Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.2 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.4.h.b.71.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66543 | − | 0.946295i | −0.942372 | − | 0.334566i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.20905 | + | 5.04457i | 0.776131 | + | 0.630571i | ||||
\(5\) | −2.08666 | + | 1.20474i | −0.186637 | + | 0.107755i | −0.590407 | − | 0.807106i | \(-0.701033\pi\) |
0.403770 | + | 0.914860i | \(0.367699\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30362 | + | 1.33000i | 0.124384 | + | 0.0718131i | 0.560901 | − | 0.827883i | \(-0.310455\pi\) |
−0.436517 | + | 0.899696i | \(0.643788\pi\) | |||||||
\(8\) | −11.7761 | − | 19.3216i | −0.520437 | − | 0.853900i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.70190 | − | 1.23654i | 0.211933 | − | 0.0391029i | ||||
\(11\) | −24.1428 | + | 41.8166i | −0.661758 | + | 1.14620i | 0.318395 | + | 0.947958i | \(0.396856\pi\) |
−0.980153 | + | 0.198241i | \(0.936477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3570 | − | 35.2594i | −0.434309 | − | 0.752245i | 0.562930 | − | 0.826505i | \(-0.309674\pi\) |
−0.997239 | + | 0.0742593i | \(0.976341\pi\) | |||||||
\(14\) | −4.88158 | − | 5.72493i | −0.0931898 | − | 0.109289i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.1046 | + | 62.6440i | 0.204759 | + | 0.978812i | ||||
\(17\) | 36.3729i | 0.518925i | 0.965753 | + | 0.259463i | \(0.0835455\pi\) | ||||
−0.965753 | + | 0.259463i | \(0.916455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.173i | 1.51141i | 0.654914 | + | 0.755703i | \(0.272705\pi\) | ||||
−0.654914 | + | 0.755703i | \(0.727295\pi\) | |||||||
\(20\) | −19.0336 | − | 3.04606i | −0.212802 | − | 0.0340560i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 103.922 | − | 88.6131i | 1.00710 | − | 0.858745i | ||||
\(23\) | 97.0560 | + | 168.106i | 0.879894 | + | 1.52402i | 0.851456 | + | 0.524426i | \(0.175720\pi\) |
0.0284384 | + | 0.999596i | \(0.490947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −59.5972 | + | 103.225i | −0.476778 | + | 0.825803i | ||||
\(26\) | 20.8944 | + | 113.245i | 0.157605 | + | 0.854200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.59405 | + | 19.8788i | 0.0512550 | + | 0.134169i | ||||
\(29\) | −153.593 | − | 88.6772i | −0.983503 | − | 0.567826i | −0.0801773 | − | 0.996781i | \(-0.525549\pi\) |
−0.903326 | + | 0.428955i | \(0.858882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.058 | + | 87.7909i | −0.880983 | + | 0.508636i | −0.870982 | − | 0.491314i | \(-0.836517\pi\) |
−0.0100006 | + | 0.999950i | \(0.503183\pi\) | |||||||
\(32\) | 24.3503 | − | 179.374i | 0.134518 | − | 0.990911i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 34.4195 | − | 96.9496i | 0.173615 | − | 0.489021i | ||||
\(35\) | −6.40918 | −0.0309529 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 199.364 | 0.885818 | 0.442909 | − | 0.896566i | \(-0.353946\pi\) | ||||
0.442909 | + | 0.896566i | \(0.353946\pi\) | |||||||
\(38\) | 118.451 | − | 333.641i | 0.505665 | − | 1.42431i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 47.8502 | + | 26.1304i | 0.189145 | + | 0.103290i | ||||
\(41\) | 201.816 | − | 116.518i | 0.768740 | − | 0.443832i | −0.0636849 | − | 0.997970i | \(-0.520285\pi\) |
0.832425 | + | 0.554138i | \(0.186952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −252.553 | − | 145.812i | −0.895674 | − | 0.517118i | −0.0198798 | − | 0.999802i | \(-0.506328\pi\) |
−0.875794 | + | 0.482685i | \(0.839662\pi\) | |||||||
\(44\) | −360.851 | + | 137.851i | −1.23637 | + | 0.472315i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −99.6182 | − | 539.918i | −0.319302 | − | 1.73058i | ||||
\(47\) | 30.9476 | − | 53.6029i | 0.0960463 | − | 0.166357i | −0.813998 | − | 0.580867i | \(-0.802714\pi\) |
0.910045 | + | 0.414510i | \(0.136047\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −167.962 | − | 290.919i | −0.489686 | − | 0.848161i | ||||
\(50\) | 256.534 | − | 218.744i | 0.725588 | − | 0.618701i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 51.4707 | − | 321.620i | 0.137264 | − | 0.857704i | ||||
\(53\) | 352.175i | 0.912735i | 0.889791 | + | 0.456367i | \(0.150850\pi\) | ||||
−0.889791 | + | 0.456367i | \(0.849150\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 116.343i | − | 0.285231i | ||||||
\(56\) | −1.43018 | − | 60.1718i | −0.00341278 | − | 0.143586i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 325.478 | + | 381.708i | 0.736851 | + | 0.864150i | ||||
\(59\) | −70.7911 | − | 122.614i | −0.156207 | − | 0.270559i | 0.777291 | − | 0.629141i | \(-0.216593\pi\) |
−0.933498 | + | 0.358583i | \(0.883260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.71518 | + | 13.3631i | −0.0161939 | + | 0.0280486i | −0.874009 | − | 0.485910i | \(-0.838488\pi\) |
0.857815 | + | 0.513959i | \(0.171822\pi\) | |||||||
\(62\) | 488.377 | − | 90.1086i | 1.00039 | − | 0.184577i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −234.645 | + | 455.067i | −0.458291 | + | 0.888802i | ||||
\(65\) | 84.9565 | + | 49.0496i | 0.162116 | + | 0.0935978i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 131.657 | − | 76.0120i | 0.240066 | − | 0.138602i | −0.375141 | − | 0.926968i | \(-0.622406\pi\) |
0.615207 | + | 0.788366i | \(0.289072\pi\) | |||||||
\(68\) | −183.486 | + | 225.841i | −0.327220 | + | 0.402754i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.0832 | + | 6.06498i | 0.0291691 | + | 0.0103558i | ||||
\(71\) | −28.0331 | −0.0468580 | −0.0234290 | − | 0.999726i | \(-0.507458\pi\) | ||||
−0.0234290 | + | 0.999726i | \(0.507458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.499 | 0.199609 | 0.0998047 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998047 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(74\) | −531.392 | − | 188.657i | −0.834771 | − | 0.296365i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −631.445 | + | 777.207i | −0.953049 | + | 1.17305i | ||||
\(77\) | −111.232 | + | 64.2199i | −0.164624 | + | 0.0950459i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 648.411 | + | 374.360i | 0.923443 | + | 0.533150i | 0.884732 | − | 0.466101i | \(-0.154342\pi\) |
0.0387108 | + | 0.999250i | \(0.487675\pi\) | |||||||
\(80\) | −102.814 | − | 114.929i | −0.143687 | − | 0.160619i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −648.187 | + | 119.595i | −0.872931 | + | 0.161061i | ||||
\(83\) | 174.444 | − | 302.146i | 0.230695 | − | 0.399576i | −0.727318 | − | 0.686301i | \(-0.759233\pi\) |
0.958013 | + | 0.286725i | \(0.0925667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −43.8198 | − | 75.8981i | −0.0559167 | − | 0.0968506i | ||||
\(86\) | 535.182 | + | 627.641i | 0.671048 | + | 0.786979i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1092.27 | − | 25.9614i | 1.32314 | − | 0.0314488i | ||||
\(89\) | − | 416.864i | − | 0.496488i | −0.968698 | − | 0.248244i | \(-0.920146\pi\) | ||
0.968698 | − | 0.248244i | \(-0.0798535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 108.299i | − | 0.124756i | ||||||
\(92\) | −245.397 | + | 1533.38i | −0.278091 | + | 1.73768i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −133.213 | + | 113.589i | −0.146169 | + | 0.124637i | ||||
\(95\) | −150.801 | − | 261.195i | −0.162861 | − | 0.282084i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −752.565 | + | 1303.48i | −0.787747 | + | 1.36442i | 0.139598 | + | 0.990208i | \(0.455419\pi\) |
−0.927344 | + | 0.374209i | \(0.877914\pi\) | |||||||
\(98\) | 172.396 | + | 934.367i | 0.177701 | + | 0.963115i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −890.770 | + | 340.289i | −0.890770 | + | 0.340289i | ||||
\(101\) | −377.088 | − | 217.712i | −0.371502 | − | 0.214487i | 0.302613 | − | 0.953114i | \(-0.402141\pi\) |
−0.674114 | + | 0.738627i | \(0.735474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1511.52 | − | 872.679i | 1.44597 | − | 0.834831i | 0.447732 | − | 0.894168i | \(-0.352232\pi\) |
0.998238 | + | 0.0593366i | \(0.0188985\pi\) | |||||||
\(104\) | −441.539 | + | 808.548i | −0.416312 | + | 0.762353i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 333.261 | − | 938.698i | 0.305370 | − | 0.860136i | ||||
\(107\) | −783.805 | −0.708161 | −0.354081 | − | 0.935215i | \(-0.615206\pi\) | ||||
−0.354081 | + | 0.935215i | \(0.615206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1581.89 | 1.39007 | 0.695035 | − | 0.718976i | \(-0.255389\pi\) | ||||
0.695035 | + | 0.718976i | \(0.255389\pi\) | |||||||
\(110\) | −110.095 | + | 310.104i | −0.0954285 | + | 0.268794i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −53.1283 | + | 161.737i | −0.0448228 | + | 0.136453i | ||||
\(113\) | 384.367 | − | 221.914i | 0.319984 | − | 0.184743i | −0.331401 | − | 0.943490i | \(-0.607521\pi\) |
0.651386 | + | 0.758747i | \(0.274188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −405.046 | − | 233.854i | −0.328442 | − | 0.189626i | ||||
\(116\) | −506.331 | − | 1325.41i | −0.405273 | − | 1.06088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 72.6600 | + | 393.808i | 0.0566855 | + | 0.307228i | ||||
\(119\) | −48.3759 | + | 83.7895i | −0.0372657 | + | 0.0645460i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −500.254 | − | 866.466i | −0.375848 | − | 0.650989i | ||||
\(122\) | 33.2097 | − | 28.3175i | 0.0246448 | − | 0.0210143i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1387.00 | − | 221.971i | −1.00449 | − | 0.160755i | ||||
\(125\) | − | 588.380i | − | 0.421010i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 425.829i | − | 0.297529i | −0.988873 | − | 0.148765i | \(-0.952470\pi\) | ||
0.988873 | − | 0.148765i | \(-0.0475297\pi\) | |||||||
\(128\) | 1056.06 | − | 990.906i | 0.729244 | − | 0.684254i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −180.030 | − | 211.132i | −0.121459 | − | 0.142443i | ||||
\(131\) | −871.836 | − | 1510.06i | −0.581471 | − | 1.00714i | −0.995305 | − | 0.0967846i | \(-0.969144\pi\) |
0.413835 | − | 0.910352i | \(-0.364189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −166.480 | + | 288.352i | −0.108539 | + | 0.187995i | ||||
\(134\) | −422.851 | + | 78.0187i | −0.272603 | + | 0.0502969i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 702.782 | − | 428.333i | 0.443110 | − | 0.270068i | ||||
\(137\) | 1274.32 | + | 735.731i | 0.794692 | + | 0.458816i | 0.841612 | − | 0.540083i | \(-0.181607\pi\) |
−0.0469195 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1107.04 | + | 639.151i | −0.675526 | + | 0.390015i | −0.798167 | − | 0.602436i | \(-0.794197\pi\) |
0.122641 | + | 0.992451i | \(0.460864\pi\) | |||||||
\(140\) | −39.7949 | − | 32.3316i | −0.0240235 | − | 0.0195180i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 74.7204 | + | 26.5276i | 0.0441577 | + | 0.0156771i | ||||
\(143\) | 1965.90 | 1.14963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 427.331 | 0.244744 | ||||||||
\(146\) | −331.843 | − | 117.813i | −0.188106 | − | 0.0667825i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1237.86 | + | 1005.71i | 0.687511 | + | 0.558572i | ||||
\(149\) | −1861.15 | + | 1074.53i | −1.02330 | + | 0.590800i | −0.915057 | − | 0.403325i | \(-0.867854\pi\) |
−0.108239 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −828.626 | − | 478.407i | −0.446574 | − | 0.257829i | 0.259808 | − | 0.965660i | \(-0.416341\pi\) |
−0.706382 | + | 0.707831i | \(0.749674\pi\) | |||||||
\(152\) | 2418.54 | − | 1474.06i | 1.29059 | − | 0.786592i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 357.252 | − | 65.9152i | 0.186936 | − | 0.0344909i | ||||
\(155\) | 211.530 | − | 366.380i | 0.109616 | − | 0.189860i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1046.60 | − | 1812.77i | −0.532024 | − | 0.921493i | −0.999301 | − | 0.0373822i | \(-0.988098\pi\) |
0.467277 | − | 0.884111i | \(-0.345235\pi\) | |||||||
\(158\) | −1374.04 | − | 1611.42i | −0.691853 | − | 0.811378i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 165.288 | + | 403.629i | 0.0816696 | + | 0.199436i | ||||
\(161\) | 516.337i | 0.252752i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1468.60i | 0.705703i | 0.935679 | + | 0.352851i | \(0.114788\pi\) | ||||
−0.935679 | + | 0.352851i | \(0.885212\pi\) | |||||||
\(164\) | 1840.87 | + | 294.606i | 0.876511 | + | 0.140273i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −750.887 | + | 640.273i | −0.351085 | + | 0.299366i | ||||
\(167\) | 1524.19 | + | 2639.98i | 0.706261 | + | 1.22328i | 0.966235 | + | 0.257664i | \(0.0829527\pi\) |
−0.259974 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 269.685 | − | 467.108i | 0.122751 | − | 0.212612i | ||||
\(170\) | 44.9766 | + | 243.768i | 0.0202915 | + | 0.109977i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −832.558 | − | 2179.37i | −0.369081 | − | 0.966137i | ||||
\(173\) | 2403.71 | + | 1387.79i | 1.05636 | + | 0.609892i | 0.924424 | − | 0.381365i | \(-0.124546\pi\) |
0.131940 | + | 0.991258i | \(0.457879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −274.579 | + | 158.528i | −0.118607 | + | 0.0684778i | ||||
\(176\) | −2935.94 | − | 964.414i | −1.25742 | − | 0.413042i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −394.476 | + | 1111.12i | −0.166108 | + | 0.467877i | ||||
\(179\) | −477.618 | −0.199435 | −0.0997174 | − | 0.995016i | \(-0.531794\pi\) | ||||
−0.0997174 | + | 0.995016i | \(0.531794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −732.350 | −0.300747 | −0.150373 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150373 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(182\) | −102.483 | + | 288.664i | −0.0417392 | + | 0.117567i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2105.12 | − | 3854.91i | 0.843433 | − | 1.54450i | ||||
\(185\) | −416.006 | + | 240.181i | −0.165326 | + | 0.0954512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1520.99 | − | 878.146i | −0.594792 | − | 0.343403i | ||||
\(188\) | 462.559 | − | 176.705i | 0.179445 | − | 0.0685509i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 154.782 | + | 838.898i | 0.0591003 | + | 0.320316i | ||||
\(191\) | −1543.00 | + | 2672.55i | −0.584542 | + | 1.01246i | 0.410391 | + | 0.911910i | \(0.365392\pi\) |
−0.994932 | + | 0.100546i | \(0.967941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 817.160 | + | 1415.36i | 0.304769 | + | 0.527876i | 0.977210 | − | 0.212275i | \(-0.0680873\pi\) |
−0.672441 | + | 0.740151i | \(0.734754\pi\) | |||||||
\(194\) | 3239.39 | − | 2762.19i | 1.19884 | − | 1.02224i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 424.676 | − | 2653.63i | 0.154765 | − | 0.967066i | ||||
\(197\) | − | 3350.67i | − | 1.21181i | −0.795539 | − | 0.605903i | \(-0.792812\pi\) | ||
0.795539 | − | 0.605903i | \(-0.207188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1046.61i | 0.372826i | 0.982471 | + | 0.186413i | \(0.0596863\pi\) | ||||
−0.982471 | + | 0.186413i | \(0.940314\pi\) | |||||||
\(200\) | 2696.30 | − | 64.0864i | 0.953286 | − | 0.0226580i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 799.083 | + | 937.133i | 0.278333 | + | 0.326418i | ||||
\(203\) | −235.881 | − | 408.558i | −0.0815547 | − | 0.141257i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −280.748 | + | 486.270i | −0.0956502 | + | 0.165671i | ||||
\(206\) | −4854.68 | + | 895.718i | −1.64195 | + | 0.302950i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1942.02 | − | 1737.30i | 0.647378 | − | 0.579136i | ||||
\(209\) | −5234.33 | − | 3022.04i | −1.73237 | − | 1.00019i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4570.77 | + | 2638.94i | −1.49130 | + | 0.861004i | −0.999950 | − | 0.00995667i | \(-0.996831\pi\) |
−0.491352 | + | 0.870961i | \(0.663497\pi\) | |||||||
\(212\) | −1776.57 | + | 2186.67i | −0.575544 | + | 0.708402i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2089.18 | + | 741.711i | 0.667352 | + | 0.236927i | ||||
\(215\) | 702.658 | 0.222888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −467.047 | −0.146107 | ||||||||
\(218\) | −4216.42 | − | 1496.94i | −1.30996 | − | 0.465070i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 586.901 | − | 722.380i | 0.179858 | − | 0.221377i | ||||
\(221\) | 1282.49 | − | 740.444i | 0.390359 | − | 0.225374i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4122.02 | + | 2379.85i | 1.23781 | + | 0.714648i | 0.968645 | − | 0.248447i | \(-0.0799202\pi\) |
0.269161 | + | 0.963095i | \(0.413254\pi\) | |||||||
\(224\) | 294.661 | − | 380.824i | 0.0878923 | − | 0.113593i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1234.50 | + | 227.773i | −0.363353 | + | 0.0670409i | ||||
\(227\) | −1115.23 | + | 1931.63i | −0.326080 | + | 0.564788i | −0.981730 | − | 0.190277i | \(-0.939061\pi\) |
0.655650 | + | 0.755065i | \(0.272395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2917.29 | + | 5052.89i | 0.841833 | + | 1.45810i | 0.888343 | + | 0.459181i | \(0.151857\pi\) |
−0.0465095 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(230\) | 858.329 | + | 1006.61i | 0.246072 | + | 0.288583i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 95.3568 | + | 4011.94i | 0.0269848 | + | 1.13533i | ||||
\(233\) | 3080.09i | 0.866022i | 0.901389 | + | 0.433011i | \(0.142549\pi\) | ||||
−0.901389 | + | 0.433011i | \(0.857451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 149.135i | 0.0413978i | ||||||||
\(236\) | 178.988 | − | 1118.43i | 0.0493693 | − | 0.308489i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 208.232 | − | 177.557i | 0.0567130 | − | 0.0483586i | ||||
\(239\) | 2645.73 | + | 4582.53i | 0.716058 | + | 1.24025i | 0.962550 | + | 0.271104i | \(0.0873887\pi\) |
−0.246492 | + | 0.969145i | \(0.579278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2501.61 | − | 4332.91i | 0.668642 | − | 1.15812i | −0.309642 | − | 0.950853i | \(-0.600209\pi\) |
0.978284 | − | 0.207268i | \(-0.0664573\pi\) | |||||||
\(242\) | 513.461 | + | 2782.89i | 0.136391 | + | 0.739220i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −115.315 | + | 44.0523i | −0.0302553 | + | 0.0115580i | ||||
\(245\) | 700.961 | + | 404.700i | 0.182787 | + | 0.105532i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4413.53 | − | 2548.15i | 1.13695 | − | 0.656417i | ||||
\(248\) | 3486.92 | + | 1904.16i | 0.892820 | + | 0.487559i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −556.781 | + | 1568.29i | −0.140856 | + | 0.396748i | ||||
\(251\) | −2577.68 | −0.648215 | −0.324107 | − | 0.946020i | \(-0.605064\pi\) | ||||
−0.324107 | + | 0.946020i | \(0.605064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9372.83 | −2.32911 | ||||||||
\(254\) | −402.960 | + | 1135.02i | −0.0995432 | + | 0.280383i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3752.54 | + | 1641.85i | −0.916147 | + | 0.400842i | ||||
\(257\) | 753.933 | − | 435.283i | 0.182992 | − | 0.105651i | −0.405705 | − | 0.914004i | \(-0.632974\pi\) |
0.588698 | + | 0.808353i | \(0.299641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 459.260 | + | 265.154i | 0.110182 | + | 0.0636134i | ||||
\(260\) | 280.065 | + | 733.121i | 0.0668033 | + | 0.174870i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 894.852 | + | 4849.99i | 0.211008 | + | 1.14364i | ||||
\(263\) | 2155.19 | − | 3732.90i | 0.505304 | − | 0.875212i | −0.494677 | − | 0.869077i | \(-0.664714\pi\) |
0.999981 | − | 0.00613515i | \(-0.00195289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −424.278 | − | 734.871i | −0.0983516 | − | 0.170350i | ||||
\(266\) | 716.608 | − | 611.043i | 0.165181 | − | 0.140848i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1200.91 | + | 192.189i | 0.273721 | + | 0.0438052i | ||||
\(269\) | 5603.52i | 1.27008i | 0.772478 | + | 0.635042i | \(0.219017\pi\) | ||||
−0.772478 | + | 0.635042i | \(0.780983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2149.22i | − | 0.481756i | −0.970555 | − | 0.240878i | \(-0.922565\pi\) | ||
0.970555 | − | 0.240878i | \(-0.0774353\pi\) | |||||||
\(272\) | −2278.55 | + | 476.653i | −0.507931 | + | 0.106255i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2700.40 | − | 3166.93i | −0.595392 | − | 0.698252i | ||||
\(275\) | −2877.69 | − | 4984.31i | −0.631023 | − | 1.09296i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1604.99 | − | 2779.93i | 0.348140 | − | 0.602995i | −0.637779 | − | 0.770219i | \(-0.720147\pi\) |
0.985919 | + | 0.167224i | \(0.0534802\pi\) | |||||||
\(278\) | 3555.57 | − | 656.025i | 0.767083 | − | 0.141531i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 75.4755 | + | 123.835i | 0.0161090 | + | 0.0264306i | ||||
\(281\) | 814.389 | + | 470.188i | 0.172891 | + | 0.0998187i | 0.583948 | − | 0.811791i | \(-0.301507\pi\) |
−0.411057 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1775.44 | + | 1025.05i | −0.372929 | + | 0.215310i | −0.674737 | − | 0.738058i | \(-0.735743\pi\) |
0.301809 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(284\) | −174.059 | − | 141.415i | −0.0363680 | − | 0.0295473i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5239.98 | − | 1860.33i | −1.08338 | − | 0.384627i | ||||
\(287\) | 619.877 | 0.127492 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3590.01 | 0.730716 | ||||||||
\(290\) | −1139.02 | − | 404.381i | −0.230640 | − | 0.0818830i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 773.020 | + | 628.043i | 0.154923 | + | 0.125868i | ||||
\(293\) | 3842.30 | − | 2218.35i | 0.766108 | − | 0.442312i | −0.0653767 | − | 0.997861i | \(-0.520825\pi\) |
0.831484 | + | 0.555548i | \(0.187492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 295.434 | + | 170.569i | 0.0583080 | + | 0.0336641i | ||||
\(296\) | −2347.74 | − | 3852.03i | −0.461013 | − | 0.756400i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5977.58 | − | 1102.90i | 1.16199 | − | 0.214394i | ||||
\(299\) | 3951.54 | − | 6844.26i | 0.764292 | − | 1.32379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −387.858 | − | 671.790i | −0.0742716 | − | 0.128642i | ||||
\(302\) | 1755.93 | + | 2059.29i | 0.334578 | + | 0.392380i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7841.35 | + | 1640.35i | −1.47938 | + | 0.309475i | ||||
\(305\) | − | 37.1790i | − | 0.00697988i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7392.80i | − | 1.37436i | −0.726486 | − | 0.687181i | \(-0.758848\pi\) | ||
0.726486 | − | 0.687181i | \(-0.241152\pi\) | |||||||
\(308\) | −1014.61 | − | 162.374i | −0.187703 | − | 0.0300393i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −910.522 | + | 776.392i | −0.166820 | + | 0.142245i | ||||
\(311\) | −2448.25 | − | 4240.50i | −0.446391 | − | 0.773172i | 0.551757 | − | 0.834005i | \(-0.313958\pi\) |
−0.998148 | + | 0.0608332i | \(0.980624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −340.861 | + | 590.388i | −0.0615546 | + | 0.106616i | −0.895160 | − | 0.445744i | \(-0.852939\pi\) |
0.833606 | + | 0.552360i | \(0.186273\pi\) | |||||||
\(314\) | 1074.23 | + | 5822.20i | 0.193065 | + | 1.04639i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2137.53 | + | 5595.38i | 0.380524 | + | 0.996091i | ||||
\(317\) | −1344.13 | − | 776.034i | −0.238151 | − | 0.137497i | 0.376176 | − | 0.926548i | \(-0.377239\pi\) |
−0.614327 | + | 0.789052i | \(0.710572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7416.37 | − | 4281.84i | 1.30168 | − | 0.751527i | ||||
\(320\) | −58.6103 | − | 1232.26i | −0.0102388 | − | 0.215266i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 488.607 | − | 1376.26i | 0.0845621 | − | 0.238186i | ||||
\(323\) | −4552.92 | −0.784307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4852.88 | 0.828276 | ||||||||
\(326\) | 1389.73 | − | 3914.45i | 0.236104 | − | 0.665035i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4627.93 | − | 2527.26i | −0.779069 | − | 0.425441i | ||||
\(329\) | 142.583 | − | 82.3206i | 0.0238932 | − | 0.0137948i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6410.22 | − | 3700.94i | −1.06446 | − | 0.614569i | −0.137801 | − | 0.990460i | \(-0.544003\pi\) |
−0.926664 | + | 0.375891i | \(0.877337\pi\) | |||||||
\(332\) | 2607.33 | − | 996.043i | 0.431011 | − | 0.164653i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1564.43 | − | 8479.02i | −0.256293 | − | 1.38908i | ||||
\(335\) | −183.149 | + | 317.223i | −0.0298701 | + | 0.0517365i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4871.58 | + | 8437.83i | 0.787454 | + | 1.36391i | 0.927522 | + | 0.373769i | \(0.121935\pi\) |
−0.140068 | + | 0.990142i | \(0.544732\pi\) | |||||||
\(338\) | −1160.85 | + | 989.842i | −0.186810 | + | 0.159291i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 110.794 | − | 692.307i | 0.0176725 | − | 0.110428i | ||||
\(341\) | − | 8478.09i | − | 1.34638i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1805.94i | − | 0.284290i | ||||||
\(344\) | 156.795 | + | 6596.82i | 0.0245750 | + | 1.03394i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5093.68 | − | 5973.67i | −0.791439 | − | 0.928169i | ||||
\(347\) | −3523.75 | − | 6103.31i | −0.545143 | − | 0.944216i | −0.998598 | − | 0.0529363i | \(-0.983142\pi\) |
0.453455 | − | 0.891279i | \(-0.350191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 603.773 | − | 1045.77i | 0.0926052 | − | 0.160397i | −0.816001 | − | 0.578050i | \(-0.803814\pi\) |
0.908607 | + | 0.417653i | \(0.137147\pi\) | |||||||
\(350\) | 881.886 | − | 162.713i | 0.134682 | − | 0.0248497i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6912.94 | + | 5348.85i | 1.04676 | + | 0.809928i | ||||
\(353\) | −1316.47 | − | 760.063i | −0.198494 | − | 0.114601i | 0.397459 | − | 0.917620i | \(-0.369892\pi\) |
−0.595953 | + | 0.803019i | \(0.703226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 58.4957 | − | 33.7725i | 0.00874544 | − | 0.00504918i | ||||
\(356\) | 2102.90 | − | 2588.33i | 0.313071 | − | 0.385340i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1273.06 | + | 451.968i | 0.187942 | + | 0.0667241i | ||||
\(359\) | 6515.20 | 0.957825 | 0.478912 | − | 0.877863i | \(-0.341031\pi\) | ||||
0.478912 | + | 0.877863i | \(0.341031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8809.35 | −1.28435 | ||||||||
\(362\) | 1952.03 | + | 693.020i | 0.283415 | + | 0.100620i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 546.322 | − | 672.434i | 0.0786678 | − | 0.0968273i | ||||
\(365\) | −259.787 | + | 149.988i | −0.0372545 | + | 0.0215089i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3492.35 | + | 2016.31i | 0.496729 | + | 0.286786i | 0.727362 | − | 0.686254i | \(-0.240746\pi\) |
−0.230633 | + | 0.973041i | \(0.574080\pi\) | |||||||
\(368\) | −9258.94 | + | 8282.93i | −1.31156 | + | 1.17331i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1336.12 | − | 246.522i | 0.187734 | − | 0.0346380i | ||||
\(371\) | −468.392 | + | 811.278i | −0.0655463 | + | 0.113530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1227.68 | − | 2126.40i | −0.170420 | − | 0.295176i | 0.768147 | − | 0.640274i | \(-0.221179\pi\) |
−0.938567 | + | 0.345098i | \(0.887846\pi\) | |||||||
\(374\) | 3223.12 | + | 3779.95i | 0.445624 | + | 0.522611i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1400.14 | + | 33.2788i | −0.192038 | + | 0.00456442i | ||||
\(377\) | 7220.81i | 0.986448i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9518.27i | 1.29003i | 0.764171 | + | 0.645014i | \(0.223149\pi\) | ||||
−0.764171 | + | 0.645014i | \(0.776851\pi\) | |||||||
\(380\) | 381.285 | − | 2382.50i | 0.0514724 | − | 0.321630i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6641.78 | − | 5663.37i | 0.889589 | − | 0.758543i | ||||
\(383\) | 4727.72 | + | 8188.65i | 0.630744 | + | 1.09248i | 0.987400 | + | 0.158245i | \(0.0505837\pi\) |
−0.356655 | + | 0.934236i | \(0.616083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 154.736 | − | 268.011i | 0.0204833 | − | 0.0354781i | ||||
\(386\) | −838.733 | − | 4545.83i | −0.110597 | − | 0.599421i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11248.2 | + | 4297.01i | −1.47176 | + | 0.562236i | ||||
\(389\) | 2568.69 | + | 1483.04i | 0.334802 | + | 0.193298i | 0.657971 | − | 0.753043i | \(-0.271415\pi\) |
−0.323169 | + | 0.946341i | \(0.604748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6114.50 | + | 3530.21i | −0.790854 | + | 0.456600i | ||||
\(392\) | −3643.06 | + | 6671.20i | −0.469394 | + | 0.859557i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3170.73 | + | 8930.99i | −0.405429 | + | 1.14197i | ||||
\(395\) | −1804.02 | −0.229798 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1296.85 | 0.163947 | 0.0819733 | − | 0.996635i | \(-0.473878\pi\) | ||||
0.0819733 | + | 0.996635i | \(0.473878\pi\) | |||||||
\(398\) | 990.405 | − | 2789.68i | 0.124735 | − | 0.351341i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7247.45 | − | 2380.68i | −0.905931 | − | 0.297585i | ||||
\(401\) | 1782.15 | − | 1028.93i | 0.221936 | − | 0.128135i | −0.384910 | − | 0.922954i | \(-0.625768\pi\) |
0.606847 | + | 0.794819i | \(0.292434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6190.90 | + | 3574.32i | 0.765238 | + | 0.441810i | ||||
\(404\) | −1243.10 | − | 3254.03i | −0.153085 | − | 0.400728i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 242.108 | + | 1312.20i | 0.0295951 | + | 0.160402i | ||||
\(407\) | −4813.22 | + | 8336.74i | −0.586198 | + | 1.01532i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2897.54 | − | 5018.69i | −0.350304 | − | 0.606744i | 0.635999 | − | 0.771690i | \(-0.280588\pi\) |
−0.986303 | + | 0.164946i | \(0.947255\pi\) | |||||||
\(410\) | 1208.47 | − | 1030.45i | 0.145566 | − | 0.124122i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13787.4 | + | 2206.48i | 1.64868 | + | 0.263849i | ||||
\(413\) | − | 376.608i | − | 0.0448709i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 840.635i | 0.0994341i | ||||||||
\(416\) | −6820.32 | + | 2792.94i | −0.803830 | + | 0.329171i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11092.0 | + | 13008.3i | 1.29791 | + | 1.52214i | ||||
\(419\) | 7052.61 | + | 12215.5i | 0.822298 | + | 1.42426i | 0.903967 | + | 0.427602i | \(0.140641\pi\) |
−0.0816695 | + | 0.996659i | \(0.526025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3210.43 | + | 5560.63i | −0.371655 | + | 0.643726i | −0.989820 | − | 0.142323i | \(-0.954543\pi\) |
0.618165 | + | 0.786048i | \(0.287876\pi\) | |||||||
\(422\) | 14680.3 | − | 2708.60i | 1.69343 | − | 0.312447i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6804.57 | − | 4147.26i | 0.779384 | − | 0.475021i | ||||
\(425\) | −3754.61 | − | 2167.73i | −0.428530 | − | 0.247412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.5457 | + | 20.5223i | −0.00402852 | + | 0.00232587i | ||||
\(428\) | −4866.68 | − | 3953.96i | −0.549626 | − | 0.446546i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1872.89 | − | 664.922i | −0.210043 | − | 0.0745707i | ||||
\(431\) | −1119.73 | −0.125140 | −0.0625700 | − | 0.998041i | \(-0.519930\pi\) | ||||
−0.0625700 | + | 0.998041i | \(0.519930\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −299.833 | −0.0332773 | −0.0166387 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166387 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(434\) | 1244.88 | + | 441.964i | 0.137687 | + | 0.0488824i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9822.04 | + | 7979.96i | 1.07888 | + | 0.876539i | ||||
\(437\) | −21042.4 | + | 12148.8i | −2.30342 | + | 1.32988i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2090.02 | + | 1206.67i | 0.227224 | + | 0.131188i | 0.609291 | − | 0.792947i | \(-0.291454\pi\) |
−0.382067 | + | 0.924135i | \(0.624788\pi\) | |||||||
\(440\) | −2247.93 | + | 1370.07i | −0.243559 | + | 0.148445i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4119.06 | + | 759.992i | −0.443266 | + | 0.0817853i | ||||
\(443\) | −2409.36 | + | 4173.14i | −0.258402 | + | 0.447566i | −0.965814 | − | 0.259236i | \(-0.916529\pi\) |
0.707412 | + | 0.706802i | \(0.249863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 502.211 | + | 869.854i | 0.0534990 | + | 0.0926630i | ||||
\(446\) | −8734.92 | − | 10244.0i | −0.927378 | − | 1.08759i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1145.77 | + | 736.225i | −0.120832 | + | 0.0776415i | ||||
\(449\) | − | 8677.13i | − | 0.912024i | −0.889974 | − | 0.456012i | \(-0.849277\pi\) | ||
0.889974 | − | 0.456012i | \(-0.150723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11252.3i | 1.17484i | ||||||||
\(452\) | 3506.02 | + | 561.089i | 0.364843 | + | 0.0583881i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4800.46 | − | 4093.29i | 0.496248 | − | 0.423145i | ||||
\(455\) | 130.472 | + | 225.984i | 0.0134431 | + | 0.0232841i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3460.04 | − | 5992.97i | 0.354166 | − | 0.613434i | −0.632809 | − | 0.774308i | \(-0.718098\pi\) |
0.986975 | + | 0.160874i | \(0.0514313\pi\) | |||||||
\(458\) | −2994.30 | − | 16228.8i | −0.305491 | − | 1.65572i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1335.26 | − | 3495.29i | −0.135341 | − | 0.354280i | ||||
\(461\) | 13470.8 | + | 7777.39i | 1.36095 | + | 0.785747i | 0.989751 | − | 0.142805i | \(-0.0456121\pi\) |
0.371203 | + | 0.928552i | \(0.378945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9994.39 | + | 5770.27i | −1.00319 | + | 0.579194i | −0.909192 | − | 0.416378i | \(-0.863299\pi\) |
−0.0940023 | + | 0.995572i | \(0.529966\pi\) | |||||||
\(464\) | 3542.31 | − | 10783.8i | 0.354413 | − | 1.07893i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2914.67 | − | 8209.76i | 0.289742 | − | 0.816116i | ||||
\(467\) | −7.01271 | −0.000694881 | −0.000347441 | − | 1.00000i | \(-0.500111\pi\) | ||||
−0.000347441 | 1.00000i | \(0.500111\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 404.383 | 0.0398138 | ||||||||
\(470\) | 141.126 | − | 397.509i | 0.0138503 | − | 0.0390122i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1535.44 | + | 2811.71i | −0.149734 | + | 0.274194i | ||||
\(473\) | 12194.7 | − | 7040.61i | 1.18544 | − | 0.684414i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12921.1 | − | 7459.98i | −1.24812 | − | 0.720605i | ||||
\(476\) | −723.051 | + | 276.218i | −0.0696239 | + | 0.0265975i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2715.57 | − | 14718.1i | −0.259848 | − | 1.40834i | ||||
\(479\) | −2830.70 | + | 4902.92i | −0.270017 | + | 0.467683i | −0.968866 | − | 0.247586i | \(-0.920363\pi\) |
0.698849 | + | 0.715269i | \(0.253696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4058.46 | − | 7029.46i | −0.384719 | − | 0.666353i | ||||
\(482\) | −10768.1 | + | 9181.81i | −1.01758 | + | 0.867677i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1264.84 | − | 7903.50i | 0.118787 | − | 0.742252i | ||||
\(485\) | − | 3626.57i | − | 0.339534i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9082.26i | − | 0.845085i | −0.906343 | − | 0.422542i | \(-0.861138\pi\) | ||
0.906343 | − | 0.422542i | \(-0.138862\pi\) | |||||||
\(488\) | 349.051 | − | 8.29632i | 0.0323786 | − | 0.000769584i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1485.40 | − | 1742.02i | −0.136946 | − | 0.160605i | ||||
\(491\) | −5098.79 | − | 8831.36i | −0.468646 | − | 0.811718i | 0.530712 | − | 0.847552i | \(-0.321925\pi\) |
−0.999358 | + | 0.0358342i | \(0.988591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3225.45 | − | 5586.65i | 0.294659 | − | 0.510365i | ||||
\(494\) | −14175.3 | + | 2615.42i | −1.29104 | + | 0.238205i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7492.24 | − | 8375.07i | −0.678249 | − | 0.758169i | ||||
\(497\) | −64.5778 | − | 37.2840i | −0.00582839 | − | 0.00336502i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2353.15 | + | 1358.59i | −0.211105 | + | 0.121881i | −0.601825 | − | 0.798628i | \(-0.705559\pi\) |
0.390720 | + | 0.920510i | \(0.372226\pi\) | |||||||
\(500\) | 2968.12 | − | 3653.28i | 0.265477 | − | 0.326759i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6870.64 | + | 2439.25i | 0.610860 | + | 0.216871i | ||||
\(503\) | 8294.45 | 0.735251 | 0.367626 | − | 0.929974i | \(-0.380171\pi\) | ||||
0.367626 | + | 0.929974i | \(0.380171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1049.14 | 0.0924479 | ||||||||
\(506\) | 24982.6 | + | 8869.47i | 2.19489 | + | 0.779241i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2148.13 | − | 2643.99i | 0.187613 | − | 0.230922i | ||||
\(509\) | −2866.64 | + | 1655.05i | −0.249629 | + | 0.144124i | −0.619595 | − | 0.784922i | \(-0.712703\pi\) |
0.369965 | + | 0.929046i | \(0.379370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 286.798 | + | 165.583i | 0.0248282 | + | 0.0143346i | ||||
\(512\) | 11555.8 | − | 825.228i | 0.997460 | − | 0.0712310i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2421.46 | + | 446.775i | −0.207794 | + | 0.0383393i | ||||
\(515\) | −2102.70 | + | 3641.98i | −0.179914 | + | 0.311621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1494.33 | + | 2588.25i | 0.127119 | + | 0.220176i | ||||
\(518\) | −973.212 | − | 1141.35i | −0.0825492 | − | 0.0968105i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −52.7443 | − | 2219.11i | −0.00444806 | − | 0.187143i | ||||
\(521\) | 5030.71i | 0.423031i | 0.977375 | + | 0.211516i | \(0.0678400\pi\) | ||||
−0.977375 | + | 0.211516i | \(0.932160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9680.16i | − | 0.809338i | −0.914463 | − | 0.404669i | \(-0.867387\pi\) | ||
0.914463 | − | 0.404669i | \(-0.132613\pi\) | |||||||
\(524\) | 2204.35 | − | 13774.1i | 0.183774 | − | 1.14833i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9276.95 | + | 7910.35i | −0.769000 | + | 0.655718i | ||||
\(527\) | −3193.21 | − | 5530.81i | −0.263944 | − | 0.457164i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12756.2 | + | 22094.4i | −1.04843 | + | 1.81593i | ||||
\(530\) | 435.479 | + | 2360.24i | 0.0356905 | + | 0.193438i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2488.30 | + | 950.571i | −0.202784 | + | 0.0774671i | ||||
\(533\) | −8216.73 | − | 4743.93i | −0.667742 | − | 0.385521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1635.54 | − | 944.278i | 0.132169 | − | 0.0763078i | ||||
\(536\) | −3019.08 | − | 1648.68i | −0.243291 | − | 0.132859i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5302.58 | − | 14935.8i | 0.424927 | − | 1.19689i | ||||
\(539\) | 16220.3 | 1.29621 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18659.8 | 1.48290 | 0.741449 | − | 0.671009i | \(-0.234139\pi\) | ||||
0.741449 | + | 0.671009i | \(0.234139\pi\) | |||||||
\(542\) | −2033.80 | + | 5728.60i | −0.161179 | + | 0.453993i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6524.36 | + | 885.691i | 0.514209 | + | 0.0698046i | ||||
\(545\) | −3300.88 | + | 1905.76i | −0.259438 | + | 0.149787i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3928.78 | + | 2268.28i | 0.307098 | + | 0.177303i | 0.645627 | − | 0.763653i | \(-0.276596\pi\) |
−0.338529 | + | 0.940956i | \(0.609929\pi\) | |||||||
\(548\) | 4200.89 | + | 10996.6i | 0.327469 | + | 0.857212i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2953.66 | + | 16008.5i | 0.228990 | + | 1.24110i | ||||
\(551\) | 11100.0 | − | 19225.8i | 0.858216 | − | 1.48647i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 995.797 | + | 1724.77i | 0.0765743 | + | 0.132631i | ||||
\(554\) | −6908.63 | + | 5890.91i | −0.529819 | + | 0.451771i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10097.9 | − | 1616.03i | −0.770229 | − | 0.123264i | ||||
\(557\) | − | 17657.1i | − | 1.34319i | −0.740918 | − | 0.671596i | \(-0.765609\pi\) | ||
0.740918 | − | 0.671596i | \(-0.234391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11873.1i | 0.898355i | ||||||||
\(560\) | −83.9898 | − | 401.497i | −0.00633789 | − | 0.0302970i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1725.76 | − | 2023.91i | −0.129532 | − | 0.151910i | ||||
\(563\) | 4972.47 | + | 8612.57i | 0.372229 | + | 0.644719i | 0.989908 | − | 0.141711i | \(-0.0452604\pi\) |
−0.617679 | + | 0.786430i | \(0.711927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −534.697 | + | 926.122i | −0.0398139 | + | 0.0689597i | ||||
\(566\) | 5702.30 | − | 1052.11i | 0.423473 | − | 0.0781334i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 330.122 | + | 541.643i | 0.0243866 | + | 0.0400121i | ||||
\(569\) | 4084.02 | + | 2357.91i | 0.300898 | + | 0.173724i | 0.642846 | − | 0.765995i | \(-0.277753\pi\) |
−0.341948 | + | 0.939719i | \(0.611087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7993.20 | − | 4614.88i | 0.585823 | − | 0.338225i | −0.177621 | − | 0.984099i | \(-0.556840\pi\) |
0.763444 | + | 0.645874i | \(0.223507\pi\) | |||||||
\(572\) | 12206.4 | + | 9917.14i | 0.892264 | + | 0.724924i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1652.24 | − | 586.587i | −0.120145 | − | 0.0426545i | ||||
\(575\) | −23137.1 | −1.67806 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4076.34 | 0.294108 | 0.147054 | − | 0.989128i | \(-0.453021\pi\) | ||||
0.147054 | + | 0.989128i | \(0.453021\pi\) | |||||||
\(578\) | −9568.92 | − | 3397.21i | −0.688607 | − | 0.244473i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2653.32 | + | 2155.70i | 0.189953 | + | 0.154329i | ||||
\(581\) | 803.706 | − | 464.020i | 0.0573896 | − | 0.0331339i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14726.8 | − | 8502.51i | −1.04618 | − | 0.604010i | ||||
\(584\) | −1466.12 | − | 2405.51i | −0.103884 | − | 0.170447i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12340.6 | + | 2276.92i | −0.869941 | + | 0.160509i | ||||
\(587\) | 4317.74 | − | 7478.55i | 0.303599 | − | 0.525848i | −0.673350 | − | 0.739324i | \(-0.735145\pi\) |
0.976948 | + | 0.213476i | \(0.0684785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10989.1 | − | 19033.6i | −0.768755 | − | 1.33152i | ||||
\(590\) | −626.052 | − | 734.209i | −0.0436850 | − | 0.0512320i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2612.59 | + | 12489.0i | 0.181380 | + | 0.867050i | ||||
\(593\) | 24260.9i | 1.68006i | 0.542537 | + | 0.840032i | \(0.317464\pi\) | ||||
−0.542537 | + | 0.840032i | \(0.682536\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 233.121i | − | 0.0160622i | ||||||
\(596\) | −16976.5 | − | 2716.85i | −1.16675 | − | 0.186723i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17009.2 | + | 14503.6i | −1.16314 | + | 0.991800i | ||||
\(599\) | −7549.02 | − | 13075.3i | −0.514932 | − | 0.891889i | −0.999850 | − | 0.0173291i | \(-0.994484\pi\) |
0.484917 | − | 0.874560i | \(-0.338850\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2964.13 | + | 5134.03i | −0.201180 | + | 0.348455i | −0.948909 | − | 0.315550i | \(-0.897811\pi\) |
0.747729 | + | 0.664004i | \(0.231144\pi\) | |||||||
\(602\) | 398.097 | + | 2157.64i | 0.0269522 | + | 0.146078i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2731.62 | − | 7150.52i | −0.184020 | − | 0.481706i | ||||
\(605\) | 2087.73 | + | 1205.35i | 0.140294 | + | 0.0809990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16115.3 | − | 9304.20i | 1.07760 | − | 0.622151i | 0.147350 | − | 0.989084i | \(-0.452926\pi\) |
0.930247 | + | 0.366933i | \(0.119592\pi\) | |||||||
\(608\) | 22452.8 | + | 3048.00i | 1.49767 | + | 0.203311i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.1823 | + | 99.0981i | −0.00233523 | + | 0.00657765i | ||||
\(611\) | −2520.01 | −0.166855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7939.25 | 0.523105 | 0.261552 | − | 0.965189i | \(-0.415766\pi\) | ||||
0.261552 | + | 0.965189i | \(0.415766\pi\) | |||||||
\(614\) | −6995.77 | + | 19705.0i | −0.459815 | + | 1.29516i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2550.71 | + | 1392.91i | 0.166836 | + | 0.0911073i | ||||
\(617\) | 25269.7 | − | 14589.5i | 1.64882 | − | 0.951946i | 0.671277 | − | 0.741206i | \(-0.265746\pi\) |
0.977542 | − | 0.210740i | \(-0.0675873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14117.6 | + | 8150.83i | 0.916698 | + | 0.529256i | 0.882580 | − | 0.470162i | \(-0.155804\pi\) |
0.0341179 | + | 0.999418i | \(0.489138\pi\) | |||||||
\(620\) | 3161.63 | − | 1207.80i | 0.204797 | − | 0.0782359i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2512.88 | + | 13619.5i | 0.161990 | + | 0.877963i | ||||
\(623\) | 554.427 | − | 960.297i | 0.0356544 | − | 0.0617552i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6740.81 | − | 11675.4i | −0.431412 | − | 0.747227i | ||||
\(626\) | 1467.22 | − | 1251.08i | 0.0936774 | − | 0.0798776i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2646.23 | − | 16535.2i | 0.168147 | − | 1.05068i | ||||
\(629\) | 7251.46i | 0.459674i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2517.83i | 0.158848i | 0.996841 | + | 0.0794242i | \(0.0253082\pi\) | ||||
−0.996841 | + | 0.0794242i | \(0.974692\pi\) | |||||||
\(632\) | −402.559 | − | 16936.8i | −0.0253369 | − | 1.06600i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2848.33 | + | 3340.41i | 0.178425 | + | 0.209250i | ||||
\(635\) | 513.012 | + | 888.562i | 0.0320602 | + | 0.0555300i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6838.42 | + | 11844.5i | −0.425350 | + | 0.736728i | ||||
\(638\) | −23819.7 | + | 4394.88i | −1.47811 | + | 0.272720i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1009.86 | + | 3339.96i | −0.0623720 | + | 0.206287i | ||||
\(641\) | −14572.0 | − | 8413.13i | −0.897907 | − | 0.518407i | −0.0213863 | − | 0.999771i | \(-0.506808\pi\) |
−0.876520 | + | 0.481365i | \(0.840141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17687.6 | − | 10211.9i | 1.08481 | − | 0.626313i | 0.152617 | − | 0.988285i | \(-0.451230\pi\) |
0.932189 | + | 0.361973i | \(0.117897\pi\) | |||||||
\(644\) | −2604.70 | + | 3205.96i | −0.159378 | + | 0.196169i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12135.5 | + | 4308.41i | 0.739109 | + | 0.262402i | ||||
\(647\) | −21477.2 | −1.30503 | −0.652515 | − | 0.757776i | \(-0.726286\pi\) | ||||
−0.652515 | + | 0.757776i | \(0.726286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6836.40 | 0.413485 | ||||||||
\(650\) | −12935.0 | − | 4592.26i | −0.780544 | − | 0.277113i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7408.45 | + | 9118.60i | −0.444996 | + | 0.547718i | ||||
\(653\) | −21836.5 | + | 12607.3i | −1.30862 | + | 0.755533i | −0.981866 | − | 0.189576i | \(-0.939289\pi\) |
−0.326756 | + | 0.945109i | \(0.605955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3638.46 | + | 2100.66i | 0.217048 | + | 0.125313i | ||||
\(656\) | 9943.90 | + | 11115.6i | 0.591835 | + | 0.661573i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −457.946 | + | 84.4938i | −0.0271316 | + | 0.00500595i | ||||
\(659\) | −6865.03 | + | 11890.6i | −0.405802 | + | 0.702870i | −0.994415 | − | 0.105545i | \(-0.966341\pi\) |
0.588612 | + | 0.808416i | \(0.299675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −772.039 | − | 1337.21i | −0.0454294 | − | 0.0786860i | 0.842417 | − | 0.538827i | \(-0.181132\pi\) |
−0.887846 | + | 0.460141i | \(0.847799\pi\) | |||||||
\(662\) | 13583.8 | + | 15930.6i | 0.797508 | + | 0.935286i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7892.20 | + | 187.584i | −0.461260 | + | 0.0109633i | ||||
\(665\) | − | 802.258i | − | 0.0467823i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34426.6i | − | 1.99851i | ||||||
\(668\) | −3853.77 | + | 24080.7i | −0.223214 | + | 1.39477i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 788.357 | − | 672.223i | 0.0454580 | − | 0.0387616i | ||||
\(671\) | −372.533 | − | 645.246i | −0.0214329 | − | 0.0371229i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2684.11 | − | 4649.02i | 0.153737 | − | 0.266280i | −0.778861 | − | 0.627196i | \(-0.784202\pi\) |
0.932598 | + | 0.360916i | \(0.117536\pi\) | |||||||
\(674\) | −5000.19 | − | 27100.4i | −0.285757 | − | 1.54877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4030.84 | − | 1539.85i | 0.229338 | − | 0.0876110i | ||||
\(677\) | 16713.8 | + | 9649.71i | 0.948838 | + | 0.547812i | 0.892720 | − | 0.450612i | \(-0.148794\pi\) |
0.0561181 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3467.25 | + | 2001.82i | −0.195966 | + | 0.113141i | ||||
\(680\) | −950.441 | + | 1740.45i | −0.0535996 | + | 0.0981520i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8022.78 | + | 22597.8i | −0.450452 | + | 1.26879i | ||||
\(683\) | 7466.11 | 0.418276 | 0.209138 | − | 0.977886i | \(-0.432934\pi\) | ||||
0.209138 | + | 0.977886i | \(0.432934\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3545.45 | −0.197759 | ||||||||
\(686\) | −1708.95 | + | 4813.60i | −0.0951136 | + | 0.267907i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5824.61 | − | 17731.7i | 0.322763 | − | 0.982581i | ||||
\(689\) | 12417.5 | − | 7169.23i | 0.686600 | − | 0.396409i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20587.2 | + | 11886.0i | 1.13339 | + | 0.654364i | 0.944786 | − | 0.327689i | \(-0.106270\pi\) |
0.188606 | + | 0.982053i | \(0.439603\pi\) | |||||||
\(692\) | 7924.00 | + | 20742.5i | 0.435297 | + | 1.13947i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3616.77 | + | 19602.5i | 0.197825 | + | 1.07219i | ||||
\(695\) | 1540.02 | − | 2667.39i | 0.0840520 | − | 0.145582i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4238.12 | + | 7340.64i | 0.230316 | + | 0.398919i | ||||
\(698\) | −2598.92 | + | 2216.07i | −0.140932 | + | 0.120171i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2504.58 | − | 400.823i | −0.135235 | − | 0.0216424i | ||||
\(701\) | − | 3501.89i | − | 0.188680i | −0.995540 | − | 0.0943399i | \(-0.969926\pi\) | ||
0.995540 | − | 0.0943399i | \(-0.0300740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24955.1i | 1.33883i | ||||||||
\(704\) | −13364.4 | − | 20798.7i | −0.715467 | − | 1.11346i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2789.71 | + | 3271.66i | 0.148714 | + | 0.174406i | ||||
\(707\) | −579.113 | − | 1003.05i | −0.0308059 | − | 0.0533574i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2079.38 | + | 3601.59i | −0.110145 | + | 0.190777i | −0.915829 | − | 0.401569i | \(-0.868465\pi\) |
0.805684 | + | 0.592346i | \(0.201798\pi\) | |||||||
\(710\) | −187.875 | + | 34.6641i | −0.00993074 | + | 0.00183228i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8054.45 | + | 4909.04i | −0.423951 | + | 0.258391i | ||||
\(713\) | −29516.3 | − | 17041.3i | −1.55034 | − | 0.895091i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4102.18 | + | 2368.40i | −0.214564 | + | 0.123878i | ||||
\(716\) | −2965.55 | − | 2409.38i | −0.154788 | − | 0.125758i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17365.8 | − | 6165.30i | −0.902627 | − | 0.320455i | ||||
\(719\) | 20077.1 | 1.04137 | 0.520687 | − | 0.853748i | \(-0.325676\pi\) | ||||
0.520687 | + | 0.853748i | \(0.325676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4642.64 | 0.239807 | ||||||||
\(722\) | 23480.7 | + | 8336.24i | 1.21033 | + | 0.429699i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4547.20 | − | 3694.39i | −0.233419 | − | 0.189642i | ||||
\(725\) | 18307.5 | − | 10569.8i | 0.937825 | − | 0.541454i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31220.9 | − | 18025.4i | −1.59274 | − | 0.919566i | −0.992835 | − | 0.119491i | \(-0.961874\pi\) |
−0.599900 | − | 0.800075i | \(-0.704793\pi\) | |||||||
\(728\) | −2092.51 | + | 1275.35i | −0.106529 | + | 0.0649278i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 834.378 | − | 153.948i | 0.0423037 | − | 0.00780530i | ||||
\(731\) | 5303.59 | − | 9186.10i | 0.268345 | − | 0.464788i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10850.9 | + | 18794.4i | 0.546779 | + | 0.947049i | 0.998493 | + | 0.0548859i | \(0.0174795\pi\) |
−0.451714 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(734\) | −7400.60 | − | 8679.14i | −0.372154 | − | 0.436448i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32517.2 | − | 13315.9i | 1.62853 | − | 0.666889i | ||||
\(737\) | 7340.58i | 0.366884i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26112.0i | 1.29979i | 0.760024 | + | 0.649895i | \(0.225187\pi\) | ||||
−0.760024 | + | 0.649895i | \(0.774813\pi\) | |||||||
\(740\) | −3794.61 | − | 607.275i | −0.188504 | − | 0.0301674i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2016.18 | − | 1719.17i | 0.0997522 | − | 0.0850576i | ||||
\(743\) | −2806.43 | − | 4860.88i | −0.138570 | − | 0.240011i | 0.788385 | − | 0.615182i | \(-0.210917\pi\) |
−0.926956 | + | 0.375171i | \(0.877584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2589.06 | − | 4484.38i | 0.127323 | − | 0.220530i | ||||
\(746\) | 1260.09 | + | 6829.51i | 0.0618432 | + | 0.335182i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5014.06 | − | 13125.2i | −0.245096 | − | 0.641585i | ||||
\(749\) | −1805.59 | − | 1042.46i | −0.0880839 | − | 0.0508553i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24027.9 | + | 13872.5i | −1.16750 | + | 0.674056i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) |
−0.214409 | + | 0.976744i | \(0.568783\pi\) | |||||||
\(752\) | 3763.46 | + | 1236.24i | 0.182499 | + | 0.0599481i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6833.02 | − | 19246.6i | 0.330032 | − | 0.929601i | ||||
\(755\) | 2305.42 | 0.111129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22792.6 | −1.09433 | −0.547167 | − | 0.837023i | \(-0.684294\pi\) | ||||
−0.547167 | + | 0.837023i | \(0.684294\pi\) | |||||||
\(758\) | 9007.10 | − | 25370.3i | 0.431600 | − | 1.21569i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3270.83 | + | 5989.57i | −0.156113 | + | 0.285874i | ||||
\(761\) | −27979.1 | + | 16153.7i | −1.33277 | + | 0.769477i | −0.985724 | − | 0.168370i | \(-0.946150\pi\) |
−0.347049 | + | 0.937847i | \(0.612816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3644.08 | + | 2103.91i | 0.172902 | + | 0.0998253i | ||||
\(764\) | −23062.4 | + | 8810.24i | −1.09211 | + | 0.417203i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4852.53 | − | 26300.1i | −0.228889 | − | 1.24055i | ||||
\(767\) | −2882.19 | + | 4992.10i | −0.135684 | + | 0.235012i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1200.97 | + | 2080.14i | 0.0563174 | + | 0.0975446i | 0.892810 | − | 0.450434i | \(-0.148731\pi\) |
−0.836492 | + | 0.547979i | \(0.815397\pi\) | |||||||
\(770\) | −666.055 | + | 567.938i | −0.0311727 | + | 0.0265806i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2066.11 | + | 12910.3i | −0.0963224 | + | 0.601880i | ||||
\(773\) | − | 21135.4i | − | 0.983424i | −0.870758 | − | 0.491712i | \(-0.836371\pi\) | ||
0.870758 | − | 0.491712i | \(-0.163629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20928.4i | − | 0.970025i | ||||||
\(776\) | 34047.6 | − | 809.252i | 1.57505 | − | 0.0374362i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5443.29 | − | 6383.68i | −0.250837 | − | 0.294172i | ||||
\(779\) | 14585.0 | + | 25262.0i | 0.670811 | + | 1.16188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 676.799 | − | 1172.25i | 0.0310087 | − | 0.0537086i | ||||
\(782\) | 19638.4 | − | 3623.41i | 0.898041 | − | 0.165694i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16023.3 | − | 14334.2i | 0.729922 | − | 0.652979i | ||||
\(785\) | 4367.81 | + | 2521.76i | 0.198591 | + | 0.114656i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3776.51 | − | 2180.37i | 0.171052 | − | 0.0987570i | −0.412030 | − | 0.911170i | \(-0.635180\pi\) |
0.583082 | + | 0.812413i | \(0.301847\pi\) | |||||||
\(788\) | 16902.7 | − | 20804.5i | 0.764130 | − | 0.940520i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4808.50 | + | 1707.14i | 0.216555 | + | 0.0768826i | ||||
\(791\) | 1180.58 | 0.0530679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 628.232 | 0.0281326 | ||||||||
\(794\) | −3456.65 | − | 1227.20i | −0.154499 | − | 0.0548510i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5279.71 | + | 6498.47i | −0.235094 | + | 0.289362i | ||||
\(797\) | 17755.1 | − | 10250.9i | 0.789106 | − | 0.455590i | −0.0505420 | − | 0.998722i | \(-0.516095\pi\) |
0.839648 | + | 0.543132i | \(0.182762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1949.69 | + | 1125.66i | 0.0863270 | + | 0.0498409i | ||||
\(800\) | 17064.8 | + | 13203.8i | 0.754163 | + | 0.583530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5723.88 | + | 1056.09i | −0.252016 | + | 0.0464985i | ||||
\(803\) | −3005.76 | + | 5206.12i | −0.132093 | + | 0.228792i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −622.050 | − | 1077.42i | −0.0272352 | − | 0.0471728i | ||||
\(806\) | −13119.1 | − | 15385.5i | −0.573324 | − | 0.672372i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 234.111 | + | 9849.74i | 0.0101931 | + | 0.428852i | ||||
\(809\) | 34550.7i | 1.50153i | 0.660568 | + | 0.750766i | \(0.270315\pi\) | ||||
−0.660568 | + | 0.750766i | \(0.729685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19709.5i | − | 0.853384i | −0.904397 | − | 0.426692i | \(-0.859679\pi\) | ||
0.904397 | − | 0.426692i | \(-0.140321\pi\) | |||||||
\(812\) | 596.402 | − | 3726.68i | 0.0257754 | − | 0.161060i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20718.3 | − | 17666.3i | 0.892109 | − | 0.760692i | ||||
\(815\) | −1769.27 | − | 3064.47i | −0.0760429 | − | 0.131710i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18251.7 | − | 31612.9i | 0.781575 | − | 1.35373i | ||||
\(818\) | 2974.03 | + | 16118.9i | 0.127121 | + | 0.688978i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4196.20 | + | 1603.02i | −0.178704 | + | 0.0682682i | ||||
\(821\) | 28891.8 | + | 16680.7i | 1.22817 | + | 0.709086i | 0.966648 | − | 0.256110i | \(-0.0824409\pi\) |
0.261526 | + | 0.965196i | \(0.415774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36540.4 | + | 21096.6i | −1.54765 | + | 0.893537i | −0.549330 | + | 0.835605i | \(0.685117\pi\) |
−0.998321 | + | 0.0579313i | \(0.981550\pi\) | |||||||
\(824\) | −34661.4 | − | 18928.2i | −1.46540 | − | 0.800237i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −356.382 | + | 1003.82i | −0.0150123 | + | 0.0422851i | ||||
\(827\) | −13992.0 | −0.588329 | −0.294165 | − | 0.955755i | \(-0.595041\pi\) | ||||
−0.294165 | + | 0.955755i | \(0.595041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23454.8 | −0.982653 | −0.491327 | − | 0.870975i | \(-0.663488\pi\) | ||||
−0.491327 | + | 0.870975i | \(0.663488\pi\) | |||||||
\(830\) | 795.489 | − | 2240.66i | 0.0332673 | − | 0.0937039i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20822.0 | − | 990.366i | 0.867637 | − | 0.0412678i | ||||
\(833\) | 10581.6 | − | 6109.28i | 0.440132 | − | 0.254110i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6360.95 | − | 3672.50i | −0.263629 | − | 0.152206i | ||||
\(836\) | −17255.3 | − | 45168.9i | −0.713860 | − | 1.86866i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7238.80 | − | 39233.4i | −0.298401 | − | 1.61730i | ||||
\(839\) | 4579.55 | − | 7932.02i | 0.188443 | − | 0.326393i | −0.756288 | − | 0.654238i | \(-0.772989\pi\) |
0.944731 | + | 0.327846i | \(0.106323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3532.81 | + | 6119.00i | 0.144852 | + | 0.250892i | ||||
\(842\) | 13819.2 | − | 11783.5i | 0.565606 | − | 0.482286i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41692.5 | − | 6672.30i | −1.70037 | − | 0.272121i | ||||
\(845\) | 1299.60i | 0.0529082i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2661.35i | − | 0.107963i | ||||||
\(848\) | −22061.6 | + | 4615.11i | −0.893396 | + | 0.186891i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7956.35 | + | 9330.90i | 0.321059 | + | 0.376526i | ||||
\(851\) | 19349.5 | + | 33514.3i | 0.779427 | + | 1.35001i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16740.3 | − | 28995.1i | 0.671955 | − | 1.16386i | −0.305394 | − | 0.952226i | \(-0.598788\pi\) |
0.977349 | − | 0.211634i | \(-0.0678784\pi\) | |||||||
\(854\) | 114.165 | − | 21.0641i | 0.00457452 | − | 0.000844028i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9230.20 | + | 15144.3i | 0.368553 | + | 0.604699i | ||||
\(857\) | −26803.0 | − | 15474.7i | −1.06835 | − | 0.616811i | −0.140618 | − | 0.990064i | \(-0.544909\pi\) |
−0.927730 | + | 0.373253i | \(0.878242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5321.93 | + | 3072.62i | −0.211388 | + | 0.122045i | −0.601956 | − | 0.798529i | \(-0.705612\pi\) |
0.390568 | + | 0.920574i | \(0.372278\pi\) | |||||||
\(860\) | 4362.84 | + | 3544.61i | 0.172990 | + | 0.140547i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2984.56 | + | 1059.59i | 0.117929 | + | 0.0418676i | ||||
\(863\) | −13685.9 | −0.539830 | −0.269915 | − | 0.962884i | \(-0.586996\pi\) | ||||
−0.269915 | + | 0.962884i | \(0.586996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6687.66 | −0.262875 | ||||||||
\(866\) | 799.185 | + | 283.731i | 0.0313596 | + | 0.0111335i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2899.92 | − | 2356.05i | −0.113398 | − | 0.0921308i | ||||
\(869\) | −31309.0 | + | 18076.3i | −1.22219 | + | 0.705633i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5360.27 | − | 3094.75i | −0.208526 | − | 0.120392i | ||||
\(872\) | −18628.6 | − | 30564.6i | −0.723444 | − | 1.18698i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 67583.3 | − | 12469.5i | 2.61561 | − | 0.482595i | ||||
\(875\) | 782.544 | − | 1355.41i | 0.0302341 | − | 0.0523669i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2574.73 | + | 4459.56i | 0.0991361 | + | 0.171709i | 0.911327 | − | 0.411683i | \(-0.135059\pi\) |
−0.812191 | + | 0.583391i | \(0.801725\pi\) | |||||||
\(878\) | −4428.94 | − | 5194.08i | −0.170238 | − | 0.199649i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7288.19 | − | 1524.63i | 0.279187 | − | 0.0584037i | ||||
\(881\) | − | 26936.4i | − | 1.03009i | −0.857162 | − | 0.515046i | \(-0.827775\pi\) | ||
0.857162 | − | 0.515046i | \(-0.172225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37301.8i | 1.42164i | 0.703376 | + | 0.710818i | \(0.251675\pi\) | ||||
−0.703376 | + | 0.710818i | \(0.748325\pi\) | |||||||
\(884\) | 11698.2 | + | 1872.14i | 0.445084 | + | 0.0712295i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10371.0 | − | 8843.25i | 0.393252 | − | 0.335321i | ||||
\(887\) | −17421.8 | − | 30175.4i | −0.659488 | − | 1.14227i | −0.980748 | − | 0.195276i | \(-0.937440\pi\) |
0.321261 | − | 0.946991i | \(-0.395893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 566.352 | − | 980.950i | 0.0213665 | − | 0.0370079i | ||||
\(890\) | −515.469 | − | 2793.78i | −0.0194141 | − | 0.105222i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13588.5 | + | 35570.4i | 0.510064 | + | 1.33519i | ||||
\(893\) | 6709.65 | + | 3873.82i | 0.251433 | + | 0.145165i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 996.628 | − | 575.404i | 0.0372219 | − | 0.0214901i | ||||
\(896\) | 3750.66 | − | 878.120i | 0.139845 | − | 0.0327410i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8211.12 | + | 23128.3i | −0.305132 | + | 0.859466i | ||||
\(899\) | 31140.2 | 1.15527 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12809.6 | −0.473641 | ||||||||
\(902\) | 10648.0 | − | 29992.4i | 0.393061 | − | 1.10714i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8814.09 | − | 4813.27i | −0.324284 | − | 0.177087i | ||||
\(905\) | 1528.17 | − | 882.289i | 0.0561304 | − | 0.0324069i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7693.07 | − | 4441.59i | −0.281636 | − | 0.162603i | 0.352528 | − | 0.935801i | \(-0.385322\pi\) |
−0.634164 | + | 0.773199i | \(0.718656\pi\) | |||||||
\(908\) | −16668.8 | + | 6367.75i | −0.609220 | + | 0.232732i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −133.916 | − | 725.809i | −0.00487833 | − | 0.0264399i | ||||
\(911\) | −22256.0 | + | 38548.6i | −0.809413 | + | 1.40194i | 0.103858 | + | 0.994592i | \(0.466881\pi\) |
−0.913271 | + | 0.407352i | \(0.866452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8423.14 | + | 14589.3i | 0.305329 | + | 0.528845i | ||||
\(914\) | −14893.6 | + | 12699.6i | −0.538991 | + | 0.459591i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7376.08 | + | 46090.1i | −0.266062 | + | 1.66251i | ||||
\(917\) | − | 4638.16i | − | 0.167029i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7223.63i | 0.259288i | 0.991561 | + | 0.129644i | \(0.0413834\pi\) | ||||
−0.991561 | + | 0.129644i | \(0.958617\pi\) | |||||||
\(920\) | 251.469 | + | 10580.0i | 0.00901160 | + | 0.379145i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28545.9 | − | 33477.5i | −1.01964 | − | 1.19579i | ||||
\(923\) | 570.670 | + | 988.430i | 0.0203509 | + | 0.0352487i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11881.6 | + | 20579.5i | −0.422339 | + | 0.731512i | ||||
\(926\) | 32099.7 | − | 5922.60i | 1.13916 | − | 0.210182i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19646.4 | + | 25391.4i | −0.694964 | + | 0.898182i | ||||
\(929\) | 30912.2 | + | 17847.2i | 1.09171 | + | 0.630298i | 0.934031 | − | 0.357193i | \(-0.116266\pi\) |
0.157677 | + | 0.987491i | \(0.449599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36415.3 | − | 21024.4i | 1.28192 | − | 0.740114i | ||||
\(932\) | −15537.7 | + | 19124.4i | −0.546089 | + | 0.672147i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.6919 | + | 6.63610i | 0.000654837 | + | 0.000232484i | ||||
\(935\) | 4231.74 | 0.148014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4657.90 | −0.162398 | −0.0811991 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811991 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(938\) | −1077.85 | − | 382.666i | −0.0375194 | − | 0.0133203i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −752.322 | + | 925.987i | −0.0261043 | + | 0.0321302i | ||||
\(941\) | −22129.9 | + | 12776.7i | −0.766645 | + | 0.442623i | −0.831676 | − | 0.555260i | \(-0.812619\pi\) |
0.0650314 | + | 0.997883i | \(0.479285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39174.9 | + | 22617.6i | 1.35282 | + | 0.781051i | ||||
\(944\) | 6753.33 | − | 6041.44i | 0.232841 | − | 0.208297i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39166.6 | + | 7226.48i | −1.34611 | + | 0.248365i | ||||
\(947\) | −26469.6 | + | 45846.6i | −0.908285 | + | 1.57319i | −0.0918380 | + | 0.995774i | \(0.529274\pi\) |
−0.816447 | + | 0.577421i | \(0.804059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2534.42 | − | 4389.75i | −0.0866922 | − | 0.150155i | ||||
\(950\) | 27380.9 | + | 32111.2i | 0.935108 | + | 1.09666i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2188.63 | − | 52.0198i | 0.0745103 | − | 0.00177098i | ||||
\(953\) | − | 744.138i | − | 0.0252938i | −0.999920 | − | 0.0126469i | \(-0.995974\pi\) | ||
0.999920 | − | 0.0126469i | \(-0.00402574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7435.63i | − | 0.251949i | ||||||
\(956\) | −6689.46 | + | 41799.7i | −0.226310 | + | 1.41412i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12184.7 | − | 10389.7i | 0.410927 | − | 0.350393i | ||||
\(959\) | 1957.04 | + | 3389.70i | 0.0658980 | + | 0.114139i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 518.981 | − | 898.901i | 0.0174207 | − | 0.0301736i | ||||
\(962\) | 4165.60 | + | 22577.0i | 0.139610 | + | 0.756666i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37390.3 | − | 14283.7i | 1.24923 | − | 0.477228i | ||||
\(965\) | −3410.28 | − | 1968.92i | −0.113762 | − | 0.0656807i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14044.5 | + | 8108.61i | −0.467054 | + | 0.269654i | −0.715006 | − | 0.699119i | \(-0.753576\pi\) |
0.247952 | + | 0.968772i | \(0.420243\pi\) | |||||||
\(968\) | −10850.4 | + | 19869.3i | −0.360274 | + | 0.659736i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3431.81 | + | 9666.37i | −0.113597 | + | 0.319968i | ||||
\(971\) | 33620.7 | 1.11116 | 0.555582 | − | 0.831462i | \(-0.312496\pi\) | ||||
0.555582 | + | 0.831462i | \(0.312496\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3400.28 | −0.112033 | ||||||||
\(974\) | −8594.50 | + | 24208.1i | −0.282737 | + | 0.796385i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −938.221 | − | 308.192i | −0.0307702 | − | 0.0101076i | ||||
\(977\) | −18376.3 | + | 10609.6i | −0.601751 | + | 0.347421i | −0.769730 | − | 0.638369i | \(-0.779609\pi\) |
0.167979 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17431.8 | + | 10064.3i | 0.569074 | + | 0.328555i | ||||
\(980\) | 2310.77 | + | 6048.85i | 0.0753211 | + | 0.197167i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5233.39 | + | 28364.3i | 0.170065 | + | 0.921733i | ||||
\(983\) | 19149.3 | − | 33167.6i | 0.621331 | − | 1.07618i | −0.367907 | − | 0.929862i | \(-0.619926\pi\) |
0.989238 | − | 0.146314i | \(-0.0467411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4036.68 | + | 6991.73i | 0.130578 | + | 0.226168i | ||||
\(986\) | −13883.8 | + | 11838.6i | −0.448429 | + | 0.382371i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40258.2 | + | 6442.76i | 1.29634 | + | 0.207461i | ||||
\(989\) | − | 56607.5i | − | 1.82004i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17803.2i | 0.570674i | 0.958427 | + | 0.285337i | \(0.0921055\pi\) | ||||
−0.958427 | + | 0.285337i | \(0.907894\pi\) | |||||||
\(992\) | 12044.7 | + | 29413.0i | 0.385505 | + | 0.941396i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 136.846 | + | 160.488i | 0.00436669 | + | 0.00512108i | ||||
\(995\) | −1260.89 | − | 2183.93i | −0.0401738 | − | 0.0695831i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4517.89 | + | 7825.21i | −0.143513 | + | 0.248573i | −0.928817 | − | 0.370538i | \(-0.879173\pi\) |
0.785304 | + | 0.619110i | \(0.212507\pi\) | |||||||
\(998\) | 7557.78 | − | 1394.46i | 0.239717 | − | 0.0442292i | ||||
\(999\) | 0 | 0 |
(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 | 108.4.h.b.35.2 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.11.11 | yes | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.35.3 | 24 | ||
9.2 | odd | 6 | 324.4.b.c.323.11 | 24 | |||
9.4 | even | 3 | 36.4.h.b.23.10 | yes | 24 | ||
9.5 | odd | 6 | inner | 108.4.h.b.71.3 | 24 | ||
9.7 | even | 3 | 324.4.b.c.323.14 | 24 | |||
12.11 | even | 2 | 36.4.h.b.11.10 | ✓ | 24 | ||
36.7 | odd | 6 | 324.4.b.c.323.12 | 24 | |||
36.11 | even | 6 | 324.4.b.c.323.13 | 24 | |||
36.23 | even | 6 | inner | 108.4.h.b.71.2 | 24 | ||
36.31 | odd | 6 | 36.4.h.b.23.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.10 | ✓ | 24 | 12.11 | even | 2 | ||
36.4.h.b.11.11 | yes | 24 | 3.2 | odd | 2 | ||
36.4.h.b.23.10 | yes | 24 | 9.4 | even | 3 | ||
36.4.h.b.23.11 | yes | 24 | 36.31 | odd | 6 | ||
108.4.h.b.35.2 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.35.3 | 24 | 4.3 | odd | 2 | inner | ||
108.4.h.b.71.2 | 24 | 36.23 | even | 6 | inner | ||
108.4.h.b.71.3 | 24 | 9.5 | odd | 6 | inner | ||
324.4.b.c.323.11 | 24 | 9.2 | odd | 6 | |||
324.4.b.c.323.12 | 24 | 36.7 | odd | 6 | |||
324.4.b.c.323.13 | 24 | 36.11 | even | 6 | |||
324.4.b.c.323.14 | 24 | 9.7 | even | 3 |