Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(-0.793353 + 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.a.1011.2 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.937379 | + | 0.541196i | −0.541196 | + | 0.312460i | −0.745564 | − | 0.666435i | \(-0.767820\pi\) |
0.204367 | + | 0.978894i | \(0.434486\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.937379 | − | 0.541196i | −0.419209 | − | 0.242030i | 0.275530 | − | 0.961292i | \(-0.411147\pi\) |
−0.694739 | + | 0.719262i | \(0.744480\pi\) | |||||||
\(6\) | 1.08239 | 0.441885 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.914214 | + | 1.58346i | −0.304738 | + | 0.527821i | ||||
\(10\) | 0.541196 | + | 0.937379i | 0.171141 | + | 0.296425i | ||||
\(11\) | −1.89097 | + | 2.72474i | −0.570149 | + | 0.821541i | ||||
\(12\) | −0.937379 | − | 0.541196i | −0.270598 | − | 0.156230i | ||||
\(13\) | 2.29610 | 0.636824 | 0.318412 | − | 0.947952i | \(-0.396851\pi\) | ||||
0.318412 | + | 0.947952i | \(0.396851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17157 | 0.302499 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.58346 | − | 0.914214i | 0.373226 | − | 0.215482i | ||||
\(19\) | 2.77164 | − | 4.80062i | 0.635858 | − | 1.10134i | −0.350475 | − | 0.936572i | \(-0.613980\pi\) |
0.986333 | − | 0.164766i | \(-0.0526867\pi\) | |||||||
\(20\) | − | 1.08239i | − | 0.242030i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | − | 1.41421i | 0.639602 | − | 0.301511i | ||||
\(23\) | −3.12132 | + | 5.40629i | −0.650840 | + | 1.12729i | 0.332079 | + | 0.943252i | \(0.392250\pi\) |
−0.982919 | + | 0.184037i | \(0.941083\pi\) | |||||||
\(24\) | 0.541196 | + | 0.937379i | 0.110471 | + | 0.191342i | ||||
\(25\) | −1.91421 | − | 3.31552i | −0.382843 | − | 0.663103i | ||||
\(26\) | −1.98848 | − | 1.14805i | −0.389973 | − | 0.225151i | ||||
\(27\) | − | 5.22625i | − | 1.00579i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.75736i | − | 0.326333i | −0.986599 | − | 0.163167i | \(-0.947829\pi\) | ||
0.986599 | − | 0.163167i | \(-0.0521708\pi\) | |||||||
\(30\) | −1.01461 | − | 0.585786i | −0.185242 | − | 0.106949i | ||||
\(31\) | −1.21193 | + | 0.699709i | −0.217669 | + | 0.125671i | −0.604871 | − | 0.796324i | \(-0.706775\pi\) |
0.387201 | + | 0.921995i | \(0.373442\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0.297934 | − | 3.57750i | 0.0518637 | − | 0.622764i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −4.80062 | + | 2.77164i | −0.778763 | + | 0.449619i | ||||
\(39\) | −2.15232 | + | 1.24264i | −0.344647 | + | 0.198982i | ||||
\(40\) | −0.541196 | + | 0.937379i | −0.0855706 | + | 0.148213i | ||||
\(41\) | 4.59220 | 0.717181 | 0.358591 | − | 0.933495i | \(-0.383257\pi\) | ||||
0.358591 | + | 0.933495i | \(0.383257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | −3.30518 | − | 0.275255i | −0.498275 | − | 0.0414963i | ||||
\(45\) | 1.71393 | − | 0.989538i | 0.255498 | − | 0.147512i | ||||
\(46\) | 5.40629 | − | 3.12132i | 0.797113 | − | 0.460214i | ||||
\(47\) | −4.25151 | − | 2.45461i | −0.620147 | − | 0.358042i | 0.156779 | − | 0.987634i | \(-0.449889\pi\) |
−0.776926 | + | 0.629592i | \(0.783222\pi\) | |||||||
\(48\) | − | 1.08239i | − | 0.156230i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.82843i | 0.541421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.14805 | + | 1.98848i | 0.159206 | + | 0.275753i | ||||
\(53\) | −2.24264 | − | 3.88437i | −0.308050 | − | 0.533559i | 0.669885 | − | 0.742464i | \(-0.266343\pi\) |
−0.977936 | + | 0.208906i | \(0.933010\pi\) | |||||||
\(54\) | −2.61313 | + | 4.52607i | −0.355601 | + | 0.615920i | ||||
\(55\) | 3.24718 | − | 1.53073i | 0.437849 | − | 0.206404i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | −0.878680 | + | 1.52192i | −0.115376 | + | 0.199838i | ||||
\(59\) | −6.24000 | + | 3.60266i | −0.812378 | + | 0.469027i | −0.847781 | − | 0.530346i | \(-0.822062\pi\) |
0.0354028 | + | 0.999373i | \(0.488729\pi\) | |||||||
\(60\) | 0.585786 | + | 1.01461i | 0.0756247 | + | 0.130986i | ||||
\(61\) | 2.77164 | − | 4.80062i | 0.354872 | − | 0.614656i | −0.632224 | − | 0.774786i | \(-0.717858\pi\) |
0.987096 | + | 0.160129i | \(0.0511911\pi\) | |||||||
\(62\) | 1.39942 | 0.177726 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.15232 | − | 1.24264i | −0.266962 | − | 0.154131i | ||||
\(66\) | −2.04677 | + | 2.94924i | −0.251940 | + | 0.363027i | ||||
\(67\) | −5.82843 | − | 10.0951i | −0.712056 | − | 1.23332i | −0.964084 | − | 0.265597i | \(-0.914431\pi\) |
0.252028 | − | 0.967720i | \(-0.418902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.75699i | − | 0.813445i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 1.58346 | + | 0.914214i | 0.186613 | + | 0.107741i | ||||
\(73\) | −7.83938 | − | 13.5782i | −0.917530 | − | 1.58921i | −0.803155 | − | 0.595771i | \(-0.796847\pi\) |
−0.114375 | − | 0.993438i | \(-0.536487\pi\) | |||||||
\(74\) | 5.19615 | − | 3.00000i | 0.604040 | − | 0.348743i | ||||
\(75\) | 3.58869 | + | 2.07193i | 0.414386 | + | 0.239246i | ||||
\(76\) | 5.54328 | 0.635858 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.48528 | 0.281403 | ||||||||
\(79\) | −7.34847 | − | 4.24264i | −0.826767 | − | 0.477334i | 0.0259772 | − | 0.999663i | \(-0.491730\pi\) |
−0.852745 | + | 0.522328i | \(0.825064\pi\) | |||||||
\(80\) | 0.937379 | − | 0.541196i | 0.104802 | − | 0.0605076i | ||||
\(81\) | 0.0857864 | + | 0.148586i | 0.00953183 | + | 0.0165096i | ||||
\(82\) | −3.97696 | − | 2.29610i | −0.439182 | − | 0.253562i | ||||
\(83\) | −13.3827 | −1.46894 | −0.734469 | − | 0.678643i | \(-0.762569\pi\) | ||||
−0.734469 | + | 0.678643i | \(0.762569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.12132 | + | 3.67423i | −0.228748 | + | 0.396203i | ||||
\(87\) | 0.951076 | + | 1.64731i | 0.101966 | + | 0.176610i | ||||
\(88\) | 2.72474 | + | 1.89097i | 0.290459 | + | 0.201578i | ||||
\(89\) | 3.08669 | + | 1.78210i | 0.327188 | + | 0.188902i | 0.654592 | − | 0.755982i | \(-0.272840\pi\) |
−0.327404 | + | 0.944885i | \(0.606174\pi\) | |||||||
\(90\) | −1.97908 | −0.208613 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.24264 | −0.650840 | ||||||||
\(93\) | 0.757359 | − | 1.31178i | 0.0785345 | − | 0.136026i | ||||
\(94\) | 2.45461 | + | 4.25151i | 0.253174 | + | 0.438510i | ||||
\(95\) | −5.19615 | + | 3.00000i | −0.533114 | + | 0.307794i | ||||
\(96\) | −0.541196 | + | 0.937379i | −0.0552356 | + | 0.0956709i | ||||
\(97\) | − | 8.60474i | − | 0.873679i | −0.899539 | − | 0.436840i | \(-0.856098\pi\) | ||
0.899539 | − | 0.436840i | \(-0.143902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.58579 | − | 5.48528i | −0.259881 | − | 0.551292i | ||||
\(100\) | 1.91421 | − | 3.31552i | 0.191421 | − | 0.331552i | ||||
\(101\) | −8.31492 | − | 14.4019i | −0.827365 | − | 1.43304i | −0.900098 | − | 0.435687i | \(-0.856506\pi\) |
0.0727333 | − | 0.997351i | \(-0.476828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.57717 | − | 3.21998i | −0.549535 | − | 0.317274i | 0.199400 | − | 0.979918i | \(-0.436101\pi\) |
−0.748934 | + | 0.662644i | \(0.769434\pi\) | |||||||
\(104\) | − | 2.29610i | − | 0.225151i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.48528i | 0.435649i | ||||||||
\(107\) | 11.0227 | + | 6.36396i | 1.06561 | + | 0.615227i | 0.926977 | − | 0.375117i | \(-0.122398\pi\) |
0.138628 | + | 0.990345i | \(0.455731\pi\) | |||||||
\(108\) | 4.52607 | − | 2.61313i | 0.435521 | − | 0.251448i | ||||
\(109\) | −3.04384 | + | 1.75736i | −0.291547 | + | 0.168324i | −0.638639 | − | 0.769506i | \(-0.720502\pi\) |
0.347093 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(110\) | −3.57750 | − | 0.297934i | −0.341102 | − | 0.0284069i | ||||
\(111\) | − | 6.49435i | − | 0.616417i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.41421 | −0.133038 | −0.0665190 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665190 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | 5.85172 | − | 3.37849i | 0.545676 | − | 0.315046i | ||||
\(116\) | 1.52192 | − | 0.878680i | 0.141307 | − | 0.0815834i | ||||
\(117\) | −2.09913 | + | 3.63579i | −0.194064 | + | 0.336129i | ||||
\(118\) | 7.20533 | 0.663304 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 1.17157i | − | 0.106949i | ||||||
\(121\) | −3.84847 | − | 10.3048i | −0.349861 | − | 0.936802i | ||||
\(122\) | −4.80062 | + | 2.77164i | −0.434628 | + | 0.250932i | ||||
\(123\) | −4.30463 | + | 2.48528i | −0.388136 | + | 0.224090i | ||||
\(124\) | −1.21193 | − | 0.699709i | −0.108835 | − | 0.0628357i | ||||
\(125\) | 9.55582i | 0.854699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 2.29610 | + | 3.97696i | 0.202160 | + | 0.350152i | ||||
\(130\) | 1.24264 | + | 2.15232i | 0.108987 | + | 0.188771i | ||||
\(131\) | −3.44415 | + | 5.96544i | −0.300917 | + | 0.521203i | −0.976344 | − | 0.216224i | \(-0.930626\pi\) |
0.675427 | + | 0.737427i | \(0.263959\pi\) | |||||||
\(132\) | 3.24718 | − | 1.53073i | 0.282630 | − | 0.133233i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.6569i | 1.00700i | ||||||||
\(135\) | −2.82843 | + | 4.89898i | −0.243432 | + | 0.421637i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.48528 | + | 14.6969i | 0.724947 | + | 1.25564i | 0.958996 | + | 0.283420i | \(0.0914689\pi\) |
−0.234050 | + | 0.972225i | \(0.575198\pi\) | |||||||
\(138\) | −3.37849 | + | 5.85172i | −0.287596 | + | 0.498132i | ||||
\(139\) | −13.3827 | −1.13510 | −0.567551 | − | 0.823338i | \(-0.692109\pi\) | ||||
−0.567551 | + | 0.823338i | \(0.692109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.31371 | 0.447495 | ||||||||
\(142\) | −1.73205 | − | 1.00000i | −0.145350 | − | 0.0839181i | ||||
\(143\) | −4.34186 | + | 6.25629i | −0.363084 | + | 0.523177i | ||||
\(144\) | −0.914214 | − | 1.58346i | −0.0761845 | − | 0.131955i | ||||
\(145\) | −0.951076 | + | 1.64731i | −0.0789826 | + | 0.136802i | ||||
\(146\) | 15.6788i | 1.29758i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 5.82655 | + | 3.36396i | 0.477330 | + | 0.275586i | 0.719303 | − | 0.694696i | \(-0.244461\pi\) |
−0.241973 | + | 0.970283i | \(0.577795\pi\) | |||||||
\(150\) | −2.07193 | − | 3.58869i | −0.169172 | − | 0.293015i | ||||
\(151\) | 5.19615 | − | 3.00000i | 0.422857 | − | 0.244137i | −0.273442 | − | 0.961888i | \(-0.588162\pi\) |
0.696299 | + | 0.717752i | \(0.254829\pi\) | |||||||
\(152\) | −4.80062 | − | 2.77164i | −0.389382 | − | 0.224810i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.51472 | 0.121665 | ||||||||
\(156\) | −2.15232 | − | 1.24264i | −0.172323 | − | 0.0994909i | ||||
\(157\) | 9.98951 | − | 5.76745i | 0.797250 | − | 0.460292i | −0.0452587 | − | 0.998975i | \(-0.514411\pi\) |
0.842509 | + | 0.538683i | \(0.181078\pi\) | |||||||
\(158\) | 4.24264 | + | 7.34847i | 0.337526 | + | 0.584613i | ||||
\(159\) | 4.20441 | + | 2.42742i | 0.333431 | + | 0.192507i | ||||
\(160\) | −1.08239 | −0.0855706 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 0.171573i | − | 0.0134800i | ||||||
\(163\) | 4.07107 | − | 7.05130i | 0.318871 | − | 0.552300i | −0.661382 | − | 0.750049i | \(-0.730030\pi\) |
0.980253 | + | 0.197749i | \(0.0633631\pi\) | |||||||
\(164\) | 2.29610 | + | 3.97696i | 0.179295 | + | 0.310549i | ||||
\(165\) | −2.21541 | + | 3.19224i | −0.172469 | + | 0.248515i | ||||
\(166\) | 11.5897 | + | 6.69133i | 0.899537 | + | 0.519348i | ||||
\(167\) | −20.2710 | −1.56861 | −0.784307 | − | 0.620373i | \(-0.786981\pi\) | ||||
−0.784307 | + | 0.620373i | \(0.786981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.72792 | −0.594456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.06774 | + | 8.77758i | 0.387540 | + | 0.671238i | ||||
\(172\) | 3.67423 | − | 2.12132i | 0.280158 | − | 0.161749i | ||||
\(173\) | 12.9071 | − | 22.3558i | 0.981310 | − | 1.69968i | 0.324002 | − | 0.946056i | \(-0.394971\pi\) |
0.657308 | − | 0.753622i | \(-0.271695\pi\) | |||||||
\(174\) | − | 1.90215i | − | 0.144202i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.41421 | − | 3.00000i | −0.106600 | − | 0.226134i | ||||
\(177\) | 3.89949 | − | 6.75412i | 0.293104 | − | 0.507671i | ||||
\(178\) | −1.78210 | − | 3.08669i | −0.133574 | − | 0.231357i | ||||
\(179\) | 2.82843 | + | 4.89898i | 0.211407 | + | 0.366167i | 0.952155 | − | 0.305616i | \(-0.0988623\pi\) |
−0.740748 | + | 0.671783i | \(0.765529\pi\) | |||||||
\(180\) | 1.71393 | + | 0.989538i | 0.127749 | + | 0.0737558i | ||||
\(181\) | 20.4567i | 1.52053i | 0.649612 | + | 0.760266i | \(0.274931\pi\) | ||||
−0.649612 | + | 0.760266i | \(0.725069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | 5.40629 | + | 3.12132i | 0.398557 | + | 0.230107i | ||||
\(185\) | 5.62427 | − | 3.24718i | 0.413505 | − | 0.238737i | ||||
\(186\) | −1.31178 | + | 0.757359i | −0.0961847 | + | 0.0555323i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 4.90923i | − | 0.358042i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | 0.878680 | − | 1.52192i | 0.0635790 | − | 0.110122i | −0.832484 | − | 0.554049i | \(-0.813082\pi\) |
0.896063 | + | 0.443927i | \(0.146415\pi\) | |||||||
\(192\) | 0.937379 | − | 0.541196i | 0.0676495 | − | 0.0390575i | ||||
\(193\) | −2.15232 | + | 1.24264i | −0.154927 | + | 0.0894472i | −0.575459 | − | 0.817830i | \(-0.695177\pi\) |
0.420532 | + | 0.907278i | \(0.361843\pi\) | |||||||
\(194\) | −4.30237 | + | 7.45193i | −0.308892 | + | 0.535017i | ||||
\(195\) | 2.69005 | 0.192638 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.4853i | − | 1.45952i | −0.683706 | − | 0.729758i | \(-0.739633\pi\) | ||
0.683706 | − | 0.729758i | \(-0.260367\pi\) | |||||||
\(198\) | −0.503284 | + | 6.04329i | −0.0357668 | + | 0.429478i | ||||
\(199\) | 21.3518 | − | 12.3275i | 1.51359 | − | 0.873870i | 0.513715 | − | 0.857961i | \(-0.328269\pi\) |
0.999873 | − | 0.0159092i | \(-0.00506428\pi\) | |||||||
\(200\) | −3.31552 | + | 1.91421i | −0.234442 | + | 0.135355i | ||||
\(201\) | 10.9269 | + | 6.30864i | 0.770724 | + | 0.444977i | ||||
\(202\) | 16.6298i | 1.17007i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.30463 | − | 2.48528i | −0.300649 | − | 0.173580i | ||||
\(206\) | 3.21998 | + | 5.57717i | 0.224347 | + | 0.388580i | ||||
\(207\) | −5.70711 | − | 9.88500i | −0.396671 | − | 0.687055i | ||||
\(208\) | −1.14805 | + | 1.98848i | −0.0796030 | + | 0.137876i | ||||
\(209\) | 7.83938 | + | 16.6298i | 0.542261 | + | 1.15031i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7279i | 1.70234i | 0.524890 | + | 0.851170i | \(0.324107\pi\) | ||||
−0.524890 | + | 0.851170i | \(0.675893\pi\) | |||||||
\(212\) | 2.24264 | − | 3.88437i | 0.154025 | − | 0.266779i | ||||
\(213\) | −1.87476 | + | 1.08239i | −0.128456 | + | 0.0741643i | ||||
\(214\) | −6.36396 | − | 11.0227i | −0.435031 | − | 0.753497i | ||||
\(215\) | −2.29610 | + | 3.97696i | −0.156593 | + | 0.271227i | ||||
\(216\) | −5.22625 | −0.355601 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.51472 | 0.238047 | ||||||||
\(219\) | 14.6969 | + | 8.48528i | 0.993127 | + | 0.573382i | ||||
\(220\) | 2.94924 | + | 2.04677i | 0.198838 | + | 0.137993i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.24718 | + | 5.62427i | −0.217936 | + | 0.377477i | ||||
\(223\) | − | 7.89377i | − | 0.528606i | −0.964440 | − | 0.264303i | \(-0.914858\pi\) | ||
0.964440 | − | 0.264303i | \(-0.0851419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 1.22474 | + | 0.707107i | 0.0814688 | + | 0.0470360i | ||||
\(227\) | 0.475538 | + | 0.823656i | 0.0315626 | + | 0.0546680i | 0.881375 | − | 0.472417i | \(-0.156618\pi\) |
−0.849813 | + | 0.527085i | \(0.823285\pi\) | |||||||
\(228\) | −5.19615 | + | 3.00000i | −0.344124 | + | 0.198680i | ||||
\(229\) | 24.6659 | + | 14.2409i | 1.62997 | + | 0.941064i | 0.984100 | + | 0.177616i | \(0.0568386\pi\) |
0.645870 | + | 0.763447i | \(0.276495\pi\) | |||||||
\(230\) | −6.75699 | −0.445542 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.75736 | −0.115376 | ||||||||
\(233\) | −7.34847 | − | 4.24264i | −0.481414 | − | 0.277945i | 0.239591 | − | 0.970874i | \(-0.422987\pi\) |
−0.721006 | + | 0.692929i | \(0.756320\pi\) | |||||||
\(234\) | 3.63579 | − | 2.09913i | 0.237679 | − | 0.137224i | ||||
\(235\) | 2.65685 | + | 4.60181i | 0.173314 | + | 0.300189i | ||||
\(236\) | −6.24000 | − | 3.60266i | −0.406189 | − | 0.234513i | ||||
\(237\) | 9.18440 | 0.596591 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.4853i | − | 1.71319i | −0.515989 | − | 0.856595i | \(-0.672575\pi\) | ||
0.515989 | − | 0.856595i | \(-0.327425\pi\) | |||||||
\(240\) | −0.585786 | + | 1.01461i | −0.0378124 | + | 0.0654929i | ||||
\(241\) | 2.29610 | + | 3.97696i | 0.147905 | + | 0.256179i | 0.930453 | − | 0.366411i | \(-0.119414\pi\) |
−0.782548 | + | 0.622590i | \(0.786080\pi\) | |||||||
\(242\) | −1.81954 | + | 10.8485i | −0.116964 | + | 0.697366i | ||||
\(243\) | 13.4174 | + | 7.74652i | 0.860725 | + | 0.496940i | ||||
\(244\) | 5.54328 | 0.354872 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.97056 | 0.316912 | ||||||||
\(247\) | 6.36396 | − | 11.0227i | 0.404929 | − | 0.701358i | ||||
\(248\) | 0.699709 | + | 1.21193i | 0.0444316 | + | 0.0769577i | ||||
\(249\) | 12.5446 | − | 7.24264i | 0.794983 | − | 0.458984i | ||||
\(250\) | 4.77791 | − | 8.27558i | 0.302182 | − | 0.523394i | ||||
\(251\) | 12.1689i | 0.768097i | 0.923313 | + | 0.384049i | \(0.125470\pi\) | ||||
−0.923313 | + | 0.384049i | \(0.874530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.82843 | − | 18.7279i | −0.555038 | − | 1.17741i | ||||
\(254\) | 3.00000 | − | 5.19615i | 0.188237 | − | 0.326036i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −19.0888 | − | 11.0209i | −1.19072 | − | 0.687465i | −0.232253 | − | 0.972655i | \(-0.574610\pi\) |
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(258\) | − | 4.59220i | − | 0.285898i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 2.48528i | − | 0.154131i | ||||||
\(261\) | 2.78272 | + | 1.60660i | 0.172246 | + | 0.0994461i | ||||
\(262\) | 5.96544 | − | 3.44415i | 0.368546 | − | 0.212780i | ||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | −3.57750 | − | 0.297934i | −0.220180 | − | 0.0183366i | ||||
\(265\) | 4.85483i | 0.298230i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.85786 | −0.236097 | ||||||||
\(268\) | 5.82843 | − | 10.0951i | 0.356028 | − | 0.616658i | ||||
\(269\) | −3.03958 | + | 1.75490i | −0.185327 | + | 0.106998i | −0.589793 | − | 0.807555i | \(-0.700791\pi\) |
0.404466 | + | 0.914553i | \(0.367457\pi\) | |||||||
\(270\) | 4.89898 | − | 2.82843i | 0.298142 | − | 0.172133i | ||||
\(271\) | −13.3827 | + | 23.1794i | −0.812938 | + | 1.40805i | 0.0978604 | + | 0.995200i | \(0.468800\pi\) |
−0.910799 | + | 0.412850i | \(0.864533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.9706i | − | 1.02523i | ||||||
\(275\) | 12.6537 | + | 1.05379i | 0.763044 | + | 0.0635462i | ||||
\(276\) | 5.85172 | − | 3.37849i | 0.352232 | − | 0.203361i | ||||
\(277\) | 16.2189 | − | 9.36396i | 0.974497 | − | 0.562626i | 0.0738925 | − | 0.997266i | \(-0.476458\pi\) |
0.900604 | + | 0.434640i | \(0.143124\pi\) | |||||||
\(278\) | 11.5897 | + | 6.69133i | 0.695105 | + | 0.401319i | ||||
\(279\) | − | 2.55873i | − | 0.153187i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000i | 0.715860i | 0.933748 | + | 0.357930i | \(0.116517\pi\) | ||||
−0.933748 | + | 0.357930i | \(0.883483\pi\) | |||||||
\(282\) | −4.60181 | − | 2.65685i | −0.274034 | − | 0.158213i | ||||
\(283\) | 11.2835 | + | 19.5436i | 0.670736 | + | 1.16175i | 0.977696 | + | 0.210027i | \(0.0673550\pi\) |
−0.306960 | + | 0.951723i | \(0.599312\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 3.24718 | − | 5.62427i | 0.192346 | − | 0.333153i | ||||
\(286\) | 6.88830 | − | 3.24718i | 0.407314 | − | 0.192010i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.82843i | 0.107741i | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 1.64731 | − | 0.951076i | 0.0967335 | − | 0.0558491i | ||||
\(291\) | 4.65685 | + | 8.06591i | 0.272990 | + | 0.472832i | ||||
\(292\) | 7.83938 | − | 13.5782i | 0.458765 | − | 0.794604i | ||||
\(293\) | 0.951076 | 0.0555625 | 0.0277812 | − | 0.999614i | \(-0.491156\pi\) | ||||
0.0277812 | + | 0.999614i | \(0.491156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.79899 | 0.454075 | ||||||||
\(296\) | 5.19615 | + | 3.00000i | 0.302020 | + | 0.174371i | ||||
\(297\) | 14.2402 | + | 9.88268i | 0.826300 | + | 0.573451i | ||||
\(298\) | −3.36396 | − | 5.82655i | −0.194869 | − | 0.337523i | ||||
\(299\) | −7.16687 | + | 12.4134i | −0.414471 | + | 0.717884i | ||||
\(300\) | 4.14386i | 0.239246i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 15.5885 | + | 9.00000i | 0.895533 | + | 0.517036i | ||||
\(304\) | 2.77164 | + | 4.80062i | 0.158964 | + | 0.275334i | ||||
\(305\) | −5.19615 | + | 3.00000i | −0.297531 | + | 0.171780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.44543 | 0.424933 | 0.212467 | − | 0.977168i | \(-0.431850\pi\) | ||||
0.212467 | + | 0.977168i | \(0.431850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.97056 | 0.396541 | ||||||||
\(310\) | −1.31178 | − | 0.757359i | −0.0745044 | − | 0.0430151i | ||||
\(311\) | −28.9174 | + | 16.6955i | −1.63976 | + | 0.946714i | −0.658841 | + | 0.752282i | \(0.728953\pi\) |
−0.980916 | + | 0.194433i | \(0.937713\pi\) | |||||||
\(312\) | 1.24264 | + | 2.15232i | 0.0703507 | + | 0.121851i | ||||
\(313\) | 8.93841 | + | 5.16059i | 0.505229 | + | 0.291694i | 0.730870 | − | 0.682516i | \(-0.239114\pi\) |
−0.225641 | + | 0.974210i | \(0.572448\pi\) | |||||||
\(314\) | −11.5349 | −0.650952 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 8.48528i | − | 0.477334i | ||||||
\(317\) | 11.4853 | − | 19.8931i | 0.645078 | − | 1.11731i | −0.339206 | − | 0.940712i | \(-0.610158\pi\) |
0.984284 | − | 0.176595i | \(-0.0565083\pi\) | |||||||
\(318\) | −2.42742 | − | 4.20441i | −0.136123 | − | 0.235772i | ||||
\(319\) | 4.78836 | + | 3.32311i | 0.268096 | + | 0.186059i | ||||
\(320\) | 0.937379 | + | 0.541196i | 0.0524011 | + | 0.0302538i | ||||
\(321\) | −13.7766 | −0.768935 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.0857864 | + | 0.148586i | −0.00476591 | + | 0.00825480i | ||||
\(325\) | −4.39523 | − | 7.61276i | −0.243803 | − | 0.422280i | ||||
\(326\) | −7.05130 | + | 4.07107i | −0.390535 | + | 0.225476i | ||||
\(327\) | 1.90215 | − | 3.29462i | 0.105189 | − | 0.182193i | ||||
\(328\) | − | 4.59220i | − | 0.253562i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.51472 | − | 1.65685i | 0.193479 | − | 0.0912068i | ||||
\(331\) | −10.2426 | + | 17.7408i | −0.562986 | + | 0.975121i | 0.434247 | + | 0.900794i | \(0.357014\pi\) |
−0.997234 | + | 0.0743275i | \(0.976319\pi\) | |||||||
\(332\) | −6.69133 | − | 11.5897i | −0.367234 | − | 0.636068i | ||||
\(333\) | −5.48528 | − | 9.50079i | −0.300592 | − | 0.520640i | ||||
\(334\) | 17.5552 | + | 10.1355i | 0.960576 | + | 0.554589i | ||||
\(335\) | 12.6173i | 0.689356i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4853i | 1.44275i | 0.692547 | + | 0.721373i | \(0.256488\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743512\pi\) | |||||||
\(338\) | 6.69258 | + | 3.86396i | 0.364028 | + | 0.210172i | ||||
\(339\) | 1.32565 | − | 0.765367i | 0.0719997 | − | 0.0415690i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.385197 | − | 4.62533i | 0.0208596 | − | 0.250476i | ||||
\(342\) | − | 10.1355i | − | 0.548064i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.24264 | −0.228748 | ||||||||
\(345\) | −3.65685 | + | 6.33386i | −0.196878 | + | 0.341003i | ||||
\(346\) | −22.3558 | + | 12.9071i | −1.20185 | + | 0.693891i | ||||
\(347\) | 6.71807 | − | 3.87868i | 0.360645 | − | 0.208218i | −0.308719 | − | 0.951153i | \(-0.599900\pi\) |
0.669364 | + | 0.742935i | \(0.266567\pi\) | |||||||
\(348\) | −0.951076 | + | 1.64731i | −0.0509830 | + | 0.0883052i | ||||
\(349\) | 29.0614 | 1.55562 | 0.777811 | − | 0.628498i | \(-0.216330\pi\) | ||||
0.777811 | + | 0.628498i | \(0.216330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 12.0000i | − | 0.640513i | ||||||
\(352\) | −0.275255 | + | 3.30518i | −0.0146711 | + | 0.176167i | ||||
\(353\) | 1.05110 | − | 0.606854i | 0.0559445 | − | 0.0322996i | −0.471767 | − | 0.881723i | \(-0.656384\pi\) |
0.527711 | + | 0.849424i | \(0.323050\pi\) | |||||||
\(354\) | −6.75412 | + | 3.89949i | −0.358978 | + | 0.207256i | ||||
\(355\) | −1.87476 | − | 1.08239i | −0.0995018 | − | 0.0574474i | ||||
\(356\) | 3.56420i | 0.188902i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.65685i | − | 0.298974i | ||||||
\(359\) | −2.15232 | − | 1.24264i | −0.113595 | − | 0.0655841i | 0.442126 | − | 0.896953i | \(-0.354224\pi\) |
−0.555721 | + | 0.831369i | \(0.687558\pi\) | |||||||
\(360\) | −0.989538 | − | 1.71393i | −0.0521532 | − | 0.0903320i | ||||
\(361\) | −5.86396 | − | 10.1567i | −0.308630 | − | 0.534562i | ||||
\(362\) | 10.2283 | − | 17.7160i | 0.537589 | − | 0.931132i | ||||
\(363\) | 9.18440 | + | 7.57675i | 0.482056 | + | 0.397676i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9706i | 0.888280i | ||||||||
\(366\) | 3.00000 | − | 5.19615i | 0.156813 | − | 0.271607i | ||||
\(367\) | −9.64834 | + | 5.57047i | −0.503639 | + | 0.290776i | −0.730215 | − | 0.683217i | \(-0.760580\pi\) |
0.226576 | + | 0.973994i | \(0.427247\pi\) | |||||||
\(368\) | −3.12132 | − | 5.40629i | −0.162710 | − | 0.281822i | ||||
\(369\) | −4.19825 | + | 7.27159i | −0.218552 | + | 0.378544i | ||||
\(370\) | −6.49435 | −0.337625 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.51472 | 0.0785345 | ||||||||
\(373\) | −17.7408 | − | 10.2426i | −0.918582 | − | 0.530344i | −0.0353999 | − | 0.999373i | \(-0.511270\pi\) |
−0.883183 | + | 0.469029i | \(0.844604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.17157 | − | 8.95743i | −0.267059 | − | 0.462560i | ||||
\(376\) | −2.45461 | + | 4.25151i | −0.126587 | + | 0.219255i | ||||
\(377\) | − | 4.03507i | − | 0.207817i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6569 | −0.598772 | −0.299386 | − | 0.954132i | \(-0.596782\pi\) | ||||
−0.299386 | + | 0.954132i | \(0.596782\pi\) | |||||||
\(380\) | −5.19615 | − | 3.00000i | −0.266557 | − | 0.153897i | ||||
\(381\) | −3.24718 | − | 5.62427i | −0.166358 | − | 0.288140i | ||||
\(382\) | −1.52192 | + | 0.878680i | −0.0778681 | + | 0.0449572i | ||||
\(383\) | −12.5271 | − | 7.23252i | −0.640105 | − | 0.369565i | 0.144550 | − | 0.989497i | \(-0.453827\pi\) |
−0.784655 | + | 0.619933i | \(0.787160\pi\) | |||||||
\(384\) | −1.08239 | −0.0552356 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.48528 | 0.126497 | ||||||||
\(387\) | 6.71807 | + | 3.87868i | 0.341499 | + | 0.197164i | ||||
\(388\) | 7.45193 | − | 4.30237i | 0.378314 | − | 0.218420i | ||||
\(389\) | 16.0000 | + | 27.7128i | 0.811232 | + | 1.40510i | 0.912002 | + | 0.410186i | \(0.134536\pi\) |
−0.100770 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(390\) | −2.32965 | − | 1.34502i | −0.117966 | − | 0.0681080i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 7.45584i | − | 0.376098i | ||||||
\(394\) | −10.2426 | + | 17.7408i | −0.516017 | + | 0.893767i | ||||
\(395\) | 4.59220 | + | 7.95393i | 0.231059 | + | 0.400205i | ||||
\(396\) | 3.45750 | − | 4.98200i | 0.173746 | − | 0.250355i | ||||
\(397\) | −1.48648 | − | 0.858221i | −0.0746044 | − | 0.0430729i | 0.462234 | − | 0.886758i | \(-0.347048\pi\) |
−0.536838 | + | 0.843685i | \(0.680381\pi\) | |||||||
\(398\) | −24.6549 | −1.23584 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.82843 | 0.191421 | ||||||||
\(401\) | −0.242641 | + | 0.420266i | −0.0121169 | + | 0.0209871i | −0.872020 | − | 0.489470i | \(-0.837190\pi\) |
0.859903 | + | 0.510457i | \(0.170524\pi\) | |||||||
\(402\) | −6.30864 | − | 10.9269i | −0.314647 | − | 0.544984i | ||||
\(403\) | −2.78272 | + | 1.60660i | −0.138617 | + | 0.0800305i | ||||
\(404\) | 8.31492 | − | 14.4019i | 0.413683 | − | 0.716519i | ||||
\(405\) | − | 0.185709i | − | 0.00922796i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.48528 | − | 18.0000i | −0.420600 | − | 0.892227i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9259 | − | 32.7807i | −0.935827 | − | 1.62090i | −0.773152 | − | 0.634220i | \(-0.781321\pi\) |
−0.162675 | − | 0.986680i | \(-0.552012\pi\) | |||||||
\(410\) | 2.48528 | + | 4.30463i | 0.122739 | + | 0.212591i | ||||
\(411\) | −15.9079 | − | 9.18440i | −0.784676 | − | 0.453033i | ||||
\(412\) | − | 6.43996i | − | 0.317274i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.4142i | 0.560978i | ||||||||
\(415\) | 12.5446 | + | 7.24264i | 0.615791 | + | 0.355527i | ||||
\(416\) | 1.98848 | − | 1.14805i | 0.0974933 | − | 0.0562878i | ||||
\(417\) | 12.5446 | − | 7.24264i | 0.614313 | − | 0.354674i | ||||
\(418\) | 1.52582 | − | 18.3215i | 0.0746301 | − | 0.896136i | ||||
\(419\) | − | 8.47343i | − | 0.413954i | −0.978346 | − | 0.206977i | \(-0.933637\pi\) | ||
0.978346 | − | 0.206977i | \(-0.0663625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6569 | 0.860542 | 0.430271 | − | 0.902700i | \(-0.358418\pi\) | ||||
0.430271 | + | 0.902700i | \(0.358418\pi\) | |||||||
\(422\) | 12.3640 | − | 21.4150i | 0.601868 | − | 1.04247i | ||||
\(423\) | 7.77359 | − | 4.48808i | 0.377965 | − | 0.218218i | ||||
\(424\) | −3.88437 | + | 2.24264i | −0.188642 | + | 0.108912i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.16478 | 0.104884 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.7279i | 0.615227i | ||||||||
\(429\) | 0.684086 | − | 8.21431i | 0.0330280 | − | 0.396591i | ||||
\(430\) | 3.97696 | − | 2.29610i | 0.191786 | − | 0.110728i | ||||
\(431\) | 2.15232 | − | 1.24264i | 0.103673 | − | 0.0598559i | −0.447267 | − | 0.894401i | \(-0.647603\pi\) |
0.550940 | + | 0.834545i | \(0.314269\pi\) | |||||||
\(432\) | 4.52607 | + | 2.61313i | 0.217760 | + | 0.125724i | ||||
\(433\) | − | 22.6758i | − | 1.08973i | −0.838523 | − | 0.544866i | \(-0.816581\pi\) | ||
0.838523 | − | 0.544866i | \(-0.183419\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.05887i | − | 0.0987155i | ||||||
\(436\) | −3.04384 | − | 1.75736i | −0.145773 | − | 0.0841622i | ||||
\(437\) | 17.3023 | + | 29.9685i | 0.827683 | + | 1.43359i | ||||
\(438\) | −8.48528 | − | 14.6969i | −0.405442 | − | 0.702247i | ||||
\(439\) | −3.24718 | + | 5.62427i | −0.154979 | + | 0.268432i | −0.933051 | − | 0.359743i | \(-0.882864\pi\) |
0.778072 | + | 0.628175i | \(0.216198\pi\) | |||||||
\(440\) | −1.53073 | − | 3.24718i | −0.0729749 | − | 0.154803i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3137 | + | 19.5959i | −0.537531 | + | 0.931030i | 0.461506 | + | 0.887137i | \(0.347309\pi\) |
−0.999036 | + | 0.0438929i | \(0.986024\pi\) | |||||||
\(444\) | 5.62427 | − | 3.24718i | 0.266916 | − | 0.154104i | ||||
\(445\) | −1.92893 | − | 3.34101i | −0.0914402 | − | 0.158379i | ||||
\(446\) | −3.94689 | + | 6.83621i | −0.186890 | + | 0.323704i | ||||
\(447\) | −7.28225 | −0.344439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.7279 | −1.92207 | −0.961035 | − | 0.276428i | \(-0.910849\pi\) | ||||
−0.961035 | + | 0.276428i | \(0.910849\pi\) | |||||||
\(450\) | −6.06218 | − | 3.50000i | −0.285774 | − | 0.164992i | ||||
\(451\) | −8.68371 | + | 12.5126i | −0.408900 | + | 0.589194i | ||||
\(452\) | −0.707107 | − | 1.22474i | −0.0332595 | − | 0.0576072i | ||||
\(453\) | −3.24718 | + | 5.62427i | −0.152566 | + | 0.264251i | ||||
\(454\) | − | 0.951076i | − | 0.0446362i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −27.2416 | − | 15.7279i | −1.27431 | − | 0.735721i | −0.298511 | − | 0.954406i | \(-0.596490\pi\) |
−0.975795 | + | 0.218685i | \(0.929823\pi\) | |||||||
\(458\) | −14.2409 | − | 24.6659i | −0.665432 | − | 1.15256i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.85172 | + | 3.37849i | 0.272838 | + | 0.157523i | ||||
\(461\) | 29.0614 | 1.35352 | 0.676762 | − | 0.736201i | \(-0.263382\pi\) | ||||
0.676762 | + | 0.736201i | \(0.263382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.31371 | −0.246949 | −0.123474 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123474 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(464\) | 1.52192 | + | 0.878680i | 0.0706533 | + | 0.0407917i | ||||
\(465\) | −1.41987 | + | 0.819760i | −0.0658447 | + | 0.0380155i | ||||
\(466\) | 4.24264 | + | 7.34847i | 0.196537 | + | 0.340411i | ||||
\(467\) | −27.8663 | − | 16.0886i | −1.28950 | − | 0.744493i | −0.310935 | − | 0.950431i | \(-0.600642\pi\) |
−0.978565 | + | 0.205938i | \(0.933976\pi\) | |||||||
\(468\) | −4.19825 | −0.194064 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 5.31371i | − | 0.245103i | ||||||
\(471\) | −6.24264 | + | 10.8126i | −0.287646 | + | 0.498217i | ||||
\(472\) | 3.60266 | + | 6.24000i | 0.165826 | + | 0.287219i | ||||
\(473\) | 11.5601 | + | 8.02270i | 0.531535 | + | 0.368884i | ||||
\(474\) | −7.95393 | − | 4.59220i | −0.365336 | − | 0.210927i | ||||
\(475\) | −21.2220 | −0.973734 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.20101 | 0.375498 | ||||||||
\(478\) | −13.2426 | + | 22.9369i | −0.605704 | + | 1.04911i | ||||
\(479\) | −4.59220 | − | 7.95393i | −0.209823 | − | 0.363424i | 0.741836 | − | 0.670582i | \(-0.233955\pi\) |
−0.951659 | + | 0.307158i | \(0.900622\pi\) | |||||||
\(480\) | 1.01461 | − | 0.585786i | 0.0463105 | − | 0.0267374i | ||||
\(481\) | −6.88830 | + | 11.9309i | −0.314080 | + | 0.544002i | ||||
\(482\) | − | 4.59220i | − | 0.209169i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | − | 8.48528i | 0.318182 | − | 0.385695i | ||||
\(485\) | −4.65685 | + | 8.06591i | −0.211457 | + | 0.366254i | ||||
\(486\) | −7.74652 | − | 13.4174i | −0.351389 | − | 0.608624i | ||||
\(487\) | 1.22183 | + | 2.11626i | 0.0553662 | + | 0.0958971i | 0.892380 | − | 0.451285i | \(-0.149034\pi\) |
−0.837014 | + | 0.547182i | \(0.815701\pi\) | |||||||
\(488\) | −4.80062 | − | 2.77164i | −0.217314 | − | 0.125466i | ||||
\(489\) | 8.81298i | 0.398537i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.9411i | 1.80252i | 0.433281 | + | 0.901259i | \(0.357356\pi\) | ||||
−0.433281 | + | 0.901259i | \(0.642644\pi\) | |||||||
\(492\) | −4.30463 | − | 2.48528i | −0.194068 | − | 0.112045i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −11.0227 | + | 6.36396i | −0.495935 | + | 0.286328i | ||||
\(495\) | −0.544751 | + | 6.54121i | −0.0244847 | + | 0.294005i | ||||
\(496\) | − | 1.39942i | − | 0.0628357i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.4853 | −0.649101 | ||||||||
\(499\) | −14.3137 | + | 24.7921i | −0.640770 | + | 1.10985i | 0.344492 | + | 0.938789i | \(0.388051\pi\) |
−0.985261 | + | 0.171056i | \(0.945282\pi\) | |||||||
\(500\) | −8.27558 | + | 4.77791i | −0.370095 | + | 0.213675i | ||||
\(501\) | 19.0016 | − | 10.9706i | 0.848928 | − | 0.490129i | ||||
\(502\) | 6.08447 | − | 10.5386i | 0.271563 | − | 0.470361i | ||||
\(503\) | 6.49435 | 0.289569 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000i | 0.800989i | ||||||||
\(506\) | −1.71832 | + | 20.6331i | −0.0763886 | + | 0.917252i | ||||
\(507\) | 7.24399 | − | 4.18232i | 0.321717 | − | 0.185743i | ||||
\(508\) | −5.19615 | + | 3.00000i | −0.230542 | + | 0.133103i | ||||
\(509\) | −28.0938 | − | 16.2200i | −1.24523 | − | 0.718937i | −0.275080 | − | 0.961421i | \(-0.588704\pi\) |
−0.970155 | + | 0.242485i | \(0.922038\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −25.0892 | − | 14.4853i | −1.10772 | − | 0.639541i | ||||
\(514\) | 11.0209 | + | 19.0888i | 0.486111 | + | 0.841969i | ||||
\(515\) | 3.48528 | + | 6.03668i | 0.153580 | + | 0.266008i | ||||
\(516\) | −2.29610 | + | 3.97696i | −0.101080 | + | 0.175076i | ||||
\(517\) | 14.7277 | − | 6.94269i | 0.647723 | − | 0.305339i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.9411i | 1.22648i | ||||||||
\(520\) | −1.24264 | + | 2.15232i | −0.0544934 | + | 0.0943853i | ||||
\(521\) | −24.5522 | + | 14.1752i | −1.07565 | + | 0.621028i | −0.929720 | − | 0.368267i | \(-0.879951\pi\) |
−0.145931 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(522\) | −1.60660 | − | 2.78272i | −0.0703190 | − | 0.121796i | ||||
\(523\) | −0.475538 | + | 0.823656i | −0.0207938 | + | 0.0360160i | −0.876235 | − | 0.481884i | \(-0.839953\pi\) |
0.855441 | + | 0.517900i | \(0.173286\pi\) | |||||||
\(524\) | −6.88830 | −0.300917 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.94924 | + | 2.04677i | 0.128349 | + | 0.0890743i | ||||
\(529\) | −7.98528 | − | 13.8309i | −0.347186 | − | 0.601344i | ||||
\(530\) | 2.42742 | − | 4.20441i | 0.105440 | − | 0.182628i | ||||
\(531\) | − | 13.1744i | − | 0.571721i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5442 | 0.456718 | ||||||||
\(534\) | 3.34101 | + | 1.92893i | 0.144580 | + | 0.0834731i | ||||
\(535\) | −6.88830 | − | 11.9309i | −0.297807 | − | 0.515817i | ||||
\(536\) | −10.0951 | + | 5.82843i | −0.436043 | + | 0.251750i | ||||
\(537\) | −5.30262 | − | 3.06147i | −0.228825 | − | 0.132112i | ||||
\(538\) | 3.50981 | 0.151319 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.65685 | −0.243432 | ||||||||
\(541\) | −9.50079 | − | 5.48528i | −0.408471 | − | 0.235831i | 0.281662 | − | 0.959514i | \(-0.409114\pi\) |
−0.690132 | + | 0.723683i | \(0.742448\pi\) | |||||||
\(542\) | 23.1794 | − | 13.3827i | 0.995642 | − | 0.574834i | ||||
\(543\) | −11.0711 | − | 19.1757i | −0.475105 | − | 0.822906i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.80430 | 0.162958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.0000i | − | 1.02617i | −0.858339 | − | 0.513083i | \(-0.828503\pi\) | ||
0.858339 | − | 0.513083i | \(-0.171497\pi\) | |||||||
\(548\) | −8.48528 | + | 14.6969i | −0.362473 | + | 0.627822i | ||||
\(549\) | 5.06774 | + | 8.77758i | 0.216286 | + | 0.374618i | ||||
\(550\) | −10.4315 | − | 7.23944i | −0.444800 | − | 0.308691i | ||||
\(551\) | −8.43641 | − | 4.87076i | −0.359403 | − | 0.207502i | ||||
\(552\) | −6.75699 | −0.287596 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.7279 | −0.795673 | ||||||||
\(555\) | −3.51472 | + | 6.08767i | −0.149191 | + | 0.258407i | ||||
\(556\) | −6.69133 | − | 11.5897i | −0.283775 | − | 0.491514i | ||||
\(557\) | 5.19615 | − | 3.00000i | 0.220168 | − | 0.127114i | −0.385860 | − | 0.922557i | \(-0.626095\pi\) |
0.606028 | + | 0.795443i | \(0.292762\pi\) | |||||||
\(558\) | −1.27937 | + | 2.21593i | −0.0541599 | + | 0.0938077i | ||||
\(559\) | − | 9.74153i | − | 0.412023i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | − | 10.3923i | 0.253095 | − | 0.438373i | ||||
\(563\) | −13.5796 | − | 23.5206i | −0.572313 | − | 0.991275i | −0.996328 | − | 0.0856201i | \(-0.972713\pi\) |
0.424015 | − | 0.905655i | \(-0.360620\pi\) | |||||||
\(564\) | 2.65685 | + | 4.60181i | 0.111874 | + | 0.193771i | ||||
\(565\) | 1.32565 | + | 0.765367i | 0.0557707 | + | 0.0321992i | ||||
\(566\) | − | 22.5671i | − | 0.948564i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | −25.9808 | − | 15.0000i | −1.08917 | − | 0.628833i | −0.155815 | − | 0.987786i | \(-0.549800\pi\) |
−0.933355 | + | 0.358954i | \(0.883134\pi\) | |||||||
\(570\) | −5.62427 | + | 3.24718i | −0.235575 | + | 0.136009i | ||||
\(571\) | 31.1769 | − | 18.0000i | 1.30471 | − | 0.753277i | 0.323505 | − | 0.946227i | \(-0.395139\pi\) |
0.981209 | + | 0.192950i | \(0.0618055\pi\) | |||||||
\(572\) | −7.58903 | − | 0.632013i | −0.317313 | − | 0.0264258i | ||||
\(573\) | 1.90215i | 0.0794635i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.8995 | 0.996678 | ||||||||
\(576\) | 0.914214 | − | 1.58346i | 0.0380922 | − | 0.0659777i | ||||
\(577\) | 28.7566 | − | 16.6026i | 1.19715 | − | 0.691177i | 0.237234 | − | 0.971453i | \(-0.423759\pi\) |
0.959919 | + | 0.280276i | \(0.0904259\pi\) | |||||||
\(578\) | −14.7224 | + | 8.50000i | −0.612372 | + | 0.353553i | ||||
\(579\) | 1.34502 | − | 2.32965i | 0.0558973 | − | 0.0968170i | ||||
\(580\) | −1.90215 | −0.0789826 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 9.31371i | − | 0.386066i | ||||||
\(583\) | 14.8247 | + | 1.23460i | 0.613975 | + | 0.0511318i | ||||
\(584\) | −13.5782 | + | 7.83938i | −0.561870 | + | 0.324396i | ||||
\(585\) | 3.93535 | − | 2.27208i | 0.162707 | − | 0.0939389i | ||||
\(586\) | −0.823656 | − | 0.475538i | −0.0340249 | − | 0.0196443i | ||||
\(587\) | − | 37.0321i | − | 1.52848i | −0.644933 | − | 0.764239i | \(-0.723115\pi\) | ||
0.644933 | − | 0.764239i | \(-0.276885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.75736i | 0.319636i | ||||||||
\(590\) | −6.75412 | − | 3.89949i | −0.278063 | − | 0.160540i | ||||
\(591\) | 11.0866 | + | 19.2025i | 0.456040 | + | 0.789884i | ||||
\(592\) | −3.00000 | − | 5.19615i | −0.123299 | − | 0.213561i | ||||
\(593\) | 14.3337 | − | 24.8268i | 0.588616 | − | 1.01951i | −0.405798 | − | 0.913963i | \(-0.633006\pi\) |
0.994414 | − | 0.105550i | \(-0.0336602\pi\) | |||||||
\(594\) | −7.39104 | − | 15.6788i | −0.303258 | − | 0.643307i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.72792i | 0.275586i | ||||||||
\(597\) | −13.3431 | + | 23.1110i | −0.546099 | + | 0.945871i | ||||
\(598\) | 12.4134 | − | 7.16687i | 0.507621 | − | 0.293075i | ||||
\(599\) | 13.0000 | + | 22.5167i | 0.531166 | + | 0.920006i | 0.999338 | + | 0.0363689i | \(0.0115791\pi\) |
−0.468173 | + | 0.883637i | \(0.655088\pi\) | |||||||
\(600\) | 2.07193 | − | 3.58869i | 0.0845862 | − | 0.146508i | ||||
\(601\) | −35.9497 | −1.46642 | −0.733210 | − | 0.680003i | \(-0.761979\pi\) | ||||
−0.733210 | + | 0.680003i | \(0.761979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3137 | 0.867961 | ||||||||
\(604\) | 5.19615 | + | 3.00000i | 0.211428 | + | 0.122068i | ||||
\(605\) | −1.96945 | + | 11.7423i | −0.0800696 | + | 0.477392i | ||||
\(606\) | −9.00000 | − | 15.5885i | −0.365600 | − | 0.633238i | ||||
\(607\) | −23.1242 | + | 40.0523i | −0.938582 | + | 1.62567i | −0.170463 | + | 0.985364i | \(0.554526\pi\) |
−0.768119 | + | 0.640307i | \(0.778807\pi\) | |||||||
\(608\) | − | 5.54328i | − | 0.224810i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −9.76191 | − | 5.63604i | −0.394924 | − | 0.228010i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9142 | + | 6.87868i | −0.481211 | + | 0.277827i | −0.720921 | − | 0.693017i | \(-0.756281\pi\) |
0.239710 | + | 0.970845i | \(0.422948\pi\) | |||||||
\(614\) | −6.44793 | − | 3.72271i | −0.260217 | − | 0.150237i | ||||
\(615\) | 5.38010 | 0.216947 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.41421 | 0.0569341 | 0.0284670 | − | 0.999595i | \(-0.490937\pi\) | ||||
0.0284670 | + | 0.999595i | \(0.490937\pi\) | |||||||
\(618\) | −6.03668 | − | 3.48528i | −0.242831 | − | 0.140199i | ||||
\(619\) | −1.48648 | + | 0.858221i | −0.0597468 | + | 0.0344948i | −0.529576 | − | 0.848263i | \(-0.677649\pi\) |
0.469829 | + | 0.882757i | \(0.344316\pi\) | |||||||
\(620\) | 0.757359 | + | 1.31178i | 0.0304163 | + | 0.0526825i | ||||
\(621\) | 28.2546 | + | 16.3128i | 1.13382 | + | 0.654610i | ||||
\(622\) | 33.3910 | 1.33886 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.48528i | − | 0.0994909i | ||||||
\(625\) | −4.39949 | + | 7.62015i | −0.175980 | + | 0.304806i | ||||
\(626\) | −5.16059 | − | 8.93841i | −0.206259 | − | 0.357251i | ||||
\(627\) | −16.3485 | − | 11.3458i | −0.652895 | − | 0.453108i | ||||
\(628\) | 9.98951 | + | 5.76745i | 0.398625 | + | 0.230146i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2132 | 0.605628 | 0.302814 | − | 0.953050i | \(-0.402074\pi\) | ||||
0.302814 | + | 0.953050i | \(0.402074\pi\) | |||||||
\(632\) | −4.24264 | + | 7.34847i | −0.168763 | + | 0.292306i | ||||
\(633\) | −13.3827 | − | 23.1794i | −0.531913 | − | 0.921300i | ||||
\(634\) | −19.8931 | + | 11.4853i | −0.790056 | + | 0.456139i | ||||
\(635\) | 3.24718 | − | 5.62427i | 0.128860 | − | 0.223193i | ||||
\(636\) | 4.85483i | 0.192507i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.48528 | − | 5.27208i | −0.0983932 | − | 0.208724i | ||||
\(639\) | −1.82843 | + | 3.16693i | −0.0723315 | + | 0.125282i | ||||
\(640\) | −0.541196 | − | 0.937379i | −0.0213927 | − | 0.0370532i | ||||
\(641\) | −1.39340 | − | 2.41344i | −0.0550359 | − | 0.0953250i | 0.837195 | − | 0.546905i | \(-0.184194\pi\) |
−0.892231 | + | 0.451580i | \(0.850861\pi\) | |||||||
\(642\) | 11.9309 | + | 6.88830i | 0.470875 | + | 0.271860i | ||||
\(643\) | − | 5.04054i | − | 0.198780i | −0.995049 | − | 0.0993898i | \(-0.968311\pi\) | ||
0.995049 | − | 0.0993898i | \(-0.0316891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 4.97056i | − | 0.195716i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.08669 | − | 1.78210i | 0.121350 | − | 0.0700616i | −0.438096 | − | 0.898928i | \(-0.644347\pi\) |
0.559446 | + | 0.828866i | \(0.311014\pi\) | |||||||
\(648\) | 0.148586 | − | 0.0857864i | 0.00583703 | − | 0.00337001i | ||||
\(649\) | 1.98330 | − | 23.8149i | 0.0778515 | − | 0.934818i | ||||
\(650\) | 8.79045i | 0.344790i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.14214 | 0.318871 | ||||||||
\(653\) | −10.7279 | + | 18.5813i | −0.419816 | + | 0.727143i | −0.995921 | − | 0.0902333i | \(-0.971239\pi\) |
0.576105 | + | 0.817376i | \(0.304572\pi\) | |||||||
\(654\) | −3.29462 | + | 1.90215i | −0.128830 | + | 0.0743800i | ||||
\(655\) | 6.45695 | − | 3.72792i | 0.252294 | − | 0.145662i | ||||
\(656\) | −2.29610 | + | 3.97696i | −0.0896477 | + | 0.155274i | ||||
\(657\) | 28.6675 | 1.11842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.21320i | − | 0.358895i | −0.983768 | − | 0.179448i | \(-0.942569\pi\) | ||
0.983768 | − | 0.179448i | \(-0.0574311\pi\) | |||||||
\(660\) | −3.87226 | − | 0.322481i | −0.150728 | − | 0.0125526i | ||||
\(661\) | −28.9645 | + | 16.7227i | −1.12659 | + | 0.650437i | −0.943075 | − | 0.332580i | \(-0.892081\pi\) |
−0.183515 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(662\) | 17.7408 | − | 10.2426i | 0.689515 | − | 0.398092i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.3827i | 0.519348i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9706i | 0.425101i | ||||||||
\(667\) | 9.50079 | + | 5.48528i | 0.367872 | + | 0.212391i | ||||
\(668\) | −10.1355 | − | 17.5552i | −0.392153 | − | 0.679230i | ||||
\(669\) | 4.27208 | + | 7.39946i | 0.165168 | + | 0.286079i | ||||
\(670\) | 6.30864 | − | 10.9269i | 0.243724 | − | 0.422143i | ||||
\(671\) | 7.83938 | + | 16.6298i | 0.302636 | + | 0.641988i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.9411i | 1.77090i | 0.464734 | + | 0.885450i | \(0.346150\pi\) | ||||
−0.464734 | + | 0.885450i | \(0.653850\pi\) | |||||||
\(674\) | 13.2426 | − | 22.9369i | 0.510087 | − | 0.883497i | ||||
\(675\) | −17.3277 | + | 10.0042i | −0.666944 | + | 0.385060i | ||||
\(676\) | −3.86396 | − | 6.69258i | −0.148614 | − | 0.257407i | ||||
\(677\) | 9.93850 | − | 17.2140i | 0.381968 | − | 0.661588i | −0.609376 | − | 0.792882i | \(-0.708580\pi\) |
0.991343 | + | 0.131294i | \(0.0419132\pi\) | |||||||
\(678\) | −1.53073 | −0.0587875 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.891519 | − | 0.514719i | −0.0341631 | − | 0.0197241i | ||||
\(682\) | −2.64626 | + | 3.81306i | −0.101330 | + | 0.146009i | ||||
\(683\) | 12.0000 | + | 20.7846i | 0.459167 | + | 0.795301i | 0.998917 | − | 0.0465244i | \(-0.0148145\pi\) |
−0.539750 | + | 0.841825i | \(0.681481\pi\) | |||||||
\(684\) | −5.06774 | + | 8.77758i | −0.193770 | + | 0.335619i | ||||
\(685\) | − | 18.3688i | − | 0.701836i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.8284 | −1.17618 | ||||||||
\(688\) | 3.67423 | + | 2.12132i | 0.140079 | + | 0.0808746i | ||||
\(689\) | −5.14933 | − | 8.91890i | −0.196174 | − | 0.339783i | ||||
\(690\) | 6.33386 | − | 3.65685i | 0.241126 | − | 0.139214i | ||||
\(691\) | 3.68290 | + | 2.12632i | 0.140104 | + | 0.0808891i | 0.568414 | − | 0.822743i | \(-0.307557\pi\) |
−0.428310 | + | 0.903632i | \(0.640891\pi\) | |||||||
\(692\) | 25.8142 | 0.981310 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.75736 | −0.294465 | ||||||||
\(695\) | 12.5446 | + | 7.24264i | 0.475845 | + | 0.274729i | ||||
\(696\) | 1.64731 | − | 0.951076i | 0.0624412 | − | 0.0360504i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −25.1679 | − | 14.5307i | −0.952620 | − | 0.549995i | ||||
\(699\) | 9.18440 | 0.347386 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.9411i | − | 1.50856i | −0.656555 | − | 0.754278i | \(-0.727987\pi\) | ||
0.656555 | − | 0.754278i | \(-0.272013\pi\) | |||||||
\(702\) | −6.00000 | + | 10.3923i | −0.226455 | + | 0.392232i | ||||
\(703\) | 16.6298 | + | 28.8037i | 0.627206 | + | 1.08635i | ||||
\(704\) | 1.89097 | − | 2.72474i | 0.0712686 | − | 0.102693i | ||||
\(705\) | −4.98096 | − | 2.87576i | −0.187594 | − | 0.108307i | ||||
\(706\) | −1.21371 | −0.0456785 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.79899 | 0.293104 | ||||||||
\(709\) | 11.6569 | − | 20.1903i | 0.437782 | − | 0.758261i | −0.559736 | − | 0.828671i | \(-0.689097\pi\) |
0.997518 | + | 0.0704099i | \(0.0224307\pi\) | |||||||
\(710\) | 1.08239 | + | 1.87476i | 0.0406215 | + | 0.0703584i | ||||
\(711\) | 13.4361 | − | 7.75736i | 0.503895 | − | 0.290924i | ||||
\(712\) | 1.78210 | − | 3.08669i | 0.0667871 | − | 0.115679i | ||||
\(713\) | − | 8.73606i | − | 0.327168i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.45584 | − | 3.51472i | 0.278833 | − | 0.131443i | ||||
\(716\) | −2.82843 | + | 4.89898i | −0.105703 | + | 0.183083i | ||||
\(717\) | 14.3337 | + | 24.8268i | 0.535303 | + | 0.927172i | ||||
\(718\) | 1.24264 | + | 2.15232i | 0.0463749 | + | 0.0803237i | ||||
\(719\) | −20.0927 | − | 11.6006i | −0.749333 | − | 0.432628i | 0.0761198 | − | 0.997099i | \(-0.475747\pi\) |
−0.825453 | + | 0.564471i | \(0.809080\pi\) | |||||||
\(720\) | 1.97908i | 0.0737558i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.7279i | 0.436468i | ||||||||
\(723\) | −4.30463 | − | 2.48528i | −0.160091 | − | 0.0924286i | ||||
\(724\) | −17.7160 | + | 10.2283i | −0.658410 | + | 0.380133i | ||||
\(725\) | −5.82655 | + | 3.36396i | −0.216393 | + | 0.124934i | ||||
\(726\) | −4.16555 | − | 11.1539i | −0.154598 | − | 0.413958i | ||||
\(727\) | − | 25.9999i | − | 0.964285i | −0.876093 | − | 0.482142i | \(-0.839859\pi\) | ||
0.876093 | − | 0.482142i | \(-0.160141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2843 | −0.640158 | ||||||||
\(730\) | 8.48528 | − | 14.6969i | 0.314054 | − | 0.543958i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5.19615 | + | 3.00000i | −0.192055 | + | 0.110883i | ||||
\(733\) | 0.475538 | − | 0.823656i | 0.0175644 | − | 0.0304224i | −0.857110 | − | 0.515134i | \(-0.827742\pi\) |
0.874674 | + | 0.484712i | \(0.161075\pi\) | |||||||
\(734\) | 11.1409 | 0.411220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.24264i | 0.230107i | ||||||||
\(737\) | 38.5280 | + | 3.20861i | 1.41920 | + | 0.118191i | ||||
\(738\) | 7.27159 | − | 4.19825i | 0.267671 | − | 0.154540i | ||||
\(739\) | 20.7846 | − | 12.0000i | 0.764574 | − | 0.441427i | −0.0663614 | − | 0.997796i | \(-0.521139\pi\) |
0.830936 | + | 0.556369i | \(0.187806\pi\) | |||||||
\(740\) | 5.62427 | + | 3.24718i | 0.206752 | + | 0.119369i | ||||
\(741\) | 13.7766i | 0.506096i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 36.4264i | − | 1.33636i | −0.744002 | − | 0.668178i | \(-0.767075\pi\) | ||
0.744002 | − | 0.668178i | \(-0.232925\pi\) | |||||||
\(744\) | −1.31178 | − | 0.757359i | −0.0480924 | − | 0.0277661i | ||||
\(745\) | −3.64113 | − | 6.30661i | −0.133401 | − | 0.231056i | ||||
\(746\) | 10.2426 | + | 17.7408i | 0.375010 | + | 0.649536i | ||||
\(747\) | 12.2346 | − | 21.1910i | 0.447641 | − | 0.775337i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.3431i | 0.377678i | ||||||||
\(751\) | −9.70711 | + | 16.8132i | −0.354217 | + | 0.613522i | −0.986984 | − | 0.160820i | \(-0.948586\pi\) |
0.632766 | + | 0.774343i | \(0.281919\pi\) | |||||||
\(752\) | 4.25151 | − | 2.45461i | 0.155037 | − | 0.0895105i | ||||
\(753\) | −6.58579 | − | 11.4069i | −0.239999 | − | 0.415691i | ||||
\(754\) | −2.01754 | + | 3.49448i | −0.0734744 | + | 0.127261i | ||||
\(755\) | −6.49435 | −0.236354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1421 | −1.38630 | −0.693150 | − | 0.720794i | \(-0.743778\pi\) | ||||
−0.693150 | + | 0.720794i | \(0.743778\pi\) | |||||||
\(758\) | 10.0951 | + | 5.82843i | 0.366672 | + | 0.211698i | ||||
\(759\) | 18.4111 | + | 12.7773i | 0.668279 | + | 0.463785i | ||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | −14.3337 | + | 24.8268i | −0.519597 | + | 0.899969i | 0.480143 | + | 0.877190i | \(0.340585\pi\) |
−0.999741 | + | 0.0227789i | \(0.992749\pi\) | |||||||
\(762\) | 6.49435i | 0.235266i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.75736 | 0.0635790 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.23252 | + | 12.5271i | 0.261322 | + | 0.452622i | ||||
\(767\) | −14.3277 | + | 8.27208i | −0.517342 | + | 0.298687i | ||||
\(768\) | 0.937379 | + | 0.541196i | 0.0338248 | + | 0.0195287i | ||||
\(769\) | −6.49435 | −0.234192 | −0.117096 | − | 0.993121i | \(-0.537359\pi\) | ||||
−0.117096 | + | 0.993121i | \(0.537359\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8579 | 0.859220 | ||||||||
\(772\) | −2.15232 | − | 1.24264i | −0.0774636 | − | 0.0447236i | ||||
\(773\) | −22.2421 | + | 12.8415i | −0.799991 | + | 0.461875i | −0.843468 | − | 0.537179i | \(-0.819490\pi\) |
0.0434768 | + | 0.999054i | \(0.486157\pi\) | |||||||
\(774\) | −3.87868 | − | 6.71807i | −0.139416 | − | 0.241476i | ||||
\(775\) | 4.63979 | + | 2.67878i | 0.166666 | + | 0.0962248i | ||||
\(776\) | −8.60474 | −0.308892 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 32.0000i | − | 1.14726i | ||||||
\(779\) | 12.7279 | − | 22.0454i | 0.456025 | − | 0.789859i | ||||
\(780\) | 1.34502 | + | 2.32965i | 0.0481596 | + | 0.0834149i | ||||
\(781\) | −3.78194 | + | 5.44949i | −0.135328 | + | 0.194998i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.18440 | −0.328224 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4853 | −0.445619 | ||||||||
\(786\) | −3.72792 | + | 6.45695i | −0.132971 | + | 0.230312i | ||||
\(787\) | −4.39523 | − | 7.61276i | −0.156673 | − | 0.271365i | 0.776994 | − | 0.629508i | \(-0.216744\pi\) |
−0.933667 | + | 0.358143i | \(0.883410\pi\) | |||||||
\(788\) | 17.7408 | − | 10.2426i | 0.631989 | − | 0.364879i | ||||
\(789\) | 12.9887 | − | 22.4971i | 0.462410 | − | 0.800918i | ||||
\(790\) | − | 9.18440i | − | 0.326766i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.48528 | + | 2.58579i | −0.194911 | + | 0.0918819i | ||||
\(793\) | 6.36396 | − | 11.0227i | 0.225991 | − | 0.391428i | ||||
\(794\) | 0.858221 | + | 1.48648i | 0.0304571 | + | 0.0527533i | ||||
\(795\) | −2.62742 | − | 4.55082i | −0.0931849 | − | 0.161401i | ||||
\(796\) | 21.3518 | + | 12.3275i | 0.756794 | + | 0.436935i | ||||
\(797\) | 26.0543i | 0.922892i | 0.887168 | + | 0.461446i | \(0.152669\pi\) | ||||
−0.887168 | + | 0.461446i | \(0.847331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.31552 | − | 1.91421i | −0.117221 | − | 0.0676777i | ||||
\(801\) | −5.64379 | + | 3.25844i | −0.199413 | + | 0.115131i | ||||
\(802\) | 0.420266 | − | 0.242641i | 0.0148401 | − | 0.00856794i | ||||
\(803\) | 51.8212 | + | 4.31566i | 1.82873 | + | 0.152296i | ||||
\(804\) | 12.6173i | 0.444977i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.21320 | 0.113180 | ||||||||
\(807\) | 1.89949 | − | 3.29002i | 0.0668654 | − | 0.115814i | ||||
\(808\) | −14.4019 | + | 8.31492i | −0.506656 | + | 0.292518i | ||||
\(809\) | −12.5446 | + | 7.24264i | −0.441045 | + | 0.254638i | −0.704041 | − | 0.710159i | \(-0.748623\pi\) |
0.262996 | + | 0.964797i | \(0.415290\pi\) | |||||||
\(810\) | −0.0928546 | + | 0.160829i | −0.00326258 | + | 0.00565095i | ||||
\(811\) | −6.88830 | −0.241881 | −0.120940 | − | 0.992660i | \(-0.538591\pi\) | ||||
−0.120940 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 28.9706i | − | 1.01604i | ||||||
\(814\) | −1.65153 | + | 19.8311i | −0.0578861 | + | 0.695080i | ||||
\(815\) | −7.63227 | + | 4.40649i | −0.267347 | + | 0.154353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.3673 | − | 11.7591i | −0.712562 | − | 0.411398i | ||||
\(818\) | 37.8519i | 1.32346i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 4.97056i | − | 0.173580i | ||||||
\(821\) | −11.9142 | − | 6.87868i | −0.415809 | − | 0.240068i | 0.277473 | − | 0.960733i | \(-0.410503\pi\) |
−0.693283 | + | 0.720666i | \(0.743836\pi\) | |||||||
\(822\) | 9.18440 | + | 15.9079i | 0.320343 | + | 0.554850i | ||||
\(823\) | −4.39340 | − | 7.60959i | −0.153144 | − | 0.265254i | 0.779238 | − | 0.626729i | \(-0.215607\pi\) |
−0.932382 | + | 0.361475i | \(0.882273\pi\) | |||||||
\(824\) | −3.21998 | + | 5.57717i | −0.112173 | + | 0.194290i | ||||
\(825\) | −12.4316 | + | 5.86030i | −0.432812 | + | 0.204030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.9706i | − | 0.590124i | −0.955478 | − | 0.295062i | \(-0.904660\pi\) | ||
0.955478 | − | 0.295062i | \(-0.0953404\pi\) | |||||||
\(828\) | 5.70711 | − | 9.88500i | 0.198336 | − | 0.343527i | ||||
\(829\) | 19.0416 | − | 10.9937i | 0.661344 | − | 0.381827i | −0.131445 | − | 0.991323i | \(-0.541962\pi\) |
0.792789 | + | 0.609496i | \(0.208628\pi\) | |||||||
\(830\) | −7.24264 | − | 12.5446i | −0.251396 | − | 0.435430i | ||||
\(831\) | −10.1355 | + | 17.5552i | −0.351596 | + | 0.608982i | ||||
\(832\) | −2.29610 | −0.0796030 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.4853 | −0.501584 | ||||||||
\(835\) | 19.0016 | + | 10.9706i | 0.657577 | + | 0.379652i | ||||
\(836\) | −10.4822 | + | 15.1040i | −0.362533 | + | 0.522383i | ||||
\(837\) | 3.65685 | + | 6.33386i | 0.126399 | + | 0.218930i | ||||
\(838\) | −4.23671 | + | 7.33820i | −0.146355 | + | 0.253494i | ||||
\(839\) | 27.0823i | 0.934986i | 0.883997 | + | 0.467493i | \(0.154843\pi\) | ||||
−0.883997 | + | 0.467493i | \(0.845157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9117 | 0.893506 | ||||||||
\(842\) | −15.2913 | − | 8.82843i | −0.526972 | − | 0.304248i | ||||
\(843\) | −6.49435 | − | 11.2485i | −0.223677 | − | 0.387421i | ||||
\(844\) | −21.4150 | + | 12.3640i | −0.737135 | + | 0.425585i | ||||
\(845\) | 7.24399 | + | 4.18232i | 0.249201 | + | 0.143876i | ||||
\(846\) | −8.97616 | −0.308607 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.48528 | 0.154025 | ||||||||
\(849\) | −21.1539 | − | 12.2132i | −0.726000 | − | 0.419156i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7279 | − | 32.4377i | −0.641985 | − | 1.11195i | ||||
\(852\) | −1.87476 | − | 1.08239i | −0.0642282 | − | 0.0370821i | ||||
\(853\) | 5.54328 | 0.189798 | 0.0948991 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0948991 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.9706i | − | 0.375185i | ||||||
\(856\) | 6.36396 | − | 11.0227i | 0.217516 | − | 0.376748i | ||||
\(857\) | −0.951076 | − | 1.64731i | −0.0324881 | − | 0.0562711i | 0.849324 | − | 0.527872i | \(-0.177010\pi\) |
−0.881812 | + | 0.471601i | \(0.843676\pi\) | |||||||
\(858\) | −4.69959 | + | 6.77176i | −0.160441 | + | 0.231184i | ||||
\(859\) | −9.98951 | − | 5.76745i | −0.340838 | − | 0.196783i | 0.319805 | − | 0.947483i | \(-0.396383\pi\) |
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(860\) | −4.59220 | −0.156593 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.48528 | −0.0846490 | ||||||||
\(863\) | 15.3640 | − | 26.6112i | 0.522995 | − | 0.905854i | −0.476647 | − | 0.879095i | \(-0.658148\pi\) |
0.999642 | − | 0.0267595i | \(-0.00851881\pi\) | |||||||
\(864\) | −2.61313 | − | 4.52607i | −0.0889003 | − | 0.153980i | ||||
\(865\) | −24.1977 | + | 13.9706i | −0.822747 | + | 0.475013i | ||||
\(866\) | −11.3379 | + | 19.6379i | −0.385278 | + | 0.667322i | ||||
\(867\) | 18.4007i | 0.624919i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.4558 | − | 12.0000i | 0.863530 | − | 0.407072i | ||||
\(870\) | −1.02944 | + | 1.78304i | −0.0349012 | + | 0.0604506i | ||||
\(871\) | −13.3827 | − | 23.1794i | −0.453454 | − | 0.785405i | ||||
\(872\) | 1.75736 | + | 3.04384i | 0.0595117 | + | 0.103077i | ||||
\(873\) | 13.6253 | + | 7.86657i | 0.461147 | + | 0.266243i | ||||
\(874\) | − | 34.6047i | − | 1.17052i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.9706i | 0.573382i | ||||||||
\(877\) | 46.7654 | + | 27.0000i | 1.57915 | + | 0.911725i | 0.994977 | + | 0.100099i | \(0.0319159\pi\) |
0.584177 | + | 0.811626i | \(0.301417\pi\) | |||||||
\(878\) | 5.62427 | − | 3.24718i | 0.189810 | − | 0.109587i | ||||
\(879\) | −0.891519 | + | 0.514719i | −0.0300702 | + | 0.0173610i | ||||
\(880\) | −0.297934 | + | 3.57750i | −0.0100434 | + | 0.120598i | ||||
\(881\) | 31.4888i | 1.06089i | 0.847721 | + | 0.530443i | \(0.177974\pi\) | ||||
−0.847721 | + | 0.530443i | \(0.822026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.4264 | −1.42776 | −0.713881 | − | 0.700267i | \(-0.753064\pi\) | ||||
−0.713881 | + | 0.700267i | \(0.753064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.31061 | + | 4.22078i | −0.245743 | + | 0.141880i | ||||
\(886\) | 19.5959 | − | 11.3137i | 0.658338 | − | 0.380091i | ||||
\(887\) | 4.59220 | − | 7.95393i | 0.154191 | − | 0.267067i | −0.778573 | − | 0.627554i | \(-0.784056\pi\) |
0.932764 | + | 0.360487i | \(0.117390\pi\) | |||||||
\(888\) | −6.49435 | −0.217936 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.85786i | 0.129316i | ||||||||
\(891\) | −0.567080 | − | 0.0472263i | −0.0189979 | − | 0.00158214i | ||||
\(892\) | 6.83621 | − | 3.94689i | 0.228893 | − | 0.132151i | ||||
\(893\) | −23.5673 | + | 13.6066i | −0.788650 | + | 0.455328i | ||||
\(894\) | 6.30661 | + | 3.64113i | 0.210925 | + | 0.121777i | ||||
\(895\) | − | 6.12293i | − | 0.204667i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 15.5147i | − | 0.518021i | ||||||
\(898\) | 35.2714 | + | 20.3640i | 1.17702 | + | 0.679554i | ||||
\(899\) | 1.22964 | + | 2.12980i | 0.0410108 | + | 0.0710328i | ||||
\(900\) | 3.50000 | + | 6.06218i | 0.116667 | + | 0.202073i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 13.7766 | − | 6.49435i | 0.458711 | − | 0.216238i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.41421i | 0.0470360i | ||||||||
\(905\) | 11.0711 | − | 19.1757i | 0.368015 | − | 0.637420i | ||||
\(906\) | 5.62427 | − | 3.24718i | 0.186854 | − | 0.107880i | ||||
\(907\) | 0.899495 | + | 1.55797i | 0.0298672 | + | 0.0517316i | 0.880573 | − | 0.473911i | \(-0.157158\pi\) |
−0.850705 | + | 0.525643i | \(0.823825\pi\) | |||||||
\(908\) | −0.475538 | + | 0.823656i | −0.0157813 | + | 0.0273340i | ||||
\(909\) | 30.4064 | 1.00852 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.2426 | 1.26704 | 0.633518 | − | 0.773728i | \(-0.281610\pi\) | ||||
0.633518 | + | 0.773728i | \(0.281610\pi\) | |||||||
\(912\) | −5.19615 | − | 3.00000i | −0.172062 | − | 0.0993399i | ||||
\(913\) | 25.3062 | − | 36.4643i | 0.837513 | − | 1.20679i | ||||
\(914\) | 15.7279 | + | 27.2416i | 0.520233 | + | 0.901071i | ||||
\(915\) | 3.24718 | − | 5.62427i | 0.107348 | − | 0.185933i | ||||
\(916\) | 28.4818i | 0.941064i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.3500 | − | 15.2132i | −0.869208 | − | 0.501837i | −0.00212280 | − | 0.999998i | \(-0.500676\pi\) |
−0.867085 | + | 0.498160i | \(0.834009\pi\) | |||||||
\(920\) | −3.37849 | − | 5.85172i | −0.111386 | − | 0.192926i | ||||
\(921\) | −6.97919 | + | 4.02944i | −0.229972 | + | 0.132774i | ||||
\(922\) | −25.1679 | − | 14.5307i | −0.828861 | − | 0.478543i | ||||
\(923\) | 4.59220 | 0.151154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.9706 | 0.755267 | ||||||||
\(926\) | 4.60181 | + | 2.65685i | 0.151225 | + | 0.0873096i | ||||
\(927\) | 10.1974 | − | 5.88750i | 0.334928 | − | 0.193371i | ||||
\(928\) | −0.878680 | − | 1.52192i | −0.0288441 | − | 0.0499594i | ||||
\(929\) | 36.5497 | + | 21.1020i | 1.19916 | + | 0.692334i | 0.960367 | − | 0.278738i | \(-0.0899160\pi\) |
0.238790 | + | 0.971071i | \(0.423249\pi\) | |||||||
\(930\) | 1.63952 | 0.0537620 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 8.48528i | − | 0.277945i | ||||||
\(933\) | 18.0711 | − | 31.3000i | 0.591620 | − | 1.02472i | ||||
\(934\) | 16.0886 | + | 27.8663i | 0.526436 | + | 0.911814i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.63579 | + | 2.09913i | 0.118840 | + | 0.0686121i | ||||
\(937\) | −35.9497 | −1.17443 | −0.587213 | − | 0.809432i | \(-0.699775\pi\) | ||||
−0.587213 | + | 0.809432i | \(0.699775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1716 | −0.364571 | ||||||||
\(940\) | −2.65685 | + | 4.60181i | −0.0866570 | + | 0.150094i | ||||
\(941\) | 20.0740 | + | 34.7692i | 0.654393 | + | 1.13344i | 0.982046 | + | 0.188644i | \(0.0604092\pi\) |
−0.327652 | + | 0.944798i | \(0.606258\pi\) | |||||||
\(942\) | 10.8126 | − | 6.24264i | 0.352293 | − | 0.203396i | ||||
\(943\) | −14.3337 | + | 24.8268i | −0.466771 | + | 0.808470i | ||||
\(944\) | − | 7.20533i | − | 0.234513i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | − | 12.7279i | −0.195077 | − | 0.413820i | ||||
\(947\) | 1.75736 | − | 3.04384i | 0.0571065 | − | 0.0989114i | −0.836059 | − | 0.548640i | \(-0.815146\pi\) |
0.893165 | + | 0.449728i | \(0.148479\pi\) | |||||||
\(948\) | 4.59220 | + | 7.95393i | 0.149148 | + | 0.258331i | ||||
\(949\) | −18.0000 | − | 31.1769i | −0.584305 | − | 1.01205i | ||||
\(950\) | 18.3788 | + | 10.6110i | 0.596288 | + | 0.344267i | ||||
\(951\) | 24.8632i | 0.806243i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.9411i | 1.48818i | 0.668080 | + | 0.744090i | \(0.267116\pi\) | ||||
−0.668080 | + | 0.744090i | \(0.732884\pi\) | |||||||
\(954\) | −7.10228 | − | 4.10051i | −0.229945 | − | 0.132759i | ||||
\(955\) | −1.64731 | + | 0.951076i | −0.0533058 | + | 0.0307761i | ||||
\(956\) | 22.9369 | − | 13.2426i | 0.741833 | − | 0.428298i | ||||
\(957\) | −6.28696 | − | 0.523577i | −0.203229 | − | 0.0169248i | ||||
\(958\) | 9.18440i | 0.296735i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.17157 | −0.0378124 | ||||||||
\(961\) | −14.5208 | + | 25.1508i | −0.468413 | + | 0.811316i | ||||
\(962\) | 11.9309 | − | 6.88830i | 0.384667 | − | 0.222088i | ||||
\(963\) | −20.1542 | + | 11.6360i | −0.649460 | + | 0.374966i | ||||
\(964\) | −2.29610 | + | 3.97696i | −0.0739524 | + | 0.128089i | ||||
\(965\) | 2.69005 | 0.0865957 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4558i | 0.625658i | 0.949810 | + | 0.312829i | \(0.101277\pi\) | ||||
−0.949810 | + | 0.312829i | \(0.898723\pi\) | |||||||
\(968\) | −10.3048 | + | 3.84847i | −0.331209 | + | 0.123694i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.06591 | − | 4.65685i | 0.258981 | − | 0.149523i | ||||
\(971\) | 31.3884 | + | 18.1221i | 1.00730 | + | 0.581566i | 0.910401 | − | 0.413728i | \(-0.135774\pi\) |
0.0969013 | + | 0.995294i | \(0.469107\pi\) | |||||||
\(972\) | 15.4930i | 0.496940i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 2.44365i | − | 0.0782996i | ||||||
\(975\) | 8.23999 | + | 4.75736i | 0.263891 | + | 0.152357i | ||||
\(976\) | 2.77164 | + | 4.80062i | 0.0887180 | + | 0.153664i | ||||
\(977\) | 22.1213 | + | 38.3153i | 0.707724 | + | 1.22581i | 0.965700 | + | 0.259662i | \(0.0836112\pi\) |
−0.257976 | + | 0.966151i | \(0.583055\pi\) | |||||||
\(978\) | 4.40649 | − | 7.63227i | 0.140904 | − | 0.244053i | ||||
\(979\) | −10.6926 | + | 5.04054i | −0.341737 | + | 0.161096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.42641i | − | 0.205179i | ||||||
\(982\) | 19.9706 | − | 34.5900i | 0.637286 | − | 1.10381i | ||||
\(983\) | 38.9736 | − | 22.5014i | 1.24306 | − | 0.717683i | 0.273347 | − | 0.961915i | \(-0.411869\pi\) |
0.969717 | + | 0.244232i | \(0.0785359\pi\) | |||||||
\(984\) | 2.48528 | + | 4.30463i | 0.0792279 | + | 0.137227i | ||||
\(985\) | −11.0866 | + | 19.2025i | −0.353247 | + | 0.611842i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.7279 | 0.404929 | ||||||||
\(989\) | 22.9369 | + | 13.2426i | 0.729352 | + | 0.421091i | ||||
\(990\) | 3.74237 | − | 5.39248i | 0.118940 | − | 0.171384i | ||||
\(991\) | 28.7990 | + | 49.8813i | 0.914830 | + | 1.58453i | 0.807150 | + | 0.590347i | \(0.201009\pi\) |
0.107680 | + | 0.994186i | \(0.465658\pi\) | |||||||
\(992\) | −0.699709 | + | 1.21193i | −0.0222158 | + | 0.0384789i | ||||
\(993\) | − | 22.1731i | − | 0.703642i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.6863 | −0.846012 | ||||||||
\(996\) | 12.5446 | + | 7.24264i | 0.397492 | + | 0.229492i | ||||
\(997\) | 3.05020 | + | 5.28311i | 0.0966009 | + | 0.167318i | 0.910276 | − | 0.414003i | \(-0.135870\pi\) |
−0.813675 | + | 0.581320i | \(0.802536\pi\) | |||||||
\(998\) | 24.7921 | − | 14.3137i | 0.784779 | − | 0.453093i | ||||
\(999\) | 27.1564 | + | 15.6788i | 0.859191 | + | 0.496054i |
(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 | 1078.2.i.a.901.2 | 16 | ||
7.2 | even | 3 | 1078.2.c.a.1077.6 | yes | 8 | ||
7.3 | odd | 6 | inner | 1078.2.i.a.1011.6 | 16 | ||
7.4 | even | 3 | inner | 1078.2.i.a.1011.7 | 16 | ||
7.5 | odd | 6 | 1078.2.c.a.1077.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 1078.2.i.a.901.3 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.a.901.6 | 16 | ||
77.10 | even | 6 | inner | 1078.2.i.a.1011.2 | 16 | ||
77.32 | odd | 6 | inner | 1078.2.i.a.1011.3 | 16 | ||
77.54 | even | 6 | 1078.2.c.a.1077.3 | yes | 8 | ||
77.65 | odd | 6 | 1078.2.c.a.1077.2 | ✓ | 8 | ||
77.76 | even | 2 | inner | 1078.2.i.a.901.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.a.1077.2 | ✓ | 8 | 77.65 | odd | 6 | ||
1078.2.c.a.1077.3 | yes | 8 | 77.54 | even | 6 | ||
1078.2.c.a.1077.6 | yes | 8 | 7.2 | even | 3 | ||
1078.2.c.a.1077.7 | yes | 8 | 7.5 | odd | 6 | ||
1078.2.i.a.901.2 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.a.901.3 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.a.901.6 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.a.901.7 | 16 | 77.76 | even | 2 | inner | ||
1078.2.i.a.1011.2 | 16 | 77.10 | even | 6 | inner | ||
1078.2.i.a.1011.3 | 16 | 77.32 | odd | 6 | inner | ||
1078.2.i.a.1011.6 | 16 | 7.3 | odd | 6 | inner | ||
1078.2.i.a.1011.7 | 16 | 7.4 | even | 3 | inner |