Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.19 | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.b.376.19 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.883008 | + | 0.509805i | −0.624381 | + | 0.360486i | −0.778573 | − | 0.627554i | \(-0.784056\pi\) |
0.154192 | + | 0.988041i | \(0.450723\pi\) | |||||||
\(3\) | −0.597446 | − | 1.62575i | −0.344936 | − | 0.938626i | ||||
\(4\) | −0.480198 | + | 0.831727i | −0.240099 | + | 0.415864i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | 1.35636 | + | 1.13097i | 0.553733 | + | 0.461716i | ||||
\(7\) | −3.32453 | + | 1.91942i | −1.25655 | + | 0.725472i | −0.972403 | − | 0.233307i | \(-0.925045\pi\) |
−0.284151 | + | 0.958779i | \(0.591712\pi\) | |||||||
\(8\) | − | 3.01845i | − | 1.06718i | ||||||
\(9\) | −2.28612 | + | 1.94260i | −0.762038 | + | 0.647532i | ||||
\(10\) | 1.01961 | 0.322429 | ||||||||
\(11\) | −1.97745 | + | 1.14168i | −0.596222 | + | 0.344229i | −0.767554 | − | 0.640984i | \(-0.778526\pi\) |
0.171332 | + | 0.985213i | \(0.445193\pi\) | |||||||
\(12\) | 1.63907 | + | 0.283769i | 0.473159 | + | 0.0819169i | ||||
\(13\) | 3.56410 | + | 0.545131i | 0.988504 | + | 0.151192i | ||||
\(14\) | 1.95706 | − | 3.38972i | 0.523046 | − | 0.905942i | ||||
\(15\) | −0.295470 | + | 1.70666i | −0.0762901 | + | 0.440658i | ||||
\(16\) | 0.578424 | + | 1.00186i | 0.144606 | + | 0.250465i | ||||
\(17\) | 7.50452 | 1.82011 | 0.910057 | − | 0.414483i | \(-0.136037\pi\) | ||||
0.910057 | + | 0.414483i | \(0.136037\pi\) | |||||||
\(18\) | 1.02831 | − | 2.88080i | 0.242376 | − | 0.679011i | ||||
\(19\) | − | 2.31692i | − | 0.531539i | −0.964037 | − | 0.265769i | \(-0.914374\pi\) | ||
0.964037 | − | 0.265769i | \(-0.0856260\pi\) | |||||||
\(20\) | 0.831727 | − | 0.480198i | 0.185980 | − | 0.107376i | ||||
\(21\) | 5.10672 | + | 4.25810i | 1.11438 | + | 0.929194i | ||||
\(22\) | 1.16407 | − | 2.01622i | 0.248180 | − | 0.429860i | ||||
\(23\) | 1.68012 | − | 2.91006i | 0.350330 | − | 0.606789i | −0.635977 | − | 0.771708i | \(-0.719403\pi\) |
0.986307 | + | 0.164919i | \(0.0527362\pi\) | |||||||
\(24\) | −4.90724 | + | 1.80336i | −1.00169 | + | 0.368110i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −3.42504 | + | 1.33564i | −0.671706 | + | 0.261941i | ||||
\(27\) | 4.52400 | + | 2.55605i | 0.870645 | + | 0.491912i | ||||
\(28\) | − | 3.68680i | − | 0.696740i | ||||||
\(29\) | −4.07714 | − | 7.06182i | −0.757107 | − | 1.31135i | −0.944320 | − | 0.329028i | \(-0.893279\pi\) |
0.187213 | − | 0.982319i | \(-0.440054\pi\) | |||||||
\(30\) | −0.609162 | − | 1.65763i | −0.111217 | − | 0.302640i | ||||
\(31\) | −3.49528 | − | 2.01800i | −0.627771 | − | 0.362444i | 0.152117 | − | 0.988362i | \(-0.451391\pi\) |
−0.779888 | + | 0.625919i | \(0.784724\pi\) | |||||||
\(32\) | 4.20660 | + | 2.42868i | 0.743629 | + | 0.429334i | ||||
\(33\) | 3.03750 | + | 2.53274i | 0.528761 | + | 0.440893i | ||||
\(34\) | −6.62655 | + | 3.82584i | −1.13644 | + | 0.656127i | ||||
\(35\) | 3.83884 | 0.648882 | ||||||||
\(36\) | −0.517922 | − | 2.83426i | −0.0863203 | − | 0.472376i | ||||
\(37\) | 0.546920i | 0.0899131i | 0.998989 | + | 0.0449565i | \(0.0143149\pi\) | ||||
−0.998989 | + | 0.0449565i | \(0.985685\pi\) | |||||||
\(38\) | 1.18118 | + | 2.04586i | 0.191613 | + | 0.331883i | ||||
\(39\) | −1.24312 | − | 6.12002i | −0.199058 | − | 0.979988i | ||||
\(40\) | −1.50922 | + | 2.61405i | −0.238629 | + | 0.413318i | ||||
\(41\) | 6.35971 | + | 3.67178i | 0.993219 | + | 0.573436i | 0.906235 | − | 0.422774i | \(-0.138944\pi\) |
0.0869844 | + | 0.996210i | \(0.472277\pi\) | |||||||
\(42\) | −6.68007 | − | 1.15651i | −1.03076 | − | 0.178453i | ||||
\(43\) | −0.826744 | − | 1.43196i | −0.126077 | − | 0.218372i | 0.796076 | − | 0.605196i | \(-0.206905\pi\) |
−0.922154 | + | 0.386824i | \(0.873572\pi\) | |||||||
\(44\) | − | 2.19293i | − | 0.330596i | ||||||
\(45\) | 2.95113 | − | 0.539279i | 0.439929 | − | 0.0803910i | ||||
\(46\) | 3.42614i | 0.505157i | ||||||||
\(47\) | 7.13335 | − | 4.11844i | 1.04051 | − | 0.600737i | 0.120530 | − | 0.992710i | \(-0.461541\pi\) |
0.919977 | + | 0.391973i | \(0.128207\pi\) | |||||||
\(48\) | 1.28319 | − | 1.53893i | 0.185213 | − | 0.222125i | ||||
\(49\) | 3.86833 | − | 6.70015i | 0.552619 | − | 0.957164i | ||||
\(50\) | −0.883008 | − | 0.509805i | −0.124876 | − | 0.0720973i | ||||
\(51\) | −4.48355 | − | 12.2005i | −0.627823 | − | 1.70841i | ||||
\(52\) | −2.16488 | + | 2.70259i | −0.300214 | + | 0.374782i | ||||
\(53\) | 7.10215 | 0.975555 | 0.487778 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487778 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(54\) | −5.29782 | + | 0.0493446i | −0.720942 | + | 0.00671495i | ||||
\(55\) | 2.28336 | 0.307888 | ||||||||
\(56\) | 5.79367 | + | 10.0349i | 0.774211 | + | 1.34097i | ||||
\(57\) | −3.76673 | + | 1.38424i | −0.498916 | + | 0.183347i | ||||
\(58\) | 7.20030 | + | 4.15710i | 0.945446 | + | 0.545853i | ||||
\(59\) | 6.45792 | + | 3.72848i | 0.840750 | + | 0.485407i | 0.857519 | − | 0.514452i | \(-0.172005\pi\) |
−0.0167693 | + | 0.999859i | \(0.505338\pi\) | |||||||
\(60\) | −1.27759 | − | 1.06529i | −0.164937 | − | 0.137528i | ||||
\(61\) | 5.77492 | + | 10.0025i | 0.739403 | + | 1.28068i | 0.952765 | + | 0.303710i | \(0.0982254\pi\) |
−0.213362 | + | 0.976973i | \(0.568441\pi\) | |||||||
\(62\) | 4.11515 | 0.522624 | ||||||||
\(63\) | 3.87161 | − | 10.8462i | 0.487777 | − | 1.36650i | ||||
\(64\) | −7.26631 | −0.908289 | ||||||||
\(65\) | −2.81404 | − | 2.25415i | −0.349039 | − | 0.279593i | ||||
\(66\) | −3.97334 | − | 0.687894i | −0.489084 | − | 0.0846739i | ||||
\(67\) | −6.43546 | − | 3.71551i | −0.786217 | − | 0.453922i | 0.0524124 | − | 0.998626i | \(-0.483309\pi\) |
−0.838629 | + | 0.544703i | \(0.816642\pi\) | |||||||
\(68\) | −3.60366 | + | 6.24172i | −0.437008 | + | 0.756919i | ||||
\(69\) | −5.73480 | − | 0.992853i | −0.690389 | − | 0.119525i | ||||
\(70\) | −3.38972 | + | 1.95706i | −0.405149 | + | 0.233913i | ||||
\(71\) | − | 7.19213i | − | 0.853549i | −0.904358 | − | 0.426774i | \(-0.859650\pi\) | ||
0.904358 | − | 0.426774i | \(-0.140350\pi\) | |||||||
\(72\) | 5.86362 | + | 6.90052i | 0.691035 | + | 0.813234i | ||||
\(73\) | − | 7.74780i | − | 0.906811i | −0.891304 | − | 0.453406i | \(-0.850209\pi\) | ||
0.891304 | − | 0.453406i | \(-0.149791\pi\) | |||||||
\(74\) | −0.278822 | − | 0.482935i | −0.0324125 | − | 0.0561400i | ||||
\(75\) | 1.10922 | − | 1.33028i | 0.128081 | − | 0.153607i | ||||
\(76\) | 1.92705 | + | 1.11258i | 0.221048 | + | 0.127622i | ||||
\(77\) | 4.38272 | − | 7.59109i | 0.499457 | − | 0.865085i | ||||
\(78\) | 4.21770 | + | 4.77028i | 0.477560 | + | 0.540128i | ||||
\(79\) | 6.19823 | + | 10.7357i | 0.697356 | + | 1.20786i | 0.969380 | + | 0.245565i | \(0.0789735\pi\) |
−0.272025 | + | 0.962290i | \(0.587693\pi\) | |||||||
\(80\) | − | 1.15685i | − | 0.129339i | ||||||
\(81\) | 1.45265 | − | 8.88199i | 0.161405 | − | 0.986888i | ||||
\(82\) | −7.48756 | −0.826863 | ||||||||
\(83\) | 5.81320 | − | 3.35625i | 0.638082 | − | 0.368397i | −0.145793 | − | 0.989315i | \(-0.546573\pi\) |
0.783875 | + | 0.620918i | \(0.213240\pi\) | |||||||
\(84\) | −5.99382 | + | 2.20267i | −0.653979 | + | 0.240331i | ||||
\(85\) | −6.49911 | − | 3.75226i | −0.704927 | − | 0.406990i | ||||
\(86\) | 1.46004 | + | 0.842957i | 0.157441 | + | 0.0908984i | ||||
\(87\) | −9.04487 | + | 10.8475i | −0.969712 | + | 1.16297i | ||||
\(88\) | 3.44610 | + | 5.96882i | 0.367355 | + | 0.636278i | ||||
\(89\) | 6.46613i | 0.685408i | 0.939443 | + | 0.342704i | \(0.111343\pi\) | ||||
−0.939443 | + | 0.342704i | \(0.888657\pi\) | |||||||
\(90\) | −2.33095 | + | 1.98069i | −0.245703 | + | 0.208783i | ||||
\(91\) | −12.8953 | + | 5.02870i | −1.35180 | + | 0.527151i | ||||
\(92\) | 1.61358 | + | 2.79481i | 0.168228 | + | 0.291379i | ||||
\(93\) | −1.19252 | + | 6.88809i | −0.123658 | + | 0.714262i | ||||
\(94\) | −4.19920 | + | 7.27323i | −0.433115 | + | 0.750177i | ||||
\(95\) | −1.15846 | + | 2.00651i | −0.118856 | + | 0.205864i | ||||
\(96\) | 1.43521 | − | 8.28988i | 0.146480 | − | 0.846083i | ||||
\(97\) | 10.1032 | − | 5.83306i | 1.02582 | − | 0.592257i | 0.110035 | − | 0.993928i | \(-0.464904\pi\) |
0.915784 | + | 0.401670i | \(0.131570\pi\) | |||||||
\(98\) | 7.88838i | 0.796847i | ||||||||
\(99\) | 2.30285 | − | 6.45139i | 0.231445 | − | 0.648389i | ||||
\(100\) | −0.960396 | −0.0960396 | ||||||||
\(101\) | −1.51884 | − | 2.63071i | −0.151130 | − | 0.261765i | 0.780513 | − | 0.625140i | \(-0.214958\pi\) |
−0.931643 | + | 0.363374i | \(0.881625\pi\) | |||||||
\(102\) | 10.1789 | + | 8.48737i | 1.00786 | + | 0.840375i | ||||
\(103\) | −9.34492 | + | 16.1859i | −0.920783 | + | 1.59484i | −0.122575 | + | 0.992459i | \(0.539115\pi\) |
−0.798207 | + | 0.602383i | \(0.794218\pi\) | |||||||
\(104\) | 1.64545 | − | 10.7581i | 0.161350 | − | 1.05491i | ||||
\(105\) | −2.29350 | − | 6.24098i | −0.223823 | − | 0.609058i | ||||
\(106\) | −6.27125 | + | 3.62071i | −0.609118 | + | 0.351674i | ||||
\(107\) | −6.42736 | −0.621357 | −0.310678 | − | 0.950515i | \(-0.600556\pi\) | ||||
−0.310678 | + | 0.950515i | \(0.600556\pi\) | |||||||
\(108\) | −4.29836 | + | 2.53533i | −0.413609 | + | 0.243962i | ||||
\(109\) | 0.188689i | 0.0180731i | 0.999959 | + | 0.00903656i | \(0.00287646\pi\) | ||||
−0.999959 | + | 0.00903656i | \(0.997124\pi\) | |||||||
\(110\) | −2.01622 | + | 1.16407i | −0.192239 | + | 0.110989i | ||||
\(111\) | 0.889154 | − | 0.326755i | 0.0843948 | − | 0.0310143i | ||||
\(112\) | −3.84597 | − | 2.22047i | −0.363410 | − | 0.209815i | ||||
\(113\) | 0.0907879 | − | 0.157249i | 0.00854061 | − | 0.0147928i | −0.861724 | − | 0.507378i | \(-0.830615\pi\) |
0.870264 | + | 0.492585i | \(0.163948\pi\) | |||||||
\(114\) | 2.62037 | − | 3.14259i | 0.245420 | − | 0.294331i | ||||
\(115\) | −2.91006 | + | 1.68012i | −0.271364 | + | 0.156672i | ||||
\(116\) | 7.83135 | 0.727122 | ||||||||
\(117\) | −9.20692 | + | 5.67738i | −0.851180 | + | 0.524874i | ||||
\(118\) | −7.60319 | −0.699931 | ||||||||
\(119\) | −24.9490 | + | 14.4043i | −2.28707 | + | 1.32044i | ||||
\(120\) | 5.15147 | + | 0.891862i | 0.470263 | + | 0.0814155i | ||||
\(121\) | −2.89314 | + | 5.01106i | −0.263013 | + | 0.455551i | ||||
\(122\) | −10.1986 | − | 5.88817i | −0.923338 | − | 0.533089i | ||||
\(123\) | 2.16980 | − | 12.5330i | 0.195645 | − | 1.13006i | ||||
\(124\) | 3.35685 | − | 1.93808i | 0.301454 | − | 0.174045i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 2.11080 | + | 11.5511i | 0.188045 | + | 1.02905i | ||||
\(127\) | 9.18483 | 0.815022 | 0.407511 | − | 0.913200i | \(-0.366397\pi\) | ||||
0.407511 | + | 0.913200i | \(0.366397\pi\) | |||||||
\(128\) | −1.99699 | + | 1.15296i | −0.176511 | + | 0.101909i | ||||
\(129\) | −1.83408 | + | 2.19960i | −0.161481 | + | 0.193664i | ||||
\(130\) | 3.63399 | + | 0.555821i | 0.318722 | + | 0.0487487i | ||||
\(131\) | 0.668898 | − | 1.15857i | 0.0584419 | − | 0.101224i | −0.835324 | − | 0.549758i | \(-0.814720\pi\) |
0.893766 | + | 0.448533i | \(0.148053\pi\) | |||||||
\(132\) | −3.56515 | + | 1.31016i | −0.310306 | + | 0.114035i | ||||
\(133\) | 4.44715 | + | 7.70268i | 0.385616 | + | 0.667907i | ||||
\(134\) | 7.57675 | 0.654531 | ||||||||
\(135\) | −2.63988 | − | 4.47561i | −0.227204 | − | 0.385199i | ||||
\(136\) | − | 22.6520i | − | 1.94239i | ||||||
\(137\) | 0.388221 | − | 0.224140i | 0.0331680 | − | 0.0191495i | −0.483324 | − | 0.875441i | \(-0.660571\pi\) |
0.516492 | + | 0.856292i | \(0.327237\pi\) | |||||||
\(138\) | 5.57004 | − | 2.04693i | 0.474153 | − | 0.174247i | ||||
\(139\) | 9.89704 | − | 17.1422i | 0.839456 | − | 1.45398i | −0.0508945 | − | 0.998704i | \(-0.516207\pi\) |
0.890350 | − | 0.455276i | \(-0.150459\pi\) | |||||||
\(140\) | −1.84340 | + | 3.19287i | −0.155796 | + | 0.269846i | ||||
\(141\) | −10.9573 | − | 9.13649i | −0.922775 | − | 0.769431i | ||||
\(142\) | 3.66658 | + | 6.35071i | 0.307693 | + | 0.532939i | ||||
\(143\) | −7.67018 | + | 2.99109i | −0.641413 | + | 0.250128i | ||||
\(144\) | −3.26855 | − | 1.16672i | −0.272379 | − | 0.0972269i | ||||
\(145\) | 8.15429i | 0.677177i | ||||||||
\(146\) | 3.94986 | + | 6.84137i | 0.326893 | + | 0.566196i | ||||
\(147\) | −13.2039 | − | 2.28596i | −1.08904 | − | 0.188542i | ||||
\(148\) | −0.454888 | − | 0.262630i | −0.0373916 | − | 0.0215880i | ||||
\(149\) | −9.24192 | − | 5.33582i | −0.757127 | − | 0.437128i | 0.0711360 | − | 0.997467i | \(-0.477338\pi\) |
−0.828263 | + | 0.560339i | \(0.810671\pi\) | |||||||
\(150\) | −0.301264 | + | 1.74013i | −0.0245981 | + | 0.142081i | ||||
\(151\) | 12.1571 | − | 7.01893i | 0.989334 | − | 0.571192i | 0.0842590 | − | 0.996444i | \(-0.473148\pi\) |
0.905075 | + | 0.425251i | \(0.139814\pi\) | |||||||
\(152\) | −6.99351 | −0.567249 | ||||||||
\(153\) | −17.1562 | + | 14.5783i | −1.38700 | + | 1.17858i | ||||
\(154\) | 8.93732i | 0.720190i | ||||||||
\(155\) | 2.01800 | + | 3.49528i | 0.162090 | + | 0.280748i | ||||
\(156\) | 5.68713 | + | 1.90489i | 0.455335 | + | 0.152513i | ||||
\(157\) | 6.23726 | − | 10.8032i | 0.497787 | − | 0.862193i | −0.502210 | − | 0.864746i | \(-0.667479\pi\) |
0.999997 | + | 0.00255322i | \(0.000812715\pi\) | |||||||
\(158\) | −10.9462 | − | 6.31978i | −0.870831 | − | 0.502775i | ||||
\(159\) | −4.24315 | − | 11.5463i | −0.336504 | − | 0.915682i | ||||
\(160\) | −2.42868 | − | 4.20660i | −0.192004 | − | 0.332561i | ||||
\(161\) | 12.8994i | 1.01662i | ||||||||
\(162\) | 3.24538 | + | 8.58344i | 0.254981 | + | 0.674379i | ||||
\(163\) | 8.11257i | 0.635425i | 0.948187 | + | 0.317713i | \(0.102915\pi\) | ||||
−0.948187 | + | 0.317713i | \(0.897085\pi\) | |||||||
\(164\) | −6.10784 | + | 3.52636i | −0.476942 | + | 0.275363i | ||||
\(165\) | −1.36418 | − | 3.71216i | −0.106202 | − | 0.288992i | ||||
\(166\) | −3.42207 | + | 5.92720i | −0.265604 | + | 0.460040i | ||||
\(167\) | 7.32936 | + | 4.23161i | 0.567163 | + | 0.327452i | 0.756015 | − | 0.654554i | \(-0.227143\pi\) |
−0.188852 | + | 0.982005i | \(0.560477\pi\) | |||||||
\(168\) | 12.8529 | − | 15.4144i | 0.991619 | − | 1.18924i | ||||
\(169\) | 12.4057 | + | 3.88581i | 0.954282 | + | 0.298908i | ||||
\(170\) | 7.65169 | 0.586857 | ||||||||
\(171\) | 4.50084 | + | 5.29675i | 0.344188 | + | 0.405053i | ||||
\(172\) | 1.58800 | 0.121084 | ||||||||
\(173\) | −13.0267 | − | 22.5630i | −0.990404 | − | 1.71543i | −0.614890 | − | 0.788613i | \(-0.710800\pi\) |
−0.375514 | − | 0.926817i | \(-0.622534\pi\) | |||||||
\(174\) | 2.45660 | − | 14.1895i | 0.186234 | − | 1.07570i | ||||
\(175\) | −3.32453 | − | 1.91942i | −0.251311 | − | 0.145094i | ||||
\(176\) | −2.28760 | − | 1.32075i | −0.172435 | − | 0.0995551i | ||||
\(177\) | 2.20331 | − | 12.7265i | 0.165611 | − | 0.956584i | ||||
\(178\) | −3.29646 | − | 5.70964i | −0.247080 | − | 0.427956i | ||||
\(179\) | −19.3448 | −1.44590 | −0.722948 | − | 0.690902i | \(-0.757213\pi\) | ||||
−0.722948 | + | 0.690902i | \(0.757213\pi\) | |||||||
\(180\) | −0.968594 | + | 2.71350i | −0.0721948 | + | 0.202252i | ||||
\(181\) | −9.00966 | −0.669683 | −0.334841 | − | 0.942274i | \(-0.608683\pi\) | ||||
−0.334841 | + | 0.942274i | \(0.608683\pi\) | |||||||
\(182\) | 8.82300 | − | 11.0145i | 0.654004 | − | 0.816447i | ||||
\(183\) | 12.8113 | − | 15.3645i | 0.947036 | − | 1.13578i | ||||
\(184\) | −8.78386 | − | 5.07136i | −0.647555 | − | 0.373866i | ||||
\(185\) | 0.273460 | − | 0.473647i | 0.0201052 | − | 0.0348232i | ||||
\(186\) | −2.45858 | − | 6.69019i | −0.180272 | − | 0.490549i | ||||
\(187\) | −14.8398 | + | 8.56776i | −1.08519 | + | 0.626536i | ||||
\(188\) | 7.91067i | 0.576945i | ||||||||
\(189\) | −19.9463 | + | 0.185783i | −1.45088 | + | 0.0135137i | ||||
\(190\) | − | 2.36236i | − | 0.171383i | ||||||
\(191\) | 0.575599 | + | 0.996967i | 0.0416489 | + | 0.0721380i | 0.886098 | − | 0.463497i | \(-0.153406\pi\) |
−0.844450 | + | 0.535635i | \(0.820072\pi\) | |||||||
\(192\) | 4.34123 | + | 11.8132i | 0.313301 | + | 0.852544i | ||||
\(193\) | 14.7966 | + | 8.54284i | 1.06509 | + | 0.614927i | 0.926835 | − | 0.375470i | \(-0.122519\pi\) |
0.138251 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(194\) | −5.94744 | + | 10.3013i | −0.427002 | + | 0.739588i | ||||
\(195\) | −1.98344 | + | 5.92165i | −0.142037 | + | 0.424058i | ||||
\(196\) | 3.71513 | + | 6.43480i | 0.265367 | + | 0.459628i | ||||
\(197\) | − | 23.3323i | − | 1.66236i | −0.556006 | − | 0.831178i | \(-0.687667\pi\) | ||
0.556006 | − | 0.831178i | \(-0.312333\pi\) | |||||||
\(198\) | 1.25551 | + | 6.87063i | 0.0892255 | + | 0.488274i | ||||
\(199\) | −22.4339 | −1.59030 | −0.795148 | − | 0.606415i | \(-0.792607\pi\) | ||||
−0.795148 | + | 0.606415i | \(0.792607\pi\) | |||||||
\(200\) | 2.61405 | − | 1.50922i | 0.184841 | − | 0.106718i | ||||
\(201\) | −2.19565 | + | 12.6823i | −0.154869 | + | 0.894538i | ||||
\(202\) | 2.68230 | + | 1.54862i | 0.188726 | + | 0.108961i | ||||
\(203\) | 27.1092 | + | 15.6515i | 1.90269 | + | 1.09852i | ||||
\(204\) | 12.3005 | + | 2.12955i | 0.861204 | + | 0.149098i | ||||
\(205\) | −3.67178 | − | 6.35971i | −0.256448 | − | 0.444181i | ||||
\(206\) | − | 19.0563i | − | 1.32772i | ||||||
\(207\) | 1.81211 | + | 9.91653i | 0.125950 | + | 0.689246i | ||||
\(208\) | 1.51542 | + | 3.88605i | 0.105075 | + | 0.269449i | ||||
\(209\) | 2.64518 | + | 4.58159i | 0.182971 | + | 0.316915i | ||||
\(210\) | 5.20686 | + | 4.34160i | 0.359308 | + | 0.299599i | ||||
\(211\) | −1.42676 | + | 2.47121i | −0.0982219 | + | 0.170125i | −0.910949 | − | 0.412520i | \(-0.864649\pi\) |
0.812727 | + | 0.582645i | \(0.197982\pi\) | |||||||
\(212\) | −3.41044 | + | 5.90705i | −0.234230 | + | 0.405698i | ||||
\(213\) | −11.6926 | + | 4.29691i | −0.801163 | + | 0.294420i | ||||
\(214\) | 5.67541 | − | 3.27670i | 0.387963 | − | 0.223991i | ||||
\(215\) | 1.65349i | 0.112767i | ||||||||
\(216\) | 7.71531 | − | 13.6555i | 0.524960 | − | 0.929137i | ||||
\(217\) | 15.4936 | 1.05177 | ||||||||
\(218\) | −0.0961945 | − | 0.166614i | −0.00651511 | − | 0.0112845i | ||||
\(219\) | −12.5960 | + | 4.62889i | −0.851157 | + | 0.312792i | ||||
\(220\) | −1.09646 | + | 1.89913i | −0.0739236 | + | 0.128039i | ||||
\(221\) | 26.7469 | + | 4.09095i | 1.79919 | + | 0.275187i | ||||
\(222\) | −0.618549 | + | 0.741823i | −0.0415143 | + | 0.0497879i | ||||
\(223\) | 7.75167 | − | 4.47543i | 0.519090 | − | 0.299697i | −0.217472 | − | 0.976067i | \(-0.569781\pi\) |
0.736562 | + | 0.676370i | \(0.236448\pi\) | |||||||
\(224\) | −18.6466 | −1.24588 | ||||||||
\(225\) | −2.82539 | − | 1.00854i | −0.188360 | − | 0.0672358i | ||||
\(226\) | 0.185137i | 0.0123151i | ||||||||
\(227\) | 10.4464 | − | 6.03126i | 0.693355 | − | 0.400309i | −0.111513 | − | 0.993763i | \(-0.535570\pi\) |
0.804868 | + | 0.593454i | \(0.202236\pi\) | |||||||
\(228\) | 0.657470 | − | 3.79760i | 0.0435420 | − | 0.251503i | ||||
\(229\) | 19.0488 | + | 10.9978i | 1.25878 | + | 0.726755i | 0.972837 | − | 0.231492i | \(-0.0743608\pi\) |
0.285940 | + | 0.958247i | \(0.407694\pi\) | |||||||
\(230\) | 1.71307 | − | 2.96712i | 0.112956 | − | 0.195646i | ||||
\(231\) | −14.9596 | − | 2.58993i | −0.984272 | − | 0.170405i | ||||
\(232\) | −21.3157 | + | 12.3067i | −1.39945 | + | 0.807971i | ||||
\(233\) | 18.6627 | 1.22263 | 0.611316 | − | 0.791387i | \(-0.290641\pi\) | ||||
0.611316 | + | 0.791387i | \(0.290641\pi\) | |||||||
\(234\) | 5.23543 | − | 9.70690i | 0.342251 | − | 0.634560i | ||||
\(235\) | −8.23689 | −0.537315 | ||||||||
\(236\) | −6.20216 | + | 3.58082i | −0.403726 | + | 0.233091i | ||||
\(237\) | 13.7504 | − | 16.4907i | 0.893182 | − | 1.07119i | ||||
\(238\) | 14.6868 | − | 25.4383i | 0.952003 | − | 1.64892i | ||||
\(239\) | −0.139921 | − | 0.0807834i | −0.00905073 | − | 0.00522544i | 0.495468 | − | 0.868626i | \(-0.334997\pi\) |
−0.504519 | + | 0.863401i | \(0.668330\pi\) | |||||||
\(240\) | −1.88074 | + | 0.691154i | −0.121401 | + | 0.0446138i | ||||
\(241\) | −1.45945 | + | 0.842613i | −0.0940114 | + | 0.0542775i | −0.546269 | − | 0.837610i | \(-0.683952\pi\) |
0.452257 | + | 0.891888i | \(0.350619\pi\) | |||||||
\(242\) | − | 5.89975i | − | 0.379250i | ||||||
\(243\) | −15.3078 | + | 2.94488i | −0.981994 | + | 0.188914i | ||||
\(244\) | −11.0924 | −0.710120 | ||||||||
\(245\) | −6.70015 | + | 3.86833i | −0.428057 | + | 0.247139i | ||||
\(246\) | 4.47342 | + | 12.1729i | 0.285215 | + | 0.776115i | ||||
\(247\) | 1.26303 | − | 8.25775i | 0.0803645 | − | 0.525428i | ||||
\(248\) | −6.09123 | + | 10.5503i | −0.386794 | + | 0.669946i | ||||
\(249\) | −8.92950 | − | 7.44562i | −0.565884 | − | 0.471847i | ||||
\(250\) | 0.509805 | + | 0.883008i | 0.0322429 | + | 0.0558463i | ||||
\(251\) | 16.3409 | 1.03143 | 0.515714 | − | 0.856761i | \(-0.327527\pi\) | ||||
0.515714 | + | 0.856761i | \(0.327527\pi\) | |||||||
\(252\) | 7.16197 | + | 8.42846i | 0.451162 | + | 0.530943i | ||||
\(253\) | 7.67264i | 0.482375i | ||||||||
\(254\) | −8.11028 | + | 4.68247i | −0.508884 | + | 0.293804i | ||||
\(255\) | −2.21736 | + | 12.8077i | −0.138857 | + | 0.802049i | ||||
\(256\) | 8.44188 | − | 14.6218i | 0.527618 | − | 0.913861i | ||||
\(257\) | 0.0607070 | − | 0.105148i | 0.00378680 | − | 0.00655893i | −0.864126 | − | 0.503276i | \(-0.832128\pi\) |
0.867913 | + | 0.496717i | \(0.165461\pi\) | |||||||
\(258\) | 0.498137 | − | 2.87729i | 0.0310127 | − | 0.179132i | ||||
\(259\) | −1.04977 | − | 1.81825i | −0.0652294 | − | 0.112981i | ||||
\(260\) | 3.22613 | − | 1.25807i | 0.200076 | − | 0.0780225i | ||||
\(261\) | 23.0391 | + | 8.22390i | 1.42608 | + | 0.509046i | ||||
\(262\) | 1.36403i | 0.0842700i | ||||||||
\(263\) | −3.71682 | − | 6.43773i | −0.229189 | − | 0.396967i | 0.728379 | − | 0.685175i | \(-0.240274\pi\) |
−0.957568 | + | 0.288207i | \(0.906941\pi\) | |||||||
\(264\) | 7.64494 | − | 9.16854i | 0.470513 | − | 0.564284i | ||||
\(265\) | −6.15064 | − | 3.55107i | −0.377831 | − | 0.218141i | ||||
\(266\) | −7.85373 | − | 4.53435i | −0.481543 | − | 0.278019i | ||||
\(267\) | 10.5123 | − | 3.86316i | 0.643342 | − | 0.236422i | ||||
\(268\) | 6.18059 | − | 3.56837i | 0.377540 | − | 0.217973i | ||||
\(269\) | 11.1991 | 0.682823 | 0.341412 | − | 0.939914i | \(-0.389095\pi\) | ||||
0.341412 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(270\) | 4.61272 | + | 2.60618i | 0.280721 | + | 0.158607i | ||||
\(271\) | − | 15.2574i | − | 0.926821i | −0.886144 | − | 0.463410i | \(-0.846626\pi\) | ||
0.886144 | − | 0.463410i | \(-0.153374\pi\) | |||||||
\(272\) | 4.34079 | + | 7.51848i | 0.263199 | + | 0.455875i | ||||
\(273\) | 15.8797 | + | 17.9601i | 0.961080 | + | 1.08700i | ||||
\(274\) | −0.228535 | + | 0.395834i | −0.0138063 | + | 0.0239132i | ||||
\(275\) | −1.97745 | − | 1.14168i | −0.119244 | − | 0.0688458i | ||||
\(276\) | 3.57962 | − | 4.29303i | 0.215468 | − | 0.258410i | ||||
\(277\) | −2.37420 | − | 4.11224i | −0.142652 | − | 0.247080i | 0.785843 | − | 0.618427i | \(-0.212230\pi\) |
−0.928494 | + | 0.371346i | \(0.878896\pi\) | |||||||
\(278\) | 20.1822i | 1.21045i | ||||||||
\(279\) | 11.9108 | − | 2.17653i | 0.713079 | − | 0.130306i | ||||
\(280\) | − | 11.5873i | − | 0.692476i | ||||||
\(281\) | −11.8137 | + | 6.82064i | −0.704746 | + | 0.406885i | −0.809113 | − | 0.587654i | \(-0.800052\pi\) |
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(282\) | 14.3332 | + | 2.48148i | 0.853533 | + | 0.147770i | ||||
\(283\) | −3.90498 | + | 6.76362i | −0.232127 | + | 0.402056i | −0.958434 | − | 0.285315i | \(-0.907902\pi\) |
0.726307 | + | 0.687371i | \(0.241235\pi\) | |||||||
\(284\) | 5.98189 | + | 3.45365i | 0.354960 | + | 0.204936i | ||||
\(285\) | 3.95421 | + | 0.684582i | 0.234227 | + | 0.0405512i | ||||
\(286\) | 5.24796 | − | 6.55146i | 0.310318 | − | 0.387396i | ||||
\(287\) | −28.1907 | −1.66405 | ||||||||
\(288\) | −14.3347 | + | 2.61948i | −0.844682 | + | 0.154354i | ||||
\(289\) | 39.3179 | 2.31282 | ||||||||
\(290\) | −4.15710 | − | 7.20030i | −0.244113 | − | 0.422816i | ||||
\(291\) | −15.5192 | − | 12.9402i | −0.909750 | − | 0.758571i | ||||
\(292\) | 6.44405 | + | 3.72048i | 0.377110 | + | 0.217724i | ||||
\(293\) | −5.15813 | − | 2.97805i | −0.301341 | − | 0.173979i | 0.341704 | − | 0.939808i | \(-0.388996\pi\) |
−0.643045 | + | 0.765828i | \(0.722329\pi\) | |||||||
\(294\) | 12.8245 | − | 4.71289i | 0.747941 | − | 0.274861i | ||||
\(295\) | −3.72848 | − | 6.45792i | −0.217081 | − | 0.375995i | ||||
\(296\) | 1.65085 | 0.0959537 | ||||||||
\(297\) | −11.8642 | + | 0.110504i | −0.688428 | + | 0.00641212i | ||||
\(298\) | 10.8809 | 0.630315 | ||||||||
\(299\) | 7.57449 | − | 9.45586i | 0.438044 | − | 0.546846i | ||||
\(300\) | 0.573785 | + | 1.56136i | 0.0331275 | + | 0.0901453i | ||||
\(301\) | 5.49707 | + | 3.17374i | 0.316846 | + | 0.182931i | ||||
\(302\) | −7.15657 | + | 12.3955i | −0.411814 | + | 0.713283i | ||||
\(303\) | −3.36944 | + | 4.04096i | −0.193569 | + | 0.232147i | ||||
\(304\) | 2.32123 | − | 1.34016i | 0.133132 | − | 0.0768636i | ||||
\(305\) | − | 11.5498i | − | 0.661342i | ||||||
\(306\) | 7.71700 | − | 21.6190i | 0.441152 | − | 1.23588i | ||||
\(307\) | 7.80536i | 0.445475i | 0.974878 | + | 0.222738i | \(0.0714993\pi\) | ||||
−0.974878 | + | 0.222738i | \(0.928501\pi\) | |||||||
\(308\) | 4.20915 | + | 7.29045i | 0.239838 | + | 0.415412i | ||||
\(309\) | 31.8973 | + | 5.52230i | 1.81457 | + | 0.314152i | ||||
\(310\) | −3.56382 | − | 2.05757i | −0.202411 | − | 0.116862i | ||||
\(311\) | 4.84636 | − | 8.39414i | 0.274812 | − | 0.475988i | −0.695276 | − | 0.718743i | \(-0.744718\pi\) |
0.970088 | + | 0.242755i | \(0.0780511\pi\) | |||||||
\(312\) | −18.4730 | + | 3.75228i | −1.04583 | + | 0.212431i | ||||
\(313\) | 13.6176 | + | 23.5864i | 0.769714 | + | 1.33318i | 0.937718 | + | 0.347397i | \(0.112934\pi\) |
−0.168004 | + | 0.985786i | \(0.553732\pi\) | |||||||
\(314\) | 12.7191i | 0.717782i | ||||||||
\(315\) | −8.77602 | + | 7.45731i | −0.494473 | + | 0.420172i | ||||
\(316\) | −11.9055 | −0.669738 | ||||||||
\(317\) | 19.4508 | − | 11.2299i | 1.09246 | − | 0.630734i | 0.158232 | − | 0.987402i | \(-0.449420\pi\) |
0.934231 | + | 0.356668i | \(0.116087\pi\) | |||||||
\(318\) | 9.63310 | + | 8.03230i | 0.540198 | + | 0.450429i | ||||
\(319\) | 16.1247 | + | 9.30958i | 0.902808 | + | 0.521236i | ||||
\(320\) | 6.29281 | + | 3.63316i | 0.351779 | + | 0.203100i | ||||
\(321\) | 3.84001 | + | 10.4493i | 0.214328 | + | 0.583222i | ||||
\(322\) | −6.57619 | − | 11.3903i | −0.366477 | − | 0.634757i | ||||
\(323\) | − | 17.3874i | − | 0.967461i | ||||||
\(324\) | 6.68984 | + | 5.47332i | 0.371658 | + | 0.304073i | ||||
\(325\) | 1.30995 | + | 3.35917i | 0.0726632 | + | 0.186333i | ||||
\(326\) | −4.13583 | − | 7.16346i | −0.229062 | − | 0.396748i | ||||
\(327\) | 0.306761 | − | 0.112731i | 0.0169639 | − | 0.00623407i | ||||
\(328\) | 11.0831 | − | 19.1964i | 0.611960 | − | 1.05995i | ||||
\(329\) | −15.8100 | + | 27.3838i | −0.871635 | + | 1.50972i | ||||
\(330\) | 3.09706 | + | 2.58240i | 0.170488 | + | 0.142157i | ||||
\(331\) | 1.13312 | − | 0.654208i | 0.0622820 | − | 0.0359585i | −0.468536 | − | 0.883445i | \(-0.655218\pi\) |
0.530818 | + | 0.847486i | \(0.321885\pi\) | |||||||
\(332\) | 6.44667i | 0.353807i | ||||||||
\(333\) | −1.06244 | − | 1.25032i | −0.0582216 | − | 0.0685172i | ||||
\(334\) | −8.62918 | −0.472168 | ||||||||
\(335\) | 3.71551 | + | 6.43546i | 0.203000 | + | 0.351607i | ||||
\(336\) | −1.31217 | + | 7.57920i | −0.0715847 | + | 0.413479i | ||||
\(337\) | 12.9160 | − | 22.3712i | 0.703580 | − | 1.21864i | −0.263621 | − | 0.964626i | \(-0.584917\pi\) |
0.967201 | − | 0.254011i | \(-0.0817499\pi\) | |||||||
\(338\) | −12.9353 | + | 2.89327i | −0.703588 | + | 0.157373i | ||||
\(339\) | −0.309889 | − | 0.0536503i | −0.0168308 | − | 0.00291388i | ||||
\(340\) | 6.24172 | − | 3.60366i | 0.338505 | − | 0.195436i | ||||
\(341\) | 9.21564 | 0.499055 | ||||||||
\(342\) | −6.67459 | − | 2.38252i | −0.360921 | − | 0.128832i | ||||
\(343\) | 2.82795i | 0.152695i | ||||||||
\(344\) | −4.32231 | + | 2.49549i | −0.233043 | + | 0.134548i | ||||
\(345\) | 4.47006 | + | 3.72724i | 0.240660 | + | 0.200668i | ||||
\(346\) | 23.0054 | + | 13.2822i | 1.23678 | + | 0.714054i | ||||
\(347\) | 8.22130 | − | 14.2397i | 0.441342 | − | 0.764428i | −0.556447 | − | 0.830883i | \(-0.687836\pi\) |
0.997789 | + | 0.0664556i | \(0.0211691\pi\) | |||||||
\(348\) | −4.67881 | − | 12.7318i | −0.250811 | − | 0.682496i | ||||
\(349\) | −6.19279 | + | 3.57541i | −0.331492 | + | 0.191387i | −0.656504 | − | 0.754323i | \(-0.727965\pi\) |
0.325011 | + | 0.945710i | \(0.394632\pi\) | |||||||
\(350\) | 3.91412 | 0.209218 | ||||||||
\(351\) | 14.7306 | + | 11.5762i | 0.786263 | + | 0.617892i | ||||
\(352\) | −11.0911 | −0.591158 | ||||||||
\(353\) | −23.2529 | + | 13.4251i | −1.23763 | + | 0.714544i | −0.968608 | − | 0.248591i | \(-0.920032\pi\) |
−0.269018 | + | 0.963135i | \(0.586699\pi\) | |||||||
\(354\) | 4.54250 | + | 12.3609i | 0.241431 | + | 0.656973i | ||||
\(355\) | −3.59606 | + | 6.22857i | −0.190859 | + | 0.330578i | ||||
\(356\) | −5.37806 | − | 3.10502i | −0.285036 | − | 0.164566i | ||||
\(357\) | 38.3235 | + | 31.9550i | 2.02829 | + | 1.69124i | ||||
\(358\) | 17.0816 | − | 9.86206i | 0.902790 | − | 0.521226i | ||||
\(359\) | 25.3831i | 1.33967i | 0.742512 | + | 0.669833i | \(0.233634\pi\) | ||||
−0.742512 | + | 0.669833i | \(0.766366\pi\) | |||||||
\(360\) | −1.62779 | − | 8.90784i | −0.0857919 | − | 0.469484i | ||||
\(361\) | 13.6319 | 0.717467 | ||||||||
\(362\) | 7.95560 | − | 4.59317i | 0.418137 | − | 0.241412i | ||||
\(363\) | 9.87523 | + | 1.70967i | 0.518315 | + | 0.0897346i | ||||
\(364\) | 2.00979 | − | 13.1401i | 0.105342 | − | 0.688731i | ||||
\(365\) | −3.87390 | + | 6.70979i | −0.202769 | + | 0.351206i | ||||
\(366\) | −3.47956 | + | 20.0982i | −0.181879 | + | 1.05055i | ||||
\(367\) | 2.75102 | + | 4.76491i | 0.143602 | + | 0.248726i | 0.928851 | − | 0.370455i | \(-0.120798\pi\) |
−0.785248 | + | 0.619181i | \(0.787465\pi\) | |||||||
\(368\) | 3.88729 | 0.202639 | ||||||||
\(369\) | −21.6718 | + | 3.96023i | −1.12819 | + | 0.206161i | ||||
\(370\) | 0.557645i | 0.0289906i | ||||||||
\(371\) | −23.6113 | + | 13.6320i | −1.22584 | + | 0.707738i | ||||
\(372\) | −5.15637 | − | 4.29950i | −0.267345 | − | 0.222919i | ||||
\(373\) | −11.5270 | + | 19.9654i | −0.596847 | + | 1.03377i | 0.396436 | + | 0.918062i | \(0.370247\pi\) |
−0.993283 | + | 0.115708i | \(0.963086\pi\) | |||||||
\(374\) | 8.73577 | − | 15.1308i | 0.451716 | − | 0.782395i | ||||
\(375\) | −1.62575 | + | 0.597446i | −0.0839533 | + | 0.0308520i | ||||
\(376\) | −12.4313 | − | 21.5317i | −0.641096 | − | 1.11041i | ||||
\(377\) | −10.6817 | − | 27.3916i | −0.550138 | − | 1.41074i | ||||
\(378\) | 17.5180 | − | 10.3328i | 0.901031 | − | 0.531461i | ||||
\(379\) | − | 13.1674i | − | 0.676363i | −0.941081 | − | 0.338181i | \(-0.890188\pi\) | ||
0.941081 | − | 0.338181i | \(-0.109812\pi\) | |||||||
\(380\) | −1.11258 | − | 1.92705i | −0.0570743 | − | 0.0988555i | ||||
\(381\) | −5.48744 | − | 14.9322i | −0.281130 | − | 0.765001i | ||||
\(382\) | −1.01652 | − | 0.586886i | −0.0520095 | − | 0.0300277i | ||||
\(383\) | −31.5880 | − | 18.2373i | −1.61407 | − | 0.931884i | −0.988414 | − | 0.151785i | \(-0.951498\pi\) |
−0.625656 | − | 0.780099i | \(-0.715169\pi\) | |||||||
\(384\) | 3.06752 | + | 2.55777i | 0.156539 | + | 0.130526i | ||||
\(385\) | −7.59109 | + | 4.38272i | −0.386878 | + | 0.223364i | ||||
\(386\) | −17.4207 | −0.886692 | ||||||||
\(387\) | 4.67176 | + | 1.66760i | 0.237479 | + | 0.0847691i | ||||
\(388\) | 11.2041i | 0.568802i | ||||||||
\(389\) | −9.44003 | − | 16.3506i | −0.478629 | − | 0.829009i | 0.521071 | − | 0.853513i | \(-0.325533\pi\) |
−0.999700 | + | 0.0245043i | \(0.992199\pi\) | |||||||
\(390\) | −1.26749 | − | 6.24003i | −0.0641820 | − | 0.315976i | ||||
\(391\) | 12.6085 | − | 21.8386i | 0.637640 | − | 1.10443i | ||||
\(392\) | −20.2241 | − | 11.6764i | −1.02147 | − | 0.589746i | ||||
\(393\) | −2.28317 | − | 0.395279i | −0.115170 | − | 0.0199392i | ||||
\(394\) | 11.8949 | + | 20.6026i | 0.599257 | + | 1.03794i | ||||
\(395\) | − | 12.3965i | − | 0.623734i | ||||||
\(396\) | 4.25997 | + | 5.01329i | 0.214072 | + | 0.251927i | ||||
\(397\) | − | 24.1425i | − | 1.21168i | −0.795587 | − | 0.605840i | \(-0.792837\pi\) | ||
0.795587 | − | 0.605840i | \(-0.207163\pi\) | |||||||
\(398\) | 19.8093 | − | 11.4369i | 0.992951 | − | 0.573280i | ||||
\(399\) | 9.86569 | − | 11.8319i | 0.493902 | − | 0.592335i | ||||
\(400\) | −0.578424 | + | 1.00186i | −0.0289212 | + | 0.0500930i | ||||
\(401\) | 16.9146 | + | 9.76567i | 0.844676 | + | 0.487674i | 0.858851 | − | 0.512225i | \(-0.171179\pi\) |
−0.0141747 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(402\) | −4.52670 | − | 12.3179i | −0.225771 | − | 0.614360i | ||||
\(403\) | −11.3575 | − | 9.09775i | −0.565756 | − | 0.453191i | ||||
\(404\) | 2.91738 | 0.145145 | ||||||||
\(405\) | −5.69903 | + | 6.96571i | −0.283187 | + | 0.346129i | ||||
\(406\) | −31.9168 | −1.58401 | ||||||||
\(407\) | −0.624407 | − | 1.08150i | −0.0309507 | − | 0.0536082i | ||||
\(408\) | −36.8265 | + | 13.5334i | −1.82318 | + | 0.670002i | ||||
\(409\) | 20.9244 | + | 12.0807i | 1.03465 | + | 0.597354i | 0.918313 | − | 0.395856i | \(-0.129552\pi\) |
0.116335 | + | 0.993210i | \(0.462885\pi\) | |||||||
\(410\) | 6.48442 | + | 3.74378i | 0.320243 | + | 0.184892i | ||||
\(411\) | −0.596336 | − | 0.497239i | −0.0294151 | − | 0.0245270i | ||||
\(412\) | −8.97483 | − | 15.5449i | −0.442158 | − | 0.765840i | ||||
\(413\) | −28.6261 | −1.40860 | ||||||||
\(414\) | −6.65560 | − | 7.83255i | −0.327105 | − | 0.384949i | ||||
\(415\) | −6.71251 | −0.329504 | ||||||||
\(416\) | 13.6688 | + | 10.9492i | 0.670169 | + | 0.536830i | ||||
\(417\) | −33.7818 | − | 5.84856i | −1.65430 | − | 0.286405i | ||||
\(418\) | −4.67143 | − | 2.69705i | −0.228487 | − | 0.131917i | ||||
\(419\) | 1.42009 | − | 2.45966i | 0.0693758 | − | 0.120162i | −0.829251 | − | 0.558876i | \(-0.811233\pi\) |
0.898627 | + | 0.438714i | \(0.144566\pi\) | |||||||
\(420\) | 6.29213 | + | 1.08934i | 0.307025 | + | 0.0531544i | ||||
\(421\) | −27.4313 | + | 15.8375i | −1.33692 | + | 0.771872i | −0.986350 | − | 0.164664i | \(-0.947346\pi\) |
−0.350571 | + | 0.936536i | \(0.614013\pi\) | |||||||
\(422\) | − | 2.90947i | − | 0.141631i | ||||||
\(423\) | −8.30720 | + | 23.2725i | −0.403910 | + | 1.13155i | ||||
\(424\) | − | 21.4375i | − | 1.04110i | ||||||
\(425\) | 3.75226 | + | 6.49911i | 0.182011 | + | 0.315253i | ||||
\(426\) | 8.13406 | − | 9.75515i | 0.394097 | − | 0.472638i | ||||
\(427\) | −38.3978 | − | 22.1690i | −1.85820 | − | 1.07283i | ||||
\(428\) | 3.08641 | − | 5.34581i | 0.149187 | − | 0.258400i | ||||
\(429\) | 9.44529 | + | 10.6828i | 0.456023 | + | 0.515769i | ||||
\(430\) | −0.842957 | − | 1.46004i | −0.0406510 | − | 0.0704096i | ||||
\(431\) | 21.7562i | 1.04796i | 0.851731 | + | 0.523979i | \(0.175553\pi\) | ||||
−0.851731 | + | 0.523979i | \(0.824447\pi\) | |||||||
\(432\) | 0.0559863 | + | 6.01089i | 0.00269364 | + | 0.289199i | ||||
\(433\) | 25.9173 | 1.24551 | 0.622753 | − | 0.782419i | \(-0.286014\pi\) | ||||
0.622753 | + | 0.782419i | \(0.286014\pi\) | |||||||
\(434\) | −13.6809 | + | 7.89869i | −0.656706 | + | 0.379149i | ||||
\(435\) | 13.2568 | − | 4.87175i | 0.635616 | − | 0.233583i | ||||
\(436\) | −0.156938 | − | 0.0906080i | −0.00751595 | − | 0.00433934i | ||||
\(437\) | −6.74238 | − | 3.89272i | −0.322532 | − | 0.186214i | ||||
\(438\) | 8.76251 | − | 10.5088i | 0.418689 | − | 0.502132i | ||||
\(439\) | −12.0337 | − | 20.8429i | −0.574336 | − | 0.994778i | −0.996113 | − | 0.0880792i | \(-0.971927\pi\) |
0.421778 | − | 0.906699i | \(-0.361406\pi\) | |||||||
\(440\) | − | 6.89220i | − | 0.328573i | ||||||
\(441\) | 4.17222 | + | 22.8319i | 0.198677 | + | 1.08723i | ||||
\(442\) | −25.7033 | + | 10.0234i | −1.22258 | + | 0.476763i | ||||
\(443\) | 9.26668 | + | 16.0504i | 0.440273 | + | 0.762575i | 0.997710 | − | 0.0676443i | \(-0.0215483\pi\) |
−0.557436 | + | 0.830220i | \(0.688215\pi\) | |||||||
\(444\) | −0.155199 | + | 0.896441i | −0.00736540 | + | 0.0425432i | ||||
\(445\) | 3.23306 | − | 5.59983i | 0.153262 | − | 0.265457i | ||||
\(446\) | −4.56319 | + | 7.90368i | −0.216073 | + | 0.374250i | ||||
\(447\) | −3.15316 | + | 18.2129i | −0.149139 | + | 0.861441i | ||||
\(448\) | 24.1571 | − | 13.9471i | 1.14131 | − | 0.658938i | ||||
\(449\) | − | 22.1356i | − | 1.04465i | −0.852748 | − | 0.522323i | \(-0.825066\pi\) | ||
0.852748 | − | 0.522323i | \(-0.174934\pi\) | |||||||
\(450\) | 3.00900 | − | 0.549854i | 0.141846 | − | 0.0259204i | ||||
\(451\) | −16.7680 | −0.789573 | ||||||||
\(452\) | 0.0871924 | + | 0.151022i | 0.00410118 | + | 0.00710346i | ||||
\(453\) | −18.6743 | − | 15.5710i | −0.877393 | − | 0.731590i | ||||
\(454\) | −6.14953 | + | 10.6513i | −0.288612 | + | 0.499890i | ||||
\(455\) | 13.6820 | + | 2.09267i | 0.641423 | + | 0.0981058i | ||||
\(456\) | 4.17825 | + | 11.3697i | 0.195665 | + | 0.532435i | ||||
\(457\) | −17.3428 | + | 10.0128i | −0.811260 | + | 0.468381i | −0.847393 | − | 0.530966i | \(-0.821829\pi\) |
0.0361334 | + | 0.999347i | \(0.488496\pi\) | |||||||
\(458\) | −22.4269 | −1.04794 | ||||||||
\(459\) | 33.9505 | + | 19.1820i | 1.58467 | + | 0.895337i | ||||
\(460\) | − | 3.22717i | − | 0.150467i | ||||||
\(461\) | 4.75751 | − | 2.74675i | 0.221580 | − | 0.127929i | −0.385102 | − | 0.922874i | \(-0.625834\pi\) |
0.606681 | + | 0.794945i | \(0.292500\pi\) | |||||||
\(462\) | 14.5298 | − | 5.33957i | 0.675989 | − | 0.248419i | ||||
\(463\) | −29.8153 | − | 17.2139i | −1.38563 | − | 0.799996i | −0.392814 | − | 0.919618i | \(-0.628498\pi\) |
−0.992820 | + | 0.119622i | \(0.961832\pi\) | |||||||
\(464\) | 4.71663 | − | 8.16945i | 0.218964 | − | 0.379257i | ||||
\(465\) | 4.47680 | − | 5.36901i | 0.207607 | − | 0.248982i | ||||
\(466\) | −16.4793 | + | 9.51431i | −0.763388 | + | 0.440742i | ||||
\(467\) | 15.2175 | 0.704182 | 0.352091 | − | 0.935966i | \(-0.385471\pi\) | ||||
0.352091 | + | 0.935966i | \(0.385471\pi\) | |||||||
\(468\) | −0.300885 | − | 10.3839i | −0.0139084 | − | 0.479997i | ||||
\(469\) | 28.5265 | 1.31723 | ||||||||
\(470\) | 7.27323 | − | 4.19920i | 0.335489 | − | 0.193695i | ||||
\(471\) | −21.2898 | − | 3.68585i | −0.980981 | − | 0.169835i | ||||
\(472\) | 11.2542 | − | 19.4929i | 0.518018 | − | 0.897233i | ||||
\(473\) | 3.26968 | + | 1.88775i | 0.150340 | + | 0.0867990i | ||||
\(474\) | −3.73461 | + | 21.5715i | −0.171536 | + | 0.990810i | ||||
\(475\) | 2.00651 | − | 1.15846i | 0.0920652 | − | 0.0531539i | ||||
\(476\) | − | 27.6677i | − | 1.26815i | ||||||
\(477\) | −16.2363 | + | 13.7966i | −0.743411 | + | 0.631703i | ||||
\(478\) | 0.164735 | 0.00753480 | ||||||||
\(479\) | 34.7928 | − | 20.0877i | 1.58973 | − | 0.917828i | 0.596374 | − | 0.802707i | \(-0.296608\pi\) |
0.993351 | − | 0.115122i | \(-0.0367258\pi\) | |||||||
\(480\) | −5.38787 | + | 6.46164i | −0.245921 | + | 0.294932i | ||||
\(481\) | −0.298143 | + | 1.94928i | −0.0135942 | + | 0.0888795i | ||||
\(482\) | 0.859137 | − | 1.48807i | 0.0391326 | − | 0.0677797i | ||||
\(483\) | 20.9712 | − | 7.70672i | 0.954224 | − | 0.350668i | ||||
\(484\) | −2.77856 | − | 4.81261i | −0.126298 | − | 0.218755i | ||||
\(485\) | −11.6661 | −0.529731 | ||||||||
\(486\) | 12.0156 | − | 10.4043i | 0.545037 | − | 0.471950i | ||||
\(487\) | − | 31.1250i | − | 1.41041i | −0.709005 | − | 0.705203i | \(-0.750856\pi\) | ||
0.709005 | − | 0.705203i | \(-0.249144\pi\) | |||||||
\(488\) | 30.1919 | − | 17.4313i | 1.36672 | − | 0.789078i | ||||
\(489\) | 13.1890 | − | 4.84683i | 0.596427 | − | 0.219181i | ||||
\(490\) | 3.94419 | − | 6.83154i | 0.178180 | − | 0.308617i | ||||
\(491\) | −9.68601 | + | 16.7767i | −0.437124 | + | 0.757120i | −0.997466 | − | 0.0711405i | \(-0.977336\pi\) |
0.560343 | + | 0.828261i | \(0.310669\pi\) | |||||||
\(492\) | 9.38208 | + | 7.82299i | 0.422977 | + | 0.352688i | ||||
\(493\) | −30.5970 | − | 52.9956i | −1.37802 | − | 2.38680i | ||||
\(494\) | 3.09458 | + | 7.93556i | 0.139232 | + | 0.357038i | ||||
\(495\) | −5.22002 | + | 4.43564i | −0.234622 | + | 0.199367i | ||||
\(496\) | − | 4.66904i | − | 0.209646i | ||||||
\(497\) | 13.8047 | + | 23.9105i | 0.619226 | + | 1.07253i | ||||
\(498\) | 11.6806 | + | 2.02224i | 0.523422 | + | 0.0906187i | ||||
\(499\) | 14.5593 | + | 8.40584i | 0.651766 | + | 0.376297i | 0.789132 | − | 0.614223i | \(-0.210531\pi\) |
−0.137367 | + | 0.990520i | \(0.543864\pi\) | |||||||
\(500\) | 0.831727 | + | 0.480198i | 0.0371960 | + | 0.0214751i | ||||
\(501\) | 2.50063 | − | 14.4439i | 0.111720 | − | 0.645304i | ||||
\(502\) | −14.4291 | + | 8.33066i | −0.644004 | + | 0.371816i | ||||
\(503\) | 7.16252 | 0.319361 | 0.159681 | − | 0.987169i | \(-0.448954\pi\) | ||||
0.159681 | + | 0.987169i | \(0.448954\pi\) | |||||||
\(504\) | −32.7388 | − | 11.6862i | −1.45830 | − | 0.520547i | ||||
\(505\) | 3.03768i | 0.135175i | ||||||||
\(506\) | −3.91155 | − | 6.77500i | −0.173890 | − | 0.301186i | ||||
\(507\) | −1.09438 | − | 22.4900i | −0.0486030 | − | 0.998818i | ||||
\(508\) | −4.41054 | + | 7.63927i | −0.195686 | + | 0.338938i | ||||
\(509\) | −19.7416 | − | 11.3978i | −0.875033 | − | 0.505201i | −0.00601565 | − | 0.999982i | \(-0.501915\pi\) |
−0.869018 | + | 0.494781i | \(0.835248\pi\) | |||||||
\(510\) | −4.57147 | − | 12.4397i | −0.202428 | − | 0.550840i | ||||
\(511\) | 14.8713 | + | 25.7578i | 0.657866 | + | 1.13946i | ||||
\(512\) | 12.6030i | 0.556979i | ||||||||
\(513\) | 5.92218 | − | 10.4818i | 0.261470 | − | 0.462781i | ||||
\(514\) | 0.123795i | 0.00546036i | ||||||||
\(515\) | 16.1859 | − | 9.34492i | 0.713235 | − | 0.411786i | ||||
\(516\) | −0.948747 | − | 2.58170i | −0.0417663 | − | 0.113653i | ||||
\(517\) | −9.40388 | + | 16.2880i | −0.413582 | + | 0.716345i | ||||
\(518\) | 1.85391 | + | 1.07035i | 0.0814560 | + | 0.0470287i | ||||
\(519\) | −28.8989 | + | 34.6583i | −1.26852 | + | 1.52133i | ||||
\(520\) | −6.80403 | + | 8.49403i | −0.298377 | + | 0.372488i | ||||
\(521\) | −38.1592 | −1.67179 | −0.835893 | − | 0.548892i | \(-0.815050\pi\) | ||||
−0.835893 | + | 0.548892i | \(0.815050\pi\) | |||||||
\(522\) | −24.5363 | + | 4.48367i | −1.07392 | + | 0.196245i | ||||
\(523\) | −3.45918 | −0.151259 | −0.0756297 | − | 0.997136i | \(-0.524097\pi\) | ||||
−0.0756297 | + | 0.997136i | \(0.524097\pi\) | |||||||
\(524\) | 0.642407 | + | 1.11268i | 0.0280637 | + | 0.0486077i | ||||
\(525\) | −1.13426 | + | 6.55160i | −0.0495033 | + | 0.285935i | ||||
\(526\) | 6.56397 | + | 3.78971i | 0.286203 | + | 0.165239i | ||||
\(527\) | −26.2304 | − | 15.1441i | −1.14261 | − | 0.659689i | ||||
\(528\) | −0.780484 | + | 4.50814i | −0.0339662 | + | 0.196192i | ||||
\(529\) | 5.85438 | + | 10.1401i | 0.254538 | + | 0.440873i | ||||
\(530\) | 7.24142 | 0.314547 | ||||||||
\(531\) | −22.0065 | + | 4.02139i | −0.955000 | + | 0.174513i | ||||
\(532\) | −8.54204 | −0.370345 | ||||||||
\(533\) | 20.6651 | + | 16.5535i | 0.895103 | + | 0.717010i | ||||
\(534\) | −7.31298 | + | 8.77042i | −0.316464 | + | 0.379533i | ||||
\(535\) | 5.56626 | + | 3.21368i | 0.240650 | + | 0.138940i | ||||
\(536\) | −11.2151 | + | 19.4251i | −0.484418 | + | 0.839037i | ||||
\(537\) | 11.5575 | + | 31.4497i | 0.498742 | + | 1.35716i | ||||
\(538\) | −9.88893 | + | 5.70937i | −0.426342 | + | 0.246149i | ||||
\(539\) | 17.6656i | 0.760910i | ||||||||
\(540\) | 4.99015 | − | 0.0464789i | 0.214742 | − | 0.00200014i | ||||
\(541\) | 39.9806i | 1.71890i | 0.511218 | + | 0.859451i | \(0.329194\pi\) | ||||
−0.511218 | + | 0.859451i | \(0.670806\pi\) | |||||||
\(542\) | 7.77829 | + | 13.4724i | 0.334106 | + | 0.578689i | ||||
\(543\) | 5.38279 | + | 14.6474i | 0.230998 | + | 0.628582i | ||||
\(544\) | 31.5685 | + | 18.2261i | 1.35349 | + | 0.781438i | ||||
\(545\) | 0.0943444 | − | 0.163409i | 0.00404127 | − | 0.00699969i | ||||
\(546\) | −23.1780 | − | 7.76342i | −0.991928 | − | 0.332244i | ||||
\(547\) | 5.20013 | + | 9.00689i | 0.222341 | + | 0.385107i | 0.955519 | − | 0.294931i | \(-0.0952967\pi\) |
−0.733177 | + | 0.680038i | \(0.761963\pi\) | |||||||
\(548\) | 0.430526i | 0.0183911i | ||||||||
\(549\) | −32.6329 | − | 11.6484i | −1.39274 | − | 0.497143i | ||||
\(550\) | 2.32813 | 0.0992719 | ||||||||
\(551\) | −16.3617 | + | 9.44643i | −0.697032 | + | 0.402432i | ||||
\(552\) | −2.99688 | + | 17.3102i | −0.127555 | + | 0.736772i | ||||
\(553\) | −41.2124 | − | 23.7940i | −1.75253 | − | 1.01182i | ||||
\(554\) | 4.19288 | + | 2.42076i | 0.178138 | + | 0.102848i | ||||
\(555\) | −0.933408 | − | 0.161599i | −0.0396210 | − | 0.00685948i | ||||
\(556\) | 9.50508 | + | 16.4633i | 0.403105 | + | 0.698198i | ||||
\(557\) | 27.0548i | 1.14635i | 0.819433 | + | 0.573175i | \(0.194288\pi\) | ||||
−0.819433 | + | 0.573175i | \(0.805712\pi\) | |||||||
\(558\) | −9.40770 | + | 7.99407i | −0.398260 | + | 0.338416i | ||||
\(559\) | −2.16599 | − | 5.55435i | −0.0916118 | − | 0.234924i | ||||
\(560\) | 2.22047 | + | 3.84597i | 0.0938322 | + | 0.162522i | ||||
\(561\) | 22.7950 | + | 19.0070i | 0.962405 | + | 0.802476i | ||||
\(562\) | 6.95439 | − | 12.0454i | 0.293353 | − | 0.508103i | ||||
\(563\) | 6.78259 | − | 11.7478i | 0.285852 | − | 0.495110i | −0.686963 | − | 0.726692i | \(-0.741057\pi\) |
0.972815 | + | 0.231582i | \(0.0743901\pi\) | |||||||
\(564\) | 12.8608 | − | 4.72620i | 0.541536 | − | 0.199009i | ||||
\(565\) | −0.157249 | + | 0.0907879i | −0.00661553 | + | 0.00381948i | ||||
\(566\) | − | 7.96311i | − | 0.334714i | ||||||
\(567\) | 12.2189 | + | 32.3167i | 0.513145 | + | 1.35717i | ||||
\(568\) | −21.7091 | −0.910892 | ||||||||
\(569\) | 4.61124 | + | 7.98690i | 0.193313 | + | 0.334828i | 0.946346 | − | 0.323154i | \(-0.104743\pi\) |
−0.753033 | + | 0.657983i | \(0.771410\pi\) | |||||||
\(570\) | −3.84060 | + | 1.41138i | −0.160865 | + | 0.0591163i | ||||
\(571\) | 5.96082 | − | 10.3244i | 0.249453 | − | 0.432064i | −0.713922 | − | 0.700226i | \(-0.753083\pi\) |
0.963374 | + | 0.268161i | \(0.0864160\pi\) | |||||||
\(572\) | 1.19543 | − | 7.81582i | 0.0499836 | − | 0.326796i | ||||
\(573\) | 1.27693 | − | 1.53141i | 0.0533444 | − | 0.0639757i | ||||
\(574\) | 24.8926 | − | 14.3718i | 1.03900 | − | 0.599866i | ||||
\(575\) | 3.36025 | 0.140132 | ||||||||
\(576\) | 16.6116 | − | 14.1155i | 0.692151 | − | 0.588146i | ||||
\(577\) | 34.5550i | 1.43854i | 0.694730 | + | 0.719271i | \(0.255524\pi\) | ||||
−0.694730 | + | 0.719271i | \(0.744476\pi\) | |||||||
\(578\) | −34.7180 | + | 20.0444i | −1.44408 | + | 0.833739i | ||||
\(579\) | 5.04831 | − | 29.1595i | 0.209801 | − | 1.21183i | ||||
\(580\) | −6.78215 | − | 3.91567i | −0.281613 | − | 0.162589i | ||||
\(581\) | −12.8841 | + | 22.3159i | −0.534523 | + | 0.925821i | ||||
\(582\) | 20.3006 | + | 3.51459i | 0.841485 | + | 0.145684i | ||||
\(583\) | −14.0441 | + | 8.10837i | −0.581648 | + | 0.335815i | ||||
\(584\) | −23.3863 | −0.967733 | ||||||||
\(585\) | 10.8121 | − | 0.313293i | 0.447026 | − | 0.0129531i | ||||
\(586\) | 6.07289 | 0.250869 | ||||||||
\(587\) | 22.8226 | − | 13.1766i | 0.941990 | − | 0.543858i | 0.0514064 | − | 0.998678i | \(-0.483630\pi\) |
0.890584 | + | 0.454820i | \(0.150296\pi\) | |||||||
\(588\) | 8.24177 | − | 9.88432i | 0.339885 | − | 0.407622i | ||||
\(589\) | −4.67555 | + | 8.09830i | −0.192653 | + | 0.333685i | ||||
\(590\) | 6.58456 | + | 3.80160i | 0.271082 | + | 0.156509i | ||||
\(591\) | −37.9324 | + | 13.9398i | −1.56033 | + | 0.573406i | ||||
\(592\) | −0.547937 | + | 0.316351i | −0.0225201 | + | 0.0130020i | ||||
\(593\) | 24.2830i | 0.997183i | 0.866837 | + | 0.498592i | \(0.166149\pi\) | ||||
−0.866837 | + | 0.498592i | \(0.833851\pi\) | |||||||
\(594\) | 10.4198 | − | 6.14598i | 0.427530 | − | 0.252173i | ||||
\(595\) | 28.8086 | 1.18104 | ||||||||
\(596\) | 8.87590 | − | 5.12450i | 0.363571 | − | 0.209908i | ||||
\(597\) | 13.4031 | + | 36.4719i | 0.548550 | + | 1.49269i | ||||
\(598\) | −1.86769 | + | 12.2111i | −0.0763757 | + | 0.499350i | ||||
\(599\) | −8.31375 | + | 14.3998i | −0.339691 | + | 0.588362i | −0.984374 | − | 0.176088i | \(-0.943656\pi\) |
0.644684 | + | 0.764449i | \(0.276989\pi\) | |||||||
\(600\) | −4.01538 | − | 3.34811i | −0.163927 | − | 0.136686i | ||||
\(601\) | 4.96659 | + | 8.60238i | 0.202591 | + | 0.350898i | 0.949363 | − | 0.314182i | \(-0.101730\pi\) |
−0.746771 | + | 0.665081i | \(0.768397\pi\) | |||||||
\(602\) | −6.47195 | −0.263777 | ||||||||
\(603\) | 21.9299 | − | 4.00740i | 0.893056 | − | 0.163194i | ||||
\(604\) | 13.4819i | 0.548571i | ||||||||
\(605\) | 5.01106 | − | 2.89314i | 0.203729 | − | 0.117623i | ||||
\(606\) | 0.915145 | − | 5.28596i | 0.0371752 | − | 0.214727i | ||||
\(607\) | −14.1047 | + | 24.4300i | −0.572492 | + | 0.991585i | 0.423817 | + | 0.905748i | \(0.360690\pi\) |
−0.996309 | + | 0.0858373i | \(0.972643\pi\) | |||||||
\(608\) | 5.62707 | − | 9.74637i | 0.228208 | − | 0.395268i | ||||
\(609\) | 9.24910 | − | 53.4236i | 0.374793 | − | 2.16483i | ||||
\(610\) | 5.88817 | + | 10.1986i | 0.238405 | + | 0.412929i | ||||
\(611\) | 27.6691 | − | 10.7899i | 1.11937 | − | 0.436514i | ||||
\(612\) | −3.88675 | − | 21.2697i | −0.157113 | − | 0.859778i | ||||
\(613\) | − | 12.3008i | − | 0.496826i | −0.968654 | − | 0.248413i | \(-0.920091\pi\) | ||
0.968654 | − | 0.248413i | \(-0.0799090\pi\) | |||||||
\(614\) | −3.97921 | − | 6.89219i | −0.160588 | − | 0.278146i | ||||
\(615\) | −8.14559 | + | 9.76897i | −0.328462 | + | 0.393923i | ||||
\(616\) | −22.9133 | − | 13.2290i | −0.923204 | − | 0.533012i | ||||
\(617\) | −0.597139 | − | 0.344759i | −0.0240399 | − | 0.0138795i | 0.487932 | − | 0.872882i | \(-0.337751\pi\) |
−0.511972 | + | 0.859002i | \(0.671085\pi\) | |||||||
\(618\) | −30.9808 | + | 11.3851i | −1.24623 | + | 0.457978i | ||||
\(619\) | 1.92390 | − | 1.11076i | 0.0773280 | − | 0.0446454i | −0.460837 | − | 0.887485i | \(-0.652451\pi\) |
0.538165 | + | 0.842839i | \(0.319118\pi\) | |||||||
\(620\) | −3.87616 | −0.155670 | ||||||||
\(621\) | 15.0391 | − | 8.87063i | 0.603500 | − | 0.355966i | ||||
\(622\) | 9.88279i | 0.396264i | ||||||||
\(623\) | −12.4112 | − | 21.4968i | −0.497244 | − | 0.861253i | ||||
\(624\) | 5.41235 | − | 4.78539i | 0.216668 | − | 0.191569i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −24.0489 | − | 13.8847i | −0.961189 | − | 0.554943i | ||||
\(627\) | 5.86816 | − | 7.03766i | 0.234352 | − | 0.281057i | ||||
\(628\) | 5.99024 | + | 10.3754i | 0.239036 | + | 0.414023i | ||||
\(629\) | 4.10437i | 0.163652i | ||||||||
\(630\) | 3.94753 | − | 11.0589i | 0.157273 | − | 0.440598i | ||||
\(631\) | 31.5030i | 1.25412i | 0.778973 | + | 0.627058i | \(0.215741\pi\) | ||||
−0.778973 | + | 0.627058i | \(0.784259\pi\) | |||||||
\(632\) | 32.4050 | − | 18.7090i | 1.28900 | − | 0.744206i | ||||
\(633\) | 4.86998 | + | 0.843128i | 0.193564 | + | 0.0335113i | ||||
\(634\) | −11.4501 | + | 19.8322i | −0.454742 | + | 0.787637i | ||||
\(635\) | −7.95429 | − | 4.59241i | −0.315657 | − | 0.182244i | ||||
\(636\) | 11.6409 | + | 2.01537i | 0.461593 | + | 0.0799145i | ||||
\(637\) | 17.4396 | − | 21.7713i | 0.690982 | − | 0.862610i | ||||
\(638\) | −18.9843 | −0.751595 | ||||||||
\(639\) | 13.9714 | + | 16.4420i | 0.552700 | + | 0.650437i | ||||
\(640\) | 2.30593 | 0.0911498 | ||||||||
\(641\) | −23.6797 | − | 41.0145i | −0.935294 | − | 1.61998i | −0.774109 | − | 0.633052i | \(-0.781802\pi\) |
−0.161184 | − | 0.986924i | \(-0.551531\pi\) | |||||||
\(642\) | −8.71785 | − | 7.26914i | −0.344066 | − | 0.286890i | ||||
\(643\) | 16.4867 | + | 9.51859i | 0.650171 | + | 0.375377i | 0.788522 | − | 0.615007i | \(-0.210847\pi\) |
−0.138350 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(644\) | −10.7288 | − | 6.19428i | −0.422774 | − | 0.244089i | ||||
\(645\) | 2.68816 | − | 0.987871i | 0.105846 | − | 0.0388974i | ||||
\(646\) | 8.86419 | + | 15.3532i | 0.348757 | + | 0.604064i | ||||
\(647\) | 31.9873 | 1.25755 | 0.628774 | − | 0.777588i | \(-0.283557\pi\) | ||||
0.628774 | + | 0.777588i | \(0.283557\pi\) | |||||||
\(648\) | −26.8098 | − | 4.38474i | −1.05319 | − | 0.172249i | ||||
\(649\) | −17.0269 | −0.668365 | ||||||||
\(650\) | −2.86922 | − | 2.29835i | −0.112540 | − | 0.0901488i | ||||
\(651\) | −9.25657 | − | 25.1886i | −0.362794 | − | 0.987220i | ||||
\(652\) | −6.74745 | − | 3.89564i | −0.264250 | − | 0.152565i | ||||
\(653\) | −6.18188 | + | 10.7073i | −0.241916 | + | 0.419010i | −0.961260 | − | 0.275644i | \(-0.911109\pi\) |
0.719344 | + | 0.694654i | \(0.244442\pi\) | |||||||
\(654\) | −0.213401 | + | 0.255931i | −0.00834464 | + | 0.0100077i | ||||
\(655\) | −1.15857 | + | 0.668898i | −0.0452689 | + | 0.0261360i | ||||
\(656\) | 8.49538i | 0.331689i | ||||||||
\(657\) | 15.0508 | + | 17.7124i | 0.587189 | + | 0.691025i | ||||
\(658\) | − | 32.2401i | − | 1.25685i | ||||||
\(659\) | −1.24479 | − | 2.15604i | −0.0484901 | − | 0.0839874i | 0.840762 | − | 0.541406i | \(-0.182108\pi\) |
−0.889252 | + | 0.457418i | \(0.848774\pi\) | |||||||
\(660\) | 3.74259 | + | 0.647945i | 0.145680 | + | 0.0252212i | ||||
\(661\) | −0.890000 | − | 0.513842i | −0.0346170 | − | 0.0199861i | 0.482592 | − | 0.875845i | \(-0.339696\pi\) |
−0.517209 | + | 0.855859i | \(0.673029\pi\) | |||||||
\(662\) | −0.667037 | + | 1.15534i | −0.0259251 | + | 0.0449036i | ||||
\(663\) | −9.32899 | − | 45.9278i | −0.362308 | − | 1.78369i | ||||
\(664\) | −10.1307 | − | 17.5469i | −0.393147 | − | 0.680950i | ||||
\(665\) | − | 8.89429i | − | 0.344906i | ||||||
\(666\) | 1.57557 | + | 0.562405i | 0.0610520 | + | 0.0217928i | ||||
\(667\) | −27.4004 | −1.06095 | ||||||||
\(668\) | −7.03909 | + | 4.06402i | −0.272351 | + | 0.157242i | ||||
\(669\) | −11.9071 | − | 9.92844i | −0.460356 | − | 0.383856i | ||||
\(670\) | −6.56166 | − | 3.78837i | −0.253499 | − | 0.146358i | ||||
\(671\) | −22.8392 | − | 13.1862i | −0.881697 | − | 0.509048i | ||||
\(672\) | 11.1404 | + | 30.3147i | 0.429749 | + | 1.16942i | ||||
\(673\) | −2.59568 | − | 4.49585i | −0.100056 | − | 0.173302i | 0.811651 | − | 0.584142i | \(-0.198569\pi\) |
−0.911708 | + | 0.410840i | \(0.865236\pi\) | |||||||
\(674\) | 26.3386i | 1.01452i | ||||||||
\(675\) | 0.0483956 | + | 5.19593i | 0.00186275 | + | 0.199991i | ||||
\(676\) | −9.18911 | + | 8.45217i | −0.353427 | + | 0.325084i | ||||
\(677\) | −9.95304 | − | 17.2392i | −0.382526 | − | 0.662555i | 0.608896 | − | 0.793250i | \(-0.291613\pi\) |
−0.991423 | + | 0.130695i | \(0.958279\pi\) | |||||||
\(678\) | 0.300985 | − | 0.110609i | 0.0115593 | − | 0.00424792i | ||||
\(679\) | −22.3922 | + | 38.7844i | −0.859332 | + | 1.48841i | ||||
\(680\) | −11.3260 | + | 19.6172i | −0.434333 | + | 0.752286i | ||||
\(681\) | −16.0465 | − | 13.3799i | −0.614903 | − | 0.512720i | ||||
\(682\) | −8.13748 | + | 4.69818i | −0.311600 | + | 0.179902i | ||||
\(683\) | − | 9.73809i | − | 0.372618i | −0.982491 | − | 0.186309i | \(-0.940348\pi\) | ||
0.982491 | − | 0.186309i | \(-0.0596525\pi\) | |||||||
\(684\) | −6.56675 | + | 1.19998i | −0.251086 | + | 0.0458826i | ||||
\(685\) | −0.448279 | −0.0171279 | ||||||||
\(686\) | −1.44170 | − | 2.49710i | −0.0550445 | − | 0.0953398i | ||||
\(687\) | 6.49905 | − | 37.5391i | 0.247954 | − | 1.43221i | ||||
\(688\) | 0.956417 | − | 1.65656i | 0.0364631 | − | 0.0631559i | ||||
\(689\) | 25.3128 | + | 3.87160i | 0.964341 | + | 0.147496i | ||||
\(690\) | −5.84726 | − | 1.01232i | −0.222601 | − | 0.0385385i | ||||
\(691\) | 22.4051 | − | 12.9356i | 0.852331 | − | 0.492093i | −0.00910599 | − | 0.999959i | \(-0.502899\pi\) |
0.861437 | + | 0.507865i | \(0.169565\pi\) | |||||||
\(692\) | 25.0216 | 0.951180 | ||||||||
\(693\) | 4.72702 | + | 25.8680i | 0.179565 | + | 0.982642i | ||||
\(694\) | 16.7650i | 0.636392i | ||||||||
\(695\) | −17.1422 | + | 9.89704i | −0.650240 | + | 0.375416i | ||||
\(696\) | 32.7425 | + | 27.3015i | 1.24110 | + | 1.03486i | ||||
\(697\) | 47.7266 | + | 27.5550i | 1.80777 | + | 1.04372i | ||||
\(698\) | 3.64552 | − | 6.31423i | 0.137985 | − | 0.238997i | ||||
\(699\) | −11.1499 | − | 30.3408i | −0.421729 | − | 1.14759i | ||||
\(700\) | 3.19287 | − | 1.84340i | 0.120679 | − | 0.0696740i | ||||
\(701\) | 11.8618 | 0.448016 | 0.224008 | − | 0.974587i | \(-0.428086\pi\) | ||||
0.224008 | + | 0.974587i | \(0.428086\pi\) | |||||||
\(702\) | −18.9089 | − | 2.71214i | −0.713669 | − | 0.102363i | ||||
\(703\) | 1.26717 | 0.0477923 | ||||||||
\(704\) | 14.3687 | − | 8.29579i | 0.541542 | − | 0.312659i | ||||
\(705\) | 4.92110 | + | 13.3911i | 0.185339 | + | 0.504338i | ||||
\(706\) | 13.6883 | − | 23.7089i | 0.515167 | − | 0.892295i | ||||
\(707\) | 10.0989 | + | 5.83058i | 0.379807 | + | 0.219281i | ||||
\(708\) | 9.52697 | + | 7.94381i | 0.358045 | + | 0.298546i | ||||
\(709\) | 28.7325 | − | 16.5887i | 1.07907 | − | 0.623001i | 0.148425 | − | 0.988924i | \(-0.452580\pi\) |
0.930645 | + | 0.365922i | \(0.119246\pi\) | |||||||
\(710\) | − | 7.33316i | − | 0.275209i | ||||||
\(711\) | −35.0249 | − | 12.5023i | −1.31354 | − | 0.468872i | ||||
\(712\) | 19.5177 | 0.731456 | ||||||||
\(713\) | −11.7450 | + | 6.78098i | −0.439854 | + | 0.253950i | ||||
\(714\) | −50.1308 | − | 8.67902i | −1.87610 | − | 0.324804i | ||||
\(715\) | 8.13812 | + | 1.24473i | 0.304348 | + | 0.0465502i | ||||
\(716\) | 9.28932 | − | 16.0896i | 0.347158 | − | 0.601296i | ||||
\(717\) | −0.0477382 | + | 0.275740i | −0.00178281 | + | 0.0102977i | ||||
\(718\) | −12.9404 | − | 22.4134i | −0.482932 | − | 0.836462i | ||||
\(719\) | −9.95480 | −0.371251 | −0.185626 | − | 0.982621i | \(-0.559431\pi\) | ||||
−0.185626 | + | 0.982621i | \(0.559431\pi\) | |||||||
\(720\) | 2.24729 | + | 2.64469i | 0.0837514 | + | 0.0985617i | ||||
\(721\) | − | 71.7473i | − | 2.67201i | ||||||
\(722\) | −12.0370 | + | 6.94959i | −0.447972 | + | 0.258637i | ||||
\(723\) | 2.24182 | + | 1.86928i | 0.0833742 | + | 0.0695193i | ||||
\(724\) | 4.32642 | − | 7.49358i | 0.160790 | − | 0.278497i | ||||
\(725\) | 4.07714 | − | 7.06182i | 0.151421 | − | 0.262269i | ||||
\(726\) | −9.59150 | + | 3.52478i | −0.355974 | + | 0.130817i | ||||
\(727\) | 10.3803 | + | 17.9792i | 0.384983 | + | 0.666811i | 0.991767 | − | 0.128056i | \(-0.0408738\pi\) |
−0.606784 | + | 0.794867i | \(0.707541\pi\) | |||||||
\(728\) | 15.1789 | + | 38.9238i | 0.562567 | + | 1.44261i | ||||
\(729\) | 13.9332 | + | 23.1272i | 0.516044 | + | 0.856562i | ||||
\(730\) | − | 7.89973i | − | 0.292382i | ||||||
\(731\) | −6.20432 | − | 10.7462i | −0.229475 | − | 0.397463i | ||||
\(732\) | 6.62713 | + | 18.0335i | 0.244946 | + | 0.666537i | ||||
\(733\) | 16.4787 | + | 9.51396i | 0.608653 | + | 0.351406i | 0.772438 | − | 0.635090i | \(-0.219037\pi\) |
−0.163785 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(734\) | −4.85834 | − | 2.80497i | −0.179325 | − | 0.103533i | ||||
\(735\) | 10.2919 | + | 8.58164i | 0.379623 | + | 0.316538i | ||||
\(736\) | 14.1352 | − | 8.16097i | 0.521031 | − | 0.300817i | ||||
\(737\) | 16.9677 | 0.625013 | ||||||||
\(738\) | 17.1174 | − | 14.5453i | 0.630101 | − | 0.535420i | ||||
\(739\) | 16.5319i | 0.608136i | 0.952650 | + | 0.304068i | \(0.0983450\pi\) | ||||
−0.952650 | + | 0.304068i | \(0.901655\pi\) | |||||||
\(740\) | 0.262630 | + | 0.454888i | 0.00965447 | + | 0.0167220i | ||||
\(741\) | −14.1796 | + | 2.88020i | −0.520901 | + | 0.105807i | ||||
\(742\) | 13.8993 | − | 24.0743i | 0.510260 | − | 0.883796i | ||||
\(743\) | −28.4897 | − | 16.4486i | −1.04519 | − | 0.603439i | −0.123889 | − | 0.992296i | \(-0.539537\pi\) |
−0.921298 | + | 0.388857i | \(0.872870\pi\) | |||||||
\(744\) | 20.7914 | + | 3.59956i | 0.762248 | + | 0.131966i | ||||
\(745\) | 5.33582 | + | 9.24192i | 0.195489 | + | 0.338598i | ||||
\(746\) | − | 23.5062i | − | 0.860622i | ||||||
\(747\) | −6.76981 | + | 18.9655i | −0.247694 | + | 0.693911i | ||||
\(748\) | − | 16.4569i | − | 0.601723i | ||||||
\(749\) | 21.3680 | − | 12.3368i | 0.780768 | − | 0.450777i | ||||
\(750\) | 1.13097 | − | 1.35636i | 0.0412971 | − | 0.0495274i | ||||
\(751\) | 1.83181 | − | 3.17279i | 0.0668437 | − | 0.115777i | −0.830667 | − | 0.556770i | \(-0.812040\pi\) |
0.897510 | + | 0.440993i | \(0.145374\pi\) | |||||||
\(752\) | 8.25220 | + | 4.76441i | 0.300927 | + | 0.173740i | ||||
\(753\) | −9.76280 | − | 26.5662i | −0.355776 | − | 0.968125i | ||||
\(754\) | 23.3965 | + | 18.7414i | 0.852049 | + | 0.682523i | ||||
\(755\) | −14.0379 | −0.510890 | ||||||||
\(756\) | 9.42366 | − | 16.6791i | 0.342735 | − | 0.606613i | ||||
\(757\) | 21.2758 | 0.773284 | 0.386642 | − | 0.922230i | \(-0.373635\pi\) | ||||
0.386642 | + | 0.922230i | \(0.373635\pi\) | |||||||
\(758\) | 6.71279 | + | 11.6269i | 0.243820 | + | 0.422308i | ||||
\(759\) | 12.4738 | − | 4.58399i | 0.452770 | − | 0.166388i | ||||
\(760\) | 6.05656 | + | 3.49676i | 0.219695 | + | 0.126841i | ||||
\(761\) | 11.3826 | + | 6.57174i | 0.412619 | + | 0.238226i | 0.691914 | − | 0.721980i | \(-0.256768\pi\) |
−0.279296 | + | 0.960205i | \(0.590101\pi\) | |||||||
\(762\) | 12.4580 | + | 10.3877i | 0.451305 | + | 0.376308i | ||||
\(763\) | −0.362173 | − | 0.627302i | −0.0131115 | − | 0.0227098i | ||||
\(764\) | −1.10561 | −0.0399994 | ||||||||
\(765\) | 22.1468 | − | 4.04703i | 0.800721 | − | 0.146321i | ||||
\(766\) | 37.1899 | 1.34373 | ||||||||
\(767\) | 20.9842 | + | 16.8091i | 0.757695 | + | 0.606942i | ||||
\(768\) | −28.8149 | − | 4.98865i | −1.03977 | − | 0.180012i | ||||
\(769\) | −43.1583 | − | 24.9175i | −1.55633 | − | 0.898547i | −0.997603 | − | 0.0691942i | \(-0.977957\pi\) |
−0.558726 | − | 0.829353i | \(-0.688709\pi\) | |||||||
\(770\) | 4.46866 | − | 7.73995i | 0.161039 | − | 0.278928i | ||||
\(771\) | −0.207213 | − | 0.0358742i | −0.00746258 | − | 0.00129198i | ||||
\(772\) | −14.2106 | + | 8.20451i | −0.511452 | + | 0.295287i | ||||
\(773\) | 18.0797i | 0.650281i | 0.945666 | + | 0.325141i | \(0.105412\pi\) | ||||
−0.945666 | + | 0.325141i | \(0.894588\pi\) | |||||||
\(774\) | −4.97535 | + | 0.909178i | −0.178835 | + | 0.0326797i | ||||
\(775\) | − | 4.03600i | − | 0.144977i | ||||||
\(776\) | −17.6068 | − | 30.4958i | −0.632047 | − | 1.09474i | ||||
\(777\) | −2.32884 | + | 2.79297i | −0.0835467 | + | 0.100197i | ||||
\(778\) | 16.6712 | + | 9.62515i | 0.597693 | + | 0.345078i | ||||
\(779\) | 8.50723 | − | 14.7350i | 0.304803 | − | 0.527935i | ||||
\(780\) | −3.97276 | − | 4.49325i | −0.142247 | − | 0.160884i | ||||
\(781\) | 8.21110 | + | 14.2220i | 0.293816 | + | 0.508905i | ||||
\(782\) | 25.7115i | 0.919443i | ||||||||
\(783\) | −0.394632 | − | 42.3691i | −0.0141030 | − | 1.51415i | ||||
\(784\) | 8.95014 | 0.319648 | ||||||||
\(785\) | −10.8032 | + | 6.23726i | −0.385584 | + | 0.222617i | ||||
\(786\) | 2.21757 | − | 0.814935i | 0.0790981 | − | 0.0290678i | ||||
\(787\) | −39.6275 | − | 22.8790i | −1.41257 | − | 0.815547i | −0.416939 | − | 0.908934i | \(-0.636897\pi\) |
−0.995630 | + | 0.0933874i | \(0.970230\pi\) | |||||||
\(788\) | 19.4061 | + | 11.2041i | 0.691314 | + | 0.399130i | ||||
\(789\) | −8.24552 | + | 9.88882i | −0.293548 | + | 0.352051i | ||||
\(790\) | 6.31978 | + | 10.9462i | 0.224848 | + | 0.389447i | ||||
\(791\) | 0.697040i | 0.0247839i | ||||||||
\(792\) | −19.4732 | − | 6.95103i | −0.691949 | − | 0.246994i | ||||
\(793\) | 15.1298 | + | 38.7979i | 0.537274 | + | 1.37775i | ||||
\(794\) | 12.3080 | + | 21.3181i | 0.436794 | + | 0.756550i | ||||
\(795\) | −2.09847 | + | 12.1210i | −0.0744252 | + | 0.429887i | ||||
\(796\) | 10.7727 | − | 18.6589i | 0.381829 | − | 0.661347i | ||||
\(797\) | 22.6184 | − | 39.1762i | 0.801185 | − | 1.38769i | −0.117651 | − | 0.993055i | \(-0.537537\pi\) |
0.918837 | − | 0.394638i | \(-0.129130\pi\) | |||||||
\(798\) | −2.67953 | + | 15.4772i | −0.0948545 | + | 0.547888i | ||||
\(799\) | 53.5324 | − | 30.9070i | 1.89384 | − | 1.09341i | ||||
\(800\) | 4.85736i | 0.171734i | ||||||||
\(801\) | −12.5611 | − | 14.7823i | −0.443824 | − | 0.522307i | ||||
\(802\) | −19.9143 | −0.703200 | ||||||||
\(803\) | 8.84550 | + | 15.3208i | 0.312151 | + | 0.540661i | ||||
\(804\) | −9.49384 | − | 7.91618i | −0.334822 | − | 0.279182i | ||||
\(805\) | 6.44972 | − | 11.1712i | 0.227323 | − | 0.393734i | ||||
\(806\) | 14.6668 | + | 2.24329i | 0.516616 | + | 0.0790167i | ||||
\(807\) | −6.69088 | − | 18.2070i | −0.235530 | − | 0.640916i | ||||
\(808\) | −7.94066 | + | 4.58454i | −0.279351 | + | 0.161284i | ||||
\(809\) | 10.8941 | 0.383016 | 0.191508 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191508 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(810\) | 1.48113 | − | 9.05617i | 0.0520417 | − | 0.318201i | ||||
\(811\) | 15.5249i | 0.545155i | 0.962134 | + | 0.272577i | \(0.0878760\pi\) | ||||
−0.962134 | + | 0.272577i | \(0.912124\pi\) | |||||||
\(812\) | −26.0355 | + | 15.0316i | −0.913669 | + | 0.527507i | ||||
\(813\) | −24.8047 | + | 9.11548i | −0.869938 | + | 0.319694i | ||||
\(814\) | 1.10271 | + | 0.636651i | 0.0386501 | + | 0.0223146i | ||||
\(815\) | 4.05628 | − | 7.02569i | 0.142085 | − | 0.246099i | ||||
\(816\) | 9.62976 | − | 11.5489i | 0.337109 | − | 0.404293i | ||||
\(817\) | −3.31775 | + | 1.91550i | −0.116073 | + | 0.0670150i | ||||
\(818\) | −24.6353 | −0.861352 | ||||||||
\(819\) | 19.7114 | − | 36.5465i | 0.688773 | − | 1.27704i | ||||
\(820\) | 7.05272 | 0.246292 | ||||||||
\(821\) | −37.4158 | + | 21.6020i | −1.30582 | + | 0.753916i | −0.981396 | − | 0.191996i | \(-0.938504\pi\) |
−0.324425 | + | 0.945911i | \(0.605171\pi\) | |||||||
\(822\) | 0.780064 | + | 0.135051i | 0.0272079 | + | 0.00471043i | ||||
\(823\) | −16.4269 | + | 28.4523i | −0.572607 | + | 0.991784i | 0.423690 | + | 0.905807i | \(0.360735\pi\) |
−0.996297 | + | 0.0859771i | \(0.972599\pi\) | |||||||
\(824\) | 48.8562 | + | 28.2072i | 1.70199 | + | 0.982643i | ||||
\(825\) | −0.674664 | + | 3.89692i | −0.0234888 | + | 0.135673i | ||||
\(826\) | 25.2770 | − | 14.5937i | 0.879501 | − | 0.507780i | ||||
\(827\) | 22.0099i | 0.765359i | 0.923881 | + | 0.382680i | \(0.124999\pi\) | ||||
−0.923881 | + | 0.382680i | \(0.875001\pi\) | |||||||
\(828\) | −9.11802 | − | 3.25471i | −0.316873 | − | 0.113109i | ||||
\(829\) | −16.6541 | −0.578419 | −0.289210 | − | 0.957266i | \(-0.593392\pi\) | ||||
−0.289210 | + | 0.957266i | \(0.593392\pi\) | |||||||
\(830\) | 5.92720 | − | 3.42207i | 0.205736 | − | 0.118782i | ||||
\(831\) | −5.26700 | + | 6.31669i | −0.182710 | + | 0.219124i | ||||
\(832\) | −25.8979 | − | 3.96109i | −0.897847 | − | 0.137326i | ||||
\(833\) | 29.0300 | − | 50.2814i | 1.00583 | − | 1.74215i | ||||
\(834\) | 32.8112 | − | 12.0578i | 1.13616 | − | 0.417528i | ||||
\(835\) | −4.23161 | − | 7.32936i | −0.146441 | − | 0.253643i | ||||
\(836\) | −5.08085 | −0.175725 | ||||||||
\(837\) | −10.6545 | − | 18.0636i | −0.368275 | − | 0.624368i | ||||
\(838\) | 2.89587i | 0.100036i | ||||||||
\(839\) | −8.84015 | + | 5.10386i | −0.305196 | + | 0.176205i | −0.644775 | − | 0.764373i | \(-0.723049\pi\) |
0.339579 | + | 0.940578i | \(0.389715\pi\) | |||||||
\(840\) | −18.8381 | + | 6.92281i | −0.649976 | + | 0.238860i | ||||
\(841\) | −18.7462 | + | 32.4694i | −0.646421 | + | 1.11963i | ||||
\(842\) | 16.1481 | − | 27.9692i | 0.556499 | − | 0.963884i | ||||
\(843\) | 18.1467 | + | 15.1311i | 0.625005 | + | 0.521144i | ||||
\(844\) | −1.37025 | − | 2.37334i | −0.0471660 | − | 0.0816939i | ||||
\(845\) | −8.80072 | − | 9.56804i | −0.302754 | − | 0.329151i | ||||
\(846\) | −4.52909 | − | 24.7848i | −0.155713 | − | 0.852119i | ||||
\(847\) | − | 22.2126i | − | 0.763233i | ||||||
\(848\) | 4.10805 | + | 7.11535i | 0.141071 | + | 0.244342i | ||||
\(849\) | 13.3290 | + | 2.30761i | 0.457449 | + | 0.0791970i | ||||
\(850\) | −6.62655 | − | 3.82584i | −0.227289 | − | 0.131225i | ||||
\(851\) | 1.59157 | + | 0.918893i | 0.0545583 | + | 0.0314992i | ||||
\(852\) | 2.04090 | − | 11.7884i | 0.0699201 | − | 0.403865i | ||||
\(853\) | −41.0378 | + | 23.6932i | −1.40511 | + | 0.811240i | −0.994911 | − | 0.100757i | \(-0.967874\pi\) |
−0.410198 | + | 0.911997i | \(0.634540\pi\) | |||||||
\(854\) | 45.2074 | 1.54697 | ||||||||
\(855\) | −1.24947 | − | 6.83755i | −0.0427309 | − | 0.233839i | ||||
\(856\) | 19.4007i | 0.663101i | ||||||||
\(857\) | 4.16755 | + | 7.21840i | 0.142361 | + | 0.246576i | 0.928385 | − | 0.371619i | \(-0.121197\pi\) |
−0.786024 | + | 0.618195i | \(0.787864\pi\) | |||||||
\(858\) | −13.7864 | − | 4.61772i | −0.470660 | − | 0.157646i | ||||
\(859\) | −3.88143 | + | 6.72284i | −0.132433 | + | 0.229380i | −0.924614 | − | 0.380906i | \(-0.875612\pi\) |
0.792181 | + | 0.610286i | \(0.208946\pi\) | |||||||
\(860\) | −1.37525 | − | 0.794002i | −0.0468957 | − | 0.0270752i | ||||
\(861\) | 16.8424 | + | 45.8310i | 0.573989 | + | 1.56192i | ||||
\(862\) | −11.0914 | − | 19.2109i | −0.377775 | − | 0.654325i | ||||
\(863\) | − | 55.9535i | − | 1.90468i | −0.305038 | − | 0.952340i | \(-0.598669\pi\) | ||
0.305038 | − | 0.952340i | \(-0.401331\pi\) | |||||||
\(864\) | 12.8228 | + | 21.7397i | 0.436242 | + | 0.739598i | ||||
\(865\) | 26.0535i | 0.885844i | ||||||||
\(866\) | −22.8852 | + | 13.2128i | −0.777670 | + | 0.448988i | ||||
\(867\) | −23.4903 | − | 63.9210i | −0.797773 | − | 2.17087i | ||||
\(868\) | −7.43997 | + | 12.8864i | −0.252529 | + | 0.437393i | ||||
\(869\) | −24.5133 | − | 14.1528i | −0.831558 | − | 0.480100i | ||||
\(870\) | −9.22224 | + | 11.0602i | −0.312663 | + | 0.374975i | ||||
\(871\) | −20.9112 | − | 16.7506i | −0.708549 | − | 0.567574i | ||||
\(872\) | 0.569548 | 0.0192873 | ||||||||
\(873\) | −11.7657 | + | 32.9614i | −0.398209 | + | 1.11557i | ||||
\(874\) | 7.93810 | 0.268510 | ||||||||
\(875\) | 1.91942 | + | 3.32453i | 0.0648882 | + | 0.112390i | ||||
\(876\) | 2.19858 | − | 12.6992i | 0.0742832 | − | 0.429066i | ||||
\(877\) | −27.9976 | − | 16.1644i | −0.945413 | − | 0.545835i | −0.0537601 | − | 0.998554i | \(-0.517121\pi\) |
−0.891653 | + | 0.452719i | \(0.850454\pi\) | |||||||
\(878\) | 21.2516 | + | 12.2696i | 0.717208 | + | 0.414080i | ||||
\(879\) | −1.75985 | + | 10.1650i | −0.0593583 | + | 0.342859i | ||||
\(880\) | 1.32075 | + | 2.28760i | 0.0445224 | + | 0.0771151i | ||||
\(881\) | −42.5371 | −1.43311 | −0.716555 | − | 0.697530i | \(-0.754282\pi\) | ||||
−0.716555 | + | 0.697530i | \(0.754282\pi\) | |||||||
\(882\) | −15.3239 | − | 18.0338i | −0.515984 | − | 0.607228i | ||||
\(883\) | 36.8578 | 1.24036 | 0.620182 | − | 0.784458i | \(-0.287059\pi\) | ||||
0.620182 | + | 0.784458i | \(0.287059\pi\) | |||||||
\(884\) | −16.2464 | + | 20.2817i | −0.546424 | + | 0.682146i | ||||
\(885\) | −8.27139 | + | 9.91984i | −0.278040 | + | 0.333452i | ||||
\(886\) | −16.3651 | − | 9.44839i | −0.549796 | − | 0.317425i | ||||
\(887\) | −7.88144 | + | 13.6511i | −0.264633 | + | 0.458358i | −0.967467 | − | 0.252996i | \(-0.918584\pi\) |
0.702834 | + | 0.711353i | \(0.251917\pi\) | |||||||
\(888\) | −0.986294 | − | 2.68387i | −0.0330979 | − | 0.0900647i | ||||
\(889\) | −30.5352 | + | 17.6295i | −1.02412 | + | 0.591275i | ||||
\(890\) | 6.59293i | 0.220995i | ||||||||
\(891\) | 7.26785 | + | 19.2221i | 0.243482 | + | 0.643965i | ||||
\(892\) | 8.59637i | 0.287828i | ||||||||
\(893\) | −9.54212 | − | 16.5274i | −0.319315 | − | 0.553069i | ||||
\(894\) | −6.50076 | − | 17.6896i | −0.217418 | − | 0.591630i | ||||
\(895\) | 16.7531 | + | 9.67239i | 0.559993 | + | 0.323312i | ||||
\(896\) | 4.42604 | − | 7.66613i | 0.147864 | − | 0.256107i | ||||
\(897\) | −19.8982 | − | 6.66485i | −0.664382 | − | 0.222533i | ||||
\(898\) | 11.2849 | + | 19.5459i | 0.376581 | + | 0.652257i | ||||
\(899\) | 32.9107i | 1.09763i | ||||||||
\(900\) | 2.19558 | − | 1.86566i | 0.0731859 | − | 0.0621887i | ||||
\(901\) | 53.2983 | 1.77562 | ||||||||
\(902\) | 14.8062 | − | 8.54839i | 0.492994 | − | 0.284630i | ||||
\(903\) | 1.87549 | − | 10.8330i | 0.0624124 | − | 0.360500i | ||||
\(904\) | −0.474649 | − | 0.274039i | −0.0157866 | − | 0.00911439i | ||||
\(905\) | 7.80260 | + | 4.50483i | 0.259367 | + | 0.149746i | ||||
\(906\) | 24.4277 | + | 4.22911i | 0.811556 | + | 0.140503i | ||||
\(907\) | 11.7945 | + | 20.4286i | 0.391629 | + | 0.678321i | 0.992665 | − | 0.120901i | \(-0.0385784\pi\) |
−0.601036 | + | 0.799222i | \(0.705245\pi\) | |||||||
\(908\) | 11.5848i | 0.384455i | ||||||||
\(909\) | 8.58264 | + | 3.06361i | 0.284668 | + | 0.101614i | ||||
\(910\) | −13.1482 | + | 5.12731i | −0.435858 | + | 0.169969i | ||||
\(911\) | −2.45500 | − | 4.25219i | −0.0813379 | − | 0.140881i | 0.822487 | − | 0.568784i | \(-0.192586\pi\) |
−0.903825 | + | 0.427903i | \(0.859253\pi\) | |||||||
\(912\) | −3.56558 | − | 2.97306i | −0.118068 | − | 0.0984479i | ||||
\(913\) | −7.66353 | + | 13.2736i | −0.253626 | + | 0.439293i | ||||
\(914\) | 10.2092 | − | 17.6828i | 0.337690 | − | 0.584896i | ||||
\(915\) | −18.7771 | + | 6.90041i | −0.620753 | + | 0.228121i | ||||
\(916\) | −18.2943 | + | 10.5622i | −0.604462 | + | 0.348986i | ||||
\(917\) | 5.13558i | 0.169592i | ||||||||
\(918\) | −39.7576 | + | 0.370308i | −1.31220 | + | 0.0122220i | ||||
\(919\) | −37.6341 | −1.24143 | −0.620717 | − | 0.784035i | \(-0.713158\pi\) | ||||
−0.620717 | + | 0.784035i | \(0.713158\pi\) | |||||||
\(920\) | 5.07136 | + | 8.78386i | 0.167198 | + | 0.289595i | ||||
\(921\) | 12.6895 | − | 4.66328i | 0.418135 | − | 0.153660i | ||||
\(922\) | −2.80062 | + | 4.85081i | −0.0922334 | + | 0.159753i | ||||
\(923\) | 3.92065 | − | 25.6335i | 0.129050 | − | 0.843737i | ||||
\(924\) | 9.33770 | − | 11.1987i | 0.307188 | − | 0.368409i | ||||
\(925\) | −0.473647 | + | 0.273460i | −0.0155734 | + | 0.00899131i | ||||
\(926\) | 35.1028 | 1.15355 | ||||||||
\(927\) | −10.0790 | − | 55.1562i | −0.331039 | − | 1.81157i | ||||
\(928\) | − | 39.6084i | − | 1.30021i | ||||||
\(929\) | 4.04204 | − | 2.33367i | 0.132615 | − | 0.0765654i | −0.432225 | − | 0.901766i | \(-0.642271\pi\) |
0.564840 | + | 0.825201i | \(0.308938\pi\) | |||||||
\(930\) | −1.21590 | + | 7.02317i | −0.0398711 | + | 0.230299i | ||||
\(931\) | −15.5237 | − | 8.96263i | −0.508770 | − | 0.293738i | ||||
\(932\) | −8.96177 | + | 15.5222i | −0.293553 | + | 0.508448i | ||||
\(933\) | −16.5422 | − | 2.86391i | −0.541568 | − | 0.0937603i | ||||
\(934\) | −13.4372 | + | 7.75796i | −0.439678 | + | 0.253848i | ||||
\(935\) | 17.1355 | 0.560391 | ||||||||
\(936\) | 17.1369 | + | 27.7906i | 0.560136 | + | 0.908365i | ||||
\(937\) | −45.6433 | −1.49110 | −0.745550 | − | 0.666450i | \(-0.767813\pi\) | ||||
−0.745550 | + | 0.666450i | \(0.767813\pi\) | |||||||
\(938\) | −25.1891 | + | 14.5430i | −0.822454 | + | 0.474844i | ||||
\(939\) | 30.2098 | − | 36.2305i | 0.985859 | − | 1.18234i | ||||
\(940\) | 3.95534 | − | 6.85084i | 0.129009 | − | 0.223450i | ||||
\(941\) | 31.9448 | + | 18.4433i | 1.04137 | + | 0.601236i | 0.920221 | − | 0.391398i | \(-0.128009\pi\) |
0.121150 | + | 0.992634i | \(0.461342\pi\) | |||||||
\(942\) | 20.6781 | − | 7.59900i | 0.673729 | − | 0.247589i | ||||
\(943\) | 21.3702 | − | 12.3381i | 0.695909 | − | 0.401783i | ||||
\(944\) | 8.62657i | 0.280771i | ||||||||
\(945\) | 17.3669 | + | 9.81227i | 0.564946 | + | 0.319193i | ||||
\(946\) | −3.84954 | −0.125159 | ||||||||
\(947\) | 22.7786 | − | 13.1512i | 0.740205 | − | 0.427358i | −0.0819386 | − | 0.996637i | \(-0.526111\pi\) |
0.822144 | + | 0.569280i | \(0.192778\pi\) | |||||||
\(948\) | 7.11291 | + | 19.3554i | 0.231017 | + | 0.628633i | ||||
\(949\) | 4.22356 | − | 27.6139i | 0.137103 | − | 0.896387i | ||||
\(950\) | −1.18118 | + | 2.04586i | −0.0383225 | + | 0.0663765i | ||||
\(951\) | −29.8778 | − | 24.9128i | −0.968854 | − | 0.807852i | ||||
\(952\) | 43.4787 | + | 75.3073i | 1.40915 | + | 2.44072i | ||||
\(953\) | 44.7832 | 1.45067 | 0.725335 | − | 0.688396i | \(-0.241685\pi\) | ||||
0.725335 | + | 0.688396i | \(0.241685\pi\) | |||||||
\(954\) | 7.30324 | − | 20.4599i | 0.236451 | − | 0.662413i | ||||
\(955\) | − | 1.15120i | − | 0.0372519i | ||||||
\(956\) | 0.134379 | − | 0.0775840i | 0.00434614 | − | 0.00250925i | ||||
\(957\) | 5.50141 | − | 31.7766i | 0.177835 | − | 1.02719i | ||||
\(958\) | −20.4816 | + | 35.4751i | −0.661729 | + | 1.14615i | ||||
\(959\) | −0.860436 | + | 1.49032i | −0.0277849 | + | 0.0481249i | ||||
\(960\) | 2.14698 | − | 12.4011i | 0.0692935 | − | 0.400245i | ||||
\(961\) | −7.35534 | − | 12.7398i | −0.237269 | − | 0.410962i | ||||
\(962\) | −0.730489 | − | 1.87322i | −0.0235519 | − | 0.0603952i | ||||
\(963\) | 14.6937 | − | 12.4858i | 0.473498 | − | 0.402348i | ||||
\(964\) | − | 1.61849i | − | 0.0521279i | ||||||
\(965\) | −8.54284 | − | 14.7966i | −0.275004 | − | 0.476321i | ||||
\(966\) | −14.5888 | + | 17.4963i | −0.469388 | + | 0.562935i | ||||
\(967\) | 39.6702 | + | 22.9036i | 1.27571 | + | 0.736531i | 0.976056 | − | 0.217518i | \(-0.0697960\pi\) |
0.299652 | + | 0.954048i | \(0.403129\pi\) | |||||||
\(968\) | 15.1256 | + | 8.73279i | 0.486157 | + | 0.280683i | ||||
\(969\) | −28.2676 | + | 10.3880i | −0.908085 | + | 0.333712i | ||||
\(970\) | 10.3013 | − | 5.94744i | 0.330754 | − | 0.190961i | ||||
\(971\) | 47.1484 | 1.51306 | 0.756532 | − | 0.653957i | \(-0.226892\pi\) | ||||
0.756532 | + | 0.653957i | \(0.226892\pi\) | |||||||
\(972\) | 4.90142 | − | 14.1460i | 0.157213 | − | 0.453734i | ||||
\(973\) | 75.9862i | 2.43601i | ||||||||
\(974\) | 15.8677 | + | 27.4836i | 0.508432 | + | 0.880631i | ||||
\(975\) | 4.67854 | − | 4.13658i | 0.149833 | − | 0.132477i | ||||
\(976\) | −6.68070 | + | 11.5713i | −0.213844 | + | 0.370389i | ||||
\(977\) | 0.391867 | + | 0.226244i | 0.0125369 | + | 0.00723820i | 0.506255 | − | 0.862384i | \(-0.331029\pi\) |
−0.493718 | + | 0.869622i | \(0.664363\pi\) | |||||||
\(978\) | −9.17505 | + | 11.0036i | −0.293386 | + | 0.351856i | ||||
\(979\) | −7.38224 | − | 12.7864i | −0.235937 | − | 0.408656i | ||||
\(980\) | − | 7.43027i | − | 0.237351i | ||||||
\(981\) | −0.366546 | − | 0.431364i | −0.0117029 | − | 0.0137724i | ||||
\(982\) | − | 19.7519i | − | 0.630309i | ||||||
\(983\) | −32.8628 | + | 18.9733i | −1.04816 | + | 0.605155i | −0.922134 | − | 0.386872i | \(-0.873556\pi\) |
−0.126026 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(984\) | −37.8301 | − | 6.54944i | −1.20598 | − | 0.208789i | ||||
\(985\) | −11.6661 | + | 20.2063i | −0.371714 | + | 0.643828i | ||||
\(986\) | 54.0348 | + | 31.1970i | 1.72082 | + | 0.993516i | ||||
\(987\) | 53.9648 | + | 9.34279i | 1.71772 | + | 0.297384i | ||||
\(988\) | 6.26170 | + | 5.01585i | 0.199211 | + | 0.159575i | ||||
\(989\) | −5.55613 | −0.176675 | ||||||||
\(990\) | 2.34801 | − | 6.57790i | 0.0746246 | − | 0.209059i | ||||
\(991\) | 31.1373 | 0.989109 | 0.494555 | − | 0.869147i | \(-0.335331\pi\) | ||||
0.494555 | + | 0.869147i | \(0.335331\pi\) | |||||||
\(992\) | −9.80217 | − | 16.9779i | −0.311219 | − | 0.539047i | ||||
\(993\) | −1.74056 | − | 1.45132i | −0.0552349 | − | 0.0460561i | ||||
\(994\) | −24.3793 | − | 14.0754i | −0.773265 | − | 0.446445i | ||||
\(995\) | 19.4283 | + | 11.2169i | 0.615919 | + | 0.355601i | ||||
\(996\) | 10.4807 | − | 3.85154i | 0.332092 | − | 0.122041i | ||||
\(997\) | −24.1727 | − | 41.8684i | −0.765557 | − | 1.32598i | −0.939951 | − | 0.341308i | \(-0.889130\pi\) |
0.174394 | − | 0.984676i | \(-0.444203\pi\) | |||||||
\(998\) | −17.1414 | −0.542600 | ||||||||
\(999\) | −1.39796 | + | 2.47427i | −0.0442294 | + | 0.0782824i |
(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 | 585.2.bt.b.571.19 | yes | 108 | |
9.7 | even | 3 | inner | 585.2.bt.b.376.36 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.571.36 | yes | 108 | |
117.25 | even | 6 | inner | 585.2.bt.b.376.19 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.19 | ✓ | 108 | 117.25 | even | 6 | inner | |
585.2.bt.b.376.36 | yes | 108 | 9.7 | even | 3 | inner | |
585.2.bt.b.571.19 | yes | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.571.36 | yes | 108 | 13.12 | even | 2 | inner |