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 | 901.6 | ||
Root | \(0.130526 - 0.991445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.a.1011.6 |
$q$-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 | ||||
\(11\) | 3.30518 | − | 0.275255i | 0.996550 | − | 0.0829925i | ||||
\(12\) | −0.937379 | − | 0.541196i | −0.270598 | − | 0.156230i | ||||
\(13\) | −2.29610 | −0.636824 | −0.318412 | − | 0.947952i | \(-0.603149\pi\) | ||||
−0.318412 | + | 0.947952i | \(0.603149\pi\) | |||||||
\(14\) | 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 | \(0.386020\pi\) |
−0.986333 | + | 0.164766i | \(0.947313\pi\) | |||||||
\(20\) | − | 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 | \(0.0521708\pi\) | ||||
−0.986599 | + | 0.163167i | \(0.947829\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | −2.94924 | + | 2.04677i | −0.513397 | + | 0.356297i | ||||
\(34\) | 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 | \(-0.616743\pi\) | ||||
−0.358591 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 1.89097 | + | 2.72474i | 0.285074 | + | 0.410771i | ||||
\(45\) | 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 | −0.987096 | − | 0.160129i | \(-0.948809\pi\) |
0.632224 | + | 0.774786i | \(0.282142\pi\) | |||||||
\(62\) | −1.39942 | −0.177726 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.15232 | + | 1.24264i | 0.266962 | + | 0.154131i | ||||
\(66\) | −3.57750 | + | 0.297934i | −0.440360 | + | 0.0366731i | ||||
\(67\) | −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 | \(0.203153\pi\) |
0.114375 | + | 0.993438i | \(0.463513\pi\) | |||||||
\(74\) | −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 | 0.852745 | − | 0.522328i | \(-0.174936\pi\) |
−0.0259772 | + | 0.999663i | \(0.508270\pi\) | |||||||
\(80\) | 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 | \(-0.237431\pi\) | ||||
0.734469 | + | 0.678643i | \(0.237431\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.12132 | + | 3.67423i | −0.228748 | + | 0.396203i | ||||
\(87\) | −0.951076 | − | 1.64731i | −0.101966 | − | 0.176610i | ||||
\(88\) | 0.275255 | + | 3.30518i | 0.0293423 | + | 0.352334i | ||||
\(89\) | 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 | \(0.143494\pi\) |
−0.0727333 | + | 0.997351i | \(0.523172\pi\) | |||||||
\(102\) | 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 | −0.138628 | − | 0.990345i | \(-0.544269\pi\) |
−0.926977 | + | 0.375117i | \(0.877602\pi\) | |||||||
\(108\) | 4.52607 | − | 2.61313i | 0.435521 | − | 0.251448i | ||||
\(109\) | 3.04384 | − | 1.75736i | 0.291547 | − | 0.168324i | −0.347093 | − | 0.937831i | \(-0.612831\pi\) |
0.638639 | + | 0.769506i | \(0.279498\pi\) | |||||||
\(110\) | −2.04677 | − | 2.94924i | −0.195152 | − | 0.281199i | ||||
\(111\) | − | 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 | ||||||||
\(121\) | 10.8485 | − | 1.81954i | 0.986224 | − | 0.165412i | ||||
\(122\) | −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 | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | −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 | −0.675427 | − | 0.737427i | \(-0.736041\pi\) |
0.976344 | + | 0.216224i | \(0.0693740\pi\) | |||||||
\(132\) | −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 | \(-0.307891\pi\) | ||||
0.567551 | + | 0.823338i | \(0.307891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.31371 | 0.447495 | ||||||||
\(142\) | 1.73205 | + | 1.00000i | 0.145350 | + | 0.0839181i | ||||
\(143\) | −7.58903 | + | 0.632013i | −0.634627 | + | 0.0528516i | ||||
\(144\) | −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 | 0.241973 | − | 0.970283i | \(-0.422205\pi\) |
−0.719303 | + | 0.694696i | \(0.755539\pi\) | |||||||
\(150\) | 2.07193 | + | 3.58869i | 0.169172 | + | 0.293015i | ||||
\(151\) | −5.19615 | + | 3.00000i | −0.422857 | + | 0.244137i | −0.696299 | − | 0.717752i | \(-0.745171\pi\) |
0.273442 | + | 0.961888i | \(0.411838\pi\) | |||||||
\(152\) | −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 | ||||
\(165\) | 3.87226 | − | 0.322481i | 0.301455 | − | 0.0251051i | ||||
\(166\) | 11.5897 | + | 6.69133i | 0.899537 | + | 0.519348i | ||||
\(167\) | 20.2710 | 1.56861 | 0.784307 | − | 0.620373i | \(-0.213019\pi\) | ||||
0.784307 | + | 0.620373i | \(0.213019\pi\) | |||||||
\(168\) | 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 | \(0.605029\pi\) |
−0.657308 | + | 0.753622i | \(0.728305\pi\) | |||||||
\(174\) | − | 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 | −0.420532 | − | 0.907278i | \(-0.638157\pi\) |
0.575459 | + | 0.817830i | \(0.304823\pi\) | |||||||
\(194\) | 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 | \(0.260367\pi\) | ||||
−0.683706 | + | 0.729758i | \(0.739633\pi\) | |||||||
\(198\) | −4.98200 | + | 3.45750i | −0.354055 | + | 0.245714i | ||||
\(199\) | 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 | \(-0.675893\pi\) | ||
0.524890 | − | 0.851170i | \(-0.324107\pi\) | |||||||
\(212\) | 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 | ||||
\(220\) | −0.297934 | − | 3.57750i | −0.0200867 | − | 0.241195i | ||||
\(221\) | 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 | 0.849813 | − | 0.527085i | \(-0.176715\pi\) |
−0.881375 | + | 0.472417i | \(0.843382\pi\) | |||||||
\(228\) | 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 | 0.721006 | − | 0.692929i | \(-0.243680\pi\) |
−0.239591 | + | 0.970874i | \(0.577013\pi\) | |||||||
\(234\) | 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 | \(0.327425\pi\) | ||||
−0.515989 | + | 0.856595i | \(0.672575\pi\) | |||||||
\(240\) | −0.585786 | + | 1.01461i | −0.0378124 | + | 0.0654929i | ||||
\(241\) | −2.29610 | − | 3.97696i | −0.147905 | − | 0.256179i | 0.782548 | − | 0.622590i | \(-0.213920\pi\) |
−0.930453 | + | 0.366411i | \(0.880586\pi\) | |||||||
\(242\) | 10.3048 | + | 3.84847i | 0.662419 | + | 0.247389i | ||||
\(243\) | 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 | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | −2.04677 | − | 2.94924i | −0.125970 | − | 0.181513i | ||||
\(265\) | 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 | \(-0.531200\pi\) |
0.910799 | − | 0.412850i | \(-0.135467\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9706i | 1.02523i | ||||||||
\(275\) | −7.23944 | − | 10.4315i | −0.436555 | − | 0.629042i | ||||
\(276\) | 5.85172 | − | 3.37849i | 0.352232 | − | 0.203361i | ||||
\(277\) | −16.2189 | + | 9.36396i | −0.974497 | + | 0.562626i | −0.900604 | − | 0.434640i | \(-0.856876\pi\) |
−0.0738925 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(278\) | 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 | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 4.60181 | + | 2.65685i | 0.274034 | + | 0.158213i | ||||
\(283\) | −11.2835 | − | 19.5436i | −0.670736 | − | 1.16175i | −0.977696 | − | 0.210027i | \(-0.932645\pi\) |
0.306960 | − | 0.951723i | \(-0.400688\pi\) | |||||||
\(284\) | 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 | \(-0.508844\pi\) | ||||
−0.0277812 | + | 0.999614i | \(0.508844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.79899 | 0.454075 | ||||||||
\(296\) | −5.19615 | − | 3.00000i | −0.302020 | − | 0.174371i | ||||
\(297\) | −1.43855 | − | 17.2737i | −0.0834733 | − | 1.00232i | ||||
\(298\) | −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 | \(-0.568150\pi\) | ||||
−0.212467 | + | 0.977168i | \(0.568150\pi\) | |||||||
\(308\) | 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 | ||||
\(319\) | 0.483722 | + | 5.80839i | 0.0270832 | + | 0.325208i | ||||
\(320\) | 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 | \(-0.743512\pi\) | ||
0.692547 | − | 0.721373i | \(-0.256488\pi\) | |||||||
\(338\) | −6.69258 | − | 3.86396i | −0.364028 | − | 0.210172i | ||||
\(339\) | 1.32565 | − | 0.765367i | 0.0719997 | − | 0.0415690i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.81306 | + | 2.64626i | −0.206489 | + | 0.143303i | ||||
\(342\) | − | 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 | −0.669364 | − | 0.742935i | \(-0.733433\pi\) |
0.308719 | + | 0.951153i | \(0.400100\pi\) | |||||||
\(348\) | 0.951076 | − | 1.64731i | 0.0509830 | − | 0.0883052i | ||||
\(349\) | −29.0614 | −1.55562 | −0.777811 | − | 0.628498i | \(-0.783670\pi\) | ||||
−0.777811 | + | 0.628498i | \(0.783670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.0000i | 0.640513i | ||||||||
\(352\) | −2.72474 | + | 1.89097i | −0.145229 | + | 0.100789i | ||||
\(353\) | 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 | 0.555721 | − | 0.831369i | \(-0.312442\pi\) |
−0.442126 | + | 0.896953i | \(0.645776\pi\) | |||||||
\(360\) | 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 | 0.883183 | − | 0.469029i | \(-0.155396\pi\) |
0.0353999 | + | 0.999373i | \(0.488730\pi\) | |||||||
\(374\) | 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 | ||||
\(396\) | −6.04329 | + | 0.503284i | −0.303687 | + | 0.0252910i | ||||
\(397\) | −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 | \(0.218679\pi\) |
0.162675 | + | 0.986680i | \(0.447988\pi\) | |||||||
\(410\) | 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 | ||||
\(418\) | −15.1040 | + | 10.4822i | −0.738762 | + | 0.512700i | ||||
\(419\) | − | 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 | ||||||
\(429\) | 6.77176 | − | 4.69959i | 0.326944 | − | 0.226898i | ||||
\(430\) | 3.97696 | − | 2.29610i | 0.191786 | − | 0.110728i | ||||
\(431\) | −2.15232 | + | 1.24264i | −0.103673 | + | 0.0598559i | −0.550940 | − | 0.834545i | \(-0.685731\pi\) |
0.447267 | + | 0.894401i | \(0.352397\pi\) | |||||||
\(432\) | 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 | −0.778072 | − | 0.628175i | \(-0.783802\pi\) |
0.933051 | + | 0.359743i | \(0.117136\pi\) | |||||||
\(440\) | 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 | ||||
\(451\) | −15.1781 | + | 1.26403i | −0.714707 | + | 0.0595207i | ||||
\(452\) | −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 | 0.975795 | − | 0.218685i | \(-0.0701767\pi\) |
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(458\) | 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 | \(-0.736618\pi\) | ||||
−0.676762 | + | 0.736201i | \(0.736618\pi\) | |||||||
\(462\) | 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 | ||||
\(473\) | 1.16781 | + | 14.0227i | 0.0536959 | + | 0.644765i | ||||
\(474\) | −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 | 0.951659 | − | 0.307158i | \(-0.0993779\pi\) |
−0.741836 | + | 0.670582i | \(0.766045\pi\) | |||||||
\(480\) | −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 | \(-0.642644\pi\) | ||
0.433281 | − | 0.901259i | \(-0.357356\pi\) | |||||||
\(492\) | 4.30463 | + | 2.48528i | 0.194068 | + | 0.112045i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 11.0227 | − | 6.36396i | 0.495935 | − | 0.286328i | ||||
\(495\) | 5.39248 | − | 3.74237i | 0.242374 | − | 0.168207i | ||||
\(496\) | − | 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 | \(-0.546249\pi\) | ||||
−0.144784 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.0000i | − | 0.800989i | ||||||
\(506\) | −17.0096 | + | 11.8046i | −0.756169 | + | 0.524780i | ||||
\(507\) | 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 | −0.855441 | − | 0.517900i | \(-0.826714\pi\) |
0.876235 | + | 0.481884i | \(0.160047\pi\) | |||||||
\(524\) | 6.88830 | 0.300917 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.297934 | − | 3.57750i | −0.0129659 | − | 0.155691i | ||||
\(529\) | −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 | 0.690132 | − | 0.723683i | \(-0.257552\pi\) |
−0.281662 | + | 0.959514i | \(0.590886\pi\) | |||||||
\(542\) | 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 | \(0.171497\pi\) | ||||
−0.858339 | + | 0.513083i | \(0.828503\pi\) | |||||||
\(548\) | −8.48528 | + | 14.6969i | −0.362473 | + | 0.627822i | ||||
\(549\) | −5.06774 | − | 8.77758i | −0.216286 | − | 0.374618i | ||||
\(550\) | −1.05379 | − | 12.6537i | −0.0449339 | − | 0.539554i | ||||
\(551\) | −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 | −0.606028 | − | 0.795443i | \(-0.707238\pi\) |
0.385860 | + | 0.922557i | \(0.373905\pi\) | |||||||
\(558\) | 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 | \(0.0272871\pi\) |
−0.424015 | + | 0.905655i | \(0.639380\pi\) | |||||||
\(564\) | 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 | 0.933355 | − | 0.358954i | \(-0.116866\pi\) |
0.155815 | + | 0.987786i | \(0.450200\pi\) | |||||||
\(570\) | −5.62427 | + | 3.24718i | −0.235575 | + | 0.136009i | ||||
\(571\) | −31.1769 | + | 18.0000i | −1.30471 | + | 0.753277i | −0.981209 | − | 0.192950i | \(-0.938194\pi\) |
−0.323505 | + | 0.946227i | \(0.604861\pi\) | |||||||
\(572\) | −4.34186 | − | 6.25629i | −0.181542 | − | 0.261589i | ||||
\(573\) | 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 | ||||||||
\(583\) | −8.48153 | − | 12.2212i | −0.351269 | − | 0.506152i | ||||
\(584\) | −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 | \(0.366994\pi\) |
−0.994414 | + | 0.105550i | \(0.966340\pi\) | |||||||
\(594\) | 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 | \(-0.238021\pi\) | ||||
0.733210 | + | 0.680003i | \(0.238021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.3137 | 0.867961 | ||||||||
\(604\) | −5.19615 | − | 3.00000i | −0.211428 | − | 0.122068i | ||||
\(605\) | −11.1539 | − | 4.16555i | −0.453469 | − | 0.169354i | ||||
\(606\) | −9.00000 | − | 15.5885i | −0.365600 | − | 0.633238i | ||||
\(607\) | 23.1242 | − | 40.0523i | 0.938582 | − | 1.62567i | 0.170463 | − | 0.985364i | \(-0.445474\pi\) |
0.768119 | − | 0.640307i | \(-0.221193\pi\) | |||||||
\(608\) | − | 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 | −0.239710 | − | 0.970845i | \(-0.577052\pi\) |
0.720921 | + | 0.693017i | \(0.243719\pi\) | |||||||
\(614\) | −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 | ||||
\(627\) | −1.65153 | − | 19.8311i | −0.0659558 | − | 0.791978i | ||||
\(628\) | 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 | ||||
\(649\) | −19.6327 | + | 13.6251i | −0.770650 | + | 0.534830i | ||||
\(650\) | 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 | \(0.0574311\pi\) | ||||
−0.983768 | + | 0.179448i | \(0.942569\pi\) | |||||||
\(660\) | 2.21541 | + | 3.19224i | 0.0862347 | + | 0.124258i | ||||
\(661\) | −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 | \(-0.653850\pi\) | ||
0.464734 | − | 0.885450i | \(-0.346150\pi\) | |||||||
\(674\) | 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 | −0.991343 | − | 0.131294i | \(-0.958087\pi\) |
0.609376 | + | 0.792882i | \(0.291420\pi\) | |||||||
\(678\) | 1.53073 | 0.0587875 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.891519 | + | 0.514719i | 0.0341631 | + | 0.0197241i | ||||
\(682\) | −4.62533 | + | 0.385197i | −0.177113 | + | 0.0147499i | ||||
\(683\) | 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 | \(0.272013\pi\) | ||||
−0.656555 | + | 0.754278i | \(0.727987\pi\) | |||||||
\(702\) | −6.00000 | + | 10.3923i | −0.226455 | + | 0.392232i | ||||
\(703\) | −16.6298 | − | 28.8037i | −0.627206 | − | 1.08635i | ||||
\(704\) | −3.30518 | + | 0.275255i | −0.124569 | + | 0.0103741i | ||||
\(705\) | −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 | ||||
\(726\) | −11.7423 | + | 1.96945i | −0.435798 | + | 0.0730932i | ||||
\(727\) | − | 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 | −0.874674 | − | 0.484712i | \(-0.838925\pi\) |
0.857110 | + | 0.515134i | \(0.172258\pi\) | |||||||
\(734\) | −11.1409 | −0.411220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.24264i | − | 0.230107i | ||||||
\(737\) | −22.0428 | − | 31.7620i | −0.811955 | − | 1.16997i | ||||
\(738\) | 7.27159 | − | 4.19825i | 0.267671 | − | 0.154540i | ||||
\(739\) | −20.7846 | + | 12.0000i | −0.764574 | + | 0.441427i | −0.830936 | − | 0.556369i | \(-0.812194\pi\) |
0.0663614 | + | 0.997796i | \(0.478861\pi\) | |||||||
\(740\) | 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 | \(0.232925\pi\) | ||||
−0.744002 | + | 0.668178i | \(0.767075\pi\) | |||||||
\(744\) | 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 | ||||
\(759\) | −1.85989 | − | 22.3331i | −0.0675099 | − | 0.810639i | ||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | 14.3337 | − | 24.8268i | 0.519597 | − | 0.899969i | −0.480143 | − | 0.877190i | \(-0.659415\pi\) |
0.999741 | − | 0.0227789i | \(-0.00725137\pi\) | |||||||
\(762\) | 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 | \(-0.462641\pi\) | ||||
0.117096 | + | 0.993121i | \(0.462641\pi\) | |||||||
\(770\) | 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 | ||||
\(781\) | 6.61037 | − | 0.550510i | 0.236537 | − | 0.0196988i | ||||
\(782\) | 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 | 0.933667 | − | 0.358143i | \(-0.116590\pi\) |
−0.776994 | + | 0.629508i | \(0.783256\pi\) | |||||||
\(788\) | −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 | ||||
\(803\) | 29.6480 | + | 42.7206i | 1.04626 | + | 1.50758i | ||||
\(804\) | 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 | −0.262996 | − | 0.964797i | \(-0.584710\pi\) |
0.704041 | + | 0.710159i | \(0.251377\pi\) | |||||||
\(810\) | 0.0928546 | − | 0.160829i | 0.00326258 | − | 0.00565095i | ||||
\(811\) | 6.88830 | 0.241881 | 0.120940 | − | 0.992660i | \(-0.461409\pi\) | ||||
0.120940 | + | 0.992660i | \(0.461409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.9706i | 1.01604i | ||||||||
\(814\) | −16.3485 | + | 11.3458i | −0.573014 | + | 0.397671i | ||||
\(815\) | −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 | 0.693283 | − | 0.720666i | \(-0.256164\pi\) |
−0.277473 | + | 0.960733i | \(0.589497\pi\) | |||||||
\(822\) | −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 | \(0.0953404\pi\) | ||||
−0.955478 | + | 0.295062i | \(0.904660\pi\) | |||||||
\(828\) | 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 | ||||
\(836\) | −18.3215 | + | 1.52582i | −0.633664 | + | 0.0527714i | ||||
\(837\) | 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 | \(-0.530253\pi\) | ||||
−0.0948991 | + | 0.995487i | \(0.530253\pi\) | |||||||
\(854\) | 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 | 0.881812 | − | 0.471601i | \(-0.156324\pi\) |
−0.849324 | + | 0.527872i | \(0.822990\pi\) | |||||||
\(858\) | 8.21431 | − | 0.684086i | 0.280432 | − | 0.0233543i | ||||
\(859\) | −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 | \(-0.968084\pi\) |
−0.584177 | − | 0.811626i | \(-0.698583\pi\) | |||||||
\(878\) | 5.62427 | − | 3.24718i | 0.189810 | − | 0.109587i | ||||
\(879\) | 0.891519 | − | 0.514719i | 0.0300702 | − | 0.0173610i | ||||
\(880\) | 2.94924 | − | 2.04677i | 0.0994189 | − | 0.0689966i | ||||
\(881\) | 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 | −0.932764 | − | 0.360487i | \(-0.882610\pi\) |
0.778573 | + | 0.627554i | \(0.215944\pi\) | |||||||
\(888\) | 6.49435 | 0.217936 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 3.85786i | − | 0.129316i | ||||||
\(891\) | 0.324439 | + | 0.467492i | 0.0108691 | + | 0.0156616i | ||||
\(892\) | 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 | ||||
\(913\) | 44.2321 | − | 3.68364i | 1.46387 | − | 0.121911i | ||||
\(914\) | 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 | 0.867085 | − | 0.498160i | \(-0.165991\pi\) |
0.00212280 | + | 0.999998i | \(0.499324\pi\) | |||||||
\(920\) | 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 | \(-0.300225\pi\) | ||||
0.587213 | + | 0.809432i | \(0.300225\pi\) | |||||||
\(938\) | 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 | \(-0.939591\pi\) |
0.327652 | − | 0.944798i | \(-0.393742\pi\) | |||||||
\(942\) | −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 | \(-0.732884\pi\) | ||
0.668080 | − | 0.744090i | \(-0.267116\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | −3.59691 | − | 5.18288i | −0.116272 | − | 0.167539i | ||||
\(958\) | 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 | \(-0.898723\pi\) | ||
0.949810 | − | 0.312829i | \(-0.101277\pi\) | |||||||
\(968\) | 1.81954 | + | 10.8485i | 0.0584821 | + | 0.348683i | ||||
\(969\) | 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 | ||||
\(990\) | 6.54121 | − | 0.544751i | 0.207893 | − | 0.0173133i | ||||
\(991\) | 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 | 0.813675 | − | 0.581320i | \(-0.197464\pi\) |
−0.910276 | + | 0.414003i | \(0.864130\pi\) | |||||||
\(998\) | −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.901.6 | 16 | ||
7.2 | even | 3 | 1078.2.c.a.1077.2 | ✓ | 8 | ||
7.3 | odd | 6 | inner | 1078.2.i.a.1011.2 | 16 | ||
7.4 | even | 3 | inner | 1078.2.i.a.1011.3 | 16 | ||
7.5 | odd | 6 | 1078.2.c.a.1077.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 1078.2.i.a.901.7 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.a.901.2 | 16 | ||
77.10 | even | 6 | inner | 1078.2.i.a.1011.6 | 16 | ||
77.32 | odd | 6 | inner | 1078.2.i.a.1011.7 | 16 | ||
77.54 | even | 6 | 1078.2.c.a.1077.7 | yes | 8 | ||
77.65 | odd | 6 | 1078.2.c.a.1077.6 | yes | 8 | ||
77.76 | even | 2 | inner | 1078.2.i.a.901.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.a.1077.2 | ✓ | 8 | 7.2 | even | 3 | ||
1078.2.c.a.1077.3 | yes | 8 | 7.5 | odd | 6 | ||
1078.2.c.a.1077.6 | yes | 8 | 77.65 | odd | 6 | ||
1078.2.c.a.1077.7 | yes | 8 | 77.54 | even | 6 | ||
1078.2.i.a.901.2 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.a.901.3 | 16 | 77.76 | even | 2 | inner | ||
1078.2.i.a.901.6 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.a.901.7 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.a.1011.2 | 16 | 7.3 | odd | 6 | inner | ||
1078.2.i.a.1011.3 | 16 | 7.4 | even | 3 | inner | ||
1078.2.i.a.1011.6 | 16 | 77.10 | even | 6 | inner | ||
1078.2.i.a.1011.7 | 16 | 77.32 | odd | 6 | inner |