Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(296,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.296");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.t (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Relative dimension: | \(52\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 296.38 | ||
Character | \(\chi\) | \(=\) | 429.296 |
Dual form | 429.2.t.a.329.38 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09482 | − | 0.632095i | 0.774156 | − | 0.446959i | −0.0601994 | − | 0.998186i | \(-0.519174\pi\) |
0.834355 | + | 0.551227i | \(0.185840\pi\) | |||||||
\(3\) | 0.177995 | − | 1.72288i | 0.102765 | − | 0.994706i | ||||
\(4\) | −0.200911 | + | 0.347987i | −0.100455 | + | 0.173994i | ||||
\(5\) | −4.13662 | −1.84995 | −0.924977 | − | 0.380024i | \(-0.875916\pi\) | ||||
−0.924977 | + | 0.380024i | \(0.875916\pi\) | |||||||
\(6\) | −0.894153 | − | 1.99876i | −0.365036 | − | 0.815989i | ||||
\(7\) | −0.620239 | + | 1.07429i | −0.234428 | + | 0.406042i | −0.959106 | − | 0.283046i | \(-0.908655\pi\) |
0.724678 | + | 0.689088i | \(0.241988\pi\) | |||||||
\(8\) | 3.03636i | 1.07352i | ||||||||
\(9\) | −2.93664 | − | 0.613327i | −0.978879 | − | 0.204442i | ||||
\(10\) | −4.52886 | + | 2.61474i | −1.43215 | + | 0.826853i | ||||
\(11\) | −2.00499 | + | 2.64197i | −0.604526 | + | 0.796585i | ||||
\(12\) | 0.563780 | + | 0.408085i | 0.162749 | + | 0.117804i | ||||
\(13\) | −2.90409 | − | 2.13688i | −0.805450 | − | 0.592664i | ||||
\(14\) | 1.56820i | 0.419119i | ||||||||
\(15\) | −0.736296 | + | 7.12691i | −0.190111 | + | 1.84016i | ||||
\(16\) | 1.51745 | + | 2.62830i | 0.379362 | + | 0.657074i | ||||
\(17\) | 2.43465 | − | 4.21694i | 0.590490 | − | 1.02276i | −0.403676 | − | 0.914902i | \(-0.632268\pi\) |
0.994166 | − | 0.107857i | \(-0.0343989\pi\) | |||||||
\(18\) | −3.60277 | + | 1.18475i | −0.849182 | + | 0.279248i | ||||
\(19\) | 1.67153 | − | 2.89518i | 0.383476 | − | 0.664200i | −0.608081 | − | 0.793875i | \(-0.708060\pi\) |
0.991556 | + | 0.129676i | \(0.0413936\pi\) | |||||||
\(20\) | 0.831091 | − | 1.43949i | 0.185838 | − | 0.321880i | ||||
\(21\) | 1.74047 | + | 1.25982i | 0.379801 | + | 0.274914i | ||||
\(22\) | −0.525121 | + | 4.15983i | −0.111956 | + | 0.886879i | ||||
\(23\) | −5.91424 | + | 3.41459i | −1.23320 | + | 0.711990i | −0.967696 | − | 0.252119i | \(-0.918873\pi\) |
−0.265507 | + | 0.964109i | \(0.585539\pi\) | |||||||
\(24\) | 5.23129 | + | 0.540456i | 1.06783 | + | 0.110320i | ||||
\(25\) | 12.1116 | 2.42233 | ||||||||
\(26\) | −4.53017 | − | 0.503840i | −0.888440 | − | 0.0988111i | ||||
\(27\) | −1.57939 | + | 4.95030i | −0.303955 | + | 0.952687i | ||||
\(28\) | −0.249225 | − | 0.431671i | −0.0470992 | − | 0.0815781i | ||||
\(29\) | −4.19202 | − | 7.26080i | −0.778439 | − | 1.34830i | −0.932841 | − | 0.360288i | \(-0.882678\pi\) |
0.154402 | − | 0.988008i | \(-0.450655\pi\) | |||||||
\(30\) | 3.69877 | + | 8.26810i | 0.675300 | + | 1.50954i | ||||
\(31\) | − | 0.243427i | − | 0.0437208i | −0.999761 | − | 0.0218604i | \(-0.993041\pi\) | ||
0.999761 | − | 0.0218604i | \(-0.00695893\pi\) | |||||||
\(32\) | −1.93646 | − | 1.11802i | −0.342321 | − | 0.197639i | ||||
\(33\) | 4.19493 | + | 3.92461i | 0.730244 | + | 0.683187i | ||||
\(34\) | − | 6.15573i | − | 1.05570i | ||||||
\(35\) | 2.56569 | − | 4.44391i | 0.433682 | − | 0.751159i | ||||
\(36\) | 0.803431 | − | 0.898689i | 0.133905 | − | 0.149781i | ||||
\(37\) | −0.983279 | + | 0.567696i | −0.161650 | + | 0.0933287i | −0.578643 | − | 0.815581i | \(-0.696417\pi\) |
0.416993 | + | 0.908910i | \(0.363084\pi\) | |||||||
\(38\) | − | 4.22627i | − | 0.685592i | ||||||
\(39\) | −4.19850 | + | 4.62305i | −0.672298 | + | 0.740280i | ||||
\(40\) | − | 12.5603i | − | 1.98595i | ||||||
\(41\) | −8.87337 | + | 5.12304i | −1.38579 | + | 0.800085i | −0.992837 | − | 0.119475i | \(-0.961879\pi\) |
−0.392950 | + | 0.919560i | \(0.628546\pi\) | |||||||
\(42\) | 2.70182 | + | 0.279131i | 0.416900 | + | 0.0430709i | ||||
\(43\) | 3.46891 | + | 2.00277i | 0.529003 | + | 0.305420i | 0.740610 | − | 0.671935i | \(-0.234536\pi\) |
−0.211607 | + | 0.977355i | \(0.567870\pi\) | |||||||
\(44\) | −0.516551 | − | 1.22851i | −0.0778730 | − | 0.185205i | ||||
\(45\) | 12.1478 | + | 2.53710i | 1.81088 | + | 0.378209i | ||||
\(46\) | −4.31669 | + | 7.47672i | −0.636461 | + | 1.10238i | ||||
\(47\) | −0.186546 | −0.0272105 | −0.0136052 | − | 0.999907i | \(-0.504331\pi\) | ||||
−0.0136052 | + | 0.999907i | \(0.504331\pi\) | |||||||
\(48\) | 4.79834 | − | 2.14656i | 0.692581 | − | 0.309829i | ||||
\(49\) | 2.73061 | + | 4.72955i | 0.390087 | + | 0.675650i | ||||
\(50\) | 13.2601 | − | 7.65571i | 1.87526 | − | 1.08268i | ||||
\(51\) | −6.83194 | − | 4.94521i | −0.956663 | − | 0.692468i | ||||
\(52\) | 1.32707 | − | 0.581265i | 0.184032 | − | 0.0806070i | ||||
\(53\) | − | 0.981050i | − | 0.134758i | −0.997727 | − | 0.0673788i | \(-0.978536\pi\) | ||
0.997727 | − | 0.0673788i | \(-0.0214636\pi\) | |||||||
\(54\) | 1.39991 | + | 6.41803i | 0.190504 | + | 0.873383i | ||||
\(55\) | 8.29387 | − | 10.9289i | 1.11834 | − | 1.47365i | ||||
\(56\) | −3.26192 | − | 1.88327i | −0.435892 | − | 0.251663i | ||||
\(57\) | −4.69053 | − | 3.39518i | −0.621275 | − | 0.449702i | ||||
\(58\) | −9.17904 | − | 5.29952i | −1.20527 | − | 0.695861i | ||||
\(59\) | 4.22819 | − | 7.32344i | 0.550464 | − | 0.953431i | −0.447778 | − | 0.894145i | \(-0.647784\pi\) |
0.998241 | − | 0.0592858i | \(-0.0188823\pi\) | |||||||
\(60\) | −2.33214 | − | 1.68809i | −0.301079 | − | 0.217932i | ||||
\(61\) | −0.321966 | − | 0.185887i | −0.0412236 | − | 0.0238004i | 0.479247 | − | 0.877680i | \(-0.340910\pi\) |
−0.520470 | + | 0.853880i | \(0.674243\pi\) | |||||||
\(62\) | −0.153869 | − | 0.266509i | −0.0195414 | − | 0.0338467i | ||||
\(63\) | 2.48030 | − | 2.77438i | 0.312489 | − | 0.349539i | ||||
\(64\) | −8.89657 | −1.11207 | ||||||||
\(65\) | 12.0131 | + | 8.83947i | 1.49004 | + | 1.09640i | ||||
\(66\) | 7.07343 | + | 1.64515i | 0.870679 | + | 0.202504i | ||||
\(67\) | −7.80314 | + | 4.50514i | −0.953305 | + | 0.550391i | −0.894106 | − | 0.447855i | \(-0.852188\pi\) |
−0.0591991 | + | 0.998246i | \(0.518855\pi\) | |||||||
\(68\) | 0.978296 | + | 1.69446i | 0.118636 | + | 0.205483i | ||||
\(69\) | 4.83022 | + | 10.7973i | 0.581490 | + | 1.29984i | ||||
\(70\) | − | 6.48706i | − | 0.775352i | ||||||
\(71\) | −5.06007 | + | 8.76429i | −0.600520 | + | 1.04013i | 0.392223 | + | 0.919870i | \(0.371706\pi\) |
−0.992742 | + | 0.120260i | \(0.961627\pi\) | |||||||
\(72\) | 1.86228 | − | 8.91669i | 0.219472 | − | 1.05084i | ||||
\(73\) | 1.57753 | 0.184636 | 0.0923182 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923182 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(74\) | −0.717676 | + | 1.24305i | −0.0834282 | + | 0.144502i | ||||
\(75\) | 2.15581 | − | 20.8669i | 0.248931 | − | 2.40950i | ||||
\(76\) | 0.671658 | + | 1.16334i | 0.0770444 | + | 0.133445i | ||||
\(77\) | −1.59467 | − | 3.79258i | −0.181729 | − | 0.432205i | ||||
\(78\) | −1.67440 | + | 7.71527i | −0.189589 | + | 0.873582i | ||||
\(79\) | − | 7.03179i | − | 0.791139i | −0.918436 | − | 0.395569i | \(-0.870547\pi\) | ||
0.918436 | − | 0.395569i | \(-0.129453\pi\) | |||||||
\(80\) | −6.27711 | − | 10.8723i | −0.701802 | − | 1.21556i | ||||
\(81\) | 8.24766 | + | 3.60223i | 0.916407 | + | 0.400248i | ||||
\(82\) | −6.47650 | + | 11.2176i | −0.715210 | + | 1.23878i | ||||
\(83\) | 4.69182i | 0.514994i | 0.966279 | + | 0.257497i | \(0.0828978\pi\) | ||||
−0.966279 | + | 0.257497i | \(0.917102\pi\) | |||||||
\(84\) | −0.788078 | + | 0.352550i | −0.0859864 | + | 0.0384664i | ||||
\(85\) | −10.0712 | + | 17.4439i | −1.09238 | + | 1.89206i | ||||
\(86\) | 5.06378 | 0.546041 | ||||||||
\(87\) | −13.2556 | + | 5.92998i | −1.42115 | + | 0.635760i | ||||
\(88\) | −8.02199 | − | 6.08786i | −0.855147 | − | 0.648968i | ||||
\(89\) | 4.62316 | + | 8.00755i | 0.490054 | + | 0.848799i | 0.999934 | − | 0.0114464i | \(-0.00364357\pi\) |
−0.509880 | + | 0.860245i | \(0.670310\pi\) | |||||||
\(90\) | 14.9033 | − | 4.90087i | 1.57095 | − | 0.516597i | ||||
\(91\) | 4.09685 | − | 1.79445i | 0.429467 | − | 0.188109i | ||||
\(92\) | − | 2.74411i | − | 0.286093i | ||||||
\(93\) | −0.419396 | − | 0.0433287i | −0.0434893 | − | 0.00449297i | ||||
\(94\) | −0.204234 | + | 0.117915i | −0.0210652 | + | 0.0121620i | ||||
\(95\) | −6.91450 | + | 11.9763i | −0.709413 | + | 1.22874i | ||||
\(96\) | −2.27089 | + | 3.13729i | −0.231772 | + | 0.320198i | ||||
\(97\) | −5.14746 | − | 2.97189i | −0.522645 | − | 0.301749i | 0.215371 | − | 0.976532i | \(-0.430904\pi\) |
−0.738016 | + | 0.674783i | \(0.764237\pi\) | |||||||
\(98\) | 5.97905 | + | 3.45201i | 0.603976 | + | 0.348705i | ||||
\(99\) | 7.50831 | − | 6.52881i | 0.754613 | − | 0.656170i | ||||
\(100\) | −2.43336 | + | 4.21470i | −0.243336 | + | 0.421470i | ||||
\(101\) | −6.80761 | − | 11.7911i | −0.677383 | − | 1.17326i | −0.975766 | − | 0.218815i | \(-0.929781\pi\) |
0.298384 | − | 0.954446i | \(-0.403552\pi\) | |||||||
\(102\) | −10.6056 | − | 1.09569i | −1.05011 | − | 0.108489i | ||||
\(103\) | −2.45798 | −0.242192 | −0.121096 | − | 0.992641i | \(-0.538641\pi\) | ||||
−0.121096 | + | 0.992641i | \(0.538641\pi\) | |||||||
\(104\) | 6.48834 | − | 8.81787i | 0.636234 | − | 0.864663i | ||||
\(105\) | −7.19965 | − | 5.21138i | −0.702614 | − | 0.508578i | ||||
\(106\) | −0.620117 | − | 1.07407i | −0.0602311 | − | 0.104323i | ||||
\(107\) | −3.86753 | − | 6.69877i | −0.373889 | − | 0.647594i | 0.616271 | − | 0.787534i | \(-0.288642\pi\) |
−0.990160 | + | 0.139940i | \(0.955309\pi\) | |||||||
\(108\) | −1.40533 | − | 1.54418i | −0.135228 | − | 0.148589i | ||||
\(109\) | 10.0251 | 0.960234 | 0.480117 | − | 0.877205i | \(-0.340594\pi\) | ||||
0.480117 | + | 0.877205i | \(0.340594\pi\) | |||||||
\(110\) | 2.17223 | − | 17.2077i | 0.207114 | − | 1.64069i | ||||
\(111\) | 0.803055 | + | 1.79512i | 0.0762226 | + | 0.170385i | ||||
\(112\) | −3.76472 | −0.355733 | ||||||||
\(113\) | 3.12909 | + | 1.80658i | 0.294360 | + | 0.169949i | 0.639906 | − | 0.768453i | \(-0.278973\pi\) |
−0.345546 | + | 0.938402i | \(0.612306\pi\) | |||||||
\(114\) | −7.28136 | − | 0.752254i | −0.681962 | − | 0.0704550i | ||||
\(115\) | 24.4650 | − | 14.1249i | 2.28137 | − | 1.31715i | ||||
\(116\) | 3.36889 | 0.312794 | ||||||||
\(117\) | 7.21765 | + | 8.05640i | 0.667272 | + | 0.744814i | ||||
\(118\) | − | 10.6905i | − | 0.984139i | ||||||
\(119\) | 3.02014 | + | 5.23103i | 0.276855 | + | 0.479528i | ||||
\(120\) | −21.6399 | − | 2.23566i | −1.97544 | − | 0.204087i | ||||
\(121\) | −2.96006 | − | 10.5942i | −0.269097 | − | 0.963113i | ||||
\(122\) | −0.469994 | −0.0425513 | ||||||||
\(123\) | 7.24698 | + | 16.1996i | 0.653438 | + | 1.46067i | ||||
\(124\) | 0.0847095 | + | 0.0489071i | 0.00760714 | + | 0.00439198i | ||||
\(125\) | −29.4182 | −2.63124 | ||||||||
\(126\) | 0.961820 | − | 4.60524i | 0.0856857 | − | 0.410267i | ||||
\(127\) | −1.33931 | + | 0.773249i | −0.118844 | + | 0.0686148i | −0.558244 | − | 0.829677i | \(-0.688525\pi\) |
0.439399 | + | 0.898292i | \(0.355191\pi\) | |||||||
\(128\) | −5.86723 | + | 3.38745i | −0.518595 | + | 0.299411i | ||||
\(129\) | 4.06799 | − | 5.62003i | 0.358166 | − | 0.494816i | ||||
\(130\) | 18.7396 | + | 2.08420i | 1.64357 | + | 0.182796i | ||||
\(131\) | 21.6050 | 1.88764 | 0.943818 | − | 0.330465i | \(-0.107206\pi\) | ||||
0.943818 | + | 0.330465i | \(0.107206\pi\) | |||||||
\(132\) | −2.20852 | + | 0.671288i | −0.192227 | + | 0.0584281i | ||||
\(133\) | 2.07350 | + | 3.59141i | 0.179795 | + | 0.311415i | ||||
\(134\) | −5.69536 | + | 9.86466i | −0.492004 | + | 0.852177i | ||||
\(135\) | 6.53336 | − | 20.4775i | 0.562302 | − | 1.76243i | ||||
\(136\) | 12.8042 | + | 7.39249i | 1.09795 | + | 0.633901i | ||||
\(137\) | −2.24066 | + | 3.88094i | −0.191433 | + | 0.331571i | −0.945725 | − | 0.324967i | \(-0.894647\pi\) |
0.754293 | + | 0.656538i | \(0.227980\pi\) | |||||||
\(138\) | 12.1132 | + | 8.76796i | 1.03114 | + | 0.746378i | ||||
\(139\) | 0.617096 | + | 0.356281i | 0.0523414 | + | 0.0302193i | 0.525942 | − | 0.850520i | \(-0.323713\pi\) |
−0.473601 | + | 0.880740i | \(0.657046\pi\) | |||||||
\(140\) | 1.03095 | + | 1.78566i | 0.0871313 | + | 0.150916i | ||||
\(141\) | −0.0332041 | + | 0.321396i | −0.00279629 | + | 0.0270664i | ||||
\(142\) | 12.7938i | 1.07363i | ||||||||
\(143\) | 11.4682 | − | 3.38812i | 0.959023 | − | 0.283329i | ||||
\(144\) | −2.84419 | − | 8.64905i | −0.237016 | − | 0.720754i | ||||
\(145\) | 17.3408 | + | 30.0352i | 1.44008 | + | 2.49429i | ||||
\(146\) | 1.72712 | − | 0.997152i | 0.142937 | − | 0.0825249i | ||||
\(147\) | 8.63448 | − | 3.86268i | 0.712160 | − | 0.318588i | ||||
\(148\) | − | 0.456225i | − | 0.0375014i | ||||||
\(149\) | 3.66256 | + | 2.11458i | 0.300049 | + | 0.173233i | 0.642465 | − | 0.766315i | \(-0.277912\pi\) |
−0.342416 | + | 0.939548i | \(0.611245\pi\) | |||||||
\(150\) | −10.8297 | − | 24.2082i | −0.884238 | − | 1.97659i | ||||
\(151\) | −0.620315 | −0.0504805 | −0.0252403 | − | 0.999681i | \(-0.508035\pi\) | ||||
−0.0252403 | + | 0.999681i | \(0.508035\pi\) | |||||||
\(152\) | 8.79081 | + | 5.07538i | 0.713029 | + | 0.411667i | ||||
\(153\) | −9.73606 | + | 10.8904i | −0.787114 | + | 0.880436i | ||||
\(154\) | −4.14315 | − | 3.14422i | −0.333864 | − | 0.253369i | ||||
\(155\) | 1.00697i | 0.0808814i | ||||||||
\(156\) | −0.765239 | − | 2.38985i | −0.0612682 | − | 0.191341i | ||||
\(157\) | −18.6856 | −1.49127 | −0.745636 | − | 0.666354i | \(-0.767854\pi\) | ||||
−0.745636 | + | 0.666354i | \(0.767854\pi\) | |||||||
\(158\) | −4.44477 | − | 7.69856i | −0.353607 | − | 0.612465i | ||||
\(159\) | −1.69023 | − | 0.174622i | −0.134044 | − | 0.0138484i | ||||
\(160\) | 8.01041 | + | 4.62481i | 0.633278 | + | 0.365623i | ||||
\(161\) | − | 8.47144i | − | 0.667643i | ||||||
\(162\) | 11.3067 | − | 1.26950i | 0.888336 | − | 0.0997417i | ||||
\(163\) | 0.0847175 | + | 0.0489117i | 0.00663559 | + | 0.00383106i | 0.503314 | − | 0.864104i | \(-0.332114\pi\) |
−0.496679 | + | 0.867935i | \(0.665447\pi\) | |||||||
\(164\) | − | 4.11709i | − | 0.321491i | ||||||
\(165\) | −17.3528 | − | 16.2346i | −1.35092 | − | 1.26386i | ||||
\(166\) | 2.96568 | + | 5.13671i | 0.230181 | + | 0.398686i | ||||
\(167\) | −1.29557 | + | 0.747996i | −0.100254 | + | 0.0578816i | −0.549289 | − | 0.835633i | \(-0.685101\pi\) |
0.449035 | + | 0.893514i | \(0.351768\pi\) | |||||||
\(168\) | −3.82525 | + | 5.28469i | −0.295125 | + | 0.407722i | ||||
\(169\) | 3.86748 | + | 12.4114i | 0.297499 | + | 0.954722i | ||||
\(170\) | 25.4639i | 1.95300i | ||||||||
\(171\) | −6.68437 | + | 7.47689i | −0.511167 | + | 0.571772i | ||||
\(172\) | −1.39388 | + | 0.804757i | −0.106282 | + | 0.0613622i | ||||
\(173\) | 2.66933 | − | 4.62341i | 0.202945 | − | 0.351511i | −0.746531 | − | 0.665351i | \(-0.768282\pi\) |
0.949476 | + | 0.313839i | \(0.101615\pi\) | |||||||
\(174\) | −10.7643 | + | 14.8711i | −0.816036 | + | 1.12738i | ||||
\(175\) | −7.51211 | + | 13.0114i | −0.567862 | + | 0.983567i | ||||
\(176\) | −9.98636 | − | 1.26064i | −0.752750 | − | 0.0950242i | ||||
\(177\) | −11.8648 | − | 8.58820i | −0.891815 | − | 0.645529i | ||||
\(178\) | 10.1231 | + | 5.84456i | 0.758757 | + | 0.438068i | ||||
\(179\) | −3.89062 | + | 2.24625i | −0.290799 | + | 0.167893i | −0.638302 | − | 0.769786i | \(-0.720363\pi\) |
0.347503 | + | 0.937679i | \(0.387030\pi\) | |||||||
\(180\) | −3.32349 | + | 3.71753i | −0.247718 | + | 0.277089i | ||||
\(181\) | −14.8734 | −1.10553 | −0.552767 | − | 0.833336i | \(-0.686428\pi\) | ||||
−0.552767 | + | 0.833336i | \(0.686428\pi\) | |||||||
\(182\) | 3.35106 | − | 4.55420i | 0.248397 | − | 0.337580i | ||||
\(183\) | −0.377570 | + | 0.521623i | −0.0279108 | + | 0.0385595i | ||||
\(184\) | −10.3679 | − | 17.9578i | −0.764333 | − | 1.32386i | ||||
\(185\) | 4.06745 | − | 2.34834i | 0.299045 | − | 0.172654i | ||||
\(186\) | −0.486551 | + | 0.217661i | −0.0356757 | + | 0.0159597i | ||||
\(187\) | 6.25961 | + | 14.8872i | 0.457748 | + | 1.08866i | ||||
\(188\) | 0.0374790 | − | 0.0649156i | 0.00273344 | − | 0.00473446i | ||||
\(189\) | −4.33844 | − | 4.76709i | −0.315575 | − | 0.346755i | ||||
\(190\) | 17.4825i | 1.26831i | ||||||||
\(191\) | 10.8325 | + | 6.25412i | 0.783809 | + | 0.452532i | 0.837778 | − | 0.546010i | \(-0.183854\pi\) |
−0.0539697 | + | 0.998543i | \(0.517187\pi\) | |||||||
\(192\) | −1.58354 | + | 15.3277i | −0.114282 | + | 1.10618i | ||||
\(193\) | −12.2549 | − | 21.2262i | −0.882130 | − | 1.52789i | −0.848968 | − | 0.528445i | \(-0.822775\pi\) |
−0.0331628 | − | 0.999450i | \(-0.510558\pi\) | |||||||
\(194\) | −7.51407 | −0.539479 | ||||||||
\(195\) | 17.3676 | − | 19.1238i | 1.24372 | − | 1.36948i | ||||
\(196\) | −2.19443 | −0.156745 | ||||||||
\(197\) | −7.62514 | + | 4.40238i | −0.543269 | + | 0.313656i | −0.746403 | − | 0.665495i | \(-0.768221\pi\) |
0.203134 | + | 0.979151i | \(0.434887\pi\) | |||||||
\(198\) | 4.09343 | − | 11.8938i | 0.290907 | − | 0.845259i | ||||
\(199\) | −0.745741 | + | 1.29166i | −0.0528642 | + | 0.0915635i | −0.891247 | − | 0.453519i | \(-0.850168\pi\) |
0.838382 | + | 0.545083i | \(0.183502\pi\) | |||||||
\(200\) | 36.7753i | 2.60041i | ||||||||
\(201\) | 6.37291 | + | 14.2458i | 0.449510 | + | 1.00482i | ||||
\(202\) | −14.9062 | − | 8.60612i | −1.04880 | − | 0.605524i | ||||
\(203\) | 10.4002 | 0.729953 | ||||||||
\(204\) | 3.09348 | − | 1.38388i | 0.216587 | − | 0.0968912i | ||||
\(205\) | 36.7058 | − | 21.1921i | 2.56364 | − | 1.48012i | ||||
\(206\) | −2.69105 | + | 1.55368i | −0.187494 | + | 0.108250i | ||||
\(207\) | 19.4622 | − | 6.40004i | 1.35272 | − | 0.444833i | ||||
\(208\) | 1.20955 | − | 10.8754i | 0.0838672 | − | 0.754075i | ||||
\(209\) | 4.29759 | + | 10.2209i | 0.297271 | + | 0.706997i | ||||
\(210\) | −11.1764 | − | 1.15466i | −0.771247 | − | 0.0796792i | ||||
\(211\) | −13.9078 | + | 8.02969i | −0.957455 | + | 0.552787i | −0.895389 | − | 0.445285i | \(-0.853102\pi\) |
−0.0620662 | + | 0.998072i | \(0.519769\pi\) | |||||||
\(212\) | 0.341393 | + | 0.197103i | 0.0234470 | + | 0.0135371i | ||||
\(213\) | 14.1992 | + | 10.2779i | 0.972911 | + | 0.704229i | ||||
\(214\) | −8.46852 | − | 4.88930i | −0.578896 | − | 0.334226i | ||||
\(215\) | −14.3496 | − | 8.28472i | −0.978631 | − | 0.565013i | ||||
\(216\) | −15.0309 | − | 4.79561i | −1.02272 | − | 0.326300i | ||||
\(217\) | 0.261510 | + | 0.150983i | 0.0177525 | + | 0.0102494i | ||||
\(218\) | 10.9757 | − | 6.33684i | 0.743370 | − | 0.429185i | ||||
\(219\) | 0.280792 | − | 2.71790i | 0.0189742 | − | 0.183659i | ||||
\(220\) | 2.13678 | + | 5.08188i | 0.144061 | + | 0.342621i | ||||
\(221\) | −16.0816 | + | 7.04382i | −1.08176 | + | 0.473819i | ||||
\(222\) | 2.01389 | + | 1.45773i | 0.135163 | + | 0.0978362i | ||||
\(223\) | −10.6584 | + | 6.15361i | −0.713737 | + | 0.412076i | −0.812443 | − | 0.583040i | \(-0.801863\pi\) |
0.0987062 | + | 0.995117i | \(0.468530\pi\) | |||||||
\(224\) | 2.40214 | − | 1.38687i | 0.160500 | − | 0.0926645i | ||||
\(225\) | −35.5675 | − | 7.42839i | −2.37117 | − | 0.495226i | ||||
\(226\) | 4.56773 | 0.303841 | ||||||||
\(227\) | 4.40336 | + | 2.54228i | 0.292262 | + | 0.168737i | 0.638961 | − | 0.769239i | \(-0.279364\pi\) |
−0.346700 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(228\) | 2.12386 | − | 0.950117i | 0.140656 | − | 0.0629230i | ||||
\(229\) | − | 7.54764i | − | 0.498762i | −0.968405 | − | 0.249381i | \(-0.919773\pi\) | ||
0.968405 | − | 0.249381i | \(-0.0802272\pi\) | |||||||
\(230\) | 17.8565 | − | 30.9284i | 1.17742 | − | 2.03936i | ||||
\(231\) | −6.81801 | + | 2.07236i | −0.448592 | + | 0.136351i | ||||
\(232\) | 22.0464 | − | 12.7285i | 1.44742 | − | 0.835667i | ||||
\(233\) | −18.0225 | −1.18070 | −0.590348 | − | 0.807149i | \(-0.701009\pi\) | ||||
−0.590348 | + | 0.807149i | \(0.701009\pi\) | |||||||
\(234\) | 12.9945 | + | 4.25807i | 0.849474 | + | 0.278359i | ||||
\(235\) | 0.771669 | 0.0503382 | ||||||||
\(236\) | 1.69898 | + | 2.94271i | 0.110594 | + | 0.191554i | ||||
\(237\) | −12.1149 | − | 1.25162i | −0.786950 | − | 0.0813015i | ||||
\(238\) | 6.61302 | + | 3.81803i | 0.428658 | + | 0.247486i | ||||
\(239\) | − | 17.3654i | − | 1.12327i | −0.827384 | − | 0.561637i | \(-0.810172\pi\) | ||
0.827384 | − | 0.561637i | \(-0.189828\pi\) | |||||||
\(240\) | −19.8489 | + | 8.87951i | −1.28124 | + | 0.573170i | ||||
\(241\) | −7.23204 | + | 12.5263i | −0.465856 | + | 0.806887i | −0.999240 | − | 0.0389866i | \(-0.987587\pi\) |
0.533383 | + | 0.845874i | \(0.320920\pi\) | |||||||
\(242\) | −9.93732 | − | 9.72776i | −0.638795 | − | 0.625324i | ||||
\(243\) | 7.67426 | − | 13.5686i | 0.492304 | − | 0.870423i | ||||
\(244\) | 0.129373 | − | 0.0746935i | 0.00828225 | − | 0.00478176i | ||||
\(245\) | −11.2955 | − | 19.5644i | −0.721642 | − | 1.24992i | ||||
\(246\) | 18.1739 | + | 13.1549i | 1.15872 | + | 0.838727i | ||||
\(247\) | −11.0409 | + | 4.83600i | −0.702518 | + | 0.307707i | ||||
\(248\) | 0.739132 | 0.0469349 | ||||||||
\(249\) | 8.08345 | + | 0.835119i | 0.512268 | + | 0.0529235i | ||||
\(250\) | −32.2076 | + | 18.5951i | −2.03699 | + | 1.17606i | ||||
\(251\) | −17.1739 | − | 9.91535i | −1.08401 | − | 0.625851i | −0.152032 | − | 0.988376i | \(-0.548582\pi\) |
−0.931974 | + | 0.362524i | \(0.881915\pi\) | |||||||
\(252\) | 0.467129 | + | 1.42052i | 0.0294263 | + | 0.0894841i | ||||
\(253\) | 2.83671 | − | 22.4715i | 0.178342 | − | 1.41277i | ||||
\(254\) | −0.977535 | + | 1.69314i | −0.0613360 | + | 0.106237i | ||||
\(255\) | 28.2611 | + | 20.4565i | 1.76978 | + | 1.28103i | ||||
\(256\) | 4.61419 | − | 7.99201i | 0.288387 | − | 0.499500i | ||||
\(257\) | −13.7477 | + | 7.93724i | −0.857558 | + | 0.495112i | −0.863194 | − | 0.504873i | \(-0.831539\pi\) |
0.00563556 | + | 0.999984i | \(0.498206\pi\) | |||||||
\(258\) | 0.901325 | − | 8.72428i | 0.0561140 | − | 0.543150i | ||||
\(259\) | − | 1.40843i | − | 0.0875156i | ||||||
\(260\) | −5.48959 | + | 2.40447i | −0.340450 | + | 0.149119i | ||||
\(261\) | 7.85721 | + | 23.8934i | 0.486349 | + | 1.47896i | ||||
\(262\) | 23.6536 | − | 13.6564i | 1.46132 | − | 0.843696i | ||||
\(263\) | 7.30094 | + | 12.6456i | 0.450195 | + | 0.779761i | 0.998398 | − | 0.0565844i | \(-0.0180210\pi\) |
−0.548202 | + | 0.836346i | \(0.684688\pi\) | |||||||
\(264\) | −11.9165 | + | 12.7373i | −0.733412 | + | 0.783928i | ||||
\(265\) | 4.05823i | 0.249295i | ||||||||
\(266\) | 4.54023 | + | 2.62130i | 0.278379 | + | 0.160722i | ||||
\(267\) | 14.6190 | − | 6.53986i | 0.894666 | − | 0.400233i | ||||
\(268\) | − | 3.62053i | − | 0.221159i | ||||||
\(269\) | 15.5837 | + | 8.99726i | 0.950155 | + | 0.548573i | 0.893129 | − | 0.449800i | \(-0.148505\pi\) |
0.0570263 | + | 0.998373i | \(0.481838\pi\) | |||||||
\(270\) | −5.79090 | − | 26.5490i | −0.352423 | − | 1.61572i | ||||
\(271\) | 1.25223 | + | 2.16892i | 0.0760674 | + | 0.131753i | 0.901550 | − | 0.432675i | \(-0.142430\pi\) |
−0.825483 | + | 0.564428i | \(0.809097\pi\) | |||||||
\(272\) | 14.7778 | 0.896039 | ||||||||
\(273\) | −2.36240 | − | 7.37779i | −0.142979 | − | 0.446524i | ||||
\(274\) | 5.66525i | 0.342250i | ||||||||
\(275\) | −24.2837 | + | 31.9987i | −1.46436 | + | 1.92959i | ||||
\(276\) | −4.72777 | − | 0.488436i | −0.284578 | − | 0.0294004i | ||||
\(277\) | −17.0065 | − | 9.81872i | −1.02182 | − | 0.589950i | −0.107191 | − | 0.994238i | \(-0.534186\pi\) |
−0.914631 | + | 0.404289i | \(0.867519\pi\) | |||||||
\(278\) | 0.900814 | 0.0540272 | ||||||||
\(279\) | −0.149300 | + | 0.714856i | −0.00893837 | + | 0.0427973i | ||||
\(280\) | 13.4933 | + | 7.79038i | 0.806380 | + | 0.465564i | ||||
\(281\) | 13.4868i | 0.804555i | 0.915518 | + | 0.402278i | \(0.131781\pi\) | ||||
−0.915518 | + | 0.402278i | \(0.868219\pi\) | |||||||
\(282\) | 0.166800 | + | 0.372859i | 0.00993282 | + | 0.0222035i | ||||
\(283\) | −25.4622 | + | 14.7006i | −1.51357 | + | 0.873861i | −0.513698 | + | 0.857971i | \(0.671725\pi\) |
−0.999874 | + | 0.0158900i | \(0.994942\pi\) | |||||||
\(284\) | −2.03324 | − | 3.52168i | −0.120651 | − | 0.208973i | ||||
\(285\) | 19.4029 | + | 14.0446i | 1.14933 | + | 0.831928i | ||||
\(286\) | 10.4141 | − | 10.9584i | 0.615797 | − | 0.647984i | ||||
\(287\) | − | 12.7100i | − | 0.750250i | ||||||
\(288\) | 5.00097 | + | 4.47089i | 0.294685 | + | 0.263450i | ||||
\(289\) | −3.35508 | − | 5.81117i | −0.197358 | − | 0.341833i | ||||
\(290\) | 37.9702 | + | 21.9221i | 2.22969 | + | 1.28731i | ||||
\(291\) | −6.03643 | + | 8.33948i | −0.353862 | + | 0.488869i | ||||
\(292\) | −0.316943 | + | 0.548962i | −0.0185477 | + | 0.0321256i | ||||
\(293\) | 6.41037 | + | 3.70103i | 0.374498 | + | 0.216216i | 0.675422 | − | 0.737432i | \(-0.263962\pi\) |
−0.300924 | + | 0.953648i | \(0.597295\pi\) | |||||||
\(294\) | 7.01164 | − | 9.68676i | 0.408927 | − | 0.564943i | ||||
\(295\) | −17.4904 | + | 30.2943i | −1.01833 | + | 1.76380i | ||||
\(296\) | −1.72373 | − | 2.98559i | −0.100190 | − | 0.173534i | ||||
\(297\) | −9.91192 | − | 14.0980i | −0.575148 | − | 0.818050i | ||||
\(298\) | 5.34647 | 0.309713 | ||||||||
\(299\) | 24.4720 | + | 2.72175i | 1.41525 | + | 0.157403i | ||||
\(300\) | 6.82830 | + | 4.94258i | 0.394232 | + | 0.285360i | ||||
\(301\) | −4.30310 | + | 2.48440i | −0.248027 | + | 0.143198i | ||||
\(302\) | −0.679134 | + | 0.392098i | −0.0390798 | + | 0.0225627i | ||||
\(303\) | −21.5264 | + | 9.62994i | −1.23666 | + | 0.553226i | ||||
\(304\) | 10.1459 | 0.581905 | ||||||||
\(305\) | 1.33185 | + | 0.768946i | 0.0762617 | + | 0.0440297i | ||||
\(306\) | −3.77548 | + | 18.0772i | −0.215830 | + | 1.03340i | ||||
\(307\) | 13.9747 | 0.797580 | 0.398790 | − | 0.917042i | \(-0.369430\pi\) | ||||
0.398790 | + | 0.917042i | \(0.369430\pi\) | |||||||
\(308\) | 1.64016 | + | 0.207047i | 0.0934566 | + | 0.0117976i | ||||
\(309\) | −0.437507 | + | 4.23481i | −0.0248889 | + | 0.240910i | ||||
\(310\) | 0.636498 | + | 1.10245i | 0.0361507 | + | 0.0626148i | ||||
\(311\) | 24.7334i | 1.40250i | 0.712916 | + | 0.701250i | \(0.247374\pi\) | ||||
−0.712916 | + | 0.701250i | \(0.752626\pi\) | |||||||
\(312\) | −14.0372 | − | 12.7482i | −0.794702 | − | 0.721723i | ||||
\(313\) | 7.09716 | 0.401155 | 0.200578 | − | 0.979678i | \(-0.435718\pi\) | ||||
0.200578 | + | 0.979678i | \(0.435718\pi\) | |||||||
\(314\) | −20.4574 | + | 11.8111i | −1.15448 | + | 0.666537i | ||||
\(315\) | −10.2601 | + | 11.4765i | −0.578090 | + | 0.646630i | ||||
\(316\) | 2.44698 | + | 1.41276i | 0.137653 | + | 0.0794741i | ||||
\(317\) | −0.369289 | −0.0207413 | −0.0103707 | − | 0.999946i | \(-0.503301\pi\) | ||||
−0.0103707 | + | 0.999946i | \(0.503301\pi\) | |||||||
\(318\) | −1.96088 | + | 0.877209i | −0.109961 | + | 0.0491914i | ||||
\(319\) | 27.5878 | + | 3.48258i | 1.54462 | + | 0.194987i | ||||
\(320\) | 36.8017 | 2.05728 | ||||||||
\(321\) | −12.2296 | + | 5.47096i | −0.682588 | + | 0.305359i | ||||
\(322\) | −5.35476 | − | 9.27471i | −0.298409 | − | 0.516860i | ||||
\(323\) | −8.13921 | − | 14.0975i | −0.452878 | − | 0.784407i | ||||
\(324\) | −2.91058 | + | 2.14636i | −0.161699 | + | 0.119242i | ||||
\(325\) | −35.1733 | − | 25.8811i | −1.95106 | − | 1.43563i | ||||
\(326\) | 0.123667 | 0.00684931 | ||||||||
\(327\) | 1.78442 | − | 17.2721i | 0.0986786 | − | 0.955150i | ||||
\(328\) | −15.5554 | − | 26.9427i | −0.858903 | − | 1.48766i | ||||
\(329\) | 0.115703 | − | 0.200403i | 0.00637891 | − | 0.0110486i | ||||
\(330\) | −29.2601 | − | 6.80536i | −1.61072 | − | 0.374623i | ||||
\(331\) | 4.03836 | + | 2.33155i | 0.221968 | + | 0.128153i | 0.606861 | − | 0.794808i | \(-0.292428\pi\) |
−0.384893 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(332\) | −1.63270 | − | 0.942637i | −0.0896058 | − | 0.0517339i | ||||
\(333\) | 3.23571 | − | 1.06405i | 0.177316 | − | 0.0583093i | ||||
\(334\) | −0.945609 | + | 1.63784i | −0.0517414 | + | 0.0896188i | ||||
\(335\) | 32.2786 | − | 18.6361i | 1.76357 | − | 1.01820i | ||||
\(336\) | −0.670100 | + | 6.48617i | −0.0365570 | + | 0.353850i | ||||
\(337\) | − | 14.0674i | − | 0.766302i | −0.923686 | − | 0.383151i | \(-0.874839\pi\) | ||
0.923686 | − | 0.383151i | \(-0.125161\pi\) | |||||||
\(338\) | 12.0794 | + | 11.1436i | 0.657032 | + | 0.606134i | ||||
\(339\) | 3.66948 | − | 5.06949i | 0.199299 | − | 0.275337i | ||||
\(340\) | −4.04684 | − | 7.00933i | −0.219471 | − | 0.380134i | ||||
\(341\) | 0.643128 | + | 0.488068i | 0.0348273 | + | 0.0264303i | ||||
\(342\) | −2.59209 | + | 12.4110i | −0.140164 | + | 0.671111i | ||||
\(343\) | −15.4579 | −0.834646 | ||||||||
\(344\) | −6.08114 | + | 10.5328i | −0.327873 | + | 0.567893i | ||||
\(345\) | −19.9808 | − | 44.6644i | −1.07573 | − | 2.40465i | ||||
\(346\) | − | 6.74908i | − | 0.362833i | ||||||
\(347\) | −1.83858 | + | 3.18452i | −0.0987004 | + | 0.170954i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) |
0.812447 | + | 0.583036i | \(0.198135\pi\) | |||||||
\(348\) | 0.599644 | − | 5.80419i | 0.0321443 | − | 0.311137i | ||||
\(349\) | 2.56390 | + | 4.44080i | 0.137242 | + | 0.237710i | 0.926452 | − | 0.376414i | \(-0.122843\pi\) |
−0.789210 | + | 0.614124i | \(0.789509\pi\) | |||||||
\(350\) | 18.9935i | 1.01524i | ||||||||
\(351\) | 15.1649 | − | 11.0012i | 0.809443 | − | 0.587198i | ||||
\(352\) | 6.83635 | − | 2.87447i | 0.364378 | − | 0.153210i | ||||
\(353\) | −4.45460 | − | 7.71560i | −0.237095 | − | 0.410660i | 0.722785 | − | 0.691073i | \(-0.242862\pi\) |
−0.959879 | + | 0.280413i | \(0.909528\pi\) | |||||||
\(354\) | −18.4184 | − | 1.90285i | −0.978928 | − | 0.101135i | ||||
\(355\) | 20.9316 | − | 36.2546i | 1.11093 | − | 1.92419i | ||||
\(356\) | −3.71537 | −0.196914 | ||||||||
\(357\) | 9.55001 | − | 4.27224i | 0.505440 | − | 0.226111i | ||||
\(358\) | −2.83969 | + | 4.91849i | −0.150082 | + | 0.259950i | ||||
\(359\) | − | 24.6971i | − | 1.30347i | −0.758449 | − | 0.651733i | \(-0.774042\pi\) | ||
0.758449 | − | 0.651733i | \(-0.225958\pi\) | |||||||
\(360\) | −7.70355 | + | 36.8850i | −0.406013 | + | 1.94401i | ||||
\(361\) | 3.91196 | + | 6.77571i | 0.205892 | + | 0.356616i | ||||
\(362\) | −16.2837 | + | 9.40142i | −0.855855 | + | 0.494128i | ||||
\(363\) | −18.7795 | + | 3.21412i | −0.985668 | + | 0.168697i | ||||
\(364\) | −0.198656 | + | 1.78618i | −0.0104124 | + | 0.0936211i | ||||
\(365\) | −6.52566 | −0.341569 | ||||||||
\(366\) | −0.0836564 | + | 0.809744i | −0.00437279 | + | 0.0423260i | ||||
\(367\) | −4.66517 | − | 8.08031i | −0.243520 | − | 0.421789i | 0.718195 | − | 0.695842i | \(-0.244969\pi\) |
−0.961714 | + | 0.274054i | \(0.911635\pi\) | |||||||
\(368\) | −17.9491 | − | 10.3629i | −0.935661 | − | 0.540204i | ||||
\(369\) | 29.2000 | − | 9.60223i | 1.52009 | − | 0.499872i | ||||
\(370\) | 2.96876 | − | 5.14204i | 0.154338 | − | 0.267322i | ||||
\(371\) | 1.05393 | + | 0.608486i | 0.0547172 | + | 0.0315910i | ||||
\(372\) | 0.0993389 | − | 0.137239i | 0.00515048 | − | 0.00711552i | ||||
\(373\) | −5.98152 | − | 3.45343i | −0.309712 | − | 0.178812i | 0.337086 | − | 0.941474i | \(-0.390559\pi\) |
−0.646797 | + | 0.762662i | \(0.723892\pi\) | |||||||
\(374\) | 16.2633 | + | 12.3422i | 0.840955 | + | 0.638198i | ||||
\(375\) | −5.23627 | + | 50.6840i | −0.270400 | + | 2.61731i | ||||
\(376\) | − | 0.566420i | − | 0.0292109i | ||||||
\(377\) | −3.34144 | + | 30.0439i | −0.172093 | + | 1.54734i | ||||
\(378\) | −7.76307 | − | 2.47681i | −0.399289 | − | 0.127393i | ||||
\(379\) | −4.47075 | + | 2.58119i | −0.229647 | + | 0.132587i | −0.610409 | − | 0.792086i | \(-0.708995\pi\) |
0.380762 | + | 0.924673i | \(0.375662\pi\) | |||||||
\(380\) | −2.77839 | − | 4.81232i | −0.142529 | − | 0.246867i | ||||
\(381\) | 1.09383 | + | 2.44510i | 0.0560384 | + | 0.125266i | ||||
\(382\) | 15.8128 | 0.809053 | ||||||||
\(383\) | 14.3171 | − | 24.7979i | 0.731569 | − | 1.26712i | −0.224643 | − | 0.974441i | \(-0.572122\pi\) |
0.956212 | − | 0.292674i | \(-0.0945452\pi\) | |||||||
\(384\) | 4.79183 | + | 10.7115i | 0.244532 | + | 0.546618i | ||||
\(385\) | 6.59653 | + | 15.6885i | 0.336190 | + | 0.799559i | ||||
\(386\) | −26.8340 | − | 15.4926i | −1.36581 | − | 0.788552i | ||||
\(387\) | −8.95856 | − | 8.00899i | −0.455389 | − | 0.407120i | ||||
\(388\) | 2.06836 | − | 1.19417i | 0.105005 | − | 0.0606247i | ||||
\(389\) | − | 19.7794i | − | 1.00285i | −0.865200 | − | 0.501427i | \(-0.832809\pi\) | ||
0.865200 | − | 0.501427i | \(-0.167191\pi\) | |||||||
\(390\) | 6.92637 | − | 31.9151i | 0.350730 | − | 1.61609i | ||||
\(391\) | 33.2533i | 1.68169i | ||||||||
\(392\) | −14.3606 | + | 8.29111i | −0.725321 | + | 0.418764i | ||||
\(393\) | 3.84557 | − | 37.2228i | 0.193983 | − | 1.87764i | ||||
\(394\) | −5.56544 | + | 9.63963i | −0.280383 | + | 0.485638i | ||||
\(395\) | 29.0879i | 1.46357i | ||||||||
\(396\) | 0.763444 | + | 3.92450i | 0.0383645 | + | 0.197214i | ||||
\(397\) | −14.7727 | − | 8.52902i | −0.741421 | − | 0.428059i | 0.0811649 | − | 0.996701i | \(-0.474136\pi\) |
−0.822586 | + | 0.568641i | \(0.807469\pi\) | |||||||
\(398\) | 1.88552i | 0.0945125i | ||||||||
\(399\) | 6.55664 | − | 2.93314i | 0.328243 | − | 0.146841i | ||||
\(400\) | 18.3788 | + | 31.8330i | 0.918940 | + | 1.59165i | ||||
\(401\) | 1.38119 | + | 2.39229i | 0.0689733 | + | 0.119465i | 0.898450 | − | 0.439077i | \(-0.144694\pi\) |
−0.829476 | + | 0.558542i | \(0.811361\pi\) | |||||||
\(402\) | 15.9819 | + | 11.5683i | 0.797104 | + | 0.576974i | ||||
\(403\) | −0.520174 | + | 0.706934i | −0.0259117 | + | 0.0352149i | ||||
\(404\) | 5.47089 | 0.272187 | ||||||||
\(405\) | −34.1175 | − | 14.9011i | −1.69531 | − | 0.740441i | ||||
\(406\) | 11.3864 | − | 6.57394i | 0.565097 | − | 0.326259i | ||||
\(407\) | 0.471621 | − | 3.73602i | 0.0233774 | − | 0.185188i | ||||
\(408\) | 15.0154 | − | 20.7442i | 0.743375 | − | 1.02699i | ||||
\(409\) | 0.528451 | − | 0.915303i | 0.0261302 | − | 0.0452588i | −0.852665 | − | 0.522459i | \(-0.825015\pi\) |
0.878795 | + | 0.477200i | \(0.158348\pi\) | |||||||
\(410\) | 26.7908 | − | 46.4031i | 1.32311 | − | 2.29169i | ||||
\(411\) | 6.28757 | + | 4.55118i | 0.310143 | + | 0.224493i | ||||
\(412\) | 0.493834 | − | 0.855346i | 0.0243295 | − | 0.0421399i | ||||
\(413\) | 5.24498 | + | 9.08457i | 0.258089 | + | 0.447022i | ||||
\(414\) | 17.2622 | − | 19.3089i | 0.848392 | − | 0.948979i | ||||
\(415\) | − | 19.4083i | − | 0.952716i | ||||||
\(416\) | 3.23459 | + | 7.38480i | 0.158589 | + | 0.362070i | ||||
\(417\) | 0.723669 | − | 0.999767i | 0.0354382 | − | 0.0489588i | ||||
\(418\) | 11.1657 | + | 8.47362i | 0.546133 | + | 0.414458i | ||||
\(419\) | 31.6187 | − | 18.2551i | 1.54467 | − | 0.891818i | 0.546140 | − | 0.837694i | \(-0.316097\pi\) |
0.998534 | − | 0.0541246i | \(-0.0172368\pi\) | |||||||
\(420\) | 3.25998 | − | 1.45837i | 0.159071 | − | 0.0711611i | ||||
\(421\) | 26.4552i | 1.28935i | 0.764458 | + | 0.644674i | \(0.223007\pi\) | ||||
−0.764458 | + | 0.644674i | \(0.776993\pi\) | |||||||
\(422\) | −10.1511 | + | 17.5822i | −0.494146 | + | 0.855886i | ||||
\(423\) | 0.547817 | + | 0.114414i | 0.0266358 | + | 0.00556298i | ||||
\(424\) | 2.97882 | 0.144664 | ||||||||
\(425\) | 29.4877 | − | 51.0741i | 1.43036 | − | 2.47746i | ||||
\(426\) | 22.0422 | + | 2.27722i | 1.06795 | + | 0.110332i | ||||
\(427\) | 0.399392 | − | 0.230589i | 0.0193279 | − | 0.0111590i | ||||
\(428\) | 3.10812 | 0.150236 | ||||||||
\(429\) | −3.79604 | − | 20.3615i | −0.183275 | − | 0.983062i | ||||
\(430\) | −20.9469 | −1.01015 | ||||||||
\(431\) | 27.8225 | − | 16.0633i | 1.34016 | − | 0.773744i | 0.353333 | − | 0.935498i | \(-0.385048\pi\) |
0.986831 | + | 0.161754i | \(0.0517151\pi\) | |||||||
\(432\) | −15.4075 | + | 3.36071i | −0.741295 | + | 0.161692i | ||||
\(433\) | 15.6033 | − | 27.0258i | 0.749849 | − | 1.29878i | −0.198046 | − | 0.980193i | \(-0.563460\pi\) |
0.947895 | − | 0.318583i | \(-0.103207\pi\) | |||||||
\(434\) | 0.381742 | 0.0183242 | ||||||||
\(435\) | 54.8336 | − | 24.5301i | 2.62907 | − | 1.17613i | ||||
\(436\) | −2.01416 | + | 3.48862i | −0.0964606 | + | 0.167075i | ||||
\(437\) | 22.8304i | 1.09212i | ||||||||
\(438\) | −1.41056 | − | 3.15311i | −0.0673990 | − | 0.150661i | ||||
\(439\) | 3.80990 | − | 2.19965i | 0.181837 | − | 0.104983i | −0.406319 | − | 0.913731i | \(-0.633188\pi\) |
0.588155 | + | 0.808748i | \(0.299854\pi\) | |||||||
\(440\) | 33.1839 | + | 25.1832i | 1.58198 | + | 1.20056i | ||||
\(441\) | −5.11804 | − | 15.5637i | −0.243716 | − | 0.741129i | ||||
\(442\) | −13.1541 | + | 17.8768i | −0.625675 | + | 0.850313i | ||||
\(443\) | − | 21.2390i | − | 1.00910i | −0.863383 | − | 0.504548i | \(-0.831659\pi\) | ||
0.863383 | − | 0.504548i | \(-0.168341\pi\) | |||||||
\(444\) | −0.786021 | − | 0.0812055i | −0.0373029 | − | 0.00385384i | ||||
\(445\) | −19.1243 | − | 33.1242i | −0.906578 | − | 1.57024i | ||||
\(446\) | −7.77934 | + | 13.4742i | −0.368362 | + | 0.638022i | ||||
\(447\) | 4.29509 | − | 5.93377i | 0.203151 | − | 0.280658i | ||||
\(448\) | 5.51800 | − | 9.55745i | 0.260701 | − | 0.451547i | ||||
\(449\) | −18.3562 | + | 31.7939i | −0.866284 | + | 1.50045i | −0.000516632 | 1.00000i | \(0.500164\pi\) | |
−0.865767 | + | 0.500447i | \(0.833169\pi\) | |||||||
\(450\) | −43.6355 | + | 14.3493i | −2.05700 | + | 0.676431i | ||||
\(451\) | 4.25603 | − | 33.7148i | 0.200409 | − | 1.58757i | ||||
\(452\) | −1.25733 | + | 0.725923i | −0.0591401 | + | 0.0341445i | ||||
\(453\) | −0.110413 | + | 1.06873i | −0.00518764 | + | 0.0502133i | ||||
\(454\) | 6.42786 | 0.301675 | ||||||||
\(455\) | −16.9471 | + | 7.42295i | −0.794493 | + | 0.347993i | ||||
\(456\) | 10.3090 | − | 14.2421i | 0.482762 | − | 0.666949i | ||||
\(457\) | 1.32900 | + | 2.30189i | 0.0621678 | + | 0.107678i | 0.895434 | − | 0.445194i | \(-0.146865\pi\) |
−0.833266 | + | 0.552872i | \(0.813532\pi\) | |||||||
\(458\) | −4.77083 | − | 8.26332i | −0.222926 | − | 0.386120i | ||||
\(459\) | 17.0299 | + | 18.7125i | 0.794887 | + | 0.873425i | ||||
\(460\) | 11.3513i | 0.529259i | ||||||||
\(461\) | −22.1383 | − | 12.7816i | −1.03109 | − | 0.595297i | −0.113790 | − | 0.993505i | \(-0.536299\pi\) |
−0.917295 | + | 0.398208i | \(0.869632\pi\) | |||||||
\(462\) | −6.15458 | + | 6.57850i | −0.286337 | + | 0.306059i | ||||
\(463\) | 10.4527i | 0.485777i | 0.970054 | + | 0.242889i | \(0.0780950\pi\) | ||||
−0.970054 | + | 0.242889i | \(0.921905\pi\) | |||||||
\(464\) | 12.7224 | − | 22.0358i | 0.590621 | − | 1.02299i | ||||
\(465\) | 1.73488 | + | 0.179234i | 0.0804532 | + | 0.00831179i | ||||
\(466\) | −19.7315 | + | 11.3920i | −0.914042 | + | 0.527722i | ||||
\(467\) | − | 30.2230i | − | 1.39855i | −0.714851 | − | 0.699276i | \(-0.753506\pi\) | ||
0.714851 | − | 0.699276i | \(-0.246494\pi\) | |||||||
\(468\) | −4.25363 | + | 0.893036i | −0.196624 | + | 0.0412806i | ||||
\(469\) | − | 11.1771i | − | 0.516109i | ||||||
\(470\) | 0.844840 | − | 0.487769i | 0.0389696 | − | 0.0224991i | ||||
\(471\) | −3.32593 | + | 32.1930i | −0.153251 | + | 1.48338i | ||||
\(472\) | 22.2366 | + | 12.8383i | 1.02352 | + | 0.590931i | ||||
\(473\) | −12.2464 | + | 5.14923i | −0.563089 | + | 0.236762i | ||||
\(474\) | −14.0548 | + | 6.28750i | −0.645560 | + | 0.288794i | ||||
\(475\) | 20.2450 | − | 35.0654i | 0.928905 | − | 1.60891i | ||||
\(476\) | −2.42711 | −0.111246 | ||||||||
\(477\) | −0.601704 | + | 2.88099i | −0.0275501 | + | 0.131911i | ||||
\(478\) | −10.9766 | − | 19.0120i | −0.502057 | − | 0.869588i | ||||
\(479\) | −14.1161 | + | 8.14992i | −0.644980 | + | 0.372379i | −0.786530 | − | 0.617552i | \(-0.788125\pi\) |
0.141551 | + | 0.989931i | \(0.454791\pi\) | |||||||
\(480\) | 9.39380 | − | 12.9778i | 0.428767 | − | 0.592352i | ||||
\(481\) | 4.06863 | + | 0.452508i | 0.185514 | + | 0.0206326i | ||||
\(482\) | 18.2854i | 0.832875i | ||||||||
\(483\) | −14.5953 | − | 1.50787i | −0.664108 | − | 0.0686105i | ||||
\(484\) | 4.28137 | + | 1.09843i | 0.194608 | + | 0.0499287i | ||||
\(485\) | 21.2931 | + | 12.2936i | 0.966870 | + | 0.558223i | ||||
\(486\) | −0.174679 | − | 19.7060i | −0.00792359 | − | 0.893883i | ||||
\(487\) | 21.0507 | + | 12.1536i | 0.953898 | + | 0.550733i | 0.894290 | − | 0.447489i | \(-0.147682\pi\) |
0.0596081 | + | 0.998222i | \(0.481015\pi\) | |||||||
\(488\) | 0.564421 | − | 0.977606i | 0.0255501 | − | 0.0442541i | ||||
\(489\) | 0.0993483 | − | 0.137252i | 0.00449268 | − | 0.00620676i | ||||
\(490\) | −24.7331 | − | 14.2797i | −1.11733 | − | 0.645089i | ||||
\(491\) | 8.25522 | + | 14.2985i | 0.372553 | + | 0.645280i | 0.989957 | − | 0.141365i | \(-0.0451492\pi\) |
−0.617405 | + | 0.786646i | \(0.711816\pi\) | |||||||
\(492\) | −7.09326 | − | 0.732820i | −0.319789 | − | 0.0330381i | ||||
\(493\) | −40.8245 | −1.83864 | ||||||||
\(494\) | −9.03104 | + | 12.2735i | −0.406326 | + | 0.552210i | ||||
\(495\) | −31.0590 | + | 27.0072i | −1.39600 | + | 1.21388i | ||||
\(496\) | 0.639799 | − | 0.369388i | 0.0287278 | − | 0.0165860i | ||||
\(497\) | −6.27690 | − | 10.8719i | −0.281558 | − | 0.487672i | ||||
\(498\) | 9.37781 | − | 4.19521i | 0.420230 | − | 0.187992i | ||||
\(499\) | − | 29.0297i | − | 1.29955i | −0.760128 | − | 0.649774i | \(-0.774864\pi\) | ||
0.760128 | − | 0.649774i | \(-0.225136\pi\) | |||||||
\(500\) | 5.91042 | − | 10.2372i | 0.264322 | − | 0.457819i | ||||
\(501\) | 1.05810 | + | 2.36525i | 0.0472726 | + | 0.105671i | ||||
\(502\) | −25.0698 | −1.11892 | ||||||||
\(503\) | −1.49478 | + | 2.58903i | −0.0666487 | + | 0.115439i | −0.897424 | − | 0.441169i | \(-0.854564\pi\) |
0.830775 | + | 0.556608i | \(0.187897\pi\) | |||||||
\(504\) | 8.42401 | + | 7.53110i | 0.375235 | + | 0.335462i | ||||
\(505\) | 28.1605 | + | 48.7754i | 1.25313 | + | 2.17048i | ||||
\(506\) | −11.0984 | − | 26.3953i | −0.493385 | − | 1.17341i | ||||
\(507\) | 22.0717 | − | 4.45406i | 0.980240 | − | 0.197812i | ||||
\(508\) | − | 0.621416i | − | 0.0275709i | ||||||
\(509\) | −2.64652 | − | 4.58390i | −0.117305 | − | 0.203178i | 0.801394 | − | 0.598137i | \(-0.204092\pi\) |
−0.918699 | + | 0.394959i | \(0.870759\pi\) | |||||||
\(510\) | 43.8713 | + | 4.53244i | 1.94266 | + | 0.200700i | ||||
\(511\) | −0.978448 | + | 1.69472i | −0.0432840 | + | 0.0749701i | ||||
\(512\) | − | 25.2162i | − | 1.11441i | ||||||
\(513\) | 11.6920 | + | 12.8472i | 0.516215 | + | 0.567219i | ||||
\(514\) | −10.0342 | + | 17.3797i | −0.442589 | + | 0.766587i | ||||
\(515\) | 10.1677 | 0.448044 | ||||||||
\(516\) | 1.13840 | + | 2.54473i | 0.0501152 | + | 0.112026i | ||||
\(517\) | 0.374022 | − | 0.492849i | 0.0164495 | − | 0.0216755i | ||||
\(518\) | −0.890262 | − | 1.54198i | −0.0391159 | − | 0.0677507i | ||||
\(519\) | −7.49046 | − | 5.42187i | −0.328794 | − | 0.237994i | ||||
\(520\) | −26.8398 | + | 36.4762i | −1.17700 | + | 1.59959i | ||||
\(521\) | − | 18.1143i | − | 0.793601i | −0.917905 | − | 0.396801i | \(-0.870120\pi\) | ||
0.917905 | − | 0.396801i | \(-0.129880\pi\) | |||||||
\(522\) | 23.7052 | + | 21.1925i | 1.03755 | + | 0.927571i | ||||
\(523\) | 20.7433 | − | 11.9761i | 0.907040 | − | 0.523680i | 0.0275622 | − | 0.999620i | \(-0.491226\pi\) |
0.879477 | + | 0.475941i | \(0.157892\pi\) | |||||||
\(524\) | −4.34067 | + | 7.51826i | −0.189623 | + | 0.328437i | ||||
\(525\) | 21.0799 | + | 15.2584i | 0.920003 | + | 0.665932i | ||||
\(526\) | 15.9865 | + | 9.22978i | 0.697043 | + | 0.402438i | ||||
\(527\) | −1.02652 | − | 0.592660i | −0.0447158 | − | 0.0258167i | ||||
\(528\) | −3.94945 | + | 16.9809i | −0.171878 | + | 0.739000i | ||||
\(529\) | 11.8188 | − | 20.4707i | 0.513861 | − | 0.890033i | ||||
\(530\) | 2.56519 | + | 4.44304i | 0.111425 | + | 0.192993i | ||||
\(531\) | −16.9083 | + | 18.9130i | −0.733759 | + | 0.820755i | ||||
\(532\) | −1.66635 | −0.0722456 | ||||||||
\(533\) | 36.7164 | + | 4.08355i | 1.59036 | + | 0.176878i | ||||
\(534\) | 11.8713 | − | 16.4006i | 0.513723 | − | 0.709721i | ||||
\(535\) | 15.9985 | + | 27.7103i | 0.691677 | + | 1.19802i | ||||
\(536\) | −13.6792 | − | 23.6931i | −0.590853 | − | 1.02339i | ||||
\(537\) | 3.17751 | + | 7.10290i | 0.137120 | + | 0.306513i | ||||
\(538\) | 22.7485 | 0.980758 | ||||||||
\(539\) | −17.9702 | − | 2.26849i | −0.774030 | − | 0.0977106i | ||||
\(540\) | 5.81331 | + | 6.38768i | 0.250165 | + | 0.274882i | ||||
\(541\) | −17.1999 | −0.739482 | −0.369741 | − | 0.929135i | \(-0.620554\pi\) | ||||
−0.369741 | + | 0.929135i | \(0.620554\pi\) | |||||||
\(542\) | 2.74193 | + | 1.58305i | 0.117776 | + | 0.0679980i | ||||
\(543\) | −2.64739 | + | 25.6251i | −0.113610 | + | 1.09968i | ||||
\(544\) | −9.42922 | + | 5.44396i | −0.404275 | + | 0.233408i | ||||
\(545\) | −41.4702 | −1.77639 | ||||||||
\(546\) | −7.24987 | − | 6.58410i | −0.310266 | − | 0.281773i | ||||
\(547\) | 13.6790i | 0.584872i | 0.956285 | + | 0.292436i | \(0.0944658\pi\) | ||||
−0.956285 | + | 0.292436i | \(0.905534\pi\) | |||||||
\(548\) | −0.900345 | − | 1.55944i | −0.0384608 | − | 0.0666161i | ||||
\(549\) | 0.831488 | + | 0.743354i | 0.0354871 | + | 0.0317256i | ||||
\(550\) | −6.36008 | + | 50.3824i | −0.271195 | + | 2.14831i | ||||
\(551\) | −28.0284 | −1.19405 | ||||||||
\(552\) | −32.7845 | + | 14.6663i | −1.39540 | + | 0.624239i | ||||
\(553\) | 7.55416 | + | 4.36139i | 0.321235 | + | 0.185465i | ||||
\(554\) | −24.8255 | −1.05473 | ||||||||
\(555\) | −3.32193 | − | 7.42573i | −0.141008 | − | 0.315205i | ||||
\(556\) | −0.247962 | + | 0.143161i | −0.0105160 | + | 0.00607139i | ||||
\(557\) | 19.9531 | − | 11.5200i | 0.845442 | − | 0.488116i | −0.0136683 | − | 0.999907i | \(-0.504351\pi\) |
0.859110 | + | 0.511790i | \(0.171018\pi\) | |||||||
\(558\) | 0.288400 | + | 0.877012i | 0.0122090 | + | 0.0371269i | ||||
\(559\) | −5.79433 | − | 13.2289i | −0.245074 | − | 0.559522i | ||||
\(560\) | 15.5732 | 0.658089 | ||||||||
\(561\) | 26.7631 | − | 8.13473i | 1.12994 | − | 0.343448i | ||||
\(562\) | 8.52495 | + | 14.7656i | 0.359603 | + | 0.622851i | ||||
\(563\) | 21.1955 | − | 36.7116i | 0.893282 | − | 1.54721i | 0.0573654 | − | 0.998353i | \(-0.481730\pi\) |
0.835917 | − | 0.548857i | \(-0.184937\pi\) | |||||||
\(564\) | −0.105171 | − | 0.0761265i | −0.00442849 | − | 0.00320550i | ||||
\(565\) | −12.9439 | − | 7.47314i | −0.544552 | − | 0.314397i | ||||
\(566\) | −18.5844 | + | 32.1891i | −0.781160 | + | 1.35301i | ||||
\(567\) | −8.98535 | + | 6.62610i | −0.377349 | + | 0.278270i | ||||
\(568\) | −26.6116 | − | 15.3642i | −1.11660 | − | 0.644667i | ||||
\(569\) | 3.72486 | + | 6.45165i | 0.156154 | + | 0.270467i | 0.933479 | − | 0.358633i | \(-0.116757\pi\) |
−0.777324 | + | 0.629100i | \(0.783424\pi\) | |||||||
\(570\) | 30.1203 | + | 3.11179i | 1.26160 | + | 0.130339i | ||||
\(571\) | − | 28.7506i | − | 1.20318i | −0.798806 | − | 0.601588i | \(-0.794535\pi\) | ||
0.798806 | − | 0.601588i | \(-0.205465\pi\) | |||||||
\(572\) | −1.12507 | + | 4.67151i | −0.0470415 | + | 0.195326i | ||||
\(573\) | 12.7032 | − | 17.5498i | 0.530685 | − | 0.733154i | ||||
\(574\) | −8.03396 | − | 13.9152i | −0.335331 | − | 0.580810i | ||||
\(575\) | −71.6311 | + | 41.3562i | −2.98722 | + | 1.72467i | ||||
\(576\) | 26.1260 | + | 5.45650i | 1.08858 | + | 0.227354i | ||||
\(577\) | 22.5576i | 0.939085i | 0.882910 | + | 0.469542i | \(0.155581\pi\) | ||||
−0.882910 | + | 0.469542i | \(0.844419\pi\) | |||||||
\(578\) | −7.34643 | − | 4.24146i | −0.305571 | − | 0.176422i | ||||
\(579\) | −38.7515 | + | 17.3357i | −1.61046 | + | 0.720446i | ||||
\(580\) | −13.9358 | −0.578654 | ||||||||
\(581\) | −5.04036 | − | 2.91005i | −0.209109 | − | 0.120729i | ||||
\(582\) | −1.33746 | + | 12.9458i | −0.0554396 | + | 0.536622i | ||||
\(583\) | 2.59191 | + | 1.96699i | 0.107346 | + | 0.0814645i | ||||
\(584\) | 4.78996i | 0.198210i | ||||||||
\(585\) | −29.8567 | − | 33.3263i | −1.23442 | − | 1.37787i | ||||
\(586\) | 9.35761 | 0.386559 | ||||||||
\(587\) | −18.8884 | − | 32.7156i | −0.779606 | − | 1.35032i | −0.932169 | − | 0.362023i | \(-0.882086\pi\) |
0.152563 | − | 0.988294i | \(-0.451247\pi\) | |||||||
\(588\) | −0.390597 | + | 3.78074i | −0.0161079 | + | 0.155915i | ||||
\(589\) | −0.704765 | − | 0.406896i | −0.0290393 | − | 0.0167659i | ||||
\(590\) | 44.2225i | 1.82061i | ||||||||
\(591\) | 6.22754 | + | 13.9208i | 0.256167 | + | 0.572625i | ||||
\(592\) | −2.98415 | − | 1.72290i | −0.122648 | − | 0.0708107i | ||||
\(593\) | 11.8238i | 0.485547i | 0.970083 | + | 0.242773i | \(0.0780572\pi\) | ||||
−0.970083 | + | 0.242773i | \(0.921943\pi\) | |||||||
\(594\) | −19.7631 | − | 9.16953i | −0.810889 | − | 0.376230i | ||||
\(595\) | −12.4932 | − | 21.6388i | −0.512170 | − | 0.887104i | ||||
\(596\) | −1.47170 | + | 0.849684i | −0.0602830 | + | 0.0348044i | ||||
\(597\) | 2.09264 | + | 1.51473i | 0.0856461 | + | 0.0619939i | ||||
\(598\) | 28.5129 | − | 12.4888i | 1.16598 | − | 0.510706i | ||||
\(599\) | 27.2805i | 1.11465i | 0.830294 | + | 0.557325i | \(0.188172\pi\) | ||||
−0.830294 | + | 0.557325i | \(0.811828\pi\) | |||||||
\(600\) | 63.3595 | + | 6.54581i | 2.58664 | + | 0.267231i | ||||
\(601\) | −17.7218 | + | 10.2317i | −0.722889 | + | 0.417360i | −0.815815 | − | 0.578313i | \(-0.803711\pi\) |
0.0929263 | + | 0.995673i | \(0.470378\pi\) | |||||||
\(602\) | −3.14075 | + | 5.43994i | −0.128008 | + | 0.221716i | ||||
\(603\) | 25.6781 | − | 8.44409i | 1.04569 | − | 0.343870i | ||||
\(604\) | 0.124628 | − | 0.215862i | 0.00507104 | − | 0.00878330i | ||||
\(605\) | 12.2447 | + | 43.8244i | 0.497816 | + | 1.78171i | ||||
\(606\) | −17.4805 | + | 24.1498i | −0.710099 | + | 0.981020i | ||||
\(607\) | 8.75317 | + | 5.05365i | 0.355280 | + | 0.205121i | 0.667008 | − | 0.745050i | \(-0.267574\pi\) |
−0.311728 | + | 0.950171i | \(0.600908\pi\) | |||||||
\(608\) | −6.47371 | + | 3.73760i | −0.262544 | + | 0.151580i | ||||
\(609\) | 1.85118 | − | 17.9184i | 0.0750138 | − | 0.726088i | ||||
\(610\) | 1.94419 | 0.0787179 | ||||||||
\(611\) | 0.541746 | + | 0.398626i | 0.0219167 | + | 0.0161267i | ||||
\(612\) | −1.83364 | − | 5.57602i | −0.0741206 | − | 0.225397i | ||||
\(613\) | 10.5185 | + | 18.2186i | 0.424839 | + | 0.735843i | 0.996405 | − | 0.0847131i | \(-0.0269974\pi\) |
−0.571566 | + | 0.820556i | \(0.693664\pi\) | |||||||
\(614\) | 15.2998 | − | 8.83336i | 0.617451 | − | 0.356485i | ||||
\(615\) | −29.9780 | − | 67.0117i | −1.20883 | − | 2.70217i | ||||
\(616\) | 11.5157 | − | 4.84198i | 0.463979 | − | 0.195089i | ||||
\(617\) | 13.6536 | − | 23.6488i | 0.549674 | − | 0.952063i | −0.448623 | − | 0.893721i | \(-0.648085\pi\) |
0.998297 | − | 0.0583419i | \(-0.0185813\pi\) | |||||||
\(618\) | 2.19781 | + | 4.91290i | 0.0884089 | + | 0.197626i | ||||
\(619\) | 2.36601i | 0.0950981i | 0.998869 | + | 0.0475491i | \(0.0151410\pi\) | ||||
−0.998869 | + | 0.0475491i | \(0.984859\pi\) | |||||||
\(620\) | −0.350411 | − | 0.202310i | −0.0140729 | − | 0.00812497i | ||||
\(621\) | −7.56233 | − | 34.6702i | −0.303466 | − | 1.39127i | ||||
\(622\) | 15.6338 | + | 27.0786i | 0.626860 | + | 1.08575i | ||||
\(623\) | −11.4699 | −0.459531 | ||||||||
\(624\) | −18.5218 | − | 4.01968i | −0.741464 | − | 0.160916i | ||||
\(625\) | 61.1336 | 2.44535 | ||||||||
\(626\) | 7.77012 | − | 4.48608i | 0.310557 | − | 0.179300i | ||||
\(627\) | 18.3744 | − | 5.58497i | 0.733803 | − | 0.223042i | ||||
\(628\) | 3.75413 | − | 6.50235i | 0.149806 | − | 0.259472i | ||||
\(629\) | 5.52857i | 0.220439i | ||||||||
\(630\) | −3.97869 | + | 19.0501i | −0.158515 | + | 0.758975i | ||||
\(631\) | −12.7129 | − | 7.33977i | −0.506091 | − | 0.292192i | 0.225135 | − | 0.974328i | \(-0.427718\pi\) |
−0.731225 | + | 0.682136i | \(0.761051\pi\) | |||||||
\(632\) | 21.3511 | 0.849300 | ||||||||
\(633\) | 11.3587 | + | 25.3908i | 0.451467 | + | 1.00919i | ||||
\(634\) | −0.404306 | + | 0.233426i | −0.0160570 | + | 0.00927053i | ||||
\(635\) | 5.54021 | − | 3.19864i | 0.219856 | − | 0.126934i | ||||
\(636\) | 0.400352 | − | 0.553096i | 0.0158750 | − | 0.0219317i | ||||
\(637\) | 2.17655 | − | 19.5700i | 0.0862381 | − | 0.775392i | ||||
\(638\) | 32.4050 | − | 13.6253i | 1.28293 | − | 0.539432i | ||||
\(639\) | 20.2350 | − | 22.6341i | 0.800482 | − | 0.895390i | ||||
\(640\) | 24.2705 | − | 14.0126i | 0.959376 | − | 0.553896i | ||||
\(641\) | −13.4694 | − | 7.77658i | −0.532010 | − | 0.307156i | 0.209824 | − | 0.977739i | \(-0.432711\pi\) |
−0.741835 | + | 0.670583i | \(0.766044\pi\) | |||||||
\(642\) | −9.93103 | + | 13.7200i | −0.391947 | + | 0.541484i | ||||
\(643\) | 0.116777 | + | 0.0674214i | 0.00460525 | + | 0.00265884i | 0.502301 | − | 0.864693i | \(-0.332487\pi\) |
−0.497696 | + | 0.867352i | \(0.665820\pi\) | |||||||
\(644\) | 2.94795 | + | 1.70200i | 0.116166 | + | 0.0670683i | ||||
\(645\) | −16.8277 | + | 23.2479i | −0.662591 | + | 0.915386i | ||||
\(646\) | −17.8220 | − | 10.2895i | −0.701196 | − | 0.404835i | ||||
\(647\) | −16.4081 | + | 9.47325i | −0.645071 | + | 0.372432i | −0.786565 | − | 0.617507i | \(-0.788143\pi\) |
0.141494 | + | 0.989939i | \(0.454809\pi\) | |||||||
\(648\) | −10.9377 | + | 25.0429i | −0.429673 | + | 0.983777i | ||||
\(649\) | 10.8709 | + | 25.8542i | 0.426720 | + | 1.01486i | ||||
\(650\) | −54.8678 | − | 6.10233i | −2.15209 | − | 0.239353i | ||||
\(651\) | 0.306673 | − | 0.423677i | 0.0120195 | − | 0.0166052i | ||||
\(652\) | −0.0340413 | + | 0.0196538i | −0.00133316 | + | 0.000769701i | ||||
\(653\) | −15.8414 | + | 9.14605i | −0.619923 | + | 0.357913i | −0.776839 | − | 0.629699i | \(-0.783178\pi\) |
0.156916 | + | 0.987612i | \(0.449845\pi\) | |||||||
\(654\) | −8.96400 | − | 20.0378i | −0.350520 | − | 0.783540i | ||||
\(655\) | −89.3716 | −3.49204 | ||||||||
\(656\) | −26.9298 | − | 15.5479i | −1.05143 | − | 0.607044i | ||||
\(657\) | −4.63264 | − | 0.967544i | −0.180737 | − | 0.0377475i | ||||
\(658\) | − | 0.292541i | − | 0.0114044i | ||||||
\(659\) | −22.9370 | + | 39.7281i | −0.893499 | + | 1.54759i | −0.0578482 | + | 0.998325i | \(0.518424\pi\) |
−0.835651 | + | 0.549261i | \(0.814909\pi\) | |||||||
\(660\) | 9.13582 | − | 2.77686i | 0.355611 | − | 0.108089i | ||||
\(661\) | −21.6055 | + | 12.4739i | −0.840355 | + | 0.485179i | −0.857385 | − | 0.514676i | \(-0.827912\pi\) |
0.0170300 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(662\) | 5.89504 | 0.229117 | ||||||||
\(663\) | 9.27324 | + | 28.9604i | 0.360143 | + | 1.12473i | ||||
\(664\) | −14.2461 | −0.552855 | ||||||||
\(665\) | −8.57729 | − | 14.8563i | −0.332613 | − | 0.576102i | ||||
\(666\) | 2.86995 | − | 3.21022i | 0.111208 | − | 0.124394i | ||||
\(667\) | 49.5852 | + | 28.6281i | 1.91995 | + | 1.10848i | ||||
\(668\) | − | 0.601121i | − | 0.0232581i | ||||||
\(669\) | 8.70481 | + | 19.4584i | 0.336547 | + | 0.752305i | ||||
\(670\) | 23.5596 | − | 40.8064i | 0.910185 | − | 1.57649i | ||||
\(671\) | 1.13665 | − | 0.477926i | 0.0438798 | − | 0.0184501i | ||||
\(672\) | −1.96185 | − | 4.38545i | −0.0756801 | − | 0.169172i | ||||
\(673\) | −25.9850 | + | 15.0025i | −1.00165 | + | 0.578303i | −0.908736 | − | 0.417371i | \(-0.862951\pi\) |
−0.0929139 | + | 0.995674i | \(0.529618\pi\) | |||||||
\(674\) | −8.89196 | − | 15.4013i | −0.342506 | − | 0.593237i | ||||
\(675\) | −19.1291 | + | 59.9563i | −0.736278 | + | 2.30772i | ||||
\(676\) | −5.09603 | − | 1.14774i | −0.196001 | − | 0.0441440i | ||||
\(677\) | 3.90531 | 0.150093 | 0.0750467 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750467 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(678\) | 0.813030 | − | 7.86965i | 0.0312242 | − | 0.302232i | ||||
\(679\) | 6.38531 | − | 3.68656i | 0.245046 | − | 0.141477i | ||||
\(680\) | −52.9660 | − | 30.5799i | −2.03115 | − | 1.17269i | ||||
\(681\) | 5.16383 | − | 7.13396i | 0.197878 | − | 0.273374i | ||||
\(682\) | 1.01262 | + | 0.127829i | 0.0387751 | + | 0.00489481i | ||||
\(683\) | 3.02787 | − | 5.24443i | 0.115858 | − | 0.200672i | −0.802264 | − | 0.596969i | \(-0.796371\pi\) |
0.918123 | + | 0.396297i | \(0.129705\pi\) | |||||||
\(684\) | −1.25890 | − | 3.82827i | −0.0481354 | − | 0.146377i | ||||
\(685\) | 9.26876 | − | 16.0540i | 0.354141 | − | 0.613391i | ||||
\(686\) | −16.9236 | + | 9.77085i | −0.646146 | + | 0.373053i | ||||
\(687\) | −13.0037 | − | 1.34344i | −0.496122 | − | 0.0512554i | ||||
\(688\) | 12.1564i | 0.463459i | ||||||||
\(689\) | −2.09639 | + | 2.84906i | −0.0798660 | + | 0.108540i | ||||
\(690\) | −50.1075 | − | 36.2697i | −1.90756 | − | 1.38076i | ||||
\(691\) | −1.34003 | + | 0.773665i | −0.0509771 | + | 0.0294316i | −0.525272 | − | 0.850934i | \(-0.676036\pi\) |
0.474295 | + | 0.880366i | \(0.342703\pi\) | |||||||
\(692\) | 1.07259 | + | 1.85778i | 0.0407738 | + | 0.0706223i | ||||
\(693\) | 2.35686 | + | 12.1155i | 0.0895296 | + | 0.460229i | ||||
\(694\) | 4.64864i | 0.176460i | ||||||||
\(695\) | −2.55269 | − | 1.47380i | −0.0968292 | − | 0.0559044i | ||||
\(696\) | −18.0055 | − | 40.2489i | −0.682498 | − | 1.52563i | ||||
\(697\) | 49.8913i | 1.88977i | ||||||||
\(698\) | 5.61402 | + | 3.24125i | 0.212494 | + | 0.122683i | ||||
\(699\) | −3.20791 | + | 31.0507i | −0.121334 | + | 1.17444i | ||||
\(700\) | −3.01853 | − | 5.22824i | −0.114090 | − | 0.197609i | ||||
\(701\) | 22.5407 | 0.851350 | 0.425675 | − | 0.904876i | \(-0.360037\pi\) | ||||
0.425675 | + | 0.904876i | \(0.360037\pi\) | |||||||
\(702\) | 9.64909 | − | 21.6300i | 0.364181 | − | 0.816371i | ||||
\(703\) | 3.79569i | 0.143157i | ||||||||
\(704\) | 17.8375 | − | 23.5045i | 0.672276 | − | 0.885859i | ||||
\(705\) | 0.137353 | − | 1.32949i | 0.00517301 | − | 0.0500716i | ||||
\(706\) | −9.75399 | − | 5.63147i | −0.367096 | − | 0.211943i | ||||
\(707\) | 16.8894 | 0.635191 | ||||||||
\(708\) | 5.37236 | − | 2.40335i | 0.201905 | − | 0.0903233i | ||||
\(709\) | 26.8935 | + | 15.5270i | 1.01001 | + | 0.583127i | 0.911193 | − | 0.411979i | \(-0.135162\pi\) |
0.0988125 | + | 0.995106i | \(0.468496\pi\) | |||||||
\(710\) | − | 52.9230i | − | 1.98617i | ||||||
\(711\) | −4.31279 | + | 20.6498i | −0.161742 | + | 0.774429i | ||||
\(712\) | −24.3138 | + | 14.0376i | −0.911199 | + | 0.526081i | ||||
\(713\) | 0.831202 | + | 1.43968i | 0.0311288 | + | 0.0539166i | ||||
\(714\) | 7.75509 | − | 10.7139i | 0.290227 | − | 0.400956i | ||||
\(715\) | −47.4398 | + | 14.0154i | −1.77415 | + | 0.524145i | ||||
\(716\) | − | 1.80518i | − | 0.0674629i | ||||||
\(717\) | −29.9185 | − | 3.09094i | −1.11733 | − | 0.115433i | ||||
\(718\) | −15.6109 | − | 27.0390i | −0.582595 | − | 1.00908i | ||||
\(719\) | 29.1335 | + | 16.8202i | 1.08650 | + | 0.627289i | 0.932641 | − | 0.360805i | \(-0.117498\pi\) |
0.153855 | + | 0.988094i | \(0.450831\pi\) | |||||||
\(720\) | 11.7653 | + | 35.7778i | 0.438468 | + | 1.33336i | ||||
\(721\) | 1.52454 | − | 2.64057i | 0.0567767 | − | 0.0983401i | ||||
\(722\) | 8.56579 | + | 4.94546i | 0.318786 | + | 0.184051i | ||||
\(723\) | 20.2940 | + | 14.6895i | 0.754741 | + | 0.546310i | ||||
\(724\) | 2.98823 | − | 5.17577i | 0.111057 | − | 0.192356i | ||||
\(725\) | −50.7723 | − | 87.9402i | −1.88564 | − | 3.26602i | ||||
\(726\) | −18.5286 | + | 15.3893i | −0.687660 | + | 0.571151i | ||||
\(727\) | 28.3059 | 1.04981 | 0.524904 | − | 0.851162i | \(-0.324101\pi\) | ||||
0.524904 | + | 0.851162i | \(0.324101\pi\) | |||||||
\(728\) | 5.44859 | + | 12.4395i | 0.201938 | + | 0.461039i | ||||
\(729\) | −22.0110 | − | 15.6370i | −0.815223 | − | 0.579147i | ||||
\(730\) | −7.14443 | + | 4.12484i | −0.264427 | + | 0.152667i | ||||
\(731\) | 16.8912 | − | 9.75212i | 0.624743 | − | 0.360695i | ||||
\(732\) | −0.105660 | − | 0.236189i | −0.00390532 | − | 0.00872980i | ||||
\(733\) | −2.55702 | −0.0944459 | −0.0472229 | − | 0.998884i | \(-0.515037\pi\) | ||||
−0.0472229 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(734\) | −10.2151 | − | 5.89766i | −0.377044 | − | 0.217687i | ||||
\(735\) | −35.7176 | + | 15.9784i | −1.31746 | + | 0.589373i | ||||
\(736\) | 15.2702 | 0.562869 | ||||||||
\(737\) | 3.74270 | − | 29.6484i | 0.137864 | − | 1.09211i | ||||
\(738\) | 25.8992 | − | 28.9699i | 0.953363 | − | 1.06640i | ||||
\(739\) | 5.02824 | + | 8.70917i | 0.184967 | + | 0.320372i | 0.943565 | − | 0.331186i | \(-0.107449\pi\) |
−0.758598 | + | 0.651558i | \(0.774116\pi\) | |||||||
\(740\) | 1.88723i | 0.0693759i | ||||||||
\(741\) | 6.36662 | + | 19.8830i | 0.233884 | + | 0.730420i | ||||
\(742\) | 1.53848 | 0.0564795 | ||||||||
\(743\) | −1.15594 | + | 0.667382i | −0.0424073 | + | 0.0244839i | −0.521054 | − | 0.853524i | \(-0.674461\pi\) |
0.478646 | + | 0.878008i | \(0.341128\pi\) | |||||||
\(744\) | 0.131561 | − | 1.27344i | 0.00482328 | − | 0.0466864i | ||||
\(745\) | −15.1506 | − | 8.74722i | −0.555076 | − | 0.320473i | ||||
\(746\) | −8.73160 | −0.319687 | ||||||||
\(747\) | 2.87762 | − | 13.7782i | 0.105287 | − | 0.504117i | ||||
\(748\) | −6.43819 | − | 0.812731i | −0.235403 | − | 0.0297164i | ||||
\(749\) | 9.59519 | 0.350600 | ||||||||
\(750\) | 26.3043 | + | 58.7998i | 0.960499 | + | 2.14706i | ||||
\(751\) | 26.3536 | + | 45.6458i | 0.961657 | + | 1.66564i | 0.718340 | + | 0.695692i | \(0.244902\pi\) |
0.243316 | + | 0.969947i | \(0.421765\pi\) | |||||||
\(752\) | −0.283074 | − | 0.490298i | −0.0103226 | − | 0.0178793i | ||||
\(753\) | −20.1398 | + | 27.8237i | −0.733936 | + | 1.01395i | ||||
\(754\) | 15.3323 | + | 35.0048i | 0.558370 | + | 1.27480i | ||||
\(755\) | 2.56601 | 0.0933867 | ||||||||
\(756\) | 2.53053 | − | 0.551963i | 0.0920344 | − | 0.0200747i | ||||
\(757\) | 20.1608 | + | 34.9196i | 0.732759 | + | 1.26918i | 0.955700 | + | 0.294343i | \(0.0951009\pi\) |
−0.222941 | + | 0.974832i | \(0.571566\pi\) | |||||||
\(758\) | −3.26312 | + | 5.65189i | −0.118522 | + | 0.205286i | ||||
\(759\) | −38.2107 | − | 8.88711i | −1.38696 | − | 0.322582i | ||||
\(760\) | −36.3643 | − | 20.9949i | −1.31907 | − | 0.761566i | ||||
\(761\) | 27.7586 | + | 16.0265i | 1.00625 | + | 0.580959i | 0.910092 | − | 0.414407i | \(-0.136011\pi\) |
0.0961585 | + | 0.995366i | \(0.469344\pi\) | |||||||
\(762\) | 2.74308 | + | 1.98555i | 0.0993714 | + | 0.0719287i | ||||
\(763\) | −6.21798 | + | 10.7699i | −0.225106 | + | 0.389895i | ||||
\(764\) | −4.35271 | + | 2.51304i | −0.157476 | + | 0.0909185i | ||||
\(765\) | 40.2744 | − | 45.0494i | 1.45612 | − | 1.62877i | ||||
\(766\) | − | 36.1991i | − | 1.30793i | ||||||
\(767\) | −27.9284 | + | 12.2328i | −1.00843 | + | 0.441701i | ||||
\(768\) | −12.9480 | − | 9.37223i | −0.467220 | − | 0.338191i | ||||
\(769\) | −8.80597 | − | 15.2524i | −0.317551 | − | 0.550015i | 0.662425 | − | 0.749128i | \(-0.269527\pi\) |
−0.979977 | + | 0.199113i | \(0.936194\pi\) | |||||||
\(770\) | 17.1386 | + | 13.0065i | 0.617634 | + | 0.468720i | ||||
\(771\) | 11.2279 | + | 25.0984i | 0.404363 | + | 0.903898i | ||||
\(772\) | 9.84860 | 0.354459 | ||||||||
\(773\) | −3.49632 | + | 6.05581i | −0.125754 | + | 0.217812i | −0.922027 | − | 0.387125i | \(-0.873468\pi\) |
0.796273 | + | 0.604937i | \(0.206802\pi\) | |||||||
\(774\) | −14.8705 | − | 3.10575i | −0.534508 | − | 0.111634i | ||||
\(775\) | − | 2.94830i | − | 0.105906i | ||||||
\(776\) | 9.02372 | − | 15.6295i | 0.323933 | − | 0.561068i | ||||
\(777\) | −2.42656 | − | 0.250693i | −0.0870522 | − | 0.00899355i | ||||
\(778\) | −12.5024 | − | 21.6549i | −0.448234 | − | 0.776365i | ||||
\(779\) | 34.2533i | 1.22725i | ||||||||
\(780\) | 3.16550 | + | 9.88589i | 0.113343 | + | 0.353972i | ||||
\(781\) | −13.0097 | − | 30.9409i | −0.465523 | − | 1.10715i | ||||
\(782\) | 21.0193 | + | 36.4065i | 0.751648 | + | 1.30189i | ||||
\(783\) | 42.5640 | − | 9.28413i | 1.52111 | − | 0.331788i | ||||
\(784\) | −8.28711 | + | 14.3537i | −0.295968 | + | 0.512632i | ||||
\(785\) | 77.2952 | 2.75878 | ||||||||
\(786\) | −19.3182 | − | 43.1831i | −0.689056 | − | 1.54029i | ||||
\(787\) | 4.74047 | − | 8.21073i | 0.168979 | − | 0.292681i | −0.769082 | − | 0.639150i | \(-0.779286\pi\) |
0.938061 | + | 0.346469i | \(0.112620\pi\) | |||||||
\(788\) | − | 3.53794i | − | 0.126034i | ||||||
\(789\) | 23.0864 | − | 10.3278i | 0.821897 | − | 0.367680i | ||||
\(790\) | 18.3863 | + | 31.8460i | 0.654156 | + | 1.13303i | ||||
\(791\) | −3.88157 | + | 2.24102i | −0.138013 | + | 0.0796816i | ||||
\(792\) | 19.8238 | + | 22.7979i | 0.704409 | + | 0.810089i | ||||
\(793\) | 0.537800 | + | 1.22784i | 0.0190979 | + | 0.0436018i | ||||
\(794\) | −21.5646 | −0.765300 | ||||||||
\(795\) | 6.99185 | + | 0.722343i | 0.247975 | + | 0.0256189i | ||||
\(796\) | −0.299655 | − | 0.519017i | −0.0106210 | − | 0.0183961i | ||||
\(797\) | −32.1913 | − | 18.5857i | −1.14027 | − | 0.658338i | −0.193776 | − | 0.981046i | \(-0.562073\pi\) |
−0.946499 | + | 0.322708i | \(0.895407\pi\) | |||||||
\(798\) | 5.32432 | − | 7.35569i | 0.188479 | − | 0.260389i | ||||
\(799\) | −0.454174 | + | 0.786653i | −0.0160675 | + | 0.0278298i | ||||
\(800\) | −23.4537 | − | 13.5410i | −0.829214 | − | 0.478747i | ||||
\(801\) | −8.66530 | − | 26.3508i | −0.306173 | − | 0.931059i | ||||
\(802\) | 3.02431 | + | 1.74609i | 0.106792 | + | 0.0616564i | ||||
\(803\) | −3.16293 | + | 4.16780i | −0.111617 | + | 0.147079i | ||||
\(804\) | −6.23773 | − | 0.644434i | −0.219988 | − | 0.0227274i | ||||
\(805\) | 35.0431i | 1.23511i | ||||||||
\(806\) | −0.122648 | + | 1.10277i | −0.00432010 | + | 0.0388433i | ||||
\(807\) | 18.2750 | − | 25.2474i | 0.643311 | − | 0.888751i | ||||
\(808\) | 35.8021 | − | 20.6704i | 1.25951 | − | 0.727181i | ||||
\(809\) | 14.5736 | + | 25.2421i | 0.512379 | + | 0.887467i | 0.999897 | + | 0.0143535i | \(0.00456903\pi\) |
−0.487518 | + | 0.873113i | \(0.662098\pi\) | |||||||
\(810\) | −46.7714 | + | 5.25146i | −1.64338 | + | 0.184518i | ||||
\(811\) | −38.5706 | −1.35440 | −0.677199 | − | 0.735800i | \(-0.736806\pi\) | ||||
−0.677199 | + | 0.735800i | \(0.736806\pi\) | |||||||
\(812\) | −2.08952 | + | 3.61915i | −0.0733277 | + | 0.127007i | ||||
\(813\) | 3.95968 | − | 1.77138i | 0.138872 | − | 0.0621251i | ||||
\(814\) | −1.84518 | − | 4.38838i | −0.0646736 | − | 0.153813i | ||||
\(815\) | −0.350444 | − | 0.202329i | −0.0122755 | − | 0.00708728i | ||||
\(816\) | 2.63038 | − | 25.4605i | 0.0920816 | − | 0.891295i | ||||
\(817\) | 11.5968 | − | 6.69540i | 0.405720 | − | 0.234243i | ||||
\(818\) | − | 1.33613i | − | 0.0467165i | ||||||
\(819\) | −13.1315 | + | 2.75693i | −0.458853 | + | 0.0963348i | ||||
\(820\) | 17.0309i | 0.594744i | ||||||||
\(821\) | −40.9400 | + | 23.6367i | −1.42882 | + | 0.824928i | −0.997028 | − | 0.0770461i | \(-0.975451\pi\) |
−0.431790 | + | 0.901974i | \(0.642118\pi\) | |||||||
\(822\) | 9.76054 | + | 1.00838i | 0.340438 | + | 0.0351714i | ||||
\(823\) | 9.28339 | − | 16.0793i | 0.323599 | − | 0.560489i | −0.657629 | − | 0.753342i | \(-0.728441\pi\) |
0.981228 | + | 0.192853i | \(0.0617739\pi\) | |||||||
\(824\) | − | 7.46331i | − | 0.259997i | ||||||
\(825\) | 50.8075 | + | 47.5335i | 1.76889 | + | 1.65490i | ||||
\(826\) | 11.4846 | + | 6.63065i | 0.399601 | + | 0.230710i | ||||
\(827\) | 4.75897i | 0.165486i | 0.996571 | + | 0.0827428i | \(0.0263680\pi\) | ||||
−0.996571 | + | 0.0827428i | \(0.973632\pi\) | |||||||
\(828\) | −1.68303 | + | 8.05844i | −0.0584895 | + | 0.280050i | ||||
\(829\) | −7.80515 | − | 13.5189i | −0.271084 | − | 0.469532i | 0.698056 | − | 0.716044i | \(-0.254049\pi\) |
−0.969140 | + | 0.246512i | \(0.920715\pi\) | |||||||
\(830\) | −12.2679 | − | 21.2486i | −0.425825 | − | 0.737550i | ||||
\(831\) | −19.9436 | + | 27.5525i | −0.691834 | + | 0.955787i | ||||
\(832\) | 25.8364 | + | 19.0109i | 0.895717 | + | 0.659084i | ||||
\(833\) | 26.5923 | 0.921370 | ||||||||
\(834\) | 0.160340 | − | 1.55199i | 0.00555212 | − | 0.0537412i | ||||
\(835\) | 5.35927 | − | 3.09417i | 0.185465 | − | 0.107078i | ||||
\(836\) | −4.42019 | − | 0.557988i | −0.152876 | − | 0.0192984i | ||||
\(837\) | 1.20504 | + | 0.384467i | 0.0416522 | + | 0.0132891i | ||||
\(838\) | 23.0779 | − | 39.9721i | 0.797212 | − | 1.38081i | ||||
\(839\) | 20.5657 | − | 35.6208i | 0.710006 | − | 1.22977i | −0.254848 | − | 0.966981i | \(-0.582026\pi\) |
0.964854 | − | 0.262785i | \(-0.0846411\pi\) | |||||||
\(840\) | 15.8236 | − | 21.8607i | 0.545967 | − | 0.754267i | ||||
\(841\) | −20.6461 | + | 35.7602i | −0.711936 | + | 1.23311i | ||||
\(842\) | 16.7222 | + | 28.9637i | 0.576285 | + | 0.998155i | ||||
\(843\) | 23.2362 | + | 2.40058i | 0.800296 | + | 0.0826803i | ||||
\(844\) | − | 6.45300i | − | 0.222122i | ||||||
\(845\) | −15.9983 | − | 51.3412i | −0.550359 | − | 1.76619i | ||||
\(846\) | 0.672082 | − | 0.221010i | 0.0231067 | − | 0.00759849i | ||||
\(847\) | 13.2172 | + | 3.39101i | 0.454148 | + | 0.116517i | ||||
\(848\) | 2.57849 | − | 1.48869i | 0.0885458 | − | 0.0511219i | ||||
\(849\) | 20.7953 | + | 46.4850i | 0.713692 | + | 1.59536i | ||||
\(850\) | − | 74.5561i | − | 2.55725i | ||||||
\(851\) | 3.87689 | − | 6.71498i | 0.132898 | − | 0.230186i | ||||
\(852\) | −6.42934 | + | 2.87620i | −0.220266 | + | 0.0985368i | ||||
\(853\) | 40.1240 | 1.37382 | 0.686910 | − | 0.726742i | \(-0.258966\pi\) | ||||
0.686910 | + | 0.726742i | \(0.258966\pi\) | |||||||
\(854\) | 0.291509 | − | 0.504908i | 0.00997523 | − | 0.0172776i | ||||
\(855\) | 27.6507 | − | 30.9291i | 0.945635 | − | 1.05775i | ||||
\(856\) | 20.3399 | − | 11.7432i | 0.695202 | − | 0.401375i | ||||
\(857\) | −36.7938 | −1.25685 | −0.628425 | − | 0.777870i | \(-0.716300\pi\) | ||||
−0.628425 | + | 0.777870i | \(0.716300\pi\) | |||||||
\(858\) | −17.0264 | − | 19.8927i | −0.581271 | − | 0.679127i | ||||
\(859\) | 2.24175 | 0.0764874 | 0.0382437 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382437 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(860\) | 5.76596 | − | 3.32898i | 0.196617 | − | 0.113517i | ||||
\(861\) | −21.8979 | − | 2.26232i | −0.746278 | − | 0.0770996i | ||||
\(862\) | 20.3071 | − | 35.1730i | 0.691664 | − | 1.19800i | ||||
\(863\) | −13.8565 | −0.471681 | −0.235841 | − | 0.971792i | \(-0.575784\pi\) | ||||
−0.235841 | + | 0.971792i | \(0.575784\pi\) | |||||||
\(864\) | 8.59295 | − | 7.82028i | 0.292338 | − | 0.266051i | ||||
\(865\) | −11.0420 | + | 19.1253i | −0.375439 | + | 0.650279i | ||||
\(866\) | − | 39.4512i | − | 1.34061i | ||||||
\(867\) | −10.6091 | + | 4.74605i | −0.360305 | + | 0.161184i | ||||
\(868\) | −0.105080 | + | 0.0606682i | −0.00356666 | + | 0.00205921i | ||||
\(869\) | 18.5778 | + | 14.0986i | 0.630210 | + | 0.478264i | ||||
\(870\) | 44.5277 | − | 61.5161i | 1.50963 | − | 2.08559i | ||||
\(871\) | 32.2880 | + | 3.59103i | 1.09404 | + | 0.121677i | ||||
\(872\) | 30.4399i | 1.03083i | ||||||||
\(873\) | 13.2935 | + | 11.8844i | 0.449916 | + | 0.402227i | ||||
\(874\) | 14.4310 | + | 24.9952i | 0.488135 | + | 0.845474i | ||||
\(875\) | 18.2463 | − | 31.6035i | 0.616838 | − | 1.06839i | ||||
\(876\) | 0.889382 | + | 0.643768i | 0.0300494 | + | 0.0217509i | ||||
\(877\) | −8.79547 | + | 15.2342i | −0.297002 | + | 0.514423i | −0.975449 | − | 0.220227i | \(-0.929320\pi\) |
0.678447 | + | 0.734650i | \(0.262653\pi\) | |||||||
\(878\) | 2.78077 | − | 4.81644i | 0.0938466 | − | 0.162547i | ||||
\(879\) | 7.51744 | − | 10.3855i | 0.253557 | − | 0.350295i | ||||
\(880\) | 41.3098 | + | 5.21479i | 1.39255 | + | 0.175790i | ||||
\(881\) | −15.4359 | + | 8.91191i | −0.520048 | + | 0.300250i | −0.736954 | − | 0.675943i | \(-0.763737\pi\) |
0.216906 | + | 0.976192i | \(0.430403\pi\) | |||||||
\(882\) | −15.4411 | − | 13.8044i | −0.519929 | − | 0.464819i | ||||
\(883\) | −13.5495 | −0.455978 | −0.227989 | − | 0.973664i | \(-0.573215\pi\) | ||||
−0.227989 | + | 0.973664i | \(0.573215\pi\) | |||||||
\(884\) | 0.779794 | − | 7.01136i | 0.0262273 | − | 0.235818i | ||||
\(885\) | 49.0803 | + | 35.5261i | 1.64982 | + | 1.19420i | ||||
\(886\) | −13.4251 | − | 23.2529i | −0.451025 | − | 0.781198i | ||||
\(887\) | 25.9762 | + | 44.9921i | 0.872195 | + | 1.51069i | 0.859721 | + | 0.510764i | \(0.170637\pi\) |
0.0124736 | + | 0.999922i | \(0.496029\pi\) | |||||||
\(888\) | −5.45063 | + | 2.43836i | −0.182911 | + | 0.0818261i | ||||
\(889\) | − | 1.91840i | − | 0.0643410i | ||||||
\(890\) | −41.8753 | − | 24.1767i | −1.40366 | − | 0.810406i | ||||
\(891\) | −26.0535 | + | 14.5677i | −0.872824 | + | 0.488036i | ||||
\(892\) | − | 4.94530i | − | 0.165581i | ||||||
\(893\) | −0.311817 | + | 0.540083i | −0.0104346 | + | 0.0180732i | ||||
\(894\) | 0.951642 | − | 9.21133i | 0.0318277 | − | 0.308073i | ||||
\(895\) | 16.0940 | − | 9.29189i | 0.537964 | − | 0.310594i | ||||
\(896\) | − | 8.40411i | − | 0.280762i | ||||||
\(897\) | 9.04514 | − | 41.6779i | 0.302008 | − | 1.39159i | ||||
\(898\) | 46.4115i | 1.54877i | ||||||||
\(899\) | −1.76747 | + | 1.02045i | −0.0589486 | + | 0.0340340i | ||||
\(900\) | 9.73087 | − | 10.8846i | 0.324362 | − | 0.362820i | ||||
\(901\) | −4.13703 | − | 2.38852i | −0.137825 | − | 0.0795730i | ||||
\(902\) | −16.6514 | − | 39.6020i | −0.554431 | − | 1.31860i | ||||
\(903\) | 3.51439 | + | 7.85594i | 0.116952 | + | 0.261429i | ||||
\(904\) | −5.48543 | + | 9.50104i | −0.182443 | + | 0.316000i | ||||
\(905\) | 61.5257 | 2.04518 | ||||||||
\(906\) | 0.554657 | + | 1.23986i | 0.0184272 | + | 0.0411916i | ||||
\(907\) | −17.3670 | − | 30.0805i | −0.576662 | − | 0.998808i | −0.995859 | − | 0.0909127i | \(-0.971022\pi\) |
0.419197 | − | 0.907895i | \(-0.362312\pi\) | |||||||
\(908\) | −1.76937 | + | 1.02154i | −0.0587185 | + | 0.0339011i | ||||
\(909\) | 12.7597 | + | 38.8015i | 0.423211 | + | 1.28697i | ||||
\(910\) | −13.8621 | + | 18.8390i | −0.459523 | + | 0.624507i | ||||
\(911\) | − | 8.73289i | − | 0.289334i | −0.989480 | − | 0.144667i | \(-0.953789\pi\) | ||
0.989480 | − | 0.144667i | \(-0.0462110\pi\) | |||||||
\(912\) | 1.80591 | − | 17.4801i | 0.0597996 | − | 0.578824i | ||||
\(913\) | −12.3957 | − | 9.40704i | −0.410237 | − | 0.311328i | ||||
\(914\) | 2.91002 | + | 1.68010i | 0.0962551 | + | 0.0555729i | ||||
\(915\) | 1.56186 | − | 2.15776i | 0.0516336 | − | 0.0713332i | ||||
\(916\) | 2.62649 | + | 1.51640i | 0.0867815 | + | 0.0501033i | ||||
\(917\) | −13.4003 | + | 23.2099i | −0.442515 | + | 0.766459i | ||||
\(918\) | 30.4728 | + | 9.72233i | 1.00575 | + | 0.320885i | ||||
\(919\) | −15.0596 | − | 8.69464i | −0.496769 | − | 0.286810i | 0.230609 | − | 0.973046i | \(-0.425928\pi\) |
−0.727378 | + | 0.686237i | \(0.759261\pi\) | |||||||
\(920\) | 42.8881 | + | 74.2844i | 1.41398 | + | 2.44909i | ||||
\(921\) | 2.48743 | − | 24.0768i | 0.0819634 | − | 0.793357i | ||||
\(922\) | −32.3167 | −1.06429 | ||||||||
\(923\) | 33.4231 | − | 14.6395i | 1.10014 | − | 0.481867i | ||||
\(924\) | 0.648656 | − | 2.78894i | 0.0213392 | − | 0.0917494i | ||||
\(925\) | −11.9091 | + | 6.87573i | −0.391569 | + | 0.226073i | ||||
\(926\) | 6.60709 | + | 11.4438i | 0.217123 | + | 0.376067i | ||||
\(927\) | 7.21819 | + | 1.50754i | 0.237076 | + | 0.0495143i | ||||
\(928\) | 18.7470i | 0.615401i | ||||||||
\(929\) | −13.3006 | + | 23.0372i | −0.436377 | + | 0.755828i | −0.997407 | − | 0.0719681i | \(-0.977072\pi\) |
0.561030 | + | 0.827796i | \(0.310405\pi\) | |||||||
\(930\) | 2.01268 | − | 0.900381i | 0.0659983 | − | 0.0295246i | ||||
\(931\) | 18.2572 | 0.598355 | ||||||||
\(932\) | 3.62092 | − | 6.27162i | 0.118607 | − | 0.205434i | ||||
\(933\) | 42.6126 | + | 4.40240i | 1.39507 | + | 0.144128i | ||||
\(934\) | −19.1038 | − | 33.0888i | −0.625096 | − | 1.08270i | ||||
\(935\) | −25.8937 | − | 61.5828i | −0.846813 | − | 2.01397i | ||||
\(936\) | −24.4621 | + | 21.9154i | −0.799570 | + | 0.716327i | ||||
\(937\) | − | 42.2335i | − | 1.37971i | −0.723948 | − | 0.689854i | \(-0.757674\pi\) | ||
0.723948 | − | 0.689854i | \(-0.242326\pi\) | |||||||
\(938\) | −7.06497 | − | 12.2369i | −0.230680 | − | 0.399549i | ||||
\(939\) | 1.26326 | − | 12.2276i | 0.0412248 | − | 0.399031i | ||||
\(940\) | −0.155037 | + | 0.268531i | −0.00505674 | + | 0.00875852i | ||||
\(941\) | 15.9049i | 0.518483i | 0.965812 | + | 0.259242i | \(0.0834726\pi\) | ||||
−0.965812 | + | 0.259242i | \(0.916527\pi\) | |||||||
\(942\) | 16.7078 | + | 37.3479i | 0.544368 | + | 1.21686i | ||||
\(943\) | 34.9861 | − | 60.5978i | 1.13931 | − | 1.97333i | ||||
\(944\) | 25.6642 | 0.835300 | ||||||||
\(945\) | 17.9465 | + | 19.7197i | 0.583799 | + | 0.641481i | ||||
\(946\) | −10.1528 | + | 13.3784i | −0.330096 | + | 0.434968i | ||||
\(947\) | 15.6897 | + | 27.1754i | 0.509848 | + | 0.883082i | 0.999935 | + | 0.0114088i | \(0.00363162\pi\) |
−0.490087 | + | 0.871673i | \(0.663035\pi\) | |||||||
\(948\) | 2.86957 | − | 3.96438i | 0.0931993 | − | 0.128757i | ||||
\(949\) | −4.58130 | − | 3.37100i | −0.148715 | − | 0.109427i | ||||
\(950\) | − | 51.1871i | − | 1.66073i | ||||||
\(951\) | −0.0657314 | + | 0.636241i | −0.00213149 | + | 0.0206315i | ||||
\(952\) | −15.8833 | + | 9.17022i | −0.514780 | + | 0.297209i | ||||
\(953\) | 17.8965 | − | 30.9977i | 0.579726 | − | 1.00411i | −0.415785 | − | 0.909463i | \(-0.636493\pi\) |
0.995510 | − | 0.0946514i | \(-0.0301736\pi\) | |||||||
\(954\) | 1.16230 | + | 3.53450i | 0.0376308 | + | 0.114434i | ||||
\(955\) | −44.8098 | − | 25.8709i | −1.45001 | − | 0.837163i | ||||
\(956\) | 6.04294 | + | 3.48889i | 0.195442 | + | 0.112839i | ||||
\(957\) | 10.9105 | − | 46.9106i | 0.352688 | − | 1.51640i | ||||
\(958\) | −10.3031 | + | 17.8454i | −0.332876 | + | 0.576559i | ||||
\(959\) | −2.77949 | − | 4.81422i | −0.0897544 | − | 0.155459i | ||||
\(960\) | 6.55051 | − | 63.4050i | 0.211417 | − | 2.04639i | ||||
\(961\) | 30.9407 | 0.998088 | ||||||||
\(962\) | 4.74045 | − | 2.07635i | 0.152838 | − | 0.0669441i | ||||
\(963\) | 7.24901 | + | 22.0439i | 0.233596 | + | 0.710355i | ||||
\(964\) | −2.90599 | − | 5.03332i | −0.0935955 | − | 0.162112i | ||||
\(965\) | 50.6941 | + | 87.8047i | 1.63190 | + | 2.82653i | ||||
\(966\) | −16.9323 | + | 7.57476i | −0.544789 | + | 0.243714i | ||||
\(967\) | −17.9153 | −0.576117 | −0.288058 | − | 0.957613i | \(-0.593010\pi\) | ||||
−0.288058 | + | 0.957613i | \(0.593010\pi\) | |||||||
\(968\) | 32.1679 | − | 8.98782i | 1.03392 | − | 0.288880i | ||||
\(969\) | −25.7371 | + | 11.5136i | −0.826794 | + | 0.369870i | ||||
\(970\) | 31.0829 | 0.998010 | ||||||||
\(971\) | 14.0000 | + | 8.08290i | 0.449281 | + | 0.259393i | 0.707527 | − | 0.706687i | \(-0.249811\pi\) |
−0.258245 | + | 0.966079i | \(0.583144\pi\) | |||||||
\(972\) | 3.17985 | + | 5.39661i | 0.101994 | + | 0.173096i | ||||
\(973\) | −0.765495 | + | 0.441959i | −0.0245406 | + | 0.0141685i | ||||
\(974\) | 30.7290 | 0.984620 | ||||||||
\(975\) | −50.8508 | + | 55.9927i | −1.62853 | + | 1.79320i | ||||
\(976\) | − | 1.12830i | − | 0.0361159i | ||||||
\(977\) | 12.3134 | + | 21.3274i | 0.393939 | + | 0.682323i | 0.992965 | − | 0.118407i | \(-0.0377786\pi\) |
−0.599026 | + | 0.800730i | \(0.704445\pi\) | |||||||
\(978\) | 0.0220121 | − | 0.213064i | 0.000703870 | − | 0.00681304i | ||||
\(979\) | −30.4251 | − | 3.84075i | −0.972392 | − | 0.122751i | ||||
\(980\) | 9.07754 | 0.289971 | ||||||||
\(981\) | −29.4402 | − | 6.14868i | −0.939952 | − | 0.196312i | ||||
\(982\) | 18.0760 | + | 10.4362i | 0.576828 | + | 0.333032i | ||||
\(983\) | −45.2956 | −1.44471 | −0.722353 | − | 0.691524i | \(-0.756939\pi\) | ||||
−0.722353 | + | 0.691524i | \(0.756939\pi\) | |||||||
\(984\) | −49.1879 | + | 22.0044i | −1.56805 | + | 0.701476i | ||||
\(985\) | 31.5423 | − | 18.2110i | 1.00502 | − | 0.580250i | ||||
\(986\) | −44.6956 | + | 25.8050i | −1.42340 | + | 0.821798i | ||||
\(987\) | −0.324677 | − | 0.235013i | −0.0103346 | − | 0.00748055i | ||||
\(988\) | 0.535375 | − | 4.81371i | 0.0170325 | − | 0.153145i | ||||
\(989\) | −27.3546 | −0.869825 | ||||||||
\(990\) | −16.9330 | + | 49.2003i | −0.538165 | + | 1.56369i | ||||
\(991\) | −12.3767 | − | 21.4371i | −0.393159 | − | 0.680971i | 0.599706 | − | 0.800221i | \(-0.295284\pi\) |
−0.992864 | + | 0.119250i | \(0.961951\pi\) | |||||||
\(992\) | −0.272155 | + | 0.471387i | −0.00864094 | + | 0.0149665i | ||||
\(993\) | 4.73578 | − | 6.54260i | 0.150285 | − | 0.207623i | ||||
\(994\) | −13.7442 | − | 7.93521i | −0.435939 | − | 0.251689i | ||||
\(995\) | 3.08485 | − | 5.34312i | 0.0977963 | − | 0.169388i | ||||
\(996\) | −1.91466 | + | 2.64516i | −0.0606684 | + | 0.0838150i | ||||
\(997\) | 7.55715 | + | 4.36312i | 0.239337 | + | 0.138181i | 0.614872 | − | 0.788627i | \(-0.289208\pi\) |
−0.375535 | + | 0.926808i | \(0.622541\pi\) | |||||||
\(998\) | −18.3495 | − | 31.7823i | −0.580844 | − | 1.00605i | ||||
\(999\) | −1.25728 | − | 5.76414i | −0.0397787 | − | 0.182369i |
(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 | 429.2.t.a.296.38 | yes | 104 | |
3.2 | odd | 2 | inner | 429.2.t.a.296.15 | ✓ | 104 | |
11.10 | odd | 2 | inner | 429.2.t.a.296.16 | yes | 104 | |
13.4 | even | 6 | inner | 429.2.t.a.329.37 | yes | 104 | |
33.32 | even | 2 | inner | 429.2.t.a.296.37 | yes | 104 | |
39.17 | odd | 6 | inner | 429.2.t.a.329.16 | yes | 104 | |
143.43 | odd | 6 | inner | 429.2.t.a.329.15 | yes | 104 | |
429.329 | even | 6 | inner | 429.2.t.a.329.38 | yes | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.t.a.296.15 | ✓ | 104 | 3.2 | odd | 2 | inner | |
429.2.t.a.296.16 | yes | 104 | 11.10 | odd | 2 | inner | |
429.2.t.a.296.37 | yes | 104 | 33.32 | even | 2 | inner | |
429.2.t.a.296.38 | yes | 104 | 1.1 | even | 1 | trivial | |
429.2.t.a.329.15 | yes | 104 | 143.43 | odd | 6 | inner | |
429.2.t.a.329.16 | yes | 104 | 39.17 | odd | 6 | inner | |
429.2.t.a.329.37 | yes | 104 | 13.4 | even | 6 | inner | |
429.2.t.a.329.38 | yes | 104 | 429.329 | even | 6 | inner |