Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(641,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.641");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.da (of order \(6\), 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: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 520) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 641.3 | ||
Root | \(2.44974i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.641 |
Dual form | 1040.2.da.f.881.3 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.275748 | + | 0.477609i | −0.159203 | + | 0.275748i | −0.934582 | − | 0.355749i | \(-0.884226\pi\) |
0.775379 | + | 0.631497i | \(0.217559\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.57306 | − | 0.908206i | 0.594561 | − | 0.343270i | −0.172338 | − | 0.985038i | \(-0.555132\pi\) |
0.766899 | + | 0.641768i | \(0.221799\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.34793 | + | 2.33468i | 0.449309 | + | 0.778226i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.759545 | − | 0.438523i | −0.229011 | − | 0.132220i | 0.381105 | − | 0.924532i | \(-0.375544\pi\) |
−0.610116 | + | 0.792312i | \(0.708877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.94577 | + | 2.07905i | −0.817009 | + | 0.576625i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.477609 | − | 0.275748i | −0.123318 | − | 0.0711977i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47282 | + | 4.28305i | 0.599748 | + | 1.03879i | 0.992858 | + | 0.119302i | \(0.0380657\pi\) |
−0.393111 | + | 0.919491i | \(0.628601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.18017 | + | 1.83607i | −0.729581 | + | 0.421224i | −0.818269 | − | 0.574836i | \(-0.805066\pi\) |
0.0886879 | + | 0.996059i | \(0.471733\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00174i | 0.218598i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.69554 | − | 4.66881i | 0.562058 | − | 0.973513i | −0.435258 | − | 0.900306i | \(-0.643343\pi\) |
0.997317 | − | 0.0732079i | \(-0.0233237\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.14124 | −0.604531 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.214596 | − | 0.371692i | 0.0398496 | − | 0.0690215i | −0.845413 | − | 0.534114i | \(-0.820645\pi\) |
0.885262 | + | 0.465092i | \(0.153979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.36449i | 0.424675i | 0.977196 | + | 0.212338i | \(0.0681077\pi\) | ||||
−0.977196 | + | 0.212338i | \(0.931892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.418885 | − | 0.241844i | 0.0729186 | − | 0.0420996i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.908206 | + | 1.57306i | 0.153515 | + | 0.265896i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.40500 | + | 4.27528i | 1.21737 | + | 0.702851i | 0.964355 | − | 0.264610i | \(-0.0852432\pi\) |
0.253019 | + | 0.967461i | \(0.418577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.180686 | − | 1.98022i | −0.0289329 | − | 0.317089i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03931 | + | 0.600045i | 0.162313 | + | 0.0937113i | 0.578956 | − | 0.815359i | \(-0.303460\pi\) |
−0.416643 | + | 0.909070i | \(0.636794\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00825 | − | 1.74634i | −0.153757 | − | 0.266315i | 0.778849 | − | 0.627212i | \(-0.215804\pi\) |
−0.932606 | + | 0.360897i | \(0.882471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.33468 | + | 1.34793i | −0.348033 | + | 0.200937i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.92633i | 1.30204i | 0.759061 | + | 0.651020i | \(0.225659\pi\) | ||||
−0.759061 | + | 0.651020i | \(0.774341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.85032 | + | 3.20485i | −0.264332 | + | 0.457836i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.72750 | −0.381926 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.45025 | −0.748650 | −0.374325 | − | 0.927298i | \(-0.622126\pi\) | ||||
−0.374325 | + | 0.927298i | \(0.622126\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.438523 | − | 0.759545i | 0.0591305 | − | 0.102417i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.02517i | − | 0.268240i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.96683 | + | 2.29025i | −0.516437 | + | 0.298165i | −0.735476 | − | 0.677551i | \(-0.763041\pi\) |
0.219039 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.952525 | − | 1.64982i | −0.121958 | − | 0.211238i | 0.798582 | − | 0.601887i | \(-0.205584\pi\) |
−0.920540 | + | 0.390649i | \(0.872251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24074 | + | 2.44839i | 0.534283 | + | 0.308468i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.07905 | − | 2.94577i | −0.257875 | − | 0.365377i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.42293 | + | 2.55358i | 0.540347 | + | 0.311970i | 0.745220 | − | 0.666819i | \(-0.232345\pi\) |
−0.204872 | + | 0.978789i | \(0.565678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.48658 | + | 2.57483i | 0.178963 | + | 0.309973i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4521 | + | 7.76656i | −1.59647 | + | 0.921721i | −0.604306 | + | 0.796752i | \(0.706550\pi\) |
−0.992161 | + | 0.124969i | \(0.960117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.7435i | 1.25743i | 0.777635 | + | 0.628716i | \(0.216419\pi\) | ||||
−0.777635 | + | 0.628716i | \(0.783581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.275748 | − | 0.477609i | 0.0318406 | − | 0.0551495i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.59308 | −0.181548 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2334 | 1.26386 | 0.631929 | − | 0.775026i | \(-0.282263\pi\) | ||||
0.631929 | + | 0.775026i | \(0.282263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.17759 | + | 5.50375i | −0.353066 | + | 0.611528i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.60910i | 0.286386i | 0.989695 | + | 0.143193i | \(0.0457369\pi\) | ||||
−0.989695 | + | 0.143193i | \(0.954263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28305 | + | 2.47282i | −0.464562 | + | 0.268215i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.118349 | + | 0.204986i | 0.0126883 | + | 0.0219768i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.645218 | + | 0.372517i | 0.0683930 | + | 0.0394867i | 0.533807 | − | 0.845607i | \(-0.320761\pi\) |
−0.465414 | + | 0.885093i | \(0.654094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.74566 | + | 5.94584i | −0.287823 | + | 0.623293i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.12930 | − | 0.652003i | −0.117103 | − | 0.0676096i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.83607 | − | 3.18017i | −0.188377 | − | 0.326279i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.46798 | − | 4.88899i | 0.859794 | − | 0.496402i | −0.00414956 | − | 0.999991i | \(-0.501321\pi\) |
0.863943 | + | 0.503589i | \(0.167988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.36439i | − | 0.237630i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.45444 | − | 5.98327i | 0.343730 | − | 0.595358i | −0.641392 | − | 0.767213i | \(-0.721643\pi\) |
0.985122 | + | 0.171855i | \(0.0549761\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4021 | 1.71468 | 0.857342 | − | 0.514747i | \(-0.172114\pi\) | ||||
0.857342 | + | 0.514747i | \(0.172114\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00174 | −0.0977601 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.84562 | + | 6.66080i | −0.371770 | + | 0.643924i | −0.989838 | − | 0.142201i | \(-0.954582\pi\) |
0.618068 | + | 0.786124i | \(0.287916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.1587i | − | 1.06881i | −0.845229 | − | 0.534404i | \(-0.820536\pi\) | ||
0.845229 | − | 0.534404i | \(-0.179464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.08382 | + | 2.35780i | −0.387619 | + | 0.223792i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.84621 | − | 11.8580i | −0.644038 | − | 1.11551i | −0.984523 | − | 0.175256i | \(-0.943925\pi\) |
0.340485 | − | 0.940250i | \(-0.389409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.66881 | + | 2.69554i | 0.435368 | + | 0.251360i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.82459 | − | 4.07500i | −0.815834 | − | 0.376734i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.77979 | + | 4.49167i | 0.713172 | + | 0.411750i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.11539 | − | 8.86012i | −0.465036 | − | 0.805466i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.573174 | + | 0.330922i | −0.0516814 | + | 0.0298383i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.56497 | − | 11.3709i | 0.582547 | − | 1.00900i | −0.412630 | − | 0.910899i | \(-0.635390\pi\) |
0.995176 | − | 0.0981016i | \(-0.0312770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.11209 | 0.0979143 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2978 | −1.68606 | −0.843030 | − | 0.537866i | \(-0.819230\pi\) | ||||
−0.843030 | + | 0.537866i | \(0.819230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.33506 | + | 5.77650i | −0.289187 | + | 0.500886i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.14124i | − | 0.270355i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.90390 | − | 2.25392i | 0.333533 | − | 0.192565i | −0.323876 | − | 0.946100i | \(-0.604986\pi\) |
0.657408 | + | 0.753534i | \(0.271653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.78060 | + | 8.28024i | 0.405485 | + | 0.702321i | 0.994378 | − | 0.105890i | \(-0.0337692\pi\) |
−0.588893 | + | 0.808211i | \(0.700436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.26330 | − | 2.46142i | −0.359034 | − | 0.207289i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.14915 | − | 0.287346i | 0.263346 | − | 0.0240291i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.371692 | + | 0.214596i | 0.0308673 | + | 0.0178213i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.02044 | − | 1.76746i | −0.0841649 | − | 0.145778i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7633 | − | 7.94624i | 1.12753 | − | 0.650981i | 0.184220 | − | 0.982885i | \(-0.441024\pi\) |
0.943313 | + | 0.331904i | \(0.107691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.4356i | − | 1.09338i | −0.837336 | − | 0.546689i | \(-0.815888\pi\) | ||
0.837336 | − | 0.546689i | \(-0.184112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.66637 | + | 11.5465i | −0.538944 | + | 0.933478i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.36449 | −0.189921 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8879 | 1.74685 | 0.873424 | − | 0.486960i | \(-0.161894\pi\) | ||||
0.873424 | + | 0.486960i | \(0.161894\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.50289 | − | 2.60309i | 0.119187 | − | 0.206438i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.79241i | − | 0.771750i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.25507 | − | 1.87932i | 0.254957 | − | 0.147199i | −0.367075 | − | 0.930191i | \(-0.619641\pi\) |
0.622032 | + | 0.782992i | \(0.286307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.241844 | + | 0.418885i | 0.0188275 | + | 0.0326102i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.3492 | + | 7.70716i | 1.03299 | + | 0.596398i | 0.917840 | − | 0.396950i | \(-0.129931\pi\) |
0.115151 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.35508 | − | 12.2488i | 0.335006 | − | 0.942216i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.57327 | − | 4.94978i | −0.655614 | − | 0.378519i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.430549 | + | 0.745733i | 0.0327340 | + | 0.0566970i | 0.881928 | − | 0.471384i | \(-0.156245\pi\) |
−0.849194 | + | 0.528081i | \(0.822912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.57306 | + | 0.908206i | −0.118912 | + | 0.0686539i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.52612i | − | 0.189875i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.90073 | + | 6.75627i | −0.291554 | + | 0.504987i | −0.974177 | − | 0.225784i | \(-0.927506\pi\) |
0.682623 | + | 0.730771i | \(0.260839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.70152 | 0.423791 | 0.211895 | − | 0.977292i | \(-0.432036\pi\) | ||||
0.211895 | + | 0.977292i | \(0.432036\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.05063 | 0.0776645 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.27528 | + | 7.40500i | −0.314325 | + | 0.544426i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.33756i | − | 0.317194i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.94135 | + | 2.85289i | −0.359430 | + | 0.207517i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.926061 | + | 1.60398i | 0.0670074 | + | 0.116060i | 0.897583 | − | 0.440846i | \(-0.145322\pi\) |
−0.830575 | + | 0.556906i | \(0.811988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.47772 | − | 4.31726i | −0.538258 | − | 0.310763i | 0.206115 | − | 0.978528i | \(-0.433918\pi\) |
−0.744373 | + | 0.667765i | \(0.767251\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.98022 | − | 0.180686i | 0.141806 | − | 0.0129392i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.66599 | + | 2.11656i | 0.261191 | + | 0.150799i | 0.624878 | − | 0.780723i | \(-0.285149\pi\) |
−0.363687 | + | 0.931521i | \(0.618482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8668 | − | 24.0179i | −0.982988 | − | 1.70259i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
−0.332432 | − | 0.943127i | \(-0.607869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.43923 | + | 1.40829i | −0.172050 | + | 0.0993330i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.779591i | − | 0.0547166i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.600045 | + | 1.03931i | −0.0419090 | + | 0.0725885i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.5335 | 1.01015 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.22064 | 0.222776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0728649 | + | 0.126206i | −0.00501623 | + | 0.00868836i | −0.868523 | − | 0.495650i | \(-0.834930\pi\) |
0.863506 | + | 0.504338i | \(0.168263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.56644i | − | 0.586963i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.74634 | − | 1.00825i | 0.119100 | − | 0.0687622i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.14745 | + | 3.71949i | 0.145778 | + | 0.252495i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.13119 | − | 2.96250i | −0.346734 | − | 0.200187i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.1891 | − | 7.47575i | −1.08899 | − | 0.502873i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.24045 | + | 2.44822i | 0.283961 | + | 0.163945i | 0.635215 | − | 0.772335i | \(-0.280911\pi\) |
−0.351254 | + | 0.936280i | \(0.614245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.34793 | − | 2.33468i | −0.0898618 | − | 0.155645i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9441 | + | 6.89595i | −0.792760 | + | 0.457700i | −0.840933 | − | 0.541139i | \(-0.817993\pi\) |
0.0481730 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6453i | 0.835628i | 0.908533 | + | 0.417814i | \(0.137204\pi\) | ||||
−0.908533 | + | 0.417814i | \(0.862796\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.439288 | − | 0.760869i | 0.0289030 | − | 0.0500615i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.2878 | 0.673975 | 0.336987 | − | 0.941509i | \(-0.390592\pi\) | ||||
0.336987 | + | 0.941509i | \(0.390592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.92633 | −0.582290 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.09759 | + | 5.36518i | −0.201210 | + | 0.348506i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.1730i | − | 1.30489i | −0.757838 | − | 0.652443i | \(-0.773744\pi\) | ||
0.757838 | − | 0.652443i | \(-0.226256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.798945 | − | 0.461271i | 0.0514645 | − | 0.0297131i | −0.474047 | − | 0.880500i | \(-0.657207\pi\) |
0.525512 | + | 0.850786i | \(0.323874\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.46428 | − | 11.1965i | −0.414684 | − | 0.718253i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.20485 | − | 1.85032i | −0.204751 | − | 0.118213i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.55075 | − | 12.0204i | 0.353186 | − | 0.764838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.24613 | − | 0.719453i | −0.0789702 | − | 0.0455935i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.13425 | − | 14.0889i | −0.513430 | − | 0.889286i | −0.999879 | − | 0.0155772i | \(-0.995041\pi\) |
0.486449 | − | 0.873709i | \(-0.338292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.09476 | + | 2.36411i | −0.257435 | + | 0.148630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 2.72750i | − | 0.170803i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.50538 | − | 14.7318i | 0.530551 | − | 0.918941i | −0.468814 | − | 0.883297i | \(-0.655318\pi\) |
0.999365 | − | 0.0356442i | \(-0.0113483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.5313 | 0.965070 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.15704 | 0.0716190 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.66899 | − | 16.7472i | 0.596215 | − | 1.03268i | −0.397159 | − | 0.917750i | \(-0.630004\pi\) |
0.993374 | − | 0.114925i | \(-0.0366629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.45025i | − | 0.334806i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.355835 | + | 0.205441i | −0.0217767 | + | 0.0125728i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.285151 | + | 0.493896i | 0.0173860 | + | 0.0301134i | 0.874587 | − | 0.484868i | \(-0.161132\pi\) |
−0.857202 | + | 0.514981i | \(0.827799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3837 | − | 11.7686i | −1.23822 | − | 0.714889i | −0.269493 | − | 0.963002i | \(-0.586856\pi\) |
−0.968731 | + | 0.248113i | \(0.920190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.08268 | − | 2.95090i | −0.126049 | − | 0.178597i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.759545 | + | 0.438523i | 0.0458023 | + | 0.0264440i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.23659 | + | 12.5341i | 0.434804 | + | 0.753103i | 0.997280 | − | 0.0737109i | \(-0.0234842\pi\) |
−0.562475 | + | 0.826814i | \(0.690151\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.52033 | + | 3.18716i | −0.330493 | + | 0.190810i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4795i | 1.46033i | 0.683273 | + | 0.730163i | \(0.260556\pi\) | ||||
−0.683273 | + | 0.730163i | \(0.739444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.89924 | − | 15.4139i | 0.529005 | − | 0.916263i | −0.470423 | − | 0.882441i | \(-0.655899\pi\) |
0.999428 | − | 0.0338224i | \(-0.0107681\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.02517 | 0.119961 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.17986 | 0.128673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.72970 | + | 6.46003i | −0.219394 | + | 0.380002i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.39251i | 0.316115i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5760 | − | 10.1475i | 1.02680 | − | 0.592824i | 0.110735 | − | 0.993850i | \(-0.464680\pi\) |
0.916067 | + | 0.401026i | \(0.131346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.29025 | − | 3.96683i | −0.133344 | − | 0.230958i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.38591 | + | 1.37751i | 0.138445 | + | 0.0799310i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.76627 | + | 19.3574i | 0.102146 | + | 1.11947i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.17208 | − | 1.83140i | −0.182836 | − | 0.105560i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.90511 | + | 3.29975i | 0.109446 | + | 0.189566i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.64982 | − | 0.952525i | 0.0944685 | − | 0.0545414i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.55636i | − | 0.545410i | −0.962098 | − | 0.272705i | \(-0.912082\pi\) | ||
0.962098 | − | 0.272705i | \(-0.0879184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.79860 | + | 8.31142i | −0.272983 | + | 0.472820i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.151461 | −0.00858856 | −0.00429428 | − | 0.999991i | \(-0.501367\pi\) | ||||
−0.00429428 | + | 0.999991i | \(0.501367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.5006 | 1.61095 | 0.805475 | − | 0.592630i | \(-0.201910\pi\) | ||||
0.805475 | + | 0.592630i | \(0.201910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.44839 | + | 4.24074i | −0.137951 | + | 0.238938i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 20.0004i | − | 1.12333i | −0.827363 | − | 0.561667i | \(-0.810160\pi\) | ||
0.827363 | − | 0.561667i | \(-0.189840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.325991 | + | 0.188211i | −0.0182520 | + | 0.0105378i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.12084 | − | 3.67340i | −0.118374 | − | 0.205029i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7280 | − | 9.08056i | −0.875129 | − | 0.505256i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.94577 | − | 2.07905i | 0.163402 | − | 0.115325i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.32949 | + | 3.07698i | 0.294721 | + | 0.170157i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.10695 | + | 14.0417i | 0.446951 | + | 0.774141i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.73156 | + | 5.04117i | −0.479930 | + | 0.277088i | −0.720387 | − | 0.693572i | \(-0.756036\pi\) |
0.240457 | + | 0.970660i | \(0.422703\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.0510i | 1.26319i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.55358 | + | 4.42293i | −0.139517 | + | 0.241651i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00198 | −0.490369 | −0.245185 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245185 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.55131 | 0.410131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.03689 | − | 1.79594i | 0.0561505 | − | 0.0972555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4368i | 1.04949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.57483 | + | 1.48658i | −0.138624 | + | 0.0800346i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.686627 | − | 1.18927i | −0.0368601 | − | 0.0638435i | 0.847007 | − | 0.531582i | \(-0.178402\pi\) |
−0.883867 | + | 0.467738i | \(0.845069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.6180 | − | 10.1717i | −0.943069 | − | 0.544481i | −0.0521480 | − | 0.998639i | \(-0.516607\pi\) |
−0.890921 | + | 0.454158i | \(0.849940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.25335 | − | 6.53079i | 0.493907 | − | 0.348588i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.13858 | − | 3.54411i | −0.326724 | − | 0.188634i | 0.327662 | − | 0.944795i | \(-0.393739\pi\) |
−0.654386 | + | 0.756161i | \(0.727073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.76656 | − | 13.4521i | −0.412206 | − | 0.713962i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.29052 | + | 2.47713i | −0.227078 | + | 0.131104i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.81284i | 0.254012i | 0.991902 | + | 0.127006i | \(0.0405368\pi\) | ||||
−0.991902 | + | 0.127006i | \(0.959463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.75768 | + | 4.77644i | −0.145141 | + | 0.251392i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.64223 | 0.296140 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.7435 | −0.562341 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.57841 | − | 7.93004i | 0.238991 | − | 0.413945i | −0.721434 | − | 0.692483i | \(-0.756517\pi\) |
0.960425 | + | 0.278538i | \(0.0898499\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.23527i | 0.168421i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.57357 | + | 4.94995i | −0.445118 | + | 0.256989i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.88828 | − | 10.1988i | −0.304884 | − | 0.528074i | 0.672352 | − | 0.740232i | \(-0.265284\pi\) |
−0.977235 | + | 0.212158i | \(0.931951\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.477609 | + | 0.275748i | 0.0246636 | + | 0.0142395i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.140616 | + | 1.54107i | 0.00724209 | + | 0.0793694i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.9745 | + | 18.4605i | 1.64242 | + | 0.948253i | 0.979969 | + | 0.199149i | \(0.0638178\pi\) |
0.662453 | + | 0.749104i | \(0.269516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.62055 | + | 6.27098i | 0.185486 | + | 0.321272i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.1140 | + | 11.0355i | −0.976679 | + | 0.563886i | −0.901266 | − | 0.433266i | \(-0.857361\pi\) |
−0.0754134 | + | 0.997152i | \(0.524028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.59308i | − | 0.0811908i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.71810 | − | 4.70788i | 0.138169 | − | 0.239315i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.1523 | 1.78229 | 0.891146 | − | 0.453716i | \(-0.149902\pi\) | ||||
0.891146 | + | 0.453716i | \(0.149902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6623 | 1.34837 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.32133 | − | 9.21682i | 0.268426 | − | 0.464927i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.2334i | 0.565214i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.03921 | − | 4.64144i | 0.403476 | − | 0.232947i | −0.284506 | − | 0.958674i | \(-0.591830\pi\) |
0.687983 | + | 0.725727i | \(0.258496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.83927 | − | 3.18571i | −0.0920788 | − | 0.159485i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.6221 | − | 14.2156i | −1.22957 | − | 0.709893i | −0.262630 | − | 0.964897i | \(-0.584590\pi\) |
−0.966940 | + | 0.255004i | \(0.917923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.91590 | − | 6.96524i | −0.244879 | − | 0.346963i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.50375 | − | 3.17759i | −0.273483 | − | 0.157896i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.74962 | − | 6.49453i | −0.185862 | − | 0.321922i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5634 | − | 10.1402i | 0.868452 | − | 0.501401i | 0.00161856 | − | 0.999999i | \(-0.499485\pi\) |
0.866834 | + | 0.498598i | \(0.166151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.48605i | 0.122628i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.16004 | + | 7.20540i | −0.204702 | + | 0.354554i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60910 | −0.128076 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.27296 | −0.258218 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.6625 | + | 25.3962i | −0.716309 | + | 1.24068i | 0.246143 | + | 0.969233i | \(0.420837\pi\) |
−0.962452 | + | 0.271450i | \(0.912497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.92975i | − | 0.142787i | −0.997448 | − | 0.0713936i | \(-0.977255\pi\) | ||
0.997448 | − | 0.0713936i | \(-0.0227447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.8401 | + | 12.0320i | −1.01328 | + | 0.585018i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.47282 | − | 4.28305i | −0.119950 | − | 0.207759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.99676 | − | 1.73018i | −0.145023 | − | 0.0837292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.731133 | + | 1.58330i | −0.0352994 | + | 0.0764424i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.4786 | + | 17.5968i | 1.46810 | + | 0.847609i | 0.999362 | − | 0.0357266i | \(-0.0113746\pi\) |
0.468741 | + | 0.883336i | \(0.344708\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.3241 | − | 17.8819i | −0.496147 | − | 0.859351i | 0.503843 | − | 0.863795i | \(-0.331919\pi\) |
−0.999990 | + | 0.00444359i | \(0.998586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.204986 | + | 0.118349i | −0.00982834 | + | 0.00567440i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.7968i | 0.947009i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.98217 | − | 8.62936i | 0.237786 | − | 0.411857i | −0.722293 | − | 0.691587i | \(-0.756912\pi\) |
0.960079 | + | 0.279730i | \(0.0902450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.97640 | −0.475067 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.1084 | −1.66805 | −0.834025 | − | 0.551727i | \(-0.813969\pi\) | ||||
−0.834025 | + | 0.551727i | \(0.813969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.372517 | + | 0.645218i | −0.0176590 | + | 0.0305863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.76463i | 0.414553i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.9768 | + | 16.1524i | −1.32031 | + | 0.762280i | −0.983778 | − | 0.179392i | \(-0.942587\pi\) |
−0.336531 | + | 0.941673i | \(0.609254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.526268 | − | 0.911523i | −0.0247810 | − | 0.0429219i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.41698 | + | 3.70485i | 0.301496 | + | 0.174069i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.94584 | − | 2.74566i | −0.278745 | − | 0.128718i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3917 | + | 10.0411i | 0.813550 | + | 0.469703i | 0.848187 | − | 0.529697i | \(-0.177694\pi\) |
−0.0346373 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.76772 | − | 13.4541i | −0.362566 | − | 0.627983i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1537 | + | 10.4810i | −0.845502 | + | 0.488151i | −0.859131 | − | 0.511756i | \(-0.828995\pi\) |
0.0136287 | + | 0.999907i | \(0.495662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.1142i | 1.63189i | 0.578127 | + | 0.815947i | \(0.303784\pi\) | ||||
−0.578127 | + | 0.815947i | \(0.696216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.652003 | − | 1.12930i | 0.0302359 | − | 0.0523702i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.6858 | 1.46625 | 0.733123 | − | 0.680096i | \(-0.238062\pi\) | ||||
0.733123 | + | 0.680096i | \(0.238062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.27672 | 0.428359 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.03555 | + | 10.4539i | −0.278103 | + | 0.481689i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.76857i | 0.0813188i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.18017 | − | 1.83607i | 0.145916 | − | 0.0842448i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.34654 | − | 12.7246i | −0.336375 | − | 0.582619i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.42202 | + | 1.97570i | 0.156356 | + | 0.0902721i | 0.576137 | − | 0.817353i | \(-0.304560\pi\) |
−0.419781 | + | 0.907626i | \(0.637893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.7019 | + | 2.80141i | −1.39989 | + | 0.127733i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.67694 | + | 2.70023i | 0.212808 | + | 0.122865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.88899 | + | 8.46798i | 0.221998 | + | 0.384511i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6267 | + | 9.02205i | −0.708111 | + | 0.408828i | −0.810361 | − | 0.585931i | \(-0.800729\pi\) |
0.102250 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.07287i | 0.0937383i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.77834 | − | 10.0084i | 0.260773 | − | 0.451672i | −0.705675 | − | 0.708536i | \(-0.749356\pi\) |
0.966448 | + | 0.256864i | \(0.0826892\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.12264 | 0.0955987 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.36439 | 0.106271 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.1073 | + | 24.4345i | −0.632798 | + | 1.09604i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.01039i | − | 0.0899973i | −0.998987 | − | 0.0449987i | \(-0.985672\pi\) | ||
0.998987 | − | 0.0449987i | \(-0.0143284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.36202 | + | 4.25046i | −0.328911 | + | 0.189897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8145 | + | 29.1236i | 0.749721 | + | 1.29856i | 0.947956 | + | 0.318401i | \(0.103146\pi\) |
−0.198235 | + | 0.980155i | \(0.563521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.98327 | + | 3.45444i | 0.266252 | + | 0.153721i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.64924 | + | 5.45761i | 0.206480 | + | 0.242381i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.8008 | − | 10.8547i | −0.833333 | − | 0.481125i | 0.0216596 | − | 0.999765i | \(-0.493105\pi\) |
−0.854992 | + | 0.518640i | \(0.826438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.75732 | + | 16.9002i | 0.431638 | + | 0.747620i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.98967 | − | 5.76754i | 0.441054 | − | 0.254643i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.4021i | 0.766830i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.91441 | − | 6.77995i | 0.172155 | − | 0.298182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.474892 | −0.0208454 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.8718 | 1.00203 | 0.501016 | − | 0.865438i | \(-0.332960\pi\) | ||||
0.501016 | + | 0.865438i | \(0.332960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.36726 | + | 5.83226i | −0.147240 | + | 0.255027i | −0.930206 | − | 0.367037i | \(-0.880372\pi\) |
0.782966 | + | 0.622064i | \(0.213706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.00174i | − | 0.0437196i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.1272 | + | 5.84697i | −0.441150 | + | 0.254698i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.03183 | − | 5.25129i | −0.131819 | − | 0.228317i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.6940 | − | 6.17418i | −0.464080 | − | 0.267936i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.30909 | + | 0.393184i | −0.186647 | + | 0.0170307i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.66080 | − | 3.84562i | −0.287972 | − | 0.166260i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.15124 | − | 3.72605i | −0.0928327 | − | 0.160791i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.81081 | − | 1.62282i | 0.121070 | − | 0.0698998i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 11.2559i | − | 0.483927i | −0.970285 | − | 0.241964i | \(-0.922209\pi\) | ||
0.970285 | − | 0.241964i | \(-0.0777915\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.57218 | + | 2.72310i | −0.0674688 | + | 0.116859i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1587 | 0.477985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1685 | 0.434774 | 0.217387 | − | 0.976086i | \(-0.430247\pi\) | ||||
0.217387 | + | 0.976086i | \(0.430247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.56787 | − | 4.44768i | 0.109594 | − | 0.189822i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.57606i | 0.0671423i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.6708 | − | 10.2023i | 0.751440 | − | 0.433844i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.35780 | − | 4.08382i | −0.100083 | − | 0.173349i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.3299 | − | 9.42807i | −0.691920 | − | 0.399480i | 0.112411 | − | 0.993662i | \(-0.464143\pi\) |
−0.804331 | + | 0.594181i | \(0.797476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.60081 | + | 3.04811i | 0.279185 | + | 0.128921i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.07166 | + | 1.19607i | 0.0874655 | + | 0.0504982i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.22434 | − | 15.9770i | −0.388760 | − | 0.673351i | 0.603523 | − | 0.797345i | \(-0.293763\pi\) |
−0.992283 | + | 0.123994i | \(0.960430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.8580 | − | 6.84621i | 0.498869 | − | 0.288022i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.5436i | 0.484787i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8990 | − | 22.3417i | 0.540753 | − | 0.936612i | −0.458108 | − | 0.888897i | \(-0.651473\pi\) |
0.998861 | − | 0.0477153i | \(-0.0151940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.0810 | 1.92843 | 0.964216 | − | 0.265118i | \(-0.0854110\pi\) | ||||
0.964216 | + | 0.265118i | \(0.0854110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.02144 | −0.0426711 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.69554 | + | 4.66881i | −0.112412 | + | 0.194703i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.69085i | 0.403435i | 0.979444 | + | 0.201718i | \(0.0646524\pi\) | ||||
−0.979444 | + | 0.201718i | \(0.935348\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.12393 | − | 2.38095i | 0.171385 | − | 0.0989489i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.36960 | + | 4.10427i | 0.0983075 | + | 0.170274i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.13971 | + | 2.39006i | 0.171449 | + | 0.0989863i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.07500 | − | 8.82459i | 0.168481 | − | 0.364852i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.4680 | + | 18.7454i | 1.34010 | + | 0.773705i | 0.986821 | − | 0.161815i | \(-0.0517348\pi\) |
0.353275 | + | 0.935520i | \(0.385068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.34138 | − | 7.51949i | −0.178883 | − | 0.309835i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.02178 | + | 1.16727i | −0.0831648 | + | 0.0480152i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.6021i | 0.846027i | 0.906123 | + | 0.423013i | \(0.139028\pi\) | ||||
−0.906123 | + | 0.423013i | \(0.860972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.49167 | + | 7.77979i | −0.184140 | + | 0.318940i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.2949 | 0.625979 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.39843 | −0.0571382 | −0.0285691 | − | 0.999592i | \(-0.509095\pi\) | ||||
−0.0285691 | + | 0.999592i | \(0.509095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2004 | + | 33.2561i | −0.783201 | + | 1.35654i | 0.146867 | + | 0.989156i | \(0.453081\pi\) |
−0.930068 | + | 0.367387i | \(0.880252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7682i | 0.560683i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.86012 | − | 5.11539i | 0.360215 | − | 0.207970i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.33388 | − | 5.77446i | −0.135318 | − | 0.234378i | 0.790401 | − | 0.612590i | \(-0.209872\pi\) |
−0.925719 | + | 0.378212i | \(0.876539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.372340 | + | 0.214970i | 0.0150880 | + | 0.00871104i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.5583 | − | 26.2949i | −0.750789 | − | 1.06378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.3895 | + | 20.4322i | 1.42937 | + | 0.825247i | 0.997071 | − | 0.0764834i | \(-0.0243692\pi\) |
0.432299 | + | 0.901730i | \(0.357703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.330922 | − | 0.573174i | −0.0133441 | − | 0.0231126i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1135 | + | 5.83904i | −0.407155 | + | 0.235071i | −0.689566 | − | 0.724222i | \(-0.742199\pi\) |
0.282412 | + | 0.959293i | \(0.408866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9724i | 0.963534i | 0.876299 | + | 0.481767i | \(0.160005\pi\) | ||||
−0.876299 | + | 0.481767i | \(0.839995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.46732 | + | 14.6658i | −0.339782 | + | 0.588519i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.35329 | 0.0542183 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.888085 | + | 1.53821i | −0.0354667 | + | 0.0614301i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.2880i | 1.68613i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.83169 | + | 3.36693i | −0.232156 | + | 0.134035i | −0.611566 | − | 0.791193i | \(-0.709460\pi\) |
0.379410 | + | 0.925228i | \(0.376127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0401846 | − | 0.0696019i | −0.00159720 | − | 0.00276643i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.3709 | + | 6.56497i | 0.451239 | + | 0.260523i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.21244 | − | 13.2877i | −0.0480385 | − | 0.526477i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.2648 | − | 20.9375i | −1.43461 | − | 0.828275i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.320045 | − | 0.554334i | −0.0126410 | − | 0.0218949i | 0.859636 | − | 0.510907i | \(-0.170691\pi\) |
−0.872277 | + | 0.489013i | \(0.837357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.2562 | − | 15.1590i | 1.03544 | − | 0.597814i | 0.116905 | − | 0.993143i | \(-0.462703\pi\) |
0.918540 | + | 0.395329i | \(0.129369\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.11209i | 0.0437886i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.22347 | + | 5.58321i | −0.126728 | + | 0.219499i | −0.922407 | − | 0.386219i | \(-0.873781\pi\) |
0.795679 | + | 0.605718i | \(0.207114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.01731 | 0.157693 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.36861 | −0.0928333 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.154888 | − | 0.268274i | 0.00606124 | − | 0.0104984i | −0.862979 | − | 0.505240i | \(-0.831404\pi\) |
0.869040 | + | 0.494742i | \(0.164737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19.2978i | − | 0.754029i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.0826 | + | 14.4815i | −0.978566 | + | 0.564975i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.55240 | + | 4.42088i | 0.0994273 | + | 0.172213i | 0.911448 | − | 0.411416i | \(-0.134966\pi\) |
−0.812020 | + | 0.583629i | \(0.801632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1957 | + | 9.92794i | 0.668835 | + | 0.386152i | 0.795635 | − | 0.605776i | \(-0.207137\pi\) |
−0.126800 | + | 0.991928i | \(0.540471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.03458 | − | 5.67062i | 0.312037 | − | 0.220228i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.77650 | − | 3.33506i | −0.224003 | − | 0.129328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.15690 | − | 2.00382i | −0.0447955 | − | 0.0775881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.33859 | + | 1.35018i | −0.0904150 | + | 0.0522011i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67082i | 0.0645012i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.192547 | − | 0.333501i | 0.00742213 | − | 0.0128555i | −0.862290 | − | 0.506414i | \(-0.830971\pi\) |
0.869713 | + | 0.493558i | \(0.164304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.14124 | 0.120906 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8350 | −0.570157 | −0.285078 | − | 0.958504i | \(-0.592020\pi\) | ||||
−0.285078 | + | 0.958504i | \(0.592020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.88043 | − | 15.3814i | 0.340800 | − | 0.590282i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.60617i | − | 0.291469i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.9469 | + | 20.7540i | −1.37547 | + | 0.794129i | −0.991610 | − | 0.129263i | \(-0.958739\pi\) |
−0.383861 | + | 0.923391i | \(0.625406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.25392 | + | 3.90390i | 0.0861178 | + | 0.149160i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.03953 | − | 3.48692i | −0.230422 | − | 0.133034i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0552 | − | 11.3314i | 0.611653 | − | 0.431690i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.55411 | + | 5.51607i | 0.363455 | + | 0.209841i | 0.670595 | − | 0.741823i | \(-0.266039\pi\) |
−0.307140 | + | 0.951664i | \(0.599372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.14735 | − | 3.71932i | −0.0815712 | − | 0.141285i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.28024 | + | 4.78060i | −0.314087 | + | 0.181338i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.93522i | 0.224813i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.83683 | + | 4.91353i | −0.107299 | + | 0.185847i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.7358 | −1.12311 | −0.561554 | − | 0.827440i | \(-0.689796\pi\) | ||||
−0.561554 | + | 0.827440i | \(0.689796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.3989 | −1.18423 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.46142 | − | 4.26330i | 0.0927023 | − | 0.160565i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12.5494i | − | 0.471968i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.3547 | + | 22.7214i | −1.47800 | + | 0.853321i | −0.999691 | − | 0.0248726i | \(-0.992082\pi\) |
−0.478305 | + | 0.878194i | \(0.658749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.1418 | + | 26.2264i | 0.567862 | + | 0.983567i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.0394 | + | 6.37358i | 0.413427 | + | 0.238692i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.287346 | + | 3.14915i | 0.0107461 | + | 0.117772i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.63483 | + | 5.56267i | 0.359819 | + | 0.207742i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.1218 | − | 45.2443i | −0.974179 | − | 1.68733i | −0.682617 | − | 0.730777i | \(-0.739158\pi\) |
−0.291563 | − | 0.956552i | \(-0.594175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3746 | − | 15.8047i | 1.01948 | − | 0.588599i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.508777i | 0.0189216i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.214596 | + | 0.371692i | −0.00796991 | + | 0.0138043i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.9248 | −1.74035 | −0.870173 | − | 0.492747i | \(-0.835993\pi\) | ||||
−0.870173 | + | 0.492747i | \(0.835993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9355 | −0.442056 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.98645 | − | 8.63679i | 0.184431 | − | 0.319443i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.6313i | − | 1.35301i | −0.736439 | − | 0.676504i | \(-0.763494\pi\) | ||
0.736439 | − | 0.676504i | \(-0.236506\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.76746 | − | 1.02044i | 0.0651938 | − | 0.0376397i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.23961 | − | 3.87912i | −0.0824971 | − | 0.142889i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1588 | + | 20.8763i | 1.33012 | + | 0.767947i | 0.985318 | − | 0.170727i | \(-0.0546116\pi\) |
0.344805 | + | 0.938674i | \(0.387945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.21043 | + | 5.96568i | 0.154674 | + | 0.219155i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4237 | − | 14.1011i | −0.896020 | − | 0.517318i | −0.0201134 | − | 0.999798i | \(-0.506403\pi\) |
−0.875907 | + | 0.482480i | \(0.839736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.94624 | + | 13.7633i | 0.291128 | + | 0.504248i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.09140 | + | 3.51687i | −0.222873 | + | 0.128676i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.9704i | 0.510469i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9708 | − | 27.6623i | 0.582784 | − | 1.00941i | −0.412364 | − | 0.911019i | \(-0.635297\pi\) |
0.995148 | − | 0.0983921i | \(-0.0313699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.97201 | 0.326958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.4356 | 0.488973 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.36247 | + | 9.28807i | −0.194902 | + | 0.337581i | −0.946868 | − | 0.321621i | \(-0.895772\pi\) |
0.751966 | + | 0.659202i | \(0.229106\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.60759i | − | 0.0946496i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.389260 | − | 0.224739i | 0.0141107 | − | 0.00814679i | −0.492928 | − | 0.870070i | \(-0.664073\pi\) |
0.507039 | + | 0.861923i | \(0.330740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1344 | − | 17.5533i | −0.366889 | − | 0.635471i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.5465 | − | 6.66637i | −0.417464 | − | 0.241023i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92381 | − | 14.9938i | 0.250004 | − | 0.541394i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.7839 | − | 6.80346i | −0.424940 | − | 0.245339i | 0.272249 | − | 0.962227i | \(-0.412233\pi\) |
−0.697188 | + | 0.716888i | \(0.745566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.69068 | + | 8.12449i | 0.168931 | + | 0.292596i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.70461 | − | 0.984159i | 0.0613107 | − | 0.0353977i | −0.469031 | − | 0.883182i | \(-0.655397\pi\) |
0.530342 | + | 0.847784i | \(0.322064\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.36449i | − | 0.0849351i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.28273 | + | 7.41791i | −0.153642 | + | 0.266116i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.40691 | −0.157894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6233 | 0.487479 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.674098 | + | 1.16757i | −0.0240903 | + | 0.0417256i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.8879i | 0.781214i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3743 | + | 8.29901i | −0.512389 | + | 0.295828i | −0.733815 | − | 0.679349i | \(-0.762262\pi\) |
0.221426 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.33240 | + | 9.23599i | 0.189839 | + | 0.328810i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.5390 | − | 12.4355i | −0.765839 | − | 0.442157i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.23598 | + | 2.87964i | 0.221446 | + | 0.102259i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.60309 | + | 1.50289i | 0.0923221 | + | 0.0533022i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.9117 | − | 22.3637i | −0.457356 | − | 0.792164i | 0.541464 | − | 0.840724i | \(-0.317870\pi\) |
−0.998820 | + | 0.0485595i | \(0.984537\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.2320 | + | 22.0732i | −1.35255 | + | 0.780895i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00850i | 0.0709669i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.71128 | − | 8.16017i | 0.166257 | − | 0.287966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.79241 | 0.345137 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.314519 | −0.0110716 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.6415 | + | 25.3599i | −0.514769 | + | 0.891607i | 0.485084 | + | 0.874468i | \(0.338789\pi\) |
−0.999853 | + | 0.0171389i | \(0.994544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.6930i | − | 1.11289i | −0.830883 | − | 0.556447i | \(-0.812164\pi\) | ||
0.830883 | − | 0.556447i | \(-0.187836\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2415 | − | 6.49031i | 0.394258 | − | 0.227625i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.87932 | + | 3.25507i | 0.0658295 | + | 0.114020i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.41282 | + | 3.70244i | 0.224356 | + | 0.129532i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.5826 | + | 1.60433i | −0.614384 | + | 0.0560597i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2146 | + | 10.5162i | 0.635695 | + | 0.367019i | 0.782954 | − | 0.622079i | \(-0.213712\pi\) |
−0.147259 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.5481 | + | 28.6621i | 0.576829 | + | 0.999097i | 0.995840 | + | 0.0911160i | \(0.0290434\pi\) |
−0.419011 | + | 0.907981i | \(0.637623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.418885 | + | 0.241844i | −0.0145837 | + | 0.00841991i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 53.6372i | − | 1.86515i | −0.360977 | − | 0.932575i | \(-0.617557\pi\) | ||
0.360977 | − | 0.932575i | \(-0.382443\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5411 | − | 44.2386i | 0.887081 | − | 1.53647i | 0.0437704 | − | 0.999042i | \(-0.486063\pi\) |
0.843310 | − | 0.537427i | \(-0.180604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.98189 | −0.276889 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.3021 | −0.634130 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.70716 | + | 13.3492i | −0.266717 | + | 0.461968i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.42743i | − | 0.256730i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.1357 | − | 9.89331i | 0.591591 | − | 0.341555i | −0.174136 | − | 0.984722i | \(-0.555713\pi\) |
0.765726 | + | 0.643167i | \(0.222380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4079 | + | 24.9552i | 0.496824 | + | 0.860524i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.6916 | − | 6.75017i | −0.402681 | − | 0.232488i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2488 | + | 4.35508i | 0.421372 | + | 0.149819i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0936 | − | 9.29167i | −0.552984 | − | 0.319265i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.90789 | + | 8.50072i | 0.168438 | + | 0.291744i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.9209 | − | 23.0483i | 1.36847 | − | 0.790087i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.1517i | 1.06661i | 0.845922 | + | 0.533307i | \(0.179051\pi\) | ||||
−0.845922 | + | 0.533307i | \(0.820949\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.94978 | − | 8.57327i | 0.169279 | − | 0.293200i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0978 | 0.447413 | 0.223707 | − | 0.974657i | \(-0.428184\pi\) | ||||
0.223707 | + | 0.974657i | \(0.428184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.4974 | 1.72295 | 0.861474 | − | 0.507801i | \(-0.169541\pi\) | ||||
0.861474 | + | 0.507801i | \(0.169541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.601091 | + | 1.04112i | −0.0204851 | + | 0.0354813i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.1831i | − | 0.618960i | −0.950906 | − | 0.309480i | \(-0.899845\pi\) | ||
0.950906 | − | 0.309480i | \(-0.100155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.745733 | + | 0.430549i | −0.0253557 | + | 0.0146391i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.05691 | − | 3.56268i | −0.0698564 | − | 0.120995i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.53228 | − | 4.92611i | −0.289438 | − | 0.167107i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.3380 | + | 1.67325i | −0.621358 | + | 0.0566961i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.8284 | + | 13.1800i | 0.772626 | + | 0.446076i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.908206 | − | 1.57306i | −0.0307030 | − | 0.0531791i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.8639 | + | 13.7778i | −0.805828 | + | 0.465245i | −0.845505 | − | 0.533968i | \(-0.820700\pi\) |
0.0396771 | + | 0.999213i | \(0.487367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.1926i | 0.377518i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5057 | − | 44.1772i | 0.859309 | − | 1.48837i | −0.0132810 | − | 0.999912i | \(-0.504228\pi\) |
0.872590 | − | 0.488454i | \(-0.162439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0045 | 1.00973 | 0.504865 | − | 0.863198i | \(-0.331542\pi\) | ||||
0.504865 | + | 0.863198i | \(0.331542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.52612 | 0.0849148 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.73608 | + | 16.8634i | −0.326906 | + | 0.566217i | −0.981896 | − | 0.189420i | \(-0.939339\pi\) |
0.654991 | + | 0.755637i | \(0.272673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.8494i | − | 0.799882i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82704 | − | 2.78690i | 0.161712 | − | 0.0933645i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3894 | − | 28.3873i | −0.548450 | − | 0.949943i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.75627 | − | 3.90073i | −0.225837 | − | 0.130387i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.73230 | − | 4.49416i | −0.324952 | − | 0.150056i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.878863 | + | 0.507412i | 0.0293117 | + | 0.0169231i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4775 | − | 23.3437i | −0.449001 | − | 0.777692i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.74939 | − | 1.01001i | 0.0582159 | − | 0.0336110i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.70152i | 0.189525i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9021 | − | 31.0073i | 0.594428 | − | 1.02958i | −0.399199 | − | 0.916864i | \(-0.630712\pi\) |
0.993627 | − | 0.112716i | \(-0.0359549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.6254 | 0.617764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6586 | 0.783843 | 0.391922 | − | 0.919999i | \(-0.371810\pi\) | ||||
0.391922 | + | 0.919999i | \(0.371810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.14415 | − | 1.98173i | 0.0378658 | − | 0.0655856i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.05063i | 0.0347326i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.3566 | + | 17.5264i | −1.00246 | + | 0.578773i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8747 | − | 22.2997i | −0.424699 | − | 0.735600i | 0.571693 | − | 0.820467i | \(-0.306287\pi\) |
−0.996392 | + | 0.0848674i | \(0.972953\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.56420 | + | 2.63514i | 0.150396 | + | 0.0868310i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.4796 | − | 50.8460i | 0.772840 | − | 1.67362i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.40500 | − | 4.27528i | −0.243475 | − | 0.140570i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.4568 | + | 40.6284i | 0.770423 | + | 1.33441i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.4301 | + | 19.3009i | −1.09680 | + | 0.633241i | −0.935380 | − | 0.353644i | \(-0.884942\pi\) |
−0.161425 | + | 0.986885i | \(0.551609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 13.5893i | − | 0.445371i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.0417650 | − | 0.0723391i | 0.00136732 | − | 0.00236828i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.33756 | 0.141853 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.1250 | 1.04948 | 0.524739 | − | 0.851263i | \(-0.324163\pi\) | ||||
0.524739 | + | 0.851263i | \(0.324163\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.85897 | + | 13.6121i | −0.256468 | + | 0.444216i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6518i | 0.868825i | 0.900714 | + | 0.434412i | \(0.143044\pi\) | ||||
−0.900714 | + | 0.434412i | \(0.856956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.60299 | − | 3.23489i | 0.182458 | − | 0.105342i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.85289 | − | 4.94135i | −0.0928045 | − | 0.160742i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.9374 | − | 8.04678i | −0.452906 | − | 0.261485i | 0.256151 | − | 0.966637i | \(-0.417546\pi\) |
−0.709057 | + | 0.705152i | \(0.750879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.3363 | − | 31.6479i | −0.725067 | − | 1.02733i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.55238 | + | 5.51507i | 0.309757 | + | 0.178838i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.4917 | − | 44.1530i | −0.825759 | − | 1.43026i | −0.901338 | − | 0.433116i | \(-0.857414\pi\) |
0.0755794 | − | 0.997140i | \(-0.475919\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.60398 | + | 0.926061i | −0.0519037 | + | 0.0299666i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.207595i | − | 0.00671060i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.09405 | − | 7.09109i | 0.132204 | − | 0.228983i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.4092 | 0.819651 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7344 | −0.668158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.31726 | − | 7.47772i | 0.138978 | − | 0.240716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.4074i | − | 0.366837i | −0.983035 | − | 0.183418i | \(-0.941284\pi\) | ||
0.983035 | − | 0.183418i | \(-0.0587163\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.67391 | − | 5.00789i | 0.278646 | − | 0.160876i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.49209 | − | 16.4408i | −0.304616 | − | 0.527610i | 0.672560 | − | 0.740042i | \(-0.265195\pi\) |
−0.977176 | + | 0.212433i | \(0.931861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0403 | + | 8.68354i | 0.482171 | + | 0.278382i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.180686 | + | 1.98022i | 0.00578658 | + | 0.0634177i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.9449 | − | 19.0208i | −1.05400 | − | 0.608528i | −0.130235 | − | 0.991483i | \(-0.541573\pi\) |
−0.923767 | + | 0.382955i | \(0.874906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.326715 | − | 0.565886i | −0.0104418 | − | 0.0180858i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.0519 | − | 15.0411i | 0.831774 | − | 0.480225i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.2502i | 0.773460i | 0.922193 | + | 0.386730i | \(0.126395\pi\) | ||||
−0.922193 | + | 0.386730i | \(0.873605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.11656 | + | 3.66599i | −0.0674392 | + | 0.116808i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.94189 | −0.284624 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.8711 | −0.345681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9946 | + | 22.5073i | −0.412787 | + | 0.714968i | −0.995193 | − | 0.0979297i | \(-0.968778\pi\) |
0.582406 | + | 0.812898i | \(0.302111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.56036i | − | 0.176453i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0179 | − | 13.8668i | 0.761419 | − | 0.439606i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.34704 | − | 4.06519i | −0.0743315 | − | 0.128746i | 0.826464 | − | 0.562990i | \(-0.190349\pi\) |
−0.900795 | + | 0.434244i | \(0.857016\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.2609 | − | 13.4297i | −0.735941 | − | 0.424896i |
(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 | 1040.2.da.f.641.3 | 16 | ||
4.3 | odd | 2 | 520.2.bu.b.121.6 | ✓ | 16 | ||
13.10 | even | 6 | inner | 1040.2.da.f.881.3 | 16 | ||
52.7 | even | 12 | 6760.2.a.bk.1.3 | 8 | |||
52.19 | even | 12 | 6760.2.a.bl.1.3 | 8 | |||
52.23 | odd | 6 | 520.2.bu.b.361.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.bu.b.121.6 | ✓ | 16 | 4.3 | odd | 2 | ||
520.2.bu.b.361.6 | yes | 16 | 52.23 | odd | 6 | ||
1040.2.da.f.641.3 | 16 | 1.1 | even | 1 | trivial | ||
1040.2.da.f.881.3 | 16 | 13.10 | even | 6 | inner | ||
6760.2.a.bk.1.3 | 8 | 52.7 | even | 12 | |||
6760.2.a.bl.1.3 | 8 | 52.19 | even | 12 |