Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.3 | ||
Root | \(1.10425 - 1.91261i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.k.3781.3 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.952306 | + | 1.64944i | −0.359938 | + | 0.623431i | −0.987950 | − | 0.154773i | \(-0.950535\pi\) |
0.628012 | + | 0.778204i | \(0.283869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50261 | + | 2.60259i | −0.453053 | + | 0.784710i | −0.998574 | − | 0.0533866i | \(-0.982998\pi\) |
0.545521 | + | 0.838097i | \(0.316332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.70849 | + | 4.69125i | 0.751201 | + | 1.30112i | 0.947241 | + | 0.320522i | \(0.103858\pi\) |
−0.196040 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.26869 | − | 3.92948i | −0.550237 | − | 0.953039i | −0.998257 | − | 0.0590155i | \(-0.981204\pi\) |
0.448020 | − | 0.894024i | \(-0.352129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.93872 | + | 3.35797i | 0.444773 | + | 0.770370i | 0.998036 | − | 0.0626366i | \(-0.0199509\pi\) |
−0.553263 | + | 0.833007i | \(0.686618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.952306 | − | 1.64944i | 0.207810 | − | 0.359938i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94438 | + | 3.36777i | 0.405432 | + | 0.702228i | 0.994372 | − | 0.105949i | \(-0.0337879\pi\) |
−0.588940 | + | 0.808177i | \(0.700455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.12189 | − | 7.13932i | 0.765415 | − | 1.32574i | −0.174612 | − | 0.984637i | \(-0.555867\pi\) |
0.940027 | − | 0.341100i | \(-0.110800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.48804 | + | 6.04146i | −0.626470 | + | 1.08508i | 0.361784 | + | 0.932262i | \(0.382168\pi\) |
−0.988255 | + | 0.152817i | \(0.951166\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50261 | − | 2.60259i | 0.261570 | − | 0.453053i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.952306 | + | 1.64944i | −0.160969 | + | 0.278807i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.725995 | + | 1.25746i | 0.119353 | + | 0.206725i | 0.919511 | − | 0.393063i | \(-0.128585\pi\) |
−0.800159 | + | 0.599788i | \(0.795251\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.70849 | − | 4.69125i | −0.433706 | − | 0.751201i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0559598 | − | 0.0969252i | 0.00873945 | − | 0.0151372i | −0.861623 | − | 0.507549i | \(-0.830551\pi\) |
0.870362 | + | 0.492412i | \(0.163885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.08087 | 0.317330 | 0.158665 | − | 0.987332i | \(-0.449281\pi\) | ||||
0.158665 | + | 0.987332i | \(0.449281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.778456 | + | 1.34832i | −0.113549 | + | 0.196673i | −0.917199 | − | 0.398429i | \(-0.869555\pi\) |
0.803650 | + | 0.595103i | \(0.202889\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.68623 | + | 2.92063i | 0.240889 | + | 0.417233i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.26869 | + | 3.92948i | 0.317680 | + | 0.550237i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.39503 | −1.15315 | −0.576573 | − | 0.817046i | \(-0.695610\pi\) | ||||
−0.576573 | + | 0.817046i | \(0.695610\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50261 | + | 2.60259i | −0.202611 | + | 0.350933i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.93872 | − | 3.35797i | −0.256790 | − | 0.444773i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.69514 | −0.350877 | −0.175438 | − | 0.984490i | \(-0.556134\pi\) | ||||
−0.175438 | + | 0.984490i | \(0.556134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.711547 | − | 1.23244i | −0.0911043 | − | 0.157797i | 0.816872 | − | 0.576819i | \(-0.195706\pi\) |
−0.907976 | + | 0.419022i | \(0.862373\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.952306 | + | 1.64944i | −0.119979 | + | 0.207810i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.70849 | + | 4.69125i | 0.335947 | + | 0.581878i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.90197 | − | 2.13517i | −0.965379 | − | 0.260852i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.94438 | − | 3.36777i | −0.234076 | − | 0.405432i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.11366 | − | 3.66096i | 0.250845 | − | 0.434476i | −0.712914 | − | 0.701252i | \(-0.752625\pi\) |
0.963759 | + | 0.266776i | \(0.0859582\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.91448 | − | 5.04802i | −0.341114 | − | 0.590826i | 0.643526 | − | 0.765424i | \(-0.277471\pi\) |
−0.984640 | + | 0.174598i | \(0.944137\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.86188 | − | 4.95693i | −0.326142 | − | 0.564894i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.12853 | − | 5.41877i | 0.351987 | − | 0.609659i | −0.634611 | − | 0.772832i | \(-0.718839\pi\) |
0.986597 | + | 0.163173i | \(0.0521728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.214571 | + | 0.371649i | 0.0235523 | + | 0.0407937i | 0.877561 | − | 0.479464i | \(-0.159169\pi\) |
−0.854009 | + | 0.520258i | \(0.825836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.26869 | − | 3.92948i | −0.246074 | − | 0.426212i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.12189 | + | 7.13932i | −0.441913 | + | 0.765415i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.70404 | −0.816626 | −0.408313 | − | 0.912842i | \(-0.633883\pi\) | ||||
−0.408313 | + | 0.912842i | \(0.633883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3173 | −1.08154 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.48804 | − | 6.04146i | 0.361693 | − | 0.626470i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93872 | + | 3.35797i | 0.198909 | + | 0.344520i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.52705 | − | 2.64493i | −0.155048 | − | 0.268552i | 0.778028 | − | 0.628229i | \(-0.216220\pi\) |
−0.933077 | + | 0.359678i | \(0.882887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50261 | + | 2.60259i | −0.151018 | + | 0.261570i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.83823 | + | 6.64801i | −0.381918 | + | 0.661502i | −0.991336 | − | 0.131347i | \(-0.958070\pi\) |
0.609418 | + | 0.792849i | \(0.291403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.08233 | + | 13.9990i | −0.796376 | + | 1.37936i | 0.125586 | + | 0.992083i | \(0.459919\pi\) |
−0.921962 | + | 0.387281i | \(0.873414\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.952306 | − | 1.64944i | 0.0929356 | − | 0.160969i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.41550 | 0.813557 | 0.406779 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406779 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00738 | −0.383837 | −0.191919 | − | 0.981411i | \(-0.561471\pi\) | ||||
−0.191919 | + | 0.981411i | \(0.561471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.725995 | − | 1.25746i | −0.0689084 | − | 0.119353i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.127891 | + | 0.221514i | −0.0120310 | + | 0.0208383i | −0.871978 | − | 0.489545i | \(-0.837163\pi\) |
0.859947 | + | 0.510383i | \(0.170496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.94438 | + | 3.36777i | 0.181315 | + | 0.314046i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.70849 | + | 4.69125i | 0.250400 | + | 0.433706i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.64194 | 0.792205 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.984349 | + | 1.70494i | 0.0894863 | + | 0.154995i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0559598 | + | 0.0969252i | −0.00504573 | + | 0.00873945i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91787 | + | 3.32185i | −0.170184 | + | 0.294767i | −0.938484 | − | 0.345323i | \(-0.887769\pi\) |
0.768300 | + | 0.640090i | \(0.221103\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.08087 | −0.183211 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.6597 | 1.80504 | 0.902521 | − | 0.430645i | \(-0.141714\pi\) | ||||
0.902521 | + | 0.430645i | \(0.141714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.38503 | −0.640363 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.37529 | −0.544678 | −0.272339 | − | 0.962201i | \(-0.587797\pi\) | ||||
−0.272339 | + | 0.962201i | \(0.587797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.06502 | 0.514429 | 0.257214 | − | 0.966354i | \(-0.417195\pi\) | ||||
0.257214 | + | 0.966354i | \(0.417195\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.778456 | − | 1.34832i | 0.0655578 | − | 0.113549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.2792 | −1.36133 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.12189 | − | 7.13932i | 0.342304 | − | 0.592888i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.68623 | − | 2.92063i | −0.139078 | − | 0.240889i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0684 | −1.56215 | −0.781073 | − | 0.624440i | \(-0.785327\pi\) | ||||
−0.781073 | + | 0.624440i | \(0.785327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.80844 | − | 6.59641i | −0.309926 | − | 0.536808i | 0.668420 | − | 0.743784i | \(-0.266971\pi\) |
−0.978346 | + | 0.206976i | \(0.933638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.26869 | − | 3.92948i | −0.183412 | − | 0.317680i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.48804 | + | 6.04146i | −0.280166 | + | 0.485262i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.20493 | + | 3.81905i | 0.175973 | + | 0.304793i | 0.940497 | − | 0.339801i | \(-0.110360\pi\) |
−0.764525 | + | 0.644594i | \(0.777026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.39503 | 0.665769 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.40659 | −0.583721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.43242 | + | 5.94512i | −0.268848 | + | 0.465658i | −0.968564 | − | 0.248763i | \(-0.919976\pi\) |
0.699717 | + | 0.714420i | \(0.253309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50261 | − | 2.60259i | 0.116978 | − | 0.202611i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.03170 | + | 15.6434i | −0.698894 | + | 1.21052i | 0.269957 | + | 0.962872i | \(0.412991\pi\) |
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.17188 | + | 14.1541i | −0.628606 | + | 1.08878i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.93872 | + | 3.35797i | 0.148258 | + | 0.256790i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.91255 | + | 5.04469i | 0.221437 | + | 0.383541i | 0.955245 | − | 0.295817i | \(-0.0955918\pi\) |
−0.733807 | + | 0.679358i | \(0.762258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.952306 | + | 1.64944i | −0.0719876 | + | 0.124686i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.69514 | 0.202579 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.32860 | 0.622509 | 0.311254 | − | 0.950327i | \(-0.399251\pi\) | ||||
0.311254 | + | 0.950327i | \(0.399251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.40709 | − | 7.63330i | 0.327576 | − | 0.567378i | −0.654454 | − | 0.756102i | \(-0.727102\pi\) |
0.982030 | + | 0.188723i | \(0.0604349\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.711547 | + | 1.23244i | 0.0525991 | + | 0.0911043i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.725995 | + | 1.25746i | 0.0533762 | + | 0.0924503i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6358 | 0.997147 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.952306 | − | 1.64944i | 0.0692701 | − | 0.119979i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.58985 | − | 4.48576i | −0.187395 | − | 0.324578i | 0.756986 | − | 0.653431i | \(-0.226671\pi\) |
−0.944381 | + | 0.328853i | \(0.893338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1088 | −0.799629 | −0.399814 | − | 0.916596i | \(-0.630925\pi\) | ||||
−0.399814 | + | 0.916596i | \(0.630925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.70849 | − | 4.69125i | −0.193959 | − | 0.335947i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.822256 | − | 1.42419i | 0.0585833 | − | 0.101469i | −0.835246 | − | 0.549876i | \(-0.814675\pi\) |
0.893830 | + | 0.448407i | \(0.148008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.25750 | + | 10.8383i | 0.443582 | + | 0.768307i | 0.997952 | − | 0.0639631i | \(-0.0203740\pi\) |
−0.554370 | + | 0.832270i | \(0.687041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.90197 | + | 2.13517i | 0.557362 | + | 0.150603i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.85060 | + | 13.5976i | 0.551004 | + | 0.954367i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0559598 | − | 0.0969252i | 0.00390840 | − | 0.00676955i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.94438 | + | 3.36777i | 0.135144 | + | 0.234076i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6525 | −0.806023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.16577 | − | 10.6794i | −0.424469 | − | 0.735202i | 0.571902 | − | 0.820322i | \(-0.306206\pi\) |
−0.996371 | + | 0.0851205i | \(0.972872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.11366 | + | 3.66096i | −0.144825 | + | 0.250845i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.08087 | 0.141914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.64337 | − | 11.5066i | −0.450981 | − | 0.781122i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.91448 | + | 5.04802i | 0.196942 | + | 0.341114i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.2894 | − | 21.2860i | 0.826678 | − | 1.43185i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1142 | −0.945159 | −0.472579 | − | 0.881288i | \(-0.656677\pi\) | ||||
−0.472579 | + | 0.881288i | \(0.656677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.17609 | + | 15.8935i | −0.609039 | + | 1.05489i | 0.382361 | + | 0.924013i | \(0.375111\pi\) |
−0.991399 | + | 0.130873i | \(0.958222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3960 | + | 19.7385i | 0.753071 | + | 1.30436i | 0.946327 | + | 0.323210i | \(0.104762\pi\) |
−0.193256 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.86188 | + | 4.95693i | 0.188298 | + | 0.326142i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.00903 | + | 13.8721i | −0.524689 | + | 0.908789i | 0.474897 | + | 0.880041i | \(0.342485\pi\) |
−0.999587 | + | 0.0287474i | \(0.990848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.778456 | + | 1.34832i | −0.0507808 | + | 0.0879550i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.12853 | + | 5.41877i | −0.203220 | + | 0.351987i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.3235 | + | 17.8809i | −0.667774 | + | 1.15662i | 0.310752 | + | 0.950491i | \(0.399419\pi\) |
−0.978525 | + | 0.206127i | \(0.933914\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.17862 | 0.204753 | 0.102376 | − | 0.994746i | \(-0.467355\pi\) | ||||
0.102376 | + | 0.994746i | \(0.467355\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.68623 | + | 2.92063i | 0.107729 | + | 0.186592i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.5020 | + | 18.1901i | −0.668228 | + | 1.15741i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.214571 | − | 0.371649i | −0.0135979 | − | 0.0235523i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.34236 | − | 9.25324i | −0.337207 | − | 0.584059i | 0.646699 | − | 0.762745i | \(-0.276149\pi\) |
−0.983906 | + | 0.178686i | \(0.942815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6866 | −0.734728 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.26869 | + | 3.92948i | 0.142071 | + | 0.246074i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.37861 | − | 14.5122i | 0.522643 | − | 0.905244i | −0.477010 | − | 0.878898i | \(-0.658279\pi\) |
0.999653 | − | 0.0263465i | \(-0.00838731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.76548 | −0.171838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.12189 | − | 7.13932i | 0.255138 | − | 0.441913i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.51186 | −0.524864 | −0.262432 | − | 0.964951i | \(-0.584525\pi\) | ||||
−0.262432 | + | 0.964951i | \(0.584525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.39503 | −0.515703 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.70404 | 0.471479 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.08990 | −0.310337 | −0.155168 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155168 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32399 | 0.384155 | 0.192078 | − | 0.981380i | \(-0.438477\pi\) | ||||
0.192078 | + | 0.981380i | \(0.438477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3173 | 0.624429 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50261 | + | 2.60259i | −0.0906106 | + | 0.156942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2318 | −1.27569 | −0.637847 | − | 0.770163i | \(-0.720175\pi\) | ||||
−0.637847 | + | 0.770163i | \(0.720175\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.48804 | + | 6.04146i | −0.208823 | + | 0.361693i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.94374 | − | 10.2949i | −0.354574 | − | 0.614139i | 0.632471 | − | 0.774584i | \(-0.282041\pi\) |
−0.987045 | + | 0.160444i | \(0.948707\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9152 | −1.06495 | −0.532473 | − | 0.846447i | \(-0.678737\pi\) | ||||
−0.532473 | + | 0.846447i | \(0.678737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.93872 | − | 3.35797i | −0.114840 | − | 0.198909i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.106582 | + | 0.184605i | 0.00629132 | + | 0.0108969i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.79388 | + | 3.10710i | −0.105523 | + | 0.182770i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.52705 | + | 2.64493i | 0.0895172 | + | 0.155048i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.98886 | 0.525135 | 0.262567 | − | 0.964914i | \(-0.415431\pi\) | ||||
0.262567 | + | 0.964914i | \(0.415431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.69514 | −0.156917 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.50261 | − | 2.60259i | 0.0871901 | − | 0.151018i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5327 | + | 18.2432i | −0.609121 | + | 1.05503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.98163 | + | 3.43228i | −0.114219 | + | 0.197833i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.83823 | − | 6.64801i | 0.220501 | − | 0.381918i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.711547 | − | 1.23244i | −0.0407431 | − | 0.0705691i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.11191 | − | 14.0502i | −0.462971 | − | 0.801890i | 0.536136 | − | 0.844132i | \(-0.319883\pi\) |
−0.999107 | + | 0.0422417i | \(0.986550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.08233 | − | 13.9990i | 0.459788 | − | 0.796376i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.88048 | −0.446861 | −0.223430 | − | 0.974720i | \(-0.571726\pi\) | ||||
−0.223430 | + | 0.974720i | \(0.571726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1030 | 1.13629 | 0.568143 | − | 0.822930i | \(-0.307662\pi\) | ||||
0.568143 | + | 0.822930i | \(0.307662\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.952306 | + | 1.64944i | −0.0536564 | + | 0.0929356i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.36681 | + | 5.83149i | 0.189099 | + | 0.327529i | 0.944950 | − | 0.327214i | \(-0.106110\pi\) |
−0.755851 | + | 0.654744i | \(0.772777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.3871 | + | 21.4552i | 0.693547 | + | 1.20126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.41550 | −0.469708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.79671 | − | 15.2363i | 0.489462 | − | 0.847773i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70849 | + | 4.69125i | 0.150240 | + | 0.260224i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.00738 | 0.221609 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.48266 | − | 2.56804i | −0.0817415 | − | 0.141580i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.62257 | + | 14.9347i | −0.473939 | + | 0.820887i | −0.999555 | − | 0.0298355i | \(-0.990502\pi\) |
0.525616 | + | 0.850722i | \(0.323835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.725995 | + | 1.25746i | 0.0397843 | + | 0.0689084i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.90197 | − | 2.13517i | −0.431731 | − | 0.116657i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.60167 | − | 6.23828i | −0.196196 | − | 0.339821i | 0.751096 | − | 0.660193i | \(-0.229525\pi\) |
−0.947292 | + | 0.320372i | \(0.896192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.127891 | − | 0.221514i | 0.00694610 | − | 0.0120310i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4823 | − | 18.1559i | −0.567648 | − | 0.983196i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7555 | −1.06670 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.94438 | − | 3.36777i | −0.104682 | − | 0.181315i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3596 | − | 19.6754i | 0.609815 | − | 1.05623i | −0.381455 | − | 0.924387i | \(-0.624577\pi\) |
0.991270 | − | 0.131844i | \(-0.0420898\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.33225 | −0.231900 | −0.115950 | − | 0.993255i | \(-0.536991\pi\) | ||||
−0.115950 | + | 0.993255i | \(0.536991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.70849 | − | 4.69125i | −0.144569 | − | 0.250400i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7645 | + | 20.3768i | 0.626163 | + | 1.08455i | 0.988315 | + | 0.152427i | \(0.0487090\pi\) |
−0.362151 | + | 0.932119i | \(0.617958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.11366 | − | 3.66096i | 0.112181 | − | 0.194304i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.64194 | −0.457380 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6177 | 0.877048 | 0.438524 | − | 0.898719i | \(-0.355501\pi\) | ||||
0.438524 | + | 0.898719i | \(0.355501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.98271 | − | 3.43416i | 0.104353 | − | 0.180745i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.984349 | − | 1.70494i | −0.0516649 | − | 0.0894863i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.91448 | − | 5.04802i | −0.152551 | − | 0.264226i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.6017 | + | 28.7549i | −0.866600 | + | 1.50100i | −0.00115093 | + | 0.999999i | \(0.500366\pi\) |
−0.865449 | + | 0.500996i | \(0.832967\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0559598 | − | 0.0969252i | 0.00291315 | − | 0.00504573i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.99464 | − | 13.8471i | 0.415061 | − | 0.718907i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4803 | + | 25.0807i | −0.749763 | + | 1.29863i | 0.198173 | + | 0.980167i | \(0.436499\pi\) |
−0.947936 | + | 0.318461i | \(0.896834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.6564 | 2.29992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.44016 | + | 2.49444i | 0.0739763 | + | 0.128131i | 0.900641 | − | 0.434565i | \(-0.143098\pi\) |
−0.826664 | + | 0.562695i | \(0.809764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.91787 | − | 3.32185i | 0.0982556 | − | 0.170184i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.91934 | − | 10.2526i | −0.302464 | − | 0.523883i | 0.674229 | − | 0.738522i | \(-0.264476\pi\) |
−0.976694 | + | 0.214639i | \(0.931143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.86188 | − | 4.95693i | −0.145855 | − | 0.252628i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.08087 | 0.105777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4580 | − | 25.0421i | −0.733051 | − | 1.26968i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.222521 | − | 0.974928i | \(-0.428571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.82239 | − | 15.2808i | 0.446167 | − | 0.772785i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.6597 | −1.04214 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.12853 | − | 5.41877i | 0.157413 | − | 0.272648i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.7710 | −1.39379 | −0.696894 | − | 0.717174i | \(-0.745435\pi\) | ||||
−0.696894 | + | 0.717174i | \(0.745435\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.38503 | 0.369714 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0164 | 1.54889 | 0.774443 | − | 0.632644i | \(-0.218030\pi\) | ||||
0.774443 | + | 0.632644i | \(0.218030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.7893 | −1.88242 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.36354 | −0.216292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7849 | + | 22.1442i | −0.632174 | + | 1.09496i | 0.354932 | + | 0.934892i | \(0.384504\pi\) |
−0.987106 | + | 0.160066i | \(0.948829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.37529 | 0.314470 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.56660 | − | 4.44548i | 0.126294 | − | 0.218748i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.214571 | + | 0.371649i | 0.0105329 | + | 0.0182435i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.06502 | −0.297005 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.1209 | + | 22.7261i | 0.641000 | + | 1.11024i | 0.985210 | + | 0.171352i | \(0.0548135\pi\) |
−0.344210 | + | 0.938893i | \(0.611853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0050 | + | 22.5253i | 0.633823 | + | 1.09781i | 0.986763 | + | 0.162168i | \(0.0518486\pi\) |
−0.352940 | + | 0.935646i | \(0.614818\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.778456 | + | 1.34832i | −0.0378498 | + | 0.0655578i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.26869 | − | 3.92948i | −0.110047 | − | 0.190608i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.71044 | 0.131168 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.2792 | 0.785967 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.02725 | − | 6.97541i | 0.193986 | − | 0.335993i | −0.752582 | − | 0.658499i | \(-0.771192\pi\) |
0.946568 | + | 0.322505i | \(0.104525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.04054 | + | 12.1946i | −0.338347 | + | 0.586034i | −0.984122 | − | 0.177494i | \(-0.943201\pi\) |
0.645775 | + | 0.763528i | \(0.276534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.12189 | + | 7.13932i | −0.197629 | + | 0.342304i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.53923 | + | 13.0583i | −0.360650 | + | 0.624665i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5384 | − | 28.6453i | −0.789333 | − | 1.36717i | −0.926376 | − | 0.376600i | \(-0.877093\pi\) |
0.137042 | − | 0.990565i | \(-0.456240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68623 | + | 2.92063i | 0.0802964 | + | 0.139078i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.08553 | + | 3.61225i | −0.0990867 | + | 0.171623i | −0.911307 | − | 0.411728i | \(-0.864925\pi\) |
0.812220 | + | 0.583351i | \(0.198259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.70404 | −0.365206 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.0684 | 0.901905 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.90893 | − | 8.50251i | 0.231667 | − | 0.401258i | −0.726632 | − | 0.687027i | \(-0.758916\pi\) |
0.958299 | + | 0.285769i | \(0.0922488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.168171 | + | 0.291281i | 0.00791887 | + | 0.0137159i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.80844 | + | 6.59641i | 0.178936 | + | 0.309926i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.3173 | −0.483681 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.154702 | − | 0.267953i | 0.00723668 | − | 0.0125343i | −0.862384 | − | 0.506254i | \(-0.831030\pi\) |
0.869621 | + | 0.493720i | \(0.164363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.26869 | + | 3.92948i | 0.105893 | + | 0.183412i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0077 | 0.652403 | 0.326202 | − | 0.945300i | \(-0.394231\pi\) | ||||
0.326202 | + | 0.945300i | \(0.394231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5872 | + | 25.2657i | 0.677923 | + | 1.17420i | 0.975605 | + | 0.219532i | \(0.0704530\pi\) |
−0.297682 | + | 0.954665i | \(0.596214\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.48804 | − | 6.04146i | 0.161754 | − | 0.280166i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.69351 | − | 6.39735i | −0.170915 | − | 0.296034i | 0.767825 | − | 0.640660i | \(-0.221339\pi\) |
−0.938740 | + | 0.344626i | \(0.888006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0469 | − | 11.0005i | 0.510100 | − | 0.507956i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.20493 | − | 3.81905i | −0.101598 | − | 0.175973i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.12673 | + | 5.41566i | −0.143767 | + | 0.249012i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.93872 | + | 3.35797i | 0.0889547 | + | 0.154074i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.39503 | −0.384382 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.1665 | − | 29.7333i | −0.784359 | − | 1.35855i | −0.929381 | − | 0.369121i | \(-0.879659\pi\) |
0.145023 | − | 0.989428i | \(-0.453675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.93270 | + | 6.81164i | −0.179316 | + | 0.310584i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.40659 | 0.337011 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.52705 | − | 2.64493i | −0.0693397 | − | 0.120100i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3592 | + | 35.2631i | 0.922562 | + | 1.59792i | 0.795436 | + | 0.606038i | \(0.207242\pi\) |
0.127126 | + | 0.991887i | \(0.459425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.43242 | − | 5.94512i | 0.155219 | − | 0.268848i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0579 | 0.453909 | 0.226954 | − | 0.973905i | \(-0.427123\pi\) | ||||
0.226954 | + | 0.973905i | \(0.427123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.4051 | −1.68464 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.50261 | + | 2.60259i | −0.0675371 | + | 0.116978i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.02570 | + | 6.97271i | 0.180577 | + | 0.312769i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.55005 | − | 13.0771i | −0.337987 | − | 0.585410i | 0.646067 | − | 0.763281i | \(-0.276413\pi\) |
−0.984054 | + | 0.177870i | \(0.943079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.03170 | − | 15.6434i | 0.403506 | − | 0.698894i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.62438 | + | 16.6699i | −0.429130 | + | 0.743274i | −0.996796 | − | 0.0799842i | \(-0.974513\pi\) |
0.567666 | + | 0.823259i | \(0.307846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.83823 | + | 6.64801i | −0.170799 | + | 0.295833i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.17188 | − | 14.1541i | 0.362926 | − | 0.628606i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.0604 | −1.24376 | −0.621878 | − | 0.783114i | \(-0.713630\pi\) | ||||
−0.621878 | + | 0.783114i | \(0.713630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1019 | 0.491119 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.93872 | − | 3.35797i | −0.0855967 | − | 0.148258i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.08233 | + | 13.9990i | −0.356150 | + | 0.616870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.33942 | − | 4.05200i | −0.102888 | − | 0.178207i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.91255 | − | 5.04469i | −0.127847 | − | 0.221437i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9781 | 1.48861 | 0.744303 | − | 0.667842i | \(-0.232782\pi\) | ||||
0.744303 | + | 0.667842i | \(0.232782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.30814 | − | 3.99781i | −0.100928 | − | 0.174812i | 0.811139 | − | 0.584853i | \(-0.198848\pi\) |
−0.912067 | + | 0.410041i | \(0.865514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.952306 | − | 1.64944i | 0.0415621 | − | 0.0719876i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.6531 | 1.37883 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.93876 | − | 6.82213i | 0.171250 | − | 0.296614i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.69514 | −0.116959 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.606267 | 0.0262603 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.41550 | 0.363834 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.32860 | −0.359406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1349 | −0.436542 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.1210 | 1.93990 | 0.969952 | − | 0.243295i | \(-0.0782284\pi\) | ||||
0.969952 | + | 0.243295i | \(0.0782284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.40709 | + | 7.63330i | −0.189126 | + | 0.327576i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00738 | −0.171657 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.41013 | + | 16.2988i | −0.402348 | + | 0.696887i | −0.994009 | − | 0.109300i | \(-0.965139\pi\) |
0.591661 | + | 0.806187i | \(0.298472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.711547 | − | 1.23244i | −0.0303681 | − | 0.0525991i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.9648 | 1.36174 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.95863 | + | 10.3207i | 0.253387 | + | 0.438879i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.725995 | − | 1.25746i | −0.0308168 | − | 0.0533762i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2456 | − | 17.7459i | 0.434121 | − | 0.751919i | −0.563103 | − | 0.826387i | \(-0.690392\pi\) |
0.997223 | + | 0.0744679i | \(0.0237258\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.63603 | + | 9.76189i | 0.238379 | + | 0.412884i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6358 | −0.575703 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3876 | 0.606366 | 0.303183 | − | 0.952932i | \(-0.401951\pi\) | ||||
0.303183 | + | 0.952932i | \(0.401951\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.127891 | + | 0.221514i | −0.00538043 | + | 0.00931917i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.952306 | + | 1.64944i | −0.0399931 | + | 0.0692701i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0338 | + | 26.0393i | −0.630249 | + | 1.09162i | 0.357252 | + | 0.934008i | \(0.383714\pi\) |
−0.987501 | + | 0.157615i | \(0.949620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.25219 | + | 12.5612i | −0.303495 | + | 0.525668i | −0.976925 | − | 0.213582i | \(-0.931487\pi\) |
0.673430 | + | 0.739251i | \(0.264820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.58985 | + | 4.48576i | 0.108193 | + | 0.187395i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.94438 | + | 3.36777i | 0.0810863 | + | 0.140446i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.32727 | − | 2.29889i | 0.0552548 | − | 0.0957041i | −0.837075 | − | 0.547088i | \(-0.815736\pi\) |
0.892330 | + | 0.451384i | \(0.149070\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.1088 | 0.461666 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.817351 | −0.0339094 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6144 | − | 21.8488i | 0.522436 | − | 0.904886i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.70849 | + | 4.69125i | 0.111982 | + | 0.193959i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.111235 | + | 0.192665i | 0.00459117 | + | 0.00795214i | 0.868312 | − | 0.496019i | \(-0.165205\pi\) |
−0.863721 | + | 0.503971i | \(0.831872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.0494 | −1.11455 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.822256 | + | 1.42419i | −0.0338231 | + | 0.0585833i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.7261 | − | 20.3103i | −0.481535 | − | 0.834043i | 0.518240 | − | 0.855235i | \(-0.326587\pi\) |
−0.999775 | + | 0.0211918i | \(0.993254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.64194 | 0.354285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.25750 | − | 10.8383i | −0.256102 | − | 0.443582i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.6959 | − | 32.3823i | 0.763895 | − | 1.32310i | −0.176934 | − | 0.984223i | \(-0.556618\pi\) |
0.940829 | − | 0.338882i | \(-0.110049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.570375 | + | 0.987919i | 0.0232661 | + | 0.0402980i | 0.877424 | − | 0.479716i | \(-0.159260\pi\) |
−0.854158 | + | 0.520014i | \(0.825927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.90197 | − | 2.13517i | −0.321793 | − | 0.0869507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.984349 | + | 1.70494i | 0.0400195 | + | 0.0693158i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2178 | − | 28.0901i | 0.658262 | − | 1.14014i | −0.322804 | − | 0.946466i | \(-0.604625\pi\) |
0.981065 | − | 0.193677i | \(-0.0620413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.85060 | − | 13.5976i | −0.318122 | − | 0.551004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.43377 | −0.341194 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.20790 | − | 5.55625i | −0.129566 | − | 0.224415i | 0.793943 | − | 0.607993i | \(-0.208025\pi\) |
−0.923508 | + | 0.383578i | \(0.874692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0559598 | + | 0.0969252i | −0.00225652 | + | 0.00390840i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0259 | 0.886730 | 0.443365 | − | 0.896341i | \(-0.353785\pi\) | ||||
0.443365 | + | 0.896341i | \(0.353785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7749 | − | 35.9831i | −0.835012 | − | 1.44628i | −0.894021 | − | 0.448026i | \(-0.852127\pi\) |
0.0590084 | − | 0.998257i | \(-0.481206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.94438 | − | 3.36777i | −0.0780254 | − | 0.135144i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.33660 | − | 12.7074i | 0.293935 | − | 0.509110i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.6525 | 0.465358 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.29411 | − | 5.70556i | 0.131345 | − | 0.227496i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.33335 | + | 14.4338i | 0.331745 | + | 0.574600i | 0.982854 | − | 0.184385i | \(-0.0590292\pi\) |
−0.651109 | + | 0.758984i | \(0.725696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.16577 | + | 10.6794i | 0.245067 | + | 0.424469i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.91787 | + | 3.32185i | −0.0761084 | + | 0.131824i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.13426 | + | 15.8210i | −0.361913 | + | 0.626851i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.11366 | − | 3.66096i | 0.0836150 | − | 0.144825i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.4494 | − | 33.6874i | 0.768206 | − | 1.33057i | −0.170329 | − | 0.985387i | \(-0.554483\pi\) |
0.938535 | − | 0.345184i | \(-0.112184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0504 | 0.554092 | 0.277046 | − | 0.960857i | \(-0.410644\pi\) | ||||
0.277046 | + | 0.960857i | \(0.410644\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.08087 | −0.0819342 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.7320 | + | 30.7127i | 0.697116 | + | 1.20744i | 0.969462 | + | 0.245242i | \(0.0788673\pi\) |
−0.272345 | + | 0.962200i | \(0.587799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.04973 | − | 7.01434i | 0.158966 | − | 0.275337i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.64337 | + | 11.5066i | 0.260374 | + | 0.450981i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.25399 | + | 16.0284i | 0.362137 | + | 0.627239i | 0.988312 | − | 0.152443i | \(-0.0487140\pi\) |
−0.626176 | + | 0.779682i | \(0.715381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.6597 | 0.807240 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.91448 | − | 5.04802i | −0.113705 | − | 0.196942i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.16040 | + | 8.93807i | −0.201021 | + | 0.348178i | −0.948858 | − | 0.315705i | \(-0.897759\pi\) |
0.747837 | + | 0.663882i | \(0.231092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1457 | −0.822471 | −0.411235 | − | 0.911529i | \(-0.634903\pi\) | ||||
−0.411235 | + | 0.911529i | \(0.634903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2894 | + | 21.2860i | −0.477283 | + | 0.826678i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.38503 | −0.286379 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.0581 | 1.24129 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.1142 | 0.545688 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.27670 | 0.165100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.5294 | −1.09973 | −0.549864 | − | 0.835254i | \(-0.685321\pi\) | ||||
−0.549864 | + | 0.835254i | \(0.685321\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2026 | − | 26.3317i | 0.584285 | − | 1.01201i | −0.410680 | − | 0.911780i | \(-0.634709\pi\) |
0.994964 | − | 0.100231i | \(-0.0319581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81688 | 0.223231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.17609 | − | 15.8935i | 0.351629 | − | 0.609039i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0436 | − | 17.3960i | −0.384307 | − | 0.665639i | 0.607366 | − | 0.794422i | \(-0.292226\pi\) |
−0.991673 | + | 0.128783i | \(0.958893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.37529 | −0.243587 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.3960 | − | 19.7385i | −0.434786 | − | 0.753071i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.7379 | − | 39.3832i | −0.866245 | − | 1.50038i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.382534 | − | 0.662568i | 0.0145523 | − | 0.0252053i | −0.858658 | − | 0.512550i | \(-0.828701\pi\) |
0.873210 | + | 0.487344i | \(0.162034\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.86188 | − | 4.95693i | −0.108714 | − | 0.188298i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.06502 | 0.230059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.507821 | −0.0192351 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.00903 | − | 13.8721i | 0.302930 | − | 0.524689i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1887 | − | 19.3794i | 0.422592 | − | 0.731951i | −0.573600 | − | 0.819136i | \(-0.694454\pi\) |
0.996192 | + | 0.0871843i | \(0.0277869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.81500 | + | 4.87573i | −0.106170 | + | 0.183892i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.778456 | − | 1.34832i | 0.0293183 | − | 0.0507808i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.31034 | − | 12.6619i | −0.274934 | − | 0.476199i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7785 | − | 23.8651i | −0.517462 | − | 0.896271i | −0.999794 | − | 0.0202824i | \(-0.993543\pi\) |
0.482332 | − | 0.875988i | \(-0.339790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.12853 | − | 5.41877i | 0.117329 | − | 0.203220i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.1283 | −1.01596 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.2792 | −0.608807 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3235 | − | 17.8809i | 0.385539 | − | 0.667774i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9605 | + | 31.1085i | 0.669813 | + | 1.16015i | 0.977956 | + | 0.208811i | \(0.0669593\pi\) |
−0.308143 | + | 0.951340i | \(0.599707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3937 | − | 26.6627i | −0.573292 | − | 0.992971i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.17862 | −0.118214 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.12189 | − | 7.13932i | 0.153083 | − | 0.265148i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.61887 | − | 14.9283i | −0.319656 | − | 0.553661i | 0.660760 | − | 0.750597i | \(-0.270234\pi\) |
−0.980416 | + | 0.196937i | \(0.936901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.72085 | − | 8.17675i | −0.174607 | − | 0.302428i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1070 | − | 17.5058i | 0.373311 | − | 0.646593i | −0.616762 | − | 0.787150i | \(-0.711556\pi\) |
0.990073 | + | 0.140557i | \(0.0448892\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.68623 | − | 2.92063i | −0.0621974 | − | 0.107729i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4305 | − | 17.3573i | 0.642061 | − | 0.639363i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.29101 | − | 3.96814i | −0.0842760 | − | 0.145970i | 0.820806 | − | 0.571206i | \(-0.193524\pi\) |
−0.905082 | + | 0.425236i | \(0.860191\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.5020 | − | 18.1901i | 0.385802 | − | 0.668228i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5208 | + | 25.1508i | 0.532717 | + | 0.922693i | 0.999270 | + | 0.0382000i | \(0.0121624\pi\) |
−0.466553 | + | 0.884493i | \(0.654504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0684 | −0.698613 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.214571 | + | 0.371649i | 0.00785076 | + | 0.0135979i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.01414 | + | 13.8809i | −0.292830 | + | 0.507197i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.5475 | 1.18767 | 0.593837 | − | 0.804586i | \(-0.297613\pi\) | ||||
0.593837 | + | 0.804586i | \(0.297613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.34236 | + | 9.25324i | 0.194686 | + | 0.337207i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.80844 | − | 6.59641i | −0.138603 | − | 0.240068i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.9972 | − | 27.7080i | 0.581428 | − | 1.00706i | −0.413882 | − | 0.910330i | \(-0.635827\pi\) |
0.995310 | − | 0.0967327i | \(-0.0308392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.6866 | 0.424195 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.4269 | 0.776726 | 0.388363 | − | 0.921507i | \(-0.373041\pi\) | ||||
0.388363 | + | 0.921507i | \(0.373041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.81625 | − | 6.60995i | 0.138158 | − | 0.239296i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.26869 | − | 3.92948i | −0.0820246 | − | 0.142071i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.29976 | − | 12.6436i | −0.263579 | − | 0.456532i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.6011 | − | 35.6821i | 0.742893 | − | 1.28673i | −0.208280 | − | 0.978069i | \(-0.566786\pi\) |
0.951173 | − | 0.308659i | \(-0.0998802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.37861 | + | 14.5122i | −0.301748 | + | 0.522643i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.9889 | − | 24.2295i | 0.503147 | − | 0.871476i | −0.496846 | − | 0.867839i | \(-0.665509\pi\) |
0.999993 | − | 0.00363766i | \(-0.00115790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.48804 | + | 6.04146i | −0.125294 | + | 0.217016i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.76548 | 0.0992109 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.433962 | 0.0155483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.35199 | + | 11.0020i | 0.227292 | + | 0.393681i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.12189 | + | 7.13932i | −0.147304 | + | 0.255138i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.20493 | + | 3.81905i | 0.0786973 | + | 0.136308i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.55242 | − | 16.5453i | −0.340507 | − | 0.589776i | 0.644020 | − | 0.765009i | \(-0.277265\pi\) |
−0.984527 | + | 0.175233i | \(0.943932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.51186 | 0.303030 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.243583 | − | 0.421899i | −0.00866083 | − | 0.0150010i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.85444 | − | 6.67609i | 0.136875 | − | 0.237075i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.39503 | 0.297741 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.83180 | − | 17.0292i | 0.348260 | − | 0.603204i | −0.637680 | − | 0.770301i | \(-0.720106\pi\) |
0.985940 | + | 0.167097i | \(0.0534393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.06429 | 0.249917 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.70404 | −0.272209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5172 | 0.618170 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.40659 | −0.261048 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.08990 | 0.179173 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.6838 | 0.692045 | 0.346022 | − | 0.938226i | \(-0.387532\pi\) | ||||
0.346022 | + | 0.938226i | \(0.387532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.82112 | + | 4.88633i | −0.0990630 | + | 0.171582i | −0.911297 | − | 0.411749i | \(-0.864918\pi\) |
0.812234 | + | 0.583332i | \(0.198251\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.32399 | −0.221792 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.43242 | + | 5.94512i | −0.120232 | + | 0.208248i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.03423 | + | 6.98749i | 0.141140 | + | 0.244461i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.3173 | −0.360514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.40512 | + | 7.62990i | 0.153740 | + | 0.266285i | 0.932599 | − | 0.360913i | \(-0.117535\pi\) |
−0.778860 | + | 0.627198i | \(0.784202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.6375 | + | 28.8169i | 0.579946 | + | 1.00450i | 0.995485 | + | 0.0949199i | \(0.0302595\pi\) |
−0.415539 | + | 0.909575i | \(0.636407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.50261 | − | 2.60259i | 0.0523140 | − | 0.0906106i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.79121 | − | 3.10247i | −0.0622865 | − | 0.107883i | 0.833201 | − | 0.552971i | \(-0.186506\pi\) |
−0.895487 | + | 0.445087i | \(0.853173\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1861 | 1.08314 | 0.541570 | − | 0.840656i | \(-0.317830\pi\) | ||||
0.541570 | + | 0.840656i | \(0.317830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.2318 | 0.736523 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65104 | − | 13.2520i | 0.265093 | − | 0.459154i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.03170 | + | 15.6434i | −0.312555 | + | 0.541361i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.48804 | − | 6.04146i | 0.120564 | − | 0.208823i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.35033 | − | 9.26705i | 0.184714 | − | 0.319934i | −0.758766 | − | 0.651363i | \(-0.774197\pi\) |
0.943480 | + | 0.331429i | \(0.107531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.4799 | − | 33.7402i | −0.671720 | − | 1.16345i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.94374 | + | 10.2949i | 0.204713 | + | 0.354574i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.17188 | + | 14.1541i | −0.281121 | + | 0.486916i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.74961 | −0.128838 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.9152 | 0.614846 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.82322 | + | 4.88996i | −0.0967788 | + | 0.167626i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3954 | + | 37.0579i | 0.732564 | + | 1.26884i | 0.955784 | + | 0.294069i | \(0.0950097\pi\) |
−0.223220 | + | 0.974768i | \(0.571657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.93872 | + | 3.35797i | 0.0663029 | + | 0.114840i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.8449 | 0.609571 | 0.304786 | − | 0.952421i | \(-0.401415\pi\) | ||||
0.304786 | + | 0.952421i | \(0.401415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.54386 | + | 14.7984i | −0.291513 | + | 0.504915i | −0.974168 | − | 0.225826i | \(-0.927492\pi\) |
0.682655 | + | 0.730741i | \(0.260825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.106582 | − | 0.184605i | −0.00363230 | − | 0.00629132i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1803 | 0.482704 | 0.241352 | − | 0.970438i | \(-0.422409\pi\) | ||||
0.241352 | + | 0.970438i | \(0.422409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.91255 | + | 5.04469i | 0.0990298 | + | 0.171525i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.79388 | − | 3.10710i | 0.0609235 | − | 0.105523i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.40189 | + | 16.2846i | 0.318937 | + | 0.552416i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3858 | − | 42.8532i | −0.385794 | − | 1.45202i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.52705 | − | 2.64493i | −0.0516828 | − | 0.0895172i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.952306 | + | 1.64944i | −0.0321938 | + | 0.0557614i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.96197 | + | 12.0585i | 0.235089 | + | 0.407186i | 0.959299 | − | 0.282394i | \(-0.0911285\pi\) |
−0.724209 | + | 0.689580i | \(0.757795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.98886 | −0.303187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.7274 | + | 27.2406i | 0.529869 | + | 0.917759i | 0.999393 | + | 0.0348397i | \(0.0110921\pi\) |
−0.469524 | + | 0.882919i | \(0.655575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6082 | + | 27.0343i | −0.525259 | + | 0.909776i | 0.474308 | + | 0.880359i | \(0.342698\pi\) |
−0.999567 | + | 0.0294167i | \(0.990635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.69514 | 0.0905960 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.99034 | + | 3.44737i | 0.0668291 | + | 0.115751i | 0.897504 | − | 0.441006i | \(-0.145378\pi\) |
−0.830675 | + | 0.556758i | \(0.812045\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.65280 | − | 6.32684i | −0.122511 | − | 0.212195i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50261 | + | 2.60259i | −0.0503392 | + | 0.0871901i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.03684 | −0.202015 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.32860 | 0.278394 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.5327 | − | 18.2432i | 0.351676 | − | 0.609121i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.7546 | + | 49.8044i | 0.959020 | + | 1.66107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.0457 | + | 32.9881i | 0.634504 | + | 1.09899i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.98163 | − | 3.43228i | 0.0659444 | − | 0.114219i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.40709 | − | 7.63330i | 0.146496 | − | 0.253739i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2302 | − | 17.7193i | 0.339690 | − | 0.588360i | −0.644685 | − | 0.764449i | \(-0.723011\pi\) |
0.984374 | + | 0.176089i | \(0.0563446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.83823 | + | 6.64801i | −0.127306 | + | 0.220501i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.25478 | −0.240361 | −0.120181 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120181 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.28967 | −0.0426817 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.711547 | + | 1.23244i | 0.0235230 | + | 0.0407431i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.6743 | + | 34.0769i | −0.649703 | + | 1.12532i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.98927 | + | 10.3737i | 0.197568 | + | 0.342198i | 0.947739 | − | 0.319046i | \(-0.103362\pi\) |
−0.750171 | + | 0.661243i | \(0.770029\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.11191 | + | 14.0502i | 0.267297 | + | 0.462971i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.8993 | 0.753740 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.725995 | + | 1.25746i | 0.0238706 | + | 0.0413450i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.08233 | + | 13.9990i | −0.265459 | + | 0.459788i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.70214 | 0.219890 | 0.109945 | − | 0.993938i | \(-0.464933\pi\) | ||||
0.109945 | + | 0.993938i | \(0.464933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.53824 | + | 11.3246i | −0.214282 | + | 0.371148i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.88048 | 0.257995 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6358 | 0.445937 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0798 | 1.08067 | 0.540335 | − | 0.841450i | \(-0.318298\pi\) | ||||
0.540335 | + | 0.841450i | \(0.318298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.1030 | −0.656035 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0151 | −0.359081 | −0.179540 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179540 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.435229 | 0.0141730 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.952306 | − | 1.64944i | 0.0309785 | − | 0.0536564i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.9084 | −1.19936 | −0.599681 | − | 0.800239i | \(-0.704706\pi\) | ||||
−0.599681 | + | 0.800239i | \(0.704706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.7877 | − | 27.3451i | 0.512490 | − | 0.887659i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.36681 | − | 5.83149i | −0.109176 | − | 0.189099i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1751 | 0.685928 | 0.342964 | − | 0.939349i | \(-0.388569\pi\) | ||||
0.342964 | + | 0.939349i | \(0.388569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.58985 | − | 4.48576i | −0.0838057 | − | 0.145156i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.3871 | − | 21.4552i | −0.400419 | − | 0.693547i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.07123 | − | 10.5157i | 0.196050 | − | 0.339569i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.83284 | − | 15.2989i | −0.284930 | − | 0.493514i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.41550 | 0.271186 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.1088 | −0.357605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2858 | − | 21.2796i | 0.395084 | − | 0.684305i | −0.598028 | − | 0.801475i | \(-0.704049\pi\) |
0.993112 | + | 0.117170i | \(0.0373822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.79671 | + | 15.2363i | −0.282591 | + | 0.489462i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5014 | + | 19.9211i | −0.369098 | + | 0.639297i | −0.989425 | − | 0.145047i | \(-0.953667\pi\) |
0.620327 | + | 0.784344i | \(0.287000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.77576 | + | 10.0039i | −0.185162 | + | 0.320711i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.70849 | − | 4.69125i | −0.0867412 | − | 0.150240i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.9723 | − | 43.2532i | −0.798933 | − | 1.38379i | −0.920311 | − | 0.391187i | \(-0.872065\pi\) |
0.121378 | − | 0.992606i | \(-0.461269\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5761 | − | 20.0505i | 0.369975 | − | 0.640815i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00738 | −0.127946 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0654 | −0.703778 | −0.351889 | − | 0.936042i | \(-0.614461\pi\) | ||||
−0.351889 | + | 0.936042i | \(0.614461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.822256 | − | 1.42419i | 0.0261992 | − | 0.0453784i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.48266 | + | 2.56804i | 0.0471935 | + | 0.0817415i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.04601 | + | 7.00789i | 0.128656 | + | 0.222838i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.96913 | 0.126084 | 0.0630418 | − | 0.998011i | \(-0.479920\pi\) | ||||
0.0630418 | + | 0.998011i | \(0.479920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.62257 | − | 14.9347i | 0.273629 | − | 0.473939i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.25750 | + | 10.8383i | 0.198376 | + | 0.343598i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.98418 | −0.0945099 | −0.0472550 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472550 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.725995 | − | 1.25746i | −0.0229695 | − | 0.0397843i |
(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 | 4020.2.q.k.841.3 | ✓ | 14 | |
67.29 | even | 3 | inner | 4020.2.q.k.3781.3 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.k.841.3 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4020.2.q.k.3781.3 | yes | 14 | 67.29 | even | 3 | inner |