Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(289,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.bl (of order \(4\), 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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.20 | ||
Character | \(\chi\) | \(=\) | 1920.289 |
Dual form | 1920.2.bl.a.1249.20 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.24079 | − | 1.86022i | 0.554899 | − | 0.831918i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.58988 | −0.600919 | −0.300460 | − | 0.953795i | \(-0.597140\pi\) | ||||
−0.300460 | + | 0.953795i | \(0.597140\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.92109 | + | 3.92109i | −1.18225 | + | 1.18225i | −0.203093 | + | 0.979160i | \(0.565099\pi\) |
−0.979160 | + | 0.203093i | \(0.934901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.10459 | − | 3.10459i | 0.861057 | − | 0.861057i | −0.130404 | − | 0.991461i | \(-0.541627\pi\) |
0.991461 | + | 0.130404i | \(0.0416273\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.438005 | − | 2.19275i | −0.113092 | − | 0.566166i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.48346i | 0.359793i | 0.983686 | + | 0.179896i | \(0.0575762\pi\) | ||||
−0.983686 | + | 0.179896i | \(0.942424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.94087 | − | 4.94087i | −1.13351 | − | 1.13351i | −0.989589 | − | 0.143924i | \(-0.954028\pi\) |
−0.143924 | − | 0.989589i | \(-0.545972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.12422 | + | 1.12422i | −0.245324 | + | 0.245324i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.61914 | 1.38019 | 0.690094 | − | 0.723720i | \(-0.257569\pi\) | ||||
0.690094 | + | 0.723720i | \(0.257569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.92087 | − | 4.61630i | −0.384174 | − | 0.923261i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.42607 | − | 4.42607i | −0.821901 | − | 0.821901i | 0.164480 | − | 0.986380i | \(-0.447406\pi\) |
−0.986380 | + | 0.164480i | \(0.947406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50391 | −0.270110 | −0.135055 | − | 0.990838i | \(-0.543121\pi\) | ||||
−0.135055 | + | 0.990838i | \(0.543121\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.54525i | 0.965305i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.97271 | + | 2.95754i | −0.333450 | + | 0.499915i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14771 | − | 2.14771i | −0.353082 | − | 0.353082i | 0.508173 | − | 0.861255i | \(-0.330321\pi\) |
−0.861255 | + | 0.508173i | \(0.830321\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.39055i | − | 0.703050i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.84881i | − | 1.06960i | −0.844977 | − | 0.534802i | \(-0.820386\pi\) | ||
0.844977 | − | 0.534802i | \(-0.179614\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.322458 | + | 0.322458i | 0.0491744 | + | 0.0491744i | 0.731266 | − | 0.682092i | \(-0.238930\pi\) |
−0.682092 | + | 0.731266i | \(0.738930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.86022 | − | 1.24079i | −0.277306 | − | 0.184966i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 13.3031i | − | 1.94046i | −0.242188 | − | 0.970229i | \(-0.577865\pi\) | ||
0.242188 | − | 0.970229i | \(-0.422135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.47227 | −0.638896 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.04897 | + | 1.04897i | 0.146885 | + | 0.146885i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.931646 | − | 0.931646i | −0.127971 | − | 0.127971i | 0.640220 | − | 0.768192i | \(-0.278843\pi\) |
−0.768192 | + | 0.640220i | \(0.778843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.42885 | + | 12.1594i | 0.327506 | + | 1.63957i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.98744 | −0.925509 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.14326 | + | 1.14326i | −0.148840 | + | 0.148840i | −0.777600 | − | 0.628760i | \(-0.783563\pi\) |
0.628760 | + | 0.777600i | \(0.283563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67458 | − | 2.67458i | −0.342445 | − | 0.342445i | 0.514841 | − | 0.857286i | \(-0.327851\pi\) |
−0.857286 | + | 0.514841i | \(0.827851\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.58988i | 0.200306i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.92308 | − | 9.62737i | −0.238529 | − | 1.19413i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.43194 | + | 5.43194i | −0.663617 | + | 0.663617i | −0.956231 | − | 0.292614i | \(-0.905475\pi\) |
0.292614 | + | 0.956231i | \(0.405475\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.68044 | − | 4.68044i | 0.563459 | − | 0.563459i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.26233i | 0.268489i | 0.990948 | + | 0.134245i | \(0.0428608\pi\) | ||||
−0.990948 | + | 0.134245i | \(0.957139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.27105 | 0.616930 | 0.308465 | − | 0.951236i | \(-0.400185\pi\) | ||||
0.308465 | + | 0.951236i | \(0.400185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.62248 | − | 1.90596i | −0.533758 | − | 0.220081i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.23407 | − | 6.23407i | 0.710438 | − | 0.710438i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.52058 | −0.733622 | −0.366811 | − | 0.930295i | \(-0.619550\pi\) | ||||
−0.366811 | + | 0.930295i | \(0.619550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.973359 | + | 0.973359i | −0.106840 | + | 0.106840i | −0.758506 | − | 0.651666i | \(-0.774070\pi\) |
0.651666 | + | 0.758506i | \(0.274070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.75957 | + | 1.84067i | 0.299318 | + | 0.199649i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.25941 | −0.671079 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.83613i | 0.724629i | 0.932056 | + | 0.362314i | \(0.118013\pi\) | ||||
−0.932056 | + | 0.362314i | \(0.881987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.93593 | + | 4.93593i | −0.517426 | + | 0.517426i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.06342 | + | 1.06342i | −0.110272 | + | 0.110272i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.3217 | + | 3.06053i | −1.57197 | + | 0.314004i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8228i | 1.60656i | 0.595599 | + | 0.803282i | \(0.296915\pi\) | ||||
−0.595599 | + | 0.803282i | \(0.703085\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.92109 | + | 3.92109i | 0.394084 | + | 0.394084i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.18050 | + | 2.18050i | −0.216968 | + | 0.216968i | −0.807220 | − | 0.590251i | \(-0.799029\pi\) |
0.590251 | + | 0.807220i | \(0.299029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.09580 | −0.797703 | −0.398851 | − | 0.917016i | \(-0.630591\pi\) | ||||
−0.398851 | + | 0.917016i | \(0.630591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.696376 | + | 3.48622i | 0.0679594 | + | 0.340220i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00752 | + | 9.00752i | 0.870790 | + | 0.870790i | 0.992559 | − | 0.121768i | \(-0.0388565\pi\) |
−0.121768 | + | 0.992559i | \(0.538856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.91170 | + | 9.91170i | 0.949369 | + | 0.949369i | 0.998779 | − | 0.0494097i | \(-0.0157340\pi\) |
−0.0494097 | + | 0.998779i | \(0.515734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.03732 | −0.288290 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.4611i | − | 0.984094i | −0.870569 | − | 0.492047i | \(-0.836249\pi\) | ||
0.870569 | − | 0.492047i | \(-0.163751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.21298 | − | 12.3131i | 0.765865 | − | 1.14820i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.10459 | − | 3.10459i | −0.287019 | − | 0.287019i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.35853i | − | 0.216206i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.7498i | − | 1.79544i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.84284 | − | 4.84284i | −0.436664 | − | 0.436664i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9708 | − | 2.15462i | −0.981255 | − | 0.192716i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.88264i | − | 0.167057i | −0.996505 | − | 0.0835284i | \(-0.973381\pi\) | ||
0.996505 | − | 0.0835284i | \(-0.0266189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.456025 | 0.0401507 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.701725 | − | 0.701725i | −0.0613100 | − | 0.0613100i | 0.675787 | − | 0.737097i | \(-0.263804\pi\) |
−0.737097 | + | 0.675787i | \(0.763804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.85540 | + | 7.85540i | 0.681150 | + | 0.681150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.19275 | + | 0.438005i | −0.188722 | + | 0.0376974i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7042 | 1.42714 | 0.713568 | − | 0.700586i | \(-0.247078\pi\) | ||||
0.713568 | + | 0.700586i | \(0.247078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.03646 | − | 5.03646i | 0.427187 | − | 0.427187i | −0.460482 | − | 0.887669i | \(-0.652323\pi\) |
0.887669 | + | 0.460482i | \(0.152323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.40672 | − | 9.40672i | −0.792189 | − | 0.792189i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.3467i | 2.03597i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.7253 | + | 2.74165i | −1.13983 | + | 0.227682i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.16237 | + | 3.16237i | −0.260828 | + | 0.260828i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.2283 | − | 12.2283i | 1.00178 | − | 1.00178i | 0.00178156 | − | 0.999998i | \(-0.499433\pi\) |
0.999998 | − | 0.00178156i | \(-0.000567087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.567736i | − | 0.0462017i | −0.999733 | − | 0.0231008i | \(-0.992646\pi\) | ||
0.999733 | − | 0.0231008i | \(-0.00735388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.48346 | 0.119931 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.86604 | + | 2.79761i | −0.149884 | + | 0.224709i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.06109 | + | 8.06109i | −0.643345 | + | 0.643345i | −0.951376 | − | 0.308031i | \(-0.900330\pi\) |
0.308031 | + | 0.951376i | \(0.400330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.31755 | −0.104488 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.5237 | −0.829381 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0969036 | − | 0.0969036i | 0.00759008 | − | 0.00759008i | −0.703302 | − | 0.710892i | \(-0.748292\pi\) |
0.710892 | + | 0.703302i | \(0.248292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.3154 | + | 6.88051i | 0.803054 | + | 0.535647i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.9619 | 1.15779 | 0.578894 | − | 0.815403i | \(-0.303484\pi\) | ||||
0.578894 | + | 0.815403i | \(0.303484\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.27691i | − | 0.482839i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.94087 | + | 4.94087i | −0.377838 | + | 0.377838i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1447 | − | 13.1447i | 0.999374 | − | 0.999374i | −0.000626029 | − | 1.00000i | \(-0.500199\pi\) |
1.00000 | 0.000626029i | \(0.000199271\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.05396 | + | 7.33938i | 0.230858 | + | 0.554805i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.61682i | 0.121527i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.56192 | − | 3.56192i | −0.266230 | − | 0.266230i | 0.561349 | − | 0.827579i | \(-0.310283\pi\) |
−0.827579 | + | 0.561349i | \(0.810283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.89499 | + | 5.89499i | −0.438171 | + | 0.438171i | −0.891396 | − | 0.453225i | \(-0.850273\pi\) |
0.453225 | + | 0.891396i | \(0.350273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.78243 | −0.279605 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.66009 | + | 1.33036i | −0.489660 | + | 0.0978102i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.81679 | − | 5.81679i | −0.425366 | − | 0.425366i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.12422 | + | 1.12422i | 0.0817748 | + | 0.0817748i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.695196 | −0.0503026 | −0.0251513 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251513 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 23.8401i | − | 1.71605i | −0.513611 | − | 0.858023i | \(-0.671693\pi\) | ||
0.513611 | − | 0.858023i | \(-0.328307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.16740 | − | 5.44776i | −0.584880 | − | 0.390122i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.90642 | − | 3.90642i | −0.278321 | − | 0.278321i | 0.554118 | − | 0.832438i | \(-0.313056\pi\) |
−0.832438 | + | 0.554118i | \(0.813056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.84627i | − | 0.272655i | −0.990664 | − | 0.136328i | \(-0.956470\pi\) | ||
0.990664 | − | 0.136328i | \(-0.0435300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.68192i | 0.541841i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.03694 | + | 7.03694i | 0.493896 | + | 0.493896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7403 | − | 8.49795i | −0.889823 | − | 0.593523i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.61914i | − | 0.460062i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.7471 | 2.68020 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.77616 | − | 8.77616i | −0.604176 | − | 0.604176i | 0.337242 | − | 0.941418i | \(-0.390506\pi\) |
−0.941418 | + | 0.337242i | \(0.890506\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.59971 | + | 1.59971i | 0.109610 | + | 0.109610i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.999948 | − | 0.199741i | 0.0681959 | − | 0.0136222i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.39104 | 0.162314 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.72720 | − | 3.72720i | 0.251861 | − | 0.251861i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.60554 | + | 4.60554i | 0.309802 | + | 0.309802i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.4599i | − | 0.901341i | −0.892690 | − | 0.450671i | \(-0.851185\pi\) | ||
0.892690 | − | 0.450671i | \(-0.148815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61630 | + | 1.92087i | −0.307754 | + | 0.128058i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.2029 | − | 16.2029i | 1.07542 | − | 1.07542i | 0.0785084 | − | 0.996913i | \(-0.474984\pi\) |
0.996913 | − | 0.0785084i | \(-0.0250157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34898 | + | 1.34898i | −0.0891433 | + | 0.0891433i | −0.750272 | − | 0.661129i | \(-0.770078\pi\) |
0.661129 | + | 0.750272i | \(0.270078\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.81631i | − | 0.580070i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0887 | 0.857470 | 0.428735 | − | 0.903430i | \(-0.358959\pi\) | ||||
0.428735 | + | 0.903430i | \(0.358959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.7468 | − | 16.5064i | −1.61430 | − | 1.07676i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.61074 | + | 4.61074i | −0.299500 | + | 0.299500i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0340 | 0.713730 | 0.356865 | − | 0.934156i | \(-0.383846\pi\) | ||||
0.356865 | + | 0.934156i | \(0.383846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.31401 | 0.535553 | 0.267776 | − | 0.963481i | \(-0.413711\pi\) | ||||
0.267776 | + | 0.963481i | \(0.413711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.54916 | + | 8.31943i | −0.354523 | + | 0.531509i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.6787 | −1.95204 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.37654i | 0.0872345i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0055 | + | 15.0055i | −0.947138 | + | 0.947138i | −0.998671 | − | 0.0515329i | \(-0.983589\pi\) |
0.0515329 | + | 0.998671i | \(0.483589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.9542 | + | 25.9542i | −1.63173 | + | 1.63173i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.25286 | − | 0.649764i | 0.203702 | − | 0.0406898i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 14.3773i | − | 0.896831i | −0.893825 | − | 0.448415i | \(-0.851989\pi\) | ||
0.893825 | − | 0.448415i | \(-0.148011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.41461 | + | 3.41461i | 0.212174 | + | 0.212174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.42607 | + | 4.42607i | −0.273967 | + | 0.273967i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.94045 | 0.304641 | 0.152320 | − | 0.988331i | \(-0.451325\pi\) | ||||
0.152320 | + | 0.988331i | \(0.451325\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.88905 | + | 0.577092i | −0.177473 | + | 0.0354505i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.83388 | + | 4.83388i | 0.295828 | + | 0.295828i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5951 | + | 11.5951i | 0.706967 | + | 0.706967i | 0.965896 | − | 0.258929i | \(-0.0833696\pi\) |
−0.258929 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.40933 | −0.207102 | −0.103551 | − | 0.994624i | \(-0.533021\pi\) | ||||
−0.103551 | + | 0.994624i | \(0.533021\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.98046i | 0.422476i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.6328 | + | 10.5690i | 1.54572 | + | 0.637337i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2957 | − | 11.2957i | −0.678690 | − | 0.678690i | 0.281014 | − | 0.959704i | \(-0.409329\pi\) |
−0.959704 | + | 0.281014i | \(0.909329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50391i | 0.0900366i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.72775i | 0.282034i | 0.990007 | + | 0.141017i | \(0.0450372\pi\) | ||||
−0.990007 | + | 0.141017i | \(0.954963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.51882 | + | 6.51882i | 0.387504 | + | 0.387504i | 0.873796 | − | 0.486292i | \(-0.161651\pi\) |
−0.486292 | + | 0.873796i | \(0.661651\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.66996 | + | 12.9982i | −0.513564 | + | 0.769948i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.8888i | 0.642746i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7993 | 0.870549 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1884 | + | 11.1884i | 0.655877 | + | 0.655877i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.60652 | + | 2.60652i | 0.152274 | + | 0.152274i | 0.779133 | − | 0.626859i | \(-0.215660\pi\) |
−0.626859 | + | 0.779133i | \(0.715660\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.708173 | + | 3.54527i | 0.0412314 | + | 0.206414i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.54525 | 0.321768 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.5497 | − | 20.5497i | 1.18842 | − | 1.18842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.512671 | − | 0.512671i | −0.0295499 | − | 0.0295499i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.08370i | 0.177154i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.29392 | + | 1.65672i | −0.474909 | + | 0.0948636i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.27735 | + | 9.27735i | −0.529486 | + | 0.529486i | −0.920419 | − | 0.390933i | \(-0.872152\pi\) |
0.390933 | + | 0.920419i | \(0.372152\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.72459 | + | 5.72459i | −0.325661 | + | 0.325661i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.87398i | 0.503197i | 0.967832 | + | 0.251599i | \(0.0809563\pi\) | ||||
−0.967832 | + | 0.251599i | \(0.919044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.6160 | −1.44790 | −0.723952 | − | 0.689850i | \(-0.757676\pi\) | ||||
−0.723952 | + | 0.689850i | \(0.757676\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.95754 | + | 1.97271i | 0.166638 | + | 0.111150i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5425 | − | 19.5425i | 1.09762 | − | 1.09762i | 0.102929 | − | 0.994689i | \(-0.467179\pi\) |
0.994689 | − | 0.102929i | \(-0.0328215\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.7100 | 1.94339 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7386 | 0.710997 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.32960 | − | 7.32960i | 0.407830 | − | 0.407830i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.2952 | − | 8.36821i | −1.12578 | − | 0.464185i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.0173 | 0.775156 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.1504i | 1.16606i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.9546 | − | 17.9546i | 0.986875 | − | 0.986875i | −0.0130395 | − | 0.999915i | \(-0.504151\pi\) |
0.999915 | + | 0.0130395i | \(0.00415073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.14771 | + | 2.14771i | −0.117694 | + | 0.117694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.36472 | + | 16.8445i | 0.183834 | + | 0.920315i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1385i | 1.64175i | 0.571108 | + | 0.820875i | \(0.306514\pi\) | ||||
−0.571108 | + | 0.820875i | \(0.693486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.39709 | − | 7.39709i | −0.401755 | − | 0.401755i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.89695 | − | 5.89695i | 0.319338 | − | 0.319338i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2396 | 0.984844 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.89922 | − | 14.5141i | −0.156089 | − | 0.781414i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1738 | + | 17.1738i | 0.921936 | + | 0.921936i | 0.997166 | − | 0.0752299i | \(-0.0239691\pi\) |
−0.0752299 | + | 0.997166i | \(0.523969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7155 | + | 11.7155i | 0.627115 | + | 0.627115i | 0.947341 | − | 0.320226i | \(-0.103759\pi\) |
−0.320226 | + | 0.947341i | \(0.603759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.39055 | −0.234350 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.34745i | − | 0.124942i | −0.998047 | − | 0.0624712i | \(-0.980102\pi\) | ||
0.998047 | − | 0.0624712i | \(-0.0198982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.20844 | + | 2.80708i | 0.223361 | + | 0.148984i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.66773 | − | 1.66773i | −0.0882659 | − | 0.0882659i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 28.6304i | − | 1.51106i | −0.655116 | − | 0.755529i | \(-0.727380\pi\) | ||
0.655116 | − | 0.755529i | \(-0.272620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.8243i | 1.56970i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.9652 | − | 13.9652i | −0.732986 | − | 0.732986i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.54028 | − | 9.80534i | 0.342334 | − | 0.513235i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12.5964i | − | 0.657527i | −0.944412 | − | 0.328764i | \(-0.893368\pi\) | ||
0.944412 | − | 0.328764i | \(-0.106632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.84881 | −0.356535 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.48121 | + | 1.48121i | 0.0769005 | + | 0.0769005i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5946 | + | 10.5946i | 0.548568 | + | 0.548568i | 0.926027 | − | 0.377458i | \(-0.123202\pi\) |
−0.377458 | + | 0.926027i | \(0.623202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.28105 | + | 6.23395i | −0.479271 | + | 0.321920i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.4822 | −1.41541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8712 | − | 25.8712i | 1.32891 | − | 1.32891i | 0.422593 | − | 0.906320i | \(-0.361120\pi\) |
0.906320 | − | 0.422593i | \(-0.138880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.33122 | − | 1.33122i | −0.0682007 | − | 0.0682007i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.25894i | − | 0.217622i | −0.994062 | − | 0.108811i | \(-0.965296\pi\) | ||
0.994062 | − | 0.108811i | \(-0.0347043\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.86158 | − | 19.3320i | −0.196805 | − | 0.985247i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.322458 | − | 0.322458i | 0.0163915 | − | 0.0163915i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.1209 | + | 22.1209i | −1.12158 | + | 1.12158i | −0.130071 | + | 0.991505i | \(0.541520\pi\) |
−0.991505 | + | 0.130071i | \(0.958480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.81926i | 0.496581i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.992388 | −0.0500594 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.09068 | + | 12.1297i | −0.407086 | + | 0.610313i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9968 | − | 12.9968i | 0.652290 | − | 0.652290i | −0.301254 | − | 0.953544i | \(-0.597405\pi\) |
0.953544 | + | 0.301254i | \(0.0974053\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.1092 | 0.556156 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.3598 | −1.76578 | −0.882892 | − | 0.469577i | \(-0.844406\pi\) | ||||
−0.882892 | + | 0.469577i | \(0.844406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.66901 | + | 4.66901i | −0.232580 | + | 0.232580i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.24079 | + | 1.86022i | −0.0616555 | + | 0.0924353i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.8427 | 0.834863 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.3933i | 1.35451i | 0.735747 | + | 0.677256i | \(0.236831\pi\) | ||||
−0.735747 | + | 0.677256i | \(0.763169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8117 | − | 11.8117i | 0.582626 | − | 0.582626i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.81765 | − | 1.81765i | 0.0894408 | − | 0.0894408i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.602930 | + | 3.01840i | 0.0295967 | + | 0.148168i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 7.12264i | − | 0.348797i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.71334 | − | 3.71334i | −0.181409 | − | 0.181409i | 0.610561 | − | 0.791969i | \(-0.290944\pi\) |
−0.791969 | + | 0.610561i | \(0.790944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7755 | − | 10.7755i | 0.525167 | − | 0.525167i | −0.393960 | − | 0.919127i | \(-0.628895\pi\) |
0.919127 | + | 0.393960i | \(0.128895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.3031 | −0.646820 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.84812 | − | 2.84954i | 0.332182 | − | 0.138223i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.25227 | + | 4.25227i | 0.205782 | + | 0.205782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.2157 | + | 17.2157i | 0.831183 | + | 0.831183i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0581 | 1.44785 | 0.723924 | − | 0.689880i | \(-0.242337\pi\) | ||||
0.723924 | + | 0.689880i | \(0.242337\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.1636i | 0.968999i | 0.874791 | + | 0.484500i | \(0.160998\pi\) | ||||
−0.874791 | + | 0.484500i | \(0.839002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.76663 | + | 11.6439i | −0.372381 | + | 0.558283i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.7043 | − | 32.7043i | −1.56446 | − | 1.56446i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.0789i | − | 1.34013i | −0.742302 | − | 0.670065i | \(-0.766266\pi\) | ||
0.742302 | − | 0.670065i | \(-0.233734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.47227i | 0.212965i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.23844 | − | 3.23844i | −0.153863 | − | 0.153863i | 0.625978 | − | 0.779841i | \(-0.284700\pi\) |
−0.779841 | + | 0.625978i | \(0.784700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7167 | + | 8.48222i | 0.602831 | + | 0.402096i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 17.2934i | − | 0.817950i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.06033 | 0.0500401 | 0.0250201 | − | 0.999687i | \(-0.492035\pi\) | ||||
0.0250201 | + | 0.999687i | \(0.492035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.8548 | + | 26.8548i | 1.26454 | + | 1.26454i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.401450 | − | 0.401450i | −0.0188618 | − | 0.0188618i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.05747 | + | 15.3064i | 0.143337 | + | 0.717575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.95861 | 0.185176 | 0.0925880 | − | 0.995705i | \(-0.470486\pi\) | ||||
0.0925880 | + | 0.995705i | \(0.470486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.04897 | − | 1.04897i | 0.0489616 | − | 0.0489616i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.2310 | + | 17.2310i | 0.802526 | + | 0.802526i | 0.983490 | − | 0.180963i | \(-0.0579216\pi\) |
−0.180963 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.4839i | − | 0.673122i | −0.941662 | − | 0.336561i | \(-0.890736\pi\) | ||
0.941662 | − | 0.336561i | \(-0.109264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.658719 | + | 3.29769i | 0.0305473 | + | 0.152927i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.0437 | + | 26.0437i | −1.20516 | + | 1.20516i | −0.232585 | + | 0.972576i | \(0.574718\pi\) |
−0.972576 | + | 0.232585i | \(0.925282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.63615 | − | 8.63615i | 0.398780 | − | 0.398780i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4001i | 0.525289i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.52877 | −0.116273 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.3178 | + | 32.2993i | −0.611062 | + | 1.48199i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.931646 | + | 0.931646i | −0.0426572 | + | 0.0426572i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5284 | −0.846586 | −0.423293 | − | 0.905993i | \(-0.639126\pi\) | ||||
−0.423293 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3355 | −0.608047 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.44135 | + | 7.44135i | −0.338593 | + | 0.338593i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.4340 | + | 19.6328i | 1.33653 | + | 0.891481i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.16579 | −0.188770 | −0.0943851 | − | 0.995536i | \(-0.530088\pi\) | ||||
−0.0943851 | + | 0.995536i | \(0.530088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.137042i | − | 0.00619727i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2554 | − | 20.2554i | 0.914115 | − | 0.914115i | −0.0824778 | − | 0.996593i | \(-0.526283\pi\) |
0.996593 | + | 0.0824778i | \(0.0262833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.56591 | − | 6.56591i | 0.295714 | − | 0.295714i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.1594 | − | 2.42885i | 0.546522 | − | 0.109169i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.59684i | − | 0.161340i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.41192 | − | 5.41192i | −0.242271 | − | 0.242271i | 0.575518 | − | 0.817789i | \(-0.304800\pi\) |
−0.817789 | + | 0.575518i | \(0.804800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5797 | − | 10.5797i | 0.472665 | − | 0.472665i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.09459 | −0.0933934 | −0.0466967 | − | 0.998909i | \(-0.514869\pi\) | ||||
−0.0466967 | + | 0.998909i | \(0.514869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.35067 | + | 6.76178i | 0.0601042 | + | 0.300895i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.43845 | − | 4.43845i | −0.197118 | − | 0.197118i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2653 | + | 26.2653i | 1.16419 | + | 1.16419i | 0.983550 | + | 0.180638i | \(0.0578161\pi\) |
0.180638 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.38036 | −0.370725 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.98744i | 0.308503i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0452 | + | 15.0600i | −0.442644 | + | 0.663623i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.1627 | + | 52.1627i | 2.29411 | + | 2.29411i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.5894i | − | 0.815985i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.2533i | − | 0.449205i | −0.974450 | − | 0.224602i | \(-0.927892\pi\) | ||
0.974450 | − | 0.224602i | \(-0.0721083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.87557 | + | 7.87557i | 0.344375 | + | 0.344375i | 0.858009 | − | 0.513634i | \(-0.171701\pi\) |
−0.513634 | + | 0.858009i | \(0.671701\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.34920 | + | 3.03025i | 0.320745 | + | 0.132251i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.23099i | − | 0.0971835i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8131 | 0.904916 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.14326 | + | 1.14326i | 0.0496133 | + | 0.0496133i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.2627 | − | 21.2627i | −0.920991 | − | 0.920991i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.9325 | − | 5.57955i | 1.20763 | − | 0.241225i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.03731 | −0.217376 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.5362 | − | 17.5362i | 0.755336 | − | 0.755336i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6782 | − | 23.6782i | −1.01800 | − | 1.01800i | −0.999835 | − | 0.0181698i | \(-0.994216\pi\) |
−0.0181698 | − | 0.999835i | \(-0.505784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.33678i | 0.357765i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.7364 | − | 6.13963i | 1.31660 | − | 0.262993i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.60366 | + | 6.60366i | −0.282352 | + | 0.282352i | −0.834046 | − | 0.551694i | \(-0.813982\pi\) |
0.551694 | + | 0.834046i | \(0.313982\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.67458 | + | 2.67458i | −0.114148 | + | 0.114148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.7373i | 1.86327i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3670 | 0.440848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.76869 | + | 5.65010i | −0.159972 | + | 0.239834i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.5466 | + | 11.5466i | −0.489245 | + | 0.489245i | −0.908068 | − | 0.418823i | \(-0.862443\pi\) |
0.418823 | + | 0.908068i | \(0.362443\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00220 | 0.0846840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.22618 | −0.347310 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3335 | − | 13.3335i | 0.561940 | − | 0.561940i | −0.367918 | − | 0.929858i | \(-0.619929\pi\) |
0.929858 | + | 0.367918i | \(0.119929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.4599 | − | 12.9800i | −0.818685 | − | 0.546073i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.58988 | 0.0667688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 13.8256i | − | 0.579600i | −0.957087 | − | 0.289800i | \(-0.906411\pi\) | ||
0.957087 | − | 0.289800i | \(-0.0935887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.8448 | + | 17.8448i | −0.746781 | + | 0.746781i | −0.973873 | − | 0.227092i | \(-0.927078\pi\) |
0.227092 | + | 0.973873i | \(0.427078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.491578 | + | 0.491578i | −0.0205360 | + | 0.0205360i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7145 | − | 30.5560i | −0.530232 | − | 1.27427i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.6737i | 0.943918i | 0.881620 | + | 0.471959i | \(0.156453\pi\) | ||||
−0.881620 | + | 0.471959i | \(0.843547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.8575 | − | 16.8575i | −0.700573 | − | 0.700573i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.54753 | − | 1.54753i | 0.0642022 | − | 0.0642022i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.30613 | 0.302589 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.62737 | + | 1.92308i | −0.398043 | + | 0.0795096i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.96994 | + | 9.96994i | 0.411504 | + | 0.411504i | 0.882262 | − | 0.470758i | \(-0.156020\pi\) |
−0.470758 | + | 0.882262i | \(0.656020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.43061 | + | 7.43061i | 0.306173 | + | 0.306173i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.52451 | −0.227248 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.5396i | 1.50050i | 0.661153 | + | 0.750251i | \(0.270067\pi\) | ||||
−0.661153 | + | 0.750251i | \(0.729933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.38740 | − | 2.92645i | −0.179866 | − | 0.119973i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.71973 | − | 2.71973i | −0.111311 | − | 0.111311i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.77638i | − | 0.317734i | −0.987300 | − | 0.158867i | \(-0.949216\pi\) | ||
0.987300 | − | 0.158867i | \(-0.0507841\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7530i | 1.29523i | 0.761966 | + | 0.647617i | \(0.224234\pi\) | ||||
−0.761966 | + | 0.647617i | \(0.775766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.43194 | + | 5.43194i | 0.221206 | + | 0.221206i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.7391 | − | 24.5055i | −1.49366 | − | 0.996288i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.7877i | 1.24963i | 0.780771 | + | 0.624817i | \(0.214826\pi\) | ||||
−0.780771 | + | 0.624817i | \(0.785174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.95173 | 0.403264 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −41.3007 | − | 41.3007i | −1.67085 | − | 1.67085i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1437 | − | 18.1437i | −0.732818 | − | 0.732818i | 0.238359 | − | 0.971177i | \(-0.423391\pi\) |
−0.971177 | + | 0.238359i | \(0.923391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.0177 | + | 2.99981i | −0.605573 | + | 0.120964i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.8136 | 0.596372 | 0.298186 | − | 0.954508i | \(-0.403619\pi\) | ||||
0.298186 | + | 0.954508i | \(0.403619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.05155 | + | 6.05155i | −0.243232 | + | 0.243232i | −0.818186 | − | 0.574954i | \(-0.805020\pi\) |
0.574954 | + | 0.818186i | \(0.305020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.68044 | − | 4.68044i | −0.187820 | − | 0.187820i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 10.8687i | − | 0.435443i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6205 | + | 17.7346i | −0.704821 | + | 0.709385i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.3984 | − | 27.3984i | 1.09419 | − | 1.09419i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.18605 | − | 3.18605i | 0.127036 | − | 0.127036i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.8534i | − | 1.42730i | −0.700502 | − | 0.713650i | \(-0.747041\pi\) | ||
0.700502 | − | 0.713650i | \(-0.252959\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.4114 | −0.493307 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.50212 | − | 2.33596i | −0.138978 | − | 0.0926997i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8846 | + | 13.8846i | −0.550126 | + | 0.550126i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.26233 | 0.0894964 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.4688 | 0.610979 | 0.305490 | − | 0.952195i | \(-0.401180\pi\) | ||||
0.305490 | + | 0.952195i | \(0.401180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.6098 | + | 11.6098i | −0.457847 | + | 0.457847i | −0.897948 | − | 0.440101i | \(-0.854943\pi\) |
0.440101 | + | 0.897948i | \(0.354943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.565832 | − | 0.848308i | 0.0222796 | − | 0.0334021i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0688 | −0.710357 | −0.355178 | − | 0.934799i | \(-0.615580\pi\) | ||||
−0.355178 | + | 0.934799i | \(0.615580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.96566i | − | 0.351933i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.69072 | − | 1.69072i | 0.0662645 | − | 0.0662645i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.64829 | − | 3.64829i | 0.142769 | − | 0.142769i | −0.632110 | − | 0.774879i | \(-0.717811\pi\) |
0.774879 | + | 0.632110i | \(0.217811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.17606 | + | 0.434671i | −0.0850257 | + | 0.0169840i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.27105i | − | 0.205643i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7113 | + | 20.7113i | 0.806796 | + | 0.806796i | 0.984148 | − | 0.177351i | \(-0.0567529\pi\) |
−0.177351 | + | 0.984148i | \(0.556753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.7363 | + | 11.7363i | −0.456488 | + | 0.456488i | −0.897501 | − | 0.441013i | \(-0.854619\pi\) |
0.441013 | + | 0.897501i | \(0.354619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.51322 | 0.252952 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.3597 | − | 4.86589i | 0.944630 | − | 0.188691i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.2968 | − | 29.2968i | −1.13438 | − | 1.13438i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.51759 | − | 9.51759i | −0.367971 | − | 0.367971i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9745 | 0.809713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.5085i | − | 1.63858i | −0.573379 | − | 0.819290i | \(-0.694368\pi\) | ||
0.573379 | − | 0.819290i | \(-0.305632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.90596 | + | 4.62248i | −0.0733604 | + | 0.177919i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5124 | + | 16.5124i | 0.634623 | + | 0.634623i | 0.949224 | − | 0.314601i | \(-0.101871\pi\) |
−0.314601 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 25.1564i | − | 0.965416i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 22.9143i | − | 0.878078i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1836 | − | 18.1836i | −0.695777 | − | 0.695777i | 0.267720 | − | 0.963497i | \(-0.413730\pi\) |
−0.963497 | + | 0.267720i | \(0.913730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7264 | − | 31.0736i | 0.791917 | − | 1.18726i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.90775i | 0.0727852i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.78475 | −0.220382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9630 | + | 13.9630i | 0.531178 | + | 0.531178i | 0.920923 | − | 0.389745i | \(-0.127437\pi\) |
−0.389745 | + | 0.920923i | \(0.627437\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.23407 | − | 6.23407i | −0.236813 | − | 0.236813i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.11975 | − | 15.6182i | −0.118339 | − | 0.592430i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.1600 | 0.384836 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.25511 | − | 9.25511i | 0.350061 | − | 0.350061i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7918 | + | 15.7918i | 0.596448 | + | 0.596448i | 0.939365 | − | 0.342918i | \(-0.111415\pi\) |
−0.342918 | + | 0.939365i | \(0.611415\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.2231i | 0.800445i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.1704 | + | 5.82683i | −1.09862 | + | 0.219451i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46675 | − | 3.46675i | 0.130380 | − | 0.130380i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4875 | − | 12.4875i | 0.468977 | − | 0.468977i | −0.432606 | − | 0.901583i | \(-0.642406\pi\) |
0.901583 | + | 0.432606i | \(0.142406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.52058i | 0.244541i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.95458 | −0.372802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45.2903 | + | 30.2092i | 1.69376 | + | 1.12976i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.80221 | − | 7.80221i | 0.291379 | − | 0.291379i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.6025 | 0.992107 | 0.496053 | − | 0.868292i | \(-0.334782\pi\) | ||||
0.496053 | + | 0.868292i | \(0.334782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8714 | 0.479355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.87890 | − | 5.87890i | 0.218638 | − | 0.218638i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.9302 | + | 28.9340i | −0.443076 | + | 1.07458i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.84475 | −0.216770 | −0.108385 | − | 0.994109i | \(-0.534568\pi\) | ||||
−0.108385 | + | 0.994109i | \(0.534568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.478355 | + | 0.478355i | −0.0176926 | + | 0.0176926i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.4267 | − | 34.4267i | 1.27158 | − | 1.27158i | 0.326318 | − | 0.945260i | \(-0.394192\pi\) |
0.945260 | − | 0.326318i | \(-0.105808\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.95888 | + | 9.80657i | 0.0722542 | + | 0.361721i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 42.5982i | − | 1.56913i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.03861 | + | 8.03861i | 0.295705 | + | 0.295705i | 0.839329 | − | 0.543624i | \(-0.182948\pi\) |
−0.543624 | + | 0.839329i | \(0.682948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.6931 | + | 21.6931i | −0.796917 | + | 0.796917i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.14206 | −0.151957 | −0.0759787 | − | 0.997109i | \(-0.524208\pi\) | ||||
−0.0759787 | + | 0.997109i | \(0.524208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.57459 | − | 37.9201i | −0.277512 | − | 1.38929i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.973359 | + | 0.973359i | 0.0356133 | + | 0.0356133i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3209 | − | 14.3209i | −0.523275 | − | 0.523275i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.0366 | −1.93533 | −0.967667 | − | 0.252232i | \(-0.918835\pi\) | ||||
−0.967667 | + | 0.252232i | \(0.918835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.2210i | 0.773335i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.05612 | − | 0.704442i | −0.0384360 | − | 0.0256373i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.39557 | − | 4.39557i | −0.159760 | − | 0.159760i | 0.622701 | − | 0.782460i | \(-0.286035\pi\) |
−0.782460 | + | 0.622701i | \(0.786035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.7048i | 1.33230i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.0961i | − | 0.619732i | −0.950780 | − | 0.309866i | \(-0.899716\pi\) | ||
0.950780 | − | 0.309866i | \(-0.100284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.7584 | − | 15.7584i | −0.570494 | − | 0.570494i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.84067 | − | 2.75957i | 0.0665495 | − | 0.0997726i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.09871i | 0.256320i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.3744 | 1.20351 | 0.601756 | − | 0.798680i | \(-0.294468\pi\) | ||||
0.601756 | + | 0.798680i | \(0.294468\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1663 | − | 10.1663i | −0.366130 | − | 0.366130i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0507 | + | 23.0507i | 0.829078 | + | 0.829078i | 0.987389 | − | 0.158312i | \(-0.0506051\pi\) |
−0.158312 | + | 0.987389i | \(0.550605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.88881 | + | 6.94249i | 0.103769 | + | 0.249382i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.82899 | 0.173239 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.8391 | + | 33.8391i | −1.21241 | + | 1.21241i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.87079 | − | 8.87079i | −0.317422 | − | 0.317422i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.25941i | 0.223693i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.99330 | + | 24.9976i | 0.178218 | + | 0.892201i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.1563 | + | 10.1563i | −0.362034 | + | 0.362034i | −0.864561 | − | 0.502527i | \(-0.832404\pi\) |
0.502527 | + | 0.864561i | \(0.332404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.49342 | − | 3.49342i | 0.124369 | − | 0.124369i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.6319i | 0.591361i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6069 | −0.589730 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.63480 | + | 2.45093i | −0.0579804 | + | 0.0869256i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6189 | + | 24.6189i | −0.872046 | + | 0.872046i | −0.992695 | − | 0.120649i | \(-0.961502\pi\) |
0.120649 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7347 | 0.698163 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.83613 | 0.241543 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.6683 | + | 20.6683i | −0.729367 | + | 0.729367i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.0577 | + | 19.5764i | −0.460223 | + | 0.689977i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3980 | 0.577236 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5505i | 0.863150i | 0.902077 | + | 0.431575i | \(0.142042\pi\) | ||||
−0.902077 | + | 0.431575i | \(0.857958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.4539 | + | 13.4539i | −0.472430 | + | 0.472430i | −0.902700 | − | 0.430270i | \(-0.858418\pi\) |
0.430270 | + | 0.902700i | \(0.358418\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.41076 | + | 2.41076i | −0.0845491 | + | 0.0845491i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0600252 | − | 0.300500i | −0.00210259 | − | 0.0105260i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.18645i | − | 0.111480i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.93593 | + | 4.93593i | 0.172475 | + | 0.172475i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.23091 | − | 7.23091i | 0.252360 | − | 0.252360i | −0.569577 | − | 0.821938i | \(-0.692893\pi\) |
0.821938 | + | 0.569577i | \(0.192893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.5825 | −1.48433 | −0.742167 | − | 0.670215i | \(-0.766202\pi\) | ||||
−0.742167 | + | 0.670215i | \(0.766202\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.5986 | − | 10.6517i | 0.891228 | − | 0.370845i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4053 | − | 18.4053i | −0.640014 | − | 0.640014i | 0.310545 | − | 0.950559i | \(-0.399488\pi\) |
−0.950559 | + | 0.310545i | \(0.899488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8176 | − | 10.8176i | −0.375710 | − | 0.375710i | 0.493842 | − | 0.869552i | \(-0.335592\pi\) |
−0.869552 | + | 0.493842i | \(0.835592\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9745 | −0.554148 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.63445i | − | 0.229870i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.5646 | − | 27.8325i | 0.642456 | − | 0.963185i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.06342 | + | 1.06342i | 0.0367573 | + | 0.0367573i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.8332i | − | 0.374004i | −0.982360 | − | 0.187002i | \(-0.940123\pi\) | ||
0.982360 | − | 0.187002i | \(-0.0598771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1802i | 0.351042i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.34302 | + | 3.34302i | 0.115140 | + | 0.115140i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6765 | − | 7.78834i | −0.401683 | − | 0.267927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.3999i | 1.07891i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.21901 | 0.316396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.2160 | − | 14.2160i | −0.487319 | − | 0.487319i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.7242 | − | 31.7242i | −1.08622 | − | 1.08622i | −0.995915 | − | 0.0903009i | \(-0.971217\pi\) |
−0.0903009 | − | 0.995915i | \(-0.528783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.06053 | + | 15.3217i | 0.104668 | + | 0.523992i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.9570 | −1.36490 | −0.682452 | − | 0.730930i | \(-0.739086\pi\) | ||||
−0.682452 | + | 0.730930i | \(0.739086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.9624 | + | 23.9624i | −0.817587 | + | 0.817587i | −0.985758 | − | 0.168171i | \(-0.946214\pi\) |
0.168171 | + | 0.985758i | \(0.446214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.69955 | + | 7.69955i | 0.262400 | + | 0.262400i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.5202i | − | 0.426192i | −0.977031 | − | 0.213096i | \(-0.931645\pi\) | ||
0.977031 | − | 0.213096i | \(-0.0683547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.14226 | − | 40.7620i | −0.276845 | − | 1.38595i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4647 | − | 10.4647i | 0.355400 | − | 0.355400i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.5678 | − | 25.5678i | 0.867327 | − | 0.867327i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.7279i | 1.14282i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.8228 | 0.535522 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.4422 | + | 3.42560i | 0.589655 | + | 0.115806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.4582 | + | 22.4582i | −0.758358 | + | 0.758358i | −0.976023 | − | 0.217666i | \(-0.930156\pi\) |
0.217666 | + | 0.976023i | \(0.430156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.68618 | 0.124332 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.4416 | −1.49728 | −0.748638 | − | 0.662979i | \(-0.769292\pi\) | ||||
−0.748638 | + | 0.662979i | \(0.769292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.6128 | − | 38.6128i | 1.29942 | − | 1.29942i | 0.370653 | − | 0.928771i | \(-0.379134\pi\) |
0.928771 | − | 0.370653i | \(-0.120866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.00764 | + | 2.00613i | 0.101101 | + | 0.0674354i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.1077 | 0.910186 | 0.455093 | − | 0.890444i | \(-0.349606\pi\) | ||||
0.455093 | + | 0.890444i | \(0.349606\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.99317i | 0.100388i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.92109 | − | 3.92109i | 0.131361 | − | 0.131361i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −65.7289 | + | 65.7289i | −2.19953 | + | 2.19953i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0456 | + | 2.20637i | −0.369212 | + | 0.0737507i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 29.0617i | − | 0.970341i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.65640 | + | 6.65640i | 0.222003 | + | 0.222003i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38206 | − | 1.38206i | 0.0460432 | − | 0.0460432i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.725026 | −0.0241274 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.65155 | + | 18.2805i | 0.121382 | + | 0.607663i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.29362 | − | 7.29362i | −0.242181 | − | 0.242181i | 0.575571 | − | 0.817752i | \(-0.304780\pi\) |
−0.817752 | + | 0.575571i | \(0.804780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.18050 | + | 2.18050i | 0.0723228 | + | 0.0723228i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.2468 | −1.06838 | −0.534192 | − | 0.845363i | \(-0.679384\pi\) | ||||
−0.534192 | + | 0.845363i | \(0.679384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.63325i | − | 0.252624i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.69321 | + | 7.03617i | −0.155153 | + | 0.232609i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.11566 | + | 1.11566i | 0.0368423 | + | 0.0368423i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5668i | 0.909346i | 0.890659 | + | 0.454673i | \(0.150244\pi\) | ||||
−0.890659 | + | 0.454673i | \(0.849756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.1202i | 0.432324i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.02360 | + | 7.02360i | 0.231185 | + | 0.231185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.78902 | + | 14.0400i | −0.190342 | + | 0.461631i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.09580i | 0.265901i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.3630 | 0.339999 | 0.169999 | − | 0.985444i | \(-0.445623\pi\) | ||||
0.169999 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0969 | + | 22.0969i | 0.724197 | + | 0.724197i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.27485 | + | 6.27485i | 0.205430 | + | 0.205430i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0380 | + | 3.60311i | −0.589904 | + | 0.117834i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.6196 | 1.62100 | 0.810501 | − | 0.585738i | \(-0.199195\pi\) | ||||
0.810501 | + | 0.585738i | \(0.199195\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.1133 | + | 18.1133i | −0.591104 | + | 0.591104i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3629 | − | 24.3629i | −0.794208 | − | 0.794208i | 0.187967 | − | 0.982175i | \(-0.439810\pi\) |
−0.982175 | + | 0.187967i | \(0.939810\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.3333i | − | 1.47625i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.48622 | − | 0.696376i | 0.113407 | − | 0.0226531i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.0132 | − | 34.0132i | 1.10528 | − | 1.10528i | 0.111518 | − | 0.993762i | \(-0.464429\pi\) |
0.993762 | − | 0.111518i | \(-0.0355714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.3644 | − | 16.3644i | 0.531212 | − | 0.531212i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 27.6373i | − | 0.896201i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9707 | 0.711700 | 0.355850 | − | 0.934543i | \(-0.384191\pi\) | ||||
0.355850 | + | 0.934543i | \(0.384191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.862594 | + | 1.29322i | −0.0279129 | + | 0.0418476i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.5437 | − | 24.5437i | 0.793385 | − | 0.793385i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.5577 | −0.857594 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7383 | −0.927041 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00752 | − | 9.00752i | 0.290263 | − | 0.290263i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.3479 | − | 29.5806i | −1.42761 | − | 0.952233i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.8251 | −0.669690 | −0.334845 | − | 0.942273i | \(-0.608684\pi\) | ||||
−0.334845 | + | 0.942273i | \(0.608684\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 10.3656i | − | 0.332991i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.3561 | + | 27.3561i | −0.877898 | + | 0.877898i | −0.993317 | − | 0.115418i | \(-0.963179\pi\) |
0.115418 | + | 0.993317i | \(0.463179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00739 | + | 8.00739i | −0.256705 | + | 0.256705i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.2681 | + | 8.43367i | −0.649099 | + | 0.270094i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 25.5428i | − | 0.817188i | −0.912716 | − | 0.408594i | \(-0.866019\pi\) | ||
0.912716 | − | 0.408594i | \(-0.133981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.8051 | − | 26.8051i | −0.856694 | − | 0.856694i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.91170 | − | 9.91170i | 0.316456 | − | 0.316456i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.0467 | −0.830760 | −0.415380 | − | 0.909648i | \(-0.636351\pi\) | ||||
−0.415380 | + | 0.909648i | \(0.636351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1139 | + | 2.41976i | −0.385980 | + | 0.0771000i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.9556 | + | 14.9556i | 0.476042 | + | 0.476042i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.13440 | + | 2.13440i | 0.0678699 | + | 0.0678699i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.2000 | 0.959334 | 0.479667 | − | 0.877451i | \(-0.340758\pi\) | ||||
0.479667 | + | 0.877451i | \(0.340758\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 25.3917i | − | 0.805780i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.15493 | − | 4.77243i | −0.226827 | − | 0.151296i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7172 | + | 32.7172i | 1.03617 | + | 1.03617i | 0.999321 | + | 0.0368444i | \(0.0117306\pi\) |
0.0368444 | + | 0.999321i | \(0.488269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.03732i | 0.0960967i |
(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 | 1920.2.bl.a.289.20 | 48 | ||
4.3 | odd | 2 | 1920.2.bl.b.289.5 | 48 | |||
5.4 | even | 2 | inner | 1920.2.bl.a.289.5 | 48 | ||
8.3 | odd | 2 | 960.2.bl.a.529.16 | 48 | |||
8.5 | even | 2 | 240.2.bl.a.109.19 | yes | 48 | ||
16.3 | odd | 4 | 960.2.bl.a.49.3 | 48 | |||
16.5 | even | 4 | inner | 1920.2.bl.a.1249.5 | 48 | ||
16.11 | odd | 4 | 1920.2.bl.b.1249.20 | 48 | |||
16.13 | even | 4 | 240.2.bl.a.229.6 | yes | 48 | ||
20.19 | odd | 2 | 1920.2.bl.b.289.20 | 48 | |||
24.5 | odd | 2 | 720.2.bm.h.109.6 | 48 | |||
40.19 | odd | 2 | 960.2.bl.a.529.3 | 48 | |||
40.29 | even | 2 | 240.2.bl.a.109.6 | ✓ | 48 | ||
48.29 | odd | 4 | 720.2.bm.h.469.19 | 48 | |||
80.19 | odd | 4 | 960.2.bl.a.49.16 | 48 | |||
80.29 | even | 4 | 240.2.bl.a.229.19 | yes | 48 | ||
80.59 | odd | 4 | 1920.2.bl.b.1249.5 | 48 | |||
80.69 | even | 4 | inner | 1920.2.bl.a.1249.20 | 48 | ||
120.29 | odd | 2 | 720.2.bm.h.109.19 | 48 | |||
240.29 | odd | 4 | 720.2.bm.h.469.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.6 | ✓ | 48 | 40.29 | even | 2 | ||
240.2.bl.a.109.19 | yes | 48 | 8.5 | even | 2 | ||
240.2.bl.a.229.6 | yes | 48 | 16.13 | even | 4 | ||
240.2.bl.a.229.19 | yes | 48 | 80.29 | even | 4 | ||
720.2.bm.h.109.6 | 48 | 24.5 | odd | 2 | |||
720.2.bm.h.109.19 | 48 | 120.29 | odd | 2 | |||
720.2.bm.h.469.6 | 48 | 240.29 | odd | 4 | |||
720.2.bm.h.469.19 | 48 | 48.29 | odd | 4 | |||
960.2.bl.a.49.3 | 48 | 16.3 | odd | 4 | |||
960.2.bl.a.49.16 | 48 | 80.19 | odd | 4 | |||
960.2.bl.a.529.3 | 48 | 40.19 | odd | 2 | |||
960.2.bl.a.529.16 | 48 | 8.3 | odd | 2 | |||
1920.2.bl.a.289.5 | 48 | 5.4 | even | 2 | inner | ||
1920.2.bl.a.289.20 | 48 | 1.1 | even | 1 | trivial | ||
1920.2.bl.a.1249.5 | 48 | 16.5 | even | 4 | inner | ||
1920.2.bl.a.1249.20 | 48 | 80.69 | even | 4 | inner | ||
1920.2.bl.b.289.5 | 48 | 4.3 | odd | 2 | |||
1920.2.bl.b.289.20 | 48 | 20.19 | odd | 2 | |||
1920.2.bl.b.1249.5 | 48 | 80.59 | odd | 4 | |||
1920.2.bl.b.1249.20 | 48 | 16.11 | odd | 4 |