Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,5,Mod(7,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.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: | \(3.72131867102\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.18 | ||
Character | \(\chi\) | \(=\) | 36.7 |
Dual form | 36.5.f.a.31.18 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.42968 | − | 2.05847i | 0.857420 | − | 0.514618i | ||||
\(3\) | 2.72970 | − | 8.57606i | 0.303300 | − | 0.952895i | ||||
\(4\) | 7.52540 | − | 14.1198i | 0.470337 | − | 0.882487i | ||||
\(5\) | 16.6139 | + | 28.7760i | 0.664554 | + | 1.15104i | 0.979406 | + | 0.201901i | \(0.0647118\pi\) |
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(6\) | −8.29157 | − | 35.0321i | −0.230321 | − | 0.973115i | ||||
\(7\) | −39.9759 | − | 23.0801i | −0.815835 | − | 0.471023i | 0.0331429 | − | 0.999451i | \(-0.489448\pi\) |
−0.848978 | + | 0.528428i | \(0.822782\pi\) | |||||||
\(8\) | −3.25547 | − | 63.9171i | −0.0508667 | − | 0.998705i | ||||
\(9\) | −66.0975 | − | 46.8201i | −0.816018 | − | 0.578026i | ||||
\(10\) | 116.215 | + | 64.4935i | 1.16215 | + | 0.644935i | ||||
\(11\) | 63.6109 | + | 36.7258i | 0.525710 | + | 0.303519i | 0.739268 | − | 0.673412i | \(-0.235172\pi\) |
−0.213558 | + | 0.976930i | \(0.568505\pi\) | |||||||
\(12\) | −100.550 | − | 103.081i | −0.698264 | − | 0.715840i | ||||
\(13\) | 151.520 | + | 262.440i | 0.896566 | + | 1.55290i | 0.831855 | + | 0.554993i | \(0.187279\pi\) |
0.0647110 | + | 0.997904i | \(0.479387\pi\) | |||||||
\(14\) | −184.614 | + | 3.13190i | −0.941910 | + | 0.0159791i | ||||
\(15\) | 292.136 | − | 63.9314i | 1.29838 | − | 0.284140i | ||||
\(16\) | −142.737 | − | 212.514i | −0.557566 | − | 0.830133i | ||||
\(17\) | −182.019 | −0.629823 | −0.314912 | − | 0.949121i | \(-0.601975\pi\) | ||||
−0.314912 | + | 0.949121i | \(0.601975\pi\) | |||||||
\(18\) | −323.071 | − | 24.5183i | −0.997133 | − | 0.0756736i | ||||
\(19\) | 314.215i | 0.870402i | 0.900333 | + | 0.435201i | \(0.143323\pi\) | ||||
−0.900333 | + | 0.435201i | \(0.856677\pi\) | |||||||
\(20\) | 531.337 | − | 18.0330i | 1.32834 | − | 0.0450824i | ||||
\(21\) | −307.059 | + | 279.834i | −0.696278 | + | 0.634544i | ||||
\(22\) | 293.764 | − | 4.98356i | 0.606950 | − | 0.0102966i | ||||
\(23\) | 290.919 | − | 167.962i | 0.549941 | − | 0.317509i | −0.199157 | − | 0.979968i | \(-0.563820\pi\) |
0.749098 | + | 0.662459i | \(0.230487\pi\) | |||||||
\(24\) | −557.044 | − | 146.556i | −0.967089 | − | 0.254437i | ||||
\(25\) | −239.540 | + | 414.896i | −0.383265 | + | 0.663834i | ||||
\(26\) | 1059.89 | + | 588.185i | 1.56788 | + | 0.870096i | ||||
\(27\) | −581.958 | + | 439.051i | −0.798297 | + | 0.602265i | ||||
\(28\) | −626.721 | + | 390.765i | −0.799389 | + | 0.498424i | ||||
\(29\) | 357.370 | − | 618.983i | 0.424935 | − | 0.736008i | −0.571480 | − | 0.820616i | \(-0.693630\pi\) |
0.996414 | + | 0.0846079i | \(0.0269638\pi\) | |||||||
\(30\) | 870.331 | − | 820.617i | 0.967034 | − | 0.911797i | ||||
\(31\) | −985.186 | + | 568.798i | −1.02517 | + | 0.591881i | −0.915597 | − | 0.402098i | \(-0.868281\pi\) |
−0.109571 | + | 0.993979i | \(0.534948\pi\) | |||||||
\(32\) | −926.995 | − | 435.035i | −0.905269 | − | 0.424839i | ||||
\(33\) | 488.601 | − | 445.280i | 0.448669 | − | 0.408889i | ||||
\(34\) | −624.267 | + | 374.681i | −0.540023 | + | 0.324118i | ||||
\(35\) | − | 1533.80i | − | 1.25208i | ||||||
\(36\) | −1158.50 | + | 580.942i | −0.893904 | + | 0.448258i | ||||
\(37\) | 1008.45 | 0.736632 | 0.368316 | − | 0.929701i | \(-0.379934\pi\) | ||||
0.368316 | + | 0.929701i | \(0.379934\pi\) | |||||||
\(38\) | 646.803 | + | 1077.66i | 0.447924 | + | 0.746300i | ||||
\(39\) | 2664.30 | − | 583.059i | 1.75168 | − | 0.383339i | ||||
\(40\) | 1785.20 | − | 1155.59i | 1.11575 | − | 0.722244i | ||||
\(41\) | −557.553 | − | 965.709i | −0.331679 | − | 0.574485i | 0.651162 | − | 0.758939i | \(-0.274282\pi\) |
−0.982841 | + | 0.184454i | \(0.940948\pi\) | |||||||
\(42\) | −477.082 | + | 1591.81i | −0.270455 | + | 0.902388i | ||||
\(43\) | −2182.06 | − | 1259.82i | −1.18013 | − | 0.681349i | −0.224087 | − | 0.974569i | \(-0.571940\pi\) |
−0.956045 | + | 0.293220i | \(0.905273\pi\) | |||||||
\(44\) | 997.257 | − | 621.796i | 0.515112 | − | 0.321176i | ||||
\(45\) | 249.164 | − | 2679.89i | 0.123044 | − | 1.32340i | ||||
\(46\) | 652.014 | − | 1174.90i | 0.308135 | − | 0.555248i | ||||
\(47\) | −980.476 | − | 566.078i | −0.443855 | − | 0.256260i | 0.261376 | − | 0.965237i | \(-0.415824\pi\) |
−0.705232 | + | 0.708977i | \(0.749157\pi\) | |||||||
\(48\) | −2212.16 | + | 644.019i | −0.960139 | + | 0.279522i | ||||
\(49\) | −135.117 | − | 234.029i | −0.0562752 | − | 0.0974714i | ||||
\(50\) | 32.5048 | + | 1916.05i | 0.0130019 | + | 0.766419i | ||||
\(51\) | −496.857 | + | 1561.00i | −0.191025 | + | 0.600156i | ||||
\(52\) | 4845.84 | − | 164.462i | 1.79210 | − | 0.0608218i | ||||
\(53\) | −1057.77 | −0.376566 | −0.188283 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188283 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(54\) | −1092.16 | + | 2703.75i | −0.374539 | + | 0.927211i | ||||
\(55\) | 2440.63i | 0.806818i | ||||||||
\(56\) | −1345.07 | + | 2630.28i | −0.428914 | + | 0.838739i | ||||
\(57\) | 2694.73 | + | 857.713i | 0.829402 | + | 0.263993i | ||||
\(58\) | −48.4939 | − | 2858.55i | −0.0144156 | − | 0.849747i | ||||
\(59\) | −878.476 | + | 507.188i | −0.252363 | + | 0.145702i | −0.620846 | − | 0.783933i | \(-0.713211\pi\) |
0.368483 | + | 0.929635i | \(0.379877\pi\) | |||||||
\(60\) | 1295.74 | − | 4606.00i | 0.359928 | − | 1.27945i | ||||
\(61\) | −430.304 | + | 745.308i | −0.115642 | + | 0.200298i | −0.918036 | − | 0.396497i | \(-0.870226\pi\) |
0.802394 | + | 0.596794i | \(0.203559\pi\) | |||||||
\(62\) | −2208.02 | + | 3978.77i | −0.574407 | + | 1.03506i | ||||
\(63\) | 1561.69 | + | 3397.22i | 0.393473 | + | 0.855937i | ||||
\(64\) | −4074.80 | + | 416.161i | −0.994825 | + | 0.101602i | ||||
\(65\) | −5034.65 | + | 8720.27i | −1.19163 | + | 2.06397i | ||||
\(66\) | 759.148 | − | 2532.94i | 0.174276 | − | 0.581483i | ||||
\(67\) | −559.041 | + | 322.762i | −0.124536 | + | 0.0719008i | −0.560974 | − | 0.827834i | \(-0.689573\pi\) |
0.436438 | + | 0.899734i | \(0.356240\pi\) | |||||||
\(68\) | −1369.76 | + | 2570.07i | −0.296229 | + | 0.555811i | ||||
\(69\) | −646.331 | − | 2953.42i | −0.135755 | − | 0.620337i | ||||
\(70\) | −3157.28 | − | 5260.44i | −0.644343 | − | 1.07356i | ||||
\(71\) | − | 9567.89i | − | 1.89801i | −0.315254 | − | 0.949007i | \(-0.602090\pi\) | ||
0.315254 | − | 0.949007i | \(-0.397910\pi\) | |||||||
\(72\) | −2777.43 | + | 4377.18i | −0.535770 | + | 0.844364i | ||||
\(73\) | 1899.10 | 0.356372 | 0.178186 | − | 0.983997i | \(-0.442977\pi\) | ||||
0.178186 | + | 0.983997i | \(0.442977\pi\) | |||||||
\(74\) | 3458.66 | − | 2075.86i | 0.631603 | − | 0.379084i | ||||
\(75\) | 2904.30 | + | 3186.85i | 0.516320 | + | 0.566552i | ||||
\(76\) | 4436.65 | + | 2364.59i | 0.768119 | + | 0.409383i | ||||
\(77\) | −1695.27 | − | 2936.29i | −0.285928 | − | 0.495242i | ||||
\(78\) | 7937.48 | − | 7484.09i | 1.30465 | − | 1.23013i | ||||
\(79\) | 6768.11 | + | 3907.57i | 1.08446 | + | 0.626113i | 0.932096 | − | 0.362212i | \(-0.117978\pi\) |
0.152363 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(80\) | 3743.90 | − | 7638.08i | 0.584985 | − | 1.19345i | ||||
\(81\) | 2176.75 | + | 6189.38i | 0.331772 | + | 0.943360i | ||||
\(82\) | −3900.11 | − | 2164.37i | −0.580028 | − | 0.321887i | ||||
\(83\) | 7052.56 | + | 4071.80i | 1.02374 | + | 0.591058i | 0.915186 | − | 0.403032i | \(-0.132044\pi\) |
0.108556 | + | 0.994090i | \(0.465377\pi\) | |||||||
\(84\) | 1640.46 | + | 6441.47i | 0.232491 | + | 0.912906i | ||||
\(85\) | −3024.04 | − | 5237.78i | −0.418552 | − | 0.724953i | ||||
\(86\) | −10077.1 | + | 170.953i | −1.36250 | + | 0.0231142i | ||||
\(87\) | −4332.92 | − | 4754.46i | −0.572456 | − | 0.628149i | ||||
\(88\) | 2140.32 | − | 4185.39i | 0.276385 | − | 0.540468i | ||||
\(89\) | 7653.39 | 0.966215 | 0.483107 | − | 0.875561i | \(-0.339508\pi\) | ||||
0.483107 | + | 0.875561i | \(0.339508\pi\) | |||||||
\(90\) | −4661.92 | − | 9704.05i | −0.575545 | − | 1.19803i | ||||
\(91\) | − | 13988.4i | − | 1.68921i | ||||||
\(92\) | −182.309 | − | 5371.70i | −0.0215394 | − | 0.634652i | ||||
\(93\) | 2188.78 | + | 10001.7i | 0.253067 | + | 1.15640i | ||||
\(94\) | −4527.97 | + | 76.8149i | −0.512446 | + | 0.00869340i | ||||
\(95\) | −9041.87 | + | 5220.33i | −1.00187 | + | 0.578430i | ||||
\(96\) | −6261.31 | + | 6762.45i | −0.679395 | + | 0.733773i | ||||
\(97\) | −6366.75 | + | 11027.5i | −0.676666 | + | 1.17202i | 0.299313 | + | 0.954155i | \(0.403243\pi\) |
−0.975979 | + | 0.217865i | \(0.930091\pi\) | |||||||
\(98\) | −945.149 | − | 524.510i | −0.0984120 | − | 0.0546137i | ||||
\(99\) | −2485.01 | − | 5405.75i | −0.253547 | − | 0.551551i | ||||
\(100\) | 4055.61 | + | 6504.52i | 0.405561 | + | 0.650452i | ||||
\(101\) | 6873.20 | − | 11904.7i | 0.673777 | − | 1.16702i | −0.303048 | − | 0.952975i | \(-0.598004\pi\) |
0.976825 | − | 0.214040i | \(-0.0686624\pi\) | |||||||
\(102\) | 1509.22 | + | 6376.51i | 0.145062 | + | 0.612890i | ||||
\(103\) | −11251.5 | + | 6496.03i | −1.06056 | + | 0.612313i | −0.925587 | − | 0.378536i | \(-0.876428\pi\) |
−0.134971 | + | 0.990850i | \(0.543094\pi\) | |||||||
\(104\) | 16281.1 | − | 10539.1i | 1.50528 | − | 0.974396i | ||||
\(105\) | −13153.9 | − | 4186.81i | −1.19310 | − | 0.379756i | ||||
\(106\) | −3627.82 | + | 2177.40i | −0.322875 | + | 0.193787i | ||||
\(107\) | 14891.8i | 1.30071i | 0.759631 | + | 0.650354i | \(0.225379\pi\) | ||||
−0.759631 | + | 0.650354i | \(0.774621\pi\) | |||||||
\(108\) | 1819.84 | + | 11521.2i | 0.156022 | + | 0.987754i | ||||
\(109\) | 7539.02 | 0.634544 | 0.317272 | − | 0.948335i | \(-0.397233\pi\) | ||||
0.317272 | + | 0.948335i | \(0.397233\pi\) | |||||||
\(110\) | 5023.96 | + | 8370.56i | 0.415203 | + | 0.691782i | ||||
\(111\) | 2752.76 | − | 8648.52i | 0.223421 | − | 0.701933i | ||||
\(112\) | 801.189 | + | 11789.8i | 0.0638703 | + | 0.939878i | ||||
\(113\) | 496.140 | + | 859.339i | 0.0388550 | + | 0.0672988i | 0.884799 | − | 0.465973i | \(-0.154296\pi\) |
−0.845944 | + | 0.533272i | \(0.820962\pi\) | |||||||
\(114\) | 11007.6 | − | 2605.34i | 0.847001 | − | 0.200472i | ||||
\(115\) | 9666.57 | + | 5581.00i | 0.730932 | + | 0.422004i | ||||
\(116\) | −6050.56 | − | 9704.08i | −0.449655 | − | 0.721171i | ||||
\(117\) | 2272.39 | − | 24440.8i | 0.166001 | − | 1.78543i | ||||
\(118\) | −1968.86 | + | 3547.81i | −0.141400 | + | 0.254798i | ||||
\(119\) | 7276.38 | + | 4201.02i | 0.513832 | + | 0.296661i | ||||
\(120\) | −5037.35 | − | 18464.4i | −0.349816 | − | 1.28225i | ||||
\(121\) | −4622.94 | − | 8007.16i | −0.315753 | − | 0.546900i | ||||
\(122\) | 58.3908 | + | 3441.94i | 0.00392306 | + | 0.231251i | ||||
\(123\) | −9803.93 | + | 2145.51i | −0.648022 | + | 0.141814i | ||||
\(124\) | 617.383 | + | 18191.1i | 0.0401524 | + | 1.18308i | ||||
\(125\) | 4848.57 | 0.310308 | ||||||||
\(126\) | 12349.2 | + | 8436.65i | 0.777852 | + | 0.531409i | ||||
\(127\) | − | 7123.52i | − | 0.441659i | −0.975312 | − | 0.220829i | \(-0.929124\pi\) | ||
0.975312 | − | 0.220829i | \(-0.0708764\pi\) | |||||||
\(128\) | −13118.6 | + | 9815.16i | −0.800697 | + | 0.599070i | ||||
\(129\) | −16760.6 | + | 15274.6i | −1.00719 | + | 0.917889i | ||||
\(130\) | 683.185 | + | 40271.4i | 0.0404252 | + | 2.38292i | ||||
\(131\) | 6027.16 | − | 3479.78i | 0.351212 | − | 0.202773i | −0.314007 | − | 0.949421i | \(-0.601671\pi\) |
0.665219 | + | 0.746648i | \(0.268338\pi\) | |||||||
\(132\) | −2610.35 | − | 10249.8i | −0.149813 | − | 0.588260i | ||||
\(133\) | 7252.12 | − | 12561.0i | 0.409979 | − | 0.710105i | ||||
\(134\) | −1252.93 | + | 2257.74i | −0.0697780 | + | 0.125737i | ||||
\(135\) | −22302.7 | − | 9452.13i | −1.22374 | − | 0.518635i | ||||
\(136\) | 592.557 | + | 11634.1i | 0.0320371 | + | 0.629008i | ||||
\(137\) | 4244.42 | − | 7351.56i | 0.226140 | − | 0.391686i | −0.730521 | − | 0.682891i | \(-0.760723\pi\) |
0.956661 | + | 0.291204i | \(0.0940559\pi\) | |||||||
\(138\) | −8296.25 | − | 8798.84i | −0.435636 | − | 0.462027i | ||||
\(139\) | 18483.9 | − | 10671.7i | 0.956673 | − | 0.552335i | 0.0615252 | − | 0.998106i | \(-0.480404\pi\) |
0.895147 | + | 0.445770i | \(0.147070\pi\) | |||||||
\(140\) | −21656.9 | − | 11542.4i | −1.10494 | − | 0.588900i | ||||
\(141\) | −7531.12 | + | 6863.39i | −0.378810 | + | 0.345224i | ||||
\(142\) | −19695.2 | − | 32814.8i | −0.976752 | − | 1.62740i | ||||
\(143\) | 22258.7i | 1.08850i | ||||||||
\(144\) | −515.388 | + | 20729.6i | −0.0248548 | + | 0.999691i | ||||
\(145\) | 23749.2 | 1.12957 | ||||||||
\(146\) | 6513.32 | − | 3909.25i | 0.305560 | − | 0.183395i | ||||
\(147\) | −2375.87 | + | 519.939i | −0.109948 | + | 0.0240612i | ||||
\(148\) | 7588.98 | − | 14239.1i | 0.346466 | − | 0.650068i | ||||
\(149\) | 6366.78 | + | 11027.6i | 0.286779 | + | 0.496716i | 0.973039 | − | 0.230640i | \(-0.0740821\pi\) |
−0.686260 | + | 0.727356i | \(0.740749\pi\) | |||||||
\(150\) | 16520.9 | + | 4951.47i | 0.734260 | + | 0.220065i | ||||
\(151\) | 3061.84 | + | 1767.75i | 0.134285 | + | 0.0775296i | 0.565638 | − | 0.824654i | \(-0.308630\pi\) |
−0.431352 | + | 0.902184i | \(0.641963\pi\) | |||||||
\(152\) | 20083.7 | − | 1022.92i | 0.869276 | − | 0.0442745i | ||||
\(153\) | 12031.0 | + | 8522.15i | 0.513947 | + | 0.364054i | ||||
\(154\) | −11858.5 | − | 6580.88i | −0.500021 | − | 0.277487i | ||||
\(155\) | −32735.5 | − | 18899.8i | −1.36256 | − | 0.786674i | ||||
\(156\) | 11817.2 | − | 42007.1i | 0.485587 | − | 1.72613i | ||||
\(157\) | −14870.6 | − | 25756.6i | −0.603292 | − | 1.04493i | −0.992319 | − | 0.123706i | \(-0.960522\pi\) |
0.389027 | − | 0.921227i | \(-0.372811\pi\) | |||||||
\(158\) | 31256.1 | − | 530.244i | 1.25205 | − | 0.0212404i | ||||
\(159\) | −2887.40 | + | 9071.53i | −0.114212 | + | 0.358828i | ||||
\(160\) | −2882.37 | − | 33902.9i | −0.112593 | − | 1.32433i | ||||
\(161\) | −15506.3 | −0.598216 | ||||||||
\(162\) | 20206.2 | + | 16746.8i | 0.769937 | + | 0.638120i | ||||
\(163\) | 5903.96i | 0.222213i | 0.993809 | + | 0.111106i | \(0.0354394\pi\) | ||||
−0.993809 | + | 0.111106i | \(0.964561\pi\) | |||||||
\(164\) | −17831.4 | + | 605.177i | −0.662976 | + | 0.0225006i | ||||
\(165\) | 20930.9 | + | 6662.18i | 0.768813 | + | 0.244708i | ||||
\(166\) | 32569.7 | − | 552.529i | 1.18195 | − | 0.0200511i | ||||
\(167\) | 17810.7 | − | 10283.0i | 0.638628 | − | 0.368712i | −0.145458 | − | 0.989364i | \(-0.546465\pi\) |
0.784086 | + | 0.620652i | \(0.213132\pi\) | |||||||
\(168\) | 18885.8 | + | 18715.3i | 0.669140 | + | 0.663100i | ||||
\(169\) | −31635.9 | + | 54795.0i | −1.10766 | + | 1.91852i | ||||
\(170\) | −21153.3 | − | 11739.0i | −0.731948 | − | 0.406195i | ||||
\(171\) | 14711.6 | − | 20768.8i | 0.503115 | − | 0.710264i | ||||
\(172\) | −34209.2 | + | 21329.7i | −1.15634 | + | 0.720987i | ||||
\(173\) | −3054.99 | + | 5291.39i | −0.102074 | + | 0.176798i | −0.912539 | − | 0.408989i | \(-0.865881\pi\) |
0.810465 | + | 0.585787i | \(0.199215\pi\) | |||||||
\(174\) | −24647.4 | − | 7387.09i | −0.814092 | − | 0.243992i | ||||
\(175\) | 19151.7 | − | 11057.2i | 0.625361 | − | 0.361053i | ||||
\(176\) | −1274.87 | − | 18760.3i | −0.0411569 | − | 0.605641i | ||||
\(177\) | 1951.70 | + | 8918.33i | 0.0622969 | + | 0.284667i | ||||
\(178\) | 26248.7 | − | 15754.3i | 0.828451 | − | 0.497231i | ||||
\(179\) | 11534.8i | 0.360001i | 0.983667 | + | 0.180001i | \(0.0576099\pi\) | ||||
−0.983667 | + | 0.180001i | \(0.942390\pi\) | |||||||
\(180\) | −35964.4 | − | 23685.3i | −1.11001 | − | 0.731029i | ||||
\(181\) | −25544.2 | −0.779713 | −0.389857 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389857 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(182\) | −28794.6 | − | 47975.6i | −0.869298 | − | 1.44836i | ||||
\(183\) | 5217.20 | + | 5724.78i | 0.155789 | + | 0.170945i | ||||
\(184\) | −11682.7 | − | 18047.9i | −0.345072 | − | 0.533079i | ||||
\(185\) | 16754.2 | + | 29019.2i | 0.489532 | + | 0.847894i | ||||
\(186\) | 28094.9 | + | 29797.0i | 0.812086 | + | 0.861283i | ||||
\(187\) | −11578.4 | − | 6684.78i | −0.331104 | − | 0.191163i | ||||
\(188\) | −15371.4 | + | 9584.15i | −0.434908 | + | 0.271168i | ||||
\(189\) | 33397.7 | − | 4119.80i | 0.934959 | − | 0.115333i | ||||
\(190\) | −20264.8 | + | 36516.5i | −0.561353 | + | 1.01154i | ||||
\(191\) | 33833.7 | + | 19533.9i | 0.927433 | + | 0.535454i | 0.885999 | − | 0.463687i | \(-0.153474\pi\) |
0.0414344 | + | 0.999141i | \(0.486807\pi\) | |||||||
\(192\) | −7553.97 | + | 36081.7i | −0.204915 | + | 0.978780i | ||||
\(193\) | −13915.2 | − | 24101.8i | −0.373572 | − | 0.647045i | 0.616541 | − | 0.787323i | \(-0.288534\pi\) |
−0.990112 | + | 0.140278i | \(0.955200\pi\) | |||||||
\(194\) | 863.947 | + | 50926.7i | 0.0229553 | + | 1.35314i | ||||
\(195\) | 61042.4 | + | 66981.2i | 1.60532 | + | 1.76150i | ||||
\(196\) | −4321.25 | + | 146.658i | −0.112486 | + | 0.00381763i | ||||
\(197\) | −21103.0 | −0.543765 | −0.271883 | − | 0.962330i | \(-0.587646\pi\) | ||||
−0.271883 | + | 0.962330i | \(0.587646\pi\) | |||||||
\(198\) | −19650.4 | − | 13424.7i | −0.501234 | − | 0.342431i | ||||
\(199\) | 5447.97i | 0.137572i | 0.997631 | + | 0.0687858i | \(0.0219125\pi\) | ||||
−0.997631 | + | 0.0687858i | \(0.978087\pi\) | |||||||
\(200\) | 27298.8 | + | 13960.1i | 0.682470 | + | 0.349001i | ||||
\(201\) | 1242.02 | + | 5675.41i | 0.0307422 | + | 0.140477i | ||||
\(202\) | −932.670 | − | 54977.7i | −0.0228573 | − | 1.34736i | ||||
\(203\) | −28572.4 | + | 16496.3i | −0.693353 | + | 0.400308i | ||||
\(204\) | 18302.0 | + | 18762.7i | 0.439783 | + | 0.450853i | ||||
\(205\) | 18526.2 | − | 32088.3i | 0.440837 | − | 0.763553i | ||||
\(206\) | −25217.0 | + | 45440.1i | −0.594236 | + | 1.07079i | ||||
\(207\) | −27093.0 | − | 2518.99i | −0.632291 | − | 0.0587875i | ||||
\(208\) | 34144.7 | − | 69659.8i | 0.789217 | − | 1.61011i | ||||
\(209\) | −11539.8 | + | 19987.5i | −0.264183 | + | 0.457579i | ||||
\(210\) | −53732.2 | + | 12717.6i | −1.21842 | + | 0.288381i | ||||
\(211\) | −59935.1 | + | 34603.5i | −1.34622 | + | 0.777241i | −0.987712 | − | 0.156286i | \(-0.950048\pi\) |
−0.358509 | + | 0.933526i | \(0.616715\pi\) | |||||||
\(212\) | −7960.17 | + | 14935.5i | −0.177113 | + | 0.332314i | ||||
\(213\) | −82054.8 | − | 26117.5i | −1.80861 | − | 0.575668i | ||||
\(214\) | 30654.4 | + | 51074.1i | 0.669367 | + | 1.11525i | ||||
\(215\) | − | 83721.5i | − | 1.81117i | ||||||
\(216\) | 29957.4 | + | 35767.8i | 0.642092 | + | 0.766628i | ||||
\(217\) | 52511.7 | 1.11516 | ||||||||
\(218\) | 25856.4 | − | 15518.9i | 0.544071 | − | 0.326548i | ||||
\(219\) | 5183.98 | − | 16286.8i | 0.108088 | − | 0.339585i | ||||
\(220\) | 34461.1 | + | 18366.7i | 0.712007 | + | 0.379477i | ||||
\(221\) | −27579.4 | − | 47769.0i | −0.564678 | − | 0.978051i | ||||
\(222\) | −8361.63 | − | 35328.1i | −0.169662 | − | 0.716828i | ||||
\(223\) | 21934.5 | + | 12663.9i | 0.441080 | + | 0.254658i | 0.704056 | − | 0.710145i | \(-0.251371\pi\) |
−0.262976 | + | 0.964802i | \(0.584704\pi\) | |||||||
\(224\) | 27016.8 | + | 38786.1i | 0.538441 | + | 0.773001i | ||||
\(225\) | 35258.5 | − | 16208.3i | 0.696464 | − | 0.320163i | ||||
\(226\) | 3470.52 | + | 1925.97i | 0.0679482 | + | 0.0377079i | ||||
\(227\) | −84184.1 | − | 48603.7i | −1.63372 | − | 0.943230i | −0.982931 | − | 0.183975i | \(-0.941104\pi\) |
−0.650792 | − | 0.759256i | \(-0.725563\pi\) | |||||||
\(228\) | 32389.6 | − | 31594.4i | 0.623069 | − | 0.607771i | ||||
\(229\) | 42946.4 | + | 74385.3i | 0.818947 | + | 1.41846i | 0.906459 | + | 0.422294i | \(0.138775\pi\) |
−0.0875119 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(230\) | 44641.6 | − | 757.323i | 0.843886 | − | 0.0143161i | ||||
\(231\) | −29809.4 | + | 6523.53i | −0.558636 | + | 0.122253i | ||||
\(232\) | −40727.0 | − | 20827.0i | −0.756671 | − | 0.386946i | ||||
\(233\) | −12774.0 | −0.235297 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(234\) | −42517.0 | − | 88501.6i | −0.776482 | − | 1.61629i | ||||
\(235\) | − | 37619.0i | − | 0.681194i | ||||||
\(236\) | 550.511 | + | 16220.7i | 0.00988421 | + | 0.291236i | ||||
\(237\) | 51986.4 | − | 47377.2i | 0.925536 | − | 0.843476i | ||||
\(238\) | 33603.3 | − | 570.064i | 0.593237 | − | 0.0100640i | ||||
\(239\) | 91748.4 | − | 52971.0i | 1.60621 | − | 0.927347i | 0.616005 | − | 0.787742i | \(-0.288750\pi\) |
0.990207 | − | 0.139605i | \(-0.0445832\pi\) | |||||||
\(240\) | −55284.8 | − | 52957.6i | −0.959806 | − | 0.919402i | ||||
\(241\) | 5089.73 | − | 8815.67i | 0.0876316 | − | 0.151782i | −0.818878 | − | 0.573968i | \(-0.805404\pi\) |
0.906510 | + | 0.422185i | \(0.138737\pi\) | |||||||
\(242\) | −32337.7 | − | 17945.8i | −0.552177 | − | 0.306431i | ||||
\(243\) | 59022.4 | − | 1772.80i | 0.999549 | − | 0.0300225i | ||||
\(244\) | 7285.38 | + | 11684.5i | 0.122369 | + | 0.196260i | ||||
\(245\) | 4489.62 | − | 7776.25i | 0.0747958 | − | 0.129550i | ||||
\(246\) | −29207.9 | + | 27539.5i | −0.482647 | + | 0.455078i | ||||
\(247\) | −82462.6 | + | 47609.8i | −1.35165 | + | 0.780373i | ||||
\(248\) | 39563.2 | + | 61118.6i | 0.643262 | + | 0.993734i | ||||
\(249\) | 54171.3 | − | 49368.4i | 0.873717 | − | 0.796251i | ||||
\(250\) | 16629.0 | − | 9980.63i | 0.266064 | − | 0.159690i | ||||
\(251\) | 21848.1i | 0.346790i | 0.984852 | + | 0.173395i | \(0.0554738\pi\) | ||||
−0.984852 | + | 0.173395i | \(0.944526\pi\) | |||||||
\(252\) | 59720.3 | + | 3514.60i | 0.940418 | + | 0.0553445i | ||||
\(253\) | 24674.2 | 0.385479 | ||||||||
\(254\) | −14663.5 | − | 24431.4i | −0.227285 | − | 0.378687i | ||||
\(255\) | −53174.2 | + | 11636.7i | −0.817751 | + | 0.178958i | ||||
\(256\) | −24788.4 | + | 60667.1i | −0.378241 | + | 0.925707i | ||||
\(257\) | −27780.7 | − | 48117.6i | −0.420608 | − | 0.728514i | 0.575391 | − | 0.817878i | \(-0.304850\pi\) |
−0.995999 | + | 0.0893643i | \(0.971516\pi\) | |||||||
\(258\) | −26041.3 | + | 86888.2i | −0.391222 | + | 1.30533i | ||||
\(259\) | −40313.7 | − | 23275.1i | −0.600971 | − | 0.346971i | ||||
\(260\) | 85240.6 | + | 136712.i | 1.26096 | + | 2.02236i | ||||
\(261\) | −52602.1 | + | 24181.1i | −0.772186 | + | 0.354973i | ||||
\(262\) | 13508.2 | − | 24341.3i | 0.196786 | − | 0.354601i | ||||
\(263\) | 21792.0 | + | 12581.6i | 0.315055 | + | 0.181897i | 0.649186 | − | 0.760629i | \(-0.275110\pi\) |
−0.334131 | + | 0.942527i | \(0.608443\pi\) | |||||||
\(264\) | −30051.7 | − | 29780.4i | −0.431182 | − | 0.427290i | ||||
\(265\) | −17573.7 | − | 30438.5i | −0.250248 | − | 0.433443i | ||||
\(266\) | −984.089 | − | 58008.6i | −0.0139082 | − | 0.819841i | ||||
\(267\) | 20891.4 | − | 65635.9i | 0.293053 | − | 0.920701i | ||||
\(268\) | 350.332 | + | 10322.5i | 0.00487765 | + | 0.143719i | ||||
\(269\) | 54154.0 | 0.748386 | 0.374193 | − | 0.927351i | \(-0.377920\pi\) | ||||
0.374193 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(270\) | −95948.1 | + | 13491.7i | −1.31616 | + | 0.185072i | ||||
\(271\) | 94942.5i | 1.29277i | 0.763011 | + | 0.646386i | \(0.223720\pi\) | ||||
−0.763011 | + | 0.646386i | \(0.776280\pi\) | |||||||
\(272\) | 25980.8 | + | 38681.6i | 0.351168 | + | 0.522837i | ||||
\(273\) | −119965. | − | 38184.0i | −1.60964 | − | 0.512338i | ||||
\(274\) | −575.954 | − | 33950.5i | −0.00767162 | − | 0.452215i | ||||
\(275\) | −30474.7 | + | 17594.6i | −0.402972 | + | 0.232656i | ||||
\(276\) | −46565.6 | − | 13099.6i | −0.611290 | − | 0.171965i | ||||
\(277\) | −54019.7 | + | 93564.9i | −0.704033 | + | 1.21942i | 0.263006 | + | 0.964794i | \(0.415286\pi\) |
−0.967039 | + | 0.254627i | \(0.918047\pi\) | |||||||
\(278\) | 41426.4 | − | 74648.9i | 0.536029 | − | 0.965904i | ||||
\(279\) | 91749.5 | + | 8530.45i | 1.17868 | + | 0.109588i | ||||
\(280\) | −98036.0 | + | 4993.24i | −1.25046 | + | 0.0636893i | ||||
\(281\) | 34463.0 | − | 59691.7i | 0.436456 | − | 0.755964i | −0.560957 | − | 0.827845i | \(-0.689567\pi\) |
0.997413 | + | 0.0718805i | \(0.0229000\pi\) | |||||||
\(282\) | −11701.2 | + | 39041.8i | −0.147141 | + | 0.490944i | ||||
\(283\) | 39154.2 | − | 22605.7i | 0.488884 | − | 0.282257i | −0.235228 | − | 0.971940i | \(-0.575584\pi\) |
0.724111 | + | 0.689683i | \(0.242250\pi\) | |||||||
\(284\) | −135097. | − | 72002.2i | −1.67497 | − | 0.892707i | ||||
\(285\) | 20088.2 | + | 91793.5i | 0.247316 | + | 1.13011i | ||||
\(286\) | 45818.9 | + | 76340.2i | 0.560160 | + | 0.933299i | ||||
\(287\) | 51473.5i | 0.624914i | ||||||||
\(288\) | 40903.6 | + | 72156.8i | 0.493148 | + | 0.869946i | ||||
\(289\) | −50390.1 | −0.603323 | ||||||||
\(290\) | 81452.0 | − | 48887.0i | 0.968514 | − | 0.581296i | ||||
\(291\) | 77193.4 | + | 84703.5i | 0.911579 | + | 1.00027i | ||||
\(292\) | 14291.5 | − | 26814.9i | 0.167615 | − | 0.314493i | ||||
\(293\) | 35853.6 | + | 62100.3i | 0.417636 | + | 0.723366i | 0.995701 | − | 0.0926242i | \(-0.0295255\pi\) |
−0.578065 | + | 0.815990i | \(0.696192\pi\) | |||||||
\(294\) | −7078.20 | + | 6673.89i | −0.0818895 | + | 0.0772119i | ||||
\(295\) | −29189.7 | − | 16852.7i | −0.335418 | − | 0.193654i | ||||
\(296\) | −3282.98 | − | 64457.2i | −0.0374701 | − | 0.735679i | ||||
\(297\) | −53143.3 | + | 6555.55i | −0.602471 | + | 0.0743184i | ||||
\(298\) | 44536.0 | + | 24715.3i | 0.501509 | + | 0.278313i | ||||
\(299\) | 88159.9 | + | 50899.1i | 0.986117 | + | 0.569335i | ||||
\(300\) | 66853.7 | − | 17025.7i | 0.742819 | − | 0.189175i | ||||
\(301\) | 58153.4 | + | 100725.i | 0.641862 | + | 1.11174i | ||||
\(302\) | 14140.0 | − | 239.878i | 0.155037 | − | 0.00263013i | ||||
\(303\) | −83333.8 | − | 91441.2i | −0.907687 | − | 0.995994i | ||||
\(304\) | 66775.2 | − | 44850.1i | 0.722550 | − | 0.485306i | ||||
\(305\) | −28596.0 | −0.307401 | ||||||||
\(306\) | 58805.0 | + | 4462.79i | 0.628017 | + | 0.0476610i | ||||
\(307\) | − | 95866.9i | − | 1.01717i | −0.861013 | − | 0.508583i | \(-0.830170\pi\) | ||
0.861013 | − | 0.508583i | \(-0.169830\pi\) | |||||||
\(308\) | −54217.4 | + | 1840.08i | −0.571528 | + | 0.0193970i | ||||
\(309\) | 24997.2 | + | 114225.i | 0.261803 | + | 1.19632i | ||||
\(310\) | −151177. | + | 2564.65i | −1.57312 | + | 0.0266873i | ||||
\(311\) | −20844.0 | + | 12034.3i | −0.215506 | + | 0.124423i | −0.603868 | − | 0.797085i | \(-0.706374\pi\) |
0.388362 | + | 0.921507i | \(0.373041\pi\) | |||||||
\(312\) | −45941.0 | − | 168396.i | −0.471945 | − | 1.72991i | ||||
\(313\) | 49654.5 | − | 86004.2i | 0.506839 | − | 0.877871i | −0.493130 | − | 0.869956i | \(-0.664147\pi\) |
0.999969 | − | 0.00791525i | \(-0.00251953\pi\) | |||||||
\(314\) | −104020. | − | 57726.1i | −1.05502 | − | 0.585481i | ||||
\(315\) | −71812.6 | + | 101380.i | −0.723735 | + | 1.02172i | ||||
\(316\) | 106107. | − | 66158.2i | 1.06260 | − | 0.662536i | ||||
\(317\) | −29720.5 | + | 51477.4i | −0.295759 | + | 0.512269i | −0.975161 | − | 0.221497i | \(-0.928906\pi\) |
0.679402 | + | 0.733766i | \(0.262239\pi\) | |||||||
\(318\) | 8770.60 | + | 37056.1i | 0.0867311 | + | 0.366442i | ||||
\(319\) | 45465.2 | − | 26249.4i | 0.446785 | − | 0.257951i | ||||
\(320\) | −79673.7 | − | 110343.i | −0.778063 | − | 1.07757i | ||||
\(321\) | 127713. | + | 40650.2i | 1.23944 | + | 0.394505i | ||||
\(322\) | −53181.8 | + | 31919.4i | −0.512922 | + | 0.307852i | ||||
\(323\) | − | 57193.1i | − | 0.548200i | ||||||
\(324\) | 103774. | + | 15842.3i | 0.988547 | + | 0.150913i | ||||
\(325\) | −145180. | −1.37449 | ||||||||
\(326\) | 12153.1 | + | 20248.7i | 0.114354 | + | 0.190529i | ||||
\(327\) | 20579.3 | − | 64655.1i | 0.192457 | − | 0.604654i | ||||
\(328\) | −59910.3 | + | 38781.0i | −0.556870 | + | 0.360472i | ||||
\(329\) | 26130.3 | + | 45259.0i | 0.241408 | + | 0.418132i | ||||
\(330\) | 85500.3 | − | 20236.6i | 0.785127 | − | 0.185827i | ||||
\(331\) | 79852.0 | + | 46102.6i | 0.728836 | + | 0.420794i | 0.817996 | − | 0.575223i | \(-0.195085\pi\) |
−0.0891599 | + | 0.996017i | \(0.528418\pi\) | |||||||
\(332\) | 110566. | − | 68938.8i | 1.00310 | − | 0.625442i | ||||
\(333\) | −66656.0 | − | 47215.7i | −0.601105 | − | 0.425793i | ||||
\(334\) | 39917.7 | − | 71930.3i | 0.357827 | − | 0.644791i | ||||
\(335\) | −18575.7 | − | 10724.7i | −0.165522 | − | 0.0955639i | ||||
\(336\) | 103297. | + | 25311.6i | 0.914977 | + | 0.224203i | ||||
\(337\) | −22954.2 | − | 39757.8i | −0.202117 | − | 0.350076i | 0.747094 | − | 0.664719i | \(-0.231449\pi\) |
−0.949210 | + | 0.314643i | \(0.898115\pi\) | |||||||
\(338\) | 4292.89 | + | 253051.i | 0.0375765 | + | 2.21500i | ||||
\(339\) | 8724.05 | − | 1909.18i | 0.0759135 | − | 0.0166130i | ||||
\(340\) | −96713.5 | + | 3282.34i | −0.836622 | + | 0.0283940i | ||||
\(341\) | −83558.1 | −0.718588 | ||||||||
\(342\) | 7704.01 | − | 101514.i | 0.0658665 | − | 0.867907i | ||||
\(343\) | 123305.i | 1.04807i | ||||||||
\(344\) | −73420.1 | + | 143573.i | −0.620438 | + | 1.21326i | ||||
\(345\) | 74249.8 | − | 67666.6i | 0.623817 | − | 0.568508i | ||||
\(346\) | 414.552 | + | 24436.4i | 0.00346279 | + | 0.204120i | ||||
\(347\) | −131615. | + | 75987.9i | −1.09306 | + | 0.631081i | −0.934391 | − | 0.356250i | \(-0.884055\pi\) |
−0.158674 | + | 0.987331i | \(0.550722\pi\) | |||||||
\(348\) | −99739.0 | + | 25400.7i | −0.823581 | + | 0.209743i | ||||
\(349\) | 93645.6 | − | 162199.i | 0.768841 | − | 1.33167i | −0.169350 | − | 0.985556i | \(-0.554167\pi\) |
0.938192 | − | 0.346116i | \(-0.112500\pi\) | |||||||
\(350\) | 42923.2 | − | 77346.0i | 0.350393 | − | 0.631396i | ||||
\(351\) | −203402. | − | 86204.1i | −1.65098 | − | 0.699703i | ||||
\(352\) | −42990.0 | − | 61717.6i | −0.346962 | − | 0.498108i | ||||
\(353\) | −22707.8 | + | 39331.1i | −0.182232 | + | 0.315636i | −0.942640 | − | 0.333810i | \(-0.891666\pi\) |
0.760408 | + | 0.649446i | \(0.224999\pi\) | |||||||
\(354\) | 25051.8 | + | 26569.5i | 0.199909 | + | 0.212020i | ||||
\(355\) | 275326. | − | 158960.i | 2.18469 | − | 1.26133i | ||||
\(356\) | 57594.8 | − | 108064.i | 0.454447 | − | 0.852671i | ||||
\(357\) | 55890.5 | − | 50935.1i | 0.438532 | − | 0.399651i | ||||
\(358\) | 23744.0 | + | 39560.6i | 0.185263 | + | 0.308672i | ||||
\(359\) | − | 71504.2i | − | 0.554808i | −0.960753 | − | 0.277404i | \(-0.910526\pi\) | ||
0.960753 | − | 0.277404i | \(-0.0894740\pi\) | |||||||
\(360\) | −172102. | − | 7201.54i | −1.32795 | − | 0.0555674i | ||||
\(361\) | 31589.8 | 0.242400 | ||||||||
\(362\) | −87608.4 | + | 52582.0i | −0.668542 | + | 0.401254i | ||||
\(363\) | −81289.1 | + | 17789.4i | −0.616906 | + | 0.135005i | ||||
\(364\) | −197513. | − | 105268.i | −1.49071 | − | 0.794499i | ||||
\(365\) | 31551.4 | + | 54648.7i | 0.236828 | + | 0.410199i | ||||
\(366\) | 29677.6 | + | 8894.69i | 0.221548 | + | 0.0664001i | ||||
\(367\) | 57406.0 | + | 33143.4i | 0.426211 | + | 0.246073i | 0.697731 | − | 0.716360i | \(-0.254193\pi\) |
−0.271520 | + | 0.962433i | \(0.587526\pi\) | |||||||
\(368\) | −77219.2 | − | 37850.0i | −0.570203 | − | 0.279492i | ||||
\(369\) | −8361.81 | + | 89935.6i | −0.0614112 | + | 0.660509i | ||||
\(370\) | 117197. | + | 65038.4i | 0.856076 | + | 0.475080i | ||||
\(371\) | 42285.5 | + | 24413.5i | 0.307216 | + | 0.177371i | ||||
\(372\) | 157693. | + | 44361.4i | 1.13953 | + | 0.320567i | ||||
\(373\) | −71784.3 | − | 124334.i | −0.515955 | − | 0.893660i | −0.999828 | − | 0.0185223i | \(-0.994104\pi\) |
0.483873 | − | 0.875138i | \(-0.339229\pi\) | |||||||
\(374\) | −53470.6 | + | 907.103i | −0.382271 | + | 0.00648505i | ||||
\(375\) | 13235.1 | − | 41581.6i | 0.0941165 | − | 0.295691i | ||||
\(376\) | −32990.2 | + | 64512.1i | −0.233351 | + | 0.456316i | ||||
\(377\) | 216594. | 1.52393 | ||||||||
\(378\) | 106063. | − | 82877.7i | 0.742300 | − | 0.580035i | ||||
\(379\) | − | 183178.i | − | 1.27525i | −0.770348 | − | 0.637624i | \(-0.779917\pi\) | ||
0.770348 | − | 0.637624i | \(-0.220083\pi\) | |||||||
\(380\) | 5666.23 | + | 166954.i | 0.0392398 | + | 1.15619i | ||||
\(381\) | −61091.7 | − | 19445.1i | −0.420855 | − | 0.133955i | ||||
\(382\) | 156249. | − | 2650.69i | 1.07075 | − | 0.0181648i | ||||
\(383\) | −15175.9 | + | 8761.79i | −0.103456 | + | 0.0597303i | −0.550835 | − | 0.834614i | \(-0.685691\pi\) |
0.447379 | + | 0.894344i | \(0.352357\pi\) | |||||||
\(384\) | 48365.5 | + | 139298.i | 0.328000 | + | 0.944678i | ||||
\(385\) | 56329.9 | − | 97566.3i | 0.380030 | − | 0.658231i | ||||
\(386\) | −97337.4 | − | 54017.4i | −0.653288 | − | 0.362543i | ||||
\(387\) | 85244.2 | + | 185435.i | 0.569171 | + | 1.23814i | ||||
\(388\) | 107794. | + | 172884.i | 0.716031 | + | 1.14839i | ||||
\(389\) | −38430.8 | + | 66564.0i | −0.253968 | + | 0.439886i | −0.964615 | − | 0.263663i | \(-0.915069\pi\) |
0.710646 | + | 0.703549i | \(0.248403\pi\) | |||||||
\(390\) | 347235. | + | 104070.i | 2.28294 | + | 0.684220i | ||||
\(391\) | −52952.8 | + | 30572.3i | −0.346366 | + | 0.199974i | ||||
\(392\) | −14518.6 | + | 9398.15i | −0.0944827 | + | 0.0611604i | ||||
\(393\) | −13390.5 | − | 61188.0i | −0.0866983 | − | 0.396169i | ||||
\(394\) | −72376.5 | + | 43439.9i | −0.466235 | + | 0.279831i | ||||
\(395\) | 259679.i | 1.66434i | ||||||||
\(396\) | −95028.7 | − | 5592.53i | −0.605989 | − | 0.0356630i | ||||
\(397\) | −73295.7 | −0.465047 | −0.232524 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232524 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(398\) | 11214.5 | + | 18684.8i | 0.0707968 | + | 0.117957i | ||||
\(399\) | −87928.1 | − | 96482.5i | −0.552309 | − | 0.606042i | ||||
\(400\) | 122362. | − | 8315.25i | 0.764765 | − | 0.0519703i | ||||
\(401\) | −142274. | − | 246426.i | −0.884784 | − | 1.53249i | −0.845961 | − | 0.533244i | \(-0.820973\pi\) |
−0.0388226 | − | 0.999246i | \(-0.512361\pi\) | |||||||
\(402\) | 15942.4 | + | 16908.2i | 0.0986509 | + | 0.104627i | ||||
\(403\) | −298550. | − | 172368.i | −1.83826 | − | 1.06132i | ||||
\(404\) | −116369. | − | 186636.i | −0.712973 | − | 1.14349i | ||||
\(405\) | −141942. | + | 165468.i | −0.865366 | + | 1.00880i | ||||
\(406\) | −64037.0 | + | 115392.i | −0.388489 | + | 0.700044i | ||||
\(407\) | 64148.4 | + | 37036.1i | 0.387255 | + | 0.223582i | ||||
\(408\) | 101392. | + | 26675.9i | 0.609095 | + | 0.160250i | ||||
\(409\) | 56577.0 | + | 97994.2i | 0.338215 | + | 0.585806i | 0.984097 | − | 0.177632i | \(-0.0568435\pi\) |
−0.645882 | + | 0.763437i | \(0.723510\pi\) | |||||||
\(410\) | −2513.94 | − | 148188.i | −0.0149550 | − | 0.881548i | ||||
\(411\) | −51461.4 | − | 56468.0i | −0.304648 | − | 0.334286i | ||||
\(412\) | 7050.91 | + | 207753.i | 0.0415385 | + | 1.22392i | ||||
\(413\) | 46823.9 | 0.274516 | ||||||||
\(414\) | −98105.6 | + | 47130.9i | −0.572392 | + | 0.274982i | ||||
\(415\) | 270593.i | 1.57116i | ||||||||
\(416\) | −26287.4 | − | 309197.i | −0.151901 | − | 1.78669i | ||||
\(417\) | −41065.4 | − | 187649.i | −0.236159 | − | 1.07913i | ||||
\(418\) | 1565.91 | + | 92305.1i | 0.00896220 | + | 0.528291i | ||||
\(419\) | −237314. | + | 137013.i | −1.35175 | + | 0.780431i | −0.988494 | − | 0.151260i | \(-0.951667\pi\) |
−0.363252 | + | 0.931691i | \(0.618334\pi\) | |||||||
\(420\) | −158106. | + | 154223.i | −0.896290 | + | 0.874283i | ||||
\(421\) | −6241.89 | + | 10811.3i | −0.0352170 | + | 0.0609976i | −0.883097 | − | 0.469191i | \(-0.844546\pi\) |
0.847880 | + | 0.530189i | \(0.177879\pi\) | |||||||
\(422\) | −134328. | + | 242054.i | −0.754294 | + | 1.35921i | ||||
\(423\) | 38303.1 | + | 83322.3i | 0.214069 | + | 0.465673i | ||||
\(424\) | 3443.55 | + | 67609.9i | 0.0191547 | + | 0.376078i | ||||
\(425\) | 43600.9 | − | 75518.9i | 0.241389 | − | 0.418098i | ||||
\(426\) | −335184. | + | 79332.8i | −1.84699 | + | 0.437153i | ||||
\(427\) | 34403.6 | − | 19862.9i | 0.188690 | − | 0.108940i | ||||
\(428\) | 210269. | + | 112067.i | 1.14786 | + | 0.611772i | ||||
\(429\) | 190892. | + | 60759.5i | 1.03722 | + | 0.330141i | ||||
\(430\) | −172338. | − | 287138.i | −0.932062 | − | 1.55294i | ||||
\(431\) | − | 119855.i | − | 0.645211i | −0.946533 | − | 0.322606i | \(-0.895441\pi\) | ||
0.946533 | − | 0.322606i | \(-0.104559\pi\) | |||||||
\(432\) | 176371. | + | 61005.6i | 0.945062 | + | 0.326890i | ||||
\(433\) | −282465. | −1.50657 | −0.753284 | − | 0.657696i | \(-0.771531\pi\) | ||||
−0.753284 | + | 0.657696i | \(0.771531\pi\) | |||||||
\(434\) | 180098. | − | 108094.i | 0.956158 | − | 0.573880i | ||||
\(435\) | 64828.1 | − | 203674.i | 0.342598 | − | 1.07636i | ||||
\(436\) | 56734.1 | − | 106449.i | 0.298450 | − | 0.559977i | ||||
\(437\) | 52776.3 | + | 91411.2i | 0.276360 | + | 0.478670i | ||||
\(438\) | −15746.5 | − | 66529.7i | −0.0820800 | − | 0.346790i | ||||
\(439\) | 148459. | + | 85712.8i | 0.770331 | + | 0.444751i | 0.832993 | − | 0.553284i | \(-0.186626\pi\) |
−0.0626618 | + | 0.998035i | \(0.519959\pi\) | |||||||
\(440\) | 155998. | − | 7945.39i | 0.805774 | − | 0.0410402i | ||||
\(441\) | −2026.39 | + | 21794.9i | −0.0104195 | + | 0.112067i | ||||
\(442\) | −192920. | − | 107061.i | −0.987488 | − | 0.548007i | ||||
\(443\) | 71888.2 | + | 41504.7i | 0.366311 | + | 0.211490i | 0.671846 | − | 0.740691i | \(-0.265502\pi\) |
−0.305535 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(444\) | −101400. | − | 103952.i | −0.514364 | − | 0.527311i | ||||
\(445\) | 127152. | + | 220234.i | 0.642102 | + | 1.11215i | ||||
\(446\) | 101296. | − | 1718.45i | 0.509242 | − | 0.00863905i | ||||
\(447\) | 111953. | − | 24499.9i | 0.560298 | − | 0.122616i | ||||
\(448\) | 172499. | + | 77410.5i | 0.859470 | + | 0.385695i | ||||
\(449\) | 252767. | 1.25380 | 0.626898 | − | 0.779101i | \(-0.284324\pi\) | ||||
0.626898 | + | 0.779101i | \(0.284324\pi\) | |||||||
\(450\) | 87561.1 | − | 128168.i | 0.432400 | − | 0.632927i | ||||
\(451\) | − | 81906.2i | − | 0.402683i | ||||||
\(452\) | 15867.3 | − | 538.519i | 0.0776653 | − | 0.00263587i | ||||
\(453\) | 23518.2 | − | 21433.1i | 0.114606 | − | 0.104445i | ||||
\(454\) | −388774. | + | 6595.37i | −1.88619 | + | 0.0319983i | ||||
\(455\) | 402530. | − | 232401.i | 1.94435 | − | 1.12257i | ||||
\(456\) | 46050.0 | − | 175032.i | 0.221462 | − | 0.841757i | ||||
\(457\) | 9489.80 | − | 16436.8i | 0.0454386 | − | 0.0787019i | −0.842412 | − | 0.538835i | \(-0.818865\pi\) |
0.887850 | + | 0.460133i | \(0.152198\pi\) | |||||||
\(458\) | 300412. | + | 166714.i | 1.43214 | + | 0.794769i | ||||
\(459\) | 105927. | − | 79915.6i | 0.502786 | − | 0.379320i | ||||
\(460\) | 151547. | − | 94490.7i | 0.716197 | − | 0.446554i | ||||
\(461\) | 97075.9 | − | 168140.i | 0.456783 | − | 0.791171i | −0.542006 | − | 0.840375i | \(-0.682335\pi\) |
0.998789 | + | 0.0492038i | \(0.0156684\pi\) | |||||||
\(462\) | −88808.1 | + | 83735.4i | −0.416072 | + | 0.392306i | ||||
\(463\) | 86227.9 | − | 49783.7i | 0.402240 | − | 0.232234i | −0.285210 | − | 0.958465i | \(-0.592063\pi\) |
0.687450 | + | 0.726232i | \(0.258730\pi\) | |||||||
\(464\) | −182552. | + | 12405.5i | −0.847914 | + | 0.0576208i | ||||
\(465\) | −251444. | + | 229150.i | −1.16288 | + | 1.05978i | ||||
\(466\) | −43810.9 | + | 26295.0i | −0.201748 | + | 0.121088i | ||||
\(467\) | − | 126990.i | − | 0.582287i | −0.956679 | − | 0.291144i | \(-0.905964\pi\) | ||
0.956679 | − | 0.291144i | \(-0.0940358\pi\) | |||||||
\(468\) | −327998. | − | 216012.i | −1.49754 | − | 0.986249i | ||||
\(469\) | 29797.6 | 0.135468 | ||||||||
\(470\) | −77437.5 | − | 129021.i | −0.350555 | − | 0.584069i | ||||
\(471\) | −261482. | + | 57223.0i | −1.17869 | + | 0.257946i | ||||
\(472\) | 35277.9 | + | 54498.5i | 0.158350 | + | 0.244625i | ||||
\(473\) | −92535.3 | − | 160276.i | −0.413605 | − | 0.716384i | ||||
\(474\) | 80772.2 | − | 269501.i | 0.359505 | − | 1.19951i | ||||
\(475\) | −130367. | − | 75267.2i | −0.577802 | − | 0.333594i | ||||
\(476\) | 114075. | − | 71126.6i | 0.503474 | − | 0.313919i | ||||
\(477\) | 69916.2 | + | 49525.1i | 0.307285 | + | 0.217665i | ||||
\(478\) | 205628. | − | 370535.i | 0.899969 | − | 1.62171i | ||||
\(479\) | −48437.8 | − | 27965.6i | −0.211112 | − | 0.121886i | 0.390716 | − | 0.920511i | \(-0.372227\pi\) |
−0.601828 | + | 0.798626i | \(0.705561\pi\) | |||||||
\(480\) | −298621. | − | 67825.3i | −1.29610 | − | 0.294381i | ||||
\(481\) | 152800. | + | 264657.i | 0.660439 | + | 1.14391i | ||||
\(482\) | −690.660 | − | 40712.0i | −0.00297283 | − | 0.175238i | ||||
\(483\) | −42327.7 | + | 132983.i | −0.181439 | + | 0.570037i | ||||
\(484\) | −147849. | + | 5017.82i | −0.631142 | + | 0.0214202i | ||||
\(485\) | −423105. | −1.79872 | ||||||||
\(486\) | 198779. | − | 127576.i | 0.841583 | − | 0.540128i | ||||
\(487\) | 274913.i | 1.15914i | 0.814921 | + | 0.579572i | \(0.196780\pi\) | ||||
−0.814921 | + | 0.579572i | \(0.803220\pi\) | |||||||
\(488\) | 49038.8 | + | 25077.5i | 0.205921 | + | 0.105304i | ||||
\(489\) | 50632.7 | + | 16116.1i | 0.211745 | + | 0.0673971i | ||||
\(490\) | −609.226 | − | 35911.8i | −0.00253739 | − | 0.149570i | ||||
\(491\) | 28037.6 | − | 16187.5i | 0.116299 | − | 0.0671455i | −0.440722 | − | 0.897644i | \(-0.645277\pi\) |
0.557021 | + | 0.830498i | \(0.311944\pi\) | |||||||
\(492\) | −43484.4 | + | 154575.i | −0.179640 | + | 0.638571i | ||||
\(493\) | −65048.1 | + | 112667.i | −0.267634 | + | 0.463555i | ||||
\(494\) | −184817. | + | 333033.i | −0.757334 | + | 1.36469i | ||||
\(495\) | 114270. | − | 161319.i | 0.466362 | − | 0.658379i | ||||
\(496\) | 261500. | + | 128178.i | 1.06294 | + | 0.521013i | ||||
\(497\) | −220828. | + | 382485.i | −0.894008 | + | 1.54847i | ||||
\(498\) | 84167.0 | − | 280828.i | 0.339377 | − | 1.13235i | ||||
\(499\) | −251446. | + | 145172.i | −1.00982 | + | 0.583019i | −0.911139 | − | 0.412100i | \(-0.864796\pi\) |
−0.0986806 | + | 0.995119i | \(0.531462\pi\) | |||||||
\(500\) | 36487.4 | − | 68460.7i | 0.145950 | − | 0.273843i | ||||
\(501\) | −39569.8 | − | 180815.i | −0.157648 | − | 0.720376i | ||||
\(502\) | 44973.7 | + | 74932.1i | 0.178464 | + | 0.297345i | ||||
\(503\) | 9486.90i | 0.0374963i | 0.999824 | + | 0.0187481i | \(0.00596807\pi\) | ||||
−0.999824 | + | 0.0187481i | \(0.994032\pi\) | |||||||
\(504\) | 212056. | − | 110879.i | 0.834815 | − | 0.436502i | ||||
\(505\) | 456761. | 1.79104 | ||||||||
\(506\) | 84624.4 | − | 50791.0i | 0.330518 | − | 0.198375i | ||||
\(507\) | 383568. | + | 420885.i | 1.49220 | + | 1.63737i | ||||
\(508\) | −100583. | − | 53607.3i | −0.389758 | − | 0.207729i | ||||
\(509\) | 146376. | + | 253530.i | 0.564980 | + | 0.978575i | 0.997052 | + | 0.0767350i | \(0.0244496\pi\) |
−0.432071 | + | 0.901839i | \(0.642217\pi\) | |||||||
\(510\) | −158417. | + | 149368.i | −0.609061 | + | 0.574271i | ||||
\(511\) | −75918.5 | − | 43831.5i | −0.290741 | − | 0.167859i | ||||
\(512\) | 39865.2 | + | 259095.i | 0.152074 | + | 0.988369i | ||||
\(513\) | −137956. | − | 182860.i | −0.524213 | − | 0.694839i | ||||
\(514\) | −194328. | − | 107842.i | −0.735544 | − | 0.408190i | ||||
\(515\) | −373860. | − | 215848.i | −1.40960 | − | 0.813831i | ||||
\(516\) | 89543.5 | + | 351604.i | 0.336306 | + | 1.32055i | ||||
\(517\) | −41579.3 | − | 72017.4i | −0.155559 | − | 0.269437i | ||||
\(518\) | −186174. | + | 3158.36i | −0.693841 | + | 0.0117707i | ||||
\(519\) | 37040.1 | + | 40643.7i | 0.137511 | + | 0.150889i | ||||
\(520\) | 573765. | + | 293412.i | 2.12191 | + | 1.08510i | ||||
\(521\) | −344253. | −1.26824 | −0.634120 | − | 0.773234i | \(-0.718638\pi\) | ||||
−0.634120 | + | 0.773234i | \(0.718638\pi\) | |||||||
\(522\) | −130632. | + | 191213.i | −0.479413 | + | 0.701742i | ||||
\(523\) | 79326.1i | 0.290010i | 0.989431 | + | 0.145005i | \(0.0463198\pi\) | ||||
−0.989431 | + | 0.145005i | \(0.953680\pi\) | |||||||
\(524\) | −3777.01 | − | 111289.i | −0.0137558 | − | 0.405312i | ||||
\(525\) | −42549.1 | − | 194429.i | −0.154373 | − | 0.705411i | ||||
\(526\) | 100639. | − | 1707.29i | 0.363742 | − | 0.00617071i | ||||
\(527\) | 179323. | − | 103532.i | 0.645675 | − | 0.372780i | ||||
\(528\) | −164370. | − | 40276.6i | −0.589595 | − | 0.144473i | ||||
\(529\) | −83497.9 | + | 144623.i | −0.298376 | + | 0.516803i | ||||
\(530\) | −122929. | − | 68219.5i | −0.437625 | − | 0.242860i | ||||
\(531\) | 81811.7 | + | 7606.48i | 0.290152 | + | 0.0269771i | ||||
\(532\) | −122784. | − | 196925.i | −0.433830 | − | 0.695790i | ||||
\(533\) | 168960. | − | 292648.i | 0.594744 | − | 1.03013i | ||||
\(534\) | −63458.5 | − | 268114.i | −0.222540 | − | 0.940237i | ||||
\(535\) | −428527. | + | 247410.i | −1.49717 | + | 0.864391i | ||||
\(536\) | 22450.0 | + | 34681.6i | 0.0781424 | + | 0.120717i | ||||
\(537\) | 98923.0 | + | 31486.5i | 0.343043 | + | 0.109188i | ||||
\(538\) | 185731. | − | 111474.i | 0.641681 | − | 0.385133i | ||||
\(539\) | − | 19849.0i | − | 0.0683223i | ||||||
\(540\) | −301299. | + | 243779.i | −1.03326 | + | 0.836003i | ||||
\(541\) | 167330. | 0.571715 | 0.285857 | − | 0.958272i | \(-0.407722\pi\) | ||||
0.285857 | + | 0.958272i | \(0.407722\pi\) | |||||||
\(542\) | 195436. | + | 325622.i | 0.665283 | + | 1.10845i | ||||
\(543\) | −69728.0 | + | 219068.i | −0.236487 | + | 0.742985i | ||||
\(544\) | 168731. | + | 79184.7i | 0.570159 | + | 0.267574i | ||||
\(545\) | 125252. | + | 216943.i | 0.421689 | + | 0.730387i | ||||
\(546\) | −490042. | + | 115985.i | −1.64380 | + | 0.389061i | ||||
\(547\) | 246877. | + | 142535.i | 0.825100 | + | 0.476372i | 0.852172 | − | 0.523262i | \(-0.175285\pi\) |
−0.0270722 | + | 0.999633i | \(0.508618\pi\) | |||||||
\(548\) | −71861.5 | − | 115254.i | −0.239296 | − | 0.383790i | ||||
\(549\) | 63337.4 | − | 29116.1i | 0.210143 | − | 0.0966026i | ||||
\(550\) | −68300.6 | + | 123075.i | −0.225787 | + | 0.406860i | ||||
\(551\) | 194494. | + | 112291.i | 0.640623 | + | 0.369864i | ||||
\(552\) | −186670. | + | 50926.5i | −0.612628 | + | 0.167134i | ||||
\(553\) | −180374. | − | 312417.i | −0.589827 | − | 1.02161i | ||||
\(554\) | 7330.30 | + | 432096.i | 0.0238837 | + | 1.40786i | ||||
\(555\) | 294604. | − | 64471.6i | 0.956429 | − | 0.209306i | ||||
\(556\) | −11583.2 | − | 341297.i | −0.0374696 | − | 1.10403i | ||||
\(557\) | 51271.9 | 0.165260 | 0.0826302 | − | 0.996580i | \(-0.473668\pi\) | ||||
0.0826302 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(558\) | 332231. | − | 159607.i | 1.06702 | − | 0.512606i | ||||
\(559\) | − | 763547.i | − | 2.44350i | ||||||
\(560\) | −325954. | + | 218930.i | −1.03939 | + | 0.698117i | ||||
\(561\) | −88934.6 | + | 81049.4i | −0.282582 | + | 0.257528i | ||||
\(562\) | −4676.52 | − | 275665.i | −0.0148064 | − | 0.872787i | ||||
\(563\) | 2488.80 | − | 1436.91i | 0.00785187 | − | 0.00453328i | −0.496069 | − | 0.868283i | \(-0.665224\pi\) |
0.503921 | + | 0.863750i | \(0.331890\pi\) | |||||||
\(564\) | 40235.0 | + | 157988.i | 0.126487 | + | 0.496666i | ||||
\(565\) | −16485.6 | + | 28553.9i | −0.0516425 | + | 0.0894474i | ||||
\(566\) | 87753.2 | − | 158128.i | 0.273924 | − | 0.493601i | ||||
\(567\) | 55833.9 | − | 297666.i | 0.173673 | − | 0.925898i | ||||
\(568\) | −611552. | + | 31148.0i | −1.89556 | + | 0.0965458i | ||||
\(569\) | 56876.7 | − | 98513.3i | 0.175675 | − | 0.304278i | −0.764720 | − | 0.644363i | \(-0.777123\pi\) |
0.940395 | + | 0.340085i | \(0.110456\pi\) | |||||||
\(570\) | 257850. | + | 273471.i | 0.793630 | + | 0.841709i | ||||
\(571\) | 27258.4 | − | 15737.7i | 0.0836043 | − | 0.0482689i | −0.457615 | − | 0.889150i | \(-0.651296\pi\) |
0.541219 | + | 0.840881i | \(0.317963\pi\) | |||||||
\(572\) | 314288. | + | 167505.i | 0.960585 | + | 0.511961i | ||||
\(573\) | 259880. | − | 236838.i | 0.791522 | − | 0.721344i | ||||
\(574\) | 105957. | + | 176538.i | 0.321592 | + | 0.535813i | ||||
\(575\) | 160935.i | 0.486760i | ||||||||
\(576\) | 288819. | + | 163276.i | 0.870524 | + | 0.492126i | ||||
\(577\) | −654654. | −1.96635 | −0.983174 | − | 0.182671i | \(-0.941526\pi\) | ||||
−0.983174 | + | 0.182671i | \(0.941526\pi\) | |||||||
\(578\) | −172822. | + | 103727.i | −0.517301 | + | 0.310480i | ||||
\(579\) | −244682. | + | 53546.6i | −0.729870 | + | 0.159726i | ||||
\(580\) | 178722. | − | 335333.i | 0.531278 | − | 0.996829i | ||||
\(581\) | −187955. | − | 325548.i | −0.556803 | − | 0.964412i | ||||
\(582\) | 439108. | + | 131605.i | 1.29636 | + | 0.388532i | ||||
\(583\) | −67285.9 | − | 38847.5i | −0.197964 | − | 0.114295i | ||||
\(584\) | −6182.48 | − | 121385.i | −0.0181275 | − | 0.355910i | ||||
\(585\) | 741062. | − | 340665.i | 2.16542 | − | 0.995441i | ||||
\(586\) | 250798. | + | 139180.i | 0.730346 | + | 0.405306i | ||||
\(587\) | −557280. | − | 321746.i | −1.61732 | − | 0.933763i | −0.987609 | − | 0.156937i | \(-0.949838\pi\) |
−0.629716 | − | 0.776825i | \(-0.716829\pi\) | |||||||
\(588\) | −10538.0 | + | 37459.6i | −0.0304791 | + | 0.108345i | ||||
\(589\) | −178725. | − | 309561.i | −0.515175 | − | 0.892309i | ||||
\(590\) | −134802. | + | 2286.86i | −0.387251 | + | 0.00656954i | ||||
\(591\) | −57604.8 | + | 180980.i | −0.164924 | + | 0.518151i | ||||
\(592\) | −143943. | − | 214310.i | −0.410721 | − | 0.611503i | ||||
\(593\) | −183090. | −0.520661 | −0.260330 | − | 0.965520i | \(-0.583831\pi\) | ||||
−0.260330 | + | 0.965520i | \(0.583831\pi\) | |||||||
\(594\) | −168770. | + | 131877.i | −0.478325 | + | 0.373764i | ||||
\(595\) | 279180.i | 0.788589i | ||||||||
\(596\) | 203620. | − | 6910.62i | 0.573228 | − | 0.0194547i | ||||
\(597\) | 46722.1 | + | 14871.3i | 0.131091 | + | 0.0417255i | ||||
\(598\) | 407134. | − | 6906.84i | 1.13851 | − | 0.0193142i | ||||
\(599\) | −24104.3 | + | 13916.6i | −0.0671800 | + | 0.0387864i | −0.533214 | − | 0.845981i | \(-0.679016\pi\) |
0.466034 | + | 0.884767i | \(0.345683\pi\) | |||||||
\(600\) | 194240. | − | 196009.i | 0.539555 | − | 0.544470i | ||||
\(601\) | 135764. | − | 235150.i | 0.375868 | − | 0.651022i | −0.614589 | − | 0.788848i | \(-0.710678\pi\) |
0.990457 | + | 0.137826i | \(0.0440113\pi\) | |||||||
\(602\) | 406786. | + | 225746.i | 1.12247 | + | 0.622912i | ||||
\(603\) | 52063.0 | + | 4840.58i | 0.143184 | + | 0.0133126i | ||||
\(604\) | 48001.8 | − | 29929.5i | 0.131578 | − | 0.0820399i | ||||
\(605\) | 153610. | − | 266060.i | 0.419670 | − | 0.726889i | ||||
\(606\) | −474037. | − | 142074.i | −1.29082 | − | 0.386873i | ||||
\(607\) | −86991.8 | + | 50224.8i | −0.236103 | + | 0.136314i | −0.613384 | − | 0.789785i | \(-0.710192\pi\) |
0.377281 | + | 0.926099i | \(0.376859\pi\) | |||||||
\(608\) | 136695. | − | 291276.i | 0.369781 | − | 0.787948i | ||||
\(609\) | 63479.0 | + | 290068.i | 0.171157 | + | 0.782106i | ||||
\(610\) | −98075.2 | + | 58864.1i | −0.263572 | + | 0.158194i | ||||
\(611\) | − | 343088.i | − | 0.919015i | ||||||
\(612\) | 210869. | − | 105743.i | 0.563002 | − | 0.282323i | ||||
\(613\) | 458408. | 1.21992 | 0.609960 | − | 0.792432i | \(-0.291185\pi\) | ||||
0.609960 | + | 0.792432i | \(0.291185\pi\) | |||||||
\(614\) | −197339. | − | 328793.i | −0.523451 | − | 0.872138i | ||||
\(615\) | −224620. | − | 246473.i | −0.593880 | − | 0.651657i | ||||
\(616\) | −182161. | + | 117916.i | −0.480057 | + | 0.310750i | ||||
\(617\) | 237317. | + | 411046.i | 0.623389 | + | 1.07974i | 0.988850 | + | 0.148915i | \(0.0475781\pi\) |
−0.365461 | + | 0.930827i | \(0.619089\pi\) | |||||||
\(618\) | 320862. | + | 340300.i | 0.840120 | + | 0.891016i | ||||
\(619\) | 5714.30 | + | 3299.15i | 0.0149136 | + | 0.00861036i | 0.507438 | − | 0.861688i | \(-0.330593\pi\) |
−0.492525 | + | 0.870298i | \(0.663926\pi\) | |||||||
\(620\) | −513209. | + | 319989.i | −1.33509 | + | 0.832438i | ||||
\(621\) | −95558.8 | + | 225475.i | −0.247792 | + | 0.584676i | ||||
\(622\) | −46715.9 | + | 84180.4i | −0.120749 | + | 0.217586i | ||||
\(623\) | −305951. | − | 176641.i | −0.788272 | − | 0.455109i | ||||
\(624\) | −504202. | − | 482977.i | −1.29490 | − | 1.24039i | ||||
\(625\) | 230266. | + | 398833.i | 0.589481 | + | 1.02101i | ||||
\(626\) | −6737.96 | − | 397179.i | −0.0171941 | − | 1.01353i | ||||
\(627\) | 139914. | + | 153526.i | 0.355898 | + | 0.390523i | ||||
\(628\) | −475584. | + | 16140.8i | −1.20589 | + | 0.0409265i | ||||
\(629\) | −183557. | −0.463948 | ||||||||
\(630\) | −37606.1 | + | 495526.i | −0.0947495 | + | 1.24849i | ||||
\(631\) | 102946.i | 0.258553i | 0.991609 | + | 0.129277i | \(0.0412655\pi\) | ||||
−0.991609 | + | 0.129277i | \(0.958734\pi\) | |||||||
\(632\) | 227727. | − | 445319.i | 0.570139 | − | 1.11490i | ||||
\(633\) | 133157. | + | 608464.i | 0.332320 | + | 1.51854i | ||||
\(634\) | 4032.97 | + | 237730.i | 0.0100334 | + | 0.591432i | ||||
\(635\) | 204987. | − | 118349.i | 0.508368 | − | 0.293506i | ||||
\(636\) | 106359. | + | 109036.i | 0.262942 | + | 0.269561i | ||||
\(637\) | 40945.7 | − | 70919.9i | 0.100909 | − | 0.174779i | ||||
\(638\) | 101898. | − | 183616.i | 0.250336 | − | 0.451096i | ||||
\(639\) | −447970. | + | 632413.i | −1.09710 | + | 1.54881i | ||||
\(640\) | −500392. | − | 214434.i | −1.22166 | − | 0.523521i | ||||
\(641\) | −202403. | + | 350572.i | −0.492607 | + | 0.853221i | −0.999964 | − | 0.00851530i | \(-0.997289\pi\) |
0.507356 | + | 0.861736i | \(0.330623\pi\) | |||||||
\(642\) | 521692. | − | 123476.i | 1.26574 | − | 0.299581i | ||||
\(643\) | 426111. | − | 246015.i | 1.03063 | − | 0.595032i | 0.113462 | − | 0.993542i | \(-0.463806\pi\) |
0.917164 | + | 0.398510i | \(0.130473\pi\) | |||||||
\(644\) | −116691. | + | 218946.i | −0.281363 | + | 0.527917i | ||||
\(645\) | −718001. | − | 228535.i | −1.72586 | − | 0.549329i | ||||
\(646\) | −117730. | − | 196154.i | −0.282113 | − | 0.470037i | ||||
\(647\) | 306912.i | 0.733171i | 0.930384 | + | 0.366586i | \(0.119473\pi\) | ||||
−0.930384 | + | 0.366586i | \(0.880527\pi\) | |||||||
\(648\) | 388521. | − | 159281.i | 0.925262 | − | 0.379328i | ||||
\(649\) | −74507.5 | −0.176893 | ||||||||
\(650\) | −497922. | + | 298849.i | −1.17851 | + | 0.707335i | ||||
\(651\) | 143341. | − | 450343.i | 0.338227 | − | 1.06263i | ||||
\(652\) | 83362.7 | + | 44429.7i | 0.196100 | + | 0.104515i | ||||
\(653\) | −97661.8 | − | 169155.i | −0.229033 | − | 0.396697i | 0.728489 | − | 0.685058i | \(-0.240223\pi\) |
−0.957522 | + | 0.288361i | \(0.906890\pi\) | |||||||
\(654\) | −62510.3 | − | 264108.i | −0.146149 | − | 0.617484i | ||||
\(655\) | 200269. | + | 115625.i | 0.466799 | + | 0.269507i | ||||
\(656\) | −125644. | + | 256330.i | −0.291966 | + | 0.595651i | ||||
\(657\) | −125526. | − | 88916.3i | −0.290806 | − | 0.205992i | ||||
\(658\) | 182783. | + | 101435.i | 0.422166 | + | 0.234281i | ||||
\(659\) | 678872. | + | 391947.i | 1.56321 | + | 0.902519i | 0.996929 | + | 0.0783055i | \(0.0249510\pi\) |
0.566279 | + | 0.824213i | \(0.308382\pi\) | |||||||
\(660\) | 251582. | − | 245405.i | 0.577553 | − | 0.563372i | ||||
\(661\) | −371075. | − | 642721.i | −0.849295 | − | 1.47102i | −0.881838 | − | 0.471552i | \(-0.843694\pi\) |
0.0325431 | − | 0.999470i | \(-0.489639\pi\) | |||||||
\(662\) | 368768. | − | 6255.97i | 0.841467 | − | 0.0142751i | ||||
\(663\) | −484953. | + | 106128.i | −1.10325 | + | 0.241436i | ||||
\(664\) | 237298. | − | 464035.i | 0.538218 | − | 1.05248i | ||||
\(665\) | 481943. | 1.08981 | ||||||||
\(666\) | −325801. | − | 24725.4i | −0.734520 | − | 0.0557436i | ||||
\(667\) | − | 240099.i | − | 0.539682i | ||||||
\(668\) | −11161.4 | − | 328867.i | −0.0250129 | − | 0.737000i | ||||
\(669\) | 168481. | − | 153543.i | 0.376442 | − | 0.343065i | ||||
\(670\) | −85784.9 | + | 1455.30i | −0.191100 | + | 0.00324193i | ||||
\(671\) | −54744.0 | + | 31606.5i | −0.121588 | + | 0.0701990i | ||||
\(672\) | 406380. | − | 125823.i | 0.899898 | − | 0.278627i | ||||
\(673\) | −211601. | + | 366503.i | −0.467183 | + | 0.809185i | −0.999297 | − | 0.0374878i | \(-0.988064\pi\) |
0.532114 | + | 0.846673i | \(0.321398\pi\) | |||||||
\(674\) | −160566. | − | 89106.0i | −0.353454 | − | 0.196149i | ||||
\(675\) | −42758.0 | − | 346623.i | −0.0938447 | − | 0.760763i | ||||
\(676\) | 535621. | + | 859046.i | 1.17210 | + | 1.87985i | ||||
\(677\) | −154122. | + | 266947.i | −0.336269 | + | 0.582435i | −0.983728 | − | 0.179665i | \(-0.942498\pi\) |
0.647459 | + | 0.762100i | \(0.275832\pi\) | |||||||
\(678\) | 25990.7 | − | 24506.1i | 0.0565404 | − | 0.0533107i | ||||
\(679\) | 509034. | − | 293891.i | 1.10410 | − | 0.637450i | ||||
\(680\) | −324940. | + | 210339.i | −0.702724 | + | 0.454886i | ||||
\(681\) | −646626. | + | 589294.i | −1.39431 | + | 1.27069i | ||||
\(682\) | −286577. | + | 172002.i | −0.616131 | + | 0.369798i | ||||
\(683\) | 760287.i | 1.62981i | 0.579597 | + | 0.814903i | \(0.303210\pi\) | ||||
−0.579597 | + | 0.814903i | \(0.696790\pi\) | |||||||
\(684\) | −182541. | − | 364018.i | −0.390165 | − | 0.778056i | ||||
\(685\) | 282065. | 0.601130 | ||||||||
\(686\) | 253819. | + | 422896.i | 0.539357 | + | 0.898639i | ||||
\(687\) | 755164. | − | 165261.i | 1.60003 | − | 0.350152i | ||||
\(688\) | 43732.4 | + | 643541.i | 0.0923904 | + | 1.35956i | ||||
\(689\) | −160273. | − | 277602.i | −0.337616 | − | 0.584768i | ||||
\(690\) | 115363. | − | 384916.i | 0.242309 | − | 0.808477i | ||||
\(691\) | 313235. | + | 180846.i | 0.656016 | + | 0.378751i | 0.790757 | − | 0.612130i | \(-0.209687\pi\) |
−0.134742 | + | 0.990881i | \(0.543020\pi\) | |||||||
\(692\) | 51723.4 | + | 82955.6i | 0.108013 | + | 0.173234i | ||||
\(693\) | −25424.5 | + | 273454.i | −0.0529403 | + | 0.569401i | ||||
\(694\) | −294978. | + | 531539.i | −0.612450 | + | 1.10361i | ||||
\(695\) | 614177. | + | 354595.i | 1.27152 | + | 0.734113i | ||||
\(696\) | −289786. | + | 292426.i | −0.598217 | + | 0.603667i | ||||
\(697\) | 101485. | + | 175777.i | 0.208899 | + | 0.361824i | ||||
\(698\) | −12707.4 | − | 749057.i | −0.0260823 | − | 1.53746i | ||||
\(699\) | −34869.3 | + | 109551.i | −0.0713656 | + | 0.224214i | ||||
\(700\) | −12001.7 | − | 353628.i | −0.0244933 | − | 0.721690i | ||||
\(701\) | 878492. | 1.78773 | 0.893864 | − | 0.448337i | \(-0.147984\pi\) | ||||
0.893864 | + | 0.448337i | \(0.147984\pi\) | |||||||
\(702\) | −875054. | + | 123046.i | −1.77566 | + | 0.249684i | ||||
\(703\) | 316870.i | 0.641167i | ||||||||
\(704\) | −274486. | − | 123178.i | −0.553827 | − | 0.248535i | ||||
\(705\) | −322622. | − | 102688.i | −0.649107 | − | 0.206606i | ||||
\(706\) | 3081.37 | + | 181636.i | 0.00618208 | + | 0.364412i | ||||
\(707\) | −549525. | + | 317268.i | −1.09938 | + | 0.634728i | ||||
\(708\) | 140612. | + | 39556.4i | 0.280515 | + | 0.0789133i | ||||
\(709\) | −431190. | + | 746844.i | −0.857781 | + | 1.48572i | 0.0162593 | + | 0.999868i | \(0.494824\pi\) |
−0.874041 | + | 0.485853i | \(0.838509\pi\) | |||||||
\(710\) | 617066. | − | 1.11193e6i | 1.22409 | − | 2.20577i | ||||
\(711\) | −264402. | − | 575164.i | −0.523029 | − | 1.13776i | ||||
\(712\) | −24915.4 | − | 489183.i | −0.0491482 | − | 0.964964i | ||||
\(713\) | −191073. | + | 330948.i | −0.375855 | + | 0.651000i | ||||
\(714\) | 86838.0 | − | 289740.i | 0.170339 | − | 0.568345i | ||||
\(715\) | −640517. | + | 369803.i | −1.25291 | + | 0.723366i | ||||
\(716\) | 162869. | + | 86803.9i | 0.317696 | + | 0.169322i | ||||
\(717\) | −203836. | − | 931435.i | −0.396500 | − | 1.81182i | ||||
\(718\) | −147189. | − | 245236.i | −0.285514 | − | 0.475703i | ||||
\(719\) | − | 424008.i | − | 0.820193i | −0.912042 | − | 0.410097i | \(-0.865495\pi\) | ||
0.912042 | − | 0.410097i | \(-0.134505\pi\) | |||||||
\(720\) | −605078. | + | 329568.i | −1.16720 | + | 0.635740i | ||||
\(721\) | 599717. | 1.15365 | ||||||||
\(722\) | 108343. | − | 65026.6i | 0.207838 | − | 0.124743i | ||||
\(723\) | −61710.3 | − | 67714.0i | −0.118054 | − | 0.129539i | ||||
\(724\) | −192230. | + | 360679.i | −0.366728 | + | 0.688087i | ||||
\(725\) | 171209. | + | 296543.i | 0.325725 | + | 0.564172i | ||||
\(726\) | −242177. | + | 228343.i | −0.459472 | + | 0.433226i | ||||
\(727\) | −78836.8 | − | 45516.5i | −0.149163 | − | 0.0861191i | 0.423561 | − | 0.905868i | \(-0.360780\pi\) |
−0.572724 | + | 0.819748i | \(0.694113\pi\) | |||||||
\(728\) | −894096. | + | 45538.7i | −1.68702 | + | 0.0859247i | ||||
\(729\) | 145910. | − | 511018.i | 0.274555 | − | 0.961571i | ||||
\(730\) | 220704. | + | 122480.i | 0.414157 | + | 0.229836i | ||||
\(731\) | 397177. | + | 229310.i | 0.743275 | + | 0.429130i | ||||
\(732\) | 120094. | − | 30584.6i | 0.224130 | − | 0.0570795i | ||||
\(733\) | 6638.99 | + | 11499.1i | 0.0123565 | + | 0.0214020i | 0.872138 | − | 0.489261i | \(-0.162733\pi\) |
−0.859781 | + | 0.510663i | \(0.829400\pi\) | |||||||
\(734\) | 265109. | − | 4497.44i | 0.492076 | − | 0.00834783i | ||||
\(735\) | −54434.2 | − | 59730.0i | −0.100762 | − | 0.110565i | ||||
\(736\) | −342750. | + | 29140.1i | −0.632735 | + | 0.0537942i | ||||
\(737\) | −47414.8 | −0.0872929 | ||||||||
\(738\) | 156452. | + | 325663.i | 0.287255 | + | 0.597937i | ||||
\(739\) | − | 622195.i | − | 1.13930i | −0.821888 | − | 0.569650i | \(-0.807079\pi\) | ||
0.821888 | − | 0.569650i | \(-0.192921\pi\) | |||||||
\(740\) | 535827. | − | 18185.3i | 0.978501 | − | 0.0332092i | ||||
\(741\) | 183206. | + | 837164.i | 0.333660 | + | 1.52466i | ||||
\(742\) | 195280. | − | 3312.84i | 0.354691 | − | 0.00601717i | ||||
\(743\) | −606588. | + | 350214.i | −1.09879 | + | 0.634389i | −0.935904 | − | 0.352255i | \(-0.885415\pi\) |
−0.162890 | + | 0.986644i | \(0.552082\pi\) | |||||||
\(744\) | 632152. | − | 172461.i | 1.14203 | − | 0.311562i | ||||
\(745\) | −211554. | + | 366422.i | −0.381161 | + | 0.660189i | ||||
\(746\) | −502135. | − | 278660.i | −0.902283 | − | 0.500722i | ||||
\(747\) | −275514. | − | 599337.i | −0.493745 | − | 1.07406i | ||||
\(748\) | −181520. | + | 113179.i | −0.324430 | + | 0.202284i | ||||
\(749\) | 343705. | − | 595314.i | 0.612663 | − | 1.06116i | ||||
\(750\) | −40202.2 | − | 169856.i | −0.0714706 | − | 0.301965i | ||||
\(751\) | 73727.4 | − | 42566.6i | 0.130722 | − | 0.0754725i | −0.433213 | − | 0.901292i | \(-0.642620\pi\) |
0.563935 | + | 0.825819i | \(0.309287\pi\) | |||||||
\(752\) | 19650.5 | + | 289165.i | 0.0347486 | + | 0.511340i | ||||
\(753\) | 187371. | + | 59638.8i | 0.330455 | + | 0.105181i | ||||
\(754\) | 742849. | − | 445853.i | 1.30665 | − | 0.784240i | ||||
\(755\) | 117477.i | 0.206091i | ||||||||
\(756\) | 193160. | − | 502571.i | 0.337966 | − | 0.879334i | ||||
\(757\) | 319528. | 0.557592 | 0.278796 | − | 0.960350i | \(-0.410065\pi\) | ||||
0.278796 | + | 0.960350i | \(0.410065\pi\) | |||||||
\(758\) | −377066. | − | 628241.i | −0.656265 | − | 1.09342i | ||||
\(759\) | 67353.0 | − | 211607.i | 0.116916 | − | 0.367321i | ||||
\(760\) | 363104. | + | 560936.i | 0.628643 | + | 0.971150i | ||||
\(761\) | −376888. | − | 652790.i | −0.650794 | − | 1.12721i | −0.982931 | − | 0.183977i | \(-0.941103\pi\) |
0.332137 | − | 0.943231i | \(-0.392230\pi\) | |||||||
\(762\) | −249552. | + | 59065.1i | −0.429785 | + | 0.101723i | ||||
\(763\) | −301379. | − | 174001.i | −0.517684 | − | 0.298885i | ||||
\(764\) | 530426. | − | 330724.i | 0.908737 | − | 0.566604i | ||||
\(765\) | −45352.5 | + | 487790.i | −0.0774958 | + | 0.833509i | ||||
\(766\) | −34012.4 | + | 61289.2i | −0.0579669 | + | 0.104454i | ||||
\(767\) | −266213. | − | 153698.i | −0.452520 | − | 0.261263i | ||||
\(768\) | 452620. | + | 378190.i | 0.767381 | + | 0.641191i | ||||
\(769\) | −425156. | − | 736392.i | −0.718945 | − | 1.24525i | −0.961418 | − | 0.275091i | \(-0.911292\pi\) |
0.242473 | − | 0.970158i | \(-0.422041\pi\) | |||||||
\(770\) | −7643.78 | − | 450575.i | −0.0128922 | − | 0.759950i | ||||
\(771\) | −488492. | + | 106902.i | −0.821768 | + | 0.179837i | ||||
\(772\) | −445029. | + | 15103.8i | −0.746713 | + | 0.0253426i | ||||
\(773\) | 13034.7 | 0.0218143 | 0.0109071 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109071 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(774\) | 674073. | + | 460510.i | 1.12519 | + | 0.768701i | ||||
\(775\) | − | 545000.i | − | 0.907388i | ||||||
\(776\) | 725575. | + | 371045.i | 1.20492 | + | 0.616173i | ||||
\(777\) | −309653. | + | 282199.i | −0.512901 | + | 0.467426i | ||||
\(778\) | 5214.93 | + | 307402.i | 0.00861567 | + | 0.507864i | ||||
\(779\) | 303441. | − | 175192.i | 0.500033 | − | 0.288694i | ||||
\(780\) | 1.40513e6 | − | 357846.i | 2.30955 | − | 0.588176i | ||||
\(781\) | 351388. | − | 608622.i | 0.576083 | − | 0.997805i | ||||
\(782\) | −118679. | + | 213855.i | −0.194071 | + | 0.349708i | ||||
\(783\) | 63790.6 | + | 517126.i | 0.104048 | + | 0.843476i | ||||
\(784\) | −30448.3 | + | 62118.7i | −0.0495372 | + | 0.101063i | ||||
\(785\) | 494114. | − | 855831.i | 0.801841 | − | 1.38883i | ||||
\(786\) | −171879. | − | 182291.i | −0.278213 | − | 0.295067i | ||||
\(787\) | 473891. | − | 273601.i | 0.765120 | − | 0.441742i | −0.0660112 | − | 0.997819i | \(-0.521027\pi\) |
0.831131 | + | 0.556077i | \(0.187694\pi\) | |||||||
\(788\) | −158808. | + | 297970.i | −0.255753 | + | 0.479866i | ||||
\(789\) | 167387. | − | 152546.i | 0.268885 | − | 0.245045i | ||||
\(790\) | 534542. | + | 890616.i | 0.856500 | + | 1.42704i | ||||
\(791\) | − | 45803.8i | − | 0.0732064i | ||||||
\(792\) | −337430. | + | 176433.i | −0.537940 | + | 0.281274i | ||||
\(793\) | −260798. | −0.414723 | ||||||||
\(794\) | −251381. | + | 150877.i | −0.398741 | + | 0.239322i | ||||
\(795\) | −309014. | + | 67624.9i | −0.488926 | + | 0.106997i | ||||
\(796\) | 76924.2 | + | 40998.2i | 0.121405 | + | 0.0647050i | ||||
\(797\) | 104227. | + | 180527.i | 0.164083 | + | 0.284201i | 0.936329 | − | 0.351123i | \(-0.114200\pi\) |
−0.772246 | + | 0.635324i | \(0.780867\pi\) | |||||||
\(798\) | −500172. | − | 149907.i | −0.785441 | − | 0.235405i | ||||
\(799\) | 178465. | + | 103037.i | 0.279550 | + | 0.161398i | ||||
\(800\) | 402547. | − | 280398.i | 0.628980 | − | 0.438122i | ||||
\(801\) | −505869. | − | 358332.i | −0.788449 | − | 0.558497i | ||||
\(802\) | −995215. | − | 552295.i | −1.54728 | − | 0.858662i | ||||
\(803\) | 120804. | + | 69746.0i | 0.187348 | + | 0.108165i | ||||
\(804\) | 89482.3 | + | 25172.7i | 0.138428 | + | 0.0389420i | ||||
\(805\) | −257620. | − | 446211.i | −0.397547 | − | 0.688571i | ||||
\(806\) | −1.37875e6 | + | 23389.8i | −2.12234 | + | 0.0360044i | ||||
\(807\) | 147824. | − | 464427.i | 0.226985 | − | 0.713133i | ||||
\(808\) | −783292. | − | 400560.i | −1.19978 | − | 0.613542i | ||||
\(809\) | 844500. | 1.29034 | 0.645168 | − | 0.764041i | \(-0.276787\pi\) | ||||
0.645168 | + | 0.764041i | \(0.276787\pi\) | |||||||
\(810\) | −146204. | + | 859684.i | −0.222837 | + | 1.31029i | ||||
\(811\) | 769174.i | 1.16945i | 0.811230 | + | 0.584727i | \(0.198798\pi\) | ||||
−0.811230 | + | 0.584727i | \(0.801202\pi\) | |||||||
\(812\) | 17905.4 | + | 527577.i | 0.0271563 | + | 0.800155i | ||||
\(813\) | 814232. | + | 259164.i | 1.23188 | + | 0.392098i | ||||
\(814\) | 296246. | − | 5025.67i | 0.447099 | − | 0.00758482i | ||||
\(815\) | −169893. | + | 98087.6i | −0.255776 | + | 0.147672i | ||||
\(816\) | 402655. | − | 117224.i | 0.604718 | − | 0.176050i | ||||
\(817\) | 395853. | − | 685638.i | 0.593048 | − | 1.02719i | ||||
\(818\) | 395759. | + | 219627.i | 0.591458 | + | 0.328230i | ||||
\(819\) | −654937. | + | 924595.i | −0.976408 | + | 1.37843i | ||||
\(820\) | −313663. | − | 503063.i | −0.466483 | − | 0.748161i | ||||
\(821\) | −322867. | + | 559222.i | −0.479002 | + | 0.829656i | −0.999710 | − | 0.0240788i | \(-0.992335\pi\) |
0.520708 | + | 0.853735i | \(0.325668\pi\) | |||||||
\(822\) | −292734. | − | 87735.3i | −0.433240 | − | 0.129847i | ||||
\(823\) | 202697. | − | 117027.i | 0.299260 | − | 0.172778i | −0.342851 | − | 0.939390i | \(-0.611392\pi\) |
0.642110 | + | 0.766612i | \(0.278059\pi\) | |||||||
\(824\) | 451837. | + | 698013.i | 0.665468 | + | 1.02804i | ||||
\(825\) | 67705.4 | + | 309381.i | 0.0994753 | + | 0.454554i | ||||
\(826\) | 160591. | − | 96385.5i | 0.235375 | − | 0.141271i | ||||
\(827\) | − | 1.14409e6i | − | 1.67282i | −0.548108 | − | 0.836408i | \(-0.684652\pi\) | ||
0.548108 | − | 0.836408i | \(-0.315348\pi\) | |||||||
\(828\) | −239453. | + | 363591.i | −0.349269 | + | 0.530338i | ||||
\(829\) | −563769. | −0.820336 | −0.410168 | − | 0.912010i | \(-0.634530\pi\) | ||||
−0.410168 | + | 0.912010i | \(0.634530\pi\) | |||||||
\(830\) | 557008. | + | 928047.i | 0.808547 | + | 1.34714i | ||||
\(831\) | 654961. | + | 718681.i | 0.948447 | + | 1.04072i | ||||
\(832\) | −726630. | − | 1.00633e6i | −1.04970 | − | 1.45377i | ||||
\(833\) | 24593.8 | + | 42597.7i | 0.0354434 | + | 0.0613898i | ||||
\(834\) | −527111. | − | 559044.i | −0.757827 | − | 0.803738i | ||||
\(835\) | 591809. | + | 341681.i | 0.848806 | + | 0.490059i | ||||
\(836\) | 195378. | + | 313353.i | 0.279552 | + | 0.448355i | ||||
\(837\) | 323606. | − | 763563.i | 0.461919 | − | 1.08992i | ||||
\(838\) | −531873. | + | 958415.i | −0.757390 | + | 1.36479i | ||||
\(839\) | −231599. | − | 133714.i | −0.329013 | − | 0.189956i | 0.326390 | − | 0.945235i | \(-0.394168\pi\) |
−0.655403 | + | 0.755279i | \(0.727501\pi\) | |||||||
\(840\) | −224787. | + | 854393.i | −0.318575 | + | 1.21087i | ||||
\(841\) | 98213.9 | + | 170111.i | 0.138861 | + | 0.240515i | ||||
\(842\) | 847.004 | + | 49927.9i | 0.00119471 | + | 0.0704238i | ||||
\(843\) | −417846. | − | 458497.i | −0.587978 | − | 0.645181i | ||||
\(844\) | 37559.3 | + | 1.10668e6i | 0.0527269 | + | 1.55359i | ||||
\(845\) | −2.10238e6 | −2.94440 | ||||||||
\(846\) | 302884. | + | 206923.i | 0.423190 | + | 0.289113i | ||||
\(847\) | 426792.i | 0.594907i | ||||||||
\(848\) | 150983. | + | 224792.i | 0.209960 | + | 0.312600i | ||||
\(849\) | −86988.4 | − | 397495.i | −0.120683 | − | 0.551463i | ||||
\(850\) | −5916.50 | − | 348757.i | −0.00818892 | − | 0.482708i | ||||
\(851\) | 293377. | − | 169381.i | 0.405105 | − | 0.233887i | ||||
\(852\) | −986268. | + | 962052.i | −1.35868 | + | 1.32532i | ||||
\(853\) | −183417. | + | 317688.i | −0.252082 | + | 0.436619i | −0.964099 | − | 0.265544i | \(-0.914449\pi\) |
0.712017 | + | 0.702162i | \(0.247782\pi\) | |||||||
\(854\) | 77106.0 | − | 138942.i | 0.105724 | − | 0.190510i | ||||
\(855\) | 842061. | + | 78291.0i | 1.15189 | + | 0.107098i | ||||
\(856\) | 951842. | − | 48479.9i | 1.29902 | − | 0.0661628i | ||||
\(857\) | −576064. | + | 997772.i | −0.784348 | + | 1.35853i | 0.145039 | + | 0.989426i | \(0.453669\pi\) |
−0.929388 | + | 0.369105i | \(0.879664\pi\) | |||||||
\(858\) | 779769. | − | 184559.i | 1.05923 | − | 0.250704i | ||||
\(859\) | −1.26237e6 | + | 728827.i | −1.71080 | + | 0.987730i | −0.777313 | + | 0.629115i | \(0.783418\pi\) |
−0.933486 | + | 0.358615i | \(0.883249\pi\) | |||||||
\(860\) | −1.18213e6 | − | 630038.i | −1.59834 | − | 0.851863i | ||||
\(861\) | 441440. | + | 140507.i | 0.595477 | + | 0.189536i | ||||
\(862\) | −246718. | − | 411064.i | −0.332037 | − | 0.553217i | ||||
\(863\) | − | 237901.i | − | 0.319430i | −0.987163 | − | 0.159715i | \(-0.948943\pi\) | ||
0.987163 | − | 0.159715i | \(-0.0510575\pi\) | |||||||
\(864\) | 730475. | − | 153826.i | 0.978539 | − | 0.206064i | ||||
\(865\) | −203020. | −0.271336 | ||||||||
\(866\) | −968764. | + | 581445.i | −1.29176 | + | 0.775306i | ||||
\(867\) | −137550. | + | 432148.i | −0.182988 | + | 0.574903i | ||||
\(868\) | 395171. | − | 741453.i | 0.524500 | − | 0.984112i | ||||
\(869\) | 287017. | + | 497128.i | 0.380074 | + | 0.658307i | ||||
\(870\) | −196918. | − | 831984.i | −0.260164 | − | 1.09920i | ||||
\(871\) | −169411. | − | 97809.7i | −0.223309 | − | 0.128928i | ||||
\(872\) | −24543.1 | − | 481873.i | −0.0322772 | − | 0.633723i | ||||
\(873\) | 937137. | − | 430800.i | 1.22963 | − | 0.565259i | ||||
\(874\) | 369173. | + | 204873.i | 0.483289 | + | 0.268201i | ||||
\(875\) | −193826. | − | 111905.i | −0.253160 | − | 0.146162i | ||||
\(876\) | −190955. | − | 195762.i | −0.248841 | − | 0.255105i | ||||
\(877\) | 331033. | + | 573367.i | 0.430400 | + | 0.745475i | 0.996908 | − | 0.0785815i | \(-0.0250391\pi\) |
−0.566507 | + | 0.824057i | \(0.691706\pi\) | |||||||
\(878\) | 685604. | − | 11630.9i | 0.889373 | − | 0.0150878i | ||||
\(879\) | 630445. | − | 137967.i | 0.815961 | − | 0.178566i | ||||
\(880\) | 518667. | − | 348367.i | 0.669766 | − | 0.449854i | ||||
\(881\) | 245234. | 0.315957 | 0.157979 | − | 0.987443i | \(-0.449502\pi\) | ||||
0.157979 | + | 0.987443i | \(0.449502\pi\) | |||||||
\(882\) | 37914.3 | + | 78920.8i | 0.0487378 | + | 0.101451i | ||||
\(883\) | − | 924835.i | − | 1.18616i | −0.805144 | − | 0.593079i | \(-0.797912\pi\) | ||
0.805144 | − | 0.593079i | \(-0.202088\pi\) | |||||||
\(884\) | −882034. | + | 29935.2i | −1.12871 | + | 0.0383070i | ||||
\(885\) | −224209. | + | 204330.i | −0.286264 | + | 0.260883i | ||||
\(886\) | 331990. | − | 5632.05i | 0.422919 | − | 0.00717462i | ||||
\(887\) | −1.09941e6 | + | 634747.i | −1.39738 | + | 0.806776i | −0.994117 | − | 0.108309i | \(-0.965456\pi\) |
−0.403260 | + | 0.915085i | \(0.632123\pi\) | |||||||
\(888\) | −561750. | − | 147794.i | −0.712389 | − | 0.187426i | ||||
\(889\) | −164412. | + | 284769.i | −0.208031 | + | 0.360321i | ||||
\(890\) | 889437. | + | 493593.i | 1.12288 | + | 0.623145i | ||||
\(891\) | −88844.6 | + | 473655.i | −0.111912 | + | 0.596632i | ||||
\(892\) | 343877. | − | 214409.i | 0.432188 | − | 0.269472i | ||||
\(893\) | 177870. | − | 308081.i | 0.223049 | − | 0.386333i | ||||
\(894\) | 333529. | − | 314478.i | 0.417310 | − | 0.393473i | ||||
\(895\) | −331926. | + | 191637.i | −0.414376 | + | 0.239240i | ||||
\(896\) | 750964. | − | 89591.1i | 0.935412 | − | 0.111596i | ||||
\(897\) | 677164. | − | 617125.i | 0.841606 | − | 0.766987i | ||||
\(898\) | 866908. | − | 520313.i | 1.07503 | − | 0.645226i | ||||
\(899\) | 813085.i | 1.00604i | ||||||||
\(900\) | 36476.8 | − | 619816.i | 0.0450330 | − | 0.765205i | ||||
\(901\) | 192535. | 0.237170 | ||||||||
\(902\) | −168601. | − | 280912.i | −0.207228 | − | 0.345269i | ||||
\(903\) | 1.02256e6 | − | 223779.i | 1.25405 | − | 0.274437i | ||||
\(904\) | 53311.3 | − | 34509.4i | 0.0652353 | − | 0.0422280i | ||||
\(905\) | −424388. | − | 735061.i | −0.518162 | − | 0.897483i | ||||
\(906\) | 36540.7 | − | 121920.i | 0.0445165 | − | 0.148532i | ||||
\(907\) | −41146.3 | − | 23755.8i | −0.0500169 | − | 0.0288772i | 0.474783 | − | 0.880103i | \(-0.342527\pi\) |
−0.524800 | + | 0.851226i | \(0.675860\pi\) | |||||||
\(908\) | −1.31979e6 | + | 822900.i | −1.60079 | + | 0.998102i | ||||
\(909\) | −1.01168e6 | + | 465068.i | −1.22438 | + | 0.562845i | ||||
\(910\) | 902158. | − | 1.62565e6i | 1.08943 | − | 1.96311i | ||||
\(911\) | −421729. | − | 243485.i | −0.508155 | − | 0.293383i | 0.223920 | − | 0.974608i | \(-0.428115\pi\) |
−0.732075 | + | 0.681224i | \(0.761448\pi\) | |||||||
\(912\) | −202361. | − | 695095.i | −0.243297 | − | 0.835708i | ||||
\(913\) | 299080. | + | 518021.i | 0.358794 | + | 0.621450i | ||||
\(914\) | −1287.73 | − | 75907.4i | −0.00154147 | − | 0.0908640i | ||||
\(915\) | −78058.5 | + | 245241.i | −0.0932349 | + | 0.292921i | ||||
\(916\) | 1.37349e6 | − | 46614.8i | 1.63695 | − | 0.0555562i | ||||
\(917\) | −321255. | −0.382042 | ||||||||
\(918\) | 198793. | − | 492133.i | 0.235894 | − | 0.583979i | ||||
\(919\) | − | 1.08957e6i | − | 1.29010i | −0.764141 | − | 0.645049i | \(-0.776837\pi\) | ||
0.764141 | − | 0.645049i | \(-0.223163\pi\) | |||||||
\(920\) | 325252. | − | 636029.i | 0.384277 | − | 0.751452i | ||||
\(921\) | −822159. | − | 261688.i | −0.969252 | − | 0.308506i | ||||
\(922\) | −13172.9 | − | 776495.i | −0.0154960 | − | 0.913434i | ||||
\(923\) | 2.51099e6 | − | 1.44972e6i | 2.94742 | − | 1.70169i | ||||
\(924\) | −132217. | + | 469994.i | −0.154861 | + | 0.550489i | ||||
\(925\) | −241564. | + | 418402.i | −0.282325 | + | 0.489001i | ||||
\(926\) | 193256. | − | 348240.i | 0.225377 | − | 0.406122i | ||||
\(927\) | 1.04784e6 | + | 97423.2i | 1.21937 | + | 0.113371i | ||||
\(928\) | −600560. | + | 418326.i | −0.697365 | + | 0.485757i | ||||
\(929\) | −671427. | + | 1.16295e6i | −0.777978 | + | 1.34750i | 0.155128 | + | 0.987894i | \(0.450421\pi\) |
−0.933106 | + | 0.359603i | \(0.882912\pi\) | |||||||
\(930\) | −390673. | + | 1.30350e6i | −0.451698 | + | 1.50711i | ||||
\(931\) | 73535.5 | − | 42455.7i | 0.0848394 | − | 0.0489820i | ||||
\(932\) | −96129.8 | + | 180367.i | −0.110669 | + | 0.207647i | ||||
\(933\) | 46308.8 | + | 211609.i | 0.0531986 | + | 0.243092i | ||||
\(934\) | −261406. | − | 435537.i | −0.299655 | − | 0.499265i | ||||
\(935\) | − | 444240.i | − | 0.508153i | ||||||
\(936\) | −1.56958e6 | − | 65678.6i | −1.79156 | − | 0.0749673i | ||||
\(937\) | 1.37506e6 | 1.56618 | 0.783089 | − | 0.621909i | \(-0.213643\pi\) | ||||
0.783089 | + | 0.621909i | \(0.213643\pi\) | |||||||
\(938\) | 102196. | − | 61337.4i | 0.116153 | − | 0.0697140i | ||||
\(939\) | −602035. | − | 660606.i | −0.682795 | − | 0.749223i | ||||
\(940\) | −531172. | − | 283098.i | −0.601145 | − | 0.320391i | ||||
\(941\) | 786864. | + | 1.36289e6i | 0.888628 | + | 1.53915i | 0.841498 | + | 0.540261i | \(0.181674\pi\) |
0.0471309 | + | 0.998889i | \(0.484992\pi\) | |||||||
\(942\) | −779007. | + | 734509.i | −0.877888 | + | 0.827743i | ||||
\(943\) | −324405. | − | 187295.i | −0.364808 | − | 0.210622i | ||||
\(944\) | 233175. | + | 114294.i | 0.261661 | + | 0.128257i | ||||
\(945\) | 673416. | + | 892607.i | 0.754084 | + | 0.999532i | ||||
\(946\) | −647290. | − | 359214.i | −0.723297 | − | 0.401394i | ||||
\(947\) | −938964. | − | 542111.i | −1.04701 | − | 0.604489i | −0.125196 | − | 0.992132i | \(-0.539956\pi\) |
−0.921810 | + | 0.387643i | \(0.873289\pi\) | |||||||
\(948\) | −277737. | − | 1.09057e6i | −0.309042 | − | 1.21349i | ||||
\(949\) | 287752. | + | 498400.i | 0.319511 | + | 0.553409i | ||||
\(950\) | −602051. | + | 10213.5i | −0.667093 | + | 0.0113169i | ||||
\(951\) | 360345. | + | 395403.i | 0.398435 | + | 0.437198i | ||||
\(952\) | 244829. | − | 478762.i | 0.270140 | − | 0.528257i | ||||
\(953\) | 461469. | 0.508108 | 0.254054 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254054 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(954\) | 341736. | + | 25934.8i | 0.375486 | + | 0.0284961i | ||||
\(955\) | 1.29813e6i | 1.42335i | ||||||||
\(956\) | −57495.6 | − | 1.69410e6i | −0.0629099 | − | 1.85363i | ||||
\(957\) | −101010. | − | 461565.i | −0.110291 | − | 0.503975i | ||||
\(958\) | −223692. | + | 3794.83i | −0.243736 | + | 0.00413487i | ||||
\(959\) | −339350. | + | 195924.i | −0.368986 | + | 0.213034i | ||||
\(960\) | −1.16379e6 | + | 382083.i | −1.26279 | + | 0.414587i | ||||
\(961\) | 185301. | − | 320951.i | 0.200646 | − | 0.347530i | ||||
\(962\) | 1.06884e6 | + | 593155.i | 1.15495 | + | 0.640941i | ||||
\(963\) | 697236. | − | 984311.i | 0.751843 | − | 1.06140i | ||||
\(964\) | −86173.2 | − | 138207.i | −0.0927295 | − | 0.148723i | ||||
\(965\) | 462369. | − | 800847.i | 0.496517 | − | 0.859993i | ||||
\(966\) | 128572. | + | 543220.i | 0.137782 | + | 0.582132i | ||||
\(967\) | −998780. | + | 576646.i | −1.06811 | + | 0.616675i | −0.927665 | − | 0.373413i | \(-0.878187\pi\) |
−0.140447 | + | 0.990088i | \(0.544854\pi\) | |||||||
\(968\) | −496745. | + | 321552.i | −0.530131 | + | 0.343163i | ||||
\(969\) | −490491. | − | 156120.i | −0.522377 | − | 0.166269i | ||||
\(970\) | −1.45111e6 | + | 870949.i | −1.54226 | + | 0.925656i | ||||
\(971\) | − | 438562.i | − | 0.465149i | −0.972579 | − | 0.232575i | \(-0.925285\pi\) | ||
0.972579 | − | 0.232575i | \(-0.0747150\pi\) | |||||||
\(972\) | 419135. | − | 846725.i | 0.443631 | − | 0.896210i | ||||
\(973\) | −985213. | −1.04065 | ||||||||
\(974\) | 565900. | + | 942864.i | 0.596516 | + | 0.993873i | ||||
\(975\) | −396298. | + | 1.24507e6i | −0.416882 | + | 1.30974i | ||||
\(976\) | 219809. | − | 14937.3i | 0.230752 | − | 0.0156810i | ||||
\(977\) | −388615. | − | 673100.i | −0.407127 | − | 0.705165i | 0.587439 | − | 0.809268i | \(-0.300136\pi\) |
−0.994566 | + | 0.104103i | \(0.966803\pi\) | |||||||
\(978\) | 206828. | − | 48953.1i | 0.216238 | − | 0.0511803i | ||||
\(979\) | 486839. | + | 281076.i | 0.507948 | + | 0.293264i | ||||
\(980\) | −76012.8 | − | 121912.i | −0.0791470 | − | 0.126939i | ||||
\(981\) | −498310. | − | 352978.i | −0.517800 | − | 0.366783i | ||||
\(982\) | 62838.4 | − | 113233.i | 0.0651632 | − | 0.117422i | ||||
\(983\) | 695782. | + | 401710.i | 0.720056 | + | 0.415724i | 0.814773 | − | 0.579780i | \(-0.196861\pi\) |
−0.0947175 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(984\) | 169051. | + | 619655.i | 0.174593 | + | 0.639970i | ||||
\(985\) | −350602. | − | 607260.i | −0.361362 | − | 0.625897i | ||||
\(986\) | 8826.81 | + | 520310.i | 0.00907925 | + | 0.535190i | ||||
\(987\) | 459472. | − | 100551.i | 0.471655 | − | 0.103218i | ||||
\(988\) | 51676.5 | + | 1.52264e6i | 0.0529394 | + | 1.55985i | ||||
\(989\) | −846405. | −0.865338 | ||||||||
\(990\) | 59839.9 | − | 788495.i | 0.0610549 | − | 0.804505i | ||||
\(991\) | 206876.i | 0.210651i | 0.994438 | + | 0.105325i | \(0.0335884\pi\) | ||||
−0.994438 | + | 0.105325i | \(0.966412\pi\) | |||||||
\(992\) | 1.16071e6 | − | 98681.8i | 1.17951 | − | 0.100280i | ||||
\(993\) | 613351. | − | 558969.i | 0.622028 | − | 0.566878i | ||||
\(994\) | 29965.6 | + | 1.76637e6i | 0.0303285 | + | 1.78776i | ||||
\(995\) | −156771. | + | 90511.8i | −0.158351 | + | 0.0914238i | ||||
\(996\) | −289410. | − | 1.13640e6i | −0.291739 | − | 1.14555i | ||||
\(997\) | 14831.3 | − | 25688.6i | 0.0149207 | − | 0.0258435i | −0.858469 | − | 0.512866i | \(-0.828584\pi\) |
0.873389 | + | 0.487023i | \(0.161917\pi\) | |||||||
\(998\) | −563546. | + | 1.01549e6i | −0.565807 | + | 1.01956i | ||||
\(999\) | −586875. | + | 442761.i | −0.588051 | + | 0.443647i |
(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 | 36.5.f.a.7.18 | yes | 44 | |
3.2 | odd | 2 | 108.5.f.a.19.5 | 44 | |||
4.3 | odd | 2 | inner | 36.5.f.a.7.12 | ✓ | 44 | |
9.2 | odd | 6 | 324.5.d.e.163.20 | 22 | |||
9.4 | even | 3 | inner | 36.5.f.a.31.12 | yes | 44 | |
9.5 | odd | 6 | 108.5.f.a.91.11 | 44 | |||
9.7 | even | 3 | 324.5.d.f.163.3 | 22 | |||
12.11 | even | 2 | 108.5.f.a.19.11 | 44 | |||
36.7 | odd | 6 | 324.5.d.f.163.4 | 22 | |||
36.11 | even | 6 | 324.5.d.e.163.19 | 22 | |||
36.23 | even | 6 | 108.5.f.a.91.5 | 44 | |||
36.31 | odd | 6 | inner | 36.5.f.a.31.18 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.12 | ✓ | 44 | 4.3 | odd | 2 | inner | |
36.5.f.a.7.18 | yes | 44 | 1.1 | even | 1 | trivial | |
36.5.f.a.31.12 | yes | 44 | 9.4 | even | 3 | inner | |
36.5.f.a.31.18 | yes | 44 | 36.31 | odd | 6 | inner | |
108.5.f.a.19.5 | 44 | 3.2 | odd | 2 | |||
108.5.f.a.19.11 | 44 | 12.11 | even | 2 | |||
108.5.f.a.91.5 | 44 | 36.23 | even | 6 | |||
108.5.f.a.91.11 | 44 | 9.5 | odd | 6 | |||
324.5.d.e.163.19 | 22 | 36.11 | even | 6 | |||
324.5.d.e.163.20 | 22 | 9.2 | odd | 6 | |||
324.5.d.f.163.3 | 22 | 9.7 | even | 3 | |||
324.5.d.f.163.4 | 22 | 36.7 | odd | 6 |