Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
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, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{60})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.406737 - 0.913545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.49 |
Dual form | 825.2.bx.e.724.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73767 | + | 0.564602i | −1.22872 | + | 0.399234i | −0.850249 | − | 0.526381i | \(-0.823549\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 1.08268 | − | 0.786610i | 0.541338 | − | 0.393305i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.564602 | + | 1.73767i | −0.230498 | + | 0.709399i | ||||
\(7\) | −1.02700 | − | 1.41355i | −0.388170 | − | 0.534270i | 0.569556 | − | 0.821953i | \(-0.307115\pi\) |
−0.957726 | + | 0.287683i | \(0.907115\pi\) | |||||||
\(8\) | 0.710666 | − | 0.978148i | 0.251258 | − | 0.345827i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.384301 | + | 3.29428i | −0.115871 | + | 0.993264i | ||||
\(12\) | − | 1.33826i | − | 0.386323i | ||||||
\(13\) | −5.09549 | + | 1.65563i | −1.41323 | + | 0.459188i | −0.913446 | − | 0.406960i | \(-0.866589\pi\) |
−0.499789 | + | 0.866147i | \(0.666589\pi\) | |||||||
\(14\) | 2.58268 | + | 1.87642i | 0.690249 | + | 0.501495i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50973 | + | 4.64646i | −0.377432 | + | 1.16162i | ||||
\(17\) | 6.97191 | + | 2.26531i | 1.69094 | + | 0.549419i | 0.986983 | − | 0.160826i | \(-0.0514158\pi\) |
0.703955 | + | 0.710245i | \(0.251416\pi\) | |||||||
\(18\) | 1.07394 | + | 1.47815i | 0.253129 | + | 0.348403i | ||||
\(19\) | 4.86606 | + | 3.53540i | 1.11635 | + | 0.811077i | 0.983652 | − | 0.180080i | \(-0.0576356\pi\) |
0.132699 | + | 0.991156i | \(0.457636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74724 | −0.381279 | ||||||||
\(22\) | −1.19217 | − | 5.94135i | −0.254172 | − | 1.26670i | ||||
\(23\) | − | 8.35772i | − | 1.74270i | −0.490658 | − | 0.871352i | \(-0.663244\pi\) | ||
0.490658 | − | 0.871352i | \(-0.336756\pi\) | |||||||
\(24\) | −0.373619 | − | 1.14988i | −0.0762647 | − | 0.234719i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.91949 | − | 5.75385i | 1.55314 | − | 1.12842i | ||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | −2.22382 | − | 0.722562i | −0.420262 | − | 0.136551i | ||||
\(29\) | 4.48048 | − | 3.25526i | 0.832005 | − | 0.604487i | −0.0881210 | − | 0.996110i | \(-0.528086\pi\) |
0.920126 | + | 0.391623i | \(0.128086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.00660190 | − | 0.0203186i | −0.00118574 | − | 0.00364932i | 0.950462 | − | 0.310841i | \(-0.100611\pi\) |
−0.951648 | + | 0.307192i | \(0.900611\pi\) | |||||||
\(32\) | − | 6.50828i | − | 1.15051i | ||||||
\(33\) | 2.43925 | + | 2.24724i | 0.424618 | + | 0.391194i | ||||
\(34\) | −13.3939 | −2.29703 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.08268 | − | 0.786610i | −0.180446 | − | 0.131102i | ||||
\(37\) | 0.659288 | + | 0.907432i | 0.108386 | + | 0.149181i | 0.859764 | − | 0.510691i | \(-0.170610\pi\) |
−0.751378 | + | 0.659872i | \(0.770610\pi\) | |||||||
\(38\) | −10.4517 | − | 3.39596i | −1.69549 | − | 0.550897i | ||||
\(39\) | −1.65563 | + | 5.09549i | −0.265112 | + | 0.815931i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.96086 | + | 2.15119i | 0.462409 | + | 0.335960i | 0.794476 | − | 0.607296i | \(-0.207746\pi\) |
−0.332066 | + | 0.943256i | \(0.607746\pi\) | |||||||
\(42\) | 3.03612 | − | 0.986494i | 0.468483 | − | 0.152219i | ||||
\(43\) | 1.96950i | 0.300346i | 0.988660 | + | 0.150173i | \(0.0479830\pi\) | ||||
−0.988660 | + | 0.150173i | \(0.952017\pi\) | |||||||
\(44\) | 2.17524 | + | 3.86894i | 0.327930 | + | 0.583264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.71878 | + | 14.5229i | 0.695747 | + | 2.14129i | ||||
\(47\) | 2.24507 | − | 3.09007i | 0.327476 | − | 0.450733i | −0.613255 | − | 0.789885i | \(-0.710140\pi\) |
0.940731 | + | 0.339152i | \(0.110140\pi\) | |||||||
\(48\) | 2.87167 | + | 3.95252i | 0.414490 | + | 0.570497i | ||||
\(49\) | 1.21974 | − | 3.75397i | 0.174248 | − | 0.536282i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.93066 | − | 4.30888i | 0.830459 | − | 0.603364i | ||||
\(52\) | −4.21443 | + | 5.80067i | −0.584437 | + | 0.804408i | ||||
\(53\) | 1.58910 | − | 0.516329i | 0.218279 | − | 0.0709232i | −0.197836 | − | 0.980235i | \(-0.563391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(54\) | 1.82709 | 0.248636 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.11251 | −0.282296 | ||||||||
\(57\) | 5.72040 | − | 1.85867i | 0.757685 | − | 0.246187i | ||||
\(58\) | −5.94766 | + | 8.18625i | −0.780966 | + | 1.07491i | ||||
\(59\) | 4.58172 | − | 3.32882i | 0.596489 | − | 0.433375i | −0.248142 | − | 0.968724i | \(-0.579820\pi\) |
0.844631 | + | 0.535349i | \(0.179820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.86761 | − | 8.82559i | 0.367160 | − | 1.13000i | −0.581458 | − | 0.813576i | \(-0.697518\pi\) |
0.948618 | − | 0.316425i | \(-0.102482\pi\) | |||||||
\(62\) | 0.0229438 | + | 0.0315794i | 0.00291387 | + | 0.00401059i | ||||
\(63\) | −1.02700 | + | 1.41355i | −0.129390 | + | 0.178090i | ||||
\(64\) | 0.655137 | + | 2.01630i | 0.0818921 | + | 0.252038i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.50739 | − | 2.52775i | −0.677913 | − | 0.311144i | ||||
\(67\) | 0.350489i | 0.0428190i | 0.999771 | + | 0.0214095i | \(0.00681538\pi\) | ||||
−0.999771 | + | 0.0214095i | \(0.993185\pi\) | |||||||
\(68\) | 9.33024 | − | 3.03158i | 1.13146 | − | 0.367633i | ||||
\(69\) | −6.76153 | − | 4.91254i | −0.813993 | − | 0.591401i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.40238 | − | 4.31607i | 0.166431 | − | 0.512223i | −0.832708 | − | 0.553713i | \(-0.813210\pi\) |
0.999139 | + | 0.0414901i | \(0.0132105\pi\) | |||||||
\(72\) | −1.14988 | − | 0.373619i | −0.135515 | − | 0.0440314i | ||||
\(73\) | 5.95986 | + | 8.20305i | 0.697549 | + | 0.960094i | 0.999976 | + | 0.00692130i | \(0.00220313\pi\) |
−0.302427 | + | 0.953173i | \(0.597797\pi\) | |||||||
\(74\) | −1.65796 | − | 1.20458i | −0.192734 | − | 0.140029i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.04935 | 0.923324 | ||||||||
\(77\) | 5.05130 | − | 2.84001i | 0.575649 | − | 0.323649i | ||||
\(78\) | − | 9.78903i | − | 1.10839i | ||||||
\(79\) | −0.792323 | − | 2.43852i | −0.0891433 | − | 0.274355i | 0.896540 | − | 0.442963i | \(-0.146073\pi\) |
−0.985683 | + | 0.168608i | \(0.946073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −6.35956 | − | 2.06635i | −0.702296 | − | 0.228190i | ||||
\(83\) | 15.2935 | + | 4.96915i | 1.67868 | + | 0.545435i | 0.984654 | − | 0.174519i | \(-0.0558371\pi\) |
0.694022 | + | 0.719954i | \(0.255837\pi\) | |||||||
\(84\) | −1.89169 | + | 1.37440i | −0.206401 | + | 0.149959i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.11198 | − | 3.42233i | −0.119908 | − | 0.369040i | ||||
\(87\) | − | 5.53818i | − | 0.593755i | ||||||
\(88\) | 2.94919 | + | 2.71704i | 0.314384 | + | 0.289637i | ||||
\(89\) | 14.5062 | 1.53765 | 0.768825 | − | 0.639459i | \(-0.220841\pi\) | ||||
0.768825 | + | 0.639459i | \(0.220841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.57337 | + | 5.50238i | 0.793905 | + | 0.576806i | ||||
\(92\) | −6.57426 | − | 9.04870i | −0.685414 | − | 0.943392i | ||||
\(93\) | −0.0203186 | − | 0.00660190i | −0.00210694 | − | 0.000684585i | ||||
\(94\) | −2.15652 | + | 6.63708i | −0.222428 | + | 0.684562i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.26531 | − | 3.82547i | −0.537389 | − | 0.390436i | ||||
\(97\) | 1.80674 | − | 0.587045i | 0.183446 | − | 0.0596054i | −0.215853 | − | 0.976426i | \(-0.569253\pi\) |
0.399300 | + | 0.916820i | \(0.369253\pi\) | |||||||
\(98\) | 7.21182i | 0.728504i | ||||||||
\(99\) | 3.25181 | − | 0.652498i | 0.326819 | − | 0.0655785i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.07354 | + | 6.38170i | 0.206325 | + | 0.635003i | 0.999656 | + | 0.0262128i | \(0.00834474\pi\) |
−0.793332 | + | 0.608790i | \(0.791655\pi\) | |||||||
\(102\) | −7.87272 | + | 10.8359i | −0.779515 | + | 1.07291i | ||||
\(103\) | −2.49620 | − | 3.43572i | −0.245958 | − | 0.338532i | 0.668133 | − | 0.744042i | \(-0.267094\pi\) |
−0.914090 | + | 0.405510i | \(0.867094\pi\) | |||||||
\(104\) | −2.00174 | + | 6.16074i | −0.196287 | + | 0.604110i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.46980 | + | 1.79442i | −0.239888 | + | 0.174289i | ||||
\(107\) | −9.24174 | + | 12.7202i | −0.893433 | + | 1.22970i | 0.0790831 | + | 0.996868i | \(0.474801\pi\) |
−0.972516 | + | 0.232837i | \(0.925199\pi\) | |||||||
\(108\) | −1.27276 | + | 0.413545i | −0.122472 | + | 0.0397934i | ||||
\(109\) | −4.23895 | −0.406018 | −0.203009 | − | 0.979177i | \(-0.565072\pi\) | ||||
−0.203009 | + | 0.979177i | \(0.565072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12165 | 0.106462 | ||||||||
\(112\) | 8.11848 | − | 2.63785i | 0.767124 | − | 0.249254i | ||||
\(113\) | 4.22996 | − | 5.82203i | 0.397921 | − | 0.547691i | −0.562300 | − | 0.826933i | \(-0.690083\pi\) |
0.960221 | + | 0.279242i | \(0.0900833\pi\) | |||||||
\(114\) | −8.89074 | + | 6.45950i | −0.832694 | + | 0.604988i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.29029 | − | 7.04879i | 0.212648 | − | 0.654463i | ||||
\(117\) | 3.14919 | + | 4.33448i | 0.291142 | + | 0.400723i | ||||
\(118\) | −6.08205 | + | 8.37122i | −0.559898 | + | 0.770633i | ||||
\(119\) | −3.95804 | − | 12.1816i | −0.362833 | − | 1.11668i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7046 | − | 2.53200i | −0.973148 | − | 0.230181i | ||||
\(122\) | 16.9550i | 1.53503i | ||||||||
\(123\) | 3.48070 | − | 1.13095i | 0.313845 | − | 0.101974i | ||||
\(124\) | −0.0231305 | − | 0.0168053i | −0.00207718 | − | 0.00150916i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.986494 | − | 3.03612i | 0.0878839 | − | 0.270479i | ||||
\(127\) | 12.0661 | + | 3.92051i | 1.07069 | + | 0.347889i | 0.790757 | − | 0.612130i | \(-0.209687\pi\) |
0.279935 | + | 0.960019i | \(0.409687\pi\) | |||||||
\(128\) | 5.37413 | + | 7.39685i | 0.475010 | + | 0.653796i | ||||
\(129\) | 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 | \(0.513494\pi\) | |||||||
\(132\) | 4.40861 | + | 0.514295i | 0.383721 | + | 0.0447637i | ||||
\(133\) | − | 10.5093i | − | 0.911268i | ||||||
\(134\) | −0.197887 | − | 0.609032i | −0.0170948 | − | 0.0526124i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.17051 | − | 5.20968i | 0.614866 | − | 0.446726i | ||||
\(137\) | 4.01379 | + | 1.30416i | 0.342921 | + | 0.111422i | 0.475414 | − | 0.879762i | \(-0.342298\pi\) |
−0.132493 | + | 0.991184i | \(0.542298\pi\) | |||||||
\(138\) | 14.5229 | + | 4.71878i | 1.23627 | + | 0.401690i | ||||
\(139\) | 7.15855 | − | 5.20099i | 0.607180 | − | 0.441142i | −0.241240 | − | 0.970465i | \(-0.577554\pi\) |
0.848420 | + | 0.529323i | \(0.177554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.18030 | − | 3.63259i | −0.0993993 | − | 0.305919i | ||||
\(142\) | 8.29167i | 0.695821i | ||||||||
\(143\) | −3.49590 | − | 17.4223i | −0.292342 | − | 1.45692i | ||||
\(144\) | 4.88558 | 0.407132 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.9877 | − | 10.8892i | −1.24039 | − | 0.901197i | ||||
\(147\) | −2.32008 | − | 3.19332i | −0.191357 | − | 0.263380i | ||||
\(148\) | 1.42759 | + | 0.463852i | 0.117347 | + | 0.0381284i | ||||
\(149\) | −2.95222 | + | 9.08598i | −0.241855 | + | 0.744353i | 0.754283 | + | 0.656549i | \(0.227985\pi\) |
−0.996138 | + | 0.0878033i | \(0.972015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.46214 | + | 3.96848i | 0.444503 | + | 0.322950i | 0.787422 | − | 0.616415i | \(-0.211416\pi\) |
−0.342919 | + | 0.939365i | \(0.611416\pi\) | |||||||
\(152\) | 6.91629 | − | 2.24724i | 0.560985 | − | 0.182275i | ||||
\(153\) | − | 7.33070i | − | 0.592652i | ||||||
\(154\) | −7.17400 | + | 7.78696i | −0.578097 | + | 0.627491i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.21566 | + | 6.81910i | 0.177395 | + | 0.545965i | ||||
\(157\) | −7.44162 | + | 10.2425i | −0.593906 | + | 0.817441i | −0.995133 | − | 0.0985374i | \(-0.968584\pi\) |
0.401228 | + | 0.915978i | \(0.368584\pi\) | |||||||
\(158\) | 2.75359 | + | 3.78999i | 0.219064 | + | 0.301515i | ||||
\(159\) | 0.516329 | − | 1.58910i | 0.0409475 | − | 0.126024i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8140 | + | 8.58338i | −0.931074 | + | 0.676465i | ||||
\(162\) | 1.07394 | − | 1.47815i | 0.0843765 | − | 0.116134i | ||||
\(163\) | −22.2602 | + | 7.23278i | −1.74355 | + | 0.566515i | −0.995295 | − | 0.0968923i | \(-0.969110\pi\) |
−0.748259 | + | 0.663407i | \(0.769110\pi\) | |||||||
\(164\) | 4.89781 | 0.382454 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.3805 | −2.28037 | ||||||||
\(167\) | −2.90254 | + | 0.943091i | −0.224605 | + | 0.0729786i | −0.419158 | − | 0.907913i | \(-0.637675\pi\) |
0.194553 | + | 0.980892i | \(0.437675\pi\) | |||||||
\(168\) | −1.24170 | + | 1.70906i | −0.0957994 | + | 0.131857i | ||||
\(169\) | 12.7057 | − | 9.23123i | 0.977362 | − | 0.710095i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.85867 | − | 5.72040i | 0.142136 | − | 0.437450i | ||||
\(172\) | 1.54923 | + | 2.13233i | 0.118128 | + | 0.162589i | ||||
\(173\) | −9.40893 | + | 12.9503i | −0.715348 | + | 0.984592i | 0.284318 | + | 0.958730i | \(0.408233\pi\) |
−0.999666 | + | 0.0258617i | \(0.991767\pi\) | |||||||
\(174\) | 3.12687 | + | 9.62351i | 0.237047 | + | 0.729557i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.7266 | − | 6.75911i | −1.11006 | − | 0.509487i | ||||
\(177\) | − | 5.66332i | − | 0.425681i | ||||||
\(178\) | −25.2069 | + | 8.19021i | −1.88934 | + | 0.613883i | ||||
\(179\) | −15.6133 | − | 11.3437i | −1.16699 | − | 0.847870i | −0.176347 | − | 0.984328i | \(-0.556428\pi\) |
−0.990646 | + | 0.136458i | \(0.956428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.76724 | + | 11.5944i | −0.280017 | + | 0.861804i | 0.707831 | + | 0.706382i | \(0.249674\pi\) |
−0.987848 | + | 0.155422i | \(0.950326\pi\) | |||||||
\(182\) | −16.2667 | − | 5.28536i | −1.20576 | − | 0.391777i | ||||
\(183\) | −5.45451 | − | 7.50749i | −0.403209 | − | 0.554970i | ||||
\(184\) | −8.17508 | − | 5.93954i | −0.602675 | − | 0.437869i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0390343 | 0.00286214 | ||||||||
\(187\) | −10.1419 | + | 22.0969i | −0.741649 | + | 1.61589i | ||||
\(188\) | − | 5.11153i | − | 0.372797i | ||||||
\(189\) | 0.539926 | + | 1.66172i | 0.0392739 | + | 0.120873i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8605 | − | 7.89064i | 0.785841 | − | 0.570947i | −0.120885 | − | 0.992666i | \(-0.538573\pi\) |
0.906726 | + | 0.421720i | \(0.138573\pi\) | |||||||
\(192\) | 2.01630 | + | 0.655137i | 0.145514 | + | 0.0472804i | ||||
\(193\) | −7.20693 | − | 2.34167i | −0.518766 | − | 0.168557i | 0.0379190 | − | 0.999281i | \(-0.487927\pi\) |
−0.556685 | + | 0.830723i | \(0.687927\pi\) | |||||||
\(194\) | −2.80806 | + | 2.04018i | −0.201607 | + | 0.146476i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.63233 | − | 5.02379i | −0.116595 | − | 0.358842i | ||||
\(197\) | − | 6.89118i | − | 0.490976i | −0.969400 | − | 0.245488i | \(-0.921052\pi\) | ||
0.969400 | − | 0.245488i | \(-0.0789483\pi\) | |||||||
\(198\) | −5.28215 | + | 2.96980i | −0.375386 | + | 0.211055i | ||||
\(199\) | −0.639398 | −0.0453257 | −0.0226629 | − | 0.999743i | \(-0.507214\pi\) | ||||
−0.0226629 | + | 0.999743i | \(0.507214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.283551 | + | 0.206012i | 0.0200002 | + | 0.0145310i | ||||
\(202\) | −7.20624 | − | 9.91854i | −0.507029 | − | 0.697866i | ||||
\(203\) | −9.20292 | − | 2.99021i | −0.645918 | − | 0.209872i | ||||
\(204\) | 3.03158 | − | 9.33024i | 0.212253 | − | 0.653248i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.27737 | + | 4.56078i | 0.437365 | + | 0.317765i | ||||
\(207\) | −7.94866 | + | 2.58268i | −0.552470 | + | 0.179508i | ||||
\(208\) | − | 26.1755i | − | 1.81495i | ||||||
\(209\) | −13.5167 | + | 14.6715i | −0.934966 | + | 1.01485i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.18090 | − | 3.63445i | −0.0812968 | − | 0.250206i | 0.902144 | − | 0.431435i | \(-0.141992\pi\) |
−0.983441 | + | 0.181229i | \(0.941992\pi\) | |||||||
\(212\) | 1.31433 | − | 1.80902i | 0.0902684 | − | 0.124244i | ||||
\(213\) | −2.66748 | − | 3.67147i | −0.182772 | − | 0.251565i | ||||
\(214\) | 8.87723 | − | 27.3213i | 0.606835 | − | 1.86765i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.978148 | + | 0.710666i | −0.0665545 | + | 0.0483547i | ||||
\(217\) | −0.0219411 | + | 0.0301993i | −0.00148946 | + | 0.00205006i | ||||
\(218\) | 7.36589 | − | 2.39332i | 0.498881 | − | 0.162096i | ||||
\(219\) | 10.1395 | 0.685165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.2758 | −2.64198 | ||||||||
\(222\) | −1.94905 | + | 0.633284i | −0.130812 | + | 0.0425033i | ||||
\(223\) | 15.7057 | − | 21.6171i | 1.05173 | − | 1.44758i | 0.164434 | − | 0.986388i | \(-0.447420\pi\) |
0.887298 | − | 0.461197i | \(-0.152580\pi\) | |||||||
\(224\) | −9.19975 | + | 6.68401i | −0.614684 | + | 0.446594i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.06312 | + | 12.5050i | −0.270275 | + | 0.831820i | ||||
\(227\) | −7.19291 | − | 9.90020i | −0.477411 | − | 0.657099i | 0.500594 | − | 0.865682i | \(-0.333115\pi\) |
−0.978005 | + | 0.208583i | \(0.933115\pi\) | |||||||
\(228\) | 4.73129 | − | 6.51206i | 0.313337 | − | 0.431272i | ||||
\(229\) | 2.06628 | + | 6.35937i | 0.136544 | + | 0.420239i | 0.995827 | − | 0.0912615i | \(-0.0290899\pi\) |
−0.859283 | + | 0.511500i | \(0.829090\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.671466 | − | 5.75590i | 0.0441792 | − | 0.378710i | ||||
\(232\) | − | 6.69598i | − | 0.439612i | ||||||
\(233\) | −6.19844 | + | 2.01399i | −0.406073 | + | 0.131941i | −0.504930 | − | 0.863161i | \(-0.668482\pi\) |
0.0988565 | + | 0.995102i | \(0.468482\pi\) | |||||||
\(234\) | −7.91949 | − | 5.75385i | −0.517714 | − | 0.376141i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.34204 | − | 7.20806i | 0.152454 | − | 0.469205i | ||||
\(237\) | −2.43852 | − | 0.792323i | −0.158399 | − | 0.0514669i | ||||
\(238\) | 13.7555 | + | 18.9328i | 0.891637 | + | 1.22723i | ||||
\(239\) | −8.77126 | − | 6.37269i | −0.567366 | − | 0.412215i | 0.266782 | − | 0.963757i | \(-0.414040\pi\) |
−0.834147 | + | 0.551542i | \(0.814040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.1803 | 1.75084 | 0.875420 | − | 0.483363i | \(-0.160585\pi\) | ||||
0.875420 | + | 0.483363i | \(0.160585\pi\) | |||||||
\(242\) | 20.0306 | − | 1.64409i | 1.28762 | − | 0.105686i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −3.83761 | − | 11.8109i | −0.245678 | − | 0.756118i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.40977 | + | 3.93043i | −0.344914 | + | 0.250595i | ||||
\(247\) | −30.6483 | − | 9.95823i | −1.95010 | − | 0.633627i | ||||
\(248\) | −0.0245663 | − | 0.00798208i | −0.00155996 | − | 0.000506862i | ||||
\(249\) | 13.0094 | − | 9.45188i | 0.824437 | − | 0.598989i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.71332 | + | 5.27307i | 0.108144 | + | 0.332833i | 0.990455 | − | 0.137833i | \(-0.0440137\pi\) |
−0.882311 | + | 0.470666i | \(0.844014\pi\) | |||||||
\(252\) | 2.33826i | 0.147297i | ||||||||
\(253\) | 27.5327 | + | 3.21188i | 1.73097 | + | 0.201929i | ||||
\(254\) | −23.1804 | −1.45447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9451 | − | 12.3113i | −1.05907 | − | 0.769457i | ||||
\(257\) | 11.1350 | + | 15.3260i | 0.694580 | + | 0.956008i | 0.999993 | + | 0.00378765i | \(0.00120565\pi\) |
−0.305413 | + | 0.952220i | \(0.598794\pi\) | |||||||
\(258\) | −3.42233 | − | 1.11198i | −0.213065 | − | 0.0692291i | ||||
\(259\) | 0.605607 | − | 1.86387i | 0.0376306 | − | 0.115815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.48048 | − | 3.25526i | −0.277335 | − | 0.201496i | ||||
\(262\) | 1.68571 | − | 0.547722i | 0.104144 | − | 0.0338384i | ||||
\(263\) | − | 3.20873i | − | 0.197859i | −0.995094 | − | 0.0989293i | \(-0.968458\pi\) | ||
0.995094 | − | 0.0989293i | \(-0.0315418\pi\) | |||||||
\(264\) | 3.93162 | − | 0.788907i | 0.241974 | − | 0.0485539i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.93355 | + | 18.2616i | 0.363809 | + | 1.11969i | ||||
\(267\) | 8.52651 | − | 11.7357i | 0.521814 | − | 0.718215i | ||||
\(268\) | 0.275698 | + | 0.379466i | 0.0168409 | + | 0.0231796i | ||||
\(269\) | 1.00252 | − | 3.08544i | 0.0611248 | − | 0.188123i | −0.915831 | − | 0.401563i | \(-0.868467\pi\) |
0.976956 | + | 0.213441i | \(0.0684669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.64212 | − | 1.19307i | 0.0997517 | − | 0.0724738i | −0.536791 | − | 0.843715i | \(-0.680364\pi\) |
0.636543 | + | 0.771241i | \(0.280364\pi\) | |||||||
\(272\) | −21.0514 | + | 28.9747i | −1.27643 | + | 1.75685i | ||||
\(273\) | 8.90304 | − | 2.89277i | 0.538836 | − | 0.175078i | ||||
\(274\) | −7.71096 | −0.465836 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.1848 | −0.673246 | ||||||||
\(277\) | −10.7627 | + | 3.49701i | −0.646668 | + | 0.210115i | −0.613944 | − | 0.789349i | \(-0.710418\pi\) |
−0.0327234 | + | 0.999464i | \(0.510418\pi\) | |||||||
\(278\) | −9.50268 | + | 13.0793i | −0.569933 | + | 0.784446i | ||||
\(279\) | −0.0172840 | + | 0.0125576i | −0.00103477 | + | 0.000751802i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.18835 | + | 9.81272i | −0.190201 | + | 0.585378i | −0.999999 | − | 0.00133051i | \(-0.999576\pi\) |
0.809798 | + | 0.586708i | \(0.199576\pi\) | |||||||
\(282\) | 4.10194 | + | 5.64583i | 0.244267 | + | 0.336205i | ||||
\(283\) | 1.23781 | − | 1.70370i | 0.0735801 | − | 0.101274i | −0.770641 | − | 0.637270i | \(-0.780064\pi\) |
0.844221 | + | 0.535996i | \(0.180064\pi\) | |||||||
\(284\) | −1.87674 | − | 5.77602i | −0.111364 | − | 0.342744i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9113 | + | 28.3003i | 0.940858 | + | 1.67343i | ||||
\(287\) | − | 6.39459i | − | 0.377461i | ||||||
\(288\) | −6.18975 | + | 2.01117i | −0.364734 | + | 0.118509i | ||||
\(289\) | 29.7227 | + | 21.5948i | 1.74839 | + | 1.27028i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.587045 | − | 1.80674i | 0.0344132 | − | 0.105913i | ||||
\(292\) | 12.9052 | + | 4.19315i | 0.755220 | + | 0.245386i | ||||
\(293\) | −13.7398 | − | 18.9111i | −0.802685 | − | 1.10480i | −0.992411 | − | 0.122964i | \(-0.960760\pi\) |
0.189726 | − | 0.981837i | \(-0.439240\pi\) | |||||||
\(294\) | 5.83448 | + | 4.23900i | 0.340274 | + | 0.247223i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.35614 | 0.0788238 | ||||||||
\(297\) | 1.38348 | − | 3.01430i | 0.0802778 | − | 0.174907i | ||||
\(298\) | − | 17.4552i | − | 1.01115i | ||||||
\(299\) | 13.8372 | + | 42.5867i | 0.800228 | + | 2.46285i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.78398 | − | 2.02268i | 0.160466 | − | 0.116585i | ||||
\(302\) | −11.7320 | − | 3.81196i | −0.675100 | − | 0.219353i | ||||
\(303\) | 6.38170 | + | 2.07354i | 0.366619 | + | 0.119122i | ||||
\(304\) | −23.7735 | + | 17.2725i | −1.36351 | + | 0.990645i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.13893 | + | 12.7383i | 0.236607 | + | 0.728201i | ||||
\(307\) | − | 32.0518i | − | 1.82929i | −0.404256 | − | 0.914646i | \(-0.632469\pi\) | ||
0.404256 | − | 0.914646i | \(-0.367531\pi\) | |||||||
\(308\) | 3.23494 | − | 7.04821i | 0.184328 | − | 0.401609i | ||||
\(309\) | −4.24678 | −0.241591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.32220 | − | 0.960634i | −0.0749751 | − | 0.0544726i | 0.549666 | − | 0.835384i | \(-0.314755\pi\) |
−0.624641 | + | 0.780912i | \(0.714755\pi\) | |||||||
\(312\) | 3.80755 | + | 5.24064i | 0.215560 | + | 0.296693i | ||||
\(313\) | −28.9245 | − | 9.39813i | −1.63491 | − | 0.531214i | −0.659516 | − | 0.751691i | \(-0.729239\pi\) |
−0.975392 | + | 0.220477i | \(0.929239\pi\) | |||||||
\(314\) | 7.14811 | − | 21.9996i | 0.403391 | − | 1.24151i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.77599 | − | 2.01688i | −0.156162 | − | 0.113458i | ||||
\(317\) | 27.9934 | − | 9.09561i | 1.57227 | − | 0.510861i | 0.612217 | − | 0.790690i | \(-0.290278\pi\) |
0.960050 | + | 0.279829i | \(0.0902778\pi\) | |||||||
\(318\) | 3.05284i | 0.171195i | ||||||||
\(319\) | 9.00190 | + | 16.0110i | 0.504010 | + | 0.896443i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.85867 | + | 14.9534i | 0.271185 | + | 0.834620i | ||||
\(322\) | 15.6826 | − | 21.5853i | 0.873958 | − | 1.20290i | ||||
\(323\) | 25.9170 | + | 35.6717i | 1.44206 | + | 1.98482i | ||||
\(324\) | −0.413545 | + | 1.27276i | −0.0229747 | + | 0.0707090i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 34.5972 | − | 25.1363i | 1.91616 | − | 1.39217i | ||||
\(327\) | −2.49159 | + | 3.42939i | −0.137786 | + | 0.189645i | ||||
\(328\) | 4.20837 | − | 1.36738i | 0.232368 | − | 0.0755010i | ||||
\(329\) | −6.67364 | −0.367929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7902 | −1.25266 | −0.626332 | − | 0.779557i | \(-0.715444\pi\) | ||||
−0.626332 | + | 0.779557i | \(0.715444\pi\) | |||||||
\(332\) | 20.4666 | − | 6.65002i | 1.12325 | − | 0.364967i | ||||
\(333\) | 0.659288 | − | 0.907432i | 0.0361287 | − | 0.0497270i | ||||
\(334\) | 4.51117 | − | 3.27756i | 0.246840 | − | 0.179340i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.63785 | − | 8.11848i | 0.143907 | − | 0.442899i | ||||
\(337\) | 8.51705 | + | 11.7227i | 0.463954 | + | 0.638577i | 0.975323 | − | 0.220784i | \(-0.0708615\pi\) |
−0.511369 | + | 0.859361i | \(0.670862\pi\) | |||||||
\(338\) | −16.8663 | + | 23.2145i | −0.917406 | + | 1.26270i | ||||
\(339\) | −2.22382 | − | 6.84421i | −0.120781 | − | 0.371727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0694723 | − | 0.0139401i | 0.00376213 | − | 0.000754899i | ||||
\(342\) | 10.9896i | 0.594247i | ||||||||
\(343\) | −18.1911 | + | 5.91066i | −0.982229 | + | 0.319146i | ||||
\(344\) | 1.92646 | + | 1.39966i | 0.103868 | + | 0.0754644i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.03783 | − | 27.8156i | 0.485877 | − | 1.49537i | ||||
\(347\) | 4.17255 | + | 1.35574i | 0.223994 | + | 0.0727802i | 0.418864 | − | 0.908049i | \(-0.362428\pi\) |
−0.194870 | + | 0.980829i | \(0.562428\pi\) | |||||||
\(348\) | −4.35639 | − | 5.99606i | −0.233527 | − | 0.321422i | ||||
\(349\) | 11.6548 | + | 8.46769i | 0.623866 | + | 0.453265i | 0.854270 | − | 0.519830i | \(-0.174005\pi\) |
−0.230404 | + | 0.973095i | \(0.574005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.35772 | 0.285974 | ||||||||
\(352\) | 21.4401 | + | 2.50114i | 1.14276 | + | 0.133311i | ||||
\(353\) | 6.01065i | 0.319914i | 0.987124 | + | 0.159957i | \(0.0511356\pi\) | ||||
−0.987124 | + | 0.159957i | \(0.948864\pi\) | |||||||
\(354\) | 3.19752 | + | 9.84096i | 0.169946 | + | 0.523041i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.7055 | − | 11.4107i | 0.832389 | − | 0.604766i | ||||
\(357\) | −12.1816 | − | 3.95804i | −0.644718 | − | 0.209482i | ||||
\(358\) | 33.5354 | + | 10.8963i | 1.77240 | + | 0.575888i | ||||
\(359\) | −1.98787 | + | 1.44428i | −0.104916 | + | 0.0762259i | −0.639006 | − | 0.769201i | \(-0.720654\pi\) |
0.534090 | + | 0.845427i | \(0.320654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.30818 | + | 16.3369i | 0.279378 | + | 0.859836i | ||||
\(362\) | − | 22.2742i | − | 1.17070i | ||||||
\(363\) | −8.34045 | + | 7.17195i | −0.437760 | + | 0.376430i | ||||
\(364\) | 12.5277 | 0.656632 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.7169 | + | 9.96589i | 0.716992 | + | 0.520926i | ||||
\(367\) | −0.869862 | − | 1.19726i | −0.0454064 | − | 0.0624966i | 0.785710 | − | 0.618595i | \(-0.212298\pi\) |
−0.831116 | + | 0.556098i | \(0.812298\pi\) | |||||||
\(368\) | 38.8338 | + | 12.6179i | 2.02435 | + | 0.657752i | ||||
\(369\) | 1.13095 | − | 3.48070i | 0.0588749 | − | 0.181198i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.36186 | − | 1.71599i | −0.122622 | − | 0.0890898i | ||||
\(372\) | −0.0271915 | + | 0.00883507i | −0.00140982 | + | 0.000458077i | ||||
\(373\) | 24.3331i | 1.25992i | 0.776627 | + | 0.629961i | \(0.216929\pi\) | ||||
−0.776627 | + | 0.629961i | \(0.783071\pi\) | |||||||
\(374\) | 5.14728 | − | 44.1232i | 0.266159 | − | 2.28156i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.42705 | − | 4.39201i | −0.0735945 | − | 0.226501i | ||||
\(377\) | −17.4408 | + | 24.0052i | −0.898245 | + | 1.23633i | ||||
\(378\) | −1.87642 | − | 2.58268i | −0.0965128 | − | 0.132839i | ||||
\(379\) | −4.92299 | + | 15.1514i | −0.252877 | + | 0.778276i | 0.741363 | + | 0.671104i | \(0.234180\pi\) |
−0.994241 | + | 0.107172i | \(0.965820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.2640 | − | 7.45726i | 0.525842 | − | 0.382047i | ||||
\(382\) | −14.4169 | + | 19.8432i | −0.737634 | + | 1.01527i | ||||
\(383\) | −3.72809 | + | 1.21133i | −0.190496 | + | 0.0618960i | −0.402712 | − | 0.915327i | \(-0.631932\pi\) |
0.212215 | + | 0.977223i | \(0.431932\pi\) | |||||||
\(384\) | 9.14301 | 0.466577 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8454 | 0.704710 | ||||||||
\(387\) | 1.87310 | − | 0.608609i | 0.0952153 | − | 0.0309373i | ||||
\(388\) | 1.49434 | − | 2.05678i | 0.0758635 | − | 0.104417i | ||||
\(389\) | −28.5510 | + | 20.7435i | −1.44759 | + | 1.05174i | −0.461209 | + | 0.887292i | \(0.652584\pi\) |
−0.986386 | + | 0.164447i | \(0.947416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9328 | − | 58.2693i | 0.957475 | − | 2.94680i | ||||
\(392\) | −2.80511 | − | 3.86090i | −0.141679 | − | 0.195005i | ||||
\(393\) | −0.570212 | + | 0.784829i | −0.0287634 | + | 0.0395894i | ||||
\(394\) | 3.89078 | + | 11.9746i | 0.196015 | + | 0.603271i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.00739 | − | 3.26435i | 0.151127 | − | 0.164040i | ||||
\(397\) | 23.2231i | 1.16553i | 0.812639 | + | 0.582767i | \(0.198030\pi\) | ||||
−0.812639 | + | 0.582767i | \(0.801970\pi\) | |||||||
\(398\) | 1.11106 | − | 0.361006i | 0.0556925 | − | 0.0180956i | ||||
\(399\) | −8.50217 | − | 6.17719i | −0.425641 | − | 0.309246i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.75973 | − | 5.41589i | 0.0878766 | − | 0.270457i | −0.897455 | − | 0.441106i | \(-0.854586\pi\) |
0.985332 | + | 0.170649i | \(0.0545864\pi\) | |||||||
\(402\) | −0.609032 | − | 0.197887i | −0.0303758 | − | 0.00986969i | ||||
\(403\) | 0.0672799 | + | 0.0926028i | 0.00335145 | + | 0.00461287i | ||||
\(404\) | 7.26488 | + | 5.27824i | 0.361441 | + | 0.262602i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.6799 | 0.877438 | ||||||||
\(407\) | −3.24270 | + | 1.82315i | −0.160735 | + | 0.0903704i | ||||
\(408\) | − | 8.86324i | − | 0.438796i | ||||||
\(409\) | −7.86540 | − | 24.2072i | −0.388919 | − | 1.19697i | −0.933597 | − | 0.358324i | \(-0.883348\pi\) |
0.544679 | − | 0.838645i | \(-0.316652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.41434 | − | 2.48066i | 0.168417 | − | 0.122362i | ||||
\(412\) | −5.40515 | − | 1.75624i | −0.266292 | − | 0.0865237i | ||||
\(413\) | −9.41086 | − | 3.05777i | −0.463078 | − | 0.150463i | ||||
\(414\) | 12.3539 | − | 8.97566i | 0.607163 | − | 0.441130i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.7753 | + | 33.1629i | 0.528301 | + | 1.62594i | ||||
\(417\) | − | 8.84846i | − | 0.433311i | ||||||
\(418\) | 15.2039 | − | 33.1258i | 0.743645 | − | 1.62023i | ||||
\(419\) | 13.4850 | 0.658786 | 0.329393 | − | 0.944193i | \(-0.393156\pi\) | ||||
0.329393 | + | 0.944193i | \(0.393156\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38633 | − | 1.73377i | −0.116303 | − | 0.0844990i | 0.528113 | − | 0.849174i | \(-0.322900\pi\) |
−0.644416 | + | 0.764675i | \(0.722900\pi\) | |||||||
\(422\) | 4.10404 | + | 5.64872i | 0.199781 | + | 0.274975i | ||||
\(423\) | −3.63259 | − | 1.18030i | −0.176623 | − | 0.0573882i | ||||
\(424\) | 0.624271 | − | 1.92131i | 0.0303173 | − | 0.0933070i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.70810 | + | 4.87372i | 0.325009 | + | 0.236133i | ||||
\(427\) | −15.4204 | + | 5.01039i | −0.746246 | + | 0.242470i | ||||
\(428\) | 21.0415i | 1.01708i | ||||||||
\(429\) | −16.1497 | − | 7.41230i | −0.779717 | − | 0.357869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.56072 | + | 10.9588i | 0.171514 | + | 0.527866i | 0.999457 | − | 0.0329464i | \(-0.0104891\pi\) |
−0.827943 | + | 0.560812i | \(0.810489\pi\) | |||||||
\(432\) | 2.87167 | − | 3.95252i | 0.138163 | − | 0.190166i | ||||
\(433\) | 6.56194 | + | 9.03174i | 0.315347 | + | 0.434038i | 0.937039 | − | 0.349224i | \(-0.113555\pi\) |
−0.621693 | + | 0.783261i | \(0.713555\pi\) | |||||||
\(434\) | 0.0210757 | − | 0.0648642i | 0.00101166 | − | 0.00311358i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.58941 | + | 3.33440i | −0.219793 | + | 0.159689i | ||||
\(437\) | 29.5479 | − | 40.6692i | 1.41347 | − | 1.94547i | ||||
\(438\) | −17.6191 | + | 5.72480i | −0.841874 | + | 0.273541i | ||||
\(439\) | −0.993624 | −0.0474231 | −0.0237115 | − | 0.999719i | \(-0.507548\pi\) | ||||
−0.0237115 | + | 0.999719i | \(0.507548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.94716 | −0.187960 | ||||||||
\(442\) | 68.2483 | − | 22.1752i | 3.24624 | − | 1.05477i | ||||
\(443\) | 6.45537 | − | 8.88506i | 0.306704 | − | 0.422142i | −0.627646 | − | 0.778499i | \(-0.715981\pi\) |
0.934350 | + | 0.356357i | \(0.115981\pi\) | |||||||
\(444\) | 1.21438 | − | 0.882299i | 0.0576320 | − | 0.0418721i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.0863 | + | 46.4307i | −0.714355 | + | 2.19856i | ||||
\(447\) | 5.61545 | + | 7.72900i | 0.265602 | + | 0.365569i | ||||
\(448\) | 2.17731 | − | 2.99681i | 0.102868 | − | 0.141586i | ||||
\(449\) | −8.96777 | − | 27.5999i | −0.423215 | − | 1.30252i | −0.904693 | − | 0.426064i | \(-0.859900\pi\) |
0.481478 | − | 0.876458i | \(-0.340100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.22451 | + | 8.92722i | −0.387277 | + | 0.420366i | ||||
\(452\) | − | 9.63070i | − | 0.452990i | ||||||
\(453\) | 6.42113 | − | 2.08635i | 0.301691 | − | 0.0980254i | ||||
\(454\) | 18.0886 | + | 13.1421i | 0.848938 | + | 0.616790i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.24724 | − | 6.91629i | 0.105237 | − | 0.323885i | ||||
\(457\) | −3.38262 | − | 1.09908i | −0.158232 | − | 0.0514129i | 0.228830 | − | 0.973466i | \(-0.426510\pi\) |
−0.387062 | + | 0.922054i | \(0.626510\pi\) | |||||||
\(458\) | −7.18103 | − | 9.88383i | −0.335547 | − | 0.461841i | ||||
\(459\) | −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 | \(0.300528\pi\) | |||||||
\(462\) | 2.08301 | + | 10.3809i | 0.0969104 | + | 0.482965i | ||||
\(463\) | 17.8743i | 0.830690i | 0.909664 | + | 0.415345i | \(0.136339\pi\) | ||||
−0.909664 | + | 0.415345i | \(0.863661\pi\) | |||||||
\(464\) | 8.36114 | + | 25.7329i | 0.388156 | + | 1.19462i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.63371 | − | 6.99930i | 0.446273 | − | 0.324236i | ||||
\(467\) | −23.9906 | − | 7.79502i | −1.11015 | − | 0.360711i | −0.304151 | − | 0.952624i | \(-0.598373\pi\) |
−0.806002 | + | 0.591913i | \(0.798373\pi\) | |||||||
\(468\) | 6.81910 | + | 2.21566i | 0.315213 | + | 0.102419i | ||||
\(469\) | 0.495432 | − | 0.359952i | 0.0228769 | − | 0.0166210i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91229 | + | 12.0408i | 0.180269 | + | 0.554810i | ||||
\(472\) | − | 6.84727i | − | 0.315171i | ||||||
\(473\) | −6.48809 | − | 0.756881i | −0.298323 | − | 0.0348014i | ||||
\(474\) | 4.68468 | 0.215175 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.8674 | − | 10.0753i | −0.635613 | − | 0.461800i | ||||
\(477\) | −0.982116 | − | 1.35177i | −0.0449680 | − | 0.0618931i | ||||
\(478\) | 18.8396 | + | 6.12135i | 0.861702 | + | 0.279984i | ||||
\(479\) | 1.61793 | − | 4.97948i | 0.0739252 | − | 0.227518i | −0.907266 | − | 0.420558i | \(-0.861834\pi\) |
0.981191 | + | 0.193039i | \(0.0618345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.86176 | − | 3.53228i | −0.221677 | − | 0.161058i | ||||
\(482\) | −47.2304 | + | 15.3461i | −2.15128 | + | 0.698995i | ||||
\(483\) | 14.6029i | 0.664456i | ||||||||
\(484\) | −13.5813 | + | 5.67904i | −0.617333 | + | 0.258138i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.564602 | − | 1.73767i | −0.0256109 | − | 0.0788222i | ||||
\(487\) | 5.31656 | − | 7.31762i | 0.240917 | − | 0.331593i | −0.671388 | − | 0.741106i | \(-0.734301\pi\) |
0.912304 | + | 0.409513i | \(0.134301\pi\) | |||||||
\(488\) | −6.59482 | − | 9.07699i | −0.298533 | − | 0.410896i | ||||
\(489\) | −7.23278 | + | 22.2602i | −0.327078 | + | 1.00664i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.1629 | − | 20.4615i | 1.27097 | − | 0.923416i | 0.271733 | − | 0.962373i | \(-0.412403\pi\) |
0.999241 | + | 0.0389565i | \(0.0124034\pi\) | |||||||
\(492\) | 2.87886 | − | 3.96241i | 0.129789 | − | 0.178639i | ||||
\(493\) | 38.6117 | − | 12.5457i | 1.73898 | − | 0.565030i | ||||
\(494\) | 58.8789 | 2.64909 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.104377 | 0.00468664 | ||||||||
\(497\) | −7.54120 | + | 2.45028i | −0.338269 | + | 0.109910i | ||||
\(498\) | −17.2694 | + | 23.7694i | −0.773862 | + | 1.06513i | ||||
\(499\) | 15.8561 | − | 11.5201i | 0.709815 | − | 0.515711i | −0.173299 | − | 0.984869i | \(-0.555443\pi\) |
0.883114 | + | 0.469158i | \(0.155443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.943091 | + | 2.90254i | −0.0421342 | + | 0.129676i | ||||
\(502\) | −5.95437 | − | 8.19549i | −0.265757 | − | 0.365783i | ||||
\(503\) | −10.8247 | + | 14.8989i | −0.482647 | + | 0.664307i | −0.979011 | − | 0.203808i | \(-0.934668\pi\) |
0.496364 | + | 0.868115i | \(0.334668\pi\) | |||||||
\(504\) | 0.652802 | + | 2.00912i | 0.0290781 | + | 0.0894932i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −49.6561 | + | 9.96384i | −2.20748 | + | 0.442947i | ||||
\(507\) | − | 15.7051i | − | 0.697489i | ||||||
\(508\) | 16.1476 | − | 5.24667i | 0.716433 | − | 0.232783i | ||||
\(509\) | 1.00187 | + | 0.727900i | 0.0444070 | + | 0.0322636i | 0.609767 | − | 0.792580i | \(-0.291263\pi\) |
−0.565360 | + | 0.824844i | \(0.691263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.47459 | − | 16.8491i | 0.242182 | − | 0.745359i | ||||
\(512\) | 19.0048 | + | 6.17504i | 0.839902 | + | 0.272901i | ||||
\(513\) | −3.53540 | − | 4.86606i | −0.156092 | − | 0.214842i | ||||
\(514\) | −28.0019 | − | 20.3446i | −1.23511 | − | 0.897362i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.63570 | 0.116030 | ||||||||
\(517\) | 9.31678 | + | 8.58340i | 0.409752 | + | 0.377498i | ||||
\(518\) | 3.58071i | 0.157327i | ||||||||
\(519\) | 4.94657 | + | 15.2240i | 0.217130 | + | 0.668258i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.8472 | + | 19.5057i | −1.17620 | + | 0.854558i | −0.991738 | − | 0.128282i | \(-0.959054\pi\) |
−0.184461 | + | 0.982840i | \(0.559054\pi\) | |||||||
\(522\) | 9.62351 | + | 3.12687i | 0.421210 | + | 0.136859i | ||||
\(523\) | −12.5072 | − | 4.06383i | −0.546901 | − | 0.177699i | 0.0225177 | − | 0.999746i | \(-0.492832\pi\) |
−0.569419 | + | 0.822047i | \(0.692832\pi\) | |||||||
\(524\) | −1.05031 | + | 0.763092i | −0.0458829 | + | 0.0333359i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.81165 | + | 5.57570i | 0.0789919 | + | 0.243112i | ||||
\(527\) | − | 0.156615i | − | 0.00682224i | ||||||
\(528\) | −14.1243 | + | 7.94115i | −0.614681 | + | 0.345594i | ||||
\(529\) | −46.8514 | −2.03702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.58172 | − | 3.32882i | −0.198830 | − | 0.144458i | ||||
\(532\) | −8.26669 | − | 11.3781i | −0.358407 | − | 0.493304i | ||||
\(533\) | −18.6486 | − | 6.05930i | −0.807761 | − | 0.262458i | ||||
\(534\) | −8.19021 | + | 25.2069i | −0.354425 | + | 1.09081i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.342830 | + | 0.249080i | 0.0148080 | + | 0.0107586i | ||||
\(537\) | −18.3545 | + | 5.96375i | −0.792057 | + | 0.257355i | ||||
\(538\) | 5.92750i | 0.255553i | ||||||||
\(539\) | 11.8979 | + | 5.46082i | 0.512479 | + | 0.235214i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0900 | + | 31.0538i | 0.433802 | + | 1.33511i | 0.894309 | + | 0.447450i | \(0.147668\pi\) |
−0.460507 | + | 0.887656i | \(0.652332\pi\) | |||||||
\(542\) | −2.17985 | + | 3.00030i | −0.0936324 | + | 0.128874i | ||||
\(543\) | 7.16572 | + | 9.86277i | 0.307511 | + | 0.423252i | ||||
\(544\) | 14.7433 | − | 45.3752i | 0.632114 | − | 1.94545i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.8372 | + | 10.0533i | −0.592179 | + | 0.430243i | ||||
\(547\) | 16.2845 | − | 22.4136i | 0.696273 | − | 0.958338i | −0.303711 | − | 0.952764i | \(-0.598226\pi\) |
0.999984 | − | 0.00557389i | \(-0.00177423\pi\) | |||||||
\(548\) | 5.37150 | − | 1.74531i | 0.229459 | − | 0.0745558i | ||||
\(549\) | −9.27977 | −0.396051 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.3110 | 1.41909 | ||||||||
\(552\) | −9.61038 | + | 3.12260i | −0.409045 | + | 0.132907i | ||||
\(553\) | −2.63324 | + | 3.62435i | −0.111977 | + | 0.154123i | ||||
\(554\) | 16.7276 | − | 12.1533i | 0.710686 | − | 0.516343i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.65924 | − | 11.2620i | 0.155186 | − | 0.477614i | ||||
\(557\) | 13.7690 | + | 18.9514i | 0.583411 | + | 0.802996i | 0.994064 | − | 0.108795i | \(-0.0346993\pi\) |
−0.410653 | + | 0.911792i | \(0.634699\pi\) | |||||||
\(558\) | 0.0229438 | − | 0.0315794i | 0.000971289 | − | 0.00133686i | ||||
\(559\) | −3.26075 | − | 10.0356i | −0.137915 | − | 0.424459i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.9155 | + | 21.1932i | 0.503073 | + | 0.894778i | ||||
\(562\) | − | 18.8514i | − | 0.795198i | ||||||
\(563\) | 21.0046 | − | 6.82482i | 0.885240 | − | 0.287632i | 0.169108 | − | 0.985597i | \(-0.445911\pi\) |
0.716131 | + | 0.697966i | \(0.245911\pi\) | |||||||
\(564\) | −4.13532 | − | 3.00448i | −0.174128 | − | 0.126512i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.18899 | + | 3.65933i | −0.0499769 | + | 0.153813i | ||||
\(567\) | 1.66172 | + | 0.539926i | 0.0697858 | + | 0.0226748i | ||||
\(568\) | −3.22513 | − | 4.43901i | −0.135323 | − | 0.186257i | ||||
\(569\) | −11.1119 | − | 8.07328i | −0.465836 | − | 0.338449i | 0.329980 | − | 0.943988i | \(-0.392958\pi\) |
−0.795816 | + | 0.605538i | \(0.792958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.5201 | −1.10983 | −0.554915 | − | 0.831907i | \(-0.687249\pi\) | ||||
−0.554915 | + | 0.831907i | \(0.687249\pi\) | |||||||
\(572\) | −17.4894 | − | 16.1127i | −0.731271 | − | 0.673708i | ||||
\(573\) | − | 13.4244i | − | 0.560811i | ||||||
\(574\) | 3.61040 | + | 11.1117i | 0.150695 | + | 0.463792i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.71517 | − | 1.24614i | 0.0714654 | − | 0.0519227i | ||||
\(577\) | 5.40927 | + | 1.75758i | 0.225191 | + | 0.0731690i | 0.419439 | − | 0.907783i | \(-0.362227\pi\) |
−0.194248 | + | 0.980952i | \(0.562227\pi\) | |||||||
\(578\) | −63.8405 | − | 20.7430i | −2.65542 | − | 0.862797i | ||||
\(579\) | −6.13058 | + | 4.45413i | −0.254778 | + | 0.185107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.68228 | − | 26.7213i | −0.360202 | − | 1.10859i | ||||
\(582\) | 3.47096i | 0.143876i | ||||||||
\(583\) | 1.09024 | + | 5.43336i | 0.0451532 | + | 0.225027i | ||||
\(584\) | 12.2593 | 0.507292 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.5524 | + | 25.1038i | 1.42735 | + | 1.03703i | ||||
\(587\) | −7.96215 | − | 10.9590i | −0.328633 | − | 0.452324i | 0.612446 | − | 0.790513i | \(-0.290186\pi\) |
−0.941078 | + | 0.338188i | \(0.890186\pi\) | |||||||
\(588\) | −5.02379 | − | 1.63233i | −0.207178 | − | 0.0673161i | ||||
\(589\) | 0.0397090 | − | 0.122212i | 0.00163618 | − | 0.00503565i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.57508 | − | 4.05054i | −0.229328 | − | 0.166617i | ||||
\(592\) | −5.21169 | + | 1.69338i | −0.214199 | + | 0.0695975i | ||||
\(593\) | − | 21.1786i | − | 0.869702i | −0.900502 | − | 0.434851i | \(-0.856801\pi\) | ||
0.900502 | − | 0.434851i | \(-0.143199\pi\) | |||||||
\(594\) | −0.702153 | + | 6.01896i | −0.0288097 | + | 0.246961i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.95083 | + | 12.1594i | 0.161833 | + | 0.498069i | ||||
\(597\) | −0.375829 | + | 0.517284i | −0.0153816 | + | 0.0211710i | ||||
\(598\) | −48.0890 | − | 66.1889i | −1.96651 | − | 2.70666i | ||||
\(599\) | 10.4573 | − | 32.1842i | 0.427273 | − | 1.31501i | −0.473529 | − | 0.880778i | \(-0.657020\pi\) |
0.900801 | − | 0.434231i | \(-0.142980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.7186 | + | 17.2325i | −0.967500 | + | 0.702930i | −0.954880 | − | 0.296990i | \(-0.904017\pi\) |
−0.0126196 | + | 0.999920i | \(0.504017\pi\) | |||||||
\(602\) | −3.69562 | + | 5.08658i | −0.150622 | + | 0.207313i | ||||
\(603\) | 0.333334 | − | 0.108307i | 0.0135744 | − | 0.00441060i | ||||
\(604\) | 9.03538 | 0.367644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.2600 | −0.498028 | ||||||||
\(607\) | −6.82370 | + | 2.21715i | −0.276965 | + | 0.0899915i | −0.444206 | − | 0.895925i | \(-0.646514\pi\) |
0.167241 | + | 0.985916i | \(0.446514\pi\) | |||||||
\(608\) | 23.0094 | − | 31.6697i | 0.933154 | − | 1.28438i | ||||
\(609\) | −7.82847 | + | 5.68772i | −0.317226 | + | 0.230478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.32372 | + | 19.4624i | −0.255830 | + | 0.787364i | ||||
\(612\) | −5.76641 | − | 7.93678i | −0.233093 | − | 0.320825i | ||||
\(613\) | 16.1667 | − | 22.2515i | 0.652967 | − | 0.898731i | −0.346257 | − | 0.938140i | \(-0.612547\pi\) |
0.999223 | + | 0.0394084i | \(0.0125473\pi\) | |||||||
\(614\) | 18.0965 | + | 55.6953i | 0.730315 | + | 2.24768i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.811840 | − | 6.95921i | 0.0327100 | − | 0.280395i | ||||
\(617\) | 24.0712i | 0.969068i | 0.874772 | + | 0.484534i | \(0.161011\pi\) | ||||
−0.874772 | + | 0.484534i | \(0.838989\pi\) | |||||||
\(618\) | 7.37950 | − | 2.39774i | 0.296847 | − | 0.0964514i | ||||
\(619\) | 21.8216 | + | 15.8543i | 0.877083 | + | 0.637238i | 0.932478 | − | 0.361227i | \(-0.117642\pi\) |
−0.0553955 | + | 0.998464i | \(0.517642\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58268 | + | 7.94866i | −0.103639 | + | 0.318969i | ||||
\(622\) | 2.83992 | + | 0.922745i | 0.113870 | + | 0.0369987i | ||||
\(623\) | −14.8978 | − | 20.5051i | −0.596870 | − | 0.821521i | ||||
\(624\) | −21.1765 | − | 15.3856i | −0.847737 | − | 0.615917i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 55.5673 | 2.22092 | ||||||||
\(627\) | 3.92463 | + | 19.5589i | 0.156735 | + | 0.781108i | ||||
\(628\) | 16.9430i | 0.676098i | ||||||||
\(629\) | 2.54088 | + | 7.82003i | 0.101312 | + | 0.311805i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.87681 | + | 5.72284i | −0.313571 | + | 0.227823i | −0.733427 | − | 0.679768i | \(-0.762080\pi\) |
0.419856 | + | 0.907591i | \(0.362080\pi\) | |||||||
\(632\) | −2.94831 | − | 0.957964i | −0.117277 | − | 0.0381058i | ||||
\(633\) | −3.63445 | − | 1.18090i | −0.144456 | − | 0.0469367i | ||||
\(634\) | −43.5078 | + | 31.6103i | −1.72792 | + | 1.25540i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.690983 | − | 2.12663i | −0.0273993 | − | 0.0843262i | ||||
\(637\) | 21.1478i | 0.837904i | ||||||||
\(638\) | −24.6821 | − | 22.7393i | −0.977175 | − | 0.900256i | ||||
\(639\) | −4.53818 | −0.179528 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3196 | − | 14.7631i | −0.802577 | − | 0.583107i | 0.109092 | − | 0.994032i | \(-0.465206\pi\) |
−0.911669 | + | 0.410925i | \(0.865206\pi\) | |||||||
\(642\) | −16.8855 | − | 23.2409i | −0.666418 | − | 0.917245i | ||||
\(643\) | 25.6079 | + | 8.32051i | 1.00988 | + | 0.328129i | 0.766806 | − | 0.641880i | \(-0.221845\pi\) |
0.243071 | + | 0.970008i | \(0.421845\pi\) | |||||||
\(644\) | −6.03897 | + | 18.5860i | −0.237969 | + | 0.732393i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −65.1754 | − | 47.3527i | −2.56429 | − | 1.86307i | ||||
\(647\) | 25.4893 | − | 8.28198i | 1.00209 | − | 0.325598i | 0.238389 | − | 0.971170i | \(-0.423381\pi\) |
0.763700 | + | 0.645572i | \(0.223381\pi\) | |||||||
\(648\) | 1.20906i | 0.0474962i | ||||||||
\(649\) | 9.20530 | + | 16.3728i | 0.361340 | + | 0.642687i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0115351 | + | 0.0355014i | 0.000452096 | + | 0.00139141i | ||||
\(652\) | −18.4112 | + | 25.3409i | −0.721039 | + | 0.992425i | ||||
\(653\) | 16.9066 | + | 23.2700i | 0.661608 | + | 0.910625i | 0.999533 | − | 0.0305480i | \(-0.00972525\pi\) |
−0.337926 | + | 0.941173i | \(0.609725\pi\) | |||||||
\(654\) | 2.39332 | − | 7.36589i | 0.0935863 | − | 0.288029i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.4655 | + | 10.5098i | −0.564784 | + | 0.410340i | ||||
\(657\) | 5.95986 | − | 8.20305i | 0.232516 | − | 0.320031i | ||||
\(658\) | 11.5966 | − | 3.76795i | 0.452081 | − | 0.146890i | ||||
\(659\) | −36.5327 | −1.42311 | −0.711556 | − | 0.702629i | \(-0.752009\pi\) | ||||
−0.711556 | + | 0.702629i | \(0.752009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7750 | −1.39149 | −0.695743 | − | 0.718291i | \(-0.744925\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(662\) | 39.6018 | − | 12.8674i | 1.53917 | − | 0.500106i | ||||
\(663\) | −23.0858 | + | 31.7748i | −0.896576 | + | 1.23403i | ||||
\(664\) | 15.7291 | − | 11.4279i | 0.610408 | − | 0.443487i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.633284 | + | 1.94905i | −0.0245393 | + | 0.0755241i | ||||
\(667\) | −27.2065 | − | 37.4466i | −1.05344 | − | 1.44994i | ||||
\(668\) | −2.40066 | + | 3.30423i | −0.0928844 | + | 0.127844i | ||||
\(669\) | −8.25698 | − | 25.4124i | −0.319233 | − | 0.982499i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.9720 | + | 12.8384i | 1.07985 | + | 0.495621i | ||||
\(672\) | 11.3715i | 0.438666i | ||||||||
\(673\) | −10.7388 | + | 3.48925i | −0.413951 | + | 0.134501i | −0.508586 | − | 0.861011i | \(-0.669832\pi\) |
0.0946349 | + | 0.995512i | \(0.469832\pi\) | |||||||
\(674\) | −21.4185 | − | 15.5614i | −0.825009 | − | 0.599404i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.49478 | − | 19.9889i | 0.249799 | − | 0.768803i | ||||
\(677\) | −41.7108 | − | 13.5527i | −1.60308 | − | 0.520872i | −0.635212 | − | 0.772338i | \(-0.719087\pi\) |
−0.967866 | + | 0.251466i | \(0.919087\pi\) | |||||||
\(678\) | 7.72851 | + | 10.6374i | 0.296812 | + | 0.408526i | ||||
\(679\) | −2.68534 | − | 1.95101i | −0.103054 | − | 0.0748729i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2373 | −0.468935 | ||||||||
\(682\) | −0.112849 | + | 0.0634474i | −0.00432121 | + | 0.00242953i | ||||
\(683\) | 18.5355i | 0.709241i | 0.935010 | + | 0.354620i | \(0.115390\pi\) | ||||
−0.935010 | + | 0.354620i | \(0.884610\pi\) | |||||||
\(684\) | −2.48739 | − | 7.65539i | −0.0951076 | − | 0.292711i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 28.2730 | − | 20.5415i | 1.07947 | − | 0.784279i | ||||
\(687\) | 6.35937 | + | 2.06628i | 0.242625 | + | 0.0788337i | ||||
\(688\) | −9.15120 | − | 2.97341i | −0.348886 | − | 0.113360i | ||||
\(689\) | −7.24238 | + | 5.26190i | −0.275913 | + | 0.200462i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.71597 | − | 26.8250i | −0.331571 | − | 1.02047i | −0.968386 | − | 0.249455i | \(-0.919749\pi\) |
0.636815 | − | 0.771017i | \(-0.280251\pi\) | |||||||
\(692\) | 21.4221i | 0.814347i | ||||||||
\(693\) | −4.26194 | − | 3.92646i | −0.161898 | − | 0.149154i | ||||
\(694\) | −8.01596 | −0.304282 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.41716 | − | 3.93580i | −0.205337 | − | 0.149186i | ||||
\(697\) | 15.7698 | + | 21.7052i | 0.597322 | + | 0.822144i | ||||
\(698\) | −25.0330 | − | 8.13371i | −0.947512 | − | 0.307865i | ||||
\(699\) | −2.01399 | + | 6.19844i | −0.0761762 | + | 0.234446i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.255153 | − | 0.185379i | −0.00963699 | − | 0.00700168i | 0.582956 | − | 0.812503i | \(-0.301896\pi\) |
−0.592593 | + | 0.805502i | \(0.701896\pi\) | |||||||
\(702\) | −9.30992 | + | 3.02498i | −0.351380 | + | 0.114170i | ||||
\(703\) | 6.74647i | 0.254448i | ||||||||
\(704\) | −6.89405 | + | 1.38334i | −0.259829 | + | 0.0521366i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.39362 | − | 10.4445i | −0.127721 | − | 0.393084i | ||||
\(707\) | 6.89129 | − | 9.48505i | 0.259174 | − | 0.356722i | ||||
\(708\) | −4.45482 | − | 6.13154i | −0.167423 | − | 0.230437i | ||||
\(709\) | −12.0593 | + | 37.1146i | −0.452895 | + | 1.39387i | 0.420693 | + | 0.907203i | \(0.361787\pi\) |
−0.873589 | + | 0.486665i | \(0.838213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.07433 | + | 1.50709i | −0.0777934 | + | 0.0565202i | ||||
\(712\) | 10.3090 | − | 14.1892i | 0.386348 | − | 0.531762i | ||||
\(713\) | −0.169817 | + | 0.0551768i | −0.00635969 | + | 0.00206639i | ||||
\(714\) | 23.4023 | 0.875808 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8272 | −0.965209 | ||||||||
\(717\) | −10.3112 | + | 3.35032i | −0.385080 | + | 0.125120i | ||||
\(718\) | 2.63882 | − | 3.63203i | 0.0984800 | − | 0.135546i | ||||
\(719\) | 23.0320 | − | 16.7337i | 0.858948 | − | 0.624062i | −0.0686507 | − | 0.997641i | \(-0.521869\pi\) |
0.927598 | + | 0.373579i | \(0.121869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29295 | + | 7.05698i | −0.0853939 | + | 0.262816i | ||||
\(722\) | −18.4477 | − | 25.3911i | −0.686552 | − | 0.944957i | ||||
\(723\) | 15.9762 | − | 21.9894i | 0.594161 | − | 0.817793i | ||||
\(724\) | 5.04156 | + | 15.5163i | 0.187368 | + | 0.576659i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.4436 | − | 17.1715i | 0.387599 | − | 0.637294i | ||||
\(727\) | 45.8400i | 1.70011i | 0.526691 | + | 0.850057i | \(0.323432\pi\) | ||||
−0.526691 | + | 0.850057i | \(0.676568\pi\) | |||||||
\(728\) | 10.7643 | − | 3.49753i | 0.398951 | − | 0.129627i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.46153 | + | 13.7312i | −0.165016 | + | 0.507866i | ||||
\(732\) | −11.8109 | − | 3.83761i | −0.436545 | − | 0.141842i | ||||
\(733\) | 22.3171 | + | 30.7169i | 0.824301 | + | 1.13455i | 0.988957 | + | 0.148202i | \(0.0473487\pi\) |
−0.164656 | + | 0.986351i | \(0.552651\pi\) | |||||||
\(734\) | 2.18751 | + | 1.58932i | 0.0807423 | + | 0.0586627i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.3944 | −2.00500 | ||||||||
\(737\) | −1.15461 | − | 0.134693i | −0.0425306 | − | 0.00496149i | ||||
\(738\) | 6.68684i | 0.246146i | ||||||||
\(739\) | −6.52725 | − | 20.0888i | −0.240109 | − | 0.738979i | −0.996403 | − | 0.0847466i | \(-0.972992\pi\) |
0.756294 | − | 0.654232i | \(-0.227008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.0710 | + | 18.9417i | −0.957741 | + | 0.695840i | ||||
\(742\) | 5.07298 | + | 1.64831i | 0.186235 | + | 0.0605113i | ||||
\(743\) | −7.58976 | − | 2.46606i | −0.278441 | − | 0.0904711i | 0.166467 | − | 0.986047i | \(-0.446764\pi\) |
−0.444909 | + | 0.895576i | \(0.646764\pi\) | |||||||
\(744\) | −0.0208973 | + | 0.0151828i | −0.000766134 | + | 0.000556629i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.7385 | − | 42.2829i | −0.503004 | − | 1.54809i | ||||
\(747\) | − | 16.0805i | − | 0.588355i | ||||||
\(748\) | 6.40126 | + | 31.9015i | 0.234053 | + | 1.16643i | ||||
\(749\) | 27.4718 | 1.00380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.78664 | + | 5.65733i | 0.284139 | + | 0.206439i | 0.720721 | − | 0.693226i | \(-0.243811\pi\) |
−0.436582 | + | 0.899664i | \(0.643811\pi\) | |||||||
\(752\) | 10.9684 | + | 15.0968i | 0.399978 | + | 0.550523i | ||||
\(753\) | 5.27307 | + | 1.71332i | 0.192161 | + | 0.0624370i | ||||
\(754\) | 16.7529 | − | 51.5600i | 0.610104 | − | 1.87771i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.89169 | + | 1.37440i | 0.0688002 | + | 0.0499863i | ||||
\(757\) | 44.3338 | − | 14.4049i | 1.61134 | − | 0.523555i | 0.641462 | − | 0.767155i | \(-0.278328\pi\) |
0.969876 | + | 0.243600i | \(0.0783283\pi\) | |||||||
\(758\) | − | 29.1076i | − | 1.05724i | ||||||
\(759\) | 18.7818 | − | 20.3865i | 0.681735 | − | 0.739984i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.79661 | − | 20.9178i | −0.246377 | − | 0.758270i | −0.995407 | − | 0.0957342i | \(-0.969480\pi\) |
0.749030 | − | 0.662536i | \(-0.230520\pi\) | |||||||
\(762\) | −13.6251 | + | 18.7533i | −0.493585 | + | 0.679361i | ||||
\(763\) | 4.35341 | + | 5.99195i | 0.157604 | + | 0.216923i | ||||
\(764\) | 5.55158 | − | 17.0860i | 0.200849 | − | 0.618151i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.79425 | − | 4.20977i | 0.209355 | − | 0.152105i | ||||
\(767\) | −17.8348 | + | 24.5476i | −0.643979 | + | 0.886361i | ||||
\(768\) | −19.9201 | + | 6.47244i | −0.718805 | + | 0.233554i | ||||
\(769\) | −48.0330 | −1.73211 | −0.866057 | − | 0.499946i | \(-0.833353\pi\) | ||||
−0.866057 | + | 0.499946i | \(0.833353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9439 | 0.682249 | ||||||||
\(772\) | −9.64476 | + | 3.13377i | −0.347123 | + | 0.112787i | ||||
\(773\) | 10.0424 | − | 13.8222i | 0.361199 | − | 0.497148i | −0.589283 | − | 0.807927i | \(-0.700590\pi\) |
0.950482 | + | 0.310778i | \(0.100590\pi\) | |||||||
\(774\) | −2.91121 | + | 2.11512i | −0.104641 | + | 0.0760263i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.709771 | − | 2.18445i | 0.0254793 | − | 0.0784172i | ||||
\(777\) | −1.15193 | − | 1.58550i | −0.0413254 | − | 0.0568795i | ||||
\(778\) | 37.9003 | − | 52.1653i | 1.35879 | − | 1.87022i | ||||
\(779\) | 6.80242 | + | 20.9357i | 0.243722 | + | 0.750099i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6794 | + | 6.27849i | 0.489488 | + | 0.224662i | ||||
\(782\) | 111.942i | 4.00304i | ||||||||
\(783\) | −5.26712 | + | 1.71139i | −0.188232 | + | 0.0611602i | ||||
\(784\) | 15.6012 | + | 11.3349i | 0.557186 | + | 0.404819i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.547722 | − | 1.68571i | 0.0195366 | − | 0.0601275i | ||||
\(787\) | −21.3910 | − | 6.95034i | −0.762505 | − | 0.247753i | −0.0981518 | − | 0.995171i | \(-0.531293\pi\) |
−0.664354 | + | 0.747418i | \(0.731293\pi\) | |||||||
\(788\) | −5.42068 | − | 7.46092i | −0.193104 | − | 0.265784i | ||||
\(789\) | −2.59591 | − | 1.88604i | −0.0924170 | − | 0.0671449i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5739 | −0.447076 | ||||||||
\(792\) | 1.67271 | − | 3.64445i | 0.0594371 | − | 0.129500i | ||||
\(793\) | 49.7184i | 1.76555i | ||||||||
\(794\) | −13.1118 | − | 40.3540i | −0.465321 | − | 1.43211i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.692261 | + | 0.502957i | −0.0245365 | + | 0.0178268i | ||||
\(797\) | −3.25051 | − | 1.05615i | −0.115139 | − | 0.0374109i | 0.250881 | − | 0.968018i | \(-0.419280\pi\) |
−0.366020 | + | 0.930607i | \(0.619280\pi\) | |||||||
\(798\) | 18.2616 | + | 5.93355i | 0.646453 | + | 0.210045i | ||||
\(799\) | 22.6524 | − | 16.4579i | 0.801383 | − | 0.582239i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.48265 | − | 13.7962i | −0.158387 | − | 0.487464i | ||||
\(802\) | 10.4046i | 0.367398i | ||||||||
\(803\) | −29.3135 | + | 16.4810i | −1.03445 | + | 0.581603i | ||||
\(804\) | 0.469045 | 0.0165420 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.169194 | − | 0.122926i | −0.00595959 | − | 0.00432990i | ||||
\(807\) | −1.90691 | − | 2.62464i | −0.0671264 | − | 0.0923916i | ||||
\(808\) | 7.71584 | + | 2.50703i | 0.271442 | + | 0.0881969i | ||||
\(809\) | 3.12679 | − | 9.62328i | 0.109932 | − | 0.338336i | −0.880924 | − | 0.473257i | \(-0.843078\pi\) |
0.990856 | + | 0.134921i | \(0.0430781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.5287 | − | 14.9150i | −0.720862 | − | 0.523737i | 0.165798 | − | 0.986160i | \(-0.446980\pi\) |
−0.886659 | + | 0.462423i | \(0.846980\pi\) | |||||||
\(812\) | −12.3159 | + | 4.00168i | −0.432204 | + | 0.140432i | ||||
\(813\) | − | 2.02977i | − | 0.0711872i | ||||||
\(814\) | 4.60538 | − | 4.99887i | 0.161419 | − | 0.175210i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.0674 | + | 34.0618i | 0.387435 | + | 1.19240i | ||||
\(817\) | −6.96297 | + | 9.58370i | −0.243603 | + | 0.335291i | ||||
\(818\) | 27.3349 | + | 37.6232i | 0.955741 | + | 1.31547i | ||||
\(819\) | 2.89277 | − | 8.90304i | 0.101082 | − | 0.311097i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.21284 | + | 0.881177i | −0.0423282 | + | 0.0307533i | −0.608748 | − | 0.793363i | \(-0.708328\pi\) |
0.566420 | + | 0.824117i | \(0.308328\pi\) | |||||||
\(822\) | −4.53239 | + | 6.23830i | −0.158085 | + | 0.217586i | ||||
\(823\) | −18.1885 | + | 5.90982i | −0.634013 | + | 0.206003i | −0.608352 | − | 0.793667i | \(-0.708169\pi\) |
−0.0256610 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(824\) | −5.13460 | −0.178872 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0794 | 0.629062 | ||||||||
\(827\) | 15.8165 | − | 5.13910i | 0.549994 | − | 0.178704i | −0.0208200 | − | 0.999783i | \(-0.506628\pi\) |
0.570814 | + | 0.821079i | \(0.306628\pi\) | |||||||
\(828\) | −6.57426 | + | 9.04870i | −0.228471 | + | 0.314464i | ||||
\(829\) | 20.7881 | − | 15.1034i | 0.722001 | − | 0.524564i | −0.165022 | − | 0.986290i | \(-0.552769\pi\) |
0.887023 | + | 0.461725i | \(0.152769\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.49701 | + | 10.7627i | −0.121310 | + | 0.373354i | ||||
\(832\) | −6.67649 | − | 9.18940i | −0.231466 | − | 0.318585i | ||||
\(833\) | 17.0078 | − | 23.4093i | 0.589286 | − | 0.811083i | ||||
\(834\) | 4.99586 | + | 15.3757i | 0.172992 | + | 0.532416i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.09338 | + | 26.5169i | −0.106987 | + | 0.917105i | ||||
\(837\) | 0.0213642i | 0.000738455i | ||||||||
\(838\) | −23.4325 | + | 7.61367i | −0.809461 | + | 0.263010i | ||||
\(839\) | −22.9737 | − | 16.6914i | −0.793141 | − | 0.576250i | 0.115753 | − | 0.993278i | \(-0.463072\pi\) |
−0.908894 | + | 0.417028i | \(0.863072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.516507 | − | 1.58965i | 0.0178106 | − | 0.0548154i | ||||
\(842\) | 5.12555 | + | 1.66539i | 0.176638 | + | 0.0573932i | ||||
\(843\) | 6.06459 | + | 8.34720i | 0.208876 | + | 0.287493i | ||||
\(844\) | −4.13743 | − | 3.00602i | −0.142416 | − | 0.103471i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.97864 | 0.239930 | ||||||||
\(847\) | 7.41457 | + | 17.7318i | 0.254768 | + | 0.609273i | ||||
\(848\) | 8.16320i | 0.280325i | ||||||||
\(849\) | −0.650755 | − | 2.00282i | −0.0223339 | − | 0.0687365i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.58406 | − | 5.51014i | 0.259978 | − | 0.188885i | ||||
\(852\) | −5.77602 | − | 1.87674i | −0.197883 | − | 0.0642962i | ||||
\(853\) | −14.3678 | − | 4.66838i | −0.491943 | − | 0.159842i | 0.0525314 | − | 0.998619i | \(-0.483271\pi\) |
−0.544475 | + | 0.838777i | \(0.683271\pi\) | |||||||
\(854\) | 23.9666 | − | 17.4128i | 0.820122 | − | 0.595853i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.87441 | + | 18.0796i | 0.200783 | + | 0.617947i | ||||
\(857\) | 2.37040i | 0.0809713i | 0.999180 | + | 0.0404856i | \(0.0128905\pi\) | ||||
−0.999180 | + | 0.0404856i | \(0.987109\pi\) | |||||||
\(858\) | 32.2479 | + | 3.76194i | 1.10092 | + | 0.128430i | ||||
\(859\) | −45.0423 | −1.53682 | −0.768411 | − | 0.639956i | \(-0.778952\pi\) | ||||
−0.768411 | + | 0.639956i | \(0.778952\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.17333 | − | 3.75865i | −0.176307 | − | 0.128094i | ||||
\(862\) | −12.3747 | − | 17.0323i | −0.421484 | − | 0.580123i | ||||
\(863\) | 23.7964 | + | 7.73191i | 0.810038 | + | 0.263197i | 0.684614 | − | 0.728906i | \(-0.259971\pi\) |
0.125424 | + | 0.992103i | \(0.459971\pi\) | |||||||
\(864\) | −2.01117 | + | 6.18975i | −0.0684214 | + | 0.210579i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.5018 | − | 11.9893i | −0.560754 | − | 0.407412i | ||||
\(867\) | 34.9411 | − | 11.3530i | 1.18666 | − | 0.385570i | ||||
\(868\) | 0.0499551i | 0.00169559i | ||||||||
\(869\) | 8.33767 | − | 1.67301i | 0.282836 | − | 0.0567530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.580278 | − | 1.78591i | −0.0196620 | − | 0.0605133i | ||||
\(872\) | −3.01248 | + | 4.14632i | −0.102015 | + | 0.140412i | ||||
\(873\) | −1.11663 | − | 1.53690i | −0.0377920 | − | 0.0520163i | ||||
\(874\) | −28.3825 | + | 87.3522i | −0.960051 | + | 2.95473i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.9778 | − | 7.97585i | 0.370906 | − | 0.269479i | ||||
\(877\) | −28.7283 | + | 39.5411i | −0.970085 | + | 1.33521i | −0.0280807 | + | 0.999606i | \(0.508940\pi\) |
−0.942004 | + | 0.335601i | \(0.891060\pi\) | |||||||
\(878\) | 1.72659 | − | 0.561002i | 0.0582695 | − | 0.0189329i | ||||
\(879\) | −23.3755 | −0.788435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.5530 | 1.50103 | 0.750515 | − | 0.660853i | \(-0.229805\pi\) | ||||
0.750515 | + | 0.660853i | \(0.229805\pi\) | |||||||
\(882\) | 6.85885 | − | 2.22857i | 0.230949 | − | 0.0750400i | ||||
\(883\) | 25.8947 | − | 35.6410i | 0.871426 | − | 1.19941i | −0.107297 | − | 0.994227i | \(-0.534220\pi\) |
0.978723 | − | 0.205187i | \(-0.0657804\pi\) | |||||||
\(884\) | −42.5230 | + | 30.8948i | −1.43020 | + | 1.03910i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.20076 | + | 19.0840i | −0.208319 | + | 0.641139i | ||||
\(887\) | 7.12941 | + | 9.81279i | 0.239382 | + | 0.329481i | 0.911757 | − | 0.410729i | \(-0.134726\pi\) |
−0.672375 | + | 0.740210i | \(0.734726\pi\) | |||||||
\(888\) | 0.797116 | − | 1.09714i | 0.0267495 | − | 0.0368175i | ||||
\(889\) | −6.85007 | − | 21.0823i | −0.229744 | − | 0.707079i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.62543 | − | 2.89102i | −0.0544538 | − | 0.0968528i | ||||
\(892\) | − | 35.7585i | − | 1.19728i | ||||||
\(893\) | 21.8493 | − | 7.09925i | 0.731158 | − | 0.237567i | ||||
\(894\) | −14.1216 | − | 10.2599i | −0.472296 | − | 0.343143i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.93655 | − | 15.1931i | 0.164919 | − | 0.507567i | ||||
\(897\) | 42.5867 | + | 13.8372i | 1.42193 | + | 0.462012i | ||||
\(898\) | 31.1660 | + | 42.8963i | 1.04002 | + | 1.43147i | ||||
\(899\) | −0.0957219 | − | 0.0695461i | −0.00319251 | − | 0.00231949i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2487 | 0.408063 | ||||||||
\(902\) | 9.25112 | − | 20.1561i | 0.308029 | − | 0.671125i | ||||
\(903\) | − | 3.44118i | − | 0.114515i | ||||||
\(904\) | −2.68872 | − | 8.27504i | −0.0894256 | − | 0.275224i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.97983 | + | 7.25077i | −0.331558 | + | 0.240891i | ||||
\(907\) | 31.2586 | + | 10.1565i | 1.03793 | + | 0.337242i | 0.777919 | − | 0.628365i | \(-0.216275\pi\) |
0.260006 | + | 0.965607i | \(0.416275\pi\) | |||||||
\(908\) | −15.5752 | − | 5.06069i | −0.516881 | − | 0.167945i | ||||
\(909\) | 5.42860 | − | 3.94411i | 0.180055 | − | 0.130818i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4328 | − | 44.4195i | −0.478179 | − | 1.47168i | −0.841622 | − | 0.540067i | \(-0.818399\pi\) |
0.363443 | − | 0.931617i | \(-0.381601\pi\) | |||||||
\(912\) | 29.3857i | 0.973058i | ||||||||
\(913\) | −22.2471 | + | 48.4714i | −0.736271 | + | 1.60417i | ||||
\(914\) | 6.49842 | 0.214949 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.23946 | + | 5.25978i | 0.239199 | + | 0.173788i | ||||
\(917\) | 0.996296 | + | 1.37128i | 0.0329006 | + | 0.0452838i | ||||
\(918\) | 12.7383 | + | 4.13893i | 0.420427 | + | 0.136605i | ||||
\(919\) | −2.26765 | + | 6.97910i | −0.0748028 | + | 0.230219i | −0.981466 | − | 0.191636i | \(-0.938621\pi\) |
0.906663 | + | 0.421855i | \(0.138621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.9304 | − | 18.8396i | −0.854437 | − | 0.620785i | ||||
\(922\) | −43.7594 | + | 14.2183i | −1.44114 | + | 0.468255i | ||||
\(923\) | 24.3143i | 0.800314i | ||||||||
\(924\) | −3.80067 | − | 6.75996i | −0.125033 | − | 0.222386i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.0919 | − | 31.0596i | −0.331640 | − | 1.02068i | ||||
\(927\) | −2.49620 | + | 3.43572i | −0.0819859 | + | 0.112844i | ||||
\(928\) | −21.1862 | − | 29.1603i | −0.695470 | − | 0.957232i | ||||
\(929\) | −3.93333 | + | 12.1055i | −0.129048 | + | 0.397170i | −0.994617 | − | 0.103621i | \(-0.966957\pi\) |
0.865569 | + | 0.500790i | \(0.166957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.2071 | − | 13.9548i | 0.629488 | − | 0.457350i | ||||
\(932\) | −5.12667 | + | 7.05626i | −0.167930 | + | 0.231135i | ||||
\(933\) | −1.55434 | + | 0.505035i | −0.0508868 | + | 0.0165341i | ||||
\(934\) | 46.0888 | 1.50807 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.47778 | 0.211733 | ||||||||
\(937\) | −18.3110 | + | 5.94961i | −0.598195 | + | 0.194365i | −0.592435 | − | 0.805618i | \(-0.701833\pi\) |
−0.00575961 | + | 0.999983i | \(0.501833\pi\) | |||||||
\(938\) | −0.657665 | + | 0.905199i | −0.0214735 | + | 0.0295558i | ||||
\(939\) | −24.6046 | + | 17.8763i | −0.802942 | + | 0.583371i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.7530 | + | 39.2496i | −0.415735 | + | 1.27950i | 0.495857 | + | 0.868404i | \(0.334854\pi\) |
−0.911592 | + | 0.411096i | \(0.865146\pi\) | |||||||
\(942\) | −13.5965 | − | 18.7140i | −0.442998 | − | 0.609735i | ||||
\(943\) | 17.9791 | − | 24.7461i | 0.585479 | − | 0.805842i | ||||
\(944\) | 8.55007 | + | 26.3144i | 0.278281 | + | 0.856461i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.7015 | − | 2.34798i | 0.380448 | − | 0.0763395i | ||||
\(947\) | − | 50.3012i | − | 1.63457i | −0.576233 | − | 0.817285i | \(-0.695478\pi\) | ||
0.576233 | − | 0.817285i | \(-0.304522\pi\) | |||||||
\(948\) | −3.26338 | + | 1.06034i | −0.105990 | + | 0.0344381i | ||||
\(949\) | −43.9496 | − | 31.9312i | −1.42666 | − | 1.03653i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.09561 | − | 27.9934i | 0.294945 | − | 0.907749i | ||||
\(952\) | −14.7282 | − | 4.78550i | −0.477345 | − | 0.155099i | ||||
\(953\) | −5.30523 | − | 7.30203i | −0.171853 | − | 0.236536i | 0.714399 | − | 0.699739i | \(-0.246700\pi\) |
−0.886252 | + | 0.463203i | \(0.846700\pi\) | |||||||
\(954\) | 2.46980 | + | 1.79442i | 0.0799628 | + | 0.0580963i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.5093 | −0.469263 | ||||||||
\(957\) | 18.2443 | + | 2.12833i | 0.589756 | + | 0.0687991i | ||||
\(958\) | 9.56617i | 0.309069i | ||||||||
\(959\) | −2.27868 | − | 7.01305i | −0.0735824 | − | 0.226463i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0792 | − | 18.2211i | 0.809005 | − | 0.587777i | ||||
\(962\) | 10.4425 | + | 3.39296i | 0.336678 | + | 0.109393i | ||||
\(963\) | 14.9534 | + | 4.85867i | 0.481868 | + | 0.156568i | ||||
\(964\) | 29.4275 | − | 21.3803i | 0.947796 | − | 0.688614i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.24484 | − | 25.3750i | −0.265273 | − | 0.816428i | ||||
\(967\) | − | 30.2503i | − | 0.972785i | −0.873740 | − | 0.486392i | \(-0.838313\pi\) | ||
0.873740 | − | 0.486392i | \(-0.161687\pi\) | |||||||
\(968\) | −10.0841 | + | 8.67130i | −0.324114 | + | 0.278706i | ||||
\(969\) | 44.0926 | 1.41646 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.3785 | − | 7.54040i | −0.333061 | − | 0.241983i | 0.408667 | − | 0.912683i | \(-0.365994\pi\) |
−0.741728 | + | 0.670700i | \(0.765994\pi\) | |||||||
\(972\) | 0.786610 | + | 1.08268i | 0.0252305 | + | 0.0347269i | ||||
\(973\) | −14.7037 | − | 4.77751i | −0.471378 | − | 0.153160i | ||||
\(974\) | −5.10687 | + | 15.7173i | −0.163635 | + | 0.503616i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.6785 | + | 26.6485i | 1.17405 | + | 0.852996i | ||||
\(977\) | 12.5151 | − | 4.06641i | 0.400394 | − | 0.130096i | −0.101896 | − | 0.994795i | \(-0.532491\pi\) |
0.502290 | + | 0.864699i | \(0.332491\pi\) | |||||||
\(978\) | − | 42.7645i | − | 1.36746i | ||||||
\(979\) | −5.57474 | + | 47.7875i | −0.178169 | + | 1.52729i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.30991 | + | 4.03149i | 0.0418222 | + | 0.128715i | ||||
\(982\) | −37.3851 | + | 51.4562i | −1.19301 | + | 1.64203i | ||||
\(983\) | 13.1881 | + | 18.1519i | 0.420635 | + | 0.578954i | 0.965772 | − | 0.259393i | \(-0.0835224\pi\) |
−0.545137 | + | 0.838347i | \(0.683522\pi\) | |||||||
\(984\) | 1.36738 | − | 4.20837i | 0.0435905 | − | 0.134158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −60.0110 | + | 43.6005i | −1.91114 | + | 1.38852i | ||||
\(987\) | −3.92266 | + | 5.39908i | −0.124860 | + | 0.171855i | ||||
\(988\) | −41.0154 | + | 13.3267i | −1.30487 | + | 0.423979i | ||||
\(989\) | 16.4605 | 0.523414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.9146 | 0.727907 | 0.363953 | − | 0.931417i | \(-0.381427\pi\) | ||||
0.363953 | + | 0.931417i | \(0.381427\pi\) | |||||||
\(992\) | −0.132239 | + | 0.0429671i | −0.00419859 | + | 0.00136421i | ||||
\(993\) | −13.3958 | + | 18.4377i | −0.425101 | + | 0.585102i | ||||
\(994\) | 11.7207 | − | 8.51555i | 0.371757 | − | 0.270097i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.65002 | − | 20.4666i | 0.210714 | − | 0.648511i | ||||
\(997\) | 9.89794 | + | 13.6234i | 0.313471 | + | 0.431456i | 0.936460 | − | 0.350775i | \(-0.114082\pi\) |
−0.622989 | + | 0.782231i | \(0.714082\pi\) | |||||||
\(998\) | −21.0483 | + | 28.9705i | −0.666272 | + | 0.917045i | ||||
\(999\) | −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.bx.e.49.1 | 16 | ||
5.2 | odd | 4 | 825.2.n.j.676.1 | 8 | |||
5.3 | odd | 4 | 165.2.m.c.16.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 825.2.bx.e.49.4 | 16 | ||
11.9 | even | 5 | inner | 825.2.bx.e.724.4 | 16 | ||
15.8 | even | 4 | 495.2.n.c.181.1 | 8 | |||
55.3 | odd | 20 | 1815.2.a.u.1.4 | 4 | |||
55.8 | even | 20 | 1815.2.a.q.1.1 | 4 | |||
55.9 | even | 10 | inner | 825.2.bx.e.724.1 | 16 | ||
55.42 | odd | 20 | 825.2.n.j.526.1 | 8 | |||
55.47 | odd | 20 | 9075.2.a.co.1.1 | 4 | |||
55.52 | even | 20 | 9075.2.a.df.1.4 | 4 | |||
55.53 | odd | 20 | 165.2.m.c.31.2 | yes | 8 | ||
165.8 | odd | 20 | 5445.2.a.bq.1.4 | 4 | |||
165.53 | even | 20 | 495.2.n.c.361.1 | 8 | |||
165.113 | even | 20 | 5445.2.a.bj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.c.16.2 | ✓ | 8 | 5.3 | odd | 4 | ||
165.2.m.c.31.2 | yes | 8 | 55.53 | odd | 20 | ||
495.2.n.c.181.1 | 8 | 15.8 | even | 4 | |||
495.2.n.c.361.1 | 8 | 165.53 | even | 20 | |||
825.2.n.j.526.1 | 8 | 55.42 | odd | 20 | |||
825.2.n.j.676.1 | 8 | 5.2 | odd | 4 | |||
825.2.bx.e.49.1 | 16 | 1.1 | even | 1 | trivial | ||
825.2.bx.e.49.4 | 16 | 5.4 | even | 2 | inner | ||
825.2.bx.e.724.1 | 16 | 55.9 | even | 10 | inner | ||
825.2.bx.e.724.4 | 16 | 11.9 | even | 5 | inner | ||
1815.2.a.q.1.1 | 4 | 55.8 | even | 20 | |||
1815.2.a.u.1.4 | 4 | 55.3 | odd | 20 | |||
5445.2.a.bj.1.1 | 4 | 165.113 | even | 20 | |||
5445.2.a.bq.1.4 | 4 | 165.8 | odd | 20 | |||
9075.2.a.co.1.1 | 4 | 55.47 | odd | 20 | |||
9075.2.a.df.1.4 | 4 | 55.52 | even | 20 |