Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 91.6 | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.5.f.a.19.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63137 | − | 3.01262i | −0.657842 | − | 0.753156i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.15179 | + | 15.8546i | −0.134487 | + | 0.990915i | ||||
\(5\) | 10.5756 | − | 18.3175i | 0.423024 | − | 0.732698i | −0.573210 | − | 0.819409i | \(-0.694302\pi\) |
0.996234 | + | 0.0867102i | \(0.0276354\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −38.6407 | + | 22.3092i | −0.788586 | + | 0.455290i | −0.839464 | − | 0.543415i | \(-0.817131\pi\) |
0.0508787 | + | 0.998705i | \(0.483798\pi\) | |||||||
\(8\) | 53.4262 | − | 35.2369i | 0.834785 | − | 0.550576i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −83.0119 | + | 16.3397i | −0.830119 | + | 0.163397i | ||||
\(11\) | −58.6904 | + | 33.8849i | −0.485045 | + | 0.280041i | −0.722516 | − | 0.691354i | \(-0.757015\pi\) |
0.237472 | + | 0.971394i | \(0.423681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.5519 | − | 25.2046i | 0.0861058 | − | 0.149140i | −0.819756 | − | 0.572713i | \(-0.805891\pi\) |
0.905862 | + | 0.423573i | \(0.139224\pi\) | |||||||
\(14\) | 168.887 | + | 57.7061i | 0.861669 | + | 0.294419i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −246.740 | − | 68.2318i | −0.963826 | − | 0.266531i | ||||
\(17\) | −402.841 | −1.39391 | −0.696957 | − | 0.717113i | \(-0.745463\pi\) | ||||
−0.696957 | + | 0.717113i | \(0.745463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 644.741i | 1.78599i | 0.450070 | + | 0.892993i | \(0.351399\pi\) | ||||
−0.450070 | + | 0.892993i | \(0.648601\pi\) | |||||||
\(20\) | 267.660 | + | 207.088i | 0.669151 | + | 0.517719i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 256.519 | + | 87.6483i | 0.529997 | + | 0.181092i | ||||
\(23\) | 335.527 | + | 193.717i | 0.634267 | + | 0.366194i | 0.782403 | − | 0.622773i | \(-0.213994\pi\) |
−0.148136 | + | 0.988967i | \(0.547327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 88.8138 | + | 153.830i | 0.142102 | + | 0.246128i | ||||
\(26\) | −114.223 | + | 22.4833i | −0.168969 | + | 0.0332593i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −270.558 | − | 660.639i | −0.345099 | − | 0.842652i | ||||
\(29\) | 362.210 | + | 627.366i | 0.430690 | + | 0.745977i | 0.996933 | − | 0.0782617i | \(-0.0249370\pi\) |
−0.566243 | + | 0.824238i | \(0.691604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1090.90 | + | 629.833i | 1.13517 | + | 0.655393i | 0.945231 | − | 0.326402i | \(-0.105836\pi\) |
0.189944 | + | 0.981795i | \(0.439169\pi\) | |||||||
\(32\) | 443.706 | + | 922.876i | 0.433307 | + | 0.901246i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1060.02 | + | 1213.61i | 0.916976 | + | 1.04983i | ||||
\(35\) | 943.733i | 0.770394i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1402.04 | −1.02413 | −0.512066 | − | 0.858946i | \(-0.671120\pi\) | ||||
−0.512066 | + | 0.858946i | \(0.671120\pi\) | |||||||
\(38\) | 1942.36 | − | 1696.55i | 1.34513 | − | 1.17490i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −80.4363 | − | 1351.28i | −0.0502727 | − | 0.844552i | ||||
\(41\) | 774.166 | − | 1340.89i | 0.460539 | − | 0.797677i | −0.538449 | − | 0.842658i | \(-0.680990\pi\) |
0.998988 | + | 0.0449815i | \(0.0143229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1620.98 | + | 935.875i | −0.876681 | + | 0.506152i | −0.869563 | − | 0.493823i | \(-0.835599\pi\) |
−0.00711825 | + | 0.999975i | \(0.502266\pi\) | |||||||
\(44\) | −410.944 | − | 1003.43i | −0.212264 | − | 0.518300i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −299.300 | − | 1520.56i | −0.141446 | − | 0.718599i | ||||
\(47\) | −3610.63 | + | 2084.60i | −1.63451 | + | 0.943683i | −0.651828 | + | 0.758367i | \(0.725998\pi\) |
−0.982679 | + | 0.185316i | \(0.940669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −205.097 | + | 355.239i | −0.0854217 | + | 0.147955i | ||||
\(50\) | 229.730 | − | 672.346i | 0.0918920 | − | 0.268938i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 368.297 | + | 284.950i | 0.136205 | + | 0.105381i | ||||
\(53\) | −906.566 | −0.322736 | −0.161368 | − | 0.986894i | \(-0.551591\pi\) | ||||
−0.161368 | + | 0.986894i | \(0.551591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1433.41i | 0.473855i | ||||||||
\(56\) | −1278.32 | + | 2553.48i | −0.407627 | + | 0.814246i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 936.910 | − | 2742.03i | 0.278511 | − | 0.815111i | ||||
\(59\) | −3916.45 | − | 2261.16i | −1.12509 | − | 0.649573i | −0.182397 | − | 0.983225i | \(-0.558386\pi\) |
−0.942696 | + | 0.333652i | \(0.891719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1314.22 | − | 2276.30i | −0.353190 | − | 0.611743i | 0.633617 | − | 0.773647i | \(-0.281570\pi\) |
−0.986806 | + | 0.161904i | \(0.948236\pi\) | |||||||
\(62\) | −973.119 | − | 4943.80i | −0.253153 | − | 1.28611i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1612.72 | − | 3765.15i | 0.393731 | − | 0.919226i | ||||
\(65\) | −307.789 | − | 533.107i | −0.0728496 | − | 0.126179i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 58.7165 | + | 33.9000i | 0.0130801 | + | 0.00755179i | 0.506526 | − | 0.862225i | \(-0.330930\pi\) |
−0.493446 | + | 0.869777i | \(0.664263\pi\) | |||||||
\(68\) | 866.831 | − | 6386.91i | 0.187463 | − | 1.38125i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2843.11 | − | 2483.31i | 0.580227 | − | 0.506798i | ||||
\(71\) | − | 1315.04i | − | 0.260869i | −0.991457 | − | 0.130434i | \(-0.958363\pi\) | ||
0.991457 | − | 0.130434i | \(-0.0416372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9470.72 | 1.77720 | 0.888602 | − | 0.458680i | \(-0.151678\pi\) | ||||
0.888602 | + | 0.458680i | \(0.151678\pi\) | |||||||
\(74\) | 3689.27 | + | 4223.80i | 0.673717 | + | 0.771330i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10222.1 | − | 1387.35i | −1.76976 | − | 0.240192i | ||||
\(77\) | 1511.89 | − | 2618.67i | 0.255000 | − | 0.441672i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3783.95 | − | 2184.67i | 0.606305 | − | 0.350050i | −0.165213 | − | 0.986258i | \(-0.552831\pi\) |
0.771518 | + | 0.636207i | \(0.219498\pi\) | |||||||
\(80\) | −3859.25 | + | 3798.05i | −0.603008 | + | 0.593445i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6076.73 | + | 1196.12i | −0.903737 | + | 0.177888i | ||||
\(83\) | −659.925 | + | 381.008i | −0.0957940 | + | 0.0553067i | −0.547132 | − | 0.837047i | \(-0.684280\pi\) |
0.451338 | + | 0.892353i | \(0.350947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4260.28 | + | 7379.03i | −0.589659 | + | 1.02132i | ||||
\(86\) | 7084.84 | + | 2420.78i | 0.957929 | + | 0.327309i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1941.61 | + | 3878.41i | −0.250724 | + | 0.500828i | ||||
\(89\) | −8083.40 | −1.02050 | −0.510251 | − | 0.860025i | \(-0.670448\pi\) | ||||
−0.510251 | + | 0.860025i | \(0.670448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1298.56i | 0.156813i | ||||||||
\(92\) | −3793.29 | + | 4902.82i | −0.448168 | + | 0.579256i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15781.0 | + | 5392.11i | 1.78599 | + | 0.610244i | ||||
\(95\) | 11810.0 | + | 6818.52i | 1.30859 | + | 0.755514i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3332.71 | − | 5772.42i | −0.354204 | − | 0.613500i | 0.632777 | − | 0.774334i | \(-0.281915\pi\) |
−0.986981 | + | 0.160834i | \(0.948582\pi\) | |||||||
\(98\) | 1609.89 | − | 316.884i | 0.167627 | − | 0.0329950i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2630.03 | + | 1077.10i | −0.263003 | + | 0.107710i | ||||
\(101\) | 4643.04 | + | 8041.97i | 0.455155 | + | 0.788352i | 0.998697 | − | 0.0510303i | \(-0.0162505\pi\) |
−0.543542 | + | 0.839382i | \(0.682917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9792.48 | − | 5653.69i | −0.923035 | − | 0.532915i | −0.0384332 | − | 0.999261i | \(-0.512237\pi\) |
−0.884602 | + | 0.466346i | \(0.845570\pi\) | |||||||
\(104\) | −110.679 | − | 1859.35i | −0.0102329 | − | 0.171907i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2385.51 | + | 2731.14i | 0.212310 | + | 0.243071i | ||||
\(107\) | − | 6261.61i | − | 0.546913i | −0.961884 | − | 0.273456i | \(-0.911833\pi\) | ||
0.961884 | − | 0.273456i | \(-0.0881669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3452.85 | 0.290620 | 0.145310 | − | 0.989386i | \(-0.453582\pi\) | ||||
0.145310 | + | 0.989386i | \(0.453582\pi\) | |||||||
\(110\) | 4318.33 | − | 3771.84i | 0.356887 | − | 0.311722i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11056.4 | − | 2868.04i | 0.881409 | − | 0.228639i | ||||
\(113\) | −1272.55 | + | 2204.13i | −0.0996597 | + | 0.172616i | −0.911544 | − | 0.411203i | \(-0.865109\pi\) |
0.811884 | + | 0.583819i | \(0.198442\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7096.79 | − | 4097.33i | 0.536619 | − | 0.309817i | ||||
\(116\) | −10726.1 | + | 4392.75i | −0.797122 | + | 0.326453i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3493.59 | + | 17748.7i | 0.250904 | + | 1.27469i | ||||
\(119\) | 15566.1 | − | 8987.07i | 1.09922 | − | 0.634636i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5024.12 | + | 8702.04i | −0.343154 | + | 0.594361i | ||||
\(122\) | −3399.42 | + | 9949.02i | −0.228394 | + | 0.668437i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12333.2 | + | 15940.6i | −0.802106 | + | 1.03672i | ||||
\(125\) | 16976.5 | 1.08650 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 530.060i | − | 0.0328638i | −0.999865 | − | 0.0164319i | \(-0.994769\pi\) | ||
0.999865 | − | 0.0164319i | \(-0.00523067\pi\) | |||||||
\(128\) | −15586.6 | + | 5048.97i | −0.951333 | + | 0.308164i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −796.142 | + | 2330.05i | −0.0471090 | + | 0.137873i | ||||
\(131\) | 802.198 | + | 463.149i | 0.0467454 | + | 0.0269885i | 0.523191 | − | 0.852216i | \(-0.324742\pi\) |
−0.476445 | + | 0.879204i | \(0.658075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14383.7 | − | 24913.2i | −0.813142 | − | 1.40840i | ||||
\(134\) | −52.3769 | − | 266.094i | −0.00291696 | − | 0.0148192i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21522.3 | + | 14194.9i | −1.16362 | + | 0.767456i | ||||
\(137\) | 834.113 | + | 1444.73i | 0.0444410 | + | 0.0769741i | 0.887390 | − | 0.461019i | \(-0.152516\pi\) |
−0.842949 | + | 0.537993i | \(0.819183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 717.766 | + | 414.402i | 0.0371495 | + | 0.0214483i | 0.518460 | − | 0.855102i | \(-0.326506\pi\) |
−0.481310 | + | 0.876550i | \(0.659839\pi\) | |||||||
\(140\) | −14962.5 | − | 2030.72i | −0.763395 | − | 0.103608i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3961.72 | + | 3460.36i | −0.196475 | + | 0.171611i | ||||
\(143\) | 1972.36i | 0.0964525i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15322.3 | 0.728768 | ||||||||
\(146\) | −24920.9 | − | 28531.7i | −1.16912 | − | 1.33851i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3016.89 | − | 22228.8i | 0.137732 | − | 1.01483i | ||||
\(149\) | 1561.38 | − | 2704.39i | 0.0703292 | − | 0.121814i | −0.828716 | − | 0.559669i | \(-0.810928\pi\) |
0.899046 | + | 0.437855i | \(0.144262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7932.37 | + | 4579.76i | −0.347896 | + | 0.200858i | −0.663758 | − | 0.747947i | \(-0.731040\pi\) |
0.315862 | + | 0.948805i | \(0.397706\pi\) | |||||||
\(152\) | 22718.7 | + | 34446.1i | 0.983322 | + | 1.49091i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11867.4 | + | 2335.94i | −0.500397 | + | 0.0984963i | ||||
\(155\) | 23073.9 | − | 13321.7i | 0.960411 | − | 0.554494i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10551.8 | + | 18276.3i | −0.428084 | + | 0.741463i | −0.996703 | − | 0.0811381i | \(-0.974145\pi\) |
0.568619 | + | 0.822601i | \(0.307478\pi\) | |||||||
\(158\) | −16538.5 | − | 5650.96i | −0.662496 | − | 0.226364i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21597.2 | + | 1632.39i | 0.843641 | + | 0.0637653i | ||||
\(161\) | −17286.7 | −0.666898 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 42771.0i | − | 1.60981i | −0.593405 | − | 0.804904i | \(-0.702217\pi\) | ||
0.593405 | − | 0.804904i | \(-0.297783\pi\) | |||||||
\(164\) | 19593.6 | + | 15159.5i | 0.728494 | + | 0.563632i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2884.34 | + | 985.532i | 0.104672 | + | 0.0357647i | ||||
\(167\) | −9568.12 | − | 5524.16i | −0.343079 | − | 0.198077i | 0.318554 | − | 0.947905i | \(-0.396803\pi\) |
−0.661633 | + | 0.749828i | \(0.730136\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13857.0 | + | 24001.0i | 0.485172 | + | 0.840342i | ||||
\(170\) | 33440.6 | − | 6582.32i | 1.15711 | − | 0.227762i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11349.9 | − | 27713.9i | −0.383651 | − | 0.936787i | ||||
\(173\) | −10967.8 | − | 18996.8i | −0.366461 | − | 0.634729i | 0.622549 | − | 0.782581i | \(-0.286097\pi\) |
−0.989009 | + | 0.147852i | \(0.952764\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6863.66 | − | 3962.73i | −0.224119 | − | 0.129395i | ||||
\(176\) | 16793.3 | − | 4356.20i | 0.542138 | − | 0.140631i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21270.4 | + | 24352.2i | 0.671329 | + | 0.768597i | ||||
\(179\) | − | 11479.2i | − | 0.358265i | −0.983825 | − | 0.179133i | \(-0.942671\pi\) | ||
0.983825 | − | 0.179133i | \(-0.0573291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45472.2 | 1.38800 | 0.693999 | − | 0.719976i | \(-0.255847\pi\) | ||||
0.693999 | + | 0.719976i | \(0.255847\pi\) | |||||||
\(182\) | 3912.08 | − | 3417.00i | 0.118104 | − | 0.103158i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24751.9 | − | 1473.38i | 0.731094 | − | 0.0435190i | ||||
\(185\) | −14827.4 | + | 25681.7i | −0.433232 | + | 0.750379i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23642.9 | − | 13650.2i | 0.676111 | − | 0.390353i | ||||
\(188\) | −25281.2 | − | 61730.8i | −0.715290 | − | 1.74657i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10534.9 | − | 53521.2i | −0.291825 | − | 1.48258i | ||||
\(191\) | −60657.0 | + | 35020.3i | −1.66270 | + | 0.959961i | −0.691283 | + | 0.722584i | \(0.742954\pi\) |
−0.971418 | + | 0.237376i | \(0.923713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17426.4 | − | 30183.5i | 0.467836 | − | 0.810316i | −0.531488 | − | 0.847066i | \(-0.678367\pi\) |
0.999325 | + | 0.0367497i | \(0.0117004\pi\) | |||||||
\(194\) | −8620.54 | + | 25229.6i | −0.229050 | + | 0.670357i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5190.87 | − | 4016.15i | −0.135122 | − | 0.104544i | ||||
\(197\) | 30858.0 | 0.795124 | 0.397562 | − | 0.917575i | \(-0.369856\pi\) | ||||
0.397562 | + | 0.917575i | \(0.369856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 34262.5i | 0.865192i | 0.901588 | + | 0.432596i | \(0.142402\pi\) | ||||
−0.901588 | + | 0.432596i | \(0.857598\pi\) | |||||||
\(200\) | 10165.5 | + | 5089.04i | 0.254137 | + | 0.127226i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12009.9 | − | 35149.1i | 0.294331 | − | 0.861414i | ||||
\(203\) | −27992.1 | − | 16161.2i | −0.679272 | − | 0.392178i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16374.5 | − | 28361.5i | −0.389638 | − | 0.674872i | ||||
\(206\) | 8735.19 | + | 44378.0i | 0.205844 | + | 1.04576i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5310.28 | + | 5226.07i | −0.122741 | + | 0.120795i | ||||
\(209\) | −21847.0 | − | 37840.1i | −0.500149 | − | 0.866283i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14989.6 | + | 8654.27i | 0.336687 | + | 0.194386i | 0.658806 | − | 0.752313i | \(-0.271062\pi\) |
−0.322119 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(212\) | 1950.74 | − | 14373.3i | 0.0434038 | − | 0.319804i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18863.9 | + | 16476.6i | −0.411911 | + | 0.359782i | ||||
\(215\) | 39589.7i | 0.856457i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −56204.3 | −1.19358 | ||||||||
\(218\) | −9085.73 | − | 10402.1i | −0.191182 | − | 0.218882i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22726.2 | − | 3084.41i | −0.469550 | − | 0.0637274i | ||||
\(221\) | −5862.10 | + | 10153.5i | −0.120024 | + | 0.207888i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −55484.8 | + | 32034.1i | −1.11574 | + | 0.644174i | −0.940311 | − | 0.340317i | \(-0.889466\pi\) |
−0.175432 | + | 0.984492i | \(0.556132\pi\) | |||||||
\(224\) | −37733.8 | − | 25761.9i | −0.752028 | − | 0.513430i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9988.77 | − | 1966.15i | 0.195567 | − | 0.0384946i | ||||
\(227\) | 11857.8 | − | 6846.11i | 0.230119 | − | 0.132859i | −0.380508 | − | 0.924778i | \(-0.624251\pi\) |
0.610627 | + | 0.791918i | \(0.290917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −32996.2 | + | 57151.0i | −0.629205 | + | 1.08982i | 0.358506 | + | 0.933527i | \(0.383286\pi\) |
−0.987711 | + | 0.156288i | \(0.950047\pi\) | |||||||
\(230\) | −31018.0 | − | 10598.4i | −0.586352 | − | 0.200347i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 41458.0 | + | 20754.7i | 0.770250 | + | 0.385602i | ||||
\(233\) | 63342.4 | 1.16676 | 0.583381 | − | 0.812198i | \(-0.301729\pi\) | ||||
0.583381 | + | 0.812198i | \(0.301729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 88183.3i | 1.59680i | ||||||||
\(236\) | 44277.3 | − | 57228.4i | 0.794982 | − | 1.02751i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −68034.7 | − | 23246.4i | −1.20109 | − | 0.410394i | ||||
\(239\) | 275.008 | + | 158.776i | 0.00481448 | + | 0.00277964i | 0.502405 | − | 0.864632i | \(-0.332449\pi\) |
−0.497591 | + | 0.867412i | \(0.665782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12752.6 | − | 22088.2i | −0.219566 | − | 0.380300i | 0.735109 | − | 0.677949i | \(-0.237131\pi\) |
−0.954675 | + | 0.297649i | \(0.903798\pi\) | |||||||
\(242\) | 39436.3 | − | 7762.48i | 0.673388 | − | 0.132547i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 38917.8 | − | 15938.4i | 0.653685 | − | 0.267710i | ||||
\(245\) | 4338.05 | + | 7513.73i | 0.0722708 | + | 0.125177i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16250.4 | + | 9382.19i | 0.266361 | + | 0.153784i | ||||
\(248\) | 80476.2 | − | 4790.41i | 1.30847 | − | 0.0778878i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −44671.5 | − | 51143.9i | −0.714744 | − | 0.818302i | ||||
\(251\) | 40987.7i | 0.650588i | 0.945613 | + | 0.325294i | \(0.105463\pi\) | ||||
−0.945613 | + | 0.325294i | \(0.894537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26256.3 | −0.410197 | ||||||||
\(254\) | −1596.87 | + | 1394.78i | −0.0247516 | + | 0.0216192i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 56224.8 | + | 33671.0i | 0.857923 | + | 0.513778i | ||||
\(257\) | 15479.1 | − | 26810.5i | 0.234357 | − | 0.405919i | −0.724728 | − | 0.689035i | \(-0.758035\pi\) |
0.959086 | + | 0.283116i | \(0.0913681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 54175.6 | − | 31278.3i | 0.807615 | − | 0.466277i | ||||
\(260\) | 9114.52 | − | 3732.76i | 0.134830 | − | 0.0552183i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −715.585 | − | 3635.44i | −0.0104246 | − | 0.0529607i | ||||
\(263\) | −13311.8 | + | 7685.54i | −0.192453 | + | 0.111113i | −0.593130 | − | 0.805107i | \(-0.702108\pi\) |
0.400678 | + | 0.916219i | \(0.368775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9587.47 | + | 16606.0i | −0.136525 | + | 0.236468i | ||||
\(266\) | −37205.5 | + | 108889.i | −0.525828 | + | 1.53893i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −663.818 | + | 857.983i | −0.00924228 | + | 0.0119456i | ||||
\(269\) | −76105.5 | −1.05175 | −0.525873 | − | 0.850563i | \(-0.676261\pi\) | ||||
−0.525873 | + | 0.850563i | \(0.676261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 78076.4i | 1.06312i | 0.847021 | + | 0.531559i | \(0.178394\pi\) | ||||
−0.847021 | + | 0.531559i | \(0.821606\pi\) | |||||||
\(272\) | 99396.9 | + | 27486.6i | 1.34349 | + | 0.371521i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2157.56 | − | 6314.48i | 0.0287383 | − | 0.0841078i | ||||
\(275\) | −10425.0 | − | 6018.90i | −0.137852 | − | 0.0795887i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2369.97 | − | 4104.90i | −0.0308875 | − | 0.0534987i | 0.850168 | − | 0.526511i | \(-0.176500\pi\) |
−0.881056 | + | 0.473012i | \(0.843167\pi\) | |||||||
\(278\) | −640.269 | − | 3252.80i | −0.00828463 | − | 0.0420890i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 33254.2 | + | 50420.1i | 0.424161 | + | 0.643113i | ||||
\(281\) | 21604.6 | + | 37420.3i | 0.273612 | + | 0.473909i | 0.969784 | − | 0.243966i | \(-0.0784484\pi\) |
−0.696172 | + | 0.717875i | \(0.745115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31277.1 | + | 18057.8i | 0.390529 | + | 0.225472i | 0.682389 | − | 0.730989i | \(-0.260941\pi\) |
−0.291860 | + | 0.956461i | \(0.594274\pi\) | |||||||
\(284\) | 20849.5 | + | 2829.69i | 0.258499 | + | 0.0350835i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5941.97 | − | 5190.00i | 0.0726438 | − | 0.0634505i | ||||
\(287\) | 69084.1i | 0.838715i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 78760.1 | 0.942997 | ||||||||
\(290\) | −40318.7 | − | 46160.4i | −0.479414 | − | 0.548876i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −20379.0 | + | 150155.i | −0.239011 | + | 1.76106i | ||||
\(293\) | −48046.7 | + | 83219.2i | −0.559665 | + | 0.969368i | 0.437859 | + | 0.899043i | \(0.355737\pi\) |
−0.997524 | + | 0.0703243i | \(0.977597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −82837.5 | + | 47826.3i | −0.951882 | + | 0.549569i | ||||
\(296\) | −74905.5 | + | 49403.4i | −0.854929 | + | 0.563862i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12255.9 | + | 2412.40i | −0.138010 | + | 0.0271654i | ||||
\(299\) | 9765.10 | − | 5637.88i | 0.109228 | − | 0.0630628i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41757.3 | − | 72325.7i | 0.460892 | − | 0.798288i | ||||
\(302\) | 34670.1 | + | 11846.2i | 0.380138 | + | 0.129887i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 43991.9 | − | 159083.i | 0.476020 | − | 1.72138i | ||||
\(305\) | −55594.6 | −0.597631 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 140641.i | − | 1.49223i | −0.665817 | − | 0.746115i | \(-0.731917\pi\) | ||
0.665817 | − | 0.746115i | \(-0.268083\pi\) | |||||||
\(308\) | 38264.9 | + | 29605.4i | 0.403366 | + | 0.312082i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −100849. | − | 34458.6i | −1.04942 | − | 0.358570i | ||||
\(311\) | 141564. | + | 81731.8i | 1.46363 | + | 0.845027i | 0.999177 | − | 0.0405712i | \(-0.0129178\pi\) |
0.464453 | + | 0.885598i | \(0.346251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25645.1 | + | 44418.7i | 0.261768 | + | 0.453395i | 0.966712 | − | 0.255868i | \(-0.0823611\pi\) |
−0.704944 | + | 0.709263i | \(0.749028\pi\) | |||||||
\(314\) | 82825.4 | − | 16303.0i | 0.840049 | − | 0.165352i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26494.8 | + | 64694.1i | 0.265330 | + | 0.647874i | ||||
\(317\) | −14025.0 | − | 24292.0i | −0.139568 | − | 0.241738i | 0.787765 | − | 0.615975i | \(-0.211238\pi\) |
−0.927333 | + | 0.374237i | \(0.877905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42516.5 | − | 24546.9i | −0.417808 | − | 0.241221i | ||||
\(320\) | −51912.4 | − | 69359.7i | −0.506957 | − | 0.677340i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 45487.6 | + | 52078.2i | 0.438714 | + | 0.502278i | ||||
\(323\) | − | 259728.i | − | 2.48951i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5169.63 | 0.0489433 | ||||||||
\(326\) | −128853. | + | 112546.i | −1.21244 | + | 1.05900i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5888.19 | − | 98918.1i | −0.0547311 | − | 0.919450i | ||||
\(329\) | 93011.4 | − | 161101.i | 0.859299 | − | 1.48835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 97678.0 | − | 56394.4i | 0.891540 | − | 0.514731i | 0.0170938 | − | 0.999854i | \(-0.494559\pi\) |
0.874446 | + | 0.485123i | \(0.161225\pi\) | |||||||
\(332\) | −4620.72 | − | 11282.7i | −0.0419212 | − | 0.102362i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8535.06 | + | 43361.2i | 0.0765092 | + | 0.388695i | ||||
\(335\) | 1241.92 | − | 717.024i | 0.0110664 | − | 0.00638917i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10409.8 | − | 18030.3i | 0.0916606 | − | 0.158761i | −0.816549 | − | 0.577276i | \(-0.804116\pi\) |
0.908210 | + | 0.418515i | \(0.137449\pi\) | |||||||
\(338\) | 35843.1 | − | 104901.i | 0.313742 | − | 0.918222i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −107825. | − | 83423.4i | −0.932739 | − | 0.721656i | ||||
\(341\) | −85367.4 | −0.734147 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 125431.i | − | 1.06615i | ||||||
\(344\) | −53625.7 | + | 107119.i | −0.453165 | + | 0.905208i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28369.8 | + | 83029.5i | −0.236976 | + | 0.693554i | ||||
\(347\) | −139615. | − | 80606.6i | −1.15950 | − | 0.669440i | −0.208318 | − | 0.978061i | \(-0.566799\pi\) |
−0.951185 | + | 0.308621i | \(0.900132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 110742. | + | 191811.i | 0.909205 | + | 1.57479i | 0.815171 | + | 0.579220i | \(0.196643\pi\) |
0.0940341 | + | 0.995569i | \(0.470024\pi\) | |||||||
\(350\) | 6122.59 | + | 31105.0i | 0.0499803 | + | 0.253919i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −57312.9 | − | 39129.0i | −0.462559 | − | 0.315801i | ||||
\(353\) | 109395. | + | 189477.i | 0.877904 | + | 1.52057i | 0.853637 | + | 0.520869i | \(0.174392\pi\) |
0.0242676 | + | 0.999705i | \(0.492275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24088.2 | − | 13907.3i | −0.191138 | − | 0.110354i | ||||
\(356\) | 17393.8 | − | 128159.i | 0.137244 | − | 1.01123i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −34582.4 | + | 30206.0i | −0.269830 | + | 0.235682i | ||||
\(359\) | − | 924.606i | − | 0.00717411i | −0.999994 | − | 0.00358705i | \(-0.998858\pi\) | ||
0.999994 | − | 0.00358705i | \(-0.00114180\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −285370. | −2.18975 | ||||||||
\(362\) | −119654. | − | 136991.i | −0.913084 | − | 1.04538i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20588.3 | − | 2794.24i | −0.155388 | − | 0.0210893i | ||||
\(365\) | 100158. | − | 173479.i | 0.751799 | − | 1.30215i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35332.0 | + | 20398.9i | −0.262323 | + | 0.151452i | −0.625394 | − | 0.780309i | \(-0.715062\pi\) |
0.363071 | + | 0.931762i | \(0.381728\pi\) | |||||||
\(368\) | −69570.1 | − | 70691.2i | −0.513721 | − | 0.521999i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 116386. | − | 22908.9i | 0.850150 | − | 0.167340i | ||||
\(371\) | 35030.3 | − | 20224.8i | 0.254505 | − | 0.146939i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 117265. | − | 203109.i | 0.842851 | − | 1.45986i | −0.0446228 | − | 0.999004i | \(-0.514209\pi\) |
0.887474 | − | 0.460858i | \(-0.152458\pi\) | |||||||
\(374\) | −103336. | − | 35308.4i | −0.738771 | − | 0.252426i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −119447. | + | 238599.i | −0.844892 | + | 1.68769i | ||||
\(377\) | 21083.4 | 0.148340 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 185553.i | − | 1.29178i | −0.763428 | − | 0.645892i | \(-0.776485\pi\) | ||
0.763428 | − | 0.645892i | \(-0.223515\pi\) | |||||||
\(380\) | −133518. | + | 172572.i | −0.924639 | + | 1.19509i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 265114. | + | 90585.2i | 1.81679 | + | 0.620770i | ||||
\(383\) | 52190.3 | + | 30132.1i | 0.355789 | + | 0.205415i | 0.667232 | − | 0.744850i | \(-0.267479\pi\) |
−0.311443 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31978.3 | − | 55388.1i | −0.215742 | − | 0.373675i | ||||
\(386\) | −136787. | + | 26924.6i | −0.918056 | + | 0.180707i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 98691.0 | − | 40417.8i | 0.655562 | − | 0.268479i | ||||
\(389\) | −6004.66 | − | 10400.4i | −0.0396816 | − | 0.0687306i | 0.845502 | − | 0.533971i | \(-0.179301\pi\) |
−0.885184 | + | 0.465241i | \(0.845968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −135164. | − | 78037.0i | −0.884113 | − | 0.510443i | ||||
\(392\) | 1559.94 | + | 26206.1i | 0.0101516 | + | 0.170542i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −81198.7 | − | 92963.4i | −0.523066 | − | 0.598852i | ||||
\(395\) | − | 92416.5i | − | 0.592318i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32276.3 | 0.204787 | 0.102394 | − | 0.994744i | \(-0.467350\pi\) | ||||
0.102394 | + | 0.994744i | \(0.467350\pi\) | |||||||
\(398\) | 103220. | − | 90157.2i | 0.651624 | − | 0.569160i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11417.8 | − | 44015.9i | −0.0713611 | − | 0.275099i | ||||
\(401\) | −93863.1 | + | 162576.i | −0.583722 | + | 1.01104i | 0.411311 | + | 0.911495i | \(0.365071\pi\) |
−0.995033 | + | 0.0995418i | \(0.968262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31749.4 | − | 18330.5i | 0.195490 | − | 0.112866i | ||||
\(404\) | −137494. | + | 56309.0i | −0.842402 | + | 0.344997i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24969.8 | + | 126856.i | 0.151483 | + | 0.769588i | ||||
\(407\) | 82286.0 | − | 47507.9i | 0.496749 | − | 0.286798i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 67272.0 | − | 116518.i | 0.402149 | − | 0.696543i | −0.591836 | − | 0.806059i | \(-0.701597\pi\) |
0.993985 | + | 0.109515i | \(0.0349299\pi\) | |||||||
\(410\) | −42355.1 | + | 123960.i | −0.251964 | + | 0.737417i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 110709. | − | 143091.i | 0.652210 | − | 0.842980i | ||||
\(413\) | 201779. | 1.18298 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16117.5i | 0.0935841i | ||||||||
\(416\) | 29717.5 | + | 2246.15i | 0.171722 | + | 0.0129793i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −56510.5 | + | 165388.i | −0.323427 | + | 0.946568i | ||||
\(419\) | 73320.7 | + | 42331.7i | 0.417637 | + | 0.241123i | 0.694066 | − | 0.719912i | \(-0.255818\pi\) |
−0.276429 | + | 0.961034i | \(0.589151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 57849.8 | + | 100199.i | 0.326391 | + | 0.565325i | 0.981793 | − | 0.189955i | \(-0.0608341\pi\) |
−0.655402 | + | 0.755280i | \(0.727501\pi\) | |||||||
\(422\) | −13371.2 | − | 67930.7i | −0.0750837 | − | 0.381453i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −48434.4 | + | 31944.6i | −0.269415 | + | 0.177691i | ||||
\(425\) | −35777.9 | − | 61969.1i | −0.198078 | − | 0.343081i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 101565. | + | 58638.4i | 0.557041 | + | 0.321608i | ||||
\(428\) | 99275.5 | + | 13473.7i | 0.541944 | + | 0.0735527i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 119269. | − | 104175.i | 0.645045 | − | 0.563413i | ||||
\(431\) | 294896.i | 1.58750i | 0.608241 | + | 0.793752i | \(0.291875\pi\) | ||||
−0.608241 | + | 0.793752i | \(0.708125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −151284. | −0.806895 | −0.403447 | − | 0.915003i | \(-0.632188\pi\) | ||||
−0.403447 | + | 0.915003i | \(0.632188\pi\) | |||||||
\(434\) | 147894. | + | 169322.i | 0.785185 | + | 0.898949i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7429.82 | + | 54743.7i | −0.0390846 | + | 0.287979i | ||||
\(437\) | −124897. | + | 216328.i | −0.654017 | + | 1.13279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17332.7 | − | 10007.1i | 0.0899369 | − | 0.0519251i | −0.454357 | − | 0.890820i | \(-0.650131\pi\) |
0.544294 | + | 0.838895i | \(0.316798\pi\) | |||||||
\(440\) | 50509.0 | + | 76581.8i | 0.260893 | + | 0.395567i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 46013.9 | − | 9057.19i | 0.235529 | − | 0.0463606i | ||||
\(443\) | 33466.7 | − | 19322.0i | 0.170532 | − | 0.0984567i | −0.412305 | − | 0.911046i | \(-0.635276\pi\) |
0.582837 | + | 0.812589i | \(0.301943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −85486.7 | + | 148067.i | −0.431696 | + | 0.747720i | ||||
\(446\) | 242508. | + | 82861.0i | 1.21915 | + | 0.416563i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21680.7 | + | 181467.i | 0.108023 | + | 0.904150i | ||||
\(449\) | −79457.9 | −0.394135 | −0.197067 | − | 0.980390i | \(-0.563142\pi\) | ||||
−0.197067 | + | 0.980390i | \(0.563142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 104930.i | 0.515878i | ||||||||
\(452\) | −32207.4 | − | 24918.7i | −0.157645 | − | 0.121969i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −51827.0 | − | 17708.5i | −0.251446 | − | 0.0859151i | ||||
\(455\) | 23786.4 | + | 13733.1i | 0.114896 | + | 0.0663354i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 131776. | + | 228243.i | 0.630963 | + | 1.09286i | 0.987355 | + | 0.158524i | \(0.0506735\pi\) |
−0.356392 | + | 0.934337i | \(0.615993\pi\) | |||||||
\(458\) | 259000. | − | 50980.5i | 1.23472 | − | 0.243037i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 49691.0 | + | 121334.i | 0.234834 | + | 0.573411i | ||||
\(461\) | −100305. | − | 173733.i | −0.471976 | − | 0.817487i | 0.527510 | − | 0.849549i | \(-0.323126\pi\) |
−0.999486 | + | 0.0320624i | \(0.989792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 205297. | + | 118528.i | 0.957679 | + | 0.552916i | 0.895458 | − | 0.445146i | \(-0.146848\pi\) |
0.0622210 | + | 0.998062i | \(0.480182\pi\) | |||||||
\(464\) | −46565.2 | − | 179510.i | −0.216285 | − | 0.833784i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −166677. | − | 190827.i | −0.767546 | − | 0.878754i | ||||
\(467\) | − | 230464.i | − | 1.05674i | −0.849014 | − | 0.528371i | \(-0.822803\pi\) | ||
0.849014 | − | 0.528371i | \(-0.177197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3025.13 | −0.0137530 | ||||||||
\(470\) | 265663. | − | 232043.i | 1.20264 | − | 1.05044i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −288918. | + | 17198.1i | −1.29685 | + | 0.0771961i | ||||
\(473\) | 63424.1 | − | 109854.i | 0.283486 | − | 0.491013i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −99180.5 | + | 57261.9i | −0.439581 | + | 0.253792i | ||||
\(476\) | 108992. | + | 266133.i | 0.481039 | + | 1.17459i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −245.315 | − | 1246.29i | −0.00107366 | − | 0.00545461i | ||||
\(479\) | 2079.74 | − | 1200.74i | 0.00906438 | − | 0.00523332i | −0.495461 | − | 0.868630i | \(-0.665001\pi\) |
0.504525 | + | 0.863397i | \(0.331668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20402.3 | + | 35337.7i | −0.0881836 | + | 0.152739i | ||||
\(482\) | −32986.6 | + | 96541.1i | −0.141985 | + | 0.415545i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −127157. | − | 98380.7i | −0.542812 | − | 0.419971i | ||||
\(485\) | −140981. | −0.599347 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 405227.i | 1.70860i | 0.519781 | + | 0.854300i | \(0.326014\pi\) | ||||
−0.519781 | + | 0.854300i | \(0.673986\pi\) | |||||||
\(488\) | −150423. | − | 75304.9i | −0.631649 | − | 0.316216i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11221.0 | − | 32840.3i | 0.0467347 | − | 0.136778i | ||||
\(491\) | 111325. | + | 64273.4i | 0.461773 | + | 0.266605i | 0.712790 | − | 0.701378i | \(-0.247431\pi\) |
−0.251016 | + | 0.967983i | \(0.580765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −145913. | − | 252729.i | −0.600345 | − | 1.03983i | ||||
\(494\) | −14495.9 | − | 73644.5i | −0.0594006 | − | 0.301777i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −226194. | − | 229839.i | −0.919429 | − | 0.934244i | ||||
\(497\) | 29337.5 | + | 50814.1i | 0.118771 | + | 0.205717i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 111377. | + | 64303.6i | 0.447296 | + | 0.258246i | 0.706687 | − | 0.707526i | \(-0.250189\pi\) |
−0.259392 | + | 0.965772i | \(0.583522\pi\) | |||||||
\(500\) | −36530.0 | + | 269157.i | −0.146120 | + | 1.07663i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 123480. | − | 107854.i | 0.489994 | − | 0.427984i | ||||
\(503\) | 368128.i | 1.45500i | 0.686109 | + | 0.727499i | \(0.259317\pi\) | ||||
−0.686109 | + | 0.727499i | \(0.740683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 196411. | 0.770165 | ||||||||
\(506\) | 69090.0 | + | 79100.3i | 0.269845 | + | 0.308942i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8403.92 | + | 1140.58i | 0.0325653 | + | 0.00441976i | ||||
\(509\) | −40698.4 | + | 70491.6i | −0.157087 | + | 0.272083i | −0.933817 | − | 0.357751i | \(-0.883544\pi\) |
0.776730 | + | 0.629834i | \(0.216877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −365955. | + | 211284.i | −1.40148 | + | 0.809143i | ||||
\(512\) | −46510.3 | − | 257985.i | −0.177423 | − | 0.984135i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −121501. | + | 23915.8i | −0.459890 | + | 0.0905230i | ||||
\(515\) | −207123. | + | 119582.i | −0.780931 | + | 0.450871i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 141273. | − | 244692.i | 0.528539 | − | 0.915457i | ||||
\(518\) | −236786. | − | 80906.0i | −0.882463 | − | 0.301523i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −35229.1 | − | 17636.4i | −0.130285 | − | 0.0652232i | ||||
\(521\) | 17832.5 | 0.0656956 | 0.0328478 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328478 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 51996.2i | 0.190094i | 0.995473 | + | 0.0950470i | \(0.0303001\pi\) | ||||
−0.995473 | + | 0.0950470i | \(0.969700\pi\) | |||||||
\(524\) | −9069.23 | + | 11722.0i | −0.0330299 | + | 0.0426911i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 58181.8 | + | 19879.8i | 0.210289 | + | 0.0718522i | ||||
\(527\) | −439461. | − | 253723.i | −1.58234 | − | 0.913562i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −64868.3 | − | 112355.i | −0.231804 | − | 0.401496i | ||||
\(530\) | 75255.7 | − | 14813.0i | 0.267909 | − | 0.0527342i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 425941. | − | 174440.i | 1.50497 | − | 0.616343i | ||||
\(533\) | −22531.1 | − | 39025.1i | −0.0793101 | − | 0.137369i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −114697. | − | 66220.2i | −0.400722 | − | 0.231357i | ||||
\(536\) | 4331.53 | − | 257.838i | 0.0150769 | − | 0.000897465i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 200262. | + | 229277.i | 0.691884 | + | 0.792129i | ||||
\(539\) | − | 27798.8i | − | 0.0956862i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −329819. | −1.12689 | −0.563444 | − | 0.826154i | \(-0.690524\pi\) | ||||
−0.563444 | + | 0.826154i | \(0.690524\pi\) | |||||||
\(542\) | 235215. | − | 205448.i | 0.800693 | − | 0.699364i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −178743. | − | 371773.i | −0.603993 | − | 1.25626i | ||||
\(545\) | 36515.9 | − | 63247.5i | 0.122939 | − | 0.212936i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 306032. | − | 176688.i | 1.02280 | − | 0.590517i | 0.107890 | − | 0.994163i | \(-0.465591\pi\) |
0.914915 | + | 0.403646i | \(0.132257\pi\) | |||||||
\(548\) | −24700.5 | + | 10115.8i | −0.0822516 | + | 0.0336853i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9299.45 | + | 47244.6i | 0.0307420 | + | 0.156181i | ||||
\(551\) | −404489. | + | 233532.i | −1.33230 | + | 0.769206i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −97476.3 | + | 168834.i | −0.318749 | + | 0.552090i | ||||
\(554\) | −6130.27 | + | 17941.3i | −0.0199738 | + | 0.0584568i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8114.69 | + | 10488.2i | −0.0262496 | + | 0.0339275i | ||||
\(557\) | 381405. | 1.22935 | 0.614676 | − | 0.788780i | \(-0.289287\pi\) | ||||
0.614676 | + | 0.788780i | \(0.289287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54475.0i | 0.174330i | ||||||||
\(560\) | 64392.6 | − | 232856.i | 0.205334 | − | 0.742526i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 55883.6 | − | 163553.i | 0.176934 | − | 0.517830i | ||||
\(563\) | −203807. | − | 117668.i | −0.642988 | − | 0.371229i | 0.142776 | − | 0.989755i | \(-0.454397\pi\) |
−0.785765 | + | 0.618526i | \(0.787730\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26916.0 | + | 46619.9i | 0.0843168 | + | 0.146041i | ||||
\(566\) | −27900.1 | − | 141743.i | −0.0870909 | − | 0.442454i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −46337.9 | − | 70257.6i | −0.143628 | − | 0.217769i | ||||
\(569\) | −110971. | − | 192208.i | −0.342757 | − | 0.593673i | 0.642186 | − | 0.766549i | \(-0.278028\pi\) |
−0.984944 | + | 0.172875i | \(0.944694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34588.3 | + | 19969.5i | 0.106086 | + | 0.0612486i | 0.552104 | − | 0.833775i | \(-0.313825\pi\) |
−0.446018 | + | 0.895024i | \(0.647158\pi\) | |||||||
\(572\) | −31271.0 | − | 4244.10i | −0.0955763 | − | 0.0129716i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 208124. | − | 181786.i | 0.631683 | − | 0.551742i | ||||
\(575\) | 68818.8i | 0.208148i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 511135. | 1.53527 | 0.767634 | − | 0.640889i | \(-0.221434\pi\) | ||||
0.767634 | + | 0.640889i | \(0.221434\pi\) | |||||||
\(578\) | −207247. | − | 237274.i | −0.620343 | − | 0.710224i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32970.5 | + | 242930.i | −0.0980098 | + | 0.722147i | ||||
\(581\) | 17000.0 | − | 29444.8i | 0.0503612 | − | 0.0872281i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 53206.7 | − | 30718.9i | 0.156541 | − | 0.0903793i | ||||
\(584\) | 505985. | − | 333719.i | 1.48358 | − | 0.978486i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 377137. | − | 74234.1i | 1.09826 | − | 0.216176i | ||||
\(587\) | 60509.5 | − | 34935.2i | 0.175609 | − | 0.101388i | −0.409619 | − | 0.912257i | \(-0.634338\pi\) |
0.585228 | + | 0.810869i | \(0.301005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −406079. | + | 703350.i | −1.17052 | + | 2.02741i | ||||
\(590\) | 362059. | + | 123710.i | 1.04010 | + | 0.355385i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 345938. | + | 95663.4i | 0.987085 | + | 0.272962i | ||||
\(593\) | −206980. | −0.588599 | −0.294299 | − | 0.955713i | \(-0.595086\pi\) | ||||
−0.294299 | + | 0.955713i | \(0.595086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 380174.i | − | 1.07386i | ||||||
\(596\) | 39517.3 | + | 30574.4i | 0.111249 | + | 0.0860726i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −42680.4 | − | 14583.2i | −0.119351 | − | 0.0407803i | ||||
\(599\) | 241159. | + | 139233.i | 0.672123 | + | 0.388051i | 0.796881 | − | 0.604137i | \(-0.206482\pi\) |
−0.124757 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −213736. | − | 370201.i | −0.591737 | − | 1.02492i | −0.993999 | − | 0.109393i | \(-0.965109\pi\) |
0.402262 | − | 0.915525i | \(-0.368224\pi\) | |||||||
\(602\) | −327769. | + | 64516.8i | −0.904430 | + | 0.178024i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −55541.6 | − | 135620.i | −0.152246 | − | 0.371748i | ||||
\(605\) | 106266. | + | 184058.i | 0.290325 | + | 0.502857i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −361479. | − | 208700.i | −0.981082 | − | 0.566428i | −0.0784853 | − | 0.996915i | \(-0.525008\pi\) |
−0.902597 | + | 0.430487i | \(0.858342\pi\) | |||||||
\(608\) | −595016. | + | 286076.i | −1.60961 | + | 0.773880i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 146290. | + | 167486.i | 0.393147 | + | 0.450109i | ||||
\(611\) | 121339.i | 0.325026i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23327.6 | −0.0620796 | −0.0310398 | − | 0.999518i | \(-0.509882\pi\) | ||||
−0.0310398 | + | 0.999518i | \(0.509882\pi\) | |||||||
\(614\) | −423699. | + | 370079.i | −1.12388 | + | 0.981652i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11499.2 | − | 193180.i | −0.0303045 | − | 0.509098i | ||||
\(617\) | 39385.7 | − | 68218.0i | 0.103459 | − | 0.179196i | −0.809649 | − | 0.586915i | \(-0.800342\pi\) |
0.913108 | + | 0.407719i | \(0.133676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 382655. | − | 220926.i | 0.998679 | − | 0.576587i | 0.0908215 | − | 0.995867i | \(-0.471051\pi\) |
0.907857 | + | 0.419280i | \(0.137717\pi\) | |||||||
\(620\) | 161561. | + | 394494.i | 0.420293 | + | 1.02626i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −126279. | − | 641545.i | −0.326401 | − | 1.65824i | ||||
\(623\) | 312348. | − | 180334.i | 0.804753 | − | 0.464625i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 124028. | − | 214823.i | 0.317512 | − | 0.549947i | ||||
\(626\) | 66334.9 | − | 194141.i | 0.169275 | − | 0.495415i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −267059. | − | 206623.i | −0.677155 | − | 0.523912i | ||||
\(629\) | 564798. | 1.42755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 211599.i | 0.531440i | 0.964050 | + | 0.265720i | \(0.0856097\pi\) | ||||
−0.964050 | + | 0.265720i | \(0.914390\pi\) | |||||||
\(632\) | 125181. | − | 250053.i | 0.313405 | − | 0.626034i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −36277.7 | + | 106173.i | −0.0902530 | + | 0.264142i | ||||
\(635\) | −9709.36 | − | 5605.70i | −0.0240793 | − | 0.0139022i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5969.11 | + | 10338.8i | 0.0147106 | + | 0.0254795i | ||||
\(638\) | 37926.0 | + | 192678.i | 0.0931743 | + | 0.473360i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −72353.7 | + | 338903.i | −0.176645 | + | 0.827401i | ||||
\(641\) | −2552.74 | − | 4421.47i | −0.00621284 | − | 0.0107610i | 0.862902 | − | 0.505371i | \(-0.168644\pi\) |
−0.869115 | + | 0.494610i | \(0.835311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −69127.8 | − | 39911.0i | −0.167198 | − | 0.0965318i | 0.414066 | − | 0.910247i | \(-0.364108\pi\) |
−0.581264 | + | 0.813715i | \(0.697442\pi\) | |||||||
\(644\) | 37197.3 | − | 274074.i | 0.0896891 | − | 0.660839i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −782463. | + | 683441.i | −1.87499 | + | 1.63771i | ||||
\(647\) | − | 531516.i | − | 1.26972i | −0.772628 | − | 0.634859i | \(-0.781058\pi\) | ||
0.772628 | − | 0.634859i | \(-0.218942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 306477. | 0.727627 | ||||||||
\(650\) | −13603.2 | − | 15574.2i | −0.0321969 | − | 0.0368619i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 678119. | + | 92034.3i | 1.59518 | + | 0.216498i | ||||
\(653\) | −235615. | + | 408097.i | −0.552556 | + | 0.957055i | 0.445533 | + | 0.895265i | \(0.353014\pi\) |
−0.998089 | + | 0.0617897i | \(0.980319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16967.4 | − | 9796.15i | 0.0395488 | − | 0.0228335i | ||||
\(656\) | −282509. | + | 278029.i | −0.656485 | + | 0.646074i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −730082. | + | 143707.i | −1.68624 | + | 0.331913i | ||||
\(659\) | 309469. | − | 178672.i | 0.712601 | − | 0.411420i | −0.0994224 | − | 0.995045i | \(-0.531700\pi\) |
0.812023 | + | 0.583625i | \(0.198366\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 282792. | − | 489809.i | 0.647237 | − | 1.12105i | −0.336543 | − | 0.941668i | \(-0.609258\pi\) |
0.983780 | − | 0.179380i | \(-0.0574090\pi\) | |||||||
\(662\) | −426922. | − | 145872.i | −0.974165 | − | 0.332857i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21831.8 | + | 43609.5i | −0.0495168 | + | 0.0989111i | ||||
\(665\) | −608463. | −1.37591 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 280664.i | 0.630864i | ||||||||
\(668\) | 108172. | − | 139812.i | 0.242417 | − | 0.313323i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5428.08 | − | 1854.69i | −0.0120920 | − | 0.00413163i | ||||
\(671\) | 154264. | + | 89064.5i | 0.342626 | + | 0.197815i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 158119. | + | 273870.i | 0.349103 | + | 0.604663i | 0.986090 | − | 0.166211i | \(-0.0531532\pi\) |
−0.636988 | + | 0.770874i | \(0.719820\pi\) | |||||||
\(674\) | −81710.5 | + | 16083.6i | −0.179870 | + | 0.0354049i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −410345. | + | 168052.i | −0.897957 | + | 0.367749i | ||||
\(677\) | −300914. | − | 521198.i | −0.656545 | − | 1.13717i | −0.981504 | − | 0.191441i | \(-0.938684\pi\) |
0.324959 | − | 0.945728i | \(-0.394649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 257556. | + | 148700.i | 0.558641 | + | 0.322531i | ||||
\(680\) | 32403.1 | + | 544353.i | 0.0700758 | + | 1.17723i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 224633. | + | 257180.i | 0.482953 | + | 0.552927i | ||||
\(683\) | 385277.i | 0.825909i | 0.910752 | + | 0.412955i | \(0.135503\pi\) | ||||
−0.910752 | + | 0.412955i | \(0.864497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35285.0 | 0.0751984 | ||||||||
\(686\) | −377877. | + | 330056.i | −0.802975 | + | 0.701357i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 463817. | − | 120315.i | 0.979873 | − | 0.254180i | ||||
\(689\) | −13192.2 | + | 22849.6i | −0.0277895 | + | 0.0481328i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −397767. | + | 229651.i | −0.833053 | + | 0.480963i | −0.854897 | − | 0.518798i | \(-0.826380\pi\) |
0.0218438 | + | 0.999761i | \(0.493046\pi\) | |||||||
\(692\) | 324788. | − | 133014.i | 0.678247 | − | 0.277769i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 124541. | + | 632712.i | 0.258578 | + | 1.31367i | ||||
\(695\) | 15181.6 | − | 8765.10i | 0.0314303 | − | 0.0181463i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −311866. | + | 540168.i | −0.641952 | + | 1.11189i | ||||
\(698\) | 286451. | − | 838349.i | 0.587948 | − | 1.72074i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 77596.9 | − | 100294.i | 0.158361 | − | 0.204681i | ||||
\(701\) | 127011. | 0.258467 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 903950.i | − | 1.82908i | ||||||
\(704\) | 32930.3 | + | 275625.i | 0.0664432 | + | 0.556126i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 282966. | − | 828150.i | 0.567707 | − | 1.66150i | ||||
\(707\) | −358820. | − | 207165.i | −0.717857 | − | 0.414455i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −247408. | − | 428523.i | −0.492177 | − | 0.852475i | 0.507783 | − | 0.861485i | \(-0.330465\pi\) |
−0.999959 | + | 0.00901014i | \(0.997132\pi\) | |||||||
\(710\) | 21487.4 | + | 109164.i | 0.0426253 | + | 0.216552i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −431865. | + | 284834.i | −0.851900 | + | 0.561864i | ||||
\(713\) | 244018. | + | 422652.i | 0.480002 | + | 0.831388i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36128.6 | + | 20858.8i | 0.0706706 | + | 0.0408017i | ||||
\(716\) | 181998. | + | 24700.8i | 0.355011 | + | 0.0481820i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2785.49 | + | 2432.98i | −0.00540322 | + | 0.00471943i | ||||
\(719\) | − | 614613.i | − | 1.18890i | −0.804134 | − | 0.594448i | \(-0.797371\pi\) | ||
0.804134 | − | 0.594448i | \(-0.202629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 504518. | 0.970523 | ||||||||
\(722\) | 750914. | + | 859712.i | 1.44051 | + | 1.64922i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −97846.7 | + | 720945.i | −0.186668 | + | 1.37539i | ||||
\(725\) | −64338.5 | + | 111438.i | −0.122404 | + | 0.212010i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −286999. | + | 165699.i | −0.543014 | + | 0.313509i | −0.746299 | − | 0.665610i | \(-0.768171\pi\) |
0.203286 | + | 0.979119i | \(0.434838\pi\) | |||||||
\(728\) | 45757.4 | + | 69377.4i | 0.0863373 | + | 0.130905i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −786182. | + | 154749.i | −1.47529 | + | 0.290390i | ||||
\(731\) | 652999. | − | 377009.i | 1.22202 | − | 0.705532i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25808.4 | − | 44701.5i | 0.0480345 | − | 0.0831982i | −0.841008 | − | 0.541022i | \(-0.818038\pi\) |
0.889043 | + | 0.457824i | \(0.151371\pi\) | |||||||
\(734\) | 154426. | + | 52764.9i | 0.286634 | + | 0.0979383i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29901.1 | + | 395603.i | −0.0551990 | + | 0.730305i | ||||
\(737\) | −4594.79 | −0.00845923 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 228968.i | − | 0.419263i | −0.977780 | − | 0.209631i | \(-0.932774\pi\) | ||
0.977780 | − | 0.209631i | \(-0.0672264\pi\) | |||||||
\(740\) | −375269. | − | 290344.i | −0.685298 | − | 0.530212i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −153107. | − | 52314.4i | −0.278092 | − | 0.0950196i | ||||
\(743\) | 910009. | + | 525394.i | 1.64842 | + | 0.951716i | 0.977700 | + | 0.210005i | \(0.0673480\pi\) |
0.670720 | + | 0.741711i | \(0.265985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33025.0 | − | 57201.0i | −0.0595018 | − | 0.103060i | ||||
\(746\) | −920459. | + | 181179.i | −1.65397 | + | 0.325560i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 165545. | + | 404223.i | 0.295878 | + | 0.722466i | ||||
\(749\) | 139692. | + | 241953.i | 0.249004 | + | 0.431288i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −233295. | − | 134693.i | −0.413643 | − | 0.238817i | 0.278711 | − | 0.960375i | \(-0.410093\pi\) |
−0.692354 | + | 0.721558i | \(0.743426\pi\) | |||||||
\(752\) | 1.03312e6 | − | 267993.i | 1.82690 | − | 0.473901i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −55478.1 | − | 63516.2i | −0.0975840 | − | 0.111723i | ||||
\(755\) | 193735.i | 0.339870i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −476176. | −0.830952 | −0.415476 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415476 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(758\) | −559002. | + | 488259.i | −0.972915 | + | 0.849791i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 871228. | − | 51860.6i | 1.50836 | − | 0.0897863i | ||||
\(761\) | 242197. | − | 419498.i | 0.418215 | − | 0.724370i | −0.577545 | − | 0.816359i | \(-0.695989\pi\) |
0.995760 | + | 0.0919890i | \(0.0293225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −133421. | + | 77030.4i | −0.229178 | + | 0.132316i | ||||
\(764\) | −424714. | − | 1.03705e6i | −0.727628 | − | 1.77670i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46555.3 | − | 236518.i | −0.0793436 | − | 0.403095i | ||||
\(767\) | −113983. | + | 65808.4i | −0.193754 | + | 0.111864i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −251061. | + | 434851.i | −0.424549 | + | 0.735340i | −0.996378 | − | 0.0850327i | \(-0.972901\pi\) |
0.571830 | + | 0.820372i | \(0.306234\pi\) | |||||||
\(770\) | −82716.6 | + | 242085.i | −0.139512 | + | 0.408307i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 441050. | + | 341238.i | 0.740037 | + | 0.572563i | ||||
\(773\) | −435529. | −0.728884 | −0.364442 | − | 0.931226i | \(-0.618740\pi\) | ||||
−0.364442 | + | 0.931226i | \(0.618740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 223752.i | 0.372531i | ||||||||
\(776\) | −381456. | − | 190964.i | −0.633463 | − | 0.317124i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15531.9 | + | 45457.0i | −0.0256606 | + | 0.0751004i | ||||
\(779\) | 864530. | + | 499136.i | 1.42464 | + | 0.822516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44560.0 | + | 77180.2i | 0.0730539 | + | 0.126533i | ||||
\(782\) | 120571. | + | 612543.i | 0.197164 | + | 1.00167i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 74844.3 | − | 73657.4i | 0.121766 | − | 0.119835i | ||||
\(785\) | 223184. | + | 386566.i | 0.362179 | + | 0.627313i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −371945. | − | 214742.i | −0.600522 | − | 0.346711i | 0.168725 | − | 0.985663i | \(-0.446035\pi\) |
−0.769247 | + | 0.638952i | \(0.779368\pi\) | |||||||
\(788\) | −66399.9 | + | 489242.i | −0.106934 | + | 0.787900i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −278416. | + | 243182.i | −0.446108 | + | 0.389652i | ||||
\(791\) | − | 113559.i | − | 0.181496i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −76497.5 | −0.121647 | ||||||||
\(794\) | −84930.9 | − | 97236.4i | −0.134718 | − | 0.154237i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −543219. | − | 73725.7i | −0.857332 | − | 0.116357i | ||||
\(797\) | 362714. | − | 628240.i | 0.571016 | − | 0.989028i | −0.425446 | − | 0.904984i | \(-0.639883\pi\) |
0.996462 | − | 0.0840446i | \(-0.0267838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.45451e6 | − | 839761.i | 2.27836 | − | 1.31541i | ||||
\(800\) | −102559. | + | 150220.i | −0.160248 | + | 0.234718i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 736768. | − | 145023.i | 1.14547 | − | 0.225469i | ||||
\(803\) | −555840. | + | 320914.i | −0.862023 | + | 0.497689i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −182817. | + | 316648.i | −0.282114 | + | 0.488635i | ||||
\(806\) | −138767. | − | 47414.6i | −0.213608 | − | 0.0729863i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 531434. | + | 266046.i | 0.814004 | + | 0.407506i | ||||
\(809\) | −144295. | −0.220473 | −0.110237 | − | 0.993905i | \(-0.535161\pi\) | ||||
−0.110237 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 321928.i | 0.489460i | 0.969591 | + | 0.244730i | \(0.0786993\pi\) | ||||
−0.969591 | + | 0.244730i | \(0.921301\pi\) | |||||||
\(812\) | 316464. | − | 409029.i | 0.479968 | − | 0.620358i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −359648. | − | 122886.i | −0.542787 | − | 0.185462i | ||||
\(815\) | −783456. | − | 452328.i | −1.17950 | − | 0.680987i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −603397. | − | 1.04511e6i | −0.903980 | − | 1.56574i | ||||
\(818\) | −528044. | + | 103938.i | −0.789156 | + | 0.155334i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 484896. | − | 198584.i | 0.721142 | − | 0.295336i | ||||
\(821\) | 453891. | + | 786162.i | 0.673388 | + | 1.16634i | 0.976937 | + | 0.213527i | \(0.0684950\pi\) |
−0.303549 | + | 0.952816i | \(0.598172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 730902. | + | 421987.i | 1.07909 | + | 0.623016i | 0.930652 | − | 0.365905i | \(-0.119241\pi\) |
0.148443 | + | 0.988921i | \(0.452574\pi\) | |||||||
\(824\) | −722394. | + | 43001.1i | −1.06395 | + | 0.0633323i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −530955. | − | 607885.i | −0.778212 | − | 0.890966i | ||||
\(827\) | − | 658309.i | − | 0.962540i | −0.876572 | − | 0.481270i | \(-0.840176\pi\) | ||
0.876572 | − | 0.481270i | \(-0.159824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.22965e6 | 1.78925 | 0.894625 | − | 0.446818i | \(-0.147443\pi\) | ||||
0.894625 | + | 0.446818i | \(0.147443\pi\) | |||||||
\(830\) | 48556.0 | − | 42411.2i | 0.0704834 | − | 0.0615636i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −71430.9 | − | 95438.0i | −0.103190 | − | 0.137872i | ||||
\(833\) | 82621.7 | − | 143105.i | 0.119071 | − | 0.206236i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −202377. | + | 116842.i | −0.290261 | + | 0.167582i | ||||
\(836\) | 646952. | − | 264952.i | 0.925677 | − | 0.379101i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −65404.3 | − | 332278.i | −0.0931362 | − | 0.473166i | ||||
\(839\) | −45546.9 | + | 26296.5i | −0.0647045 | + | 0.0373572i | −0.532003 | − | 0.846742i | \(-0.678561\pi\) |
0.467299 | + | 0.884099i | \(0.345227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 91248.2 | − | 158047.i | 0.129013 | − | 0.223456i | ||||
\(842\) | 149637. | − | 437940.i | 0.211064 | − | 0.617718i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −169465. | + | 219033.i | −0.237900 | + | 0.307486i | ||||
\(845\) | 586183. | 0.820956 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 448337.i | − | 0.624939i | ||||||
\(848\) | 223686. | + | 61856.6i | 0.311062 | + | 0.0860191i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −92544.7 | + | 270849.i | −0.128090 | + | 0.374877i | ||||
\(851\) | −470421. | − | 271598.i | −0.649572 | − | 0.375031i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 322258. | + | 558168.i | 0.442900 | + | 0.767126i | 0.997903 | − | 0.0647226i | \(-0.0206163\pi\) |
−0.555003 | + | 0.831848i | \(0.687283\pi\) | |||||||
\(854\) | −90598.9 | − | 460276.i | −0.124224 | − | 0.631106i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −220639. | − | 334534.i | −0.301117 | − | 0.456555i | ||||
\(857\) | 175819. | + | 304528.i | 0.239390 | + | 0.414635i | 0.960539 | − | 0.278144i | \(-0.0897194\pi\) |
−0.721150 | + | 0.692779i | \(0.756386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −658817. | − | 380368.i | −0.892851 | − | 0.515487i | −0.0179767 | − | 0.999838i | \(-0.505722\pi\) |
−0.874874 | + | 0.484351i | \(0.839056\pi\) | |||||||
\(860\) | −627681. | − | 85188.9i | −0.848676 | − | 0.115182i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 888412. | − | 775981.i | 1.19564 | − | 1.04433i | ||||
\(863\) | 363360.i | 0.487883i | 0.969790 | + | 0.243942i | \(0.0784406\pi\) | ||||
−0.969790 | + | 0.243942i | \(0.921559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −463964. | −0.620086 | ||||||||
\(866\) | 398084. | + | 455761.i | 0.530809 | + | 0.607717i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 120940. | − | 891100.i | 0.160521 | − | 1.18273i | ||||
\(869\) | −148054. | + | 256438.i | −0.196057 | + | 0.339580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1708.87 | − | 986.617i | 0.00225254 | − | 0.00130051i | ||||
\(872\) | 184473. | − | 121668.i | 0.242605 | − | 0.160008i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 980365. | − | 192971.i | 1.28341 | − | 0.252621i | ||||
\(875\) | −655985. | + | 378733.i | −0.856796 | + | 0.494672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36035.0 | + | 62414.4i | −0.0468516 | + | 0.0811494i | −0.888500 | − | 0.458876i | \(-0.848252\pi\) |
0.841649 | + | 0.540026i | \(0.181585\pi\) | |||||||
\(878\) | −75756.3 | − | 25884.7i | −0.0982720 | − | 0.0335780i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 97804.3 | − | 353680.i | 0.126297 | − | 0.456714i | ||||
\(881\) | −1.34754e6 | −1.73616 | −0.868082 | − | 0.496422i | \(-0.834647\pi\) | ||||
−0.868082 | + | 0.496422i | \(0.834647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 675925.i | 0.866916i | 0.901174 | + | 0.433458i | \(0.142707\pi\) | ||||
−0.901174 | + | 0.433458i | \(0.857293\pi\) | |||||||
\(884\) | −148365. | − | 114790.i | −0.189858 | − | 0.146892i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −146273. | − | 49979.2i | −0.186336 | − | 0.0636681i | ||||
\(887\) | −888008. | − | 512692.i | −1.12868 | − | 0.651642i | −0.185075 | − | 0.982724i | \(-0.559253\pi\) |
−0.943602 | + | 0.331082i | \(0.892586\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11825.2 | + | 20481.9i | 0.0149626 | + | 0.0259159i | ||||
\(890\) | 671018. | − | 132081.i | 0.847138 | − | 0.166747i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −388498. | − | 948622.i | −0.488269 | − | 1.19224i | ||||
\(893\) | −1.34402e6 | − | 2.32792e6i | −1.68540 | − | 2.91921i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −210269. | − | 121399.i | −0.262500 | − | 0.151555i | ||||
\(896\) | 489640. | − | 542821.i | 0.609904 | − | 0.676147i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 209083. | + | 239377.i | 0.259278 | + | 0.296845i | ||||
\(899\) | 912528.i | 1.12908i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 365202. | 0.449867 | ||||||||
\(902\) | 316115. | − | 276110.i | 0.388537 | − | 0.339367i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9678.86 | + | 162599.i | 0.0118437 | + | 0.198967i | ||||
\(905\) | 480895. | − | 832935.i | 0.587156 | − | 1.01698i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.39930e6 | + | 807885.i | −1.70097 | + | 0.982053i | −0.756181 | + | 0.654363i | \(0.772937\pi\) |
−0.944785 | + | 0.327690i | \(0.893730\pi\) | |||||||
\(908\) | 83027.1 | + | 202733.i | 0.100704 | + | 0.245896i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21218.2 | − | 107796.i | −0.0256227 | − | 0.130173i | ||||
\(911\) | −246841. | + | 142514.i | −0.297427 | + | 0.171719i | −0.641286 | − | 0.767302i | \(-0.721599\pi\) |
0.343860 | + | 0.939021i | \(0.388266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25820.8 | − | 44723.0i | 0.0309762 | − | 0.0536524i | ||||
\(914\) | 340858. | − | 997583.i | 0.408020 | − | 1.19414i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −835108. | − | 646119.i | −0.995295 | − | 0.770055i | ||||
\(917\) | −41330.0 | −0.0491503 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 662333.i | 0.784233i | 0.919916 | + | 0.392117i | \(0.128257\pi\) | ||||
−0.919916 | + | 0.392117i | \(0.871743\pi\) | |||||||
\(920\) | 234777. | − | 468974.i | 0.277384 | − | 0.554081i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −259453. | + | 759336.i | −0.305209 | + | 0.893249i | ||||
\(923\) | −33145.1 | − | 19136.3i | −0.0389059 | − | 0.0224623i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −124520. | − | 215675.i | −0.145531 | − | 0.252067i | ||||
\(926\) | −183131. | − | 930373.i | −0.213570 | − | 1.08501i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −418267. | + | 612641.i | −0.485688 | + | 0.711394i | ||||
\(929\) | 620275. | + | 1.07435e6i | 0.718708 | + | 1.24484i | 0.961512 | + | 0.274764i | \(0.0885997\pi\) |
−0.242803 | + | 0.970076i | \(0.578067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −229037. | − | 132235.i | −0.264245 | − | 0.152562i | ||||
\(932\) | −136300. | + | 1.00427e6i | −0.156914 | + | 1.15616i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −694300. | + | 606435.i | −0.795891 | + | 0.695169i | ||||
\(935\) | − | 577438.i | − | 0.660514i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −593717. | −0.676239 | −0.338119 | − | 0.941103i | \(-0.609791\pi\) | ||||
−0.338119 | + | 0.941103i | \(0.609791\pi\) | |||||||
\(938\) | 7960.23 | + | 9113.57i | 0.00904732 | + | 0.0103582i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.39812e6 | − | 189752.i | −1.58229 | − | 0.214749i | ||||
\(941\) | −613509. | + | 1.06263e6i | −0.692854 | + | 1.20006i | 0.278044 | + | 0.960568i | \(0.410314\pi\) |
−0.970899 | + | 0.239491i | \(0.923020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 519507. | − | 299938.i | 0.584209 | − | 0.337293i | ||||
\(944\) | 812060. | + | 825145.i | 0.911264 | + | 0.925947i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −497840. | + | 97992.9i | −0.556298 | + | 0.109500i | ||||
\(947\) | −1.48474e6 | + | 857213.i | −1.65558 | + | 0.955848i | −0.680857 | + | 0.732416i | \(0.738393\pi\) |
−0.974720 | + | 0.223431i | \(0.928274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 137817. | − | 238706.i | 0.153027 | − | 0.265051i | ||||
\(950\) | 433489. | + | 148116.i | 0.480320 | + | 0.164118i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 514960. | − | 1.02865e6i | 0.568198 | − | 1.13499i | ||||
\(953\) | 1.23751e6 | 1.36258 | 0.681290 | − | 0.732014i | \(-0.261419\pi\) | ||||
0.681290 | + | 0.732014i | \(0.261419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.48144e6i | 1.62434i | ||||||||
\(956\) | −3109.09 | + | 4018.50i | −0.00340187 | + | 0.00439691i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9089.93 | − | 3105.89i | −0.00990443 | − | 0.00338419i | ||||
\(959\) | −64461.5 | − | 37216.8i | −0.0700911 | − | 0.0404671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 331619. | + | 574381.i | 0.359081 | + | 0.621947i | ||||
\(962\) | 160145. | − | 31522.3i | 0.173047 | − | 0.0340619i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 377642. | − | 154659.i | 0.406374 | − | 0.166426i | ||||
\(965\) | −368589. | − | 638416.i | −0.395811 | − | 0.685565i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 858506. | + | 495659.i | 0.918101 | + | 0.530066i | 0.883029 | − | 0.469319i | \(-0.155501\pi\) |
0.0350720 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(968\) | 38212.7 | + | 641952.i | 0.0407809 | + | 0.685096i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 370974. | + | 424724.i | 0.394276 | + | 0.451402i | ||||
\(971\) | 1.45182e6i | 1.53984i | 0.638141 | + | 0.769920i | \(0.279704\pi\) | ||||
−0.638141 | + | 0.769920i | \(0.720296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36980.0 | −0.0390608 | ||||||||
\(974\) | 1.22080e6 | − | 1.06630e6i | 1.28684 | − | 1.12399i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 168954. | + | 651324.i | 0.177366 | + | 0.683750i | ||||
\(977\) | 306090. | − | 530163.i | 0.320671 | − | 0.555418i | −0.659956 | − | 0.751304i | \(-0.729425\pi\) |
0.980627 | + | 0.195886i | \(0.0627583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 474418. | − | 273905.i | 0.494989 | − | 0.285782i | ||||
\(980\) | −128462. | + | 52610.3i | −0.133759 | + | 0.0547796i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −99305.1 | − | 504507.i | −0.102979 | − | 0.523171i | ||||
\(983\) | 1.04512e6 | − | 603401.i | 1.08158 | − | 0.624452i | 0.150259 | − | 0.988647i | \(-0.451989\pi\) |
0.931323 | + | 0.364195i | \(0.118656\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 326341. | − | 565239.i | 0.336356 | − | 0.582586i | ||||
\(986\) | −377426. | + | 1.10460e6i | −0.388220 | + | 1.13620i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −183719. | + | 237456.i | −0.188209 | + | 0.243260i | ||||
\(989\) | −725178. | −0.741399 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 860509.i | − | 0.876210i | −0.898924 | − | 0.438105i | \(-0.855650\pi\) | ||
0.898924 | − | 0.438105i | \(-0.144350\pi\) | |||||||
\(992\) | −97217.8 | + | 1.28623e6i | −0.0987921 | + | 1.30706i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 75885.8 | − | 222093.i | 0.0768047 | − | 0.224783i | ||||
\(995\) | 627601. | + | 362346.i | 0.633924 | + | 0.365996i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 243483. | + | 421725.i | 0.244951 | + | 0.424267i | 0.962118 | − | 0.272634i | \(-0.0878949\pi\) |
−0.717167 | + | 0.696901i | \(0.754562\pi\) | |||||||
\(998\) | −99351.8 | − | 504744.i | −0.0997504 | − | 0.506769i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.f.a.91.6 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.31.17 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.91.9 | 44 | ||
9.2 | odd | 6 | 36.5.f.a.7.14 | ✓ | 44 | ||
9.4 | even | 3 | 324.5.d.e.163.21 | 22 | |||
9.5 | odd | 6 | 324.5.d.f.163.2 | 22 | |||
9.7 | even | 3 | inner | 108.5.f.a.19.9 | 44 | ||
12.11 | even | 2 | 36.5.f.a.31.14 | yes | 44 | ||
36.7 | odd | 6 | inner | 108.5.f.a.19.6 | 44 | ||
36.11 | even | 6 | 36.5.f.a.7.17 | yes | 44 | ||
36.23 | even | 6 | 324.5.d.f.163.1 | 22 | |||
36.31 | odd | 6 | 324.5.d.e.163.22 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.14 | ✓ | 44 | 9.2 | odd | 6 | ||
36.5.f.a.7.17 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.14 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.17 | yes | 44 | 3.2 | odd | 2 | ||
108.5.f.a.19.6 | 44 | 36.7 | odd | 6 | inner | ||
108.5.f.a.19.9 | 44 | 9.7 | even | 3 | inner | ||
108.5.f.a.91.6 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.9 | 44 | 4.3 | odd | 2 | inner | ||
324.5.d.e.163.21 | 22 | 9.4 | even | 3 | |||
324.5.d.e.163.22 | 22 | 36.31 | odd | 6 | |||
324.5.d.f.163.1 | 22 | 36.23 | even | 6 | |||
324.5.d.f.163.2 | 22 | 9.5 | odd | 6 |