Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (of order \(4\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 487.14 | ||
Character | \(\chi\) | \(=\) | 1110.487 |
Dual form | 1110.2.o.a.253.14 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.02734 | − | 0.943349i | −0.906652 | − | 0.421878i | ||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −0.516238 | − | 0.516238i | −0.195120 | − | 0.195120i | 0.602784 | − | 0.797904i | \(-0.294058\pi\) |
−0.797904 | + | 0.602784i | \(0.794058\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.02734 | + | 0.943349i | 0.641100 | + | 0.298313i | ||||
\(11\) | 0.497352i | 0.149957i | 0.997185 | + | 0.0749787i | \(0.0238889\pi\) | ||||
−0.997185 | + | 0.0749787i | \(0.976111\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −1.53056 | −0.424500 | −0.212250 | − | 0.977215i | \(-0.568079\pi\) | ||||
−0.212250 | + | 0.977215i | \(0.568079\pi\) | |||||||
\(14\) | 0.516238 | + | 0.516238i | 0.137970 | + | 0.137970i | ||||
\(15\) | −0.766495 | − | 2.10059i | −0.197908 | − | 0.542370i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.55573i | 0.619856i | 0.950760 | + | 0.309928i | \(0.100305\pi\) | ||||
−0.950760 | + | 0.309928i | \(0.899695\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 2.36425 | − | 2.36425i | 0.542396 | − | 0.542396i | −0.381835 | − | 0.924231i | \(-0.624708\pi\) |
0.924231 | + | 0.381835i | \(0.124708\pi\) | |||||||
\(20\) | −2.02734 | − | 0.943349i | −0.453326 | − | 0.210939i | ||||
\(21\) | − | 0.730071i | − | 0.159315i | ||||||
\(22\) | − | 0.497352i | − | 0.106036i | ||||||
\(23\) | 5.13868 | 1.07149 | 0.535744 | − | 0.844380i | \(-0.320031\pi\) | ||||
0.535744 | + | 0.844380i | \(0.320031\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | 3.22019 | + | 3.82497i | 0.644037 | + | 0.764994i | ||||
\(26\) | 1.53056 | 0.300167 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −0.516238 | − | 0.516238i | −0.0975599 | − | 0.0975599i | ||||
\(29\) | −7.56116 | − | 7.56116i | −1.40407 | − | 1.40407i | −0.786568 | − | 0.617504i | \(-0.788144\pi\) |
−0.617504 | − | 0.786568i | \(-0.711856\pi\) | |||||||
\(30\) | 0.766495 | + | 2.10059i | 0.139942 | + | 0.383514i | ||||
\(31\) | 5.92380 | − | 5.92380i | 1.06395 | − | 1.06395i | 0.0661351 | − | 0.997811i | \(-0.478933\pi\) |
0.997811 | − | 0.0661351i | \(-0.0210668\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.351681 | + | 0.351681i | −0.0612198 | + | 0.0612198i | ||||
\(34\) | − | 2.55573i | − | 0.438305i | ||||||
\(35\) | 0.559596 | + | 1.53358i | 0.0945890 | + | 0.259223i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 4.64120 | − | 3.93182i | 0.763009 | − | 0.646388i | ||||
\(38\) | −2.36425 | + | 2.36425i | −0.383532 | + | 0.383532i | ||||
\(39\) | −1.08227 | − | 1.08227i | −0.173301 | − | 0.173301i | ||||
\(40\) | 2.02734 | + | 0.943349i | 0.320550 | + | 0.149157i | ||||
\(41\) | 2.70364i | 0.422238i | 0.977460 | + | 0.211119i | \(0.0677108\pi\) | ||||
−0.977460 | + | 0.211119i | \(0.932289\pi\) | |||||||
\(42\) | 0.730071i | 0.112652i | ||||||||
\(43\) | 9.05230 | 1.38046 | 0.690232 | − | 0.723588i | \(-0.257509\pi\) | ||||
0.690232 | + | 0.723588i | \(0.257509\pi\) | |||||||
\(44\) | 0.497352i | 0.0749787i | ||||||||
\(45\) | 0.943349 | − | 2.02734i | 0.140626 | − | 0.302217i | ||||
\(46\) | −5.13868 | −0.757656 | ||||||||
\(47\) | −9.26908 | − | 9.26908i | −1.35203 | − | 1.35203i | −0.883384 | − | 0.468650i | \(-0.844740\pi\) |
−0.468650 | − | 0.883384i | \(-0.655260\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 6.46700i | − | 0.923857i | ||||||
\(50\) | −3.22019 | − | 3.82497i | −0.455403 | − | 0.540933i | ||||
\(51\) | −1.80718 | + | 1.80718i | −0.253055 | + | 0.253055i | ||||
\(52\) | −1.53056 | −0.212250 | ||||||||
\(53\) | −0.413793 | + | 0.413793i | −0.0568388 | + | 0.0568388i | −0.734955 | − | 0.678116i | \(-0.762797\pi\) |
0.678116 | + | 0.734955i | \(0.262797\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | 0.469177 | − | 1.00830i | 0.0632638 | − | 0.135959i | ||||
\(56\) | 0.516238 | + | 0.516238i | 0.0689852 | + | 0.0689852i | ||||
\(57\) | 3.34355 | 0.442865 | ||||||||
\(58\) | 7.56116 | + | 7.56116i | 0.992829 | + | 0.992829i | ||||
\(59\) | 5.91307 | − | 5.91307i | 0.769817 | − | 0.769817i | −0.208257 | − | 0.978074i | \(-0.566779\pi\) |
0.978074 | + | 0.208257i | \(0.0667792\pi\) | |||||||
\(60\) | −0.766495 | − | 2.10059i | −0.0989541 | − | 0.271185i | ||||
\(61\) | 10.7956 | − | 10.7956i | 1.38223 | − | 1.38223i | 0.541586 | − | 0.840645i | \(-0.317824\pi\) |
0.840645 | − | 0.541586i | \(-0.182176\pi\) | |||||||
\(62\) | −5.92380 | + | 5.92380i | −0.752323 | + | 0.752323i | ||||
\(63\) | 0.516238 | − | 0.516238i | 0.0650399 | − | 0.0650399i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.10295 | + | 1.44385i | 0.384874 | + | 0.179087i | ||||
\(66\) | 0.351681 | − | 0.351681i | 0.0432889 | − | 0.0432889i | ||||
\(67\) | −9.29726 | + | 9.29726i | −1.13584 | + | 1.13584i | −0.146653 | + | 0.989188i | \(0.546850\pi\) |
−0.989188 | + | 0.146653i | \(0.953150\pi\) | |||||||
\(68\) | 2.55573i | 0.309928i | ||||||||
\(69\) | 3.63359 | + | 3.63359i | 0.437433 | + | 0.437433i | ||||
\(70\) | −0.559596 | − | 1.53358i | −0.0668845 | − | 0.183298i | ||||
\(71\) | −4.10631 | −0.487329 | −0.243664 | − | 0.969860i | \(-0.578350\pi\) | ||||
−0.243664 | + | 0.969860i | \(0.578350\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −2.63103 | − | 2.63103i | −0.307938 | − | 0.307938i | 0.536171 | − | 0.844109i | \(-0.319870\pi\) |
−0.844109 | + | 0.536171i | \(0.819870\pi\) | |||||||
\(74\) | −4.64120 | + | 3.93182i | −0.539529 | + | 0.457065i | ||||
\(75\) | −0.427648 | + | 4.98168i | −0.0493805 | + | 0.575235i | ||||
\(76\) | 2.36425 | − | 2.36425i | 0.271198 | − | 0.271198i | ||||
\(77\) | 0.256752 | − | 0.256752i | 0.0292596 | − | 0.0292596i | ||||
\(78\) | 1.08227 | + | 1.08227i | 0.122543 | + | 0.122543i | ||||
\(79\) | −0.827925 | + | 0.827925i | −0.0931489 | + | 0.0931489i | −0.752146 | − | 0.658997i | \(-0.770981\pi\) |
0.658997 | + | 0.752146i | \(0.270981\pi\) | |||||||
\(80\) | −2.02734 | − | 0.943349i | −0.226663 | − | 0.105470i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 2.70364i | − | 0.298567i | ||||||
\(83\) | 11.2038 | − | 11.2038i | 1.22978 | − | 1.22978i | 0.265729 | − | 0.964048i | \(-0.414387\pi\) |
0.964048 | − | 0.265729i | \(-0.0856126\pi\) | |||||||
\(84\) | − | 0.730071i | − | 0.0796573i | ||||||
\(85\) | 2.41095 | − | 5.18133i | 0.261504 | − | 0.561994i | ||||
\(86\) | −9.05230 | −0.976135 | ||||||||
\(87\) | − | 10.6931i | − | 1.14642i | ||||||
\(88\) | − | 0.497352i | − | 0.0530179i | ||||||
\(89\) | 6.24255 | + | 6.24255i | 0.661709 | + | 0.661709i | 0.955783 | − | 0.294074i | \(-0.0950112\pi\) |
−0.294074 | + | 0.955783i | \(0.595011\pi\) | |||||||
\(90\) | −0.943349 | + | 2.02734i | −0.0994377 | + | 0.213700i | ||||
\(91\) | 0.790132 | + | 0.790132i | 0.0828284 | + | 0.0828284i | ||||
\(92\) | 5.13868 | 0.535744 | ||||||||
\(93\) | 8.37752 | 0.868708 | ||||||||
\(94\) | 9.26908 | + | 9.26908i | 0.956032 | + | 0.956032i | ||||
\(95\) | −7.02344 | + | 2.56282i | −0.720590 | + | 0.262940i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 3.13965i | 0.318783i | 0.987215 | + | 0.159391i | \(0.0509532\pi\) | ||||
−0.987215 | + | 0.159391i | \(0.949047\pi\) | |||||||
\(98\) | 6.46700i | 0.653265i | ||||||||
\(99\) | −0.497352 | −0.0499858 | ||||||||
\(100\) | 3.22019 | + | 3.82497i | 0.322019 | + | 0.382497i | ||||
\(101\) | 4.17592i | 0.415519i | 0.978180 | + | 0.207760i | \(0.0666172\pi\) | ||||
−0.978180 | + | 0.207760i | \(0.933383\pi\) | |||||||
\(102\) | 1.80718 | − | 1.80718i | 0.178937 | − | 0.178937i | ||||
\(103\) | 15.6656i | 1.54357i | 0.635881 | + | 0.771787i | \(0.280637\pi\) | ||||
−0.635881 | + | 0.771787i | \(0.719363\pi\) | |||||||
\(104\) | 1.53056 | 0.150083 | ||||||||
\(105\) | −0.688712 | + | 1.48010i | −0.0672114 | + | 0.144443i | ||||
\(106\) | 0.413793 | − | 0.413793i | 0.0401911 | − | 0.0401911i | ||||
\(107\) | −0.609066 | − | 0.609066i | −0.0588806 | − | 0.0588806i | 0.677053 | − | 0.735934i | \(-0.263257\pi\) |
−0.735934 | + | 0.677053i | \(0.763257\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −0.255676 | + | 0.255676i | −0.0244894 | + | 0.0244894i | −0.719245 | − | 0.694756i | \(-0.755512\pi\) |
0.694756 | + | 0.719245i | \(0.255512\pi\) | |||||||
\(110\) | −0.469177 | + | 1.00830i | −0.0447342 | + | 0.0961376i | ||||
\(111\) | 6.06205 | + | 0.501607i | 0.575384 | + | 0.0476104i | ||||
\(112\) | −0.516238 | − | 0.516238i | −0.0487799 | − | 0.0487799i | ||||
\(113\) | 12.8460i | 1.20845i | 0.796813 | + | 0.604226i | \(0.206518\pi\) | ||||
−0.796813 | + | 0.604226i | \(0.793482\pi\) | |||||||
\(114\) | −3.34355 | −0.313153 | ||||||||
\(115\) | −10.4178 | − | 4.84756i | −0.971467 | − | 0.452038i | ||||
\(116\) | −7.56116 | − | 7.56116i | −0.702036 | − | 0.702036i | ||||
\(117\) | − | 1.53056i | − | 0.141500i | ||||||
\(118\) | −5.91307 | + | 5.91307i | −0.544343 | + | 0.544343i | ||||
\(119\) | 1.31937 | − | 1.31937i | 0.120946 | − | 0.120946i | ||||
\(120\) | 0.766495 | + | 2.10059i | 0.0699711 | + | 0.191757i | ||||
\(121\) | 10.7526 | 0.977513 | ||||||||
\(122\) | −10.7956 | + | 10.7956i | −0.977385 | + | 0.977385i | ||||
\(123\) | −1.91176 | + | 1.91176i | −0.172378 | + | 0.172378i | ||||
\(124\) | 5.92380 | − | 5.92380i | 0.531973 | − | 0.531973i | ||||
\(125\) | −2.92012 | − | 10.7923i | −0.261183 | − | 0.965289i | ||||
\(126\) | −0.516238 | + | 0.516238i | −0.0459902 | + | 0.0459902i | ||||
\(127\) | −0.504136 | − | 0.504136i | −0.0447349 | − | 0.0447349i | 0.684385 | − | 0.729120i | \(-0.260071\pi\) |
−0.729120 | + | 0.684385i | \(0.760071\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.40095 | + | 6.40095i | 0.563572 | + | 0.563572i | ||||
\(130\) | −3.10295 | − | 1.44385i | −0.272147 | − | 0.126634i | ||||
\(131\) | 15.2212 | − | 15.2212i | 1.32988 | − | 1.32988i | 0.424407 | − | 0.905472i | \(-0.360483\pi\) |
0.905472 | − | 0.424407i | \(-0.139517\pi\) | |||||||
\(132\) | −0.351681 | + | 0.351681i | −0.0306099 | + | 0.0306099i | ||||
\(133\) | −2.44103 | −0.211664 | ||||||||
\(134\) | 9.29726 | − | 9.29726i | 0.803161 | − | 0.803161i | ||||
\(135\) | 2.10059 | − | 0.766495i | 0.180790 | − | 0.0659694i | ||||
\(136\) | − | 2.55573i | − | 0.219152i | ||||||
\(137\) | −10.5042 | − | 10.5042i | −0.897430 | − | 0.897430i | 0.0977781 | − | 0.995208i | \(-0.468826\pi\) |
−0.995208 | + | 0.0977781i | \(0.968826\pi\) | |||||||
\(138\) | −3.63359 | − | 3.63359i | −0.309312 | − | 0.309312i | ||||
\(139\) | 0.111253 | 0.00943637 | 0.00471819 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471819 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(140\) | 0.559596 | + | 1.53358i | 0.0472945 | + | 0.129611i | ||||
\(141\) | − | 13.1085i | − | 1.10393i | ||||||
\(142\) | 4.10631 | 0.344594 | ||||||||
\(143\) | − | 0.761226i | − | 0.0636569i | ||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 8.19620 | + | 22.4618i | 0.680657 | + | 1.86535i | ||||
\(146\) | 2.63103 | + | 2.63103i | 0.217745 | + | 0.217745i | ||||
\(147\) | 4.57286 | − | 4.57286i | 0.377163 | − | 0.377163i | ||||
\(148\) | 4.64120 | − | 3.93182i | 0.381505 | − | 0.323194i | ||||
\(149\) | − | 16.2537i | − | 1.33155i | −0.746150 | − | 0.665777i | \(-0.768100\pi\) | ||
0.746150 | − | 0.665777i | \(-0.231900\pi\) | |||||||
\(150\) | 0.427648 | − | 4.98168i | 0.0349173 | − | 0.406752i | ||||
\(151\) | − | 15.7270i | − | 1.27985i | −0.768438 | − | 0.639924i | \(-0.778966\pi\) | ||
0.768438 | − | 0.639924i | \(-0.221034\pi\) | |||||||
\(152\) | −2.36425 | + | 2.36425i | −0.191766 | + | 0.191766i | ||||
\(153\) | −2.55573 | −0.206619 | ||||||||
\(154\) | −0.256752 | + | 0.256752i | −0.0206897 | + | 0.0206897i | ||||
\(155\) | −17.5977 | + | 6.42132i | −1.41348 | + | 0.515773i | ||||
\(156\) | −1.08227 | − | 1.08227i | −0.0866507 | − | 0.0866507i | ||||
\(157\) | −3.60469 | − | 3.60469i | −0.287685 | − | 0.287685i | 0.548479 | − | 0.836164i | \(-0.315207\pi\) |
−0.836164 | + | 0.548479i | \(0.815207\pi\) | |||||||
\(158\) | 0.827925 | − | 0.827925i | 0.0658662 | − | 0.0658662i | ||||
\(159\) | −0.585191 | −0.0464087 | ||||||||
\(160\) | 2.02734 | + | 0.943349i | 0.160275 | + | 0.0745783i | ||||
\(161\) | −2.65278 | − | 2.65278i | −0.209068 | − | 0.209068i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | − | 12.0896i | − | 0.946929i | −0.880813 | − | 0.473465i | \(-0.843003\pi\) | ||
0.880813 | − | 0.473465i | \(-0.156997\pi\) | |||||||
\(164\) | 2.70364i | 0.211119i | ||||||||
\(165\) | 1.04473 | − | 0.381218i | 0.0813324 | − | 0.0296778i | ||||
\(166\) | −11.2038 | + | 11.2038i | −0.869583 | + | 0.869583i | ||||
\(167\) | 11.3927i | 0.881596i | 0.897606 | + | 0.440798i | \(0.145305\pi\) | ||||
−0.897606 | + | 0.440798i | \(0.854695\pi\) | |||||||
\(168\) | 0.730071i | 0.0563262i | ||||||||
\(169\) | −10.6574 | −0.819800 | ||||||||
\(170\) | −2.41095 | + | 5.18133i | −0.184911 | + | 0.397390i | ||||
\(171\) | 2.36425 | + | 2.36425i | 0.180799 | + | 0.180799i | ||||
\(172\) | 9.05230 | 0.690232 | ||||||||
\(173\) | 13.4370 | + | 13.4370i | 1.02160 | + | 1.02160i | 0.999762 | + | 0.0218360i | \(0.00695117\pi\) |
0.0218360 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(174\) | 10.6931i | 0.810641i | ||||||||
\(175\) | 0.312213 | − | 3.63698i | 0.0236011 | − | 0.274930i | ||||
\(176\) | 0.497352i | 0.0374893i | ||||||||
\(177\) | 8.36235 | 0.628553 | ||||||||
\(178\) | −6.24255 | − | 6.24255i | −0.467899 | − | 0.467899i | ||||
\(179\) | −7.63199 | − | 7.63199i | −0.570442 | − | 0.570442i | 0.361810 | − | 0.932252i | \(-0.382159\pi\) |
−0.932252 | + | 0.361810i | \(0.882159\pi\) | |||||||
\(180\) | 0.943349 | − | 2.02734i | 0.0703131 | − | 0.151109i | ||||
\(181\) | 9.48047 | 0.704677 | 0.352339 | − | 0.935873i | \(-0.385387\pi\) | ||||
0.352339 | + | 0.935873i | \(0.385387\pi\) | |||||||
\(182\) | −0.790132 | − | 0.790132i | −0.0585685 | − | 0.0585685i | ||||
\(183\) | 15.2672 | 1.12859 | ||||||||
\(184\) | −5.13868 | −0.378828 | ||||||||
\(185\) | −13.1184 | + | 3.59286i | −0.964481 | + | 0.264152i | ||||
\(186\) | −8.37752 | −0.614269 | ||||||||
\(187\) | −1.27110 | −0.0929520 | ||||||||
\(188\) | −9.26908 | − | 9.26908i | −0.676017 | − | 0.676017i | ||||
\(189\) | 0.730071 | 0.0531049 | ||||||||
\(190\) | 7.02344 | − | 2.56282i | 0.509534 | − | 0.185926i | ||||
\(191\) | 13.3339 | + | 13.3339i | 0.964808 | + | 0.964808i | 0.999401 | − | 0.0345933i | \(-0.0110136\pi\) |
−0.0345933 | + | 0.999401i | \(0.511014\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 8.67065 | 0.624127 | 0.312064 | − | 0.950061i | \(-0.398980\pi\) | ||||
0.312064 | + | 0.950061i | \(0.398980\pi\) | |||||||
\(194\) | − | 3.13965i | − | 0.225413i | ||||||
\(195\) | 1.17316 | + | 3.21508i | 0.0840120 | + | 0.230236i | ||||
\(196\) | − | 6.46700i | − | 0.461928i | ||||||
\(197\) | 5.35975 | + | 5.35975i | 0.381867 | + | 0.381867i | 0.871774 | − | 0.489908i | \(-0.162970\pi\) |
−0.489908 | + | 0.871774i | \(0.662970\pi\) | |||||||
\(198\) | 0.497352 | 0.0353453 | ||||||||
\(199\) | −13.1621 | − | 13.1621i | −0.933037 | − | 0.933037i | 0.0648573 | − | 0.997895i | \(-0.479341\pi\) |
−0.997895 | + | 0.0648573i | \(0.979341\pi\) | |||||||
\(200\) | −3.22019 | − | 3.82497i | −0.227702 | − | 0.270466i | ||||
\(201\) | −13.1483 | −0.927410 | ||||||||
\(202\) | − | 4.17592i | − | 0.293816i | ||||||
\(203\) | 7.80672i | 0.547924i | ||||||||
\(204\) | −1.80718 | + | 1.80718i | −0.126528 | + | 0.126528i | ||||
\(205\) | 2.55048 | − | 5.48119i | 0.178133 | − | 0.382823i | ||||
\(206\) | − | 15.6656i | − | 1.09147i | ||||||
\(207\) | 5.13868i | 0.357163i | ||||||||
\(208\) | −1.53056 | −0.106125 | ||||||||
\(209\) | 1.17586 | + | 1.17586i | 0.0813363 | + | 0.0813363i | ||||
\(210\) | 0.688712 | − | 1.48010i | 0.0475256 | − | 0.102137i | ||||
\(211\) | −24.6681 | −1.69822 | −0.849112 | − | 0.528213i | \(-0.822862\pi\) | ||||
−0.849112 | + | 0.528213i | \(0.822862\pi\) | |||||||
\(212\) | −0.413793 | + | 0.413793i | −0.0284194 | + | 0.0284194i | ||||
\(213\) | −2.90360 | − | 2.90360i | −0.198951 | − | 0.198951i | ||||
\(214\) | 0.609066 | + | 0.609066i | 0.0416349 | + | 0.0416349i | ||||
\(215\) | −18.3521 | − | 8.53948i | −1.25160 | − | 0.582388i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | −6.11618 | −0.415194 | ||||||||
\(218\) | 0.255676 | − | 0.255676i | 0.0173166 | − | 0.0173166i | ||||
\(219\) | − | 3.72083i | − | 0.251431i | ||||||
\(220\) | 0.469177 | − | 1.00830i | 0.0316319 | − | 0.0679796i | ||||
\(221\) | − | 3.91170i | − | 0.263129i | ||||||
\(222\) | −6.06205 | − | 0.501607i | −0.406858 | − | 0.0336657i | ||||
\(223\) | −11.0405 | + | 11.0405i | −0.739328 | + | 0.739328i | −0.972448 | − | 0.233120i | \(-0.925106\pi\) |
0.233120 | + | 0.972448i | \(0.425106\pi\) | |||||||
\(224\) | 0.516238 | + | 0.516238i | 0.0344926 | + | 0.0344926i | ||||
\(225\) | −3.82497 | + | 3.22019i | −0.254998 | + | 0.214679i | ||||
\(226\) | − | 12.8460i | − | 0.854505i | ||||||
\(227\) | 28.9019i | 1.91829i | 0.282922 | + | 0.959143i | \(0.408696\pi\) | ||||
−0.282922 | + | 0.959143i | \(0.591304\pi\) | |||||||
\(228\) | 3.34355 | 0.221432 | ||||||||
\(229\) | 27.5614i | 1.82131i | 0.413171 | + | 0.910654i | \(0.364421\pi\) | ||||
−0.413171 | + | 0.910654i | \(0.635579\pi\) | |||||||
\(230\) | 10.4178 | + | 4.84756i | 0.686931 | + | 0.319639i | ||||
\(231\) | 0.363102 | 0.0238904 | ||||||||
\(232\) | 7.56116 | + | 7.56116i | 0.496414 | + | 0.496414i | ||||
\(233\) | −7.51093 | − | 7.51093i | −0.492057 | − | 0.492057i | 0.416897 | − | 0.908954i | \(-0.363118\pi\) |
−0.908954 | + | 0.416897i | \(0.863118\pi\) | |||||||
\(234\) | 1.53056i | 0.100056i | ||||||||
\(235\) | 10.0476 | + | 27.5355i | 0.655431 | + | 1.79622i | ||||
\(236\) | 5.91307 | − | 5.91307i | 0.384908 | − | 0.384908i | ||||
\(237\) | −1.17086 | −0.0760557 | ||||||||
\(238\) | −1.31937 | + | 1.31937i | −0.0855219 | + | 0.0855219i | ||||
\(239\) | −6.73852 | + | 6.73852i | −0.435879 | + | 0.435879i | −0.890622 | − | 0.454744i | \(-0.849731\pi\) |
0.454744 | + | 0.890622i | \(0.349731\pi\) | |||||||
\(240\) | −0.766495 | − | 2.10059i | −0.0494770 | − | 0.135593i | ||||
\(241\) | −8.91683 | − | 8.91683i | −0.574384 | − | 0.574384i | 0.358967 | − | 0.933350i | \(-0.383129\pi\) |
−0.933350 | + | 0.358967i | \(0.883129\pi\) | |||||||
\(242\) | −10.7526 | −0.691206 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 10.7956 | − | 10.7956i | 0.691116 | − | 0.691116i | ||||
\(245\) | −6.10063 | + | 13.1108i | −0.389755 | + | 0.837617i | ||||
\(246\) | 1.91176 | − | 1.91176i | 0.121890 | − | 0.121890i | ||||
\(247\) | −3.61862 | + | 3.61862i | −0.230247 | + | 0.230247i | ||||
\(248\) | −5.92380 | + | 5.92380i | −0.376162 | + | 0.376162i | ||||
\(249\) | 15.8446 | 1.00411 | ||||||||
\(250\) | 2.92012 | + | 10.7923i | 0.184684 | + | 0.682563i | ||||
\(251\) | −8.72803 | + | 8.72803i | −0.550908 | + | 0.550908i | −0.926703 | − | 0.375795i | \(-0.877370\pi\) |
0.375795 | + | 0.926703i | \(0.377370\pi\) | |||||||
\(252\) | 0.516238 | − | 0.516238i | 0.0325200 | − | 0.0325200i | ||||
\(253\) | 2.55573i | 0.160677i | ||||||||
\(254\) | 0.504136 | + | 0.504136i | 0.0316323 | + | 0.0316323i | ||||
\(255\) | 5.36855 | − | 1.95896i | 0.336192 | − | 0.122675i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 6.57411i | − | 0.410082i | −0.978753 | − | 0.205041i | \(-0.934267\pi\) | ||
0.978753 | − | 0.205041i | \(-0.0657327\pi\) | |||||||
\(258\) | −6.40095 | − | 6.40095i | −0.398505 | − | 0.398505i | ||||
\(259\) | −4.42572 | − | 0.366209i | −0.275001 | − | 0.0227551i | ||||
\(260\) | 3.10295 | + | 1.44385i | 0.192437 | + | 0.0895437i | ||||
\(261\) | 7.56116 | − | 7.56116i | 0.468024 | − | 0.468024i | ||||
\(262\) | −15.2212 | + | 15.2212i | −0.940366 | + | 0.940366i | ||||
\(263\) | 0.841547 | + | 0.841547i | 0.0518920 | + | 0.0518920i | 0.732577 | − | 0.680685i | \(-0.238318\pi\) |
−0.680685 | + | 0.732577i | \(0.738318\pi\) | |||||||
\(264\) | 0.351681 | − | 0.351681i | 0.0216445 | − | 0.0216445i | ||||
\(265\) | 1.22925 | − | 0.448546i | 0.0755121 | − | 0.0275540i | ||||
\(266\) | 2.44103 | 0.149669 | ||||||||
\(267\) | 8.82830i | 0.540283i | ||||||||
\(268\) | −9.29726 | + | 9.29726i | −0.567920 | + | 0.567920i | ||||
\(269\) | 16.4147i | 1.00082i | 0.865788 | + | 0.500412i | \(0.166818\pi\) | ||||
−0.865788 | + | 0.500412i | \(0.833182\pi\) | |||||||
\(270\) | −2.10059 | + | 0.766495i | −0.127838 | + | 0.0466474i | ||||
\(271\) | 3.57932 | 0.217428 | 0.108714 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108714 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(272\) | 2.55573i | 0.154964i | ||||||||
\(273\) | 1.11742i | 0.0676291i | ||||||||
\(274\) | 10.5042 | + | 10.5042i | 0.634579 | + | 0.634579i | ||||
\(275\) | −1.90236 | + | 1.60157i | −0.114716 | + | 0.0965781i | ||||
\(276\) | 3.63359 | + | 3.63359i | 0.218717 | + | 0.218717i | ||||
\(277\) | −11.1501 | −0.669946 | −0.334973 | − | 0.942228i | \(-0.608727\pi\) | ||||
−0.334973 | + | 0.942228i | \(0.608727\pi\) | |||||||
\(278\) | −0.111253 | −0.00667252 | ||||||||
\(279\) | 5.92380 | + | 5.92380i | 0.354649 | + | 0.354649i | ||||
\(280\) | −0.559596 | − | 1.53358i | −0.0334422 | − | 0.0916490i | ||||
\(281\) | −12.0088 | − | 12.0088i | −0.716383 | − | 0.716383i | 0.251480 | − | 0.967863i | \(-0.419083\pi\) |
−0.967863 | + | 0.251480i | \(0.919083\pi\) | |||||||
\(282\) | 13.1085i | 0.780597i | ||||||||
\(283\) | 23.9142i | 1.42155i | 0.703419 | + | 0.710776i | \(0.251656\pi\) | ||||
−0.703419 | + | 0.710776i | \(0.748344\pi\) | |||||||
\(284\) | −4.10631 | −0.243664 | ||||||||
\(285\) | −6.77851 | − | 3.15414i | −0.401524 | − | 0.186835i | ||||
\(286\) | 0.761226i | 0.0450122i | ||||||||
\(287\) | 1.39572 | − | 1.39572i | 0.0823870 | − | 0.0823870i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 10.4682 | 0.615778 | ||||||||
\(290\) | −8.19620 | − | 22.4618i | −0.481297 | − | 1.31900i | ||||
\(291\) | −2.22007 | + | 2.22007i | −0.130143 | + | 0.130143i | ||||
\(292\) | −2.63103 | − | 2.63103i | −0.153969 | − | 0.153969i | ||||
\(293\) | 17.4755 | − | 17.4755i | 1.02093 | − | 1.02093i | 0.0211515 | − | 0.999776i | \(-0.493267\pi\) |
0.999776 | − | 0.0211515i | \(-0.00673323\pi\) | |||||||
\(294\) | −4.57286 | + | 4.57286i | −0.266694 | + | 0.266694i | ||||
\(295\) | −17.5659 | + | 6.40970i | −1.02273 | + | 0.373187i | ||||
\(296\) | −4.64120 | + | 3.93182i | −0.269764 | + | 0.228533i | ||||
\(297\) | −0.351681 | − | 0.351681i | −0.0204066 | − | 0.0204066i | ||||
\(298\) | 16.2537i | 0.941552i | ||||||||
\(299\) | −7.86504 | −0.454847 | ||||||||
\(300\) | −0.427648 | + | 4.98168i | −0.0246902 | + | 0.287617i | ||||
\(301\) | −4.67315 | − | 4.67315i | −0.269356 | − | 0.269356i | ||||
\(302\) | 15.7270i | 0.904989i | ||||||||
\(303\) | −2.95282 | + | 2.95282i | −0.169635 | + | 0.169635i | ||||
\(304\) | 2.36425 | − | 2.36425i | 0.135599 | − | 0.135599i | ||||
\(305\) | −32.0702 | + | 11.7023i | −1.83634 | + | 0.670070i | ||||
\(306\) | 2.55573 | 0.146102 | ||||||||
\(307\) | −6.16080 | + | 6.16080i | −0.351615 | + | 0.351615i | −0.860710 | − | 0.509095i | \(-0.829980\pi\) |
0.509095 | + | 0.860710i | \(0.329980\pi\) | |||||||
\(308\) | 0.256752 | − | 0.256752i | 0.0146298 | − | 0.0146298i | ||||
\(309\) | −11.0772 | + | 11.0772i | −0.630161 | + | 0.630161i | ||||
\(310\) | 17.5977 | − | 6.42132i | 0.999485 | − | 0.364707i | ||||
\(311\) | −12.1752 | + | 12.1752i | −0.690392 | + | 0.690392i | −0.962318 | − | 0.271926i | \(-0.912339\pi\) |
0.271926 | + | 0.962318i | \(0.412339\pi\) | |||||||
\(312\) | 1.08227 | + | 1.08227i | 0.0612713 | + | 0.0612713i | ||||
\(313\) | 3.47014 | 0.196144 | 0.0980720 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980720 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(314\) | 3.60469 | + | 3.60469i | 0.203424 | + | 0.203424i | ||||
\(315\) | −1.53358 | + | 0.559596i | −0.0864075 | + | 0.0315297i | ||||
\(316\) | −0.827925 | + | 0.827925i | −0.0465744 | + | 0.0465744i | ||||
\(317\) | 6.39255 | − | 6.39255i | 0.359041 | − | 0.359041i | −0.504418 | − | 0.863460i | \(-0.668293\pi\) |
0.863460 | + | 0.504418i | \(0.168293\pi\) | |||||||
\(318\) | 0.585191 | 0.0328159 | ||||||||
\(319\) | 3.76056 | − | 3.76056i | 0.210551 | − | 0.210551i | ||||
\(320\) | −2.02734 | − | 0.943349i | −0.113332 | − | 0.0527348i | ||||
\(321\) | − | 0.861349i | − | 0.0480758i | ||||||
\(322\) | 2.65278 | + | 2.65278i | 0.147834 | + | 0.147834i | ||||
\(323\) | 6.04239 | + | 6.04239i | 0.336208 | + | 0.336208i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −4.92868 | − | 5.85434i | −0.273394 | − | 0.324740i | ||||
\(326\) | 12.0896i | 0.669580i | ||||||||
\(327\) | −0.361581 | −0.0199955 | ||||||||
\(328\) | − | 2.70364i | − | 0.149284i | ||||||
\(329\) | 9.57011i | 0.527617i | ||||||||
\(330\) | −1.04473 | + | 0.381218i | −0.0575107 | + | 0.0209854i | ||||
\(331\) | −12.6298 | − | 12.6298i | −0.694194 | − | 0.694194i | 0.268958 | − | 0.963152i | \(-0.413321\pi\) |
−0.963152 | + | 0.268958i | \(0.913321\pi\) | |||||||
\(332\) | 11.2038 | − | 11.2038i | 0.614888 | − | 0.614888i | ||||
\(333\) | 3.93182 | + | 4.64120i | 0.215463 | + | 0.254336i | ||||
\(334\) | − | 11.3927i | − | 0.623383i | ||||||
\(335\) | 27.6192 | − | 10.0781i | 1.50900 | − | 0.550626i | ||||
\(336\) | − | 0.730071i | − | 0.0398286i | ||||||
\(337\) | 11.4706 | − | 11.4706i | 0.624845 | − | 0.624845i | −0.321921 | − | 0.946766i | \(-0.604329\pi\) |
0.946766 | + | 0.321921i | \(0.104329\pi\) | |||||||
\(338\) | 10.6574 | 0.579686 | ||||||||
\(339\) | −9.08351 | + | 9.08351i | −0.493349 | + | 0.493349i | ||||
\(340\) | 2.41095 | − | 5.18133i | 0.130752 | − | 0.280997i | ||||
\(341\) | 2.94621 | + | 2.94621i | 0.159546 | + | 0.159546i | ||||
\(342\) | −2.36425 | − | 2.36425i | −0.127844 | − | 0.127844i | ||||
\(343\) | −6.95218 | + | 6.95218i | −0.375382 | + | 0.375382i | ||||
\(344\) | −9.05230 | −0.488068 | ||||||||
\(345\) | −3.93877 | − | 10.7943i | −0.212056 | − | 0.581143i | ||||
\(346\) | −13.4370 | − | 13.4370i | −0.722379 | − | 0.722379i | ||||
\(347\) | −2.52563 | −0.135583 | −0.0677914 | − | 0.997700i | \(-0.521595\pi\) | ||||
−0.0677914 | + | 0.997700i | \(0.521595\pi\) | |||||||
\(348\) | − | 10.6931i | − | 0.573210i | ||||||
\(349\) | − | 5.42724i | − | 0.290514i | −0.989394 | − | 0.145257i | \(-0.953599\pi\) | ||
0.989394 | − | 0.145257i | \(-0.0464008\pi\) | |||||||
\(350\) | −0.312213 | + | 3.63698i | −0.0166885 | + | 0.194405i | ||||
\(351\) | 1.08227 | − | 1.08227i | 0.0577672 | − | 0.0577672i | ||||
\(352\) | − | 0.497352i | − | 0.0265090i | ||||||
\(353\) | − | 16.8913i | − | 0.899034i | −0.893272 | − | 0.449517i | \(-0.851596\pi\) | ||
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(354\) | −8.36235 | −0.444454 | ||||||||
\(355\) | 8.32486 | + | 3.87368i | 0.441838 | + | 0.205594i | ||||
\(356\) | 6.24255 | + | 6.24255i | 0.330854 | + | 0.330854i | ||||
\(357\) | 1.86587 | 0.0987522 | ||||||||
\(358\) | 7.63199 | + | 7.63199i | 0.403363 | + | 0.403363i | ||||
\(359\) | 10.2084i | 0.538781i | 0.963031 | + | 0.269391i | \(0.0868223\pi\) | ||||
−0.963031 | + | 0.269391i | \(0.913178\pi\) | |||||||
\(360\) | −0.943349 | + | 2.02734i | −0.0497189 | + | 0.106850i | ||||
\(361\) | 7.82065i | 0.411613i | ||||||||
\(362\) | −9.48047 | −0.498282 | ||||||||
\(363\) | 7.60327 | + | 7.60327i | 0.399068 | + | 0.399068i | ||||
\(364\) | 0.790132 | + | 0.790132i | 0.0414142 | + | 0.0414142i | ||||
\(365\) | 2.85200 | + | 7.81595i | 0.149280 | + | 0.409105i | ||||
\(366\) | −15.2672 | −0.798032 | ||||||||
\(367\) | −13.8736 | − | 13.8736i | −0.724195 | − | 0.724195i | 0.245262 | − | 0.969457i | \(-0.421126\pi\) |
−0.969457 | + | 0.245262i | \(0.921126\pi\) | |||||||
\(368\) | 5.13868 | 0.267872 | ||||||||
\(369\) | −2.70364 | −0.140746 | ||||||||
\(370\) | 13.1184 | − | 3.59286i | 0.681991 | − | 0.186784i | ||||
\(371\) | 0.427231 | 0.0221807 | ||||||||
\(372\) | 8.37752 | 0.434354 | ||||||||
\(373\) | −6.36168 | − | 6.36168i | −0.329395 | − | 0.329395i | 0.522961 | − | 0.852356i | \(-0.324827\pi\) |
−0.852356 | + | 0.522961i | \(0.824827\pi\) | |||||||
\(374\) | 1.27110 | 0.0657270 | ||||||||
\(375\) | 5.56645 | − | 9.69612i | 0.287450 | − | 0.500705i | ||||
\(376\) | 9.26908 | + | 9.26908i | 0.478016 | + | 0.478016i | ||||
\(377\) | 11.5728 | + | 11.5728i | 0.596029 | + | 0.596029i | ||||
\(378\) | −0.730071 | −0.0375508 | ||||||||
\(379\) | 10.4081i | 0.534627i | 0.963610 | + | 0.267313i | \(0.0861359\pi\) | ||||
−0.963610 | + | 0.267313i | \(0.913864\pi\) | |||||||
\(380\) | −7.02344 | + | 2.56282i | −0.360295 | + | 0.131470i | ||||
\(381\) | − | 0.712957i | − | 0.0365259i | ||||||
\(382\) | −13.3339 | − | 13.3339i | −0.682222 | − | 0.682222i | ||||
\(383\) | −20.7631 | −1.06094 | −0.530472 | − | 0.847703i | \(-0.677985\pi\) | ||||
−0.530472 | + | 0.847703i | \(0.677985\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | −0.762730 | + | 0.278316i | −0.0388723 | + | 0.0141843i | ||||
\(386\) | −8.67065 | −0.441325 | ||||||||
\(387\) | 9.05230i | 0.460154i | ||||||||
\(388\) | 3.13965i | 0.159391i | ||||||||
\(389\) | 20.8063 | − | 20.8063i | 1.05492 | − | 1.05492i | 0.0565210 | − | 0.998401i | \(-0.481999\pi\) |
0.998401 | − | 0.0565210i | \(-0.0180008\pi\) | |||||||
\(390\) | −1.17316 | − | 3.21508i | −0.0594055 | − | 0.162802i | ||||
\(391\) | 13.1331i | 0.664169i | ||||||||
\(392\) | 6.46700i | 0.326633i | ||||||||
\(393\) | 21.5260 | 1.08584 | ||||||||
\(394\) | −5.35975 | − | 5.35975i | −0.270020 | − | 0.270020i | ||||
\(395\) | 2.45951 | − | 0.897461i | 0.123751 | − | 0.0451561i | ||||
\(396\) | −0.497352 | −0.0249929 | ||||||||
\(397\) | 5.88311 | − | 5.88311i | 0.295265 | − | 0.295265i | −0.543891 | − | 0.839156i | \(-0.683050\pi\) |
0.839156 | + | 0.543891i | \(0.183050\pi\) | |||||||
\(398\) | 13.1621 | + | 13.1621i | 0.659757 | + | 0.659757i | ||||
\(399\) | −1.72607 | − | 1.72607i | −0.0864116 | − | 0.0864116i | ||||
\(400\) | 3.22019 | + | 3.82497i | 0.161009 | + | 0.191249i | ||||
\(401\) | −14.5564 | + | 14.5564i | −0.726914 | + | 0.726914i | −0.970004 | − | 0.243090i | \(-0.921839\pi\) |
0.243090 | + | 0.970004i | \(0.421839\pi\) | |||||||
\(402\) | 13.1483 | 0.655778 | ||||||||
\(403\) | −9.06671 | + | 9.06671i | −0.451645 | + | 0.451645i | ||||
\(404\) | 4.17592i | 0.207760i | ||||||||
\(405\) | 2.02734 | + | 0.943349i | 0.100739 | + | 0.0468754i | ||||
\(406\) | − | 7.80672i | − | 0.387441i | ||||||
\(407\) | 1.95550 | + | 2.30831i | 0.0969306 | + | 0.114419i | ||||
\(408\) | 1.80718 | − | 1.80718i | 0.0894686 | − | 0.0894686i | ||||
\(409\) | 11.0869 | + | 11.0869i | 0.548211 | + | 0.548211i | 0.925923 | − | 0.377712i | \(-0.123289\pi\) |
−0.377712 | + | 0.925923i | \(0.623289\pi\) | |||||||
\(410\) | −2.55048 | + | 5.48119i | −0.125959 | + | 0.270697i | ||||
\(411\) | − | 14.8551i | − | 0.732749i | ||||||
\(412\) | 15.6656i | 0.771787i | ||||||||
\(413\) | −6.10511 | −0.300413 | ||||||||
\(414\) | − | 5.13868i | − | 0.252552i | ||||||
\(415\) | −33.2830 | + | 12.1448i | −1.63380 | + | 0.596164i | ||||
\(416\) | 1.53056 | 0.0750417 | ||||||||
\(417\) | 0.0786679 | + | 0.0786679i | 0.00385238 | + | 0.00385238i | ||||
\(418\) | −1.17586 | − | 1.17586i | −0.0575134 | − | 0.0575134i | ||||
\(419\) | 22.0253i | 1.07601i | 0.842942 | + | 0.538004i | \(0.180822\pi\) | ||||
−0.842942 | + | 0.538004i | \(0.819178\pi\) | |||||||
\(420\) | −0.688712 | + | 1.48010i | −0.0336057 | + | 0.0722215i | ||||
\(421\) | 22.6650 | − | 22.6650i | 1.10463 | − | 1.10463i | 0.110782 | − | 0.993845i | \(-0.464664\pi\) |
0.993845 | − | 0.110782i | \(-0.0353356\pi\) | |||||||
\(422\) | 24.6681 | 1.20083 | ||||||||
\(423\) | 9.26908 | − | 9.26908i | 0.450678 | − | 0.450678i | ||||
\(424\) | 0.413793 | − | 0.413793i | 0.0200956 | − | 0.0200956i | ||||
\(425\) | −9.77561 | + | 8.22994i | −0.474187 | + | 0.399211i | ||||
\(426\) | 2.90360 | + | 2.90360i | 0.140680 | + | 0.140680i | ||||
\(427\) | −11.1462 | −0.539401 | ||||||||
\(428\) | −0.609066 | − | 0.609066i | −0.0294403 | − | 0.0294403i | ||||
\(429\) | 0.538268 | − | 0.538268i | 0.0259878 | − | 0.0259878i | ||||
\(430\) | 18.3521 | + | 8.53948i | 0.885015 | + | 0.411810i | ||||
\(431\) | 17.9692 | − | 17.9692i | 0.865547 | − | 0.865547i | −0.126428 | − | 0.991976i | \(-0.540351\pi\) |
0.991976 | + | 0.126428i | \(0.0403514\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −18.0984 | + | 18.0984i | −0.869755 | + | 0.869755i | −0.992445 | − | 0.122690i | \(-0.960848\pi\) |
0.122690 | + | 0.992445i | \(0.460848\pi\) | |||||||
\(434\) | 6.11618 | 0.293586 | ||||||||
\(435\) | −10.0873 | + | 21.6785i | −0.483650 | + | 1.03940i | ||||
\(436\) | −0.255676 | + | 0.255676i | −0.0122447 | + | 0.0122447i | ||||
\(437\) | 12.1491 | − | 12.1491i | 0.581171 | − | 0.581171i | ||||
\(438\) | 3.72083i | 0.177788i | ||||||||
\(439\) | −24.7771 | − | 24.7771i | −1.18255 | − | 1.18255i | −0.979083 | − | 0.203463i | \(-0.934780\pi\) |
−0.203463 | − | 0.979083i | \(-0.565220\pi\) | |||||||
\(440\) | −0.469177 | + | 1.00830i | −0.0223671 | + | 0.0480688i | ||||
\(441\) | 6.46700 | 0.307952 | ||||||||
\(442\) | 3.91170i | 0.186060i | ||||||||
\(443\) | −11.6985 | − | 11.6985i | −0.555811 | − | 0.555811i | 0.372301 | − | 0.928112i | \(-0.378569\pi\) |
−0.928112 | + | 0.372301i | \(0.878569\pi\) | |||||||
\(444\) | 6.06205 | + | 0.501607i | 0.287692 | + | 0.0238052i | ||||
\(445\) | −6.76685 | − | 18.5446i | −0.320779 | − | 0.879101i | ||||
\(446\) | 11.0405 | − | 11.0405i | 0.522784 | − | 0.522784i | ||||
\(447\) | 11.4931 | − | 11.4931i | 0.543605 | − | 0.543605i | ||||
\(448\) | −0.516238 | − | 0.516238i | −0.0243900 | − | 0.0243900i | ||||
\(449\) | 16.3835 | − | 16.3835i | 0.773187 | − | 0.773187i | −0.205475 | − | 0.978662i | \(-0.565874\pi\) |
0.978662 | + | 0.205475i | \(0.0658740\pi\) | |||||||
\(450\) | 3.82497 | − | 3.22019i | 0.180311 | − | 0.151801i | ||||
\(451\) | −1.34466 | −0.0633177 | ||||||||
\(452\) | 12.8460i | 0.604226i | ||||||||
\(453\) | 11.1207 | − | 11.1207i | 0.522496 | − | 0.522496i | ||||
\(454\) | − | 28.9019i | − | 1.35643i | ||||||
\(455\) | −0.856493 | − | 2.34723i | −0.0401530 | − | 0.110040i | ||||
\(456\) | −3.34355 | −0.156576 | ||||||||
\(457\) | − | 36.6470i | − | 1.71427i | −0.515089 | − | 0.857137i | \(-0.672241\pi\) | ||
0.515089 | − | 0.857137i | \(-0.327759\pi\) | |||||||
\(458\) | − | 27.5614i | − | 1.28786i | ||||||
\(459\) | −1.80718 | − | 1.80718i | −0.0843518 | − | 0.0843518i | ||||
\(460\) | −10.4178 | − | 4.84756i | −0.485734 | − | 0.226019i | ||||
\(461\) | −4.87965 | − | 4.87965i | −0.227268 | − | 0.227268i | 0.584283 | − | 0.811550i | \(-0.301376\pi\) |
−0.811550 | + | 0.584283i | \(0.801376\pi\) | |||||||
\(462\) | −0.363102 | −0.0168931 | ||||||||
\(463\) | 3.03199 | 0.140908 | 0.0704542 | − | 0.997515i | \(-0.477555\pi\) | ||||
0.0704542 | + | 0.997515i | \(0.477555\pi\) | |||||||
\(464\) | −7.56116 | − | 7.56116i | −0.351018 | − | 0.351018i | ||||
\(465\) | −16.9840 | − | 7.90292i | −0.787616 | − | 0.366489i | ||||
\(466\) | 7.51093 | + | 7.51093i | 0.347937 | + | 0.347937i | ||||
\(467\) | − | 7.88298i | − | 0.364781i | −0.983226 | − | 0.182390i | \(-0.941616\pi\) | ||
0.983226 | − | 0.182390i | \(-0.0583835\pi\) | |||||||
\(468\) | − | 1.53056i | − | 0.0707500i | ||||||
\(469\) | 9.59920 | 0.443250 | ||||||||
\(470\) | −10.0476 | − | 27.5355i | −0.463460 | − | 1.27012i | ||||
\(471\) | − | 5.09780i | − | 0.234894i | ||||||
\(472\) | −5.91307 | + | 5.91307i | −0.272171 | + | 0.272171i | ||||
\(473\) | 4.50218i | 0.207011i | ||||||||
\(474\) | 1.17086 | 0.0537795 | ||||||||
\(475\) | 16.6565 | + | 1.42986i | 0.764253 | + | 0.0656066i | ||||
\(476\) | 1.31937 | − | 1.31937i | 0.0604731 | − | 0.0604731i | ||||
\(477\) | −0.413793 | − | 0.413793i | −0.0189463 | − | 0.0189463i | ||||
\(478\) | 6.73852 | − | 6.73852i | 0.308213 | − | 0.308213i | ||||
\(479\) | 22.2999 | − | 22.2999i | 1.01891 | − | 1.01891i | 0.0190898 | − | 0.999818i | \(-0.493923\pi\) |
0.999818 | − | 0.0190898i | \(-0.00607685\pi\) | |||||||
\(480\) | 0.766495 | + | 2.10059i | 0.0349855 | + | 0.0958785i | ||||
\(481\) | −7.10363 | + | 6.01788i | −0.323897 | + | 0.274392i | ||||
\(482\) | 8.91683 | + | 8.91683i | 0.406151 | + | 0.406151i | ||||
\(483\) | − | 3.75160i | − | 0.170704i | ||||||
\(484\) | 10.7526 | 0.488756 | ||||||||
\(485\) | 2.96178 | − | 6.36512i | 0.134488 | − | 0.289025i | ||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 12.8810i | 0.583695i | 0.956465 | + | 0.291847i | \(0.0942699\pi\) | ||||
−0.956465 | + | 0.291847i | \(0.905730\pi\) | |||||||
\(488\) | −10.7956 | + | 10.7956i | −0.488693 | + | 0.488693i | ||||
\(489\) | 8.54863 | − | 8.54863i | 0.386582 | − | 0.386582i | ||||
\(490\) | 6.10063 | − | 13.1108i | 0.275599 | − | 0.592285i | ||||
\(491\) | 0.897235 | 0.0404916 | 0.0202458 | − | 0.999795i | \(-0.493555\pi\) | ||||
0.0202458 | + | 0.999795i | \(0.493555\pi\) | |||||||
\(492\) | −1.91176 | + | 1.91176i | −0.0861890 | + | 0.0861890i | ||||
\(493\) | 19.3243 | − | 19.3243i | 0.870323 | − | 0.870323i | ||||
\(494\) | 3.61862 | − | 3.61862i | 0.162809 | − | 0.162809i | ||||
\(495\) | 1.00830 | + | 0.469177i | 0.0453197 | + | 0.0210879i | ||||
\(496\) | 5.92380 | − | 5.92380i | 0.265986 | − | 0.265986i | ||||
\(497\) | 2.11983 | + | 2.11983i | 0.0950875 | + | 0.0950875i | ||||
\(498\) | −15.8446 | −0.710012 | ||||||||
\(499\) | 17.8190 | + | 17.8190i | 0.797689 | + | 0.797689i | 0.982731 | − | 0.185042i | \(-0.0592421\pi\) |
−0.185042 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(500\) | −2.92012 | − | 10.7923i | −0.130592 | − | 0.482645i | ||||
\(501\) | −8.05588 | + | 8.05588i | −0.359910 | + | 0.359910i | ||||
\(502\) | 8.72803 | − | 8.72803i | 0.389551 | − | 0.389551i | ||||
\(503\) | 17.9635 | 0.800955 | 0.400477 | − | 0.916307i | \(-0.368844\pi\) | ||||
0.400477 | + | 0.916307i | \(0.368844\pi\) | |||||||
\(504\) | −0.516238 | + | 0.516238i | −0.0229951 | + | 0.0229951i | ||||
\(505\) | 3.93935 | − | 8.46599i | 0.175299 | − | 0.376731i | ||||
\(506\) | − | 2.55573i | − | 0.113616i | ||||||
\(507\) | −7.53592 | − | 7.53592i | −0.334682 | − | 0.334682i | ||||
\(508\) | −0.504136 | − | 0.504136i | −0.0223674 | − | 0.0223674i | ||||
\(509\) | 8.36462 | 0.370755 | 0.185378 | − | 0.982667i | \(-0.440649\pi\) | ||||
0.185378 | + | 0.982667i | \(0.440649\pi\) | |||||||
\(510\) | −5.36855 | + | 1.95896i | −0.237723 | + | 0.0867441i | ||||
\(511\) | 2.71647i | 0.120170i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.34355i | 0.147622i | ||||||||
\(514\) | 6.57411i | 0.289972i | ||||||||
\(515\) | 14.7781 | − | 31.7594i | 0.651200 | − | 1.39948i | ||||
\(516\) | 6.40095 | + | 6.40095i | 0.281786 | + | 0.281786i | ||||
\(517\) | 4.61000 | − | 4.61000i | 0.202747 | − | 0.202747i | ||||
\(518\) | 4.42572 | + | 0.366209i | 0.194455 | + | 0.0160903i | ||||
\(519\) | 19.0028i | 0.834131i | ||||||||
\(520\) | −3.10295 | − | 1.44385i | −0.136074 | − | 0.0633170i | ||||
\(521\) | 16.5234i | 0.723904i | 0.932197 | + | 0.361952i | \(0.117890\pi\) | ||||
−0.932197 | + | 0.361952i | \(0.882110\pi\) | |||||||
\(522\) | −7.56116 | + | 7.56116i | −0.330943 | + | 0.330943i | ||||
\(523\) | 14.2767 | 0.624278 | 0.312139 | − | 0.950036i | \(-0.398954\pi\) | ||||
0.312139 | + | 0.950036i | \(0.398954\pi\) | |||||||
\(524\) | 15.2212 | − | 15.2212i | 0.664939 | − | 0.664939i | ||||
\(525\) | 2.79250 | − | 2.35096i | 0.121875 | − | 0.102605i | ||||
\(526\) | −0.841547 | − | 0.841547i | −0.0366932 | − | 0.0366932i | ||||
\(527\) | 15.1397 | + | 15.1397i | 0.659494 | + | 0.659494i | ||||
\(528\) | −0.351681 | + | 0.351681i | −0.0153050 | + | 0.0153050i | ||||
\(529\) | 3.40599 | 0.148087 | ||||||||
\(530\) | −1.22925 | + | 0.448546i | −0.0533951 | + | 0.0194836i | ||||
\(531\) | 5.91307 | + | 5.91307i | 0.256606 | + | 0.256606i | ||||
\(532\) | −2.44103 | −0.105832 | ||||||||
\(533\) | − | 4.13808i | − | 0.179240i | ||||||
\(534\) | − | 8.82830i | − | 0.382038i | ||||||
\(535\) | 0.660220 | + | 1.80934i | 0.0285438 | + | 0.0782247i | ||||
\(536\) | 9.29726 | − | 9.29726i | 0.401580 | − | 0.401580i | ||||
\(537\) | − | 10.7933i | − | 0.465764i | ||||||
\(538\) | − | 16.4147i | − | 0.707689i | ||||||
\(539\) | 3.21637 | 0.138539 | ||||||||
\(540\) | 2.10059 | − | 0.766495i | 0.0903951 | − | 0.0329847i | ||||
\(541\) | −2.99943 | − | 2.99943i | −0.128955 | − | 0.128955i | 0.639683 | − | 0.768639i | \(-0.279066\pi\) |
−0.768639 | + | 0.639683i | \(0.779066\pi\) | |||||||
\(542\) | −3.57932 | −0.153745 | ||||||||
\(543\) | 6.70370 | + | 6.70370i | 0.287683 | + | 0.287683i | ||||
\(544\) | − | 2.55573i | − | 0.109576i | ||||||
\(545\) | 0.759534 | − | 0.277150i | 0.0325349 | − | 0.0118718i | ||||
\(546\) | − | 1.11742i | − | 0.0478210i | ||||||
\(547\) | −20.8842 | −0.892944 | −0.446472 | − | 0.894798i | \(-0.647320\pi\) | ||||
−0.446472 | + | 0.894798i | \(0.647320\pi\) | |||||||
\(548\) | −10.5042 | − | 10.5042i | −0.448715 | − | 0.448715i | ||||
\(549\) | 10.7956 | + | 10.7956i | 0.460744 | + | 0.460744i | ||||
\(550\) | 1.90236 | − | 1.60157i | 0.0811168 | − | 0.0682910i | ||||
\(551\) | −35.7529 | −1.52313 | ||||||||
\(552\) | −3.63359 | − | 3.63359i | −0.154656 | − | 0.154656i | ||||
\(553\) | 0.854813 | 0.0363504 | ||||||||
\(554\) | 11.1501 | 0.473723 | ||||||||
\(555\) | −11.8166 | − | 6.73555i | −0.501587 | − | 0.285908i | ||||
\(556\) | 0.111253 | 0.00471819 | ||||||||
\(557\) | −10.1584 | −0.430426 | −0.215213 | − | 0.976567i | \(-0.569045\pi\) | ||||
−0.215213 | + | 0.976567i | \(0.569045\pi\) | |||||||
\(558\) | −5.92380 | − | 5.92380i | −0.250774 | − | 0.250774i | ||||
\(559\) | −13.8551 | −0.586007 | ||||||||
\(560\) | 0.559596 | + | 1.53358i | 0.0236472 | + | 0.0648056i | ||||
\(561\) | −0.898803 | − | 0.898803i | −0.0379475 | − | 0.0379475i | ||||
\(562\) | 12.0088 | + | 12.0088i | 0.506559 | + | 0.506559i | ||||
\(563\) | 13.4772 | 0.567996 | 0.283998 | − | 0.958825i | \(-0.408339\pi\) | ||||
0.283998 | + | 0.958825i | \(0.408339\pi\) | |||||||
\(564\) | − | 13.1085i | − | 0.551966i | ||||||
\(565\) | 12.1183 | − | 26.0432i | 0.509820 | − | 1.09565i | ||||
\(566\) | − | 23.9142i | − | 1.00519i | ||||||
\(567\) | 0.516238 | + | 0.516238i | 0.0216800 | + | 0.0216800i | ||||
\(568\) | 4.10631 | 0.172297 | ||||||||
\(569\) | 0.956429 | + | 0.956429i | 0.0400956 | + | 0.0400956i | 0.726870 | − | 0.686775i | \(-0.240974\pi\) |
−0.686775 | + | 0.726870i | \(0.740974\pi\) | |||||||
\(570\) | 6.77851 | + | 3.15414i | 0.283920 | + | 0.132112i | ||||
\(571\) | −1.80272 | −0.0754415 | −0.0377208 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377208 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(572\) | − | 0.761226i | − | 0.0318285i | ||||||
\(573\) | 18.8570i | 0.787763i | ||||||||
\(574\) | −1.39572 | + | 1.39572i | −0.0582564 | + | 0.0582564i | ||||
\(575\) | 16.5475 | + | 19.6553i | 0.690078 | + | 0.819682i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | − | 21.8641i | − | 0.910216i | −0.890436 | − | 0.455108i | \(-0.849601\pi\) | ||
0.890436 | − | 0.455108i | \(-0.150399\pi\) | |||||||
\(578\) | −10.4682 | −0.435421 | ||||||||
\(579\) | 6.13108 | + | 6.13108i | 0.254799 | + | 0.254799i | ||||
\(580\) | 8.19620 | + | 22.4618i | 0.340329 | + | 0.932676i | ||||
\(581\) | −11.5677 | −0.479907 | ||||||||
\(582\) | 2.22007 | − | 2.22007i | 0.0920247 | − | 0.0920247i | ||||
\(583\) | −0.205801 | − | 0.205801i | −0.00852340 | − | 0.00852340i | ||||
\(584\) | 2.63103 | + | 2.63103i | 0.108873 | + | 0.108873i | ||||
\(585\) | −1.44385 | + | 3.10295i | −0.0596958 | + | 0.128291i | ||||
\(586\) | −17.4755 | + | 17.4755i | −0.721905 | + | 0.721905i | ||||
\(587\) | 13.4925 | 0.556896 | 0.278448 | − | 0.960451i | \(-0.410180\pi\) | ||||
0.278448 | + | 0.960451i | \(0.410180\pi\) | |||||||
\(588\) | 4.57286 | − | 4.57286i | 0.188581 | − | 0.188581i | ||||
\(589\) | − | 28.0107i | − | 1.15416i | ||||||
\(590\) | 17.5659 | − | 6.40970i | 0.723176 | − | 0.263883i | ||||
\(591\) | 7.57983i | 0.311793i | ||||||||
\(592\) | 4.64120 | − | 3.93182i | 0.190752 | − | 0.161597i | ||||
\(593\) | −21.6151 | + | 21.6151i | −0.887628 | + | 0.887628i | −0.994295 | − | 0.106667i | \(-0.965982\pi\) |
0.106667 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(594\) | 0.351681 | + | 0.351681i | 0.0144296 | + | 0.0144296i | ||||
\(595\) | −3.91942 | + | 1.43018i | −0.160681 | + | 0.0586316i | ||||
\(596\) | − | 16.2537i | − | 0.665777i | ||||||
\(597\) | − | 18.6140i | − | 0.761822i | ||||||
\(598\) | 7.86504 | 0.321625 | ||||||||
\(599\) | − | 1.58656i | − | 0.0648249i | −0.999475 | − | 0.0324125i | \(-0.989681\pi\) | ||
0.999475 | − | 0.0324125i | \(-0.0103190\pi\) | |||||||
\(600\) | 0.427648 | − | 4.98168i | 0.0174586 | − | 0.203376i | ||||
\(601\) | 39.5787 | 1.61445 | 0.807224 | − | 0.590245i | \(-0.200969\pi\) | ||||
0.807224 | + | 0.590245i | \(0.200969\pi\) | |||||||
\(602\) | 4.67315 | + | 4.67315i | 0.190463 | + | 0.190463i | ||||
\(603\) | −9.29726 | − | 9.29726i | −0.378614 | − | 0.378614i | ||||
\(604\) | − | 15.7270i | − | 0.639924i | ||||||
\(605\) | −21.7992 | − | 10.1435i | −0.886264 | − | 0.412392i | ||||
\(606\) | 2.95282 | − | 2.95282i | 0.119950 | − | 0.119950i | ||||
\(607\) | −29.3879 | −1.19282 | −0.596409 | − | 0.802680i | \(-0.703407\pi\) | ||||
−0.596409 | + | 0.802680i | \(0.703407\pi\) | |||||||
\(608\) | −2.36425 | + | 2.36425i | −0.0958830 | + | 0.0958830i | ||||
\(609\) | −5.52018 | + | 5.52018i | −0.223689 | + | 0.223689i | ||||
\(610\) | 32.0702 | − | 11.7023i | 1.29849 | − | 0.473811i | ||||
\(611\) | 14.1869 | + | 14.1869i | 0.573939 | + | 0.573939i | ||||
\(612\) | −2.55573 | −0.103309 | ||||||||
\(613\) | 11.9588 | + | 11.9588i | 0.483011 | + | 0.483011i | 0.906092 | − | 0.423081i | \(-0.139051\pi\) |
−0.423081 | + | 0.906092i | \(0.639051\pi\) | |||||||
\(614\) | 6.16080 | − | 6.16080i | 0.248630 | − | 0.248630i | ||||
\(615\) | 5.67925 | − | 2.07233i | 0.229009 | − | 0.0835644i | ||||
\(616\) | −0.256752 | + | 0.256752i | −0.0103448 | + | 0.0103448i | ||||
\(617\) | 19.8923 | − | 19.8923i | 0.800835 | − | 0.800835i | −0.182391 | − | 0.983226i | \(-0.558384\pi\) |
0.983226 | + | 0.182391i | \(0.0583836\pi\) | |||||||
\(618\) | 11.0772 | − | 11.0772i | 0.445591 | − | 0.445591i | ||||
\(619\) | −25.0352 | −1.00625 | −0.503125 | − | 0.864213i | \(-0.667817\pi\) | ||||
−0.503125 | + | 0.864213i | \(0.667817\pi\) | |||||||
\(620\) | −17.5977 | + | 6.42132i | −0.706742 | + | 0.257887i | ||||
\(621\) | −3.63359 | + | 3.63359i | −0.145811 | + | 0.145811i | ||||
\(622\) | 12.1752 | − | 12.1752i | 0.488181 | − | 0.488181i | ||||
\(623\) | − | 6.44528i | − | 0.258225i | ||||||
\(624\) | −1.08227 | − | 1.08227i | −0.0433254 | − | 0.0433254i | ||||
\(625\) | −4.26081 | + | 24.6342i | −0.170432 | + | 0.985369i | ||||
\(626\) | −3.47014 | −0.138695 | ||||||||
\(627\) | 1.66292i | 0.0664108i | ||||||||
\(628\) | −3.60469 | − | 3.60469i | −0.143843 | − | 0.143843i | ||||
\(629\) | 10.0487 | + | 11.8617i | 0.400668 | + | 0.472956i | ||||
\(630\) | 1.53358 | − | 0.559596i | 0.0610993 | − | 0.0222948i | ||||
\(631\) | −14.6446 | + | 14.6446i | −0.582990 | + | 0.582990i | −0.935724 | − | 0.352733i | \(-0.885252\pi\) |
0.352733 | + | 0.935724i | \(0.385252\pi\) | |||||||
\(632\) | 0.827925 | − | 0.827925i | 0.0329331 | − | 0.0329331i | ||||
\(633\) | −17.4430 | − | 17.4430i | −0.693297 | − | 0.693297i | ||||
\(634\) | −6.39255 | + | 6.39255i | −0.253881 | + | 0.253881i | ||||
\(635\) | 0.546478 | + | 1.49763i | 0.0216863 | + | 0.0594317i | ||||
\(636\) | −0.585191 | −0.0232043 | ||||||||
\(637\) | 9.89811i | 0.392177i | ||||||||
\(638\) | −3.76056 | + | 3.76056i | −0.148882 | + | 0.148882i | ||||
\(639\) | − | 4.10631i | − | 0.162443i | ||||||
\(640\) | 2.02734 | + | 0.943349i | 0.0801375 | + | 0.0372891i | ||||
\(641\) | 18.7683 | 0.741305 | 0.370652 | − | 0.928772i | \(-0.379134\pi\) | ||||
0.370652 | + | 0.928772i | \(0.379134\pi\) | |||||||
\(642\) | 0.861349i | 0.0339947i | ||||||||
\(643\) | 33.3318i | 1.31448i | 0.753683 | + | 0.657238i | \(0.228275\pi\) | ||||
−0.753683 | + | 0.657238i | \(0.771725\pi\) | |||||||
\(644\) | −2.65278 | − | 2.65278i | −0.104534 | − | 0.104534i | ||||
\(645\) | −6.93855 | − | 19.0152i | −0.273205 | − | 0.748723i | ||||
\(646\) | −6.04239 | − | 6.04239i | −0.237735 | − | 0.237735i | ||||
\(647\) | 20.5310 | 0.807156 | 0.403578 | − | 0.914945i | \(-0.367766\pi\) | ||||
0.403578 | + | 0.914945i | \(0.367766\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.94088 | + | 2.94088i | 0.115440 | + | 0.115440i | ||||
\(650\) | 4.92868 | + | 5.85434i | 0.193319 | + | 0.229626i | ||||
\(651\) | −4.32479 | − | 4.32479i | −0.169502 | − | 0.169502i | ||||
\(652\) | − | 12.0896i | − | 0.473465i | ||||||
\(653\) | − | 26.4235i | − | 1.03403i | −0.855976 | − | 0.517016i | \(-0.827043\pi\) | ||
0.855976 | − | 0.517016i | \(-0.172957\pi\) | |||||||
\(654\) | 0.361581 | 0.0141389 | ||||||||
\(655\) | −45.2173 | + | 16.4995i | −1.76678 | + | 0.644690i | ||||
\(656\) | 2.70364i | 0.105560i | ||||||||
\(657\) | 2.63103 | − | 2.63103i | 0.102646 | − | 0.102646i | ||||
\(658\) | − | 9.57011i | − | 0.373082i | ||||||
\(659\) | 39.4006 | 1.53483 | 0.767414 | − | 0.641152i | \(-0.221543\pi\) | ||||
0.767414 | + | 0.641152i | \(0.221543\pi\) | |||||||
\(660\) | 1.04473 | − | 0.381218i | 0.0406662 | − | 0.0148389i | ||||
\(661\) | 7.90042 | − | 7.90042i | 0.307291 | − | 0.307291i | −0.536567 | − | 0.843858i | \(-0.680279\pi\) |
0.843858 | + | 0.536567i | \(0.180279\pi\) | |||||||
\(662\) | 12.6298 | + | 12.6298i | 0.490870 | + | 0.490870i | ||||
\(663\) | 2.76599 | − | 2.76599i | 0.107422 | − | 0.107422i | ||||
\(664\) | −11.2038 | + | 11.2038i | −0.434792 | + | 0.434792i | ||||
\(665\) | 4.94879 | + | 2.30274i | 0.191906 | + | 0.0892966i | ||||
\(666\) | −3.93182 | − | 4.64120i | −0.152355 | − | 0.179843i | ||||
\(667\) | −38.8543 | − | 38.8543i | −1.50445 | − | 1.50445i | ||||
\(668\) | 11.3927i | 0.440798i | ||||||||
\(669\) | −15.6137 | −0.603659 | ||||||||
\(670\) | −27.6192 | + | 10.0781i | −1.06702 | + | 0.389351i | ||||
\(671\) | 5.36920 | + | 5.36920i | 0.207276 | + | 0.207276i | ||||
\(672\) | 0.730071i | 0.0281631i | ||||||||
\(673\) | −31.7666 | + | 31.7666i | −1.22451 | + | 1.22451i | −0.258503 | + | 0.966011i | \(0.583229\pi\) |
−0.966011 | + | 0.258503i | \(0.916771\pi\) | |||||||
\(674\) | −11.4706 | + | 11.4706i | −0.441832 | + | 0.441832i | ||||
\(675\) | −4.98168 | − | 0.427648i | −0.191745 | − | 0.0164602i | ||||
\(676\) | −10.6574 | −0.409900 | ||||||||
\(677\) | 21.1045 | − | 21.1045i | 0.811110 | − | 0.811110i | −0.173690 | − | 0.984800i | \(-0.555569\pi\) |
0.984800 | + | 0.173690i | \(0.0555691\pi\) | |||||||
\(678\) | 9.08351 | − | 9.08351i | 0.348850 | − | 0.348850i | ||||
\(679\) | 1.62081 | − | 1.62081i | 0.0622008 | − | 0.0622008i | ||||
\(680\) | −2.41095 | + | 5.18133i | −0.0924556 | + | 0.198695i | ||||
\(681\) | −20.4367 | + | 20.4367i | −0.783137 | + | 0.783137i | ||||
\(682\) | −2.94621 | − | 2.94621i | −0.112816 | − | 0.112816i | ||||
\(683\) | 35.4086 | 1.35487 | 0.677437 | − | 0.735581i | \(-0.263091\pi\) | ||||
0.677437 | + | 0.735581i | \(0.263091\pi\) | |||||||
\(684\) | 2.36425 | + | 2.36425i | 0.0903993 | + | 0.0903993i | ||||
\(685\) | 11.3864 | + | 31.2045i | 0.435051 | + | 1.19226i | ||||
\(686\) | 6.95218 | − | 6.95218i | 0.265435 | − | 0.265435i | ||||
\(687\) | −19.4888 | + | 19.4888i | −0.743546 | + | 0.743546i | ||||
\(688\) | 9.05230 | 0.345116 | ||||||||
\(689\) | 0.633334 | − | 0.633334i | 0.0241281 | − | 0.0241281i | ||||
\(690\) | 3.93877 | + | 10.7943i | 0.149946 | + | 0.410930i | ||||
\(691\) | 22.4704i | 0.854814i | 0.904059 | + | 0.427407i | \(0.140573\pi\) | ||||
−0.904059 | + | 0.427407i | \(0.859427\pi\) | |||||||
\(692\) | 13.4370 | + | 13.4370i | 0.510799 | + | 0.510799i | ||||
\(693\) | 0.256752 | + | 0.256752i | 0.00975321 | + | 0.00975321i | ||||
\(694\) | 2.52563 | 0.0958715 | ||||||||
\(695\) | −0.225548 | − | 0.104951i | −0.00855551 | − | 0.00398100i | ||||
\(696\) | 10.6931i | 0.405321i | ||||||||
\(697\) | −6.90979 | −0.261727 | ||||||||
\(698\) | 5.42724i | 0.205424i | ||||||||
\(699\) | − | 10.6221i | − | 0.401763i | ||||||
\(700\) | 0.312213 | − | 3.63698i | 0.0118005 | − | 0.137465i | ||||
\(701\) | 15.2902 | + | 15.2902i | 0.577504 | + | 0.577504i | 0.934215 | − | 0.356711i | \(-0.116102\pi\) |
−0.356711 | + | 0.934215i | \(0.616102\pi\) | |||||||
\(702\) | −1.08227 | + | 1.08227i | −0.0408475 | + | 0.0408475i | ||||
\(703\) | 1.67715 | − | 20.2688i | 0.0632549 | − | 0.764451i | ||||
\(704\) | 0.497352i | 0.0187447i | ||||||||
\(705\) | −12.3658 | + | 26.5753i | −0.465725 | + | 1.00088i | ||||
\(706\) | 16.8913i | 0.635713i | ||||||||
\(707\) | 2.15577 | − | 2.15577i | 0.0810760 | − | 0.0810760i | ||||
\(708\) | 8.36235 | 0.314276 | ||||||||
\(709\) | 11.5740 | − | 11.5740i | 0.434672 | − | 0.434672i | −0.455542 | − | 0.890214i | \(-0.650555\pi\) |
0.890214 | + | 0.455542i | \(0.150555\pi\) | |||||||
\(710\) | −8.32486 | − | 3.87368i | −0.312427 | − | 0.145377i | ||||
\(711\) | −0.827925 | − | 0.827925i | −0.0310496 | − | 0.0310496i | ||||
\(712\) | −6.24255 | − | 6.24255i | −0.233949 | − | 0.233949i | ||||
\(713\) | 30.4405 | − | 30.4405i | 1.14001 | − | 1.14001i | ||||
\(714\) | −1.86587 | −0.0698283 | ||||||||
\(715\) | −0.718102 | + | 1.54326i | −0.0268555 | + | 0.0577147i | ||||
\(716\) | −7.63199 | − | 7.63199i | −0.285221 | − | 0.285221i | ||||
\(717\) | −9.52971 | −0.355893 | ||||||||
\(718\) | − | 10.2084i | − | 0.380976i | ||||||
\(719\) | 33.1940i | 1.23793i | 0.785420 | + | 0.618963i | \(0.212447\pi\) | ||||
−0.785420 | + | 0.618963i | \(0.787553\pi\) | |||||||
\(720\) | 0.943349 | − | 2.02734i | 0.0351565 | − | 0.0755544i | ||||
\(721\) | 8.08716 | − | 8.08716i | 0.301182 | − | 0.301182i | ||||
\(722\) | − | 7.82065i | − | 0.291054i | ||||||
\(723\) | − | 12.6103i | − | 0.468982i | ||||||
\(724\) | 9.48047 | 0.352339 | ||||||||
\(725\) | 4.57288 | − | 53.2695i | 0.169832 | − | 1.97838i | ||||
\(726\) | −7.60327 | − | 7.60327i | −0.282184 | − | 0.282184i | ||||
\(727\) | 25.8130 | 0.957352 | 0.478676 | − | 0.877992i | \(-0.341117\pi\) | ||||
0.478676 | + | 0.877992i | \(0.341117\pi\) | |||||||
\(728\) | −0.790132 | − | 0.790132i | −0.0292842 | − | 0.0292842i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −2.85200 | − | 7.81595i | −0.105557 | − | 0.289281i | ||||
\(731\) | 23.1353i | 0.855689i | ||||||||
\(732\) | 15.2672 | 0.564294 | ||||||||
\(733\) | −29.0185 | − | 29.0185i | −1.07182 | − | 1.07182i | −0.997213 | − | 0.0746110i | \(-0.976228\pi\) |
−0.0746110 | − | 0.997213i | \(-0.523772\pi\) | |||||||
\(734\) | 13.8736 | + | 13.8736i | 0.512083 | + | 0.512083i | ||||
\(735\) | −13.5845 | + | 4.95692i | −0.501073 | + | 0.182839i | ||||
\(736\) | −5.13868 | −0.189414 | ||||||||
\(737\) | −4.62401 | − | 4.62401i | −0.170328 | − | 0.170328i | ||||
\(738\) | 2.70364 | 0.0995225 | ||||||||
\(739\) | −33.6130 | −1.23647 | −0.618236 | − | 0.785992i | \(-0.712153\pi\) | ||||
−0.618236 | + | 0.785992i | \(0.712153\pi\) | |||||||
\(740\) | −13.1184 | + | 3.59286i | −0.482241 | + | 0.132076i | ||||
\(741\) | −5.11750 | −0.187996 | ||||||||
\(742\) | −0.427231 | −0.0156842 | ||||||||
\(743\) | −15.7302 | − | 15.7302i | −0.577084 | − | 0.577084i | 0.357015 | − | 0.934099i | \(-0.383795\pi\) |
−0.934099 | + | 0.357015i | \(0.883795\pi\) | |||||||
\(744\) | −8.37752 | −0.307135 | ||||||||
\(745\) | −15.3329 | + | 32.9517i | −0.561754 | + | 1.20726i | ||||
\(746\) | 6.36168 | + | 6.36168i | 0.232918 | + | 0.232918i | ||||
\(747\) | 11.2038 | + | 11.2038i | 0.409926 | + | 0.409926i | ||||
\(748\) | −1.27110 | −0.0464760 | ||||||||
\(749\) | 0.628846i | 0.0229775i | ||||||||
\(750\) | −5.56645 | + | 9.69612i | −0.203258 | + | 0.354052i | ||||
\(751\) | 12.7266i | 0.464401i | 0.972668 | + | 0.232201i | \(0.0745926\pi\) | ||||
−0.972668 | + | 0.232201i | \(0.925407\pi\) | |||||||
\(752\) | −9.26908 | − | 9.26908i | −0.338009 | − | 0.338009i | ||||
\(753\) | −12.3433 | −0.449815 | ||||||||
\(754\) | −11.5728 | − | 11.5728i | −0.421456 | − | 0.421456i | ||||
\(755\) | −14.8361 | + | 31.8840i | −0.539940 | + | 1.16038i | ||||
\(756\) | 0.730071 | 0.0265524 | ||||||||
\(757\) | 49.4794i | 1.79836i | 0.437578 | + | 0.899181i | \(0.355836\pi\) | ||||
−0.437578 | + | 0.899181i | \(0.644164\pi\) | |||||||
\(758\) | − | 10.4081i | − | 0.378038i | ||||||
\(759\) | −1.80718 | + | 1.80718i | −0.0655963 | + | 0.0655963i | ||||
\(760\) | 7.02344 | − | 2.56282i | 0.254767 | − | 0.0929632i | ||||
\(761\) | 10.2526i | 0.371657i | 0.982582 | + | 0.185828i | \(0.0594968\pi\) | ||||
−0.982582 | + | 0.185828i | \(0.940503\pi\) | |||||||
\(762\) | 0.712957i | 0.0258277i | ||||||||
\(763\) | 0.263980 | 0.00955671 | ||||||||
\(764\) | 13.3339 | + | 13.3339i | 0.482404 | + | 0.482404i | ||||
\(765\) | 5.18133 | + | 2.41095i | 0.187331 | + | 0.0871680i | ||||
\(766\) | 20.7631 | 0.750200 | ||||||||
\(767\) | −9.05030 | + | 9.05030i | −0.326787 | + | 0.326787i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −18.0896 | − | 18.0896i | −0.652327 | − | 0.652327i | 0.301226 | − | 0.953553i | \(-0.402604\pi\) |
−0.953553 | + | 0.301226i | \(0.902604\pi\) | |||||||
\(770\) | 0.762730 | − | 0.278316i | 0.0274869 | − | 0.0100298i | ||||
\(771\) | 4.64860 | − | 4.64860i | 0.167415 | − | 0.167415i | ||||
\(772\) | 8.67065 | 0.312064 | ||||||||
\(773\) | 21.4323 | − | 21.4323i | 0.770866 | − | 0.770866i | −0.207392 | − | 0.978258i | \(-0.566498\pi\) |
0.978258 | + | 0.207392i | \(0.0664976\pi\) | |||||||
\(774\) | − | 9.05230i | − | 0.325378i | ||||||
\(775\) | 41.7341 | + | 3.58263i | 1.49913 | + | 0.128692i | ||||
\(776\) | − | 3.13965i | − | 0.112707i | ||||||
\(777\) | −2.87051 | − | 3.38841i | −0.102979 | − | 0.121558i | ||||
\(778\) | −20.8063 | + | 20.8063i | −0.745943 | + | 0.745943i | ||||
\(779\) | 6.39209 | + | 6.39209i | 0.229020 | + | 0.229020i | ||||
\(780\) | 1.17316 | + | 3.21508i | 0.0420060 | + | 0.115118i | ||||
\(781\) | − | 2.04228i | − | 0.0730785i | ||||||
\(782\) | − | 13.1331i | − | 0.469638i | ||||||
\(783\) | 10.6931 | 0.382140 | ||||||||
\(784\) | − | 6.46700i | − | 0.230964i | ||||||
\(785\) | 3.90744 | + | 10.7084i | 0.139462 | + | 0.382199i | ||||
\(786\) | −21.5260 | −0.767806 | ||||||||
\(787\) | 16.7084 | + | 16.7084i | 0.595590 | + | 0.595590i | 0.939136 | − | 0.343546i | \(-0.111628\pi\) |
−0.343546 | + | 0.939136i | \(0.611628\pi\) | |||||||
\(788\) | 5.35975 | + | 5.35975i | 0.190933 | + | 0.190933i | ||||
\(789\) | 1.19013i | 0.0423696i | ||||||||
\(790\) | −2.45951 | + | 0.897461i | −0.0875053 | + | 0.0319302i | ||||
\(791\) | 6.63161 | − | 6.63161i | 0.235793 | − | 0.235793i | ||||
\(792\) | 0.497352 | 0.0176726 | ||||||||
\(793\) | −16.5232 | + | 16.5232i | −0.586757 | + | 0.586757i | ||||
\(794\) | −5.88311 | + | 5.88311i | −0.208784 | + | 0.208784i | ||||
\(795\) | 1.18638 | + | 0.552040i | 0.0420766 | + | 0.0195788i | ||||
\(796\) | −13.1621 | − | 13.1621i | −0.466519 | − | 0.466519i | ||||
\(797\) | 13.0313 | 0.461591 | 0.230796 | − | 0.973002i | \(-0.425867\pi\) | ||||
0.230796 | + | 0.973002i | \(0.425867\pi\) | |||||||
\(798\) | 1.72607 | + | 1.72607i | 0.0611022 | + | 0.0611022i | ||||
\(799\) | 23.6893 | − | 23.6893i | 0.838067 | − | 0.838067i | ||||
\(800\) | −3.22019 | − | 3.82497i | −0.113851 | − | 0.135233i | ||||
\(801\) | −6.24255 | + | 6.24255i | −0.220570 | + | 0.220570i | ||||
\(802\) | 14.5564 | − | 14.5564i | 0.514006 | − | 0.514006i | ||||
\(803\) | 1.30855 | − | 1.30855i | 0.0461776 | − | 0.0461776i | ||||
\(804\) | −13.1483 | −0.463705 | ||||||||
\(805\) | 2.87558 | + | 7.88058i | 0.101351 | + | 0.277754i | ||||
\(806\) | 9.06671 | − | 9.06671i | 0.319361 | − | 0.319361i | ||||
\(807\) | −11.6070 | + | 11.6070i | −0.408584 | + | 0.408584i | ||||
\(808\) | − | 4.17592i | − | 0.146908i | ||||||
\(809\) | 4.63922 | + | 4.63922i | 0.163106 | + | 0.163106i | 0.783941 | − | 0.620835i | \(-0.213206\pi\) |
−0.620835 | + | 0.783941i | \(0.713206\pi\) | |||||||
\(810\) | −2.02734 | − | 0.943349i | −0.0712333 | − | 0.0331459i | ||||
\(811\) | 55.6848 | 1.95536 | 0.977679 | − | 0.210105i | \(-0.0673805\pi\) | ||||
0.977679 | + | 0.210105i | \(0.0673805\pi\) | |||||||
\(812\) | 7.80672i | 0.273962i | ||||||||
\(813\) | 2.53096 | + | 2.53096i | 0.0887647 | + | 0.0887647i | ||||
\(814\) | −1.95550 | − | 2.30831i | −0.0685403 | − | 0.0809063i | ||||
\(815\) | −11.4047 | + | 24.5096i | −0.399489 | + | 0.858536i | ||||
\(816\) | −1.80718 | + | 1.80718i | −0.0632638 | + | 0.0632638i | ||||
\(817\) | 21.4019 | − | 21.4019i | 0.748758 | − | 0.748758i | ||||
\(818\) | −11.0869 | − | 11.0869i | −0.387644 | − | 0.387644i | ||||
\(819\) | −0.790132 | + | 0.790132i | −0.0276095 | + | 0.0276095i | ||||
\(820\) | 2.55048 | − | 5.48119i | 0.0890666 | − | 0.191412i | ||||
\(821\) | −17.4399 | −0.608658 | −0.304329 | − | 0.952567i | \(-0.598432\pi\) | ||||
−0.304329 | + | 0.952567i | \(0.598432\pi\) | |||||||
\(822\) | 14.8551i | 0.518132i | ||||||||
\(823\) | −18.0594 | + | 18.0594i | −0.629511 | + | 0.629511i | −0.947945 | − | 0.318434i | \(-0.896843\pi\) |
0.318434 | + | 0.947945i | \(0.396843\pi\) | |||||||
\(824\) | − | 15.6656i | − | 0.545736i | ||||||
\(825\) | −2.47765 | − | 0.212691i | −0.0862606 | − | 0.00740497i | ||||
\(826\) | 6.10511 | 0.212424 | ||||||||
\(827\) | − | 18.6866i | − | 0.649797i | −0.945749 | − | 0.324899i | \(-0.894670\pi\) | ||
0.945749 | − | 0.324899i | \(-0.105330\pi\) | |||||||
\(828\) | 5.13868i | 0.178581i | ||||||||
\(829\) | −0.406665 | − | 0.406665i | −0.0141241 | − | 0.0141241i | 0.700009 | − | 0.714134i | \(-0.253179\pi\) |
−0.714134 | + | 0.700009i | \(0.753179\pi\) | |||||||
\(830\) | 33.2830 | − | 12.1448i | 1.15527 | − | 0.421551i | ||||
\(831\) | −7.88433 | − | 7.88433i | −0.273504 | − | 0.273504i | ||||
\(832\) | −1.53056 | −0.0530625 | ||||||||
\(833\) | 16.5279 | 0.572658 | ||||||||
\(834\) | −0.0786679 | − | 0.0786679i | −0.00272405 | − | 0.00272405i | ||||
\(835\) | 10.7473 | − | 23.0969i | 0.371926 | − | 0.799301i | ||||
\(836\) | 1.17586 | + | 1.17586i | 0.0406681 | + | 0.0406681i | ||||
\(837\) | 8.37752i | 0.289569i | ||||||||
\(838\) | − | 22.0253i | − | 0.760853i | ||||||
\(839\) | −33.2804 | −1.14897 | −0.574483 | − | 0.818516i | \(-0.694797\pi\) | ||||
−0.574483 | + | 0.818516i | \(0.694797\pi\) | |||||||
\(840\) | 0.688712 | − | 1.48010i | 0.0237628 | − | 0.0510683i | ||||
\(841\) | 85.3422i | 2.94283i | ||||||||
\(842\) | −22.6650 | + | 22.6650i | −0.781089 | + | 0.781089i | ||||
\(843\) | − | 16.9830i | − | 0.584924i | ||||||
\(844\) | −24.6681 | −0.849112 | ||||||||
\(845\) | 21.6061 | + | 10.0536i | 0.743273 | + | 0.345856i | ||||
\(846\) | −9.26908 | + | 9.26908i | −0.318677 | + | 0.318677i | ||||
\(847\) | −5.55092 | − | 5.55092i | −0.190732 | − | 0.190732i | ||||
\(848\) | −0.413793 | + | 0.413793i | −0.0142097 | + | 0.0142097i | ||||
\(849\) | −16.9099 | + | 16.9099i | −0.580346 | + | 0.580346i | ||||
\(850\) | 9.77561 | − | 8.22994i | 0.335300 | − | 0.282284i | ||||
\(851\) | 23.8496 | − | 20.2044i | 0.817555 | − | 0.692597i | ||||
\(852\) | −2.90360 | − | 2.90360i | −0.0994756 | − | 0.0994756i | ||||
\(853\) | − | 13.7096i | − | 0.469409i | −0.972067 | − | 0.234705i | \(-0.924588\pi\) | ||
0.972067 | − | 0.234705i | \(-0.0754123\pi\) | |||||||
\(854\) | 11.1462 | 0.381414 | ||||||||
\(855\) | −2.56282 | − | 7.02344i | −0.0876465 | − | 0.240197i | ||||
\(856\) | 0.609066 | + | 0.609066i | 0.0208174 | + | 0.0208174i | ||||
\(857\) | 11.0849i | 0.378651i | 0.981914 | + | 0.189326i | \(0.0606302\pi\) | ||||
−0.981914 | + | 0.189326i | \(0.939370\pi\) | |||||||
\(858\) | −0.538268 | + | 0.538268i | −0.0183762 | + | 0.0183762i | ||||
\(859\) | 15.5947 | − | 15.5947i | 0.532084 | − | 0.532084i | −0.389108 | − | 0.921192i | \(-0.627217\pi\) |
0.921192 | + | 0.389108i | \(0.127217\pi\) | |||||||
\(860\) | −18.3521 | − | 8.53948i | −0.625800 | − | 0.291194i | ||||
\(861\) | 1.97385 | 0.0672687 | ||||||||
\(862\) | −17.9692 | + | 17.9692i | −0.612034 | + | 0.612034i | ||||
\(863\) | −0.801311 | + | 0.801311i | −0.0272770 | + | 0.0272770i | −0.720614 | − | 0.693337i | \(-0.756140\pi\) |
0.693337 | + | 0.720614i | \(0.256140\pi\) | |||||||
\(864\) | 0.707107 | − | 0.707107i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | −14.5656 | − | 39.9172i | −0.495244 | − | 1.35722i | ||||
\(866\) | 18.0984 | − | 18.0984i | 0.615010 | − | 0.615010i | ||||
\(867\) | 7.40215 | + | 7.40215i | 0.251390 | + | 0.251390i | ||||
\(868\) | −6.11618 | −0.207597 | ||||||||
\(869\) | −0.411770 | − | 0.411770i | −0.0139684 | − | 0.0139684i | ||||
\(870\) | 10.0873 | − | 21.6785i | 0.341992 | − | 0.734970i | ||||
\(871\) | 14.2300 | − | 14.2300i | 0.482165 | − | 0.482165i | ||||
\(872\) | 0.255676 | − | 0.255676i | 0.00865830 | − | 0.00865830i | ||||
\(873\) | −3.13965 | −0.106261 | ||||||||
\(874\) | −12.1491 | + | 12.1491i | −0.410950 | + | 0.410950i | ||||
\(875\) | −4.06390 | + | 7.07885i | −0.137385 | + | 0.239309i | ||||
\(876\) | − | 3.72083i | − | 0.125715i | ||||||
\(877\) | −7.57864 | − | 7.57864i | −0.255912 | − | 0.255912i | 0.567477 | − | 0.823389i | \(-0.307920\pi\) |
−0.823389 | + | 0.567477i | \(0.807920\pi\) | |||||||
\(878\) | 24.7771 | + | 24.7771i | 0.836186 | + | 0.836186i | ||||
\(879\) | 24.7140 | 0.833584 | ||||||||
\(880\) | 0.469177 | − | 1.00830i | 0.0158159 | − | 0.0339898i | ||||
\(881\) | 23.3650i | 0.787188i | 0.919284 | + | 0.393594i | \(0.128768\pi\) | ||||
−0.919284 | + | 0.393594i | \(0.871232\pi\) | |||||||
\(882\) | −6.46700 | −0.217755 | ||||||||
\(883\) | − | 12.2410i | − | 0.411943i | −0.978558 | − | 0.205972i | \(-0.933965\pi\) | ||
0.978558 | − | 0.205972i | \(-0.0660355\pi\) | |||||||
\(884\) | − | 3.91170i | − | 0.131565i | ||||||
\(885\) | −16.9533 | − | 7.88861i | −0.569879 | − | 0.265173i | ||||
\(886\) | 11.6985 | + | 11.6985i | 0.393018 | + | 0.393018i | ||||
\(887\) | 9.25112 | − | 9.25112i | 0.310622 | − | 0.310622i | −0.534528 | − | 0.845151i | \(-0.679511\pi\) |
0.845151 | + | 0.534528i | \(0.179511\pi\) | |||||||
\(888\) | −6.06205 | − | 0.501607i | −0.203429 | − | 0.0168328i | ||||
\(889\) | 0.520509i | 0.0174573i | ||||||||
\(890\) | 6.76685 | + | 18.5446i | 0.226825 | + | 0.621618i | ||||
\(891\) | − | 0.497352i | − | 0.0166619i | ||||||
\(892\) | −11.0405 | + | 11.0405i | −0.369664 | + | 0.369664i | ||||
\(893\) | −43.8288 | −1.46668 | ||||||||
\(894\) | −11.4931 | + | 11.4931i | −0.384387 | + | 0.384387i | ||||
\(895\) | 8.27299 | + | 22.6722i | 0.276535 | + | 0.757850i | ||||
\(896\) | 0.516238 | + | 0.516238i | 0.0172463 | + | 0.0172463i | ||||
\(897\) | −5.56142 | − | 5.56142i | −0.185690 | − | 0.185690i | ||||
\(898\) | −16.3835 | + | 16.3835i | −0.546726 | + | 0.546726i | ||||
\(899\) | −89.5816 | −2.98771 | ||||||||
\(900\) | −3.82497 | + | 3.22019i | −0.127499 | + | 0.107340i | ||||
\(901\) | −1.05754 | − | 1.05754i | −0.0352319 | − | 0.0352319i | ||||
\(902\) | 1.34466 | 0.0447724 | ||||||||
\(903\) | − | 6.60883i | − | 0.219928i | ||||||
\(904\) | − | 12.8460i | − | 0.427253i | ||||||
\(905\) | −19.2201 | − | 8.94339i | −0.638898 | − | 0.297288i | ||||
\(906\) | −11.1207 | + | 11.1207i | −0.369460 | + | 0.369460i | ||||
\(907\) | − | 28.2255i | − | 0.937213i | −0.883407 | − | 0.468606i | \(-0.844756\pi\) | ||
0.883407 | − | 0.468606i | \(-0.155244\pi\) | |||||||
\(908\) | 28.9019i | 0.959143i | ||||||||
\(909\) | −4.17592 | −0.138506 | ||||||||
\(910\) | 0.856493 | + | 2.34723i | 0.0283925 | + | 0.0778100i | ||||
\(911\) | −11.7600 | − | 11.7600i | −0.389626 | − | 0.389626i | 0.484928 | − | 0.874554i | \(-0.338846\pi\) |
−0.874554 | + | 0.484928i | \(0.838846\pi\) | |||||||
\(912\) | 3.34355 | 0.110716 | ||||||||
\(913\) | 5.57223 | + | 5.57223i | 0.184414 | + | 0.184414i | ||||
\(914\) | 36.6470i | 1.21217i | ||||||||
\(915\) | −30.9518 | − | 14.4023i | −1.02324 | − | 0.476127i | ||||
\(916\) | 27.5614i | 0.910654i | ||||||||
\(917\) | −15.7155 | −0.518971 | ||||||||
\(918\) | 1.80718 | + | 1.80718i | 0.0596457 | + | 0.0596457i | ||||
\(919\) | 16.8392 | + | 16.8392i | 0.555476 | + | 0.555476i | 0.928016 | − | 0.372540i | \(-0.121513\pi\) |
−0.372540 | + | 0.928016i | \(0.621513\pi\) | |||||||
\(920\) | 10.4178 | + | 4.84756i | 0.343466 | + | 0.159819i | ||||
\(921\) | −8.71269 | −0.287093 | ||||||||
\(922\) | 4.87965 | + | 4.87965i | 0.160703 | + | 0.160703i | ||||
\(923\) | 6.28494 | 0.206871 | ||||||||
\(924\) | 0.363102 | 0.0119452 | ||||||||
\(925\) | 29.9846 | + | 5.09126i | 0.985889 | + | 0.167400i | ||||
\(926\) | −3.03199 | −0.0996373 | ||||||||
\(927\) | −15.6656 | −0.514524 | ||||||||
\(928\) | 7.56116 | + | 7.56116i | 0.248207 | + | 0.248207i | ||||
\(929\) | 24.9345 | 0.818075 | 0.409038 | − | 0.912518i | \(-0.365865\pi\) | ||||
0.409038 | + | 0.912518i | \(0.365865\pi\) | |||||||
\(930\) | 16.9840 | + | 7.90292i | 0.556929 | + | 0.259147i | ||||
\(931\) | −15.2896 | − | 15.2896i | −0.501096 | − | 0.501096i | ||||
\(932\) | −7.51093 | − | 7.51093i | −0.246029 | − | 0.246029i | ||||
\(933\) | −17.2183 | −0.563703 | ||||||||
\(934\) | 7.88298i | 0.257939i | ||||||||
\(935\) | 2.57695 | + | 1.19909i | 0.0842751 | + | 0.0392144i | ||||
\(936\) | 1.53056i | 0.0500278i | ||||||||
\(937\) | −3.73610 | − | 3.73610i | −0.122053 | − | 0.122053i | 0.643442 | − | 0.765495i | \(-0.277506\pi\) |
−0.765495 | + | 0.643442i | \(0.777506\pi\) | |||||||
\(938\) | −9.59920 | −0.313425 | ||||||||
\(939\) | 2.45376 | + | 2.45376i | 0.0800755 | + | 0.0800755i | ||||
\(940\) | 10.0476 | + | 27.5355i | 0.327715 | + | 0.898110i | ||||
\(941\) | 21.1387 | 0.689100 | 0.344550 | − | 0.938768i | \(-0.388031\pi\) | ||||
0.344550 | + | 0.938768i | \(0.388031\pi\) | |||||||
\(942\) | 5.09780i | 0.166095i | ||||||||
\(943\) | 13.8931i | 0.452423i | ||||||||
\(944\) | 5.91307 | − | 5.91307i | 0.192454 | − | 0.192454i | ||||
\(945\) | −1.48010 | − | 0.688712i | −0.0481476 | − | 0.0224038i | ||||
\(946\) | − | 4.50218i | − | 0.146379i | ||||||
\(947\) | − | 1.08920i | − | 0.0353942i | −0.999843 | − | 0.0176971i | \(-0.994367\pi\) | ||
0.999843 | − | 0.0176971i | \(-0.00563346\pi\) | |||||||
\(948\) | −1.17086 | −0.0380279 | ||||||||
\(949\) | 4.02694 | + | 4.02694i | 0.130720 | + | 0.130720i | ||||
\(950\) | −16.6565 | − | 1.42986i | −0.540409 | − | 0.0463909i | ||||
\(951\) | 9.04043 | 0.293156 | ||||||||
\(952\) | −1.31937 | + | 1.31937i | −0.0427609 | + | 0.0427609i | ||||
\(953\) | −6.11358 | − | 6.11358i | −0.198038 | − | 0.198038i | 0.601120 | − | 0.799159i | \(-0.294721\pi\) |
−0.799159 | + | 0.601120i | \(0.794721\pi\) | |||||||
\(954\) | 0.413793 | + | 0.413793i | 0.0133970 | + | 0.0133970i | ||||
\(955\) | −14.4538 | − | 39.6109i | −0.467714 | − | 1.28178i | ||||
\(956\) | −6.73852 | + | 6.73852i | −0.217939 | + | 0.217939i | ||||
\(957\) | 5.31823 | 0.171914 | ||||||||
\(958\) | −22.2999 | + | 22.2999i | −0.720476 | + | 0.720476i | ||||
\(959\) | 10.8453i | 0.350213i | ||||||||
\(960\) | −0.766495 | − | 2.10059i | −0.0247385 | − | 0.0677963i | ||||
\(961\) | − | 39.1828i | − | 1.26396i | ||||||
\(962\) | 7.10363 | − | 6.01788i | 0.229030 | − | 0.194024i | ||||
\(963\) | 0.609066 | − | 0.609066i | 0.0196269 | − | 0.0196269i | ||||
\(964\) | −8.91683 | − | 8.91683i | −0.287192 | − | 0.287192i | ||||
\(965\) | −17.5783 | − | 8.17945i | −0.565867 | − | 0.263306i | ||||
\(966\) | 3.75160i | 0.120706i | ||||||||
\(967\) | − | 20.1527i | − | 0.648066i | −0.946046 | − | 0.324033i | \(-0.894961\pi\) | ||
0.946046 | − | 0.324033i | \(-0.105039\pi\) | |||||||
\(968\) | −10.7526 | −0.345603 | ||||||||
\(969\) | 8.54523i | 0.274512i | ||||||||
\(970\) | −2.96178 | + | 6.36512i | −0.0950971 | + | 0.204372i | ||||
\(971\) | −16.1896 | −0.519550 | −0.259775 | − | 0.965669i | \(-0.583648\pi\) | ||||
−0.259775 | + | 0.965669i | \(0.583648\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −0.0574331 | − | 0.0574331i | −0.00184122 | − | 0.00184122i | ||||
\(974\) | − | 12.8810i | − | 0.412734i | ||||||
\(975\) | 0.654539 | − | 7.62474i | 0.0209620 | − | 0.244187i | ||||
\(976\) | 10.7956 | − | 10.7956i | 0.345558 | − | 0.345558i | ||||
\(977\) | −6.24061 | −0.199655 | −0.0998273 | − | 0.995005i | \(-0.531829\pi\) | ||||
−0.0998273 | + | 0.995005i | \(0.531829\pi\) | |||||||
\(978\) | −8.54863 | + | 8.54863i | −0.273355 | + | 0.273355i | ||||
\(979\) | −3.10474 | + | 3.10474i | −0.0992281 | + | 0.0992281i | ||||
\(980\) | −6.10063 | + | 13.1108i | −0.194878 | + | 0.418808i | ||||
\(981\) | −0.255676 | − | 0.255676i | −0.00816312 | − | 0.00816312i | ||||
\(982\) | −0.897235 | −0.0286319 | ||||||||
\(983\) | −3.22372 | − | 3.22372i | −0.102821 | − | 0.102821i | 0.653825 | − | 0.756646i | \(-0.273163\pi\) |
−0.756646 | + | 0.653825i | \(0.773163\pi\) | |||||||
\(984\) | 1.91176 | − | 1.91176i | 0.0609448 | − | 0.0609448i | ||||
\(985\) | −5.80991 | − | 15.9221i | −0.185119 | − | 0.507322i | ||||
\(986\) | −19.3243 | + | 19.3243i | −0.615411 | + | 0.615411i | ||||
\(987\) | −6.76709 | + | 6.76709i | −0.215399 | + | 0.215399i | ||||
\(988\) | −3.61862 | + | 3.61862i | −0.115124 | + | 0.115124i | ||||
\(989\) | 46.5169 | 1.47915 | ||||||||
\(990\) | −1.00830 | − | 0.469177i | −0.0320459 | − | 0.0149114i | ||||
\(991\) | 4.95581 | − | 4.95581i | 0.157427 | − | 0.157427i | −0.623999 | − | 0.781425i | \(-0.714493\pi\) |
0.781425 | + | 0.623999i | \(0.214493\pi\) | |||||||
\(992\) | −5.92380 | + | 5.92380i | −0.188081 | + | 0.188081i | ||||
\(993\) | − | 17.8612i | − | 0.566807i | ||||||
\(994\) | −2.11983 | − | 2.11983i | −0.0672370 | − | 0.0672370i | ||||
\(995\) | 14.2676 | + | 39.1005i | 0.452312 | + | 1.23957i | ||||
\(996\) | 15.8446 | 0.502054 | ||||||||
\(997\) | 28.8366i | 0.913265i | 0.889655 | + | 0.456633i | \(0.150945\pi\) | ||||
−0.889655 | + | 0.456633i | \(0.849055\pi\) | |||||||
\(998\) | −17.8190 | − | 17.8190i | −0.564051 | − | 0.564051i | ||||
\(999\) | −0.501607 | + | 6.06205i | −0.0158701 | + | 0.191795i |
(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 | 1110.2.o.a.487.14 | yes | 36 | |
5.3 | odd | 4 | 1110.2.l.a.43.5 | ✓ | 36 | ||
37.31 | odd | 4 | 1110.2.l.a.697.5 | yes | 36 | ||
185.68 | even | 4 | inner | 1110.2.o.a.253.14 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.5 | ✓ | 36 | 5.3 | odd | 4 | ||
1110.2.l.a.697.5 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.253.14 | yes | 36 | 185.68 | even | 4 | inner | |
1110.2.o.a.487.14 | yes | 36 | 1.1 | even | 1 | trivial |