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 | 71.2 | ||
Character | \(\chi\) | \(=\) | 108.71 |
Dual form | 108.4.h.b.35.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0.403770 | − | 0.914860i | \(-0.367699\pi\) |
−0.590407 | + | 0.807106i | \(0.701033\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30362 | − | 1.33000i | 0.124384 | − | 0.0718131i | −0.436517 | − | 0.899696i | \(-0.643788\pi\) |
0.560901 | + | 0.827883i | \(0.310455\pi\) | |||||||
\(8\) | −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 | −0.980153 | − | 0.198241i | \(-0.936477\pi\) |
0.318395 | − | 0.947958i | \(-0.396856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3570 | + | 35.2594i | −0.434309 | + | 0.752245i | −0.997239 | − | 0.0742593i | \(-0.976341\pi\) |
0.562930 | + | 0.826505i | \(0.309674\pi\) | |||||||
\(14\) | −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 | \(-0.916455\pi\) | ||
0.965753 | − | 0.259463i | \(-0.0835455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 125.173i | − | 1.51141i | −0.654914 | − | 0.755703i | \(-0.727295\pi\) | ||
0.654914 | − | 0.755703i | \(-0.272705\pi\) | |||||||
\(20\) | −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 | 0.0284384 | − | 0.999596i | \(-0.490947\pi\) |
0.851456 | − | 0.524426i | \(-0.175720\pi\) | |||||||
\(24\) | 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 | −0.903326 | − | 0.428955i | \(-0.858882\pi\) |
−0.0801773 | + | 0.996781i | \(0.525549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.058 | − | 87.7909i | −0.880983 | − | 0.508636i | −0.0100006 | − | 0.999950i | \(-0.503183\pi\) |
−0.870982 | + | 0.491314i | \(0.836517\pi\) | |||||||
\(32\) | 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 | 0.832425 | − | 0.554138i | \(-0.186952\pi\) |
−0.0636849 | + | 0.997970i | \(0.520285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −252.553 | + | 145.812i | −0.895674 | + | 0.517118i | −0.875794 | − | 0.482685i | \(-0.839662\pi\) |
−0.0198798 | + | 0.999802i | \(0.506328\pi\) | |||||||
\(44\) | −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 | 0.910045 | − | 0.414510i | \(-0.136047\pi\) |
−0.813998 | + | 0.580867i | \(0.802714\pi\) | |||||||
\(48\) | 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 | \(-0.849150\pi\) | ||
0.889791 | − | 0.456367i | \(-0.150850\pi\) | |||||||
\(54\) | 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 | −0.933498 | − | 0.358583i | \(-0.883260\pi\) |
0.777291 | + | 0.629141i | \(0.216593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.71518 | − | 13.3631i | −0.0161939 | − | 0.0280486i | 0.857815 | − | 0.513959i | \(-0.171822\pi\) |
−0.874009 | + | 0.485910i | \(0.838488\pi\) | |||||||
\(62\) | 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 | 0.615207 | − | 0.788366i | \(-0.289072\pi\) |
−0.375141 | + | 0.926968i | \(0.622406\pi\) | |||||||
\(68\) | −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 | 0.0387108 | − | 0.999250i | \(-0.487675\pi\) |
0.884732 | + | 0.466101i | \(0.154342\pi\) | |||||||
\(80\) | −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 | 0.958013 | − | 0.286725i | \(-0.0925667\pi\) |
−0.727318 | + | 0.686301i | \(0.759233\pi\) | |||||||
\(84\) | 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 | \(0.0798535\pi\) | ||||
−0.968698 | + | 0.248244i | \(0.920146\pi\) | |||||||
\(90\) | 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 | −0.927344 | − | 0.374209i | \(-0.877914\pi\) |
0.139598 | − | 0.990208i | \(-0.455419\pi\) | |||||||
\(98\) | 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 | −0.674114 | − | 0.738627i | \(-0.735474\pi\) |
0.302613 | + | 0.953114i | \(0.402141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1511.52 | + | 872.679i | 1.44597 | + | 0.834831i | 0.998238 | − | 0.0593366i | \(-0.0188985\pi\) |
0.447732 | + | 0.894168i | \(0.352232\pi\) | |||||||
\(104\) | −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 | 0.651386 | − | 0.758747i | \(-0.274188\pi\) |
−0.331401 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(114\) | 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 | \(0.0475297\pi\) | ||||
−0.988873 | + | 0.148765i | \(0.952470\pi\) | |||||||
\(128\) | 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 | 0.413835 | + | 0.910352i | \(0.364189\pi\) |
−0.995305 | + | 0.0967846i | \(0.969144\pi\) | |||||||
\(132\) | 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 | −0.0469195 | − | 0.998899i | \(-0.514940\pi\) |
0.841612 | + | 0.540083i | \(0.181607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1107.04 | − | 639.151i | −0.675526 | − | 0.390015i | 0.122641 | − | 0.992451i | \(-0.460864\pi\) |
−0.798167 | + | 0.602436i | \(0.794197\pi\) | |||||||
\(140\) | −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 | −0.108239 | − | 0.994125i | \(-0.534521\pi\) |
−0.915057 | + | 0.403325i | \(0.867854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −828.626 | + | 478.407i | −0.446574 | + | 0.257829i | −0.706382 | − | 0.707831i | \(-0.749674\pi\) |
0.259808 | + | 0.965660i | \(0.416341\pi\) | |||||||
\(152\) | 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 | 0.467277 | + | 0.884111i | \(0.345235\pi\) |
−0.999301 | + | 0.0373822i | \(0.988098\pi\) | |||||||
\(158\) | −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 | \(-0.885212\pi\) | ||
0.935679 | − | 0.352851i | \(-0.114788\pi\) | |||||||
\(164\) | 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 | −0.259974 | − | 0.965616i | \(-0.583714\pi\) |
0.966235 | − | 0.257664i | \(-0.0829527\pi\) | |||||||
\(168\) | 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 | 0.131940 | − | 0.991258i | \(-0.457879\pi\) |
0.924424 | + | 0.381365i | \(0.124546\pi\) | |||||||
\(174\) | 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 | −0.994932 | − | 0.100546i | \(-0.967941\pi\) |
0.410391 | − | 0.911910i | \(-0.365392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 817.160 | − | 1415.36i | 0.304769 | − | 0.527876i | −0.672441 | − | 0.740151i | \(-0.734754\pi\) |
0.977210 | + | 0.212275i | \(0.0680873\pi\) | |||||||
\(194\) | 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 | \(0.207188\pi\) | ||||
−0.795539 | + | 0.605903i | \(0.792812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1046.61i | − | 0.372826i | −0.982471 | − | 0.186413i | \(-0.940314\pi\) | ||
0.982471 | − | 0.186413i | \(-0.0596863\pi\) | |||||||
\(200\) | 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 | −0.491352 | − | 0.870961i | \(-0.663497\pi\) |
−0.999950 | + | 0.00995667i | \(0.996831\pi\) | |||||||
\(212\) | −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 | 0.269161 | − | 0.963095i | \(-0.413254\pi\) |
0.968645 | + | 0.248447i | \(0.0799202\pi\) | |||||||
\(224\) | 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 | 0.655650 | − | 0.755065i | \(-0.272395\pi\) |
−0.981730 | + | 0.190277i | \(0.939061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2917.29 | − | 5052.89i | 0.841833 | − | 1.45810i | −0.0465095 | − | 0.998918i | \(-0.514810\pi\) |
0.888343 | − | 0.459181i | \(-0.151857\pi\) | |||||||
\(230\) | 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 | \(-0.857451\pi\) | ||
0.901389 | − | 0.433011i | \(-0.142549\pi\) | |||||||
\(234\) | 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 | −0.246492 | − | 0.969145i | \(-0.579278\pi\) |
0.962550 | − | 0.271104i | \(-0.0873887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2501.61 | + | 4332.91i | 0.668642 | + | 1.15812i | 0.978284 | + | 0.207268i | \(0.0664573\pi\) |
−0.309642 | + | 0.950853i | \(0.600209\pi\) | |||||||
\(242\) | 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 | 0.588698 | − | 0.808353i | \(-0.299641\pi\) |
−0.405705 | + | 0.914004i | \(0.632974\pi\) | |||||||
\(258\) | 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 | 0.999981 | + | 0.00613515i | \(0.00195289\pi\) |
−0.494677 | + | 0.869077i | \(0.664714\pi\) | |||||||
\(264\) | 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 | \(-0.780983\pi\) | ||
0.772478 | − | 0.635042i | \(-0.219017\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2149.22i | 0.481756i | 0.970555 | + | 0.240878i | \(0.0774353\pi\) | ||||
−0.970555 | + | 0.240878i | \(0.922565\pi\) | |||||||
\(272\) | −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 | 0.985919 | − | 0.167224i | \(-0.0534802\pi\) |
−0.637779 | + | 0.770219i | \(0.720147\pi\) | |||||||
\(278\) | 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 | −0.411057 | − | 0.911610i | \(-0.634840\pi\) |
0.583948 | + | 0.811791i | \(0.301507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1775.44 | − | 1025.05i | −0.372929 | − | 0.215310i | 0.301809 | − | 0.953369i | \(-0.402410\pi\) |
−0.674737 | + | 0.738058i | \(0.735743\pi\) | |||||||
\(284\) | −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 | 0.831484 | − | 0.555548i | \(-0.187492\pi\) |
−0.0653767 | + | 0.997861i | \(0.520825\pi\) | |||||||
\(294\) | 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 | \(0.241152\pi\) | ||||
−0.726486 | + | 0.687181i | \(0.758848\pi\) | |||||||
\(308\) | −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 | −0.998148 | − | 0.0608332i | \(-0.980624\pi\) |
0.551757 | + | 0.834005i | \(0.313958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −340.861 | − | 590.388i | −0.0615546 | − | 0.106616i | 0.833606 | − | 0.552360i | \(-0.186273\pi\) |
−0.895160 | + | 0.445744i | \(0.852939\pi\) | |||||||
\(314\) | 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 | −0.614327 | − | 0.789052i | \(-0.710572\pi\) |
0.376176 | + | 0.926548i | \(0.377239\pi\) | |||||||
\(318\) | 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 | −0.926664 | − | 0.375891i | \(-0.877337\pi\) |
−0.137801 | + | 0.990460i | \(0.544003\pi\) | |||||||
\(332\) | 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 | −0.140068 | − | 0.990142i | \(-0.544732\pi\) |
0.927522 | − | 0.373769i | \(-0.121935\pi\) | |||||||
\(338\) | −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 | 0.453455 | + | 0.891279i | \(0.350191\pi\) |
−0.998598 | + | 0.0529363i | \(0.983142\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 603.773 | + | 1045.77i | 0.0926052 | + | 0.160397i | 0.908607 | − | 0.417653i | \(-0.137147\pi\) |
−0.816001 | + | 0.578050i | \(0.803814\pi\) | |||||||
\(350\) | 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 | −0.595953 | − | 0.803019i | \(-0.703226\pi\) |
0.397459 | + | 0.917620i | \(0.369892\pi\) | |||||||
\(354\) | 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 | −0.230633 | − | 0.973041i | \(-0.574080\pi\) |
0.727362 | + | 0.686254i | \(0.240746\pi\) | |||||||
\(368\) | −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 | −0.938567 | − | 0.345098i | \(-0.887846\pi\) |
0.768147 | + | 0.640274i | \(0.221179\pi\) | |||||||
\(374\) | 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 | \(-0.776851\pi\) | ||
0.764171 | − | 0.645014i | \(-0.223149\pi\) | |||||||
\(380\) | 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 | −0.356655 | − | 0.934236i | \(-0.616083\pi\) |
0.987400 | − | 0.158245i | \(-0.0505837\pi\) | |||||||
\(384\) | 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 | −0.323169 | − | 0.946341i | \(-0.604748\pi\) |
0.657971 | + | 0.753043i | \(0.271415\pi\) | |||||||
\(390\) | 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 | 0.606847 | − | 0.794819i | \(-0.292434\pi\) |
−0.384910 | + | 0.922954i | \(0.625768\pi\) | |||||||
\(402\) | 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 | −0.986303 | − | 0.164946i | \(-0.947255\pi\) |
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(410\) | 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 | −0.0816695 | − | 0.996659i | \(-0.526025\pi\) |
0.903967 | − | 0.427602i | \(-0.140641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3210.43 | − | 5560.63i | −0.371655 | − | 0.643726i | 0.618165 | − | 0.786048i | \(-0.287876\pi\) |
−0.989820 | + | 0.142323i | \(0.954543\pi\) | |||||||
\(422\) | 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 | −0.382067 | − | 0.924135i | \(-0.624788\pi\) |
0.609291 | + | 0.792947i | \(0.291454\pi\) | |||||||
\(440\) | −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 | 0.707412 | − | 0.706802i | \(-0.249863\pi\) |
−0.965814 | + | 0.259236i | \(0.916529\pi\) | |||||||
\(444\) | 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 | \(0.150723\pi\) | ||||
−0.889974 | + | 0.456012i | \(0.849277\pi\) | |||||||
\(450\) | 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 | 0.986975 | − | 0.160874i | \(-0.0514313\pi\) |
−0.632809 | + | 0.774308i | \(0.718098\pi\) | |||||||
\(458\) | −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 | 0.371203 | − | 0.928552i | \(-0.378945\pi\) |
0.989751 | + | 0.142805i | \(0.0456121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9994.39 | − | 5770.27i | −1.00319 | − | 0.579194i | −0.0940023 | − | 0.995572i | \(-0.529966\pi\) |
−0.909192 | + | 0.416378i | \(0.863299\pi\) | |||||||
\(464\) | 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 | 0.698849 | − | 0.715269i | \(-0.253696\pi\) |
−0.968866 | + | 0.247586i | \(0.920363\pi\) | |||||||
\(480\) | 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 | \(0.138862\pi\) | ||||
−0.906343 | + | 0.422542i | \(0.861138\pi\) | |||||||
\(488\) | 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 | −0.999358 | − | 0.0358342i | \(-0.988591\pi\) |
0.530712 | + | 0.847552i | \(0.321925\pi\) | |||||||
\(492\) | 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 | 0.390720 | − | 0.920510i | \(-0.372226\pi\) |
−0.601825 | + | 0.798628i | \(0.705559\pi\) | |||||||
\(500\) | 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 | 0.369965 | − | 0.929046i | \(-0.379370\pi\) |
−0.619595 | + | 0.784922i | \(0.712703\pi\) | |||||||
\(510\) | 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 | \(-0.932160\pi\) | ||
0.977375 | − | 0.211516i | \(-0.0678400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9680.16i | 0.809338i | 0.914463 | + | 0.404669i | \(0.132613\pi\) | ||||
−0.914463 | + | 0.404669i | \(0.867387\pi\) | |||||||
\(524\) | 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 | −0.338529 | − | 0.940956i | \(-0.609929\pi\) |
0.645627 | + | 0.763653i | \(0.276596\pi\) | |||||||
\(548\) | 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 | \(0.234391\pi\) | ||||
−0.740918 | + | 0.671596i | \(0.765609\pi\) | |||||||
\(558\) | 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 | −0.617679 | − | 0.786430i | \(-0.711927\pi\) |
0.989908 | + | 0.141711i | \(0.0452604\pi\) | |||||||
\(564\) | 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 | −0.341948 | − | 0.939719i | \(-0.611087\pi\) |
0.642846 | + | 0.765995i | \(0.277753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7993.20 | + | 4614.88i | 0.585823 | + | 0.338225i | 0.763444 | − | 0.645874i | \(-0.223507\pi\) |
−0.177621 | + | 0.984099i | \(0.556840\pi\) | |||||||
\(572\) | 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 | 0.976948 | − | 0.213476i | \(-0.0684785\pi\) |
−0.673350 | + | 0.739324i | \(0.735145\pi\) | |||||||
\(588\) | 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 | \(-0.682536\pi\) | ||
0.542537 | − | 0.840032i | \(-0.317464\pi\) | |||||||
\(594\) | 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 | 0.484917 | + | 0.874560i | \(0.338850\pi\) |
−0.999850 | + | 0.0173291i | \(0.994484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2964.13 | − | 5134.03i | −0.201180 | − | 0.348455i | 0.747729 | − | 0.664004i | \(-0.231144\pi\) |
−0.948909 | + | 0.315550i | \(0.897811\pi\) | |||||||
\(602\) | 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 | 0.930247 | − | 0.366933i | \(-0.119592\pi\) |
0.147350 | + | 0.989084i | \(0.452926\pi\) | |||||||
\(608\) | 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 | 0.977542 | + | 0.210740i | \(0.0675873\pi\) |
0.671277 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14117.6 | − | 8150.83i | 0.916698 | − | 0.529256i | 0.0341179 | − | 0.999418i | \(-0.489138\pi\) |
0.882580 | + | 0.470162i | \(0.155804\pi\) | |||||||
\(620\) | 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 | \(-0.974692\pi\) | ||
0.996841 | − | 0.0794242i | \(-0.0253082\pi\) | |||||||
\(632\) | −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 | −0.876520 | − | 0.481365i | \(-0.840141\pi\) |
−0.0213863 | + | 0.999771i | \(0.506808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17687.6 | + | 10211.9i | 1.08481 | + | 0.626313i | 0.932189 | − | 0.361973i | \(-0.117897\pi\) |
0.152617 | + | 0.988285i | \(0.451230\pi\) | |||||||
\(644\) | −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 | −0.326756 | − | 0.945109i | \(-0.605955\pi\) |
−0.981866 | + | 0.189576i | \(0.939289\pi\) | |||||||
\(654\) | 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 | 0.588612 | − | 0.808416i | \(-0.299675\pi\) |
−0.994415 | + | 0.105545i | \(0.966341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −772.039 | + | 1337.21i | −0.0454294 | + | 0.0786860i | −0.887846 | − | 0.460141i | \(-0.847799\pi\) |
0.842417 | + | 0.538827i | \(0.181132\pi\) | |||||||
\(662\) | 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 | 0.932598 | − | 0.360916i | \(-0.117536\pi\) |
−0.778861 | + | 0.627196i | \(0.784202\pi\) | |||||||
\(674\) | −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 | 0.0561181 | − | 0.998424i | \(-0.482128\pi\) |
0.892720 | + | 0.450612i | \(0.148794\pi\) | |||||||
\(678\) | 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 | 0.188606 | − | 0.982053i | \(-0.439603\pi\) |
0.944786 | + | 0.327689i | \(0.106270\pi\) | |||||||
\(692\) | 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 | \(0.0300740\pi\) | ||||
−0.995540 | + | 0.0943399i | \(0.969926\pi\) | |||||||
\(702\) | 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 | 0.805684 | − | 0.592346i | \(-0.201798\pi\) |
−0.915829 | + | 0.401569i | \(0.868465\pi\) | |||||||
\(710\) | −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 | −0.599900 | + | 0.800075i | \(0.704793\pi\) |
−0.992835 | + | 0.119491i | \(0.961874\pi\) | |||||||
\(728\) | −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 | −0.451714 | − | 0.892163i | \(-0.649187\pi\) |
0.998493 | − | 0.0548859i | \(-0.0174795\pi\) | |||||||
\(734\) | −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 | \(-0.774813\pi\) | ||
0.760024 | − | 0.649895i | \(-0.225187\pi\) | |||||||
\(740\) | −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 | −0.926956 | − | 0.375171i | \(-0.877584\pi\) |
0.788385 | + | 0.615182i | \(0.210917\pi\) | |||||||
\(744\) | 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 | −0.214409 | − | 0.976744i | \(-0.568783\pi\) |
−0.953090 | + | 0.302688i | \(0.902116\pi\) | |||||||
\(752\) | 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 | −0.347049 | − | 0.937847i | \(-0.612816\pi\) |
−0.985724 | + | 0.168370i | \(0.946150\pi\) | |||||||
\(762\) | 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 | −0.836492 | − | 0.547979i | \(-0.815397\pi\) |
0.892810 | + | 0.450434i | \(0.148731\pi\) | |||||||
\(770\) | −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 | \(0.163629\pi\) | ||||
−0.870758 | + | 0.491712i | \(0.836371\pi\) | |||||||
\(774\) | 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 | 0.583082 | − | 0.812413i | \(-0.301847\pi\) |
−0.412030 | + | 0.911170i | \(0.635180\pi\) | |||||||
\(788\) | 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 | 0.839648 | − | 0.543132i | \(-0.182762\pi\) |
−0.0505420 | + | 0.998722i | \(0.516095\pi\) | |||||||
\(798\) | 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 | \(-0.729685\pi\) | ||
0.660568 | − | 0.750766i | \(-0.270315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19709.5i | 0.853384i | 0.904397 | + | 0.426692i | \(0.140321\pi\) | ||||
−0.904397 | + | 0.426692i | \(0.859679\pi\) | |||||||
\(812\) | 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 | 0.261526 | − | 0.965196i | \(-0.415774\pi\) |
0.966648 | + | 0.256110i | \(0.0824409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36540.4 | − | 21096.6i | −1.54765 | − | 0.893537i | −0.998321 | − | 0.0579313i | \(-0.981550\pi\) |
−0.549330 | − | 0.835605i | \(-0.685117\pi\) | |||||||
\(824\) | −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 | 0.944731 | − | 0.327846i | \(-0.106323\pi\) |
−0.756288 | + | 0.654238i | \(0.772989\pi\) | |||||||
\(840\) | 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 | 0.977349 | + | 0.211634i | \(0.0678784\pi\) |
−0.305394 | + | 0.952226i | \(0.598788\pi\) | |||||||
\(854\) | 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 | −0.927730 | − | 0.373253i | \(-0.878242\pi\) |
−0.140618 | + | 0.990064i | \(0.544909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5321.93 | − | 3072.62i | −0.211388 | − | 0.122045i | 0.390568 | − | 0.920574i | \(-0.372278\pi\) |
−0.601956 | + | 0.798529i | \(0.705612\pi\) | |||||||
\(860\) | 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 | −0.812191 | − | 0.583391i | \(-0.801725\pi\) |
0.911327 | + | 0.411683i | \(0.135059\pi\) | |||||||
\(878\) | −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 | \(0.172225\pi\) | ||||
−0.857162 | + | 0.515046i | \(0.827775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37301.8i | − | 1.42164i | −0.703376 | − | 0.710818i | \(-0.748325\pi\) | ||
0.703376 | − | 0.710818i | \(-0.251675\pi\) | |||||||
\(884\) | 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 | 0.321261 | + | 0.946991i | \(0.395893\pi\) |
−0.980748 | + | 0.195276i | \(0.937440\pi\) | |||||||
\(888\) | 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 | −0.634164 | − | 0.773199i | \(-0.718656\pi\) |
0.352528 | + | 0.935801i | \(0.385322\pi\) | |||||||
\(908\) | −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 | −0.913271 | − | 0.407352i | \(-0.866452\pi\) |
0.103858 | − | 0.994592i | \(-0.466881\pi\) | |||||||
\(912\) | 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 | \(-0.958617\pi\) | ||
0.991561 | − | 0.129644i | \(-0.0413834\pi\) | |||||||
\(920\) | 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 | 0.157677 | − | 0.987491i | \(-0.449599\pi\) |
0.934031 | + | 0.357193i | \(0.116266\pi\) | |||||||
\(930\) | 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 | 0.0650314 | − | 0.997883i | \(-0.479285\pi\) |
−0.831676 | + | 0.555260i | \(0.812619\pi\) | |||||||
\(942\) | 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 | −0.816447 | − | 0.577421i | \(-0.804059\pi\) |
−0.0918380 | − | 0.995774i | \(-0.529274\pi\) | |||||||
\(948\) | 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 | \(0.00402574\pi\) | ||||
−0.999920 | + | 0.0126469i | \(0.995974\pi\) | |||||||
\(954\) | 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 | 0.247952 | − | 0.968772i | \(-0.420243\pi\) |
−0.715006 | + | 0.699119i | \(0.753576\pi\) | |||||||
\(968\) | −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 | 0.167979 | − | 0.985791i | \(-0.446276\pi\) |
−0.769730 | + | 0.638369i | \(0.779609\pi\) | |||||||
\(978\) | 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 | 0.989238 | + | 0.146314i | \(0.0467411\pi\) |
−0.367907 | + | 0.929862i | \(0.619926\pi\) | |||||||
\(984\) | 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 | \(-0.907894\pi\) | ||
0.958427 | − | 0.285337i | \(-0.0921055\pi\) | |||||||
\(992\) | 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 | 0.785304 | − | 0.619110i | \(-0.212507\pi\) |
−0.928817 | + | 0.370538i | \(0.879173\pi\) | |||||||
\(998\) | 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.71.2 | 24 | ||
3.2 | odd | 2 | 36.4.h.b.23.11 | yes | 24 | ||
4.3 | odd | 2 | inner | 108.4.h.b.71.3 | 24 | ||
9.2 | odd | 6 | inner | 108.4.h.b.35.3 | 24 | ||
9.4 | even | 3 | 324.4.b.c.323.13 | 24 | |||
9.5 | odd | 6 | 324.4.b.c.323.12 | 24 | |||
9.7 | even | 3 | 36.4.h.b.11.10 | ✓ | 24 | ||
12.11 | even | 2 | 36.4.h.b.23.10 | yes | 24 | ||
36.7 | odd | 6 | 36.4.h.b.11.11 | yes | 24 | ||
36.11 | even | 6 | inner | 108.4.h.b.35.2 | 24 | ||
36.23 | even | 6 | 324.4.b.c.323.14 | 24 | |||
36.31 | odd | 6 | 324.4.b.c.323.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.h.b.11.10 | ✓ | 24 | 9.7 | even | 3 | ||
36.4.h.b.11.11 | yes | 24 | 36.7 | odd | 6 | ||
36.4.h.b.23.10 | yes | 24 | 12.11 | even | 2 | ||
36.4.h.b.23.11 | yes | 24 | 3.2 | odd | 2 | ||
108.4.h.b.35.2 | 24 | 36.11 | even | 6 | inner | ||
108.4.h.b.35.3 | 24 | 9.2 | odd | 6 | inner | ||
108.4.h.b.71.2 | 24 | 1.1 | even | 1 | trivial | ||
108.4.h.b.71.3 | 24 | 4.3 | odd | 2 | inner | ||
324.4.b.c.323.11 | 24 | 36.31 | odd | 6 | |||
324.4.b.c.323.12 | 24 | 9.5 | odd | 6 | |||
324.4.b.c.323.13 | 24 | 9.4 | even | 3 | |||
324.4.b.c.323.14 | 24 | 36.23 | even | 6 |