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 | 177.2 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 539.177 |
Dual form | 539.2.e.j.67.2 |
$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
0.925615 | − | 0.378467i | \(-0.123549\pi\) | |||||||
\(3\) | 1.61803 | + | 2.80252i | 0.934172 | + | 1.61803i | 0.776103 | + | 0.630606i | \(0.217194\pi\) |
0.158069 | + | 0.987428i | \(0.449473\pi\) | |||||||
\(4\) | −1.50000 | − | 2.59808i | −0.750000 | − | 1.29904i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 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 | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 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 | \(-0.118773\pi\) |
−0.781293 | + | 0.624164i | \(0.785440\pi\) | |||||||
\(18\) | 8.35410 | + | 14.4697i | 1.96908 | + | 3.41055i | ||||
\(19\) | −1.23607 | + | 2.14093i | −0.283573 | + | 0.491164i | −0.972262 | − | 0.233893i | \(-0.924853\pi\) |
0.688689 | + | 0.725057i | \(0.258187\pi\) | |||||||
\(20\) | 6.00000 | 1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.23607 | 0.476731 | ||||||||
\(23\) | 3.23607 | − | 5.60503i | 0.674767 | − | 1.16873i | −0.301770 | − | 0.953381i | \(-0.597578\pi\) |
0.976537 | − | 0.215350i | \(-0.0690891\pi\) | |||||||
\(24\) | −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 | −0.983166 | − | 0.182714i | \(-0.941512\pi\) |
0.333348 | − | 0.942804i | \(-0.391822\pi\) | |||||||
\(32\) | −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 | −0.884778 | − | 0.466013i | \(-0.845690\pi\) |
0.845968 | + | 0.533233i | \(0.179023\pi\) | |||||||
\(38\) | 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 | \(-0.322877\pi\) | ||||
0.528174 | + | 0.849136i | \(0.322877\pi\) | |||||||
\(42\) | 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 | −0.471732 | − | 0.881742i | \(-0.656371\pi\) |
0.999477 | − | 0.0323386i | \(-0.0102955\pi\) | |||||||
\(48\) | 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 | −0.995258 | − | 0.0972717i | \(-0.968988\pi\) |
0.413389 | − | 0.910554i | \(-0.364345\pi\) | |||||||
\(54\) | −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 | \(-0.0991086\pi\) |
−0.741268 | + | 0.671209i | \(0.765775\pi\) | |||||||
\(60\) | 9.70820 | + | 16.8151i | 1.25332 | + | 2.17082i | ||||
\(61\) | −1.38197 | + | 2.39364i | −0.176943 | + | 0.306474i | −0.940832 | − | 0.338874i | \(-0.889954\pi\) |
0.763889 | + | 0.645347i | \(0.223287\pi\) | |||||||
\(62\) | −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 | 0.646326 | − | 0.763062i | \(-0.276305\pi\) |
−0.983994 | + | 0.178204i | \(0.942971\pi\) | |||||||
\(68\) | 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 | \(-0.265797\pi\) |
−0.977576 | + | 0.210583i | \(0.932464\pi\) | |||||||
\(74\) | 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 | 0.496839 | + | 0.867843i | \(0.334494\pi\) |
−0.999993 | + | 0.00364646i | \(0.998839\pi\) | |||||||
\(80\) | 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 | \(-0.821047\pi\) | ||||
−0.846085 | + | 0.533048i | \(0.821047\pi\) | |||||||
\(84\) | 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 | \(-0.799529\pi\) |
0.914146 | + | 0.405385i | \(0.132862\pi\) | |||||||
\(90\) | −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 | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(98\) | 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 | \(-0.318642\pi\) |
−0.998935 | + | 0.0461372i | \(0.985309\pi\) | |||||||
\(102\) | 4.47214 | + | 7.74597i | 0.442807 | + | 0.766965i | ||||
\(103\) | −2.85410 | + | 4.94345i | −0.281223 | + | 0.487093i | −0.971686 | − | 0.236275i | \(-0.924073\pi\) |
0.690463 | + | 0.723368i | \(0.257407\pi\) | |||||||
\(104\) | −2.76393 | −0.271026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.9443 | −1.84003 | ||||||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 21.7082 | + | 37.5997i | 2.08887 | + | 3.61803i | ||||
\(109\) | −2.23607 | − | 3.87298i | −0.214176 | − | 0.370965i | 0.738841 | − | 0.673880i | \(-0.235373\pi\) |
−0.953018 | + | 0.302915i | \(0.902040\pi\) | |||||||
\(110\) | −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 | 0.385053 | + | 0.922895i | \(0.374183\pi\) |
−0.991776 | + | 0.127982i | \(0.959150\pi\) | |||||||
\(132\) | 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 | 0.659239 | − | 0.751934i | \(-0.270879\pi\) |
−0.980813 | + | 0.194951i | \(0.937545\pi\) | |||||||
\(138\) | 23.4164 | − | 40.5584i | 1.99334 | − | 3.45256i | ||||
\(139\) | 10.4721 | 0.888235 | 0.444117 | − | 0.895969i | \(-0.353517\pi\) | ||||
0.444117 | + | 0.895969i | \(0.353517\pi\) | |||||||
\(140\) | 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 | 0.422744 | + | 0.906249i | \(0.361067\pi\) |
−0.996207 | + | 0.0870170i | \(0.972267\pi\) | |||||||
\(150\) | 3.61803 | + | 6.26662i | 0.295411 | + | 0.511667i | ||||
\(151\) | 4.47214 | + | 7.74597i | 0.363937 | + | 0.630358i | 0.988605 | − | 0.150533i | \(-0.0480989\pi\) |
−0.624668 | + | 0.780891i | \(0.714766\pi\) | |||||||
\(152\) | 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 | \(-0.256042\pi\) |
−0.970664 | + | 0.240438i | \(0.922709\pi\) | |||||||
\(158\) | 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 | −0.113196 | + | 0.993573i | \(0.536109\pi\) |
−0.803861 | + | 0.594817i | \(0.797224\pi\) | |||||||
\(164\) | −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 | \(-0.333029\pi\) | ||||
0.500829 | + | 0.865546i | \(0.333029\pi\) | |||||||
\(168\) | 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 | 0.326622 | + | 0.945155i | \(0.394089\pi\) |
−0.981839 | + | 0.189714i | \(0.939244\pi\) | |||||||
\(174\) | −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 | 0.649080 | − | 0.760720i | \(-0.275154\pi\) |
−0.983343 | + | 0.181760i | \(0.941821\pi\) | |||||||
\(180\) | −22.4164 | + | 38.8264i | −1.67082 | + | 2.89395i | ||||
\(181\) | −1.41641 | −0.105281 | −0.0526404 | − | 0.998614i | \(-0.516764\pi\) | ||||
−0.0526404 | + | 0.998614i | \(0.516764\pi\) | |||||||
\(182\) | 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 | −0.186265 | − | 0.982500i | \(-0.559638\pi\) |
0.944002 | − | 0.329940i | \(-0.107028\pi\) | |||||||
\(192\) | −21.0344 | − | 36.4327i | −1.51803 | − | 2.62931i | ||||
\(193\) | 11.9443 | + | 20.6881i | 0.859768 | + | 1.48916i | 0.872151 | + | 0.489238i | \(0.162725\pi\) |
−0.0123830 | + | 0.999923i | \(0.503942\pi\) | |||||||
\(194\) | 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 | 0.962854 | + | 0.270022i | \(0.0870311\pi\) |
−0.247581 | + | 0.968867i | \(0.579636\pi\) | |||||||
\(200\) | −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 | \(-0.633714\pi\) | ||||
−0.407828 | + | 0.913059i | \(0.633714\pi\) | |||||||
\(224\) | 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 | −0.606040 | − | 0.795434i | \(-0.707243\pi\) |
−0.385846 | − | 0.922563i | \(-0.626090\pi\) | |||||||
\(228\) | 12.0000 | + | 20.7846i | 0.794719 | + | 1.37649i | ||||
\(229\) | 2.23607 | − | 3.87298i | 0.147764 | − | 0.255934i | −0.782637 | − | 0.622478i | \(-0.786126\pi\) |
0.930401 | + | 0.366544i | \(0.119459\pi\) | |||||||
\(230\) | 28.9443 | 1.90853 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.05573 | 0.0693119 | ||||||||
\(233\) | 8.70820 | − | 15.0831i | 0.570493 | − | 0.988124i | −0.426022 | − | 0.904713i | \(-0.640085\pi\) |
0.996515 | − | 0.0834107i | \(-0.0265813\pi\) | |||||||
\(234\) | 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 | 0.858220 | + | 0.513281i | \(0.171570\pi\) |
0.0154046 | + | 0.999881i | \(0.495096\pi\) | |||||||
\(242\) | 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 | \(-0.688763\pi\) | ||||
−0.558866 | + | 0.829258i | \(0.688763\pi\) | |||||||
\(252\) | 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 | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 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 | \(-0.300791\pi\) |
−0.994779 | + | 0.102056i | \(0.967458\pi\) | |||||||
\(270\) | −32.3607 | − | 56.0503i | −1.96941 | − | 3.41112i | ||||
\(271\) | −0.763932 | + | 1.32317i | −0.0464056 | + | 0.0803768i | −0.888295 | − | 0.459273i | \(-0.848110\pi\) |
0.841890 | + | 0.539650i | \(0.181443\pi\) | |||||||
\(272\) | 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 | 0.522337 | − | 0.852739i | \(-0.325060\pi\) |
−0.999662 | + | 0.0259878i | \(0.991727\pi\) | |||||||
\(278\) | 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 | \(-0.222665\pi\) |
−0.940168 | + | 0.340712i | \(0.889332\pi\) | |||||||
\(284\) | 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 | \(-0.645658\pi\) | ||||
−0.441795 | + | 0.897116i | \(0.645658\pi\) | |||||||
\(294\) | 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 | \(-0.582154\pi\) | ||||
−0.255238 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(308\) | 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 | −0.990300 | − | 0.138945i | \(-0.955629\pi\) |
0.374820 | − | 0.927097i | \(-0.377704\pi\) | |||||||
\(312\) | −4.47214 | − | 7.74597i | −0.253185 | − | 0.438529i | ||||
\(313\) | −1.47214 | + | 2.54981i | −0.0832100 | + | 0.144124i | −0.904627 | − | 0.426204i | \(-0.859851\pi\) |
0.821417 | + | 0.570328i | \(0.193184\pi\) | |||||||
\(314\) | −15.5279 | −0.876288 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.8328 | 1.50946 | ||||||||
\(317\) | −7.00000 | + | 12.1244i | −0.393159 | + | 0.680972i | −0.992864 | − | 0.119249i | \(-0.961951\pi\) |
0.599705 | + | 0.800221i | \(0.295285\pi\) | |||||||
\(318\) | −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 | 0.391035 | + | 0.920376i | \(0.372117\pi\) |
−0.992586 | + | 0.121542i | \(0.961216\pi\) | |||||||
\(332\) | 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 | 0.822097 | − | 0.569347i | \(-0.192804\pi\) |
−0.904118 | + | 0.427284i | \(0.859470\pi\) | |||||||
\(348\) | −2.29180 | + | 3.96951i | −0.122853 | + | 0.212788i | ||||
\(349\) | 2.76393 | 0.147950 | 0.0739749 | − | 0.997260i | \(-0.476432\pi\) | ||||
0.0739749 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(350\) | 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 | \(-0.305630\pi\) |
−0.996215 | + | 0.0869220i | \(0.972297\pi\) | |||||||
\(354\) | 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 | −0.757785 | − | 0.652505i | \(-0.773718\pi\) |
0.943978 | + | 0.330008i | \(0.107052\pi\) | |||||||
\(360\) | 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 | \(-0.0191773\pi\) |
−0.551237 | + | 0.834349i | \(0.685844\pi\) | |||||||
\(368\) | −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 | −0.933181 | − | 0.359408i | \(-0.882979\pi\) |
0.777847 | + | 0.628454i | \(0.216312\pi\) | |||||||
\(374\) | 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 | −0.293756 | − | 0.955881i | \(-0.594905\pi\) |
0.974695 | − | 0.223540i | \(-0.0717614\pi\) | |||||||
\(384\) | −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 | 0.999988 | + | 0.00485030i | \(0.00154390\pi\) |
−0.495794 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(390\) | −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 | \(-0.834224\pi\) |
0.864624 | + | 0.502420i | \(0.167557\pi\) | |||||||
\(398\) | 45.1246 | 2.26189 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −2.52786 | + | 4.37839i | −0.126236 | + | 0.218646i | −0.922215 | − | 0.386677i | \(-0.873623\pi\) |
0.795980 | + | 0.605323i | \(0.206956\pi\) | |||||||
\(402\) | −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 | −0.937831 | − | 0.347093i | \(-0.887169\pi\) |
0.168324 | − | 0.985732i | \(-0.446164\pi\) | |||||||
\(410\) | 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 | \(-0.448045\pi\) | ||||
0.162497 | + | 0.986709i | \(0.448045\pi\) | |||||||
\(420\) | 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 | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | −7.23607 | + | 12.5332i | −0.348145 | + | 0.603006i | ||||
\(433\) | −0.472136 | −0.0226894 | −0.0113447 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113447 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(434\) | 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 | \(-0.821725\pi\) |
0.883680 | + | 0.468092i | \(0.155058\pi\) | |||||||
\(440\) | 4.47214 | 0.213201 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.41641 | 0.162502 | ||||||||
\(443\) | 3.52786 | − | 6.11044i | 0.167614 | − | 0.290316i | −0.769967 | − | 0.638084i | \(-0.779727\pi\) |
0.937580 | + | 0.347768i | \(0.113060\pi\) | |||||||
\(444\) | 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 | 0.414568 | + | 0.910018i | \(0.363933\pi\) |
−0.995383 | + | 0.0959828i | \(0.969401\pi\) | |||||||
\(458\) | −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 | \(-0.576188\pi\) | ||||
−0.237073 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(462\) | 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 | 0.138772 | + | 0.990324i | \(0.455684\pi\) |
−0.927032 | + | 0.374982i | \(0.877649\pi\) | |||||||
\(468\) | 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 | 0.999879 | + | 0.0155300i | \(0.00494354\pi\) |
−0.486490 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(480\) | 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 | 0.755631 | − | 0.654998i | \(-0.227330\pi\) |
−0.945060 | + | 0.326897i | \(0.893997\pi\) | |||||||
\(488\) | 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 | −0.959098 | − | 0.283075i | \(-0.908645\pi\) |
0.724699 | + | 0.689065i | \(0.241979\pi\) | |||||||
\(500\) | 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 | \(-0.475732\pi\) | ||||
0.0761650 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(504\) | 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 | −0.270185 | − | 0.962808i | \(-0.587085\pi\) |
0.968909 | − | 0.247417i | \(-0.0795818\pi\) | |||||||
\(510\) | −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 | \(-0.268529\pi\) |
−0.979347 | + | 0.202185i | \(0.935196\pi\) | |||||||
\(522\) | −3.94427 | − | 6.83168i | −0.172636 | − | 0.299014i | ||||
\(523\) | 22.0000 | − | 38.1051i | 0.961993 | − | 1.66622i | 0.244507 | − | 0.969648i | \(-0.421374\pi\) |
0.717486 | − | 0.696573i | \(-0.245293\pi\) | |||||||
\(524\) | 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 | −0.260607 | − | 0.965445i | \(-0.583923\pi\) |
0.966403 | − | 0.257030i | \(-0.0827440\pi\) | |||||||
\(542\) | 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 | 0.998127 | − | 0.0611800i | \(-0.0194864\pi\) |
−0.552047 | + | 0.833813i | \(0.686153\pi\) | |||||||
\(558\) | 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 | 0.897562 | + | 0.440889i | \(0.145337\pi\) |
−0.0669600 | + | 0.997756i | \(0.521330\pi\) | |||||||
\(564\) | −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 | −0.985403 | − | 0.170235i | \(-0.945547\pi\) |
0.640130 | + | 0.768267i | \(0.278881\pi\) | |||||||
\(570\) | −17.8885 | − | 30.9839i | −0.749269 | − | 1.29777i | ||||
\(571\) | 16.4721 | + | 28.5306i | 0.689337 | + | 1.19397i | 0.972053 | + | 0.234764i | \(0.0754316\pi\) |
−0.282715 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(572\) | 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 | −0.993873 | − | 0.110526i | \(-0.964746\pi\) |
0.401218 | − | 0.915983i | \(-0.368587\pi\) | |||||||
\(578\) | −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 | \(-0.412693\pi\) | ||||
0.270855 | + | 0.962620i | \(0.412693\pi\) | |||||||
\(588\) | 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 | 0.316782 | + | 0.948498i | \(0.397398\pi\) |
−0.979815 | + | 0.199908i | \(0.935936\pi\) | |||||||
\(594\) | −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 | 0.829016 | − | 0.559225i | \(-0.188901\pi\) |
−0.898811 | + | 0.438336i | \(0.855568\pi\) | |||||||
\(600\) | 3.61803 | − | 6.26662i | 0.147706 | − | 0.255834i | ||||
\(601\) | −3.12461 | −0.127456 | −0.0637278 | − | 0.997967i | \(-0.520299\pi\) | ||||
−0.0637278 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(602\) | 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 | \(-0.865327\pi\) |
0.811484 | + | 0.584374i | \(0.198660\pi\) | |||||||
\(608\) | 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 | 0.733647 | + | 0.679531i | \(0.237817\pi\) |
0.221668 | + | 0.975122i | \(0.428850\pi\) | |||||||
\(614\) | −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 | −0.994837 | − | 0.101487i | \(-0.967640\pi\) |
0.409528 | − | 0.912297i | \(-0.365693\pi\) | |||||||
\(620\) | −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 | 0.999816 | − | 0.0191823i | \(-0.00610630\pi\) |
−0.516520 | + | 0.856275i | \(0.672773\pi\) | |||||||
\(642\) | 14.4721 | − | 25.0665i | 0.571170 | − | 0.989295i | ||||
\(643\) | 29.1246 | 1.14856 | 0.574281 | − | 0.818658i | \(-0.305282\pi\) | ||||
0.574281 | + | 0.818658i | \(0.305282\pi\) | |||||||
\(644\) | 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 | \(-0.309497\pi\) |
−0.997198 | + | 0.0748132i | \(0.976164\pi\) | |||||||
\(648\) | 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 | 0.0493971 | + | 0.998779i | \(0.484270\pi\) |
−0.889667 | + | 0.456610i | \(0.849063\pi\) | |||||||
\(654\) | −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 | \(-0.0863776\pi\) |
−0.713837 | + | 0.700312i | \(0.753044\pi\) | |||||||
\(662\) | 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 | \(-0.810632\pi\) |
0.899453 | + | 0.437017i | \(0.143965\pi\) | |||||||
\(678\) | 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 | −0.996378 | − | 0.0850292i | \(-0.972902\pi\) |
0.424552 | − | 0.905404i | \(-0.360432\pi\) | |||||||
\(684\) | −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 | −0.129011 | + | 0.991643i | \(0.541180\pi\) |
−0.794283 | + | 0.607548i | \(0.792153\pi\) | |||||||
\(692\) | 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 | −0.892344 | − | 0.451355i | \(-0.850941\pi\) |
0.837057 | + | 0.547115i | \(0.184274\pi\) | |||||||
\(710\) | −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 | −0.364262 | − | 0.931296i | \(-0.618679\pi\) |
0.988657 | − | 0.150188i | \(-0.0479879\pi\) | |||||||
\(720\) | −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 | \(-0.105097\pi\) | ||||
0.945987 | + | 0.324206i | \(0.105097\pi\) | |||||||
\(728\) | 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 | \(-0.754728\pi\) |
0.961975 | + | 0.273138i | \(0.0880617\pi\) | |||||||
\(734\) | 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 | 0.793815 | − | 0.608160i | \(-0.208092\pi\) |
−0.923589 | + | 0.383384i | \(0.874759\pi\) | |||||||
\(740\) | −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 | 0.265853 | + | 0.964014i | \(0.414347\pi\) |
−0.967787 | + | 0.251772i | \(0.918987\pi\) | |||||||
\(752\) | −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 | \(-0.730006\pi\) |
0.980267 | + | 0.197676i | \(0.0633395\pi\) | |||||||
\(762\) | 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 | \(-0.693721\pi\) | ||||
−0.571714 | + | 0.820453i | \(0.693721\pi\) | |||||||
\(770\) | 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 | \(-0.130176\pi\) |
−0.803146 | + | 0.595782i | \(0.796842\pi\) | |||||||
\(774\) | 66.8328 | + | 115.758i | 2.40226 | + | 4.16083i | ||||
\(775\) | 3.61803 | − | 6.26662i | 0.129964 | − | 0.225104i | ||||
\(776\) | −21.0557 | −0.755857 |