Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(131,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.e (of order \(2\), degree \(1\), 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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 131.47 | ||
Character | \(\chi\) | \(=\) | 572.131 |
Dual form | 572.2.e.b.131.48 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.936395 | − | 1.05979i | 0.662131 | − | 0.749388i | ||||
\(3\) | − | 2.78715i | − | 1.60916i | −0.593843 | − | 0.804581i | \(-0.702390\pi\) | ||
0.593843 | − | 0.804581i | \(-0.297610\pi\) | |||||||
\(4\) | −0.246329 | − | 1.98477i | −0.123165 | − | 0.992386i | ||||
\(5\) | 1.09997 | 0.491923 | 0.245961 | − | 0.969280i | \(-0.420896\pi\) | ||||
0.245961 | + | 0.969280i | \(0.420896\pi\) | |||||||
\(6\) | −2.95381 | − | 2.60987i | −1.20589 | − | 1.06548i | ||||
\(7\) | 3.18482 | 1.20375 | 0.601874 | − | 0.798591i | \(-0.294421\pi\) | ||||
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(8\) | −2.33411 | − | 1.59747i | −0.825233 | − | 0.564792i | ||||
\(9\) | −4.76820 | −1.58940 | ||||||||
\(10\) | 1.03001 | − | 1.16575i | 0.325717 | − | 0.368641i | ||||
\(11\) | 3.20589 | − | 0.849864i | 0.966612 | − | 0.256244i | ||||
\(12\) | −5.53186 | + | 0.686556i | −1.59691 | + | 0.198192i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 2.98224 | − | 3.37525i | 0.797038 | − | 0.902074i | ||||
\(15\) | − | 3.06579i | − | 0.791583i | ||||||
\(16\) | −3.87864 | + | 0.977815i | −0.969661 | + | 0.244454i | ||||
\(17\) | 0.404034i | 0.0979926i | 0.998799 | + | 0.0489963i | \(0.0156022\pi\) | ||||
−0.998799 | + | 0.0489963i | \(0.984398\pi\) | |||||||
\(18\) | −4.46492 | + | 5.05332i | −1.05239 | + | 1.19108i | ||||
\(19\) | −0.124854 | −0.0286434 | −0.0143217 | − | 0.999897i | \(-0.504559\pi\) | ||||
−0.0143217 | + | 0.999897i | \(0.504559\pi\) | |||||||
\(20\) | −0.270955 | − | 2.18320i | −0.0605875 | − | 0.488177i | ||||
\(21\) | − | 8.87656i | − | 1.93702i | ||||||
\(22\) | 2.10130 | − | 4.19339i | 0.447998 | − | 0.894034i | ||||
\(23\) | 4.72467i | 0.985162i | 0.870267 | + | 0.492581i | \(0.163946\pi\) | ||||
−0.870267 | + | 0.492581i | \(0.836054\pi\) | |||||||
\(24\) | −4.45240 | + | 6.50552i | −0.908841 | + | 1.32793i | ||||
\(25\) | −3.79006 | −0.758012 | ||||||||
\(26\) | 1.05979 | + | 0.936395i | 0.207843 | + | 0.183642i | ||||
\(27\) | 4.92825i | 0.948442i | ||||||||
\(28\) | −0.784513 | − | 6.32113i | −0.148259 | − | 1.19458i | ||||
\(29\) | 9.08186i | 1.68646i | 0.537553 | + | 0.843230i | \(0.319349\pi\) | ||||
−0.537553 | + | 0.843230i | \(0.680651\pi\) | |||||||
\(30\) | −3.24911 | − | 2.87079i | −0.593203 | − | 0.524132i | ||||
\(31\) | 10.4536i | 1.87752i | 0.344578 | + | 0.938758i | \(0.388022\pi\) | ||||
−0.344578 | + | 0.938758i | \(0.611978\pi\) | |||||||
\(32\) | −2.59566 | + | 5.02619i | −0.458852 | + | 0.888513i | ||||
\(33\) | −2.36870 | − | 8.93530i | −0.412337 | − | 1.55544i | ||||
\(34\) | 0.428193 | + | 0.378335i | 0.0734345 | + | 0.0648839i | ||||
\(35\) | 3.50321 | 0.592151 | ||||||||
\(36\) | 1.17455 | + | 9.46380i | 0.195758 | + | 1.57730i | ||||
\(37\) | 2.86681 | 0.471301 | 0.235650 | − | 0.971838i | \(-0.424278\pi\) | ||||
0.235650 | + | 0.971838i | \(0.424278\pi\) | |||||||
\(38\) | −0.116912 | + | 0.132319i | −0.0189657 | + | 0.0214650i | ||||
\(39\) | 2.78715 | 0.446301 | ||||||||
\(40\) | −2.56746 | − | 1.75718i | −0.405951 | − | 0.277834i | ||||
\(41\) | − | 3.30715i | − | 0.516490i | −0.966079 | − | 0.258245i | \(-0.916856\pi\) | ||
0.966079 | − | 0.258245i | \(-0.0831442\pi\) | |||||||
\(42\) | −9.40733 | − | 8.31196i | −1.45158 | − | 1.28256i | ||||
\(43\) | 7.57237 | 1.15478 | 0.577388 | − | 0.816470i | \(-0.304072\pi\) | ||||
0.577388 | + | 0.816470i | \(0.304072\pi\) | |||||||
\(44\) | −2.47649 | − | 6.15362i | −0.373345 | − | 0.927693i | ||||
\(45\) | −5.24490 | −0.781863 | ||||||||
\(46\) | 5.00718 | + | 4.42416i | 0.738268 | + | 0.652306i | ||||
\(47\) | 4.17057i | 0.608340i | 0.952618 | + | 0.304170i | \(0.0983791\pi\) | ||||
−0.952618 | + | 0.304170i | \(0.901621\pi\) | |||||||
\(48\) | 2.72532 | + | 10.8104i | 0.393366 | + | 1.56034i | ||||
\(49\) | 3.14305 | 0.449007 | ||||||||
\(50\) | −3.54899 | + | 4.01668i | −0.501903 | + | 0.568045i | ||||
\(51\) | 1.12610 | 0.157686 | ||||||||
\(52\) | 1.98477 | − | 0.246329i | 0.275238 | − | 0.0341597i | ||||
\(53\) | −11.5475 | −1.58618 | −0.793089 | − | 0.609106i | \(-0.791528\pi\) | ||||
−0.793089 | + | 0.609106i | \(0.791528\pi\) | |||||||
\(54\) | 5.22293 | + | 4.61479i | 0.710751 | + | 0.627993i | ||||
\(55\) | 3.52639 | − | 0.934827i | 0.475499 | − | 0.126052i | ||||
\(56\) | −7.43372 | − | 5.08765i | −0.993372 | − | 0.679866i | ||||
\(57\) | 0.347986i | 0.0460919i | ||||||||
\(58\) | 9.62491 | + | 8.50421i | 1.26381 | + | 1.11666i | ||||
\(59\) | − | 6.68623i | − | 0.870473i | −0.900316 | − | 0.435237i | \(-0.856665\pi\) | ||
0.900316 | − | 0.435237i | \(-0.143335\pi\) | |||||||
\(60\) | −6.08489 | + | 0.755193i | −0.785556 | + | 0.0974951i | ||||
\(61\) | − | 1.02508i | − | 0.131249i | −0.997844 | − | 0.0656243i | \(-0.979096\pi\) | ||
0.997844 | − | 0.0656243i | \(-0.0209039\pi\) | |||||||
\(62\) | 11.0786 | + | 9.78866i | 1.40699 | + | 1.24316i | ||||
\(63\) | −15.1859 | −1.91324 | ||||||||
\(64\) | 2.89616 | + | 7.45736i | 0.362020 | + | 0.932170i | ||||
\(65\) | 1.09997i | 0.136435i | ||||||||
\(66\) | −11.6876 | − | 5.85663i | −1.43865 | − | 0.720902i | ||||
\(67\) | − | 11.3802i | − | 1.39032i | −0.718856 | − | 0.695159i | \(-0.755334\pi\) | ||
0.718856 | − | 0.695159i | \(-0.244666\pi\) | |||||||
\(68\) | 0.801915 | − | 0.0995253i | 0.0972465 | − | 0.0120692i | ||||
\(69\) | 13.1684 | 1.58528 | ||||||||
\(70\) | 3.28039 | − | 3.71268i | 0.392081 | − | 0.443751i | ||||
\(71\) | − | 12.4986i | − | 1.48331i | −0.670784 | − | 0.741653i | \(-0.734042\pi\) | ||
0.670784 | − | 0.741653i | \(-0.265958\pi\) | |||||||
\(72\) | 11.1295 | + | 7.61708i | 1.31163 | + | 0.897681i | ||||
\(73\) | − | 2.91778i | − | 0.341501i | −0.985314 | − | 0.170750i | \(-0.945381\pi\) | ||
0.985314 | − | 0.170750i | \(-0.0546192\pi\) | |||||||
\(74\) | 2.68447 | − | 3.03823i | 0.312063 | − | 0.353187i | ||||
\(75\) | 10.5635i | 1.21976i | ||||||||
\(76\) | 0.0307551 | + | 0.247806i | 0.00352785 | + | 0.0284253i | ||||
\(77\) | 10.2102 | − | 2.70666i | 1.16356 | − | 0.308452i | ||||
\(78\) | 2.60987 | − | 2.95381i | 0.295510 | − | 0.334453i | ||||
\(79\) | −10.8405 | −1.21965 | −0.609824 | − | 0.792537i | \(-0.708760\pi\) | ||||
−0.609824 | + | 0.792537i | \(0.708760\pi\) | |||||||
\(80\) | −4.26640 | + | 1.07557i | −0.476998 | + | 0.120252i | ||||
\(81\) | −0.568841 | −0.0632045 | ||||||||
\(82\) | −3.50490 | − | 3.09680i | −0.387052 | − | 0.341984i | ||||
\(83\) | −3.91349 | −0.429561 | −0.214781 | − | 0.976662i | \(-0.568904\pi\) | ||||
−0.214781 | + | 0.976662i | \(0.568904\pi\) | |||||||
\(84\) | −17.6179 | + | 2.18656i | −1.92228 | + | 0.238573i | ||||
\(85\) | 0.444426i | 0.0482048i | ||||||||
\(86\) | 7.09073 | − | 8.02516i | 0.764613 | − | 0.865375i | ||||
\(87\) | 25.3125 | 2.71379 | ||||||||
\(88\) | −8.84054 | − | 3.13764i | −0.942405 | − | 0.334474i | ||||
\(89\) | −4.50758 | −0.477803 | −0.238901 | − | 0.971044i | \(-0.576787\pi\) | ||||
−0.238901 | + | 0.971044i | \(0.576787\pi\) | |||||||
\(90\) | −4.91129 | + | 5.55851i | −0.517696 | + | 0.585919i | ||||
\(91\) | 3.18482i | 0.333859i | ||||||||
\(92\) | 9.37739 | − | 1.16382i | 0.977661 | − | 0.121337i | ||||
\(93\) | 29.1356 | 3.02123 | ||||||||
\(94\) | 4.41995 | + | 3.90530i | 0.455883 | + | 0.402801i | ||||
\(95\) | −0.137336 | −0.0140903 | ||||||||
\(96\) | 14.0087 | + | 7.23449i | 1.42976 | + | 0.738367i | ||||
\(97\) | 3.28224 | 0.333261 | 0.166630 | − | 0.986019i | \(-0.446711\pi\) | ||||
0.166630 | + | 0.986019i | \(0.446711\pi\) | |||||||
\(98\) | 2.94314 | − | 3.33099i | 0.297302 | − | 0.336480i | ||||
\(99\) | −15.2863 | + | 4.05232i | −1.53633 | + | 0.407274i | ||||
\(100\) | 0.933602 | + | 7.52241i | 0.0933602 | + | 0.752241i | ||||
\(101\) | 2.94323i | 0.292862i | 0.989221 | + | 0.146431i | \(0.0467787\pi\) | ||||
−0.989221 | + | 0.146431i | \(0.953221\pi\) | |||||||
\(102\) | 1.05448 | − | 1.19344i | 0.104409 | − | 0.118168i | ||||
\(103\) | − | 14.8477i | − | 1.46299i | −0.681848 | − | 0.731494i | \(-0.738823\pi\) | ||
0.681848 | − | 0.731494i | \(-0.261177\pi\) | |||||||
\(104\) | 1.59747 | − | 2.33411i | 0.156645 | − | 0.228879i | ||||
\(105\) | − | 9.76397i | − | 0.952866i | ||||||
\(106\) | −10.8131 | + | 12.2380i | −1.05026 | + | 1.18866i | ||||
\(107\) | 12.0169 | 1.16172 | 0.580858 | − | 0.814005i | \(-0.302717\pi\) | ||||
0.580858 | + | 0.814005i | \(0.302717\pi\) | |||||||
\(108\) | 9.78146 | − | 1.21397i | 0.941221 | − | 0.116815i | ||||
\(109\) | 0.213984i | 0.0204960i | 0.999947 | + | 0.0102480i | \(0.00326209\pi\) | ||||
−0.999947 | + | 0.0102480i | \(0.996738\pi\) | |||||||
\(110\) | 2.31137 | − | 4.61262i | 0.220381 | − | 0.439796i | ||||
\(111\) | − | 7.99023i | − | 0.758399i | ||||||
\(112\) | −12.3528 | + | 3.11416i | −1.16723 | + | 0.294260i | ||||
\(113\) | −13.5331 | −1.27309 | −0.636545 | − | 0.771240i | \(-0.719637\pi\) | ||||
−0.636545 | + | 0.771240i | \(0.719637\pi\) | |||||||
\(114\) | 0.368794 | + | 0.325852i | 0.0345407 | + | 0.0305189i | ||||
\(115\) | 5.19701i | 0.484624i | ||||||||
\(116\) | 18.0254 | − | 2.23713i | 1.67362 | − | 0.207712i | ||||
\(117\) | − | 4.76820i | − | 0.440821i | ||||||
\(118\) | −7.08603 | − | 6.26096i | −0.652322 | − | 0.576368i | ||||
\(119\) | 1.28677i | 0.117958i | ||||||||
\(120\) | −4.89751 | + | 7.15590i | −0.447080 | + | 0.653241i | ||||
\(121\) | 9.55546 | − | 5.44914i | 0.868679 | − | 0.495376i | ||||
\(122\) | −1.08638 | − | 0.959883i | −0.0983561 | − | 0.0869038i | ||||
\(123\) | −9.21753 | −0.831116 | ||||||||
\(124\) | 20.7479 | − | 2.57502i | 1.86322 | − | 0.231243i | ||||
\(125\) | −9.66883 | −0.864806 | ||||||||
\(126\) | −14.2200 | + | 16.0939i | −1.26681 | + | 1.43376i | ||||
\(127\) | 21.9470 | 1.94748 | 0.973741 | − | 0.227659i | \(-0.0731072\pi\) | ||||
0.973741 | + | 0.227659i | \(0.0731072\pi\) | |||||||
\(128\) | 10.6152 | + | 3.91370i | 0.938262 | + | 0.345925i | ||||
\(129\) | − | 21.1053i | − | 1.85822i | ||||||
\(130\) | 1.16575 | + | 1.03001i | 0.102243 | + | 0.0903378i | ||||
\(131\) | −0.729152 | −0.0637063 | −0.0318532 | − | 0.999493i | \(-0.510141\pi\) | ||||
−0.0318532 | + | 0.999493i | \(0.510141\pi\) | |||||||
\(132\) | −17.1511 | + | 6.90235i | −1.49281 | + | 0.600772i | ||||
\(133\) | −0.397636 | −0.0344794 | ||||||||
\(134\) | −12.0607 | − | 10.6564i | −1.04189 | − | 0.920572i | ||||
\(135\) | 5.42094i | 0.466560i | ||||||||
\(136\) | 0.645433 | − | 0.943060i | 0.0553454 | − | 0.0808667i | ||||
\(137\) | −3.03978 | −0.259706 | −0.129853 | − | 0.991533i | \(-0.541451\pi\) | ||||
−0.129853 | + | 0.991533i | \(0.541451\pi\) | |||||||
\(138\) | 12.3308 | − | 13.9558i | 1.04967 | − | 1.18799i | ||||
\(139\) | −13.8449 | −1.17431 | −0.587156 | − | 0.809474i | \(-0.699752\pi\) | ||||
−0.587156 | + | 0.809474i | \(0.699752\pi\) | |||||||
\(140\) | −0.862943 | − | 6.95308i | −0.0729320 | − | 0.587642i | ||||
\(141\) | 11.6240 | 0.978918 | ||||||||
\(142\) | −13.2459 | − | 11.7036i | −1.11157 | − | 0.982143i | ||||
\(143\) | 0.849864 | + | 3.20589i | 0.0710692 | + | 0.268090i | ||||
\(144\) | 18.4942 | − | 4.66242i | 1.54118 | − | 0.388535i | ||||
\(145\) | 9.98980i | 0.829608i | ||||||||
\(146\) | −3.09225 | − | 2.73220i | −0.255917 | − | 0.226118i | ||||
\(147\) | − | 8.76015i | − | 0.722525i | ||||||
\(148\) | −0.706179 | − | 5.68997i | −0.0580476 | − | 0.467712i | ||||
\(149\) | 12.6321i | 1.03487i | 0.855724 | + | 0.517433i | \(0.173112\pi\) | ||||
−0.855724 | + | 0.517433i | \(0.826888\pi\) | |||||||
\(150\) | 11.1951 | + | 9.89157i | 0.914076 | + | 0.807644i | ||||
\(151\) | −8.74541 | −0.711691 | −0.355846 | − | 0.934545i | \(-0.615807\pi\) | ||||
−0.355846 | + | 0.934545i | \(0.615807\pi\) | |||||||
\(152\) | 0.291423 | + | 0.199450i | 0.0236375 | + | 0.0161776i | ||||
\(153\) | − | 1.92652i | − | 0.155750i | ||||||
\(154\) | 6.69225 | − | 13.3552i | 0.539277 | − | 1.07619i | ||||
\(155\) | 11.4986i | 0.923593i | ||||||||
\(156\) | −0.686556 | − | 5.53186i | −0.0549685 | − | 0.442903i | ||||
\(157\) | 10.8981 | 0.869766 | 0.434883 | − | 0.900487i | \(-0.356790\pi\) | ||||
0.434883 | + | 0.900487i | \(0.356790\pi\) | |||||||
\(158\) | −10.1510 | + | 11.4887i | −0.807566 | + | 0.913989i | ||||
\(159\) | 32.1848i | 2.55242i | ||||||||
\(160\) | −2.85515 | + | 5.52867i | −0.225720 | + | 0.437080i | ||||
\(161\) | 15.0472i | 1.18589i | ||||||||
\(162\) | −0.532660 | + | 0.602854i | −0.0418497 | + | 0.0473647i | ||||
\(163\) | 15.6207i | 1.22350i | 0.791050 | + | 0.611752i | \(0.209535\pi\) | ||||
−0.791050 | + | 0.611752i | \(0.790465\pi\) | |||||||
\(164\) | −6.56394 | + | 0.814648i | −0.512558 | + | 0.0636133i | ||||
\(165\) | −2.60550 | − | 9.82858i | −0.202838 | − | 0.765154i | ||||
\(166\) | −3.66457 | + | 4.14750i | −0.284426 | + | 0.321908i | ||||
\(167\) | −5.30031 | −0.410151 | −0.205075 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205075 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(168\) | −14.1801 | + | 20.7189i | −1.09402 | + | 1.59850i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0.471000 | + | 0.416158i | 0.0361241 | + | 0.0319179i | ||||
\(171\) | 0.595328 | 0.0455259 | ||||||||
\(172\) | −1.86530 | − | 15.0294i | −0.142228 | − | 1.14598i | ||||
\(173\) | 22.9386i | 1.74399i | 0.489514 | + | 0.871995i | \(0.337174\pi\) | ||||
−0.489514 | + | 0.871995i | \(0.662826\pi\) | |||||||
\(174\) | 23.7025 | − | 26.8261i | 1.79688 | − | 2.03368i | ||||
\(175\) | −12.0706 | −0.912455 | ||||||||
\(176\) | −11.6035 | + | 6.43109i | −0.874646 | + | 0.484761i | ||||
\(177\) | −18.6355 | −1.40073 | ||||||||
\(178\) | −4.22088 | + | 4.77711i | −0.316368 | + | 0.358060i | ||||
\(179\) | − | 15.5156i | − | 1.15969i | −0.814727 | − | 0.579844i | \(-0.803113\pi\) | ||
0.814727 | − | 0.579844i | \(-0.196887\pi\) | |||||||
\(180\) | 1.29197 | + | 10.4099i | 0.0962978 | + | 0.775910i | ||||
\(181\) | 15.2516 | 1.13364 | 0.566821 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566821 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(182\) | 3.37525 | + | 2.98224i | 0.250190 | + | 0.221059i | ||||
\(183\) | −2.85706 | −0.211200 | ||||||||
\(184\) | 7.54753 | − | 11.0279i | 0.556411 | − | 0.812988i | ||||
\(185\) | 3.15341 | 0.231844 | ||||||||
\(186\) | 27.2825 | − | 30.8778i | 2.00045 | − | 2.26407i | ||||
\(187\) | 0.343374 | + | 1.29529i | 0.0251100 | + | 0.0947208i | ||||
\(188\) | 8.27763 | − | 1.02733i | 0.603709 | − | 0.0749260i | ||||
\(189\) | 15.6956i | 1.14168i | ||||||||
\(190\) | −0.128600 | + | 0.145548i | −0.00932965 | + | 0.0105591i | ||||
\(191\) | − | 12.5325i | − | 0.906820i | −0.891302 | − | 0.453410i | \(-0.850207\pi\) | ||
0.891302 | − | 0.453410i | \(-0.149793\pi\) | |||||||
\(192\) | 20.7848 | − | 8.07204i | 1.50001 | − | 0.582549i | ||||
\(193\) | 3.99734i | 0.287735i | 0.989597 | + | 0.143867i | \(0.0459539\pi\) | ||||
−0.989597 | + | 0.143867i | \(0.954046\pi\) | |||||||
\(194\) | 3.07347 | − | 3.47850i | 0.220662 | − | 0.249741i | ||||
\(195\) | 3.06579 | 0.219546 | ||||||||
\(196\) | −0.774225 | − | 6.23824i | −0.0553018 | − | 0.445588i | ||||
\(197\) | 4.27512i | 0.304590i | 0.988335 | + | 0.152295i | \(0.0486663\pi\) | ||||
−0.988335 | + | 0.152295i | \(0.951334\pi\) | |||||||
\(198\) | −10.0194 | + | 19.9950i | −0.712049 | + | 1.42098i | ||||
\(199\) | − | 17.2819i | − | 1.22508i | −0.790440 | − | 0.612540i | \(-0.790148\pi\) | ||
0.790440 | − | 0.612540i | \(-0.209852\pi\) | |||||||
\(200\) | 8.84643 | + | 6.05452i | 0.625537 | + | 0.428119i | ||||
\(201\) | −31.7184 | −2.23725 | ||||||||
\(202\) | 3.11922 | + | 2.75603i | 0.219467 | + | 0.193913i | ||||
\(203\) | 28.9241i | 2.03007i | ||||||||
\(204\) | −0.277392 | − | 2.23506i | −0.0194213 | − | 0.156485i | ||||
\(205\) | − | 3.63778i | − | 0.254073i | ||||||
\(206\) | −15.7355 | − | 13.9033i | −1.09635 | − | 0.968690i | ||||
\(207\) | − | 22.5282i | − | 1.56582i | ||||||
\(208\) | −0.977815 | − | 3.87864i | −0.0677993 | − | 0.268936i | ||||
\(209\) | −0.400267 | + | 0.106109i | −0.0276871 | + | 0.00733969i | ||||
\(210\) | −10.3478 | − | 9.14293i | −0.714066 | − | 0.630922i | ||||
\(211\) | −6.88191 | −0.473770 | −0.236885 | − | 0.971538i | \(-0.576126\pi\) | ||||
−0.236885 | + | 0.971538i | \(0.576126\pi\) | |||||||
\(212\) | 2.84450 | + | 22.9193i | 0.195361 | + | 1.57410i | ||||
\(213\) | −34.8354 | −2.38688 | ||||||||
\(214\) | 11.2525 | − | 12.7354i | 0.769208 | − | 0.870576i | ||||
\(215\) | 8.32941 | 0.568061 | ||||||||
\(216\) | 7.87274 | − | 11.5031i | 0.535672 | − | 0.782686i | ||||
\(217\) | 33.2927i | 2.26005i | ||||||||
\(218\) | 0.226779 | + | 0.200374i | 0.0153594 | + | 0.0135710i | ||||
\(219\) | −8.13230 | −0.549530 | ||||||||
\(220\) | −2.72407 | − | 6.76881i | −0.183657 | − | 0.456353i | ||||
\(221\) | −0.404034 | −0.0271782 | ||||||||
\(222\) | −8.46800 | − | 7.48201i | −0.568335 | − | 0.502160i | ||||
\(223\) | − | 6.34123i | − | 0.424640i | −0.977200 | − | 0.212320i | \(-0.931898\pi\) | ||
0.977200 | − | 0.212320i | \(-0.0681019\pi\) | |||||||
\(224\) | −8.26670 | + | 16.0075i | −0.552342 | + | 1.06954i | ||||
\(225\) | 18.0718 | 1.20479 | ||||||||
\(226\) | −12.6724 | + | 14.3423i | −0.842952 | + | 0.954038i | ||||
\(227\) | 15.4340 | 1.02439 | 0.512197 | − | 0.858868i | \(-0.328832\pi\) | ||||
0.512197 | + | 0.858868i | \(0.328832\pi\) | |||||||
\(228\) | 0.690673 | − | 0.0857191i | 0.0457409 | − | 0.00567689i | ||||
\(229\) | 14.5539 | 0.961751 | 0.480875 | − | 0.876789i | \(-0.340319\pi\) | ||||
0.480875 | + | 0.876789i | \(0.340319\pi\) | |||||||
\(230\) | 5.50776 | + | 4.86645i | 0.363171 | + | 0.320884i | ||||
\(231\) | −7.54386 | − | 28.4573i | −0.496350 | − | 1.87235i | ||||
\(232\) | 14.5080 | − | 21.1981i | 0.952499 | − | 1.39172i | ||||
\(233\) | 8.01550i | 0.525113i | 0.964917 | + | 0.262557i | \(0.0845656\pi\) | ||||
−0.964917 | + | 0.262557i | \(0.915434\pi\) | |||||||
\(234\) | −5.05332 | − | 4.46492i | −0.330346 | − | 0.291881i | ||||
\(235\) | 4.58751i | 0.299256i | ||||||||
\(236\) | −13.2707 | + | 1.64701i | −0.863846 | + | 0.107212i | ||||
\(237\) | 30.2140i | 1.96261i | ||||||||
\(238\) | 1.36371 | + | 1.20493i | 0.0883965 | + | 0.0781039i | ||||
\(239\) | −8.04188 | −0.520186 | −0.260093 | − | 0.965584i | \(-0.583753\pi\) | ||||
−0.260093 | + | 0.965584i | \(0.583753\pi\) | |||||||
\(240\) | 2.99777 | + | 11.8911i | 0.193506 | + | 0.767568i | ||||
\(241\) | 1.69843i | 0.109405i | 0.998503 | + | 0.0547026i | \(0.0174211\pi\) | ||||
−0.998503 | + | 0.0547026i | \(0.982579\pi\) | |||||||
\(242\) | 3.17272 | − | 15.2294i | 0.203950 | − | 0.978981i | ||||
\(243\) | 16.3702i | 1.05015i | ||||||||
\(244\) | −2.03456 | + | 0.252508i | −0.130249 | + | 0.0161652i | ||||
\(245\) | 3.45727 | 0.220877 | ||||||||
\(246\) | −8.63124 | + | 9.76868i | −0.550308 | + | 0.622829i | ||||
\(247\) | − | 0.124854i | − | 0.00794425i | ||||||
\(248\) | 16.6993 | − | 24.3998i | 1.06041 | − | 1.54939i | ||||
\(249\) | 10.9075i | 0.691234i | ||||||||
\(250\) | −9.05384 | + | 10.2470i | −0.572615 | + | 0.648075i | ||||
\(251\) | 9.67025i | 0.610381i | 0.952291 | + | 0.305190i | \(0.0987201\pi\) | ||||
−0.952291 | + | 0.305190i | \(0.901280\pi\) | |||||||
\(252\) | 3.74072 | + | 30.1405i | 0.235643 | + | 1.89867i | ||||
\(253\) | 4.01532 | + | 15.1468i | 0.252441 | + | 0.952269i | ||||
\(254\) | 20.5511 | − | 23.2593i | 1.28949 | − | 1.45942i | ||||
\(255\) | 1.23868 | 0.0775693 | ||||||||
\(256\) | 14.0878 | − | 7.58519i | 0.880485 | − | 0.474074i | ||||
\(257\) | −15.6489 | −0.976150 | −0.488075 | − | 0.872802i | \(-0.662301\pi\) | ||||
−0.488075 | + | 0.872802i | \(0.662301\pi\) | |||||||
\(258\) | −22.3673 | − | 19.7629i | −1.39253 | − | 1.23039i | ||||
\(259\) | 9.13026 | 0.567327 | ||||||||
\(260\) | 2.18320 | − | 0.270955i | 0.135396 | − | 0.0168039i | ||||
\(261\) | − | 43.3042i | − | 2.68046i | ||||||
\(262\) | −0.682774 | + | 0.772751i | −0.0421819 | + | 0.0477407i | ||||
\(263\) | −29.5589 | −1.82268 | −0.911341 | − | 0.411651i | \(-0.864952\pi\) | ||||
−0.911341 | + | 0.411651i | \(0.864952\pi\) | |||||||
\(264\) | −8.74508 | + | 24.6399i | −0.538223 | + | 1.51648i | ||||
\(265\) | −12.7020 | −0.780277 | ||||||||
\(266\) | −0.372344 | + | 0.421412i | −0.0228299 | + | 0.0258385i | ||||
\(267\) | 12.5633i | 0.768862i | ||||||||
\(268\) | −22.5872 | + | 2.80329i | −1.37973 | + | 0.171238i | ||||
\(269\) | −6.14686 | −0.374781 | −0.187390 | − | 0.982286i | \(-0.560003\pi\) | ||||
−0.187390 | + | 0.982286i | \(0.560003\pi\) | |||||||
\(270\) | 5.74508 | + | 5.07614i | 0.349635 | + | 0.308924i | ||||
\(271\) | 22.3148 | 1.35553 | 0.677765 | − | 0.735279i | \(-0.262949\pi\) | ||||
0.677765 | + | 0.735279i | \(0.262949\pi\) | |||||||
\(272\) | −0.395070 | − | 1.56710i | −0.0239546 | − | 0.0950196i | ||||
\(273\) | 8.87656 | 0.537234 | ||||||||
\(274\) | −2.84643 | + | 3.22154i | −0.171959 | + | 0.194620i | ||||
\(275\) | −12.1505 | + | 3.22103i | −0.732704 | + | 0.194236i | ||||
\(276\) | −3.24375 | − | 26.1362i | −0.195251 | − | 1.57321i | ||||
\(277\) | − | 16.8127i | − | 1.01018i | −0.863067 | − | 0.505090i | \(-0.831459\pi\) | ||
0.863067 | − | 0.505090i | \(-0.168541\pi\) | |||||||
\(278\) | −12.9643 | + | 14.6728i | −0.777549 | + | 0.880015i | ||||
\(279\) | − | 49.8447i | − | 2.98413i | ||||||
\(280\) | −8.17689 | − | 5.59628i | −0.488663 | − | 0.334442i | ||||
\(281\) | − | 22.3218i | − | 1.33161i | −0.746127 | − | 0.665804i | \(-0.768089\pi\) | ||
0.746127 | − | 0.665804i | \(-0.231911\pi\) | |||||||
\(282\) | 10.8847 | − | 12.3191i | 0.648172 | − | 0.733589i | ||||
\(283\) | 9.23091 | 0.548720 | 0.274360 | − | 0.961627i | \(-0.411534\pi\) | ||||
0.274360 | + | 0.961627i | \(0.411534\pi\) | |||||||
\(284\) | −24.8068 | + | 3.07876i | −1.47201 | + | 0.182691i | ||||
\(285\) | 0.382775i | 0.0226736i | ||||||||
\(286\) | 4.19339 | + | 2.10130i | 0.247961 | + | 0.124252i | ||||
\(287\) | − | 10.5327i | − | 0.621724i | ||||||
\(288\) | 12.3766 | − | 23.9659i | 0.729300 | − | 1.41220i | ||||
\(289\) | 16.8368 | 0.990397 | ||||||||
\(290\) | 10.5871 | + | 9.35440i | 0.621698 | + | 0.549309i | ||||
\(291\) | − | 9.14808i | − | 0.536270i | ||||||
\(292\) | −5.79114 | + | 0.718736i | −0.338901 | + | 0.0420608i | ||||
\(293\) | − | 1.84539i | − | 0.107809i | −0.998546 | − | 0.0539045i | \(-0.982833\pi\) | ||
0.998546 | − | 0.0539045i | \(-0.0171667\pi\) | |||||||
\(294\) | −9.28396 | − | 8.20296i | −0.541452 | − | 0.478406i | ||||
\(295\) | − | 7.35468i | − | 0.428206i | ||||||
\(296\) | −6.69146 | − | 4.57965i | −0.388933 | − | 0.266187i | ||||
\(297\) | 4.18834 | + | 15.7994i | 0.243032 | + | 0.916776i | ||||
\(298\) | 13.3875 | + | 11.8287i | 0.775516 | + | 0.685217i | ||||
\(299\) | −4.72467 | −0.273235 | ||||||||
\(300\) | 20.9661 | − | 2.60209i | 1.21048 | − | 0.150232i | ||||
\(301\) | 24.1166 | 1.39006 | ||||||||
\(302\) | −8.18915 | + | 9.26833i | −0.471233 | + | 0.533333i | ||||
\(303\) | 8.20322 | 0.471263 | ||||||||
\(304\) | 0.484263 | − | 0.122084i | 0.0277744 | − | 0.00700199i | ||||
\(305\) | − | 1.12756i | − | 0.0645642i | ||||||
\(306\) | −2.04171 | − | 1.80398i | −0.116717 | − | 0.103127i | ||||
\(307\) | 34.7935 | 1.98577 | 0.992885 | − | 0.119077i | \(-0.0379935\pi\) | ||||
0.992885 | + | 0.119077i | \(0.0379935\pi\) | |||||||
\(308\) | −7.88716 | − | 19.5981i | −0.449413 | − | 1.11671i | ||||
\(309\) | −41.3828 | −2.35418 | ||||||||
\(310\) | 12.1862 | + | 10.7673i | 0.692129 | + | 0.611539i | ||||
\(311\) | − | 18.1045i | − | 1.02661i | −0.858205 | − | 0.513307i | \(-0.828420\pi\) | ||
0.858205 | − | 0.513307i | \(-0.171580\pi\) | |||||||
\(312\) | −6.50552 | − | 4.45240i | −0.368303 | − | 0.252067i | ||||
\(313\) | −31.1943 | −1.76321 | −0.881604 | − | 0.471989i | \(-0.843536\pi\) | ||||
−0.881604 | + | 0.471989i | \(0.843536\pi\) | |||||||
\(314\) | 10.2050 | − | 11.5498i | 0.575899 | − | 0.651792i | ||||
\(315\) | −16.7040 | −0.941165 | ||||||||
\(316\) | 2.67032 | + | 21.5158i | 0.150217 | + | 1.21036i | ||||
\(317\) | −21.9345 | −1.23196 | −0.615982 | − | 0.787760i | \(-0.711241\pi\) | ||||
−0.615982 | + | 0.787760i | \(0.711241\pi\) | |||||||
\(318\) | 34.1092 | + | 30.1376i | 1.91275 | + | 1.69003i | ||||
\(319\) | 7.71834 | + | 29.1155i | 0.432144 | + | 1.63015i | ||||
\(320\) | 3.18570 | + | 8.20290i | 0.178086 | + | 0.458556i | ||||
\(321\) | − | 33.4928i | − | 1.86939i | ||||||
\(322\) | 15.9469 | + | 14.0901i | 0.888688 | + | 0.785212i | ||||
\(323\) | − | 0.0504451i | − | 0.00280684i | ||||||
\(324\) | 0.140122 | + | 1.12902i | 0.00778456 | + | 0.0627233i | ||||
\(325\) | − | 3.79006i | − | 0.210235i | ||||||
\(326\) | 16.5547 | + | 14.6271i | 0.916879 | + | 0.810120i | ||||
\(327\) | 0.596406 | 0.0329813 | ||||||||
\(328\) | −5.28308 | + | 7.71926i | −0.291709 | + | 0.426225i | ||||
\(329\) | 13.2825i | 0.732288i | ||||||||
\(330\) | −12.8561 | − | 6.44214i | −0.707703 | − | 0.354628i | ||||
\(331\) | 23.3853i | 1.28537i | 0.766129 | + | 0.642687i | \(0.222180\pi\) | ||||
−0.766129 | + | 0.642687i | \(0.777820\pi\) | |||||||
\(332\) | 0.964007 | + | 7.76739i | 0.0529068 | + | 0.426291i | ||||
\(333\) | −13.6695 | −0.749086 | ||||||||
\(334\) | −4.96319 | + | 5.61724i | −0.271573 | + | 0.307362i | ||||
\(335\) | − | 12.5180i | − | 0.683929i | ||||||
\(336\) | 8.67963 | + | 34.4290i | 0.473513 | + | 1.87826i | ||||
\(337\) | 12.3138i | 0.670778i | 0.942080 | + | 0.335389i | \(0.108868\pi\) | ||||
−0.942080 | + | 0.335389i | \(0.891132\pi\) | |||||||
\(338\) | −0.936395 | + | 1.05979i | −0.0509332 | + | 0.0576452i | ||||
\(339\) | 37.7189i | 2.04861i | ||||||||
\(340\) | 0.882085 | − | 0.109475i | 0.0478378 | − | 0.00593712i | ||||
\(341\) | 8.88410 | + | 33.5130i | 0.481101 | + | 1.81483i | ||||
\(342\) | 0.557462 | − | 0.630925i | 0.0301441 | − | 0.0341165i | ||||
\(343\) | −12.2837 | −0.663256 | ||||||||
\(344\) | −17.6748 | − | 12.0967i | −0.952960 | − | 0.652208i | ||||
\(345\) | 14.4848 | 0.779838 | ||||||||
\(346\) | 24.3102 | + | 21.4796i | 1.30693 | + | 1.15475i | ||||
\(347\) | −27.3443 | −1.46792 | −0.733959 | − | 0.679194i | \(-0.762330\pi\) | ||||
−0.733959 | + | 0.679194i | \(0.762330\pi\) | |||||||
\(348\) | −6.23521 | − | 50.2396i | −0.334242 | − | 2.69312i | ||||
\(349\) | − | 11.6046i | − | 0.621182i | −0.950544 | − | 0.310591i | \(-0.899473\pi\) | ||
0.950544 | − | 0.310591i | \(-0.100527\pi\) | |||||||
\(350\) | −11.3029 | + | 12.7924i | −0.604165 | + | 0.683783i | ||||
\(351\) | −4.92825 | −0.263051 | ||||||||
\(352\) | −4.04983 | + | 18.3194i | −0.215856 | + | 0.976425i | ||||
\(353\) | 29.7044 | 1.58101 | 0.790503 | − | 0.612458i | \(-0.209819\pi\) | ||||
0.790503 | + | 0.612458i | \(0.209819\pi\) | |||||||
\(354\) | −17.4502 | + | 19.7498i | −0.927469 | + | 1.04969i | ||||
\(355\) | − | 13.7481i | − | 0.729672i | ||||||
\(356\) | 1.11035 | + | 8.94653i | 0.0588484 | + | 0.474165i | ||||
\(357\) | 3.58643 | 0.189814 | ||||||||
\(358\) | −16.4433 | − | 14.5287i | −0.869057 | − | 0.767866i | ||||
\(359\) | −2.22396 | −0.117376 | −0.0586881 | − | 0.998276i | \(-0.518692\pi\) | ||||
−0.0586881 | + | 0.998276i | \(0.518692\pi\) | |||||||
\(360\) | 12.2422 | + | 8.37858i | 0.645219 | + | 0.441590i | ||||
\(361\) | −18.9844 | −0.999180 | ||||||||
\(362\) | 14.2815 | − | 16.1635i | 0.750619 | − | 0.849537i | ||||
\(363\) | −15.1876 | − | 26.6325i | −0.797140 | − | 1.39784i | ||||
\(364\) | 6.32113 | − | 0.784513i | 0.331317 | − | 0.0411197i | ||||
\(365\) | − | 3.20948i | − | 0.167992i | ||||||
\(366\) | −2.67534 | + | 3.02790i | −0.139842 | + | 0.158271i | ||||
\(367\) | 11.3410i | 0.591994i | 0.955189 | + | 0.295997i | \(0.0956518\pi\) | ||||
−0.955189 | + | 0.295997i | \(0.904348\pi\) | |||||||
\(368\) | −4.61985 | − | 18.3253i | −0.240826 | − | 0.955273i | ||||
\(369\) | 15.7692i | 0.820910i | ||||||||
\(370\) | 2.95284 | − | 3.34197i | 0.153511 | − | 0.173741i | ||||
\(371\) | −36.7768 | −1.90936 | ||||||||
\(372\) | −7.17696 | − | 57.8276i | −0.372108 | − | 2.99822i | ||||
\(373\) | − | 28.1110i | − | 1.45553i | −0.685826 | − | 0.727765i | \(-0.740559\pi\) | ||
0.685826 | − | 0.727765i | \(-0.259441\pi\) | |||||||
\(374\) | 1.69427 | + | 0.848995i | 0.0876087 | + | 0.0439005i | ||||
\(375\) | 26.9485i | 1.39161i | ||||||||
\(376\) | 6.66237 | − | 9.73458i | 0.343586 | − | 0.502023i | ||||
\(377\) | −9.08186 | −0.467740 | ||||||||
\(378\) | 16.6341 | + | 14.6972i | 0.855565 | + | 0.755945i | ||||
\(379\) | − | 4.65148i | − | 0.238930i | −0.992838 | − | 0.119465i | \(-0.961882\pi\) | ||
0.992838 | − | 0.119465i | \(-0.0381180\pi\) | |||||||
\(380\) | 0.0338298 | + | 0.272580i | 0.00173543 | + | 0.0139831i | ||||
\(381\) | − | 61.1696i | − | 3.13381i | ||||||
\(382\) | −13.2819 | − | 11.7354i | −0.679560 | − | 0.600434i | ||||
\(383\) | − | 1.48954i | − | 0.0761119i | −0.999276 | − | 0.0380560i | \(-0.987883\pi\) | ||
0.999276 | − | 0.0380560i | \(-0.0121165\pi\) | |||||||
\(384\) | 10.9081 | − | 29.5862i | 0.556650 | − | 1.50982i | ||||
\(385\) | 11.2309 | − | 2.97725i | 0.572380 | − | 0.151735i | ||||
\(386\) | 4.23636 | + | 3.74309i | 0.215625 | + | 0.190518i | ||||
\(387\) | −36.1066 | −1.83540 | ||||||||
\(388\) | −0.808510 | − | 6.51449i | −0.0410459 | − | 0.330723i | ||||
\(389\) | −2.10222 | −0.106587 | −0.0532934 | − | 0.998579i | \(-0.516972\pi\) | ||||
−0.0532934 | + | 0.998579i | \(0.516972\pi\) | |||||||
\(390\) | 2.87079 | − | 3.24911i | 0.145368 | − | 0.164525i | ||||
\(391\) | −1.90893 | −0.0965385 | ||||||||
\(392\) | −7.33623 | − | 5.02093i | −0.370536 | − | 0.253596i | ||||
\(393\) | 2.03226i | 0.102514i | ||||||||
\(394\) | 4.53075 | + | 4.00320i | 0.228256 | + | 0.201678i | ||||
\(395\) | −11.9242 | −0.599972 | ||||||||
\(396\) | 11.8084 | + | 29.3417i | 0.593395 | + | 1.47448i | ||||
\(397\) | −10.3607 | −0.519991 | −0.259995 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259995 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(398\) | −18.3152 | − | 16.1827i | −0.918060 | − | 0.811163i | ||||
\(399\) | 1.10827i | 0.0554829i | ||||||||
\(400\) | 14.7003 | − | 3.70598i | 0.735015 | − | 0.185299i | ||||
\(401\) | −24.2259 | −1.20978 | −0.604891 | − | 0.796308i | \(-0.706783\pi\) | ||||
−0.604891 | + | 0.796308i | \(0.706783\pi\) | |||||||
\(402\) | −29.7010 | + | 33.6150i | −1.48135 | + | 1.67656i | ||||
\(403\) | −10.4536 | −0.520729 | ||||||||
\(404\) | 5.84164 | − | 0.725003i | 0.290633 | − | 0.0360703i | ||||
\(405\) | −0.625709 | −0.0310918 | ||||||||
\(406\) | 30.6536 | + | 27.0843i | 1.52131 | + | 1.34417i | ||||
\(407\) | 9.19068 | − | 2.43640i | 0.455565 | − | 0.120768i | ||||
\(408\) | −2.62845 | − | 1.79892i | −0.130128 | − | 0.0890597i | ||||
\(409\) | − | 20.2912i | − | 1.00333i | −0.865061 | − | 0.501667i | \(-0.832720\pi\) | ||
0.865061 | − | 0.501667i | \(-0.167280\pi\) | |||||||
\(410\) | −3.85530 | − | 3.40640i | −0.190400 | − | 0.168230i | ||||
\(411\) | 8.47232i | 0.417909i | ||||||||
\(412\) | −29.4693 | + | 3.65742i | −1.45185 | + | 0.180188i | ||||
\(413\) | − | 21.2944i | − | 1.04783i | ||||||
\(414\) | −23.8753 | − | 21.0953i | −1.17340 | − | 1.03678i | ||||
\(415\) | −4.30473 | −0.211311 | ||||||||
\(416\) | −5.02619 | − | 2.59566i | −0.246429 | − | 0.127263i | ||||
\(417\) | 38.5879i | 1.88966i | ||||||||
\(418\) | −0.262355 | + | 0.523561i | −0.0128322 | + | 0.0256082i | ||||
\(419\) | 9.15253i | 0.447130i | 0.974689 | + | 0.223565i | \(0.0717696\pi\) | ||||
−0.974689 | + | 0.223565i | \(0.928230\pi\) | |||||||
\(420\) | −19.3793 | + | 2.40515i | −0.945611 | + | 0.117359i | ||||
\(421\) | 6.93713 | 0.338095 | 0.169048 | − | 0.985608i | \(-0.445931\pi\) | ||||
0.169048 | + | 0.985608i | \(0.445931\pi\) | |||||||
\(422\) | −6.44418 | + | 7.29341i | −0.313698 | + | 0.355037i | ||||
\(423\) | − | 19.8861i | − | 0.966897i | ||||||
\(424\) | 26.9533 | + | 18.4469i | 1.30897 | + | 0.895860i | ||||
\(425\) | − | 1.53131i | − | 0.0742795i | ||||||
\(426\) | −32.6197 | + | 36.9183i | −1.58043 | + | 1.78870i | ||||
\(427\) | − | 3.26470i | − | 0.157990i | ||||||
\(428\) | −2.96011 | − | 23.8508i | −0.143082 | − | 1.15287i | ||||
\(429\) | 8.93530 | − | 2.36870i | 0.431400 | − | 0.114362i | ||||
\(430\) | 7.79961 | − | 8.82746i | 0.376131 | − | 0.425698i | ||||
\(431\) | −19.6520 | −0.946602 | −0.473301 | − | 0.880901i | \(-0.656938\pi\) | ||||
−0.473301 | + | 0.880901i | \(0.656938\pi\) | |||||||
\(432\) | −4.81892 | − | 19.1149i | −0.231850 | − | 0.919667i | ||||
\(433\) | 11.9743 | 0.575450 | 0.287725 | − | 0.957713i | \(-0.407101\pi\) | ||||
0.287725 | + | 0.957713i | \(0.407101\pi\) | |||||||
\(434\) | 35.2834 | + | 31.1751i | 1.69366 | + | 1.49645i | ||||
\(435\) | 27.8431 | 1.33497 | ||||||||
\(436\) | 0.424710 | − | 0.0527106i | 0.0203399 | − | 0.00252438i | ||||
\(437\) | − | 0.589892i | − | 0.0282184i | ||||||
\(438\) | −7.61505 | + | 8.61857i | −0.363861 | + | 0.411811i | ||||
\(439\) | 15.7369 | 0.751080 | 0.375540 | − | 0.926806i | \(-0.377457\pi\) | ||||
0.375540 | + | 0.926806i | \(0.377457\pi\) | |||||||
\(440\) | −9.72436 | − | 3.45132i | −0.463591 | − | 0.164535i | ||||
\(441\) | −14.9867 | −0.713652 | ||||||||
\(442\) | −0.378335 | + | 0.428193i | −0.0179956 | + | 0.0203671i | ||||
\(443\) | − | 8.81640i | − | 0.418880i | −0.977821 | − | 0.209440i | \(-0.932836\pi\) | ||
0.977821 | − | 0.209440i | \(-0.0671641\pi\) | |||||||
\(444\) | −15.8588 | + | 1.96823i | −0.752625 | + | 0.0934079i | ||||
\(445\) | −4.95822 | −0.235042 | ||||||||
\(446\) | −6.72040 | − | 5.93790i | −0.318220 | − | 0.281167i | ||||
\(447\) | 35.2077 | 1.66527 | ||||||||
\(448\) | 9.22375 | + | 23.7503i | 0.435781 | + | 1.12210i | ||||
\(449\) | 7.59029 | 0.358208 | 0.179104 | − | 0.983830i | \(-0.442680\pi\) | ||||
0.179104 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(450\) | 16.9223 | − | 19.1524i | 0.797726 | − | 0.902852i | ||||
\(451\) | −2.81063 | − | 10.6024i | −0.132347 | − | 0.499246i | ||||
\(452\) | 3.33360 | + | 26.8602i | 0.156800 | + | 1.26340i | ||||
\(453\) | 24.3748i | 1.14523i | ||||||||
\(454\) | 14.4524 | − | 16.3569i | 0.678283 | − | 0.767668i | ||||
\(455\) | 3.50321i | 0.164233i | ||||||||
\(456\) | 0.555898 | − | 0.812238i | 0.0260323 | − | 0.0380365i | ||||
\(457\) | − | 16.6392i | − | 0.778349i | −0.921164 | − | 0.389175i | \(-0.872760\pi\) | ||
0.921164 | − | 0.389175i | \(-0.127240\pi\) | |||||||
\(458\) | 13.6282 | − | 15.4242i | 0.636805 | − | 0.720724i | ||||
\(459\) | −1.99118 | −0.0929403 | ||||||||
\(460\) | 10.3149 | − | 1.28017i | 0.480934 | − | 0.0596885i | ||||
\(461\) | 19.6073i | 0.913204i | 0.889671 | + | 0.456602i | \(0.150934\pi\) | ||||
−0.889671 | + | 0.456602i | \(0.849066\pi\) | |||||||
\(462\) | −37.2229 | − | 18.6523i | −1.73177 | − | 0.867783i | ||||
\(463\) | 37.5026i | 1.74289i | 0.490489 | + | 0.871447i | \(0.336818\pi\) | ||||
−0.490489 | + | 0.871447i | \(0.663182\pi\) | |||||||
\(464\) | −8.88038 | − | 35.2253i | −0.412261 | − | 1.63529i | ||||
\(465\) | 32.0484 | 1.48621 | ||||||||
\(466\) | 8.49479 | + | 7.50568i | 0.393513 | + | 0.347694i | ||||
\(467\) | 17.4618i | 0.808035i | 0.914751 | + | 0.404017i | \(0.132387\pi\) | ||||
−0.914751 | + | 0.404017i | \(0.867613\pi\) | |||||||
\(468\) | −9.46380 | + | 1.17455i | −0.437464 | + | 0.0542935i | ||||
\(469\) | − | 36.2440i | − | 1.67359i | ||||||
\(470\) | 4.86182 | + | 4.29573i | 0.224259 | + | 0.198147i | ||||
\(471\) | − | 30.3747i | − | 1.39959i | ||||||
\(472\) | −10.6811 | + | 15.6064i | −0.491636 | + | 0.718344i | ||||
\(473\) | 24.2762 | − | 6.43548i | 1.11622 | − | 0.295904i | ||||
\(474\) | 32.0206 | + | 28.2922i | 1.47076 | + | 1.29950i | ||||
\(475\) | 0.473203 | 0.0217120 | ||||||||
\(476\) | 2.55395 | − | 0.316970i | 0.117060 | − | 0.0145283i | ||||
\(477\) | 55.0611 | 2.52107 | ||||||||
\(478\) | −7.53037 | + | 8.52274i | −0.344431 | + | 0.389821i | ||||
\(479\) | 37.9234 | 1.73277 | 0.866383 | − | 0.499380i | \(-0.166439\pi\) | ||||
0.866383 | + | 0.499380i | \(0.166439\pi\) | |||||||
\(480\) | 15.4092 | + | 7.95774i | 0.703332 | + | 0.363220i | ||||
\(481\) | 2.86681i | 0.130715i | ||||||||
\(482\) | 1.79998 | + | 1.59040i | 0.0819870 | + | 0.0724406i | ||||
\(483\) | 41.9388 | 1.90828 | ||||||||
\(484\) | −13.1691 | − | 17.6231i | −0.598595 | − | 0.801052i | ||||
\(485\) | 3.61037 | 0.163938 | ||||||||
\(486\) | 17.3490 | + | 15.3290i | 0.786969 | + | 0.695336i | ||||
\(487\) | 19.3802i | 0.878202i | 0.898438 | + | 0.439101i | \(0.144703\pi\) | ||||
−0.898438 | + | 0.439101i | \(0.855297\pi\) | |||||||
\(488\) | −1.63754 | + | 2.39266i | −0.0741281 | + | 0.108311i | ||||
\(489\) | 43.5371 | 1.96882 | ||||||||
\(490\) | 3.23737 | − | 3.66400i | 0.146249 | − | 0.165522i | ||||
\(491\) | −26.1029 | −1.17801 | −0.589004 | − | 0.808130i | \(-0.700480\pi\) | ||||
−0.589004 | + | 0.808130i | \(0.700480\pi\) | |||||||
\(492\) | 2.27055 | + | 18.2947i | 0.102364 | + | 0.824788i | ||||
\(493\) | −3.66938 | −0.165261 | ||||||||
\(494\) | −0.132319 | − | 0.116912i | −0.00595332 | − | 0.00526014i | ||||
\(495\) | −16.8146 | + | 4.45745i | −0.755758 | + | 0.200347i | ||||
\(496\) | −10.2216 | − | 40.5456i | −0.458966 | − | 1.82055i | ||||
\(497\) | − | 39.8056i | − | 1.78553i | ||||||
\(498\) | 11.5597 | + | 10.2137i | 0.518002 | + | 0.457687i | ||||
\(499\) | − | 7.99822i | − | 0.358049i | −0.983845 | − | 0.179025i | \(-0.942706\pi\) | ||
0.983845 | − | 0.179025i | \(-0.0572942\pi\) | |||||||
\(500\) | 2.38171 | + | 19.1904i | 0.106514 | + | 0.858222i | ||||
\(501\) | 14.7728i | 0.659999i | ||||||||
\(502\) | 10.2485 | + | 9.05517i | 0.457412 | + | 0.404152i | ||||
\(503\) | 6.47440 | 0.288679 | 0.144340 | − | 0.989528i | \(-0.453894\pi\) | ||||
0.144340 | + | 0.989528i | \(0.453894\pi\) | |||||||
\(504\) | 35.4455 | + | 24.2590i | 1.57887 | + | 1.08058i | ||||
\(505\) | 3.23747i | 0.144066i | ||||||||
\(506\) | 19.8124 | + | 9.92794i | 0.880768 | + | 0.441351i | ||||
\(507\) | 2.78715i | 0.123782i | ||||||||
\(508\) | −5.40619 | − | 43.5598i | −0.239861 | − | 1.93265i | ||||
\(509\) | −0.678175 | −0.0300596 | −0.0150298 | − | 0.999887i | \(-0.504784\pi\) | ||||
−0.0150298 | + | 0.999887i | \(0.504784\pi\) | |||||||
\(510\) | 1.15990 | − | 1.31275i | 0.0513610 | − | 0.0581295i | ||||
\(511\) | − | 9.29261i | − | 0.411081i | ||||||
\(512\) | 5.15296 | − | 22.0329i | 0.227731 | − | 0.973724i | ||||
\(513\) | − | 0.615310i | − | 0.0271666i | ||||||
\(514\) | −14.6535 | + | 16.5846i | −0.646340 | + | 0.731515i | ||||
\(515\) | − | 16.3321i | − | 0.719677i | ||||||
\(516\) | −41.8893 | + | 5.19886i | −1.84407 | + | 0.228867i | ||||
\(517\) | 3.54442 | + | 13.3704i | 0.155883 | + | 0.588029i | ||||
\(518\) | 8.54953 | − | 9.67620i | 0.375645 | − | 0.425148i | ||||
\(519\) | 63.9334 | 2.80636 | ||||||||
\(520\) | 1.75718 | − | 2.56746i | 0.0770573 | − | 0.112591i | ||||
\(521\) | 31.0733 | 1.36135 | 0.680674 | − | 0.732587i | \(-0.261687\pi\) | ||||
0.680674 | + | 0.732587i | \(0.261687\pi\) | |||||||
\(522\) | −45.8935 | − | 40.5498i | −2.00871 | − | 1.77482i | ||||
\(523\) | 21.7315 | 0.950254 | 0.475127 | − | 0.879917i | \(-0.342402\pi\) | ||||
0.475127 | + | 0.879917i | \(0.342402\pi\) | |||||||
\(524\) | 0.179611 | + | 1.44720i | 0.00784636 | + | 0.0632213i | ||||
\(525\) | 33.6427i | 1.46829i | ||||||||
\(526\) | −27.6788 | + | 31.3264i | −1.20686 | + | 1.36590i | ||||
\(527\) | −4.22359 | −0.183983 | ||||||||
\(528\) | 17.9244 | + | 32.3407i | 0.780059 | + | 1.40745i | ||||
\(529\) | 0.677499 | 0.0294565 | ||||||||
\(530\) | −11.8941 | + | 13.4615i | −0.516646 | + | 0.584730i | ||||
\(531\) | 31.8813i | 1.38353i | ||||||||
\(532\) | 0.0979493 | + | 0.789217i | 0.00424664 | + | 0.0342169i | ||||
\(533\) | 3.30715 | 0.143249 | ||||||||
\(534\) | 13.3145 | + | 11.7642i | 0.576176 | + | 0.509088i | ||||
\(535\) | 13.2182 | 0.571474 | ||||||||
\(536\) | −18.1796 | + | 26.5628i | −0.785240 | + | 1.14734i | ||||
\(537\) | −43.2442 | −1.86613 | ||||||||
\(538\) | −5.75589 | + | 6.51441i | −0.248154 | + | 0.280856i | ||||
\(539\) | 10.0763 | − | 2.67116i | 0.434016 | − | 0.115055i | ||||
\(540\) | 10.7593 | − | 1.33534i | 0.463008 | − | 0.0574637i | ||||
\(541\) | − | 7.64816i | − | 0.328820i | −0.986392 | − | 0.164410i | \(-0.947428\pi\) | ||
0.986392 | − | 0.164410i | \(-0.0525720\pi\) | |||||||
\(542\) | 20.8955 | − | 23.6491i | 0.897539 | − | 1.01582i | ||||
\(543\) | − | 42.5084i | − | 1.82421i | ||||||
\(544\) | −2.03075 | − | 1.04873i | −0.0870676 | − | 0.0449641i | ||||
\(545\) | 0.235377i | 0.0100824i | ||||||||
\(546\) | 8.31196 | − | 9.40733i | 0.355719 | − | 0.402596i | ||||
\(547\) | 38.7151 | 1.65534 | 0.827669 | − | 0.561216i | \(-0.189666\pi\) | ||||
0.827669 | + | 0.561216i | \(0.189666\pi\) | |||||||
\(548\) | 0.748786 | + | 6.03327i | 0.0319866 | + | 0.257728i | ||||
\(549\) | 4.88781i | 0.208607i | ||||||||
\(550\) | −7.96405 | + | 15.8932i | −0.339588 | + | 0.677689i | ||||
\(551\) | − | 1.13390i | − | 0.0483059i | ||||||
\(552\) | −30.7364 | − | 21.0361i | −1.30823 | − | 0.895356i | ||||
\(553\) | −34.5249 | −1.46815 | ||||||||
\(554\) | −17.8180 | − | 15.7434i | −0.757016 | − | 0.668871i | ||||
\(555\) | − | 8.78904i | − | 0.373074i | ||||||
\(556\) | 3.41041 | + | 27.4790i | 0.144634 | + | 1.16537i | ||||
\(557\) | 23.1336i | 0.980202i | 0.871666 | + | 0.490101i | \(0.163040\pi\) | ||||
−0.871666 | + | 0.490101i | \(0.836960\pi\) | |||||||
\(558\) | −52.8252 | − | 46.6743i | −2.23627 | − | 1.97588i | ||||
\(559\) | 7.57237i | 0.320277i | ||||||||
\(560\) | −13.5877 | + | 3.42549i | −0.574185 | + | 0.144753i | ||||
\(561\) | 3.61016 | − | 0.957034i | 0.152421 | − | 0.0404060i | ||||
\(562\) | −23.6565 | − | 20.9020i | −0.997890 | − | 0.881699i | ||||
\(563\) | −1.43427 | −0.0604474 | −0.0302237 | − | 0.999543i | \(-0.509622\pi\) | ||||
−0.0302237 | + | 0.999543i | \(0.509622\pi\) | |||||||
\(564\) | −2.86333 | − | 23.0710i | −0.120568 | − | 0.971465i | ||||
\(565\) | −14.8861 | −0.626262 | ||||||||
\(566\) | 8.64377 | − | 9.78287i | 0.363325 | − | 0.411205i | ||||
\(567\) | −1.81165 | −0.0760823 | ||||||||
\(568\) | −19.9661 | + | 29.1730i | −0.837759 | + | 1.22407i | ||||
\(569\) | − | 0.761746i | − | 0.0319341i | −0.999873 | − | 0.0159670i | \(-0.994917\pi\) | ||
0.999873 | − | 0.0159670i | \(-0.00508268\pi\) | |||||||
\(570\) | 0.405663 | + | 0.358429i | 0.0169914 | + | 0.0150129i | ||||
\(571\) | 17.2745 | 0.722916 | 0.361458 | − | 0.932388i | \(-0.382279\pi\) | ||||
0.361458 | + | 0.932388i | \(0.382279\pi\) | |||||||
\(572\) | 6.15362 | − | 2.47649i | 0.257296 | − | 0.103547i | ||||
\(573\) | −34.9300 | −1.45922 | ||||||||
\(574\) | −11.1625 | − | 9.86274i | −0.465912 | − | 0.411663i | ||||
\(575\) | − | 17.9068i | − | 0.746764i | ||||||
\(576\) | −13.8095 | − | 35.5582i | −0.575396 | − | 1.48159i | ||||
\(577\) | 34.8927 | 1.45260 | 0.726301 | − | 0.687377i | \(-0.241238\pi\) | ||||
0.726301 | + | 0.687377i | \(0.241238\pi\) | |||||||
\(578\) | 15.7659 | − | 17.8435i | 0.655773 | − | 0.742192i | ||||
\(579\) | 11.1412 | 0.463012 | ||||||||
\(580\) | 19.8275 | − | 2.46078i | 0.823292 | − | 0.102178i | ||||
\(581\) | −12.4637 | −0.517083 | ||||||||
\(582\) | −9.69509 | − | 8.56622i | −0.401874 | − | 0.355081i | ||||
\(583\) | −37.0202 | + | 9.81384i | −1.53322 | + | 0.406448i | ||||
\(584\) | −4.66108 | + | 6.81044i | −0.192877 | + | 0.281818i | ||||
\(585\) | − | 5.24490i | − | 0.216850i | ||||||
\(586\) | −1.95574 | − | 1.72802i | −0.0807907 | − | 0.0713837i | ||||
\(587\) | 27.0974i | 1.11843i | 0.829023 | + | 0.559214i | \(0.188897\pi\) | ||||
−0.829023 | + | 0.559214i | \(0.811103\pi\) | |||||||
\(588\) | −17.3869 | + | 2.15788i | −0.717024 | + | 0.0889895i | ||||
\(589\) | − | 1.30517i | − | 0.0537784i | ||||||
\(590\) | −7.79445 | − | 6.88688i | −0.320892 | − | 0.283528i | ||||
\(591\) | 11.9154 | 0.490134 | ||||||||
\(592\) | −11.1193 | + | 2.80321i | −0.457002 | + | 0.115211i | ||||
\(593\) | 42.5287i | 1.74645i | 0.487321 | + | 0.873223i | \(0.337974\pi\) | ||||
−0.487321 | + | 0.873223i | \(0.662026\pi\) | |||||||
\(594\) | 20.6661 | + | 10.3557i | 0.847940 | + | 0.424901i | ||||
\(595\) | 1.41542i | 0.0580264i | ||||||||
\(596\) | 25.0719 | − | 3.11167i | 1.02699 | − | 0.127459i | ||||
\(597\) | −48.1672 | −1.97135 | ||||||||
\(598\) | −4.42416 | + | 5.00718i | −0.180917 | + | 0.204759i | ||||
\(599\) | − | 27.8633i | − | 1.13846i | −0.822177 | − | 0.569232i | \(-0.807241\pi\) | ||
0.822177 | − | 0.569232i | \(-0.192759\pi\) | |||||||
\(600\) | 16.8748 | − | 24.6563i | 0.688913 | − | 1.00659i | ||||
\(601\) | 30.8864i | 1.25988i | 0.776643 | + | 0.629940i | \(0.216921\pi\) | ||||
−0.776643 | + | 0.629940i | \(0.783079\pi\) | |||||||
\(602\) | 22.5827 | − | 25.5587i | 0.920401 | − | 1.04169i | ||||
\(603\) | 54.2633i | 2.20977i | ||||||||
\(604\) | 2.15425 | + | 17.3576i | 0.0876551 | + | 0.706272i | ||||
\(605\) | 10.5108 | − | 5.99390i | 0.427323 | − | 0.243687i | ||||
\(606\) | 7.68146 | − | 8.69373i | 0.312038 | − | 0.353159i | ||||
\(607\) | −35.6261 | −1.44602 | −0.723010 | − | 0.690838i | \(-0.757242\pi\) | ||||
−0.723010 | + | 0.690838i | \(0.757242\pi\) | |||||||
\(608\) | 0.324078 | − | 0.627538i | 0.0131431 | − | 0.0254500i | ||||
\(609\) | 80.6157 | 3.26671 | ||||||||
\(610\) | −1.19499 | − | 1.05585i | −0.0483836 | − | 0.0427499i | ||||
\(611\) | −4.17057 | −0.168723 | ||||||||
\(612\) | −3.82369 | + | 0.474557i | −0.154564 | + | 0.0191828i | ||||
\(613\) | 7.52250i | 0.303831i | 0.988393 | + | 0.151916i | \(0.0485442\pi\) | ||||
−0.988393 | + | 0.151916i | \(0.951456\pi\) | |||||||
\(614\) | 32.5805 | − | 36.8740i | 1.31484 | − | 1.48811i | ||||
\(615\) | −10.1390 | −0.408845 | ||||||||
\(616\) | −28.1555 | − | 9.99282i | −1.13442 | − | 0.402622i | ||||
\(617\) | −32.4036 | −1.30452 | −0.652260 | − | 0.757995i | \(-0.726179\pi\) | ||||
−0.652260 | + | 0.757995i | \(0.726179\pi\) | |||||||
\(618\) | −38.7506 | + | 43.8573i | −1.55878 | + | 1.76420i | ||||
\(619\) | 1.89280i | 0.0760782i | 0.999276 | + | 0.0380391i | \(0.0121112\pi\) | ||||
−0.999276 | + | 0.0380391i | \(0.987889\pi\) | |||||||
\(620\) | 22.8222 | − | 2.83245i | 0.916561 | − | 0.113754i | ||||
\(621\) | −23.2844 | −0.934369 | ||||||||
\(622\) | −19.1871 | − | 16.9530i | −0.769332 | − | 0.679753i | ||||
\(623\) | −14.3558 | −0.575154 | ||||||||
\(624\) | −10.8104 | + | 2.72532i | −0.432761 | + | 0.109100i | ||||
\(625\) | 8.31485 | 0.332594 | ||||||||
\(626\) | −29.2102 | + | 33.0596i | −1.16748 | + | 1.32133i | ||||
\(627\) | 0.295741 | + | 1.11560i | 0.0118107 | + | 0.0445530i | ||||
\(628\) | −2.68453 | − | 21.6303i | −0.107124 | − | 0.863143i | ||||
\(629\) | 1.15829i | 0.0461840i | ||||||||
\(630\) | −15.6416 | + | 17.7028i | −0.623175 | + | 0.705298i | ||||
\(631\) | 6.27266i | 0.249711i | 0.992175 | + | 0.124855i | \(0.0398467\pi\) | ||||
−0.992175 | + | 0.124855i | \(0.960153\pi\) | |||||||
\(632\) | 25.3029 | + | 17.3173i | 1.00649 | + | 0.688847i | ||||
\(633\) | 19.1809i | 0.762372i | ||||||||
\(634\) | −20.5394 | + | 23.2461i | −0.815722 | + | 0.923219i | ||||
\(635\) | 24.1411 | 0.958011 | ||||||||
\(636\) | 63.8794 | − | 7.92804i | 2.53298 | − | 0.314367i | ||||
\(637\) | 3.14305i | 0.124532i | ||||||||
\(638\) | 38.0838 | + | 19.0837i | 1.50775 | + | 0.755531i | ||||
\(639\) | 59.5957i | 2.35757i | ||||||||
\(640\) | 11.6765 | + | 4.30496i | 0.461553 | + | 0.170168i | ||||
\(641\) | 18.5629 | 0.733190 | 0.366595 | − | 0.930381i | \(-0.380523\pi\) | ||||
0.366595 | + | 0.930381i | \(0.380523\pi\) | |||||||
\(642\) | −35.4955 | − | 31.3625i | −1.40090 | − | 1.23778i | ||||
\(643\) | − | 40.9531i | − | 1.61503i | −0.589846 | − | 0.807516i | \(-0.700812\pi\) | ||
0.589846 | − | 0.807516i | \(-0.299188\pi\) | |||||||
\(644\) | 29.8653 | − | 3.70656i | 1.17686 | − | 0.146059i | ||||
\(645\) | − | 23.2153i | − | 0.914102i | ||||||
\(646\) | −0.0534614 | − | 0.0472365i | −0.00210341 | − | 0.00185850i | ||||
\(647\) | 23.2745i | 0.915016i | 0.889206 | + | 0.457508i | \(0.151258\pi\) | ||||
−0.889206 | + | 0.457508i | \(0.848742\pi\) | |||||||
\(648\) | 1.32774 | + | 0.908707i | 0.0521585 | + | 0.0356974i | ||||
\(649\) | −5.68239 | − | 21.4353i | −0.223053 | − | 0.841410i | ||||
\(650\) | −4.01668 | − | 3.54899i | −0.157547 | − | 0.139203i | ||||
\(651\) | 92.7916 | 3.63679 | ||||||||
\(652\) | 31.0034 | − | 3.84782i | 1.21419 | − | 0.150692i | ||||
\(653\) | 28.8171 | 1.12770 | 0.563851 | − | 0.825877i | \(-0.309319\pi\) | ||||
0.563851 | + | 0.825877i | \(0.309319\pi\) | |||||||
\(654\) | 0.558472 | − | 0.632068i | 0.0218380 | − | 0.0247158i | ||||
\(655\) | −0.802047 | −0.0313386 | ||||||||
\(656\) | 3.23378 | + | 12.8273i | 0.126258 | + | 0.500820i | ||||
\(657\) | 13.9126i | 0.542782i | ||||||||
\(658\) | 14.0767 | + | 12.4377i | 0.548768 | + | 0.484871i | ||||
\(659\) | −20.4704 | −0.797413 | −0.398707 | − | 0.917079i | \(-0.630541\pi\) | ||||
−0.398707 | + | 0.917079i | \(0.630541\pi\) | |||||||
\(660\) | −18.8657 | + | 7.59240i | −0.734346 | + | 0.295534i | ||||
\(661\) | 26.3215 | 1.02379 | 0.511893 | − | 0.859049i | \(-0.328944\pi\) | ||||
0.511893 | + | 0.859049i | \(0.328944\pi\) | |||||||
\(662\) | 24.7836 | + | 21.8979i | 0.963243 | + | 0.851086i | ||||
\(663\) | 1.12610i | 0.0437342i | ||||||||
\(664\) | 9.13453 | + | 6.25169i | 0.354488 | + | 0.242613i | ||||
\(665\) | −0.437389 | −0.0169612 | ||||||||
\(666\) | −12.8001 | + | 14.4869i | −0.495993 | + | 0.561356i | ||||
\(667\) | −42.9088 | −1.66144 | ||||||||
\(668\) | 1.30562 | + | 10.5199i | 0.0505160 | + | 0.407028i | ||||
\(669\) | −17.6740 | −0.683315 | ||||||||
\(670\) | −13.2665 | − | 11.7217i | −0.512528 | − | 0.452851i | ||||
\(671\) | −0.871181 | − | 3.28631i | −0.0336316 | − | 0.126866i | ||||
\(672\) | 44.6152 | + | 23.0405i | 1.72107 | + | 0.888807i | ||||
\(673\) | 8.62898i | 0.332623i | 0.986073 | + | 0.166311i | \(0.0531857\pi\) | ||||
−0.986073 | + | 0.166311i | \(0.946814\pi\) | |||||||
\(674\) | 13.0501 | + | 11.5306i | 0.502673 | + | 0.444143i | ||||
\(675\) | − | 18.6784i | − | 0.718931i | ||||||
\(676\) | 0.246329 | + | 1.98477i | 0.00947420 | + | 0.0763374i | ||||
\(677\) | 5.05795i | 0.194393i | 0.995265 | + | 0.0971965i | \(0.0309875\pi\) | ||||
−0.995265 | + | 0.0971965i | \(0.969012\pi\) | |||||||
\(678\) | 39.9742 | + | 35.3197i | 1.53520 | + | 1.35645i | ||||
\(679\) | 10.4533 | 0.401161 | ||||||||
\(680\) | 0.709959 | − | 1.03734i | 0.0272257 | − | 0.0397802i | ||||
\(681\) | − | 43.0170i | − | 1.64842i | ||||||
\(682\) | 43.8359 | + | 21.9661i | 1.67856 | + | 0.841124i | ||||
\(683\) | − | 30.4518i | − | 1.16521i | −0.812757 | − | 0.582603i | \(-0.802034\pi\) | ||
0.812757 | − | 0.582603i | \(-0.197966\pi\) | |||||||
\(684\) | −0.146647 | − | 1.18159i | −0.00560717 | − | 0.0451792i | ||||
\(685\) | −3.34367 | −0.127755 | ||||||||
\(686\) | −11.5024 | + | 13.0182i | −0.439163 | + | 0.497036i | ||||
\(687\) | − | 40.5640i | − | 1.54761i | ||||||
\(688\) | −29.3705 | + | 7.40438i | −1.11974 | + | 0.282289i | ||||
\(689\) | − | 11.5475i | − | 0.439927i | ||||||
\(690\) | 13.5635 | − | 15.3510i | 0.516355 | − | 0.584401i | ||||
\(691\) | 31.0783i | 1.18227i | 0.806571 | + | 0.591137i | \(0.201321\pi\) | ||||
−0.806571 | + | 0.591137i | \(0.798679\pi\) | |||||||
\(692\) | 45.5279 | − | 5.65045i | 1.73071 | − | 0.214798i | ||||
\(693\) | −48.6842 | + | 12.9059i | −1.84936 | + | 0.490255i | ||||
\(694\) | −25.6051 | + | 28.9793i | −0.971954 | + | 1.10004i | ||||
\(695\) | −15.2291 | −0.577671 | ||||||||
\(696\) | −59.0823 | − | 40.4360i | −2.23951 | − | 1.53272i | ||||
\(697\) | 1.33620 | 0.0506122 | ||||||||
\(698\) | −12.2985 | − | 10.8665i | −0.465506 | − | 0.411304i | ||||
\(699\) | 22.3404 | 0.844992 | ||||||||
\(700\) | 2.97335 | + | 23.9575i | 0.112382 | + | 0.905507i | ||||
\(701\) | − | 46.7314i | − | 1.76502i | −0.470292 | − | 0.882511i | \(-0.655852\pi\) | ||
0.470292 | − | 0.882511i | \(-0.344148\pi\) | |||||||
\(702\) | −4.61479 | + | 5.22293i | −0.174174 | + | 0.197127i | ||||
\(703\) | −0.357932 | −0.0134997 | ||||||||
\(704\) | 15.6225 | + | 21.4461i | 0.588796 | + | 0.808282i | ||||
\(705\) | 12.7861 | 0.481552 | ||||||||
\(706\) | 27.8151 | − | 31.4806i | 1.04683 | − | 1.18479i | ||||
\(707\) | 9.37364i | 0.352532i | ||||||||
\(708\) | 4.59048 | + | 36.9873i | 0.172521 | + | 1.39007i | ||||
\(709\) | −11.0151 | −0.413680 | −0.206840 | − | 0.978375i | \(-0.566318\pi\) | ||||
−0.206840 | + | 0.978375i | \(0.566318\pi\) | |||||||
\(710\) | −14.5701 | − | 12.8736i | −0.546808 | − | 0.483139i | ||||
\(711\) | 51.6895 | 1.93851 | ||||||||
\(712\) | 10.5212 | + | 7.20074i | 0.394299 | + | 0.269859i | ||||
\(713\) | −49.3896 | −1.84966 | ||||||||
\(714\) | 3.35831 | − | 3.80088i | 0.125682 | − | 0.142244i | ||||
\(715\) | 0.934827 | + | 3.52639i | 0.0349605 | + | 0.131880i | ||||
\(716\) | −30.7949 | + | 3.82194i | −1.15086 | + | 0.142833i | ||||
\(717\) | 22.4139i | 0.837063i | ||||||||
\(718\) | −2.08251 | + | 2.35694i | −0.0777185 | + | 0.0879603i | ||||
\(719\) | 24.2300i | 0.903626i | 0.892113 | + | 0.451813i | \(0.149223\pi\) | ||||
−0.892113 | + | 0.451813i | \(0.850777\pi\) | |||||||
\(720\) | 20.3431 | − | 5.12854i | 0.758142 | − | 0.191129i | ||||
\(721\) | − | 47.2872i | − | 1.76107i | ||||||
\(722\) | −17.7769 | + | 20.1196i | −0.661588 | + | 0.748773i | ||||
\(723\) | 4.73377 | 0.176051 | ||||||||
\(724\) | −3.75691 | − | 30.2709i | −0.139624 | − | 1.12501i | ||||
\(725\) | − | 34.4208i | − | 1.27836i | ||||||
\(726\) | −42.4465 | − | 8.84285i | −1.57534 | − | 0.328189i | ||||
\(727\) | 16.8363i | 0.624425i | 0.950012 | + | 0.312212i | \(0.101070\pi\) | ||||
−0.950012 | + | 0.312212i | \(0.898930\pi\) | |||||||
\(728\) | 5.08765 | − | 7.43372i | 0.188561 | − | 0.275512i | ||||
\(729\) | 43.9197 | 1.62665 | ||||||||
\(730\) | −3.40139 | − | 3.00534i | −0.125891 | − | 0.111233i | ||||
\(731\) | 3.05949i | 0.113159i | ||||||||
\(732\) | 0.703778 | + | 5.67062i | 0.0260124 | + | 0.209592i | ||||
\(733\) | 38.8850i | 1.43625i | 0.695913 | + | 0.718126i | \(0.255000\pi\) | ||||
−0.695913 | + | 0.718126i | \(0.745000\pi\) | |||||||
\(734\) | 12.0191 | + | 10.6196i | 0.443633 | + | 0.391977i | ||||
\(735\) | − | 9.63593i | − | 0.355427i | ||||||
\(736\) | −23.7471 | − | 12.2636i | −0.875329 | − | 0.452043i | ||||
\(737\) | −9.67165 | − | 36.4838i | −0.356260 | − | 1.34390i | ||||
\(738\) | 16.7121 | + | 14.7662i | 0.615180 | + | 0.543550i | ||||
\(739\) | 31.7483 | 1.16788 | 0.583941 | − | 0.811796i | \(-0.301510\pi\) | ||||
0.583941 | + | 0.811796i | \(0.301510\pi\) | |||||||
\(740\) | −0.776778 | − | 6.25881i | −0.0285549 | − | 0.230078i | ||||
\(741\) | −0.347986 | −0.0127836 | ||||||||
\(742\) | −34.4376 | + | 38.9759i | −1.26424 | + | 1.43085i | ||||
\(743\) | −9.59026 | −0.351832 | −0.175916 | − | 0.984405i | \(-0.556289\pi\) | ||||
−0.175916 | + | 0.984405i | \(0.556289\pi\) | |||||||
\(744\) | −68.0059 | − | 46.5434i | −2.49322 | − | 1.70636i | ||||
\(745\) | 13.8950i | 0.509074i | ||||||||
\(746\) | −29.7919 | − | 26.3230i | −1.09076 | − | 0.963752i | ||||
\(747\) | 18.6603 | 0.682745 | ||||||||
\(748\) | 2.48627 | − | 1.00059i | 0.0909070 | − | 0.0365850i | ||||
\(749\) | 38.2715 | 1.39841 | ||||||||
\(750\) | 28.5598 | + | 25.2344i | 1.04286 | + | 0.921430i | ||||
\(751\) | 1.35655i | 0.0495012i | 0.999694 | + | 0.0247506i | \(0.00787916\pi\) | ||||
−0.999694 | + | 0.0247506i | \(0.992121\pi\) | |||||||
\(752\) | −4.07805 | − | 16.1762i | −0.148711 | − | 0.589884i | ||||
\(753\) | 26.9524 | 0.982201 | ||||||||
\(754\) | −8.50421 | + | 9.62491i | −0.309705 | + | 0.350519i | ||||
\(755\) | −9.61971 | −0.350097 | ||||||||
\(756\) | 31.1521 | − | 3.86628i | 1.13299 | − | 0.140615i | ||||
\(757\) | 5.81206 | 0.211243 | 0.105621 | − | 0.994406i | \(-0.466317\pi\) | ||||
0.105621 | + | 0.994406i | \(0.466317\pi\) | |||||||
\(758\) | −4.92961 | − | 4.35562i | −0.179052 | − | 0.158203i | ||||
\(759\) | 42.2163 | − | 11.1913i | 1.53236 | − | 0.406219i | ||||
\(760\) | 0.320557 | + | 0.219390i | 0.0116278 | + | 0.00795811i | ||||
\(761\) | − | 22.1576i | − | 0.803212i | −0.915813 | − | 0.401606i | \(-0.868452\pi\) | ||
0.915813 | − | 0.401606i | \(-0.131548\pi\) | |||||||
\(762\) | −64.8272 | − | 57.2789i | −2.34844 | − | 2.07500i | ||||
\(763\) | 0.681500i | 0.0246720i | ||||||||
\(764\) | −24.8742 | + | 3.08712i | −0.899916 | + | 0.111688i | ||||
\(765\) | − | 2.11911i | − | 0.0766168i | ||||||
\(766\) | −1.57861 | − | 1.39480i | −0.0570373 | − | 0.0503961i | ||||
\(767\) | 6.68623 | 0.241426 | ||||||||
\(768\) | −21.1411 | − | 39.2647i | −0.762862 | − | 1.41684i | ||||
\(769\) | − | 32.8214i | − | 1.18357i | −0.806096 | − | 0.591785i | \(-0.798423\pi\) | ||
0.806096 | − | 0.591785i | \(-0.201577\pi\) | |||||||
\(770\) | 7.36129 | − | 14.6903i | 0.265283 | − | 0.529403i | ||||
\(771\) | 43.6158i | 1.57078i | ||||||||
\(772\) | 7.93381 | − | 0.984661i | 0.285544 | − | 0.0354387i | ||||
\(773\) | −48.6899 | −1.75125 | −0.875627 | − | 0.482988i | \(-0.839552\pi\) | ||||
−0.875627 | + | 0.482988i | \(0.839552\pi\) | |||||||
\(774\) | −33.8101 | + | 38.2656i | −1.21528 | + | 1.37543i | ||||
\(775\) | − | 39.6196i | − | 1.42318i | ||||||
\(776\) | −7.66111 | − | 5.24328i | −0.275018 | − | 0.188223i | ||||
\(777\) | − | 25.4474i | − | 0.912921i | ||||||
\(778\) | −1.96851 | + | 2.22792i | −0.0705745 | + | 0.0798749i | ||||
\(779\) | 0.412910i | 0.0147940i | ||||||||
\(780\) | −0.755193 | − | 6.08489i | −0.0270403 | − | 0.217874i | ||||
\(781\) | −10.6221 | − | 40.0690i | −0.380088 | − | 1.43378i | ||||
\(782\) | −1.78751 | + | 2.02307i | −0.0639212 | + | 0.0723448i | ||||
\(783\) | −44.7577 | −1.59951 | ||||||||
\(784\) | −12.1908 | + | 3.07332i | −0.435385 | + | 0.109761i | ||||
\(785\) | 11.9877 | 0.427858 | ||||||||
\(786\) | 2.15377 | + | 1.90299i | 0.0768226 | + | 0.0678775i | ||||
\(787\) | −19.6216 | −0.699434 | −0.349717 | − | 0.936855i | \(-0.613722\pi\) | ||||
−0.349717 | + | 0.936855i | \(0.613722\pi\) | |||||||
\(788\) | 8.48514 | − | 1.05309i | 0.302271 | − | 0.0375147i | ||||
\(789\) | 82.3852i | 2.93299i | ||||||||
\(790\) | −11.1658 | + | 12.6372i | −0.397260 | + | 0.449612i | ||||
\(791\) | −43.1005 | −1.53248 | ||||||||
\(792\) | 42.1535 | + | 14.9609i | 1.49786 | + | 0.531613i | ||||
\(793\) | 1.02508 | 0.0364018 | ||||||||
\(794\) | −9.70174 | + | 10.9803i | −0.344302 | + | 0.389675i | ||||
\(795\) | 35.4024i | 1.25559i | ||||||||
\(796\) | −34.3006 | + | 4.25703i | −1.21575 | + | 0.150886i | ||||
\(797\) | 24.6757 | 0.874058 | 0.437029 | − | 0.899447i | \(-0.356031\pi\) | ||||
0.437029 | + | 0.899447i | \(0.356031\pi\) | |||||||
\(798\) | 1.17454 | + | 1.03778i | 0.0415782 | + | 0.0367370i | ||||
\(799\) | −1.68505 | −0.0596128 | ||||||||
\(800\) | 9.83770 | − | 19.0495i | 0.347815 | − | 0.673503i | ||||
\(801\) | 21.4931 | 0.759421 | ||||||||
\(802\) | −22.6850 | + | 25.6744i | −0.801034 | + | 0.906596i | ||||
\(803\) | −2.47972 | − | 9.35410i | −0.0875074 | − | 0.330099i | ||||
\(804\) | 7.81318 | + | 62.9539i | 0.275549 | + | 2.22021i | ||||
\(805\) | 16.5515i | 0.583364i | ||||||||
\(806\) | −9.78866 | + | 11.0786i | −0.344791 | + | 0.390228i | ||||
\(807\) | 17.1322i | 0.603083i | ||||||||
\(808\) | 4.70173 | − | 6.86983i | 0.165406 | − | 0.241680i | ||||
\(809\) | − | 28.9665i | − | 1.01841i | −0.860646 | − | 0.509204i | \(-0.829940\pi\) | ||
0.860646 | − | 0.509204i | \(-0.170060\pi\) | |||||||
\(810\) | −0.585911 | + | 0.663123i | −0.0205868 | + | 0.0232998i | ||||
\(811\) | −56.4774 | −1.98319 | −0.991595 | − | 0.129377i | \(-0.958702\pi\) | ||||
−0.991595 | + | 0.129377i | \(0.958702\pi\) | |||||||
\(812\) | 57.4077 | − | 7.12484i | 2.01461 | − | 0.250033i | ||||
\(813\) | − | 62.1948i | − | 2.18127i | ||||||
\(814\) | 6.02402 | − | 12.0217i | 0.211142 | − | 0.421359i | ||||
\(815\) | 17.1823i | 0.601870i | ||||||||
\(816\) | −4.36775 | + | 1.10112i | −0.152902 | + | 0.0385469i | ||||
\(817\) | −0.945439 | −0.0330767 | ||||||||
\(818\) | −21.5045 | − | 19.0005i | −0.751886 | − | 0.664338i | ||||
\(819\) | − | 15.1859i | − | 0.530637i | ||||||
\(820\) | −7.22016 | + | 0.896091i | −0.252139 | + | 0.0312928i | ||||
\(821\) | 8.69317i | 0.303394i | 0.988427 | + | 0.151697i | \(0.0484738\pi\) | ||||
−0.988427 | + | 0.151697i | \(0.951526\pi\) | |||||||
\(822\) | 8.97891 | + | 7.93343i | 0.313176 | + | 0.276710i | ||||
\(823\) | − | 18.9006i | − | 0.658835i | −0.944184 | − | 0.329418i | \(-0.893148\pi\) | ||
0.944184 | − | 0.329418i | \(-0.106852\pi\) | |||||||
\(824\) | −23.7188 | + | 34.6562i | −0.826284 | + | 1.20731i | ||||
\(825\) | 8.97750 | + | 33.8653i | 0.312557 | + | 1.17904i | ||||
\(826\) | −22.5677 | − | 19.9400i | −0.785231 | − | 0.693801i | ||||
\(827\) | −13.0032 | −0.452166 | −0.226083 | − | 0.974108i | \(-0.572592\pi\) | ||||
−0.226083 | + | 0.974108i | \(0.572592\pi\) | |||||||
\(828\) | −44.7133 | + | 5.54935i | −1.55390 | + | 0.192853i | ||||
\(829\) | 27.6999 | 0.962058 | 0.481029 | − | 0.876705i | \(-0.340263\pi\) | ||||
0.481029 | + | 0.876705i | \(0.340263\pi\) | |||||||
\(830\) | −4.03093 | + | 4.56213i | −0.139916 | + | 0.158354i | ||||
\(831\) | −46.8596 | −1.62554 | ||||||||
\(832\) | −7.45736 | + | 2.89616i | −0.258537 | + | 0.100406i | ||||
\(833\) | 1.26990i | 0.0439994i | ||||||||
\(834\) | 40.8953 | + | 36.1335i | 1.41609 | + | 1.25120i | ||||
\(835\) | −5.83020 | −0.201762 | ||||||||
\(836\) | 0.309199 | + | 0.768302i | 0.0106939 | + | 0.0265723i | ||||
\(837\) | −51.5178 | −1.78071 | ||||||||
\(838\) | 9.69980 | + | 8.57038i | 0.335074 | + | 0.296059i | ||||
\(839\) | − | 7.03051i | − | 0.242720i | −0.992609 | − | 0.121360i | \(-0.961274\pi\) | ||
0.992609 | − | 0.121360i | \(-0.0387256\pi\) | |||||||
\(840\) | −15.5977 | + | 22.7902i | −0.538171 | + | 0.786337i | ||||
\(841\) | −53.4802 | −1.84415 | ||||||||
\(842\) | 6.49589 | − | 7.35193i | 0.223863 | − | 0.253364i | ||||
\(843\) | −62.2142 | −2.14277 | ||||||||
\(844\) | 1.69521 | + | 13.6590i | 0.0583517 | + | 0.470163i | ||||
\(845\) | −1.09997 | −0.0378402 | ||||||||
\(846\) | −21.0752 | − | 18.6213i | −0.724581 | − | 0.640213i | ||||
\(847\) | 30.4324 | − | 17.3545i | 1.04567 | − | 0.596308i | ||||
\(848\) | 44.7888 | − | 11.2914i | 1.53805 | − | 0.387747i | ||||
\(849\) | − | 25.7279i | − | 0.882980i | ||||||
\(850\) | −1.62288 | − | 1.43391i | −0.0556642 | − | 0.0491828i | ||||
\(851\) | 13.5447i | 0.464307i | ||||||||
\(852\) | 8.58097 | + | 69.1403i | 0.293979 | + | 2.36871i | ||||
\(853\) | − | 35.2284i | − | 1.20620i | −0.797666 | − | 0.603099i | \(-0.793932\pi\) | ||
0.797666 | − | 0.603099i | \(-0.206068\pi\) | |||||||
\(854\) | −3.45991 | − | 3.05705i | −0.118396 | − | 0.104610i | ||||
\(855\) | 0.654845 | 0.0223952 | ||||||||
\(856\) | −28.0488 | − | 19.1966i | −0.958687 | − | 0.656128i | ||||
\(857\) | 35.6180i | 1.21669i | 0.793674 | + | 0.608343i | \(0.208166\pi\) | ||||
−0.793674 | + | 0.608343i | \(0.791834\pi\) | |||||||
\(858\) | 5.85663 | − | 11.6876i | 0.199942 | − | 0.399009i | ||||
\(859\) | − | 22.6595i | − | 0.773133i | −0.922262 | − | 0.386567i | \(-0.873661\pi\) | ||
0.922262 | − | 0.386567i | \(-0.126339\pi\) | |||||||
\(860\) | −2.05178 | − | 16.5320i | −0.0699650 | − | 0.563736i | ||||
\(861\) | −29.3561 | −1.00045 | ||||||||
\(862\) | −18.4020 | + | 20.8271i | −0.626775 | + | 0.709372i | ||||
\(863\) | − | 26.4145i | − | 0.899162i | −0.893240 | − | 0.449581i | \(-0.851573\pi\) | ||
0.893240 | − | 0.449581i | \(-0.148427\pi\) | |||||||
\(864\) | −24.7703 | − | 12.7921i | −0.842703 | − | 0.435195i | ||||
\(865\) | 25.2319i | 0.857909i | ||||||||
\(866\) | 11.2127 | − | 12.6903i | 0.381024 | − | 0.431235i | ||||
\(867\) | − | 46.9266i | − | 1.59371i | ||||||
\(868\) | 66.0784 | − | 8.20096i | 2.24285 | − | 0.278359i | ||||
\(869\) | −34.7533 | + | 9.21291i | −1.17893 | + | 0.312527i | ||||
\(870\) | 26.0721 | − | 29.5079i | 0.883928 | − | 1.00041i | ||||
\(871\) | 11.3802 | 0.385605 | ||||||||
\(872\) | 0.341834 | − | 0.499463i | 0.0115760 | − | 0.0169140i | ||||
\(873\) | −15.6504 | −0.529685 | ||||||||
\(874\) | −0.625165 | − | 0.552372i | −0.0211465 | − | 0.0186843i | ||||
\(875\) | −30.7934 | −1.04101 | ||||||||
\(876\) | 2.00322 | + | 16.1408i | 0.0676827 | + | 0.545346i | ||||
\(877\) | − | 20.8866i | − | 0.705291i | −0.935757 | − | 0.352645i | \(-0.885282\pi\) | ||
0.935757 | − | 0.352645i | \(-0.114718\pi\) | |||||||
\(878\) | 14.7359 | − | 16.6779i | 0.497314 | − | 0.562851i | ||||
\(879\) | −5.14338 | −0.173482 | ||||||||
\(880\) | −12.7635 | + | 7.07402i | −0.430259 | + | 0.238465i | ||||
\(881\) | 21.9853 | 0.740704 | 0.370352 | − | 0.928891i | \(-0.379237\pi\) | ||||
0.370352 | + | 0.928891i | \(0.379237\pi\) | |||||||
\(882\) | −14.0335 | + | 15.8828i | −0.472532 | + | 0.534803i | ||||
\(883\) | − | 17.3585i | − | 0.584161i | −0.956394 | − | 0.292080i | \(-0.905653\pi\) | ||
0.956394 | − | 0.292080i | \(-0.0943475\pi\) | |||||||
\(884\) | 0.0995253 | + | 0.801915i | 0.00334740 | + | 0.0269713i | ||||
\(885\) | −20.4986 | −0.689052 | ||||||||
\(886\) | −9.34358 | − | 8.25564i | −0.313904 | − | 0.277354i | ||||
\(887\) | 36.0313 | 1.20981 | 0.604906 | − | 0.796297i | \(-0.293211\pi\) | ||||
0.604906 | + | 0.796297i | \(0.293211\pi\) | |||||||
\(888\) | −12.7642 | + | 18.6501i | −0.428338 | + | 0.625856i | ||||
\(889\) | 69.8972 | 2.34428 | ||||||||
\(890\) | −4.64285 | + | 5.25469i | −0.155629 | + | 0.176138i | ||||
\(891\) | −1.82364 | + | 0.483437i | −0.0610943 | + | 0.0161958i | ||||
\(892\) | −12.5859 | + | 1.56203i | −0.421407 | + | 0.0523006i | ||||
\(893\) | − | 0.520711i | − | 0.0174249i | ||||||
\(894\) | 32.9683 | − | 37.3129i | 1.10262 | − | 1.24793i | ||||
\(895\) | − | 17.0667i | − | 0.570477i | ||||||
\(896\) | 33.8075 | + | 12.4644i | 1.12943 | + | 0.416406i | ||||
\(897\) | 13.1684i | 0.439679i | ||||||||
\(898\) | 7.10751 | − | 8.04415i | 0.237181 | − | 0.268437i | ||||
\(899\) | −94.9378 | −3.16635 | ||||||||
\(900\) | −4.45161 | − | 35.8684i | −0.148387 | − | 1.19561i | ||||
\(901\) | − | 4.66560i | − | 0.155434i | ||||||
\(902\) | −13.8682 | − | 6.94931i | −0.461760 | − | 0.231387i | ||||
\(903\) | − | 67.2166i | − | 2.23683i | ||||||
\(904\) | 31.5878 | + | 21.6188i | 1.05060 | + | 0.719030i | ||||
\(905\) | 16.7763 | 0.557664 | ||||||||
\(906\) | 25.8322 | + | 22.8244i | 0.858219 | + | 0.758290i | ||||
\(907\) | − | 34.0513i | − | 1.13065i | −0.824867 | − | 0.565327i | \(-0.808750\pi\) | ||
0.824867 | − | 0.565327i | \(-0.191250\pi\) | |||||||
\(908\) | −3.80186 | − | 30.6331i | −0.126169 | − | 1.01659i | ||||
\(909\) | − | 14.0339i | − | 0.465476i | ||||||
\(910\) | 3.71268 | + | 3.28039i | 0.123074 | + | 0.108744i | ||||
\(911\) | − | 46.4260i | − | 1.53816i | −0.639151 | − | 0.769082i | \(-0.720714\pi\) | ||
0.639151 | − | 0.769082i | \(-0.279286\pi\) | |||||||
\(912\) | −0.340266 | − | 1.34971i | −0.0112673 | − | 0.0446935i | ||||
\(913\) | −12.5462 | + | 3.32593i | −0.415219 | + | 0.110072i | ||||
\(914\) | −17.6341 | − | 15.5809i | −0.583286 | − | 0.515369i | ||||
\(915\) | −3.14269 | −0.103894 | ||||||||
\(916\) | −3.58506 | − | 28.8862i | −0.118454 | − | 0.954428i | ||||
\(917\) | −2.32221 | −0.0766863 | ||||||||
\(918\) | −1.86453 | + | 2.11024i | −0.0615387 | + | 0.0696483i | ||||
\(919\) | −26.2047 | −0.864415 | −0.432207 | − | 0.901774i | \(-0.642265\pi\) | ||||
−0.432207 | + | 0.901774i | \(0.642265\pi\) | |||||||
\(920\) | 8.30208 | − | 12.1304i | 0.273711 | − | 0.399928i | ||||
\(921\) | − | 96.9747i | − | 3.19543i | ||||||
\(922\) | 20.7797 | + | 18.3602i | 0.684344 | + | 0.604661i | ||||
\(923\) | 12.4986 | 0.411395 | ||||||||
\(924\) | −54.6229 | + | 21.9827i | −1.79696 | + | 0.723178i | ||||
\(925\) | −10.8654 | −0.357252 | ||||||||
\(926\) | 39.7451 | + | 35.1173i | 1.30610 | + | 1.15402i | ||||
\(927\) | 70.7969i | 2.32528i | ||||||||
\(928\) | −45.6471 | − | 23.5734i | −1.49844 | − | 0.773836i | ||||
\(929\) | −27.2396 | −0.893703 | −0.446852 | − | 0.894608i | \(-0.647455\pi\) | ||||
−0.446852 | + | 0.894608i | \(0.647455\pi\) | |||||||
\(930\) | 30.0100 | − | 33.9647i | 0.984066 | − | 1.11375i | ||||
\(931\) | −0.392421 | −0.0128611 | ||||||||
\(932\) | 15.9089 | − | 1.97445i | 0.521115 | − | 0.0646753i | ||||
\(933\) | −50.4601 | −1.65199 | ||||||||
\(934\) | 18.5059 | + | 16.3511i | 0.605532 | + | 0.535025i | ||||
\(935\) | 0.377702 | + | 1.42478i | 0.0123522 | + | 0.0465953i | ||||
\(936\) | −7.61708 | + | 11.1295i | −0.248972 | + | 0.363780i | ||||
\(937\) | 52.1689i | 1.70429i | 0.523310 | + | 0.852143i | \(0.324697\pi\) | ||||
−0.523310 | + | 0.852143i | \(0.675303\pi\) | |||||||
\(938\) | −38.4112 | − | 33.9387i | −1.25417 | − | 1.10814i | ||||
\(939\) | 86.9433i | 2.83729i | ||||||||
\(940\) | 9.10517 | − | 1.13004i | 0.296978 | − | 0.0368578i | ||||
\(941\) | 50.2788i | 1.63904i | 0.573050 | + | 0.819520i | \(0.305760\pi\) | ||||
−0.573050 | + | 0.819520i | \(0.694240\pi\) | |||||||
\(942\) | −32.1910 | − | 28.4427i | −1.04884 | − | 0.926715i | ||||
\(943\) | 15.6252 | 0.508826 | ||||||||
\(944\) | 6.53790 | + | 25.9335i | 0.212790 | + | 0.844064i | ||||
\(945\) | 17.2647i | 0.561621i | ||||||||
\(946\) | 15.9118 | − | 31.7539i | 0.517338 | − | 1.03241i | ||||
\(947\) | 37.1438i | 1.20701i | 0.797359 | + | 0.603505i | \(0.206230\pi\) | ||||
−0.797359 | + | 0.603505i | \(0.793770\pi\) | |||||||
\(948\) | 59.9679 | − | 7.44259i | 1.94767 | − | 0.241724i | ||||
\(949\) | 2.91778 | 0.0947153 | ||||||||
\(950\) | 0.443105 | − | 0.501498i | 0.0143762 | − | 0.0162707i | ||||
\(951\) | 61.1347i | 1.98243i | ||||||||
\(952\) | 2.05558 | − | 3.00347i | 0.0666219 | − | 0.0973431i | ||||
\(953\) | 22.0491i | 0.714242i | 0.934058 | + | 0.357121i | \(0.116242\pi\) | ||||
−0.934058 | + | 0.357121i | \(0.883758\pi\) | |||||||
\(954\) | 51.5589 | − | 58.3534i | 1.66928 | − | 1.88926i | ||||
\(955\) | − | 13.7854i | − | 0.446086i | ||||||
\(956\) | 1.98095 | + | 15.9613i | 0.0640685 | + | 0.516225i | ||||
\(957\) | 81.1491 | − | 21.5122i | 2.62318 | − | 0.695390i | ||||
\(958\) | 35.5113 | − | 40.1910i | 1.14732 | − | 1.29851i | ||||
\(959\) | −9.68113 | −0.312620 | ||||||||
\(960\) | 22.8627 | − | 8.87903i | 0.737890 | − | 0.286569i | ||||
\(961\) | −78.2769 | −2.52506 | ||||||||
\(962\) | 3.03823 | + | 2.68447i | 0.0979565 | + | 0.0865507i | ||||
\(963\) | −57.2989 | −1.84643 | ||||||||
\(964\) | 3.37099 | − | 0.418372i | 0.108572 | − | 0.0134749i | ||||
\(965\) | 4.39696i | 0.141543i | ||||||||
\(966\) | 39.2713 | − | 44.4465i | 1.26353 | − | 1.43004i | ||||
\(967\) | −15.8934 | −0.511098 | −0.255549 | − | 0.966796i | \(-0.582256\pi\) | ||||
−0.255549 | + | 0.966796i | \(0.582256\pi\) | |||||||
\(968\) | −31.0084 | − | 2.54569i | −0.996647 | − | 0.0818215i | ||||
\(969\) | −0.140598 | −0.00451666 | ||||||||
\(970\) | 3.38073 | − | 3.82625i | 0.108549 | − | 0.122854i | ||||
\(971\) | − | 35.6585i | − | 1.14433i | −0.820137 | − | 0.572167i | \(-0.806103\pi\) | ||
0.820137 | − | 0.572167i | \(-0.193897\pi\) | |||||||
\(972\) | 32.4911 | − | 4.03246i | 1.04215 | − | 0.129341i | ||||
\(973\) | −44.0936 | −1.41357 | ||||||||
\(974\) | 20.5391 | + | 18.1476i | 0.658114 | + | 0.581485i | ||||
\(975\) | −10.5635 | −0.338302 | ||||||||
\(976\) | 1.00234 | + | 3.97594i | 0.0320842 | + | 0.127267i | ||||
\(977\) | −42.8948 | −1.37233 | −0.686163 | − | 0.727448i | \(-0.740706\pi\) | ||||
−0.686163 | + | 0.727448i | \(0.740706\pi\) | |||||||
\(978\) | 40.7679 | − | 46.1404i | 1.30361 | − | 1.47541i | ||||
\(979\) | −14.4508 | + | 3.83083i | −0.461850 | + | 0.122434i | ||||
\(980\) | −0.851626 | − | 6.86189i | −0.0272042 | − | 0.219195i | ||||
\(981\) | − | 1.02032i | − | 0.0325763i | ||||||
\(982\) | −24.4426 | + | 27.6637i | −0.779996 | + | 0.882785i | ||||
\(983\) | − | 41.2474i | − | 1.31559i | −0.753198 | − | 0.657794i | \(-0.771490\pi\) | ||
0.753198 | − | 0.657794i | \(-0.228510\pi\) | |||||||
\(984\) | 21.5147 | + | 14.7247i | 0.685865 | + | 0.469408i | ||||
\(985\) | 4.70252i | 0.149835i | ||||||||
\(986\) | −3.43599 | + | 3.88879i | −0.109424 | + | 0.123844i | ||||
\(987\) | 37.0203 | 1.17837 | ||||||||
\(988\) | −0.247806 | + | 0.0307551i | −0.00788376 | + | 0.000978450i | ||||
\(989\) | 35.7770i | 1.13764i | ||||||||
\(990\) | −11.0211 | + | 21.9939i | −0.350273 | + | 0.699012i | ||||
\(991\) | 8.84218i | 0.280881i | 0.990089 | + | 0.140441i | \(0.0448519\pi\) | ||||
−0.990089 | + | 0.140441i | \(0.955148\pi\) | |||||||
\(992\) | −52.5416 | − | 27.1339i | −1.66820 | − | 0.861502i | ||||
\(993\) | 65.1784 | 2.06837 | ||||||||
\(994\) | −42.1858 | − | 37.2738i | −1.33805 | − | 1.18225i | ||||
\(995\) | − | 19.0096i | − | 0.602645i | ||||||
\(996\) | 21.6489 | − | 2.68683i | 0.685971 | − | 0.0851355i | ||||
\(997\) | − | 32.0386i | − | 1.01467i | −0.861748 | − | 0.507336i | \(-0.830630\pi\) | ||
0.861748 | − | 0.507336i | \(-0.169370\pi\) | |||||||
\(998\) | −8.47647 | − | 7.48949i | −0.268318 | − | 0.237076i | ||||
\(999\) | 14.1284i | 0.447002i |
(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 | 572.2.e.b.131.47 | yes | 64 | |
4.3 | odd | 2 | inner | 572.2.e.b.131.17 | ✓ | 64 | |
11.10 | odd | 2 | inner | 572.2.e.b.131.18 | yes | 64 | |
44.43 | even | 2 | inner | 572.2.e.b.131.48 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.e.b.131.17 | ✓ | 64 | 4.3 | odd | 2 | inner | |
572.2.e.b.131.18 | yes | 64 | 11.10 | odd | 2 | inner | |
572.2.e.b.131.47 | yes | 64 | 1.1 | even | 1 | trivial | |
572.2.e.b.131.48 | yes | 64 | 44.43 | even | 2 | inner |