Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.18 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.a.533.18 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.71008 | + | 0.274986i | 0.987317 | + | 0.158763i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.05001 | − | 0.893014i | −0.916791 | − | 0.399368i | ||||
\(6\) | 1.40366 | − | 1.01477i | 0.573040 | − | 0.414277i | ||||
\(7\) | 2.76585 | + | 2.76585i | 1.04539 | + | 1.04539i | 0.998920 | + | 0.0464734i | \(0.0147983\pi\) |
0.0464734 | + | 0.998920i | \(0.485202\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.84877 | + | 0.940499i | 0.949588 | + | 0.313500i | ||||
\(10\) | −2.08103 | + | 0.818117i | −0.658079 | + | 0.258711i | ||||
\(11\) | − | 4.37906i | − | 1.32034i | −0.751117 | − | 0.660169i | \(-0.770485\pi\) | ||
0.751117 | − | 0.660169i | \(-0.229515\pi\) | |||||||
\(12\) | 0.274986 | − | 1.71008i | 0.0793817 | − | 0.493658i | ||||
\(13\) | −0.0858524 | + | 0.0858524i | −0.0238112 | + | 0.0238112i | −0.718912 | − | 0.695101i | \(-0.755360\pi\) |
0.695101 | + | 0.718912i | \(0.255360\pi\) | |||||||
\(14\) | 3.91150 | 1.04539 | ||||||||
\(15\) | −3.26011 | − | 2.09085i | −0.841758 | − | 0.539855i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.90493 | − | 4.90493i | 1.18962 | − | 1.18962i | 0.212447 | − | 0.977173i | \(-0.431857\pi\) |
0.977173 | − | 0.212447i | \(-0.0681432\pi\) | |||||||
\(18\) | 2.67941 | − | 1.34935i | 0.631544 | − | 0.318044i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | −0.893014 | + | 2.05001i | −0.199684 | + | 0.458395i | ||||
\(21\) | 3.96926 | + | 5.49040i | 0.866164 | + | 1.19810i | ||||
\(22\) | −3.09646 | − | 3.09646i | −0.660169 | − | 0.660169i | ||||
\(23\) | 4.04057 | + | 4.04057i | 0.842517 | + | 0.842517i | 0.989186 | − | 0.146669i | \(-0.0468551\pi\) |
−0.146669 | + | 0.989186i | \(0.546855\pi\) | |||||||
\(24\) | −1.01477 | − | 1.40366i | −0.207138 | − | 0.286520i | ||||
\(25\) | 3.40505 | + | 3.66137i | 0.681010 | + | 0.732274i | ||||
\(26\) | 0.121414i | 0.0238112i | ||||||||
\(27\) | 4.61300 | + | 2.39170i | 0.887772 | + | 0.460283i | ||||
\(28\) | 2.76585 | − | 2.76585i | 0.522696 | − | 0.522696i | ||||
\(29\) | −7.73552 | −1.43645 | −0.718225 | − | 0.695811i | \(-0.755045\pi\) | ||||
−0.718225 | + | 0.695811i | \(0.755045\pi\) | |||||||
\(30\) | −3.78370 | + | 0.826793i | −0.690807 | + | 0.150951i | ||||
\(31\) | −4.80009 | −0.862122 | −0.431061 | − | 0.902323i | \(-0.641861\pi\) | ||||
−0.431061 | + | 0.902323i | \(0.641861\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.20418 | − | 7.48856i | 0.209621 | − | 1.30359i | ||||
\(34\) | − | 6.93661i | − | 1.18962i | ||||||
\(35\) | −3.20007 | − | 8.13995i | −0.540910 | − | 1.37590i | ||||
\(36\) | 0.940499 | − | 2.84877i | 0.156750 | − | 0.474794i | ||||
\(37\) | −1.15860 | − | 1.15860i | −0.190473 | − | 0.190473i | 0.605427 | − | 0.795901i | \(-0.293002\pi\) |
−0.795901 | + | 0.605427i | \(0.793002\pi\) | |||||||
\(38\) | 0.707107 | + | 0.707107i | 0.114708 | + | 0.114708i | ||||
\(39\) | −0.170423 | + | 0.123206i | −0.0272895 | + | 0.0197288i | ||||
\(40\) | 0.818117 | + | 2.08103i | 0.129356 | + | 0.329040i | ||||
\(41\) | − | 3.99475i | − | 0.623874i | −0.950103 | − | 0.311937i | \(-0.899022\pi\) | ||
0.950103 | − | 0.311937i | \(-0.100978\pi\) | |||||||
\(42\) | 6.68899 | + | 1.07561i | 1.03213 | + | 0.165970i | ||||
\(43\) | −2.22743 | + | 2.22743i | −0.339680 | + | 0.339680i | −0.856247 | − | 0.516567i | \(-0.827210\pi\) |
0.516567 | + | 0.856247i | \(0.327210\pi\) | |||||||
\(44\) | −4.37906 | −0.660169 | ||||||||
\(45\) | −5.00011 | − | 4.47202i | −0.745372 | − | 0.666649i | ||||
\(46\) | 5.71423 | 0.842517 | ||||||||
\(47\) | −9.37516 | + | 9.37516i | −1.36751 | + | 1.36751i | −0.503528 | + | 0.863979i | \(0.667965\pi\) |
−0.863979 | + | 0.503528i | \(0.832035\pi\) | |||||||
\(48\) | −1.71008 | − | 0.274986i | −0.246829 | − | 0.0396909i | ||||
\(49\) | 8.29985i | 1.18569i | ||||||||
\(50\) | 4.99671 | + | 0.181243i | 0.706642 | + | 0.0256317i | ||||
\(51\) | 9.73662 | − | 7.03904i | 1.36340 | − | 0.985663i | ||||
\(52\) | 0.0858524 | + | 0.0858524i | 0.0119056 | + | 0.0119056i | ||||
\(53\) | 1.61864 | + | 1.61864i | 0.222337 | + | 0.222337i | 0.809482 | − | 0.587145i | \(-0.199748\pi\) |
−0.587145 | + | 0.809482i | \(0.699748\pi\) | |||||||
\(54\) | 4.95307 | − | 1.57069i | 0.674028 | − | 0.213744i | ||||
\(55\) | −3.91056 | + | 8.97711i | −0.527300 | + | 1.21047i | ||||
\(56\) | − | 3.91150i | − | 0.522696i | ||||||
\(57\) | −0.274986 | + | 1.71008i | −0.0364228 | + | 0.226506i | ||||
\(58\) | −5.46984 | + | 5.46984i | −0.718225 | + | 0.718225i | ||||
\(59\) | −13.6615 | −1.77857 | −0.889286 | − | 0.457351i | \(-0.848798\pi\) | ||||
−0.889286 | + | 0.457351i | \(0.848798\pi\) | |||||||
\(60\) | −2.09085 | + | 3.26011i | −0.269928 | + | 0.420879i | ||||
\(61\) | 13.0690 | 1.67331 | 0.836655 | − | 0.547730i | \(-0.184508\pi\) | ||||
0.836655 | + | 0.547730i | \(0.184508\pi\) | |||||||
\(62\) | −3.39418 | + | 3.39418i | −0.431061 | + | 0.431061i | ||||
\(63\) | 5.27798 | + | 10.4805i | 0.664963 | + | 1.32042i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.252665 | − | 0.0993306i | 0.0313393 | − | 0.0123204i | ||||
\(66\) | −4.44373 | − | 6.14670i | −0.546985 | − | 0.756606i | ||||
\(67\) | −9.57951 | − | 9.57951i | −1.17032 | − | 1.17032i | −0.982132 | − | 0.188191i | \(-0.939738\pi\) |
−0.188191 | − | 0.982132i | \(-0.560262\pi\) | |||||||
\(68\) | −4.90493 | − | 4.90493i | −0.594810 | − | 0.594810i | ||||
\(69\) | 5.79861 | + | 8.02081i | 0.698070 | + | 0.965592i | ||||
\(70\) | −8.01860 | − | 3.49303i | −0.958407 | − | 0.417496i | ||||
\(71\) | 10.1120i | 1.20007i | 0.799973 | + | 0.600036i | \(0.204847\pi\) | ||||
−0.799973 | + | 0.600036i | \(0.795153\pi\) | |||||||
\(72\) | −1.34935 | − | 2.67941i | −0.159022 | − | 0.315772i | ||||
\(73\) | −3.04806 | + | 3.04806i | −0.356748 | + | 0.356748i | −0.862613 | − | 0.505865i | \(-0.831174\pi\) |
0.505865 | + | 0.862613i | \(0.331174\pi\) | |||||||
\(74\) | −1.63851 | −0.190473 | ||||||||
\(75\) | 4.81609 | + | 7.19759i | 0.556115 | + | 0.831106i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 12.1118 | − | 12.1118i | 1.38027 | − | 1.38027i | ||||
\(78\) | −0.0333871 | + | 0.207627i | −0.00378034 | + | 0.0235092i | ||||
\(79\) | 1.24732i | 0.140334i | 0.997535 | + | 0.0701671i | \(0.0223532\pi\) | ||||
−0.997535 | + | 0.0701671i | \(0.977647\pi\) | |||||||
\(80\) | 2.05001 | + | 0.893014i | 0.229198 | + | 0.0998420i | ||||
\(81\) | 7.23092 | + | 5.35852i | 0.803436 | + | 0.595391i | ||||
\(82\) | −2.82471 | − | 2.82471i | −0.311937 | − | 0.311937i | ||||
\(83\) | 9.27133 | + | 9.27133i | 1.01766 | + | 1.01766i | 0.999841 | + | 0.0178196i | \(0.00567245\pi\) |
0.0178196 | + | 0.999841i | \(0.494328\pi\) | |||||||
\(84\) | 5.49040 | − | 3.96926i | 0.599052 | − | 0.433082i | ||||
\(85\) | −14.4353 | + | 5.67496i | −1.56573 | + | 0.615536i | ||||
\(86\) | 3.15007i | 0.339680i | ||||||||
\(87\) | −13.2284 | − | 2.12716i | −1.41823 | − | 0.228056i | ||||
\(88\) | −3.09646 | + | 3.09646i | −0.330084 | + | 0.330084i | ||||
\(89\) | −4.47665 | −0.474524 | −0.237262 | − | 0.971446i | \(-0.576250\pi\) | ||||
−0.237262 | + | 0.971446i | \(0.576250\pi\) | |||||||
\(90\) | −6.69780 | + | 0.373418i | −0.706010 | + | 0.0393617i | ||||
\(91\) | −0.474910 | −0.0497841 | ||||||||
\(92\) | 4.04057 | − | 4.04057i | 0.421258 | − | 0.421258i | ||||
\(93\) | −8.20856 | − | 1.31996i | −0.851188 | − | 0.136874i | ||||
\(94\) | 13.2585i | 1.36751i | ||||||||
\(95\) | 0.893014 | − | 2.05001i | 0.0916213 | − | 0.210326i | ||||
\(96\) | −1.40366 | + | 1.01477i | −0.143260 | + | 0.103569i | ||||
\(97\) | −1.05430 | − | 1.05430i | −0.107048 | − | 0.107048i | 0.651554 | − | 0.758602i | \(-0.274117\pi\) |
−0.758602 | + | 0.651554i | \(0.774117\pi\) | |||||||
\(98\) | 5.86888 | + | 5.86888i | 0.592846 | + | 0.592846i | ||||
\(99\) | 4.11850 | − | 12.4749i | 0.413925 | − | 1.25378i | ||||
\(100\) | 3.66137 | − | 3.40505i | 0.366137 | − | 0.340505i | ||||
\(101\) | − | 1.32352i | − | 0.131695i | −0.997830 | − | 0.0658476i | \(-0.979025\pi\) | ||
0.997830 | − | 0.0658476i | \(-0.0209751\pi\) | |||||||
\(102\) | 1.90747 | − | 11.8622i | 0.188868 | − | 1.17453i | ||||
\(103\) | 8.88033 | − | 8.88033i | 0.875005 | − | 0.875005i | −0.118008 | − | 0.993013i | \(-0.537651\pi\) |
0.993013 | + | 0.118008i | \(0.0376508\pi\) | |||||||
\(104\) | 0.121414 | 0.0119056 | ||||||||
\(105\) | −3.23400 | − | 14.8000i | −0.315606 | − | 1.44433i | ||||
\(106\) | 2.28910 | 0.222337 | ||||||||
\(107\) | −7.02479 | + | 7.02479i | −0.679112 | + | 0.679112i | −0.959799 | − | 0.280687i | \(-0.909438\pi\) |
0.280687 | + | 0.959799i | \(0.409438\pi\) | |||||||
\(108\) | 2.39170 | − | 4.61300i | 0.230142 | − | 0.443886i | ||||
\(109\) | − | 0.223709i | − | 0.0214274i | −0.999943 | − | 0.0107137i | \(-0.996590\pi\) | ||
0.999943 | − | 0.0107137i | \(-0.00341035\pi\) | |||||||
\(110\) | 3.58259 | + | 9.11296i | 0.341586 | + | 0.868887i | ||||
\(111\) | −1.66271 | − | 2.29991i | −0.157817 | − | 0.218298i | ||||
\(112\) | −2.76585 | − | 2.76585i | −0.261348 | − | 0.261348i | ||||
\(113\) | −4.90305 | − | 4.90305i | −0.461240 | − | 0.461240i | 0.437822 | − | 0.899062i | \(-0.355750\pi\) |
−0.899062 | + | 0.437822i | \(0.855750\pi\) | |||||||
\(114\) | 1.01477 | + | 1.40366i | 0.0950416 | + | 0.131464i | ||||
\(115\) | −4.67491 | − | 11.8915i | −0.435937 | − | 1.10889i | ||||
\(116\) | 7.73552i | 0.718225i | ||||||||
\(117\) | −0.325317 | + | 0.163829i | −0.0300756 | + | 0.0151460i | ||||
\(118\) | −9.66012 | + | 9.66012i | −0.889286 | + | 0.889286i | ||||
\(119\) | 27.1326 | 2.48724 | ||||||||
\(120\) | 0.826793 | + | 3.78370i | 0.0754756 | + | 0.345403i | ||||
\(121\) | −8.17619 | −0.743290 | ||||||||
\(122\) | 9.24116 | − | 9.24116i | 0.836655 | − | 0.836655i | ||||
\(123\) | 1.09850 | − | 6.83135i | 0.0990484 | − | 0.615962i | ||||
\(124\) | 4.80009i | 0.431061i | ||||||||
\(125\) | −3.71073 | − | 10.5466i | −0.331897 | − | 0.943316i | ||||
\(126\) | 11.1430 | + | 3.67876i | 0.992693 | + | 0.327730i | ||||
\(127\) | 1.71446 | + | 1.71446i | 0.152134 | + | 0.152134i | 0.779070 | − | 0.626936i | \(-0.215691\pi\) |
−0.626936 | + | 0.779070i | \(0.715691\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −4.42161 | + | 3.19658i | −0.389301 | + | 0.281443i | ||||
\(130\) | 0.108424 | − | 0.248899i | 0.00950942 | − | 0.0218299i | ||||
\(131\) | 1.03462i | 0.0903948i | 0.998978 | + | 0.0451974i | \(0.0143917\pi\) | ||||
−0.998978 | + | 0.0451974i | \(0.985608\pi\) | |||||||
\(132\) | −7.48856 | − | 1.20418i | −0.651795 | − | 0.104811i | ||||
\(133\) | −2.76585 | + | 2.76585i | −0.239830 | + | 0.239830i | ||||
\(134\) | −13.5475 | −1.17032 | ||||||||
\(135\) | −7.32086 | − | 9.02248i | −0.630079 | − | 0.776531i | ||||
\(136\) | −6.93661 | −0.594810 | ||||||||
\(137\) | −3.90513 | + | 3.90513i | −0.333638 | + | 0.333638i | −0.853966 | − | 0.520328i | \(-0.825810\pi\) |
0.520328 | + | 0.853966i | \(0.325810\pi\) | |||||||
\(138\) | 9.77180 | + | 1.57133i | 0.831831 | + | 0.133761i | ||||
\(139\) | − | 0.884659i | − | 0.0750358i | −0.999296 | − | 0.0375179i | \(-0.988055\pi\) | ||
0.999296 | − | 0.0375179i | \(-0.0119451\pi\) | |||||||
\(140\) | −8.13995 | + | 3.20007i | −0.687952 | + | 0.270455i | ||||
\(141\) | −18.6103 | + | 13.4543i | −1.56727 | + | 1.13305i | ||||
\(142\) | 7.15026 | + | 7.15026i | 0.600036 | + | 0.600036i | ||||
\(143\) | 0.375953 | + | 0.375953i | 0.0314388 | + | 0.0314388i | ||||
\(144\) | −2.84877 | − | 0.940499i | −0.237397 | − | 0.0783749i | ||||
\(145\) | 15.8579 | + | 6.90793i | 1.31692 | + | 0.573672i | ||||
\(146\) | 4.31060i | 0.356748i | ||||||||
\(147\) | −2.28234 | + | 14.1934i | −0.188245 | + | 1.17065i | ||||
\(148\) | −1.15860 | + | 1.15860i | −0.0952366 | + | 0.0952366i | ||||
\(149\) | −14.4191 | −1.18126 | −0.590629 | − | 0.806943i | \(-0.701120\pi\) | ||||
−0.590629 | + | 0.806943i | \(0.701120\pi\) | |||||||
\(150\) | 8.49495 | + | 1.68397i | 0.693610 | + | 0.137495i | ||||
\(151\) | 12.5541 | 1.02164 | 0.510820 | − | 0.859687i | \(-0.329342\pi\) | ||||
0.510820 | + | 0.859687i | \(0.329342\pi\) | |||||||
\(152\) | 0.707107 | − | 0.707107i | 0.0573539 | − | 0.0573539i | ||||
\(153\) | 18.5861 | − | 9.35991i | 1.50259 | − | 0.756704i | ||||
\(154\) | − | 17.1287i | − | 1.38027i | ||||||
\(155\) | 9.84022 | + | 4.28655i | 0.790386 | + | 0.344304i | ||||
\(156\) | 0.123206 | + | 0.170423i | 0.00986441 | + | 0.0136448i | ||||
\(157\) | −9.08703 | − | 9.08703i | −0.725224 | − | 0.725224i | 0.244440 | − | 0.969664i | \(-0.421396\pi\) |
−0.969664 | + | 0.244440i | \(0.921396\pi\) | |||||||
\(158\) | 0.881987 | + | 0.881987i | 0.0701671 | + | 0.0701671i | ||||
\(159\) | 2.32290 | + | 3.21311i | 0.184218 | + | 0.254816i | ||||
\(160\) | 2.08103 | − | 0.818117i | 0.164520 | − | 0.0646778i | ||||
\(161\) | 22.3512i | 1.76152i | ||||||||
\(162\) | 8.90208 | − | 1.32399i | 0.699414 | − | 0.104023i | ||||
\(163\) | −2.97919 | + | 2.97919i | −0.233348 | + | 0.233348i | −0.814089 | − | 0.580740i | \(-0.802763\pi\) |
0.580740 | + | 0.814089i | \(0.302763\pi\) | |||||||
\(164\) | −3.99475 | −0.311937 | ||||||||
\(165\) | −9.15597 | + | 14.2762i | −0.712791 | + | 1.11140i | ||||
\(166\) | 13.1116 | 1.01766 | ||||||||
\(167\) | 6.66427 | − | 6.66427i | 0.515697 | − | 0.515697i | −0.400569 | − | 0.916266i | \(-0.631188\pi\) |
0.916266 | + | 0.400569i | \(0.131188\pi\) | |||||||
\(168\) | 1.07561 | − | 6.68899i | 0.0829851 | − | 0.516067i | ||||
\(169\) | 12.9853i | 0.998866i | ||||||||
\(170\) | −6.19449 | + | 14.2201i | −0.475096 | + | 1.09063i | ||||
\(171\) | −0.940499 | + | 2.84877i | −0.0719217 | + | 0.217851i | ||||
\(172\) | 2.22743 | + | 2.22743i | 0.169840 | + | 0.169840i | ||||
\(173\) | −3.33173 | − | 3.33173i | −0.253307 | − | 0.253307i | 0.569018 | − | 0.822325i | \(-0.307323\pi\) |
−0.822325 | + | 0.569018i | \(0.807323\pi\) | |||||||
\(174\) | −10.8580 | + | 7.84975i | −0.823144 | + | 0.595088i | ||||
\(175\) | −0.708933 | + | 19.5447i | −0.0535903 | + | 1.47744i | ||||
\(176\) | 4.37906i | 0.330084i | ||||||||
\(177\) | −23.3622 | − | 3.75672i | −1.75601 | − | 0.282372i | ||||
\(178\) | −3.16547 | + | 3.16547i | −0.237262 | + | 0.237262i | ||||
\(179\) | 20.3926 | 1.52421 | 0.762105 | − | 0.647453i | \(-0.224166\pi\) | ||||
0.762105 | + | 0.647453i | \(0.224166\pi\) | |||||||
\(180\) | −4.47202 | + | 5.00011i | −0.333324 | + | 0.372686i | ||||
\(181\) | −19.7998 | −1.47171 | −0.735855 | − | 0.677139i | \(-0.763220\pi\) | ||||
−0.735855 | + | 0.677139i | \(0.763220\pi\) | |||||||
\(182\) | −0.335812 | + | 0.335812i | −0.0248920 | + | 0.0248920i | ||||
\(183\) | 22.3490 | + | 3.59379i | 1.65209 | + | 0.265661i | ||||
\(184\) | − | 5.71423i | − | 0.421258i | ||||||
\(185\) | 1.34050 | + | 3.40979i | 0.0985552 | + | 0.250693i | ||||
\(186\) | −6.73768 | + | 4.87097i | −0.494031 | + | 0.357157i | ||||
\(187\) | −21.4790 | − | 21.4790i | −1.57070 | − | 1.57070i | ||||
\(188\) | 9.37516 | + | 9.37516i | 0.683754 | + | 0.683754i | ||||
\(189\) | 6.14378 | + | 19.3740i | 0.446894 | + | 1.40925i | ||||
\(190\) | −0.818117 | − | 2.08103i | −0.0593525 | − | 0.150974i | ||||
\(191\) | 16.0949i | 1.16458i | 0.812979 | + | 0.582292i | \(0.197844\pi\) | ||||
−0.812979 | + | 0.582292i | \(0.802156\pi\) | |||||||
\(192\) | −0.274986 | + | 1.71008i | −0.0198454 | + | 0.123415i | ||||
\(193\) | −2.75631 | + | 2.75631i | −0.198404 | + | 0.198404i | −0.799315 | − | 0.600912i | \(-0.794804\pi\) |
0.600912 | + | 0.799315i | \(0.294804\pi\) | |||||||
\(194\) | −1.49100 | −0.107048 | ||||||||
\(195\) | 0.459393 | − | 0.100384i | 0.0328978 | − | 0.00718865i | ||||
\(196\) | 8.29985 | 0.592846 | ||||||||
\(197\) | 9.52900 | − | 9.52900i | 0.678913 | − | 0.678913i | −0.280841 | − | 0.959754i | \(-0.590613\pi\) |
0.959754 | + | 0.280841i | \(0.0906134\pi\) | |||||||
\(198\) | −5.90888 | − | 11.7333i | −0.419926 | − | 0.833851i | ||||
\(199\) | − | 7.61755i | − | 0.539994i | −0.962861 | − | 0.269997i | \(-0.912977\pi\) | ||
0.962861 | − | 0.269997i | \(-0.0870227\pi\) | |||||||
\(200\) | 0.181243 | − | 4.99671i | 0.0128158 | − | 0.353321i | ||||
\(201\) | −13.7475 | − | 19.0160i | −0.969675 | − | 1.34128i | ||||
\(202\) | −0.935870 | − | 0.935870i | −0.0658476 | − | 0.0658476i | ||||
\(203\) | −21.3953 | − | 21.3953i | −1.50166 | − | 1.50166i | ||||
\(204\) | −7.03904 | − | 9.73662i | −0.492831 | − | 0.681700i | ||||
\(205\) | −3.56736 | + | 8.18925i | −0.249155 | + | 0.571962i | ||||
\(206\) | − | 12.5587i | − | 0.875005i | ||||||
\(207\) | 7.71048 | + | 15.3108i | 0.535916 | + | 1.06417i | ||||
\(208\) | 0.0858524 | − | 0.0858524i | 0.00595279 | − | 0.00595279i | ||||
\(209\) | 4.37906 | 0.302906 | ||||||||
\(210\) | −12.7519 | − | 8.17837i | −0.879968 | − | 0.564361i | ||||
\(211\) | 5.54199 | 0.381526 | 0.190763 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190763 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(212\) | 1.61864 | − | 1.61864i | 0.111168 | − | 0.111168i | ||||
\(213\) | −2.78066 | + | 17.2923i | −0.190528 | + | 1.18485i | ||||
\(214\) | 9.93455i | 0.679112i | ||||||||
\(215\) | 6.55538 | − | 2.57712i | 0.447073 | − | 0.175758i | ||||
\(216\) | −1.57069 | − | 4.95307i | −0.106872 | − | 0.337014i | ||||
\(217\) | −13.2763 | − | 13.2763i | −0.901257 | − | 0.901257i | ||||
\(218\) | −0.158186 | − | 0.158186i | −0.0107137 | − | 0.0107137i | ||||
\(219\) | −6.05060 | + | 4.37426i | −0.408862 | + | 0.295585i | ||||
\(220\) | 8.97711 | + | 3.91056i | 0.605236 | + | 0.263650i | ||||
\(221\) | 0.842199i | 0.0566525i | ||||||||
\(222\) | −2.80199 | − | 0.450568i | −0.188057 | − | 0.0302402i | ||||
\(223\) | 9.53065 | − | 9.53065i | 0.638219 | − | 0.638219i | −0.311897 | − | 0.950116i | \(-0.600964\pi\) |
0.950116 | + | 0.311897i | \(0.100964\pi\) | |||||||
\(224\) | −3.91150 | −0.261348 | ||||||||
\(225\) | 6.25668 | + | 13.6328i | 0.417112 | + | 0.908855i | ||||
\(226\) | −6.93395 | −0.461240 | ||||||||
\(227\) | 13.7533 | − | 13.7533i | 0.912836 | − | 0.912836i | −0.0836582 | − | 0.996495i | \(-0.526660\pi\) |
0.996495 | + | 0.0836582i | \(0.0266604\pi\) | |||||||
\(228\) | 1.71008 | + | 0.274986i | 0.113253 | + | 0.0182114i | ||||
\(229\) | 6.49460i | 0.429175i | 0.976705 | + | 0.214588i | \(0.0688407\pi\) | ||||
−0.976705 | + | 0.214588i | \(0.931159\pi\) | |||||||
\(230\) | −11.7142 | − | 5.10289i | −0.772412 | − | 0.336474i | ||||
\(231\) | 24.0428 | − | 17.3816i | 1.58190 | − | 1.14363i | ||||
\(232\) | 5.46984 | + | 5.46984i | 0.359113 | + | 0.359113i | ||||
\(233\) | −7.94673 | − | 7.94673i | −0.520608 | − | 0.520608i | 0.397147 | − | 0.917755i | \(-0.370000\pi\) |
−0.917755 | + | 0.397147i | \(0.870000\pi\) | |||||||
\(234\) | −0.114189 | + | 0.345879i | −0.00746479 | + | 0.0226108i | ||||
\(235\) | 27.5913 | − | 10.8470i | 1.79986 | − | 0.707579i | ||||
\(236\) | 13.6615i | 0.889286i | ||||||||
\(237\) | −0.342995 | + | 2.13302i | −0.0222799 | + | 0.138554i | ||||
\(238\) | 19.1856 | − | 19.1856i | 1.24362 | − | 1.24362i | ||||
\(239\) | 7.51189 | 0.485903 | 0.242952 | − | 0.970038i | \(-0.421884\pi\) | ||||
0.242952 | + | 0.970038i | \(0.421884\pi\) | |||||||
\(240\) | 3.26011 | + | 2.09085i | 0.210439 | + | 0.134964i | ||||
\(241\) | 11.2111 | 0.722170 | 0.361085 | − | 0.932533i | \(-0.382406\pi\) | ||||
0.361085 | + | 0.932533i | \(0.382406\pi\) | |||||||
\(242\) | −5.78144 | + | 5.78144i | −0.371645 | + | 0.371645i | ||||
\(243\) | 10.8920 | + | 11.1519i | 0.698720 | + | 0.715396i | ||||
\(244\) | − | 13.0690i | − | 0.836655i | ||||||
\(245\) | 7.41188 | − | 17.0147i | 0.473528 | − | 1.08703i | ||||
\(246\) | −4.05373 | − | 5.60725i | −0.258457 | − | 0.357505i | ||||
\(247\) | −0.0858524 | − | 0.0858524i | −0.00546266 | − | 0.00546266i | ||||
\(248\) | 3.39418 | + | 3.39418i | 0.215531 | + | 0.215531i | ||||
\(249\) | 13.3053 | + | 18.4042i | 0.843186 | + | 1.16632i | ||||
\(250\) | −10.0814 | − | 4.83369i | −0.637606 | − | 0.305709i | ||||
\(251\) | − | 10.7576i | − | 0.679015i | −0.940603 | − | 0.339508i | \(-0.889740\pi\) | ||
0.940603 | − | 0.339508i | \(-0.110260\pi\) | |||||||
\(252\) | 10.4805 | − | 5.27798i | 0.660212 | − | 0.332481i | ||||
\(253\) | 17.6939 | − | 17.6939i | 1.11241 | − | 1.11241i | ||||
\(254\) | 2.42462 | 0.152134 | ||||||||
\(255\) | −26.2461 | + | 5.73515i | −1.64359 | + | 0.359149i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.67697 | − | 2.67697i | 0.166985 | − | 0.166985i | −0.618668 | − | 0.785653i | \(-0.712327\pi\) |
0.785653 | + | 0.618668i | \(0.212327\pi\) | |||||||
\(258\) | −0.866225 | + | 5.38688i | −0.0539288 | + | 0.335372i | ||||
\(259\) | − | 6.40905i | − | 0.398239i | ||||||
\(260\) | −0.0993306 | − | 0.252665i | −0.00616022 | − | 0.0156696i | ||||
\(261\) | −22.0367 | − | 7.27525i | −1.36404 | − | 0.450327i | ||||
\(262\) | 0.731584 | + | 0.731584i | 0.0451974 | + | 0.0451974i | ||||
\(263\) | −16.7660 | − | 16.7660i | −1.03384 | − | 1.03384i | −0.999407 | − | 0.0344303i | \(-0.989038\pi\) |
−0.0344303 | − | 0.999407i | \(-0.510962\pi\) | |||||||
\(264\) | −6.14670 | + | 4.44373i | −0.378303 | + | 0.273492i | ||||
\(265\) | −1.87275 | − | 4.76368i | −0.115042 | − | 0.292631i | ||||
\(266\) | 3.91150i | 0.239830i | ||||||||
\(267\) | −7.65545 | − | 1.23102i | −0.468506 | − | 0.0753371i | ||||
\(268\) | −9.57951 | + | 9.57951i | −0.585162 | + | 0.585162i | ||||
\(269\) | 12.5500 | 0.765186 | 0.382593 | − | 0.923917i | \(-0.375031\pi\) | ||||
0.382593 | + | 0.923917i | \(0.375031\pi\) | |||||||
\(270\) | −11.5565 | − | 1.20323i | −0.703305 | − | 0.0732261i | ||||
\(271\) | −12.9702 | −0.787886 | −0.393943 | − | 0.919135i | \(-0.628889\pi\) | ||||
−0.393943 | + | 0.919135i | \(0.628889\pi\) | |||||||
\(272\) | −4.90493 | + | 4.90493i | −0.297405 | + | 0.297405i | ||||
\(273\) | −0.812135 | − | 0.130594i | −0.0491526 | − | 0.00790389i | ||||
\(274\) | 5.52269i | 0.333638i | ||||||||
\(275\) | 16.0334 | − | 14.9109i | 0.966848 | − | 0.899163i | ||||
\(276\) | 8.02081 | − | 5.79861i | 0.482796 | − | 0.349035i | ||||
\(277\) | 10.2241 | + | 10.2241i | 0.614306 | + | 0.614306i | 0.944065 | − | 0.329759i | \(-0.106967\pi\) |
−0.329759 | + | 0.944065i | \(0.606967\pi\) | |||||||
\(278\) | −0.625548 | − | 0.625548i | −0.0375179 | − | 0.0375179i | ||||
\(279\) | −13.6743 | − | 4.51448i | −0.818661 | − | 0.270275i | ||||
\(280\) | −3.49303 | + | 8.01860i | −0.208748 | + | 0.479203i | ||||
\(281\) | − | 3.48157i | − | 0.207693i | −0.994593 | − | 0.103846i | \(-0.966885\pi\) | ||
0.994593 | − | 0.103846i | \(-0.0331150\pi\) | |||||||
\(282\) | −3.64590 | + | 22.6731i | −0.217110 | + | 1.35016i | ||||
\(283\) | −3.43456 | + | 3.43456i | −0.204164 | + | 0.204164i | −0.801781 | − | 0.597618i | \(-0.796114\pi\) |
0.597618 | + | 0.801781i | \(0.296114\pi\) | |||||||
\(284\) | 10.1120 | 0.600036 | ||||||||
\(285\) | 2.09085 | − | 3.26011i | 0.123851 | − | 0.193112i | ||||
\(286\) | 0.531678 | 0.0314388 | ||||||||
\(287\) | 11.0489 | − | 11.0489i | 0.652194 | − | 0.652194i | ||||
\(288\) | −2.67941 | + | 1.34935i | −0.157886 | + | 0.0795111i | ||||
\(289\) | − | 31.1166i | − | 1.83039i | ||||||
\(290\) | 16.0979 | − | 6.32856i | 0.945299 | − | 0.371626i | ||||
\(291\) | −1.51302 | − | 2.09286i | −0.0886949 | − | 0.122685i | ||||
\(292\) | 3.04806 | + | 3.04806i | 0.178374 | + | 0.178374i | ||||
\(293\) | −4.27164 | − | 4.27164i | −0.249552 | − | 0.249552i | 0.571235 | − | 0.820787i | \(-0.306465\pi\) |
−0.820787 | + | 0.571235i | \(0.806465\pi\) | |||||||
\(294\) | 8.42241 | + | 11.6501i | 0.491205 | + | 0.679449i | ||||
\(295\) | 28.0061 | + | 12.1999i | 1.63058 | + | 0.710305i | ||||
\(296\) | 1.63851i | 0.0952366i | ||||||||
\(297\) | 10.4734 | − | 20.2006i | 0.607729 | − | 1.17216i | ||||
\(298\) | −10.1958 | + | 10.1958i | −0.590629 | + | 0.590629i | ||||
\(299\) | −0.693785 | −0.0401226 | ||||||||
\(300\) | 7.19759 | − | 4.81609i | 0.415553 | − | 0.278057i | ||||
\(301\) | −12.3215 | −0.710199 | ||||||||
\(302\) | 8.87711 | − | 8.87711i | 0.510820 | − | 0.510820i | ||||
\(303\) | 0.363950 | − | 2.26333i | 0.0209084 | − | 0.130025i | ||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | −26.7915 | − | 11.6708i | −1.53408 | − | 0.668267i | ||||
\(306\) | 6.52387 | − | 19.7608i | 0.372945 | − | 1.12965i | ||||
\(307\) | −12.5877 | − | 12.5877i | −0.718417 | − | 0.718417i | 0.249864 | − | 0.968281i | \(-0.419614\pi\) |
−0.968281 | + | 0.249864i | \(0.919614\pi\) | |||||||
\(308\) | −12.1118 | − | 12.1118i | −0.690136 | − | 0.690136i | ||||
\(309\) | 17.6281 | − | 12.7441i | 1.00283 | − | 0.724988i | ||||
\(310\) | 9.98914 | − | 3.92704i | 0.567345 | − | 0.223041i | ||||
\(311\) | − | 2.19199i | − | 0.124296i | −0.998067 | − | 0.0621481i | \(-0.980205\pi\) | ||
0.998067 | − | 0.0621481i | \(-0.0197951\pi\) | |||||||
\(312\) | 0.207627 | + | 0.0333871i | 0.0117546 | + | 0.00189017i | ||||
\(313\) | 12.2938 | − | 12.2938i | 0.694888 | − | 0.694888i | −0.268416 | − | 0.963303i | \(-0.586500\pi\) |
0.963303 | + | 0.268416i | \(0.0865001\pi\) | |||||||
\(314\) | −12.8510 | −0.725224 | ||||||||
\(315\) | −1.46063 | − | 26.1985i | −0.0822970 | − | 1.47612i | ||||
\(316\) | 1.24732 | 0.0701671 | ||||||||
\(317\) | −5.00014 | + | 5.00014i | −0.280836 | + | 0.280836i | −0.833442 | − | 0.552606i | \(-0.813633\pi\) |
0.552606 | + | 0.833442i | \(0.313633\pi\) | |||||||
\(318\) | 3.91455 | + | 0.629471i | 0.219517 | + | 0.0352990i | ||||
\(319\) | 33.8743i | 1.89660i | ||||||||
\(320\) | 0.893014 | − | 2.05001i | 0.0499210 | − | 0.114599i | ||||
\(321\) | −13.9447 | + | 10.0813i | −0.778317 | + | 0.562681i | ||||
\(322\) | 15.8047 | + | 15.8047i | 0.880761 | + | 0.880761i | ||||
\(323\) | 4.90493 | + | 4.90493i | 0.272917 | + | 0.272917i | ||||
\(324\) | 5.35852 | − | 7.23092i | 0.297695 | − | 0.401718i | ||||
\(325\) | −0.606669 | − | 0.0220054i | −0.0336520 | − | 0.00122064i | ||||
\(326\) | 4.21322i | 0.233348i | ||||||||
\(327\) | 0.0615169 | − | 0.382561i | 0.00340189 | − | 0.0211557i | ||||
\(328\) | −2.82471 | + | 2.82471i | −0.155969 | + | 0.155969i | ||||
\(329\) | −51.8605 | −2.85916 | ||||||||
\(330\) | 3.62058 | + | 16.5691i | 0.199306 | + | 0.912098i | ||||
\(331\) | 15.5843 | 0.856592 | 0.428296 | − | 0.903639i | \(-0.359114\pi\) | ||||
0.428296 | + | 0.903639i | \(0.359114\pi\) | |||||||
\(332\) | 9.27133 | − | 9.27133i | 0.508830 | − | 0.508830i | ||||
\(333\) | −2.21092 | − | 4.39025i | −0.121158 | − | 0.240584i | ||||
\(334\) | − | 9.42471i | − | 0.515697i | ||||||
\(335\) | 11.0834 | + | 28.1927i | 0.605552 | + | 1.54033i | ||||
\(336\) | −3.96926 | − | 5.49040i | −0.216541 | − | 0.299526i | ||||
\(337\) | −12.8769 | − | 12.8769i | −0.701449 | − | 0.701449i | 0.263272 | − | 0.964722i | \(-0.415198\pi\) |
−0.964722 | + | 0.263272i | \(0.915198\pi\) | |||||||
\(338\) | 9.18196 | + | 9.18196i | 0.499433 | + | 0.499433i | ||||
\(339\) | −7.03634 | − | 9.73288i | −0.382162 | − | 0.528618i | ||||
\(340\) | 5.67496 | + | 14.4353i | 0.307768 | + | 0.782864i | ||||
\(341\) | 21.0199i | 1.13829i | ||||||||
\(342\) | 1.34935 | + | 2.67941i | 0.0729644 | + | 0.144886i | ||||
\(343\) | −3.59519 | + | 3.59519i | −0.194122 | + | 0.194122i | ||||
\(344\) | 3.15007 | 0.169840 | ||||||||
\(345\) | −4.72449 | − | 21.6209i | −0.254358 | − | 1.16403i | ||||
\(346\) | −4.71178 | −0.253307 | ||||||||
\(347\) | 5.40671 | − | 5.40671i | 0.290247 | − | 0.290247i | −0.546931 | − | 0.837178i | \(-0.684204\pi\) |
0.837178 | + | 0.546931i | \(0.184204\pi\) | |||||||
\(348\) | −2.12716 | + | 13.2284i | −0.114028 | + | 0.709116i | ||||
\(349\) | 4.70970i | 0.252104i | 0.992024 | + | 0.126052i | \(0.0402307\pi\) | ||||
−0.992024 | + | 0.126052i | \(0.959769\pi\) | |||||||
\(350\) | 13.3189 | + | 14.3215i | 0.711923 | + | 0.765514i | ||||
\(351\) | −0.601370 | + | 0.190704i | −0.0320988 | + | 0.0101790i | ||||
\(352\) | 3.09646 | + | 3.09646i | 0.165042 | + | 0.165042i | ||||
\(353\) | 1.82994 | + | 1.82994i | 0.0973976 | + | 0.0973976i | 0.754127 | − | 0.656729i | \(-0.228060\pi\) |
−0.656729 | + | 0.754127i | \(0.728060\pi\) | |||||||
\(354\) | −19.1760 | + | 13.8632i | −1.01919 | + | 0.736821i | ||||
\(355\) | 9.03015 | − | 20.7296i | 0.479271 | − | 1.10022i | ||||
\(356\) | 4.47665i | 0.237262i | ||||||||
\(357\) | 46.3990 | + | 7.46109i | 2.45569 | + | 0.394883i | ||||
\(358\) | 14.4197 | − | 14.4197i | 0.762105 | − | 0.762105i | ||||
\(359\) | −9.20818 | −0.485989 | −0.242995 | − | 0.970028i | \(-0.578130\pi\) | ||||
−0.242995 | + | 0.970028i | \(0.578130\pi\) | |||||||
\(360\) | 0.373418 | + | 6.69780i | 0.0196809 | + | 0.353005i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −14.0006 | + | 14.0006i | −0.735855 | + | 0.735855i | ||||
\(363\) | −13.9820 | − | 2.24834i | −0.733863 | − | 0.118007i | ||||
\(364\) | 0.474910i | 0.0248920i | ||||||||
\(365\) | 8.97050 | − | 3.52658i | 0.469537 | − | 0.184590i | ||||
\(366\) | 18.3443 | − | 13.2620i | 0.958874 | − | 0.693214i | ||||
\(367\) | 14.0925 | + | 14.0925i | 0.735621 | + | 0.735621i | 0.971727 | − | 0.236107i | \(-0.0758715\pi\) |
−0.236107 | + | 0.971727i | \(0.575871\pi\) | |||||||
\(368\) | −4.04057 | − | 4.04057i | −0.210629 | − | 0.210629i | ||||
\(369\) | 3.75705 | − | 11.3801i | 0.195584 | − | 0.592424i | ||||
\(370\) | 3.35896 | + | 1.46321i | 0.174624 | + | 0.0760689i | ||||
\(371\) | 8.95381i | 0.464859i | ||||||||
\(372\) | −1.31996 | + | 8.20856i | −0.0684368 | + | 0.425594i | ||||
\(373\) | −6.94081 | + | 6.94081i | −0.359382 | + | 0.359382i | −0.863585 | − | 0.504203i | \(-0.831786\pi\) |
0.504203 | + | 0.863585i | \(0.331786\pi\) | |||||||
\(374\) | −30.3759 | −1.57070 | ||||||||
\(375\) | −3.44548 | − | 19.0559i | −0.177924 | − | 0.984044i | ||||
\(376\) | 13.2585 | 0.683754 | ||||||||
\(377\) | 0.664113 | − | 0.664113i | 0.0342036 | − | 0.0342036i | ||||
\(378\) | 18.0438 | + | 9.35515i | 0.928071 | + | 0.481177i | ||||
\(379\) | 34.8937i | 1.79237i | 0.443683 | + | 0.896184i | \(0.353671\pi\) | ||||
−0.443683 | + | 0.896184i | \(0.646329\pi\) | |||||||
\(380\) | −2.05001 | − | 0.893014i | −0.105163 | − | 0.0458107i | ||||
\(381\) | 2.46042 | + | 3.40333i | 0.126051 | + | 0.174358i | ||||
\(382\) | 11.3808 | + | 11.3808i | 0.582292 | + | 0.582292i | ||||
\(383\) | 3.00238 | + | 3.00238i | 0.153415 | + | 0.153415i | 0.779641 | − | 0.626227i | \(-0.215401\pi\) |
−0.626227 | + | 0.779641i | \(0.715401\pi\) | |||||||
\(384\) | 1.01477 | + | 1.40366i | 0.0517846 | + | 0.0716300i | ||||
\(385\) | −35.6454 | + | 14.0133i | −1.81666 | + | 0.714184i | ||||
\(386\) | 3.89801i | 0.198404i | ||||||||
\(387\) | −8.44033 | + | 4.25054i | −0.429046 | + | 0.216067i | ||||
\(388\) | −1.05430 | + | 1.05430i | −0.0535239 | + | 0.0535239i | ||||
\(389\) | −4.18737 | −0.212308 | −0.106154 | − | 0.994350i | \(-0.533854\pi\) | ||||
−0.106154 | + | 0.994350i | \(0.533854\pi\) | |||||||
\(390\) | 0.253858 | − | 0.395822i | 0.0128546 | − | 0.0200432i | ||||
\(391\) | 39.6374 | 2.00455 | ||||||||
\(392\) | 5.86888 | − | 5.86888i | 0.296423 | − | 0.296423i | ||||
\(393\) | −0.284505 | + | 1.76928i | −0.0143514 | + | 0.0892483i | ||||
\(394\) | − | 13.4760i | − | 0.678913i | ||||||
\(395\) | 1.11387 | − | 2.55701i | 0.0560450 | − | 0.128657i | ||||
\(396\) | −12.4749 | − | 4.11850i | −0.626888 | − | 0.206963i | ||||
\(397\) | −6.47953 | − | 6.47953i | −0.325198 | − | 0.325198i | 0.525559 | − | 0.850757i | \(-0.323856\pi\) |
−0.850757 | + | 0.525559i | \(0.823856\pi\) | |||||||
\(398\) | −5.38642 | − | 5.38642i | −0.269997 | − | 0.269997i | ||||
\(399\) | −5.49040 | + | 3.96926i | −0.274864 | + | 0.198712i | ||||
\(400\) | −3.40505 | − | 3.66137i | −0.170253 | − | 0.183068i | ||||
\(401\) | 12.0856i | 0.603528i | 0.953383 | + | 0.301764i | \(0.0975754\pi\) | ||||
−0.953383 | + | 0.301764i | \(0.902425\pi\) | |||||||
\(402\) | −23.1673 | − | 3.72537i | −1.15548 | − | 0.185805i | ||||
\(403\) | 0.412100 | − | 0.412100i | 0.0205281 | − | 0.0205281i | ||||
\(404\) | −1.32352 | −0.0658476 | ||||||||
\(405\) | −10.0382 | − | 17.4423i | −0.498803 | − | 0.866716i | ||||
\(406\) | −30.2575 | −1.50166 | ||||||||
\(407\) | −5.07360 | + | 5.07360i | −0.251489 | + | 0.251489i | ||||
\(408\) | −11.8622 | − | 1.90747i | −0.587266 | − | 0.0944340i | ||||
\(409\) | − | 14.2278i | − | 0.703521i | −0.936090 | − | 0.351760i | \(-0.885583\pi\) | ||
0.936090 | − | 0.351760i | \(-0.114417\pi\) | |||||||
\(410\) | 3.26817 | + | 8.31318i | 0.161403 | + | 0.410559i | ||||
\(411\) | −7.75196 | + | 5.60424i | −0.382376 | + | 0.276437i | ||||
\(412\) | −8.88033 | − | 8.88033i | −0.437502 | − | 0.437502i | ||||
\(413\) | −37.7856 | − | 37.7856i | −1.85931 | − | 1.85931i | ||||
\(414\) | 16.2785 | + | 5.37422i | 0.800044 | + | 0.264129i | ||||
\(415\) | −10.7269 | − | 27.2857i | −0.526561 | − | 1.33940i | ||||
\(416\) | − | 0.121414i | − | 0.00595279i | ||||||
\(417\) | 0.243269 | − | 1.51284i | 0.0119129 | − | 0.0740841i | ||||
\(418\) | 3.09646 | − | 3.09646i | 0.151453 | − | 0.151453i | ||||
\(419\) | 27.8666 | 1.36137 | 0.680686 | − | 0.732576i | \(-0.261682\pi\) | ||||
0.680686 | + | 0.732576i | \(0.261682\pi\) | |||||||
\(420\) | −14.8000 | + | 3.23400i | −0.722164 | + | 0.157803i | ||||
\(421\) | 30.3012 | 1.47679 | 0.738396 | − | 0.674368i | \(-0.235584\pi\) | ||||
0.738396 | + | 0.674368i | \(0.235584\pi\) | |||||||
\(422\) | 3.91878 | − | 3.91878i | 0.190763 | − | 0.190763i | ||||
\(423\) | −35.5249 | + | 17.8903i | −1.72728 | + | 0.869856i | ||||
\(424\) | − | 2.28910i | − | 0.111168i | ||||||
\(425\) | 34.6603 | + | 1.25721i | 1.68127 | + | 0.0609838i | ||||
\(426\) | 10.2613 | + | 14.1938i | 0.497162 | + | 0.687690i | ||||
\(427\) | 36.1468 | + | 36.1468i | 1.74927 | + | 1.74927i | ||||
\(428\) | 7.02479 | + | 7.02479i | 0.339556 | + | 0.339556i | ||||
\(429\) | 0.539529 | + | 0.746293i | 0.0260487 | + | 0.0360314i | ||||
\(430\) | 2.81305 | − | 6.45766i | 0.135658 | − | 0.311416i | ||||
\(431\) | 23.2155i | 1.11825i | 0.829082 | + | 0.559126i | \(0.188863\pi\) | ||||
−0.829082 | + | 0.559126i | \(0.811137\pi\) | |||||||
\(432\) | −4.61300 | − | 2.39170i | −0.221943 | − | 0.115071i | ||||
\(433\) | 20.5816 | − | 20.5816i | 0.989090 | − | 0.989090i | −0.0108515 | − | 0.999941i | \(-0.503454\pi\) |
0.999941 | + | 0.0108515i | \(0.00345420\pi\) | |||||||
\(434\) | −18.7756 | −0.901257 | ||||||||
\(435\) | 25.2187 | + | 16.1738i | 1.20914 | + | 0.775476i | ||||
\(436\) | −0.223709 | −0.0107137 | ||||||||
\(437\) | −4.04057 | + | 4.04057i | −0.193287 | + | 0.193287i | ||||
\(438\) | −1.18536 | + | 7.37149i | −0.0566386 | + | 0.352223i | ||||
\(439\) | − | 29.7544i | − | 1.42010i | −0.704151 | − | 0.710050i | \(-0.748672\pi\) | ||
0.704151 | − | 0.710050i | \(-0.251328\pi\) | |||||||
\(440\) | 9.11296 | − | 3.58259i | 0.434443 | − | 0.170793i | ||||
\(441\) | −7.80600 | + | 23.6443i | −0.371714 | + | 1.12592i | ||||
\(442\) | 0.595525 | + | 0.595525i | 0.0283262 | + | 0.0283262i | ||||
\(443\) | −12.8988 | − | 12.8988i | −0.612842 | − | 0.612842i | 0.330844 | − | 0.943686i | \(-0.392667\pi\) |
−0.943686 | + | 0.330844i | \(0.892667\pi\) | |||||||
\(444\) | −2.29991 | + | 1.66271i | −0.109149 | + | 0.0789086i | ||||
\(445\) | 9.17717 | + | 3.99771i | 0.435040 | + | 0.189510i | ||||
\(446\) | − | 13.4784i | − | 0.638219i | ||||||
\(447\) | −24.6578 | − | 3.96505i | −1.16628 | − | 0.187541i | ||||
\(448\) | −2.76585 | + | 2.76585i | −0.130674 | + | 0.130674i | ||||
\(449\) | 6.08743 | 0.287284 | 0.143642 | − | 0.989630i | \(-0.454119\pi\) | ||||
0.143642 | + | 0.989630i | \(0.454119\pi\) | |||||||
\(450\) | 14.0640 | + | 5.21572i | 0.662984 | + | 0.245871i | ||||
\(451\) | −17.4932 | −0.823725 | ||||||||
\(452\) | −4.90305 | + | 4.90305i | −0.230620 | + | 0.230620i | ||||
\(453\) | 21.4686 | + | 3.45221i | 1.00868 | + | 0.162199i | ||||
\(454\) | − | 19.4501i | − | 0.912836i | ||||||
\(455\) | 0.973568 | + | 0.424101i | 0.0456416 | + | 0.0198822i | ||||
\(456\) | 1.40366 | − | 1.01477i | 0.0657322 | − | 0.0475208i | ||||
\(457\) | 13.6315 | + | 13.6315i | 0.637656 | + | 0.637656i | 0.949977 | − | 0.312321i | \(-0.101106\pi\) |
−0.312321 | + | 0.949977i | \(0.601106\pi\) | |||||||
\(458\) | 4.59237 | + | 4.59237i | 0.214588 | + | 0.214588i | ||||
\(459\) | 34.3575 | − | 10.8953i | 1.60367 | − | 0.508549i | ||||
\(460\) | −11.8915 | + | 4.67491i | −0.554443 | + | 0.217969i | ||||
\(461\) | 20.6355i | 0.961091i | 0.876970 | + | 0.480546i | \(0.159561\pi\) | ||||
−0.876970 | + | 0.480546i | \(0.840439\pi\) | |||||||
\(462\) | 4.71016 | − | 29.2915i | 0.219137 | − | 1.36276i | ||||
\(463\) | 1.47081 | − | 1.47081i | 0.0683543 | − | 0.0683543i | −0.672103 | − | 0.740458i | \(-0.734609\pi\) |
0.740458 | + | 0.672103i | \(0.234609\pi\) | |||||||
\(464\) | 7.73552 | 0.359113 | ||||||||
\(465\) | 15.6489 | + | 10.0363i | 0.725698 | + | 0.465422i | ||||
\(466\) | −11.2384 | −0.520608 | ||||||||
\(467\) | −24.9074 | + | 24.9074i | −1.15258 | + | 1.15258i | −0.166541 | + | 0.986035i | \(0.553260\pi\) |
−0.986035 | + | 0.166541i | \(0.946740\pi\) | |||||||
\(468\) | 0.163829 | + | 0.325317i | 0.00757301 | + | 0.0150378i | ||||
\(469\) | − | 52.9910i | − | 2.44690i | ||||||
\(470\) | 11.8400 | − | 27.1800i | 0.546139 | − | 1.25372i | ||||
\(471\) | −13.0408 | − | 18.0384i | −0.600887 | − | 0.831165i | ||||
\(472\) | 9.66012 | + | 9.66012i | 0.444643 | + | 0.444643i | ||||
\(473\) | 9.75407 | + | 9.75407i | 0.448493 | + | 0.448493i | ||||
\(474\) | 1.26574 | + | 1.75080i | 0.0581372 | + | 0.0804171i | ||||
\(475\) | −3.66137 | + | 3.40505i | −0.167995 | + | 0.156235i | ||||
\(476\) | − | 27.1326i | − | 1.24362i | ||||||
\(477\) | 3.08879 | + | 6.13344i | 0.141426 | + | 0.280831i | ||||
\(478\) | 5.31171 | − | 5.31171i | 0.242952 | − | 0.242952i | ||||
\(479\) | 11.4278 | 0.522150 | 0.261075 | − | 0.965318i | \(-0.415923\pi\) | ||||
0.261075 | + | 0.965318i | \(0.415923\pi\) | |||||||
\(480\) | 3.78370 | − | 0.826793i | 0.172702 | − | 0.0377378i | ||||
\(481\) | 0.198938 | 0.00907078 | ||||||||
\(482\) | 7.92744 | − | 7.92744i | 0.361085 | − | 0.361085i | ||||
\(483\) | −6.14628 | + | 38.2224i | −0.279665 | + | 1.73918i | ||||
\(484\) | 8.17619i | 0.371645i | ||||||||
\(485\) | 1.21982 | + | 3.10282i | 0.0553890 | + | 0.140892i | ||||
\(486\) | 15.5874 | + | 0.183816i | 0.707058 | + | 0.00833808i | ||||
\(487\) | −6.40458 | − | 6.40458i | −0.290219 | − | 0.290219i | 0.546948 | − | 0.837167i | \(-0.315790\pi\) |
−0.837167 | + | 0.546948i | \(0.815790\pi\) | |||||||
\(488\) | −9.24116 | − | 9.24116i | −0.418328 | − | 0.418328i | ||||
\(489\) | −5.91390 | + | 4.27543i | −0.267436 | + | 0.193342i | ||||
\(490\) | −6.79025 | − | 17.2722i | −0.306752 | − | 0.780280i | ||||
\(491\) | − | 8.15301i | − | 0.367940i | −0.982932 | − | 0.183970i | \(-0.941105\pi\) | ||
0.982932 | − | 0.183970i | \(-0.0588950\pi\) | |||||||
\(492\) | −6.83135 | − | 1.09850i | −0.307981 | − | 0.0495242i | ||||
\(493\) | −37.9422 | + | 37.9422i | −1.70883 | + | 1.70883i | ||||
\(494\) | −0.121414 | −0.00546266 | ||||||||
\(495\) | −19.5832 | + | 21.8958i | −0.880201 | + | 0.984142i | ||||
\(496\) | 4.80009 | 0.215531 | ||||||||
\(497\) | −27.9683 | + | 27.9683i | −1.25455 | + | 1.25455i | ||||
\(498\) | 22.4220 | + | 3.60552i | 1.00475 | + | 0.161567i | ||||
\(499\) | 1.46257i | 0.0654738i | 0.999464 | + | 0.0327369i | \(0.0104223\pi\) | ||||
−0.999464 | + | 0.0327369i | \(0.989578\pi\) | |||||||
\(500\) | −10.5466 | + | 3.71073i | −0.471658 | + | 0.165949i | ||||
\(501\) | 13.2290 | − | 9.56387i | 0.591030 | − | 0.427282i | ||||
\(502\) | −7.60679 | − | 7.60679i | −0.339508 | − | 0.339508i | ||||
\(503\) | 27.1555 | + | 27.1555i | 1.21081 | + | 1.21081i | 0.970762 | + | 0.240043i | \(0.0771615\pi\) |
0.240043 | + | 0.970762i | \(0.422839\pi\) | |||||||
\(504\) | 3.67876 | − | 11.1430i | 0.163865 | − | 0.496346i | ||||
\(505\) | −1.18192 | + | 2.71323i | −0.0525949 | + | 0.120737i | ||||
\(506\) | − | 25.0230i | − | 1.11241i | ||||||
\(507\) | −3.57077 | + | 22.2059i | −0.158583 | + | 0.986197i | ||||
\(508\) | 1.71446 | − | 1.71446i | 0.0760670 | − | 0.0760670i | ||||
\(509\) | −3.41038 | −0.151162 | −0.0755812 | − | 0.997140i | \(-0.524081\pi\) | ||||
−0.0755812 | + | 0.997140i | \(0.524081\pi\) | |||||||
\(510\) | −14.5034 | + | 22.6141i | −0.642223 | + | 1.00137i | ||||
\(511\) | −16.8609 | −0.745884 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.39170 | + | 4.61300i | −0.105596 | + | 0.203669i | ||||
\(514\) | − | 3.78581i | − | 0.166985i | ||||||
\(515\) | −26.1350 | + | 10.2745i | −1.15165 | + | 0.452747i | ||||
\(516\) | 3.19658 | + | 4.42161i | 0.140722 | + | 0.194651i | ||||
\(517\) | 41.0544 | + | 41.0544i | 1.80557 | + | 1.80557i | ||||
\(518\) | −4.53188 | − | 4.53188i | −0.199119 | − | 0.199119i | ||||
\(519\) | −4.78135 | − | 6.61371i | −0.209878 | − | 0.290310i | ||||
\(520\) | −0.248899 | − | 0.108424i | −0.0109149 | − | 0.00475471i | ||||
\(521\) | − | 26.3131i | − | 1.15280i | −0.817169 | − | 0.576399i | \(-0.804457\pi\) | ||
0.817169 | − | 0.576399i | \(-0.195543\pi\) | |||||||
\(522\) | −20.7267 | + | 10.4379i | −0.907182 | + | 0.456855i | ||||
\(523\) | 1.67071 | − | 1.67071i | 0.0730549 | − | 0.0730549i | −0.669635 | − | 0.742690i | \(-0.733550\pi\) |
0.742690 | + | 0.669635i | \(0.233550\pi\) | |||||||
\(524\) | 1.03462 | 0.0451974 | ||||||||
\(525\) | −6.58685 | + | 33.2280i | −0.287474 | + | 1.45019i | ||||
\(526\) | −23.7107 | −1.03384 | ||||||||
\(527\) | −23.5441 | + | 23.5441i | −1.02560 | + | 1.02560i | ||||
\(528\) | −1.20418 | + | 7.48856i | −0.0524053 | + | 0.325898i | ||||
\(529\) | 9.65240i | 0.419669i | ||||||||
\(530\) | −4.69267 | − | 2.04420i | −0.203836 | − | 0.0887942i | ||||
\(531\) | −38.9183 | − | 12.8486i | −1.68891 | − | 0.557582i | ||||
\(532\) | 2.76585 | + | 2.76585i | 0.119915 | + | 0.119915i | ||||
\(533\) | 0.342959 | + | 0.342959i | 0.0148552 | + | 0.0148552i | ||||
\(534\) | −6.28368 | + | 4.54276i | −0.271921 | + | 0.196584i | ||||
\(535\) | 20.6741 | − | 8.12763i | 0.893819 | − | 0.351388i | ||||
\(536\) | 13.5475i | 0.585162i | ||||||||
\(537\) | 34.8729 | + | 5.60767i | 1.50488 | + | 0.241989i | ||||
\(538\) | 8.87418 | − | 8.87418i | 0.382593 | − | 0.382593i | ||||
\(539\) | 36.3456 | 1.56551 | ||||||||
\(540\) | −9.02248 | + | 7.32086i | −0.388266 | + | 0.315039i | ||||
\(541\) | −23.9511 | −1.02974 | −0.514870 | − | 0.857269i | \(-0.672160\pi\) | ||||
−0.514870 | + | 0.857269i | \(0.672160\pi\) | |||||||
\(542\) | −9.17134 | + | 9.17134i | −0.393943 | + | 0.393943i | ||||
\(543\) | −33.8594 | − | 5.44469i | −1.45304 | − | 0.233654i | ||||
\(544\) | 6.93661i | 0.297405i | ||||||||
\(545\) | −0.199775 | + | 0.458605i | −0.00855743 | + | 0.0196445i | ||||
\(546\) | −0.666610 | + | 0.481922i | −0.0285283 | + | 0.0206244i | ||||
\(547\) | −18.6458 | − | 18.6458i | −0.797236 | − | 0.797236i | 0.185423 | − | 0.982659i | \(-0.440634\pi\) |
−0.982659 | + | 0.185423i | \(0.940634\pi\) | |||||||
\(548\) | 3.90513 | + | 3.90513i | 0.166819 | + | 0.166819i | ||||
\(549\) | 37.2304 | + | 12.2914i | 1.58896 | + | 0.524582i | ||||
\(550\) | 0.793675 | − | 21.8809i | 0.0338424 | − | 0.933006i | ||||
\(551\) | − | 7.73552i | − | 0.329544i | ||||||
\(552\) | 1.57133 | − | 9.77180i | 0.0668804 | − | 0.415915i | ||||
\(553\) | −3.44989 | + | 3.44989i | −0.146704 | + | 0.146704i | ||||
\(554\) | 14.4590 | 0.614306 | ||||||||
\(555\) | 1.35471 | + | 6.19965i | 0.0575043 | + | 0.263160i | ||||
\(556\) | −0.884659 | −0.0375179 | ||||||||
\(557\) | 4.22121 | − | 4.22121i | 0.178859 | − | 0.178859i | −0.612000 | − | 0.790858i | \(-0.709635\pi\) |
0.790858 | + | 0.612000i | \(0.209635\pi\) | |||||||
\(558\) | −12.8614 | + | 6.47700i | −0.544468 | + | 0.274193i | ||||
\(559\) | − | 0.382461i | − | 0.0161764i | ||||||
\(560\) | 3.20007 | + | 8.13995i | 0.135228 | + | 0.343976i | ||||
\(561\) | −30.8244 | − | 42.6373i | −1.30141 | − | 1.80015i | ||||
\(562\) | −2.46184 | − | 2.46184i | −0.103846 | − | 0.103846i | ||||
\(563\) | −11.0358 | − | 11.0358i | −0.465105 | − | 0.465105i | 0.435219 | − | 0.900325i | \(-0.356671\pi\) |
−0.900325 | + | 0.435219i | \(0.856671\pi\) | |||||||
\(564\) | 13.4543 | + | 18.6103i | 0.566526 | + | 0.783636i | ||||
\(565\) | 5.67279 | + | 14.4298i | 0.238656 | + | 0.607065i | ||||
\(566\) | 4.85720i | 0.204164i | ||||||||
\(567\) | 5.17879 | + | 34.8205i | 0.217489 | + | 1.46232i | ||||
\(568\) | 7.15026 | − | 7.15026i | 0.300018 | − | 0.300018i | ||||
\(569\) | −16.3299 | −0.684585 | −0.342293 | − | 0.939593i | \(-0.611203\pi\) | ||||
−0.342293 | + | 0.939593i | \(0.611203\pi\) | |||||||
\(570\) | −0.826793 | − | 3.78370i | −0.0346306 | − | 0.158482i | ||||
\(571\) | 28.8841 | 1.20876 | 0.604381 | − | 0.796695i | \(-0.293421\pi\) | ||||
0.604381 | + | 0.796695i | \(0.293421\pi\) | |||||||
\(572\) | 0.375953 | − | 0.375953i | 0.0157194 | − | 0.0157194i | ||||
\(573\) | −4.42587 | + | 27.5236i | −0.184893 | + | 1.14981i | ||||
\(574\) | − | 15.6255i | − | 0.652194i | ||||||
\(575\) | −1.03566 | + | 28.5524i | −0.0431902 | + | 1.19072i | ||||
\(576\) | −0.940499 | + | 2.84877i | −0.0391874 | + | 0.118699i | ||||
\(577\) | −10.6942 | − | 10.6942i | −0.445205 | − | 0.445205i | 0.448552 | − | 0.893757i | \(-0.351940\pi\) |
−0.893757 | + | 0.448552i | \(0.851940\pi\) | |||||||
\(578\) | −22.0028 | − | 22.0028i | −0.915194 | − | 0.915194i | ||||
\(579\) | −5.47147 | + | 3.95557i | −0.227386 | + | 0.164388i | ||||
\(580\) | 6.90793 | − | 15.8579i | 0.286836 | − | 0.658462i | ||||
\(581\) | 51.2862i | 2.12771i | ||||||||
\(582\) | −2.54974 | − | 0.410006i | −0.105690 | − | 0.0169953i | ||||
\(583\) | 7.08811 | − | 7.08811i | 0.293560 | − | 0.293560i | ||||
\(584\) | 4.31060 | 0.178374 | ||||||||
\(585\) | 0.813205 | − | 0.0453381i | 0.0336219 | − | 0.00187450i | ||||
\(586\) | −6.04102 | −0.249552 | ||||||||
\(587\) | 26.1994 | − | 26.1994i | 1.08136 | − | 1.08136i | 0.0849807 | − | 0.996383i | \(-0.472917\pi\) |
0.996383 | − | 0.0849807i | \(-0.0270829\pi\) | |||||||
\(588\) | 14.1934 | + | 2.28234i | 0.585327 | + | 0.0941223i | ||||
\(589\) | − | 4.80009i | − | 0.197784i | ||||||
\(590\) | 28.4299 | − | 11.1767i | 1.17044 | − | 0.460137i | ||||
\(591\) | 18.9157 | − | 13.6750i | 0.778089 | − | 0.562516i | ||||
\(592\) | 1.15860 | + | 1.15860i | 0.0476183 | + | 0.0476183i | ||||
\(593\) | −13.6587 | − | 13.6587i | −0.560897 | − | 0.560897i | 0.368665 | − | 0.929562i | \(-0.379815\pi\) |
−0.929562 | + | 0.368665i | \(0.879815\pi\) | |||||||
\(594\) | −6.87817 | − | 21.6898i | −0.282215 | − | 0.889944i | ||||
\(595\) | −55.6220 | − | 24.2298i | −2.28028 | − | 0.993324i | ||||
\(596\) | 14.4191i | 0.590629i | ||||||||
\(597\) | 2.09472 | − | 13.0266i | 0.0857313 | − | 0.533145i | ||||
\(598\) | −0.490580 | + | 0.490580i | −0.0200613 | + | 0.0200613i | ||||
\(599\) | −29.0472 | −1.18684 | −0.593418 | − | 0.804894i | \(-0.702222\pi\) | ||||
−0.593418 | + | 0.804894i | \(0.702222\pi\) | |||||||
\(600\) | 1.68397 | − | 8.49495i | 0.0687477 | − | 0.346805i | ||||
\(601\) | −14.9410 | −0.609458 | −0.304729 | − | 0.952439i | \(-0.598566\pi\) | ||||
−0.304729 | + | 0.952439i | \(0.598566\pi\) | |||||||
\(602\) | −8.71261 | + | 8.71261i | −0.355100 | + | 0.355100i | ||||
\(603\) | −18.2803 | − | 36.2993i | −0.744430 | − | 1.47822i | ||||
\(604\) | − | 12.5541i | − | 0.510820i | ||||||
\(605\) | 16.7612 | + | 7.30145i | 0.681441 | + | 0.296846i | ||||
\(606\) | −1.34306 | − | 1.85777i | −0.0545583 | − | 0.0754666i | ||||
\(607\) | 8.68114 | + | 8.68114i | 0.352357 | + | 0.352357i | 0.860986 | − | 0.508629i | \(-0.169848\pi\) |
−0.508629 | + | 0.860986i | \(0.669848\pi\) | |||||||
\(608\) | −0.707107 | − | 0.707107i | −0.0286770 | − | 0.0286770i | ||||
\(609\) | −30.7043 | − | 42.4711i | −1.24420 | − | 1.72102i | ||||
\(610\) | −27.1969 | + | 10.6920i | −1.10117 | + | 0.432905i | ||||
\(611\) | − | 1.60976i | − | 0.0651239i | ||||||
\(612\) | −9.35991 | − | 18.5861i | −0.378352 | − | 0.751297i | ||||
\(613\) | −5.07536 | + | 5.07536i | −0.204992 | + | 0.204992i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.597143 | + | 0.802135i | \(0.296303\pi\) | |||||||
\(614\) | −17.8017 | −0.718417 | ||||||||
\(615\) | −8.35242 | + | 13.0233i | −0.336802 | + | 0.525151i | ||||
\(616\) | −17.1287 | −0.690136 | ||||||||
\(617\) | 4.31435 | − | 4.31435i | 0.173689 | − | 0.173689i | −0.614909 | − | 0.788598i | \(-0.710807\pi\) |
0.788598 | + | 0.614909i | \(0.210807\pi\) | |||||||
\(618\) | 3.45346 | − | 21.4764i | 0.138919 | − | 0.863907i | ||||
\(619\) | − | 6.95816i | − | 0.279672i | −0.990175 | − | 0.139836i | \(-0.955342\pi\) | ||
0.990175 | − | 0.139836i | \(-0.0446575\pi\) | |||||||
\(620\) | 4.28655 | − | 9.84022i | 0.172152 | − | 0.395193i | ||||
\(621\) | 8.97531 | + | 28.3030i | 0.360167 | + | 1.13576i | ||||
\(622\) | −1.54997 | − | 1.54997i | −0.0621481 | − | 0.0621481i | ||||
\(623\) | −12.3818 | − | 12.3818i | −0.496064 | − | 0.496064i | ||||
\(624\) | 0.170423 | − | 0.123206i | 0.00682238 | − | 0.00493221i | ||||
\(625\) | −1.81124 | + | 24.9343i | −0.0724496 | + | 0.997372i | ||||
\(626\) | − | 17.3861i | − | 0.694888i | ||||||
\(627\) | 7.48856 | + | 1.20418i | 0.299064 | + | 0.0480904i | ||||
\(628\) | −9.08703 | + | 9.08703i | −0.362612 | + | 0.362612i | ||||
\(629\) | −11.3657 | −0.453181 | ||||||||
\(630\) | −19.5579 | − | 17.4923i | −0.779207 | − | 0.696910i | ||||
\(631\) | −16.5313 | −0.658102 | −0.329051 | − | 0.944312i | \(-0.606729\pi\) | ||||
−0.329051 | + | 0.944312i | \(0.606729\pi\) | |||||||
\(632\) | 0.881987 | − | 0.881987i | 0.0350835 | − | 0.0350835i | ||||
\(633\) | 9.47726 | + | 1.52397i | 0.376687 | + | 0.0605724i | ||||
\(634\) | 7.07127i | 0.280836i | ||||||||
\(635\) | −1.98362 | − | 5.04570i | −0.0787176 | − | 0.200233i | ||||
\(636\) | 3.21311 | − | 2.32290i | 0.127408 | − | 0.0921090i | ||||
\(637\) | −0.712562 | − | 0.712562i | −0.0282327 | − | 0.0282327i | ||||
\(638\) | 23.9528 | + | 23.9528i | 0.948300 | + | 0.948300i | ||||
\(639\) | −9.51031 | + | 28.8067i | −0.376222 | + | 1.13958i | ||||
\(640\) | −0.818117 | − | 2.08103i | −0.0323389 | − | 0.0822599i | ||||
\(641\) | − | 16.7295i | − | 0.660775i | −0.943845 | − | 0.330388i | \(-0.892820\pi\) | ||
0.943845 | − | 0.330388i | \(-0.107180\pi\) | |||||||
\(642\) | −2.73187 | + | 16.9889i | −0.107818 | + | 0.670499i | ||||
\(643\) | 21.5217 | − | 21.5217i | 0.848733 | − | 0.848733i | −0.141242 | − | 0.989975i | \(-0.545110\pi\) |
0.989975 | + | 0.141242i | \(0.0451095\pi\) | |||||||
\(644\) | 22.3512 | 0.880761 | ||||||||
\(645\) | 11.9189 | − | 2.60445i | 0.469307 | − | 0.102550i | ||||
\(646\) | 6.93661 | 0.272917 | ||||||||
\(647\) | −7.41491 | + | 7.41491i | −0.291510 | + | 0.291510i | −0.837677 | − | 0.546166i | \(-0.816087\pi\) |
0.546166 | + | 0.837677i | \(0.316087\pi\) | |||||||
\(648\) | −1.32399 | − | 8.90208i | −0.0520113 | − | 0.349707i | ||||
\(649\) | 59.8244i | 2.34831i | ||||||||
\(650\) | −0.444540 | + | 0.413420i | −0.0174363 | + | 0.0162157i | ||||
\(651\) | −19.0528 | − | 26.3545i | −0.746739 | − | 1.03291i | ||||
\(652\) | 2.97919 | + | 2.97919i | 0.116674 | + | 0.116674i | ||||
\(653\) | 19.0621 | + | 19.0621i | 0.745959 | + | 0.745959i | 0.973718 | − | 0.227758i | \(-0.0731396\pi\) |
−0.227758 | + | 0.973718i | \(0.573140\pi\) | |||||||
\(654\) | −0.227012 | − | 0.314010i | −0.00887688 | − | 0.0122788i | ||||
\(655\) | 0.923926 | − | 2.12097i | 0.0361008 | − | 0.0828731i | ||||
\(656\) | 3.99475i | 0.155969i | ||||||||
\(657\) | −11.5499 | + | 5.81651i | −0.450604 | + | 0.226924i | ||||
\(658\) | −36.6709 | + | 36.6709i | −1.42958 | + | 1.42958i | ||||
\(659\) | 43.8126 | 1.70670 | 0.853349 | − | 0.521341i | \(-0.174568\pi\) | ||||
0.853349 | + | 0.521341i | \(0.174568\pi\) | |||||||
\(660\) | 14.2762 | + | 9.15597i | 0.555702 | + | 0.356396i | ||||
\(661\) | −16.9162 | −0.657963 | −0.328982 | − | 0.944336i | \(-0.606705\pi\) | ||||
−0.328982 | + | 0.944336i | \(0.606705\pi\) | |||||||
\(662\) | 11.0198 | − | 11.0198i | 0.428296 | − | 0.428296i | ||||
\(663\) | −0.231593 | + | 1.44023i | −0.00899434 | + | 0.0559339i | ||||
\(664\) | − | 13.1116i | − | 0.508830i | ||||||
\(665\) | 8.13995 | − | 3.20007i | 0.315654 | − | 0.124093i | ||||
\(666\) | −4.66774 | − | 1.54102i | −0.180871 | − | 0.0597133i | ||||
\(667\) | −31.2559 | − | 31.2559i | −1.21023 | − | 1.21023i | ||||
\(668\) | −6.66427 | − | 6.66427i | −0.257848 | − | 0.257848i | ||||
\(669\) | 18.9190 | − | 13.6774i | 0.731451 | − | 0.528799i | ||||
\(670\) | 27.7724 | + | 12.0981i | 1.07294 | + | 0.467390i | ||||
\(671\) | − | 57.2299i | − | 2.20933i | ||||||
\(672\) | −6.68899 | − | 1.07561i | −0.258033 | − | 0.0414925i | ||||
\(673\) | −29.1932 | + | 29.1932i | −1.12532 | + | 1.12532i | −0.134386 | + | 0.990929i | \(0.542906\pi\) |
−0.990929 | + | 0.134386i | \(0.957094\pi\) | |||||||
\(674\) | −18.2107 | −0.701449 | ||||||||
\(675\) | 6.95060 | + | 25.0338i | 0.267529 | + | 0.963550i | ||||
\(676\) | 12.9853 | 0.499433 | ||||||||
\(677\) | −10.7238 | + | 10.7238i | −0.412148 | + | 0.412148i | −0.882486 | − | 0.470338i | \(-0.844132\pi\) |
0.470338 | + | 0.882486i | \(0.344132\pi\) | |||||||
\(678\) | −11.8576 | − | 1.90674i | −0.455390 | − | 0.0732280i | ||||
\(679\) | − | 5.83207i | − | 0.223814i | ||||||
\(680\) | 14.2201 | + | 6.19449i | 0.545316 | + | 0.237548i | ||||
\(681\) | 27.3012 | − | 19.7373i | 1.04618 | − | 0.756333i | ||||
\(682\) | 14.8633 | + | 14.8633i | 0.569146 | + | 0.569146i | ||||
\(683\) | 35.6719 | + | 35.6719i | 1.36495 | + | 1.36495i | 0.867488 | + | 0.497459i | \(0.165733\pi\) |
0.497459 | + | 0.867488i | \(0.334267\pi\) | |||||||
\(684\) | 2.84877 | + | 0.940499i | 0.108925 | + | 0.0359609i | ||||
\(685\) | 11.4929 | − | 4.51821i | 0.439121 | − | 0.172632i | ||||
\(686\) | 5.08436i | 0.194122i | ||||||||
\(687\) | −1.78593 | + | 11.1063i | −0.0681373 | + | 0.423732i | ||||
\(688\) | 2.22743 | − | 2.22743i | 0.0849201 | − | 0.0849201i | ||||
\(689\) | −0.277928 | −0.0105882 | ||||||||
\(690\) | −18.6290 | − | 11.9476i | −0.709195 | − | 0.454837i | ||||
\(691\) | −26.9995 | −1.02711 | −0.513554 | − | 0.858057i | \(-0.671671\pi\) | ||||
−0.513554 | + | 0.858057i | \(0.671671\pi\) | |||||||
\(692\) | −3.33173 | + | 3.33173i | −0.126653 | + | 0.126653i | ||||
\(693\) | 45.8949 | − | 23.1126i | 1.74340 | − | 0.877975i | ||||
\(694\) | − | 7.64624i | − | 0.290247i | ||||||
\(695\) | −0.790013 | + | 1.81356i | −0.0299669 | + | 0.0687921i | ||||
\(696\) | 7.84975 | + | 10.8580i | 0.297544 | + | 0.411572i | ||||
\(697\) | −19.5939 | − | 19.5939i | −0.742173 | − | 0.742173i | ||||
\(698\) | 3.33026 | + | 3.33026i | 0.126052 | + | 0.126052i | ||||
\(699\) | −11.4043 | − | 15.7748i | −0.431351 | − | 0.596658i | ||||
\(700\) | 19.5447 | + | 0.708933i | 0.738719 | + | 0.0267951i | ||||
\(701\) | 43.3103i | 1.63581i | 0.575354 | + | 0.817905i | \(0.304864\pi\) | ||||
−0.575354 | + | 0.817905i | \(0.695136\pi\) | |||||||
\(702\) | −0.290385 | + | 0.560081i | −0.0109599 | + | 0.0211389i | ||||
\(703\) | 1.15860 | − | 1.15860i | 0.0436975 | − | 0.0436975i | ||||
\(704\) | 4.37906 | 0.165042 | ||||||||
\(705\) | 50.1661 | − | 10.9620i | 1.88937 | − | 0.412853i | ||||
\(706\) | 2.58792 | 0.0973976 | ||||||||
\(707\) | 3.66066 | − | 3.66066i | 0.137673 | − | 0.137673i | ||||
\(708\) | −3.75672 | + | 23.3622i | −0.141186 | + | 0.878007i | ||||
\(709\) | − | 5.62201i | − | 0.211139i | −0.994412 | − | 0.105569i | \(-0.966333\pi\) | ||
0.994412 | − | 0.105569i | \(-0.0336665\pi\) | |||||||
\(710\) | −8.27279 | − | 21.0434i | −0.310472 | − | 0.789743i | ||||
\(711\) | −1.17310 | + | 3.55331i | −0.0439947 | + | 0.133260i | ||||
\(712\) | 3.16547 | + | 3.16547i | 0.118631 | + | 0.118631i | ||||
\(713\) | −19.3951 | − | 19.3951i | −0.726353 | − | 0.726353i | ||||
\(714\) | 38.0848 | − | 27.5332i | 1.42529 | − | 1.03041i | ||||
\(715\) | −0.434975 | − | 1.10644i | −0.0162671 | − | 0.0413784i | ||||
\(716\) | − | 20.3926i | − | 0.762105i | ||||||
\(717\) | 12.8459 | + | 2.06567i | 0.479741 | + | 0.0771437i | ||||
\(718\) | −6.51117 | + | 6.51117i | −0.242995 | + | 0.242995i | ||||
\(719\) | −36.9146 | −1.37668 | −0.688340 | − | 0.725388i | \(-0.741660\pi\) | ||||
−0.688340 | + | 0.725388i | \(0.741660\pi\) | |||||||
\(720\) | 5.00011 | + | 4.47202i | 0.186343 | + | 0.166662i | ||||
\(721\) | 49.1233 | 1.82945 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | 19.1719 | + | 3.08290i | 0.713010 | + | 0.114654i | ||||
\(724\) | 19.7998i | 0.735855i | ||||||||
\(725\) | −26.3399 | − | 28.3226i | −0.978238 | − | 1.05188i | ||||
\(726\) | −11.4766 | + | 8.29692i | −0.425935 | + | 0.307928i | ||||
\(727\) | 23.0361 | + | 23.0361i | 0.854362 | + | 0.854362i | 0.990667 | − | 0.136305i | \(-0.0435227\pi\) |
−0.136305 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(728\) | 0.335812 | + | 0.335812i | 0.0124460 | + | 0.0124460i | ||||
\(729\) | 15.5595 | + | 22.0658i | 0.576279 | + | 0.817253i | ||||
\(730\) | 3.84943 | − | 8.83677i | 0.142474 | − | 0.327063i | ||||
\(731\) | 21.8508i | 0.808181i | ||||||||
\(732\) | 3.59379 | − | 22.3490i | 0.132830 | − | 0.826044i | ||||
\(733\) | −32.4240 | + | 32.4240i | −1.19761 | + | 1.19761i | −0.222726 | + | 0.974881i | \(0.571495\pi\) |
−0.974881 | + | 0.222726i | \(0.928505\pi\) | |||||||
\(734\) | 19.9298 | 0.735621 | ||||||||
\(735\) | 17.3538 | − | 27.0585i | 0.640103 | − | 0.998066i | ||||
\(736\) | −5.71423 | −0.210629 | ||||||||
\(737\) | −41.9493 | + | 41.9493i | −1.54522 | + | 1.54522i | ||||
\(738\) | −5.39030 | − | 10.7036i | −0.198420 | − | 0.394004i | ||||
\(739\) | 36.8773i | 1.35655i | 0.734806 | + | 0.678277i | \(0.237273\pi\) | ||||
−0.734806 | + | 0.678277i | \(0.762727\pi\) | |||||||
\(740\) | 3.40979 | − | 1.34050i | 0.125346 | − | 0.0492776i | ||||
\(741\) | −0.123206 | − | 0.170423i | −0.00452610 | − | 0.00626064i | ||||
\(742\) | 6.33130 | + | 6.33130i | 0.232429 | + | 0.232429i | ||||
\(743\) | 25.4177 | + | 25.4177i | 0.932483 | + | 0.932483i | 0.997861 | − | 0.0653772i | \(-0.0208251\pi\) |
−0.0653772 | + | 0.997861i | \(0.520825\pi\) | |||||||
\(744\) | 4.87097 | + | 6.73768i | 0.178579 | + | 0.247015i | ||||
\(745\) | 29.5592 | + | 12.8765i | 1.08297 | + | 0.471757i | ||||
\(746\) | 9.81579i | 0.359382i | ||||||||
\(747\) | 17.6922 | + | 35.1315i | 0.647323 | + | 1.28540i | ||||
\(748\) | −21.4790 | + | 21.4790i | −0.785349 | + | 0.785349i | ||||
\(749\) | −38.8590 | −1.41988 | ||||||||
\(750\) | −15.9109 | − | 11.0383i | −0.580984 | − | 0.403060i | ||||
\(751\) | 4.92408 | 0.179682 | 0.0898412 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898412 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(752\) | 9.37516 | − | 9.37516i | 0.341877 | − | 0.341877i | ||||
\(753\) | 2.95820 | − | 18.3964i | 0.107803 | − | 0.670403i | ||||
\(754\) | − | 0.939198i | − | 0.0342036i | ||||||
\(755\) | −25.7361 | − | 11.2110i | −0.936631 | − | 0.408011i | ||||
\(756\) | 19.3740 | − | 6.14378i | 0.704624 | − | 0.223447i | ||||
\(757\) | 13.6895 | + | 13.6895i | 0.497555 | + | 0.497555i | 0.910676 | − | 0.413121i | \(-0.135561\pi\) |
−0.413121 | + | 0.910676i | \(0.635561\pi\) | |||||||
\(758\) | 24.6735 | + | 24.6735i | 0.896184 | + | 0.896184i | ||||
\(759\) | 35.1236 | − | 25.3925i | 1.27491 | − | 0.921688i | ||||
\(760\) | −2.08103 | + | 0.818117i | −0.0754869 | + | 0.0296762i | ||||
\(761\) | − | 20.7833i | − | 0.753394i | −0.926337 | − | 0.376697i | \(-0.877060\pi\) | ||
0.926337 | − | 0.376697i | \(-0.122940\pi\) | |||||||
\(762\) | 4.14630 | + | 0.666737i | 0.150204 | + | 0.0241533i | ||||
\(763\) | 0.618745 | − | 0.618745i | 0.0224001 | − | 0.0224001i | ||||
\(764\) | 16.0949 | 0.582292 | ||||||||
\(765\) | −46.4601 | + | 2.59026i | −1.67977 | + | 0.0936510i | ||||
\(766\) | 4.24601 | 0.153415 | ||||||||
\(767\) | 1.17287 | − | 1.17287i | 0.0423499 | − | 0.0423499i | ||||
\(768\) | 1.71008 | + | 0.274986i | 0.0617073 | + | 0.00992271i | ||||
\(769\) | − | 41.2077i | − | 1.48599i | −0.669297 | − | 0.742995i | \(-0.733405\pi\) | ||
0.669297 | − | 0.742995i | \(-0.266595\pi\) | |||||||
\(770\) | −15.2962 | + | 35.1140i | −0.551236 | + | 1.26542i | ||||
\(771\) | 5.31397 | − | 3.84171i | 0.191378 | − | 0.138356i | ||||
\(772\) | 2.75631 | + | 2.75631i | 0.0992018 | + | 0.0992018i | ||||
\(773\) | −12.8806 | − | 12.8806i | −0.463282 | − | 0.463282i | 0.436448 | − | 0.899729i | \(-0.356236\pi\) |
−0.899729 | + | 0.436448i | \(0.856236\pi\) | |||||||
\(774\) | −2.96263 | + | 8.97380i | −0.106490 | + | 0.322557i | ||||
\(775\) | −16.3446 | − | 17.5749i | −0.587114 | − | 0.631310i | ||||
\(776\) | 1.49100i | 0.0535239i | ||||||||
\(777\) | 1.76240 | − | 10.9600i | 0.0632257 | − | 0.393188i | ||||
\(778\) | −2.96092 | + | 2.96092i | −0.106154 | + | 0.106154i | ||||
\(779\) | 3.99475 | 0.143127 | ||||||||
\(780\) | −0.100384 | − | 0.459393i | −0.00359432 | − | 0.0164489i | ||||
\(781\) | 44.2811 | 1.58450 | ||||||||
\(782\) | 28.0279 | − | 28.0279i | 1.00227 | − | 1.00227i | ||||
\(783\) | −35.6840 | − | 18.5011i | −1.27524 | − | 0.661174i | ||||
\(784\) | − | 8.29985i | − | 0.296423i | ||||||
\(785\) | 10.5136 | + | 26.7433i | 0.375247 | + | 0.954510i | ||||
\(786\) | 1.04989 | + | 1.45224i | 0.0374484 | + | 0.0517998i | ||||
\(787\) | −20.6001 | − | 20.6001i | −0.734316 | − | 0.734316i | 0.237156 | − | 0.971472i | \(-0.423785\pi\) |
−0.971472 | + | 0.237156i | \(0.923785\pi\) | |||||||
\(788\) | −9.52900 | − | 9.52900i | −0.339457 | − | 0.339457i | ||||
\(789\) | −24.0609 | − | 33.2817i | −0.856589 | − | 1.18486i | ||||
\(790\) | −1.02045 | − | 2.59570i | −0.0363061 | − | 0.0923510i | ||||
\(791\) | − | 27.1222i | − | 0.964354i | ||||||
\(792\) | −11.7333 | + | 5.90888i | −0.416925 | + | 0.209963i | ||||
\(793\) | −1.12200 | + | 1.12200i | −0.0398435 | + | 0.0398435i | ||||
\(794\) | −9.16344 | −0.325198 | ||||||||
\(795\) | −1.89261 | − | 8.66127i | −0.0671240 | − | 0.307184i | ||||
\(796\) | −7.61755 | −0.269997 | ||||||||
\(797\) | 29.3132 | − | 29.3132i | 1.03833 | − | 1.03833i | 0.0390930 | − | 0.999236i | \(-0.487553\pi\) |
0.999236 | − | 0.0390930i | \(-0.0124469\pi\) | |||||||
\(798\) | −1.07561 | + | 6.68899i | −0.0380762 | + | 0.236788i | ||||
\(799\) | 91.9689i | 3.25363i | ||||||||
\(800\) | −4.99671 | − | 0.181243i | −0.176661 | − | 0.00640791i | ||||
\(801\) | −12.7529 | − | 4.21029i | −0.450603 | − | 0.148763i | ||||
\(802\) | 8.54583 | + | 8.54583i | 0.301764 | + | 0.301764i | ||||
\(803\) | 13.3476 | + | 13.3476i | 0.471028 | + | 0.471028i | ||||
\(804\) | −19.0160 | + | 13.7475i | −0.670642 | + | 0.484838i | ||||
\(805\) | 19.9599 | − | 45.8201i | 0.703496 | − | 1.61495i | ||||
\(806\) | − | 0.582797i | − | 0.0205281i | ||||||
\(807\) | 21.4615 | + | 3.45107i | 0.755481 | + | 0.121484i | ||||
\(808\) | −0.935870 | + | 0.935870i | −0.0329238 | + | 0.0329238i | ||||
\(809\) | −3.65445 | −0.128483 | −0.0642417 | − | 0.997934i | \(-0.520463\pi\) | ||||
−0.0642417 | + | 0.997934i | \(0.520463\pi\) | |||||||
\(810\) | −19.4317 | − | 5.23549i | −0.682759 | − | 0.183956i | ||||
\(811\) | 5.62337 | 0.197463 | 0.0987316 | − | 0.995114i | \(-0.468521\pi\) | ||||
0.0987316 | + | 0.995114i | \(0.468521\pi\) | |||||||
\(812\) | −21.3953 | + | 21.3953i | −0.750828 | + | 0.750828i | ||||
\(813\) | −22.1802 | − | 3.56664i | −0.777893 | − | 0.125087i | ||||
\(814\) | 7.17515i | 0.251489i | ||||||||
\(815\) | 8.76783 | − | 3.44690i | 0.307124 | − | 0.120740i | ||||
\(816\) | −9.73662 | + | 7.03904i | −0.340850 | + | 0.246416i | ||||
\(817\) | −2.22743 | − | 2.22743i | −0.0779280 | − | 0.0779280i | ||||
\(818\) | −10.0606 | − | 10.0606i | −0.351760 | − | 0.351760i | ||||
\(819\) | −1.35291 | − | 0.446652i | −0.0472744 | − | 0.0156073i | ||||
\(820\) | 8.18925 | + | 3.56736i | 0.285981 | + | 0.124578i | ||||
\(821\) | − | 29.9356i | − | 1.04476i | −0.852713 | − | 0.522379i | \(-0.825045\pi\) | ||
0.852713 | − | 0.522379i | \(-0.174955\pi\) | |||||||
\(822\) | −1.51867 | + | 9.44426i | −0.0529695 | + | 0.329406i | ||||
\(823\) | −25.9697 | + | 25.9697i | −0.905246 | + | 0.905246i | −0.995884 | − | 0.0906383i | \(-0.971109\pi\) |
0.0906383 | + | 0.995884i | \(0.471109\pi\) | |||||||
\(824\) | −12.5587 | −0.437502 | ||||||||
\(825\) | 31.5187 | − | 21.0900i | 1.09734 | − | 0.734259i | ||||
\(826\) | −53.4369 | −1.85931 | ||||||||
\(827\) | −20.1949 | + | 20.1949i | −0.702247 | + | 0.702247i | −0.964892 | − | 0.262645i | \(-0.915405\pi\) |
0.262645 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(828\) | 15.3108 | − | 7.71048i | 0.532086 | − | 0.267958i | ||||
\(829\) | − | 54.6415i | − | 1.89778i | −0.315613 | − | 0.948888i | \(-0.602210\pi\) | ||
0.315613 | − | 0.948888i | \(-0.397790\pi\) | |||||||
\(830\) | −26.8789 | − | 11.7089i | −0.932982 | − | 0.406421i | ||||
\(831\) | 14.6726 | + | 20.2955i | 0.508985 | + | 0.704044i | ||||
\(832\) | −0.0858524 | − | 0.0858524i | −0.00297640 | − | 0.00297640i | ||||
\(833\) | 40.7102 | + | 40.7102i | 1.41052 | + | 1.41052i | ||||
\(834\) | −0.897722 | − | 1.24176i | −0.0310856 | − | 0.0429985i | ||||
\(835\) | −19.6131 | + | 7.71051i | −0.678739 | + | 0.266833i | ||||
\(836\) | − | 4.37906i | − | 0.151453i | ||||||
\(837\) | −22.1428 | − | 11.4804i | −0.765368 | − | 0.396820i | ||||
\(838\) | 19.7046 | − | 19.7046i | 0.680686 | − | 0.680686i | ||||
\(839\) | −16.3986 | −0.566144 | −0.283072 | − | 0.959099i | \(-0.591354\pi\) | ||||
−0.283072 | + | 0.959099i | \(0.591354\pi\) | |||||||
\(840\) | −8.17837 | + | 12.7519i | −0.282181 | + | 0.439984i | ||||
\(841\) | 30.8383 | 1.06339 | ||||||||
\(842\) | 21.4262 | − | 21.4262i | 0.738396 | − | 0.738396i | ||||
\(843\) | 0.957383 | − | 5.95377i | 0.0329740 | − | 0.205059i | ||||
\(844\) | − | 5.54199i | − | 0.190763i | ||||||
\(845\) | 11.5960 | − | 26.6199i | 0.398915 | − | 0.915751i | ||||
\(846\) | −12.4696 | + | 37.7703i | −0.428713 | + | 1.29857i | ||||
\(847\) | −22.6141 | − | 22.6141i | −0.777030 | − | 0.777030i | ||||
\(848\) | −1.61864 | − | 1.61864i | −0.0555842 | − | 0.0555842i | ||||
\(849\) | −6.81784 | + | 4.92893i | −0.233988 | + | 0.169160i | ||||
\(850\) | 25.3975 | − | 23.6195i | 0.871127 | − | 0.810143i | ||||
\(851\) | − | 9.36283i | − | 0.320954i | ||||||
\(852\) | 17.2923 | + | 2.78066i | 0.592426 | + | 0.0952638i | ||||
\(853\) | 26.5007 | − | 26.5007i | 0.907366 | − | 0.907366i | −0.0886927 | − | 0.996059i | \(-0.528269\pi\) |
0.996059 | + | 0.0886927i | \(0.0282689\pi\) | |||||||
\(854\) | 51.1193 | 1.74927 | ||||||||
\(855\) | 4.47202 | − | 5.00011i | 0.152940 | − | 0.171000i | ||||
\(856\) | 9.93455 | 0.339556 | ||||||||
\(857\) | −22.7533 | + | 22.7533i | −0.777239 | + | 0.777239i | −0.979360 | − | 0.202121i | \(-0.935216\pi\) |
0.202121 | + | 0.979360i | \(0.435216\pi\) | |||||||
\(858\) | 0.909213 | + | 0.146204i | 0.0310400 | + | 0.00499133i | ||||
\(859\) | 41.5266i | 1.41687i | 0.705776 | + | 0.708435i | \(0.250598\pi\) | ||||
−0.705776 | + | 0.708435i | \(0.749402\pi\) | |||||||
\(860\) | −2.57712 | − | 6.55538i | −0.0878792 | − | 0.223537i | ||||
\(861\) | 21.9328 | − | 15.8562i | 0.747467 | − | 0.540377i | ||||
\(862\) | 16.4159 | + | 16.4159i | 0.559126 | + | 0.559126i | ||||
\(863\) | −7.36244 | − | 7.36244i | −0.250620 | − | 0.250620i | 0.570605 | − | 0.821225i | \(-0.306709\pi\) |
−0.821225 | + | 0.570605i | \(0.806709\pi\) | |||||||
\(864\) | −4.95307 | + | 1.57069i | −0.168507 | + | 0.0534361i | ||||
\(865\) | 3.85478 | + | 9.80534i | 0.131067 | + | 0.333392i | ||||
\(866\) | − | 29.1068i | − | 0.989090i | ||||||
\(867\) | 8.55664 | − | 53.2120i | 0.290599 | − | 1.80717i | ||||
\(868\) | −13.2763 | + | 13.2763i | −0.450628 | + | 0.450628i | ||||
\(869\) | 5.46208 | 0.185288 | ||||||||
\(870\) | 29.2689 | − | 6.39568i | 0.992310 | − | 0.216834i | ||||
\(871\) | 1.64485 | 0.0557335 | ||||||||
\(872\) | −0.158186 | + | 0.158186i | −0.00535686 | + | 0.00535686i | ||||
\(873\) | −2.01188 | − | 3.99502i | −0.0680920 | − | 0.135211i | ||||
\(874\) | 5.71423i | 0.193287i | ||||||||
\(875\) | 18.9070 | − | 39.4336i | 0.639172 | − | 1.33310i | ||||
\(876\) | 4.37426 | + | 6.05060i | 0.147792 | + | 0.204431i | ||||
\(877\) | −1.47878 | − | 1.47878i | −0.0499350 | − | 0.0499350i | 0.681698 | − | 0.731633i | \(-0.261242\pi\) |
−0.731633 | + | 0.681698i | \(0.761242\pi\) | |||||||
\(878\) | −21.0395 | − | 21.0395i | −0.710050 | − | 0.710050i | ||||
\(879\) | −6.13022 | − | 8.47951i | −0.206767 | − | 0.286007i | ||||
\(880\) | 3.91056 | − | 8.97711i | 0.131825 | − | 0.302618i | ||||
\(881\) | 21.9350i | 0.739009i | 0.929229 | + | 0.369504i | \(0.120473\pi\) | ||||
−0.929229 | + | 0.369504i | \(0.879527\pi\) | |||||||
\(882\) | 11.1994 | + | 22.2387i | 0.377103 | + | 0.748817i | ||||
\(883\) | 16.2095 | − | 16.2095i | 0.545493 | − | 0.545493i | −0.379641 | − | 0.925134i | \(-0.623952\pi\) |
0.925134 | + | 0.379641i | \(0.123952\pi\) | |||||||
\(884\) | 0.842199 | 0.0283262 | ||||||||
\(885\) | 44.5380 | + | 28.5641i | 1.49713 | + | 0.960172i | ||||
\(886\) | −18.2417 | −0.612842 | ||||||||
\(887\) | 10.8840 | − | 10.8840i | 0.365449 | − | 0.365449i | −0.500366 | − | 0.865814i | \(-0.666801\pi\) |
0.865814 | + | 0.500366i | \(0.166801\pi\) | |||||||
\(888\) | −0.450568 | + | 2.80199i | −0.0151201 | + | 0.0940287i | ||||
\(889\) | 9.48390i | 0.318080i | ||||||||
\(890\) | 9.31605 | − | 3.66243i | 0.312275 | − | 0.122765i | ||||
\(891\) | 23.4653 | − | 31.6647i | 0.786117 | − | 1.06081i | ||||
\(892\) | −9.53065 | − | 9.53065i | −0.319110 | − | 0.319110i | ||||
\(893\) | −9.37516 | − | 9.37516i | −0.313728 | − | 0.313728i | ||||
\(894\) | −20.2394 | + | 14.6320i | −0.676908 | + | 0.489368i | ||||
\(895\) | −41.8049 | − | 18.2108i | −1.39738 | − | 0.608721i | ||||
\(896\) | 3.91150i | 0.130674i | ||||||||
\(897\) | −1.18643 | − | 0.190781i | −0.0396137 | − | 0.00637001i | ||||
\(898\) | 4.30447 | − | 4.30447i | 0.143642 | − | 0.143642i | ||||
\(899\) | 37.1312 | 1.23840 | ||||||||
\(900\) | 13.6328 | − | 6.25668i | 0.454428 | − | 0.208556i | ||||
\(901\) | 15.8786 | 0.528992 | ||||||||
\(902\) | −12.3696 | + | 12.3696i | −0.411862 | + | 0.411862i | ||||
\(903\) | −21.0708 | − | 3.38824i | −0.701191 | − | 0.112754i | ||||
\(904\) | 6.93395i | 0.230620i | ||||||||
\(905\) | 40.5898 | + | 17.6815i | 1.34925 | + | 0.587754i | ||||
\(906\) | 17.6217 | − | 12.7395i | 0.585441 | − | 0.423242i | ||||
\(907\) | 10.1424 | + | 10.1424i | 0.336773 | + | 0.336773i | 0.855151 | − | 0.518379i | \(-0.173464\pi\) |
−0.518379 | + | 0.855151i | \(0.673464\pi\) | |||||||
\(908\) | −13.7533 | − | 13.7533i | −0.456418 | − | 0.456418i | ||||
\(909\) | 1.24477 | − | 3.77040i | 0.0412864 | − | 0.125056i | ||||
\(910\) | 0.988301 | − | 0.388532i | 0.0327619 | − | 0.0128797i | ||||
\(911\) | − | 33.7497i | − | 1.11818i | −0.829108 | − | 0.559088i | \(-0.811151\pi\) | ||
0.829108 | − | 0.559088i | \(-0.188849\pi\) | |||||||
\(912\) | 0.274986 | − | 1.71008i | 0.00910571 | − | 0.0566265i | ||||
\(913\) | 40.5997 | − | 40.5997i | 1.34366 | − | 1.34366i | ||||
\(914\) | 19.2779 | 0.637656 | ||||||||
\(915\) | −42.6063 | − | 27.3253i | −1.40852 | − | 0.903346i | ||||
\(916\) | 6.49460 | 0.214588 | ||||||||
\(917\) | −2.86159 | + | 2.86159i | −0.0944980 | + | 0.0944980i | ||||
\(918\) | 16.5903 | − | 31.9986i | 0.547562 | − | 1.05611i | ||||
\(919\) | 43.6233i | 1.43900i | 0.694493 | + | 0.719499i | \(0.255629\pi\) | ||||
−0.694493 | + | 0.719499i | \(0.744371\pi\) | |||||||
\(920\) | −5.10289 | + | 11.7142i | −0.168237 | + | 0.386206i | ||||
\(921\) | −18.0645 | − | 24.9874i | −0.595246 | − | 0.823363i | ||||
\(922\) | 14.5915 | + | 14.5915i | 0.480546 | + | 0.480546i | ||||
\(923\) | −0.868139 | − | 0.868139i | −0.0285751 | − | 0.0285751i | ||||
\(924\) | −17.3816 | − | 24.0428i | −0.571814 | − | 0.790951i | ||||
\(925\) | 0.296969 | − | 8.18718i | 0.00976429 | − | 0.269193i | ||||
\(926\) | − | 2.08004i | − | 0.0683543i | ||||||
\(927\) | 33.6499 | − | 16.9460i | 1.10521 | − | 0.556581i | ||||
\(928\) | 5.46984 | − | 5.46984i | 0.179556 | − | 0.179556i | ||||
\(929\) | 50.9123 | 1.67038 | 0.835190 | − | 0.549962i | \(-0.185358\pi\) | ||||
0.835190 | + | 0.549962i | \(0.185358\pi\) | |||||||
\(930\) | 18.1621 | − | 3.96869i | 0.595560 | − | 0.130138i | ||||
\(931\) | −8.29985 | −0.272017 | ||||||||
\(932\) | −7.94673 | + | 7.94673i | −0.260304 | + | 0.260304i | ||||
\(933\) | 0.602766 | − | 3.74848i | 0.0197337 | − | 0.122720i | ||||
\(934\) | 35.2243i | 1.15258i | ||||||||
\(935\) | 24.8510 | + | 63.2131i | 0.812715 | + | 2.06729i | ||||
\(936\) | 0.345879 | + | 0.114189i | 0.0113054 | + | 0.00373240i | ||||
\(937\) | 11.7524 | + | 11.7524i | 0.383934 | + | 0.383934i | 0.872517 | − | 0.488583i | \(-0.162486\pi\) |
−0.488583 | + | 0.872517i | \(0.662486\pi\) | |||||||
\(938\) | −37.4703 | − | 37.4703i | −1.22345 | − | 1.22345i | ||||
\(939\) | 24.4041 | − | 17.6428i | 0.796397 | − | 0.575751i | ||||
\(940\) | −10.8470 | − | 27.5913i | −0.353790 | − | 0.899928i | ||||
\(941\) | 35.7875i | 1.16664i | 0.812242 | + | 0.583320i | \(0.198247\pi\) | ||||
−0.812242 | + | 0.583320i | \(0.801753\pi\) | |||||||
\(942\) | −21.9763 | − | 3.53385i | −0.716026 | − | 0.115139i | ||||
\(943\) | 16.1410 | − | 16.1410i | 0.525625 | − | 0.525625i | ||||
\(944\) | 13.6615 | 0.444643 | ||||||||
\(945\) | 4.70643 | − | 45.2032i | 0.153100 | − | 1.47046i | ||||
\(946\) | 13.7943 | 0.448493 | ||||||||
\(947\) | 35.8866 | − | 35.8866i | 1.16616 | − | 1.16616i | 0.183055 | − | 0.983103i | \(-0.441401\pi\) |
0.983103 | − | 0.183055i | \(-0.0585986\pi\) | |||||||
\(948\) | 2.13302 | + | 0.342995i | 0.0692771 | + | 0.0111400i | ||||
\(949\) | − | 0.523366i | − | 0.0169892i | ||||||
\(950\) | −0.181243 | + | 4.99671i | −0.00588030 | + | 0.162115i | ||||
\(951\) | −9.92562 | + | 7.17568i | −0.321860 | + | 0.232687i | ||||
\(952\) | −19.1856 | − | 19.1856i | −0.621810 | − | 0.621810i | ||||
\(953\) | 7.52954 | + | 7.52954i | 0.243906 | + | 0.243906i | 0.818464 | − | 0.574558i | \(-0.194826\pi\) |
−0.574558 | + | 0.818464i | \(0.694826\pi\) | |||||||
\(954\) | 6.52110 | + | 2.15289i | 0.211128 | + | 0.0697025i | ||||
\(955\) | 14.3730 | − | 32.9946i | 0.465098 | − | 1.06768i | ||||
\(956\) | − | 7.51189i | − | 0.242952i | ||||||
\(957\) | −9.31498 | + | 57.9279i | −0.301111 | + | 1.87254i | ||||
\(958\) | 8.08069 | − | 8.08069i | 0.261075 | − | 0.261075i | ||||
\(959\) | −21.6020 | −0.697566 | ||||||||
\(960\) | 2.09085 | − | 3.26011i | 0.0674819 | − | 0.105220i | ||||
\(961\) | −7.95909 | −0.256745 | ||||||||
\(962\) | 0.140670 | − | 0.140670i | 0.00453539 | − | 0.00453539i | ||||
\(963\) | −26.6188 | + | 13.4052i | −0.857778 | + | 0.431976i | ||||
\(964\) | − | 11.2111i | − | 0.361085i | ||||||
\(965\) | 8.11188 | − | 3.18903i | 0.261131 | − | 0.102659i | ||||
\(966\) | 22.6813 | + | 31.3734i | 0.729758 | + | 1.00942i | ||||
\(967\) | 26.9948 | + | 26.9948i | 0.868094 | + | 0.868094i | 0.992261 | − | 0.124167i | \(-0.0396259\pi\) |
−0.124167 | + | 0.992261i | \(0.539626\pi\) | |||||||
\(968\) | 5.78144 | + | 5.78144i | 0.185823 | + | 0.185823i | ||||
\(969\) | 7.03904 | + | 9.73662i | 0.226127 | + | 0.312785i | ||||
\(970\) | 3.05657 | + | 1.33149i | 0.0981405 | + | 0.0427515i | ||||
\(971\) | 5.51830i | 0.177091i | 0.996072 | + | 0.0885453i | \(0.0282218\pi\) | ||||
−0.996072 | + | 0.0885453i | \(0.971778\pi\) | |||||||
\(972\) | 11.1519 | − | 10.8920i | 0.357698 | − | 0.349360i | ||||
\(973\) | 2.44683 | − | 2.44683i | 0.0784419 | − | 0.0784419i | ||||
\(974\) | −9.05744 | −0.290219 | ||||||||
\(975\) | −1.03140 | − | 0.204457i | −0.0330313 | − | 0.00654786i | ||||
\(976\) | −13.0690 | −0.418328 | ||||||||
\(977\) | 24.9913 | − | 24.9913i | 0.799542 | − | 0.799542i | −0.183482 | − | 0.983023i | \(-0.558737\pi\) |
0.983023 | + | 0.183482i | \(0.0587368\pi\) | |||||||
\(978\) | −1.15858 | + | 7.20495i | −0.0370472 | + | 0.230389i | ||||
\(979\) | 19.6036i | 0.626532i | ||||||||
\(980\) | −17.0147 | − | 7.41188i | −0.543516 | − | 0.236764i | ||||
\(981\) | 0.210398 | − | 0.637294i | 0.00671749 | − | 0.0203472i | ||||
\(982\) | −5.76505 | − | 5.76505i | −0.183970 | − | 0.183970i | ||||
\(983\) | 5.21812 | + | 5.21812i | 0.166432 | + | 0.166432i | 0.785409 | − | 0.618977i | \(-0.212453\pi\) |
−0.618977 | + | 0.785409i | \(0.712453\pi\) | |||||||
\(984\) | −5.60725 | + | 4.05373i | −0.178753 | + | 0.129228i | ||||
\(985\) | −28.0440 | + | 11.0250i | −0.893558 | + | 0.351285i | ||||
\(986\) | 53.6583i | 1.70883i | ||||||||
\(987\) | −88.6858 | − | 14.2609i | −2.82290 | − | 0.453931i | ||||
\(988\) | −0.0858524 | + | 0.0858524i | −0.00273133 | + | 0.00273133i | ||||
\(989\) | −18.0002 | −0.572373 | ||||||||
\(990\) | 1.63522 | + | 29.3301i | 0.0519708 | + | 0.932172i | ||||
\(991\) | −34.4931 | −1.09571 | −0.547855 | − | 0.836574i | \(-0.684555\pi\) | ||||
−0.547855 | + | 0.836574i | \(0.684555\pi\) | |||||||
\(992\) | 3.39418 | − | 3.39418i | 0.107765 | − | 0.107765i | ||||
\(993\) | 26.6505 | + | 4.28547i | 0.845727 | + | 0.135995i | ||||
\(994\) | 39.5531i | 1.25455i | ||||||||
\(995\) | −6.80258 | + | 15.6160i | −0.215656 | + | 0.495062i | ||||
\(996\) | 18.4042 | − | 13.3053i | 0.583160 | − | 0.421593i | ||||
\(997\) | −26.5745 | − | 26.5745i | −0.841623 | − | 0.841623i | 0.147447 | − | 0.989070i | \(-0.452894\pi\) |
−0.989070 | + | 0.147447i | \(0.952894\pi\) | |||||||
\(998\) | 1.03420 | + | 1.03420i | 0.0327369 | + | 0.0327369i | ||||
\(999\) | −2.57360 | − | 8.11567i | −0.0814252 | − | 0.256768i |
(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 | 570.2.k.a.77.18 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.77.5 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.a.533.5 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.a.533.18 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.5 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.a.77.18 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.533.5 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.a.533.18 | yes | 36 | 15.8 | even | 4 | inner |