Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(40,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.40");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.g (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 94.3 | ||
Root | \(1.60675 + 1.36085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.94 |
Dual form | 363.3.g.g.112.3 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.10675 | − | 0.684524i | 1.05337 | − | 0.342262i | 0.269383 | − | 0.963033i | \(-0.413180\pi\) |
0.783992 | + | 0.620771i | \(0.213180\pi\) | |||||||
\(3\) | −1.40126 | − | 1.01807i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0.733748 | − | 0.533099i | 0.183437 | − | 0.133275i | ||||
\(5\) | 2.68691 | − | 8.26946i | 0.537382 | − | 1.65389i | −0.201064 | − | 0.979578i | \(-0.564440\pi\) |
0.738445 | − | 0.674313i | \(-0.235560\pi\) | |||||||
\(6\) | −3.64900 | − | 1.18563i | −0.608166 | − | 0.197605i | ||||
\(7\) | −3.92164 | − | 5.39767i | −0.560234 | − | 0.771096i | 0.431122 | − | 0.902294i | \(-0.358118\pi\) |
−0.991356 | + | 0.131197i | \(0.958118\pi\) | |||||||
\(8\) | −4.02726 | + | 5.54305i | −0.503408 | + | 0.692882i | ||||
\(9\) | 0.927051 | + | 2.85317i | 0.103006 | + | 0.317019i | ||||
\(10\) | − | 19.2609i | − | 1.92609i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.57091 | −0.130909 | ||||||||
\(13\) | −10.6087 | + | 3.44698i | −0.816055 | + | 0.265152i | −0.687160 | − | 0.726506i | \(-0.741143\pi\) |
−0.128895 | + | 0.991658i | \(0.541143\pi\) | |||||||
\(14\) | −11.9567 | − | 8.68708i | −0.854053 | − | 0.620506i | ||||
\(15\) | −12.1840 | + | 8.85218i | −0.812265 | + | 0.590145i | ||||
\(16\) | −5.81115 | + | 17.8849i | −0.363197 | + | 1.11780i | ||||
\(17\) | −7.44380 | − | 2.41864i | −0.437870 | − | 0.142273i | 0.0817825 | − | 0.996650i | \(-0.473939\pi\) |
−0.519653 | + | 0.854377i | \(0.673939\pi\) | |||||||
\(18\) | 3.90613 | + | 5.37632i | 0.217007 | + | 0.298685i | ||||
\(19\) | 4.96218 | − | 6.82986i | 0.261168 | − | 0.359466i | −0.658216 | − | 0.752829i | \(-0.728688\pi\) |
0.919383 | + | 0.393363i | \(0.128688\pi\) | |||||||
\(20\) | −2.43693 | − | 7.50009i | −0.121846 | − | 0.375005i | ||||
\(21\) | 11.5561i | 0.550288i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.30611 | 0.404613 | 0.202307 | − | 0.979322i | \(-0.435156\pi\) | ||||
0.202307 | + | 0.979322i | \(0.435156\pi\) | |||||||
\(24\) | 11.2865 | − | 3.66720i | 0.470270 | − | 0.152800i | ||||
\(25\) | −40.9390 | − | 29.7439i | −1.63756 | − | 1.18976i | ||||
\(26\) | −19.9904 | + | 14.5238i | −0.768860 | + | 0.558610i | ||||
\(27\) | 1.60570 | − | 4.94183i | 0.0594703 | − | 0.183031i | ||||
\(28\) | −5.75499 | − | 1.86991i | −0.205535 | − | 0.0667825i | ||||
\(29\) | −4.21943 | − | 5.80755i | −0.145498 | − | 0.200260i | 0.730048 | − | 0.683396i | \(-0.239498\pi\) |
−0.875545 | + | 0.483136i | \(0.839498\pi\) | |||||||
\(30\) | −19.6090 | + | 26.9895i | −0.653635 | + | 0.899651i | ||||
\(31\) | −8.47458 | − | 26.0821i | −0.273374 | − | 0.841357i | −0.989645 | − | 0.143536i | \(-0.954153\pi\) |
0.716272 | − | 0.697822i | \(-0.245847\pi\) | |||||||
\(32\) | 14.2504i | 0.445326i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.3378 | −0.509936 | ||||||||
\(35\) | −55.1729 | + | 17.9268i | −1.57637 | + | 0.512193i | ||||
\(36\) | 2.20125 | + | 1.59930i | 0.0611457 | + | 0.0444250i | ||||
\(37\) | 42.8306 | − | 31.1183i | 1.15758 | − | 0.841035i | 0.168114 | − | 0.985768i | \(-0.446232\pi\) |
0.989471 | + | 0.144733i | \(0.0462323\pi\) | |||||||
\(38\) | 5.77887 | − | 17.7855i | 0.152076 | − | 0.468040i | ||||
\(39\) | 18.3748 | + | 5.97035i | 0.471150 | + | 0.153086i | ||||
\(40\) | 35.0172 | + | 48.1970i | 0.875429 | + | 1.20492i | ||||
\(41\) | −28.1276 | + | 38.7143i | −0.686039 | + | 0.944252i | −0.999987 | − | 0.00518868i | \(-0.998348\pi\) |
0.313948 | + | 0.949440i | \(0.398348\pi\) | |||||||
\(42\) | 7.91040 | + | 24.3457i | 0.188343 | + | 0.579660i | ||||
\(43\) | − | 45.8381i | − | 1.06600i | −0.846114 | − | 0.533002i | \(-0.821064\pi\) | ||
0.846114 | − | 0.533002i | \(-0.178936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.0851 | 0.579668 | ||||||||
\(46\) | 19.6056 | − | 6.37026i | 0.426209 | − | 0.138484i | ||||
\(47\) | 13.0073 | + | 9.45032i | 0.276750 | + | 0.201071i | 0.717499 | − | 0.696560i | \(-0.245287\pi\) |
−0.440749 | + | 0.897631i | \(0.645287\pi\) | |||||||
\(48\) | 26.3510 | − | 19.1452i | 0.548980 | − | 0.398857i | ||||
\(49\) | 1.38621 | − | 4.26632i | 0.0282900 | − | 0.0870677i | ||||
\(50\) | −106.609 | − | 34.6393i | −2.13217 | − | 0.692785i | ||||
\(51\) | 7.96833 | + | 10.9675i | 0.156242 | + | 0.215048i | ||||
\(52\) | −5.94655 | + | 8.18472i | −0.114357 | + | 0.157398i | ||||
\(53\) | −16.9750 | − | 52.2436i | −0.320283 | − | 0.985728i | −0.973525 | − | 0.228580i | \(-0.926592\pi\) |
0.653243 | − | 0.757149i | \(-0.273408\pi\) | |||||||
\(54\) | − | 11.5103i | − | 0.213155i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 45.7131 | 0.816305 | ||||||||
\(57\) | −13.9066 | + | 4.51853i | −0.243976 | + | 0.0792725i | ||||
\(58\) | −12.8647 | − | 9.34674i | −0.221805 | − | 0.161151i | ||||
\(59\) | 57.6112 | − | 41.8570i | 0.976460 | − | 0.709440i | 0.0195456 | − | 0.999809i | \(-0.493778\pi\) |
0.956915 | + | 0.290369i | \(0.0937781\pi\) | |||||||
\(60\) | −4.22088 | + | 12.9905i | −0.0703480 | + | 0.216509i | ||||
\(61\) | −1.23762 | − | 0.402127i | −0.0202889 | − | 0.00659225i | 0.298855 | − | 0.954299i | \(-0.403395\pi\) |
−0.319144 | + | 0.947706i | \(0.603395\pi\) | |||||||
\(62\) | −35.7076 | − | 49.1473i | −0.575929 | − | 0.792699i | ||||
\(63\) | 11.7649 | − | 16.1930i | 0.186745 | − | 0.257032i | ||||
\(64\) | −13.4898 | − | 41.5174i | −0.210779 | − | 0.648710i | ||||
\(65\) | 96.9901i | 1.49216i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −28.9406 | −0.431949 | −0.215975 | − | 0.976399i | \(-0.569293\pi\) | ||||
−0.215975 | + | 0.976399i | \(0.569293\pi\) | |||||||
\(68\) | −6.75125 | + | 2.19361i | −0.0992831 | + | 0.0322590i | ||||
\(69\) | −13.0403 | − | 9.47431i | −0.188989 | − | 0.137309i | ||||
\(70\) | −103.964 | + | 75.5344i | −1.48520 | + | 1.07906i | ||||
\(71\) | 6.81447 | − | 20.9728i | 0.0959784 | − | 0.295391i | −0.891529 | − | 0.452964i | \(-0.850367\pi\) |
0.987507 | + | 0.157572i | \(0.0503668\pi\) | |||||||
\(72\) | −19.5488 | − | 6.35178i | −0.271510 | − | 0.0882191i | ||||
\(73\) | 73.6065 | + | 101.311i | 1.00831 | + | 1.38782i | 0.920086 | + | 0.391717i | \(0.128119\pi\) |
0.0882227 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(74\) | 68.9322 | − | 94.8770i | 0.931516 | − | 1.28212i | ||||
\(75\) | 27.0846 | + | 83.3579i | 0.361128 | + | 1.11144i | ||||
\(76\) | − | 7.65674i | − | 0.100747i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 42.7980 | 0.548693 | ||||||||
\(79\) | 40.7779 | − | 13.2495i | 0.516175 | − | 0.167716i | −0.0393335 | − | 0.999226i | \(-0.512523\pi\) |
0.555509 | + | 0.831511i | \(0.312523\pi\) | |||||||
\(80\) | 132.284 | + | 96.1101i | 1.65355 | + | 1.20138i | ||||
\(81\) | −7.28115 | + | 5.29007i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −32.7569 | + | 100.815i | −0.399474 | + | 1.22946i | ||||
\(83\) | 126.694 | + | 41.1653i | 1.52643 | + | 0.495968i | 0.947595 | − | 0.319475i | \(-0.103506\pi\) |
0.578838 | + | 0.815443i | \(0.303506\pi\) | |||||||
\(84\) | 6.16053 | + | 8.47924i | 0.0733396 | + | 0.100943i | ||||
\(85\) | −40.0016 | + | 55.0575i | −0.470607 | + | 0.647735i | ||||
\(86\) | −31.3773 | − | 96.5694i | −0.364852 | − | 1.12290i | ||||
\(87\) | 12.4336i | 0.142915i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.48441 | −0.106566 | −0.0532832 | − | 0.998579i | \(-0.516969\pi\) | ||||
−0.0532832 | + | 0.998579i | \(0.516969\pi\) | |||||||
\(90\) | 54.9547 | − | 17.8559i | 0.610608 | − | 0.198398i | ||||
\(91\) | 60.2093 | + | 43.7446i | 0.661640 | + | 0.480710i | ||||
\(92\) | 6.82834 | − | 4.96108i | 0.0742211 | − | 0.0539248i | ||||
\(93\) | −14.6784 | + | 45.1755i | −0.157832 | + | 0.485758i | ||||
\(94\) | 33.8720 | + | 11.0057i | 0.360340 | + | 0.117082i | ||||
\(95\) | −43.1463 | − | 59.3858i | −0.454172 | − | 0.625114i | ||||
\(96\) | 14.5080 | − | 19.9685i | 0.151125 | − | 0.208006i | ||||
\(97\) | 48.2128 | + | 148.384i | 0.497039 | + | 1.52973i | 0.813755 | + | 0.581208i | \(0.197420\pi\) |
−0.316716 | + | 0.948520i | \(0.602580\pi\) | |||||||
\(98\) | − | 9.93695i | − | 0.101397i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −45.8954 | −0.458954 | ||||||||
\(101\) | −52.3806 | + | 17.0195i | −0.518620 | + | 0.168510i | −0.556619 | − | 0.830768i | \(-0.687902\pi\) |
0.0379991 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(102\) | 24.2948 | + | 17.6512i | 0.238184 | + | 0.173051i | ||||
\(103\) | 65.5447 | − | 47.6210i | 0.636356 | − | 0.462340i | −0.222240 | − | 0.974992i | \(-0.571337\pi\) |
0.858596 | + | 0.512652i | \(0.171337\pi\) | |||||||
\(104\) | 23.6173 | − | 72.6866i | 0.227090 | − | 0.698910i | ||||
\(105\) | 95.5623 | + | 31.0501i | 0.910117 | + | 0.295715i | ||||
\(106\) | −71.5240 | − | 98.4443i | −0.674755 | − | 0.928720i | ||||
\(107\) | 45.9640 | − | 63.2641i | 0.429571 | − | 0.591253i | −0.538284 | − | 0.842763i | \(-0.680927\pi\) |
0.967855 | + | 0.251510i | \(0.0809272\pi\) | |||||||
\(108\) | −1.45631 | − | 4.48206i | −0.0134844 | − | 0.0415006i | ||||
\(109\) | 2.67841i | 0.0245725i | 0.999925 | + | 0.0122863i | \(0.00391094\pi\) | ||||
−0.999925 | + | 0.0122863i | \(0.996089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −91.6975 | −0.826104 | ||||||||
\(112\) | 119.326 | − | 38.7713i | 1.06541 | − | 0.346173i | ||||
\(113\) | −149.025 | − | 108.273i | −1.31881 | − | 0.958171i | −0.999946 | − | 0.0103704i | \(-0.996699\pi\) |
−0.318863 | − | 0.947801i | \(-0.603301\pi\) | |||||||
\(114\) | −26.2047 | + | 19.0388i | −0.229866 | + | 0.167007i | ||||
\(115\) | 25.0047 | − | 76.9565i | 0.217432 | − | 0.669187i | ||||
\(116\) | −6.19200 | − | 2.01190i | −0.0533793 | − | 0.0173440i | ||||
\(117\) | −19.6696 | − | 27.0729i | −0.168117 | − | 0.231393i | ||||
\(118\) | 92.7201 | − | 127.618i | 0.785764 | − | 1.08151i | ||||
\(119\) | 16.1369 | + | 49.6642i | 0.135604 | + | 0.417346i | ||||
\(120\) | − | 103.186i | − | 0.859887i | ||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.88262 | −0.0236280 | ||||||||
\(123\) | 78.8281 | − | 25.6128i | 0.640879 | − | 0.208234i | ||||
\(124\) | −20.1226 | − | 14.6199i | −0.162279 | − | 0.117902i | ||||
\(125\) | −180.105 | + | 130.854i | −1.44084 | + | 1.04683i | ||||
\(126\) | 13.7012 | − | 42.1680i | 0.108740 | − | 0.334667i | ||||
\(127\) | 113.277 | + | 36.8060i | 0.891947 | + | 0.289811i | 0.718909 | − | 0.695104i | \(-0.244642\pi\) |
0.173038 | + | 0.984915i | \(0.444642\pi\) | |||||||
\(128\) | −90.3441 | − | 124.348i | −0.705813 | − | 0.971469i | ||||
\(129\) | −46.6666 | + | 64.2311i | −0.361757 | + | 0.497915i | ||||
\(130\) | 66.3921 | + | 204.334i | 0.510708 | + | 1.57180i | ||||
\(131\) | 17.9999i | 0.137403i | 0.997637 | + | 0.0687017i | \(0.0218857\pi\) | ||||
−0.997637 | + | 0.0687017i | \(0.978114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56.3253 | −0.423498 | ||||||||
\(134\) | −60.9706 | + | 19.8105i | −0.455004 | + | 0.147840i | ||||
\(135\) | −36.5519 | − | 26.5565i | −0.270755 | − | 0.196715i | ||||
\(136\) | 43.3848 | − | 31.5209i | 0.319006 | − | 0.231771i | ||||
\(137\) | 28.6028 | − | 88.0304i | 0.208780 | − | 0.642558i | −0.790757 | − | 0.612130i | \(-0.790313\pi\) |
0.999537 | − | 0.0304278i | \(-0.00968697\pi\) | |||||||
\(138\) | −33.9579 | − | 11.0336i | −0.246072 | − | 0.0799537i | ||||
\(139\) | −127.442 | − | 175.408i | −0.916847 | − | 1.26193i | −0.964774 | − | 0.263081i | \(-0.915261\pi\) |
0.0479268 | − | 0.998851i | \(-0.484739\pi\) | |||||||
\(140\) | −30.9263 | + | 42.5664i | −0.220902 | + | 0.304046i | ||||
\(141\) | −8.60540 | − | 26.4847i | −0.0610312 | − | 0.187835i | ||||
\(142\) | − | 48.8490i | − | 0.344007i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −56.4158 | −0.391776 | ||||||||
\(145\) | −59.3625 | + | 19.2880i | −0.409397 | + | 0.133021i | ||||
\(146\) | 224.420 | + | 163.051i | 1.53712 | + | 1.11679i | ||||
\(147\) | −6.28586 | + | 4.56695i | −0.0427610 | + | 0.0310677i | ||||
\(148\) | 14.8378 | − | 45.6660i | 0.100255 | − | 0.308554i | ||||
\(149\) | −133.834 | − | 43.4853i | −0.898214 | − | 0.291847i | −0.176714 | − | 0.984262i | \(-0.556547\pi\) |
−0.721500 | + | 0.692415i | \(0.756547\pi\) | |||||||
\(150\) | 114.121 | + | 157.074i | 0.760806 | + | 1.04716i | ||||
\(151\) | 6.76470 | − | 9.31081i | 0.0447994 | − | 0.0616610i | −0.786030 | − | 0.618189i | \(-0.787867\pi\) |
0.830829 | + | 0.556528i | \(0.187867\pi\) | |||||||
\(152\) | 17.8743 | + | 55.0113i | 0.117594 | + | 0.361917i | ||||
\(153\) | − | 23.4806i | − | 0.153468i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −238.455 | −1.53842 | ||||||||
\(156\) | 16.6653 | − | 5.41488i | 0.106829 | − | 0.0347108i | ||||
\(157\) | 121.134 | + | 88.0087i | 0.771551 | + | 0.560565i | 0.902432 | − | 0.430833i | \(-0.141780\pi\) |
−0.130880 | + | 0.991398i | \(0.541780\pi\) | |||||||
\(158\) | 76.8391 | − | 55.8269i | 0.486323 | − | 0.353335i | ||||
\(159\) | −29.4015 | + | 90.4886i | −0.184915 | + | 0.569110i | ||||
\(160\) | 117.843 | + | 38.2896i | 0.736521 | + | 0.239310i | ||||
\(161\) | −36.4952 | − | 50.2313i | −0.226678 | − | 0.311996i | ||||
\(162\) | −11.7184 | + | 16.1290i | −0.0723357 | + | 0.0995615i | ||||
\(163\) | −16.9395 | − | 52.1343i | −0.103923 | − | 0.319842i | 0.885553 | − | 0.464538i | \(-0.153780\pi\) |
−0.989476 | + | 0.144696i | \(0.953780\pi\) | |||||||
\(164\) | 43.4014i | 0.264643i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 295.091 | 1.77766 | ||||||||
\(167\) | −40.8400 | + | 13.2697i | −0.244551 | + | 0.0794594i | −0.428728 | − | 0.903434i | \(-0.641038\pi\) |
0.184177 | + | 0.982893i | \(0.441038\pi\) | |||||||
\(168\) | −64.0558 | − | 46.5393i | −0.381285 | − | 0.277020i | ||||
\(169\) | −36.0606 | + | 26.1996i | −0.213376 | + | 0.155027i | ||||
\(170\) | −46.5852 | + | 143.374i | −0.274030 | + | 0.843379i | ||||
\(171\) | 24.0870 | + | 7.82632i | 0.140859 | + | 0.0457680i | ||||
\(172\) | −24.4363 | − | 33.6337i | −0.142071 | − | 0.195545i | ||||
\(173\) | 9.54745 | − | 13.1409i | 0.0551876 | − | 0.0759592i | −0.780531 | − | 0.625117i | \(-0.785051\pi\) |
0.835719 | + | 0.549158i | \(0.185051\pi\) | |||||||
\(174\) | 8.51108 | + | 26.1944i | 0.0489142 | + | 0.150543i | ||||
\(175\) | 337.620i | 1.92926i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −123.342 | −0.696845 | ||||||||
\(178\) | −19.9813 | + | 6.49231i | −0.112254 | + | 0.0364736i | ||||
\(179\) | −105.458 | − | 76.6195i | −0.589149 | − | 0.428042i | 0.252862 | − | 0.967502i | \(-0.418628\pi\) |
−0.842011 | + | 0.539461i | \(0.818628\pi\) | |||||||
\(180\) | 19.1399 | − | 13.9059i | 0.106333 | − | 0.0772552i | ||||
\(181\) | −31.3778 | + | 96.5709i | −0.173358 | + | 0.533541i | −0.999555 | − | 0.0298408i | \(-0.990500\pi\) |
0.826197 | + | 0.563382i | \(0.190500\pi\) | |||||||
\(182\) | 156.790 | + | 50.9442i | 0.861483 | + | 0.279913i | ||||
\(183\) | 1.32483 | + | 1.82347i | 0.00723951 | + | 0.00996433i | ||||
\(184\) | −37.4782 | + | 51.5843i | −0.203686 | + | 0.280349i | ||||
\(185\) | −142.249 | − | 437.798i | −0.768915 | − | 2.36648i | ||||
\(186\) | 105.221i | 0.565705i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 14.5820 | 0.0775639 | ||||||||
\(189\) | −32.9714 | + | 10.7131i | −0.174452 | + | 0.0566828i | ||||
\(190\) | −131.549 | − | 95.5763i | −0.692365 | − | 0.503033i | ||||
\(191\) | 130.878 | − | 95.0887i | 0.685227 | − | 0.497847i | −0.189860 | − | 0.981811i | \(-0.560804\pi\) |
0.875088 | + | 0.483964i | \(0.160804\pi\) | |||||||
\(192\) | −23.3651 | + | 71.9103i | −0.121693 | + | 0.374533i | ||||
\(193\) | −32.5181 | − | 10.5658i | −0.168488 | − | 0.0547450i | 0.223558 | − | 0.974691i | \(-0.428233\pi\) |
−0.392046 | + | 0.919946i | \(0.628233\pi\) | |||||||
\(194\) | 203.144 | + | 279.604i | 1.04714 | + | 1.44126i | ||||
\(195\) | 98.7431 | − | 135.908i | 0.506375 | − | 0.696965i | ||||
\(196\) | −1.25724 | − | 3.86939i | −0.00641449 | − | 0.0197418i | ||||
\(197\) | − | 61.8792i | − | 0.314107i | −0.987590 | − | 0.157054i | \(-0.949800\pi\) | ||
0.987590 | − | 0.157054i | \(-0.0501996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 238.301 | 1.19749 | 0.598747 | − | 0.800938i | \(-0.295666\pi\) | ||||
0.598747 | + | 0.800938i | \(0.295666\pi\) | |||||||
\(200\) | 329.745 | − | 107.140i | 1.64872 | − | 0.535702i | ||||
\(201\) | 40.5533 | + | 29.4637i | 0.201758 | + | 0.146585i | ||||
\(202\) | −98.7025 | + | 71.7116i | −0.488626 | + | 0.355008i | ||||
\(203\) | −14.8002 | + | 45.5502i | −0.0729072 | + | 0.224385i | ||||
\(204\) | 11.6935 | + | 3.79945i | 0.0573211 | + | 0.0186248i | ||||
\(205\) | 244.570 | + | 336.622i | 1.19302 | + | 1.64206i | ||||
\(206\) | 105.488 | − | 145.192i | 0.512080 | − | 0.704817i | ||||
\(207\) | 8.62724 | + | 26.5519i | 0.0416775 | + | 0.128270i | ||||
\(208\) | − | 209.767i | − | 1.00849i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 222.580 | 1.05991 | ||||||||
\(211\) | −179.220 | + | 58.2321i | −0.849384 | + | 0.275982i | −0.701188 | − | 0.712976i | \(-0.747347\pi\) |
−0.148196 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(212\) | −40.3064 | − | 29.2843i | −0.190124 | − | 0.138134i | ||||
\(213\) | −30.9007 | + | 22.4506i | −0.145074 | + | 0.105402i | ||||
\(214\) | 53.5289 | − | 164.745i | 0.250135 | − | 0.769837i | ||||
\(215\) | −379.057 | − | 123.163i | −1.76305 | − | 0.572851i | ||||
\(216\) | 20.9263 | + | 28.8026i | 0.0968809 | + | 0.133345i | ||||
\(217\) | −107.548 | + | 148.028i | −0.495614 | + | 0.682154i | ||||
\(218\) | 1.83343 | + | 5.64273i | 0.00841024 | + | 0.0258841i | ||||
\(219\) | − | 216.899i | − | 0.990408i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 87.3062 | 0.395050 | ||||||||
\(222\) | −193.184 | + | 62.7692i | −0.870196 | + | 0.282744i | ||||
\(223\) | 208.939 | + | 151.803i | 0.936947 | + | 0.680732i | 0.947684 | − | 0.319210i | \(-0.103418\pi\) |
−0.0107365 | + | 0.999942i | \(0.503418\pi\) | |||||||
\(224\) | 76.9192 | − | 55.8851i | 0.343389 | − | 0.249487i | ||||
\(225\) | 46.9119 | − | 144.380i | 0.208497 | − | 0.641689i | ||||
\(226\) | −388.075 | − | 126.093i | −1.71715 | − | 0.557934i | ||||
\(227\) | 26.0441 | + | 35.8466i | 0.114732 | + | 0.157914i | 0.862521 | − | 0.506022i | \(-0.168885\pi\) |
−0.747789 | + | 0.663936i | \(0.768885\pi\) | |||||||
\(228\) | −7.79513 | + | 10.7291i | −0.0341891 | + | 0.0470573i | ||||
\(229\) | −1.18625 | − | 3.65089i | −0.00518011 | − | 0.0159427i | 0.948433 | − | 0.316978i | \(-0.102668\pi\) |
−0.953613 | + | 0.301035i | \(0.902668\pi\) | |||||||
\(230\) | − | 179.244i | − | 0.779323i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 49.1843 | 0.212001 | ||||||||
\(233\) | −229.530 | + | 74.5789i | −0.985109 | + | 0.320081i | −0.756900 | − | 0.653531i | \(-0.773287\pi\) |
−0.228209 | + | 0.973612i | \(0.573287\pi\) | |||||||
\(234\) | −59.9711 | − | 43.5715i | −0.256287 | − | 0.186203i | ||||
\(235\) | 113.098 | − | 82.1708i | 0.481270 | − | 0.349663i | ||||
\(236\) | 19.9582 | − | 61.4250i | 0.0845685 | − | 0.260275i | ||||
\(237\) | −70.6293 | − | 22.9489i | −0.298014 | − | 0.0968306i | ||||
\(238\) | 67.9927 | + | 93.5839i | 0.285684 | + | 0.393210i | ||||
\(239\) | −272.376 | + | 374.893i | −1.13965 | + | 1.56859i | −0.371353 | + | 0.928492i | \(0.621106\pi\) |
−0.768294 | + | 0.640098i | \(0.778894\pi\) | |||||||
\(240\) | −87.5172 | − | 269.350i | −0.364655 | − | 1.12229i | ||||
\(241\) | 447.213i | 1.85565i | 0.373011 | + | 0.927827i | \(0.378325\pi\) | ||||
−0.373011 | + | 0.927827i | \(0.621675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | −1.12248 | + | 0.364714i | −0.00460031 | + | 0.00149473i | ||||
\(245\) | −31.5555 | − | 22.9264i | −0.128798 | − | 0.0935772i | ||||
\(246\) | 148.538 | − | 107.919i | 0.603814 | − | 0.438697i | ||||
\(247\) | −29.1000 | + | 89.5606i | −0.117814 | + | 0.362594i | ||||
\(248\) | 178.704 | + | 58.0644i | 0.720580 | + | 0.234131i | ||||
\(249\) | −135.622 | − | 186.667i | −0.544665 | − | 0.749667i | ||||
\(250\) | −289.863 | + | 398.963i | −1.15945 | + | 1.59585i | ||||
\(251\) | 117.622 | + | 362.002i | 0.468612 | + | 1.44224i | 0.854383 | + | 0.519645i | \(0.173936\pi\) |
−0.385771 | + | 0.922595i | \(0.626064\pi\) | |||||||
\(252\) | − | 18.1535i | − | 0.0720376i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 263.841 | 1.03875 | ||||||||
\(255\) | 112.105 | − | 36.4252i | 0.439628 | − | 0.142844i | ||||
\(256\) | −134.184 | − | 97.4906i | −0.524157 | − | 0.380823i | ||||
\(257\) | −2.69498 | + | 1.95802i | −0.0104863 | + | 0.00761874i | −0.593016 | − | 0.805191i | \(-0.702063\pi\) |
0.582530 | + | 0.812809i | \(0.302063\pi\) | |||||||
\(258\) | −54.3471 | + | 167.263i | −0.210648 | + | 0.648307i | ||||
\(259\) | −335.933 | − | 109.151i | −1.29704 | − | 0.421433i | ||||
\(260\) | 51.7054 | + | 71.1663i | 0.198867 | + | 0.273717i | ||||
\(261\) | 12.6583 | − | 17.4226i | 0.0484992 | − | 0.0667534i | ||||
\(262\) | 12.3213 | + | 37.9212i | 0.0470280 | + | 0.144737i | ||||
\(263\) | − | 379.793i | − | 1.44408i | −0.691850 | − | 0.722041i | \(-0.743204\pi\) | ||
0.691850 | − | 0.722041i | \(-0.256796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −477.636 | −1.80240 | ||||||||
\(266\) | −118.663 | + | 38.5560i | −0.446102 | + | 0.144947i | ||||
\(267\) | 13.2901 | + | 9.65583i | 0.0497757 | + | 0.0361641i | ||||
\(268\) | −21.2351 | + | 15.4282i | −0.0792355 | + | 0.0575680i | ||||
\(269\) | −57.8531 | + | 178.053i | −0.215067 | + | 0.661909i | 0.784082 | + | 0.620658i | \(0.213134\pi\) |
−0.999149 | + | 0.0412510i | \(0.986866\pi\) | |||||||
\(270\) | −95.1843 | − | 30.9273i | −0.352534 | − | 0.114545i | ||||
\(271\) | −179.367 | − | 246.878i | −0.661872 | − | 0.910988i | 0.337670 | − | 0.941265i | \(-0.390361\pi\) |
−0.999542 | + | 0.0302763i | \(0.990361\pi\) | |||||||
\(272\) | 86.5140 | − | 119.076i | 0.318066 | − | 0.437781i | ||||
\(273\) | −39.8335 | − | 122.595i | −0.145910 | − | 0.449066i | ||||
\(274\) | − | 205.037i | − | 0.748311i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.6190 | −0.0529675 | ||||||||
\(277\) | 456.671 | − | 148.381i | 1.64863 | − | 0.535673i | 0.670189 | − | 0.742190i | \(-0.266213\pi\) |
0.978443 | + | 0.206517i | \(0.0662129\pi\) | |||||||
\(278\) | −388.559 | − | 282.305i | −1.39769 | − | 1.01548i | ||||
\(279\) | 66.5602 | − | 48.3588i | 0.238567 | − | 0.173329i | ||||
\(280\) | 122.827 | − | 378.022i | 0.438668 | − | 1.35008i | ||||
\(281\) | −8.61488 | − | 2.79915i | −0.0306579 | − | 0.00996137i | 0.293648 | − | 0.955914i | \(-0.405131\pi\) |
−0.324306 | + | 0.945952i | \(0.605131\pi\) | |||||||
\(282\) | −36.2588 | − | 49.9060i | −0.128577 | − | 0.176972i | ||||
\(283\) | 156.764 | − | 215.768i | 0.553938 | − | 0.762430i | −0.436602 | − | 0.899655i | \(-0.643818\pi\) |
0.990540 | + | 0.137224i | \(0.0438181\pi\) | |||||||
\(284\) | −6.18047 | − | 19.0215i | −0.0217622 | − | 0.0669772i | ||||
\(285\) | 127.141i | 0.446109i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 319.274 | 1.11245 | ||||||||
\(288\) | −40.6589 | + | 13.2109i | −0.141177 | + | 0.0458711i | ||||
\(289\) | −184.246 | − | 133.862i | −0.637528 | − | 0.463191i | ||||
\(290\) | −111.859 | + | 81.2701i | −0.385720 | + | 0.280242i | ||||
\(291\) | 83.5070 | − | 257.008i | 0.286966 | − | 0.883189i | ||||
\(292\) | 108.017 | + | 35.0970i | 0.369922 | + | 0.120195i | ||||
\(293\) | 100.061 | + | 137.722i | 0.341506 | + | 0.470042i | 0.944880 | − | 0.327415i | \(-0.106178\pi\) |
−0.603375 | + | 0.797458i | \(0.706178\pi\) | |||||||
\(294\) | −10.1165 | + | 13.9242i | −0.0344100 | + | 0.0473613i | ||||
\(295\) | −191.338 | − | 588.879i | −0.648605 | − | 1.99620i | ||||
\(296\) | 362.734i | 1.22545i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −311.721 | −1.04604 | ||||||||
\(299\) | −98.7259 | + | 32.0780i | −0.330187 | + | 0.107284i | ||||
\(300\) | 64.3113 | + | 46.7249i | 0.214371 | + | 0.155750i | ||||
\(301\) | −247.419 | + | 179.761i | −0.821991 | + | 0.597211i | ||||
\(302\) | 7.87805 | − | 24.2461i | 0.0260863 | − | 0.0802853i | ||||
\(303\) | 90.7259 | + | 29.4786i | 0.299425 | + | 0.0972892i | ||||
\(304\) | 93.3152 | + | 128.437i | 0.306958 | + | 0.422491i | ||||
\(305\) | −6.65075 | + | 9.15397i | −0.0218057 | + | 0.0300130i | ||||
\(306\) | −16.0730 | − | 49.4678i | −0.0525263 | − | 0.161659i | ||||
\(307\) | − | 228.869i | − | 0.745501i | −0.927932 | − | 0.372750i | \(-0.878415\pi\) | ||
0.927932 | − | 0.372750i | \(-0.121585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −140.327 | −0.454132 | ||||||||
\(310\) | −502.365 | + | 163.228i | −1.62053 | + | 0.526543i | ||||
\(311\) | −228.596 | − | 166.085i | −0.735036 | − | 0.534035i | 0.156117 | − | 0.987739i | \(-0.450102\pi\) |
−0.891153 | + | 0.453704i | \(0.850102\pi\) | |||||||
\(312\) | −107.094 | + | 77.8086i | −0.343251 | + | 0.249386i | ||||
\(313\) | −108.210 | + | 333.037i | −0.345719 | + | 1.06402i | 0.615478 | + | 0.788154i | \(0.288963\pi\) |
−0.961198 | + | 0.275861i | \(0.911037\pi\) | |||||||
\(314\) | 315.442 | + | 102.493i | 1.00459 | + | 0.326412i | ||||
\(315\) | −102.296 | − | 140.799i | −0.324750 | − | 0.446980i | ||||
\(316\) | 22.8574 | − | 31.4605i | 0.0723335 | − | 0.0995585i | ||||
\(317\) | 115.700 | + | 356.089i | 0.364986 | + | 1.12331i | 0.949990 | + | 0.312280i | \(0.101093\pi\) |
−0.585004 | + | 0.811030i | \(0.698907\pi\) | |||||||
\(318\) | 210.763i | 0.662776i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −379.572 | −1.18616 | ||||||||
\(321\) | −128.815 | + | 41.8545i | −0.401293 | + | 0.130388i | ||||
\(322\) | −111.271 | − | 80.8429i | −0.345561 | − | 0.251065i | ||||
\(323\) | −53.4564 | + | 38.8384i | −0.165500 | + | 0.120243i | ||||
\(324\) | −2.52240 | + | 7.76316i | −0.00778519 | + | 0.0239604i | ||||
\(325\) | 536.837 | + | 174.429i | 1.65181 | + | 0.536705i | ||||
\(326\) | −71.3744 | − | 98.2384i | −0.218940 | − | 0.301345i | ||||
\(327\) | 2.72681 | − | 3.75314i | 0.00833888 | − | 0.0114775i | ||||
\(328\) | −101.318 | − | 311.826i | −0.308897 | − | 0.950688i | ||||
\(329\) | − | 107.270i | − | 0.326048i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 262.925 | 0.794334 | 0.397167 | − | 0.917746i | \(-0.369993\pi\) | ||||
0.397167 | + | 0.917746i | \(0.369993\pi\) | |||||||
\(332\) | 114.907 | − | 37.3354i | 0.346104 | − | 0.112456i | ||||
\(333\) | 128.492 | + | 93.3548i | 0.385862 | + | 0.280345i | ||||
\(334\) | −76.9561 | + | 55.9119i | −0.230408 | + | 0.167401i | ||||
\(335\) | −77.7608 | + | 239.323i | −0.232122 | + | 0.714397i | ||||
\(336\) | −206.679 | − | 67.1539i | −0.615115 | − | 0.199863i | ||||
\(337\) | −18.5752 | − | 25.5665i | −0.0551192 | − | 0.0758650i | 0.780568 | − | 0.625071i | \(-0.214930\pi\) |
−0.835687 | + | 0.549206i | \(0.814930\pi\) | |||||||
\(338\) | −58.0364 | + | 79.8803i | −0.171705 | + | 0.236332i | ||||
\(339\) | 98.5929 | + | 303.438i | 0.290835 | + | 0.895097i | ||||
\(340\) | 61.7232i | 0.181539i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 56.1025 | 0.164042 | ||||||||
\(343\) | −339.386 | + | 110.273i | −0.989464 | + | 0.321497i | ||||
\(344\) | 254.083 | + | 184.602i | 0.738614 | + | 0.536635i | ||||
\(345\) | −113.385 | + | 82.3793i | −0.328653 | + | 0.238781i | ||||
\(346\) | 11.1188 | − | 34.2201i | 0.0321352 | − | 0.0989020i | ||||
\(347\) | 393.282 | + | 127.785i | 1.13338 | + | 0.368257i | 0.814859 | − | 0.579659i | \(-0.196814\pi\) |
0.318520 | + | 0.947916i | \(0.396814\pi\) | |||||||
\(348\) | 6.62833 | + | 9.12311i | 0.0190469 | + | 0.0262158i | ||||
\(349\) | 215.843 | − | 297.082i | 0.618460 | − | 0.851237i | −0.378780 | − | 0.925487i | \(-0.623656\pi\) |
0.997240 | + | 0.0742497i | \(0.0236562\pi\) | |||||||
\(350\) | 231.109 | + | 711.281i | 0.660312 | + | 2.03223i | ||||
\(351\) | 57.9614i | 0.165132i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −415.577 | −1.17727 | −0.588636 | − | 0.808398i | \(-0.700335\pi\) | ||||
−0.588636 | + | 0.808398i | \(0.700335\pi\) | |||||||
\(354\) | −259.850 | + | 84.4303i | −0.734039 | + | 0.238504i | ||||
\(355\) | −155.124 | − | 112.704i | −0.436968 | − | 0.317476i | ||||
\(356\) | −6.95917 | + | 5.05613i | −0.0195482 | + | 0.0142026i | ||||
\(357\) | 27.9499 | − | 86.0209i | 0.0782910 | − | 0.240955i | ||||
\(358\) | −274.621 | − | 89.2297i | −0.767097 | − | 0.249245i | ||||
\(359\) | 90.9611 | + | 125.197i | 0.253374 | + | 0.348739i | 0.916689 | − | 0.399601i | \(-0.130851\pi\) |
−0.663316 | + | 0.748340i | \(0.730851\pi\) | |||||||
\(360\) | −105.051 | + | 144.591i | −0.291810 | + | 0.401642i | ||||
\(361\) | 89.5314 | + | 275.549i | 0.248009 | + | 0.763295i | ||||
\(362\) | 224.929i | 0.621352i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 67.4987 | 0.185436 | ||||||||
\(365\) | 1035.56 | − | 336.473i | 2.83715 | − | 0.921845i | ||||
\(366\) | 4.03930 | + | 2.93472i | 0.0110363 | + | 0.00801836i | ||||
\(367\) | 88.1312 | − | 64.0311i | 0.240139 | − | 0.174472i | −0.461206 | − | 0.887293i | \(-0.652583\pi\) |
0.701345 | + | 0.712822i | \(0.252583\pi\) | |||||||
\(368\) | −54.0792 | + | 166.439i | −0.146954 | + | 0.452279i | ||||
\(369\) | −136.534 | − | 44.3627i | −0.370011 | − | 0.120224i | ||||
\(370\) | −599.367 | − | 824.958i | −1.61991 | − | 2.22962i | ||||
\(371\) | −215.424 | + | 296.506i | −0.580658 | + | 0.799207i | ||||
\(372\) | 13.3128 | + | 40.9725i | 0.0357870 | + | 0.110141i | ||||
\(373\) | − | 721.229i | − | 1.93359i | −0.255555 | − | 0.966795i | \(-0.582258\pi\) | ||
0.255555 | − | 0.966795i | \(-0.417742\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 385.593 | 1.02825 | ||||||||
\(376\) | −104.767 | + | 34.0410i | −0.278636 | + | 0.0905345i | ||||
\(377\) | 64.7813 | + | 47.0664i | 0.171834 | + | 0.124844i | ||||
\(378\) | −62.1291 | + | 45.1394i | −0.164363 | + | 0.119416i | ||||
\(379\) | −3.99789 | + | 12.3042i | −0.0105485 | + | 0.0324650i | −0.956192 | − | 0.292739i | \(-0.905433\pi\) |
0.945644 | + | 0.325204i | \(0.105433\pi\) | |||||||
\(380\) | −63.3171 | − | 20.5730i | −0.166624 | − | 0.0541394i | ||||
\(381\) | −121.259 | − | 166.899i | −0.318266 | − | 0.438056i | ||||
\(382\) | 210.637 | − | 289.917i | 0.551407 | − | 0.758946i | ||||
\(383\) | −30.7820 | − | 94.7372i | −0.0803707 | − | 0.247356i | 0.902795 | − | 0.430071i | \(-0.141511\pi\) |
−0.983166 | + | 0.182715i | \(0.941511\pi\) | |||||||
\(384\) | 266.221i | 0.693283i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −75.7401 | −0.196218 | ||||||||
\(387\) | 130.784 | − | 42.4943i | 0.337943 | − | 0.109804i | ||||
\(388\) | 114.479 | + | 83.1741i | 0.295050 | + | 0.214366i | ||||
\(389\) | −163.520 | + | 118.805i | −0.420361 | + | 0.305410i | −0.777783 | − | 0.628533i | \(-0.783656\pi\) |
0.357422 | + | 0.933943i | \(0.383656\pi\) | |||||||
\(390\) | 114.994 | − | 353.916i | 0.294857 | − | 0.907478i | ||||
\(391\) | −69.2728 | − | 22.5081i | −0.177168 | − | 0.0575655i | ||||
\(392\) | 18.0658 | + | 24.8654i | 0.0460862 | + | 0.0634322i | ||||
\(393\) | 18.3252 | − | 25.2224i | 0.0466290 | − | 0.0641792i | ||||
\(394\) | −42.3578 | − | 130.364i | −0.107507 | − | 0.330873i | ||||
\(395\) | − | 372.811i | − | 0.943826i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 332.729 | 0.838108 | 0.419054 | − | 0.907961i | \(-0.362362\pi\) | ||||
0.419054 | + | 0.907961i | \(0.362362\pi\) | |||||||
\(398\) | 502.041 | − | 163.123i | 1.26141 | − | 0.409857i | ||||
\(399\) | 78.9262 | + | 57.3433i | 0.197810 | + | 0.143717i | ||||
\(400\) | 769.869 | − | 559.343i | 1.92467 | − | 1.39836i | ||||
\(401\) | 202.987 | − | 624.730i | 0.506202 | − | 1.55793i | −0.292537 | − | 0.956254i | \(-0.594500\pi\) |
0.798740 | − | 0.601677i | \(-0.205500\pi\) | |||||||
\(402\) | 105.604 | + | 34.3129i | 0.262697 | + | 0.0853554i | ||||
\(403\) | 179.809 | + | 247.486i | 0.446176 | + | 0.614108i | ||||
\(404\) | −29.3611 | + | 40.4121i | −0.0726760 | + | 0.100030i | ||||
\(405\) | 24.1822 | + | 74.4251i | 0.0597091 | + | 0.183766i | ||||
\(406\) | 106.094i | 0.261315i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −92.8839 | −0.227657 | ||||||||
\(409\) | 446.099 | − | 144.946i | 1.09071 | − | 0.354392i | 0.292187 | − | 0.956361i | \(-0.405617\pi\) |
0.798519 | + | 0.601969i | \(0.205617\pi\) | |||||||
\(410\) | 745.673 | + | 541.763i | 1.81872 | + | 1.32137i | ||||
\(411\) | −129.701 | + | 94.2336i | −0.315575 | + | 0.229279i | ||||
\(412\) | 22.7066 | − | 69.8837i | 0.0551131 | − | 0.169621i | ||||
\(413\) | −451.860 | − | 146.818i | −1.09409 | − | 0.355492i | ||||
\(414\) | 36.3508 | + | 50.0326i | 0.0878040 | + | 0.120852i | ||||
\(415\) | 680.830 | − | 937.082i | 1.64055 | − | 2.25803i | ||||
\(416\) | −49.1210 | − | 151.179i | −0.118079 | − | 0.363411i | ||||
\(417\) | 375.538i | 0.900570i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 242.229 | 0.578112 | 0.289056 | − | 0.957312i | \(-0.406659\pi\) | ||||
0.289056 | + | 0.957312i | \(0.406659\pi\) | |||||||
\(420\) | 86.6715 | − | 28.1613i | 0.206361 | − | 0.0670506i | ||||
\(421\) | 596.706 | + | 433.532i | 1.41735 | + | 1.02977i | 0.992201 | + | 0.124646i | \(0.0397796\pi\) |
0.425153 | + | 0.905122i | \(0.360220\pi\) | |||||||
\(422\) | −337.710 | + | 245.361i | −0.800262 | + | 0.581424i | ||||
\(423\) | −14.9050 | + | 45.8728i | −0.0352364 | + | 0.108446i | ||||
\(424\) | 357.952 | + | 116.306i | 0.844226 | + | 0.274306i | ||||
\(425\) | 232.802 | + | 320.424i | 0.547769 | + | 0.753940i | ||||
\(426\) | −49.7319 | + | 68.4501i | −0.116742 | + | 0.160681i | ||||
\(427\) | 2.68295 | + | 8.25727i | 0.00628325 | + | 0.0193379i | ||||
\(428\) | − | 70.9233i | − | 0.165709i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −882.885 | −2.05322 | ||||||||
\(431\) | −467.387 | + | 151.863i | −1.08443 | + | 0.352351i | −0.796090 | − | 0.605178i | \(-0.793102\pi\) |
−0.288335 | + | 0.957529i | \(0.593102\pi\) | |||||||
\(432\) | 79.0531 | + | 57.4355i | 0.182993 | + | 0.132952i | ||||
\(433\) | 325.762 | − | 236.680i | 0.752337 | − | 0.546604i | −0.144214 | − | 0.989547i | \(-0.546065\pi\) |
0.896550 | + | 0.442942i | \(0.146065\pi\) | |||||||
\(434\) | −125.249 | + | 385.476i | −0.288592 | + | 0.888194i | ||||
\(435\) | 102.819 | + | 33.4079i | 0.236365 | + | 0.0767997i | ||||
\(436\) | 1.42786 | + | 1.96528i | 0.00327490 | + | 0.00450751i | ||||
\(437\) | 46.1786 | − | 63.5594i | 0.105672 | − | 0.145445i | ||||
\(438\) | −148.473 | − | 456.952i | −0.338979 | − | 1.04327i | ||||
\(439\) | − | 68.4030i | − | 0.155815i | −0.996961 | − | 0.0779077i | \(-0.975176\pi\) | ||
0.996961 | − | 0.0779077i | \(-0.0248240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.4576 | 0.0305161 | ||||||||
\(442\) | 183.932 | − | 59.7632i | 0.416136 | − | 0.135211i | ||||
\(443\) | −253.579 | − | 184.236i | −0.572413 | − | 0.415883i | 0.263568 | − | 0.964641i | \(-0.415101\pi\) |
−0.835981 | + | 0.548758i | \(0.815101\pi\) | |||||||
\(444\) | −67.2829 | + | 48.8839i | −0.151538 | + | 0.110099i | ||||
\(445\) | −25.4837 | + | 78.4309i | −0.0572668 | + | 0.176249i | ||||
\(446\) | 544.096 | + | 176.787i | 1.21995 | + | 0.396384i | ||||
\(447\) | 143.265 | + | 197.187i | 0.320503 | + | 0.441134i | ||||
\(448\) | −171.195 | + | 235.630i | −0.382132 | + | 0.525960i | ||||
\(449\) | 101.701 | + | 313.004i | 0.226506 | + | 0.697112i | 0.998135 | + | 0.0610405i | \(0.0194419\pi\) |
−0.771630 | + | 0.636072i | \(0.780558\pi\) | |||||||
\(450\) | − | 336.285i | − | 0.747300i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −167.068 | −0.369619 | ||||||||
\(453\) | −18.9582 | + | 6.15989i | −0.0418503 | + | 0.0135980i | ||||
\(454\) | 79.4062 | + | 57.6920i | 0.174903 | + | 0.127075i | ||||
\(455\) | 523.521 | − | 380.360i | 1.15060 | − | 0.835956i | ||||
\(456\) | 30.9591 | − | 95.2824i | 0.0678928 | − | 0.208953i | ||||
\(457\) | 84.2148 | + | 27.3630i | 0.184277 | + | 0.0598754i | 0.399702 | − | 0.916645i | \(-0.369114\pi\) |
−0.215425 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(458\) | −4.99824 | − | 6.87949i | −0.0109132 | − | 0.0150207i | ||||
\(459\) | −23.9050 | + | 32.9024i | −0.0520806 | + | 0.0716828i | ||||
\(460\) | −22.6783 | − | 69.7967i | −0.0493007 | − | 0.151732i | ||||
\(461\) | 607.310i | 1.31737i | 0.752417 | + | 0.658687i | \(0.228888\pi\) | ||||
−0.752417 | + | 0.658687i | \(0.771112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.7126 | −0.0879321 | −0.0439660 | − | 0.999033i | \(-0.513999\pi\) | ||||
−0.0439660 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(464\) | 128.387 | − | 41.7155i | 0.276696 | − | 0.0899040i | ||||
\(465\) | 334.137 | + | 242.765i | 0.718575 | + | 0.522075i | ||||
\(466\) | −432.512 | + | 314.238i | −0.928137 | + | 0.674331i | ||||
\(467\) | −138.378 | + | 425.883i | −0.296312 | + | 0.911956i | 0.686465 | + | 0.727163i | \(0.259161\pi\) |
−0.982777 | + | 0.184793i | \(0.940839\pi\) | |||||||
\(468\) | −28.8651 | − | 9.37886i | −0.0616777 | − | 0.0200403i | ||||
\(469\) | 113.495 | + | 156.212i | 0.241993 | + | 0.333075i | ||||
\(470\) | 182.022 | − | 250.532i | 0.387281 | − | 0.533046i | ||||
\(471\) | −80.1401 | − | 246.646i | −0.170149 | − | 0.523664i | ||||
\(472\) | 487.911i | 1.03371i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −164.507 | −0.347062 | ||||||||
\(475\) | −406.294 | + | 132.013i | −0.855356 | + | 0.277922i | ||||
\(476\) | 38.3164 | + | 27.8385i | 0.0804966 | + | 0.0584842i | ||||
\(477\) | 133.323 | − | 96.8650i | 0.279504 | − | 0.203071i | ||||
\(478\) | −317.204 | + | 976.253i | −0.663606 | + | 2.04237i | ||||
\(479\) | 55.6296 | + | 18.0752i | 0.116137 | + | 0.0377352i | 0.366509 | − | 0.930415i | \(-0.380553\pi\) |
−0.250372 | + | 0.968150i | \(0.580553\pi\) | |||||||
\(480\) | −126.147 | − | 173.627i | −0.262807 | − | 0.361723i | ||||
\(481\) | −347.114 | + | 477.762i | −0.721651 | + | 0.993267i | ||||
\(482\) | 306.128 | + | 942.165i | 0.635120 | + | 1.95470i | ||||
\(483\) | 107.542i | 0.222654i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1356.60 | 2.79710 | ||||||||
\(486\) | 32.8410 | − | 10.6707i | 0.0675740 | − | 0.0219561i | ||||
\(487\) | 528.517 | + | 383.990i | 1.08525 | + | 0.788480i | 0.978591 | − | 0.205815i | \(-0.0659846\pi\) |
0.106659 | + | 0.994296i | \(0.465985\pi\) | |||||||
\(488\) | 7.21324 | − | 5.24072i | 0.0147812 | − | 0.0107392i | ||||
\(489\) | −29.3400 | + | 90.2993i | −0.0600000 | + | 0.184661i | ||||
\(490\) | −82.1732 | − | 26.6997i | −0.167700 | − | 0.0544891i | ||||
\(491\) | −173.259 | − | 238.471i | −0.352871 | − | 0.485685i | 0.595275 | − | 0.803522i | \(-0.297043\pi\) |
−0.948145 | + | 0.317838i | \(0.897043\pi\) | |||||||
\(492\) | 44.1858 | − | 60.8166i | 0.0898086 | − | 0.123611i | ||||
\(493\) | 17.3622 | + | 53.4355i | 0.0352175 | + | 0.108388i | ||||
\(494\) | 208.601i | 0.422270i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 515.722 | 1.03976 | ||||||||
\(497\) | −139.928 | + | 45.4654i | −0.281545 | + | 0.0914797i | ||||
\(498\) | −413.499 | − | 300.424i | −0.830318 | − | 0.603262i | ||||
\(499\) | −33.4297 | + | 24.2881i | −0.0669933 | + | 0.0486735i | −0.620778 | − | 0.783986i | \(-0.713183\pi\) |
0.553785 | + | 0.832660i | \(0.313183\pi\) | |||||||
\(500\) | −62.3936 | + | 192.028i | −0.124787 | + | 0.384056i | ||||
\(501\) | 70.7369 | + | 22.9838i | 0.141191 | + | 0.0458759i | ||||
\(502\) | 495.598 | + | 682.133i | 0.987248 | + | 1.35883i | ||||
\(503\) | 359.909 | − | 495.373i | 0.715526 | − | 0.984837i | −0.284135 | − | 0.958784i | \(-0.591706\pi\) |
0.999661 | − | 0.0260523i | \(-0.00829365\pi\) | |||||||
\(504\) | 42.3784 | + | 130.427i | 0.0840840 | + | 0.258784i | ||||
\(505\) | 478.889i | 0.948295i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 77.2034 | 0.152275 | ||||||||
\(508\) | 102.738 | − | 33.3817i | 0.202241 | − | 0.0657120i | ||||
\(509\) | 242.692 | + | 176.326i | 0.476801 | + | 0.346416i | 0.800086 | − | 0.599885i | \(-0.204787\pi\) |
−0.323285 | + | 0.946302i | \(0.604787\pi\) | |||||||
\(510\) | 211.244 | − | 153.477i | 0.414203 | − | 0.300936i | ||||
\(511\) | 258.184 | − | 794.608i | 0.505252 | − | 1.55501i | ||||
\(512\) | 235.292 | + | 76.4511i | 0.459555 | + | 0.149318i | ||||
\(513\) | −25.7843 | − | 35.4890i | −0.0502617 | − | 0.0691793i | ||||
\(514\) | −4.33733 | + | 5.96982i | −0.00843839 | + | 0.0116144i | ||||
\(515\) | −217.687 | − | 669.972i | −0.422694 | − | 1.30092i | ||||
\(516\) | 72.0074i | 0.139549i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −782.442 | −1.51051 | ||||||||
\(519\) | −26.7569 | + | 8.69384i | −0.0515547 | + | 0.0167511i | ||||
\(520\) | −537.621 | − | 390.605i | −1.03389 | − | 0.751163i | ||||
\(521\) | −514.374 | + | 373.714i | −0.987282 | + | 0.717302i | −0.959324 | − | 0.282307i | \(-0.908900\pi\) |
−0.0279575 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(522\) | 14.7416 | − | 45.3700i | 0.0282407 | − | 0.0869158i | ||||
\(523\) | 7.82910 | + | 2.54383i | 0.0149696 | + | 0.00486392i | 0.316492 | − | 0.948595i | \(-0.397495\pi\) |
−0.301523 | + | 0.953459i | \(0.597495\pi\) | |||||||
\(524\) | 9.59571 | + | 13.2074i | 0.0183124 | + | 0.0252049i | ||||
\(525\) | 343.723 | − | 473.093i | 0.654710 | − | 0.901130i | ||||
\(526\) | −259.978 | − | 800.129i | −0.494254 | − | 1.52116i | ||||
\(527\) | 214.647i | 0.407299i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −442.396 | −0.836288 | ||||||||
\(530\) | −1006.26 | + | 326.954i | −1.89860 | + | 0.616894i | ||||
\(531\) | 172.833 | + | 125.571i | 0.325487 | + | 0.236480i | ||||
\(532\) | −41.3286 | + | 30.0270i | −0.0776853 | + | 0.0564417i | ||||
\(533\) | 164.950 | − | 507.665i | 0.309475 | − | 0.952467i | ||||
\(534\) | 34.6086 | + | 11.2450i | 0.0648100 | + | 0.0210581i | ||||
\(535\) | −399.658 | − | 550.083i | −0.747025 | − | 1.02819i | ||||
\(536\) | 116.551 | − | 160.419i | 0.217447 | − | 0.299290i | ||||
\(537\) | 69.7692 | + | 214.727i | 0.129924 | + | 0.399865i | ||||
\(538\) | 414.716i | 0.770847i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −40.9772 | −0.0758837 | ||||||||
\(541\) | −195.789 | + | 63.6156i | −0.361901 | + | 0.117589i | −0.484323 | − | 0.874889i | \(-0.660934\pi\) |
0.122422 | + | 0.992478i | \(0.460934\pi\) | |||||||
\(542\) | −546.876 | − | 397.328i | −1.00900 | − | 0.733078i | ||||
\(543\) | 142.285 | − | 103.376i | 0.262034 | − | 0.190379i | ||||
\(544\) | 34.4666 | − | 106.077i | 0.0633578 | − | 0.194995i | ||||
\(545\) | 22.1490 | + | 7.19663i | 0.0406403 | + | 0.0132048i | ||||
\(546\) | −167.838 | − | 231.010i | −0.307396 | − | 0.423095i | ||||
\(547\) | −547.844 | + | 754.043i | −1.00154 | + | 1.37851i | −0.0771705 | + | 0.997018i | \(0.524589\pi\) |
−0.924373 | + | 0.381489i | \(0.875411\pi\) | |||||||
\(548\) | −25.9417 | − | 79.8403i | −0.0473388 | − | 0.145694i | ||||
\(549\) | − | 3.90393i | − | 0.00711099i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.6023 | −0.109986 | ||||||||
\(552\) | 105.033 | − | 34.1274i | 0.190278 | − | 0.0618249i | ||||
\(553\) | −231.433 | − | 168.146i | −0.418504 | − | 0.304061i | ||||
\(554\) | 860.521 | − | 625.205i | 1.55329 | − | 1.12853i | ||||
\(555\) | −246.383 | + | 758.289i | −0.443933 | + | 1.36629i | ||||
\(556\) | −187.020 | − | 60.7666i | −0.336368 | − | 0.109292i | ||||
\(557\) | 438.296 | + | 603.262i | 0.786887 | + | 1.08306i | 0.994489 | + | 0.104843i | \(0.0334340\pi\) |
−0.207602 | + | 0.978213i | \(0.566566\pi\) | |||||||
\(558\) | 107.123 | − | 147.442i | 0.191976 | − | 0.264233i | ||||
\(559\) | 158.003 | + | 486.284i | 0.282653 | + | 0.869918i | ||||
\(560\) | − | 1090.94i | − | 1.94810i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0655 | −0.0357037 | ||||||||
\(563\) | 728.799 | − | 236.801i | 1.29449 | − | 0.420606i | 0.420830 | − | 0.907140i | \(-0.361739\pi\) |
0.873662 | + | 0.486534i | \(0.161739\pi\) | |||||||
\(564\) | −20.4332 | − | 14.8456i | −0.0362290 | − | 0.0263219i | ||||
\(565\) | −1295.78 | + | 941.439i | −2.29342 | + | 1.66626i | ||||
\(566\) | 182.565 | − | 561.878i | 0.322553 | − | 0.992717i | ||||
\(567\) | 57.1081 | + | 18.5555i | 0.100720 | + | 0.0327258i | ||||
\(568\) | 88.8096 | + | 122.236i | 0.156355 | + | 0.215204i | ||||
\(569\) | −520.926 | + | 716.992i | −0.915511 | + | 1.26009i | 0.0497389 | + | 0.998762i | \(0.484161\pi\) |
−0.965250 | + | 0.261330i | \(0.915839\pi\) | |||||||
\(570\) | 87.0311 | + | 267.854i | 0.152686 | + | 0.469919i | ||||
\(571\) | − | 504.852i | − | 0.884154i | −0.896977 | − | 0.442077i | \(-0.854242\pi\) | ||
0.896977 | − | 0.442077i | \(-0.145758\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −280.202 | −0.489008 | ||||||||
\(574\) | 672.629 | − | 218.550i | 1.17183 | − | 0.380750i | ||||
\(575\) | −380.983 | − | 276.800i | −0.662579 | − | 0.481392i | ||||
\(576\) | 105.950 | − | 76.9775i | 0.183942 | − | 0.133642i | ||||
\(577\) | 267.335 | − | 822.772i | 0.463319 | − | 1.42595i | −0.397766 | − | 0.917487i | \(-0.630214\pi\) |
0.861085 | − | 0.508462i | \(-0.169786\pi\) | |||||||
\(578\) | −479.791 | − | 155.894i | −0.830088 | − | 0.269712i | ||||
\(579\) | 34.8096 | + | 47.9113i | 0.0601202 | + | 0.0827483i | ||||
\(580\) | −33.2747 | + | 45.7987i | −0.0573702 | + | 0.0789633i | ||||
\(581\) | −274.651 | − | 845.288i | −0.472721 | − | 1.45488i | ||||
\(582\) | − | 598.614i | − | 1.02855i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −858.004 | −1.46918 | ||||||||
\(585\) | −276.729 | + | 89.9148i | −0.473041 | + | 0.153700i | ||||
\(586\) | 305.078 | + | 221.652i | 0.520611 | + | 0.378246i | ||||
\(587\) | 593.518 | − | 431.216i | 1.01110 | − | 0.734610i | 0.0466636 | − | 0.998911i | \(-0.485141\pi\) |
0.964440 | + | 0.264301i | \(0.0851411\pi\) | |||||||
\(588\) | −2.17761 | + | 6.70198i | −0.00370341 | + | 0.0113979i | ||||
\(589\) | −220.189 | − | 71.5439i | −0.373836 | − | 0.121467i | ||||
\(590\) | −806.204 | − | 1109.64i | −1.36645 | − | 1.88075i | ||||
\(591\) | −62.9976 | + | 86.7087i | −0.106595 | + | 0.146715i | ||||
\(592\) | 307.651 | + | 946.854i | 0.519681 | + | 1.59941i | ||||
\(593\) | − | 1126.19i | − | 1.89915i | −0.313544 | − | 0.949574i | \(-0.601516\pi\) | ||
0.313544 | − | 0.949574i | \(-0.398484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 454.054 | 0.763117 | ||||||||
\(596\) | −121.382 | + | 39.4395i | −0.203662 | + | 0.0661737i | ||||
\(597\) | −333.922 | − | 242.608i | −0.559333 | − | 0.406379i | ||||
\(598\) | −186.032 | + | 135.161i | −0.311091 | + | 0.226021i | ||||
\(599\) | −11.3484 | + | 34.9266i | −0.0189455 | + | 0.0583082i | −0.960082 | − | 0.279718i | \(-0.909759\pi\) |
0.941137 | + | 0.338026i | \(0.109759\pi\) | |||||||
\(600\) | −571.134 | − | 185.573i | −0.951890 | − | 0.309288i | ||||
\(601\) | −377.478 | − | 519.554i | −0.628083 | − | 0.864482i | 0.369827 | − | 0.929101i | \(-0.379417\pi\) |
−0.997910 | + | 0.0646184i | \(0.979417\pi\) | |||||||
\(602\) | −398.200 | + | 548.075i | −0.661461 | + | 0.910424i | ||||
\(603\) | −26.8294 | − | 82.5725i | −0.0444932 | − | 0.136936i | ||||
\(604\) | − | 10.4381i | − | 0.0172815i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 211.315 | 0.348705 | ||||||||
\(607\) | 628.641 | − | 204.258i | 1.03565 | − | 0.336504i | 0.258630 | − | 0.965976i | \(-0.416729\pi\) |
0.777023 | + | 0.629472i | \(0.216729\pi\) | |||||||
\(608\) | 97.3285 | + | 70.7133i | 0.160080 | + | 0.116305i | ||||
\(609\) | 67.1123 | − | 48.7600i | 0.110201 | − | 0.0800656i | ||||
\(610\) | −7.74534 | + | 23.8377i | −0.0126973 | + | 0.0390782i | ||||
\(611\) | −170.565 | − | 55.4200i | −0.279158 | − | 0.0907038i | ||||
\(612\) | −12.5175 | − | 17.2289i | −0.0204534 | − | 0.0281517i | ||||
\(613\) | −428.918 | + | 590.355i | −0.699703 | + | 0.963059i | 0.300254 | + | 0.953859i | \(0.402928\pi\) |
−0.999958 | + | 0.00919982i | \(0.997072\pi\) | |||||||
\(614\) | −156.666 | − | 482.169i | −0.255157 | − | 0.785291i | ||||
\(615\) | − | 720.685i | − | 1.17184i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −329.848 | −0.534600 | −0.267300 | − | 0.963613i | \(-0.586132\pi\) | ||||
−0.267300 | + | 0.963613i | \(0.586132\pi\) | |||||||
\(618\) | −295.633 | + | 96.0570i | −0.478371 | + | 0.155432i | ||||
\(619\) | −835.925 | − | 607.335i | −1.35044 | − | 0.981155i | −0.998989 | − | 0.0449503i | \(-0.985687\pi\) |
−0.351455 | − | 0.936205i | \(-0.614313\pi\) | |||||||
\(620\) | −174.966 | + | 127.120i | −0.282203 | + | 0.205033i | ||||
\(621\) | 14.9428 | − | 45.9892i | 0.0240625 | − | 0.0740568i | ||||
\(622\) | −595.284 | − | 193.419i | −0.957048 | − | 0.310964i | ||||
\(623\) | 37.1944 | + | 51.1937i | 0.0597021 | + | 0.0821729i | ||||
\(624\) | −213.558 | + | 293.937i | −0.342240 | + | 0.471053i | ||||
\(625\) | 207.233 | + | 637.797i | 0.331573 | + | 1.02048i | ||||
\(626\) | 775.697i | 1.23913i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 135.799 | 0.216240 | ||||||||
\(629\) | −394.086 | + | 128.046i | −0.626528 | + | 0.203571i | ||||
\(630\) | −311.892 | − | 226.603i | −0.495067 | − | 0.359688i | ||||
\(631\) | 691.507 | − | 502.409i | 1.09589 | − | 0.796211i | 0.115506 | − | 0.993307i | \(-0.463151\pi\) |
0.980384 | + | 0.197096i | \(0.0631510\pi\) | |||||||
\(632\) | −90.7804 | + | 279.393i | −0.143640 | + | 0.442078i | ||||
\(633\) | 310.418 | + | 100.861i | 0.490392 | + | 0.159338i | ||||
\(634\) | 487.504 | + | 670.991i | 0.768933 | + | 1.05835i | ||||
\(635\) | 608.732 | − | 837.847i | 0.958632 | − | 1.31944i | ||||
\(636\) | 26.6661 | + | 82.0698i | 0.0419278 | + | 0.129041i | ||||
\(637\) | 50.0384i | 0.0785532i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 66.1562 | 0.103531 | ||||||||
\(640\) | −1271.04 | + | 412.985i | −1.98600 | + | 0.645289i | ||||
\(641\) | −366.468 | − | 266.254i | −0.571713 | − | 0.415374i | 0.264014 | − | 0.964519i | \(-0.414953\pi\) |
−0.835727 | + | 0.549145i | \(0.814953\pi\) | |||||||
\(642\) | −242.730 | + | 176.354i | −0.378085 | + | 0.274695i | ||||
\(643\) | −81.9683 | + | 252.273i | −0.127478 | + | 0.392337i | −0.994344 | − | 0.106204i | \(-0.966130\pi\) |
0.866866 | + | 0.498540i | \(0.166130\pi\) | |||||||
\(644\) | −53.5566 | − | 17.4016i | −0.0831624 | − | 0.0270211i | ||||
\(645\) | 405.767 | + | 558.491i | 0.629097 | + | 0.865877i | ||||
\(646\) | −86.0335 | + | 118.415i | −0.133179 | + | 0.183305i | ||||
\(647\) | −105.937 | − | 326.040i | −0.163735 | − | 0.503925i | 0.835206 | − | 0.549938i | \(-0.185349\pi\) |
−0.998941 | + | 0.0460124i | \(0.985349\pi\) | |||||||
\(648\) | − | 61.6643i | − | 0.0951610i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1250.38 | 1.92366 | ||||||||
\(651\) | 301.406 | − | 97.9327i | 0.462989 | − | 0.150434i | ||||
\(652\) | −40.2221 | − | 29.2231i | −0.0616903 | − | 0.0448206i | ||||
\(653\) | −439.431 | + | 319.266i | −0.672942 | + | 0.488921i | −0.871009 | − | 0.491267i | \(-0.836534\pi\) |
0.198067 | + | 0.980189i | \(0.436534\pi\) | |||||||
\(654\) | 3.17560 | − | 9.77349i | 0.00485566 | − | 0.0149442i | ||||
\(655\) | 148.849 | + | 48.3640i | 0.227250 | + | 0.0738381i | ||||
\(656\) | −528.947 | − | 728.033i | −0.806322 | − | 1.10981i | ||||
\(657\) | −220.820 | + | 303.932i | −0.336103 | + | 0.462606i | ||||
\(658\) | −73.4287 | − | 225.990i | −0.111594 | − | 0.343450i | ||||
\(659\) | 309.878i | 0.470224i | 0.971968 | + | 0.235112i | \(0.0755457\pi\) | ||||
−0.971968 | + | 0.235112i | \(0.924454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 389.483 | 0.589234 | 0.294617 | − | 0.955615i | \(-0.404808\pi\) | ||||
0.294617 | + | 0.955615i | \(0.404808\pi\) | |||||||
\(662\) | 553.916 | − | 179.978i | 0.836731 | − | 0.271870i | ||||
\(663\) | −122.339 | − | 88.8841i | −0.184523 | − | 0.134064i | ||||
\(664\) | −738.412 | + | 536.487i | −1.11207 | + | 0.807963i | ||||
\(665\) | −151.341 | + | 465.779i | −0.227580 | + | 0.700420i | ||||
\(666\) | 334.604 | + | 108.719i | 0.502408 | + | 0.163242i | ||||
\(667\) | −39.2665 | − | 54.0457i | −0.0588703 | − | 0.0810280i | ||||
\(668\) | −22.8922 | + | 31.5084i | −0.0342698 | + | 0.0471683i | ||||
\(669\) | −138.231 | − | 425.431i | −0.206623 | − | 0.635921i | ||||
\(670\) | 557.423i | 0.831974i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −164.679 | −0.245058 | ||||||||
\(673\) | 686.613 | − | 223.094i | 1.02023 | − | 0.331492i | 0.249308 | − | 0.968424i | \(-0.419797\pi\) |
0.770920 | + | 0.636932i | \(0.219797\pi\) | |||||||
\(674\) | −56.6341 | − | 41.1471i | −0.0840268 | − | 0.0610491i | ||||
\(675\) | −212.725 | + | 154.554i | −0.315149 | + | 0.228969i | ||||
\(676\) | −12.4924 | + | 38.4478i | −0.0184799 | + | 0.0568754i | ||||
\(677\) | −804.636 | − | 261.442i | −1.18853 | − | 0.386177i | −0.353002 | − | 0.935623i | \(-0.614839\pi\) |
−0.835530 | + | 0.549445i | \(0.814839\pi\) | |||||||
\(678\) | 415.421 | + | 571.778i | 0.612715 | + | 0.843331i | ||||
\(679\) | 611.853 | − | 842.144i | 0.901109 | − | 1.24027i | ||||
\(680\) | −144.090 | − | 443.462i | −0.211897 | − | 0.652150i | ||||
\(681\) | − | 76.7451i | − | 0.112695i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.2192 | 0.0720632 | 0.0360316 | − | 0.999351i | \(-0.488528\pi\) | ||||
0.0360316 | + | 0.999351i | \(0.488528\pi\) | |||||||
\(684\) | 21.8460 | − | 7.09819i | 0.0319386 | − | 0.0103775i | ||||
\(685\) | −651.110 | − | 473.059i | −0.950526 | − | 0.690598i | ||||
\(686\) | −639.517 | + | 464.636i | −0.932240 | + | 0.677312i | ||||
\(687\) | −2.05464 | + | 6.32352i | −0.00299074 | + | 0.00920455i | ||||
\(688\) | 819.809 | + | 266.372i | 1.19158 | + | 0.387169i | ||||
\(689\) | 360.165 | + | 495.725i | 0.522737 | + | 0.719485i | ||||
\(690\) | −182.484 | + | 251.167i | −0.264469 | + | 0.364011i | ||||
\(691\) | 218.071 | + | 671.154i | 0.315588 | + | 0.971280i | 0.975512 | + | 0.219947i | \(0.0705885\pi\) |
−0.659924 | + | 0.751333i | \(0.729411\pi\) | |||||||
\(692\) | − | 14.7319i | − | 0.0212888i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 916.019 | 1.31991 | ||||||||
\(695\) | −1792.96 | + | 582.567i | −2.57979 | + | 0.838226i | ||||
\(696\) | −68.9200 | − | 50.0733i | −0.0990229 | − | 0.0719444i | ||||
\(697\) | 303.012 | − | 220.151i | 0.434737 | − | 0.315855i | ||||
\(698\) | 251.366 | − | 773.626i | 0.360124 | − | 1.10835i | ||||
\(699\) | 397.558 | + | 129.174i | 0.568753 | + | 0.184799i | ||||
\(700\) | 179.985 | + | 247.728i | 0.257122 | + | 0.353898i | ||||
\(701\) | 33.4914 | − | 46.0969i | 0.0477766 | − | 0.0657588i | −0.784460 | − | 0.620179i | \(-0.787060\pi\) |
0.832237 | + | 0.554420i | \(0.187060\pi\) | |||||||
\(702\) | 39.6759 | + | 122.110i | 0.0565184 | + | 0.173946i | ||||
\(703\) | − | 446.942i | − | 0.635764i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −242.136 | −0.343455 | ||||||||
\(706\) | −875.517 | + | 284.473i | −1.24011 | + | 0.402936i | ||||
\(707\) | 297.283 | + | 215.989i | 0.420486 | + | 0.305501i | ||||
\(708\) | −90.5017 | + | 65.7533i | −0.127827 | + | 0.0928720i | ||||
\(709\) | 148.802 | − | 457.965i | 0.209876 | − | 0.645931i | −0.789602 | − | 0.613619i | \(-0.789713\pi\) |
0.999478 | − | 0.0323120i | \(-0.0102870\pi\) | |||||||
\(710\) | −403.955 | − | 131.253i | −0.568951 | − | 0.184863i | ||||
\(711\) | 75.6063 | + | 104.063i | 0.106338 | + | 0.146362i | ||||
\(712\) | 38.1962 | − | 52.5726i | 0.0536464 | − | 0.0738379i | ||||
\(713\) | −78.8654 | − | 242.723i | −0.110611 | − | 0.340424i | ||||
\(714\) | − | 200.357i | − | 0.280612i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −118.225 | −0.165119 | ||||||||
\(717\) | 763.337 | − | 248.023i | 1.06463 | − | 0.345918i | ||||
\(718\) | 277.333 | + | 201.494i | 0.386257 | + | 0.280632i | ||||
\(719\) | −799.053 | + | 580.546i | −1.11134 | + | 0.807435i | −0.982874 | − | 0.184279i | \(-0.941005\pi\) |
−0.128465 | + | 0.991714i | \(0.541005\pi\) | |||||||
\(720\) | −151.584 | + | 466.528i | −0.210534 | + | 0.647956i | ||||
\(721\) | −514.085 | − | 167.036i | −0.713017 | − | 0.231673i | ||||
\(722\) | 377.240 | + | 519.227i | 0.522494 | + | 0.719151i | ||||
\(723\) | 455.296 | − | 626.661i | 0.629731 | − | 0.866750i | ||||
\(724\) | 28.4585 | + | 87.5862i | 0.0393073 | + | 0.120975i | ||||
\(725\) | 363.258i | 0.501045i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −146.472 | −0.201474 | −0.100737 | − | 0.994913i | \(-0.532120\pi\) | ||||
−0.100737 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(728\) | −484.957 | + | 157.572i | −0.666150 | + | 0.216445i | ||||
\(729\) | −21.8435 | − | 15.8702i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 1951.34 | − | 1417.73i | 2.67306 | − | 1.94210i | ||||
\(731\) | −110.866 | + | 341.210i | −0.151663 | + | 0.466771i | ||||
\(732\) | 1.94418 | + | 0.631704i | 0.00265599 | + | 0.000862983i | ||||
\(733\) | −82.5567 | − | 113.630i | −0.112629 | − | 0.155020i | 0.748981 | − | 0.662591i | \(-0.230543\pi\) |
−0.861610 | + | 0.507571i | \(0.830543\pi\) | |||||||
\(734\) | 141.839 | − | 195.225i | 0.193242 | − | 0.265974i | ||||
\(735\) | 20.8766 | + | 64.2516i | 0.0284036 | + | 0.0874172i | ||||
\(736\) | 132.616i | 0.180185i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −318.011 | −0.430909 | ||||||||
\(739\) | 629.811 | − | 204.638i | 0.852248 | − | 0.276912i | 0.149861 | − | 0.988707i | \(-0.452117\pi\) |
0.702387 | + | 0.711795i | \(0.252117\pi\) | |||||||
\(740\) | −337.765 | − | 245.401i | −0.456439 | − | 0.331623i | ||||
\(741\) | 131.956 | − | 95.8717i | 0.178078 | − | 0.129381i | ||||
\(742\) | −250.879 | + | 772.126i | −0.338112 | + | 1.04060i | ||||
\(743\) | 182.565 | + | 59.3188i | 0.245713 | + | 0.0798369i | 0.429284 | − | 0.903169i | \(-0.358766\pi\) |
−0.183572 | + | 0.983006i | \(0.558766\pi\) | |||||||
\(744\) | −191.296 | − | 263.297i | −0.257119 | − | 0.353894i | ||||
\(745\) | −719.199 | + | 989.893i | −0.965368 | + | 1.32872i | ||||
\(746\) | −493.698 | − | 1519.45i | −0.661794 | − | 2.03679i | ||||
\(747\) | 399.642i | 0.534995i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −521.733 | −0.696573 | ||||||||
\(750\) | 812.347 | − | 263.948i | 1.08313 | − | 0.351930i | ||||
\(751\) | 970.697 | + | 705.253i | 1.29254 | + | 0.939085i | 0.999853 | − | 0.0171236i | \(-0.00545089\pi\) |
0.292686 | + | 0.956209i | \(0.405451\pi\) | |||||||
\(752\) | −244.605 | + | 177.716i | −0.325272 | + | 0.236324i | ||||
\(753\) | 203.727 | − | 627.006i | 0.270553 | − | 0.832677i | ||||
\(754\) | 168.696 | + | 54.8126i | 0.223735 | + | 0.0726958i | ||||
\(755\) | −58.8192 | − | 80.9577i | −0.0779063 | − | 0.107229i | ||||
\(756\) | −18.4816 | + | 25.4377i | −0.0244465 | + | 0.0336478i | ||||
\(757\) | −176.792 | − | 544.111i | −0.233543 | − | 0.718773i | −0.997311 | − | 0.0732818i | \(-0.976653\pi\) |
0.763768 | − | 0.645491i | \(-0.223347\pi\) | |||||||
\(758\) | 28.6586i | 0.0378082i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 502.940 | 0.661764 | ||||||||
\(761\) | −68.4331 | + | 22.2353i | −0.0899253 | + | 0.0292185i | −0.353634 | − | 0.935384i | \(-0.615054\pi\) |
0.263709 | + | 0.964602i | \(0.415054\pi\) | |||||||
\(762\) | −369.710 | − | 268.610i | −0.485184 | − | 0.352507i | ||||
\(763\) | 14.4572 | − | 10.5037i | 0.0189478 | − | 0.0137664i | ||||
\(764\) | 45.3401 | − | 139.542i | 0.0593457 | − | 0.182647i | ||||
\(765\) | −194.172 | − | 63.0903i | −0.253820 | − | 0.0824710i | ||||
\(766\) | −129.700 | − | 178.516i | −0.169321 | − | 0.233050i | ||||
\(767\) | −466.900 | + | 642.633i | −0.608736 | + | 0.837853i | ||||
\(768\) | 88.7743 | + | 273.219i | 0.115591 | + | 0.355754i | ||||
\(769\) | − | 87.6070i | − | 0.113923i | −0.998376 | − | 0.0569616i | \(-0.981859\pi\) | ||
0.998376 | − | 0.0569616i | \(-0.0181413\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.76976 | 0.00748348 | ||||||||
\(772\) | −29.4928 | + | 9.58278i | −0.0382030 | + | 0.0124129i | ||||
\(773\) | 621.175 | + | 451.310i | 0.803590 | + | 0.583842i | 0.911965 | − | 0.410268i | \(-0.134565\pi\) |
−0.108375 | + | 0.994110i | \(0.534565\pi\) | |||||||
\(774\) | 246.441 | − | 179.050i | 0.318399 | − | 0.231330i | ||||
\(775\) | −428.843 | + | 1319.84i | −0.553345 | + | 1.70302i | ||||
\(776\) | −1016.66 | − | 330.334i | −1.31013 | − | 0.425688i | ||||
\(777\) | 359.605 | + | 494.953i | 0.462812 | + | 0.637005i | ||||
\(778\) | −263.172 | + | 362.225i | −0.338267 | + | 0.465585i | ||||
\(779\) | 124.839 | + | 384.215i | 0.160256 | + | 0.493216i | ||||
\(780\) | − | 152.362i | − | 0.195336i | ||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −161.348 | −0.206327 | ||||||||
\(783\) | −35.4751 | + | 11.5266i | −0.0453066 | + | 0.0147210i | ||||
\(784\) | 68.2470 | + | 49.5844i | 0.0870498 | + | 0.0632454i | ||||
\(785\) | 1053.26 | − | 765.238i | 1.34173 | − | 0.974825i | ||||
\(786\) | 21.3412 | − | 65.6814i | 0.0271516 | − | 0.0835641i | ||||
\(787\) | 298.166 | + | 96.8800i | 0.378864 | + | 0.123100i | 0.492257 | − | 0.870450i | \(-0.336172\pi\) |
−0.113393 | + | 0.993550i | \(0.536172\pi\) | |||||||
\(788\) | −32.9878 | − | 45.4037i | −0.0418626 | − | 0.0576190i | ||||
\(789\) | −386.658 | + | 532.189i | −0.490061 | + | 0.674511i | ||||
\(790\) | −255.198 | − | 785.419i | −0.323036 | − | 0.994202i | ||||
\(791\) | 1229.00i | 1.55373i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.5157 | 0.0183048 | ||||||||
\(794\) | 700.976 | − | 227.761i | 0.882841 | − | 0.286853i | ||||
\(795\) | 669.292 | + | 486.269i | 0.841877 | + | 0.611659i | ||||
\(796\) | 174.853 | − | 127.038i | 0.219665 | − | 0.159596i | ||||
\(797\) | −207.482 | + | 638.564i | −0.260329 | + | 0.801210i | 0.732404 | + | 0.680870i | \(0.238398\pi\) |
−0.992733 | + | 0.120339i | \(0.961602\pi\) | |||||||
\(798\) | 205.531 | + | 66.7809i | 0.257557 | + | 0.0836854i | ||||
\(799\) | −73.9665 | − | 101.806i | −0.0925738 | − | 0.127417i | ||||
\(800\) | 423.864 | − | 583.399i | 0.529830 | − | 0.729249i | ||||
\(801\) | −8.79253 | − | 27.0606i | −0.0109769 | − | 0.0337835i | ||||
\(802\) | − | 1455.10i | − | 1.81434i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 45.4630 | 0.0565460 | ||||||||
\(805\) | −513.445 | + | 166.828i | −0.637820 | + | 0.207240i | ||||
\(806\) | 548.222 | + | 398.307i | 0.680176 | + | 0.494177i | ||||
\(807\) | 262.339 | − | 190.600i | 0.325079 | − | 0.236184i | ||||
\(808\) | 116.611 | − | 358.890i | 0.144320 | − | 0.444171i | ||||
\(809\) | −1008.04 | − | 327.532i | −1.24603 | − | 0.404860i | −0.389535 | − | 0.921012i | \(-0.627364\pi\) |
−0.856497 | + | 0.516152i | \(0.827364\pi\) | |||||||
\(810\) | 101.892 | + | 140.242i | 0.125792 | + | 0.173138i | ||||
\(811\) | 510.745 | − | 702.980i | 0.629772 | − | 0.866806i | −0.368247 | − | 0.929728i | \(-0.620042\pi\) |
0.998018 | + | 0.0629219i | \(0.0200419\pi\) | |||||||
\(812\) | 13.4232 | + | 41.3124i | 0.0165310 | + | 0.0508773i | ||||
\(813\) | 528.549i | 0.650122i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −476.637 | −0.584831 | ||||||||
\(816\) | −242.457 | + | 78.7791i | −0.297129 | + | 0.0965430i | ||||
\(817\) | −313.068 | − | 227.457i | −0.383192 | − | 0.278406i | ||||
\(818\) | 840.599 | − | 610.731i | 1.02763 | − | 0.746614i | ||||
\(819\) | −68.9937 | + | 212.341i | −0.0842414 | + | 0.259268i | ||||
\(820\) | 358.906 | + | 116.616i | 0.437690 | + | 0.142214i | ||||
\(821\) | −440.634 | − | 606.481i | −0.536704 | − | 0.738710i | 0.451429 | − | 0.892307i | \(-0.350914\pi\) |
−0.988134 | + | 0.153597i | \(0.950914\pi\) | |||||||
\(822\) | −208.743 | + | 287.310i | −0.253945 | + | 0.349526i | ||||
\(823\) | 366.120 | + | 1126.80i | 0.444861 | + | 1.36914i | 0.882636 | + | 0.470056i | \(0.155766\pi\) |
−0.437776 | + | 0.899084i | \(0.644234\pi\) | |||||||
\(824\) | 555.100i | 0.673665i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1052.46 | −1.27416 | ||||||||
\(827\) | 95.4326 | − | 31.0079i | 0.115396 | − | 0.0374945i | −0.250750 | − | 0.968052i | \(-0.580677\pi\) |
0.366146 | + | 0.930557i | \(0.380677\pi\) | |||||||
\(828\) | 20.4850 | + | 14.8832i | 0.0247404 | + | 0.0179749i | ||||
\(829\) | −201.561 | + | 146.443i | −0.243138 | + | 0.176650i | −0.702680 | − | 0.711506i | \(-0.748013\pi\) |
0.459542 | + | 0.888156i | \(0.348013\pi\) | |||||||
\(830\) | 792.882 | − | 2440.24i | 0.955280 | − | 2.94005i | ||||
\(831\) | −790.978 | − | 257.004i | −0.951838 | − | 0.309271i | ||||
\(832\) | 286.220 | + | 393.947i | 0.344014 | + | 0.473494i | ||||
\(833\) | −20.6373 | + | 28.4048i | −0.0247747 | + | 0.0340995i | ||||
\(834\) | 257.065 | + | 791.164i | 0.308231 | + | 0.948637i | ||||
\(835\) | 373.379i | 0.447161i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −142.501 | −0.170252 | ||||||||
\(838\) | 510.315 | − | 165.811i | 0.608968 | − | 0.197866i | ||||
\(839\) | 98.4416 | + | 71.5220i | 0.117332 | + | 0.0852467i | 0.644904 | − | 0.764264i | \(-0.276897\pi\) |
−0.527572 | + | 0.849510i | \(0.676897\pi\) | |||||||
\(840\) | −556.967 | + | 404.660i | −0.663056 | + | 0.481738i | ||||
\(841\) | 243.959 | − | 750.829i | 0.290082 | − | 0.892782i | ||||
\(842\) | 1553.87 | + | 504.884i | 1.84545 | + | 0.599625i | ||||
\(843\) | 9.22194 | + | 12.6929i | 0.0109394 | + | 0.0150568i | ||||
\(844\) | −100.459 | + | 138.270i | −0.119027 | + | 0.163827i | ||||
\(845\) | 119.765 | + | 368.598i | 0.141733 | + | 0.436210i | ||||
\(846\) | 106.845i | 0.126295i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1033.01 | 1.21818 | ||||||||
\(849\) | −439.335 | + | 142.749i | −0.517474 | + | 0.168137i | ||||
\(850\) | 709.793 | + | 515.695i | 0.835051 | + | 0.606700i | ||||
\(851\) | 398.587 | − | 289.590i | 0.468374 | − | 0.340294i | ||||
\(852\) | −10.7049 | + | 32.9463i | −0.0125644 | + | 0.0386693i | ||||
\(853\) | 137.068 | + | 44.5362i | 0.160690 | + | 0.0522112i | 0.388257 | − | 0.921551i | \(-0.373077\pi\) |
−0.227568 | + | 0.973762i | \(0.573077\pi\) | |||||||
\(854\) | 11.3046 | + | 15.5594i | 0.0132372 | + | 0.0182195i | ||||
\(855\) | 129.439 | − | 178.157i | 0.151391 | − | 0.208371i | ||||
\(856\) | 165.567 | + | 509.562i | 0.193419 | + | 0.595283i | ||||
\(857\) | − | 527.163i | − | 0.615126i | −0.951528 | − | 0.307563i | \(-0.900487\pi\) | ||
0.951528 | − | 0.307563i | \(-0.0995134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 122.027 | 0.142057 | 0.0710284 | − | 0.997474i | \(-0.477372\pi\) | ||||
0.0710284 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(860\) | −343.790 | + | 111.704i | −0.399756 | + | 0.129889i | ||||
\(861\) | −447.385 | − | 325.044i | −0.519611 | − | 0.377519i | ||||
\(862\) | −880.713 | + | 639.876i | −1.02171 | + | 0.742315i | ||||
\(863\) | 261.197 | − | 803.880i | 0.302661 | − | 0.931495i | −0.677879 | − | 0.735174i | \(-0.737100\pi\) |
0.980540 | − | 0.196321i | \(-0.0628995\pi\) | |||||||
\(864\) | 70.4233 | + | 22.8819i | 0.0815085 | + | 0.0264837i | ||||
\(865\) | −83.0153 | − | 114.261i | −0.0959714 | − | 0.132093i | ||||
\(866\) | 524.285 | − | 721.616i | 0.605410 | − | 0.833275i | ||||
\(867\) | 121.894 | + | 375.151i | 0.140593 | + | 0.432700i | ||||
\(868\) | 165.949i | 0.191185i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 239.482 | 0.275267 | ||||||||
\(871\) | 307.023 | − | 99.7578i | 0.352495 | − | 0.114532i | ||||
\(872\) | −14.8465 | − | 10.7866i | −0.0170259 | − | 0.0123700i | ||||
\(873\) | −378.668 | + | 275.118i | −0.433755 | + | 0.315141i | ||||
\(874\) | 53.7788 | − | 165.514i | 0.0615318 | − | 0.189375i | ||||
\(875\) | 1412.61 | + | 458.986i | 1.61442 | + | 0.524556i | ||||
\(876\) | −115.629 | − | 159.150i | −0.131996 | − | 0.181678i | ||||
\(877\) | 537.597 | − | 739.939i | 0.612996 | − | 0.843716i | −0.383824 | − | 0.923406i | \(-0.625393\pi\) |
0.996820 | + | 0.0796899i | \(0.0253930\pi\) | |||||||
\(878\) | −46.8235 | − | 144.108i | −0.0533297 | − | 0.164132i | ||||
\(879\) | − | 294.854i | − | 0.335443i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 618.978 | 0.702586 | 0.351293 | − | 0.936266i | \(-0.385742\pi\) | ||||
0.351293 | + | 0.936266i | \(0.385742\pi\) | |||||||
\(882\) | 28.3518 | − | 9.21206i | 0.0321449 | − | 0.0104445i | ||||
\(883\) | 47.3926 | + | 34.4327i | 0.0536722 | + | 0.0389952i | 0.614298 | − | 0.789074i | \(-0.289439\pi\) |
−0.560626 | + | 0.828069i | \(0.689439\pi\) | |||||||
\(884\) | 64.0608 | − | 46.5429i | 0.0724669 | − | 0.0526503i | ||||
\(885\) | −331.408 | + | 1019.97i | −0.374472 | + | 1.15251i | ||||
\(886\) | −660.341 | − | 214.558i | −0.745306 | − | 0.242165i | ||||
\(887\) | −623.392 | − | 858.025i | −0.702809 | − | 0.967334i | −0.999922 | − | 0.0124914i | \(-0.996024\pi\) |
0.297113 | − | 0.954842i | \(-0.403976\pi\) | |||||||
\(888\) | 369.290 | − | 508.284i | 0.415867 | − | 0.572392i | ||||
\(889\) | −245.566 | − | 755.774i | −0.276227 | − | 0.850139i | ||||
\(890\) | 182.678i | 0.205257i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 234.235 | 0.262595 | ||||||||
\(893\) | 129.089 | − | 41.9435i | 0.144556 | − | 0.0469692i | ||||
\(894\) | 436.802 | + | 317.355i | 0.488593 | + | 0.354983i | ||||
\(895\) | −916.957 | + | 666.208i | −1.02453 | + | 0.744367i | ||||
\(896\) | −316.893 | + | 975.296i | −0.353675 | + | 1.08850i | ||||
\(897\) | 170.998 | + | 55.5607i | 0.190634 | + | 0.0619406i | ||||
\(898\) | 428.517 | + | 589.803i | 0.477190 | + | 0.656796i | ||||
\(899\) | −115.715 | + | 159.268i | −0.128715 | + | 0.177161i | ||||
\(900\) | −42.5474 | − | 130.947i | −0.0472749 | − | 0.145497i | ||||
\(901\) | 429.947i | 0.477189i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 529.708 | 0.586609 | ||||||||
\(904\) | 1200.33 | − | 390.011i | 1.32780 | − | 0.431428i | ||||
\(905\) | 714.280 | + | 518.955i | 0.789259 | + | 0.573431i | ||||
\(906\) | −35.7236 | + | 25.9547i | −0.0394300 | + | 0.0286476i | ||||
\(907\) | −385.722 | + | 1187.13i | −0.425272 | + | 1.30885i | 0.477461 | + | 0.878653i | \(0.341557\pi\) |
−0.902733 | + | 0.430201i | \(0.858443\pi\) | |||||||
\(908\) | 38.2196 | + | 12.4183i | 0.0420921 | + | 0.0136765i | ||||
\(909\) | −97.1190 | − | 133.673i | −0.106842 | − | 0.147055i | ||||
\(910\) | 842.561 | − | 1159.69i | 0.925891 | − | 1.27438i | ||||
\(911\) | −191.384 | − | 589.019i | −0.210081 | − | 0.646563i | −0.999466 | − | 0.0326649i | \(-0.989601\pi\) |
0.789385 | − | 0.613898i | \(-0.210399\pi\) | |||||||
\(912\) | − | 274.976i | − | 0.301509i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 196.150 | 0.214606 | ||||||||
\(915\) | 18.6388 | − | 6.05612i | 0.0203703 | − | 0.00661871i | ||||
\(916\) | −2.81669 | − | 2.04645i | −0.00307499 | − | 0.00223411i | ||||
\(917\) | 97.1573 | − | 70.5889i | 0.105951 | − | 0.0769781i | ||||
\(918\) | −27.8393 | + | 85.6807i | −0.0303261 | + | 0.0933341i | ||||
\(919\) | 1620.79 | + | 526.627i | 1.76365 | + | 0.573043i | 0.997568 | − | 0.0697040i | \(-0.0222055\pi\) |
0.766078 | + | 0.642747i | \(0.222205\pi\) | |||||||
\(920\) | 325.873 | + | 448.526i | 0.354210 | + | 0.487529i | ||||
\(921\) | −233.005 | + | 320.704i | −0.252992 | + | 0.348213i | ||||
\(922\) | 415.718 | + | 1279.45i | 0.450887 | + | 1.38769i | ||||
\(923\) | 245.984i | 0.266504i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2679.02 | −2.89624 | ||||||||
\(926\) | −85.7711 | + | 27.8687i | −0.0926254 | + | 0.0300958i | ||||
\(927\) | 196.634 | + | 142.863i | 0.212119 | + | 0.154113i | ||||
\(928\) | 82.7601 | − | 60.1287i | 0.0891811 | − | 0.0647939i | ||||
\(929\) | −156.082 | + | 480.371i | −0.168011 | + | 0.517084i | −0.999246 | − | 0.0388376i | \(-0.987635\pi\) |
0.831235 | + | 0.555922i | \(0.187635\pi\) | |||||||
\(930\) | 870.121 | + | 282.720i | 0.935614 | + | 0.304000i | ||||
\(931\) | −22.2597 | − | 30.6379i | −0.0239095 | − | 0.0329086i | ||||
\(932\) | −128.660 | + | 177.085i | −0.138047 | + | 0.190005i | ||||
\(933\) | 151.236 | + | 465.456i | 0.162096 | + | 0.498881i | ||||
\(934\) | 991.952i | 1.06205i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 229.282 | 0.244959 | ||||||||
\(937\) | −1242.03 | + | 403.561i | −1.32554 | + | 0.430694i | −0.884394 | − | 0.466740i | \(-0.845428\pi\) |
−0.441147 | + | 0.897435i | \(0.645428\pi\) | |||||||
\(938\) | 346.035 | + | 251.409i | 0.368908 | + | 0.268027i | ||||
\(939\) | 490.686 | − | 356.505i | 0.522563 | − | 0.379664i | ||||
\(940\) | 39.1805 | − | 120.585i | 0.0416814 | − | 0.128282i | ||||
\(941\) | −30.2766 | − | 9.83747i | −0.0321749 | − | 0.0104543i | 0.292885 | − | 0.956148i | \(-0.405385\pi\) |
−0.325060 | + | 0.945693i | \(0.605385\pi\) | |||||||
\(942\) | −337.670 | − | 464.763i | −0.358461 | − | 0.493379i | ||||
\(943\) | −261.758 | + | 360.280i | −0.277581 | + | 0.382057i | ||||
\(944\) | 413.819 | + | 1273.61i | 0.438368 | + | 1.34916i | ||||
\(945\) | 301.440i | 0.318985i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −749.175 | −0.791103 | −0.395552 | − | 0.918444i | \(-0.629447\pi\) | ||||
−0.395552 | + | 0.918444i | \(0.629447\pi\) | |||||||
\(948\) | −64.0582 | + | 20.8138i | −0.0675719 | + | 0.0219555i | ||||
\(949\) | −1130.09 | − | 821.056i | −1.19082 | − | 0.865181i | ||||
\(950\) | −765.593 | + | 556.236i | −0.805887 | + | 0.585512i | ||||
\(951\) | 200.399 | − | 616.765i | 0.210725 | − | 0.648544i | ||||
\(952\) | −340.279 | − | 110.563i | −0.357436 | − | 0.116138i | ||||
\(953\) | −853.888 | − | 1175.28i | −0.896000 | − | 1.23324i | −0.971726 | − | 0.236110i | \(-0.924127\pi\) |
0.0757259 | − | 0.997129i | \(-0.475873\pi\) | |||||||
\(954\) | 214.572 | − | 295.333i | 0.224918 | − | 0.309573i | ||||
\(955\) | −434.674 | − | 1337.79i | −0.455156 | − | 1.40083i | ||||
\(956\) | 420.280i | 0.439624i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 129.571 | 0.135251 | ||||||||
\(959\) | −587.329 | + | 190.835i | −0.612439 | + | 0.198994i | ||||
\(960\) | 531.879 | + | 386.433i | 0.554041 | + | 0.402534i | ||||
\(961\) | 169.009 | − | 122.792i | 0.175868 | − | 0.127776i | ||||
\(962\) | −404.243 | + | 1244.13i | −0.420211 | + | 1.29328i | ||||
\(963\) | 223.114 | + | 72.4942i | 0.231687 | + | 0.0752795i | ||||
\(964\) | 238.409 | + | 328.142i | 0.247312 | + | 0.340396i | ||||
\(965\) | −174.747 | + | 240.518i | −0.181085 | + | 0.249242i | ||||
\(966\) | 73.6150 | + | 226.564i | 0.0762060 | + | 0.234538i | ||||
\(967\) | − | 950.193i | − | 0.982619i | −0.870985 | − | 0.491310i | \(-0.836518\pi\) | ||
0.870985 | − | 0.491310i | \(-0.163482\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 114.447 | 0.118108 | ||||||||
\(970\) | 2858.01 | − | 928.622i | 2.94640 | − | 0.957343i | ||||
\(971\) | 533.187 | + | 387.383i | 0.549111 | + | 0.398952i | 0.827458 | − | 0.561528i | \(-0.189786\pi\) |
−0.278347 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(972\) | 11.4380 | − | 8.31020i | 0.0117675 | − | 0.00854959i | ||||
\(973\) | −447.017 | + | 1375.78i | −0.459422 | + | 1.41395i | ||||
\(974\) | 1376.30 | + | 447.188i | 1.41304 | + | 0.459125i | ||||
\(975\) | −574.666 | − | 790.960i | −0.589401 | − | 0.811241i | ||||
\(976\) | 14.3840 | − | 19.7979i | 0.0147377 | − | 0.0202847i | ||||
\(977\) | 63.8513 | + | 196.514i | 0.0653544 | + | 0.201140i | 0.978401 | − | 0.206714i | \(-0.0662770\pi\) |
−0.913047 | + | 0.407855i | \(0.866277\pi\) | |||||||
\(978\) | 210.322i | 0.215053i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −35.3758 | −0.0360978 | ||||||||
\(981\) | −7.64194 | + | 2.48302i | −0.00778995 | + | 0.00253111i | ||||
\(982\) | −528.253 | − | 383.799i | −0.537936 | − | 0.390834i | ||||
\(983\) | −184.812 | + | 134.274i | −0.188009 | + | 0.136596i | −0.677808 | − | 0.735239i | \(-0.737070\pi\) |
0.489800 | + | 0.871835i | \(0.337070\pi\) | |||||||
\(984\) | −175.488 | + | 540.098i | −0.178342 | + | 0.548880i | ||||
\(985\) | −511.707 | − | 166.264i | −0.519500 | − | 0.168796i | ||||
\(986\) | 73.1558 | + | 100.690i | 0.0741945 | + | 0.102120i | ||||
\(987\) | −109.208 | + | 150.313i | −0.110647 | + | 0.152292i | ||||
\(988\) | 26.3926 | + | 81.2282i | 0.0267132 | + | 0.0822148i | ||||
\(989\) | − | 426.575i | − | 0.431319i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1872.78 | −1.88979 | −0.944895 | − | 0.327373i | \(-0.893837\pi\) | ||||
−0.944895 | + | 0.327373i | \(0.893837\pi\) | |||||||
\(992\) | 371.681 | − | 120.766i | 0.374678 | − | 0.121740i | ||||
\(993\) | −368.425 | − | 267.677i | −0.371023 | − | 0.269564i | ||||
\(994\) | −263.671 | + | 191.568i | −0.265263 | + | 0.192725i | ||||
\(995\) | 640.294 | − | 1970.62i | 0.643511 | − | 1.98052i | ||||
\(996\) | −199.024 | − | 64.6669i | −0.199823 | − | 0.0649266i | ||||
\(997\) | 903.041 | + | 1242.93i | 0.905758 | + | 1.24667i | 0.968595 | + | 0.248645i | \(0.0799854\pi\) |
−0.0628363 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(998\) | −53.8021 | + | 74.0523i | −0.0539100 | + | 0.0742007i | ||||
\(999\) | −85.0083 | − | 261.629i | −0.0850934 | − | 0.261890i |
(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 | 363.3.g.g.94.3 | 16 | ||
11.2 | odd | 10 | inner | 363.3.g.g.112.3 | 16 | ||
11.3 | even | 5 | 363.3.c.e.241.5 | 16 | |||
11.4 | even | 5 | 33.3.g.a.19.3 | yes | 16 | ||
11.5 | even | 5 | 363.3.g.f.40.2 | 16 | |||
11.6 | odd | 10 | 33.3.g.a.7.3 | ✓ | 16 | ||
11.7 | odd | 10 | 363.3.g.f.118.2 | 16 | |||
11.8 | odd | 10 | 363.3.c.e.241.12 | 16 | |||
11.9 | even | 5 | 363.3.g.a.112.2 | 16 | |||
11.10 | odd | 2 | 363.3.g.a.94.2 | 16 | |||
33.8 | even | 10 | 1089.3.c.m.604.5 | 16 | |||
33.14 | odd | 10 | 1089.3.c.m.604.12 | 16 | |||
33.17 | even | 10 | 99.3.k.c.73.2 | 16 | |||
33.26 | odd | 10 | 99.3.k.c.19.2 | 16 | |||
44.15 | odd | 10 | 528.3.bf.b.481.1 | 16 | |||
44.39 | even | 10 | 528.3.bf.b.337.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.7.3 | ✓ | 16 | 11.6 | odd | 10 | ||
33.3.g.a.19.3 | yes | 16 | 11.4 | even | 5 | ||
99.3.k.c.19.2 | 16 | 33.26 | odd | 10 | |||
99.3.k.c.73.2 | 16 | 33.17 | even | 10 | |||
363.3.c.e.241.5 | 16 | 11.3 | even | 5 | |||
363.3.c.e.241.12 | 16 | 11.8 | odd | 10 | |||
363.3.g.a.94.2 | 16 | 11.10 | odd | 2 | |||
363.3.g.a.112.2 | 16 | 11.9 | even | 5 | |||
363.3.g.f.40.2 | 16 | 11.5 | even | 5 | |||
363.3.g.f.118.2 | 16 | 11.7 | odd | 10 | |||
363.3.g.g.94.3 | 16 | 1.1 | even | 1 | trivial | ||
363.3.g.g.112.3 | 16 | 11.2 | odd | 10 | inner | ||
528.3.bf.b.337.1 | 16 | 44.39 | even | 10 | |||
528.3.bf.b.481.1 | 16 | 44.15 | odd | 10 | |||
1089.3.c.m.604.5 | 16 | 33.8 | even | 10 | |||
1089.3.c.m.604.12 | 16 | 33.14 | odd | 10 |