Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(27,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, 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("76.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.6 | ||
Character | \(\chi\) | \(=\) | 76.27 |
Dual form | 76.4.f.a.31.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45296 | + | 1.40819i | −0.867252 | + | 0.497870i | ||||
\(3\) | 0.676811 | − | 1.17227i | 0.130252 | − | 0.225604i | −0.793521 | − | 0.608542i | \(-0.791755\pi\) |
0.923774 | + | 0.382939i | \(0.125088\pi\) | |||||||
\(4\) | 4.03401 | − | 6.90846i | 0.504251 | − | 0.863557i | ||||
\(5\) | −5.49309 | + | 9.51431i | −0.491317 | + | 0.850986i | −0.999950 | − | 0.00999751i | \(-0.996818\pi\) |
0.508633 | + | 0.860983i | \(0.330151\pi\) | |||||||
\(6\) | −0.00941024 | + | 3.82861i | −0.000640286 | + | 0.260504i | ||||
\(7\) | − | 11.1169i | − | 0.600258i | −0.953899 | − | 0.300129i | \(-0.902970\pi\) | ||
0.953899 | − | 0.300129i | \(-0.0970298\pi\) | |||||||
\(8\) | −0.166844 | + | 22.6268i | −0.00737355 | + | 0.999973i | ||||
\(9\) | 12.5839 | + | 21.7959i | 0.466069 | + | 0.807255i | ||||
\(10\) | 0.0763748 | − | 31.0735i | 0.00241518 | − | 0.982631i | ||||
\(11\) | 30.2803i | 0.829988i | 0.909824 | + | 0.414994i | \(0.136216\pi\) | ||||
−0.909824 | + | 0.414994i | \(0.863784\pi\) | |||||||
\(12\) | −5.36832 | − | 9.40467i | −0.129142 | − | 0.226241i | ||||
\(13\) | −50.5440 | + | 29.1816i | −1.07834 | + | 0.622578i | −0.930447 | − | 0.366426i | \(-0.880581\pi\) |
−0.147890 | + | 0.989004i | \(0.547248\pi\) | |||||||
\(14\) | 15.6548 | + | 27.2694i | 0.298851 | + | 0.520575i | ||||
\(15\) | 7.43557 | + | 12.8788i | 0.127990 | + | 0.221686i | ||||
\(16\) | −31.4535 | − | 55.7375i | −0.491462 | − | 0.870899i | ||||
\(17\) | −42.7132 | + | 73.9814i | −0.609380 | + | 1.05548i | 0.381962 | + | 0.924178i | \(0.375248\pi\) |
−0.991343 | + | 0.131300i | \(0.958085\pi\) | |||||||
\(18\) | −61.5604 | − | 35.7439i | −0.806107 | − | 0.468051i | ||||
\(19\) | −71.4136 | + | 41.9416i | −0.862285 | + | 0.506424i | ||||
\(20\) | 43.5700 | + | 76.3296i | 0.487128 | + | 0.853391i | ||||
\(21\) | −13.0321 | − | 7.52407i | −0.135420 | − | 0.0781850i | ||||
\(22\) | −42.6404 | − | 74.2764i | −0.413226 | − | 0.719808i | ||||
\(23\) | 66.3834 | − | 38.3265i | 0.601821 | − | 0.347462i | −0.167937 | − | 0.985798i | \(-0.553710\pi\) |
0.769758 | + | 0.638336i | \(0.220377\pi\) | |||||||
\(24\) | 26.4118 | + | 15.5097i | 0.224637 | + | 0.131912i | ||||
\(25\) | 2.15192 | + | 3.72724i | 0.0172154 | + | 0.0298179i | ||||
\(26\) | 82.8891 | − | 142.757i | 0.625227 | − | 1.07680i | ||||
\(27\) | 70.6153 | 0.503331 | ||||||||
\(28\) | −76.8009 | − | 44.8458i | −0.518357 | − | 0.302681i | ||||
\(29\) | 48.1403 | − | 27.7938i | 0.308256 | − | 0.177972i | −0.337890 | − | 0.941186i | \(-0.609713\pi\) |
0.646146 | + | 0.763214i | \(0.276380\pi\) | |||||||
\(30\) | −36.3749 | − | 21.1204i | −0.221370 | − | 0.128535i | ||||
\(31\) | 256.345 | 1.48519 | 0.742594 | − | 0.669742i | \(-0.233595\pi\) | ||||
0.742594 | + | 0.669742i | \(0.233595\pi\) | |||||||
\(32\) | 155.643 | + | 92.4294i | 0.859815 | + | 0.510605i | ||||
\(33\) | 35.4967 | + | 20.4941i | 0.187248 | + | 0.108108i | ||||
\(34\) | 0.593876 | − | 241.621i | 0.00299555 | − | 1.21876i | ||||
\(35\) | 105.770 | + | 61.0664i | 0.510811 | + | 0.294917i | ||||
\(36\) | 201.339 | + | 0.989740i | 0.932126 | + | 0.00458213i | ||||
\(37\) | − | 10.8550i | − | 0.0482309i | −0.999709 | − | 0.0241154i | \(-0.992323\pi\) | ||
0.999709 | − | 0.0241154i | \(-0.00767693\pi\) | |||||||
\(38\) | 116.113 | − | 203.445i | 0.495685 | − | 0.868503i | ||||
\(39\) | 79.0017i | 0.324369i | ||||||||
\(40\) | −214.362 | − | 125.878i | −0.847340 | − | 0.497578i | ||||
\(41\) | −243.046 | − | 140.323i | −0.925791 | − | 0.534506i | −0.0403132 | − | 0.999187i | \(-0.512836\pi\) |
−0.885478 | + | 0.464681i | \(0.846169\pi\) | |||||||
\(42\) | 42.5624 | + | 0.104613i | 0.156370 | + | 0.000384337i | ||||
\(43\) | −346.008 | − | 199.768i | −1.22711 | − | 0.708472i | −0.260685 | − | 0.965424i | \(-0.583948\pi\) |
−0.966424 | + | 0.256952i | \(0.917282\pi\) | |||||||
\(44\) | 209.190 | + | 122.151i | 0.716742 | + | 0.418522i | ||||
\(45\) | −276.497 | −0.915950 | ||||||||
\(46\) | −108.865 | + | 187.493i | −0.348940 | + | 0.600965i | ||||
\(47\) | −96.5469 | + | 55.7414i | −0.299634 | + | 0.172994i | −0.642279 | − | 0.766471i | \(-0.722011\pi\) |
0.342644 | + | 0.939465i | \(0.388677\pi\) | |||||||
\(48\) | −86.6276 | − | 0.851705i | −0.260492 | − | 0.00256111i | ||||
\(49\) | 219.414 | 0.639690 | ||||||||
\(50\) | −10.5272 | − | 6.11245i | −0.0297755 | − | 0.0172886i | ||||
\(51\) | 57.8175 | + | 100.143i | 0.158746 | + | 0.274957i | ||||
\(52\) | −2.29518 | + | 466.900i | −0.00612084 | + | 1.24514i | ||||
\(53\) | 448.024 | − | 258.667i | 1.16115 | − | 0.670389i | 0.209569 | − | 0.977794i | \(-0.432794\pi\) |
0.951579 | + | 0.307404i | \(0.0994605\pi\) | |||||||
\(54\) | −173.216 | + | 99.4397i | −0.436514 | + | 0.250593i | ||||
\(55\) | −288.096 | − | 166.333i | −0.706308 | − | 0.407787i | ||||
\(56\) | 251.541 | + | 1.85480i | 0.600242 | + | 0.00442603i | ||||
\(57\) | 0.833362 | + | 112.103i | 0.00193652 | + | 0.260497i | ||||
\(58\) | −78.9471 | + | 135.968i | −0.178729 | + | 0.307818i | ||||
\(59\) | −212.955 | + | 368.850i | −0.469906 | + | 0.813901i | −0.999408 | − | 0.0344079i | \(-0.989045\pi\) |
0.529502 | + | 0.848309i | \(0.322379\pi\) | |||||||
\(60\) | 118.968 | + | 0.584819i | 0.255978 | + | 0.00125833i | ||||
\(61\) | 353.240 | + | 611.829i | 0.741438 | + | 1.28421i | 0.951841 | + | 0.306594i | \(0.0991892\pi\) |
−0.210402 | + | 0.977615i | \(0.567477\pi\) | |||||||
\(62\) | −628.802 | + | 360.981i | −1.28803 | + | 0.739431i | ||||
\(63\) | 242.303 | − | 139.894i | 0.484561 | − | 0.279762i | ||||
\(64\) | −511.944 | − | 7.55031i | −0.999891 | − | 0.0147467i | ||||
\(65\) | − | 641.188i | − | 1.22353i | ||||||
\(66\) | −115.932 | − | 0.284945i | −0.216215 | − | 0.000531429i | ||||
\(67\) | −452.689 | − | 784.081i | −0.825445 | − | 1.42971i | −0.901579 | − | 0.432615i | \(-0.857591\pi\) |
0.0761337 | − | 0.997098i | \(-0.475742\pi\) | |||||||
\(68\) | 338.792 | + | 593.524i | 0.604184 | + | 1.05846i | ||||
\(69\) | − | 103.759i | − | 0.181031i | ||||||
\(70\) | −345.442 | − | 0.849055i | −0.589832 | − | 0.00144973i | ||||
\(71\) | −48.8602 | + | 84.6283i | −0.0816709 | + | 0.141458i | −0.903968 | − | 0.427601i | \(-0.859359\pi\) |
0.822297 | + | 0.569059i | \(0.192692\pi\) | |||||||
\(72\) | −495.270 | + | 281.096i | −0.810669 | + | 0.460104i | ||||
\(73\) | 8.45627 | − | 14.6467i | 0.0135580 | − | 0.0234831i | −0.859167 | − | 0.511696i | \(-0.829018\pi\) |
0.872725 | + | 0.488213i | \(0.162351\pi\) | |||||||
\(74\) | 15.2858 | + | 26.6267i | 0.0240127 | + | 0.0418283i | ||||
\(75\) | 5.82578 | 0.00896937 | ||||||||
\(76\) | 1.66834 | + | 662.551i | 0.00251804 | + | 0.999997i | ||||
\(77\) | 336.625 | 0.498207 | ||||||||
\(78\) | −111.249 | − | 193.788i | −0.161494 | − | 0.281310i | ||||
\(79\) | 263.354 | − | 456.142i | 0.375059 | − | 0.649621i | −0.615277 | − | 0.788311i | \(-0.710956\pi\) |
0.990336 | + | 0.138690i | \(0.0442892\pi\) | |||||||
\(80\) | 703.082 | + | 6.91256i | 0.982586 | + | 0.00966059i | ||||
\(81\) | −291.971 | + | 505.708i | −0.400509 | + | 0.693701i | ||||
\(82\) | 793.783 | + | 1.95102i | 1.06901 | + | 0.00262749i | ||||
\(83\) | 645.249i | 0.853316i | 0.904413 | + | 0.426658i | \(0.140309\pi\) | ||||
−0.904413 | + | 0.426658i | \(0.859691\pi\) | |||||||
\(84\) | −104.551 | + | 59.6793i | −0.135803 | + | 0.0775184i | ||||
\(85\) | −469.255 | − | 812.773i | −0.598798 | − | 1.03715i | ||||
\(86\) | 1130.05 | + | 2.77753i | 1.41694 | + | 0.00348266i | ||||
\(87\) | − | 75.2446i | − | 0.0927249i | ||||||
\(88\) | −685.147 | − | 5.05210i | −0.829965 | − | 0.00611995i | ||||
\(89\) | 351.665 | − | 203.034i | 0.418836 | − | 0.241815i | −0.275743 | − | 0.961231i | \(-0.588924\pi\) |
0.694579 | + | 0.719416i | \(0.255591\pi\) | |||||||
\(90\) | 678.236 | − | 389.360i | 0.794359 | − | 0.456024i | ||||
\(91\) | 324.410 | + | 561.895i | 0.373708 | + | 0.647281i | ||||
\(92\) | 3.01443 | − | 613.216i | 0.00341605 | − | 0.694915i | ||||
\(93\) | 173.497 | − | 300.505i | 0.193449 | − | 0.335064i | ||||
\(94\) | 158.331 | − | 272.688i | 0.173730 | − | 0.299208i | ||||
\(95\) | −6.76368 | − | 909.840i | −0.00730462 | − | 0.982607i | ||||
\(96\) | 213.693 | − | 119.899i | 0.227187 | − | 0.127470i | ||||
\(97\) | −471.054 | − | 271.963i | −0.493075 | − | 0.284677i | 0.232774 | − | 0.972531i | \(-0.425220\pi\) |
−0.725849 | + | 0.687854i | \(0.758553\pi\) | |||||||
\(98\) | −538.212 | + | 308.976i | −0.554772 | + | 0.318482i | ||||
\(99\) | −659.986 | + | 381.043i | −0.670011 | + | 0.386831i | ||||
\(100\) | 34.4303 | + | 0.169252i | 0.0344303 | + | 0.000169252i | ||||
\(101\) | 361.195 | + | 625.608i | 0.355844 | + | 0.616340i | 0.987262 | − | 0.159103i | \(-0.0508601\pi\) |
−0.631418 | + | 0.775443i | \(0.717527\pi\) | |||||||
\(102\) | −282.844 | − | 164.228i | −0.274566 | − | 0.159422i | ||||
\(103\) | 381.220 | 0.364686 | 0.182343 | − | 0.983235i | \(-0.441632\pi\) | ||||
0.182343 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(104\) | −651.853 | − | 1148.52i | −0.614610 | − | 1.08290i | ||||
\(105\) | 143.173 | − | 82.6607i | 0.133069 | − | 0.0768273i | ||||
\(106\) | −734.733 | + | 1265.40i | −0.673241 | + | 1.15950i | ||||
\(107\) | 129.584 | 0.117078 | 0.0585388 | − | 0.998285i | \(-0.481356\pi\) | ||||
0.0585388 | + | 0.998285i | \(0.481356\pi\) | |||||||
\(108\) | 284.863 | − | 487.843i | 0.253805 | − | 0.434655i | ||||
\(109\) | 490.565 | + | 283.228i | 0.431079 | + | 0.248883i | 0.699806 | − | 0.714333i | \(-0.253270\pi\) |
−0.268727 | + | 0.963216i | \(0.586603\pi\) | |||||||
\(110\) | 940.916 | + | 2.31266i | 0.815571 | + | 0.00200457i | ||||
\(111\) | −12.7249 | − | 7.34675i | −0.0108811 | − | 0.00628219i | ||||
\(112\) | −619.631 | + | 349.667i | −0.522765 | + | 0.295004i | ||||
\(113\) | 111.350i | 0.0926981i | 0.998925 | + | 0.0463490i | \(0.0147586\pi\) | ||||
−0.998925 | + | 0.0463490i | \(0.985241\pi\) | |||||||
\(114\) | −159.906 | − | 273.809i | −0.131373 | − | 0.224953i | ||||
\(115\) | 842.123i | 0.682855i | ||||||||
\(116\) | 2.18603 | − | 444.695i | 0.00174972 | − | 0.355939i | ||||
\(117\) | −1272.08 | − | 734.434i | −1.00516 | − | 0.580328i | ||||
\(118\) | 2.96089 | − | 1204.65i | 0.00230993 | − | 0.939809i | ||||
\(119\) | 822.447 | + | 474.840i | 0.633559 | + | 0.365786i | ||||
\(120\) | −292.646 | + | 166.094i | −0.222623 | + | 0.126352i | ||||
\(121\) | 414.102 | 0.311121 | ||||||||
\(122\) | −1728.05 | − | 1003.36i | −1.28238 | − | 0.744592i | ||||
\(123\) | −328.993 | + | 189.944i | −0.241173 | + | 0.139241i | ||||
\(124\) | 1034.10 | − | 1770.95i | 0.748908 | − | 1.28254i | ||||
\(125\) | −1420.56 | −1.01647 | ||||||||
\(126\) | −397.363 | + | 684.363i | −0.280952 | + | 0.483872i | ||||
\(127\) | −987.493 | − | 1710.39i | −0.689967 | − | 1.19506i | −0.971848 | − | 0.235609i | \(-0.924292\pi\) |
0.281881 | − | 0.959449i | \(-0.409042\pi\) | |||||||
\(128\) | 1266.41 | − | 702.394i | 0.874499 | − | 0.485027i | ||||
\(129\) | −468.364 | + | 270.410i | −0.319668 | + | 0.184560i | ||||
\(130\) | 902.914 | + | 1572.81i | 0.609160 | + | 1.06111i | ||||
\(131\) | 2493.43 | + | 1439.58i | 1.66299 | + | 0.960128i | 0.971276 | + | 0.237956i | \(0.0764773\pi\) |
0.691714 | + | 0.722172i | \(0.256856\pi\) | |||||||
\(132\) | 284.776 | − | 162.555i | 0.187777 | − | 0.107186i | ||||
\(133\) | 466.262 | + | 793.901i | 0.303985 | + | 0.517594i | ||||
\(134\) | 2214.56 | + | 1285.85i | 1.42768 | + | 0.828957i | ||||
\(135\) | −387.896 | + | 671.856i | −0.247295 | + | 0.428327i | ||||
\(136\) | −1666.84 | − | 978.806i | −1.05096 | − | 0.617146i | ||||
\(137\) | 1038.08 | + | 1798.01i | 0.647366 | + | 1.12127i | 0.983750 | + | 0.179546i | \(0.0574628\pi\) |
−0.336384 | + | 0.941725i | \(0.609204\pi\) | |||||||
\(138\) | 146.112 | + | 254.517i | 0.0901297 | + | 0.156999i | ||||
\(139\) | 768.219 | − | 443.531i | 0.468773 | − | 0.270646i | −0.246953 | − | 0.969027i | \(-0.579429\pi\) |
0.715726 | + | 0.698381i | \(0.246096\pi\) | |||||||
\(140\) | 848.552 | − | 484.365i | 0.512255 | − | 0.292403i | ||||
\(141\) | 150.906i | 0.0901315i | ||||||||
\(142\) | 0.679342 | − | 276.394i | 0.000401473 | − | 0.163341i | ||||
\(143\) | −883.628 | − | 1530.49i | −0.516732 | − | 0.895006i | ||||
\(144\) | 819.042 | − | 1386.95i | 0.473983 | − | 0.802634i | ||||
\(145\) | 610.695i | 0.349762i | ||||||||
\(146\) | −0.117574 | + | 47.8357i | −6.66474e−5 | + | 0.0271158i | ||||
\(147\) | 148.502 | − | 257.212i | 0.0833211 | − | 0.144316i | ||||
\(148\) | −74.9910 | − | 43.7890i | −0.0416501 | − | 0.0243205i | ||||
\(149\) | −350.682 | + | 607.398i | −0.192812 | + | 0.333960i | −0.946181 | − | 0.323638i | \(-0.895094\pi\) |
0.753369 | + | 0.657598i | \(0.228427\pi\) | |||||||
\(150\) | −14.2904 | + | 8.20379i | −0.00777870 | + | 0.00446558i | ||||
\(151\) | 2623.46 | 1.41387 | 0.706934 | − | 0.707280i | \(-0.250078\pi\) | ||||
0.706934 | + | 0.707280i | \(0.250078\pi\) | |||||||
\(152\) | −937.089 | − | 1622.86i | −0.500052 | − | 0.865995i | ||||
\(153\) | −2149.99 | −1.13605 | ||||||||
\(154\) | −825.726 | + | 474.031i | −0.432071 | + | 0.248042i | ||||
\(155\) | −1408.12 | + | 2438.94i | −0.729698 | + | 1.26387i | ||||
\(156\) | 545.780 | + | 318.693i | 0.280111 | + | 0.163563i | ||||
\(157\) | −1240.06 | + | 2147.85i | −0.630368 | + | 1.09183i | 0.357109 | + | 0.934063i | \(0.383762\pi\) |
−0.987477 | + | 0.157766i | \(0.949571\pi\) | |||||||
\(158\) | −3.66162 | + | 1489.75i | −0.00184369 | + | 0.750115i | ||||
\(159\) | − | 700.274i | − | 0.349279i | ||||||
\(160\) | −1734.36 | + | 973.115i | −0.856959 | + | 0.480822i | ||||
\(161\) | −426.073 | − | 737.980i | −0.208567 | − | 0.361248i | ||||
\(162\) | 4.05951 | − | 1651.63i | 0.00196880 | − | 0.801015i | ||||
\(163\) | 1057.41i | 0.508115i | 0.967189 | + | 0.254057i | \(0.0817652\pi\) | ||||
−0.967189 | + | 0.254057i | \(0.918235\pi\) | |||||||
\(164\) | −1949.86 | + | 1113.01i | −0.928407 | + | 0.529948i | ||||
\(165\) | −389.974 | + | 225.151i | −0.183996 | + | 0.106230i | ||||
\(166\) | −908.632 | − | 1582.77i | −0.424840 | − | 0.740040i | ||||
\(167\) | 358.486 | + | 620.915i | 0.166111 | + | 0.287712i | 0.937049 | − | 0.349198i | \(-0.113546\pi\) |
−0.770939 | + | 0.636909i | \(0.780212\pi\) | |||||||
\(168\) | 172.420 | − | 293.619i | 0.0791814 | − | 0.134840i | ||||
\(169\) | 604.631 | − | 1047.25i | 0.275207 | − | 0.476673i | ||||
\(170\) | 2295.60 | + | 1332.90i | 1.03567 | + | 0.601345i | ||||
\(171\) | −1812.81 | − | 1028.74i | −0.810697 | − | 0.460055i | ||||
\(172\) | −2775.89 | + | 1584.52i | −1.23058 | + | 0.702431i | ||||
\(173\) | 331.370 | + | 191.316i | 0.145628 | + | 0.0840781i | 0.571043 | − | 0.820920i | \(-0.306539\pi\) |
−0.425416 | + | 0.904998i | \(0.639872\pi\) | |||||||
\(174\) | 105.959 | + | 184.572i | 0.0461649 | + | 0.0804158i | ||||
\(175\) | 41.4355 | − | 23.9228i | 0.0178984 | − | 0.0103337i | ||||
\(176\) | 1687.75 | − | 952.424i | 0.722835 | − | 0.407907i | ||||
\(177\) | 288.261 | + | 499.283i | 0.122413 | + | 0.212025i | ||||
\(178\) | −576.709 | + | 993.243i | −0.242844 | + | 0.418240i | ||||
\(179\) | −3190.57 | −1.33226 | −0.666129 | − | 0.745837i | \(-0.732050\pi\) | ||||
−0.666129 | + | 0.745837i | \(0.732050\pi\) | |||||||
\(180\) | −1115.39 | + | 1910.17i | −0.461869 | + | 0.790975i | ||||
\(181\) | 3875.11 | − | 2237.30i | 1.59135 | − | 0.918768i | 0.598277 | − | 0.801289i | \(-0.295852\pi\) |
0.993075 | − | 0.117479i | \(-0.0374812\pi\) | |||||||
\(182\) | −1587.02 | − | 921.474i | −0.646360 | − | 0.375298i | ||||
\(183\) | 956.306 | 0.386296 | ||||||||
\(184\) | 856.129 | + | 1508.44i | 0.343015 | + | 0.604367i | ||||
\(185\) | 103.277 | + | 59.6272i | 0.0410438 | + | 0.0236967i | ||||
\(186\) | −2.41226 | + | 981.443i | −0.000950945 | + | 0.386897i | ||||
\(187\) | −2240.18 | − | 1293.37i | −0.876033 | − | 0.505778i | ||||
\(188\) | −4.38415 | + | 891.851i | −0.00170078 | + | 0.345984i | ||||
\(189\) | − | 785.027i | − | 0.302128i | ||||||
\(190\) | 1297.82 | + | 2222.28i | 0.495545 | + | 0.848531i | ||||
\(191\) | − | 1560.35i | − | 0.591114i | −0.955325 | − | 0.295557i | \(-0.904495\pi\) | ||
0.955325 | − | 0.295557i | \(-0.0955052\pi\) | |||||||
\(192\) | −355.340 | + | 595.027i | −0.133565 | + | 0.223658i | ||||
\(193\) | 3841.10 | + | 2217.66i | 1.43258 | + | 0.827102i | 0.997317 | − | 0.0732002i | \(-0.0233212\pi\) |
0.435265 | + | 0.900302i | \(0.356655\pi\) | |||||||
\(194\) | 1538.45 | + | 3.78132i | 0.569352 | + | 0.00139940i | ||||
\(195\) | −751.647 | − | 433.963i | −0.276033 | − | 0.159368i | ||||
\(196\) | 885.117 | − | 1515.81i | 0.322564 | − | 0.552409i | ||||
\(197\) | −2775.80 | −1.00390 | −0.501948 | − | 0.864898i | \(-0.667383\pi\) | ||||
−0.501948 | + | 0.864898i | \(0.667383\pi\) | |||||||
\(198\) | 1082.34 | − | 1864.07i | 0.388477 | − | 0.669058i | ||||
\(199\) | 1586.73 | − | 916.101i | 0.565229 | − | 0.326335i | −0.190013 | − | 0.981782i | \(-0.560853\pi\) |
0.755241 | + | 0.655447i | \(0.227520\pi\) | |||||||
\(200\) | −84.6945 | + | 48.0692i | −0.0299440 | + | 0.0169950i | ||||
\(201\) | −1225.54 | −0.430064 | ||||||||
\(202\) | −1766.97 | − | 1025.96i | −0.615463 | − | 0.357358i | ||||
\(203\) | −308.982 | − | 535.172i | −0.106829 | − | 0.185033i | ||||
\(204\) | 925.068 | + | 4.54743i | 0.317489 | + | 0.00156071i | ||||
\(205\) | 2670.15 | − | 1541.61i | 0.909714 | − | 0.525223i | ||||
\(206\) | −935.116 | + | 536.829i | −0.316275 | + | 0.181566i | ||||
\(207\) | 1670.72 | + | 964.589i | 0.560980 | + | 0.323882i | ||||
\(208\) | 3216.30 | + | 1899.33i | 1.07216 | + | 0.633150i | ||||
\(209\) | −1270.00 | − | 2162.43i | −0.420326 | − | 0.715685i | ||||
\(210\) | −234.795 | + | 404.377i | −0.0771541 | + | 0.132879i | ||||
\(211\) | −2918.37 | + | 5054.76i | −0.952174 | + | 1.64921i | −0.211466 | + | 0.977385i | \(0.567824\pi\) |
−0.740708 | + | 0.671828i | \(0.765510\pi\) | |||||||
\(212\) | 20.3446 | − | 4138.62i | 0.00659089 | − | 1.34076i | ||||
\(213\) | 66.1382 | + | 114.555i | 0.0212756 | + | 0.0368505i | ||||
\(214\) | −317.863 | + | 182.478i | −0.101536 | + | 0.0582895i | ||||
\(215\) | 3801.30 | − | 2194.68i | 1.20580 | − | 0.696168i | ||||
\(216\) | −11.7818 | + | 1597.80i | −0.00371133 | + | 0.503317i | ||||
\(217\) | − | 2849.77i | − | 0.891497i | ||||||
\(218\) | −1602.17 | − | 3.93794i | −0.497765 | − | 0.00122344i | ||||
\(219\) | −11.4466 | − | 19.8261i | −0.00353191 | − | 0.00611745i | ||||
\(220\) | −2311.29 | + | 1319.31i | −0.708304 | + | 0.404310i | ||||
\(221\) | − | 4985.75i | − | 1.51755i | ||||||
\(222\) | 41.5594 | + | 0.102148i | 0.0125643 | + | 3.08816e-5i | ||||
\(223\) | 2062.77 | − | 3572.83i | 0.619432 | − | 1.07289i | −0.370157 | − | 0.928969i | \(-0.620696\pi\) |
0.989589 | − | 0.143919i | \(-0.0459705\pi\) | |||||||
\(224\) | 1027.53 | − | 1730.28i | 0.306495 | − | 0.516111i | ||||
\(225\) | −54.1589 | + | 93.8061i | −0.0160471 | + | 0.0277944i | ||||
\(226\) | −156.801 | − | 273.136i | −0.0461516 | − | 0.0803926i | ||||
\(227\) | −3334.74 | −0.975041 | −0.487520 | − | 0.873112i | \(-0.662099\pi\) | ||||
−0.487520 | + | 0.873112i | \(0.662099\pi\) | |||||||
\(228\) | 777.818 | + | 446.466i | 0.225931 | + | 0.129684i | ||||
\(229\) | −2836.98 | −0.818659 | −0.409329 | − | 0.912387i | \(-0.634237\pi\) | ||||
−0.409329 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(230\) | −1185.87 | − | 2065.69i | −0.339973 | − | 0.592207i | ||||
\(231\) | 227.831 | − | 394.615i | 0.0648926 | − | 0.112397i | ||||
\(232\) | 620.853 | + | 1093.90i | 0.175694 | + | 0.309560i | ||||
\(233\) | 2863.92 | − | 4960.45i | 0.805242 | − | 1.39472i | −0.110886 | − | 0.993833i | \(-0.535369\pi\) |
0.916128 | − | 0.400887i | \(-0.131298\pi\) | |||||||
\(234\) | 4154.57 | + | 10.2114i | 1.16065 | + | 0.00285274i | ||||
\(235\) | − | 1224.77i | − | 0.339979i | ||||||
\(236\) | 1689.12 | + | 2959.14i | 0.465899 | + | 0.816201i | ||||
\(237\) | −356.482 | − | 617.444i | −0.0977045 | − | 0.169229i | ||||
\(238\) | −2686.09 | − | 6.60208i | −0.731569 | − | 0.00179811i | ||||
\(239\) | 6005.30i | 1.62531i | 0.582742 | + | 0.812657i | \(0.301980\pi\) | ||||
−0.582742 | + | 0.812657i | \(0.698020\pi\) | |||||||
\(240\) | 483.957 | − | 819.523i | 0.130164 | − | 0.220417i | ||||
\(241\) | 4052.85 | − | 2339.92i | 1.08327 | − | 0.625424i | 0.151491 | − | 0.988459i | \(-0.451593\pi\) |
0.931776 | + | 0.363035i | \(0.118259\pi\) | |||||||
\(242\) | −1015.77 | + | 583.133i | −0.269820 | + | 0.154898i | ||||
\(243\) | 1348.53 | + | 2335.71i | 0.356000 | + | 0.616610i | ||||
\(244\) | 5651.77 | + | 27.7829i | 1.48286 | + | 0.00728941i | ||||
\(245\) | −1205.26 | + | 2087.57i | −0.314290 | + | 0.544367i | ||||
\(246\) | 539.528 | − | 929.208i | 0.139834 | − | 0.240830i | ||||
\(247\) | 2385.61 | − | 4203.86i | 0.614545 | − | 1.08294i | ||||
\(248\) | −42.7696 | + | 5800.26i | −0.0109511 | + | 1.48515i | ||||
\(249\) | 756.406 | + | 436.711i | 0.192511 | + | 0.111146i | ||||
\(250\) | 3484.56 | − | 2000.41i | 0.881532 | − | 0.506068i | ||||
\(251\) | 3128.51 | − | 1806.25i | 0.786733 | − | 0.454221i | −0.0520779 | − | 0.998643i | \(-0.516584\pi\) |
0.838811 | + | 0.544422i | \(0.183251\pi\) | |||||||
\(252\) | 11.0029 | − | 2238.28i | 0.00275046 | − | 0.559516i | ||||
\(253\) | 1160.54 | + | 2010.11i | 0.288389 | + | 0.499504i | ||||
\(254\) | 4830.83 | + | 2804.93i | 1.19336 | + | 0.692903i | ||||
\(255\) | −1270.39 | −0.311979 | ||||||||
\(256\) | −2117.35 | + | 3506.29i | −0.516931 | + | 0.856027i | ||||
\(257\) | −3768.74 | + | 2175.88i | −0.914737 | + | 0.528124i | −0.881952 | − | 0.471339i | \(-0.843771\pi\) |
−0.0327847 | + | 0.999462i | \(0.510438\pi\) | |||||||
\(258\) | 768.088 | − | 1322.85i | 0.185345 | − | 0.319213i | ||||
\(259\) | −120.674 | −0.0289510 | ||||||||
\(260\) | −4429.62 | − | 2586.56i | −1.05659 | − | 0.616968i | ||||
\(261\) | 1211.58 | + | 699.506i | 0.287337 | + | 0.165894i | ||||
\(262\) | −8143.47 | − | 20.0156i | −1.92025 | − | 0.00471973i | ||||
\(263\) | −4904.09 | − | 2831.38i | −1.14981 | − | 0.663841i | −0.200967 | − | 0.979598i | \(-0.564408\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(264\) | −469.637 | + | 799.758i | −0.109486 | + | 0.186446i | ||||
\(265\) | 5683.52i | 1.31749i | ||||||||
\(266\) | −2261.68 | − | 1290.82i | −0.521326 | − | 0.297539i | ||||
\(267\) | − | 549.661i | − | 0.125988i | ||||||
\(268\) | −7242.94 | − | 35.6047i | −1.65087 | − | 0.00811532i | ||||
\(269\) | 1997.02 | + | 1152.98i | 0.452641 | + | 0.261332i | 0.708945 | − | 0.705264i | \(-0.249172\pi\) |
−0.256304 | + | 0.966596i | \(0.582505\pi\) | |||||||
\(270\) | 5.39324 | − | 2194.27i | 0.00121564 | − | 0.494588i | ||||
\(271\) | −7149.18 | − | 4127.58i | −1.60252 | − | 0.925213i | −0.990982 | − | 0.133994i | \(-0.957220\pi\) |
−0.611534 | − | 0.791219i | \(-0.709447\pi\) | |||||||
\(272\) | 5467.02 | + | 53.7507i | 1.21870 | + | 0.0119820i | ||||
\(273\) | 878.257 | 0.194705 | ||||||||
\(274\) | −5078.30 | − | 2948.62i | −1.11968 | − | 0.650120i | ||||
\(275\) | −112.862 | + | 65.1609i | −0.0247485 | + | 0.0142885i | ||||
\(276\) | −716.815 | − | 418.565i | −0.156330 | − | 0.0912849i | ||||
\(277\) | 3798.27 | 0.823885 | 0.411943 | − | 0.911210i | \(-0.364850\pi\) | ||||
0.411943 | + | 0.911210i | \(0.364850\pi\) | |||||||
\(278\) | −1259.83 | + | 2169.76i | −0.271798 | + | 0.468106i | ||||
\(279\) | 3225.80 | + | 5587.25i | 0.692200 | + | 1.19893i | ||||
\(280\) | −1399.38 | + | 2383.05i | −0.298676 | + | 0.508623i | ||||
\(281\) | −5145.99 | + | 2971.04i | −1.09247 | + | 0.630738i | −0.934233 | − | 0.356663i | \(-0.883914\pi\) |
−0.158237 | + | 0.987401i | \(0.550581\pi\) | |||||||
\(282\) | −212.503 | − | 370.165i | −0.0448737 | − | 0.0781667i | ||||
\(283\) | 5134.70 | + | 2964.52i | 1.07854 | + | 0.622695i | 0.930502 | − | 0.366287i | \(-0.119371\pi\) |
0.148037 | + | 0.988982i | \(0.452705\pi\) | |||||||
\(284\) | 387.548 | + | 678.940i | 0.0809745 | + | 0.141858i | ||||
\(285\) | −1071.16 | − | 607.861i | −0.222631 | − | 0.126339i | ||||
\(286\) | 4322.72 | + | 2509.91i | 0.893734 | + | 0.518930i | ||||
\(287\) | −1559.96 | + | 2701.93i | −0.320842 | + | 0.555714i | ||||
\(288\) | −55.9869 | + | 4555.50i | −0.0114551 | + | 0.932067i | ||||
\(289\) | −1192.33 | − | 2065.18i | −0.242689 | − | 0.420349i | ||||
\(290\) | −859.974 | − | 1498.01i | −0.174136 | − | 0.303332i | ||||
\(291\) | −637.629 | + | 368.135i | −0.128448 | + | 0.0741597i | ||||
\(292\) | −67.0733 | − | 117.505i | −0.0134424 | − | 0.0235494i | ||||
\(293\) | 690.794i | 0.137736i | 0.997626 | + | 0.0688679i | \(0.0219387\pi\) | ||||
−0.997626 | + | 0.0688679i | \(0.978061\pi\) | |||||||
\(294\) | −2.06474 | + | 840.049i | −0.000409585 | + | 0.166642i | ||||
\(295\) | −2339.57 | − | 4052.25i | −0.461745 | − | 0.799766i | ||||
\(296\) | 245.613 | + | 1.81109i | 0.0482296 | + | 0.000355633i | ||||
\(297\) | 2138.26i | 0.417758i | ||||||||
\(298\) | 4.87581 | − | 1983.75i | 0.000947812 | − | 0.385622i | ||||
\(299\) | −2236.85 | + | 3874.34i | −0.432644 | + | 0.749362i | ||||
\(300\) | 23.5012 | − | 40.2471i | 0.00452281 | − | 0.00774556i | ||||
\(301\) | −2220.81 | + | 3846.55i | −0.425266 | + | 0.736583i | ||||
\(302\) | −6435.23 | + | 3694.32i | −1.22618 | + | 0.703922i | ||||
\(303\) | 977.843 | 0.185398 | ||||||||
\(304\) | 4583.93 | + | 2661.21i | 0.864824 | + | 0.502075i | ||||
\(305\) | −7761.51 | −1.45712 | ||||||||
\(306\) | 5273.82 | − | 3027.58i | 0.985243 | − | 0.565606i | ||||
\(307\) | −2367.48 | + | 4100.59i | −0.440128 | + | 0.762324i | −0.997699 | − | 0.0678058i | \(-0.978400\pi\) |
0.557571 | + | 0.830129i | \(0.311733\pi\) | |||||||
\(308\) | 1357.95 | − | 2325.56i | 0.251221 | − | 0.430230i | ||||
\(309\) | 258.014 | − | 446.893i | 0.0475012 | − | 0.0822745i | ||||
\(310\) | 19.5783 | − | 7965.53i | 0.00358700 | − | 1.45939i | ||||
\(311\) | − | 28.1167i | − | 0.00512653i | −0.999997 | − | 0.00256327i | \(-0.999184\pi\) | ||
0.999997 | − | 0.00256327i | \(-0.000815914\pi\) | |||||||
\(312\) | −1787.56 | − | 13.1810i | −0.324360 | − | 0.00239175i | ||||
\(313\) | 2620.51 | + | 4538.86i | 0.473227 | + | 0.819654i | 0.999530 | − | 0.0306433i | \(-0.00975560\pi\) |
−0.526303 | + | 0.850297i | \(0.676422\pi\) | |||||||
\(314\) | 17.2416 | − | 7014.83i | 0.00309872 | − | 1.26073i | ||||
\(315\) | 3073.80i | 0.549806i | ||||||||
\(316\) | −2088.87 | − | 3659.45i | −0.371861 | − | 0.651456i | ||||
\(317\) | −5251.59 | + | 3032.01i | −0.930469 | + | 0.537207i | −0.886960 | − | 0.461846i | \(-0.847187\pi\) |
−0.0435091 | + | 0.999053i | \(0.513854\pi\) | |||||||
\(318\) | 986.118 | + | 1717.74i | 0.173896 | + | 0.302913i | ||||
\(319\) | 841.605 | + | 1457.70i | 0.147714 | + | 0.255849i | ||||
\(320\) | 2883.99 | − | 4829.32i | 0.503813 | − | 0.843648i | ||||
\(321\) | 87.7035 | − | 151.907i | 0.0152496 | − | 0.0264132i | ||||
\(322\) | 2084.35 | + | 1210.24i | 0.360734 | + | 0.209454i | ||||
\(323\) | −52.5931 | − | 7074.74i | −0.00905992 | − | 1.21873i | ||||
\(324\) | 2315.85 | + | 4057.10i | 0.397094 | + | 0.695662i | ||||
\(325\) | −217.534 | − | 125.593i | −0.0371280 | − | 0.0214358i | ||||
\(326\) | −1489.03 | − | 2593.78i | −0.252975 | − | 0.440664i | ||||
\(327\) | 664.039 | − | 383.383i | 0.112298 | − | 0.0648352i | ||||
\(328\) | 3215.61 | − | 5475.95i | 0.541318 | − | 0.921825i | ||||
\(329\) | 619.674 | + | 1073.31i | 0.103841 | + | 0.179858i | ||||
\(330\) | 639.533 | − | 1101.44i | 0.106682 | − | 0.183735i | ||||
\(331\) | 7840.67 | 1.30200 | 0.651000 | − | 0.759078i | \(-0.274350\pi\) | ||||
0.651000 | + | 0.759078i | \(0.274350\pi\) | |||||||
\(332\) | 4457.67 | + | 2602.94i | 0.736887 | + | 0.430286i | ||||
\(333\) | 236.593 | − | 136.597i | 0.0389346 | − | 0.0224789i | ||||
\(334\) | −1753.72 | − | 1018.26i | −0.287303 | − | 0.166817i | ||||
\(335\) | 9946.66 | 1.62222 | ||||||||
\(336\) | −9.46836 | + | 963.034i | −0.00153733 | + | 0.156363i | ||||
\(337\) | −4444.09 | − | 2565.80i | −0.718354 | − | 0.414742i | 0.0957927 | − | 0.995401i | \(-0.469461\pi\) |
−0.814146 | + | 0.580660i | \(0.802795\pi\) | |||||||
\(338\) | −8.40667 | + | 3420.30i | −0.00135285 | + | 0.550413i | ||||
\(339\) | 130.532 | + | 75.3626i | 0.0209130 | + | 0.0120741i | ||||
\(340\) | −7507.98 | − | 36.9076i | −1.19758 | − | 0.00588705i | ||||
\(341\) | 7762.20i | 1.23269i | ||||||||
\(342\) | 5895.41 | − | 29.3353i | 0.932126 | − | 0.00463822i | ||||
\(343\) | − | 6252.32i | − | 0.984238i | ||||||
\(344\) | 4577.83 | − | 7795.72i | 0.717501 | − | 1.22185i | ||||
\(345\) | 987.196 | + | 569.958i | 0.154055 | + | 0.0889435i | ||||
\(346\) | −1082.25 | − | 2.66003i | −0.168156 | − | 0.000413306i | ||||
\(347\) | 2890.21 | + | 1668.66i | 0.447131 | + | 0.258151i | 0.706618 | − | 0.707595i | \(-0.250220\pi\) |
−0.259487 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(348\) | −519.824 | − | 303.537i | −0.0800732 | − | 0.0467566i | ||||
\(349\) | 2551.53 | 0.391347 | 0.195674 | − | 0.980669i | \(-0.437311\pi\) | ||||
0.195674 | + | 0.980669i | \(0.437311\pi\) | |||||||
\(350\) | −67.9517 | + | 117.031i | −0.0103776 | + | 0.0178730i | ||||
\(351\) | −3569.18 | + | 2060.67i | −0.542760 | + | 0.313363i | ||||
\(352\) | −2798.79 | + | 4712.93i | −0.423796 | + | 0.713636i | ||||
\(353\) | 4101.98 | 0.618488 | 0.309244 | − | 0.950983i | \(-0.399924\pi\) | ||||
0.309244 | + | 0.950983i | \(0.399924\pi\) | |||||||
\(354\) | −1410.18 | − | 818.794i | −0.211723 | − | 0.122933i | ||||
\(355\) | −536.787 | − | 929.742i | −0.0802526 | − | 0.139002i | ||||
\(356\) | 15.9689 | − | 3248.50i | 0.00237739 | − | 0.483624i | ||||
\(357\) | 1113.28 | − | 642.753i | 0.165045 | − | 0.0952888i | ||||
\(358\) | 7826.33 | − | 4492.92i | 1.15540 | − | 0.663291i | ||||
\(359\) | 5042.01 | + | 2911.00i | 0.741245 | + | 0.427958i | 0.822522 | − | 0.568733i | \(-0.192566\pi\) |
−0.0812767 | + | 0.996692i | \(0.525900\pi\) | |||||||
\(360\) | 46.1319 | − | 6256.24i | 0.00675380 | − | 0.915925i | ||||
\(361\) | 3340.81 | − | 5990.40i | 0.487070 | − | 0.873363i | ||||
\(362\) | −6354.95 | + | 10944.9i | −0.922676 | + | 1.58909i | ||||
\(363\) | 280.268 | − | 485.439i | 0.0405242 | − | 0.0701900i | ||||
\(364\) | 5190.50 | + | 25.5154i | 0.747407 | + | 0.00367409i | ||||
\(365\) | 92.9021 | + | 160.911i | 0.0133225 | + | 0.0230753i | ||||
\(366\) | −2345.78 | + | 1346.66i | −0.335016 | + | 0.192325i | ||||
\(367\) | −4029.38 | + | 2326.36i | −0.573111 | + | 0.330886i | −0.758391 | − | 0.651800i | \(-0.774014\pi\) |
0.185280 | + | 0.982686i | \(0.440681\pi\) | |||||||
\(368\) | −4224.21 | − | 2494.54i | −0.598376 | − | 0.353362i | ||||
\(369\) | − | 7063.21i | − | 0.996466i | ||||||
\(370\) | −337.302 | − | 0.829045i | −0.0473932 | − | 0.000116487i | ||||
\(371\) | −2875.58 | − | 4980.66i | −0.402407 | − | 0.696989i | ||||
\(372\) | −1376.14 | − | 2410.84i | −0.191800 | − | 0.336011i | ||||
\(373\) | − | 9800.87i | − | 1.36051i | −0.732976 | − | 0.680254i | \(-0.761869\pi\) | ||
0.732976 | − | 0.680254i | \(-0.238131\pi\) | |||||||
\(374\) | 7316.38 | + | 17.9827i | 1.01155 | + | 0.00248627i | ||||
\(375\) | −961.447 | + | 1665.28i | −0.132397 | + | 0.229319i | ||||
\(376\) | −1245.14 | − | 2193.85i | −0.170780 | − | 0.300902i | ||||
\(377\) | −1622.13 | + | 2809.62i | −0.221603 | + | 0.383827i | ||||
\(378\) | 1105.47 | + | 1925.64i | 0.150421 | + | 0.262021i | ||||
\(379\) | 3854.61 | 0.522422 | 0.261211 | − | 0.965282i | \(-0.415878\pi\) | ||||
0.261211 | + | 0.965282i | \(0.415878\pi\) | |||||||
\(380\) | −6312.88 | − | 3623.58i | −0.852220 | − | 0.489173i | ||||
\(381\) | −2673.38 | −0.359479 | ||||||||
\(382\) | 2197.26 | + | 3827.47i | 0.294298 | + | 0.512644i | ||||
\(383\) | −2887.26 | + | 5000.89i | −0.385202 | + | 0.667189i | −0.991797 | − | 0.127822i | \(-0.959201\pi\) |
0.606595 | + | 0.795011i | \(0.292535\pi\) | |||||||
\(384\) | 33.7247 | − | 1959.96i | 0.00448179 | − | 0.260466i | ||||
\(385\) | −1849.11 | + | 3202.75i | −0.244778 | + | 0.423967i | ||||
\(386\) | −12544.9 | − | 30.8339i | −1.65420 | − | 0.00406582i | ||||
\(387\) | − | 10055.4i | − | 1.32079i | ||||||
\(388\) | −3779.08 | + | 2157.15i | −0.494468 | + | 0.282250i | ||||
\(389\) | −3409.67 | − | 5905.72i | −0.444414 | − | 0.769748i | 0.553597 | − | 0.832785i | \(-0.313255\pi\) |
−0.998011 | + | 0.0630370i | \(0.979921\pi\) | |||||||
\(390\) | 2454.86 | + | 6.03374i | 0.318735 | + | 0.000783411i | ||||
\(391\) | 6548.18i | 0.846945i | ||||||||
\(392\) | −36.6079 | + | 4964.63i | −0.00471678 | + | 0.639672i | ||||
\(393\) | 3375.16 | − | 1948.65i | 0.433216 | − | 0.250118i | ||||
\(394\) | 6808.92 | − | 3908.85i | 0.870631 | − | 0.499810i | ||||
\(395\) | 2893.25 | + | 5011.26i | 0.368545 | + | 0.638339i | ||||
\(396\) | −29.9696 | + | 6096.62i | −0.00380311 | + | 0.773653i | ||||
\(397\) | 4803.59 | − | 8320.05i | 0.607267 | − | 1.05182i | −0.384422 | − | 0.923158i | \(-0.625599\pi\) |
0.991689 | − | 0.128660i | \(-0.0410676\pi\) | |||||||
\(398\) | −2602.15 | + | 4481.58i | −0.327723 | + | 0.564425i | ||||
\(399\) | 1246.24 | − | 9.26444i | 0.156366 | − | 0.00116241i | ||||
\(400\) | 140.062 | − | 237.178i | 0.0175077 | − | 0.0296472i | ||||
\(401\) | 8084.37 | + | 4667.51i | 1.00677 | + | 0.581258i | 0.910244 | − | 0.414072i | \(-0.135894\pi\) |
0.0965247 | + | 0.995331i | \(0.469227\pi\) | |||||||
\(402\) | 3006.20 | − | 1725.79i | 0.372974 | − | 0.214116i | ||||
\(403\) | −12956.7 | + | 7480.54i | −1.60153 | + | 0.924646i | ||||
\(404\) | 5779.05 | + | 28.4085i | 0.711679 | + | 0.00349846i | ||||
\(405\) | −3207.64 | − | 5555.80i | −0.393553 | − | 0.681654i | ||||
\(406\) | 1511.54 | + | 877.651i | 0.184770 | + | 0.107283i | ||||
\(407\) | 328.692 | 0.0400310 | ||||||||
\(408\) | −2275.56 | + | 1291.52i | −0.276120 | + | 0.156715i | ||||
\(409\) | −8611.47 | + | 4971.83i | −1.04110 | + | 0.601079i | −0.920145 | − | 0.391579i | \(-0.871929\pi\) |
−0.120955 | + | 0.992658i | \(0.538596\pi\) | |||||||
\(410\) | −4378.88 | + | 7541.58i | −0.527458 | + | 0.908420i | ||||
\(411\) | 2810.33 | 0.337284 | ||||||||
\(412\) | 1537.84 | − | 2633.64i | 0.183893 | − | 0.314927i | ||||
\(413\) | 4100.48 | + | 2367.41i | 0.488551 | + | 0.282065i | ||||
\(414\) | −5456.52 | − | 13.4115i | −0.647762 | − | 0.00159212i | ||||
\(415\) | −6139.10 | − | 3544.41i | −0.726160 | − | 0.419249i | ||||
\(416\) | −10564.1 | − | 129.832i | −1.24506 | − | 0.0153018i | ||||
\(417\) | − | 1200.75i | − | 0.141009i | ||||||
\(418\) | 6160.37 | + | 3515.94i | 0.720846 | + | 0.411412i | ||||
\(419\) | − | 8870.59i | − | 1.03426i | −0.855906 | − | 0.517132i | \(-0.827000\pi\) | ||
0.855906 | − | 0.517132i | \(-0.173000\pi\) | |||||||
\(420\) | 6.50140 | − | 1322.56i | 0.000755323 | − | 0.153653i | ||||
\(421\) | 4342.60 | + | 2507.20i | 0.502721 | + | 0.290246i | 0.729837 | − | 0.683622i | \(-0.239596\pi\) |
−0.227115 | + | 0.973868i | \(0.572929\pi\) | |||||||
\(422\) | 40.5764 | − | 16508.7i | 0.00468063 | − | 1.90434i | ||||
\(423\) | −2429.86 | − | 1402.88i | −0.279300 | − | 0.161254i | ||||
\(424\) | 5778.05 | + | 10180.5i | 0.661809 | + | 1.16606i | ||||
\(425\) | −367.662 | −0.0419628 | ||||||||
\(426\) | −323.549 | − | 187.863i | −0.0367981 | − | 0.0213662i | ||||
\(427\) | 6801.67 | − | 3926.95i | 0.770857 | − | 0.445054i | ||||
\(428\) | 522.741 | − | 895.222i | 0.0590366 | − | 0.101103i | ||||
\(429\) | −2392.20 | −0.269222 | ||||||||
\(430\) | −6233.91 | + | 10736.4i | −0.699130 | + | 1.20408i | ||||
\(431\) | −6100.30 | − | 10566.0i | −0.681766 | − | 1.18085i | −0.974441 | − | 0.224642i | \(-0.927879\pi\) |
0.292675 | − | 0.956212i | \(-0.405455\pi\) | |||||||
\(432\) | −2221.10 | − | 3935.93i | −0.247368 | − | 0.438350i | ||||
\(433\) | 6740.59 | − | 3891.68i | 0.748111 | − | 0.431922i | −0.0769000 | − | 0.997039i | \(-0.524502\pi\) |
0.825011 | + | 0.565117i | \(0.191169\pi\) | |||||||
\(434\) | 4013.01 | + | 6990.36i | 0.443849 | + | 0.773152i | ||||
\(435\) | 715.900 | + | 413.325i | 0.0789076 | + | 0.0455573i | ||||
\(436\) | 3935.61 | − | 2246.50i | 0.432297 | − | 0.246761i | ||||
\(437\) | −3133.20 | + | 5521.25i | −0.342978 | + | 0.604387i | ||||
\(438\) | 55.9968 | + | 32.5136i | 0.00610875 | + | 0.00354694i | ||||
\(439\) | −6265.82 | + | 10852.7i | −0.681211 | + | 1.17989i | 0.293401 | + | 0.955989i | \(0.405213\pi\) |
−0.974612 | + | 0.223902i | \(0.928120\pi\) | |||||||
\(440\) | 3811.64 | − | 6490.95i | 0.412984 | − | 0.703282i | ||||
\(441\) | 2761.07 | + | 4782.31i | 0.298139 | + | 0.516393i | ||||
\(442\) | 7020.88 | + | 12229.8i | 0.755541 | + | 1.31610i | ||||
\(443\) | 3564.50 | − | 2057.97i | 0.382291 | − | 0.220716i | −0.296524 | − | 0.955025i | \(-0.595827\pi\) |
0.678814 | + | 0.734310i | \(0.262494\pi\) | |||||||
\(444\) | −102.087 | + | 58.2729i | −0.0109118 | + | 0.00622862i | ||||
\(445\) | 4461.13i | 0.475231i | ||||||||
\(446\) | −28.6804 | + | 11668.8i | −0.00304497 | + | 1.23886i | ||||
\(447\) | 474.690 | + | 822.188i | 0.0502284 | + | 0.0869981i | ||||
\(448\) | −83.9363 | + | 5691.25i | −0.00885182 | + | 0.600193i | ||||
\(449\) | − | 9120.54i | − | 0.958630i | −0.877643 | − | 0.479315i | \(-0.840885\pi\) | ||
0.877643 | − | 0.479315i | \(-0.159115\pi\) | |||||||
\(450\) | 0.753015 | − | 306.368i | 7.88833e−5 | − | 0.0320941i | ||||
\(451\) | 4249.02 | − | 7359.52i | 0.443633 | − | 0.768395i | ||||
\(452\) | 769.254 | + | 449.185i | 0.0800501 | + | 0.0467431i | ||||
\(453\) | 1775.59 | − | 3075.40i | 0.184160 | − | 0.318974i | ||||
\(454\) | 8179.97 | − | 4695.94i | 0.845606 | − | 0.485444i | ||||
\(455\) | −7128.05 | −0.734436 | ||||||||
\(456\) | −2536.66 | + | 0.152645i | −0.260505 | + | 1.56760e-5i | ||||
\(457\) | −4614.11 | −0.472295 | −0.236148 | − | 0.971717i | \(-0.575885\pi\) | ||||
−0.236148 | + | 0.971717i | \(0.575885\pi\) | |||||||
\(458\) | 6958.99 | − | 3995.00i | 0.709983 | − | 0.407586i | ||||
\(459\) | −3016.20 | + | 5224.22i | −0.306720 | + | 0.531254i | ||||
\(460\) | 5817.77 | + | 3397.13i | 0.589684 | + | 0.344330i | ||||
\(461\) | 2873.32 | − | 4976.73i | 0.290290 | − | 0.502797i | −0.683588 | − | 0.729868i | \(-0.739582\pi\) |
0.973878 | + | 0.227071i | \(0.0729148\pi\) | |||||||
\(462\) | −3.16772 | + | 1288.80i | −0.000318995 | + | 0.129785i | ||||
\(463\) | 6925.58i | 0.695160i | 0.937650 | + | 0.347580i | \(0.112997\pi\) | ||||
−0.937650 | + | 0.347580i | \(0.887003\pi\) | |||||||
\(464\) | −3063.34 | − | 1809.01i | −0.306491 | − | 0.180994i | ||||
\(465\) | 1906.07 | + | 3301.40i | 0.190090 | + | 0.329245i | ||||
\(466\) | −39.8193 | + | 16200.7i | −0.00395836 | + | 1.61048i | ||||
\(467\) | − | 18984.4i | − | 1.88114i | −0.339598 | − | 0.940571i | \(-0.610291\pi\) | ||
0.339598 | − | 0.940571i | \(-0.389709\pi\) | |||||||
\(468\) | −10205.4 | + | 5825.37i | −1.00800 | + | 0.575380i | ||||
\(469\) | −8716.58 | + | 5032.52i | −0.858197 | + | 0.495480i | ||||
\(470\) | 1724.71 | + | 3004.31i | 0.169266 | + | 0.294848i | ||||
\(471\) | 1678.57 | + | 2907.38i | 0.164214 | + | 0.284426i | ||||
\(472\) | −8310.36 | − | 4880.04i | −0.810414 | − | 0.475894i | ||||
\(473\) | 6049.03 | − | 10477.2i | 0.588023 | − | 1.01849i | ||||
\(474\) | 1743.91 | + | 1012.57i | 0.168989 | + | 0.0981202i | ||||
\(475\) | −310.003 | − | 175.921i | −0.0299451 | − | 0.0169932i | ||||
\(476\) | 6598.17 | − | 3766.33i | 0.635350 | − | 0.362667i | ||||
\(477\) | 11275.7 | + | 6510.05i | 1.08235 | + | 0.624895i | ||||
\(478\) | −8456.59 | − | 14730.7i | −0.809195 | − | 1.40956i | ||||
\(479\) | −17324.7 | + | 10002.4i | −1.65258 | + | 0.954117i | −0.676573 | + | 0.736376i | \(0.736536\pi\) |
−0.976007 | + | 0.217741i | \(0.930131\pi\) | |||||||
\(480\) | −33.0816 | + | 2691.76i | −0.00314576 | + | 0.255961i | ||||
\(481\) | 316.765 | + | 548.653i | 0.0300275 | + | 0.0520092i | ||||
\(482\) | −6646.43 | + | 11446.9i | −0.628085 | + | 1.08173i | ||||
\(483\) | −1153.48 | −0.108665 | ||||||||
\(484\) | 1670.49 | − | 2860.80i | 0.156883 | − | 0.268670i | ||||
\(485\) | 5175.08 | − | 2987.84i | 0.484512 | − | 0.279733i | ||||
\(486\) | −6597.00 | − | 3830.43i | −0.615733 | − | 0.357514i | ||||
\(487\) | 13640.7 | 1.26924 | 0.634620 | − | 0.772824i | \(-0.281157\pi\) | ||||
0.634620 | + | 0.772824i | \(0.281157\pi\) | |||||||
\(488\) | −13902.7 | + | 7890.61i | −1.28964 | + | 0.731949i | ||||
\(489\) | 1239.57 | + | 715.667i | 0.114633 | + | 0.0661831i | ||||
\(490\) | 16.7577 | − | 6817.95i | 0.00154497 | − | 0.628579i | ||||
\(491\) | −1730.54 | − | 999.126i | −0.159059 | − | 0.0918329i | 0.418358 | − | 0.908282i | \(-0.362606\pi\) |
−0.577417 | + | 0.816450i | \(0.695939\pi\) | |||||||
\(492\) | −14.9394 | + | 3039.07i | −0.00136894 | + | 0.278479i | ||||
\(493\) | 4748.64i | 0.433810i | ||||||||
\(494\) | 68.0277 | + | 13671.3i | 0.00619577 | + | 1.24514i | ||||
\(495\) | − | 8372.42i | − | 0.760227i | ||||||
\(496\) | −8062.94 | − | 14288.0i | −0.729913 | − | 1.29345i | ||||
\(497\) | 940.808 | + | 543.175i | 0.0849114 | + | 0.0490236i | ||||
\(498\) | −2470.40 | − | 6.07195i | −0.222292 | − | 0.000546366i | ||||
\(499\) | 2266.18 | + | 1308.38i | 0.203303 | + | 0.117377i | 0.598195 | − | 0.801350i | \(-0.295885\pi\) |
−0.394892 | + | 0.918727i | \(0.629218\pi\) | |||||||
\(500\) | −5730.53 | + | 9813.84i | −0.512554 | + | 0.877777i | ||||
\(501\) | 970.508 | 0.0865451 | ||||||||
\(502\) | −5130.58 | + | 8836.19i | −0.456153 | + | 0.785615i | ||||
\(503\) | 14048.8 | − | 8111.08i | 1.24534 | − | 0.718997i | 0.275163 | − | 0.961398i | \(-0.411268\pi\) |
0.970176 | + | 0.242401i | \(0.0779349\pi\) | |||||||
\(504\) | 3124.93 | + | 5505.89i | 0.276181 | + | 0.486611i | ||||
\(505\) | −7936.31 | −0.699329 | ||||||||
\(506\) | −5677.36 | − | 3296.46i | −0.498794 | − | 0.289616i | ||||
\(507\) | −818.441 | − | 1417.58i | −0.0716928 | − | 0.124176i | ||||
\(508\) | −15799.7 | − | 77.6679i | −1.37992 | − | 0.00678338i | ||||
\(509\) | −2646.12 | + | 1527.74i | −0.230427 | + | 0.133037i | −0.610769 | − | 0.791809i | \(-0.709140\pi\) |
0.380342 | + | 0.924846i | \(0.375806\pi\) | |||||||
\(510\) | 3116.20 | − | 1788.94i | 0.270564 | − | 0.155325i | ||||
\(511\) | −162.826 | − | 94.0078i | −0.0140959 | − | 0.00813828i | ||||
\(512\) | 256.254 | − | 11582.4i | 0.0221190 | − | 0.999755i | ||||
\(513\) | −5042.90 | + | 2961.72i | −0.434014 | + | 0.254899i | ||||
\(514\) | 6180.50 | − | 10644.4i | 0.530370 | − | 0.913436i | ||||
\(515\) | −2094.07 | + | 3627.04i | −0.179177 | + | 0.310343i | ||||
\(516\) | −21.2682 | + | 4326.51i | −0.00181449 | + | 0.369116i | ||||
\(517\) | −1687.87 | − | 2923.47i | −0.143583 | − | 0.248693i | ||||
\(518\) | 296.008 | − | 169.932i | 0.0251078 | − | 0.0144138i | ||||
\(519\) | 448.549 | − | 258.970i | 0.0379367 | − | 0.0219027i | ||||
\(520\) | 14508.0 | + | 106.979i | 1.22350 | + | 0.00902178i | ||||
\(521\) | − | 2837.83i | − | 0.238633i | −0.992856 | − | 0.119316i | \(-0.961930\pi\) | ||
0.992856 | − | 0.119316i | \(-0.0380702\pi\) | |||||||
\(522\) | −3956.99 | − | 9.72580i | −0.331787 | − | 0.000815491i | ||||
\(523\) | 2285.69 | + | 3958.94i | 0.191102 | + | 0.330999i | 0.945616 | − | 0.325286i | \(-0.105460\pi\) |
−0.754514 | + | 0.656284i | \(0.772127\pi\) | |||||||
\(524\) | 20003.8 | − | 11418.4i | 1.66769 | − | 0.951941i | ||||
\(525\) | − | 64.7648i | − | 0.00538394i | ||||||
\(526\) | 16016.6 | + | 39.3669i | 1.32768 | + | 0.00326327i | ||||
\(527\) | −10949.3 | + | 18964.7i | −0.905044 | + | 1.56758i | ||||
\(528\) | 25.7899 | − | 2623.11i | 0.00212569 | − | 0.216205i | ||||
\(529\) | −3145.67 | + | 5448.45i | −0.258541 | + | 0.447806i | ||||
\(530\) | −8003.47 | − | 13941.4i | −0.655941 | − | 1.14260i | ||||
\(531\) | −10719.2 | −0.876033 | ||||||||
\(532\) | 7365.54 | − | 18.5468i | 0.600256 | − | 0.00151148i | ||||
\(533\) | 16379.4 | 1.33109 | ||||||||
\(534\) | 774.027 | + | 1348.30i | 0.0627255 | + | 0.109263i | ||||
\(535\) | −711.814 | + | 1232.90i | −0.0575223 | + | 0.0996315i | ||||
\(536\) | 17816.8 | − | 10112.1i | 1.43576 | − | 0.814881i | ||||
\(537\) | −2159.41 | + | 3740.21i | −0.173530 | + | 0.300562i | ||||
\(538\) | −6522.21 | − | 16.0308i | −0.522663 | − | 0.00128464i | ||||
\(539\) | 6643.92i | 0.530935i | ||||||||
\(540\) | 3076.71 | + | 5390.04i | 0.245186 | + | 0.429538i | ||||
\(541\) | −10093.9 | − | 17483.1i | −0.802164 | − | 1.38939i | −0.918189 | − | 0.396142i | \(-0.870349\pi\) |
0.116026 | − | 0.993246i | \(-0.462984\pi\) | |||||||
\(542\) | 23349.1 | + | 57.3891i | 1.85042 | + | 0.00454810i | ||||
\(543\) | − | 6056.91i | − | 0.478687i | ||||||
\(544\) | −13486.1 | + | 7566.75i | −1.06289 | + | 0.596363i | ||||
\(545\) | −5389.43 | + | 3111.59i | −0.423592 | + | 0.244561i | ||||
\(546\) | −2154.33 | + | 1236.75i | −0.168858 | + | 0.0969379i | ||||
\(547\) | 3257.31 | + | 5641.83i | 0.254611 | + | 0.441000i | 0.964790 | − | 0.263022i | \(-0.0847191\pi\) |
−0.710178 | + | 0.704022i | \(0.751386\pi\) | |||||||
\(548\) | 16609.1 | + | 81.6466i | 1.29472 | + | 0.00636454i | ||||
\(549\) | −8890.24 | + | 15398.3i | −0.691122 | + | 1.19706i | ||||
\(550\) | 185.087 | − | 318.768i | 0.0143493 | − | 0.0247133i | ||||
\(551\) | −2272.16 | + | 4003.93i | −0.175675 | + | 0.309570i | ||||
\(552\) | 2347.73 | + | 17.3116i | 0.181026 | + | 0.00133484i | ||||
\(553\) | −5070.91 | − | 2927.69i | −0.389940 | − | 0.225132i | ||||
\(554\) | −9317.01 | + | 5348.69i | −0.714516 | + | 0.410188i | ||||
\(555\) | 139.799 | − | 80.7127i | 0.0106921 | − | 0.00617309i | ||||
\(556\) | 34.8844 | − | 7096.41i | 0.00266084 | − | 0.541286i | ||||
\(557\) | −933.783 | − | 1617.36i | −0.0710335 | − | 0.123034i | 0.828321 | − | 0.560254i | \(-0.189296\pi\) |
−0.899355 | + | 0.437220i | \(0.855963\pi\) | |||||||
\(558\) | −15780.7 | − | 9162.76i | −1.19722 | − | 0.695144i | ||||
\(559\) | 23318.2 | 1.76432 | ||||||||
\(560\) | 76.8465 | − | 7816.12i | 0.00579885 | − | 0.589806i | ||||
\(561\) | −3032.36 | + | 1750.73i | −0.228211 | + | 0.131758i | ||||
\(562\) | 8439.12 | − | 14534.4i | 0.633421 | − | 1.09092i | ||||
\(563\) | 6701.41 | 0.501653 | 0.250827 | − | 0.968032i | \(-0.419298\pi\) | ||||
0.250827 | + | 0.968032i | \(0.419298\pi\) | |||||||
\(564\) | 1042.52 | + | 608.754i | 0.0778337 | + | 0.0454489i | ||||
\(565\) | −1059.41 | − | 611.653i | −0.0788848 | − | 0.0455441i | ||||
\(566\) | −16769.8 | − | 41.2181i | −1.24539 | − | 0.00306100i | ||||
\(567\) | 5621.93 | + | 3245.82i | 0.416400 | + | 0.240409i | ||||
\(568\) | −1906.72 | − | 1119.67i | −0.140852 | − | 0.0827117i | ||||
\(569\) | − | 25055.1i | − | 1.84598i | −0.384824 | − | 0.922990i | \(-0.625738\pi\) | ||
0.384824 | − | 0.922990i | \(-0.374262\pi\) | |||||||
\(570\) | 3483.49 | − | 17.3337i | 0.255977 | − | 0.00127373i | ||||
\(571\) | − | 24262.3i | − | 1.77819i | −0.457723 | − | 0.889095i | \(-0.651335\pi\) | ||
0.457723 | − | 0.889095i | \(-0.348665\pi\) | |||||||
\(572\) | −14137.9 | − | 69.4987i | −1.03345 | − | 0.00508022i | ||||
\(573\) | −1829.15 | − | 1056.06i | −0.133357 | − | 0.0769939i | ||||
\(574\) | 21.6894 | − | 8824.44i | 0.00157717 | − | 0.641681i | ||||
\(575\) | 285.704 | + | 164.951i | 0.0207212 | + | 0.0119634i | ||||
\(576\) | −6277.67 | − | 11253.3i | −0.454114 | − | 0.814040i | ||||
\(577\) | −9291.86 | −0.670408 | −0.335204 | − | 0.942146i | \(-0.608805\pi\) | ||||
−0.335204 | + | 0.942146i | \(0.608805\pi\) | |||||||
\(578\) | 5832.89 | + | 3386.76i | 0.419751 | + | 0.243721i | ||||
\(579\) | 5199.40 | − | 3001.87i | 0.373194 | − | 0.215464i | ||||
\(580\) | 4218.96 | + | 2463.55i | 0.302039 | + | 0.176368i | ||||
\(581\) | 7173.19 | 0.512210 | ||||||||
\(582\) | 1045.67 | − | 1800.92i | 0.0744751 | − | 0.128266i | ||||
\(583\) | 7832.52 | + | 13566.3i | 0.556415 | + | 0.963739i | ||||
\(584\) | 329.997 | + | 193.782i | 0.0233825 | + | 0.0137307i | ||||
\(585\) | 13975.3 | − | 8068.62i | 0.987703 | − | 0.570250i | ||||
\(586\) | −972.768 | − | 1694.49i | −0.0685745 | − | 0.119452i | ||||
\(587\) | 17376.9 | + | 10032.6i | 1.22184 | + | 0.705431i | 0.965310 | − | 0.261105i | \(-0.0840869\pi\) |
0.256532 | + | 0.966536i | \(0.417420\pi\) | |||||||
\(588\) | −1177.88 | − | 2063.51i | −0.0826107 | − | 0.144724i | ||||
\(589\) | −18306.5 | + | 10751.5i | −1.28066 | + | 0.752135i | ||||
\(590\) | 11445.2 | + | 6645.45i | 0.798629 | + | 0.463710i | ||||
\(591\) | −1878.69 | + | 3253.99i | −0.130760 | + | 0.226483i | ||||
\(592\) | −605.028 | + | 341.427i | −0.0420042 | + | 0.0237036i | ||||
\(593\) | 12641.7 | + | 21896.0i | 0.875431 | + | 1.51629i | 0.856303 | + | 0.516474i | \(0.172756\pi\) |
0.0191287 | + | 0.999817i | \(0.493911\pi\) | |||||||
\(594\) | −3011.07 | − | 5245.05i | −0.207989 | − | 0.362302i | ||||
\(595\) | −9035.55 | + | 5216.68i | −0.622557 | + | 0.359433i | ||||
\(596\) | 2781.53 | + | 4872.92i | 0.191168 | + | 0.334904i | ||||
\(597\) | − | 2480.11i | − | 0.170024i | ||||||
\(598\) | 31.1008 | − | 12653.5i | 0.00212676 | − | 0.865286i | ||||
\(599\) | 3248.61 | + | 5626.76i | 0.221594 | + | 0.383812i | 0.955292 | − | 0.295664i | \(-0.0955407\pi\) |
−0.733698 | + | 0.679475i | \(0.762207\pi\) | |||||||
\(600\) | −0.971998 | + | 131.819i | −6.61361e−5 | + | 0.00896913i | ||||
\(601\) | 18229.6i | 1.23727i | 0.785677 | + | 0.618637i | \(0.212315\pi\) | ||||
−0.785677 | + | 0.618637i | \(0.787685\pi\) | |||||||
\(602\) | 30.8776 | − | 12562.7i | 0.00209050 | − | 0.850530i | ||||
\(603\) | 11393.2 | − | 19733.5i | 0.769428 | − | 1.33269i | ||||
\(604\) | 10583.1 | − | 18124.0i | 0.712944 | − | 1.22096i | ||||
\(605\) | −2274.70 | + | 3939.89i | −0.152859 | + | 0.264759i | ||||
\(606\) | −2398.61 | + | 1376.99i | −0.160787 | + | 0.0923041i | ||||
\(607\) | −17719.7 | −1.18488 | −0.592438 | − | 0.805616i | \(-0.701834\pi\) | ||||
−0.592438 | + | 0.805616i | \(0.701834\pi\) | |||||||
\(608\) | −14991.7 | − | 72.7937i | −0.999988 | − | 0.00485555i | ||||
\(609\) | −836.489 | −0.0556589 | ||||||||
\(610\) | 19038.7 | − | 10929.7i | 1.26369 | − | 0.725458i | ||||
\(611\) | 3253.25 | − | 5634.79i | 0.215405 | − | 0.373092i | ||||
\(612\) | −8673.06 | + | 14853.1i | −0.572856 | + | 0.981046i | ||||
\(613\) | −7340.05 | + | 12713.3i | −0.483625 | + | 0.837662i | −0.999823 | − | 0.0188067i | \(-0.994013\pi\) |
0.516199 | + | 0.856469i | \(0.327347\pi\) | |||||||
\(614\) | 32.9170 | − | 13392.4i | 0.00216355 | − | 0.880253i | ||||
\(615\) | − | 4173.52i | − | 0.273646i | ||||||
\(616\) | −56.1639 | + | 7616.74i | −0.00367355 | + | 0.498193i | ||||
\(617\) | 5414.43 | + | 9378.07i | 0.353285 | + | 0.611908i | 0.986823 | − | 0.161804i | \(-0.0517312\pi\) |
−0.633538 | + | 0.773712i | \(0.718398\pi\) | |||||||
\(618\) | −3.58737 | + | 1459.54i | −0.000233504 | + | 0.0950022i | ||||
\(619\) | 2009.72i | 0.130497i | 0.997869 | + | 0.0652485i | \(0.0207840\pi\) | ||||
−0.997869 | + | 0.0652485i | \(0.979216\pi\) | |||||||
\(620\) | 11168.9 | + | 19566.7i | 0.723476 | + | 1.26745i | ||||
\(621\) | 4687.68 | − | 2706.44i | 0.302915 | − | 0.174888i | ||||
\(622\) | 39.5936 | + | 68.9691i | 0.00255235 | + | 0.00444600i | ||||
\(623\) | −2257.11 | − | 3909.43i | −0.145151 | − | 0.251410i | ||||
\(624\) | 4403.36 | − | 2484.88i | 0.282493 | − | 0.159415i | ||||
\(625\) | 7534.25 | − | 13049.7i | 0.482192 | − | 0.835181i | ||||
\(626\) | −12819.6 | − | 7443.46i | −0.818488 | − | 0.475240i | ||||
\(627\) | −3394.50 | + | 25.2345i | −0.216210 | + | 0.00160729i | ||||
\(628\) | 9835.91 | + | 17231.4i | 0.624993 | + | 1.09491i | ||||
\(629\) | 803.064 | + | 463.649i | 0.0509066 | + | 0.0293910i | ||||
\(630\) | −4328.49 | − | 7539.90i | −0.273732 | − | 0.476821i | ||||
\(631\) | −5014.42 | + | 2895.08i | −0.316356 | + | 0.182648i | −0.649767 | − | 0.760133i | \(-0.725134\pi\) |
0.333411 | + | 0.942782i | \(0.391800\pi\) | |||||||
\(632\) | 10277.1 | + | 6034.96i | 0.646837 | + | 0.379838i | ||||
\(633\) | 3950.36 | + | 6842.23i | 0.248046 | + | 0.429628i | ||||
\(634\) | 8612.29 | − | 14832.6i | 0.539492 | − | 0.929146i | ||||
\(635\) | 21697.6 | 1.35597 | ||||||||
\(636\) | −4837.81 | − | 2824.91i | −0.301622 | − | 0.176124i | ||||
\(637\) | −11090.0 | + | 6402.84i | −0.689801 | + | 0.398257i | ||||
\(638\) | −4117.14 | − | 2390.55i | −0.255485 | − | 0.148343i | ||||
\(639\) | −2459.40 | −0.152257 | ||||||||
\(640\) | −273.714 | + | 15907.3i | −0.0169055 | + | 0.982488i | ||||
\(641\) | 4059.52 | + | 2343.76i | 0.250142 | + | 0.144420i | 0.619829 | − | 0.784737i | \(-0.287202\pi\) |
−0.369687 | + | 0.929156i | \(0.620535\pi\) | |||||||
\(642\) | −1.21941 | + | 496.125i | −7.49632e−5 | + | 0.0304992i | ||||
\(643\) | −8610.56 | − | 4971.31i | −0.528099 | − | 0.304898i | 0.212143 | − | 0.977239i | \(-0.431956\pi\) |
−0.740242 | + | 0.672341i | \(0.765289\pi\) | |||||||
\(644\) | −6817.08 | − | 33.5113i | −0.417128 | − | 0.00205051i | ||||
\(645\) | − | 5941.54i | − | 0.362710i | ||||||
\(646\) | 10091.6 | + | 17280.0i | 0.614625 | + | 1.05243i | ||||
\(647\) | − | 1376.69i | − | 0.0836527i | −0.999125 | − | 0.0418263i | \(-0.986682\pi\) | ||
0.999125 | − | 0.0418263i | \(-0.0133176\pi\) | |||||||
\(648\) | −11393.8 | − | 6690.74i | −0.690729 | − | 0.405613i | ||||
\(649\) | −11168.9 | − | 6448.36i | −0.675527 | − | 0.390016i | ||||
\(650\) | 710.459 | + | 1.74622i | 0.0428716 | + | 0.000105373i | ||||
\(651\) | −3340.70 | − | 1928.75i | −0.201125 | − | 0.116120i | ||||
\(652\) | 7305.07 | + | 4265.60i | 0.438786 | + | 0.256218i | ||||
\(653\) | 10986.5 | 0.658401 | 0.329201 | − | 0.944260i | \(-0.393221\pi\) | ||||
0.329201 | + | 0.944260i | \(0.393221\pi\) | |||||||
\(654\) | −1088.98 | + | 1875.51i | −0.0651111 | + | 0.112138i | ||||
\(655\) | −27393.2 | + | 15815.5i | −1.63411 | + | 0.943454i | ||||
\(656\) | −176.584 | + | 17960.4i | −0.0105098 | + | 1.06896i | ||||
\(657\) | 425.650 | 0.0252758 | ||||||||
\(658\) | −3031.45 | − | 1760.16i | −0.179602 | − | 0.104283i | ||||
\(659\) | 1775.73 | + | 3075.65i | 0.104966 | + | 0.181806i | 0.913724 | − | 0.406335i | \(-0.133193\pi\) |
−0.808758 | + | 0.588141i | \(0.799860\pi\) | |||||||
\(660\) | −17.7085 | + | 3602.38i | −0.00104440 | + | 0.212458i | ||||
\(661\) | −1417.79 | + | 818.563i | −0.0834278 | + | 0.0481671i | −0.541134 | − | 0.840937i | \(-0.682005\pi\) |
0.457706 | + | 0.889104i | \(0.348671\pi\) | |||||||
\(662\) | −19232.8 | + | 11041.1i | −1.12916 | + | 0.648227i | ||||
\(663\) | −5844.65 | − | 3374.41i | −0.342364 | − | 0.197664i | ||||
\(664\) | −14599.9 | − | 107.656i | −0.853293 | − | 0.00629196i | ||||
\(665\) | −10114.6 | + | 75.1915i | −0.589818 | + | 0.00438466i | ||||
\(666\) | −387.999 | + | 668.235i | −0.0225745 | + | 0.0388792i | ||||
\(667\) | 2130.47 | − | 3690.09i | 0.123677 | − | 0.214214i | ||||
\(668\) | 5735.70 | + | 28.1955i | 0.332217 | + | 0.00163311i | ||||
\(669\) | −2792.21 | − | 4836.25i | −0.161365 | − | 0.279492i | ||||
\(670\) | −24398.7 | + | 14006.8i | −1.40687 | + | 0.807655i | ||||
\(671\) | −18526.4 | + | 10696.2i | −1.06588 | + | 0.615384i | ||||
\(672\) | −1332.91 | − | 2375.62i | −0.0765149 | − | 0.136371i | ||||
\(673\) | 11725.8i | 0.671616i | 0.941930 | + | 0.335808i | \(0.109009\pi\) | ||||
−0.941930 | + | 0.335808i | \(0.890991\pi\) | |||||||
\(674\) | 14514.3 | + | 35.6744i | 0.829481 | + | 0.00203876i | ||||
\(675\) | 151.959 | + | 263.200i | 0.00866503 | + | 0.0150083i | ||||
\(676\) | −4795.80 | − | 8401.69i | −0.272861 | − | 0.478020i | ||||
\(677\) | − | 15569.8i | − | 0.883895i | −0.897041 | − | 0.441948i | \(-0.854288\pi\) | ||
0.897041 | − | 0.441948i | \(-0.145712\pi\) | |||||||
\(678\) | −426.314 | − | 1.04783i | −0.0241482 | − | 5.93533e-5i | ||||
\(679\) | −3023.40 | + | 5236.68i | −0.170880 | + | 0.295972i | ||||
\(680\) | 18468.7 | − | 10482.1i | 1.04154 | − | 0.591134i | ||||
\(681\) | −2256.99 | + | 3909.21i | −0.127001 | + | 0.219973i | ||||
\(682\) | −10930.6 | − | 19040.3i | −0.613718 | − | 1.06905i | ||||
\(683\) | −8307.82 | −0.465432 | −0.232716 | − | 0.972545i | \(-0.574761\pi\) | ||||
−0.232716 | + | 0.972545i | \(0.574761\pi\) | |||||||
\(684\) | −14419.9 | + | 8373.80i | −0.806078 | + | 0.468100i | ||||
\(685\) | −22809.1 | −1.27225 | ||||||||
\(686\) | 8804.45 | + | 15336.7i | 0.490022 | + | 0.853582i | ||||
\(687\) | −1920.10 | + | 3325.71i | −0.106632 | + | 0.184692i | ||||
\(688\) | −251.390 | + | 25569.0i | −0.0139304 | + | 1.41688i | ||||
\(689\) | −15096.6 | + | 26148.1i | −0.834740 | + | 1.44581i | ||||
\(690\) | −3224.16 | − | 7.92458i | −0.177886 | − | 0.000437223i | ||||
\(691\) | − | 1635.93i | − | 0.0900632i | −0.998986 | − | 0.0450316i | \(-0.985661\pi\) | ||
0.998986 | − | 0.0450316i | \(-0.0143389\pi\) | |||||||
\(692\) | 2658.45 | − | 1517.48i | 0.146039 | − | 0.0833612i | ||||
\(693\) | 4236.04 | + | 7337.03i | 0.232199 | + | 0.402180i | ||||
\(694\) | −9439.35 | − | 23.2008i | −0.516301 | − | 0.00126900i | ||||
\(695\) | 9745.43i | 0.531892i | ||||||||
\(696\) | 1702.54 | + | 12.5541i | 0.0927224 | + | 0.000683711i | ||||
\(697\) | 20762.5 | − | 11987.3i | 1.12832 | − | 0.651435i | ||||
\(698\) | −6258.80 | + | 3593.04i | −0.339397 | + | 0.194840i | ||||
\(699\) | −3876.66 | − | 6714.57i | −0.209769 | − | 0.363331i | ||||
\(700\) | 1.88156 | − | 382.760i | 0.000101595 | − | 0.0206671i | ||||
\(701\) | 9950.48 | − | 17234.7i | 0.536126 | − | 0.928597i | −0.462982 | − | 0.886368i | \(-0.653221\pi\) |
0.999108 | − | 0.0422296i | \(-0.0134461\pi\) | |||||||
\(702\) | 5853.24 | − | 10080.8i | 0.314696 | − | 0.541988i | ||||
\(703\) | 455.274 | + | 775.191i | 0.0244253 | + | 0.0415888i | ||||
\(704\) | 228.626 | − | 15501.8i | 0.0122396 | − | 0.829897i | ||||
\(705\) | −1435.76 | − | 828.938i | −0.0767006 | − | 0.0442831i | ||||
\(706\) | −10062.0 | + | 5776.36i | −0.536385 | + | 0.307926i | ||||
\(707\) | 6954.85 | − | 4015.38i | 0.369963 | − | 0.213598i | ||||
\(708\) | 4612.12 | + | 22.6722i | 0.244822 | + | 0.00120349i | ||||
\(709\) | −1459.56 | − | 2528.04i | −0.0773133 | − | 0.133911i | 0.824777 | − | 0.565459i | \(-0.191301\pi\) |
−0.902090 | + | 0.431548i | \(0.857967\pi\) | |||||||
\(710\) | 2625.97 | + | 1524.72i | 0.138804 | + | 0.0805940i | ||||
\(711\) | 13256.0 | 0.699212 | ||||||||
\(712\) | 4535.33 | + | 7990.92i | 0.238720 | + | 0.420607i | ||||
\(713\) | 17017.0 | − | 9824.78i | 0.893818 | − | 0.516046i | ||||
\(714\) | −1825.72 | + | 3144.36i | −0.0956942 | + | 0.164810i | ||||
\(715\) | 19415.4 | 1.01552 | ||||||||
\(716\) | −12870.8 | + | 22041.9i | −0.671792 | + | 1.15048i | ||||
\(717\) | 7039.83 | + | 4064.45i | 0.366677 | + | 0.211701i | ||||
\(718\) | −16467.1 | − | 40.4740i | −0.855914 | − | 0.00210373i | ||||
\(719\) | −28355.7 | − | 16371.2i | −1.47078 | − | 0.849155i | −0.471318 | − | 0.881964i | \(-0.656221\pi\) |
−0.999462 | + | 0.0328088i | \(0.989555\pi\) | |||||||
\(720\) | 8696.81 | + | 15411.3i | 0.450154 | + | 0.797700i | ||||
\(721\) | − | 4238.00i | − | 0.218906i | ||||||
\(722\) | 240.744 | + | 19398.7i | 0.0124094 | + | 0.999923i | ||||
\(723\) | − | 6334.72i | − | 0.325852i | ||||||
\(724\) | 175.967 | − | 35796.3i | 0.00903281 | − | 1.83751i | ||||
\(725\) | 207.188 | + | 119.620i | 0.0106135 | + | 0.00612770i | ||||
\(726\) | −3.89680 | + | 1585.43i | −0.000199206 | + | 0.0810481i | ||||
\(727\) | 1764.01 | + | 1018.45i | 0.0899908 | + | 0.0519562i | 0.544320 | − | 0.838878i | \(-0.316788\pi\) |
−0.454329 | + | 0.890834i | \(0.650121\pi\) | |||||||
\(728\) | −12768.0 | + | 7246.61i | −0.650019 | + | 0.368925i | ||||
\(729\) | −12115.6 | −0.615538 | ||||||||
\(730\) | −454.478 | − | 263.885i | −0.0230425 | − | 0.0133792i | ||||
\(731\) | 29558.2 | − | 17065.4i | 1.49555 | − | 0.863458i | ||||
\(732\) | 3857.75 | − | 6606.60i | 0.194790 | − | 0.333589i | ||||
\(733\) | 34794.9 | 1.75331 | 0.876657 | − | 0.481115i | \(-0.159768\pi\) | ||||
0.876657 | + | 0.481115i | \(0.159768\pi\) | |||||||
\(734\) | 6607.94 | − | 11380.6i | 0.332294 | − | 0.572296i | ||||
\(735\) | 1631.46 | + | 2825.78i | 0.0818741 | + | 0.141810i | ||||
\(736\) | 13874.6 | + | 170.519i | 0.694871 | + | 0.00853994i | ||||
\(737\) | 23742.2 | − | 13707.6i | 1.18664 | − | 0.685109i | ||||
\(738\) | 9946.33 | + | 17325.7i | 0.496110 | + | 0.864186i | ||||
\(739\) | −22320.9 | − | 12887.0i | −1.11108 | − | 0.641482i | −0.171970 | − | 0.985102i | \(-0.555013\pi\) |
−0.939109 | + | 0.343620i | \(0.888347\pi\) | |||||||
\(740\) | 828.554 | − | 472.951i | 0.0411598 | − | 0.0234946i | ||||
\(741\) | −3313.45 | − | 5641.80i | −0.164268 | − | 0.279698i | ||||
\(742\) | 14067.4 | + | 8167.98i | 0.695998 | + | 0.404119i | ||||
\(743\) | 13842.3 | − | 23975.6i | 0.683480 | − | 1.18382i | −0.290432 | − | 0.956896i | \(-0.593799\pi\) |
0.973912 | − | 0.226926i | \(-0.0728676\pi\) | |||||||
\(744\) | 6770.52 | + | 3975.81i | 0.333628 | + | 0.195915i | ||||
\(745\) | −3852.65 | − | 6672.99i | −0.189463 | − | 0.328160i | ||||
\(746\) | 13801.5 | + | 24041.1i | 0.677356 | + | 1.17990i | ||||
\(747\) | −14063.8 | + | 8119.71i | −0.688843 | + | 0.397704i | ||||
\(748\) | −17972.1 | + | 10258.7i | −0.878509 | + | 0.501466i | ||||
\(749\) | − | 1440.57i | − | 0.0702769i | ||||||
\(750\) | 13.3678 | − | 5438.75i | 0.000650829 | − | 0.264793i | ||||
\(751\) | 8367.99 | + | 14493.8i | 0.406594 | + | 0.704242i | 0.994506 | − | 0.104683i | \(-0.0333829\pi\) |
−0.587911 | + | 0.808926i | \(0.700050\pi\) | |||||||
\(752\) | 6143.63 | + | 3628.02i | 0.297919 | + | 0.175931i | ||||
\(753\) | − | 4889.95i | − | 0.236653i | ||||||
\(754\) | 22.5538 | − | 9176.15i | 0.00108934 | − | 0.443204i | ||||
\(755\) | −14410.9 | + | 24960.4i | −0.694657 | + | 1.20318i | ||||
\(756\) | −5423.32 | − | 3166.80i | −0.260905 | − | 0.152349i | ||||
\(757\) | 6037.04 | − | 10456.5i | 0.289854 | − | 0.502043i | −0.683920 | − | 0.729557i | \(-0.739726\pi\) |
0.973775 | + | 0.227514i | \(0.0730598\pi\) | |||||||
\(758\) | −9455.19 | + | 5428.02i | −0.453071 | + | 0.260098i | ||||
\(759\) | 3141.86 | 0.150253 | ||||||||
\(760\) | 20587.9 | − | 1.23888i | 0.982634 | − | 5.91303e-5i | ||||
\(761\) | 31305.7 | 1.49124 | 0.745618 | − | 0.666374i | \(-0.232155\pi\) | ||||
0.745618 | + | 0.666374i | \(0.232155\pi\) | |||||||
\(762\) | 6557.70 | − | 3764.63i | 0.311759 | − | 0.178974i | ||||
\(763\) | 3148.62 | − | 5453.58i | 0.149394 | − | 0.258758i | ||||
\(764\) | −10779.6 | − | 6294.45i | −0.510461 | − | 0.298070i | ||||
\(765\) | 11810.1 | − | 20455.6i | 0.558162 | − | 0.966764i | ||||
\(766\) | 40.1439 | − | 16332.8i | 0.00189355 | − | 0.770401i | ||||
\(767\) | − | 24857.5i | − | 1.17021i | ||||||
\(768\) | 2677.27 | + | 4855.20i | 0.125791 | + | 0.228121i | ||||
\(769\) | −10763.5 | − | 18642.9i | −0.504734 | − | 0.874224i | −0.999985 | − | 0.00547464i | \(-0.998257\pi\) |
0.495251 | − | 0.868750i | \(-0.335076\pi\) | |||||||
\(770\) | 25.7097 | − | 10460.1i | 0.00120326 | − | 0.489554i | ||||
\(771\) | 5890.64i | 0.275157i | ||||||||
\(772\) | 30815.6 | − | 17590.0i | 1.43663 | − | 0.820050i | ||||
\(773\) | −12953.8 | + | 7478.91i | −0.602739 | + | 0.347992i | −0.770118 | − | 0.637901i | \(-0.779803\pi\) |
0.167379 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(774\) | 14159.9 | + | 24665.5i | 0.657580 | + | 1.14545i | ||||
\(775\) | 551.633 | + | 955.457i | 0.0255681 | + | 0.0442852i | ||||
\(776\) | 6232.25 | − | 10613.1i | 0.288305 | − | 0.490962i | ||||
\(777\) | −81.6734 | + | 141.462i | −0.00377093 | + | 0.00653145i | ||||
\(778\) | 16680.1 | + | 9685.02i | 0.768653 | + | 0.446305i | ||||
\(779\) | 23242.2 | − | 172.781i | 1.06898 | − | 0.00794673i | ||||
\(780\) | −6030.17 | + | 3442.11i | −0.276814 | + | 0.158009i | ||||
\(781\) | −2562.57 | − | 1479.50i | −0.117409 | − | 0.0677858i | ||||
\(782\) | −9221.07 | − | 16062.4i | −0.421668 | − | 0.734515i | ||||
\(783\) | 3399.44 | − | 1962.67i | 0.155155 | − | 0.0895786i | ||||
\(784\) | −6901.34 | − | 12229.6i | −0.314383 | − | 0.557105i | ||||
\(785\) | −13623.5 | − | 23596.7i | −0.619420 | − | 1.07287i | ||||
\(786\) | −5535.05 | + | 9532.81i | −0.251182 | + | 0.432600i | ||||
\(787\) | −29401.4 | −1.33170 | −0.665848 | − | 0.746087i | \(-0.731930\pi\) | ||||
−0.665848 | + | 0.746087i | \(0.731930\pi\) | |||||||
\(788\) | −11197.6 | + | 19176.5i | −0.506216 | + | 0.866922i | ||||
\(789\) | −6638.29 | + | 3832.62i | −0.299530 | + | 0.172934i | ||||
\(790\) | −14153.8 | − | 8218.17i | −0.637431 | − | 0.370113i | ||||
\(791\) | 1237.87 | 0.0556428 | ||||||||
\(792\) | −8511.68 | − | 14997.0i | −0.381880 | − | 0.672845i | ||||
\(793\) | −35708.3 | − | 20616.2i | −1.59904 | − | 0.923207i | ||||
\(794\) | −66.7881 | + | 27173.1i | −0.00298517 | + | 1.21453i | ||||
\(795\) | 6662.63 | + | 3846.67i | 0.297232 | + | 0.171607i | ||||
\(796\) | 72.0527 | − | 14657.4i | 0.00320834 | − | 0.652662i | ||||
\(797\) | 25313.5i | 1.12503i | 0.826787 | + | 0.562515i | \(0.190166\pi\) | ||||
−0.826787 | + | 0.562515i | \(0.809834\pi\) | |||||||
\(798\) | −3043.92 | + | 1777.66i | −0.135030 | + | 0.0788579i | ||||
\(799\) | − | 9523.57i | − | 0.421677i | ||||||
\(800\) | −9.57414 | + | 779.020i | −0.000423121 | + | 0.0344282i | ||||
\(801\) | 8850.59 | + | 5109.89i | 0.390412 | + | 0.225405i | ||||
\(802\) | −26403.4 | − | 64.8962i | −1.16251 | − | 0.00285731i | ||||
\(803\) | 443.506 | + | 256.059i | 0.0194907 | + | 0.0112529i | ||||
\(804\) | −4943.84 | + | 8466.59i | −0.216860 | + | 0.371385i | ||||
\(805\) | 9361.83 | 0.409889 | ||||||||
\(806\) | 21248.2 | − | 36594.9i | 0.928580 | − | 1.59926i | ||||
\(807\) | 2703.21 | − | 1560.70i | 0.117915 | − | 0.0680782i | ||||
\(808\) | −14215.8 | + | 8068.31i | −0.618947 | + | 0.351290i | ||||
\(809\) | −16328.0 | −0.709593 | −0.354796 | − | 0.934944i | \(-0.615450\pi\) | ||||
−0.354796 | + | 0.934944i | \(0.615450\pi\) | |||||||
\(810\) | 15691.8 | + | 9111.18i | 0.680685 | + | 0.395228i | ||||
\(811\) | 2699.59 | + | 4675.84i | 0.116887 | + | 0.202455i | 0.918533 | − | 0.395345i | \(-0.129375\pi\) |
−0.801645 | + | 0.597800i | \(0.796042\pi\) | |||||||
\(812\) | −4943.65 | − | 24.3019i | −0.213655 | − | 0.00105028i | ||||
\(813\) | −9677.28 | + | 5587.18i | −0.417463 | + | 0.241022i | ||||
\(814\) | −806.267 | + | 462.860i | −0.0347170 | + | 0.0199303i | ||||
\(815\) | −10060.5 | − | 5808.45i | −0.432399 | − | 0.249645i | ||||
\(816\) | 3763.15 | − | 6372.45i | 0.161442 | − | 0.273383i | ||||
\(817\) | 33088.2 | − | 245.976i | 1.41690 | − | 0.0105332i | ||||
\(818\) | 14122.3 | − | 24322.3i | 0.603636 | − | 1.03962i | ||||
\(819\) | −8164.66 | + | 14141.6i | −0.348347 | + | 0.603355i | ||||
\(820\) | 121.250 | − | 24665.5i | 0.00516370 | − | 1.05043i | ||||
\(821\) | −9044.64 | − | 15665.8i | −0.384482 | − | 0.665943i | 0.607215 | − | 0.794538i | \(-0.292287\pi\) |
−0.991697 | + | 0.128595i | \(0.958953\pi\) | |||||||
\(822\) | −6893.63 | + | 3957.48i | −0.292510 | + | 0.167923i | ||||
\(823\) | 9311.48 | − | 5375.98i | 0.394383 | − | 0.227697i | −0.289674 | − | 0.957125i | \(-0.593547\pi\) |
0.684058 | + | 0.729428i | \(0.260214\pi\) | |||||||
\(824\) | −63.6043 | + | 8625.78i | −0.00268903 | + | 0.364676i | ||||
\(825\) | 176.406i | 0.00744447i | ||||||||
\(826\) | −13392.1 | − | 32.9161i | −0.564128 | − | 0.00138656i | ||||
\(827\) | 10475.6 | + | 18144.3i | 0.440474 | + | 0.762923i | 0.997725 | − | 0.0674210i | \(-0.0214771\pi\) |
−0.557251 | + | 0.830344i | \(0.688144\pi\) | |||||||
\(828\) | 13403.5 | − | 7650.92i | 0.562565 | − | 0.321120i | ||||
\(829\) | − | 4453.30i | − | 0.186574i | −0.995639 | − | 0.0932868i | \(-0.970263\pi\) | ||
0.995639 | − | 0.0932868i | \(-0.0297374\pi\) | |||||||
\(830\) | 20050.1 | + | 49.2808i | 0.838495 | + | 0.00206092i | ||||
\(831\) | 2570.71 | − | 4452.61i | 0.107313 | − | 0.185871i | ||||
\(832\) | 26096.0 | − | 14557.7i | 1.08740 | − | 0.606609i | ||||
\(833\) | −9371.85 | + | 16232.5i | −0.389814 | + | 0.675178i | ||||
\(834\) | 1690.88 | + | 2945.38i | 0.0702042 | + | 0.122290i | ||||
\(835\) | −7876.78 | −0.326452 | ||||||||
\(836\) | −20062.2 | + | 50.5178i | −0.829985 | + | 0.00208994i | ||||
\(837\) | 18101.9 | 0.747541 | ||||||||
\(838\) | 12491.5 | + | 21759.2i | 0.514929 | + | 0.896968i | ||||
\(839\) | −11536.3 | + | 19981.5i | −0.474706 | + | 0.822216i | −0.999580 | − | 0.0289643i | \(-0.990779\pi\) |
0.524874 | + | 0.851180i | \(0.324112\pi\) | |||||||
\(840\) | 1846.46 | + | 3253.33i | 0.0758440 | + | 0.133632i | ||||
\(841\) | −10649.5 | + | 18445.5i | −0.436652 | + | 0.756304i | ||||
\(842\) | −14182.8 | − | 34.8597i | −0.580491 | − | 0.00142677i | ||||
\(843\) | 8043.33i | 0.328620i | ||||||||
\(844\) | 23147.9 | + | 40552.3i | 0.944055 | + | 1.65387i | ||||
\(845\) | 6642.58 | + | 11505.3i | 0.270428 | + | 0.468395i | ||||
\(846\) | 7935.88 | + | 19.5054i | 0.322507 | + | 0.000792683i | ||||
\(847\) | − | 4603.54i | − | 0.186753i | ||||||
\(848\) | −28509.4 | − | 16835.8i | −1.15450 | − | 0.681773i | ||||
\(849\) | 6950.45 | − | 4012.84i | 0.280964 | − | 0.162215i | ||||
\(850\) | 901.859 | − | 517.737i | 0.0363924 | − | 0.0208920i | ||||
\(851\) | −416.032 | − | 720.588i | −0.0167584 | − | 0.0290264i | ||||
\(852\) | 1058.20 | + | 5.20187i | 0.0425508 | + | 0.000209170i | ||||
\(853\) | −2324.59 | + | 4026.31i | −0.0933089 | + | 0.161616i | −0.908902 | − | 0.417011i | \(-0.863078\pi\) |
0.815593 | + | 0.578626i | \(0.196411\pi\) | |||||||
\(854\) | −11154.3 | + | 19210.7i | −0.446948 | + | 0.769761i | ||||
\(855\) | 19745.6 | − | 11596.7i | 0.789809 | − | 0.463859i | ||||
\(856\) | −21.6203 | + | 2932.06i | −0.000863278 | + | 0.117075i | ||||
\(857\) | 3370.00 | + | 1945.67i | 0.134325 | + | 0.0775528i | 0.565657 | − | 0.824641i | \(-0.308623\pi\) |
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(858\) | 5867.96 | − | 3368.66i | 0.233483 | − | 0.134038i | ||||
\(859\) | −4961.47 | + | 2864.51i | −0.197070 | + | 0.113778i | −0.595288 | − | 0.803512i | \(-0.702962\pi\) |
0.398218 | + | 0.917291i | \(0.369629\pi\) | |||||||
\(860\) | 172.615 | − | 35114.5i | 0.00684434 | − | 1.39232i | ||||
\(861\) | 2111.60 | + | 3657.39i | 0.0835807 | + | 0.144766i | ||||
\(862\) | 29842.8 | + | 17327.7i | 1.17917 | + | 0.684667i | ||||
\(863\) | −38455.0 | −1.51683 | −0.758415 | − | 0.651772i | \(-0.774026\pi\) | ||||
−0.758415 | + | 0.651772i | \(0.774026\pi\) | |||||||
\(864\) | 10990.8 | + | 6526.93i | 0.432772 | + | 0.257003i | ||||
\(865\) | −3640.49 | + | 2101.84i | −0.143099 | + | 0.0826180i | ||||
\(866\) | −11054.2 | + | 19038.2i | −0.433760 | + | 0.747047i | ||||
\(867\) | −3227.93 | −0.126443 | ||||||||
\(868\) | −19687.5 | − | 11496.0i | −0.769858 | − | 0.449538i | ||||
\(869\) | 13812.1 | + | 7974.44i | 0.539177 | + | 0.311294i | ||||
\(870\) | −2338.11 | − | 5.74679i | −0.0911143 | − | 0.000223948i | ||||
\(871\) | 45761.5 | + | 26420.4i | 1.78022 | + | 1.02781i | ||||
\(872\) | −6490.38 | + | 11052.7i | −0.252055 | + | 0.429232i | ||||
\(873\) | − | 13689.4i | − | 0.530716i | ||||||
\(874\) | −89.3460 | − | 17955.5i | −0.00345787 | − | 0.694915i | ||||
\(875\) | 15792.2i | 0.610143i | ||||||||
\(876\) | −183.143 | − | 0.900292i | −0.00706374 | − | 3.47238e-5i | ||||
\(877\) | −2499.32 | − | 1442.99i | −0.0962328 | − | 0.0555600i | 0.451111 | − | 0.892468i | \(-0.351028\pi\) |
−0.547344 | + | 0.836908i | \(0.684361\pi\) | |||||||
\(878\) | 87.1188 | − | 35444.8i | 0.00334865 | − | 1.36242i | ||||
\(879\) | 809.797 | + | 467.537i | 0.0310737 | + | 0.0179404i | ||||
\(880\) | −209.315 | + | 21289.5i | −0.00801817 | + | 0.815534i | ||||
\(881\) | −39870.5 | −1.52471 | −0.762356 | − | 0.647157i | \(-0.775958\pi\) | ||||
−0.762356 | + | 0.647157i | \(0.775958\pi\) | |||||||
\(882\) | −13507.2 | − | 7842.71i | −0.515658 | − | 0.299408i | ||||
\(883\) | −15090.9 | + | 8712.74i | −0.575141 | + | 0.332058i | −0.759200 | − | 0.650857i | \(-0.774410\pi\) |
0.184059 | + | 0.982915i | \(0.441076\pi\) | |||||||
\(884\) | −34443.9 | − | 20112.6i | −1.31049 | − | 0.765225i | ||||
\(885\) | −6333.78 | −0.240574 | ||||||||
\(886\) | −5845.57 | + | 10067.6i | −0.221654 | + | 0.381747i | ||||
\(887\) | −9438.62 | − | 16348.2i | −0.357292 | − | 0.618847i | 0.630216 | − | 0.776420i | \(-0.282966\pi\) |
−0.987507 | + | 0.157573i | \(0.949633\pi\) | |||||||
\(888\) | 168.357 | − | 286.699i | 0.00636225 | − | 0.0108344i | ||||
\(889\) | −19014.3 | + | 10977.9i | −0.717344 | + | 0.414159i | ||||
\(890\) | −6282.11 | − | 10943.0i | −0.236603 | − | 0.412145i | ||||
\(891\) | −15313.0 | − | 8840.97i | −0.575764 | − | 0.332417i | ||||
\(892\) | −16361.5 | − | 28663.4i | −0.614151 | − | 1.07592i | ||||
\(893\) | 4556.88 | − | 8030.02i | 0.170762 | − | 0.300912i | ||||
\(894\) | −2322.19 | − | 1348.34i | −0.0868743 | − | 0.0504420i | ||||
\(895\) | 17526.1 | − | 30356.0i | 0.654561 | − | 1.13373i | ||||
\(896\) | −7808.47 | − | 14078.6i | −0.291141 | − | 0.524926i | ||||
\(897\) | 3027.85 | + | 5244.40i | 0.112706 | + | 0.195212i | ||||
\(898\) | 12843.4 | + | 22372.3i | 0.477273 | + | 0.831373i | ||||
\(899\) | 12340.5 | − | 7124.79i | 0.457818 | − | 0.264321i | ||||
\(900\) | 429.577 | + | 752.569i | 0.0159103 | + | 0.0278729i | ||||
\(901\) | 44193.9i | 1.63409i | ||||||||
\(902\) | −59.0775 | + | 24036.0i | −0.00218078 | + | 0.887264i | ||||
\(903\) | 3006.13 | + | 5206.77i | 0.110784 | + | 0.191883i | ||||
\(904\) | −2519.48 | − | 18.5780i | −0.0926956 | − | 0.000683514i | ||||
\(905\) | 49158.7i | 1.80562i | ||||||||
\(906\) | −24.6874 | + | 10044.2i | −0.000905280 | + | 0.368318i | ||||
\(907\) | −1251.55 | + | 2167.75i | −0.0458182 | + | 0.0793595i | −0.888025 | − | 0.459795i | \(-0.847923\pi\) |
0.842207 | + | 0.539155i | \(0.181256\pi\) | |||||||
\(908\) | −13452.4 | + | 23037.9i | −0.491665 | + | 0.842003i | ||||
\(909\) | −9090.45 | + | 15745.1i | −0.331696 | + | 0.574513i | ||||
\(910\) | 17484.8 | − | 10037.6i | 0.636941 | − | 0.365654i | ||||
\(911\) | 14956.7 | 0.543950 | 0.271975 | − | 0.962304i | \(-0.412323\pi\) | ||||
0.271975 | + | 0.962304i | \(0.412323\pi\) | |||||||
\(912\) | 6222.11 | − | 3572.47i | 0.225915 | − | 0.129711i | ||||
\(913\) | −19538.3 | −0.708242 | ||||||||
\(914\) | 11318.2 | − | 6497.54i | 0.409599 | − | 0.235142i | ||||
\(915\) | −5253.08 | + | 9098.59i | −0.189794 | + | 0.328733i | ||||
\(916\) | −11444.4 | + | 19599.2i | −0.412810 | + | 0.706959i | ||||
\(917\) | 16003.7 | − | 27719.3i | 0.576325 | − | 0.998223i | ||||
\(918\) | 41.9367 | − | 17062.2i | 0.00150775 | − | 0.613438i | ||||
\(919\) | − | 4558.20i | − | 0.163614i | −0.996648 | − | 0.0818069i | \(-0.973931\pi\) | ||
0.996648 | − | 0.0818069i | \(-0.0260691\pi\) | |||||||
\(920\) | −19054.5 | − | 140.503i | −0.682837 | − | 0.00503506i | ||||
\(921\) | 3204.67 | + | 5550.65i | 0.114655 | + | 0.198589i | ||||
\(922\) | −39.9500 | + | 16253.9i | −0.00142699 | + | 0.580579i | ||||
\(923\) | − | 5703.27i | − | 0.203386i | ||||||
\(924\) | −1807.11 | − | 3165.84i | −0.0643393 | − | 0.112715i | ||||
\(925\) | 40.4590 | − | 23.3590i | 0.00143814 | − | 0.000830313i | ||||
\(926\) | −9752.53 | − | 16988.2i | −0.346099 | − | 0.602879i | ||||
\(927\) | 4797.21 | + | 8309.02i | 0.169969 | + | 0.294395i | ||||
\(928\) | 10061.7 | + | 123.658i | 0.355916 | + | 0.00437420i | ||||
\(929\) | −16535.5 | + | 28640.3i | −0.583974 | + | 1.01147i | 0.411028 | + | 0.911623i | \(0.365170\pi\) |
−0.995002 | + | 0.0998504i | \(0.968164\pi\) | |||||||
\(930\) | −9324.50 | − | 5414.11i | −0.328777 | − | 0.190898i | ||||
\(931\) | −15669.1 | + | 9202.55i | −0.551595 | + | 0.323954i | ||||
\(932\) | −22716.0 | − | 39795.7i | −0.798376 | − | 1.39866i | ||||
\(933\) | −32.9604 | − | 19.0297i | −0.00115656 | − | 0.000667743i | ||||
\(934\) | 26733.6 | + | 46567.9i | 0.936564 | + | 1.63142i | ||||
\(935\) | 24611.0 | − | 14209.2i | 0.860820 | − | 0.496995i | ||||
\(936\) | 16830.1 | − | 28660.5i | 0.587724 | − | 1.00085i | ||||
\(937\) | 4759.96 | + | 8244.49i | 0.165956 | + | 0.287445i | 0.936994 | − | 0.349344i | \(-0.113596\pi\) |
−0.771038 | + | 0.636789i | \(0.780262\pi\) | |||||||
\(938\) | 14294.7 | − | 24619.2i | 0.497588 | − | 0.856977i | ||||
\(939\) | 7094.37 | 0.246556 | ||||||||
\(940\) | −8461.27 | − | 4940.73i | −0.293592 | − | 0.171435i | ||||
\(941\) | −6605.11 | + | 3813.46i | −0.228821 | + | 0.132110i | −0.610028 | − | 0.792380i | \(-0.708842\pi\) |
0.381207 | + | 0.924490i | \(0.375508\pi\) | |||||||
\(942\) | −8211.61 | − | 4767.92i | −0.284022 | − | 0.164912i | ||||
\(943\) | −21512.3 | −0.742881 | ||||||||
\(944\) | 27257.0 | + | 267.985i | 0.939766 | + | 0.00923959i | ||||
\(945\) | 7468.99 | + | 4312.22i | 0.257107 | + | 0.148441i | ||||
\(946\) | −84.1046 | + | 34218.4i | −0.00289057 | + | 1.17604i | ||||
\(947\) | −21689.0 | − | 12522.2i | −0.744244 | − | 0.429689i | 0.0793664 | − | 0.996846i | \(-0.474710\pi\) |
−0.823610 | + | 0.567156i | \(0.808044\pi\) | |||||||
\(948\) | −5703.64 | − | 28.0378i | −0.195407 | − | 0.000960576i | ||||
\(949\) | 987.069i | 0.0337636i | ||||||||
\(950\) | 1008.15 | − | 5.01653i | 0.0344303 | − | 0.000171324i | ||||
\(951\) | 8208.38i | 0.279890i | ||||||||
\(952\) | −10881.3 | + | 18530.1i | −0.370447 | + | 0.630845i | ||||
\(953\) | 12760.8 | + | 7367.46i | 0.433750 | + | 0.250426i | 0.700943 | − | 0.713217i | \(-0.252763\pi\) |
−0.267193 | + | 0.963643i | \(0.586096\pi\) | |||||||
\(954\) | −36826.3 | − | 90.5145i | −1.24979 | − | 0.00307182i | ||||
\(955\) | 14845.6 | + | 8571.13i | 0.503029 | + | 0.290424i | ||||
\(956\) | 41487.3 | + | 24225.4i | 1.40355 | + | 0.819567i | ||||
\(957\) | 2278.43 | 0.0769605 | ||||||||
\(958\) | 28411.5 | − | 48932.0i | 0.958176 | − | 1.65023i | ||||
\(959\) | 19988.3 | − | 11540.3i | 0.673052 | − | 0.388587i | ||||
\(960\) | −3709.36 | − | 6649.36i | −0.124707 | − | 0.223549i | ||||
\(961\) | 35921.5 | 1.20578 | ||||||||
\(962\) | −1549.62 | − | 899.758i | −0.0519352 | − | 0.0301552i | ||||
\(963\) | 1630.66 | + | 2824.39i | 0.0545662 | + | 0.0945115i | ||||
\(964\) | 184.038 | − | 37438.2i | 0.00614882 | − | 1.25083i | ||||
\(965\) | −42199.0 | + | 24363.6i | −1.40770 | + | 0.812738i | ||||
\(966\) | 2829.45 | − | 1624.32i | 0.0942401 | − | 0.0541011i | ||||
\(967\) | 49598.3 | + | 28635.6i | 1.64940 | + | 0.952284i | 0.977309 | + | 0.211821i | \(0.0679393\pi\) |
0.672096 | + | 0.740464i | \(0.265394\pi\) | |||||||
\(968\) | −69.0905 | + | 9369.80i | −0.00229406 | + | 0.311112i | ||||
\(969\) | −8329.10 | − | 4726.60i | −0.276129 | − | 0.156698i | ||||
\(970\) | −8486.83 | + | 14616.5i | −0.280923 | + | 0.483823i | ||||
\(971\) | 15.2876 | − | 26.4790i | 0.000505256 | − | 0.000875130i | −0.865773 | − | 0.500438i | \(-0.833173\pi\) |
0.866278 | + | 0.499562i | \(0.166506\pi\) | |||||||
\(972\) | 21576.1 | + | 106.064i | 0.711991 | + | 0.00349999i | ||||
\(973\) | −4930.71 | − | 8540.24i | −0.162458 | − | 0.281385i | ||||
\(974\) | −33460.1 | + | 19208.7i | −1.10075 | + | 0.631917i | ||||
\(975\) | −294.458 | + | 170.005i | −0.00967201 | + | 0.00558414i | ||||
\(976\) | 22991.2 | − | 38932.9i | 0.754028 | − | 1.27686i | ||||
\(977\) | − | 36344.9i | − | 1.19015i | −0.803670 | − | 0.595075i | \(-0.797122\pi\) | ||
0.803670 | − | 0.595075i | \(-0.202878\pi\) | |||||||
\(978\) | −4048.41 | − | 9.95049i | −0.132366 | − | 0.000325339i | ||||
\(979\) | 6147.92 | + | 10648.5i | 0.200703 | + | 0.347628i | ||||
\(980\) | 9559.86 | + | 16747.8i | 0.311611 | + | 0.545905i | ||||
\(981\) | 14256.4i | 0.463987i | ||||||||
\(982\) | 5651.89 | + | 13.8917i | 0.183665 | + | 0.000451426i | ||||
\(983\) | 3159.11 | − | 5471.73i | 0.102502 | − | 0.177539i | −0.810213 | − | 0.586136i | \(-0.800648\pi\) |
0.912715 | + | 0.408597i | \(0.133982\pi\) | |||||||
\(984\) | −4242.93 | − | 7475.74i | −0.137459 | − | 0.242193i | ||||
\(985\) | 15247.7 | − | 26409.8i | 0.493231 | − | 0.854301i | ||||
\(986\) | −6686.99 | − | 11648.2i | −0.215981 | − | 0.376222i | ||||
\(987\) | 1677.61 | 0.0541022 | ||||||||
\(988\) | −19418.6 | − | 33439.3i | −0.625292 | − | 1.07677i | ||||
\(989\) | −30625.6 | −0.984667 | ||||||||
\(990\) | 11789.9 | + | 20537.2i | 0.378494 | + | 0.659308i | ||||
\(991\) | 13047.5 | − | 22598.9i | 0.418232 | − | 0.724398i | −0.577530 | − | 0.816369i | \(-0.695983\pi\) |
0.995762 | + | 0.0919711i | \(0.0293167\pi\) | |||||||
\(992\) | 39898.3 | + | 23693.8i | 1.27699 | + | 0.758344i | ||||
\(993\) | 5306.65 | − | 9191.38i | 0.169588 | − | 0.293736i | ||||
\(994\) | −3072.66 | − | 7.55221i | −0.0980470 | − | 0.000240987i | ||||
\(995\) | 20128.9i | 0.641336i | ||||||||
\(996\) | 6068.35 | − | 3463.90i | 0.193055 | − | 0.110199i | ||||
\(997\) | 14964.0 | + | 25918.4i | 0.475340 | + | 0.823313i | 0.999601 | − | 0.0282443i | \(-0.00899164\pi\) |
−0.524261 | + | 0.851558i | \(0.675658\pi\) | |||||||
\(998\) | −7401.29 | − | 18.1914i | −0.234753 | − | 0.000576994i | ||||
\(999\) | − | 766.526i | − | 0.0242761i |
(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 | 76.4.f.a.27.6 | ✓ | 56 | |
4.3 | odd | 2 | inner | 76.4.f.a.27.15 | yes | 56 | |
19.12 | odd | 6 | inner | 76.4.f.a.31.15 | yes | 56 | |
76.31 | even | 6 | inner | 76.4.f.a.31.6 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.f.a.27.6 | ✓ | 56 | 1.1 | even | 1 | trivial | |
76.4.f.a.27.15 | yes | 56 | 4.3 | odd | 2 | inner | |
76.4.f.a.31.6 | yes | 56 | 76.31 | even | 6 | inner | |
76.4.f.a.31.15 | yes | 56 | 19.12 | odd | 6 | inner |