Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,5,Mod(11,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.11");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.g (of order \(6\), 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: | \(2.89435896635\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Character | \(\chi\) | \(=\) | 28.23 |
Dual form | 28.5.g.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.98249 | − | 0.373846i | −0.995623 | − | 0.0934616i | ||||
\(3\) | −10.4527 | + | 6.03487i | −1.16141 | + | 0.670542i | −0.951642 | − | 0.307209i | \(-0.900605\pi\) |
−0.209770 | + | 0.977751i | \(0.567272\pi\) | |||||||
\(4\) | 15.7205 | + | 2.97768i | 0.982530 | + | 0.186105i | ||||
\(5\) | 13.8853 | − | 24.0501i | 0.555412 | − | 0.962002i | −0.442459 | − | 0.896789i | \(-0.645894\pi\) |
0.997871 | − | 0.0652135i | \(-0.0207729\pi\) | |||||||
\(6\) | 43.8839 | − | 20.1261i | 1.21900 | − | 0.559059i | ||||
\(7\) | 34.1259 | − | 35.1628i | 0.696446 | − | 0.717609i | ||||
\(8\) | −61.4935 | − | 17.7356i | −0.960836 | − | 0.277119i | ||||
\(9\) | 32.3394 | − | 56.0135i | 0.399252 | − | 0.691525i | ||||
\(10\) | −64.2891 | + | 90.5882i | −0.642891 | + | 0.905882i | ||||
\(11\) | 91.7023 | − | 52.9444i | 0.757871 | − | 0.437557i | −0.0706601 | − | 0.997500i | \(-0.522511\pi\) |
0.828531 | + | 0.559944i | \(0.189177\pi\) | |||||||
\(12\) | −182.291 | + | 63.7463i | −1.26591 | + | 0.442683i | ||||
\(13\) | 111.726 | 0.661103 | 0.330552 | − | 0.943788i | \(-0.392765\pi\) | ||||
0.330552 | + | 0.943788i | \(0.392765\pi\) | |||||||
\(14\) | −149.051 | + | 127.278i | −0.760467 | + | 0.649377i | ||||
\(15\) | 335.184i | 1.48971i | ||||||||
\(16\) | 238.267 | + | 93.6211i | 0.930730 | + | 0.365707i | ||||
\(17\) | −268.141 | − | 464.434i | −0.927823 | − | 1.60704i | −0.786957 | − | 0.617008i | \(-0.788344\pi\) |
−0.140867 | − | 0.990029i | \(-0.544989\pi\) | |||||||
\(18\) | −149.732 | + | 210.983i | −0.462135 | + | 0.651183i | ||||
\(19\) | −15.8167 | − | 9.13175i | −0.0438135 | − | 0.0252957i | 0.477933 | − | 0.878396i | \(-0.341386\pi\) |
−0.521747 | + | 0.853100i | \(0.674719\pi\) | |||||||
\(20\) | 289.897 | − | 336.732i | 0.724742 | − | 0.841831i | ||||
\(21\) | −144.505 | + | 573.492i | −0.327675 | + | 1.30044i | ||||
\(22\) | −384.997 | + | 176.568i | −0.795448 | + | 0.364810i | ||||
\(23\) | −246.453 | − | 142.290i | −0.465885 | − | 0.268979i | 0.248631 | − | 0.968598i | \(-0.420019\pi\) |
−0.714515 | + | 0.699620i | \(0.753353\pi\) | |||||||
\(24\) | 749.806 | − | 185.720i | 1.30175 | − | 0.322431i | ||||
\(25\) | −73.1034 | − | 126.619i | −0.116966 | − | 0.202590i | ||||
\(26\) | −444.950 | − | 41.7685i | −0.658209 | − | 0.0617877i | ||||
\(27\) | − | 196.993i | − | 0.270223i | ||||||
\(28\) | 641.179 | − | 451.161i | 0.817830 | − | 0.575460i | ||||
\(29\) | 1348.88 | 1.60389 | 0.801947 | − | 0.597395i | \(-0.203797\pi\) | ||||
0.801947 | + | 0.597395i | \(0.203797\pi\) | |||||||
\(30\) | 125.307 | − | 1334.87i | 0.139230 | − | 1.48319i | ||||
\(31\) | 418.793 | − | 241.790i | 0.435789 | − | 0.251603i | −0.266021 | − | 0.963967i | \(-0.585709\pi\) |
0.701810 | + | 0.712364i | \(0.252376\pi\) | |||||||
\(32\) | −913.896 | − | 461.920i | −0.892476 | − | 0.451094i | ||||
\(33\) | −639.025 | + | 1106.82i | −0.586800 | + | 1.01637i | ||||
\(34\) | 894.242 | + | 1949.85i | 0.773566 | + | 1.68672i | ||||
\(35\) | −371.820 | − | 1308.98i | −0.303526 | − | 1.06855i | ||||
\(36\) | 675.181 | − | 784.263i | 0.520973 | − | 0.605141i | ||||
\(37\) | −807.077 | + | 1397.90i | −0.589537 | + | 1.02111i | 0.404756 | + | 0.914425i | \(0.367357\pi\) |
−0.994293 | + | 0.106684i | \(0.965977\pi\) | |||||||
\(38\) | 59.5758 | + | 42.2801i | 0.0412575 | + | 0.0292799i | ||||
\(39\) | −1167.84 | + | 674.255i | −0.767813 | + | 0.443297i | ||||
\(40\) | −1280.40 | + | 1232.66i | −0.800249 | + | 0.770411i | ||||
\(41\) | −209.077 | −0.124376 | −0.0621882 | − | 0.998064i | \(-0.519808\pi\) | ||||
−0.0621882 | + | 0.998064i | \(0.519808\pi\) | |||||||
\(42\) | 789.886 | − | 2229.91i | 0.447781 | − | 1.26412i | ||||
\(43\) | 2072.51i | 1.12088i | 0.828194 | + | 0.560442i | \(0.189369\pi\) | ||||
−0.828194 | + | 0.560442i | \(0.810631\pi\) | |||||||
\(44\) | 1599.26 | − | 559.251i | 0.826062 | − | 0.288869i | ||||
\(45\) | −898.085 | − | 1555.53i | −0.443499 | − | 0.768163i | ||||
\(46\) | 928.303 | + | 658.803i | 0.438706 | + | 0.311344i | ||||
\(47\) | −1737.55 | − | 1003.17i | −0.786577 | − | 0.454130i | 0.0521793 | − | 0.998638i | \(-0.483383\pi\) |
−0.838756 | + | 0.544507i | \(0.816717\pi\) | |||||||
\(48\) | −3055.53 | + | 459.317i | −1.32618 | + | 0.199356i | ||||
\(49\) | −71.8495 | − | 2399.92i | −0.0299248 | − | 0.999552i | ||||
\(50\) | 243.798 | + | 531.588i | 0.0975191 | + | 0.212635i | ||||
\(51\) | 5605.60 | + | 3236.39i | 2.15517 | + | 1.24429i | ||||
\(52\) | 1756.39 | + | 332.685i | 0.649554 | + | 0.123035i | ||||
\(53\) | 829.490 | + | 1436.72i | 0.295297 | + | 0.511470i | 0.975054 | − | 0.221968i | \(-0.0712479\pi\) |
−0.679757 | + | 0.733438i | \(0.737915\pi\) | |||||||
\(54\) | −73.6449 | + | 784.521i | −0.0252555 | + | 0.269040i | ||||
\(55\) | − | 2940.60i | − | 0.972098i | ||||||
\(56\) | −2722.15 | + | 1557.04i | −0.868034 | + | 0.496505i | ||||
\(57\) | 220.436 | 0.0678473 | ||||||||
\(58\) | −5371.89 | − | 504.272i | −1.59687 | − | 0.149903i | ||||
\(59\) | −2933.77 | + | 1693.81i | −0.842795 | + | 0.486588i | −0.858213 | − | 0.513293i | \(-0.828425\pi\) |
0.0154181 | + | 0.999881i | \(0.495092\pi\) | |||||||
\(60\) | −998.071 | + | 5269.26i | −0.277242 | + | 1.46368i | ||||
\(61\) | 992.473 | − | 1719.01i | 0.266722 | − | 0.461976i | −0.701291 | − | 0.712875i | \(-0.747393\pi\) |
0.968013 | + | 0.250899i | \(0.0807261\pi\) | |||||||
\(62\) | −1758.23 | + | 806.364i | −0.457397 | + | 0.209772i | ||||
\(63\) | −865.983 | − | 3048.65i | −0.218187 | − | 0.768117i | ||||
\(64\) | 3466.90 | + | 2181.25i | 0.846410 | + | 0.532532i | ||||
\(65\) | 1551.36 | − | 2687.03i | 0.367185 | − | 0.635983i | ||||
\(66\) | 2958.69 | − | 4169.02i | 0.679223 | − | 0.957075i | ||||
\(67\) | 5169.03 | − | 2984.34i | 1.15149 | − | 0.664812i | 0.202239 | − | 0.979336i | \(-0.435178\pi\) |
0.949249 | + | 0.314524i | \(0.101845\pi\) | |||||||
\(68\) | −2832.37 | − | 8099.56i | −0.612537 | − | 1.75163i | ||||
\(69\) | 3434.80 | 0.721446 | ||||||||
\(70\) | 991.414 | + | 5351.99i | 0.202329 | + | 1.09224i | ||||
\(71\) | 2300.43i | 0.456343i | 0.973621 | + | 0.228172i | \(0.0732747\pi\) | ||||
−0.973621 | + | 0.228172i | \(0.926725\pi\) | |||||||
\(72\) | −2982.10 | + | 2870.91i | −0.575250 | + | 0.553801i | ||||
\(73\) | −443.902 | − | 768.861i | −0.0832993 | − | 0.144279i | 0.821366 | − | 0.570402i | \(-0.193212\pi\) |
−0.904665 | + | 0.426123i | \(0.859879\pi\) | |||||||
\(74\) | 3736.77 | − | 5265.39i | 0.682391 | − | 0.961540i | ||||
\(75\) | 1528.26 | + | 882.340i | 0.271690 | + | 0.156860i | ||||
\(76\) | −221.454 | − | 190.652i | −0.0383404 | − | 0.0330077i | ||||
\(77\) | 1267.75 | − | 5031.29i | 0.213822 | − | 0.848589i | ||||
\(78\) | 4903.00 | − | 2248.62i | 0.805884 | − | 0.369596i | ||||
\(79\) | −2530.89 | − | 1461.21i | −0.405526 | − | 0.234131i | 0.283339 | − | 0.959020i | \(-0.408558\pi\) |
−0.688866 | + | 0.724889i | \(0.741891\pi\) | |||||||
\(80\) | 5560.00 | − | 4430.37i | 0.868750 | − | 0.692246i | ||||
\(81\) | 3808.32 | + | 6596.20i | 0.580448 | + | 1.00536i | ||||
\(82\) | 832.647 | + | 78.1626i | 0.123832 | + | 0.0116244i | ||||
\(83\) | 1600.35i | 0.232305i | 0.993231 | + | 0.116153i | \(0.0370562\pi\) | ||||
−0.993231 | + | 0.116153i | \(0.962944\pi\) | |||||||
\(84\) | −3979.36 | + | 8585.28i | −0.563968 | + | 1.21674i | ||||
\(85\) | −14892.9 | −2.06130 | ||||||||
\(86\) | 774.802 | − | 8253.77i | 0.104760 | − | 1.11598i | ||||
\(87\) | −14099.4 | + | 8140.29i | −1.86278 | + | 1.07548i | ||||
\(88\) | −6578.10 | + | 1629.34i | −0.849444 | + | 0.210400i | ||||
\(89\) | −4526.47 | + | 7840.08i | −0.571452 | + | 0.989784i | 0.424965 | + | 0.905210i | \(0.360286\pi\) |
−0.996417 | + | 0.0845743i | \(0.973047\pi\) | |||||||
\(90\) | 2995.09 | + | 6530.63i | 0.369764 | + | 0.806250i | ||||
\(91\) | 3812.76 | − | 3928.62i | 0.460423 | − | 0.474413i | ||||
\(92\) | −3450.67 | − | 2970.72i | −0.407688 | − | 0.350983i | ||||
\(93\) | −2918.35 | + | 5054.73i | −0.337420 | + | 0.584429i | ||||
\(94\) | 6544.74 | + | 4644.71i | 0.740690 | + | 0.525657i | ||||
\(95\) | −439.238 | + | 253.594i | −0.0486691 | + | 0.0280991i | ||||
\(96\) | 12340.3 | − | 686.928i | 1.33901 | − | 0.0745365i | ||||
\(97\) | 1186.89 | 0.126144 | 0.0630722 | − | 0.998009i | \(-0.479910\pi\) | ||||
0.0630722 | + | 0.998009i | \(0.479910\pi\) | |||||||
\(98\) | −611.063 | + | 9584.54i | −0.0636259 | + | 0.997974i | ||||
\(99\) | − | 6848.76i | − | 0.698782i | ||||||
\(100\) | −772.191 | − | 2208.19i | −0.0772191 | − | 0.220819i | ||||
\(101\) | 4047.53 | + | 7010.53i | 0.396778 | + | 0.687240i | 0.993326 | − | 0.115337i | \(-0.0367949\pi\) |
−0.596548 | + | 0.802577i | \(0.703462\pi\) | |||||||
\(102\) | −21114.3 | − | 14984.5i | −2.02944 | − | 1.44027i | ||||
\(103\) | 6318.38 | + | 3647.92i | 0.595567 | + | 0.343851i | 0.767296 | − | 0.641293i | \(-0.221602\pi\) |
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(104\) | −6870.45 | − | 1981.54i | −0.635211 | − | 0.183204i | ||||
\(105\) | 11786.0 | + | 11438.5i | 1.06903 | + | 1.03750i | ||||
\(106\) | −2766.33 | − | 6031.83i | −0.246202 | − | 0.536830i | ||||
\(107\) | 13822.6 | + | 7980.49i | 1.20732 | + | 0.697047i | 0.962173 | − | 0.272438i | \(-0.0878301\pi\) |
0.245148 | + | 0.969486i | \(0.421163\pi\) | |||||||
\(108\) | 586.581 | − | 3096.82i | 0.0502898 | − | 0.265502i | ||||
\(109\) | −10338.6 | − | 17906.9i | −0.870177 | − | 1.50719i | −0.861813 | − | 0.507227i | \(-0.830671\pi\) |
−0.00836466 | − | 0.999965i | \(-0.502663\pi\) | |||||||
\(110\) | −1099.33 | + | 11710.9i | −0.0908538 | + | 0.967843i | ||||
\(111\) | − | 19482.4i | − | 1.58124i | ||||||
\(112\) | 11423.0 | − | 5183.24i | 0.910638 | − | 0.413204i | ||||
\(113\) | 2432.90 | 0.190532 | 0.0952659 | − | 0.995452i | \(-0.469630\pi\) | ||||
0.0952659 | + | 0.995452i | \(0.469630\pi\) | |||||||
\(114\) | −877.884 | − | 82.4091i | −0.0675503 | − | 0.00634111i | ||||
\(115\) | −6844.15 | + | 3951.47i | −0.517516 | + | 0.298788i | ||||
\(116\) | 21205.0 | + | 4016.52i | 1.57587 | + | 0.298493i | ||||
\(117\) | 3613.17 | − | 6258.19i | 0.263947 | − | 0.457169i | ||||
\(118\) | 12316.9 | − | 5648.82i | 0.884584 | − | 0.405689i | ||||
\(119\) | −25481.3 | − | 6420.61i | −1.79940 | − | 0.453401i | ||||
\(120\) | 5944.70 | − | 20611.6i | 0.412827 | − | 1.43136i | ||||
\(121\) | −1714.29 | + | 2969.23i | −0.117088 | + | 0.202803i | ||||
\(122\) | −4595.16 | + | 6474.92i | −0.308732 | + | 0.435026i | ||||
\(123\) | 2185.42 | − | 1261.75i | 0.144452 | − | 0.0833996i | ||||
\(124\) | 7303.61 | − | 2554.03i | 0.475000 | − | 0.166105i | ||||
\(125\) | 13296.4 | 0.850968 | ||||||||
\(126\) | 2309.04 | + | 12465.0i | 0.145442 | + | 0.785147i | ||||
\(127\) | 12796.1i | 0.793358i | 0.917957 | + | 0.396679i | \(0.129837\pi\) | ||||
−0.917957 | + | 0.396679i | \(0.870163\pi\) | |||||||
\(128\) | −12991.4 | − | 9982.90i | −0.792934 | − | 0.609308i | ||||
\(129\) | −12507.4 | − | 21663.4i | −0.751599 | − | 1.30181i | ||||
\(130\) | −7182.80 | + | 10121.1i | −0.425018 | + | 0.598881i | ||||
\(131\) | 19959.9 | + | 11523.8i | 1.16310 | + | 0.671513i | 0.952044 | − | 0.305962i | \(-0.0989779\pi\) |
0.211051 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(132\) | −13341.5 | + | 15497.0i | −0.765700 | + | 0.889405i | ||||
\(133\) | −860.856 | + | 244.529i | −0.0486662 | + | 0.0138238i | ||||
\(134\) | −21701.3 | + | 9952.69i | −1.20858 | + | 0.554282i | ||||
\(135\) | −4737.68 | − | 2735.30i | −0.259955 | − | 0.150085i | ||||
\(136\) | 8251.90 | + | 33315.3i | 0.446145 | + | 1.80122i | ||||
\(137\) | −795.466 | − | 1377.79i | −0.0423819 | − | 0.0734076i | 0.844056 | − | 0.536255i | \(-0.180161\pi\) |
−0.886438 | + | 0.462847i | \(0.846828\pi\) | |||||||
\(138\) | −13679.1 | − | 1284.09i | −0.718288 | − | 0.0674274i | ||||
\(139\) | − | 2377.96i | − | 0.123076i | −0.998105 | − | 0.0615381i | \(-0.980399\pi\) | ||
0.998105 | − | 0.0615381i | \(-0.0196006\pi\) | |||||||
\(140\) | −1947.48 | − | 21684.9i | −0.0993610 | − | 1.10637i | ||||
\(141\) | 24216.1 | 1.21805 | ||||||||
\(142\) | 860.006 | − | 9161.43i | 0.0426506 | − | 0.454346i | ||||
\(143\) | 10245.6 | − | 5915.29i | 0.501031 | − | 0.289270i | ||||
\(144\) | 12949.5 | − | 10318.5i | 0.624491 | − | 0.497613i | ||||
\(145\) | 18729.6 | − | 32440.5i | 0.890823 | − | 1.54295i | ||||
\(146\) | 1480.40 | + | 3227.93i | 0.0694502 | + | 0.151432i | ||||
\(147\) | 15234.3 | + | 24652.1i | 0.704996 | + | 1.14083i | ||||
\(148\) | −16850.1 | + | 19572.4i | −0.769271 | + | 0.893554i | ||||
\(149\) | −14331.9 | + | 24823.6i | −0.645553 | + | 1.11813i | 0.338620 | + | 0.940923i | \(0.390040\pi\) |
−0.984173 | + | 0.177208i | \(0.943294\pi\) | |||||||
\(150\) | −5756.42 | − | 4085.25i | −0.255841 | − | 0.181566i | ||||
\(151\) | 14414.1 | − | 8322.00i | 0.632171 | − | 0.364984i | −0.149421 | − | 0.988774i | \(-0.547741\pi\) |
0.781592 | + | 0.623790i | \(0.214408\pi\) | |||||||
\(152\) | 810.664 | + | 842.061i | 0.0350876 | + | 0.0364466i | ||||
\(153\) | −34686.1 | −1.48174 | ||||||||
\(154\) | −6929.72 | + | 19563.1i | −0.292196 | + | 0.824891i | ||||
\(155\) | − | 13429.3i | − | 0.558973i | ||||||
\(156\) | −20366.8 | + | 7122.15i | −0.836899 | + | 0.292659i | ||||
\(157\) | −1014.83 | − | 1757.74i | −0.0411713 | − | 0.0713108i | 0.844705 | − | 0.535231i | \(-0.179776\pi\) |
−0.885877 | + | 0.463921i | \(0.846442\pi\) | |||||||
\(158\) | 9532.98 | + | 6765.42i | 0.381869 | + | 0.271007i | ||||
\(159\) | −17340.8 | − | 10011.7i | −0.685924 | − | 0.396018i | ||||
\(160\) | −23798.9 | + | 15565.3i | −0.929646 | + | 0.608021i | ||||
\(161\) | −13413.7 | + | 3810.23i | −0.517485 | + | 0.146994i | ||||
\(162\) | −12700.6 | − | 27693.0i | −0.483944 | − | 1.05521i | ||||
\(163\) | −5223.77 | − | 3015.94i | −0.196611 | − | 0.113514i | 0.398463 | − | 0.917185i | \(-0.369544\pi\) |
−0.595074 | + | 0.803671i | \(0.702877\pi\) | |||||||
\(164\) | −3286.79 | − | 622.564i | −0.122204 | − | 0.0231471i | ||||
\(165\) | 17746.1 | + | 30737.2i | 0.651832 | + | 1.12901i | ||||
\(166\) | 598.285 | − | 6373.38i | 0.0217116 | − | 0.231288i | ||||
\(167\) | 14573.6i | 0.522558i | 0.965263 | + | 0.261279i | \(0.0841443\pi\) | ||||
−0.965263 | + | 0.261279i | \(0.915856\pi\) | |||||||
\(168\) | 19057.3 | − | 32703.1i | 0.675217 | − | 1.15870i | ||||
\(169\) | −16078.2 | −0.562943 | ||||||||
\(170\) | 59310.7 | + | 5567.65i | 2.05228 | + | 0.192652i | ||||
\(171\) | −1023.00 | + | 590.631i | −0.0349852 | + | 0.0201987i | ||||
\(172\) | −6171.28 | + | 32580.9i | −0.208602 | + | 1.10130i | ||||
\(173\) | −7042.10 | + | 12197.3i | −0.235294 | + | 0.407540i | −0.959358 | − | 0.282192i | \(-0.908939\pi\) |
0.724064 | + | 0.689732i | \(0.242272\pi\) | |||||||
\(174\) | 59194.0 | − | 27147.6i | 1.95515 | − | 0.896672i | ||||
\(175\) | −6947.00 | − | 1750.46i | −0.226841 | − | 0.0571577i | ||||
\(176\) | 26806.3 | − | 4029.62i | 0.865391 | − | 0.130088i | ||||
\(177\) | 20443.9 | − | 35409.9i | 0.652555 | − | 1.13026i | ||||
\(178\) | 20957.6 | − | 29530.8i | 0.661458 | − | 0.932043i | ||||
\(179\) | −18506.6 | + | 10684.8i | −0.577591 | + | 0.333473i | −0.760176 | − | 0.649718i | \(-0.774887\pi\) |
0.182584 | + | 0.983190i | \(0.441554\pi\) | |||||||
\(180\) | −9486.46 | − | 27127.9i | −0.292792 | − | 0.837280i | ||||
\(181\) | 1099.65 | 0.0335659 | 0.0167830 | − | 0.999859i | \(-0.494658\pi\) | ||||
0.0167830 | + | 0.999859i | \(0.494658\pi\) | |||||||
\(182\) | −16653.0 | + | 14220.3i | −0.502747 | + | 0.429305i | ||||
\(183\) | 23957.8i | 0.715393i | ||||||||
\(184\) | 12631.7 | + | 13120.9i | 0.373100 | + | 0.387550i | ||||
\(185\) | 22413.0 | + | 38820.5i | 0.654873 | + | 1.13427i | ||||
\(186\) | 13512.0 | − | 19039.4i | 0.390565 | − | 0.550335i | ||||
\(187\) | −49178.3 | − | 28393.1i | −1.40634 | − | 0.811951i | ||||
\(188\) | −24328.0 | − | 20944.2i | −0.688319 | − | 0.592582i | ||||
\(189\) | −6926.82 | − | 6722.54i | −0.193914 | − | 0.188196i | ||||
\(190\) | 1844.07 | − | 845.730i | 0.0510822 | − | 0.0234274i | ||||
\(191\) | −36690.2 | − | 21183.1i | −1.00573 | − | 0.580661i | −0.0957944 | − | 0.995401i | \(-0.530539\pi\) |
−0.909940 | + | 0.414740i | \(0.863872\pi\) | |||||||
\(192\) | −49402.0 | − | 1877.70i | −1.34012 | − | 0.0509358i | ||||
\(193\) | 4551.63 | + | 7883.66i | 0.122195 | + | 0.211648i | 0.920633 | − | 0.390429i | \(-0.127673\pi\) |
−0.798438 | + | 0.602077i | \(0.794340\pi\) | |||||||
\(194\) | −4726.79 | − | 443.715i | −0.125592 | − | 0.0117896i | ||||
\(195\) | 37448.9i | 0.984851i | ||||||||
\(196\) | 6016.70 | − | 37941.9i | 0.156620 | − | 0.987659i | ||||
\(197\) | 22723.2 | 0.585514 | 0.292757 | − | 0.956187i | \(-0.405427\pi\) | ||||
0.292757 | + | 0.956187i | \(0.405427\pi\) | |||||||
\(198\) | −2560.38 | + | 27275.1i | −0.0653092 | + | 0.695723i | ||||
\(199\) | 65585.4 | − | 37865.8i | 1.65616 | − | 0.956182i | 0.681691 | − | 0.731640i | \(-0.261245\pi\) |
0.974464 | − | 0.224542i | \(-0.0720886\pi\) | |||||||
\(200\) | 2249.72 | + | 9082.77i | 0.0562430 | + | 0.227069i | ||||
\(201\) | −36020.2 | + | 62388.9i | −0.891568 | + | 1.54424i | ||||
\(202\) | −13498.4 | − | 29432.5i | −0.330811 | − | 0.721315i | ||||
\(203\) | 46031.6 | − | 47430.3i | 1.11703 | − | 1.15097i | ||||
\(204\) | 78485.7 | + | 67569.3i | 1.88595 | + | 1.62364i | ||||
\(205\) | −2903.10 | + | 5028.31i | −0.0690802 | + | 0.119650i | ||||
\(206\) | −23799.1 | − | 16889.9i | −0.560824 | − | 0.398009i | ||||
\(207\) | −15940.3 | + | 9203.13i | −0.372011 | + | 0.214781i | ||||
\(208\) | 26620.7 | + | 10459.9i | 0.615309 | + | 0.241770i | ||||
\(209\) | −1933.90 | −0.0442732 | ||||||||
\(210\) | −42661.5 | − | 49959.7i | −0.967382 | − | 1.13287i | ||||
\(211\) | − | 44419.0i | − | 0.997709i | −0.866686 | − | 0.498854i | \(-0.833754\pi\) | ||
0.866686 | − | 0.498854i | \(-0.166246\pi\) | |||||||
\(212\) | 8761.90 | + | 25055.9i | 0.194951 | + | 0.557491i | ||||
\(213\) | −13882.8 | − | 24045.7i | −0.305997 | − | 0.530003i | ||||
\(214\) | −52065.0 | − | 36949.8i | −1.13689 | − | 0.806834i | ||||
\(215\) | 49844.1 | + | 28777.5i | 1.07829 | + | 0.622553i | ||||
\(216\) | −3493.79 | + | 12113.8i | −0.0748840 | + | 0.259640i | ||||
\(217\) | 5789.65 | − | 22977.3i | 0.122951 | − | 0.487954i | ||||
\(218\) | 34478.9 | + | 75179.3i | 0.725504 | + | 1.58192i | ||||
\(219\) | 9279.95 | + | 5357.78i | 0.193490 | + | 0.111711i | ||||
\(220\) | 8756.15 | − | 46227.6i | 0.180912 | − | 0.955115i | ||||
\(221\) | −29958.4 | − | 51889.5i | −0.613387 | − | 1.06242i | ||||
\(222\) | −7283.43 | + | 77588.6i | −0.147785 | + | 1.57432i | ||||
\(223\) | 52005.7i | 1.04578i | 0.852400 | + | 0.522891i | \(0.175147\pi\) | ||||
−0.852400 | + | 0.522891i | \(0.824853\pi\) | |||||||
\(224\) | −47429.9 | + | 16371.7i | −0.945271 | + | 0.326286i | ||||
\(225\) | −9456.49 | −0.186795 | ||||||||
\(226\) | −9689.00 | − | 909.530i | −0.189698 | − | 0.0178074i | ||||
\(227\) | −41419.9 | + | 23913.8i | −0.803818 | + | 0.464085i | −0.844804 | − | 0.535075i | \(-0.820283\pi\) |
0.0409864 | + | 0.999160i | \(0.486950\pi\) | |||||||
\(228\) | 3465.36 | + | 656.387i | 0.0666620 | + | 0.0126267i | ||||
\(229\) | −7319.37 | + | 12677.5i | −0.139573 | + | 0.241748i | −0.927335 | − | 0.374232i | \(-0.877906\pi\) |
0.787762 | + | 0.615980i | \(0.211240\pi\) | |||||||
\(230\) | 28734.0 | − | 13178.0i | 0.543176 | − | 0.249112i | ||||
\(231\) | 17111.8 | + | 60241.3i | 0.320679 | + | 1.12894i | ||||
\(232\) | −82947.1 | − | 23923.1i | −1.54108 | − | 0.444470i | ||||
\(233\) | 45670.4 | − | 79103.5i | 0.841247 | − | 1.45708i | −0.0475945 | − | 0.998867i | \(-0.515156\pi\) |
0.888841 | − | 0.458215i | \(-0.151511\pi\) | |||||||
\(234\) | −16729.0 | + | 23572.4i | −0.305519 | + | 0.430499i | ||||
\(235\) | −48252.8 | + | 27858.7i | −0.873749 | + | 0.504459i | ||||
\(236\) | −51163.9 | + | 17891.7i | −0.918628 | + | 0.321239i | ||||
\(237\) | 35272.9 | 0.627978 | ||||||||
\(238\) | 99078.9 | + | 35096.1i | 1.74915 | + | 0.619591i | ||||
\(239\) | 26705.3i | 0.467521i | 0.972294 | + | 0.233761i | \(0.0751032\pi\) | ||||
−0.972294 | + | 0.233761i | \(0.924897\pi\) | |||||||
\(240\) | −31380.3 | + | 79863.3i | −0.544797 | + | 1.38652i | ||||
\(241\) | 38815.0 | + | 67229.5i | 0.668290 | + | 1.15751i | 0.978382 | + | 0.206806i | \(0.0663068\pi\) |
−0.310092 | + | 0.950707i | \(0.600360\pi\) | |||||||
\(242\) | 7937.17 | − | 11184.1i | 0.135530 | − | 0.190972i | ||||
\(243\) | −65795.8 | − | 37987.2i | −1.11426 | − | 0.643317i | ||||
\(244\) | 20720.8 | − | 24068.4i | 0.348038 | − | 0.404267i | ||||
\(245\) | −58716.0 | − | 31595.7i | −0.978192 | − | 0.526376i | ||||
\(246\) | −9175.12 | + | 4207.91i | −0.151615 | + | 0.0695338i | ||||
\(247\) | −1767.14 | − | 1020.26i | −0.0289652 | − | 0.0167231i | ||||
\(248\) | −30041.4 | + | 7440.97i | −0.488446 | + | 0.120984i | ||||
\(249\) | −9657.91 | − | 16728.0i | −0.155770 | − | 0.269802i | ||||
\(250\) | −52952.7 | − | 4970.80i | −0.847243 | − | 0.0795328i | ||||
\(251\) | − | 34401.1i | − | 0.546040i | −0.962008 | − | 0.273020i | \(-0.911978\pi\) | ||
0.962008 | − | 0.273020i | \(-0.0880225\pi\) | |||||||
\(252\) | −4535.75 | − | 50504.9i | −0.0714246 | − | 0.795303i | ||||
\(253\) | −30133.8 | −0.470774 | ||||||||
\(254\) | 4783.76 | − | 50960.2i | 0.0741485 | − | 0.789885i | ||||
\(255\) | 155671. | − | 89876.6i | 2.39402 | − | 1.38219i | ||||
\(256\) | 48006.2 | + | 44613.6i | 0.732516 | + | 0.680749i | ||||
\(257\) | 19658.6 | − | 34049.6i | 0.297636 | − | 0.515521i | −0.677959 | − | 0.735100i | \(-0.737135\pi\) |
0.975595 | + | 0.219579i | \(0.0704685\pi\) | |||||||
\(258\) | 41711.7 | + | 90950.1i | 0.626640 | + | 1.36636i | ||||
\(259\) | 21611.8 | + | 76083.6i | 0.322175 | + | 1.13420i | ||||
\(260\) | 32389.2 | − | 37621.9i | 0.479130 | − | 0.556537i | ||||
\(261\) | 43621.8 | − | 75555.2i | 0.640358 | − | 1.10913i | ||||
\(262\) | −75181.9 | − | 53355.5i | −1.09524 | − | 0.777279i | ||||
\(263\) | −1083.26 | + | 625.421i | −0.0156611 | + | 0.00904193i | −0.507810 | − | 0.861469i | \(-0.669545\pi\) |
0.492149 | + | 0.870511i | \(0.336212\pi\) | |||||||
\(264\) | 58926.1 | − | 56729.0i | 0.845473 | − | 0.813948i | ||||
\(265\) | 46070.9 | 0.656047 | ||||||||
\(266\) | 3519.77 | − | 652.009i | 0.0497451 | − | 0.00921489i | ||||
\(267\) | − | 109267.i | − | 1.53273i | ||||||
\(268\) | 90146.0 | − | 31523.6i | 1.25510 | − | 0.438900i | ||||
\(269\) | −8417.85 | − | 14580.1i | −0.116331 | − | 0.201492i | 0.801980 | − | 0.597351i | \(-0.203780\pi\) |
−0.918311 | + | 0.395859i | \(0.870447\pi\) | |||||||
\(270\) | 17845.2 | + | 12664.5i | 0.244790 | + | 0.173724i | ||||
\(271\) | −14619.6 | − | 8440.62i | −0.199066 | − | 0.114931i | 0.397154 | − | 0.917752i | \(-0.369998\pi\) |
−0.596220 | + | 0.802821i | \(0.703331\pi\) | |||||||
\(272\) | −20408.3 | − | 135763.i | −0.275848 | − | 1.83503i | ||||
\(273\) | −16145.0 | + | 64074.2i | −0.216627 | + | 0.859722i | ||||
\(274\) | 2652.85 | + | 5784.41i | 0.0353356 | + | 0.0770473i | ||||
\(275\) | −13407.5 | − | 7740.83i | −0.177289 | − | 0.102358i | ||||
\(276\) | 53996.7 | + | 10227.7i | 0.708842 | + | 0.134265i | ||||
\(277\) | 33756.2 | + | 58467.5i | 0.439941 | + | 0.761999i | 0.997684 | − | 0.0680137i | \(-0.0216662\pi\) |
−0.557744 | + | 0.830013i | \(0.688333\pi\) | |||||||
\(278\) | −888.990 | + | 9470.19i | −0.0115029 | + | 0.122538i | ||||
\(279\) | − | 31277.4i | − | 0.401812i | ||||||
\(280\) | −351.006 | + | 87087.9i | −0.00447711 | + | 1.11082i | ||||
\(281\) | 66489.6 | 0.842056 | 0.421028 | − | 0.907048i | \(-0.361669\pi\) | ||||
0.421028 | + | 0.907048i | \(0.361669\pi\) | |||||||
\(282\) | −96440.4 | − | 9053.10i | −1.21272 | − | 0.113841i | ||||
\(283\) | −20437.5 | + | 11799.6i | −0.255185 | + | 0.147331i | −0.622136 | − | 0.782909i | \(-0.713735\pi\) |
0.366951 | + | 0.930240i | \(0.380402\pi\) | |||||||
\(284\) | −6849.93 | + | 36163.8i | −0.0849277 | + | 0.448371i | ||||
\(285\) | 3060.82 | − | 5301.50i | 0.0376832 | − | 0.0652693i | ||||
\(286\) | −43014.3 | + | 19727.3i | −0.525873 | + | 0.241177i | ||||
\(287\) | −7134.93 | + | 7351.73i | −0.0866215 | + | 0.0892537i | ||||
\(288\) | −55428.6 | + | 36252.3i | −0.668266 | + | 0.437069i | ||||
\(289\) | −102039. | + | 176736.i | −1.22171 | + | 2.11607i | ||||
\(290\) | −86718.0 | + | 122192.i | −1.03113 | + | 1.45294i | ||||
\(291\) | −12406.2 | + | 7162.74i | −0.146506 | + | 0.0845850i | ||||
\(292\) | −4688.93 | − | 13408.7i | −0.0549931 | − | 0.157260i | ||||
\(293\) | −66255.7 | −0.771770 | −0.385885 | − | 0.922547i | \(-0.626104\pi\) | ||||
−0.385885 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(294\) | −51454.2 | − | 103872.i | −0.595287 | − | 1.20172i | ||||
\(295\) | 94076.5i | 1.08103i | ||||||||
\(296\) | 74422.5 | − | 71647.6i | 0.849417 | − | 0.817745i | ||||
\(297\) | −10429.6 | − | 18064.7i | −0.118238 | − | 0.204794i | ||||
\(298\) | 66357.0 | − | 93501.9i | 0.747230 | − | 1.05290i | ||||
\(299\) | −27535.3 | − | 15897.5i | −0.307998 | − | 0.177823i | ||||
\(300\) | 21397.6 | + | 18421.5i | 0.237751 | + | 0.204683i | ||||
\(301\) | 72875.5 | + | 70726.4i | 0.804356 | + | 0.780636i | ||||
\(302\) | −60515.3 | + | 27753.6i | −0.663516 | + | 0.304303i | ||||
\(303\) | −84615.4 | − | 48852.7i | −0.921646 | − | 0.532112i | ||||
\(304\) | −2913.66 | − | 3656.57i | −0.0315277 | − | 0.0395664i | ||||
\(305\) | −27561.6 | − | 47738.0i | −0.296281 | − | 0.513174i | ||||
\(306\) | 138137. | + | 12967.3i | 1.47526 | + | 0.138486i | ||||
\(307\) | 145787.i | 1.54683i | 0.633902 | + | 0.773413i | \(0.281452\pi\) | ||||
−0.633902 | + | 0.773413i | \(0.718548\pi\) | |||||||
\(308\) | 34911.2 | − | 75319.3i | 0.368013 | − | 0.793971i | ||||
\(309\) | −88058.8 | −0.922266 | ||||||||
\(310\) | −5020.51 | + | 53482.2i | −0.0522425 | + | 0.556527i | ||||
\(311\) | −95505.9 | + | 55140.4i | −0.987437 | + | 0.570097i | −0.904507 | − | 0.426458i | \(-0.859761\pi\) |
−0.0829301 | + | 0.996555i | \(0.526428\pi\) | |||||||
\(312\) | 83773.1 | − | 20749.8i | 0.860588 | − | 0.213160i | ||||
\(313\) | 59038.8 | − | 102258.i | 0.602627 | − | 1.04378i | −0.389794 | − | 0.920902i | \(-0.627454\pi\) |
0.992422 | − | 0.122879i | \(-0.0392128\pi\) | |||||||
\(314\) | 3384.43 | + | 7379.58i | 0.0343263 | + | 0.0748466i | ||||
\(315\) | −85344.8 | − | 21504.6i | −0.860113 | − | 0.216725i | ||||
\(316\) | −35435.8 | − | 30507.1i | −0.354869 | − | 0.305511i | ||||
\(317\) | −50129.2 | + | 86826.4i | −0.498853 | + | 0.864039i | −0.999999 | − | 0.00132398i | \(-0.999579\pi\) |
0.501146 | + | 0.865363i | \(0.332912\pi\) | |||||||
\(318\) | 65316.9 | + | 46354.5i | 0.645909 | + | 0.458393i | ||||
\(319\) | 123695. | − | 71415.4i | 1.21554 | − | 0.701795i | ||||
\(320\) | 100598. | − | 53091.7i | 0.982403 | − | 0.518474i | ||||
\(321\) | −192645. | −1.86960 | ||||||||
\(322\) | 54844.5 | − | 10159.5i | 0.528959 | − | 0.0979854i | ||||
\(323\) | 9794.39i | 0.0938798i | ||||||||
\(324\) | 40227.2 | + | 115035.i | 0.383204 | + | 1.09583i | ||||
\(325\) | −8167.59 | − | 14146.7i | −0.0773263 | − | 0.133933i | ||||
\(326\) | 19676.1 | + | 13963.9i | 0.185142 | + | 0.131392i | ||||
\(327\) | 216132. | + | 124784.i | 2.02127 | + | 1.16698i | ||||
\(328\) | 12856.9 | + | 3708.11i | 0.119505 | + | 0.0344671i | ||||
\(329\) | −94569.8 | + | 26862.9i | −0.873696 | + | 0.248177i | ||||
\(330\) | −59182.8 | − | 129045.i | −0.543460 | − | 1.18499i | ||||
\(331\) | −73168.2 | − | 42243.7i | −0.667831 | − | 0.385572i | 0.127424 | − | 0.991848i | \(-0.459329\pi\) |
−0.795254 | + | 0.606276i | \(0.792663\pi\) | |||||||
\(332\) | −4765.33 | + | 25158.3i | −0.0432331 | + | 0.228247i | ||||
\(333\) | 52200.8 | + | 90414.4i | 0.470748 | + | 0.815359i | ||||
\(334\) | 5448.30 | − | 58039.3i | 0.0488391 | − | 0.520271i | ||||
\(335\) | − | 165754.i | − | 1.47698i | ||||||
\(336\) | −88121.6 | + | 123116.i | −0.780556 | + | 1.09052i | ||||
\(337\) | 208442. | 1.83538 | 0.917688 | − | 0.397302i | \(-0.130053\pi\) | ||||
0.917688 | + | 0.397302i | \(0.130053\pi\) | |||||||
\(338\) | 64031.3 | + | 6010.78i | 0.560478 | + | 0.0526135i | ||||
\(339\) | −25430.4 | + | 14682.2i | −0.221286 | + | 0.127759i | ||||
\(340\) | −234123. | − | 44346.2i | −2.02529 | − | 0.383618i | ||||
\(341\) | 25602.9 | − | 44345.5i | 0.220181 | − | 0.381365i | ||||
\(342\) | 4294.90 | − | 1969.74i | 0.0367199 | − | 0.0168405i | ||||
\(343\) | −86840.1 | − | 79373.1i | −0.738128 | − | 0.674660i | ||||
\(344\) | 36757.3 | − | 127446.i | 0.310618 | − | 1.07699i | ||||
\(345\) | 47693.3 | − | 82607.2i | 0.400700 | − | 0.694032i | ||||
\(346\) | 32605.0 | − | 45942.9i | 0.272353 | − | 0.383766i | ||||
\(347\) | 66168.9 | − | 38202.7i | 0.549535 | − | 0.317274i | −0.199399 | − | 0.979918i | \(-0.563899\pi\) |
0.748934 | + | 0.662644i | \(0.230566\pi\) | |||||||
\(348\) | −245889. | + | 85985.8i | −2.03039 | + | 0.710016i | ||||
\(349\) | −1612.29 | −0.0132371 | −0.00661854 | − | 0.999978i | \(-0.502107\pi\) | ||||
−0.00661854 | + | 0.999978i | \(0.502107\pi\) | |||||||
\(350\) | 27012.0 | + | 9568.28i | 0.220506 | + | 0.0781084i | ||||
\(351\) | − | 22009.3i | − | 0.178645i | ||||||
\(352\) | −108262. | + | 6026.47i | −0.873761 | + | 0.0486382i | ||||
\(353\) | 14472.4 | + | 25067.0i | 0.116143 | + | 0.201165i | 0.918236 | − | 0.396034i | \(-0.129614\pi\) |
−0.802093 | + | 0.597199i | \(0.796280\pi\) | |||||||
\(354\) | −94655.5 | + | 133377.i | −0.755335 | + | 1.06432i | ||||
\(355\) | 55325.4 | + | 31942.1i | 0.439003 | + | 0.253459i | ||||
\(356\) | −94503.5 | + | 109771.i | −0.745672 | + | 0.866142i | ||||
\(357\) | 305097. | − | 86663.9i | 2.39387 | − | 0.679989i | ||||
\(358\) | 77696.9 | − | 35633.5i | 0.606230 | − | 0.278030i | ||||
\(359\) | 145311. | + | 83895.3i | 1.12748 | + | 0.650951i | 0.943300 | − | 0.331941i | \(-0.107704\pi\) |
0.184181 | + | 0.982892i | \(0.441037\pi\) | |||||||
\(360\) | 27638.1 | + | 111583.i | 0.213257 | + | 0.860980i | ||||
\(361\) | −64993.7 | − | 112572.i | −0.498720 | − | 0.863809i | ||||
\(362\) | −4379.36 | − | 411.101i | −0.0334190 | − | 0.00313712i | ||||
\(363\) | − | 41382.0i | − | 0.314050i | ||||||
\(364\) | 71636.6 | − | 50406.6i | 0.540670 | − | 0.380438i | ||||
\(365\) | −24654.9 | −0.185062 | ||||||||
\(366\) | 8956.53 | − | 95411.7i | 0.0668617 | − | 0.712261i | ||||
\(367\) | −64226.4 | + | 37081.1i | −0.476849 | + | 0.275309i | −0.719103 | − | 0.694904i | \(-0.755447\pi\) |
0.242253 | + | 0.970213i | \(0.422114\pi\) | |||||||
\(368\) | −45400.3 | − | 56976.1i | −0.335245 | − | 0.420724i | ||||
\(369\) | −6761.42 | + | 11711.1i | −0.0496575 | + | 0.0860094i | ||||
\(370\) | −74746.7 | − | 162981.i | −0.545995 | − | 1.19051i | ||||
\(371\) | 78826.2 | + | 19862.1i | 0.572694 | + | 0.144304i | ||||
\(372\) | −60929.2 | + | 70772.9i | −0.440291 | + | 0.511424i | ||||
\(373\) | −12468.1 | + | 21595.3i | −0.0896151 | + | 0.155218i | −0.907348 | − | 0.420379i | \(-0.861897\pi\) |
0.817733 | + | 0.575597i | \(0.195230\pi\) | |||||||
\(374\) | 185238. | + | 131460.i | 1.32430 | + | 0.939835i | ||||
\(375\) | −138983. | + | 80242.0i | −0.988325 | + | 0.570610i | ||||
\(376\) | 89056.0 | + | 92505.1i | 0.629923 | + | 0.654320i | ||||
\(377\) | 150705. | 1.06034 | ||||||||
\(378\) | 25072.8 | + | 29362.0i | 0.175477 | + | 0.205496i | ||||
\(379\) | − | 200932.i | − | 1.39885i | −0.714706 | − | 0.699425i | \(-0.753440\pi\) | ||
0.714706 | − | 0.699425i | \(-0.246560\pi\) | |||||||
\(380\) | −7660.16 | + | 2678.71i | −0.0530482 | + | 0.0185506i | ||||
\(381\) | −77222.7 | − | 133754.i | −0.531979 | − | 0.921415i | ||||
\(382\) | 138199. | + | 98078.0i | 0.947063 | + | 0.672117i | ||||
\(383\) | −63309.8 | − | 36551.9i | −0.431592 | − | 0.249180i | 0.268433 | − | 0.963298i | \(-0.413494\pi\) |
−0.700025 | + | 0.714119i | \(0.746828\pi\) | |||||||
\(384\) | 196041. | + | 25946.7i | 1.32949 | + | 0.175962i | ||||
\(385\) | −103400. | − | 100350.i | −0.697586 | − | 0.677014i | ||||
\(386\) | −15179.6 | − | 33098.2i | −0.101879 | − | 0.222142i | ||||
\(387\) | 116089. | + | 67023.9i | 0.775119 | + | 0.447515i | ||||
\(388\) | 18658.5 | + | 3534.18i | 0.123941 | + | 0.0234761i | ||||
\(389\) | −40109.3 | − | 69471.4i | −0.265061 | − | 0.459099i | 0.702519 | − | 0.711665i | \(-0.252059\pi\) |
−0.967580 | + | 0.252566i | \(0.918725\pi\) | |||||||
\(390\) | 14000.1 | − | 149140.i | 0.0920457 | − | 0.980540i | ||||
\(391\) | 152615.i | 0.998259i | ||||||||
\(392\) | −38145.9 | + | 148854.i | −0.248242 | + | 0.968698i | ||||
\(393\) | −278180. | −1.80111 | ||||||||
\(394\) | −90495.0 | − | 8494.99i | −0.582951 | − | 0.0547231i | ||||
\(395\) | −70284.4 | + | 40578.7i | −0.450469 | + | 0.260078i | ||||
\(396\) | 20393.4 | − | 107666.i | 0.130047 | − | 0.686574i | ||||
\(397\) | −40799.5 | + | 70666.8i | −0.258865 | + | 0.448368i | −0.965938 | − | 0.258773i | \(-0.916682\pi\) |
0.707073 | + | 0.707141i | \(0.250015\pi\) | |||||||
\(398\) | −275349. | + | 126281.i | −1.73827 | + | 0.797210i | ||||
\(399\) | 7522.57 | − | 7751.15i | 0.0472520 | − | 0.0486878i | ||||
\(400\) | −5563.93 | − | 37013.1i | −0.0347746 | − | 0.231332i | ||||
\(401\) | 52874.3 | − | 91580.9i | 0.328818 | − | 0.569530i | −0.653460 | − | 0.756961i | \(-0.726683\pi\) |
0.982278 | + | 0.187432i | \(0.0600164\pi\) | |||||||
\(402\) | 166774. | − | 234997.i | 1.03199 | − | 1.45415i | ||||
\(403\) | 46790.3 | − | 27014.4i | 0.288102 | − | 0.166336i | ||||
\(404\) | 42754.0 | + | 122261.i | 0.261948 | + | 0.749076i | ||||
\(405\) | 211519. | 1.28955 | ||||||||
\(406\) | −201052. | + | 171682.i | −1.21971 | + | 1.04153i | ||||
\(407\) | 170921.i | 1.03182i | ||||||||
\(408\) | −287308. | − | 298436.i | −1.72595 | − | 1.79280i | ||||
\(409\) | 50630.6 | + | 87694.8i | 0.302668 | + | 0.524236i | 0.976739 | − | 0.214430i | \(-0.0687893\pi\) |
−0.674071 | + | 0.738666i | \(0.735456\pi\) | |||||||
\(410\) | 13441.4 | − | 18939.9i | 0.0799606 | − | 0.112670i | ||||
\(411\) | 16629.5 | + | 9601.07i | 0.0984457 | + | 0.0568376i | ||||
\(412\) | 88465.6 | + | 76161.1i | 0.521170 | + | 0.448682i | ||||
\(413\) | −40558.2 | + | 160963.i | −0.237782 | + | 0.943680i | ||||
\(414\) | 66922.6 | − | 30692.2i | 0.390456 | − | 0.179072i | ||||
\(415\) | 38488.5 | + | 22221.4i | 0.223478 | + | 0.129025i | ||||
\(416\) | −102106. | − | 51608.7i | −0.590019 | − | 0.298220i | ||||
\(417\) | 14350.7 | + | 24856.1i | 0.0825278 | + | 0.142942i | ||||
\(418\) | 7701.74 | + | 722.981i | 0.0440795 | + | 0.00413785i | ||||
\(419\) | − | 240347.i | − | 1.36902i | −0.729002 | − | 0.684512i | \(-0.760015\pi\) | ||
0.729002 | − | 0.684512i | \(-0.239985\pi\) | |||||||
\(420\) | 151222. | + | 214913.i | 0.857267 | + | 1.21833i | ||||
\(421\) | −153159. | −0.864129 | −0.432065 | − | 0.901843i | \(-0.642215\pi\) | ||||
−0.432065 | + | 0.901843i | \(0.642215\pi\) | |||||||
\(422\) | −16605.9 | + | 176898.i | −0.0932474 | + | 0.993342i | ||||
\(423\) | −112383. | + | 64884.1i | −0.628085 | + | 0.362625i | ||||
\(424\) | −25527.1 | − | 103060.i | −0.141994 | − | 0.573271i | ||||
\(425\) | −39204.1 | + | 67903.4i | −0.217047 | + | 0.375936i | ||||
\(426\) | 46298.7 | + | 100952.i | 0.255123 | + | 0.556282i | ||||
\(427\) | −26576.4 | − | 93561.0i | −0.145761 | − | 0.513144i | ||||
\(428\) | 193535. | + | 166616.i | 1.05651 | + | 0.909558i | ||||
\(429\) | −71396.0 | + | 123662.i | −0.387935 | + | 0.671924i | ||||
\(430\) | −187745. | − | 133240.i | −1.01539 | − | 0.720607i | ||||
\(431\) | 117845. | − | 68038.0i | 0.634391 | − | 0.366266i | −0.148059 | − | 0.988978i | \(-0.547303\pi\) |
0.782451 | + | 0.622712i | \(0.213969\pi\) | |||||||
\(432\) | 18442.7 | − | 46936.8i | 0.0988225 | − | 0.251505i | ||||
\(433\) | 130510. | 0.696094 | 0.348047 | − | 0.937477i | \(-0.386845\pi\) | ||||
0.348047 | + | 0.937477i | \(0.386845\pi\) | |||||||
\(434\) | −31647.2 | + | 89342.3i | −0.168018 | + | 0.474327i | ||||
\(435\) | 452122.i | 2.38933i | ||||||||
\(436\) | −109206. | − | 312291.i | −0.574480 | − | 1.64281i | ||||
\(437\) | 2598.71 | + | 4501.10i | 0.0136080 | + | 0.0235698i | ||||
\(438\) | −34954.3 | − | 24806.6i | −0.182202 | − | 0.129306i | ||||
\(439\) | −275353. | − | 158975.i | −1.42877 | − | 0.824899i | −0.431744 | − | 0.901996i | \(-0.642102\pi\) |
−0.997024 | + | 0.0770971i | \(0.975435\pi\) | |||||||
\(440\) | −52153.3 | + | 180827.i | −0.269387 | + | 0.934026i | ||||
\(441\) | −136752. | − | 73587.6i | −0.703163 | − | 0.378379i | ||||
\(442\) | 99910.5 | + | 217849.i | 0.511407 | + | 1.11510i | ||||
\(443\) | 216455. | + | 124970.i | 1.10296 | + | 0.636794i | 0.936997 | − | 0.349338i | \(-0.113593\pi\) |
0.165963 | + | 0.986132i | \(0.446927\pi\) | |||||||
\(444\) | 58012.4 | − | 306273.i | 0.294276 | − | 1.55361i | ||||
\(445\) | 125703. | + | 217724.i | 0.634783 | + | 1.09948i | ||||
\(446\) | 19442.1 | − | 207112.i | 0.0977404 | − | 1.04120i | ||||
\(447\) | − | 345965.i | − | 1.73148i | ||||||
\(448\) | 195010. | − | 47468.8i | 0.971629 | − | 0.236511i | ||||
\(449\) | −12867.9 | −0.0638287 | −0.0319144 | − | 0.999491i | \(-0.510160\pi\) | ||||
−0.0319144 | + | 0.999491i | \(0.510160\pi\) | |||||||
\(450\) | 37660.4 | + | 3535.27i | 0.185977 | + | 0.0174581i | ||||
\(451\) | −19172.8 | + | 11069.4i | −0.0942613 | + | 0.0544218i | ||||
\(452\) | 38246.3 | + | 7244.39i | 0.187203 | + | 0.0354589i | ||||
\(453\) | −100444. | + | 173975.i | −0.489474 | + | 0.847794i | ||||
\(454\) | 173895. | − | 79751.9i | 0.843674 | − | 0.386927i | ||||
\(455\) | −41542.1 | − | 146247.i | −0.200662 | − | 0.706423i | ||||
\(456\) | −13555.4 | − | 3909.57i | −0.0651901 | − | 0.0188018i | ||||
\(457\) | 24313.5 | − | 42112.1i | 0.116416 | − | 0.201639i | −0.801929 | − | 0.597420i | \(-0.796193\pi\) |
0.918345 | + | 0.395781i | \(0.129526\pi\) | |||||||
\(458\) | 33888.8 | − | 47751.8i | 0.161557 | − | 0.227645i | ||||
\(459\) | −91490.0 | + | 52821.8i | −0.434258 | + | 0.250719i | ||||
\(460\) | −119360. | + | 41739.4i | −0.564081 | + | 0.197256i | ||||
\(461\) | −36777.8 | −0.173055 | −0.0865274 | − | 0.996249i | \(-0.527577\pi\) | ||||
−0.0865274 | + | 0.996249i | \(0.527577\pi\) | |||||||
\(462\) | −45626.5 | − | 246308.i | −0.213763 | − | 1.15397i | ||||
\(463\) | − | 327574.i | − | 1.52809i | −0.645166 | − | 0.764043i | \(-0.723212\pi\) | ||
0.645166 | − | 0.764043i | \(-0.276788\pi\) | |||||||
\(464\) | 321392. | + | 126283.i | 1.49279 | + | 0.586556i | ||||
\(465\) | 81044.4 | + | 140373.i | 0.374815 | + | 0.649198i | ||||
\(466\) | −211455. | + | 297955.i | −0.973746 | + | 1.37208i | ||||
\(467\) | 59405.5 | + | 34297.8i | 0.272391 | + | 0.157265i | 0.629974 | − | 0.776616i | \(-0.283066\pi\) |
−0.357583 | + | 0.933881i | \(0.616399\pi\) | |||||||
\(468\) | 75435.6 | − | 87622.9i | 0.344417 | − | 0.400061i | ||||
\(469\) | 71459.8 | − | 283601.i | 0.324875 | − | 1.28932i | ||||
\(470\) | 202581. | − | 92908.1i | 0.917072 | − | 0.420589i | ||||
\(471\) | 21215.5 | + | 12248.8i | 0.0956337 | + | 0.0552142i | ||||
\(472\) | 210449. | − | 52126.2i | 0.944631 | − | 0.233976i | ||||
\(473\) | 109728. | + | 190054.i | 0.490450 | + | 0.849485i | ||||
\(474\) | −140474. | − | 13186.6i | −0.625229 | − | 0.0586918i | ||||
\(475\) | 2670.25i | 0.0118349i | ||||||||
\(476\) | −381460. | − | 176810.i | −1.68359 | − | 0.780358i | ||||
\(477\) | 107301. | 0.471592 | ||||||||
\(478\) | 9983.67 | − | 106354.i | 0.0436953 | − | 0.465475i | ||||
\(479\) | −317660. | + | 183401.i | −1.38450 | + | 0.799340i | −0.992688 | − | 0.120707i | \(-0.961484\pi\) |
−0.391809 | + | 0.920047i | \(0.628150\pi\) | |||||||
\(480\) | 154828. | − | 306324.i | 0.671998 | − | 1.32953i | ||||
\(481\) | −90171.8 | + | 156182.i | −0.389745 | + | 0.675058i | ||||
\(482\) | −129447. | − | 282252.i | −0.557182 | − | 1.21491i | ||||
\(483\) | 117216. | − | 120777.i | 0.502448 | − | 0.517716i | ||||
\(484\) | −35790.8 | + | 41573.2i | −0.152785 | + | 0.177469i | ||||
\(485\) | 16480.4 | − | 28544.8i | 0.0700621 | − | 0.121351i | ||||
\(486\) | 247830. | + | 175881.i | 1.04926 | + | 0.744642i | ||||
\(487\) | −118968. | + | 68686.5i | −0.501619 | + | 0.289610i | −0.729382 | − | 0.684107i | \(-0.760192\pi\) |
0.227763 | + | 0.973717i | \(0.426859\pi\) | |||||||
\(488\) | −91518.3 | + | 88106.0i | −0.384298 | + | 0.369969i | ||||
\(489\) | 72803.4 | 0.304462 | ||||||||
\(490\) | 222024. | + | 147780.i | 0.924714 | + | 0.615495i | ||||
\(491\) | 178509.i | 0.740451i | 0.928942 | + | 0.370226i | \(0.120720\pi\) | ||||
−0.928942 | + | 0.370226i | \(0.879280\pi\) | |||||||
\(492\) | 38112.9 | − | 13327.9i | 0.157450 | − | 0.0550593i | ||||
\(493\) | −361689. | − | 626463.i | −1.48813 | − | 2.57752i | ||||
\(494\) | 6656.20 | + | 4723.81i | 0.0272755 | + | 0.0193570i | ||||
\(495\) | −164713. | − | 95097.1i | −0.672229 | − | 0.388112i | ||||
\(496\) | 122421. | − | 18402.8i | 0.497615 | − | 0.0748031i | ||||
\(497\) | 80889.5 | + | 78504.1i | 0.327476 | + | 0.317819i | ||||
\(498\) | 32208.9 | + | 70229.7i | 0.129872 | + | 0.283180i | ||||
\(499\) | 209807. | + | 121132.i | 0.842594 | + | 0.486472i | 0.858145 | − | 0.513407i | \(-0.171617\pi\) |
−0.0155514 | + | 0.999879i | \(0.504950\pi\) | |||||||
\(500\) | 209025. | + | 39592.3i | 0.836102 | + | 0.158369i | ||||
\(501\) | −87950.0 | − | 152334.i | −0.350397 | − | 0.606905i | ||||
\(502\) | −12860.7 | + | 137002.i | −0.0510337 | + | 0.543650i | ||||
\(503\) | 390543.i | 1.54359i | 0.635869 | + | 0.771797i | \(0.280642\pi\) | ||||
−0.635869 | + | 0.771797i | \(0.719358\pi\) | |||||||
\(504\) | −817.505 | + | 202831.i | −0.00321832 | + | 0.798497i | ||||
\(505\) | 224805. | 0.881502 | ||||||||
\(506\) | 120007. | + | 11265.4i | 0.468713 | + | 0.0439993i | ||||
\(507\) | 168061. | − | 97029.9i | 0.653808 | − | 0.377476i | ||||
\(508\) | −38102.6 | + | 201160.i | −0.147648 | + | 0.779498i | ||||
\(509\) | 43311.3 | − | 75017.4i | 0.167173 | − | 0.289552i | −0.770252 | − | 0.637740i | \(-0.779870\pi\) |
0.937425 | + | 0.348188i | \(0.113203\pi\) | |||||||
\(510\) | −653558. | + | 299736.i | −2.51272 | + | 1.15239i | ||||
\(511\) | −42183.9 | − | 10629.2i | −0.161549 | − | 0.0407060i | ||||
\(512\) | −174506. | − | 195620.i | −0.665686 | − | 0.746232i | ||||
\(513\) | −1798.89 | + | 3115.76i | −0.00683548 | + | 0.0118394i | ||||
\(514\) | −91019.3 | + | 128253.i | −0.344514 | + | 0.485447i | ||||
\(515\) | 175465. | − | 101305.i | 0.661571 | − | 0.381958i | ||||
\(516\) | −132115. | − | 377802.i | −0.496196 | − | 1.41894i | ||||
\(517\) | −212450. | −0.794831 | ||||||||
\(518\) | −57625.4 | − | 311082.i | −0.214761 | − | 1.15935i | ||||
\(519\) | − | 169993.i | − | 0.631097i | ||||||
\(520\) | −143054. | + | 137720.i | −0.529047 | + | 0.509321i | ||||
\(521\) | 212972. | + | 368878.i | 0.784598 | + | 1.35896i | 0.929239 | + | 0.369479i | \(0.120464\pi\) |
−0.144642 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(522\) | −201970. | + | 284590.i | −0.741217 | + | 1.04443i | ||||
\(523\) | 379033. | + | 218835.i | 1.38571 | + | 0.800042i | 0.992829 | − | 0.119545i | \(-0.0381436\pi\) |
0.392885 | + | 0.919587i | \(0.371477\pi\) | |||||||
\(524\) | 279465. | + | 240594.i | 1.01780 | + | 0.876240i | ||||
\(525\) | 83178.7 | − | 23627.3i | 0.301782 | − | 0.0857225i | ||||
\(526\) | 4547.89 | − | 2085.76i | 0.0164376 | − | 0.00753865i | ||||
\(527\) | −224591. | − | 129668.i | −0.808670 | − | 0.466886i | ||||
\(528\) | −255881. | + | 203893.i | −0.917845 | + | 0.731366i | ||||
\(529\) | −99427.7 | − | 172214.i | −0.355301 | − | 0.615399i | ||||
\(530\) | −183477. | − | 17223.4i | −0.653176 | − | 0.0613152i | ||||
\(531\) | 219108.i | 0.777085i | ||||||||
\(532\) | −14261.2 | + | 1280.77i | −0.0503886 | + | 0.00452530i | ||||
\(533\) | −23359.4 | −0.0822257 | ||||||||
\(534\) | −40849.0 | + | 435154.i | −0.143251 | + | 1.52602i | ||||
\(535\) | 383863. | − | 221623.i | 1.34112 | − | 0.774297i | ||||
\(536\) | −370791. | + | 91841.5i | −1.29062 | + | 0.319676i | ||||
\(537\) | 128963. | − | 223370.i | 0.447214 | − | 0.774598i | ||||
\(538\) | 28073.3 | + | 61212.3i | 0.0969903 | + | 0.211482i | ||||
\(539\) | −133651. | − | 216275.i | −0.460040 | − | 0.744437i | ||||
\(540\) | −66333.8 | − | 57107.6i | −0.227482 | − | 0.195842i | ||||
\(541\) | −29263.4 | + | 50685.6i | −0.0999838 | + | 0.173177i | −0.911678 | − | 0.410906i | \(-0.865212\pi\) |
0.811694 | + | 0.584083i | \(0.198546\pi\) | |||||||
\(542\) | 55066.9 | + | 39080.2i | 0.187453 | + | 0.133033i | ||||
\(543\) | −11494.4 | + | 6636.27i | −0.0389839 | + | 0.0225073i | ||||
\(544\) | 30521.5 | + | 548304.i | 0.103136 | + | 1.85278i | ||||
\(545\) | −574217. | −1.93323 | ||||||||
\(546\) | 88251.2 | − | 249139.i | 0.296030 | − | 0.835713i | ||||
\(547\) | 430943.i | 1.44027i | 0.693832 | + | 0.720137i | \(0.255921\pi\) | ||||
−0.693832 | + | 0.720137i | \(0.744079\pi\) | |||||||
\(548\) | −8402.49 | − | 24028.1i | −0.0279800 | − | 0.0800126i | ||||
\(549\) | −64191.9 | − | 111184.i | −0.212979 | − | 0.368890i | ||||
\(550\) | 50501.4 | + | 35840.1i | 0.166947 | + | 0.118480i | ||||
\(551\) | −21334.7 | − | 12317.6i | −0.0702722 | − | 0.0405717i | ||||
\(552\) | −211218. | − | 60918.4i | −0.693191 | − | 0.199926i | ||||
\(553\) | −137749. | + | 39128.2i | −0.450442 | + | 0.127950i | ||||
\(554\) | −112576. | − | 245466.i | −0.366797 | − | 0.799782i | ||||
\(555\) | −468553. | − | 270519.i | −1.52115 | − | 0.878238i | ||||
\(556\) | 7080.79 | − | 37382.6i | 0.0229051 | − | 0.120926i | ||||
\(557\) | 34006.4 | + | 58900.9i | 0.109610 | + | 0.189850i | 0.915612 | − | 0.402062i | \(-0.131706\pi\) |
−0.806002 | + | 0.591912i | \(0.798373\pi\) | |||||||
\(558\) | −11693.0 | + | 124562.i | −0.0375540 | + | 0.400053i | ||||
\(559\) | 231555.i | 0.741020i | ||||||||
\(560\) | 33955.4 | − | 346696.i | 0.108276 | − | 1.10553i | ||||
\(561\) | 685395. | 2.17779 | ||||||||
\(562\) | −264794. | − | 24856.9i | −0.838370 | − | 0.0786999i | ||||
\(563\) | 201482. | − | 116326.i | 0.635652 | − | 0.366994i | −0.147286 | − | 0.989094i | \(-0.547054\pi\) |
0.782938 | + | 0.622100i | \(0.213720\pi\) | |||||||
\(564\) | 380689. | + | 72107.8i | 1.19677 | + | 0.226686i | ||||
\(565\) | 33781.6 | − | 58511.4i | 0.105824 | − | 0.183292i | ||||
\(566\) | 85803.5 | − | 39351.4i | 0.267838 | − | 0.122836i | ||||
\(567\) | 361903. | + | 91189.8i | 1.12571 | + | 0.283648i | ||||
\(568\) | 40799.5 | − | 141461.i | 0.126461 | − | 0.438471i | ||||
\(569\) | 119989. | − | 207827.i | 0.370610 | − | 0.641916i | −0.619049 | − | 0.785352i | \(-0.712482\pi\) |
0.989660 | + | 0.143436i | \(0.0458152\pi\) | |||||||
\(570\) | −14171.6 | + | 19968.9i | −0.0436184 | + | 0.0614616i | ||||
\(571\) | 177375. | − | 102407.i | 0.544026 | − | 0.314093i | −0.202683 | − | 0.979244i | \(-0.564966\pi\) |
0.746709 | + | 0.665151i | \(0.231633\pi\) | |||||||
\(572\) | 178679. | − | 62483.1i | 0.546112 | − | 0.190972i | ||||
\(573\) | 511349. | 1.55743 | ||||||||
\(574\) | 31163.2 | − | 26610.9i | 0.0945842 | − | 0.0807672i | ||||
\(575\) | 41607.5i | 0.125845i | ||||||||
\(576\) | 234297. | − | 123653.i | 0.706190 | − | 0.372699i | ||||
\(577\) | −131819. | − | 228317.i | −0.395937 | − | 0.685782i | 0.597284 | − | 0.802030i | \(-0.296247\pi\) |
−0.993220 | + | 0.116248i | \(0.962913\pi\) | |||||||
\(578\) | 472440. | − | 665703.i | 1.41414 | − | 1.99262i | ||||
\(579\) | −95153.8 | − | 54937.1i | −0.283837 | − | 0.163873i | ||||
\(580\) | 391035. | − | 454210.i | 1.16241 | − | 1.35021i | ||||
\(581\) | 56272.8 | + | 54613.3i | 0.166704 | + | 0.161788i | ||||
\(582\) | 52085.5 | − | 23887.5i | 0.153770 | − | 0.0705221i | ||||
\(583\) | 152132. | + | 87833.7i | 0.447594 | + | 0.258419i | ||||
\(584\) | 13660.8 | + | 55152.8i | 0.0400546 | + | 0.161712i | ||||
\(585\) | −100340. | − | 173794.i | −0.293199 | − | 0.507835i | ||||
\(586\) | 263863. | + | 24769.4i | 0.768392 | + | 0.0721309i | ||||
\(587\) | − | 600519.i | − | 1.74281i | −0.490563 | − | 0.871406i | \(-0.663209\pi\) | ||
0.490563 | − | 0.871406i | \(-0.336791\pi\) | |||||||
\(588\) | 166084. | + | 432906.i | 0.480367 | + | 1.25210i | ||||
\(589\) | −8831.88 | −0.0254579 | ||||||||
\(590\) | 35170.1 | − | 374659.i | 0.101035 | − | 1.07630i | ||||
\(591\) | −237519. | + | 137132.i | −0.680023 | + | 0.392611i | ||||
\(592\) | −323172. | + | 257513.i | −0.922127 | + | 0.734778i | ||||
\(593\) | 231916. | − | 401691.i | 0.659510 | − | 1.14231i | −0.321232 | − | 0.947000i | \(-0.604097\pi\) |
0.980743 | − | 0.195305i | \(-0.0625697\pi\) | |||||||
\(594\) | 34782.6 | + | 75841.5i | 0.0985800 | + | 0.214948i | ||||
\(595\) | −508232. | + | 523676.i | −1.43558 | + | 1.47921i | ||||
\(596\) | −299222. | + | 347563.i | −0.842365 | + | 0.978456i | ||||
\(597\) | −457030. | + | 791599.i | −1.28232 | + | 2.22104i | ||||
\(598\) | 103716. | + | 73605.8i | 0.290030 | + | 0.205830i | ||||
\(599\) | −465405. | + | 268702.i | −1.29711 | + | 0.748888i | −0.979904 | − | 0.199468i | \(-0.936079\pi\) |
−0.317208 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(600\) | −78329.0 | − | 81362.8i | −0.217581 | − | 0.226008i | ||||
\(601\) | −691321. | −1.91395 | −0.956975 | − | 0.290169i | \(-0.906288\pi\) | ||||
−0.956975 | + | 0.290169i | \(0.906288\pi\) | |||||||
\(602\) | −263785. | − | 308911.i | −0.727876 | − | 0.852395i | ||||
\(603\) | − | 386047.i | − | 1.06171i | ||||||
\(604\) | 251377. | − | 87905.2i | 0.689052 | − | 0.240958i | ||||
\(605\) | 47606.8 | + | 82457.4i | 0.130064 | + | 0.225278i | ||||
\(606\) | 318717. | + | 226189.i | 0.867879 | + | 0.615922i | ||||
\(607\) | −324117. | − | 187129.i | −0.879679 | − | 0.507883i | −0.00912673 | − | 0.999958i | \(-0.502905\pi\) |
−0.870553 | + | 0.492075i | \(0.836239\pi\) | |||||||
\(608\) | 10236.6 | + | 15651.5i | 0.0276917 | + | 0.0423398i | ||||
\(609\) | −194919. | + | 773570.i | −0.525556 | + | 2.08576i | ||||
\(610\) | 91917.0 | + | 200420.i | 0.247022 | + | 0.538619i | ||||
\(611\) | −194130. | − | 112081.i | −0.520008 | − | 0.300227i | ||||
\(612\) | −545282. | − | 103284.i | −1.45585 | − | 0.275759i | ||||
\(613\) | 334821. | + | 579927.i | 0.891029 | + | 1.54331i | 0.838644 | + | 0.544681i | \(0.183349\pi\) |
0.0523854 | + | 0.998627i | \(0.483318\pi\) | |||||||
\(614\) | 54501.9 | − | 580595.i | 0.144569 | − | 1.54006i | ||||
\(615\) | − | 70079.3i | − | 0.185285i | ||||||
\(616\) | −167191. | + | 286907.i | −0.440608 | + | 0.756101i | ||||
\(617\) | −423423. | −1.11225 | −0.556127 | − | 0.831097i | \(-0.687713\pi\) | ||||
−0.556127 | + | 0.831097i | \(0.687713\pi\) | |||||||
\(618\) | 350694. | + | 32920.5i | 0.918229 | + | 0.0861964i | ||||
\(619\) | 395702. | − | 228459.i | 1.03273 | − | 0.596248i | 0.114966 | − | 0.993369i | \(-0.463324\pi\) |
0.917766 | + | 0.397122i | \(0.129991\pi\) | |||||||
\(620\) | 39988.3 | − | 211116.i | 0.104028 | − | 0.549208i | ||||
\(621\) | −28030.0 | + | 48549.4i | −0.0726842 | + | 0.125893i | ||||
\(622\) | 400966. | − | 183892.i | 1.03640 | − | 0.475314i | ||||
\(623\) | 121210. | + | 426713.i | 0.312292 | + | 1.09941i | ||||
\(624\) | −341383. | + | 51317.8i | −0.876744 | + | 0.131795i | ||||
\(625\) | 230314. | − | 398915.i | 0.589604 | − | 1.02122i | ||||
\(626\) | −273350. | + | 385171.i | −0.697543 | + | 0.982890i | ||||
\(627\) | 20214.5 | − | 11670.8i | 0.0514195 | − | 0.0296870i | ||||
\(628\) | −10719.7 | − | 30654.4i | −0.0271808 | − | 0.0777272i | ||||
\(629\) | 865641. | 2.18795 | ||||||||
\(630\) | 331845. | + | 117548.i | 0.836093 | + | 0.296164i | ||||
\(631\) | − | 622726.i | − | 1.56401i | −0.623275 | − | 0.782003i | \(-0.714198\pi\) | ||
0.623275 | − | 0.782003i | \(-0.285802\pi\) | |||||||
\(632\) | 129718. | + | 134742.i | 0.324762 | + | 0.337340i | ||||
\(633\) | 268063. | + | 464299.i | 0.669005 | + | 1.15875i | ||||
\(634\) | 232099. | − | 327045.i | 0.577424 | − | 0.813633i | ||||
\(635\) | 307746. | + | 177677.i | 0.763212 | + | 0.440641i | ||||
\(636\) | −242795. | − | 209025.i | −0.600240 | − | 0.516754i | ||||
\(637\) | −8027.49 | − | 268135.i | −0.0197834 | − | 0.660807i | ||||
\(638\) | −519313. | + | 238168.i | −1.27582 | + | 0.585117i | ||||
\(639\) | 128855. | + | 74394.4i | 0.315573 | + | 0.182196i | ||||
\(640\) | −420479. | + | 173829.i | −1.02656 | + | 0.424387i | ||||
\(641\) | −277608. | − | 480831.i | −0.675641 | − | 1.17024i | −0.976281 | − | 0.216506i | \(-0.930534\pi\) |
0.300640 | − | 0.953738i | \(-0.402800\pi\) | |||||||
\(642\) | 767207. | + | 72019.6i | 1.86141 | + | 0.174735i | ||||
\(643\) | 173062.i | 0.418581i | 0.977853 | + | 0.209291i | \(0.0671155\pi\) | ||||
−0.977853 | + | 0.209291i | \(0.932885\pi\) | |||||||
\(644\) | −222216. | + | 19956.8i | −0.535801 | + | 0.0481192i | ||||
\(645\) | −694674. | −1.66979 | ||||||||
\(646\) | 3661.59 | − | 39006.1i | 0.00877415 | − | 0.0934689i | ||||
\(647\) | −260240. | + | 150250.i | −0.621678 | + | 0.358926i | −0.777522 | − | 0.628856i | \(-0.783524\pi\) |
0.155844 | + | 0.987782i | \(0.450190\pi\) | |||||||
\(648\) | −117199. | − | 473166.i | −0.279109 | − | 1.12684i | ||||
\(649\) | −179356. | + | 310653.i | −0.425820 | + | 0.737542i | ||||
\(650\) | 27238.7 | + | 59392.4i | 0.0644702 | + | 0.140574i | ||||
\(651\) | 78147.4 | + | 275114.i | 0.184396 | + | 0.649160i | ||||
\(652\) | −73139.6 | − | 62966.8i | −0.172051 | − | 0.148121i | ||||
\(653\) | 56179.8 | − | 97306.2i | 0.131751 | − | 0.228199i | −0.792601 | − | 0.609741i | \(-0.791273\pi\) |
0.924352 | + | 0.381542i | \(0.124607\pi\) | |||||||
\(654\) | −814095. | − | 577752.i | −1.90335 | − | 1.35078i | ||||
\(655\) | 554298. | − | 320024.i | 1.29199 | − | 0.745933i | ||||
\(656\) | −49816.1 | − | 19574.0i | −0.115761 | − | 0.0454854i | ||||
\(657\) | −57422.1 | −0.133030 | ||||||||
\(658\) | 386666. | − | 71626.8i | 0.893067 | − | 0.165434i | ||||
\(659\) | 42480.9i | 0.0978190i | 0.998803 | + | 0.0489095i | \(0.0155746\pi\) | ||||
−0.998803 | + | 0.0489095i | \(0.984425\pi\) | |||||||
\(660\) | 187452. | + | 536045.i | 0.430331 | + | 1.23059i | ||||
\(661\) | 312257. | + | 540845.i | 0.714676 | + | 1.23786i | 0.963084 | + | 0.269200i | \(0.0867592\pi\) |
−0.248408 | + | 0.968655i | \(0.579907\pi\) | |||||||
\(662\) | 275599. | + | 195589.i | 0.628871 | + | 0.446301i | ||||
\(663\) | 626293. | + | 361591.i | 1.42479 | + | 0.822603i | ||||
\(664\) | 28383.2 | − | 98411.1i | 0.0643762 | − | 0.223207i | ||||
\(665\) | −6072.29 | + | 24099.0i | −0.0137312 | + | 0.0544949i | ||||
\(666\) | −174088. | − | 379590.i | −0.392483 | − | 0.855787i | ||||
\(667\) | −332435. | − | 191931.i | −0.747230 | − | 0.431414i | ||||
\(668\) | −43395.6 | + | 229104.i | −0.0972507 | + | 0.513429i | ||||
\(669\) | −313848. | − | 543600.i | −0.701240 | − | 1.21458i | ||||
\(670\) | −61966.5 | + | 660114.i | −0.138041 | + | 1.47051i | ||||
\(671\) | − | 210183.i | − | 0.466824i | ||||||
\(672\) | 396970. | − | 457363.i | 0.879061 | − | 1.01280i | ||||
\(673\) | −364018. | −0.803698 | −0.401849 | − | 0.915706i | \(-0.631632\pi\) | ||||
−0.401849 | + | 0.915706i | \(0.631632\pi\) | |||||||
\(674\) | −830118. | − | 77925.2i | −1.82734 | − | 0.171537i | ||||
\(675\) | −24943.0 | + | 14400.8i | −0.0547445 | + | 0.0316068i | ||||
\(676\) | −252757. | − | 47875.7i | −0.553108 | − | 0.104766i | ||||
\(677\) | −219412. | + | 380033.i | −0.478722 | + | 0.829170i | −0.999702 | − | 0.0243981i | \(-0.992233\pi\) |
0.520981 | + | 0.853569i | \(0.325566\pi\) | |||||||
\(678\) | 106765. | − | 48964.9i | 0.232258 | − | 0.106519i | ||||
\(679\) | 40503.7 | − | 41734.5i | 0.0878528 | − | 0.0905223i | ||||
\(680\) | 915815. | + | 264134.i | 1.98057 | + | 0.571225i | ||||
\(681\) | 288634. | − | 499928.i | 0.622376 | − | 1.07799i | ||||
\(682\) | −118542. | + | 167034.i | −0.254860 | + | 0.359117i | ||||
\(683\) | −736037. | + | 424951.i | −1.57782 | + | 0.910957i | −0.582661 | + | 0.812716i | \(0.697988\pi\) |
−0.995163 | + | 0.0982412i | \(0.968678\pi\) | |||||||
\(684\) | −17840.8 | + | 6238.83i | −0.0381331 | + | 0.0133349i | ||||
\(685\) | −44181.1 | −0.0941577 | ||||||||
\(686\) | 316167. | + | 348568.i | 0.671843 | + | 0.740694i | ||||
\(687\) | − | 176686.i | − | 0.374359i | ||||||
\(688\) | −194031. | + | 493811.i | −0.409915 | + | 1.04324i | ||||
\(689\) | 92676.0 | + | 160520.i | 0.195222 | + | 0.338135i | ||||
\(690\) | −220821. | + | 311153.i | −0.463811 | + | 0.653544i | ||||
\(691\) | −702961. | − | 405855.i | −1.47223 | − | 0.849992i | −0.472716 | − | 0.881215i | \(-0.656726\pi\) |
−0.999512 | + | 0.0312229i | \(0.990060\pi\) | |||||||
\(692\) | −147025. | + | 170778.i | −0.307028 | + | 0.356631i | ||||
\(693\) | −240822. | − | 233720.i | −0.501452 | − | 0.486664i | ||||
\(694\) | −277799. | + | 127405.i | −0.576782 | + | 0.264525i | ||||
\(695\) | −57190.0 | − | 33018.7i | −0.118400 | − | 0.0683581i | ||||
\(696\) | 1.01139e6 | − | 250513.i | 2.08786 | − | 0.517145i | ||||
\(697\) | 56062.1 | + | 97102.3i | 0.115399 | + | 0.199878i | ||||
\(698\) | 6420.93 | + | 602.748i | 0.0131791 | + | 0.00123716i | ||||
\(699\) | 1.10246e6i | 2.25636i | ||||||||
\(700\) | −103998. | − | 48203.9i | −0.212240 | − | 0.0983754i | ||||
\(701\) | 428193. | 0.871373 | 0.435686 | − | 0.900099i | \(-0.356506\pi\) | ||||
0.435686 | + | 0.900099i | \(0.356506\pi\) | |||||||
\(702\) | −8228.09 | + | 87651.8i | −0.0166965 | + | 0.177863i | ||||
\(703\) | 25530.5 | − | 14740.0i | 0.0516593 | − | 0.0298255i | ||||
\(704\) | 433407. | + | 16473.2i | 0.874482 | + | 0.0332377i | ||||
\(705\) | 336248. | − | 582399.i | 0.676521 | − | 1.17177i | ||||
\(706\) | −48265.1 | − | 105239.i | −0.0968331 | − | 0.211139i | ||||
\(707\) | 384636. | + | 96917.8i | 0.769504 | + | 0.193894i | ||||
\(708\) | 426827. | − | 495785.i | 0.851502 | − | 0.989069i | ||||
\(709\) | 162620. | − | 281666.i | 0.323506 | − | 0.560328i | −0.657703 | − | 0.753277i | \(-0.728472\pi\) |
0.981209 | + | 0.192949i | \(0.0618051\pi\) | |||||||
\(710\) | −208391. | − | 147892.i | −0.413393 | − | 0.293379i | ||||
\(711\) | −163695. | + | 94509.3i | −0.323814 | + | 0.186954i | ||||
\(712\) | 417397. | − | 401834.i | 0.823360 | − | 0.792659i | ||||
\(713\) | −137617. | −0.270703 | ||||||||
\(714\) | −1.24744e6 | + | 231079.i | −2.44695 | + | 0.453278i | ||||
\(715\) | − | 328542.i | − | 0.642657i | ||||||
\(716\) | −322749. | + | 112863.i | −0.629562 | + | 0.220154i | ||||
\(717\) | −161163. | − | 279143.i | −0.313493 | − | 0.542985i | ||||
\(718\) | −547335. | − | 388436.i | −1.06171 | − | 0.753478i | ||||
\(719\) | 220013. | + | 127025.i | 0.425590 | + | 0.245714i | 0.697466 | − | 0.716618i | \(-0.254311\pi\) |
−0.271876 | + | 0.962332i | \(0.587644\pi\) | |||||||
\(720\) | −68353.6 | − | 454711.i | −0.131855 | − | 0.877143i | ||||
\(721\) | 343891. | − | 97683.7i | 0.661531 | − | 0.187911i | ||||
\(722\) | 216752. | + | 472616.i | 0.415804 | + | 0.906639i | ||||
\(723\) | −811443. | − | 468487.i | −1.55232 | − | 0.896233i | ||||
\(724\) | 17287.1 | + | 3274.41i | 0.0329795 | + | 0.00624678i | ||||
\(725\) | −98607.5 | − | 170793.i | −0.187600 | − | 0.324933i | ||||
\(726\) | −15470.5 | + | 164804.i | −0.0293516 | + | 0.312675i | ||||
\(727\) | 610597.i | 1.15528i | 0.816293 | + | 0.577638i | \(0.196025\pi\) | ||||
−0.816293 | + | 0.577638i | \(0.803975\pi\) | |||||||
\(728\) | −304137. | + | 173963.i | −0.573860 | + | 0.328241i | ||||
\(729\) | 300045. | 0.564588 | ||||||||
\(730\) | 98187.7 | + | 9217.12i | 0.184252 | + | 0.0172962i | ||||
\(731\) | 962546. | − | 555726.i | 1.80130 | − | 1.03998i | ||||
\(732\) | −71338.6 | + | 376628.i | −0.133138 | + | 0.702895i | ||||
\(733\) | 314941. | − | 545495.i | 0.586168 | − | 1.01527i | −0.408561 | − | 0.912731i | \(-0.633969\pi\) |
0.994729 | − | 0.102541i | \(-0.0326973\pi\) | |||||||
\(734\) | 269644. | − | 123664.i | 0.500493 | − | 0.229537i | ||||
\(735\) | 804417. | − | 24082.8i | 1.48904 | − | 0.0445793i | ||||
\(736\) | 159506. | + | 243880.i | 0.294457 | + | 0.450215i | ||||
\(737\) | 316008. | − | 547342.i | 0.581786 | − | 1.00768i | ||||
\(738\) | 31305.5 | − | 44111.7i | 0.0574788 | − | 0.0809919i | ||||
\(739\) | 627353. | − | 362203.i | 1.14874 | − | 0.663228i | 0.200163 | − | 0.979763i | \(-0.435853\pi\) |
0.948581 | + | 0.316535i | \(0.102519\pi\) | |||||||
\(740\) | 236748. | + | 677015.i | 0.432338 | + | 1.23633i | ||||
\(741\) | 24628.5 | 0.0448541 | ||||||||
\(742\) | −306499. | − | 108569.i | −0.556701 | − | 0.197197i | ||||
\(743\) | − | 578121.i | − | 1.04723i | −0.851956 | − | 0.523613i | \(-0.824584\pi\) | ||
0.851956 | − | 0.523613i | \(-0.175416\pi\) | |||||||
\(744\) | 269108. | − | 259074.i | 0.486162 | − | 0.468035i | ||||
\(745\) | 398006. | + | 689367.i | 0.717096 | + | 1.24205i | ||||
\(746\) | 57727.3 | − | 81342.0i | 0.103730 | − | 0.146163i | ||||
\(747\) | 89641.2 | + | 51754.4i | 0.160645 | + | 0.0927483i | ||||
\(748\) | −688561. | − | 592790.i | −1.23066 | − | 1.05949i | ||||
\(749\) | 752326. | − | 213701.i | 1.34104 | − | 0.380928i | ||||
\(750\) | 583497. | − | 267605.i | 1.03733 | − | 0.475742i | ||||
\(751\) | 495739. | + | 286215.i | 0.878968 | + | 0.507472i | 0.870318 | − | 0.492490i | \(-0.163913\pi\) |
0.00864991 | + | 0.999963i | \(0.497247\pi\) | |||||||
\(752\) | −320082. | − | 401694.i | −0.566012 | − | 0.710329i | ||||
\(753\) | 207606. | + | 359584.i | 0.366142 | + | 0.634177i | ||||
\(754\) | −600182. | − | 56340.5i | −1.05570 | − | 0.0991010i | ||||
\(755\) | − | 462214.i | − | 0.810866i | ||||||
\(756\) | −88875.3 | − | 126307.i | −0.155503 | − | 0.220996i | ||||
\(757\) | −181064. | −0.315966 | −0.157983 | − | 0.987442i | \(-0.550499\pi\) | ||||
−0.157983 | + | 0.987442i | \(0.550499\pi\) | |||||||
\(758\) | −75117.7 | + | 800210.i | −0.130739 | + | 1.39273i | ||||
\(759\) | 314979. | − | 181853.i | 0.546762 | − | 0.315673i | ||||
\(760\) | 31507.9 | − | 7804.23i | 0.0545498 | − | 0.0135115i | ||||
\(761\) | −522138. | + | 904369.i | −0.901604 | + | 1.56162i | −0.0761914 | + | 0.997093i | \(0.524276\pi\) |
−0.825412 | + | 0.564530i | \(0.809057\pi\) | |||||||
\(762\) | 257535. | + | 561542.i | 0.443534 | + | 0.967102i | ||||
\(763\) | −982472. | − | 247556.i | −1.68761 | − | 0.425231i | ||||
\(764\) | −513711. | − | 442260.i | −0.880100 | − | 0.757689i | ||||
\(765\) | −481627. | + | 834202.i | −0.822977 | + | 1.42544i | ||||
\(766\) | 238466. | + | 169236.i | 0.406414 | + | 0.288426i | ||||
\(767\) | −327780. | + | 189244.i | −0.557175 | + | 0.321685i | ||||
\(768\) | −771032. | − | 176622.i | −1.30722 | − | 0.299448i | ||||
\(769\) | −479929. | −0.811567 | −0.405783 | − | 0.913969i | \(-0.633001\pi\) | ||||
−0.405783 | + | 0.913969i | \(0.633001\pi\) | |||||||
\(770\) | 374273. | + | 438300.i | 0.631258 | + | 0.739248i | ||||
\(771\) | 474548.i | 0.798309i | ||||||||
\(772\) | 48078.9 | + | 137488.i | 0.0806714 | + | 0.230691i | ||||
\(773\) | −472697. | − | 818735.i | −0.791086 | − | 1.37020i | −0.925295 | − | 0.379248i | \(-0.876183\pi\) |
0.134209 | − | 0.990953i | \(-0.457151\pi\) | |||||||
\(774\) | −437266. | − | 310321.i | −0.729901 | − | 0.518000i | ||||
\(775\) | −61230.5 | − | 35351.4i | −0.101945 | − | 0.0588577i | ||||
\(776\) | −72986.1 | − | 21050.3i | −0.121204 | − | 0.0349570i | ||||
\(777\) | −685057. | − | 664855.i | −1.13471 | − | 1.10125i | ||||
\(778\) | 133763. | + | 291664.i | 0.220993 | + | 0.481863i | ||||
\(779\) | 3306.90 | + | 1909.24i | 0.00544936 | + | 0.00314619i | ||||
\(780\) | −111511. | + | 588715.i | −0.183286 | + | 0.967645i | ||||
\(781\) | 121795. | + | 210954.i | 0.199676 | + | 0.345849i | ||||
\(782\) | 57054.5 | − | 607787.i | 0.0932988 | − | 0.993889i | ||||
\(783\) | − | 265718.i | − | 0.433409i | ||||||
\(784\) | 207564. | − | 578549.i | 0.337692 | − | 0.941257i | ||||
\(785\) | −56365.0 | −0.0914682 | ||||||||
\(786\) | 1.10785e6 | + | 103996.i | 1.79323 | + | 0.168335i | ||||
\(787\) | −781750. | + | 451343.i | −1.26217 | + | 0.728715i | −0.973494 | − | 0.228712i | \(-0.926549\pi\) |
−0.288677 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(788\) | 357220. | + | 67662.4i | 0.575285 | + | 0.108967i | ||||
\(789\) | 7548.68 | − | 13074.7i | 0.0121260 | − | 0.0210028i | ||||
\(790\) | 295077. | − | 135329.i | 0.472804 | − | 0.216838i | ||||
\(791\) | 83024.8 | − | 85547.7i | 0.132695 | − | 0.136727i | ||||
\(792\) | −121467. | + | 421154.i | −0.193646 | + | 0.671414i | ||||
\(793\) | 110885. | − | 192059.i | 0.176331 | − | 0.305414i | ||||
\(794\) | 188902. | − | 266177.i | 0.299637 | − | 0.422211i | ||||
\(795\) | −481566. | + | 278032.i | −0.761941 | + | 0.439907i | ||||
\(796\) | 1.14379e6 | − | 399976.i | 1.80517 | − | 0.631259i | ||||
\(797\) | −808501. | −1.27281 | −0.636406 | − | 0.771355i | \(-0.719580\pi\) | ||||
−0.636406 | + | 0.771355i | \(0.719580\pi\) | |||||||
\(798\) | −32856.3 | + | 28056.6i | −0.0515956 | + | 0.0440585i | ||||
\(799\) | 1.07597e6i | 1.68541i | ||||||||
\(800\) | 8321.10 | + | 149484.i | 0.0130017 | + | 0.233569i | ||||
\(801\) | 292767. | + | 507087.i | 0.456307 | + | 0.790346i | ||||
\(802\) | −244809. | + | 344953.i | −0.380608 | + | 0.536305i | ||||
\(803\) | −81413.7 | − | 47004.2i | −0.126260 | − | 0.0728963i | ||||
\(804\) | −752030. | + | 873526.i | −1.16338 | + | 1.35134i | ||||
\(805\) | −94617.7 | + | 375507.i | −0.146009 | + | 0.579464i | ||||
\(806\) | −196441. | + | 90092.2i | −0.302386 | + | 0.138681i | ||||
\(807\) | 175979. | + | 101601.i | 0.270217 | + | 0.156010i | ||||
\(808\) | −124561. | − | 502888.i | −0.190791 | − | 0.770279i | ||||
\(809\) | 386141. | + | 668816.i | 0.589996 | + | 1.02190i | 0.994232 | + | 0.107249i | \(0.0342041\pi\) |
−0.404236 | + | 0.914655i | \(0.632463\pi\) | |||||||
\(810\) | −842371. | − | 79075.4i | −1.28391 | − | 0.120523i | ||||
\(811\) | 381341.i | 0.579791i | 0.957058 | + | 0.289895i | \(0.0936205\pi\) | ||||
−0.957058 | + | 0.289895i | \(0.906379\pi\) | |||||||
\(812\) | 864870. | − | 608560.i | 1.31171 | − | 0.922977i | ||||
\(813\) | 203752. | 0.308263 | ||||||||
\(814\) | 63898.0 | − | 680690.i | 0.0964359 | − | 1.02731i | ||||
\(815\) | −145067. | + | 83754.6i | −0.218401 | + | 0.126094i | ||||
\(816\) | 1.03263e6 | + | 1.29593e6i | 1.55084 | + | 1.94626i | ||||
\(817\) | 18925.7 | − | 32780.3i | 0.0283536 | − | 0.0491098i | ||||
\(818\) | −168852. | − | 368172.i | −0.252347 | − | 0.550229i | ||||
\(819\) | −96753.2 | − | 340615.i | −0.144244 | − | 0.507804i | ||||
\(820\) | −60610.7 | + | 70402.9i | −0.0901409 | + | 0.104704i | ||||
\(821\) | −305496. | + | 529134.i | −0.453230 | + | 0.785017i | −0.998585 | − | 0.0531881i | \(-0.983062\pi\) |
0.545355 | + | 0.838205i | \(0.316395\pi\) | |||||||
\(822\) | −62637.7 | − | 44453.1i | −0.0927026 | − | 0.0657897i | ||||
\(823\) | 449491. | − | 259514.i | 0.663623 | − | 0.383143i | −0.130033 | − | 0.991510i | \(-0.541508\pi\) |
0.793656 | + | 0.608367i | \(0.208175\pi\) | |||||||
\(824\) | −323841. | − | 336383.i | −0.476955 | − | 0.495427i | ||||
\(825\) | 186860. | 0.274541 | ||||||||
\(826\) | 221698. | − | 625869.i | 0.324939 | − | 0.917326i | ||||
\(827\) | 144933.i | 0.211912i | 0.994371 | + | 0.105956i | \(0.0337903\pi\) | ||||
−0.994371 | + | 0.105956i | \(0.966210\pi\) | |||||||
\(828\) | −277993. | + | 97212.6i | −0.405484 | + | 0.141795i | ||||
\(829\) | −277028. | − | 479827.i | −0.403102 | − | 0.698193i | 0.590997 | − | 0.806674i | \(-0.298735\pi\) |
−0.994099 | + | 0.108481i | \(0.965401\pi\) | |||||||
\(830\) | −144973. | − | 102885.i | −0.210441 | − | 0.149347i | ||||
\(831\) | −705687. | − | 407429.i | −1.02190 | − | 0.589997i | ||||
\(832\) | 387344. | + | 243703.i | 0.559564 | + | 0.352058i | ||||
\(833\) | −1.09534e6 | + | 676887.i | −1.57855 | + | 0.975498i | ||||
\(834\) | −47859.1 | − | 104354.i | −0.0688069 | − | 0.150030i | ||||
\(835\) | 350497. | + | 202359.i | 0.502702 | + | 0.290235i | ||||
\(836\) | −30401.8 | − | 5758.53i | −0.0434998 | − | 0.00823947i | ||||
\(837\) | −47630.9 | − | 82499.2i | −0.0679889 | − | 0.117760i | ||||
\(838\) | −89852.9 | + | 957181.i | −0.127951 | + | 1.36303i | ||||
\(839\) | 213623.i | 0.303475i | 0.988421 | + | 0.151738i | \(0.0484869\pi\) | ||||
−0.988421 | + | 0.151738i | \(0.951513\pi\) | |||||||
\(840\) | −521896. | − | 912423.i | −0.739648 | − | 1.29312i | ||||
\(841\) | 1.11218e6 | 1.57248 | ||||||||
\(842\) | 609955. | + | 57258.0i | 0.860347 | + | 0.0807629i | ||||
\(843\) | −694996. | + | 401256.i | −0.977974 | + | 0.564634i | ||||
\(844\) | 132266. | − | 698288.i | 0.185679 | − | 0.980279i | ||||
\(845\) | −223251. | + | 386682.i | −0.312665 | + | 0.541552i | ||||
\(846\) | 471819. | − | 216387.i | 0.659227 | − | 0.302336i | ||||
\(847\) | 45905.1 | + | 161607.i | 0.0639873 | + | 0.225265i | ||||
\(848\) | 63132.9 | + | 419980.i | 0.0877938 | + | 0.584033i | ||||
\(849\) | 142418. | − | 246676.i | 0.197583 | − | 0.342225i | ||||
\(850\) | 181515. | − | 255768.i | 0.251232 | − | 0.354005i | ||||
\(851\) | 397813. | − | 229677.i | 0.549313 | − | 0.317146i | ||||
\(852\) | −146644. | − | 419348.i | −0.202015 | − | 0.577691i | ||||
\(853\) | 1.16857e6 | 1.60605 | 0.803024 | − | 0.595947i | \(-0.203223\pi\) | ||||
0.803024 | + | 0.595947i | \(0.203223\pi\) | |||||||
\(854\) | 70862.7 | + | 382541.i | 0.0971633 | + | 0.524521i | ||||
\(855\) | 32804.4i | 0.0448745i | ||||||||
\(856\) | −708462. | − | 735901.i | −0.966872 | − | 1.00432i | ||||
\(857\) | −401117. | − | 694756.i | −0.546147 | − | 0.945955i | −0.998534 | − | 0.0541328i | \(-0.982761\pi\) |
0.452386 | − | 0.891822i | \(-0.350573\pi\) | |||||||
\(858\) | 330564. | − | 465790.i | 0.449036 | − | 0.632726i | ||||
\(859\) | −912156. | − | 526633.i | −1.23618 | − | 0.713711i | −0.267871 | − | 0.963455i | \(-0.586320\pi\) |
−0.968312 | + | 0.249744i | \(0.919653\pi\) | |||||||
\(860\) | 697883. | + | 600816.i | 0.943595 | + | 0.812352i | ||||
\(861\) | 30212.6 | − | 119904.i | 0.0407550 | − | 0.161744i | ||||
\(862\) | −494753. | + | 226905.i | −0.665846 | + | 0.305372i | ||||
\(863\) | 91314.2 | + | 52720.3i | 0.122607 | + | 0.0707874i | 0.560049 | − | 0.828459i | \(-0.310782\pi\) |
−0.437442 | + | 0.899247i | \(0.644115\pi\) | |||||||
\(864\) | −90994.9 | + | 180031.i | −0.121896 | + | 0.241168i | ||||
\(865\) | 195563. | + | 338726.i | 0.261370 | + | 0.452706i | ||||
\(866\) | −519755. | − | 48790.7i | −0.693047 | − | 0.0650580i | ||||
\(867\) | − | 2.46316e6i | − | 3.27683i | ||||||
\(868\) | 159435. | − | 343974.i | 0.211614 | − | 0.456548i | ||||
\(869\) | −309451. | −0.409782 | ||||||||
\(870\) | 169024. | − | 1.80057e6i | 0.223311 | − | 2.37888i | ||||
\(871\) | 577517. | − | 333430.i | 0.761252 | − | 0.439509i | ||||
\(872\) | 318164. | + | 1.28452e6i | 0.418426 | + | 1.68931i | ||||
\(873\) | 38383.4 | − | 66482.0i | 0.0503634 | − | 0.0872319i | ||||
\(874\) | −8666.62 | − | 18897.1i | −0.0113456 | − | 0.0247384i | ||||
\(875\) | 453751. | − | 467538.i | 0.592654 | − | 0.610662i | ||||
\(876\) | 129932. | + | 111860.i | 0.169319 | + | 0.145769i | ||||
\(877\) | −728314. | + | 1.26148e6i | −0.946933 | + | 1.64014i | −0.195100 | + | 0.980783i | \(0.562503\pi\) |
−0.751833 | + | 0.659353i | \(0.770830\pi\) | |||||||
\(878\) | 1.03716e6 | + | 736058.i | 1.34542 | + | 0.954823i | ||||
\(879\) | 692552. | − | 399845.i | 0.896343 | − | 0.517504i | ||||
\(880\) | 275302. | − | 700646.i | 0.355503 | − | 0.904760i | ||||
\(881\) | 541199. | 0.697277 | 0.348638 | − | 0.937257i | \(-0.386644\pi\) | ||||
0.348638 | + | 0.937257i | \(0.386644\pi\) | |||||||
\(882\) | 517102. | + | 344186.i | 0.664721 | + | 0.442442i | ||||
\(883\) | 16040.6i | 0.0205731i | 0.999947 | + | 0.0102865i | \(0.00327437\pi\) | ||||
−0.999947 | + | 0.0102865i | \(0.996726\pi\) | |||||||
\(884\) | −316451. | − | 904935.i | −0.404950 | − | 1.15801i | ||||
\(885\) | −567740. | − | 983354.i | −0.724874 | − | 1.25552i | ||||
\(886\) | −815310. | − | 578614.i | −1.03862 | − | 0.737091i | ||||
\(887\) | 580624. | + | 335223.i | 0.737985 | + | 0.426076i | 0.821336 | − | 0.570444i | \(-0.193229\pi\) |
−0.0833509 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(888\) | −345533. | + | 1.19804e6i | −0.438191 | + | 1.51931i | ||||
\(889\) | 449946. | + | 436677.i | 0.569321 | + | 0.552531i | ||||
\(890\) | −419215. | − | 914077.i | −0.529246 | − | 1.15399i | ||||
\(891\) | 698463. | + | 403258.i | 0.879808 | + | 0.507958i | ||||
\(892\) | −154856. | + | 817554.i | −0.194625 | + | 1.02751i | ||||
\(893\) | 18321.5 | + | 31733.7i | 0.0229751 | + | 0.0397940i | ||||
\(894\) | −129338. | + | 1.37780e6i | −0.161827 | + | 1.72390i | ||||
\(895\) | 593447.i | 0.740859i | ||||||||
\(896\) | −794371. | + | 116140.i | −0.989481 | + | 0.144666i | ||||
\(897\) | 383758. | 0.476950 | ||||||||
\(898\) | 51246.5 | + | 4810.63i | 0.0635494 | + | 0.00596553i | ||||
\(899\) | 564900. | − | 326145.i | 0.698960 | − | 0.403545i | ||||
\(900\) | −148661. | − | 28158.4i | −0.183532 | − | 0.0347634i | ||||
\(901\) | 444841. | − | 770487.i | 0.547968 | − | 0.949108i | ||||
\(902\) | 80493.9 | − | 36916.3i | 0.0989350 | − | 0.0453738i | ||||
\(903\) | −1.18857e6 | − | 299488.i | −1.45764 | − | 0.367285i | ||||
\(904\) | −149607. | − | 43149.0i | −0.183070 | − | 0.0528000i | ||||
\(905\) | 15269.0 | − | 26446.7i | 0.0186429 | − | 0.0322905i | ||||
\(906\) | 465059. | − | 655303.i | 0.566567 | − | 0.798336i | ||||
\(907\) | −1.07365e6 | + | 619873.i | −1.30511 | + | 0.753508i | −0.981277 | − | 0.192604i | \(-0.938307\pi\) |
−0.323838 | + | 0.946112i | \(0.604973\pi\) | |||||||
\(908\) | −722349. | + | 252601.i | −0.876144 | + | 0.306382i | ||||
\(909\) | 523579. | 0.633658 | ||||||||
\(910\) | 110767. | + | 597959.i | 0.133761 | + | 0.722085i | ||||
\(911\) | 1.12252e6i | 1.35256i | 0.736645 | + | 0.676279i | \(0.236409\pi\) | ||||
−0.736645 | + | 0.676279i | \(0.763591\pi\) | |||||||
\(912\) | 52522.6 | + | 20637.4i | 0.0631475 | + | 0.0248123i | ||||
\(913\) | 84729.5 | + | 146756.i | 0.101647 | + | 0.176057i | ||||
\(914\) | −112572. | + | 158622.i | −0.134752 | + | 0.189876i | ||||
\(915\) | 576186. | + | 332661.i | 0.688209 | + | 0.397338i | ||||
\(916\) | −152814. | + | 177502.i | −0.182126 | + | 0.211550i | ||||
\(917\) | 1.08636e6 | − | 308585.i | 1.29192 | − | 0.366974i | ||||
\(918\) | 384105. | − | 176159.i | 0.455790 | − | 0.209035i | ||||
\(919\) | 106736. | + | 61624.3i | 0.126381 | + | 0.0729661i | 0.561858 | − | 0.827234i | \(-0.310087\pi\) |
−0.435477 | + | 0.900200i | \(0.643420\pi\) | |||||||
\(920\) | 490953. | − | 121605.i | 0.580048 | − | 0.143673i | ||||
\(921\) | −879805. | − | 1.52387e6i | −1.03721 | − | 1.79650i | ||||
\(922\) | 146467. | + | 13749.2i | 0.172297 | + | 0.0161740i | ||||
\(923\) | 257018.i | 0.301690i | ||||||||
\(924\) | 89626.1 | + | 997975.i | 0.104976 | + | 1.16890i | ||||
\(925\) | 236000. | 0.275822 | ||||||||
\(926\) | −122462. | + | 1.30456e6i | −0.142817 | + | 1.52140i | ||||
\(927\) | 408665. | − | 235943.i | 0.475563 | − | 0.274566i | ||||
\(928\) | −1.23273e6 | − | 623073.i | −1.43144 | − | 0.723507i | ||||
\(929\) | 63711.1 | − | 110351.i | 0.0738216 | − | 0.127863i | −0.826752 | − | 0.562567i | \(-0.809814\pi\) |
0.900573 | + | 0.434704i | \(0.143147\pi\) | |||||||
\(930\) | −270281. | − | 589332.i | −0.312499 | − | 0.681388i | ||||
\(931\) | −20779.1 | + | 38614.9i | −0.0239733 | + | 0.0445508i | ||||
\(932\) | 953506. | − | 1.10755e6i | 1.09772 | − | 1.27507i | ||||
\(933\) | 665530. | − | 1.15273e6i | 0.764548 | − | 1.32424i | ||||
\(934\) | −223760. | − | 158799.i | −0.256501 | − | 0.182035i | ||||
\(935\) | −1.36571e6 | + | 788494.i | −1.56220 | + | 0.901935i | ||||
\(936\) | −333179. | + | 320756.i | −0.380300 | + | 0.366120i | ||||
\(937\) | −1.48894e6 | −1.69589 | −0.847944 | − | 0.530085i | \(-0.822160\pi\) | ||||
−0.847944 | + | 0.530085i | \(0.822160\pi\) | |||||||
\(938\) | −390611. | + | 1.10272e6i | −0.443955 | + | 1.25332i | ||||
\(939\) | 1.42517e6i | 1.61635i | ||||||||
\(940\) | −841511. | + | 294272.i | −0.952366 | + | 0.333037i | ||||
\(941\) | −303825. | − | 526241.i | −0.343119 | − | 0.594299i | 0.641891 | − | 0.766796i | \(-0.278150\pi\) |
−0.985010 | + | 0.172496i | \(0.944817\pi\) | |||||||
\(942\) | −79911.3 | − | 56711.9i | −0.0900547 | − | 0.0639106i | ||||
\(943\) | 51527.6 | + | 29749.5i | 0.0579451 | + | 0.0334546i | ||||
\(944\) | −857597. | + | 128917.i | −0.962364 | + | 0.144666i | ||||
\(945\) | −257859. | + | 73245.7i | −0.288747 | + | 0.0820198i | ||||
\(946\) | −365940. | − | 797911.i | −0.408909 | − | 0.891605i | ||||
\(947\) | 72005.3 | + | 41572.3i | 0.0802906 | + | 0.0463558i | 0.539608 | − | 0.841917i | \(-0.318573\pi\) |
−0.459317 | + | 0.888272i | \(0.651906\pi\) | |||||||
\(948\) | 554506. | + | 105031.i | 0.617007 | + | 0.116870i | ||||
\(949\) | −49595.6 | − | 85902.1i | −0.0550694 | − | 0.0953830i | ||||
\(950\) | 998.263 | − | 10634.2i | 0.00110611 | − | 0.0117831i | ||||
\(951\) | − | 1.21009e6i | − | 1.33801i | ||||||
\(952\) | 1.45306e6 | + | 846753.i | 1.60328 | + | 0.934293i | ||||
\(953\) | 356578. | 0.392616 | 0.196308 | − | 0.980542i | \(-0.437105\pi\) | ||||
0.196308 | + | 0.980542i | \(0.437105\pi\) | |||||||
\(954\) | −427325. | − | 40114.0i | −0.469528 | − | 0.0440758i | ||||
\(955\) | −1.01891e6 | + | 588267.i | −1.11719 | + | 0.645012i | ||||
\(956\) | −79519.8 | + | 419820.i | −0.0870081 | + | 0.459354i | ||||
\(957\) | −861965. | + | 1.49297e6i | −0.941166 | + | 1.63015i | ||||
\(958\) | 1.33364e6 | − | 611638.i | 1.45314 | − | 0.666444i | ||||
\(959\) | −75592.8 | − | 19047.4i | −0.0821946 | − | 0.0207108i | ||||
\(960\) | −731121. | + | 1.16205e6i | −0.793317 | + | 1.26090i | ||||
\(961\) | −344835. | + | 597272.i | −0.373392 | + | 0.646734i | ||||
\(962\) | 417497. | − | 588284.i | 0.451131 | − | 0.635677i | ||||
\(963\) | 894031. | − | 516169.i | 0.964051 | − | 0.556595i | ||||
\(964\) | 410002. | + | 1.17246e6i | 0.441196 | + | 1.26166i | ||||
\(965\) | 252803. | 0.271474 | ||||||||
\(966\) | −511963. | + | 437174.i | −0.548636 | + | 0.468490i | ||||
\(967\) | − | 1.07395e6i | − | 1.14850i | −0.818679 | − | 0.574251i | \(-0.805293\pi\) | ||
0.818679 | − | 0.574251i | \(-0.194707\pi\) | |||||||
\(968\) | 158079. | − | 152185.i | 0.168703 | − | 0.162413i | ||||
\(969\) | −59107.9 | − | 102378.i | −0.0629503 | − | 0.109033i | ||||
\(970\) | −76304.3 | + | 107518.i | −0.0810971 | + | 0.114272i | ||||
\(971\) | 1.27167e6 | + | 734201.i | 1.34877 | + | 0.778711i | 0.988075 | − | 0.153974i | \(-0.0492072\pi\) |
0.360692 | + | 0.932685i | \(0.382540\pi\) | |||||||
\(972\) | −921228. | − | 793096.i | −0.975067 | − | 0.839447i | ||||
\(973\) | −83615.7 | − | 81149.8i | −0.0883206 | − | 0.0857160i | ||||
\(974\) | 499469. | − | 229067.i | 0.526491 | − | 0.241460i | ||||
\(975\) | 170747. | + | 98580.7i | 0.179615 | + | 0.103701i | ||||
\(976\) | 397409. | − | 316667.i | 0.417194 | − | 0.332433i | ||||
\(977\) | −531841. | − | 921176.i | −0.557177 | − | 0.965058i | −0.997731 | − | 0.0673321i | \(-0.978551\pi\) |
0.440554 | − | 0.897726i | \(-0.354782\pi\) | |||||||
\(978\) | −289939. | − | 27217.3i | −0.303130 | − | 0.0284555i | ||||
\(979\) | 958605.i | 1.00017i | ||||||||
\(980\) | −828961. | − | 671537.i | −0.863142 | − | 0.699226i | ||||
\(981\) | −1.33737e6 | −1.38968 | ||||||||
\(982\) | 66734.8 | − | 710909.i | 0.0692037 | − | 0.737210i | ||||
\(983\) | −907239. | + | 523795.i | −0.938890 | + | 0.542068i | −0.889612 | − | 0.456717i | \(-0.849025\pi\) |
−0.0492778 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(984\) | −156767. | + | 38829.8i | −0.161907 | + | 0.0401028i | ||||
\(985\) | 315519. | − | 546495.i | 0.325202 | − | 0.563266i | ||||
\(986\) | 1.20622e6 | + | 2.63010e6i | 1.24072 | + | 2.70532i | ||||
\(987\) | 826396. | − | 851507.i | 0.848309 | − | 0.874085i | ||||
\(988\) | −24742.3 | − | 21300.9i | −0.0253469 | − | 0.0218215i | ||||
\(989\) | 294898. | − | 510778.i | 0.301494 | − | 0.522203i | ||||
\(990\) | 620417. | + | 440301.i | 0.633013 | + | 0.449241i | ||||
\(991\) | 1.32227e6 | − | 763412.i | 1.34639 | − | 0.777341i | 0.358657 | − | 0.933469i | \(-0.383235\pi\) |
0.987737 | + | 0.156128i | \(0.0499013\pi\) | |||||||
\(992\) | −494421. | + | 27522.1i | −0.502428 | + | 0.0279678i | ||||
\(993\) | 1.01974e6 | 1.03417 | ||||||||
\(994\) | −292793. | − | 342882.i | −0.296339 | − | 0.347034i | ||||
\(995\) | − | 2.10311e6i | − | 2.12430i | ||||||
\(996\) | −102016. | − | 291730.i | −0.102837 | − | 0.294078i | ||||
\(997\) | 737619. | + | 1.27759e6i | 0.742065 | + | 1.28529i | 0.951554 | + | 0.307483i | \(0.0994866\pi\) |
−0.209489 | + | 0.977811i | \(0.567180\pi\) | |||||||
\(998\) | −790268. | − | 560842.i | −0.793439 | − | 0.563092i | ||||
\(999\) | 275375. | + | 158988.i | 0.275927 | + | 0.159307i |
(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 | 28.5.g.a.23.1 | yes | 28 | |
4.3 | odd | 2 | inner | 28.5.g.a.23.10 | yes | 28 | |
7.2 | even | 3 | 196.5.c.h.99.10 | 14 | |||
7.4 | even | 3 | inner | 28.5.g.a.11.10 | yes | 28 | |
7.5 | odd | 6 | 196.5.c.g.99.10 | 14 | |||
28.11 | odd | 6 | inner | 28.5.g.a.11.1 | ✓ | 28 | |
28.19 | even | 6 | 196.5.c.g.99.9 | 14 | |||
28.23 | odd | 6 | 196.5.c.h.99.9 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.5.g.a.11.1 | ✓ | 28 | 28.11 | odd | 6 | inner | |
28.5.g.a.11.10 | yes | 28 | 7.4 | even | 3 | inner | |
28.5.g.a.23.1 | yes | 28 | 1.1 | even | 1 | trivial | |
28.5.g.a.23.10 | yes | 28 | 4.3 | odd | 2 | inner | |
196.5.c.g.99.9 | 14 | 28.19 | even | 6 | |||
196.5.c.g.99.10 | 14 | 7.5 | odd | 6 | |||
196.5.c.h.99.9 | 14 | 28.23 | odd | 6 | |||
196.5.c.h.99.10 | 14 | 7.2 | even | 3 |