Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 351.2 | ||
Root | \(0.394508 - 0.683308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.351 |
Dual form | 475.2.l.c.226.2 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0366369 | − | 0.207778i | −0.0259062 | − | 0.146921i | 0.969111 | − | 0.246625i | \(-0.0793216\pi\) |
−0.995017 | + | 0.0997037i | \(0.968211\pi\) | |||||||
\(3\) | −0.0612035 | + | 0.0513559i | −0.0353359 | + | 0.0296503i | −0.660285 | − | 0.751016i | \(-0.729564\pi\) |
0.624949 | + | 0.780666i | \(0.285120\pi\) | |||||||
\(4\) | 1.83756 | − | 0.668816i | 0.918778 | − | 0.334408i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0129129 | + | 0.0108352i | 0.00527169 | + | 0.00442347i | ||||
\(7\) | −0.843614 | + | 1.46118i | −0.318856 | + | 0.552275i | −0.980250 | − | 0.197764i | \(-0.936632\pi\) |
0.661394 | + | 0.750039i | \(0.269965\pi\) | |||||||
\(8\) | −0.417271 | − | 0.722735i | −0.147528 | − | 0.255526i | ||||
\(9\) | −0.519836 | + | 2.94814i | −0.173279 | + | 0.982712i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.44339 | + | 2.50003i | 0.435199 | + | 0.753787i | 0.997312 | − | 0.0732738i | \(-0.0233447\pi\) |
−0.562113 | + | 0.827061i | \(0.690011\pi\) | |||||||
\(12\) | −0.0781173 | + | 0.135303i | −0.0225505 | + | 0.0390586i | ||||
\(13\) | 4.95325 | + | 4.15627i | 1.37378 | + | 1.15274i | 0.971449 | + | 0.237250i | \(0.0762461\pi\) |
0.402336 | + | 0.915492i | \(0.368198\pi\) | |||||||
\(14\) | 0.334509 | + | 0.121751i | 0.0894014 | + | 0.0325394i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.86110 | − | 2.40075i | 0.715274 | − | 0.600186i | ||||
\(17\) | −0.518598 | − | 2.94112i | −0.125778 | − | 0.713325i | −0.980842 | − | 0.194803i | \(-0.937593\pi\) |
0.855064 | − | 0.518523i | \(-0.173518\pi\) | |||||||
\(18\) | 0.631604 | 0.148871 | ||||||||
\(19\) | −4.34933 | − | 0.288668i | −0.997805 | − | 0.0662249i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0234081 | − | 0.132754i | −0.00510807 | − | 0.0289693i | ||||
\(22\) | 0.466570 | − | 0.391499i | 0.0994731 | − | 0.0834678i | ||||
\(23\) | 7.75955 | − | 2.82424i | 1.61798 | − | 0.588896i | 0.634982 | − | 0.772527i | \(-0.281008\pi\) |
0.982995 | + | 0.183631i | \(0.0587853\pi\) | |||||||
\(24\) | 0.0626552 | + | 0.0228046i | 0.0127894 | + | 0.00465497i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.682111 | − | 1.18145i | 0.133773 | − | 0.231702i | ||||
\(27\) | −0.239432 | − | 0.414708i | −0.0460786 | − | 0.0798105i | ||||
\(28\) | −0.572926 | + | 3.24923i | −0.108273 | + | 0.614046i | ||||
\(29\) | 1.26021 | − | 7.14701i | 0.234015 | − | 1.32717i | −0.610662 | − | 0.791891i | \(-0.709097\pi\) |
0.844677 | − | 0.535276i | \(-0.179792\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.02800 | + | 3.51260i | −0.364240 | + | 0.630882i | −0.988654 | − | 0.150212i | \(-0.952005\pi\) |
0.624414 | + | 0.781094i | \(0.285338\pi\) | |||||||
\(32\) | −1.88224 | − | 1.57939i | −0.332736 | − | 0.279199i | ||||
\(33\) | −0.216732 | − | 0.0788839i | −0.0377281 | − | 0.0137319i | ||||
\(34\) | −0.592100 | + | 0.215507i | −0.101544 | + | 0.0369591i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.01653 | + | 5.76504i | 0.169422 | + | 0.960840i | ||||
\(37\) | −7.96989 | −1.31024 | −0.655121 | − | 0.755524i | \(-0.727382\pi\) | ||||
−0.655121 | + | 0.755524i | \(0.727382\pi\) | |||||||
\(38\) | 0.0993671 | + | 0.914272i | 0.0161195 | + | 0.148315i | ||||
\(39\) | −0.516605 | −0.0827230 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.17950 | − | 3.50702i | 0.652728 | − | 0.547704i | −0.255169 | − | 0.966896i | \(-0.582131\pi\) |
0.907897 | + | 0.419192i | \(0.137687\pi\) | |||||||
\(42\) | −0.0267258 | + | 0.00972740i | −0.00412388 | + | 0.00150097i | ||||
\(43\) | −5.01011 | − | 1.82353i | −0.764034 | − | 0.278086i | −0.0695352 | − | 0.997580i | \(-0.522152\pi\) |
−0.694499 | + | 0.719494i | \(0.744374\pi\) | |||||||
\(44\) | 4.32437 | + | 3.62858i | 0.651923 | + | 0.547029i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.871103 | − | 1.50879i | −0.128437 | − | 0.222460i | ||||
\(47\) | −0.286452 | + | 1.62455i | −0.0417833 | + | 0.236965i | −0.998546 | − | 0.0539044i | \(-0.982833\pi\) |
0.956763 | + | 0.290869i | \(0.0939445\pi\) | |||||||
\(48\) | −0.0518169 | + | 0.293868i | −0.00747912 | + | 0.0424162i | ||||
\(49\) | 2.07663 | + | 3.59683i | 0.296662 | + | 0.513833i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.182783 | + | 0.153374i | 0.0255948 | + | 0.0214766i | ||||
\(52\) | 11.8817 | + | 4.32457i | 1.64769 | + | 0.599710i | ||||
\(53\) | 1.79663 | − | 0.653921i | 0.246787 | − | 0.0898230i | −0.215665 | − | 0.976467i | \(-0.569192\pi\) |
0.462452 | + | 0.886644i | \(0.346970\pi\) | |||||||
\(54\) | −0.0773952 | + | 0.0649423i | −0.0105322 | + | 0.00883753i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.40806 | 0.188160 | ||||||||
\(57\) | 0.281019 | − | 0.205696i | 0.0372219 | − | 0.0272451i | ||||
\(58\) | −1.53116 | −0.201052 | ||||||||
\(59\) | 0.616931 | + | 3.49879i | 0.0803175 | + | 0.455503i | 0.998269 | + | 0.0588110i | \(0.0187309\pi\) |
−0.917952 | + | 0.396692i | \(0.870158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.42370 | − | 2.70201i | 0.950508 | − | 0.345956i | 0.180201 | − | 0.983630i | \(-0.442325\pi\) |
0.770307 | + | 0.637673i | \(0.220103\pi\) | |||||||
\(62\) | 0.804142 | + | 0.292684i | 0.102126 | + | 0.0371709i | ||||
\(63\) | −3.86922 | − | 3.24666i | −0.487476 | − | 0.409041i | ||||
\(64\) | 3.47569 | − | 6.02008i | 0.434462 | − | 0.752510i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.00844998 | + | 0.0479222i | −0.00104012 | + | 0.00589882i | ||||
\(67\) | −0.393370 | + | 2.23091i | −0.0480578 | + | 0.272550i | −0.999362 | − | 0.0357028i | \(-0.988633\pi\) |
0.951305 | + | 0.308252i | \(0.0997441\pi\) | |||||||
\(68\) | −2.92002 | − | 5.05762i | −0.354104 | − | 0.613326i | ||||
\(69\) | −0.329870 | + | 0.571352i | −0.0397117 | + | 0.0687827i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79389 | − | 3.56469i | −1.16232 | − | 0.423050i | −0.312395 | − | 0.949952i | \(-0.601131\pi\) |
−0.849926 | + | 0.526902i | \(0.823354\pi\) | |||||||
\(72\) | 2.34764 | − | 0.854469i | 0.276671 | − | 0.100700i | ||||
\(73\) | −1.08155 | + | 0.907529i | −0.126586 | + | 0.106218i | −0.703883 | − | 0.710316i | \(-0.748552\pi\) |
0.577297 | + | 0.816534i | \(0.304108\pi\) | |||||||
\(74\) | 0.291992 | + | 1.65597i | 0.0339434 | + | 0.192503i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.18520 | + | 2.37846i | −0.938907 | + | 0.272828i | ||||
\(77\) | −4.87066 | −0.555063 | ||||||||
\(78\) | 0.0189268 | + | 0.107339i | 0.00214304 | + | 0.0121538i | ||||
\(79\) | −1.84675 | + | 1.54961i | −0.207776 | + | 0.174344i | −0.740737 | − | 0.671795i | \(-0.765524\pi\) |
0.532961 | + | 0.846140i | \(0.321079\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.40329 | − | 3.05855i | −0.933699 | − | 0.339838i | ||||
\(82\) | −0.881806 | − | 0.739923i | −0.0973792 | − | 0.0817108i | ||||
\(83\) | −5.70029 | + | 9.87319i | −0.625688 | + | 1.08372i | 0.362719 | + | 0.931898i | \(0.381848\pi\) |
−0.988407 | + | 0.151825i | \(0.951485\pi\) | |||||||
\(84\) | −0.131802 | − | 0.228287i | −0.0143807 | − | 0.0249082i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.195335 | + | 1.10780i | −0.0210635 | + | 0.119457i | ||||
\(87\) | 0.289912 | + | 0.502142i | 0.0310818 | + | 0.0538352i | ||||
\(88\) | 1.20457 | − | 2.08638i | 0.128408 | − | 0.222409i | ||||
\(89\) | −7.74938 | − | 6.50250i | −0.821433 | − | 0.689264i | 0.131874 | − | 0.991266i | \(-0.457901\pi\) |
−0.953307 | + | 0.302002i | \(0.902345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2517 | + | 3.73131i | −1.07467 | + | 0.391148i | ||||
\(92\) | 12.3697 | − | 10.3794i | 1.28963 | − | 1.08213i | ||||
\(93\) | −0.0562718 | − | 0.319133i | −0.00583512 | − | 0.0330926i | ||||
\(94\) | 0.348041 | 0.0358977 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.196310 | 0.0200358 | ||||||||
\(97\) | 1.71360 | + | 9.71828i | 0.173989 | + | 0.986742i | 0.939304 | + | 0.343086i | \(0.111472\pi\) |
−0.765315 | + | 0.643656i | \(0.777417\pi\) | |||||||
\(98\) | 0.671262 | − | 0.563256i | 0.0678077 | − | 0.0568974i | ||||
\(99\) | −8.12075 | + | 2.95571i | −0.816166 | + | 0.297060i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.19421 | + | 2.68026i | 0.317836 | + | 0.266696i | 0.787722 | − | 0.616031i | \(-0.211260\pi\) |
−0.469886 | + | 0.882727i | \(0.655705\pi\) | |||||||
\(102\) | 0.0251711 | − | 0.0435976i | 0.00249231 | − | 0.00431680i | ||||
\(103\) | −6.28180 | − | 10.8804i | −0.618964 | − | 1.07208i | −0.989675 | − | 0.143329i | \(-0.954219\pi\) |
0.370711 | − | 0.928748i | \(-0.379114\pi\) | |||||||
\(104\) | 0.937034 | − | 5.31418i | 0.0918837 | − | 0.521098i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.201694 | − | 0.349344i | −0.0195902 | − | 0.0339313i | ||||
\(107\) | 7.47116 | − | 12.9404i | 0.722264 | − | 1.25100i | −0.237826 | − | 0.971308i | \(-0.576435\pi\) |
0.960090 | − | 0.279690i | \(-0.0902318\pi\) | |||||||
\(108\) | −0.717332 | − | 0.601913i | −0.0690253 | − | 0.0579191i | ||||
\(109\) | −4.89106 | − | 1.78020i | −0.468479 | − | 0.170512i | 0.0969843 | − | 0.995286i | \(-0.469080\pi\) |
−0.565463 | + | 0.824774i | \(0.691303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.487785 | − | 0.409301i | 0.0462985 | − | 0.0388491i | ||||
\(112\) | 1.09427 | + | 6.20589i | 0.103398 | + | 0.586401i | ||||
\(113\) | −8.57064 | −0.806258 | −0.403129 | − | 0.915143i | \(-0.632077\pi\) | ||||
−0.403129 | + | 0.915143i | \(0.632077\pi\) | |||||||
\(114\) | −0.0530349 | − | 0.0508536i | −0.00496717 | − | 0.00476288i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.46433 | − | 13.9759i | −0.228807 | − | 1.29763i | ||||
\(117\) | −14.8281 | + | 12.4423i | −1.37086 | + | 1.15029i | ||||
\(118\) | 0.704370 | − | 0.256370i | 0.0648425 | − | 0.0236007i | ||||
\(119\) | 4.73500 | + | 1.72340i | 0.434057 | + | 0.157984i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.33324 | − | 2.30924i | 0.121204 | − | 0.209931i | ||||
\(122\) | −0.833400 | − | 1.44349i | −0.0754525 | − | 0.130688i | ||||
\(123\) | −0.0756943 | + | 0.429284i | −0.00682512 | + | 0.0387072i | ||||
\(124\) | −1.37728 | + | 7.81096i | −0.123684 | + | 0.701445i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.532830 | + | 0.922889i | −0.0474683 | + | 0.0822175i | ||||
\(127\) | −9.98688 | − | 8.37999i | −0.886192 | − | 0.743604i | 0.0812503 | − | 0.996694i | \(-0.474109\pi\) |
−0.967443 | + | 0.253090i | \(0.918553\pi\) | |||||||
\(128\) | −5.99600 | − | 2.18236i | −0.529976 | − | 0.192896i | ||||
\(129\) | 0.400285 | − | 0.145692i | 0.0352431 | − | 0.0128274i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0324867 | + | 0.184241i | 0.00283838 | + | 0.0160972i | 0.986194 | − | 0.165594i | \(-0.0529541\pi\) |
−0.983356 | + | 0.181691i | \(0.941843\pi\) | |||||||
\(132\) | −0.451015 | −0.0392558 | ||||||||
\(133\) | 4.09095 | − | 6.11164i | 0.354730 | − | 0.529946i | ||||
\(134\) | 0.477948 | 0.0412884 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.90925 | + | 1.60205i | −0.163717 | + | 0.137375i | ||||
\(137\) | 2.02559 | − | 0.737254i | 0.173058 | − | 0.0629879i | −0.254038 | − | 0.967194i | \(-0.581759\pi\) |
0.427096 | + | 0.904206i | \(0.359537\pi\) | |||||||
\(138\) | 0.130800 | + | 0.0476073i | 0.0111344 | + | 0.00405260i | ||||
\(139\) | −6.04955 | − | 5.07617i | −0.513116 | − | 0.430555i | 0.349108 | − | 0.937082i | \(-0.386485\pi\) |
−0.862224 | + | 0.506527i | \(0.830929\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0658982 | − | 0.114139i | −0.00554963 | − | 0.00961225i | ||||
\(142\) | −0.381846 | + | 2.16556i | −0.0320438 | + | 0.181730i | ||||
\(143\) | −3.24131 | + | 18.3824i | −0.271052 | + | 1.53721i | ||||
\(144\) | 5.59042 | + | 9.68290i | 0.465869 | + | 0.806908i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.228189 | + | 0.191474i | 0.0188851 | + | 0.0158465i | ||||
\(147\) | −0.311815 | − | 0.113492i | −0.0257181 | − | 0.00936063i | ||||
\(148\) | −14.6451 | + | 5.33039i | −1.20382 | + | 0.438155i | ||||
\(149\) | 13.7096 | − | 11.5037i | 1.12313 | − | 0.942421i | 0.124375 | − | 0.992235i | \(-0.460307\pi\) |
0.998759 | + | 0.0498141i | \(0.0158629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.93984 | 0.239241 | 0.119620 | − | 0.992820i | \(-0.461832\pi\) | ||||
0.119620 | + | 0.992820i | \(0.461832\pi\) | |||||||
\(152\) | 1.60622 | + | 3.26387i | 0.130282 | + | 0.264735i | ||||
\(153\) | 8.94040 | 0.722788 | ||||||||
\(154\) | 0.178446 | + | 1.01202i | 0.0143796 | + | 0.0815507i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.949291 | + | 0.345514i | −0.0760041 | + | 0.0276632i | ||||
\(157\) | 6.35878 | + | 2.31441i | 0.507486 | + | 0.184710i | 0.583058 | − | 0.812431i | \(-0.301856\pi\) |
−0.0755720 | + | 0.997140i | \(0.524078\pi\) | |||||||
\(158\) | 0.389634 | + | 0.326942i | 0.0309976 | + | 0.0260101i | ||||
\(159\) | −0.0763776 | + | 0.132290i | −0.00605714 | + | 0.0104913i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.41933 | + | 13.7207i | −0.190670 | + | 1.08134i | ||||
\(162\) | −0.327629 | + | 1.85808i | −0.0257410 | + | 0.145984i | ||||
\(163\) | −0.453917 | − | 0.786207i | −0.0355535 | − | 0.0615805i | 0.847701 | − | 0.530474i | \(-0.177986\pi\) |
−0.883255 | + | 0.468894i | \(0.844653\pi\) | |||||||
\(164\) | 5.33452 | − | 9.23965i | 0.416556 | − | 0.721496i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.26028 | + | 0.822673i | 0.175431 | + | 0.0638518i | ||||
\(167\) | 13.4109 | − | 4.88117i | 1.03777 | − | 0.377716i | 0.233733 | − | 0.972301i | \(-0.424906\pi\) |
0.804033 | + | 0.594585i | \(0.202683\pi\) | |||||||
\(168\) | −0.0861785 | + | 0.0723123i | −0.00664881 | + | 0.00557902i | ||||
\(169\) | 5.00268 | + | 28.3716i | 0.384822 | + | 2.18243i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.11197 | − | 12.6724i | 0.237978 | − | 0.969080i | ||||
\(172\) | −10.4260 | −0.794971 | ||||||||
\(173\) | −2.44452 | − | 13.8636i | −0.185854 | − | 1.05403i | −0.924854 | − | 0.380323i | \(-0.875813\pi\) |
0.739000 | − | 0.673705i | \(-0.235298\pi\) | |||||||
\(174\) | 0.0937127 | − | 0.0786343i | 0.00710434 | − | 0.00596125i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.1316 | + | 3.68761i | 0.763699 | + | 0.277964i | ||||
\(177\) | −0.217442 | − | 0.182455i | −0.0163439 | − | 0.0137142i | ||||
\(178\) | −1.06717 | + | 1.84839i | −0.0799875 | + | 0.138542i | ||||
\(179\) | −7.87488 | − | 13.6397i | −0.588596 | − | 1.01948i | −0.994417 | − | 0.105525i | \(-0.966348\pi\) |
0.405821 | − | 0.913953i | \(-0.366986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.791542 | − | 4.48906i | 0.0588348 | − | 0.333669i | −0.941156 | − | 0.337973i | \(-0.890259\pi\) |
0.999991 | + | 0.00430380i | \(0.00136995\pi\) | |||||||
\(182\) | 1.15088 | + | 1.99338i | 0.0853087 | + | 0.147759i | ||||
\(183\) | −0.315593 | + | 0.546623i | −0.0233293 | + | 0.0404075i | ||||
\(184\) | −5.27902 | − | 4.42962i | −0.389174 | − | 0.326556i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0642474 | + | 0.0233841i | −0.00471085 | + | 0.00171461i | ||||
\(187\) | 6.60433 | − | 5.54169i | 0.482956 | − | 0.405249i | ||||
\(188\) | 0.560153 | + | 3.17678i | 0.0408533 | + | 0.231691i | ||||
\(189\) | 0.807951 | 0.0587698 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.95887 | −0.720599 | −0.360299 | − | 0.932837i | \(-0.617325\pi\) | ||||
−0.360299 | + | 0.932837i | \(0.617325\pi\) | |||||||
\(192\) | 0.0964416 | + | 0.546947i | 0.00696007 | + | 0.0394725i | ||||
\(193\) | 16.3943 | − | 13.7564i | 1.18009 | − | 0.990210i | 0.180108 | − | 0.983647i | \(-0.442355\pi\) |
0.999978 | − | 0.00656365i | \(-0.00208929\pi\) | |||||||
\(194\) | 1.95647 | − | 0.712096i | 0.140466 | − | 0.0511255i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.22154 | + | 5.22049i | 0.444396 | + | 0.372892i | ||||
\(197\) | 0.683372 | − | 1.18364i | 0.0486883 | − | 0.0843305i | −0.840654 | − | 0.541572i | \(-0.817829\pi\) |
0.889342 | + | 0.457242i | \(0.151163\pi\) | |||||||
\(198\) | 0.911652 | + | 1.57903i | 0.0647883 | + | 0.112217i | ||||
\(199\) | −3.11454 | + | 17.6634i | −0.220784 | + | 1.25213i | 0.649799 | + | 0.760106i | \(0.274853\pi\) |
−0.870583 | + | 0.492022i | \(0.836258\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0904949 | − | 0.156742i | −0.00638302 | − | 0.0110557i | ||||
\(202\) | 0.439874 | − | 0.761885i | 0.0309495 | − | 0.0536060i | ||||
\(203\) | 9.37996 | + | 7.87072i | 0.658344 | + | 0.552416i | ||||
\(204\) | 0.438453 | + | 0.159584i | 0.0306979 | + | 0.0111731i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.03057 | + | 1.70385i | −0.141476 | + | 0.118713i | ||||
\(207\) | 4.29257 | + | 24.3443i | 0.298354 | + | 1.69205i | ||||
\(208\) | 24.1499 | 1.67449 | ||||||||
\(209\) | −5.55611 | − | 11.2901i | −0.384324 | − | 0.780953i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.60629 | + | 20.4523i | 0.248267 | + | 1.40799i | 0.812781 | + | 0.582570i | \(0.197953\pi\) |
−0.564513 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(212\) | 2.86406 | − | 2.40323i | 0.196705 | − | 0.165055i | ||||
\(213\) | 0.782488 | − | 0.284802i | 0.0536152 | − | 0.0195143i | ||||
\(214\) | −2.96246 | − | 1.07825i | −0.202510 | − | 0.0737075i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.199816 | + | 0.346091i | −0.0135957 | + | 0.0235485i | ||||
\(217\) | −3.42170 | − | 5.92656i | −0.232280 | − | 0.402321i | ||||
\(218\) | −0.190694 | + | 1.08148i | −0.0129154 | + | 0.0732469i | ||||
\(219\) | 0.0195878 | − | 0.111088i | 0.00132362 | − | 0.00750662i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.65533 | − | 16.7235i | 0.649488 | − | 1.12495i | ||||
\(222\) | −0.102915 | − | 0.0863557i | −0.00690719 | − | 0.00579582i | ||||
\(223\) | 1.83236 | + | 0.666925i | 0.122704 | + | 0.0446606i | 0.402642 | − | 0.915357i | \(-0.368092\pi\) |
−0.279938 | + | 0.960018i | \(0.590314\pi\) | |||||||
\(224\) | 3.89565 | − | 1.41790i | 0.260289 | − | 0.0947375i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.314002 | + | 1.78079i | 0.0208871 | + | 0.118457i | ||||
\(227\) | −12.6099 | −0.836950 | −0.418475 | − | 0.908228i | \(-0.637435\pi\) | ||||
−0.418475 | + | 0.908228i | \(0.637435\pi\) | |||||||
\(228\) | 0.378815 | − | 0.565928i | 0.0250877 | − | 0.0374795i | ||||
\(229\) | −6.12765 | −0.404926 | −0.202463 | − | 0.979290i | \(-0.564895\pi\) | ||||
−0.202463 | + | 0.979290i | \(0.564895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.298102 | − | 0.250137i | 0.0196136 | − | 0.0164578i | ||||
\(232\) | −5.69125 | + | 2.07145i | −0.373649 | + | 0.135997i | ||||
\(233\) | 6.20868 | + | 2.25977i | 0.406744 | + | 0.148043i | 0.537286 | − | 0.843400i | \(-0.319450\pi\) |
−0.130542 | + | 0.991443i | \(0.541672\pi\) | |||||||
\(234\) | 3.12849 | + | 2.62512i | 0.204516 | + | 0.171609i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.47369 | + | 6.01660i | 0.226118 | + | 0.391648i | ||||
\(237\) | 0.0334462 | − | 0.189683i | 0.00217256 | − | 0.0123212i | ||||
\(238\) | 0.184609 | − | 1.04697i | 0.0119664 | − | 0.0678650i | ||||
\(239\) | 1.10191 | + | 1.90856i | 0.0712766 | + | 0.123455i | 0.899461 | − | 0.437001i | \(-0.143959\pi\) |
−0.828184 | + | 0.560456i | \(0.810626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0956409 | − | 0.0802523i | −0.00616077 | − | 0.00516950i | 0.639702 | − | 0.768623i | \(-0.279058\pi\) |
−0.645863 | + | 0.763453i | \(0.723502\pi\) | |||||||
\(242\) | −0.528656 | − | 0.192415i | −0.0339833 | − | 0.0123689i | ||||
\(243\) | 2.02134 | − | 0.735707i | 0.129669 | − | 0.0471956i | ||||
\(244\) | 11.8343 | − | 9.93017i | 0.757615 | − | 0.635714i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0919690 | 0.00586373 | ||||||||
\(247\) | −20.3435 | − | 19.5068i | −1.29443 | − | 1.24119i | ||||
\(248\) | 3.38491 | 0.214942 | ||||||||
\(249\) | −0.158168 | − | 0.897017i | −0.0100235 | − | 0.0568462i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.49264 | + | 1.27122i | −0.220453 | + | 0.0802385i | −0.449886 | − | 0.893086i | \(-0.648535\pi\) |
0.229432 | + | 0.973325i | \(0.426313\pi\) | |||||||
\(252\) | −9.28133 | − | 3.37813i | −0.584669 | − | 0.212802i | ||||
\(253\) | 18.2608 | + | 15.3226i | 1.14804 | + | 0.963323i | ||||
\(254\) | −1.37529 | + | 2.38207i | −0.0862935 | + | 0.149465i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.18042 | − | 12.3658i | 0.136276 | − | 0.772861i | ||||
\(257\) | 4.68428 | − | 26.5659i | 0.292198 | − | 1.65713i | −0.386182 | − | 0.922423i | \(-0.626206\pi\) |
0.678379 | − | 0.734712i | \(-0.262683\pi\) | |||||||
\(258\) | −0.0449368 | − | 0.0778328i | −0.00279764 | − | 0.00484566i | ||||
\(259\) | 6.72351 | − | 11.6455i | 0.417779 | − | 0.723614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.4153 | + | 7.43055i | 1.26367 | + | 0.459940i | ||||
\(262\) | 0.0370911 | − | 0.0135001i | 0.00229150 | − | 0.000834036i | ||||
\(263\) | −15.8386 | + | 13.2902i | −0.976652 | + | 0.819508i | −0.983581 | − | 0.180468i | \(-0.942239\pi\) |
0.00692932 | + | 0.999976i | \(0.497794\pi\) | |||||||
\(264\) | 0.0334238 | + | 0.189556i | 0.00205709 | + | 0.0116663i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.41975 | − | 0.626099i | −0.0870502 | − | 0.0383886i | ||||
\(267\) | 0.808231 | 0.0494629 | ||||||||
\(268\) | 0.769230 | + | 4.36252i | 0.0469882 | + | 0.266483i | ||||
\(269\) | −10.5139 | + | 8.82218i | −0.641042 | + | 0.537898i | −0.904338 | − | 0.426817i | \(-0.859635\pi\) |
0.263296 | + | 0.964715i | \(0.415190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.05880 | + | 1.84125i | 0.307300 | + | 0.111848i | 0.491067 | − | 0.871122i | \(-0.336607\pi\) |
−0.183767 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(272\) | −8.54463 | − | 7.16979i | −0.518094 | − | 0.434733i | ||||
\(273\) | 0.435815 | − | 0.754854i | 0.0263767 | − | 0.0456859i | ||||
\(274\) | −0.227397 | − | 0.393863i | −0.0137375 | − | 0.0237941i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.224026 | + | 1.27051i | −0.0134848 | + | 0.0764759i | ||||
\(277\) | 11.3993 | + | 19.7441i | 0.684916 | + | 1.18631i | 0.973463 | + | 0.228843i | \(0.0734944\pi\) |
−0.288547 | + | 0.957466i | \(0.593172\pi\) | |||||||
\(278\) | −0.833082 | + | 1.44294i | −0.0499649 | + | 0.0865418i | ||||
\(279\) | −9.30140 | − | 7.80481i | −0.556861 | − | 0.467261i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1900 | − | 5.89267i | 0.965814 | − | 0.351528i | 0.189505 | − | 0.981880i | \(-0.439312\pi\) |
0.776309 | + | 0.630352i | \(0.217090\pi\) | |||||||
\(282\) | −0.0213013 | + | 0.0178739i | −0.00126848 | + | 0.00106438i | ||||
\(283\) | −2.83026 | − | 16.0512i | −0.168242 | − | 0.954146i | −0.945659 | − | 0.325161i | \(-0.894582\pi\) |
0.777417 | − | 0.628986i | \(-0.216530\pi\) | |||||||
\(284\) | −20.3809 | −1.20939 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.93821 | 0.232871 | ||||||||
\(287\) | 1.59851 | + | 9.06558i | 0.0943568 | + | 0.535124i | ||||
\(288\) | 5.63470 | − | 4.72807i | 0.332028 | − | 0.278604i | ||||
\(289\) | 7.59356 | − | 2.76383i | 0.446680 | − | 0.162578i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.603969 | − | 0.506790i | −0.0354053 | − | 0.0297086i | ||||
\(292\) | −1.38044 | + | 2.39099i | −0.0807841 | + | 0.139922i | ||||
\(293\) | 12.6441 | + | 21.9002i | 0.738675 | + | 1.27942i | 0.953092 | + | 0.302681i | \(0.0978817\pi\) |
−0.214416 | + | 0.976742i | \(0.568785\pi\) | |||||||
\(294\) | −0.0121571 | + | 0.0689465i | −0.000709018 | + | 0.00402104i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.32561 | + | 5.76012i | 0.193297 | + | 0.334800i | ||||
\(297\) | 0.691187 | − | 1.19717i | 0.0401067 | − | 0.0694669i | ||||
\(298\) | −2.89250 | − | 2.42710i | −0.167558 | − | 0.140598i | ||||
\(299\) | 50.1733 | + | 18.2616i | 2.90160 | + | 1.05609i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.89110 | − | 5.78232i | 0.397197 | − | 0.333287i | ||||
\(302\) | −0.107707 | − | 0.610834i | −0.00619782 | − | 0.0351496i | ||||
\(303\) | −0.333144 | −0.0191386 | ||||||||
\(304\) | −13.1369 | + | 9.61573i | −0.753451 | + | 0.551500i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.327549 | − | 1.85762i | −0.0187247 | − | 0.106193i | ||||
\(307\) | −13.1982 | + | 11.0746i | −0.753259 | + | 0.632059i | −0.936362 | − | 0.351035i | \(-0.885830\pi\) |
0.183104 | + | 0.983094i | \(0.441386\pi\) | |||||||
\(308\) | −8.95011 | + | 3.25757i | −0.509980 | + | 0.185617i | ||||
\(309\) | 0.943241 | + | 0.343312i | 0.0536591 | + | 0.0195303i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4862 | + | 21.6267i | −0.708028 | + | 1.22634i | 0.257560 | + | 0.966262i | \(0.417082\pi\) |
−0.965588 | + | 0.260078i | \(0.916252\pi\) | |||||||
\(312\) | 0.215565 | + | 0.373369i | 0.0122039 | + | 0.0211378i | ||||
\(313\) | 2.92827 | − | 16.6071i | 0.165516 | − | 0.938687i | −0.783015 | − | 0.622002i | \(-0.786319\pi\) |
0.948531 | − | 0.316684i | \(-0.102570\pi\) | |||||||
\(314\) | 0.247917 | − | 1.40601i | 0.0139908 | − | 0.0793457i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.35710 | + | 4.08263i | −0.132598 | + | 0.229666i | ||||
\(317\) | −18.4779 | − | 15.5048i | −1.03782 | − | 0.870834i | −0.0460593 | − | 0.998939i | \(-0.514666\pi\) |
−0.991761 | + | 0.128104i | \(0.959111\pi\) | |||||||
\(318\) | 0.0302852 | + | 0.0110229i | 0.00169831 | + | 0.000618134i | ||||
\(319\) | 19.6867 | − | 7.16538i | 1.10224 | − | 0.401184i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.207305 | + | 1.17569i | 0.0115707 | + | 0.0656205i | ||||
\(322\) | 2.93950 | 0.163812 | ||||||||
\(323\) | 1.40655 | + | 12.9416i | 0.0782624 | + | 0.720089i | ||||
\(324\) | −17.4871 | −0.971506 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.146727 | + | 0.123118i | −0.00812644 | + | 0.00681889i | ||||
\(327\) | 0.390774 | − | 0.142230i | 0.0216099 | − | 0.00786534i | ||||
\(328\) | −4.27863 | − | 1.55729i | −0.236248 | − | 0.0859872i | ||||
\(329\) | −2.13211 | − | 1.78905i | −0.117547 | − | 0.0986335i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.77017 | − | 13.4583i | −0.427087 | − | 0.739736i | 0.569526 | − | 0.821973i | \(-0.307127\pi\) |
−0.996613 | + | 0.0822371i | \(0.973794\pi\) | |||||||
\(332\) | −3.87126 | + | 21.9550i | −0.212463 | + | 1.20494i | ||||
\(333\) | 4.14304 | − | 23.4963i | 0.227037 | − | 1.28759i | ||||
\(334\) | −1.50553 | − | 2.60766i | −0.0823792 | − | 0.142685i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.385681 | − | 0.323625i | −0.0210406 | − | 0.0176552i | ||||
\(337\) | 10.3419 | + | 3.76416i | 0.563361 | + | 0.205047i | 0.607973 | − | 0.793958i | \(-0.291983\pi\) |
−0.0446119 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(338\) | 5.71172 | − | 2.07890i | 0.310677 | − | 0.113077i | ||||
\(339\) | 0.524554 | − | 0.440153i | 0.0284898 | − | 0.0239058i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7088 | −0.634067 | ||||||||
\(342\) | −2.74705 | − | 0.182324i | −0.148544 | − | 0.00985894i | ||||
\(343\) | −18.8181 | −1.01608 | ||||||||
\(344\) | 0.772645 | + | 4.38189i | 0.0416582 | + | 0.236255i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.79099 | + | 1.01584i | −0.150045 | + | 0.0546118i | ||||
\(347\) | 28.6321 | + | 10.4212i | 1.53705 | + | 0.559441i | 0.965336 | − | 0.261010i | \(-0.0840555\pi\) |
0.571716 | + | 0.820451i | \(0.306278\pi\) | |||||||
\(348\) | 0.868569 | + | 0.728816i | 0.0465602 | + | 0.0390686i | ||||
\(349\) | −2.80872 | + | 4.86485i | −0.150347 | + | 0.260409i | −0.931355 | − | 0.364112i | \(-0.881373\pi\) |
0.781008 | + | 0.624521i | \(0.214706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.537673 | − | 3.04929i | 0.0286988 | − | 0.162759i | ||||
\(352\) | 1.23170 | − | 6.98532i | 0.0656499 | − | 0.372319i | ||||
\(353\) | −3.74308 | − | 6.48321i | −0.199224 | − | 0.345067i | 0.749053 | − | 0.662510i | \(-0.230509\pi\) |
−0.948277 | + | 0.317444i | \(0.897176\pi\) | |||||||
\(354\) | −0.0299438 | + | 0.0518642i | −0.00159150 | + | 0.00275655i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.5889 | − | 6.76581i | −0.985210 | − | 0.358587i | ||||
\(357\) | −0.378305 | + | 0.137692i | −0.0200220 | + | 0.00728743i | ||||
\(358\) | −2.54552 | + | 2.13594i | −0.134535 | + | 0.112888i | ||||
\(359\) | −4.42550 | − | 25.0982i | −0.233569 | − | 1.32463i | −0.845607 | − | 0.533806i | \(-0.820761\pi\) |
0.612038 | − | 0.790828i | \(-0.290350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8333 | + | 2.51102i | 0.991229 | + | 0.132159i | ||||
\(362\) | −0.961728 | −0.0505473 | ||||||||
\(363\) | 0.0369940 | + | 0.209803i | 0.00194168 | + | 0.0110118i | ||||
\(364\) | −16.3425 | + | 13.7130i | −0.856580 | + | 0.718756i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.125139 | + | 0.0455468i | 0.00654111 | + | 0.00238077i | ||||
\(367\) | 25.6366 | + | 21.5117i | 1.33822 | + | 1.12290i | 0.982079 | + | 0.188468i | \(0.0603521\pi\) |
0.356141 | + | 0.934432i | \(0.384092\pi\) | |||||||
\(368\) | 15.4205 | − | 26.7091i | 0.803850 | − | 1.39231i | ||||
\(369\) | 8.16651 | + | 14.1448i | 0.425132 | + | 0.736350i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.560167 | + | 3.17686i | −0.0290824 | + | 0.164935i | ||||
\(372\) | −0.316844 | − | 0.548790i | −0.0164276 | − | 0.0284534i | ||||
\(373\) | −5.23935 | + | 9.07481i | −0.271283 | + | 0.469876i | −0.969191 | − | 0.246312i | \(-0.920781\pi\) |
0.697908 | + | 0.716188i | \(0.254115\pi\) | |||||||
\(374\) | −1.39341 | − | 1.16921i | −0.0720513 | − | 0.0604582i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.29365 | − | 0.470849i | 0.0667148 | − | 0.0242822i | ||||
\(377\) | 35.9471 | − | 30.1632i | 1.85137 | − | 1.55348i | ||||
\(378\) | −0.0296008 | − | 0.167875i | −0.00152250 | − | 0.00863454i | ||||
\(379\) | −14.2962 | −0.734344 | −0.367172 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367172 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.04159 | 0.0533625 | ||||||||
\(382\) | 0.364862 | + | 2.06924i | 0.0186680 | + | 0.105871i | ||||
\(383\) | −28.3295 | + | 23.7712i | −1.44757 | + | 1.21465i | −0.513238 | + | 0.858246i | \(0.671554\pi\) |
−0.934331 | + | 0.356408i | \(0.884001\pi\) | |||||||
\(384\) | 0.479053 | − | 0.174361i | 0.0244466 | − | 0.00889783i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.45893 | − | 2.90238i | −0.176055 | − | 0.147727i | ||||
\(387\) | 7.98045 | − | 13.8225i | 0.405669 | − | 0.702639i | ||||
\(388\) | 9.64857 | + | 16.7118i | 0.489832 | + | 0.848413i | ||||
\(389\) | −2.88385 | + | 16.3551i | −0.146217 | + | 0.829237i | 0.820165 | + | 0.572127i | \(0.193881\pi\) |
−0.966382 | + | 0.257110i | \(0.917230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3305 | − | 21.3571i | −0.623581 | − | 1.08007i | ||||
\(392\) | 1.73304 | − | 3.00171i | 0.0875316 | − | 0.151609i | ||||
\(393\) | −0.0114502 | − | 0.00960783i | −0.000577584 | − | 0.000484651i | ||||
\(394\) | −0.270970 | − | 0.0986252i | −0.0136513 | − | 0.00496866i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.9455 | + | 10.8626i | −0.650536 | + | 0.545865i | ||||
\(397\) | 4.62570 | + | 26.2337i | 0.232157 | + | 1.31663i | 0.848518 | + | 0.529166i | \(0.177495\pi\) |
−0.616361 | + | 0.787464i | \(0.711394\pi\) | |||||||
\(398\) | 3.78419 | 0.189684 | ||||||||
\(399\) | 0.0634878 | + | 0.584148i | 0.00317836 | + | 0.0292440i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.224832 | + | 1.27508i | 0.0112276 | + | 0.0636747i | 0.989907 | − | 0.141720i | \(-0.0452633\pi\) |
−0.978679 | + | 0.205395i | \(0.934152\pi\) | |||||||
\(402\) | −0.0292521 | + | 0.0245454i | −0.00145896 | + | 0.00122421i | ||||
\(403\) | −24.6445 | + | 8.96988i | −1.22763 | + | 0.446821i | ||||
\(404\) | 7.66215 | + | 2.78879i | 0.381206 | + | 0.138748i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.29171 | − | 2.23731i | 0.0641066 | − | 0.111036i | ||||
\(407\) | −11.5037 | − | 19.9250i | −0.570216 | − | 0.987643i | ||||
\(408\) | 0.0345782 | − | 0.196102i | 0.00171187 | − | 0.00970852i | ||||
\(409\) | 4.69402 | − | 26.6211i | 0.232104 | − | 1.31633i | −0.616522 | − | 0.787337i | \(-0.711459\pi\) |
0.848627 | − | 0.528992i | \(-0.177430\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0861109 | + | 0.149148i | −0.00424754 | + | 0.00735695i | ||||
\(412\) | −18.8201 | − | 15.7920i | −0.927202 | − | 0.778015i | ||||
\(413\) | −5.63282 | − | 2.05018i | −0.277173 | − | 0.100883i | ||||
\(414\) | 4.90096 | − | 1.78380i | 0.240869 | − | 0.0876692i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.75884 | − | 15.6462i | −0.135263 | − | 0.767117i | ||||
\(417\) | 0.630945 | 0.0308975 | ||||||||
\(418\) | −2.14228 | + | 1.56807i | −0.104782 | + | 0.0766970i | ||||
\(419\) | −4.15498 | −0.202984 | −0.101492 | − | 0.994836i | \(-0.532362\pi\) | ||||
−0.101492 | + | 0.994836i | \(0.532362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2274 | + | 16.9728i | −0.985822 | + | 0.827203i | −0.984957 | − | 0.172797i | \(-0.944720\pi\) |
−0.000864321 | 1.00000i | \(0.500275\pi\) | ||||||||
\(422\) | 4.11742 | − | 1.49862i | 0.200433 | − | 0.0729516i | ||||
\(423\) | −4.64049 | − | 1.68900i | −0.225628 | − | 0.0821219i | ||||
\(424\) | −1.22230 | − | 1.02563i | −0.0593599 | − | 0.0498089i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.0878437 | − | 0.152150i | −0.00425604 | − | 0.00737168i | ||||
\(427\) | −2.31461 | + | 13.1268i | −0.112012 | + | 0.635252i | ||||
\(428\) | 5.07391 | − | 28.7756i | 0.245257 | − | 1.39092i | ||||
\(429\) | −0.745664 | − | 1.29153i | −0.0360010 | − | 0.0623555i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.44700 | − | 6.24878i | −0.358710 | − | 0.300993i | 0.445567 | − | 0.895249i | \(-0.353002\pi\) |
−0.804276 | + | 0.594256i | \(0.797447\pi\) | |||||||
\(432\) | −1.68064 | − | 0.611705i | −0.0808600 | − | 0.0294306i | ||||
\(433\) | −0.620049 | + | 0.225679i | −0.0297976 | + | 0.0108455i | −0.356876 | − | 0.934152i | \(-0.616158\pi\) |
0.327078 | + | 0.944997i | \(0.393936\pi\) | |||||||
\(434\) | −1.10605 | + | 0.928086i | −0.0530921 | + | 0.0445496i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.1782 | −0.487449 | ||||||||
\(437\) | −34.5641 | + | 10.0436i | −1.65342 | + | 0.480452i | ||||
\(438\) | −0.0237993 | −0.00113717 | ||||||||
\(439\) | 4.72146 | + | 26.7767i | 0.225343 | + | 1.27798i | 0.862029 | + | 0.506860i | \(0.169194\pi\) |
−0.636686 | + | 0.771123i | \(0.719695\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6835 | + | 4.25243i | −0.556355 | + | 0.202497i | ||||
\(442\) | −3.82853 | − | 1.39347i | −0.182104 | − | 0.0662806i | ||||
\(443\) | −28.9473 | − | 24.2897i | −1.37533 | − | 1.15404i | −0.970905 | − | 0.239466i | \(-0.923028\pi\) |
−0.404424 | − | 0.914572i | \(-0.632528\pi\) | |||||||
\(444\) | 0.622586 | − | 1.07835i | 0.0295466 | − | 0.0511763i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0714405 | − | 0.405159i | 0.00338280 | − | 0.0191848i | ||||
\(447\) | −0.248292 | + | 1.40814i | −0.0117438 | + | 0.0666025i | ||||
\(448\) | 5.86429 | + | 10.1572i | 0.277062 | + | 0.479885i | ||||
\(449\) | 8.27496 | − | 14.3327i | 0.390520 | − | 0.676400i | −0.601998 | − | 0.798497i | \(-0.705629\pi\) |
0.992518 | + | 0.122097i | \(0.0389620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8003 | + | 5.38687i | 0.696919 | + | 0.253658i | ||||
\(452\) | −15.7490 | + | 5.73218i | −0.740772 | + | 0.269619i | ||||
\(453\) | −0.179928 | + | 0.150978i | −0.00845377 | + | 0.00709356i | ||||
\(454\) | 0.461989 | + | 2.62007i | 0.0216822 | + | 0.122966i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.265925 | − | 0.117271i | −0.0124531 | − | 0.00549173i | ||||
\(457\) | −11.4492 | −0.535571 | −0.267785 | − | 0.963479i | \(-0.586292\pi\) | ||||
−0.267785 | + | 0.963479i | \(0.586292\pi\) | |||||||
\(458\) | 0.224498 | + | 1.27319i | 0.0104901 | + | 0.0594923i | ||||
\(459\) | −1.09553 | + | 0.919262i | −0.0511352 | + | 0.0429075i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1108 | + | 3.68002i | 0.470905 | + | 0.171396i | 0.566562 | − | 0.824019i | \(-0.308273\pi\) |
−0.0956571 | + | 0.995414i | \(0.530495\pi\) | |||||||
\(462\) | −0.0628946 | − | 0.0527748i | −0.00292612 | − | 0.00245531i | ||||
\(463\) | 8.54409 | − | 14.7988i | 0.397078 | − | 0.687758i | −0.596286 | − | 0.802772i | \(-0.703358\pi\) |
0.993364 | + | 0.115013i | \(0.0366911\pi\) | |||||||
\(464\) | −13.5526 | − | 23.4737i | −0.629162 | − | 1.08974i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.242065 | − | 1.37282i | 0.0112134 | − | 0.0635946i | ||||
\(467\) | 15.9280 | + | 27.5880i | 0.737058 | + | 1.27662i | 0.953815 | + | 0.300396i | \(0.0971189\pi\) |
−0.216756 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(468\) | −18.9259 | + | 32.7807i | −0.874851 | + | 1.51529i | ||||
\(469\) | −2.92792 | − | 2.45682i | −0.135199 | − | 0.113445i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.508038 | + | 0.184911i | −0.0234092 | + | 0.00852024i | ||||
\(472\) | 2.27127 | − | 1.90582i | 0.104544 | − | 0.0877225i | ||||
\(473\) | −2.67267 | − | 15.1575i | −0.122890 | − | 0.696941i | ||||
\(474\) | −0.0406374 | −0.00186654 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.85346 | 0.451633 | ||||||||
\(477\) | 0.993894 | + | 5.63665i | 0.0455073 | + | 0.258085i | ||||
\(478\) | 0.356187 | − | 0.298877i | 0.0162916 | − | 0.0136703i | ||||
\(479\) | 3.61807 | − | 1.31687i | 0.165314 | − | 0.0601693i | −0.258038 | − | 0.966135i | \(-0.583076\pi\) |
0.423351 | + | 0.905966i | \(0.360854\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.4769 | − | 33.1250i | −1.79999 | − | 1.51037i | ||||
\(482\) | −0.0131707 | + | 0.0228123i | −0.000599909 | + | 0.00103907i | ||||
\(483\) | −0.556566 | − | 0.964000i | −0.0253246 | − | 0.0438635i | ||||
\(484\) | 0.905448 | − | 5.13505i | 0.0411567 | − | 0.233411i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.226919 | − | 0.393036i | −0.0102933 | − | 0.0178285i | ||||
\(487\) | 17.7037 | − | 30.6638i | 0.802233 | − | 1.38951i | −0.115910 | − | 0.993260i | \(-0.536978\pi\) |
0.918143 | − | 0.396249i | \(-0.129688\pi\) | |||||||
\(488\) | −5.05053 | − | 4.23790i | −0.228627 | − | 0.191841i | ||||
\(489\) | 0.0681576 | + | 0.0248074i | 0.00308220 | + | 0.00112183i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5179 | − | 13.0210i | 0.700311 | − | 0.587631i | −0.221551 | − | 0.975149i | \(-0.571112\pi\) |
0.921862 | + | 0.387518i | \(0.126667\pi\) | |||||||
\(492\) | 0.148019 | + | 0.839458i | 0.00667322 | + | 0.0378457i | ||||
\(493\) | −21.6737 | −0.976136 | ||||||||
\(494\) | −3.30777 | + | 4.94162i | −0.148824 | + | 0.222334i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.63055 | + | 14.9186i | 0.118115 | + | 0.669866i | ||||
\(497\) | 13.4709 | − | 11.3034i | 0.604253 | − | 0.507029i | ||||
\(498\) | −0.180586 | + | 0.0657279i | −0.00809225 | + | 0.00294534i | ||||
\(499\) | −0.553880 | − | 0.201596i | −0.0247951 | − | 0.00902467i | 0.329593 | − | 0.944123i | \(-0.393089\pi\) |
−0.354388 | + | 0.935099i | \(0.615311\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.570118 | + | 0.987473i | −0.0254710 | + | 0.0441170i | ||||
\(502\) | 0.392091 | + | 0.679121i | 0.0174999 | + | 0.0303107i | ||||
\(503\) | 1.97091 | − | 11.1776i | 0.0878787 | − | 0.498385i | −0.908820 | − | 0.417190i | \(-0.863015\pi\) |
0.996698 | − | 0.0811953i | \(-0.0258738\pi\) | |||||||
\(504\) | −0.731962 | + | 4.15116i | −0.0326042 | + | 0.184908i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.51468 | − | 4.35556i | 0.111791 | − | 0.193628i | ||||
\(507\) | −1.76323 | − | 1.47953i | −0.0783078 | − | 0.0657080i | ||||
\(508\) | −23.9561 | − | 8.71931i | −1.06288 | − | 0.386857i | ||||
\(509\) | −11.1499 | + | 4.05822i | −0.494209 | + | 0.179877i | −0.577088 | − | 0.816682i | \(-0.695811\pi\) |
0.0828785 | + | 0.996560i | \(0.473589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.413654 | − | 2.34595i | −0.0182990 | − | 0.103779i | ||||
\(512\) | −15.4108 | −0.681069 | ||||||||
\(513\) | 0.921654 | + | 1.87282i | 0.0406920 | + | 0.0826869i | ||||
\(514\) | −5.69143 | −0.251038 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.638105 | − | 0.535434i | 0.0280910 | − | 0.0235712i | ||||
\(517\) | −4.47488 | + | 1.62872i | −0.196805 | + | 0.0716312i | ||||
\(518\) | −2.66600 | − | 0.970346i | −0.117137 | − | 0.0426346i | ||||
\(519\) | 0.861589 | + | 0.722959i | 0.0378196 | + | 0.0317344i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.2611 | + | 21.2368i | 0.537166 | + | 0.930400i | 0.999055 | + | 0.0434617i | \(0.0138386\pi\) |
−0.461889 | + | 0.886938i | \(0.652828\pi\) | |||||||
\(522\) | 0.795955 | − | 4.51408i | 0.0348380 | − | 0.197576i | ||||
\(523\) | −3.68721 | + | 20.9112i | −0.161230 | + | 0.914382i | 0.791636 | + | 0.610993i | \(0.209230\pi\) |
−0.952867 | + | 0.303390i | \(0.901882\pi\) | |||||||
\(524\) | 0.182919 | + | 0.316826i | 0.00799087 | + | 0.0138406i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.34169 | + | 2.80401i | 0.145705 | + | 0.122261i | ||||
\(527\) | 11.3827 | + | 4.14296i | 0.495838 | + | 0.180470i | ||||
\(528\) | −0.809471 | + | 0.294623i | −0.0352277 | + | 0.0128218i | ||||
\(529\) | 34.6152 | − | 29.0456i | 1.50501 | − | 1.26285i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.6356 | −0.461546 | ||||||||
\(532\) | 3.42979 | − | 13.9666i | 0.148700 | − | 0.605528i | ||||
\(533\) | 35.2782 | 1.52807 | ||||||||
\(534\) | −0.0296111 | − | 0.167933i | −0.00128140 | − | 0.00726717i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.77650 | − | 0.646594i | 0.0767332 | − | 0.0279286i | ||||
\(537\) | 1.18245 | + | 0.430376i | 0.0510264 | + | 0.0185721i | ||||
\(538\) | 2.21825 | + | 1.86134i | 0.0956357 | + | 0.0802479i | ||||
\(539\) | −5.99478 | + | 10.3833i | −0.258214 | + | 0.447239i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.57449 | − | 14.6006i | 0.110686 | − | 0.627730i | −0.878110 | − | 0.478458i | \(-0.841196\pi\) |
0.988796 | − | 0.149272i | \(-0.0476930\pi\) | |||||||
\(542\) | 0.197233 | − | 1.11857i | 0.00847190 | − | 0.0480465i | ||||
\(543\) | 0.182094 | + | 0.315396i | 0.00781441 | + | 0.0135350i | ||||
\(544\) | −3.66903 | + | 6.35495i | −0.157308 | + | 0.272466i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.172809 | − | 0.0628974i | −0.00739555 | − | 0.00269176i | ||||
\(547\) | 7.48131 | − | 2.72298i | 0.319878 | − | 0.116426i | −0.177091 | − | 0.984195i | \(-0.556669\pi\) |
0.496969 | + | 0.867769i | \(0.334446\pi\) | |||||||
\(548\) | 3.22905 | − | 2.70949i | 0.137938 | − | 0.115744i | ||||
\(549\) | 4.10678 | + | 23.2907i | 0.175273 | + | 0.994022i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.54419 | + | 30.7209i | −0.321393 | + | 1.30876i | ||||
\(552\) | 0.550581 | 0.0234343 | ||||||||
\(553\) | −0.706315 | − | 4.00571i | −0.0300355 | − | 0.170340i | ||||
\(554\) | 3.68476 | − | 3.09188i | 0.156551 | − | 0.131362i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.5114 | − | 5.28172i | −0.615421 | − | 0.223995i | ||||
\(557\) | 6.20896 | + | 5.20994i | 0.263082 | + | 0.220752i | 0.764781 | − | 0.644290i | \(-0.222847\pi\) |
−0.501699 | + | 0.865042i | \(0.667292\pi\) | |||||||
\(558\) | −1.28089 | + | 2.21857i | −0.0542246 | + | 0.0939197i | ||||
\(559\) | −17.2372 | − | 29.8558i | −0.729057 | − | 1.26276i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.119610 | + | 0.678342i | −0.00504994 | + | 0.0286396i | ||||
\(562\) | −1.81752 | − | 3.14804i | −0.0766675 | − | 0.132792i | ||||
\(563\) | 4.14912 | − | 7.18648i | 0.174864 | − | 0.302874i | −0.765250 | − | 0.643733i | \(-0.777385\pi\) |
0.940114 | + | 0.340859i | \(0.110718\pi\) | |||||||
\(564\) | −0.197430 | − | 0.165663i | −0.00831329 | − | 0.00697568i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.23141 | + | 1.17614i | −0.135826 | + | 0.0494367i | ||||
\(567\) | 11.5582 | − | 9.69850i | 0.485400 | − | 0.407299i | ||||
\(568\) | 1.51039 | + | 8.56583i | 0.0633745 | + | 0.359414i | ||||
\(569\) | −7.28643 | −0.305463 | −0.152732 | − | 0.988268i | \(-0.548807\pi\) | ||||
−0.152732 | + | 0.988268i | \(0.548807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6974 | −0.866159 | −0.433080 | − | 0.901356i | \(-0.642573\pi\) | ||||
−0.433080 | + | 0.901356i | \(0.642573\pi\) | |||||||
\(572\) | 6.33834 | + | 35.9465i | 0.265019 | + | 1.50300i | ||||
\(573\) | 0.609518 | − | 0.511446i | 0.0254630 | − | 0.0213660i | ||||
\(574\) | 1.82507 | − | 0.664270i | 0.0761768 | − | 0.0277261i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.9412 | + | 13.3763i | 0.664218 | + | 0.557345i | ||||
\(577\) | 7.29547 | − | 12.6361i | 0.303715 | − | 0.526049i | −0.673260 | − | 0.739406i | \(-0.735106\pi\) |
0.976974 | + | 0.213357i | \(0.0684398\pi\) | |||||||
\(578\) | −0.852469 | − | 1.47652i | −0.0354580 | − | 0.0614151i | ||||
\(579\) | −0.296914 | + | 1.68389i | −0.0123393 | + | 0.0699799i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.61769 | − | 16.6583i | −0.399009 | − | 0.691104i | ||||
\(582\) | −0.0831724 | + | 0.144059i | −0.00344761 | + | 0.00597143i | ||||
\(583\) | 4.22807 | + | 3.54777i | 0.175109 | + | 0.146934i | ||||
\(584\) | 1.10720 | + | 0.402989i | 0.0458164 | + | 0.0166758i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.08715 | − | 3.42952i | 0.168838 | − | 0.141672i | ||||
\(587\) | 1.82464 | + | 10.3481i | 0.0753110 | + | 0.427110i | 0.999030 | + | 0.0440388i | \(0.0140225\pi\) |
−0.923719 | + | 0.383071i | \(0.874866\pi\) | |||||||
\(588\) | −0.648883 | −0.0267595 | ||||||||
\(589\) | 9.83443 | − | 14.6920i | 0.405220 | − | 0.605375i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0189618 | + | 0.107538i | 0.000779985 | + | 0.00442352i | ||||
\(592\) | −22.8026 | + | 19.1337i | −0.937183 | + | 0.786389i | ||||
\(593\) | 22.8495 | − | 8.31653i | 0.938316 | − | 0.341519i | 0.172815 | − | 0.984954i | \(-0.444714\pi\) |
0.765501 | + | 0.643435i | \(0.222491\pi\) | |||||||
\(594\) | −0.274069 | − | 0.0997530i | −0.0112452 | − | 0.00409292i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.4983 | − | 30.3079i | 0.716757 | − | 1.24146i | ||||
\(597\) | −0.716500 | − | 1.24101i | −0.0293244 | − | 0.0507913i | ||||
\(598\) | 1.95617 | − | 11.0940i | 0.0799936 | − | 0.453666i | ||||
\(599\) | −6.58292 | + | 37.3336i | −0.268971 | + | 1.52541i | 0.488513 | + | 0.872557i | \(0.337539\pi\) |
−0.757484 | + | 0.652854i | \(0.773572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9738 | + | 22.4713i | −0.529213 | + | 0.916623i | 0.470207 | + | 0.882556i | \(0.344179\pi\) |
−0.999420 | + | 0.0340669i | \(0.989154\pi\) | |||||||
\(602\) | −1.45391 | − | 1.21998i | −0.0592569 | − | 0.0497225i | ||||
\(603\) | −6.37255 | − | 2.31942i | −0.259510 | − | 0.0944541i | ||||
\(604\) | 5.40211 | − | 1.96621i | 0.219809 | − | 0.0800039i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.0122054 | + | 0.0692202i | 0.000495810 | + | 0.00281188i | ||||
\(607\) | 11.5300 | 0.467988 | 0.233994 | − | 0.972238i | \(-0.424820\pi\) | ||||
0.233994 | + | 0.972238i | \(0.424820\pi\) | |||||||
\(608\) | 7.73056 | + | 7.41261i | 0.313516 | + | 0.300621i | ||||
\(609\) | −0.978294 | −0.0396425 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.17093 | + | 6.85623i | −0.330561 | + | 0.277373i | ||||
\(612\) | 16.4285 | − | 5.97948i | 0.664082 | − | 0.241706i | ||||
\(613\) | 21.2917 | + | 7.74954i | 0.859963 | + | 0.313001i | 0.734096 | − | 0.679046i | \(-0.237606\pi\) |
0.125868 | + | 0.992047i | \(0.459829\pi\) | |||||||
\(614\) | 2.78459 | + | 2.33655i | 0.112377 | + | 0.0942956i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.03239 | + | 3.52020i | 0.0818872 | + | 0.141833i | ||||
\(617\) | −1.03785 | + | 5.88595i | −0.0417823 | + | 0.236959i | −0.998546 | − | 0.0539072i | \(-0.982832\pi\) |
0.956764 | + | 0.290867i | \(0.0939436\pi\) | |||||||
\(618\) | 0.0367753 | − | 0.208563i | 0.00147932 | − | 0.00838963i | ||||
\(619\) | 17.1031 | + | 29.6234i | 0.687431 | + | 1.19067i | 0.972666 | + | 0.232208i | \(0.0745951\pi\) |
−0.285235 | + | 0.958458i | \(0.592072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.02912 | − | 2.54173i | −0.121554 | − | 0.101996i | ||||
\(622\) | 4.95103 | + | 1.80203i | 0.198518 | + | 0.0722547i | ||||
\(623\) | 16.0388 | − | 5.83766i | 0.642582 | − | 0.233881i | ||||
\(624\) | −1.47806 | + | 1.24024i | −0.0591697 | + | 0.0496492i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.55787 | −0.142201 | ||||||||
\(627\) | 0.919866 | + | 0.405656i | 0.0367359 | + | 0.0162003i | ||||
\(628\) | 13.2325 | 0.528035 | ||||||||
\(629\) | 4.13317 | + | 23.4404i | 0.164800 | + | 0.934629i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.3916 | − | 4.87414i | 0.533111 | − | 0.194036i | −0.0614161 | − | 0.998112i | \(-0.519562\pi\) |
0.594527 | + | 0.804076i | \(0.297339\pi\) | |||||||
\(632\) | 1.89055 | + | 0.688105i | 0.0752021 | + | 0.0273713i | ||||
\(633\) | −1.27106 | − | 1.06655i | −0.0505202 | − | 0.0423915i | ||||
\(634\) | −2.54458 | + | 4.40735i | −0.101058 | + | 0.175038i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0518706 | + | 0.294173i | −0.00205680 | + | 0.0116647i | ||||
\(637\) | −4.66333 | + | 26.4471i | −0.184768 | + | 1.04787i | ||||
\(638\) | −2.21007 | − | 3.82795i | −0.0874975 | − | 0.151550i | ||||
\(639\) | 15.6004 | − | 27.0207i | 0.617142 | − | 1.06892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.3475 | + | 13.5934i | 1.47514 | + | 0.536906i | 0.949490 | − | 0.313797i | \(-0.101601\pi\) |
0.525647 | + | 0.850703i | \(0.323823\pi\) | |||||||
\(642\) | 0.236687 | − | 0.0861471i | 0.00934130 | − | 0.00339996i | ||||
\(643\) | −12.1851 | + | 10.2245i | −0.480532 | + | 0.403214i | −0.850619 | − | 0.525783i | \(-0.823772\pi\) |
0.370087 | + | 0.928997i | \(0.379328\pi\) | |||||||
\(644\) | 4.73096 | + | 26.8306i | 0.186426 | + | 1.05727i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.63745 | − | 0.766390i | 0.103769 | − | 0.0301532i | ||||
\(647\) | −18.8549 | −0.741262 | −0.370631 | − | 0.928780i | \(-0.620858\pi\) | ||||
−0.370631 | + | 0.928780i | \(0.620858\pi\) | |||||||
\(648\) | 1.29593 | + | 7.34960i | 0.0509090 | + | 0.288719i | ||||
\(649\) | −7.85659 | + | 6.59246i | −0.308398 | + | 0.258777i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.513784 | + | 0.187002i | 0.0201368 | + | 0.00732919i | ||||
\(652\) | −1.35993 | − | 1.14111i | −0.0532588 | − | 0.0446894i | ||||
\(653\) | −21.2626 | + | 36.8279i | −0.832070 | + | 1.44119i | 0.0643232 | + | 0.997929i | \(0.479511\pi\) |
−0.896394 | + | 0.443259i | \(0.853822\pi\) | |||||||
\(654\) | −0.0438691 | − | 0.0759835i | −0.00171542 | − | 0.00297119i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.53850 | − | 20.0678i | 0.138155 | − | 0.783517i | ||||
\(657\) | −2.11329 | − | 3.66032i | −0.0824473 | − | 0.142803i | ||||
\(658\) | −0.293612 | + | 0.508551i | −0.0114462 | + | 0.0198254i | ||||
\(659\) | −35.1057 | − | 29.4572i | −1.36752 | − | 1.14749i | −0.973578 | − | 0.228354i | \(-0.926666\pi\) |
−0.393945 | − | 0.919134i | \(-0.628890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.3834 | − | 15.7903i | 1.68742 | − | 0.614170i | 0.693121 | − | 0.720822i | \(-0.256235\pi\) |
0.994296 | + | 0.106652i | \(0.0340131\pi\) | |||||||
\(662\) | −2.51167 | + | 2.10754i | −0.0976189 | + | 0.0819120i | ||||
\(663\) | 0.267910 | + | 1.51940i | 0.0104048 | + | 0.0590084i | ||||
\(664\) | 9.51427 | 0.369225 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.03382 | −0.195056 | ||||||||
\(667\) | −10.4062 | − | 59.0167i | −0.402931 | − | 2.28514i | ||||
\(668\) | 21.3787 | − | 17.9388i | 0.827166 | − | 0.694074i | ||||
\(669\) | −0.146397 | + | 0.0532843i | −0.00566005 | + | 0.00206009i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4704 | + | 14.6594i | 0.674437 | + | 0.565920i | ||||
\(672\) | −0.165610 | + | 0.286845i | −0.00638855 | + | 0.0110653i | ||||
\(673\) | 2.74410 | + | 4.75292i | 0.105777 | + | 0.183212i | 0.914056 | − | 0.405589i | \(-0.132934\pi\) |
−0.808278 | + | 0.588801i | \(0.799600\pi\) | |||||||
\(674\) | 0.403213 | − | 2.28674i | 0.0155312 | − | 0.0880818i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.1681 | + | 48.7885i | 1.08339 | + | 1.87648i | ||||
\(677\) | −14.7154 | + | 25.4878i | −0.565557 | + | 0.979574i | 0.431440 | + | 0.902141i | \(0.358006\pi\) |
−0.996998 | + | 0.0774324i | \(0.975328\pi\) | |||||||
\(678\) | −0.110672 | − | 0.0928650i | −0.00425034 | − | 0.00356646i | ||||
\(679\) | −15.6458 | − | 5.69460i | −0.600430 | − | 0.218539i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.771771 | − | 0.647593i | 0.0295743 | − | 0.0248158i | ||||
\(682\) | 0.428975 | + | 2.43284i | 0.0164263 | + | 0.0931581i | ||||
\(683\) | 27.4543 | 1.05051 | 0.525254 | − | 0.850945i | \(-0.323970\pi\) | ||||
0.525254 | + | 0.850945i | \(0.323970\pi\) | |||||||
\(684\) | −2.75705 | − | 25.3675i | −0.105419 | − | 0.969951i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.689437 | + | 3.90999i | 0.0263228 | + | 0.149284i | ||||
\(687\) | 0.375033 | − | 0.314690i | 0.0143084 | − | 0.0120062i | ||||
\(688\) | −18.7122 | + | 6.81069i | −0.713397 | + | 0.259655i | ||||
\(689\) | 11.6170 | + | 4.22826i | 0.442574 | + | 0.161084i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.71390 | + | 2.96856i | −0.0651997 | + | 0.112929i | −0.896783 | − | 0.442471i | \(-0.854102\pi\) |
0.831583 | + | 0.555401i | \(0.187435\pi\) | |||||||
\(692\) | −13.7641 | − | 23.8402i | −0.523233 | − | 0.906267i | ||||
\(693\) | 2.53195 | − | 14.3594i | 0.0961806 | − | 0.545468i | ||||
\(694\) | 1.11631 | − | 6.33094i | 0.0423747 | − | 0.240319i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.241944 | − | 0.419059i | 0.00917085 | − | 0.0158844i | ||||
\(697\) | −12.4820 | − | 10.4737i | −0.472790 | − | 0.396718i | ||||
\(698\) | 1.11371 | + | 0.405358i | 0.0421546 | + | 0.0153430i | ||||
\(699\) | −0.496045 | + | 0.180546i | −0.0187622 | + | 0.00682887i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.566267 | − | 3.21146i | −0.0213876 | − | 0.121295i | 0.972245 | − | 0.233966i | \(-0.0751705\pi\) |
−0.993632 | + | 0.112671i | \(0.964059\pi\) | |||||||
\(702\) | −0.653276 | −0.0246563 | ||||||||
\(703\) | 34.6637 | + | 2.30065i | 1.30737 | + | 0.0867707i | ||||
\(704\) | 20.0672 | 0.756309 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.20994 | + | 1.01526i | −0.0455365 | + | 0.0382097i | ||||
\(707\) | −6.61103 | + | 2.40622i | −0.248634 | + | 0.0904952i | ||||
\(708\) | −0.521590 | − | 0.189843i | −0.0196025 | − | 0.00713474i | ||||
\(709\) | −13.1285 | − | 11.0161i | −0.493052 | − | 0.413720i | 0.362067 | − | 0.932152i | \(-0.382071\pi\) |
−0.855118 | + | 0.518433i | \(0.826516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.60845 | − | 6.25001i | −0.135327 | − | 0.234394i | ||||
\(712\) | −1.46599 | + | 8.31406i | −0.0549404 | + | 0.311583i | ||||
\(713\) | −5.81593 | + | 32.9838i | −0.217808 | + | 1.23525i | ||||
\(714\) | 0.0424693 | + | 0.0735590i | 0.00158937 | + | 0.00275288i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.5930 | − | 19.7968i | −0.881710 | − | 0.739843i | ||||
\(717\) | −0.165457 | − | 0.0602213i | −0.00617909 | − | 0.00224900i | ||||
\(718\) | −5.05273 | + | 1.83904i | −0.188566 | + | 0.0686325i | ||||
\(719\) | 4.76900 | − | 4.00167i | 0.177854 | − | 0.149237i | −0.549515 | − | 0.835484i | \(-0.685187\pi\) |
0.727369 | + | 0.686247i | \(0.240743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.1977 | 0.789442 | ||||||||
\(722\) | −0.168259 | − | 4.00516i | −0.00626197 | − | 0.149056i | ||||
\(723\) | 0.00997498 | 0.000370974 | ||||||||
\(724\) | −1.54785 | − | 8.77829i | −0.0575253 | − | 0.326242i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0422373 | − | 0.0153731i | 0.00156757 | − | 0.000570549i | ||||
\(727\) | −39.7667 | − | 14.4739i | −1.47487 | − | 0.536807i | −0.525449 | − | 0.850825i | \(-0.676103\pi\) |
−0.949417 | + | 0.314017i | \(0.898325\pi\) | |||||||
\(728\) | 6.97449 | + | 5.85229i | 0.258492 | + | 0.216900i | ||||
\(729\) | 13.3280 | − | 23.0847i | 0.493628 | − | 0.854989i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.76498 | + | 15.6810i | −0.102266 | + | 0.579982i | ||||
\(732\) | −0.214330 | + | 1.21552i | −0.00792185 | + | 0.0449270i | ||||
\(733\) | −11.3815 | − | 19.7134i | −0.420386 | − | 0.728129i | 0.575591 | − | 0.817737i | \(-0.304772\pi\) |
−0.995977 | + | 0.0896082i | \(0.971439\pi\) | |||||||
\(734\) | 3.53041 | − | 6.11485i | 0.130310 | − | 0.225703i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.0659 | − | 6.93941i | −0.702778 | − | 0.255790i | ||||
\(737\) | −6.14514 | + | 2.23665i | −0.226359 | + | 0.0823879i | ||||
\(738\) | 2.63979 | − | 2.21505i | 0.0971720 | − | 0.0815370i | ||||
\(739\) | 3.11567 | + | 17.6698i | 0.114612 | + | 0.649996i | 0.986942 | + | 0.161078i | \(0.0514971\pi\) |
−0.872330 | + | 0.488918i | \(0.837392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.24689 | + | 0.149127i | 0.0825414 | + | 0.00547833i | ||||
\(742\) | 0.680606 | 0.0249858 | ||||||||
\(743\) | 3.00948 | + | 17.0676i | 0.110407 | + | 0.626150i | 0.988922 | + | 0.148435i | \(0.0474237\pi\) |
−0.878515 | + | 0.477715i | \(0.841465\pi\) | |||||||
\(744\) | −0.207168 | + | 0.173835i | −0.00759516 | + | 0.00637310i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.07750 | + | 0.756149i | 0.0760628 | + | 0.0276846i | ||||
\(747\) | −26.1443 | − | 21.9377i | −0.956570 | − | 0.802658i | ||||
\(748\) | 8.42945 | − | 14.6002i | 0.308211 | − | 0.533838i | ||||
\(749\) | 12.6055 | + | 21.8334i | 0.460597 | + | 0.797777i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.379642 | + | 2.15305i | −0.0138533 | + | 0.0785661i | −0.990951 | − | 0.134227i | \(-0.957145\pi\) |
0.977097 | + | 0.212793i | \(0.0682560\pi\) | |||||||
\(752\) | 3.08056 | + | 5.33569i | 0.112337 | + | 0.194573i | ||||
\(753\) | 0.148477 | − | 0.257170i | 0.00541081 | − | 0.00937181i | ||||
\(754\) | −7.58424 | − | 6.36394i | −0.276202 | − | 0.231761i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.48466 | − | 0.540370i | 0.0539964 | − | 0.0196531i | ||||
\(757\) | 11.9799 | − | 10.0523i | 0.435417 | − | 0.365358i | −0.398574 | − | 0.917136i | \(-0.630495\pi\) |
0.833991 | + | 0.551778i | \(0.186050\pi\) | |||||||
\(758\) | 0.523767 | + | 2.97043i | 0.0190241 | + | 0.107891i | ||||
\(759\) | −1.90453 | −0.0691299 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2993 | 0.953349 | 0.476675 | − | 0.879080i | \(-0.341842\pi\) | ||||
0.476675 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(762\) | −0.0381608 | − | 0.216421i | −0.00138242 | − | 0.00784009i | ||||
\(763\) | 6.72737 | − | 5.64493i | 0.243547 | − | 0.204360i | ||||
\(764\) | −18.3000 | + | 6.66065i | −0.662070 | + | 0.240974i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.97705 | + | 5.01534i | 0.215960 | + | 0.181212i | ||||
\(767\) | −11.4861 | + | 19.8945i | −0.414739 | + | 0.718349i | ||||
\(768\) | 0.501605 | + | 0.868806i | 0.0181001 | + | 0.0313503i | ||||
\(769\) | 0.0147166 | − | 0.0834622i | 0.000530695 | − | 0.00300972i | −0.984541 | − | 0.175153i | \(-0.943958\pi\) |
0.985072 | + | 0.172143i | \(0.0550692\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.07762 | + | 1.86649i | 0.0388095 | + | 0.0672200i | ||||
\(772\) | 20.9249 | − | 36.2430i | 0.753104 | − | 1.30441i | ||||
\(773\) | 0.00879051 | + | 0.00737611i | 0.000316173 | + | 0.000265300i | 0.642946 | − | 0.765912i | \(-0.277712\pi\) |
−0.642630 | + | 0.766177i | \(0.722157\pi\) | |||||||
\(774\) | −3.16440 | − | 1.15175i | −0.113742 | − | 0.0413987i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.30871 | − | 5.29364i | 0.226470 | − | 0.190030i | ||||
\(777\) | 0.186560 | + | 1.05803i | 0.00669281 | + | 0.0379568i | ||||
\(778\) | 3.50389 | 0.125621 | ||||||||
\(779\) | −19.1904 | + | 14.0467i | −0.687567 | + | 0.503275i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.22461 | − | 29.6302i | −0.186951 | − | 1.06025i | ||||
\(782\) | −3.98578 | + | 3.34447i | −0.142531 | + | 0.119598i | ||||
\(783\) | −3.26566 | + | 1.18860i | −0.116705 | + | 0.0424771i | ||||
\(784\) | 14.5765 | + | 5.30542i | 0.520590 | + | 0.189479i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.00157680 | + | 0.00273110i | −5.62426e−5 | + | 9.74150e-5i | ||||
\(787\) | 15.0534 | + | 26.0733i | 0.536596 | + | 0.929411i | 0.999084 | + | 0.0427861i | \(0.0136234\pi\) |
−0.462488 | + | 0.886625i | \(0.653043\pi\) | |||||||
\(788\) | 0.464101 | − | 2.63205i | 0.0165329 | − | 0.0937628i | ||||
\(789\) | 0.286851 | − | 1.62681i | 0.0102122 | − | 0.0579161i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.23031 | − | 12.5233i | 0.257080 | − | 0.445276i | ||||
\(792\) | 5.52475 | + | 4.63582i | 0.196314 | + | 0.164727i | ||||
\(793\) | 48.0017 | + | 17.4712i | 1.70459 | + | 0.620421i | ||||
\(794\) | 5.28131 | − | 1.92224i | 0.187427 | − | 0.0682178i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.09044 | + | 34.5406i | 0.215870 | + | 1.22426i | ||||
\(797\) | −38.2339 | −1.35432 | −0.677158 | − | 0.735838i | \(-0.736789\pi\) | ||||
−0.677158 | + | 0.735838i | \(0.736789\pi\) | |||||||
\(798\) | 0.119047 | − | 0.0345928i | 0.00421423 | − | 0.00122457i | ||||
\(799\) | 4.92654 | 0.174288 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.1987 | − | 19.4660i | 0.819685 | − | 0.687798i | ||||
\(802\) | 0.256698 | − | 0.0934304i | 0.00906431 | − | 0.00329914i | ||||
\(803\) | −3.82995 | − | 1.39399i | −0.135156 | − | 0.0491927i | ||||
\(804\) | −0.271121 | − | 0.227497i | −0.00956169 | − | 0.00802321i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.76665 | + | 4.79197i | 0.0974509 | + | 0.168790i | ||||
\(807\) | 0.190415 | − | 1.07990i | 0.00670292 | − | 0.0380142i | ||||
\(808\) | 0.604267 | − | 3.42697i | 0.0212580 | − | 0.120560i | ||||
\(809\) | −1.85001 | − | 3.20432i | −0.0650431 | − | 0.112658i | 0.831670 | − | 0.555270i | \(-0.187385\pi\) |
−0.896713 | + | 0.442612i | \(0.854052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.3508 | + | 26.3064i | 1.10088 | + | 0.923744i | 0.997484 | − | 0.0708964i | \(-0.0225860\pi\) |
0.103392 | + | 0.994641i | \(0.467030\pi\) | |||||||
\(812\) | 22.5002 | + | 8.18942i | 0.789604 | + | 0.287392i | ||||
\(813\) | −0.404175 | + | 0.147108i | −0.0141750 | + | 0.00515929i | ||||
\(814\) | −3.71851 | + | 3.12020i | −0.130334 | + | 0.109363i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.891172 | 0.0311973 | ||||||||
\(817\) | 21.2642 | + | 9.37739i | 0.743940 | + | 0.328073i | ||||
\(818\) | −5.70327 | −0.199410 | ||||||||
\(819\) | −5.67122 | − | 32.1631i | −0.198168 | − | 1.12387i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3884 | + | 5.96489i | −0.571959 | + | 0.208176i | −0.611776 | − | 0.791031i | \(-0.709545\pi\) |
0.0398170 | + | 0.999207i | \(0.487323\pi\) | |||||||
\(822\) | 0.0341447 | + | 0.0124276i | 0.00119093 | + | 0.000433464i | ||||
\(823\) | 4.98291 | + | 4.18116i | 0.173693 | + | 0.145746i | 0.725490 | − | 0.688233i | \(-0.241613\pi\) |
−0.551797 | + | 0.833979i | \(0.686058\pi\) | |||||||
\(824\) | −5.24243 | + | 9.08016i | −0.182629 | + | 0.316322i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.219613 | + | 1.24549i | −0.00764133 | + | 0.0433361i | ||||
\(827\) | −0.281701 | + | 1.59761i | −0.00979571 | + | 0.0555542i | −0.989314 | − | 0.145802i | \(-0.953424\pi\) |
0.979518 | + | 0.201356i | \(0.0645349\pi\) | |||||||
\(828\) | 24.1697 | + | 41.8632i | 0.839955 | + | 1.45485i | ||||
\(829\) | −16.3252 | + | 28.2760i | −0.566996 | + | 0.982066i | 0.429865 | + | 0.902893i | \(0.358561\pi\) |
−0.996861 | + | 0.0791727i | \(0.974772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.71165 | − | 0.622990i | −0.0593765 | − | 0.0216113i | ||||
\(832\) | 42.2371 | − | 15.3730i | 1.46431 | − | 0.532964i | ||||
\(833\) | 9.50176 | − | 7.97292i | 0.329216 | − | 0.276245i | ||||
\(834\) | −0.0231159 | − | 0.131097i | −0.000800437 | − | 0.00453951i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.7607 | − | 17.0302i | −0.614265 | − | 0.589001i | ||||
\(837\) | 1.94227 | 0.0671347 | ||||||||
\(838\) | 0.152226 | + | 0.863314i | 0.00525854 | + | 0.0298227i | ||||
\(839\) | −8.85542 | + | 7.43058i | −0.305723 | + | 0.256532i | −0.782722 | − | 0.622372i | \(-0.786169\pi\) |
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2406 | − | 8.09491i | −0.766916 | − | 0.279135i | ||||
\(842\) | 4.26764 | + | 3.58098i | 0.147073 | + | 0.123409i | ||||
\(843\) | −0.688261 | + | 1.19210i | −0.0237050 | + | 0.0410582i | ||||
\(844\) | 20.3056 | + | 35.1703i | 0.698947 | + | 1.21061i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.180924 | + | 1.02607i | −0.00622030 | + | 0.0352771i | ||||
\(847\) | 2.24948 | + | 3.89622i | 0.0772931 | + | 0.133876i | ||||
\(848\) | 3.57044 | − | 6.18419i | 0.122610 | − | 0.212366i | ||||
\(849\) | 0.997547 | + | 0.837041i | 0.0342357 | + | 0.0287272i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −61.8427 | + | 22.5089i | −2.11994 | + | 0.771596i | ||||
\(852\) | 1.24739 | − | 1.04668i | 0.0427347 | − | 0.0358587i | ||||
\(853\) | −8.28547 | − | 46.9892i | −0.283689 | − | 1.60888i | −0.709931 | − | 0.704271i | \(-0.751274\pi\) |
0.426242 | − | 0.904609i | \(-0.359837\pi\) | |||||||
\(854\) | 2.81227 | 0.0962339 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.4700 | −0.426216 | ||||||||
\(857\) | 6.69167 | + | 37.9503i | 0.228583 | + | 1.29636i | 0.855716 | + | 0.517447i | \(0.173117\pi\) |
−0.627132 | + | 0.778913i | \(0.715772\pi\) | |||||||
\(858\) | −0.241033 | + | 0.202250i | −0.00822872 | + | 0.00690471i | ||||
\(859\) | −18.0347 | + | 6.56408i | −0.615335 | + | 0.223964i | −0.630836 | − | 0.775916i | \(-0.717288\pi\) |
0.0155009 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.563405 | − | 0.472753i | −0.0192008 | − | 0.0161114i | ||||
\(862\) | −1.02553 | + | 1.77626i | −0.0349295 | + | 0.0604997i | ||||
\(863\) | −4.58397 | − | 7.93967i | −0.156040 | − | 0.270269i | 0.777397 | − | 0.629010i | \(-0.216540\pi\) |
−0.933437 | + | 0.358741i | \(0.883206\pi\) | |||||||
\(864\) | −0.204316 | + | 1.15873i | −0.00695097 | + | 0.0394209i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.0696079 | + | 0.120564i | 0.00236537 | + | 0.00409695i | ||||
\(867\) | −0.322814 | + | 0.559130i | −0.0109633 | + | 0.0189890i | ||||
\(868\) | −10.2513 | − | 8.60190i | −0.347953 | − | 0.291967i | ||||
\(869\) | −6.53965 | − | 2.38024i | −0.221842 | − | 0.0807440i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2207 | + | 9.41533i | −0.380201 | + | 0.319026i | ||||
\(872\) | 0.754286 | + | 4.27777i | 0.0255434 | + | 0.144864i | ||||
\(873\) | −29.5416 | −0.999832 | ||||||||
\(874\) | 3.35317 | + | 6.81370i | 0.113423 | + | 0.230477i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0383037 | − | 0.217231i | −0.00129416 | − | 0.00733955i | ||||
\(877\) | 2.78066 | − | 2.33325i | 0.0938961 | − | 0.0787882i | −0.594631 | − | 0.803999i | \(-0.702702\pi\) |
0.688527 | + | 0.725210i | \(0.258257\pi\) | |||||||
\(878\) | 5.39064 | − | 1.96203i | 0.181925 | − | 0.0662154i | ||||
\(879\) | −1.89857 | − | 0.691022i | −0.0640370 | − | 0.0233076i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.17191 | − | 7.22596i | 0.140555 | − | 0.243449i | −0.787151 | − | 0.616761i | \(-0.788445\pi\) |
0.927706 | + | 0.373312i | \(0.121778\pi\) | |||||||
\(882\) | 1.31161 | + | 2.27177i | 0.0441642 | + | 0.0764946i | ||||
\(883\) | −4.89899 | + | 27.7836i | −0.164864 | + | 0.934991i | 0.784340 | + | 0.620331i | \(0.213002\pi\) |
−0.949204 | + | 0.314660i | \(0.898109\pi\) | |||||||
\(884\) | 6.55725 | − | 37.1880i | 0.220544 | − | 1.25077i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.98633 | + | 6.90452i | −0.133923 | + | 0.231962i | ||||
\(887\) | 6.77332 | + | 5.68349i | 0.227426 | + | 0.190833i | 0.749379 | − | 0.662141i | \(-0.230352\pi\) |
−0.521953 | + | 0.852974i | \(0.674796\pi\) | |||||||
\(888\) | −0.499355 | − | 0.181750i | −0.0167573 | − | 0.00609914i | ||||
\(889\) | 20.6698 | − | 7.52318i | 0.693242 | − | 0.252319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.48278 | − | 25.4231i | −0.150179 | − | 0.851707i | ||||
\(892\) | 3.81312 | 0.127673 | ||||||||
\(893\) | 1.71483 | − | 6.98301i | 0.0573846 | − | 0.233678i | ||||
\(894\) | 0.301677 | 0.0100896 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.24714 | − | 6.92017i | 0.275517 | − | 0.231187i | ||||
\(897\) | −4.00862 | + | 1.45902i | −0.133844 | + | 0.0487152i | ||||
\(898\) | −3.28118 | − | 1.19425i | −0.109495 | − | 0.0398528i | ||||
\(899\) | 22.5489 | + | 18.9208i | 0.752048 | + | 0.631043i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.85499 | − | 4.94498i | −0.0951134 | − | 0.164741i | ||||
\(902\) | 0.577037 | − | 3.27254i | 0.0192132 | − | 0.108964i | ||||
\(903\) | −0.124804 | + | 0.707797i | −0.00415321 | + | 0.0235540i | ||||
\(904\) | 3.57628 | + | 6.19431i | 0.118945 | + | 0.206020i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.0379619 | + | 0.0318539i | 0.00126120 | + | 0.00105827i | ||||
\(907\) | 3.97425 | + | 1.44651i | 0.131963 | + | 0.0480305i | 0.407157 | − | 0.913358i | \(-0.366520\pi\) |
−0.275195 | + | 0.961389i | \(0.588742\pi\) | |||||||
\(908\) | −23.1714 | + | 8.43371i | −0.768971 | + | 0.279882i | ||||
\(909\) | −9.56225 | + | 8.02368i | −0.317160 | + | 0.266129i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.1182 | 0.335231 | 0.167616 | − | 0.985852i | \(-0.446393\pi\) | ||||
0.167616 | + | 0.985852i | \(0.446393\pi\) | |||||||
\(912\) | 0.310199 | − | 1.26317i | 0.0102717 | − | 0.0418278i | ||||
\(913\) | −32.9110 | −1.08920 | ||||||||
\(914\) | 0.419463 | + | 2.37890i | 0.0138746 | + | 0.0786869i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.2599 | + | 4.09826i | −0.372037 | + | 0.135410i | ||||
\(917\) | −0.296616 | − | 0.107959i | −0.00979513 | − | 0.00356513i | ||||
\(918\) | 0.231140 | + | 0.193949i | 0.00762875 | + | 0.00640128i | ||||
\(919\) | 23.9378 | − | 41.4616i | 0.789637 | − | 1.36769i | −0.136553 | − | 0.990633i | \(-0.543602\pi\) |
0.926190 | − | 0.377058i | \(-0.123064\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.239030 | − | 1.35561i | 0.00787630 | − | 0.0446687i | ||||
\(922\) | 0.394201 | − | 2.23562i | 0.0129823 | − | 0.0736263i | ||||
\(923\) | −33.6958 | − | 58.3629i | −1.10911 | − | 1.92104i | ||||
\(924\) | 0.380483 | − | 0.659016i | 0.0125170 | − | 0.0216800i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.38790 | − | 1.23309i | −0.111333 | − | 0.0405220i | ||||
\(927\) | 35.3424 | − | 12.8636i | 1.16080 | − | 0.422496i | ||||
\(928\) | −13.6599 | + | 11.4620i | −0.448408 | + | 0.376259i | ||||
\(929\) | −3.75604 | − | 21.3015i | −0.123232 | − | 0.698881i | −0.982342 | − | 0.187092i | \(-0.940094\pi\) |
0.859111 | − | 0.511789i | \(-0.171017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.99367 | − | 16.2433i | −0.261982 | − | 0.532351i | ||||
\(932\) | 12.9202 | 0.423214 | ||||||||
\(933\) | −0.346460 | − | 1.96487i | −0.0113426 | − | 0.0643271i | ||||
\(934\) | 5.14864 | − | 4.32023i | 0.168469 | − | 0.141362i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15.1798 | + | 5.52501i | 0.496168 | + | 0.180591i | ||||
\(937\) | −27.6414 | − | 23.1939i | −0.903006 | − | 0.757712i | 0.0677696 | − | 0.997701i | \(-0.478412\pi\) |
−0.970776 | + | 0.239989i | \(0.922856\pi\) | |||||||
\(938\) | −0.403203 | + | 0.698368i | −0.0131651 | + | 0.0228025i | ||||
\(939\) | 0.673649 | + | 1.16679i | 0.0219837 | + | 0.0380769i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.41858 | + | 47.7441i | −0.274438 | + | 1.55641i | 0.466305 | + | 0.884624i | \(0.345585\pi\) |
−0.740742 | + | 0.671789i | \(0.765526\pi\) | |||||||
\(942\) | 0.0570334 | + | 0.0987847i | 0.00185825 | + | 0.00321858i | ||||
\(943\) | 22.5264 | − | 39.0168i | 0.733559 | − | 1.27056i | ||||
\(944\) | 10.1648 | + | 8.52928i | 0.330836 | + | 0.277604i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.05148 | + | 1.11065i | −0.0992120 | + | 0.0361102i | ||||
\(947\) | −26.9727 | + | 22.6328i | −0.876495 | + | 0.735466i | −0.965455 | − | 0.260569i | \(-0.916090\pi\) |
0.0889606 | + | 0.996035i | \(0.471645\pi\) | |||||||
\(948\) | −0.0654036 | − | 0.370922i | −0.00212421 | − | 0.0120470i | ||||
\(949\) | −9.12913 | −0.296344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.92717 | 0.0624928 | ||||||||
\(952\) | −0.730219 | − | 4.14128i | −0.0236665 | − | 0.134220i | ||||
\(953\) | −34.1607 | + | 28.6643i | −1.10657 | + | 0.928527i | −0.997850 | − | 0.0655452i | \(-0.979121\pi\) |
−0.108725 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(954\) | 1.13476 | − | 0.413019i | 0.0367392 | − | 0.0133720i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.30130 | + | 2.77012i | 0.106772 | + | 0.0895920i | ||||
\(957\) | −0.836912 | + | 1.44957i | −0.0270535 | + | 0.0468581i | ||||
\(958\) | −0.406172 | − | 0.703510i | −0.0131228 | − | 0.0227294i | ||||
\(959\) | −0.631553 | + | 3.58171i | −0.0203939 | + | 0.115660i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.27442 | + | 12.5997i | 0.234659 | + | 0.406441i | ||||
\(962\) | −5.43635 | + | 9.41604i | −0.175275 | + | 0.303585i | ||||
\(963\) | 34.2664 | + | 28.7529i | 1.10422 | + | 0.926549i | ||||
\(964\) | −0.229419 | − | 0.0835019i | −0.00738910 | − | 0.00268941i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.179908 | + | 0.150960i | −0.00578843 | + | 0.00485707i | ||||
\(967\) | −0.469769 | − | 2.66419i | −0.0151067 | − | 0.0856746i | 0.976322 | − | 0.216321i | \(-0.0694058\pi\) |
−0.991429 | + | 0.130647i | \(0.958295\pi\) | |||||||
\(968\) | −2.22529 | −0.0715236 | ||||||||
\(969\) | −0.750712 | − | 0.719836i | −0.0241163 | − | 0.0231245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.24026 | − | 7.03387i | −0.0398019 | − | 0.225728i | 0.958418 | − | 0.285368i | \(-0.0921158\pi\) |
−0.998220 | + | 0.0596403i | \(0.981005\pi\) | |||||||
\(972\) | 3.22227 | − | 2.70380i | 0.103354 | − | 0.0867246i | ||||
\(973\) | 12.5207 | − | 4.55716i | 0.401395 | − | 0.146096i | ||||
\(974\) | −7.01988 | − | 2.55503i | −0.224932 | − | 0.0818684i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.7531 | − | 25.5531i | 0.472235 | − | 0.817935i | ||||
\(977\) | −14.4495 | − | 25.0272i | −0.462280 | − | 0.800692i | 0.536794 | − | 0.843713i | \(-0.319635\pi\) |
−0.999074 | + | 0.0430210i | \(0.986302\pi\) | |||||||
\(978\) | 0.00265734 | − | 0.0150705i | 8.49725e−5 | − | 0.000481903i | ||||
\(979\) | 5.07105 | − | 28.7593i | 0.162071 | − | 0.919152i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.79083 | − | 13.4941i | 0.248742 | − | 0.430834i | ||||
\(982\) | −3.27402 | − | 2.74722i | −0.104478 | − | 0.0876675i | ||||
\(983\) | 9.71738 | + | 3.53684i | 0.309936 | + | 0.112808i | 0.492305 | − | 0.870423i | \(-0.336154\pi\) |
−0.182369 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(984\) | 0.341843 | − | 0.124421i | 0.0108976 | − | 0.00396639i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.794059 | + | 4.50333i | 0.0252880 | + | 0.143415i | ||||
\(987\) | 0.222371 | 0.00707814 | ||||||||
\(988\) | −50.4289 | − | 22.2388i | −1.60436 | − | 0.707511i | ||||
\(989\) | −44.0262 | −1.39995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2226 | − | 20.3251i | 0.769455 | − | 0.645650i | −0.171114 | − | 0.985251i | \(-0.554737\pi\) |
0.940569 | + | 0.339602i | \(0.110292\pi\) | |||||||
\(992\) | 9.36494 | − | 3.40856i | 0.297337 | − | 0.108222i | ||||
\(993\) | 1.16673 | + | 0.424653i | 0.0370249 | + | 0.0134760i | ||||
\(994\) | −2.84214 | − | 2.38484i | −0.0901473 | − | 0.0756426i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.890582 | − | 1.54253i | −0.0282192 | − | 0.0488771i | ||||
\(997\) | −1.36787 | + | 7.75758i | −0.0433209 | + | 0.245685i | −0.998777 | − | 0.0494495i | \(-0.984253\pi\) |
0.955456 | + | 0.295134i | \(0.0953644\pi\) | |||||||
\(998\) | −0.0215948 | + | 0.122470i | −0.000683571 | + | 0.00387672i | ||||
\(999\) | 1.90824 | + | 3.30518i | 0.0603742 | + | 0.104571i |
(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 | 475.2.l.c.351.2 | 18 | ||
5.2 | odd | 4 | 475.2.u.b.199.4 | 36 | |||
5.3 | odd | 4 | 475.2.u.b.199.3 | 36 | |||
5.4 | even | 2 | 95.2.k.a.66.2 | yes | 18 | ||
15.14 | odd | 2 | 855.2.bs.c.541.2 | 18 | |||
19.6 | even | 9 | 9025.2.a.cc.1.6 | 9 | |||
19.13 | odd | 18 | 9025.2.a.cf.1.4 | 9 | |||
19.17 | even | 9 | inner | 475.2.l.c.226.2 | 18 | ||
95.17 | odd | 36 | 475.2.u.b.74.3 | 36 | |||
95.44 | even | 18 | 1805.2.a.v.1.4 | 9 | |||
95.74 | even | 18 | 95.2.k.a.36.2 | ✓ | 18 | ||
95.89 | odd | 18 | 1805.2.a.s.1.6 | 9 | |||
95.93 | odd | 36 | 475.2.u.b.74.4 | 36 | |||
285.74 | odd | 18 | 855.2.bs.c.226.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.36.2 | ✓ | 18 | 95.74 | even | 18 | ||
95.2.k.a.66.2 | yes | 18 | 5.4 | even | 2 | ||
475.2.l.c.226.2 | 18 | 19.17 | even | 9 | inner | ||
475.2.l.c.351.2 | 18 | 1.1 | even | 1 | trivial | ||
475.2.u.b.74.3 | 36 | 95.17 | odd | 36 | |||
475.2.u.b.74.4 | 36 | 95.93 | odd | 36 | |||
475.2.u.b.199.3 | 36 | 5.3 | odd | 4 | |||
475.2.u.b.199.4 | 36 | 5.2 | odd | 4 | |||
855.2.bs.c.226.2 | 18 | 285.74 | odd | 18 | |||
855.2.bs.c.541.2 | 18 | 15.14 | odd | 2 | |||
1805.2.a.s.1.6 | 9 | 95.89 | odd | 18 | |||
1805.2.a.v.1.4 | 9 | 95.44 | even | 18 | |||
9025.2.a.cc.1.6 | 9 | 19.6 | even | 9 | |||
9025.2.a.cf.1.4 | 9 | 19.13 | odd | 18 |