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 | 31.12 | ||
Character | \(\chi\) | \(=\) | 36.31 |
Dual form | 36.5.f.a.7.12 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0678484 | + | 3.99942i | 0.0169621 | + | 0.999856i | ||||
\(3\) | −2.72970 | − | 8.57606i | −0.303300 | − | 0.952895i | ||||
\(4\) | −15.9908 | + | 0.542709i | −0.999425 | + | 0.0339193i | ||||
\(5\) | 16.6139 | − | 28.7760i | 0.664554 | − | 1.15104i | −0.314852 | − | 0.949141i | \(-0.601955\pi\) |
0.979406 | − | 0.201901i | \(-0.0647118\pi\) | |||||||
\(6\) | 34.1141 | − | 11.4991i | 0.947613 | − | 0.319419i | ||||
\(7\) | 39.9759 | − | 23.0801i | 0.815835 | − | 0.471023i | −0.0331429 | − | 0.999451i | \(-0.510552\pi\) |
0.848978 | + | 0.528428i | \(0.177218\pi\) | |||||||
\(8\) | −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 | \(-0.764828\pi\) |
0.213558 | + | 0.976930i | \(0.431495\pi\) | |||||||
\(12\) | 48.3044 | + | 135.657i | 0.335447 | + | 0.942059i | ||||
\(13\) | 151.520 | − | 262.440i | 0.896566 | − | 1.55290i | 0.0647110 | − | 0.997904i | \(-0.479387\pi\) |
0.831855 | − | 0.554993i | \(-0.187279\pi\) | |||||||
\(14\) | 95.0195 | + | 158.315i | 0.484793 | + | 0.807728i | ||||
\(15\) | −292.136 | − | 63.9314i | −1.29838 | − | 0.284140i | ||||
\(16\) | 255.411 | − | 17.3567i | 0.997699 | − | 0.0677996i | ||||
\(17\) | −182.019 | −0.629823 | −0.314912 | − | 0.949121i | \(-0.601975\pi\) | ||||
−0.314912 | + | 0.949121i | \(0.601975\pi\) | |||||||
\(18\) | −191.738 | − | 261.175i | −0.591784 | − | 0.806096i | ||||
\(19\) | 314.215i | 0.870402i | 0.900333 | + | 0.435201i | \(0.143323\pi\) | ||||
−0.900333 | + | 0.435201i | \(0.856677\pi\) | |||||||
\(20\) | −250.052 | + | 469.168i | −0.625129 | + | 1.17292i | ||||
\(21\) | −307.059 | − | 279.834i | −0.696278 | − | 0.634544i | ||||
\(22\) | −151.198 | − | 251.915i | −0.312392 | − | 0.520486i | ||||
\(23\) | −290.919 | − | 167.962i | −0.549941 | − | 0.317509i | 0.199157 | − | 0.979968i | \(-0.436180\pi\) |
−0.749098 | + | 0.662459i | \(0.769513\pi\) | |||||||
\(24\) | −539.271 | + | 202.394i | −0.936234 | + | 0.351378i | ||||
\(25\) | −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 | 0.996414 | − | 0.0846079i | \(-0.0269638\pi\) |
−0.571480 | + | 0.820616i | \(0.693630\pi\) | |||||||
\(30\) | 235.868 | − | 1172.71i | 0.262075 | − | 1.30301i | ||||
\(31\) | 985.186 | + | 568.798i | 1.02517 | + | 0.591881i | 0.915597 | − | 0.402098i | \(-0.131719\pi\) |
0.109571 | + | 0.993979i | \(0.465052\pi\) | |||||||
\(32\) | 86.7460 | + | 1020.32i | 0.0847129 | + | 0.996405i | ||||
\(33\) | 488.601 | + | 445.280i | 0.448669 | + | 0.408889i | ||||
\(34\) | −12.3497 | − | 727.971i | −0.0106831 | − | 0.629733i | ||||
\(35\) | − | 1533.80i | − | 1.25208i | ||||||
\(36\) | 1031.54 | − | 784.562i | 0.795942 | − | 0.605372i | ||||
\(37\) | 1008.45 | 0.736632 | 0.368316 | − | 0.929701i | \(-0.379934\pi\) | ||||
0.368316 | + | 0.929701i | \(0.379934\pi\) | |||||||
\(38\) | −1256.68 | + | 21.3190i | −0.870277 | + | 0.0147638i | ||||
\(39\) | −2664.30 | − | 583.059i | −1.75168 | − | 0.383339i | ||||
\(40\) | −1893.37 | − | 968.231i | −1.18336 | − | 0.605144i | ||||
\(41\) | −557.553 | + | 965.709i | −0.331679 | + | 0.574485i | −0.982841 | − | 0.184454i | \(-0.940948\pi\) |
0.651162 | + | 0.758939i | \(0.274282\pi\) | |||||||
\(42\) | 1098.34 | − | 1247.04i | 0.622643 | − | 0.706941i | ||||
\(43\) | 2182.06 | − | 1259.82i | 1.18013 | − | 0.681349i | 0.224087 | − | 0.974569i | \(-0.428060\pi\) |
0.956045 | + | 0.293220i | \(0.0947268\pi\) | |||||||
\(44\) | 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 | \(-0.584176\pi\) |
0.705232 | + | 0.708977i | \(0.250843\pi\) | |||||||
\(48\) | −846.047 | − | 2143.04i | −0.367208 | − | 0.930139i | ||||
\(49\) | −135.117 | + | 234.029i | −0.0562752 | + | 0.0974714i | ||||
\(50\) | 1643.09 | − | 986.173i | 0.657237 | − | 0.394469i | ||||
\(51\) | 496.857 | + | 1561.00i | 0.191025 | + | 0.600156i | ||||
\(52\) | −2280.49 | + | 4278.85i | −0.843377 | + | 1.58241i | ||||
\(53\) | −1057.77 | −0.376566 | −0.188283 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188283 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(54\) | −1716.47 | + | 2357.29i | −0.588637 | + | 0.808397i | ||||
\(55\) | 2440.63i | 0.806818i | ||||||||
\(56\) | −1605.36 | − | 2480.01i | −0.511912 | − | 0.790820i | ||||
\(57\) | 2694.73 | − | 857.713i | 0.829402 | − | 0.263993i | ||||
\(58\) | −2451.33 | + | 1471.27i | −0.728695 | + | 0.437358i | ||||
\(59\) | 878.476 | + | 507.188i | 0.252363 | + | 0.145702i | 0.620846 | − | 0.783933i | \(-0.286789\pi\) |
−0.368483 | + | 0.929635i | \(0.620123\pi\) | |||||||
\(60\) | 4706.18 | + | 863.769i | 1.30727 | + | 0.239936i | ||||
\(61\) | −430.304 | − | 745.308i | −0.115642 | − | 0.200298i | 0.802394 | − | 0.596794i | \(-0.203559\pi\) |
−0.918036 | + | 0.396497i | \(0.870226\pi\) | |||||||
\(62\) | −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 | ||||
\(66\) | −1747.71 | + | 1984.33i | −0.401220 | + | 0.455540i | ||||
\(67\) | 559.041 | + | 322.762i | 0.124536 | + | 0.0719008i | 0.560974 | − | 0.827834i | \(-0.310427\pi\) |
−0.436438 | + | 0.899734i | \(0.643760\pi\) | |||||||
\(68\) | 2910.63 | − | 98.7833i | 0.629461 | − | 0.0213632i | ||||
\(69\) | −646.331 | + | 2953.42i | −0.135755 | + | 0.620337i | ||||
\(70\) | 6134.31 | − | 104.066i | 1.25190 | − | 0.0212379i | ||||
\(71\) | − | 9567.89i | − | 1.89801i | −0.315254 | − | 0.949007i | \(-0.602090\pi\) | ||
0.315254 | − | 0.949007i | \(-0.397910\pi\) | |||||||
\(72\) | 3207.79 | + | 4072.34i | 0.618786 | + | 0.785560i | ||||
\(73\) | 1899.10 | 0.356372 | 0.178186 | − | 0.983997i | \(-0.442977\pi\) | ||||
0.178186 | + | 0.983997i | \(0.442977\pi\) | |||||||
\(74\) | 68.4216 | + | 4033.22i | 0.0124948 | + | 0.736526i | ||||
\(75\) | −2904.30 | + | 3186.85i | −0.516320 | + | 0.566552i | ||||
\(76\) | −170.527 | − | 5024.55i | −0.0295234 | − | 0.869902i | ||||
\(77\) | −1695.27 | + | 2936.29i | −0.285928 | + | 0.495242i | ||||
\(78\) | 2151.13 | − | 10695.2i | 0.353572 | − | 1.75793i | ||||
\(79\) | −6768.11 | + | 3907.57i | −1.08446 | + | 0.626113i | −0.932096 | − | 0.362212i | \(-0.882022\pi\) |
−0.152363 | + | 0.988325i | \(0.548688\pi\) | |||||||
\(80\) | 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 | \(-0.867956\pi\) |
−0.108556 | + | 0.994090i | \(0.534623\pi\) | |||||||
\(84\) | 5061.98 | + | 4308.12i | 0.717401 | + | 0.610562i | ||||
\(85\) | −3024.04 | + | 5237.78i | −0.418552 | + | 0.724953i | ||||
\(86\) | 5186.58 | + | 8641.52i | 0.701269 | + | 1.16840i | ||||
\(87\) | 4332.92 | − | 4754.46i | 0.572456 | − | 0.628149i | ||||
\(88\) | 2554.49 | + | 3946.27i | 0.329867 | + | 0.509590i | ||||
\(89\) | 7653.39 | 0.966215 | 0.483107 | − | 0.875561i | \(-0.339508\pi\) | ||||
0.483107 | + | 0.875561i | \(0.339508\pi\) | |||||||
\(90\) | −10701.1 | + | 1178.34i | −1.32112 | + | 0.145474i | ||||
\(91\) | − | 13988.4i | − | 1.68921i | ||||||
\(92\) | 4743.18 | + | 2527.96i | 0.560395 | + | 0.298673i | ||||
\(93\) | 2188.78 | − | 10001.7i | 0.253067 | − | 1.15640i | ||||
\(94\) | 2330.51 | + | 3882.93i | 0.263752 | + | 0.439445i | ||||
\(95\) | 9041.87 | + | 5220.33i | 1.00187 | + | 0.578430i | ||||
\(96\) | 8513.52 | − | 3529.10i | 0.923776 | − | 0.382932i | ||||
\(97\) | −6366.75 | − | 11027.5i | −0.676666 | − | 1.17202i | −0.975979 | − | 0.217865i | \(-0.930091\pi\) |
0.299313 | − | 0.954155i | \(-0.403243\pi\) | |||||||
\(98\) | −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 | 0.976825 | + | 0.214040i | \(0.0686624\pi\) |
−0.303048 | + | 0.952975i | \(0.598004\pi\) | |||||||
\(102\) | −6209.41 | + | 2093.05i | −0.596829 | + | 0.201178i | ||||
\(103\) | 11251.5 | + | 6496.03i | 1.06056 | + | 0.612313i | 0.925587 | − | 0.378536i | \(-0.123572\pi\) |
0.134971 | + | 0.990850i | \(0.456906\pi\) | |||||||
\(104\) | −17267.7 | − | 8830.34i | −1.59649 | − | 0.816414i | ||||
\(105\) | −13153.9 | + | 4186.81i | −1.19310 | + | 0.379756i | ||||
\(106\) | −71.7682 | − | 4230.49i | −0.00638734 | − | 0.376512i | ||||
\(107\) | 14891.8i | 1.30071i | 0.759631 | + | 0.650354i | \(0.225379\pi\) | ||||
−0.759631 | + | 0.650354i | \(0.774621\pi\) | |||||||
\(108\) | −9544.25 | − | 6704.94i | −0.818266 | − | 0.574840i | ||||
\(109\) | 7539.02 | 0.634544 | 0.317272 | − | 0.948335i | \(-0.397233\pi\) | ||||
0.317272 | + | 0.948335i | \(0.397233\pi\) | |||||||
\(110\) | −9761.10 | + | 165.592i | −0.806702 | + | 0.0136853i | ||||
\(111\) | −2752.76 | − | 8648.52i | −0.223421 | − | 0.701933i | ||||
\(112\) | 9809.70 | − | 6588.76i | 0.782023 | − | 0.525252i | ||||
\(113\) | 496.140 | − | 859.339i | 0.0388550 | − | 0.0672988i | −0.845944 | − | 0.533272i | \(-0.820962\pi\) |
0.884799 | + | 0.465973i | \(0.154296\pi\) | |||||||
\(114\) | 3613.19 | + | 10719.2i | 0.278023 | + | 0.824805i | ||||
\(115\) | −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 | ||||
\(120\) | −3135.27 | + | 18880.6i | −0.217727 | + | 1.31115i | ||||
\(121\) | −4622.94 | + | 8007.16i | −0.315753 | + | 0.546900i | ||||
\(122\) | 2951.61 | − | 1771.54i | 0.198307 | − | 0.119023i | ||||
\(123\) | 9803.93 | + | 2145.51i | 0.648022 | + | 0.141814i | ||||
\(124\) | −16062.6 | − | 8560.86i | −1.04465 | − | 0.556767i | ||||
\(125\) | 4848.57 | 0.310308 | ||||||||
\(126\) | −13692.9 | − | 6015.38i | −0.862488 | − | 0.378898i | ||||
\(127\) | − | 7123.52i | − | 0.441659i | −0.975312 | − | 0.220829i | \(-0.929124\pi\) | ||
0.975312 | − | 0.220829i | \(-0.0708764\pi\) | |||||||
\(128\) | −1940.87 | − | 16268.6i | −0.118461 | − | 0.992959i | ||||
\(129\) | −16760.6 | − | 15274.6i | −1.00719 | − | 0.917889i | ||||
\(130\) | 34534.5 | − | 20727.4i | 2.04346 | − | 1.22647i | ||||
\(131\) | −6027.16 | − | 3479.78i | −0.351212 | − | 0.202773i | 0.314007 | − | 0.949421i | \(-0.398329\pi\) |
−0.665219 | + | 0.746648i | \(0.731662\pi\) | |||||||
\(132\) | −8054.77 | − | 6855.22i | −0.462280 | − | 0.393435i | ||||
\(133\) | 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 | 0.956661 | − | 0.291204i | \(-0.0940559\pi\) |
−0.730521 | + | 0.682891i | \(0.760723\pi\) | |||||||
\(138\) | −11855.9 | − | 2384.57i | −0.622550 | − | 0.125214i | ||||
\(139\) | −18483.9 | − | 10671.7i | −0.956673 | − | 0.552335i | −0.0615252 | − | 0.998106i | \(-0.519596\pi\) |
−0.895147 | + | 0.445770i | \(0.852930\pi\) | |||||||
\(140\) | 832.406 | + | 24526.7i | 0.0424697 | + | 1.25136i | ||||
\(141\) | −7531.12 | − | 6863.39i | −0.378810 | − | 0.345224i | ||||
\(142\) | 38266.1 | − | 649.166i | 1.89774 | − | 0.0321943i | ||||
\(143\) | 22258.7i | 1.08850i | ||||||||
\(144\) | −16069.4 | + | 13105.6i | −0.774951 | + | 0.632022i | ||||
\(145\) | 23749.2 | 1.12957 | ||||||||
\(146\) | 128.851 | + | 7595.32i | 0.00604481 | + | 0.356320i | ||||
\(147\) | 2375.87 | + | 519.939i | 0.109948 | + | 0.0240612i | ||||
\(148\) | −16125.9 | + | 547.294i | −0.736208 | + | 0.0249860i | ||||
\(149\) | 6366.78 | − | 11027.6i | 0.286779 | − | 0.496716i | −0.686260 | − | 0.727356i | \(-0.740749\pi\) |
0.973039 | + | 0.230640i | \(0.0740821\pi\) | |||||||
\(150\) | −12942.6 | − | 11399.3i | −0.575228 | − | 0.506636i | ||||
\(151\) | −3061.84 | + | 1767.75i | −0.134285 | + | 0.0775296i | −0.565638 | − | 0.824654i | \(-0.691370\pi\) |
0.431352 | + | 0.902184i | \(0.358037\pi\) | |||||||
\(152\) | 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 | ||||
\(156\) | 42920.7 | + | 7877.64i | 1.76367 | + | 0.323703i | ||||
\(157\) | −14870.6 | + | 25756.6i | −0.603292 | + | 1.04493i | 0.389027 | + | 0.921227i | \(0.372811\pi\) |
−0.992319 | + | 0.123706i | \(0.960522\pi\) | |||||||
\(158\) | −16087.2 | − | 26803.4i | −0.644417 | − | 1.07368i | ||||
\(159\) | 2887.40 | + | 9071.53i | 0.114212 | + | 0.358828i | ||||
\(160\) | 30801.9 | + | 14455.2i | 1.20320 | + | 0.564657i | ||||
\(161\) | −15506.3 | −0.598216 | ||||||||
\(162\) | 24901.7 | + | 8285.82i | 0.948852 | + | 0.315722i | ||||
\(163\) | 5903.96i | 0.222213i | 0.993809 | + | 0.111106i | \(0.0354394\pi\) | ||||
−0.993809 | + | 0.111106i | \(0.964561\pi\) | |||||||
\(164\) | 8391.61 | − | 15745.0i | 0.312002 | − | 0.585405i | ||||
\(165\) | 20930.9 | − | 6662.18i | 0.768813 | − | 0.244708i | ||||
\(166\) | −16763.4 | − | 27929.9i | −0.608338 | − | 1.01357i | ||||
\(167\) | −17810.7 | − | 10283.0i | −0.638628 | − | 0.368712i | 0.145458 | − | 0.989364i | \(-0.453535\pi\) |
−0.784086 | + | 0.620652i | \(0.786868\pi\) | |||||||
\(168\) | −16886.6 | + | 20537.3i | −0.598305 | + | 0.727654i | ||||
\(169\) | −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 | 0.810465 | − | 0.585787i | \(-0.199215\pi\) |
−0.912539 | + | 0.408989i | \(0.865881\pi\) | |||||||
\(174\) | 19309.1 | + | 17006.6i | 0.637769 | + | 0.561719i | ||||
\(175\) | −19151.7 | − | 11057.2i | −0.625361 | − | 0.361053i | ||||
\(176\) | −15609.5 | + | 10484.2i | −0.503922 | + | 0.338463i | ||||
\(177\) | 1951.70 | − | 8918.33i | 0.0622969 | − | 0.284667i | ||||
\(178\) | 519.270 | + | 30609.1i | 0.0163890 | + | 0.966076i | ||||
\(179\) | 11534.8i | 0.360001i | 0.983667 | + | 0.180001i | \(0.0576099\pi\) | ||||
−0.983667 | + | 0.180001i | \(0.942390\pi\) | |||||||
\(180\) | −5438.72 | − | 42718.3i | −0.167862 | − | 1.31847i | ||||
\(181\) | −25544.2 | −0.779713 | −0.389857 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389857 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(182\) | 55945.4 | − | 949.087i | 1.68897 | − | 0.0286526i | ||||
\(183\) | −5217.20 | + | 5724.78i | −0.155789 | + | 0.170945i | ||||
\(184\) | −9788.59 | + | 19141.5i | −0.289124 | + | 0.565380i | ||||
\(185\) | 16754.2 | − | 29019.2i | 0.489532 | − | 0.847894i | ||||
\(186\) | 40149.4 | + | 8075.25i | 1.16052 | + | 0.233416i | ||||
\(187\) | 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 | \(-0.846526\pi\) |
−0.0414344 | + | 0.999141i | \(0.513193\pi\) | |||||||
\(192\) | 14692.0 | + | 33809.8i | 0.398546 | + | 0.917148i | ||||
\(193\) | −13915.2 | + | 24101.8i | −0.373572 | + | 0.647045i | −0.990112 | − | 0.140278i | \(-0.955200\pi\) |
0.616541 | + | 0.787323i | \(0.288534\pi\) | |||||||
\(194\) | 43671.8 | − | 26211.5i | 1.16037 | − | 0.696449i | ||||
\(195\) | −61042.4 | + | 66981.2i | −1.60532 | + | 1.76150i | ||||
\(196\) | 2033.61 | − | 3815.64i | 0.0529366 | − | 0.0993242i | ||||
\(197\) | −21103.0 | −0.543765 | −0.271883 | − | 0.962330i | \(-0.587646\pi\) | ||||
−0.271883 | + | 0.962330i | \(0.587646\pi\) | |||||||
\(198\) | 21788.5 | + | 9571.86i | 0.555772 | + | 0.244155i | ||||
\(199\) | 5447.97i | 0.137572i | 0.997631 | + | 0.0687858i | \(0.0219125\pi\) | ||||
−0.997631 | + | 0.0687858i | \(0.978087\pi\) | |||||||
\(200\) | −25739.2 | + | 16661.4i | −0.643479 | + | 0.416535i | ||||
\(201\) | 1242.02 | − | 5675.41i | 0.0307422 | − | 0.140477i | ||||
\(202\) | −47145.7 | + | 28296.5i | −1.15542 | + | 0.693475i | ||||
\(203\) | 28572.4 | + | 16496.3i | 0.693353 | + | 0.400308i | ||||
\(204\) | −8792.31 | − | 24692.1i | −0.211272 | − | 0.593331i | ||||
\(205\) | 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 | ||||
\(210\) | −17637.3 | − | 52324.1i | −0.399939 | − | 1.18649i | ||||
\(211\) | 59935.1 | + | 34603.5i | 1.34622 | + | 0.777241i | 0.987712 | − | 0.156286i | \(-0.0499520\pi\) |
0.358509 | + | 0.933526i | \(0.383285\pi\) | |||||||
\(212\) | 16914.6 | − | 574.063i | 0.376349 | − | 0.0127729i | ||||
\(213\) | −82054.8 | + | 26117.5i | −1.80861 | + | 0.575668i | ||||
\(214\) | −59558.7 | + | 1010.38i | −1.30052 | + | 0.0220627i | ||||
\(215\) | − | 83721.5i | − | 1.81117i | ||||||
\(216\) | 26168.3 | − | 38626.4i | 0.560878 | − | 0.827898i | ||||
\(217\) | 52511.7 | 1.11516 | ||||||||
\(218\) | 511.510 | + | 30151.8i | 0.0107632 | + | 0.634453i | ||||
\(219\) | −5183.98 | − | 16286.8i | −0.108088 | − | 0.339585i | ||||
\(220\) | −1324.55 | − | 39027.5i | −0.0273667 | − | 0.806354i | ||||
\(221\) | −27579.4 | + | 47769.0i | −0.564678 | + | 0.978051i | ||||
\(222\) | 34402.3 | − | 11596.3i | 0.698043 | − | 0.235295i | ||||
\(223\) | −21934.5 | + | 12663.9i | −0.441080 | + | 0.254658i | −0.704056 | − | 0.710145i | \(-0.748629\pi\) |
0.262976 | + | 0.964802i | \(0.415296\pi\) | |||||||
\(224\) | 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 | 0.650792 | − | 0.759256i | \(-0.274437\pi\) |
0.982931 | − | 0.183975i | \(-0.0588964\pi\) | |||||||
\(228\) | −42625.3 | + | 15178.0i | −0.819971 | + | 0.291974i | ||||
\(229\) | 42946.4 | − | 74385.3i | 0.818947 | − | 1.41846i | −0.0875119 | − | 0.996163i | \(-0.527892\pi\) |
0.906459 | − | 0.422294i | \(-0.138775\pi\) | |||||||
\(230\) | −22976.6 | − | 38282.1i | −0.434341 | − | 0.723669i | ||||
\(231\) | 29809.4 | + | 6523.53i | 0.558636 | + | 0.122253i | ||||
\(232\) | 38400.2 | − | 24857.2i | 0.713440 | − | 0.461823i | ||||
\(233\) | −12774.0 | −0.235297 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(234\) | −97594.8 | + | 10746.5i | −1.78236 | + | 0.196262i | ||||
\(235\) | − | 37619.0i | − | 0.681194i | ||||||
\(236\) | −14322.8 | − | 7633.59i | −0.257160 | − | 0.137058i | ||||
\(237\) | 51986.4 | + | 47377.2i | 0.925536 | + | 0.843476i | ||||
\(238\) | −17295.3 | − | 28816.3i | −0.305334 | − | 0.508726i | ||||
\(239\) | −91748.4 | − | 52971.0i | −1.60621 | − | 0.927347i | −0.990207 | − | 0.139605i | \(-0.955417\pi\) |
−0.616005 | − | 0.787742i | \(-0.711250\pi\) | |||||||
\(240\) | −75724.3 | − | 11258.3i | −1.31466 | − | 0.195456i | ||||
\(241\) | 5089.73 | + | 8815.67i | 0.0876316 | + | 0.151782i | 0.906510 | − | 0.422185i | \(-0.138737\pi\) |
−0.818878 | + | 0.573968i | \(0.805404\pi\) | |||||||
\(242\) | −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 | ||||
\(246\) | −7915.61 | + | 39355.6i | −0.130802 | + | 0.650334i | ||||
\(247\) | 82462.6 | + | 47609.8i | 1.35165 | + | 0.780373i | ||||
\(248\) | 33148.7 | − | 64822.0i | 0.538968 | − | 1.05395i | ||||
\(249\) | 54171.3 | + | 49368.4i | 0.873717 | + | 0.796251i | ||||
\(250\) | 328.967 | + | 19391.5i | 0.00526347 | + | 0.310264i | ||||
\(251\) | 21848.1i | 0.346790i | 0.984852 | + | 0.173395i | \(0.0554738\pi\) | ||||
−0.984852 | + | 0.173395i | \(0.944526\pi\) | |||||||
\(252\) | 23129.0 | − | 55171.7i | 0.364214 | − | 0.868791i | ||||
\(253\) | 24674.2 | 0.385479 | ||||||||
\(254\) | 28490.0 | − | 483.319i | 0.441595 | − | 0.00749146i | ||||
\(255\) | 53174.2 | + | 11636.7i | 0.817751 | + | 0.178958i | ||||
\(256\) | 64933.5 | − | 8866.17i | 0.990806 | − | 0.135287i | ||||
\(257\) | −27780.7 | + | 48117.6i | −0.420608 | + | 0.728514i | −0.995999 | − | 0.0893643i | \(-0.971516\pi\) |
0.575391 | + | 0.817878i | \(0.304850\pi\) | |||||||
\(258\) | 59952.4 | − | 68069.2i | 0.900673 | − | 1.02261i | ||||
\(259\) | 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 | \(-0.724890\pi\) |
0.334131 | + | 0.942527i | \(0.391557\pi\) | |||||||
\(264\) | 26870.4 | − | 32679.6i | 0.385537 | − | 0.468887i | ||||
\(265\) | −17573.7 | + | 30438.5i | −0.250248 | + | 0.433443i | ||||
\(266\) | −49744.9 | + | 29856.6i | −0.703049 | + | 0.421965i | ||||
\(267\) | −20891.4 | − | 65635.9i | −0.293053 | − | 0.920701i | ||||
\(268\) | −9114.67 | − | 4857.83i | −0.126903 | − | 0.0676352i | ||||
\(269\) | 54154.0 | 0.748386 | 0.374193 | − | 0.927351i | \(-0.377920\pi\) | ||||
0.374193 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(270\) | 39316.3 | + | 88556.7i | 0.539318 | + | 1.21477i | ||||
\(271\) | 94942.5i | 1.29277i | 0.763011 | + | 0.646386i | \(0.223720\pi\) | ||||
−0.763011 | + | 0.646386i | \(0.776280\pi\) | |||||||
\(272\) | −46489.6 | + | 3159.25i | −0.628374 | + | 0.0427017i | ||||
\(273\) | −119965. | + | 38184.0i | −1.60964 | + | 0.512338i | ||||
\(274\) | −29114.0 | + | 17474.0i | −0.387794 | + | 0.232751i | ||||
\(275\) | 30474.7 | + | 17594.6i | 0.402972 | + | 0.232656i | ||||
\(276\) | 8732.50 | − | 47578.4i | 0.114636 | − | 0.624585i | ||||
\(277\) | −54019.7 | − | 93564.9i | −0.704033 | − | 1.21942i | −0.967039 | − | 0.254627i | \(-0.918047\pi\) |
0.263006 | − | 0.964794i | \(-0.415286\pi\) | |||||||
\(278\) | 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 | 0.997413 | − | 0.0718805i | \(-0.0229000\pi\) |
−0.560957 | + | 0.827845i | \(0.689567\pi\) | |||||||
\(282\) | 26938.7 | − | 30585.8i | 0.338749 | − | 0.384611i | ||||
\(283\) | −39154.2 | − | 22605.7i | −0.488884 | − | 0.282257i | 0.235228 | − | 0.971940i | \(-0.424416\pi\) |
−0.724111 | + | 0.689683i | \(0.757750\pi\) | |||||||
\(284\) | 5192.58 | + | 152998.i | 0.0643793 | + | 1.89692i | ||||
\(285\) | 20088.2 | − | 91793.5i | 0.247316 | − | 1.13011i | ||||
\(286\) | −89022.0 | + | 1510.22i | −1.08834 | + | 0.0184632i | ||||
\(287\) | 51473.5i | 0.624914i | ||||||||
\(288\) | −53505.2 | − | 63379.1i | −0.645076 | − | 0.764119i | ||||
\(289\) | −50390.1 | −0.603323 | ||||||||
\(290\) | 1611.34 | + | 94983.0i | 0.0191598 | + | 1.12941i | ||||
\(291\) | −77193.4 | + | 84703.5i | −0.911579 | + | 1.00027i | ||||
\(292\) | −30368.2 | + | 1030.66i | −0.356167 | + | 0.0120879i | ||||
\(293\) | 35853.6 | − | 62100.3i | 0.417636 | − | 0.723366i | −0.578065 | − | 0.815990i | \(-0.696192\pi\) |
0.995701 | + | 0.0926242i | \(0.0295255\pi\) | |||||||
\(294\) | −1918.26 | + | 9537.40i | −0.0221928 | + | 0.110341i | ||||
\(295\) | 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 | ||||
\(300\) | 44712.5 | − | 52536.5i | 0.496806 | − | 0.583739i | ||||
\(301\) | 58153.4 | − | 100725.i | 0.641862 | − | 1.11174i | ||||
\(302\) | −7277.73 | − | 12125.6i | −0.0797962 | − | 0.132951i | ||||
\(303\) | 83333.8 | − | 91441.2i | 0.907687 | − | 0.995994i | ||||
\(304\) | 5453.74 | + | 80254.0i | 0.0590129 | + | 0.868400i | ||||
\(305\) | −28596.0 | −0.307401 | ||||||||
\(306\) | 34900.0 | + | 47538.8i | 0.372720 | + | 0.507698i | ||||
\(307\) | − | 95866.9i | − | 1.01717i | −0.861013 | − | 0.508583i | \(-0.830170\pi\) | ||
0.861013 | − | 0.508583i | \(-0.169830\pi\) | |||||||
\(308\) | 25515.2 | − | 47873.7i | 0.268966 | − | 0.504656i | ||||
\(309\) | 24997.2 | − | 114225.i | 0.261803 | − | 1.19632i | ||||
\(310\) | 77809.5 | + | 129641.i | 0.809673 | + | 1.34902i | ||||
\(311\) | 20844.0 | + | 12034.3i | 0.215506 | + | 0.124423i | 0.603868 | − | 0.797085i | \(-0.293626\pi\) |
−0.388362 | + | 0.921507i | \(0.626959\pi\) | |||||||
\(312\) | −28593.9 | + | 172193.i | −0.293741 | + | 1.76891i | ||||
\(313\) | 49654.5 | + | 86004.2i | 0.506839 | + | 0.877871i | 0.999969 | + | 0.00791525i | \(0.00251953\pi\) |
−0.493130 | + | 0.869956i | \(0.664147\pi\) | |||||||
\(314\) | −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 | 0.679402 | − | 0.733766i | \(-0.262239\pi\) |
−0.975161 | + | 0.221497i | \(0.928906\pi\) | |||||||
\(318\) | −36085.0 | + | 12163.4i | −0.356839 | + | 0.120282i | ||||
\(319\) | −45465.2 | − | 26249.4i | −0.446785 | − | 0.257951i | ||||
\(320\) | −55722.7 | + | 124171.i | −0.544167 | + | 1.21261i | ||||
\(321\) | 127713. | − | 40650.2i | 1.23944 | − | 0.394505i | ||||
\(322\) | −1052.08 | − | 62016.5i | −0.0101470 | − | 0.598129i | ||||
\(323\) | − | 57193.1i | − | 0.548200i | ||||||
\(324\) | −31449.0 | + | 100154.i | −0.299583 | + | 0.954070i | ||||
\(325\) | −145180. | −1.37449 | ||||||||
\(326\) | −23612.5 | + | 400.574i | −0.222181 | + | 0.00376919i | ||||
\(327\) | −20579.3 | − | 64655.1i | −0.192457 | − | 0.604654i | ||||
\(328\) | 63540.5 | + | 32493.3i | 0.590613 | + | 0.302028i | ||||
\(329\) | 26130.3 | − | 45259.0i | 0.241408 | − | 0.418132i | ||||
\(330\) | 28065.0 | + | 83259.7i | 0.257713 | + | 0.764552i | ||||
\(331\) | −79852.0 | + | 46102.6i | −0.728836 | + | 0.420794i | −0.817996 | − | 0.575223i | \(-0.804915\pi\) |
0.0891599 | + | 0.996017i | \(0.471582\pi\) | |||||||
\(332\) | 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 | ||||
\(336\) | −83283.1 | − | 66143.2i | −0.737698 | − | 0.585877i | ||||
\(337\) | −22954.2 | + | 39757.8i | −0.202117 | + | 0.350076i | −0.949210 | − | 0.314643i | \(-0.898115\pi\) |
0.747094 | + | 0.664719i | \(0.231449\pi\) | |||||||
\(338\) | 217002. | − | 130243.i | 1.89946 | − | 1.14004i | ||||
\(339\) | −8724.05 | − | 1909.18i | −0.0759135 | − | 0.0166130i | ||||
\(340\) | 45514.1 | − | 85397.5i | 0.393721 | − | 0.738733i | ||||
\(341\) | −83558.1 | −0.718588 | ||||||||
\(342\) | 82065.2 | − | 60247.1i | 0.701628 | − | 0.515091i | ||||
\(343\) | 123305.i | 1.04807i | ||||||||
\(344\) | −87627.4 | − | 135370.i | −0.740497 | − | 1.14395i | ||||
\(345\) | 74249.8 | + | 67666.6i | 0.623817 | + | 0.568508i | ||||
\(346\) | 20955.3 | − | 12577.2i | 0.175041 | − | 0.105059i | ||||
\(347\) | 131615. | + | 75987.9i | 1.09306 | + | 0.631081i | 0.934391 | − | 0.356250i | \(-0.115945\pi\) |
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(348\) | −66706.5 | + | 78379.1i | −0.550820 | + | 0.647205i | ||||
\(349\) | 93645.6 | + | 162199.i | 0.768841 | + | 1.33167i | 0.938192 | + | 0.346116i | \(0.112500\pi\) |
−0.169350 | + | 0.985556i | \(0.554167\pi\) | |||||||
\(350\) | 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 | 0.760408 | − | 0.649446i | \(-0.224999\pi\) |
−0.942640 | + | 0.333810i | \(0.891666\pi\) | |||||||
\(354\) | 35800.6 | + | 7200.58i | 0.285683 | + | 0.0574594i | ||||
\(355\) | −275326. | − | 158960.i | −2.18469 | − | 1.26133i | ||||
\(356\) | −122384. | + | 4153.56i | −0.965659 | + | 0.0327733i | ||||
\(357\) | 55890.5 | + | 50935.1i | 0.438532 | + | 0.399651i | ||||
\(358\) | −46132.5 | + | 782.617i | −0.359949 | + | 0.00610637i | ||||
\(359\) | − | 71504.2i | − | 0.554808i | −0.960753 | − | 0.277404i | \(-0.910526\pi\) | ||
0.960753 | − | 0.277404i | \(-0.0894740\pi\) | |||||||
\(360\) | 170480. | − | 24650.1i | 1.31543 | − | 0.190202i | ||||
\(361\) | 31589.8 | 0.242400 | ||||||||
\(362\) | −1733.13 | − | 102162.i | −0.0132256 | − | 0.779601i | ||||
\(363\) | 81289.1 | + | 17789.4i | 0.616906 | + | 0.135005i | ||||
\(364\) | 7591.61 | + | 223685.i | 0.0572969 | + | 1.68824i | ||||
\(365\) | 31551.4 | − | 54648.7i | 0.236828 | − | 0.410199i | ||||
\(366\) | −23249.8 | − | 20477.4i | −0.173563 | − | 0.152867i | ||||
\(367\) | −57406.0 | + | 33143.4i | −0.426211 | + | 0.246073i | −0.697731 | − | 0.716360i | \(-0.745807\pi\) |
0.271520 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(368\) | −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 | ||||
\(372\) | −29572.3 | + | 161122.i | −0.213697 | + | 1.16431i | ||||
\(373\) | −71784.3 | + | 124334.i | −0.515955 | + | 0.893660i | 0.483873 | + | 0.875138i | \(0.339229\pi\) |
−0.999828 | + | 0.0185223i | \(0.994104\pi\) | |||||||
\(374\) | 27520.9 | + | 45853.3i | 0.196752 | + | 0.327814i | ||||
\(375\) | −13235.1 | − | 41581.6i | −0.0941165 | − | 0.295691i | ||||
\(376\) | −39374.0 | − | 60826.4i | −0.278506 | − | 0.430245i | ||||
\(377\) | 216594. | 1.52393 | ||||||||
\(378\) | −14210.9 | + | 133851.i | −0.0994574 | + | 0.936781i | ||||
\(379\) | − | 183178.i | − | 1.27525i | −0.770348 | − | 0.637624i | \(-0.779917\pi\) | ||
0.770348 | − | 0.637624i | \(-0.220083\pi\) | |||||||
\(380\) | −147420. | − | 78570.1i | −1.02091 | − | 0.544114i | ||||
\(381\) | −61091.7 | + | 19445.1i | −0.420855 | + | 0.133955i | ||||
\(382\) | −80419.9 | − | 133990.i | −0.551108 | − | 0.918218i | ||||
\(383\) | 15175.9 | + | 8761.79i | 0.103456 | + | 0.0597303i | 0.550835 | − | 0.834614i | \(-0.314309\pi\) |
−0.447379 | + | 0.894344i | \(0.647643\pi\) | |||||||
\(384\) | −134223. | + | 61053.5i | −0.910256 | + | 0.414046i | ||||
\(385\) | 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 | 0.710646 | − | 0.703549i | \(-0.248403\pi\) |
−0.964615 | + | 0.263663i | \(0.915069\pi\) | |||||||
\(390\) | −272028. | − | 239590.i | −1.78848 | − | 1.57521i | ||||
\(391\) | 52952.8 | + | 30572.3i | 0.346366 | + | 0.199974i | ||||
\(392\) | 15398.3 | + | 7874.40i | 0.100208 | + | 0.0512443i | ||||
\(393\) | −13390.5 | + | 61188.0i | −0.0866983 | + | 0.396169i | ||||
\(394\) | −1431.80 | − | 84399.8i | −0.00922340 | − | 0.543687i | ||||
\(395\) | 259679.i | 1.66434i | ||||||||
\(396\) | −36803.6 | + | 87790.9i | −0.234693 | + | 0.559834i | ||||
\(397\) | −73295.7 | −0.465047 | −0.232524 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232524 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(398\) | −21788.8 | + | 369.636i | −0.137552 | + | 0.00233350i | ||||
\(399\) | 87928.1 | − | 96482.5i | 0.552309 | − | 0.606042i | ||||
\(400\) | −68382.4 | − | 101811.i | −0.427390 | − | 0.636321i | ||||
\(401\) | −142274. | + | 246426.i | −0.884784 | + | 1.53249i | −0.0388226 | + | 0.999246i | \(0.512361\pi\) |
−0.845961 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(402\) | 22782.6 | + | 4582.28i | 0.140978 | + | 0.0283550i | ||||
\(403\) | 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 | ||||
\(408\) | 98157.5 | − | 36839.5i | 0.589662 | − | 0.221306i | ||||
\(409\) | 56577.0 | − | 97994.2i | 0.338215 | − | 0.585806i | −0.645882 | − | 0.763437i | \(-0.723510\pi\) |
0.984097 | + | 0.177632i | \(0.0568435\pi\) | |||||||
\(410\) | −127078. | + | 76271.3i | −0.755965 | + | 0.453725i | ||||
\(411\) | 51461.4 | − | 56468.0i | 0.304648 | − | 0.334286i | ||||
\(412\) | −183445. | − | 97770.4i | −1.08072 | − | 0.575988i | ||||
\(413\) | 46823.9 | 0.274516 | ||||||||
\(414\) | 11912.7 | + | 108186.i | 0.0695040 | + | 0.631203i | ||||
\(415\) | 270593.i | 1.57116i | ||||||||
\(416\) | 280916. | + | 131833.i | 1.62327 | + | 0.761793i | ||||
\(417\) | −41065.4 | + | 187649.i | −0.236159 | + | 1.07913i | ||||
\(418\) | 79155.6 | − | 47508.7i | 0.453032 | − | 0.271907i | ||||
\(419\) | 237314. | + | 137013.i | 1.35175 | + | 0.780431i | 0.988494 | − | 0.151260i | \(-0.0483331\pi\) |
0.363252 | + | 0.931691i | \(0.381666\pi\) | |||||||
\(420\) | 208070. | − | 74089.2i | 1.17953 | − | 0.420007i | ||||
\(421\) | −6241.89 | − | 10811.3i | −0.0352170 | − | 0.0609976i | 0.847880 | − | 0.530189i | \(-0.177879\pi\) |
−0.883097 | + | 0.469191i | \(0.844546\pi\) | |||||||
\(422\) | −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 | ||||
\(426\) | −110022. | − | 326400.i | −0.606263 | − | 1.79858i | ||||
\(427\) | −34403.6 | − | 19862.9i | −0.188690 | − | 0.108940i | ||||
\(428\) | −8081.91 | − | 238132.i | −0.0441191 | − | 1.29996i | ||||
\(429\) | 190892. | − | 60759.5i | 1.03722 | − | 0.330141i | ||||
\(430\) | 334838. | − | 5680.37i | 1.81091 | − | 0.0307213i | ||||
\(431\) | − | 119855.i | − | 0.645211i | −0.946533 | − | 0.322606i | \(-0.895441\pi\) | ||
0.946533 | − | 0.322606i | \(-0.104559\pi\) | |||||||
\(432\) | 156259. | + | 102038.i | 0.837293 | + | 0.546755i | ||||
\(433\) | −282465. | −1.50657 | −0.753284 | − | 0.657696i | \(-0.771531\pi\) | ||||
−0.753284 | + | 0.657696i | \(0.771531\pi\) | |||||||
\(434\) | 3562.83 | + | 210016.i | 0.0189154 | + | 1.11500i | ||||
\(435\) | −64828.1 | − | 203674.i | −0.342598 | − | 1.07636i | ||||
\(436\) | −120555. | + | 4091.49i | −0.634179 | + | 0.0215233i | ||||
\(437\) | 52776.3 | − | 91411.2i | 0.276360 | − | 0.478670i | ||||
\(438\) | 64786.2 | − | 21838.0i | 0.337703 | − | 0.113832i | ||||
\(439\) | −148459. | + | 85712.8i | −0.770331 | + | 0.444751i | −0.832993 | − | 0.553284i | \(-0.813374\pi\) |
0.0626618 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(440\) | 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 | \(-0.734498\pi\) |
0.305535 | + | 0.952181i | \(0.401165\pi\) | |||||||
\(444\) | 48712.5 | + | 136803.i | 0.247101 | + | 0.693951i | ||||
\(445\) | 127152. | − | 220234.i | 0.642102 | − | 1.11215i | ||||
\(446\) | −52136.4 | − | 86866.0i | −0.262103 | − | 0.436697i | ||||
\(447\) | −111953. | − | 24499.9i | −0.560298 | − | 0.122616i | ||||
\(448\) | −153289. | + | 110683.i | −0.763757 | + | 0.551476i | ||||
\(449\) | 252767. | 1.25380 | 0.626898 | − | 0.779101i | \(-0.284324\pi\) | ||||
0.626898 | + | 0.779101i | \(0.284324\pi\) | |||||||
\(450\) | −62431.5 | + | 142113.i | −0.308304 | + | 0.701794i | ||||
\(451\) | − | 81906.2i | − | 0.402683i | ||||||
\(452\) | −7467.29 | + | 14010.8i | −0.0365499 | + | 0.0685780i | ||||
\(453\) | 23518.2 | + | 21433.1i | 0.114606 | + | 0.104445i | ||||
\(454\) | 200099. | + | 333390.i | 0.970806 | + | 1.61749i | ||||
\(455\) | −402530. | − | 232401.i | −1.94435 | − | 1.12257i | ||||
\(456\) | −63595.2 | − | 169447.i | −0.305840 | − | 0.814900i | ||||
\(457\) | 9489.80 | + | 16436.8i | 0.0454386 | + | 0.0787019i | 0.887850 | − | 0.460133i | \(-0.152198\pi\) |
−0.842412 | + | 0.538835i | \(0.818865\pi\) | |||||||
\(458\) | 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 | 0.998789 | − | 0.0492038i | \(-0.0156684\pi\) |
−0.542006 | + | 0.840375i | \(0.682335\pi\) | |||||||
\(462\) | −24067.8 | + | 119663.i | −0.112760 | + | 0.560630i | ||||
\(463\) | −86227.9 | − | 49783.7i | −0.402240 | − | 0.232234i | 0.285210 | − | 0.958465i | \(-0.407937\pi\) |
−0.687450 | + | 0.726232i | \(0.741270\pi\) | |||||||
\(464\) | 102020. | + | 151892.i | 0.473858 | + | 0.705504i | ||||
\(465\) | −251444. | − | 229150.i | −1.16288 | − | 1.05978i | ||||
\(466\) | −866.698 | − | 51088.8i | −0.00399113 | − | 0.235263i | ||||
\(467\) | − | 126990.i | − | 0.582287i | −0.956679 | − | 0.291144i | \(-0.905964\pi\) | ||
0.956679 | − | 0.291144i | \(-0.0940358\pi\) | |||||||
\(468\) | −49601.6 | − | 389594.i | −0.226466 | − | 1.77877i | ||||
\(469\) | 29797.6 | 0.135468 | ||||||||
\(470\) | 150454. | − | 2552.38i | 0.681096 | − | 0.0115545i | ||||
\(471\) | 261482. | + | 57223.0i | 1.17869 | + | 0.257946i | ||||
\(472\) | 29558.2 | − | 57800.8i | 0.132676 | − | 0.259448i | ||||
\(473\) | −92535.3 | + | 160276.i | −0.413605 | + | 0.716384i | ||||
\(474\) | −185954. | + | 211130.i | −0.827655 | + | 0.939710i | ||||
\(475\) | 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 | \(-0.627773\pi\) |
0.601828 | + | 0.798626i | \(0.294439\pi\) | |||||||
\(480\) | 39888.8 | − | 303618.i | 0.173129 | − | 1.31778i | ||||
\(481\) | 152800. | − | 264657.i | 0.660439 | − | 1.14391i | ||||
\(482\) | −34912.3 | + | 20954.1i | −0.150274 | + | 0.0901935i | ||||
\(483\) | 42327.7 | + | 132983.i | 0.181439 | + | 0.570037i | ||||
\(484\) | 69578.9 | − | 130550.i | 0.297021 | − | 0.557295i | ||||
\(485\) | −423105. | −1.79872 | ||||||||
\(486\) | 3085.61 | − | 236176.i | 0.0130638 | − | 0.999915i | ||||
\(487\) | 274913.i | 1.15914i | 0.814921 | + | 0.579572i | \(0.196780\pi\) | ||||
−0.814921 | + | 0.579572i | \(0.803220\pi\) | |||||||
\(488\) | −46237.1 | + | 29930.1i | −0.194156 | + | 0.125681i | ||||
\(489\) | 50632.7 | − | 16116.1i | 0.211745 | − | 0.0673971i | ||||
\(490\) | −30795.9 | + | 18483.5i | −0.128263 | + | 0.0769825i | ||||
\(491\) | −28037.6 | − | 16187.5i | −0.116299 | − | 0.0671455i | 0.440722 | − | 0.897644i | \(-0.354723\pi\) |
−0.557021 | + | 0.830498i | \(0.688056\pi\) | |||||||
\(492\) | −157937. | − | 28987.7i | −0.652460 | − | 0.119752i | ||||
\(493\) | −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 | ||||
\(498\) | −193770. | + | 220004.i | −0.781316 | + | 0.887097i | ||||
\(499\) | 251446. | + | 145172.i | 1.00982 | + | 0.583019i | 0.911139 | − | 0.412100i | \(-0.135204\pi\) |
0.0986806 | + | 0.995119i | \(0.468538\pi\) | |||||||
\(500\) | −77532.4 | + | 2631.36i | −0.310130 | + | 0.0105254i | ||||
\(501\) | −39569.8 | + | 180815.i | −0.157648 | + | 0.720376i | ||||
\(502\) | −87380.0 | + | 1482.36i | −0.346740 | + | 0.00588229i | ||||
\(503\) | 9486.90i | 0.0374963i | 0.999824 | + | 0.0187481i | \(0.00596807\pi\) | ||||
−0.999824 | + | 0.0187481i | \(0.994032\pi\) | |||||||
\(504\) | 222224. | + | 88759.5i | 0.874844 | + | 0.349425i | ||||
\(505\) | 456761. | 1.79104 | ||||||||
\(506\) | 1674.10 | + | 98682.4i | 0.00653854 | + | 0.385424i | ||||
\(507\) | −383568. | + | 420885.i | −1.49220 | + | 1.63737i | ||||
\(508\) | 3865.99 | + | 113911.i | 0.0149808 | + | 0.441405i | ||||
\(509\) | 146376. | − | 253530.i | 0.564980 | − | 0.978575i | −0.432071 | − | 0.901839i | \(-0.642217\pi\) |
0.997052 | − | 0.0767350i | \(-0.0244496\pi\) | |||||||
\(510\) | −42932.4 | + | 213456.i | −0.165061 | + | 0.820669i | ||||
\(511\) | 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 | ||||
\(516\) | 276305. | + | 235157.i | 1.03774 | + | 0.883197i | ||||
\(517\) | −41579.3 | + | 72017.4i | −0.155559 | + | 0.269437i | ||||
\(518\) | 95822.3 | + | 159652.i | 0.357114 | + | 0.594999i | ||||
\(519\) | −37040.1 | + | 40643.7i | −0.137511 | + | 0.150889i | ||||
\(520\) | −540985. | + | 350189.i | −2.00068 | + | 1.29508i | ||||
\(521\) | −344253. | −1.26824 | −0.634120 | − | 0.773234i | \(-0.718638\pi\) | ||||
−0.634120 | + | 0.773234i | \(0.718638\pi\) | |||||||
\(522\) | 93141.6 | − | 212019.i | 0.341824 | − | 0.778096i | ||||
\(523\) | 79326.1i | 0.290010i | 0.989431 | + | 0.145005i | \(0.0463198\pi\) | ||||
−0.989431 | + | 0.145005i | \(0.953680\pi\) | |||||||
\(524\) | 98267.5 | + | 52373.4i | 0.357888 | + | 0.190743i | ||||
\(525\) | −42549.1 | + | 194429.i | −0.154373 | + | 0.705411i | ||||
\(526\) | −51797.9 | − | 86302.0i | −0.187215 | − | 0.311924i | ||||
\(527\) | −179323. | − | 103532.i | −0.645675 | − | 0.372780i | ||||
\(528\) | 132523. | + | 105249.i | 0.475359 | + | 0.377529i | ||||
\(529\) | −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 | ||||
\(534\) | 261088. | − | 88007.0i | 0.915598 | − | 0.308628i | ||||
\(535\) | 428527. | + | 247410.i | 1.49717 | + | 0.864391i | ||||
\(536\) | 18810.1 | − | 36783.1i | 0.0654729 | − | 0.128032i | ||||
\(537\) | 98923.0 | − | 31486.5i | 0.343043 | − | 0.109188i | ||||
\(538\) | 3674.26 | + | 216585.i | 0.0126942 | + | 0.748278i | ||||
\(539\) | − | 19849.0i | − | 0.0683223i | ||||||
\(540\) | −351508. | + | 163251.i | −1.20545 | + | 0.559845i | ||||
\(541\) | 167330. | 0.571715 | 0.285857 | − | 0.958272i | \(-0.407722\pi\) | ||||
0.285857 | + | 0.958272i | \(0.407722\pi\) | |||||||
\(542\) | −379715. | + | 6441.69i | −1.29259 | + | 0.0219281i | ||||
\(543\) | 69728.0 | + | 219068.i | 0.236487 | + | 0.742985i | ||||
\(544\) | −15789.4 | − | 185717.i | −0.0533541 | − | 0.627559i | ||||
\(545\) | 125252. | − | 216943.i | 0.421689 | − | 0.730387i | ||||
\(546\) | −160854. | − | 477200.i | −0.539567 | − | 1.60072i | ||||
\(547\) | −246877. | + | 142535.i | −0.825100 | + | 0.476372i | −0.852172 | − | 0.523262i | \(-0.824715\pi\) |
0.0270722 | + | 0.999633i | \(0.491382\pi\) | |||||||
\(548\) | −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 | ||||
\(552\) | 190879. | + | 31696.9i | 0.626439 | + | 0.104025i | ||||
\(553\) | −180374. | + | 312417.i | −0.589827 | + | 1.02161i | ||||
\(554\) | 370541. | − | 222396.i | 1.20730 | − | 0.724616i | ||||
\(555\) | −294604. | − | 64471.6i | −0.956429 | − | 0.209306i | ||||
\(556\) | 301363. | + | 160617.i | 0.974857 | + | 0.519568i | ||||
\(557\) | 51271.9 | 0.165260 | 0.0826302 | − | 0.996580i | \(-0.473668\pi\) | ||||
0.0826302 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(558\) | −40342.0 | − | 366366.i | −0.129565 | − | 1.17665i | ||||
\(559\) | − | 763547.i | − | 2.44350i | ||||||
\(560\) | −26621.7 | − | 391749.i | −0.0848905 | − | 1.24920i | ||||
\(561\) | −88934.6 | − | 81049.4i | −0.282582 | − | 0.257528i | ||||
\(562\) | −236394. | + | 141882.i | −0.748452 | + | 0.449216i | ||||
\(563\) | −2488.80 | − | 1436.91i | −0.00785187 | − | 0.00453328i | 0.496069 | − | 0.868283i | \(-0.334776\pi\) |
−0.503921 | + | 0.863750i | \(0.668110\pi\) | |||||||
\(564\) | 124153. | + | 105664.i | 0.390302 | + | 0.332176i | ||||
\(565\) | −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 | 0.940395 | − | 0.340085i | \(-0.110456\pi\) |
−0.764720 | + | 0.644363i | \(0.777123\pi\) | |||||||
\(570\) | 368484. | + | 74113.3i | 1.13415 | + | 0.228111i | ||||
\(571\) | −27258.4 | − | 15737.7i | −0.0836043 | − | 0.0482689i | 0.457615 | − | 0.889150i | \(-0.348704\pi\) |
−0.541219 | + | 0.840881i | \(0.682037\pi\) | |||||||
\(572\) | −12080.0 | − | 355934.i | −0.0369211 | − | 1.08787i | ||||
\(573\) | 259880. | + | 236838.i | 0.791522 | + | 0.721344i | ||||
\(574\) | −205864. | + | 3492.39i | −0.624824 | + | 0.0105998i | ||||
\(575\) | 160935.i | 0.486760i | ||||||||
\(576\) | 249850. | − | 218290.i | 0.753067 | − | 0.657944i | ||||
\(577\) | −654654. | −1.96635 | −0.983174 | − | 0.182671i | \(-0.941526\pi\) | ||||
−0.983174 | + | 0.182671i | \(0.941526\pi\) | |||||||
\(578\) | −3418.89 | − | 201531.i | −0.0102336 | − | 0.603236i | ||||
\(579\) | 244682. | + | 53546.6i | 0.729870 | + | 0.159726i | ||||
\(580\) | −379768. | + | 12888.9i | −1.12892 | + | 0.0383142i | ||||
\(581\) | −187955. | + | 325548.i | −0.556803 | + | 0.964412i | ||||
\(582\) | −344003. | − | 302982.i | −1.01558 | − | 0.894482i | ||||
\(583\) | 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 | 0.629716 | − | 0.776825i | \(-0.283171\pi\) |
0.987609 | − | 0.156937i | \(-0.0501620\pi\) | |||||||
\(588\) | −38274.3 | − | 7024.84i | −0.110701 | − | 0.0203180i | ||||
\(589\) | −178725. | + | 309561.i | −0.515175 | + | 0.892309i | ||||
\(590\) | 69381.6 | + | 115599.i | 0.199315 | + | 0.332085i | ||||
\(591\) | 57604.8 | + | 180980.i | 0.164924 | + | 0.518151i | ||||
\(592\) | 257569. | − | 17503.3i | 0.734937 | − | 0.0499433i | ||||
\(593\) | −183090. | −0.520661 | −0.260330 | − | 0.965520i | \(-0.583831\pi\) | ||||
−0.260330 | + | 0.965520i | \(0.583831\pi\) | |||||||
\(594\) | 22612.7 | − | 212988.i | 0.0640886 | − | 0.603645i | ||||
\(595\) | 279180.i | 0.788589i | ||||||||
\(596\) | −95825.2 | + | 179795.i | −0.269766 | + | 0.506158i | ||||
\(597\) | 46722.1 | − | 14871.3i | 0.131091 | − | 0.0417255i | ||||
\(598\) | −209549. | − | 349135.i | −0.585980 | − | 0.976318i | ||||
\(599\) | 24104.3 | + | 13916.6i | 0.0671800 | + | 0.0387864i | 0.533214 | − | 0.845981i | \(-0.320984\pi\) |
−0.466034 | + | 0.884767i | \(0.654317\pi\) | |||||||
\(600\) | 213149. | + | 175260.i | 0.592082 | + | 0.486833i | ||||
\(601\) | 135764. | + | 235150.i | 0.375868 | + | 0.651022i | 0.990457 | − | 0.137826i | \(-0.0440113\pi\) |
−0.614589 | + | 0.788848i | \(0.710678\pi\) | |||||||
\(602\) | 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 | ||||
\(606\) | 371366. | + | 327083.i | 1.01125 | + | 0.890662i | ||||
\(607\) | 86991.8 | + | 50224.8i | 0.236103 | + | 0.136314i | 0.613384 | − | 0.789785i | \(-0.289808\pi\) |
−0.377281 | + | 0.926099i | \(0.623141\pi\) | |||||||
\(608\) | −320600. | + | 27256.9i | −0.867274 | + | 0.0737343i | ||||
\(609\) | 63479.0 | − | 290068.i | 0.171157 | − | 0.782106i | ||||
\(610\) | −1940.19 | − | 114368.i | −0.00521417 | − | 0.307357i | ||||
\(611\) | − | 343088.i | − | 0.919015i | ||||||
\(612\) | −187760. | + | 142805.i | −0.501303 | + | 0.381278i | ||||
\(613\) | 458408. | 1.21992 | 0.609960 | − | 0.792432i | \(-0.291185\pi\) | ||||
0.609960 | + | 0.792432i | \(0.291185\pi\) | |||||||
\(614\) | 383412. | − | 6504.41i | 1.01702 | − | 0.0172533i | ||||
\(615\) | 224620. | − | 246473.i | 0.593880 | − | 0.651657i | ||||
\(616\) | 193198. | + | 98797.8i | 0.509146 | + | 0.260367i | ||||
\(617\) | 237317. | − | 411046.i | 0.623389 | − | 1.07974i | −0.365461 | − | 0.930827i | \(-0.619089\pi\) |
0.988850 | − | 0.148915i | \(-0.0475781\pi\) | |||||||
\(618\) | 458532. | + | 92224.6i | 1.20058 | + | 0.241474i | ||||
\(619\) | −5714.30 | + | 3299.15i | −0.0149136 | + | 0.00861036i | −0.507438 | − | 0.861688i | \(-0.669407\pi\) |
0.492525 | + | 0.870298i | \(0.336074\pi\) | |||||||
\(620\) | −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 | ||||
\(624\) | −690611. | − | 102676.i | −1.77364 | − | 0.263694i | ||||
\(625\) | 230266. | − | 398833.i | 0.589481 | − | 1.02101i | ||||
\(626\) | −340598. | + | 204425.i | −0.869148 | + | 0.521657i | ||||
\(627\) | −139914. | + | 153526.i | −0.355898 | + | 0.390523i | ||||
\(628\) | 223814. | − | 419938.i | 0.567502 | − | 1.06479i | ||||
\(629\) | −183557. | −0.463948 | ||||||||
\(630\) | −400590. | + | 294088.i | −1.00930 | + | 0.740962i | ||||
\(631\) | 102946.i | 0.258553i | 0.991609 | + | 0.129277i | \(0.0412655\pi\) | ||||
−0.991609 | + | 0.129277i | \(0.958734\pi\) | |||||||
\(632\) | 271794. | + | 419877.i | 0.680465 | + | 1.05121i | ||||
\(633\) | 133157. | − | 608464.i | 0.332320 | − | 1.51854i | ||||
\(634\) | 203864. | − | 122358.i | 0.507179 | − | 0.304405i | ||||
\(635\) | −204987. | − | 118349.i | −0.508368 | − | 0.293506i | ||||
\(636\) | −51095.1 | − | 143494.i | −0.126318 | − | 0.354747i | ||||
\(637\) | 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 | 0.507356 | − | 0.861736i | \(-0.330623\pi\) |
−0.999964 | + | 0.00851530i | \(0.997289\pi\) | |||||||
\(642\) | 171242. | + | 508020.i | 0.415471 | + | 1.23257i | ||||
\(643\) | −426111. | − | 246015.i | −1.03063 | − | 0.595032i | −0.113462 | − | 0.993542i | \(-0.536194\pi\) |
−0.917164 | + | 0.398510i | \(0.869527\pi\) | |||||||
\(644\) | 247959. | − | 8415.43i | 0.597871 | − | 0.0202911i | ||||
\(645\) | −718001. | + | 228535.i | −1.72586 | + | 0.549329i | ||||
\(646\) | 228740. | − | 3880.46i | 0.548121 | − | 0.00929861i | ||||
\(647\) | 306912.i | 0.733171i | 0.930384 | + | 0.366586i | \(0.119473\pi\) | ||||
−0.930384 | + | 0.366586i | \(0.880527\pi\) | |||||||
\(648\) | −402694. | − | 118983.i | −0.959015 | − | 0.283356i | ||||
\(649\) | −74507.5 | −0.176893 | ||||||||
\(650\) | −9850.24 | − | 580637.i | −0.0233142 | − | 1.37429i | ||||
\(651\) | −143341. | − | 450343.i | −0.338227 | − | 1.06263i | ||||
\(652\) | −3204.13 | − | 94409.1i | −0.00753729 | − | 0.222085i | ||||
\(653\) | −97661.8 | + | 169155.i | −0.229033 | + | 0.396697i | −0.957522 | − | 0.288361i | \(-0.906890\pi\) |
0.728489 | + | 0.685058i | \(0.240223\pi\) | |||||||
\(654\) | 257187. | − | 86692.0i | 0.601303 | − | 0.202686i | ||||
\(655\) | −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 | −0.566279 | + | 0.824213i | \(0.691618\pi\) |
−0.996929 | + | 0.0783055i | \(0.975049\pi\) | |||||||
\(660\) | −331087. | + | 117893.i | −0.760071 | + | 0.270645i | ||||
\(661\) | −371075. | + | 642721.i | −0.849295 | + | 1.47102i | 0.0325431 | + | 0.999470i | \(0.489639\pi\) |
−0.881838 | + | 0.471552i | \(0.843694\pi\) | |||||||
\(662\) | −189802. | − | 316234.i | −0.433096 | − | 0.721594i | ||||
\(663\) | 484953. | + | 106128.i | 1.10325 | + | 0.241436i | ||||
\(664\) | 283217. | + | 437524.i | 0.642367 | + | 0.992352i | ||||
\(665\) | 481943. | 1.08981 | ||||||||
\(666\) | −193358. | − | 263382.i | −0.435927 | − | 0.593797i | ||||
\(667\) | − | 240099.i | − | 0.539682i | ||||||
\(668\) | 290388. | + | 154768.i | 0.650767 | + | 0.346838i | ||||
\(669\) | 168481. | + | 153543.i | 0.376442 | + | 0.343065i | ||||
\(670\) | 44152.8 | + | 73564.3i | 0.0983577 | + | 0.163877i | ||||
\(671\) | 54744.0 | + | 31606.5i | 0.121588 | + | 0.0701990i | ||||
\(672\) | 258884. | − | 337572.i | 0.573280 | − | 0.747529i | ||||
\(673\) | −211601. | − | 366503.i | −0.467183 | − | 0.809185i | 0.532114 | − | 0.846673i | \(-0.321398\pi\) |
−0.999297 | + | 0.0374878i | \(0.988064\pi\) | |||||||
\(674\) | −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 | 0.647459 | − | 0.762100i | \(-0.275832\pi\) |
−0.983728 | + | 0.179665i | \(0.942498\pi\) | |||||||
\(678\) | 7043.72 | − | 35020.7i | 0.0153230 | − | 0.0761843i | ||||
\(679\) | −509034. | − | 293891.i | −1.10410 | − | 0.637450i | ||||
\(680\) | 344629. | + | 176236.i | 0.745305 | + | 0.381134i | ||||
\(681\) | −646626. | − | 589294.i | −1.39431 | − | 1.27069i | ||||
\(682\) | −5669.28 | − | 334184.i | −0.0121887 | − | 0.718484i | ||||
\(683\) | 760287.i | 1.62981i | 0.579597 | + | 0.814903i | \(0.303210\pi\) | ||||
−0.579597 | + | 0.814903i | \(0.696790\pi\) | |||||||
\(684\) | 246522. | + | 324126.i | 0.526918 | + | 0.692790i | ||||
\(685\) | 282065. | 0.601130 | ||||||||
\(686\) | −493148. | + | 8366.02i | −1.04792 | + | 0.0177775i | ||||
\(687\) | −755164. | − | 165261.i | −1.60003 | − | 0.350152i | ||||
\(688\) | 535457. | − | 359644.i | 1.13122 | − | 0.759794i | ||||
\(689\) | −160273. | + | 277602.i | −0.337616 | + | 0.584768i | ||||
\(690\) | −265590. | + | 301548.i | −0.557845 | + | 0.633370i | ||||
\(691\) | −313235. | + | 180846.i | −0.656016 | + | 0.378751i | −0.790757 | − | 0.612130i | \(-0.790313\pi\) |
0.134742 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | −317997. | − | 261470.i | −0.656455 | − | 0.539763i | ||||
\(697\) | 101485. | − | 175777.i | 0.208899 | − | 0.361824i | ||||
\(698\) | −642349. | + | 385534.i | −1.31844 | + | 0.791319i | ||||
\(699\) | 34869.3 | + | 109551.i | 0.0713656 | + | 0.224214i | ||||
\(700\) | 312252. | + | 166420.i | 0.637248 | + | 0.339633i | ||||
\(701\) | 878492. | 1.78773 | 0.893864 | − | 0.448337i | \(-0.147984\pi\) | ||||
0.893864 | + | 0.448337i | \(0.147984\pi\) | |||||||
\(702\) | 358567. | + | 807644.i | 0.727606 | + | 1.63887i | ||||
\(703\) | 316870.i | 0.641167i | ||||||||
\(704\) | 243918. | − | 176123.i | 0.492151 | − | 0.355361i | ||||
\(705\) | −322622. | + | 102688.i | −0.649107 | + | 0.206606i | ||||
\(706\) | 155761. | − | 93486.7i | 0.312499 | − | 0.187560i | ||||
\(707\) | 549525. | + | 317268.i | 1.09938 | + | 0.634728i | ||||
\(708\) | −26369.2 | + | 143670.i | −0.0526054 | + | 0.286616i | ||||
\(709\) | −431190. | − | 746844.i | −0.857781 | − | 1.48572i | −0.874041 | − | 0.485853i | \(-0.838509\pi\) |
0.0162593 | − | 0.999868i | \(-0.494824\pi\) | |||||||
\(710\) | 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 | ||||
\(714\) | −199919. | + | 226986.i | −0.392155 | + | 0.445248i | ||||
\(715\) | 640517. | + | 369803.i | 1.25291 | + | 0.723366i | ||||
\(716\) | −6260.03 | − | 184450.i | −0.0122110 | − | 0.359794i | ||||
\(717\) | −203836. | + | 931435.i | −0.396500 | + | 1.81182i | ||||
\(718\) | 285976. | − | 4851.44i | 0.554728 | − | 0.00941070i | ||||
\(719\) | − | 424008.i | − | 0.820193i | −0.912042 | − | 0.410097i | \(-0.865495\pi\) | ||
0.912042 | − | 0.410097i | \(-0.134505\pi\) | |||||||
\(720\) | 110153. | + | 680148.i | 0.212487 | + | 1.31201i | ||||
\(721\) | 599717. | 1.15365 | ||||||||
\(722\) | 2143.31 | + | 126341.i | 0.00411160 | + | 0.242365i | ||||
\(723\) | 61710.3 | − | 67714.0i | 0.118054 | − | 0.129539i | ||||
\(724\) | 408472. | − | 13863.1i | 0.779265 | − | 0.0264473i | ||||
\(725\) | 171209. | − | 296543.i | 0.325725 | − | 0.564172i | ||||
\(726\) | −65632.1 | + | 326317.i | −0.124521 | + | 0.619107i | ||||
\(727\) | 78836.8 | − | 45516.5i | 0.149163 | − | 0.0861191i | −0.423561 | − | 0.905868i | \(-0.639220\pi\) |
0.572724 | + | 0.819748i | \(0.305887\pi\) | |||||||
\(728\) | −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 | ||||
\(732\) | 80320.3 | − | 94375.1i | 0.149901 | − | 0.176131i | ||||
\(733\) | 6638.99 | − | 11499.1i | 0.0123565 | − | 0.0214020i | −0.859781 | − | 0.510663i | \(-0.829400\pi\) |
0.872138 | + | 0.489261i | \(0.162733\pi\) | |||||||
\(734\) | −136449. | − | 227342.i | −0.253267 | − | 0.421976i | ||||
\(735\) | 54434.2 | − | 59730.0i | 0.100762 | − | 0.110565i | ||||
\(736\) | 146139. | − | 311400.i | 0.269780 | − | 0.574862i | ||||
\(737\) | −47414.8 | −0.0872929 | ||||||||
\(738\) | 359123. | − | 39544.4i | 0.659373 | − | 0.0726060i | ||||
\(739\) | − | 622195.i | − | 1.13930i | −0.821888 | − | 0.569650i | \(-0.807079\pi\) | ||
0.821888 | − | 0.569650i | \(-0.192921\pi\) | |||||||
\(740\) | −252165. | + | 473132.i | −0.460490 | + | 0.864011i | ||||
\(741\) | 183206. | − | 837164.i | 0.333660 | − | 1.52466i | ||||
\(742\) | −100509. | − | 167461.i | −0.182557 | − | 0.304163i | ||||
\(743\) | 606588. | + | 350214.i | 1.09879 | + | 0.634389i | 0.935904 | − | 0.352255i | \(-0.114585\pi\) |
0.162890 | + | 0.986644i | \(0.447918\pi\) | |||||||
\(744\) | −646403. | − | 107340.i | −1.16777 | − | 0.193917i | ||||
\(745\) | −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 | ||||
\(750\) | 165404. | − | 55754.1i | 0.294052 | − | 0.0991185i | ||||
\(751\) | −73727.4 | − | 42566.6i | −0.130722 | − | 0.0754725i | 0.433213 | − | 0.901292i | \(-0.357380\pi\) |
−0.563935 | + | 0.825819i | \(0.690713\pi\) | |||||||
\(752\) | 240599. | − | 161600.i | 0.425459 | − | 0.285763i | ||||
\(753\) | 187371. | − | 59638.8i | 0.330455 | − | 0.105181i | ||||
\(754\) | 14695.6 | + | 866252.i | 0.0258490 | + | 1.52371i | ||||
\(755\) | 117477.i | 0.206091i | ||||||||
\(756\) | −536291. | − | 47753.7i | −0.938333 | − | 0.0835533i | ||||
\(757\) | 319528. | 0.557592 | 0.278796 | − | 0.960350i | \(-0.410065\pi\) | ||||
0.278796 | + | 0.960350i | \(0.410065\pi\) | |||||||
\(758\) | 732606. | − | 12428.3i | 1.27506 | − | 0.0216309i | ||||
\(759\) | −67353.0 | − | 211607.i | −0.116916 | − | 0.367321i | ||||
\(760\) | 304233. | − | 594925.i | 0.526719 | − | 1.03000i | ||||
\(761\) | −376888. | + | 652790.i | −0.650794 | + | 1.12721i | 0.332137 | + | 0.943231i | \(0.392230\pi\) |
−0.982931 | + | 0.183977i | \(0.941103\pi\) | |||||||
\(762\) | −81914.0 | − | 243012.i | −0.141074 | − | 0.418522i | ||||
\(763\) | 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 | ||||
\(768\) | −253286. | − | 532671.i | −0.429426 | − | 0.903102i | ||||
\(769\) | −425156. | + | 736392.i | −0.718945 | + | 1.24525i | 0.242473 | + | 0.970158i | \(0.422041\pi\) |
−0.961418 | + | 0.275091i | \(0.911292\pi\) | |||||||
\(770\) | −386387. | + | 231907.i | −0.651690 | + | 0.391140i | ||||
\(771\) | 488492. | + | 106902.i | 0.821768 | + | 0.179837i | ||||
\(772\) | 209434. | − | 392958.i | 0.351409 | − | 0.659344i | ||||
\(773\) | 13034.7 | 0.0218143 | 0.0109071 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109071 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(774\) | −747417. | − | 328346.i | −1.24762 | − | 0.548088i | ||||
\(775\) | − | 545000.i | − | 0.907388i | ||||||
\(776\) | −684122. | + | 442844.i | −1.13608 | + | 0.735407i | ||||
\(777\) | −309653. | − | 282199.i | −0.512901 | − | 0.467426i | ||||
\(778\) | 263610. | − | 158217.i | 0.435515 | − | 0.261393i | ||||
\(779\) | −303441. | − | 175192.i | −0.500033 | − | 0.288694i | ||||
\(780\) | 939766. | − | 1.10421e6i | 1.54465 | − | 1.81494i | ||||
\(781\) | 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 | ||||
\(786\) | −245625. | − | 49402.6i | −0.397583 | − | 0.0799659i | ||||
\(787\) | −473891. | − | 273601.i | −0.765120 | − | 0.441742i | 0.0660112 | − | 0.997819i | \(-0.478973\pi\) |
−0.831131 | + | 0.556077i | \(0.812306\pi\) | |||||||
\(788\) | 337454. | − | 11452.8i | 0.543452 | − | 0.0184441i | ||||
\(789\) | 167387. | + | 152546.i | 0.268885 | + | 0.245045i | ||||
\(790\) | −1.03857e6 | + | 17618.8i | −1.66410 | + | 0.0282307i | ||||
\(791\) | − | 45803.8i | − | 0.0732064i | ||||||
\(792\) | −353610. | − | 141237.i | −0.563734 | − | 0.225163i | ||||
\(793\) | −260798. | −0.414723 | ||||||||
\(794\) | −4972.99 | − | 293140.i | −0.00788818 | − | 0.464981i | ||||
\(795\) | 309014. | + | 67624.9i | 0.488926 | + | 0.106997i | ||||
\(796\) | −2956.66 | − | 87117.4i | −0.00466633 | − | 0.137492i | ||||
\(797\) | 104227. | − | 180527.i | 0.164083 | − | 0.284201i | −0.772246 | − | 0.635324i | \(-0.780867\pi\) |
0.936329 | + | 0.351123i | \(0.114200\pi\) | |||||||
\(798\) | 391840. | + | 345116.i | 0.615323 | + | 0.541950i | ||||
\(799\) | −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 | ||||
\(804\) | −16780.7 | + | 91428.4i | −0.0259596 | + | 0.141439i | ||||
\(805\) | −257620. | + | 446211.i | −0.397547 | + | 0.688571i | ||||
\(806\) | 709629. | + | 1.18233e6i | 1.09235 | + | 1.81999i | ||||
\(807\) | −147824. | − | 464427.i | −0.226985 | − | 0.713133i | ||||
\(808\) | 738541. | − | 478071.i | 1.13123 | − | 0.732267i | ||||
\(809\) | 844500. | 1.29034 | 0.645168 | − | 0.764041i | \(-0.276787\pi\) | ||||
0.645168 | + | 0.764041i | \(0.276787\pi\) | |||||||
\(810\) | 652146. | − | 578912.i | 0.993973 | − | 0.882353i | ||||
\(811\) | 769174.i | 1.16945i | 0.811230 | + | 0.584727i | \(0.198798\pi\) | ||||
−0.811230 | + | 0.584727i | \(0.801202\pi\) | |||||||
\(812\) | −465848. | − | 248282.i | −0.706532 | − | 0.376559i | ||||
\(813\) | 814232. | − | 259164.i | 1.23188 | − | 0.392098i | ||||
\(814\) | −152475. | − | 254044.i | −0.230118 | − | 0.383407i | ||||
\(815\) | 169893. | + | 98087.6i | 0.255776 | + | 0.147672i | ||||
\(816\) | 153997. | + | 390074.i | 0.231276 | + | 0.585823i | ||||
\(817\) | 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 | 0.520708 | − | 0.853735i | \(-0.325668\pi\) |
−0.999710 | + | 0.0240788i | \(0.992335\pi\) | |||||||
\(822\) | 229331. | + | 201985.i | 0.339406 | + | 0.298934i | ||||
\(823\) | −202697. | − | 117027.i | −0.299260 | − | 0.172778i | 0.342851 | − | 0.939390i | \(-0.388608\pi\) |
−0.642110 | + | 0.766612i | \(0.721941\pi\) | |||||||
\(824\) | 378579. | − | 740309.i | 0.557574 | − | 1.09033i | ||||
\(825\) | 67705.4 | − | 309381.i | 0.0994753 | − | 0.454554i | ||||
\(826\) | 3176.92 | + | 187268.i | 0.00465636 | + | 0.274476i | ||||
\(827\) | − | 1.14409e6i | − | 1.67282i | −0.548108 | − | 0.836408i | \(-0.684652\pi\) | ||
0.548108 | − | 0.836408i | \(-0.315348\pi\) | |||||||
\(828\) | −431872. | + | 54984.2i | −0.629933 | + | 0.0802005i | ||||
\(829\) | −563769. | −0.820336 | −0.410168 | − | 0.912010i | \(-0.634530\pi\) | ||||
−0.410168 | + | 0.912010i | \(0.634530\pi\) | |||||||
\(830\) | −1.08222e6 | + | 18359.3i | −1.57093 | + | 0.0266502i | ||||
\(831\) | −654961. | + | 718681.i | −0.948447 | + | 1.04072i | ||||
\(832\) | −508196. | + | 1.13245e6i | −0.734149 | + | 1.63595i | ||||
\(833\) | 24593.8 | − | 42597.7i | 0.0354434 | − | 0.0613898i | ||||
\(834\) | −753275. | − | 151506.i | −1.08298 | − | 0.217820i | ||||
\(835\) | −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 | \(-0.605832\pi\) |
0.655403 | + | 0.755279i | \(0.272499\pi\) | |||||||
\(840\) | 310431. | + | 827133.i | 0.439954 | + | 1.17224i | ||||
\(841\) | 98213.9 | − | 170111.i | 0.138861 | − | 0.240515i | ||||
\(842\) | 42815.4 | − | 25697.5i | 0.0603914 | − | 0.0362465i | ||||
\(843\) | 417846. | − | 458497.i | 0.587978 | − | 0.645181i | ||||
\(844\) | −977189. | − | 520811.i | −1.37181 | − | 0.731131i | ||||
\(845\) | −2.10238e6 | −2.94440 | ||||||||
\(846\) | −335840. | − | 147537.i | −0.469237 | − | 0.206139i | ||||
\(847\) | 426792.i | 0.594907i | ||||||||
\(848\) | −270167. | + | 18359.4i | −0.375699 | + | 0.0255310i | ||||
\(849\) | −86988.4 | + | 397495.i | −0.120683 | + | 0.551463i | ||||
\(850\) | −299074. | + | 179502.i | −0.413943 | + | 0.248446i | ||||
\(851\) | −293377. | − | 169381.i | −0.405105 | − | 0.233887i | ||||
\(852\) | 1.29795e6 | − | 462171.i | 1.78804 | − | 0.636683i | ||||
\(853\) | −183417. | − | 317688.i | −0.252082 | − | 0.436619i | 0.712017 | − | 0.702162i | \(-0.247782\pi\) |
−0.964099 | + | 0.265544i | \(0.914449\pi\) | |||||||
\(854\) | 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 | −0.929388 | − | 0.369105i | \(-0.879664\pi\) |
0.145039 | − | 0.989426i | \(-0.453669\pi\) | |||||||
\(858\) | 255955. | + | 759335.i | 0.347687 | + | 1.03148i | ||||
\(859\) | 1.26237e6 | + | 728827.i | 1.71080 | + | 0.987730i | 0.933486 | + | 0.358615i | \(0.116751\pi\) |
0.777313 | + | 0.629115i | \(0.216582\pi\) | |||||||
\(860\) | 45436.4 | + | 1.33877e6i | 0.0614338 | + | 1.81013i | ||||
\(861\) | 441440. | − | 140507.i | 0.595477 | − | 0.189536i | ||||
\(862\) | 479351. | − | 8131.97i | 0.645118 | − | 0.0109441i | ||||
\(863\) | − | 237901.i | − | 0.319430i | −0.987163 | − | 0.159715i | \(-0.948943\pi\) | ||
0.987163 | − | 0.159715i | \(-0.0510575\pi\) | |||||||
\(864\) | −397489. | + | 631869.i | −0.532474 | + | 0.846447i | ||||
\(865\) | −203020. | −0.271336 | ||||||||
\(866\) | −19164.8 | − | 1.12970e6i | −0.0255545 | − | 1.50635i | ||||
\(867\) | 137550. | + | 432148.i | 0.182988 | + | 0.574903i | ||||
\(868\) | −839703. | + | 28498.5i | −1.11452 | + | 0.0378254i | ||||
\(869\) | 287017. | − | 497128.i | 0.380074 | − | 0.658307i | ||||
\(870\) | 810181. | − | 273094.i | 1.07039 | − | 0.360806i | ||||
\(871\) | 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 | ||||
\(876\) | 91735.0 | + | 257626.i | 0.119544 | + | 0.335723i | ||||
\(877\) | 331033. | − | 573367.i | 0.430400 | − | 0.745475i | −0.566507 | − | 0.824057i | \(-0.691706\pi\) |
0.996908 | + | 0.0785815i | \(0.0250391\pi\) | |||||||
\(878\) | −352875. | − | 587935.i | −0.457753 | − | 0.762676i | ||||
\(879\) | −630445. | − | 137967.i | −0.815961 | − | 0.178566i | ||||
\(880\) | 42361.2 | + | 623362.i | 0.0547019 | + | 0.804962i | ||||
\(881\) | 245234. | 0.315957 | 0.157979 | − | 0.987443i | \(-0.449502\pi\) | ||||
0.157979 | + | 0.987443i | \(0.449502\pi\) | |||||||
\(882\) | 87029.6 | − | 9583.15i | 0.111874 | − | 0.0123189i | ||||
\(883\) | − | 924835.i | − | 1.18616i | −0.805144 | − | 0.593079i | \(-0.797912\pi\) | ||
0.805144 | − | 0.593079i | \(-0.202088\pi\) | |||||||
\(884\) | 415092. | − | 778832.i | 0.531178 | − | 0.996642i | ||||
\(885\) | −224209. | − | 204330.i | −0.286264 | − | 0.260883i | ||||
\(886\) | −170872. | − | 284695.i | −0.217673 | − | 0.362671i | ||||
\(887\) | 1.09941e6 | + | 634747.i | 1.39738 | + | 0.806776i | 0.994117 | − | 0.108309i | \(-0.0345436\pi\) |
0.403260 | + | 0.915085i | \(0.367877\pi\) | |||||||
\(888\) | −543827. | + | 204104.i | −0.689660 | + | 0.258836i | ||||
\(889\) | −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 | ||||
\(894\) | 90389.6 | − | 449409.i | 0.113095 | − | 0.562298i | ||||
\(895\) | 331926. | + | 191637.i | 0.414376 | + | 0.239240i | ||||
\(896\) | −453070. | − | 605558.i | −0.564351 | − | 0.754293i | ||||
\(897\) | 677164. | + | 617125.i | 0.841606 | + | 0.766987i | ||||
\(898\) | 17149.8 | + | 1.01092e6i | 0.0212670 | + | 1.25362i | ||||
\(899\) | 813085.i | 1.00604i | ||||||||
\(900\) | −572608. | − | 240048.i | −0.706923 | − | 0.296356i | ||||
\(901\) | 192535. | 0.237170 | ||||||||
\(902\) | 327578. | − | 5557.20i | 0.402625 | − | 0.00683035i | ||||
\(903\) | −1.02256e6 | − | 223779.i | −1.25405 | − | 0.274437i | ||||
\(904\) | −56541.7 | − | 28914.3i | −0.0691881 | − | 0.0353814i | ||||
\(905\) | −424388. | + | 735061.i | −0.518162 | + | 0.897483i | ||||
\(906\) | −84124.2 | + | 95513.6i | −0.102486 | + | 0.116361i | ||||
\(907\) | 41146.3 | − | 23755.8i | 0.0500169 | − | 0.0288772i | −0.474783 | − | 0.880103i | \(-0.657473\pi\) |
0.524800 | + | 0.851226i | \(0.324140\pi\) | |||||||
\(908\) | −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 | \(-0.571885\pi\) |
0.732075 | + | 0.681224i | \(0.238552\pi\) | |||||||
\(912\) | 673376. | − | 265841.i | 0.809595 | − | 0.319619i | ||||
\(913\) | 299080. | − | 518021.i | 0.358794 | − | 0.621450i | ||||
\(914\) | −65093.9 | + | 39068.9i | −0.0779198 | + | 0.0467670i | ||||
\(915\) | 78058.5 | + | 245241.i | 0.0932349 | + | 0.292921i | ||||
\(916\) | −646377. | + | 1.21279e6i | −0.770363 | + | 1.44542i | ||||
\(917\) | −321255. | −0.382042 | ||||||||
\(918\) | 312429. | − | 429071.i | 0.370737 | − | 0.509148i | ||||
\(919\) | − | 1.08957e6i | − | 1.29010i | −0.764141 | − | 0.645049i | \(-0.776837\pi\) | ||
0.764141 | − | 0.645049i | \(-0.223163\pi\) | |||||||
\(920\) | 388191. | + | 599691.i | 0.458637 | + | 0.708520i | ||||
\(921\) | −822159. | + | 261688.i | −0.969252 | + | 0.308506i | ||||
\(922\) | −665878. | + | 399656.i | −0.783309 | + | 0.470137i | ||||
\(923\) | −2.51099e6 | − | 1.44972e6i | −2.94742 | − | 1.70169i | ||||
\(924\) | −480216. | − | 88138.6i | −0.562461 | − | 0.103234i | ||||
\(925\) | −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 | −0.933106 | − | 0.359603i | \(-0.882912\pi\) |
0.155128 | − | 0.987894i | \(-0.450421\pi\) | |||||||
\(930\) | 899410. | − | 1.02118e6i | 1.03990 | − | 1.18069i | ||||
\(931\) | −73535.5 | − | 42455.7i | −0.0848394 | − | 0.0489820i | ||||
\(932\) | 204267. | − | 6932.59i | 0.235162 | − | 0.00798111i | ||||
\(933\) | 46308.8 | − | 211609.i | 0.0531986 | − | 0.243092i | ||||
\(934\) | 507889. | − | 8616.09i | 0.582204 | − | 0.00987681i | ||||
\(935\) | − | 444240.i | − | 0.508153i | ||||||
\(936\) | 1.55479e6 | − | 224811.i | 1.77468 | − | 0.256605i | ||||
\(937\) | 1.37506e6 | 1.56618 | 0.783089 | − | 0.621909i | \(-0.213643\pi\) | ||||
0.783089 | + | 0.621909i | \(0.213643\pi\) | |||||||
\(938\) | 2021.72 | + | 119173.i | 0.00229781 | + | 0.135448i | ||||
\(939\) | 602035. | − | 660606.i | 0.682795 | − | 0.749223i | ||||
\(940\) | 20416.1 | + | 601557.i | 0.0231056 | + | 0.680802i | ||||
\(941\) | 786864. | − | 1.36289e6i | 0.888628 | − | 1.53915i | 0.0471309 | − | 0.998889i | \(-0.484992\pi\) |
0.841498 | − | 0.540261i | \(-0.181674\pi\) | |||||||
\(942\) | −211118. | + | 1.04966e6i | −0.237916 | + | 1.18290i | ||||
\(943\) | 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 | \(-0.460044\pi\) |
0.921810 | + | 0.387643i | \(0.126711\pi\) | |||||||
\(948\) | −857016. | − | 729385.i | −0.953614 | − | 0.811597i | ||||
\(949\) | 287752. | − | 498400.i | 0.319511 | − | 0.553409i | ||||
\(950\) | 309871. | + | 516285.i | 0.343347 | + | 0.572061i | ||||
\(951\) | −360345. | + | 395403.i | −0.398435 | + | 0.437198i | ||||
\(952\) | 292205. | + | 451409.i | 0.322414 | + | 0.498077i | ||||
\(953\) | 461469. | 0.508108 | 0.254054 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254054 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(954\) | 202816. | + | 276264.i | 0.222846 | + | 0.303548i | ||||
\(955\) | 1.29813e6i | 1.42335i | ||||||||
\(956\) | 1.49588e6 | + | 797255.i | 1.63674 | + | 0.872332i | ||||
\(957\) | −101010. | + | 461565.i | −0.110291 | + | 0.503975i | ||||
\(958\) | 115133. | + | 191826.i | 0.125449 | + | 0.209014i | ||||
\(959\) | 339350. | + | 195924.i | 0.368986 | + | 0.213034i | ||||
\(960\) | 1.21700e6 | + | 138932.i | 1.32053 | + | 0.150751i | ||||
\(961\) | 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 | ||||
\(966\) | −528985. | + | 178309.i | −0.566877 | + | 0.191082i | ||||
\(967\) | 998780. | + | 576646.i | 1.06811 | + | 0.616675i | 0.927665 | − | 0.373413i | \(-0.121813\pi\) |
0.140447 | + | 0.990088i | \(0.455146\pi\) | |||||||
\(968\) | 526845. | + | 269418.i | 0.562253 | + | 0.287525i | ||||
\(969\) | −490491. | + | 156120.i | −0.522377 | + | 0.166269i | ||||
\(970\) | −28707.0 | − | 1.69218e6i | −0.0305101 | − | 1.79847i | ||||
\(971\) | − | 438562.i | − | 0.465149i | −0.972579 | − | 0.232575i | \(-0.925285\pi\) | ||
0.972579 | − | 0.232575i | \(-0.0747150\pi\) | |||||||
\(972\) | 944777. | − | 3683.47i | 0.999992 | − | 0.00389874i | ||||
\(973\) | −985213. | −1.04065 | ||||||||
\(974\) | −1.09949e6 | + | 18652.4i | −1.15898 | + | 0.0196615i | ||||
\(975\) | 396298. | + | 1.24507e6i | 0.416882 | + | 1.30974i | ||||
\(976\) | −122840. | − | 182891.i | −0.128956 | − | 0.191996i | ||||
\(977\) | −388615. | + | 673100.i | −0.407127 | + | 0.705165i | −0.994566 | − | 0.104103i | \(-0.966803\pi\) |
0.587439 | + | 0.809268i | \(0.300136\pi\) | |||||||
\(978\) | 67890.3 | + | 201408.i | 0.0709790 | + | 0.210572i | ||||
\(979\) | −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 | \(-0.803139\pi\) |
0.0947175 | + | 0.995504i | \(0.469805\pi\) | |||||||
\(984\) | 105218. | − | 633624.i | 0.108668 | − | 0.654397i | ||||
\(985\) | −350602. | + | 607260.i | −0.361362 | + | 0.625897i | ||||
\(986\) | 446188. | − | 267799.i | 0.458949 | − | 0.275458i | ||||
\(987\) | −459472. | − | 100551.i | −0.471655 | − | 0.103218i | ||||
\(988\) | −1.34448e6 | − | 716565.i | −1.37734 | − | 0.734077i | ||||
\(989\) | −846405. | −0.865338 | ||||||||
\(990\) | 637431. | − | 467961.i | 0.650373 | − | 0.477462i | ||||
\(991\) | 206876.i | 0.210651i | 0.994438 | + | 0.105325i | \(0.0335884\pi\) | ||||
−0.994438 | + | 0.105325i | \(0.966412\pi\) | |||||||
\(992\) | −494894. | + | 1.05455e6i | −0.502909 | + | 1.07162i | ||||
\(993\) | 613351. | + | 558969.i | 0.622028 | + | 0.566878i | ||||
\(994\) | 1.51474e6 | − | 909136.i | 1.53308 | − | 0.920145i | ||||
\(995\) | 156771. | + | 90511.8i | 0.158351 | + | 0.0914238i | ||||
\(996\) | −893035. | − | 760040.i | −0.900223 | − | 0.766157i | ||||
\(997\) | 14831.3 | + | 25688.6i | 0.0149207 | + | 0.0258435i | 0.873389 | − | 0.487023i | \(-0.161917\pi\) |
−0.858469 | + | 0.512866i | \(0.828584\pi\) | |||||||
\(998\) | −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.31.12 | yes | 44 | |
3.2 | odd | 2 | 108.5.f.a.91.11 | 44 | |||
4.3 | odd | 2 | inner | 36.5.f.a.31.18 | yes | 44 | |
9.2 | odd | 6 | 108.5.f.a.19.5 | 44 | |||
9.4 | even | 3 | 324.5.d.f.163.3 | 22 | |||
9.5 | odd | 6 | 324.5.d.e.163.20 | 22 | |||
9.7 | even | 3 | inner | 36.5.f.a.7.18 | yes | 44 | |
12.11 | even | 2 | 108.5.f.a.91.5 | 44 | |||
36.7 | odd | 6 | inner | 36.5.f.a.7.12 | ✓ | 44 | |
36.11 | even | 6 | 108.5.f.a.19.11 | 44 | |||
36.23 | even | 6 | 324.5.d.e.163.19 | 22 | |||
36.31 | odd | 6 | 324.5.d.f.163.4 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.12 | ✓ | 44 | 36.7 | odd | 6 | inner | |
36.5.f.a.7.18 | yes | 44 | 9.7 | even | 3 | inner | |
36.5.f.a.31.12 | yes | 44 | 1.1 | even | 1 | trivial | |
36.5.f.a.31.18 | yes | 44 | 4.3 | odd | 2 | inner | |
108.5.f.a.19.5 | 44 | 9.2 | odd | 6 | |||
108.5.f.a.19.11 | 44 | 36.11 | even | 6 | |||
108.5.f.a.91.5 | 44 | 12.11 | even | 2 | |||
108.5.f.a.91.11 | 44 | 3.2 | odd | 2 | |||
324.5.d.e.163.19 | 22 | 36.23 | even | 6 | |||
324.5.d.e.163.20 | 22 | 9.5 | odd | 6 | |||
324.5.d.f.163.3 | 22 | 9.4 | even | 3 | |||
324.5.d.f.163.4 | 22 | 36.31 | odd | 6 |