0.753166i | \(0.728526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 324.093 | 0.449505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 791.292 | + | 43.4738i | 1.09446 | + | 0.0601297i | ||||
\(724\) | 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 | 0.655118 | − | 0.755527i | \(-0.272619\pi\) |
−0.755527 | + | 0.655118i | \(0.772619\pi\) | |||||||
\(734\) | 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 | \(-0.203421\pi\) |
−0.596447 | + | 0.802653i | \(0.703421\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.89467 | + | 125.494i | −0.00930455 | + | 0.169358i | ||||
\(742\) | 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 | ||||||||
\(747\) | 63.1454 | − | 50.6082i | 0.0845319 | − | 0.0677486i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1030.88 | + | 1030.88i | −1.37634 | + | 1.37634i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1014.28 | 1.35058 | 0.675289 | − | 0.737553i | \(-0.264019\pi\) | ||||
0.675289 | + | 0.737553i | \(0.264019\pi\) | |||||||
\(752\) | 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 | 0.417057 | − | 0.908880i | \(-0.363062\pi\) |
0.908880 | − | 0.417057i | \(-0.136938\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −66.0261 | − | 73.7028i | −0.0869909 | − | 0.0971052i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.1069 | −0.0710997 | −0.0355499 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355499 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.1829 | + | 28.1829i | −0.0369370 | + | 0.0369370i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 720.386 | − | 577.358i | 0.941681 | − | 0.754716i | ||||
\(766\) | 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 | ||||||||
\(771\) | 18.6161 | − | 338.843i | 0.0241454 | − | 0.439485i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 339.143 | + | 339.143i | 0.438736 | + | 0.438736i | 0.891586 | − | 0.452850i | \(-0.149593\pi\) |
−0.452850 | + | 0.891586i | \(0.649593\pi\) | |||||||
\(774\) | 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 | −0.980954 | − | 0.194241i | \(-0.937776\pi\) |
−0.194241 | − | 0.980954i | \(-0.562224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −387.389 | − | 21.2832i | −0.490987 | − | 0.0269749i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2181.15 | −2.75746 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 91.7980i | 0.115760i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.5937 | + | 465.846i | −0.0321933 | + | 0.585970i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 707.837 | − | 707.837i | 0.888127 | − | 0.888127i | −0.106216 | − | 0.994343i | \(-0.533873\pi\) |
0.994343 | + | 0.106216i | \(0.0338735\pi\) | |||||||
\(798\) | 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 | \(-0.740062\pi\) | ||||
−0.684689 | + | 0.728836i | \(0.740062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 217.697 | − | 217.697i | 0.268431 | − | 0.268431i | −0.560037 | − | 0.828468i | \(-0.689213\pi\) |
0.828468 | + | 0.560037i | \(0.189213\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 511.411 | + | 28.0970i | 0.629042 | + | 0.0345597i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 479.986i | 0.588940i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −373.351 | −0.456978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 291.258 | − | 233.431i | 0.355627 | − | 0.285019i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −761.374 | − | 761.374i | −0.927374 | − | 0.927374i | 0.0701619 | − | 0.997536i | \(-0.477648\pi\) |
−0.997536 | + | 0.0701619i | \(0.977648\pi\) | |||||||
\(822\) | 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 | 0.773962 | − | 0.633232i | \(-0.218272\pi\) |
−0.633232 | + | 0.773962i | \(0.718272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −821.995 | − | 821.995i | −0.991550 | − | 0.991550i | 0.00841482 | − | 0.999965i | \(-0.497321\pi\) |
−0.999965 | + | 0.00841482i | \(0.997321\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | 1001.26 | + | 166.369i | 1.19625 | + | 0.198768i | ||||
\(838\) | 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 | ||||||||
\(843\) | 408.786 | + | 22.4588i | 0.484919 | + | 0.0266415i | ||||
\(844\) | 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 | −0.662160 | − | 0.749362i | \(-0.730360\pi\) |
0.749362 | + | 0.662160i | \(0.230360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −62.4887 | + | 566.981i | −0.0730862 | + | 0.663135i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1113.91 | −1.29977 | −0.649887 | − | 0.760030i | \(-0.725184\pi\) | ||||
−0.649887 | + | 0.760030i | \(0.725184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −78.5892 | + | 78.5892i | −0.0914891 | + | 0.0914891i | −0.751370 | − | 0.659881i | \(-0.770607\pi\) |
0.659881 | + | 0.751370i | \(0.270607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.24334 | + | 168.244i | −0.0107356 | + | 0.195405i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 814.226i | − | 0.943483i | −0.881737 | − | 0.471741i | \(-0.843626\pi\) | ||
0.881737 | − | 0.471741i | \(-0.156374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −894.658 | −1.03429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 341.552 | + | 18.7650i | 0.393947 | + | 0.0216436i | ||||
\(868\) | 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 | 0.727823 | − | 0.685765i | \(-0.240532\pi\) |
−0.685765 | + | 0.727823i | \(0.740532\pi\) | |||||||
\(878\) | 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 | \(-0.143406\pi\) |
−0.435435 | + | 0.900220i | \(0.643406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −63.8153 | + | 1161.54i | −0.0721077 | + | 1.31248i | ||||
\(886\) | 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 | ||||||||
\(891\) | −108.664 | − | 171.086i | −0.121957 | − | 0.192016i | ||||
\(892\) | 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 | \(-0.650249\pi\) |
0.890651 | + | 0.454687i | \(0.150249\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1001.98 | − | 1250.20i | −1.10229 | − | 1.37536i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1451.84i | − | 1.59367i | −0.604195 | − | 0.796837i | \(-0.706505\pi\) | ||
0.604195 | − | 0.796837i | \(-0.293495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.4983 | −0.0246422 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.8550 | + | 415.998i | −0.0249782 | + | 0.454643i | ||||
\(916\) | 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 | ||||||||
\(933\) | 942.100 | + | 51.7592i | 1.00975 | + | 0.0554761i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −256.669 | −0.274512 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 177.635i | − | 0.189579i | −0.995497 | − | 0.0947893i | \(-0.969782\pi\) | ||
0.995497 | − | 0.0947893i | \(-0.0302177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0949 | − | 311.154i | 0.0182054 | − | 0.331368i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.5787 | − | 49.5787i | 0.0526872 | − | 0.0526872i | −0.680272 | − | 0.732959i | \(-0.738138\pi\) |
0.732959 | + | 0.680272i | \(0.238138\pi\) | |||||||
\(942\) | 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 | −0.143057 | − | 0.989714i | \(-0.545693\pi\) |
0.989714 | + | 0.143057i | \(0.0456931\pi\) | |||||||
\(948\) | 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 | \(-0.392181\pi\) | ||||
0.332283 | + | 0.943180i | \(0.392181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 219.954 | − | 219.954i | 0.230318 | − | 0.230318i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −69.0630 | − | 3.79434i | −0.0721662 | − | 0.00396483i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 652.649i | 0.680552i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 452.174 | 0.470525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −668.259 | − | 833.807i | −0.693935 | − | 0.865843i | ||||
\(964\) | 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 | −0.933097 | − | 0.359625i | \(-0.882905\pi\) |
−0.359625 | − | 0.933097i | \(-0.617095\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −18.2694 | − | 22.7953i | −0.0186232 | − | 0.0232368i | ||||
\(982\) | 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 | ||||||||
\(987\) | −2017.00 | − | 110.815i | −2.04357 | − | 0.112274i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −280.561 | + | 280.561i | −0.283682 | + | 0.283682i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 728.452 | 0.735067 | 0.367534 | − | 0.930010i | \(-0.380202\pi\) | ||||
0.367534 | + | 0.930010i | \(0.380202\pi\) | |||||||
\(992\) | 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 | −0.0409850 | − | 0.999160i | \(-0.513050\pi\) |
0.999160 | + | 0.0409850i | \(0.0130496\pi\) | |||||||
\(998\) | 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.c.161.1 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.c.161.6 | 20 | ||
4.3 | odd | 2 | 384.3.i.d.161.10 | 20 | |||
8.3 | odd | 2 | 48.3.i.b.29.1 | yes | 20 | ||
8.5 | even | 2 | 192.3.i.b.17.10 | 20 | |||
12.11 | even | 2 | 384.3.i.d.161.5 | 20 | |||
16.3 | odd | 4 | 48.3.i.b.5.10 | yes | 20 | ||
16.5 | even | 4 | inner | 384.3.i.c.353.6 | 20 | ||
16.11 | odd | 4 | 384.3.i.d.353.5 | 20 | |||
16.13 | even | 4 | 192.3.i.b.113.5 | 20 | |||
24.5 | odd | 2 | 192.3.i.b.17.5 | 20 | |||
24.11 | even | 2 | 48.3.i.b.29.10 | yes | 20 | ||
48.5 | odd | 4 | inner | 384.3.i.c.353.1 | 20 | ||
48.11 | even | 4 | 384.3.i.d.353.10 | 20 | |||
48.29 | odd | 4 | 192.3.i.b.113.10 | 20 | |||
48.35 | even | 4 | 48.3.i.b.5.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.1 | ✓ | 20 | 48.35 | even | 4 | ||
48.3.i.b.5.10 | yes | 20 | 16.3 | odd | 4 | ||
48.3.i.b.29.1 | yes | 20 | 8.3 | odd | 2 | ||
48.3.i.b.29.10 | yes | 20 | 24.11 | even | 2 | ||
192.3.i.b.17.5 | 20 | 24.5 | odd | 2 | |||
192.3.i.b.17.10 | 20 | 8.5 | even | 2 | |||
192.3.i.b.113.5 | 20 | 16.13 | even | 4 | |||
192.3.i.b.113.10 | 20 | 48.29 | odd | 4 | |||
384.3.i.c.161.1 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.c.161.6 | 20 | 3.2 | odd | 2 | inner | ||
384.3.i.c.353.1 | 20 | 48.5 | odd | 4 | inner | ||
384.3.i.c.353.6 | 20 | 16.5 | even | 4 | inner | ||
384.3.i.d.161.5 | 20 | 12.11 | even | 2 | |||
384.3.i.d.161.10 | 20 | 4.3 | odd | 2 | |||
384.3.i.d.353.5 | 20 | 16.11 | odd | 4 | |||
384.3.i.d.353.10 | 20 | 48.11 | even | 4 |