Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.4 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.4 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12043 | − | 2.12043i | −0.948283 | − | 0.948283i | 0.0504437 | − | 0.998727i | \(-0.483936\pi\) |
−0.998727 | + | 0.0504437i | \(0.983936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.03827 | − | 4.03827i | 1.21759 | − | 1.21759i | 0.249110 | − | 0.968475i | \(-0.419862\pi\) |
0.968475 | − | 0.249110i | \(-0.0801380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.91665 | − | 4.91665i | −1.36363 | − | 1.36363i | −0.869237 | − | 0.494396i | \(-0.835389\pi\) |
−0.494396 | − | 0.869237i | \(-0.664611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.76253i | 1.15508i | 0.816361 | + | 0.577542i | \(0.195988\pi\) | ||||
−0.816361 | + | 0.577542i | \(0.804012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.21762 | − | 2.21762i | 0.508756 | − | 0.508756i | −0.405388 | − | 0.914145i | \(-0.632864\pi\) |
0.914145 | + | 0.405388i | \(0.132864\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.91384i | − | 1.44164i | −0.693125 | − | 0.720818i | \(-0.743767\pi\) | ||
0.693125 | − | 0.720818i | \(-0.256233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.99241i | 0.798482i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.61285 | + | 2.61285i | −0.485193 | + | 0.485193i | −0.906786 | − | 0.421592i | \(-0.861471\pi\) |
0.421592 | + | 0.906786i | \(0.361471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.712246i | − | 0.127923i | −0.997952 | − | 0.0639615i | \(-0.979627\pi\) | ||
0.997952 | − | 0.0639615i | \(-0.0203735\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.12043 | + | 2.12043i | 0.358417 | + | 0.358417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.73777 | − | 5.73777i | 0.943283 | − | 0.943283i | −0.0551925 | − | 0.998476i | \(-0.517577\pi\) |
0.998476 | + | 0.0551925i | \(0.0175773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.59400 | 0.561288 | 0.280644 | − | 0.959812i | \(-0.409452\pi\) | ||||
0.280644 | + | 0.959812i | \(0.409452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.36325 | − | 3.36325i | −0.512891 | − | 0.512891i | 0.402520 | − | 0.915411i | \(-0.368134\pi\) |
−0.915411 | + | 0.402520i | \(0.868134\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.04590 | 0.881885 | 0.440942 | − | 0.897535i | \(-0.354644\pi\) | ||||
0.440942 | + | 0.897535i | \(0.354644\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.53235 | − | 4.53235i | −0.622566 | − | 0.622566i | 0.323621 | − | 0.946187i | \(-0.395100\pi\) |
−0.946187 | + | 0.323621i | \(0.895100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.1257 | −2.30923 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.82118 | + | 4.82118i | −0.627664 | + | 0.627664i | −0.947480 | − | 0.319815i | \(-0.896379\pi\) |
0.319815 | + | 0.947480i | \(0.396379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.72581 | − | 6.72581i | −0.861151 | − | 0.861151i | 0.130321 | − | 0.991472i | \(-0.458399\pi\) |
−0.991472 | + | 0.130321i | \(0.958399\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.8508i | 2.58622i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.87274 | − | 3.87274i | 0.473130 | − | 0.473130i | −0.429796 | − | 0.902926i | \(-0.641414\pi\) |
0.902926 | + | 0.429796i | \(0.141414\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7448i | 1.74988i | 0.484229 | + | 0.874941i | \(0.339100\pi\) | ||||
−0.484229 | + | 0.874941i | \(0.660900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.61241i | 0.539842i | 0.962882 | + | 0.269921i | \(0.0869976\pi\) | ||||
−0.962882 | + | 0.269921i | \(0.913002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.03827 | + | 4.03827i | −0.460204 | + | 0.460204i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.43429i | − | 0.836423i | −0.908350 | − | 0.418211i | \(-0.862657\pi\) | ||
0.908350 | − | 0.418211i | \(-0.137343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.44737 | + | 2.44737i | 0.268633 | + | 0.268633i | 0.828549 | − | 0.559916i | \(-0.189167\pi\) |
−0.559916 | + | 0.828549i | \(0.689167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0986 | − | 10.0986i | 1.09535 | − | 1.09535i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.23689 | −0.449109 | −0.224555 | − | 0.974461i | \(-0.572093\pi\) | ||||
−0.224555 | + | 0.974461i | \(0.572093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91665 | + | 4.91665i | 0.515405 | + | 0.515405i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.40458 | −0.964890 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.76292 | −0.686670 | −0.343335 | − | 0.939213i | \(-0.611557\pi\) | ||||
−0.343335 | + | 0.939213i | \(0.611557\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7637 | + | 12.7637i | 1.27003 | + | 1.27003i | 0.946070 | + | 0.323963i | \(0.105015\pi\) |
0.323963 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.09658 | −0.502181 | −0.251091 | − | 0.967964i | \(-0.580789\pi\) | ||||
−0.251091 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.45316 | + | 3.45316i | −0.333829 | + | 0.333829i | −0.854039 | − | 0.520209i | \(-0.825854\pi\) |
0.520209 | + | 0.854039i | \(0.325854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6452 | + | 12.6452i | 1.21119 | + | 1.21119i | 0.970635 | + | 0.240558i | \(0.0773304\pi\) |
0.240558 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.90657i | − | 0.555644i | −0.960633 | − | 0.277822i | \(-0.910388\pi\) | ||
0.960633 | − | 0.277822i | \(-0.0896125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6603 | + | 14.6603i | −1.36708 | + | 1.36708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.76253i | − | 0.436581i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 21.6153i | − | 1.96503i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.13652 | + | 2.13652i | −0.191096 | + | 0.191096i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.07038i | 0.272452i | 0.990678 | + | 0.136226i | \(0.0434974\pi\) | ||||
−0.990678 | + | 0.136226i | \(0.956503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.95401 | − | 6.95401i | −0.607575 | − | 0.607575i | 0.334737 | − | 0.942312i | \(-0.391353\pi\) |
−0.942312 | + | 0.334737i | \(0.891353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.21762 | + | 2.21762i | −0.192292 | + | 0.192292i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.5548 | −0.987193 | −0.493596 | − | 0.869691i | \(-0.664318\pi\) | ||||
−0.493596 | + | 0.869691i | \(0.664318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.19355 | − | 6.19355i | −0.525330 | − | 0.525330i | 0.393846 | − | 0.919176i | \(-0.371144\pi\) |
−0.919176 | + | 0.393846i | \(0.871144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −39.7095 | −3.32068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0807 | 0.920201 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.38965 | − | 2.38965i | −0.195767 | − | 0.195767i | 0.602415 | − | 0.798183i | \(-0.294205\pi\) |
−0.798183 | + | 0.602415i | \(0.794205\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2639 | −0.998018 | −0.499009 | − | 0.866597i | \(-0.666303\pi\) | ||||
−0.499009 | + | 0.866597i | \(0.666303\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.51026 | + | 1.51026i | −0.121307 | + | 0.121307i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.81144 | − | 4.81144i | −0.383995 | − | 0.383995i | 0.488544 | − | 0.872539i | \(-0.337528\pi\) |
−0.872539 | + | 0.488544i | \(0.837528\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.91384i | 0.544887i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.02781 | − | 6.02781i | 0.472134 | − | 0.472134i | −0.430470 | − | 0.902605i | \(-0.641652\pi\) |
0.902605 | + | 0.430470i | \(0.141652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.75117i | − | 0.367656i | −0.982958 | − | 0.183828i | \(-0.941151\pi\) | ||
0.982958 | − | 0.183828i | \(-0.0588490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.3469i | 2.71899i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.6615 | + | 13.6615i | −1.03867 | + | 1.03867i | −0.0394449 | + | 0.999222i | \(0.512559\pi\) |
−0.999222 | + | 0.0394449i | \(0.987441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.99241i | − | 0.301798i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.71026 | − | 9.71026i | −0.725779 | − | 0.725779i | 0.243997 | − | 0.969776i | \(-0.421541\pi\) |
−0.969776 | + | 0.243997i | \(0.921541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.99969 | + | 3.99969i | −0.297295 | + | 0.297295i | −0.839953 | − | 0.542659i | \(-0.817418\pi\) |
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.3330 | −1.78900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.2324 | + | 19.2324i | 1.40641 | + | 1.40641i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9802 | 1.15629 | 0.578143 | − | 0.815936i | \(-0.303778\pi\) | ||||
0.578143 | + | 0.815936i | \(0.303778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.55024 | −0.255552 | −0.127776 | − | 0.991803i | \(-0.540784\pi\) | ||||
−0.127776 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4049 | + | 10.4049i | 0.741320 | + | 0.741320i | 0.972832 | − | 0.231512i | \(-0.0743671\pi\) |
−0.231512 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0463 | −1.42104 | −0.710521 | − | 0.703676i | \(-0.751541\pi\) | ||||
−0.710521 | + | 0.703676i | \(0.751541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.61285 | − | 2.61285i | 0.183386 | − | 0.183386i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.62081 | − | 7.62081i | −0.532260 | − | 0.532260i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.9107i | − | 1.23891i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2434 | − | 14.2434i | 0.980558 | − | 0.980558i | −0.0192564 | − | 0.999815i | \(-0.506130\pi\) |
0.999815 | + | 0.0192564i | \(0.00612987\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.2630i | 0.972731i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.712246i | 0.0483504i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.4157 | − | 23.4157i | 1.57511 | − | 1.57511i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.0811i | − | 1.14384i | −0.820311 | − | 0.571918i | \(-0.806199\pi\) | ||
0.820311 | − | 0.571918i | \(-0.193801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.8882 | + | 15.8882i | 1.05453 | + | 1.05453i | 0.998425 | + | 0.0561098i | \(0.0178697\pi\) |
0.0561098 | + | 0.998425i | \(0.482130\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2648 | + | 17.2648i | −1.14089 | + | 1.14089i | −0.152605 | + | 0.988287i | \(0.548766\pi\) |
−0.988287 | + | 0.152605i | \(0.951234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.37677 | −0.548780 | −0.274390 | − | 0.961618i | \(-0.588476\pi\) | ||||
−0.274390 | + | 0.961618i | \(0.588476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8199 | − | 12.8199i | −0.836276 | − | 0.836276i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.24270 | 0.403807 | 0.201903 | − | 0.979405i | \(-0.435287\pi\) | ||||
0.201903 | + | 0.979405i | \(0.435287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.39859 | −0.154507 | −0.0772535 | − | 0.997011i | \(-0.524615\pi\) | ||||
−0.0772535 | + | 0.997011i | \(0.524615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.12043 | − | 2.12043i | −0.135469 | − | 0.135469i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.8065 | −1.38751 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5027 | + | 10.5027i | −0.662927 | + | 0.662927i | −0.956069 | − | 0.293142i | \(-0.905299\pi\) |
0.293142 | + | 0.956069i | \(0.405299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.9200 | − | 27.9200i | −1.75531 | − | 1.75531i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.99198i | − | 0.124256i | −0.998068 | − | 0.0621282i | \(-0.980211\pi\) | ||
0.998068 | − | 0.0621282i | \(-0.0197888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.73777 | + | 5.73777i | −0.356528 | + | 0.356528i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.76661i | − | 0.293922i | −0.989142 | − | 0.146961i | \(-0.953051\pi\) | ||
0.989142 | − | 0.146961i | \(-0.0469492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.2210i | 1.18074i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1764 | + | 10.1764i | −0.620468 | + | 0.620468i | −0.945651 | − | 0.325183i | \(-0.894574\pi\) |
0.325183 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.8185i | 1.81135i | 0.423977 | + | 0.905673i | \(0.360634\pi\) | ||||
−0.423977 | + | 0.905673i | \(0.639366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.1224 | + | 16.1224i | 0.972220 | + | 0.972220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3689 | − | 10.3689i | 0.623007 | − | 0.623007i | −0.323292 | − | 0.946299i | \(-0.604790\pi\) |
0.946299 | + | 0.323292i | \(0.104790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1234 | −0.603909 | −0.301954 | − | 0.953322i | \(-0.597639\pi\) | ||||
−0.301954 | + | 0.953322i | \(0.597639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7990 | − | 13.7990i | −0.820266 | − | 0.820266i | 0.165880 | − | 0.986146i | \(-0.446954\pi\) |
−0.986146 | + | 0.165880i | \(0.946954\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.59400 | −0.212147 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.68174 | −0.334220 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.85735 | + | 4.85735i | 0.283770 | + | 0.283770i | 0.834610 | − | 0.550841i | \(-0.185693\pi\) |
−0.550841 | + | 0.834610i | \(0.685693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.4459 | 1.19041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.9929 | + | 33.9929i | −1.96586 | + | 1.96586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.36325 | + | 3.36325i | 0.193854 | + | 0.193854i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.5231i | 1.63323i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4100 | − | 21.4100i | 1.22193 | − | 1.22193i | 0.254989 | − | 0.966944i | \(-0.417928\pi\) |
0.966944 | − | 0.254989i | \(-0.0820719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.23033i | − | 0.183175i | −0.995797 | − | 0.0915876i | \(-0.970806\pi\) | ||
0.995797 | − | 0.0915876i | \(-0.0291941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.53030i | − | 0.369114i | −0.982822 | − | 0.184557i | \(-0.940915\pi\) | ||
0.982822 | − | 0.184557i | \(-0.0590851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.7296 | − | 12.7296i | 0.714965 | − | 0.714965i | −0.252605 | − | 0.967570i | \(-0.581287\pi\) |
0.967570 | + | 0.252605i | \(0.0812872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1028i | 1.18153i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5615 | + | 10.5615i | 0.587656 | + | 0.587656i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.6293 | − | 19.6293i | 1.08884 | − | 1.08884i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.04590 | −0.333321 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.98204 | − | 7.98204i | −0.438732 | − | 0.438732i | 0.452853 | − | 0.891585i | \(-0.350406\pi\) |
−0.891585 | + | 0.452853i | \(0.850406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.4237 | −0.897323 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.43831 | −0.0783498 | −0.0391749 | − | 0.999232i | \(-0.512473\pi\) | ||||
−0.0391749 | + | 0.999232i | \(0.512473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.87624 | − | 2.87624i | −0.155757 | − | 0.155757i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3928 | + | 13.3928i | −0.718966 | + | 0.718966i | −0.968393 | − | 0.249428i | \(-0.919758\pi\) |
0.249428 | + | 0.968393i | \(0.419758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.01384 | − | 2.01384i | −0.107798 | − | 0.107798i | 0.651150 | − | 0.758949i | \(-0.274287\pi\) |
−0.758949 | + | 0.651150i | \(0.774287\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.9746i | − | 0.584119i | −0.956400 | − | 0.292060i | \(-0.905659\pi\) | ||
0.956400 | − | 0.292060i | \(-0.0943406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.2652 | − | 31.2652i | 1.65938 | − | 1.65938i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.8112i | − | 0.728926i | −0.931218 | − | 0.364463i | \(-0.881253\pi\) | ||
0.931218 | − | 0.364463i | \(-0.118747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.16435i | 0.482334i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.78028 | − | 9.78028i | 0.511923 | − | 0.511923i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.72353i | 0.0899673i | 0.998988 | + | 0.0449837i | \(0.0143236\pi\) | ||||
−0.998988 | + | 0.0449837i | \(0.985676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.53235 | + | 4.53235i | 0.235308 | + | 0.235308i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.17122 | − | 5.17122i | 0.267756 | − | 0.267756i | −0.560440 | − | 0.828195i | \(-0.689368\pi\) |
0.828195 | + | 0.560440i | \(0.189368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.6929 | 1.32325 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.73174 | + | 4.73174i | 0.243053 | + | 0.243053i | 0.818112 | − | 0.575059i | \(-0.195021\pi\) |
−0.575059 | + | 0.818112i | \(0.695021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9260 | 0.609388 | 0.304694 | − | 0.952450i | \(-0.401446\pi\) | ||||
0.304694 | + | 0.952450i | \(0.401446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.1257 | 0.872807 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5999 | + | 21.5999i | 1.09516 | + | 1.09516i | 0.994968 | + | 0.100189i | \(0.0319448\pi\) |
0.100189 | + | 0.994968i | \(0.468055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.9274 | 1.66521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7639 | + | 15.7639i | −0.793165 | + | 0.793165i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.1706 | − | 24.1706i | −1.21309 | − | 1.21309i | −0.970005 | − | 0.243084i | \(-0.921841\pi\) |
−0.243084 | − | 0.970005i | \(-0.578159\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.3793i | 1.61694i | 0.588536 | + | 0.808471i | \(0.299705\pi\) | ||||
−0.588536 | + | 0.808471i | \(0.700295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.50186 | + | 3.50186i | −0.174440 | + | 0.174440i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 46.3413i | − | 2.29706i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5253i | 0.767676i | 0.923400 | + | 0.383838i | \(0.125398\pi\) | ||||
−0.923400 | + | 0.383838i | \(0.874602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.82118 | − | 4.82118i | 0.237235 | − | 0.237235i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.3789i | − | 0.509481i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.1080 | + | 24.1080i | 1.17775 | + | 1.17775i | 0.980315 | + | 0.197438i | \(0.0632622\pi\) |
0.197438 | + | 0.980315i | \(0.436738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4110 | + | 21.4110i | −1.04351 | + | 1.04351i | −0.0444969 | + | 0.999010i | \(0.514168\pi\) |
−0.999010 | + | 0.0444969i | \(0.985832\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.0140 | −0.922314 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.72581 | + | 6.72581i | 0.325485 | + | 0.325485i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.7984 | 0.905485 | 0.452742 | − | 0.891641i | \(-0.350446\pi\) | ||||
0.452742 | + | 0.891641i | \(0.350446\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4453 | 1.27088 | 0.635440 | − | 0.772150i | \(-0.280819\pi\) | ||||
0.635440 | + | 0.772150i | \(0.280819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.3322 | − | 15.3322i | −0.733441 | − | 0.733441i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.11296 | −0.339483 | −0.169742 | − | 0.985489i | \(-0.554293\pi\) | ||||
−0.169742 | + | 0.985489i | \(0.554293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0108636 | − | 0.0108636i | 0.000516147 | − | 0.000516147i | −0.706849 | − | 0.707365i | \(-0.749884\pi\) |
0.707365 | + | 0.706849i | \(0.249884\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.98401 | + | 8.98401i | 0.425883 | + | 0.425883i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.7577i | − | 1.54593i | −0.634448 | − | 0.772966i | \(-0.718772\pi\) | ||
0.634448 | − | 0.772966i | \(-0.281228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.5135 | − | 14.5135i | 0.683416 | − | 0.683416i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 20.8508i | − | 0.977499i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.0528i | − | 0.470252i | −0.971965 | − | 0.235126i | \(-0.924450\pi\) | ||
0.971965 | − | 0.235126i | \(-0.0755502\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1351 | − | 15.1351i | 0.704910 | − | 0.704910i | −0.260550 | − | 0.965460i | \(-0.583904\pi\) |
0.965460 | + | 0.260550i | \(0.0839039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.6714i | − | 0.495940i | −0.968768 | − | 0.247970i | \(-0.920236\pi\) | ||
0.968768 | − | 0.247970i | \(-0.0797635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.67348 | − | 3.67348i | −0.169989 | − | 0.169989i | 0.616986 | − | 0.786974i | \(-0.288354\pi\) |
−0.786974 | + | 0.616986i | \(0.788354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.87274 | + | 3.87274i | −0.178826 | + | 0.178826i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.1634 | −1.24898 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.85363 | + | 8.85363i | 0.406233 | + | 0.406233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.41155 | 0.201569 | 0.100784 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100784 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56.4212 | −2.57258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3403 | + | 14.3403i | 0.651158 | + | 0.651158i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.97116 | −0.451837 | −0.225918 | − | 0.974146i | \(-0.572538\pi\) | ||||
−0.225918 | + | 0.974146i | \(0.572538\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2732 | − | 30.2732i | 1.36621 | − | 1.36621i | 0.500440 | − | 0.865771i | \(-0.333172\pi\) |
0.865771 | − | 0.500440i | \(-0.166828\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4438 | − | 12.4438i | −0.560439 | − | 0.560439i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.7448i | − | 0.661394i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4161 | + | 10.4161i | −0.466289 | + | 0.466289i | −0.900710 | − | 0.434421i | \(-0.856953\pi\) |
0.434421 | + | 0.900710i | \(0.356953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.37172i | − | 0.373277i | −0.982429 | − | 0.186638i | \(-0.940241\pi\) | ||
0.982429 | − | 0.186638i | \(-0.0597592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 54.1288i | − | 2.40870i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0580 | − | 17.0580i | 0.756083 | − | 0.756083i | −0.219524 | − | 0.975607i | \(-0.570450\pi\) |
0.975607 | + | 0.219524i | \(0.0704503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.61241i | − | 0.204041i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8069 | + | 10.8069i | 0.476210 | + | 0.476210i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.4150 | − | 24.4150i | 1.07377 | − | 1.07377i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.2025 | 0.534601 | 0.267300 | − | 0.963613i | \(-0.413868\pi\) | ||||
0.267300 | + | 0.963613i | \(0.413868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.77429 | + | 8.77429i | 0.383673 | + | 0.383673i | 0.872423 | − | 0.488751i | \(-0.162547\pi\) |
−0.488751 | + | 0.872423i | \(0.662547\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.39209 | 0.147762 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.8012 | −1.07831 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.6704 | − | 17.6704i | −0.765391 | − | 0.765391i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.6443 | 0.633129 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.03827 | − | 4.03827i | 0.173941 | − | 0.173941i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2625 | − | 23.2625i | −1.00013 | − | 1.00013i | −1.00000 | 0.000132738i | \(-0.999958\pi\) | |
−0.000132738 | − | 1.00000i | \(-0.500042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 53.6265i | − | 2.29711i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.7224 | + | 24.7224i | −1.05705 | + | 1.05705i | −0.0587833 | + | 0.998271i | \(0.518722\pi\) |
−0.998271 | + | 0.0587833i | \(0.981278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5886i | 0.493690i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.43429i | 0.316138i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9473 | − | 15.9473i | 0.675708 | − | 0.675708i | −0.283318 | − | 0.959026i | \(-0.591435\pi\) |
0.959026 | + | 0.283318i | \(0.0914352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.0718i | 1.39879i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.75478 | − | 8.75478i | −0.368970 | − | 0.368970i | 0.498132 | − | 0.867101i | \(-0.334020\pi\) |
−0.867101 | + | 0.498132i | \(0.834020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.5244 | + | 12.5244i | −0.526908 | + | 0.526908i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.3805 | −1.02209 | −0.511043 | − | 0.859555i | \(-0.670741\pi\) | ||||
−0.511043 | + | 0.859555i | \(0.670741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.52629 | + | 9.52629i | 0.398663 | + | 0.398663i | 0.877761 | − | 0.479098i | \(-0.159036\pi\) |
−0.479098 | + | 0.877761i | \(0.659036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.6029 | 1.15112 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.46394 | 0.0609448 | 0.0304724 | − | 0.999536i | \(-0.490299\pi\) | ||||
0.0304724 | + | 0.999536i | \(0.490299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44737 | − | 2.44737i | −0.101534 | − | 0.101534i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.6057 | −1.51605 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.13883 | − | 7.13883i | 0.294651 | − | 0.294651i | −0.544263 | − | 0.838914i | \(-0.683191\pi\) |
0.838914 | + | 0.544263i | \(0.183191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57949 | − | 1.57949i | −0.0650816 | − | 0.0650816i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7385i | 0.605237i | 0.953112 | + | 0.302619i | \(0.0978609\pi\) | ||||
−0.953112 | + | 0.302619i | \(0.902139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0986 | + | 10.0986i | −0.414002 | + | 0.414002i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8924i | 0.731062i | 0.930799 | + | 0.365531i | \(0.119113\pi\) | ||||
−0.930799 | + | 0.365531i | \(0.880887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.69170i | 0.272960i | 0.990643 | + | 0.136480i | \(0.0435790\pi\) | ||||
−0.990643 | + | 0.136480i | \(0.956421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45.8336 | + | 45.8336i | −1.86340 | + | 1.86340i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.0776i | − | 1.09904i | −0.835479 | − | 0.549522i | \(-0.814810\pi\) | ||
0.835479 | − | 0.549522i | \(-0.185190\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.7255 | − | 29.7255i | −1.20257 | − | 1.20257i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9059 | − | 22.9059i | 0.925159 | − | 0.925159i | −0.0722294 | − | 0.997388i | \(-0.523011\pi\) |
0.997388 | + | 0.0722294i | \(0.0230114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3945 | 0.418466 | 0.209233 | − | 0.977866i | \(-0.432903\pi\) | ||||
0.209233 | + | 0.977866i | \(0.432903\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.53232 | + | 8.53232i | 0.342943 | + | 0.342943i | 0.857473 | − | 0.514530i | \(-0.172033\pi\) |
−0.514530 | + | 0.857473i | \(0.672033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.23689 | 0.169747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.0227 | 1.16091 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3263 | + | 27.3263i | 1.08957 | + | 1.08957i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.74199 | 0.148966 | 0.0744831 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744831 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.51051 | − | 6.51051i | 0.258362 | − | 0.258362i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.91665 | − | 4.91665i | −0.194805 | − | 0.194805i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1283i | 0.597531i | 0.954326 | + | 0.298766i | \(0.0965749\pi\) | ||||
−0.954326 | + | 0.298766i | \(0.903425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.845317 | − | 0.845317i | 0.0333361 | − | 0.0333361i | −0.690242 | − | 0.723578i | \(-0.742496\pi\) |
0.723578 | + | 0.690242i | \(0.242496\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.9117i | 0.940064i | 0.882649 | + | 0.470032i | \(0.155758\pi\) | ||||
−0.882649 | + | 0.470032i | \(0.844242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.9385i | 1.52847i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.8544 | + | 19.8544i | −0.776964 | + | 0.776964i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.202350 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.4909i | 1.15231i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.03903 | − | 9.03903i | −0.352111 | − | 0.352111i | 0.508784 | − | 0.860894i | \(-0.330095\pi\) |
−0.860894 | + | 0.508784i | \(0.830095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.4210 | + | 31.4210i | −1.22213 | + | 1.22213i | −0.255261 | + | 0.966872i | \(0.582161\pi\) |
−0.966872 | + | 0.255261i | \(0.917839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.40458 | 0.364694 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0648 | + | 18.0648i | 0.699472 | + | 0.699472i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −54.3213 | −2.09705 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8543 | 0.649684 | 0.324842 | − | 0.945768i | \(-0.394689\pi\) | ||||
0.324842 | + | 0.945768i | \(0.394689\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8816 | − | 20.8816i | −0.802545 | − | 0.802545i | 0.180948 | − | 0.983493i | \(-0.442084\pi\) |
−0.983493 | + | 0.180948i | \(0.942084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.76292 | 0.259537 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.9351 | − | 18.9351i | 0.724533 | − | 0.724533i | −0.244992 | − | 0.969525i | \(-0.578785\pi\) |
0.969525 | + | 0.244992i | \(0.0787854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.5011 | + | 24.5011i | 0.936138 | + | 0.936138i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.5679i | 1.69790i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.24775 | − | 2.24775i | 0.0855083 | − | 0.0855083i | −0.663059 | − | 0.748567i | \(-0.730742\pi\) |
0.748567 | + | 0.663059i | \(0.230742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.2659i | 0.996323i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.1165i | 0.648335i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.17318 | − | 8.17318i | 0.308697 | − | 0.308697i | −0.535707 | − | 0.844404i | \(-0.679955\pi\) |
0.844404 | + | 0.535707i | \(0.179955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 25.4483i | − | 0.959802i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.7637 | − | 12.7637i | −0.480027 | − | 0.480027i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4595 | + | 11.4595i | −0.430372 | + | 0.430372i | −0.888755 | − | 0.458383i | \(-0.848429\pi\) |
0.458383 | + | 0.888755i | \(0.348429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.92435 | −0.184418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.2011 | + | 84.2011i | 3.14894 | + | 3.14894i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6156 | 0.880714 | 0.440357 | − | 0.897823i | \(-0.354852\pi\) | ||||
0.440357 | + | 0.897823i | \(0.354852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.09658 | 0.189807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.4316 | − | 10.4316i | −0.387418 | − | 0.387418i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2623 | 0.417695 | 0.208848 | − | 0.977948i | \(-0.433029\pi\) | ||||
0.208848 | + | 0.977948i | \(0.433029\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0176 | − | 16.0176i | 0.592432 | − | 0.592432i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.10898 | + | 8.10898i | 0.299512 | + | 0.299512i | 0.840823 | − | 0.541311i | \(-0.182072\pi\) |
−0.541311 | + | 0.840823i | \(0.682072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 31.2783i | − | 1.15215i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7952 | − | 35.7952i | 1.31675 | − | 1.31675i | 0.400410 | − | 0.916336i | \(-0.368868\pi\) |
0.916336 | − | 0.400410i | \(-0.131132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.0620i | − | 0.882748i | −0.897323 | − | 0.441374i | \(-0.854491\pi\) | ||
0.897323 | − | 0.441374i | \(-0.145509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.1341i | 0.371286i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.45316 | − | 3.45316i | 0.126176 | − | 0.126176i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 39.8810i | − | 1.45528i | −0.685961 | − | 0.727639i | \(-0.740618\pi\) | ||
0.685961 | − | 0.727639i | \(-0.259382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.0046 | + | 26.0046i | 0.946404 | + | 0.946404i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5955 | + | 11.5955i | −0.421446 | + | 0.421446i | −0.885701 | − | 0.464255i | \(-0.846322\pi\) |
0.464255 | + | 0.885701i | \(0.346322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.8050 | 0.645430 | 0.322715 | − | 0.946496i | \(-0.395404\pi\) | ||||
0.322715 | + | 0.946496i | \(0.395404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6452 | − | 12.6452i | −0.457788 | − | 0.457788i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.4081 | 1.71181 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.78949 | −0.244835 | −0.122418 | − | 0.992479i | \(-0.539065\pi\) | ||||
−0.122418 | + | 0.992479i | \(0.539065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.3304 | + | 20.3304i | 0.731235 | + | 0.731235i | 0.970864 | − | 0.239629i | \(-0.0770259\pi\) |
−0.239629 | + | 0.970864i | \(0.577026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.84358 | 0.102144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.97011 | − | 7.97011i | 0.285559 | − | 0.285559i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.5434 | + | 59.5434i | 2.13063 | + | 2.13063i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.4046i | 0.728272i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8828 | − | 11.8828i | 0.423577 | − | 0.423577i | −0.462856 | − | 0.886433i | \(-0.653175\pi\) |
0.886433 | + | 0.462856i | \(0.153175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.90657i | 0.210014i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.1368i | 2.34859i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.57631 | + | 4.57631i | −0.162101 | + | 0.162101i | −0.783497 | − | 0.621396i | \(-0.786566\pi\) |
0.621396 | + | 0.783497i | \(0.286566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.7938i | 1.01865i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.6262 | + | 18.6262i | 0.657303 | + | 0.657303i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6603 | − | 14.6603i | 0.516707 | − | 0.516707i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.1471 | 0.884123 | 0.442062 | − | 0.896985i | \(-0.354247\pi\) | ||||
0.442062 | + | 0.896985i | \(0.354247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5249 | − | 24.5249i | −0.861187 | − | 0.861187i | 0.130289 | − | 0.991476i | \(-0.458409\pi\) |
−0.991476 | + | 0.130289i | \(0.958409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.5630 | −0.895434 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.9168 | −0.521873 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.4111 | − | 24.4111i | −0.851955 | − | 0.851955i | 0.138419 | − | 0.990374i | \(-0.455798\pi\) |
−0.990374 | + | 0.138419i | \(0.955798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7338 | −0.548445 | −0.274223 | − | 0.961666i | \(-0.588421\pi\) | ||||
−0.274223 | + | 0.961666i | \(0.588421\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.0353 | + | 25.0353i | −0.870564 | + | 0.870564i | −0.992534 | − | 0.121970i | \(-0.961079\pi\) |
0.121970 | + | 0.992534i | \(0.461079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.0067 | − | 21.0067i | −0.729592 | − | 0.729592i | 0.240947 | − | 0.970538i | \(-0.422542\pi\) |
−0.970538 | + | 0.240947i | \(0.922542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.76253i | 0.165012i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0745 | + | 10.0745i | −0.348642 | + | 0.348642i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.34682i | 0.253640i | 0.991926 | + | 0.126820i | \(0.0404771\pi\) | ||||
−0.991926 | + | 0.126820i | \(0.959523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3461i | 0.529175i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 74.9504 | − | 74.9504i | 2.57837 | − | 2.57837i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.6153i | 0.742710i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.6700 | − | 39.6700i | −1.35987 | − | 1.35987i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.5322 | − | 27.5322i | 0.942685 | − | 0.942685i | −0.0557594 | − | 0.998444i | \(-0.517758\pi\) |
0.998444 | + | 0.0557594i | \(0.0177580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.8983 | −0.508915 | −0.254457 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254457 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.6121 | − | 13.6121i | −0.464439 | − | 0.464439i | 0.435668 | − | 0.900107i | \(-0.356512\pi\) |
−0.900107 | + | 0.435668i | \(0.856512\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.8205 | −1.49167 | −0.745834 | − | 0.666132i | \(-0.767949\pi\) | ||||
−0.745834 | + | 0.666132i | \(0.767949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.9365 | 1.96990 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.0217 | − | 30.0217i | −1.01842 | − | 1.01842i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.0818 | −1.29035 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.13652 | − | 2.13652i | 0.0722275 | − | 0.0722275i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3765 | + | 15.3765i | 0.519229 | + | 0.519229i | 0.917338 | − | 0.398109i | \(-0.130333\pi\) |
−0.398109 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.9612i | − | 0.672509i | −0.941771 | − | 0.336254i | \(-0.890840\pi\) | ||
0.941771 | − | 0.336254i | \(-0.109160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8680 | − | 16.8680i | 0.567654 | − | 0.567654i | −0.363816 | − | 0.931471i | \(-0.618526\pi\) |
0.931471 | + | 0.363816i | \(0.118526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.0819i | 0.842167i | 0.907022 | + | 0.421084i | \(0.138350\pi\) | ||||
−0.907022 | + | 0.421084i | \(0.861650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.07038i | − | 0.102977i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4075 | − | 13.4075i | 0.448664 | − | 0.448664i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.1797i | 1.37649i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.86099 | + | 1.86099i | 0.0620674 | + | 0.0620674i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.5855 | − | 21.5855i | 0.719116 | − | 0.719116i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9621 | 0.563839 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00255 | + | 6.00255i | 0.199311 | + | 0.199311i | 0.799705 | − | 0.600393i | \(-0.204989\pi\) |
−0.600393 | + | 0.799705i | \(0.704989\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6496 | −0.485363 | −0.242682 | − | 0.970106i | \(-0.578027\pi\) | ||||
−0.242682 | + | 0.970106i | \(0.578027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.7663 | 0.654168 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.95401 | + | 6.95401i | 0.229642 | + | 0.229642i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.17227 | −0.137631 | −0.0688153 | − | 0.997629i | \(-0.521922\pi\) | ||||
−0.0688153 | + | 0.997629i | \(0.521922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.4949 | − | 72.4949i | 2.38620 | − | 2.38620i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.9075 | + | 22.9075i | 0.753195 | + | 0.753195i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 38.1876i | − | 1.25290i | −0.779463 | − | 0.626448i | \(-0.784508\pi\) | ||
0.779463 | − | 0.626448i | \(-0.215492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.21762 | − | 2.21762i | 0.0726794 | − | 0.0726794i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 81.5618i | − | 2.66736i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0796i | 1.47269i | 0.676609 | + | 0.736343i | \(0.263449\pi\) | ||||
−0.676609 | + | 0.736343i | \(0.736551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.09966 | − | 3.09966i | 0.101046 | − | 0.101046i | −0.654777 | − | 0.755822i | \(-0.727237\pi\) |
0.755822 | + | 0.654777i | \(0.227237\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 24.8483i | − | 0.809173i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6180 | − | 16.6180i | −0.540012 | − | 0.540012i | 0.383520 | − | 0.923532i | \(-0.374712\pi\) |
−0.923532 | + | 0.383520i | \(0.874712\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.6776 | − | 22.6776i | 0.736146 | − | 0.736146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 57.9097 | 1.87588 | 0.937939 | − | 0.346801i | \(-0.112732\pi\) | ||||
0.937939 | + | 0.346801i | \(0.112732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.8848 | − | 33.8848i | −1.09649 | − | 1.09649i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5548 | 0.373124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4927 | 0.983636 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.52801 | + | 7.52801i | 0.242335 | + | 0.242335i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.9630 | −1.22081 | −0.610404 | − | 0.792090i | \(-0.708993\pi\) | ||||
−0.610404 | + | 0.792090i | \(0.708993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.00112 | − | 1.00112i | 0.0321273 | − | 0.0321273i | −0.690861 | − | 0.722988i | \(-0.742768\pi\) |
0.722988 | + | 0.690861i | \(0.242768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.19355 | + | 6.19355i | 0.198556 | + | 0.198556i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 24.6595i | − | 0.788928i | −0.918911 | − | 0.394464i | \(-0.870930\pi\) | ||
0.918911 | − | 0.394464i | \(-0.129070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.1097 | + | 17.1097i | −0.546829 | + | 0.546829i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.2723i | − | 0.646586i | −0.946299 | − | 0.323293i | \(-0.895210\pi\) | ||
0.946299 | − | 0.323293i | \(-0.104790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44.1258i | − | 1.40596i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.2530 | + | 23.2530i | −0.739401 | + | 0.739401i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4804i | 1.60356i | 0.597618 | + | 0.801781i | \(0.296114\pi\) | ||||
−0.597618 | + | 0.801781i | \(0.703886\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.5066 | + | 42.5066i | 1.34755 | + | 1.34755i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1175 | − | 28.1175i | 0.890492 | − | 0.890492i | −0.104077 | − | 0.994569i | \(-0.533189\pi\) |
0.994569 | + | 0.104077i | \(0.0331890\pi\) | |||||||
\(998\) | 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 | 4032.2.v.e.1583.4 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.17 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.17 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.4 | ✓ | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.4 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.17 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.17 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.4 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.4 | ✓ | 40 | 12.11 | even | 2 | ||
1008.2.v.e.323.17 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.4 | yes | 40 | 16.5 | even | 4 | ||
1008.2.v.e.827.17 | yes | 40 | 48.5 | odd | 4 | ||
4032.2.v.e.1583.4 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.1583.17 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.4 | 40 | 48.11 | even | 4 | inner | ||
4032.2.v.e.3599.17 | 40 | 16.11 | odd | 4 | inner |