Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.n (of order \(5\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 526.1 | ||
Root | \(-0.104528 - 0.994522i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.526 |
Dual form | 825.2.n.j.676.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.564602 | + | 1.73767i | −0.399234 | + | 1.22872i | 0.526381 | + | 0.850249i | \(0.323549\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −1.08268 | − | 0.786610i | −0.541338 | − | 0.393305i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.564602 | − | 1.73767i | −0.230498 | − | 0.709399i | ||||
\(7\) | 1.41355 | + | 1.02700i | 0.534270 | + | 0.388170i | 0.821953 | − | 0.569556i | \(-0.192885\pi\) |
−0.287683 | + | 0.957726i | \(0.592885\pi\) | |||||||
\(8\) | −0.978148 | + | 0.710666i | −0.345827 | + | 0.251258i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.384301 | − | 3.29428i | −0.115871 | − | 0.993264i | ||||
\(12\) | 1.33826 | 0.386323 | ||||||||
\(13\) | 1.65563 | − | 5.09549i | 0.459188 | − | 1.41323i | −0.406960 | − | 0.913446i | \(-0.633411\pi\) |
0.866147 | − | 0.499789i | \(-0.166589\pi\) | |||||||
\(14\) | −2.58268 | + | 1.87642i | −0.690249 | + | 0.501495i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50973 | − | 4.64646i | −0.377432 | − | 1.16162i | ||||
\(17\) | −2.26531 | − | 6.97191i | −0.549419 | − | 1.69094i | −0.710245 | − | 0.703955i | \(-0.751416\pi\) |
0.160826 | − | 0.986983i | \(-0.448584\pi\) | |||||||
\(18\) | 1.47815 | + | 1.07394i | 0.348403 | + | 0.253129i | ||||
\(19\) | −4.86606 | + | 3.53540i | −1.11635 | + | 0.811077i | −0.983652 | − | 0.180080i | \(-0.942364\pi\) |
−0.132699 | + | 0.991156i | \(0.542364\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74724 | −0.381279 | ||||||||
\(22\) | 5.94135 | + | 1.19217i | 1.26670 | + | 0.254172i | ||||
\(23\) | −8.35772 | −1.74270 | −0.871352 | − | 0.490658i | \(-0.836756\pi\) | ||||
−0.871352 | + | 0.490658i | \(0.836756\pi\) | |||||||
\(24\) | 0.373619 | − | 1.14988i | 0.0762647 | − | 0.234719i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.91949 | + | 5.75385i | 1.55314 | + | 1.12842i | ||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −0.722562 | − | 2.22382i | −0.136551 | − | 0.420262i | ||||
\(29\) | −4.48048 | − | 3.25526i | −0.832005 | − | 0.604487i | 0.0881210 | − | 0.996110i | \(-0.471914\pi\) |
−0.920126 | + | 0.391623i | \(0.871914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.00660190 | + | 0.0203186i | −0.00118574 | + | 0.00364932i | −0.951648 | − | 0.307192i | \(-0.900611\pi\) |
0.950462 | + | 0.310841i | \(0.100611\pi\) | |||||||
\(32\) | 6.50828 | 1.15051 | ||||||||
\(33\) | 2.24724 | + | 2.43925i | 0.391194 | + | 0.424618i | ||||
\(34\) | 13.3939 | 2.29703 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.08268 | + | 0.786610i | −0.180446 | + | 0.131102i | ||||
\(37\) | −0.907432 | − | 0.659288i | −0.149181 | − | 0.108386i | 0.510691 | − | 0.859764i | \(-0.329390\pi\) |
−0.659872 | + | 0.751378i | \(0.729390\pi\) | |||||||
\(38\) | −3.39596 | − | 10.4517i | −0.550897 | − | 1.69549i | ||||
\(39\) | 1.65563 | + | 5.09549i | 0.265112 | + | 0.815931i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.96086 | − | 2.15119i | 0.462409 | − | 0.335960i | −0.332066 | − | 0.943256i | \(-0.607746\pi\) |
0.794476 | + | 0.607296i | \(0.207746\pi\) | |||||||
\(42\) | 0.986494 | − | 3.03612i | 0.152219 | − | 0.468483i | ||||
\(43\) | 1.96950 | 0.300346 | 0.150173 | − | 0.988660i | \(-0.452017\pi\) | ||||
0.150173 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(44\) | −2.17524 | + | 3.86894i | −0.327930 | + | 0.583264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.71878 | − | 14.5229i | 0.695747 | − | 2.14129i | ||||
\(47\) | 3.09007 | − | 2.24507i | 0.450733 | − | 0.327476i | −0.339152 | − | 0.940731i | \(-0.610140\pi\) |
0.789885 | + | 0.613255i | \(0.210140\pi\) | |||||||
\(48\) | 3.95252 | + | 2.87167i | 0.570497 | + | 0.414490i | ||||
\(49\) | −1.21974 | − | 3.75397i | −0.174248 | − | 0.536282i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.93066 | + | 4.30888i | 0.830459 | + | 0.603364i | ||||
\(52\) | −5.80067 | + | 4.21443i | −0.804408 | + | 0.584437i | ||||
\(53\) | −0.516329 | + | 1.58910i | −0.0709232 | + | 0.218279i | −0.980235 | − | 0.197836i | \(-0.936609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(54\) | −1.82709 | −0.248636 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.11251 | −0.282296 | ||||||||
\(57\) | 1.85867 | − | 5.72040i | 0.246187 | − | 0.757685i | ||||
\(58\) | 8.18625 | − | 5.94766i | 1.07491 | − | 0.780966i | ||||
\(59\) | −4.58172 | − | 3.32882i | −0.596489 | − | 0.433375i | 0.248142 | − | 0.968724i | \(-0.420180\pi\) |
−0.844631 | + | 0.535349i | \(0.820180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.86761 | + | 8.82559i | 0.367160 | + | 1.13000i | 0.948618 | + | 0.316425i | \(0.102482\pi\) |
−0.581458 | + | 0.813576i | \(0.697518\pi\) | |||||||
\(62\) | −0.0315794 | − | 0.0229438i | −0.00401059 | − | 0.00291387i | ||||
\(63\) | 1.41355 | − | 1.02700i | 0.178090 | − | 0.129390i | ||||
\(64\) | −0.655137 | + | 2.01630i | −0.0818921 | + | 0.252038i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.50739 | + | 2.52775i | −0.677913 | + | 0.311144i | ||||
\(67\) | −0.350489 | −0.0428190 | −0.0214095 | − | 0.999771i | \(-0.506815\pi\) | ||||
−0.0214095 | + | 0.999771i | \(0.506815\pi\) | |||||||
\(68\) | −3.03158 | + | 9.33024i | −0.367633 | + | 1.13146i | ||||
\(69\) | 6.76153 | − | 4.91254i | 0.813993 | − | 0.591401i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.40238 | + | 4.31607i | 0.166431 | + | 0.512223i | 0.999139 | − | 0.0414901i | \(-0.0132105\pi\) |
−0.832708 | + | 0.553713i | \(0.813210\pi\) | |||||||
\(72\) | 0.373619 | + | 1.14988i | 0.0440314 | + | 0.135515i | ||||
\(73\) | 8.20305 | + | 5.95986i | 0.960094 | + | 0.697549i | 0.953173 | − | 0.302427i | \(-0.0977969\pi\) |
0.00692130 | + | 0.999976i | \(0.497797\pi\) | |||||||
\(74\) | 1.65796 | − | 1.20458i | 0.192734 | − | 0.140029i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.04935 | 0.923324 | ||||||||
\(77\) | 2.84001 | − | 5.05130i | 0.323649 | − | 0.575649i | ||||
\(78\) | −9.78903 | −1.10839 | ||||||||
\(79\) | 0.792323 | − | 2.43852i | 0.0891433 | − | 0.274355i | −0.896540 | − | 0.442963i | \(-0.853927\pi\) |
0.985683 | + | 0.168608i | \(0.0539273\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 2.06635 | + | 6.35956i | 0.228190 | + | 0.702296i | ||||
\(83\) | 4.96915 | + | 15.2935i | 0.545435 | + | 1.67868i | 0.719954 | + | 0.694022i | \(0.244163\pi\) |
−0.174519 | + | 0.984654i | \(0.555837\pi\) | |||||||
\(84\) | 1.89169 | + | 1.37440i | 0.206401 | + | 0.149959i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.11198 | + | 3.42233i | −0.119908 | + | 0.369040i | ||||
\(87\) | 5.53818 | 0.593755 | ||||||||
\(88\) | 2.71704 | + | 2.94919i | 0.289637 | + | 0.314384i | ||||
\(89\) | −14.5062 | −1.53765 | −0.768825 | − | 0.639459i | \(-0.779159\pi\) | ||||
−0.768825 | + | 0.639459i | \(0.779159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.57337 | − | 5.50238i | 0.793905 | − | 0.576806i | ||||
\(92\) | 9.04870 | + | 6.57426i | 0.943392 | + | 0.685414i | ||||
\(93\) | −0.00660190 | − | 0.0203186i | −0.000684585 | − | 0.00210694i | ||||
\(94\) | 2.15652 | + | 6.63708i | 0.222428 | + | 0.684562i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.26531 | + | 3.82547i | −0.537389 | + | 0.390436i | ||||
\(97\) | 0.587045 | − | 1.80674i | 0.0596054 | − | 0.183446i | −0.916820 | − | 0.399300i | \(-0.869253\pi\) |
0.976426 | + | 0.215853i | \(0.0692533\pi\) | |||||||
\(98\) | 7.21182 | 0.728504 | ||||||||
\(99\) | −3.25181 | − | 0.652498i | −0.326819 | − | 0.0655785i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.07354 | − | 6.38170i | 0.206325 | − | 0.635003i | −0.793332 | − | 0.608790i | \(-0.791655\pi\) |
0.999656 | − | 0.0262128i | \(-0.00834474\pi\) | |||||||
\(102\) | −10.8359 | + | 7.87272i | −1.07291 | + | 0.779515i | ||||
\(103\) | −3.43572 | − | 2.49620i | −0.338532 | − | 0.245958i | 0.405510 | − | 0.914090i | \(-0.367094\pi\) |
−0.744042 | + | 0.668133i | \(0.767094\pi\) | |||||||
\(104\) | 2.00174 | + | 6.16074i | 0.196287 | + | 0.604110i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.46980 | − | 1.79442i | −0.239888 | − | 0.174289i | ||||
\(107\) | −12.7202 | + | 9.24174i | −1.22970 | + | 0.893433i | −0.996868 | − | 0.0790831i | \(-0.974801\pi\) |
−0.232837 | + | 0.972516i | \(0.574801\pi\) | |||||||
\(108\) | 0.413545 | − | 1.27276i | 0.0397934 | − | 0.122472i | ||||
\(109\) | 4.23895 | 0.406018 | 0.203009 | − | 0.979177i | \(-0.434928\pi\) | ||||
0.203009 | + | 0.979177i | \(0.434928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12165 | 0.106462 | ||||||||
\(112\) | 2.63785 | − | 8.11848i | 0.249254 | − | 0.767124i | ||||
\(113\) | −5.82203 | + | 4.22996i | −0.547691 | + | 0.397921i | −0.826933 | − | 0.562300i | \(-0.809917\pi\) |
0.279242 | + | 0.960221i | \(0.409917\pi\) | |||||||
\(114\) | 8.89074 | + | 6.45950i | 0.832694 | + | 0.604988i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.29029 | + | 7.04879i | 0.212648 | + | 0.654463i | ||||
\(117\) | −4.33448 | − | 3.14919i | −0.400723 | − | 0.291142i | ||||
\(118\) | 8.37122 | − | 6.08205i | 0.770633 | − | 0.559898i | ||||
\(119\) | 3.95804 | − | 12.1816i | 0.362833 | − | 1.11668i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7046 | + | 2.53200i | −0.973148 | + | 0.230181i | ||||
\(122\) | −16.9550 | −1.53503 | ||||||||
\(123\) | −1.13095 | + | 3.48070i | −0.101974 | + | 0.313845i | ||||
\(124\) | 0.0231305 | − | 0.0168053i | 0.00207718 | − | 0.00150916i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.986494 | + | 3.03612i | 0.0878839 | + | 0.270479i | ||||
\(127\) | −3.92051 | − | 12.0661i | −0.347889 | − | 1.07069i | −0.960019 | − | 0.279935i | \(-0.909687\pi\) |
0.612130 | − | 0.790757i | \(-0.290313\pi\) | |||||||
\(128\) | 7.39685 | + | 5.37413i | 0.653796 | + | 0.475010i | ||||
\(129\) | −1.59336 | + | 1.15764i | −0.140287 | + | 0.101925i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.970102 | −0.0847582 | −0.0423791 | − | 0.999102i | \(-0.513494\pi\) | ||||
−0.0423791 | + | 0.999102i | \(0.513494\pi\) | |||||||
\(132\) | −0.514295 | − | 4.40861i | −0.0447637 | − | 0.383721i | ||||
\(133\) | −10.5093 | −0.911268 | ||||||||
\(134\) | 0.197887 | − | 0.609032i | 0.0170948 | − | 0.0526124i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.17051 | + | 5.20968i | 0.614866 | + | 0.446726i | ||||
\(137\) | −1.30416 | − | 4.01379i | −0.111422 | − | 0.342921i | 0.879762 | − | 0.475414i | \(-0.157702\pi\) |
−0.991184 | + | 0.132493i | \(0.957702\pi\) | |||||||
\(138\) | 4.71878 | + | 14.5229i | 0.401690 | + | 1.23627i | ||||
\(139\) | −7.15855 | − | 5.20099i | −0.607180 | − | 0.441142i | 0.241240 | − | 0.970465i | \(-0.422446\pi\) |
−0.848420 | + | 0.529323i | \(0.822446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.18030 | + | 3.63259i | −0.0993993 | + | 0.305919i | ||||
\(142\) | −8.29167 | −0.695821 | ||||||||
\(143\) | −17.4223 | − | 3.49590i | −1.45692 | − | 0.292342i | ||||
\(144\) | −4.88558 | −0.407132 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.9877 | + | 10.8892i | −1.24039 | + | 0.901197i | ||||
\(147\) | 3.19332 | + | 2.32008i | 0.263380 | + | 0.191357i | ||||
\(148\) | 0.463852 | + | 1.42759i | 0.0381284 | + | 0.117347i | ||||
\(149\) | 2.95222 | + | 9.08598i | 0.241855 | + | 0.744353i | 0.996138 | + | 0.0878033i | \(0.0279847\pi\) |
−0.754283 | + | 0.656549i | \(0.772015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.46214 | − | 3.96848i | 0.444503 | − | 0.322950i | −0.342919 | − | 0.939365i | \(-0.611416\pi\) |
0.787422 | + | 0.616415i | \(0.211416\pi\) | |||||||
\(152\) | 2.24724 | − | 6.91629i | 0.182275 | − | 0.560985i | ||||
\(153\) | −7.33070 | −0.592652 | ||||||||
\(154\) | 7.17400 | + | 7.78696i | 0.578097 | + | 0.627491i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.21566 | − | 6.81910i | 0.177395 | − | 0.545965i | ||||
\(157\) | −10.2425 | + | 7.44162i | −0.817441 | + | 0.593906i | −0.915978 | − | 0.401228i | \(-0.868584\pi\) |
0.0985374 | + | 0.995133i | \(0.468584\pi\) | |||||||
\(158\) | 3.78999 | + | 2.75359i | 0.301515 | + | 0.219064i | ||||
\(159\) | −0.516329 | − | 1.58910i | −0.0409475 | − | 0.126024i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8140 | − | 8.58338i | −0.931074 | − | 0.676465i | ||||
\(162\) | 1.47815 | − | 1.07394i | 0.116134 | − | 0.0843765i | ||||
\(163\) | 7.23278 | − | 22.2602i | 0.566515 | − | 1.74355i | −0.0968923 | − | 0.995295i | \(-0.530890\pi\) |
0.663407 | − | 0.748259i | \(-0.269110\pi\) | |||||||
\(164\) | −4.89781 | −0.382454 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.3805 | −2.28037 | ||||||||
\(167\) | −0.943091 | + | 2.90254i | −0.0729786 | + | 0.224605i | −0.980892 | − | 0.194553i | \(-0.937675\pi\) |
0.907913 | + | 0.419158i | \(0.137675\pi\) | |||||||
\(168\) | 1.70906 | − | 1.24170i | 0.131857 | − | 0.0957994i | ||||
\(169\) | −12.7057 | − | 9.23123i | −0.977362 | − | 0.710095i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.85867 | + | 5.72040i | 0.142136 | + | 0.437450i | ||||
\(172\) | −2.13233 | − | 1.54923i | −0.162589 | − | 0.118128i | ||||
\(173\) | 12.9503 | − | 9.40893i | 0.984592 | − | 0.715348i | 0.0258617 | − | 0.999666i | \(-0.491767\pi\) |
0.958730 | + | 0.284318i | \(0.0917670\pi\) | |||||||
\(174\) | −3.12687 | + | 9.62351i | −0.237047 | + | 0.729557i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.7266 | + | 6.75911i | −1.11006 | + | 0.509487i | ||||
\(177\) | 5.66332 | 0.425681 | ||||||||
\(178\) | 8.19021 | − | 25.2069i | 0.613883 | − | 1.88934i | ||||
\(179\) | 15.6133 | − | 11.3437i | 1.16699 | − | 0.847870i | 0.176347 | − | 0.984328i | \(-0.443572\pi\) |
0.990646 | + | 0.136458i | \(0.0435719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.76724 | − | 11.5944i | −0.280017 | − | 0.861804i | −0.987848 | − | 0.155422i | \(-0.950326\pi\) |
0.707831 | − | 0.706382i | \(-0.249674\pi\) | |||||||
\(182\) | 5.28536 | + | 16.2667i | 0.391777 | + | 1.20576i | ||||
\(183\) | −7.50749 | − | 5.45451i | −0.554970 | − | 0.403209i | ||||
\(184\) | 8.17508 | − | 5.93954i | 0.602675 | − | 0.437869i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0390343 | 0.00286214 | ||||||||
\(187\) | −22.0969 | + | 10.1419i | −1.61589 | + | 0.741649i | ||||
\(188\) | −5.11153 | −0.372797 | ||||||||
\(189\) | −0.539926 | + | 1.66172i | −0.0392739 | + | 0.120873i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8605 | + | 7.89064i | 0.785841 | + | 0.570947i | 0.906726 | − | 0.421720i | \(-0.138573\pi\) |
−0.120885 | + | 0.992666i | \(0.538573\pi\) | |||||||
\(192\) | −0.655137 | − | 2.01630i | −0.0472804 | − | 0.145514i | ||||
\(193\) | −2.34167 | − | 7.20693i | −0.168557 | − | 0.518766i | 0.830723 | − | 0.556685i | \(-0.187927\pi\) |
−0.999281 | + | 0.0379190i | \(0.987927\pi\) | |||||||
\(194\) | 2.80806 | + | 2.04018i | 0.201607 | + | 0.146476i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.63233 | + | 5.02379i | −0.116595 | + | 0.358842i | ||||
\(197\) | 6.89118 | 0.490976 | 0.245488 | − | 0.969400i | \(-0.421052\pi\) | ||||
0.245488 | + | 0.969400i | \(0.421052\pi\) | |||||||
\(198\) | 2.96980 | − | 5.28215i | 0.211055 | − | 0.375386i | ||||
\(199\) | 0.639398 | 0.0453257 | 0.0226629 | − | 0.999743i | \(-0.492786\pi\) | ||||
0.0226629 | + | 0.999743i | \(0.492786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.283551 | − | 0.206012i | 0.0200002 | − | 0.0145310i | ||||
\(202\) | 9.91854 | + | 7.20624i | 0.697866 | + | 0.507029i | ||||
\(203\) | −2.99021 | − | 9.20292i | −0.209872 | − | 0.645918i | ||||
\(204\) | −3.03158 | − | 9.33024i | −0.212253 | − | 0.653248i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.27737 | − | 4.56078i | 0.437365 | − | 0.317765i | ||||
\(207\) | −2.58268 | + | 7.94866i | −0.179508 | + | 0.552470i | ||||
\(208\) | −26.1755 | −1.81495 | ||||||||
\(209\) | 13.5167 | + | 14.6715i | 0.934966 | + | 1.01485i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18090 | + | 3.63445i | −0.0812968 | + | 0.250206i | −0.983441 | − | 0.181229i | \(-0.941992\pi\) |
0.902144 | + | 0.431435i | \(0.141992\pi\) | |||||||
\(212\) | 1.80902 | − | 1.31433i | 0.124244 | − | 0.0902684i | ||||
\(213\) | −3.67147 | − | 2.66748i | −0.251565 | − | 0.182772i | ||||
\(214\) | −8.87723 | − | 27.3213i | −0.606835 | − | 1.86765i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.978148 | − | 0.710666i | −0.0665545 | − | 0.0483547i | ||||
\(217\) | −0.0301993 | + | 0.0219411i | −0.00205006 | + | 0.00148946i | ||||
\(218\) | −2.39332 | + | 7.36589i | −0.162096 | + | 0.498881i | ||||
\(219\) | −10.1395 | −0.685165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.2758 | −2.64198 | ||||||||
\(222\) | −0.633284 | + | 1.94905i | −0.0425033 | + | 0.130812i | ||||
\(223\) | −21.6171 | + | 15.7057i | −1.44758 | + | 1.05173i | −0.461197 | + | 0.887298i | \(0.652580\pi\) |
−0.986388 | + | 0.164434i | \(0.947420\pi\) | |||||||
\(224\) | 9.19975 | + | 6.68401i | 0.614684 | + | 0.446594i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.06312 | − | 12.5050i | −0.270275 | − | 0.831820i | ||||
\(227\) | 9.90020 | + | 7.19291i | 0.657099 | + | 0.477411i | 0.865682 | − | 0.500594i | \(-0.166885\pi\) |
−0.208583 | + | 0.978005i | \(0.566885\pi\) | |||||||
\(228\) | −6.51206 | + | 4.73129i | −0.431272 | + | 0.313337i | ||||
\(229\) | −2.06628 | + | 6.35937i | −0.136544 | + | 0.420239i | −0.995827 | − | 0.0912615i | \(-0.970910\pi\) |
0.859283 | + | 0.511500i | \(0.170910\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.671466 | + | 5.75590i | 0.0441792 | + | 0.378710i | ||||
\(232\) | 6.69598 | 0.439612 | ||||||||
\(233\) | 2.01399 | − | 6.19844i | 0.131941 | − | 0.406073i | −0.863161 | − | 0.504930i | \(-0.831518\pi\) |
0.995102 | + | 0.0988565i | \(0.0315185\pi\) | |||||||
\(234\) | 7.91949 | − | 5.75385i | 0.517714 | − | 0.376141i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.34204 | + | 7.20806i | 0.152454 | + | 0.469205i | ||||
\(237\) | 0.792323 | + | 2.43852i | 0.0514669 | + | 0.158399i | ||||
\(238\) | 18.9328 | + | 13.7555i | 1.22723 | + | 0.891637i | ||||
\(239\) | 8.77126 | − | 6.37269i | 0.567366 | − | 0.412215i | −0.266782 | − | 0.963757i | \(-0.585960\pi\) |
0.834147 | + | 0.551542i | \(0.185960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1803 | 1.75084 | 0.875420 | − | 0.483363i | \(-0.160585\pi\) | ||||
0.875420 | + | 0.483363i | \(0.160585\pi\) | |||||||
\(242\) | 1.64409 | − | 20.0306i | 0.105686 | − | 1.28762i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.83761 | − | 11.8109i | 0.245678 | − | 0.756118i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.40977 | − | 3.93043i | −0.344914 | − | 0.250595i | ||||
\(247\) | 9.95823 | + | 30.6483i | 0.633627 | + | 1.95010i | ||||
\(248\) | −0.00798208 | − | 0.0245663i | −0.000506862 | − | 0.00155996i | ||||
\(249\) | −13.0094 | − | 9.45188i | −0.824437 | − | 0.598989i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.71332 | − | 5.27307i | 0.108144 | − | 0.332833i | −0.882311 | − | 0.470666i | \(-0.844014\pi\) |
0.990455 | + | 0.137833i | \(0.0440137\pi\) | |||||||
\(252\) | −2.33826 | −0.147297 | ||||||||
\(253\) | 3.21188 | + | 27.5327i | 0.201929 | + | 1.73097i | ||||
\(254\) | 23.1804 | 1.45447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9451 | + | 12.3113i | −1.05907 | + | 0.769457i | ||||
\(257\) | −15.3260 | − | 11.1350i | −0.956008 | − | 0.694580i | −0.00378765 | − | 0.999993i | \(-0.501206\pi\) |
−0.952220 | + | 0.305413i | \(0.901206\pi\) | |||||||
\(258\) | −1.11198 | − | 3.42233i | −0.0692291 | − | 0.213065i | ||||
\(259\) | −0.605607 | − | 1.86387i | −0.0376306 | − | 0.115815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.48048 | + | 3.25526i | −0.277335 | + | 0.201496i | ||||
\(262\) | 0.547722 | − | 1.68571i | 0.0338384 | − | 0.104144i | ||||
\(263\) | −3.20873 | −0.197859 | −0.0989293 | − | 0.995094i | \(-0.531542\pi\) | ||||
−0.0989293 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(264\) | −3.93162 | − | 0.788907i | −0.241974 | − | 0.0485539i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.93355 | − | 18.2616i | 0.363809 | − | 1.11969i | ||||
\(267\) | 11.7357 | − | 8.52651i | 0.718215 | − | 0.521814i | ||||
\(268\) | 0.379466 | + | 0.275698i | 0.0231796 | + | 0.0168409i | ||||
\(269\) | −1.00252 | − | 3.08544i | −0.0611248 | − | 0.188123i | 0.915831 | − | 0.401563i | \(-0.131533\pi\) |
−0.976956 | + | 0.213441i | \(0.931533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.64212 | + | 1.19307i | 0.0997517 | + | 0.0724738i | 0.636543 | − | 0.771241i | \(-0.280364\pi\) |
−0.536791 | + | 0.843715i | \(0.680364\pi\) | |||||||
\(272\) | −28.9747 | + | 21.0514i | −1.75685 | + | 1.27643i | ||||
\(273\) | −2.89277 | + | 8.90304i | −0.175078 | + | 0.538836i | ||||
\(274\) | 7.71096 | 0.465836 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.1848 | −0.673246 | ||||||||
\(277\) | −3.49701 | + | 10.7627i | −0.210115 | + | 0.646668i | 0.789349 | + | 0.613944i | \(0.210418\pi\) |
−0.999464 | + | 0.0327234i | \(0.989582\pi\) | |||||||
\(278\) | 13.0793 | − | 9.50268i | 0.784446 | − | 0.569933i | ||||
\(279\) | 0.0172840 | + | 0.0125576i | 0.00103477 | + | 0.000751802i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.18835 | − | 9.81272i | −0.190201 | − | 0.585378i | 0.809798 | − | 0.586708i | \(-0.199576\pi\) |
−0.999999 | + | 0.00133051i | \(0.999576\pi\) | |||||||
\(282\) | −5.64583 | − | 4.10194i | −0.336205 | − | 0.244267i | ||||
\(283\) | −1.70370 | + | 1.23781i | −0.101274 | + | 0.0735801i | −0.637270 | − | 0.770641i | \(-0.719936\pi\) |
0.535996 | + | 0.844221i | \(0.319936\pi\) | |||||||
\(284\) | 1.87674 | − | 5.77602i | 0.111364 | − | 0.342744i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9113 | − | 28.3003i | 0.940858 | − | 1.67343i | ||||
\(287\) | 6.39459 | 0.377461 | ||||||||
\(288\) | 2.01117 | − | 6.18975i | 0.118509 | − | 0.364734i | ||||
\(289\) | −29.7227 | + | 21.5948i | −1.74839 | + | 1.27028i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.587045 | + | 1.80674i | 0.0344132 | + | 0.105913i | ||||
\(292\) | −4.19315 | − | 12.9052i | −0.245386 | − | 0.755220i | ||||
\(293\) | −18.9111 | − | 13.7398i | −1.10480 | − | 0.802685i | −0.122964 | − | 0.992411i | \(-0.539240\pi\) |
−0.981837 | + | 0.189726i | \(0.939240\pi\) | |||||||
\(294\) | −5.83448 | + | 4.23900i | −0.340274 | + | 0.247223i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.35614 | 0.0788238 | ||||||||
\(297\) | 3.01430 | − | 1.38348i | 0.174907 | − | 0.0802778i | ||||
\(298\) | −17.4552 | −1.01115 | ||||||||
\(299\) | −13.8372 | + | 42.5867i | −0.800228 | + | 2.46285i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.78398 | + | 2.02268i | 0.160466 | + | 0.116585i | ||||
\(302\) | 3.81196 | + | 11.7320i | 0.219353 | + | 0.675100i | ||||
\(303\) | 2.07354 | + | 6.38170i | 0.119122 | + | 0.366619i | ||||
\(304\) | 23.7735 | + | 17.2725i | 1.36351 | + | 0.990645i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.13893 | − | 12.7383i | 0.236607 | − | 0.728201i | ||||
\(307\) | 32.0518 | 1.82929 | 0.914646 | − | 0.404256i | \(-0.132469\pi\) | ||||
0.914646 | + | 0.404256i | \(0.132469\pi\) | |||||||
\(308\) | −7.04821 | + | 3.23494i | −0.401609 | + | 0.184328i | ||||
\(309\) | 4.24678 | 0.241591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.32220 | + | 0.960634i | −0.0749751 | + | 0.0544726i | −0.624641 | − | 0.780912i | \(-0.714755\pi\) |
0.549666 | + | 0.835384i | \(0.314755\pi\) | |||||||
\(312\) | −5.24064 | − | 3.80755i | −0.296693 | − | 0.215560i | ||||
\(313\) | −9.39813 | − | 28.9245i | −0.531214 | − | 1.63491i | −0.751691 | − | 0.659516i | \(-0.770761\pi\) |
0.220477 | − | 0.975392i | \(-0.429239\pi\) | |||||||
\(314\) | −7.14811 | − | 21.9996i | −0.403391 | − | 1.24151i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.77599 | + | 2.01688i | −0.156162 | + | 0.113458i | ||||
\(317\) | 9.09561 | − | 27.9934i | 0.510861 | − | 1.57227i | −0.279829 | − | 0.960050i | \(-0.590278\pi\) |
0.790690 | − | 0.612217i | \(-0.209722\pi\) | |||||||
\(318\) | 3.05284 | 0.171195 | ||||||||
\(319\) | −9.00190 | + | 16.0110i | −0.504010 | + | 0.896443i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.85867 | − | 14.9534i | 0.271185 | − | 0.834620i | ||||
\(322\) | 21.5853 | − | 15.6826i | 1.20290 | − | 0.873958i | ||||
\(323\) | 35.6717 | + | 25.9170i | 1.98482 | + | 1.44206i | ||||
\(324\) | 0.413545 | + | 1.27276i | 0.0229747 | + | 0.0707090i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.5972 | + | 25.1363i | 1.91616 | + | 1.39217i | ||||
\(327\) | −3.42939 | + | 2.49159i | −0.189645 | + | 0.137786i | ||||
\(328\) | −1.36738 | + | 4.20837i | −0.0755010 | + | 0.232368i | ||||
\(329\) | 6.67364 | 0.367929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7902 | −1.25266 | −0.626332 | − | 0.779557i | \(-0.715444\pi\) | ||||
−0.626332 | + | 0.779557i | \(0.715444\pi\) | |||||||
\(332\) | 6.65002 | − | 20.4666i | 0.364967 | − | 1.12325i | ||||
\(333\) | −0.907432 | + | 0.659288i | −0.0497270 | + | 0.0361287i | ||||
\(334\) | −4.51117 | − | 3.27756i | −0.246840 | − | 0.179340i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.63785 | + | 8.11848i | 0.143907 | + | 0.442899i | ||||
\(337\) | −11.7227 | − | 8.51705i | −0.638577 | − | 0.463954i | 0.220784 | − | 0.975323i | \(-0.429138\pi\) |
−0.859361 | + | 0.511369i | \(0.829138\pi\) | |||||||
\(338\) | 23.2145 | − | 16.8663i | 1.26270 | − | 0.917406i | ||||
\(339\) | 2.22382 | − | 6.84421i | 0.120781 | − | 0.371727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0694723 | + | 0.0139401i | 0.00376213 | + | 0.000754899i | ||||
\(342\) | −10.9896 | −0.594247 | ||||||||
\(343\) | 5.91066 | − | 18.1911i | 0.319146 | − | 0.982229i | ||||
\(344\) | −1.92646 | + | 1.39966i | −0.103868 | + | 0.0754644i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.03783 | + | 27.8156i | 0.485877 | + | 1.49537i | ||||
\(347\) | −1.35574 | − | 4.17255i | −0.0727802 | − | 0.223994i | 0.908049 | − | 0.418864i | \(-0.137572\pi\) |
−0.980829 | + | 0.194870i | \(0.937572\pi\) | |||||||
\(348\) | −5.99606 | − | 4.35639i | −0.321422 | − | 0.233527i | ||||
\(349\) | −11.6548 | + | 8.46769i | −0.623866 | + | 0.453265i | −0.854270 | − | 0.519830i | \(-0.825995\pi\) |
0.230404 | + | 0.973095i | \(0.425995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.35772 | 0.285974 | ||||||||
\(352\) | −2.50114 | − | 21.4401i | −0.133311 | − | 1.14276i | ||||
\(353\) | 6.01065 | 0.319914 | 0.159957 | − | 0.987124i | \(-0.448864\pi\) | ||||
0.159957 | + | 0.987124i | \(0.448864\pi\) | |||||||
\(354\) | −3.19752 | + | 9.84096i | −0.169946 | + | 0.523041i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.7055 | + | 11.4107i | 0.832389 | + | 0.604766i | ||||
\(357\) | 3.95804 | + | 12.1816i | 0.209482 | + | 0.644718i | ||||
\(358\) | 10.8963 | + | 33.5354i | 0.575888 | + | 1.77240i | ||||
\(359\) | 1.98787 | + | 1.44428i | 0.104916 | + | 0.0762259i | 0.639006 | − | 0.769201i | \(-0.279346\pi\) |
−0.534090 | + | 0.845427i | \(0.679346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.30818 | − | 16.3369i | 0.279378 | − | 0.859836i | ||||
\(362\) | 22.2742 | 1.17070 | ||||||||
\(363\) | 7.17195 | − | 8.34045i | 0.376430 | − | 0.437760i | ||||
\(364\) | −12.5277 | −0.656632 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.7169 | − | 9.96589i | 0.716992 | − | 0.520926i | ||||
\(367\) | 1.19726 | + | 0.869862i | 0.0624966 | + | 0.0454064i | 0.618595 | − | 0.785710i | \(-0.287702\pi\) |
−0.556098 | + | 0.831116i | \(0.687702\pi\) | |||||||
\(368\) | 12.6179 | + | 38.8338i | 0.657752 | + | 2.02435i | ||||
\(369\) | −1.13095 | − | 3.48070i | −0.0588749 | − | 0.181198i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.36186 | + | 1.71599i | −0.122622 | + | 0.0890898i | ||||
\(372\) | −0.00883507 | + | 0.0271915i | −0.000458077 | + | 0.00140982i | ||||
\(373\) | 24.3331 | 1.25992 | 0.629961 | − | 0.776627i | \(-0.283071\pi\) | ||||
0.629961 | + | 0.776627i | \(0.283071\pi\) | |||||||
\(374\) | −5.14728 | − | 44.1232i | −0.266159 | − | 2.28156i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.42705 | + | 4.39201i | −0.0735945 | + | 0.226501i | ||||
\(377\) | −24.0052 | + | 17.4408i | −1.23633 | + | 0.898245i | ||||
\(378\) | −2.58268 | − | 1.87642i | −0.132839 | − | 0.0965128i | ||||
\(379\) | 4.92299 | + | 15.1514i | 0.252877 | + | 0.778276i | 0.994241 | + | 0.107172i | \(0.0341795\pi\) |
−0.741363 | + | 0.671104i | \(0.765820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.2640 | + | 7.45726i | 0.525842 | + | 0.382047i | ||||
\(382\) | −19.8432 | + | 14.4169i | −1.01527 | + | 0.737634i | ||||
\(383\) | 1.21133 | − | 3.72809i | 0.0618960 | − | 0.190496i | −0.915327 | − | 0.402712i | \(-0.868068\pi\) |
0.977223 | + | 0.212215i | \(0.0680678\pi\) | |||||||
\(384\) | −9.14301 | −0.466577 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8454 | 0.704710 | ||||||||
\(387\) | 0.608609 | − | 1.87310i | 0.0309373 | − | 0.0952153i | ||||
\(388\) | −2.05678 | + | 1.49434i | −0.104417 | + | 0.0758635i | ||||
\(389\) | 28.5510 | + | 20.7435i | 1.44759 | + | 1.05174i | 0.986386 | + | 0.164447i | \(0.0525840\pi\) |
0.461209 | + | 0.887292i | \(0.347416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9328 | + | 58.2693i | 0.957475 | + | 2.94680i | ||||
\(392\) | 3.86090 | + | 2.80511i | 0.195005 | + | 0.141679i | ||||
\(393\) | 0.784829 | − | 0.570212i | 0.0395894 | − | 0.0287634i | ||||
\(394\) | −3.89078 | + | 11.9746i | −0.196015 | + | 0.603271i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.00739 | + | 3.26435i | 0.151127 | + | 0.164040i | ||||
\(397\) | −23.2231 | −1.16553 | −0.582767 | − | 0.812639i | \(-0.698030\pi\) | ||||
−0.582767 | + | 0.812639i | \(0.698030\pi\) | |||||||
\(398\) | −0.361006 | + | 1.11106i | −0.0180956 | + | 0.0556925i | ||||
\(399\) | 8.50217 | − | 6.17719i | 0.425641 | − | 0.309246i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.75973 | + | 5.41589i | 0.0878766 | + | 0.270457i | 0.985332 | − | 0.170649i | \(-0.0545864\pi\) |
−0.897455 | + | 0.441106i | \(0.854586\pi\) | |||||||
\(402\) | 0.197887 | + | 0.609032i | 0.00986969 | + | 0.0303758i | ||||
\(403\) | 0.0926028 | + | 0.0672799i | 0.00461287 | + | 0.00335145i | ||||
\(404\) | −7.26488 | + | 5.27824i | −0.361441 | + | 0.262602i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.6799 | 0.877438 | ||||||||
\(407\) | −1.82315 | + | 3.24270i | −0.0903704 | + | 0.160735i | ||||
\(408\) | −8.86324 | −0.438796 | ||||||||
\(409\) | 7.86540 | − | 24.2072i | 0.388919 | − | 1.19697i | −0.544679 | − | 0.838645i | \(-0.683348\pi\) |
0.933597 | − | 0.358324i | \(-0.116652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.41434 | + | 2.48066i | 0.168417 | + | 0.122362i | ||||
\(412\) | 1.75624 | + | 5.40515i | 0.0865237 | + | 0.266292i | ||||
\(413\) | −3.05777 | − | 9.41086i | −0.150463 | − | 0.463078i | ||||
\(414\) | −12.3539 | − | 8.97566i | −0.607163 | − | 0.441130i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.7753 | − | 33.1629i | 0.528301 | − | 1.62594i | ||||
\(417\) | 8.84846 | 0.433311 | ||||||||
\(418\) | −33.1258 | + | 15.2039i | −1.62023 | + | 0.743645i | ||||
\(419\) | −13.4850 | −0.658786 | −0.329393 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329393 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38633 | + | 1.73377i | −0.116303 | + | 0.0844990i | −0.644416 | − | 0.764675i | \(-0.722900\pi\) |
0.528113 | + | 0.849174i | \(0.322900\pi\) | |||||||
\(422\) | −5.64872 | − | 4.10404i | −0.274975 | − | 0.199781i | ||||
\(423\) | −1.18030 | − | 3.63259i | −0.0573882 | − | 0.176623i | ||||
\(424\) | −0.624271 | − | 1.92131i | −0.0303173 | − | 0.0933070i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.70810 | − | 4.87372i | 0.325009 | − | 0.236133i | ||||
\(427\) | −5.01039 | + | 15.4204i | −0.242470 | + | 0.746246i | ||||
\(428\) | 21.0415 | 1.01708 | ||||||||
\(429\) | 16.1497 | − | 7.41230i | 0.779717 | − | 0.357869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.56072 | − | 10.9588i | 0.171514 | − | 0.527866i | −0.827943 | − | 0.560812i | \(-0.810489\pi\) |
0.999457 | + | 0.0329464i | \(0.0104891\pi\) | |||||||
\(432\) | 3.95252 | − | 2.87167i | 0.190166 | − | 0.138163i | ||||
\(433\) | 9.03174 | + | 6.56194i | 0.434038 | + | 0.315347i | 0.783261 | − | 0.621693i | \(-0.213555\pi\) |
−0.349224 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(434\) | −0.0210757 | − | 0.0648642i | −0.00101166 | − | 0.00311358i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.58941 | − | 3.33440i | −0.219793 | − | 0.159689i | ||||
\(437\) | 40.6692 | − | 29.5479i | 1.94547 | − | 1.41347i | ||||
\(438\) | 5.72480 | − | 17.6191i | 0.273541 | − | 0.841874i | ||||
\(439\) | 0.993624 | 0.0474231 | 0.0237115 | − | 0.999719i | \(-0.492452\pi\) | ||||
0.0237115 | + | 0.999719i | \(0.492452\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.94716 | −0.187960 | ||||||||
\(442\) | 22.1752 | − | 68.2483i | 1.05477 | − | 3.24624i | ||||
\(443\) | −8.88506 | + | 6.45537i | −0.422142 | + | 0.306704i | −0.778499 | − | 0.627646i | \(-0.784019\pi\) |
0.356357 | + | 0.934350i | \(0.384019\pi\) | |||||||
\(444\) | −1.21438 | − | 0.882299i | −0.0576320 | − | 0.0418721i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.0863 | − | 46.4307i | −0.714355 | − | 2.19856i | ||||
\(447\) | −7.72900 | − | 5.61545i | −0.365569 | − | 0.265602i | ||||
\(448\) | −2.99681 | + | 2.17731i | −0.141586 | + | 0.102868i | ||||
\(449\) | 8.96777 | − | 27.5999i | 0.423215 | − | 1.30252i | −0.481478 | − | 0.876458i | \(-0.659900\pi\) |
0.904693 | − | 0.426064i | \(-0.140100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.22451 | − | 8.92722i | −0.387277 | − | 0.420366i | ||||
\(452\) | 9.63070 | 0.452990 | ||||||||
\(453\) | −2.08635 | + | 6.42113i | −0.0980254 | + | 0.301691i | ||||
\(454\) | −18.0886 | + | 13.1421i | −0.848938 | + | 0.616790i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.24724 | + | 6.91629i | 0.105237 | + | 0.323885i | ||||
\(457\) | 1.09908 | + | 3.38262i | 0.0514129 | + | 0.158232i | 0.973466 | − | 0.228830i | \(-0.0734899\pi\) |
−0.922054 | + | 0.387062i | \(0.873490\pi\) | |||||||
\(458\) | −9.88383 | − | 7.18103i | −0.461841 | − | 0.335547i | ||||
\(459\) | 5.93066 | − | 4.30888i | 0.276820 | − | 0.201121i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.1829 | 1.17288 | 0.586441 | − | 0.809992i | \(-0.300528\pi\) | ||||
0.586441 | + | 0.809992i | \(0.300528\pi\) | |||||||
\(462\) | −10.3809 | − | 2.08301i | −0.482965 | − | 0.0969104i | ||||
\(463\) | 17.8743 | 0.830690 | 0.415345 | − | 0.909664i | \(-0.363661\pi\) | ||||
0.415345 | + | 0.909664i | \(0.363661\pi\) | |||||||
\(464\) | −8.36114 | + | 25.7329i | −0.388156 | + | 1.19462i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.63371 | + | 6.99930i | 0.446273 | + | 0.324236i | ||||
\(467\) | 7.79502 | + | 23.9906i | 0.360711 | + | 1.11015i | 0.952624 | + | 0.304151i | \(0.0983729\pi\) |
−0.591913 | + | 0.806002i | \(0.701627\pi\) | |||||||
\(468\) | 2.21566 | + | 6.81910i | 0.102419 | + | 0.315213i | ||||
\(469\) | −0.495432 | − | 0.359952i | −0.0228769 | − | 0.0166210i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91229 | − | 12.0408i | 0.180269 | − | 0.554810i | ||||
\(472\) | 6.84727 | 0.315171 | ||||||||
\(473\) | −0.756881 | − | 6.48809i | −0.0348014 | − | 0.298323i | ||||
\(474\) | −4.68468 | −0.215175 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.8674 | + | 10.0753i | −0.635613 | + | 0.461800i | ||||
\(477\) | 1.35177 | + | 0.982116i | 0.0618931 | + | 0.0449680i | ||||
\(478\) | 6.12135 | + | 18.8396i | 0.279984 | + | 0.861702i | ||||
\(479\) | −1.61793 | − | 4.97948i | −0.0739252 | − | 0.227518i | 0.907266 | − | 0.420558i | \(-0.138166\pi\) |
−0.981191 | + | 0.193039i | \(0.938166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.86176 | + | 3.53228i | −0.221677 | + | 0.161058i | ||||
\(482\) | −15.3461 | + | 47.2304i | −0.698995 | + | 2.15128i | ||||
\(483\) | 14.6029 | 0.664456 | ||||||||
\(484\) | 13.5813 | + | 5.67904i | 0.617333 | + | 0.258138i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.564602 | + | 1.73767i | −0.0256109 | + | 0.0788222i | ||||
\(487\) | 7.31762 | − | 5.31656i | 0.331593 | − | 0.240917i | −0.409513 | − | 0.912304i | \(-0.634301\pi\) |
0.741106 | + | 0.671388i | \(0.234301\pi\) | |||||||
\(488\) | −9.07699 | − | 6.59482i | −0.410896 | − | 0.298533i | ||||
\(489\) | 7.23278 | + | 22.2602i | 0.327078 | + | 1.00664i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.1629 | + | 20.4615i | 1.27097 | + | 0.923416i | 0.999241 | − | 0.0389565i | \(-0.0124034\pi\) |
0.271733 | + | 0.962373i | \(0.412403\pi\) | |||||||
\(492\) | 3.96241 | − | 2.87886i | 0.178639 | − | 0.129789i | ||||
\(493\) | −12.5457 | + | 38.6117i | −0.565030 | + | 1.73898i | ||||
\(494\) | −58.8789 | −2.64909 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.104377 | 0.00468664 | ||||||||
\(497\) | −2.45028 | + | 7.54120i | −0.109910 | + | 0.338269i | ||||
\(498\) | 23.7694 | − | 17.2694i | 1.06513 | − | 0.773862i | ||||
\(499\) | −15.8561 | − | 11.5201i | −0.709815 | − | 0.515711i | 0.173299 | − | 0.984869i | \(-0.444557\pi\) |
−0.883114 | + | 0.469158i | \(0.844557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.943091 | − | 2.90254i | −0.0421342 | − | 0.129676i | ||||
\(502\) | 8.19549 | + | 5.95437i | 0.365783 | + | 0.265757i | ||||
\(503\) | 14.8989 | − | 10.8247i | 0.664307 | − | 0.482647i | −0.203808 | − | 0.979011i | \(-0.565332\pi\) |
0.868115 | + | 0.496364i | \(0.165332\pi\) | |||||||
\(504\) | −0.652802 | + | 2.00912i | −0.0290781 | + | 0.0894932i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −49.6561 | − | 9.96384i | −2.20748 | − | 0.442947i | ||||
\(507\) | 15.7051 | 0.697489 | ||||||||
\(508\) | −5.24667 | + | 16.1476i | −0.232783 | + | 0.716433i | ||||
\(509\) | −1.00187 | + | 0.727900i | −0.0444070 | + | 0.0322636i | −0.609767 | − | 0.792580i | \(-0.708737\pi\) |
0.565360 | + | 0.824844i | \(0.308737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.47459 | + | 16.8491i | 0.242182 | + | 0.745359i | ||||
\(512\) | −6.17504 | − | 19.0048i | −0.272901 | − | 0.839902i | ||||
\(513\) | −4.86606 | − | 3.53540i | −0.214842 | − | 0.156092i | ||||
\(514\) | 28.0019 | − | 20.3446i | 1.23511 | − | 0.897362i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.63570 | 0.116030 | ||||||||
\(517\) | −8.58340 | − | 9.31678i | −0.377498 | − | 0.409752i | ||||
\(518\) | 3.58071 | 0.157327 | ||||||||
\(519\) | −4.94657 | + | 15.2240i | −0.217130 | + | 0.668258i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.8472 | − | 19.5057i | −1.17620 | − | 0.854558i | −0.184461 | − | 0.982840i | \(-0.559054\pi\) |
−0.991738 | + | 0.128282i | \(0.959054\pi\) | |||||||
\(522\) | −3.12687 | − | 9.62351i | −0.136859 | − | 0.421210i | ||||
\(523\) | −4.06383 | − | 12.5072i | −0.177699 | − | 0.546901i | 0.822047 | − | 0.569419i | \(-0.192832\pi\) |
−0.999746 | + | 0.0225177i | \(0.992832\pi\) | |||||||
\(524\) | 1.05031 | + | 0.763092i | 0.0458829 | + | 0.0333359i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.81165 | − | 5.57570i | 0.0789919 | − | 0.243112i | ||||
\(527\) | 0.156615 | 0.00682224 | ||||||||
\(528\) | 7.94115 | − | 14.1243i | 0.345594 | − | 0.614681i | ||||
\(529\) | 46.8514 | 2.03702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.58172 | + | 3.32882i | −0.198830 | + | 0.144458i | ||||
\(532\) | 11.3781 | + | 8.26669i | 0.493304 | + | 0.358407i | ||||
\(533\) | −6.05930 | − | 18.6486i | −0.262458 | − | 0.807761i | ||||
\(534\) | 8.19021 | + | 25.2069i | 0.354425 | + | 1.09081i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.342830 | − | 0.249080i | 0.0148080 | − | 0.0107586i | ||||
\(537\) | −5.96375 | + | 18.3545i | −0.257355 | + | 0.792057i | ||||
\(538\) | 5.92750 | 0.255553 | ||||||||
\(539\) | −11.8979 | + | 5.46082i | −0.512479 | + | 0.235214i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0900 | − | 31.0538i | 0.433802 | − | 1.33511i | −0.460507 | − | 0.887656i | \(-0.652332\pi\) |
0.894309 | − | 0.447450i | \(-0.147668\pi\) | |||||||
\(542\) | −3.00030 | + | 2.17985i | −0.128874 | + | 0.0936324i | ||||
\(543\) | 9.86277 | + | 7.16572i | 0.423252 | + | 0.307511i | ||||
\(544\) | −14.7433 | − | 45.3752i | −0.632114 | − | 1.94545i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.8372 | − | 10.0533i | −0.592179 | − | 0.430243i | ||||
\(547\) | 22.4136 | − | 16.2845i | 0.958338 | − | 0.696273i | 0.00557389 | − | 0.999984i | \(-0.498226\pi\) |
0.952764 | + | 0.303711i | \(0.0982258\pi\) | |||||||
\(548\) | −1.74531 | + | 5.37150i | −0.0745558 | + | 0.229459i | ||||
\(549\) | 9.27977 | 0.396051 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.3110 | 1.41909 | ||||||||
\(552\) | −3.12260 | + | 9.61038i | −0.132907 | + | 0.409045i | ||||
\(553\) | 3.62435 | − | 2.63324i | 0.154123 | − | 0.111977i | ||||
\(554\) | −16.7276 | − | 12.1533i | −0.710686 | − | 0.516343i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.65924 | + | 11.2620i | 0.155186 | + | 0.477614i | ||||
\(557\) | −18.9514 | − | 13.7690i | −0.802996 | − | 0.583411i | 0.108795 | − | 0.994064i | \(-0.465301\pi\) |
−0.911792 | + | 0.410653i | \(0.865301\pi\) | |||||||
\(558\) | −0.0315794 | + | 0.0229438i | −0.00133686 | + | 0.000971289i | ||||
\(559\) | 3.26075 | − | 10.0356i | 0.137915 | − | 0.424459i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.9155 | − | 21.1932i | 0.503073 | − | 0.894778i | ||||
\(562\) | 18.8514 | 0.795198 | ||||||||
\(563\) | −6.82482 | + | 21.0046i | −0.287632 | + | 0.885240i | 0.697966 | + | 0.716131i | \(0.254089\pi\) |
−0.985597 | + | 0.169108i | \(0.945911\pi\) | |||||||
\(564\) | 4.13532 | − | 3.00448i | 0.174128 | − | 0.126512i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.18899 | − | 3.65933i | −0.0499769 | − | 0.153813i | ||||
\(567\) | −0.539926 | − | 1.66172i | −0.0226748 | − | 0.0697858i | ||||
\(568\) | −4.43901 | − | 3.22513i | −0.186257 | − | 0.135323i | ||||
\(569\) | 11.1119 | − | 8.07328i | 0.465836 | − | 0.338449i | −0.329980 | − | 0.943988i | \(-0.607042\pi\) |
0.795816 | + | 0.605538i | \(0.207042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.5201 | −1.10983 | −0.554915 | − | 0.831907i | \(-0.687249\pi\) | ||||
−0.554915 | + | 0.831907i | \(0.687249\pi\) | |||||||
\(572\) | 16.1127 | + | 17.4894i | 0.673708 | + | 0.731271i | ||||
\(573\) | −13.4244 | −0.560811 | ||||||||
\(574\) | −3.61040 | + | 11.1117i | −0.150695 | + | 0.463792i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.71517 | + | 1.24614i | 0.0714654 | + | 0.0519227i | ||||
\(577\) | −1.75758 | − | 5.40927i | −0.0731690 | − | 0.225191i | 0.907783 | − | 0.419439i | \(-0.137773\pi\) |
−0.980952 | + | 0.194248i | \(0.937773\pi\) | |||||||
\(578\) | −20.7430 | − | 63.8405i | −0.862797 | − | 2.65542i | ||||
\(579\) | 6.13058 | + | 4.45413i | 0.254778 | + | 0.185107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.68228 | + | 26.7213i | −0.360202 | + | 1.10859i | ||||
\(582\) | −3.47096 | −0.143876 | ||||||||
\(583\) | 5.43336 | + | 1.09024i | 0.225027 | + | 0.0451532i | ||||
\(584\) | −12.2593 | −0.507292 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.5524 | − | 25.1038i | 1.42735 | − | 1.03703i | ||||
\(587\) | 10.9590 | + | 7.96215i | 0.452324 | + | 0.328633i | 0.790513 | − | 0.612446i | \(-0.209814\pi\) |
−0.338188 | + | 0.941078i | \(0.609814\pi\) | |||||||
\(588\) | −1.63233 | − | 5.02379i | −0.0673161 | − | 0.207178i | ||||
\(589\) | −0.0397090 | − | 0.122212i | −0.00163618 | − | 0.00503565i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.57508 | + | 4.05054i | −0.229328 | + | 0.166617i | ||||
\(592\) | −1.69338 | + | 5.21169i | −0.0695975 | + | 0.214199i | ||||
\(593\) | −21.1786 | −0.869702 | −0.434851 | − | 0.900502i | \(-0.643199\pi\) | ||||
−0.434851 | + | 0.900502i | \(0.643199\pi\) | |||||||
\(594\) | 0.702153 | + | 6.01896i | 0.0288097 | + | 0.246961i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.95083 | − | 12.1594i | 0.161833 | − | 0.498069i | ||||
\(597\) | −0.517284 | + | 0.375829i | −0.0211710 | + | 0.0153816i | ||||
\(598\) | −66.1889 | − | 48.0890i | −2.70666 | − | 1.96651i | ||||
\(599\) | −10.4573 | − | 32.1842i | −0.427273 | − | 1.31501i | −0.900801 | − | 0.434231i | \(-0.857020\pi\) |
0.473529 | − | 0.880778i | \(-0.342980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.7186 | − | 17.2325i | −0.967500 | − | 0.702930i | −0.0126196 | − | 0.999920i | \(-0.504017\pi\) |
−0.954880 | + | 0.296990i | \(0.904017\pi\) | |||||||
\(602\) | −5.08658 | + | 3.69562i | −0.207313 | + | 0.150622i | ||||
\(603\) | −0.108307 | + | 0.333334i | −0.00441060 | + | 0.0135744i | ||||
\(604\) | −9.03538 | −0.367644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.2600 | −0.498028 | ||||||||
\(607\) | −2.21715 | + | 6.82370i | −0.0899915 | + | 0.276965i | −0.985916 | − | 0.167241i | \(-0.946514\pi\) |
0.895925 | + | 0.444206i | \(0.146514\pi\) | |||||||
\(608\) | −31.6697 | + | 23.0094i | −1.28438 | + | 0.933154i | ||||
\(609\) | 7.82847 | + | 5.68772i | 0.317226 | + | 0.230478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.32372 | − | 19.4624i | −0.255830 | − | 0.787364i | ||||
\(612\) | 7.93678 | + | 5.76641i | 0.320825 | + | 0.233093i | ||||
\(613\) | −22.2515 | + | 16.1667i | −0.898731 | + | 0.652967i | −0.938140 | − | 0.346257i | \(-0.887453\pi\) |
0.0394084 | + | 0.999223i | \(0.487453\pi\) | |||||||
\(614\) | −18.0965 | + | 55.6953i | −0.730315 | + | 2.24768i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.811840 | + | 6.95921i | 0.0327100 | + | 0.280395i | ||||
\(617\) | −24.0712 | −0.969068 | −0.484534 | − | 0.874772i | \(-0.661011\pi\) | ||||
−0.484534 | + | 0.874772i | \(0.661011\pi\) | |||||||
\(618\) | −2.39774 | + | 7.37950i | −0.0964514 | + | 0.296847i | ||||
\(619\) | −21.8216 | + | 15.8543i | −0.877083 | + | 0.637238i | −0.932478 | − | 0.361227i | \(-0.882358\pi\) |
0.0553955 | + | 0.998464i | \(0.482358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58268 | − | 7.94866i | −0.103639 | − | 0.318969i | ||||
\(622\) | −0.922745 | − | 2.83992i | −0.0369987 | − | 0.113870i | ||||
\(623\) | −20.5051 | − | 14.8978i | −0.821521 | − | 0.596870i | ||||
\(624\) | 21.1765 | − | 15.3856i | 0.847737 | − | 0.615917i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 55.5673 | 2.22092 | ||||||||
\(627\) | −19.5589 | − | 3.92463i | −0.781108 | − | 0.156735i | ||||
\(628\) | 16.9430 | 0.676098 | ||||||||
\(629\) | −2.54088 | + | 7.82003i | −0.101312 | + | 0.311805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.87681 | − | 5.72284i | −0.313571 | − | 0.227823i | 0.419856 | − | 0.907591i | \(-0.362080\pi\) |
−0.733427 | + | 0.679768i | \(0.762080\pi\) | |||||||
\(632\) | 0.957964 | + | 2.94831i | 0.0381058 | + | 0.117277i | ||||
\(633\) | −1.18090 | − | 3.63445i | −0.0469367 | − | 0.144456i | ||||
\(634\) | 43.5078 | + | 31.6103i | 1.72792 | + | 1.25540i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.690983 | + | 2.12663i | −0.0273993 | + | 0.0843262i | ||||
\(637\) | −21.1478 | −0.837904 | ||||||||
\(638\) | −22.7393 | − | 24.6821i | −0.900256 | − | 0.977175i | ||||
\(639\) | 4.53818 | 0.179528 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3196 | + | 14.7631i | −0.802577 | + | 0.583107i | −0.911669 | − | 0.410925i | \(-0.865206\pi\) |
0.109092 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(642\) | 23.2409 | + | 16.8855i | 0.917245 | + | 0.666418i | ||||
\(643\) | 8.32051 | + | 25.6079i | 0.328129 | + | 1.00988i | 0.970008 | + | 0.243071i | \(0.0781549\pi\) |
−0.641880 | + | 0.766806i | \(0.721845\pi\) | |||||||
\(644\) | 6.03897 | + | 18.5860i | 0.237969 | + | 0.732393i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −65.1754 | + | 47.3527i | −2.56429 | + | 1.86307i | ||||
\(647\) | 8.28198 | − | 25.4893i | 0.325598 | − | 1.00209i | −0.645572 | − | 0.763700i | \(-0.723381\pi\) |
0.971170 | − | 0.238389i | \(-0.0766192\pi\) | |||||||
\(648\) | 1.20906 | 0.0474962 | ||||||||
\(649\) | −9.20530 | + | 16.3728i | −0.361340 | + | 0.642687i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0115351 | − | 0.0355014i | 0.000452096 | − | 0.00139141i | ||||
\(652\) | −25.3409 | + | 18.4112i | −0.992425 | + | 0.721039i | ||||
\(653\) | 23.2700 | + | 16.9066i | 0.910625 | + | 0.661608i | 0.941173 | − | 0.337926i | \(-0.109725\pi\) |
−0.0305480 | + | 0.999533i | \(0.509725\pi\) | |||||||
\(654\) | −2.39332 | − | 7.36589i | −0.0935863 | − | 0.288029i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.4655 | − | 10.5098i | −0.564784 | − | 0.410340i | ||||
\(657\) | 8.20305 | − | 5.95986i | 0.320031 | − | 0.232516i | ||||
\(658\) | −3.76795 | + | 11.5966i | −0.146890 | + | 0.452081i | ||||
\(659\) | 36.5327 | 1.42311 | 0.711556 | − | 0.702629i | \(-0.247991\pi\) | ||||
0.711556 | + | 0.702629i | \(0.247991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7750 | −1.39149 | −0.695743 | − | 0.718291i | \(-0.744925\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(662\) | 12.8674 | − | 39.6018i | 0.500106 | − | 1.53917i | ||||
\(663\) | 31.7748 | − | 23.0858i | 1.23403 | − | 0.896576i | ||||
\(664\) | −15.7291 | − | 11.4279i | −0.610408 | − | 0.443487i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.633284 | − | 1.94905i | −0.0245393 | − | 0.0755241i | ||||
\(667\) | 37.4466 | + | 27.2065i | 1.44994 | + | 1.05344i | ||||
\(668\) | 3.30423 | − | 2.40066i | 0.127844 | − | 0.0928844i | ||||
\(669\) | 8.25698 | − | 25.4124i | 0.319233 | − | 0.982499i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.9720 | − | 12.8384i | 1.07985 | − | 0.495621i | ||||
\(672\) | −11.3715 | −0.438666 | ||||||||
\(673\) | 3.48925 | − | 10.7388i | 0.134501 | − | 0.413951i | −0.861011 | − | 0.508586i | \(-0.830168\pi\) |
0.995512 | + | 0.0946349i | \(0.0301684\pi\) | |||||||
\(674\) | 21.4185 | − | 15.5614i | 0.825009 | − | 0.599404i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.49478 | + | 19.9889i | 0.249799 | + | 0.768803i | ||||
\(677\) | 13.5527 | + | 41.7108i | 0.520872 | + | 1.60308i | 0.772338 | + | 0.635212i | \(0.219087\pi\) |
−0.251466 | + | 0.967866i | \(0.580913\pi\) | |||||||
\(678\) | 10.6374 | + | 7.72851i | 0.408526 | + | 0.296812i | ||||
\(679\) | 2.68534 | − | 1.95101i | 0.103054 | − | 0.0748729i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2373 | −0.468935 | ||||||||
\(682\) | −0.0634474 | + | 0.112849i | −0.00242953 | + | 0.00432121i | ||||
\(683\) | 18.5355 | 0.709241 | 0.354620 | − | 0.935010i | \(-0.384610\pi\) | ||||
0.354620 | + | 0.935010i | \(0.384610\pi\) | |||||||
\(684\) | 2.48739 | − | 7.65539i | 0.0951076 | − | 0.292711i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28.2730 | + | 20.5415i | 1.07947 | + | 0.784279i | ||||
\(687\) | −2.06628 | − | 6.35937i | −0.0788337 | − | 0.242625i | ||||
\(688\) | −2.97341 | − | 9.15120i | −0.113360 | − | 0.348886i | ||||
\(689\) | 7.24238 | + | 5.26190i | 0.275913 | + | 0.200462i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.71597 | + | 26.8250i | −0.331571 | + | 1.02047i | 0.636815 | + | 0.771017i | \(0.280251\pi\) |
−0.968386 | + | 0.249455i | \(0.919749\pi\) | |||||||
\(692\) | −21.4221 | −0.814347 | ||||||||
\(693\) | −3.92646 | − | 4.26194i | −0.149154 | − | 0.161898i | ||||
\(694\) | 8.01596 | 0.304282 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.41716 | + | 3.93580i | −0.205337 | + | 0.149186i | ||||
\(697\) | −21.7052 | − | 15.7698i | −0.822144 | − | 0.597322i | ||||
\(698\) | −8.13371 | − | 25.0330i | −0.307865 | − | 0.947512i | ||||
\(699\) | 2.01399 | + | 6.19844i | 0.0761762 | + | 0.234446i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.255153 | + | 0.185379i | −0.00963699 | + | 0.00700168i | −0.592593 | − | 0.805502i | \(-0.701896\pi\) |
0.582956 | + | 0.812503i | \(0.301896\pi\) | |||||||
\(702\) | −3.02498 | + | 9.30992i | −0.114170 | + | 0.351380i | ||||
\(703\) | 6.74647 | 0.254448 | ||||||||
\(704\) | 6.89405 | + | 1.38334i | 0.259829 | + | 0.0521366i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.39362 | + | 10.4445i | −0.127721 | + | 0.393084i | ||||
\(707\) | 9.48505 | − | 6.89129i | 0.356722 | − | 0.259174i | ||||
\(708\) | −6.13154 | − | 4.45482i | −0.230437 | − | 0.167423i | ||||
\(709\) | 12.0593 | + | 37.1146i | 0.452895 | + | 1.39387i | 0.873589 | + | 0.486665i | \(0.161787\pi\) |
−0.420693 | + | 0.907203i | \(0.638213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.07433 | − | 1.50709i | −0.0777934 | − | 0.0565202i | ||||
\(712\) | 14.1892 | − | 10.3090i | 0.531762 | − | 0.386348i | ||||
\(713\) | 0.0551768 | − | 0.169817i | 0.00206639 | − | 0.00635969i | ||||
\(714\) | −23.4023 | −0.875808 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8272 | −0.965209 | ||||||||
\(717\) | −3.35032 | + | 10.3112i | −0.125120 | + | 0.385080i | ||||
\(718\) | −3.63203 | + | 2.63882i | −0.135546 | + | 0.0984800i | ||||
\(719\) | −23.0320 | − | 16.7337i | −0.858948 | − | 0.624062i | 0.0686507 | − | 0.997641i | \(-0.478131\pi\) |
−0.927598 | + | 0.373579i | \(0.878131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29295 | − | 7.05698i | −0.0853939 | − | 0.262816i | ||||
\(722\) | 25.3911 | + | 18.4477i | 0.944957 | + | 0.686552i | ||||
\(723\) | −21.9894 | + | 15.9762i | −0.817793 | + | 0.594161i | ||||
\(724\) | −5.04156 | + | 15.5163i | −0.187368 | + | 0.576659i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.4436 | + | 17.1715i | 0.387599 | + | 0.637294i | ||||
\(727\) | −45.8400 | −1.70011 | −0.850057 | − | 0.526691i | \(-0.823432\pi\) | ||||
−0.850057 | + | 0.526691i | \(0.823432\pi\) | |||||||
\(728\) | −3.49753 | + | 10.7643i | −0.129627 | + | 0.398951i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.46153 | − | 13.7312i | −0.165016 | − | 0.507866i | ||||
\(732\) | 3.83761 | + | 11.8109i | 0.141842 | + | 0.436545i | ||||
\(733\) | 30.7169 | + | 22.3171i | 1.13455 | + | 0.824301i | 0.986351 | − | 0.164656i | \(-0.0526513\pi\) |
0.148202 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(734\) | −2.18751 | + | 1.58932i | −0.0807423 | + | 0.0586627i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.3944 | −2.00500 | ||||||||
\(737\) | 0.134693 | + | 1.15461i | 0.00496149 | + | 0.0425306i | ||||
\(738\) | 6.68684 | 0.246146 | ||||||||
\(739\) | 6.52725 | − | 20.0888i | 0.240109 | − | 0.738979i | −0.756294 | − | 0.654232i | \(-0.772992\pi\) |
0.996403 | − | 0.0847466i | \(-0.0270081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.0710 | − | 18.9417i | −0.957741 | − | 0.695840i | ||||
\(742\) | −1.64831 | − | 5.07298i | −0.0605113 | − | 0.186235i | ||||
\(743\) | −2.46606 | − | 7.58976i | −0.0904711 | − | 0.278441i | 0.895576 | − | 0.444909i | \(-0.146764\pi\) |
−0.986047 | + | 0.166467i | \(0.946764\pi\) | |||||||
\(744\) | 0.0208973 | + | 0.0151828i | 0.000766134 | + | 0.000556629i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.7385 | + | 42.2829i | −0.503004 | + | 1.54809i | ||||
\(747\) | 16.0805 | 0.588355 | ||||||||
\(748\) | 31.9015 | + | 6.40126i | 1.16643 | + | 0.234053i | ||||
\(749\) | −27.4718 | −1.00380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.78664 | − | 5.65733i | 0.284139 | − | 0.206439i | −0.436582 | − | 0.899664i | \(-0.643811\pi\) |
0.720721 | + | 0.693226i | \(0.243811\pi\) | |||||||
\(752\) | −15.0968 | − | 10.9684i | −0.550523 | − | 0.399978i | ||||
\(753\) | 1.71332 | + | 5.27307i | 0.0624370 | + | 0.192161i | ||||
\(754\) | −16.7529 | − | 51.5600i | −0.610104 | − | 1.87771i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.89169 | − | 1.37440i | 0.0688002 | − | 0.0499863i | ||||
\(757\) | 14.4049 | − | 44.3338i | 0.523555 | − | 1.61134i | −0.243600 | − | 0.969876i | \(-0.578328\pi\) |
0.767155 | − | 0.641462i | \(-0.221672\pi\) | |||||||
\(758\) | −29.1076 | −1.05724 | ||||||||
\(759\) | −18.7818 | − | 20.3865i | −0.681735 | − | 0.739984i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.79661 | + | 20.9178i | −0.246377 | + | 0.758270i | 0.749030 | + | 0.662536i | \(0.230520\pi\) |
−0.995407 | + | 0.0957342i | \(0.969480\pi\) | |||||||
\(762\) | −18.7533 | + | 13.6251i | −0.679361 | + | 0.493585i | ||||
\(763\) | 5.99195 | + | 4.35341i | 0.216923 | + | 0.157604i | ||||
\(764\) | −5.55158 | − | 17.0860i | −0.200849 | − | 0.618151i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.79425 | + | 4.20977i | 0.209355 | + | 0.152105i | ||||
\(767\) | −24.5476 | + | 17.8348i | −0.886361 | + | 0.643979i | ||||
\(768\) | 6.47244 | − | 19.9201i | 0.233554 | − | 0.718805i | ||||
\(769\) | 48.0330 | 1.73211 | 0.866057 | − | 0.499946i | \(-0.166647\pi\) | ||||
0.866057 | + | 0.499946i | \(0.166647\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9439 | 0.682249 | ||||||||
\(772\) | −3.13377 | + | 9.64476i | −0.112787 | + | 0.347123i | ||||
\(773\) | −13.8222 | + | 10.0424i | −0.497148 | + | 0.361199i | −0.807927 | − | 0.589283i | \(-0.799410\pi\) |
0.310778 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(774\) | 2.91121 | + | 2.11512i | 0.104641 | + | 0.0760263i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.709771 | + | 2.18445i | 0.0254793 | + | 0.0784172i | ||||
\(777\) | 1.58550 | + | 1.15193i | 0.0568795 | + | 0.0413254i | ||||
\(778\) | −52.1653 | + | 37.9003i | −1.87022 | + | 1.35879i | ||||
\(779\) | −6.80242 | + | 20.9357i | −0.243722 | + | 0.750099i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6794 | − | 6.27849i | 0.489488 | − | 0.224662i | ||||
\(782\) | −111.942 | −4.00304 | ||||||||
\(783\) | 1.71139 | − | 5.26712i | 0.0611602 | − | 0.188232i | ||||
\(784\) | −15.6012 | + | 11.3349i | −0.557186 | + | 0.404819i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.547722 | + | 1.68571i | 0.0195366 | + | 0.0601275i | ||||
\(787\) | 6.95034 | + | 21.3910i | 0.247753 | + | 0.762505i | 0.995171 | + | 0.0981518i | \(0.0312931\pi\) |
−0.747418 | + | 0.664354i | \(0.768707\pi\) | |||||||
\(788\) | −7.46092 | − | 5.42068i | −0.265784 | − | 0.193104i | ||||
\(789\) | 2.59591 | − | 1.88604i | 0.0924170 | − | 0.0671449i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5739 | −0.447076 | ||||||||
\(792\) | 3.64445 | − | 1.67271i | 0.129500 | − | 0.0594371i | ||||
\(793\) | 49.7184 | 1.76555 | ||||||||
\(794\) | 13.1118 | − | 40.3540i | 0.465321 | − | 1.43211i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.692261 | − | 0.502957i | −0.0245365 | − | 0.0178268i | ||||
\(797\) | 1.05615 | + | 3.25051i | 0.0374109 | + | 0.115139i | 0.968018 | − | 0.250881i | \(-0.0807203\pi\) |
−0.930607 | + | 0.366020i | \(0.880720\pi\) | |||||||
\(798\) | 5.93355 | + | 18.2616i | 0.210045 | + | 0.646453i | ||||
\(799\) | −22.6524 | − | 16.4579i | −0.801383 | − | 0.582239i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.48265 | + | 13.7962i | −0.158387 | + | 0.487464i | ||||
\(802\) | −10.4046 | −0.367398 | ||||||||
\(803\) | 16.4810 | − | 29.3135i | 0.581603 | − | 1.03445i | ||||
\(804\) | −0.469045 | −0.0165420 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.169194 | + | 0.122926i | −0.00595959 | + | 0.00432990i | ||||
\(807\) | 2.62464 | + | 1.90691i | 0.0923916 | + | 0.0671264i | ||||
\(808\) | 2.50703 | + | 7.71584i | 0.0881969 | + | 0.271442i | ||||
\(809\) | −3.12679 | − | 9.62328i | −0.109932 | − | 0.338336i | 0.880924 | − | 0.473257i | \(-0.156922\pi\) |
−0.990856 | + | 0.134921i | \(0.956922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.5287 | + | 14.9150i | −0.720862 | + | 0.523737i | −0.886659 | − | 0.462423i | \(-0.846980\pi\) |
0.165798 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(812\) | −4.00168 | + | 12.3159i | −0.140432 | + | 0.432204i | ||||
\(813\) | −2.02977 | −0.0711872 | ||||||||
\(814\) | −4.60538 | − | 4.99887i | −0.161419 | − | 0.175210i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.0674 | − | 34.0618i | 0.387435 | − | 1.19240i | ||||
\(817\) | −9.58370 | + | 6.96297i | −0.335291 | + | 0.243603i | ||||
\(818\) | 37.6232 | + | 27.3349i | 1.31547 | + | 0.955741i | ||||
\(819\) | −2.89277 | − | 8.90304i | −0.101082 | − | 0.311097i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.21284 | − | 0.881177i | −0.0423282 | − | 0.0307533i | 0.566420 | − | 0.824117i | \(-0.308328\pi\) |
−0.608748 | + | 0.793363i | \(0.708328\pi\) | |||||||
\(822\) | −6.23830 | + | 4.53239i | −0.217586 | + | 0.158085i | ||||
\(823\) | 5.90982 | − | 18.1885i | 0.206003 | − | 0.634013i | −0.793667 | − | 0.608352i | \(-0.791831\pi\) |
0.999671 | − | 0.0256610i | \(-0.00816904\pi\) | |||||||
\(824\) | 5.13460 | 0.178872 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0794 | 0.629062 | ||||||||
\(827\) | 5.13910 | − | 15.8165i | 0.178704 | − | 0.549994i | −0.821079 | − | 0.570814i | \(-0.806628\pi\) |
0.999783 | + | 0.0208200i | \(0.00662770\pi\) | |||||||
\(828\) | 9.04870 | − | 6.57426i | 0.314464 | − | 0.228471i | ||||
\(829\) | −20.7881 | − | 15.1034i | −0.722001 | − | 0.524564i | 0.165022 | − | 0.986290i | \(-0.447231\pi\) |
−0.887023 | + | 0.461725i | \(0.847231\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.49701 | − | 10.7627i | −0.121310 | − | 0.373354i | ||||
\(832\) | 9.18940 | + | 6.67649i | 0.318585 | + | 0.231466i | ||||
\(833\) | −23.4093 | + | 17.0078i | −0.811083 | + | 0.589286i | ||||
\(834\) | −4.99586 | + | 15.3757i | −0.172992 | + | 0.532416i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.09338 | − | 26.5169i | −0.106987 | − | 0.917105i | ||||
\(837\) | −0.0213642 | −0.000738455 | ||||||||
\(838\) | 7.61367 | − | 23.4325i | 0.263010 | − | 0.809461i | ||||
\(839\) | 22.9737 | − | 16.6914i | 0.793141 | − | 0.576250i | −0.115753 | − | 0.993278i | \(-0.536928\pi\) |
0.908894 | + | 0.417028i | \(0.136928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.516507 | + | 1.58965i | 0.0178106 | + | 0.0548154i | ||||
\(842\) | −1.66539 | − | 5.12555i | −0.0573932 | − | 0.176638i | ||||
\(843\) | 8.34720 | + | 6.06459i | 0.287493 | + | 0.208876i | ||||
\(844\) | 4.13743 | − | 3.00602i | 0.142416 | − | 0.103471i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.97864 | 0.239930 | ||||||||
\(847\) | −17.7318 | − | 7.41457i | −0.609273 | − | 0.254768i | ||||
\(848\) | 8.16320 | 0.280325 | ||||||||
\(849\) | 0.650755 | − | 2.00282i | 0.0223339 | − | 0.0687365i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.58406 | + | 5.51014i | 0.259978 | + | 0.188885i | ||||
\(852\) | 1.87674 | + | 5.77602i | 0.0642962 | + | 0.197883i | ||||
\(853\) | −4.66838 | − | 14.3678i | −0.159842 | − | 0.491943i | 0.838777 | − | 0.544475i | \(-0.183271\pi\) |
−0.998619 | + | 0.0525314i | \(0.983271\pi\) | |||||||
\(854\) | −23.9666 | − | 17.4128i | −0.820122 | − | 0.595853i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.87441 | − | 18.0796i | 0.200783 | − | 0.617947i | ||||
\(857\) | −2.37040 | −0.0809713 | −0.0404856 | − | 0.999180i | \(-0.512891\pi\) | ||||
−0.0404856 | + | 0.999180i | \(0.512891\pi\) | |||||||
\(858\) | 3.76194 | + | 32.2479i | 0.128430 | + | 1.10092i | ||||
\(859\) | 45.0423 | 1.53682 | 0.768411 | − | 0.639956i | \(-0.221048\pi\) | ||||
0.768411 | + | 0.639956i | \(0.221048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.17333 | + | 3.75865i | −0.176307 | + | 0.128094i | ||||
\(862\) | 17.0323 | + | 12.3747i | 0.580123 | + | 0.421484i | ||||
\(863\) | 7.73191 | + | 23.7964i | 0.263197 | + | 0.810038i | 0.992103 | + | 0.125424i | \(0.0400292\pi\) |
−0.728906 | + | 0.684614i | \(0.759971\pi\) | |||||||
\(864\) | 2.01117 | + | 6.18975i | 0.0684214 | + | 0.210579i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.5018 | + | 11.9893i | −0.560754 | + | 0.407412i | ||||
\(867\) | 11.3530 | − | 34.9411i | 0.385570 | − | 1.18666i | ||||
\(868\) | 0.0499551 | 0.00169559 | ||||||||
\(869\) | −8.33767 | − | 1.67301i | −0.282836 | − | 0.0567530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.580278 | + | 1.78591i | −0.0196620 | + | 0.0605133i | ||||
\(872\) | −4.14632 | + | 3.01248i | −0.140412 | + | 0.102015i | ||||
\(873\) | −1.53690 | − | 1.11663i | −0.0520163 | − | 0.0377920i | ||||
\(874\) | 28.3825 | + | 87.3522i | 0.960051 | + | 2.95473i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.9778 | + | 7.97585i | 0.370906 | + | 0.269479i | ||||
\(877\) | −39.5411 | + | 28.7283i | −1.33521 | + | 0.970085i | −0.335601 | + | 0.942004i | \(0.608940\pi\) |
−0.999606 | + | 0.0280807i | \(0.991060\pi\) | |||||||
\(878\) | −0.561002 | + | 1.72659i | −0.0189329 | + | 0.0582695i | ||||
\(879\) | 23.3755 | 0.788435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.5530 | 1.50103 | 0.750515 | − | 0.660853i | \(-0.229805\pi\) | ||||
0.750515 | + | 0.660853i | \(0.229805\pi\) | |||||||
\(882\) | 2.22857 | − | 6.85885i | 0.0750400 | − | 0.230949i | ||||
\(883\) | −35.6410 | + | 25.8947i | −1.19941 | + | 0.871426i | −0.994227 | − | 0.107297i | \(-0.965780\pi\) |
−0.205187 | + | 0.978723i | \(0.565780\pi\) | |||||||
\(884\) | 42.5230 | + | 30.8948i | 1.43020 | + | 1.03910i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.20076 | − | 19.0840i | −0.208319 | − | 0.641139i | ||||
\(887\) | −9.81279 | − | 7.12941i | −0.329481 | − | 0.239382i | 0.410729 | − | 0.911757i | \(-0.365274\pi\) |
−0.740210 | + | 0.672375i | \(0.765274\pi\) | |||||||
\(888\) | −1.09714 | + | 0.797116i | −0.0368175 | + | 0.0267495i | ||||
\(889\) | 6.85007 | − | 21.0823i | 0.229744 | − | 0.707079i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.62543 | + | 2.89102i | −0.0544538 | + | 0.0968528i | ||||
\(892\) | 35.7585 | 1.19728 | ||||||||
\(893\) | −7.09925 | + | 21.8493i | −0.237567 | + | 0.731158i | ||||
\(894\) | 14.1216 | − | 10.2599i | 0.472296 | − | 0.343143i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.93655 | + | 15.1931i | 0.164919 | + | 0.507567i | ||||
\(897\) | −13.8372 | − | 42.5867i | −0.462012 | − | 1.42193i | ||||
\(898\) | 42.8963 | + | 31.1660i | 1.43147 | + | 1.04002i | ||||
\(899\) | 0.0957219 | − | 0.0695461i | 0.00319251 | − | 0.00231949i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2487 | 0.408063 | ||||||||
\(902\) | 20.1561 | − | 9.25112i | 0.671125 | − | 0.308029i | ||||
\(903\) | −3.44118 | −0.114515 | ||||||||
\(904\) | 2.68872 | − | 8.27504i | 0.0894256 | − | 0.275224i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.97983 | − | 7.25077i | −0.331558 | − | 0.240891i | ||||
\(907\) | −10.1565 | − | 31.2586i | −0.337242 | − | 1.03793i | −0.965607 | − | 0.260006i | \(-0.916275\pi\) |
0.628365 | − | 0.777919i | \(-0.283725\pi\) | |||||||
\(908\) | −5.06069 | − | 15.5752i | −0.167945 | − | 0.516881i | ||||
\(909\) | −5.42860 | − | 3.94411i | −0.180055 | − | 0.130818i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4328 | + | 44.4195i | −0.478179 | + | 1.47168i | 0.363443 | + | 0.931617i | \(0.381601\pi\) |
−0.841622 | + | 0.540067i | \(0.818399\pi\) | |||||||
\(912\) | −29.3857 | −0.973058 | ||||||||
\(913\) | 48.4714 | − | 22.2471i | 1.60417 | − | 0.736271i | ||||
\(914\) | −6.49842 | −0.214949 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.23946 | − | 5.25978i | 0.239199 | − | 0.173788i | ||||
\(917\) | −1.37128 | − | 0.996296i | −0.0452838 | − | 0.0329006i | ||||
\(918\) | 4.13893 | + | 12.7383i | 0.136605 | + | 0.420427i | ||||
\(919\) | 2.26765 | + | 6.97910i | 0.0748028 | + | 0.230219i | 0.981466 | − | 0.191636i | \(-0.0613792\pi\) |
−0.906663 | + | 0.421855i | \(0.861379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.9304 | + | 18.8396i | −0.854437 | + | 0.620785i | ||||
\(922\) | −14.2183 | + | 43.7594i | −0.468255 | + | 1.44114i | ||||
\(923\) | 24.3143 | 0.800314 | ||||||||
\(924\) | 3.80067 | − | 6.75996i | 0.125033 | − | 0.222386i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.0919 | + | 31.0596i | −0.331640 | + | 1.02068i | ||||
\(927\) | −3.43572 | + | 2.49620i | −0.112844 | + | 0.0819859i | ||||
\(928\) | −29.1603 | − | 21.1862i | −0.957232 | − | 0.695470i | ||||
\(929\) | 3.93333 | + | 12.1055i | 0.129048 | + | 0.397170i | 0.994617 | − | 0.103621i | \(-0.0330428\pi\) |
−0.865569 | + | 0.500790i | \(0.833043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.2071 | + | 13.9548i | 0.629488 | + | 0.457350i | ||||
\(932\) | −7.05626 | + | 5.12667i | −0.231135 | + | 0.167930i | ||||
\(933\) | 0.505035 | − | 1.55434i | 0.0165341 | − | 0.0508868i | ||||
\(934\) | −46.0888 | −1.50807 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.47778 | 0.211733 | ||||||||
\(937\) | −5.94961 | + | 18.3110i | −0.194365 | + | 0.598195i | 0.805618 | + | 0.592435i | \(0.201833\pi\) |
−0.999983 | + | 0.00575961i | \(0.998167\pi\) | |||||||
\(938\) | 0.905199 | − | 0.657665i | 0.0295558 | − | 0.0214735i | ||||
\(939\) | 24.6046 | + | 17.8763i | 0.802942 | + | 0.583371i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.7530 | − | 39.2496i | −0.415735 | − | 1.27950i | −0.911592 | − | 0.411096i | \(-0.865146\pi\) |
0.495857 | − | 0.868404i | \(-0.334854\pi\) | |||||||
\(942\) | 18.7140 | + | 13.5965i | 0.609735 | + | 0.442998i | ||||
\(943\) | −24.7461 | + | 17.9791i | −0.805842 | + | 0.585479i | ||||
\(944\) | −8.55007 | + | 26.3144i | −0.278281 | + | 0.856461i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.7015 | + | 2.34798i | 0.380448 | + | 0.0763395i | ||||
\(947\) | 50.3012 | 1.63457 | 0.817285 | − | 0.576233i | \(-0.195478\pi\) | ||||
0.817285 | + | 0.576233i | \(0.195478\pi\) | |||||||
\(948\) | 1.06034 | − | 3.26338i | 0.0344381 | − | 0.105990i | ||||
\(949\) | 43.9496 | − | 31.9312i | 1.42666 | − | 1.03653i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.09561 | + | 27.9934i | 0.294945 | + | 0.907749i | ||||
\(952\) | 4.78550 | + | 14.7282i | 0.155099 | + | 0.477345i | ||||
\(953\) | −7.30203 | − | 5.30523i | −0.236536 | − | 0.171853i | 0.463203 | − | 0.886252i | \(-0.346700\pi\) |
−0.699739 | + | 0.714399i | \(0.746700\pi\) | |||||||
\(954\) | −2.46980 | + | 1.79442i | −0.0799628 | + | 0.0580963i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.5093 | −0.469263 | ||||||||
\(957\) | −2.12833 | − | 18.2443i | −0.0687991 | − | 0.589756i | ||||
\(958\) | 9.56617 | 0.309069 | ||||||||
\(959\) | 2.27868 | − | 7.01305i | 0.0735824 | − | 0.226463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0792 | + | 18.2211i | 0.809005 | + | 0.587777i | ||||
\(962\) | −3.39296 | − | 10.4425i | −0.109393 | − | 0.336678i | ||||
\(963\) | 4.85867 | + | 14.9534i | 0.156568 | + | 0.481868i | ||||
\(964\) | −29.4275 | − | 21.3803i | −0.947796 | − | 0.688614i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.24484 | + | 25.3750i | −0.265273 | + | 0.816428i | ||||
\(967\) | 30.2503 | 0.972785 | 0.486392 | − | 0.873740i | \(-0.338313\pi\) | ||||
0.486392 | + | 0.873740i | \(0.338313\pi\) | |||||||
\(968\) | 8.67130 | − | 10.0841i | 0.278706 | − | 0.324114i | ||||
\(969\) | −44.0926 | −1.41646 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.3785 | + | 7.54040i | −0.333061 | + | 0.241983i | −0.741728 | − | 0.670700i | \(-0.765994\pi\) |
0.408667 | + | 0.912683i | \(0.365994\pi\) | |||||||
\(972\) | −1.08268 | − | 0.786610i | −0.0347269 | − | 0.0252305i | ||||
\(973\) | −4.77751 | − | 14.7037i | −0.153160 | − | 0.471378i | ||||
\(974\) | 5.10687 | + | 15.7173i | 0.163635 | + | 0.503616i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.6785 | − | 26.6485i | 1.17405 | − | 0.852996i | ||||
\(977\) | 4.06641 | − | 12.5151i | 0.130096 | − | 0.400394i | −0.864699 | − | 0.502290i | \(-0.832491\pi\) |
0.994795 | + | 0.101896i | \(0.0324909\pi\) | |||||||
\(978\) | −42.7645 | −1.36746 | ||||||||
\(979\) | 5.57474 | + | 47.7875i | 0.178169 | + | 1.52729i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.30991 | − | 4.03149i | 0.0418222 | − | 0.128715i | ||||
\(982\) | −51.4562 | + | 37.3851i | −1.64203 | + | 1.19301i | ||||
\(983\) | 18.1519 | + | 13.1881i | 0.578954 | + | 0.420635i | 0.838347 | − | 0.545137i | \(-0.183522\pi\) |
−0.259393 | + | 0.965772i | \(0.583522\pi\) | |||||||
\(984\) | −1.36738 | − | 4.20837i | −0.0435905 | − | 0.134158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −60.0110 | − | 43.6005i | −1.91114 | − | 1.38852i | ||||
\(987\) | −5.39908 | + | 3.92266i | −0.171855 | + | 0.124860i | ||||
\(988\) | 13.3267 | − | 41.0154i | 0.423979 | − | 1.30487i | ||||
\(989\) | −16.4605 | −0.523414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.9146 | 0.727907 | 0.363953 | − | 0.931417i | \(-0.381427\pi\) | ||||
0.363953 | + | 0.931417i | \(0.381427\pi\) | |||||||
\(992\) | −0.0429671 | + | 0.132239i | −0.00136421 | + | 0.00419859i | ||||
\(993\) | 18.4377 | − | 13.3958i | 0.585102 | − | 0.425101i | ||||
\(994\) | −11.7207 | − | 8.51555i | −0.371757 | − | 0.270097i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.65002 | + | 20.4666i | 0.210714 | + | 0.648511i | ||||
\(997\) | −13.6234 | − | 9.89794i | −0.431456 | − | 0.313471i | 0.350775 | − | 0.936460i | \(-0.385918\pi\) |
−0.782231 | + | 0.622989i | \(0.785918\pi\) | |||||||
\(998\) | 28.9705 | − | 21.0483i | 0.917045 | − | 0.666272i | ||||
\(999\) | 0.346608 | − | 1.06675i | 0.0109662 | − | 0.0337505i |
(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 | 825.2.n.j.526.1 | 8 | ||
5.2 | odd | 4 | 825.2.bx.e.724.1 | 16 | |||
5.3 | odd | 4 | 825.2.bx.e.724.4 | 16 | |||
5.4 | even | 2 | 165.2.m.c.31.2 | yes | 8 | ||
11.4 | even | 5 | 9075.2.a.co.1.1 | 4 | |||
11.5 | even | 5 | inner | 825.2.n.j.676.1 | 8 | ||
11.7 | odd | 10 | 9075.2.a.df.1.4 | 4 | |||
15.14 | odd | 2 | 495.2.n.c.361.1 | 8 | |||
55.4 | even | 10 | 1815.2.a.u.1.4 | 4 | |||
55.27 | odd | 20 | 825.2.bx.e.49.4 | 16 | |||
55.29 | odd | 10 | 1815.2.a.q.1.1 | 4 | |||
55.38 | odd | 20 | 825.2.bx.e.49.1 | 16 | |||
55.49 | even | 10 | 165.2.m.c.16.2 | ✓ | 8 | ||
165.29 | even | 10 | 5445.2.a.bq.1.4 | 4 | |||
165.59 | odd | 10 | 5445.2.a.bj.1.1 | 4 | |||
165.104 | odd | 10 | 495.2.n.c.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.c.16.2 | ✓ | 8 | 55.49 | even | 10 | ||
165.2.m.c.31.2 | yes | 8 | 5.4 | even | 2 | ||
495.2.n.c.181.1 | 8 | 165.104 | odd | 10 | |||
495.2.n.c.361.1 | 8 | 15.14 | odd | 2 | |||
825.2.n.j.526.1 | 8 | 1.1 | even | 1 | trivial | ||
825.2.n.j.676.1 | 8 | 11.5 | even | 5 | inner | ||
825.2.bx.e.49.1 | 16 | 55.38 | odd | 20 | |||
825.2.bx.e.49.4 | 16 | 55.27 | odd | 20 | |||
825.2.bx.e.724.1 | 16 | 5.2 | odd | 4 | |||
825.2.bx.e.724.4 | 16 | 5.3 | odd | 4 | |||
1815.2.a.q.1.1 | 4 | 55.29 | odd | 10 | |||
1815.2.a.u.1.4 | 4 | 55.4 | even | 10 | |||
5445.2.a.bj.1.1 | 4 | 165.59 | odd | 10 | |||
5445.2.a.bq.1.4 | 4 | 165.29 | even | 10 | |||
9075.2.a.co.1.1 | 4 | 11.4 | even | 5 | |||
9075.2.a.df.1.4 | 4 | 11.7 | odd | 10 |