Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 197.10 | ||
Character | \(\chi\) | \(=\) | 405.197 |
Dual form | 405.2.r.a.368.10 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.639298 | − | 0.0559313i | 0.452052 | − | 0.0395494i | 0.141143 | − | 0.989989i | \(-0.454922\pi\) |
0.310909 | + | 0.950440i | \(0.399367\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.56404 | + | 0.275783i | −0.782021 | + | 0.137891i | ||||
\(5\) | 1.26232 | + | 1.84568i | 0.564526 | + | 0.825415i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.52875 | − | 2.47086i | 1.33374 | − | 0.933897i | 0.333781 | − | 0.942651i | \(-0.391675\pi\) |
0.999962 | + | 0.00875387i | \(0.00278648\pi\) | |||||||
\(8\) | −2.22421 | + | 0.595975i | −0.786377 | + | 0.210709i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.910229 | + | 1.10934i | 0.287840 | + | 0.350804i | ||||
\(11\) | 0.157893 | + | 0.433806i | 0.0476064 | + | 0.130798i | 0.961217 | − | 0.275792i | \(-0.0889401\pi\) |
−0.913611 | + | 0.406590i | \(0.866718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.462462 | + | 5.28596i | −0.128264 | + | 1.46606i | 0.610457 | + | 0.792050i | \(0.290986\pi\) |
−0.738720 | + | 0.674012i | \(0.764570\pi\) | |||||||
\(14\) | 2.11772 | − | 1.77698i | 0.565986 | − | 0.474918i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59619 | − | 0.580964i | 0.399047 | − | 0.145241i | ||||
\(17\) | 4.93057 | + | 1.32114i | 1.19584 | + | 0.320424i | 0.801191 | − | 0.598409i | \(-0.204200\pi\) |
0.394647 | + | 0.918833i | \(0.370867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03667 | + | 0.598524i | 0.237829 | + | 0.137311i | 0.614179 | − | 0.789167i | \(-0.289487\pi\) |
−0.376349 | + | 0.926478i | \(0.622821\pi\) | |||||||
\(20\) | −2.48333 | − | 2.53860i | −0.555289 | − | 0.567649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.125204 | + | 0.268500i | 0.0266935 | + | 0.0572444i | ||||
\(23\) | 1.57814 | − | 2.25381i | 0.329064 | − | 0.469952i | −0.620195 | − | 0.784448i | \(-0.712946\pi\) |
0.949259 | + | 0.314496i | \(0.101835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.81310 | + | 4.65968i | −0.362621 | + | 0.931937i | ||||
\(26\) | 3.40517i | 0.667808i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.83770 | + | 4.83770i | −0.914239 | + | 0.914239i | ||||
\(29\) | 0.00462297 | + | 0.00387914i | 0.000858465 | + | 0.000720337i | 0.643217 | − | 0.765684i | \(-0.277599\pi\) |
−0.642358 | + | 0.766404i | \(0.722044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.387533 | − | 2.19781i | −0.0696030 | − | 0.394738i | −0.999629 | − | 0.0272441i | \(-0.991327\pi\) |
0.930026 | − | 0.367494i | \(-0.119784\pi\) | |||||||
\(32\) | 5.16180 | − | 2.40699i | 0.912486 | − | 0.425499i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.22599 | + | 0.568830i | 0.553253 | + | 0.0975535i | ||||
\(35\) | 9.01483 | + | 3.39395i | 1.52379 | + | 0.573683i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.94341 | + | 7.25290i | −0.319494 | + | 1.19237i | 0.600238 | + | 0.799822i | \(0.295073\pi\) |
−0.919732 | + | 0.392547i | \(0.871594\pi\) | |||||||
\(38\) | 0.696220 | + | 0.324653i | 0.112942 | + | 0.0526656i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.90764 | − | 3.35288i | −0.617853 | − | 0.530137i | ||||
\(41\) | −3.02828 | − | 3.60897i | −0.472939 | − | 0.563626i | 0.475855 | − | 0.879524i | \(-0.342139\pi\) |
−0.948793 | + | 0.315898i | \(0.897694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.806157 | − | 1.72881i | 0.122938 | − | 0.263641i | −0.835201 | − | 0.549945i | \(-0.814649\pi\) |
0.958139 | + | 0.286304i | \(0.0924266\pi\) | |||||||
\(44\) | −0.366587 | − | 0.634947i | −0.0552651 | − | 0.0957219i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.882840 | − | 1.52912i | 0.130168 | − | 0.225457i | ||||
\(47\) | −6.47343 | − | 9.24502i | −0.944247 | − | 1.34853i | −0.937290 | − | 0.348549i | \(-0.886674\pi\) |
−0.00695690 | − | 0.999976i | \(-0.502214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.95281 | − | 10.8602i | 0.564687 | − | 1.55146i | ||||
\(50\) | −0.898490 | + | 3.08033i | −0.127066 | + | 0.435625i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.734468 | − | 8.39501i | −0.101852 | − | 1.16418i | ||||
\(53\) | −3.94023 | − | 3.94023i | −0.541233 | − | 0.541233i | 0.382657 | − | 0.923890i | \(-0.375009\pi\) |
−0.923890 | + | 0.382657i | \(0.875009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.601359 | + | 0.839022i | −0.0810872 | + | 0.113134i | ||||
\(56\) | −6.37611 | + | 7.59875i | −0.852044 | + | 1.01543i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.00317242 | + | 0.00222135i | 0.000416559 | + | 0.000291678i | ||||
\(59\) | 0.388624 | + | 0.141448i | 0.0505945 | + | 0.0184149i | 0.367193 | − | 0.930145i | \(-0.380319\pi\) |
−0.316599 | + | 0.948559i | \(0.602541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.399307 | − | 2.26458i | 0.0511260 | − | 0.289950i | −0.948515 | − | 0.316731i | \(-0.897415\pi\) |
0.999641 | + | 0.0267812i | \(0.00852575\pi\) | |||||||
\(62\) | −0.370675 | − | 1.38338i | −0.0470758 | − | 0.175689i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.223194 | − | 0.128861i | 0.0278993 | − | 0.0161077i | ||||
\(65\) | −10.3400 | + | 5.81901i | −1.28252 | + | 0.721759i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.84619 | − | 0.511475i | −0.714226 | − | 0.0624866i | −0.275750 | − | 0.961230i | \(-0.588926\pi\) |
−0.438476 | + | 0.898743i | \(0.644482\pi\) | |||||||
\(68\) | −8.07597 | − | 0.706556i | −0.979355 | − | 0.0856824i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.95299 | + | 1.66553i | 0.711518 | + | 0.199069i | ||||
\(71\) | −0.648656 | + | 0.374502i | −0.0769813 | + | 0.0444452i | −0.537997 | − | 0.842947i | \(-0.680819\pi\) |
0.461015 | + | 0.887392i | \(0.347485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.97508 | − | 11.1032i | −0.348207 | − | 1.29953i | −0.888821 | − | 0.458255i | \(-0.848475\pi\) |
0.540614 | − | 0.841271i | \(-0.318192\pi\) | |||||||
\(74\) | −0.836752 | + | 4.74546i | −0.0972705 | + | 0.551648i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.78647 | − | 0.650220i | −0.204922 | − | 0.0745854i | ||||
\(77\) | 1.62904 | + | 1.14066i | 0.185646 | + | 0.129991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.01095 | + | 1.20481i | −0.113741 | + | 0.135551i | −0.819911 | − | 0.572491i | \(-0.805977\pi\) |
0.706170 | + | 0.708043i | \(0.250422\pi\) | |||||||
\(80\) | 3.08717 | + | 2.21269i | 0.345156 | + | 0.247387i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.13783 | − | 2.13783i | −0.236084 | − | 0.236084i | ||||
\(83\) | −0.930629 | − | 10.6371i | −0.102150 | − | 1.16758i | −0.858289 | − | 0.513167i | \(-0.828472\pi\) |
0.756139 | − | 0.654411i | \(-0.227083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.78554 | + | 10.7680i | 0.410599 | + | 1.16795i | ||||
\(86\) | 0.418680 | − | 1.15031i | 0.0451474 | − | 0.124041i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.609724 | − | 0.870776i | −0.0649968 | − | 0.0928250i | ||||
\(89\) | −6.36010 | + | 11.0160i | −0.674169 | + | 1.16770i | 0.302542 | + | 0.953136i | \(0.402165\pi\) |
−0.976711 | + | 0.214559i | \(0.931168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4289 | + | 19.7955i | 1.19808 | + | 2.07513i | ||||
\(92\) | −1.84671 | + | 3.96028i | −0.192533 | + | 0.412888i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.65554 | − | 5.54825i | −0.480182 | − | 0.572259i | ||||
\(95\) | 0.203927 | + | 2.66890i | 0.0209224 | + | 0.273824i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.76434 | − | 3.62057i | −0.788349 | − | 0.367613i | −0.0136208 | − | 0.999907i | \(-0.504336\pi\) |
−0.774729 | + | 0.632294i | \(0.782114\pi\) | |||||||
\(98\) | 1.91959 | − | 7.16401i | 0.193908 | − | 0.723675i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.55071 | − | 7.78797i | 0.155071 | − | 0.778797i | ||||
\(101\) | 15.4590 | + | 2.72585i | 1.53823 | + | 0.271232i | 0.877569 | − | 0.479450i | \(-0.159164\pi\) |
0.660663 | + | 0.750682i | \(0.270275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6867 | + | 5.91592i | −1.25006 | + | 0.582912i | −0.931068 | − | 0.364845i | \(-0.881122\pi\) |
−0.318992 | + | 0.947758i | \(0.603344\pi\) | |||||||
\(104\) | −2.12169 | − | 12.0327i | −0.208049 | − | 1.17990i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.73936 | − | 2.29860i | −0.266071 | − | 0.223260i | ||||
\(107\) | −2.86472 | + | 2.86472i | −0.276943 | + | 0.276943i | −0.831887 | − | 0.554945i | \(-0.812739\pi\) |
0.554945 | + | 0.831887i | \(0.312739\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.64284i | − | 0.636269i | −0.948046 | − | 0.318134i | \(-0.896944\pi\) | ||
0.948046 | − | 0.318134i | \(-0.103056\pi\) | |||||||
\(110\) | −0.337520 | + | 0.570019i | −0.0321812 | + | 0.0543492i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.19706 | − | 5.99403i | 0.396585 | − | 0.566382i | ||||
\(113\) | 2.96857 | + | 6.36611i | 0.279259 | + | 0.598874i | 0.995043 | − | 0.0994488i | \(-0.0317080\pi\) |
−0.715783 | + | 0.698322i | \(0.753930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.15193 | + | 0.0677124i | 0.573671 | + | 0.00631422i | ||||
\(116\) | −0.00830033 | − | 0.00479220i | −0.000770666 | − | 0.000444944i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.256358 | + | 0.0686908i | 0.0235996 | + | 0.00632350i | ||||
\(119\) | 20.6631 | − | 7.52076i | 1.89418 | − | 0.689427i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.26323 | − | 6.93367i | 0.751203 | − | 0.630334i | ||||
\(122\) | 0.128615 | − | 1.47008i | 0.0116443 | − | 0.133094i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.21224 | + | 3.33059i | 0.108862 | + | 0.299096i | ||||
\(125\) | −10.8890 | + | 2.53559i | −0.973944 | + | 0.226790i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.09882 | − | 2.17007i | 0.718654 | − | 0.192563i | 0.119083 | − | 0.992884i | \(-0.462005\pi\) |
0.599571 | + | 0.800322i | \(0.295338\pi\) | |||||||
\(128\) | −9.19534 | + | 6.43865i | −0.812761 | + | 0.569102i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.28487 | + | 4.29841i | −0.551219 | + | 0.376995i | ||||
\(131\) | 11.2646 | − | 1.98625i | 0.984193 | − | 0.173540i | 0.341682 | − | 0.939816i | \(-0.389004\pi\) |
0.642512 | + | 0.766276i | \(0.277892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.13704 | − | 0.449432i | 0.445437 | − | 0.0389707i | ||||
\(134\) | −3.76606 | −0.325338 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.7540 | −1.00790 | ||||||||
\(137\) | −10.2700 | + | 0.898508i | −0.877424 | + | 0.0767647i | −0.516961 | − | 0.856009i | \(-0.672937\pi\) |
−0.360463 | + | 0.932773i | \(0.617381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.70385 | + | 0.300434i | −0.144518 | + | 0.0254825i | −0.245439 | − | 0.969412i | \(-0.578932\pi\) |
0.100921 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(140\) | −15.0356 | − | 2.82215i | −1.27074 | − | 0.238515i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.393738 | + | 0.275698i | −0.0330417 | + | 0.0231361i | ||||
\(143\) | −2.36610 | + | 0.633995i | −0.197863 | + | 0.0530173i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.00132399 | + | 0.0134293i | −0.000109952 | + | 0.00111524i | ||||
\(146\) | −2.52298 | − | 6.93182i | −0.208803 | − | 0.573681i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.03935 | − | 11.8798i | 0.0854339 | − | 0.976513i | ||||
\(149\) | 3.51771 | − | 2.95171i | 0.288182 | − | 0.241813i | −0.487223 | − | 0.873277i | \(-0.661990\pi\) |
0.775405 | + | 0.631464i | \(0.217546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16351 | + | 1.51539i | −0.338821 | + | 0.123321i | −0.505827 | − | 0.862635i | \(-0.668813\pi\) |
0.167005 | + | 0.985956i | \(0.446590\pi\) | |||||||
\(152\) | −2.66249 | − | 0.713411i | −0.215956 | − | 0.0578653i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.10524 | + | 0.638110i | 0.0890627 | + | 0.0514204i | ||||
\(155\) | 3.56727 | − | 3.48960i | 0.286530 | − | 0.280291i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.351788 | + | 0.754412i | 0.0280757 | + | 0.0602086i | 0.919846 | − | 0.392281i | \(-0.128314\pi\) |
−0.891770 | + | 0.452489i | \(0.850536\pi\) | |||||||
\(158\) | −0.578913 | + | 0.826774i | −0.0460559 | + | 0.0657746i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.9584 | + | 6.48867i | 0.866336 | + | 0.512974i | ||||
\(161\) | − | 11.8525i | − | 0.934107i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1572 | + | 10.1572i | −0.795571 | + | 0.795571i | −0.982394 | − | 0.186823i | \(-0.940181\pi\) |
0.186823 | + | 0.982394i | \(0.440181\pi\) | |||||||
\(164\) | 5.73166 | + | 4.80943i | 0.447567 | + | 0.375554i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18990 | − | 6.74824i | −0.0923540 | − | 0.523765i | ||||
\(167\) | 20.3353 | − | 9.48250i | 1.57359 | − | 0.733778i | 0.577038 | − | 0.816718i | \(-0.304209\pi\) |
0.996555 | + | 0.0829395i | \(0.0264308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.9250 | − | 2.63168i | −1.14808 | − | 0.202437i | ||||
\(170\) | 3.02235 | + | 6.67221i | 0.231804 | + | 0.511735i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.784088 | + | 2.92626i | −0.0597861 | + | 0.223125i | ||||
\(173\) | −2.09324 | − | 0.976093i | −0.159146 | − | 0.0742110i | 0.341413 | − | 0.939913i | \(-0.389094\pi\) |
−0.500559 | + | 0.865702i | \(0.666872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.11543 | + | 20.9228i | 0.386690 | + | 1.58161i | ||||
\(176\) | 0.504052 | + | 0.600706i | 0.0379943 | + | 0.0452799i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.44986 | + | 7.39824i | −0.258578 | + | 0.554522i | ||||
\(179\) | 10.3891 | + | 17.9945i | 0.776520 | + | 1.34497i | 0.933936 | + | 0.357440i | \(0.116350\pi\) |
−0.157416 | + | 0.987532i | \(0.550316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.61486 | − | 2.79701i | 0.120031 | − | 0.207900i | −0.799748 | − | 0.600335i | \(-0.795034\pi\) |
0.919780 | + | 0.392435i | \(0.128367\pi\) | |||||||
\(182\) | 8.41369 | + | 12.0160i | 0.623664 | + | 0.890685i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.16689 | + | 5.95348i | −0.159745 | + | 0.438896i | ||||
\(185\) | −15.8398 | + | 5.56855i | −1.16456 | + | 0.409408i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.205381 | + | 2.34751i | 0.0150189 | + | 0.171667i | ||||
\(188\) | 12.6743 | + | 12.6743i | 0.924372 | + | 0.924372i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.279645 | + | 1.69482i | 0.0202876 | + | 0.122955i | ||||
\(191\) | −0.296698 | + | 0.353591i | −0.0214683 | + | 0.0255850i | −0.776672 | − | 0.629905i | \(-0.783094\pi\) |
0.755203 | + | 0.655490i | \(0.227538\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.86360 | − | 1.30491i | −0.134145 | − | 0.0939292i | 0.504578 | − | 0.863366i | \(-0.331648\pi\) |
−0.638723 | + | 0.769437i | \(0.720537\pi\) | |||||||
\(194\) | −5.16623 | − | 1.88035i | −0.370914 | − | 0.135001i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.18729 | + | 18.0760i | −0.227663 | + | 1.29114i | ||||
\(197\) | −6.91110 | − | 25.7926i | −0.492396 | − | 1.83765i | −0.544153 | − | 0.838986i | \(-0.683149\pi\) |
0.0517571 | − | 0.998660i | \(-0.483518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.6539 | − | 11.9246i | 1.46412 | − | 0.845309i | 0.464921 | − | 0.885352i | \(-0.346083\pi\) |
0.999198 | + | 0.0400428i | \(0.0127494\pi\) | |||||||
\(200\) | 1.25566 | − | 11.4447i | 0.0887889 | − | 0.809261i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0354 | + | 0.877983i | 0.706088 | + | 0.0617747i | ||||
\(203\) | 0.0258981 | + | 0.00226579i | 0.00181769 | + | 0.000159027i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.83836 | − | 10.1449i | 0.198240 | − | 0.708552i | ||||
\(206\) | −7.77970 | + | 4.49161i | −0.542038 | + | 0.312946i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.33278 | + | 8.70605i | 0.161749 | + | 0.603656i | ||||
\(209\) | −0.0959604 | + | 0.544219i | −0.00663772 | + | 0.0376444i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3867 | + | 7.42015i | 1.40348 | + | 0.510825i | 0.929209 | − | 0.369555i | \(-0.120490\pi\) |
0.474270 | + | 0.880379i | \(0.342712\pi\) | |||||||
\(212\) | 7.24934 | + | 5.07605i | 0.497887 | + | 0.348624i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.67118 | + | 1.99163i | −0.114239 | + | 0.136145i | ||||
\(215\) | 4.20846 | − | 0.694397i | 0.287015 | − | 0.0473575i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.79799 | − | 6.79799i | −0.461477 | − | 0.461477i | ||||
\(218\) | −0.371543 | − | 4.24675i | −0.0251640 | − | 0.287626i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.709163 | − | 1.47811i | 0.0478118 | − | 0.0996542i | ||||
\(221\) | −9.26370 | + | 25.4518i | −0.623144 | + | 1.71207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.30605 | − | 9.00598i | −0.422285 | − | 0.603085i | 0.550489 | − | 0.834842i | \(-0.314441\pi\) |
−0.972774 | + | 0.231757i | \(0.925552\pi\) | |||||||
\(224\) | 12.2674 | − | 21.2477i | 0.819649 | − | 1.41967i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.25386 | + | 3.90381i | 0.149925 | + | 0.259677i | ||||
\(227\) | −4.18215 | + | 8.96865i | −0.277579 | + | 0.595270i | −0.994831 | − | 0.101544i | \(-0.967622\pi\) |
0.717252 | + | 0.696814i | \(0.245400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.25137 | + | 7.45009i | 0.413102 | + | 0.492316i | 0.931968 | − | 0.362540i | \(-0.118090\pi\) |
−0.518866 | + | 0.854855i | \(0.673646\pi\) | |||||||
\(230\) | 3.93670 | − | 0.300797i | 0.259579 | − | 0.0198340i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0125943 | − | 0.00587283i | −0.000826858 | − | 0.000385570i | ||||
\(233\) | 2.61861 | − | 9.77279i | 0.171551 | − | 0.640236i | −0.825563 | − | 0.564311i | \(-0.809142\pi\) |
0.997113 | − | 0.0759259i | \(-0.0241913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.89186 | − | 23.6181i | 0.580041 | − | 1.54067i | ||||
\(236\) | −0.646833 | − | 0.114054i | −0.0421053 | − | 0.00742429i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.7892 | − | 5.96371i | 0.829002 | − | 0.386570i | ||||
\(239\) | 0.554723 | + | 3.14599i | 0.0358821 | + | 0.203497i | 0.997478 | − | 0.0709702i | \(-0.0226095\pi\) |
−0.961596 | + | 0.274468i | \(0.911498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5334 | − | 13.0341i | −1.00060 | − | 0.839600i | −0.0135291 | − | 0.999908i | \(-0.504307\pi\) |
−0.987067 | + | 0.160309i | \(0.948751\pi\) | |||||||
\(242\) | 4.89485 | − | 4.89485i | 0.314653 | − | 0.314653i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.65203i | 0.233797i | ||||||||
\(245\) | 25.0343 | − | 6.41346i | 1.59938 | − | 0.409741i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.64320 | + | 5.20303i | −0.231811 | + | 0.331061i | ||||
\(248\) | 2.17179 | + | 4.65743i | 0.137909 | + | 0.295747i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.81951 | + | 2.23003i | −0.431303 | + | 0.141040i | ||||
\(251\) | −12.3046 | − | 7.10409i | −0.776662 | − | 0.448406i | 0.0585840 | − | 0.998282i | \(-0.481341\pi\) |
−0.835246 | + | 0.549876i | \(0.814675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.22689 | + | 0.328745i | 0.0771341 | + | 0.0206680i | ||||
\(254\) | 5.05618 | − | 1.84030i | 0.317253 | − | 0.115471i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.91329 | + | 4.96184i | −0.369581 | + | 0.310115i | ||||
\(257\) | −2.46595 | + | 28.1859i | −0.153822 | + | 1.75819i | 0.391701 | + | 0.920093i | \(0.371887\pi\) |
−0.545522 | + | 0.838096i | \(0.683669\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0631 | + | 30.3956i | 0.687426 | + | 1.88869i | ||||
\(260\) | 14.5674 | − | 11.9528i | 0.903432 | − | 0.741279i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.09034 | − | 1.89985i | 0.438043 | − | 0.117373i | ||||
\(263\) | 4.29988 | − | 3.01081i | 0.265142 | − | 0.185655i | −0.433444 | − | 0.901181i | \(-0.642702\pi\) |
0.698586 | + | 0.715526i | \(0.253813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.29860 | − | 12.2463i | 0.141202 | − | 0.752282i | ||||
\(266\) | 3.25896 | − | 0.574642i | 0.199819 | − | 0.0352336i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.28474 | − | 0.812310i | 0.567156 | − | 0.0496197i | ||||
\(269\) | −11.2342 | −0.684961 | −0.342480 | − | 0.939525i | \(-0.611267\pi\) | ||||
−0.342480 | + | 0.939525i | \(0.611267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3871 | −0.934699 | −0.467349 | − | 0.884073i | \(-0.654791\pi\) | ||||
−0.467349 | + | 0.884073i | \(0.654791\pi\) | |||||||
\(272\) | 8.63764 | − | 0.755696i | 0.523734 | − | 0.0458208i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.51532 | + | 1.14883i | −0.393605 | + | 0.0694032i | ||||
\(275\) | −2.30768 | − | 0.0508059i | −0.139158 | − | 0.00306371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4512 | + | 9.41860i | −0.808202 | + | 0.565909i | −0.903026 | − | 0.429585i | \(-0.858660\pi\) |
0.0948247 | + | 0.995494i | \(0.469771\pi\) | |||||||
\(278\) | −1.07246 | + | 0.287365i | −0.0643219 | + | 0.0172350i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.0736 | − | 2.17624i | −1.31915 | − | 0.130055i | ||||
\(281\) | 3.30030 | + | 9.06751i | 0.196880 | + | 0.540922i | 0.998369 | − | 0.0570865i | \(-0.0181811\pi\) |
−0.801490 | + | 0.598009i | \(0.795959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.35265 | + | 15.4609i | −0.0804068 | + | 0.919054i | 0.843674 | + | 0.536856i | \(0.180388\pi\) |
−0.924080 | + | 0.382198i | \(0.875167\pi\) | |||||||
\(284\) | 0.911245 | − | 0.764625i | 0.0540724 | − | 0.0453721i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.47718 | + | 0.537651i | −0.0873477 | + | 0.0317920i | ||||
\(287\) | −19.6033 | − | 5.25269i | −1.15715 | − | 0.310057i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.84266 | + | 4.52796i | 0.461333 | + | 0.266351i | ||||
\(290\) | −9.53107e−5 | 0.00865934i | −5.59684e−6 | 0.000508494i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.71521 | + | 16.5453i | 0.451499 | + | 0.968242i | ||||
\(293\) | −5.53310 | + | 7.90208i | −0.323247 | + | 0.461645i | −0.947582 | − | 0.319512i | \(-0.896481\pi\) |
0.624335 | + | 0.781157i | \(0.285370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.229500 | + | 0.895829i | 0.0133620 | + | 0.0521572i | ||||
\(296\) | − | 17.2902i | − | 1.00497i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.08377 | − | 2.08377i | 0.120709 | − | 0.120709i | ||||
\(299\) | 11.1837 | + | 9.38426i | 0.646772 | + | 0.542706i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.42692 | − | 8.09244i | −0.0822460 | − | 0.466440i | ||||
\(302\) | −2.57696 | + | 1.20166i | −0.148288 | + | 0.0691476i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00245 | + | 0.353085i | 0.114848 | + | 0.0202508i | ||||
\(305\) | 4.68376 | − | 2.12163i | 0.268191 | − | 0.121484i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.13471 | + | 4.23478i | −0.0647610 | + | 0.241692i | −0.990717 | − | 0.135940i | \(-0.956595\pi\) |
0.925956 | + | 0.377631i | \(0.123261\pi\) | |||||||
\(308\) | −2.86246 | − | 1.33479i | −0.163104 | − | 0.0760566i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.08537 | − | 2.43042i | 0.118441 | − | 0.138038i | ||||
\(311\) | 5.33012 | + | 6.35219i | 0.302243 | + | 0.360199i | 0.895694 | − | 0.444671i | \(-0.146679\pi\) |
−0.593451 | + | 0.804870i | \(0.702235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.37462 | − | 9.38140i | 0.247268 | − | 0.530268i | −0.743025 | − | 0.669264i | \(-0.766610\pi\) |
0.990293 | + | 0.138996i | \(0.0443874\pi\) | |||||||
\(314\) | 0.267093 | + | 0.462618i | 0.0150729 | + | 0.0261070i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.24891 | − | 2.16317i | 0.0702566 | − | 0.121688i | ||||
\(317\) | 0.779004 | + | 1.11253i | 0.0437532 | + | 0.0624861i | 0.840433 | − | 0.541916i | \(-0.182301\pi\) |
−0.796679 | + | 0.604402i | \(0.793412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.000952860 | 0.00261796i | −5.33499e−5 | 0.000146578i | ||||||
\(320\) | 0.519580 | + | 0.249282i | 0.0290454 | + | 0.0139353i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.662925 | − | 7.57727i | −0.0369434 | − | 0.422265i | ||||
\(323\) | 4.32066 | + | 4.32066i | 0.240408 | + | 0.240408i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.7924 | − | 11.7389i | −1.31977 | − | 0.651158i | ||||
\(326\) | −5.92535 | + | 7.06156i | −0.328175 | + | 0.391104i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.88639 | + | 6.22232i | 0.490669 | + | 0.343570i | ||||
\(329\) | −45.6863 | − | 16.6284i | −2.51877 | − | 0.916756i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24032 | − | 7.03423i | 0.0681744 | − | 0.386636i | −0.931560 | − | 0.363588i | \(-0.881552\pi\) |
0.999734 | − | 0.0230485i | \(-0.00733722\pi\) | |||||||
\(332\) | 4.38908 | + | 16.3803i | 0.240882 | + | 0.898985i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4699 | − | 7.19952i | 0.682324 | − | 0.393940i | ||||
\(335\) | −6.43573 | − | 11.4359i | −0.351622 | − | 0.624808i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.6457 | + | 2.50617i | 1.56043 | + | 0.136520i | 0.834406 | − | 0.551151i | \(-0.185811\pi\) |
0.726023 | + | 0.687671i | \(0.241367\pi\) | |||||||
\(338\) | −9.68871 | − | 0.847653i | −0.526997 | − | 0.0461062i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.89037 | − | 15.7976i | −0.482148 | − | 0.856744i | ||||
\(341\) | 0.892235 | − | 0.515132i | 0.0483172 | − | 0.0278960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.08105 | − | 18.9628i | −0.274351 | − | 1.02389i | ||||
\(344\) | −0.762735 | + | 4.32568i | −0.0411239 | + | 0.233225i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.39280 | − | 0.506936i | −0.0748772 | − | 0.0272531i | ||||
\(347\) | −24.1565 | − | 16.9146i | −1.29679 | − | 0.908021i | −0.297874 | − | 0.954605i | \(-0.596277\pi\) |
−0.998914 | + | 0.0465844i | \(0.985166\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.2402 | + | 15.7790i | −0.708730 | + | 0.844632i | −0.993484 | − | 0.113969i | \(-0.963644\pi\) |
0.284754 | + | 0.958601i | \(0.408088\pi\) | |||||||
\(350\) | 4.44052 | + | 13.0898i | 0.237356 | + | 0.699678i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.85918 | + | 1.85918i | 0.0990944 | + | 0.0990944i | ||||
\(353\) | −0.152839 | − | 1.74696i | −0.00813482 | − | 0.0929814i | 0.991042 | − | 0.133552i | \(-0.0426382\pi\) |
−0.999177 | + | 0.0405701i | \(0.987083\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.51002 | − | 0.724474i | −0.0801437 | − | 0.0384511i | ||||
\(356\) | 6.90944 | − | 18.9835i | 0.366199 | − | 1.00612i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.64820 | + | 10.9228i | 0.404220 | + | 0.577286i | ||||
\(359\) | −9.41628 | + | 16.3095i | −0.496972 | + | 0.860781i | −0.999994 | − | 0.00349274i | \(-0.998888\pi\) |
0.503022 | + | 0.864274i | \(0.332222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.78354 | − | 15.2135i | −0.462291 | − | 0.800712i | ||||
\(362\) | 0.875933 | − | 1.87844i | 0.0460380 | − | 0.0987288i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.3346 | − | 27.8091i | −1.22307 | − | 1.45759i | ||||
\(365\) | 16.7374 | − | 19.5068i | 0.876076 | − | 1.02103i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3645 | − | 11.3614i | −1.27182 | − | 0.593058i | −0.334783 | − | 0.942295i | \(-0.608663\pi\) |
−0.937034 | + | 0.349237i | \(0.886441\pi\) | |||||||
\(368\) | 1.20961 | − | 4.51434i | 0.0630555 | − | 0.235326i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.81486 | + | 4.44590i | −0.510251 | + | 0.231131i | ||||
\(371\) | −23.6399 | − | 4.16835i | −1.22732 | − | 0.216410i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.86161 | − | 1.33439i | 0.148169 | − | 0.0690922i | −0.347120 | − | 0.937821i | \(-0.612840\pi\) |
0.495288 | + | 0.868729i | \(0.335062\pi\) | |||||||
\(374\) | 0.262599 | + | 1.48927i | 0.0135786 | + | 0.0770083i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.9081 | + | 16.7049i | 1.02668 | + | 0.861487i | ||||
\(377\) | −0.0226429 | + | 0.0226429i | −0.00116617 | + | 0.00116617i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.29800i | − | 0.374873i | −0.982277 | − | 0.187436i | \(-0.939982\pi\) | ||
0.982277 | − | 0.187436i | \(-0.0600179\pi\) | |||||||
\(380\) | −1.05499 | − | 4.11804i | −0.0541197 | − | 0.211251i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.169902 | + | 0.242645i | −0.00869293 | + | 0.0124148i | ||||
\(383\) | 7.76938 | + | 16.6615i | 0.396997 | + | 0.851362i | 0.998617 | + | 0.0525799i | \(0.0167444\pi\) |
−0.601620 | + | 0.798783i | \(0.705478\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0489420 | + | 4.44657i | −0.00249432 | + | 0.226618i | ||||
\(386\) | −1.26438 | − | 0.729990i | −0.0643552 | − | 0.0371555i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.1423 | + | 3.52146i | 0.667197 | + | 0.178775i | ||||
\(389\) | −19.7491 | + | 7.18808i | −1.00132 | + | 0.364450i | −0.790093 | − | 0.612987i | \(-0.789968\pi\) |
−0.211226 | + | 0.977437i | \(0.567746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.7587 | − | 9.02763i | 0.544091 | − | 0.456547i | ||||
\(392\) | −2.31943 | + | 26.5112i | −0.117149 | + | 1.33902i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.86086 | − | 16.1026i | −0.295266 | − | 0.811237i | ||||
\(395\) | −3.49984 | − | 0.345050i | −0.176096 | − | 0.0173614i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.7796 | + | 8.78326i | −1.64516 | + | 0.440819i | −0.958252 | − | 0.285926i | \(-0.907699\pi\) |
−0.686907 | + | 0.726745i | \(0.741032\pi\) | |||||||
\(398\) | 12.5371 | − | 8.77854i | 0.628426 | − | 0.440029i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.186940 | + | 8.49107i | −0.00934699 | + | 0.424554i | ||||
\(401\) | 26.7887 | − | 4.72357i | 1.33776 | − | 0.235884i | 0.541433 | − | 0.840744i | \(-0.317882\pi\) |
0.796332 | + | 0.604860i | \(0.206771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7968 | − | 1.03208i | 0.587638 | − | 0.0514117i | ||||
\(404\) | −24.9303 | −1.24033 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0166833 | 0.000827980 | ||||||||
\(407\) | −3.45320 | + | 0.302116i | −0.171169 | + | 0.0149753i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.3695 | + | 2.35741i | −0.661081 | + | 0.116566i | −0.494115 | − | 0.869396i | \(-0.664508\pi\) |
−0.166965 | + | 0.985963i | \(0.553397\pi\) | |||||||
\(410\) | 1.24714 | − | 6.64438i | 0.0615917 | − | 0.328143i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.2111 | − | 12.7515i | 0.897195 | − | 0.628222i | ||||
\(413\) | 1.72085 | − | 0.461102i | 0.0846777 | − | 0.0226893i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4580 | − | 15.1451i | 0.906070 | − | 0.743444i | ||||
\(416\) | 10.3361 | + | 28.3982i | 0.506769 | + | 1.39234i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0309084 | + | 0.353285i | −0.00151178 | + | 0.0172797i | ||||
\(419\) | 9.78730 | − | 8.21252i | 0.478141 | − | 0.401208i | −0.371613 | − | 0.928388i | \(-0.621195\pi\) |
0.849754 | + | 0.527180i | \(0.176751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9246 | − | 6.16004i | 0.824853 | − | 0.300222i | 0.105108 | − | 0.994461i | \(-0.466481\pi\) |
0.719745 | + | 0.694239i | \(0.244259\pi\) | |||||||
\(422\) | 13.4482 | + | 3.60343i | 0.654648 | + | 0.175412i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.1122 | + | 6.41562i | 0.539656 | + | 0.311570i | ||||
\(425\) | −15.0957 | + | 20.5795i | −0.732251 | + | 0.998254i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.18641 | − | 8.97778i | −0.202595 | − | 0.434465i | ||||
\(428\) | 3.69050 | − | 5.27058i | 0.178387 | − | 0.254763i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.65162 | − | 0.679311i | 0.127873 | − | 0.0327593i | ||||
\(431\) | − | 4.80209i | − | 0.231309i | −0.993290 | − | 0.115654i | \(-0.963104\pi\) | ||
0.993290 | − | 0.115654i | \(-0.0368965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.6615 | − | 23.6615i | 1.13710 | − | 1.13710i | 0.148130 | − | 0.988968i | \(-0.452675\pi\) |
0.988968 | − | 0.148130i | \(-0.0473253\pi\) | |||||||
\(434\) | −4.72616 | − | 3.96572i | −0.226863 | − | 0.190360i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.83198 | + | 10.3897i | 0.0877360 | + | 0.497576i | ||||
\(437\) | 2.98497 | − | 1.39192i | 0.142791 | − | 0.0665844i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.531654 | + | 0.0937450i | 0.0253745 | + | 0.00447420i | 0.186321 | − | 0.982489i | \(-0.440344\pi\) |
−0.160947 | + | 0.986963i | \(0.551455\pi\) | |||||||
\(440\) | 0.837512 | − | 2.22455i | 0.0399268 | − | 0.106051i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.49871 | + | 16.7894i | −0.213982 | + | 0.798591i | ||||
\(443\) | −4.71408 | − | 2.19821i | −0.223973 | − | 0.104440i | 0.307393 | − | 0.951583i | \(-0.400543\pi\) |
−0.531366 | + | 0.847142i | \(0.678321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.3606 | + | 2.16699i | −1.34442 | + | 0.102725i | ||||
\(446\) | −4.53516 | − | 5.40479i | −0.214746 | − | 0.255924i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.469199 | − | 1.00620i | 0.0221676 | − | 0.0475385i | ||||
\(449\) | −6.99817 | − | 12.1212i | −0.330264 | − | 0.572034i | 0.652300 | − | 0.757961i | \(-0.273804\pi\) |
−0.982564 | + | 0.185927i | \(0.940471\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08745 | − | 1.88352i | 0.0512060 | − | 0.0886914i | ||||
\(452\) | −6.39863 | − | 9.13819i | −0.300966 | − | 0.429824i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.17201 | + | 5.96755i | −0.101937 | + | 0.280071i | ||||
\(455\) | −22.1093 | + | 46.0825i | −1.03650 | + | 2.16038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.334574 | + | 3.82420i | 0.0156507 | + | 0.178888i | 0.999997 | + | 0.00264047i | \(0.000840488\pi\) |
−0.984346 | + | 0.176248i | \(0.943604\pi\) | |||||||
\(458\) | 4.41318 | + | 4.41318i | 0.206214 | + | 0.206214i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.64056 | + | 1.59069i | −0.449493 | + | 0.0741664i | ||||
\(461\) | 14.3235 | − | 17.0701i | 0.667111 | − | 0.795032i | −0.321276 | − | 0.946985i | \(-0.604112\pi\) |
0.988388 | + | 0.151953i | \(0.0485563\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.977400 | − | 0.684383i | −0.0454236 | − | 0.0318060i | 0.550644 | − | 0.834740i | \(-0.314382\pi\) |
−0.596068 | + | 0.802934i | \(0.703271\pi\) | |||||||
\(464\) | 0.00963277 | + | 0.00350604i | 0.000447190 | + | 0.000162764i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.12747 | − | 6.39418i | 0.0522289 | − | 0.296205i | ||||
\(467\) | −0.233069 | − | 0.869824i | −0.0107851 | − | 0.0402506i | 0.960324 | − | 0.278888i | \(-0.0899659\pi\) |
−0.971109 | + | 0.238638i | \(0.923299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8935 | + | 12.6402i | −1.01095 | + | 0.583672i | ||||
\(470\) | 4.36355 | − | 15.5963i | 0.201276 | − | 0.719404i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.948680 | − | 0.0829988i | −0.0436665 | − | 0.00382033i | ||||
\(473\) | 0.877255 | + | 0.0767499i | 0.0403362 | + | 0.00352896i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.66853 | + | 3.74539i | −0.214207 | + | 0.171850i | ||||
\(476\) | −30.2439 | + | 17.4613i | −1.38623 | + | 0.800338i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.530593 | + | 1.98020i | 0.0242687 | + | 0.0905722i | ||||
\(479\) | 5.10504 | − | 28.9521i | 0.233255 | − | 1.32286i | −0.613001 | − | 0.790082i | \(-0.710038\pi\) |
0.846257 | − | 0.532775i | \(-0.178851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.4398 | − | 13.6270i | −1.70711 | − | 0.621336i | ||||
\(482\) | −10.6595 | − | 7.46386i | −0.485527 | − | 0.339969i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0119 | + | 13.1234i | −0.500539 | + | 0.596519i | ||||
\(485\) | −3.11864 | − | 18.9008i | −0.141610 | − | 0.858243i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.6006 | + | 22.6006i | 1.02413 | + | 1.02413i | 0.999702 | + | 0.0244298i | \(0.00777702\pi\) |
0.0244298 | + | 0.999702i | \(0.492223\pi\) | |||||||
\(488\) | 0.461492 | + | 5.27488i | 0.0208908 | + | 0.238783i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.6456 | − | 5.50031i | 0.706798 | − | 0.248479i | ||||
\(491\) | 4.34237 | − | 11.9306i | 0.195968 | − | 0.538419i | −0.802320 | − | 0.596894i | \(-0.796401\pi\) |
0.998289 | + | 0.0584746i | \(0.0186237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0176690 | + | 0.0252339i | 0.000795772 | + | 0.00113648i | ||||
\(494\) | −2.03808 | + | 3.53005i | −0.0916974 | + | 0.158824i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.89542 | − | 3.28297i | −0.0851071 | − | 0.147410i | ||||
\(497\) | −1.36361 | + | 2.92426i | −0.0611661 | + | 0.131171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.76871 | − | 9.25839i | −0.347775 | − | 0.414463i | 0.563594 | − | 0.826052i | \(-0.309418\pi\) |
−0.911369 | + | 0.411589i | \(0.864974\pi\) | |||||||
\(500\) | 16.3316 | − | 6.96878i | 0.730372 | − | 0.311653i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.26367 | − | 3.85341i | −0.368825 | − | 0.171986i | ||||
\(503\) | −5.65132 | + | 21.0910i | −0.251980 | + | 0.940402i | 0.717766 | + | 0.696285i | \(0.245165\pi\) |
−0.969746 | + | 0.244117i | \(0.921502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4832 | + | 31.9734i | 0.644493 | + | 1.42280i | ||||
\(506\) | 0.802737 | + | 0.141544i | 0.0356860 | + | 0.00629241i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0684 | + | 5.62760i | −0.535450 | + | 0.249684i | ||||
\(509\) | 0.934268 | + | 5.29850i | 0.0414107 | + | 0.234852i | 0.998487 | − | 0.0549834i | \(-0.0175106\pi\) |
−0.957077 | + | 0.289835i | \(0.906399\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.9326 | − | 31.8293i | −1.67804 | − | 1.40804i | ||||
\(512\) | 12.3723 | − | 12.3723i | 0.546785 | − | 0.546785i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.1571i | 0.800876i | ||||||||
\(515\) | −26.9336 | − | 15.9479i | −1.18684 | − | 0.702749i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.98844 | − | 4.26794i | 0.131432 | − | 0.187704i | ||||
\(518\) | 8.77266 | + | 18.8130i | 0.385449 | + | 0.826597i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.5303 | − | 19.1051i | 0.856461 | − | 0.837813i | ||||
\(521\) | 2.74885 | + | 1.58705i | 0.120429 | + | 0.0695300i | 0.559005 | − | 0.829165i | \(-0.311183\pi\) |
−0.438575 | + | 0.898694i | \(0.644517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6055 | − | 3.10969i | −0.507473 | − | 0.135977i | −0.00400710 | − | 0.999992i | \(-0.501276\pi\) |
−0.503466 | + | 0.864015i | \(0.667942\pi\) | |||||||
\(524\) | −17.0706 | + | 6.21317i | −0.745731 | + | 0.271424i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.58051 | − | 2.16530i | 0.112515 | − | 0.0944116i | ||||
\(527\) | 0.992860 | − | 11.3484i | 0.0432496 | − | 0.494346i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.27731 | + | 14.4993i | 0.229448 | + | 0.630404i | ||||
\(530\) | 0.784539 | − | 7.95757i | 0.0340782 | − | 0.345655i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.91060 | + | 2.11964i | −0.342968 | + | 0.0918980i | ||||
\(533\) | 20.4773 | − | 14.3384i | 0.886972 | − | 0.621064i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.90355 | − | 1.67118i | −0.384934 | − | 0.0722513i | ||||
\(536\) | 13.3080 | − | 2.34655i | 0.574817 | − | 0.101356i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.18199 | + | 0.628343i | −0.309638 | + | 0.0270898i | ||||
\(539\) | 5.33536 | 0.229810 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7781 | 1.45223 | 0.726116 | − | 0.687572i | \(-0.241324\pi\) | ||||
0.726116 | + | 0.687572i | \(0.241324\pi\) | |||||||
\(542\) | −9.83692 | + | 0.860619i | −0.422532 | + | 0.0369668i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.6306 | − | 5.04834i | 1.22753 | − | 0.216446i | ||||
\(545\) | 12.2606 | − | 8.38538i | 0.525186 | − | 0.359190i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.7446 | − | 8.22365i | 0.502162 | − | 0.351618i | −0.294887 | − | 0.955532i | \(-0.595282\pi\) |
0.797049 | + | 0.603914i | \(0.206393\pi\) | |||||||
\(548\) | 15.8149 | − | 4.23759i | 0.675579 | − | 0.181021i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.47813 | + | 0.0965912i | −0.0630278 | + | 0.00411866i | ||||
\(551\) | 0.00247076 | + | 0.00678836i | 0.000105258 | + | 0.000289194i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.590495 | + | 6.74939i | −0.0251104 | + | 0.287013i | ||||
\(554\) | −8.07250 | + | 6.77363i | −0.342968 | + | 0.287784i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.58203 | − | 0.939783i | 0.109503 | − | 0.0398557i | ||||
\(557\) | 9.77642 | + | 2.61958i | 0.414240 | + | 0.110995i | 0.459919 | − | 0.887961i | \(-0.347878\pi\) |
−0.0456789 | + | 0.998956i | \(0.514545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.76560 | + | 5.06082i | 0.370745 | + | 0.214050i | ||||
\(560\) | 16.3611 | + | 0.180082i | 0.691383 | + | 0.00760984i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.61703 | + | 5.61224i | 0.110393 | + | 0.236738i | ||||
\(563\) | 16.1451 | − | 23.0577i | 0.680437 | − | 0.971765i | −0.319273 | − | 0.947663i | \(-0.603439\pi\) |
0.999710 | − | 0.0241016i | \(-0.00767253\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00256 | + | 13.5151i | −0.336670 | + | 0.568585i | ||||
\(566\) | 9.95976i | 0.418640i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.21955 | − | 1.21955i | 0.0511713 | − | 0.0511713i | ||||
\(569\) | 7.66040 | + | 6.42784i | 0.321141 | + | 0.269469i | 0.789078 | − | 0.614292i | \(-0.210558\pi\) |
−0.467938 | + | 0.883761i | \(0.655003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.25288 | + | 24.1193i | 0.177978 | + | 1.00936i | 0.934651 | + | 0.355568i | \(0.115712\pi\) |
−0.756673 | + | 0.653794i | \(0.773176\pi\) | |||||||
\(572\) | 3.52584 | − | 1.64413i | 0.147423 | − | 0.0687444i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.8261 | − | 2.26159i | −0.535353 | − | 0.0943971i | ||||
\(575\) | 7.64073 | + | 11.4400i | 0.318640 | + | 0.477081i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.13963 | + | 15.4493i | −0.172335 | + | 0.643163i | 0.824655 | + | 0.565636i | \(0.191369\pi\) |
−0.996990 | + | 0.0775272i | \(0.975298\pi\) | |||||||
\(578\) | 5.26705 | + | 2.45606i | 0.219080 | + | 0.102159i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.00163278 | − | 0.0213691i | −6.77973e−5 | − | 0.000887302i | ||||
\(581\) | −29.5668 | − | 35.2364i | −1.22664 | − | 1.46185i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.08716 | − | 2.33143i | 0.0450258 | − | 0.0965581i | ||||
\(584\) | 13.2344 | + | 22.9227i | 0.547643 | + | 0.948546i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.09532 | + | 5.36125i | −0.127867 | + | 0.221471i | ||||
\(587\) | 11.3970 | + | 16.2765i | 0.470403 | + | 0.671805i | 0.982316 | − | 0.187233i | \(-0.0599518\pi\) |
−0.511913 | + | 0.859037i | \(0.671063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.913697 | − | 2.51036i | 0.0376482 | − | 0.103438i | ||||
\(590\) | 0.196823 | + | 0.559865i | 0.00810309 | + | 0.0230493i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.11163 | + | 12.7060i | 0.0456878 | + | 0.522214i | ||||
\(593\) | 24.0438 | + | 24.0438i | 0.987362 | + | 0.987362i | 0.999921 | − | 0.0125593i | \(-0.00399784\pi\) |
−0.0125593 | + | 0.999921i | \(0.503998\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.9644 | + | 28.6440i | 1.63838 | + | 1.17429i | ||||
\(596\) | −4.68781 | + | 5.58672i | −0.192020 | + | 0.228841i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.67460 | + | 5.37382i | 0.313838 | + | 0.219752i | ||||
\(599\) | 32.8027 | + | 11.9392i | 1.34028 | + | 0.487823i | 0.909901 | − | 0.414825i | \(-0.136157\pi\) |
0.430381 | + | 0.902647i | \(0.358379\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.52626 | + | 25.6697i | −0.184630 | + | 1.04709i | 0.741800 | + | 0.670621i | \(0.233972\pi\) |
−0.926430 | + | 0.376467i | \(0.877139\pi\) | |||||||
\(602\) | −1.36484 | − | 5.09367i | −0.0556269 | − | 0.207602i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.09398 | − | 3.51836i | 0.247961 | − | 0.143160i | ||||
\(605\) | 23.2282 | + | 6.49881i | 0.944361 | + | 0.264214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.56643 | − | 0.312022i | −0.144757 | − | 0.0126646i | 0.0145470 | − | 0.999894i | \(-0.495369\pi\) |
−0.159304 | + | 0.987230i | \(0.550925\pi\) | |||||||
\(608\) | 6.79175 | + | 0.594201i | 0.275442 | + | 0.0240980i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.87565 | − | 1.61832i | 0.116432 | − | 0.0655239i | ||||
\(611\) | 51.8625 | − | 29.9428i | 2.09813 | − | 1.21136i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.71891 | + | 17.6112i | 0.190595 | + | 0.711310i | 0.993363 | + | 0.115019i | \(0.0366928\pi\) |
−0.802768 | + | 0.596291i | \(0.796640\pi\) | |||||||
\(614\) | −0.488558 | + | 2.77075i | −0.0197166 | + | 0.111818i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.30313 | − | 1.56621i | −0.173378 | − | 0.0631044i | ||||
\(617\) | −2.52278 | − | 1.76647i | −0.101563 | − | 0.0711153i | 0.521692 | − | 0.853134i | \(-0.325301\pi\) |
−0.623255 | + | 0.782019i | \(0.714190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9284 | − | 27.3250i | 0.921572 | − | 1.09829i | −0.0733171 | − | 0.997309i | \(-0.523359\pi\) |
0.994889 | − | 0.100978i | \(-0.0321970\pi\) | |||||||
\(620\) | −4.61699 | + | 6.44168i | −0.185423 | + | 0.258704i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.76282 | + | 3.76282i | 0.150875 | + | 0.150875i | ||||
\(623\) | 4.77580 | + | 54.5877i | 0.191339 | + | 2.18701i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.4253 | − | 16.8970i | −0.737013 | − | 0.675879i | ||||
\(626\) | 2.27197 | − | 6.24218i | 0.0908062 | − | 0.249488i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.758266 | − | 1.08292i | −0.0302581 | − | 0.0432130i | ||||
\(629\) | −19.1642 | + | 33.1934i | −0.764127 | + | 1.32351i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.459598 | + | 0.796047i | 0.0182963 | + | 0.0316901i | 0.875029 | − | 0.484071i | \(-0.160842\pi\) |
−0.856732 | + | 0.515761i | \(0.827509\pi\) | |||||||
\(632\) | 1.53054 | − | 3.28225i | 0.0608815 | − | 0.130561i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.560241 | + | 0.667669i | 0.0222500 | + | 0.0265165i | ||||
\(635\) | 14.2286 | + | 12.2085i | 0.564643 | + | 0.484481i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 55.5788 | + | 25.9168i | 2.20211 | + | 1.02686i | ||||
\(638\) | −0.000462735 | 0.00172695i | −1.83199e−5 | 6.83707e-5i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.4912 | − | 8.84408i | −0.928570 | − | 0.349593i | ||||
\(641\) | −28.1175 | − | 4.95787i | −1.11057 | − | 0.195824i | −0.411875 | − | 0.911240i | \(-0.635126\pi\) |
−0.698699 | + | 0.715416i | \(0.746237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.3252 | − | 16.0061i | 1.35365 | − | 0.631220i | 0.395764 | − | 0.918352i | \(-0.370480\pi\) |
0.957891 | + | 0.287133i | \(0.0927020\pi\) | |||||||
\(644\) | 3.26871 | + | 18.5378i | 0.128805 | + | 0.730492i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00385 | + | 2.52053i | 0.118185 | + | 0.0991688i | ||||
\(647\) | −30.2410 | + | 30.2410i | −1.18890 | + | 1.18890i | −0.211525 | + | 0.977373i | \(0.567843\pi\) |
−0.977373 | + | 0.211525i | \(0.932157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.190921i | 0.00749431i | ||||||||
\(650\) | −15.8670 | − | 6.17392i | −0.622355 | − | 0.242161i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0851 | − | 18.6874i | 0.512451 | − | 0.731856i | ||||
\(653\) | −15.4696 | − | 33.1747i | −0.605374 | − | 1.29823i | −0.935178 | − | 0.354178i | \(-0.884761\pi\) |
0.329804 | − | 0.944049i | \(-0.393017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8855 | + | 18.2836i | 0.698845 | + | 0.714400i | ||||
\(656\) | −6.93039 | − | 4.00126i | −0.270586 | − | 0.156223i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30.1372 | − | 8.07523i | −1.17487 | − | 0.314805i | ||||
\(659\) | 29.4659 | − | 10.7247i | 1.14783 | − | 0.417776i | 0.303095 | − | 0.952960i | \(-0.401980\pi\) |
0.844735 | + | 0.535184i | \(0.179758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.28171 | − | 2.75368i | 0.127644 | − | 0.107106i | −0.576731 | − | 0.816934i | \(-0.695672\pi\) |
0.704375 | + | 0.709828i | \(0.251227\pi\) | |||||||
\(662\) | 0.399503 | − | 4.56634i | 0.0155271 | − | 0.177476i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.40938 | + | 23.1046i | 0.326347 | + | 0.896632i | ||||
\(665\) | 7.31409 | + | 8.91402i | 0.283628 | + | 0.345671i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0160385 | − | 0.00429751i | 0.000621014 | − | 0.000166400i | ||||
\(668\) | −29.1901 | + | 20.4392i | −1.12940 | + | 0.790815i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.75397 | − | 6.95096i | −0.183662 | − | 0.268539i | ||||
\(671\) | 1.04544 | − | 0.184339i | 0.0403587 | − | 0.00711633i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.3733 | − | 2.48234i | 1.09371 | − | 0.0956872i | 0.474005 | − | 0.880522i | \(-0.342808\pi\) |
0.619705 | + | 0.784835i | \(0.287252\pi\) | |||||||
\(674\) | 18.4533 | 0.710793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.0691 | 0.925735 | ||||||||
\(677\) | −42.4749 | + | 3.71607i | −1.63244 | + | 0.142820i | −0.866189 | − | 0.499717i | \(-0.833437\pi\) |
−0.766255 | + | 0.642537i | \(0.777882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.3444 | + | 6.40849i | −1.39477 | + | 0.245935i | ||||
\(680\) | −14.8373 | − | 21.6941i | −0.568983 | − | 0.831933i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.541592 | − | 0.379227i | 0.0207386 | − | 0.0145213i | ||||
\(683\) | 16.5292 | − | 4.42899i | 0.632473 | − | 0.169471i | 0.0716812 | − | 0.997428i | \(-0.477164\pi\) |
0.560792 | + | 0.827957i | \(0.310497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.6224 | − | 17.8210i | −0.558692 | − | 0.680904i | ||||
\(686\) | −4.30892 | − | 11.8386i | −0.164515 | − | 0.452002i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.282400 | − | 3.22785i | 0.0107664 | − | 0.123061i | ||||
\(689\) | 22.6501 | − | 19.0057i | 0.862901 | − | 0.724060i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.7479 | + | 10.4634i | −1.09362 | + | 0.398045i | −0.824961 | − | 0.565190i | \(-0.808803\pi\) |
−0.268660 | + | 0.963235i | \(0.586581\pi\) | |||||||
\(692\) | 3.54310 | + | 0.949372i | 0.134689 | + | 0.0360897i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3892 | − | 9.46233i | −0.622127 | − | 0.359185i | ||||
\(695\) | −2.70530 | − | 2.76552i | −0.102618 | − | 0.104902i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1632 | − | 21.7951i | −0.384959 | − | 0.825547i | ||||
\(698\) | −7.58187 | + | 10.8280i | −0.286978 | + | 0.409847i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.7709 | − | 31.3134i | −0.520491 | − | 1.18353i | ||||
\(701\) | 33.1045i | 1.25034i | 0.780488 | + | 0.625171i | \(0.214971\pi\) | ||||
−0.780488 | + | 0.625171i | \(0.785029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.35572 | + | 6.35572i | −0.239710 | + | 0.239710i | ||||
\(704\) | 0.0911416 | + | 0.0764768i | 0.00343503 | + | 0.00288233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.195420 | − | 1.10828i | −0.00735472 | − | 0.0417107i | ||||
\(707\) | 61.2863 | − | 28.5783i | 2.30491 | − | 1.07480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6991 | + | 6.47105i | 1.37827 | + | 0.243025i | 0.813182 | − | 0.582009i | \(-0.197733\pi\) |
0.565083 | + | 0.825034i | \(0.308844\pi\) | |||||||
\(710\) | −1.00587 | − | 0.378697i | −0.0377498 | − | 0.0142122i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.58092 | − | 28.2924i | 0.284107 | − | 1.06030i | ||||
\(713\) | −5.56503 | − | 2.59502i | −0.208412 | − | 0.0971841i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.15693 | − | 3.56677i | −0.155460 | − | 0.133390i | ||||
\(716\) | −21.2116 | − | 25.2790i | −0.792716 | − | 0.944722i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.10759 | + | 10.9533i | −0.190614 | + | 0.408772i | ||||
\(719\) | −21.5770 | − | 37.3725i | −0.804687 | − | 1.39376i | −0.916502 | − | 0.400029i | \(-0.869000\pi\) |
0.111816 | − | 0.993729i | \(-0.464333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.1509 | + | 52.2229i | −1.12288 | + | 1.94488i | ||||
\(722\) | −6.46621 | − | 9.23470i | −0.240647 | − | 0.343680i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.75433 | + | 4.82000i | −0.0651993 | + | 0.179134i | ||||
\(725\) | −0.0264575 | + | 0.0145083i | −0.000982606 | + | 0.000538826i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.590839 | + | 6.75332i | 0.0219130 | + | 0.250467i | 0.999248 | + | 0.0387690i | \(0.0123436\pi\) |
−0.977335 | + | 0.211698i | \(0.932101\pi\) | |||||||
\(728\) | −37.2180 | − | 37.2180i | −1.37939 | − | 1.37939i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.60915 | − | 13.4068i | 0.355651 | − | 0.496207i | ||||
\(731\) | 6.25882 | − | 7.45897i | 0.231491 | − | 0.275880i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8024 | − | 14.5660i | −0.768353 | − | 0.538006i | 0.122408 | − | 0.992480i | \(-0.460938\pi\) |
−0.890760 | + | 0.454474i | \(0.849827\pi\) | |||||||
\(734\) | −16.2116 | − | 5.90055i | −0.598382 | − | 0.217793i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.72113 | − | 15.4323i | 0.100302 | − | 0.568841i | ||||
\(737\) | −0.701189 | − | 2.61687i | −0.0258286 | − | 0.0963937i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3022 | + | 18.0723i | −1.15147 | + | 0.664801i | −0.949245 | − | 0.314538i | \(-0.898150\pi\) |
−0.202224 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(740\) | 23.2384 | − | 13.0778i | 0.854259 | − | 0.480749i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.3461 | − | 1.34261i | −0.563371 | − | 0.0492886i | ||||
\(743\) | −35.7603 | − | 3.12862i | −1.31192 | − | 0.114778i | −0.590365 | − | 0.807136i | \(-0.701016\pi\) |
−0.721554 | + | 0.692358i | \(0.756572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.88838 | + | 2.76658i | 0.362282 | + | 0.101360i | ||||
\(746\) | 1.75479 | − | 1.01313i | 0.0642473 | − | 0.0370932i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.968627 | − | 3.61497i | −0.0354165 | − | 0.132176i | ||||
\(749\) | −3.03056 | + | 17.1872i | −0.110734 | + | 0.628006i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6234 | + | 7.50630i | 0.752558 | + | 0.273909i | 0.689682 | − | 0.724113i | \(-0.257750\pi\) |
0.0628763 | + | 0.998021i | \(0.479973\pi\) | |||||||
\(752\) | −15.7038 | − | 10.9959i | −0.572660 | − | 0.400981i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0132091 | + | 0.0157420i | −0.000481047 | + | 0.000573290i | ||||
\(755\) | −8.05261 | − | 5.77161i | −0.293065 | − | 0.210051i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9998 | − | 19.9998i | −0.726906 | − | 0.726906i | 0.243096 | − | 0.970002i | \(-0.421837\pi\) |
−0.970002 | + | 0.243096i | \(0.921837\pi\) | |||||||
\(758\) | −0.408186 | − | 4.66559i | −0.0148260 | − | 0.169462i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.04417 | − | 5.81466i | −0.0741500 | − | 0.210920i | ||||
\(761\) | −17.7365 | + | 48.7306i | −0.642947 | + | 1.76648i | −0.000683402 | 1.00000i | \(0.500218\pi\) | |
−0.642264 | + | 0.766484i | \(0.722005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4135 | − | 23.4409i | −0.594209 | − | 0.848619i | ||||
\(764\) | 0.366534 | − | 0.634856i | 0.0132607 | − | 0.0229683i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.89884 | + | 10.2171i | 0.213134 | + | 0.369159i | ||||
\(767\) | −0.927410 | + | 1.98884i | −0.0334868 | + | 0.0718127i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9226 | + | 34.4686i | 1.04298 | + | 1.24297i | 0.969350 | + | 0.245684i | \(0.0790126\pi\) |
0.0736257 | + | 0.997286i | \(0.476543\pi\) | |||||||
\(770\) | 0.217414 | + | 2.84542i | 0.00783506 | + | 0.102542i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.27462 | + | 1.52698i | 0.117856 | + | 0.0549572i | ||||
\(773\) | −6.21709 | + | 23.2025i | −0.223613 | + | 0.834536i | 0.759342 | + | 0.650691i | \(0.225521\pi\) |
−0.982955 | + | 0.183844i | \(0.941146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9437 | + | 2.17907i | 0.393111 | + | 0.0782746i | ||||
\(776\) | 19.4273 | + | 3.42556i | 0.697399 | + | 0.122970i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.2235 | + | 5.69992i | −0.438234 | + | 0.204352i | ||||
\(779\) | −0.979290 | − | 5.55383i | −0.0350867 | − | 0.198987i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.264879 | − | 0.222260i | −0.00947813 | − | 0.00795309i | ||||
\(782\) | 6.37309 | − | 6.37309i | 0.227901 | − | 0.227901i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 19.6314i | − | 0.701122i | ||||||
\(785\) | −0.948338 | + | 1.60160i | −0.0338476 | + | 0.0571635i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.8846 | + | 26.9699i | −0.673162 | + | 0.961375i | 0.326706 | + | 0.945126i | \(0.394061\pi\) |
−0.999868 | + | 0.0162488i | \(0.994828\pi\) | |||||||
\(788\) | 17.9224 | + | 38.4347i | 0.638460 | + | 1.36918i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.25674 | − | 0.0248392i | −0.0802911 | − | 0.000883739i | ||||
\(791\) | 26.2051 | + | 15.1295i | 0.931746 | + | 0.537944i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7858 | + | 3.15800i | 0.418527 | + | 0.112144i | ||||
\(794\) | −20.4646 | + | 7.44852i | −0.726263 | + | 0.264338i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.0150 | + | 24.3465i | −1.02841 | + | 0.862939i | ||||
\(797\) | −4.05225 | + | 46.3175i | −0.143538 | + | 1.64065i | 0.493449 | + | 0.869774i | \(0.335736\pi\) |
−0.636988 | + | 0.770874i | \(0.719820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.7037 | − | 54.1355i | −0.697068 | − | 1.91518i | ||||
\(800\) | 1.85692 | + | 28.4165i | 0.0656522 | + | 1.00467i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.8618 | − | 4.51810i | 0.595410 | − | 0.159540i | ||||
\(803\) | 4.34687 | − | 3.04371i | 0.153398 | − | 0.107410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8760 | − | 14.9616i | 0.771026 | − | 0.527328i | ||||
\(806\) | 7.48391 | − | 1.31962i | 0.263610 | − | 0.0464815i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.0087 | + | 3.15035i | −1.26678 | + | 0.110829i | ||||
\(809\) | 14.6731 | 0.515879 | 0.257939 | − | 0.966161i | \(-0.416957\pi\) | ||||
0.257939 | + | 0.966161i | \(0.416957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.4369 | 1.06878 | 0.534392 | − | 0.845237i | \(-0.320541\pi\) | ||||
0.534392 | + | 0.845237i | \(0.320541\pi\) | |||||||
\(812\) | −0.0411306 | + | 0.00359846i | −0.00144340 | + | 0.000126281i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.19073 | + | 0.386284i | −0.0767849 | + | 0.0135393i | ||||
\(815\) | −31.5685 | − | 5.92535i | −1.10580 | − | 0.207556i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.87046 | − | 1.30971i | 0.0654390 | − | 0.0458209i | ||||
\(818\) | −8.41525 | + | 2.25486i | −0.294232 | + | 0.0788393i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.64152 | + | 16.6499i | −0.0573242 | + | 0.581439i | ||||
\(821\) | −5.06906 | − | 13.9271i | −0.176911 | − | 0.486060i | 0.819266 | − | 0.573414i | \(-0.194381\pi\) |
−0.996177 | + | 0.0873536i | \(0.972159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.04135 | + | 11.9027i | −0.0362993 | + | 0.414903i | 0.956205 | + | 0.292696i | \(0.0945525\pi\) |
−0.992505 | + | 0.122206i | \(0.961003\pi\) | |||||||
\(824\) | 24.6922 | − | 20.7192i | 0.860193 | − | 0.721788i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.07435 | − | 0.391031i | 0.0373813 | − | 0.0136057i | ||||
\(827\) | −5.37558 | − | 1.44038i | −0.186927 | − | 0.0500870i | 0.164141 | − | 0.986437i | \(-0.447515\pi\) |
−0.351068 | + | 0.936350i | \(0.614181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.1754 | − | 19.7312i | −1.18696 | − | 0.685293i | −0.229347 | − | 0.973345i | \(-0.573659\pi\) |
−0.957615 | + | 0.288052i | \(0.906992\pi\) | |||||||
\(830\) | 10.9531 | − | 10.7146i | 0.380188 | − | 0.371910i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.577937 | + | 1.23939i | 0.0200364 | + | 0.0429681i | ||||
\(833\) | 33.8375 | − | 48.3250i | 1.17240 | − | 1.67436i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.1713 | + | 25.5626i | 1.49401 | + | 0.884630i | ||||
\(836\) | − | 0.877645i | − | 0.0303540i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.79766 | − | 5.79766i | 0.200277 | − | 0.200277i | ||||
\(839\) | −34.4322 | − | 28.8921i | −1.18873 | − | 0.997464i | −0.999881 | − | 0.0154586i | \(-0.995079\pi\) |
−0.188851 | − | 0.982006i | \(-0.560476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03579 | − | 28.5594i | −0.173648 | − | 0.984807i | ||||
\(842\) | 10.4753 | − | 4.88471i | 0.361003 | − | 0.168338i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.9320 | − | 5.98313i | −1.16799 | − | 0.205948i | ||||
\(845\) | −13.9829 | − | 30.8689i | −0.481025 | − | 1.06192i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.0268 | − | 44.8845i | 0.413244 | − | 1.54225i | ||||
\(848\) | −8.57848 | − | 4.00021i | −0.294586 | − | 0.137368i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.49962 | + | 14.0008i | −0.291535 | + | 0.480222i | ||||
\(851\) | 13.2797 | + | 15.8261i | 0.455222 | + | 0.542513i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.70943 | + | 7.95489i | −0.127008 | + | 0.272370i | −0.959522 | − | 0.281635i | \(-0.909123\pi\) |
0.832513 | + | 0.554005i | \(0.186901\pi\) | |||||||
\(854\) | −3.17850 | − | 5.50532i | −0.108766 | − | 0.188388i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.66443 | − | 8.07903i | 0.159427 | − | 0.276135i | ||||
\(857\) | 19.8301 | + | 28.3204i | 0.677385 | + | 0.967406i | 0.999784 | + | 0.0208017i | \(0.00662187\pi\) |
−0.322399 | + | 0.946604i | \(0.604489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.70299 | − | 18.4163i | 0.228703 | − | 0.628357i | −0.771264 | − | 0.636516i | \(-0.780375\pi\) |
0.999967 | + | 0.00815913i | \(0.00259716\pi\) | |||||||
\(860\) | −6.39071 | + | 2.24669i | −0.217922 | + | 0.0766114i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.268587 | − | 3.06997i | −0.00914812 | − | 0.104563i | ||||
\(863\) | −29.8911 | − | 29.8911i | −1.01750 | − | 1.01750i | −0.999844 | − | 0.0176605i | \(-0.994378\pi\) |
−0.0176605 | − | 0.999844i | \(-0.505622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.840774 | − | 5.09560i | −0.0285872 | − | 0.173255i | ||||
\(866\) | 13.8033 | − | 16.4501i | 0.469055 | − | 0.558998i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.5071 | + | 8.75757i | 0.424519 | + | 0.297251i | ||||
\(869\) | −0.682275 | − | 0.248328i | −0.0231446 | − | 0.00842394i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.40728 | − | 30.6662i | 0.183219 | − | 1.03908i | ||||
\(872\) | 3.95897 | + | 14.7751i | 0.134068 | + | 0.500347i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.83043 | − | 1.05680i | 0.0619154 | − | 0.0357469i | ||||
\(875\) | −32.1596 | + | 35.8527i | −1.08719 | + | 1.21204i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.6921 | − | 2.86019i | −1.10393 | − | 0.0965817i | −0.479413 | − | 0.877590i | \(-0.659150\pi\) |
−0.624521 | + | 0.781008i | \(0.714706\pi\) | |||||||
\(878\) | 0.345129 | + | 0.0301948i | 0.0116475 | + | 0.00101903i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.472439 | + | 1.68860i | −0.0159259 | + | 0.0569228i | ||||
\(881\) | 10.5631 | − | 6.09860i | 0.355879 | − | 0.205467i | −0.311392 | − | 0.950281i | \(-0.600795\pi\) |
0.667272 | + | 0.744814i | \(0.267462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.21415 | + | 34.3877i | 0.310081 | + | 1.15724i | 0.928483 | + | 0.371376i | \(0.121114\pi\) |
−0.618402 | + | 0.785862i | \(0.712220\pi\) | |||||||
\(884\) | 7.46965 | − | 42.3625i | 0.251232 | − | 1.42480i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.13665 | − | 1.14165i | −0.105378 | − | 0.0383544i | ||||
\(887\) | −8.21054 | − | 5.74909i | −0.275683 | − | 0.193035i | 0.427556 | − | 0.903989i | \(-0.359375\pi\) |
−0.703239 | + | 0.710954i | \(0.748264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2168 | − | 27.6687i | 0.778666 | − | 0.927978i | ||||
\(890\) | −18.0096 | + | 2.97159i | −0.603684 | + | 0.0996080i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.3466 | + | 12.3466i | 0.413396 | + | 0.413396i | ||||
\(893\) | −1.17747 | − | 13.4586i | −0.0394027 | − | 0.450374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0978 | + | 41.8899i | −0.671795 | + | 1.40022i | ||||
\(896\) | −16.5391 | + | 45.4408i | −0.552532 | + | 1.51807i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.15187 | − | 7.35763i | −0.171920 | − | 0.245527i | ||||
\(899\) | 0.00673405 | − | 0.0116637i | 0.000224593 | − | 0.000389007i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2220 | − | 24.6332i | −0.473803 | − | 0.820651i | ||||
\(902\) | 0.589856 | − | 1.26495i | 0.0196401 | − | 0.0421183i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.3968 | − | 12.3904i | −0.345791 | − | 0.412098i | ||||
\(905\) | 7.20086 | − | 0.550206i | 0.239365 | − | 0.0182895i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0298 | − | 7.47482i | −0.532261 | − | 0.248197i | 0.137857 | − | 0.990452i | \(-0.455979\pi\) |
−0.670118 | + | 0.742255i | \(0.733756\pi\) | |||||||
\(908\) | 4.06766 | − | 15.1807i | 0.134990 | − | 0.503790i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.5570 | + | 30.6970i | −0.383110 | + | 1.01760i | ||||
\(911\) | −15.2588 | − | 2.69054i | −0.505547 | − | 0.0891416i | −0.0849428 | − | 0.996386i | \(-0.527071\pi\) |
−0.420604 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.46752 | − | 2.08324i | 0.147853 | − | 0.0689451i | ||||
\(914\) | 0.427785 | + | 2.42609i | 0.0141499 | + | 0.0802478i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.8320 | − | 9.92824i | −0.390941 | − | 0.328038i | ||||
\(917\) | 34.8423 | − | 34.8423i | 1.15059 | − | 1.15059i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6392i | 0.614851i | 0.951572 | + | 0.307426i | \(0.0994676\pi\) | ||||
−0.951572 | + | 0.307426i | \(0.900532\pi\) | |||||||
\(920\) | −13.7235 | + | 3.51579i | −0.452452 | + | 0.115912i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.20222 | − | 11.7140i | 0.270126 | − | 0.385779i | ||||
\(923\) | −1.67962 | − | 3.60196i | −0.0552855 | − | 0.118560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.2726 | − | 22.2059i | −0.995357 | − | 0.730126i | ||||
\(926\) | −0.663128 | − | 0.382857i | −0.0217917 | − | 0.0125815i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.0331999 | + | 0.00889589i | 0.00108984 | + | 0.000292022i | ||||
\(929\) | 9.92982 | − | 3.61416i | 0.325787 | − | 0.118577i | −0.173949 | − | 0.984755i | \(-0.555653\pi\) |
0.499736 | + | 0.866178i | \(0.333431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5979 | − | 8.89269i | 0.347332 | − | 0.291446i | ||||
\(932\) | −1.40045 | + | 16.0072i | −0.0458733 | + | 0.524334i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.197650 | − | 0.543040i | −0.00646732 | − | 0.0177688i | ||||
\(935\) | −4.07351 | + | 3.34237i | −0.133218 | + | 0.109307i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.3508 | + | 3.84529i | −0.468820 | + | 0.125620i | −0.485492 | − | 0.874241i | \(-0.661360\pi\) |
0.0166719 | + | 0.999861i | \(0.494693\pi\) | |||||||
\(938\) | −13.2895 | + | 9.30540i | −0.433917 | + | 0.303832i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.39378 | + | 39.3919i | −0.241159 | + | 1.28482i | ||||
\(941\) | −16.9600 | + | 2.99051i | −0.552882 | + | 0.0974879i | −0.443107 | − | 0.896469i | \(-0.646124\pi\) |
−0.109774 | + | 0.993957i | \(0.535013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.9130 | + | 1.12974i | −0.420504 | + | 0.0367894i | ||||
\(944\) | 0.702492 | 0.0228642 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.565120 | 0.0183736 | ||||||||
\(947\) | 59.3613 | − | 5.19344i | 1.92898 | − | 0.168764i | 0.942678 | − | 0.333704i | \(-0.108299\pi\) |
0.986304 | + | 0.164940i | \(0.0527431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0667 | − | 10.5914i | 1.94985 | − | 0.343811i | ||||
\(950\) | −2.77510 | + | 2.65554i | −0.0900360 | + | 0.0861569i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −41.4769 | + | 29.0424i | −1.34427 | + | 0.941271i | ||||
\(953\) | 7.58847 | − | 2.03332i | 0.245815 | − | 0.0658658i | −0.133808 | − | 0.991007i | \(-0.542721\pi\) |
0.379623 | + | 0.925141i | \(0.376054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.02715 | − | 0.101267i | −0.0332377 | − | 0.00327691i | ||||
\(956\) | −1.73522 | − | 4.76748i | −0.0561211 | − | 0.154191i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.64431 | − | 18.7946i | 0.0531253 | − | 0.607225i | ||||
\(959\) | −34.0202 | + | 28.5463i | −1.09857 | + | 0.921808i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4503 | − | 8.89918i | 0.788719 | − | 0.287070i | ||||
\(962\) | −24.6973 | − | 6.61763i | −0.796274 | − | 0.213361i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.8895 | + | 16.1020i | 0.898261 | + | 0.518611i | ||||
\(965\) | 0.0559891 | − | 5.08682i | 0.00180235 | − | 0.163751i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.1660 | − | 28.2347i | −0.423392 | − | 0.907966i | −0.996102 | − | 0.0882085i | \(-0.971886\pi\) |
0.572710 | − | 0.819758i | \(-0.305892\pi\) | |||||||
\(968\) | −14.2469 | + | 20.3466i | −0.457911 | + | 0.653965i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.05089 | − | 11.9088i | −0.0979581 | − | 0.382370i | ||||
\(971\) | 46.4614i | 1.49102i | 0.666496 | + | 0.745509i | \(0.267793\pi\) | ||||
−0.666496 | + | 0.745509i | \(0.732207\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.27012 | + | 5.27012i | −0.168952 | + | 0.168952i | ||||
\(974\) | 15.7126 | + | 13.1844i | 0.503464 | + | 0.422456i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.678273 | − | 3.84668i | −0.0217110 | − | 0.123129i | ||||
\(977\) | −30.9924 | + | 14.4520i | −0.991534 | + | 0.462360i | −0.849549 | − | 0.527509i | \(-0.823126\pi\) |
−0.141985 | + | 0.989869i | \(0.545348\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.78303 | − | 1.01970i | −0.184826 | − | 0.0325899i | ||||
\(980\) | −37.3860 | + | 16.9349i | −1.19425 | + | 0.540967i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.10878 | − | 7.87006i | 0.0672937 | − | 0.251144i | ||||
\(983\) | −32.2428 | − | 15.0350i | −1.02838 | − | 0.479543i | −0.166175 | − | 0.986096i | \(-0.553142\pi\) |
−0.862209 | + | 0.506553i | \(0.830919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.8810 | − | 45.3142i | 1.23885 | − | 1.44383i | ||||
\(986\) | 0.0127071 | + | 0.0151438i | 0.000404677 | + | 0.000482275i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.26321 | − | 9.14249i | 0.135631 | − | 0.290861i | ||||
\(989\) | −2.62418 | − | 4.54522i | −0.0834442 | − | 0.144530i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.77369 | + | 4.80418i | −0.0881092 | + | 0.152610i | −0.906712 | − | 0.421751i | \(-0.861416\pi\) |
0.818603 | + | 0.574360i | \(0.194749\pi\) | |||||||
\(992\) | −7.29047 | − | 10.4119i | −0.231473 | − | 0.330577i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.708192 | + | 1.94574i | −0.0224625 | + | 0.0617152i | ||||
\(995\) | 48.0808 | + | 23.0681i | 1.52426 | + | 0.731307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.65905 | + | 30.3931i | 0.0842129 | + | 0.962558i | 0.914330 | + | 0.404969i | \(0.132718\pi\) |
−0.830117 | + | 0.557589i | \(0.811727\pi\) | |||||||
\(998\) | −5.48435 | − | 5.48435i | −0.173604 | − | 0.173604i | ||||
\(999\) | 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 | 405.2.r.a.197.10 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.92.7 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.278.7 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.443.7 | 192 | |||
15.8 | even | 4 | 135.2.q.a.38.10 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.632.10 | 192 | |||
27.5 | odd | 18 | inner | 405.2.r.a.287.7 | 192 | ||
27.22 | even | 9 | 135.2.q.a.32.10 | ✓ | 192 | ||
135.22 | odd | 36 | 675.2.ba.b.518.10 | 192 | |||
135.49 | even | 18 | 675.2.ba.b.32.7 | 192 | |||
135.103 | odd | 36 | 135.2.q.a.113.7 | yes | 192 | ||
135.113 | even | 36 | inner | 405.2.r.a.368.10 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.10 | ✓ | 192 | 27.22 | even | 9 | ||
135.2.q.a.38.10 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.92.7 | yes | 192 | 3.2 | odd | 2 | ||
135.2.q.a.113.7 | yes | 192 | 135.103 | odd | 36 | ||
405.2.r.a.197.10 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.278.7 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.287.7 | 192 | 27.5 | odd | 18 | inner | ||
405.2.r.a.368.10 | 192 | 135.113 | even | 36 | inner | ||
675.2.ba.b.32.7 | 192 | 135.49 | even | 18 | |||
675.2.ba.b.443.7 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.518.10 | 192 | 135.22 | odd | 36 | |||
675.2.ba.b.632.10 | 192 | 15.14 | odd | 2 |