Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(89,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.12 | ||
Character | \(\chi\) | \(=\) | 231.89 |
Dual form | 231.2.n.a.122.12 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.408229 | − | 0.235691i | −0.288661 | − | 0.166659i | 0.348677 | − | 0.937243i | \(-0.386631\pi\) |
−0.637338 | + | 0.770584i | \(0.719964\pi\) | |||||||
\(3\) | −1.32879 | − | 1.11100i | −0.767178 | − | 0.641435i | ||||
\(4\) | −0.888900 | − | 1.53962i | −0.444450 | − | 0.769810i | ||||
\(5\) | 1.95312 | − | 3.38291i | 0.873462 | − | 1.51288i | 0.0150708 | − | 0.999886i | \(-0.495203\pi\) |
0.858392 | − | 0.512995i | \(-0.171464\pi\) | |||||||
\(6\) | 0.280598 | + | 0.766725i | 0.114554 | + | 0.313014i | ||||
\(7\) | −2.47945 | + | 0.923218i | −0.937144 | + | 0.348944i | ||||
\(8\) | 1.78079i | 0.629603i | ||||||||
\(9\) | 0.531368 | + | 2.95257i | 0.177123 | + | 0.984189i | ||||
\(10\) | −1.59464 | + | 0.920666i | −0.504269 | + | 0.291140i | ||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | ||||
\(12\) | −0.529352 | + | 3.03340i | −0.152811 | + | 0.875666i | ||||
\(13\) | − | 1.06912i | − | 0.296520i | −0.988948 | − | 0.148260i | \(-0.952633\pi\) | ||
0.988948 | − | 0.148260i | \(-0.0473673\pi\) | |||||||
\(14\) | 1.22978 | + | 0.207500i | 0.328672 | + | 0.0554566i | ||||
\(15\) | −6.35369 | + | 2.32526i | −1.64052 | + | 0.600379i | ||||
\(16\) | −1.35808 | + | 2.35227i | −0.339521 | + | 0.588068i | ||||
\(17\) | −2.07932 | − | 3.60148i | −0.504309 | − | 0.873488i | −0.999988 | − | 0.00498221i | \(-0.998414\pi\) |
0.495679 | − | 0.868506i | \(-0.334919\pi\) | |||||||
\(18\) | 0.478973 | − | 1.33056i | 0.112895 | − | 0.313616i | ||||
\(19\) | 5.11329 | + | 2.95216i | 1.17307 | + | 0.677272i | 0.954401 | − | 0.298527i | \(-0.0964953\pi\) |
0.218669 | + | 0.975799i | \(0.429829\pi\) | |||||||
\(20\) | −6.94452 | −1.55284 | ||||||||
\(21\) | 4.32036 | + | 1.52790i | 0.942780 | + | 0.333415i | ||||
\(22\) | 0.471382 | 0.100499 | ||||||||
\(23\) | −4.27331 | − | 2.46720i | −0.891047 | − | 0.514446i | −0.0167624 | − | 0.999860i | \(-0.505336\pi\) |
−0.874285 | + | 0.485413i | \(0.838669\pi\) | |||||||
\(24\) | 1.97845 | − | 2.36629i | 0.403849 | − | 0.483017i | ||||
\(25\) | −5.12937 | − | 8.88432i | −1.02587 | − | 1.77686i | ||||
\(26\) | −0.251982 | + | 0.436445i | −0.0494176 | + | 0.0855939i | ||||
\(27\) | 2.57422 | − | 4.51369i | 0.495408 | − | 0.868660i | ||||
\(28\) | 3.62539 | + | 2.99676i | 0.685134 | + | 0.566334i | ||||
\(29\) | − | 4.40659i | − | 0.818283i | −0.912471 | − | 0.409142i | \(-0.865828\pi\) | ||
0.912471 | − | 0.409142i | \(-0.134172\pi\) | |||||||
\(30\) | 3.14180 | + | 0.548269i | 0.573612 | + | 0.100100i | ||||
\(31\) | −4.27970 | + | 2.47089i | −0.768657 | + | 0.443784i | −0.832395 | − | 0.554182i | \(-0.813031\pi\) |
0.0637383 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(32\) | 4.19323 | − | 2.42096i | 0.741265 | − | 0.427970i | ||||
\(33\) | 1.70627 | + | 0.297757i | 0.297023 | + | 0.0518328i | ||||
\(34\) | 1.96030i | 0.336189i | ||||||||
\(35\) | −1.71951 | + | 10.1909i | −0.290649 | + | 1.72258i | ||||
\(36\) | 4.07349 | − | 3.44264i | 0.678916 | − | 0.573773i | ||||
\(37\) | 0.718698 | − | 1.24482i | 0.118153 | − | 0.204648i | −0.800883 | − | 0.598821i | \(-0.795636\pi\) |
0.919036 | + | 0.394174i | \(0.128969\pi\) | |||||||
\(38\) | −1.39159 | − | 2.41031i | −0.225746 | − | 0.391004i | ||||
\(39\) | −1.18779 | + | 1.42063i | −0.190198 | + | 0.227484i | ||||
\(40\) | 6.02423 | + | 3.47809i | 0.952514 | + | 0.549934i | ||||
\(41\) | 2.23267 | 0.348685 | 0.174342 | − | 0.984685i | \(-0.444220\pi\) | ||||
0.174342 | + | 0.984685i | \(0.444220\pi\) | |||||||
\(42\) | −1.40358 | − | 1.64200i | −0.216578 | − | 0.253366i | ||||
\(43\) | 5.91566 | 0.902129 | 0.451065 | − | 0.892491i | \(-0.351044\pi\) | ||||
0.451065 | + | 0.892491i | \(0.351044\pi\) | |||||||
\(44\) | 1.53962 | + | 0.888900i | 0.232106 | + | 0.134007i | ||||
\(45\) | 11.0261 | + | 3.96915i | 1.64367 | + | 0.591686i | ||||
\(46\) | 1.16299 | + | 2.01436i | 0.171474 | + | 0.297001i | ||||
\(47\) | 1.55717 | − | 2.69711i | 0.227137 | − | 0.393413i | −0.729821 | − | 0.683638i | \(-0.760397\pi\) |
0.956959 | + | 0.290225i | \(0.0937301\pi\) | |||||||
\(48\) | 4.41798 | − | 1.61685i | 0.637680 | − | 0.233372i | ||||
\(49\) | 5.29534 | − | 4.57814i | 0.756477 | − | 0.654021i | ||||
\(50\) | 4.83578i | 0.683883i | ||||||||
\(51\) | −1.23826 | + | 7.09573i | −0.173391 | + | 0.993601i | ||||
\(52\) | −1.64604 | + | 0.950339i | −0.228264 | + | 0.131788i | ||||
\(53\) | −5.23203 | + | 3.02072i | −0.718675 | + | 0.414927i | −0.814265 | − | 0.580494i | \(-0.802860\pi\) |
0.0955899 | + | 0.995421i | \(0.469526\pi\) | |||||||
\(54\) | −2.11471 | + | 1.23590i | −0.287775 | + | 0.168184i | ||||
\(55\) | 3.90624i | 0.526718i | ||||||||
\(56\) | −1.64405 | − | 4.41537i | −0.219696 | − | 0.590028i | ||||
\(57\) | −3.51465 | − | 9.60366i | −0.465527 | − | 1.27204i | ||||
\(58\) | −1.03859 | + | 1.79890i | −0.136374 | + | 0.236207i | ||||
\(59\) | −0.240199 | − | 0.416038i | −0.0312713 | − | 0.0541635i | 0.849966 | − | 0.526837i | \(-0.176622\pi\) |
−0.881238 | + | 0.472674i | \(0.843289\pi\) | |||||||
\(60\) | 9.22781 | + | 7.71534i | 1.19130 | + | 0.996046i | ||||
\(61\) | −2.78463 | − | 1.60771i | −0.356536 | − | 0.205846i | 0.311024 | − | 0.950402i | \(-0.399328\pi\) |
−0.667560 | + | 0.744556i | \(0.732661\pi\) | |||||||
\(62\) | 2.32946 | 0.295842 | ||||||||
\(63\) | −4.04336 | − | 6.83017i | −0.509416 | − | 0.860520i | ||||
\(64\) | 3.14994 | 0.393743 | ||||||||
\(65\) | −3.61673 | − | 2.08812i | −0.448600 | − | 0.258999i | ||||
\(66\) | −0.626368 | − | 0.523704i | −0.0771005 | − | 0.0644635i | ||||
\(67\) | −7.40799 | − | 12.8310i | −0.905031 | − | 1.56756i | −0.820876 | − | 0.571106i | \(-0.806514\pi\) |
−0.0841542 | − | 0.996453i | \(-0.526819\pi\) | |||||||
\(68\) | −3.69661 | + | 6.40271i | −0.448280 | + | 0.776443i | ||||
\(69\) | 2.93729 | + | 8.02603i | 0.353608 | + | 0.966221i | ||||
\(70\) | 3.10385 | − | 3.75494i | 0.370981 | − | 0.448802i | ||||
\(71\) | − | 10.0055i | − | 1.18743i | −0.804674 | − | 0.593717i | \(-0.797660\pi\) | ||
0.804674 | − | 0.593717i | \(-0.202340\pi\) | |||||||
\(72\) | −5.25789 | + | 0.946253i | −0.619648 | + | 0.111517i | ||||
\(73\) | 10.7524 | − | 6.20787i | 1.25847 | − | 0.726577i | 0.285691 | − | 0.958322i | \(-0.407777\pi\) |
0.972777 | + | 0.231745i | \(0.0744435\pi\) | |||||||
\(74\) | −0.586787 | + | 0.338781i | −0.0682126 | + | 0.0393825i | ||||
\(75\) | −3.05461 | + | 17.5041i | −0.352716 | + | 2.02120i | ||||
\(76\) | − | 10.4967i | − | 1.20405i | ||||||
\(77\) | 1.68566 | − | 2.03925i | 0.192098 | − | 0.232395i | ||||
\(78\) | 0.819720 | − | 0.299993i | 0.0928150 | − | 0.0339675i | ||||
\(79\) | −2.94229 | + | 5.09619i | −0.331033 | + | 0.573367i | −0.982715 | − | 0.185126i | \(-0.940731\pi\) |
0.651681 | + | 0.758493i | \(0.274064\pi\) | |||||||
\(80\) | 5.30501 | + | 9.18854i | 0.593118 | + | 1.02731i | ||||
\(81\) | −8.43530 | + | 3.13780i | −0.937255 | + | 0.348644i | ||||
\(82\) | −0.911441 | − | 0.526220i | −0.100652 | − | 0.0581113i | ||||
\(83\) | 7.65786 | 0.840559 | 0.420280 | − | 0.907395i | \(-0.361932\pi\) | ||||
0.420280 | + | 0.907395i | \(0.361932\pi\) | |||||||
\(84\) | −1.48799 | − | 8.00986i | −0.162352 | − | 0.873947i | ||||
\(85\) | −16.2446 | −1.76198 | ||||||||
\(86\) | −2.41494 | − | 1.39427i | −0.260410 | − | 0.150348i | ||||
\(87\) | −4.89571 | + | 5.85544i | −0.524875 | + | 0.627769i | ||||
\(88\) | −0.890393 | − | 1.54221i | −0.0949162 | − | 0.164400i | ||||
\(89\) | 0.824642 | − | 1.42832i | 0.0874119 | − | 0.151402i | −0.819005 | − | 0.573787i | \(-0.805474\pi\) |
0.906416 | + | 0.422385i | \(0.138807\pi\) | |||||||
\(90\) | −3.56567 | − | 4.21907i | −0.375854 | − | 0.444729i | ||||
\(91\) | 0.987030 | + | 2.65083i | 0.103469 | + | 0.277882i | ||||
\(92\) | 8.77237i | 0.914582i | ||||||||
\(93\) | 8.43198 | + | 1.47145i | 0.874355 | + | 0.152582i | ||||
\(94\) | −1.27137 | + | 0.734024i | −0.131131 | + | 0.0757088i | ||||
\(95\) | 19.9738 | − | 11.5319i | 2.04926 | − | 1.18314i | ||||
\(96\) | −8.26161 | − | 1.44172i | −0.843197 | − | 0.147145i | ||||
\(97\) | − | 5.22606i | − | 0.530626i | −0.964162 | − | 0.265313i | \(-0.914525\pi\) | ||
0.964162 | − | 0.265313i | \(-0.0854753\pi\) | |||||||
\(98\) | −3.24074 | + | 0.620867i | −0.327364 | + | 0.0627171i | ||||
\(99\) | −1.93646 | − | 2.29131i | −0.194622 | − | 0.230286i | ||||
\(100\) | −9.11898 | + | 15.7945i | −0.911898 | + | 1.57945i | ||||
\(101\) | 1.34223 | + | 2.32480i | 0.133557 | + | 0.231327i | 0.925045 | − | 0.379857i | \(-0.124027\pi\) |
−0.791489 | + | 0.611184i | \(0.790694\pi\) | |||||||
\(102\) | 2.17789 | − | 2.60483i | 0.215644 | − | 0.257917i | ||||
\(103\) | 10.9732 | + | 6.33537i | 1.08122 | + | 0.624242i | 0.931225 | − | 0.364445i | \(-0.118741\pi\) |
0.149994 | + | 0.988687i | \(0.452075\pi\) | |||||||
\(104\) | 1.90387 | 0.186690 | ||||||||
\(105\) | 13.6069 | − | 11.6312i | 1.32790 | − | 1.13509i | ||||
\(106\) | 2.84782 | 0.276605 | ||||||||
\(107\) | −8.45146 | − | 4.87945i | −0.817034 | − | 0.471715i | 0.0323588 | − | 0.999476i | \(-0.489698\pi\) |
−0.849392 | + | 0.527762i | \(0.823031\pi\) | |||||||
\(108\) | −9.23759 | + | 0.0489034i | −0.888887 | + | 0.00470573i | ||||
\(109\) | 4.39285 | + | 7.60864i | 0.420759 | + | 0.728776i | 0.996014 | − | 0.0891983i | \(-0.0284305\pi\) |
−0.575255 | + | 0.817974i | \(0.695097\pi\) | |||||||
\(110\) | 0.920666 | − | 1.59464i | 0.0877820 | − | 0.152043i | ||||
\(111\) | −2.33799 | + | 0.855636i | −0.221913 | + | 0.0812133i | ||||
\(112\) | 1.19564 | − | 7.08614i | 0.112978 | − | 0.669578i | ||||
\(113\) | 7.33403i | 0.689927i | 0.938616 | + | 0.344964i | \(0.112109\pi\) | ||||
−0.938616 | + | 0.344964i | \(0.887891\pi\) | |||||||
\(114\) | −0.828714 | + | 4.74886i | −0.0776162 | + | 0.444771i | ||||
\(115\) | −16.6926 | + | 9.63748i | −1.55659 | + | 0.898699i | ||||
\(116\) | −6.78447 | + | 3.91702i | −0.629922 | + | 0.363686i | ||||
\(117\) | 3.15664 | − | 0.568096i | 0.291832 | − | 0.0525205i | ||||
\(118\) | 0.226451i | 0.0208465i | ||||||||
\(119\) | 8.48052 | + | 7.01003i | 0.777408 | + | 0.642608i | ||||
\(120\) | −4.14079 | − | 11.3146i | −0.378001 | − | 1.03287i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 0.757845 | + | 1.31263i | 0.0686121 | + | 0.118840i | ||||
\(123\) | −2.96675 | − | 2.48049i | −0.267503 | − | 0.223659i | ||||
\(124\) | 7.60845 | + | 4.39274i | 0.683259 | + | 0.394480i | ||||
\(125\) | −20.5419 | −1.83732 | ||||||||
\(126\) | 0.0408078 | + | 3.74125i | 0.00363545 | + | 0.333297i | ||||
\(127\) | −14.2480 | −1.26430 | −0.632152 | − | 0.774844i | \(-0.717828\pi\) | ||||
−0.632152 | + | 0.774844i | \(0.717828\pi\) | |||||||
\(128\) | −9.67235 | − | 5.58434i | −0.854923 | − | 0.493590i | ||||
\(129\) | −7.86067 | − | 6.57228i | −0.692093 | − | 0.578657i | ||||
\(130\) | 0.984301 | + | 1.70486i | 0.0863289 | + | 0.149526i | ||||
\(131\) | 10.7855 | − | 18.6811i | 0.942338 | − | 1.63218i | 0.181342 | − | 0.983420i | \(-0.441956\pi\) |
0.760996 | − | 0.648757i | \(-0.224711\pi\) | |||||||
\(132\) | −1.05827 | − | 2.89167i | −0.0921102 | − | 0.251688i | ||||
\(133\) | −15.4036 | − | 2.59905i | −1.33566 | − | 0.225366i | ||||
\(134\) | 6.98399i | 0.603325i | ||||||||
\(135\) | −10.2416 | − | 17.5241i | −0.881459 | − | 1.50824i | ||||
\(136\) | 6.41347 | − | 3.70282i | 0.549951 | − | 0.317514i | ||||
\(137\) | 2.39232 | − | 1.38121i | 0.204390 | − | 0.118005i | −0.394312 | − | 0.918977i | \(-0.629017\pi\) |
0.598701 | + | 0.800972i | \(0.295684\pi\) | |||||||
\(138\) | 0.692578 | − | 3.96875i | 0.0589562 | − | 0.337842i | ||||
\(139\) | 20.6106i | 1.74817i | 0.485776 | + | 0.874083i | \(0.338537\pi\) | ||||
−0.485776 | + | 0.874083i | \(0.661463\pi\) | |||||||
\(140\) | 17.2186 | − | 6.41130i | 1.45523 | − | 0.541854i | ||||
\(141\) | −5.06564 | + | 1.85387i | −0.426604 | + | 0.156124i | ||||
\(142\) | −2.35820 | + | 4.08453i | −0.197896 | + | 0.342766i | ||||
\(143\) | 0.534559 | + | 0.925884i | 0.0447021 | + | 0.0774263i | ||||
\(144\) | −7.66688 | − | 2.75991i | −0.638907 | − | 0.229993i | ||||
\(145\) | −14.9071 | − | 8.60661i | −1.23797 | − | 0.714740i | ||||
\(146\) | −5.85256 | −0.484361 | ||||||||
\(147\) | −12.1227 | + | 0.200289i | −0.999864 | + | 0.0165195i | ||||
\(148\) | −2.55540 | −0.210053 | ||||||||
\(149\) | 13.8040 | + | 7.96975i | 1.13087 | + | 0.652907i | 0.944153 | − | 0.329507i | \(-0.106883\pi\) |
0.186715 | + | 0.982414i | \(0.440216\pi\) | |||||||
\(150\) | 5.37254 | − | 6.42574i | 0.438666 | − | 0.524659i | ||||
\(151\) | 8.92946 | + | 15.4663i | 0.726669 | + | 1.25863i | 0.958283 | + | 0.285820i | \(0.0922661\pi\) |
−0.231614 | + | 0.972808i | \(0.574401\pi\) | |||||||
\(152\) | −5.25717 | + | 9.10568i | −0.426412 | + | 0.738568i | ||||
\(153\) | 9.52873 | − | 8.05304i | 0.770353 | − | 0.651049i | ||||
\(154\) | −1.16877 | + | 0.435188i | −0.0941819 | + | 0.0350685i | ||||
\(155\) | 19.3038i | 1.55052i | ||||||||
\(156\) | 3.24306 | + | 0.565940i | 0.259653 | + | 0.0453115i | ||||
\(157\) | 2.79410 | − | 1.61317i | 0.222994 | − | 0.128745i | −0.384342 | − | 0.923191i | \(-0.625572\pi\) |
0.607336 | + | 0.794445i | \(0.292238\pi\) | |||||||
\(158\) | 2.40225 | − | 1.38694i | 0.191113 | − | 0.110339i | ||||
\(159\) | 10.3083 | + | 1.79888i | 0.817500 | + | 0.142660i | ||||
\(160\) | − | 18.9137i | − | 1.49526i | ||||||
\(161\) | 12.8732 | + | 2.17209i | 1.01455 | + | 0.171185i | ||||
\(162\) | 4.18308 | + | 0.707183i | 0.328654 | + | 0.0555615i | ||||
\(163\) | 8.37708 | − | 14.5095i | 0.656143 | − | 1.13647i | −0.325463 | − | 0.945555i | \(-0.605520\pi\) |
0.981606 | − | 0.190919i | \(-0.0611466\pi\) | |||||||
\(164\) | −1.98462 | − | 3.43746i | −0.154973 | − | 0.268421i | ||||
\(165\) | 4.33983 | − | 5.19058i | 0.337855 | − | 0.404086i | ||||
\(166\) | −3.12616 | − | 1.80489i | −0.242637 | − | 0.140086i | ||||
\(167\) | −10.6160 | −0.821488 | −0.410744 | − | 0.911751i | \(-0.634731\pi\) | ||||
−0.410744 | + | 0.911751i | \(0.634731\pi\) | |||||||
\(168\) | −2.72086 | + | 7.69364i | −0.209919 | + | 0.593577i | ||||
\(169\) | 11.8570 | 0.912076 | ||||||||
\(170\) | 6.63153 | + | 3.82871i | 0.508615 | + | 0.293649i | ||||
\(171\) | −5.99941 | + | 16.6660i | −0.458786 | + | 1.27448i | ||||
\(172\) | −5.25842 | − | 9.10786i | −0.400951 | − | 0.694468i | ||||
\(173\) | −7.00634 | + | 12.1353i | −0.532682 | + | 0.922632i | 0.466590 | + | 0.884474i | \(0.345482\pi\) |
−0.999272 | + | 0.0381583i | \(0.987851\pi\) | |||||||
\(174\) | 3.37864 | − | 1.23648i | 0.256134 | − | 0.0937374i | ||||
\(175\) | 20.9202 | + | 17.2927i | 1.58142 | + | 1.30721i | ||||
\(176\) | − | 2.71617i | − | 0.204739i | ||||||
\(177\) | −0.143042 | + | 0.819688i | −0.0107517 | + | 0.0616115i | ||||
\(178\) | −0.673285 | + | 0.388721i | −0.0504649 | + | 0.0291359i | ||||
\(179\) | −3.44243 | + | 1.98749i | −0.257299 | + | 0.148552i | −0.623102 | − | 0.782141i | \(-0.714128\pi\) |
0.365803 | + | 0.930692i | \(0.380794\pi\) | |||||||
\(180\) | −3.69009 | − | 20.5041i | −0.275043 | − | 1.52829i | ||||
\(181\) | − | 4.57190i | − | 0.339827i | −0.985459 | − | 0.169913i | \(-0.945651\pi\) | ||
0.985459 | − | 0.169913i | \(-0.0543488\pi\) | |||||||
\(182\) | 0.221842 | − | 1.31478i | 0.0164440 | − | 0.0974577i | ||||
\(183\) | 1.91403 | + | 5.23003i | 0.141489 | + | 0.386615i | ||||
\(184\) | 4.39355 | − | 7.60986i | 0.323897 | − | 0.561006i | ||||
\(185\) | −2.80741 | − | 4.86258i | −0.206405 | − | 0.357504i | ||||
\(186\) | −3.09537 | − | 2.58803i | −0.226963 | − | 0.189763i | ||||
\(187\) | 3.60148 | + | 2.07932i | 0.263367 | + | 0.152055i | ||||
\(188\) | −5.53669 | −0.403804 | ||||||||
\(189\) | −2.21552 | + | 13.5680i | −0.161155 | + | 0.986929i | ||||
\(190\) | −10.8718 | −0.788724 | ||||||||
\(191\) | 9.48395 | + | 5.47556i | 0.686234 | + | 0.396198i | 0.802200 | − | 0.597056i | \(-0.203663\pi\) |
−0.115965 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(192\) | −4.18561 | − | 3.49958i | −0.302071 | − | 0.252560i | ||||
\(193\) | 4.74840 | + | 8.22447i | 0.341797 | + | 0.592010i | 0.984767 | − | 0.173882i | \(-0.0556310\pi\) |
−0.642969 | + | 0.765892i | \(0.722298\pi\) | |||||||
\(194\) | −1.23174 | + | 2.13343i | −0.0884334 | + | 0.153171i | ||||
\(195\) | 2.48598 | + | 6.79285i | 0.178025 | + | 0.486446i | ||||
\(196\) | −11.7556 | − | 4.08329i | −0.839687 | − | 0.291664i | ||||
\(197\) | 12.4496i | 0.886997i | 0.896275 | + | 0.443498i | \(0.146263\pi\) | ||||
−0.896275 | + | 0.443498i | \(0.853737\pi\) | |||||||
\(198\) | 0.250477 | + | 1.39179i | 0.0178006 | + | 0.0989099i | ||||
\(199\) | 19.4647 | − | 11.2380i | 1.37982 | − | 0.796638i | 0.387680 | − | 0.921794i | \(-0.373277\pi\) |
0.992137 | + | 0.125156i | \(0.0399433\pi\) | |||||||
\(200\) | 15.8211 | − | 9.13430i | 1.11872 | − | 0.645893i | ||||
\(201\) | −4.41156 | + | 25.2800i | −0.311168 | + | 1.78311i | ||||
\(202\) | − | 1.26540i | − | 0.0890334i | ||||||
\(203\) | 4.06824 | + | 10.9259i | 0.285535 | + | 0.766849i | ||||
\(204\) | 12.0254 | − | 4.40094i | 0.841948 | − | 0.308128i | ||||
\(205\) | 4.36068 | − | 7.55292i | 0.304563 | − | 0.527519i | ||||
\(206\) | −2.98638 | − | 5.17256i | −0.208071 | − | 0.360389i | ||||
\(207\) | 5.01386 | − | 13.9282i | 0.348488 | − | 0.968079i | ||||
\(208\) | 2.51486 | + | 1.45195i | 0.174374 | + | 0.100675i | ||||
\(209\) | −5.90432 | −0.408410 | ||||||||
\(210\) | −8.29611 | + | 1.54116i | −0.572486 | + | 0.106350i | ||||
\(211\) | 2.77052 | 0.190731 | 0.0953654 | − | 0.995442i | \(-0.469598\pi\) | ||||
0.0953654 | + | 0.995442i | \(0.469598\pi\) | |||||||
\(212\) | 9.30150 | + | 5.37022i | 0.638830 | + | 0.368829i | ||||
\(213\) | −11.1161 | + | 13.2952i | −0.761662 | + | 0.910973i | ||||
\(214\) | 2.30009 | + | 3.98387i | 0.157231 | + | 0.272331i | ||||
\(215\) | 11.5540 | − | 20.0121i | 0.787976 | − | 1.36481i | ||||
\(216\) | 8.03792 | + | 4.58413i | 0.546911 | + | 0.311911i | ||||
\(217\) | 8.33013 | − | 10.0775i | 0.565486 | − | 0.684108i | ||||
\(218\) | − | 4.14142i | − | 0.280492i | ||||||
\(219\) | −21.1846 | − | 3.69688i | −1.43152 | − | 0.249812i | ||||
\(220\) | 6.01413 | − | 3.47226i | 0.405472 | − | 0.234100i | ||||
\(221\) | −3.85041 | + | 2.22304i | −0.259007 | + | 0.149538i | ||||
\(222\) | 1.15610 | + | 0.201749i | 0.0775925 | + | 0.0135405i | ||||
\(223\) | 10.9682i | 0.734484i | 0.930125 | + | 0.367242i | \(0.119698\pi\) | ||||
−0.930125 | + | 0.367242i | \(0.880302\pi\) | |||||||
\(224\) | −8.16182 | + | 9.87392i | −0.545335 | + | 0.659729i | ||||
\(225\) | 23.5060 | − | 19.8656i | 1.56706 | − | 1.32438i | ||||
\(226\) | 1.72856 | − | 2.99396i | 0.114982 | − | 0.199155i | ||||
\(227\) | −6.32034 | − | 10.9472i | −0.419496 | − | 0.726588i | 0.576393 | − | 0.817173i | \(-0.304460\pi\) |
−0.995889 | + | 0.0905845i | \(0.971126\pi\) | |||||||
\(228\) | −11.6618 | + | 13.9479i | −0.772322 | + | 0.923723i | ||||
\(229\) | −0.565883 | − | 0.326713i | −0.0373946 | − | 0.0215898i | 0.481186 | − | 0.876618i | \(-0.340206\pi\) |
−0.518581 | + | 0.855029i | \(0.673539\pi\) | |||||||
\(230\) | 9.08586 | 0.599104 | ||||||||
\(231\) | −4.50549 | + | 0.836982i | −0.296440 | + | 0.0550693i | ||||
\(232\) | 7.84719 | 0.515194 | ||||||||
\(233\) | −20.3793 | − | 11.7660i | −1.33509 | − | 0.770815i | −0.349016 | − | 0.937117i | \(-0.613484\pi\) |
−0.986075 | + | 0.166302i | \(0.946817\pi\) | |||||||
\(234\) | −1.42253 | − | 0.512079i | −0.0929935 | − | 0.0334757i | ||||
\(235\) | −6.08270 | − | 10.5355i | −0.396792 | − | 0.687263i | ||||
\(236\) | −0.427026 | + | 0.739631i | −0.0277970 | + | 0.0481459i | ||||
\(237\) | 9.57154 | − | 3.50290i | 0.621739 | − | 0.227538i | ||||
\(238\) | −1.80979 | − | 4.86048i | −0.117311 | − | 0.315058i | ||||
\(239\) | 12.8951i | 0.834118i | 0.908879 | + | 0.417059i | \(0.136939\pi\) | ||||
−0.908879 | + | 0.417059i | \(0.863061\pi\) | |||||||
\(240\) | 3.15921 | − | 18.1035i | 0.203926 | − | 1.16858i | ||||
\(241\) | 18.6347 | − | 10.7588i | 1.20037 | − | 0.693034i | 0.239732 | − | 0.970839i | \(-0.422940\pi\) |
0.960637 | + | 0.277806i | \(0.0896071\pi\) | |||||||
\(242\) | −0.408229 | + | 0.235691i | −0.0262419 | + | 0.0151508i | ||||
\(243\) | 14.6948 | + | 5.20212i | 0.942674 | + | 0.333716i | ||||
\(244\) | 5.71637i | 0.365953i | ||||||||
\(245\) | −5.14500 | − | 26.8553i | −0.328702 | − | 1.71572i | ||||
\(246\) | 0.626484 | + | 1.71184i | 0.0399431 | + | 0.109143i | ||||
\(247\) | 3.15621 | − | 5.46672i | 0.200825 | − | 0.347839i | ||||
\(248\) | −4.40012 | − | 7.62123i | −0.279408 | − | 0.483949i | ||||
\(249\) | −10.1757 | − | 8.50786i | −0.644858 | − | 0.539164i | ||||
\(250\) | 8.38579 | + | 4.84154i | 0.530364 | + | 0.306206i | ||||
\(251\) | 2.36882 | 0.149519 | 0.0747594 | − | 0.997202i | \(-0.476181\pi\) | ||||
0.0747594 | + | 0.997202i | \(0.476181\pi\) | |||||||
\(252\) | −6.92172 | + | 12.2966i | −0.436027 | + | 0.774611i | ||||
\(253\) | 4.93440 | 0.310223 | ||||||||
\(254\) | 5.81644 | + | 3.35812i | 0.364956 | + | 0.210707i | ||||
\(255\) | 21.5857 | + | 18.0478i | 1.35175 | + | 1.13019i | ||||
\(256\) | −0.517587 | − | 0.896487i | −0.0323492 | − | 0.0560304i | ||||
\(257\) | 1.14080 | − | 1.97593i | 0.0711612 | − | 0.123255i | −0.828249 | − | 0.560360i | \(-0.810663\pi\) |
0.899410 | + | 0.437105i | \(0.143996\pi\) | |||||||
\(258\) | 1.65992 | + | 4.53568i | 0.103342 | + | 0.282379i | ||||
\(259\) | −0.632734 | + | 3.74999i | −0.0393162 | + | 0.233013i | ||||
\(260\) | 7.42451i | 0.460449i | ||||||||
\(261\) | 13.0108 | − | 2.34152i | 0.805345 | − | 0.144937i | ||||
\(262\) | −8.80594 | + | 5.08411i | −0.544033 | + | 0.314097i | ||||
\(263\) | −10.5208 | + | 6.07421i | −0.648742 | + | 0.374552i | −0.787974 | − | 0.615708i | \(-0.788870\pi\) |
0.139232 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(264\) | −0.530241 | + | 3.03849i | −0.0326341 | + | 0.187006i | ||||
\(265\) | 23.5993i | 1.44969i | ||||||||
\(266\) | 5.67563 | + | 4.69150i | 0.347995 | + | 0.287654i | ||||
\(267\) | −2.68264 | + | 0.981765i | −0.164175 | + | 0.0600831i | ||||
\(268\) | −13.1699 | + | 22.8110i | −0.804481 | + | 1.39340i | ||||
\(269\) | 1.12011 | + | 1.94008i | 0.0682941 | + | 0.118289i | 0.898151 | − | 0.439688i | \(-0.144911\pi\) |
−0.829856 | + | 0.557977i | \(0.811578\pi\) | |||||||
\(270\) | 0.0506510 | + | 9.56771i | 0.00308252 | + | 0.582272i | ||||
\(271\) | −15.4313 | − | 8.90928i | −0.937387 | − | 0.541200i | −0.0482464 | − | 0.998835i | \(-0.515363\pi\) |
−0.889140 | + | 0.457635i | \(0.848697\pi\) | |||||||
\(272\) | 11.2956 | 0.684893 | ||||||||
\(273\) | 1.63351 | − | 4.61898i | 0.0988642 | − | 0.279553i | ||||
\(274\) | −1.30215 | −0.0786659 | ||||||||
\(275\) | 8.88432 | + | 5.12937i | 0.535745 | + | 0.309312i | ||||
\(276\) | 9.74608 | − | 11.6566i | 0.586645 | − | 0.701647i | ||||
\(277\) | 3.19654 | + | 5.53657i | 0.192062 | + | 0.332660i | 0.945933 | − | 0.324361i | \(-0.105149\pi\) |
−0.753872 | + | 0.657022i | \(0.771816\pi\) | |||||||
\(278\) | 4.85773 | − | 8.41383i | 0.291347 | − | 0.504628i | ||||
\(279\) | −9.56955 | − | 11.3232i | −0.572914 | − | 0.677899i | ||||
\(280\) | −18.1478 | − | 3.06207i | −1.08454 | − | 0.182994i | ||||
\(281\) | 6.57145i | 0.392020i | 0.980602 | + | 0.196010i | \(0.0627985\pi\) | ||||
−0.980602 | + | 0.196010i | \(0.937202\pi\) | |||||||
\(282\) | 2.50488 | + | 0.437121i | 0.149163 | + | 0.0260302i | ||||
\(283\) | 2.21575 | − | 1.27926i | 0.131713 | − | 0.0760444i | −0.432696 | − | 0.901540i | \(-0.642438\pi\) |
0.564409 | + | 0.825496i | \(0.309104\pi\) | |||||||
\(284\) | −15.4047 | + | 8.89388i | −0.914098 | + | 0.527755i | ||||
\(285\) | −39.3528 | − | 6.86738i | −2.33106 | − | 0.406789i | ||||
\(286\) | − | 0.503963i | − | 0.0298000i | ||||||
\(287\) | −5.53580 | + | 2.06124i | −0.326768 | + | 0.121671i | ||||
\(288\) | 9.37620 | + | 11.0944i | 0.552498 | + | 0.653742i | ||||
\(289\) | −0.147121 | + | 0.254821i | −0.00865416 | + | 0.0149895i | ||||
\(290\) | 4.05700 | + | 7.02693i | 0.238235 | + | 0.412635i | ||||
\(291\) | −5.80614 | + | 6.94434i | −0.340362 | + | 0.407084i | ||||
\(292\) | −19.1155 | − | 11.0364i | −1.11865 | − | 0.645854i | ||||
\(293\) | 26.2396 | 1.53293 | 0.766467 | − | 0.642284i | \(-0.222013\pi\) | ||||
0.766467 | + | 0.642284i | \(0.222013\pi\) | |||||||
\(294\) | 4.99604 | + | 2.77545i | 0.291375 | + | 0.161867i | ||||
\(295\) | −1.87655 | −0.109257 | ||||||||
\(296\) | 2.21676 | + | 1.27985i | 0.128847 | + | 0.0743897i | ||||
\(297\) | 0.0275078 | + | 5.19608i | 0.00159617 | + | 0.301507i | ||||
\(298\) | −3.75679 | − | 6.50696i | −0.217625 | − | 0.376938i | ||||
\(299\) | −2.63773 | + | 4.56868i | −0.152544 | + | 0.264213i | ||||
\(300\) | 29.6649 | − | 10.8565i | 1.71270 | − | 0.626798i | ||||
\(301\) | −14.6676 | + | 5.46144i | −0.845425 | + | 0.314792i | ||||
\(302\) | − | 8.41837i | − | 0.484423i | ||||||
\(303\) | 0.799314 | − | 4.58039i | 0.0459194 | − | 0.263136i | ||||
\(304\) | −13.8886 | + | 8.01857i | −0.796564 | + | 0.459896i | ||||
\(305\) | −10.8775 | + | 6.28010i | −0.622841 | + | 0.359598i | ||||
\(306\) | −5.78793 | + | 1.04164i | −0.330874 | + | 0.0595468i | ||||
\(307\) | 0.463588i | 0.0264584i | 0.999912 | + | 0.0132292i | \(0.00421111\pi\) | ||||
−0.999912 | + | 0.0132292i | \(0.995789\pi\) | |||||||
\(308\) | −4.63806 | − | 0.782577i | −0.264278 | − | 0.0445915i | ||||
\(309\) | −7.54247 | − | 20.6095i | −0.429076 | − | 1.17244i | ||||
\(310\) | 4.54972 | − | 7.88035i | 0.258407 | − | 0.447574i | ||||
\(311\) | −14.0883 | − | 24.4017i | −0.798876 | − | 1.38369i | −0.920349 | − | 0.391099i | \(-0.872095\pi\) |
0.121473 | − | 0.992595i | \(-0.461238\pi\) | |||||||
\(312\) | −2.52985 | − | 2.11520i | −0.143224 | − | 0.119749i | ||||
\(313\) | 1.05728 | + | 0.610419i | 0.0597609 | + | 0.0345029i | 0.529583 | − | 0.848258i | \(-0.322349\pi\) |
−0.469822 | + | 0.882761i | \(0.655682\pi\) | |||||||
\(314\) | −1.52084 | −0.0858261 | ||||||||
\(315\) | −31.0030 | + | 0.338166i | −1.74682 | + | 0.0190535i | ||||
\(316\) | 10.4616 | 0.588511 | ||||||||
\(317\) | 29.0062 | + | 16.7467i | 1.62915 | + | 0.940591i | 0.984347 | + | 0.176243i | \(0.0563944\pi\) |
0.644804 | + | 0.764348i | \(0.276939\pi\) | |||||||
\(318\) | −3.78416 | − | 3.16392i | −0.212205 | − | 0.177424i | ||||
\(319\) | 2.20330 | + | 3.81622i | 0.123361 | + | 0.213667i | ||||
\(320\) | 6.15222 | − | 10.6560i | 0.343919 | − | 0.595686i | ||||
\(321\) | 5.80916 | + | 15.8733i | 0.324236 | + | 0.885963i | ||||
\(322\) | −4.74328 | − | 3.92081i | −0.264332 | − | 0.218498i | ||||
\(323\) | − | 24.5539i | − | 1.36622i | ||||||
\(324\) | 12.3291 | + | 10.1980i | 0.684953 | + | 0.566553i | ||||
\(325\) | −9.49839 | + | 5.48390i | −0.526876 | + | 0.304192i | ||||
\(326\) | −6.83952 | + | 3.94880i | −0.378806 | + | 0.218704i | ||||
\(327\) | 2.61600 | − | 14.9907i | 0.144665 | − | 0.828990i | ||||
\(328\) | 3.97591i | 0.219533i | ||||||||
\(329\) | −1.37092 | + | 8.12495i | −0.0755812 | + | 0.447943i | ||||
\(330\) | −2.99501 | + | 1.09608i | −0.164870 | + | 0.0603375i | ||||
\(331\) | 2.16592 | − | 3.75149i | 0.119050 | − | 0.206200i | −0.800342 | − | 0.599544i | \(-0.795348\pi\) |
0.919391 | + | 0.393344i | \(0.128682\pi\) | |||||||
\(332\) | −6.80707 | − | 11.7902i | −0.373586 | − | 0.647070i | ||||
\(333\) | 4.05731 | + | 1.46055i | 0.222339 | + | 0.0800374i | ||||
\(334\) | 4.33374 | + | 2.50209i | 0.237132 | + | 0.136908i | ||||
\(335\) | −57.8748 | −3.16204 | ||||||||
\(336\) | −9.46145 | + | 8.08765i | −0.516164 | + | 0.441217i | ||||
\(337\) | 2.61781 | 0.142601 | 0.0713006 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713006 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(338\) | −4.84036 | − | 2.79458i | −0.263281 | − | 0.152005i | ||||
\(339\) | 8.14809 | − | 9.74538i | 0.442543 | − | 0.529297i | ||||
\(340\) | 14.4399 | + | 25.0106i | 0.783111 | + | 1.35639i | ||||
\(341\) | 2.47089 | − | 4.27970i | 0.133806 | − | 0.231759i | ||||
\(342\) | 6.37716 | − | 5.38954i | 0.344837 | − | 0.291433i | ||||
\(343\) | −8.90289 | + | 16.2400i | −0.480711 | + | 0.876879i | ||||
\(344\) | 10.5345i | 0.567983i | ||||||||
\(345\) | 32.8882 | + | 5.73925i | 1.77064 | + | 0.308991i | ||||
\(346\) | 5.72037 | − | 3.30266i | 0.307529 | − | 0.177552i | ||||
\(347\) | −13.7933 | + | 7.96356i | −0.740463 | + | 0.427506i | −0.822238 | − | 0.569144i | \(-0.807275\pi\) |
0.0817747 | + | 0.996651i | \(0.473941\pi\) | |||||||
\(348\) | 13.3669 | + | 2.33264i | 0.716543 | + | 0.125043i | ||||
\(349\) | − | 5.93887i | − | 0.317901i | −0.987287 | − | 0.158950i | \(-0.949189\pi\) | ||
0.987287 | − | 0.158950i | \(-0.0508110\pi\) | |||||||
\(350\) | −4.46448 | − | 11.9901i | −0.238636 | − | 0.640896i | ||||
\(351\) | −4.82567 | − | 2.75214i | −0.257575 | − | 0.146899i | ||||
\(352\) | −2.42096 | + | 4.19323i | −0.129038 | + | 0.223500i | ||||
\(353\) | 8.63189 | + | 14.9509i | 0.459429 | + | 0.795754i | 0.998931 | − | 0.0462300i | \(-0.0147207\pi\) |
−0.539502 | + | 0.841984i | \(0.681387\pi\) | |||||||
\(354\) | 0.251587 | − | 0.300906i | 0.0133717 | − | 0.0159930i | ||||
\(355\) | −33.8477 | − | 19.5420i | −1.79645 | − | 1.03718i | ||||
\(356\) | −2.93210 | −0.155401 | ||||||||
\(357\) | −3.48070 | − | 18.7367i | −0.184218 | − | 0.991651i | ||||
\(358\) | 1.87373 | 0.0990297 | ||||||||
\(359\) | −27.2535 | − | 15.7348i | −1.43838 | − | 0.830451i | −0.440645 | − | 0.897681i | \(-0.645250\pi\) |
−0.997737 | + | 0.0672305i | \(0.978584\pi\) | |||||||
\(360\) | −7.06821 | + | 19.6351i | −0.372527 | + | 1.03486i | ||||
\(361\) | 7.93050 | + | 13.7360i | 0.417395 | + | 0.722949i | ||||
\(362\) | −1.07756 | + | 1.86638i | −0.0566351 | + | 0.0980948i | ||||
\(363\) | −1.62655 | + | 0.595267i | −0.0853716 | + | 0.0312434i | ||||
\(364\) | 3.20389 | − | 3.87597i | 0.167930 | − | 0.203156i | ||||
\(365\) | − | 48.4989i | − | 2.53855i | ||||||
\(366\) | 0.451307 | − | 2.58617i | 0.0235902 | − | 0.135181i | ||||
\(367\) | 3.35150 | − | 1.93499i | 0.174947 | − | 0.101006i | −0.409970 | − | 0.912099i | \(-0.634461\pi\) |
0.584916 | + | 0.811094i | \(0.301127\pi\) | |||||||
\(368\) | 11.6070 | − | 6.70133i | 0.605059 | − | 0.349331i | ||||
\(369\) | 1.18637 | + | 6.59211i | 0.0617600 | + | 0.343172i | ||||
\(370\) | 2.64672i | 0.137597i | ||||||||
\(371\) | 10.1838 | − | 12.3200i | 0.528715 | − | 0.639623i | ||||
\(372\) | −5.22971 | − | 14.2900i | −0.271148 | − | 0.740902i | ||||
\(373\) | 1.49777 | − | 2.59421i | 0.0775514 | − | 0.134323i | −0.824642 | − | 0.565656i | \(-0.808623\pi\) |
0.902193 | + | 0.431333i | \(0.141956\pi\) | |||||||
\(374\) | −0.980152 | − | 1.69767i | −0.0506825 | − | 0.0877846i | ||||
\(375\) | 27.2959 | + | 22.8220i | 1.40955 | + | 1.17852i | ||||
\(376\) | 4.80297 | + | 2.77299i | 0.247694 | + | 0.143006i | ||||
\(377\) | −4.71117 | −0.242637 | ||||||||
\(378\) | 4.10230 | − | 5.01668i | 0.211000 | − | 0.258030i | ||||
\(379\) | −30.0561 | −1.54388 | −0.771938 | − | 0.635697i | \(-0.780713\pi\) | ||||
−0.771938 | + | 0.635697i | \(0.780713\pi\) | |||||||
\(380\) | −35.5093 | − | 20.5013i | −1.82159 | − | 1.05170i | ||||
\(381\) | 18.9326 | + | 15.8295i | 0.969946 | + | 0.810969i | ||||
\(382\) | −2.58108 | − | 4.47056i | −0.132060 | − | 0.228734i | ||||
\(383\) | 10.2996 | − | 17.8395i | 0.526286 | − | 0.911554i | −0.473245 | − | 0.880931i | \(-0.656917\pi\) |
0.999531 | − | 0.0306231i | \(-0.00974917\pi\) | |||||||
\(384\) | 6.64835 | + | 18.1664i | 0.339272 | + | 0.927049i | ||||
\(385\) | −3.60631 | − | 9.68533i | −0.183795 | − | 0.493610i | ||||
\(386\) | − | 4.47662i | − | 0.227854i | ||||||
\(387\) | 3.14339 | + | 17.4664i | 0.159788 | + | 0.887865i | ||||
\(388\) | −8.04614 | + | 4.64544i | −0.408481 | + | 0.235837i | ||||
\(389\) | 8.68694 | − | 5.01541i | 0.440445 | − | 0.254291i | −0.263341 | − | 0.964703i | \(-0.584824\pi\) |
0.703787 | + | 0.710412i | \(0.251491\pi\) | |||||||
\(390\) | 0.586165 | − | 3.35896i | 0.0296816 | − | 0.170087i | ||||
\(391\) | 20.5204i | 1.03776i | ||||||||
\(392\) | 8.15270 | + | 9.42986i | 0.411773 | + | 0.476280i | ||||
\(393\) | −35.0864 | + | 12.8406i | −1.76988 | + | 0.647721i | ||||
\(394\) | 2.93426 | − | 5.08228i | 0.147826 | − | 0.256042i | ||||
\(395\) | 11.4933 | + | 19.9070i | 0.578290 | + | 1.00163i | ||||
\(396\) | −1.80643 | + | 5.01816i | −0.0907765 | + | 0.252172i | ||||
\(397\) | −29.6673 | − | 17.1284i | −1.48896 | − | 0.859650i | −0.489037 | − | 0.872263i | \(-0.662652\pi\) |
−0.999920 | + | 0.0126130i | \(0.995985\pi\) | |||||||
\(398\) | −10.5947 | −0.531066 | ||||||||
\(399\) | 17.5807 | + | 20.5670i | 0.880134 | + | 1.02964i | ||||
\(400\) | 27.8644 | 1.39322 | ||||||||
\(401\) | 23.6000 | + | 13.6255i | 1.17853 | + | 0.680423i | 0.955673 | − | 0.294429i | \(-0.0951293\pi\) |
0.222854 | + | 0.974852i | \(0.428463\pi\) | |||||||
\(402\) | 7.75919 | − | 9.28026i | 0.386993 | − | 0.462857i | ||||
\(403\) | 2.64167 | + | 4.57551i | 0.131591 | + | 0.227922i | ||||
\(404\) | 2.38621 | − | 4.13303i | 0.118718 | − | 0.205626i | ||||
\(405\) | −5.86028 | + | 34.6643i | −0.291199 | + | 1.72248i | ||||
\(406\) | 0.914366 | − | 5.41912i | 0.0453792 | − | 0.268946i | ||||
\(407\) | 1.43740i | 0.0712491i | ||||||||
\(408\) | −12.6360 | − | 2.20508i | −0.625574 | − | 0.109168i | ||||
\(409\) | 10.1269 | − | 5.84676i | 0.500742 | − | 0.289104i | −0.228278 | − | 0.973596i | \(-0.573309\pi\) |
0.729020 | + | 0.684492i | \(0.239976\pi\) | |||||||
\(410\) | −3.56031 | + | 2.05554i | −0.175831 | + | 0.101516i | ||||
\(411\) | −4.71341 | − | 0.822528i | −0.232495 | − | 0.0405723i | ||||
\(412\) | − | 22.5260i | − | 1.10978i | ||||||
\(413\) | 0.979656 | + | 0.809788i | 0.0482057 | + | 0.0398470i | ||||
\(414\) | −5.32956 | + | 4.50418i | −0.261934 | + | 0.221368i | ||||
\(415\) | 14.9567 | − | 25.9058i | 0.734197 | − | 1.27167i | ||||
\(416\) | −2.58830 | − | 4.48306i | −0.126902 | − | 0.219800i | ||||
\(417\) | 22.8983 | − | 27.3871i | 1.12134 | − | 1.34115i | ||||
\(418\) | 2.41031 | + | 1.39159i | 0.117892 | + | 0.0680651i | ||||
\(419\) | 8.63636 | 0.421914 | 0.210957 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210957 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(420\) | −30.0028 | − | 10.6105i | −1.46399 | − | 0.517740i | ||||
\(421\) | 23.5610 | 1.14829 | 0.574146 | − | 0.818753i | \(-0.305334\pi\) | ||||
0.574146 | + | 0.818753i | \(0.305334\pi\) | |||||||
\(422\) | −1.13101 | − | 0.652988i | −0.0550566 | − | 0.0317869i | ||||
\(423\) | 8.79082 | + | 3.16450i | 0.427424 | + | 0.153863i | ||||
\(424\) | −5.37925 | − | 9.31713i | −0.261239 | − | 0.452480i | ||||
\(425\) | −21.3312 | + | 36.9467i | −1.03471 | + | 1.79218i | ||||
\(426\) | 7.67146 | − | 2.80753i | 0.371684 | − | 0.136025i | ||||
\(427\) | 8.38863 | + | 1.41541i | 0.405954 | + | 0.0684964i | ||||
\(428\) | 17.3494i | 0.838614i | ||||||||
\(429\) | 0.318338 | − | 1.82420i | 0.0153695 | − | 0.0880732i | ||||
\(430\) | −9.43334 | + | 5.44634i | −0.454916 | + | 0.262646i | ||||
\(431\) | 7.17728 | − | 4.14380i | 0.345717 | − | 0.199600i | −0.317080 | − | 0.948399i | \(-0.602702\pi\) |
0.662797 | + | 0.748799i | \(0.269369\pi\) | |||||||
\(432\) | 7.12142 | + | 12.1852i | 0.342629 | + | 0.586262i | ||||
\(433\) | 8.45254i | 0.406203i | 0.979158 | + | 0.203101i | \(0.0651021\pi\) | ||||
−0.979158 | + | 0.203101i | \(0.934898\pi\) | |||||||
\(434\) | −5.77578 | + | 2.15060i | −0.277246 | + | 0.103232i | ||||
\(435\) | 10.2465 | + | 27.9981i | 0.491280 | + | 1.34241i | ||||
\(436\) | 7.80961 | − | 13.5266i | 0.374012 | − | 0.647809i | ||||
\(437\) | −14.5671 | − | 25.2310i | −0.696840 | − | 1.20696i | ||||
\(438\) | 7.77682 | + | 6.50218i | 0.371591 | + | 0.310686i | ||||
\(439\) | −9.30550 | − | 5.37254i | −0.444127 | − | 0.256417i | 0.261219 | − | 0.965279i | \(-0.415875\pi\) |
−0.705347 | + | 0.708862i | \(0.749209\pi\) | |||||||
\(440\) | −6.95618 | −0.331623 | ||||||||
\(441\) | 16.3311 | + | 13.2022i | 0.777669 | + | 0.628674i | ||||
\(442\) | 2.09580 | 0.0996870 | ||||||||
\(443\) | 11.8729 | + | 6.85484i | 0.564100 | + | 0.325684i | 0.754790 | − | 0.655967i | \(-0.227739\pi\) |
−0.190689 | + | 0.981650i | \(0.561072\pi\) | |||||||
\(444\) | 3.39560 | + | 2.83905i | 0.161148 | + | 0.134735i | ||||
\(445\) | −3.22125 | − | 5.57937i | −0.152702 | − | 0.264488i | ||||
\(446\) | 2.58510 | − | 4.47753i | 0.122408 | − | 0.212017i | ||||
\(447\) | −9.48826 | − | 25.9263i | −0.448779 | − | 1.22627i | ||||
\(448\) | −7.81012 | + | 2.90808i | −0.368994 | + | 0.137394i | ||||
\(449\) | 16.9934i | 0.801968i | 0.916085 | + | 0.400984i | \(0.131332\pi\) | ||||
−0.916085 | + | 0.400984i | \(0.868668\pi\) | |||||||
\(450\) | −14.2780 | + | 2.56958i | −0.673070 | + | 0.121131i | ||||
\(451\) | −1.93355 | + | 1.11634i | −0.0910473 | + | 0.0525662i | ||||
\(452\) | 11.2916 | − | 6.51921i | 0.531112 | − | 0.306638i | ||||
\(453\) | 5.31762 | − | 30.4721i | 0.249844 | − | 1.43170i | ||||
\(454\) | 5.95859i | 0.279650i | ||||||||
\(455\) | 10.8953 | + | 1.83836i | 0.510779 | + | 0.0861834i | ||||
\(456\) | 17.1021 | − | 6.25884i | 0.800877 | − | 0.293097i | ||||
\(457\) | −6.03723 | + | 10.4568i | −0.282410 | + | 0.489148i | −0.971978 | − | 0.235073i | \(-0.924467\pi\) |
0.689568 | + | 0.724221i | \(0.257800\pi\) | |||||||
\(458\) | 0.154006 | + | 0.266747i | 0.00719624 | + | 0.0124643i | ||||
\(459\) | −21.6086 | + | 0.114395i | −1.00860 | + | 0.00533950i | ||||
\(460\) | 29.6761 | + | 17.1335i | 1.38365 | + | 0.798853i | ||||
\(461\) | −36.9486 | −1.72087 | −0.860434 | − | 0.509563i | \(-0.829807\pi\) | ||||
−0.860434 | + | 0.509563i | \(0.829807\pi\) | |||||||
\(462\) | 2.03654 | + | 0.720224i | 0.0947484 | + | 0.0335078i | ||||
\(463\) | −8.35061 | −0.388086 | −0.194043 | − | 0.980993i | \(-0.562160\pi\) | ||||
−0.194043 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(464\) | 10.3655 | + | 5.98452i | 0.481206 | + | 0.277824i | ||||
\(465\) | 21.4464 | − | 25.6507i | 0.994555 | − | 1.18952i | ||||
\(466\) | 5.54627 | + | 9.60642i | 0.256926 | + | 0.445009i | ||||
\(467\) | −5.02423 | + | 8.70222i | −0.232494 | + | 0.402691i | −0.958541 | − | 0.284954i | \(-0.908022\pi\) |
0.726048 | + | 0.687644i | \(0.241355\pi\) | |||||||
\(468\) | −3.68059 | − | 4.35505i | −0.170135 | − | 0.201312i | ||||
\(469\) | 30.2136 | + | 24.9747i | 1.39513 | + | 1.15322i | ||||
\(470\) | 5.73455i | 0.264515i | ||||||||
\(471\) | −5.50501 | − | 0.960668i | −0.253657 | − | 0.0442653i | ||||
\(472\) | 0.740874 | − | 0.427744i | 0.0341015 | − | 0.0196885i | ||||
\(473\) | −5.12311 | + | 2.95783i | −0.235561 | + | 0.136001i | ||||
\(474\) | −4.73298 | − | 0.825943i | −0.217393 | − | 0.0379368i | ||||
\(475\) | − | 60.5709i | − | 2.77918i | ||||||
\(476\) | 3.25445 | − | 19.2880i | 0.149168 | − | 0.884063i | ||||
\(477\) | −11.6990 | − | 13.8428i | −0.535660 | − | 0.633819i | ||||
\(478\) | 3.03927 | − | 5.26417i | 0.139013 | − | 0.240777i | ||||
\(479\) | 1.11912 | + | 1.93837i | 0.0511337 | + | 0.0885662i | 0.890459 | − | 0.455063i | \(-0.150383\pi\) |
−0.839326 | + | 0.543629i | \(0.817050\pi\) | |||||||
\(480\) | −21.0131 | + | 25.1324i | −0.959113 | + | 1.14713i | ||||
\(481\) | −1.33086 | − | 0.768374i | −0.0606821 | − | 0.0350348i | ||||
\(482\) | −10.1430 | −0.462000 | ||||||||
\(483\) | −14.6926 | − | 17.1884i | −0.668538 | − | 0.782098i | ||||
\(484\) | −1.77780 | −0.0808091 | ||||||||
\(485\) | −17.6793 | − | 10.2071i | −0.802774 | − | 0.463482i | ||||
\(486\) | −4.77276 | − | 5.58709i | −0.216497 | − | 0.253436i | ||||
\(487\) | 1.46555 | + | 2.53840i | 0.0664103 | + | 0.115026i | 0.897319 | − | 0.441383i | \(-0.145512\pi\) |
−0.830908 | + | 0.556409i | \(0.812179\pi\) | |||||||
\(488\) | 2.86299 | − | 4.95884i | 0.129601 | − | 0.224476i | ||||
\(489\) | −27.2514 | + | 9.97320i | −1.23235 | + | 0.451004i | ||||
\(490\) | −4.22921 | + | 12.1757i | −0.191056 | + | 0.550043i | ||||
\(491\) | 22.0744i | 0.996206i | 0.867118 | + | 0.498103i | \(0.165970\pi\) | ||||
−0.867118 | + | 0.498103i | \(0.834030\pi\) | |||||||
\(492\) | −1.18187 | + | 6.77258i | −0.0532828 | + | 0.305331i | ||||
\(493\) | −15.8703 | + | 9.16270i | −0.714761 | + | 0.412667i | ||||
\(494\) | −2.57691 | + | 1.48778i | −0.115941 | + | 0.0669384i | ||||
\(495\) | −11.5334 | + | 2.07565i | −0.518390 | + | 0.0932937i | ||||
\(496\) | − | 13.4227i | − | 0.602697i | ||||||
\(497\) | 9.23726 | + | 24.8081i | 0.414348 | + | 1.11280i | ||||
\(498\) | 2.14878 | + | 5.87147i | 0.0962892 | + | 0.263107i | ||||
\(499\) | 20.8831 | − | 36.1706i | 0.934855 | − | 1.61922i | 0.159964 | − | 0.987123i | \(-0.448862\pi\) |
0.774891 | − | 0.632094i | \(-0.217805\pi\) | |||||||
\(500\) | 18.2597 | + | 31.6267i | 0.816597 | + | 1.41439i | ||||
\(501\) | 14.1064 | + | 11.7943i | 0.630227 | + | 0.526931i | ||||
\(502\) | −0.967021 | − | 0.558310i | −0.0431603 | − | 0.0249186i | ||||
\(503\) | 23.4080 | 1.04371 | 0.521855 | − | 0.853034i | \(-0.325240\pi\) | ||||
0.521855 | + | 0.853034i | \(0.325240\pi\) | |||||||
\(504\) | 12.1631 | − | 7.20036i | 0.541786 | − | 0.320730i | ||||
\(505\) | 10.4861 | 0.466626 | ||||||||
\(506\) | −2.01436 | − | 1.16299i | −0.0895493 | − | 0.0517013i | ||||
\(507\) | −15.7554 | − | 13.1731i | −0.699724 | − | 0.585037i | ||||
\(508\) | 12.6650 | + | 21.9365i | 0.561920 | + | 0.973274i | ||||
\(509\) | 7.33533 | − | 12.7052i | 0.325133 | − | 0.563147i | −0.656406 | − | 0.754407i | \(-0.727924\pi\) |
0.981539 | + | 0.191261i | \(0.0612577\pi\) | |||||||
\(510\) | −4.55822 | − | 12.4552i | −0.201841 | − | 0.551524i | ||||
\(511\) | −20.9287 | + | 25.3189i | −0.925831 | + | 1.12004i | ||||
\(512\) | 22.8253i | 1.00875i | ||||||||
\(513\) | 26.4879 | − | 15.4803i | 1.16947 | − | 0.683473i | ||||
\(514\) | −0.931415 | + | 0.537753i | −0.0410830 | + | 0.0237193i | ||||
\(515\) | 42.8639 | − | 24.7475i | 1.88881 | − | 1.09050i | ||||
\(516\) | −3.13147 | + | 17.9445i | −0.137855 | + | 0.789964i | ||||
\(517\) | 3.11435i | 0.136969i | ||||||||
\(518\) | 1.14214 | − | 1.38172i | 0.0501827 | − | 0.0607094i | ||||
\(519\) | 22.7923 | − | 8.34129i | 1.00047 | − | 0.366142i | ||||
\(520\) | 3.71849 | − | 6.44062i | 0.163067 | − | 0.282440i | ||||
\(521\) | −4.63455 | − | 8.02728i | −0.203044 | − | 0.351682i | 0.746464 | − | 0.665426i | \(-0.231750\pi\) |
−0.949508 | + | 0.313744i | \(0.898417\pi\) | |||||||
\(522\) | −5.86324 | − | 2.11064i | −0.256627 | − | 0.0923802i | ||||
\(523\) | 36.0039 | + | 20.7868i | 1.57434 | + | 0.908945i | 0.995627 | + | 0.0934133i | \(0.0297778\pi\) |
0.578712 | + | 0.815532i | \(0.303556\pi\) | |||||||
\(524\) | −38.3491 | −1.67529 | ||||||||
\(525\) | −8.58637 | − | 46.2206i | −0.374740 | − | 2.01723i | ||||
\(526\) | 5.72654 | 0.249689 | ||||||||
\(527\) | 17.7977 | + | 10.2755i | 0.775281 | + | 0.447608i | ||||
\(528\) | −3.01766 | + | 3.60922i | −0.131327 | + | 0.157071i | ||||
\(529\) | 0.674136 | + | 1.16764i | 0.0293103 | + | 0.0507669i | ||||
\(530\) | 5.56214 | − | 9.63391i | 0.241604 | − | 0.418470i | ||||
\(531\) | 1.10074 | − | 0.930274i | 0.0477682 | − | 0.0403704i | ||||
\(532\) | 9.69074 | + | 26.0260i | 0.420147 | + | 1.12837i | ||||
\(533\) | − | 2.38699i | − | 0.103392i | ||||||
\(534\) | 1.32652 | + | 0.231489i | 0.0574043 | + | 0.0100175i | ||||
\(535\) | −33.0135 | + | 19.0603i | −1.42730 | + | 0.824050i | ||||
\(536\) | 22.8493 | − | 13.1921i | 0.986940 | − | 0.569810i | ||||
\(537\) | 6.78236 | + | 1.18358i | 0.292680 | + | 0.0510751i | ||||
\(538\) | − | 1.05600i | − | 0.0455272i | ||||||
\(539\) | −2.29682 | + | 6.61246i | −0.0989312 | + | 0.284819i | ||||
\(540\) | −17.8767 | + | 31.3454i | −0.769290 | + | 1.34889i | ||||
\(541\) | −18.1823 | + | 31.4927i | −0.781719 | + | 1.35398i | 0.149220 | + | 0.988804i | \(0.452324\pi\) |
−0.930939 | + | 0.365173i | \(0.881010\pi\) | |||||||
\(542\) | 4.19967 | + | 7.27405i | 0.180391 | + | 0.312447i | ||||
\(543\) | −5.07937 | + | 6.07510i | −0.217977 | + | 0.260707i | ||||
\(544\) | −17.4381 | − | 10.0679i | −0.747653 | − | 0.431657i | ||||
\(545\) | 34.3191 | 1.47007 | ||||||||
\(546\) | −1.75549 | + | 1.50060i | −0.0751282 | + | 0.0642196i | ||||
\(547\) | 0.291428 | 0.0124606 | 0.00623028 | − | 0.999981i | \(-0.498017\pi\) | ||||
0.00623028 | + | 0.999981i | \(0.498017\pi\) | |||||||
\(548\) | −4.25307 | − | 2.45551i | −0.181682 | − | 0.104894i | ||||
\(549\) | 3.26720 | − | 9.07610i | 0.139441 | − | 0.387359i | ||||
\(550\) | −2.41789 | − | 4.18791i | −0.103099 | − | 0.178573i | ||||
\(551\) | 13.0090 | − | 22.5322i | 0.554200 | − | 0.959903i | ||||
\(552\) | −14.2926 | + | 5.23068i | −0.608335 | + | 0.222632i | ||||
\(553\) | 2.59036 | − | 15.3521i | 0.110153 | − | 0.652839i | ||||
\(554\) | − | 3.01358i | − | 0.128035i | ||||||
\(555\) | −1.67185 | + | 9.58037i | −0.0709662 | + | 0.406664i | ||||
\(556\) | 31.7325 | − | 18.3207i | 1.34576 | − | 0.776972i | ||||
\(557\) | −29.6985 | + | 17.1464i | −1.25836 | + | 0.726517i | −0.972756 | − | 0.231830i | \(-0.925529\pi\) |
−0.285608 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(558\) | 1.23780 | + | 6.87789i | 0.0524003 | + | 0.291164i | ||||
\(559\) | − | 6.32454i | − | 0.267499i | ||||||
\(560\) | −21.6365 | − | 17.8848i | −0.914310 | − | 0.755773i | ||||
\(561\) | −2.47550 | − | 6.76422i | −0.104516 | − | 0.285585i | ||||
\(562\) | 1.54883 | − | 2.68265i | 0.0653335 | − | 0.113161i | ||||
\(563\) | 11.4094 | + | 19.7616i | 0.480848 | + | 0.832854i | 0.999759 | − | 0.0219750i | \(-0.00699543\pi\) |
−0.518910 | + | 0.854829i | \(0.673662\pi\) | |||||||
\(564\) | 7.35710 | + | 6.15125i | 0.309790 | + | 0.259014i | ||||
\(565\) | 24.8103 | + | 14.3242i | 1.04378 | + | 0.602625i | ||||
\(566\) | −1.20604 | −0.0506938 | ||||||||
\(567\) | 18.0180 | − | 15.5676i | 0.756685 | − | 0.653779i | ||||
\(568\) | 17.8176 | 0.747612 | ||||||||
\(569\) | −14.7142 | − | 8.49522i | −0.616850 | − | 0.356138i | 0.158792 | − | 0.987312i | \(-0.449240\pi\) |
−0.775641 | + | 0.631174i | \(0.782573\pi\) | |||||||
\(570\) | 14.4464 | + | 12.0786i | 0.605092 | + | 0.505915i | ||||
\(571\) | −8.93189 | − | 15.4705i | −0.373788 | − | 0.647420i | 0.616357 | − | 0.787467i | \(-0.288608\pi\) |
−0.990145 | + | 0.140047i | \(0.955275\pi\) | |||||||
\(572\) | 0.950339 | − | 1.64604i | 0.0397357 | − | 0.0688242i | ||||
\(573\) | −6.51885 | − | 17.8125i | −0.272329 | − | 0.744129i | ||||
\(574\) | 2.74569 | + | 0.463278i | 0.114603 | + | 0.0193369i | ||||
\(575\) | 50.6207i | 2.11103i | ||||||||
\(576\) | 1.67378 | + | 9.30041i | 0.0697408 | + | 0.387517i | ||||
\(577\) | 8.92725 | − | 5.15415i | 0.371646 | − | 0.214570i | −0.302531 | − | 0.953139i | \(-0.597832\pi\) |
0.674177 | + | 0.738569i | \(0.264498\pi\) | |||||||
\(578\) | 0.120118 | − | 0.0693501i | 0.00499624 | − | 0.00288458i | ||||
\(579\) | 2.82774 | − | 16.2041i | 0.117517 | − | 0.673418i | ||||
\(580\) | 30.6016i | 1.27066i | ||||||||
\(581\) | −18.9873 | + | 7.06987i | −0.787725 | + | 0.293308i | ||||
\(582\) | 4.00695 | − | 1.46642i | 0.166093 | − | 0.0607852i | ||||
\(583\) | 3.02072 | − | 5.23203i | 0.125105 | − | 0.216689i | ||||
\(584\) | 11.0549 | + | 19.1476i | 0.457455 | + | 0.792335i | ||||
\(585\) | 4.24349 | − | 11.7882i | 0.175447 | − | 0.487382i | ||||
\(586\) | −10.7118 | − | 6.18444i | −0.442499 | − | 0.255477i | ||||
\(587\) | 38.7455 | 1.59920 | 0.799599 | − | 0.600535i | \(-0.205046\pi\) | ||||
0.799599 | + | 0.600535i | \(0.205046\pi\) | |||||||
\(588\) | 11.0842 | + | 18.4863i | 0.457106 | + | 0.762362i | ||||
\(589\) | −29.1778 | −1.20225 | ||||||||
\(590\) | 0.766063 | + | 0.442287i | 0.0315383 | + | 0.0182087i | ||||
\(591\) | 13.8315 | − | 16.5429i | 0.568951 | − | 0.680484i | ||||
\(592\) | 1.95211 | + | 3.38115i | 0.0802311 | + | 0.138964i | ||||
\(593\) | 16.4622 | − | 28.5133i | 0.676020 | − | 1.17090i | −0.300150 | − | 0.953892i | \(-0.597037\pi\) |
0.976170 | − | 0.217009i | \(-0.0696299\pi\) | |||||||
\(594\) | 1.21344 | − | 2.12767i | 0.0497880 | − | 0.0872994i | ||||
\(595\) | 40.2778 | − | 14.9973i | 1.65123 | − | 0.614831i | ||||
\(596\) | − | 28.3372i | − | 1.16074i | ||||||
\(597\) | −38.3499 | − | 6.69236i | −1.56956 | − | 0.273900i | ||||
\(598\) | 2.15359 | − | 1.24338i | 0.0880669 | − | 0.0508455i | ||||
\(599\) | 16.2703 | − | 9.39369i | 0.664788 | − | 0.383816i | −0.129311 | − | 0.991604i | \(-0.541276\pi\) |
0.794099 | + | 0.607788i | \(0.207943\pi\) | |||||||
\(600\) | −31.1711 | − | 5.43961i | −1.27255 | − | 0.222071i | ||||
\(601\) | − | 14.9145i | − | 0.608377i | −0.952612 | − | 0.304188i | \(-0.901615\pi\) | ||
0.952612 | − | 0.304188i | \(-0.0983852\pi\) | |||||||
\(602\) | 7.27493 | + | 1.22750i | 0.296504 | + | 0.0500290i | ||||
\(603\) | 33.9481 | − | 28.6906i | 1.38247 | − | 1.16837i | ||||
\(604\) | 15.8748 | − | 27.4959i | 0.645936 | − | 1.11879i | ||||
\(605\) | −1.95312 | − | 3.38291i | −0.0794057 | − | 0.137535i | ||||
\(606\) | −1.40586 | + | 1.68145i | −0.0571091 | + | 0.0683044i | ||||
\(607\) | 10.3735 | + | 5.98914i | 0.421047 | + | 0.243092i | 0.695525 | − | 0.718502i | \(-0.255172\pi\) |
−0.274478 | + | 0.961593i | \(0.588505\pi\) | |||||||
\(608\) | 28.5883 | 1.15941 | ||||||||
\(609\) | 6.73282 | − | 19.0381i | 0.272828 | − | 0.771461i | ||||
\(610\) | 5.92065 | 0.239720 | ||||||||
\(611\) | −2.88353 | − | 1.66480i | −0.116655 | − | 0.0673508i | ||||
\(612\) | −20.8687 | − | 7.51228i | −0.843567 | − | 0.303666i | ||||
\(613\) | 1.23060 | + | 2.13146i | 0.0497035 | + | 0.0860890i | 0.889807 | − | 0.456338i | \(-0.150839\pi\) |
−0.840103 | + | 0.542427i | \(0.817506\pi\) | |||||||
\(614\) | 0.109264 | − | 0.189250i | 0.00440952 | − | 0.00763751i | ||||
\(615\) | −14.1857 | + | 5.19154i | −0.572023 | + | 0.209343i | ||||
\(616\) | 3.63148 | + | 3.00179i | 0.146316 | + | 0.120946i | ||||
\(617\) | − | 17.5483i | − | 0.706468i | −0.935535 | − | 0.353234i | \(-0.885082\pi\) | ||
0.935535 | − | 0.353234i | \(-0.114918\pi\) | |||||||
\(618\) | −1.77843 | + | 10.1911i | −0.0715389 | + | 0.409946i | ||||
\(619\) | −32.9669 | + | 19.0334i | −1.32505 | + | 0.765019i | −0.984530 | − | 0.175218i | \(-0.943937\pi\) |
−0.340522 | + | 0.940237i | \(0.610604\pi\) | |||||||
\(620\) | 29.7205 | − | 17.1591i | 1.19360 | − | 0.689126i | ||||
\(621\) | −22.1366 | + | 12.9373i | −0.888311 | + | 0.519156i | ||||
\(622\) | 13.2820i | 0.532558i | ||||||||
\(623\) | −0.726005 | + | 4.30278i | −0.0290868 | + | 0.172387i | ||||
\(624\) | −1.72860 | − | 4.72334i | −0.0691994 | − | 0.189085i | ||||
\(625\) | −14.4740 | + | 25.0696i | −0.578959 | + | 1.00279i | ||||
\(626\) | −0.287741 | − | 0.498381i | −0.0115004 | − | 0.0199193i | ||||
\(627\) | 7.84561 | + | 6.55969i | 0.313323 | + | 0.261969i | ||||
\(628\) | −4.96735 | − | 2.86790i | −0.198219 | − | 0.114442i | ||||
\(629\) | −5.97761 | −0.238343 | ||||||||
\(630\) | 12.7360 | + | 7.16908i | 0.507415 | + | 0.285623i | ||||
\(631\) | 1.25547 | 0.0499794 | 0.0249897 | − | 0.999688i | \(-0.492045\pi\) | ||||
0.0249897 | + | 0.999688i | \(0.492045\pi\) | |||||||
\(632\) | −9.07523 | − | 5.23959i | −0.360993 | − | 0.208420i | ||||
\(633\) | −3.68145 | − | 3.07805i | −0.146324 | − | 0.122341i | ||||
\(634\) | −7.89411 | − | 13.6730i | −0.313515 | − | 0.543024i | ||||
\(635\) | −27.8280 | + | 48.1996i | −1.10432 | + | 1.91274i | ||||
\(636\) | −6.39344 | − | 17.4699i | −0.253516 | − | 0.692725i | ||||
\(637\) | −4.89458 | − | 5.66134i | −0.193930 | − | 0.224311i | ||||
\(638\) | − | 2.07719i | − | 0.0822366i | ||||||
\(639\) | 29.5419 | − | 5.31660i | 1.16866 | − | 0.210322i | ||||
\(640\) | −37.7826 | + | 21.8138i | −1.49349 | + | 0.862265i | ||||
\(641\) | −35.6839 | + | 20.6021i | −1.40943 | + | 0.813735i | −0.995333 | − | 0.0964984i | \(-0.969236\pi\) |
−0.414097 | + | 0.910233i | \(0.635902\pi\) | |||||||
\(642\) | 1.36973 | − | 7.84911i | 0.0540591 | − | 0.309780i | ||||
\(643\) | − | 17.3235i | − | 0.683174i | −0.939850 | − | 0.341587i | \(-0.889036\pi\) | ||
0.939850 | − | 0.341587i | \(-0.110964\pi\) | |||||||
\(644\) | −8.09881 | − | 21.7506i | −0.319138 | − | 0.857095i | ||||
\(645\) | −37.5862 | + | 13.7554i | −1.47996 | + | 0.541620i | ||||
\(646\) | −5.78713 | + | 10.0236i | −0.227692 | + | 0.394374i | ||||
\(647\) | −10.0149 | − | 17.3464i | −0.393728 | − | 0.681957i | 0.599210 | − | 0.800592i | \(-0.295482\pi\) |
−0.992938 | + | 0.118635i | \(0.962148\pi\) | |||||||
\(648\) | −5.58775 | − | 15.0215i | −0.219508 | − | 0.590098i | ||||
\(649\) | 0.416038 | + | 0.240199i | 0.0163309 | + | 0.00942865i | ||||
\(650\) | 5.17002 | 0.202785 | ||||||||
\(651\) | −22.2651 | + | 4.13617i | −0.872639 | + | 0.162109i | ||||
\(652\) | −29.7855 | −1.16649 | ||||||||
\(653\) | −38.2992 | − | 22.1121i | −1.49876 | − | 0.865312i | −0.498765 | − | 0.866737i | \(-0.666213\pi\) |
−0.999999 | + | 0.00142529i | \(0.999546\pi\) | |||||||
\(654\) | −4.60111 | + | 5.50308i | −0.179918 | + | 0.215187i | ||||
\(655\) | −42.1310 | − | 72.9730i | −1.64619 | − | 2.85129i | ||||
\(656\) | −3.03216 | + | 5.25185i | −0.118386 | + | 0.205050i | ||||
\(657\) | 24.0426 | + | 28.4484i | 0.937992 | + | 1.10988i | ||||
\(658\) | 2.47462 | − | 2.99372i | 0.0964709 | − | 0.116707i | ||||
\(659\) | − | 34.0478i | − | 1.32631i | −0.748480 | − | 0.663157i | \(-0.769216\pi\) | ||
0.748480 | − | 0.663157i | \(-0.230784\pi\) | |||||||
\(660\) | −11.8492 | − | 2.06778i | −0.461229 | − | 0.0804881i | ||||
\(661\) | −27.2842 | + | 15.7526i | −1.06123 | + | 0.612704i | −0.925773 | − | 0.378079i | \(-0.876585\pi\) |
−0.135461 | + | 0.990783i | \(0.543251\pi\) | |||||||
\(662\) | −1.76838 | + | 1.02098i | −0.0687302 | + | 0.0396814i | ||||
\(663\) | 7.58618 | + | 1.32385i | 0.294623 | + | 0.0514141i | ||||
\(664\) | 13.6370i | 0.529218i | ||||||||
\(665\) | −38.8775 | + | 47.0328i | −1.50760 | + | 1.82385i | ||||
\(666\) | −1.31207 | − | 1.55251i | −0.0508418 | − | 0.0601585i | ||||
\(667\) | −10.8719 | + | 18.8307i | −0.420963 | + | 0.729129i | ||||
\(668\) | 9.43652 | + | 16.3445i | 0.365110 | + | 0.632389i | ||||
\(669\) | 12.1856 | − | 14.5744i | 0.471124 | − | 0.563480i | ||||
\(670\) | 23.6262 | + | 13.6406i | 0.912759 | + | 0.526981i | ||||
\(671\) | 3.21542 | 0.124130 | ||||||||
\(672\) | 21.8153 | − | 4.05260i | 0.841542 | − | 0.156332i | ||||
\(673\) | 24.6061 | 0.948496 | 0.474248 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474248 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(674\) | −1.06867 | − | 0.616994i | −0.0411635 | − | 0.0237657i | ||||
\(675\) | −53.3052 | + | 0.282195i | −2.05172 | + | 0.0108617i | ||||
\(676\) | −10.5397 | − | 18.2552i | −0.405372 | − | 0.702125i | ||||
\(677\) | −19.9027 | + | 34.4725i | −0.764924 | + | 1.32489i | 0.175363 | + | 0.984504i | \(0.443890\pi\) |
−0.940287 | + | 0.340384i | \(0.889443\pi\) | |||||||
\(678\) | −5.62318 | + | 2.05791i | −0.215957 | + | 0.0790337i | ||||
\(679\) | 4.82479 | + | 12.9578i | 0.185159 | + | 0.497273i | ||||
\(680\) | − | 28.9282i | − | 1.10935i | ||||||
\(681\) | −3.76385 | + | 21.5684i | −0.144231 | + | 0.826502i | ||||
\(682\) | −2.01737 | + | 1.16473i | −0.0772492 | + | 0.0445999i | ||||
\(683\) | −25.8221 | + | 14.9084i | −0.988055 | + | 0.570454i | −0.904692 | − | 0.426066i | \(-0.859899\pi\) |
−0.0833625 | + | 0.996519i | \(0.526566\pi\) | |||||||
\(684\) | 30.9922 | − | 5.57761i | 1.18502 | − | 0.213265i | ||||
\(685\) | − | 10.7907i | − | 0.412290i | ||||||
\(686\) | 7.46204 | − | 4.53131i | 0.284902 | − | 0.173006i | ||||
\(687\) | 0.388963 | + | 1.06283i | 0.0148399 | + | 0.0405494i | ||||
\(688\) | −8.03396 | + | 13.9152i | −0.306292 | + | 0.530513i | ||||
\(689\) | 3.22950 | + | 5.59366i | 0.123034 | + | 0.213102i | ||||
\(690\) | −12.0732 | − | 10.0944i | −0.459619 | − | 0.384286i | ||||
\(691\) | −20.7657 | − | 11.9891i | −0.789965 | − | 0.456086i | 0.0499853 | − | 0.998750i | \(-0.484083\pi\) |
−0.839950 | + | 0.542663i | \(0.817416\pi\) | |||||||
\(692\) | 24.9117 | 0.947001 | ||||||||
\(693\) | 6.91674 | + | 3.89342i | 0.262745 | + | 0.147899i | ||||
\(694\) | 7.50776 | 0.284991 | ||||||||
\(695\) | 69.7237 | + | 40.2550i | 2.64477 | + | 1.52696i | ||||
\(696\) | −10.4273 | − | 8.71821i | −0.395245 | − | 0.330463i | ||||
\(697\) | −4.64243 | − | 8.04093i | −0.175845 | − | 0.304572i | ||||
\(698\) | −1.39974 | + | 2.42442i | −0.0529809 | + | 0.0917656i | ||||
\(699\) | 14.0078 | + | 38.2758i | 0.529824 | + | 1.44773i | ||||
\(700\) | 8.02825 | − | 47.5806i | 0.303439 | − | 1.79838i | ||||
\(701\) | − | 1.73905i | − | 0.0656829i | −0.999461 | − | 0.0328414i | \(-0.989544\pi\) | ||
0.999461 | − | 0.0328414i | \(-0.0104556\pi\) | |||||||
\(702\) | 1.32132 | + | 2.26087i | 0.0498701 | + | 0.0853311i | ||||
\(703\) | 7.34983 | − | 4.24343i | 0.277204 | − | 0.160044i | ||||
\(704\) | −2.72793 | + | 1.57497i | −0.102813 | + | 0.0593589i | ||||
\(705\) | −3.62233 | + | 20.7574i | −0.136425 | + | 0.781769i | ||||
\(706\) | − | 8.13783i | − | 0.306271i | ||||||
\(707\) | −5.47428 | − | 4.52507i | −0.205882 | − | 0.170183i | ||||
\(708\) | 1.38916 | − | 0.508390i | 0.0522077 | − | 0.0191065i | ||||
\(709\) | −16.6746 | + | 28.8813i | −0.626228 | + | 1.08466i | 0.362074 | + | 0.932149i | \(0.382069\pi\) |
−0.988302 | + | 0.152509i | \(0.951265\pi\) | |||||||
\(710\) | 9.21172 | + | 15.9552i | 0.345710 | + | 0.598787i | ||||
\(711\) | −16.6103 | − | 5.97935i | −0.622934 | − | 0.224243i | ||||
\(712\) | 2.54354 | + | 1.46851i | 0.0953230 | + | 0.0550348i | ||||
\(713\) | 24.3847 | 0.913213 | ||||||||
\(714\) | −2.99515 | + | 8.46923i | −0.112091 | + | 0.316953i | ||||
\(715\) | 4.17624 | 0.156182 | ||||||||
\(716\) | 6.11995 | + | 3.53335i | 0.228713 | + | 0.132048i | ||||
\(717\) | 14.3265 | − | 17.1349i | 0.535032 | − | 0.639916i | ||||
\(718\) | 7.41710 | + | 12.8468i | 0.276804 | + | 0.479438i | ||||
\(719\) | −8.19635 | + | 14.1965i | −0.305672 | + | 0.529440i | −0.977411 | − | 0.211348i | \(-0.932215\pi\) |
0.671738 | + | 0.740788i | \(0.265548\pi\) | |||||||
\(720\) | −24.3109 | + | 20.5459i | −0.906012 | + | 0.765700i | ||||
\(721\) | −33.0564 | − | 5.57758i | −1.23108 | − | 0.207720i | ||||
\(722\) | − | 7.47659i | − | 0.278250i | ||||||
\(723\) | −36.7146 | − | 6.40700i | −1.36543 | − | 0.238279i | ||||
\(724\) | −7.03899 | + | 4.06396i | −0.261602 | + | 0.151036i | ||||
\(725\) | −39.1496 | + | 22.6030i | −1.45398 | + | 0.839455i | ||||
\(726\) | 0.804302 | + | 0.140357i | 0.0298505 | + | 0.00520915i | ||||
\(727\) | 13.3976i | 0.496890i | 0.968646 | + | 0.248445i | \(0.0799195\pi\) | ||||
−0.968646 | + | 0.248445i | \(0.920081\pi\) | |||||||
\(728\) | −4.72055 | + | 1.75769i | −0.174955 | + | 0.0651443i | ||||
\(729\) | −13.7468 | − | 23.2384i | −0.509141 | − | 0.860683i | ||||
\(730\) | −11.4308 | + | 19.7987i | −0.423071 | + | 0.732781i | ||||
\(731\) | −12.3005 | − | 21.3051i | −0.454951 | − | 0.787999i | ||||
\(732\) | 6.35087 | − | 7.59586i | 0.234735 | − | 0.280751i | ||||
\(733\) | −15.8778 | − | 9.16703i | −0.586458 | − | 0.338592i | 0.177237 | − | 0.984168i | \(-0.443284\pi\) |
−0.763696 | + | 0.645576i | \(0.776617\pi\) | |||||||
\(734\) | −1.82424 | −0.0673338 | ||||||||
\(735\) | −22.9995 | + | 41.4011i | −0.848351 | + | 1.52710i | ||||
\(736\) | −23.8920 | −0.880670 | ||||||||
\(737\) | 12.8310 | + | 7.40799i | 0.472637 | + | 0.272877i | ||||
\(738\) | 1.06939 | − | 2.97071i | 0.0393648 | − | 0.109353i | ||||
\(739\) | 3.86930 | + | 6.70183i | 0.142335 | + | 0.246531i | 0.928375 | − | 0.371644i | \(-0.121206\pi\) |
−0.786041 | + | 0.618175i | \(0.787872\pi\) | |||||||
\(740\) | −4.99101 | + | 8.64469i | −0.183473 | + | 0.317785i | ||||
\(741\) | −10.2674 | + | 3.75758i | −0.377184 | + | 0.138038i | ||||
\(742\) | −7.06103 | + | 2.62916i | −0.259218 | + | 0.0965195i | ||||
\(743\) | 18.1032i | 0.664144i | 0.943254 | + | 0.332072i | \(0.107748\pi\) | ||||
−0.943254 | + | 0.332072i | \(0.892252\pi\) | |||||||
\(744\) | −2.62033 | + | 15.0155i | −0.0960661 | + | 0.550497i | ||||
\(745\) | 53.9218 | − | 31.1318i | 1.97554 | − | 1.14058i | ||||
\(746\) | −1.22286 | + | 0.706020i | −0.0447722 | + | 0.0258492i | ||||
\(747\) | 4.06914 | + | 22.6103i | 0.148882 | + | 0.827269i | ||||
\(748\) | − | 7.39322i | − | 0.270323i | ||||||
\(749\) | 25.4598 | + | 4.29582i | 0.930280 | + | 0.156966i | ||||
\(750\) | −5.76402 | − | 15.7500i | −0.210472 | − | 0.575108i | ||||
\(751\) | 7.09821 | − | 12.2945i | 0.259017 | − | 0.448631i | −0.706962 | − | 0.707252i | \(-0.749935\pi\) |
0.965979 | + | 0.258621i | \(0.0832680\pi\) | |||||||
\(752\) | 4.22955 | + | 7.32579i | 0.154236 | + | 0.267144i | ||||
\(753\) | −3.14767 | − | 2.63176i | −0.114707 | − | 0.0959065i | ||||
\(754\) | 1.92323 | + | 1.11038i | 0.0700400 | + | 0.0404376i | ||||
\(755\) | 69.7613 | 2.53887 | ||||||||
\(756\) | 22.8590 | − | 8.64956i | 0.831373 | − | 0.314581i | ||||
\(757\) | −20.4284 | −0.742484 | −0.371242 | − | 0.928536i | \(-0.621068\pi\) | ||||
−0.371242 | + | 0.928536i | \(0.621068\pi\) | |||||||
\(758\) | 12.2697 | + | 7.08394i | 0.445657 | + | 0.257300i | ||||
\(759\) | −6.55678 | − | 5.48210i | −0.237996 | − | 0.198988i | ||||
\(760\) | 20.5358 | + | 35.5690i | 0.744911 | + | 1.29022i | ||||
\(761\) | 2.30246 | − | 3.98799i | 0.0834643 | − | 0.144564i | −0.821272 | − | 0.570538i | \(-0.806735\pi\) |
0.904736 | + | 0.425973i | \(0.140068\pi\) | |||||||
\(762\) | −3.99796 | − | 10.9243i | −0.144831 | − | 0.395745i | ||||
\(763\) | −17.9163 | − | 14.8097i | −0.648613 | − | 0.536147i | ||||
\(764\) | − | 19.4689i | − | 0.704360i | ||||||
\(765\) | −8.63188 | − | 47.9634i | −0.312086 | − | 1.73412i | ||||
\(766\) | −8.40920 | + | 4.85505i | −0.303837 | + | 0.175420i | ||||
\(767\) | −0.444794 | + | 0.256802i | −0.0160606 | + | 0.00927257i | ||||
\(768\) | −0.308230 | + | 1.76628i | −0.0111223 | + | 0.0637352i | ||||
\(769\) | 9.58284i | 0.345566i | 0.984960 | + | 0.172783i | \(0.0552759\pi\) | ||||
−0.984960 | + | 0.172783i | \(0.944724\pi\) | |||||||
\(770\) | −0.810544 | + | 4.80380i | −0.0292100 | + | 0.173117i | ||||
\(771\) | −3.71113 | + | 1.35816i | −0.133653 | + | 0.0489131i | ||||
\(772\) | 8.44170 | − | 14.6215i | 0.303824 | − | 0.526238i | ||||
\(773\) | 4.15980 | + | 7.20498i | 0.149617 | + | 0.259145i | 0.931086 | − | 0.364799i | \(-0.118862\pi\) |
−0.781469 | + | 0.623944i | \(0.785529\pi\) | |||||||
\(774\) | 2.83344 | − | 7.87114i | 0.101846 | − | 0.282922i | ||||
\(775\) | 43.9043 | + | 25.3482i | 1.57709 | + | 0.910533i | ||||
\(776\) | 9.30650 | 0.334084 | ||||||||
\(777\) | 5.00700 | − | 4.27998i | 0.179625 | − | 0.153544i | ||||
\(778\) | −4.72834 | −0.169519 | ||||||||
\(779\) | 11.4163 | + | 6.59121i | 0.409031 | + | 0.236154i | ||||
\(780\) | 8.24861 | − | 9.86562i | 0.295348 | − | 0.353246i | ||||
\(781\) | 5.00275 | + | 8.66502i | 0.179012 | + | 0.310059i | ||||
\(782\) | 4.83646 | − | 8.37700i | 0.172951 | − | 0.299561i | ||||
\(783\) | −19.8900 | − | 11.3435i | −0.710810 | − | 0.405384i | ||||
\(784\) | 3.57752 | + | 18.6736i | 0.127769 | + | 0.666913i | ||||
\(785\) | − | 12.6029i | − | 0.449817i | ||||||
\(786\) | 17.3497 | + | 3.02766i | 0.618843 | + | 0.107993i | ||||
\(787\) | 47.0972 | − | 27.1916i | 1.67883 | − | 0.969274i | 0.716425 | − | 0.697664i | \(-0.245777\pi\) |
0.962407 | − | 0.271610i | \(-0.0875562\pi\) | |||||||
\(788\) | 19.1676 | − | 11.0664i | 0.682819 | − | 0.394226i | ||||
\(789\) | 20.7284 | + | 3.61728i | 0.737951 | + | 0.128778i | ||||
\(790\) | − | 10.8355i | − | 0.385508i | ||||||
\(791\) | −6.77091 | − | 18.1843i | −0.240746 | − | 0.646561i | ||||
\(792\) | 4.08034 | − | 3.44842i | 0.144989 | − | 0.122534i | ||||
\(793\) | −1.71883 | + | 2.97710i | −0.0610375 | + | 0.105720i | ||||
\(794\) | 8.07402 | + | 13.9846i | 0.286536 | + | 0.496295i | ||||
\(795\) | 26.2188 | − | 31.3585i | 0.929884 | − | 1.11217i | ||||
\(796\) | −34.6043 | − | 19.9788i | −1.22652 | − | 0.708131i | ||||
\(797\) | −18.5539 | −0.657212 | −0.328606 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328606 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(798\) | −2.32948 | − | 12.5396i | −0.0824626 | − | 0.443898i | ||||
\(799\) | −12.9514 | −0.458189 | ||||||||
\(800\) | −43.0172 | − | 24.8360i | −1.52089 | − | 0.878085i | ||||
\(801\) | 4.65540 | + | 1.67585i | 0.164491 | + | 0.0592131i | ||||
\(802\) | −6.42280 | − | 11.1246i | −0.226797 | − | 0.392824i | ||||
\(803\) | −6.20787 | + | 10.7524i | −0.219071 | + | 0.379442i | ||||
\(804\) | 42.8430 | − | 15.6793i | 1.51096 | − | 0.552965i | ||||
\(805\) | 32.4910 | − | 39.3065i | 1.14516 | − | 1.38537i | ||||
\(806\) | − | 2.49047i | − | 0.0877231i | ||||||
\(807\) | 0.667040 | − | 3.82240i | 0.0234809 | − | 0.134555i | ||||
\(808\) | −4.13998 | + | 2.39022i | −0.145644 | + | 0.0840876i | ||||
\(809\) | 12.5255 | − | 7.23159i | 0.440373 | − | 0.254249i | −0.263383 | − | 0.964691i | \(-0.584838\pi\) |
0.703756 | + | 0.710442i | \(0.251505\pi\) | |||||||
\(810\) | 10.5624 | − | 12.7698i | 0.371125 | − | 0.448683i | ||||
\(811\) | 27.1561i | 0.953578i | 0.879018 | + | 0.476789i | \(0.158199\pi\) | ||||
−0.879018 | + | 0.476789i | \(0.841801\pi\) | |||||||
\(812\) | 13.2055 | − | 15.9756i | 0.463422 | − | 0.560633i | ||||
\(813\) | 10.6068 | + | 28.9827i | 0.371997 | + | 1.01647i | ||||
\(814\) | 0.338781 | − | 0.586787i | 0.0118743 | − | 0.0205669i | ||||
\(815\) | −32.7229 | − | 56.6777i | −1.14623 | − | 1.98533i | ||||
\(816\) | −15.0094 | − | 12.5493i | −0.525435 | − | 0.439314i | ||||
\(817\) | 30.2485 | + | 17.4640i | 1.05826 | + | 0.610987i | ||||
\(818\) | −5.51211 | −0.192726 | ||||||||
\(819\) | −7.30226 | + | 4.32283i | −0.255162 | + | 0.151052i | ||||
\(820\) | −15.5048 | −0.541452 | ||||||||
\(821\) | −33.6203 | − | 19.4107i | −1.17336 | − | 0.677438i | −0.218889 | − | 0.975750i | \(-0.570243\pi\) |
−0.954469 | + | 0.298311i | \(0.903577\pi\) | |||||||
\(822\) | 1.73029 | + | 1.44669i | 0.0603507 | + | 0.0504590i | ||||
\(823\) | −4.75046 | − | 8.22804i | −0.165591 | − | 0.286811i | 0.771274 | − | 0.636503i | \(-0.219620\pi\) |
−0.936865 | + | 0.349692i | \(0.886286\pi\) | |||||||
\(824\) | −11.2819 | + | 19.5409i | −0.393025 | + | 0.680739i | ||||
\(825\) | −6.10669 | − | 16.6863i | −0.212608 | − | 0.580943i | ||||
\(826\) | −0.209064 | − | 0.561474i | −0.00727426 | − | 0.0195362i | ||||
\(827\) | 2.24422i | 0.0780391i | 0.999238 | + | 0.0390195i | \(0.0124235\pi\) | ||||
−0.999238 | + | 0.0390195i | \(0.987577\pi\) | |||||||
\(828\) | −25.9010 | + | 4.66136i | −0.900122 | + | 0.161993i | ||||
\(829\) | 11.3765 | − | 6.56822i | 0.395122 | − | 0.228124i | −0.289255 | − | 0.957252i | \(-0.593408\pi\) |
0.684377 | + | 0.729128i | \(0.260074\pi\) | |||||||
\(830\) | −12.2115 | + | 7.05033i | −0.423868 | + | 0.244720i | ||||
\(831\) | 1.90359 | − | 10.9083i | 0.0660347 | − | 0.378405i | ||||
\(832\) | − | 3.36766i | − | 0.116753i | ||||||
\(833\) | −27.4988 | − | 9.55165i | −0.952777 | − | 0.330945i | ||||
\(834\) | −15.8026 | + | 5.78329i | −0.547201 | + | 0.200259i | ||||
\(835\) | −20.7343 | + | 35.9128i | −0.717539 | + | 1.24281i | ||||
\(836\) | 5.24835 | + | 9.09041i | 0.181518 | + | 0.314398i | ||||
\(837\) | 0.135937 | + | 25.6778i | 0.00469868 | + | 0.887556i | ||||
\(838\) | −3.52561 | − | 2.03551i | −0.121790 | − | 0.0703156i | ||||
\(839\) | 5.42803 | 0.187396 | 0.0936982 | − | 0.995601i | \(-0.470131\pi\) | ||||
0.0936982 | + | 0.995601i | \(0.470131\pi\) | |||||||
\(840\) | 20.7127 | + | 24.2310i | 0.714655 | + | 0.836050i | ||||
\(841\) | 9.58196 | 0.330412 | ||||||||
\(842\) | −9.61827 | − | 5.55311i | −0.331468 | − | 0.191373i | ||||
\(843\) | 7.30086 | − | 8.73208i | 0.251455 | − | 0.300749i | ||||
\(844\) | −2.46272 | − | 4.26555i | −0.0847703 | − | 0.146826i | ||||
\(845\) | 23.1581 | − | 40.1111i | 0.796664 | − | 1.37986i | ||||
\(846\) | −2.84282 | − | 3.36376i | −0.0977381 | − | 0.115648i | ||||
\(847\) | −0.440194 | + | 2.60888i | −0.0151253 | + | 0.0896420i | ||||
\(848\) | − | 16.4095i | − | 0.563506i | ||||||
\(849\) | −4.36553 | − | 0.761820i | −0.149825 | − | 0.0261456i | ||||
\(850\) | 17.4160 | − | 10.0551i | 0.597363 | − | 0.344888i | ||||
\(851\) | −6.14245 | + | 3.54634i | −0.210560 | + | 0.121567i | ||||
\(852\) | 30.3506 | + | 5.29643i | 1.03980 | + | 0.181453i | ||||
\(853\) | − | 6.40649i | − | 0.219354i | −0.993967 | − | 0.109677i | \(-0.965018\pi\) | ||
0.993967 | − | 0.109677i | \(-0.0349817\pi\) | |||||||
\(854\) | −3.09088 | − | 2.55493i | −0.105768 | − | 0.0874280i | ||||
\(855\) | 44.6620 | + | 52.8462i | 1.52741 | + | 1.80730i | ||||
\(856\) | 8.68926 | − | 15.0502i | 0.296993 | − | 0.514407i | ||||
\(857\) | 14.4948 | + | 25.1058i | 0.495134 | + | 0.857596i | 0.999984 | − | 0.00561020i | \(-0.00178579\pi\) |
−0.504851 | + | 0.863207i | \(0.668452\pi\) | |||||||
\(858\) | −0.559902 | + | 0.669661i | −0.0191147 | + | 0.0228619i | ||||
\(859\) | 19.0459 | + | 10.9962i | 0.649839 | + | 0.375184i | 0.788394 | − | 0.615170i | \(-0.210913\pi\) |
−0.138556 | + | 0.990355i | \(0.544246\pi\) | |||||||
\(860\) | −41.0814 | −1.40086 | ||||||||
\(861\) | 9.64595 | + | 3.41130i | 0.328733 | + | 0.116257i | ||||
\(862\) | −3.90663 | −0.133060 | ||||||||
\(863\) | 11.3830 | + | 6.57195i | 0.387480 | + | 0.223712i | 0.681068 | − | 0.732220i | \(-0.261516\pi\) |
−0.293588 | + | 0.955932i | \(0.594849\pi\) | |||||||
\(864\) | −0.133191 | − | 25.1590i | −0.00453124 | − | 0.855927i | ||||
\(865\) | 27.3685 | + | 47.4035i | 0.930555 | + | 1.61177i | ||||
\(866\) | 1.99219 | − | 3.45057i | 0.0676972 | − | 0.117255i | ||||
\(867\) | 0.478598 | − | 0.175152i | 0.0162540 | − | 0.00594849i | ||||
\(868\) | −22.9202 | − | 3.86732i | −0.777963 | − | 0.131265i | ||||
\(869\) | − | 5.88458i | − | 0.199621i | ||||||
\(870\) | 2.41600 | − | 13.8446i | 0.0819100 | − | 0.469377i | ||||
\(871\) | −13.7179 | + | 7.92002i | −0.464813 | + | 0.268360i | ||||
\(872\) | −13.5494 | + | 7.82273i | −0.458839 | + | 0.264911i | ||||
\(873\) | 15.4303 | − | 2.77696i | 0.522236 | − | 0.0939860i | ||||
\(874\) | 13.7334i | 0.464538i | ||||||||
\(875\) | 50.9326 | − | 18.9646i | 1.72183 | − | 0.641122i | ||||
\(876\) | 13.1392 | + | 35.9023i | 0.443931 | + | 1.21303i | ||||
\(877\) | −21.8068 | + | 37.7706i | −0.736365 | + | 1.27542i | 0.217757 | + | 0.976003i | \(0.430126\pi\) |
−0.954122 | + | 0.299418i | \(0.903207\pi\) | |||||||
\(878\) | 2.53252 | + | 4.38645i | 0.0854683 | + | 0.148035i | ||||
\(879\) | −34.8669 | − | 29.1521i | −1.17603 | − | 0.983277i | ||||
\(880\) | −9.18854 | − | 5.30501i | −0.309746 | − | 0.178832i | ||||
\(881\) | 35.2188 | 1.18655 | 0.593276 | − | 0.804999i | \(-0.297834\pi\) | ||||
0.593276 | + | 0.804999i | \(0.297834\pi\) | |||||||
\(882\) | −3.55518 | − | 9.23858i | −0.119709 | − | 0.311079i | ||||
\(883\) | −0.651143 | −0.0219127 | −0.0109564 | − | 0.999940i | \(-0.503488\pi\) | ||||
−0.0109564 | + | 0.999940i | \(0.503488\pi\) | |||||||
\(884\) | 6.84526 | + | 3.95211i | 0.230231 | + | 0.132924i | ||||
\(885\) | 2.49355 | + | 2.08485i | 0.0838197 | + | 0.0700814i | ||||
\(886\) | −3.23125 | − | 5.59669i | −0.108556 | − | 0.188024i | ||||
\(887\) | −0.626447 | + | 1.08504i | −0.0210340 | + | 0.0364320i | −0.876351 | − | 0.481673i | \(-0.840029\pi\) |
0.855317 | + | 0.518105i | \(0.173363\pi\) | |||||||
\(888\) | −1.52370 | − | 4.16347i | −0.0511322 | − | 0.139717i | ||||
\(889\) | 35.3272 | − | 13.1540i | 1.18483 | − | 0.441171i | ||||
\(890\) | 3.03688i | 0.101796i | ||||||||
\(891\) | 5.73628 | − | 6.93506i | 0.192173 | − | 0.232333i | ||||
\(892\) | 16.8868 | − | 9.74961i | 0.565413 | − | 0.326441i | ||||
\(893\) | 15.9246 | − | 9.19406i | 0.532896 | − | 0.307667i | ||||
\(894\) | −2.23722 | + | 12.8202i | −0.0748239 | + | 0.428771i | ||||
\(895\) | 15.5272i | 0.519017i | ||||||||
\(896\) | 29.1377 | + | 4.91639i | 0.973421 | + | 0.164245i | ||||
\(897\) | 8.58078 | − | 3.14031i | 0.286504 | − | 0.104852i | ||||
\(898\) | 4.00519 | − | 6.93719i | 0.133655 | − | 0.231497i | ||||
\(899\) | 10.8882 | + | 18.8589i | 0.363141 | + | 0.628979i | ||||
\(900\) | −51.4800 | − | 18.5317i | −1.71600 | − | 0.617723i | ||||
\(901\) | 21.7581 | + | 12.5621i | 0.724868 | + | 0.418503i | ||||
\(902\) | 1.05244 | 0.0350424 | ||||||||
\(903\) | 25.5578 | + | 9.03853i | 0.850510 | + | 0.300783i | ||||
\(904\) | −13.0603 | −0.434380 | ||||||||
\(905\) | −15.4663 | − | 8.92948i | −0.514118 | − | 0.296826i | ||||
\(906\) | −9.35279 | + | 11.1863i | −0.310726 | + | 0.371638i | ||||
\(907\) | 6.45593 | + | 11.1820i | 0.214366 | + | 0.371292i | 0.953076 | − | 0.302731i | \(-0.0978982\pi\) |
−0.738710 | + | 0.674023i | \(0.764565\pi\) | |||||||
\(908\) | −11.2363 | + | 19.4618i | −0.372890 | + | 0.645864i | ||||
\(909\) | −6.15092 | + | 5.19834i | −0.204013 | + | 0.172418i | ||||
\(910\) | −4.01448 | − | 3.31839i | −0.133079 | − | 0.110003i | ||||
\(911\) | 12.4393i | 0.412134i | 0.978538 | + | 0.206067i | \(0.0660664\pi\) | ||||
−0.978538 | + | 0.206067i | \(0.933934\pi\) | |||||||
\(912\) | 27.3636 | + | 4.77517i | 0.906099 | + | 0.158122i | ||||
\(913\) | −6.63190 | + | 3.82893i | −0.219484 | + | 0.126719i | ||||
\(914\) | 4.92914 | − | 2.84584i | 0.163042 | − | 0.0941321i | ||||
\(915\) | 21.4310 | + | 3.73989i | 0.708488 | + | 0.123637i | ||||
\(916\) | 1.16166i | 0.0383823i | ||||||||
\(917\) | −9.49547 | + | 56.2763i | −0.313568 | + | 1.85841i | ||||
\(918\) | 8.84821 | + | 5.04625i | 0.292034 | + | 0.166551i | ||||
\(919\) | 5.32262 | − | 9.21905i | 0.175577 | − | 0.304109i | −0.764784 | − | 0.644287i | \(-0.777154\pi\) |
0.940361 | + | 0.340179i | \(0.110488\pi\) | |||||||
\(920\) | −17.1623 | − | 29.7259i | −0.565824 | − | 0.980035i | ||||
\(921\) | 0.515046 | − | 0.616012i | 0.0169713 | − | 0.0202983i | ||||
\(922\) | 15.0835 | + | 8.70845i | 0.496748 | + | 0.286797i | ||||
\(923\) | −10.6971 | −0.352098 | ||||||||
\(924\) | 5.29356 | + | 6.19275i | 0.174145 | + | 0.203727i | ||||
\(925\) | −14.7459 | −0.484841 | ||||||||
\(926\) | 3.40896 | + | 1.96816i | 0.112025 | + | 0.0646778i | ||||
\(927\) | −12.8748 | + | 35.7654i | −0.422864 | + | 1.17469i | ||||
\(928\) | −10.6682 | − | 18.4778i | −0.350200 | − | 0.606565i | ||||
\(929\) | 12.4288 | − | 21.5273i | 0.407775 | − | 0.706287i | −0.586865 | − | 0.809685i | \(-0.699638\pi\) |
0.994640 | + | 0.103398i | \(0.0329715\pi\) | |||||||
\(930\) | −14.8007 | + | 5.41660i | −0.485333 | + | 0.177617i | ||||
\(931\) | 40.5920 | − | 7.77671i | 1.33035 | − | 0.254871i | ||||
\(932\) | 41.8351i | 1.37035i | ||||||||
\(933\) | −8.38980 | + | 48.0768i | −0.274670 | + | 1.57397i | ||||
\(934\) | 4.10207 | − | 2.36833i | 0.134224 | − | 0.0774941i | ||||
\(935\) | 14.0683 | − | 8.12232i | 0.460082 | − | 0.265628i | ||||
\(936\) | 1.01166 | + | 5.62131i | 0.0330670 | + | 0.183738i | ||||
\(937\) | 15.1506i | 0.494950i | 0.968894 | + | 0.247475i | \(0.0796008\pi\) | ||||
−0.968894 | + | 0.247475i | \(0.920399\pi\) | |||||||
\(938\) | −6.44774 | − | 17.3164i | −0.210526 | − | 0.565402i | ||||
\(939\) | −0.726726 | − | 1.98575i | −0.0237158 | − | 0.0648026i | ||||
\(940\) | −10.8138 | + | 18.7301i | −0.352708 | + | 0.610908i | ||||
\(941\) | −3.89566 | − | 6.74748i | −0.126995 | − | 0.219962i | 0.795516 | − | 0.605933i | \(-0.207200\pi\) |
−0.922511 | + | 0.385971i | \(0.873867\pi\) | |||||||
\(942\) | 2.02088 | + | 1.68965i | 0.0658439 | + | 0.0550519i | ||||
\(943\) | −9.54091 | − | 5.50844i | −0.310695 | − | 0.179380i | ||||
\(944\) | 1.30484 | 0.0424691 | ||||||||
\(945\) | 41.5722 | + | 33.9949i | 1.35234 | + | 1.10585i | ||||
\(946\) | 2.78853 | 0.0906630 | ||||||||
\(947\) | −16.0640 | − | 9.27454i | −0.522009 | − | 0.301382i | 0.215747 | − | 0.976449i | \(-0.430781\pi\) |
−0.737756 | + | 0.675067i | \(0.764115\pi\) | |||||||
\(948\) | −13.9013 | − | 11.6228i | −0.451492 | − | 0.377491i | ||||
\(949\) | −6.63695 | − | 11.4955i | −0.215445 | − | 0.373161i | ||||
\(950\) | −14.2760 | + | 24.7268i | −0.463175 | + | 0.802242i | ||||
\(951\) | −19.9376 | − | 54.4787i | −0.646520 | − | 1.76659i | ||||
\(952\) | −12.4834 | + | 15.1020i | −0.404588 | + | 0.489458i | ||||
\(953\) | 17.3867i | 0.563211i | 0.959530 | + | 0.281606i | \(0.0908670\pi\) | ||||
−0.959530 | + | 0.281606i | \(0.909133\pi\) | |||||||
\(954\) | 1.51324 | + | 8.40838i | 0.0489930 | + | 0.272231i | ||||
\(955\) | 37.0466 | − | 21.3889i | 1.19880 | − | 0.692128i | ||||
\(956\) | 19.8536 | − | 11.4625i | 0.642112 | − | 0.370723i | ||||
\(957\) | 1.31209 | − | 7.51881i | 0.0424139 | − | 0.243049i | ||||
\(958\) | − | 1.05506i | − | 0.0340875i | ||||||
\(959\) | −4.65648 | + | 5.63327i | −0.150366 | + | 0.181908i | ||||
\(960\) | −20.0138 | + | 7.32443i | −0.645941 | + | 0.236395i | ||||
\(961\) | −3.28944 | + | 5.69747i | −0.106111 | + | 0.183789i | ||||
\(962\) | 0.362197 | + | 0.627344i | 0.0116777 | + | 0.0202264i | ||||
\(963\) | 9.91607 | − | 27.5463i | 0.319541 | − | 0.887667i | ||||
\(964\) | −33.1288 | − | 19.1269i | −1.06701 | − | 0.616037i | ||||
\(965\) | 37.0968 | 1.19419 | ||||||||
\(966\) | 1.94681 | + | 10.4797i | 0.0626375 | + | 0.337179i | ||||
\(967\) | 14.3108 | 0.460205 | 0.230103 | − | 0.973166i | \(-0.426094\pi\) | ||||
0.230103 | + | 0.973166i | \(0.426094\pi\) | |||||||
\(968\) | 1.54221 | + | 0.890393i | 0.0495684 | + | 0.0286183i | ||||
\(969\) | −27.2793 | + | 32.6270i | −0.876339 | + | 1.04813i | ||||
\(970\) | 4.81146 | + | 8.33369i | 0.154487 | + | 0.267579i | ||||
\(971\) | −3.47472 | + | 6.01839i | −0.111509 | + | 0.193139i | −0.916379 | − | 0.400312i | \(-0.868902\pi\) |
0.804870 | + | 0.593451i | \(0.202235\pi\) | |||||||
\(972\) | −5.05295 | − | 27.2486i | −0.162073 | − | 0.873999i | ||||
\(973\) | −19.0281 | − | 51.1029i | −0.610012 | − | 1.63828i | ||||
\(974\) | − | 1.38167i | − | 0.0442714i | ||||||
\(975\) | 18.7140 | + | 3.26574i | 0.599327 | + | 0.104587i | ||||
\(976\) | 7.56354 | − | 4.36681i | 0.242103 | − | 0.139778i | ||||
\(977\) | −40.2337 | + | 23.2289i | −1.28719 | + | 0.743160i | −0.978152 | − | 0.207890i | \(-0.933340\pi\) |
−0.309038 | + | 0.951050i | \(0.600007\pi\) | |||||||
\(978\) | 13.4754 | + | 2.35157i | 0.430896 | + | 0.0751948i | ||||
\(979\) | 1.64928i | 0.0527114i | ||||||||
\(980\) | −36.7735 | + | 31.7930i | −1.17469 | + | 1.01559i | ||||
\(981\) | −20.1308 | + | 17.0132i | −0.642727 | + | 0.543189i | ||||
\(982\) | 5.20274 | − | 9.01142i | 0.166026 | − | 0.287566i | ||||
\(983\) | −3.37017 | − | 5.83731i | −0.107492 | − | 0.186181i | 0.807262 | − | 0.590194i | \(-0.200949\pi\) |
−0.914754 | + | 0.404012i | \(0.867615\pi\) | |||||||
\(984\) | 4.41723 | − | 5.28315i | 0.140816 | − | 0.168421i | ||||
\(985\) | 42.1158 | + | 24.3156i | 1.34192 | + | 0.774758i | ||||
\(986\) | 8.63826 | 0.275098 | ||||||||
\(987\) | 10.8485 | − | 9.27327i | 0.345310 | − | 0.295171i | ||||
\(988\) | −11.2222 | −0.357026 | ||||||||
\(989\) | −25.2795 | − | 14.5951i | −0.803840 | − | 0.464097i | ||||
\(990\) | 5.19749 | + | 1.87099i | 0.165187 | + | 0.0594638i | ||||
\(991\) | −4.43379 | − | 7.67955i | −0.140844 | − | 0.243949i | 0.786971 | − | 0.616990i | \(-0.211648\pi\) |
−0.927815 | + | 0.373041i | \(0.878315\pi\) | |||||||
\(992\) | −11.9638 | + | 20.7220i | −0.379852 | + | 0.657924i | ||||
\(993\) | −7.04595 | + | 2.57861i | −0.223596 | + | 0.0818296i | ||||
\(994\) | 2.07614 | − | 12.3045i | 0.0658510 | − | 0.390276i | ||||
\(995\) | − | 87.7964i | − | 2.78333i | ||||||
\(996\) | −4.05370 | + | 23.2293i | −0.128446 | + | 0.736049i | ||||
\(997\) | 8.35506 | − | 4.82380i | 0.264608 | − | 0.152771i | −0.361827 | − | 0.932245i | \(-0.617847\pi\) |
0.626435 | + | 0.779474i | \(0.284514\pi\) | |||||||
\(998\) | −17.0502 | + | 9.84391i | −0.539713 | + | 0.311603i | ||||
\(999\) | −3.76866 | − | 6.44843i | −0.119235 | − | 0.204019i |
(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 | 231.2.n.a.89.12 | ✓ | 52 | |
3.2 | odd | 2 | inner | 231.2.n.a.89.15 | yes | 52 | |
7.3 | odd | 6 | inner | 231.2.n.a.122.15 | yes | 52 | |
21.17 | even | 6 | inner | 231.2.n.a.122.12 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.n.a.89.12 | ✓ | 52 | 1.1 | even | 1 | trivial | |
231.2.n.a.89.15 | yes | 52 | 3.2 | odd | 2 | inner | |
231.2.n.a.122.12 | yes | 52 | 21.17 | even | 6 | inner | |
231.2.n.a.122.15 | yes | 52 | 7.3 | odd | 6 | inner |