Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(439,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.10 | ||
Character | \(\chi\) | \(=\) | 930.439 |
Dual form | 930.2.s.c.769.4 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.981775 | + | 2.00901i | 0.439063 | + | 0.898456i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0.669647 | + | 0.386621i | 0.253103 | + | 0.146129i | 0.621184 | − | 0.783665i | \(-0.286652\pi\) |
−0.368081 | + | 0.929794i | \(0.619985\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −2.00901 | + | 0.981775i | −0.635304 | + | 0.310464i | ||||
\(11\) | 0.0912000 | + | 0.157963i | 0.0274978 | + | 0.0476277i | 0.879447 | − | 0.475997i | \(-0.157913\pi\) |
−0.851949 | + | 0.523625i | \(0.824579\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 3.35207 | − | 1.93532i | 0.929698 | − | 0.536761i | 0.0429816 | − | 0.999076i | \(-0.486314\pi\) |
0.886716 | + | 0.462315i | \(0.152981\pi\) | |||||||
\(14\) | −0.386621 | + | 0.669647i | −0.103329 | + | 0.178971i | ||||
\(15\) | −0.154263 | + | 2.23074i | −0.0398304 | + | 0.575975i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.39463 | + | 3.11459i | 1.30839 | + | 0.755400i | 0.981828 | − | 0.189776i | \(-0.0607760\pi\) |
0.326563 | + | 0.945175i | \(0.394109\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −0.298547 | + | 0.517099i | −0.0684915 | + | 0.118631i | −0.898237 | − | 0.439511i | \(-0.855152\pi\) |
0.829746 | + | 0.558141i | \(0.188485\pi\) | |||||||
\(20\) | −0.981775 | − | 2.00901i | −0.219532 | − | 0.449228i | ||||
\(21\) | 0.386621 | + | 0.669647i | 0.0843676 | + | 0.146129i | ||||
\(22\) | −0.157963 | + | 0.0912000i | −0.0336778 | + | 0.0194439i | ||||
\(23\) | 3.42650i | 0.714475i | 0.934014 | + | 0.357237i | \(0.116281\pi\) | ||||
−0.934014 | + | 0.357237i | \(0.883719\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −3.07224 | + | 3.94479i | −0.614447 | + | 0.788958i | ||||
\(26\) | 1.93532 | + | 3.35207i | 0.379547 | + | 0.657395i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −0.669647 | − | 0.386621i | −0.126551 | − | 0.0730645i | ||||
\(29\) | −7.12532 | −1.32314 | −0.661569 | − | 0.749884i | \(-0.730109\pi\) | ||||
−0.661569 | + | 0.749884i | \(0.730109\pi\) | |||||||
\(30\) | −2.23074 | − | 0.154263i | −0.407276 | − | 0.0281644i | ||||
\(31\) | −4.63168 | − | 3.08991i | −0.831874 | − | 0.554964i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.182400i | 0.0317518i | ||||||||
\(34\) | −3.11459 | + | 5.39463i | −0.534148 | + | 0.925172i | ||||
\(35\) | −0.119282 | + | 1.72490i | −0.0201624 | + | 0.291561i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 5.54979 | + | 3.20418i | 0.912381 | + | 0.526763i | 0.881196 | − | 0.472750i | \(-0.156739\pi\) |
0.0311843 | + | 0.999514i | \(0.490072\pi\) | |||||||
\(38\) | −0.517099 | − | 0.298547i | −0.0838846 | − | 0.0484308i | ||||
\(39\) | 3.87064 | 0.619798 | ||||||||
\(40\) | 2.00901 | − | 0.981775i | 0.317652 | − | 0.155232i | ||||
\(41\) | 0.930631 | + | 1.61190i | 0.145340 | + | 0.251736i | 0.929500 | − | 0.368823i | \(-0.120239\pi\) |
−0.784160 | + | 0.620559i | \(0.786906\pi\) | |||||||
\(42\) | −0.669647 | + | 0.386621i | −0.103329 | + | 0.0596569i | ||||
\(43\) | −5.78617 | − | 3.34064i | −0.882382 | − | 0.509444i | −0.0109390 | − | 0.999940i | \(-0.503482\pi\) |
−0.871443 | + | 0.490497i | \(0.836815\pi\) | |||||||
\(44\) | −0.0912000 | − | 0.157963i | −0.0137489 | − | 0.0238138i | ||||
\(45\) | −1.24897 | + | 1.85475i | −0.186185 | + | 0.276489i | ||||
\(46\) | −3.42650 | −0.505210 | ||||||||
\(47\) | − | 6.17291i | − | 0.900412i | −0.892925 | − | 0.450206i | \(-0.851351\pi\) | ||
0.892925 | − | 0.450206i | \(-0.148649\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | −3.20105 | − | 5.54438i | −0.457293 | − | 0.792054i | ||||
\(50\) | −3.94479 | − | 3.07224i | −0.557878 | − | 0.434480i | ||||
\(51\) | 3.11459 | + | 5.39463i | 0.436130 | + | 0.755400i | ||||
\(52\) | −3.35207 | + | 1.93532i | −0.464849 | + | 0.268381i | ||||
\(53\) | 7.49604 | − | 4.32784i | 1.02966 | − | 0.594475i | 0.112773 | − | 0.993621i | \(-0.464027\pi\) |
0.916888 | + | 0.399146i | \(0.130693\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.227811 | + | 0.338306i | −0.0307181 | + | 0.0456172i | ||||
\(56\) | 0.386621 | − | 0.669647i | 0.0516644 | − | 0.0894853i | ||||
\(57\) | −0.517099 | + | 0.298547i | −0.0684915 | + | 0.0395436i | ||||
\(58\) | − | 7.12532i | − | 0.935600i | ||||||
\(59\) | −6.03735 | + | 10.4570i | −0.785996 | + | 1.36139i | 0.142406 | + | 0.989808i | \(0.454516\pi\) |
−0.928402 | + | 0.371577i | \(0.878817\pi\) | |||||||
\(60\) | 0.154263 | − | 2.23074i | 0.0199152 | − | 0.287987i | ||||
\(61\) | 0.975597 | 0.124912 | 0.0624562 | − | 0.998048i | \(-0.480107\pi\) | ||||
0.0624562 | + | 0.998048i | \(0.480107\pi\) | |||||||
\(62\) | 3.08991 | − | 4.63168i | 0.392419 | − | 0.588224i | ||||
\(63\) | 0.773241i | 0.0974193i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.17906 | + | 4.83430i | 0.890452 | + | 0.599621i | ||||
\(66\) | −0.182400 | −0.0224519 | ||||||||
\(67\) | 0.371098 | − | 0.214254i | 0.0453369 | − | 0.0261753i | −0.477160 | − | 0.878816i | \(-0.658334\pi\) |
0.522497 | + | 0.852641i | \(0.325001\pi\) | |||||||
\(68\) | −5.39463 | − | 3.11459i | −0.654195 | − | 0.377700i | ||||
\(69\) | −1.71325 | + | 2.96744i | −0.206251 | + | 0.357237i | ||||
\(70\) | −1.72490 | − | 0.119282i | −0.206165 | − | 0.0142570i | ||||
\(71\) | 4.02888 | + | 6.97823i | 0.478141 | + | 0.828164i | 0.999686 | − | 0.0250598i | \(-0.00797761\pi\) |
−0.521545 | + | 0.853224i | \(0.674644\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | −9.05991 | + | 5.23074i | −1.06038 | + | 0.612212i | −0.925538 | − | 0.378655i | \(-0.876387\pi\) |
−0.134844 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(74\) | −3.20418 | + | 5.54979i | −0.372478 | + | 0.645151i | ||||
\(75\) | −4.63303 | + | 1.88017i | −0.534976 | + | 0.217103i | ||||
\(76\) | 0.298547 | − | 0.517099i | 0.0342457 | − | 0.0593153i | ||||
\(77\) | 0.141039i | 0.0160729i | ||||||||
\(78\) | 3.87064i | 0.438264i | ||||||||
\(79\) | 3.64065 | − | 6.30578i | 0.409605 | − | 0.709456i | −0.585241 | − | 0.810860i | \(-0.699000\pi\) |
0.994845 | + | 0.101404i | \(0.0323333\pi\) | |||||||
\(80\) | 0.981775 | + | 2.00901i | 0.109766 | + | 0.224614i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.61190 | + | 0.930631i | −0.178005 | + | 0.102771i | ||||
\(83\) | 6.97624 | − | 4.02773i | 0.765742 | − | 0.442101i | −0.0656117 | − | 0.997845i | \(-0.520900\pi\) |
0.831353 | + | 0.555744i | \(0.187567\pi\) | |||||||
\(84\) | −0.386621 | − | 0.669647i | −0.0421838 | − | 0.0730645i | ||||
\(85\) | −0.960930 | + | 13.8957i | −0.104228 | + | 1.50720i | ||||
\(86\) | 3.34064 | − | 5.78617i | 0.360231 | − | 0.623938i | ||||
\(87\) | −6.17071 | − | 3.56266i | −0.661569 | − | 0.381957i | ||||
\(88\) | 0.157963 | − | 0.0912000i | 0.0168389 | − | 0.00972196i | ||||
\(89\) | −0.839983 | −0.0890380 | −0.0445190 | − | 0.999009i | \(-0.514176\pi\) | ||||
−0.0445190 | + | 0.999009i | \(0.514176\pi\) | |||||||
\(90\) | −1.85475 | − | 1.24897i | −0.195507 | − | 0.131653i | ||||
\(91\) | 2.99294 | 0.313745 | ||||||||
\(92\) | − | 3.42650i | − | 0.357237i | ||||||
\(93\) | −2.46620 | − | 4.99178i | −0.255733 | − | 0.517624i | ||||
\(94\) | 6.17291 | 0.636687 | ||||||||
\(95\) | −1.33196 | − | 0.0921094i | −0.136657 | − | 0.00945022i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | − | 9.51682i | − | 0.966287i | −0.875541 | − | 0.483143i | \(-0.839495\pi\) | ||
0.875541 | − | 0.483143i | \(-0.160505\pi\) | |||||||
\(98\) | 5.54438 | − | 3.20105i | 0.560067 | − | 0.323355i | ||||
\(99\) | −0.0912000 | + | 0.157963i | −0.00916595 | + | 0.0158759i | ||||
\(100\) | 3.07224 | − | 3.94479i | 0.307224 | − | 0.394479i | ||||
\(101\) | 11.7568 | 1.16985 | 0.584923 | − | 0.811089i | \(-0.301125\pi\) | ||||
0.584923 | + | 0.811089i | \(0.301125\pi\) | |||||||
\(102\) | −5.39463 | + | 3.11459i | −0.534148 | + | 0.308391i | ||||
\(103\) | −8.33883 | + | 4.81443i | −0.821650 | + | 0.474380i | −0.850985 | − | 0.525190i | \(-0.823994\pi\) |
0.0293353 | + | 0.999570i | \(0.490661\pi\) | |||||||
\(104\) | −1.93532 | − | 3.35207i | −0.189774 | − | 0.328698i | ||||
\(105\) | −0.965752 | + | 1.43417i | −0.0942477 | + | 0.139960i | ||||
\(106\) | 4.32784 | + | 7.49604i | 0.420357 | + | 0.728080i | ||||
\(107\) | −6.18652 | − | 3.57179i | −0.598073 | − | 0.345298i | 0.170210 | − | 0.985408i | \(-0.445555\pi\) |
−0.768283 | + | 0.640110i | \(0.778889\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −15.9921 | −1.53177 | −0.765883 | − | 0.642979i | \(-0.777698\pi\) | ||||
−0.765883 | + | 0.642979i | \(0.777698\pi\) | |||||||
\(110\) | −0.338306 | − | 0.227811i | −0.0322562 | − | 0.0217210i | ||||
\(111\) | 3.20418 | + | 5.54979i | 0.304127 | + | 0.526763i | ||||
\(112\) | 0.669647 | + | 0.386621i | 0.0632757 | + | 0.0365322i | ||||
\(113\) | 12.2956 | − | 7.09885i | 1.15667 | − | 0.667804i | 0.206167 | − | 0.978517i | \(-0.433901\pi\) |
0.950504 | + | 0.310713i | \(0.100568\pi\) | |||||||
\(114\) | −0.298547 | − | 0.517099i | −0.0279615 | − | 0.0484308i | ||||
\(115\) | −6.88387 | + | 3.36405i | −0.641924 | + | 0.313700i | ||||
\(116\) | 7.12532 | 0.661569 | ||||||||
\(117\) | 3.35207 | + | 1.93532i | 0.309899 | + | 0.178920i | ||||
\(118\) | −10.4570 | − | 6.03735i | −0.962645 | − | 0.555783i | ||||
\(119\) | 2.40833 | + | 4.17135i | 0.220771 | + | 0.382387i | ||||
\(120\) | 2.23074 | + | 0.154263i | 0.203638 | + | 0.0140822i | ||||
\(121\) | 5.48337 | − | 9.49747i | 0.498488 | − | 0.863406i | ||||
\(122\) | 0.975597i | 0.0883264i | ||||||||
\(123\) | 1.86126i | 0.167824i | ||||||||
\(124\) | 4.63168 | + | 3.08991i | 0.415937 | + | 0.277482i | ||||
\(125\) | −10.9414 | − | 2.29925i | −0.978625 | − | 0.205652i | ||||
\(126\) | −0.773241 | −0.0688858 | ||||||||
\(127\) | 10.3908 | + | 5.99913i | 0.922034 | + | 0.532337i | 0.884283 | − | 0.466951i | \(-0.154647\pi\) |
0.0377506 | + | 0.999287i | \(0.487981\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −3.34064 | − | 5.78617i | −0.294127 | − | 0.509444i | ||||
\(130\) | −4.83430 | + | 7.17906i | −0.423996 | + | 0.629645i | ||||
\(131\) | 4.14488 | − | 7.17915i | 0.362140 | − | 0.627245i | −0.626173 | − | 0.779684i | \(-0.715379\pi\) |
0.988313 | + | 0.152439i | \(0.0487128\pi\) | |||||||
\(132\) | − | 0.182400i | − | 0.0158759i | ||||||
\(133\) | −0.399843 | + | 0.230849i | −0.0346707 | + | 0.0200172i | ||||
\(134\) | 0.214254 | + | 0.371098i | 0.0185087 | + | 0.0320580i | ||||
\(135\) | −2.00901 | + | 0.981775i | −0.172908 | + | 0.0844977i | ||||
\(136\) | 3.11459 | − | 5.39463i | 0.267074 | − | 0.462586i | ||||
\(137\) | 11.1202 | − | 6.42025i | 0.950063 | − | 0.548519i | 0.0569622 | − | 0.998376i | \(-0.481859\pi\) |
0.893100 | + | 0.449857i | \(0.148525\pi\) | |||||||
\(138\) | −2.96744 | − | 1.71325i | −0.252605 | − | 0.145842i | ||||
\(139\) | −3.85068 | −0.326611 | −0.163305 | − | 0.986576i | \(-0.552216\pi\) | ||||
−0.163305 | + | 0.986576i | \(0.552216\pi\) | |||||||
\(140\) | 0.119282 | − | 1.72490i | 0.0100812 | − | 0.145781i | ||||
\(141\) | 3.08646 | − | 5.34590i | 0.259926 | − | 0.450206i | ||||
\(142\) | −6.97823 | + | 4.02888i | −0.585600 | + | 0.338096i | ||||
\(143\) | 0.611418 | + | 0.353002i | 0.0511294 | + | 0.0295195i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.99546 | − | 14.3148i | −0.580941 | − | 1.18878i | ||||
\(146\) | −5.23074 | − | 9.05991i | −0.432899 | − | 0.749803i | ||||
\(147\) | − | 6.40210i | − | 0.528036i | ||||||
\(148\) | −5.54979 | − | 3.20418i | −0.456190 | − | 0.263382i | ||||
\(149\) | 6.29694 | − | 10.9066i | 0.515865 | − | 0.893505i | −0.483965 | − | 0.875087i | \(-0.660804\pi\) |
0.999830 | − | 0.0184175i | \(-0.00586282\pi\) | |||||||
\(150\) | −1.88017 | − | 4.63303i | −0.153515 | − | 0.378285i | ||||
\(151\) | 12.8986 | 1.04967 | 0.524835 | − | 0.851204i | \(-0.324127\pi\) | ||||
0.524835 | + | 0.851204i | \(0.324127\pi\) | |||||||
\(152\) | 0.517099 | + | 0.298547i | 0.0419423 | + | 0.0242154i | ||||
\(153\) | 6.22919i | 0.503600i | ||||||||
\(154\) | −0.141039 | −0.0113653 | ||||||||
\(155\) | 1.66039 | − | 12.3387i | 0.133366 | − | 0.991067i | ||||
\(156\) | −3.87064 | −0.309899 | ||||||||
\(157\) | 14.4319i | 1.15179i | 0.817522 | + | 0.575897i | \(0.195347\pi\) | ||||
−0.817522 | + | 0.575897i | \(0.804653\pi\) | |||||||
\(158\) | 6.30578 | + | 3.64065i | 0.501661 | + | 0.289634i | ||||
\(159\) | 8.65569 | 0.686441 | ||||||||
\(160\) | −2.00901 | + | 0.981775i | −0.158826 | + | 0.0776161i | ||||
\(161\) | −1.32476 | + | 2.29455i | −0.104405 | + | 0.180835i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | − | 1.86439i | − | 0.146030i | −0.997331 | − | 0.0730150i | \(-0.976738\pi\) | ||
0.997331 | − | 0.0730150i | \(-0.0232621\pi\) | |||||||
\(164\) | −0.930631 | − | 1.61190i | −0.0726700 | − | 0.125868i | ||||
\(165\) | −0.366443 | + | 0.179076i | −0.0285276 | + | 0.0139410i | ||||
\(166\) | 4.02773 | + | 6.97624i | 0.312613 | + | 0.541461i | ||||
\(167\) | −0.608695 | − | 0.351430i | −0.0471022 | − | 0.0271945i | 0.476264 | − | 0.879302i | \(-0.341991\pi\) |
−0.523366 | + | 0.852108i | \(0.675324\pi\) | |||||||
\(168\) | 0.669647 | − | 0.386621i | 0.0516644 | − | 0.0298284i | ||||
\(169\) | 0.990925 | − | 1.71633i | 0.0762250 | − | 0.132026i | ||||
\(170\) | −13.8957 | − | 0.960930i | −1.06575 | − | 0.0737000i | ||||
\(171\) | −0.597095 | −0.0456610 | ||||||||
\(172\) | 5.78617 | + | 3.34064i | 0.441191 | + | 0.254722i | ||||
\(173\) | 6.36230 | − | 3.67328i | 0.483717 | − | 0.279274i | −0.238247 | − | 0.971205i | \(-0.576573\pi\) |
0.721964 | + | 0.691930i | \(0.243240\pi\) | |||||||
\(174\) | 3.56266 | − | 6.17071i | 0.270084 | − | 0.467800i | ||||
\(175\) | −3.58245 | + | 1.45383i | −0.270808 | + | 0.109899i | ||||
\(176\) | 0.0912000 | + | 0.157963i | 0.00687446 | + | 0.0119069i | ||||
\(177\) | −10.4570 | + | 6.03735i | −0.785996 | + | 0.453795i | ||||
\(178\) | − | 0.839983i | − | 0.0629594i | ||||||
\(179\) | −0.245463 | + | 0.425154i | −0.0183467 | + | 0.0317775i | −0.875053 | − | 0.484027i | \(-0.839174\pi\) |
0.856706 | + | 0.515805i | \(0.172507\pi\) | |||||||
\(180\) | 1.24897 | − | 1.85475i | 0.0930924 | − | 0.138245i | ||||
\(181\) | 8.47857 | + | 14.6853i | 0.630207 | + | 1.09155i | 0.987509 | + | 0.157562i | \(0.0503633\pi\) |
−0.357302 | + | 0.933989i | \(0.616303\pi\) | |||||||
\(182\) | 2.99294i | 0.221851i | ||||||||
\(183\) | 0.844892 | + | 0.487799i | 0.0624562 | + | 0.0360591i | ||||
\(184\) | 3.42650 | 0.252605 | ||||||||
\(185\) | −0.988569 | + | 14.2954i | −0.0726810 | + | 1.05102i | ||||
\(186\) | 4.99178 | − | 2.46620i | 0.366015 | − | 0.180830i | ||||
\(187\) | 1.13620i | 0.0830875i | ||||||||
\(188\) | 6.17291i | 0.450206i | ||||||||
\(189\) | −0.386621 | + | 0.669647i | −0.0281225 | + | 0.0487096i | ||||
\(190\) | 0.0921094 | − | 1.33196i | 0.00668232 | − | 0.0966308i | ||||
\(191\) | −4.93870 | − | 8.55408i | −0.357352 | − | 0.618952i | 0.630166 | − | 0.776461i | \(-0.282987\pi\) |
−0.987518 | + | 0.157509i | \(0.949654\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 7.56580 | + | 4.36812i | 0.544598 | + | 0.314424i | 0.746941 | − | 0.664891i | \(-0.231522\pi\) |
−0.202342 | + | 0.979315i | \(0.564855\pi\) | |||||||
\(194\) | 9.51682 | 0.683268 | ||||||||
\(195\) | 3.80010 | + | 7.77615i | 0.272131 | + | 0.556862i | ||||
\(196\) | 3.20105 | + | 5.54438i | 0.228646 | + | 0.396027i | ||||
\(197\) | 1.14893 | − | 0.663337i | 0.0818582 | − | 0.0472608i | −0.458512 | − | 0.888688i | \(-0.651617\pi\) |
0.540370 | + | 0.841427i | \(0.318284\pi\) | |||||||
\(198\) | −0.157963 | − | 0.0912000i | −0.0112259 | − | 0.00648130i | ||||
\(199\) | −12.3167 | − | 21.3331i | −0.873107 | − | 1.51226i | −0.858766 | − | 0.512368i | \(-0.828768\pi\) |
−0.0143404 | − | 0.999897i | \(-0.504565\pi\) | |||||||
\(200\) | 3.94479 | + | 3.07224i | 0.278939 | + | 0.217240i | ||||
\(201\) | 0.428507 | 0.0302246 | ||||||||
\(202\) | 11.7568i | 0.827206i | ||||||||
\(203\) | −4.77145 | − | 2.75480i | −0.334890 | − | 0.193349i | ||||
\(204\) | −3.11459 | − | 5.39463i | −0.218065 | − | 0.377700i | ||||
\(205\) | −2.32465 | + | 3.45217i | −0.162361 | + | 0.241110i | ||||
\(206\) | −4.81443 | − | 8.33883i | −0.335437 | − | 0.580994i | ||||
\(207\) | −2.96744 | + | 1.71325i | −0.206251 | + | 0.119079i | ||||
\(208\) | 3.35207 | − | 1.93532i | 0.232424 | − | 0.134190i | ||||
\(209\) | −0.108910 | −0.00753347 | ||||||||
\(210\) | −1.43417 | − | 0.965752i | −0.0989669 | − | 0.0666432i | ||||
\(211\) | 8.11534 | − | 14.0562i | 0.558683 | − | 0.967667i | −0.438924 | − | 0.898524i | \(-0.644640\pi\) |
0.997607 | − | 0.0691431i | \(-0.0220265\pi\) | |||||||
\(212\) | −7.49604 | + | 4.32784i | −0.514830 | + | 0.297238i | ||||
\(213\) | 8.05777i | 0.552109i | ||||||||
\(214\) | 3.57179 | − | 6.18652i | 0.244162 | − | 0.422902i | ||||
\(215\) | 1.03067 | − | 14.9042i | 0.0702913 | − | 1.01646i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.90697 | − | 3.85985i | −0.129453 | − | 0.262024i | ||||
\(218\) | − | 15.9921i | − | 1.08312i | ||||||
\(219\) | −10.4615 | −0.706921 | ||||||||
\(220\) | 0.227811 | − | 0.338306i | 0.0153590 | − | 0.0228086i | ||||
\(221\) | 24.1109 | 1.62188 | ||||||||
\(222\) | −5.54979 | + | 3.20418i | −0.372478 | + | 0.215050i | ||||
\(223\) | −17.2965 | − | 9.98614i | −1.15826 | − | 0.668722i | −0.207373 | − | 0.978262i | \(-0.566492\pi\) |
−0.950886 | + | 0.309540i | \(0.899825\pi\) | |||||||
\(224\) | −0.386621 | + | 0.669647i | −0.0258322 | + | 0.0447427i | ||||
\(225\) | −4.95241 | − | 0.688239i | −0.330160 | − | 0.0458826i | ||||
\(226\) | 7.09885 | + | 12.2956i | 0.472209 | + | 0.817889i | ||||
\(227\) | 20.2265 | − | 11.6778i | 1.34248 | − | 0.775080i | 0.355307 | − | 0.934750i | \(-0.384376\pi\) |
0.987171 | + | 0.159670i | \(0.0510429\pi\) | |||||||
\(228\) | 0.517099 | − | 0.298547i | 0.0342457 | − | 0.0197718i | ||||
\(229\) | 6.66108 | − | 11.5373i | 0.440176 | − | 0.762408i | −0.557526 | − | 0.830160i | \(-0.688249\pi\) |
0.997702 | + | 0.0677518i | \(0.0215826\pi\) | |||||||
\(230\) | −3.36405 | − | 6.88387i | −0.221819 | − | 0.453909i | ||||
\(231\) | −0.0705196 | + | 0.122144i | −0.00463985 | + | 0.00803646i | ||||
\(232\) | 7.12532i | 0.467800i | ||||||||
\(233\) | 10.6233i | 0.695957i | 0.937503 | + | 0.347978i | \(0.113132\pi\) | ||||
−0.937503 | + | 0.347978i | \(0.886868\pi\) | |||||||
\(234\) | −1.93532 | + | 3.35207i | −0.126516 | + | 0.219132i | ||||
\(235\) | 12.4014 | − | 6.06041i | 0.808980 | − | 0.395338i | ||||
\(236\) | 6.03735 | − | 10.4570i | 0.392998 | − | 0.680693i | ||||
\(237\) | 6.30578 | − | 3.64065i | 0.409605 | − | 0.236485i | ||||
\(238\) | −4.17135 | + | 2.40833i | −0.270389 | + | 0.156109i | ||||
\(239\) | −4.64700 | − | 8.04884i | −0.300589 | − | 0.520636i | 0.675680 | − | 0.737195i | \(-0.263850\pi\) |
−0.976270 | + | 0.216559i | \(0.930517\pi\) | |||||||
\(240\) | −0.154263 | + | 2.23074i | −0.00995761 | + | 0.143994i | ||||
\(241\) | −4.18140 | + | 7.24239i | −0.269347 | + | 0.466523i | −0.968693 | − | 0.248260i | \(-0.920141\pi\) |
0.699346 | + | 0.714783i | \(0.253475\pi\) | |||||||
\(242\) | 9.49747 | + | 5.48337i | 0.610520 | + | 0.352484i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −0.975597 | −0.0624562 | ||||||||
\(245\) | 7.99600 | − | 11.8743i | 0.510846 | − | 0.758619i | ||||
\(246\) | −1.86126 | −0.118670 | ||||||||
\(247\) | 2.31114i | 0.147054i | ||||||||
\(248\) | −3.08991 | + | 4.63168i | −0.196209 | + | 0.294112i | ||||
\(249\) | 8.05547 | 0.510495 | ||||||||
\(250\) | 2.29925 | − | 10.9414i | 0.145418 | − | 0.691993i | ||||
\(251\) | −9.11474 | + | 15.7872i | −0.575317 | + | 0.996479i | 0.420690 | + | 0.907205i | \(0.361788\pi\) |
−0.996007 | + | 0.0892742i | \(0.971545\pi\) | |||||||
\(252\) | − | 0.773241i | − | 0.0487096i | ||||||
\(253\) | −0.541261 | + | 0.312497i | −0.0340288 | + | 0.0196465i | ||||
\(254\) | −5.99913 | + | 10.3908i | −0.376419 | + | 0.651977i | ||||
\(255\) | −7.78004 | + | 11.5536i | −0.487205 | + | 0.723512i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.29328 | − | 0.746676i | 0.0806727 | − | 0.0465764i | −0.459121 | − | 0.888374i | \(-0.651836\pi\) |
0.539794 | + | 0.841797i | \(0.318502\pi\) | |||||||
\(258\) | 5.78617 | − | 3.34064i | 0.360231 | − | 0.207979i | ||||
\(259\) | 2.47760 | + | 4.29133i | 0.153951 | + | 0.266650i | ||||
\(260\) | −7.17906 | − | 4.83430i | −0.445226 | − | 0.299810i | ||||
\(261\) | −3.56266 | − | 6.17071i | −0.220523 | − | 0.381957i | ||||
\(262\) | 7.17915 | + | 4.14488i | 0.443529 | + | 0.256072i | ||||
\(263\) | 21.7443i | 1.34081i | 0.741996 | + | 0.670404i | \(0.233879\pi\) | ||||
−0.741996 | + | 0.670404i | \(0.766121\pi\) | |||||||
\(264\) | 0.182400 | 0.0112259 | ||||||||
\(265\) | 16.0541 | + | 10.8107i | 0.986196 | + | 0.664093i | ||||
\(266\) | −0.230849 | − | 0.399843i | −0.0141543 | − | 0.0245159i | ||||
\(267\) | −0.727447 | − | 0.419992i | −0.0445190 | − | 0.0257031i | ||||
\(268\) | −0.371098 | + | 0.214254i | −0.0226684 | + | 0.0130876i | ||||
\(269\) | 6.95564 | + | 12.0475i | 0.424093 | + | 0.734551i | 0.996335 | − | 0.0855341i | \(-0.0272596\pi\) |
−0.572242 | + | 0.820085i | \(0.693926\pi\) | |||||||
\(270\) | −0.981775 | − | 2.00901i | −0.0597489 | − | 0.122264i | ||||
\(271\) | 16.6543 | 1.01168 | 0.505838 | − | 0.862629i | \(-0.331184\pi\) | ||||
0.505838 | + | 0.862629i | \(0.331184\pi\) | |||||||
\(272\) | 5.39463 | + | 3.11459i | 0.327098 | + | 0.188850i | ||||
\(273\) | 2.59196 | + | 1.49647i | 0.156873 | + | 0.0905705i | ||||
\(274\) | 6.42025 | + | 11.1202i | 0.387861 | + | 0.671796i | ||||
\(275\) | −0.903319 | − | 0.125535i | −0.0544722 | − | 0.00757004i | ||||
\(276\) | 1.71325 | − | 2.96744i | 0.103126 | − | 0.178619i | ||||
\(277\) | − | 15.3671i | − | 0.923321i | −0.887057 | − | 0.461660i | \(-0.847254\pi\) | ||
0.887057 | − | 0.461660i | \(-0.152746\pi\) | |||||||
\(278\) | − | 3.85068i | − | 0.230949i | ||||||
\(279\) | 0.360101 | − | 5.55611i | 0.0215587 | − | 0.332635i | ||||
\(280\) | 1.72490 | + | 0.119282i | 0.103083 | + | 0.00712848i | ||||
\(281\) | 17.4465 | 1.04077 | 0.520384 | − | 0.853932i | \(-0.325789\pi\) | ||||
0.520384 | + | 0.853932i | \(0.325789\pi\) | |||||||
\(282\) | 5.34590 | + | 3.08646i | 0.318344 | + | 0.183796i | ||||
\(283\) | − | 28.9290i | − | 1.71965i | −0.510588 | − | 0.859826i | \(-0.670572\pi\) | ||
0.510588 | − | 0.859826i | \(-0.329428\pi\) | |||||||
\(284\) | −4.02888 | − | 6.97823i | −0.239070 | − | 0.414082i | ||||
\(285\) | −1.10746 | − | 0.745751i | −0.0656002 | − | 0.0441745i | ||||
\(286\) | −0.353002 | + | 0.611418i | −0.0208735 | + | 0.0361539i | ||||
\(287\) | 1.43920i | 0.0849536i | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 10.9014 | + | 18.8817i | 0.641258 | + | 1.11069i | ||||
\(290\) | 14.3148 | − | 6.99546i | 0.840596 | − | 0.410787i | ||||
\(291\) | 4.75841 | − | 8.24181i | 0.278943 | − | 0.483143i | ||||
\(292\) | 9.05991 | − | 5.23074i | 0.530191 | − | 0.306106i | ||||
\(293\) | 7.37274 | + | 4.25665i | 0.430720 | + | 0.248676i | 0.699653 | − | 0.714482i | \(-0.253338\pi\) |
−0.268933 | + | 0.963159i | \(0.586671\pi\) | |||||||
\(294\) | 6.40210 | 0.373378 | ||||||||
\(295\) | −26.9355 | − | 1.86267i | −1.56825 | − | 0.108449i | ||||
\(296\) | 3.20418 | − | 5.54979i | 0.186239 | − | 0.322575i | ||||
\(297\) | −0.157963 | + | 0.0912000i | −0.00916595 | + | 0.00529196i | ||||
\(298\) | 10.9066 | + | 6.29694i | 0.631803 | + | 0.364772i | ||||
\(299\) | 6.63137 | + | 11.4859i | 0.383502 | + | 0.664245i | ||||
\(300\) | 4.63303 | − | 1.88017i | 0.267488 | − | 0.108552i | ||||
\(301\) | −2.58312 | − | 4.47410i | −0.148889 | − | 0.257883i | ||||
\(302\) | 12.8986i | 0.742229i | ||||||||
\(303\) | 10.1817 | + | 5.87840i | 0.584923 | + | 0.337705i | ||||
\(304\) | −0.298547 | + | 0.517099i | −0.0171229 | + | 0.0296577i | ||||
\(305\) | 0.957817 | + | 1.95998i | 0.0548444 | + | 0.112228i | ||||
\(306\) | −6.22919 | −0.356099 | ||||||||
\(307\) | −18.6892 | − | 10.7902i | −1.06665 | − | 0.615830i | −0.139385 | − | 0.990238i | \(-0.544513\pi\) |
−0.927264 | + | 0.374408i | \(0.877846\pi\) | |||||||
\(308\) | − | 0.141039i | − | 0.00803646i | ||||||
\(309\) | −9.62886 | −0.547766 | ||||||||
\(310\) | 12.3387 | + | 1.66039i | 0.700790 | + | 0.0943039i | ||||
\(311\) | 7.50012 | 0.425293 | 0.212646 | − | 0.977129i | \(-0.431792\pi\) | ||||
0.212646 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(312\) | − | 3.87064i | − | 0.219132i | ||||||
\(313\) | −10.1694 | − | 5.87130i | −0.574808 | − | 0.331866i | 0.184259 | − | 0.982878i | \(-0.441011\pi\) |
−0.759067 | + | 0.651012i | \(0.774345\pi\) | |||||||
\(314\) | −14.4319 | −0.814442 | ||||||||
\(315\) | −1.55345 | + | 0.759149i | −0.0875269 | + | 0.0427732i | ||||
\(316\) | −3.64065 | + | 6.30578i | −0.204802 | + | 0.354728i | ||||
\(317\) | −21.7925 | − | 12.5819i | −1.22399 | − | 0.706672i | −0.258225 | − | 0.966085i | \(-0.583138\pi\) |
−0.965766 | + | 0.259413i | \(0.916471\pi\) | |||||||
\(318\) | 8.65569i | 0.485387i | ||||||||
\(319\) | −0.649829 | − | 1.12554i | −0.0363834 | − | 0.0630180i | ||||
\(320\) | −0.981775 | − | 2.00901i | −0.0548829 | − | 0.112307i | ||||
\(321\) | −3.57179 | − | 6.18652i | −0.199358 | − | 0.345298i | ||||
\(322\) | −2.29455 | − | 1.32476i | −0.127870 | − | 0.0738258i | ||||
\(323\) | −3.22111 | + | 1.85971i | −0.179227 | + | 0.103477i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −2.66393 | + | 19.1690i | −0.147768 | + | 1.06330i | ||||
\(326\) | 1.86439 | 0.103259 | ||||||||
\(327\) | −13.8496 | − | 7.99606i | −0.765883 | − | 0.442183i | ||||
\(328\) | 1.61190 | − | 0.930631i | 0.0890023 | − | 0.0513855i | ||||
\(329\) | 2.38658 | − | 4.13367i | 0.131576 | − | 0.227897i | ||||
\(330\) | −0.179076 | − | 0.366443i | −0.00985780 | − | 0.0201720i | ||||
\(331\) | −16.4267 | − | 28.4518i | −0.902891 | − | 1.56385i | −0.823724 | − | 0.566991i | \(-0.808107\pi\) |
−0.0791671 | − | 0.996861i | \(-0.525226\pi\) | |||||||
\(332\) | −6.97624 | + | 4.02773i | −0.382871 | + | 0.221051i | ||||
\(333\) | 6.40835i | 0.351175i | ||||||||
\(334\) | 0.351430 | − | 0.608695i | 0.0192294 | − | 0.0333063i | ||||
\(335\) | 0.794773 | + | 0.535191i | 0.0434231 | + | 0.0292406i | ||||
\(336\) | 0.386621 | + | 0.669647i | 0.0210919 | + | 0.0365322i | ||||
\(337\) | − | 12.7086i | − | 0.692281i | −0.938183 | − | 0.346140i | \(-0.887492\pi\) | ||
0.938183 | − | 0.346140i | \(-0.112508\pi\) | |||||||
\(338\) | 1.71633 | + | 0.990925i | 0.0933562 | + | 0.0538992i | ||||
\(339\) | 14.1977 | 0.771114 | ||||||||
\(340\) | 0.960930 | − | 13.8957i | 0.0521138 | − | 0.753600i | ||||
\(341\) | 0.0656824 | − | 1.01343i | 0.00355690 | − | 0.0548805i | ||||
\(342\) | − | 0.597095i | − | 0.0322872i | ||||||
\(343\) | − | 10.3631i | − | 0.559553i | ||||||
\(344\) | −3.34064 | + | 5.78617i | −0.180115 | + | 0.311969i | ||||
\(345\) | −7.64363 | − | 0.528581i | −0.411519 | − | 0.0284578i | ||||
\(346\) | 3.67328 | + | 6.36230i | 0.197477 | + | 0.342040i | ||||
\(347\) | −26.0657 | − | 15.0491i | −1.39928 | − | 0.807876i | −0.404964 | − | 0.914332i | \(-0.632716\pi\) |
−0.994317 | + | 0.106457i | \(0.966049\pi\) | |||||||
\(348\) | 6.17071 | + | 3.56266i | 0.330785 | + | 0.190979i | ||||
\(349\) | 8.86982 | 0.474790 | 0.237395 | − | 0.971413i | \(-0.423706\pi\) | ||||
0.237395 | + | 0.971413i | \(0.423706\pi\) | |||||||
\(350\) | −1.45383 | − | 3.58245i | −0.0777102 | − | 0.191490i | ||||
\(351\) | 1.93532 | + | 3.35207i | 0.103300 | + | 0.178920i | ||||
\(352\) | −0.157963 | + | 0.0912000i | −0.00841946 | + | 0.00486098i | ||||
\(353\) | 10.3613 | + | 5.98210i | 0.551476 | + | 0.318395i | 0.749717 | − | 0.661758i | \(-0.230190\pi\) |
−0.198241 | + | 0.980153i | \(0.563523\pi\) | |||||||
\(354\) | −6.03735 | − | 10.4570i | −0.320882 | − | 0.555783i | ||||
\(355\) | −10.0639 | + | 14.9451i | −0.534135 | + | 0.793205i | ||||
\(356\) | 0.839983 | 0.0445190 | ||||||||
\(357\) | 4.81667i | 0.254925i | ||||||||
\(358\) | −0.425154 | − | 0.245463i | −0.0224701 | − | 0.0129731i | ||||
\(359\) | −2.64689 | − | 4.58455i | −0.139697 | − | 0.241963i | 0.787685 | − | 0.616079i | \(-0.211280\pi\) |
−0.927382 | + | 0.374116i | \(0.877946\pi\) | |||||||
\(360\) | 1.85475 | + | 1.24897i | 0.0977537 | + | 0.0658263i | ||||
\(361\) | 9.32174 | + | 16.1457i | 0.490618 | + | 0.849775i | ||||
\(362\) | −14.6853 | + | 8.47857i | −0.771843 | + | 0.445624i | ||||
\(363\) | 9.49747 | − | 5.48337i | 0.498488 | − | 0.287802i | ||||
\(364\) | −2.99294 | −0.156873 | ||||||||
\(365\) | −19.4034 | − | 13.0660i | −1.01562 | − | 0.683907i | ||||
\(366\) | −0.487799 | + | 0.844892i | −0.0254976 | + | 0.0441632i | ||||
\(367\) | −19.4298 | + | 11.2178i | −1.01423 | + | 0.585564i | −0.912427 | − | 0.409240i | \(-0.865794\pi\) |
−0.101801 | + | 0.994805i | \(0.532460\pi\) | |||||||
\(368\) | 3.42650i | 0.178619i | ||||||||
\(369\) | −0.930631 | + | 1.61190i | −0.0484467 | + | 0.0839121i | ||||
\(370\) | −14.2954 | − | 0.988569i | −0.743181 | − | 0.0513932i | ||||
\(371\) | 6.69294 | 0.347480 | ||||||||
\(372\) | 2.46620 | + | 4.99178i | 0.127866 | + | 0.258812i | ||||
\(373\) | − | 3.89756i | − | 0.201808i | −0.994896 | − | 0.100904i | \(-0.967826\pi\) | ||
0.994896 | − | 0.100904i | \(-0.0321735\pi\) | |||||||
\(374\) | −1.13620 | −0.0587517 | ||||||||
\(375\) | −8.32587 | − | 7.46189i | −0.429946 | − | 0.385331i | ||||
\(376\) | −6.17291 | −0.318344 | ||||||||
\(377\) | −23.8846 | + | 13.7898i | −1.23012 | + | 0.710209i | ||||
\(378\) | −0.669647 | − | 0.386621i | −0.0344429 | − | 0.0198856i | ||||
\(379\) | 11.7489 | − | 20.3497i | 0.603499 | − | 1.04529i | −0.388787 | − | 0.921327i | \(-0.627106\pi\) |
0.992287 | − | 0.123964i | \(-0.0395607\pi\) | |||||||
\(380\) | 1.33196 | + | 0.0921094i | 0.0683283 | + | 0.00472511i | ||||
\(381\) | 5.99913 | + | 10.3908i | 0.307345 | + | 0.532337i | ||||
\(382\) | 8.55408 | − | 4.93870i | 0.437665 | − | 0.252686i | ||||
\(383\) | −5.23407 | + | 3.02189i | −0.267449 | + | 0.154412i | −0.627728 | − | 0.778433i | \(-0.716015\pi\) |
0.360279 | + | 0.932845i | \(0.382682\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −0.283349 | + | 0.138469i | −0.0144408 | + | 0.00705703i | ||||
\(386\) | −4.36812 | + | 7.56580i | −0.222331 | + | 0.385089i | ||||
\(387\) | − | 6.68129i | − | 0.339629i | ||||||
\(388\) | 9.51682i | 0.483143i | ||||||||
\(389\) | 3.21583 | − | 5.56997i | 0.163049 | − | 0.282409i | −0.772912 | − | 0.634513i | \(-0.781201\pi\) |
0.935961 | + | 0.352105i | \(0.114534\pi\) | |||||||
\(390\) | −7.77615 | + | 3.80010i | −0.393761 | + | 0.192425i | ||||
\(391\) | −10.6722 | + | 18.4847i | −0.539714 | + | 0.934812i | ||||
\(392\) | −5.54438 | + | 3.20105i | −0.280033 | + | 0.161677i | ||||
\(393\) | 7.17915 | − | 4.14488i | 0.362140 | − | 0.209082i | ||||
\(394\) | 0.663337 | + | 1.14893i | 0.0334185 | + | 0.0578825i | ||||
\(395\) | 16.2427 | + | 1.12323i | 0.817257 | + | 0.0565159i | ||||
\(396\) | 0.0912000 | − | 0.157963i | 0.00458297 | − | 0.00793794i | ||||
\(397\) | 29.5449 | + | 17.0578i | 1.48282 | + | 0.856105i | 0.999810 | − | 0.0195106i | \(-0.00621081\pi\) |
0.483008 | + | 0.875616i | \(0.339544\pi\) | |||||||
\(398\) | 21.3331 | − | 12.3167i | 1.06933 | − | 0.617380i | ||||
\(399\) | −0.461698 | −0.0231138 | ||||||||
\(400\) | −3.07224 | + | 3.94479i | −0.153612 | + | 0.197239i | ||||
\(401\) | −36.6374 | −1.82959 | −0.914793 | − | 0.403924i | \(-0.867646\pi\) | ||||
−0.914793 | + | 0.403924i | \(0.867646\pi\) | |||||||
\(402\) | 0.428507i | 0.0213720i | ||||||||
\(403\) | −21.5057 | − | 1.39382i | −1.07127 | − | 0.0694312i | ||||
\(404\) | −11.7568 | −0.584923 | ||||||||
\(405\) | −2.23074 | − | 0.154263i | −0.110846 | − | 0.00766537i | ||||
\(406\) | 2.75480 | − | 4.77145i | 0.136718 | − | 0.236803i | ||||
\(407\) | 1.16888i | 0.0579394i | ||||||||
\(408\) | 5.39463 | − | 3.11459i | 0.267074 | − | 0.154195i | ||||
\(409\) | −10.5653 | + | 18.2997i | −0.522422 | + | 0.904861i | 0.477238 | + | 0.878774i | \(0.341638\pi\) |
−0.999660 | + | 0.0260870i | \(0.991695\pi\) | |||||||
\(410\) | −3.45217 | − | 2.32465i | −0.170490 | − | 0.114806i | ||||
\(411\) | 12.8405 | 0.633375 | ||||||||
\(412\) | 8.33883 | − | 4.81443i | 0.410825 | − | 0.237190i | ||||
\(413\) | −8.08579 | + | 4.66833i | −0.397876 | + | 0.229714i | ||||
\(414\) | −1.71325 | − | 2.96744i | −0.0842017 | − | 0.145842i | ||||
\(415\) | 14.9409 | + | 10.0610i | 0.733418 | + | 0.493875i | ||||
\(416\) | 1.93532 | + | 3.35207i | 0.0948869 | + | 0.164349i | ||||
\(417\) | −3.33479 | − | 1.92534i | −0.163305 | − | 0.0942844i | ||||
\(418\) | − | 0.108910i | − | 0.00532697i | ||||||
\(419\) | −22.8606 | −1.11681 | −0.558406 | − | 0.829568i | \(-0.688587\pi\) | ||||
−0.558406 | + | 0.829568i | \(0.688587\pi\) | |||||||
\(420\) | 0.965752 | − | 1.43417i | 0.0471239 | − | 0.0699802i | ||||
\(421\) | −6.83483 | − | 11.8383i | −0.333109 | − | 0.576962i | 0.650010 | − | 0.759925i | \(-0.274765\pi\) |
−0.983120 | + | 0.182963i | \(0.941431\pi\) | |||||||
\(422\) | 14.0562 | + | 8.11534i | 0.684244 | + | 0.395049i | ||||
\(423\) | 5.34590 | − | 3.08646i | 0.259926 | − | 0.150069i | ||||
\(424\) | −4.32784 | − | 7.49604i | −0.210179 | − | 0.364040i | ||||
\(425\) | −28.8600 | + | 11.7119i | −1.39992 | + | 0.568112i | ||||
\(426\) | −8.05777 | −0.390400 | ||||||||
\(427\) | 0.653305 | + | 0.377186i | 0.0316157 | + | 0.0182533i | ||||
\(428\) | 6.18652 | + | 3.57179i | 0.299037 | + | 0.172649i | ||||
\(429\) | 0.353002 | + | 0.611418i | 0.0170431 | + | 0.0295195i | ||||
\(430\) | 14.9042 | + | 1.03067i | 0.718745 | + | 0.0497035i | ||||
\(431\) | −9.10321 | + | 15.7672i | −0.438486 | + | 0.759480i | −0.997573 | − | 0.0696289i | \(-0.977818\pi\) |
0.559087 | + | 0.829109i | \(0.311152\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 2.97874i | − | 0.143149i | −0.997435 | − | 0.0715746i | \(-0.977198\pi\) | ||
0.997435 | − | 0.0715746i | \(-0.0228024\pi\) | |||||||
\(434\) | 3.85985 | − | 1.90697i | 0.185279 | − | 0.0915373i | ||||
\(435\) | 1.09917 | − | 15.8947i | 0.0527012 | − | 0.762094i | ||||
\(436\) | 15.9921 | 0.765883 | ||||||||
\(437\) | −1.77184 | − | 1.02297i | −0.0847586 | − | 0.0489354i | ||||
\(438\) | − | 10.4615i | − | 0.499869i | ||||||
\(439\) | 1.88163 | + | 3.25908i | 0.0898052 | + | 0.155547i | 0.907429 | − | 0.420206i | \(-0.138042\pi\) |
−0.817623 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(440\) | 0.338306 | + | 0.227811i | 0.0161281 | + | 0.0108605i | ||||
\(441\) | 3.20105 | − | 5.54438i | 0.152431 | − | 0.264018i | ||||
\(442\) | 24.1109i | 1.14684i | ||||||||
\(443\) | −23.4960 | + | 13.5654i | −1.11633 | + | 0.644512i | −0.940461 | − | 0.339903i | \(-0.889606\pi\) |
−0.175866 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(444\) | −3.20418 | − | 5.54979i | −0.152063 | − | 0.263382i | ||||
\(445\) | −0.824674 | − | 1.68753i | −0.0390933 | − | 0.0799968i | ||||
\(446\) | 9.98614 | − | 17.2965i | 0.472858 | − | 0.819013i | ||||
\(447\) | 10.9066 | − | 6.29694i | 0.515865 | − | 0.297835i | ||||
\(448\) | −0.669647 | − | 0.386621i | −0.0316378 | − | 0.0182661i | ||||
\(449\) | −41.4038 | −1.95397 | −0.976983 | − | 0.213316i | \(-0.931574\pi\) | ||||
−0.976983 | + | 0.213316i | \(0.931574\pi\) | |||||||
\(450\) | 0.688239 | − | 4.95241i | 0.0324439 | − | 0.233459i | ||||
\(451\) | −0.169747 | + | 0.294011i | −0.00799308 | + | 0.0138444i | ||||
\(452\) | −12.2956 | + | 7.09885i | −0.578335 | + | 0.333902i | ||||
\(453\) | 11.1705 | + | 6.44928i | 0.524835 | + | 0.303014i | ||||
\(454\) | 11.6778 | + | 20.2265i | 0.548064 | + | 0.949275i | ||||
\(455\) | 2.93839 | + | 6.01284i | 0.137754 | + | 0.281886i | ||||
\(456\) | 0.298547 | + | 0.517099i | 0.0139808 | + | 0.0242154i | ||||
\(457\) | − | 24.6010i | − | 1.15079i | −0.817877 | − | 0.575393i | \(-0.804849\pi\) | ||
0.817877 | − | 0.575393i | \(-0.195151\pi\) | |||||||
\(458\) | 11.5373 | + | 6.66108i | 0.539104 | + | 0.311252i | ||||
\(459\) | −3.11459 | + | 5.39463i | −0.145377 | + | 0.251800i | ||||
\(460\) | 6.88387 | − | 3.36405i | 0.320962 | − | 0.156850i | ||||
\(461\) | −5.75649 | −0.268106 | −0.134053 | − | 0.990974i | \(-0.542799\pi\) | ||||
−0.134053 | + | 0.990974i | \(0.542799\pi\) | |||||||
\(462\) | −0.122144 | − | 0.0705196i | −0.00568263 | − | 0.00328087i | ||||
\(463\) | 30.2945i | 1.40791i | 0.710246 | + | 0.703953i | \(0.248583\pi\) | ||||
−0.710246 | + | 0.703953i | \(0.751417\pi\) | |||||||
\(464\) | −7.12532 | −0.330785 | ||||||||
\(465\) | 7.60728 | − | 9.85542i | 0.352779 | − | 0.457034i | ||||
\(466\) | −10.6233 | −0.492116 | ||||||||
\(467\) | − | 24.8358i | − | 1.14927i | −0.818412 | − | 0.574633i | \(-0.805145\pi\) | ||
0.818412 | − | 0.574633i | \(-0.194855\pi\) | |||||||
\(468\) | −3.35207 | − | 1.93532i | −0.154950 | − | 0.0894602i | ||||
\(469\) | 0.331340 | 0.0152998 | ||||||||
\(470\) | 6.06041 | + | 12.4014i | 0.279546 | + | 0.572036i | ||||
\(471\) | −7.21597 | + | 12.4984i | −0.332494 | + | 0.575897i | ||||
\(472\) | 10.4570 | + | 6.03735i | 0.481323 | + | 0.277892i | ||||
\(473\) | − | 1.21867i | − | 0.0560344i | ||||||
\(474\) | 3.64065 | + | 6.30578i | 0.167220 | + | 0.289634i | ||||
\(475\) | −1.12264 | − | 2.76636i | −0.0515102 | − | 0.126929i | ||||
\(476\) | −2.40833 | − | 4.17135i | −0.110386 | − | 0.191194i | ||||
\(477\) | 7.49604 | + | 4.32784i | 0.343220 | + | 0.198158i | ||||
\(478\) | 8.04884 | − | 4.64700i | 0.368145 | − | 0.212549i | ||||
\(479\) | −19.4463 | + | 33.6819i | −0.888523 | + | 1.53897i | −0.0469010 | + | 0.998900i | \(0.514935\pi\) |
−0.841622 | + | 0.540067i | \(0.818399\pi\) | |||||||
\(480\) | −2.23074 | − | 0.154263i | −0.101819 | − | 0.00704109i | ||||
\(481\) | 24.8044 | 1.13098 | ||||||||
\(482\) | −7.24239 | − | 4.18140i | −0.329882 | − | 0.190457i | ||||
\(483\) | −2.29455 | + | 1.32476i | −0.104405 | + | 0.0602785i | ||||
\(484\) | −5.48337 | + | 9.49747i | −0.249244 | + | 0.431703i | ||||
\(485\) | 19.1194 | − | 9.34338i | 0.868166 | − | 0.424261i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 1.68240 | − | 0.971337i | 0.0762370 | − | 0.0440155i | −0.461397 | − | 0.887194i | \(-0.652652\pi\) |
0.537634 | + | 0.843178i | \(0.319318\pi\) | |||||||
\(488\) | − | 0.975597i | − | 0.0441632i | ||||||
\(489\) | 0.932193 | − | 1.61461i | 0.0421552 | − | 0.0730150i | ||||
\(490\) | 11.8743 | + | 7.99600i | 0.536425 | + | 0.361222i | ||||
\(491\) | 14.8550 | + | 25.7295i | 0.670395 | + | 1.16116i | 0.977792 | + | 0.209576i | \(0.0672085\pi\) |
−0.307398 | + | 0.951581i | \(0.599458\pi\) | |||||||
\(492\) | − | 1.86126i | − | 0.0839121i | ||||||
\(493\) | −38.4385 | − | 22.1925i | −1.73118 | − | 0.999498i | ||||
\(494\) | −2.31114 | −0.103983 | ||||||||
\(495\) | −0.406887 | − | 0.0281375i | −0.0182882 | − | 0.00126469i | ||||
\(496\) | −4.63168 | − | 3.08991i | −0.207969 | − | 0.138741i | ||||
\(497\) | 6.23060i | 0.279481i | ||||||||
\(498\) | 8.05547i | 0.360974i | ||||||||
\(499\) | −1.99859 | + | 3.46166i | −0.0894693 | + | 0.154965i | −0.907287 | − | 0.420512i | \(-0.861850\pi\) |
0.817818 | + | 0.575477i | \(0.195184\pi\) | |||||||
\(500\) | 10.9414 | + | 2.29925i | 0.489313 | + | 0.102826i | ||||
\(501\) | −0.351430 | − | 0.608695i | −0.0157007 | − | 0.0271945i | ||||
\(502\) | −15.7872 | − | 9.11474i | −0.704617 | − | 0.406811i | ||||
\(503\) | 20.2717 | + | 11.7039i | 0.903871 | + | 0.521850i | 0.878454 | − | 0.477827i | \(-0.158575\pi\) |
0.0254170 | + | 0.999677i | \(0.491909\pi\) | |||||||
\(504\) | 0.773241 | 0.0344429 | ||||||||
\(505\) | 11.5425 | + | 23.6195i | 0.513636 | + | 1.05106i | ||||
\(506\) | −0.312497 | − | 0.541261i | −0.0138922 | − | 0.0240620i | ||||
\(507\) | 1.71633 | − | 0.990925i | 0.0762250 | − | 0.0440085i | ||||
\(508\) | −10.3908 | − | 5.99913i | −0.461017 | − | 0.266168i | ||||
\(509\) | 16.9298 | + | 29.3232i | 0.750399 | + | 1.29973i | 0.947629 | + | 0.319372i | \(0.103472\pi\) |
−0.197230 | + | 0.980357i | \(0.563195\pi\) | |||||||
\(510\) | −11.5536 | − | 7.78004i | −0.511600 | − | 0.344506i | ||||
\(511\) | −8.08925 | −0.357847 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −0.517099 | − | 0.298547i | −0.0228305 | − | 0.0131812i | ||||
\(514\) | 0.746676 | + | 1.29328i | 0.0329345 | + | 0.0570442i | ||||
\(515\) | −17.8591 | − | 12.0261i | −0.786965 | − | 0.529934i | ||||
\(516\) | 3.34064 | + | 5.78617i | 0.147064 | + | 0.254722i | ||||
\(517\) | 0.975092 | − | 0.562970i | 0.0428845 | − | 0.0247594i | ||||
\(518\) | −4.29133 | + | 2.47760i | −0.188550 | + | 0.108860i | ||||
\(519\) | 7.34656 | 0.322478 | ||||||||
\(520\) | 4.83430 | − | 7.17906i | 0.211998 | − | 0.314822i | ||||
\(521\) | −9.26685 | + | 16.0507i | −0.405988 | + | 0.703192i | −0.994436 | − | 0.105343i | \(-0.966406\pi\) |
0.588448 | + | 0.808535i | \(0.299739\pi\) | |||||||
\(522\) | 6.17071 | − | 3.56266i | 0.270084 | − | 0.155933i | ||||
\(523\) | 19.2334i | 0.841019i | 0.907288 | + | 0.420509i | \(0.138149\pi\) | ||||
−0.907288 | + | 0.420509i | \(0.861851\pi\) | |||||||
\(524\) | −4.14488 | + | 7.17915i | −0.181070 | + | 0.313623i | ||||
\(525\) | −3.82941 | − | 0.532175i | −0.167129 | − | 0.0232260i | ||||
\(526\) | −21.7443 | −0.948095 | ||||||||
\(527\) | −15.3624 | − | 31.0947i | −0.669197 | − | 1.35451i | ||||
\(528\) | 0.182400i | 0.00793794i | ||||||||
\(529\) | 11.2591 | 0.489526 | ||||||||
\(530\) | −10.8107 | + | 16.0541i | −0.469585 | + | 0.697346i | ||||
\(531\) | −12.0747 | −0.523998 | ||||||||
\(532\) | 0.399843 | − | 0.230849i | 0.0173354 | − | 0.0100086i | ||||
\(533\) | 6.23908 | + | 3.60214i | 0.270245 | + | 0.156026i | ||||
\(534\) | 0.419992 | − | 0.727447i | 0.0181748 | − | 0.0314797i | ||||
\(535\) | 1.10199 | − | 15.9355i | 0.0476430 | − | 0.688950i | ||||
\(536\) | −0.214254 | − | 0.371098i | −0.00925435 | − | 0.0160290i | ||||
\(537\) | −0.425154 | + | 0.245463i | −0.0183467 | + | 0.0105925i | ||||
\(538\) | −12.0475 | + | 6.95564i | −0.519406 | + | 0.299879i | ||||
\(539\) | 0.583871 | − | 1.01130i | 0.0251491 | − | 0.0435596i | ||||
\(540\) | 2.00901 | − | 0.981775i | 0.0864540 | − | 0.0422489i | ||||
\(541\) | −4.65254 | + | 8.05844i | −0.200028 | + | 0.346459i | −0.948537 | − | 0.316665i | \(-0.897437\pi\) |
0.748509 | + | 0.663125i | \(0.230770\pi\) | |||||||
\(542\) | 16.6543i | 0.715362i | ||||||||
\(543\) | 16.9571i | 0.727700i | ||||||||
\(544\) | −3.11459 | + | 5.39463i | −0.133537 | + | 0.231293i | ||||
\(545\) | −15.7007 | − | 32.1283i | −0.672542 | − | 1.37623i | ||||
\(546\) | −1.49647 | + | 2.59196i | −0.0640430 | + | 0.110926i | ||||
\(547\) | 0.685180 | − | 0.395589i | 0.0292962 | − | 0.0169141i | −0.485280 | − | 0.874359i | \(-0.661282\pi\) |
0.514577 | + | 0.857444i | \(0.327949\pi\) | |||||||
\(548\) | −11.1202 | + | 6.42025i | −0.475031 | + | 0.274259i | ||||
\(549\) | 0.487799 | + | 0.844892i | 0.0208187 | + | 0.0360591i | ||||
\(550\) | 0.125535 | − | 0.903319i | 0.00535283 | − | 0.0385177i | ||||
\(551\) | 2.12724 | − | 3.68450i | 0.0906237 | − | 0.156965i | ||||
\(552\) | 2.96744 | + | 1.71325i | 0.126302 | + | 0.0729208i | ||||
\(553\) | 4.87589 | − | 2.81510i | 0.207344 | − | 0.119710i | ||||
\(554\) | 15.3671 | 0.652886 | ||||||||
\(555\) | −8.00381 | + | 11.8859i | −0.339743 | + | 0.504527i | ||||
\(556\) | 3.85068 | 0.163305 | ||||||||
\(557\) | 25.2701i | 1.07073i | 0.844621 | + | 0.535365i | \(0.179826\pi\) | ||||
−0.844621 | + | 0.535365i | \(0.820174\pi\) | |||||||
\(558\) | 5.55611 | + | 0.360101i | 0.235209 | + | 0.0152443i | ||||
\(559\) | −25.8609 | −1.09380 | ||||||||
\(560\) | −0.119282 | + | 1.72490i | −0.00504059 | + | 0.0728904i | ||||
\(561\) | −0.568102 | + | 0.983981i | −0.0239853 | + | 0.0415437i | ||||
\(562\) | 17.4465i | 0.735934i | ||||||||
\(563\) | −38.7751 | + | 22.3868i | −1.63418 | + | 0.943492i | −0.651389 | + | 0.758744i | \(0.725814\pi\) |
−0.982786 | + | 0.184748i | \(0.940853\pi\) | |||||||
\(564\) | −3.08646 | + | 5.34590i | −0.129963 | + | 0.225103i | ||||
\(565\) | 26.3331 | + | 17.7324i | 1.10784 | + | 0.746010i | ||||
\(566\) | 28.9290 | 1.21598 | ||||||||
\(567\) | −0.669647 | + | 0.386621i | −0.0281225 | + | 0.0162365i | ||||
\(568\) | 6.97823 | − | 4.02888i | 0.292800 | − | 0.169048i | ||||
\(569\) | −14.8782 | − | 25.7699i | −0.623728 | − | 1.08033i | −0.988785 | − | 0.149344i | \(-0.952284\pi\) |
0.365057 | − | 0.930985i | \(-0.381049\pi\) | |||||||
\(570\) | 0.745751 | − | 1.10746i | 0.0312361 | − | 0.0463864i | ||||
\(571\) | −5.85732 | − | 10.1452i | −0.245121 | − | 0.424562i | 0.717045 | − | 0.697027i | \(-0.245494\pi\) |
−0.962166 | + | 0.272465i | \(0.912161\pi\) | |||||||
\(572\) | −0.611418 | − | 0.353002i | −0.0255647 | − | 0.0147598i | ||||
\(573\) | − | 9.87740i | − | 0.412634i | ||||||
\(574\) | −1.43920 | −0.0600712 | ||||||||
\(575\) | −13.5168 | − | 10.5270i | −0.563691 | − | 0.439007i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 26.0152 | + | 15.0199i | 1.08303 | + | 0.625286i | 0.931712 | − | 0.363199i | \(-0.118315\pi\) |
0.151316 | + | 0.988485i | \(0.451649\pi\) | |||||||
\(578\) | −18.8817 | + | 10.9014i | −0.785377 | + | 0.453438i | ||||
\(579\) | 4.36812 | + | 7.56580i | 0.181533 | + | 0.314424i | ||||
\(580\) | 6.99546 | + | 14.3148i | 0.290471 | + | 0.594391i | ||||
\(581\) | 6.22882 | 0.258415 | ||||||||
\(582\) | 8.24181 | + | 4.75841i | 0.341634 | + | 0.197242i | ||||
\(583\) | 1.36728 | + | 0.789399i | 0.0566269 | + | 0.0326936i | ||||
\(584\) | 5.23074 | + | 9.05991i | 0.216450 | + | 0.374902i | ||||
\(585\) | −0.597095 | + | 8.63439i | −0.0246868 | + | 0.356988i | ||||
\(586\) | −4.25665 | + | 7.37274i | −0.175841 | + | 0.304565i | ||||
\(587\) | − | 37.1122i | − | 1.53178i | −0.642969 | − | 0.765892i | \(-0.722298\pi\) | ||
0.642969 | − | 0.765892i | \(-0.277702\pi\) | |||||||
\(588\) | 6.40210i | 0.264018i | ||||||||
\(589\) | 2.98057 | − | 1.47255i | 0.122812 | − | 0.0606755i | ||||
\(590\) | 1.86267 | − | 26.9355i | 0.0766851 | − | 1.10892i | ||||
\(591\) | 1.32667 | 0.0545721 | ||||||||
\(592\) | 5.54979 | + | 3.20418i | 0.228095 | + | 0.131691i | ||||
\(593\) | − | 11.8545i | − | 0.486806i | −0.969925 | − | 0.243403i | \(-0.921736\pi\) | ||
0.969925 | − | 0.243403i | \(-0.0782638\pi\) | |||||||
\(594\) | −0.0912000 | − | 0.157963i | −0.00374198 | − | 0.00648130i | ||||
\(595\) | −6.01585 | + | 8.93369i | −0.246626 | + | 0.366246i | ||||
\(596\) | −6.29694 | + | 10.9066i | −0.257933 | + | 0.446752i | ||||
\(597\) | − | 24.6334i | − | 1.00818i | ||||||
\(598\) | −11.4859 | + | 6.63137i | −0.469692 | + | 0.271177i | ||||
\(599\) | 8.73826 | + | 15.1351i | 0.357036 | + | 0.618404i | 0.987464 | − | 0.157843i | \(-0.0504541\pi\) |
−0.630428 | + | 0.776247i | \(0.717121\pi\) | |||||||
\(600\) | 1.88017 | + | 4.63303i | 0.0767576 | + | 0.189143i | ||||
\(601\) | −12.7413 | + | 22.0685i | −0.519728 | + | 0.900195i | 0.480009 | + | 0.877263i | \(0.340633\pi\) |
−0.999737 | + | 0.0229313i | \(0.992700\pi\) | |||||||
\(602\) | 4.47410 | − | 2.58312i | 0.182351 | − | 0.105280i | ||||
\(603\) | 0.371098 | + | 0.214254i | 0.0151123 | + | 0.00872509i | ||||
\(604\) | −12.8986 | −0.524835 | ||||||||
\(605\) | 24.4639 | + | 1.69176i | 0.994600 | + | 0.0687797i | ||||
\(606\) | −5.87840 | + | 10.1817i | −0.238794 | + | 0.413603i | ||||
\(607\) | 30.6602 | − | 17.7016i | 1.24446 | − | 0.718488i | 0.274459 | − | 0.961599i | \(-0.411501\pi\) |
0.969998 | + | 0.243111i | \(0.0781680\pi\) | |||||||
\(608\) | −0.517099 | − | 0.298547i | −0.0209711 | − | 0.0121077i | ||||
\(609\) | −2.75480 | − | 4.77145i | −0.111630 | − | 0.193349i | ||||
\(610\) | −1.95998 | + | 0.957817i | −0.0793574 | + | 0.0387809i | ||||
\(611\) | −11.9466 | − | 20.6920i | −0.483306 | − | 0.837111i | ||||
\(612\) | − | 6.22919i | − | 0.251800i | ||||||
\(613\) | 4.02516 | + | 2.32392i | 0.162574 | + | 0.0938624i | 0.579080 | − | 0.815271i | \(-0.303412\pi\) |
−0.416505 | + | 0.909133i | \(0.636745\pi\) | |||||||
\(614\) | 10.7902 | − | 18.6892i | 0.435458 | − | 0.754235i | ||||
\(615\) | −3.73929 | + | 1.82734i | −0.150783 | + | 0.0736855i | ||||
\(616\) | 0.141039 | 0.00568263 | ||||||||
\(617\) | 33.5728 | + | 19.3833i | 1.35159 | + | 0.780341i | 0.988472 | − | 0.151401i | \(-0.0483786\pi\) |
0.363119 | + | 0.931743i | \(0.381712\pi\) | |||||||
\(618\) | − | 9.62886i | − | 0.387329i | ||||||
\(619\) | −26.0289 | −1.04619 | −0.523096 | − | 0.852274i | \(-0.675223\pi\) | ||||
−0.523096 | + | 0.852274i | \(0.675223\pi\) | |||||||
\(620\) | −1.66039 | + | 12.3387i | −0.0666829 | + | 0.495533i | ||||
\(621\) | −3.42650 | −0.137501 | ||||||||
\(622\) | 7.50012i | 0.300727i | ||||||||
\(623\) | −0.562492 | − | 0.324755i | −0.0225358 | − | 0.0130110i | ||||
\(624\) | 3.87064 | 0.154950 | ||||||||
\(625\) | −6.12273 | − | 24.2386i | −0.244909 | − | 0.969546i | ||||
\(626\) | 5.87130 | − | 10.1694i | 0.234664 | − | 0.406451i | ||||
\(627\) | −0.0943189 | − | 0.0544551i | −0.00376674 | − | 0.00217473i | ||||
\(628\) | − | 14.4319i | − | 0.575897i | ||||||
\(629\) | 19.9594 | + | 34.5707i | 0.795834 | + | 1.37842i | ||||
\(630\) | −0.759149 | − | 1.55345i | −0.0302452 | − | 0.0618909i | ||||
\(631\) | −3.96941 | − | 6.87523i | −0.158020 | − | 0.273698i | 0.776135 | − | 0.630567i | \(-0.217178\pi\) |
−0.934155 | + | 0.356869i | \(0.883844\pi\) | |||||||
\(632\) | −6.30578 | − | 3.64065i | −0.250831 | − | 0.144817i | ||||
\(633\) | 14.0562 | − | 8.11534i | 0.558683 | − | 0.322556i | ||||
\(634\) | 12.5819 | − | 21.7925i | 0.499692 | − | 0.865493i | ||||
\(635\) | −1.85088 | + | 26.7650i | −0.0734500 | + | 1.06214i | ||||
\(636\) | −8.65569 | −0.343220 | ||||||||
\(637\) | −21.4603 | − | 12.3901i | −0.850288 | − | 0.490914i | ||||
\(638\) | 1.12554 | − | 0.649829i | 0.0445604 | − | 0.0257270i | ||||
\(639\) | −4.02888 | + | 6.97823i | −0.159380 | + | 0.276055i | ||||
\(640\) | 2.00901 | − | 0.981775i | 0.0794131 | − | 0.0388081i | ||||
\(641\) | 4.48266 | + | 7.76419i | 0.177054 | + | 0.306667i | 0.940870 | − | 0.338767i | \(-0.110010\pi\) |
−0.763816 | + | 0.645434i | \(0.776676\pi\) | |||||||
\(642\) | 6.18652 | − | 3.57179i | 0.244162 | − | 0.140967i | ||||
\(643\) | − | 3.96229i | − | 0.156257i | −0.996943 | − | 0.0781287i | \(-0.975106\pi\) | ||
0.996943 | − | 0.0781287i | \(-0.0248945\pi\) | |||||||
\(644\) | 1.32476 | − | 2.29455i | 0.0522027 | − | 0.0904177i | ||||
\(645\) | 8.34470 | − | 12.3921i | 0.328572 | − | 0.487938i | ||||
\(646\) | −1.85971 | − | 3.22111i | −0.0731692 | − | 0.126733i | ||||
\(647\) | 4.25345i | 0.167220i | 0.996499 | + | 0.0836102i | \(0.0266451\pi\) | ||||
−0.996499 | + | 0.0836102i | \(0.973355\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −2.20243 | −0.0864528 | ||||||||
\(650\) | −19.1690 | − | 2.66393i | −0.751869 | − | 0.104488i | ||||
\(651\) | 0.278445 | − | 4.29621i | 0.0109131 | − | 0.168382i | ||||
\(652\) | 1.86439i | 0.0730150i | ||||||||
\(653\) | 22.0646i | 0.863455i | 0.902004 | + | 0.431727i | \(0.142096\pi\) | ||||
−0.902004 | + | 0.431727i | \(0.857904\pi\) | |||||||
\(654\) | 7.99606 | − | 13.8496i | 0.312671 | − | 0.541561i | ||||
\(655\) | 18.4923 | + | 1.27880i | 0.722555 | + | 0.0499669i | ||||
\(656\) | 0.930631 | + | 1.61190i | 0.0363350 | + | 0.0629341i | ||||
\(657\) | −9.05991 | − | 5.23074i | −0.353461 | − | 0.204071i | ||||
\(658\) | 4.13367 | + | 2.38658i | 0.161147 | + | 0.0930384i | ||||
\(659\) | −6.39574 | −0.249143 | −0.124571 | − | 0.992211i | \(-0.539756\pi\) | ||||
−0.124571 | + | 0.992211i | \(0.539756\pi\) | |||||||
\(660\) | 0.366443 | − | 0.179076i | 0.0142638 | − | 0.00697052i | ||||
\(661\) | −13.5355 | − | 23.4443i | −0.526472 | − | 0.911876i | −0.999524 | − | 0.0308417i | \(-0.990181\pi\) |
0.473052 | − | 0.881034i | \(-0.343152\pi\) | |||||||
\(662\) | 28.4518 | − | 16.4267i | 1.10581 | − | 0.638440i | ||||
\(663\) | 20.8807 | + | 12.0555i | 0.810938 | + | 0.468196i | ||||
\(664\) | −4.02773 | − | 6.97624i | −0.156306 | − | 0.270731i | ||||
\(665\) | −0.856334 | − | 0.576645i | −0.0332072 | − | 0.0223614i | ||||
\(666\) | −6.40835 | −0.248319 | ||||||||
\(667\) | − | 24.4149i | − | 0.945349i | ||||||
\(668\) | 0.608695 | + | 0.351430i | 0.0235511 | + | 0.0135972i | ||||
\(669\) | −9.98614 | − | 17.2965i | −0.386087 | − | 0.668722i | ||||
\(670\) | −0.535191 | + | 0.794773i | −0.0206762 | + | 0.0307048i | ||||
\(671\) | 0.0889745 | + | 0.154108i | 0.00343482 | + | 0.00594929i | ||||
\(672\) | −0.669647 | + | 0.386621i | −0.0258322 | + | 0.0149142i | ||||
\(673\) | −6.01517 | + | 3.47286i | −0.231868 | + | 0.133869i | −0.611433 | − | 0.791296i | \(-0.709407\pi\) |
0.379566 | + | 0.925165i | \(0.376073\pi\) | |||||||
\(674\) | 12.7086 | 0.489516 | ||||||||
\(675\) | −3.94479 | − | 3.07224i | −0.151835 | − | 0.118250i | ||||
\(676\) | −0.990925 | + | 1.71633i | −0.0381125 | + | 0.0660128i | ||||
\(677\) | 5.78792 | − | 3.34166i | 0.222448 | − | 0.128430i | −0.384635 | − | 0.923069i | \(-0.625673\pi\) |
0.607083 | + | 0.794638i | \(0.292339\pi\) | |||||||
\(678\) | 14.1977i | 0.545260i | ||||||||
\(679\) | 3.67940 | − | 6.37291i | 0.141202 | − | 0.244570i | ||||
\(680\) | 13.8957 | + | 0.960930i | 0.532876 | + | 0.0368500i | ||||
\(681\) | 23.3555 | 0.894985 | ||||||||
\(682\) | 1.01343 | + | 0.0656824i | 0.0388064 | + | 0.00251511i | ||||
\(683\) | − | 5.17502i | − | 0.198017i | −0.995087 | − | 0.0990083i | \(-0.968433\pi\) | ||
0.995087 | − | 0.0990083i | \(-0.0315671\pi\) | |||||||
\(684\) | 0.597095 | 0.0228305 | ||||||||
\(685\) | 23.8159 | + | 16.0373i | 0.909958 | + | 0.612755i | ||||
\(686\) | 10.3631 | 0.395663 | ||||||||
\(687\) | 11.5373 | − | 6.66108i | 0.440176 | − | 0.254136i | ||||
\(688\) | −5.78617 | − | 3.34064i | −0.220596 | − | 0.127361i | ||||
\(689\) | 16.7515 | − | 29.0145i | 0.638182 | − | 1.10536i | ||||
\(690\) | 0.528581 | − | 7.64363i | 0.0201227 | − | 0.290988i | ||||
\(691\) | −21.5450 | − | 37.3170i | −0.819610 | − | 1.41961i | −0.905970 | − | 0.423341i | \(-0.860857\pi\) |
0.0863607 | − | 0.996264i | \(-0.472476\pi\) | |||||||
\(692\) | −6.36230 | + | 3.67328i | −0.241858 | + | 0.139637i | ||||
\(693\) | −0.122144 | + | 0.0705196i | −0.00463985 | + | 0.00267882i | ||||
\(694\) | 15.0491 | − | 26.0657i | 0.571254 | − | 0.989442i | ||||
\(695\) | −3.78051 | − | 7.73606i | −0.143403 | − | 0.293445i | ||||
\(696\) | −3.56266 | + | 6.17071i | −0.135042 | + | 0.233900i | ||||
\(697\) | 11.5941i | 0.439160i | ||||||||
\(698\) | 8.86982i | 0.335727i | ||||||||
\(699\) | −5.31166 | + | 9.20007i | −0.200905 | + | 0.347978i | ||||
\(700\) | 3.58245 | − | 1.45383i | 0.135404 | − | 0.0549494i | ||||
\(701\) | −7.89296 | + | 13.6710i | −0.298113 | + | 0.516347i | −0.975704 | − | 0.219092i | \(-0.929691\pi\) |
0.677591 | + | 0.735439i | \(0.263024\pi\) | |||||||
\(702\) | −3.35207 | + | 1.93532i | −0.126516 | + | 0.0730439i | ||||
\(703\) | −3.31375 | + | 1.91320i | −0.124981 | + | 0.0721576i | ||||
\(704\) | −0.0912000 | − | 0.157963i | −0.00343723 | − | 0.00595346i | ||||
\(705\) | 13.7702 | + | 0.952249i | 0.518614 | + | 0.0358638i | ||||
\(706\) | −5.98210 | + | 10.3613i | −0.225139 | + | 0.389953i | ||||
\(707\) | 7.87290 | + | 4.54542i | 0.296091 | + | 0.170948i | ||||
\(708\) | 10.4570 | − | 6.03735i | 0.392998 | − | 0.226898i | ||||
\(709\) | 12.5564 | 0.471567 | 0.235783 | − | 0.971806i | \(-0.424234\pi\) | ||||
0.235783 | + | 0.971806i | \(0.424234\pi\) | |||||||
\(710\) | −14.9451 | − | 10.0639i | −0.560880 | − | 0.377690i | ||||
\(711\) | 7.28129 | 0.273070 | ||||||||
\(712\) | 0.839983i | 0.0314797i | ||||||||
\(713\) | 10.5876 | − | 15.8705i | 0.396508 | − | 0.594353i | ||||
\(714\) | −4.81667 | −0.180259 | ||||||||
\(715\) | −0.108910 | + | 1.57491i | −0.00407301 | + | 0.0588984i | ||||
\(716\) | 0.245463 | − | 0.425154i | 0.00917337 | − | 0.0158887i | ||||
\(717\) | − | 9.29400i | − | 0.347091i | ||||||
\(718\) | 4.58455 | − | 2.64689i | 0.171094 | − | 0.0987810i | ||||
\(719\) | 7.65650 | − | 13.2615i | 0.285539 | − | 0.494569i | −0.687200 | − | 0.726468i | \(-0.741161\pi\) |
0.972740 | + | 0.231899i | \(0.0744939\pi\) | |||||||
\(720\) | −1.24897 | + | 1.85475i | −0.0465462 | + | 0.0691223i | ||||
\(721\) | −7.44543 | −0.277282 | ||||||||
\(722\) | −16.1457 | + | 9.32174i | −0.600882 | + | 0.346919i | ||||
\(723\) | −7.24239 | + | 4.18140i | −0.269347 | + | 0.155508i | ||||
\(724\) | −8.47857 | − | 14.6853i | −0.315103 | − | 0.545775i | ||||
\(725\) | 21.8907 | − | 28.1079i | 0.812999 | − | 1.04390i | ||||
\(726\) | 5.48337 | + | 9.49747i | 0.203507 | + | 0.352484i | ||||
\(727\) | 1.68725 | + | 0.974136i | 0.0625768 | + | 0.0361287i | 0.530962 | − | 0.847396i | \(-0.321831\pi\) |
−0.468385 | + | 0.883524i | \(0.655164\pi\) | |||||||
\(728\) | − | 2.99294i | − | 0.110926i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 13.0660 | − | 19.4034i | 0.483595 | − | 0.718152i | ||||
\(731\) | −20.8095 | − | 36.0431i | −0.769667 | − | 1.33310i | ||||
\(732\) | −0.844892 | − | 0.487799i | −0.0312281 | − | 0.0180296i | ||||
\(733\) | 7.42242 | − | 4.28533i | 0.274153 | − | 0.158282i | −0.356620 | − | 0.934249i | \(-0.616071\pi\) |
0.630774 | + | 0.775967i | \(0.282738\pi\) | |||||||
\(734\) | −11.2178 | − | 19.4298i | −0.414057 | − | 0.717167i | ||||
\(735\) | 12.8619 | − | 6.28542i | 0.474417 | − | 0.231841i | ||||
\(736\) | −3.42650 | −0.126302 | ||||||||
\(737\) | 0.0676884 | + | 0.0390799i | 0.00249333 | + | 0.00143953i | ||||
\(738\) | −1.61190 | − | 0.930631i | −0.0593348 | − | 0.0342570i | ||||
\(739\) | 16.2472 | + | 28.1409i | 0.597662 | + | 1.03518i | 0.993165 | + | 0.116716i | \(0.0372367\pi\) |
−0.395504 | + | 0.918464i | \(0.629430\pi\) | |||||||
\(740\) | 0.988569 | − | 14.2954i | 0.0363405 | − | 0.525508i | ||||
\(741\) | −1.15557 | + | 2.00150i | −0.0424509 | + | 0.0735271i | ||||
\(742\) | 6.69294i | 0.245705i | ||||||||
\(743\) | 39.0832i | 1.43383i | 0.697163 | + | 0.716913i | \(0.254445\pi\) | ||||
−0.697163 | + | 0.716913i | \(0.745555\pi\) | |||||||
\(744\) | −4.99178 | + | 2.46620i | −0.183008 | + | 0.0904152i | ||||
\(745\) | 28.0937 | + | 1.94276i | 1.02927 | + | 0.0711773i | ||||
\(746\) | 3.89756 | 0.142700 | ||||||||
\(747\) | 6.97624 | + | 4.02773i | 0.255247 | + | 0.147367i | ||||
\(748\) | − | 1.13620i | − | 0.0415437i | ||||||
\(749\) | −2.76186 | − | 4.78367i | −0.100916 | − | 0.174792i | ||||
\(750\) | 7.46189 | − | 8.32587i | 0.272470 | − | 0.304018i | ||||
\(751\) | 11.3158 | − | 19.5996i | 0.412920 | − | 0.715199i | −0.582287 | − | 0.812983i | \(-0.697842\pi\) |
0.995208 | + | 0.0977840i | \(0.0311754\pi\) | |||||||
\(752\) | − | 6.17291i | − | 0.225103i | ||||||
\(753\) | −15.7872 | + | 9.11474i | −0.575317 | + | 0.332160i | ||||
\(754\) | −13.7898 | − | 23.8846i | −0.502194 | − | 0.869825i | ||||
\(755\) | 12.6635 | + | 25.9133i | 0.460871 | + | 0.943082i | ||||
\(756\) | 0.386621 | − | 0.669647i | 0.0140613 | − | 0.0243548i | ||||
\(757\) | 13.7398 | − | 7.93270i | 0.499383 | − | 0.288319i | −0.229076 | − | 0.973409i | \(-0.573570\pi\) |
0.728459 | + | 0.685090i | \(0.240237\pi\) | |||||||
\(758\) | 20.3497 | + | 11.7489i | 0.739133 | + | 0.426738i | ||||
\(759\) | −0.624994 | −0.0226858 | ||||||||
\(760\) | −0.0921094 | + | 1.33196i | −0.00334116 | + | 0.0483154i | ||||
\(761\) | −21.8886 | + | 37.9122i | −0.793462 | + | 1.37432i | 0.130349 | + | 0.991468i | \(0.458390\pi\) |
−0.923811 | + | 0.382849i | \(0.874943\pi\) | |||||||
\(762\) | −10.3908 | + | 5.99913i | −0.376419 | + | 0.217326i | ||||
\(763\) | −10.7091 | − | 6.18288i | −0.387694 | − | 0.223835i | ||||
\(764\) | 4.93870 | + | 8.55408i | 0.178676 | + | 0.309476i | ||||
\(765\) | −12.5145 | + | 6.11566i | −0.452462 | + | 0.221112i | ||||
\(766\) | −3.02189 | − | 5.23407i | −0.109185 | − | 0.189115i | ||||
\(767\) | 46.7368i | 1.68757i | ||||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −10.3459 | + | 17.9196i | −0.373081 | + | 0.646196i | −0.990038 | − | 0.140801i | \(-0.955032\pi\) |
0.616956 | + | 0.786997i | \(0.288365\pi\) | |||||||
\(770\) | −0.138469 | − | 0.283349i | −0.00499007 | − | 0.0102112i | ||||
\(771\) | 1.49335 | 0.0537818 | ||||||||
\(772\) | −7.56580 | − | 4.36812i | −0.272299 | − | 0.157212i | ||||
\(773\) | − | 4.79978i | − | 0.172636i | −0.996268 | − | 0.0863180i | \(-0.972490\pi\) | ||
0.996268 | − | 0.0863180i | \(-0.0275101\pi\) | |||||||
\(774\) | 6.68129 | 0.240154 | ||||||||
\(775\) | 26.4187 | − | 8.77807i | 0.948986 | − | 0.315318i | ||||
\(776\) | −9.51682 | −0.341634 | ||||||||
\(777\) | 4.95520i | 0.177767i | ||||||||
\(778\) | 5.56997 | + | 3.21583i | 0.199693 | + | 0.115293i | ||||
\(779\) | −1.11135 | −0.0398182 | ||||||||
\(780\) | −3.80010 | − | 7.77615i | −0.136065 | − | 0.278431i | ||||
\(781\) | −0.734869 | + | 1.27283i | −0.0262957 | + | 0.0455454i | ||||
\(782\) | −18.4847 | − | 10.6722i | −0.661012 | − | 0.381635i | ||||
\(783\) | − | 7.12532i | − | 0.254638i | ||||||
\(784\) | −3.20105 | − | 5.54438i | −0.114323 | − | 0.198014i | ||||
\(785\) | −28.9939 | + | 14.1689i | −1.03484 | + | 0.505711i | ||||
\(786\) | 4.14488 | + | 7.17915i | 0.147843 | + | 0.256072i | ||||
\(787\) | −32.8966 | − | 18.9928i | −1.17264 | − | 0.677022i | −0.218336 | − | 0.975874i | \(-0.570063\pi\) |
−0.954299 | + | 0.298852i | \(0.903396\pi\) | |||||||
\(788\) | −1.14893 | + | 0.663337i | −0.0409291 | + | 0.0236304i | ||||
\(789\) | −10.8721 | + | 18.8311i | −0.387058 | + | 0.670404i | ||||
\(790\) | −1.12323 | + | 16.2427i | −0.0399628 | + | 0.577888i | ||||
\(791\) | 10.9783 | 0.390342 | ||||||||
\(792\) | 0.157963 | + | 0.0912000i | 0.00561297 | + | 0.00324065i | ||||
\(793\) | 3.27027 | − | 1.88809i | 0.116131 | − | 0.0670481i | ||||
\(794\) | −17.0578 | + | 29.5449i | −0.605358 | + | 1.04851i | ||||
\(795\) | 8.49794 | + | 17.3894i | 0.301391 | + | 0.616737i | ||||
\(796\) | 12.3167 | + | 21.3331i | 0.436553 | + | 0.756132i | ||||
\(797\) | −1.01175 | + | 0.584137i | −0.0358382 | + | 0.0206912i | −0.517812 | − | 0.855494i | \(-0.673253\pi\) |
0.481974 | + | 0.876186i | \(0.339920\pi\) | |||||||
\(798\) | − | 0.461698i | − | 0.0163439i | ||||||
\(799\) | 19.2261 | − | 33.3006i | 0.680171 | − | 1.17809i | ||||
\(800\) | −3.94479 | − | 3.07224i | −0.139469 | − | 0.108620i | ||||
\(801\) | −0.419992 | − | 0.727447i | −0.0148397 | − | 0.0257031i | ||||
\(802\) | − | 36.6374i | − | 1.29371i | ||||||
\(803\) | −1.65253 | − | 0.954087i | −0.0583164 | − | 0.0336690i | ||||
\(804\) | −0.428507 | −0.0151123 | ||||||||
\(805\) | −5.91037 | − | 0.408721i | −0.208313 | − | 0.0144055i | ||||
\(806\) | 1.39382 | − | 21.5057i | 0.0490952 | − | 0.757506i | ||||
\(807\) | 13.9113i | 0.489700i | ||||||||
\(808\) | − | 11.7568i | − | 0.413603i | ||||||
\(809\) | 26.1993 | − | 45.3786i | 0.921119 | − | 1.59543i | 0.123433 | − | 0.992353i | \(-0.460610\pi\) |
0.797687 | − | 0.603072i | \(-0.206057\pi\) | |||||||
\(810\) | 0.154263 | − | 2.23074i | 0.00542023 | − | 0.0783802i | ||||
\(811\) | −12.9976 | − | 22.5125i | −0.456408 | − | 0.790522i | 0.542360 | − | 0.840146i | \(-0.317531\pi\) |
−0.998768 | + | 0.0496241i | \(0.984198\pi\) | |||||||
\(812\) | 4.77145 | + | 2.75480i | 0.167445 | + | 0.0966744i | ||||
\(813\) | 14.4230 | + | 8.32714i | 0.505838 | + | 0.292045i | ||||
\(814\) | −1.16888 | −0.0409693 | ||||||||
\(815\) | 3.74557 | − | 1.83041i | 0.131202 | − | 0.0641164i | ||||
\(816\) | 3.11459 | + | 5.39463i | 0.109033 | + | 0.188850i | ||||
\(817\) | 3.45489 | − | 1.99468i | 0.120871 | − | 0.0697851i | ||||
\(818\) | −18.2997 | − | 10.5653i | −0.639833 | − | 0.369408i | ||||
\(819\) | 1.49647 | + | 2.59196i | 0.0522909 | + | 0.0905705i | ||||
\(820\) | 2.32465 | − | 3.45217i | 0.0811803 | − | 0.120555i | ||||
\(821\) | −34.7207 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(822\) | 12.8405i | 0.447864i | ||||||||
\(823\) | 23.9449 | + | 13.8246i | 0.834667 | + | 0.481895i | 0.855448 | − | 0.517889i | \(-0.173282\pi\) |
−0.0207808 | + | 0.999784i | \(0.506615\pi\) | |||||||
\(824\) | 4.81443 | + | 8.33883i | 0.167719 | + | 0.290497i | ||||
\(825\) | −0.719530 | − | 0.560376i | −0.0250508 | − | 0.0195098i | ||||
\(826\) | −4.66833 | − | 8.08579i | −0.162432 | − | 0.281341i | ||||
\(827\) | −13.7054 | + | 7.91284i | −0.476585 | + | 0.275156i | −0.718992 | − | 0.695018i | \(-0.755396\pi\) |
0.242407 | + | 0.970175i | \(0.422063\pi\) | |||||||
\(828\) | 2.96744 | − | 1.71325i | 0.103126 | − | 0.0595396i | ||||
\(829\) | 40.3193 | 1.40035 | 0.700173 | − | 0.713973i | \(-0.253106\pi\) | ||||
0.700173 | + | 0.713973i | \(0.253106\pi\) | |||||||
\(830\) | −10.0610 | + | 14.9409i | −0.349222 | + | 0.518605i | ||||
\(831\) | 7.68356 | − | 13.3083i | 0.266540 | − | 0.461660i | ||||
\(832\) | −3.35207 | + | 1.93532i | −0.116212 | + | 0.0670951i | ||||
\(833\) | − | 39.8799i | − | 1.38176i | ||||||
\(834\) | 1.92534 | − | 3.33479i | 0.0666691 | − | 0.115474i | ||||
\(835\) | 0.108425 | − | 1.56790i | 0.00375220 | − | 0.0542593i | ||||
\(836\) | 0.108910 | 0.00376674 | ||||||||
\(837\) | 3.08991 | − | 4.63168i | 0.106803 | − | 0.160094i | ||||
\(838\) | − | 22.8606i | − | 0.789706i | ||||||
\(839\) | 34.2514 | 1.18249 | 0.591245 | − | 0.806492i | \(-0.298637\pi\) | ||||
0.591245 | + | 0.806492i | \(0.298637\pi\) | |||||||
\(840\) | 1.43417 | + | 0.965752i | 0.0494835 | + | 0.0333216i | ||||
\(841\) | 21.7701 | 0.750695 | ||||||||
\(842\) | 11.8383 | − | 6.83483i | 0.407974 | − | 0.235544i | ||||
\(843\) | 15.1091 | + | 8.72323i | 0.520384 | + | 0.300444i | ||||
\(844\) | −8.11534 | + | 14.0562i | −0.279342 | + | 0.483834i | ||||
\(845\) | 4.42099 | + | 0.305725i | 0.152087 | + | 0.0105173i | ||||
\(846\) | 3.08646 | + | 5.34590i | 0.106115 | + | 0.183796i | ||||
\(847\) | 7.34384 | − | 4.23997i | 0.252337 | − | 0.145687i | ||||
\(848\) | 7.49604 | − | 4.32784i | 0.257415 | − | 0.148619i | ||||
\(849\) | 14.4645 | − | 25.0533i | 0.496421 | − | 0.859826i | ||||
\(850\) | −11.7119 | − | 28.8600i | −0.401716 | − | 0.989890i | ||||
\(851\) | −10.9791 | + | 19.0164i | −0.376359 | + | 0.651873i | ||||
\(852\) | − | 8.05777i | − | 0.276055i | ||||||
\(853\) | − | 32.9827i | − | 1.12931i | −0.825328 | − | 0.564654i | \(-0.809010\pi\) | ||
0.825328 | − | 0.564654i | \(-0.190990\pi\) | |||||||
\(854\) | −0.377186 | + | 0.653305i | −0.0129070 | + | 0.0223557i | ||||
\(855\) | −0.586213 | − | 1.19957i | −0.0200481 | − | 0.0410244i | ||||
\(856\) | −3.57179 | + | 6.18652i | −0.122081 | + | 0.211451i | ||||
\(857\) | −16.7037 | + | 9.64390i | −0.570588 | + | 0.329429i | −0.757384 | − | 0.652969i | \(-0.773523\pi\) |
0.186796 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(858\) | −0.611418 | + | 0.353002i | −0.0208735 | + | 0.0120513i | ||||
\(859\) | −18.9369 | − | 32.7997i | −0.646120 | − | 1.11911i | −0.984042 | − | 0.177938i | \(-0.943057\pi\) |
0.337922 | − | 0.941174i | \(-0.390276\pi\) | |||||||
\(860\) | −1.03067 | + | 14.9042i | −0.0351456 | + | 0.508230i | ||||
\(861\) | −0.719602 | + | 1.24639i | −0.0245240 | + | 0.0424768i | ||||
\(862\) | −15.7672 | − | 9.10321i | −0.537034 | − | 0.310057i | ||||
\(863\) | 0.655557 | − | 0.378486i | 0.0223154 | − | 0.0128838i | −0.488801 | − | 0.872395i | \(-0.662566\pi\) |
0.511116 | + | 0.859512i | \(0.329232\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 13.6260 | + | 9.17559i | 0.463298 | + | 0.311980i | ||||
\(866\) | 2.97874 | 0.101222 | ||||||||
\(867\) | 21.8028i | 0.740461i | ||||||||
\(868\) | 1.90697 | + | 3.85985i | 0.0647266 | + | 0.131012i | ||||
\(869\) | 1.32811 | 0.0450530 | ||||||||
\(870\) | 15.8947 | + | 1.09917i | 0.538882 | + | 0.0372653i | ||||
\(871\) | 0.829299 | − | 1.43639i | 0.0280997 | − | 0.0486702i | ||||
\(872\) | 15.9921i | 0.541561i | ||||||||
\(873\) | 8.24181 | − | 4.75841i | 0.278943 | − | 0.161048i | ||||
\(874\) | 1.02297 | − | 1.77184i | 0.0346026 | − | 0.0599334i | ||||
\(875\) | −6.43791 | − | 5.76985i | −0.217641 | − | 0.195056i | ||||
\(876\) | 10.4615 | 0.353461 | ||||||||
\(877\) | 1.71623 | − | 0.990863i | 0.0579528 | − | 0.0334591i | −0.470744 | − | 0.882270i | \(-0.656014\pi\) |
0.528696 | + | 0.848811i | \(0.322681\pi\) | |||||||
\(878\) | −3.25908 | + | 1.88163i | −0.109989 | + | 0.0635019i | ||||
\(879\) | 4.25665 | + | 7.37274i | 0.143573 | + | 0.248676i | ||||
\(880\) | −0.227811 | + | 0.338306i | −0.00767952 | + | 0.0114043i | ||||
\(881\) | −25.1594 | − | 43.5774i | −0.847643 | − | 1.46816i | −0.883306 | − | 0.468796i | \(-0.844688\pi\) |
0.0356635 | − | 0.999364i | \(-0.488646\pi\) | |||||||
\(882\) | 5.54438 | + | 3.20105i | 0.186689 | + | 0.107785i | ||||
\(883\) | 11.1079i | 0.373809i | 0.982378 | + | 0.186905i | \(0.0598456\pi\) | ||||
−0.982378 | + | 0.186905i | \(0.940154\pi\) | |||||||
\(884\) | −24.1109 | −0.810938 | ||||||||
\(885\) | −22.3955 | − | 15.0809i | −0.752817 | − | 0.506939i | ||||
\(886\) | −13.5654 | − | 23.4960i | −0.455739 | − | 0.789362i | ||||
\(887\) | −15.3394 | − | 8.85623i | −0.515048 | − | 0.297363i | 0.219858 | − | 0.975532i | \(-0.429441\pi\) |
−0.734906 | + | 0.678169i | \(0.762774\pi\) | |||||||
\(888\) | 5.54979 | − | 3.20418i | 0.186239 | − | 0.107525i | ||||
\(889\) | 4.63878 | + | 8.03459i | 0.155580 | + | 0.269472i | ||||
\(890\) | 1.68753 | − | 0.824674i | 0.0565663 | − | 0.0276432i | ||||
\(891\) | −0.182400 | −0.00611063 | ||||||||
\(892\) | 17.2965 | + | 9.98614i | 0.579130 | + | 0.334361i | ||||
\(893\) | 3.19201 | + | 1.84291i | 0.106816 | + | 0.0616705i | ||||
\(894\) | 6.29694 | + | 10.9066i | 0.210601 | + | 0.364772i | ||||
\(895\) | −1.09513 | − | 0.0757314i | −0.0366060 | − | 0.00253142i | ||||
\(896\) | 0.386621 | − | 0.669647i | 0.0129161 | − | 0.0223713i | ||||
\(897\) | 13.2627i | 0.442830i | ||||||||
\(898\) | − | 41.4038i | − | 1.38166i | ||||||
\(899\) | 33.0022 | + | 22.0166i | 1.10068 | + | 0.734294i | ||||
\(900\) | 4.95241 | + | 0.688239i | 0.165080 | + | 0.0229413i | ||||
\(901\) | 53.9179 | 1.79627 | ||||||||
\(902\) | −0.294011 | − | 0.169747i | −0.00978948 | − | 0.00565196i | ||||
\(903\) | − | 5.16625i | − | 0.171922i | ||||||
\(904\) | −7.09885 | − | 12.2956i | −0.236104 | − | 0.408945i | ||||
\(905\) | −21.1789 | + | 31.4512i | −0.704010 | + | 1.04547i | ||||
\(906\) | −6.44928 | + | 11.1705i | −0.214263 | + | 0.371114i | ||||
\(907\) | 0.154060i | 0.00511547i | 0.999997 | + | 0.00255774i | \(0.000814153\pi\) | ||||
−0.999997 | + | 0.00255774i | \(0.999186\pi\) | |||||||
\(908\) | −20.2265 | + | 11.6778i | −0.671239 | + | 0.387540i | ||||
\(909\) | 5.87840 | + | 10.1817i | 0.194974 | + | 0.337705i | ||||
\(910\) | −6.01284 | + | 2.93839i | −0.199324 | + | 0.0974068i | ||||
\(911\) | −5.64684 | + | 9.78062i | −0.187088 | + | 0.324046i | −0.944278 | − | 0.329148i | \(-0.893238\pi\) |
0.757190 | + | 0.653195i | \(0.226572\pi\) | |||||||
\(912\) | −0.517099 | + | 0.298547i | −0.0171229 | + | 0.00988589i | ||||
\(913\) | 1.27247 | + | 0.734659i | 0.0421125 | + | 0.0243137i | ||||
\(914\) | 24.6010 | 0.813729 | ||||||||
\(915\) | −0.150498 | + | 2.17630i | −0.00497531 | + | 0.0719464i | ||||
\(916\) | −6.66108 | + | 11.5373i | −0.220088 | + | 0.381204i | ||||
\(917\) | 5.55122 | − | 3.20500i | 0.183317 | − | 0.105838i | ||||
\(918\) | −5.39463 | − | 3.11459i | −0.178049 | − | 0.102797i | ||||
\(919\) | −1.62927 | − | 2.82198i | −0.0537446 | − | 0.0930884i | 0.837901 | − | 0.545822i | \(-0.183782\pi\) |
−0.891646 | + | 0.452733i | \(0.850449\pi\) | |||||||
\(920\) | 3.36405 | + | 6.88387i | 0.110910 | + | 0.226955i | ||||
\(921\) | −10.7902 | − | 18.6892i | −0.355550 | − | 0.615830i | ||||
\(922\) | − | 5.75649i | − | 0.189580i | ||||||
\(923\) | 27.0102 | + | 15.5944i | 0.889052 | + | 0.513295i | ||||
\(924\) | 0.0705196 | − | 0.122144i | 0.00231993 | − | 0.00401823i | ||||
\(925\) | −29.6901 | + | 12.0488i | −0.976204 | + | 0.396162i | ||||
\(926\) | −30.2945 | −0.995540 | ||||||||
\(927\) | −8.33883 | − | 4.81443i | −0.273883 | − | 0.158127i | ||||
\(928\) | − | 7.12532i | − | 0.233900i | ||||||
\(929\) | 5.49130 | 0.180164 | 0.0900819 | − | 0.995934i | \(-0.471287\pi\) | ||||
0.0900819 | + | 0.995934i | \(0.471287\pi\) | |||||||
\(930\) | 9.85542 | + | 7.60728i | 0.323172 | + | 0.249453i | ||||
\(931\) | 3.82266 | 0.125283 | ||||||||
\(932\) | − | 10.6233i | − | 0.347978i | ||||||
\(933\) | 6.49529 | + | 3.75006i | 0.212646 | + | 0.122771i | ||||
\(934\) | 24.8358 | 0.812653 | ||||||||
\(935\) | −2.28264 | + | 1.11550i | −0.0746504 | + | 0.0364806i | ||||
\(936\) | 1.93532 | − | 3.35207i | 0.0632579 | − | 0.109566i | ||||
\(937\) | 39.2023 | + | 22.6335i | 1.28068 | + | 0.739403i | 0.976973 | − | 0.213362i | \(-0.0684412\pi\) |
0.303710 | + | 0.952764i | \(0.401775\pi\) | |||||||
\(938\) | 0.331340i | 0.0108186i | ||||||||
\(939\) | −5.87130 | − | 10.1694i | −0.191603 | − | 0.331866i | ||||
\(940\) | −12.4014 | + | 6.06041i | −0.404490 | + | 0.197669i | ||||
\(941\) | −0.692766 | − | 1.19991i | −0.0225835 | − | 0.0391158i | 0.854513 | − | 0.519430i | \(-0.173856\pi\) |
−0.877096 | + | 0.480315i | \(0.840523\pi\) | |||||||
\(942\) | −12.4984 | − | 7.21597i | −0.407221 | − | 0.235109i | ||||
\(943\) | −5.52318 | + | 3.18881i | −0.179859 | + | 0.103842i | ||||
\(944\) | −6.03735 | + | 10.4570i | −0.196499 | + | 0.340346i | ||||
\(945\) | −1.72490 | − | 0.119282i | −0.0561110 | − | 0.00388025i | ||||
\(946\) | 1.21867 | 0.0396223 | ||||||||
\(947\) | 11.0470 | + | 6.37797i | 0.358978 | + | 0.207256i | 0.668633 | − | 0.743593i | \(-0.266880\pi\) |
−0.309654 | + | 0.950849i | \(0.600213\pi\) | |||||||
\(948\) | −6.30578 | + | 3.64065i | −0.204802 | + | 0.118243i | ||||
\(949\) | −20.2463 | + | 35.0676i | −0.657223 | + | 1.13834i | ||||
\(950\) | 2.76636 | − | 1.12264i | 0.0897525 | − | 0.0364232i | ||||
\(951\) | −12.5819 | − | 21.7925i | −0.407997 | − | 0.706672i | ||||
\(952\) | 4.17135 | − | 2.40833i | 0.135194 | − | 0.0780545i | ||||
\(953\) | 34.8545i | 1.12905i | 0.825417 | + | 0.564524i | \(0.190940\pi\) | ||||
−0.825417 | + | 0.564524i | \(0.809060\pi\) | |||||||
\(954\) | −4.32784 | + | 7.49604i | −0.140119 | + | 0.242693i | ||||
\(955\) | 12.3365 | − | 18.3201i | 0.399201 | − | 0.592824i | ||||
\(956\) | 4.64700 | + | 8.04884i | 0.150295 | + | 0.260318i | ||||
\(957\) | − | 1.29966i | − | 0.0420120i | ||||||
\(958\) | −33.6819 | − | 19.4463i | −1.08821 | − | 0.628281i | ||||
\(959\) | 9.92881 | 0.320618 | ||||||||
\(960\) | 0.154263 | − | 2.23074i | 0.00497880 | − | 0.0719968i | ||||
\(961\) | 11.9049 | + | 28.6229i | 0.384029 | + | 0.923321i | ||||
\(962\) | 24.8044i | 0.799726i | ||||||||
\(963\) | − | 7.14358i | − | 0.230199i | ||||||
\(964\) | 4.18140 | − | 7.24239i | 0.134674 | − | 0.233262i | ||||
\(965\) | −1.34767 | + | 19.4883i | −0.0433832 | + | 0.627350i | ||||
\(966\) | −1.32476 | − | 2.29455i | −0.0426233 | − | 0.0738258i | ||||
\(967\) | 38.4657 | + | 22.2082i | 1.23697 | + | 0.714168i | 0.968475 | − | 0.249112i | \(-0.0801387\pi\) |
0.268500 | + | 0.963280i | \(0.413472\pi\) | |||||||
\(968\) | −9.49747 | − | 5.48337i | −0.305260 | − | 0.176242i | ||||
\(969\) | −3.71941 | −0.119485 | ||||||||
\(970\) | 9.34338 | + | 19.1194i | 0.299998 | + | 0.613886i | ||||
\(971\) | 3.59816 | + | 6.23220i | 0.115470 | + | 0.200001i | 0.917968 | − | 0.396655i | \(-0.129829\pi\) |
−0.802497 | + | 0.596656i | \(0.796496\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −2.57860 | − | 1.48875i | −0.0826661 | − | 0.0477273i | ||||
\(974\) | 0.971337 | + | 1.68240i | 0.0311236 | + | 0.0539077i | ||||
\(975\) | −11.8915 | + | 15.2689i | −0.380833 | + | 0.488995i | ||||
\(976\) | 0.975597 | 0.0312281 | ||||||||
\(977\) | − | 42.7392i | − | 1.36735i | −0.729788 | − | 0.683673i | \(-0.760381\pi\) | ||
0.729788 | − | 0.683673i | \(-0.239619\pi\) | |||||||
\(978\) | 1.61461 | + | 0.932193i | 0.0516294 | + | 0.0298082i | ||||
\(979\) | −0.0766065 | − | 0.132686i | −0.00244835 | − | 0.00424067i | ||||
\(980\) | −7.99600 | + | 11.8743i | −0.255423 | + | 0.379310i | ||||
\(981\) | −7.99606 | − | 13.8496i | −0.255294 | − | 0.442183i | ||||
\(982\) | −25.7295 | + | 14.8550i | −0.821062 | + | 0.474041i | ||||
\(983\) | −0.451740 | + | 0.260812i | −0.0144083 | + | 0.00831862i | −0.507187 | − | 0.861836i | \(-0.669315\pi\) |
0.492779 | + | 0.870155i | \(0.335981\pi\) | |||||||
\(984\) | 1.86126 | 0.0593348 | ||||||||
\(985\) | 2.46065 | + | 1.65697i | 0.0784027 | + | 0.0527955i | ||||
\(986\) | 22.1925 | − | 38.4385i | 0.706752 | − | 1.22413i | ||||
\(987\) | 4.13367 | − | 2.38658i | 0.131576 | − | 0.0759655i | ||||
\(988\) | − | 2.31114i | − | 0.0735271i | ||||||
\(989\) | 11.4467 | − | 19.8263i | 0.363985 | − | 0.630440i | ||||
\(990\) | 0.0281375 | − | 0.406887i | 0.000894268 | − | 0.0129317i | ||||
\(991\) | −61.1300 | −1.94186 | −0.970930 | − | 0.239365i | \(-0.923061\pi\) | ||||
−0.970930 | + | 0.239365i | \(0.923061\pi\) | |||||||
\(992\) | 3.08991 | − | 4.63168i | 0.0981047 | − | 0.147056i | ||||
\(993\) | − | 32.8533i | − | 1.04257i | ||||||
\(994\) | −6.23060 | −0.197623 | ||||||||
\(995\) | 30.7662 | − | 45.6887i | 0.975355 | − | 1.44843i | ||||
\(996\) | −8.05547 | −0.255247 | ||||||||
\(997\) | −16.8876 | + | 9.75004i | −0.534834 | + | 0.308787i | −0.742983 | − | 0.669310i | \(-0.766590\pi\) |
0.208148 | + | 0.978097i | \(0.433256\pi\) | |||||||
\(998\) | −3.46166 | − | 1.99859i | −0.109577 | − | 0.0632643i | ||||
\(999\) | −3.20418 | + | 5.54979i | −0.101376 | + | 0.175588i |
(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 | 930.2.s.c.439.10 | yes | 24 | |
5.4 | even | 2 | inner | 930.2.s.c.439.5 | ✓ | 24 | |
31.25 | even | 3 | inner | 930.2.s.c.769.11 | yes | 24 | |
155.149 | even | 6 | inner | 930.2.s.c.769.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.s.c.439.5 | ✓ | 24 | 5.4 | even | 2 | inner | |
930.2.s.c.439.10 | yes | 24 | 1.1 | even | 1 | trivial | |
930.2.s.c.769.4 | yes | 24 | 155.149 | even | 6 | inner | |
930.2.s.c.769.11 | yes | 24 | 31.25 | even | 3 | inner |