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 | 91.7 | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.5.f.a.19.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58866 | + | 3.04940i | −0.647164 | + | 0.762350i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.59770 | − | 15.7877i | −0.162356 | − | 0.986732i | ||||
\(5\) | 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 | −0.390996 | − | 0.920392i | \(-0.627869\pi\) |
0.601585 | + | 0.798809i | \(0.294536\pi\) | |||||||
\(8\) | 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 | \(0.694633\pi\) |
−0.996143 | + | 0.0877473i | \(0.972033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5350 | − | 32.1036i | 0.109675 | − | 0.189962i | −0.805964 | − | 0.591965i | \(-0.798352\pi\) |
0.915639 | + | 0.402003i | \(0.131686\pi\) | |||||||
\(14\) | −8.54488 | + | 46.8884i | −0.0435963 | + | 0.239227i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −242.504 | + | 82.0235i | −0.947281 | + | 0.320404i | ||||
\(17\) | −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 | \(-0.979931\pi\) | ||
0.998013 | − | 0.0630057i | \(-0.0200686\pi\) | |||||||
\(20\) | −165.158 | − | 62.2643i | −0.412896 | − | 0.155661i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 157.332 | − | 863.330i | 0.325066 | − | 1.78374i | ||||
\(23\) | −174.319 | − | 100.643i | −0.329525 | − | 0.190252i | 0.326105 | − | 0.945334i | \(-0.394264\pi\) |
−0.655630 | + | 0.755082i | \(0.727597\pi\) | |||||||
\(24\) | 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 | −0.374773 | − | 0.927117i | \(-0.622279\pi\) |
−0.990293 | + | 0.138996i | \(0.955613\pi\) | |||||||
\(32\) | 377.637 | − | 951.823i | 0.368786 | − | 0.929514i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 735.233 | − | 866.094i | 0.636015 | − | 0.749216i | ||||
\(35\) | − | 131.443i | − | 0.107301i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1521.29 | −1.11124 | −0.555622 | − | 0.831435i | \(-0.687520\pi\) | ||||
−0.555622 | + | 0.831435i | \(0.687520\pi\) | |||||||
\(38\) | 138.718 | + | 117.758i | 0.0960648 | + | 0.0815501i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 617.407 | − | 342.453i | 0.385879 | − | 0.214033i | ||||
\(41\) | −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 | −0.509329 | − | 0.860572i | \(-0.670106\pi\) |
0.490613 | + | 0.871378i | \(0.336773\pi\) | |||||||
\(44\) | 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 | 0.186807 | − | 0.982397i | \(-0.440186\pi\) |
0.944184 | + | 0.329419i | \(0.106853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1129.51 | + | 1956.38i | −0.470435 | + | 0.814817i | ||||
\(50\) | −1980.60 | − | 360.941i | −0.792239 | − | 0.144376i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −554.991 | − | 209.230i | −0.205248 | − | 0.0773780i | ||||
\(53\) | −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 | ||||||||
\(56\) | 762.458 | + | 13.1019i | 0.243131 | + | 0.00417791i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4833.61 | + | 880.870i | 1.43686 | + | 0.261852i | ||||
\(59\) | −2453.33 | − | 1416.43i | −0.704778 | − | 0.406904i | 0.104346 | − | 0.994541i | \(-0.466725\pi\) |
−0.809125 | + | 0.587637i | \(0.800058\pi\) | |||||||
\(60\) | 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 | 0.587073 | − | 0.809534i | \(-0.300280\pi\) |
−0.407541 | + | 0.913187i | \(0.633614\pi\) | |||||||
\(68\) | 737.801 | + | 4484.04i | 0.159559 | + | 0.969732i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 400.823 | + | 340.261i | 0.0818006 | + | 0.0694411i | ||||
\(71\) | 1162.75i | 0.230659i | 0.993327 | + | 0.115329i | \(0.0367923\pi\) | ||||
−0.993327 | + | 0.115329i | \(0.963208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2162.87 | −0.405867 | −0.202934 | − | 0.979192i | \(-0.565048\pi\) | ||||
−0.202934 | + | 0.979192i | \(0.565048\pi\) | |||||||
\(74\) | 3938.11 | − | 4639.03i | 0.719158 | − | 0.847157i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −718.185 | + | 118.170i | −0.124339 | + | 0.0204587i | ||||
\(77\) | −1307.02 | + | 2263.82i | −0.220445 | + | 0.381822i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6482.54 | − | 3742.70i | 1.03870 | − | 0.599695i | 0.119237 | − | 0.992866i | \(-0.461955\pi\) |
0.919466 | + | 0.393171i | \(0.128622\pi\) | |||||||
\(80\) | −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 | −0.428190 | − | 0.903689i | \(-0.640848\pi\) |
0.568523 | + | 0.822667i | \(0.307515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1566.60 | + | 2713.43i | −0.216830 | + | 0.375561i | ||||
\(86\) | 28.6565 | − | 157.247i | 0.00387459 | − | 0.0212611i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −14038.7 | − | 241.238i | −1.81285 | − | 0.0311516i | ||||
\(89\) | 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 | ||||||
\(92\) | −1136.10 | + | 3013.54i | −0.134227 | + | 0.356042i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2068.85 | + | 11352.5i | −0.234139 | + | 1.28480i | ||||
\(95\) | −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 | −0.0493798 | − | 0.998780i | \(-0.515724\pi\) |
−0.889659 | + | 0.456626i | \(0.849058\pi\) | |||||||
\(104\) | 2074.71 | − | 1150.77i | 0.191819 | − | 0.106395i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3663.28 | − | 4315.29i | 0.326031 | − | 0.384059i | ||||
\(107\) | 6602.72i | 0.576707i | 0.957524 | + | 0.288353i | \(0.0931078\pi\) | ||||
−0.957524 | + | 0.288353i | \(0.906892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12045.3 | 1.01383 | 0.506913 | − | 0.861997i | \(-0.330786\pi\) | ||||
0.506913 | + | 0.861997i | \(0.330786\pi\) | |||||||
\(110\) | −7380.12 | − | 6265.04i | −0.609928 | − | 0.517772i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2013.70 | + | 2291.13i | −0.160531 | + | 0.182647i | ||||
\(113\) | 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 | ||||
\(122\) | −20688.4 | − | 3770.21i | −1.38997 | − | 0.253307i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8549.63 | + | 22678.2i | −0.556037 | + | 1.47491i | ||||
\(125\) | 12447.0 | 0.796607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26549.7i | 1.64608i | 0.567980 | + | 0.823042i | \(0.307725\pi\) | ||||
−0.567980 | + | 0.823042i | \(0.692275\pi\) | |||||||
\(128\) | −16008.1 | − | 3489.47i | −0.977056 | − | 0.212981i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1609.26 | + | 293.269i | 0.0952226 | + | 0.0173532i | ||||
\(131\) | 1142.84 | + | 659.821i | 0.0665954 | + | 0.0384489i | 0.532928 | − | 0.846161i | \(-0.321092\pi\) |
−0.466333 | + | 0.884609i | \(0.654425\pi\) | |||||||
\(132\) | 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 | 0.175772 | − | 0.984431i | \(-0.443758\pi\) |
−0.764656 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(140\) | −2075.19 | + | 341.450i | −0.105877 | + | 0.0174209i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3545.69 | − | 3009.96i | −0.175843 | − | 0.149274i | ||||
\(143\) | 8132.70i | 0.397706i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13550.2 | −0.644478 | ||||||||
\(146\) | 5598.92 | − | 6595.45i | 0.262663 | − | 0.309413i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3951.86 | + | 24017.7i | 0.180417 | + | 1.09650i | ||||
\(149\) | 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 | 0.148020 | − | 0.988984i | \(-0.452710\pi\) |
0.930496 | + | 0.366303i | \(0.119377\pi\) | |||||||
\(152\) | 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 | \(0.130948\pi\) | |||||||
\(158\) | −5368.10 | + | 29456.4i | −0.215033 | + | 1.17996i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7010.39 | − | 8857.86i | −0.273844 | − | 0.346010i | ||||
\(161\) | −2398.36 | −0.0925257 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 407.281i | − | 0.0153292i | −0.999971 | − | 0.00766459i | \(-0.997560\pi\) | ||
0.999971 | − | 0.00766459i | \(-0.00243974\pi\) | |||||||
\(164\) | 39433.9 | + | 14866.5i | 1.46616 | + | 0.552739i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −800.556 | + | 4392.91i | −0.0290520 | + | 0.159417i | ||||
\(167\) | 20561.9 | + | 11871.4i | 0.737277 | + | 0.425667i | 0.821078 | − | 0.570816i | \(-0.193373\pi\) |
−0.0838016 | + | 0.996482i | \(0.526706\pi\) | |||||||
\(168\) | 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 | ||||
\(176\) | 37077.0 | − | 42185.2i | 1.19696 | − | 1.36187i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17446.8 | + | 20552.1i | −0.550650 | + | 0.648658i | ||||
\(179\) | − | 45743.4i | − | 1.42765i | −0.700323 | − | 0.713826i | \(-0.746961\pi\) | ||
0.700323 | − | 0.713826i | \(-0.253039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24226.2 | −0.739483 | −0.369742 | − | 0.929135i | \(-0.620554\pi\) | ||||
−0.369742 | + | 0.929135i | \(0.620554\pi\) | |||||||
\(182\) | 1346.91 | + | 1143.40i | 0.0406626 | + | 0.0345188i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6248.52 | − | 11265.4i | −0.184562 | − | 0.332745i | ||||
\(185\) | −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 | −0.208257 | − | 0.978074i | \(-0.566779\pi\) |
0.742908 | + | 0.669393i | \(0.233446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9144.35 | + | 15838.5i | −0.245493 | + | 0.425205i | −0.962270 | − | 0.272097i | \(-0.912283\pi\) |
0.716777 | + | 0.697302i | \(0.245616\pi\) | |||||||
\(194\) | 47405.5 | + | 8639.10i | 1.25958 | + | 0.229544i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 33820.9 | + | 12750.4i | 0.880385 | + | 0.331903i | ||||
\(197\) | −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 | \(0.203906\pi\) | ||||
−0.801744 | + | 0.597667i | \(0.796094\pi\) | |||||||
\(200\) | −553.433 | + | 32206.7i | −0.0138358 | + | 0.805168i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 37601.5 | + | 6852.44i | 0.921515 | + | 0.167935i | ||||
\(203\) | −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 | −0.0257275 | − | 0.999669i | \(-0.508190\pi\) |
−0.878602 | + | 0.477554i | \(0.841524\pi\) | |||||||
\(212\) | 3676.08 | + | 22341.6i | 0.0817924 | + | 0.497099i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20134.3 | − | 17092.2i | −0.439653 | − | 0.373224i | ||||
\(215\) | 440.814i | 0.00953626i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18048.7 | −0.383290 | ||||||||
\(218\) | −31181.1 | + | 36730.9i | −0.656113 | + | 0.772891i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 38209.2 | − | 6286.92i | 0.789447 | − | 0.129895i | ||||
\(221\) | −5264.34 | + | 9118.10i | −0.107785 | + | 0.186689i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −71531.9 | + | 41298.9i | −1.43843 | + | 0.830480i | −0.997741 | − | 0.0671780i | \(-0.978600\pi\) |
−0.440693 | + | 0.897658i | \(0.645267\pi\) | |||||||
\(224\) | −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 | −0.728376 | − | 0.685178i | \(-0.759724\pi\) |
0.229194 | + | 0.973381i | \(0.426391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22667.9 | + | 39262.0i | −0.432256 | + | 0.748690i | −0.997067 | − | 0.0765307i | \(-0.975616\pi\) |
0.564811 | + | 0.825220i | \(0.308949\pi\) | |||||||
\(230\) | 1592.42 | − | 8738.10i | 0.0301024 | − | 0.165182i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1350.64 | − | 78599.9i | 0.0250937 | − | 1.46031i | ||||
\(233\) | −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 | ||||||
\(236\) | −15989.2 | + | 42412.0i | −0.287080 | + | 0.761491i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2426.92 | − | 13317.3i | 0.0428452 | − | 0.235105i | ||||
\(239\) | 31946.2 | + | 18444.1i | 0.559272 | + | 0.322896i | 0.752853 | − | 0.658188i | \(-0.228677\pi\) |
−0.193581 | + | 0.981084i | \(0.562010\pi\) | |||||||
\(240\) | 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 | ||||
\(248\) | −47023.0 | − | 84777.4i | −0.764551 | − | 1.37840i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −32221.0 | + | 37955.8i | −0.515536 | + | 0.607293i | ||||
\(251\) | − | 1475.47i | − | 0.0234198i | −0.999931 | − | 0.0117099i | \(-0.996273\pi\) | ||
0.999931 | − | 0.0117099i | \(-0.00372746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44159.6 | 0.689897 | ||||||||
\(254\) | −80960.7 | − | 68728.1i | −1.25489 | − | 1.06529i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 52080.3 | − | 39782.1i | 0.794682 | − | 0.607026i | ||||
\(257\) | 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 | −0.376099 | − | 0.926580i | \(-0.622735\pi\) |
0.614392 | + | 0.789001i | \(0.289401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7805.54 | + | 13519.6i | −0.111151 | + | 0.192518i | ||||
\(266\) | 2132.96 | + | 388.707i | 0.0301453 | + | 0.00549363i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5252.43 | − | 13932.3i | 0.0731292 | − | 0.193978i | ||||
\(269\) | −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 | \(-0.931259\pi\) | ||
0.976772 | − | 0.214281i | \(-0.0687409\pi\) | |||||||
\(272\) | 68876.2 | − | 23296.4i | 0.930960 | − | 0.314884i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −101579. | − | 18511.6i | −1.35301 | − | 0.246571i | ||||
\(275\) | −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 | 0.173970 | − | 0.984751i | \(-0.444341\pi\) |
−0.765835 | + | 0.643038i | \(0.777674\pi\) | |||||||
\(284\) | 18357.2 | − | 3020.48i | 0.227598 | − | 0.0374489i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24799.9 | − | 21052.8i | −0.303192 | − | 0.257381i | ||||
\(287\) | 31383.9i | 0.381016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2853.15 | −0.0341609 | ||||||||
\(290\) | 35076.7 | − | 41319.9i | 0.417083 | − | 0.491318i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5618.48 | + | 34146.7i | 0.0658951 | + | 0.400482i | ||||
\(293\) | −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 | ||||
\(302\) | −20363.6 | + | 111742.i | −0.223276 | + | 1.22518i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3731.26 | + | 11031.5i | 0.0403746 | + | 0.119368i | ||||
\(305\) | 57996.0 | 0.623446 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 123447.i | − | 1.30980i | −0.755716 | − | 0.654900i | \(-0.772711\pi\) | ||
0.755716 | − | 0.654900i | \(-0.227289\pi\) | |||||||
\(308\) | 39135.8 | + | 14754.1i | 0.412547 | + | 0.155529i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11983.7 | − | 65758.1i | 0.124700 | − | 0.684268i | ||||
\(311\) | 52431.9 | + | 30271.6i | 0.542094 | + | 0.312978i | 0.745927 | − | 0.666027i | \(-0.232007\pi\) |
−0.203833 | + | 0.979006i | \(0.565340\pi\) | |||||||
\(312\) | 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 | ||||
\(320\) | 45158.7 | + | 1552.45i | 0.441003 | + | 0.0151607i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6208.53 | − | 7313.56i | 0.0598794 | − | 0.0705370i | ||||
\(323\) | 12920.1i | 0.123840i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18657.5 | 0.176639 | ||||||||
\(326\) | 1241.96 | + | 1054.31i | 0.0116862 | + | 0.00992050i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −147415. | + | 81765.6i | −1.37023 | + | 0.760017i | ||||
\(329\) | 17186.8 | − | 29768.4i | 0.158783 | − | 0.275019i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 37439.2 | − | 21615.5i | 0.341720 | − | 0.197292i | −0.319312 | − | 0.947650i | \(-0.603452\pi\) |
0.661032 | + | 0.750357i | \(0.270119\pi\) | |||||||
\(332\) | −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 | \(0.183285\pi\) | |||||||
\(338\) | −106985. | − | 19496.8i | −0.936462 | − | 0.170659i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 46908.4 | + | 17684.3i | 0.405782 | + | 0.152979i | ||||
\(341\) | 332321. | 2.85791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55525.0i | 0.471955i | ||||||||
\(344\) | −2557.01 | − | 43.9392i | −0.0216081 | − | 0.000371309i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11122.8 | + | 2027.00i | 0.0929098 | + | 0.0169317i | ||||
\(347\) | −25222.5 | − | 14562.2i | −0.209473 | − | 0.120940i | 0.391593 | − | 0.920138i | \(-0.371924\pi\) |
−0.601067 | + | 0.799199i | \(0.705257\pi\) | |||||||
\(348\) | 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 | ||||
\(356\) | −17507.8 | − | 106405.i | −0.138144 | − | 0.839577i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 139490. | + | 118414.i | 1.08837 | + | 0.923925i | ||||
\(359\) | 66839.6i | 0.518615i | 0.965795 | + | 0.259307i | \(0.0834942\pi\) | ||||
−0.965795 | + | 0.259307i | \(0.916506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 128252. | 0.984121 | ||||||||
\(362\) | 62713.4 | − | 73875.4i | 0.478567 | − | 0.563745i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6973.37 | + | 1147.39i | −0.0526308 | + | 0.00865984i | ||||
\(365\) | −11929.9 | + | 20663.2i | −0.0895472 | + | 0.155100i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −81901.3 | + | 47285.7i | −0.608077 | + | 0.351073i | −0.772212 | − | 0.635364i | \(-0.780850\pi\) |
0.164136 | + | 0.986438i | \(0.447517\pi\) | |||||||
\(368\) | 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 | \(-0.0588554\pi\) | |||||||
\(374\) | −44685.5 | + | 245204.i | −0.319465 | + | 1.75301i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 184604. | + | 3172.19i | 1.30576 | + | 0.0224379i | ||||
\(377\) | −45533.4 | −0.320366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 51191.3i | 0.356384i | 0.983996 | + | 0.178192i | \(0.0570248\pi\) | ||||
−0.983996 | + | 0.178192i | \(0.942975\pi\) | |||||||
\(380\) | −2832.41 | + | 7513.07i | −0.0196150 | + | 0.0520296i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16151.5 | + | 88628.2i | −0.110684 | + | 0.607359i | ||||
\(383\) | 132128. | + | 76284.0i | 0.900734 | + | 0.520039i | 0.877438 | − | 0.479690i | \(-0.159251\pi\) |
0.0232957 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(384\) | 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 | ||||
\(392\) | −126432. | + | 70127.0i | −0.822780 | + | 0.456366i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 93968.9 | − | 110694.i | 0.605329 | − | 0.713069i | ||||
\(395\) | − | 82575.7i | − | 0.529247i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −126087. | −0.799998 | −0.399999 | − | 0.916516i | \(-0.630990\pi\) | ||||
−0.399999 | + | 0.916516i | \(0.630990\pi\) | |||||||
\(398\) | −144348. | − | 122538.i | −0.911264 | − | 0.773578i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −96778.6 | − | 85059.8i | −0.604866 | − | 0.531624i | ||||
\(401\) | 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 | \(0.208214\pi\) | |||||||
\(410\) | −114343. | − | 20837.7i | −0.680209 | − | 0.123960i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −64927.4 | + | 172223.i | −0.382502 | + | 1.01460i | ||||
\(413\) | −33754.1 | −0.197891 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12314.7i | − | 0.0715036i | ||||||
\(416\) | −23557.4 | − | 29765.6i | −0.136126 | − | 0.172000i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −39273.0 | − | 7157.04i | −0.224771 | − | 0.0409620i | ||||
\(419\) | −182385. | − | 105300.i | −1.03887 | − | 0.599792i | −0.119357 | − | 0.992851i | \(-0.538083\pi\) |
−0.919513 | + | 0.393060i | \(0.871417\pi\) | |||||||
\(420\) | 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 | ||||
\(428\) | 104242. | − | 17151.9i | 0.569055 | − | 0.0936320i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1344.22 | − | 1141.12i | −0.00726997 | − | 0.00617153i | ||||
\(431\) | 150083.i | 0.807933i | 0.914774 | + | 0.403967i | \(0.132369\pi\) | ||||
−0.914774 | + | 0.403967i | \(0.867631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 71221.5 | 0.379871 | 0.189935 | − | 0.981797i | \(-0.439172\pi\) | ||||
0.189935 | + | 0.981797i | \(0.439172\pi\) | |||||||
\(434\) | 46722.0 | − | 55037.8i | 0.248051 | − | 0.292201i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31290.0 | − | 190167.i | −0.164601 | − | 1.00038i | ||||
\(437\) | −4578.26 | + | 7929.78i | −0.0239739 | + | 0.0415239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −94609.3 | + | 54622.7i | −0.490913 | + | 0.283429i | −0.724953 | − | 0.688798i | \(-0.758139\pi\) |
0.234040 | + | 0.972227i | \(0.424805\pi\) | |||||||
\(440\) | −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 | −0.913486 | − | 0.406871i | \(-0.866620\pi\) |
−0.104382 | + | 0.994537i | \(0.533287\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37174.8 | − | 64388.7i | 0.187728 | − | 0.325154i | ||||
\(446\) | 59234.5 | − | 325038.i | 0.297786 | − | 1.63405i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 41402.6 | + | 25840.0i | 0.206287 | + | 0.128747i | ||||
\(449\) | 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 | ||||||
\(452\) | −55853.8 | − | 21056.7i | −0.273386 | − | 0.103066i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21300.3 | − | 116881.i | 0.103341 | − | 0.567066i | ||||
\(455\) | −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 | 0.105521 | − | 0.994417i | \(-0.466349\pi\) |
−0.808430 | + | 0.588592i | \(0.799682\pi\) | |||||||
\(464\) | 236186. | + | 207587.i | 1.09703 | + | 0.964194i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 131844. | − | 155310.i | 0.607138 | − | 0.715200i | ||||
\(467\) | 172090.i | 0.789080i | 0.918879 | + | 0.394540i | \(0.129096\pi\) | ||||
−0.918879 | + | 0.394540i | \(0.870904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11088.2 | 0.0504097 | ||||||||
\(470\) | 97045.8 | + | 82382.8i | 0.439320 | + | 0.372942i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −87940.6 | − | 158548.i | −0.394735 | − | 0.711665i | ||||
\(473\) | 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 | −0.851912 | − | 0.523685i | \(-0.824557\pi\) |
0.0275690 | + | 0.999620i | \(0.491223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28197.2 | + | 48839.0i | −0.121875 | + | 0.211094i | ||||
\(482\) | 33005.5 | + | 6014.87i | 0.142067 | + | 0.0258900i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −501389. | − | 189022.i | −2.14034 | − | 0.806904i | ||||
\(485\) | −132893. | −0.564959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 392112.i | 1.65330i | 0.562716 | + | 0.826650i | \(0.309757\pi\) | ||||
−0.562716 | + | 0.826650i | \(0.690243\pi\) | |||||||
\(488\) | −5780.89 | + | 336416.i | −0.0242748 | + | 1.41266i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −98067.5 | − | 17871.7i | −0.408444 | − | 0.0744343i | ||||
\(491\) | −181620. | − | 104859.i | −0.753358 | − | 0.434951i | 0.0735480 | − | 0.997292i | \(-0.476568\pi\) |
−0.826906 | + | 0.562340i | \(0.809901\pi\) | |||||||
\(492\) | 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 | 0.717332 | − | 0.696731i | \(-0.245363\pi\) |
−0.244721 | + | 0.969594i | \(0.578696\pi\) | |||||||
\(500\) | −32333.5 | − | 196509.i | −0.129334 | − | 0.786037i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4499.29 | + | 3819.48i | 0.0178541 | + | 0.0151564i | ||||
\(503\) | − | 232332.i | − | 0.918275i | −0.888365 | − | 0.459137i | \(-0.848159\pi\) | ||
0.888365 | − | 0.459137i | \(-0.151841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −105409. | −0.413328 | ||||||||
\(506\) | −114314. | + | 134660.i | −0.446477 | + | 0.525943i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 419159. | − | 68968.2i | 1.62424 | − | 0.267252i | ||||
\(509\) | −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 | ||||
\(518\) | 12999.3 | − | 71331.1i | 0.0484461 | − | 0.265839i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 449.672 | − | 26168.4i | 0.00166299 | − | 0.0967766i | ||||
\(521\) | −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 | \(-0.957278\pi\) | ||
0.991007 | − | 0.133811i | \(-0.0427215\pi\) | |||||||
\(524\) | 7448.30 | − | 19756.9i | 0.0271266 | − | 0.0719543i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13648.9 | + | 74896.0i | −0.0493318 | + | 0.270699i | ||||
\(527\) | 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 | ||||
\(536\) | 28888.4 | + | 52082.7i | 0.100553 | + | 0.181286i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 152017. | − | 179073.i | 0.525202 | − | 0.618681i | ||||
\(539\) | − | 495602.i | − | 1.70591i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 438165. | 1.49707 | 0.748536 | − | 0.663094i | \(-0.230757\pi\) | ||||
0.748536 | + | 0.663094i | \(0.230757\pi\) | |||||||
\(542\) | 95977.1 | + | 81475.6i | 0.326715 | + | 0.277351i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −107257. | + | 270337.i | −0.362432 | + | 0.913500i | ||||
\(545\) | 66439.2 | − | 115076.i | 0.223682 | − | 0.387429i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −270221. | + | 156012.i | −0.903118 | + | 0.521416i | −0.878211 | − | 0.478274i | \(-0.841263\pi\) |
−0.0249077 | + | 0.999690i | \(0.507929\pi\) | |||||||
\(548\) | 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 | ||||
\(554\) | 261814. | + | 47712.6i | 0.853048 | + | 0.155458i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −74153.2 | + | 196694.i | −0.239873 | + | 0.636271i | ||||
\(557\) | −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 | ||||||||
\(560\) | 10781.4 | + | 31875.5i | 0.0343796 | + | 0.101644i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 486861. | + | 88724.8i | 1.54146 | + | 0.280913i | ||||
\(563\) | 74780.6 | + | 43174.6i | 0.235924 | + | 0.136211i | 0.613302 | − | 0.789849i | \(-0.289841\pi\) |
−0.377378 | + | 0.926059i | \(0.623174\pi\) | |||||||
\(564\) | 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 | 0.0394467 | − | 0.999222i | \(-0.487440\pi\) |
−0.845628 | + | 0.533773i | \(0.820774\pi\) | |||||||
\(572\) | 128397. | − | 21126.3i | 0.392430 | − | 0.0645701i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −95702.2 | − | 81242.3i | −0.290468 | − | 0.246580i | ||||
\(575\) | − | 101308.i | − | 0.306414i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −500884. | −1.50448 | −0.752238 | − | 0.658892i | \(-0.771026\pi\) | ||||
−0.752238 | + | 0.658892i | \(0.771026\pi\) | |||||||
\(578\) | 7385.83 | − | 8700.40i | 0.0221077 | − | 0.0260426i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 35199.2 | + | 213926.i | 0.104635 | + | 0.635927i | ||||
\(581\) | 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 | 0.448666 | − | 0.893699i | \(-0.351899\pi\) |
0.998300 | + | 0.0582932i | \(0.0185658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34453.5 | + | 59675.2i | −0.0993122 | + | 0.172014i | ||||
\(590\) | 22411.4 | − | 122978.i | 0.0643821 | − | 0.353285i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 368919. | − | 124782.i | 1.05266 | − | 0.356048i | ||||
\(593\) | 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 | ||||||||
\(596\) | −388305. | − | 146390.i | −1.09315 | − | 0.412115i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5351.10 | − | 29363.2i | 0.0149637 | − | 0.0821108i | ||||
\(599\) | 165665. | + | 95646.9i | 0.461719 | + | 0.266574i | 0.712767 | − | 0.701401i | \(-0.247442\pi\) |
−0.251048 | + | 0.967975i | \(0.580775\pi\) | |||||||
\(600\) | 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 | 0.578523 | − | 0.815666i | \(-0.303629\pi\) |
−0.417126 | + | 0.908849i | \(0.636962\pi\) | |||||||
\(608\) | −43298.5 | − | 17178.7i | −0.117129 | − | 0.0464712i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −150132. | + | 176853.i | −0.403472 | + | 0.475284i | ||||
\(611\) | − | 106942.i | − | 0.286461i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −572114. | −1.52252 | −0.761258 | − | 0.648450i | \(-0.775418\pi\) | ||||
−0.761258 | + | 0.648450i | \(0.775418\pi\) | |||||||
\(614\) | 376440. | + | 319563.i | 0.998526 | + | 0.847655i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −146300. | + | 81147.5i | −0.385553 | + | 0.213852i | ||||
\(617\) | 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 | 0.101786 | − | 0.994806i | \(-0.467544\pi\) |
0.912420 | + | 0.409254i | \(0.134211\pi\) | |||||||
\(620\) | 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 | ||||
\(626\) | −206150. | − | 37568.4i | −0.526058 | − | 0.0958680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −82647.8 | − | 31158.0i | −0.209562 | − | 0.0790042i | ||||
\(629\) | 432079. | 1.09210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 402529.i | 1.01097i | 0.862835 | + | 0.505486i | \(0.168687\pi\) | ||||
−0.862835 | + | 0.505486i | \(0.831313\pi\) | |||||||
\(632\) | 478995. | + | 8230.94i | 1.19921 | + | 0.0206070i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 102304. | + | 18643.8i | 0.254517 | + | 0.0463827i | ||||
\(635\) | 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 | 0.198415 | − | 0.980118i | \(-0.436420\pi\) |
−0.749599 | + | 0.661892i | \(0.769754\pi\) | |||||||
\(644\) | 6230.22 | + | 37864.6i | 0.0150221 | + | 0.0912981i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39398.7 | − | 33445.8i | −0.0944097 | − | 0.0801451i | ||||
\(647\) | 265174.i | 0.633464i | 0.948515 | + | 0.316732i | \(0.102586\pi\) | ||||
−0.948515 | + | 0.316732i | \(0.897414\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 621494. | 1.47553 | ||||||||
\(650\) | −48297.9 | + | 56894.3i | −0.114315 | + | 0.134661i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6430.04 | + | 1057.99i | −0.0151258 | + | 0.00248879i | ||||
\(653\) | −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 | −0.937802 | − | 0.347171i | \(-0.887142\pi\) |
−0.168242 | + | 0.985746i | \(0.553809\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 410614. | − | 711204.i | 0.939789 | − | 1.62776i | 0.173926 | − | 0.984759i | \(-0.444355\pi\) |
0.765863 | − | 0.643004i | \(-0.222312\pi\) | |||||||
\(662\) | −31002.8 | + | 170122.i | −0.0707433 | + | 0.388191i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 71433.6 | + | 1227.50i | 0.162019 | + | 0.00278410i | ||||
\(665\) | −5979.36 | −0.0135211 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 247241.i | 0.555736i | ||||||||
\(668\) | 134009. | − | 355464.i | 0.300318 | − | 0.796604i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7362.12 | + | 40398.3i | −0.0164004 | + | 0.0899939i | ||||
\(671\) | −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 | ||||
\(680\) | −175357. | + | 97263.9i | −0.379231 | + | 0.210346i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −860265. | + | 1.01338e6i | −1.84954 | + | 2.17873i | ||||
\(683\) | 764551.i | 1.63895i | 0.573117 | + | 0.819474i | \(0.305734\pi\) | ||||
−0.573117 | + | 0.819474i | \(0.694266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 284757. | 0.606868 | ||||||||
\(686\) | −169318. | − | 143735.i | −0.359795 | − | 0.305433i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6753.22 | − | 7683.62i | 0.0142671 | − | 0.0162326i | ||||
\(689\) | −26229.4 | + | 45430.7i | −0.0552523 | + | 0.0956998i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 278107. | − | 160565.i | 0.582445 | − | 0.336275i | −0.179659 | − | 0.983729i | \(-0.557500\pi\) |
0.762105 | + | 0.647454i | \(0.224166\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 472131. | + | 86040.5i | 0.969063 | + | 0.176601i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 33847.9 | − | 89782.9i | 0.0690774 | − | 0.183230i | ||||
\(701\) | 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 | ||||||||
\(704\) | −762323. | − | 475777.i | −1.53813 | − | 0.959972i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −609002. | − | 110984.i | −1.22183 | − | 0.222664i | ||||
\(707\) | −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 | ||||
\(716\) | −722183. | + | 118828.i | −1.40871 | + | 0.231788i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −203821. | − | 173025.i | −0.395366 | − | 0.335629i | ||||
\(719\) | 348658.i | 0.674438i | 0.941426 | + | 0.337219i | \(0.109486\pi\) | ||||
−0.941426 | + | 0.337219i | \(0.890514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −137065. | −0.263668 | ||||||||
\(722\) | −332000. | + | 391091.i | −0.636888 | + | 0.750245i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 62932.5 | + | 382476.i | 0.120060 | + | 0.729672i | ||||
\(725\) | 309106. | − | 535387.i | 0.588073 | − | 1.01857i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 523789. | − | 302410.i | 0.991032 | − | 0.572173i | 0.0854497 | − | 0.996342i | \(-0.472767\pi\) |
0.905583 | + | 0.424170i | \(0.139434\pi\) | |||||||
\(728\) | 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 | \(0.0207222\pi\) | |||||||
\(734\) | 67821.2 | − | 372156.i | 0.125885 | − | 0.690770i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −161624. | + | 127914.i | −0.298366 | + | 0.236136i | ||||
\(737\) | −204160. | −0.375868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 844449.i | 1.54627i | 0.634244 | + | 0.773133i | \(0.281312\pi\) | ||||
−0.634244 | + | 0.773133i | \(0.718688\pi\) | |||||||
\(740\) | 251254. | + | 94722.2i | 0.458828 | + | 0.172977i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12092.1 | − | 66353.1i | 0.0219631 | − | 0.120518i | ||||
\(743\) | 537216. | + | 310162.i | 0.973131 | + | 0.561837i | 0.900189 | − | 0.435499i | \(-0.143428\pi\) |
0.0729415 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(744\) | 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 | −0.180139 | − | 0.983641i | \(-0.557655\pi\) |
−0.941928 | + | 0.335816i | \(0.890988\pi\) | |||||||
\(752\) | −487549. | + | 554719.i | −0.862149 | + | 0.980928i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 117870. | − | 138849.i | 0.207330 | − | 0.244231i | ||||
\(755\) | − | 313247.i | − | 0.549533i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −769023. | −1.34198 | −0.670992 | − | 0.741465i | \(-0.734132\pi\) | ||||
−0.670992 | + | 0.741465i | \(0.734132\pi\) | |||||||
\(758\) | −156103. | − | 132517.i | −0.271689 | − | 0.230639i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15578.2 | − | 28085.9i | −0.0269706 | − | 0.0486252i | ||||
\(761\) | 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 | \(0.152440\pi\) | |||||||
\(770\) | −113479. | − | 20680.2i | −0.191396 | − | 0.0348798i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 273808. | + | 103225.i | 0.459421 | + | 0.173201i | ||||
\(773\) | 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 | ||||||
\(776\) | 13246.4 | − | 770866.i | 0.0219975 | − | 1.28013i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −267187. | − | 48691.7i | −0.441423 | − | 0.0804443i | ||||
\(779\) | 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 | −0.159181 | − | 0.987249i | \(-0.550885\pi\) |
−0.934574 | + | 0.355770i | \(0.884219\pi\) | |||||||
\(788\) | 94297.2 | + | 573098.i | 0.151861 | + | 0.922946i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 251807. | + | 213760.i | 0.403472 | + | 0.342510i | ||||
\(791\) | − | 44451.9i | − | 0.0710456i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 194887. | 0.309911 | ||||||||
\(794\) | 326396. | − | 384490.i | 0.517730 | − | 0.609879i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 747335. | − | 122966.i | 1.17948 | − | 0.194070i | ||||
\(797\) | −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 | ||||
\(806\) | 40269.4 | − | 220971.i | 0.0619876 | − | 0.340146i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10506.9 | − | 611442.i | 0.0160935 | − | 0.936554i | ||||
\(809\) | 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 | \(0.125167\pi\) | ||||
−0.923678 | + | 0.383169i | \(0.874833\pi\) | |||||||
\(812\) | −82605.3 | + | 219114.i | −0.125284 | + | 0.332321i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −239348. | + | 1.31338e6i | −0.361228 | + | 1.98217i | ||||
\(815\) | −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 | 0.919584 | − | 0.392893i | \(-0.128526\pi\) |
0.119536 | + | 0.992830i | \(0.461859\pi\) | |||||||
\(824\) | −357101. | − | 643815.i | −0.525940 | − | 0.948215i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 87377.7 | − | 102930.i | 0.128068 | − | 0.150862i | ||||
\(827\) | − | 375951.i | − | 0.549693i | −0.961488 | − | 0.274847i | \(-0.911373\pi\) | ||
0.961488 | − | 0.274847i | \(-0.0886271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 423699. | 0.616522 | 0.308261 | − | 0.951302i | \(-0.400253\pi\) | ||||
0.308261 | + | 0.951302i | \(0.400253\pi\) | |||||||
\(830\) | 37552.5 | + | 31878.6i | 0.0545108 | + | 0.0462746i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 151749. | + | 5216.79i | 0.219220 | + | 0.00753628i | ||||
\(833\) | 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 | 0.373539 | − | 0.927614i | \(-0.378144\pi\) |
0.990107 | + | 0.140313i | \(0.0448108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −400727. | + | 694079.i | −0.566573 | + | 0.981334i | ||||
\(842\) | 331052. | + | 60330.3i | 0.466951 | + | 0.0850965i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −262399. | + | 696024.i | −0.368364 | + | 0.977100i | ||||
\(845\) | 299914. | 0.420032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 399036.i | − | 0.556218i | ||||||
\(848\) | 343174. | − | 116074.i | 0.477224 | − | 0.161414i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 562531. | + | 102515.i | 0.778589 | + | 0.141889i | ||||
\(851\) | 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 | 0.969606 | − | 0.244671i | \(-0.0786799\pi\) |
0.272912 | + | 0.962039i | \(0.412013\pi\) | |||||||
\(860\) | 6959.44 | − | 1145.10i | 0.00940974 | − | 0.00154827i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −457662. | − | 388512.i | −0.615928 | − | 0.522866i | ||||
\(863\) | − | 676878.i | − | 0.908844i | −0.890787 | − | 0.454422i | \(-0.849846\pi\) | ||
0.890787 | − | 0.454422i | \(-0.150154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31180.7 | −0.0416729 | ||||||||
\(866\) | −184368. | + | 217183.i | −0.245839 | + | 0.289594i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 46885.2 | + | 284948.i | 0.0622295 | + | 0.378204i | ||||
\(869\) | −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 | \(0.757664\pi\) | |||||||
\(878\) | 78344.6 | − | 429901.i | 0.101629 | − | 0.557673i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −198512. | − | 586905.i | −0.256343 | − | 0.757883i | ||||
\(881\) | −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 | \(0.154886\pi\) | ||||
−0.883933 | + | 0.467614i | \(0.845114\pi\) | |||||||
\(884\) | 157629. | + | 59425.7i | 0.201712 | + | 0.0760449i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 165415. | − | 907682.i | 0.210720 | − | 1.15629i | ||||
\(887\) | −1.26218e6 | − | 728722.i | −1.60426 | − | 0.926221i | −0.990621 | − | 0.136636i | \(-0.956371\pi\) |
−0.613641 | − | 0.789585i | \(-0.710296\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | −185974. | + | 59362.3i | −0.231652 | + | 0.0739426i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25243.7 | + | 29736.7i | −0.0313040 | + | 0.0368757i | ||||
\(899\) | 1.86060e6i | 2.30215i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 401926. | 0.495104 | ||||||||
\(902\) | 1.76211e6 | + | 1.49587e6i | 2.16581 | + | 1.83857i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 208797. | − | 115812.i | 0.255498 | − | 0.141715i | ||||
\(905\) | −133627. | + | 231448.i | −0.163153 | + | 0.282590i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3010.76 | − | 1738.27i | 0.00365984 | − | 0.00211301i | −0.498169 | − | 0.867080i | \(-0.665994\pi\) |
0.501829 | + | 0.864967i | \(0.332661\pi\) | |||||||
\(908\) | 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 | −0.863589 | − | 0.504197i | \(-0.831789\pi\) |
0.00485282 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −122453. | + | 212094.i | −0.146901 | + | 0.254441i | ||||
\(914\) | 260270. | + | 47431.1i | 0.311552 | + | 0.0567768i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 678742. | + | 255884.i | 0.808936 | + | 0.304967i | ||||
\(917\) | 15723.8 | 0.0186990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 873279.i | − | 1.03400i | −0.855984 | − | 0.517002i | \(-0.827048\pi\) | ||
0.855984 | − | 0.517002i | \(-0.172952\pi\) | |||||||
\(920\) | −142091. | − | 2441.67i | −0.167877 | − | 0.00288477i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 684680. | + | 124775.i | 0.805427 | + | 0.146780i | ||||
\(923\) | 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 | ||||
\(932\) | 132304. | + | 804088.i | 0.152315 | + | 0.925704i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −524771. | − | 445481.i | −0.601556 | − | 0.510665i | ||||
\(935\) | − | 687384.i | − | 0.786278i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10958e6 | −1.26380 | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||||
−0.631901 | + | 0.775049i | \(0.717725\pi\) | |||||||
\(938\) | −28703.5 | + | 33812.3i | −0.0326234 | + | 0.0384299i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −502437. | + | 82670.6i | −0.568624 | + | 0.0935611i | ||||
\(941\) | 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 | −0.565805 | − | 0.824539i | \(-0.691434\pi\) |
0.431170 | + | 0.902271i | \(0.358101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40088.8 | + | 69435.9i | −0.0445134 | + | 0.0770995i | ||||
\(950\) | −16419.2 | + | 90097.6i | −0.0181931 | + | 0.0998311i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −216554. | − | 3721.22i | −0.238942 | − | 0.00410593i | ||||
\(953\) | −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 | ||||||
\(956\) | 208204. | − | 552270.i | 0.227811 | − | 0.604276i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 156622. | − | 859436.i | 0.170656 | − | 0.936446i | ||||
\(959\) | 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 | 0.520857 | − | 0.853644i | \(-0.325613\pi\) |
−0.478849 | + | 0.877897i | \(0.658946\pi\) | |||||||
\(968\) | 1.87433e6 | − | 1.03962e6i | 2.00030 | − | 1.10949i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 344013. | − | 405243.i | 0.365622 | − | 0.430697i | ||||
\(971\) | − | 1.18319e6i | − | 1.25492i | −0.778648 | − | 0.627461i | \(-0.784094\pi\) | ||
0.778648 | − | 0.627461i | \(-0.215906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −156541. | −0.165350 | ||||||||
\(974\) | −1.19571e6 | − | 1.01504e6i | −1.26039 | − | 1.06996i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.01090e6 | − | 888494.i | −1.06123 | − | 0.932727i | ||||
\(977\) | 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 | −0.963381 | − | 0.268137i | \(-0.913592\pi\) |
−0.249476 | + | 0.968381i | \(0.580259\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −200225. | + | 346799.i | −0.206369 | + | 0.357442i | ||||
\(986\) | −1.37285e6 | − | 250185.i | −1.41211 | − | 0.257341i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9517.90 | + | 25246.6i | −0.00975051 | + | 0.0258636i | ||||
\(989\) | 8043.24 | 0.00822316 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.02847e6i | − | 1.04724i | −0.851953 | − | 0.523619i | \(-0.824582\pi\) | ||
0.851953 | − | 0.523619i | \(-0.175418\pi\) | |||||||
\(992\) | −1.21629e6 | + | 962611.i | −1.23599 | + | 0.978200i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −54519.6 | − | 9935.56i | −0.0551797 | − | 0.0100559i | ||||
\(995\) | 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.91.7 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.31.16 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.91.21 | 44 | ||
9.2 | odd | 6 | 36.5.f.a.7.2 | ✓ | 44 | ||
9.4 | even | 3 | 324.5.d.e.163.9 | 22 | |||
9.5 | odd | 6 | 324.5.d.f.163.14 | 22 | |||
9.7 | even | 3 | inner | 108.5.f.a.19.21 | 44 | ||
12.11 | even | 2 | 36.5.f.a.31.2 | yes | 44 | ||
36.7 | odd | 6 | inner | 108.5.f.a.19.7 | 44 | ||
36.11 | even | 6 | 36.5.f.a.7.16 | yes | 44 | ||
36.23 | even | 6 | 324.5.d.f.163.13 | 22 | |||
36.31 | odd | 6 | 324.5.d.e.163.10 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.2 | ✓ | 44 | 9.2 | odd | 6 | ||
36.5.f.a.7.16 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.2 | yes | 44 | 12.11 | even | 2 | ||
36.5.f.a.31.16 | yes | 44 | 3.2 | odd | 2 | ||
108.5.f.a.19.7 | 44 | 36.7 | odd | 6 | inner | ||
108.5.f.a.19.21 | 44 | 9.7 | even | 3 | inner | ||
108.5.f.a.91.7 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.91.21 | 44 | 4.3 | odd | 2 | inner | ||
324.5.d.e.163.9 | 22 | 9.4 | even | 3 | |||
324.5.d.e.163.10 | 22 | 36.31 | odd | 6 | |||
324.5.d.f.163.13 | 22 | 36.23 | even | 6 | |||
324.5.d.f.163.14 | 22 | 9.5 | odd | 6 |