Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(26,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("475.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.e (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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.1 | ||
Root | \(0.203566 - 0.352587i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.201 |
Dual form | 475.2.e.g.26.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22810 | + | 2.12713i | −0.868399 | + | 1.50411i | −0.00476685 | + | 0.999989i | \(0.501517\pi\) |
−0.863632 | + | 0.504123i | \(0.831816\pi\) | |||||||
\(3\) | −0.780522 | + | 1.35190i | −0.450635 | + | 0.780522i | −0.998426 | − | 0.0560930i | \(-0.982136\pi\) |
0.547791 | + | 0.836615i | \(0.315469\pi\) | |||||||
\(4\) | −2.01647 | − | 3.49262i | −1.00823 | − | 1.74631i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.91712 | − | 3.32055i | −0.782662 | − | 1.35561i | ||||
\(7\) | 4.50527 | 1.70283 | 0.851417 | − | 0.524490i | \(-0.175744\pi\) | ||||
0.851417 | + | 0.524490i | \(0.175744\pi\) | |||||||
\(8\) | 4.99330 | 1.76540 | ||||||||
\(9\) | 0.281570 | + | 0.487693i | 0.0938566 | + | 0.162564i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.19869 | 0.662930 | 0.331465 | − | 0.943467i | \(-0.392457\pi\) | ||||
0.331465 | + | 0.943467i | \(0.392457\pi\) | |||||||
\(12\) | 6.29559 | 1.81738 | ||||||||
\(13\) | 1.87925 | + | 3.25495i | 0.521209 | + | 0.902761i | 0.999696 | + | 0.0246661i | \(0.00785227\pi\) |
−0.478486 | + | 0.878095i | \(0.658814\pi\) | |||||||
\(14\) | −5.53293 | + | 9.58332i | −1.47874 | + | 2.56125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.09935 | + | 3.63617i | −0.524836 | + | 0.909043i | ||||
\(17\) | −0.332943 | + | 0.576674i | −0.0807506 | + | 0.139864i | −0.903573 | − | 0.428435i | \(-0.859065\pi\) |
0.822822 | + | 0.568299i | \(0.192398\pi\) | |||||||
\(18\) | −1.38318 | −0.326020 | ||||||||
\(19\) | 3.79804 | − | 2.13891i | 0.871329 | − | 0.490699i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.51647 | + | 6.09070i | −0.767356 | + | 1.32910i | ||||
\(22\) | −2.70022 | + | 4.67691i | −0.575688 | + | 0.997121i | ||||
\(23\) | 0.244013 | + | 0.422643i | 0.0508802 | + | 0.0881272i | 0.890344 | − | 0.455289i | \(-0.150464\pi\) |
−0.839464 | + | 0.543416i | \(0.817131\pi\) | |||||||
\(24\) | −3.89738 | + | 6.75046i | −0.795550 | + | 1.37793i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.23163 | −1.81047 | ||||||||
\(27\) | −5.56222 | −1.07045 | ||||||||
\(28\) | −9.08474 | − | 15.7352i | −1.71685 | − | 2.97368i | ||||
\(29\) | −1.79804 | − | 3.11429i | −0.333887 | − | 0.578309i | 0.649383 | − | 0.760461i | \(-0.275027\pi\) |
−0.983270 | + | 0.182152i | \(0.941694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.83424 | 1.22747 | 0.613733 | − | 0.789514i | \(-0.289667\pi\) | ||||
0.613733 | + | 0.789514i | \(0.289667\pi\) | |||||||
\(32\) | −0.163119 | − | 0.282531i | −0.0288357 | − | 0.0499449i | ||||
\(33\) | −1.71613 | + | 2.97242i | −0.298739 | + | 0.517432i | ||||
\(34\) | −0.817776 | − | 1.41643i | −0.140247 | − | 0.242916i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.13555 | − | 1.96683i | 0.189259 | − | 0.327806i | ||||
\(37\) | −3.01171 | −0.495123 | −0.247561 | − | 0.968872i | \(-0.579629\pi\) | ||||
−0.247561 | + | 0.968872i | \(0.579629\pi\) | |||||||
\(38\) | −0.114636 | + | 10.7057i | −0.0185964 | + | 1.73670i | ||||
\(39\) | −5.86718 | −0.939500 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0362063 | + | 0.0627112i | −0.00565448 | + | 0.00979384i | −0.868839 | − | 0.495095i | \(-0.835133\pi\) |
0.863184 | + | 0.504889i | \(0.168467\pi\) | |||||||
\(42\) | −8.63716 | − | 14.9600i | −1.33274 | − | 2.30838i | ||||
\(43\) | −0.210271 | + | 0.364199i | −0.0320660 | + | 0.0555399i | −0.881613 | − | 0.471973i | \(-0.843542\pi\) |
0.849547 | + | 0.527513i | \(0.176875\pi\) | |||||||
\(44\) | −4.43359 | − | 7.67920i | −0.668389 | − | 1.15768i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.19869 | −0.176737 | ||||||||
\(47\) | −2.51139 | − | 4.34986i | −0.366324 | − | 0.634492i | 0.622664 | − | 0.782490i | \(-0.286050\pi\) |
−0.988988 | + | 0.147998i | \(0.952717\pi\) | |||||||
\(48\) | −3.27717 | − | 5.67623i | −0.473019 | − | 0.819293i | ||||
\(49\) | 13.2975 | 1.89964 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.519739 | − | 0.900215i | −0.0727780 | − | 0.126055i | ||||
\(52\) | 7.57888 | − | 13.1270i | 1.05100 | − | 1.82039i | ||||
\(53\) | −1.30900 | − | 2.26725i | −0.179804 | − | 0.311430i | 0.762009 | − | 0.647566i | \(-0.224213\pi\) |
−0.941813 | + | 0.336136i | \(0.890880\pi\) | |||||||
\(54\) | 6.83097 | − | 11.8316i | 0.929577 | − | 1.61008i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22.4962 | 3.00618 | ||||||||
\(57\) | −0.0728572 | + | 6.80405i | −0.00965017 | + | 0.901218i | ||||
\(58\) | 8.83269 | 1.15979 | ||||||||
\(59\) | −6.26783 | + | 10.8562i | −0.816002 | + | 1.41336i | 0.0926038 | + | 0.995703i | \(0.470481\pi\) |
−0.908606 | + | 0.417654i | \(0.862852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.53293 | − | 6.11922i | −0.452346 | − | 0.783486i | 0.546185 | − | 0.837664i | \(-0.316079\pi\) |
−0.998531 | + | 0.0541782i | \(0.982746\pi\) | |||||||
\(62\) | −8.39315 | + | 14.5374i | −1.06593 | + | 1.84625i | ||||
\(63\) | 1.26855 | + | 2.19719i | 0.159822 | + | 0.276820i | ||||
\(64\) | −7.59607 | −0.949509 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.21516 | − | 7.30087i | −0.518850 | − | 0.898675i | ||||
\(67\) | −2.86334 | − | 4.95944i | −0.349812 | − | 0.605892i | 0.636404 | − | 0.771356i | \(-0.280421\pi\) |
−0.986216 | + | 0.165464i | \(0.947088\pi\) | |||||||
\(68\) | 2.68548 | 0.325662 | ||||||||
\(69\) | −0.761831 | −0.0917136 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.48626 | + | 6.03838i | −0.413743 | + | 0.716624i | −0.995296 | − | 0.0968847i | \(-0.969112\pi\) |
0.581552 | + | 0.813509i | \(0.302446\pi\) | |||||||
\(72\) | 1.40596 | + | 2.43520i | 0.165694 | + | 0.286991i | ||||
\(73\) | 1.47882 | − | 2.56139i | 0.173083 | − | 0.299788i | −0.766413 | − | 0.642348i | \(-0.777961\pi\) |
0.939496 | + | 0.342560i | \(0.111294\pi\) | |||||||
\(74\) | 3.69869 | − | 6.40632i | 0.429964 | − | 0.744720i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.1290 | − | 8.95208i | −1.73542 | − | 1.02687i | ||||
\(77\) | 9.90571 | 1.12886 | ||||||||
\(78\) | 7.20549 | − | 12.4803i | 0.815861 | − | 1.41311i | ||||
\(79\) | −5.66849 | + | 9.81811i | −0.637755 | + | 1.10462i | 0.348170 | + | 0.937431i | \(0.386803\pi\) |
−0.985924 | + | 0.167192i | \(0.946530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.49673 | − | 6.05651i | 0.388525 | − | 0.672946i | ||||
\(82\) | −0.0889301 | − | 0.154031i | −0.00982068 | − | 0.0170099i | ||||
\(83\) | −15.6999 | −1.72328 | −0.861642 | − | 0.507517i | \(-0.830564\pi\) | ||||
−0.861642 | + | 0.507517i | \(0.830564\pi\) | |||||||
\(84\) | 28.3634 | 3.09470 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.516467 | − | 0.894547i | −0.0556921 | − | 0.0964615i | ||||
\(87\) | 5.61363 | 0.601845 | ||||||||
\(88\) | 10.9787 | 1.17034 | ||||||||
\(89\) | 0.668486 | + | 1.15785i | 0.0708594 | + | 0.122732i | 0.899278 | − | 0.437377i | \(-0.144092\pi\) |
−0.828419 | + | 0.560109i | \(0.810759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.46652 | + | 14.6644i | 0.887533 | + | 1.53725i | ||||
\(92\) | 0.984089 | − | 1.70449i | 0.102598 | − | 0.177706i | ||||
\(93\) | −5.33428 | + | 9.23924i | −0.553139 | + | 0.958065i | ||||
\(94\) | 12.3370 | 1.27246 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.509273 | 0.0519775 | ||||||||
\(97\) | −2.19319 | + | 3.79871i | −0.222685 | + | 0.385701i | −0.955622 | − | 0.294595i | \(-0.904815\pi\) |
0.732938 | + | 0.680296i | \(0.238149\pi\) | |||||||
\(98\) | −16.3307 | + | 28.2856i | −1.64965 | + | 2.85727i | ||||
\(99\) | 0.619085 | + | 1.07229i | 0.0622204 | + | 0.107769i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.28430 | + | 9.15267i | 0.525807 | + | 0.910725i | 0.999548 | + | 0.0300608i | \(0.00957008\pi\) |
−0.473741 | + | 0.880664i | \(0.657097\pi\) | |||||||
\(102\) | 2.55317 | 0.252801 | ||||||||
\(103\) | 5.75615 | 0.567171 | 0.283585 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283585 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(104\) | 9.38364 | + | 16.2529i | 0.920142 | + | 1.59373i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.43032 | 0.624568 | ||||||||
\(107\) | −1.30229 | −0.125897 | −0.0629486 | − | 0.998017i | \(-0.520050\pi\) | ||||
−0.0629486 | + | 0.998017i | \(0.520050\pi\) | |||||||
\(108\) | 11.2160 | + | 19.4267i | 1.07926 | + | 1.86934i | ||||
\(109\) | 6.01647 | − | 10.4208i | 0.576273 | − | 0.998134i | −0.419629 | − | 0.907696i | \(-0.637840\pi\) |
0.995902 | − | 0.0904385i | \(-0.0288269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.35071 | − | 4.07155i | 0.223120 | − | 0.386454i | ||||
\(112\) | −9.45813 | + | 16.3820i | −0.893709 | + | 1.54795i | ||||
\(113\) | 7.74626 | 0.728707 | 0.364353 | − | 0.931261i | \(-0.381290\pi\) | ||||
0.364353 | + | 0.931261i | \(0.381290\pi\) | |||||||
\(114\) | −14.3836 | − | 8.51104i | −1.34715 | − | 0.797132i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.25136 | + | 12.5597i | −0.673272 | + | 1.16614i | ||||
\(117\) | −1.05828 | + | 1.83299i | −0.0978378 | + | 0.169460i | ||||
\(118\) | −15.3951 | − | 26.6650i | −1.41723 | − | 2.45472i | ||||
\(119\) | −1.50000 | + | 2.59808i | −0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.16576 | −0.560523 | ||||||||
\(122\) | 17.3552 | 1.57127 | ||||||||
\(123\) | −0.0565197 | − | 0.0978950i | −0.00509621 | − | 0.00882689i | ||||
\(124\) | −13.7810 | − | 23.8694i | −1.23757 | − | 2.14354i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.23163 | −0.555157 | ||||||||
\(127\) | 1.96818 | + | 3.40898i | 0.174647 | + | 0.302498i | 0.940039 | − | 0.341066i | \(-0.110788\pi\) |
−0.765392 | + | 0.643565i | \(0.777455\pi\) | |||||||
\(128\) | 9.65499 | − | 16.7229i | 0.853389 | − | 1.47811i | ||||
\(129\) | −0.328242 | − | 0.568531i | −0.0289001 | − | 0.0500564i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.16248 | − | 14.1378i | 0.713160 | − | 1.23523i | −0.250505 | − | 0.968115i | \(-0.580597\pi\) |
0.963665 | − | 0.267114i | \(-0.0860699\pi\) | |||||||
\(132\) | 13.8421 | 1.20480 | ||||||||
\(133\) | 17.1112 | − | 9.63635i | 1.48373 | − | 0.835578i | ||||
\(134\) | 14.0659 | 1.21511 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.66248 | + | 2.87951i | −0.142557 | + | 0.246916i | ||||
\(137\) | 8.21529 | + | 14.2293i | 0.701879 | + | 1.21569i | 0.967806 | + | 0.251697i | \(0.0809887\pi\) |
−0.265927 | + | 0.963993i | \(0.585678\pi\) | |||||||
\(138\) | 0.935605 | − | 1.62052i | 0.0796440 | − | 0.137947i | ||||
\(139\) | 1.33424 | + | 2.31098i | 0.113169 | + | 0.196015i | 0.917046 | − | 0.398781i | \(-0.130567\pi\) |
−0.803877 | + | 0.594795i | \(0.797233\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.84079 | 0.660313 | ||||||||
\(142\) | −8.56297 | − | 14.8315i | −0.718588 | − | 1.24463i | ||||
\(143\) | 4.13188 | + | 7.15663i | 0.345526 | + | 0.598468i | ||||
\(144\) | −2.36445 | −0.197037 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.63228 | + | 6.29129i | 0.300610 | + | 0.520671i | ||||
\(147\) | −10.3790 | + | 17.9769i | −0.856045 | + | 1.48271i | ||||
\(148\) | 6.07302 | + | 10.5188i | 0.499199 | + | 0.864639i | ||||
\(149\) | 8.98299 | − | 15.5590i | 0.735915 | − | 1.27464i | −0.218405 | − | 0.975858i | \(-0.570085\pi\) |
0.954321 | − | 0.298784i | \(-0.0965812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7344 | −1.03631 | −0.518154 | − | 0.855288i | \(-0.673380\pi\) | ||||
−0.518154 | + | 0.855288i | \(0.673380\pi\) | |||||||
\(152\) | 18.9647 | − | 10.6802i | 1.53824 | − | 0.866278i | ||||
\(153\) | −0.374987 | −0.0303159 | ||||||||
\(154\) | −12.1652 | + | 21.0708i | −0.980301 | + | 1.69793i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.8310 | + | 20.4918i | 0.947236 | + | 1.64066i | ||||
\(157\) | 10.0270 | − | 17.3674i | 0.800245 | − | 1.38607i | −0.119209 | − | 0.992869i | \(-0.538036\pi\) |
0.919454 | − | 0.393197i | \(-0.128631\pi\) | |||||||
\(158\) | −13.9230 | − | 24.1153i | −1.10765 | − | 1.91851i | ||||
\(159\) | 4.08680 | 0.324104 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.09935 | + | 1.90412i | 0.0866406 | + | 0.150066i | ||||
\(162\) | 8.58867 | + | 14.8760i | 0.674790 | + | 1.16877i | ||||
\(163\) | −14.2331 | −1.11482 | −0.557412 | − | 0.830236i | \(-0.688206\pi\) | ||||
−0.557412 | + | 0.830236i | \(0.688206\pi\) | |||||||
\(164\) | 0.292035 | 0.0228041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.2810 | − | 33.3957i | 1.49650 | − | 2.59201i | ||||
\(167\) | −2.80815 | − | 4.86386i | −0.217301 | − | 0.376376i | 0.736681 | − | 0.676241i | \(-0.236392\pi\) |
−0.953982 | + | 0.299864i | \(0.903059\pi\) | |||||||
\(168\) | −17.5588 | + | 30.4127i | −1.35469 | + | 2.34639i | ||||
\(169\) | −0.563139 | + | 0.975386i | −0.0433184 | + | 0.0750297i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.11254 | + | 1.25002i | 0.161550 | + | 0.0955918i | ||||
\(172\) | 1.69601 | 0.129320 | ||||||||
\(173\) | 5.34524 | − | 9.25824i | 0.406391 | − | 0.703891i | −0.588091 | − | 0.808795i | \(-0.700120\pi\) |
0.994482 | + | 0.104904i | \(0.0334536\pi\) | |||||||
\(174\) | −6.89411 | + | 11.9409i | −0.522641 | + | 0.905241i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.61581 | + | 7.99482i | −0.347930 | + | 0.602632i | ||||
\(177\) | −9.78437 | − | 16.9470i | −0.735438 | − | 1.27382i | ||||
\(178\) | −3.28388 | −0.246137 | ||||||||
\(179\) | 7.68942 | 0.574734 | 0.287367 | − | 0.957821i | \(-0.407220\pi\) | ||||
0.287367 | + | 0.957821i | \(0.407220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.06314 | + | 5.30551i | 0.227681 | + | 0.394356i | 0.957121 | − | 0.289690i | \(-0.0935522\pi\) |
−0.729439 | + | 0.684046i | \(0.760219\pi\) | |||||||
\(182\) | −41.5910 | −3.08293 | ||||||||
\(183\) | 11.0301 | 0.815371 | ||||||||
\(184\) | 1.21843 | + | 2.11038i | 0.0898239 | + | 0.155580i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.1021 | − | 22.6935i | −0.960691 | − | 1.66397i | ||||
\(187\) | −0.732039 | + | 1.26793i | −0.0535320 | + | 0.0927201i | ||||
\(188\) | −10.1283 | + | 17.5427i | −0.738680 | + | 1.27943i | ||||
\(189\) | −25.0593 | −1.82280 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.85517 | 0.423666 | 0.211833 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211833 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(192\) | 5.92891 | − | 10.2692i | 0.427882 | − | 0.741113i | ||||
\(193\) | −1.29559 | + | 2.24402i | −0.0932584 | + | 0.161528i | −0.908880 | − | 0.417057i | \(-0.863062\pi\) |
0.815622 | + | 0.578585i | \(0.196395\pi\) | |||||||
\(194\) | −5.38692 | − | 9.33041i | −0.386758 | − | 0.669885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.8140 | − | 46.4431i | −1.91528 | − | 3.31737i | ||||
\(197\) | −19.8628 | −1.41517 | −0.707584 | − | 0.706629i | \(-0.750215\pi\) | ||||
−0.707584 | + | 0.706629i | \(0.750215\pi\) | |||||||
\(198\) | −3.04120 | −0.216128 | ||||||||
\(199\) | 6.38092 | + | 11.0521i | 0.452331 | + | 0.783460i | 0.998530 | − | 0.0541948i | \(-0.0172592\pi\) |
−0.546199 | + | 0.837655i | \(0.683926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.93959 | 0.630550 | ||||||||
\(202\) | −25.9586 | −1.82644 | ||||||||
\(203\) | −8.10065 | − | 14.0307i | −0.568554 | − | 0.984765i | ||||
\(204\) | −2.09607 | + | 3.63051i | −0.146755 | + | 0.254186i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.06914 | + | 12.2441i | −0.492530 | + | 0.853088i | ||||
\(207\) | −0.137413 | + | 0.238007i | −0.00955089 | + | 0.0165426i | ||||
\(208\) | −15.7808 | −1.09420 | ||||||||
\(209\) | 8.35071 | − | 4.70279i | 0.577631 | − | 0.325299i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92759 | + | 11.9989i | −0.476915 | + | 0.826041i | −0.999650 | − | 0.0264545i | \(-0.991578\pi\) |
0.522735 | + | 0.852495i | \(0.324912\pi\) | |||||||
\(212\) | −5.27909 | + | 9.14366i | −0.362570 | + | 0.627989i | ||||
\(213\) | −5.44221 | − | 9.42619i | −0.372894 | − | 0.645872i | ||||
\(214\) | 1.59935 | − | 2.77015i | 0.109329 | − | 0.189363i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −27.7738 | −1.88977 | ||||||||
\(217\) | 30.7901 | 2.09017 | ||||||||
\(218\) | 14.7777 | + | 25.5957i | 1.00087 | + | 1.73356i | ||||
\(219\) | 2.30850 | + | 3.99844i | 0.155994 | + | 0.270190i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.50273 | −0.168352 | ||||||||
\(222\) | 5.77382 | + | 10.0006i | 0.387514 | + | 0.671193i | ||||
\(223\) | 10.8480 | − | 18.7893i | 0.726437 | − | 1.25823i | −0.231943 | − | 0.972729i | \(-0.574508\pi\) |
0.958380 | − | 0.285496i | \(-0.0921584\pi\) | |||||||
\(224\) | −0.734898 | − | 1.27288i | −0.0491024 | − | 0.0850479i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.51320 | + | 16.4773i | −0.632808 | + | 1.09606i | ||||
\(227\) | −8.19628 | −0.544006 | −0.272003 | − | 0.962296i | \(-0.587686\pi\) | ||||
−0.272003 | + | 0.962296i | \(0.587686\pi\) | |||||||
\(228\) | 23.9109 | − | 13.4657i | 1.58354 | − | 0.891786i | ||||
\(229\) | −16.6619 | −1.10105 | −0.550526 | − | 0.834818i | \(-0.685573\pi\) | ||||
−0.550526 | + | 0.834818i | \(0.685573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.73163 | + | 13.3916i | −0.508704 | + | 0.881101i | ||||
\(232\) | −8.97814 | − | 15.5506i | −0.589444 | − | 1.02095i | ||||
\(233\) | 6.10677 | − | 10.5772i | 0.400068 | − | 0.692937i | −0.593666 | − | 0.804711i | \(-0.702320\pi\) |
0.993734 | + | 0.111774i | \(0.0356533\pi\) | |||||||
\(234\) | −2.59935 | − | 4.50220i | −0.169925 | − | 0.294318i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 50.5555 | 3.29088 | ||||||||
\(237\) | −8.84876 | − | 15.3265i | −0.574789 | − | 0.995563i | ||||
\(238\) | −3.68430 | − | 6.38140i | −0.238818 | − | 0.413645i | ||||
\(239\) | 2.03948 | 0.131923 | 0.0659614 | − | 0.997822i | \(-0.478989\pi\) | ||||
0.0659614 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.76183 | − | 15.1759i | −0.564399 | − | 0.977568i | −0.997105 | − | 0.0760330i | \(-0.975775\pi\) |
0.432706 | − | 0.901535i | \(-0.357559\pi\) | |||||||
\(242\) | 7.57218 | − | 13.1154i | 0.486758 | − | 0.843089i | ||||
\(243\) | −2.88478 | − | 4.99659i | −0.185059 | − | 0.320531i | ||||
\(244\) | −14.2481 | + | 24.6784i | −0.912141 | + | 1.57987i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.277648 | 0.0177022 | ||||||||
\(247\) | 14.0995 | + | 8.34289i | 0.897129 | + | 0.530846i | ||||
\(248\) | 34.1254 | 2.16697 | ||||||||
\(249\) | 12.2541 | − | 21.2247i | 0.776572 | − | 1.34506i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.66903 | + | 2.89084i | 0.105348 | + | 0.182468i | 0.913880 | − | 0.405984i | \(-0.133071\pi\) |
−0.808532 | + | 0.588452i | \(0.799738\pi\) | |||||||
\(252\) | 5.11597 | − | 8.86112i | 0.322276 | − | 0.558198i | ||||
\(253\) | 0.536509 | + | 0.929261i | 0.0337301 | + | 0.0584222i | ||||
\(254\) | −9.66849 | −0.606655 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1185 | + | 27.9181i | 1.00741 | + | 1.74488i | ||||
\(257\) | −13.7922 | − | 23.8889i | −0.860337 | − | 1.49015i | −0.871604 | − | 0.490210i | \(-0.836920\pi\) |
0.0112676 | − | 0.999937i | \(-0.496413\pi\) | |||||||
\(258\) | 1.61246 | 0.100387 | ||||||||
\(259\) | −13.5686 | −0.843112 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.01255 | − | 1.75378i | 0.0626750 | − | 0.108556i | ||||
\(262\) | 20.0487 | + | 34.7254i | 1.23861 | + | 2.14534i | ||||
\(263\) | −6.81310 | + | 11.8006i | −0.420114 | + | 0.727658i | −0.995950 | − | 0.0899066i | \(-0.971343\pi\) |
0.575837 | + | 0.817565i | \(0.304676\pi\) | |||||||
\(264\) | −8.56914 | + | 14.8422i | −0.527394 | + | 0.913473i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.516467 | + | 48.2322i | −0.0316666 | + | 2.95731i | ||||
\(267\) | −2.08707 | −0.127727 | ||||||||
\(268\) | −11.5476 | + | 20.0011i | −0.705385 | + | 1.22176i | ||||
\(269\) | 1.80404 | − | 3.12469i | 0.109994 | − | 0.190515i | −0.805773 | − | 0.592224i | \(-0.798250\pi\) |
0.915768 | + | 0.401708i | \(0.131583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.28157 | + | 9.14795i | −0.320833 | + | 0.555698i | −0.980660 | − | 0.195719i | \(-0.937296\pi\) |
0.659828 | + | 0.751417i | \(0.270629\pi\) | |||||||
\(272\) | −1.39793 | − | 2.42128i | −0.0847617 | − | 0.146812i | ||||
\(273\) | −26.4332 | −1.59981 | ||||||||
\(274\) | −40.3568 | −2.43804 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.53621 | + | 2.66079i | 0.0924688 | + | 0.160161i | ||||
\(277\) | 6.73487 | 0.404659 | 0.202330 | − | 0.979317i | \(-0.435149\pi\) | ||||
0.202330 | + | 0.979317i | \(0.435149\pi\) | |||||||
\(278\) | −6.55434 | −0.393103 | ||||||||
\(279\) | 1.92432 | + | 3.33301i | 0.115206 | + | 0.199542i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.7152 | − | 20.2912i | −0.698868 | − | 1.21047i | −0.968859 | − | 0.247612i | \(-0.920354\pi\) |
0.269992 | − | 0.962863i | \(-0.412979\pi\) | |||||||
\(282\) | −9.62928 | + | 16.6784i | −0.573415 | + | 0.993185i | ||||
\(283\) | −7.34157 | + | 12.7160i | −0.436411 | + | 0.755886i | −0.997410 | − | 0.0719306i | \(-0.977084\pi\) |
0.560999 | + | 0.827817i | \(0.310417\pi\) | |||||||
\(284\) | 28.1197 | 1.66860 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2975 | −1.20022 | ||||||||
\(287\) | −0.163119 | + | 0.282531i | −0.00962863 | + | 0.0166773i | ||||
\(288\) | 0.0918589 | − | 0.159104i | 0.00541284 | − | 0.00937531i | ||||
\(289\) | 8.27830 | + | 14.3384i | 0.486959 | + | 0.843437i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.42367 | − | 5.92996i | −0.200699 | − | 0.347621i | ||||
\(292\) | −11.9280 | −0.698031 | ||||||||
\(293\) | 18.1855 | 1.06241 | 0.531206 | − | 0.847243i | \(-0.321739\pi\) | ||||
0.531206 | + | 0.847243i | \(0.321739\pi\) | |||||||
\(294\) | −25.4929 | − | 44.1550i | −1.48678 | − | 2.57517i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.0384 | −0.874089 | ||||||||
\(297\) | −12.2296 | −0.709634 | ||||||||
\(298\) | 22.0641 | + | 38.2161i | 1.27814 | + | 2.21380i | ||||
\(299\) | −0.917122 | + | 1.58850i | −0.0530385 | + | 0.0918654i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.947326 | + | 1.64082i | −0.0546030 | + | 0.0945752i | ||||
\(302\) | 15.6391 | − | 27.0877i | 0.899928 | − | 1.55872i | ||||
\(303\) | −16.4981 | −0.947788 | ||||||||
\(304\) | −0.195962 | + | 18.3006i | −0.0112392 | + | 1.04961i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.460522 | − | 0.797647i | 0.0263263 | − | 0.0455985i | ||||
\(307\) | 14.6901 | − | 25.4439i | 0.838406 | − | 1.45216i | −0.0528200 | − | 0.998604i | \(-0.516821\pi\) |
0.891226 | − | 0.453559i | \(-0.149846\pi\) | |||||||
\(308\) | −19.9745 | − | 34.5969i | −1.13815 | − | 1.97134i | ||||
\(309\) | −4.49281 | + | 7.78177i | −0.255587 | + | 0.442689i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.193232 | −0.0109572 | −0.00547859 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547859 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(312\) | −29.2966 | −1.65859 | ||||||||
\(313\) | −10.6377 | − | 18.4251i | −0.601281 | − | 1.04145i | −0.992627 | − | 0.121206i | \(-0.961324\pi\) |
0.391346 | − | 0.920243i | \(-0.372009\pi\) | |||||||
\(314\) | 24.6285 | + | 42.6578i | 1.38986 | + | 2.40732i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45.7213 | 2.57202 | ||||||||
\(317\) | 9.58506 | + | 16.6018i | 0.538351 | + | 0.932451i | 0.998993 | + | 0.0448649i | \(0.0142857\pi\) |
−0.460642 | + | 0.887586i | \(0.652381\pi\) | |||||||
\(318\) | −5.01901 | + | 8.69317i | −0.281452 | + | 0.487489i | ||||
\(319\) | −3.95333 | − | 6.84736i | −0.221344 | − | 0.383379i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.01647 | − | 1.76057i | 0.0567337 | − | 0.0982656i | ||||
\(322\) | −5.40043 | −0.300954 | ||||||||
\(323\) | −0.0310783 | + | 2.90236i | −0.00172924 | + | 0.161492i | ||||
\(324\) | −28.2042 | −1.56690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.4797 | − | 30.2758i | 0.968112 | − | 1.67682i | ||||
\(327\) | 9.39197 | + | 16.2674i | 0.519377 | + | 0.899588i | ||||
\(328\) | −0.180789 | + | 0.313136i | −0.00998240 | + | 0.0172900i | ||||
\(329\) | −11.3145 | − | 19.5973i | −0.623789 | − | 1.08043i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.6070 | −1.13266 | −0.566331 | − | 0.824178i | \(-0.691638\pi\) | ||||
−0.566331 | + | 0.824178i | \(0.691638\pi\) | |||||||
\(332\) | 31.6583 | + | 54.8337i | 1.73747 | + | 3.00939i | ||||
\(333\) | −0.848007 | − | 1.46879i | −0.0464705 | − | 0.0804893i | ||||
\(334\) | 13.7948 | 0.754816 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.7646 | − | 25.5730i | −0.805473 | − | 1.39512i | ||||
\(337\) | −5.10368 | + | 8.83982i | −0.278015 | + | 0.481536i | −0.970891 | − | 0.239520i | \(-0.923010\pi\) |
0.692876 | + | 0.721056i | \(0.256343\pi\) | |||||||
\(338\) | −1.38318 | − | 2.39575i | −0.0752353 | − | 0.130311i | ||||
\(339\) | −6.04613 | + | 10.4722i | −0.328381 | + | 0.568772i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0264 | 0.813725 | ||||||||
\(342\) | −5.25339 | + | 2.95850i | −0.284071 | + | 0.159977i | ||||
\(343\) | 28.3719 | 1.53194 | ||||||||
\(344\) | −1.04994 | + | 1.81856i | −0.0566092 | + | 0.0980500i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.1290 | + | 22.7401i | 0.705820 | + | 1.22252i | ||||
\(347\) | 2.72055 | − | 4.71213i | 0.146047 | − | 0.252960i | −0.783716 | − | 0.621119i | \(-0.786678\pi\) |
0.929763 | + | 0.368159i | \(0.120012\pi\) | |||||||
\(348\) | −11.3197 | − | 19.6063i | −0.606800 | − | 1.05101i | ||||
\(349\) | −1.55114 | −0.0830304 | −0.0415152 | − | 0.999138i | \(-0.513219\pi\) | ||||
−0.0415152 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4528 | − | 18.1048i | −0.557928 | − | 0.966360i | ||||
\(352\) | −0.358649 | − | 0.621199i | −0.0191161 | − | 0.0331100i | ||||
\(353\) | 32.9335 | 1.75287 | 0.876437 | − | 0.481517i | \(-0.159914\pi\) | ||||
0.876437 | + | 0.481517i | \(0.159914\pi\) | |||||||
\(354\) | 48.0648 | 2.55461 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.69596 | − | 4.66954i | 0.142886 | − | 0.247485i | ||||
\(357\) | −2.34157 | − | 4.05571i | −0.123929 | − | 0.214651i | ||||
\(358\) | −9.44339 | + | 16.3564i | −0.499098 | + | 0.864464i | ||||
\(359\) | 1.74864 | − | 3.02873i | 0.0922894 | − | 0.159850i | −0.816185 | − | 0.577791i | \(-0.803915\pi\) |
0.908474 | + | 0.417941i | \(0.137248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.85017 | − | 16.2473i | 0.518430 | − | 0.855120i | ||||
\(362\) | −15.0474 | −0.790873 | ||||||||
\(363\) | 4.81251 | − | 8.33551i | 0.252591 | − | 0.437501i | ||||
\(364\) | 34.1449 | − | 59.1408i | 1.78968 | − | 3.09982i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.5461 | + | 23.4626i | −0.708068 | + | 1.22641i | ||||
\(367\) | 9.75196 | + | 16.8909i | 0.509048 | + | 0.881697i | 0.999945 | + | 0.0104794i | \(0.00333575\pi\) |
−0.490897 | + | 0.871218i | \(0.663331\pi\) | |||||||
\(368\) | −2.04907 | −0.106815 | ||||||||
\(369\) | −0.0407784 | −0.00212284 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.89738 | − | 10.2146i | −0.306177 | − | 0.530314i | ||||
\(372\) | 43.0256 | 2.23077 | ||||||||
\(373\) | −23.5158 | −1.21760 | −0.608802 | − | 0.793322i | \(-0.708350\pi\) | ||||
−0.608802 | + | 0.793322i | \(0.708350\pi\) | |||||||
\(374\) | −1.79804 | − | 3.11429i | −0.0929743 | − | 0.161036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.5401 | − | 21.7201i | −0.646708 | − | 1.12013i | ||||
\(377\) | 6.75791 | − | 11.7050i | 0.348050 | − | 0.602841i | ||||
\(378\) | 30.7754 | − | 53.3046i | 1.58292 | − | 2.74169i | ||||
\(379\) | −7.05148 | −0.362210 | −0.181105 | − | 0.983464i | \(-0.557967\pi\) | ||||
−0.181105 | + | 0.983464i | \(0.557967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.14483 | −0.314809 | ||||||||
\(382\) | −7.19075 | + | 12.4547i | −0.367911 | + | 0.637240i | ||||
\(383\) | 1.54204 | − | 2.67090i | 0.0787947 | − | 0.136476i | −0.823935 | − | 0.566684i | \(-0.808226\pi\) |
0.902730 | + | 0.430207i | \(0.141560\pi\) | |||||||
\(384\) | 15.0719 | + | 26.1052i | 0.769133 | + | 1.33218i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.18222 | − | 5.51177i | −0.161971 | − | 0.280542i | ||||
\(387\) | −0.236823 | −0.0120384 | ||||||||
\(388\) | 17.6900 | 0.898072 | ||||||||
\(389\) | −4.69542 | − | 8.13270i | −0.238067 | − | 0.412345i | 0.722092 | − | 0.691797i | \(-0.243181\pi\) |
−0.960160 | + | 0.279452i | \(0.909847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.324970 | −0.0164344 | ||||||||
\(392\) | 66.3984 | 3.35362 | ||||||||
\(393\) | 12.7420 | + | 22.0698i | 0.642749 | + | 1.11327i | ||||
\(394\) | 24.3936 | − | 42.2509i | 1.22893 | − | 2.12857i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.49673 | − | 4.32446i | 0.125465 | − | 0.217312i | ||||
\(397\) | −13.3797 | + | 23.1744i | −0.671510 | + | 1.16309i | 0.305966 | + | 0.952042i | \(0.401021\pi\) |
−0.977476 | + | 0.211047i | \(0.932313\pi\) | |||||||
\(398\) | −31.3456 | −1.57122 | ||||||||
\(399\) | −0.328242 | + | 30.6541i | −0.0164326 | + | 1.53462i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.5851 | − | 21.7980i | 0.628468 | − | 1.08854i | −0.359391 | − | 0.933187i | \(-0.617016\pi\) |
0.987859 | − | 0.155352i | \(-0.0496511\pi\) | |||||||
\(402\) | −10.9787 | + | 19.0157i | −0.547569 | + | 0.948417i | ||||
\(403\) | 12.8432 | + | 22.2451i | 0.639767 | + | 1.10811i | ||||
\(404\) | 21.3112 | − | 36.9121i | 1.06027 | − | 1.83645i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 39.7937 | 1.97493 | ||||||||
\(407\) | −6.62183 | −0.328232 | ||||||||
\(408\) | −2.59521 | − | 4.49504i | −0.128482 | − | 0.222538i | ||||
\(409\) | 14.1608 | + | 24.5271i | 0.700204 | + | 1.21279i | 0.968395 | + | 0.249423i | \(0.0802410\pi\) |
−0.268191 | + | 0.963366i | \(0.586426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.6489 | −1.26516 | ||||||||
\(412\) | −11.6071 | − | 20.1041i | −0.571840 | − | 0.990457i | ||||
\(413\) | −28.2383 | + | 48.9102i | −1.38952 | + | 2.40671i | ||||
\(414\) | −0.337515 | − | 0.584593i | −0.0165880 | − | 0.0287312i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.613083 | − | 1.06189i | 0.0300589 | − | 0.0520635i | ||||
\(417\) | −4.16563 | −0.203992 | ||||||||
\(418\) | −0.252049 | + | 23.5386i | −0.0123281 | + | 1.15131i | ||||
\(419\) | 13.0449 | 0.637287 | 0.318643 | − | 0.947875i | \(-0.396773\pi\) | ||||
0.318643 | + | 0.947875i | \(0.396773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.66248 | + | 2.87951i | −0.0810246 | + | 0.140339i | −0.903690 | − | 0.428187i | \(-0.859153\pi\) |
0.822666 | + | 0.568525i | \(0.192486\pi\) | |||||||
\(422\) | −17.0156 | − | 29.4718i | −0.828305 | − | 1.43467i | ||||
\(423\) | 1.41426 | − | 2.44958i | 0.0687638 | − | 0.119102i | ||||
\(424\) | −6.53621 | − | 11.3210i | −0.317426 | − | 0.549798i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 26.7344 | 1.29528 | ||||||||
\(427\) | −15.9168 | − | 27.5688i | −0.770270 | − | 1.33415i | ||||
\(428\) | 2.62603 | + | 4.54841i | 0.126934 | + | 0.219856i | ||||
\(429\) | −12.9001 | −0.622823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0242034 | − | 0.0419216i | −0.00116584 | − | 0.00201929i | 0.865442 | − | 0.501009i | \(-0.167038\pi\) |
−0.866608 | + | 0.498990i | \(0.833704\pi\) | |||||||
\(432\) | 11.6770 | − | 20.2252i | 0.561811 | − | 0.973085i | ||||
\(433\) | −4.78436 | − | 8.28676i | −0.229922 | − | 0.398236i | 0.727863 | − | 0.685723i | \(-0.240514\pi\) |
−0.957785 | + | 0.287486i | \(0.907180\pi\) | |||||||
\(434\) | −37.8134 | + | 65.4948i | −1.81510 | + | 3.14385i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.5280 | −2.32407 | ||||||||
\(437\) | 1.83076 | + | 1.08329i | 0.0875773 | + | 0.0518209i | ||||
\(438\) | −11.3403 | −0.541861 | ||||||||
\(439\) | 11.1257 | − | 19.2703i | 0.531002 | − | 0.919723i | −0.468343 | − | 0.883547i | \(-0.655149\pi\) |
0.999345 | − | 0.0361764i | \(-0.0115178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.74417 | + | 6.48509i | 0.178294 | + | 0.308814i | ||||
\(442\) | 3.07361 | − | 5.32364i | 0.146197 | − | 0.253220i | ||||
\(443\) | 10.0579 | + | 17.4207i | 0.477863 | + | 0.827684i | 0.999678 | − | 0.0253753i | \(-0.00807806\pi\) |
−0.521815 | + | 0.853059i | \(0.674745\pi\) | |||||||
\(444\) | −18.9605 | −0.899827 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.6449 | + | 46.1504i | 1.26167 | + | 2.18528i | ||||
\(447\) | 14.0229 | + | 24.2883i | 0.663258 | + | 1.14880i | ||||
\(448\) | −34.2224 | −1.61686 | ||||||||
\(449\) | −12.4973 | −0.589783 | −0.294891 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294891 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0796065 | + | 0.137883i | −0.00374852 | + | 0.00649263i | ||||
\(452\) | −15.6201 | − | 27.0548i | −0.734707 | − | 1.27255i | ||||
\(453\) | 9.93945 | − | 17.2156i | 0.466996 | − | 0.808861i | ||||
\(454\) | 10.0659 | − | 17.4346i | 0.472415 | − | 0.818246i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.363798 | + | 33.9746i | −0.0170364 | + | 1.59101i | ||||
\(457\) | 28.3179 | 1.32465 | 0.662327 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662327 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(458\) | 20.4626 | − | 35.4422i | 0.956153 | − | 1.65610i | ||||
\(459\) | 1.85190 | − | 3.20759i | 0.0864394 | − | 0.149717i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.65976 | + | 4.60683i | −0.123877 | + | 0.214562i | −0.921293 | − | 0.388868i | \(-0.872866\pi\) |
0.797416 | + | 0.603430i | \(0.206200\pi\) | |||||||
\(462\) | −18.9904 | − | 32.8924i | −0.883515 | − | 1.53029i | ||||
\(463\) | 17.9327 | 0.833401 | 0.416701 | − | 0.909044i | \(-0.363186\pi\) | ||||
0.416701 | + | 0.909044i | \(0.363186\pi\) | |||||||
\(464\) | 15.0988 | 0.700944 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.9995 | + | 25.9798i | 0.694836 | + | 1.20349i | ||||
\(467\) | −28.7791 | −1.33174 | −0.665868 | − | 0.746069i | \(-0.731939\pi\) | ||||
−0.665868 | + | 0.746069i | \(0.731939\pi\) | |||||||
\(468\) | 8.53593 | 0.394574 | ||||||||
\(469\) | −12.9001 | − | 22.3436i | −0.595672 | − | 1.03173i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.6527 | + | 27.1112i | 0.721237 | + | 1.24922i | ||||
\(472\) | −31.2972 | + | 54.2083i | −1.44057 | + | 2.49514i | ||||
\(473\) | −0.462320 | + | 0.800762i | −0.0212575 | + | 0.0368191i | ||||
\(474\) | 43.4687 | 1.99658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0988 | 0.554548 | ||||||||
\(477\) | 0.737147 | − | 1.27678i | 0.0337516 | − | 0.0584595i | ||||
\(478\) | −2.50469 | + | 4.33824i | −0.114562 | + | 0.198427i | ||||
\(479\) | 4.02574 | + | 6.97279i | 0.183941 | + | 0.318595i | 0.943219 | − | 0.332171i | \(-0.107781\pi\) |
−0.759278 | + | 0.650766i | \(0.774448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65976 | − | 9.80298i | −0.258063 | − | 0.446978i | ||||
\(482\) | 43.0417 | 1.96049 | ||||||||
\(483\) | −3.43226 | −0.156173 | ||||||||
\(484\) | 12.4330 | + | 21.5347i | 0.565138 | + | 0.978849i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.1712 | 0.642819 | ||||||||
\(487\) | −1.09761 | −0.0497376 | −0.0248688 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248688 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(488\) | −17.6410 | − | 30.5551i | −0.798571 | − | 1.38316i | ||||
\(489\) | 11.1093 | − | 19.2418i | 0.502379 | − | 0.870145i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.55267 | + | 11.3496i | −0.295718 | + | 0.512199i | −0.975152 | − | 0.221538i | \(-0.928892\pi\) |
0.679434 | + | 0.733737i | \(0.262226\pi\) | |||||||
\(492\) | −0.227940 | + | 0.394804i | −0.0102763 | + | 0.0177991i | ||||
\(493\) | 2.39458 | 0.107846 | ||||||||
\(494\) | −35.0621 | + | 19.7456i | −1.57752 | + | 0.888395i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3474 | + | 24.8505i | −0.644219 | + | 1.11582i | ||||
\(497\) | −15.7066 | + | 27.2046i | −0.704536 | + | 1.22029i | ||||
\(498\) | 30.0985 | + | 52.1322i | 1.34875 | + | 2.33610i | ||||
\(499\) | −12.0703 | + | 20.9064i | −0.540342 | + | 0.935900i | 0.458542 | + | 0.888673i | \(0.348372\pi\) |
−0.998884 | + | 0.0472275i | \(0.984961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.76729 | 0.391694 | ||||||||
\(502\) | −8.19895 | −0.365937 | ||||||||
\(503\) | −9.48090 | − | 16.4214i | −0.422733 | − | 0.732194i | 0.573473 | − | 0.819224i | \(-0.305596\pi\) |
−0.996206 | + | 0.0870300i | \(0.972262\pi\) | |||||||
\(504\) | 6.33424 | + | 10.9712i | 0.282150 | + | 0.488697i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.63555 | −0.117165 | ||||||||
\(507\) | −0.879086 | − | 1.52262i | −0.0390416 | − | 0.0676220i | ||||
\(508\) | 7.93753 | − | 13.7482i | 0.352171 | − | 0.609978i | ||||
\(509\) | −10.9803 | − | 19.0184i | −0.486692 | − | 0.842974i | 0.513191 | − | 0.858274i | \(-0.328463\pi\) |
−0.999883 | + | 0.0152997i | \(0.995130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.66248 | − | 11.5398i | 0.294731 | − | 0.510489i | ||||
\(512\) | −40.5609 | −1.79255 | ||||||||
\(513\) | −21.1255 | + | 11.8971i | −0.932714 | + | 0.525268i | ||||
\(514\) | 67.7531 | 2.98846 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.32378 | + | 2.29285i | −0.0582761 | + | 0.100937i | ||||
\(517\) | −5.52177 | − | 9.56399i | −0.242847 | − | 0.420624i | ||||
\(518\) | 16.6636 | − | 28.8622i | 0.732157 | − | 1.26813i | ||||
\(519\) | 8.34417 | + | 14.4525i | 0.366268 | + | 0.634395i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.56968 | 0.287823 | 0.143912 | − | 0.989591i | \(-0.454032\pi\) | ||||
0.143912 | + | 0.989591i | \(0.454032\pi\) | |||||||
\(522\) | 2.48702 | + | 4.30764i | 0.108854 | + | 0.188540i | ||||
\(523\) | 2.09889 | + | 3.63538i | 0.0917779 | + | 0.158964i | 0.908259 | − | 0.418408i | \(-0.137412\pi\) |
−0.816481 | + | 0.577372i | \(0.804078\pi\) | |||||||
\(524\) | −65.8375 | −2.87613 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7344 | − | 28.9848i | −0.729653 | − | 1.26380i | ||||
\(527\) | −2.27541 | + | 3.94113i | −0.0991186 | + | 0.171678i | ||||
\(528\) | −7.20549 | − | 12.4803i | −0.313579 | − | 0.543134i | ||||
\(529\) | 11.3809 | − | 19.7123i | 0.494822 | − | 0.857058i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.05933 | −0.306349 | ||||||||
\(532\) | −68.1603 | − | 40.3316i | −2.95513 | − | 1.74860i | ||||
\(533\) | −0.272162 | −0.0117887 | ||||||||
\(534\) | 2.56314 | − | 4.43949i | 0.110918 | − | 0.192115i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.2975 | − | 24.7640i | −0.617558 | − | 1.06964i | ||||
\(537\) | −6.00176 | + | 10.3954i | −0.258995 | + | 0.448593i | ||||
\(538\) | 4.43108 | + | 7.67486i | 0.191038 | + | 0.330887i | ||||
\(539\) | 29.2371 | 1.25933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.31505 | + | 4.00978i | 0.0995316 | + | 0.172394i | 0.911491 | − | 0.411320i | \(-0.134932\pi\) |
−0.811959 | + | 0.583714i | \(0.801599\pi\) | |||||||
\(542\) | −12.9726 | − | 22.4692i | −0.557221 | − | 0.965136i | ||||
\(543\) | −9.56340 | −0.410405 | ||||||||
\(544\) | 0.217238 | 0.00931400 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 32.4627 | − | 56.2271i | 1.38928 | − | 2.40630i | ||||
\(547\) | −19.0199 | − | 32.9435i | −0.813233 | − | 1.40856i | −0.910590 | − | 0.413312i | \(-0.864372\pi\) |
0.0973563 | − | 0.995250i | \(-0.468961\pi\) | |||||||
\(548\) | 33.1317 | − | 57.3858i | 1.41532 | − | 2.45140i | ||||
\(549\) | 1.98953 | − | 3.44597i | 0.0849113 | − | 0.147071i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4902 | − | 7.98236i | −0.574701 | − | 0.340060i | ||||
\(552\) | −3.80405 | −0.161911 | ||||||||
\(553\) | −25.5381 | + | 44.2333i | −1.08599 | + | 1.88099i | ||||
\(554\) | −8.27110 | + | 14.3260i | −0.351406 | + | 0.608652i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.38092 | − | 9.32002i | 0.228202 | − | 0.395257i | ||||
\(557\) | 18.2153 | + | 31.5498i | 0.771807 | + | 1.33681i | 0.936572 | + | 0.350476i | \(0.113980\pi\) |
−0.164765 | + | 0.986333i | \(0.552687\pi\) | |||||||
\(558\) | −9.45302 | −0.400178 | ||||||||
\(559\) | −1.58060 | −0.0668523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14275 | − | 1.97929i | −0.0482468 | − | 0.0835659i | ||||
\(562\) | 57.5496 | 2.42758 | ||||||||
\(563\) | −20.6856 | −0.871795 | −0.435897 | − | 0.899996i | \(-0.643569\pi\) | ||||
−0.435897 | + | 0.899996i | \(0.643569\pi\) | |||||||
\(564\) | −15.8107 | − | 27.3849i | −0.665750 | − | 1.15311i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.0324 | − | 31.2330i | −0.757958 | − | 1.31282i | ||||
\(567\) | 15.7537 | − | 27.2862i | 0.661594 | − | 1.14591i | ||||
\(568\) | −17.4080 | + | 30.1515i | −0.730422 | + | 1.26513i | ||||
\(569\) | −27.1132 | −1.13664 | −0.568322 | − | 0.822806i | \(-0.692407\pi\) | ||||
−0.568322 | + | 0.822806i | \(0.692407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.4687 | 1.94466 | 0.972328 | − | 0.233622i | \(-0.0750578\pi\) | ||||
0.972328 | + | 0.233622i | \(0.0750578\pi\) | |||||||
\(572\) | 16.6636 | − | 28.8622i | 0.696741 | − | 1.20679i | ||||
\(573\) | −4.57009 | + | 7.91564i | −0.190918 | + | 0.330680i | ||||
\(574\) | −0.400654 | − | 0.693954i | −0.0167230 | − | 0.0289651i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.13882 | − | 3.70455i | −0.0891177 | − | 0.154356i | ||||
\(577\) | −18.0398 | −0.751008 | −0.375504 | − | 0.926821i | \(-0.622530\pi\) | ||||
−0.375504 | + | 0.926821i | \(0.622530\pi\) | |||||||
\(578\) | −40.6664 | −1.69150 | ||||||||
\(579\) | −2.02247 | − | 3.50302i | −0.0840509 | − | 0.145580i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −70.7322 | −2.93447 | ||||||||
\(582\) | 16.8184 | 0.697147 | ||||||||
\(583\) | −2.87808 | − | 4.98497i | −0.119198 | − | 0.206457i | ||||
\(584\) | 7.38419 | − | 12.7898i | 0.305560 | − | 0.529245i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.3337 | + | 38.6831i | −0.922597 | + | 1.59798i | ||||
\(587\) | 13.0168 | − | 22.5458i | 0.537262 | − | 0.930565i | −0.461788 | − | 0.886990i | \(-0.652792\pi\) |
0.999050 | − | 0.0435750i | \(-0.0138747\pi\) | |||||||
\(588\) | 83.7156 | 3.45237 | ||||||||
\(589\) | 25.9567 | − | 14.6178i | 1.06953 | − | 0.602316i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.5034 | − | 26.8526i | 0.637724 | − | 1.10457i | ||||
\(592\) | 6.32263 | − | 10.9511i | 0.259858 | − | 0.450088i | ||||
\(593\) | −9.07803 | − | 15.7236i | −0.372790 | − | 0.645691i | 0.617203 | − | 0.786804i | \(-0.288266\pi\) |
−0.989994 | + | 0.141112i | \(0.954932\pi\) | |||||||
\(594\) | 15.0192 | − | 26.0140i | 0.616245 | − | 1.06737i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −72.4556 | −2.96790 | ||||||||
\(597\) | −19.9218 | −0.815345 | ||||||||
\(598\) | −2.25264 | − | 3.90168i | −0.0921172 | − | 0.159552i | ||||
\(599\) | −20.0357 | − | 34.7028i | −0.818635 | − | 1.41792i | −0.906688 | − | 0.421802i | \(-0.861398\pi\) |
0.0880531 | − | 0.996116i | \(-0.471935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0473 | 0.613793 | 0.306897 | − | 0.951743i | \(-0.400709\pi\) | ||||
0.306897 | + | 0.951743i | \(0.400709\pi\) | |||||||
\(602\) | −2.32683 | − | 4.03018i | −0.0948344 | − | 0.164258i | ||||
\(603\) | 1.61246 | − | 2.79286i | 0.0656643 | − | 0.113734i | ||||
\(604\) | 25.6784 | + | 44.4763i | 1.04484 | + | 1.80972i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 20.2613 | − | 35.0936i | 0.823059 | − | 1.42558i | ||||
\(607\) | 29.3860 | 1.19274 | 0.596370 | − | 0.802709i | \(-0.296609\pi\) | ||||
0.596370 | + | 0.802709i | \(0.296609\pi\) | |||||||
\(608\) | −1.22384 | − | 0.724166i | −0.0496333 | − | 0.0293688i | ||||
\(609\) | 25.2910 | 1.02484 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.43905 | − | 16.3489i | 0.381863 | − | 0.661406i | ||||
\(612\) | 0.756148 | + | 1.30969i | 0.0305655 | + | 0.0529410i | ||||
\(613\) | −17.3539 | + | 30.0578i | −0.700917 | + | 1.21402i | 0.267229 | + | 0.963633i | \(0.413892\pi\) |
−0.968145 | + | 0.250390i | \(0.919441\pi\) | |||||||
\(614\) | 36.0818 | + | 62.4955i | 1.45614 | + | 2.52211i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 49.4622 | 1.99289 | ||||||||
\(617\) | 5.36376 | + | 9.29031i | 0.215937 | + | 0.374014i | 0.953562 | − | 0.301197i | \(-0.0973861\pi\) |
−0.737625 | + | 0.675210i | \(0.764053\pi\) | |||||||
\(618\) | −11.0352 | − | 19.1136i | −0.443903 | − | 0.768862i | ||||
\(619\) | −36.1437 | −1.45274 | −0.726370 | − | 0.687304i | \(-0.758794\pi\) | ||||
−0.726370 | + | 0.687304i | \(0.758794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.35725 | − | 2.35083i | −0.0544647 | − | 0.0943357i | ||||
\(622\) | 0.237309 | − | 0.411031i | 0.00951521 | − | 0.0164808i | ||||
\(623\) | 3.01171 | + | 5.21644i | 0.120662 | + | 0.208992i | ||||
\(624\) | 12.3172 | − | 21.3341i | 0.493084 | − | 0.854046i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 52.2569 | 2.08861 | ||||||||
\(627\) | −0.160191 | + | 14.9600i | −0.00639739 | + | 0.597445i | ||||
\(628\) | −80.8768 | −3.22734 | ||||||||
\(629\) | 1.00273 | − | 1.73678i | 0.0399814 | − | 0.0692499i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7882 | + | 27.3460i | 0.628519 | + | 1.08863i | 0.987849 | + | 0.155417i | \(0.0496720\pi\) |
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(632\) | −28.3045 | + | 49.0248i | −1.12589 | + | 1.95010i | ||||
\(633\) | −10.8143 | − | 18.7309i | −0.429829 | − | 0.744485i | ||||
\(634\) | −47.0857 | −1.87001 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.24090 | − | 14.2737i | −0.326773 | − | 0.565987i | ||||
\(637\) | 24.9893 | + | 43.2827i | 0.990111 | + | 1.71492i | ||||
\(638\) | 19.4204 | 0.768859 | ||||||||
\(639\) | −3.92650 | −0.155330 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.91331 | + | 17.1704i | −0.391552 | + | 0.678188i | −0.992654 | − | 0.120984i | \(-0.961395\pi\) |
0.601102 | + | 0.799172i | \(0.294728\pi\) | |||||||
\(642\) | 2.49665 | + | 4.32432i | 0.0985349 | + | 0.170667i | ||||
\(643\) | 6.72843 | − | 11.6540i | 0.265343 | − | 0.459588i | −0.702310 | − | 0.711871i | \(-0.747848\pi\) |
0.967654 | + | 0.252283i | \(0.0811814\pi\) | |||||||
\(644\) | 4.43359 | − | 7.67920i | 0.174708 | − | 0.302603i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.13555 | − | 3.63051i | −0.241400 | − | 0.142840i | ||||
\(647\) | −4.19511 | −0.164927 | −0.0824634 | − | 0.996594i | \(-0.526279\pi\) | ||||
−0.0824634 | + | 0.996594i | \(0.526279\pi\) | |||||||
\(648\) | 17.4602 | − | 30.2420i | 0.685902 | − | 1.18802i | ||||
\(649\) | −13.7810 | + | 23.8694i | −0.540953 | + | 0.936957i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.0324 | + | 41.6253i | −0.941904 | + | 1.63143i | ||||
\(652\) | 28.7006 | + | 49.7109i | 1.12400 | + | 1.94683i | ||||
\(653\) | 12.1680 | 0.476170 | 0.238085 | − | 0.971244i | \(-0.423480\pi\) | ||||
0.238085 | + | 0.971244i | \(0.423480\pi\) | |||||||
\(654\) | −46.1372 | −1.80411 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.152019 | − | 0.263305i | −0.00593535 | − | 0.0102803i | ||||
\(657\) | 1.66556 | 0.0649798 | ||||||||
\(658\) | 55.5814 | 2.16679 | ||||||||
\(659\) | −4.12236 | − | 7.14013i | −0.160584 | − | 0.278140i | 0.774494 | − | 0.632581i | \(-0.218004\pi\) |
−0.935078 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5599 | − | 18.2902i | −0.410731 | − | 0.711407i | 0.584239 | − | 0.811582i | \(-0.301393\pi\) |
−0.994970 | + | 0.100175i | \(0.968060\pi\) | |||||||
\(662\) | 25.3075 | − | 43.8338i | 0.983603 | − | 1.70365i | ||||
\(663\) | 1.95344 | − | 3.38345i | 0.0758652 | − | 0.131402i | ||||
\(664\) | −78.3941 | −3.04228 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.16576 | 0.161420 | ||||||||
\(667\) | 0.877489 | − | 1.51986i | 0.0339765 | − | 0.0588490i | ||||
\(668\) | −11.3251 | + | 19.6156i | −0.438180 | + | 0.758951i | ||||
\(669\) | 16.9342 | + | 29.3310i | 0.654716 | + | 1.13400i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.76783 | − | 13.4543i | −0.299874 | − | 0.519397i | ||||
\(672\) | 2.29442 | 0.0885090 | ||||||||
\(673\) | 30.2802 | 1.16722 | 0.583608 | − | 0.812036i | \(-0.301641\pi\) | ||||
0.583608 | + | 0.812036i | \(0.301641\pi\) | |||||||
\(674\) | −12.5357 | − | 21.7124i | −0.482856 | − | 0.836331i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.54221 | 0.174700 | ||||||||
\(677\) | −49.9003 | −1.91783 | −0.958913 | − | 0.283701i | \(-0.908438\pi\) | ||||
−0.958913 | + | 0.283701i | \(0.908438\pi\) | |||||||
\(678\) | −14.8505 | − | 25.7219i | −0.570331 | − | 0.987842i | ||||
\(679\) | −9.88092 | + | 17.1142i | −0.379195 | + | 0.656785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.39738 | − | 11.0806i | 0.245148 | − | 0.424609i | ||||
\(682\) | −18.4539 | + | 31.9632i | −0.706638 | + | 1.22393i | ||||
\(683\) | −3.11357 | −0.119137 | −0.0595687 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595687 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(684\) | 0.105997 | − | 9.89894i | 0.00405290 | − | 0.378496i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.8436 | + | 60.3509i | −1.33034 | + | 2.30421i | ||||
\(687\) | 13.0050 | − | 22.5254i | 0.496172 | − | 0.859396i | ||||
\(688\) | −0.882861 | − | 1.52916i | −0.0336588 | − | 0.0582987i | ||||
\(689\) | 4.91985 | − | 8.52143i | 0.187431 | − | 0.324641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.2831 | −1.15202 | −0.576012 | − | 0.817441i | \(-0.695392\pi\) | ||||
−0.576012 | + | 0.817441i | \(0.695392\pi\) | |||||||
\(692\) | −43.1140 | −1.63895 | ||||||||
\(693\) | 2.78915 | + | 4.83094i | 0.105951 | + | 0.183512i | ||||
\(694\) | 6.68222 | + | 11.5740i | 0.253654 | + | 0.439341i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 28.0305 | 1.06250 | ||||||||
\(697\) | −0.0241093 | − | 0.0417585i | −0.000913204 | − | 0.00158172i | ||||
\(698\) | 1.90495 | − | 3.29948i | 0.0721035 | − | 0.124887i | ||||
\(699\) | 9.53293 | + | 16.5115i | 0.360569 | + | 0.624523i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2849 | + | 38.5987i | −0.841691 | + | 1.45785i | 0.0467733 | + | 0.998906i | \(0.485106\pi\) |
−0.888464 | + | 0.458946i | \(0.848227\pi\) | |||||||
\(702\) | 51.3483 | 1.93802 | ||||||||
\(703\) | −11.4386 | + | 6.44177i | −0.431415 | + | 0.242956i | ||||
\(704\) | −16.7014 | −0.629458 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.4457 | + | 70.0540i | −1.52219 | + | 2.63652i | ||||
\(707\) | 23.8072 | + | 41.2353i | 0.895363 | + | 1.55081i | ||||
\(708\) | −39.4597 | + | 68.3462i | −1.48299 | + | 2.56861i | ||||
\(709\) | −4.67176 | − | 8.09172i | −0.175452 | − | 0.303891i | 0.764866 | − | 0.644190i | \(-0.222805\pi\) |
−0.940317 | + | 0.340299i | \(0.889472\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.38429 | −0.239430 | ||||||||
\(712\) | 3.33795 | + | 5.78150i | 0.125095 | + | 0.216671i | ||||
\(713\) | 1.66764 | + | 2.88844i | 0.0624538 | + | 0.108173i | ||||
\(714\) | 11.5027 | 0.430479 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.5055 | − | 26.8562i | −0.579466 | − | 1.00366i | ||||
\(717\) | −1.59186 | + | 2.75718i | −0.0594490 | + | 0.102969i | ||||
\(718\) | 4.29500 | + | 7.43916i | 0.160288 | + | 0.277627i | ||||
\(719\) | −12.6987 | + | 21.9948i | −0.473581 | + | 0.820267i | −0.999543 | − | 0.0302417i | \(-0.990372\pi\) |
0.525961 | + | 0.850508i | \(0.323706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.9330 | 0.965797 | ||||||||
\(722\) | 22.4631 | + | 40.9059i | 0.835992 | + | 1.52236i | ||||
\(723\) | 27.3552 | 1.01735 | ||||||||
\(724\) | 12.3534 | − | 21.3968i | 0.459112 | − | 0.795205i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.8205 | + | 20.4737i | 0.438700 | + | 0.759851i | ||||
\(727\) | −15.7189 | + | 27.2259i | −0.582980 | + | 1.00975i | 0.412143 | + | 0.911119i | \(0.364780\pi\) |
−0.995124 | + | 0.0986328i | \(0.968553\pi\) | |||||||
\(728\) | 42.2759 | + | 73.2240i | 1.56685 | + | 2.71386i | ||||
\(729\) | 29.9869 | 1.11063 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.140016 | − | 0.242515i | −0.00517869 | − | 0.00896975i | ||||
\(732\) | −22.2419 | − | 38.5241i | −0.822085 | − | 1.42389i | ||||
\(733\) | 25.3946 | 0.937971 | 0.468985 | − | 0.883206i | \(-0.344620\pi\) | ||||
0.468985 | + | 0.883206i | \(0.344620\pi\) | |||||||
\(734\) | −47.9056 | −1.76823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0796065 | − | 0.137883i | 0.00293434 | − | 0.00508242i | ||||
\(737\) | −6.29559 | − | 10.9043i | −0.231901 | − | 0.401664i | ||||
\(738\) | 0.0500800 | − | 0.0867411i | 0.00184347 | − | 0.00319299i | ||||
\(739\) | −17.7541 | + | 30.7510i | −0.653095 | + | 1.13119i | 0.329273 | + | 0.944235i | \(0.393196\pi\) |
−0.982368 | + | 0.186959i | \(0.940137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.2838 | + | 12.5493i | −0.818614 | + | 0.461011i | ||||
\(742\) | 28.9703 | 1.06353 | ||||||||
\(743\) | 8.55493 | − | 14.8176i | 0.313850 | − | 0.543604i | −0.665342 | − | 0.746538i | \(-0.731714\pi\) |
0.979192 | + | 0.202934i | \(0.0650477\pi\) | |||||||
\(744\) | −26.6357 | + | 46.1343i | −0.976511 | + | 1.69137i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.8798 | − | 50.0213i | 1.05737 | − | 1.83141i | ||||
\(747\) | −4.42060 | − | 7.65671i | −0.161741 | − | 0.280144i | ||||
\(748\) | 5.90453 | 0.215891 | ||||||||
\(749\) | −5.86718 | −0.214382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.72562 | + | 6.45297i | 0.135950 | + | 0.235472i | 0.925960 | − | 0.377622i | \(-0.123258\pi\) |
−0.790010 | + | 0.613094i | \(0.789925\pi\) | |||||||
\(752\) | 21.0891 | 0.769041 | ||||||||
\(753\) | −5.21086 | −0.189894 | ||||||||
\(754\) | 16.5988 | + | 28.7500i | 0.604493 | + | 1.04701i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 50.5313 | + | 87.5228i | 1.83781 | + | 3.18317i | ||||
\(757\) | 26.8838 | − | 46.5640i | 0.977107 | − | 1.69240i | 0.304306 | − | 0.952574i | \(-0.401575\pi\) |
0.672801 | − | 0.739824i | \(-0.265091\pi\) | |||||||
\(758\) | 8.65994 | − | 14.9994i | 0.314543 | − | 0.544804i | ||||
\(759\) | −1.67503 | −0.0607997 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.3939 | 0.848029 | 0.424014 | − | 0.905655i | \(-0.360621\pi\) | ||||
0.424014 | + | 0.905655i | \(0.360621\pi\) | |||||||
\(762\) | 7.54647 | − | 13.0709i | 0.273380 | − | 0.473508i | ||||
\(763\) | 27.1058 | − | 46.9487i | 0.981297 | − | 1.69966i | ||||
\(764\) | −11.8068 | − | 20.4499i | −0.427154 | − | 0.739852i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.78757 | + | 6.56027i | 0.136851 | + | 0.237032i | ||||
\(767\) | −47.1152 | −1.70123 | ||||||||
\(768\) | −50.3235 | −1.81589 | ||||||||
\(769\) | 6.62236 | + | 11.4703i | 0.238808 | + | 0.413628i | 0.960373 | − | 0.278719i | \(-0.0899099\pi\) |
−0.721564 | + | 0.692347i | \(0.756577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.0606 | 1.55079 | ||||||||
\(772\) | 10.4500 | 0.376105 | ||||||||
\(773\) | −8.90262 | − | 15.4198i | −0.320205 | − | 0.554611i | 0.660325 | − | 0.750980i | \(-0.270418\pi\) |
−0.980530 | + | 0.196369i | \(0.937085\pi\) | |||||||
\(774\) | 0.290843 | − | 0.503755i | 0.0104541 | − | 0.0181071i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.9512 | + | 18.9681i | −0.393127 | + | 0.680916i | ||||
\(777\) | 10.5906 | − | 18.3434i | 0.379935 | − | 0.658068i | ||||
\(778\) | 23.0658 | 0.826949 | ||||||||
\(779\) | −0.00337965 | + | 0.315621i | −0.000121088 | + | 0.0113083i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.66521 | + | 13.2765i | −0.274283 | + | 0.475072i | ||||
\(782\) | 0.399096 | − | 0.691255i | 0.0142716 | − | 0.0247192i | ||||
\(783\) | 10.0011 | + | 17.3224i | 0.357409 | + | 0.619051i | ||||
\(784\) | −27.9160 | + | 48.3520i | −0.997001 | + | 1.72686i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −62.5939 | −2.23265 | ||||||||
\(787\) | 43.5779 | 1.55339 | 0.776693 | − | 0.629880i | \(-0.216896\pi\) | ||||
0.776693 | + | 0.629880i | \(0.216896\pi\) | |||||||
\(788\) | 40.0527 | + | 69.3734i | 1.42682 | + | 2.47132i | ||||
\(789\) | −10.6356 | − | 18.4213i | −0.378636 | − | 0.655816i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8990 | 1.24087 | ||||||||
\(792\) | 3.09128 | + | 5.35425i | 0.109844 | + | 0.190255i | ||||
\(793\) | 13.2785 | − | 22.9991i | 0.471534 | − | 0.816721i | ||||
\(794\) | −32.8634 | − | 56.9210i | −1.16628 | − | 2.02005i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.7338 | − | 44.5723i | 0.912111 | − | 1.57982i | ||||
\(797\) | 16.1311 | 0.571395 | 0.285697 | − | 0.958320i | \(-0.407775\pi\) | ||||
0.285697 | + | 0.958320i | \(0.407775\pi\) | |||||||
\(798\) | −64.8023 | − | 38.3446i | −2.29398 | − | 1.35738i | ||||
\(799\) | 3.34460 | 0.118323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.376451 | + | 0.652032i | −0.0133012 | + | 0.0230384i | ||||
\(802\) | 30.9115 | + | 53.5403i | 1.09152 | + | 1.89057i | ||||
\(803\) | 3.25147 | − | 5.63170i | 0.114742 | − | 0.198739i | ||||
\(804\) | −18.0264 | − | 31.2226i | −0.635742 | − | 1.10114i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −63.0912 | −2.22229 | ||||||||
\(807\) | 2.81618 | + | 4.87777i | 0.0991344 | + | 0.171706i | ||||
\(808\) | 26.3861 | + | 45.7021i | 0.928259 | + | 1.60779i | ||||
\(809\) | 28.7134 | 1.00951 | 0.504755 | − | 0.863263i | \(-0.331583\pi\) | ||||
0.504755 | + | 0.863263i | \(0.331583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7711 | − | 18.6561i | −0.378225 | − | 0.655104i | 0.612579 | − | 0.790409i | \(-0.290132\pi\) |
−0.990804 | + | 0.135305i | \(0.956799\pi\) | |||||||
\(812\) | −32.6694 | + | 56.5850i | −1.14647 | + | 1.98575i | ||||
\(813\) | −8.24477 | − | 14.2804i | −0.289157 | − | 0.500834i | ||||
\(814\) | 8.13228 | − | 14.0855i | 0.285036 | − | 0.493697i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.36445 | 0.152786 | ||||||||
\(817\) | −0.0196275 | + | 1.83299i | −0.000686680 | + | 0.0641282i | ||||
\(818\) | −69.5634 | −2.43223 | ||||||||
\(819\) | −4.76783 | + | 8.25813i | −0.166602 | + | 0.288562i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6602 | − | 28.8563i | −0.581445 | − | 1.00709i | −0.995308 | − | 0.0967536i | \(-0.969154\pi\) |
0.413863 | − | 0.910339i | \(-0.364179\pi\) | |||||||
\(822\) | 31.4994 | − | 54.5586i | 1.09867 | − | 1.90295i | ||||
\(823\) | 18.6195 | + | 32.2499i | 0.649035 | + | 1.12416i | 0.983354 | + | 0.181701i | \(0.0581604\pi\) |
−0.334319 | + | 0.942460i | \(0.608506\pi\) | |||||||
\(824\) | 28.7422 | 1.00128 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.3590 | − | 120.133i | −2.41331 | − | 4.17997i | ||||
\(827\) | 14.5256 | + | 25.1591i | 0.505105 | + | 0.874868i | 0.999983 | + | 0.00590503i | \(0.00187964\pi\) |
−0.494877 | + | 0.868963i | \(0.664787\pi\) | |||||||
\(828\) | 1.10836 | 0.0385181 | ||||||||
\(829\) | 34.5380 | 1.19956 | 0.599778 | − | 0.800166i | \(-0.295256\pi\) | ||||
0.599778 | + | 0.800166i | \(0.295256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.25672 | + | 9.10490i | −0.182353 | + | 0.315845i | ||||
\(832\) | −14.2749 | − | 24.7249i | −0.494893 | − | 0.857180i | ||||
\(833\) | −4.42731 | + | 7.66832i | −0.153397 | + | 0.265692i | ||||
\(834\) | 5.11581 | − | 8.86085i | 0.177146 | − | 0.306826i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −33.2640 | − | 19.6829i | −1.15046 | − | 0.680746i | ||||
\(837\) | −38.0136 | −1.31394 | ||||||||
\(838\) | −16.0205 | + | 27.7483i | −0.553419 | + | 0.958550i | ||||
\(839\) | 22.3622 | − | 38.7324i | 0.772028 | − | 1.33719i | −0.164422 | − | 0.986390i | \(-0.552576\pi\) |
0.936450 | − | 0.350801i | \(-0.114091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.03413 | − | 13.9155i | 0.277039 | − | 0.479845i | ||||
\(842\) | −4.08340 | − | 7.07266i | −0.140723 | − | 0.243740i | ||||
\(843\) | 36.5758 | 1.25974 | ||||||||
\(844\) | 55.8770 | 1.92337 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.47372 | + | 6.01665i | 0.119429 | + | 0.206857i | ||||
\(847\) | −27.7784 | −0.954478 | ||||||||
\(848\) | 10.9921 | 0.377471 | ||||||||
\(849\) | −11.4605 | − | 19.8502i | −0.393324 | − | 0.681257i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.734898 | − | 1.27288i | −0.0251920 | − | 0.0436338i | ||||
\(852\) | −21.9481 | + | 38.0152i | −0.751929 | + | 1.30238i | ||||
\(853\) | 8.13013 | − | 14.0818i | 0.278370 | − | 0.482152i | −0.692610 | − | 0.721313i | \(-0.743539\pi\) |
0.970980 | + | 0.239161i | \(0.0768724\pi\) | |||||||
\(854\) | 78.1900 | 2.67561 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50273 | −0.222259 | ||||||||
\(857\) | 8.31896 | − | 14.4089i | 0.284170 | − | 0.492197i | −0.688237 | − | 0.725485i | \(-0.741615\pi\) |
0.972408 | + | 0.233288i | \(0.0749486\pi\) | |||||||
\(858\) | 15.8426 | − | 27.4403i | 0.540859 | − | 0.936795i | ||||
\(859\) | −20.1362 | − | 34.8769i | −0.687038 | − | 1.18999i | −0.972792 | − | 0.231682i | \(-0.925577\pi\) |
0.285753 | − | 0.958303i | \(-0.407756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.254637 | − | 0.441044i | −0.00867799 | − | 0.0150307i | ||||
\(862\) | 0.118897 | 0.00404965 | ||||||||
\(863\) | −32.9634 | −1.12209 | −0.561044 | − | 0.827786i | \(-0.689600\pi\) | ||||
−0.561044 | + | 0.827786i | \(0.689600\pi\) | |||||||
\(864\) | 0.907306 | + | 1.57150i | 0.0308672 | + | 0.0534635i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.5027 | 0.798655 | ||||||||
\(867\) | −25.8456 | −0.877762 | ||||||||
\(868\) | −62.0873 | − | 107.538i | −2.10738 | − | 3.65009i | ||||
\(869\) | −12.4633 | + | 21.5870i | −0.422787 | + | 0.732288i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.7618 | − | 18.6400i | 0.364651 | − | 0.631594i | ||||
\(872\) | 30.0420 | − | 52.0343i | 1.01735 | − | 1.76210i | ||||
\(873\) | −2.47014 | −0.0836016 | ||||||||
\(874\) | −4.55267 | + | 2.56389i | −0.153996 | + | 0.0867248i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.31004 | − | 16.1255i | 0.314557 | − | 0.544829i | ||||
\(877\) | −0.106600 | + | 0.184636i | −0.00359962 | + | 0.00623472i | −0.867820 | − | 0.496879i | \(-0.834479\pi\) |
0.864220 | + | 0.503114i | \(0.167812\pi\) | |||||||
\(878\) | 27.3271 | + | 47.3319i | 0.922244 | + | 1.59737i | ||||
\(879\) | −14.1942 | + | 24.5851i | −0.478759 | + | 0.829236i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.8661 | 1.74741 | 0.873707 | − | 0.486453i | \(-0.161710\pi\) | ||||
0.873707 | + | 0.486453i | \(0.161710\pi\) | |||||||
\(882\) | −18.3929 | −0.619321 | ||||||||
\(883\) | −20.8225 | − | 36.0657i | −0.700734 | − | 1.21371i | −0.968209 | − | 0.250142i | \(-0.919523\pi\) |
0.267475 | − | 0.963565i | \(-0.413811\pi\) | |||||||
\(884\) | 5.04667 | + | 8.74109i | 0.169738 | + | 0.293995i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.4083 | −1.65990 | ||||||||
\(887\) | −2.04663 | − | 3.54486i | −0.0687190 | − | 0.119025i | 0.829619 | − | 0.558330i | \(-0.188558\pi\) |
−0.898338 | + | 0.439306i | \(0.855225\pi\) | |||||||
\(888\) | 11.7378 | − | 20.3305i | 0.393895 | − | 0.682246i | ||||
\(889\) | 8.86718 | + | 15.3584i | 0.297396 | + | 0.515104i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.68823 | − | 13.3164i | 0.257565 | − | 0.446116i | ||||
\(892\) | −87.4987 | −2.92967 | ||||||||
\(893\) | −18.8423 | − | 11.1493i | −0.630533 | − | 0.373097i | ||||
\(894\) | −68.8859 | −2.30389 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 43.4984 | − | 75.3414i | 1.45318 | − | 2.51698i | ||||
\(897\) | −1.43167 | − | 2.47972i | −0.0478020 | − | 0.0827955i | ||||
\(898\) | 15.3479 | − | 26.5834i | 0.512167 | − | 0.887099i | ||||
\(899\) | −12.2882 | − | 21.2838i | −0.409835 | − | 0.709855i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.74328 | 0.0580772 | ||||||||
\(902\) | −0.195530 | − | 0.338668i | −0.00651043 | − | 0.0112764i | ||||
\(903\) | −1.47882 | − | 2.56139i | −0.0492120 | − | 0.0852377i | ||||
\(904\) | 38.6794 | 1.28646 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.4133 | + | 42.2851i | 0.811078 | + | 1.40483i | ||||
\(907\) | −4.20363 | + | 7.28090i | −0.139579 | + | 0.241758i | −0.927337 | − | 0.374226i | \(-0.877908\pi\) |
0.787758 | + | 0.615985i | \(0.211242\pi\) | |||||||
\(908\) | 16.5275 | + | 28.6265i | 0.548486 | + | 0.950005i | ||||
\(909\) | −2.97580 | + | 5.15423i | −0.0987009 | + | 0.170955i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.87918 | 0.294180 | 0.147090 | − | 0.989123i | \(-0.453009\pi\) | ||||
0.147090 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(912\) | −24.5877 | − | 14.5490i | −0.814181 | − | 0.481764i | ||||
\(913\) | −34.5192 | −1.14242 | ||||||||
\(914\) | −34.7772 | + | 60.2359i | −1.15033 | + | 1.99243i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.5983 | + | 58.1939i | 1.11012 | + | 1.92278i | ||||
\(917\) | 36.7742 | − | 63.6948i | 1.21439 | − | 2.10339i | ||||
\(918\) | 4.54865 | + | 7.87849i | 0.150128 | + | 0.260029i | ||||
\(919\) | −45.9834 | −1.51685 | −0.758427 | − | 0.651758i | \(-0.774032\pi\) | ||||
−0.758427 | + | 0.651758i | \(0.774032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.9319 | + | 39.7191i | 0.755630 | + | 1.30879i | ||||
\(922\) | −6.53290 | − | 11.3153i | −0.215150 | − | 0.372650i | ||||
\(923\) | −26.2062 | −0.862587 | ||||||||
\(924\) | 62.3623 | 2.05157 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.0231 | + | 38.1452i | −0.723725 | + | 1.25353i | ||||
\(927\) | 1.62076 | + | 2.80724i | 0.0532327 | + | 0.0922017i | ||||
\(928\) | −0.586589 | + | 1.01600i | −0.0192557 | + | 0.0333519i | ||||
\(929\) | 11.0889 | − | 19.2065i | 0.363814 | − | 0.630145i | −0.624771 | − | 0.780808i | \(-0.714808\pi\) |
0.988585 | + | 0.150663i | \(0.0481409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.5044 | − | 28.4421i | 1.65521 | − | 0.932152i | ||||
\(932\) | −49.2564 | −1.61345 | ||||||||
\(933\) | 0.150822 | − | 0.261231i | 0.00493769 | − | 0.00855233i | ||||
\(934\) | 35.3436 | − | 61.2170i | 1.15648 | − | 2.00308i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.28430 | + | 9.15267i | −0.172723 | + | 0.299165i | ||||
\(937\) | −17.1637 | − | 29.7284i | −0.560714 | − | 0.971186i | −0.997434 | − | 0.0715882i | \(-0.977193\pi\) |
0.436720 | − | 0.899598i | \(-0.356140\pi\) | |||||||
\(938\) | 63.3706 | 2.06912 | ||||||||
\(939\) | 33.2120 | 1.08383 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8606 | − | 29.2035i | −0.549641 | − | 0.952006i | −0.998299 | − | 0.0583025i | \(-0.981431\pi\) |
0.448658 | − | 0.893704i | \(-0.351902\pi\) | |||||||
\(942\) | −76.8923 | −2.50529 | ||||||||
\(943\) | −0.0353393 | −0.00115080 | ||||||||
\(944\) | −26.3167 | − | 45.5818i | −0.856535 | − | 1.48356i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.13555 | − | 1.96683i | −0.0369200 | − | 0.0639473i | ||||
\(947\) | 11.0732 | − | 19.1794i | 0.359832 | − | 0.623248i | −0.628100 | − | 0.778132i | \(-0.716167\pi\) |
0.987933 | + | 0.154885i | \(0.0495006\pi\) | |||||||
\(948\) | −35.6865 | + | 61.8108i | −1.15904 | + | 2.00752i | ||||
\(949\) | 11.1163 | 0.360849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.9254 | −0.970398 | ||||||||
\(952\) | −7.48995 | + | 12.9730i | −0.242751 | + | 0.420457i | ||||
\(953\) | 18.6484 | − | 32.2999i | 0.604079 | − | 1.04630i | −0.388117 | − | 0.921610i | \(-0.626874\pi\) |
0.992196 | − | 0.124686i | \(-0.0397924\pi\) | |||||||
\(954\) | 1.81058 | + | 3.13602i | 0.0586198 | + | 0.101532i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.11254 | − | 7.12313i | −0.133009 | − | 0.230378i | ||||
\(957\) | 12.3426 | 0.398981 | ||||||||
\(958\) | −19.7761 | −0.638936 | ||||||||
\(959\) | 37.0121 | + | 64.1069i | 1.19518 | + | 2.07012i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7069 | 0.506674 | ||||||||
\(962\) | 27.8030 | 0.896405 | ||||||||
\(963\) | −0.366686 | − | 0.635118i | −0.0118163 | − | 0.0204664i | ||||
\(964\) | −35.3359 | + | 61.2036i | −1.13809 | + | 1.97123i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.21516 | − | 7.30087i | 0.135621 | − | 0.234902i | ||||
\(967\) | 9.33679 | − | 16.1718i | 0.300251 | − | 0.520050i | −0.675942 | − | 0.736955i | \(-0.736263\pi\) |
0.976193 | + | 0.216905i | \(0.0695963\pi\) | |||||||
\(968\) | −30.7875 | −0.989547 | ||||||||
\(969\) | −3.89946 | − | 2.30738i | −0.125269 | − | 0.0741236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.2903 | + | 24.7515i | −0.458598 | + | 0.794314i | −0.998887 | − | 0.0471649i | \(-0.984981\pi\) |
0.540290 | + | 0.841479i | \(0.318315\pi\) | |||||||
\(972\) | −11.6341 | + | 20.1509i | −0.373165 | + | 0.646341i | ||||
\(973\) | 6.01113 | + | 10.4116i | 0.192708 | + | 0.333780i | ||||
\(974\) | 1.34798 | − | 2.33477i | 0.0431921 | − | 0.0748109i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.6674 | 0.949630 | ||||||||
\(977\) | 58.1909 | 1.86169 | 0.930846 | − | 0.365411i | \(-0.119072\pi\) | ||||
0.930846 | + | 0.365411i | \(0.119072\pi\) | |||||||
\(978\) | 27.2866 | + | 47.2618i | 0.872530 | + | 1.51127i | ||||
\(979\) | 1.46980 | + | 2.54576i | 0.0469749 | + | 0.0813628i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.77622 | 0.216348 | ||||||||
\(982\) | −16.0947 | − | 27.8768i | −0.513602 | − | 0.889586i | ||||
\(983\) | −24.0363 | + | 41.6320i | −0.766638 | + | 1.32786i | 0.172738 | + | 0.984968i | \(0.444738\pi\) |
−0.939376 | + | 0.342888i | \(0.888595\pi\) | |||||||
\(984\) | −0.282220 | − | 0.488819i | −0.00899684 | − | 0.0155830i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.94078 | + | 5.09359i | −0.0936536 | + | 0.162213i | ||||
\(987\) | 35.3249 | 1.12440 | ||||||||
\(988\) | 0.707444 | − | 66.0674i | 0.0225068 | − | 2.10188i | ||||
\(989\) | −0.205235 | −0.00652609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1976 | + | 33.2512i | −0.609832 | + | 1.05626i | 0.381436 | + | 0.924395i | \(0.375430\pi\) |
−0.991268 | + | 0.131865i | \(0.957904\pi\) | |||||||
\(992\) | −1.11480 | − | 1.93089i | −0.0353949 | − | 0.0613057i | ||||
\(993\) | 16.0842 | − | 27.8587i | 0.510417 | − | 0.884069i | ||||
\(994\) | −38.5785 | − | 66.8200i | −1.22364 | − | 2.11940i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −98.8399 | −3.13186 | ||||||||
\(997\) | −18.9109 | − | 32.7546i | −0.598914 | − | 1.03735i | −0.992982 | − | 0.118268i | \(-0.962266\pi\) |
0.394068 | − | 0.919081i | \(-0.371067\pi\) | |||||||
\(998\) | −29.6472 | − | 51.3504i | −0.938465 | − | 1.62547i | ||||
\(999\) | 16.7518 | 0.530004 |
(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 | 475.2.e.g.201.1 | 12 | ||
5.2 | odd | 4 | 95.2.i.b.49.1 | ✓ | 12 | ||
5.3 | odd | 4 | 95.2.i.b.49.6 | yes | 12 | ||
5.4 | even | 2 | inner | 475.2.e.g.201.6 | 12 | ||
15.2 | even | 4 | 855.2.be.d.334.6 | 12 | |||
15.8 | even | 4 | 855.2.be.d.334.1 | 12 | |||
19.7 | even | 3 | inner | 475.2.e.g.26.1 | 12 | ||
19.8 | odd | 6 | 9025.2.a.bt.1.1 | 6 | |||
19.11 | even | 3 | 9025.2.a.bu.1.6 | 6 | |||
95.7 | odd | 12 | 95.2.i.b.64.6 | yes | 12 | ||
95.8 | even | 12 | 1805.2.b.g.1084.6 | 6 | |||
95.27 | even | 12 | 1805.2.b.g.1084.1 | 6 | |||
95.49 | even | 6 | 9025.2.a.bu.1.1 | 6 | |||
95.64 | even | 6 | inner | 475.2.e.g.26.6 | 12 | ||
95.68 | odd | 12 | 1805.2.b.f.1084.1 | 6 | |||
95.83 | odd | 12 | 95.2.i.b.64.1 | yes | 12 | ||
95.84 | odd | 6 | 9025.2.a.bt.1.6 | 6 | |||
95.87 | odd | 12 | 1805.2.b.f.1084.6 | 6 | |||
285.83 | even | 12 | 855.2.be.d.64.6 | 12 | |||
285.197 | even | 12 | 855.2.be.d.64.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.1 | ✓ | 12 | 5.2 | odd | 4 | ||
95.2.i.b.49.6 | yes | 12 | 5.3 | odd | 4 | ||
95.2.i.b.64.1 | yes | 12 | 95.83 | odd | 12 | ||
95.2.i.b.64.6 | yes | 12 | 95.7 | odd | 12 | ||
475.2.e.g.26.1 | 12 | 19.7 | even | 3 | inner | ||
475.2.e.g.26.6 | 12 | 95.64 | even | 6 | inner | ||
475.2.e.g.201.1 | 12 | 1.1 | even | 1 | trivial | ||
475.2.e.g.201.6 | 12 | 5.4 | even | 2 | inner | ||
855.2.be.d.64.1 | 12 | 285.197 | even | 12 | |||
855.2.be.d.64.6 | 12 | 285.83 | even | 12 | |||
855.2.be.d.334.1 | 12 | 15.8 | even | 4 | |||
855.2.be.d.334.6 | 12 | 15.2 | even | 4 | |||
1805.2.b.f.1084.1 | 6 | 95.68 | odd | 12 | |||
1805.2.b.f.1084.6 | 6 | 95.87 | odd | 12 | |||
1805.2.b.g.1084.1 | 6 | 95.27 | even | 12 | |||
1805.2.b.g.1084.6 | 6 | 95.8 | even | 12 | |||
9025.2.a.bt.1.1 | 6 | 19.8 | odd | 6 | |||
9025.2.a.bt.1.6 | 6 | 95.84 | odd | 6 | |||
9025.2.a.bu.1.1 | 6 | 95.49 | even | 6 | |||
9025.2.a.bu.1.6 | 6 | 19.11 | even | 3 |