Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,3,Mod(577,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.577");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.f (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: | \(27.6294988061\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 775.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.775 |
Dual form | 1014.3.f.a.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.73205 | − | 4.73205i | −0.946410 | − | 0.946410i | 0.0522252 | − | 0.998635i | \(-0.483369\pi\) |
−0.998635 | + | 0.0522252i | \(0.983369\pi\) | |||||||
\(6\) | 1.73205 | + | 1.73205i | 0.288675 | + | 0.288675i | ||||
\(7\) | 2.73205 | − | 2.73205i | 0.390293 | − | 0.390293i | −0.484499 | − | 0.874792i | \(-0.660998\pi\) |
0.874792 | + | 0.484499i | \(0.160998\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 9.46410i | 0.946410i | ||||||||
\(11\) | −1.73205 | + | 1.73205i | −0.157459 | + | 0.157459i | −0.781440 | − | 0.623981i | \(-0.785514\pi\) |
0.623981 | + | 0.781440i | \(0.285514\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.46410 | −0.390293 | ||||||||
\(15\) | 8.19615 | + | 8.19615i | 0.546410 | + | 0.546410i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | − | 29.3205i | − | 1.72474i | −0.506282 | − | 0.862368i | \(-0.668981\pi\) | ||
0.506282 | − | 0.862368i | \(-0.331019\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | 11.2679 | + | 11.2679i | 0.593050 | + | 0.593050i | 0.938454 | − | 0.345404i | \(-0.112258\pi\) |
−0.345404 | + | 0.938454i | \(0.612258\pi\) | |||||||
\(20\) | 9.46410 | − | 9.46410i | 0.473205 | − | 0.473205i | ||||
\(21\) | −4.73205 | + | 4.73205i | −0.225336 | + | 0.225336i | ||||
\(22\) | 3.46410 | 0.157459 | ||||||||
\(23\) | − | 29.3205i | − | 1.27480i | −0.770531 | − | 0.637402i | \(-0.780009\pi\) | ||
0.770531 | − | 0.637402i | \(-0.219991\pi\) | |||||||
\(24\) | −3.46410 | + | 3.46410i | −0.144338 | + | 0.144338i | ||||
\(25\) | 19.7846i | 0.791384i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 5.46410 | + | 5.46410i | 0.195146 | + | 0.195146i | ||||
\(29\) | 31.8564 | 1.09850 | 0.549248 | − | 0.835659i | \(-0.314914\pi\) | ||||
0.549248 | + | 0.835659i | \(0.314914\pi\) | |||||||
\(30\) | − | 16.3923i | − | 0.546410i | ||||||
\(31\) | −26.9808 | − | 26.9808i | −0.870347 | − | 0.870347i | 0.122163 | − | 0.992510i | \(-0.461017\pi\) |
−0.992510 | + | 0.122163i | \(0.961017\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 3.00000 | − | 3.00000i | 0.0909091 | − | 0.0909091i | ||||
\(34\) | −29.3205 | + | 29.3205i | −0.862368 | + | 0.862368i | ||||
\(35\) | −25.8564 | −0.738754 | ||||||||
\(36\) | 6.00000i | 0.166667i | ||||||||
\(37\) | 30.8564 | − | 30.8564i | 0.833957 | − | 0.833957i | −0.154099 | − | 0.988055i | \(-0.549247\pi\) |
0.988055 | + | 0.154099i | \(0.0492473\pi\) | |||||||
\(38\) | − | 22.5359i | − | 0.593050i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −18.9282 | −0.473205 | ||||||||
\(41\) | 14.4449 | + | 14.4449i | 0.352314 | + | 0.352314i | 0.860970 | − | 0.508656i | \(-0.169858\pi\) |
−0.508656 | + | 0.860970i | \(0.669858\pi\) | |||||||
\(42\) | 9.46410 | 0.225336 | ||||||||
\(43\) | − | 25.1769i | − | 0.585510i | −0.956188 | − | 0.292755i | \(-0.905428\pi\) | ||
0.956188 | − | 0.292755i | \(-0.0945720\pi\) | |||||||
\(44\) | −3.46410 | − | 3.46410i | −0.0787296 | − | 0.0787296i | ||||
\(45\) | −14.1962 | − | 14.1962i | −0.315470 | − | 0.315470i | ||||
\(46\) | −29.3205 | + | 29.3205i | −0.637402 | + | 0.637402i | ||||
\(47\) | 41.1962 | − | 41.1962i | 0.876514 | − | 0.876514i | −0.116658 | − | 0.993172i | \(-0.537218\pi\) |
0.993172 | + | 0.116658i | \(0.0372182\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 34.0718i | 0.695343i | ||||||||
\(50\) | 19.7846 | − | 19.7846i | 0.395692 | − | 0.395692i | ||||
\(51\) | 50.7846i | 0.995777i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.28719 | 0.0431545 | 0.0215772 | − | 0.999767i | \(-0.493131\pi\) | ||||
0.0215772 | + | 0.999767i | \(0.493131\pi\) | |||||||
\(54\) | 5.19615 | + | 5.19615i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 16.3923 | 0.298042 | ||||||||
\(56\) | − | 10.9282i | − | 0.195146i | ||||||
\(57\) | −19.5167 | − | 19.5167i | −0.342398 | − | 0.342398i | ||||
\(58\) | −31.8564 | − | 31.8564i | −0.549248 | − | 0.549248i | ||||
\(59\) | −54.6218 | + | 54.6218i | −0.925793 | + | 0.925793i | −0.997431 | − | 0.0716379i | \(-0.977177\pi\) |
0.0716379 | + | 0.997431i | \(0.477177\pi\) | |||||||
\(60\) | −16.3923 | + | 16.3923i | −0.273205 | + | 0.273205i | ||||
\(61\) | −7.42563 | −0.121732 | −0.0608658 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608658 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(62\) | 53.9615i | 0.870347i | ||||||||
\(63\) | 8.19615 | − | 8.19615i | 0.130098 | − | 0.130098i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | −0.0909091 | ||||||||
\(67\) | 60.6936 | + | 60.6936i | 0.905874 | + | 0.905874i | 0.995936 | − | 0.0900619i | \(-0.0287065\pi\) |
−0.0900619 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(68\) | 58.6410 | 0.862368 | ||||||||
\(69\) | 50.7846i | 0.736009i | ||||||||
\(70\) | 25.8564 | + | 25.8564i | 0.369377 | + | 0.369377i | ||||
\(71\) | −38.9090 | − | 38.9090i | −0.548014 | − | 0.548014i | 0.377852 | − | 0.925866i | \(-0.376663\pi\) |
−0.925866 | + | 0.377852i | \(0.876663\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −40.3205 | + | 40.3205i | −0.552336 | + | 0.552336i | −0.927114 | − | 0.374779i | \(-0.877719\pi\) |
0.374779 | + | 0.927114i | \(0.377719\pi\) | |||||||
\(74\) | −61.7128 | −0.833957 | ||||||||
\(75\) | − | 34.2679i | − | 0.456906i | ||||||
\(76\) | −22.5359 | + | 22.5359i | −0.296525 | + | 0.296525i | ||||
\(77\) | 9.46410i | 0.122910i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −148.210 | −1.87608 | −0.938039 | − | 0.346528i | \(-0.887360\pi\) | ||||
−0.938039 | + | 0.346528i | \(0.887360\pi\) | |||||||
\(80\) | 18.9282 | + | 18.9282i | 0.236603 | + | 0.236603i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 28.8897i | − | 0.352314i | ||||||
\(83\) | −73.7987 | − | 73.7987i | −0.889141 | − | 0.889141i | 0.105300 | − | 0.994441i | \(-0.466420\pi\) |
−0.994441 | + | 0.105300i | \(0.966420\pi\) | |||||||
\(84\) | −9.46410 | − | 9.46410i | −0.112668 | − | 0.112668i | ||||
\(85\) | −138.746 | + | 138.746i | −1.63231 | + | 1.63231i | ||||
\(86\) | −25.1769 | + | 25.1769i | −0.292755 | + | 0.292755i | ||||
\(87\) | −55.1769 | −0.634217 | ||||||||
\(88\) | 6.92820i | 0.0787296i | ||||||||
\(89\) | −25.5167 | + | 25.5167i | −0.286704 | + | 0.286704i | −0.835775 | − | 0.549071i | \(-0.814981\pi\) |
0.549071 | + | 0.835775i | \(0.314981\pi\) | |||||||
\(90\) | 28.3923i | 0.315470i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 58.6410 | 0.637402 | ||||||||
\(93\) | 46.7321 | + | 46.7321i | 0.502495 | + | 0.502495i | ||||
\(94\) | −82.3923 | −0.876514 | ||||||||
\(95\) | − | 106.641i | − | 1.12254i | ||||||
\(96\) | −6.92820 | − | 6.92820i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 86.0333 | + | 86.0333i | 0.886941 | + | 0.886941i | 0.994228 | − | 0.107287i | \(-0.0342163\pi\) |
−0.107287 | + | 0.994228i | \(0.534216\pi\) | |||||||
\(98\) | 34.0718 | − | 34.0718i | 0.347671 | − | 0.347671i | ||||
\(99\) | −5.19615 | + | 5.19615i | −0.0524864 | + | 0.0524864i | ||||
\(100\) | −39.5692 | −0.395692 | ||||||||
\(101\) | − | 104.536i | − | 1.03501i | −0.855681 | − | 0.517504i | \(-0.826861\pi\) | ||
0.855681 | − | 0.517504i | \(-0.173139\pi\) | |||||||
\(102\) | 50.7846 | − | 50.7846i | 0.497888 | − | 0.497888i | ||||
\(103\) | − | 36.6795i | − | 0.356112i | −0.984020 | − | 0.178056i | \(-0.943019\pi\) | ||
0.984020 | − | 0.178056i | \(-0.0569808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 44.7846 | 0.426520 | ||||||||
\(106\) | −2.28719 | − | 2.28719i | −0.0215772 | − | 0.0215772i | ||||
\(107\) | −123.464 | −1.15387 | −0.576935 | − | 0.816790i | \(-0.695751\pi\) | ||||
−0.576935 | + | 0.816790i | \(0.695751\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | −119.315 | − | 119.315i | −1.09464 | − | 1.09464i | −0.995027 | − | 0.0996097i | \(-0.968241\pi\) |
−0.0996097 | − | 0.995027i | \(-0.531759\pi\) | |||||||
\(110\) | −16.3923 | − | 16.3923i | −0.149021 | − | 0.149021i | ||||
\(111\) | −53.4449 | + | 53.4449i | −0.481485 | + | 0.481485i | ||||
\(112\) | −10.9282 | + | 10.9282i | −0.0975732 | + | 0.0975732i | ||||
\(113\) | −184.277 | −1.63077 | −0.815384 | − | 0.578920i | \(-0.803474\pi\) | ||||
−0.815384 | + | 0.578920i | \(0.803474\pi\) | |||||||
\(114\) | 39.0333i | 0.342398i | ||||||||
\(115\) | −138.746 | + | 138.746i | −1.20649 | + | 1.20649i | ||||
\(116\) | 63.7128i | 0.549248i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 109.244 | 0.925793 | ||||||||
\(119\) | −80.1051 | − | 80.1051i | −0.673152 | − | 0.673152i | ||||
\(120\) | 32.7846 | 0.273205 | ||||||||
\(121\) | 115.000i | 0.950413i | ||||||||
\(122\) | 7.42563 | + | 7.42563i | 0.0608658 | + | 0.0608658i | ||||
\(123\) | −25.0192 | − | 25.0192i | −0.203408 | − | 0.203408i | ||||
\(124\) | 53.9615 | − | 53.9615i | 0.435174 | − | 0.435174i | ||||
\(125\) | −24.6795 | + | 24.6795i | −0.197436 | + | 0.197436i | ||||
\(126\) | −16.3923 | −0.130098 | ||||||||
\(127\) | 173.962i | 1.36978i | 0.728648 | + | 0.684888i | \(0.240149\pi\) | ||||
−0.728648 | + | 0.684888i | \(0.759851\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 43.6077i | 0.338044i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 121.110 | 0.924506 | 0.462253 | − | 0.886748i | \(-0.347041\pi\) | ||||
0.462253 | + | 0.886748i | \(0.347041\pi\) | |||||||
\(132\) | 6.00000 | + | 6.00000i | 0.0454545 | + | 0.0454545i | ||||
\(133\) | 61.5692 | 0.462926 | ||||||||
\(134\) | − | 121.387i | − | 0.905874i | ||||||
\(135\) | 24.5885 | + | 24.5885i | 0.182137 | + | 0.182137i | ||||
\(136\) | −58.6410 | − | 58.6410i | −0.431184 | − | 0.431184i | ||||
\(137\) | 130.053 | − | 130.053i | 0.949289 | − | 0.949289i | −0.0494861 | − | 0.998775i | \(-0.515758\pi\) |
0.998775 | + | 0.0494861i | \(0.0157583\pi\) | |||||||
\(138\) | 50.7846 | − | 50.7846i | 0.368004 | − | 0.368004i | ||||
\(139\) | −27.1384 | −0.195241 | −0.0976203 | − | 0.995224i | \(-0.531123\pi\) | ||||
−0.0976203 | + | 0.995224i | \(0.531123\pi\) | |||||||
\(140\) | − | 51.7128i | − | 0.369377i | ||||||
\(141\) | −71.3538 | + | 71.3538i | −0.506056 | + | 0.506056i | ||||
\(142\) | 77.8179i | 0.548014i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −150.746 | − | 150.746i | −1.03963 | − | 1.03963i | ||||
\(146\) | 80.6410 | 0.552336 | ||||||||
\(147\) | − | 59.0141i | − | 0.401456i | ||||||
\(148\) | 61.7128 | + | 61.7128i | 0.416978 | + | 0.416978i | ||||
\(149\) | 168.224 | + | 168.224i | 1.12902 | + | 1.12902i | 0.990336 | + | 0.138686i | \(0.0442878\pi\) |
0.138686 | + | 0.990336i | \(0.455712\pi\) | |||||||
\(150\) | −34.2679 | + | 34.2679i | −0.228453 | + | 0.228453i | ||||
\(151\) | 38.4064 | − | 38.4064i | 0.254347 | − | 0.254347i | −0.568403 | − | 0.822750i | \(-0.692439\pi\) |
0.822750 | + | 0.568403i | \(0.192439\pi\) | |||||||
\(152\) | 45.0718 | 0.296525 | ||||||||
\(153\) | − | 87.9615i | − | 0.574912i | ||||||
\(154\) | 9.46410 | − | 9.46410i | 0.0614552 | − | 0.0614552i | ||||
\(155\) | 255.349i | 1.64741i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −227.215 | −1.44723 | −0.723616 | − | 0.690203i | \(-0.757521\pi\) | ||||
−0.723616 | + | 0.690203i | \(0.757521\pi\) | |||||||
\(158\) | 148.210 | + | 148.210i | 0.938039 | + | 0.938039i | ||||
\(159\) | −3.96152 | −0.0249152 | ||||||||
\(160\) | − | 37.8564i | − | 0.236603i | ||||||
\(161\) | −80.1051 | − | 80.1051i | −0.497547 | − | 0.497547i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −12.4449 | + | 12.4449i | −0.0763489 | + | 0.0763489i | −0.744250 | − | 0.667901i | \(-0.767193\pi\) |
0.667901 | + | 0.744250i | \(0.267193\pi\) | |||||||
\(164\) | −28.8897 | + | 28.8897i | −0.176157 | + | 0.176157i | ||||
\(165\) | −28.3923 | −0.172075 | ||||||||
\(166\) | 147.597i | 0.889141i | ||||||||
\(167\) | −119.512 | + | 119.512i | −0.715638 | + | 0.715638i | −0.967709 | − | 0.252071i | \(-0.918888\pi\) |
0.252071 | + | 0.967709i | \(0.418888\pi\) | |||||||
\(168\) | 18.9282i | 0.112668i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 277.492 | 1.63231 | ||||||||
\(171\) | 33.8038 | + | 33.8038i | 0.197683 | + | 0.197683i | ||||
\(172\) | 50.3538 | 0.292755 | ||||||||
\(173\) | − | 69.3975i | − | 0.401141i | −0.979679 | − | 0.200571i | \(-0.935720\pi\) | ||
0.979679 | − | 0.200571i | \(-0.0642796\pi\) | |||||||
\(174\) | 55.1769 | + | 55.1769i | 0.317109 | + | 0.317109i | ||||
\(175\) | 54.0526 | + | 54.0526i | 0.308872 | + | 0.308872i | ||||
\(176\) | 6.92820 | − | 6.92820i | 0.0393648 | − | 0.0393648i | ||||
\(177\) | 94.6077 | − | 94.6077i | 0.534507 | − | 0.534507i | ||||
\(178\) | 51.0333 | 0.286704 | ||||||||
\(179\) | 165.282i | 0.923363i | 0.887046 | + | 0.461682i | \(0.152754\pi\) | ||||
−0.887046 | + | 0.461682i | \(0.847246\pi\) | |||||||
\(180\) | 28.3923 | − | 28.3923i | 0.157735 | − | 0.157735i | ||||
\(181\) | − | 283.856i | − | 1.56827i | −0.620592 | − | 0.784134i | \(-0.713108\pi\) | ||
0.620592 | − | 0.784134i | \(-0.286892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8616 | 0.0702818 | ||||||||
\(184\) | −58.6410 | − | 58.6410i | −0.318701 | − | 0.318701i | ||||
\(185\) | −292.028 | −1.57853 | ||||||||
\(186\) | − | 93.4641i | − | 0.502495i | ||||||
\(187\) | 50.7846 | + | 50.7846i | 0.271575 | + | 0.271575i | ||||
\(188\) | 82.3923 | + | 82.3923i | 0.438257 | + | 0.438257i | ||||
\(189\) | −14.1962 | + | 14.1962i | −0.0751119 | + | 0.0751119i | ||||
\(190\) | −106.641 | + | 106.641i | −0.561269 | + | 0.561269i | ||||
\(191\) | 9.28203 | 0.0485970 | 0.0242985 | − | 0.999705i | \(-0.492265\pi\) | ||||
0.0242985 | + | 0.999705i | \(0.492265\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | 21.7180 | − | 21.7180i | 0.112528 | − | 0.112528i | −0.648601 | − | 0.761129i | \(-0.724645\pi\) |
0.761129 | + | 0.648601i | \(0.224645\pi\) | |||||||
\(194\) | − | 172.067i | − | 0.886941i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −68.1436 | −0.347671 | ||||||||
\(197\) | 112.732 | + | 112.732i | 0.572244 | + | 0.572244i | 0.932755 | − | 0.360511i | \(-0.117398\pi\) |
−0.360511 | + | 0.932755i | \(0.617398\pi\) | |||||||
\(198\) | 10.3923 | 0.0524864 | ||||||||
\(199\) | 245.100i | 1.23166i | 0.787880 | + | 0.615829i | \(0.211179\pi\) | ||||
−0.787880 | + | 0.615829i | \(0.788821\pi\) | |||||||
\(200\) | 39.5692 | + | 39.5692i | 0.197846 | + | 0.197846i | ||||
\(201\) | −105.124 | − | 105.124i | −0.523007 | − | 0.523007i | ||||
\(202\) | −104.536 | + | 104.536i | −0.517504 | + | 0.517504i | ||||
\(203\) | 87.0333 | − | 87.0333i | 0.428736 | − | 0.428736i | ||||
\(204\) | −101.569 | −0.497888 | ||||||||
\(205\) | − | 136.708i | − | 0.666867i | ||||||
\(206\) | −36.6795 | + | 36.6795i | −0.178056 | + | 0.178056i | ||||
\(207\) | − | 87.9615i | − | 0.424935i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −39.0333 | −0.186762 | ||||||||
\(210\) | −44.7846 | − | 44.7846i | −0.213260 | − | 0.213260i | ||||
\(211\) | 345.282 | 1.63641 | 0.818204 | − | 0.574928i | \(-0.194970\pi\) | ||||
0.818204 | + | 0.574928i | \(0.194970\pi\) | |||||||
\(212\) | 4.57437i | 0.0215772i | ||||||||
\(213\) | 67.3923 | + | 67.3923i | 0.316396 | + | 0.316396i | ||||
\(214\) | 123.464 | + | 123.464i | 0.576935 | + | 0.576935i | ||||
\(215\) | −119.138 | + | 119.138i | −0.554132 | + | 0.554132i | ||||
\(216\) | −10.3923 | + | 10.3923i | −0.0481125 | + | 0.0481125i | ||||
\(217\) | −147.426 | −0.679381 | ||||||||
\(218\) | 238.631i | 1.09464i | ||||||||
\(219\) | 69.8372 | − | 69.8372i | 0.318891 | − | 0.318891i | ||||
\(220\) | 32.7846i | 0.149021i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 106.890 | 0.481485 | ||||||||
\(223\) | −170.588 | − | 170.588i | −0.764971 | − | 0.764971i | 0.212246 | − | 0.977216i | \(-0.431922\pi\) |
−0.977216 | + | 0.212246i | \(0.931922\pi\) | |||||||
\(224\) | 21.8564 | 0.0975732 | ||||||||
\(225\) | 59.3538i | 0.263795i | ||||||||
\(226\) | 184.277 | + | 184.277i | 0.815384 | + | 0.815384i | ||||
\(227\) | −169.368 | − | 169.368i | −0.746114 | − | 0.746114i | 0.227633 | − | 0.973747i | \(-0.426901\pi\) |
−0.973747 | + | 0.227633i | \(0.926901\pi\) | |||||||
\(228\) | 39.0333 | − | 39.0333i | 0.171199 | − | 0.171199i | ||||
\(229\) | −141.823 | + | 141.823i | −0.619315 | + | 0.619315i | −0.945356 | − | 0.326041i | \(-0.894285\pi\) |
0.326041 | + | 0.945356i | \(0.394285\pi\) | |||||||
\(230\) | 277.492 | 1.20649 | ||||||||
\(231\) | − | 16.3923i | − | 0.0709624i | ||||||
\(232\) | 63.7128 | − | 63.7128i | 0.274624 | − | 0.274624i | ||||
\(233\) | 128.038i | 0.549521i | 0.961513 | + | 0.274761i | \(0.0885986\pi\) | ||||
−0.961513 | + | 0.274761i | \(0.911401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −389.885 | −1.65908 | ||||||||
\(236\) | −109.244 | − | 109.244i | −0.462896 | − | 0.462896i | ||||
\(237\) | 256.708 | 1.08315 | ||||||||
\(238\) | 160.210i | 0.673152i | ||||||||
\(239\) | −88.0192 | − | 88.0192i | −0.368281 | − | 0.368281i | 0.498569 | − | 0.866850i | \(-0.333859\pi\) |
−0.866850 | + | 0.498569i | \(0.833859\pi\) | |||||||
\(240\) | −32.7846 | − | 32.7846i | −0.136603 | − | 0.136603i | ||||
\(241\) | 147.459 | − | 147.459i | 0.611863 | − | 0.611863i | −0.331568 | − | 0.943431i | \(-0.607578\pi\) |
0.943431 | + | 0.331568i | \(0.107578\pi\) | |||||||
\(242\) | 115.000 | − | 115.000i | 0.475207 | − | 0.475207i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 14.8513i | − | 0.0608658i | ||||||
\(245\) | 161.229 | − | 161.229i | 0.658079 | − | 0.658079i | ||||
\(246\) | 50.0385i | 0.203408i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −107.923 | −0.435174 | ||||||||
\(249\) | 127.823 | + | 127.823i | 0.513346 | + | 0.513346i | ||||
\(250\) | 49.3590 | 0.197436 | ||||||||
\(251\) | 181.377i | 0.722617i | 0.932446 | + | 0.361308i | \(0.117670\pi\) | ||||
−0.932446 | + | 0.361308i | \(0.882330\pi\) | |||||||
\(252\) | 16.3923 | + | 16.3923i | 0.0650488 | + | 0.0650488i | ||||
\(253\) | 50.7846 | + | 50.7846i | 0.200730 | + | 0.200730i | ||||
\(254\) | 173.962 | − | 173.962i | 0.684888 | − | 0.684888i | ||||
\(255\) | 240.315 | − | 240.315i | 0.942413 | − | 0.942413i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 297.664i | − | 1.15823i | −0.815247 | − | 0.579113i | \(-0.803399\pi\) | ||
0.815247 | − | 0.579113i | \(-0.196601\pi\) | |||||||
\(258\) | 43.6077 | − | 43.6077i | 0.169022 | − | 0.169022i | ||||
\(259\) | − | 168.603i | − | 0.650975i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 95.5692 | 0.366166 | ||||||||
\(262\) | −121.110 | − | 121.110i | −0.462253 | − | 0.462253i | ||||
\(263\) | 22.8897 | 0.0870332 | 0.0435166 | − | 0.999053i | \(-0.486144\pi\) | ||||
0.0435166 | + | 0.999053i | \(0.486144\pi\) | |||||||
\(264\) | − | 12.0000i | − | 0.0454545i | ||||||
\(265\) | −10.8231 | − | 10.8231i | −0.0408418 | − | 0.0408418i | ||||
\(266\) | −61.5692 | − | 61.5692i | −0.231463 | − | 0.231463i | ||||
\(267\) | 44.1962 | − | 44.1962i | 0.165529 | − | 0.165529i | ||||
\(268\) | −121.387 | + | 121.387i | −0.452937 | + | 0.452937i | ||||
\(269\) | 220.774 | 0.820722 | 0.410361 | − | 0.911923i | \(-0.365403\pi\) | ||||
0.410361 | + | 0.911923i | \(0.365403\pi\) | |||||||
\(270\) | − | 49.1769i | − | 0.182137i | ||||||
\(271\) | −148.953 | + | 148.953i | −0.549641 | + | 0.549641i | −0.926337 | − | 0.376696i | \(-0.877060\pi\) |
0.376696 | + | 0.926337i | \(0.377060\pi\) | |||||||
\(272\) | 117.282i | 0.431184i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −260.105 | −0.949289 | ||||||||
\(275\) | −34.2679 | − | 34.2679i | −0.124611 | − | 0.124611i | ||||
\(276\) | −101.569 | −0.368004 | ||||||||
\(277\) | 27.2154i | 0.0982505i | 0.998793 | + | 0.0491253i | \(0.0156434\pi\) | ||||
−0.998793 | + | 0.0491253i | \(0.984357\pi\) | |||||||
\(278\) | 27.1384 | + | 27.1384i | 0.0976203 | + | 0.0976203i | ||||
\(279\) | −80.9423 | − | 80.9423i | −0.290116 | − | 0.290116i | ||||
\(280\) | −51.7128 | + | 51.7128i | −0.184689 | + | 0.184689i | ||||
\(281\) | 51.6218 | − | 51.6218i | 0.183707 | − | 0.183707i | −0.609262 | − | 0.792969i | \(-0.708534\pi\) |
0.792969 | + | 0.609262i | \(0.208534\pi\) | |||||||
\(282\) | 142.708 | 0.506056 | ||||||||
\(283\) | − | 93.8076i | − | 0.331476i | −0.986170 | − | 0.165738i | \(-0.946999\pi\) | ||
0.986170 | − | 0.165738i | \(-0.0530006\pi\) | |||||||
\(284\) | 77.8179 | − | 77.8179i | 0.274007 | − | 0.274007i | ||||
\(285\) | 184.708i | 0.648097i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 78.9282 | 0.275011 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | −570.692 | −1.97471 | ||||||||
\(290\) | 301.492i | 1.03963i | ||||||||
\(291\) | −149.014 | − | 149.014i | −0.512076 | − | 0.512076i | ||||
\(292\) | −80.6410 | − | 80.6410i | −0.276168 | − | 0.276168i | ||||
\(293\) | 120.042 | − | 120.042i | 0.409701 | − | 0.409701i | −0.471934 | − | 0.881634i | \(-0.656444\pi\) |
0.881634 | + | 0.471934i | \(0.156444\pi\) | |||||||
\(294\) | −59.0141 | + | 59.0141i | −0.200728 | + | 0.200728i | ||||
\(295\) | 516.946 | 1.75236 | ||||||||
\(296\) | − | 123.426i | − | 0.416978i | ||||||
\(297\) | 9.00000 | − | 9.00000i | 0.0303030 | − | 0.0303030i | ||||
\(298\) | − | 336.449i | − | 1.12902i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 68.5359 | 0.228453 | ||||||||
\(301\) | −68.7846 | − | 68.7846i | −0.228520 | − | 0.228520i | ||||
\(302\) | −76.8128 | −0.254347 | ||||||||
\(303\) | 181.061i | 0.597563i | ||||||||
\(304\) | −45.0718 | − | 45.0718i | −0.148262 | − | 0.148262i | ||||
\(305\) | 35.1384 | + | 35.1384i | 0.115208 | + | 0.115208i | ||||
\(306\) | −87.9615 | + | 87.9615i | −0.287456 | + | 0.287456i | ||||
\(307\) | −7.48849 | + | 7.48849i | −0.0243925 | + | 0.0243925i | −0.719198 | − | 0.694805i | \(-0.755491\pi\) |
0.694805 | + | 0.719198i | \(0.255491\pi\) | |||||||
\(308\) | −18.9282 | −0.0614552 | ||||||||
\(309\) | 63.5307i | 0.205601i | ||||||||
\(310\) | 255.349 | − | 255.349i | 0.823705 | − | 0.823705i | ||||
\(311\) | − | 289.377i | − | 0.930472i | −0.885187 | − | 0.465236i | \(-0.845969\pi\) | ||
0.885187 | − | 0.465236i | \(-0.154031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 346.841 | 1.10812 | 0.554059 | − | 0.832477i | \(-0.313078\pi\) | ||||
0.554059 | + | 0.832477i | \(0.313078\pi\) | |||||||
\(314\) | 227.215 | + | 227.215i | 0.723616 | + | 0.723616i | ||||
\(315\) | −77.5692 | −0.246251 | ||||||||
\(316\) | − | 296.420i | − | 0.938039i | ||||||
\(317\) | 97.0192 | + | 97.0192i | 0.306054 | + | 0.306054i | 0.843377 | − | 0.537322i | \(-0.180564\pi\) |
−0.537322 | + | 0.843377i | \(0.680564\pi\) | |||||||
\(318\) | 3.96152 | + | 3.96152i | 0.0124576 | + | 0.0124576i | ||||
\(319\) | −55.1769 | + | 55.1769i | −0.172968 | + | 0.172968i | ||||
\(320\) | −37.8564 | + | 37.8564i | −0.118301 | + | 0.118301i | ||||
\(321\) | 213.846 | 0.666187 | ||||||||
\(322\) | 160.210i | 0.497547i | ||||||||
\(323\) | 330.382 | − | 330.382i | 1.02285 | − | 1.02285i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.8897 | 0.0763489 | ||||||||
\(327\) | 206.660 | + | 206.660i | 0.631989 | + | 0.631989i | ||||
\(328\) | 57.7795 | 0.176157 | ||||||||
\(329\) | − | 225.100i | − | 0.684194i | ||||||
\(330\) | 28.3923 | + | 28.3923i | 0.0860373 | + | 0.0860373i | ||||
\(331\) | 126.130 | + | 126.130i | 0.381056 | + | 0.381056i | 0.871483 | − | 0.490427i | \(-0.163159\pi\) |
−0.490427 | + | 0.871483i | \(0.663159\pi\) | |||||||
\(332\) | 147.597 | − | 147.597i | 0.444570 | − | 0.444570i | ||||
\(333\) | 92.5692 | − | 92.5692i | 0.277986 | − | 0.277986i | ||||
\(334\) | 239.023 | 0.715638 | ||||||||
\(335\) | − | 574.410i | − | 1.71466i | ||||||
\(336\) | 18.9282 | − | 18.9282i | 0.0563339 | − | 0.0563339i | ||||
\(337\) | − | 423.061i | − | 1.25538i | −0.778465 | − | 0.627688i | \(-0.784002\pi\) | ||
0.778465 | − | 0.627688i | \(-0.215998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 319.177 | 0.941525 | ||||||||
\(340\) | −277.492 | − | 277.492i | −0.816154 | − | 0.816154i | ||||
\(341\) | 93.4641 | 0.274088 | ||||||||
\(342\) | − | 67.6077i | − | 0.197683i | ||||||
\(343\) | 226.956 | + | 226.956i | 0.661680 | + | 0.661680i | ||||
\(344\) | −50.3538 | − | 50.3538i | −0.146377 | − | 0.146377i | ||||
\(345\) | 240.315 | − | 240.315i | 0.696566 | − | 0.696566i | ||||
\(346\) | −69.3975 | + | 69.3975i | −0.200571 | + | 0.200571i | ||||
\(347\) | −191.867 | −0.552930 | −0.276465 | − | 0.961024i | \(-0.589163\pi\) | ||||
−0.276465 | + | 0.961024i | \(0.589163\pi\) | |||||||
\(348\) | − | 110.354i | − | 0.317109i | ||||||
\(349\) | −36.7898 | + | 36.7898i | −0.105415 | + | 0.105415i | −0.757847 | − | 0.652432i | \(-0.773749\pi\) |
0.652432 | + | 0.757847i | \(0.273749\pi\) | |||||||
\(350\) | − | 108.105i | − | 0.308872i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.8564 | −0.0393648 | ||||||||
\(353\) | −117.870 | − | 117.870i | −0.333911 | − | 0.333911i | 0.520159 | − | 0.854070i | \(-0.325873\pi\) |
−0.854070 | + | 0.520159i | \(0.825873\pi\) | |||||||
\(354\) | −189.215 | −0.534507 | ||||||||
\(355\) | 368.238i | 1.03729i | ||||||||
\(356\) | −51.0333 | − | 51.0333i | −0.143352 | − | 0.143352i | ||||
\(357\) | 138.746 | + | 138.746i | 0.388645 | + | 0.388645i | ||||
\(358\) | 165.282 | − | 165.282i | 0.461682 | − | 0.461682i | ||||
\(359\) | −13.1192 | + | 13.1192i | −0.0365437 | + | 0.0365437i | −0.725143 | − | 0.688599i | \(-0.758226\pi\) |
0.688599 | + | 0.725143i | \(0.258226\pi\) | |||||||
\(360\) | −56.7846 | −0.157735 | ||||||||
\(361\) | − | 107.067i | − | 0.296583i | ||||||
\(362\) | −283.856 | + | 283.856i | −0.784134 | + | 0.784134i | ||||
\(363\) | − | 199.186i | − | 0.548721i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 381.597 | 1.04547 | ||||||||
\(366\) | −12.8616 | − | 12.8616i | −0.0351409 | − | 0.0351409i | ||||
\(367\) | −600.708 | −1.63681 | −0.818403 | − | 0.574645i | \(-0.805140\pi\) | ||||
−0.818403 | + | 0.574645i | \(0.805140\pi\) | |||||||
\(368\) | 117.282i | 0.318701i | ||||||||
\(369\) | 43.3346 | + | 43.3346i | 0.117438 | + | 0.117438i | ||||
\(370\) | 292.028 | + | 292.028i | 0.789265 | + | 0.789265i | ||||
\(371\) | 6.24871 | − | 6.24871i | 0.0168429 | − | 0.0168429i | ||||
\(372\) | −93.4641 | + | 93.4641i | −0.251248 | + | 0.251248i | ||||
\(373\) | 671.836 | 1.80117 | 0.900584 | − | 0.434682i | \(-0.143139\pi\) | ||||
0.900584 | + | 0.434682i | \(0.143139\pi\) | |||||||
\(374\) | − | 101.569i | − | 0.271575i | ||||||
\(375\) | 42.7461 | − | 42.7461i | 0.113990 | − | 0.113990i | ||||
\(376\) | − | 164.785i | − | 0.438257i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 28.3923 | 0.0751119 | ||||||||
\(379\) | −158.799 | − | 158.799i | −0.418994 | − | 0.418994i | 0.465863 | − | 0.884857i | \(-0.345744\pi\) |
−0.884857 | + | 0.465863i | \(0.845744\pi\) | |||||||
\(380\) | 213.282 | 0.561269 | ||||||||
\(381\) | − | 301.310i | − | 0.790840i | ||||||
\(382\) | −9.28203 | − | 9.28203i | −0.0242985 | − | 0.0242985i | ||||
\(383\) | −233.445 | − | 233.445i | −0.609517 | − | 0.609517i | 0.333303 | − | 0.942820i | \(-0.391837\pi\) |
−0.942820 | + | 0.333303i | \(0.891837\pi\) | |||||||
\(384\) | 13.8564 | − | 13.8564i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 44.7846 | − | 44.7846i | 0.116324 | − | 0.116324i | ||||
\(386\) | −43.4359 | −0.112528 | ||||||||
\(387\) | − | 75.5307i | − | 0.195170i | ||||||
\(388\) | −172.067 | + | 172.067i | −0.443471 | + | 0.443471i | ||||
\(389\) | 27.6950i | 0.0711953i | 0.999366 | + | 0.0355976i | \(0.0113335\pi\) | ||||
−0.999366 | + | 0.0355976i | \(0.988667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −859.692 | −2.19870 | ||||||||
\(392\) | 68.1436 | + | 68.1436i | 0.173836 | + | 0.173836i | ||||
\(393\) | −209.769 | −0.533764 | ||||||||
\(394\) | − | 225.464i | − | 0.572244i | ||||||
\(395\) | 701.338 | + | 701.338i | 1.77554 | + | 1.77554i | ||||
\(396\) | −10.3923 | − | 10.3923i | −0.0262432 | − | 0.0262432i | ||||
\(397\) | 398.692 | − | 398.692i | 1.00426 | − | 1.00426i | 0.00427158 | − | 0.999991i | \(-0.498640\pi\) |
0.999991 | − | 0.00427158i | \(-0.00135969\pi\) | |||||||
\(398\) | 245.100 | − | 245.100i | 0.615829 | − | 0.615829i | ||||
\(399\) | −106.641 | −0.267271 | ||||||||
\(400\) | − | 79.1384i | − | 0.197846i | ||||||
\(401\) | 139.450 | − | 139.450i | 0.347756 | − | 0.347756i | −0.511517 | − | 0.859273i | \(-0.670916\pi\) |
0.859273 | + | 0.511517i | \(0.170916\pi\) | |||||||
\(402\) | 210.249i | 0.523007i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 209.072 | 0.517504 | ||||||||
\(405\) | −42.5885 | − | 42.5885i | −0.105157 | − | 0.105157i | ||||
\(406\) | −174.067 | −0.428736 | ||||||||
\(407\) | 106.890i | 0.262628i | ||||||||
\(408\) | 101.569 | + | 101.569i | 0.248944 | + | 0.248944i | ||||
\(409\) | −401.813 | − | 401.813i | −0.982427 | − | 0.982427i | 0.0174209 | − | 0.999848i | \(-0.494454\pi\) |
−0.999848 | + | 0.0174209i | \(0.994454\pi\) | |||||||
\(410\) | −136.708 | + | 136.708i | −0.333433 | + | 0.333433i | ||||
\(411\) | −225.258 | + | 225.258i | −0.548072 | + | 0.548072i | ||||
\(412\) | 73.3590 | 0.178056 | ||||||||
\(413\) | 298.459i | 0.722661i | ||||||||
\(414\) | −87.9615 | + | 87.9615i | −0.212467 | + | 0.212467i | ||||
\(415\) | 698.438i | 1.68298i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.0052 | 0.112722 | ||||||||
\(418\) | 39.0333 | + | 39.0333i | 0.0933812 | + | 0.0933812i | ||||
\(419\) | 139.177 | 0.332164 | 0.166082 | − | 0.986112i | \(-0.446888\pi\) | ||||
0.166082 | + | 0.986112i | \(0.446888\pi\) | |||||||
\(420\) | 89.5692i | 0.213260i | ||||||||
\(421\) | −360.244 | − | 360.244i | −0.855685 | − | 0.855685i | 0.135141 | − | 0.990826i | \(-0.456851\pi\) |
−0.990826 | + | 0.135141i | \(0.956851\pi\) | |||||||
\(422\) | −345.282 | − | 345.282i | −0.818204 | − | 0.818204i | ||||
\(423\) | 123.588 | − | 123.588i | 0.292171 | − | 0.292171i | ||||
\(424\) | 4.57437 | − | 4.57437i | 0.0107886 | − | 0.0107886i | ||||
\(425\) | 580.095 | 1.36493 | ||||||||
\(426\) | − | 134.785i | − | 0.316396i | ||||||
\(427\) | −20.2872 | + | 20.2872i | −0.0475110 | + | 0.0475110i | ||||
\(428\) | − | 246.928i | − | 0.576935i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 238.277 | 0.554132 | ||||||||
\(431\) | −213.522 | − | 213.522i | −0.495410 | − | 0.495410i | 0.414596 | − | 0.910006i | \(-0.363923\pi\) |
−0.910006 | + | 0.414596i | \(0.863923\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 446.708i | 1.03166i | 0.856692 | + | 0.515829i | \(0.172516\pi\) | ||||
−0.856692 | + | 0.515829i | \(0.827484\pi\) | |||||||
\(434\) | 147.426 | + | 147.426i | 0.339690 | + | 0.339690i | ||||
\(435\) | 261.100 | + | 261.100i | 0.600230 | + | 0.600230i | ||||
\(436\) | 238.631 | − | 238.631i | 0.547318 | − | 0.547318i | ||||
\(437\) | 330.382 | − | 330.382i | 0.756023 | − | 0.756023i | ||||
\(438\) | −139.674 | −0.318891 | ||||||||
\(439\) | 164.238i | 0.374119i | 0.982349 | + | 0.187060i | \(0.0598958\pi\) | ||||
−0.982349 | + | 0.187060i | \(0.940104\pi\) | |||||||
\(440\) | 32.7846 | − | 32.7846i | 0.0745105 | − | 0.0745105i | ||||
\(441\) | 102.215i | 0.231781i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −458.736 | −1.03552 | −0.517761 | − | 0.855526i | \(-0.673234\pi\) | ||||
−0.517761 | + | 0.855526i | \(0.673234\pi\) | |||||||
\(444\) | −106.890 | − | 106.890i | −0.240743 | − | 0.240743i | ||||
\(445\) | 241.492 | 0.542679 | ||||||||
\(446\) | 341.177i | 0.764971i | ||||||||
\(447\) | −291.373 | − | 291.373i | −0.651841 | − | 0.651841i | ||||
\(448\) | −21.8564 | − | 21.8564i | −0.0487866 | − | 0.0487866i | ||||
\(449\) | −221.776 | + | 221.776i | −0.493932 | + | 0.493932i | −0.909543 | − | 0.415610i | \(-0.863568\pi\) |
0.415610 | + | 0.909543i | \(0.363568\pi\) | |||||||
\(450\) | 59.3538 | − | 59.3538i | 0.131897 | − | 0.131897i | ||||
\(451\) | −50.0385 | −0.110950 | ||||||||
\(452\) | − | 368.554i | − | 0.815384i | ||||||
\(453\) | −66.5218 | + | 66.5218i | −0.146847 | + | 0.146847i | ||||
\(454\) | 338.736i | 0.746114i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −78.0666 | −0.171199 | ||||||||
\(457\) | −52.9615 | − | 52.9615i | −0.115890 | − | 0.115890i | 0.646784 | − | 0.762673i | \(-0.276114\pi\) |
−0.762673 | + | 0.646784i | \(0.776114\pi\) | |||||||
\(458\) | 283.646 | 0.619315 | ||||||||
\(459\) | 152.354i | 0.331926i | ||||||||
\(460\) | −277.492 | − | 277.492i | −0.603244 | − | 0.603244i | ||||
\(461\) | −67.4500 | − | 67.4500i | −0.146312 | − | 0.146312i | 0.630156 | − | 0.776468i | \(-0.282991\pi\) |
−0.776468 | + | 0.630156i | \(0.782991\pi\) | |||||||
\(462\) | −16.3923 | + | 16.3923i | −0.0354812 | + | 0.0354812i | ||||
\(463\) | −549.247 | + | 549.247i | −1.18628 | + | 1.18628i | −0.208191 | + | 0.978088i | \(0.566758\pi\) |
−0.978088 | + | 0.208191i | \(0.933242\pi\) | |||||||
\(464\) | −127.426 | −0.274624 | ||||||||
\(465\) | − | 442.277i | − | 0.951133i | ||||||
\(466\) | 128.038 | − | 128.038i | 0.274761 | − | 0.274761i | ||||
\(467\) | − | 30.1821i | − | 0.0646297i | −0.999478 | − | 0.0323148i | \(-0.989712\pi\) | ||
0.999478 | − | 0.0323148i | \(-0.0102879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 331.636 | 0.707113 | ||||||||
\(470\) | 389.885 | + | 389.885i | 0.829542 | + | 0.829542i | ||||
\(471\) | 393.549 | 0.835560 | ||||||||
\(472\) | 218.487i | 0.462896i | ||||||||
\(473\) | 43.6077 | + | 43.6077i | 0.0921939 | + | 0.0921939i | ||||
\(474\) | −256.708 | − | 256.708i | −0.541577 | − | 0.541577i | ||||
\(475\) | −222.932 | + | 222.932i | −0.469330 | + | 0.469330i | ||||
\(476\) | 160.210 | − | 160.210i | 0.336576 | − | 0.336576i | ||||
\(477\) | 6.86156 | 0.0143848 | ||||||||
\(478\) | 176.038i | 0.368281i | ||||||||
\(479\) | 258.870 | − | 258.870i | 0.540439 | − | 0.540439i | −0.383218 | − | 0.923658i | \(-0.625184\pi\) |
0.923658 | + | 0.383218i | \(0.125184\pi\) | |||||||
\(480\) | 65.5692i | 0.136603i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −294.918 | −0.611863 | ||||||||
\(483\) | 138.746 | + | 138.746i | 0.287259 | + | 0.287259i | ||||
\(484\) | −230.000 | −0.475207 | ||||||||
\(485\) | − | 814.228i | − | 1.67882i | ||||||
\(486\) | 15.5885 | + | 15.5885i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 274.560 | + | 274.560i | 0.563779 | + | 0.563779i | 0.930379 | − | 0.366600i | \(-0.119478\pi\) |
−0.366600 | + | 0.930379i | \(0.619478\pi\) | |||||||
\(488\) | −14.8513 | + | 14.8513i | −0.0304329 | + | 0.0304329i | ||||
\(489\) | 21.5551 | − | 21.5551i | 0.0440800 | − | 0.0440800i | ||||
\(490\) | −322.459 | −0.658079 | ||||||||
\(491\) | 220.726i | 0.449543i | 0.974412 | + | 0.224771i | \(0.0721635\pi\) | ||||
−0.974412 | + | 0.224771i | \(0.927836\pi\) | |||||||
\(492\) | 50.0385 | − | 50.0385i | 0.101704 | − | 0.101704i | ||||
\(493\) | − | 934.046i | − | 1.89462i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 49.1769 | 0.0993473 | ||||||||
\(496\) | 107.923 | + | 107.923i | 0.217587 | + | 0.217587i | ||||
\(497\) | −212.603 | −0.427772 | ||||||||
\(498\) | − | 255.646i | − | 0.513346i | ||||||
\(499\) | 625.065 | + | 625.065i | 1.25264 | + | 1.25264i | 0.954534 | + | 0.298102i | \(0.0963534\pi\) |
0.298102 | + | 0.954534i | \(0.403647\pi\) | |||||||
\(500\) | −49.3590 | − | 49.3590i | −0.0987180 | − | 0.0987180i | ||||
\(501\) | 207.000 | − | 207.000i | 0.413174 | − | 0.413174i | ||||
\(502\) | 181.377 | − | 181.377i | 0.361308 | − | 0.361308i | ||||
\(503\) | −696.018 | −1.38373 | −0.691867 | − | 0.722025i | \(-0.743211\pi\) | ||||
−0.691867 | + | 0.722025i | \(0.743211\pi\) | |||||||
\(504\) | − | 32.7846i | − | 0.0650488i | ||||||
\(505\) | −494.669 | + | 494.669i | −0.979543 | + | 0.979543i | ||||
\(506\) | − | 101.569i | − | 0.200730i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −347.923 | −0.684888 | ||||||||
\(509\) | −401.678 | − | 401.678i | −0.789151 | − | 0.789151i | 0.192204 | − | 0.981355i | \(-0.438437\pi\) |
−0.981355 | + | 0.192204i | \(0.938437\pi\) | |||||||
\(510\) | −480.631 | −0.942413 | ||||||||
\(511\) | 220.315i | 0.431146i | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −58.5500 | − | 58.5500i | −0.114133 | − | 0.114133i | ||||
\(514\) | −297.664 | + | 297.664i | −0.579113 | + | 0.579113i | ||||
\(515\) | −173.569 | + | 173.569i | −0.337028 | + | 0.337028i | ||||
\(516\) | −87.2154 | −0.169022 | ||||||||
\(517\) | 142.708i | 0.276030i | ||||||||
\(518\) | −168.603 | + | 168.603i | −0.325488 | + | 0.325488i | ||||
\(519\) | 120.200i | 0.231599i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −602.651 | −1.15672 | −0.578360 | − | 0.815782i | \(-0.696307\pi\) | ||||
−0.578360 | + | 0.815782i | \(0.696307\pi\) | |||||||
\(522\) | −95.5692 | − | 95.5692i | −0.183083 | − | 0.183083i | ||||
\(523\) | 854.677 | 1.63418 | 0.817091 | − | 0.576509i | \(-0.195586\pi\) | ||||
0.817091 | + | 0.576509i | \(0.195586\pi\) | |||||||
\(524\) | 242.221i | 0.462253i | ||||||||
\(525\) | −93.6218 | − | 93.6218i | −0.178327 | − | 0.178327i | ||||
\(526\) | −22.8897 | − | 22.8897i | −0.0435166 | − | 0.0435166i | ||||
\(527\) | −791.090 | + | 791.090i | −1.50112 | + | 1.50112i | ||||
\(528\) | −12.0000 | + | 12.0000i | −0.0227273 | + | 0.0227273i | ||||
\(529\) | −330.692 | −0.625127 | ||||||||
\(530\) | 21.6462i | 0.0408418i | ||||||||
\(531\) | −163.865 | + | 163.865i | −0.308598 | + | 0.308598i | ||||
\(532\) | 123.138i | 0.231463i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −88.3923 | −0.165529 | ||||||||
\(535\) | 584.238 | + | 584.238i | 1.09203 | + | 1.09203i | ||||
\(536\) | 242.774 | 0.452937 | ||||||||
\(537\) | − | 286.277i | − | 0.533104i | ||||||
\(538\) | −220.774 | − | 220.774i | −0.410361 | − | 0.410361i | ||||
\(539\) | −59.0141 | − | 59.0141i | −0.109488 | − | 0.109488i | ||||
\(540\) | −49.1769 | + | 49.1769i | −0.0910684 | + | 0.0910684i | ||||
\(541\) | 344.244 | − | 344.244i | 0.636310 | − | 0.636310i | −0.313333 | − | 0.949643i | \(-0.601446\pi\) |
0.949643 | + | 0.313333i | \(0.101446\pi\) | |||||||
\(542\) | 297.905 | 0.549641 | ||||||||
\(543\) | 491.654i | 0.905440i | ||||||||
\(544\) | 117.282 | − | 117.282i | 0.215592 | − | 0.215592i | ||||
\(545\) | 1129.21i | 2.07195i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 842.200 | 1.53967 | 0.769835 | − | 0.638242i | \(-0.220338\pi\) | ||||
0.769835 | + | 0.638242i | \(0.220338\pi\) | |||||||
\(548\) | 260.105 | + | 260.105i | 0.474644 | + | 0.474644i | ||||
\(549\) | −22.2769 | −0.0405772 | ||||||||
\(550\) | 68.5359i | 0.124611i | ||||||||
\(551\) | 358.956 | + | 358.956i | 0.651463 | + | 0.651463i | ||||
\(552\) | 101.569 | + | 101.569i | 0.184002 | + | 0.184002i | ||||
\(553\) | −404.918 | + | 404.918i | −0.732220 | + | 0.732220i | ||||
\(554\) | 27.2154 | − | 27.2154i | 0.0491253 | − | 0.0491253i | ||||
\(555\) | 505.808 | 0.911365 | ||||||||
\(556\) | − | 54.2769i | − | 0.0976203i | ||||||
\(557\) | −99.2576 | + | 99.2576i | −0.178200 | + | 0.178200i | −0.790571 | − | 0.612370i | \(-0.790216\pi\) |
0.612370 | + | 0.790571i | \(0.290216\pi\) | |||||||
\(558\) | 161.885i | 0.290116i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 103.426 | 0.184689 | ||||||||
\(561\) | −87.9615 | − | 87.9615i | −0.156794 | − | 0.156794i | ||||
\(562\) | −103.244 | −0.183707 | ||||||||
\(563\) | 647.174i | 1.14951i | 0.818326 | + | 0.574755i | \(0.194903\pi\) | ||||
−0.818326 | + | 0.574755i | \(0.805097\pi\) | |||||||
\(564\) | −142.708 | − | 142.708i | −0.253028 | − | 0.253028i | ||||
\(565\) | 872.008 | + | 872.008i | 1.54338 | + | 1.54338i | ||||
\(566\) | −93.8076 | + | 93.8076i | −0.165738 | + | 0.165738i | ||||
\(567\) | 24.5885 | − | 24.5885i | 0.0433659 | − | 0.0433659i | ||||
\(568\) | −155.636 | −0.274007 | ||||||||
\(569\) | 701.223i | 1.23238i | 0.787598 | + | 0.616189i | \(0.211324\pi\) | ||||
−0.787598 | + | 0.616189i | \(0.788676\pi\) | |||||||
\(570\) | 184.708 | − | 184.708i | 0.324049 | − | 0.324049i | ||||
\(571\) | 218.746i | 0.383093i | 0.981484 | + | 0.191547i | \(0.0613503\pi\) | ||||
−0.981484 | + | 0.191547i | \(0.938650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0770 | −0.0280575 | ||||||||
\(574\) | −78.9282 | − | 78.9282i | −0.137506 | − | 0.137506i | ||||
\(575\) | 580.095 | 1.00886 | ||||||||
\(576\) | − | 24.0000i | − | 0.0416667i | ||||||
\(577\) | 12.3590 | + | 12.3590i | 0.0214194 | + | 0.0214194i | 0.717735 | − | 0.696316i | \(-0.245179\pi\) |
−0.696316 | + | 0.717735i | \(0.745179\pi\) | |||||||
\(578\) | 570.692 | + | 570.692i | 0.987357 | + | 0.987357i | ||||
\(579\) | −37.6166 | + | 37.6166i | −0.0649683 | + | 0.0649683i | ||||
\(580\) | 301.492 | − | 301.492i | 0.519814 | − | 0.519814i | ||||
\(581\) | −403.244 | −0.694051 | ||||||||
\(582\) | 298.028i | 0.512076i | ||||||||
\(583\) | −3.96152 | + | 3.96152i | −0.00679507 | + | 0.00679507i | ||||
\(584\) | 161.282i | 0.276168i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −240.084 | −0.409701 | ||||||||
\(587\) | 106.219 | + | 106.219i | 0.180953 | + | 0.180953i | 0.791771 | − | 0.610818i | \(-0.209159\pi\) |
−0.610818 | + | 0.791771i | \(0.709159\pi\) | |||||||
\(588\) | 118.028 | 0.200728 | ||||||||
\(589\) | − | 608.036i | − | 1.03232i | ||||||
\(590\) | −516.946 | − | 516.946i | −0.876180 | − | 0.876180i | ||||
\(591\) | −195.258 | − | 195.258i | −0.330385 | − | 0.330385i | ||||
\(592\) | −123.426 | + | 123.426i | −0.208489 | + | 0.208489i | ||||
\(593\) | −770.645 | + | 770.645i | −1.29957 | + | 1.29957i | −0.370895 | + | 0.928675i | \(0.620949\pi\) |
−0.928675 | + | 0.370895i | \(0.879051\pi\) | |||||||
\(594\) | −18.0000 | −0.0303030 | ||||||||
\(595\) | 758.123i | 1.27416i | ||||||||
\(596\) | −336.449 | + | 336.449i | −0.564511 | + | 0.564511i | ||||
\(597\) | − | 424.526i | − | 0.711098i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −130.392 | −0.217683 | −0.108842 | − | 0.994059i | \(-0.534714\pi\) | ||||
−0.108842 | + | 0.994059i | \(0.534714\pi\) | |||||||
\(600\) | −68.5359 | − | 68.5359i | −0.114226 | − | 0.114226i | ||||
\(601\) | −551.108 | −0.916984 | −0.458492 | − | 0.888698i | \(-0.651610\pi\) | ||||
−0.458492 | + | 0.888698i | \(0.651610\pi\) | |||||||
\(602\) | 137.569i | 0.228520i | ||||||||
\(603\) | 182.081 | + | 182.081i | 0.301958 | + | 0.301958i | ||||
\(604\) | 76.8128 | + | 76.8128i | 0.127173 | + | 0.127173i | ||||
\(605\) | 544.186 | − | 544.186i | 0.899481 | − | 0.899481i | ||||
\(606\) | 181.061 | − | 181.061i | 0.298781 | − | 0.298781i | ||||
\(607\) | 63.6001 | 0.104778 | 0.0523889 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523889 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(608\) | 90.1436i | 0.148262i | ||||||||
\(609\) | −150.746 | + | 150.746i | −0.247531 | + | 0.247531i | ||||
\(610\) | − | 70.2769i | − | 0.115208i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 175.923 | 0.287456 | ||||||||
\(613\) | 26.3487 | + | 26.3487i | 0.0429832 | + | 0.0429832i | 0.728272 | − | 0.685289i | \(-0.240324\pi\) |
−0.685289 | + | 0.728272i | \(0.740324\pi\) | |||||||
\(614\) | 14.9770 | 0.0243925 | ||||||||
\(615\) | 236.785i | 0.385016i | ||||||||
\(616\) | 18.9282 | + | 18.9282i | 0.0307276 | + | 0.0307276i | ||||
\(617\) | −375.391 | − | 375.391i | −0.608413 | − | 0.608413i | 0.334118 | − | 0.942531i | \(-0.391562\pi\) |
−0.942531 | + | 0.334118i | \(0.891562\pi\) | |||||||
\(618\) | 63.5307 | − | 63.5307i | 0.102801 | − | 0.102801i | ||||
\(619\) | −264.070 | + | 264.070i | −0.426608 | + | 0.426608i | −0.887471 | − | 0.460863i | \(-0.847540\pi\) |
0.460863 | + | 0.887471i | \(0.347540\pi\) | |||||||
\(620\) | −510.697 | −0.823705 | ||||||||
\(621\) | 152.354i | 0.245336i | ||||||||
\(622\) | −289.377 | + | 289.377i | −0.465236 | + | 0.465236i | ||||
\(623\) | 139.426i | 0.223797i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 728.184 | 1.16510 | ||||||||
\(626\) | −346.841 | − | 346.841i | −0.554059 | − | 0.554059i | ||||
\(627\) | 67.6077 | 0.107827 | ||||||||
\(628\) | − | 454.431i | − | 0.723616i | ||||||
\(629\) | −904.726 | − | 904.726i | −1.43836 | − | 1.43836i | ||||
\(630\) | 77.5692 | + | 77.5692i | 0.123126 | + | 0.123126i | ||||
\(631\) | 441.594 | − | 441.594i | 0.699831 | − | 0.699831i | −0.264543 | − | 0.964374i | \(-0.585221\pi\) |
0.964374 | + | 0.264543i | \(0.0852210\pi\) | |||||||
\(632\) | −296.420 | + | 296.420i | −0.469020 | + | 0.469020i | ||||
\(633\) | −598.046 | −0.944780 | ||||||||
\(634\) | − | 194.038i | − | 0.306054i | ||||||
\(635\) | 823.195 | − | 823.195i | 1.29637 | − | 1.29637i | ||||
\(636\) | − | 7.92305i | − | 0.0124576i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 110.354 | 0.172968 | ||||||||
\(639\) | −116.727 | − | 116.727i | −0.182671 | − | 0.182671i | ||||
\(640\) | 75.7128 | 0.118301 | ||||||||
\(641\) | − | 829.910i | − | 1.29471i | −0.762188 | − | 0.647356i | \(-0.775875\pi\) | ||
0.762188 | − | 0.647356i | \(-0.224125\pi\) | |||||||
\(642\) | −213.846 | − | 213.846i | −0.333094 | − | 0.333094i | ||||
\(643\) | −424.196 | − | 424.196i | −0.659714 | − | 0.659714i | 0.295598 | − | 0.955312i | \(-0.404481\pi\) |
−0.955312 | + | 0.295598i | \(0.904481\pi\) | |||||||
\(644\) | 160.210 | − | 160.210i | 0.248774 | − | 0.248774i | ||||
\(645\) | 206.354 | − | 206.354i | 0.319928 | − | 0.319928i | ||||
\(646\) | −660.764 | −1.02285 | ||||||||
\(647\) | 477.913i | 0.738660i | 0.929298 | + | 0.369330i | \(0.120413\pi\) | ||||
−0.929298 | + | 0.369330i | \(0.879587\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 189.215i | − | 0.291549i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 255.349 | 0.392241 | ||||||||
\(652\) | −24.8897 | − | 24.8897i | −0.0381744 | − | 0.0381744i | ||||
\(653\) | −243.380 | −0.372710 | −0.186355 | − | 0.982482i | \(-0.559667\pi\) | ||||
−0.186355 | + | 0.982482i | \(0.559667\pi\) | |||||||
\(654\) | − | 413.321i | − | 0.631989i | ||||||
\(655\) | −573.100 | − | 573.100i | −0.874962 | − | 0.874962i | ||||
\(656\) | −57.7795 | − | 57.7795i | −0.0880784 | − | 0.0880784i | ||||
\(657\) | −120.962 | + | 120.962i | −0.184112 | + | 0.184112i | ||||
\(658\) | −225.100 | + | 225.100i | −0.342097 | + | 0.342097i | ||||
\(659\) | −190.677 | −0.289343 | −0.144671 | − | 0.989480i | \(-0.546212\pi\) | ||||
−0.144671 | + | 0.989480i | \(0.546212\pi\) | |||||||
\(660\) | − | 56.7846i | − | 0.0860373i | ||||||
\(661\) | 446.149 | − | 446.149i | 0.674960 | − | 0.674960i | −0.283895 | − | 0.958855i | \(-0.591627\pi\) |
0.958855 | + | 0.283895i | \(0.0916267\pi\) | |||||||
\(662\) | − | 252.259i | − | 0.381056i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −295.195 | −0.444570 | ||||||||
\(665\) | −291.349 | − | 291.349i | −0.438118 | − | 0.438118i | ||||
\(666\) | −185.138 | −0.277986 | ||||||||
\(667\) | − | 934.046i | − | 1.40037i | ||||||
\(668\) | −239.023 | − | 239.023i | −0.357819 | − | 0.357819i | ||||
\(669\) | 295.468 | + | 295.468i | 0.441656 | + | 0.441656i | ||||
\(670\) | −574.410 | + | 574.410i | −0.857329 | + | 0.857329i | ||||
\(671\) | 12.8616 | − | 12.8616i | 0.0191678 | − | 0.0191678i | ||||
\(672\) | −37.8564 | −0.0563339 | ||||||||
\(673\) | − | 176.221i | − | 0.261843i | −0.991393 | − | 0.130922i | \(-0.958206\pi\) | ||
0.991393 | − | 0.130922i | \(-0.0417936\pi\) | |||||||
\(674\) | −423.061 | + | 423.061i | −0.627688 | + | 0.627688i | ||||
\(675\) | − | 102.804i | − | 0.152302i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 672.600 | 0.993500 | 0.496750 | − | 0.867894i | \(-0.334527\pi\) | ||||
0.496750 | + | 0.867894i | \(0.334527\pi\) | |||||||
\(678\) | −319.177 | − | 319.177i | −0.470762 | − | 0.470762i | ||||
\(679\) | 470.095 | 0.692334 | ||||||||
\(680\) | 554.985i | 0.816154i | ||||||||
\(681\) | 293.354 | + | 293.354i | 0.430769 | + | 0.430769i | ||||
\(682\) | −93.4641 | − | 93.4641i | −0.137044 | − | 0.137044i | ||||
\(683\) | −306.191 | + | 306.191i | −0.448303 | + | 0.448303i | −0.894790 | − | 0.446487i | \(-0.852675\pi\) |
0.446487 | + | 0.894790i | \(0.352675\pi\) | |||||||
\(684\) | −67.6077 | + | 67.6077i | −0.0988417 | + | 0.0988417i | ||||
\(685\) | −1230.83 | −1.79683 | ||||||||
\(686\) | − | 453.913i | − | 0.661680i | ||||||
\(687\) | 245.645 | − | 245.645i | 0.357562 | − | 0.357562i | ||||
\(688\) | 100.708i | 0.146377i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −480.631 | −0.696566 | ||||||||
\(691\) | 474.865 | + | 474.865i | 0.687215 | + | 0.687215i | 0.961615 | − | 0.274401i | \(-0.0884795\pi\) |
−0.274401 | + | 0.961615i | \(0.588479\pi\) | |||||||
\(692\) | 138.795 | 0.200571 | ||||||||
\(693\) | 28.3923i | 0.0409701i | ||||||||
\(694\) | 191.867 | + | 191.867i | 0.276465 | + | 0.276465i | ||||
\(695\) | 128.420 | + | 128.420i | 0.184778 | + | 0.184778i | ||||
\(696\) | −110.354 | + | 110.354i | −0.158554 | + | 0.158554i | ||||
\(697\) | 423.531 | − | 423.531i | 0.607648 | − | 0.607648i | ||||
\(698\) | 73.5795 | 0.105415 | ||||||||
\(699\) | − | 221.769i | − | 0.317266i | ||||||
\(700\) | −108.105 | + | 108.105i | −0.154436 | + | 0.154436i | ||||
\(701\) | 204.480i | 0.291697i | 0.989307 | + | 0.145848i | \(0.0465912\pi\) | ||||
−0.989307 | + | 0.145848i | \(0.953409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 695.377 | 0.989156 | ||||||||
\(704\) | 13.8564 | + | 13.8564i | 0.0196824 | + | 0.0196824i | ||||
\(705\) | 675.300 | 0.957872 | ||||||||
\(706\) | 235.741i | 0.333911i | ||||||||
\(707\) | −285.597 | − | 285.597i | −0.403957 | − | 0.403957i | ||||
\(708\) | 189.215 | + | 189.215i | 0.267253 | + | 0.267253i | ||||
\(709\) | 629.018 | − | 629.018i | 0.887190 | − | 0.887190i | −0.107062 | − | 0.994252i | \(-0.534144\pi\) |
0.994252 | + | 0.107062i | \(0.0341444\pi\) | |||||||
\(710\) | 368.238 | − | 368.238i | 0.518646 | − | 0.518646i | ||||
\(711\) | −444.631 | −0.625360 | ||||||||
\(712\) | 102.067i | 0.143352i | ||||||||
\(713\) | −791.090 | + | 791.090i | −1.10952 | + | 1.10952i | ||||
\(714\) | − | 277.492i | − | 0.388645i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −330.564 | −0.461682 | ||||||||
\(717\) | 152.454 | + | 152.454i | 0.212627 | + | 0.212627i | ||||
\(718\) | 26.2384 | 0.0365437 | ||||||||
\(719\) | − | 863.290i | − | 1.20068i | −0.799745 | − | 0.600340i | \(-0.795032\pi\) | ||
0.799745 | − | 0.600340i | \(-0.204968\pi\) | |||||||
\(720\) | 56.7846 | + | 56.7846i | 0.0788675 | + | 0.0788675i | ||||
\(721\) | −100.210 | − | 100.210i | −0.138988 | − | 0.138988i | ||||
\(722\) | −107.067 | + | 107.067i | −0.148292 | + | 0.148292i | ||||
\(723\) | −255.406 | + | 255.406i | −0.353259 | + | 0.353259i | ||||
\(724\) | 567.713 | 0.784134 | ||||||||
\(725\) | 630.267i | 0.869333i | ||||||||
\(726\) | −199.186 | + | 199.186i | −0.274361 | + | 0.274361i | ||||
\(727\) | 605.577i | 0.832980i | 0.909140 | + | 0.416490i | \(0.136740\pi\) | ||||
−0.909140 | + | 0.416490i | \(0.863260\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −381.597 | − | 381.597i | −0.522736 | − | 0.522736i | ||||
\(731\) | −738.200 | −1.00985 | ||||||||
\(732\) | 25.7231i | 0.0351409i | ||||||||
\(733\) | −205.946 | − | 205.946i | −0.280963 | − | 0.280963i | 0.552530 | − | 0.833493i | \(-0.313663\pi\) |
−0.833493 | + | 0.552530i | \(0.813663\pi\) | |||||||
\(734\) | 600.708 | + | 600.708i | 0.818403 | + | 0.818403i | ||||
\(735\) | −279.258 | + | 279.258i | −0.379942 | + | 0.379942i | ||||
\(736\) | 117.282 | − | 117.282i | 0.159351 | − | 0.159351i | ||||
\(737\) | −210.249 | −0.285276 | ||||||||
\(738\) | − | 86.6692i | − | 0.117438i | ||||||
\(739\) | 58.7884 | − | 58.7884i | 0.0795513 | − | 0.0795513i | −0.666212 | − | 0.745763i | \(-0.732085\pi\) |
0.745763 | + | 0.666212i | \(0.232085\pi\) | |||||||
\(740\) | − | 584.056i | − | 0.789265i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.4974 | −0.0168429 | ||||||||
\(743\) | 885.509 | + | 885.509i | 1.19180 | + | 1.19180i | 0.976561 | + | 0.215241i | \(0.0690536\pi\) |
0.215241 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(744\) | 186.928 | 0.251248 | ||||||||
\(745\) | − | 1592.09i | − | 2.13704i | ||||||
\(746\) | −671.836 | − | 671.836i | −0.900584 | − | 0.900584i | ||||
\(747\) | −221.396 | − | 221.396i | −0.296380 | − | 0.296380i | ||||
\(748\) | −101.569 | + | 101.569i | −0.135788 | + | 0.135788i | ||||
\(749\) | −337.310 | + | 337.310i | −0.450347 | + | 0.450347i | ||||
\(750\) | −85.4923 | −0.113990 | ||||||||
\(751\) | − | 19.5720i | − | 0.0260612i | −0.999915 | − | 0.0130306i | \(-0.995852\pi\) | ||
0.999915 | − | 0.0130306i | \(-0.00414789\pi\) | |||||||
\(752\) | −164.785 | + | 164.785i | −0.219128 | + | 0.219128i | ||||
\(753\) | − | 314.154i | − | 0.417203i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −363.482 | −0.481433 | ||||||||
\(756\) | −28.3923 | − | 28.3923i | −0.0375560 | − | 0.0375560i | ||||
\(757\) | 677.836 | 0.895424 | 0.447712 | − | 0.894178i | \(-0.352239\pi\) | ||||
0.447712 | + | 0.894178i | \(0.352239\pi\) | |||||||
\(758\) | 317.597i | 0.418994i | ||||||||
\(759\) | −87.9615 | − | 87.9615i | −0.115891 | − | 0.115891i | ||||
\(760\) | −213.282 | − | 213.282i | −0.280634 | − | 0.280634i | ||||
\(761\) | 62.4449 | − | 62.4449i | 0.0820563 | − | 0.0820563i | −0.664887 | − | 0.746944i | \(-0.731520\pi\) |
0.746944 | + | 0.664887i | \(0.231520\pi\) | |||||||
\(762\) | −301.310 | + | 301.310i | −0.395420 | + | 0.395420i | ||||
\(763\) | −651.951 | −0.854458 | ||||||||
\(764\) | 18.5641i | 0.0242985i | ||||||||
\(765\) | −416.238 | + | 416.238i | −0.544102 | + | 0.544102i | ||||
\(766\) | 466.890i | 0.609517i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 71.5950 | + | 71.5950i | 0.0931014 | + | 0.0931014i | 0.752124 | − | 0.659022i | \(-0.229030\pi\) |
−0.659022 | + | 0.752124i | \(0.729030\pi\) | |||||||
\(770\) | −89.5692 | −0.116324 | ||||||||
\(771\) | 515.569i | 0.668702i | ||||||||
\(772\) | 43.4359 | + | 43.4359i | 0.0562642 | + | 0.0562642i | ||||
\(773\) | 778.817 | + | 778.817i | 1.00752 | + | 1.00752i | 0.999971 | + | 0.00755317i | \(0.00240427\pi\) |
0.00755317 | + | 0.999971i | \(0.497596\pi\) | |||||||
\(774\) | −75.5307 | + | 75.5307i | −0.0975849 | + | 0.0975849i | ||||
\(775\) | 533.804 | − | 533.804i | 0.688779 | − | 0.688779i | ||||
\(776\) | 344.133 | 0.443471 | ||||||||
\(777\) | 292.028i | 0.375841i | ||||||||
\(778\) | 27.6950 | − | 27.6950i | 0.0355976 | − | 0.0355976i | ||||
\(779\) | 325.528i | 0.417879i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 134.785 | 0.172580 | ||||||||
\(782\) | 859.692 | + | 859.692i | 1.09935 | + | 1.09935i | ||||
\(783\) | −165.531 | −0.211406 | ||||||||
\(784\) | − | 136.287i | − | 0.173836i | ||||||
\(785\) | 1075.19 | + | 1075.19i | 1.36967 | + | 1.36967i | ||||
\(786\) | 209.769 | + | 209.769i | 0.266882 | + | 0.266882i | ||||
\(787\) | −548.883 | + | 548.883i | −0.697437 | + | 0.697437i | −0.963857 | − | 0.266420i | \(-0.914159\pi\) |
0.266420 | + | 0.963857i | \(0.414159\pi\) | |||||||
\(788\) | −225.464 | + | 225.464i | −0.286122 | + | 0.286122i | ||||
\(789\) | −39.6462 | −0.0502486 | ||||||||
\(790\) | − | 1402.68i | − | 1.77554i | ||||||
\(791\) | −503.454 | + | 503.454i | −0.636478 | + | 0.636478i | ||||
\(792\) | 20.7846i | 0.0262432i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −797.384 | −1.00426 | ||||||||
\(795\) | 18.7461 | + | 18.7461i | 0.0235800 | + | 0.0235800i | ||||
\(796\) | −490.200 | −0.615829 | ||||||||
\(797\) | − | 41.5871i | − | 0.0521795i | −0.999660 | − | 0.0260898i | \(-0.991694\pi\) | ||
0.999660 | − | 0.0260898i | \(-0.00830557\pi\) | |||||||
\(798\) | 106.641 | + | 106.641i | 0.133635 | + | 0.133635i | ||||
\(799\) | −1207.89 | − | 1207.89i | −1.51175 | − | 1.51175i | ||||
\(800\) | −79.1384 | + | 79.1384i | −0.0989230 | + | 0.0989230i | ||||
\(801\) | −76.5500 | + | 76.5500i | −0.0955680 | + | 0.0955680i | ||||
\(802\) | −278.900 | −0.347756 | ||||||||
\(803\) | − | 139.674i | − | 0.173941i | ||||||
\(804\) | 210.249 | − | 210.249i | 0.261503 | − | 0.261503i | ||||
\(805\) | 758.123i | 0.941768i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −382.392 | −0.473844 | ||||||||
\(808\) | −209.072 | − | 209.072i | −0.258752 | − | 0.258752i | ||||
\(809\) | −1338.40 | −1.65439 | −0.827194 | − | 0.561916i | \(-0.810064\pi\) | ||||
−0.827194 | + | 0.561916i | \(0.810064\pi\) | |||||||
\(810\) | 85.1769i | 0.105157i | ||||||||
\(811\) | −257.258 | − | 257.258i | −0.317210 | − | 0.317210i | 0.530484 | − | 0.847695i | \(-0.322010\pi\) |
−0.847695 | + | 0.530484i | \(0.822010\pi\) | |||||||
\(812\) | 174.067 | + | 174.067i | 0.214368 | + | 0.214368i | ||||
\(813\) | 257.993 | − | 257.993i | 0.317335 | − | 0.317335i | ||||
\(814\) | 106.890 | − | 106.890i | 0.131314 | − | 0.131314i | ||||
\(815\) | 117.779 | 0.144515 | ||||||||
\(816\) | − | 203.138i | − | 0.248944i | ||||||
\(817\) | 283.692 | − | 283.692i | 0.347236 | − | 0.347236i | ||||
\(818\) | 803.626i | 0.982427i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 273.415 | 0.333433 | ||||||||
\(821\) | 306.873 | + | 306.873i | 0.373779 | + | 0.373779i | 0.868852 | − | 0.495072i | \(-0.164858\pi\) |
−0.495072 | + | 0.868852i | \(0.664858\pi\) | |||||||
\(822\) | 450.515 | 0.548072 | ||||||||
\(823\) | 1037.92i | 1.26114i | 0.776131 | + | 0.630571i | \(0.217179\pi\) | ||||
−0.776131 | + | 0.630571i | \(0.782821\pi\) | |||||||
\(824\) | −73.3590 | − | 73.3590i | −0.0890279 | − | 0.0890279i | ||||
\(825\) | 59.3538 | + | 59.3538i | 0.0719440 | + | 0.0719440i | ||||
\(826\) | 298.459 | − | 298.459i | 0.361330 | − | 0.361330i | ||||
\(827\) | −658.153 | + | 658.153i | −0.795831 | + | 0.795831i | −0.982435 | − | 0.186604i | \(-0.940252\pi\) |
0.186604 | + | 0.982435i | \(0.440252\pi\) | |||||||
\(828\) | 175.923 | 0.212467 | ||||||||
\(829\) | 372.354i | 0.449160i | 0.974456 | + | 0.224580i | \(0.0721010\pi\) | ||||
−0.974456 | + | 0.224580i | \(0.927899\pi\) | |||||||
\(830\) | 698.438 | − | 698.438i | 0.841492 | − | 0.841492i | ||||
\(831\) | − | 47.1384i | − | 0.0567250i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 999.002 | 1.19928 | ||||||||
\(834\) | −47.0052 | − | 47.0052i | −0.0563611 | − | 0.0563611i | ||||
\(835\) | 1131.07 | 1.35457 | ||||||||
\(836\) | − | 78.0666i | − | 0.0933812i | ||||||
\(837\) | 140.196 | + | 140.196i | 0.167498 | + | 0.167498i | ||||
\(838\) | −139.177 | − | 139.177i | −0.166082 | − | 0.166082i | ||||
\(839\) | −1018.87 | + | 1018.87i | −1.21438 | + | 1.21438i | −0.244813 | + | 0.969570i | \(0.578727\pi\) |
−0.969570 | + | 0.244813i | \(0.921273\pi\) | |||||||
\(840\) | 89.5692 | − | 89.5692i | 0.106630 | − | 0.106630i | ||||
\(841\) | 173.831 | 0.206695 | ||||||||
\(842\) | 720.487i | 0.855685i | ||||||||
\(843\) | −89.4115 | + | 89.4115i | −0.106064 | + | 0.106064i | ||||
\(844\) | 690.564i | 0.818204i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −247.177 | −0.292171 | ||||||||
\(847\) | 314.186 | + | 314.186i | 0.370940 | + | 0.370940i | ||||
\(848\) | −9.14875 | −0.0107886 | ||||||||
\(849\) | 162.480i | 0.191378i | ||||||||
\(850\) | −580.095 | − | 580.095i | −0.682464 | − | 0.682464i | ||||
\(851\) | −904.726 | − | 904.726i | −1.06313 | − | 1.06313i | ||||
\(852\) | −134.785 | + | 134.785i | −0.158198 | + | 0.158198i | ||||
\(853\) | 366.790 | − | 366.790i | 0.430000 | − | 0.430000i | −0.458628 | − | 0.888628i | \(-0.651659\pi\) |
0.888628 | + | 0.458628i | \(0.151659\pi\) | |||||||
\(854\) | 40.5744 | 0.0475110 | ||||||||
\(855\) | − | 319.923i | − | 0.374179i | ||||||
\(856\) | −246.928 | + | 246.928i | −0.288468 | + | 0.288468i | ||||
\(857\) | − | 469.244i | − | 0.547542i | −0.961795 | − | 0.273771i | \(-0.911729\pi\) | ||
0.961795 | − | 0.273771i | \(-0.0882711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1238.66 | −1.44197 | −0.720987 | − | 0.692948i | \(-0.756311\pi\) | ||||
−0.720987 | + | 0.692948i | \(0.756311\pi\) | |||||||
\(860\) | −238.277 | − | 238.277i | −0.277066 | − | 0.277066i | ||||
\(861\) | −136.708 | −0.158778 | ||||||||
\(862\) | 427.044i | 0.495410i | ||||||||
\(863\) | 5.71143 | + | 5.71143i | 0.00661811 | + | 0.00661811i | 0.710408 | − | 0.703790i | \(-0.248510\pi\) |
−0.703790 | + | 0.710408i | \(0.748510\pi\) | |||||||
\(864\) | −20.7846 | − | 20.7846i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | −328.392 | + | 328.392i | −0.379644 | + | 0.379644i | ||||
\(866\) | 446.708 | − | 446.708i | 0.515829 | − | 0.515829i | ||||
\(867\) | 988.468 | 1.14010 | ||||||||
\(868\) | − | 294.851i | − | 0.339690i | ||||||
\(869\) | 256.708 | − | 256.708i | 0.295406 | − | 0.295406i | ||||
\(870\) | − | 522.200i | − | 0.600230i | ||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −477.261 | −0.547318 | ||||||||
\(873\) | 258.100 | + | 258.100i | 0.295647 | + | 0.295647i | ||||
\(874\) | −660.764 | −0.756023 | ||||||||
\(875\) | 134.851i | 0.154116i | ||||||||
\(876\) | 139.674 | + | 139.674i | 0.159446 | + | 0.159446i | ||||
\(877\) | −591.287 | − | 591.287i | −0.674216 | − | 0.674216i | 0.284469 | − | 0.958685i | \(-0.408183\pi\) |
−0.958685 | + | 0.284469i | \(0.908183\pi\) | |||||||
\(878\) | 164.238 | − | 164.238i | 0.187060 | − | 0.187060i | ||||
\(879\) | −207.919 | + | 207.919i | −0.236541 | + | 0.236541i | ||||
\(880\) | −65.5692 | −0.0745105 | ||||||||
\(881\) | − | 663.997i | − | 0.753686i | −0.926277 | − | 0.376843i | \(-0.877010\pi\) | ||
0.926277 | − | 0.376843i | \(-0.122990\pi\) | |||||||
\(882\) | 102.215 | − | 102.215i | 0.115890 | − | 0.115890i | ||||
\(883\) | 570.192i | 0.645744i | 0.946443 | + | 0.322872i | \(0.104648\pi\) | ||||
−0.946443 | + | 0.322872i | \(0.895352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −895.377 | −1.01173 | ||||||||
\(886\) | 458.736 | + | 458.736i | 0.517761 | + | 0.517761i | ||||
\(887\) | 481.031 | 0.542312 | 0.271156 | − | 0.962535i | \(-0.412594\pi\) | ||||
0.271156 | + | 0.962535i | \(0.412594\pi\) | |||||||
\(888\) | 213.779i | 0.240743i | ||||||||
\(889\) | 475.272 | + | 475.272i | 0.534614 | + | 0.534614i | ||||
\(890\) | −241.492 | − | 241.492i | −0.271340 | − | 0.271340i | ||||
\(891\) | −15.5885 | + | 15.5885i | −0.0174955 | + | 0.0174955i | ||||
\(892\) | 341.177 | − | 341.177i | 0.382485 | − | 0.382485i | ||||
\(893\) | 928.392 | 1.03963 | ||||||||
\(894\) | 582.746i | 0.651841i | ||||||||
\(895\) | 782.123 | − | 782.123i | 0.873880 | − | 0.873880i | ||||
\(896\) | 43.7128i | 0.0487866i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 443.551 | 0.493932 | ||||||||
\(899\) | −859.510 | − | 859.510i | −0.956074 | − | 0.956074i | ||||
\(900\) | −118.708 | −0.131897 | ||||||||
\(901\) | − | 67.0615i | − | 0.0744301i | ||||||
\(902\) | 50.0385 | + | 50.0385i | 0.0554750 | + | 0.0554750i | ||||
\(903\) | 119.138 | + | 119.138i | 0.131936 | + | 0.131936i | ||||
\(904\) | −368.554 | + | 368.554i | −0.407692 | + | 0.407692i | ||||
\(905\) | −1343.22 | + | 1343.22i | −1.48422 | + | 1.48422i | ||||
\(906\) | 133.044 | 0.146847 | ||||||||
\(907\) | − | 193.331i | − | 0.213154i | −0.994304 | − | 0.106577i | \(-0.966011\pi\) | ||
0.994304 | − | 0.106577i | \(-0.0339891\pi\) | |||||||
\(908\) | 338.736 | − | 338.736i | 0.373057 | − | 0.373057i | ||||
\(909\) | − | 313.608i | − | 0.345003i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −868.743 | −0.953615 | −0.476808 | − | 0.879008i | \(-0.658206\pi\) | ||||
−0.476808 | + | 0.879008i | \(0.658206\pi\) | |||||||
\(912\) | 78.0666 | + | 78.0666i | 0.0855994 | + | 0.0855994i | ||||
\(913\) | 255.646 | 0.280007 | ||||||||
\(914\) | 105.923i | 0.115890i | ||||||||
\(915\) | −60.8616 | − | 60.8616i | −0.0665154 | − | 0.0665154i | ||||
\(916\) | −283.646 | − | 283.646i | −0.309657 | − | 0.309657i | ||||
\(917\) | 330.879 | − | 330.879i | 0.360828 | − | 0.360828i | ||||
\(918\) | 152.354 | − | 152.354i | 0.165963 | − | 0.165963i | ||||
\(919\) | 389.108 | 0.423403 | 0.211702 | − | 0.977334i | \(-0.432100\pi\) | ||||
0.211702 | + | 0.977334i | \(0.432100\pi\) | |||||||
\(920\) | 554.985i | 0.603244i | ||||||||
\(921\) | 12.9705 | − | 12.9705i | 0.0140830 | − | 0.0140830i | ||||
\(922\) | 134.900i | 0.146312i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 32.7846 | 0.0354812 | ||||||||
\(925\) | 610.482 | + | 610.482i | 0.659980 | + | 0.659980i | ||||
\(926\) | 1098.49 | 1.18628 | ||||||||
\(927\) | − | 110.038i | − | 0.118704i | ||||||
\(928\) | 127.426 | + | 127.426i | 0.137312 | + | 0.137312i | ||||
\(929\) | 429.870 | + | 429.870i | 0.462724 | + | 0.462724i | 0.899547 | − | 0.436823i | \(-0.143897\pi\) |
−0.436823 | + | 0.899547i | \(0.643897\pi\) | |||||||
\(930\) | −442.277 | + | 442.277i | −0.475567 | + | 0.475567i | ||||
\(931\) | −383.919 | + | 383.919i | −0.412373 | + | 0.412373i | ||||
\(932\) | −256.077 | −0.274761 | ||||||||
\(933\) | 501.215i | 0.537208i | ||||||||
\(934\) | −30.1821 | + | 30.1821i | −0.0323148 | + | 0.0323148i | ||||
\(935\) | − | 480.631i | − | 0.514044i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 916.441 | 0.978059 | 0.489029 | − | 0.872267i | \(-0.337351\pi\) | ||||
0.489029 | + | 0.872267i | \(0.337351\pi\) | |||||||
\(938\) | −331.636 | − | 331.636i | −0.353556 | − | 0.353556i | ||||
\(939\) | −600.746 | −0.639772 | ||||||||
\(940\) | − | 779.769i | − | 0.829542i | ||||||
\(941\) | −835.601 | − | 835.601i | −0.887993 | − | 0.887993i | 0.106337 | − | 0.994330i | \(-0.466088\pi\) |
−0.994330 | + | 0.106337i | \(0.966088\pi\) | |||||||
\(942\) | −393.549 | − | 393.549i | −0.417780 | − | 0.417780i | ||||
\(943\) | 423.531 | − | 423.531i | 0.449131 | − | 0.449131i | ||||
\(944\) | 218.487 | − | 218.487i | 0.231448 | − | 0.231448i | ||||
\(945\) | 134.354 | 0.142173 | ||||||||
\(946\) | − | 87.2154i | − | 0.0921939i | ||||||
\(947\) | 378.506 | − | 378.506i | 0.399690 | − | 0.399690i | −0.478434 | − | 0.878124i | \(-0.658795\pi\) |
0.878124 | + | 0.478434i | \(0.158795\pi\) | |||||||
\(948\) | 513.415i | 0.541577i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 445.864 | 0.469330 | ||||||||
\(951\) | −168.042 | − | 168.042i | −0.176701 | − | 0.176701i | ||||
\(952\) | −320.420 | −0.336576 | ||||||||
\(953\) | 839.556i | 0.880961i | 0.897762 | + | 0.440481i | \(0.145192\pi\) | ||||
−0.897762 | + | 0.440481i | \(0.854808\pi\) | |||||||
\(954\) | −6.86156 | − | 6.86156i | −0.00719241 | − | 0.00719241i | ||||
\(955\) | −43.9230 | − | 43.9230i | −0.0459927 | − | 0.0459927i | ||||
\(956\) | 176.038 | − | 176.038i | 0.184141 | − | 0.184141i | ||||
\(957\) | 95.5692 | − | 95.5692i | 0.0998633 | − | 0.0998633i | ||||
\(958\) | −517.741 | −0.540439 | ||||||||
\(959\) | − | 710.620i | − | 0.741001i | ||||||
\(960\) | 65.5692 | − | 65.5692i | 0.0683013 | − | 0.0683013i | ||||
\(961\) | 494.923i | 0.515008i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −370.392 | −0.384623 | ||||||||
\(964\) | 294.918 | + | 294.918i | 0.305931 | + | 0.305931i | ||||
\(965\) | −205.541 | −0.212996 | ||||||||
\(966\) | − | 277.492i | − | 0.287259i | ||||||
\(967\) | 375.745 | + | 375.745i | 0.388567 | + | 0.388567i | 0.874176 | − | 0.485609i | \(-0.161402\pi\) |
−0.485609 | + | 0.874176i | \(0.661402\pi\) | |||||||
\(968\) | 230.000 | + | 230.000i | 0.237603 | + | 0.237603i | ||||
\(969\) | −572.238 | + | 572.238i | −0.590545 | + | 0.590545i | ||||
\(970\) | −814.228 | + | 814.228i | −0.839410 | + | 0.839410i | ||||
\(971\) | 134.523 | 0.138541 | 0.0692703 | − | 0.997598i | \(-0.477933\pi\) | ||||
0.0692703 | + | 0.997598i | \(0.477933\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −74.1436 | + | 74.1436i | −0.0762010 | + | 0.0762010i | ||||
\(974\) | − | 549.121i | − | 0.563779i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.7025 | 0.0304329 | ||||||||
\(977\) | −708.060 | − | 708.060i | −0.724729 | − | 0.724729i | 0.244836 | − | 0.969565i | \(-0.421266\pi\) |
−0.969565 | + | 0.244836i | \(0.921266\pi\) | |||||||
\(978\) | −43.1103 | −0.0440800 | ||||||||
\(979\) | − | 88.3923i | − | 0.0902884i | ||||||
\(980\) | 322.459 | + | 322.459i | 0.329040 | + | 0.329040i | ||||
\(981\) | −357.946 | − | 357.946i | −0.364879 | − | 0.364879i | ||||
\(982\) | 220.726 | − | 220.726i | 0.224771 | − | 0.224771i | ||||
\(983\) | 904.881 | − | 904.881i | 0.920530 | − | 0.920530i | −0.0765369 | − | 0.997067i | \(-0.524386\pi\) |
0.997067 | + | 0.0765369i | \(0.0243863\pi\) | |||||||
\(984\) | −100.077 | −0.101704 | ||||||||
\(985\) | − | 1066.91i | − | 1.08315i | ||||||
\(986\) | −934.046 | + | 934.046i | −0.947308 | + | 0.947308i | ||||
\(987\) | 389.885i | 0.395020i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −738.200 | −0.746410 | ||||||||
\(990\) | −49.1769 | − | 49.1769i | −0.0496737 | − | 0.0496737i | ||||
\(991\) | 29.0155 | 0.0292790 | 0.0146395 | − | 0.999893i | \(-0.495340\pi\) | ||||
0.0146395 | + | 0.999893i | \(0.495340\pi\) | |||||||
\(992\) | − | 215.846i | − | 0.217587i | ||||||
\(993\) | −218.463 | − | 218.463i | −0.220003 | − | 0.220003i | ||||
\(994\) | 212.603 | + | 212.603i | 0.213886 | + | 0.213886i | ||||
\(995\) | 1159.83 | − | 1159.83i | 1.16565 | − | 1.16565i | ||||
\(996\) | −255.646 | + | 255.646i | −0.256673 | + | 0.256673i | ||||
\(997\) | 336.123 | 0.337134 | 0.168567 | − | 0.985690i | \(-0.446086\pi\) | ||||
0.168567 | + | 0.985690i | \(0.446086\pi\) | |||||||
\(998\) | − | 1250.13i | − | 1.25264i | ||||||
\(999\) | −160.335 | + | 160.335i | −0.160495 | + | 0.160495i |
(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 | 1014.3.f.a.775.1 | 4 | ||
13.5 | odd | 4 | inner | 1014.3.f.a.577.1 | 4 | ||
13.8 | odd | 4 | 78.3.f.a.31.1 | ✓ | 4 | ||
13.12 | even | 2 | 78.3.f.a.73.1 | yes | 4 | ||
39.8 | even | 4 | 234.3.i.b.109.1 | 4 | |||
39.38 | odd | 2 | 234.3.i.b.73.1 | 4 | |||
52.47 | even | 4 | 624.3.ba.a.577.2 | 4 | |||
52.51 | odd | 2 | 624.3.ba.a.385.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.f.a.31.1 | ✓ | 4 | 13.8 | odd | 4 | ||
78.3.f.a.73.1 | yes | 4 | 13.12 | even | 2 | ||
234.3.i.b.73.1 | 4 | 39.38 | odd | 2 | |||
234.3.i.b.109.1 | 4 | 39.8 | even | 4 | |||
624.3.ba.a.385.2 | 4 | 52.51 | odd | 2 | |||
624.3.ba.a.577.2 | 4 | 52.47 | even | 4 | |||
1014.3.f.a.577.1 | 4 | 13.5 | odd | 4 | inner | ||
1014.3.f.a.775.1 | 4 | 1.1 | even | 1 | trivial |