Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(113,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.bs (of order \(12\), degree \(4\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 137.2 | ||
Character | \(\chi\) | \(=\) | 360.137 |
Dual form | 360.2.bs.a.113.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.71407 | − | 0.248907i | −0.989620 | − | 0.143706i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.528278 | + | 2.17277i | 0.236253 | + | 0.971692i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.980572 | + | 0.262743i | −0.370621 | + | 0.0993077i | −0.439322 | − | 0.898330i | \(-0.644781\pi\) |
0.0687007 | + | 0.997637i | \(0.478115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87609 | + | 0.853289i | 0.958697 | + | 0.284430i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.66231 | − | 2.11444i | −1.10423 | − | 0.637526i | −0.166900 | − | 0.985974i | \(-0.553376\pi\) |
−0.937328 | + | 0.348448i | \(0.886709\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.89065 | − | 1.04250i | −1.07907 | − | 0.289136i | −0.324856 | − | 0.945764i | \(-0.605316\pi\) |
−0.754215 | + | 0.656627i | \(0.771982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.364690 | − | 3.85578i | −0.0941624 | − | 0.995557i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.61068 | + | 2.61068i | −0.633182 | + | 0.633182i | −0.948865 | − | 0.315683i | \(-0.897766\pi\) |
0.315683 | + | 0.948865i | \(0.397766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.281469i | 0.0645734i | 0.999479 | + | 0.0322867i | \(0.0102790\pi\) | ||||
−0.999479 | + | 0.0322867i | \(0.989721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.74617 | − | 0.206290i | 0.381046 | − | 0.0450163i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.36908 | + | 8.84152i | −0.493987 | + | 1.84358i | 0.0416437 | + | 0.999133i | \(0.486741\pi\) |
−0.535631 | + | 0.844452i | \(0.679926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.44185 | + | 2.29565i | −0.888369 | + | 0.459130i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.71744 | − | 2.17848i | −0.907872 | − | 0.419248i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.93812 | + | 5.08896i | −0.545594 | + | 0.944997i | 0.452975 | + | 0.891523i | \(0.350363\pi\) |
−0.998569 | + | 0.0534738i | \(0.982971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.835561 | − | 1.44723i | −0.150071 | − | 0.259931i | 0.781182 | − | 0.624303i | \(-0.214617\pi\) |
−0.931253 | + | 0.364372i | \(0.881284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.75117 | + | 4.53587i | 1.00115 | + | 0.789594i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.08889 | − | 1.99175i | −0.184057 | − | 0.336668i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09788 | − | 3.09788i | −0.509289 | − | 0.509289i | 0.405019 | − | 0.914308i | \(-0.367265\pi\) |
−0.914308 | + | 0.405019i | \(0.867265\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.40937 | + | 2.75532i | 1.02632 | + | 0.441204i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9685 | − | 6.33265i | 1.71299 | − | 0.988993i | 0.782514 | − | 0.622633i | \(-0.213937\pi\) |
0.930473 | − | 0.366360i | \(-0.119396\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.26685 | − | 8.45998i | −0.345691 | − | 1.29014i | −0.891803 | − | 0.452423i | \(-0.850560\pi\) |
0.546113 | − | 0.837712i | \(-0.316107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.334624 | + | 6.69985i | −0.0498828 | + | 0.998755i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.481889 | + | 1.79843i | 0.0702907 | + | 0.262329i | 0.992124 | − | 0.125257i | \(-0.0399757\pi\) |
−0.921834 | + | 0.387586i | \(0.873309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.16969 | + | 2.98472i | −0.738527 | + | 0.426389i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.12470 | − | 3.82507i | 0.717602 | − | 0.535618i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.91696 | + | 1.91696i | 0.263315 | + | 0.263315i | 0.826399 | − | 0.563084i | \(-0.190385\pi\) |
−0.563084 | + | 0.826399i | \(0.690385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.65946 | − | 9.07436i | 0.358602 | − | 1.22359i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0700596 | − | 0.482459i | 0.00927962 | − | 0.0639032i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.31085 | + | 7.46661i | 0.561225 | + | 0.972070i | 0.997390 | + | 0.0722032i | \(0.0230030\pi\) |
−0.436165 | + | 0.899867i | \(0.643664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82244 | − | 4.88861i | 0.361377 | − | 0.625923i | −0.626811 | − | 0.779171i | \(-0.715640\pi\) |
0.988188 | + | 0.153249i | \(0.0489735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.04441 | − | 0.0810368i | −0.383560 | − | 0.0102097i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.209760 | − | 9.00420i | 0.0260175 | − | 1.11683i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50752 | + | 5.62615i | −0.184173 | + | 0.687344i | 0.810633 | + | 0.585555i | \(0.199123\pi\) |
−0.994806 | + | 0.101789i | \(0.967543\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.26149 | − | 14.5653i | 0.753795 | − | 1.75346i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.92890i | 0.228919i | 0.993428 | + | 0.114459i | \(0.0365136\pi\) | ||||
−0.993428 | + | 0.114459i | \(0.963486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.05914 | − | 4.05914i | 0.475087 | − | 0.475087i | −0.428470 | − | 0.903556i | \(-0.640947\pi\) |
0.903556 | + | 0.428470i | \(0.140947\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.18505 | − | 2.82931i | 0.945128 | − | 0.326700i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.14671 | + | 1.11111i | 0.472562 | + | 0.126623i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.19722 | + | 1.84591i | 0.359715 | + | 0.207682i | 0.668956 | − | 0.743302i | \(-0.266742\pi\) |
−0.309241 | + | 0.950984i | \(0.600075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.54380 | + | 4.90827i | 0.838200 | + | 0.545363i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.950284 | + | 0.254628i | −0.104307 | + | 0.0279490i | −0.310595 | − | 0.950542i | \(-0.600528\pi\) |
0.206288 | + | 0.978491i | \(0.433862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.05156 | − | 4.29323i | −0.764849 | − | 0.465667i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.30282 | − | 7.99154i | 0.675733 | − | 0.856783i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.94741 | −0.736423 | −0.368212 | − | 0.929742i | \(-0.620030\pi\) | ||||
−0.368212 | + | 0.929742i | \(0.620030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.08897 | 0.428640 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.07199 | + | 2.68864i | 0.111160 | + | 0.278799i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.611567 | + | 0.148694i | −0.0627455 | + | 0.0152557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.20533 | − | 0.858865i | 0.325452 | − | 0.0872045i | −0.0923940 | − | 0.995723i | \(-0.529452\pi\) |
0.417846 | + | 0.908518i | \(0.362785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.72891 | − | 9.20632i | −0.877289 | − | 0.925270i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.37496 | + | 3.10323i | 0.534828 | + | 0.308783i | 0.742980 | − | 0.669313i | \(-0.233412\pi\) |
−0.208152 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5754 | + | 4.17342i | 1.53469 | + | 0.411219i | 0.924546 | − | 0.381070i | \(-0.124444\pi\) |
0.610146 | + | 0.792289i | \(0.291111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.37068 | + | 3.68505i | 0.133765 | + | 0.359624i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.51835 | + | 9.51835i | −0.920173 | + | 0.920173i | −0.997041 | − | 0.0768681i | \(-0.975508\pi\) |
0.0768681 | + | 0.997041i | \(0.475508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0583i | 1.05919i | 0.848249 | + | 0.529597i | \(0.177657\pi\) | ||||
−0.848249 | + | 0.529597i | \(0.822343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.53891 | + | 6.08108i | 0.430814 | + | 0.577191i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.42849 | + | 5.33120i | −0.134381 | + | 0.501517i | 0.865619 | + | 0.500704i | \(0.166925\pi\) |
−1.00000 | 0.000812894i | \(0.999741\pi\) | ||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.4621 | − | 0.476681i | −1.90810 | − | 0.0444507i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.3003 | − | 6.31815i | −0.952263 | − | 0.584114i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87402 | − | 3.24589i | 0.171791 | − | 0.297551i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.44167 | + | 5.96116i | 0.312880 | + | 0.541923i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.3770 | + | 8.12449i | −1.83733 | + | 0.732561i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.33444 | − | 8.43836i | −0.656013 | − | 0.754750i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.93844 | + | 7.93844i | 0.704422 | + | 0.704422i | 0.965357 | − | 0.260934i | \(-0.0840306\pi\) |
−0.260934 | + | 0.965357i | \(0.584031\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.77979 | + | 15.0653i | 0.156702 | + | 1.32642i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.94678 | + | 3.43338i | −0.519573 | + | 0.299975i | −0.736760 | − | 0.676155i | \(-0.763645\pi\) |
0.217187 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0739542 | − | 0.276001i | −0.00641264 | − | 0.0239323i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.24121 | − | 11.4007i | 0.192893 | − | 0.981220i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.49250 | − | 20.4983i | −0.469256 | − | 1.75129i | −0.642381 | − | 0.766386i | \(-0.722053\pi\) |
0.173125 | − | 0.984900i | \(-0.444614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7241 | − | 6.76891i | 0.994425 | − | 0.574132i | 0.0878311 | − | 0.996135i | \(-0.472006\pi\) |
0.906594 | + | 0.422004i | \(0.138673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.378350 | − | 3.20259i | −0.0318628 | − | 0.269707i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0445 | + | 12.0445i | 1.00721 | + | 1.00721i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6093 | − | 3.69546i | −1.04714 | − | 0.306891i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.60414 | − | 3.82926i | 0.792136 | − | 0.315832i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.79849 | + | 3.11508i | 0.147338 | + | 0.255198i | 0.930243 | − | 0.366944i | \(-0.119596\pi\) |
−0.782905 | + | 0.622142i | \(0.786263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.41050 | − | 4.17511i | 0.196164 | − | 0.339766i | −0.751117 | − | 0.660169i | \(-0.770485\pi\) |
0.947281 | + | 0.320403i | \(0.103818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.73620 | + | 5.28088i | −0.787125 | + | 0.426934i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.70310 | − | 2.58002i | 0.217118 | − | 0.207232i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13261 | − | 7.95901i | 0.170201 | − | 0.635198i | −0.827119 | − | 0.562027i | \(-0.810022\pi\) |
0.997319 | − | 0.0731706i | \(-0.0233118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.80867 | − | 3.76296i | −0.222742 | − | 0.298422i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.29221i | − | 0.732329i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.95634 | + | 4.95634i | −0.388210 | + | 0.388210i | −0.874049 | − | 0.485838i | \(-0.838514\pi\) |
0.485838 | + | 0.874049i | \(0.338514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.81718 | + | 14.8922i | −0.530717 | + | 1.15935i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8848 | + | 3.72041i | 1.07443 | + | 0.287894i | 0.752314 | − | 0.658805i | \(-0.228938\pi\) |
0.322121 | + | 0.946699i | \(0.395604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.79200 | + | 1.61196i | 0.214769 | + | 0.123997i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.240174 | + | 0.809531i | −0.0183666 | + | 0.0619064i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0437 | − | 3.76299i | 1.06772 | − | 0.286095i | 0.318164 | − | 0.948036i | \(-0.396934\pi\) |
0.749556 | + | 0.661941i | \(0.230267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.75238 | − | 3.41812i | 0.283653 | − | 0.258385i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.53062 | − | 13.8713i | −0.415707 | − | 1.04263i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.8707 | −1.63469 | −0.817347 | − | 0.576146i | \(-0.804556\pi\) | ||||
−0.817347 | + | 0.576146i | \(0.804556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.8617 | −1.77363 | −0.886814 | − | 0.462127i | \(-0.847086\pi\) | ||||
−0.886814 | + | 0.462127i | \(0.847086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.05468 | + | 7.67691i | −0.447575 | + | 0.567494i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.09444 | − | 8.36752i | 0.374551 | − | 0.615193i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0812 | − | 4.04100i | 1.10285 | − | 0.295507i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.19817 | + | 0.896677i | 0.378111 | + | 0.0652237i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5962 | − | 8.42713i | −1.05615 | − | 0.609766i | −0.131782 | − | 0.991279i | \(-0.542070\pi\) |
−0.924363 | + | 0.381513i | \(0.875403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6162 | − | 6.32793i | −1.69993 | − | 0.455494i | −0.727007 | − | 0.686631i | \(-0.759089\pi\) |
−0.972921 | + | 0.231136i | \(0.925756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.60075 | + | 15.3816i | −0.186244 | + | 1.10150i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.2754 | + | 13.2754i | −0.945832 | + | 0.945832i | −0.998606 | − | 0.0527741i | \(-0.983194\pi\) |
0.0527741 | + | 0.998606i | \(0.483194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3515i | 1.79712i | 0.438852 | + | 0.898559i | \(0.355385\pi\) | ||||
−0.438852 | + | 0.898559i | \(0.644615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.98439 | − | 9.26840i | 0.281037 | − | 0.653743i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.54394 | − | 5.76207i | 0.108363 | − | 0.404418i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.5538 | + | 20.4865i | 1.36569 | + | 1.43084i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.3581 | + | 23.4075i | −0.997954 | + | 1.62693i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.595148 | − | 1.03083i | 0.0411673 | − | 0.0713038i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.35077 | + | 10.9999i | 0.437205 | + | 0.757261i | 0.997473 | − | 0.0710502i | \(-0.0226350\pi\) |
−0.560268 | + | 0.828312i | \(0.689302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.480117 | − | 3.30628i | 0.0328971 | − | 0.226543i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.1841 | − | 9.39455i | 1.17194 | − | 0.640703i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.19958 | + | 1.19958i | 0.0814327 | + | 0.0814327i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.96801 | + | 5.94732i | −0.538428 | + | 0.401882i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8788 | − | 7.43560i | 0.866324 | − | 0.500172i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.71629 | + | 6.40529i | 0.114931 | + | 0.428930i | 0.999282 | − | 0.0378938i | \(-0.0120648\pi\) |
−0.884350 | + | 0.466824i | \(0.845398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.7340 | + | 2.81232i | −0.982267 | + | 0.187488i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0441550 | − | 0.164789i | −0.00293067 | − | 0.0109374i | 0.964445 | − | 0.264284i | \(-0.0851355\pi\) |
−0.967376 | + | 0.253346i | \(0.918469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7967 | − | 6.81084i | 0.779550 | − | 0.450073i | −0.0567210 | − | 0.998390i | \(-0.518065\pi\) |
0.836271 | + | 0.548317i | \(0.184731\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.83120 | − | 2.93667i | −0.449460 | − | 0.193218i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.81013 | + | 5.81013i | 0.380634 | + | 0.380634i | 0.871331 | − | 0.490697i | \(-0.163258\pi\) |
−0.490697 | + | 0.871331i | \(0.663258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.65301 | + | 1.99711i | −0.238296 | + | 0.130277i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.02080 | − | 3.95984i | −0.326136 | − | 0.257219i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5650 | − | 18.2991i | −0.683394 | − | 1.18367i | −0.973939 | − | 0.226812i | \(-0.927170\pi\) |
0.290544 | − | 0.956861i | \(-0.406164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2304 | + | 24.6478i | −0.916662 | + | 1.58771i | −0.112212 | + | 0.993684i | \(0.535794\pi\) |
−0.804450 | + | 0.594021i | \(0.797540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7089 | − | 10.2908i | −0.751127 | − | 0.660157i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.21614 | − | 9.65578i | −0.588798 | − | 0.616885i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.293430 | − | 1.09510i | 0.0186705 | − | 0.0696793i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.69224 | − | 0.199919i | 0.107241 | − | 0.0126693i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.25994i | − | 0.205766i | −0.994693 | − | 0.102883i | \(-0.967193\pi\) | ||
0.994693 | − | 0.102883i | \(-0.0328067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.3711 | − | 27.3711i | 1.72081 | − | 1.72081i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.0183 | + | 9.11409i | 0.689991 | + | 0.570747i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.9940 | − | 7.50097i | −1.74622 | − | 0.467898i | −0.762405 | − | 0.647100i | \(-0.775982\pi\) |
−0.983812 | + | 0.179203i | \(0.942648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.85165 | + | 2.22375i | 0.239330 | + | 0.138177i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.7926 | + | 12.1293i | −0.791845 | + | 0.750783i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4961 | − | 4.95600i | 1.14052 | − | 0.305600i | 0.361357 | − | 0.932427i | \(-0.382314\pi\) |
0.779158 | + | 0.626827i | \(0.215647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.15243 | + | 5.17780i | −0.193652 | + | 0.318070i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9084 | + | 1.72926i | 0.728780 | + | 0.105829i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.67111 | −0.284803 | −0.142401 | − | 0.989809i | \(-0.545482\pi\) | ||||
−0.142401 | + | 0.989809i | \(0.545482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0525 | −0.792886 | −0.396443 | − | 0.918059i | \(-0.629756\pi\) | ||||
−0.396443 | + | 0.918059i | \(0.629756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00879 | − | 1.01777i | −0.424191 | − | 0.0615983i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.1214 | + | 0.984614i | 1.27367 | + | 0.0593745i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5784 | − | 6.58576i | 1.47677 | − | 0.395700i | 0.571525 | − | 0.820585i | \(-0.306352\pi\) |
0.905248 | + | 0.424885i | \(0.139685\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.16824 | − | 4.87535i | −0.0699408 | − | 0.291880i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.62412 | + | 1.51504i | 0.156542 | + | 0.0903796i | 0.576225 | − | 0.817291i | \(-0.304525\pi\) |
−0.419683 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.77609 | − | 2.08360i | −0.462241 | − | 0.123857i | 0.0201806 | − | 0.999796i | \(-0.493576\pi\) |
−0.482421 | + | 0.875939i | \(0.660243\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.08528 | − | 0.102649i | 0.0642865 | − | 0.00608039i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.09151 | + | 9.09151i | −0.536655 | + | 0.536655i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.36874i | 0.198161i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.70794 | + | 0.674329i | −0.334605 | + | 0.0395299i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.13277 | + | 7.95962i | −0.124598 | + | 0.465006i | −0.999825 | − | 0.0187062i | \(-0.994045\pi\) |
0.875227 | + | 0.483712i | \(0.160712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.9459 | + | 13.3109i | −0.811961 | + | 0.774992i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.6705 | + | 17.9530i | 0.735216 | + | 1.04174i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.4345 | − | 31.9295i | 1.06609 | − | 1.84653i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.44561 | + | 7.70002i | 0.256241 | + | 0.443822i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.44065 | − | 6.65703i | −0.484903 | − | 0.382436i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.1129 | + | 3.54997i | 0.693580 | + | 0.203271i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.15439 | − | 1.15439i | −0.0658844 | − | 0.0658844i | 0.673397 | − | 0.739281i | \(-0.264835\pi\) |
−0.739281 | + | 0.673397i | \(0.764835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.6586 | − | 11.0304i | −1.45967 | − | 0.627496i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.86996 | + | 2.81167i | −0.276150 | + | 0.159435i | −0.631679 | − | 0.775230i | \(-0.717634\pi\) |
0.355529 | + | 0.934665i | \(0.384301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.94609 | − | 14.7270i | −0.223046 | − | 0.832420i | −0.983178 | − | 0.182651i | \(-0.941532\pi\) |
0.760131 | − | 0.649769i | \(-0.225134\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.43222 | − | 6.65761i | −0.0806964 | − | 0.375114i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.13440 | + | 26.6259i | 0.400708 | + | 1.49546i | 0.811837 | + | 0.583884i | \(0.198468\pi\) |
−0.411129 | + | 0.911577i | \(0.634865\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.5206 | − | 12.4249i | 1.20492 | − | 0.695661i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.6843 | − | 13.9460i | 1.04286 | − | 0.778387i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.734825 | − | 0.734825i | −0.0408867 | − | 0.0408867i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.6749 | − | 4.30096i | 1.09136 | − | 0.238574i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.75249 | − | 18.9548i | 0.152213 | − | 1.04820i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.945053 | − | 1.63688i | −0.0521025 | − | 0.0902441i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9037 | − | 22.3499i | 0.709253 | − | 1.22846i | −0.255881 | − | 0.966708i | \(-0.582366\pi\) |
0.965135 | − | 0.261754i | \(-0.0843010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.26640 | − | 11.5532i | −0.343397 | − | 0.633110i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.0207 | − | 0.303328i | −0.711398 | − | 0.0165726i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.30633 | + | 23.5355i | −0.343528 | + | 1.28206i | 0.550795 | + | 0.834640i | \(0.314324\pi\) |
−0.894323 | + | 0.447422i | \(0.852342\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.77551 | − | 8.78250i | 0.205057 | − | 0.477000i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.06696i | 0.382697i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.30984 | − | 9.30984i | 0.502684 | − | 0.502684i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 34.9549 | + | 5.91022i | 1.88191 | + | 0.318196i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.43538 | + | 0.384609i | 0.0770552 | + | 0.0206469i | 0.297141 | − | 0.954834i | \(-0.403967\pi\) |
−0.220085 | + | 0.975481i | \(0.570634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0207 | + | 6.36282i | 0.589926 | + | 0.340594i | 0.765068 | − | 0.643949i | \(-0.222705\pi\) |
−0.175142 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0828 | + | 13.3936i | 0.858438 | + | 0.714897i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6377 | − | 3.65422i | 0.725862 | − | 0.194494i | 0.123077 | − | 0.992397i | \(-0.460724\pi\) |
0.602786 | + | 0.797903i | \(0.294057\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.19106 | + | 1.01900i | −0.222438 | + | 0.0540827i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.02013 | + | 5.09724i | −0.212768 | + | 0.269775i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.2014 | −1.22452 | −0.612262 | − | 0.790655i | \(-0.709740\pi\) | ||||
−0.612262 | + | 0.790655i | \(0.709740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9208 | 0.995830 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.41551 | − | 11.0745i | −0.231754 | − | 0.581261i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.9639 | + | 6.67522i | 0.573878 | + | 0.349397i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2481 | + | 2.74598i | −0.534948 | + | 0.143339i | −0.516172 | − | 0.856485i | \(-0.672644\pi\) |
−0.0187758 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.9499 | − | 8.85400i | 1.92353 | − | 0.460921i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.38339 | − | 1.37605i | −0.123739 | − | 0.0714409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0303 | + | 5.09915i | 0.985351 | + | 0.264024i | 0.715296 | − | 0.698821i | \(-0.246292\pi\) |
0.270054 | + | 0.962845i | \(0.412958\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4714 | + | 16.2896i | 0.540741 | + | 0.841189i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.7364 | − | 16.7364i | 0.861968 | − | 0.861968i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5293i | 0.540852i | 0.962741 | + | 0.270426i | \(0.0871646\pi\) | ||||
−0.962741 | + | 0.270426i | \(0.912835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.6311 | − | 15.5830i | −0.595881 | − | 0.798341i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.55008 | − | 28.1773i | 0.385791 | − | 1.43979i | −0.451125 | − | 0.892461i | \(-0.648977\pi\) |
0.836916 | − | 0.547331i | \(-0.184356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.223565 | + | 9.59682i | −0.0113940 | + | 0.489099i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.699153 | − | 26.2659i | 0.0355399 | − | 1.33517i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.74483 | + | 16.8785i | −0.494082 | + | 0.855776i | −0.999977 | − | 0.00681963i | \(-0.997829\pi\) |
0.505894 | + | 0.862595i | \(0.331163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8975 | − | 29.2673i | −0.854541 | − | 1.48011i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.0478 | − | 4.40486i | 0.557288 | − | 0.222196i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.32173 | + | 7.92197i | −0.116819 | + | 0.398597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.214255 | + | 0.214255i | 0.0107532 | + | 0.0107532i | 0.712463 | − | 0.701710i | \(-0.247580\pi\) |
−0.701710 | + | 0.712463i | \(0.747580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0580644 | + | 0.491493i | 0.00290686 | + | 0.0246054i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5015 | + | 6.06307i | −0.524422 | + | 0.302775i | −0.738742 | − | 0.673988i | \(-0.764580\pi\) |
0.214320 | + | 0.976764i | \(0.431247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.74214 | + | 6.50174i | 0.0867820 | + | 0.323875i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.67932 | + | 18.9839i | −0.331898 | + | 0.943315i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.79513 | + | 17.8957i | 0.237686 | + | 0.887056i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8210 | + | 9.71162i | −0.831745 | + | 0.480208i | −0.854450 | − | 0.519534i | \(-0.826106\pi\) |
0.0227044 | + | 0.999742i | \(0.492772\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.31238 | + | 36.5027i | 0.212714 | + | 1.80054i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.18890 | − | 6.18890i | −0.304536 | − | 0.304536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05526 | − | 1.93023i | −0.0518008 | − | 0.0947514i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7808 | + | 8.68420i | −1.06661 | + | 0.425267i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.242058 | − | 0.419257i | −0.0118253 | − | 0.0204820i | 0.860052 | − | 0.510206i | \(-0.170431\pi\) |
−0.871878 | + | 0.489724i | \(0.837098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.06103 | + | 13.9621i | −0.392871 | + | 0.680472i | −0.992827 | − | 0.119561i | \(-0.961851\pi\) |
0.599956 | + | 0.800033i | \(0.295185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.148627 | + | 5.58365i | −0.00722648 | + | 0.271486i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.60302 | − | 17.5894i | 0.271786 | − | 0.853212i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.48316 | + | 5.53521i | −0.0717750 | + | 0.267868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6471 | − | 23.6430i | −0.852012 | − | 1.14150i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.5311i | − | 0.988949i | −0.869192 | − | 0.494474i | \(-0.835361\pi\) | ||
0.869192 | − | 0.494474i | \(-0.164639\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0908 | − | 18.0908i | 0.869389 | − | 0.869389i | −0.123016 | − | 0.992405i | \(-0.539257\pi\) |
0.992405 | + | 0.123016i | \(0.0392566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.6934 | + | 9.47282i | 0.992173 | + | 0.454187i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.48862 | − | 0.666822i | −0.119047 | − | 0.0318984i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.7433 | − | 18.3270i | −1.51502 | − | 0.874699i | −0.999845 | − | 0.0176165i | \(-0.994392\pi\) |
−0.515179 | − | 0.857083i | \(-0.672274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.4153 | + | 4.17309i | −0.829301 | + | 0.198719i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.05102 | + | 2.42521i | −0.430027 | + | 0.115225i | −0.467339 | − | 0.884078i | \(-0.654787\pi\) |
0.0373118 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.67016 | − | 15.0951i | −0.173982 | − | 0.715577i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.30738 | − | 5.78714i | −0.109136 | − | 0.273722i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.35277 | 0.299806 | 0.149903 | − | 0.988701i | \(-0.452104\pi\) | ||||
0.149903 | + | 0.988701i | \(0.452104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.5599 | −2.52204 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.17099 | + | 6.55646i | −0.242954 | + | 0.308049i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.16011 | + | 8.88438i | 0.101268 | + | 0.416506i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9472 | − | 4.00508i | 0.699199 | − | 0.187350i | 0.108327 | − | 0.994115i | \(-0.465451\pi\) |
0.590872 | + | 0.806766i | \(0.298784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.0030 | − | 6.62841i | 0.840308 | − | 0.309388i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.28581 | + | 3.05176i | 0.246185 | + | 0.142135i | 0.618016 | − | 0.786166i | \(-0.287937\pi\) |
−0.371831 | + | 0.928300i | \(0.621270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8625 | − | 6.66190i | −1.15546 | − | 0.309605i | −0.370309 | − | 0.928909i | \(-0.620748\pi\) |
−0.785151 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.27549 | + | 3.74953i | −0.244645 | + | 0.173880i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0615 | − | 24.0615i | 1.11343 | − | 1.11343i | 0.120749 | − | 0.992683i | \(-0.461470\pi\) |
0.992683 | − | 0.120749i | \(-0.0385296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.91294i | − | 0.273034i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.63650 | + | 13.1115i | −0.259716 | + | 0.604146i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.58620 | + | 35.7762i | −0.440774 | + | 1.64499i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.646155 | − | 1.25024i | −0.0296476 | − | 0.0573651i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.87763 | + | 7.14908i | 0.177545 | + | 0.327334i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.9283 | + | 27.5886i | −0.727781 | + | 1.26055i | 0.230037 | + | 0.973182i | \(0.426115\pi\) |
−0.957819 | + | 0.287373i | \(0.907218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.82324 | + | 15.2823i | 0.402305 | + | 0.696813i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.31289 | + | 15.9275i | −0.105240 | + | 0.724727i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.55942 | + | 6.51072i | 0.161625 | + | 0.295636i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.615541 | − | 0.615541i | −0.0278928 | − | 0.0278928i | 0.693023 | − | 0.720916i | \(-0.256278\pi\) |
−0.720916 | + | 0.693023i | \(0.756278\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.72919 | − | 7.26186i | 0.439969 | − | 0.328393i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.5023 | + | 12.4143i | −0.970384 | + | 0.560252i | −0.899353 | − | 0.437222i | \(-0.855962\pi\) |
−0.0710310 | + | 0.997474i | \(0.522629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.61517 | − | 20.9561i | −0.252895 | − | 0.943816i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.3919 | − | 23.8294i | 0.691815 | − | 1.07105i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.506806 | − | 1.89143i | −0.0227334 | − | 0.0848421i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.45894 | − | 4.30642i | 0.333908 | − | 0.192782i | −0.323667 | − | 0.946171i | \(-0.604916\pi\) |
0.657575 | + | 0.753389i | \(0.271582\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.8734 | − | 9.83306i | −1.02191 | − | 0.439309i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0273 | + | 17.0273i | 0.759208 | + | 0.759208i | 0.976178 | − | 0.216970i | \(-0.0696173\pi\) |
−0.216970 | + | 0.976178i | \(0.569617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.90314 | + | 13.3179i | −0.173687 | + | 0.592639i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.38446 | − | 3.45796i | −0.194721 | − | 0.153574i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.76039 | + | 4.78114i | 0.122352 | + | 0.211920i | 0.920695 | − | 0.390283i | \(-0.127623\pi\) |
−0.798343 | + | 0.602204i | \(0.794290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.91377 | + | 5.04679i | −0.128897 | + | 0.223257i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.613174 | − | 1.32781i | 0.0270723 | − | 0.0586244i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.839732 | + | 36.0465i | −0.0370030 | + | 1.58840i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.03785 | − | 7.60534i | 0.0896244 | − | 0.334483i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.0085 | + | 2.95447i | −1.09775 | + | 0.129687i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1806i | 0.884126i | 0.896984 | + | 0.442063i | \(0.145753\pi\) | ||||
−0.896984 | + | 0.442063i | \(0.854247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0855088 | − | 0.0855088i | 0.00373904 | − | 0.00373904i | −0.705235 | − | 0.708974i | \(-0.749158\pi\) |
0.708974 | + | 0.705235i | \(0.249158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.28265 | + | 4.92491i | −0.317841 | + | 0.214941i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.95964 | + | 1.59688i | 0.259606 | + | 0.0695612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.6414 | − | 30.3925i | −2.28876 | − | 1.32141i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.02722 | + | 25.1530i | 0.261559 | + | 1.09155i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.2762 | + | 13.2035i | −2.13439 | + | 0.571908i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.7095 | − | 15.6528i | −1.11152 | − | 0.676731i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 37.4880 | + | 5.44377i | 1.61773 | + | 0.234916i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.2440 | 1.08734 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.7856 | −0.721671 | −0.360835 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360835 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.9007 | + | 5.93934i | 1.75522 | + | 0.254882i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0272 | + | 5.84186i | −1.02921 | + | 0.250238i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.58350 | − | 2.29994i | 0.367004 | − | 0.0983384i | −0.0706037 | − | 0.997504i | \(-0.522493\pi\) |
0.437608 | + | 0.899166i | \(0.355826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.2890 | − | 11.6517i | 0.524482 | − | 0.497284i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.43239 | − | 0.826989i | −0.0610217 | − | 0.0352309i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.62010 | − | 0.970004i | −0.153942 | − | 0.0412488i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.8150 | + | 13.0745i | −0.459070 | + | 0.554982i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.716676 | − | 0.716676i | 0.0303665 | − | 0.0303665i | −0.691760 | − | 0.722127i | \(-0.743165\pi\) |
0.722127 | + | 0.691760i | \(0.243165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.2780i | 1.49210i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.8561 | + | 3.17275i | −1.13387 | + | 0.133954i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.55543 | − | 28.1972i | 0.318423 | − | 1.18837i | −0.602337 | − | 0.798242i | \(-0.705764\pi\) |
0.920760 | − | 0.390130i | \(-0.127570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.3381 | − | 0.287426i | −0.519067 | − | 0.0120921i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.68685 | − | 2.83083i | −0.364814 | − | 0.118884i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.1381 | + | 26.2200i | −0.634623 | + | 1.09920i | 0.351971 | + | 0.936011i | \(0.385511\pi\) |
−0.986595 | + | 0.163189i | \(0.947822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2794 | + | 26.4647i | 0.639423 | + | 1.10751i | 0.985560 | + | 0.169329i | \(0.0541602\pi\) |
−0.346136 | + | 0.938184i | \(0.612506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.9214 | + | 18.0778i | 0.957555 | + | 0.755211i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.77396 | − | 44.7113i | −0.407602 | − | 1.86459i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.11358 | − | 7.11358i | −0.296142 | − | 0.296142i | 0.543359 | − | 0.839501i | \(-0.317152\pi\) |
−0.839501 | + | 0.543359i | \(0.817152\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.9047 | + | 16.7248i | 1.61683 | + | 0.695057i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.864920 | − | 0.499362i | 0.0358829 | − | 0.0207170i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.96722 | − | 11.0738i | −0.122890 | − | 0.458630i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.28647 | − | 25.7179i | 0.342603 | − | 1.06330i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.48476 | + | 9.27324i | 0.102557 | + | 0.382748i | 0.998057 | − | 0.0623146i | \(-0.0198482\pi\) |
−0.895500 | + | 0.445062i | \(0.853182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.407352 | − | 0.235185i | 0.0167846 | − | 0.00969061i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.0593 | − | 19.4507i | 1.07194 | − | 0.800093i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.723344 | − | 0.723344i | −0.0297042 | − | 0.0297042i | 0.692099 | − | 0.721803i | \(-0.256686\pi\) |
−0.721803 | + | 0.692099i | \(0.756686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.04258 | + | 2.35707i | 0.329714 | + | 0.0966306i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.31015 | − | 43.4543i | 0.258257 | − | 1.77847i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.49913 | − | 6.06066i | −0.142970 | − | 0.247632i | 0.785643 | − | 0.618680i | \(-0.212332\pi\) |
−0.928614 | + | 0.371047i | \(0.878999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.49249 | − | 7.78122i | 0.183252 | − | 0.317402i | −0.759734 | − | 0.650234i | \(-0.774671\pi\) |
0.942986 | + | 0.332832i | \(0.108004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.13651 | + | 14.8950i | −0.372067 | + | 0.606570i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.1341 | + | 10.6271i | −0.452664 | + | 0.432053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.12710 | + | 19.1346i | −0.208103 | + | 0.776649i | 0.780379 | + | 0.625307i | \(0.215026\pi\) |
−0.988481 | + | 0.151342i | \(0.951640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.08064 | + | 9.49230i | −0.165356 | + | 0.384648i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.49944i | − | 0.303395i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6163 | + | 16.6163i | −0.671124 | + | 0.671124i | −0.957975 | − | 0.286851i | \(-0.907392\pi\) |
0.286851 | + | 0.957975i | \(0.407392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.4174 | − | 39.9825i | −1.14590 | − | 1.61225i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3965 | + | 3.05370i | 0.458808 | + | 0.122937i | 0.480818 | − | 0.876821i | \(-0.340340\pi\) |
−0.0220100 | + | 0.999758i | \(0.507007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.05521 | + | 2.91863i | 0.203186 | + | 0.117309i | 0.598141 | − | 0.801391i | \(-0.295906\pi\) |
−0.394955 | + | 0.918701i | \(0.629240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.4370 | − | 36.5484i | 1.22140 | − | 1.46664i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.81243 | − | 1.82539i | 0.272934 | − | 0.0731325i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.4600 | − | 20.3938i | 0.578399 | − | 0.815754i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.27671 | + | 1.61878i | −0.0509868 | + | 0.0646477i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.1751 | 0.644945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1124 | 1.83571 | 0.917853 | − | 0.396920i | \(-0.129921\pi\) | ||||
0.917853 | + | 0.396920i | \(0.129921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.14774 | − | 20.4353i | −0.323844 | − | 0.812231i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.0547 | + | 21.4421i | −0.518059 | + | 0.850903i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.2250 | − | 6.22312i | 0.920208 | − | 0.246569i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.64591 | + | 5.54770i | −0.0651112 | + | 0.219464i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.2725 | − | 19.2099i | −1.31418 | − | 0.758744i | −0.331398 | − | 0.943491i | \(-0.607520\pi\) |
−0.982786 | + | 0.184747i | \(0.940854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.9724 | + | 4.54774i | 0.669326 | + | 0.179345i | 0.577451 | − | 0.816425i | \(-0.304047\pi\) |
0.0918748 | + | 0.995771i | \(0.470714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.7931 | + | 11.8257i | −1.25185 | + | 0.465637i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.1467 | + | 22.1467i | −0.870677 | + | 0.870677i | −0.992546 | − | 0.121870i | \(-0.961111\pi\) |
0.121870 | + | 0.992546i | \(0.461111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.4601i | − | 1.43118i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.75758 | − | 2.35475i | −0.0688851 | − | 0.0922899i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.56014 | + | 31.9469i | −0.334984 | + | 1.25018i | 0.568902 | + | 0.822405i | \(0.307368\pi\) |
−0.903886 | + | 0.427773i | \(0.859298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6015 | − | 11.1072i | −0.414234 | − | 0.433994i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.1381 | − | 8.21084i | 0.590593 | − | 0.320335i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0315958 | + | 0.0547256i | −0.00123080 | + | 0.00213181i | −0.866640 | − | 0.498934i | \(-0.833725\pi\) |
0.865409 | + | 0.501066i | \(0.167058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.681072 | − | 1.17965i | −0.0264906 | − | 0.0458832i | 0.852476 | − | 0.522766i | \(-0.175100\pi\) |
−0.878967 | + | 0.476883i | \(0.841767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.9260 | + | 9.53953i | −0.929210 | + | 0.370485i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.560617 | − | 0.306490i | 0.0217398 | − | 0.0118852i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.0336 | − | 38.0336i | −1.47267 | − | 1.47267i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.34753 | − | 11.4063i | −0.0520985 | − | 0.440994i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6733 | + | 11.9357i | −0.798084 | + | 0.460774i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.37147 | + | 23.7787i | 0.245602 | + | 0.916600i | 0.973080 | + | 0.230469i | \(0.0740259\pi\) |
−0.727478 | + | 0.686131i | \(0.759307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9552 | − | 1.15313i | 0.999015 | − | 0.0443841i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.45281 | + | 16.6181i | 0.171135 | + | 0.638686i | 0.997178 | + | 0.0750779i | \(0.0239205\pi\) |
−0.826042 | + | 0.563608i | \(0.809413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.91739 | + | 1.68436i | −0.111959 | + | 0.0646397i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0346678 | + | 0.293450i | 0.00132847 | + | 0.0112450i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.80388 | + | 7.80388i | 0.298607 | + | 0.298607i | 0.840468 | − | 0.541861i | \(-0.182280\pi\) |
−0.541861 | + | 0.840468i | \(0.682280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.6364 | − | 22.7627i | 1.59085 | − | 0.869718i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.9157 | + | 8.73800i | −0.836137 | + | 0.333375i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.45979 | − | 9.45664i | −0.208002 | − | 0.360269i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3258 | − | 26.5451i | 0.583023 | − | 1.00982i | −0.412096 | − | 0.911140i | \(-0.635203\pi\) |
0.995119 | − | 0.0986844i | \(-0.0314634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.9782 | + | 6.73399i | 0.417028 | + | 0.255803i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.9009 | + | 21.8979i | 0.792815 | + | 0.830634i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1026 | + | 45.1676i | −0.458420 | + | 1.71085i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.51280 | − | 11.4052i | −0.321984 | − | 0.431383i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.37006i | 0.353902i | 0.984220 | + | 0.176951i | \(0.0566234\pi\) | ||||
−0.984220 | + | 0.176951i | \(0.943377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.871958 | − | 0.871958i | 0.0328865 | − | 0.0328865i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.75862 | − | 2.51393i | 0.254544 | − | 0.0946799i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.08589 | − | 1.63071i | −0.228883 | − | 0.0613291i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.62031 | + | 0.935488i | 0.0608522 | + | 0.0351330i | 0.530117 | − | 0.847924i | \(-0.322148\pi\) |
−0.469265 | + | 0.883057i | \(0.655481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.62039 | + | 8.03716i | 0.285787 | + | 0.301417i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.7753 | − | 3.95902i | 0.553338 | − | 0.148266i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.8070 | + | 32.5326i | −0.740740 | + | 1.21665i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.5544 | + | 33.9958i | 0.506199 | + | 1.26960i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.7584 | 0.811452 | 0.405726 | − | 0.913995i | \(-0.367019\pi\) | ||||
0.405726 | + | 0.913995i | \(0.367019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3694 | −0.609627 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.5270 | − | 38.7061i | 1.13531 | − | 1.43950i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.36817 | − | 29.3493i | 0.0508126 | − | 1.09000i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.6944 | + | 4.20530i | −0.582073 | + | 0.155966i | −0.537828 | − | 0.843055i | \(-0.680755\pi\) |
−0.0442451 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5085 | + | 20.5537i | 0.648462 | + | 0.761247i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0043 | + | 16.1683i | 1.03578 | + | 0.598005i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.2446 | − | 11.5873i | −1.59727 | − | 0.427988i | −0.653057 | − | 0.757309i | \(-0.726514\pi\) |
−0.944218 | + | 0.329321i | \(0.893180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.3937 | + | 18.8447i | 0.494036 | + | 0.695096i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4172 | − | 17.4172i | 0.641569 | − | 0.641569i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.2703i | 0.561726i | 0.959748 | + | 0.280863i | \(0.0906206\pi\) | ||||
−0.959748 | + | 0.280863i | \(0.909379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.775538 | + | 1.80404i | −0.0284901 | + | 0.0662730i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.17205 | − | 11.8382i | 0.116371 | − | 0.434303i | −0.883015 | − | 0.469345i | \(-0.844490\pi\) |
0.999386 | + | 0.0350425i | \(0.0111567\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.81825 | + | 5.55334i | −0.213164 | + | 0.203459i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.95038 | − | 0.0785337i | −0.107949 | − | 0.00287340i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.83254 | − | 11.8343i | 0.249656 | − | 0.432416i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.95028 | + | 3.37798i | 0.0711667 | + | 0.123264i | 0.899413 | − | 0.437100i | \(-0.143994\pi\) |
−0.828246 | + | 0.560364i | \(0.810661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.811421 | + | 5.58777i | −0.0295698 | + | 0.203630i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3450 | + | 3.03185i | 0.376492 | + | 0.110340i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.02600 | − | 8.02600i | −0.291710 | − | 0.291710i | 0.546045 | − | 0.837756i | \(-0.316133\pi\) |
−0.837756 | + | 0.546045i | \(0.816133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −53.7290 | + | 40.1032i | −1.95024 | + | 1.45566i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.0744 | − | 13.3220i | 0.836447 | − | 0.482923i | −0.0196080 | − | 0.999808i | \(-0.506242\pi\) |
0.856055 | + | 0.516885i | \(0.172908\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.90550 | − | 10.8435i | −0.105186 | − | 0.392560i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.6176 | − | 18.3647i | −0.600809 | − | 0.663979i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.98808 | − | 33.5440i | −0.324541 | − | 1.21120i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.3021 | − | 21.5364i | 1.34515 | − | 0.776621i | 0.357590 | − | 0.933879i | \(-0.383599\pi\) |
0.987558 | + | 0.157258i | \(0.0502653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.1167 | + | 19.8251i | 1.66085 | + | 0.713983i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.43913 | − | 1.43913i | −0.0517620 | − | 0.0517620i | 0.680752 | − | 0.732514i | \(-0.261653\pi\) |
−0.732514 | + | 0.680752i | \(0.761653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.03378 | + | 4.51023i | 0.252661 | + | 0.162012i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.04849 | − | 4.77037i | −0.216989 | − | 0.171136i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.78244 | + | 3.08729i | 0.0638627 | + | 0.110613i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.07854 | − | 7.06424i | 0.145942 | − | 0.252778i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.9466 | − | 17.6063i | 0.891518 | − | 0.629197i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.4197 | + | 0.429101i | 0.657427 | + | 0.0153153i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.88152 | − | 18.2181i | 0.174007 | − | 0.649405i | −0.822711 | − | 0.568460i | \(-0.807540\pi\) |
0.996719 | − | 0.0809450i | \(-0.0257938\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.9372 | + | 3.89116i | −1.17259 | + | 0.138529i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.60295i | − | 0.199218i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0775 | + | 16.0775i | −0.570928 | + | 0.570928i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.69228 | − | 8.09047i | 0.237351 | − | 0.286939i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.8838 | − | 6.13169i | −0.810585 | − | 0.217196i | −0.170359 | − | 0.985382i | \(-0.554493\pi\) |
−0.640226 | + | 0.768186i | \(0.721159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.95318 | − | 3.43707i | −0.210609 | − | 0.121595i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.9814 | − | 5.92814i | −0.706007 | − | 0.209461i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4486 | + | 6.28304i | −0.827484 | + | 0.221724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.1898 | − | 4.90887i | 0.711598 | − | 0.173015i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.00662 | + | 1.16267i | 0.281846 | + | 0.0409280i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.46997 | 0.157156 | 0.0785778 | − | 0.996908i | \(-0.474962\pi\) | ||||
0.0785778 | + | 0.996908i | \(0.474962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2622 | 1.51914 | 0.759571 | − | 0.650424i | \(-0.225409\pi\) | ||||
0.759571 | + | 0.650424i | \(0.225409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.3730 | + | 3.24887i | 0.784656 | + | 0.113943i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.3873 | − | 8.15065i | −0.468937 | − | 0.285505i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.38122 | − | 0.638047i | 0.0833085 | − | 0.0223224i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.7602 | + | 3.48907i | 0.410936 | + | 0.121918i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.3735 | + | 23.3097i | 1.40905 | + | 0.813513i | 0.995296 | − | 0.0968772i | \(-0.0308854\pi\) |
0.413750 | + | 0.910391i | \(0.364219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.4955 | + | 8.43920i | 1.09787 | + | 0.294172i | 0.761895 | − | 0.647700i | \(-0.224269\pi\) |
0.335970 | + | 0.941873i | \(0.390936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.9586 | − | 6.94496i | −1.25192 | − | 0.241793i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.08734 | − | 6.08734i | 0.211678 | − | 0.211678i | −0.593302 | − | 0.804980i | \(-0.702176\pi\) |
0.804980 | + | 0.593302i | \(0.202176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.7231i | 0.893400i | 0.894684 | + | 0.446700i | \(0.147401\pi\) | ||||
−0.894684 | + | 0.446700i | \(0.852599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.7684 | + | 5.17075i | −1.51831 | + | 0.179371i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.70425 | − | 21.2885i | 0.197640 | − | 0.737604i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.748581 | + | 32.1338i | −0.0259057 | + | 1.11203i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.788942 | + | 8.64749i | 0.0272698 | + | 0.298901i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.00802753 | + | 0.0139041i | −0.000277141 | + | 0.000480022i | −0.866164 | − | 0.499760i | \(-0.833422\pi\) |
0.865887 | + | 0.500240i | \(0.166755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.76504 | − | 4.78919i | −0.0953462 | − | 0.165145i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.12084 | − | 3.25005i | −0.141929 | − | 0.111938i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.02747 | + | 6.91792i | −0.0697469 | + | 0.237984i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.94106 | − | 4.94106i | −0.169777 | − | 0.169777i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.8102 | + | 5.50696i | 0.439644 | + | 0.188998i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.7291 | − | 20.0509i | 1.19050 | − | 0.687335i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.68364 | + | 10.0155i | 0.0918859 | + | 0.342923i | 0.996529 | − | 0.0832473i | \(-0.0265291\pi\) |
−0.904643 | + | 0.426170i | \(0.859862\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.88580 | − | 0.0941863i | −0.0644931 | − | 0.00322110i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.23292 | + | 4.60132i | 0.0421157 | + | 0.157178i | 0.983781 | − | 0.179372i | \(-0.0574066\pi\) |
−0.941666 | + | 0.336550i | \(0.890740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0689 | − | 17.9377i | 1.06006 | − | 0.612025i | 0.134610 | − | 0.990899i | \(-0.457022\pi\) |
0.925448 | + | 0.378874i | \(0.123688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.8464 | − | 13.3206i | 0.608205 | − | 0.453964i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.1155 | − | 35.1155i | −1.19535 | − | 1.19535i | −0.975544 | − | 0.219803i | \(-0.929459\pi\) |
−0.219803 | − | 0.975544i | \(-0.570541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.5950 | + | 28.5257i | 0.530248 | + | 0.969903i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.838501 | − | 5.77426i | 0.0284770 | − | 0.196104i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.80613 | − | 13.5206i | −0.264805 | − | 0.458656i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7305 | − | 20.3178i | 0.397472 | − | 0.688442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.95167 | + | 0.264896i | 0.336813 | + | 0.00896536i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.40907 | + | 6.34734i | 0.318085 | + | 0.214579i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.52326 | − | 20.6131i | 0.186507 | − | 0.696055i | −0.807795 | − | 0.589463i | \(-0.799339\pi\) |
0.994303 | − | 0.106592i | \(-0.0339939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.63694 | − | 13.1125i | 0.190129 | − | 0.442274i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 46.9670i | − | 1.58236i | −0.611584 | − | 0.791180i | \(-0.709467\pi\) | ||
0.611584 | − | 0.791180i | \(-0.290533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.3061 | + | 19.3061i | −0.649703 | + | 0.649703i | −0.952921 | − | 0.303218i | \(-0.901939\pi\) |
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.2174 | − | 19.3447i | 0.914904 | − | 0.650264i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6307 | − | 3.11644i | −0.390522 | − | 0.104640i | 0.0582149 | − | 0.998304i | \(-0.481459\pi\) |
−0.448736 | + | 0.893664i | \(0.648126\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.86998 | − | 5.69844i | −0.331029 | − | 0.191119i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.2495 | − | 33.9265i | −0.577880 | − | 1.13658i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.506204 | + | 0.135637i | −0.0169395 | + | 0.00453891i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5538 | − | 47.5200i | −0.386201 | − | 1.58842i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.5455 | + | 50.1410i | −1.32039 | + | 1.67416i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.81990 | 0.327512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0091 | −0.333453 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.70351 | − | 14.3049i | −0.189801 | − | 0.476039i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.6056 | − | 51.8460i | −0.419025 | − | 1.72342i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.14289 | + | 1.11008i | −0.137562 | + | 0.0368598i | −0.326943 | − | 0.945044i | \(-0.606019\pi\) |
0.189381 | + | 0.981904i | \(0.439352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.8109 | + | 13.5116i | 0.424911 | + | 0.448151i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.7547 | + | 18.3336i | 1.05208 | + | 0.607419i | 0.923231 | − | 0.384245i | \(-0.125538\pi\) |
0.128849 | + | 0.991664i | \(0.458872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.01863 | + | 1.07679i | 0.132997 | + | 0.0356365i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.8787 | − | 9.09987i | −0.657170 | − | 0.300833i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.92915 | − | 4.92915i | 0.162775 | − | 0.162775i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.3075i | − | 0.702870i | −0.936212 | − | 0.351435i | \(-0.885694\pi\) | ||
0.936212 | − | 0.351435i | \(-0.114306\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.69137 | + | 2.26604i | 0.0557325 | + | 0.0746685i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.01087 | − | 7.50468i | 0.0661886 | − | 0.247019i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8720 | + | 6.64866i | 0.686266 | + | 0.218607i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.2352 | + | 25.2935i | 1.35434 | + | 0.830747i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5804 | + | 25.2540i | −0.478367 | + | 0.828556i | −0.999692 | − | 0.0248023i | \(-0.992104\pi\) |
0.521326 | + | 0.853358i | \(0.325438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.840107 | − | 1.45511i | −0.0275334 | − | 0.0476892i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.04731 | − | 3.60724i | 0.296196 | − | 0.118096i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.7472 | + | 30.6332i | 0.547693 | + | 1.00181i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.6450 | + | 13.6450i | 0.445761 | + | 0.445761i | 0.893943 | − | 0.448181i | \(-0.147928\pi\) |
−0.448181 | + | 0.893943i | \(0.647928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.09824 | + | 26.2254i | 0.101107 | + | 0.855833i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.1984 | − | 11.0842i | 0.625849 | − | 0.361334i | −0.153294 | − | 0.988181i | \(-0.548988\pi\) |
0.779143 | + | 0.626847i | \(0.215655\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0051 | + | 111.980i | 0.977100 | + | 3.64659i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.797805 | + | 11.7681i | 0.0259526 | + | 0.382817i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.22747 | − | 19.5092i | −0.169870 | − | 0.633964i | −0.997369 | − | 0.0724959i | \(-0.976904\pi\) |
0.827499 | − | 0.561468i | \(-0.189763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0243 | + | 11.5610i | −0.650017 | + | 0.375287i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.60150 | − | 47.4146i | −0.181641 | − | 1.53752i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.3870 | − | 20.3870i | −0.660399 | − | 0.660399i | 0.295075 | − | 0.955474i | \(-0.404655\pi\) |
−0.955474 | + | 0.295075i | \(0.904655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.5993 | − | 36.1661i | 0.342987 | − | 1.17031i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.9805 | + | 15.9406i | −1.29239 | + | 0.515286i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.7716 | + | 18.6569i | 0.347832 | + | 0.602463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1037 | − | 24.4283i | 0.454957 | − | 0.788009i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.4975 | + | 19.2537i | −1.14389 | + | 0.620443i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.27324 | − | 54.6553i | 0.0409870 | − | 1.75942i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.12383 | + | 22.8544i | −0.196929 | + | 0.734949i | 0.794830 | + | 0.606832i | \(0.207560\pi\) |
−0.991759 | + | 0.128117i | \(0.959107\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.07664 | + | 1.44245i | 0.0345867 | + | 0.0463380i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.0761i | 1.02937i | 0.857379 | + | 0.514686i | \(0.172092\pi\) | ||||
−0.857379 | + | 0.514686i | \(0.827908\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.71784 | + | 9.71784i | −0.311540 | + | 0.311540i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.7947 | + | 2.47495i | −1.11432 | + | 0.0792619i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.3058 | − | 6.24476i | −0.745618 | − | 0.199788i | −0.134044 | − | 0.990975i | \(-0.542796\pi\) |
−0.611573 | + | 0.791188i | \(0.709463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.4435 | + | 14.6898i | 0.813179 | + | 0.469489i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.43594 | + | 31.8047i | −0.301266 | + | 1.01545i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.39530 | + | 1.44566i | −0.172083 | + | 0.0461096i | −0.343832 | − | 0.939031i | \(-0.611725\pi\) |
0.171749 | + | 0.985141i | \(0.445058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.8574 | − | 21.8313i | −1.14251 | − | 0.695602i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.21246 | + | 3.04096i | 0.0385930 | + | 0.0967949i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 80.1694 | 2.54924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1955 | 0.387401 | 0.193701 | − | 0.981061i | \(-0.437951\pi\) | ||||
0.193701 | + | 0.981061i | \(0.437951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.6810 | + | 35.0976i | −0.878429 | + | 1.11379i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −55.0829 | + | 13.3926i | −1.74625 | + | 0.424575i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.3044 | + | 13.4790i | −1.59316 | + | 0.426885i | −0.942967 | − | 0.332886i | \(-0.891978\pi\) |
−0.650191 | + | 0.759771i | \(0.725311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.86541 | + | 21.3627i | 0.248851 | + | 0.675887i |
(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 | 360.2.bs.a.137.2 | yes | 72 | |
3.2 | odd | 2 | 1080.2.bt.a.737.8 | 72 | |||
4.3 | odd | 2 | 720.2.cu.e.497.17 | 72 | |||
5.3 | odd | 4 | inner | 360.2.bs.a.353.11 | yes | 72 | |
9.4 | even | 3 | 1080.2.bt.a.17.15 | 72 | |||
9.5 | odd | 6 | inner | 360.2.bs.a.257.11 | yes | 72 | |
15.8 | even | 4 | 1080.2.bt.a.953.15 | 72 | |||
20.3 | even | 4 | 720.2.cu.e.353.8 | 72 | |||
36.23 | even | 6 | 720.2.cu.e.257.8 | 72 | |||
45.13 | odd | 12 | 1080.2.bt.a.233.8 | 72 | |||
45.23 | even | 12 | inner | 360.2.bs.a.113.2 | ✓ | 72 | |
180.23 | odd | 12 | 720.2.cu.e.113.17 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bs.a.113.2 | ✓ | 72 | 45.23 | even | 12 | inner | |
360.2.bs.a.137.2 | yes | 72 | 1.1 | even | 1 | trivial | |
360.2.bs.a.257.11 | yes | 72 | 9.5 | odd | 6 | inner | |
360.2.bs.a.353.11 | yes | 72 | 5.3 | odd | 4 | inner | |
720.2.cu.e.113.17 | 72 | 180.23 | odd | 12 | |||
720.2.cu.e.257.8 | 72 | 36.23 | even | 6 | |||
720.2.cu.e.353.8 | 72 | 20.3 | even | 4 | |||
720.2.cu.e.497.17 | 72 | 4.3 | odd | 2 | |||
1080.2.bt.a.17.15 | 72 | 9.4 | even | 3 | |||
1080.2.bt.a.233.8 | 72 | 45.13 | odd | 12 | |||
1080.2.bt.a.737.8 | 72 | 3.2 | odd | 2 | |||
1080.2.bt.a.953.15 | 72 | 15.8 | even | 4 |