Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(33,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.i (of order \(16\), degree \(8\), 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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{16})\) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Character | \(\chi\) | \(=\) | 512.97 |
Dual form | 512.2.i.b.417.3 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.152968 | − | 0.769021i | −0.0883160 | − | 0.443995i | −0.999489 | − | 0.0319702i | \(-0.989822\pi\) |
0.911173 | − | 0.412024i | \(-0.135178\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.78737 | − | 1.86246i | 1.24655 | − | 0.832919i | 0.255553 | − | 0.966795i | \(-0.417742\pi\) |
0.990998 | + | 0.133876i | \(0.0427425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.13672 | − | 1.29927i | −1.18557 | − | 0.491078i | −0.299258 | − | 0.954172i | \(-0.596739\pi\) |
−0.886309 | + | 0.463094i | \(0.846739\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.20364 | − | 0.912779i | 0.734548 | − | 0.304260i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79402 | + | 0.356853i | 0.540918 | + | 0.107595i | 0.457985 | − | 0.888960i | \(-0.348571\pi\) |
0.0829328 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34710 | − | 2.90464i | −1.20567 | − | 0.805603i | −0.220200 | − | 0.975455i | \(-0.570671\pi\) |
−0.985470 | + | 0.169852i | \(0.945671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.85865 | − | 1.85865i | −0.479902 | − | 0.479902i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.16196 | + | 1.16196i | −0.281818 | + | 0.281818i | −0.833834 | − | 0.552016i | \(-0.813859\pi\) |
0.552016 | + | 0.833834i | \(0.313859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.00265155 | − | 0.00396832i | 0.000608307 | − | 0.000910395i | −0.831165 | − | 0.556025i | \(-0.812326\pi\) |
0.831774 | + | 0.555115i | \(0.187326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.519350 | + | 2.61095i | −0.113331 | + | 0.569755i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.78945 | + | 4.32013i | 0.373127 | + | 0.900809i | 0.993217 | + | 0.116278i | \(0.0370962\pi\) |
−0.620090 | + | 0.784531i | \(0.712904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.38726 | − | 5.76336i | 0.477452 | − | 1.15267i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.34588 | − | 3.51086i | −0.451465 | − | 0.675665i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.70191 | − | 0.338531i | 0.316037 | − | 0.0628637i | −0.0345231 | − | 0.999404i | \(-0.510991\pi\) |
0.350560 | + | 0.936540i | \(0.385991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.42685i | − | 1.69311i | −0.532300 | − | 0.846556i | \(-0.678672\pi\) | ||
0.532300 | − | 0.846556i | \(-0.321328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.43423i | − | 0.249667i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.1630 | + | 2.22047i | −1.88690 | + | 0.375327i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47130 | + | 2.20195i | 0.241880 | + | 0.361999i | 0.932470 | − | 0.361248i | \(-0.117649\pi\) |
−0.690590 | + | 0.723246i | \(0.742649\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.56876 | + | 3.78733i | −0.251203 | + | 0.606458i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.497436 | + | 1.20092i | 0.0776864 | + | 0.187552i | 0.957951 | − | 0.286931i | \(-0.0926351\pi\) |
−0.880265 | + | 0.474483i | \(0.842635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.104068 | + | 0.523183i | −0.0158702 | + | 0.0797847i | −0.987909 | − | 0.155037i | \(-0.950450\pi\) |
0.972039 | + | 0.234821i | \(0.0754505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.44236 | − | 6.64846i | 0.662228 | − | 0.991094i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.378819 | + | 0.378819i | −0.0552564 | + | 0.0552564i | −0.734195 | − | 0.678939i | \(-0.762440\pi\) |
0.678939 | + | 0.734195i | \(0.262440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.20113 | + | 3.20113i | 0.457305 | + | 0.457305i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07132 | + | 0.715832i | 0.150015 | + | 0.100237i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.63594 | + | 0.723233i | 0.499435 | + | 0.0993438i | 0.438378 | − | 0.898791i | \(-0.355553\pi\) |
0.0610565 | + | 0.998134i | \(0.480553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.66523 | − | 2.34662i | 0.763900 | − | 0.316418i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.00345732 | − | 0.00143207i | −0.000457934 | − | 0.000189682i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1857 | − | 7.47403i | 1.45625 | − | 0.973036i | 0.459874 | − | 0.887984i | \(-0.347895\pi\) |
0.996377 | − | 0.0850514i | \(-0.0271054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29788 | + | 6.52488i | 0.166176 | + | 0.835425i | 0.970475 | + | 0.241200i | \(0.0775410\pi\) |
−0.804299 | + | 0.594225i | \(0.797459\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.09815 | −1.02027 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.5268 | −2.17393 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.46964 | − | 7.38837i | −0.179545 | − | 0.902633i | −0.960550 | − | 0.278108i | \(-0.910293\pi\) |
0.781005 | − | 0.624525i | \(-0.214707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.04854 | − | 2.03697i | 0.367001 | − | 0.245222i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.03495 | + | 2.08554i | 0.597538 | + | 0.247508i | 0.660890 | − | 0.750483i | \(-0.270179\pi\) |
−0.0633517 | + | 0.997991i | \(0.520179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.53632 | + | 1.87901i | −0.530936 | + | 0.219921i | −0.632013 | − | 0.774958i | \(-0.717771\pi\) |
0.101077 | + | 0.994879i | \(0.467771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.79732 | − | 0.954247i | −0.553947 | − | 0.110187i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.16369 | − | 3.45027i | −0.588457 | − | 0.393194i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3984 | + | 11.3984i | 1.28242 | + | 1.28242i | 0.939287 | + | 0.343133i | \(0.111488\pi\) |
0.343133 | + | 0.939287i | \(0.388512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.71871 | − | 2.71871i | 0.302079 | − | 0.302079i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.35370 | + | 5.01916i | −0.368116 | + | 0.550925i | −0.968572 | − | 0.248733i | \(-0.919986\pi\) |
0.600456 | + | 0.799658i | \(0.294986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.07471 | + | 5.40294i | −0.116569 | + | 0.586032i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.520675 | − | 1.25702i | −0.0558223 | − | 0.134767i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.25907 | − | 10.2823i | 0.451460 | − | 1.08992i | −0.520307 | − | 0.853980i | \(-0.674182\pi\) |
0.971767 | − | 0.235942i | \(-0.0758177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.86171 | + | 14.7591i | 1.03379 | + | 1.54717i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.24944 | + | 1.44200i | −0.751732 | + | 0.149529i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.0159996i | − | 0.00164152i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2846i | 1.24731i | 0.781698 | + | 0.623657i | \(0.214354\pi\) | ||||
−0.781698 | + | 0.623657i | \(0.785646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.27911 | − | 0.851169i | 0.430067 | − | 0.0855457i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.04551 | + | 1.56472i | 0.104032 | + | 0.155695i | 0.879833 | − | 0.475282i | \(-0.157654\pi\) |
−0.775801 | + | 0.630978i | \(0.782654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50995 | + | 10.8880i | −0.444379 | + | 1.07283i | 0.530017 | + | 0.847987i | \(0.322186\pi\) |
−0.974396 | + | 0.224839i | \(0.927814\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.41517 | + | 8.24495i | 0.333287 | + | 0.804625i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.90641 | + | 14.6115i | −0.280973 | + | 1.41255i | 0.540042 | + | 0.841638i | \(0.318408\pi\) |
−0.821014 | + | 0.570907i | \(0.806592\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.04402 | + | 12.0387i | −0.770478 | + | 1.15310i | 0.213870 | + | 0.976862i | \(0.431393\pi\) |
−0.984347 | + | 0.176239i | \(0.943607\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.46829 | − | 1.46829i | 0.139364 | − | 0.139364i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.94034 | + | 9.94034i | 0.935109 | + | 0.935109i | 0.998019 | − | 0.0629105i | \(-0.0200383\pi\) |
−0.0629105 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0340 | + | 8.70901i | 1.21542 | + | 0.812119i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.2308 | − | 2.43285i | −1.13073 | − | 0.224917i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.15446 | − | 2.13505i | 0.472508 | − | 0.195719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.07151 | − | 2.92911i | −0.642864 | − | 0.266283i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.847439 | − | 0.566240i | 0.0764110 | − | 0.0510562i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.809807 | − | 4.07117i | −0.0724313 | − | 0.364137i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3100 | 1.18107 | 0.590534 | − | 0.807013i | \(-0.298917\pi\) | ||||
0.590534 | + | 0.807013i | \(0.298917\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.418258 | 0.0368255 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.318596 | − | 1.60169i | −0.0278359 | − | 0.139940i | 0.964368 | − | 0.264563i | \(-0.0852279\pi\) |
−0.992204 | + | 0.124623i | \(0.960228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0134731 | + | 0.00900242i | −0.00116826 | + | 0.000780609i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.0777 | − | 5.41695i | −1.12555 | − | 0.466217i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.96260 | + | 2.88400i | −0.594855 | + | 0.246397i | −0.659738 | − | 0.751496i | \(-0.729333\pi\) |
0.0648827 | + | 0.997893i | \(0.479333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.03376 | + | 0.802365i | 0.342139 | + | 0.0680557i | 0.363169 | − | 0.931723i | \(-0.381695\pi\) |
−0.0210303 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.349267 | + | 0.233372i | 0.0294136 | + | 0.0196535i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.76227 | − | 6.76227i | −0.565489 | − | 0.565489i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.11336 | − | 4.11336i | 0.341596 | − | 0.341596i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.97207 | − | 2.95141i | 0.162654 | − | 0.243428i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.992028 | + | 4.98726i | −0.0812701 | + | 0.408573i | 0.918639 | + | 0.395098i | \(0.129289\pi\) |
−0.999909 | + | 0.0134748i | \(0.995711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.957754 | − | 2.31222i | −0.0779409 | − | 0.188166i | 0.880106 | − | 0.474777i | \(-0.157471\pi\) |
−0.958047 | + | 0.286611i | \(0.907471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.49994 | + | 3.62117i | −0.121263 | + | 0.292754i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.5572 | − | 26.2761i | −1.41022 | − | 2.11055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6061 | − | 2.50752i | 1.00608 | − | 0.200122i | 0.335564 | − | 0.942017i | \(-0.391073\pi\) |
0.670515 | + | 0.741896i | \(0.266073\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 2.90675i | − | 0.230520i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 15.8760i | − | 1.25120i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1793 | − | 2.42260i | 0.953953 | − | 0.189753i | 0.306510 | − | 0.951867i | \(-0.400839\pi\) |
0.647443 | + | 0.762114i | \(0.275839\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.67120 | − | 3.99773i | −0.207952 | − | 0.311223i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.69682 | − | 11.3391i | 0.363451 | − | 0.877448i | −0.631339 | − | 0.775507i | \(-0.717495\pi\) |
0.994790 | − | 0.101942i | \(-0.0325055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.48548 | + | 13.2431i | 0.421960 | + | 1.01870i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.00222087 | − | 0.0111650i | 0.000169834 | − | 0.000853812i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.09606 | − | 4.63358i | 0.235389 | − | 0.352285i | −0.694903 | − | 0.719103i | \(-0.744553\pi\) |
0.930293 | + | 0.366818i | \(0.119553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.9763 | + | 14.9763i | −1.13210 | + | 1.13210i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.45873 | − | 7.45873i | −0.560633 | − | 0.560633i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.829076 | + | 0.553971i | 0.0619681 | + | 0.0414057i | 0.586168 | − | 0.810189i | \(-0.300636\pi\) |
−0.524200 | + | 0.851595i | \(0.675636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2786 | − | 3.43692i | −1.28430 | − | 0.255464i | −0.494691 | − | 0.869069i | \(-0.664719\pi\) |
−0.789613 | + | 0.613605i | \(0.789719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.81923 | − | 1.99619i | 0.356248 | − | 0.147563i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.20211 | + | 3.39743i | 0.603031 | + | 0.249784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.49924 | + | 1.66994i | −0.182763 | + | 0.122118i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.79681 | + | 14.0605i | 0.203438 | + | 1.02275i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00046 | −0.434178 | −0.217089 | − | 0.976152i | \(-0.569656\pi\) | ||||
−0.217089 | + | 0.976152i | \(0.569656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.98517 | 0.646767 | 0.323383 | − | 0.946268i | \(-0.395180\pi\) | ||||
0.323383 | + | 0.946268i | \(0.395180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.68103 | + | 13.4785i | 0.191993 | + | 0.965213i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.91120 | − | 6.62245i | 0.706144 | − | 0.471830i | −0.149921 | − | 0.988698i | \(-0.547902\pi\) |
0.856065 | + | 0.516868i | \(0.172902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.782393 | + | 0.324078i | 0.0554624 | + | 0.0229733i | 0.410242 | − | 0.911977i | \(-0.365444\pi\) |
−0.354780 | + | 0.934950i | \(0.615444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.45701 | + | 2.26037i | −0.384908 | + | 0.159434i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.77826 | − | 1.14937i | −0.405554 | − | 0.0806697i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.62320 | + | 2.42095i | 0.253055 | + | 0.169086i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.88664 | + | 7.88664i | 0.548160 | + | 0.548160i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.00617304 | − | 0.00617304i | 0.000426998 | − | 0.000426998i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82250 | − | 7.21737i | 0.331994 | − | 0.496865i | −0.627491 | − | 0.778624i | \(-0.715918\pi\) |
0.959485 | + | 0.281759i | \(0.0909180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.833642 | − | 4.19100i | 0.0571202 | − | 0.287163i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.684334 | + | 1.65213i | 0.0466712 | + | 0.112674i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.2480 | + | 29.5693i | −0.831450 | + | 2.00730i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.13891 | + | 3.20110i | 0.144534 | + | 0.216310i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.42627 | − | 1.67609i | 0.566812 | − | 0.112746i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1030i | 0.676547i | 0.941048 | + | 0.338273i | \(0.109843\pi\) | ||||
−0.941048 | + | 0.338273i | \(0.890157\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 14.8794i | − | 0.991963i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3254 | + | 3.44624i | −1.14993 | + | 0.228735i | −0.733016 | − | 0.680212i | \(-0.761888\pi\) |
−0.416912 | + | 0.908947i | \(0.636888\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.76160 | − | 5.62963i | −0.248574 | − | 0.372017i | 0.686110 | − | 0.727498i | \(-0.259317\pi\) |
−0.934683 | + | 0.355481i | \(0.884317\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.86345 | + | 4.49876i | −0.122606 | + | 0.295997i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2794 | − | 27.2309i | −0.738939 | − | 1.78396i | −0.610152 | − | 0.792285i | \(-0.708892\pi\) |
−0.128787 | − | 0.991672i | \(-0.541108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.350373 | + | 1.76144i | −0.0228558 | + | 0.114904i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.02202 | − | 10.5092i | 0.456129 | − | 0.682646i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.91117 | − | 4.91117i | 0.317677 | − | 0.317677i | −0.530197 | − | 0.847874i | \(-0.677882\pi\) |
0.847874 | + | 0.530197i | \(0.177882\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9105 | − | 15.9105i | −1.02488 | − | 1.02488i | −0.999682 | − | 0.0252016i | \(-0.991977\pi\) |
−0.0252016 | − | 0.999682i | \(-0.508023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.0392 | − | 8.71251i | −0.836465 | − | 0.558908i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.8848 | + | 2.96076i | 0.950952 | + | 0.189156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0230531 | + | 0.00954890i | −0.00146683 | + | 0.000607582i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.37285 | + | 1.81129i | 0.277118 | + | 0.114786i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4114 | + | 8.96124i | −0.846523 | + | 0.565628i | −0.901461 | − | 0.432861i | \(-0.857504\pi\) |
0.0549377 | + | 0.998490i | \(0.482504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.66867 | + | 8.38897i | 0.104908 | + | 0.527410i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.31938 | 0.270490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.4126 | 0.836653 | 0.418327 | − | 0.908297i | \(-0.362617\pi\) | ||||
0.418327 | + | 0.908297i | \(0.362617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.75411 | − | 8.81851i | −0.108995 | − | 0.547956i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.44140 | − | 2.29947i | 0.213017 | − | 0.142334i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.51629 | − | 2.28492i | −0.340149 | − | 0.140894i | 0.206069 | − | 0.978538i | \(-0.433933\pi\) |
−0.546218 | + | 0.837643i | \(0.683933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4817 | − | 4.75588i | 0.705316 | − | 0.292152i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.55881 | − | 1.70245i | −0.523791 | − | 0.104188i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.39748 | + | 4.94284i | 0.451032 | + | 0.301370i | 0.760261 | − | 0.649617i | \(-0.225071\pi\) |
−0.309229 | + | 0.950988i | \(0.600071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.27670 | + | 3.27670i | 0.199046 | + | 0.199046i | 0.799591 | − | 0.600545i | \(-0.205050\pi\) |
−0.600545 | + | 0.799591i | \(0.705050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.84153 | − | 9.84153i | 0.595637 | − | 0.595637i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.33947 | − | 9.48769i | 0.382285 | − | 0.572129i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81203 | − | 9.10969i | 0.108874 | − | 0.547348i | −0.887392 | − | 0.461016i | \(-0.847485\pi\) |
0.996266 | − | 0.0863327i | \(-0.0275148\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.60463 | − | 20.7734i | −0.515146 | − | 1.24367i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.02651 | − | 16.9635i | 0.419166 | − | 1.01196i | −0.563424 | − | 0.826168i | \(-0.690516\pi\) |
0.982590 | − | 0.185789i | \(-0.0594840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.58111 | − | 3.86291i | −0.153431 | − | 0.229626i | 0.746789 | − | 0.665061i | \(-0.231595\pi\) |
−0.900220 | + | 0.435435i | \(0.856595\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0123040 | + | 0.00244742i | −0.000728828 | + | 0.000144973i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.41324i | − | 0.260505i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2997i | 0.841158i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.44714 | − | 1.87915i | 0.553801 | − | 0.110158i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.12834 | − | 6.17849i | −0.241180 | − | 0.360951i | 0.691057 | − | 0.722801i | \(-0.257146\pi\) |
−0.932237 | + | 0.361849i | \(0.882146\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.2585 | − | 41.6658i | 1.00483 | − | 2.42588i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.95570 | − | 7.13569i | −0.171507 | − | 0.414055i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.76947 | − | 23.9778i | 0.275826 | − | 1.38667i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00619 | − | 1.50586i | 0.0579956 | − | 0.0867966i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.04337 | − | 1.04337i | 0.0599402 | − | 0.0599402i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.7700 | + | 15.7700i | 0.902988 | + | 0.902988i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.22026 | + | 2.81989i | 0.240863 | + | 0.160939i | 0.670143 | − | 0.742232i | \(-0.266233\pi\) |
−0.429280 | + | 0.903171i | \(0.641233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.06298 | + | 1.80274i | 0.515575 | + | 0.102554i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.5642 | + | 11.8317i | −1.61972 | + | 0.670912i | −0.994025 | − | 0.109152i | \(-0.965186\pi\) |
−0.625699 | + | 0.780064i | \(0.715186\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.76475 | − | 3.63048i | −0.495413 | − | 0.205207i | 0.120966 | − | 0.992657i | \(-0.461401\pi\) |
−0.616379 | + | 0.787450i | \(0.711401\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.5726 | + | 15.0825i | −1.27182 | + | 0.849803i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.95679 | − | 19.8921i | −0.222235 | − | 1.11725i | −0.917267 | − | 0.398274i | \(-0.869609\pi\) |
0.695031 | − | 0.718980i | \(-0.255391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.17407 | 0.177714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6811 | 0.651977 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.00153004 | + | 0.00769205i | 8.51339e−5 | + | 0.000427997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.1182 | + | 18.1198i | −1.50425 | + | 1.00510i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.4885 | + | 4.34449i | 0.580016 | + | 0.240251i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.68043 | − | 0.696058i | 0.0926453 | − | 0.0383749i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.0847 | − | 4.98965i | −1.37878 | − | 0.274256i | −0.550622 | − | 0.834754i | \(-0.685610\pi\) |
−0.828155 | + | 0.560498i | \(0.810610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.25211 | + | 3.50935i | 0.287814 | + | 0.192311i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.8570 | − | 17.8570i | −0.975632 | − | 0.975632i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.30903 | − | 1.30903i | 0.0713075 | − | 0.0713075i | −0.670554 | − | 0.741861i | \(-0.733943\pi\) |
0.741861 | + | 0.670554i | \(0.233943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.12378 | − | 9.16489i | 0.332598 | − | 0.497768i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.36400 | − | 16.9120i | 0.182171 | − | 0.915834i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.21298 | + | 7.75682i | 0.173485 | + | 0.418829i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.70364 | − | 11.3556i | 0.253235 | − | 0.611364i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1922 | + | 25.7299i | 0.922925 | + | 1.38125i | 0.924470 | + | 0.381256i | \(0.124508\pi\) |
−0.00154489 | + | 0.999999i | \(0.500492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.252228 | − | 0.0501713i | 0.0135015 | − | 0.00268561i | −0.188335 | − | 0.982105i | \(-0.560309\pi\) |
0.201836 | + | 0.979419i | \(0.435309\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.0760i | 1.17833i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.17608i | 0.328719i | 0.986400 | + | 0.164360i | \(0.0525558\pi\) | ||||
−0.986400 | + | 0.164360i | \(0.947444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.9185 | − | 3.56422i | 0.951016 | − | 0.189169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.43036 | − | 3.63729i | −0.128628 | − | 0.192506i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.7708 | + | 26.0029i | −0.568459 | + | 1.37238i | 0.334395 | + | 0.942433i | \(0.391468\pi\) |
−0.902854 | + | 0.429948i | \(0.858532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.27098 | + | 17.5537i | 0.382683 | + | 0.923878i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.17084 | + | 5.88620i | −0.0614530 | + | 0.308945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.14484 | + | 13.6862i | −0.478663 | + | 0.716370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.85490 | − | 6.85490i | 0.357823 | − | 0.357823i | −0.505187 | − | 0.863010i | \(-0.668576\pi\) |
0.863010 | + | 0.505187i | \(0.168576\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.19234 | + | 2.19234i | 0.114129 | + | 0.114129i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4652 | − | 6.99265i | −0.543328 | − | 0.363040i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4393 | + | 3.07108i | 0.799419 | + | 0.159014i | 0.577863 | − | 0.816133i | \(-0.303887\pi\) |
0.221555 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00694 | + | 1.24552i | −0.155278 | + | 0.0643182i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.38169 | − | 3.47181i | −0.431679 | − | 0.178807i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8812 | − | 17.2933i | 1.32943 | − | 0.888295i | 0.330961 | − | 0.943645i | \(-0.392627\pi\) |
0.998467 | + | 0.0553495i | \(0.0176273\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.03600 | − | 10.2356i | −0.104307 | − | 0.524388i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.3304 | −1.34542 | −0.672711 | − | 0.739905i | \(-0.734870\pi\) | ||||
−0.672711 | + | 0.739905i | \(0.734870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.8191 | −1.06104 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.248223 | + | 1.24790i | 0.0126179 | + | 0.0634343i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.4392 | + | 13.6570i | −1.03631 | + | 0.692439i | −0.952654 | − | 0.304056i | \(-0.901659\pi\) |
−0.0836539 | + | 0.996495i | \(0.526659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.09912 | − | 2.94055i | −0.359018 | − | 0.148710i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.18300 | + | 0.490015i | −0.0596745 | + | 0.0247180i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 53.0007 | + | 10.5425i | 2.66675 | + | 0.530450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8836 | + | 15.2903i | 1.14850 | + | 0.767400i | 0.976034 | − | 0.217616i | \(-0.0698281\pi\) |
0.172461 | + | 0.985016i | \(0.444828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.00898400 | + | 0.00898400i | 0.000449762 | + | 0.000449762i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4437 | + | 24.4437i | −1.22066 | + | 1.22066i | −0.253263 | + | 0.967398i | \(0.581504\pi\) |
−0.967398 | + | 0.253263i | \(0.918496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.3816 | + | 40.9795i | −1.36397 | + | 2.04133i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.51456 | − | 12.6415i | 0.124950 | − | 0.628164i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85377 | + | 4.47539i | 0.0918878 | + | 0.221837i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0633 | + | 29.1234i | −0.596492 | + | 1.44006i | 0.280641 | + | 0.959813i | \(0.409453\pi\) |
−0.877134 | + | 0.480247i | \(0.840547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.28291 | + | 4.91323i | 0.161934 | + | 0.242352i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.7971 | + | 8.91069i | −2.20432 | + | 0.438466i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.2364i | 0.993367i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.22478i | − | 0.157918i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3813 | − | 2.26388i | 0.556012 | − | 0.110598i | 0.0909169 | − | 0.995858i | \(-0.471020\pi\) |
0.465095 | + | 0.885261i | \(0.346020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.35311 | + | 5.01829i | 0.163421 | + | 0.244576i | 0.904138 | − | 0.427240i | \(-0.140514\pi\) |
−0.740717 | + | 0.671817i | \(0.765514\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.489004 | + | 1.18056i | −0.0237762 | + | 0.0574007i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.92291 | + | 9.47073i | 0.190289 | + | 0.459398i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.40650 | − | 22.1530i | 0.213246 | − | 1.07206i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.16592 | + | 6.23474i | −0.201132 | + | 0.301016i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6711 | − | 19.6711i | 0.947521 | − | 0.947521i | −0.0511686 | − | 0.998690i | \(-0.516295\pi\) |
0.998690 | + | 0.0511686i | \(0.0162946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2910 | − | 18.2910i | −0.879011 | − | 0.879011i | 0.114421 | − | 0.993432i | \(-0.463499\pi\) |
−0.993432 | + | 0.114421i | \(0.963499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.79247 | − | 2.53405i | −0.181835 | − | 0.121498i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0218885 | + | 0.00435389i | 0.00104707 | + | 0.000208275i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.7707 | − | 4.46137i | 0.514057 | − | 0.212929i | −0.110547 | − | 0.993871i | \(-0.535260\pi\) |
0.624604 | + | 0.780941i | \(0.285260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.97609 | + | 4.13223i | 0.475052 | + | 0.196773i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.77026 | + | 6.52828i | −0.464199 | + | 0.310168i | −0.765586 | − | 0.643334i | \(-0.777551\pi\) |
0.301386 | + | 0.953502i | \(0.402551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.27880 | − | 36.5930i | −0.345048 | − | 1.73467i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.98706 | 0.188581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.5341 | 1.25222 | 0.626111 | − | 0.779734i | \(-0.284646\pi\) | ||||
0.626111 | + | 0.779734i | \(0.284646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.463860 | + | 2.33198i | 0.0218423 | + | 0.109809i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.63164 | + | 1.09023i | −0.0766613 | + | 0.0512234i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 54.9765 | + | 22.7720i | 2.57734 | + | 1.06757i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.9069 | − | 9.90258i | 1.11832 | − | 0.463223i | 0.254525 | − | 0.967066i | \(-0.418081\pi\) |
0.863795 | + | 0.503843i | \(0.168081\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.80532 | + | 1.35366i | 0.317645 | + | 0.0631835i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.9755 | − | 16.0199i | −1.11665 | − | 0.746121i | −0.146640 | − | 0.989190i | \(-0.546846\pi\) |
−0.970009 | + | 0.243069i | \(0.921846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.4799 | − | 19.4799i | −0.905307 | − | 0.905307i | 0.0905817 | − | 0.995889i | \(-0.471127\pi\) |
−0.995889 | + | 0.0905817i | \(0.971127\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.5212 | + | 17.5212i | −0.812527 | + | 0.812527i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7398 | + | 17.5698i | −0.543252 | + | 0.813035i | −0.996944 | − | 0.0781243i | \(-0.975107\pi\) |
0.453691 | + | 0.891159i | \(0.350107\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.98965 | + | 25.0847i | −0.230401 | + | 1.15830i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.85667 | − | 9.31081i | −0.177706 | − | 0.429020i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.373399 | + | 0.901465i | −0.0171689 | + | 0.0414494i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0165409 | − | 0.0247552i | −0.000758950 | − | 0.00113585i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.67247 | − | 1.72506i | 0.397085 | − | 0.0789851i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 12.7073i | − | 0.580611i | −0.956934 | − | 0.290305i | \(-0.906243\pi\) | ||
0.956934 | − | 0.290305i | \(-0.0937569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13.8457i | − | 0.631310i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.2090 | + | 2.42852i | −0.555528 | + | 0.110501i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.8797 | + | 34.2418i | 1.03891 | + | 1.55484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.38031 | + | 12.9892i | −0.243805 | + | 0.588597i | −0.997655 | − | 0.0684497i | \(-0.978195\pi\) |
0.753850 | + | 0.657047i | \(0.228195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.72607 | − | 8.99553i | −0.168499 | − | 0.406792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.14334 | − | 10.7753i | 0.0967275 | − | 0.486282i | −0.901806 | − | 0.432141i | \(-0.857758\pi\) |
0.998533 | − | 0.0541404i | \(-0.0172419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.58420 | + | 2.37092i | −0.0713487 | + | 0.106781i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3422 | − | 10.3422i | 0.464848 | − | 0.464848i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0835 | − | 13.0835i | −0.586876 | − | 0.586876i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.97175 | − | 5.32655i | −0.356864 | − | 0.238449i | 0.364195 | − | 0.931323i | \(-0.381344\pi\) |
−0.721059 | + | 0.692874i | \(0.756344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.43849 | − | 1.87743i | −0.421681 | − | 0.0838775i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.63705 | + | 3.16337i | −0.340519 | + | 0.141048i | −0.546389 | − | 0.837532i | \(-0.683998\pi\) |
0.205869 | + | 0.978579i | \(0.433998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.82846 | + | 2.41423i | 0.259363 | + | 0.107432i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.34513 | − | 6.24422i | 0.415032 | − | 0.277316i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.95926 | + | 14.8772i | 0.131167 | + | 0.659420i | 0.989288 | + | 0.145974i | \(0.0466314\pi\) |
−0.858122 | + | 0.513446i | \(0.828369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6705 | 0.737459 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0201524 | −0.000889751 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.70756 | + | 38.7485i | 0.339636 | + | 1.70746i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.814791 | + | 0.544426i | −0.0358345 | + | 0.0239438i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.03692 | − | 1.67215i | −0.177201 | − | 0.0733992i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0424 | − | 4.15970i | 0.439966 | − | 0.182240i | −0.151694 | − | 0.988427i | \(-0.548473\pi\) |
0.591660 | + | 0.806188i | \(0.298473\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.45679 | + | 0.687599i | 0.151155 | + | 0.0300666i | 0.270088 | − | 0.962836i | \(-0.412947\pi\) |
−0.118933 | + | 0.992902i | \(0.537947\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.8080 | + | 9.22622i | 0.602631 | + | 0.402665i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.9537 | + | 10.9537i | 0.477149 | + | 0.477149i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.802117 | − | 0.802117i | 0.0348746 | − | 0.0348746i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.8271 | − | 26.6801i | 0.773630 | − | 1.15782i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32583 | − | 6.66538i | 0.0574279 | − | 0.288710i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.1121 | + | 46.1407i | 0.826289 | + | 1.99484i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.299194 | − | 0.722317i | 0.0129112 | − | 0.0311703i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.60057 | + | 6.88524i | 0.198161 | + | 0.296568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.58170 | − | 0.911357i | 0.196983 | − | 0.0391823i | −0.0956128 | − | 0.995419i | \(-0.530481\pi\) |
0.292595 | + | 0.956236i | \(0.405481\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8133i | 0.592786i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 48.5381i | 2.07915i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.46021 | + | 1.48393i | −0.318975 | + | 0.0634482i | −0.351981 | − | 0.936007i | \(-0.614492\pi\) |
0.0330060 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.81583 | + | 13.1938i | 0.376251 | + | 0.563099i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.00316930 | − | 0.00765136i | 0.000135017 | − | 0.000325959i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.9439 | − | 50.5631i | −0.890626 | − | 2.15016i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.35803 | − | 6.82729i | 0.0576453 | − | 0.289803i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.06578 | + | 12.0713i | −0.341758 | + | 0.511477i | −0.962042 | − | 0.272900i | \(-0.912017\pi\) |
0.620284 | + | 0.784377i | \(0.287017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.97205 | − | 1.97205i | 0.0834089 | − | 0.0834089i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66652 | + | 1.66652i | 0.0703606 | + | 0.0703606i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.7599 | − | 9.19410i | −0.579912 | − | 0.387485i | 0.230738 | − | 0.973016i | \(-0.425886\pi\) |
−0.810650 | + | 0.585531i | \(0.800886\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.2210 | + | 9.19392i | 1.94453 | + | 0.386791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.0602 | + | 4.99548i | −0.506479 | + | 0.209790i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.7745 | + | 4.46295i | 0.451691 | + | 0.187097i | 0.596919 | − | 0.802302i | \(-0.296391\pi\) |
−0.145228 | + | 0.989398i | \(0.546391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3434 | + | 25.6202i | −1.60462 | + | 1.07217i | −0.656471 | + | 0.754351i | \(0.727951\pi\) |
−0.948150 | + | 0.317822i | \(0.897049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.917878 | + | 4.61448i | 0.0383449 | + | 0.192773i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.1703 | 1.21649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.30739 | 0.220949 | 0.110475 | − | 0.993879i | \(-0.464763\pi\) | ||||
0.110475 | + | 0.993879i | \(0.464763\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.37444 | − | 6.90979i | −0.0571199 | − | 0.287161i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0408 | − | 11.3863i | 0.706973 | − | 0.472384i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.26487 | + | 2.59499i | 0.259464 | + | 0.107474i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −38.6228 | + | 15.9981i | −1.59686 | + | 0.661439i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.07653 | + | 0.214135i | 0.0444331 | + | 0.00883830i | 0.217257 | − | 0.976114i | \(-0.430289\pi\) |
−0.172824 | + | 0.984953i | \(0.555289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0374087 | − | 0.0249957i | −0.00154140 | − | 0.00102993i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.60890 | − | 6.60890i | −0.271854 | − | 0.271854i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.71203 | + | 9.71203i | −0.398825 | + | 0.398825i | −0.877819 | − | 0.478993i | \(-0.841002\pi\) |
0.478993 | + | 0.877819i | \(0.341002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3910 | − | 15.5512i | 0.425987 | − | 0.637535i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.129542 | − | 0.651251i | 0.00530179 | − | 0.0266539i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.51141 | + | 3.64886i | 0.0617545 | + | 0.149088i | 0.951745 | − | 0.306891i | \(-0.0992889\pi\) |
−0.889990 | + | 0.455980i | \(0.849289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.10853 | + | 9.91887i | −0.167591 | + | 0.404599i | −0.985254 | − | 0.171097i | \(-0.945269\pi\) |
0.817664 | + | 0.575696i | \(0.195269\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.98251 | − | 14.9399i | −0.406519 | − | 0.608399i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.1663 | + | 5.00589i | −1.02316 | + | 0.203518i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 43.0657i | − | 1.74798i | −0.485943 | − | 0.873991i | \(-0.661524\pi\) | ||
0.485943 | − | 0.873991i | \(-0.338476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.61942i | 0.187188i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.74710 | − | 0.546431i | 0.111136 | − | 0.0221062i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.9537 | − | 38.8424i | −1.04826 | − | 1.56883i | −0.799872 | − | 0.600170i | \(-0.795099\pi\) |
−0.248387 | − | 0.968661i | \(-0.579901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.30753 | − | 3.15665i | 0.0527245 | − | 0.127288i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.4503 | − | 25.2293i | −0.420715 | − | 1.01570i | −0.982137 | − | 0.188166i | \(-0.939746\pi\) |
0.561422 | − | 0.827529i | \(-0.310254\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.81639 | + | 39.2957i | −0.314167 | + | 1.57943i | 0.424546 | + | 0.905406i | \(0.360434\pi\) |
−0.738713 | + | 0.674020i | \(0.764566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9695 | − | 16.4170i | 0.440191 | − | 0.658792i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.7190 | + | 26.7190i | −1.07047 | + | 1.07047i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2158 | + | 12.2158i | 0.488631 | + | 0.488631i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.00569148 | − | 0.00380292i | −0.000227296 | − | 0.000151874i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.26819 | − | 0.848995i | −0.170184 | − | 0.0338516i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.5309 | + | 12.6463i | −1.21542 | + | 0.503442i | −0.895950 | − | 0.444155i | \(-0.853504\pi\) |
−0.319467 | + | 0.947597i | \(0.603504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.28800 | − | 2.60458i | −0.249926 | − | 0.103523i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.0998 | − | 24.7893i | 1.47226 | − | 0.983733i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.61751 | − | 23.2138i | −0.182953 | − | 0.919765i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.9989 | 0.514227 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0254 | −1.18593 | −0.592966 | − | 0.805227i | \(-0.702043\pi\) | ||||
−0.592966 | + | 0.805227i | \(0.702043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.92684 | + | 9.68687i | 0.0759871 | + | 0.382013i | 1.00000 | 0.000348458i | \(-0.000110918\pi\) | |
−0.924013 | + | 0.382361i | \(0.875111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.16584 | − | 0.778990i | 0.0459049 | − | 0.0306727i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0095 | − | 13.2588i | −1.25842 | − | 0.521257i | −0.348999 | − | 0.937123i | \(-0.613478\pi\) |
−0.909426 | + | 0.415867i | \(0.863478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7345 | − | 9.41693i | 0.892406 | − | 0.369647i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.6130 | + | 4.89583i | 0.964660 | + | 0.191883i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.9545 | − | 20.6832i | −1.21134 | − | 0.809394i | −0.225043 | − | 0.974349i | \(-0.572252\pi\) |
−0.986301 | + | 0.164954i | \(0.947252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.87114 | − | 3.87114i | −0.151258 | − | 0.151258i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.28132 | + | 8.28132i | −0.323085 | + | 0.323085i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.96386 | − | 10.4222i | 0.271273 | − | 0.405989i | −0.670673 | − | 0.741753i | \(-0.733994\pi\) |
0.941946 | + | 0.335764i | \(0.108994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.07042 | + | 20.4634i | −0.158321 | + | 0.795934i | 0.817256 | + | 0.576275i | \(0.195494\pi\) |
−0.975577 | + | 0.219659i | \(0.929506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.57790 | − | 6.22359i | −0.100117 | − | 0.241704i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0207878 | + | 0.0501862i | −0.000806116 | + | 0.00194614i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50799 | + | 6.74668i | 0.174550 | + | 0.261233i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.76942 | − | 1.54543i | 0.300383 | − | 0.0597499i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1689i | 0.469776i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.76884i | 0.145278i | 0.997358 | + | 0.0726390i | \(0.0231421\pi\) | ||||
−0.997358 | + | 0.0726390i | \(0.976858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.8346 | + | 5.13882i | −0.994373 | + | 0.197793i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4716 | + | 18.6650i | 0.479321 | + | 0.717354i | 0.989789 | − | 0.142543i | \(-0.0455278\pi\) |
−0.510468 | + | 0.859897i | \(0.670528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9610 | − | 38.5334i | 0.612529 | − | 1.47878i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.30046 | + | 12.7964i | 0.203114 | + | 0.490361i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.81275 | − | 39.2773i | 0.298946 | − | 1.50291i | −0.480811 | − | 0.876824i | \(-0.659658\pi\) |
0.779758 | − | 0.626081i | \(-0.215342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0360 | + | 21.0064i | −0.536289 | + | 0.802613i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.75390 | + | 3.75390i | −0.143220 | + | 0.143220i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.7051 | − | 13.7051i | −0.522122 | − | 0.522122i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.3968 | − | 18.9741i | −1.08027 | − | 0.721811i | −0.117752 | − | 0.993043i | \(-0.537569\pi\) |
−0.962514 | + | 0.271232i | \(0.912569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.5283 | − | 2.88985i | −0.551883 | − | 0.109776i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.7380 | − | 5.27624i | 0.483179 | − | 0.200139i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.97343 | − | 0.817420i | −0.0747488 | − | 0.0309620i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.2158 | + | 12.8396i | −0.726807 | + | 0.485637i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.21632 | + | 16.1695i | 0.121479 | + | 0.610715i | 0.992778 | + | 0.119963i | \(0.0382777\pi\) |
−0.871300 | + | 0.490752i | \(0.836722\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0126393 | 0.000476699 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.40818 | 0.0530353 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.24648 | − | 6.26648i | −0.0468787 | − | 0.235675i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.10981 | − | 1.40973i | 0.0792355 | − | 0.0529435i | −0.515321 | − | 0.856997i | \(-0.672327\pi\) |
0.594557 | + | 0.804053i | \(0.297327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.5222 | + | 14.7138i | 1.33219 | + | 0.551810i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.7252 | − | 16.8689i | 1.52517 | − | 0.631746i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.4434 | − | 6.25449i | −1.17592 | − | 0.233905i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.52805 | − | 3.02554i | −0.169103 | − | 0.112991i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.6165 | − | 13.6165i | −0.507809 | − | 0.507809i | 0.406044 | − | 0.913854i | \(-0.366908\pi\) |
−0.913854 | + | 0.406044i | \(0.866908\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.2929 | − | 28.2929i | 1.05368 | − | 1.05368i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.80170 | + | 14.6693i | −0.364529 | + | 0.545557i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.11183 | − | 10.6169i | 0.0784314 | − | 0.394301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.57477 | − | 18.2871i | −0.280933 | − | 0.678231i | 0.718925 | − | 0.695087i | \(-0.244634\pi\) |
−0.999858 | + | 0.0168560i | \(0.994634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.291465 | + | 0.703658i | −0.0107950 | + | 0.0260614i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.486997 | − | 0.728843i | −0.0180122 | − | 0.0269572i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5625 | − | 6.87491i | 1.27660 | − | 0.253931i | 0.490176 | − | 0.871623i | \(-0.336932\pi\) |
0.786420 | + | 0.617693i | \(0.211932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 11.8996i | − | 0.438923i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 13.7793i | − | 0.507569i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3933 | − | 5.05105i | 0.934109 | − | 0.185806i | 0.295505 | − | 0.955341i | \(-0.404512\pi\) |
0.638604 | + | 0.769535i | \(0.279512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0108697 | + | 0.0162676i | 0.000399308 | + | 0.000597607i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2227 | + | 24.6798i | −0.375034 | + | 0.905413i | 0.617846 | + | 0.786299i | \(0.288005\pi\) |
−0.992881 | + | 0.119114i | \(0.961995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.52344 | + | 15.7490i | 0.239000 | + | 0.576998i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.80897 | + | 14.1216i | −0.102775 | + | 0.516684i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.1008 | − | 42.0559i | 1.02678 | − | 1.53669i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.2054 | + | 18.2054i | −0.664326 | + | 0.664326i | −0.956397 | − | 0.292071i | \(-0.905656\pi\) |
0.292071 | + | 0.956397i | \(0.405656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.94290 | + | 8.94290i | 0.325898 | + | 0.325898i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.97605 | − | 4.66124i | −0.253884 | − | 0.169640i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.14973 | + | 1.62108i | 0.296207 | + | 0.0589192i | 0.340957 | − | 0.940079i | \(-0.389249\pi\) |
−0.0447498 | + | 0.998998i | \(0.514249\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.19604 | − | 2.56649i | 0.224902 | − | 0.0931575i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.0579 | + | 15.3499i | 1.34335 | + | 0.556433i | 0.934433 | − | 0.356139i | \(-0.115907\pi\) |
0.408916 | + | 0.912572i | \(0.365907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.8734 | − | 27.3107i | 1.47972 | − | 0.988714i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.56341 | + | 12.8871i | 0.0926803 | + | 0.465936i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −70.3346 | −2.53964 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.7180 | 1.61257 | 0.806287 | − | 0.591525i | \(-0.201474\pi\) | ||||
0.806287 | + | 0.591525i | \(0.201474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.05169 | − | 10.3146i | −0.0738899 | − | 0.371470i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.7197 | − | 19.8581i | 1.06894 | − | 0.714245i | 0.108887 | − | 0.994054i | \(-0.465271\pi\) |
0.960056 | + | 0.279809i | \(0.0902712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −54.3303 | − | 22.5044i | −1.95160 | − | 0.808380i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.51330 | + | 2.69790i | −0.233663 | + | 0.0967865i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.00608460 | + | 0.00121030i | 0.000218003 | + | 4.33636e-5i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.28857 | + | 5.53825i | 0.296588 | + | 0.198174i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.18101 | − | 5.18101i | −0.185154 | − | 0.185154i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.4678 | − | 30.4678i | 1.08744 | − | 1.08744i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8406 | + | 19.2173i | −0.457717 | + | 0.685022i | −0.986505 | − | 0.163732i | \(-0.947647\pi\) |
0.528788 | + | 0.848754i | \(0.322647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.913339 | + | 4.59167i | −0.0325157 | + | 0.163468i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.2648 | − | 44.0952i | −0.649423 | − | 1.56785i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.3104 | − | 32.1342i | 0.472667 | − | 1.14112i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.41371 | − | 8.10219i | −0.192004 | − | 0.287355i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.16130 | − | 1.82230i | 0.324510 | − | 0.0645491i | −0.0301471 | − | 0.999545i | \(-0.509598\pi\) |
0.354657 | + | 0.934996i | \(0.384598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.880347i | − | 0.0311445i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 26.5461i | − | 0.937961i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.80879 | + | 1.75218i | −0.310856 | + | 0.0618330i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.5684 | − | 44.2523i | −1.04215 | − | 1.55969i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.66957 | − | 6.44491i | 0.0939733 | − | 0.226872i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.1941 | + | 24.6108i | 0.358406 | + | 0.865268i | 0.995525 | + | 0.0945027i | \(0.0301261\pi\) |
−0.637119 | + | 0.770766i | \(0.719874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.07144 | + | 10.4138i | −0.0727380 | + | 0.365679i | −0.999961 | − | 0.00883095i | \(-0.997189\pi\) |
0.927223 | + | 0.374510i | \(0.122189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.01863 | − | 3.02109i | 0.0707963 | − | 0.105954i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.4361 | − | 29.4361i | 1.03110 | − | 1.03110i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.00180022 | + | 0.00180022i | 6.29816e−5 | + | 6.29816e-5i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.2035 | + | 23.5222i | 1.23011 | + | 0.821933i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.6020 | − | 10.6621i | −1.87072 | − | 0.372110i | −0.876677 | − | 0.481079i | \(-0.840245\pi\) |
−0.994045 | + | 0.108969i | \(0.965245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4170 | − | 10.5281i | 0.885982 | − | 0.366986i | 0.107168 | − | 0.994241i | \(-0.465822\pi\) |
0.778814 | + | 0.627255i | \(0.215822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.26597 | − | 3.42388i | −0.287784 | − | 0.119204i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.6824 | + | 15.1559i | −0.788743 | + | 0.527021i | −0.883473 | − | 0.468482i | \(-0.844801\pi\) |
0.0947301 | + | 0.995503i | \(0.469801\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.14763 | − | 10.7969i | −0.0745902 | − | 0.374990i | 0.925402 | − | 0.378988i | \(-0.123728\pi\) |
−0.999992 | + | 0.00399713i | \(0.998728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.28273 | −0.252635 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.43921 | −0.257753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.02692 | − | 40.3540i | −0.277783 | − | 1.39651i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.0963 | + | 22.1142i | −1.14398 | + | 0.764380i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.6575 | + | 7.31397i | 0.609604 | + | 0.252506i | 0.666059 | − | 0.745899i | \(-0.267980\pi\) |
−0.0564551 | + | 0.998405i | \(0.517980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0106 | + | 9.94552i | −0.827952 | + | 0.342949i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.1201 | − | 2.80866i | −0.486322 | − | 0.0967356i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.9549 | + | 26.6970i | 1.37449 | + | 0.918405i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.3756 | + | 18.3756i | 0.631393 | + | 0.631393i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.57583 | + | 2.57583i | −0.0884023 | + | 0.0884023i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.87989 | + | 10.2965i | −0.235840 | + | 0.352959i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.92566 | − | 44.8723i | 0.305609 | − | 1.53640i | −0.456957 | − | 0.889489i | \(-0.651061\pi\) |
0.762566 | − | 0.646911i | \(-0.223939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0146041 | − | 0.0352574i | −0.000499450 | − | 0.00120578i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.18475 | − | 10.1029i | 0.142948 | − | 0.345108i | −0.836148 | − | 0.548503i | \(-0.815198\pi\) |
0.979097 | + | 0.203396i | \(0.0651978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.25686 | − | 4.87424i | −0.111123 | − | 0.166307i | 0.771740 | − | 0.635938i | \(-0.219387\pi\) |
−0.882862 | + | 0.469632i | \(0.844387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39387 | + | 0.675083i | −0.115663 | + | 0.0230068i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.43064i | − | 0.0486996i | −0.999704 | − | 0.0243498i | \(-0.992248\pi\) | ||
0.999704 | − | 0.0243498i | \(-0.00775154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 18.6818i | − | 0.635201i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.9968 | − | 2.18739i | 0.373469 | − | 0.0742877i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.3814 | + | 24.5165i | 0.555701 | + | 0.831666i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0719 | + | 36.3868i | −0.510692 | + | 1.23292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.2132 | + | 27.0709i | 0.379508 | + | 0.916213i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.74942 | + | 13.8223i | −0.0929474 | + | 0.467278i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5649 | + | 30.7776i | −0.694428 | + | 1.03929i | 0.301872 | + | 0.953348i | \(0.402388\pi\) |
−0.996301 | + | 0.0859368i | \(0.972612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.11989 | + | 4.11989i | −0.138960 | + | 0.138960i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.5814 | + | 10.5814i | 0.356496 | + | 0.356496i | 0.862520 | − | 0.506023i | \(-0.168885\pi\) |
−0.506023 | + | 0.862520i | \(0.668885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.6957 | + | 31.2011i | 1.57144 | + | 1.05000i | 0.967469 | + | 0.252991i | \(0.0814144\pi\) |
0.603968 | + | 0.797009i | \(0.293586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.6819 | − | 6.89866i | −1.16582 | − | 0.231896i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.8447 | − | 19.8179i | 1.60647 | − | 0.665421i | 0.614156 | − | 0.789185i | \(-0.289497\pi\) |
0.992312 | + | 0.123764i | \(0.0394966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.7495 | − | 17.2932i | −1.40023 | − | 0.579996i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.84760 | − | 3.90724i | 0.195902 | − | 0.130898i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.000498818 | 0.00250773i | 1.66923e−5 | 8.39179e-5i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.34270 | 0.111734 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.1690 | −0.640034 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.19128 | − | 16.0437i | −0.106435 | − | 0.535086i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.06520 | + | 3.38446i | −0.168746 | + | 0.112753i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.31196 | − | 0.543430i | −0.0436592 | − | 0.0180842i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.5629 | + | 22.6007i | −1.81373 | + | 0.751272i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.2228 | − | 7.80190i | −1.30237 | − | 0.259058i | −0.505300 | − | 0.862943i | \(-0.668618\pi\) |
−0.797071 | + | 0.603886i | \(0.793618\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.73218 | + | 2.49376i | 0.123789 | + | 0.0827129i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9692 | + | 28.9692i | 0.959794 | + | 0.959794i | 0.999222 | − | 0.0394285i | \(-0.0125537\pi\) |
−0.0394285 | + | 0.999222i | \(0.512554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.80771 | + | 7.80771i | −0.258397 | + | 0.258397i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.71517 | − | 14.5398i | 0.321174 | − | 0.480670i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.08168 | + | 5.43799i | −0.0357204 | + | 0.179578i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.60437 | + | 11.1159i | 0.151884 | + | 0.366681i | 0.981447 | − | 0.191732i | \(-0.0614105\pi\) |
−0.829563 | + | 0.558413i | \(0.811411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.52299 | − | 3.67682i | 0.0501842 | − | 0.121155i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.8297 | − | 23.6908i | −0.521040 | − | 0.779792i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.2030 | − | 3.22298i | 0.532752 | − | 0.105971i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.1099i | 0.923249i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 27.6140i | − | 0.905987i | −0.891514 | − | 0.452994i | \(-0.850356\pi\) | ||
0.891514 | − | 0.452994i | \(-0.149644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0211911 | − | 0.00421517i | 0.000694510 | − | 0.000138147i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.4682 | + | 20.1566i | 0.440929 | + | 0.659897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.85611 | + | 9.30948i | −0.126108 | + | 0.304453i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.53902 | + | 20.6150i | 0.278958 | + | 0.673464i | 0.999807 | − | 0.0196280i | \(-0.00624818\pi\) |
−0.720850 | + | 0.693091i | \(0.756248\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.45119 | + | 7.29563i | −0.0473578 | + | 0.238084i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.1132 | − | 31.5981i | 0.688270 | − | 1.03007i | −0.308614 | − | 0.951187i | \(-0.599865\pi\) |
0.996884 | − | 0.0788810i | \(-0.0251347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.29797 | + | 4.29797i | −0.139961 | + | 0.139961i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 33.9829 | + | 33.9829i | 1.10546 | + | 1.10546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.9627 | + | 16.0114i | 0.778683 | + | 0.520299i | 0.880239 | − | 0.474531i | \(-0.157382\pi\) |
−0.101556 | + | 0.994830i | \(0.532382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.1777 | + | 5.00816i | 0.817303 | + | 0.162572i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.6922 | + | 6.08571i | −0.476427 | + | 0.197343i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.7611 | − | 19.3691i | −1.51474 | − | 0.627426i | −0.538211 | − | 0.842810i | \(-0.680899\pi\) |
−0.976529 | + | 0.215385i | \(0.930899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.7255 | + | 11.1756i | −0.541226 | + | 0.361635i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.485531 | − | 2.44093i | −0.0156950 | − | 0.0789040i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.5868 | 0.826241 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −57.8654 | −1.86663 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.93238 | + | 34.8514i | 0.223393 | + | 1.12307i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.0450 | − | 16.7346i | 0.806228 | − | 0.538704i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.7556 | − | 20.6095i | −1.60003 | − | 0.662755i | −0.608612 | − | 0.793468i | \(-0.708274\pi\) |
−0.991420 | + | 0.130712i | \(0.958274\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.00568130 | − | 0.00235327i | 0.000182510 | − | 7.55980e-5i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0337 | − | 3.98496i | −0.642913 | − | 0.127883i | −0.137142 | − | 0.990551i | \(-0.543792\pi\) |
−0.505771 | + | 0.862668i | \(0.668792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.6103 | − | 7.75773i | −0.372208 | − | 0.248701i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0827 | + | 18.0827i | 0.579110 | + | 0.579110i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.15858 | − | 8.15858i | 0.261016 | − | 0.261016i | −0.564451 | − | 0.825467i | \(-0.690912\pi\) |
0.825467 | + | 0.564451i | \(0.190912\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3101 | − | 16.9268i | 0.361473 | − | 0.540983i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.73746 | + | 33.8715i | −0.215111 | + | 1.08143i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.28561 | + | 7.93217i | 0.104795 | + | 0.252997i | 0.967576 | − | 0.252581i | \(-0.0812794\pi\) |
−0.862781 | + | 0.505578i | \(0.831279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2921 | − | 36.9185i | 0.487248 | − | 1.17632i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.792336 | − | 1.18581i | −0.0252203 | − | 0.0377449i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.44644 | + | 0.486627i | −0.0777923 | + | 0.0154738i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.7977i | 0.692427i | 0.938156 | + | 0.346213i | \(0.112533\pi\) | ||||
−0.938156 | + | 0.346213i | \(0.887467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0539i | 0.636391i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.78441 | − | 0.553853i | 0.0882716 | − | 0.0175583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.81651 | − | 13.1948i | −0.279222 | − | 0.417885i | 0.665178 | − | 0.746685i | \(-0.268356\pi\) |
−0.944400 | + | 0.328800i | \(0.893356\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.27925 | − | 10.3310i | 0.135390 | − | 0.326859i |
(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 | 512.2.i.b.97.3 | 56 | ||
4.3 | odd | 2 | 512.2.i.a.97.5 | 56 | |||
8.3 | odd | 2 | 256.2.i.a.177.3 | 56 | |||
8.5 | even | 2 | 64.2.i.a.21.7 | ✓ | 56 | ||
24.5 | odd | 2 | 576.2.bd.a.469.1 | 56 | |||
64.3 | odd | 16 | 512.2.i.a.417.5 | 56 | |||
64.29 | even | 16 | 64.2.i.a.61.7 | yes | 56 | ||
64.35 | odd | 16 | 256.2.i.a.81.3 | 56 | |||
64.61 | even | 16 | inner | 512.2.i.b.417.3 | 56 | ||
192.29 | odd | 16 | 576.2.bd.a.253.1 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.2.i.a.21.7 | ✓ | 56 | 8.5 | even | 2 | ||
64.2.i.a.61.7 | yes | 56 | 64.29 | even | 16 | ||
256.2.i.a.81.3 | 56 | 64.35 | odd | 16 | |||
256.2.i.a.177.3 | 56 | 8.3 | odd | 2 | |||
512.2.i.a.97.5 | 56 | 4.3 | odd | 2 | |||
512.2.i.a.417.5 | 56 | 64.3 | odd | 16 | |||
512.2.i.b.97.3 | 56 | 1.1 | even | 1 | trivial | ||
512.2.i.b.417.3 | 56 | 64.61 | even | 16 | inner | ||
576.2.bd.a.253.1 | 56 | 192.29 | odd | 16 | |||
576.2.bd.a.469.1 | 56 | 24.5 | odd | 2 |