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 | 91.21 | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.5.f.a.19.21 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.93519 | − | 0.717143i | 0.983797 | − | 0.179286i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.9714 | − | 5.64418i | 0.935713 | − | 0.352761i | ||||
\(5\) | 5.51579 | − | 9.55363i | 0.220632 | − | 0.382145i | −0.734368 | − | 0.678751i | \(-0.762521\pi\) |
0.955000 | + | 0.296606i | \(0.0958548\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.3188 | + | 5.95759i | −0.210589 | + | 0.121583i | −0.601585 | − | 0.798809i | \(-0.705464\pi\) |
0.390996 | + | 0.920392i | \(0.372131\pi\) | |||||||
\(8\) | 54.8676 | − | 32.9476i | 0.857307 | − | 0.514806i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.8544 | − | 41.5509i | 0.148544 | − | 0.415509i | ||||
\(11\) | 189.995 | − | 109.694i | 1.57021 | − | 0.906559i | 0.574063 | − | 0.818811i | \(-0.305367\pi\) |
0.996143 | − | 0.0877473i | \(-0.0279668\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5350 | − | 32.1036i | 0.109675 | − | 0.189962i | −0.805964 | − | 0.591965i | \(-0.798352\pi\) |
0.915639 | + | 0.402003i | \(0.131686\pi\) | |||||||
\(14\) | −36.3341 | + | 30.8443i | −0.185378 | + | 0.157369i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 192.286 | − | 169.003i | 0.751119 | − | 0.660167i | ||||
\(17\) | −284.021 | −0.982771 | −0.491386 | − | 0.870942i | \(-0.663509\pi\) | ||||
−0.491386 | + | 0.870942i | \(0.663509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 45.4901i | 0.126011i | 0.998013 | + | 0.0630057i | \(0.0200686\pi\) | ||||
−0.998013 | + | 0.0630057i | \(0.979931\pi\) | |||||||
\(20\) | 28.6568 | − | 174.163i | 0.0716419 | − | 0.435409i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 669.000 | − | 567.918i | 1.38223 | − | 1.17338i | ||||
\(23\) | 174.319 | + | 100.643i | 0.329525 | + | 0.190252i | 0.655630 | − | 0.755082i | \(-0.272403\pi\) |
−0.326105 | + | 0.945334i | \(0.605736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 251.652 | + | 435.874i | 0.402643 | + | 0.697399i | ||||
\(26\) | 49.9160 | − | 139.626i | 0.0738402 | − | 0.206547i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −120.862 | + | 147.435i | −0.154161 | + | 0.188055i | ||||
\(29\) | −614.153 | − | 1063.74i | −0.730265 | − | 1.26486i | −0.956770 | − | 0.290846i | \(-0.906063\pi\) |
0.226505 | − | 0.974010i | \(-0.427270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1311.83 | + | 757.384i | 1.36507 | + | 0.788121i | 0.990293 | − | 0.138996i | \(-0.0443875\pi\) |
0.374773 | + | 0.927117i | \(0.377721\pi\) | |||||||
\(32\) | 635.484 | − | 802.954i | 0.620590 | − | 0.784135i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1117.68 | + | 203.683i | −0.966847 | + | 0.176197i | ||||
\(35\) | 131.443i | 0.107301i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1521.29 | −1.11124 | −0.555622 | − | 0.831435i | \(-0.687520\pi\) | ||||
−0.555622 | + | 0.831435i | \(0.687520\pi\) | |||||||
\(38\) | 32.6229 | + | 179.012i | 0.0225920 | + | 0.123970i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.1303 | − | 705.917i | −0.00758145 | − | 0.441198i | ||||
\(41\) | −1316.97 | + | 2281.07i | −0.783447 | + | 1.35697i | 0.146476 | + | 0.989214i | \(0.453207\pi\) |
−0.929923 | + | 0.367755i | \(0.880126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.6057 | − | 19.9796i | 0.0187159 | − | 0.0108056i | −0.490613 | − | 0.871378i | \(-0.663227\pi\) |
0.509329 | + | 0.860572i | \(0.329894\pi\) | |||||||
\(44\) | 2225.36 | − | 2714.63i | 1.14946 | − | 1.40219i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 758.153 | + | 271.038i | 0.358295 | + | 0.128090i | ||||
\(47\) | −2498.36 | + | 1442.43i | −1.13099 | + | 0.652978i | −0.944184 | − | 0.329419i | \(-0.893147\pi\) |
−0.186807 | + | 0.982397i | \(0.559814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1129.51 | + | 1956.38i | −0.470435 | + | 0.814817i | ||||
\(50\) | 1302.88 | + | 1534.78i | 0.521153 | + | 0.613911i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 96.2969 | − | 585.252i | 0.0356128 | − | 0.216439i | ||||
\(53\) | −1415.13 | −0.503783 | −0.251892 | − | 0.967755i | \(-0.581053\pi\) | ||||
−0.251892 | + | 0.967755i | \(0.581053\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2420.19i | − | 0.800062i | ||||||
\(56\) | −369.883 | + | 666.859i | −0.117947 | + | 0.212646i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3179.66 | − | 3745.60i | −0.945203 | − | 1.11344i | ||||
\(59\) | 2453.33 | + | 1416.43i | 0.704778 | + | 0.406904i | 0.809125 | − | 0.587637i | \(-0.199942\pi\) |
−0.104346 | + | 0.994541i | \(0.533275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2628.64 | + | 4552.93i | 0.706433 | + | 1.22358i | 0.966172 | + | 0.257899i | \(0.0830300\pi\) |
−0.259739 | + | 0.965679i | \(0.583637\pi\) | |||||||
\(62\) | 5705.44 | + | 2039.68i | 1.48425 | + | 0.530614i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1924.92 | − | 3615.51i | 0.469950 | − | 0.882693i | ||||
\(65\) | −204.471 | − | 354.154i | −0.0483954 | − | 0.0838233i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −805.917 | − | 465.296i | −0.179531 | − | 0.103653i | 0.407541 | − | 0.913187i | \(-0.366386\pi\) |
−0.587073 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(68\) | −4252.19 | + | 1603.07i | −0.919592 | + | 0.346684i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 94.2635 | + | 517.254i | 0.0192375 | + | 0.105562i | ||||
\(71\) | − | 1162.75i | − | 0.230659i | −0.993327 | − | 0.115329i | \(-0.963208\pi\) | ||
0.993327 | − | 0.115329i | \(-0.0367923\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2162.87 | −0.405867 | −0.202934 | − | 0.979192i | \(-0.565048\pi\) | ||||
−0.202934 | + | 0.979192i | \(0.565048\pi\) | |||||||
\(74\) | −5986.57 | + | 1090.98i | −1.09324 | + | 0.199230i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 256.754 | + | 681.051i | 0.0444519 | + | 0.117911i | ||||
\(77\) | −1307.02 | + | 2263.82i | −0.220445 | + | 0.381822i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6482.54 | + | 3742.70i | −1.03870 | + | 0.599695i | −0.919466 | − | 0.393171i | \(-0.871378\pi\) |
−0.119237 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(80\) | −553.978 | − | 2769.22i | −0.0865591 | − | 0.432690i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3546.69 | + | 9920.88i | −0.527467 | + | 1.47544i | ||||
\(83\) | −966.756 | + | 558.157i | −0.140333 | + | 0.0810215i | −0.568523 | − | 0.822667i | \(-0.692485\pi\) |
0.428190 | + | 0.903689i | \(0.359152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1566.60 | + | 2713.43i | −0.216830 | + | 0.375561i | ||||
\(86\) | 121.852 | − | 103.441i | 0.0164754 | − | 0.0139861i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6810.44 | − | 12278.5i | 0.879447 | − | 1.58555i | ||||
\(89\) | 6739.71 | 0.850866 | 0.425433 | − | 0.904990i | \(-0.360122\pi\) | ||||
0.425433 | + | 0.904990i | \(0.360122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 441.696i | 0.0533385i | ||||||||
\(92\) | 3177.85 | + | 522.881i | 0.375455 | + | 0.0617771i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8797.09 | + | 7467.91i | −0.995596 | + | 0.845168i | ||||
\(95\) | 434.596 | + | 250.914i | 0.0481546 | + | 0.0278021i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6023.28 | − | 10432.6i | −0.640161 | − | 1.10879i | −0.985396 | − | 0.170276i | \(-0.945534\pi\) |
0.345235 | − | 0.938516i | \(-0.387799\pi\) | |||||||
\(98\) | −3041.85 | + | 8508.73i | −0.316727 | + | 0.885957i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6227.74 | + | 5105.28i | 0.622774 | + | 0.510528i | ||||
\(101\) | −4777.60 | − | 8275.04i | −0.468346 | − | 0.811199i | 0.530999 | − | 0.847372i | \(-0.321817\pi\) |
−0.999346 | + | 0.0361728i | \(0.988483\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9962.26 | + | 5751.71i | 0.939039 | + | 0.542154i | 0.889659 | − | 0.456626i | \(-0.150942\pi\) |
0.0493798 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(104\) | −40.7622 | − | 2372.13i | −0.00376870 | − | 0.219317i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5568.79 | + | 1014.85i | −0.495620 | + | 0.0903211i | ||||
\(107\) | − | 6602.72i | − | 0.576707i | −0.957524 | − | 0.288353i | \(-0.906892\pi\) | ||
0.957524 | − | 0.288353i | \(-0.0931078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12045.3 | 1.01383 | 0.506913 | − | 0.861997i | \(-0.330786\pi\) | ||||
0.506913 | + | 0.861997i | \(0.330786\pi\) | |||||||
\(110\) | −1735.62 | − | 9523.89i | −0.143440 | − | 0.787099i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −977.325 | + | 2889.48i | −0.0779117 | + | 0.230347i | ||||
\(113\) | 1865.35 | − | 3230.88i | 0.146084 | − | 0.253025i | −0.783693 | − | 0.621149i | \(-0.786666\pi\) |
0.929777 | + | 0.368124i | \(0.120000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1923.01 | − | 1110.25i | 0.145407 | − | 0.0839510i | ||||
\(116\) | −15198.7 | − | 12459.4i | −1.12951 | − | 0.925933i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10670.1 | + | 3814.54i | 0.766311 | + | 0.273954i | ||||
\(119\) | 2930.77 | − | 1692.08i | 0.206960 | − | 0.119489i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16744.9 | − | 29003.0i | 1.14370 | − | 1.98094i | ||||
\(122\) | 13609.3 | + | 16031.5i | 0.914356 | + | 1.07710i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 23914.7 | + | 3934.92i | 1.55533 | + | 0.255913i | ||||
\(125\) | 12447.0 | 0.796607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 26549.7i | − | 1.64608i | −0.567980 | − | 0.823042i | \(-0.692275\pi\) | ||
0.567980 | − | 0.823042i | \(-0.307725\pi\) | |||||||
\(128\) | 4982.07 | − | 15608.2i | 0.304082 | − | 0.952646i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1058.61 | − | 1247.03i | −0.0626396 | − | 0.0737886i | ||||
\(131\) | −1142.84 | − | 659.821i | −0.0665954 | − | 0.0384489i | 0.466333 | − | 0.884609i | \(-0.345575\pi\) |
−0.532928 | + | 0.846161i | \(0.678908\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −271.011 | − | 469.405i | −0.0153209 | − | 0.0265366i | ||||
\(134\) | −3505.12 | − | 1253.07i | −0.195206 | − | 0.0697856i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15583.6 | + | 9357.79i | −0.842537 | + | 0.505936i | ||||
\(137\) | 12906.5 | + | 22354.7i | 0.687648 | + | 1.19104i | 0.972597 | + | 0.232499i | \(0.0746901\pi\) |
−0.284949 | + | 0.958543i | \(0.591977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11377.8 | + | 6569.00i | 0.588885 | + | 0.339993i | 0.764656 | − | 0.644438i | \(-0.222909\pi\) |
−0.175772 | + | 0.984431i | \(0.556242\pi\) | |||||||
\(140\) | 741.889 | + | 1967.89i | 0.0378515 | + | 0.100403i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −833.858 | − | 4575.64i | −0.0413538 | − | 0.226921i | ||||
\(143\) | − | 8132.70i | − | 0.397706i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13550.2 | −0.644478 | ||||||||
\(146\) | −8511.29 | + | 1551.08i | −0.399291 | + | 0.0727662i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22775.9 | + | 8586.46i | −1.03981 | + | 0.392004i | ||||
\(149\) | 12968.2 | − | 22461.6i | 0.584128 | − | 1.01174i | −0.410856 | − | 0.911700i | \(-0.634770\pi\) |
0.994984 | − | 0.100038i | \(-0.0318965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24591.2 | + | 14197.8i | −1.07852 | + | 0.622681i | −0.930496 | − | 0.366303i | \(-0.880623\pi\) |
−0.148020 | + | 0.988984i | \(0.547290\pi\) | |||||||
\(152\) | 1498.79 | + | 2495.93i | 0.0648714 | + | 0.108030i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3519.88 | + | 9845.88i | −0.148418 | + | 0.415158i | ||||
\(155\) | 14471.5 | − | 8355.15i | 0.602353 | − | 0.347769i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2760.19 | − | 4780.78i | 0.111980 | − | 0.193954i | −0.804589 | − | 0.593832i | \(-0.797614\pi\) |
0.916568 | + | 0.399878i | \(0.130948\pi\) | |||||||
\(158\) | −22826.0 | + | 19377.1i | −0.914356 | + | 0.776203i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4165.93 | − | 10500.1i | −0.162732 | − | 0.410161i | ||||
\(161\) | −2398.36 | −0.0925257 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 407.281i | 0.0153292i | 0.999971 | + | 0.00766459i | \(0.00243974\pi\) | ||||
−0.999971 | + | 0.00766459i | \(0.997560\pi\) | |||||||
\(164\) | −6842.21 | + | 41584.0i | −0.254395 | + | 1.54610i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3404.09 | + | 2889.76i | −0.123534 | + | 0.104868i | ||||
\(167\) | −20561.9 | − | 11871.4i | −0.737277 | − | 0.425667i | 0.0838016 | − | 0.996482i | \(-0.473294\pi\) |
−0.821078 | + | 0.570816i | \(0.806627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13593.4 | + | 23544.5i | 0.475943 | + | 0.824357i | ||||
\(170\) | −4218.95 | + | 11801.3i | −0.145984 | + | 0.408351i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 405.328 | − | 494.444i | 0.0137009 | − | 0.0167132i | ||||
\(173\) | −1413.25 | − | 2447.82i | −0.0472200 | − | 0.0817874i | 0.841449 | − | 0.540336i | \(-0.181703\pi\) |
−0.888669 | + | 0.458549i | \(0.848370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5193.52 | − | 2998.48i | −0.169584 | − | 0.0979095i | ||||
\(176\) | 17994.9 | − | 53202.2i | 0.580931 | − | 1.71753i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26522.0 | − | 4833.34i | 0.837080 | − | 0.152548i | ||||
\(179\) | 45743.4i | 1.42765i | 0.700323 | + | 0.713826i | \(0.253039\pi\) | ||||
−0.700323 | + | 0.713826i | \(0.746961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24226.2 | −0.739483 | −0.369742 | − | 0.929135i | \(-0.620554\pi\) | ||||
−0.369742 | + | 0.929135i | \(0.620554\pi\) | |||||||
\(182\) | 316.759 | + | 1738.16i | 0.00956283 | + | 0.0524743i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12880.4 | − | 221.334i | 0.380447 | − | 0.00653752i | ||||
\(185\) | −8391.13 | + | 14533.9i | −0.245176 | + | 0.424657i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −53962.5 | + | 31155.3i | −1.54315 | + | 0.890940i | ||||
\(188\) | −29262.6 | + | 35696.4i | −0.827938 | + | 1.00997i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1890.16 | + | 675.726i | 0.0523589 | + | 0.0187182i | ||||
\(191\) | −19504.6 | + | 11261.0i | −0.534651 | + | 0.308681i | −0.742908 | − | 0.669393i | \(-0.766554\pi\) |
0.208257 | + | 0.978074i | \(0.433221\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9144.35 | + | 15838.5i | −0.245493 | + | 0.425205i | −0.962270 | − | 0.272097i | \(-0.912283\pi\) |
0.716777 | + | 0.697302i | \(0.245616\pi\) | |||||||
\(194\) | −31184.4 | − | 36734.8i | −0.828579 | − | 0.976055i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5868.28 | + | 35664.9i | −0.152756 | + | 0.928387i | ||||
\(197\) | −36300.2 | −0.935356 | −0.467678 | − | 0.883899i | \(-0.654909\pi\) | ||||
−0.467678 | + | 0.883899i | \(0.654909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 47336.5i | − | 1.19533i | −0.801744 | − | 0.597667i | \(-0.796094\pi\) | ||
0.801744 | − | 0.597667i | \(-0.203906\pi\) | |||||||
\(200\) | 28168.6 | + | 15624.1i | 0.704214 | + | 0.390602i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −24735.1 | − | 29137.6i | −0.606194 | − | 0.714088i | ||||
\(203\) | 12674.7 | + | 7317.73i | 0.307571 | + | 0.177576i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14528.3 | + | 25163.8i | 0.345706 | + | 0.598781i | ||||
\(206\) | 43328.2 | + | 15489.7i | 1.02102 | + | 0.365014i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1861.57 | − | 9305.56i | −0.0430280 | − | 0.215088i | ||||
\(209\) | 4989.97 | + | 8642.89i | 0.114237 | + | 0.197864i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40261.7 | + | 23245.1i | 0.904330 | + | 0.522115i | 0.878602 | − | 0.477554i | \(-0.158476\pi\) |
0.0257275 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(212\) | −21186.5 | + | 7987.24i | −0.471397 | + | 0.177715i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4735.09 | − | 25982.9i | −0.103395 | − | 0.567363i | ||||
\(215\) | − | 440.814i | − | 0.00953626i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18048.7 | −0.383290 | ||||||||
\(218\) | 47400.4 | − | 8638.18i | 0.997400 | − | 0.181765i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13660.0 | − | 36233.6i | −0.282231 | − | 0.748629i | ||||
\(221\) | −5264.34 | + | 9118.10i | −0.107785 | + | 0.186689i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 71531.9 | − | 41298.9i | 1.43843 | − | 0.830480i | 0.440693 | − | 0.897658i | \(-0.354733\pi\) |
0.997741 | + | 0.0671780i | \(0.0213996\pi\) | |||||||
\(224\) | −1773.79 | + | 12071.5i | −0.0353514 | + | 0.240583i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5023.49 | − | 14051.8i | 0.0983533 | − | 0.275116i | ||||
\(227\) | 25722.3 | − | 14850.8i | 0.499182 | − | 0.288203i | −0.229194 | − | 0.973381i | \(-0.573609\pi\) |
0.728376 | + | 0.685178i | \(0.240276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22667.9 | + | 39262.0i | −0.432256 | + | 0.748690i | −0.997067 | − | 0.0765307i | \(-0.975616\pi\) |
0.564811 | + | 0.825220i | \(0.308949\pi\) | |||||||
\(230\) | 6771.21 | − | 5748.13i | 0.128000 | − | 0.108660i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −68744.9 | − | 38130.3i | −1.27722 | − | 0.708425i | ||||
\(233\) | −50931.3 | −0.938151 | −0.469075 | − | 0.883158i | \(-0.655413\pi\) | ||||
−0.469075 | + | 0.883158i | \(0.655413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31824.5i | 0.576270i | ||||||||
\(236\) | 44724.5 | + | 7358.94i | 0.803010 | + | 0.132127i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10319.7 | − | 8760.43i | 0.182184 | − | 0.154658i | ||||
\(239\) | −31946.2 | − | 18444.1i | −0.559272 | − | 0.322896i | 0.193581 | − | 0.981084i | \(-0.437990\pi\) |
−0.752853 | + | 0.658188i | \(0.771323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4193.64 | − | 7263.59i | −0.0722033 | − | 0.125060i | 0.827663 | − | 0.561225i | \(-0.189670\pi\) |
−0.899867 | + | 0.436165i | \(0.856336\pi\) | |||||||
\(242\) | 45094.9 | − | 126141.i | 0.770011 | − | 2.15389i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 65052.0 | + | 53327.3i | 1.09265 | + | 0.895715i | ||||
\(245\) | 12460.3 | + | 21581.9i | 0.207586 | + | 0.359549i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1460.40 | + | 843.160i | 0.0239374 | + | 0.0138203i | ||||
\(248\) | 96930.9 | − | 1665.64i | 1.57601 | − | 0.0270818i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 48981.2 | − | 8926.26i | 0.783699 | − | 0.142820i | ||||
\(251\) | 1475.47i | 0.0234198i | 0.999931 | + | 0.0117099i | \(0.00372746\pi\) | ||||
−0.999931 | + | 0.0117099i | \(0.996273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44159.6 | 0.689897 | ||||||||
\(254\) | −19039.9 | − | 104478.i | −0.295119 | − | 1.61941i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8412.13 | − | 64993.9i | 0.128359 | − | 0.991728i | ||||
\(257\) | 17336.5 | − | 30027.8i | 0.262480 | − | 0.454629i | −0.704420 | − | 0.709783i | \(-0.748793\pi\) |
0.966900 | + | 0.255154i | \(0.0821263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15698.0 | − | 9063.23i | 0.234015 | − | 0.135109i | ||||
\(260\) | −5060.12 | − | 4148.11i | −0.0748539 | − | 0.0613626i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4970.49 | − | 1776.94i | −0.0724097 | − | 0.0258863i | ||||
\(263\) | −16482.5 | + | 9516.19i | −0.238294 | + | 0.137579i | −0.614392 | − | 0.789001i | \(-0.710599\pi\) |
0.376099 | + | 0.926580i | \(0.377265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7805.54 | + | 13519.6i | −0.111151 | + | 0.192518i | ||||
\(266\) | −1403.11 | − | 1652.84i | −0.0198303 | − | 0.0233598i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14691.9 | − | 2417.40i | −0.204555 | − | 0.0336573i | ||||
\(269\) | −58724.1 | −0.811544 | −0.405772 | − | 0.913974i | \(-0.632997\pi\) | ||||
−0.405772 | + | 0.913974i | \(0.632997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31474.1i | 0.428563i | 0.976772 | + | 0.214281i | \(0.0687409\pi\) | ||||
−0.976772 | + | 0.214281i | \(0.931259\pi\) | |||||||
\(272\) | −54613.4 | + | 48000.3i | −0.738178 | + | 0.648793i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 66820.8 | + | 78714.0i | 0.890043 | + | 1.04846i | ||||
\(275\) | 95625.2 | + | 55209.2i | 1.26447 | + | 0.730040i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −33265.8 | − | 57618.0i | −0.433549 | − | 0.750929i | 0.563627 | − | 0.826029i | \(-0.309405\pi\) |
−0.997176 | + | 0.0751008i | \(0.976072\pi\) | |||||||
\(278\) | 49484.8 | + | 17690.7i | 0.640299 | + | 0.228905i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4330.73 | + | 7211.98i | 0.0552389 | + | 0.0919895i | ||||
\(281\) | −61859.9 | − | 107145.i | −0.783424 | − | 1.35693i | −0.929936 | − | 0.367721i | \(-0.880138\pi\) |
0.146512 | − | 0.989209i | \(-0.453195\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 47401.9 | + | 27367.5i | 0.591865 | + | 0.341713i | 0.765835 | − | 0.643038i | \(-0.222326\pi\) |
−0.173970 | + | 0.984751i | \(0.555659\pi\) | |||||||
\(284\) | −6562.78 | − | 17408.0i | −0.0813675 | − | 0.215830i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5832.30 | − | 32003.7i | −0.0713030 | − | 0.391262i | ||||
\(287\) | − | 31383.9i | − | 0.381016i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2853.15 | −0.0341609 | ||||||||
\(290\) | −53322.4 | + | 9717.39i | −0.634036 | + | 0.115546i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32381.2 | + | 12207.6i | −0.379776 | + | 0.143174i | ||||
\(293\) | −44309.0 | + | 76745.4i | −0.516127 | + | 0.893958i | 0.483698 | + | 0.875235i | \(0.339293\pi\) |
−0.999825 | + | 0.0187226i | \(0.994040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27064.1 | − | 15625.5i | 0.310993 | − | 0.179552i | ||||
\(296\) | −83469.8 | + | 50122.9i | −0.952677 | + | 0.572075i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34924.2 | − | 97690.7i | 0.393273 | − | 1.10007i | ||||
\(299\) | 6462.01 | − | 3730.84i | 0.0722812 | − | 0.0417316i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238.061 | + | 412.333i | −0.00262757 | + | 0.00455109i | ||||
\(302\) | −86589.3 | + | 73506.3i | −0.949403 | + | 0.805955i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7687.95 | + | 8747.13i | 0.0831886 | + | 0.0946495i | ||||
\(305\) | 57996.0 | 0.623446 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 123447.i | 1.30980i | 0.755716 | + | 0.654900i | \(0.227289\pi\) | ||||
−0.755716 | + | 0.654900i | \(0.772711\pi\) | |||||||
\(308\) | −6790.48 | + | 41269.7i | −0.0715813 | + | 0.435040i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 50956.4 | − | 43257.2i | 0.530243 | − | 0.450127i | ||||
\(311\) | −52431.9 | − | 30271.6i | −0.542094 | − | 0.312978i | 0.203833 | − | 0.979006i | \(-0.434660\pi\) |
−0.745927 | + | 0.666027i | \(0.767993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26193.1 | + | 45367.8i | 0.267361 | + | 0.463083i | 0.968180 | − | 0.250257i | \(-0.0805150\pi\) |
−0.700818 | + | 0.713340i | \(0.747182\pi\) | |||||||
\(314\) | 7433.35 | − | 20792.7i | 0.0753920 | − | 0.210888i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −75928.4 | + | 92622.1i | −0.760378 | + | 0.927557i | ||||
\(317\) | −12998.7 | − | 22514.4i | −0.129354 | − | 0.224048i | 0.794072 | − | 0.607823i | \(-0.207957\pi\) |
−0.923427 | + | 0.383775i | \(0.874624\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −233372. | − | 134737.i | −2.29333 | − | 1.32406i | ||||
\(320\) | −23923.8 | − | 38332.3i | −0.233631 | − | 0.374339i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9437.99 | + | 1719.97i | −0.0910265 | + | 0.0165885i | ||||
\(323\) | − | 12920.1i | − | 0.123840i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18657.5 | 0.176639 | ||||||||
\(326\) | 292.079 | + | 1602.73i | 0.00274830 | + | 0.0150808i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2896.29 | + | 168548.i | 0.0269212 | + | 1.56666i | ||||
\(329\) | 17186.8 | − | 29768.4i | 0.158783 | − | 0.275019i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −37439.2 | + | 21615.5i | −0.341720 | + | 0.197292i | −0.661032 | − | 0.750357i | \(-0.729881\pi\) |
0.319312 | + | 0.947650i | \(0.396548\pi\) | |||||||
\(332\) | −11323.4 | + | 13812.9i | −0.102731 | + | 0.125317i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −89428.5 | − | 31970.5i | −0.801647 | − | 0.286587i | ||||
\(335\) | −8890.54 | + | 5132.95i | −0.0792206 | + | 0.0457381i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5926.38 | + | 10264.8i | −0.0521831 | + | 0.0903837i | −0.890937 | − | 0.454127i | \(-0.849951\pi\) |
0.838754 | + | 0.544511i | \(0.183285\pi\) | |||||||
\(338\) | 70377.3 | + | 82903.5i | 0.616027 | + | 0.725671i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8139.12 | + | 49466.1i | −0.0704076 | + | 0.427907i | ||||
\(341\) | 332321. | 2.85791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 55525.0i | − | 0.471955i | ||||||
\(344\) | 1240.45 | − | 2236.41i | 0.0104825 | − | 0.0188988i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7316.83 | − | 8619.12i | −0.0611182 | − | 0.0719964i | ||||
\(347\) | 25222.5 | + | 14562.2i | 0.209473 | + | 0.120940i | 0.601067 | − | 0.799199i | \(-0.294743\pi\) |
−0.391593 | + | 0.920138i | \(0.628076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −59988.4 | − | 103903.i | −0.492512 | − | 0.853055i | 0.507451 | − | 0.861681i | \(-0.330588\pi\) |
−0.999963 | + | 0.00862528i | \(0.997254\pi\) | |||||||
\(350\) | −22587.8 | − | 8075.08i | −0.184390 | − | 0.0659191i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32659.8 | − | 222266.i | 0.263589 | − | 1.79385i | ||||
\(353\) | 77379.0 | + | 134024.i | 0.620975 | + | 1.07556i | 0.989305 | + | 0.145865i | \(0.0465964\pi\) |
−0.368330 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11108.5 | − | 6413.49i | −0.0881451 | − | 0.0508906i | ||||
\(356\) | 100903. | − | 38040.2i | 0.796167 | − | 0.300153i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 32804.5 | + | 180009.i | 0.255957 | + | 1.40452i | ||||
\(359\) | − | 66839.6i | − | 0.518615i | −0.965795 | − | 0.259307i | \(-0.916506\pi\) | ||
0.965795 | − | 0.259307i | \(-0.0834942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 128252. | 0.984121 | ||||||||
\(362\) | −95334.7 | + | 17373.6i | −0.727501 | + | 0.132579i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2493.01 | + | 6612.82i | 0.0188158 | + | 0.0499096i | ||||
\(365\) | −11929.9 | + | 20663.2i | −0.0895472 | + | 0.155100i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 81901.3 | − | 47285.7i | 0.608077 | − | 0.351073i | −0.164136 | − | 0.986438i | \(-0.552483\pi\) |
0.772212 | + | 0.635364i | \(0.219150\pi\) | |||||||
\(368\) | 50528.1 | − | 10108.1i | 0.373110 | − | 0.0746403i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22597.8 | + | 63211.2i | −0.165068 | + | 0.461732i | ||||
\(371\) | 14602.5 | − | 8430.74i | 0.106091 | − | 0.0612517i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 90530.4 | − | 156803.i | 0.650694 | − | 1.12704i | −0.332260 | − | 0.943188i | \(-0.607811\pi\) |
0.982955 | − | 0.183848i | \(-0.0588554\pi\) | |||||||
\(374\) | −190010. | + | 161301.i | −1.35842 | + | 1.15317i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −89554.6 | + | 161457.i | −0.633450 | + | 1.14204i | ||||
\(377\) | −45533.4 | −0.320366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 51191.3i | − | 0.356384i | −0.983996 | − | 0.178192i | \(-0.942975\pi\) | ||
0.983996 | − | 0.178192i | \(-0.0570248\pi\) | |||||||
\(380\) | 7922.71 | + | 1303.60i | 0.0548664 | + | 0.00902769i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −68678.6 | + | 58301.7i | −0.470646 | + | 0.399535i | ||||
\(383\) | −132128. | − | 76284.0i | −0.900734 | − | 0.520039i | −0.0232957 | − | 0.999729i | \(-0.507416\pi\) |
−0.877438 | + | 0.479690i | \(0.840749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14418.5 | + | 24973.5i | 0.0972742 | + | 0.168484i | ||||
\(386\) | −24626.3 | + | 68885.2i | −0.165282 | + | 0.462329i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −149061. | − | 122195.i | −0.990147 | − | 0.811687i | ||||
\(389\) | 33948.4 | + | 58800.3i | 0.224347 | + | 0.388580i | 0.956123 | − | 0.292965i | \(-0.0946418\pi\) |
−0.731776 | + | 0.681545i | \(0.761308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49510.2 | − | 28584.7i | −0.323848 | − | 0.186974i | ||||
\(392\) | 2484.03 | + | 144556.i | 0.0161653 | + | 0.940731i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −142848. | + | 26032.5i | −0.920201 | + | 0.167696i | ||||
\(395\) | 82575.7i | 0.529247i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −126087. | −0.799998 | −0.399999 | − | 0.916516i | \(-0.630990\pi\) | ||||
−0.399999 | + | 0.916516i | \(0.630990\pi\) | |||||||
\(398\) | −33947.0 | − | 186278.i | −0.214306 | − | 1.17597i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 122053. | + | 41282.8i | 0.762833 | + | 0.258017i | ||||
\(401\) | 35445.4 | − | 61393.2i | 0.220430 | − | 0.381796i | −0.734509 | − | 0.678599i | \(-0.762587\pi\) |
0.954939 | + | 0.296803i | \(0.0959206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48629.5 | − | 28076.3i | 0.299426 | − | 0.172874i | ||||
\(404\) | −118233. | − | 96923.5i | −0.724398 | − | 0.593836i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 55125.1 | + | 19707.1i | 0.334424 | + | 0.119556i | ||||
\(407\) | −289038. | + | 166876.i | −1.74488 | + | 1.00741i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21772.1 | + | 37710.4i | −0.130153 | + | 0.225432i | −0.923735 | − | 0.383031i | \(-0.874880\pi\) |
0.793582 | + | 0.608463i | \(0.208214\pi\) | |||||||
\(410\) | 75217.6 | + | 88605.3i | 0.447458 | + | 0.527099i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 181613. | + | 29882.5i | 1.06992 | + | 0.176044i | ||||
\(413\) | −33754.1 | −0.197891 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12314.7i | 0.0715036i | ||||||||
\(416\) | −13999.0 | − | 35284.1i | −0.0808930 | − | 0.203888i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25834.7 | + | 30432.9i | 0.147860 | + | 0.174177i | ||||
\(419\) | 182385. | + | 105300.i | 1.03887 | + | 0.599792i | 0.919513 | − | 0.393060i | \(-0.128583\pi\) |
0.119357 | + | 0.992851i | \(0.461917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −42063.0 | − | 72855.3i | −0.237321 | − | 0.411052i | 0.722624 | − | 0.691242i | \(-0.242936\pi\) |
−0.959945 | + | 0.280190i | \(0.909603\pi\) | |||||||
\(422\) | 175107. | + | 62600.4i | 0.983285 | + | 0.351522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −77644.7 | + | 46625.0i | −0.431897 | + | 0.259350i | ||||
\(425\) | −71474.4 | − | 123797.i | −0.395706 | − | 0.685383i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54249.0 | − | 31320.7i | −0.297533 | − | 0.171781i | ||||
\(428\) | −37266.9 | − | 98852.0i | −0.203440 | − | 0.539632i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −316.126 | − | 1734.69i | −0.00170972 | − | 0.00938175i | ||||
\(431\) | − | 150083.i | − | 0.807933i | −0.914774 | − | 0.403967i | \(-0.867631\pi\) | ||
0.914774 | − | 0.403967i | \(-0.132369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 71221.5 | 0.379871 | 0.189935 | − | 0.981797i | \(-0.439172\pi\) | ||||
0.189935 | + | 0.981797i | \(0.439172\pi\) | |||||||
\(434\) | −71025.1 | + | 12943.5i | −0.377079 | + | 0.0687183i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 180335. | − | 67985.7i | 0.948651 | − | 0.357639i | ||||
\(437\) | −4578.26 | + | 7929.78i | −0.0239739 | + | 0.0415239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 94609.3 | − | 54622.7i | 0.490913 | − | 0.283429i | −0.234040 | − | 0.972227i | \(-0.575195\pi\) |
0.724953 | + | 0.688798i | \(0.241861\pi\) | |||||||
\(440\) | −79739.3 | − | 132790.i | −0.411876 | − | 0.685899i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14177.2 | + | 39656.7i | −0.0725680 | + | 0.202989i | ||||
\(443\) | 199756. | − | 115329.i | 1.01787 | − | 0.587666i | 0.104382 | − | 0.994537i | \(-0.466713\pi\) |
0.913486 | + | 0.406871i | \(0.133380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37174.8 | − | 64388.7i | 0.187728 | − | 0.325154i | ||||
\(446\) | 251874. | − | 213818.i | 1.26623 | − | 1.07491i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1676.80 | + | 48775.7i | 0.00835458 | + | 0.243023i | ||||
\(449\) | 9751.64 | 0.0483710 | 0.0241855 | − | 0.999707i | \(-0.492301\pi\) | ||||
0.0241855 | + | 0.999707i | \(0.492301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 577854.i | 2.84096i | ||||||||
\(452\) | 9691.23 | − | 58899.1i | 0.0474353 | − | 0.288292i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 90572.1 | − | 76887.2i | 0.439423 | − | 0.373029i | ||||
\(455\) | 4219.80 | + | 2436.30i | 0.0203831 | + | 0.0117682i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33069.5 | − | 57278.1i | −0.158342 | − | 0.274256i | 0.775929 | − | 0.630820i | \(-0.217281\pi\) |
−0.934271 | + | 0.356564i | \(0.883948\pi\) | |||||||
\(458\) | −61046.1 | + | 170760.i | −0.291023 | + | 0.814056i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22523.8 | − | 27475.9i | 0.106445 | − | 0.129848i | ||||
\(461\) | −86994.6 | − | 150679.i | −0.409346 | − | 0.709008i | 0.585471 | − | 0.810694i | \(-0.300910\pi\) |
−0.994817 | + | 0.101686i | \(0.967576\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 150682. | + | 86996.3i | 0.702909 | + | 0.405825i | 0.808430 | − | 0.588592i | \(-0.200318\pi\) |
−0.105521 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(464\) | −297869. | − | 100750.i | −1.38353 | − | 0.467960i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −200424. | + | 36525.0i | −0.922950 | + | 0.168197i | ||||
\(467\) | − | 172090.i | − | 0.789080i | −0.918879 | − | 0.394540i | \(-0.870904\pi\) | ||
0.918879 | − | 0.394540i | \(-0.129096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11088.2 | 0.0504097 | ||||||||
\(470\) | 22822.7 | + | 125236.i | 0.103317 | + | 0.566933i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 181277. | − | 3115.02i | 0.813688 | − | 0.0139822i | ||||
\(473\) | 4383.27 | − | 7592.05i | 0.0195919 | − | 0.0339341i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19828.0 | + | 11447.7i | −0.0878802 | + | 0.0507376i | ||||
\(476\) | 34327.3 | − | 41874.6i | 0.151505 | − | 0.184815i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −138941. | − | 49671.2i | −0.608101 | − | 0.217395i | ||||
\(479\) | 189138. | − | 109199.i | 0.824343 | − | 0.475935i | −0.0275690 | − | 0.999620i | \(-0.508777\pi\) |
0.851912 | + | 0.523685i | \(0.175443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28197.2 | + | 48839.0i | −0.121875 | + | 0.211094i | ||||
\(482\) | −21711.8 | − | 25576.2i | −0.0934548 | − | 0.110088i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 86996.3 | − | 528726.i | 0.371373 | − | 2.25705i | ||||
\(485\) | −132893. | −0.564959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 392112.i | − | 1.65330i | −0.562716 | − | 0.826650i | \(-0.690243\pi\) | ||
0.562716 | − | 0.826650i | \(-0.309757\pi\) | |||||||
\(488\) | 294235. | + | 163201.i | 1.23553 | + | 0.685306i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 64511.1 | + | 75993.1i | 0.268684 | + | 0.316506i | ||||
\(491\) | 181620. | + | 104859.i | 0.753358 | + | 0.434951i | 0.826906 | − | 0.562340i | \(-0.190099\pi\) |
−0.0735480 | + | 0.997292i | \(0.523432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 174432. | + | 302125.i | 0.717683 | + | 1.24306i | ||||
\(494\) | 6351.60 | + | 2270.68i | 0.0260273 | + | 0.00930470i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 380247. | − | 76067.9i | 1.54562 | − | 0.309199i | ||||
\(497\) | 6927.19 | + | 11998.2i | 0.0280443 | + | 0.0485741i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −117681. | − | 67943.0i | −0.472611 | − | 0.272862i | 0.244721 | − | 0.969594i | \(-0.421304\pi\) |
−0.717332 | + | 0.696731i | \(0.754637\pi\) | |||||||
\(500\) | 186349. | − | 70253.0i | 0.745395 | − | 0.281012i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1058.12 | + | 5806.24i | 0.00419883 | + | 0.0230403i | ||||
\(503\) | 232332.i | 0.918275i | 0.888365 | + | 0.459137i | \(0.151841\pi\) | ||||
−0.888365 | + | 0.459137i | \(0.848159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −105409. | −0.413328 | ||||||||
\(506\) | 173776. | − | 31668.7i | 0.678718 | − | 0.123689i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −149851. | − | 397486.i | −0.580675 | − | 1.54026i | ||||
\(509\) | −72659.4 | + | 125850.i | −0.280451 | + | 0.485755i | −0.971496 | − | 0.237057i | \(-0.923817\pi\) |
0.691045 | + | 0.722812i | \(0.257151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22318.3 | − | 12885.5i | 0.0854711 | − | 0.0493467i | ||||
\(512\) | −13506.6 | − | 261796.i | −0.0515234 | − | 0.998672i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46688.3 | − | 130598.i | 0.176719 | − | 0.494321i | ||||
\(515\) | 109899. | − | 63450.5i | 0.414363 | − | 0.239233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −316450. | + | 548108.i | −1.18393 | + | 2.05062i | ||||
\(518\) | 55274.9 | − | 46923.2i | 0.206001 | − | 0.174875i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −22887.3 | − | 12694.8i | −0.0846425 | − | 0.0469481i | ||||
\(521\) | −443088. | −1.63235 | −0.816177 | − | 0.577803i | \(-0.803910\pi\) | ||||
−0.816177 | + | 0.577803i | \(0.803910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 73202.4i | 0.267622i | 0.991007 | + | 0.133811i | \(0.0427215\pi\) | ||||
−0.991007 | + | 0.133811i | \(0.957278\pi\) | |||||||
\(524\) | −20834.1 | − | 3428.04i | −0.0758775 | − | 0.0124848i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58037.4 | + | 49268.3i | −0.209767 | + | 0.178072i | ||||
\(527\) | −372587. | − | 215113.i | −1.34155 | − | 0.774543i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −119662. | − | 207261.i | −0.427609 | − | 0.740640i | ||||
\(530\) | −21020.8 | + | 58799.9i | −0.0748338 | + | 0.209327i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6706.83 | − | 5498.02i | −0.0236970 | − | 0.0194260i | ||||
\(533\) | 48820.3 | + | 84559.2i | 0.171849 | + | 0.297651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −63079.9 | − | 36419.2i | −0.220386 | − | 0.127240i | ||||
\(536\) | −59549.1 | + | 1023.28i | −0.207274 | + | 0.00356176i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −231090. | + | 42113.6i | −0.798394 | + | 0.145498i | ||||
\(539\) | 495602.i | 1.70591i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 438165. | 1.49707 | 0.748536 | − | 0.663094i | \(-0.230757\pi\) | ||||
0.748536 | + | 0.663094i | \(0.230757\pi\) | |||||||
\(542\) | 22571.4 | + | 123856.i | 0.0768351 | + | 0.421619i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −180491. | + | 228056.i | −0.609898 | + | 0.770625i | ||||
\(545\) | 66439.2 | − | 115076.i | 0.223682 | − | 0.387429i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 270221. | − | 156012.i | 0.903118 | − | 0.521416i | 0.0249077 | − | 0.999690i | \(-0.492071\pi\) |
0.878211 | + | 0.478274i | \(0.158737\pi\) | |||||||
\(548\) | 319402. | + | 261834.i | 1.06359 | + | 0.871898i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 415896. | + | 148682.i | 1.37486 | + | 0.491510i | ||||
\(551\) | 48389.8 | − | 27937.9i | 0.159386 | − | 0.0920217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44594.9 | − | 77240.6i | 0.145826 | − | 0.252578i | ||||
\(554\) | −172227. | − | 202881.i | −0.561155 | − | 0.661032i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 207419. | + | 34128.6i | 0.670963 | + | 0.110400i | ||||
\(557\) | −312549. | −1.00741 | −0.503707 | − | 0.863874i | \(-0.668031\pi\) | ||||
−0.503707 | + | 0.863874i | \(0.668031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1481.29i | − | 0.00474042i | ||||||
\(560\) | 22214.3 | + | 25274.7i | 0.0708363 | + | 0.0805955i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −320268. | − | 377272.i | −1.01401 | − | 1.19449i | ||||
\(563\) | −74780.6 | − | 43174.6i | −0.235924 | − | 0.136211i | 0.377378 | − | 0.926059i | \(-0.376826\pi\) |
−0.613302 | + | 0.789849i | \(0.710159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20577.7 | − | 35641.7i | −0.0644615 | − | 0.111651i | ||||
\(566\) | 206162. | + | 73702.3i | 0.643539 | + | 0.230064i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38309.8 | − | 63797.4i | −0.118744 | − | 0.197745i | ||||
\(569\) | 277479. | + | 480608.i | 0.857049 | + | 1.48445i | 0.874731 | + | 0.484609i | \(0.161038\pi\) |
−0.0176822 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 262848. | + | 151755.i | 0.806181 | + | 0.465449i | 0.845628 | − | 0.533773i | \(-0.179226\pi\) |
−0.0394467 | + | 0.999222i | \(0.512560\pi\) | |||||||
\(572\) | −45902.4 | − | 121758.i | −0.140295 | − | 0.372139i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22506.8 | − | 123502.i | −0.0683108 | − | 0.374843i | ||||
\(575\) | 101308.i | 0.306414i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −500884. | −1.50448 | −0.752238 | − | 0.658892i | \(-0.771026\pi\) | ||||
−0.752238 | + | 0.658892i | \(0.771026\pi\) | |||||||
\(578\) | −11227.7 | + | 2046.12i | −0.0336074 | + | 0.00612456i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −202865. | + | 76479.5i | −0.603047 | + | 0.227347i | ||||
\(581\) | 6650.54 | − | 11519.1i | 0.0197017 | − | 0.0341244i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −268867. | + | 155230.i | −0.791043 | + | 0.456709i | ||||
\(584\) | −118671. | + | 71261.2i | −0.347953 | + | 0.208943i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −119327. | + | 333783.i | −0.347490 | + | 0.972007i | ||||
\(587\) | −498580. | + | 287855.i | −1.44697 | + | 0.835406i | −0.998300 | − | 0.0582932i | \(-0.981434\pi\) |
−0.448666 | + | 0.893699i | \(0.648101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34453.5 | + | 59675.2i | −0.0993122 | + | 0.172014i | ||||
\(590\) | 95296.8 | − | 80898.1i | 0.273763 | − | 0.232399i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −292524. | + | 257103.i | −0.834676 | + | 0.733607i | ||||
\(593\) | 138143. | 0.392843 | 0.196421 | − | 0.980520i | \(-0.437068\pi\) | ||||
0.196421 | + | 0.980520i | \(0.437068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 37332.6i | − | 0.105452i | ||||||
\(596\) | 67375.1 | − | 409477.i | 0.189674 | − | 1.15275i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22753.7 | − | 19315.8i | 0.0636282 | − | 0.0540144i | ||||
\(599\) | −165665. | − | 95646.9i | −0.461719 | − | 0.266574i | 0.251048 | − | 0.967975i | \(-0.419225\pi\) |
−0.712767 | + | 0.701401i | \(0.752558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 203120. | + | 351814.i | 0.562346 | + | 0.974012i | 0.997291 | + | 0.0735551i | \(0.0234345\pi\) |
−0.434945 | + | 0.900457i | \(0.643232\pi\) | |||||||
\(602\) | −641.112 | + | 1793.33i | −0.00176905 | + | 0.00494843i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −288031. | + | 351358.i | −0.789524 | + | 0.963110i | ||||
\(605\) | −184722. | − | 319948.i | −0.504671 | − | 0.874117i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −59466.9 | − | 34333.2i | −0.161398 | − | 0.0931831i | 0.417126 | − | 0.908849i | \(-0.363038\pi\) |
−0.578523 | + | 0.815666i | \(0.696371\pi\) | |||||||
\(608\) | 36526.5 | + | 28908.2i | 0.0988100 | + | 0.0782014i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 228225. | − | 41591.4i | 0.613344 | − | 0.111775i | ||||
\(611\) | 106942.i | 0.286461i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −572114. | −1.52252 | −0.761258 | − | 0.648450i | \(-0.775418\pi\) | ||||
−0.761258 | + | 0.648450i | \(0.775418\pi\) | |||||||
\(614\) | 88529.3 | + | 485788.i | 0.234828 | + | 1.28858i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2874.39 | + | 167274.i | 0.00757504 | + | 0.440825i | ||||
\(617\) | 10190.4 | − | 17650.3i | 0.0267684 | − | 0.0463642i | −0.852331 | − | 0.523003i | \(-0.824812\pi\) |
0.879099 | + | 0.476639i | \(0.158145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −388604. | + | 224361.i | −1.01421 | + | 0.585552i | −0.912420 | − | 0.409254i | \(-0.865789\pi\) |
−0.101786 | + | 0.994806i | \(0.532456\pi\) | |||||||
\(620\) | 169501. | − | 206768.i | 0.440951 | − | 0.537899i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −228038. | − | 81523.2i | −0.589423 | − | 0.210717i | ||||
\(623\) | −69546.0 | + | 40152.4i | −0.179183 | + | 0.103451i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −88627.6 | + | 153508.i | −0.226887 | + | 0.392979i | ||||
\(626\) | 135610. | + | 159747.i | 0.346053 | + | 0.407646i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14340.3 | − | 87154.1i | 0.0363612 | − | 0.220988i | ||||
\(629\) | 432079. | 1.09210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 402529.i | − | 1.01097i | −0.862835 | − | 0.505486i | \(-0.831313\pi\) | ||
0.862835 | − | 0.505486i | \(-0.168687\pi\) | |||||||
\(632\) | −232369. | + | 418937.i | −0.581760 | + | 1.04885i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −67298.3 | − | 79276.4i | −0.167427 | − | 0.197227i | ||||
\(635\) | −253646. | − | 146443.i | −0.629043 | − | 0.363178i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41871.2 | + | 72523.0i | 0.103190 | + | 0.178730i | ||||
\(638\) | −1.01499e6 | − | 362856.i | −2.49356 | − | 0.891441i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −121634. | − | 133688.i | −0.296959 | − | 0.326387i | ||||
\(641\) | 176906. | + | 306411.i | 0.430554 | + | 0.745741i | 0.996921 | − | 0.0784117i | \(-0.0249849\pi\) |
−0.566367 | + | 0.824153i | \(0.691652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 227886. | + | 131570.i | 0.551184 | + | 0.318226i | 0.749599 | − | 0.661892i | \(-0.230246\pi\) |
−0.198415 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(644\) | −35906.8 | + | 13536.8i | −0.0865775 | + | 0.0326395i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9265.58 | − | 50843.2i | −0.0222028 | − | 0.121834i | ||||
\(647\) | − | 265174.i | − | 0.633464i | −0.948515 | − | 0.316732i | \(-0.897414\pi\) | ||
0.948515 | − | 0.316732i | \(-0.102586\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 621494. | 1.47553 | ||||||||
\(650\) | 73420.8 | − | 13380.1i | 0.173777 | − | 0.0316689i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2298.77 | + | 6097.57i | 0.00540754 | + | 0.0143437i | ||||
\(653\) | −2938.96 | + | 5090.43i | −0.00689235 | + | 0.0119379i | −0.869451 | − | 0.494019i | \(-0.835527\pi\) |
0.862559 | + | 0.505957i | \(0.168861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12607.4 | + | 7278.87i | −0.0293861 | + | 0.0169661i | ||||
\(656\) | 132270. | + | 661190.i | 0.307365 | + | 1.53645i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 46285.0 | − | 129470.i | 0.106903 | − | 0.299031i | ||||
\(659\) | 480334. | − | 277321.i | 1.10604 | − | 0.638575i | 0.168242 | − | 0.985746i | \(-0.446191\pi\) |
0.937802 | + | 0.347171i | \(0.112858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 410614. | − | 711204.i | 0.939789 | − | 1.62776i | 0.173926 | − | 0.984759i | \(-0.444355\pi\) |
0.765863 | − | 0.643004i | \(-0.222312\pi\) | |||||||
\(662\) | −131829. | + | 111910.i | −0.300812 | + | 0.255361i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34653.7 | + | 62477.0i | −0.0785984 | + | 0.141705i | ||||
\(665\) | −5979.36 | −0.0135211 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 247241.i | − | 0.555736i | ||||||
\(668\) | −374845. | − | 61676.8i | −0.840039 | − | 0.138219i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −31304.9 | + | 26574.9i | −0.0697368 | + | 0.0592001i | ||||
\(671\) | 998855. | + | 576689.i | 2.21849 | + | 1.28085i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −258432. | − | 447618.i | −0.570580 | − | 0.988274i | −0.996506 | − | 0.0835158i | \(-0.973385\pi\) |
0.425926 | − | 0.904758i | \(-0.359948\pi\) | |||||||
\(674\) | −15960.1 | + | 44643.9i | −0.0351330 | + | 0.0982749i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 336402. | + | 275770.i | 0.736148 | + | 0.603468i | ||||
\(677\) | −345343. | − | 598152.i | −0.753483 | − | 1.30507i | −0.946125 | − | 0.323801i | \(-0.895039\pi\) |
0.192642 | − | 0.981269i | \(-0.438294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 124307. | + | 71768.4i | 0.269621 | + | 0.155666i | ||||
\(680\) | 3445.26 | + | 200495.i | 0.00745083 | + | 0.433597i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.30774e6 | − | 238321.i | 2.81160 | − | 0.512382i | ||||
\(683\) | − | 764551.i | − | 1.63895i | −0.573117 | − | 0.819474i | \(-0.694266\pi\) | ||
0.573117 | − | 0.819474i | \(-0.305734\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 284757. | 0.606868 | ||||||||
\(686\) | −39819.4 | − | 218502.i | −0.0846148 | − | 0.464308i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3277.60 | − | 9690.27i | 0.00692435 | − | 0.0204719i | ||||
\(689\) | −26229.4 | + | 45430.7i | −0.0552523 | + | 0.0956998i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −278107. | + | 160565.i | −0.582445 | + | 0.336275i | −0.762105 | − | 0.647454i | \(-0.775834\pi\) |
0.179659 | + | 0.983729i | \(0.442500\pi\) | |||||||
\(692\) | −34974.2 | − | 28670.6i | −0.0730358 | − | 0.0598722i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 109698. | + | 39216.9i | 0.227762 | + | 0.0814244i | ||||
\(695\) | 125516. | − | 72466.4i | 0.259853 | − | 0.150026i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 374048. | − | 647870.i | 0.769949 | − | 1.33359i | ||||
\(698\) | −310579. | − | 365858.i | −0.637472 | − | 0.750933i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −94678.2 | − | 15578.3i | −0.193221 | − | 0.0317925i | ||||
\(701\) | 621799. | 1.26536 | 0.632680 | − | 0.774413i | \(-0.281955\pi\) | ||||
0.632680 | + | 0.774413i | \(0.281955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 69203.8i | − | 0.140029i | ||||||
\(704\) | −30873.9 | − | 898079.i | −0.0622940 | − | 1.81205i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 400616. | + | 471920.i | 0.803745 | + | 0.946801i | ||||
\(707\) | 98598.6 | + | 56925.9i | 0.197257 | + | 0.113886i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 262435. | + | 454550.i | 0.522070 | + | 0.904252i | 0.999670 | + | 0.0256748i | \(0.00817343\pi\) |
−0.477600 | + | 0.878577i | \(0.658493\pi\) | |||||||
\(710\) | −48313.4 | − | 17271.9i | −0.0958409 | − | 0.0342629i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 369792. | − | 222057.i | 0.729454 | − | 0.438031i | ||||
\(713\) | 152451. | + | 264053.i | 0.299882 | + | 0.519412i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −77696.8 | − | 44858.2i | −0.151982 | − | 0.0877466i | ||||
\(716\) | 258184. | + | 684843.i | 0.503620 | + | 1.33587i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −47933.5 | − | 263026.i | −0.0929801 | − | 0.510211i | ||||
\(719\) | − | 348658.i | − | 0.674438i | −0.941426 | − | 0.337219i | \(-0.890514\pi\) | ||
0.941426 | − | 0.337219i | \(-0.109486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −137065. | −0.263668 | ||||||||
\(722\) | 504694. | − | 91974.7i | 0.968175 | − | 0.176439i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −362701. | + | 136737.i | −0.691944 | + | 0.260861i | ||||
\(725\) | 309106. | − | 535387.i | 0.588073 | − | 1.01857i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −523789. | + | 302410.i | −0.991032 | + | 0.572173i | −0.905583 | − | 0.424170i | \(-0.860566\pi\) |
−0.0854497 | + | 0.996342i | \(0.527233\pi\) | |||||||
\(728\) | 14552.8 | + | 24234.8i | 0.0274590 | + | 0.0457275i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32128.0 | + | 89869.2i | −0.0602890 | + | 0.168642i | ||||
\(731\) | −9828.75 | + | 5674.63i | −0.0183935 | + | 0.0106195i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 237805. | − | 411891.i | 0.442602 | − | 0.766609i | −0.555280 | − | 0.831664i | \(-0.687389\pi\) |
0.997882 | + | 0.0650546i | \(0.0207222\pi\) | |||||||
\(734\) | 288386. | − | 244813.i | 0.535282 | − | 0.454404i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 191589. | − | 76013.1i | 0.353683 | − | 0.140324i | ||||
\(737\) | −204160. | −0.375868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 844449.i | − | 1.54627i | −0.634244 | − | 0.773133i | \(-0.718688\pi\) | ||
0.634244 | − | 0.773133i | \(-0.281312\pi\) | |||||||
\(740\) | −43595.3 | + | 264954.i | −0.0796116 | + | 0.483845i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 51417.4 | − | 43648.6i | 0.0933905 | − | 0.0792798i | ||||
\(743\) | −537216. | − | 310162.i | −0.973131 | − | 0.561837i | −0.0729415 | − | 0.997336i | \(-0.523239\pi\) |
−0.900189 | + | 0.435499i | \(0.856572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −143060. | − | 247787.i | −0.257754 | − | 0.446443i | ||||
\(746\) | 243804. | − | 681974.i | 0.438090 | − | 1.22543i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −632049. | + | 771013.i | −1.12966 | + | 1.37803i | ||||
\(749\) | 39336.3 | + | 68132.4i | 0.0701180 | + | 0.121448i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 632847. | + | 365374.i | 1.12207 | + | 0.647825i | 0.941928 | − | 0.335816i | \(-0.109012\pi\) |
0.180139 | + | 0.983641i | \(0.442345\pi\) | |||||||
\(752\) | −236626. | + | 699589.i | −0.418434 | + | 1.23711i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −179182. | + | 32653.9i | −0.315176 | + | 0.0574371i | ||||
\(755\) | 313247.i | 0.549533i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −769023. | −1.34198 | −0.670992 | − | 0.741465i | \(-0.734132\pi\) | ||||
−0.670992 | + | 0.741465i | \(0.734132\pi\) | |||||||
\(758\) | −36711.5 | − | 201447.i | −0.0638945 | − | 0.350609i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 32112.2 | − | 551.810i | 0.0555960 | − | 0.000955349i | ||||
\(761\) | 137697. | − | 238498.i | 0.237769 | − | 0.411828i | −0.722305 | − | 0.691575i | \(-0.756917\pi\) |
0.960074 | + | 0.279747i | \(0.0902505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −124293. | + | 71760.8i | −0.213500 | + | 0.123264i | ||||
\(764\) | −228452. | + | 278680.i | −0.391389 | + | 0.477441i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −574654. | − | 205437.i | −0.979375 | − | 0.350124i | ||||
\(767\) | 90945.2 | − | 52507.2i | 0.154593 | − | 0.0892541i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26421.1 | − | 45762.6i | 0.0446784 | − | 0.0773853i | −0.842821 | − | 0.538193i | \(-0.819107\pi\) |
0.887500 | + | 0.460808i | \(0.152440\pi\) | |||||||
\(770\) | 74649.0 | + | 87935.4i | 0.125905 | + | 0.148314i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −47508.6 | + | 288737.i | −0.0797145 | + | 0.484471i | ||||
\(773\) | 195309. | 0.326861 | 0.163430 | − | 0.986555i | \(-0.447744\pi\) | ||||
0.163430 | + | 0.986555i | \(0.447744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 762389.i | 1.26933i | ||||||||
\(776\) | −674213. | − | 373961.i | −1.11963 | − | 0.621017i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 175761. | + | 207045.i | 0.290379 | + | 0.342062i | ||||
\(779\) | −103766. | − | 59909.3i | −0.170994 | − | 0.0987232i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −127546. | − | 220917.i | −0.209106 | − | 0.362182i | ||||
\(782\) | −215331. | − | 76980.4i | −0.352122 | − | 0.125883i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 113443. | + | 567076.i | 0.184563 | + | 0.922590i | ||||
\(785\) | −30449.2 | − | 52739.6i | −0.0494125 | − | 0.0855849i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 677438. | + | 391119.i | 1.09375 | + | 0.631480i | 0.934574 | − | 0.355770i | \(-0.115781\pi\) |
0.159181 | + | 0.987249i | \(0.449115\pi\) | |||||||
\(788\) | −543466. | + | 204885.i | −0.875225 | + | 0.329958i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 59218.6 | + | 324951.i | 0.0948864 | + | 0.520672i | ||||
\(791\) | 44451.9i | 0.0710456i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 194887. | 0.309911 | ||||||||
\(794\) | −496176. | + | 90422.3i | −0.787036 | + | 0.143428i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −267176. | − | 708694.i | −0.421668 | − | 1.11849i | ||||
\(797\) | −586714. | + | 1.01622e6i | −0.923655 | + | 1.59982i | −0.129944 | + | 0.991521i | \(0.541480\pi\) |
−0.793711 | + | 0.608296i | \(0.791854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 709586. | − | 409680.i | 1.11151 | − | 0.641728i | ||||
\(800\) | 509908. | + | 74926.0i | 0.796731 | + | 0.117072i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 95456.6 | − | 267013.i | 0.148408 | − | 0.415130i | ||||
\(803\) | −410934. | + | 237253.i | −0.637295 | + | 0.367943i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13228.8 | + | 22913.0i | −0.0204141 | + | 0.0353583i | ||||
\(806\) | 171232. | − | 145360.i | 0.263581 | − | 0.223756i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −534778. | − | 296622.i | −0.819126 | − | 0.454340i | ||||
\(809\) | 421614. | 0.644196 | 0.322098 | − | 0.946706i | \(-0.395612\pi\) | ||||
0.322098 | + | 0.946706i | \(0.395612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 504037.i | − | 0.766339i | −0.923678 | − | 0.383169i | \(-0.874833\pi\) | ||
0.923678 | − | 0.383169i | \(-0.125167\pi\) | |||||||
\(812\) | 231061. | + | 38018.6i | 0.350440 | + | 0.0576612i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.01774e6 | + | 863970.i | −1.53600 | + | 1.30392i | ||||
\(815\) | 3891.01 | + | 2246.48i | 0.00585797 | + | 0.00338210i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 908.875 | + | 1574.22i | 0.00136163 | + | 0.00235842i | ||||
\(818\) | −58633.6 | + | 164011.i | −0.0876275 | + | 0.245113i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 359538. | + | 294737.i | 0.534709 | + | 0.438335i | ||||
\(821\) | −35777.1 | − | 61967.7i | −0.0530785 | − | 0.0919346i | 0.838265 | − | 0.545262i | \(-0.183570\pi\) |
−0.891344 | + | 0.453328i | \(0.850237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −703826. | − | 406354.i | −1.03912 | − | 0.599936i | −0.119536 | − | 0.992830i | \(-0.538141\pi\) |
−0.919584 | + | 0.392893i | \(0.871474\pi\) | |||||||
\(824\) | 736111. | − | 12649.2i | 1.08415 | − | 0.0186298i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −132829. | + | 24206.5i | −0.194685 | + | 0.0354790i | ||||
\(827\) | 375951.i | 0.549693i | 0.961488 | + | 0.274847i | \(0.0886271\pi\) | ||||
−0.961488 | + | 0.274847i | \(0.911373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 423699. | 0.616522 | 0.308261 | − | 0.951302i | \(-0.400253\pi\) | ||||
0.308261 | + | 0.951302i | \(0.400253\pi\) | |||||||
\(830\) | 8831.40 | + | 48460.7i | 0.0128196 | + | 0.0703450i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −80392.5 | − | 128810.i | −0.116137 | − | 0.186082i | ||||
\(833\) | 320806. | − | 555652.i | 0.462330 | − | 0.800779i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −226830. | + | 130961.i | −0.325333 | + | 0.187831i | ||||
\(836\) | 123489. | + | 101232.i | 0.176691 | + | 0.144845i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 793234. | + | 283579.i | 1.12957 | + | 0.403819i | ||||
\(839\) | −959899. | + | 554198.i | −1.36365 | + | 0.787302i | −0.990107 | − | 0.140313i | \(-0.955189\pi\) |
−0.373539 | + | 0.927614i | \(0.621856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −400727. | + | 694079.i | −0.566573 | + | 0.981334i | ||||
\(842\) | −217773. | − | 256534.i | −0.307171 | − | 0.361843i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 733974. | + | 120768.i | 1.03038 | + | 0.169537i | ||||
\(845\) | 299914. | 0.420032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 399036.i | 0.556218i | ||||||||
\(848\) | −272110. | + | 239160.i | −0.378401 | + | 0.332581i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −370046. | − | 435909.i | −0.512174 | − | 0.603334i | ||||
\(851\) | −265190. | − | 153108.i | −0.366183 | − | 0.211416i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 254659. | + | 441083.i | 0.349995 | + | 0.606209i | 0.986248 | − | 0.165272i | \(-0.0528501\pi\) |
−0.636253 | + | 0.771480i | \(0.719517\pi\) | |||||||
\(854\) | −235941. | − | 84348.4i | −0.323510 | − | 0.115654i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −217543. | − | 362276.i | −0.296892 | − | 0.494415i | ||||
\(857\) | −328394. | − | 568795.i | −0.447130 | − | 0.774452i | 0.551068 | − | 0.834460i | \(-0.314220\pi\) |
−0.998198 | + | 0.0600088i | \(0.980887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −916830. | − | 529332.i | −1.24252 | − | 0.717368i | −0.272912 | − | 0.962039i | \(-0.587987\pi\) |
−0.969606 | + | 0.244671i | \(0.921320\pi\) | |||||||
\(860\) | −2488.03 | − | 6599.60i | −0.00336403 | − | 0.00892321i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −107631. | − | 590603.i | −0.144851 | − | 0.794842i | ||||
\(863\) | 676878.i | 0.908844i | 0.890787 | + | 0.454422i | \(0.150154\pi\) | ||||
−0.890787 | + | 0.454422i | \(0.849846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31180.7 | −0.0416729 | ||||||||
\(866\) | 280270. | − | 51076.0i | 0.373716 | − | 0.0681053i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −270215. | + | 101870.i | −0.358649 | + | 0.135210i | ||||
\(869\) | −821100. | + | 1.42219e6i | −1.08732 | + | 1.88329i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29875.4 | + | 17248.6i | −0.0393801 | + | 0.0227361i | ||||
\(872\) | 660896. | − | 396862.i | 0.869161 | − | 0.521924i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12329.5 | + | 34488.5i | −0.0161408 | + | 0.0451493i | ||||
\(875\) | −128438. | + | 74154.0i | −0.167756 | + | 0.0968541i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −737914. | + | 1.27810e6i | −0.959415 | + | 1.66176i | −0.235490 | + | 0.971877i | \(0.575669\pi\) |
−0.723925 | + | 0.689879i | \(0.757664\pi\) | |||||||
\(878\) | 333133. | − | 282799.i | 0.432144 | − | 0.366850i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −409018. | − | 465369.i | −0.528175 | − | 0.600942i | ||||
\(881\) | −599513. | −0.772408 | −0.386204 | − | 0.922413i | \(-0.626214\pi\) | ||||
−0.386204 | + | 0.922413i | \(0.626214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 729187.i | − | 0.935229i | −0.883933 | − | 0.467614i | \(-0.845114\pi\) | ||
0.883933 | − | 0.467614i | \(-0.154886\pi\) | |||||||
\(884\) | −27350.3 | + | 166224.i | −0.0349992 | + | 0.212710i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 703369. | − | 597094.i | 0.896015 | − | 0.760634i | ||||
\(887\) | 1.26218e6 | + | 728722.i | 1.60426 | + | 0.926221i | 0.990621 | + | 0.136636i | \(0.0436290\pi\) |
0.613641 | + | 0.789585i | \(0.289704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 158172. | + | 273962.i | 0.200137 | + | 0.346647i | ||||
\(890\) | 100114. | − | 280041.i | 0.126391 | − | 0.353543i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 837834. | − | 1.02204e6i | 1.05300 | − | 1.28452i | ||||
\(893\) | −65616.2 | − | 113651.i | −0.0822826 | − | 0.142518i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 437015. | + | 252311.i | 0.545570 | + | 0.314985i | ||||
\(896\) | 41577.7 | + | 190739.i | 0.0517898 | + | 0.237588i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38374.5 | − | 6993.32i | 0.0475872 | − | 0.00867223i | ||||
\(899\) | − | 1.86060e6i | − | 2.30215i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 401926. | 0.495104 | ||||||||
\(902\) | 414404. | + | 2.27397e6i | 0.509344 | + | 2.79493i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4102.27 | − | 238729.i | −0.00501981 | − | 0.292125i | ||||
\(905\) | −133627. | + | 231448.i | −0.163153 | + | 0.282590i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3010.76 | + | 1738.27i | −0.00365984 | + | 0.00211301i | −0.501829 | − | 0.864967i | \(-0.667339\pi\) |
0.498169 | + | 0.867080i | \(0.334006\pi\) | |||||||
\(908\) | 301279. | − | 367519.i | 0.365424 | − | 0.445767i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18352.9 | + | 6561.11i | 0.0221627 | + | 0.00792309i | ||||
\(911\) | 712683. | − | 411468.i | 0.858736 | − | 0.495791i | −0.00485282 | − | 0.999988i | \(-0.501545\pi\) |
0.863589 | + | 0.504197i | \(0.168211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −122453. | + | 212094.i | −0.146901 | + | 0.254441i | ||||
\(914\) | −171211. | − | 201685.i | −0.204946 | − | 0.241424i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −117769. | + | 715750.i | −0.140359 | + | 0.853042i | ||||
\(917\) | 15723.8 | 0.0186990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 873279.i | 1.03400i | 0.855984 | + | 0.517002i | \(0.172952\pi\) | ||||
−0.855984 | + | 0.517002i | \(0.827048\pi\) | |||||||
\(920\) | 68931.1 | − | 124276.i | 0.0814403 | − | 0.146828i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −450398. | − | 530563.i | −0.529828 | − | 0.624130i | ||||
\(923\) | −37328.5 | − | 21551.6i | −0.0438164 | − | 0.0252974i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −382837. | − | 663092.i | −0.447435 | − | 0.774980i | ||||
\(926\) | 655351. | + | 234286.i | 0.764279 | + | 0.273228i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.24442e6 | − | 182856.i | −1.44501 | − | 0.212330i | ||||
\(929\) | 172980. | + | 299611.i | 0.200431 | + | 0.347157i | 0.948667 | − | 0.316275i | \(-0.102432\pi\) |
−0.748236 | + | 0.663433i | \(0.769099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −88995.8 | − | 51381.7i | −0.102676 | − | 0.0592802i | ||||
\(932\) | −762513. | + | 287465.i | −0.877840 | + | 0.330943i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −123413. | − | 677205.i | −0.141471 | − | 0.776295i | ||||
\(935\) | 687384.i | 0.786278i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10958e6 | −1.26380 | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||||
−0.631901 | + | 0.775049i | \(0.717725\pi\) | |||||||
\(938\) | 43634.0 | − | 7951.80i | 0.0495929 | − | 0.00903774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 179623. | + | 476458.i | 0.203286 | + | 0.539224i | ||||
\(941\) | 161271. | − | 279330.i | 0.182129 | − | 0.315456i | −0.760477 | − | 0.649365i | \(-0.775035\pi\) |
0.942605 | + | 0.333909i | \(0.108368\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −459147. | + | 265089.i | −0.516331 | + | 0.298104i | ||||
\(944\) | 711124. | − | 142259.i | 0.797997 | − | 0.159638i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11804.4 | − | 33019.6i | 0.0131905 | − | 0.0368969i | ||||
\(947\) | 120742. | − | 69710.2i | 0.134635 | − | 0.0777314i | −0.431170 | − | 0.902271i | \(-0.641899\pi\) |
0.565805 | + | 0.824539i | \(0.308566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40088.8 | + | 69435.9i | −0.0445134 | + | 0.0770995i | ||||
\(950\) | −69817.2 | + | 59268.3i | −0.0773597 | + | 0.0656712i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 105054. | − | 189402.i | 0.115915 | − | 0.208983i | ||||
\(953\) | −1.68438e6 | −1.85462 | −0.927308 | − | 0.374300i | \(-0.877883\pi\) | ||||
−0.927308 | + | 0.374300i | \(0.877883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 248453.i | 0.272419i | ||||||||
\(956\) | −582382. | − | 95824.8i | −0.637224 | − | 0.104848i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 665983. | − | 565357.i | 0.725658 | − | 0.616016i | ||||
\(959\) | −266360. | − | 153783.i | −0.289622 | − | 0.167213i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 685501. | + | 1.18732e6i | 0.742269 | + | 1.28565i | ||||
\(962\) | −75936.8 | + | 212412.i | −0.0820545 | + | 0.229525i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −103782. | − | 85076.6i | −0.111678 | − | 0.0915495i | ||||
\(965\) | 100877. | + | 174723.i | 0.108327 | + | 0.187628i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39280.8 | − | 22678.8i | −0.0420075 | − | 0.0242530i | 0.478849 | − | 0.877897i | \(-0.341054\pi\) |
−0.520857 | + | 0.853644i | \(0.674387\pi\) | |||||||
\(968\) | −36825.3 | − | 2.14303e6i | −0.0393003 | − | 2.28706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −522957. | + | 95302.9i | −0.555805 | + | 0.101289i | ||||
\(971\) | 1.18319e6i | 1.25492i | 0.778648 | + | 0.627461i | \(0.215906\pi\) | ||||
−0.778648 | + | 0.627461i | \(0.784094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −156541. | −0.165350 | ||||||||
\(974\) | −281200. | − | 1.54303e6i | −0.296413 | − | 1.62651i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.27491e6 | + | 431220.i | 1.33838 | + | 0.452688i | ||||
\(977\) | 562965. | − | 975083.i | 0.589783 | − | 1.02153i | −0.404478 | − | 0.914548i | \(-0.632547\pi\) |
0.994261 | − | 0.106986i | \(-0.0341199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.28051e6 | − | 739303.i | 1.33604 | − | 0.771360i | ||||
\(980\) | 308361. | + | 252784.i | 0.321076 | + | 0.263206i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 789909. | + | 282390.i | 0.819132 | + | 0.292838i | ||||
\(983\) | 1.17197e6 | − | 676638.i | 1.21286 | − | 0.700243i | 0.249476 | − | 0.968381i | \(-0.419741\pi\) |
0.963381 | + | 0.268137i | \(0.0864081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −200225. | + | 346799.i | −0.206369 | + | 0.357442i | ||||
\(986\) | 903090. | + | 1.06383e6i | 0.928918 | + | 1.09425i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26623.2 | + | 4380.56i | 0.0272738 | + | 0.00448761i | ||||
\(989\) | 8043.24 | 0.00822316 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.02847e6i | 1.04724i | 0.851953 | + | 0.523619i | \(0.175418\pi\) | ||||
−0.851953 | + | 0.523619i | \(0.824582\pi\) | |||||||
\(992\) | 1.44179e6 | − | 572032.i | 1.46514 | − | 0.581296i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 35864.2 | + | 42247.5i | 0.0362985 | + | 0.0427591i | ||||
\(995\) | −452235. | − | 261098.i | −0.456791 | − | 0.263729i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −564030. | − | 976929.i | −0.567430 | − | 0.982817i | −0.996819 | − | 0.0796977i | \(-0.974605\pi\) |
0.429389 | − | 0.903119i | \(-0.358729\pi\) | |||||||
\(998\) | −511821. | − | 182975.i | −0.513874 | − | 0.183709i | ||||
\(999\) | 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.91.21 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.31.2 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.91.7 | 44 | ||
9.2 | odd | 6 | 36.5.f.a.7.16 | yes | 44 | ||
9.4 | even | 3 | 324.5.d.e.163.10 | 22 | |||
9.5 | odd | 6 | 324.5.d.f.163.13 | 22 | |||
9.7 | even | 3 | inner | 108.5.f.a.19.7 | 44 | ||
12.11 | even | 2 | 36.5.f.a.31.16 | yes | 44 | ||
36.7 | odd | 6 | inner | 108.5.f.a.19.21 | 44 | ||
36.11 | even | 6 | 36.5.f.a.7.2 | ✓ | 44 | ||
36.23 | even | 6 | 324.5.d.f.163.14 | 22 | |||
36.31 | odd | 6 | 324.5.d.e.163.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.2 | ✓ | 44 | 36.11 | even | 6 | ||
36.5.f.a.7.16 | yes | 44 | 9.2 | odd | 6 | ||
36.5.f.a.31.2 | yes | 44 | 3.2 | odd | 2 | ||
36.5.f.a.31.16 | yes | 44 | 12.11 | even | 2 | ||
108.5.f.a.19.7 | 44 | 9.7 | even | 3 | inner | ||
108.5.f.a.19.21 | 44 | 36.7 | odd | 6 | inner | ||
108.5.f.a.91.7 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.91.21 | 44 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.9 | 22 | 36.31 | odd | 6 | |||
324.5.d.e.163.10 | 22 | 9.4 | even | 3 | |||
324.5.d.f.163.13 | 22 | 9.5 | odd | 6 | |||
324.5.d.f.163.14 | 22 | 36.23 | even | 6 |