Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(847,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.847");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bi (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{12} + 28x^{8} + 80x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{49}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 847.2 | ||
Root | \(-1.31813 - 0.512386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.847 |
Dual form | 1440.2.bi.d.1423.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.83051 | + | 1.28422i | −0.818631 | + | 0.574320i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.94984 | − | 2.94984i | 1.11494 | − | 1.11494i | 0.122462 | − | 0.992473i | \(-0.460921\pi\) |
0.992473 | − | 0.122462i | \(-0.0390789\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61148 | 0.485880 | 0.242940 | − | 0.970041i | \(-0.421888\pi\) | ||||
0.242940 | + | 0.970041i | \(0.421888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50967 | + | 2.50967i | 0.696057 | + | 0.696057i | 0.963558 | − | 0.267501i | \(-0.0861978\pi\) |
−0.267501 | + | 0.963558i | \(0.586198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.59398 | − | 4.59398i | −1.11420 | − | 1.11420i | −0.992576 | − | 0.121629i | \(-0.961188\pi\) |
−0.121629 | − | 0.992576i | \(-0.538812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09259 | + | 1.09259i | 0.227821 | + | 0.227821i | 0.811782 | − | 0.583961i | \(-0.198498\pi\) |
−0.583961 | + | 0.811782i | \(0.698498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.70156 | − | 4.70156i | 0.340312 | − | 0.940312i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.75362 | −0.882725 | −0.441362 | − | 0.897329i | \(-0.645505\pi\) | ||||
−0.441362 | + | 0.897329i | \(0.645505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.01934i | 0.901500i | 0.892650 | + | 0.450750i | \(0.148843\pi\) | ||||
−0.892650 | + | 0.450750i | \(0.851157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.61148 | + | 9.18797i | −0.272390 | + | 1.55305i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.50967 | + | 2.50967i | −0.412587 | + | 0.412587i | −0.882639 | − | 0.470052i | \(-0.844235\pi\) |
0.470052 | + | 0.882639i | \(0.344235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.18797 | 1.43492 | 0.717460 | − | 0.696600i | \(-0.245305\pi\) | ||||
0.717460 | + | 0.696600i | \(0.245305\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40312 | − | 7.40312i | 1.12897 | − | 1.12897i | 0.138620 | − | 0.990346i | \(-0.455733\pi\) |
0.990346 | − | 0.138620i | \(-0.0442667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.32206 | − | 7.32206i | 1.06803 | − | 1.06803i | 0.0705213 | − | 0.997510i | \(-0.477534\pi\) |
0.997510 | − | 0.0705213i | \(-0.0224663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 10.4031i | − | 1.48616i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.11473 | + | 3.11473i | 0.427841 | + | 0.427841i | 0.887892 | − | 0.460051i | \(-0.152169\pi\) |
−0.460051 | + | 0.887892i | \(0.652169\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.94984 | + | 2.06950i | −0.397756 | + | 0.279051i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.61148i | − | 0.209797i | −0.994483 | − | 0.104899i | \(-0.966548\pi\) | ||
0.994483 | − | 0.104899i | \(-0.0334518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.78003i | − | 0.868093i | −0.900890 | − | 0.434047i | \(-0.857085\pi\) | ||
0.900890 | − | 0.434047i | \(-0.142915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.81695 | − | 1.37102i | −0.969573 | − | 0.170054i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.40312 | − | 7.40312i | −0.904436 | − | 0.904436i | 0.0913805 | − | 0.995816i | \(-0.470872\pi\) |
−0.995816 | + | 0.0913805i | \(0.970872\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 5.00000i | 0.585206 | − | 0.585206i | −0.351123 | − | 0.936329i | \(-0.614200\pi\) |
0.936329 | + | 0.351123i | \(0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.75362 | − | 4.75362i | 0.541725 | − | 0.541725i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01934 | 0.564720 | 0.282360 | − | 0.959309i | \(-0.408883\pi\) | ||||
0.282360 | + | 0.959309i | \(0.408883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.57648 | − | 7.57648i | 0.831627 | − | 0.831627i | −0.156112 | − | 0.987739i | \(-0.549896\pi\) |
0.987739 | + | 0.156112i | \(0.0498961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.3090 | + | 2.50967i | 1.55203 | + | 0.272212i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.74204i | 0.290655i | 0.989384 | + | 0.145328i | \(0.0464236\pi\) | ||||
−0.989384 | + | 0.145328i | \(0.953576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8062 | 1.55212 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.13688 | + | 7.32206i | 0.527032 | + | 0.751227i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.40312 | + | 2.40312i | 0.244000 | + | 0.244000i | 0.818503 | − | 0.574503i | \(-0.194804\pi\) |
−0.574503 | + | 0.818503i | \(0.694804\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.79790i | − | 0.875424i | −0.899115 | − | 0.437712i | \(-0.855789\pi\) | ||
0.899115 | − | 0.437712i | \(-0.144211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.96918 | + | 7.96918i | 0.785227 | + | 0.785227i | 0.980707 | − | 0.195481i | \(-0.0626268\pi\) |
−0.195481 | + | 0.980707i | \(0.562627\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.61148 | + | 1.61148i | 0.155788 | + | 0.155788i | 0.780697 | − | 0.624909i | \(-0.214864\pi\) |
−0.624909 | + | 0.780697i | \(0.714864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7994 | 1.13017 | 0.565087 | − | 0.825031i | \(-0.308843\pi\) | ||||
0.565087 | + | 0.825031i | \(0.308843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.59398 | + | 4.59398i | −0.432166 | + | 0.432166i | −0.889364 | − | 0.457199i | \(-0.848853\pi\) |
0.457199 | + | 0.889364i | \(0.348853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.40312 | − | 0.596876i | −0.317343 | − | 0.0556590i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.1030 | −2.48453 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40312 | −0.763920 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.92310 | + | 10.7915i | 0.261450 | + | 0.965217i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.83019 | − | 3.83019i | 0.339874 | − | 0.339874i | −0.516446 | − | 0.856320i | \(-0.672745\pi\) |
0.856320 | + | 0.516446i | \(0.172745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5415 | −1.18313 | −0.591563 | − | 0.806259i | \(-0.701489\pi\) | ||||
−0.591563 | + | 0.806259i | \(0.701489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7994 | − | 11.7994i | −1.02313 | − | 1.02313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.0399 | + | 11.0399i | 0.943203 | + | 0.943203i | 0.998472 | − | 0.0552681i | \(-0.0176013\pi\) |
−0.0552681 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.04429 | + | 4.04429i | 0.338200 | + | 0.338200i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.70156 | − | 6.10469i | 0.722625 | − | 0.506967i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.79790 | −0.720752 | −0.360376 | − | 0.932807i | \(-0.617352\pi\) | ||||
−0.360376 | + | 0.932807i | \(0.617352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.880344i | 0.0716414i | 0.999358 | + | 0.0358207i | \(0.0114045\pi\) | ||||
−0.999358 | + | 0.0358207i | \(0.988595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.44593 | − | 9.18797i | −0.517750 | − | 0.737995i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.28970 | + | 9.28970i | −0.741398 | + | 0.741398i | −0.972847 | − | 0.231449i | \(-0.925653\pi\) |
0.231449 | + | 0.972847i | \(0.425653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.44593 | 0.508010 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.32206 | + | 7.32206i | −0.566598 | + | 0.566598i | −0.931174 | − | 0.364576i | \(-0.881214\pi\) |
0.364576 | + | 0.931174i | \(0.381214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 0.403124i | − | 0.0310096i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.86835 | + | 7.86835i | 0.598220 | + | 0.598220i | 0.939839 | − | 0.341619i | \(-0.110975\pi\) |
−0.341619 | + | 0.939839i | \(0.610975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.84952 | − | 18.8882i | −0.668961 | − | 1.42781i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 26.4333i | − | 1.97572i | −0.155343 | − | 0.987861i | \(-0.549648\pi\) | ||
0.155343 | − | 0.987861i | \(-0.450352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7994i | 0.877040i | 0.898721 | + | 0.438520i | \(0.144497\pi\) | ||||
−0.898721 | + | 0.438520i | \(0.855503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.37102 | − | 7.81695i | 0.100799 | − | 0.574713i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.40312 | − | 7.40312i | −0.541370 | − | 0.541370i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 19.0145i | − | 1.37584i | −0.725787 | − | 0.687919i | \(-0.758524\pi\) | ||
0.725787 | − | 0.687919i | \(-0.241476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4031 | + | 12.4031i | −0.892796 | + | 0.892796i | −0.994786 | − | 0.101989i | \(-0.967479\pi\) |
0.101989 | + | 0.994786i | \(0.467479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.34420 | − | 9.34420i | 0.665747 | − | 0.665747i | −0.290982 | − | 0.956729i | \(-0.593982\pi\) |
0.956729 | + | 0.290982i | \(0.0939820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9577 | −1.48565 | −0.742826 | − | 0.669485i | \(-0.766515\pi\) | ||||
−0.742826 | + | 0.669485i | \(0.766515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.0224 | + | 14.0224i | −0.984181 | + | 0.984181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.8187 | + | 11.7994i | −1.17467 | + | 0.824103i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.44593i | − | 0.445874i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.04429 | + | 23.0588i | −0.275818 | + | 1.57259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.8062 | + | 14.8062i | 1.00511 | + | 1.00511i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.0588i | − | 1.55110i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.83019 | + | 3.83019i | 0.256488 | + | 0.256488i | 0.823624 | − | 0.567136i | \(-0.191949\pi\) |
−0.567136 | + | 0.823624i | \(0.691949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.6339 | + | 15.6339i | 1.03766 | + | 1.03766i | 0.999263 | + | 0.0383956i | \(0.0122247\pi\) |
0.0383956 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.78003 | −0.448037 | −0.224018 | − | 0.974585i | \(-0.571918\pi\) | ||||
−0.224018 | + | 0.974585i | \(0.571918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0399 | + | 11.0399i | −0.723249 | + | 0.723249i | −0.969266 | − | 0.246017i | \(-0.920878\pi\) |
0.246017 | + | 0.969266i | \(0.420878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 22.8062i | −0.260931 | + | 1.48772i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.08857 | 0.523206 | 0.261603 | − | 0.965176i | \(-0.415749\pi\) | ||||
0.261603 | + | 0.965176i | \(0.415749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.80625 | −0.438429 | −0.219215 | − | 0.975677i | \(-0.570349\pi\) | ||||
−0.219215 | + | 0.975677i | \(0.570349\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.3599 | + | 19.0431i | 0.853532 | + | 1.21662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0387 | − | 10.0387i | 0.638746 | − | 0.638746i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9874 | 1.26159 | 0.630797 | − | 0.775948i | \(-0.282728\pi\) | ||||
0.630797 | + | 0.775948i | \(0.282728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.76069 | + | 1.76069i | 0.110694 | + | 0.110694i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.7820 | + | 13.7820i | 0.859694 | + | 0.859694i | 0.991302 | − | 0.131607i | \(-0.0420138\pi\) |
−0.131607 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8062i | 0.920016i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.95170 | − | 2.95170i | −0.182009 | − | 0.182009i | 0.610221 | − | 0.792231i | \(-0.291080\pi\) |
−0.792231 | + | 0.610221i | \(0.791080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.70156 | − | 1.70156i | −0.595962 | − | 0.104526i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.3051 | −1.11608 | −0.558042 | − | 0.829813i | \(-0.688447\pi\) | ||||
−0.558042 | + | 0.829813i | \(0.688447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6797i | 0.770237i | 0.922867 | + | 0.385119i | \(0.125840\pi\) | ||||
−0.922867 | + | 0.385119i | \(0.874160\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.74204 | − | 7.57648i | 0.165351 | − | 0.456879i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.52901 | − | 7.52901i | 0.452374 | − | 0.452374i | −0.443768 | − | 0.896142i | \(-0.646358\pi\) |
0.896142 | + | 0.443768i | \(0.146358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.5639 | −1.64432 | −0.822162 | − | 0.569253i | \(-0.807232\pi\) | ||||
−0.822162 | + | 0.569253i | \(0.807232\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.40312 | + | 7.40312i | −0.440070 | + | 0.440070i | −0.892035 | − | 0.451965i | \(-0.850723\pi\) |
0.451965 | + | 0.892035i | \(0.350723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.1030 | − | 27.1030i | 1.59984 | − | 1.59984i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2094i | 1.48290i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.11473 | − | 3.11473i | −0.181965 | − | 0.181965i | 0.610247 | − | 0.792211i | \(-0.291070\pi\) |
−0.792211 | + | 0.610247i | \(0.791070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.06950 | + | 2.94984i | 0.120491 | + | 0.171746i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.48408i | 0.317152i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 43.6761i | − | 2.51745i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.70704 | + | 12.4109i | 0.498564 | + | 0.710648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | + | 20.0000i | 1.14146 | + | 1.14146i | 0.988183 | + | 0.153277i | \(0.0489827\pi\) |
0.153277 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.08857i | − | 0.458661i | −0.973349 | − | 0.229330i | \(-0.926346\pi\) | ||
0.973349 | − | 0.229330i | \(-0.0736537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8062 | + | 19.8062i | −1.11952 | + | 1.11952i | −0.127703 | + | 0.991812i | \(0.540760\pi\) |
−0.991812 | + | 0.127703i | \(0.959240\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.59058 | − | 4.59058i | 0.257833 | − | 0.257833i | −0.566339 | − | 0.824172i | \(-0.691641\pi\) |
0.824172 | + | 0.566339i | \(0.191641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.66037 | −0.428898 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.3759 | + | 18.3759i | −1.02246 | + | 1.02246i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0697 | − | 7.52901i | 0.891388 | − | 0.417634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 43.1978i | − | 2.38157i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.80625 | −0.154245 | −0.0771227 | − | 0.997022i | \(-0.524573\pi\) | ||||
−0.0771227 | + | 0.997022i | \(0.524573\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.0588 | + | 4.04429i | 1.25983 | + | 0.220963i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.40312 | − | 2.40312i | −0.130907 | − | 0.130907i | 0.638618 | − | 0.769524i | \(-0.279507\pi\) |
−0.769524 | + | 0.638618i | \(0.779507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.08857i | 0.438021i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0387 | − | 10.0387i | −0.542038 | − | 0.542038i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.74204 | − | 2.74204i | −0.147200 | − | 0.147200i | 0.629666 | − | 0.776866i | \(-0.283192\pi\) |
−0.776866 | + | 0.629666i | \(0.783192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.78003 | 0.362926 | 0.181463 | − | 0.983398i | \(-0.441917\pi\) | ||||
0.181463 | + | 0.983398i | \(0.441917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7820 | − | 13.7820i | 0.733539 | − | 0.733539i | −0.237780 | − | 0.971319i | \(-0.576420\pi\) |
0.971319 | + | 0.237780i | \(0.0764197\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.1916 | −1.85734 | −0.928671 | − | 0.370904i | \(-0.879048\pi\) | ||||
−0.928671 | + | 0.370904i | \(0.879048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.73147 | + | 15.5737i | −0.142972 | + | 0.815163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7492 | + | 14.7492i | −0.769902 | + | 0.769902i | −0.978089 | − | 0.208187i | \(-0.933244\pi\) |
0.208187 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.3759 | 0.954031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3090 | − | 14.3090i | −0.740894 | − | 0.740894i | 0.231856 | − | 0.972750i | \(-0.425520\pi\) |
−0.972750 | + | 0.231856i | \(0.925520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.9300 | − | 11.9300i | −0.614427 | − | 0.614427i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8062i | 0.966012i | 0.875617 | + | 0.483006i | \(0.160455\pi\) | ||||
−0.875617 | + | 0.483006i | \(0.839545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.0105 | + | 26.0105i | 1.32907 | + | 1.32907i | 0.906180 | + | 0.422892i | \(0.138985\pi\) |
0.422892 | + | 0.906180i | \(0.361015\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.59688 | + | 14.8062i | −0.132349 | + | 0.754596i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.3196 | −1.89218 | −0.946090 | − | 0.323905i | \(-0.895004\pi\) | ||||
−0.946090 | + | 0.323905i | \(0.895004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.0387i | − | 0.507678i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.18797 | + | 6.44593i | −0.462297 | + | 0.324330i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3284 | + | 19.3284i | −0.970063 | + | 0.970063i | −0.999565 | − | 0.0295016i | \(-0.990608\pi\) |
0.0295016 | + | 0.999565i | \(0.490608\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.8919 | 0.643789 | 0.321894 | − | 0.946776i | \(-0.395680\pi\) | ||||
0.321894 | + | 0.946776i | \(0.395680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5969 | + | 12.5969i | −0.627495 | + | 0.627495i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.04429 | + | 4.04429i | −0.200468 | + | 0.200468i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.40312i | 0.168274i | 0.996454 | + | 0.0841368i | \(0.0268133\pi\) | ||||
−0.996454 | + | 0.0841368i | \(0.973187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.75362 | − | 4.75362i | −0.233910 | − | 0.233910i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.13899 | + | 23.5987i | −0.203175 | + | 1.15842i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.9174i | 1.55927i | 0.626235 | + | 0.779634i | \(0.284595\pi\) | ||||
−0.626235 | + | 0.779634i | \(0.715405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3788i | 1.48057i | 0.672293 | + | 0.740285i | \(0.265309\pi\) | ||||
−0.672293 | + | 0.740285i | \(0.734691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.4158 | + | 13.7820i | −1.42688 | + | 0.668523i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0000 | − | 20.0000i | −0.967868 | − | 0.967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27.1030i | − | 1.30551i | −0.757570 | − | 0.652754i | \(-0.773614\pi\) | ||
0.757570 | − | 0.652754i | \(-0.226386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4031 | − | 12.4031i | 0.596056 | − | 0.596056i | −0.343205 | − | 0.939261i | \(-0.611512\pi\) |
0.939261 | + | 0.343205i | \(0.111512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.37036 | − | 4.37036i | 0.209063 | − | 0.209063i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9190 | 0.521136 | 0.260568 | − | 0.965455i | \(-0.416090\pi\) | ||||
0.260568 | + | 0.965455i | \(0.416090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6339 | − | 15.6339i | 0.742789 | − | 0.742789i | −0.230325 | − | 0.973114i | \(-0.573979\pi\) |
0.973114 | + | 0.230325i | \(0.0739789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.52138 | − | 5.01934i | −0.166929 | − | 0.237939i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.44593i | − | 0.304202i | −0.988365 | − | 0.152101i | \(-0.951396\pi\) | ||
0.988365 | − | 0.152101i | \(-0.0486039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8062 | 0.697199 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.1030 | + | 19.0145i | −1.27061 | + | 0.891412i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.80625 | − | 9.80625i | −0.458717 | − | 0.458717i | 0.439517 | − | 0.898234i | \(-0.355150\pi\) |
−0.898234 | + | 0.439517i | \(0.855150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.3051i | 0.852555i | 0.904592 | + | 0.426278i | \(0.140175\pi\) | ||||
−0.904592 | + | 0.426278i | \(0.859825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7492 | − | 14.7492i | −0.685454 | − | 0.685454i | 0.275770 | − | 0.961224i | \(-0.411067\pi\) |
−0.961224 | + | 0.275770i | \(0.911067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.7994 | − | 10.7994i | −0.499739 | − | 0.499739i | 0.411618 | − | 0.911357i | \(-0.364964\pi\) |
−0.911357 | + | 0.411618i | \(0.864964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.6761 | −2.01677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.9300 | − | 11.9300i | 0.548542 | − | 0.548542i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.8062 | − | 6.80625i | −0.862890 | − | 0.312292i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.08857 | 0.369576 | 0.184788 | − | 0.982778i | \(-0.440840\pi\) | ||||
0.184788 | + | 0.982778i | \(0.440840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5969 | −0.574368 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.48509 | − | 1.31281i | −0.339880 | − | 0.0596118i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.06950 | + | 2.06950i | −0.0937778 | + | 0.0937778i | −0.752439 | − | 0.658662i | \(-0.771123\pi\) |
0.658662 | + | 0.752439i | \(0.271123\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2804 | 0.509076 | 0.254538 | − | 0.967063i | \(-0.418077\pi\) | ||||
0.254538 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.8380 | + | 21.8380i | 0.983536 | + | 0.983536i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.8062i | − | 0.841883i | −0.907088 | − | 0.420942i | \(-0.861700\pi\) | ||
0.907088 | − | 0.420942i | \(-0.138300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.13688 | − | 5.13688i | −0.229042 | − | 0.229042i | 0.583250 | − | 0.812292i | \(-0.301781\pi\) |
−0.812292 | + | 0.583250i | \(0.801781\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2984 | + | 16.1047i | 0.502774 | + | 0.716649i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8422 | −0.569220 | −0.284610 | − | 0.958643i | \(-0.591864\pi\) | ||||
−0.284610 | + | 0.958643i | \(0.591864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 29.4984i | − | 1.30493i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.8219 | − | 4.35352i | −1.09378 | − | 0.191839i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7994 | − | 11.7994i | 0.518935 | − | 0.518935i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.44593 | 0.282401 | 0.141201 | − | 0.989981i | \(-0.454904\pi\) | ||||
0.141201 | + | 0.989981i | \(0.454904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.19375 | − | 5.19375i | 0.227107 | − | 0.227107i | −0.584376 | − | 0.811483i | \(-0.698661\pi\) |
0.811483 | + | 0.584376i | \(0.198661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.0588 | − | 23.0588i | 1.00446 | − | 1.00446i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.6125i | − | 0.896196i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.0588 | + | 23.0588i | 0.998786 | + | 0.998786i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.01934 | − | 0.880344i | −0.217005 | − | 0.0380606i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 16.7645i | − | 0.722096i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.27799i | 0.355898i | 0.984040 | + | 0.177949i | \(0.0569463\pi\) | ||||
−0.984040 | + | 0.177949i | \(0.943054\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5989 | + | 15.1530i | −0.925195 | + | 0.649082i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2094 | + | 22.2094i | 0.949604 | + | 0.949604i | 0.998790 | − | 0.0491855i | \(-0.0156625\pi\) |
−0.0491855 | + | 0.998790i | \(0.515663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.0145i | 0.810044i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8062 | − | 14.8062i | 0.629626 | − | 0.629626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7146 | − | 13.7146i | 0.581104 | − | 0.581104i | −0.354102 | − | 0.935207i | \(-0.615214\pi\) |
0.935207 | + | 0.354102i | \(0.115214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.1588 | 1.57165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.74204 | − | 2.74204i | 0.115563 | − | 0.115563i | −0.646960 | − | 0.762524i | \(-0.723960\pi\) |
0.762524 | + | 0.646960i | \(0.223960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.50967 | − | 14.3090i | 0.105583 | − | 0.601986i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.7519i | 1.54072i | 0.637610 | + | 0.770359i | \(0.279923\pi\) | ||||
−0.637610 | + | 0.770359i | \(0.720077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6125 | −0.737060 | −0.368530 | − | 0.929616i | \(-0.620139\pi\) | ||||
−0.368530 | + | 0.929616i | \(0.620139\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.99599 | − | 3.27777i | 0.291753 | − | 0.136692i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4031 | + | 12.4031i | 0.516349 | + | 0.516349i | 0.916465 | − | 0.400116i | \(-0.131030\pi\) |
−0.400116 | + | 0.916465i | \(0.631030\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 44.6989i | − | 1.85442i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.01934 | + | 5.01934i | 0.207880 | + | 0.207880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.61148 | − | 1.61148i | −0.0665130 | − | 0.0665130i | 0.673068 | − | 0.739581i | \(-0.264976\pi\) |
−0.739581 | + | 0.673068i | \(0.764976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0774 | 0.827273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.59398 | − | 4.59398i | 0.188652 | − | 0.188652i | −0.606461 | − | 0.795113i | \(-0.707411\pi\) |
0.795113 | + | 0.606461i | \(0.207411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 49.6125 | − | 34.8062i | 2.03391 | − | 1.42692i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.1030 | −1.10740 | −0.553700 | − | 0.832716i | \(-0.686785\pi\) | ||||
−0.553700 | + | 0.832716i | \(0.686785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.2094 | 0.824358 | 0.412179 | − | 0.911103i | \(-0.364768\pi\) | ||||
0.412179 | + | 0.911103i | \(0.364768\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.3820 | − | 10.7915i | 0.625369 | − | 0.438735i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.8882 | − | 18.8882i | 0.766648 | − | 0.766648i | −0.210867 | − | 0.977515i | \(-0.567629\pi\) |
0.977515 | + | 0.210867i | \(0.0676285\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.7519 | 1.48682 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3284 | + | 19.3284i | 0.780666 | + | 0.780666i | 0.979943 | − | 0.199278i | \(-0.0638595\pi\) |
−0.199278 | + | 0.979943i | \(0.563860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.33602 | + | 7.33602i | 0.295337 | + | 0.295337i | 0.839184 | − | 0.543847i | \(-0.183033\pi\) |
−0.543847 | + | 0.839184i | \(0.683033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.8062i | − | 0.434340i | −0.976134 | − | 0.217170i | \(-0.930317\pi\) | ||
0.976134 | − | 0.217170i | \(-0.0696826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.08857 | + | 8.08857i | 0.324062 | + | 0.324062i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.2094 | − | 16.0000i | −0.768375 | − | 0.640000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.0588 | 0.919413 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0967i | 0.999083i | 0.866290 | + | 0.499542i | \(0.166498\pi\) | ||||
−0.866290 | + | 0.499542i | \(0.833502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.09241 | + | 11.9300i | −0.0830348 | + | 0.473428i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.1084 | − | 26.1084i | 1.03445 | − | 1.03445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.74204 | 0.108304 | 0.0541520 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541520 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.7810 | + | 19.7810i | −0.777671 | + | 0.777671i | −0.979434 | − | 0.201763i | \(-0.935333\pi\) |
0.201763 | + | 0.979434i | \(0.435333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.59688i | − | 0.101936i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.1904 | + | 15.1904i | 0.594447 | + | 0.594447i | 0.938829 | − | 0.344383i | \(-0.111912\pi\) |
−0.344383 | + | 0.938829i | \(0.611912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.7879 | − | 17.3902i | 0.968543 | − | 0.679493i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.83445i | − | 0.188323i | −0.995557 | − | 0.0941617i | \(-0.969983\pi\) | ||
0.995557 | − | 0.0941617i | \(-0.0300171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.8574i | 1.04463i | 0.852752 | + | 0.522315i | \(0.174932\pi\) | ||||
−0.852752 | + | 0.522315i | \(0.825068\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.7519 | + | 6.44593i | 1.42518 | + | 0.249962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.19375 | − | 5.19375i | −0.201103 | − | 0.201103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.9259i | − | 0.421789i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | − | 15.0000i | 0.578208 | − | 0.578208i | −0.356202 | − | 0.934409i | \(-0.615928\pi\) |
0.934409 | + | 0.356202i | \(0.115928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1421 | − | 18.1421i | 0.697258 | − | 0.697258i | −0.266560 | − | 0.963818i | \(-0.585887\pi\) |
0.963818 | + | 0.266560i | \(0.0858872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1777 | 0.544089 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.13056 | − | 1.13056i | 0.0432595 | − | 0.0432595i | −0.685146 | − | 0.728406i | \(-0.740262\pi\) |
0.728406 | + | 0.685146i | \(0.240262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.3864 | − | 6.03105i | −1.31384 | − | 0.230434i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.6339i | 0.595604i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.13688 | − | 7.32206i | −0.194853 | − | 0.277741i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.2094 | − | 42.2094i | −1.59879 | − | 1.59879i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.33496i | − | 0.125960i | −0.998015 | − | 0.0629798i | \(-0.979940\pi\) | ||
0.998015 | − | 0.0629798i | \(-0.0200604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0387 | + | 10.0387i | 0.378616 | + | 0.378616i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.9524 | − | 25.9524i | −0.976041 | − | 0.976041i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8574 | 1.00865 | 0.504325 | − | 0.863514i | \(-0.331741\pi\) | ||||
0.504325 | + | 0.863514i | \(0.331741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.48408 | + | 5.48408i | −0.205380 | + | 0.205380i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5969 | − | 2.20937i | −0.471096 | − | 0.0826259i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.08857 | 0.301653 | 0.150826 | − | 0.988560i | \(-0.451807\pi\) | ||||
0.150826 | + | 0.988560i | \(0.451807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.0156 | 1.75095 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.08857 | + | 22.3494i | −0.300402 | + | 0.830037i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.7069 | + | 35.7069i | −1.32430 | + | 1.32430i | −0.414034 | + | 0.910261i | \(0.635881\pi\) |
−0.910261 | + | 0.414034i | \(0.864119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68.0197 | −2.51580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.50967 | + | 2.50967i | 0.0926967 | + | 0.0926967i | 0.751935 | − | 0.659238i | \(-0.229121\pi\) |
−0.659238 | + | 0.751935i | \(0.729121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.9300 | − | 11.9300i | −0.439447 | − | 0.439447i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 48.4187i | − | 1.78111i | −0.454873 | − | 0.890556i | \(-0.650315\pi\) | ||
0.454873 | − | 0.890556i | \(-0.349685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.18116 | − | 9.18116i | −0.336824 | − | 0.336824i | 0.518346 | − | 0.855171i | \(-0.326548\pi\) |
−0.855171 | + | 0.518346i | \(0.826548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1047 | − | 11.2984i | 0.590030 | − | 0.413943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.50723 | 0.347387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0580i | 0.549475i | 0.961519 | + | 0.274737i | \(0.0885909\pi\) | ||||
−0.961519 | + | 0.274737i | \(0.911409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.13056 | − | 1.61148i | −0.0411451 | − | 0.0586479i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0504 | − | 11.0504i | 0.401633 | − | 0.401633i | −0.477175 | − | 0.878808i | \(-0.658339\pi\) |
0.878808 | + | 0.477175i | \(0.158339\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1978 | 1.56592 | 0.782960 | − | 0.622073i | \(-0.213709\pi\) | ||||
0.782960 | + | 0.622073i | \(0.213709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.8062 | − | 34.8062i | 1.26007 | − | 1.26007i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.04429 | − | 4.04429i | 0.146031 | − | 0.146031i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.40312i | 0.0505980i | 0.999680 | + | 0.0252990i | \(0.00805377\pi\) | ||||
−0.999680 | + | 0.0252990i | \(0.991946\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4642 | − | 25.4642i | −0.915882 | − | 0.915882i | 0.0808446 | − | 0.996727i | \(-0.474238\pi\) |
−0.996727 | + | 0.0808446i | \(0.974238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.5987 | + | 8.54071i | 0.847691 | + | 0.306792i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 36.7519i | − | 1.31677i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.07491 | − | 28.9349i | 0.181131 | − | 1.03273i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 20.0000i | 0.712923 | + | 0.712923i | 0.967146 | − | 0.254223i | \(-0.0818196\pi\) |
−0.254223 | + | 0.967146i | \(0.581820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.1030i | 0.963673i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0156 | − | 17.0156i | 0.604242 | − | 0.604242i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.00924 | + | 6.00924i | −0.212858 | + | 0.212858i | −0.805481 | − | 0.592622i | \(-0.798093\pi\) |
0.592622 | + | 0.805481i | \(0.298093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −67.2748 | −2.38001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.05741 | − | 8.05741i | 0.284340 | − | 0.284340i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.7994 | + | 8.27799i | −0.415873 | + | 0.291761i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.74204i | 0.0964049i | 0.998838 | + | 0.0482025i | \(0.0153493\pi\) | ||||
−0.998838 | + | 0.0482025i | \(0.984651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.8062 | 1.50313 | 0.751565 | − | 0.659659i | \(-0.229299\pi\) | ||||
0.751565 | + | 0.659659i | \(0.229299\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.6125 | − | 29.6125i | −1.03601 | − | 1.03601i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.9452i | 1.39410i | 0.717023 | + | 0.697049i | \(0.245504\pi\) | ||||
−0.717023 | + | 0.697049i | \(0.754496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.59087 | − | 5.59087i | −0.194886 | − | 0.194886i | 0.602918 | − | 0.797803i | \(-0.294005\pi\) |
−0.797803 | + | 0.602918i | \(0.794005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.7519 | + | 36.7519i | 1.27799 | + | 1.27799i | 0.941792 | + | 0.336196i | \(0.109140\pi\) |
0.336196 | + | 0.941792i | \(0.390860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.27799 | −0.287506 | −0.143753 | − | 0.989614i | \(-0.545917\pi\) | ||||
−0.143753 | + | 0.989614i | \(0.545917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −47.7918 | + | 47.7918i | −1.65589 | + | 1.65589i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.00000 | − | 22.8062i | 0.138426 | − | 0.789243i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.1030 | −0.935701 | −0.467850 | − | 0.883808i | \(-0.654971\pi\) | ||||
−0.467850 | + | 0.883808i | \(0.654971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.40312 | −0.220797 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.517700 | + | 0.737925i | 0.0178094 | + | 0.0253854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.7879 | + | 24.7879i | −0.851722 | + | 0.851722i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.48408 | −0.187992 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.3090 | − | 14.3090i | −0.489932 | − | 0.489932i | 0.418353 | − | 0.908285i | \(-0.362608\pi\) |
−0.908285 | + | 0.418353i | \(0.862608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7820 | + | 13.7820i | 0.470782 | + | 0.470782i | 0.902168 | − | 0.431385i | \(-0.141975\pi\) |
−0.431385 | + | 0.902168i | \(0.641975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.6125i | − | 0.873887i | −0.899489 | − | 0.436944i | \(-0.856061\pi\) | ||
0.899489 | − | 0.436944i | \(-0.143939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.9662 | − | 21.9662i | −0.747737 | − | 0.747737i | 0.226317 | − | 0.974054i | \(-0.427332\pi\) |
−0.974054 | + | 0.226317i | \(0.927332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.5078 | − | 4.29844i | −0.833291 | − | 0.146151i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.08857 | 0.274386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 37.1588i | − | 1.25908i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.4558 | + | 23.2104i | 1.36765 | + | 0.784654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3090 | − | 14.3090i | 0.483182 | − | 0.483182i | −0.422965 | − | 0.906146i | \(-0.639011\pi\) |
0.906146 | + | 0.422965i | \(0.139011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.9017 | −1.58016 | −0.790079 | − | 0.613005i | \(-0.789961\pi\) | ||||
−0.790079 | + | 0.613005i | \(0.789961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.8062 | + | 14.8062i | −0.498270 | + | 0.498270i | −0.910899 | − | 0.412629i | \(-0.864611\pi\) |
0.412629 | + | 0.910899i | \(0.364611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.3365 | + | 26.3365i | −0.884294 | + | 0.884294i | −0.993968 | − | 0.109674i | \(-0.965019\pi\) |
0.109674 | + | 0.993968i | \(0.465019\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 22.5969i | − | 0.757875i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.2882 | − | 29.2882i | −0.980093 | − | 0.980093i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.9462 | + | 48.3866i | 1.13470 | + | 1.61739i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 23.8600i | − | 0.795776i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 28.6181i | − | 0.953406i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.1530 | − | 21.5989i | −0.503702 | − | 0.717972i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5969 | − | 12.5969i | −0.418272 | − | 0.418272i | 0.466336 | − | 0.884608i | \(-0.345574\pi\) |
−0.884608 | + | 0.466336i | \(0.845574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.1030i | 0.897964i | 0.893541 | + | 0.448982i | \(0.148213\pi\) | ||||
−0.893541 | + | 0.448982i | \(0.851787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2094 | − | 12.2094i | 0.404071 | − | 0.404071i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.9452 | + | 39.9452i | −1.31911 | + | 1.31911i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.2168 | 1.72247 | 0.861237 | − | 0.508204i | \(-0.169691\pi\) | ||||
0.861237 | + | 0.508204i | \(0.169691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.52901 | + | 16.0697i | 0.247552 | + | 0.528369i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.1978i | − | 1.41727i | −0.705573 | − | 0.708637i | \(-0.749310\pi\) | ||
0.705573 | − | 0.708637i | \(-0.250690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.6125 | −1.36379 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.0588 | + | 4.04429i | 0.754102 | + | 0.132262i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4031 | + | 22.4031i | 0.731878 | + | 0.731878i | 0.970992 | − | 0.239113i | \(-0.0768568\pi\) |
−0.239113 | + | 0.970992i | \(0.576857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 10.2166i | − | 0.333050i | −0.986037 | − | 0.166525i | \(-0.946745\pi\) | ||
0.986037 | − | 0.166525i | \(-0.0532547\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0387 | + | 10.0387i | 0.326904 | + | 0.326904i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.3759 | + | 18.3759i | 0.597138 | + | 0.597138i | 0.939550 | − | 0.342412i | \(-0.111244\pi\) |
−0.342412 | + | 0.939550i | \(0.611244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.0967 | 0.814673 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.85195 | − | 1.85195i | 0.0599904 | − | 0.0599904i | −0.676475 | − | 0.736466i | \(-0.736493\pi\) |
0.736466 | + | 0.676475i | \(0.236493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.4187 | + | 34.8062i | 0.790172 | + | 1.12630i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 65.1320 | 2.10322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.80625 | 0.187298 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77576 | − | 38.6324i | 0.218119 | − | 1.24362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.06950 | + | 2.06950i | −0.0665505 | + | 0.0665505i | −0.739599 | − | 0.673048i | \(-0.764985\pi\) |
0.673048 | + | 0.739599i | \(0.264985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.3634 | −1.23114 | −0.615569 | − | 0.788083i | \(-0.711074\pi\) | ||||
−0.615569 | + | 0.788083i | \(0.711074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.7994 | + | 11.7994i | 0.378270 | + | 0.378270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.33602 | − | 7.33602i | −0.234700 | − | 0.234700i | 0.579951 | − | 0.814651i | \(-0.303072\pi\) |
−0.814651 | + | 0.579951i | \(0.803072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.41875i | 0.141224i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.18116 | − | 9.18116i | −0.292834 | − | 0.292834i | 0.545365 | − | 0.838199i | \(-0.316391\pi\) |
−0.838199 | + | 0.545365i | \(0.816391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.10469 | + | 29.1047i | −0.162649 | + | 0.927352i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.1771 | 0.514403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.7957i | − | 1.35945i | −0.733466 | − | 0.679726i | \(-0.762099\pi\) | ||
0.733466 | − | 0.679726i | \(-0.237901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.3634 | − | 26.9143i | 1.21620 | − | 0.853240i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50967 | + | 2.50967i | −0.0794820 | + | 0.0794820i | −0.745730 | − | 0.666248i | \(-0.767899\pi\) |
0.666248 | + | 0.745730i | \(0.267899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.2.bi.d.847.2 | 16 | ||
3.2 | odd | 2 | inner | 1440.2.bi.d.847.8 | 16 | ||
4.3 | odd | 2 | 360.2.w.d.307.5 | yes | 16 | ||
5.3 | odd | 4 | inner | 1440.2.bi.d.1423.7 | 16 | ||
8.3 | odd | 2 | inner | 1440.2.bi.d.847.7 | 16 | ||
8.5 | even | 2 | 360.2.w.d.307.1 | yes | 16 | ||
12.11 | even | 2 | 360.2.w.d.307.4 | yes | 16 | ||
15.8 | even | 4 | inner | 1440.2.bi.d.1423.1 | 16 | ||
20.3 | even | 4 | 360.2.w.d.163.1 | ✓ | 16 | ||
24.5 | odd | 2 | 360.2.w.d.307.8 | yes | 16 | ||
24.11 | even | 2 | inner | 1440.2.bi.d.847.1 | 16 | ||
40.3 | even | 4 | inner | 1440.2.bi.d.1423.2 | 16 | ||
40.13 | odd | 4 | 360.2.w.d.163.5 | yes | 16 | ||
60.23 | odd | 4 | 360.2.w.d.163.8 | yes | 16 | ||
120.53 | even | 4 | 360.2.w.d.163.4 | yes | 16 | ||
120.83 | odd | 4 | inner | 1440.2.bi.d.1423.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.w.d.163.1 | ✓ | 16 | 20.3 | even | 4 | ||
360.2.w.d.163.4 | yes | 16 | 120.53 | even | 4 | ||
360.2.w.d.163.5 | yes | 16 | 40.13 | odd | 4 | ||
360.2.w.d.163.8 | yes | 16 | 60.23 | odd | 4 | ||
360.2.w.d.307.1 | yes | 16 | 8.5 | even | 2 | ||
360.2.w.d.307.4 | yes | 16 | 12.11 | even | 2 | ||
360.2.w.d.307.5 | yes | 16 | 4.3 | odd | 2 | ||
360.2.w.d.307.8 | yes | 16 | 24.5 | odd | 2 | ||
1440.2.bi.d.847.1 | 16 | 24.11 | even | 2 | inner | ||
1440.2.bi.d.847.2 | 16 | 1.1 | even | 1 | trivial | ||
1440.2.bi.d.847.7 | 16 | 8.3 | odd | 2 | inner | ||
1440.2.bi.d.847.8 | 16 | 3.2 | odd | 2 | inner | ||
1440.2.bi.d.1423.1 | 16 | 15.8 | even | 4 | inner | ||
1440.2.bi.d.1423.2 | 16 | 40.3 | even | 4 | inner | ||
1440.2.bi.d.1423.7 | 16 | 5.3 | odd | 4 | inner | ||
1440.2.bi.d.1423.8 | 16 | 120.83 | odd | 4 | inner |