Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(109,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.g (of order \(3\), 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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1767277521.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.373419 + 0.0835272i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.541 |
Dual form | 567.2.g.k.109.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18584 | − | 2.05393i | −0.838513 | − | 1.45235i | −0.891138 | − | 0.453733i | \(-0.850092\pi\) |
0.0526243 | − | 0.998614i | \(-0.483241\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.81242 | + | 3.13920i | −0.906209 | + | 1.56960i | ||||
\(5\) | −1.22875 | −0.549512 | −0.274756 | − | 0.961514i | \(-0.588597\pi\) | ||||
−0.274756 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61263 | − | 0.417345i | 0.987480 | − | 0.157741i | ||||
\(8\) | 3.85358 | 1.36245 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.45709 | + | 2.52376i | 0.460773 | + | 0.798082i | ||||
\(11\) | −2.66102 | −0.802328 | −0.401164 | − | 0.916006i | \(-0.631394\pi\) | ||||
−0.401164 | + | 0.916006i | \(0.631394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.81242 | + | 3.13920i | 0.502674 | + | 0.870658i | 0.999995 | + | 0.00309084i | \(0.000983846\pi\) |
−0.497321 | + | 0.867567i | \(0.665683\pi\) | |||||||
\(14\) | −3.95535 | − | 4.87125i | −1.05711 | − | 1.30190i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.944883 | − | 1.63659i | −0.236221 | − | 0.409146i | ||||
\(17\) | 3.36579 | + | 5.82972i | 0.816324 | + | 1.41391i | 0.908373 | + | 0.418160i | \(0.137325\pi\) |
−0.0920492 | + | 0.995754i | \(0.529342\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.25730 | + | 2.17771i | −0.288445 | + | 0.499601i | −0.973439 | − | 0.228948i | \(-0.926471\pi\) |
0.684994 | + | 0.728549i | \(0.259805\pi\) | |||||||
\(20\) | 2.22700 | − | 3.85728i | 0.497972 | − | 0.862514i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.15554 | + | 5.46555i | 0.672763 | + | 1.16526i | ||||
\(23\) | 7.99651 | 1.66739 | 0.833694 | − | 0.552227i | \(-0.186222\pi\) | ||||
0.833694 | + | 0.552227i | \(0.186222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.49018 | −0.698037 | ||||||||
\(26\) | 4.29846 | − | 7.44516i | 0.842998 | − | 1.46012i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.42505 | + | 8.95796i | −0.647273 | + | 1.69290i | ||||
\(29\) | 1.12484 | − | 1.94827i | 0.208877 | − | 0.361785i | −0.742484 | − | 0.669864i | \(-0.766353\pi\) |
0.951361 | + | 0.308078i | \(0.0996859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.11263 | − | 8.85533i | 0.918255 | − | 1.59046i | 0.116191 | − | 0.993227i | \(-0.462932\pi\) |
0.802064 | − | 0.597237i | \(-0.203735\pi\) | |||||||
\(32\) | 1.61263 | − | 2.79315i | 0.285075 | − | 0.493764i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.98256 | − | 13.8262i | 1.36900 | − | 2.37117i | ||||
\(35\) | −3.21025 | + | 0.512810i | −0.542632 | + | 0.0866807i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.76951 | − | 3.06488i | 0.290906 | − | 0.503863i | −0.683119 | − | 0.730308i | \(-0.739377\pi\) |
0.974024 | + | 0.226444i | \(0.0727101\pi\) | |||||||
\(38\) | 5.96382 | 0.967459 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.73507 | −0.748680 | ||||||||
\(41\) | 0.932674 | + | 1.61544i | 0.145659 | + | 0.252289i | 0.929619 | − | 0.368523i | \(-0.120136\pi\) |
−0.783959 | + | 0.620812i | \(0.786803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.56972 | + | 4.45088i | −0.391879 | + | 0.678753i | −0.992697 | − | 0.120632i | \(-0.961508\pi\) |
0.600819 | + | 0.799385i | \(0.294841\pi\) | |||||||
\(44\) | 4.82288 | − | 8.35348i | 0.727077 | − | 1.25933i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.48256 | − | 16.4243i | −1.39813 | − | 2.42163i | ||||
\(47\) | −1.07321 | − | 1.85885i | −0.156544 | − | 0.271142i | 0.777076 | − | 0.629406i | \(-0.216702\pi\) |
−0.933620 | + | 0.358265i | \(0.883369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65165 | − | 2.18073i | 0.950235 | − | 0.311533i | ||||
\(50\) | 4.13879 | + | 7.16859i | 0.585313 | + | 1.01379i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.1394 | −1.82211 | ||||||||
\(53\) | 1.48605 | + | 2.57391i | 0.204124 | + | 0.353553i | 0.949853 | − | 0.312696i | \(-0.101232\pi\) |
−0.745729 | + | 0.666249i | \(0.767899\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.26972 | 0.440888 | ||||||||
\(56\) | 10.0680 | − | 1.60827i | 1.34539 | − | 0.214914i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.33549 | −0.700584 | ||||||||
\(59\) | −4.36405 | + | 7.55875i | −0.568150 | + | 0.984065i | 0.428599 | + | 0.903495i | \(0.359007\pi\) |
−0.996749 | + | 0.0805702i | \(0.974326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.50239 | + | 12.9945i | 0.960583 | + | 1.66378i | 0.721041 | + | 0.692893i | \(0.243664\pi\) |
0.239542 | + | 0.970886i | \(0.423003\pi\) | |||||||
\(62\) | −24.2510 | −3.07988 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.4288 | −1.42860 | ||||||||
\(65\) | −2.22700 | − | 3.85728i | −0.276225 | − | 0.478436i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.32463 | − | 2.29432i | 0.161829 | − | 0.280296i | −0.773696 | − | 0.633557i | \(-0.781594\pi\) |
0.935525 | + | 0.353261i | \(0.114927\pi\) | |||||||
\(68\) | −24.4009 | −2.95904 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.86011 | + | 5.98553i | 0.580895 | + | 0.715407i | ||||
\(71\) | 10.1150 | 1.20043 | 0.600216 | − | 0.799838i | \(-0.295081\pi\) | ||||
0.600216 | + | 0.799838i | \(0.295081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.64707 | − | 6.31691i | −0.426857 | − | 0.739338i | 0.569735 | − | 0.821829i | \(-0.307046\pi\) |
−0.996592 | + | 0.0824907i | \(0.973713\pi\) | |||||||
\(74\) | −8.39340 | −0.975713 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.55751 | − | 7.89384i | −0.522782 | − | 0.905486i | ||||
\(77\) | −6.95226 | + | 1.11056i | −0.792283 | + | 0.126560i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.156882 | + | 0.271728i | 0.0176506 | + | 0.0305717i | 0.874716 | − | 0.484636i | \(-0.161048\pi\) |
−0.857065 | + | 0.515208i | \(0.827715\pi\) | |||||||
\(80\) | 1.16102 | + | 2.01095i | 0.129806 | + | 0.224831i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.21200 | − | 3.83129i | 0.244274 | − | 0.423096i | ||||
\(83\) | 3.84686 | − | 6.66295i | 0.422247 | − | 0.731354i | −0.573912 | − | 0.818917i | \(-0.694575\pi\) |
0.996159 | + | 0.0875633i | \(0.0279080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.13570 | − | 7.16324i | −0.448580 | − | 0.776963i | ||||
\(86\) | 12.1891 | 1.31438 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.2545 | −1.09313 | ||||||||
\(89\) | −3.59628 | + | 6.22894i | −0.381205 | + | 0.660266i | −0.991235 | − | 0.132112i | \(-0.957824\pi\) |
0.610030 | + | 0.792378i | \(0.291157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.04530 | + | 7.44516i | 0.633720 | + | 0.780465i | ||||
\(92\) | −14.4930 | + | 25.1026i | −1.51100 | + | 2.61713i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.54530 | + | 4.40859i | −0.262528 | + | 0.454712i | ||||
\(95\) | 1.54490 | − | 2.67585i | 0.158504 | − | 0.274536i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.59195 | − | 11.4176i | 0.669311 | − | 1.15928i | −0.308786 | − | 0.951132i | \(-0.599923\pi\) |
0.978097 | − | 0.208149i | \(-0.0667440\pi\) | |||||||
\(98\) | −12.3668 | − | 11.0760i | −1.24924 | − | 1.11885i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.32567 | − | 10.9564i | 0.632567 | − | 1.09564i | ||||
\(101\) | 2.78302 | 0.276921 | 0.138460 | − | 0.990368i | \(-0.455785\pi\) | ||||
0.138460 | + | 0.990368i | \(0.455785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00647 | 0.591835 | 0.295917 | − | 0.955214i | \(-0.404375\pi\) | ||||
0.295917 | + | 0.955214i | \(0.404375\pi\) | |||||||
\(104\) | 6.98430 | + | 12.0972i | 0.684867 | + | 1.18622i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.52442 | − | 6.10447i | 0.342322 | − | 0.592919i | ||||
\(107\) | −5.86818 | + | 10.1640i | −0.567299 | + | 0.982590i | 0.429533 | + | 0.903051i | \(0.358678\pi\) |
−0.996832 | + | 0.0795391i | \(0.974655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.99237 | + | 6.91499i | 0.382400 | + | 0.662336i | 0.991405 | − | 0.130830i | \(-0.0417644\pi\) |
−0.609005 | + | 0.793166i | \(0.708431\pi\) | |||||||
\(110\) | −3.87735 | − | 6.71577i | −0.369691 | − | 0.640323i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.15165 | − | 3.88145i | −0.297803 | − | 0.366762i | ||||
\(113\) | 2.32005 | + | 4.01844i | 0.218252 | + | 0.378023i | 0.954274 | − | 0.298935i | \(-0.0966313\pi\) |
−0.736022 | + | 0.676958i | \(0.763298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.82567 | −0.916249 | ||||||||
\(116\) | 4.07735 | + | 7.06217i | 0.378572 | + | 0.655706i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.7002 | 1.90561 | ||||||||
\(119\) | 11.2266 | + | 13.8262i | 1.02914 | + | 1.26745i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.91897 | −0.356270 | ||||||||
\(122\) | 17.7932 | − | 30.8188i | 1.61092 | − | 2.79020i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.5324 | + | 32.0991i | 1.66426 | + | 2.88259i | ||||
\(125\) | 10.4323 | 0.933091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.32633 | −0.295164 | −0.147582 | − | 0.989050i | \(-0.547149\pi\) | ||||
−0.147582 | + | 0.989050i | \(0.547149\pi\) | |||||||
\(128\) | 10.3274 | + | 17.8876i | 0.912824 | + | 1.58106i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.28172 | + | 9.14820i | −0.463237 | + | 0.802351i | ||||
\(131\) | 8.44702 | 0.738020 | 0.369010 | − | 0.929425i | \(-0.379697\pi\) | ||||
0.369010 | + | 0.929425i | \(0.379697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37600 | + | 6.21427i | −0.206026 | + | 0.538846i | ||||
\(134\) | −6.28317 | −0.542783 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.9703 | + | 22.4653i | 1.11220 | + | 1.92638i | ||||
\(137\) | −13.9965 | −1.19580 | −0.597901 | − | 0.801570i | \(-0.703999\pi\) | ||||
−0.597901 | + | 0.801570i | \(0.703999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82005 | + | 4.88446i | 0.239193 | + | 0.414295i | 0.960483 | − | 0.278339i | \(-0.0897837\pi\) |
−0.721290 | + | 0.692633i | \(0.756450\pi\) | |||||||
\(140\) | 4.20851 | − | 11.0071i | 0.355684 | − | 0.930266i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.9948 | − | 20.7755i | −1.00658 | − | 1.74344i | ||||
\(143\) | −4.82288 | − | 8.35348i | −0.403310 | − | 0.698553i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.38214 | + | 2.39393i | −0.114780 | + | 0.198805i | ||||
\(146\) | −8.64965 | + | 14.9816i | −0.715850 | + | 1.23989i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.41418 | + | 11.1097i | 0.527243 | + | 0.913211i | ||||
\(149\) | −8.76945 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.56075 | −0.778042 | −0.389021 | − | 0.921229i | \(-0.627187\pi\) | ||||
−0.389021 | + | 0.921229i | \(0.627187\pi\) | |||||||
\(152\) | −4.84511 | + | 8.39198i | −0.392991 | + | 0.680680i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.5253 | + | 12.9625i | 0.848149 | + | 1.04455i | ||||
\(155\) | −6.28212 | + | 10.8809i | −0.504592 | + | 0.873979i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07953 | + | 1.86981i | −0.0861562 | + | 0.149227i | −0.905883 | − | 0.423527i | \(-0.860792\pi\) |
0.819727 | + | 0.572754i | \(0.194125\pi\) | |||||||
\(158\) | 0.372073 | − | 0.644449i | 0.0296005 | − | 0.0512696i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.98151 | + | 3.43207i | −0.156652 | + | 0.271329i | ||||
\(161\) | 20.8919 | − | 3.33730i | 1.64651 | − | 0.263016i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.4871 | + | 18.1643i | −0.821416 | + | 1.42273i | 0.0832119 | + | 0.996532i | \(0.473482\pi\) |
−0.904628 | + | 0.426202i | \(0.859851\pi\) | |||||||
\(164\) | −6.76158 | −0.527991 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.2470 | −1.41624 | ||||||||
\(167\) | 2.13704 | + | 3.70147i | 0.165370 | + | 0.286428i | 0.936786 | − | 0.349902i | \(-0.113785\pi\) |
−0.771417 | + | 0.636330i | \(0.780452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0697192 | + | 0.120757i | −0.00536302 | + | 0.00928902i | ||||
\(170\) | −9.80853 | + | 16.9889i | −0.752280 | + | 1.30299i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.31481 | − | 16.1337i | −0.710248 | − | 1.23019i | ||||
\(173\) | 0.908300 | + | 1.57322i | 0.0690567 | + | 0.119610i | 0.898486 | − | 0.439001i | \(-0.144668\pi\) |
−0.829430 | + | 0.558611i | \(0.811334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.11855 | + | 1.45661i | −0.689298 | + | 0.110109i | ||||
\(176\) | 2.51435 | + | 4.35499i | 0.189526 | + | 0.328269i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.0584 | 1.27858 | ||||||||
\(179\) | 4.02507 | + | 6.97162i | 0.300848 | + | 0.521083i | 0.976328 | − | 0.216295i | \(-0.0693971\pi\) |
−0.675481 | + | 0.737378i | \(0.736064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.3467 | 1.88401 | 0.942004 | − | 0.335601i | \(-0.108939\pi\) | ||||
0.942004 | + | 0.335601i | \(0.108939\pi\) | |||||||
\(182\) | 8.12309 | − | 21.2454i | 0.602124 | − | 1.57481i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 30.8152 | 2.27173 | ||||||||
\(185\) | −2.17428 | + | 3.76596i | −0.159856 | + | 0.276879i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.95644 | − | 15.5130i | −0.654960 | − | 1.13442i | ||||
\(188\) | 7.78042 | 0.567445 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.32801 | −0.531630 | ||||||||
\(191\) | −3.57560 | − | 6.19313i | −0.258722 | − | 0.448119i | 0.707178 | − | 0.707035i | \(-0.249968\pi\) |
−0.965900 | + | 0.258917i | \(0.916635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.67777 | + | 9.83418i | −0.408695 | + | 0.707880i | −0.994744 | − | 0.102396i | \(-0.967349\pi\) |
0.586049 | + | 0.810276i | \(0.300683\pi\) | |||||||
\(194\) | −31.2679 | −2.24490 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.20981 | + | 24.8333i | −0.372129 | + | 1.77380i | ||||
\(197\) | −20.0998 | −1.43205 | −0.716024 | − | 0.698075i | \(-0.754040\pi\) | ||||
−0.716024 | + | 0.698075i | \(0.754040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.16251 | − | 8.94173i | −0.365961 | − | 0.633862i | 0.622969 | − | 0.782246i | \(-0.285926\pi\) |
−0.988930 | + | 0.148384i | \(0.952593\pi\) | |||||||
\(200\) | −13.4497 | −0.951038 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.30021 | − | 5.71613i | −0.232202 | − | 0.402186i | ||||
\(203\) | 2.12568 | − | 5.55956i | 0.149193 | − | 0.390204i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.14602 | − | 1.98496i | −0.0800415 | − | 0.138636i | ||||
\(206\) | −7.12269 | − | 12.3369i | −0.496261 | − | 0.859550i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.42505 | − | 5.93235i | 0.237484 | − | 0.411335i | ||||
\(209\) | 3.34570 | − | 5.79493i | 0.231427 | − | 0.400844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.299369 | − | 0.518522i | −0.0206094 | − | 0.0356965i | 0.855537 | − | 0.517742i | \(-0.173227\pi\) |
−0.876146 | + | 0.482046i | \(0.839894\pi\) | |||||||
\(212\) | −10.7734 | −0.739917 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.8348 | 1.90275 | ||||||||
\(215\) | 3.15753 | − | 5.46900i | 0.215342 | − | 0.372983i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.66167 | − | 25.2694i | 0.655877 | − | 1.71540i | ||||
\(218\) | 9.46860 | − | 16.4001i | 0.641295 | − | 1.11076i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.92609 | + | 10.2643i | −0.399537 | + | 0.692019i | ||||
\(221\) | −12.2004 | + | 21.1318i | −0.820690 | + | 1.42148i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.51002 | + | 2.61543i | −0.101119 | + | 0.175142i | −0.912146 | − | 0.409866i | \(-0.865575\pi\) |
0.811027 | + | 0.585008i | \(0.198909\pi\) | |||||||
\(224\) | 3.04749 | − | 7.97049i | 0.203619 | − | 0.532551i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.50239 | − | 9.53043i | 0.366014 | − | 0.633954i | ||||
\(227\) | 20.1080 | 1.33462 | 0.667309 | − | 0.744781i | \(-0.267446\pi\) | ||||
0.667309 | + | 0.744781i | \(0.267446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0065 | −1.32206 | −0.661032 | − | 0.750357i | \(-0.729881\pi\) | ||||
−0.661032 | + | 0.750357i | \(0.729881\pi\) | |||||||
\(230\) | 11.6516 | + | 20.1812i | 0.768287 | + | 1.33071i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.33465 | − | 7.50783i | 0.284584 | − | 0.492913i | ||||
\(233\) | −0.151398 | + | 0.262229i | −0.00991839 | + | 0.0171792i | −0.870942 | − | 0.491386i | \(-0.836491\pi\) |
0.861024 | + | 0.508565i | \(0.169824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.31870 | + | 2.28406i | 0.0860226 | + | 0.148995i | ||||
\(236\) | −15.8190 | − | 27.3992i | −1.02973 | − | 1.78354i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0852 | − | 39.4542i | 0.977826 | − | 2.55743i | ||||
\(239\) | 1.77340 | + | 3.07162i | 0.114712 | + | 0.198686i | 0.917664 | − | 0.397356i | \(-0.130072\pi\) |
−0.802953 | + | 0.596043i | \(0.796739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00647 | 0.386911 | 0.193455 | − | 0.981109i | \(-0.438031\pi\) | ||||
0.193455 | + | 0.981109i | \(0.438031\pi\) | |||||||
\(242\) | 4.64726 | + | 8.04929i | 0.298737 | + | 0.517428i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −54.3899 | −3.48196 | ||||||||
\(245\) | −8.17318 | + | 2.67956i | −0.522165 | + | 0.171191i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.11502 | −0.579975 | ||||||||
\(248\) | 19.7019 | − | 34.1247i | 1.25107 | − | 2.16692i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.3710 | − | 21.4272i | −0.782409 | − | 1.35517i | ||||
\(251\) | 21.0113 | 1.32622 | 0.663109 | − | 0.748523i | \(-0.269236\pi\) | ||||
0.663109 | + | 0.748523i | \(0.269236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2789 | −1.33779 | ||||||||
\(254\) | 3.94448 | + | 6.83205i | 0.247499 | + | 0.428681i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0645 | − | 22.6284i | 0.816530 | − | 1.41427i | ||||
\(257\) | −20.5690 | −1.28306 | −0.641530 | − | 0.767098i | \(-0.721700\pi\) | ||||
−0.641530 | + | 0.767098i | \(0.721700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.34396 | − | 8.74589i | 0.207783 | − | 0.543443i | ||||
\(260\) | 16.1450 | 1.00127 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.0168 | − | 17.3496i | −0.618839 | − | 1.07186i | ||||
\(263\) | 14.2030 | 0.875796 | 0.437898 | − | 0.899025i | \(-0.355723\pi\) | ||||
0.437898 | + | 0.899025i | \(0.355723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.82597 | − | 3.16268i | −0.112169 | − | 0.194282i | ||||
\(266\) | 15.5812 | − | 2.48897i | 0.955347 | − | 0.152608i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.80156 | + | 8.31654i | 0.293302 | + | 0.508013i | ||||
\(269\) | −15.5662 | − | 26.9615i | −0.949090 | − | 1.64387i | −0.747348 | − | 0.664433i | \(-0.768673\pi\) |
−0.201742 | − | 0.979439i | \(-0.564660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.821392 | − | 1.42269i | 0.0498960 | − | 0.0864225i | −0.839999 | − | 0.542588i | \(-0.817444\pi\) |
0.889895 | + | 0.456166i | \(0.150778\pi\) | |||||||
\(272\) | 6.36056 | − | 11.0168i | 0.385665 | − | 0.667992i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5976 | + | 28.7478i | 1.00270 | + | 1.73672i | ||||
\(275\) | 9.28745 | 0.560055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0950 | −1.32756 | −0.663779 | − | 0.747929i | \(-0.731049\pi\) | ||||
−0.663779 | + | 0.747929i | \(0.731049\pi\) | |||||||
\(278\) | 6.68823 | − | 11.5844i | 0.401133 | − | 0.694783i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.3710 | + | 1.97616i | −0.739307 | + | 0.118098i | ||||
\(281\) | 7.74070 | − | 13.4073i | 0.461771 | − | 0.799811i | −0.537278 | − | 0.843405i | \(-0.680547\pi\) |
0.999049 | + | 0.0435938i | \(0.0138807\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1174 | − | 22.7200i | 0.779749 | − | 1.35057i | −0.152337 | − | 0.988329i | \(-0.548680\pi\) |
0.932086 | − | 0.362237i | \(-0.117987\pi\) | |||||||
\(284\) | −18.3326 | + | 31.7531i | −1.08784 | + | 1.88420i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.4383 | + | 19.8117i | −0.676361 | + | 1.17149i | ||||
\(287\) | 3.11093 | + | 3.83129i | 0.183632 | + | 0.226154i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1571 | + | 24.5208i | −0.832770 | + | 1.44240i | ||||
\(290\) | 6.55596 | 0.384979 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.4400 | 1.54729 | ||||||||
\(293\) | −8.45425 | − | 14.6432i | −0.493903 | − | 0.855464i | 0.506073 | − | 0.862491i | \(-0.331097\pi\) |
−0.999975 | + | 0.00702646i | \(0.997763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.36230 | − | 9.28778i | 0.312205 | − | 0.540755i | ||||
\(296\) | 6.81895 | − | 11.8108i | 0.396343 | − | 0.686487i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.3991 | + | 18.0118i | 0.602406 | + | 1.04340i | ||||
\(299\) | 14.4930 | + | 25.1026i | 0.838153 | + | 1.45172i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85617 | + | 12.7010i | −0.279905 | + | 0.732071i | ||||
\(302\) | 11.3375 | + | 19.6371i | 0.652399 | + | 1.12999i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.75201 | 0.272546 | ||||||||
\(305\) | −9.21853 | − | 15.9670i | −0.527852 | − | 0.914266i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.6835 | −0.838034 | −0.419017 | − | 0.907978i | \(-0.637625\pi\) | ||||
−0.419017 | + | 0.907978i | \(0.637625\pi\) | |||||||
\(308\) | 9.11412 | − | 23.8373i | 0.519325 | − | 1.35826i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.7983 | 1.69243 | ||||||||
\(311\) | 5.91109 | − | 10.2383i | 0.335187 | − | 0.580561i | −0.648334 | − | 0.761356i | \(-0.724534\pi\) |
0.983521 | + | 0.180795i | \(0.0578671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.177560 | + | 0.307543i | 0.0100363 | + | 0.0173833i | 0.871000 | − | 0.491283i | \(-0.163472\pi\) |
−0.860964 | + | 0.508666i | \(0.830139\pi\) | |||||||
\(314\) | 5.12061 | 0.288973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.13734 | −0.0639805 | ||||||||
\(317\) | −5.22486 | − | 9.04972i | −0.293457 | − | 0.508283i | 0.681168 | − | 0.732127i | \(-0.261472\pi\) |
−0.974625 | + | 0.223845i | \(0.928139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.99321 | + | 5.18440i | −0.167588 | + | 0.290270i | ||||
\(320\) | 14.0431 | 0.785031 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −31.6290 | − | 38.9530i | −1.76261 | − | 2.17077i | ||||
\(323\) | −16.9272 | −0.941857 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.32567 | − | 10.9564i | −0.350885 | − | 0.607751i | ||||
\(326\) | 49.7441 | 2.75507 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.59414 | + | 6.22523i | 0.198453 | + | 0.343731i | ||||
\(329\) | −3.57968 | − | 4.40859i | −0.197354 | − | 0.243054i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.43352 | − | 12.8752i | −0.408583 | − | 0.707686i | 0.586148 | − | 0.810204i | \(-0.300644\pi\) |
−0.994731 | + | 0.102517i | \(0.967310\pi\) | |||||||
\(332\) | 13.9442 | + | 24.1521i | 0.765289 | + | 1.32552i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.06837 | − | 8.77868i | 0.277329 | − | 0.480348i | ||||
\(335\) | −1.62763 | + | 2.81914i | −0.0889269 | + | 0.154026i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.70676 | − | 8.15235i | −0.256394 | − | 0.444087i | 0.708879 | − | 0.705330i | \(-0.249201\pi\) |
−0.965273 | + | 0.261243i | \(0.915868\pi\) | |||||||
\(338\) | 0.330703 | 0.0179878 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 29.9825 | 1.62603 | ||||||||
\(341\) | −13.6048 | + | 23.5642i | −0.736742 | + | 1.27607i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4682 | − | 8.47347i | 0.889197 | − | 0.457524i | ||||
\(344\) | −9.90262 | + | 17.1518i | −0.533914 | + | 0.924766i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.15419 | − | 3.73117i | 0.115810 | − | 0.200589i | ||||
\(347\) | 13.2932 | − | 23.0245i | 0.713618 | − | 1.23602i | −0.249872 | − | 0.968279i | \(-0.580389\pi\) |
0.963490 | − | 0.267744i | \(-0.0862781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.77648 | + | 8.27311i | −0.255679 | + | 0.442850i | −0.965080 | − | 0.261956i | \(-0.915632\pi\) |
0.709401 | + | 0.704806i | \(0.248966\pi\) | |||||||
\(350\) | 13.8049 | + | 17.0016i | 0.737902 | + | 0.908772i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.29124 | + | 7.43264i | −0.228724 | + | 0.396161i | ||||
\(353\) | −17.0729 | −0.908697 | −0.454349 | − | 0.890824i | \(-0.650128\pi\) | ||||
−0.454349 | + | 0.890824i | \(0.650128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4288 | −0.659651 | ||||||||
\(356\) | −13.0359 | − | 22.5789i | −0.690903 | − | 1.19668i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.54614 | − | 16.5344i | 0.504529 | − | 0.873870i | ||||
\(359\) | 12.8333 | − | 22.2280i | 0.677318 | − | 1.17315i | −0.298467 | − | 0.954420i | \(-0.596475\pi\) |
0.975786 | − | 0.218730i | \(-0.0701912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.33839 | + | 10.9784i | 0.333599 | + | 0.577811i | ||||
\(362\) | −30.0571 | − | 52.0604i | −1.57977 | − | 2.73624i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −34.3285 | + | 5.48367i | −1.79930 | + | 0.287423i | ||||
\(365\) | 4.48132 | + | 7.76187i | 0.234563 | + | 0.406275i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3752 | −0.541579 | −0.270790 | − | 0.962639i | \(-0.587285\pi\) | ||||
−0.270790 | + | 0.962639i | \(0.587285\pi\) | |||||||
\(368\) | −7.55577 | − | 13.0870i | −0.393872 | − | 0.682205i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.3134 | 0.536166 | ||||||||
\(371\) | 4.95669 | + | 6.10447i | 0.257339 | + | 0.316928i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8152 | −1.02599 | −0.512996 | − | 0.858391i | \(-0.671465\pi\) | ||||
−0.512996 | + | 0.858391i | \(0.671465\pi\) | |||||||
\(374\) | −21.2417 | + | 36.7918i | −1.09838 | + | 1.90246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.13570 | − | 7.16324i | −0.213282 | − | 0.369416i | ||||
\(377\) | 8.15470 | 0.419988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1716 | 0.727948 | 0.363974 | − | 0.931409i | \(-0.381420\pi\) | ||||
0.363974 | + | 0.931409i | \(0.381420\pi\) | |||||||
\(380\) | 5.60002 | + | 9.69952i | 0.287275 | + | 0.497575i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.48016 | + | 14.6881i | −0.433883 | + | 0.751507i | ||||
\(383\) | 13.4487 | 0.687197 | 0.343598 | − | 0.939117i | \(-0.388354\pi\) | ||||
0.343598 | + | 0.939117i | \(0.388354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.54255 | − | 1.36460i | 0.435369 | − | 0.0695464i | ||||
\(386\) | 26.9316 | 1.37078 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.8947 | + | 41.3869i | 1.21307 | + | 2.10110i | ||||
\(389\) | −20.9297 | −1.06118 | −0.530590 | − | 0.847629i | \(-0.678029\pi\) | ||||
−0.530590 | + | 0.847629i | \(0.678029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.9146 | + | 46.6174i | 1.36113 | + | 2.35754i | ||||
\(392\) | 25.6327 | − | 8.40363i | 1.29465 | − | 0.424447i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.8350 | + | 41.2835i | 1.20079 | + | 2.07983i | ||||
\(395\) | −0.192768 | − | 0.333884i | −0.00969921 | − | 0.0167995i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5708 | − | 21.7732i | 0.630909 | − | 1.09277i | −0.356458 | − | 0.934312i | \(-0.616016\pi\) |
0.987366 | − | 0.158454i | \(-0.0506511\pi\) | |||||||
\(398\) | −12.2438 | + | 21.2069i | −0.613726 | + | 1.06300i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.29782 | + | 5.71198i | 0.164891 | + | 0.285599i | ||||
\(401\) | −21.1603 | −1.05669 | −0.528347 | − | 0.849029i | \(-0.677188\pi\) | ||||
−0.528347 | + | 0.849029i | \(0.677188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0649 | 1.84633 | ||||||||
\(404\) | −5.04400 | + | 8.73646i | −0.250948 | + | 0.434655i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.9396 | + | 2.22674i | −0.691813 | + | 0.110511i | ||||
\(407\) | −4.70870 | + | 8.15571i | −0.233402 | + | 0.404264i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.271903 | + | 0.470950i | −0.0134447 | + | 0.0232870i | −0.872670 | − | 0.488311i | \(-0.837613\pi\) |
0.859225 | + | 0.511598i | \(0.170946\pi\) | |||||||
\(410\) | −2.71798 | + | 4.70769i | −0.134232 | + | 0.232496i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.8862 | + | 18.8555i | −0.536326 | + | 0.928944i | ||||
\(413\) | −8.24702 | + | 21.5695i | −0.405810 | + | 1.06137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.72681 | + | 8.18707i | −0.232030 | + | 0.401888i | ||||
\(416\) | 11.6910 | 0.573200 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.8698 | −0.776219 | ||||||||
\(419\) | −11.9044 | − | 20.6190i | −0.581566 | − | 1.00730i | −0.995294 | − | 0.0969018i | \(-0.969107\pi\) |
0.413728 | − | 0.910401i | \(-0.364227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.45490 | − | 2.51997i | 0.0709077 | − | 0.122816i | −0.828392 | − | 0.560149i | \(-0.810744\pi\) |
0.899299 | + | 0.437334i | \(0.144077\pi\) | |||||||
\(422\) | −0.710005 | + | 1.22976i | −0.0345625 | + | 0.0598640i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.72660 | + | 9.91876i | 0.278108 | + | 0.481698i | ||||
\(425\) | −11.7472 | − | 20.3468i | −0.569824 | − | 0.986965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0242 | + | 30.8188i | 1.21100 | + | 1.49143i | ||||
\(428\) | −21.2712 | − | 36.8428i | −1.02818 | − | 1.78086i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.9773 | −0.722268 | ||||||||
\(431\) | −15.6897 | − | 27.1754i | −0.755747 | − | 1.30899i | −0.945002 | − | 0.327065i | \(-0.893941\pi\) |
0.189255 | − | 0.981928i | \(-0.439393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.9281 | −1.29408 | −0.647042 | − | 0.762455i | \(-0.723994\pi\) | ||||
−0.647042 | + | 0.762455i | \(0.723994\pi\) | |||||||
\(434\) | −63.3588 | + | 10.1210i | −3.04132 | + | 0.485824i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.9434 | −1.38614 | ||||||||
\(437\) | −10.0540 | + | 17.4141i | −0.480949 | + | 0.833028i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6647 | + | 21.9359i | 0.604453 | + | 1.04694i | 0.992138 | + | 0.125151i | \(0.0399416\pi\) |
−0.387685 | + | 0.921792i | \(0.626725\pi\) | |||||||
\(440\) | 12.6001 | 0.600687 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 57.8709 | 2.75264 | ||||||||
\(443\) | −6.51570 | − | 11.2855i | −0.309570 | − | 0.536191i | 0.668698 | − | 0.743534i | \(-0.266852\pi\) |
−0.978268 | + | 0.207343i | \(0.933518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.41891 | − | 7.65378i | 0.209477 | − | 0.362824i | ||||
\(446\) | 7.16256 | 0.339157 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.8592 | + | 4.76974i | −1.41071 | + | 0.225349i | ||||
\(449\) | 19.4353 | 0.917206 | 0.458603 | − | 0.888641i | \(-0.348350\pi\) | ||||
0.458603 | + | 0.888641i | \(0.348350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.48187 | − | 4.29872i | −0.116866 | − | 0.202419i | ||||
\(452\) | −16.8196 | −0.791126 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.8449 | − | 41.3005i | −1.11909 | − | 1.93833i | ||||
\(455\) | −7.42814 | − | 9.14820i | −0.348236 | − | 0.428874i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3487 | + | 24.8528i | 0.671206 | + | 1.16256i | 0.977562 | + | 0.210646i | \(0.0675567\pi\) |
−0.306356 | + | 0.951917i | \(0.599110\pi\) | |||||||
\(458\) | 23.7244 | + | 41.0919i | 1.10857 | + | 1.92010i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.8082 | − | 30.8448i | 0.830313 | − | 1.43814i | ||||
\(461\) | −11.5240 | + | 19.9601i | −0.536725 | + | 0.929635i | 0.462353 | + | 0.886696i | \(0.347005\pi\) |
−0.999078 | + | 0.0429386i | \(0.986328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6074 | − | 25.3007i | −0.678863 | − | 1.17583i | −0.975324 | − | 0.220780i | \(-0.929140\pi\) |
0.296460 | − | 0.955045i | \(-0.404194\pi\) | |||||||
\(464\) | −4.25135 | −0.197364 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.718132 | 0.0332668 | ||||||||
\(467\) | 2.18254 | − | 3.78027i | 0.100996 | − | 0.174930i | −0.811099 | − | 0.584908i | \(-0.801130\pi\) |
0.912095 | + | 0.409978i | \(0.134464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.50323 | − | 6.54703i | 0.115589 | − | 0.302314i | ||||
\(470\) | 3.12753 | − | 5.41704i | 0.144262 | − | 0.249869i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.8172 | + | 29.1283i | −0.774075 | + | 1.34074i | ||||
\(473\) | 6.83808 | − | 11.8439i | 0.314415 | − | 0.544583i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.38821 | − | 7.60061i | 0.201345 | − | 0.348740i | ||||
\(476\) | −63.7504 | + | 10.1836i | −2.92200 | + | 0.466763i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.20592 | − | 7.28487i | 0.192374 | − | 0.333202i | ||||
\(479\) | 15.9229 | 0.727535 | 0.363767 | − | 0.931490i | \(-0.381490\pi\) | ||||
0.363767 | + | 0.931490i | \(0.381490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8284 | 0.584923 | ||||||||
\(482\) | −7.12269 | − | 12.3369i | −0.324430 | − | 0.561929i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.10281 | − | 12.3024i | 0.322855 | − | 0.559201i | ||||
\(485\) | −8.09983 | + | 14.0293i | −0.367794 | + | 0.637038i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.1329 | + | 33.1391i | 0.866993 | + | 1.50168i | 0.865055 | + | 0.501677i | \(0.167283\pi\) |
0.00193753 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(488\) | 28.9111 | + | 50.0755i | 1.30874 | + | 2.26681i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.1957 | + | 13.6096i | 0.686472 | + | 0.614820i | ||||
\(491\) | 6.69540 | + | 11.5968i | 0.302159 | + | 0.523355i | 0.976625 | − | 0.214951i | \(-0.0689593\pi\) |
−0.674466 | + | 0.738306i | \(0.735626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1439 | 0.682045 | ||||||||
\(494\) | 10.8089 | + | 18.7216i | 0.486317 | + | 0.842325i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.3233 | −0.867643 | ||||||||
\(497\) | 26.4268 | − | 4.22145i | 1.18540 | − | 0.189358i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.40706 | 0.242053 | 0.121027 | − | 0.992649i | \(-0.461381\pi\) | ||||
0.121027 | + | 0.992649i | \(0.461381\pi\) | |||||||
\(500\) | −18.9076 | + | 32.7490i | −0.845576 | + | 1.46458i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.9159 | − | 43.1556i | −1.11205 | − | 1.92613i | ||||
\(503\) | −9.49157 | −0.423208 | −0.211604 | − | 0.977355i | \(-0.567869\pi\) | ||||
−0.211604 | + | 0.977355i | \(0.567869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.41962 | −0.152171 | ||||||||
\(506\) | 25.2333 | + | 43.7053i | 1.12176 | + | 1.94294i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.02870 | − | 10.4420i | 0.267480 | − | 0.463289i | ||||
\(509\) | 37.2297 | 1.65018 | 0.825088 | − | 0.565005i | \(-0.191126\pi\) | ||||
0.825088 | + | 0.565005i | \(0.191126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1648 | − | 14.9816i | −0.538137 | − | 0.662749i | ||||
\(512\) | −20.6597 | −0.913039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.3915 | + | 42.2473i | 1.07586 | + | 1.86345i | ||||
\(515\) | −7.38042 | −0.325220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.85583 | + | 4.94645i | 0.125599 | + | 0.217544i | ||||
\(518\) | −21.9288 | + | 3.50294i | −0.963497 | + | 0.153910i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.58193 | − | 14.8643i | −0.376342 | − | 0.651844i | ||||
\(521\) | −7.60082 | − | 13.1650i | −0.332998 | − | 0.576769i | 0.650100 | − | 0.759848i | \(-0.274727\pi\) |
−0.983098 | + | 0.183079i | \(0.941394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.39824 | + | 4.15387i | −0.104867 | + | 0.181636i | −0.913684 | − | 0.406425i | \(-0.866775\pi\) |
0.808817 | + | 0.588061i | \(0.200109\pi\) | |||||||
\(524\) | −15.3095 | + | 26.5169i | −0.668800 | + | 1.15840i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.8425 | − | 29.1720i | −0.734366 | − | 1.27196i | ||||
\(527\) | 68.8321 | 2.99837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.9442 | 1.78018 | ||||||||
\(530\) | −4.33061 | + | 7.50084i | −0.188110 | + | 0.325816i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.2015 | − | 18.7216i | −0.659070 | − | 0.811685i | ||||
\(533\) | −3.38079 | + | 5.85570i | −0.146438 | + | 0.253639i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.21050 | − | 12.4890i | 0.311737 | − | 0.539945i | ||||
\(536\) | 5.10456 | − | 8.84135i | 0.220483 | − | 0.381888i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.9180 | + | 63.9439i | −1.59165 | + | 2.75682i | ||||
\(539\) | −17.7002 | + | 5.80297i | −0.762400 | + | 0.249952i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.22660 | − | 5.58864i | 0.138722 | − | 0.240274i | −0.788291 | − | 0.615303i | \(-0.789034\pi\) |
0.927013 | + | 0.375029i | \(0.122367\pi\) | |||||||
\(542\) | −3.89615 | −0.167354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.7111 | 0.930854 | ||||||||
\(545\) | −4.90561 | − | 8.49676i | −0.210133 | − | 0.363961i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1281 | + | 22.7385i | −0.561316 | + | 0.972227i | 0.436066 | + | 0.899915i | \(0.356371\pi\) |
−0.997382 | + | 0.0723129i | \(0.976962\pi\) | |||||||
\(548\) | 25.3675 | − | 43.9378i | 1.08365 | − | 1.87693i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.0134 | − | 19.0758i | −0.469613 | − | 0.813394i | ||||
\(551\) | 2.82852 | + | 4.89913i | 0.120499 | + | 0.208710i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.523278 | + | 0.644449i | 0.0222521 | + | 0.0274048i | ||||
\(554\) | 26.2010 | + | 45.3815i | 1.11318 | + | 1.92808i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4444 | −0.867036 | ||||||||
\(557\) | −0.00716610 | − | 0.0124121i | −0.000303638 | − | 0.000525916i | 0.865874 | − | 0.500263i | \(-0.166763\pi\) |
−0.866177 | + | 0.499737i | \(0.833430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.6296 | −0.787949 | ||||||||
\(560\) | 3.87257 | + | 4.76931i | 0.163646 | + | 0.201540i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −36.7168 | −1.54881 | ||||||||
\(563\) | −8.59130 | + | 14.8806i | −0.362080 | + | 0.627141i | −0.988303 | − | 0.152503i | \(-0.951267\pi\) |
0.626223 | + | 0.779644i | \(0.284600\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.85075 | − | 4.93764i | −0.119932 | − | 0.207728i | ||||
\(566\) | −62.2205 | −2.61532 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.9791 | 1.63553 | ||||||||
\(569\) | −14.7390 | − | 25.5286i | −0.617889 | − | 1.07022i | −0.989870 | − | 0.141975i | \(-0.954655\pi\) |
0.371981 | − | 0.928240i | \(-0.378679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4161 | − | 28.4335i | 0.686991 | − | 1.18990i | −0.285815 | − | 0.958285i | \(-0.592264\pi\) |
0.972807 | − | 0.231619i | \(-0.0744023\pi\) | |||||||
\(572\) | 34.9643 | 1.46193 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.18016 | − | 10.9329i | 0.174477 | − | 0.456331i | ||||
\(575\) | −27.9093 | −1.16390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9787 | − | 27.6759i | −0.665201 | − | 1.15216i | −0.979231 | − | 0.202748i | \(-0.935013\pi\) |
0.314030 | − | 0.949413i | \(-0.398321\pi\) | |||||||
\(578\) | 67.1520 | 2.79315 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.01002 | − | 8.67761i | −0.208030 | − | 0.360318i | ||||
\(581\) | 7.26966 | − | 19.0133i | 0.301596 | − | 0.788804i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.95440 | − | 6.84922i | −0.163775 | − | 0.283666i | ||||
\(584\) | −14.0543 | − | 24.3427i | −0.581570 | − | 1.00731i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.0507 | + | 34.7289i | −0.828288 | + | 1.43464i | ||||
\(587\) | −2.37316 | + | 4.11044i | −0.0979509 | + | 0.169656i | −0.910836 | − | 0.412768i | \(-0.864562\pi\) |
0.812885 | + | 0.582424i | \(0.197895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8562 | + | 22.2676i | 0.529732 | + | 0.917522i | ||||
\(590\) | −25.4353 | −1.04715 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.68792 | −0.274872 | ||||||||
\(593\) | −0.970397 | + | 1.68078i | −0.0398494 | + | 0.0690212i | −0.885262 | − | 0.465092i | \(-0.846021\pi\) |
0.845413 | + | 0.534113i | \(0.179354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.7946 | − | 16.9889i | −0.565523 | − | 0.696476i | ||||
\(596\) | 15.8939 | − | 27.5290i | 0.651040 | − | 1.12763i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.3727 | − | 59.5353i | 1.40560 | − | 2.43458i | ||||
\(599\) | −4.40067 | + | 7.62219i | −0.179807 | + | 0.311434i | −0.941814 | − | 0.336134i | \(-0.890881\pi\) |
0.762008 | + | 0.647568i | \(0.224214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.48016 | − | 12.9560i | 0.305122 | − | 0.528487i | −0.672166 | − | 0.740400i | \(-0.734636\pi\) |
0.977289 | + | 0.211913i | \(0.0679694\pi\) | |||||||
\(602\) | 31.8455 | − | 5.08704i | 1.29793 | − | 0.207332i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.3281 | − | 30.0131i | 0.705069 | − | 1.22122i | ||||
\(605\) | 4.81542 | 0.195775 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.79138 | 0.113299 | 0.0566494 | − | 0.998394i | \(-0.481958\pi\) | ||||
0.0566494 | + | 0.998394i | \(0.481958\pi\) | |||||||
\(608\) | 4.05512 | + | 7.02367i | 0.164457 | + | 0.284847i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.8633 | + | 37.8684i | −0.885221 | + | 1.53325i | ||||
\(611\) | 3.89021 | − | 6.73804i | 0.157381 | − | 0.272592i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.3218 | − | 23.0740i | −0.538062 | − | 0.931950i | −0.999008 | − | 0.0445225i | \(-0.985823\pi\) |
0.460947 | − | 0.887428i | \(-0.347510\pi\) | |||||||
\(614\) | 17.4123 | + | 30.1590i | 0.702703 | + | 1.21712i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.7911 | + | 4.27964i | −1.07944 | + | 0.172432i | ||||
\(617\) | −19.0560 | − | 33.0060i | −0.767166 | − | 1.32877i | −0.939094 | − | 0.343661i | \(-0.888333\pi\) |
0.171927 | − | 0.985110i | \(-0.445001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9315 | −0.961890 | −0.480945 | − | 0.876751i | \(-0.659706\pi\) | ||||
−0.480945 | + | 0.876751i | \(0.659706\pi\) | |||||||
\(620\) | −22.7716 | − | 39.4417i | −0.914531 | − | 1.58401i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.0384 | −1.12424 | ||||||||
\(623\) | −6.79613 | + | 17.7748i | −0.272281 | + | 0.712132i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.63231 | 0.185293 | ||||||||
\(626\) | 0.421114 | − | 0.729391i | 0.0168311 | − | 0.0291523i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.91314 | − | 6.77775i | −0.156151 | − | 0.270462i | ||||
\(629\) | 23.8232 | 0.949893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.6748 | −0.663812 | −0.331906 | − | 0.943313i | \(-0.607692\pi\) | ||||
−0.331906 | + | 0.943313i | \(0.607692\pi\) | |||||||
\(632\) | 0.604558 | + | 1.04712i | 0.0240480 | + | 0.0416524i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3917 | + | 21.4630i | −0.492135 | + | 0.852404i | ||||
\(635\) | 4.08721 | 0.162196 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9013 | + | 16.9285i | 0.748898 | + | 0.670730i | ||||
\(638\) | 14.1978 | 0.562098 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.6898 | − | 21.9793i | −0.501607 | − | 0.868809i | ||||
\(641\) | −32.0213 | −1.26477 | −0.632383 | − | 0.774656i | \(-0.717923\pi\) | ||||
−0.632383 | + | 0.774656i | \(0.717923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.75969 | + | 3.04788i | 0.0693956 | + | 0.120197i | 0.898635 | − | 0.438696i | \(-0.144560\pi\) |
−0.829240 | + | 0.558893i | \(0.811226\pi\) | |||||||
\(644\) | −27.3884 | + | 71.6325i | −1.07925 | + | 2.82271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0730 | + | 34.7674i | 0.789760 | + | 1.36790i | ||||
\(647\) | 20.7773 | + | 35.9873i | 0.816839 | + | 1.41481i | 0.908000 | + | 0.418971i | \(0.137609\pi\) |
−0.0911605 | + | 0.995836i | \(0.529058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.6128 | − | 20.1140i | 0.455843 | − | 0.789543i | ||||
\(650\) | −15.0024 | + | 25.9850i | −0.588444 | + | 1.01921i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.0142 | − | 65.8424i | −1.48875 | − | 2.57859i | ||||
\(653\) | −10.2858 | −0.402513 | −0.201257 | − | 0.979539i | \(-0.564503\pi\) | ||||
−0.201257 | + | 0.979539i | \(0.564503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3792 | −0.405550 | ||||||||
\(656\) | 1.76254 | − | 3.05280i | 0.0688155 | − | 0.119192i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.81002 | + | 12.5803i | −0.187514 | + | 0.490430i | ||||
\(659\) | 10.1776 | − | 17.6281i | 0.396461 | − | 0.686691i | −0.596825 | − | 0.802371i | \(-0.703571\pi\) |
0.993287 | + | 0.115680i | \(0.0369047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.32637 | − | 14.4217i | 0.323858 | − | 0.560939i | −0.657422 | − | 0.753522i | \(-0.728353\pi\) |
0.981281 | + | 0.192584i | \(0.0616866\pi\) | |||||||
\(662\) | −17.6299 | + | 30.5358i | −0.685204 | + | 1.18681i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.8242 | − | 25.6762i | 0.575290 | − | 0.996431i | ||||
\(665\) | 2.91950 | − | 7.63576i | 0.113214 | − | 0.296102i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.99477 | − | 15.5794i | 0.348279 | − | 0.603236i | ||||
\(668\) | −15.4929 | −0.599437 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.72041 | 0.298265 | ||||||||
\(671\) | −19.9640 | − | 34.5787i | −0.770703 | − | 1.33490i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.10939 | + | 8.84973i | −0.196953 | + | 0.341132i | −0.947539 | − | 0.319641i | \(-0.896438\pi\) |
0.750586 | + | 0.660772i | \(0.229771\pi\) | |||||||
\(674\) | −11.1629 | + | 19.3347i | −0.429979 | + | 0.744746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.252721 | − | 0.437725i | −0.00972003 | − | 0.0168356i | ||||
\(677\) | 3.19342 | + | 5.53117i | 0.122733 | + | 0.212580i | 0.920845 | − | 0.389930i | \(-0.127501\pi\) |
−0.798111 | + | 0.602510i | \(0.794167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.4572 | − | 32.5810i | 0.478065 | − | 1.25035i | ||||
\(680\) | −15.9373 | − | 27.6041i | −0.611166 | − | 1.05857i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 64.5323 | 2.47107 | ||||||||
\(683\) | −15.4061 | − | 26.6842i | −0.589499 | − | 1.02104i | −0.994298 | − | 0.106636i | \(-0.965992\pi\) |
0.404800 | − | 0.914405i | \(-0.367341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1981 | 0.657107 | ||||||||
\(686\) | −36.9325 | − | 23.7763i | −1.41009 | − | 0.907783i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.71234 | 0.370279 | ||||||||
\(689\) | −5.38668 | + | 9.32999i | −0.205216 | + | 0.355444i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.43402 | + | 4.21585i | 0.0925945 | + | 0.160378i | 0.908602 | − | 0.417663i | \(-0.137151\pi\) |
−0.816008 | + | 0.578041i | \(0.803817\pi\) | |||||||
\(692\) | −6.58487 | −0.250319 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −63.0544 | −2.39351 | ||||||||
\(695\) | −3.46512 | − | 6.00176i | −0.131439 | − | 0.227660i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.27837 | + | 10.8745i | −0.237810 | + | 0.411900i | ||||
\(698\) | 22.6565 | 0.857562 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.9540 | − | 31.2650i | 0.451820 | − | 1.18170i | ||||
\(701\) | −44.4038 | −1.67711 | −0.838554 | − | 0.544819i | \(-0.816598\pi\) | ||||
−0.838554 | + | 0.544819i | \(0.816598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.44961 | + | 7.70696i | 0.167820 | + | 0.290673i | ||||
\(704\) | 30.4122 | 1.14620 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.2456 | + | 35.0665i | 0.761955 | + | 1.31974i | ||||
\(707\) | 7.27100 | − | 1.16148i | 0.273454 | − | 0.0436819i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.2884 | + | 23.0162i | 0.499056 | + | 0.864391i | 0.999999 | − | 0.00108957i | \(-0.000346820\pi\) |
−0.500943 | + | 0.865480i | \(0.667013\pi\) | |||||||
\(710\) | 14.7385 | + | 25.5279i | 0.553126 | + | 0.958043i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8586 | + | 24.0037i | −0.519372 | + | 0.899578i | ||||
\(713\) | 40.8832 | − | 70.8117i | 1.53109 | − | 2.65192i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.92609 | + | 10.2643i | 0.221623 | + | 0.383863i | ||||
\(716\) | −29.1804 | −1.09052 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −60.8730 | −2.27176 | ||||||||
\(719\) | −16.9462 | + | 29.3517i | −0.631987 | + | 1.09463i | 0.355157 | + | 0.934807i | \(0.384427\pi\) |
−0.987145 | + | 0.159828i | \(0.948906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6927 | − | 2.50677i | 0.584425 | − | 0.0933569i | ||||
\(722\) | 15.0326 | − | 26.0372i | 0.559455 | − | 0.969005i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −45.9389 | + | 79.5685i | −1.70731 | + | 2.95714i | ||||
\(725\) | −3.92589 | + | 6.79984i | −0.145804 | + | 0.252540i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9709 | − | 20.7341i | 0.443974 | − | 0.768986i | −0.554006 | − | 0.832513i | \(-0.686901\pi\) |
0.997980 | + | 0.0635267i | \(0.0202348\pi\) | |||||||
\(728\) | 23.2961 | + | 28.6905i | 0.863410 | + | 1.06334i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.6282 | − | 18.4086i | 0.393368 | − | 0.681334i | ||||
\(731\) | −34.5965 | −1.27960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5703 | −1.38769 | −0.693846 | − | 0.720124i | \(-0.744085\pi\) | ||||
−0.693846 | + | 0.720124i | \(0.744085\pi\) | |||||||
\(734\) | 12.3033 | + | 21.3099i | 0.454121 | + | 0.786561i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.8954 | − | 22.3355i | 0.475331 | − | 0.823297i | ||||
\(737\) | −3.52486 | + | 6.10523i | −0.129840 | + | 0.224889i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.82055 | + | 4.88534i | 0.103756 | + | 0.179710i | 0.913229 | − | 0.407446i | \(-0.133581\pi\) |
−0.809473 | + | 0.587156i | \(0.800247\pi\) | |||||||
\(740\) | −7.88140 | − | 13.6510i | −0.289726 | − | 0.501820i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.66032 | − | 17.4196i | 0.244508 | − | 0.639494i | ||||
\(743\) | 7.58516 | + | 13.1379i | 0.278273 | + | 0.481982i | 0.970956 | − | 0.239260i | \(-0.0769048\pi\) |
−0.692683 | + | 0.721242i | \(0.743571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7754 | 0.394781 | ||||||||
\(746\) | 23.4976 | + | 40.6990i | 0.860308 | + | 1.49010i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 64.9312 | 2.37412 | ||||||||
\(749\) | −11.0895 | + | 29.0038i | −0.405201 | + | 1.05978i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8935 | 0.944869 | 0.472434 | − | 0.881366i | \(-0.343375\pi\) | ||||
0.472434 | + | 0.881366i | \(0.343375\pi\) | |||||||
\(752\) | −2.02811 | + | 3.51280i | −0.0739577 | + | 0.128099i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.67014 | − | 16.7492i | −0.352166 | − | 0.609969i | ||||
\(755\) | 11.7477 | 0.427543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9054 | 1.34135 | 0.670675 | − | 0.741752i | \(-0.266005\pi\) | ||||
0.670675 | + | 0.741752i | \(0.266005\pi\) | |||||||
\(758\) | −16.8052 | − | 29.1075i | −0.610394 | − | 1.05723i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.95341 | − | 10.3116i | 0.215953 | − | 0.374041i | ||||
\(761\) | −28.4009 | −1.02953 | −0.514765 | − | 0.857331i | \(-0.672121\pi\) | ||||
−0.514765 | + | 0.857331i | \(0.672121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3165 | + | 16.4001i | 0.482090 | + | 0.593724i | ||||
\(764\) | 25.9219 | 0.937823 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.9480 | − | 27.6227i | −0.576223 | − | 0.998048i | ||||
\(767\) | −31.6379 | −1.14238 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.63076 | + | 4.55661i | 0.0948677 | + | 0.164316i | 0.909553 | − | 0.415587i | \(-0.136424\pi\) |
−0.814686 | + | 0.579903i | \(0.803091\pi\) | |||||||
\(770\) | −12.9329 | − | 15.9276i | −0.466068 | − | 0.573991i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.5810 | − | 35.6473i | −0.740726 | − | 1.28297i | ||||
\(773\) | −20.6873 | − | 35.8315i | −0.744071 | − | 1.28877i | −0.950627 | − | 0.310335i | \(-0.899559\pi\) |
0.206556 | − | 0.978435i | \(-0.433774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8440 | + | 30.9067i | −0.640976 | + | 1.11020i | ||||
\(776\) | 25.4026 | − | 43.9986i | 0.911901 | − | 1.57946i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.8192 | + | 42.9882i | 0.889813 | + | 1.54120i | ||||
\(779\) | −4.69061 | −0.168059 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.9163 | −0.963140 | ||||||||
\(782\) | 63.8326 | − | 110.561i | 2.28265 | − | 3.95366i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.85398 | − | 8.82545i | −0.351928 | − | 0.315195i | ||||
\(785\) | 1.32647 | − | 2.29752i | 0.0473438 | − | 0.0820019i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.68064 | + | 4.64301i | −0.0955547 | + | 0.165506i | −0.909840 | − | 0.414959i | \(-0.863796\pi\) |
0.814285 | + | 0.580465i | \(0.197129\pi\) | |||||||
\(788\) | 36.4292 | − | 63.0972i | 1.29774 | − | 2.24774i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.457183 | + | 0.791864i | −0.0162658 | + | 0.0281733i | ||||
\(791\) | 7.73849 | + | 9.53043i | 0.275149 | + | 0.338863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.1949 | + | 47.1030i | −0.965721 | + | 1.67268i | ||||
\(794\) | −59.6275 | −2.11610 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.4265 | 1.32655 | ||||||||
\(797\) | 15.2102 | + | 26.3448i | 0.538773 | + | 0.933182i | 0.998970 | + | 0.0453658i | \(0.0144453\pi\) |
−0.460197 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.22439 | − | 12.5130i | 0.255581 | − | 0.442679i | ||||
\(800\) | −5.62837 | + | 9.74862i | −0.198993 | + | 0.344666i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.0926 | + | 43.4617i | 0.886052 | + | 1.53469i | ||||
\(803\) | 9.70492 | + | 16.8094i | 0.342479 | + | 0.593191i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.6708 | + | 4.10069i | −0.904778 | + | 0.144530i | ||||
\(806\) | −43.9529 | − | 76.1287i | −1.54817 | − | 2.68152i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.7246 | 0.377290 | ||||||||
\(809\) | 21.7729 | + | 37.7117i | 0.765494 | + | 1.32587i | 0.939985 | + | 0.341216i | \(0.110839\pi\) |
−0.174491 | + | 0.984659i | \(0.555828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.4078 | 0.611272 | 0.305636 | − | 0.952148i | \(-0.401131\pi\) | ||||
0.305636 | + | 0.952148i | \(0.401131\pi\) | |||||||
\(812\) | 13.6000 | + | 16.7492i | 0.477265 | + | 0.587781i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.3350 | 0.782842 | ||||||||
\(815\) | 12.8860 | − | 22.3192i | 0.451378 | − | 0.781809i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.46182 | − | 11.1922i | −0.226071 | − | 0.391566i | ||||
\(818\) | 1.28973 | 0.0450944 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.30826 | 0.290137 | ||||||||
\(821\) | 11.5318 | + | 19.9736i | 0.402462 | + | 0.697085i | 0.994022 | − | 0.109176i | \(-0.0348211\pi\) |
−0.591560 | + | 0.806261i | \(0.701488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.03902 | + | 8.72784i | −0.175649 | + | 0.304233i | −0.940386 | − | 0.340110i | \(-0.889536\pi\) |
0.764737 | + | 0.644343i | \(0.222869\pi\) | |||||||
\(824\) | 23.1464 | 0.806344 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 54.0819 | − | 8.63911i | 1.88175 | − | 0.300593i | ||||
\(827\) | 28.4954 | 0.990882 | 0.495441 | − | 0.868642i | \(-0.335007\pi\) | ||||
0.495441 | + | 0.868642i | \(0.335007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.907602 | + | 1.57201i | 0.0315223 | + | 0.0545983i | 0.881356 | − | 0.472452i | \(-0.156631\pi\) |
−0.849834 | + | 0.527051i | \(0.823298\pi\) | |||||||
\(830\) | 22.4209 | 0.778241 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.7137 | − | 35.8772i | −0.718120 | − | 1.24382i | ||||
\(833\) | 35.1011 | + | 31.4374i | 1.21618 | + | 1.08924i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.62588 | − | 4.54816i | −0.0908725 | − | 0.157396i | ||||
\(836\) | 12.1276 | + | 21.0057i | 0.419443 | + | 0.726496i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.2333 | + | 48.9015i | −0.975302 | + | 1.68927i | ||||
\(839\) | 3.43860 | − | 5.95583i | 0.118714 | − | 0.205618i | −0.800544 | − | 0.599273i | \(-0.795456\pi\) |
0.919258 | + | 0.393655i | \(0.128790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.9695 | + | 20.7318i | 0.412741 | + | 0.714888i | ||||
\(842\) | −6.90112 | −0.237828 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.17032 | 0.0747057 | ||||||||
\(845\) | 0.0856672 | − | 0.148380i | 0.00294704 | − | 0.00510442i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2388 | + | 1.63556i | −0.351810 | + | 0.0561985i | ||||
\(848\) | 2.80828 | − | 4.86408i | 0.0964367 | − | 0.167033i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.8606 | + | 48.2560i | −0.955611 | + | 1.65517i | ||||
\(851\) | 14.1499 | − | 24.5083i | 0.485052 | − | 0.840135i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.34635 | − | 2.33195i | 0.0460982 | − | 0.0798445i | −0.842056 | − | 0.539391i | \(-0.818655\pi\) |
0.888154 | + | 0.459546i | \(0.151988\pi\) | |||||||
\(854\) | 33.6250 | − | 87.9439i | 1.15063 | − | 3.00938i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.6135 | + | 39.1678i | −0.772914 | + | 1.33873i | ||||
\(857\) | 23.6722 | 0.808625 | 0.404313 | − | 0.914621i | \(-0.367511\pi\) | ||||
0.404313 | + | 0.914621i | \(0.367511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0275 | −0.444492 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(860\) | 11.4455 | + | 19.8242i | 0.390289 | + | 0.676001i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.2109 | + | 64.4512i | −1.26741 | + | 2.19522i | ||||
\(863\) | 9.87796 | − | 17.1091i | 0.336250 | − | 0.582401i | −0.647475 | − | 0.762087i | \(-0.724175\pi\) |
0.983724 | + | 0.179686i | \(0.0575081\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.11607 | − | 1.93309i | −0.0379475 | − | 0.0657270i | ||||
\(866\) | 31.9324 | + | 55.3085i | 1.08511 | + | 1.87946i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 61.8148 | + | 76.1287i | 2.09813 | + | 2.58397i | ||||
\(869\) | −0.417466 | − | 0.723073i | −0.0141616 | − | 0.0245286i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.60311 | 0.325389 | ||||||||
\(872\) | 15.3849 | + | 26.6475i | 0.520999 | + | 0.902398i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 47.6897 | 1.61313 | ||||||||
\(875\) | 27.2557 | − | 4.35385i | 0.921409 | − | 0.147187i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6814 | 0.428222 | 0.214111 | − | 0.976809i | \(-0.431315\pi\) | ||||
0.214111 | + | 0.976809i | \(0.431315\pi\) | |||||||
\(878\) | 30.0365 | − | 52.0248i | 1.01368 | − | 1.75575i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.08950 | − | 5.35117i | −0.104147 | − | 0.180388i | ||||
\(881\) | 43.7202 | 1.47297 | 0.736485 | − | 0.676454i | \(-0.236484\pi\) | ||||
0.736485 | + | 0.676454i | \(0.236484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.03795 | −0.0349298 | −0.0174649 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174649 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(884\) | −44.2246 | − | 76.5992i | −1.48743 | − | 2.57631i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.4531 | + | 26.7656i | −0.519157 | + | 0.899207i | ||||
\(887\) | 6.38256 | 0.214305 | 0.107153 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107153 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.69046 | + | 1.38823i | −0.291469 | + | 0.0465596i | ||||
\(890\) | −20.9604 | −0.702596 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.47358 | − | 9.48052i | −0.183269 | − | 0.317431i | ||||
\(893\) | 5.39739 | 0.180617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.94578 | − | 8.56634i | −0.165319 | − | 0.286341i | ||||
\(896\) | 34.4470 | + | 42.4236i | 1.15079 | + | 1.41727i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.0470 | − | 39.9186i | −0.769090 | − | 1.33210i | ||||
\(899\) | −11.5017 | − | 19.9216i | −0.383604 | − | 0.664422i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0034 | + | 17.3265i | −0.333263 | + | 0.577228i | ||||
\(902\) | −5.88617 | + | 10.1952i | −0.195988 | + | 0.339461i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.94049 | + | 15.4854i | 0.297356 | + | 0.515036i | ||||
\(905\) | −31.1447 | −1.03528 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.4262 | −1.50835 | −0.754176 | − | 0.656672i | \(-0.771964\pi\) | ||||
−0.754176 | + | 0.656672i | \(0.771964\pi\) | |||||||
\(908\) | −36.4442 | + | 63.1232i | −1.20944 | + | 2.09482i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.98121 | + | 26.1051i | −0.330874 | + | 0.865377i | ||||
\(911\) | 2.24354 | − | 3.88592i | 0.0743318 | − | 0.128746i | −0.826464 | − | 0.562990i | \(-0.809651\pi\) |
0.900795 | + | 0.434244i | \(0.142984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2366 | + | 17.7303i | −0.338781 | + | 0.586786i | ||||
\(914\) | 34.0305 | − | 58.9426i | 1.12563 | − | 1.94965i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.2601 | − | 62.8043i | 1.19807 | − | 2.07511i | ||||
\(917\) | 22.0689 | − | 3.52532i | 0.728780 | − | 0.116416i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3189 | − | 29.9972i | 0.571298 | − | 0.989517i | −0.425135 | − | 0.905130i | \(-0.639773\pi\) |
0.996433 | − | 0.0843873i | \(-0.0268933\pi\) | |||||||
\(920\) | −37.8640 | −1.24834 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 54.6622 | 1.80020 | ||||||||
\(923\) | 18.3326 | + | 31.7531i | 0.603426 | + | 1.04517i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.17592 | + | 10.6970i | −0.203063 | + | 0.351715i | ||||
\(926\) | −34.6440 | + | 60.0051i | −1.13847 | + | 1.97189i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.62788 | − | 6.28368i | −0.119091 | − | 0.206272i | ||||
\(929\) | 7.63640 | + | 13.2266i | 0.250542 | + | 0.433952i | 0.963675 | − | 0.267077i | \(-0.0860578\pi\) |
−0.713133 | + | 0.701029i | \(0.752725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.61412 | + | 17.2272i | −0.118448 | + | 0.564598i | ||||
\(932\) | −0.548792 | − | 0.950535i | −0.0179763 | − | 0.0311358i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.3525 | −0.338746 | ||||||||
\(935\) | 11.0052 | + | 19.0615i | 0.359908 | + | 0.623379i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6920 | 0.545305 | 0.272652 | − | 0.962113i | \(-0.412099\pi\) | ||||
0.272652 | + | 0.962113i | \(0.412099\pi\) | |||||||
\(938\) | −16.4156 | + | 2.62224i | −0.535987 | + | 0.0856193i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.56015 | −0.311818 | ||||||||
\(941\) | 10.6239 | − | 18.4012i | 0.346330 | − | 0.599862i | −0.639264 | − | 0.768987i | \(-0.720761\pi\) |
0.985595 | + | 0.169125i | \(0.0540943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.45814 | + | 12.9179i | 0.242870 | + | 0.420664i | ||||
\(944\) | 16.4940 | 0.536836 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.4354 | −1.05456 | ||||||||
\(947\) | 19.6573 | + | 34.0475i | 0.638777 | + | 1.10639i | 0.985701 | + | 0.168501i | \(0.0538927\pi\) |
−0.346924 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.2200 | − | 22.8977i | 0.429140 | − | 0.743292i | ||||
\(950\) | −20.8148 | −0.675322 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 43.2625 | + | 53.2804i | 1.40214 | + | 1.72683i | ||||
\(953\) | 15.1311 | 0.490143 | 0.245072 | − | 0.969505i | \(-0.421189\pi\) | ||||
0.245072 | + | 0.969505i | \(0.421189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.39351 | + | 7.60977i | 0.142170 | + | 0.246247i | ||||
\(956\) | −12.8566 | −0.415811 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.8819 | − | 32.7045i | −0.610047 | − | 1.05663i | ||||
\(959\) | −36.5677 | + | 5.84137i | −1.18083 | + | 0.188628i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.7779 | − | 63.7012i | −1.18638 | − | 2.05488i | ||||
\(962\) | −15.2123 | − | 26.3486i | −0.490466 | − | 0.849512i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.8862 | + | 18.8555i | −0.350622 | + | 0.607295i | ||||
\(965\) | 6.97653 | − | 12.0837i | 0.224582 | − | 0.388988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6941 | − | 27.1829i | −0.504687 | − | 0.874143i | −0.999985 | − | 0.00542015i | \(-0.998275\pi\) |
0.495299 | − | 0.868723i | \(-0.335059\pi\) | |||||||
\(968\) | −15.1021 | −0.485399 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.4203 | 1.23360 | ||||||||
\(971\) | 17.4760 | − | 30.2694i | 0.560833 | − | 0.971391i | −0.436591 | − | 0.899660i | \(-0.643814\pi\) |
0.997424 | − | 0.0717309i | \(-0.0228523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.40624 | + | 11.5844i | 0.301550 | + | 0.371377i | ||||
\(974\) | 45.3769 | − | 78.5951i | 1.45397 | − | 2.51835i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1778 | − | 24.5566i | 0.453819 | − | 0.786038i | ||||
\(977\) | −3.84316 | + | 6.65655i | −0.122954 | + | 0.212962i | −0.920931 | − | 0.389725i | \(-0.872570\pi\) |
0.797978 | + | 0.602687i | \(0.205903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.56978 | − | 16.5753i | 0.305851 | − | 0.529750i | ||||
\(980\) | 6.40153 | − | 30.5137i | 0.204489 | − | 0.974726i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.8793 | − | 27.5037i | 0.506729 | − | 0.877680i | ||||
\(983\) | −2.18071 | −0.0695538 | −0.0347769 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347769 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.6975 | 0.786928 | ||||||||
\(986\) | −17.9581 | − | 31.1044i | −0.571904 | − | 0.990566i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.5202 | − | 28.6139i | 0.525579 | − | 0.910329i | ||||
\(989\) | −20.5488 | + | 35.5915i | −0.653413 | + | 1.13175i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85159 | + | 4.93909i | 0.0905837 | + | 0.156895i | 0.907757 | − | 0.419497i | \(-0.137793\pi\) |
−0.817173 | + | 0.576392i | \(0.804460\pi\) | |||||||
\(992\) | −16.4895 | − | 28.5607i | −0.523543 | − | 0.906803i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −40.0084 | − | 49.2728i | −1.26899 | − | 1.56284i | ||||
\(995\) | 6.34341 | + | 10.9871i | 0.201100 | + | 0.348315i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3797 | 0.993804 | 0.496902 | − | 0.867807i | \(-0.334471\pi\) | ||||
0.496902 | + | 0.867807i | \(0.334471\pi\) | |||||||
\(998\) | −6.41189 | − | 11.1057i | −0.202965 | − | 0.351545i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.2.g.k.541.1 | 8 | ||
3.2 | odd | 2 | 567.2.g.j.541.4 | 8 | |||
7.4 | even | 3 | 567.2.h.j.298.4 | 8 | |||
9.2 | odd | 6 | 567.2.e.c.163.4 | ✓ | 8 | ||
9.4 | even | 3 | 567.2.h.j.352.4 | 8 | |||
9.5 | odd | 6 | 567.2.h.k.352.1 | 8 | |||
9.7 | even | 3 | 567.2.e.d.163.1 | yes | 8 | ||
21.11 | odd | 6 | 567.2.h.k.298.1 | 8 | |||
63.2 | odd | 6 | 3969.2.a.x.1.1 | 4 | |||
63.4 | even | 3 | inner | 567.2.g.k.109.1 | 8 | ||
63.11 | odd | 6 | 567.2.e.c.487.4 | yes | 8 | ||
63.16 | even | 3 | 3969.2.a.s.1.4 | 4 | |||
63.25 | even | 3 | 567.2.e.d.487.1 | yes | 8 | ||
63.32 | odd | 6 | 567.2.g.j.109.4 | 8 | |||
63.47 | even | 6 | 3969.2.a.w.1.1 | 4 | |||
63.61 | odd | 6 | 3969.2.a.t.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.4 | ✓ | 8 | 9.2 | odd | 6 | ||
567.2.e.c.487.4 | yes | 8 | 63.11 | odd | 6 | ||
567.2.e.d.163.1 | yes | 8 | 9.7 | even | 3 | ||
567.2.e.d.487.1 | yes | 8 | 63.25 | even | 3 | ||
567.2.g.j.109.4 | 8 | 63.32 | odd | 6 | |||
567.2.g.j.541.4 | 8 | 3.2 | odd | 2 | |||
567.2.g.k.109.1 | 8 | 63.4 | even | 3 | inner | ||
567.2.g.k.541.1 | 8 | 1.1 | even | 1 | trivial | ||
567.2.h.j.298.4 | 8 | 7.4 | even | 3 | |||
567.2.h.j.352.4 | 8 | 9.4 | even | 3 | |||
567.2.h.k.298.1 | 8 | 21.11 | odd | 6 | |||
567.2.h.k.352.1 | 8 | 9.5 | odd | 6 | |||
3969.2.a.s.1.4 | 4 | 63.16 | even | 3 | |||
3969.2.a.t.1.4 | 4 | 63.61 | odd | 6 | |||
3969.2.a.w.1.1 | 4 | 63.47 | even | 6 | |||
3969.2.a.x.1.1 | 4 | 63.2 | odd | 6 |