Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [990,2,Mod(91,990)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(990, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("990.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 990.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: | \(7.90518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 990.91 |
Dual form | 990.2.n.e.631.1 |
$q$-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 \(\left(\mathbb{Z}/990\mathbb{Z}\right)^\times\).
\(n\) | \(397\) | \(541\) | \(551\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | − | 0.587785i | 0.572061 | − | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 3.07768i | −0.377964 | + | 1.16326i | 0.563492 | + | 0.826121i | \(0.309457\pi\) |
−0.941457 | + | 0.337134i | \(0.890543\pi\) | |||||||
\(8\) | −0.309017 | − | 0.951057i | −0.109254 | − | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.04508 | + | 1.31433i | −0.918128 | + | 0.396285i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73607 | + | 1.98787i | −0.758849 | + | 0.551336i | −0.898557 | − | 0.438857i | \(-0.855384\pi\) |
0.139708 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(14\) | 1.00000 | + | 3.07768i | 0.267261 | + | 0.822546i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −4.92705 | − | 3.57971i | −1.19499 | − | 0.868208i | −0.201203 | − | 0.979550i | \(-0.564485\pi\) |
−0.993782 | + | 0.111342i | \(0.964485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.381966 | + | 1.17557i | 0.0876290 | + | 0.269694i | 0.985263 | − | 0.171048i | \(-0.0547153\pi\) |
−0.897634 | + | 0.440742i | \(0.854715\pi\) | |||||||
\(20\) | −0.809017 | + | 0.587785i | −0.180902 | + | 0.131433i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.69098 | + | 2.85317i | −0.360519 | + | 0.608298i | ||||
\(23\) | −6.85410 | −1.42918 | −0.714590 | − | 0.699544i | \(-0.753386\pi\) | ||||
−0.714590 | + | 0.699544i | \(0.753386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −1.04508 | + | 3.21644i | −0.204958 | + | 0.630796i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.61803 | + | 1.90211i | 0.494762 | + | 0.359466i | ||||
\(29\) | 0.809017 | − | 2.48990i | 0.150231 | − | 0.462363i | −0.847416 | − | 0.530930i | \(-0.821843\pi\) |
0.997646 | + | 0.0685673i | \(0.0218428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.11803 | − | 0.812299i | 0.200805 | − | 0.145893i | −0.482839 | − | 0.875709i | \(-0.660394\pi\) |
0.683644 | + | 0.729816i | \(0.260394\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.09017 | −1.04446 | ||||||||
\(35\) | 2.61803 | − | 1.90211i | 0.442529 | − | 0.321516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.97214 | + | 6.06961i | −0.324217 | + | 0.997838i | 0.647576 | + | 0.762001i | \(0.275783\pi\) |
−0.971793 | + | 0.235837i | \(0.924217\pi\) | |||||||
\(38\) | 1.00000 | + | 0.726543i | 0.162221 | + | 0.117861i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.309017 | + | 0.951057i | −0.0488599 | + | 0.150375i | ||||
\(41\) | −0.381966 | − | 1.17557i | −0.0596531 | − | 0.183593i | 0.916789 | − | 0.399371i | \(-0.130771\pi\) |
−0.976443 | + | 0.215778i | \(0.930771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0901699 | −0.0137508 | −0.00687539 | − | 0.999976i | \(-0.502189\pi\) | ||||
−0.00687539 | + | 0.999976i | \(0.502189\pi\) | |||||||
\(44\) | 0.309017 | + | 3.30220i | 0.0465861 | + | 0.497825i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.54508 | + | 4.02874i | −0.817578 | + | 0.594005i | ||||
\(47\) | 1.33688 | + | 4.11450i | 0.195004 | + | 0.600161i | 0.999977 | + | 0.00684879i | \(0.00218005\pi\) |
−0.804972 | + | 0.593312i | \(0.797820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.80902 | − | 2.04087i | −0.401288 | − | 0.291553i | ||||
\(50\) | 0.809017 | + | 0.587785i | 0.114412 | + | 0.0831254i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.04508 | + | 3.21644i | 0.144927 | + | 0.446040i | ||||
\(53\) | 6.85410 | − | 4.97980i | 0.941483 | − | 0.684028i | −0.00729395 | − | 0.999973i | \(-0.502322\pi\) |
0.948777 | + | 0.315946i | \(0.102322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.23607 | + | 0.726543i | 0.436351 | + | 0.0979670i | ||||
\(56\) | 3.23607 | 0.432438 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.809017 | − | 2.48990i | −0.106229 | − | 0.326940i | ||||
\(59\) | −4.35410 | + | 13.4005i | −0.566856 | + | 1.74460i | 0.0955164 | + | 0.995428i | \(0.469550\pi\) |
−0.662372 | + | 0.749175i | \(0.730450\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(62\) | 0.427051 | − | 1.31433i | 0.0542355 | − | 0.166920i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 3.38197 | 0.419481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.09017 | −0.621863 | −0.310932 | − | 0.950432i | \(-0.600641\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(68\) | −4.92705 | + | 3.57971i | −0.597493 | + | 0.434104i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | − | 3.07768i | 0.119523 | − | 0.367854i | ||||
\(71\) | 8.47214 | + | 6.15537i | 1.00546 | + | 0.730508i | 0.963251 | − | 0.268601i | \(-0.0865614\pi\) |
0.0422061 | + | 0.999109i | \(0.486561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.14590 | − | 12.7598i | 0.485241 | − | 1.49342i | −0.346391 | − | 0.938090i | \(-0.612593\pi\) |
0.831632 | − | 0.555327i | \(-0.187407\pi\) | |||||||
\(74\) | 1.97214 | + | 6.06961i | 0.229256 | + | 0.705578i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.23607 | 0.141787 | ||||||||
\(77\) | −1.00000 | − | 10.6861i | −0.113961 | − | 1.21780i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.30902 | − | 2.40414i | 0.372293 | − | 0.270487i | −0.385868 | − | 0.922554i | \(-0.626098\pi\) |
0.758161 | + | 0.652067i | \(0.226098\pi\) | |||||||
\(80\) | 0.309017 | + | 0.951057i | 0.0345492 | + | 0.106331i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | − | 0.726543i | −0.110432 | − | 0.0802332i | ||||
\(83\) | 3.23607 | + | 2.35114i | 0.355205 | + | 0.258071i | 0.751049 | − | 0.660246i | \(-0.229548\pi\) |
−0.395845 | + | 0.918318i | \(0.629548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88197 | + | 5.79210i | 0.204128 | + | 0.628241i | ||||
\(86\) | −0.0729490 | + | 0.0530006i | −0.00786629 | + | 0.00571520i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.19098 | + | 2.48990i | 0.233560 | + | 0.265424i | ||||
\(89\) | −17.2361 | −1.82702 | −0.913510 | − | 0.406817i | \(-0.866639\pi\) | ||||
−0.913510 | + | 0.406817i | \(0.866639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38197 | − | 10.4086i | −0.354526 | − | 1.09112i | ||||
\(92\) | −2.11803 | + | 6.51864i | −0.220820 | + | 0.679615i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.50000 | + | 2.54290i | 0.360997 | + | 0.262280i | ||||
\(95\) | 0.381966 | − | 1.17557i | 0.0391889 | − | 0.120611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.0902 | + | 10.9637i | −1.53217 | + | 1.11319i | −0.577160 | + | 0.816631i | \(0.695839\pi\) |
−0.955015 | + | 0.296559i | \(0.904161\pi\) | |||||||
\(98\) | −3.47214 | −0.350739 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.6353 | − | 9.18005i | 1.25725 | − | 0.913449i | 0.258635 | − | 0.965975i | \(-0.416727\pi\) |
0.998620 | + | 0.0525259i | \(0.0167272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09017 | − | 6.43288i | 0.205951 | − | 0.633851i | −0.793722 | − | 0.608280i | \(-0.791860\pi\) |
0.999673 | − | 0.0255706i | \(-0.00814025\pi\) | |||||||
\(104\) | 2.73607 | + | 1.98787i | 0.268294 | + | 0.194927i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.61803 | − | 8.05748i | 0.254286 | − | 0.782612i | ||||
\(107\) | −1.94427 | − | 5.98385i | −0.187960 | − | 0.578481i | 0.812027 | − | 0.583620i | \(-0.198364\pi\) |
−0.999987 | + | 0.00513899i | \(0.998364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.47214 | −0.236788 | −0.118394 | − | 0.992967i | \(-0.537775\pi\) | ||||
−0.118394 | + | 0.992967i | \(0.537775\pi\) | |||||||
\(110\) | 3.04508 | − | 1.31433i | 0.290337 | − | 0.125316i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.61803 | − | 1.90211i | 0.247381 | − | 0.179733i | ||||
\(113\) | 6.04508 | + | 18.6049i | 0.568674 | + | 1.75020i | 0.656775 | + | 0.754086i | \(0.271920\pi\) |
−0.0881015 | + | 0.996112i | \(0.528080\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.54508 | + | 4.02874i | 0.517082 | + | 0.375682i | ||||
\(116\) | −2.11803 | − | 1.53884i | −0.196655 | − | 0.142878i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.35410 | + | 13.4005i | 0.400828 | + | 1.23362i | ||||
\(119\) | 15.9443 | − | 11.5842i | 1.46161 | − | 1.06192i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.54508 | − | 8.00448i | 0.685917 | − | 0.727680i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.427051 | − | 1.31433i | −0.0383503 | − | 0.118030i | ||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8541 | − | 8.61251i | −1.05188 | − | 0.764237i | −0.0793121 | − | 0.996850i | \(-0.525272\pi\) |
−0.972569 | + | 0.232613i | \(0.925272\pi\) | |||||||
\(128\) | −0.309017 | + | 0.951057i | −0.0273135 | + | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.73607 | − | 1.98787i | 0.239969 | − | 0.174348i | ||||
\(131\) | 3.38197 | 0.295484 | 0.147742 | − | 0.989026i | \(-0.452800\pi\) | ||||
0.147742 | + | 0.989026i | \(0.452800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | −4.11803 | + | 2.99193i | −0.355744 | + | 0.258463i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.88197 | + | 5.79210i | −0.161377 | + | 0.496668i | ||||
\(137\) | −10.3541 | − | 7.52270i | −0.884611 | − | 0.642707i | 0.0498566 | − | 0.998756i | \(-0.484124\pi\) |
−0.934467 | + | 0.356049i | \(0.884124\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.70820 | − | 8.33499i | 0.229707 | − | 0.706965i | −0.768073 | − | 0.640363i | \(-0.778784\pi\) |
0.997780 | − | 0.0666024i | \(-0.0212159\pi\) | |||||||
\(140\) | −1.00000 | − | 3.07768i | −0.0845154 | − | 0.260112i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.4721 | 0.878802 | ||||||||
\(143\) | 5.71885 | − | 9.64932i | 0.478234 | − | 0.806917i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.11803 | + | 1.53884i | −0.175893 | + | 0.127794i | ||||
\(146\) | −4.14590 | − | 12.7598i | −0.343117 | − | 1.05601i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.16312 | + | 3.75123i | 0.424406 | + | 0.308349i | ||||
\(149\) | −6.16312 | − | 4.47777i | −0.504902 | − | 0.366833i | 0.305984 | − | 0.952037i | \(-0.401015\pi\) |
−0.810886 | + | 0.585204i | \(0.801015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47214 | + | 19.9192i | 0.526695 | + | 1.62100i | 0.760940 | + | 0.648823i | \(0.224738\pi\) |
−0.234245 | + | 0.972178i | \(0.575262\pi\) | |||||||
\(152\) | 1.00000 | − | 0.726543i | 0.0811107 | − | 0.0589304i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.09017 | − | 8.05748i | −0.571342 | − | 0.649290i | ||||
\(155\) | −1.38197 | −0.111002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.86475 | − | 8.81678i | −0.228632 | − | 0.703656i | −0.997903 | − | 0.0647330i | \(-0.979380\pi\) |
0.769271 | − | 0.638923i | \(-0.220620\pi\) | |||||||
\(158\) | 1.26393 | − | 3.88998i | 0.100553 | − | 0.309470i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.809017 | + | 0.587785i | 0.0639584 | + | 0.0464685i | ||||
\(161\) | 6.85410 | − | 21.0948i | 0.540179 | − | 1.66250i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.690983 | + | 0.502029i | −0.0541220 | + | 0.0393219i | −0.614517 | − | 0.788903i | \(-0.710649\pi\) |
0.560395 | + | 0.828225i | \(0.310649\pi\) | |||||||
\(164\) | −1.23607 | −0.0965207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | −10.7361 | + | 7.80021i | −0.830782 | + | 0.603598i | −0.919780 | − | 0.392433i | \(-0.871633\pi\) |
0.0889985 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.482779 | + | 1.48584i | −0.0371369 | + | 0.114295i | ||||
\(170\) | 4.92705 | + | 3.57971i | 0.377888 | + | 0.274551i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0278640 | + | 0.0857567i | −0.00212461 | + | 0.00653889i | ||||
\(173\) | 2.94427 | + | 9.06154i | 0.223849 | + | 0.688936i | 0.998406 | + | 0.0564325i | \(0.0179726\pi\) |
−0.774558 | + | 0.632503i | \(0.782027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.23607 | −0.244624 | ||||||||
\(176\) | 3.23607 | + | 0.726543i | 0.243928 | + | 0.0547652i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.9443 | + | 10.1311i | −1.04517 | + | 0.759359i | ||||
\(179\) | −5.60739 | − | 17.2578i | −0.419116 | − | 1.28991i | −0.908517 | − | 0.417848i | \(-0.862785\pi\) |
0.489401 | − | 0.872059i | \(-0.337215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.7082 | − | 12.8658i | −1.31624 | − | 0.956305i | −0.999971 | − | 0.00763529i | \(-0.997570\pi\) |
−0.316270 | − | 0.948669i | \(-0.602430\pi\) | |||||||
\(182\) | −8.85410 | − | 6.43288i | −0.656310 | − | 0.476837i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.11803 | + | 6.51864i | 0.156144 | + | 0.480560i | ||||
\(185\) | 5.16312 | − | 3.75123i | 0.379600 | − | 0.275796i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.7082 | + | 4.42477i | 1.44121 | + | 0.323571i | ||||
\(188\) | 4.32624 | 0.315523 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.381966 | − | 1.17557i | −0.0277107 | − | 0.0852848i | ||||
\(191\) | −2.85410 | + | 8.78402i | −0.206516 | + | 0.635590i | 0.793132 | + | 0.609050i | \(0.208449\pi\) |
−0.999648 | + | 0.0265400i | \(0.991551\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9443 | + | 12.3107i | 1.21968 | + | 0.886146i | 0.996073 | − | 0.0885344i | \(-0.0282183\pi\) |
0.223602 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(194\) | −5.76393 | + | 17.7396i | −0.413826 | + | 1.27363i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.80902 | + | 2.04087i | −0.200644 | + | 0.145776i | ||||
\(197\) | −10.9443 | −0.779747 | −0.389874 | − | 0.920868i | \(-0.627481\pi\) | ||||
−0.389874 | + | 0.920868i | \(0.627481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9787 | 1.84158 | 0.920791 | − | 0.390056i | \(-0.127544\pi\) | ||||
0.920791 | + | 0.390056i | \(0.127544\pi\) | |||||||
\(200\) | 0.809017 | − | 0.587785i | 0.0572061 | − | 0.0415627i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.82624 | − | 14.8536i | 0.339573 | − | 1.04510i | ||||
\(203\) | 6.85410 | + | 4.97980i | 0.481064 | + | 0.349513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.381966 | + | 1.17557i | −0.0266777 | + | 0.0821054i | ||||
\(206\) | −2.09017 | − | 6.43288i | −0.145629 | − | 0.448200i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.38197 | 0.234497 | ||||||||
\(209\) | −2.70820 | − | 3.07768i | −0.187330 | − | 0.212888i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4164 | − | 14.8334i | 1.40552 | − | 1.02117i | 0.411569 | − | 0.911379i | \(-0.364981\pi\) |
0.993954 | − | 0.109794i | \(-0.0350191\pi\) | |||||||
\(212\) | −2.61803 | − | 8.05748i | −0.179807 | − | 0.553390i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.09017 | − | 3.69822i | −0.347957 | − | 0.252805i | ||||
\(215\) | 0.0729490 | + | 0.0530006i | 0.00497508 | + | 0.00361461i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.38197 | + | 4.25325i | 0.0938140 | + | 0.288730i | ||||
\(218\) | −2.00000 | + | 1.45309i | −0.135457 | + | 0.0984153i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.69098 | − | 2.85317i | 0.114006 | − | 0.192361i | ||||
\(221\) | 20.5967 | 1.38549 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.23607 | + | 6.88191i | 0.149738 | + | 0.460847i | 0.997590 | − | 0.0693868i | \(-0.0221043\pi\) |
−0.847852 | + | 0.530234i | \(0.822104\pi\) | |||||||
\(224\) | 1.00000 | − | 3.07768i | 0.0668153 | − | 0.205636i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.8262 | + | 11.4984i | 1.05275 | + | 0.764865i | ||||
\(227\) | −6.29180 | + | 19.3642i | −0.417601 | + | 1.28524i | 0.492302 | + | 0.870424i | \(0.336155\pi\) |
−0.909904 | + | 0.414820i | \(0.863845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.618034 | + | 0.449028i | −0.0408408 | + | 0.0296726i | −0.608018 | − | 0.793923i | \(-0.708035\pi\) |
0.567178 | + | 0.823596i | \(0.308035\pi\) | |||||||
\(230\) | 6.85410 | 0.451946 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.61803 | −0.171882 | ||||||||
\(233\) | −3.59017 | + | 2.60841i | −0.235200 | + | 0.170883i | −0.699142 | − | 0.714983i | \(-0.746435\pi\) |
0.463942 | + | 0.885865i | \(0.346435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.33688 | − | 4.11450i | 0.0872085 | − | 0.268400i | ||||
\(236\) | 11.3992 | + | 8.28199i | 0.742024 | + | 0.539112i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.09017 | − | 18.7436i | 0.394767 | − | 1.21497i | ||||
\(239\) | 1.00000 | + | 3.07768i | 0.0646846 | + | 0.199079i | 0.978175 | − | 0.207780i | \(-0.0666240\pi\) |
−0.913491 | + | 0.406859i | \(0.866624\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.8885 | −1.53880 | −0.769398 | − | 0.638769i | \(-0.779444\pi\) | ||||
−0.769398 | + | 0.638769i | \(0.779444\pi\) | |||||||
\(242\) | 1.39919 | − | 10.9106i | 0.0899431 | − | 0.701363i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.07295 | + | 3.30220i | 0.0685482 | + | 0.210970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.38197 | − | 2.45714i | −0.215189 | − | 0.156344i | ||||
\(248\) | −1.11803 | − | 0.812299i | −0.0709952 | − | 0.0515811i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.309017 | − | 0.951057i | −0.0195440 | − | 0.0601501i | ||||
\(251\) | 6.78115 | − | 4.92680i | 0.428023 | − | 0.310977i | −0.352835 | − | 0.935685i | \(-0.614782\pi\) |
0.780858 | + | 0.624709i | \(0.214782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.8713 | − | 9.00854i | 1.31217 | − | 0.566362i | ||||
\(254\) | −14.6525 | −0.919378 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −9.38197 | + | 28.8747i | −0.585231 | + | 1.80116i | 0.0131100 | + | 0.999914i | \(0.495827\pi\) |
−0.598341 | + | 0.801242i | \(0.704173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.7082 | − | 12.1392i | −1.03820 | − | 0.754294i | ||||
\(260\) | 1.04508 | − | 3.21644i | 0.0648134 | − | 0.199475i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.73607 | − | 1.98787i | 0.169035 | − | 0.122811i | ||||
\(263\) | −6.85410 | −0.422642 | −0.211321 | − | 0.977417i | \(-0.567777\pi\) | ||||
−0.211321 | + | 0.977417i | \(0.567777\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47214 | −0.520439 | ||||||||
\(266\) | −3.23607 | + | 2.35114i | −0.198416 | + | 0.144158i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.57295 | + | 4.84104i | −0.0960832 | + | 0.295714i | ||||
\(269\) | 2.59017 | + | 1.88187i | 0.157925 | + | 0.114740i | 0.663942 | − | 0.747784i | \(-0.268882\pi\) |
−0.506016 | + | 0.862524i | \(0.668882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.97214 | + | 6.06961i | −0.119799 | + | 0.368703i | −0.992918 | − | 0.118805i | \(-0.962094\pi\) |
0.873119 | + | 0.487507i | \(0.162094\pi\) | |||||||
\(272\) | 1.88197 | + | 5.79210i | 0.114111 | + | 0.351197i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.7984 | −0.773178 | ||||||||
\(275\) | −2.19098 | − | 2.48990i | −0.132121 | − | 0.150147i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0172 | − | 13.8168i | 1.14263 | − | 0.830172i | 0.155150 | − | 0.987891i | \(-0.450414\pi\) |
0.987484 | + | 0.157719i | \(0.0504139\pi\) | |||||||
\(278\) | −2.70820 | − | 8.33499i | −0.162427 | − | 0.499900i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.61803 | − | 1.90211i | −0.156457 | − | 0.113673i | ||||
\(281\) | −6.09017 | − | 4.42477i | −0.363309 | − | 0.263959i | 0.391122 | − | 0.920339i | \(-0.372087\pi\) |
−0.754431 | + | 0.656379i | \(0.772087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.89919 | − | 21.2335i | −0.410114 | − | 1.26220i | −0.916549 | − | 0.399923i | \(-0.869037\pi\) |
0.506435 | − | 0.862278i | \(-0.330963\pi\) | |||||||
\(284\) | 8.47214 | − | 6.15537i | 0.502729 | − | 0.365254i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.04508 | − | 11.1679i | −0.0617972 | − | 0.660373i | ||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.20820 | + | 19.1069i | 0.365188 | + | 1.12393i | ||||
\(290\) | −0.809017 | + | 2.48990i | −0.0475071 | + | 0.146212i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.8541 | − | 7.88597i | −0.635188 | − | 0.461491i | ||||
\(293\) | 6.18034 | − | 19.0211i | 0.361059 | − | 1.11123i | −0.591353 | − | 0.806413i | \(-0.701406\pi\) |
0.952412 | − | 0.304813i | \(-0.0985941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3992 | − | 8.28199i | 0.663686 | − | 0.482196i | ||||
\(296\) | 6.38197 | 0.370944 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.61803 | −0.441301 | ||||||||
\(299\) | 18.7533 | − | 13.6251i | 1.08453 | − | 0.787958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0901699 | − | 0.277515i | 0.00519731 | − | 0.0159957i | ||||
\(302\) | 16.9443 | + | 12.3107i | 0.975033 | + | 0.708403i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.381966 | − | 1.17557i | 0.0219073 | − | 0.0674236i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.4508 | −1.90914 | −0.954570 | − | 0.297985i | \(-0.903685\pi\) | ||||
−0.954570 | + | 0.297985i | \(0.903685\pi\) | |||||||
\(308\) | −10.4721 | − | 2.35114i | −0.596705 | − | 0.133969i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.11803 | + | 0.812299i | −0.0635001 | + | 0.0461355i | ||||
\(311\) | −2.85410 | − | 8.78402i | −0.161841 | − | 0.498096i | 0.836948 | − | 0.547282i | \(-0.184337\pi\) |
−0.998790 | + | 0.0491856i | \(0.984337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.85410 | − | 4.97980i | −0.387417 | − | 0.281475i | 0.376979 | − | 0.926222i | \(-0.376963\pi\) |
−0.764396 | + | 0.644747i | \(0.776963\pi\) | |||||||
\(314\) | −7.50000 | − | 5.44907i | −0.423249 | − | 0.307509i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.26393 | − | 3.88998i | −0.0711017 | − | 0.218829i | ||||
\(317\) | −22.1803 | + | 16.1150i | −1.24577 | + | 0.905106i | −0.997969 | − | 0.0637041i | \(-0.979709\pi\) |
−0.247803 | + | 0.968810i | \(0.579709\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.809017 | + | 8.64527i | 0.0452963 | + | 0.484042i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.85410 | − | 21.0948i | −0.381964 | − | 1.17556i | ||||
\(323\) | 2.32624 | − | 7.15942i | 0.129435 | − | 0.398361i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.73607 | − | 1.98787i | −0.151770 | − | 0.110267i | ||||
\(326\) | −0.263932 | + | 0.812299i | −0.0146178 | + | 0.0449891i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00000 | + | 0.726543i | −0.0552158 | + | 0.0401166i | ||||
\(329\) | −14.0000 | −0.771845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.23607 | 0.507660 | 0.253830 | − | 0.967249i | \(-0.418310\pi\) | ||||
0.253830 | + | 0.967249i | \(0.418310\pi\) | |||||||
\(332\) | 3.23607 | − | 2.35114i | 0.177602 | − | 0.129036i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.10081 | + | 12.6210i | −0.224387 | + | 0.690591i | ||||
\(335\) | 4.11803 | + | 2.99193i | 0.224992 | + | 0.163466i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.70820 | + | 14.4904i | −0.256472 | + | 0.789340i | 0.737064 | + | 0.675823i | \(0.236212\pi\) |
−0.993536 | + | 0.113517i | \(0.963788\pi\) | |||||||
\(338\) | 0.482779 | + | 1.48584i | 0.0262597 | + | 0.0808191i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.09017 | 0.330286 | ||||||||
\(341\) | −2.33688 | + | 3.94298i | −0.126549 | + | 0.213525i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.23607 | + | 6.71040i | −0.498701 | + | 0.362327i | ||||
\(344\) | 0.0278640 | + | 0.0857567i | 0.00150233 | + | 0.00462369i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.70820 | + | 5.60034i | 0.414396 | + | 0.301076i | ||||
\(347\) | 29.0344 | + | 21.0948i | 1.55865 | + | 1.13243i | 0.937105 | + | 0.349048i | \(0.113495\pi\) |
0.621546 | + | 0.783378i | \(0.286505\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.52786 | − | 10.8576i | −0.188842 | − | 0.581197i | 0.811151 | − | 0.584837i | \(-0.198841\pi\) |
−0.999993 | + | 0.00363995i | \(0.998841\pi\) | |||||||
\(350\) | −2.61803 | + | 1.90211i | −0.139940 | + | 0.101672i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.04508 | − | 1.31433i | 0.162304 | − | 0.0700539i | ||||
\(353\) | −23.6180 | −1.25706 | −0.628531 | − | 0.777785i | \(-0.716343\pi\) | ||||
−0.628531 | + | 0.777785i | \(0.716343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.23607 | − | 9.95959i | −0.171753 | − | 0.528600i | ||||
\(356\) | −5.32624 | + | 16.3925i | −0.282290 | + | 0.868799i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.6803 | − | 10.6659i | −0.775880 | − | 0.563710i | ||||
\(359\) | 3.76393 | − | 11.5842i | 0.198653 | − | 0.611390i | −0.801262 | − | 0.598314i | \(-0.795838\pi\) |
0.999915 | − | 0.0130763i | \(-0.00416243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1353 | − | 10.2699i | 0.743961 | − | 0.540519i | ||||
\(362\) | −21.8885 | −1.15044 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.9443 | −0.573636 | ||||||||
\(365\) | −10.8541 | + | 7.88597i | −0.568130 | + | 0.412770i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.27051 | + | 25.4540i | −0.431717 | + | 1.32869i | 0.464696 | + | 0.885470i | \(0.346163\pi\) |
−0.896414 | + | 0.443219i | \(0.853837\pi\) | |||||||
\(368\) | 5.54508 | + | 4.02874i | 0.289058 | + | 0.210013i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.97214 | − | 6.06961i | 0.102526 | − | 0.315544i | ||||
\(371\) | 8.47214 | + | 26.0746i | 0.439851 | + | 1.35372i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5279 | −0.596890 | −0.298445 | − | 0.954427i | \(-0.596468\pi\) | ||||
−0.298445 | + | 0.954427i | \(0.596468\pi\) | |||||||
\(374\) | 18.5451 | − | 8.00448i | 0.958944 | − | 0.413902i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.50000 | − | 2.54290i | 0.180499 | − | 0.131140i | ||||
\(377\) | 2.73607 | + | 8.42075i | 0.140915 | + | 0.433691i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | + | 7.26543i | 0.513665 | + | 0.373200i | 0.814212 | − | 0.580567i | \(-0.197169\pi\) |
−0.300547 | + | 0.953767i | \(0.597169\pi\) | |||||||
\(380\) | −1.00000 | − | 0.726543i | −0.0512989 | − | 0.0372708i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.85410 | + | 8.78402i | 0.146029 | + | 0.449430i | ||||
\(383\) | −0.263932 | + | 0.191758i | −0.0134863 | + | 0.00979837i | −0.594508 | − | 0.804090i | \(-0.702653\pi\) |
0.581022 | + | 0.813888i | \(0.302653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.47214 | + | 9.23305i | −0.278886 | + | 0.470560i | ||||
\(386\) | 20.9443 | 1.06604 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.76393 | + | 17.7396i | 0.292619 | + | 0.900590i | ||||
\(389\) | −2.11803 | + | 6.51864i | −0.107389 | + | 0.330508i | −0.990284 | − | 0.139062i | \(-0.955591\pi\) |
0.882895 | + | 0.469570i | \(0.155591\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.7705 | + | 24.5357i | 1.70785 | + | 1.24082i | ||||
\(392\) | −1.07295 | + | 3.30220i | −0.0541921 | + | 0.166786i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.85410 | + | 6.43288i | −0.446063 | + | 0.324084i | ||||
\(395\) | −4.09017 | −0.205799 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20163 | 0.110496 | 0.0552482 | − | 0.998473i | \(-0.482405\pi\) | ||||
0.0552482 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(398\) | 21.0172 | − | 15.2699i | 1.05350 | − | 0.765411i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | 17.8541 | + | 12.9718i | 0.891591 | + | 0.647779i | 0.936292 | − | 0.351221i | \(-0.114234\pi\) |
−0.0447011 | + | 0.999000i | \(0.514234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.44427 | + | 4.44501i | −0.0719443 | + | 0.221422i | ||||
\(404\) | −4.82624 | − | 14.8536i | −0.240114 | − | 0.738996i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.47214 | 0.420465 | ||||||||
\(407\) | −1.97214 | − | 21.0745i | −0.0977551 | − | 1.04462i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5000 | + | 7.62870i | −0.519192 | + | 0.377215i | −0.816299 | − | 0.577629i | \(-0.803978\pi\) |
0.297108 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(410\) | 0.381966 | + | 1.17557i | 0.0188640 | + | 0.0580573i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.47214 | − | 3.97574i | −0.269593 | − | 0.195871i | ||||
\(413\) | −36.8885 | − | 26.8011i | −1.81517 | − | 1.31880i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.23607 | − | 3.80423i | −0.0606762 | − | 0.186742i | ||||
\(416\) | 2.73607 | − | 1.98787i | 0.134147 | − | 0.0974633i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.00000 | − | 0.898056i | −0.195646 | − | 0.0439254i | ||||
\(419\) | −22.8541 | −1.11650 | −0.558248 | − | 0.829674i | \(-0.688526\pi\) | ||||
−0.558248 | + | 0.829674i | \(0.688526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.763932 | − | 2.35114i | −0.0372318 | − | 0.114588i | 0.930713 | − | 0.365750i | \(-0.119187\pi\) |
−0.967945 | + | 0.251162i | \(0.919187\pi\) | |||||||
\(422\) | 7.79837 | − | 24.0009i | 0.379619 | − | 1.16835i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.85410 | − | 4.97980i | −0.332865 | − | 0.241840i | ||||
\(425\) | 1.88197 | − | 5.79210i | 0.0912888 | − | 0.280958i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.29180 | −0.304125 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0901699 | 0.00434838 | ||||||||
\(431\) | 18.0902 | − | 13.1433i | 0.871373 | − | 0.633089i | −0.0595822 | − | 0.998223i | \(-0.518977\pi\) |
0.930955 | + | 0.365134i | \(0.118977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.05573 | + | 21.7153i | −0.339077 | + | 1.04357i | 0.625602 | + | 0.780142i | \(0.284853\pi\) |
−0.964679 | + | 0.263428i | \(0.915147\pi\) | |||||||
\(434\) | 3.61803 | + | 2.62866i | 0.173671 | + | 0.126180i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.763932 | + | 2.35114i | −0.0365857 | + | 0.112599i | ||||
\(437\) | −2.61803 | − | 8.05748i | −0.125238 | − | 0.385442i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.67376 | 0.0798843 | 0.0399422 | − | 0.999202i | \(-0.487283\pi\) | ||||
0.0399422 | + | 0.999202i | \(0.487283\pi\) | |||||||
\(440\) | −0.309017 | − | 3.30220i | −0.0147318 | − | 0.157426i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.6631 | − | 12.1065i | 0.792584 | − | 0.575846i | ||||
\(443\) | 5.76393 | + | 17.7396i | 0.273853 | + | 0.842832i | 0.989521 | + | 0.144391i | \(0.0461224\pi\) |
−0.715668 | + | 0.698441i | \(0.753878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.9443 | + | 10.1311i | 0.661022 | + | 0.480261i | ||||
\(446\) | 5.85410 | + | 4.25325i | 0.277200 | + | 0.201397i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | − | 3.07768i | −0.0472456 | − | 0.145407i | ||||
\(449\) | −9.00000 | + | 6.53888i | −0.424736 | + | 0.308589i | −0.779541 | − | 0.626352i | \(-0.784547\pi\) |
0.354804 | + | 0.934941i | \(0.384547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.70820 | + | 3.07768i | 0.127524 | + | 0.144922i | ||||
\(452\) | 19.5623 | 0.920133 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.29180 | + | 19.3642i | 0.295289 | + | 0.908805i | ||||
\(455\) | −3.38197 | + | 10.4086i | −0.158549 | + | 0.487964i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.76393 | − | 2.73466i | −0.176069 | − | 0.127922i | 0.496260 | − | 0.868174i | \(-0.334706\pi\) |
−0.672330 | + | 0.740252i | \(0.734706\pi\) | |||||||
\(458\) | −0.236068 | + | 0.726543i | −0.0110307 | + | 0.0339491i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.54508 | − | 4.02874i | 0.258541 | − | 0.187841i | ||||
\(461\) | −23.2148 | −1.08122 | −0.540610 | − | 0.841273i | \(-0.681807\pi\) | ||||
−0.540610 | + | 0.841273i | \(0.681807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8885 | 0.552507 | 0.276254 | − | 0.961085i | \(-0.410907\pi\) | ||||
0.276254 | + | 0.961085i | \(0.410907\pi\) | |||||||
\(464\) | −2.11803 | + | 1.53884i | −0.0983273 | + | 0.0714389i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.37132 | + | 4.22050i | −0.0635253 | + | 0.195511i | ||||
\(467\) | 23.0902 | + | 16.7760i | 1.06849 | + | 0.776300i | 0.975639 | − | 0.219380i | \(-0.0704035\pi\) |
0.0928462 | + | 0.995680i | \(0.470404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.09017 | − | 15.6659i | 0.235042 | − | 0.723386i | ||||
\(470\) | −1.33688 | − | 4.11450i | −0.0616657 | − | 0.189788i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.0902 | 0.648553 | ||||||||
\(473\) | 0.274575 | − | 0.118513i | 0.0126250 | − | 0.00544923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | + | 0.726543i | −0.0458831 | + | 0.0333361i | ||||
\(476\) | −6.09017 | − | 18.7436i | −0.279142 | − | 0.859112i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.61803 | + | 1.90211i | 0.119746 | + | 0.0870006i | ||||
\(479\) | 10.3262 | + | 7.50245i | 0.471818 | + | 0.342796i | 0.798149 | − | 0.602460i | \(-0.205813\pi\) |
−0.326331 | + | 0.945255i | \(0.605813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.66970 | − | 20.5272i | −0.304112 | − | 0.935960i | ||||
\(482\) | −19.3262 | + | 14.0413i | −0.880286 | + | 0.639565i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.28115 | − | 9.64932i | −0.240052 | − | 0.438606i | ||||
\(485\) | 18.6525 | 0.846965 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.52786 | + | 10.8576i | 0.159863 | + | 0.492007i | 0.998621 | − | 0.0524969i | \(-0.0167180\pi\) |
−0.838758 | + | 0.544504i | \(0.816718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.80902 | + | 2.04087i | 0.126898 | + | 0.0921971i | ||||
\(491\) | −8.66312 | + | 26.6623i | −0.390961 | + | 1.20325i | 0.541102 | + | 0.840957i | \(0.318007\pi\) |
−0.932063 | + | 0.362297i | \(0.881993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.8992 | + | 9.37181i | −0.580950 | + | 0.422085i | ||||
\(494\) | −4.18034 | −0.188082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.38197 | −0.0620521 | ||||||||
\(497\) | −27.4164 | + | 19.9192i | −1.22979 | + | 0.893498i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0344 | + | 30.8828i | −0.449203 | + | 1.38251i | 0.428604 | + | 0.903492i | \(0.359005\pi\) |
−0.877808 | + | 0.479013i | \(0.840995\pi\) | |||||||
\(500\) | −0.809017 | − | 0.587785i | −0.0361803 | − | 0.0262866i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.59017 | − | 7.97172i | 0.115605 | − | 0.355795i | ||||
\(503\) | 7.51722 | + | 23.1356i | 0.335176 | + | 1.03157i | 0.966635 | + | 0.256157i | \(0.0824565\pi\) |
−0.631459 | + | 0.775409i | \(0.717544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6180 | −0.694993 | ||||||||
\(506\) | 11.5902 | − | 19.5559i | 0.515246 | − | 0.869366i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.8541 | + | 8.61251i | −0.525941 | + | 0.382118i | ||||
\(509\) | −2.71885 | − | 8.36775i | −0.120511 | − | 0.370894i | 0.872546 | − | 0.488532i | \(-0.162468\pi\) |
−0.993056 | + | 0.117638i | \(0.962468\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.1246 | + | 25.5195i | 1.55382 | + | 1.12892i | ||||
\(512\) | 0.809017 | + | 0.587785i | 0.0357538 | + | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.38197 | + | 28.8747i | 0.413821 | + | 1.27361i | ||||
\(515\) | −5.47214 | + | 3.97574i | −0.241131 | + | 0.175192i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.47871 | − | 10.7719i | −0.416873 | − | 0.473747i | ||||
\(518\) | −20.6525 | −0.907418 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.04508 | − | 3.21644i | −0.0458300 | − | 0.141050i | ||||
\(521\) | 0.729490 | − | 2.24514i | 0.0319595 | − | 0.0983614i | −0.933804 | − | 0.357784i | \(-0.883532\pi\) |
0.965764 | + | 0.259423i | \(0.0835323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.4164 | − | 22.8254i | −1.37374 | − | 0.998083i | −0.997434 | − | 0.0715891i | \(-0.977193\pi\) |
−0.376309 | − | 0.926494i | \(-0.622807\pi\) | |||||||
\(524\) | 1.04508 | − | 3.21644i | 0.0456547 | − | 0.140511i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.54508 | + | 4.02874i | −0.241777 | + | 0.175661i | ||||
\(527\) | −8.41641 | −0.366624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.9787 | 1.04255 | ||||||||
\(530\) | −6.85410 | + | 4.97980i | −0.297723 | + | 0.216309i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.23607 | + | 3.80423i | −0.0535903 | + | 0.164934i | ||||
\(533\) | 3.38197 | + | 2.45714i | 0.146489 | + | 0.106431i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.94427 | + | 5.98385i | −0.0840582 | + | 0.258705i | ||||
\(536\) | 1.57295 | + | 4.84104i | 0.0679410 | + | 0.209101i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.20163 | 0.138032 | ||||||||
\(539\) | 11.2361 | + | 2.52265i | 0.483972 | + | 0.108658i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0902 | + | 15.3229i | −0.906737 | + | 0.658783i | −0.940188 | − | 0.340657i | \(-0.889350\pi\) |
0.0334503 | + | 0.999440i | \(0.489350\pi\) | |||||||
\(542\) | 1.97214 | + | 6.06961i | 0.0847105 | + | 0.260712i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.92705 | + | 3.57971i | 0.211246 | + | 0.153479i | ||||
\(545\) | 2.00000 | + | 1.45309i | 0.0856706 | + | 0.0622433i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6074 | + | 32.6462i | 0.453539 | + | 1.39585i | 0.872842 | + | 0.488004i | \(0.162275\pi\) |
−0.419302 | + | 0.907847i | \(0.637725\pi\) | |||||||
\(548\) | −10.3541 | + | 7.52270i | −0.442305 | + | 0.321354i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.23607 | − | 0.726543i | −0.137986 | − | 0.0309799i | ||||
\(551\) | 3.23607 | 0.137861 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.09017 | + | 12.5882i | 0.173932 | + | 0.535307i | ||||
\(554\) | 7.26393 | − | 22.3561i | 0.308615 | − | 0.949819i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.09017 | − | 5.15131i | −0.300690 | − | 0.218464i | ||||
\(557\) | 10.8541 | − | 33.4055i | 0.459903 | − | 1.41544i | −0.405378 | − | 0.914149i | \(-0.632860\pi\) |
0.865281 | − | 0.501287i | \(-0.167140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.246711 | − | 0.179246i | 0.0104348 | − | 0.00758130i | ||||
\(560\) | −3.23607 | −0.136749 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.52786 | −0.317544 | ||||||||
\(563\) | 13.7984 | − | 10.0251i | 0.581532 | − | 0.422508i | −0.257744 | − | 0.966213i | \(-0.582979\pi\) |
0.839276 | + | 0.543705i | \(0.182979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.04508 | − | 18.6049i | 0.254319 | − | 0.782712i | ||||
\(566\) | −18.0623 | − | 13.1230i | −0.759215 | − | 0.551602i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.23607 | − | 9.95959i | 0.135782 | − | 0.417895i | ||||
\(569\) | 7.85410 | + | 24.1724i | 0.329261 | + | 1.01336i | 0.969480 | + | 0.245169i | \(0.0788435\pi\) |
−0.640219 | + | 0.768192i | \(0.721156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.3607 | −1.18686 | −0.593429 | − | 0.804887i | \(-0.702226\pi\) | ||||
−0.593429 | + | 0.804887i | \(0.702226\pi\) | |||||||
\(572\) | −7.40983 | − | 8.42075i | −0.309821 | − | 0.352089i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.23607 | − | 2.35114i | 0.135071 | − | 0.0981347i | ||||
\(575\) | −2.11803 | − | 6.51864i | −0.0883281 | − | 0.271846i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7984 | − | 10.0251i | −0.574434 | − | 0.417351i | 0.262279 | − | 0.964992i | \(-0.415526\pi\) |
−0.836713 | + | 0.547641i | \(0.815526\pi\) | |||||||
\(578\) | 16.2533 | + | 11.8087i | 0.676048 | + | 0.491177i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.809017 | + | 2.48990i | 0.0335926 | + | 0.103387i | ||||
\(581\) | −10.4721 | + | 7.60845i | −0.434457 | + | 0.315652i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.3262 | + | 24.1724i | −0.593332 | + | 1.00112i | ||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.18034 | − | 19.0211i | −0.255307 | − | 0.785756i | ||||
\(587\) | 8.12461 | − | 25.0050i | 0.335339 | − | 1.03207i | −0.631216 | − | 0.775607i | \(-0.717444\pi\) |
0.966555 | − | 0.256459i | \(-0.0825560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.38197 | + | 1.00406i | 0.0569429 | + | 0.0413715i | ||||
\(590\) | 4.35410 | − | 13.4005i | 0.179256 | − | 0.551692i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.16312 | − | 3.75123i | 0.212203 | − | 0.154174i | ||||
\(593\) | 17.6738 | 0.725774 | 0.362887 | − | 0.931833i | \(-0.381791\pi\) | ||||
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.7082 | −0.807958 | ||||||||
\(596\) | −6.16312 | + | 4.47777i | −0.252451 | + | 0.183417i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.16312 | − | 22.0458i | 0.292922 | − | 0.901520i | ||||
\(599\) | 14.7082 | + | 10.6861i | 0.600961 | + | 0.436624i | 0.846220 | − | 0.532834i | \(-0.178873\pi\) |
−0.245259 | + | 0.969458i | \(0.578873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.85410 | + | 18.0171i | −0.238794 | + | 0.734932i | 0.757802 | + | 0.652485i | \(0.226273\pi\) |
−0.996595 | + | 0.0824468i | \(0.973727\pi\) | |||||||
\(602\) | −0.0901699 | − | 0.277515i | −0.00367505 | − | 0.0113106i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.9443 | 0.852210 | ||||||||
\(605\) | −10.8090 | + | 2.04087i | −0.439449 | + | 0.0829732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.61803 | − | 2.62866i | 0.146851 | − | 0.106694i | −0.511934 | − | 0.859025i | \(-0.671071\pi\) |
0.658785 | + | 0.752331i | \(0.271071\pi\) | |||||||
\(608\) | −0.381966 | − | 1.17557i | −0.0154908 | − | 0.0476757i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.8369 | − | 8.60000i | −0.478869 | − | 0.347919i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.85410 | + | 5.70634i | 0.0748865 | + | 0.230477i | 0.981492 | − | 0.191502i | \(-0.0613357\pi\) |
−0.906606 | + | 0.421979i | \(0.861336\pi\) | |||||||
\(614\) | −27.0623 | + | 19.6619i | −1.09215 | + | 0.793490i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.85410 | + | 4.25325i | −0.397033 | + | 0.171368i | ||||
\(617\) | −26.3607 | −1.06124 | −0.530621 | − | 0.847610i | \(-0.678041\pi\) | ||||
−0.530621 | + | 0.847610i | \(0.678041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.94427 | + | 9.06154i | 0.118340 | + | 0.364214i | 0.992629 | − | 0.121192i | \(-0.0386717\pi\) |
−0.874289 | + | 0.485406i | \(0.838672\pi\) | |||||||
\(620\) | −0.427051 | + | 1.31433i | −0.0171508 | + | 0.0527847i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.47214 | − | 5.42882i | −0.299605 | − | 0.217676i | ||||
\(623\) | 17.2361 | − | 53.0472i | 0.690548 | − | 2.12529i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | −8.47214 | −0.338615 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.27051 | −0.369934 | ||||||||
\(629\) | 31.4443 | − | 22.8456i | 1.25377 | − | 0.910914i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.75329 | + | 5.39607i | −0.0697973 | + | 0.214814i | −0.979871 | − | 0.199633i | \(-0.936025\pi\) |
0.910073 | + | 0.414447i | \(0.136025\pi\) | |||||||
\(632\) | −3.30902 | − | 2.40414i | −0.131626 | − | 0.0956316i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.47214 | + | 26.0746i | −0.336472 | + | 1.03555i | ||||
\(635\) | 4.52786 | + | 13.9353i | 0.179683 | + | 0.553007i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.7426 | 0.465261 | ||||||||
\(638\) | 5.73607 | + | 6.51864i | 0.227093 | + | 0.258075i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.809017 | − | 0.587785i | 0.0319792 | − | 0.0232343i | ||||
\(641\) | −3.76393 | − | 11.5842i | −0.148666 | − | 0.457548i | 0.848798 | − | 0.528717i | \(-0.177327\pi\) |
−0.997464 | + | 0.0711694i | \(0.977327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.88197 | + | 2.82041i | 0.153090 | + | 0.111226i | 0.661693 | − | 0.749775i | \(-0.269838\pi\) |
−0.508604 | + | 0.861001i | \(0.669838\pi\) | |||||||
\(644\) | −17.9443 | − | 13.0373i | −0.707103 | − | 0.513741i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.32624 | − | 7.15942i | −0.0915246 | − | 0.281684i | ||||
\(647\) | −10.0172 | + | 7.27794i | −0.393818 | + | 0.286125i | −0.767018 | − | 0.641625i | \(-0.778260\pi\) |
0.373200 | + | 0.927751i | \(0.378260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.35410 | − | 46.5285i | −0.170913 | − | 1.82640i | ||||
\(650\) | −3.38197 | −0.132652 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.263932 | + | 0.812299i | 0.0103364 | + | 0.0318121i | ||||
\(653\) | −7.58359 | + | 23.3399i | −0.296769 | + | 0.913361i | 0.685853 | + | 0.727740i | \(0.259429\pi\) |
−0.982622 | + | 0.185620i | \(0.940571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.73607 | − | 1.98787i | −0.106907 | − | 0.0776725i | ||||
\(656\) | −0.381966 | + | 1.17557i | −0.0149133 | + | 0.0458983i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.3262 | + | 8.22899i | −0.441543 | + | 0.320800i | ||||
\(659\) | 15.4164 | 0.600538 | 0.300269 | − | 0.953855i | \(-0.402924\pi\) | ||||
0.300269 | + | 0.953855i | \(0.402924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.36068 | 0.325193 | 0.162596 | − | 0.986693i | \(-0.448013\pi\) | ||||
0.162596 | + | 0.986693i | \(0.448013\pi\) | |||||||
\(662\) | 7.47214 | − | 5.42882i | 0.290413 | − | 0.210997i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.23607 | − | 3.80423i | 0.0479687 | − | 0.147633i | ||||
\(665\) | 3.23607 | + | 2.35114i | 0.125489 | + | 0.0911733i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.54508 | + | 17.0660i | −0.214707 | + | 0.660799i | ||||
\(668\) | 4.10081 | + | 12.6210i | 0.158665 | + | 0.488321i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.09017 | 0.196650 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7082 | − | 9.23305i | 0.489865 | − | 0.355908i | −0.315267 | − | 0.949003i | \(-0.602094\pi\) |
0.805132 | + | 0.593095i | \(0.202094\pi\) | |||||||
\(674\) | 4.70820 | + | 14.4904i | 0.181353 | + | 0.558148i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.26393 | + | 0.918300i | 0.0486128 | + | 0.0353192i | ||||
\(677\) | 22.0344 | + | 16.0090i | 0.846852 | + | 0.615274i | 0.924276 | − | 0.381724i | \(-0.124670\pi\) |
−0.0774240 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.6525 | − | 57.4064i | −0.715816 | − | 2.20306i | ||||
\(680\) | 4.92705 | − | 3.57971i | 0.188944 | − | 0.137276i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.427051 | + | 4.56352i | 0.0163526 | + | 0.174746i | ||||
\(683\) | −21.1246 | −0.808311 | −0.404155 | − | 0.914690i | \(-0.632435\pi\) | ||||
−0.404155 | + | 0.914690i | \(0.632435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.95492 | + | 12.1720i | 0.151110 | + | 0.465067i | ||||
\(686\) | −3.52786 | + | 10.8576i | −0.134694 | + | 0.414547i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0729490 | + | 0.0530006i | 0.00278116 | + | 0.00202063i | ||||
\(689\) | −8.85410 | + | 27.2501i | −0.337314 | + | 1.03815i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.7082 | − | 12.1392i | 0.635610 | − | 0.461798i | −0.222729 | − | 0.974880i | \(-0.571497\pi\) |
0.858339 | + | 0.513083i | \(0.171497\pi\) | |||||||
\(692\) | 9.52786 | 0.362195 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.8885 | 1.36231 | ||||||||
\(695\) | −7.09017 | + | 5.15131i | −0.268945 | + | 0.195400i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.32624 | + | 7.15942i | −0.0881125 | + | 0.271183i | ||||
\(698\) | −9.23607 | − | 6.71040i | −0.349590 | − | 0.253992i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00000 | + | 3.07768i | −0.0377964 | + | 0.116326i | ||||
\(701\) | 1.09017 | + | 3.35520i | 0.0411752 | + | 0.126724i | 0.969531 | − | 0.244968i | \(-0.0787776\pi\) |
−0.928356 | + | 0.371692i | \(0.878778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.88854 | −0.297522 | ||||||||
\(704\) | 1.69098 | − | 2.85317i | 0.0637313 | − | 0.107533i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.1074 | + | 13.8823i | −0.719116 | + | 0.522468i | ||||
\(707\) | 15.6180 | + | 48.0674i | 0.587377 | + | 1.80776i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.56231 | + | 6.22088i | 0.321564 | + | 0.233630i | 0.736843 | − | 0.676064i | \(-0.236316\pi\) |
−0.415278 | + | 0.909694i | \(0.636316\pi\) | |||||||
\(710\) | −8.47214 | − | 6.15537i | −0.317954 | − | 0.231007i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.32624 | + | 16.3925i | 0.199609 | + | 0.614334i | ||||
\(713\) | −7.66312 | + | 5.56758i | −0.286986 | + | 0.208508i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.2984 | + | 4.44501i | −0.385137 | + | 0.166234i | ||||
\(716\) | −18.1459 | −0.678144 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.76393 | − | 11.5842i | −0.140469 | − | 0.432318i | ||||
\(719\) | −12.5623 | + | 38.6628i | −0.468495 | + | 1.44188i | 0.386038 | + | 0.922483i | \(0.373843\pi\) |
−0.854533 | + | 0.519397i | \(0.826157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.7082 | + | 12.8658i | 0.659488 | + | 0.479146i | ||||
\(722\) | 5.39919 | − | 16.6170i | 0.200937 | − | 0.618420i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.7082 | + | 12.8658i | −0.658120 | + | 0.478152i | ||||
\(725\) | 2.61803 | 0.0972313 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.1803 | −1.86109 | −0.930543 | − | 0.366183i | \(-0.880664\pi\) | ||||
−0.930543 | + | 0.366183i | \(0.880664\pi\) | |||||||
\(728\) | −8.85410 | + | 6.43288i | −0.328155 | + | 0.238418i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.14590 | + | 12.7598i | −0.153447 | + | 0.472260i | ||||
\(731\) | 0.444272 | + | 0.322782i | 0.0164320 | + | 0.0119385i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8607 | − | 48.8142i | 0.585828 | − | 1.80299i | −0.0100937 | − | 0.999949i | \(-0.503213\pi\) |
0.595921 | − | 0.803043i | \(-0.296787\pi\) | |||||||
\(734\) | 8.27051 | + | 25.4540i | 0.305270 | + | 0.939525i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.85410 | 0.252646 | ||||||||
\(737\) | 15.5000 | − | 6.69015i | 0.570950 | − | 0.246435i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.8541 | + | 15.8779i | −0.803916 | + | 0.584079i | −0.912060 | − | 0.410056i | \(-0.865509\pi\) |
0.108144 | + | 0.994135i | \(0.465509\pi\) | |||||||
\(740\) | −1.97214 | − | 6.06961i | −0.0724972 | − | 0.223123i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.1803 | + | 16.1150i | 0.814266 | + | 0.591599i | ||||
\(743\) | 8.73607 | + | 6.34712i | 0.320495 | + | 0.232853i | 0.736387 | − | 0.676561i | \(-0.236530\pi\) |
−0.415892 | + | 0.909414i | \(0.636530\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.35410 | + | 7.24518i | 0.0862476 | + | 0.265443i | ||||
\(746\) | −9.32624 | + | 6.77591i | −0.341458 | + | 0.248084i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.2984 | − | 17.3763i | 0.376546 | − | 0.635340i | ||||
\(749\) | 20.3607 | 0.743963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.97214 | − | 27.6134i | −0.327398 | − | 1.00763i | −0.970347 | − | 0.241718i | \(-0.922289\pi\) |
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(752\) | 1.33688 | − | 4.11450i | 0.0487510 | − | 0.150040i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.16312 | + | 5.20431i | 0.260865 | + | 0.189530i | ||||
\(755\) | 6.47214 | − | 19.9192i | 0.235545 | − | 0.724933i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.5689 | − | 31.6546i | 1.58354 | − | 1.15051i | 0.671044 | − | 0.741417i | \(-0.265846\pi\) |
0.912494 | − | 0.409090i | \(-0.134154\pi\) | |||||||
\(758\) | 12.3607 | 0.448960 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.23607 | −0.0448369 | ||||||||
\(761\) | −8.09017 | + | 5.87785i | −0.293268 | + | 0.213072i | −0.724684 | − | 0.689081i | \(-0.758014\pi\) |
0.431416 | + | 0.902153i | \(0.358014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.47214 | − | 7.60845i | 0.0894973 | − | 0.275444i | ||||
\(764\) | 7.47214 | + | 5.42882i | 0.270332 | + | 0.196408i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.100813 | + | 0.310271i | −0.00364252 | + | 0.0112105i | ||||
\(767\) | −14.7254 | − | 45.3202i | −0.531704 | − | 1.63642i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.4508 | −0.881720 | −0.440860 | − | 0.897576i | \(-0.645327\pi\) | ||||
−0.440860 | + | 0.897576i | \(0.645327\pi\) | |||||||
\(770\) | 1.00000 | + | 10.6861i | 0.0360375 | + | 0.385102i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.9443 | − | 12.3107i | 0.609838 | − | 0.443073i | ||||
\(773\) | −6.05573 | − | 18.6376i | −0.217809 | − | 0.670348i | −0.998942 | − | 0.0459835i | \(-0.985358\pi\) |
0.781133 | − | 0.624365i | \(-0.214642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.11803 | + | 0.812299i | 0.0401610 | + | 0.0291787i | ||||
\(776\) | 15.0902 | + | 10.9637i | 0.541706 | + | 0.393572i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.11803 | + | 6.51864i | 0.0759352 | + | 0.233705i | ||||
\(779\) | 1.23607 | − | 0.898056i | 0.0442867 | − | 0.0321762i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.8885 | − | 7.60845i | −1.21263 | − | 0.272252i | ||||
\(782\) | 41.7426 | 1.49271 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.07295 | + | 3.30220i | 0.0383196 | + | 0.117936i | ||||
\(785\) | −2.86475 | + | 8.81678i | −0.102247 | + | 0.314684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0172 | − | 12.3637i | −0.606598 | − | 0.440720i | 0.241616 | − | 0.970372i | \(-0.422322\pi\) |
−0.848215 | + | 0.529652i | \(0.822322\pi\) | |||||||
\(788\) | −3.38197 | + | 10.4086i | −0.120478 | + | 0.370792i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.30902 | + | 2.40414i | −0.117730 | + | 0.0855355i | ||||
\(791\) | −63.3050 | −2.25086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.78115 | − | 1.29408i | 0.0632108 | − | 0.0459253i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.02786 | − | 24.7072i | 0.284540 | − | 0.875724i | ||||
\(797\) | −17.5623 | − | 12.7598i | −0.622089 | − | 0.451974i | 0.231562 | − | 0.972820i | \(-0.425616\pi\) |
−0.853651 | + | 0.520846i | \(0.825616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.14183 | − | 25.0580i | 0.288037 | − | 0.886488i | ||||
\(800\) | −0.309017 | − | 0.951057i | −0.0109254 | − | 0.0336249i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.0689 | 0.779279 | ||||||||
\(803\) | 4.14590 | + | 44.3036i | 0.146306 | + | 1.56344i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.9443 | + | 13.0373i | −0.632452 | + | 0.459504i | ||||
\(806\) | 1.44427 | + | 4.44501i | 0.0508723 | + | 0.156569i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.6353 | − | 9.18005i | −0.444507 | − | 0.322953i | ||||
\(809\) | −2.14590 | − | 1.55909i | −0.0754458 | − | 0.0548146i | 0.549423 | − | 0.835544i | \(-0.314848\pi\) |
−0.624869 | + | 0.780730i | \(0.714848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41641 | − | 4.35926i | −0.0497368 | − | 0.153074i | 0.923103 | − | 0.384552i | \(-0.125644\pi\) |
−0.972840 | + | 0.231478i | \(0.925644\pi\) | |||||||
\(812\) | 6.85410 | − | 4.97980i | 0.240532 | − | 0.174757i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.9828 | − | 15.8904i | −0.490096 | − | 0.556960i | ||||
\(815\) | 0.854102 | 0.0299179 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0344419 | − | 0.106001i | −0.00120497 | − | 0.00370851i | ||||
\(818\) | −4.01064 | + | 12.3435i | −0.140229 | + | 0.431580i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | + | 0.726543i | 0.0349215 | + | 0.0253720i | ||||
\(821\) | 13.3820 | − | 41.1855i | 0.467034 | − | 1.43738i | −0.389373 | − | 0.921080i | \(-0.627308\pi\) |
0.856407 | − | 0.516302i | \(-0.172692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3262 | − | 7.50245i | 0.359950 | − | 0.261519i | −0.393081 | − | 0.919504i | \(-0.628591\pi\) |
0.753031 | + | 0.657985i | \(0.228591\pi\) | |||||||
\(824\) | −6.76393 | −0.235633 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.5967 | −1.58651 | ||||||||
\(827\) | 24.5066 | − | 17.8051i | 0.852177 | − | 0.619143i | −0.0735683 | − | 0.997290i | \(-0.523439\pi\) |
0.925745 | + | 0.378147i | \(0.123439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0000 | − | 33.8545i | 0.382046 | − | 1.17582i | −0.556555 | − | 0.830811i | \(-0.687877\pi\) |
0.938601 | − | 0.345005i | \(-0.112123\pi\) | |||||||
\(830\) | −3.23607 | − | 2.35114i | −0.112326 | − | 0.0816093i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.04508 | − | 3.21644i | 0.0362318 | − | 0.111510i | ||||
\(833\) | 6.53444 | + | 20.1109i | 0.226405 | + | 0.696803i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.2705 | 0.459245 | ||||||||
\(836\) | −3.76393 | + | 1.62460i | −0.130178 | + | 0.0561879i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.4894 | + | 13.4333i | −0.638704 | + | 0.464046i | ||||
\(839\) | 7.21478 | + | 22.2048i | 0.249082 | + | 0.766595i | 0.994938 | + | 0.100488i | \(0.0320405\pi\) |
−0.745856 | + | 0.666107i | \(0.767959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.9164 | + | 13.0170i | 0.617807 | + | 0.448863i | ||||
\(842\) | −2.00000 | − | 1.45309i | −0.0689246 | − | 0.0500766i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.79837 | − | 24.0009i | −0.268431 | − | 0.826146i | ||||
\(845\) | 1.26393 | − | 0.918300i | 0.0434806 | − | 0.0315905i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.0902 | + | 31.2259i | 0.587225 | + | 1.07293i | ||||
\(848\) | −8.47214 | −0.290934 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.88197 | − | 5.79210i | −0.0645509 | − | 0.198667i | ||||
\(851\) | 13.5172 | − | 41.6017i | 0.463364 | − | 1.42609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2705 | + | 16.1805i | 0.762528 | + | 0.554009i | 0.899685 | − | 0.436541i | \(-0.143796\pi\) |
−0.137157 | + | 0.990549i | \(0.543796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.09017 | + | 3.69822i | −0.173978 | + | 0.126403i | ||||
\(857\) | −24.1591 | −0.825258 | −0.412629 | − | 0.910899i | \(-0.635389\pi\) | ||||
−0.412629 | + | 0.910899i | \(0.635389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.1246 | −0.652523 | −0.326262 | − | 0.945279i | \(-0.605789\pi\) | ||||
−0.326262 | + | 0.945279i | \(0.605789\pi\) | |||||||
\(860\) | 0.0729490 | − | 0.0530006i | 0.00248754 | − | 0.00180730i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.90983 | − | 21.2663i | 0.235350 | − | 0.724332i | ||||
\(863\) | −35.8713 | − | 26.0620i | −1.22107 | − | 0.887162i | −0.224885 | − | 0.974385i | \(-0.572201\pi\) |
−0.996189 | + | 0.0872230i | \(0.972201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.94427 | − | 9.06154i | 0.100108 | − | 0.308102i | ||||
\(866\) | 7.05573 | + | 21.7153i | 0.239763 | + | 0.737916i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.47214 | 0.151794 | ||||||||
\(869\) | −6.91641 | + | 11.6699i | −0.234623 | + | 0.395876i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9271 | − | 10.1186i | 0.471900 | − | 0.342856i | ||||
\(872\) | 0.763932 | + | 2.35114i | 0.0258700 | + | 0.0796197i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.85410 | − | 4.97980i | −0.231843 | − | 0.168444i | ||||
\(875\) | 2.61803 | + | 1.90211i | 0.0885057 | + | 0.0643032i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.86068 | + | 18.0373i | 0.197901 | + | 0.609077i | 0.999930 | + | 0.0117923i | \(0.00375371\pi\) |
−0.802029 | + | 0.597285i | \(0.796246\pi\) | |||||||
\(878\) | 1.35410 | − | 0.983813i | 0.0456987 | − | 0.0332021i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.19098 | − | 2.48990i | −0.0738580 | − | 0.0839345i | ||||
\(881\) | −8.00000 | −0.269527 | −0.134763 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134763 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.44427 | − | 4.44501i | −0.0486036 | − | 0.149587i | 0.923809 | − | 0.382853i | \(-0.125058\pi\) |
−0.972413 | + | 0.233267i | \(0.925058\pi\) | |||||||
\(884\) | 6.36475 | − | 19.5887i | 0.214070 | − | 0.658838i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0902 | + | 10.9637i | 0.506964 | + | 0.368331i | ||||
\(887\) | 13.1180 | − | 40.3732i | 0.440460 | − | 1.35560i | −0.446926 | − | 0.894571i | \(-0.647481\pi\) |
0.887386 | − | 0.461027i | \(-0.152519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.3607 | − | 27.8707i | 1.28658 | − | 0.934752i | ||||
\(890\) | 17.2361 | 0.577754 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.23607 | 0.242281 | ||||||||
\(893\) | −4.32624 | + | 3.14320i | −0.144772 | + | 0.105183i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.60739 | + | 17.2578i | −0.187434 | + | 0.576864i | ||||
\(896\) | −2.61803 | − | 1.90211i | −0.0874624 | − | 0.0635451i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.43769 | + | 10.5801i | −0.114717 | + | 0.353064i | ||||
\(899\) | −1.11803 | − | 3.44095i | −0.0372885 | − | 0.114762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.5967 | −1.71894 | ||||||||
\(902\) | 4.00000 | + | 0.898056i | 0.133185 | + | 0.0299020i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.8262 | − | 11.4984i | 0.526373 | − | 0.382432i | ||||
\(905\) | 6.76393 | + | 20.8172i | 0.224841 | + | 0.691989i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0172 | + | 13.8168i | 0.631456 | + | 0.458780i | 0.856904 | − | 0.515475i | \(-0.172385\pi\) |
−0.225448 | + | 0.974255i | \(0.572385\pi\) | |||||||
\(908\) | 16.4721 | + | 11.9677i | 0.546647 | + | 0.397162i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.38197 | + | 10.4086i | 0.112111 | + | 0.345042i | ||||
\(911\) | 2.85410 | − | 2.07363i | 0.0945606 | − | 0.0687023i | −0.539500 | − | 0.841985i | \(-0.681387\pi\) |
0.634061 | + | 0.773283i | \(0.281387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.9443 | − | 2.90617i | −0.428393 | − | 0.0961802i | ||||
\(914\) | −4.65248 | −0.153890 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.236068 | + | 0.726543i | 0.00779991 | + | 0.0240056i | ||||
\(917\) | −3.38197 | + | 10.4086i | −0.111682 | + | 0.343723i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.4894 | − | 27.2376i | −1.23666 | − | 0.898486i | −0.239289 | − | 0.970948i | \(-0.576914\pi\) |
−0.997371 | + | 0.0724626i | \(0.976914\pi\) | |||||||
\(920\) | 2.11803 | − | 6.51864i | 0.0698295 | − | 0.214913i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.7812 | + | 13.6453i | −0.618524 | + | 0.449384i | ||||
\(923\) | −35.4164 | −1.16575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.38197 | −0.209838 | ||||||||
\(926\) | 9.61803 | − | 6.98791i | 0.316068 | − | 0.229637i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.809017 | + | 2.48990i | −0.0265573 | + | 0.0817349i | ||||
\(929\) | −24.6525 | − | 17.9111i | −0.808821 | − | 0.587643i | 0.104667 | − | 0.994507i | \(-0.466622\pi\) |
−0.913489 | + | 0.406864i | \(0.866622\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32624 | − | 4.08174i | 0.0434657 | − | 0.133774i | ||||
\(932\) | 1.37132 | + | 4.22050i | 0.0449192 | + | 0.138247i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.5410 | 0.933891 | ||||||||
\(935\) | −13.3435 | − | 15.1639i | −0.436378 | − | 0.495913i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.5066 | − | 25.0705i | 1.12728 | − | 0.819017i | 0.141984 | − | 0.989869i | \(-0.454652\pi\) |
0.985297 | + | 0.170852i | \(0.0546519\pi\) | |||||||
\(938\) | −5.09017 | − | 15.6659i | −0.166200 | − | 0.511511i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.50000 | − | 2.54290i | −0.114157 | − | 0.0829402i | ||||
\(941\) | 0.826238 | + | 0.600297i | 0.0269346 | + | 0.0195691i | 0.601171 | − | 0.799120i | \(-0.294701\pi\) |
−0.574237 | + | 0.818689i | \(0.694701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.61803 | + | 8.05748i | 0.0852549 | + | 0.262388i | ||||
\(944\) | 11.3992 | − | 8.28199i | 0.371012 | − | 0.269556i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.152476 | − | 0.257270i | 0.00495742 | − | 0.00836457i | ||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0213 | + | 43.1531i | 0.455150 | + | 1.40081i | ||||
\(950\) | −0.381966 | + | 1.17557i | −0.0123926 | + | 0.0381405i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.9443 | − | 11.5842i | −0.516757 | − | 0.375446i | ||||
\(953\) | 18.2984 | − | 56.3166i | 0.592742 | − | 1.82427i | 0.0270855 | − | 0.999633i | \(-0.491377\pi\) |
0.565657 | − | 0.824641i | \(-0.308623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.47214 | − | 5.42882i | 0.241793 | − | 0.175673i | ||||
\(956\) | 3.23607 | 0.104662 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.7639 | 0.412384 | ||||||||
\(959\) | 33.5066 | − | 24.3440i | 1.08198 | − | 0.786107i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.98936 | + | 27.6664i | −0.289979 | + | 0.892464i | ||||
\(962\) | −17.4615 | − | 12.6865i | −0.562981 | − | 0.409030i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.38197 | + | 22.7194i | −0.237757 | + | 0.731741i | ||||
\(965\) | −6.47214 | − | 19.9192i | −0.208345 | − | 0.641221i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.3050 | 1.71417 | 0.857086 | − | 0.515174i | \(-0.172273\pi\) | ||||
0.857086 | + | 0.515174i | \(0.172273\pi\) | |||||||
\(968\) | −9.94427 | − | 4.70228i | −0.319621 | − | 0.151137i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.0902 | − | 10.9637i | 0.484516 | − | 0.352022i | ||||
\(971\) | −2.58359 | − | 7.95148i | −0.0829114 | − | 0.255175i | 0.901004 | − | 0.433811i | \(-0.142832\pi\) |
−0.983915 | + | 0.178636i | \(0.942832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9443 | + | 16.6700i | 0.735560 | + | 0.534415i | ||||
\(974\) | 9.23607 | + | 6.71040i | 0.295943 | + | 0.215015i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.3262 | − | 16.9475i | 0.746272 | − | 0.542199i | −0.148397 | − | 0.988928i | \(-0.547411\pi\) |
0.894669 | + | 0.446729i | \(0.147411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52.4853 | − | 22.6538i | 1.67744 | − | 0.724020i | ||||
\(980\) | 3.47214 | 0.110913 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.66312 | + | 26.6623i | 0.276451 | + | 0.850829i | ||||
\(983\) | 15.8197 | − | 48.6879i | 0.504569 | − | 1.55290i | −0.296925 | − | 0.954901i | \(-0.595961\pi\) |
0.801494 | − | 0.598002i | \(-0.204039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.85410 | + | 6.43288i | 0.282115 | + | 0.204969i | ||||
\(986\) | −4.92705 | + | 15.1639i | −0.156909 | + | 0.482917i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.38197 | + | 2.45714i | −0.107595 | + | 0.0781721i | ||||
\(989\) | 0.618034 | 0.0196523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5197 | 1.73188 | 0.865938 | − | 0.500151i | \(-0.166722\pi\) | ||||
0.865938 | + | 0.500151i | \(0.166722\pi\) | |||||||
\(992\) | −1.11803 | + | 0.812299i | −0.0354976 | + | 0.0257905i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.4721 | + | 32.2299i | −0.332156 | + | 1.02227i | ||||
\(995\) | −21.0172 | − | 15.2699i | −0.666291 | − | 0.484089i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.73607 | + | 23.8092i | −0.245004 | + | 0.754044i | 0.750632 | + | 0.660720i | \(0.229749\pi\) |
−0.995636 | + | 0.0933236i | \(0.970251\pi\) | |||||||
\(998\) | 10.0344 | + | 30.8828i | 0.317635 | + | 0.977579i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 990.2.n.e.91.1 | 4 | ||
3.2 | odd | 2 | 330.2.m.b.91.1 | ✓ | 4 | ||
11.4 | even | 5 | inner | 990.2.n.e.631.1 | 4 | ||
33.2 | even | 10 | 3630.2.a.bb.1.2 | 2 | |||
33.20 | odd | 10 | 3630.2.a.bj.1.1 | 2 | |||
33.26 | odd | 10 | 330.2.m.b.301.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.b.91.1 | ✓ | 4 | 3.2 | odd | 2 | ||
330.2.m.b.301.1 | yes | 4 | 33.26 | odd | 10 | ||
990.2.n.e.91.1 | 4 | 1.1 | even | 1 | trivial | ||
990.2.n.e.631.1 | 4 | 11.4 | even | 5 | inner | ||
3630.2.a.bb.1.2 | 2 | 33.2 | even | 10 | |||
3630.2.a.bj.1.1 | 2 | 33.20 | odd | 10 |