Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [539,2,Mod(67,539)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(539, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("539.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 539.e (of order \(3\), 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: | \(4.30393666895\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.67 |
Dual form | 539.2.e.i.177.2 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11803 | + | 1.93649i | 0.790569 | + | 1.36931i | 0.925615 | + | 0.378467i | \(0.123549\pi\) |
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −1.61803 | + | 2.80252i | −0.934172 | + | 1.61803i | −0.158069 | + | 0.987428i | \(0.550527\pi\) |
−0.776103 | + | 0.630606i | \(0.782806\pi\) | |||||||
\(4\) | −1.50000 | + | 2.59808i | −0.750000 | + | 1.29904i | ||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −7.23607 | −2.95411 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | −3.73607 | − | 6.47106i | −1.24536 | − | 2.15702i | ||||
\(10\) | −2.23607 | + | 3.87298i | −0.707107 | + | 1.22474i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −4.85410 | − | 8.40755i | −1.40126 | − | 2.42705i | ||||
\(13\) | −1.23607 | −0.342824 | −0.171412 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171412 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.47214 | −1.67110 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −0.618034 | + | 1.07047i | −0.149895 | + | 0.259626i | −0.931189 | − | 0.364538i | \(-0.881227\pi\) |
0.781293 | + | 0.624164i | \(0.214560\pi\) | |||||||
\(18\) | 8.35410 | − | 14.4697i | 1.96908 | − | 3.41055i | ||||
\(19\) | 1.23607 | + | 2.14093i | 0.283573 | + | 0.491164i | 0.972262 | − | 0.233893i | \(-0.0751467\pi\) |
−0.688689 | + | 0.725057i | \(0.741813\pi\) | |||||||
\(20\) | −6.00000 | −1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.23607 | 0.476731 | ||||||||
\(23\) | 3.23607 | + | 5.60503i | 0.674767 | + | 1.16873i | 0.976537 | + | 0.215350i | \(0.0690891\pi\) |
−0.301770 | + | 0.953381i | \(0.597578\pi\) | |||||||
\(24\) | 3.61803 | − | 6.26662i | 0.738528 | − | 1.27917i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −1.38197 | − | 2.39364i | −0.271026 | − | 0.469431i | ||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | −7.23607 | − | 12.5332i | −1.32112 | − | 2.28825i | ||||
\(31\) | 3.61803 | − | 6.26662i | 0.649818 | − | 1.12552i | −0.333348 | − | 0.942804i | \(-0.608178\pi\) |
0.983166 | − | 0.182714i | \(-0.0584883\pi\) | |||||||
\(32\) | −3.35410 | + | 5.80948i | −0.592927 | + | 1.02698i | ||||
\(33\) | 1.61803 | + | 2.80252i | 0.281664 | + | 0.487856i | ||||
\(34\) | −2.76393 | −0.474010 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 22.4164 | 3.73607 | ||||||||
\(37\) | −0.236068 | − | 0.408882i | −0.0388093 | − | 0.0672197i | 0.845968 | − | 0.533233i | \(-0.179023\pi\) |
−0.884778 | + | 0.466013i | \(0.845690\pi\) | |||||||
\(38\) | −2.76393 | + | 4.78727i | −0.448369 | + | 0.776598i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | −2.23607 | − | 3.87298i | −0.353553 | − | 0.612372i | ||||
\(41\) | −6.76393 | −1.05635 | −0.528174 | − | 0.849136i | \(-0.677123\pi\) | ||||
−0.528174 | + | 0.849136i | \(0.677123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 7.47214 | − | 12.9421i | 1.11388 | − | 1.92930i | ||||
\(46\) | −7.23607 | + | 12.5332i | −1.06690 | + | 1.84793i | ||||
\(47\) | −3.61803 | − | 6.26662i | −0.527744 | − | 0.914080i | −0.999477 | − | 0.0323386i | \(-0.989705\pi\) |
0.471732 | − | 0.881742i | \(-0.343629\pi\) | |||||||
\(48\) | −3.23607 | −0.467086 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.23607 | 0.316228 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 1.85410 | − | 3.21140i | 0.257118 | − | 0.445341i | ||||
\(53\) | −4.23607 | + | 7.33708i | −0.581869 | + | 1.00783i | 0.413389 | + | 0.910554i | \(0.364345\pi\) |
−0.995258 | + | 0.0972717i | \(0.968988\pi\) | |||||||
\(54\) | 16.1803 | + | 28.0252i | 2.20187 | + | 3.81374i | ||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | −0.527864 | − | 0.914287i | −0.0693119 | − | 0.120052i | ||||
\(59\) | −1.61803 | + | 2.80252i | −0.210650 | + | 0.364857i | −0.951918 | − | 0.306352i | \(-0.900891\pi\) |
0.741268 | + | 0.671209i | \(0.234225\pi\) | |||||||
\(60\) | 9.70820 | − | 16.8151i | 1.25332 | − | 2.17082i | ||||
\(61\) | 1.38197 | + | 2.39364i | 0.176943 | + | 0.306474i | 0.940832 | − | 0.338874i | \(-0.110046\pi\) |
−0.763889 | + | 0.645347i | \(0.776713\pi\) | |||||||
\(62\) | 16.1803 | 2.05491 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | −1.23607 | − | 2.14093i | −0.153315 | − | 0.265550i | ||||
\(66\) | −3.61803 | + | 6.26662i | −0.445349 | + | 0.771367i | ||||
\(67\) | −2.76393 | + | 4.78727i | −0.337668 | + | 0.584858i | −0.983994 | − | 0.178204i | \(-0.942971\pi\) |
0.646326 | + | 0.763062i | \(0.276305\pi\) | |||||||
\(68\) | −1.85410 | − | 3.21140i | −0.224843 | − | 0.389439i | ||||
\(69\) | −20.9443 | −2.52139 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.52786 | −0.181324 | −0.0906621 | − | 0.995882i | \(-0.528898\pi\) | ||||
−0.0906621 | + | 0.995882i | \(0.528898\pi\) | |||||||
\(72\) | 8.35410 | + | 14.4697i | 0.984540 | + | 1.70527i | ||||
\(73\) | 2.61803 | − | 4.53457i | 0.306418 | − | 0.530731i | −0.671158 | − | 0.741314i | \(-0.734203\pi\) |
0.977576 | + | 0.210583i | \(0.0675362\pi\) | |||||||
\(74\) | 0.527864 | − | 0.914287i | 0.0613629 | − | 0.106284i | ||||
\(75\) | 1.61803 | + | 2.80252i | 0.186834 | + | 0.323607i | ||||
\(76\) | −7.41641 | −0.850720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.94427 | 1.01274 | ||||||||
\(79\) | −4.47214 | − | 7.74597i | −0.503155 | − | 0.871489i | −0.999993 | − | 0.00364646i | \(-0.998839\pi\) |
0.496839 | − | 0.867843i | \(-0.334494\pi\) | |||||||
\(80\) | −1.00000 | + | 1.73205i | −0.111803 | + | 0.193649i | ||||
\(81\) | −12.2082 | + | 21.1452i | −1.35647 | + | 2.34947i | ||||
\(82\) | −7.56231 | − | 13.0983i | −0.835117 | − | 1.44647i | ||||
\(83\) | 15.4164 | 1.69217 | 0.846085 | − | 0.533048i | \(-0.178953\pi\) | ||||
0.846085 | + | 0.533048i | \(0.178953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47214 | −0.268141 | ||||||||
\(86\) | 8.94427 | + | 15.4919i | 0.964486 | + | 1.67054i | ||||
\(87\) | 0.763932 | − | 1.32317i | 0.0819021 | − | 0.141859i | ||||
\(88\) | −1.11803 | + | 1.93649i | −0.119183 | + | 0.206431i | ||||
\(89\) | −1.00000 | − | 1.73205i | −0.106000 | − | 0.183597i | 0.808146 | − | 0.588982i | \(-0.200471\pi\) |
−0.914146 | + | 0.405385i | \(0.867138\pi\) | |||||||
\(90\) | 33.4164 | 3.52240 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −19.4164 | −2.02430 | ||||||||
\(93\) | 11.7082 | + | 20.2792i | 1.21408 | + | 2.10286i | ||||
\(94\) | 8.09017 | − | 14.0126i | 0.834437 | − | 1.44529i | ||||
\(95\) | −2.47214 | + | 4.28187i | −0.253636 | + | 0.439310i | ||||
\(96\) | −10.8541 | − | 18.7999i | −1.10779 | − | 1.91875i | ||||
\(97\) | −9.41641 | −0.956091 | −0.478046 | − | 0.878335i | \(-0.658655\pi\) | ||||
−0.478046 | + | 0.878335i | \(0.658655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.47214 | −0.750978 | ||||||||
\(100\) | 1.50000 | + | 2.59808i | 0.150000 | + | 0.259808i | ||||
\(101\) | 4.61803 | − | 7.99867i | 0.459512 | − | 0.795897i | −0.539424 | − | 0.842035i | \(-0.681358\pi\) |
0.998935 | + | 0.0461372i | \(0.0146911\pi\) | |||||||
\(102\) | 4.47214 | − | 7.74597i | 0.442807 | − | 0.766965i | ||||
\(103\) | 2.85410 | + | 4.94345i | 0.281223 | + | 0.487093i | 0.971686 | − | 0.236275i | \(-0.0759266\pi\) |
−0.690463 | + | 0.723368i | \(0.742593\pi\) | |||||||
\(104\) | 2.76393 | 0.271026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.9443 | −1.84003 | ||||||||
\(107\) | 2.00000 | + | 3.46410i | 0.193347 | + | 0.334887i | 0.946357 | − | 0.323122i | \(-0.104732\pi\) |
−0.753010 | + | 0.658009i | \(0.771399\pi\) | |||||||
\(108\) | −21.7082 | + | 37.5997i | −2.08887 | + | 3.61803i | ||||
\(109\) | −2.23607 | + | 3.87298i | −0.214176 | + | 0.370965i | −0.953018 | − | 0.302915i | \(-0.902040\pi\) |
0.738841 | + | 0.673880i | \(0.235373\pi\) | |||||||
\(110\) | 2.23607 | + | 3.87298i | 0.213201 | + | 0.369274i | ||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | −8.94427 | − | 15.4919i | −0.837708 | − | 1.45095i | ||||
\(115\) | −6.47214 | + | 11.2101i | −0.603530 | + | 1.04534i | ||||
\(116\) | 0.708204 | − | 1.22665i | 0.0657551 | − | 0.113891i | ||||
\(117\) | 4.61803 | + | 7.99867i | 0.426937 | + | 0.739477i | ||||
\(118\) | −7.23607 | −0.666134 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.4721 | 1.32112 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −3.09017 | + | 5.35233i | −0.279771 | + | 0.484577i | ||||
\(123\) | 10.9443 | − | 18.9560i | 0.986812 | − | 1.70921i | ||||
\(124\) | 10.8541 | + | 18.7999i | 0.974727 | + | 1.68828i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9443 | 1.85850 | 0.929252 | − | 0.369447i | \(-0.120453\pi\) | ||||
0.929252 | + | 0.369447i | \(0.120453\pi\) | |||||||
\(128\) | −7.82624 | − | 13.5554i | −0.691748 | − | 1.19814i | ||||
\(129\) | −12.9443 | + | 22.4201i | −1.13968 | + | 1.97398i | ||||
\(130\) | 2.76393 | − | 4.78727i | 0.242413 | − | 0.419871i | ||||
\(131\) | 6.94427 | + | 12.0278i | 0.606724 | + | 1.05088i | 0.991776 | + | 0.127982i | \(0.0408500\pi\) |
−0.385053 | + | 0.922895i | \(0.625817\pi\) | |||||||
\(132\) | −9.70820 | −0.844991 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.3607 | −1.06780 | ||||||||
\(135\) | 14.4721 | + | 25.0665i | 1.24556 | + | 2.15738i | ||||
\(136\) | 1.38197 | − | 2.39364i | 0.118503 | − | 0.205253i | ||||
\(137\) | −3.76393 | + | 6.51932i | −0.321574 | + | 0.556983i | −0.980813 | − | 0.194951i | \(-0.937545\pi\) |
0.659239 | + | 0.751934i | \(0.270879\pi\) | |||||||
\(138\) | −23.4164 | − | 40.5584i | −1.99334 | − | 3.45256i | ||||
\(139\) | −10.4721 | −0.888235 | −0.444117 | − | 0.895969i | \(-0.646483\pi\) | ||||
−0.444117 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.4164 | 1.97202 | ||||||||
\(142\) | −1.70820 | − | 2.95870i | −0.143349 | − | 0.248288i | ||||
\(143\) | −0.618034 | + | 1.07047i | −0.0516826 | + | 0.0895169i | ||||
\(144\) | 3.73607 | − | 6.47106i | 0.311339 | − | 0.539255i | ||||
\(145\) | −0.472136 | − | 0.817763i | −0.0392088 | − | 0.0679116i | ||||
\(146\) | 11.7082 | 0.968978 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.41641 | 0.116428 | ||||||||
\(149\) | −7.00000 | − | 12.1244i | −0.573462 | − | 0.993266i | −0.996207 | − | 0.0870170i | \(-0.972267\pi\) |
0.422744 | − | 0.906249i | \(-0.361067\pi\) | |||||||
\(150\) | −3.61803 | + | 6.26662i | −0.295411 | + | 0.511667i | ||||
\(151\) | 4.47214 | − | 7.74597i | 0.363937 | − | 0.630358i | −0.624668 | − | 0.780891i | \(-0.714766\pi\) |
0.988605 | + | 0.150533i | \(0.0480989\pi\) | |||||||
\(152\) | −2.76393 | − | 4.78727i | −0.224184 | − | 0.388299i | ||||
\(153\) | 9.23607 | 0.746692 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4721 | 1.16243 | ||||||||
\(156\) | 6.00000 | + | 10.3923i | 0.480384 | + | 0.832050i | ||||
\(157\) | 3.47214 | − | 6.01392i | 0.277107 | − | 0.479963i | −0.693558 | − | 0.720401i | \(-0.743958\pi\) |
0.970664 | + | 0.240438i | \(0.0772911\pi\) | |||||||
\(158\) | 10.0000 | − | 17.3205i | 0.795557 | − | 1.37795i | ||||
\(159\) | −13.7082 | − | 23.7433i | −1.08713 | − | 1.88297i | ||||
\(160\) | −13.4164 | −1.06066 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −54.5967 | −4.28953 | ||||||||
\(163\) | −11.7082 | − | 20.2792i | −0.917057 | − | 1.58839i | −0.803861 | − | 0.594817i | \(-0.797224\pi\) |
−0.113196 | − | 0.993573i | \(-0.536109\pi\) | |||||||
\(164\) | 10.1459 | − | 17.5732i | 0.792262 | − | 1.37224i | ||||
\(165\) | −3.23607 | + | 5.60503i | −0.251928 | + | 0.436351i | ||||
\(166\) | 17.2361 | + | 29.8537i | 1.33778 | + | 2.31710i | ||||
\(167\) | −12.9443 | −1.00166 | −0.500829 | − | 0.865546i | \(-0.666971\pi\) | ||||
−0.500829 | + | 0.865546i | \(0.666971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | −2.76393 | − | 4.78727i | −0.211984 | − | 0.367167i | ||||
\(171\) | 9.23607 | − | 15.9973i | 0.706300 | − | 1.22335i | ||||
\(172\) | −12.0000 | + | 20.7846i | −0.914991 | + | 1.58481i | ||||
\(173\) | 8.61803 | + | 14.9269i | 0.655217 | + | 1.13487i | 0.981839 | + | 0.189714i | \(0.0607561\pi\) |
−0.326622 | + | 0.945155i | \(0.605911\pi\) | |||||||
\(174\) | 3.41641 | 0.258997 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −5.23607 | − | 9.06914i | −0.393567 | − | 0.681678i | ||||
\(178\) | 2.23607 | − | 3.87298i | 0.167600 | − | 0.290292i | ||||
\(179\) | −4.47214 | + | 7.74597i | −0.334263 | + | 0.578961i | −0.983343 | − | 0.181760i | \(-0.941821\pi\) |
0.649080 | + | 0.760720i | \(0.275154\pi\) | |||||||
\(180\) | 22.4164 | + | 38.8264i | 1.67082 | + | 2.89395i | ||||
\(181\) | 1.41641 | 0.105281 | 0.0526404 | − | 0.998614i | \(-0.483236\pi\) | ||||
0.0526404 | + | 0.998614i | \(0.483236\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.94427 | −0.661180 | ||||||||
\(184\) | −7.23607 | − | 12.5332i | −0.533450 | − | 0.923963i | ||||
\(185\) | 0.472136 | − | 0.817763i | 0.0347121 | − | 0.0601232i | ||||
\(186\) | −26.1803 | + | 45.3457i | −1.91964 | + | 3.32491i | ||||
\(187\) | 0.618034 | + | 1.07047i | 0.0451951 | + | 0.0782802i | ||||
\(188\) | 21.7082 | 1.58323 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.0557 | −0.802067 | ||||||||
\(191\) | 10.4721 | + | 18.1383i | 0.757737 | + | 1.31244i | 0.944002 | + | 0.329940i | \(0.107028\pi\) |
−0.186265 | + | 0.982500i | \(0.559638\pi\) | |||||||
\(192\) | 21.0344 | − | 36.4327i | 1.51803 | − | 2.62931i | ||||
\(193\) | 11.9443 | − | 20.6881i | 0.859768 | − | 1.48916i | −0.0123830 | − | 0.999923i | \(-0.503942\pi\) |
0.872151 | − | 0.489238i | \(-0.162725\pi\) | |||||||
\(194\) | −10.5279 | − | 18.2348i | −0.755857 | − | 1.30918i | ||||
\(195\) | 8.00000 | 0.572892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | −8.35410 | − | 14.4697i | −0.593700 | − | 1.02832i | ||||
\(199\) | −10.0902 | + | 17.4767i | −0.715273 | + | 1.23889i | 0.247581 | + | 0.968867i | \(0.420364\pi\) |
−0.962854 | + | 0.270022i | \(0.912969\pi\) | |||||||
\(200\) | −1.11803 | + | 1.93649i | −0.0790569 | + | 0.136931i | ||||
\(201\) | −8.94427 | − | 15.4919i | −0.630880 | − | 1.09272i | ||||
\(202\) | 20.6525 | 1.45310 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | −6.76393 | − | 11.7155i | −0.472414 | − | 0.818244i | ||||
\(206\) | −6.38197 | + | 11.0539i | −0.444653 | + | 0.770161i | ||||
\(207\) | 24.1803 | − | 41.8816i | 1.68065 | − | 2.91097i | ||||
\(208\) | −0.618034 | − | 1.07047i | −0.0428529 | − | 0.0742235i | ||||
\(209\) | 2.47214 | 0.171001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8885 | 1.50687 | 0.753435 | − | 0.657523i | \(-0.228396\pi\) | ||||
0.753435 | + | 0.657523i | \(0.228396\pi\) | |||||||
\(212\) | −12.7082 | − | 22.0113i | −0.872803 | − | 1.51174i | ||||
\(213\) | 2.47214 | − | 4.28187i | 0.169388 | − | 0.293389i | ||||
\(214\) | −4.47214 | + | 7.74597i | −0.305709 | + | 0.529503i | ||||
\(215\) | 8.00000 | + | 13.8564i | 0.545595 | + | 0.944999i | ||||
\(216\) | −32.3607 | −2.20187 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | 8.47214 | + | 14.6742i | 0.572494 | + | 0.991589i | ||||
\(220\) | −3.00000 | + | 5.19615i | −0.202260 | + | 0.350325i | ||||
\(221\) | 0.763932 | − | 1.32317i | 0.0513876 | − | 0.0890060i | ||||
\(222\) | 1.70820 | + | 2.95870i | 0.114647 | + | 0.198575i | ||||
\(223\) | 12.1803 | 0.815656 | 0.407828 | − | 0.913059i | \(-0.366286\pi\) | ||||
0.407828 | + | 0.913059i | \(0.366286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.47214 | −0.498142 | ||||||||
\(226\) | 2.23607 | + | 3.87298i | 0.148741 | + | 0.257627i | ||||
\(227\) | 14.9443 | − | 25.8842i | 0.991886 | − | 1.71800i | 0.385846 | − | 0.922563i | \(-0.373910\pi\) |
0.606040 | − | 0.795434i | \(-0.292757\pi\) | |||||||
\(228\) | 12.0000 | − | 20.7846i | 0.794719 | − | 1.37649i | ||||
\(229\) | −2.23607 | − | 3.87298i | −0.147764 | − | 0.255934i | 0.782637 | − | 0.622478i | \(-0.213874\pi\) |
−0.930401 | + | 0.366544i | \(0.880541\pi\) | |||||||
\(230\) | −28.9443 | −1.90853 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.05573 | 0.0693119 | ||||||||
\(233\) | 8.70820 | + | 15.0831i | 0.570493 | + | 0.988124i | 0.996515 | + | 0.0834107i | \(0.0265813\pi\) |
−0.426022 | + | 0.904713i | \(0.640085\pi\) | |||||||
\(234\) | −10.3262 | + | 17.8856i | −0.675047 | + | 1.16922i | ||||
\(235\) | 7.23607 | − | 12.5332i | 0.472029 | − | 0.817578i | ||||
\(236\) | −4.85410 | − | 8.40755i | −0.315975 | − | 0.547285i | ||||
\(237\) | 28.9443 | 1.88013 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8885 | 1.67459 | 0.837295 | − | 0.546751i | \(-0.184136\pi\) | ||||
0.837295 | + | 0.546751i | \(0.184136\pi\) | |||||||
\(240\) | −3.23607 | − | 5.60503i | −0.208887 | − | 0.361803i | ||||
\(241\) | −13.5623 | + | 23.4906i | −0.873625 | + | 1.51316i | −0.0154046 | + | 0.999881i | \(0.504904\pi\) |
−0.858220 | + | 0.513281i | \(0.828430\pi\) | |||||||
\(242\) | 1.11803 | − | 1.93649i | 0.0718699 | − | 0.124482i | ||||
\(243\) | −17.7984 | − | 30.8277i | −1.14177 | − | 1.97760i | ||||
\(244\) | −8.29180 | −0.530828 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 48.9443 | 3.12057 | ||||||||
\(247\) | −1.52786 | − | 2.64634i | −0.0972157 | − | 0.168382i | ||||
\(248\) | −8.09017 | + | 14.0126i | −0.513726 | + | 0.889800i | ||||
\(249\) | −24.9443 | + | 43.2047i | −1.58078 | + | 2.73799i | ||||
\(250\) | 13.4164 | + | 23.2379i | 0.848528 | + | 1.46969i | ||||
\(251\) | 17.7082 | 1.11773 | 0.558866 | − | 0.829258i | \(-0.311237\pi\) | ||||
0.558866 | + | 0.829258i | \(0.311237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.47214 | 0.406900 | ||||||||
\(254\) | 23.4164 | + | 40.5584i | 1.46928 | + | 2.54486i | ||||
\(255\) | 4.00000 | − | 6.92820i | 0.250490 | − | 0.433861i | ||||
\(256\) | 4.50000 | − | 7.79423i | 0.281250 | − | 0.487139i | ||||
\(257\) | 3.00000 | + | 5.19615i | 0.187135 | + | 0.324127i | 0.944294 | − | 0.329104i | \(-0.106747\pi\) |
−0.757159 | + | 0.653231i | \(0.773413\pi\) | |||||||
\(258\) | −57.8885 | −3.60398 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.41641 | 0.459946 | ||||||||
\(261\) | 1.76393 | + | 3.05522i | 0.109185 | + | 0.189113i | ||||
\(262\) | −15.5279 | + | 26.8950i | −0.959315 | + | 1.66158i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −3.61803 | − | 6.26662i | −0.222675 | − | 0.385684i | ||||
\(265\) | −16.9443 | −1.04088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.47214 | 0.396088 | ||||||||
\(268\) | −8.29180 | − | 14.3618i | −0.506502 | − | 0.877287i | ||||
\(269\) | 6.70820 | − | 11.6190i | 0.409006 | − | 0.708420i | −0.585772 | − | 0.810476i | \(-0.699209\pi\) |
0.994779 | + | 0.102056i | \(0.0325420\pi\) | |||||||
\(270\) | −32.3607 | + | 56.0503i | −1.96941 | + | 3.41112i | ||||
\(271\) | 0.763932 | + | 1.32317i | 0.0464056 | + | 0.0803768i | 0.888295 | − | 0.459273i | \(-0.151890\pi\) |
−0.841890 | + | 0.539650i | \(0.818557\pi\) | |||||||
\(272\) | −1.23607 | −0.0749476 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.8328 | −1.01691 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 31.4164 | − | 54.4148i | 1.89105 | − | 3.27539i | ||||
\(277\) | −7.94427 | + | 13.7599i | −0.477325 | + | 0.826751i | −0.999662 | − | 0.0259878i | \(-0.991727\pi\) |
0.522337 | + | 0.852739i | \(0.325060\pi\) | |||||||
\(278\) | −11.7082 | − | 20.2792i | −0.702211 | − | 1.21627i | ||||
\(279\) | −54.0689 | −3.23702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4721 | −0.744025 | −0.372013 | − | 0.928228i | \(-0.621332\pi\) | ||||
−0.372013 | + | 0.928228i | \(0.621332\pi\) | |||||||
\(282\) | 26.1803 | + | 45.3457i | 1.55902 | + | 2.70030i | ||||
\(283\) | 2.94427 | − | 5.09963i | 0.175019 | − | 0.303141i | −0.765149 | − | 0.643853i | \(-0.777335\pi\) |
0.940168 | + | 0.340712i | \(0.110668\pi\) | |||||||
\(284\) | 2.29180 | − | 3.96951i | 0.135993 | − | 0.235547i | ||||
\(285\) | −8.00000 | − | 13.8564i | −0.473879 | − | 0.820783i | ||||
\(286\) | −2.76393 | −0.163435 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 50.1246 | 2.95362 | ||||||||
\(289\) | 7.73607 | + | 13.3993i | 0.455063 | + | 0.788192i | ||||
\(290\) | 1.05573 | − | 1.82857i | 0.0619945 | − | 0.107378i | ||||
\(291\) | 15.2361 | − | 26.3896i | 0.893154 | − | 1.54699i | ||||
\(292\) | 7.85410 | + | 13.6037i | 0.459627 | + | 0.796097i | ||||
\(293\) | 15.1246 | 0.883589 | 0.441795 | − | 0.897116i | \(-0.354342\pi\) | ||||
0.441795 | + | 0.897116i | \(0.354342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.47214 | −0.376822 | ||||||||
\(296\) | 0.527864 | + | 0.914287i | 0.0306815 | + | 0.0531419i | ||||
\(297\) | 7.23607 | − | 12.5332i | 0.419879 | − | 0.727252i | ||||
\(298\) | 15.6525 | − | 27.1109i | 0.906724 | − | 1.57049i | ||||
\(299\) | −4.00000 | − | 6.92820i | −0.231326 | − | 0.400668i | ||||
\(300\) | −9.70820 | −0.560503 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 20.0000 | 1.15087 | ||||||||
\(303\) | 14.9443 | + | 25.8842i | 0.858526 | + | 1.48701i | ||||
\(304\) | −1.23607 | + | 2.14093i | −0.0708934 | + | 0.122791i | ||||
\(305\) | −2.76393 | + | 4.78727i | −0.158262 | + | 0.274118i | ||||
\(306\) | 10.3262 | + | 17.8856i | 0.590312 | + | 1.02245i | ||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | 16.1803 | + | 28.0252i | 0.918982 | + | 1.59172i | ||||
\(311\) | 10.8541 | − | 18.7999i | 0.615480 | − | 1.06604i | −0.374820 | − | 0.927097i | \(-0.622296\pi\) |
0.990300 | − | 0.138945i | \(-0.0443710\pi\) | |||||||
\(312\) | −4.47214 | + | 7.74597i | −0.253185 | + | 0.438529i | ||||
\(313\) | 1.47214 | + | 2.54981i | 0.0832100 | + | 0.144124i | 0.904627 | − | 0.426204i | \(-0.140149\pi\) |
−0.821417 | + | 0.570328i | \(0.806816\pi\) | |||||||
\(314\) | 15.5279 | 0.876288 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.8328 | 1.50946 | ||||||||
\(317\) | −7.00000 | − | 12.1244i | −0.393159 | − | 0.680972i | 0.599705 | − | 0.800221i | \(-0.295285\pi\) |
−0.992864 | + | 0.119249i | \(0.961951\pi\) | |||||||
\(318\) | 30.6525 | − | 53.0916i | 1.71891 | − | 2.97723i | ||||
\(319\) | −0.236068 | + | 0.408882i | −0.0132173 | + | 0.0228930i | ||||
\(320\) | −13.0000 | − | 22.5167i | −0.726722 | − | 1.25872i | ||||
\(321\) | −12.9443 | −0.722479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.05573 | −0.170025 | ||||||||
\(324\) | −36.6246 | − | 63.4357i | −2.03470 | − | 3.52420i | ||||
\(325\) | −0.618034 | + | 1.07047i | −0.0342824 | + | 0.0593788i | ||||
\(326\) | 26.1803 | − | 45.3457i | 1.44999 | − | 2.51146i | ||||
\(327\) | −7.23607 | − | 12.5332i | −0.400155 | − | 0.693090i | ||||
\(328\) | 15.1246 | 0.835117 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −14.4721 | −0.796665 | ||||||||
\(331\) | −10.9443 | − | 18.9560i | −0.601552 | − | 1.04192i | −0.992586 | − | 0.121542i | \(-0.961216\pi\) |
0.391035 | − | 0.920376i | \(-0.372117\pi\) | |||||||
\(332\) | −23.1246 | + | 40.0530i | −1.26913 | + | 2.19819i | ||||
\(333\) | −1.76393 | + | 3.05522i | −0.0966629 | + | 0.167425i | ||||
\(334\) | −14.4721 | − | 25.0665i | −0.791880 | − | 1.37158i | ||||
\(335\) | −11.0557 | −0.604039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4721 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(338\) | −12.8262 | − | 22.2157i | −0.697655 | − | 1.20837i | ||||
\(339\) | −3.23607 | + | 5.60503i | −0.175759 | + | 0.304424i | ||||
\(340\) | 3.70820 | − | 6.42280i | 0.201106 | − | 0.348325i | ||||
\(341\) | −3.61803 | − | 6.26662i | −0.195928 | − | 0.339356i | ||||
\(342\) | 41.3050 | 2.23352 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.8885 | −0.964486 | ||||||||
\(345\) | −20.9443 | − | 36.2765i | −1.12760 | − | 1.95306i | ||||
\(346\) | −19.2705 | + | 33.3775i | −1.03599 | + | 1.79439i | ||||
\(347\) | −1.52786 | + | 2.64634i | −0.0820200 | + | 0.142063i | −0.904118 | − | 0.427284i | \(-0.859470\pi\) |
0.822097 | + | 0.569347i | \(0.192804\pi\) | |||||||
\(348\) | 2.29180 | + | 3.96951i | 0.122853 | + | 0.212788i | ||||
\(349\) | −2.76393 | −0.147950 | −0.0739749 | − | 0.997260i | \(-0.523568\pi\) | ||||
−0.0739749 | + | 0.997260i | \(0.523568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 3.35410 | + | 5.80948i | 0.178774 | + | 0.309646i | ||||
\(353\) | 7.94427 | − | 13.7599i | 0.422831 | − | 0.732365i | −0.573384 | − | 0.819287i | \(-0.694370\pi\) |
0.996215 | + | 0.0869220i | \(0.0277031\pi\) | |||||||
\(354\) | 11.7082 | − | 20.2792i | 0.622284 | − | 1.07783i | ||||
\(355\) | −1.52786 | − | 2.64634i | −0.0810906 | − | 0.140453i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | 3.52786 | + | 6.11044i | 0.186194 | + | 0.322497i | 0.943978 | − | 0.330008i | \(-0.107052\pi\) |
−0.757785 | + | 0.652505i | \(0.773718\pi\) | |||||||
\(360\) | −16.7082 | + | 28.9395i | −0.880600 | + | 1.52524i | ||||
\(361\) | 6.44427 | − | 11.1618i | 0.339172 | − | 0.587463i | ||||
\(362\) | 1.58359 | + | 2.74286i | 0.0832318 | + | 0.144162i | ||||
\(363\) | 3.23607 | 0.169850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4721 | 0.548137 | ||||||||
\(366\) | −10.0000 | − | 17.3205i | −0.522708 | − | 0.905357i | ||||
\(367\) | −8.56231 | + | 14.8303i | −0.446949 | + | 0.774138i | −0.998186 | − | 0.0602108i | \(-0.980823\pi\) |
0.551237 | + | 0.834349i | \(0.314156\pi\) | |||||||
\(368\) | −3.23607 | + | 5.60503i | −0.168692 | + | 0.292183i | ||||
\(369\) | 25.2705 | + | 43.7698i | 1.31553 | + | 2.27857i | ||||
\(370\) | 2.11146 | 0.109769 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −70.2492 | −3.64225 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | −1.38197 | + | 2.39364i | −0.0714598 | + | 0.123772i | ||||
\(375\) | −19.4164 | + | 33.6302i | −1.00266 | + | 1.73666i | ||||
\(376\) | 8.09017 | + | 14.0126i | 0.417219 | + | 0.722644i | ||||
\(377\) | 0.583592 | 0.0300565 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.3050 | −1.29983 | −0.649914 | − | 0.760008i | \(-0.725195\pi\) | ||||
−0.649914 | + | 0.760008i | \(0.725195\pi\) | |||||||
\(380\) | −7.41641 | − | 12.8456i | −0.380454 | − | 0.658965i | ||||
\(381\) | −33.8885 | + | 58.6967i | −1.73616 | + | 3.00712i | ||||
\(382\) | −23.4164 | + | 40.5584i | −1.19809 | + | 2.07515i | ||||
\(383\) | −13.3262 | − | 23.0817i | −0.680939 | − | 1.17942i | −0.974695 | − | 0.223540i | \(-0.928239\pi\) |
0.293756 | − | 0.955881i | \(-0.405095\pi\) | |||||||
\(384\) | 50.6525 | 2.58485 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.4164 | 2.71882 | ||||||||
\(387\) | −29.8885 | − | 51.7685i | −1.51932 | − | 2.63154i | ||||
\(388\) | 14.1246 | − | 24.4645i | 0.717069 | − | 1.24200i | ||||
\(389\) | 9.94427 | − | 17.2240i | 0.504195 | − | 0.873291i | −0.495794 | − | 0.868440i | \(-0.665123\pi\) |
0.999988 | − | 0.00485030i | \(-0.00154390\pi\) | |||||||
\(390\) | 8.94427 | + | 15.4919i | 0.452911 | + | 0.784465i | ||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.9443 | −2.26714 | ||||||||
\(394\) | −2.23607 | − | 3.87298i | −0.112651 | − | 0.195118i | ||||
\(395\) | 8.94427 | − | 15.4919i | 0.450035 | − | 0.779484i | ||||
\(396\) | 11.2082 | − | 19.4132i | 0.563233 | − | 0.975549i | ||||
\(397\) | 0.0557281 | + | 0.0965239i | 0.00279691 | + | 0.00484439i | 0.867420 | − | 0.497576i | \(-0.165776\pi\) |
−0.864624 | + | 0.502420i | \(0.832443\pi\) | |||||||
\(398\) | −45.1246 | −2.26189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −2.52786 | − | 4.37839i | −0.126236 | − | 0.218646i | 0.795980 | − | 0.605323i | \(-0.206956\pi\) |
−0.922215 | + | 0.386677i | \(0.873623\pi\) | |||||||
\(402\) | 20.0000 | − | 34.6410i | 0.997509 | − | 1.72774i | ||||
\(403\) | −4.47214 | + | 7.74597i | −0.222773 | + | 0.385854i | ||||
\(404\) | 13.8541 | + | 23.9960i | 0.689267 | + | 1.19385i | ||||
\(405\) | −48.8328 | −2.42652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.472136 | −0.0234029 | ||||||||
\(408\) | 4.47214 | + | 7.74597i | 0.221404 | + | 0.383482i | ||||
\(409\) | 15.5623 | − | 26.9547i | 0.769507 | − | 1.33282i | −0.168324 | − | 0.985732i | \(-0.553836\pi\) |
0.937831 | − | 0.347093i | \(-0.112831\pi\) | |||||||
\(410\) | 15.1246 | − | 26.1966i | 0.746951 | − | 1.29376i | ||||
\(411\) | −12.1803 | − | 21.0970i | −0.600812 | − | 1.04064i | ||||
\(412\) | −17.1246 | −0.843669 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 108.138 | 5.31468 | ||||||||
\(415\) | 15.4164 | + | 26.7020i | 0.756762 | + | 1.31075i | ||||
\(416\) | 4.14590 | − | 7.18091i | 0.203269 | − | 0.352073i | ||||
\(417\) | 16.9443 | − | 29.3483i | 0.829765 | − | 1.43719i | ||||
\(418\) | 2.76393 | + | 4.78727i | 0.135188 | + | 0.234153i | ||||
\(419\) | −6.65248 | −0.324995 | −0.162497 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162497 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3607 | −1.08979 | −0.544896 | − | 0.838503i | \(-0.683431\pi\) | ||||
−0.544896 | + | 0.838503i | \(0.683431\pi\) | |||||||
\(422\) | 24.4721 | + | 42.3870i | 1.19128 | + | 2.06337i | ||||
\(423\) | −27.0344 | + | 46.8250i | −1.31446 | + | 2.27671i | ||||
\(424\) | 9.47214 | − | 16.4062i | 0.460008 | − | 0.796757i | ||||
\(425\) | 0.618034 | + | 1.07047i | 0.0299791 | + | 0.0519252i | ||||
\(426\) | 11.0557 | 0.535652 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −2.00000 | − | 3.46410i | −0.0965609 | − | 0.167248i | ||||
\(430\) | −17.8885 | + | 30.9839i | −0.862662 | + | 1.49417i | ||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 7.23607 | + | 12.5332i | 0.348145 | + | 0.603006i | ||||
\(433\) | 0.472136 | 0.0226894 | 0.0113447 | − | 0.999936i | \(-0.496389\pi\) | ||||
0.0113447 | + | 0.999936i | \(0.496389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.05573 | 0.146511 | ||||||||
\(436\) | −6.70820 | − | 11.6190i | −0.321265 | − | 0.556447i | ||||
\(437\) | −8.00000 | + | 13.8564i | −0.382692 | + | 0.662842i | ||||
\(438\) | −18.9443 | + | 32.8124i | −0.905192 | + | 1.56784i | ||||
\(439\) | −0.763932 | − | 1.32317i | −0.0364605 | − | 0.0631514i | 0.847219 | − | 0.531243i | \(-0.178275\pi\) |
−0.883680 | + | 0.468092i | \(0.844942\pi\) | |||||||
\(440\) | −4.47214 | −0.213201 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.41641 | 0.162502 | ||||||||
\(443\) | 3.52786 | + | 6.11044i | 0.167614 | + | 0.290316i | 0.937580 | − | 0.347768i | \(-0.113060\pi\) |
−0.769967 | + | 0.638084i | \(0.779727\pi\) | |||||||
\(444\) | −2.29180 | + | 3.96951i | −0.108764 | + | 0.188384i | ||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | 13.6180 | + | 23.5871i | 0.644833 | + | 1.11688i | ||||
\(447\) | 45.3050 | 2.14285 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5279 | −0.921577 | −0.460788 | − | 0.887510i | \(-0.652433\pi\) | ||||
−0.460788 | + | 0.887510i | \(0.652433\pi\) | |||||||
\(450\) | −8.35410 | − | 14.4697i | −0.393816 | − | 0.682110i | ||||
\(451\) | −3.38197 | + | 5.85774i | −0.159251 | + | 0.275830i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | 14.4721 | + | 25.0665i | 0.679960 | + | 1.17773i | ||||
\(454\) | 66.8328 | 3.13662 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 17.8885 | 0.837708 | ||||||||
\(457\) | −12.4164 | − | 21.5058i | −0.580815 | − | 1.00600i | −0.995383 | − | 0.0959828i | \(-0.969401\pi\) |
0.414568 | − | 0.910018i | \(-0.363933\pi\) | |||||||
\(458\) | 5.00000 | − | 8.66025i | 0.233635 | − | 0.404667i | ||||
\(459\) | −8.94427 | + | 15.4919i | −0.417483 | + | 0.723102i | ||||
\(460\) | −19.4164 | − | 33.6302i | −0.905295 | − | 1.56802i | ||||
\(461\) | 10.1803 | 0.474146 | 0.237073 | − | 0.971492i | \(-0.423812\pi\) | ||||
0.237073 | + | 0.971492i | \(0.423812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.4721 | −0.672577 | −0.336289 | − | 0.941759i | \(-0.609172\pi\) | ||||
−0.336289 | + | 0.941759i | \(0.609172\pi\) | |||||||
\(464\) | −0.236068 | − | 0.408882i | −0.0109592 | − | 0.0189819i | ||||
\(465\) | −23.4164 | + | 40.5584i | −1.08591 | + | 1.88085i | ||||
\(466\) | −19.4721 | + | 33.7267i | −0.902029 | + | 1.56236i | ||||
\(467\) | 17.0344 | + | 29.5045i | 0.788260 | + | 1.36531i | 0.927032 | + | 0.374982i | \(0.122351\pi\) |
−0.138772 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(468\) | −27.7082 | −1.28081 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 32.3607 | 1.49269 | ||||||||
\(471\) | 11.2361 | + | 19.4614i | 0.517731 | + | 0.896736i | ||||
\(472\) | 3.61803 | − | 6.26662i | 0.166534 | − | 0.288445i | ||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 32.3607 | + | 56.0503i | 1.48638 | + | 2.57448i | ||||
\(475\) | 2.47214 | 0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 63.3050 | 2.89853 | ||||||||
\(478\) | 28.9443 | + | 50.1329i | 1.32388 | + | 2.29303i | ||||
\(479\) | −11.2361 | + | 19.4614i | −0.513389 | + | 0.889216i | 0.486490 | + | 0.873686i | \(0.338277\pi\) |
−0.999879 | + | 0.0155300i | \(0.995056\pi\) | |||||||
\(480\) | 21.7082 | − | 37.5997i | 0.990839 | − | 1.71618i | ||||
\(481\) | 0.291796 | + | 0.505406i | 0.0133048 | + | 0.0230445i | ||||
\(482\) | −60.6525 | −2.76264 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | −9.41641 | − | 16.3097i | −0.427577 | − | 0.740585i | ||||
\(486\) | 39.7984 | − | 68.9328i | 1.80529 | − | 3.12686i | ||||
\(487\) | −4.18034 | + | 7.24056i | −0.189429 | + | 0.328101i | −0.945060 | − | 0.326897i | \(-0.893997\pi\) |
0.755631 | + | 0.654998i | \(0.227330\pi\) | |||||||
\(488\) | −3.09017 | − | 5.35233i | −0.139885 | − | 0.242289i | ||||
\(489\) | 75.7771 | 3.42676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 32.8328 | + | 56.8681i | 1.48022 | + | 2.56381i | ||||
\(493\) | 0.291796 | − | 0.505406i | 0.0131418 | − | 0.0227623i | ||||
\(494\) | 3.41641 | − | 5.91739i | 0.153711 | − | 0.266236i | ||||
\(495\) | −7.47214 | − | 12.9421i | −0.335848 | − | 0.581705i | ||||
\(496\) | 7.23607 | 0.324909 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −111.554 | −4.99886 | ||||||||
\(499\) | −5.23607 | − | 9.06914i | −0.234399 | − | 0.405990i | 0.724699 | − | 0.689065i | \(-0.241979\pi\) |
−0.959098 | + | 0.283075i | \(0.908645\pi\) | |||||||
\(500\) | −18.0000 | + | 31.1769i | −0.804984 | + | 1.39427i | ||||
\(501\) | 20.9443 | − | 36.2765i | 0.935721 | − | 1.62072i | ||||
\(502\) | 19.7984 | + | 34.2918i | 0.883645 | + | 1.53052i | ||||
\(503\) | −3.41641 | −0.152330 | −0.0761650 | − | 0.997095i | \(-0.524268\pi\) | ||||
−0.0761650 | + | 0.997095i | \(0.524268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.4721 | 0.821999 | ||||||||
\(506\) | 7.23607 | + | 12.5332i | 0.321682 | + | 0.557170i | ||||
\(507\) | 18.5623 | − | 32.1509i | 0.824381 | − | 1.42787i | ||||
\(508\) | −31.4164 | + | 54.4148i | −1.39388 | + | 2.41427i | ||||
\(509\) | −15.7639 | − | 27.3039i | −0.698724 | − | 1.21023i | −0.968909 | − | 0.247417i | \(-0.920418\pi\) |
0.270185 | − | 0.962808i | \(-0.412915\pi\) | |||||||
\(510\) | 17.8885 | 0.792118 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.1803 | −0.494106 | ||||||||
\(513\) | 17.8885 | + | 30.9839i | 0.789799 | + | 1.36797i | ||||
\(514\) | −6.70820 | + | 11.6190i | −0.295886 | + | 0.512490i | ||||
\(515\) | −5.70820 | + | 9.88690i | −0.251534 | + | 0.435669i | ||||
\(516\) | −38.8328 | − | 67.2604i | −1.70952 | − | 2.96097i | ||||
\(517\) | −7.23607 | −0.318242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −55.7771 | −2.44834 | ||||||||
\(520\) | 2.76393 | + | 4.78727i | 0.121206 | + | 0.209936i | ||||
\(521\) | 7.18034 | − | 12.4367i | 0.314576 | − | 0.544862i | −0.664771 | − | 0.747047i | \(-0.731471\pi\) |
0.979347 | + | 0.202185i | \(0.0648042\pi\) | |||||||
\(522\) | −3.94427 | + | 6.83168i | −0.172636 | + | 0.299014i | ||||
\(523\) | −22.0000 | − | 38.1051i | −0.961993 | − | 1.66622i | −0.717486 | − | 0.696573i | \(-0.754707\pi\) |
−0.244507 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(524\) | −41.6656 | −1.82017 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.47214 | + | 7.74597i | 0.194809 | + | 0.337420i | ||||
\(528\) | −1.61803 | + | 2.80252i | −0.0704159 | + | 0.121964i | ||||
\(529\) | −9.44427 | + | 16.3580i | −0.410621 | + | 0.711216i | ||||
\(530\) | −18.9443 | − | 32.8124i | −0.822887 | − | 1.42528i | ||||
\(531\) | 24.1803 | 1.04934 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.36068 | 0.362141 | ||||||||
\(534\) | 7.23607 | + | 12.5332i | 0.313135 | + | 0.542366i | ||||
\(535\) | −4.00000 | + | 6.92820i | −0.172935 | + | 0.299532i | ||||
\(536\) | 6.18034 | − | 10.7047i | 0.266950 | − | 0.462371i | ||||
\(537\) | −14.4721 | − | 25.0665i | −0.624519 | − | 1.08170i | ||||
\(538\) | 30.0000 | 1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −86.8328 | −3.73669 | ||||||||
\(541\) | 16.4164 | + | 28.4341i | 0.705797 | + | 1.22248i | 0.966403 | + | 0.257030i | \(0.0827440\pi\) |
−0.260607 | + | 0.965445i | \(0.583923\pi\) | |||||||
\(542\) | −1.70820 | + | 2.95870i | −0.0733736 | + | 0.127087i | ||||
\(543\) | −2.29180 | + | 3.96951i | −0.0983504 | + | 0.170348i | ||||
\(544\) | −4.14590 | − | 7.18091i | −0.177754 | − | 0.307879i | ||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | −11.2918 | − | 19.5580i | −0.482362 | − | 0.835475i | ||||
\(549\) | 10.3262 | − | 17.8856i | 0.440713 | − | 0.763337i | ||||
\(550\) | 1.11803 | − | 1.93649i | 0.0476731 | − | 0.0825723i | ||||
\(551\) | −0.583592 | − | 1.01081i | −0.0248619 | − | 0.0430620i | ||||
\(552\) | 46.8328 | 1.99334 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35.5279 | −1.50943 | ||||||||
\(555\) | 1.52786 | + | 2.64634i | 0.0648542 | + | 0.112331i | ||||
\(556\) | 15.7082 | − | 27.2074i | 0.666176 | − | 1.15385i | ||||
\(557\) | 10.5279 | − | 18.2348i | 0.446080 | − | 0.772633i | −0.552047 | − | 0.833813i | \(-0.686153\pi\) |
0.998127 | + | 0.0611800i | \(0.0194864\pi\) | |||||||
\(558\) | −60.4508 | − | 104.704i | −2.55909 | − | 4.43247i | ||||
\(559\) | −9.88854 | −0.418241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | −13.9443 | − | 24.1522i | −0.588204 | − | 1.01880i | ||||
\(563\) | −19.7082 | + | 34.1356i | −0.830602 | + | 1.43864i | 0.0669600 | + | 0.997756i | \(0.478670\pi\) |
−0.897562 | + | 0.440889i | \(0.854663\pi\) | |||||||
\(564\) | −35.1246 | + | 60.8376i | −1.47901 | + | 2.56173i | ||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | 13.1672 | 0.553458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.41641 | 0.143349 | ||||||||
\(569\) | −8.23607 | − | 14.2653i | −0.345274 | − | 0.598032i | 0.640130 | − | 0.768267i | \(-0.278881\pi\) |
−0.985403 | + | 0.170235i | \(0.945547\pi\) | |||||||
\(570\) | 17.8885 | − | 30.9839i | 0.749269 | − | 1.29777i | ||||
\(571\) | 16.4721 | − | 28.5306i | 0.689337 | − | 1.19397i | −0.282715 | − | 0.959204i | \(-0.591235\pi\) |
0.972053 | − | 0.234764i | \(-0.0754316\pi\) | |||||||
\(572\) | −1.85410 | − | 3.21140i | −0.0775239 | − | 0.134275i | ||||
\(573\) | −67.7771 | −2.83143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.47214 | 0.269907 | ||||||||
\(576\) | 48.5689 | + | 84.1238i | 2.02370 | + | 3.50516i | ||||
\(577\) | 14.2361 | − | 24.6576i | 0.592655 | − | 1.02651i | −0.401218 | − | 0.915983i | \(-0.631413\pi\) |
0.993873 | − | 0.110526i | \(-0.0352537\pi\) | |||||||
\(578\) | −17.2984 | + | 29.9617i | −0.719517 | + | 1.24624i | ||||
\(579\) | 38.6525 | + | 66.9481i | 1.60634 | + | 2.78227i | ||||
\(580\) | 2.83282 | 0.117626 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 68.1378 | 2.82440 | ||||||||
\(583\) | 4.23607 | + | 7.33708i | 0.175440 | + | 0.303871i | ||||
\(584\) | −5.85410 | + | 10.1396i | −0.242244 | + | 0.419580i | ||||
\(585\) | −9.23607 | + | 15.9973i | −0.381864 | + | 0.661409i | ||||
\(586\) | 16.9098 | + | 29.2887i | 0.698539 | + | 1.20990i | ||||
\(587\) | −13.1246 | −0.541711 | −0.270855 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270855 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8885 | 0.737085 | ||||||||
\(590\) | −7.23607 | − | 12.5332i | −0.297904 | − | 0.515985i | ||||
\(591\) | 3.23607 | − | 5.60503i | 0.133114 | − | 0.230560i | ||||
\(592\) | 0.236068 | − | 0.408882i | 0.00970233 | − | 0.0168049i | ||||
\(593\) | 16.1459 | + | 27.9655i | 0.663033 | + | 1.14841i | 0.979815 | + | 0.199908i | \(0.0640643\pi\) |
−0.316782 | + | 0.948498i | \(0.602602\pi\) | |||||||
\(594\) | 32.3607 | 1.32777 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.0000 | 1.72039 | ||||||||
\(597\) | −32.6525 | − | 56.5557i | −1.33638 | − | 2.31467i | ||||
\(598\) | 8.94427 | − | 15.4919i | 0.365758 | − | 0.633512i | ||||
\(599\) | −1.70820 | + | 2.95870i | −0.0697953 | + | 0.120889i | −0.898811 | − | 0.438336i | \(-0.855568\pi\) |
0.829016 | + | 0.559225i | \(0.188901\pi\) | |||||||
\(600\) | −3.61803 | − | 6.26662i | −0.147706 | − | 0.255834i | ||||
\(601\) | 3.12461 | 0.127456 | 0.0637278 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637278 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41.3050 | 1.68207 | ||||||||
\(604\) | 13.4164 | + | 23.2379i | 0.545906 | + | 0.945537i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | −33.4164 | + | 57.8789i | −1.35745 | + | 2.35117i | ||||
\(607\) | 2.47214 | + | 4.28187i | 0.100341 | + | 0.173796i | 0.911825 | − | 0.410579i | \(-0.134673\pi\) |
−0.811484 | + | 0.584374i | \(0.801340\pi\) | |||||||
\(608\) | −16.5836 | −0.672553 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.3607 | −0.500469 | ||||||||
\(611\) | 4.47214 | + | 7.74597i | 0.180923 | + | 0.313368i | ||||
\(612\) | −13.8541 | + | 23.9960i | −0.560019 | + | 0.969981i | ||||
\(613\) | 23.6525 | − | 40.9673i | 0.955315 | − | 1.65465i | 0.221668 | − | 0.975122i | \(-0.428850\pi\) |
0.733647 | − | 0.679531i | \(-0.237817\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | 43.7771 | 1.76526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4164 | 1.34529 | 0.672647 | − | 0.739964i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739964i | \(0.265157\pi\) | |||||||
\(618\) | −20.6525 | − | 35.7711i | −0.830764 | − | 1.43893i | ||||
\(619\) | 14.5623 | − | 25.2227i | 0.585308 | − | 1.01378i | −0.409528 | − | 0.912297i | \(-0.634307\pi\) |
0.994837 | − | 0.101487i | \(-0.0323599\pi\) | |||||||
\(620\) | −21.7082 | + | 37.5997i | −0.871822 | + | 1.51004i | ||||
\(621\) | 46.8328 | + | 81.1168i | 1.87934 | + | 3.25511i | ||||
\(622\) | 48.5410 | 1.94632 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | −3.29180 | + | 5.70156i | −0.131567 | + | 0.227880i | ||||
\(627\) | −4.00000 | + | 6.92820i | −0.159745 | + | 0.276686i | ||||
\(628\) | 10.4164 | + | 18.0417i | 0.415660 | + | 0.719944i | ||||
\(629\) | 0.583592 | 0.0232693 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | 10.0000 | + | 17.3205i | 0.397779 | + | 0.688973i | ||||
\(633\) | −35.4164 | + | 61.3430i | −1.40768 | + | 2.43817i | ||||
\(634\) | 15.6525 | − | 27.1109i | 0.621639 | − | 1.07671i | ||||
\(635\) | 20.9443 | + | 36.2765i | 0.831148 | + | 1.43959i | ||||
\(636\) | 82.2492 | 3.26139 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.05573 | −0.0417967 | ||||||||
\(639\) | 5.70820 | + | 9.88690i | 0.225813 | + | 0.391120i | ||||
\(640\) | 15.6525 | − | 27.1109i | 0.618718 | − | 1.07165i | ||||
\(641\) | 12.2361 | − | 21.1935i | 0.483296 | − | 0.837093i | −0.516520 | − | 0.856275i | \(-0.672773\pi\) |
0.999816 | + | 0.0191823i | \(0.00610630\pi\) | |||||||
\(642\) | −14.4721 | − | 25.0665i | −0.571170 | − | 0.989295i | ||||
\(643\) | −29.1246 | −1.14856 | −0.574281 | − | 0.818658i | \(-0.694718\pi\) | ||||
−0.574281 | + | 0.818658i | \(0.694718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −51.7771 | −2.03872 | ||||||||
\(646\) | −3.41641 | − | 5.91739i | −0.134417 | − | 0.232817i | ||||
\(647\) | 11.0344 | − | 19.1122i | 0.433809 | − | 0.751379i | −0.563389 | − | 0.826192i | \(-0.690503\pi\) |
0.997198 | + | 0.0748132i | \(0.0238360\pi\) | |||||||
\(648\) | 27.2984 | − | 47.2822i | 1.07238 | − | 1.85742i | ||||
\(649\) | 1.61803 | + | 2.80252i | 0.0635134 | + | 0.110008i | ||||
\(650\) | −2.76393 | −0.108410 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 70.2492 | 2.75117 | ||||||||
\(653\) | −21.4721 | − | 37.1908i | −0.840270 | − | 1.45539i | −0.889667 | − | 0.456610i | \(-0.849063\pi\) |
0.0493971 | − | 0.998779i | \(-0.484270\pi\) | |||||||
\(654\) | 16.1803 | − | 28.0252i | 0.632701 | − | 1.09587i | ||||
\(655\) | −13.8885 | + | 24.0557i | −0.542670 | + | 0.939933i | ||||
\(656\) | −3.38197 | − | 5.85774i | −0.132044 | − | 0.228706i | ||||
\(657\) | −39.1246 | −1.52640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | −9.70820 | − | 16.8151i | −0.377891 | − | 0.654527i | ||||
\(661\) | −6.41641 | + | 11.1135i | −0.249569 | + | 0.432267i | −0.963406 | − | 0.268045i | \(-0.913622\pi\) |
0.713837 | + | 0.700312i | \(0.246956\pi\) | |||||||
\(662\) | 24.4721 | − | 42.3870i | 0.951137 | − | 1.64742i | ||||
\(663\) | 2.47214 | + | 4.28187i | 0.0960098 | + | 0.166294i | ||||
\(664\) | −34.4721 | −1.33778 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.88854 | −0.305675 | ||||||||
\(667\) | −1.52786 | − | 2.64634i | −0.0591591 | − | 0.102467i | ||||
\(668\) | 19.4164 | − | 33.6302i | 0.751243 | − | 1.30119i | ||||
\(669\) | −19.7082 | + | 34.1356i | −0.761963 | + | 1.31976i | ||||
\(670\) | −12.3607 | − | 21.4093i | −0.477535 | − | 0.827114i | ||||
\(671\) | 2.76393 | 0.106700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.41641 | 0.208787 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(674\) | −22.8885 | − | 39.6441i | −0.881634 | − | 1.52703i | ||||
\(675\) | 7.23607 | − | 12.5332i | 0.278516 | − | 0.482405i | ||||
\(676\) | 17.2082 | − | 29.8055i | 0.661854 | − | 1.14636i | ||||
\(677\) | −1.85410 | − | 3.21140i | −0.0712589 | − | 0.123424i | 0.828194 | − | 0.560441i | \(-0.189368\pi\) |
−0.899453 | + | 0.437017i | \(0.856035\pi\) | |||||||
\(678\) | −14.4721 | −0.555799 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.52786 | 0.211984 | ||||||||
\(681\) | 48.3607 | + | 83.7632i | 1.85319 | + | 3.20981i | ||||
\(682\) | 8.09017 | − | 14.0126i | 0.309789 | − | 0.536570i | ||||
\(683\) | −14.9443 | + | 25.8842i | −0.571827 | + | 0.990433i | 0.424552 | + | 0.905404i | \(0.360432\pi\) |
−0.996378 | + | 0.0850292i | \(0.972902\pi\) | |||||||
\(684\) | 27.7082 | + | 47.9920i | 1.05945 | + | 1.83502i | ||||
\(685\) | −15.0557 | −0.575250 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.4721 | 0.552146 | ||||||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | 5.23607 | − | 9.06914i | 0.199478 | − | 0.345507i | ||||
\(690\) | 46.8328 | − | 81.1168i | 1.78289 | − | 3.08806i | ||||
\(691\) | 24.2705 | + | 42.0378i | 0.923294 | + | 1.59919i | 0.794283 | + | 0.607548i | \(0.207847\pi\) |
0.129011 | + | 0.991643i | \(0.458820\pi\) | |||||||
\(692\) | −51.7082 | −1.96565 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.83282 | −0.259370 | ||||||||
\(695\) | −10.4721 | − | 18.1383i | −0.397231 | − | 0.688024i | ||||
\(696\) | −1.70820 | + | 2.95870i | −0.0647493 | + | 0.112149i | ||||
\(697\) | 4.18034 | − | 7.24056i | 0.158342 | − | 0.274256i | ||||
\(698\) | −3.09017 | − | 5.35233i | −0.116965 | − | 0.202589i | ||||
\(699\) | −56.3607 | −2.13176 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.4721 | −0.924300 | −0.462150 | − | 0.886802i | \(-0.652922\pi\) | ||||
−0.462150 | + | 0.886802i | \(0.652922\pi\) | |||||||
\(702\) | −20.0000 | − | 34.6410i | −0.754851 | − | 1.30744i | ||||
\(703\) | 0.583592 | − | 1.01081i | 0.0220106 | − | 0.0381235i | ||||
\(704\) | −6.50000 | + | 11.2583i | −0.244978 | + | 0.424314i | ||||
\(705\) | 23.4164 | + | 40.5584i | 0.881913 | + | 1.52752i | ||||
\(706\) | 35.5279 | 1.33711 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 31.4164 | 1.18070 | ||||||||
\(709\) | −1.47214 | − | 2.54981i | −0.0552872 | − | 0.0957603i | 0.837057 | − | 0.547115i | \(-0.184274\pi\) |
−0.892344 | + | 0.451355i | \(0.850941\pi\) | |||||||
\(710\) | 3.41641 | − | 5.91739i | 0.128216 | − | 0.222076i | ||||
\(711\) | −33.4164 | + | 57.8789i | −1.25321 | + | 2.17063i | ||||
\(712\) | 2.23607 | + | 3.87298i | 0.0838002 | + | 0.145146i | ||||
\(713\) | 46.8328 | 1.75390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.47214 | −0.0924526 | ||||||||
\(716\) | −13.4164 | − | 23.2379i | −0.501395 | − | 0.868441i | ||||
\(717\) | −41.8885 | + | 72.5531i | −1.56436 | + | 2.70954i | ||||
\(718\) | −7.88854 | + | 13.6634i | −0.294398 | + | 0.509912i | ||||
\(719\) | −16.7426 | − | 28.9991i | −0.624395 | − | 1.08148i | −0.988657 | − | 0.150188i | \(-0.952012\pi\) |
0.364262 | − | 0.931296i | \(-0.381321\pi\) | |||||||
\(720\) | 14.9443 | 0.556940 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 28.8197 | 1.07256 | ||||||||
\(723\) | −43.8885 | − | 76.0172i | −1.63223 | − | 2.82711i | ||||
\(724\) | −2.12461 | + | 3.67994i | −0.0789606 | + | 0.136764i | ||||
\(725\) | −0.236068 | + | 0.408882i | −0.00876734 | + | 0.0151855i | ||||
\(726\) | 3.61803 | + | 6.26662i | 0.134278 | + | 0.232576i | ||||
\(727\) | −51.0132 | −1.89197 | −0.945987 | − | 0.324206i | \(-0.894903\pi\) | ||||
−0.945987 | + | 0.324206i | \(0.894903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 11.7082 | + | 20.2792i | 0.433340 | + | 0.750567i | ||||
\(731\) | −4.94427 | + | 8.56373i | −0.182871 | + | 0.316741i | ||||
\(732\) | 13.4164 | − | 23.2379i | 0.495885 | − | 0.858898i | ||||
\(733\) | −6.61803 | − | 11.4628i | −0.244443 | − | 0.423387i | 0.717532 | − | 0.696525i | \(-0.245272\pi\) |
−0.961975 | + | 0.273138i | \(0.911938\pi\) | |||||||
\(734\) | −38.2918 | −1.41338 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.4164 | −1.60035 | ||||||||
\(737\) | 2.76393 | + | 4.78727i | 0.101811 | + | 0.176341i | ||||
\(738\) | −56.5066 | + | 97.8723i | −2.08004 | + | 3.60273i | ||||
\(739\) | −3.52786 | + | 6.11044i | −0.129775 | + | 0.224776i | −0.923589 | − | 0.383384i | \(-0.874759\pi\) |
0.793815 | + | 0.608160i | \(0.208092\pi\) | |||||||
\(740\) | 1.41641 | + | 2.45329i | 0.0520682 | + | 0.0901847i | ||||
\(741\) | 9.88854 | 0.363265 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8885 | −1.24325 | −0.621625 | − | 0.783315i | \(-0.713527\pi\) | ||||
−0.621625 | + | 0.783315i | \(0.713527\pi\) | |||||||
\(744\) | −26.1803 | − | 45.3457i | −0.959818 | − | 1.66245i | ||||
\(745\) | 14.0000 | − | 24.2487i | 0.512920 | − | 0.888404i | ||||
\(746\) | 6.70820 | − | 11.6190i | 0.245605 | − | 0.425400i | ||||
\(747\) | −57.5967 | − | 99.7605i | −2.10735 | − | 3.65005i | ||||
\(748\) | −3.70820 | −0.135585 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −86.8328 | −3.17069 | ||||||||
\(751\) | −19.2361 | − | 33.3178i | −0.701934 | − | 1.21579i | −0.967787 | − | 0.251772i | \(-0.918987\pi\) |
0.265853 | − | 0.964014i | \(-0.414347\pi\) | |||||||
\(752\) | 3.61803 | − | 6.26662i | 0.131936 | − | 0.228520i | ||||
\(753\) | −28.6525 | + | 49.6275i | −1.04415 | + | 1.80853i | ||||
\(754\) | 0.652476 | + | 1.13012i | 0.0237618 | + | 0.0411566i | ||||
\(755\) | 17.8885 | 0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8885 | −0.722861 | −0.361431 | − | 0.932399i | \(-0.617712\pi\) | ||||
−0.361431 | + | 0.932399i | \(0.617712\pi\) | |||||||
\(758\) | −28.2918 | − | 49.0028i | −1.02760 | − | 1.77986i | ||||
\(759\) | −10.4721 | + | 18.1383i | −0.380114 | + | 0.658378i | ||||
\(760\) | 5.52786 | − | 9.57454i | 0.200517 | − | 0.347305i | ||||
\(761\) | −8.79837 | − | 15.2392i | −0.318941 | − | 0.552422i | 0.661327 | − | 0.750098i | \(-0.269994\pi\) |
−0.980267 | + | 0.197676i | \(0.936660\pi\) | |||||||
\(762\) | −151.554 | −5.49023 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −62.8328 | −2.27321 | ||||||||
\(765\) | 9.23607 | + | 15.9973i | 0.333931 | + | 0.578385i | ||||
\(766\) | 29.7984 | − | 51.6123i | 1.07666 | − | 1.86483i | ||||
\(767\) | 2.00000 | − | 3.46410i | 0.0722158 | − | 0.125081i | ||||
\(768\) | 14.5623 | + | 25.2227i | 0.525472 | + | 0.910144i | ||||
\(769\) | 31.7082 | 1.14343 | 0.571714 | − | 0.820453i | \(-0.306279\pi\) | ||||
0.571714 | + | 0.820453i | \(0.306279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.4164 | −0.699265 | ||||||||
\(772\) | 35.8328 | + | 62.0643i | 1.28965 | + | 2.23374i | ||||
\(773\) | −3.18034 | + | 5.50851i | −0.114389 | + | 0.198127i | −0.917535 | − | 0.397654i | \(-0.869824\pi\) |
0.803146 | + | 0.595782i | \(0.203158\pi\) | |||||||
\(774\) | 66.8328 | − | 115.758i | 2.40226 | − | 4.16083i | ||||
\(775\) | −3.61803 | − | 6.26662i | −0.129964 | − | 0.225104i | ||||
\(776\) | 21.0557 | 0.755857 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.4721 | 1.59440 | ||||||||
\(779\) | −8.36068 | − | 14.4811i | −0.299552 | − | 0.518840i | ||||
\(780\) | −12.0000 | + | 20.7846i | −0.429669 | + | 0.744208i | ||||
\(781\) | −0.763932 | + | 1.32317i | −0.0273356 | + | 0.0473467i | ||||
\(782\) | −8.94427 | − | 15.4919i | −0.319847 | − | 0.553990i | ||||
\(783\) | −6.83282 | −0.244185 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.8885 | 0.495703 | ||||||||
\(786\) | −50.2492 | − | 87.0342i | −1.79233 | − | 3.10441i | ||||
\(787\) | 8.29180 | − | 14.3618i | 0.295571 | − | 0.511943i | −0.679547 | − | 0.733632i | \(-0.737824\pi\) |
0.975117 | + | 0.221689i | \(0.0711569\pi\) | |||||||
\(788\) | 3.00000 | − | 5.19615i | 0.106871 | − | 0.185105i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.7082 | 0.593700 | ||||||||
\(793\) | −1.70820 | − | 2.95870i | −0.0606601 | − | 0.105066i | ||||
\(794\) | −0.124612 | + | 0.215834i | −0.00442231 | + | 0.00765966i | ||||
\(795\) | 27.4164 | − | 47.4866i | 0.972360 | − | 1.68418i | ||||
\(796\) | −30.2705 | − | 52.4301i | −1.07291 | − | 1.85833i | ||||
\(797\) | 2.94427 | 0.104291 | 0.0521457 | − | 0.998639i | \(-0.483394\pi\) | ||||
0.0521457 | + | 0.998639i | \(0.483394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.94427 | 0.316426 | ||||||||
\(800\) | 3.35410 | + | 5.80948i | 0.118585 | + | 0.205396i | ||||
\(801\) | −7.47214 | + | 12.9421i | −0.264015 | + | 0.457287i | ||||
\(802\) | 5.65248 | − | 9.79038i | 0.199596 | − | 0.345710i | ||||
\(803\) | −2.61803 | − | 4.53457i | −0.0923884 | − | 0.160021i | ||||
\(804\) | 53.6656 | 1.89264 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 21.7082 | + | 37.5997i | 0.764165 | + | 1.32357i | ||||
\(808\) | −10.3262 | + | 17.8856i | −0.363276 | + | 0.629212i | ||||
\(809\) | −19.4721 | + | 33.7267i | −0.684604 | + | 1.18577i | 0.288957 | + | 0.957342i | \(0.406691\pi\) |
−0.973561 | + | 0.228427i | \(0.926642\pi\) | |||||||
\(810\) | −54.5967 | − | 94.5643i | −1.91833 | − | 3.32265i | ||||
\(811\) | 18.8328 | 0.661310 | 0.330655 | − | 0.943752i | \(-0.392730\pi\) | ||||
0.330655 | + | 0.943752i | \(0.392730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.94427 | −0.173403 | ||||||||
\(814\) | −0.527864 | − | 0.914287i | −0.0185016 | − | 0.0320458i | ||||
\(815\) | 23.4164 | − | 40.5584i | 0.820241 | − | 1.42070i | ||||
\(816\) | 2.00000 | − | 3.46410i | 0.0700140 | − | 0.121268i | ||||
\(817\) | 9.88854 | + | 17.1275i | 0.345956 | + | 0.599214i | ||||
\(818\) | 69.5967 | 2.43339 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.5836 | 1.41724 | ||||||||
\(821\) | 4.41641 | + | 7.64944i | 0.154134 | + | 0.266967i | 0.932743 | − | 0.360541i | \(-0.117408\pi\) |
−0.778610 | + | 0.627509i | \(0.784075\pi\) | |||||||
\(822\) | 27.2361 | − | 47.1743i | 0.949967 | − | 1.64539i | ||||
\(823\) | 24.9443 | − | 43.2047i | 0.869503 | − | 1.50602i | 0.00699691 | − | 0.999976i | \(-0.497773\pi\) |
0.862506 | − | 0.506047i | \(-0.168894\pi\) | |||||||
\(824\) | −6.38197 | − | 11.0539i | −0.222326 | − | 0.385080i | ||||
\(825\) | 3.23607 | 0.112665 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.94427 | 0.171929 | 0.0859646 | − | 0.996298i | \(-0.472603\pi\) | ||||
0.0859646 | + | 0.996298i | \(0.472603\pi\) | |||||||
\(828\) | 72.5410 | + | 125.645i | 2.52097 | + | 4.36646i | ||||
\(829\) | 8.41641 | − | 14.5776i | 0.292314 | − | 0.506303i | −0.682043 | − | 0.731312i | \(-0.738908\pi\) |
0.974356 | + | 0.225010i | \(0.0722415\pi\) | |||||||
\(830\) | −34.4721 | + | 59.7075i | −1.19655 | + | 2.07248i | ||||
\(831\) | −25.7082 | − | 44.5279i | −0.891808 | − | 1.54466i | ||||
\(832\) | 16.0689 | 0.557088 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 75.7771 | 2.62395 | ||||||||
\(835\) | −12.9443 | − | 22.4201i | −0.447955 | − | 0.775881i | ||||
\(836\) | −3.70820 | + | 6.42280i | −0.128251 | + | 0.222137i | ||||
\(837\) | 52.3607 | − | 90.6914i | 1.80985 | − | 3.13475i | ||||
\(838\) | −7.43769 | − | 12.8825i | −0.256931 | − | 0.445017i | ||||
\(839\) | −14.0689 | −0.485712 | −0.242856 | − | 0.970062i | \(-0.578084\pi\) | ||||
−0.242856 | + | 0.970062i | \(0.578084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | −25.0000 | − | 43.3013i | −0.861557 | − | 1.49226i | ||||
\(843\) | 20.1803 | − | 34.9534i | 0.695048 | − | 1.20386i | ||||
\(844\) | −32.8328 | + | 56.8681i | −1.13015 | + | 1.95748i | ||||
\(845\) | −11.4721 | − | 19.8703i | −0.394653 | − | 0.683560i | ||||
\(846\) | −120.902 | −4.15669 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.47214 | −0.290934 | ||||||||
\(849\) | 9.52786 | + | 16.5027i | 0.326995 | + | 0.566373i | ||||
\(850\) | −1.38197 | + | 2.39364i | −0.0474010 | + | 0.0821010i | ||||
\(851\) | 1.52786 | − | 2.64634i | 0.0523745 | − | 0.0907153i | ||||
\(852\) | 7.41641 | + | 12.8456i | 0.254082 | + | 0.440083i | ||||
\(853\) | 0.652476 | 0.0223403 | 0.0111702 | − | 0.999938i | \(-0.496444\pi\) | ||||
0.0111702 | + | 0.999938i | \(0.496444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.9443 | 1.26347 | ||||||||
\(856\) | −4.47214 | − | 7.74597i | −0.152854 | − | 0.264752i | ||||
\(857\) | −5.38197 | + | 9.32184i | −0.183844 | + | 0.318428i | −0.943187 | − | 0.332264i | \(-0.892188\pi\) |
0.759342 | + | 0.650692i | \(0.225521\pi\) | |||||||
\(858\) | 4.47214 | − | 7.74597i | 0.152676 | − | 0.264443i | ||||
\(859\) | −20.2705 | − | 35.1096i | −0.691621 | − | 1.19792i | −0.971307 | − | 0.237831i | \(-0.923564\pi\) |
0.279686 | − | 0.960092i | \(-0.409770\pi\) | |||||||
\(860\) | −48.0000 | −1.63679 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.8328 | −0.913929 | ||||||||
\(863\) | 10.4721 | + | 18.1383i | 0.356476 | + | 0.617434i | 0.987369 | − | 0.158435i | \(-0.0506449\pi\) |
−0.630894 | + | 0.775869i | \(0.717312\pi\) | |||||||
\(864\) | −48.5410 | + | 84.0755i | −1.65140 | + | 2.86031i | ||||
\(865\) | −17.2361 | + | 29.8537i | −0.586044 | + | 1.01506i | ||||
\(866\) | 0.527864 | + | 0.914287i | 0.0179376 | + | 0.0310687i | ||||
\(867\) | −50.0689 | −1.70043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.94427 | −0.303414 | ||||||||
\(870\) | 3.41641 | + | 5.91739i | 0.115827 | + | 0.200618i | ||||
\(871\) | 3.41641 | − | 5.91739i | 0.115761 | − | 0.200503i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | 35.1803 | + | 60.9341i | 1.19067 | + | 2.06231i | ||||
\(874\) | −35.7771 | −1.21018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.8328 | −1.71748 | ||||||||
\(877\) | −20.7082 | − | 35.8677i | −0.699266 | − | 1.21116i | −0.968721 | − | 0.248152i | \(-0.920177\pi\) |
0.269455 | − | 0.963013i | \(-0.413157\pi\) | |||||||
\(878\) | 1.70820 | − | 2.95870i | 0.0576491 | − | 0.0998512i | ||||
\(879\) | −24.4721 | + | 42.3870i | −0.825425 | + | 1.42968i | ||||
\(880\) | 1.00000 | + | 1.73205i | 0.0337100 | + | 0.0583874i | ||||
\(881\) | 29.4164 | 0.991064 | 0.495532 | − | 0.868590i | \(-0.334973\pi\) | ||||
0.495532 | + | 0.868590i | \(0.334973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.94427 | 0.300999 | 0.150499 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150499 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(884\) | 2.29180 | + | 3.96951i | 0.0770814 | + | 0.133509i | ||||
\(885\) | 10.4721 | − | 18.1383i | 0.352017 | − | 0.609711i | ||||
\(886\) | −7.88854 | + | 13.6634i | −0.265021 | + | 0.459030i | ||||
\(887\) | −20.1803 | − | 34.9534i | −0.677589 | − | 1.17362i | −0.975705 | − | 0.219090i | \(-0.929691\pi\) |
0.298115 | − | 0.954530i | \(-0.403642\pi\) | |||||||
\(888\) | −3.41641 | −0.114647 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.94427 | 0.299813 | ||||||||
\(891\) | 12.2082 | + | 21.1452i | 0.408990 | + | 0.708392i | ||||
\(892\) | −18.2705 | + | 31.6455i | −0.611742 | + | 1.05957i | ||||
\(893\) | 8.94427 | − | 15.4919i | 0.299309 | − | 0.518418i | ||||
\(894\) | 50.6525 | + | 87.7327i | 1.69407 | + | 2.93422i | ||||
\(895\) | −17.8885 | −0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.8885 | 0.864393 | ||||||||
\(898\) | −21.8328 | − | 37.8155i | −0.728570 | − | 1.26192i | ||||
\(899\) | −1.70820 | + | 2.95870i | −0.0569718 | + | 0.0986780i | ||||
\(900\) | 11.2082 | − | 19.4132i | 0.373607 | − | 0.647106i | ||||
\(901\) | −5.23607 | − | 9.06914i | −0.174439 | − | 0.302137i | ||||
\(902\) | −15.1246 | −0.503594 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.47214 | −0.148741 | ||||||||
\(905\) | 1.41641 | + | 2.45329i | 0.0470830 | + | 0.0815501i | ||||
\(906\) | −32.3607 | + | 56.0503i | −1.07511 | + | 1.86215i | ||||
\(907\) | −6.76393 | + | 11.7155i | −0.224593 | + | 0.389006i | −0.956197 | − | 0.292723i | \(-0.905438\pi\) |
0.731604 | + | 0.681729i | \(0.238772\pi\) | |||||||
\(908\) | 44.8328 | + | 77.6527i | 1.48783 | + | 2.57700i | ||||
\(909\) | −69.0132 | −2.28902 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5279 | 1.11083 | 0.555414 | − | 0.831574i | \(-0.312560\pi\) | ||||
0.555414 | + | 0.831574i | \(0.312560\pi\) | |||||||
\(912\) | −4.00000 | − | 6.92820i | −0.132453 | − | 0.229416i | ||||
\(913\) | 7.70820 | − | 13.3510i | 0.255104 | − | 0.441854i | ||||
\(914\) | 27.7639 | − | 48.0885i | 0.918349 | − | 1.59063i | ||||
\(915\) | −8.94427 | − | 15.4919i | −0.295689 | − | 0.512148i | ||||
\(916\) | 13.4164 | 0.443291 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −40.0000 | −1.32020 | ||||||||
\(919\) | −3.05573 | − | 5.29268i | −0.100799 | − | 0.174589i | 0.811215 | − | 0.584748i | \(-0.198807\pi\) |
−0.912014 | + | 0.410159i | \(0.865473\pi\) | |||||||
\(920\) | 14.4721 | − | 25.0665i | 0.477132 | − | 0.826417i | ||||
\(921\) | −14.4721 | + | 25.0665i | −0.476873 | + | 0.825968i | ||||
\(922\) | 11.3820 | + | 19.7141i | 0.374845 | + | 0.649251i | ||||
\(923\) | 1.88854 | 0.0621622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.472136 | −0.0155237 | ||||||||
\(926\) | −16.1803 | − | 28.0252i | −0.531719 | − | 0.920964i | ||||
\(927\) | 21.3262 | − | 36.9381i | 0.700446 | − | 1.21321i | ||||
\(928\) | 1.58359 | − | 2.74286i | 0.0519840 | − | 0.0900389i | ||||
\(929\) | −14.1246 | − | 24.4645i | −0.463413 | − | 0.802656i | 0.535715 | − | 0.844399i | \(-0.320042\pi\) |
−0.999128 | + | 0.0417432i | \(0.986709\pi\) | |||||||
\(930\) | −104.721 | −3.43395 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −52.2492 | −1.71148 | ||||||||
\(933\) | 35.1246 | + | 60.8376i | 1.14993 | + | 1.99173i | ||||
\(934\) | −38.0902 | + | 65.9741i | −1.24635 | + | 2.15874i | ||||
\(935\) | −1.23607 | + | 2.14093i | −0.0404237 | + | 0.0700160i | ||||
\(936\) | −10.3262 | − | 17.8856i | −0.337524 | − | 0.584608i | ||||
\(937\) | 20.6525 | 0.674687 | 0.337343 | − | 0.941382i | \(-0.390472\pi\) | ||||
0.337343 | + | 0.941382i | \(0.390472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.52786 | −0.310930 | ||||||||
\(940\) | 21.7082 | + | 37.5997i | 0.708044 | + | 1.22637i | ||||
\(941\) | 20.7984 | − | 36.0238i | 0.678008 | − | 1.17434i | −0.297572 | − | 0.954699i | \(-0.596177\pi\) |
0.975580 | − | 0.219644i | \(-0.0704897\pi\) | |||||||
\(942\) | −25.1246 | + | 43.5171i | −0.818604 | + | 1.41786i | ||||
\(943\) | −21.8885 | − | 37.9121i | −0.712789 | − | 1.23459i | ||||
\(944\) | −3.23607 | −0.105325 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8885 | 0.581607 | ||||||||
\(947\) | 29.4164 | + | 50.9507i | 0.955905 | + | 1.65568i | 0.732284 | + | 0.681000i | \(0.238454\pi\) |
0.223621 | + | 0.974676i | \(0.428212\pi\) | |||||||
\(948\) | −43.4164 | + | 75.1994i | −1.41010 | + | 2.44236i | ||||
\(949\) | −3.23607 | + | 5.60503i | −0.105047 | + | 0.181947i | ||||
\(950\) | 2.76393 | + | 4.78727i | 0.0896738 | + | 0.155320i | ||||
\(951\) | 45.3050 | 1.46911 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.05573 | 0.163771 | 0.0818855 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818855 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(954\) | 70.7771 | + | 122.590i | 2.29149 | + | 3.96898i | ||||
\(955\) | −20.9443 | + | 36.2765i | −0.677741 | + | 1.17388i | ||||
\(956\) | −38.8328 | + | 67.2604i | −1.25594 | + | 2.17536i | ||||
\(957\) | −0.763932 | − | 1.32317i | −0.0246944 | − | 0.0427720i | ||||
\(958\) | −50.2492 | −1.62348 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 84.1378 | 2.71553 | ||||||||
\(961\) | −10.6803 | − | 18.4989i | −0.344527 | − | 0.596738i | ||||
\(962\) | −0.652476 | + | 1.13012i | −0.0210367 | + | 0.0364366i | ||||
\(963\) | 14.9443 | − | 25.8842i | 0.481572 | − | 0.834108i | ||||
\(964\) | −40.6869 | − | 70.4718i | −1.31044 | − | 2.26974i | ||||
\(965\) | 47.7771 | 1.53800 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8885 | 0.703888 | 0.351944 | − | 0.936021i | \(-0.385521\pi\) | ||||
0.351944 | + | 0.936021i | \(0.385521\pi\) | |||||||
\(968\) | 1.11803 | + | 1.93649i | 0.0359350 | + | 0.0622412i | ||||
\(969\) | 4.94427 | − | 8.56373i | 0.158833 | − | 0.275107i | ||||
\(970\) | 21.0557 | − | 36.4696i | 0.676059 | − | 1.17097i | ||||
\(971\) | 14.5623 | + | 25.2227i | 0.467327 | + | 0.809433i | 0.999303 | − | 0.0373256i | \(-0.0118839\pi\) |
−0.531977 | + | 0.846759i | \(0.678551\pi\) | |||||||
\(972\) | 106.790 | 3.42530 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.6950 | −0.599028 | ||||||||
\(975\) | −2.00000 | − | 3.46410i | −0.0640513 | − | 0.110940i | ||||
\(976\) | −1.38197 | + | 2.39364i | −0.0442357 | + | 0.0766184i | ||||
\(977\) | −2.52786 | + | 4.37839i | −0.0808735 | + | 0.140077i | −0.903625 | − | 0.428324i | \(-0.859104\pi\) |
0.822752 | + | 0.568401i | \(0.192438\pi\) | |||||||
\(978\) | 84.7214 | + | 146.742i | 2.70909 | + | 4.69228i | ||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.4164 | 1.06690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0902 | + | 38.2613i | −0.704567 | + | 1.22035i | 0.262281 | + | 0.964992i | \(0.415525\pi\) |
−0.966848 | + | 0.255354i | \(0.917808\pi\) | |||||||
\(984\) | −24.4721 | + | 42.3870i | −0.780143 | + | 1.35125i | ||||
\(985\) | −2.00000 | − | 3.46410i | −0.0637253 | − | 0.110375i | ||||
\(986\) | 1.30495 | 0.0415581 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.16718 | 0.291647 | ||||||||
\(989\) | 25.8885 | + | 44.8403i | 0.823208 | + | 1.42584i | ||||
\(990\) | 16.7082 | − | 28.9395i | 0.531022 | − | 0.919756i | ||||
\(991\) | 13.1246 | − | 22.7325i | 0.416917 | − | 0.722121i | −0.578711 | − | 0.815533i | \(-0.696444\pi\) |
0.995628 | + | 0.0934115i | \(0.0297772\pi\) | |||||||
\(992\) | 24.2705 | + | 42.0378i | 0.770589 | + | 1.33470i | ||||
\(993\) | 70.8328 | 2.24781 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.3607 | −1.27952 | ||||||||
\(996\) | −74.8328 | − | 129.614i | −2.37117 | − | 4.10698i | ||||
\(997\) | −16.3262 | + | 28.2779i | −0.517057 | + | 0.895569i | 0.482747 | + | 0.875760i | \(0.339639\pi\) |
−0.999804 | + | 0.0198092i | \(0.993694\pi\) | |||||||
\(998\) | 11.7082 | − | 20.2792i | 0.370617 | − | 0.641927i | ||||
\(999\) | −3.41641 | − | 5.91739i | −0.108090 | − | 0.187218i |
(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 | 539.2.e.i.67.2 | 4 | ||
7.2 | even | 3 | inner | 539.2.e.i.177.2 | 4 | ||
7.3 | odd | 6 | 539.2.a.f.1.1 | 2 | |||
7.4 | even | 3 | 77.2.a.d.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | 539.2.e.j.177.2 | 4 | |||
7.6 | odd | 2 | 539.2.e.j.67.2 | 4 | |||
21.11 | odd | 6 | 693.2.a.h.1.2 | 2 | |||
21.17 | even | 6 | 4851.2.a.y.1.2 | 2 | |||
28.3 | even | 6 | 8624.2.a.ce.1.2 | 2 | |||
28.11 | odd | 6 | 1232.2.a.m.1.1 | 2 | |||
35.4 | even | 6 | 1925.2.a.r.1.2 | 2 | |||
35.18 | odd | 12 | 1925.2.b.h.1849.4 | 4 | |||
35.32 | odd | 12 | 1925.2.b.h.1849.1 | 4 | |||
56.11 | odd | 6 | 4928.2.a.bv.1.2 | 2 | |||
56.53 | even | 6 | 4928.2.a.bm.1.1 | 2 | |||
77.4 | even | 15 | 847.2.f.a.148.1 | 4 | |||
77.10 | even | 6 | 5929.2.a.m.1.2 | 2 | |||
77.18 | odd | 30 | 847.2.f.m.148.1 | 4 | |||
77.25 | even | 15 | 847.2.f.a.372.1 | 4 | |||
77.32 | odd | 6 | 847.2.a.f.1.2 | 2 | |||
77.39 | odd | 30 | 847.2.f.b.729.1 | 4 | |||
77.46 | odd | 30 | 847.2.f.b.323.1 | 4 | |||
77.53 | even | 15 | 847.2.f.n.323.1 | 4 | |||
77.60 | even | 15 | 847.2.f.n.729.1 | 4 | |||
77.74 | odd | 30 | 847.2.f.m.372.1 | 4 | |||
231.32 | even | 6 | 7623.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
539.2.a.f.1.1 | 2 | 7.3 | odd | 6 | |||
539.2.e.i.67.2 | 4 | 1.1 | even | 1 | trivial | ||
539.2.e.i.177.2 | 4 | 7.2 | even | 3 | inner | ||
539.2.e.j.67.2 | 4 | 7.6 | odd | 2 | |||
539.2.e.j.177.2 | 4 | 7.5 | odd | 6 | |||
693.2.a.h.1.2 | 2 | 21.11 | odd | 6 | |||
847.2.a.f.1.2 | 2 | 77.32 | odd | 6 | |||
847.2.f.a.148.1 | 4 | 77.4 | even | 15 | |||
847.2.f.a.372.1 | 4 | 77.25 | even | 15 | |||
847.2.f.b.323.1 | 4 | 77.46 | odd | 30 | |||
847.2.f.b.729.1 | 4 | 77.39 | odd | 30 | |||
847.2.f.m.148.1 | 4 | 77.18 | odd | 30 | |||
847.2.f.m.372.1 | 4 | 77.74 | odd | 30 | |||
847.2.f.n.323.1 | 4 | 77.53 | even | 15 | |||
847.2.f.n.729.1 | 4 | 77.60 | even | 15 | |||
1232.2.a.m.1.1 | 2 | 28.11 | odd | 6 | |||
1925.2.a.r.1.2 | 2 | 35.4 | even | 6 | |||
1925.2.b.h.1849.1 | 4 | 35.32 | odd | 12 | |||
1925.2.b.h.1849.4 | 4 | 35.18 | odd | 12 | |||
4851.2.a.y.1.2 | 2 | 21.17 | even | 6 | |||
4928.2.a.bm.1.1 | 2 | 56.53 | even | 6 | |||
4928.2.a.bv.1.2 | 2 | 56.11 | odd | 6 | |||
5929.2.a.m.1.2 | 2 | 77.10 | even | 6 | |||
7623.2.a.bl.1.1 | 2 | 231.32 | even | 6 | |||
8624.2.a.ce.1.2 | 2 | 28.3 | even | 6 |