Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.5 | ||
Root | \(-1.35949 + 0.389597i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.c.143.4 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.207468i | 0.119782i | 0.998205 | + | 0.0598908i | \(0.0190753\pi\) | ||||
−0.998205 | + | 0.0598908i | \(0.980925\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32185 | − | 1.32185i | −0.499611 | − | 0.499611i | 0.411706 | − | 0.911317i | \(-0.364933\pi\) |
−0.911317 | + | 0.411706i | \(0.864933\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.95696 | 0.985652 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.39286 | + | 2.39286i | 0.721473 | + | 0.721473i | 0.968905 | − | 0.247432i | \(-0.0795867\pi\) |
−0.247432 | + | 0.968905i | \(0.579587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.20208 | −1.16545 | −0.582724 | − | 0.812670i | \(-0.698013\pi\) | ||||
−0.582724 | + | 0.812670i | \(0.698013\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.29071 | + | 3.29071i | 0.798114 | + | 0.798114i | 0.982798 | − | 0.184684i | \(-0.0591262\pi\) |
−0.184684 | + | 0.982798i | \(0.559126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.838342 | − | 0.838342i | −0.192329 | − | 0.192329i | 0.604373 | − | 0.796702i | \(-0.293424\pi\) |
−0.796702 | + | 0.604373i | \(0.793424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.274241 | − | 0.274241i | 0.0598443 | − | 0.0598443i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67277 | − | 2.67277i | 0.557311 | − | 0.557311i | −0.371230 | − | 0.928541i | \(-0.621064\pi\) |
0.928541 | + | 0.371230i | \(0.121064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.23588i | 0.237845i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.55451 | − | 2.55451i | 0.474361 | − | 0.474361i | −0.428961 | − | 0.903323i | \(-0.641120\pi\) |
0.903323 | + | 0.428961i | \(0.141120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.23723i | 1.12024i | 0.828412 | + | 0.560120i | \(0.189245\pi\) | ||||
−0.828412 | + | 0.560120i | \(0.810755\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.496441 | + | 0.496441i | −0.0864192 | + | 0.0864192i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.29451 | −0.706013 | −0.353006 | − | 0.935621i | \(-0.614841\pi\) | ||||
−0.353006 | + | 0.935621i | \(0.614841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.871798i | − | 0.139599i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.06598i | 1.10352i | 0.834002 | + | 0.551761i | \(0.186044\pi\) | ||||
−0.834002 | + | 0.551761i | \(0.813956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.43258 | 1.43845 | 0.719227 | − | 0.694775i | \(-0.244496\pi\) | ||||
0.719227 | + | 0.694775i | \(0.244496\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.31820 | − | 8.31820i | 1.21333 | − | 1.21333i | 0.243410 | − | 0.969923i | \(-0.421734\pi\) |
0.969923 | − | 0.243410i | \(-0.0782662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.50544i | − | 0.500777i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.682716 | + | 0.682716i | −0.0955994 | + | 0.0955994i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.66672i | 1.05311i | 0.850143 | + | 0.526553i | \(0.176516\pi\) | ||||
−0.850143 | + | 0.526553i | \(0.823484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.173929 | − | 0.173929i | 0.0230375 | − | 0.0230375i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.07557 | − | 7.07557i | 0.921161 | − | 0.921161i | −0.0759506 | − | 0.997112i | \(-0.524199\pi\) |
0.997112 | + | 0.0759506i | \(0.0241991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.74267 | + | 8.74267i | 1.11938 | + | 1.11938i | 0.991832 | + | 0.127552i | \(0.0407120\pi\) |
0.127552 | + | 0.991832i | \(0.459288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.90865 | − | 3.90865i | −0.492443 | − | 0.492443i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5494 | −1.53315 | −0.766574 | − | 0.642156i | \(-0.778040\pi\) | ||||
−0.766574 | + | 0.642156i | \(0.778040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.554514 | + | 0.554514i | 0.0667556 | + | 0.0667556i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4624 | 1.24166 | 0.620829 | − | 0.783946i | \(-0.286796\pi\) | ||||
0.620829 | + | 0.783946i | \(0.286796\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.79095 | − | 4.79095i | −0.560738 | − | 0.560738i | 0.368779 | − | 0.929517i | \(-0.379776\pi\) |
−0.929517 | + | 0.368779i | \(0.879776\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.32598i | − | 0.720912i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.69963 | 0.978784 | 0.489392 | − | 0.872064i | \(-0.337219\pi\) | ||||
0.489392 | + | 0.872064i | \(0.337219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.61447 | 0.957163 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.14519i | 0.454993i | 0.973779 | + | 0.227497i | \(0.0730541\pi\) | ||||
−0.973779 | + | 0.227497i | \(0.926946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.529980 | + | 0.529980i | 0.0568198 | + | 0.0568198i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.548482 | −0.0581390 | −0.0290695 | − | 0.999577i | \(-0.509254\pi\) | ||||
−0.0290695 | + | 0.999577i | \(0.509254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.55451 | + | 5.55451i | 0.582271 | + | 0.582271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.29403 | −0.134184 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2022 | + | 12.2022i | 1.23895 | + | 1.23895i | 0.960431 | + | 0.278518i | \(0.0898433\pi\) |
0.278518 | + | 0.960431i | \(0.410157\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.07557 | + | 7.07557i | 0.711122 | + | 0.711122i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.46843 | + | 6.46843i | −0.643633 | + | 0.643633i | −0.951447 | − | 0.307814i | \(-0.900403\pi\) |
0.307814 | + | 0.951447i | \(0.400403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.55234 | + | 6.55234i | −0.645621 | + | 0.645621i | −0.951932 | − | 0.306310i | \(-0.900905\pi\) |
0.306310 | + | 0.951932i | \(0.400905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3708i | 1.58262i | 0.611413 | + | 0.791312i | \(0.290601\pi\) | ||||
−0.611413 | + | 0.791312i | \(0.709399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | − | 2.00000i | 0.191565 | − | 0.191565i | −0.604807 | − | 0.796372i | \(-0.706750\pi\) |
0.796372 | + | 0.604807i | \(0.206750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.890973i | − | 0.0845674i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8688 | − | 11.8688i | 1.11652 | − | 1.11652i | 0.124275 | − | 0.992248i | \(-0.460339\pi\) |
0.992248 | − | 0.124275i | \(-0.0396606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.4254 | −1.14873 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 8.69963i | − | 0.797493i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.451518i | 0.0410471i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.46597 | −0.132182 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55946 | − | 5.55946i | 0.493322 | − | 0.493322i | −0.416029 | − | 0.909351i | \(-0.636579\pi\) |
0.909351 | + | 0.416029i | \(0.136579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.95696i | 0.172300i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16166 | + | 3.16166i | −0.276235 | + | 0.276235i | −0.831604 | − | 0.555369i | \(-0.812577\pi\) |
0.555369 | + | 0.831604i | \(0.312577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.21632i | 0.192179i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.507360 | − | 0.507360i | 0.0433467 | − | 0.0433467i | −0.685101 | − | 0.728448i | \(-0.740242\pi\) |
0.728448 | + | 0.685101i | \(0.240242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.52106 | + | 5.52106i | −0.468290 | + | 0.468290i | −0.901360 | − | 0.433070i | \(-0.857430\pi\) |
0.433070 | + | 0.901360i | \(0.357430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.72576 | + | 1.72576i | 0.145335 | + | 0.145335i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0550 | − | 10.0550i | −0.840840 | − | 0.840840i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.727266 | 0.0599839 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.82875 | − | 2.82875i | −0.231741 | − | 0.231741i | 0.581678 | − | 0.813419i | \(-0.302396\pi\) |
−0.813419 | + | 0.581678i | \(0.802396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.12820 | −0.580085 | −0.290042 | − | 0.957014i | \(-0.593669\pi\) | ||||
−0.290042 | + | 0.957014i | \(0.593669\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.73048 | + | 9.73048i | 0.786663 | + | 0.786663i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.7371i | − | 1.65500i | −0.561464 | − | 0.827501i | \(-0.689762\pi\) | ||
0.561464 | − | 0.827501i | \(-0.310238\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.59060 | −0.126143 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.06598 | −0.556878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8985i | 0.853640i | 0.904337 | + | 0.426820i | \(0.140366\pi\) | ||||
−0.904337 | + | 0.426820i | \(0.859634\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.20680 | − | 1.20680i | −0.0933853 | − | 0.0933853i | 0.658871 | − | 0.752256i | \(-0.271034\pi\) |
−0.752256 | + | 0.658871i | \(0.771034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.65751 | 0.358270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.47894 | − | 2.47894i | −0.189569 | − | 0.189569i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.12438 | −0.389599 | −0.194800 | − | 0.980843i | \(-0.562406\pi\) | ||||
−0.194800 | + | 0.980843i | \(0.562406\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.46795 | + | 1.46795i | 0.110338 | + | 0.110338i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6301 | − | 12.6301i | −0.944017 | − | 0.944017i | 0.0544970 | − | 0.998514i | \(-0.482644\pi\) |
−0.998514 | + | 0.0544970i | \(0.982644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.46843 | − | 8.46843i | 0.629453 | − | 0.629453i | −0.318477 | − | 0.947931i | \(-0.603171\pi\) |
0.947931 | + | 0.318477i | \(0.103171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.81382 | + | 1.81382i | −0.134082 | + | 0.134082i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.7484i | 1.15164i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.63364 | − | 1.63364i | 0.118830 | − | 0.118830i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3534i | 0.821501i | 0.911748 | + | 0.410750i | \(0.134733\pi\) | ||||
−0.911748 | + | 0.410750i | \(0.865267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0245 | − | 11.0245i | 0.793561 | − | 0.793561i | −0.188510 | − | 0.982071i | \(-0.560366\pi\) |
0.982071 | + | 0.188510i | \(0.0603658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.1953 | −1.51010 | −0.755050 | − | 0.655667i | \(-0.772388\pi\) | ||||
−0.755050 | + | 0.655667i | \(0.772388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.68045i | 0.615341i | 0.951493 | + | 0.307670i | \(0.0995494\pi\) | ||||
−0.951493 | + | 0.307670i | \(0.900451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.60359i | − | 0.183643i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.75335 | −0.473993 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.90326 | − | 7.90326i | 0.549315 | − | 0.549315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.01206i | − | 0.277520i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.28986 | − | 6.28986i | 0.433012 | − | 0.433012i | −0.456640 | − | 0.889652i | \(-0.650947\pi\) |
0.889652 | + | 0.456640i | \(0.150947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.17061i | 0.148728i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.24467 | − | 8.24467i | 0.559684 | − | 0.559684i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.993968 | − | 0.993968i | 0.0671661 | − | 0.0671661i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8278 | − | 13.8278i | −0.930160 | − | 0.930160i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.50264 | − | 3.50264i | −0.234554 | − | 0.234554i | 0.580036 | − | 0.814591i | \(-0.303038\pi\) |
−0.814591 | + | 0.580036i | \(0.803038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.622404 | −0.0413104 | −0.0206552 | − | 0.999787i | \(-0.506575\pi\) | ||||
−0.0206552 | + | 0.999787i | \(0.506575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.35940 | + | 9.35940i | 0.618487 | + | 0.618487i | 0.945143 | − | 0.326657i | \(-0.105922\pi\) |
−0.326657 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.31244 | 0.0863521 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.79047 | + | 1.79047i | 0.117297 | + | 0.117297i | 0.763319 | − | 0.646022i | \(-0.223568\pi\) |
−0.646022 | + | 0.763319i | \(0.723568\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.80489i | 0.117240i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9056 | −1.35227 | −0.676136 | − | 0.736777i | \(-0.736347\pi\) | ||||
−0.676136 | + | 0.736777i | \(0.736347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.70055 | −0.238374 | −0.119187 | − | 0.992872i | \(-0.538029\pi\) | ||||
−0.119187 | + | 0.992872i | \(0.538029\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.49486i | 0.352495i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52278 | + | 3.52278i | 0.224149 | + | 0.224149i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.859993 | −0.0544999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.630086 | − | 0.630086i | −0.0397707 | − | 0.0397707i | 0.686942 | − | 0.726712i | \(-0.258953\pi\) |
−0.726712 | + | 0.686942i | \(0.758953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7911 | 0.804170 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.62414 | + | 3.62414i | 0.226068 | + | 0.226068i | 0.811048 | − | 0.584980i | \(-0.198898\pi\) |
−0.584980 | + | 0.811048i | \(0.698898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.67668 | + | 5.67668i | 0.352732 | + | 0.352732i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.55359 | − | 7.55359i | 0.467555 | − | 0.467555i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.25957 | − | 5.25957i | 0.324319 | − | 0.324319i | −0.526102 | − | 0.850421i | \(-0.676347\pi\) |
0.850421 | + | 0.526102i | \(0.176347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.113792i | − | 0.00696398i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.82875 | + | 8.82875i | −0.538299 | + | 0.538299i | −0.923029 | − | 0.384730i | \(-0.874294\pi\) |
0.384730 | + | 0.923029i | \(0.374294\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.9177i | − | 1.87812i | −0.343760 | − | 0.939058i | \(-0.611701\pi\) | ||
0.343760 | − | 0.939058i | \(-0.388299\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.15238 | + | 1.15238i | −0.0697454 | + | 0.0697454i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9322 | 1.13753 | 0.568764 | − | 0.822501i | \(-0.307422\pi\) | ||||
0.568764 | + | 0.822501i | \(0.307422\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.4432i | 1.10417i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.51750i | − | 0.388802i | −0.980922 | − | 0.194401i | \(-0.937724\pi\) | ||
0.980922 | − | 0.194401i | \(-0.0622762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0721 | 0.955390 | 0.477695 | − | 0.878526i | \(-0.341472\pi\) | ||||
0.477695 | + | 0.878526i | \(0.341472\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.34015 | − | 9.34015i | 0.551332 | − | 0.551332i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.65751i | 0.273971i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.53157 | + | 2.53157i | −0.148403 | + | 0.148403i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.829872i | 0.0484816i | 0.999706 | + | 0.0242408i | \(0.00771685\pi\) | ||||
−0.999706 | + | 0.0242408i | \(0.992283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.95728 | + | 2.95728i | −0.171599 | + | 0.171599i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.2312 | + | 11.2312i | −0.649517 | + | 0.649517i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.4684 | − | 12.4684i | −0.718668 | − | 0.718668i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.34199 | − | 1.34199i | −0.0770954 | − | 0.0770954i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4115 | −1.62153 | −0.810766 | − | 0.585371i | \(-0.800949\pi\) | ||||
−0.810766 | + | 0.585371i | \(0.800949\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.35940 | − | 1.35940i | −0.0773336 | − | 0.0773336i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8087 | −1.80370 | −0.901852 | − | 0.432046i | \(-0.857792\pi\) | ||||
−0.901852 | + | 0.432046i | \(0.857792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7727 | − | 18.7727i | −1.06110 | − | 1.06110i | −0.998008 | − | 0.0630896i | \(-0.979905\pi\) |
−0.0630896 | − | 0.998008i | \(-0.520095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.6205i | 0.596506i | 0.954487 | + | 0.298253i | \(0.0964039\pi\) | ||||
−0.954487 | + | 0.298253i | \(0.903596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.2252 | 0.684478 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.39641 | −0.189569 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.51748i | − | 0.307001i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.414936 | + | 0.414936i | 0.0229460 | + | 0.0229460i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.9908 | −1.21239 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.4098 | − | 22.4098i | −1.23175 | − | 1.23175i | −0.963290 | − | 0.268462i | \(-0.913485\pi\) |
−0.268462 | − | 0.963290i | \(-0.586515\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6987 | −0.695883 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.95728 | + | 2.95728i | 0.161093 | + | 0.161093i | 0.783051 | − | 0.621958i | \(-0.213662\pi\) |
−0.621958 | + | 0.783051i | \(0.713662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.46240 | + | 2.46240i | 0.133739 | + | 0.133739i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.9248 | + | 14.9248i | −0.808223 | + | 0.808223i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8866 | + | 13.8866i | −0.749805 | + | 0.749805i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.8901i | − | 0.745659i | −0.927900 | − | 0.372830i | \(-0.878388\pi\) | ||
0.927900 | − | 0.372830i | \(-0.121612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4914 | + | 13.4914i | −0.722176 | + | 0.722176i | −0.969048 | − | 0.246872i | \(-0.920597\pi\) |
0.246872 | + | 0.969048i | \(0.420597\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.19326i | − | 0.277196i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.9785 | + | 15.9785i | −0.850448 | + | 0.850448i | −0.990188 | − | 0.139740i | \(-0.955373\pi\) |
0.139740 | + | 0.990188i | \(0.455373\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.80489 | 0.0955251 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 28.2831i | − | 1.49273i | −0.665539 | − | 0.746363i | \(-0.731798\pi\) | ||
0.665539 | − | 0.746363i | \(-0.268202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.5944i | − | 0.926019i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0936755 | −0.00491669 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.8285 | + | 16.8285i | −0.878439 | + | 0.878439i | −0.993373 | − | 0.114934i | \(-0.963334\pi\) |
0.114934 | + | 0.993373i | \(0.463334\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.8938i | 1.08769i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1342 | − | 10.1342i | 0.526143 | − | 0.526143i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.03845i | 0.416215i | 0.978106 | + | 0.208108i | \(0.0667304\pi\) | ||||
−0.978106 | + | 0.208108i | \(0.933270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.7343 | + | 10.7343i | −0.552844 | + | 0.552844i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.30677 | + | 2.30677i | −0.118491 | + | 0.118491i | −0.763866 | − | 0.645375i | \(-0.776701\pi\) |
0.645375 | + | 0.763866i | \(0.276701\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15341 | + | 1.15341i | 0.0590910 | + | 0.0590910i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.85530 | + | 7.85530i | 0.401387 | + | 0.401387i | 0.878722 | − | 0.477335i | \(-0.158397\pi\) |
−0.477335 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.8917 | 1.41782 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.2171 | − | 27.2171i | −1.37996 | − | 1.37996i | −0.844660 | − | 0.535303i | \(-0.820197\pi\) |
−0.535303 | − | 0.844660i | \(-0.679803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.5906 | 0.889595 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.655943 | − | 0.655943i | −0.0330879 | − | 0.0330879i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.38693i | − | 0.220174i | −0.993922 | − | 0.110087i | \(-0.964887\pi\) | ||
0.993922 | − | 0.110087i | \(-0.0351129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.459815 | −0.0230196 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.5944 | −1.22818 | −0.614092 | − | 0.789234i | \(-0.710478\pi\) | ||||
−0.614092 | + | 0.789234i | \(0.710478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 26.2094i | − | 1.30558i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2761 | − | 10.2761i | −0.509369 | − | 0.509369i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.06598 | −0.349390 | −0.174695 | − | 0.984623i | \(-0.555894\pi\) | ||||
−0.174695 | + | 0.984623i | \(0.555894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.105261 | + | 0.105261i | 0.00519214 | + | 0.00519214i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.7057 | −0.920445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.14544 | − | 1.14544i | −0.0560926 | − | 0.0560926i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.54400 | − | 4.54400i | −0.221989 | − | 0.221989i | 0.587347 | − | 0.809336i | \(-0.300173\pi\) |
−0.809336 | + | 0.587347i | \(0.800173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.47539 | − | 5.47539i | 0.266854 | − | 0.266854i | −0.560977 | − | 0.827831i | \(-0.689574\pi\) |
0.827831 | + | 0.560977i | \(0.189574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.5966 | − | 24.5966i | 1.19593 | − | 1.19593i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 23.1129i | − | 1.11851i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.08609 | − | 2.08609i | 0.100717 | − | 0.100717i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.6658i | − | 0.610090i | −0.952338 | − | 0.305045i | \(-0.901328\pi\) | ||
0.952338 | − | 0.305045i | \(-0.0986716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0499 | + | 11.0499i | −0.531022 | + | 0.531022i | −0.920876 | − | 0.389854i | \(-0.872525\pi\) |
0.389854 | + | 0.920876i | \(0.372525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.48139 | −0.214374 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.4936i | 0.978108i | 0.872254 | + | 0.489054i | \(0.162658\pi\) | ||||
−0.872254 | + | 0.489054i | \(0.837342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 10.3654i | − | 0.493592i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0123 | 0.523212 | 0.261606 | − | 0.965175i | \(-0.415748\pi\) | ||||
0.261606 | + | 0.965175i | \(0.415748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.586876 | − | 0.586876i | 0.0277583 | − | 0.0277583i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.4423i | − | 0.728767i | −0.931249 | − | 0.364383i | \(-0.881280\pi\) | ||
0.931249 | − | 0.364383i | \(-0.118720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.9079 | + | 16.9079i | −0.796161 | + | 0.796161i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.47887i | − | 0.0694835i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.14212 | + | 3.14212i | −0.146982 | + | 0.146982i | −0.776769 | − | 0.629786i | \(-0.783143\pi\) |
0.629786 | + | 0.776769i | \(0.283143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.06691 | + | 4.06691i | −0.189827 | + | 0.189827i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.45636 | + | 8.45636i | 0.393852 | + | 0.393852i | 0.876058 | − | 0.482206i | \(-0.160164\pi\) |
−0.482206 | + | 0.876058i | \(0.660164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5859 | + | 21.5859i | 1.00318 | + | 1.00318i | 0.999995 | + | 0.00318643i | \(0.00101428\pi\) |
0.00318643 | + | 0.999995i | \(0.498986\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.4880 | 1.04062 | 0.520311 | − | 0.853977i | \(-0.325816\pi\) | ||||
0.520311 | + | 0.853977i | \(0.325816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.5883 | + | 16.5883i | 0.765978 | + | 0.765978i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.30229 | 0.198239 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.5708 | + | 22.5708i | 1.03781 | + | 1.03781i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6702i | 1.03800i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.852623 | −0.0389573 | −0.0194787 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194787 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0459 | 0.822821 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.46597i | − | 0.0667037i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.49958 | + | 2.49958i | 0.113267 | + | 0.113267i | 0.761469 | − | 0.648202i | \(-0.224479\pi\) |
−0.648202 | + | 0.761469i | \(0.724479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.26110 | −0.102250 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1177 | − | 22.1177i | −0.998157 | − | 0.998157i | 0.00184099 | − | 0.999998i | \(-0.499414\pi\) |
−0.999998 | + | 0.00184099i | \(0.999414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8123 | 0.757189 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.8297 | − | 13.8297i | −0.620346 | − | 0.620346i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.73911 | + | 7.73911i | 0.346450 | + | 0.346450i | 0.858786 | − | 0.512335i | \(-0.171219\pi\) |
−0.512335 | + | 0.858786i | \(0.671219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.250373 | − | 0.250373i | 0.0111858 | − | 0.0111858i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.9144 | − | 13.9144i | 0.620413 | − | 0.620413i | −0.325224 | − | 0.945637i | \(-0.605440\pi\) |
0.945637 | + | 0.325224i | \(0.105440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.966284i | 0.0429142i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.48049 | − | 4.48049i | 0.198594 | − | 0.198594i | −0.600803 | − | 0.799397i | \(-0.705152\pi\) |
0.799397 | + | 0.600803i | \(0.205152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6658i | 0.560302i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.03609 | − | 1.03609i | 0.0457444 | − | 0.0457444i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.8085 | 1.75078 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.06314i | − | 0.0466669i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.26728i | − | 0.143142i | −0.997435 | − | 0.0715711i | \(-0.977199\pi\) | ||
0.997435 | − | 0.0715711i | \(-0.0228013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1372 | −0.443270 | −0.221635 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221635 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.5249 | + | 20.5249i | −0.894079 | + | 0.894079i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.71262i | 0.378809i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.9222 | − | 20.9222i | 0.907945 | − | 0.907945i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 29.6919i | − | 1.28610i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.62034 | − | 2.62034i | 0.113076 | − | 0.113076i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.38801 | − | 8.38801i | 0.361297 | − | 0.361297i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3823 | − | 18.3823i | −0.790319 | − | 0.790319i | 0.191227 | − | 0.981546i | \(-0.438753\pi\) |
−0.981546 | + | 0.191227i | \(0.938753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.75693 | + | 1.75693i | 0.0753970 | + | 0.0753970i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.60503 | −0.154140 | −0.0770699 | − | 0.997026i | \(-0.524556\pi\) | ||||
−0.0770699 | + | 0.997026i | \(0.524556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.8517 | + | 25.8517i | 1.10332 | + | 1.10332i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.28311 | −0.182467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.4996 | − | 11.4996i | −0.489012 | − | 0.489012i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5670i | 0.913823i | 0.889512 | + | 0.456911i | \(0.151044\pi\) | ||||
−0.889512 | + | 0.456911i | \(0.848956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.6365 | −1.67644 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.26728 | −0.137945 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.5306i | 1.11813i | 0.829123 | + | 0.559066i | \(0.188840\pi\) | ||||
−0.829123 | + | 0.559066i | \(0.811160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.3870 | − | 11.3870i | −0.478209 | − | 0.478209i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.23630 | 0.387206 | 0.193603 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193603 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.6530 | + | 31.6530i | 1.32464 | + | 1.32464i | 0.909975 | + | 0.414663i | \(0.136100\pi\) |
0.414663 | + | 0.909975i | \(0.363900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.35546 | −0.0984007 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8539 | − | 23.8539i | −0.993051 | − | 0.993051i | 0.00692502 | − | 0.999976i | \(-0.497796\pi\) |
−0.999976 | + | 0.00692502i | \(0.997796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.28723 | + | 2.28723i | 0.0950541 | + | 0.0950541i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.47931 | − | 5.47931i | 0.227320 | − | 0.227320i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.3454 | + | 18.3454i | −0.759787 | + | 0.759787i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 24.2348i | − | 1.00028i | −0.865946 | − | 0.500138i | \(-0.833282\pi\) | ||
0.865946 | − | 0.500138i | \(-0.166718\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.22893 | − | 5.22893i | 0.215454 | − | 0.215454i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 4.39734i | − | 0.180882i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4929 | + | 15.4929i | −0.636219 | + | 0.636219i | −0.949621 | − | 0.313402i | \(-0.898531\pi\) |
0.313402 | + | 0.949621i | \(0.398531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.80091 | −0.0737065 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.1812i | 0.783722i | 0.920024 | + | 0.391861i | \(0.128169\pi\) | ||||
−0.920024 | + | 0.391861i | \(0.871831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7464i | 0.887056i | 0.896261 | + | 0.443528i | \(0.146273\pi\) | ||||
−0.896261 | + | 0.443528i | \(0.853727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.1079 | −1.51115 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.2541 | + | 20.2541i | −0.822088 | + | 0.822088i | −0.986407 | − | 0.164319i | \(-0.947457\pi\) |
0.164319 | + | 0.986407i | \(0.447457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.40110i | − | 0.0567756i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.9538 | + | 34.9538i | −1.41408 | + | 1.41408i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.00698i | − | 0.242620i | −0.992615 | − | 0.121310i | \(-0.961291\pi\) | ||
0.992615 | − | 0.121310i | \(-0.0387094\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9289 | − | 20.9289i | 0.842566 | − | 0.842566i | −0.146626 | − | 0.989192i | \(-0.546841\pi\) |
0.989192 | + | 0.146626i | \(0.0468413\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.30074 | − | 3.30074i | 0.132668 | − | 0.132668i | −0.637655 | − | 0.770322i | \(-0.720095\pi\) |
0.770322 | + | 0.637655i | \(0.220095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.30321 | + | 3.30321i | 0.132553 | + | 0.132553i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.725009 | + | 0.725009i | 0.0290469 | + | 0.0290469i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.832374 | 0.0332418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.1320 | − | 14.1320i | −0.563479 | − | 0.563479i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.39734 | −0.175055 | −0.0875276 | − | 0.996162i | \(-0.527897\pi\) | ||||
−0.0875276 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.30494 | + | 1.30494i | 0.0518669 | + | 0.0518669i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7301i | 0.583630i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.9369 | 1.22384 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.74978 | 0.345596 | 0.172798 | − | 0.984957i | \(-0.444719\pi\) | ||||
0.172798 | + | 0.984957i | \(0.444719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.4968i | − | 1.04493i | −0.852660 | − | 0.522466i | \(-0.825012\pi\) | ||
0.852660 | − | 0.522466i | \(-0.174988\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.8343 | + | 15.8343i | 0.622512 | + | 0.622512i | 0.946173 | − | 0.323661i | \(-0.104914\pi\) |
−0.323661 | + | 0.946173i | \(0.604914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.8616 | 1.32919 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.71050 | + | 1.71050i | 0.0670399 | + | 0.0670399i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.4608 | 1.03549 | 0.517746 | − | 0.855534i | \(-0.326771\pi\) | ||||
0.517746 | + | 0.855534i | \(0.326771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.1666 | − | 14.1666i | −0.552693 | − | 0.552693i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.5128 | − | 30.5128i | −1.18861 | − | 1.18861i | −0.977452 | − | 0.211156i | \(-0.932277\pi\) |
−0.211156 | − | 0.977452i | \(-0.567723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.81695 | + | 4.81695i | −0.187358 | + | 0.187358i | −0.794553 | − | 0.607195i | \(-0.792295\pi\) |
0.607195 | + | 0.794553i | \(0.292295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.86883 | − | 2.86883i | 0.111416 | − | 0.111416i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.6552i | − | 0.528733i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.726685 | − | 0.726685i | 0.0280953 | − | 0.0280953i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.8399i | 1.61521i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.80519 | + | 2.80519i | −0.108132 | + | 0.108132i | −0.759103 | − | 0.650971i | \(-0.774362\pi\) |
0.650971 | + | 0.759103i | \(0.274362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.5498 | 0.674492 | 0.337246 | − | 0.941417i | \(-0.390505\pi\) | ||||
0.337246 | + | 0.941417i | \(0.390505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 32.2590i | − | 1.23799i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 0.129129i | − | 0.00494823i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.7834 | −0.833518 | −0.416759 | − | 0.909017i | \(-0.636834\pi\) | ||||
−0.416759 | + | 0.909017i | \(0.636834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.94178 | + | 1.94178i | −0.0740833 | + | 0.0740833i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32.2162i | − | 1.22734i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.2147 | − | 31.2147i | 1.18746 | − | 1.18746i | 0.209694 | − | 0.977767i | \(-0.432753\pi\) |
0.977767 | − | 0.209694i | \(-0.0672469\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 18.7057i | − | 0.710569i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.2521 | + | 23.2521i | −0.880736 | + | 0.880736i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.371464 | + | 0.371464i | −0.0140501 | + | 0.0140501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.9248 | + | 20.9248i | 0.790318 | + | 0.790318i | 0.981546 | − | 0.191227i | \(-0.0612468\pi\) |
−0.191227 | + | 0.981546i | \(0.561247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.60027 | + | 3.60027i | 0.135787 | + | 0.135787i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.1005 | 0.643132 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.3703 | − | 26.3703i | −0.990357 | − | 0.990357i | 0.00959736 | − | 0.999954i | \(-0.496945\pi\) |
−0.999954 | + | 0.00959736i | \(0.996945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.7244 | 0.964741 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.6707 | + | 16.6707i | 0.624322 | + | 0.624322i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 4.33724i | − | 0.161977i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.65374 | −0.0989679 | −0.0494840 | − | 0.998775i | \(-0.515758\pi\) | ||||
−0.0494840 | + | 0.998775i | \(0.515758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3224 | 0.645119 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 0.767746i | − | 0.0285528i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.8999 | + | 30.8999i | 1.14601 | + | 1.14601i | 0.987329 | + | 0.158685i | \(0.0507255\pi\) |
0.158685 | + | 0.987329i | \(0.449275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.7034 | 0.914940 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.0399 | + | 31.0399i | 1.14805 | + | 1.14805i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.2726 | 1.70912 | 0.854559 | − | 0.519354i | \(-0.173828\pi\) | ||||
0.854559 | + | 0.519354i | \(0.173828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.0288 | − | 30.0288i | −1.10613 | − | 1.10613i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0504 | + | 12.0504i | 0.443280 | + | 0.443280i | 0.893113 | − | 0.449833i | \(-0.148516\pi\) |
−0.449833 | + | 0.893113i | \(0.648516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.730865 | + | 0.730865i | −0.0268490 | + | 0.0268490i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.4100 | + | 21.4100i | −0.785456 | + | 0.785456i | −0.980746 | − | 0.195290i | \(-0.937435\pi\) |
0.195290 | + | 0.980746i | \(0.437435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2571i | 0.448465i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.6397 | − | 21.6397i | 0.790696 | − | 0.790696i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50828i | 0.310472i | 0.987877 | + | 0.155236i | \(0.0496137\pi\) | ||||
−0.987877 | + | 0.155236i | \(0.950386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.130723 | − | 0.130723i | 0.00476379 | − | 0.00476379i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.2794 | 1.06418 | 0.532089 | − | 0.846688i | \(-0.321407\pi\) | ||||
0.532089 | + | 0.846688i | \(0.321407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.65374i | 0.0963248i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.3132i | 1.42510i | 0.701621 | + | 0.712551i | \(0.252460\pi\) | ||||
−0.701621 | + | 0.712551i | \(0.747540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.28739 | −0.191416 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.7321 | + | 29.7321i | −1.07357 | + | 1.07357i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.4222i | 0.952809i | 0.879226 | + | 0.476404i | \(0.158060\pi\) | ||||
−0.879226 | + | 0.476404i | \(0.841940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.751892 | + | 0.751892i | −0.0270787 | + | 0.0270787i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.08416i | − | 0.290767i | −0.989375 | − | 0.145383i | \(-0.953558\pi\) | ||
0.989375 | − | 0.145383i | \(-0.0464416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.17773 | + | 1.17773i | −0.0422508 | + | 0.0422508i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.92371 | − | 5.92371i | 0.212239 | − | 0.212239i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.0350 | + | 25.0350i | 0.895823 | + | 0.895823i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.15707 | + | 3.15707i | 0.112824 | + | 0.112824i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.5596 | 1.44579 | 0.722897 | − | 0.690955i | \(-0.242810\pi\) | ||||
0.722897 | + | 0.690955i | \(0.242810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.09119 | + | 1.09119i | 0.0388474 | + | 0.0388474i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.3775 | −1.11566 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.7374 | − | 36.7374i | −1.30458 | − | 1.30458i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.85060i | 0.0655517i | 0.999463 | + | 0.0327759i | \(0.0104347\pi\) | ||||
−0.999463 | + | 0.0327759i | \(0.989565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.7455 | 1.93676 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.62184 | −0.0573048 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 22.9281i | − | 0.809115i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.83168 | − | 1.83168i | −0.0644783 | − | 0.0644783i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.5823 | −0.934584 | −0.467292 | − | 0.884103i | \(-0.654770\pi\) | ||||
−0.467292 | + | 0.884103i | \(0.654770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.49812 | − | 6.49812i | −0.228180 | − | 0.228180i | 0.583752 | − | 0.811932i | \(-0.301584\pi\) |
−0.811932 | + | 0.583752i | \(0.801584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.41443 | 0.224964 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.90773 | − | 7.90773i | −0.276656 | − | 0.276656i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.4245 | + | 16.4245i | 0.573917 | + | 0.573917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | − | 6.00000i | 0.209401 | − | 0.209401i | −0.594612 | − | 0.804013i | \(-0.702694\pi\) |
0.804013 | + | 0.594612i | \(0.202694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.1106 | + | 15.1106i | −0.526722 | + | 0.526722i | −0.919593 | − | 0.392871i | \(-0.871482\pi\) |
0.392871 | + | 0.919593i | \(0.371482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.3792i | − | 0.465241i | −0.972568 | − | 0.232621i | \(-0.925270\pi\) | ||
0.972568 | − | 0.232621i | \(-0.0747301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.81788 | + | 5.81788i | −0.202063 | + | 0.202063i | −0.800883 | − | 0.598820i | \(-0.795636\pi\) |
0.598820 | + | 0.800883i | \(0.295636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.92783i | 0.136255i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5354 | − | 11.5354i | 0.399677 | − | 0.399677i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.70845 | −0.266443 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27.4305i | − | 0.947006i | −0.880792 | − | 0.473503i | \(-0.842989\pi\) | ||
0.880792 | − | 0.473503i | \(-0.157011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9489i | 0.549963i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.35217 | 0.0465713 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.596838 | − | 0.596838i | 0.0205076 | − | 0.0205076i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.33445i | 0.114438i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4782 | + | 11.4782i | −0.393469 | + | 0.393469i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6692i | 0.570742i | 0.958417 | + | 0.285371i | \(0.0921169\pi\) | ||||
−0.958417 | + | 0.285371i | \(0.907883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.73331 | − | 4.73331i | 0.161687 | − | 0.161687i | −0.621627 | − | 0.783314i | \(-0.713528\pi\) |
0.783314 | + | 0.621627i | \(0.213528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.3237 | − | 26.3237i | 0.898152 | − | 0.898152i | −0.0971203 | − | 0.995273i | \(-0.530963\pi\) |
0.995273 | + | 0.0971203i | \(0.0309632\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.93778 | + | 1.93778i | 0.0660394 | + | 0.0660394i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.71130 | + | 8.71130i | 0.296536 | + | 0.296536i | 0.839655 | − | 0.543119i | \(-0.182757\pi\) |
−0.543119 | + | 0.839655i | \(0.682757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.966284 | −0.0328167 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.8170 | + | 20.8170i | 0.706167 | + | 0.706167i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.7334 | 1.78680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.0815 | + | 36.0815i | 1.22117 | + | 1.22117i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.6674i | − | 1.13687i | −0.822730 | − | 0.568433i | \(-0.807550\pi\) | ||
0.822730 | − | 0.568433i | \(-0.192450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.172172 | −0.00580721 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.3058 | 0.919956 | 0.459978 | − | 0.887930i | \(-0.347857\pi\) | ||||
0.459978 | + | 0.887930i | \(0.347857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.9628i | − | 0.941023i | −0.882394 | − | 0.470511i | \(-0.844070\pi\) | ||
0.882394 | − | 0.470511i | \(-0.155930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.4497 | − | 12.4497i | −0.418020 | − | 0.418020i | 0.466501 | − | 0.884521i | \(-0.345514\pi\) |
−0.884521 | + | 0.466501i | \(0.845514\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6975 | −0.492939 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.6132 | + | 20.6132i | 0.690567 | + | 0.690567i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.9470 | −0.466718 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.33011 | − | 2.33011i | −0.0778002 | − | 0.0778002i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.9331 | + | 15.9331i | 0.531398 | + | 0.531398i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.2289 | + | 25.2289i | −0.840498 | + | 0.840498i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.58680 | − | 2.58680i | 0.0860833 | − | 0.0860833i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.3527i | − | 1.27348i | −0.771078 | − | 0.636740i | \(-0.780282\pi\) | ||
0.771078 | − | 0.636740i | \(-0.219718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1269 | + | 19.1269i | −0.634398 | + | 0.634398i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.0192i | − | 0.795791i | −0.917431 | − | 0.397895i | \(-0.869741\pi\) | ||
0.917431 | − | 0.397895i | \(-0.130259\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.91884 | + | 9.91884i | −0.328266 | + | 0.328266i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.35846 | 0.276021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1211i | 0.828668i | 0.910125 | + | 0.414334i | \(0.135986\pi\) | ||||
−0.910125 | + | 0.414334i | \(0.864014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 5.89448i | − | 0.194230i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.9639 | −1.44709 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.3750 | + | 19.3750i | −0.636358 | + | 0.636358i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 39.8307i | − | 1.30680i | −0.757012 | − | 0.653401i | \(-0.773342\pi\) | ||
0.757012 | − | 0.653401i | \(-0.226658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.93876 | + | 2.93876i | −0.0963139 | + | 0.0963139i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 6.59927i | − | 0.216051i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2763 | + | 18.2763i | −0.597060 | + | 0.597060i | −0.939529 | − | 0.342469i | \(-0.888737\pi\) |
0.342469 | + | 0.939529i | \(0.388737\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.89474 | − | 3.89474i | 0.127100 | − | 0.127100i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.34852 | − | 2.34852i | −0.0765597 | − | 0.0765597i | 0.667790 | − | 0.744350i | \(-0.267240\pi\) |
−0.744350 | + | 0.667790i | \(0.767240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.8857 | + | 18.8857i | 0.615004 | + | 0.615004i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.7829 | 0.610363 | 0.305181 | − | 0.952294i | \(-0.401283\pi\) | ||||
0.305181 | + | 0.952294i | \(0.401283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.1320 | + | 20.1320i | 0.653511 | + | 0.653511i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.20341 | −0.0714505 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.07454 | + | 9.07454i | 0.293953 | + | 0.293953i | 0.838640 | − | 0.544687i | \(-0.183351\pi\) |
−0.544687 | + | 0.838640i | \(0.683351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.53633i | 0.0819879i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34130 | −0.0433130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.90304 | −0.254937 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 48.4077i | 1.55992i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3057 | − | 13.3057i | −0.427882 | − | 0.427882i | 0.460024 | − | 0.887906i | \(-0.347841\pi\) |
−0.887906 | + | 0.460024i | \(0.847841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.14470 | 0.0367730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.6349 | − | 18.6349i | −0.598023 | − | 0.598023i | 0.341763 | − | 0.939786i | \(-0.388976\pi\) |
−0.939786 | + | 0.341763i | \(0.888976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5960 | 0.467926 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.28407 | + | 7.28407i | 0.233038 | + | 0.233038i | 0.813960 | − | 0.580921i | \(-0.197308\pi\) |
−0.580921 | + | 0.813960i | \(0.697308\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.31244 | − | 1.31244i | −0.0419457 | − | 0.0419457i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.91391 | − | 5.91391i | 0.188817 | − | 0.188817i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.0322 | − | 31.0322i | 0.989772 | − | 0.989772i | −0.0101761 | − | 0.999948i | \(-0.503239\pi\) |
0.999948 | + | 0.0101761i | \(0.00323922\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.56238i | − | 0.145222i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.2111 | − | 25.2111i | 0.801666 | − | 0.801666i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1060i | 1.27401i | 0.770860 | + | 0.637004i | \(0.219827\pi\) | ||||
−0.770860 | + | 0.637004i | \(0.780173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.64931 | − | 4.64931i | 0.147541 | − | 0.147541i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.58204 | 0.0817740 | 0.0408870 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408870 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 5.30749i | − | 0.167921i |
(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 | 1600.2.j.c.1007.5 | 16 | ||
4.3 | odd | 2 | 400.2.j.c.307.8 | yes | 16 | ||
5.2 | odd | 4 | 1600.2.s.c.943.5 | 16 | |||
5.3 | odd | 4 | 1600.2.s.c.943.4 | 16 | |||
5.4 | even | 2 | inner | 1600.2.j.c.1007.4 | 16 | ||
16.5 | even | 4 | 400.2.s.c.107.4 | yes | 16 | ||
16.11 | odd | 4 | 1600.2.s.c.207.4 | 16 | |||
20.3 | even | 4 | 400.2.s.c.243.4 | yes | 16 | ||
20.7 | even | 4 | 400.2.s.c.243.5 | yes | 16 | ||
20.19 | odd | 2 | 400.2.j.c.307.1 | yes | 16 | ||
80.27 | even | 4 | inner | 1600.2.j.c.143.5 | 16 | ||
80.37 | odd | 4 | 400.2.j.c.43.1 | ✓ | 16 | ||
80.43 | even | 4 | inner | 1600.2.j.c.143.4 | 16 | ||
80.53 | odd | 4 | 400.2.j.c.43.8 | yes | 16 | ||
80.59 | odd | 4 | 1600.2.s.c.207.5 | 16 | |||
80.69 | even | 4 | 400.2.s.c.107.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.c.43.1 | ✓ | 16 | 80.37 | odd | 4 | ||
400.2.j.c.43.8 | yes | 16 | 80.53 | odd | 4 | ||
400.2.j.c.307.1 | yes | 16 | 20.19 | odd | 2 | ||
400.2.j.c.307.8 | yes | 16 | 4.3 | odd | 2 | ||
400.2.s.c.107.4 | yes | 16 | 16.5 | even | 4 | ||
400.2.s.c.107.5 | yes | 16 | 80.69 | even | 4 | ||
400.2.s.c.243.4 | yes | 16 | 20.3 | even | 4 | ||
400.2.s.c.243.5 | yes | 16 | 20.7 | even | 4 | ||
1600.2.j.c.143.4 | 16 | 80.43 | even | 4 | inner | ||
1600.2.j.c.143.5 | 16 | 80.27 | even | 4 | inner | ||
1600.2.j.c.1007.4 | 16 | 5.4 | even | 2 | inner | ||
1600.2.j.c.1007.5 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.s.c.207.4 | 16 | 16.11 | odd | 4 | |||
1600.2.s.c.207.5 | 16 | 80.59 | odd | 4 | |||
1600.2.s.c.943.4 | 16 | 5.3 | odd | 4 | |||
1600.2.s.c.943.5 | 16 | 5.2 | odd | 4 |