Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [972,2,Mod(35,972)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(972, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([27, 31]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("972.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 972 = 2^{2} \cdot 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 972.p (of order \(54\), degree \(18\), not 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: | \(7.76145907647\) |
Analytic rank: | \(0\) |
Dimension: | \(936\) |
Relative dimension: | \(52\) over \(\Q(\zeta_{54})\) |
Twist minimal: | no (minimal twist has level 324) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{54}]$ |
Embedding invariants
Embedding label | 251.30 | ||
Character | \(\chi\) | \(=\) | 972.251 |
Dual form | 972.2.p.a.395.30 |
$q$-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 \(\left(\mathbb{Z}/972\mathbb{Z}\right)^\times\).
\(n\) | \(245\) | \(487\) |
\(\chi(n)\) | \(e\left(\frac{1}{54}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.456796 | − | 1.33841i | 0.323004 | − | 0.946398i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.58267 | − | 1.22276i | −0.791337 | − | 0.611380i | ||||
\(5\) | 0.874721 | + | 3.69074i | 0.391187 | + | 1.65055i | 0.711092 | + | 0.703099i | \(0.248201\pi\) |
−0.319905 | + | 0.947450i | \(0.603651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85958 | − | 2.12888i | 1.08082 | − | 0.804641i | 0.0991206 | − | 0.995075i | \(-0.468397\pi\) |
0.981700 | + | 0.190434i | \(0.0609896\pi\) | |||||||
\(8\) | −2.35951 | + | 1.55971i | −0.834213 | + | 0.551442i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.33928 | + | 0.515181i | 1.68843 | + | 0.162915i | ||||
\(11\) | 0.253209 | − | 0.268386i | 0.0763453 | − | 0.0809213i | −0.688075 | − | 0.725640i | \(-0.741544\pi\) |
0.764420 | + | 0.644718i | \(0.223025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.86762 | + | 0.937956i | 0.517986 | + | 0.260142i | 0.688530 | − | 0.725208i | \(-0.258256\pi\) |
−0.170544 | + | 0.985350i | \(0.554553\pi\) | |||||||
\(14\) | −1.54306 | − | 4.79975i | −0.412401 | − | 1.28279i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00972 | + | 3.87046i | 0.252429 | + | 0.967615i | ||||
\(17\) | −2.09840 | + | 5.76530i | −0.508936 | + | 1.39829i | 0.373399 | + | 0.927671i | \(0.378192\pi\) |
−0.882336 | + | 0.470620i | \(0.844030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03264 | + | 2.83716i | 0.236904 | + | 0.650888i | 0.999989 | + | 0.00459076i | \(0.00146129\pi\) |
−0.763085 | + | 0.646298i | \(0.776316\pi\) | |||||||
\(20\) | 3.12849 | − | 6.91081i | 0.699551 | − | 1.54530i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.243545 | − | 0.461494i | −0.0519239 | − | 0.0983909i | ||||
\(23\) | −3.75651 | + | 5.04586i | −0.783286 | + | 1.05214i | 0.213877 | + | 0.976861i | \(0.431391\pi\) |
−0.997163 | + | 0.0752748i | \(0.976017\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.38825 | + | 4.21274i | −1.67765 | + | 0.842547i | ||||
\(26\) | 2.10849 | − | 2.07119i | 0.413509 | − | 0.406194i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.12890 | − | 0.127258i | −1.34723 | − | 0.0240495i | ||||
\(29\) | 3.89902 | − | 5.92817i | 0.724030 | − | 1.10083i | −0.266540 | − | 0.963824i | \(-0.585880\pi\) |
0.990570 | − | 0.137010i | \(-0.0437493\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.55754 | − | 1.10321i | 0.459347 | − | 0.198143i | −0.153816 | − | 0.988100i | \(-0.549156\pi\) |
0.613163 | + | 0.789957i | \(0.289897\pi\) | |||||||
\(32\) | 5.64149 | + | 0.416598i | 0.997285 | + | 0.0736448i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.75779 | + | 5.44208i | 1.15895 | + | 0.933309i | ||||
\(35\) | 10.3585 | + | 8.69179i | 1.75090 | + | 1.46918i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.159326 | + | 0.133690i | −0.0261930 | + | 0.0219785i | −0.655790 | − | 0.754943i | \(-0.727664\pi\) |
0.629597 | + | 0.776922i | \(0.283220\pi\) | |||||||
\(38\) | 4.26898 | − | 0.0860925i | 0.692520 | − | 0.0139661i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.82041 | − | 7.34403i | −1.23651 | − | 1.16119i | ||||
\(41\) | 10.2366 | − | 0.596211i | 1.59868 | − | 0.0931125i | 0.764507 | − | 0.644615i | \(-0.222982\pi\) |
0.834173 | + | 0.551502i | \(0.185945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.05296 | − | 2.11152i | 1.07557 | − | 0.322003i | 0.300434 | − | 0.953803i | \(-0.402869\pi\) |
0.775132 | + | 0.631799i | \(0.217683\pi\) | |||||||
\(44\) | −0.728918 | + | 0.115154i | −0.109889 | + | 0.0173601i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.03747 | + | 7.33267i | 0.742734 | + | 1.08114i | ||||
\(47\) | 2.93833 | − | 6.81180i | 0.428599 | − | 0.993604i | −0.557911 | − | 0.829901i | \(-0.688397\pi\) |
0.986510 | − | 0.163703i | \(-0.0523438\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.63746 | − | 5.46949i | 0.233923 | − | 0.781356i | ||||
\(50\) | 1.80664 | + | 13.1513i | 0.255498 | + | 1.85987i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.80895 | − | 3.76814i | −0.250856 | − | 0.522546i | ||||
\(53\) | −6.38357 | + | 3.68555i | −0.876850 | + | 0.506250i | −0.869619 | − | 0.493724i | \(-0.835635\pi\) |
−0.00723169 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.21203 | + | 0.699765i | 0.163430 | + | 0.0943563i | ||||
\(56\) | −3.42678 | + | 9.48325i | −0.457922 | + | 1.26725i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.15326 | − | 7.92645i | −0.807963 | − | 1.04079i | ||||
\(59\) | −2.92703 | − | 3.10247i | −0.381067 | − | 0.403908i | 0.508242 | − | 0.861214i | \(-0.330296\pi\) |
−0.889309 | + | 0.457307i | \(0.848814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.15413 | + | 0.134898i | −0.147771 | + | 0.0172719i | −0.189657 | − | 0.981850i | \(-0.560737\pi\) |
0.0418860 | + | 0.999122i | \(0.486663\pi\) | |||||||
\(62\) | −0.308278 | − | 3.92697i | −0.0391513 | − | 0.498726i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.13459 | − | 7.36032i | 0.391824 | − | 0.920040i | ||||
\(65\) | −1.82810 | + | 7.71336i | −0.226748 | + | 0.956725i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.04241 | + | 6.14618i | 0.493858 | + | 0.750875i | 0.993311 | − | 0.115466i | \(-0.0368360\pi\) |
−0.499453 | + | 0.866341i | \(0.666466\pi\) | |||||||
\(68\) | 10.3707 | − | 6.55876i | 1.25763 | − | 0.795366i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 16.3649 | − | 9.89349i | 1.95598 | − | 1.18250i | ||||
\(71\) | 0.398446 | + | 2.25970i | 0.0472869 | + | 0.268177i | 0.999280 | − | 0.0379425i | \(-0.0120804\pi\) |
−0.951993 | + | 0.306120i | \(0.900969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.219535 | − | 1.24504i | 0.0256946 | − | 0.145721i | −0.969261 | − | 0.246033i | \(-0.920873\pi\) |
0.994956 | + | 0.100312i | \(0.0319840\pi\) | |||||||
\(74\) | 0.106153 | + | 0.274312i | 0.0123400 | + | 0.0318882i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.83483 | − | 5.75297i | 0.210469 | − | 0.659910i | ||||
\(77\) | 0.152711 | − | 1.30652i | 0.0174030 | − | 0.148892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0782584 | + | 0.00455803i | 0.00880476 | + | 0.000512819i | 0.0625466 | − | 0.998042i | \(-0.480078\pi\) |
−0.0537419 | + | 0.998555i | \(0.517115\pi\) | |||||||
\(80\) | −13.4016 | + | 7.11218i | −1.49835 | + | 0.795165i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.87804 | − | 13.9730i | 0.428258 | − | 1.54306i | ||||
\(83\) | 0.294342 | − | 5.05366i | 0.0323083 | − | 0.554711i | −0.942852 | − | 0.333211i | \(-0.891868\pi\) |
0.975160 | − | 0.221500i | \(-0.0710953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.1137 | − | 2.70161i | −2.50704 | − | 0.293031i | ||||
\(86\) | 0.395692 | − | 10.4043i | 0.0426686 | − | 1.12192i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.178845 | + | 1.02819i | −0.0190649 | + | 0.109606i | ||||
\(89\) | 8.23009 | + | 1.45119i | 0.872387 | + | 0.153825i | 0.591880 | − | 0.806026i | \(-0.298386\pi\) |
0.280508 | + | 0.959852i | \(0.409497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.33742 | − | 1.29379i | 0.769171 | − | 0.135626i | ||||
\(92\) | 12.1152 | − | 3.39266i | 1.26310 | − | 0.353709i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.77476 | − | 7.04429i | −0.801905 | − | 0.726563i | ||||
\(95\) | −9.56793 | + | 6.29293i | −0.981649 | + | 0.645641i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4281 | − | 2.94552i | −1.26188 | − | 0.299072i | −0.455378 | − | 0.890298i | \(-0.650496\pi\) |
−0.806506 | + | 0.591226i | \(0.798644\pi\) | |||||||
\(98\) | −6.57243 | − | 4.69003i | −0.663915 | − | 0.473764i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.4270 | + | 3.58942i | 1.84270 | + | 0.358942i | ||||
\(101\) | −0.0948622 | − | 0.811598i | −0.00943914 | − | 0.0807570i | 0.987698 | − | 0.156375i | \(-0.0499810\pi\) |
−0.997137 | + | 0.0756184i | \(0.975907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.31110 | + | 6.89767i | −0.720384 | + | 0.679647i | −0.956386 | − | 0.292105i | \(-0.905644\pi\) |
0.236002 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(104\) | −5.86963 | + | 0.699839i | −0.575564 | + | 0.0686249i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.01679 | + | 10.2274i | 0.195888 | + | 0.993370i | ||||
\(107\) | 9.81977 | − | 17.0083i | 0.949313 | − | 1.64426i | 0.202436 | − | 0.979295i | \(-0.435114\pi\) |
0.746877 | − | 0.664963i | \(-0.231552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.261103 | + | 0.452244i | 0.0250091 | + | 0.0433171i | 0.878259 | − | 0.478185i | \(-0.158705\pi\) |
−0.853250 | + | 0.521502i | \(0.825372\pi\) | |||||||
\(110\) | 1.49022 | − | 1.30254i | 0.142087 | − | 0.124192i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.1271 | + | 8.91834i | 1.05141 | + | 0.842704i | ||||
\(113\) | −19.3462 | − | 5.79188i | −1.81994 | − | 0.544854i | −0.820306 | − | 0.571924i | \(-0.806197\pi\) |
−0.999634 | + | 0.0270702i | \(0.991382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.9089 | − | 9.45056i | −2.04301 | − | 0.881269i | ||||
\(116\) | −13.4196 | + | 4.61480i | −1.24598 | + | 0.428474i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.48943 | + | 2.50037i | −0.505343 | + | 0.230177i | ||||
\(119\) | 6.27309 | + | 20.9536i | 0.575054 | + | 1.92081i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.631677 | + | 10.8455i | 0.0574252 | + | 0.985952i | ||||
\(122\) | −0.346652 | + | 1.60631i | −0.0313844 | + | 0.145429i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.39671 | − | 1.38123i | −0.484639 | − | 0.124038i | ||||
\(125\) | −10.6951 | − | 12.7459i | −0.956598 | − | 1.14003i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.72655 | + | 3.24937i | −0.241942 | + | 0.288335i | −0.873327 | − | 0.487134i | \(-0.838042\pi\) |
0.631385 | + | 0.775469i | \(0.282487\pi\) | |||||||
\(128\) | −8.41925 | − | 7.55753i | −0.744163 | − | 0.667998i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.48856 | + | 5.97018i | 0.832202 | + | 0.523620i | ||||
\(131\) | −5.26366 | − | 12.2025i | −0.459888 | − | 1.06614i | −0.977578 | − | 0.210572i | \(-0.932467\pi\) |
0.517690 | − | 0.855568i | \(-0.326792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.99289 | + | 5.91471i | 0.779782 | + | 0.512871i | ||||
\(134\) | 10.0727 | − | 2.60284i | 0.870145 | − | 0.224851i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.04102 | − | 16.8762i | −0.346515 | − | 1.44712i | ||||
\(137\) | 8.19288 | + | 16.3134i | 0.699965 | + | 1.39374i | 0.909400 | + | 0.415922i | \(0.136541\pi\) |
−0.209435 | + | 0.977823i | \(0.567163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0551 | − | 7.48577i | −0.852866 | − | 0.634935i | 0.0793465 | − | 0.996847i | \(-0.474717\pi\) |
−0.932212 | + | 0.361912i | \(0.882124\pi\) | |||||||
\(140\) | −5.76612 | − | 26.4222i | −0.487326 | − | 2.23308i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.20641 | + | 0.498939i | 0.269076 | + | 0.0418700i | ||||
\(143\) | 0.724633 | − | 0.263745i | 0.0605969 | − | 0.0220555i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.2899 | + | 9.20477i | 2.10021 | + | 0.764414i | ||||
\(146\) | −1.56610 | − | 0.862559i | −0.129611 | − | 0.0713859i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.415632 | − | 0.0167709i | 0.0341647 | − | 0.00137856i | ||||
\(149\) | 1.62011 | − | 3.22591i | 0.132725 | − | 0.264277i | −0.817447 | − | 0.576004i | \(-0.804611\pi\) |
0.950172 | + | 0.311727i | \(0.100908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.22213 | + | 4.92682i | 0.424971 | + | 0.400939i | 0.868793 | − | 0.495176i | \(-0.164896\pi\) |
−0.443822 | + | 0.896115i | \(0.646378\pi\) | |||||||
\(152\) | −6.86168 | − | 5.08368i | −0.556555 | − | 0.412341i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.67890 | − | 0.801203i | −0.135290 | − | 0.0645628i | ||||
\(155\) | 6.30881 | + | 8.47420i | 0.506735 | + | 0.680664i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.89799 | − | 1.87186i | 0.630328 | − | 0.149390i | 0.0969799 | − | 0.995286i | \(-0.469082\pi\) |
0.533348 | + | 0.845896i | \(0.320934\pi\) | |||||||
\(158\) | 0.0418487 | − | 0.102660i | 0.00332930 | − | 0.00816716i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.39718 | + | 21.1857i | 0.268571 | + | 1.67488i | ||||
\(161\) | 22.4262i | 1.76743i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.68098i | − | 0.601621i | −0.953684 | − | 0.300810i | \(-0.902743\pi\) | ||
0.953684 | − | 0.300810i | \(-0.0972571\pi\) | |||||||
\(164\) | −16.9302 | − | 11.5732i | −1.32202 | − | 0.903718i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.62941 | − | 2.70244i | −0.514542 | − | 0.209750i | ||||
\(167\) | −0.436113 | + | 0.103361i | −0.0337474 | + | 0.00799828i | −0.247455 | − | 0.968899i | \(-0.579594\pi\) |
0.213707 | + | 0.976898i | \(0.431446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.15480 | − | 6.92410i | −0.396523 | − | 0.532623i | ||||
\(170\) | −14.1741 | + | 29.7015i | −1.08711 | + | 2.27800i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.7444 | − | 5.28223i | −1.04800 | − | 0.402766i | ||||
\(173\) | 5.36388 | + | 5.06056i | 0.407808 | + | 0.384747i | 0.862630 | − | 0.505835i | \(-0.168816\pi\) |
−0.454822 | + | 0.890582i | \(0.650297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.0185 | + | 29.9042i | −1.13529 | + | 2.26055i | ||||
\(176\) | 1.29445 | + | 0.709041i | 0.0975725 | + | 0.0534460i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.70175 | − | 10.3523i | 0.427364 | − | 0.775939i | ||||
\(179\) | −20.8808 | − | 7.59999i | −1.56070 | − | 0.568050i | −0.589807 | − | 0.807545i | \(-0.700796\pi\) |
−0.970898 | + | 0.239495i | \(0.923018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.8404 | + | 5.76543i | −1.17741 | + | 0.428541i | −0.855285 | − | 0.518158i | \(-0.826618\pi\) |
−0.322121 | + | 0.946698i | \(0.604396\pi\) | |||||||
\(182\) | 1.62009 | − | 10.4115i | 0.120089 | − | 0.771749i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.993422 | − | 17.7648i | 0.0732360 | − | 1.30964i | ||||
\(185\) | −0.632782 | − | 0.471088i | −0.0465230 | − | 0.0346351i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.01599 | + | 2.02301i | 0.0742966 | + | 0.147937i | ||||
\(188\) | −12.9796 | + | 7.18800i | −0.946635 | + | 0.524239i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.05191 | + | 15.6804i | 0.293957 | + | 1.13757i | ||||
\(191\) | −6.08575 | − | 4.00266i | −0.440349 | − | 0.289622i | 0.309910 | − | 0.950766i | \(-0.399701\pi\) |
−0.750259 | + | 0.661144i | \(0.770071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.19455 | + | 12.0423i | 0.373912 | + | 0.866826i | 0.996446 | + | 0.0842331i | \(0.0268440\pi\) |
−0.622534 | + | 0.782593i | \(0.713897\pi\) | |||||||
\(194\) | −9.61943 | + | 15.2884i | −0.690634 | + | 1.09764i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.27943 | + | 6.65420i | −0.662817 | + | 0.475300i | ||||
\(197\) | 11.4542 | − | 13.6505i | 0.816076 | − | 0.972561i | −0.183870 | − | 0.982950i | \(-0.558863\pi\) |
0.999946 | + | 0.0103894i | \(0.00330712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.13451 | − | 9.69433i | −0.576640 | − | 0.687213i | 0.396340 | − | 0.918104i | \(-0.370280\pi\) |
−0.972980 | + | 0.230891i | \(0.925836\pi\) | |||||||
\(200\) | 13.2215 | − | 23.0233i | 0.934902 | − | 1.62799i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.12958 | − | 0.243770i | −0.0794771 | − | 0.0171516i | ||||
\(203\) | −1.47080 | − | 25.2526i | −0.103230 | − | 1.77239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1546 | + | 37.2589i | 0.779070 | + | 2.60228i | ||||
\(206\) | 5.89221 | + | 12.9361i | 0.410530 | + | 0.901298i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.74455 | + | 8.17564i | −0.120963 | + | 0.566879i | ||||
\(209\) | 1.02293 | + | 0.441247i | 0.0707573 | + | 0.0305217i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.55626 | − | 1.06468i | −0.244823 | − | 0.0732953i | 0.162041 | − | 0.986784i | \(-0.448192\pi\) |
−0.406864 | + | 0.913489i | \(0.633378\pi\) | |||||||
\(212\) | 14.6097 | + | 1.97254i | 1.00340 | + | 0.135474i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.2785 | − | 20.9122i | −1.24949 | − | 1.42953i | ||||
\(215\) | 13.9624 | + | 24.1836i | 0.952229 | + | 1.64931i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.96488 | − | 8.59942i | 0.337038 | − | 0.583767i | ||||
\(218\) | 0.724557 | − | 0.142879i | 0.0490732 | − | 0.00967700i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.06260 | − | 2.58952i | −0.0716406 | − | 0.174585i | ||||
\(221\) | −9.32662 | + | 8.79921i | −0.627377 | + | 0.591899i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.09225 | − | 9.34481i | −0.0731426 | − | 0.625775i | −0.979240 | − | 0.202705i | \(-0.935027\pi\) |
0.906097 | − | 0.423070i | \(-0.139047\pi\) | |||||||
\(224\) | 17.0192 | − | 10.8188i | 1.13714 | − | 0.722859i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.5892 | + | 23.2474i | −1.10350 | + | 1.54640i | ||||
\(227\) | 4.88161 | + | 1.15696i | 0.324004 | + | 0.0767904i | 0.389399 | − | 0.921069i | \(-0.372683\pi\) |
−0.0653952 | + | 0.997859i | \(0.520831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.99822 | − | 2.62967i | 0.264210 | − | 0.173774i | −0.410491 | − | 0.911865i | \(-0.634643\pi\) |
0.674701 | + | 0.738091i | \(0.264272\pi\) | |||||||
\(230\) | −22.6566 | + | 25.0060i | −1.49393 | + | 1.64885i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0464631 | + | 20.0689i | 0.00305045 | + | 1.31759i | ||||
\(233\) | −9.17615 | + | 1.61800i | −0.601149 | + | 0.105999i | −0.465937 | − | 0.884818i | \(-0.654283\pi\) |
−0.135212 | + | 0.990817i | \(0.543172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.7108 | + | 4.88616i | 1.80765 | + | 0.318738i | ||||
\(236\) | 0.838960 | + | 8.48926i | 0.0546116 | + | 0.552604i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 30.9100 | + | 1.17556i | 2.00360 | + | 0.0762002i | ||||
\(239\) | 16.2720 | + | 1.90192i | 1.05255 | + | 0.123025i | 0.624730 | − | 0.780841i | \(-0.285209\pi\) |
0.427816 | + | 0.903866i | \(0.359283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.619928 | − | 10.6438i | 0.0399331 | − | 0.685625i | −0.917636 | − | 0.397422i | \(-0.869905\pi\) |
0.957569 | − | 0.288203i | \(-0.0930579\pi\) | |||||||
\(242\) | 14.8042 | + | 4.10873i | 0.951651 | + | 0.264119i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.99155 | + | 1.19772i | 0.127496 | + | 0.0766761i | ||||
\(245\) | 21.6188 | + | 1.25915i | 1.38117 | + | 0.0804442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.732544 | + | 6.26732i | −0.0466107 | + | 0.398780i | ||||
\(248\) | −4.31384 | + | 6.59207i | −0.273929 | + | 0.418597i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.9447 | + | 8.49212i | −1.38791 | + | 0.537089i | ||||
\(251\) | 3.47543 | − | 19.7101i | 0.219367 | − | 1.24409i | −0.653798 | − | 0.756669i | \(-0.726825\pi\) |
0.873165 | − | 0.487424i | \(-0.162063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.403057 | + | 2.28585i | 0.0253400 | + | 0.143710i | ||||
\(254\) | 3.10351 | + | 5.13354i | 0.194732 | + | 0.322107i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.9609 | + | 7.81614i | −0.872559 | + | 0.488509i | ||||
\(257\) | 6.90020 | + | 10.4912i | 0.430423 | + | 0.654426i | 0.983958 | − | 0.178400i | \(-0.0570921\pi\) |
−0.553536 | + | 0.832826i | \(0.686722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.170995 | + | 0.721484i | −0.0106251 | + | 0.0448308i | ||||
\(260\) | 12.3249 | − | 9.97242i | 0.764357 | − | 0.618463i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.7364 | + | 1.47085i | −1.15754 | + | 0.0908697i | ||||
\(263\) | −12.1229 | + | 1.41697i | −0.747531 | + | 0.0873739i | −0.481325 | − | 0.876542i | \(-0.659844\pi\) |
−0.266206 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.1863 | − | 20.3362i | −1.17860 | − | 1.24925i | ||||
\(266\) | 12.0242 | − | 9.33434i | 0.737252 | − | 0.572325i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.11749 | − | 14.6703i | 0.0682615 | − | 0.896131i | ||||
\(269\) | −13.4840 | − | 7.78500i | −0.822135 | − | 0.474660i | 0.0290174 | − | 0.999579i | \(-0.490762\pi\) |
−0.851152 | + | 0.524919i | \(0.824096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.8391 | − | 16.0729i | 1.69110 | − | 0.976360i | 0.737476 | − | 0.675373i | \(-0.236017\pi\) |
0.953628 | − | 0.300987i | \(-0.0973160\pi\) | |||||||
\(272\) | −24.4332 | − | 2.30045i | −1.48148 | − | 0.139485i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.5764 | − | 3.51354i | 1.54513 | − | 0.212261i | ||||
\(275\) | −0.993340 | + | 3.31799i | −0.0599007 | + | 0.200082i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.88948 | − | 11.3351i | 0.293781 | − | 0.681060i | −0.705847 | − | 0.708365i | \(-0.749433\pi\) |
0.999627 | + | 0.0273048i | \(0.00869247\pi\) | |||||||
\(278\) | −14.6122 | + | 10.0384i | −0.876380 | + | 0.602064i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −37.9977 | − | 4.35214i | −2.27079 | − | 0.260090i | ||||
\(281\) | −11.6621 | + | 3.49140i | −0.695702 | + | 0.208279i | −0.615079 | − | 0.788465i | \(-0.710876\pi\) |
−0.0806225 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.56653 | − | 0.0912401i | 0.0931206 | − | 0.00542366i | −0.0115212 | − | 0.999934i | \(-0.503667\pi\) |
0.104642 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(284\) | 2.13246 | − | 4.06357i | 0.126538 | − | 0.241129i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0219887 | − | 1.09033i | −0.00130022 | − | 0.0644727i | ||||
\(287\) | 28.0030 | − | 23.4973i | 1.65296 | − | 1.38700i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8127 | − | 13.2684i | −0.930157 | − | 0.780495i | ||||
\(290\) | 23.8721 | − | 29.6435i | 1.40182 | − | 1.74073i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.86984 | + | 1.70206i | −0.109424 | + | 0.0996056i | ||||
\(293\) | −1.49400 | + | 0.644447i | −0.0872802 | + | 0.0376490i | −0.439272 | − | 0.898354i | \(-0.644764\pi\) |
0.351992 | + | 0.936003i | \(0.385504\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.89008 | − | 13.5167i | 0.517600 | − | 0.786973i | ||||
\(296\) | 0.167413 | − | 0.563946i | 0.00973067 | − | 0.0327787i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.57753 | − | 3.64196i | −0.207240 | − | 0.210973i | ||||
\(299\) | −11.7485 | + | 5.90034i | −0.679436 | + | 0.341226i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6733 | − | 21.0530i | 0.903396 | − | 1.21347i | ||||
\(302\) | 8.97955 | − | 4.73878i | 0.516715 | − | 0.272686i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.93843 | + | 6.86152i | −0.570008 | + | 0.393535i | ||||
\(305\) | −1.50741 | − | 4.14158i | −0.0863141 | − | 0.237146i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.69558 | + | 4.65857i | −0.0967719 | + | 0.265879i | −0.978628 | − | 0.205641i | \(-0.934072\pi\) |
0.881856 | + | 0.471520i | \(0.156294\pi\) | |||||||
\(308\) | −1.83925 | + | 1.88107i | −0.104801 | + | 0.107184i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.2238 | − | 4.57278i | 0.807856 | − | 0.259716i | ||||
\(311\) | −21.5229 | − | 10.8092i | −1.22045 | − | 0.612933i | −0.282354 | − | 0.959310i | \(-0.591115\pi\) |
−0.938095 | + | 0.346377i | \(0.887412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.49585 | + | 3.70539i | −0.197597 | + | 0.209441i | −0.818594 | − | 0.574372i | \(-0.805246\pi\) |
0.620997 | + | 0.783813i | \(0.286728\pi\) | |||||||
\(314\) | 1.10246 | − | 11.4258i | 0.0622155 | − | 0.644795i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.118284 | − | 0.102905i | −0.00665401 | − | 0.00578887i | ||||
\(317\) | −10.7411 | + | 7.99645i | −0.603280 | + | 0.449125i | −0.854966 | − | 0.518683i | \(-0.826422\pi\) |
0.251686 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.603770 | − | 2.54751i | −0.0338046 | − | 0.142633i | ||||
\(320\) | 29.9069 | + | 5.13073i | 1.67185 | + | 0.286816i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.0154 | + | 10.2442i | 1.67269 | + | 0.570887i | ||||
\(323\) | −18.5240 | −1.03070 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.6175 | −1.08818 | ||||||||
\(326\) | −10.2803 | − | 3.50864i | −0.569372 | − | 0.194326i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −23.2233 | + | 17.3728i | −1.28229 | + | 0.959255i | ||||
\(329\) | −6.09913 | − | 25.7343i | −0.336256 | − | 1.41878i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.8006 | + | 19.9523i | −1.47309 | + | 1.09668i | −0.500064 | + | 0.865989i | \(0.666690\pi\) |
−0.973028 | + | 0.230687i | \(0.925903\pi\) | |||||||
\(332\) | −6.64526 | + | 7.63839i | −0.364706 | + | 0.419211i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.0608759 | + | 0.630912i | −0.00333098 | + | 0.0345219i | ||||
\(335\) | −19.1480 | + | 20.2957i | −1.04616 | + | 1.10887i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4222 | + | 10.2564i | 1.11247 | + | 0.558703i | 0.907494 | − | 0.420065i | \(-0.137993\pi\) |
0.204974 | + | 0.978767i | \(0.434289\pi\) | |||||||
\(338\) | −11.6220 | + | 3.73633i | −0.632152 | + | 0.203229i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.2781 | + | 32.5383i | 1.80476 | + | 1.76464i | ||||
\(341\) | 0.351504 | − | 0.965750i | 0.0190350 | − | 0.0522983i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.57371 | + | 4.32373i | 0.0849723 | + | 0.233460i | ||||
\(344\) | −13.3482 | + | 15.9827i | −0.719685 | + | 0.861731i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.22330 | − | 4.86742i | 0.495848 | − | 0.261674i | ||||
\(347\) | 2.31099 | − | 3.10420i | 0.124060 | − | 0.166642i | −0.735754 | − | 0.677249i | \(-0.763172\pi\) |
0.859814 | + | 0.510607i | \(0.170579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2338 | + | 5.64183i | −0.601332 | + | 0.302000i | −0.723300 | − | 0.690534i | \(-0.757376\pi\) |
0.121968 | + | 0.992534i | \(0.461079\pi\) | |||||||
\(350\) | 33.1637 | + | 33.7610i | 1.77268 | + | 1.80460i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.54028 | − | 1.40861i | 0.0820974 | − | 0.0750791i | ||||
\(353\) | 11.3170 | − | 17.2067i | 0.602344 | − | 0.915819i | −0.397655 | − | 0.917535i | \(-0.630176\pi\) |
0.999999 | + | 0.00171576i | \(0.000546142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.99143 | + | 3.44717i | −0.424141 | + | 0.182957i | ||||
\(356\) | −11.2511 | − | 12.3602i | −0.596307 | − | 0.655088i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.7102 | + | 24.4754i | −1.04171 | + | 1.29356i | ||||
\(359\) | 18.7882 | + | 15.7651i | 0.991601 | + | 0.832052i | 0.985799 | − | 0.167931i | \(-0.0537086\pi\) |
0.00580232 | + | 0.999983i | \(0.498153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.57173 | − | 6.35344i | 0.398512 | − | 0.334392i | ||||
\(362\) | 0.480671 | + | 23.8345i | 0.0252635 | + | 1.25271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.1947 | − | 6.92426i | −0.691592 | − | 0.362930i | ||||
\(365\) | 4.78717 | − | 0.278821i | 0.250572 | − | 0.0145941i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.46037 | + | 2.23349i | −0.389428 | + | 0.116587i | −0.475531 | − | 0.879699i | \(-0.657744\pi\) |
0.0861026 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(368\) | −23.3228 | − | 9.44452i | −1.21579 | − | 0.492330i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.919561 | + | 0.631729i | −0.0478057 | + | 0.0328420i | ||||
\(371\) | −10.4082 | + | 24.1290i | −0.540368 | + | 1.25271i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.70087 | − | 9.02152i | 0.139846 | − | 0.467117i | −0.859160 | − | 0.511707i | \(-0.829013\pi\) |
0.999005 | + | 0.0445906i | \(0.0141983\pi\) | |||||||
\(374\) | 3.17171 | − | 0.435710i | 0.164005 | − | 0.0225301i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.69145 | + | 20.6555i | 0.190372 | + | 1.06522i | ||||
\(377\) | 12.8423 | − | 7.41449i | 0.661411 | − | 0.381866i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00647 | + | 0.581088i | 0.0516991 | + | 0.0298485i | 0.525627 | − | 0.850715i | \(-0.323831\pi\) |
−0.473928 | + | 0.880564i | \(0.657164\pi\) | |||||||
\(380\) | 22.8377 | + | 1.73963i | 1.17155 | + | 0.0892409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.13714 | + | 6.31682i | −0.416332 | + | 0.323196i | ||||
\(383\) | −18.3800 | − | 19.4816i | −0.939172 | − | 0.995464i | 0.0608246 | − | 0.998148i | \(-0.480627\pi\) |
−0.999996 | + | 0.00268457i | \(0.999145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.95561 | − | 0.579228i | 0.252561 | − | 0.0295202i | ||||
\(386\) | 18.4904 | − | 1.45154i | 0.941137 | − | 0.0738817i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.0680 | + | 19.8584i | 0.815729 | + | 1.00816i | ||||
\(389\) | 2.27968 | − | 9.61872i | 0.115584 | − | 0.487688i | −0.884204 | − | 0.467101i | \(-0.845298\pi\) |
0.999788 | − | 0.0205871i | \(-0.00655353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.2083 | − | 32.2456i | −1.07255 | − | 1.63073i | ||||
\(392\) | 4.66723 | + | 15.4593i | 0.235731 | + | 0.780812i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.0378 | − | 21.5659i | −0.656834 | − | 1.08647i | ||||
\(395\) | 0.0516318 | + | 0.292818i | 0.00259788 | + | 0.0147333i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.49961 | − | 14.1760i | 0.125452 | − | 0.711472i | −0.855587 | − | 0.517659i | \(-0.826803\pi\) |
0.981039 | − | 0.193813i | \(-0.0620854\pi\) | |||||||
\(398\) | −16.6908 | + | 6.45896i | −0.836633 | + | 0.323758i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −24.7750 | − | 28.2127i | −1.23875 | − | 1.41064i | ||||
\(401\) | −0.316914 | + | 2.71138i | −0.0158259 | + | 0.135400i | −0.998841 | − | 0.0481231i | \(-0.984676\pi\) |
0.983015 | + | 0.183523i | \(0.0587501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.81129 | + | 0.338469i | 0.289481 | + | 0.0168603i | ||||
\(404\) | −0.842253 | + | 1.40049i | −0.0419037 | + | 0.0696769i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.4702 | − | 9.56678i | −1.71073 | − | 0.474792i | ||||
\(407\) | −0.00446216 | + | 0.0766123i | −0.000221181 | + | 0.00379753i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.5810 | + | 2.87310i | 1.21545 | + | 0.142066i | 0.699551 | − | 0.714583i | \(-0.253384\pi\) |
0.515900 | + | 0.856649i | \(0.327458\pi\) | |||||||
\(410\) | 54.9630 | + | 2.09034i | 2.71443 | + | 0.103234i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 20.0053 | − | 1.97704i | 0.985589 | − | 0.0974019i | ||||
\(413\) | −14.9749 | − | 2.64048i | −0.736866 | − | 0.129929i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9092 | − | 3.33420i | 0.928217 | − | 0.163670i | ||||
\(416\) | 10.1454 | + | 6.06952i | 0.497421 | + | 0.297583i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.05784 | − | 1.16753i | 0.0517405 | − | 0.0571059i | ||||
\(419\) | −7.64662 | + | 5.02926i | −0.373562 | + | 0.245696i | −0.722382 | − | 0.691494i | \(-0.756953\pi\) |
0.348820 | + | 0.937190i | \(0.386582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3360 | + | 3.63470i | 0.747430 | + | 0.177144i | 0.586644 | − | 0.809845i | \(-0.300449\pi\) |
0.160786 | + | 0.986989i | \(0.448597\pi\) | |||||||
\(422\) | −3.04946 | + | 4.27339i | −0.148445 | + | 0.208026i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.31369 | − | 18.6526i | 0.452313 | − | 0.905852i | ||||
\(425\) | −6.68581 | − | 57.2008i | −0.324310 | − | 2.77465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.01313 | + | 2.84275i | −0.145816 | + | 0.137570i | ||||
\(428\) | −36.3386 | + | 14.9114i | −1.75649 | + | 0.720772i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.7456 | − | 7.64044i | 1.86848 | − | 0.368455i | ||||
\(431\) | −13.6704 | + | 23.6778i | −0.658479 | + | 1.14052i | 0.322530 | + | 0.946559i | \(0.395467\pi\) |
−0.981009 | + | 0.193960i | \(0.937867\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5032 | − | 23.3882i | −0.648922 | − | 1.12397i | −0.983381 | − | 0.181556i | \(-0.941887\pi\) |
0.334458 | − | 0.942411i | \(-0.391447\pi\) | |||||||
\(434\) | −9.24160 | − | 10.5732i | −0.443611 | − | 0.507531i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.139744 | − | 1.03502i | 0.00669254 | − | 0.0495685i | ||||
\(437\) | −18.1950 | − | 5.44723i | −0.870386 | − | 0.260577i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.55305 | + | 2.82671i | 0.312760 | + | 0.134911i | 0.546673 | − | 0.837346i | \(-0.315894\pi\) |
−0.233913 | + | 0.972257i | \(0.575153\pi\) | |||||||
\(440\) | −3.95123 | + | 0.239313i | −0.188367 | + | 0.0114088i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.51658 | + | 16.5023i | 0.357527 | + | 0.784933i | ||||
\(443\) | 1.77205 | + | 5.91905i | 0.0841926 | + | 0.281223i | 0.989710 | − | 0.143086i | \(-0.0457024\pi\) |
−0.905518 | + | 0.424308i | \(0.860517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.84308 | + | 31.6445i | 0.0873704 | + | 1.50009i | ||||
\(446\) | −13.0061 | − | 2.80679i | −0.615857 | − | 0.132906i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.70562 | − | 27.7206i | −0.316811 | − | 1.30968i | ||||
\(449\) | 14.9846 | + | 17.8579i | 0.707166 | + | 0.842768i | 0.993317 | − | 0.115417i | \(-0.0368204\pi\) |
−0.286151 | + | 0.958185i | \(0.592376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.43197 | − | 2.89831i | 0.114517 | − | 0.136476i | ||||
\(452\) | 23.5367 | + | 32.8224i | 1.10707 | + | 1.54384i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.77839 | − | 6.00509i | 0.177329 | − | 0.281833i | ||||
\(455\) | 11.1932 | + | 25.9488i | 0.524746 | + | 1.21650i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.6280 | − | 18.1712i | −1.29238 | − | 0.850014i | −0.297868 | − | 0.954607i | \(-0.596275\pi\) |
−0.994515 | + | 0.104594i | \(0.966646\pi\) | |||||||
\(458\) | −1.69320 | − | 6.55248i | −0.0791182 | − | 0.306177i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 23.1188 | + | 41.7464i | 1.07792 | + | 1.94644i | ||||
\(461\) | −0.466380 | − | 0.928638i | −0.0217215 | − | 0.0432510i | 0.882510 | − | 0.470293i | \(-0.155852\pi\) |
−0.904232 | + | 0.427042i | \(0.859556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2791 | + | 13.6083i | 0.849501 | + | 0.632430i | 0.931314 | − | 0.364218i | \(-0.118664\pi\) |
−0.0818131 | + | 0.996648i | \(0.526071\pi\) | |||||||
\(464\) | 26.8817 | + | 9.10523i | 1.24795 | + | 0.422700i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.02608 | + | 13.0205i | −0.0938564 | + | 0.603164i | ||||
\(467\) | −10.0689 | + | 3.66477i | −0.465932 | + | 0.169585i | −0.564309 | − | 0.825564i | \(-0.690857\pi\) |
0.0983769 | + | 0.995149i | \(0.468635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.6441 | + | 8.96971i | 1.13796 | + | 0.414183i | ||||
\(470\) | 19.1979 | − | 34.8564i | 0.885532 | − | 1.60781i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.7453 | + | 2.75499i | 0.540623 | + | 0.126809i | ||||
\(473\) | 1.21917 | − | 2.42757i | 0.0560575 | − | 0.111620i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.6142 | − | 19.4485i | −0.945846 | − | 0.892360i | ||||
\(476\) | 15.6929 | − | 40.8332i | 0.719285 | − | 1.87159i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.97851 | − | 20.9097i | 0.456407 | − | 0.956389i | ||||
\(479\) | 7.69314 | + | 10.3337i | 0.351508 | + | 0.472158i | 0.942350 | − | 0.334630i | \(-0.108611\pi\) |
−0.590841 | + | 0.806788i | \(0.701204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.422957 | + | 0.100243i | −0.0192852 | + | 0.00457067i | ||||
\(482\) | −13.9625 | − | 5.69175i | −0.635975 | − | 0.259252i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.2617 | − | 17.9372i | 0.557349 | − | 0.815329i | ||||
\(485\) | − | 48.4454i | − | 2.19979i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 21.1052i | − | 0.956369i | −0.878259 | − | 0.478185i | \(-0.841295\pi\) | ||
0.878259 | − | 0.478185i | \(-0.158705\pi\) | |||||||
\(488\) | 2.51277 | − | 2.11840i | 0.113748 | − | 0.0958953i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.5606 | − | 28.3596i | 0.522256 | − | 1.28115i | ||||
\(491\) | 14.1512 | − | 3.35389i | 0.638633 | − | 0.151359i | 0.101472 | − | 0.994838i | \(-0.467645\pi\) |
0.537161 | + | 0.843480i | \(0.319497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.9960 | + | 34.9187i | 1.17080 | + | 1.57266i | ||||
\(494\) | 8.05360 | + | 3.84333i | 0.362349 | + | 0.172920i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.85234 | + | 8.78491i | 0.307679 | + | 0.394454i | ||||
\(497\) | 5.95002 | + | 5.61355i | 0.266895 | + | 0.251802i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.99823 | + | 9.95230i | −0.223752 | + | 0.445526i | −0.977298 | − | 0.211868i | \(-0.932045\pi\) |
0.753547 | + | 0.657395i | \(0.228342\pi\) | |||||||
\(500\) | 1.34166 | + | 33.2502i | 0.0600008 | + | 1.48699i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.7927 | − | 13.6551i | −1.10655 | − | 0.609455i | ||||
\(503\) | 22.2568 | + | 8.10083i | 0.992384 | + | 0.361198i | 0.786643 | − | 0.617408i | \(-0.211817\pi\) |
0.205741 | + | 0.978607i | \(0.434040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91242 | − | 1.06003i | 0.129601 | − | 0.0471709i | ||||
\(506\) | 3.24352 | + | 0.504713i | 0.144192 | + | 0.0224372i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.28844 | − | 1.80879i | 0.367740 | − | 0.0802520i | ||||
\(509\) | 21.4334 | + | 15.9566i | 0.950018 | + | 0.707262i | 0.956199 | − | 0.292719i | \(-0.0945600\pi\) |
−0.00618061 | + | 0.999981i | \(0.501967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.02277 | − | 4.02767i | −0.0894822 | − | 0.178174i | ||||
\(512\) | 4.08389 | + | 22.2558i | 0.180484 | + | 0.983578i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.1936 | − | 4.44292i | 0.758375 | − | 0.195969i | ||||
\(515\) | −31.8527 | − | 20.9498i | −1.40360 | − | 0.923159i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.08418 | − | 2.51341i | −0.0476822 | − | 0.110540i | ||||
\(518\) | 0.887530 | + | 0.558432i | 0.0389959 | + | 0.0245361i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.71721 | − | 21.0511i | −0.338422 | − | 0.923151i | ||||
\(521\) | 15.7683 | − | 18.7919i | 0.690823 | − | 0.823290i | −0.300632 | − | 0.953740i | \(-0.597198\pi\) |
0.991455 | + | 0.130450i | \(0.0416422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0537 | − | 17.9403i | −0.658253 | − | 0.784475i | 0.328881 | − | 0.944371i | \(-0.393329\pi\) |
−0.987134 | + | 0.159896i | \(0.948884\pi\) | |||||||
\(524\) | −6.59011 | + | 25.7488i | −0.287890 | + | 1.12484i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.64122 | + | 16.8727i | −0.158765 | + | 0.735684i | ||||
\(527\) | 0.993629 | + | 17.0600i | 0.0432832 | + | 0.743143i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.75293 | − | 15.8759i | −0.206649 | − | 0.690256i | ||||
\(530\) | −35.9824 | + | 16.3895i | −1.56298 | + | 0.711916i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.00054 | − | 20.3572i | −0.303512 | − | 0.882597i | ||||
\(533\) | 19.6773 | + | 8.48794i | 0.852317 | + | 0.367654i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 71.3629 | + | 21.3646i | 3.08529 | + | 0.923674i | ||||
\(536\) | −19.1244 | − | 8.19699i | −0.826047 | − | 0.354056i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.5790 | + | 14.4910i | −0.714769 | + | 0.624750i | ||||
\(539\) | −1.05331 | − | 1.82439i | −0.0453694 | − | 0.0785822i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2815 | − | 36.8606i | 0.914962 | − | 1.58476i | 0.108004 | − | 0.994150i | \(-0.465554\pi\) |
0.806957 | − | 0.590610i | \(-0.201113\pi\) | |||||||
\(542\) | −8.79533 | − | 44.6021i | −0.377792 | − | 1.91583i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.2399 | + | 31.6507i | −0.610531 | + | 1.35701i | ||||
\(545\) | −1.44072 | + | 1.35925i | −0.0617137 | + | 0.0582239i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.55324 | − | 30.3999i | −0.151926 | − | 1.29981i | −0.827061 | − | 0.562112i | \(-0.809989\pi\) |
0.675135 | − | 0.737694i | \(-0.264085\pi\) | |||||||
\(548\) | 6.98066 | − | 35.8367i | 0.298199 | − | 1.53087i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.98707 | + | 2.84514i | 0.170009 | + | 0.121317i | ||||
\(551\) | 20.8454 | + | 4.94046i | 0.888046 | + | 0.210471i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.233490 | − | 0.153569i | 0.00992900 | − | 0.00653041i | ||||
\(554\) | −12.9375 | − | 11.7220i | −0.549661 | − | 0.498018i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.76071 | + | 24.1426i | 0.286718 | + | 1.02387i | ||||
\(557\) | 6.28172 | − | 1.10764i | 0.266165 | − | 0.0469320i | −0.0389729 | − | 0.999240i | \(-0.512409\pi\) |
0.305138 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.1528 | + | 2.67184i | 0.640894 | + | 0.113007i | ||||
\(560\) | −23.1821 | + | 48.8683i | −0.979623 | + | 2.06506i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.654278 | + | 17.2035i | −0.0275991 | + | 0.725686i | ||||
\(563\) | −5.15676 | − | 0.602739i | −0.217332 | − | 0.0254024i | 0.00673023 | − | 0.999977i | \(-0.497858\pi\) |
−0.224062 | + | 0.974575i | \(0.571932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.45376 | − | 76.4681i | 0.187371 | − | 3.21704i | ||||
\(566\) | 0.593469 | − | 2.13834i | 0.0249454 | − | 0.0898810i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.46462 | − | 4.71033i | −0.187331 | − | 0.197641i | ||||
\(569\) | −35.7367 | − | 2.08142i | −1.49816 | − | 0.0872578i | −0.710643 | − | 0.703552i | \(-0.751596\pi\) |
−0.787516 | + | 0.616295i | \(0.788633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26983 | − | 10.8641i | 0.0531407 | − | 0.454647i | −0.940304 | − | 0.340335i | \(-0.889459\pi\) |
0.993445 | − | 0.114312i | \(-0.0364664\pi\) | |||||||
\(572\) | −1.46935 | − | 0.468630i | −0.0614368 | − | 0.0195944i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.6573 | − | 48.2129i | −0.778742 | − | 2.01237i | ||||
\(575\) | 10.2536 | − | 58.1511i | 0.427605 | − | 2.42507i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.60819 | + | 9.12049i | 0.0669498 | + | 0.379691i | 0.999811 | + | 0.0194545i | \(0.00619295\pi\) |
−0.932861 | + | 0.360237i | \(0.882696\pi\) | |||||||
\(578\) | −24.9817 | + | 15.1029i | −1.03910 | + | 0.628196i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −28.7705 | − | 45.4916i | −1.19463 | − | 1.88894i | ||||
\(581\) | −9.91694 | − | 15.0780i | −0.411424 | − | 0.625540i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.627225 | + | 2.64647i | −0.0259770 | + | 0.109606i | ||||
\(584\) | 1.42392 | + | 3.28011i | 0.0589221 | + | 0.135732i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.180082 | + | 2.29396i | 0.00743911 | + | 0.0947626i | ||||
\(587\) | 18.4325 | − | 2.15446i | 0.760793 | − | 0.0889239i | 0.273155 | − | 0.961970i | \(-0.411933\pi\) |
0.487638 | + | 0.873046i | \(0.337859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.77101 | + | 6.11691i | 0.237790 | + | 0.252043i | ||||
\(590\) | −14.0299 | − | 18.0729i | −0.577603 | − | 0.744051i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.678317 | − | 0.481675i | −0.0278787 | − | 0.0197967i | ||||
\(593\) | 5.66767 | + | 3.27223i | 0.232743 | + | 0.134374i | 0.611837 | − | 0.790984i | \(-0.290431\pi\) |
−0.379094 | + | 0.925358i | \(0.623764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −71.8470 | + | 41.4809i | −2.94544 | + | 1.70055i | ||||
\(596\) | −6.50863 | + | 3.12456i | −0.266604 | + | 0.127987i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.53038 | + | 18.4196i | 0.103475 | + | 0.753234i | ||||
\(599\) | −0.528274 | + | 1.76456i | −0.0215847 | + | 0.0720979i | −0.968103 | − | 0.250551i | \(-0.919388\pi\) |
0.946519 | + | 0.322649i | \(0.104573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.82735 | − | 11.1910i | 0.196912 | − | 0.456492i | −0.790940 | − | 0.611894i | \(-0.790408\pi\) |
0.987851 | + | 0.155402i | \(0.0496672\pi\) | |||||||
\(602\) | −21.0179 | − | 30.5942i | −0.856627 | − | 1.24693i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.24061 | − | 14.1830i | −0.0911690 | − | 0.577096i | ||||
\(605\) | −39.4753 | + | 11.8181i | −1.60490 | + | 0.480475i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.1472 | − | 2.04709i | 1.42658 | − | 0.0830890i | 0.672611 | − | 0.739996i | \(-0.265173\pi\) |
0.753972 | + | 0.656907i | \(0.228136\pi\) | |||||||
\(608\) | 4.64368 | + | 16.4360i | 0.188326 | + | 0.666568i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.23170 | + | 0.125675i | −0.252314 | + | 0.00508842i | ||||
\(611\) | 11.8769 | − | 9.96587i | 0.480486 | − | 0.403176i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.2490 | + | 22.8647i | 1.10058 | + | 0.923495i | 0.997464 | − | 0.0711743i | \(-0.0226747\pi\) |
0.103115 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(614\) | 5.46053 | + | 4.39740i | 0.220369 | + | 0.177464i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.67748 | + | 3.32094i | 0.0675875 | + | 0.133804i | ||||
\(617\) | 40.8912 | − | 17.6387i | 1.64622 | − | 0.710108i | 0.647564 | − | 0.762011i | \(-0.275788\pi\) |
0.998652 | + | 0.0519027i | \(0.0165286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2520 | − | 27.7508i | 0.733609 | − | 1.11540i | −0.255298 | − | 0.966862i | \(-0.582174\pi\) |
0.988907 | − | 0.148536i | \(-0.0474561\pi\) | |||||||
\(620\) | 0.377121 | − | 21.1260i | 0.0151455 | − | 0.848442i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.2987 | + | 23.8688i | −0.974288 | + | 0.957051i | ||||
\(623\) | 26.6240 | − | 13.3711i | 1.06667 | − | 0.535701i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.65991 | − | 12.9755i | 0.386396 | − | 0.519020i | ||||
\(626\) | 3.36243 | + | 6.37149i | 0.134390 | + | 0.254656i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.7888 | − | 6.69480i | −0.590136 | − | 0.267152i | ||||
\(629\) | −0.436436 | − | 1.19910i | −0.0174018 | − | 0.0478111i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5396 | + | 34.4522i | −0.499193 | + | 1.37152i | 0.392863 | + | 0.919597i | \(0.371485\pi\) |
−0.892056 | + | 0.451925i | \(0.850738\pi\) | |||||||
\(632\) | −0.191761 | + | 0.111306i | −0.00762784 | + | 0.00442751i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.79602 | + | 18.0287i | 0.230190 | + | 0.716012i | ||||
\(635\) | −14.3776 | − | 7.22068i | −0.570556 | − | 0.286544i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.18830 | − | 8.67909i | 0.324432 | − | 0.343878i | ||||
\(638\) | −3.68541 | − | 0.355600i | −0.145907 | − | 0.0140783i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.5284 | − | 37.6840i | 0.811455 | − | 1.48959i | ||||
\(641\) | 6.61816 | − | 4.92704i | 0.261402 | − | 0.194606i | −0.458477 | − | 0.888706i | \(-0.651605\pi\) |
0.719879 | + | 0.694100i | \(0.244197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0807862 | − | 0.340864i | −0.00318590 | − | 0.0134424i | 0.971429 | − | 0.237332i | \(-0.0762728\pi\) |
−0.974615 | + | 0.223889i | \(0.928125\pi\) | |||||||
\(644\) | 27.4219 | − | 35.4934i | 1.08057 | − | 1.39864i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.46167 | + | 24.7926i | −0.332920 | + | 0.975453i | ||||
\(647\) | −1.81191 | −0.0712337 | −0.0356168 | − | 0.999366i | \(-0.511340\pi\) | ||||
−0.0356168 | + | 0.999366i | \(0.511340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.57381 | −0.0617774 | ||||||||
\(650\) | −8.96118 | + | 26.2562i | −0.351487 | + | 1.02985i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.39199 | + | 12.1565i | −0.367819 | + | 0.476085i | ||||
\(653\) | 9.69506 | + | 40.9067i | 0.379397 | + | 1.60080i | 0.743029 | + | 0.669260i | \(0.233389\pi\) |
−0.363631 | + | 0.931543i | \(0.618463\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.4321 | − | 30.1006i | 1.57981 | − | 1.17613i | ||||
\(656\) | 12.6436 | + | 39.0182i | 0.493651 | + | 1.52340i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −37.2290 | − | 3.59218i | −1.45134 | − | 0.140038i | ||||
\(659\) | 30.5270 | − | 32.3568i | 1.18916 | − | 1.26044i | 0.231408 | − | 0.972857i | \(-0.425667\pi\) |
0.957756 | − | 0.287583i | \(-0.0928519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0414178 | − | 0.0208008i | −0.00161097 | − | 0.000809058i | 0.447994 | − | 0.894037i | \(-0.352139\pi\) |
−0.449604 | + | 0.893228i | \(0.648435\pi\) | |||||||
\(662\) | 14.4619 | + | 44.9842i | 0.562078 | + | 1.74836i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.18776 | + | 12.3833i | 0.278939 | + | 0.480564i | ||||
\(665\) | −13.9634 | + | 38.3641i | −0.541477 | + | 1.48770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.2661 | + | 41.9432i | 0.591104 | + | 1.62405i | ||||
\(668\) | 0.816610 | + | 0.369675i | 0.0315956 | + | 0.0143031i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.4172 | + | 34.8988i | 0.711517 | + | 1.34826i | ||||
\(671\) | −0.256030 | + | 0.343908i | −0.00988393 | + | 0.0132764i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0993 | + | 13.1076i | −1.00606 | + | 0.505260i | −0.873971 | − | 0.485978i | \(-0.838463\pi\) |
−0.132085 | + | 0.991238i | \(0.542167\pi\) | |||||||
\(674\) | 23.0561 | − | 22.6482i | 0.888086 | − | 0.872375i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.308138 | + | 17.2617i | −0.0118515 | + | 0.663911i | ||||
\(677\) | −24.0436 | + | 36.5565i | −0.924071 | + | 1.40498i | −0.00976724 | + | 0.999952i | \(0.503109\pi\) |
−0.914304 | + | 0.405029i | \(0.867261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.8099 | + | 18.0350i | −1.60452 | + | 0.692121i | ||||
\(680\) | 58.7509 | − | 29.6763i | 2.25299 | − | 1.13803i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.13200 | − | 0.911607i | −0.0433466 | − | 0.0349072i | ||||
\(683\) | 24.5285 | + | 20.5819i | 0.938557 | + | 0.787543i | 0.977334 | − | 0.211705i | \(-0.0679016\pi\) |
−0.0387764 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.0419 | + | 44.5074i | −2.02663 | + | 1.70054i | ||||
\(686\) | 6.50578 | − | 0.131202i | 0.248392 | − | 0.00500932i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.2940 | + | 25.1662i | 0.583079 | + | 0.959451i | ||||
\(689\) | −15.3790 | + | 0.895725i | −0.585893 | + | 0.0341244i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.8395 | + | 10.1309i | −1.28732 | + | 0.385397i | −0.856080 | − | 0.516843i | \(-0.827107\pi\) |
−0.431235 | + | 0.902240i | \(0.641922\pi\) | |||||||
\(692\) | −2.30143 | − | 14.5680i | −0.0874872 | − | 0.553791i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.09903 | − | 4.51103i | −0.117638 | − | 0.171236i | ||||
\(695\) | 18.8326 | − | 43.6589i | 0.714361 | − | 1.65607i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0430 | + | 60.2679i | −0.683428 | + | 2.28281i | ||||
\(698\) | 2.41951 | + | 17.6126i | 0.0915799 | + | 0.666646i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 60.3351 | − | 28.9647i | 2.28045 | − | 1.09476i | ||||
\(701\) | 28.7233 | − | 16.5834i | 1.08487 | − | 0.626347i | 0.152660 | − | 0.988279i | \(-0.451216\pi\) |
0.932205 | + | 0.361932i | \(0.117883\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.543827 | − | 0.313978i | −0.0205108 | − | 0.0118419i | ||||
\(704\) | −1.18170 | − | 2.70498i | −0.0445369 | − | 0.101948i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.8600 | − | 23.0067i | −0.672170 | − | 0.865870i | ||||
\(707\) | −1.99906 | − | 2.11888i | −0.0751824 | − | 0.0796887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.4678 | − | 1.92481i | 0.618460 | − | 0.0722877i | 0.198907 | − | 0.980018i | \(-0.436261\pi\) |
0.419553 | + | 0.907731i | \(0.362187\pi\) | |||||||
\(710\) | 0.963262 | + | 12.2705i | 0.0361506 | + | 0.460502i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21.6824 | + | 9.41248i | −0.812583 | + | 0.352748i | ||||
\(713\) | −4.04074 | + | 17.0492i | −0.151327 | + | 0.638498i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.60727 | + | 2.44373i | 0.0601083 | + | 0.0913902i | ||||
\(716\) | 23.7545 | + | 37.5605i | 0.887749 | + | 1.40370i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.6826 | − | 17.9448i | 1.10774 | − | 0.669693i | ||||
\(719\) | 2.85237 | + | 16.1766i | 0.106375 | + | 0.603284i | 0.990662 | + | 0.136340i | \(0.0435340\pi\) |
−0.884287 | + | 0.466944i | \(0.845355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.22238 | + | 35.2889i | −0.231734 | + | 1.31423i | ||||
\(722\) | −5.04476 | − | 13.0363i | −0.187746 | − | 0.485161i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32.1199 | + | 10.2442i | 1.19373 | + | 0.380722i | ||||
\(725\) | −7.73212 | + | 66.1526i | −0.287164 | + | 2.45684i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.9318 | − | 1.85982i | −1.18429 | − | 0.0689768i | −0.545331 | − | 0.838221i | \(-0.683596\pi\) |
−0.638955 | + | 0.769244i | \(0.720633\pi\) | |||||||
\(728\) | −15.2948 | + | 14.4970i | −0.566863 | + | 0.537294i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.81358 | − | 6.53455i | 0.0671237 | − | 0.241854i | ||||
\(731\) | −2.62638 | + | 45.0932i | −0.0971402 | + | 1.66783i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.3169 | + | 2.25782i | 0.713485 | + | 0.0833944i | 0.465089 | − | 0.885264i | \(-0.346022\pi\) |
0.248396 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(734\) | −0.418549 | + | 11.0053i | −0.0154489 | + | 0.406212i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.2944 | + | 26.9013i | −0.858643 | + | 0.991593i | ||||
\(737\) | 2.67312 | + | 0.471343i | 0.0984656 | + | 0.0173621i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5280 | + | 2.56167i | −0.534420 | + | 0.0942326i | −0.434344 | − | 0.900747i | \(-0.643020\pi\) |
−0.100076 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(740\) | 0.425459 | + | 1.51932i | 0.0156402 | + | 0.0558513i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.5400 | + | 24.9525i | 1.01103 | + | 0.916035i | ||||
\(743\) | 1.61301 | − | 1.06090i | 0.0591758 | − | 0.0389205i | −0.519576 | − | 0.854424i | \(-0.673910\pi\) |
0.578752 | + | 0.815503i | \(0.303540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3231 | + | 3.15764i | 0.488122 | + | 0.115687i | ||||
\(746\) | −10.8407 | − | 7.73586i | −0.396908 | − | 0.283230i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.865666 | − | 4.44407i | 0.0316519 | − | 0.162491i | ||||
\(749\) | −8.12828 | − | 69.5418i | −0.297001 | − | 2.54100i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.4272 | − | 17.3851i | 0.672417 | − | 0.634393i | −0.272326 | − | 0.962205i | \(-0.587793\pi\) |
0.944743 | + | 0.327812i | \(0.106311\pi\) | |||||||
\(752\) | 29.3317 | + | 4.49468i | 1.06962 | + | 0.163904i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.05732 | − | 20.5751i | −0.147759 | − | 0.749302i | ||||
\(755\) | −13.6157 | + | 23.5831i | −0.495526 | + | 0.858277i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.88889 | − | 17.1281i | −0.359418 | − | 0.622530i | 0.628446 | − | 0.777853i | \(-0.283691\pi\) |
−0.987864 | + | 0.155324i | \(0.950358\pi\) | |||||||
\(758\) | 1.23749 | − | 1.08164i | 0.0449476 | − | 0.0392868i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.7605 | − | 29.7715i | 0.462871 | − | 1.07992i | ||||
\(761\) | −9.77015 | − | 2.92499i | −0.354168 | − | 0.106031i | 0.104777 | − | 0.994496i | \(-0.466587\pi\) |
−0.458944 | + | 0.888465i | \(0.651772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.70942 | + | 0.737371i | 0.0618851 | + | 0.0266946i | ||||
\(764\) | 4.73747 | + | 13.7763i | 0.171396 | + | 0.498410i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.4702 | + | 15.7008i | −1.24546 | + | 0.567291i | ||||
\(767\) | −2.55661 | − | 8.53968i | −0.0923140 | − | 0.308350i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.97182 | − | 51.0242i | −0.107167 | − | 1.83998i | −0.441190 | − | 0.897413i | \(-0.645444\pi\) |
0.334024 | − | 0.942565i | \(-0.391593\pi\) | |||||||
\(770\) | 1.48846 | − | 6.89722i | 0.0536404 | − | 0.248559i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.50359 | − | 25.4108i | 0.234069 | − | 0.914554i | ||||
\(773\) | 24.5742 | + | 29.2863i | 0.883871 | + | 1.05336i | 0.998204 | + | 0.0599139i | \(0.0190826\pi\) |
−0.114333 | + | 0.993443i | \(0.536473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.8057 | + | 20.0283i | −0.603679 | + | 0.719437i | ||||
\(776\) | 33.9185 | − | 12.4343i | 1.21760 | − | 0.446366i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8324 | − | 7.44493i | −0.424213 | − | 0.266914i | ||||
\(779\) | 12.2622 | + | 28.4270i | 0.439340 | + | 1.01850i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.707361 | + | 0.465239i | 0.0253114 | + | 0.0166476i | ||||
\(782\) | −52.8457 | + | 13.6557i | −1.88976 | + | 0.488326i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.8228 | + | 0.815080i | 0.815101 | + | 0.0291100i | ||||
\(785\) | 13.8171 | + | 27.5121i | 0.493152 | + | 0.981947i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7469 | − | 16.9344i | −0.810838 | − | 0.603647i | 0.109849 | − | 0.993948i | \(-0.464963\pi\) |
−0.920687 | + | 0.390302i | \(0.872371\pi\) | |||||||
\(788\) | −34.8196 | + | 7.59867i | −1.24040 | + | 0.270692i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.415496 | + | 0.0646539i | 0.0147827 | + | 0.00230028i | ||||
\(791\) | −67.6523 | + | 24.6234i | −2.40544 | + | 0.875509i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.28200 | − | 0.830581i | −0.0810362 | − | 0.0294948i | ||||
\(794\) | −17.8314 | − | 9.82103i | −0.632814 | − | 0.348535i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.02044 | + | 25.2895i | 0.0361686 | + | 0.896363i | ||||
\(797\) | 6.09784 | − | 12.1418i | 0.215997 | − | 0.430085i | −0.759375 | − | 0.650654i | \(-0.774495\pi\) |
0.975371 | + | 0.220569i | \(0.0707913\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.1063 | + | 31.2342i | 1.17122 | + | 1.10499i | ||||
\(800\) | −49.0773 | + | 20.2716i | −1.73514 | + | 0.716709i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.48416 | + | 1.66271i | 0.123030 | + | 0.0587122i | ||||
\(803\) | −0.278564 | − | 0.374176i | −0.00983031 | − | 0.0132044i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −82.7693 | + | 19.6167i | −2.91723 | + | 0.691397i | ||||
\(806\) | 3.10758 | − | 7.62326i | 0.109460 | − | 0.268518i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.48969 | + | 1.76702i | 0.0524071 | + | 0.0621634i | ||||
\(809\) | − | 16.0043i | − | 0.562683i | −0.959608 | − | 0.281341i | \(-0.909221\pi\) | ||
0.959608 | − | 0.281341i | \(-0.0907793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.6868i | − | 0.515725i | −0.966182 | − | 0.257862i | \(-0.916982\pi\) | ||
0.966182 | − | 0.257862i | \(-0.0830181\pi\) | |||||||
\(812\) | −28.5501 | + | 41.7652i | −1.00191 | + | 1.46567i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.100500 | + | 0.0409684i | 0.00352253 | + | 0.00143594i | ||||
\(815\) | 28.3485 | − | 6.71871i | 0.993004 | − | 0.235346i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2739 | + | 17.8299i | 0.464394 | + | 0.623789i | ||||
\(818\) | 15.0739 | − | 31.5869i | 0.527046 | − | 1.10441i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.9046 | − | 72.6081i | 0.974472 | − | 2.53559i | ||||
\(821\) | 7.19381 | + | 6.78701i | 0.251066 | + | 0.236868i | 0.801477 | − | 0.598025i | \(-0.204048\pi\) |
−0.550412 | + | 0.834893i | \(0.685529\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.12742 | + | 4.23604i | −0.0741571 | + | 0.147659i | −0.927656 | − | 0.373435i | \(-0.878180\pi\) |
0.853499 | + | 0.521094i | \(0.174476\pi\) | |||||||
\(824\) | 6.49224 | − | 27.6783i | 0.226168 | − | 0.964221i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.3745 | + | 18.8363i | −0.360975 | + | 0.655400i | ||||
\(827\) | −35.4582 | − | 12.9057i | −1.23300 | − | 0.448776i | −0.358377 | − | 0.933577i | \(-0.616670\pi\) |
−0.874624 | + | 0.484801i | \(0.838892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.4864 | + | 8.91232i | −0.850448 | + | 0.309538i | −0.730223 | − | 0.683209i | \(-0.760584\pi\) |
−0.120225 | + | 0.992747i | \(0.538362\pi\) | |||||||
\(830\) | 4.17513 | − | 26.8313i | 0.144921 | − | 0.931328i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.7579 | − | 10.8062i | 0.442301 | − | 0.374638i | ||||
\(833\) | 28.0972 | + | 20.9176i | 0.973511 | + | 0.724752i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.762954 | − | 1.51917i | −0.0264031 | − | 0.0525729i | ||||
\(836\) | −1.07942 | − | 1.94914i | −0.0373325 | − | 0.0674125i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.23826 | + | 12.5317i | 0.111864 | + | 0.432899i | ||||
\(839\) | 15.7619 | + | 10.3667i | 0.544160 | + | 0.357900i | 0.791635 | − | 0.610995i | \(-0.209230\pi\) |
−0.247475 | + | 0.968894i | \(0.579601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.45457 | − | 19.5999i | −0.291537 | − | 0.675858i | ||||
\(842\) | 11.8701 | − | 18.8655i | 0.409072 | − | 0.650148i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.32657 | + | 6.03349i | 0.148927 | + | 0.207681i | ||||
\(845\) | 21.0460 | − | 25.0817i | 0.724005 | − | 0.862836i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8950 | + | 29.6688i | 0.855404 | + | 1.01943i | ||||
\(848\) | −20.7104 | − | 20.9860i | −0.711198 | − | 0.720662i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −79.6121 | − | 17.1808i | −2.73067 | − | 0.589295i | ||||
\(851\) | −0.0760743 | − | 1.30615i | −0.00260779 | − | 0.0447741i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.54855 | + | 5.17251i | 0.0530213 | + | 0.177104i | 0.980399 | − | 0.197024i | \(-0.0631276\pi\) |
−0.927377 | + | 0.374127i | \(0.877942\pi\) | |||||||
\(854\) | 2.42837 | + | 5.33136i | 0.0830970 | + | 0.182435i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.35827 | + | 55.4474i | 0.114783 | + | 1.89515i | ||||
\(857\) | −31.1800 | − | 13.4498i | −1.06509 | − | 0.459435i | −0.209885 | − | 0.977726i | \(-0.567309\pi\) |
−0.855204 | + | 0.518291i | \(0.826568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.5742 | − | 9.45269i | −1.07730 | − | 0.322522i | −0.301476 | − | 0.953474i | \(-0.597479\pi\) |
−0.775822 | + | 0.630952i | \(0.782664\pi\) | |||||||
\(860\) | 7.47279 | − | 55.3475i | 0.254820 | − | 1.88733i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.4460 | + | 29.1125i | 0.866694 | + | 0.991575i | ||||
\(863\) | −16.8495 | − | 29.1842i | −0.573563 | − | 0.993441i | −0.996196 | − | 0.0871400i | \(-0.972227\pi\) |
0.422633 | − | 0.906301i | \(-0.361106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.9853 | + | 24.2233i | −0.475515 | + | 0.823616i | ||||
\(866\) | −37.4712 | + | 7.38914i | −1.27332 | + | 0.251093i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.3728 | + | 7.53923i | −0.623614 | + | 0.255898i | ||||
\(869\) | 0.0210390 | − | 0.0198493i | 0.000713700 | − | 0.000673342i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.78485 | + | 15.2704i | 0.0604773 | + | 0.517416i | ||||
\(872\) | −1.32145 | − | 0.659828i | −0.0447498 | − | 0.0223446i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.6020 | + | 21.8641i | −0.527747 | + | 0.739564i | ||||
\(875\) | −57.7180 | − | 13.6794i | −1.95123 | − | 0.462449i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.3803 | + | 28.5317i | −1.46485 | + | 0.963445i | −0.468031 | + | 0.883712i | \(0.655037\pi\) |
−0.996816 | + | 0.0797337i | \(0.974593\pi\) | |||||||
\(878\) | 6.77670 | − | 7.47942i | 0.228702 | − | 0.252418i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.48461 | + | 5.39767i | −0.0500461 | + | 0.181956i | ||||
\(881\) | −28.2935 | + | 4.98890i | −0.953232 | + | 0.168080i | −0.628573 | − | 0.777751i | \(-0.716361\pi\) |
−0.324659 | + | 0.945831i | \(0.605249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5035 | − | 4.49695i | −0.858260 | − | 0.151334i | −0.272835 | − | 0.962061i | \(-0.587961\pi\) |
−0.585425 | + | 0.810727i | \(0.699072\pi\) | |||||||
\(884\) | 25.5203 | − | 2.52207i | 0.858342 | − | 0.0848265i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.73158 | + | 0.332077i | 0.293343 | + | 0.0111563i | ||||
\(887\) | −10.1567 | − | 1.18715i | −0.341028 | − | 0.0398604i | −0.0561446 | − | 0.998423i | \(-0.517881\pi\) |
−0.284883 | + | 0.958562i | \(0.591955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.879262 | + | 15.0963i | −0.0294895 | + | 0.506315i | ||||
\(890\) | 43.1951 | + | 11.9883i | 1.44790 | + | 0.401848i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.69778 | + | 16.1254i | −0.324706 | + | 0.539917i | ||||
\(893\) | 22.3604 | + | 1.30234i | 0.748262 | + | 0.0435813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.78470 | − | 83.7134i | 0.327066 | − | 2.79823i | ||||
\(896\) | −40.1646 | − | 3.68781i | −1.34181 | − | 0.123201i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.7461 | − | 11.8981i | 1.02601 | − | 0.397043i | ||||
\(899\) | 3.43185 | − | 19.4630i | 0.114459 | − | 0.649127i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.85307 | − | 44.5369i | −0.261624 | − | 1.48374i | ||||
\(902\) | −2.76821 | − | 4.57891i | −0.0921712 | − | 0.152461i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 54.6813 | − | 16.5086i | 1.81867 | − | 0.549066i | ||||
\(905\) | −35.1346 | − | 53.4196i | −1.16791 | − | 1.77573i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.5008 | + | 44.3062i | −0.348672 | + | 1.47116i | 0.462639 | + | 0.886547i | \(0.346903\pi\) |
−0.811311 | + | 0.584615i | \(0.801246\pi\) | |||||||
\(908\) | −6.31131 | − | 7.80014i | −0.209448 | − | 0.258857i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 39.8431 | − | 3.12779i | 1.32079 | − | 0.103685i | ||||
\(911\) | −46.9874 | + | 5.49204i | −1.55676 | + | 0.181959i | −0.850493 | − | 0.525986i | \(-0.823696\pi\) |
−0.706267 | + | 0.707945i | \(0.749622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.28180 | − | 1.35863i | −0.0424214 | − | 0.0449640i | ||||
\(914\) | −36.9409 | + | 28.6770i | −1.22190 | + | 0.948551i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.54335 | − | 0.726951i | −0.315321 | − | 0.0240191i | ||||
\(917\) | −41.0296 | − | 23.6884i | −1.35492 | − | 0.782261i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.4935 | − | 15.8734i | 0.906928 | − | 0.523615i | 0.0274862 | − | 0.999622i | \(-0.491250\pi\) |
0.879441 | + | 0.476007i | \(0.157916\pi\) | |||||||
\(920\) | 66.4344 | − | 11.8728i | 2.19028 | − | 0.391435i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.45594 | + | 0.200008i | −0.0479487 | + | 0.00658691i | ||||
\(923\) | −1.37535 | + | 4.59400i | −0.0452703 | + | 0.151213i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.773263 | − | 1.79263i | 0.0254247 | − | 0.0589412i | ||||
\(926\) | 26.5632 | − | 18.2487i | 0.872922 | − | 0.599688i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.4660 | − | 31.8194i | 0.803135 | − | 1.04452i | ||||
\(929\) | 46.6009 | − | 13.9514i | 1.52893 | − | 0.457730i | 0.591614 | − | 0.806221i | \(-0.298491\pi\) |
0.937312 | + | 0.348491i | \(0.113306\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.2087 | − | 1.00229i | 0.563992 | − | 0.0328488i | ||||
\(932\) | 16.5013 | + | 8.65945i | 0.540518 | + | 0.283650i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.305536 | + | 15.1503i | 0.00999746 | + | 0.495733i | ||||
\(935\) | −6.57767 | + | 5.51932i | −0.215113 | + | 0.180501i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2580 | + | 16.1594i | 0.629132 | + | 0.527904i | 0.900659 | − | 0.434527i | \(-0.143084\pi\) |
−0.271527 | + | 0.962431i | \(0.587529\pi\) | |||||||
\(938\) | 23.2624 | − | 28.8865i | 0.759546 | − | 0.943178i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −37.8826 | − | 41.6169i | −1.23559 | − | 1.35739i | ||||
\(941\) | −34.8606 | + | 15.0374i | −1.13642 | + | 0.490205i | −0.879345 | − | 0.476186i | \(-0.842019\pi\) |
−0.257078 | + | 0.966391i | \(0.582760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.4453 | + | 53.8919i | −1.15426 | + | 1.75496i | ||||
\(944\) | 9.05253 | − | 14.4616i | 0.294635 | − | 0.470684i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.69216 | − | 2.74065i | −0.0875298 | − | 0.0891062i | ||||
\(947\) | 5.05797 | − | 2.54021i | 0.164362 | − | 0.0825457i | −0.364716 | − | 0.931119i | \(-0.618834\pi\) |
0.529078 | + | 0.848573i | \(0.322538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.57781 | − | 2.11936i | 0.0512178 | − | 0.0687974i | ||||
\(950\) | −35.4466 | + | 18.7063i | −1.15004 | + | 0.606911i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −47.4830 | − | 39.6560i | −1.53893 | − | 1.28526i | ||||
\(953\) | 11.0342 | + | 30.3161i | 0.357432 | + | 0.982035i | 0.979917 | + | 0.199404i | \(0.0639006\pi\) |
−0.622486 | + | 0.782631i | \(0.713877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.44944 | − | 25.9621i | 0.305777 | − | 0.840114i | ||||
\(956\) | −23.4276 | − | 22.9068i | −0.757704 | − | 0.740859i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.3449 | − | 5.57618i | 0.560388 | − | 0.180158i | ||||
\(959\) | 58.1574 | + | 29.2077i | 1.87800 | + | 0.943167i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.9496 | + | 16.9056i | −0.514502 | + | 0.545341i | ||||
\(962\) | −0.0590395 | + | 0.611879i | −0.00190351 | + | 0.0197278i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.9959 | + | 16.0876i | −0.450778 | + | 0.518146i | ||||
\(965\) | −39.9013 | + | 29.7054i | −1.28447 | + | 0.956251i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.73696 | + | 28.4255i | 0.216646 | + | 0.914101i | 0.967346 | + | 0.253458i | \(0.0815681\pi\) |
−0.750700 | + | 0.660643i | \(0.770284\pi\) | |||||||
\(968\) | −18.4063 | − | 24.6048i | −0.591600 | − | 0.790828i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −64.8398 | − | 22.1297i | −2.08188 | − | 0.710542i | ||||
\(971\) | −23.4277 | −0.751829 | −0.375915 | − | 0.926654i | \(-0.622671\pi\) | ||||
−0.375915 | + | 0.926654i | \(0.622671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.6898 | −1.43269 | ||||||||
\(974\) | −28.2474 | − | 9.64079i | −0.905106 | − | 0.308911i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.68746 | − | 4.33079i | −0.0540142 | − | 0.138625i | ||||
\(977\) | −2.82117 | − | 11.9035i | −0.0902572 | − | 0.380825i | 0.909104 | − | 0.416570i | \(-0.136768\pi\) |
−0.999361 | + | 0.0357446i | \(0.988620\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47341 | − | 1.84138i | 0.0790504 | − | 0.0588509i | ||||
\(980\) | −32.6758 | − | 28.4274i | −1.04379 | − | 0.908080i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.97533 | − | 20.4721i | 0.0630352 | − | 0.653290i | ||||
\(983\) | −26.0766 | + | 27.6396i | −0.831715 | + | 0.881566i | −0.994461 | − | 0.105102i | \(-0.966483\pi\) |
0.162747 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60.3998 | + | 30.3339i | 1.92450 | + | 0.966519i | ||||
\(986\) | 58.6104 | − | 18.8426i | 1.86653 | − | 0.600069i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.82280 | − | 9.02339i | 0.280691 | − | 0.287072i | ||||
\(989\) | −15.8400 | + | 43.5202i | −0.503684 | + | 1.38386i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9022 | − | 46.4384i | −0.536916 | − | 1.47517i | −0.850690 | − | 0.525668i | \(-0.823816\pi\) |
0.313774 | − | 0.949498i | \(-0.398407\pi\) | |||||||
\(992\) | 14.8879 | − | 5.15831i | 0.472692 | − | 0.163776i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.2312 | − | 5.39931i | 0.324513 | − | 0.171256i | ||||
\(995\) | 28.6638 | − | 38.5022i | 0.908704 | − | 1.22060i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.96485 | − | 4.50232i | 0.283920 | − | 0.142590i | −0.301140 | − | 0.953580i | \(-0.597367\pi\) |
0.585060 | + | 0.810990i | \(0.301071\pi\) | |||||||
\(998\) | 11.0371 | + | 11.2359i | 0.349372 | + | 0.355665i | ||||
\(999\) | 0 | 0 |
(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 | 972.2.p.a.251.30 | 936 | ||
3.2 | odd | 2 | 324.2.p.a.83.23 | ✓ | 936 | ||
4.3 | odd | 2 | inner | 972.2.p.a.251.29 | 936 | ||
12.11 | even | 2 | 324.2.p.a.83.24 | yes | 936 | ||
81.40 | even | 27 | 324.2.p.a.203.24 | yes | 936 | ||
81.41 | odd | 54 | inner | 972.2.p.a.395.29 | 936 | ||
324.203 | even | 54 | inner | 972.2.p.a.395.30 | 936 | ||
324.283 | odd | 54 | 324.2.p.a.203.23 | yes | 936 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.2.p.a.83.23 | ✓ | 936 | 3.2 | odd | 2 | ||
324.2.p.a.83.24 | yes | 936 | 12.11 | even | 2 | ||
324.2.p.a.203.23 | yes | 936 | 324.283 | odd | 54 | ||
324.2.p.a.203.24 | yes | 936 | 81.40 | even | 27 | ||
972.2.p.a.251.29 | 936 | 4.3 | odd | 2 | inner | ||
972.2.p.a.251.30 | 936 | 1.1 | even | 1 | trivial | ||
972.2.p.a.395.29 | 936 | 81.41 | odd | 54 | inner | ||
972.2.p.a.395.30 | 936 | 324.203 | even | 54 | inner |