Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 418.3 | ||
Character | \(\chi\) | \(=\) | 525.418 |
Dual form | 525.2.bc.e.157.3 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.259789 | − | 0.969545i | −0.183698 | − | 0.685572i | −0.994905 | − | 0.100813i | \(-0.967856\pi\) |
0.811207 | − | 0.584759i | \(-0.198811\pi\) | |||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | 0.859523 | − | 0.496246i | 0.429762 | − | 0.248123i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00375i | 0.409778i | ||||||||
\(7\) | 1.06195 | + | 2.42328i | 0.401379 | + | 0.915912i | ||||
\(8\) | −2.12394 | − | 2.12394i | −0.750926 | − | 0.750926i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.78283 | − | 3.08796i | −0.537545 | − | 0.931054i | −0.999036 | − | 0.0439095i | \(-0.986019\pi\) |
0.461491 | − | 0.887145i | \(-0.347315\pi\) | |||||||
\(12\) | −0.958673 | + | 0.256876i | −0.276745 | + | 0.0741536i | ||||
\(13\) | 2.78368 | − | 2.78368i | 0.772054 | − | 0.772054i | −0.206411 | − | 0.978465i | \(-0.566178\pi\) |
0.978465 | + | 0.206411i | \(0.0661785\pi\) | |||||||
\(14\) | 2.07359 | − | 1.65915i | 0.554191 | − | 0.443426i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.514988 | + | 0.891986i | −0.128747 | + | 0.222997i | ||||
\(17\) | 0.135713 | − | 0.506489i | 0.0329153 | − | 0.122842i | −0.947513 | − | 0.319716i | \(-0.896412\pi\) |
0.980429 | + | 0.196874i | \(0.0630791\pi\) | |||||||
\(18\) | 0.259789 | − | 0.969545i | 0.0612328 | − | 0.228524i | ||||
\(19\) | 2.06188 | − | 3.57128i | 0.473028 | − | 0.819308i | −0.526496 | − | 0.850178i | \(-0.676494\pi\) |
0.999523 | + | 0.0308699i | \(0.00982775\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.398574 | − | 2.61556i | −0.0869761 | − | 0.570761i | ||||
\(22\) | −2.53075 | + | 2.53075i | −0.539559 | + | 0.539559i | ||||
\(23\) | 2.49427 | − | 0.668338i | 0.520092 | − | 0.139358i | 0.0107826 | − | 0.999942i | \(-0.496568\pi\) |
0.509309 | + | 0.860584i | \(0.329901\pi\) | |||||||
\(24\) | 1.50185 | + | 2.60128i | 0.306564 | + | 0.530985i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.42207 | − | 1.97574i | −0.671124 | − | 0.387474i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 2.11531 | + | 1.55587i | 0.399756 | + | 0.294032i | ||||
\(29\) | − | 6.14396i | − | 1.14091i | −0.821331 | − | 0.570453i | \(-0.806768\pi\) | ||
0.821331 | − | 0.570453i | \(-0.193232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.71173 | + | 0.988266i | −0.307435 | + | 0.177498i | −0.645778 | − | 0.763525i | \(-0.723467\pi\) |
0.338343 | + | 0.941023i | \(0.390134\pi\) | |||||||
\(32\) | −4.80410 | − | 1.28726i | −0.849253 | − | 0.227557i | ||||
\(33\) | 0.922863 | + | 3.44417i | 0.160650 | + | 0.599553i | ||||
\(34\) | −0.526321 | −0.0902633 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.992492 | 0.165415 | ||||||||
\(37\) | 0.0409435 | + | 0.152803i | 0.00673106 | + | 0.0251207i | 0.969210 | − | 0.246237i | \(-0.0791941\pi\) |
−0.962479 | + | 0.271357i | \(0.912527\pi\) | |||||||
\(38\) | −3.99817 | − | 1.07131i | −0.648589 | − | 0.173789i | ||||
\(39\) | −3.40930 | + | 1.96836i | −0.545925 | + | 0.315190i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.28475i | 1.29386i | 0.762549 | + | 0.646930i | \(0.223948\pi\) | ||||
−0.762549 | + | 0.646930i | \(0.776052\pi\) | |||||||
\(42\) | −2.43236 | + | 1.06593i | −0.375321 | + | 0.164476i | ||||
\(43\) | −9.01253 | − | 9.01253i | −1.37440 | − | 1.37440i | −0.853805 | − | 0.520594i | \(-0.825711\pi\) |
−0.520594 | − | 0.853805i | \(-0.674289\pi\) | |||||||
\(44\) | −3.06477 | − | 1.76945i | −0.462032 | − | 0.266754i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.29597 | − | 2.24468i | −0.191080 | − | 0.330960i | ||||
\(47\) | 5.19095 | − | 1.39091i | 0.757178 | − | 0.202885i | 0.140478 | − | 0.990084i | \(-0.455136\pi\) |
0.616700 | + | 0.787198i | \(0.288469\pi\) | |||||||
\(48\) | 0.728304 | − | 0.728304i | 0.105122 | − | 0.105122i | ||||
\(49\) | −4.74453 | + | 5.14679i | −0.677790 | + | 0.735256i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.262178 | + | 0.454106i | −0.0367123 | + | 0.0635875i | ||||
\(52\) | 1.01125 | − | 3.77403i | 0.140235 | − | 0.523363i | ||||
\(53\) | 1.48765 | − | 5.55200i | 0.204345 | − | 0.762626i | −0.785303 | − | 0.619111i | \(-0.787493\pi\) |
0.989648 | − | 0.143514i | \(-0.0458404\pi\) | |||||||
\(54\) | −0.501874 | + | 0.869271i | −0.0682963 | + | 0.118293i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.89138 | − | 7.40241i | 0.386376 | − | 0.989188i | ||||
\(57\) | −2.91594 | + | 2.91594i | −0.386225 | + | 0.386225i | ||||
\(58\) | −5.95685 | + | 1.59613i | −0.782173 | + | 0.209583i | ||||
\(59\) | −1.30044 | − | 2.25243i | −0.169303 | − | 0.293242i | 0.768872 | − | 0.639403i | \(-0.220818\pi\) |
−0.938175 | + | 0.346161i | \(0.887485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.67653 | + | 5.00940i | 1.11092 | + | 0.641387i | 0.939066 | − | 0.343736i | \(-0.111692\pi\) |
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(62\) | 1.40286 | + | 1.40286i | 0.178163 | + | 0.178163i | ||||
\(63\) | −0.291963 | + | 2.62959i | −0.0367838 | + | 0.331298i | ||||
\(64\) | 7.05216i | 0.881521i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.09953 | − | 1.78951i | 0.381526 | − | 0.220274i | ||||
\(67\) | −5.32418 | − | 1.42661i | −0.650452 | − | 0.174288i | −0.0815189 | − | 0.996672i | \(-0.525977\pi\) |
−0.568933 | + | 0.822384i | \(0.692644\pi\) | |||||||
\(68\) | −0.134694 | − | 0.502686i | −0.0163341 | − | 0.0609596i | ||||
\(69\) | −2.58226 | −0.310868 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.23274 | −0.858369 | −0.429184 | − | 0.903217i | \(-0.641199\pi\) | ||||
−0.429184 | + | 0.903217i | \(0.641199\pi\) | |||||||
\(72\) | −0.777416 | − | 2.90136i | −0.0916194 | − | 0.341928i | ||||
\(73\) | 14.8625 | + | 3.98240i | 1.73953 | + | 0.466105i | 0.982342 | − | 0.187096i | \(-0.0599077\pi\) |
0.757185 | + | 0.653201i | \(0.226574\pi\) | |||||||
\(74\) | 0.137513 | − | 0.0793931i | 0.0159855 | − | 0.00922926i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.09280i | − | 0.469476i | ||||||
\(77\) | 5.58969 | − | 7.59955i | 0.637005 | − | 0.866049i | ||||
\(78\) | 2.79411 | + | 2.79411i | 0.316371 | + | 0.316371i | ||||
\(79\) | 13.1146 | + | 7.57171i | 1.47551 | + | 0.851884i | 0.999618 | − | 0.0276214i | \(-0.00879330\pi\) |
0.475888 | + | 0.879506i | \(0.342127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 8.03244 | − | 2.15229i | 0.887035 | − | 0.237680i | ||||
\(83\) | −9.42372 | + | 9.42372i | −1.03439 | + | 1.03439i | −0.0350007 | + | 0.999387i | \(0.511143\pi\) |
−0.999387 | + | 0.0350007i | \(0.988857\pi\) | |||||||
\(84\) | −1.64054 | − | 2.05034i | −0.178998 | − | 0.223710i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.39670 | + | 11.0794i | −0.689774 | + | 1.19472i | ||||
\(87\) | −1.59017 | + | 5.93461i | −0.170485 | + | 0.636257i | ||||
\(88\) | −2.77201 | + | 10.3453i | −0.295497 | + | 1.10281i | ||||
\(89\) | 5.52672 | − | 9.57257i | 0.585831 | − | 1.01469i | −0.408940 | − | 0.912561i | \(-0.634101\pi\) |
0.994771 | − | 0.102128i | \(-0.0325653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.70175 | + | 3.78950i | 1.01702 | + | 0.397247i | ||||
\(92\) | 1.81222 | − | 1.81222i | 0.188937 | − | 0.188937i | ||||
\(93\) | 1.90918 | − | 0.511564i | 0.197973 | − | 0.0530467i | ||||
\(94\) | −2.69710 | − | 4.67152i | −0.278185 | − | 0.481830i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.30724 | + | 2.48679i | 0.439606 | + | 0.253807i | ||||
\(97\) | 2.48828 | + | 2.48828i | 0.252647 | + | 0.252647i | 0.822055 | − | 0.569408i | \(-0.192828\pi\) |
−0.569408 | + | 0.822055i | \(0.692828\pi\) | |||||||
\(98\) | 6.22262 | + | 3.26295i | 0.628580 | + | 0.329608i | ||||
\(99\) | − | 3.56567i | − | 0.358363i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.739502 | − | 0.426952i | 0.0735832 | − | 0.0424833i | −0.462757 | − | 0.886485i | \(-0.653140\pi\) |
0.536340 | + | 0.844002i | \(0.319806\pi\) | |||||||
\(102\) | 0.508387 | + | 0.136222i | 0.0503378 | + | 0.0134880i | ||||
\(103\) | 1.57114 | + | 5.86357i | 0.154809 | + | 0.577755i | 0.999122 | + | 0.0419040i | \(0.0133424\pi\) |
−0.844313 | + | 0.535851i | \(0.819991\pi\) | |||||||
\(104\) | −11.8247 | −1.15951 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.76939 | −0.560373 | ||||||||
\(107\) | 3.02740 | + | 11.2984i | 0.292670 | + | 1.09226i | 0.943051 | + | 0.332650i | \(0.107943\pi\) |
−0.650381 | + | 0.759608i | \(0.725391\pi\) | |||||||
\(108\) | −0.958673 | − | 0.256876i | −0.0922484 | − | 0.0247179i | ||||
\(109\) | −10.8565 | + | 6.26802i | −1.03987 | + | 0.600367i | −0.919796 | − | 0.392398i | \(-0.871646\pi\) |
−0.120071 | + | 0.992765i | \(0.538312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.158193i | − | 0.0150151i | ||||||
\(112\) | −2.70842 | − | 0.300715i | −0.255922 | − | 0.0284149i | ||||
\(113\) | 7.25767 | + | 7.25767i | 0.682744 | + | 0.682744i | 0.960618 | − | 0.277874i | \(-0.0896296\pi\) |
−0.277874 | + | 0.960618i | \(0.589630\pi\) | |||||||
\(114\) | 3.58466 | + | 2.06961i | 0.335734 | + | 0.193836i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.04892 | − | 5.28088i | −0.283085 | − | 0.490317i | ||||
\(117\) | 3.80258 | − | 1.01890i | 0.351549 | − | 0.0941971i | ||||
\(118\) | −1.84600 | + | 1.84600i | −0.169938 | + | 0.169938i | ||||
\(119\) | 1.37148 | − | 0.208995i | 0.125724 | − | 0.0191585i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.856990 | + | 1.48435i | −0.0779082 | + | 0.134941i | ||||
\(122\) | 2.60277 | − | 9.71367i | 0.235644 | − | 0.879435i | ||||
\(123\) | 2.14425 | − | 8.00245i | 0.193341 | − | 0.721557i | ||||
\(124\) | −0.980846 | + | 1.69887i | −0.0880825 | + | 0.152563i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.62536 | − | 0.400068i | 0.233885 | − | 0.0356409i | ||||
\(127\) | 1.06249 | − | 1.06249i | 0.0942804 | − | 0.0942804i | −0.658393 | − | 0.752674i | \(-0.728764\pi\) |
0.752674 | + | 0.658393i | \(0.228764\pi\) | |||||||
\(128\) | −2.77081 | + | 0.742437i | −0.244908 | + | 0.0656228i | ||||
\(129\) | 6.37282 | + | 11.0381i | 0.561096 | + | 0.971846i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3808 | + | 5.99337i | 0.906976 | + | 0.523643i | 0.879457 | − | 0.475979i | \(-0.157906\pi\) |
0.0275190 | + | 0.999621i | \(0.491239\pi\) | |||||||
\(132\) | 2.50238 | + | 2.50238i | 0.217804 | + | 0.217804i | ||||
\(133\) | 10.8438 | + | 1.20398i | 0.940277 | + | 0.104399i | ||||
\(134\) | 5.53265i | 0.477948i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.36400 | + | 0.787505i | −0.116962 | + | 0.0675280i | ||||
\(137\) | 6.10553 | + | 1.63597i | 0.521630 | + | 0.139770i | 0.510021 | − | 0.860162i | \(-0.329638\pi\) |
0.0116098 | + | 0.999933i | \(0.496304\pi\) | |||||||
\(138\) | 0.670842 | + | 2.50362i | 0.0571059 | + | 0.213122i | ||||
\(139\) | 5.07872 | 0.430772 | 0.215386 | − | 0.976529i | \(-0.430899\pi\) | ||||
0.215386 | + | 0.976529i | \(0.430899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.37407 | −0.452578 | ||||||||
\(142\) | 1.87899 | + | 7.01247i | 0.157681 | + | 0.588474i | ||||
\(143\) | −13.5587 | − | 3.63305i | −1.13384 | − | 0.303811i | ||||
\(144\) | −0.891986 | + | 0.514988i | −0.0743322 | + | 0.0429157i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 15.4445i | − | 1.27819i | ||||||
\(147\) | 5.91495 | − | 3.74344i | 0.487857 | − | 0.308754i | ||||
\(148\) | 0.111020 | + | 0.111020i | 0.00912577 | + | 0.00912577i | ||||
\(149\) | 13.1991 | + | 7.62048i | 1.08131 | + | 0.624294i | 0.931249 | − | 0.364383i | \(-0.118720\pi\) |
0.150060 | + | 0.988677i | \(0.452053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.46500 | − | 12.9298i | −0.607493 | − | 1.05221i | −0.991652 | − | 0.128942i | \(-0.958842\pi\) |
0.384159 | − | 0.923267i | \(-0.374491\pi\) | |||||||
\(152\) | −11.9645 | + | 3.20588i | −0.970449 | + | 0.260031i | ||||
\(153\) | 0.370776 | − | 0.370776i | 0.0299754 | − | 0.0299754i | ||||
\(154\) | −8.82025 | − | 3.44518i | −0.710756 | − | 0.277621i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.95358 | + | 3.38370i | −0.156412 | + | 0.270913i | ||||
\(157\) | −1.70656 | + | 6.36897i | −0.136198 | + | 0.508299i | 0.863792 | + | 0.503849i | \(0.168083\pi\) |
−0.999990 | + | 0.00445019i | \(0.998583\pi\) | |||||||
\(158\) | 3.93409 | − | 14.6822i | 0.312980 | − | 1.16806i | ||||
\(159\) | −2.87393 | + | 4.97779i | −0.227917 | + | 0.394764i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.26836 | + | 5.33457i | 0.336394 | + | 0.420423i | ||||
\(162\) | 0.709756 | − | 0.709756i | 0.0557637 | − | 0.0557637i | ||||
\(163\) | 1.35039 | − | 0.361835i | 0.105770 | − | 0.0283411i | −0.205546 | − | 0.978648i | \(-0.565897\pi\) |
0.311316 | + | 0.950306i | \(0.399230\pi\) | |||||||
\(164\) | 4.11127 | + | 7.12093i | 0.321036 | + | 0.556051i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.5849 | + | 6.68855i | 0.899163 | + | 0.519132i | ||||
\(167\) | 4.18179 | + | 4.18179i | 0.323597 | + | 0.323597i | 0.850145 | − | 0.526548i | \(-0.176514\pi\) |
−0.526548 | + | 0.850145i | \(0.676514\pi\) | |||||||
\(168\) | −4.70874 | + | 6.40183i | −0.363287 | + | 0.493912i | ||||
\(169\) | − | 2.49776i | − | 0.192135i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.57128 | − | 2.06188i | 0.273103 | − | 0.157676i | ||||
\(172\) | −12.2189 | − | 3.27405i | −0.931683 | − | 0.249644i | ||||
\(173\) | 0.619668 | + | 2.31263i | 0.0471125 | + | 0.175826i | 0.985473 | − | 0.169832i | \(-0.0543224\pi\) |
−0.938361 | + | 0.345658i | \(0.887656\pi\) | |||||||
\(174\) | 6.16698 | 0.467518 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.67255 | 0.276829 | ||||||||
\(177\) | 0.673159 | + | 2.51226i | 0.0505977 | + | 0.188833i | ||||
\(178\) | −10.7168 | − | 2.87156i | −0.803259 | − | 0.215233i | ||||
\(179\) | 1.63071 | − | 0.941493i | 0.121885 | − | 0.0703705i | −0.437818 | − | 0.899064i | \(-0.644249\pi\) |
0.559703 | + | 0.828693i | \(0.310915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.7439i | − | 1.31889i | −0.751751 | − | 0.659447i | \(-0.770791\pi\) | ||
0.751751 | − | 0.659447i | \(-0.229209\pi\) | |||||||
\(182\) | 1.15368 | − | 10.3908i | 0.0855166 | − | 0.770214i | ||||
\(183\) | −7.08436 | − | 7.08436i | −0.523691 | − | 0.523691i | ||||
\(184\) | −6.71719 | − | 3.87817i | −0.495198 | − | 0.285903i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.991969 | − | 1.71814i | −0.0727347 | − | 0.125980i | ||||
\(187\) | −1.80597 | + | 0.483908i | −0.132066 | + | 0.0353869i | ||||
\(188\) | 3.77151 | − | 3.77151i | 0.275066 | − | 0.275066i | ||||
\(189\) | 0.962603 | − | 2.46443i | 0.0700191 | − | 0.179261i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.37301 | + | 9.30633i | −0.388778 | + | 0.673382i | −0.992285 | − | 0.123975i | \(-0.960436\pi\) |
0.603508 | + | 0.797357i | \(0.293769\pi\) | |||||||
\(192\) | 1.82523 | − | 6.81187i | 0.131725 | − | 0.491604i | ||||
\(193\) | 0.833614 | − | 3.11109i | 0.0600049 | − | 0.223941i | −0.929412 | − | 0.369045i | \(-0.879685\pi\) |
0.989416 | + | 0.145104i | \(0.0463515\pi\) | |||||||
\(194\) | 1.76607 | − | 3.05893i | 0.126797 | − | 0.219618i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.52396 | + | 6.77824i | −0.108854 | + | 0.484160i | ||||
\(197\) | 10.9317 | − | 10.9317i | 0.778852 | − | 0.778852i | −0.200784 | − | 0.979636i | \(-0.564349\pi\) |
0.979636 | + | 0.200784i | \(0.0643489\pi\) | |||||||
\(198\) | −3.45708 | + | 0.926321i | −0.245684 | + | 0.0658307i | ||||
\(199\) | −6.19974 | − | 10.7383i | −0.439488 | − | 0.761215i | 0.558162 | − | 0.829732i | \(-0.311507\pi\) |
−0.997650 | + | 0.0685166i | \(0.978173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.77353 | + | 2.75600i | 0.336699 | + | 0.194393i | ||||
\(202\) | −0.606063 | − | 0.606063i | −0.0426425 | − | 0.0426425i | ||||
\(203\) | 14.8885 | − | 6.52458i | 1.04497 | − | 0.457935i | ||||
\(204\) | 0.520419i | 0.0364366i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.27683 | − | 3.04658i | 0.367654 | − | 0.212265i | ||||
\(207\) | 2.49427 | + | 0.668338i | 0.173364 | + | 0.0464527i | ||||
\(208\) | 1.04944 | + | 3.91657i | 0.0727657 | + | 0.271565i | ||||
\(209\) | −14.7040 | −1.01709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4216 | −0.923982 | −0.461991 | − | 0.886885i | \(-0.652865\pi\) | ||||
−0.461991 | + | 0.886885i | \(0.652865\pi\) | |||||||
\(212\) | −1.47648 | − | 5.51031i | −0.101405 | − | 0.378450i | ||||
\(213\) | 6.98629 | + | 1.87197i | 0.478693 | + | 0.128265i | ||||
\(214\) | 10.1678 | − | 5.87040i | 0.695058 | − | 0.401292i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.00370i | 0.204376i | ||||||||
\(217\) | −4.21261 | − | 3.09850i | −0.285970 | − | 0.210340i | ||||
\(218\) | 8.89753 | + | 8.89753i | 0.602617 | + | 0.602617i | ||||
\(219\) | −13.3254 | − | 7.69341i | −0.900445 | − | 0.519872i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.03212 | − | 1.78769i | −0.0694280 | − | 0.120253i | ||||
\(222\) | −0.153376 | + | 0.0410969i | −0.0102939 | + | 0.00275824i | ||||
\(223\) | −1.60905 | + | 1.60905i | −0.107750 | + | 0.107750i | −0.758927 | − | 0.651176i | \(-0.774276\pi\) |
0.651176 | + | 0.758927i | \(0.274276\pi\) | |||||||
\(224\) | −1.98234 | − | 13.0087i | −0.132451 | − | 0.869178i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.15118 | − | 8.92210i | 0.342651 | − | 0.593489i | ||||
\(227\) | −6.67262 | + | 24.9026i | −0.442878 | + | 1.65284i | 0.278603 | + | 0.960407i | \(0.410129\pi\) |
−0.721480 | + | 0.692435i | \(0.756538\pi\) | |||||||
\(228\) | −1.05929 | + | 3.95334i | −0.0701534 | + | 0.261816i | ||||
\(229\) | −0.669566 | + | 1.15972i | −0.0442462 | + | 0.0766366i | −0.887300 | − | 0.461192i | \(-0.847422\pi\) |
0.843054 | + | 0.537829i | \(0.180755\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.36614 | + | 5.89388i | −0.484656 | + | 0.387789i | ||||
\(232\) | −13.0494 | + | 13.0494i | −0.856736 | + | 0.856736i | ||||
\(233\) | −20.7283 | + | 5.55413i | −1.35796 | + | 0.363863i | −0.863065 | − | 0.505093i | \(-0.831458\pi\) |
−0.494890 | + | 0.868956i | \(0.664792\pi\) | |||||||
\(234\) | −1.97574 | − | 3.42207i | −0.129158 | − | 0.223708i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.23552 | − | 1.29068i | −0.145520 | − | 0.0840161i | ||||
\(237\) | −10.7080 | − | 10.7080i | −0.695561 | − | 0.695561i | ||||
\(238\) | −0.558926 | − | 1.27542i | −0.0362298 | − | 0.0826732i | ||||
\(239\) | 12.8433i | 0.830767i | 0.909646 | + | 0.415384i | \(0.136353\pi\) | ||||
−0.909646 | + | 0.415384i | \(0.863647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0766 | + | 12.7459i | −1.42208 | + | 0.821036i | −0.996476 | − | 0.0838747i | \(-0.973270\pi\) |
−0.425601 | + | 0.904911i | \(0.639937\pi\) | |||||||
\(242\) | 1.66178 | + | 0.445273i | 0.106823 | + | 0.0286232i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 9.94357 | 0.636572 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.31579 | −0.530196 | ||||||||
\(247\) | −4.20169 | − | 15.6809i | −0.267347 | − | 0.997753i | ||||
\(248\) | 5.73462 | + | 1.53659i | 0.364149 | + | 0.0975734i | ||||
\(249\) | 11.5417 | − | 6.66358i | 0.731423 | − | 0.422287i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0858i | 0.762849i | 0.924400 | + | 0.381425i | \(0.124566\pi\) | ||||
−0.924400 | + | 0.381425i | \(0.875434\pi\) | |||||||
\(252\) | 1.05398 | + | 2.40508i | 0.0663942 | + | 0.151506i | ||||
\(253\) | −6.51067 | − | 6.51067i | −0.409322 | − | 0.409322i | ||||
\(254\) | −1.30615 | − | 0.754106i | −0.0819552 | − | 0.0473168i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.49182 | + | 14.7083i | 0.530739 | + | 0.919266i | ||||
\(257\) | −10.0104 | + | 2.68228i | −0.624431 | + | 0.167316i | −0.557141 | − | 0.830418i | \(-0.688102\pi\) |
−0.0672896 | + | 0.997733i | \(0.521435\pi\) | |||||||
\(258\) | 9.04630 | − | 9.04630i | 0.563198 | − | 0.563198i | ||||
\(259\) | −0.326804 | + | 0.261486i | −0.0203066 | + | 0.0162480i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.07198 | − | 5.32083i | 0.190151 | − | 0.329351i | ||||
\(262\) | 3.11402 | − | 11.6217i | 0.192385 | − | 0.717990i | ||||
\(263\) | 2.05827 | − | 7.68155i | 0.126918 | − | 0.473665i | −0.872983 | − | 0.487751i | \(-0.837817\pi\) |
0.999901 | + | 0.0140863i | \(0.00448397\pi\) | |||||||
\(264\) | 5.35511 | − | 9.27532i | 0.329584 | − | 0.570856i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.64978 | − | 10.8263i | −0.101155 | − | 0.663806i | ||||
\(267\) | −7.81597 | + | 7.81597i | −0.478329 | + | 0.478329i | ||||
\(268\) | −5.28421 | + | 1.41590i | −0.322784 | + | 0.0864898i | ||||
\(269\) | −0.857638 | − | 1.48547i | −0.0522911 | − | 0.0905709i | 0.838695 | − | 0.544601i | \(-0.183319\pi\) |
−0.890986 | + | 0.454030i | \(0.849986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0645 | − | 5.81076i | −0.611377 | − | 0.352979i | 0.162127 | − | 0.986770i | \(-0.448164\pi\) |
−0.773504 | + | 0.633791i | \(0.781498\pi\) | |||||||
\(272\) | 0.381890 | + | 0.381890i | 0.0231555 | + | 0.0231555i | ||||
\(273\) | −8.39038 | − | 6.17137i | −0.507809 | − | 0.373508i | ||||
\(274\) | − | 6.34459i | − | 0.383291i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.21951 | + | 1.28144i | −0.133599 | + | 0.0771334i | ||||
\(277\) | 8.83410 | + | 2.36709i | 0.530790 | + | 0.142225i | 0.514253 | − | 0.857639i | \(-0.328069\pi\) |
0.0165369 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(278\) | −1.31940 | − | 4.92405i | −0.0791321 | − | 0.295325i | ||||
\(279\) | −1.97653 | −0.118332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0644 | 0.898669 | 0.449334 | − | 0.893364i | \(-0.351661\pi\) | ||||
0.449334 | + | 0.893364i | \(0.351661\pi\) | |||||||
\(282\) | 1.39612 | + | 5.21040i | 0.0831379 | + | 0.310275i | ||||
\(283\) | −15.4679 | − | 4.14461i | −0.919470 | − | 0.246371i | −0.232111 | − | 0.972689i | \(-0.574563\pi\) |
−0.687359 | + | 0.726318i | \(0.741230\pi\) | |||||||
\(284\) | −6.21671 | + | 3.58922i | −0.368894 | + | 0.212981i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0896i | 0.833137i | ||||||||
\(287\) | −20.0762 | + | 8.79798i | −1.18506 | + | 0.519329i | ||||
\(288\) | −3.51685 | − | 3.51685i | −0.207232 | − | 0.207232i | ||||
\(289\) | 14.4843 | + | 8.36253i | 0.852019 | + | 0.491913i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.75948 | − | 3.04751i | −0.103143 | − | 0.178648i | ||||
\(292\) | 14.7509 | − | 3.95250i | 0.863233 | − | 0.231302i | ||||
\(293\) | −6.20477 | + | 6.20477i | −0.362487 | + | 0.362487i | −0.864728 | − | 0.502241i | \(-0.832509\pi\) |
0.502241 | + | 0.864728i | \(0.332509\pi\) | |||||||
\(294\) | −5.16608 | − | 4.76231i | −0.301292 | − | 0.277743i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.237583 | − | 0.411506i | 0.0138092 | − | 0.0239183i | ||||
\(297\) | −0.922863 | + | 3.44417i | −0.0535499 | + | 0.199851i | ||||
\(298\) | 3.95943 | − | 14.7768i | 0.229364 | − | 0.855997i | ||||
\(299\) | 5.08282 | − | 8.80370i | 0.293947 | − | 0.509131i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2690 | − | 31.4107i | 0.707173 | − | 1.81048i | ||||
\(302\) | −10.5967 | + | 10.5967i | −0.609769 | + | 0.609769i | ||||
\(303\) | −0.824807 | + | 0.221006i | −0.0473839 | + | 0.0126965i | ||||
\(304\) | 2.12369 | + | 3.67834i | 0.121802 | + | 0.210967i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.455807 | − | 0.263160i | −0.0260568 | − | 0.0150439i | ||||
\(307\) | −6.26397 | − | 6.26397i | −0.357504 | − | 0.357504i | 0.505388 | − | 0.862892i | \(-0.331349\pi\) |
−0.862892 | + | 0.505388i | \(0.831349\pi\) | |||||||
\(308\) | 1.03322 | − | 9.30585i | 0.0588735 | − | 0.530250i | ||||
\(309\) | − | 6.07042i | − | 0.345334i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.78463 | + | 3.33976i | −0.328016 | + | 0.189380i | −0.654960 | − | 0.755664i | \(-0.727315\pi\) |
0.326944 | + | 0.945044i | \(0.393981\pi\) | |||||||
\(312\) | 11.4218 | + | 3.06047i | 0.646633 | + | 0.173265i | ||||
\(313\) | 0.480011 | + | 1.79143i | 0.0271318 | + | 0.101257i | 0.978164 | − | 0.207835i | \(-0.0666416\pi\) |
−0.951032 | + | 0.309092i | \(0.899975\pi\) | |||||||
\(314\) | 6.61835 | 0.373495 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.0297 | 0.845488 | ||||||||
\(317\) | 0.446453 | + | 1.66619i | 0.0250753 | + | 0.0935824i | 0.977329 | − | 0.211724i | \(-0.0679078\pi\) |
−0.952254 | + | 0.305306i | \(0.901241\pi\) | |||||||
\(318\) | 5.57280 | + | 1.49323i | 0.312507 | + | 0.0837361i | ||||
\(319\) | −18.9723 | + | 10.9537i | −1.06224 | + | 0.613287i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11.6970i | − | 0.652861i | ||||||
\(322\) | 4.06323 | − | 5.52423i | 0.226435 | − | 0.307853i | ||||
\(323\) | −1.52899 | − | 1.52899i | −0.0850752 | − | 0.0850752i | ||||
\(324\) | 0.859523 | + | 0.496246i | 0.0477513 | + | 0.0275692i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.701630 | − | 1.21526i | −0.0388597 | − | 0.0673070i | ||||
\(327\) | 12.1089 | − | 3.24457i | 0.669623 | − | 0.179425i | ||||
\(328\) | 17.5963 | − | 17.5963i | 0.971594 | − | 0.971594i | ||||
\(329\) | 8.88309 | + | 11.1020i | 0.489741 | + | 0.612075i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0089 | + | 22.5320i | −0.715032 | + | 1.23847i | 0.247915 | + | 0.968782i | \(0.420255\pi\) |
−0.962947 | + | 0.269690i | \(0.913079\pi\) | |||||||
\(332\) | −3.42342 | + | 12.7764i | −0.187885 | + | 0.701196i | ||||
\(333\) | −0.0409435 | + | 0.152803i | −0.00224369 | + | 0.00837356i | ||||
\(334\) | 2.96806 | − | 5.14082i | 0.162405 | − | 0.281293i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.53830 | + | 0.991459i | 0.138476 | + | 0.0540885i | ||||
\(337\) | 14.7150 | − | 14.7150i | 0.801579 | − | 0.801579i | −0.181763 | − | 0.983342i | \(-0.558180\pi\) |
0.983342 | + | 0.181763i | \(0.0581805\pi\) | |||||||
\(338\) | −2.42169 | + | 0.648890i | −0.131723 | + | 0.0352950i | ||||
\(339\) | −5.13195 | − | 8.88879i | −0.278729 | − | 0.482773i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.10345 | + | 3.52383i | 0.330520 | + | 0.190826i | ||||
\(342\) | −2.92686 | − | 2.92686i | −0.158267 | − | 0.158267i | ||||
\(343\) | −17.5105 | − | 6.03166i | −0.945480 | − | 0.325679i | ||||
\(344\) | 38.2842i | 2.06414i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.08122 | − | 1.20159i | 0.111887 | − | 0.0645980i | ||||
\(347\) | −12.3723 | − | 3.31515i | −0.664181 | − | 0.177967i | −0.0890489 | − | 0.996027i | \(-0.528383\pi\) |
−0.575132 | + | 0.818060i | \(0.695049\pi\) | |||||||
\(348\) | 1.57823 | + | 5.89005i | 0.0846023 | + | 0.315740i | ||||
\(349\) | 12.7510 | 0.682546 | 0.341273 | − | 0.939964i | \(-0.389142\pi\) | ||||
0.341273 | + | 0.939964i | \(0.389142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.93672 | −0.210127 | ||||||||
\(352\) | 4.58992 | + | 17.1298i | 0.244644 | + | 0.913023i | ||||
\(353\) | 16.6743 | + | 4.46786i | 0.887483 | + | 0.237800i | 0.673633 | − | 0.739066i | \(-0.264733\pi\) |
0.213850 | + | 0.976866i | \(0.431400\pi\) | |||||||
\(354\) | 2.26087 | − | 1.30532i | 0.120164 | − | 0.0693768i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.9705i | − | 0.581433i | ||||||
\(357\) | −1.37884 | − | 0.153092i | −0.0729761 | − | 0.00810250i | ||||
\(358\) | −1.33646 | − | 1.33646i | −0.0706342 | − | 0.0706342i | ||||
\(359\) | −6.50719 | − | 3.75693i | −0.343437 | − | 0.198283i | 0.318354 | − | 0.947972i | \(-0.396870\pi\) |
−0.661791 | + | 0.749689i | \(0.730203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.997305 | + | 1.72738i | 0.0524897 | + | 0.0909149i | ||||
\(362\) | −17.2035 | + | 4.60967i | −0.904197 | + | 0.242279i | ||||
\(363\) | 1.21197 | − | 1.21197i | 0.0636118 | − | 0.0636118i | ||||
\(364\) | 10.2194 | − | 1.55729i | 0.535642 | − | 0.0816244i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.02817 | + | 8.70904i | −0.262826 | + | 0.455229i | ||||
\(367\) | 1.78295 | − | 6.65407i | 0.0930693 | − | 0.347340i | −0.903650 | − | 0.428271i | \(-0.859123\pi\) |
0.996720 | + | 0.0809315i | \(0.0257895\pi\) | |||||||
\(368\) | −0.688373 | + | 2.56904i | −0.0358839 | + | 0.133921i | ||||
\(369\) | −4.14237 | + | 7.17480i | −0.215643 | + | 0.373505i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.0338 | − | 2.29095i | 0.780518 | − | 0.118940i | ||||
\(372\) | 1.38713 | − | 1.38713i | 0.0719191 | − | 0.0719191i | ||||
\(373\) | 6.50499 | − | 1.74301i | 0.336816 | − | 0.0902494i | −0.0864472 | − | 0.996256i | \(-0.527551\pi\) |
0.423263 | + | 0.906007i | \(0.360885\pi\) | |||||||
\(374\) | 0.938342 | + | 1.62526i | 0.0485205 | + | 0.0840400i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.9795 | − | 8.07106i | −0.720937 | − | 0.416233i | ||||
\(377\) | −17.1028 | − | 17.1028i | −0.880840 | − | 0.880840i | ||||
\(378\) | −2.63945 | − | 0.293057i | −0.135758 | − | 0.0150732i | ||||
\(379\) | − | 37.6021i | − | 1.93149i | −0.259496 | − | 0.965744i | \(-0.583556\pi\) | ||
0.259496 | − | 0.965744i | \(-0.416444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.30127 | + | 0.751291i | −0.0666663 | + | 0.0384898i | ||||
\(382\) | 10.4188 | + | 2.79170i | 0.533070 | + | 0.142836i | ||||
\(383\) | 4.00163 | + | 14.9343i | 0.204474 | + | 0.763106i | 0.989609 | + | 0.143782i | \(0.0459265\pi\) |
−0.785136 | + | 0.619324i | \(0.787407\pi\) | |||||||
\(384\) | 2.86856 | 0.146385 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.23291 | −0.164551 | ||||||||
\(387\) | −3.29882 | − | 12.3113i | −0.167688 | − | 0.625821i | ||||
\(388\) | 3.37353 | + | 0.903935i | 0.171265 | + | 0.0458904i | ||||
\(389\) | 16.0657 | − | 9.27555i | 0.814565 | − | 0.470289i | −0.0339739 | − | 0.999423i | \(-0.510816\pi\) |
0.848539 | + | 0.529134i | \(0.177483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.35402i | − | 0.0684759i | ||||||
\(392\) | 21.0086 | − | 0.854385i | 1.06109 | − | 0.0431530i | ||||
\(393\) | −8.47590 | − | 8.47590i | −0.427553 | − | 0.427553i | ||||
\(394\) | −13.4387 | − | 7.75885i | −0.677033 | − | 0.390885i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.76945 | − | 3.06477i | −0.0889181 | − | 0.154011i | ||||
\(397\) | 4.39567 | − | 1.17781i | 0.220612 | − | 0.0591128i | −0.146820 | − | 0.989163i | \(-0.546904\pi\) |
0.367432 | + | 0.930050i | \(0.380237\pi\) | |||||||
\(398\) | −8.80061 | + | 8.80061i | −0.441135 | + | 0.441135i | ||||
\(399\) | −10.1627 | − | 3.96954i | −0.508771 | − | 0.198726i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1701 | − | 19.3471i | 0.557806 | − | 0.966148i | −0.439873 | − | 0.898060i | \(-0.644977\pi\) |
0.997679 | − | 0.0680885i | \(-0.0216900\pi\) | |||||||
\(402\) | 1.43196 | − | 5.34413i | 0.0714195 | − | 0.266541i | ||||
\(403\) | −2.01388 | + | 7.51592i | −0.100319 | + | 0.374395i | ||||
\(404\) | 0.423746 | − | 0.733949i | 0.0210821 | − | 0.0365153i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1937 | − | 12.7401i | −0.505907 | − | 0.632279i | ||||
\(407\) | 0.398854 | − | 0.398854i | 0.0197705 | − | 0.0197705i | ||||
\(408\) | 1.52134 | − | 0.407643i | 0.0753177 | − | 0.0201813i | ||||
\(409\) | 3.04693 | + | 5.27744i | 0.150661 | + | 0.260953i | 0.931471 | − | 0.363816i | \(-0.118526\pi\) |
−0.780810 | + | 0.624769i | \(0.785193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.47407 | − | 3.16045i | −0.270016 | − | 0.155894i | ||||
\(412\) | 4.26020 | + | 4.26020i | 0.209885 | + | 0.209885i | ||||
\(413\) | 4.07726 | − | 5.54331i | 0.200629 | − | 0.272768i | ||||
\(414\) | − | 2.59194i | − | 0.127387i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.9564 | + | 9.78978i | −0.831356 | + | 0.479984i | ||||
\(417\) | −4.90567 | − | 1.31447i | −0.240232 | − | 0.0643699i | ||||
\(418\) | 3.81992 | + | 14.2561i | 0.186839 | + | 0.697291i | ||||
\(419\) | −23.3177 | −1.13914 | −0.569572 | − | 0.821942i | \(-0.692891\pi\) | ||||
−0.569572 | + | 0.821942i | \(0.692891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0119079 | −0.000580356 | −0.000290178 | − | 1.00000i | \(-0.500092\pi\) | ||||
−0.000290178 | 1.00000i | \(0.500092\pi\) | ||||||||
\(422\) | 3.48679 | + | 13.0129i | 0.169734 | + | 0.633456i | ||||
\(423\) | 5.19095 | + | 1.39091i | 0.252393 | + | 0.0676284i | ||||
\(424\) | −14.9518 | + | 8.63243i | −0.726124 | + | 0.419228i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 7.25985i | − | 0.351741i | ||||||
\(427\) | −2.92511 | + | 26.3453i | −0.141556 | + | 1.27494i | ||||
\(428\) | 8.20890 | + | 8.20890i | 0.396792 | + | 0.396792i | ||||
\(429\) | 12.1564 | + | 7.01851i | 0.586918 | + | 0.338857i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.44866 | − | 16.3656i | −0.455126 | − | 0.788301i | 0.543569 | − | 0.839364i | \(-0.317072\pi\) |
−0.998695 | + | 0.0510628i | \(0.983739\pi\) | |||||||
\(432\) | 0.994881 | − | 0.266578i | 0.0478662 | − | 0.0128257i | ||||
\(433\) | 18.7716 | − | 18.7716i | 0.902105 | − | 0.902105i | −0.0935133 | − | 0.995618i | \(-0.529810\pi\) |
0.995618 | + | 0.0935133i | \(0.0298098\pi\) | |||||||
\(434\) | −1.90974 | + | 4.88927i | −0.0916707 | + | 0.234692i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.22096 | + | 10.7750i | −0.297930 | + | 0.516029i | ||||
\(437\) | 2.75607 | − | 10.2858i | 0.131840 | − | 0.492035i | ||||
\(438\) | −3.99732 | + | 14.9182i | −0.190999 | + | 0.712820i | ||||
\(439\) | 3.40990 | − | 5.90612i | 0.162746 | − | 0.281884i | −0.773107 | − | 0.634276i | \(-0.781298\pi\) |
0.935852 | + | 0.352392i | \(0.114632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.68228 | + | 2.08499i | −0.318204 | + | 0.0992852i | ||||
\(442\) | −1.46511 | + | 1.46511i | −0.0696881 | + | 0.0696881i | ||||
\(443\) | 6.66435 | − | 1.78571i | 0.316633 | − | 0.0848415i | −0.0970026 | − | 0.995284i | \(-0.530926\pi\) |
0.413635 | + | 0.910443i | \(0.364259\pi\) | |||||||
\(444\) | −0.0785028 | − | 0.135971i | −0.00372558 | − | 0.00645289i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.97807 | + | 1.14204i | 0.0936641 | + | 0.0540770i | ||||
\(447\) | −10.7770 | − | 10.7770i | −0.509734 | − | 0.509734i | ||||
\(448\) | −17.0893 | + | 7.48904i | −0.807395 | + | 0.353824i | ||||
\(449\) | 27.2653i | 1.28673i | 0.765560 | + | 0.643365i | \(0.222462\pi\) | ||||
−0.765560 | + | 0.643365i | \(0.777538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.5830 | − | 14.7703i | 1.20465 | − | 0.695508i | ||||
\(452\) | 9.83972 | + | 2.63655i | 0.462822 | + | 0.124013i | ||||
\(453\) | 3.86417 | + | 14.4213i | 0.181554 | + | 0.677570i | ||||
\(454\) | 25.8776 | 1.21450 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.3866 | 0.580054 | ||||||||
\(457\) | 4.49326 | + | 16.7691i | 0.210186 | + | 0.784425i | 0.987806 | + | 0.155690i | \(0.0497602\pi\) |
−0.777620 | + | 0.628735i | \(0.783573\pi\) | |||||||
\(458\) | 1.29835 | + | 0.347892i | 0.0606679 | + | 0.0162559i | ||||
\(459\) | −0.454106 | + | 0.262178i | −0.0211958 | + | 0.0122374i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8808i | 1.95058i | 0.220920 | + | 0.975292i | \(0.429094\pi\) | ||||
−0.220920 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(462\) | 7.62803 | + | 5.61064i | 0.354888 | + | 0.261031i | ||||
\(463\) | 15.4654 | + | 15.4654i | 0.718740 | + | 0.718740i | 0.968347 | − | 0.249607i | \(-0.0803016\pi\) |
−0.249607 | + | 0.968347i | \(0.580302\pi\) | |||||||
\(464\) | 5.48033 | + | 3.16407i | 0.254418 | + | 0.146888i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7700 | + | 18.6541i | 0.498909 | + | 0.864135i | ||||
\(467\) | 32.4120 | − | 8.68477i | 1.49985 | − | 0.401883i | 0.586800 | − | 0.809732i | \(-0.300388\pi\) |
0.913049 | + | 0.407849i | \(0.133721\pi\) | |||||||
\(468\) | 2.76278 | − | 2.76278i | 0.127710 | − | 0.127710i | ||||
\(469\) | −2.19694 | − | 14.4169i | −0.101445 | − | 0.665713i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.29682 | − | 5.71026i | 0.151910 | − | 0.263115i | ||||
\(472\) | −2.02197 | + | 7.54610i | −0.0930688 | + | 0.347337i | ||||
\(473\) | −11.7625 | + | 43.8982i | −0.540839 | + | 2.01844i | ||||
\(474\) | −7.60009 | + | 13.1637i | −0.349083 | + | 0.604630i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.07511 | − | 0.860229i | 0.0492775 | − | 0.0394285i | ||||
\(477\) | 4.06435 | − | 4.06435i | 0.186094 | − | 0.186094i | ||||
\(478\) | 12.4522 | − | 3.33656i | 0.569551 | − | 0.152611i | ||||
\(479\) | 8.19191 | + | 14.1888i | 0.374298 | + | 0.648303i | 0.990222 | − | 0.139503i | \(-0.0445505\pi\) |
−0.615924 | + | 0.787806i | \(0.711217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.539329 | + | 0.311381i | 0.0245913 | + | 0.0141978i | ||||
\(482\) | 18.0930 | + | 18.0930i | 0.824113 | + | 0.824113i | ||||
\(483\) | −2.74223 | − | 6.25753i | −0.124776 | − | 0.284727i | ||||
\(484\) | 1.70111i | 0.0773232i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.869271 | + | 0.501874i | −0.0394309 | + | 0.0227654i | ||||
\(487\) | −4.22392 | − | 1.13179i | −0.191404 | − | 0.0512865i | 0.161844 | − | 0.986816i | \(-0.448256\pi\) |
−0.353248 | + | 0.935530i | \(0.614923\pi\) | |||||||
\(488\) | −7.78877 | − | 29.0681i | −0.352581 | − | 1.31585i | ||||
\(489\) | −1.39802 | −0.0632208 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8633 | 1.52823 | 0.764116 | − | 0.645079i | \(-0.223176\pi\) | ||||
0.764116 | + | 0.645079i | \(0.223176\pi\) | |||||||
\(492\) | −2.12815 | − | 7.94237i | −0.0959445 | − | 0.358070i | ||||
\(493\) | −3.11185 | − | 0.833817i | −0.140151 | − | 0.0375532i | ||||
\(494\) | −14.1118 | + | 8.14746i | −0.634920 | + | 0.366571i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.03578i | − | 0.0914093i | ||||||
\(497\) | −7.68081 | − | 17.5269i | −0.344531 | − | 0.786190i | ||||
\(498\) | −9.45904 | − | 9.45904i | −0.423870 | − | 0.423870i | ||||
\(499\) | −15.2390 | − | 8.79824i | −0.682192 | − | 0.393864i | 0.118489 | − | 0.992955i | \(-0.462195\pi\) |
−0.800680 | + | 0.599092i | \(0.795528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.95698 | − | 5.12163i | −0.132108 | − | 0.228818i | ||||
\(502\) | 11.7177 | − | 3.13976i | 0.522988 | − | 0.140134i | ||||
\(503\) | −9.37063 | + | 9.37063i | −0.417816 | + | 0.417816i | −0.884450 | − | 0.466635i | \(-0.845466\pi\) |
0.466635 | + | 0.884450i | \(0.345466\pi\) | |||||||
\(504\) | 6.20521 | − | 4.96499i | 0.276402 | − | 0.221158i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.62099 | + | 8.00379i | −0.205428 | + | 0.355812i | ||||
\(507\) | −0.646467 | + | 2.41265i | −0.0287106 | + | 0.107150i | ||||
\(508\) | 0.385977 | − | 1.44049i | 0.0171250 | − | 0.0639112i | ||||
\(509\) | −13.8907 | + | 24.0594i | −0.615695 | + | 1.06641i | 0.374567 | + | 0.927200i | \(0.377791\pi\) |
−0.990262 | + | 0.139215i | \(0.955542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.13279 | + | 40.2451i | 0.271299 | + | 1.78034i | ||||
\(512\) | 7.99749 | − | 7.99749i | 0.353442 | − | 0.353442i | ||||
\(513\) | −3.98325 | + | 1.06731i | −0.175865 | + | 0.0471228i | ||||
\(514\) | 5.20118 | + | 9.00870i | 0.229414 | + | 0.397357i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.9552 | + | 6.32497i | 0.482275 | + | 0.278441i | ||||
\(517\) | −13.5497 | − | 13.5497i | −0.595914 | − | 0.595914i | ||||
\(518\) | 0.338423 | + | 0.248920i | 0.0148695 | + | 0.0109369i | ||||
\(519\) | − | 2.39421i | − | 0.105094i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2942 | − | 8.83010i | 0.670050 | − | 0.386854i | −0.126045 | − | 0.992024i | \(-0.540228\pi\) |
0.796096 | + | 0.605171i | \(0.206895\pi\) | |||||||
\(522\) | −5.95685 | − | 1.59613i | −0.260724 | − | 0.0698608i | ||||
\(523\) | −1.08429 | − | 4.04661i | −0.0474125 | − | 0.176946i | 0.938159 | − | 0.346204i | \(-0.112530\pi\) |
−0.985572 | + | 0.169258i | \(0.945863\pi\) | |||||||
\(524\) | 11.8967 | 0.519711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.98233 | −0.348046 | ||||||||
\(527\) | 0.268242 | + | 1.00109i | 0.0116848 | + | 0.0436082i | ||||
\(528\) | −3.54742 | − | 0.950527i | −0.154381 | − | 0.0413664i | ||||
\(529\) | −14.1439 | + | 8.16597i | −0.614951 | + | 0.355042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.60089i | − | 0.112869i | ||||||
\(532\) | 9.91797 | − | 4.34634i | 0.429999 | − | 0.188438i | ||||
\(533\) | 23.0621 | + | 23.0621i | 0.998930 | + | 0.998930i | ||||
\(534\) | 9.60844 | + | 5.54743i | 0.415798 | + | 0.240061i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.27821 | + | 14.3383i | 0.357564 | + | 0.619319i | ||||
\(537\) | −1.81883 | + | 0.487353i | −0.0784881 | + | 0.0210308i | ||||
\(538\) | −1.21743 | + | 1.21743i | −0.0524871 | + | 0.0524871i | ||||
\(539\) | 24.3518 | + | 5.47503i | 1.04891 | + | 0.235826i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.49606 | − | 16.4477i | 0.408267 | − | 0.707140i | −0.586428 | − | 0.810001i | \(-0.699466\pi\) |
0.994696 | + | 0.102861i | \(0.0327998\pi\) | |||||||
\(542\) | −3.01914 | + | 11.2676i | −0.129683 | + | 0.483984i | ||||
\(543\) | −4.59246 | + | 17.1393i | −0.197081 | + | 0.735517i | ||||
\(544\) | −1.30396 | + | 2.25853i | −0.0559069 | + | 0.0968336i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.80370 | + | 9.73811i | −0.162783 | + | 0.416753i | ||||
\(547\) | 4.10986 | − | 4.10986i | 0.175725 | − | 0.175725i | −0.613764 | − | 0.789489i | \(-0.710345\pi\) |
0.789489 | + | 0.613764i | \(0.210345\pi\) | |||||||
\(548\) | 6.05969 | − | 1.62369i | 0.258857 | − | 0.0693605i | ||||
\(549\) | 5.00940 | + | 8.67653i | 0.213796 | + | 0.370305i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.9418 | − | 12.6681i | −0.934752 | − | 0.539680i | ||||
\(552\) | 5.48457 | + | 5.48457i | 0.233439 | + | 0.233439i | ||||
\(553\) | −4.42131 | + | 39.8210i | −0.188013 | + | 1.69336i | ||||
\(554\) | − | 9.18001i | − | 0.390021i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.36528 | − | 2.52029i | 0.185129 | − | 0.106884i | ||||
\(557\) | −27.2967 | − | 7.31412i | −1.15660 | − | 0.309909i | −0.370991 | − | 0.928637i | \(-0.620982\pi\) |
−0.785606 | + | 0.618727i | \(0.787649\pi\) | |||||||
\(558\) | 0.513481 | + | 1.91634i | 0.0217374 | + | 0.0811250i | ||||
\(559\) | −50.1760 | −2.12222 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.86968 | 0.0789379 | ||||||||
\(562\) | −3.91357 | − | 14.6057i | −0.165084 | − | 0.616102i | ||||
\(563\) | −23.8998 | − | 6.40394i | −1.00726 | − | 0.269894i | −0.282775 | − | 0.959186i | \(-0.591255\pi\) |
−0.724483 | + | 0.689292i | \(0.757922\pi\) | |||||||
\(564\) | −4.61914 | + | 2.66686i | −0.194501 | + | 0.112295i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.0735i | 0.675621i | ||||||||
\(567\) | −1.56764 | + | 2.13131i | −0.0658348 | + | 0.0895067i | ||||
\(568\) | 15.3619 | + | 15.3619i | 0.644572 | + | 0.644572i | ||||
\(569\) | −31.0893 | − | 17.9494i | −1.30333 | − | 0.752479i | −0.322357 | − | 0.946618i | \(-0.604475\pi\) |
−0.980974 | + | 0.194140i | \(0.937809\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.51101 | + | 6.08125i | 0.146931 | + | 0.254492i | 0.930092 | − | 0.367327i | \(-0.119727\pi\) |
−0.783161 | + | 0.621820i | \(0.786394\pi\) | |||||||
\(572\) | −13.4569 | + | 3.60577i | −0.562662 | + | 0.150765i | ||||
\(573\) | 7.59859 | − | 7.59859i | 0.317436 | − | 0.317436i | ||||
\(574\) | 13.7456 | + | 17.1792i | 0.573731 | + | 0.717046i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.52608 | + | 6.10735i | −0.146920 | + | 0.254473i | ||||
\(577\) | 6.47806 | − | 24.1765i | 0.269685 | − | 1.00648i | −0.689635 | − | 0.724157i | \(-0.742229\pi\) |
0.959320 | − | 0.282321i | \(-0.0911045\pi\) | |||||||
\(578\) | 4.34498 | − | 16.2157i | 0.180727 | − | 0.674484i | ||||
\(579\) | −1.61042 | + | 2.78933i | −0.0669267 | + | 0.115921i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.8438 | − | 12.8288i | −1.36259 | − | 0.532227i | ||||
\(582\) | −2.49760 | + | 2.49760i | −0.103529 | + | 0.103529i | ||||
\(583\) | −19.7966 | + | 5.30448i | −0.819891 | + | 0.219689i | ||||
\(584\) | −23.1087 | − | 40.0255i | −0.956246 | − | 1.65627i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.62774 | + | 4.40388i | 0.315099 | + | 0.181923i | ||||
\(587\) | 22.0509 | + | 22.0509i | 0.910139 | + | 0.910139i | 0.996283 | − | 0.0861436i | \(-0.0274544\pi\) |
−0.0861436 | + | 0.996283i | \(0.527454\pi\) | |||||||
\(588\) | 3.22637 | − | 6.15285i | 0.133053 | − | 0.253739i | ||||
\(589\) | 8.15074i | 0.335845i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.3885 | + | 7.72988i | −0.550731 | + | 0.317965i | ||||
\(592\) | −0.157384 | − | 0.0421708i | −0.00646843 | − | 0.00173321i | ||||
\(593\) | −11.1621 | − | 41.6575i | −0.458372 | − | 1.71067i | −0.677981 | − | 0.735079i | \(-0.737145\pi\) |
0.219609 | − | 0.975588i | \(-0.429522\pi\) | |||||||
\(594\) | 3.57903 | 0.146849 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.1265 | 0.619607 | ||||||||
\(597\) | 3.20922 | + | 11.9770i | 0.131345 | + | 0.490185i | ||||
\(598\) | −9.85604 | − | 2.64092i | −0.403043 | − | 0.107995i | ||||
\(599\) | 23.6940 | − | 13.6797i | 0.968111 | − | 0.558939i | 0.0694514 | − | 0.997585i | \(-0.477875\pi\) |
0.898660 | + | 0.438646i | \(0.144542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.61565i | − | 0.310649i | −0.987864 | − | 0.155324i | \(-0.950358\pi\) | ||
0.987864 | − | 0.155324i | \(-0.0496423\pi\) | |||||||
\(602\) | −33.6414 | − | 3.73520i | −1.37112 | − | 0.152235i | ||||
\(603\) | −3.89757 | − | 3.89757i | −0.158721 | − | 0.158721i | ||||
\(604\) | −12.8327 | − | 7.40895i | −0.522154 | − | 0.301466i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.428551 | + | 0.742273i | 0.0174087 | + | 0.0301528i | ||||
\(607\) | −15.0249 | + | 4.02590i | −0.609840 | + | 0.163406i | −0.550505 | − | 0.834832i | \(-0.685565\pi\) |
−0.0593354 | + | 0.998238i | \(0.518898\pi\) | |||||||
\(608\) | −14.5026 | + | 14.5026i | −0.588159 | + | 0.588159i | ||||
\(609\) | −16.0699 | + | 2.44883i | −0.651184 | + | 0.0992314i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5781 | − | 18.3218i | 0.427944 | − | 0.741221i | ||||
\(612\) | 0.134694 | − | 0.502686i | 0.00544469 | − | 0.0203199i | ||||
\(613\) | −0.880848 | + | 3.28737i | −0.0355771 | + | 0.132776i | −0.981430 | − | 0.191819i | \(-0.938561\pi\) |
0.945853 | + | 0.324595i | \(0.105228\pi\) | |||||||
\(614\) | −4.44590 | + | 7.70052i | −0.179422 | + | 0.310768i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.0132 | + | 4.26882i | −1.12868 | + | 0.171996i | ||||
\(617\) | 19.3906 | − | 19.3906i | 0.780637 | − | 0.780637i | −0.199301 | − | 0.979938i | \(-0.563867\pi\) |
0.979938 | + | 0.199301i | \(0.0638671\pi\) | |||||||
\(618\) | −5.88554 | + | 1.57703i | −0.236751 | + | 0.0634373i | ||||
\(619\) | 15.4314 | + | 26.7280i | 0.620240 | + | 1.07429i | 0.989441 | + | 0.144938i | \(0.0462982\pi\) |
−0.369200 | + | 0.929350i | \(0.620368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.23630 | − | 1.29113i | −0.0897397 | − | 0.0518113i | ||||
\(622\) | 4.74083 | + | 4.74083i | 0.190090 | + | 0.190090i | ||||
\(623\) | 29.0661 | + | 3.22719i | 1.16451 | + | 0.129295i | ||||
\(624\) | − | 4.05473i | − | 0.162319i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.61217 | − | 0.930785i | 0.0644351 | − | 0.0372016i | ||||
\(627\) | 14.2029 | + | 3.80566i | 0.567210 | + | 0.151984i | ||||
\(628\) | 1.69375 | + | 6.32115i | 0.0675879 | + | 0.252241i | ||||
\(629\) | 0.0829496 | 0.00330742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0017 | −0.756446 | −0.378223 | − | 0.925714i | \(-0.623465\pi\) | ||||
−0.378223 | + | 0.925714i | \(0.623465\pi\) | |||||||
\(632\) | −11.7727 | − | 43.9365i | −0.468295 | − | 1.74770i | ||||
\(633\) | 12.9643 | + | 3.47377i | 0.515284 | + | 0.138070i | ||||
\(634\) | 1.49946 | − | 0.865713i | 0.0595512 | − | 0.0343819i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.70470i | 0.226206i | ||||||||
\(637\) | 1.11978 | + | 27.5343i | 0.0443671 | + | 1.09095i | ||||
\(638\) | 15.5489 | + | 15.5489i | 0.615585 | + | 0.615585i | ||||
\(639\) | −6.26374 | − | 3.61637i | −0.247790 | − | 0.143061i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.84861 | + | 15.3262i | 0.349499 | + | 0.605350i | 0.986161 | − | 0.165793i | \(-0.0530185\pi\) |
−0.636661 | + | 0.771143i | \(0.719685\pi\) | |||||||
\(642\) | −11.3407 | + | 3.03874i | −0.447583 | + | 0.119930i | ||||
\(643\) | 1.20751 | − | 1.20751i | 0.0476194 | − | 0.0476194i | −0.682896 | − | 0.730516i | \(-0.739280\pi\) |
0.730516 | + | 0.682896i | \(0.239280\pi\) | |||||||
\(644\) | 6.31601 | + | 2.46703i | 0.248886 | + | 0.0972145i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.08521 | + | 1.87964i | −0.0426970 | + | 0.0739534i | ||||
\(647\) | −0.977939 | + | 3.64972i | −0.0384468 | + | 0.143485i | −0.982481 | − | 0.186362i | \(-0.940330\pi\) |
0.944034 | + | 0.329847i | \(0.106997\pi\) | |||||||
\(648\) | 0.777416 | − | 2.90136i | 0.0305398 | − | 0.113976i | ||||
\(649\) | −4.63695 | + | 8.03143i | −0.182016 | + | 0.315261i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.26712 | + | 4.08322i | 0.128048 | + | 0.160034i | ||||
\(652\) | 0.981129 | − | 0.981129i | 0.0384240 | − | 0.0384240i | ||||
\(653\) | 8.72296 | − | 2.33731i | 0.341356 | − | 0.0914660i | −0.0840686 | − | 0.996460i | \(-0.526791\pi\) |
0.425424 | + | 0.904994i | \(0.360125\pi\) | |||||||
\(654\) | −6.29151 | − | 10.8972i | −0.246017 | − | 0.426115i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.38988 | − | 4.26655i | −0.288526 | − | 0.166581i | ||||
\(657\) | 10.8801 | + | 10.8801i | 0.424474 | + | 0.424474i | ||||
\(658\) | 8.45619 | − | 11.4967i | 0.329657 | − | 0.448190i | ||||
\(659\) | − | 40.3378i | − | 1.57134i | −0.618648 | − | 0.785668i | \(-0.712319\pi\) | ||
0.618648 | − | 0.785668i | \(-0.287681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8392 | − | 13.7636i | 0.927238 | − | 0.535341i | 0.0413010 | − | 0.999147i | \(-0.486850\pi\) |
0.885937 | + | 0.463806i | \(0.153516\pi\) | |||||||
\(662\) | 25.2254 | + | 6.75912i | 0.980412 | + | 0.262701i | ||||
\(663\) | 0.534265 | + | 1.99390i | 0.0207491 | + | 0.0774368i | ||||
\(664\) | 40.0308 | 1.55350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.158786 | 0.00615284 | ||||||||
\(667\) | −4.10624 | − | 15.3247i | −0.158994 | − | 0.593375i | ||||
\(668\) | 5.66955 | + | 1.51915i | 0.219361 | + | 0.0587777i | ||||
\(669\) | 1.97068 | − | 1.13777i | 0.0761909 | − | 0.0439889i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 35.7237i | − | 1.37910i | ||||||
\(672\) | −1.45210 | + | 13.0785i | −0.0560159 | + | 0.504513i | ||||
\(673\) | −22.5966 | − | 22.5966i | −0.871035 | − | 0.871035i | 0.121550 | − | 0.992585i | \(-0.461213\pi\) |
−0.992585 | + | 0.121550i | \(0.961213\pi\) | |||||||
\(674\) | −18.0897 | − | 10.4441i | −0.696789 | − | 0.402291i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.23950 | − | 2.14688i | −0.0476732 | − | 0.0825723i | ||||
\(677\) | −8.93720 | + | 2.39472i | −0.343484 | + | 0.0920364i | −0.426437 | − | 0.904517i | \(-0.640232\pi\) |
0.0829529 | + | 0.996553i | \(0.473565\pi\) | |||||||
\(678\) | −7.28486 | + | 7.28486i | −0.279774 | + | 0.279774i | ||||
\(679\) | −3.38736 | + | 8.67221i | −0.129995 | + | 0.332809i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.8905 | − | 22.3270i | 0.493966 | − | 0.855574i | ||||
\(682\) | 1.83090 | − | 6.83302i | 0.0701089 | − | 0.261650i | ||||
\(683\) | −1.20450 | + | 4.49527i | −0.0460891 | + | 0.172007i | −0.985134 | − | 0.171788i | \(-0.945046\pi\) |
0.939045 | + | 0.343794i | \(0.111712\pi\) | |||||||
\(684\) | 2.04640 | − | 3.54447i | 0.0782460 | − | 0.135526i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.29893 | + | 18.5442i | −0.0495933 | + | 0.708022i | ||||
\(687\) | 0.946910 | − | 0.946910i | 0.0361269 | − | 0.0361269i | ||||
\(688\) | 12.6804 | − | 3.39770i | 0.483436 | − | 0.129536i | ||||
\(689\) | −11.3138 | − | 19.5961i | −0.431023 | − | 0.746554i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.52332 | − | 3.76624i | −0.248159 | − | 0.143275i | 0.370762 | − | 0.928728i | \(-0.379097\pi\) |
−0.618921 | + | 0.785453i | \(0.712430\pi\) | |||||||
\(692\) | 1.68025 | + | 1.68025i | 0.0638736 | + | 0.0638736i | ||||
\(693\) | 8.64059 | − | 3.78656i | 0.328229 | − | 0.143839i | ||||
\(694\) | 12.8568i | 0.488036i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.9822 | − | 9.22732i | 0.605804 | − | 0.349761i | ||||
\(697\) | 4.19613 | + | 1.12435i | 0.158940 | + | 0.0425878i | ||||
\(698\) | −3.31257 | − | 12.3627i | −0.125383 | − | 0.467934i | ||||
\(699\) | 21.4595 | 0.811673 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.2736 | −1.70996 | −0.854981 | − | 0.518660i | \(-0.826431\pi\) | ||||
−0.854981 | + | 0.518660i | \(0.826431\pi\) | |||||||
\(702\) | 1.02272 | + | 3.81683i | 0.0385999 | + | 0.144057i | ||||
\(703\) | 0.630123 | + | 0.168841i | 0.0237655 | + | 0.00636796i | ||||
\(704\) | 21.7768 | − | 12.5728i | 0.820744 | − | 0.473857i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 17.3272i | − | 0.652117i | ||||||
\(707\) | 1.81993 | + | 1.33862i | 0.0684457 | + | 0.0503438i | ||||
\(708\) | 1.82530 | + | 1.82530i | 0.0685988 | + | 0.0685988i | ||||
\(709\) | 27.8909 | + | 16.1028i | 1.04747 | + | 0.604754i | 0.921939 | − | 0.387336i | \(-0.126605\pi\) |
0.125527 | + | 0.992090i | \(0.459938\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.57171 | + | 13.1146i | 0.283961 | + | 0.491836i | ||||
\(712\) | −32.0700 | + | 8.59313i | −1.20187 | + | 0.322041i | ||||
\(713\) | −3.60902 | + | 3.60902i | −0.135159 | + | 0.135159i | ||||
\(714\) | 0.209778 | + | 1.37662i | 0.00785074 | + | 0.0515188i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.934424 | − | 1.61847i | 0.0349211 | − | 0.0604851i | ||||
\(717\) | 3.32410 | − | 12.4057i | 0.124141 | − | 0.463300i | ||||
\(718\) | −1.95202 | + | 7.28503i | −0.0728486 | + | 0.271875i | ||||
\(719\) | 14.8623 | − | 25.7422i | 0.554270 | − | 0.960023i | −0.443690 | − | 0.896180i | \(-0.646331\pi\) |
0.997960 | − | 0.0638430i | \(-0.0203357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5406 | + | 10.0341i | −0.467036 | + | 0.373690i | ||||
\(722\) | 1.41569 | − | 1.41569i | 0.0526864 | − | 0.0526864i | ||||
\(723\) | 24.6232 | − | 6.59777i | 0.915747 | − | 0.245374i | ||||
\(724\) | −8.80534 | − | 15.2513i | −0.327248 | − | 0.566810i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.48991 | − | 0.860202i | −0.0552958 | − | 0.0319251i | ||||
\(727\) | −8.03461 | − | 8.03461i | −0.297987 | − | 0.297987i | 0.542238 | − | 0.840225i | \(-0.317577\pi\) |
−0.840225 | + | 0.542238i | \(0.817577\pi\) | |||||||
\(728\) | −12.5573 | − | 28.6546i | −0.465404 | − | 1.06201i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.78787 | + | 3.34163i | −0.214072 | + | 0.123595i | ||||
\(732\) | −9.60475 | − | 2.57358i | −0.355002 | − | 0.0951224i | ||||
\(733\) | −7.77556 | − | 29.0188i | −0.287197 | − | 1.07183i | −0.947219 | − | 0.320587i | \(-0.896120\pi\) |
0.660022 | − | 0.751246i | \(-0.270547\pi\) | |||||||
\(734\) | −6.91461 | −0.255223 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.8431 | −0.473401 | ||||||||
\(737\) | 5.08682 | + | 18.9843i | 0.187375 | + | 0.699294i | ||||
\(738\) | 8.03244 | + | 2.15229i | 0.295678 | + | 0.0792267i | ||||
\(739\) | 35.8813 | − | 20.7161i | 1.31992 | − | 0.762054i | 0.336202 | − | 0.941790i | \(-0.390858\pi\) |
0.983715 | + | 0.179736i | \(0.0575243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.2341i | 0.596374i | ||||||||
\(742\) | −6.12680 | − | 13.9808i | −0.224922 | − | 0.513252i | ||||
\(743\) | −10.5103 | − | 10.5103i | −0.385585 | − | 0.385585i | 0.487525 | − | 0.873109i | \(-0.337900\pi\) |
−0.873109 | + | 0.487525i | \(0.837900\pi\) | |||||||
\(744\) | −5.14152 | − | 2.96846i | −0.188497 | − | 0.108829i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.37985 | − | 5.85407i | −0.123745 | − | 0.214333i | ||||
\(747\) | −12.8730 | + | 3.44932i | −0.471000 | + | 0.126204i | ||||
\(748\) | −1.31214 | + | 1.31214i | −0.0479764 | + | 0.0479764i | ||||
\(749\) | −24.1642 | + | 19.3346i | −0.882941 | + | 0.706469i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.0235 | − | 36.4138i | 0.767159 | − | 1.32876i | −0.171938 | − | 0.985108i | \(-0.555003\pi\) |
0.939097 | − | 0.343651i | \(-0.111664\pi\) | |||||||
\(752\) | −1.43261 | + | 5.34656i | −0.0522418 | + | 0.194969i | ||||
\(753\) | 3.12804 | − | 11.6740i | 0.113992 | − | 0.425424i | ||||
\(754\) | −12.1388 | + | 21.0251i | −0.442071 | + | 0.765689i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.395582 | − | 2.59592i | −0.0143872 | − | 0.0944126i | ||||
\(757\) | −12.0838 | + | 12.0838i | −0.439193 | + | 0.439193i | −0.891740 | − | 0.452547i | \(-0.850515\pi\) |
0.452547 | + | 0.891740i | \(0.350515\pi\) | |||||||
\(758\) | −36.4569 | + | 9.76860i | −1.32417 | + | 0.354811i | ||||
\(759\) | 4.60374 | + | 7.97391i | 0.167105 | + | 0.289435i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.6620 | − | 7.31041i | −0.458997 | − | 0.265002i | 0.252625 | − | 0.967564i | \(-0.418706\pi\) |
−0.711623 | + | 0.702562i | \(0.752039\pi\) | |||||||
\(762\) | 1.06647 | + | 1.06647i | 0.0386340 | + | 0.0386340i | ||||
\(763\) | −26.7182 | − | 19.6520i | −0.967264 | − | 0.711451i | ||||
\(764\) | 10.6653i | 0.385858i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4399 | − | 7.75952i | 0.485603 | − | 0.280363i | ||||
\(767\) | −9.89008 | − | 2.65004i | −0.357110 | − | 0.0956874i | ||||
\(768\) | −4.39569 | − | 16.4049i | −0.158616 | − | 0.591962i | ||||
\(769\) | −5.95109 | −0.214602 | −0.107301 | − | 0.994227i | \(-0.534221\pi\) | ||||
−0.107301 | + | 0.994227i | \(0.534221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3635 | 0.373233 | ||||||||
\(772\) | −0.827355 | − | 3.08773i | −0.0297772 | − | 0.111130i | ||||
\(773\) | −4.58677 | − | 1.22902i | −0.164975 | − | 0.0442049i | 0.175386 | − | 0.984500i | \(-0.443883\pi\) |
−0.340361 | + | 0.940295i | \(0.610549\pi\) | |||||||
\(774\) | −11.0794 | + | 6.39670i | −0.398241 | + | 0.229925i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 10.5699i | − | 0.379438i | ||||||
\(777\) | 0.383346 | − | 0.167993i | 0.0137525 | − | 0.00602673i | ||||
\(778\) | −13.1668 | − | 13.1668i | −0.472051 | − | 0.472051i | ||||
\(779\) | 29.5872 | + | 17.0822i | 1.06007 | + | 0.612032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8948 | + | 22.3344i | 0.461411 | + | 0.799188i | ||||
\(782\) | −1.31279 | + | 0.351760i | −0.0469452 | + | 0.0125789i | ||||
\(783\) | −4.34444 | + | 4.34444i | −0.155258 | + | 0.155258i | ||||
\(784\) | −2.14749 | − | 6.88259i | −0.0766961 | − | 0.245807i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.01582 | + | 10.4197i | −0.214577 | + | 0.371659i | ||||
\(787\) | −4.26300 | + | 15.9097i | −0.151959 | + | 0.567120i | 0.847387 | + | 0.530976i | \(0.178174\pi\) |
−0.999347 | + | 0.0361447i | \(0.988492\pi\) | |||||||
\(788\) | 3.97124 | − | 14.8209i | 0.141470 | − | 0.527971i | ||||
\(789\) | −3.97626 | + | 6.88709i | −0.141559 | + | 0.245187i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.88005 | + | 25.2946i | −0.351294 | + | 0.899373i | ||||
\(792\) | −7.57326 | + | 7.57326i | −0.269104 | + | 0.269104i | ||||
\(793\) | 38.0972 | − | 10.2081i | 1.35287 | − | 0.362501i | ||||
\(794\) | −2.28389 | − | 3.95581i | −0.0810522 | − | 0.140387i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.6576 | − | 6.15319i | −0.377750 | − | 0.218094i | ||||
\(797\) | 33.5483 | + | 33.5483i | 1.18834 | + | 1.18834i | 0.977525 | + | 0.210818i | \(0.0676127\pi\) |
0.210818 | + | 0.977525i | \(0.432387\pi\) | |||||||
\(798\) | −1.20849 | + | 10.8844i | −0.0427803 | + | 0.385305i | ||||
\(799\) | − | 2.81792i | − | 0.0996910i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.57257 | − | 5.52672i | 0.338230 | − | 0.195277i | ||||
\(802\) | −21.6598 | − | 5.80371i | −0.764832 | − | 0.204936i | ||||
\(803\) | −14.1999 | − | 52.9948i | −0.501104 | − | 1.87015i | ||||
\(804\) | 5.47061 | 0.192934 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.81021 | 0.275103 | ||||||||
\(807\) | 0.443946 | + | 1.65683i | 0.0156276 | + | 0.0583232i | ||||
\(808\) | −2.47748 | − | 0.663838i | −0.0871573 | − | 0.0233537i | ||||
\(809\) | 5.58195 | − | 3.22274i | 0.196251 | − | 0.113306i | −0.398655 | − | 0.917101i | \(-0.630523\pi\) |
0.594906 | + | 0.803796i | \(0.297189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.116404i | 0.00408751i | 0.999998 | + | 0.00204375i | \(0.000650547\pi\) | ||||
−0.999998 | + | 0.00204375i | \(0.999349\pi\) | |||||||
\(812\) | 9.55922 | − | 12.9964i | 0.335463 | − | 0.456084i | ||||
\(813\) | 8.21766 | + | 8.21766i | 0.288206 | + | 0.288206i | ||||
\(814\) | −0.490325 | − | 0.283089i | −0.0171859 | − | 0.00992227i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.270037 | − | 0.467718i | −0.00945319 | − | 0.0163734i | ||||
\(817\) | −50.7690 | + | 13.6035i | −1.77618 | + | 0.475927i | ||||
\(818\) | 4.32516 | − | 4.32516i | 0.151226 | − | 0.151226i | ||||
\(819\) | 6.50722 | + | 8.13268i | 0.227381 | + | 0.284179i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.698986 | − | 1.21068i | 0.0243948 | − | 0.0422530i | −0.853570 | − | 0.520978i | \(-0.825567\pi\) |
0.877965 | + | 0.478725i | \(0.158901\pi\) | |||||||
\(822\) | −1.64210 | + | 6.12841i | −0.0572749 | + | 0.213753i | ||||
\(823\) | 4.22216 | − | 15.7573i | 0.147175 | − | 0.549265i | −0.852474 | − | 0.522770i | \(-0.824899\pi\) |
0.999649 | − | 0.0264952i | \(-0.00843466\pi\) | |||||||
\(824\) | 9.11687 | − | 15.7909i | 0.317601 | − | 0.550101i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.43371 | − | 2.51300i | −0.223858 | − | 0.0874386i | ||||
\(827\) | 29.7712 | − | 29.7712i | 1.03524 | − | 1.03524i | 0.0358886 | − | 0.999356i | \(-0.488574\pi\) |
0.999356 | − | 0.0358886i | \(-0.0114262\pi\) | |||||||
\(828\) | 2.47554 | − | 0.663320i | 0.0860311 | − | 0.0230520i | ||||
\(829\) | −3.31772 | − | 5.74647i | −0.115229 | − | 0.199583i | 0.802642 | − | 0.596461i | \(-0.203427\pi\) |
−0.917871 | + | 0.396878i | \(0.870094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.92044 | − | 4.57287i | −0.274757 | − | 0.158631i | ||||
\(832\) | 19.6310 | + | 19.6310i | 0.680582 | + | 0.680582i | ||||
\(833\) | 1.96290 | + | 3.10154i | 0.0680104 | + | 0.107462i | ||||
\(834\) | 5.09775i | 0.176521i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.6384 | + | 7.29677i | −0.437108 | + | 0.252364i | ||||
\(837\) | 1.90918 | + | 0.511564i | 0.0659910 | + | 0.0176822i | ||||
\(838\) | 6.05768 | + | 22.6076i | 0.209259 | + | 0.780965i | ||||
\(839\) | 18.1682 | 0.627234 | 0.313617 | − | 0.949550i | \(-0.398459\pi\) | ||||
0.313617 | + | 0.949550i | \(0.398459\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.74827 | −0.301664 | ||||||||
\(842\) | 0.00309354 | + | 0.0115453i | 0.000106610 | + | 0.000397876i | ||||
\(843\) | −14.5511 | − | 3.89896i | −0.501167 | − | 0.134287i | ||||
\(844\) | −11.5362 | + | 6.66042i | −0.397092 | + | 0.229261i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 5.39421i | − | 0.185457i | ||||||
\(847\) | −4.50707 | − | 0.500418i | −0.154865 | − | 0.0171946i | ||||
\(848\) | 4.18618 | + | 4.18618i | 0.143754 | + | 0.143754i | ||||
\(849\) | 13.8681 | + | 8.00677i | 0.475953 | + | 0.274791i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.204248 | + | 0.353768i | 0.00700154 | + | 0.0121270i | ||||
\(852\) | 6.93384 | − | 1.85792i | 0.237549 | − | 0.0636512i | ||||
\(853\) | −34.0703 | + | 34.0703i | −1.16654 | + | 1.16654i | −0.183530 | + | 0.983014i | \(0.558752\pi\) |
−0.983014 | + | 0.183530i | \(0.941248\pi\) | |||||||
\(854\) | 26.3029 | − | 4.00820i | 0.900067 | − | 0.137158i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.5671 | − | 30.4271i | 0.600432 | − | 1.03998i | ||||
\(857\) | 9.53874 | − | 35.5991i | 0.325837 | − | 1.21604i | −0.587631 | − | 0.809129i | \(-0.699939\pi\) |
0.913468 | − | 0.406911i | \(-0.133394\pi\) | |||||||
\(858\) | 3.64666 | − | 13.6095i | 0.124495 | − | 0.464622i | ||||
\(859\) | −6.11471 | + | 10.5910i | −0.208631 | + | 0.361360i | −0.951284 | − | 0.308317i | \(-0.900234\pi\) |
0.742652 | + | 0.669677i | \(0.233567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6692 | − | 3.30209i | 0.738486 | − | 0.112535i | ||||
\(862\) | −13.4125 | + | 13.4125i | −0.456831 | + | 0.456831i | ||||
\(863\) | 40.1292 | − | 10.7526i | 1.36601 | − | 0.366022i | 0.499993 | − | 0.866030i | \(-0.333336\pi\) |
0.866021 | + | 0.500007i | \(0.166669\pi\) | |||||||
\(864\) | 2.48679 | + | 4.30724i | 0.0846022 | + | 0.146535i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.0765 | − | 13.3233i | −0.784173 | − | 0.452743i | ||||
\(867\) | −11.8264 | − | 11.8264i | −0.401645 | − | 0.401645i | ||||
\(868\) | −5.15845 | − | 0.572740i | −0.175089 | − | 0.0194401i | ||||
\(869\) | − | 53.9964i | − | 1.83170i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7920 | + | 10.8496i | −0.636744 | + | 0.367624i | ||||
\(872\) | 36.3715 | + | 9.74572i | 1.23169 | + | 0.330032i | ||||
\(873\) | 0.910774 | + | 3.39905i | 0.0308250 | + | 0.115041i | ||||
\(874\) | −10.6885 | −0.361545 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.2713 | −0.515969 | ||||||||
\(877\) | −0.648098 | − | 2.41873i | −0.0218847 | − | 0.0816748i | 0.954120 | − | 0.299425i | \(-0.0967949\pi\) |
−0.976005 | + | 0.217750i | \(0.930128\pi\) | |||||||
\(878\) | −6.61211 | − | 1.77171i | −0.223148 | − | 0.0597923i | ||||
\(879\) | 7.59927 | − | 4.38744i | 0.256317 | − | 0.147985i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.7030i | 1.64084i | 0.571758 | + | 0.820422i | \(0.306262\pi\) | ||||
−0.571758 | + | 0.820422i | \(0.693738\pi\) | |||||||
\(882\) | 3.75747 | + | 5.93711i | 0.126521 | + | 0.199913i | ||||
\(883\) | 5.87749 | + | 5.87749i | 0.197793 | + | 0.197793i | 0.799053 | − | 0.601260i | \(-0.205334\pi\) |
−0.601260 | + | 0.799053i | \(0.705334\pi\) | |||||||
\(884\) | −1.77426 | − | 1.02437i | −0.0596749 | − | 0.0344533i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.46265 | − | 5.99748i | −0.116330 | − | 0.201489i | ||||
\(887\) | −9.36397 | + | 2.50907i | −0.314411 | + | 0.0842463i | −0.412574 | − | 0.910924i | \(-0.635370\pi\) |
0.0981626 | + | 0.995170i | \(0.468703\pi\) | |||||||
\(888\) | −0.335993 | + | 0.335993i | −0.0112752 | + | 0.0112752i | ||||
\(889\) | 3.70300 | + | 1.44639i | 0.124195 | + | 0.0485104i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.78283 | − | 3.08796i | 0.0597272 | − | 0.103450i | ||||
\(892\) | −0.584533 | + | 2.18151i | −0.0195716 | + | 0.0730422i | ||||
\(893\) | 5.73578 | − | 21.4062i | 0.191941 | − | 0.716332i | ||||
\(894\) | −7.64903 | + | 13.2485i | −0.255822 | + | 0.443097i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.74159 | − | 5.92601i | −0.158406 | − | 0.197974i | ||||
\(897\) | −7.18819 | + | 7.18819i | −0.240007 | + | 0.240007i | ||||
\(898\) | 26.4350 | − | 7.08322i | 0.882146 | − | 0.236370i | ||||
\(899\) | 6.07187 | + | 10.5168i | 0.202508 | + | 0.350754i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.61013 | − | 1.50696i | −0.0869561 | − | 0.0502041i | ||||
\(902\) | −20.9667 | − | 20.9667i | −0.698114 | − | 0.698114i | ||||
\(903\) | −19.9806 | + | 27.1650i | −0.664914 | + | 0.903993i | ||||
\(904\) | − | 30.8297i | − | 1.02538i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.9782 | − | 7.49297i | 0.431172 | − | 0.248937i | ||||
\(907\) | 31.8869 | + | 8.54407i | 1.05879 | + | 0.283701i | 0.745878 | − | 0.666082i | \(-0.232030\pi\) |
0.312909 | + | 0.949783i | \(0.398697\pi\) | |||||||
\(908\) | 6.62252 | + | 24.7156i | 0.219776 | + | 0.820216i | ||||
\(909\) | 0.853903 | 0.0283222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1445 | 1.09813 | 0.549064 | − | 0.835781i | \(-0.314984\pi\) | ||||
0.549064 | + | 0.835781i | \(0.314984\pi\) | |||||||
\(912\) | −1.09930 | − | 4.10265i | −0.0364015 | − | 0.135852i | ||||
\(913\) | 45.9010 | + | 12.2991i | 1.51910 | + | 0.407042i | ||||
\(914\) | 15.0911 | − | 8.71284i | 0.499169 | − | 0.288195i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.32908i | 0.0439140i | ||||||||
\(917\) | −3.49968 | + | 31.5202i | −0.115570 | + | 1.04089i | ||||
\(918\) | 0.372165 | + | 0.372165i | 0.0122833 | + | 0.0122833i | ||||
\(919\) | −27.8600 | − | 16.0850i | −0.919015 | − | 0.530594i | −0.0356945 | − | 0.999363i | \(-0.511364\pi\) |
−0.883321 | + | 0.468769i | \(0.844698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.42930 | + | 7.67177i | 0.145950 | + | 0.252793i | ||||
\(922\) | 40.6053 | − | 10.8802i | 1.33727 | − | 0.358319i | ||||
\(923\) | −20.1336 | + | 20.1336i | −0.662707 | + | 0.662707i | ||||
\(924\) | −3.40655 | + | 8.72134i | −0.112067 | + | 0.286911i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.9767 | − | 19.0122i | 0.360716 | − | 0.624779i | ||||
\(927\) | −1.57114 | + | 5.86357i | −0.0516030 | + | 0.192585i | ||||
\(928\) | −7.90885 | + | 29.5162i | −0.259621 | + | 0.968918i | ||||
\(929\) | 20.2533 | − | 35.0798i | 0.664490 | − | 1.15093i | −0.314934 | − | 0.949114i | \(-0.601982\pi\) |
0.979423 | − | 0.201816i | \(-0.0646843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.59799 | + | 27.5561i | 0.281788 | + | 0.903115i | ||||
\(932\) | −15.0602 | + | 15.0602i | −0.493314 | + | 0.493314i | ||||
\(933\) | 6.45191 | − | 1.72878i | 0.211226 | − | 0.0565979i | ||||
\(934\) | −16.8406 | − | 29.1687i | −0.551040 | − | 0.954429i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.2405 | − | 5.91237i | −0.334722 | − | 0.193252i | ||||
\(937\) | −10.0291 | − | 10.0291i | −0.327637 | − | 0.327637i | 0.524050 | − | 0.851687i | \(-0.324420\pi\) |
−0.851687 | + | 0.524050i | \(0.824420\pi\) | |||||||
\(938\) | −13.4071 | + | 5.87540i | −0.437759 | + | 0.191838i | ||||
\(939\) | − | 1.85462i | − | 0.0605232i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.3581 | + | 18.6820i | −1.05485 | + | 0.609015i | −0.924002 | − | 0.382388i | \(-0.875102\pi\) |
−0.130843 | + | 0.991403i | \(0.541768\pi\) | |||||||
\(942\) | −6.39284 | − | 1.71296i | −0.208290 | − | 0.0558111i | ||||
\(943\) | 5.53701 | + | 20.6644i | 0.180310 | + | 0.672926i | ||||
\(944\) | 2.67885 | 0.0871893 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.6170 | 1.48314 | ||||||||
\(947\) | −0.500489 | − | 1.86785i | −0.0162637 | − | 0.0606970i | 0.957317 | − | 0.289040i | \(-0.0933360\pi\) |
−0.973581 | + | 0.228343i | \(0.926669\pi\) | |||||||
\(948\) | −14.5176 | − | 3.88998i | −0.471510 | − | 0.126341i | ||||
\(949\) | 52.4582 | − | 30.2868i | 1.70287 | − | 0.983150i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.72496i | − | 0.0559358i | ||||||
\(952\) | −3.35684 | − | 2.46905i | −0.108796 | − | 0.0800225i | ||||
\(953\) | −14.5970 | − | 14.5970i | −0.472845 | − | 0.472845i | 0.429989 | − | 0.902834i | \(-0.358517\pi\) |
−0.902834 | + | 0.429989i | \(0.858517\pi\) | |||||||
\(954\) | −4.99644 | − | 2.88470i | −0.161766 | − | 0.0933955i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.37346 | + | 11.0392i | 0.206132 | + | 0.357032i | ||||
\(957\) | 21.1608 | − | 5.67003i | 0.684033 | − | 0.183286i | ||||
\(958\) | 11.6285 | − | 11.6285i | 0.375700 | − | 0.375700i | ||||
\(959\) | 2.51935 | + | 16.5327i | 0.0813541 | + | 0.533869i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5467 | + | 23.4635i | −0.436989 | + | 0.756887i | ||||
\(962\) | 0.161787 | − | 0.603797i | 0.00521622 | − | 0.0194672i | ||||
\(963\) | −3.02740 | + | 11.2984i | −0.0975565 | + | 0.364086i | ||||
\(964\) | −12.6502 | + | 21.9108i | −0.407436 | + | 0.705700i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.35456 | + | 4.28435i | −0.172280 | + | 0.137847i | ||||
\(967\) | −34.5723 | + | 34.5723i | −1.11177 | + | 1.11177i | −0.118858 | + | 0.992911i | \(0.537923\pi\) |
−0.992911 | + | 0.118858i | \(0.962077\pi\) | |||||||
\(968\) | 4.97287 | − | 1.33248i | 0.159834 | − | 0.0428274i | ||||
\(969\) | 1.08116 | + | 1.87262i | 0.0347318 | + | 0.0601573i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.45937 | − | 1.41992i | −0.0789251 | − | 0.0455674i | 0.460018 | − | 0.887910i | \(-0.347843\pi\) |
−0.538943 | + | 0.842342i | \(0.681176\pi\) | |||||||
\(972\) | −0.701798 | − | 0.701798i | −0.0225102 | − | 0.0225102i | ||||
\(973\) | 5.39334 | + | 12.3071i | 0.172903 | + | 0.394549i | ||||
\(974\) | 4.38930i | 0.140642i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.93662 | + | 5.15956i | −0.286054 | + | 0.165154i | ||||
\(977\) | −36.0763 | − | 9.66661i | −1.15418 | − | 0.309262i | −0.369543 | − | 0.929214i | \(-0.620486\pi\) |
−0.784640 | + | 0.619951i | \(0.787152\pi\) | |||||||
\(978\) | 0.363191 | + | 1.35545i | 0.0116136 | + | 0.0433424i | ||||
\(979\) | −39.4129 | −1.25964 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5360 | −0.400245 | ||||||||
\(982\) | −8.79732 | − | 32.8320i | −0.280734 | − | 1.04771i | ||||
\(983\) | −30.9698 | − | 8.29834i | −0.987784 | − | 0.264676i | −0.271465 | − | 0.962448i | \(-0.587508\pi\) |
−0.716320 | + | 0.697772i | \(0.754175\pi\) | |||||||
\(984\) | −21.5510 | + | 12.4425i | −0.687021 | + | 0.396651i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.23369i | 0.102982i | ||||||||
\(987\) | −5.70699 | − | 13.0228i | −0.181655 | − | 0.414522i | ||||
\(988\) | −11.3930 | − | 11.3930i | −0.362461 | − | 0.362461i | ||||
\(989\) | −28.5031 | − | 16.4563i | −0.906346 | − | 0.523279i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.9999 | − | 36.3729i | −0.667084 | − | 1.15542i | −0.978716 | − | 0.205221i | \(-0.934209\pi\) |
0.311632 | − | 0.950203i | \(-0.399125\pi\) | |||||||
\(992\) | 9.49546 | − | 2.54430i | 0.301481 | − | 0.0807817i | ||||
\(993\) | 18.3973 | − | 18.3973i | 0.583821 | − | 0.583821i | ||||
\(994\) | −14.9978 | + | 12.0002i | −0.475700 | + | 0.380623i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.61355 | − | 11.4550i | 0.209558 | − | 0.362966i | ||||
\(997\) | −5.68114 | + | 21.2023i | −0.179924 | + | 0.671484i | 0.815737 | + | 0.578423i | \(0.196332\pi\) |
−0.995660 | + | 0.0930609i | \(0.970335\pi\) | |||||||
\(998\) | −4.57137 | + | 17.0606i | −0.144704 | + | 0.540044i | ||||
\(999\) | 0.0790967 | − | 0.136999i | 0.00250251 | − | 0.00433447i |
(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 | 525.2.bc.e.418.3 | 32 | ||
5.2 | odd | 4 | inner | 525.2.bc.e.82.6 | 32 | ||
5.3 | odd | 4 | 105.2.u.a.82.3 | yes | 32 | ||
5.4 | even | 2 | 105.2.u.a.103.6 | yes | 32 | ||
7.3 | odd | 6 | inner | 525.2.bc.e.493.6 | 32 | ||
15.8 | even | 4 | 315.2.bz.d.82.6 | 32 | |||
15.14 | odd | 2 | 315.2.bz.d.208.3 | 32 | |||
35.3 | even | 12 | 105.2.u.a.52.6 | ✓ | 32 | ||
35.4 | even | 6 | 735.2.v.b.178.3 | 32 | |||
35.9 | even | 6 | 735.2.m.c.538.11 | 32 | |||
35.13 | even | 4 | 735.2.v.b.607.3 | 32 | |||
35.17 | even | 12 | inner | 525.2.bc.e.157.3 | 32 | ||
35.18 | odd | 12 | 735.2.v.b.472.6 | 32 | |||
35.19 | odd | 6 | 735.2.m.c.538.12 | 32 | |||
35.23 | odd | 12 | 735.2.m.c.97.12 | 32 | |||
35.24 | odd | 6 | 105.2.u.a.73.3 | yes | 32 | ||
35.33 | even | 12 | 735.2.m.c.97.11 | 32 | |||
35.34 | odd | 2 | 735.2.v.b.313.6 | 32 | |||
105.38 | odd | 12 | 315.2.bz.d.262.3 | 32 | |||
105.59 | even | 6 | 315.2.bz.d.73.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.u.a.52.6 | ✓ | 32 | 35.3 | even | 12 | ||
105.2.u.a.73.3 | yes | 32 | 35.24 | odd | 6 | ||
105.2.u.a.82.3 | yes | 32 | 5.3 | odd | 4 | ||
105.2.u.a.103.6 | yes | 32 | 5.4 | even | 2 | ||
315.2.bz.d.73.6 | 32 | 105.59 | even | 6 | |||
315.2.bz.d.82.6 | 32 | 15.8 | even | 4 | |||
315.2.bz.d.208.3 | 32 | 15.14 | odd | 2 | |||
315.2.bz.d.262.3 | 32 | 105.38 | odd | 12 | |||
525.2.bc.e.82.6 | 32 | 5.2 | odd | 4 | inner | ||
525.2.bc.e.157.3 | 32 | 35.17 | even | 12 | inner | ||
525.2.bc.e.418.3 | 32 | 1.1 | even | 1 | trivial | ||
525.2.bc.e.493.6 | 32 | 7.3 | odd | 6 | inner | ||
735.2.m.c.97.11 | 32 | 35.33 | even | 12 | |||
735.2.m.c.97.12 | 32 | 35.23 | odd | 12 | |||
735.2.m.c.538.11 | 32 | 35.9 | even | 6 | |||
735.2.m.c.538.12 | 32 | 35.19 | odd | 6 | |||
735.2.v.b.178.3 | 32 | 35.4 | even | 6 | |||
735.2.v.b.313.6 | 32 | 35.34 | odd | 2 | |||
735.2.v.b.472.6 | 32 | 35.18 | odd | 12 | |||
735.2.v.b.607.3 | 32 | 35.13 | even | 4 |