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 | 19.4 | ||
Character | \(\chi\) | \(=\) | 108.19 |
Dual form | 108.5.f.a.91.4 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.61656 | − | 1.70894i | −0.904141 | − | 0.427234i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.1591 | + | 12.3610i | 0.634942 | + | 0.772560i | ||||
\(5\) | 2.83091 | + | 4.90328i | 0.113236 | + | 0.196131i | 0.917073 | − | 0.398718i | \(-0.130545\pi\) |
−0.803837 | + | 0.594850i | \(0.797212\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −45.1595 | − | 26.0728i | −0.921621 | − | 0.532098i | −0.0374695 | − | 0.999298i | \(-0.511930\pi\) |
−0.884152 | + | 0.467199i | \(0.845263\pi\) | |||||||
\(8\) | −15.6169 | − | 62.0654i | −0.244014 | − | 0.969772i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.85878 | − | 22.5709i | −0.0185878 | − | 0.225709i | ||||
\(11\) | 92.3736 | + | 53.3319i | 0.763418 | + | 0.440760i | 0.830522 | − | 0.556986i | \(-0.188042\pi\) |
−0.0671034 | + | 0.997746i | \(0.521376\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.0686 | + | 105.774i | 0.361352 | + | 0.625881i | 0.988184 | − | 0.153274i | \(-0.0489818\pi\) |
−0.626831 | + | 0.779155i | \(0.715648\pi\) | |||||||
\(14\) | 118.765 | + | 171.469i | 0.605945 | + | 0.874840i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −49.5864 | + | 251.152i | −0.193697 | + | 0.981061i | ||||
\(17\) | 122.675 | 0.424481 | 0.212240 | − | 0.977217i | \(-0.431924\pi\) | ||||
0.212240 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 593.624i | − | 1.64439i | −0.569207 | − | 0.822194i | \(-0.692750\pi\) | ||
0.569207 | − | 0.822194i | \(-0.307250\pi\) | |||||||
\(20\) | −31.8498 | + | 84.8055i | −0.0796244 | + | 0.212014i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −242.934 | − | 350.739i | −0.501930 | − | 0.724667i | ||||
\(23\) | 473.649 | − | 273.461i | 0.895366 | − | 0.516940i | 0.0196720 | − | 0.999806i | \(-0.493738\pi\) |
0.875694 | + | 0.482867i | \(0.160404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 296.472 | − | 513.504i | 0.474355 | − | 0.821607i | ||||
\(26\) | −40.0976 | − | 486.900i | −0.0593160 | − | 0.720266i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −136.493 | − | 823.090i | −0.174099 | − | 1.04986i | ||||
\(29\) | 367.933 | − | 637.279i | 0.437495 | − | 0.757763i | −0.560001 | − | 0.828492i | \(-0.689199\pi\) |
0.997496 | + | 0.0707290i | \(0.0225326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −507.427 | + | 292.963i | −0.528020 | + | 0.304853i | −0.740210 | − | 0.672376i | \(-0.765274\pi\) |
0.212190 | + | 0.977228i | \(0.431941\pi\) | |||||||
\(32\) | 608.535 | − | 823.566i | 0.594272 | − | 0.804264i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −443.662 | − | 209.644i | −0.383791 | − | 0.181353i | ||||
\(35\) | − | 295.239i | − | 0.241012i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2289.29 | 1.67223 | 0.836117 | − | 0.548551i | \(-0.184820\pi\) | ||||
0.836117 | + | 0.548551i | \(0.184820\pi\) | |||||||
\(38\) | −1014.47 | + | 2146.88i | −0.702539 | + | 1.48676i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 260.114 | − | 252.275i | 0.162571 | − | 0.157672i | ||||
\(41\) | −1434.13 | − | 2483.99i | −0.853142 | − | 1.47769i | −0.878358 | − | 0.478004i | \(-0.841360\pi\) |
0.0252152 | − | 0.999682i | \(-0.491973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1943.81 | + | 1122.26i | 1.05128 | + | 0.606955i | 0.923007 | − | 0.384784i | \(-0.125724\pi\) |
0.128270 | + | 0.991739i | \(0.459057\pi\) | |||||||
\(44\) | 279.197 | + | 1683.63i | 0.144213 | + | 0.869643i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2180.31 | + | 179.555i | −1.03039 | + | 0.0848557i | ||||
\(47\) | −913.531 | − | 527.427i | −0.413550 | − | 0.238763i | 0.278764 | − | 0.960360i | \(-0.410075\pi\) |
−0.692314 | + | 0.721597i | \(0.743409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 159.084 | + | 275.542i | 0.0662574 | + | 0.114761i | ||||
\(50\) | −1949.76 | + | 1350.47i | −0.779902 | + | 0.540188i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −687.066 | + | 1829.43i | −0.254092 | + | 0.676564i | ||||
\(53\) | 4752.60 | 1.69192 | 0.845960 | − | 0.533246i | \(-0.179028\pi\) | ||||
0.845960 | + | 0.533246i | \(0.179028\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 603.911i | 0.199640i | ||||||||
\(56\) | −912.971 | + | 3210.02i | −0.291126 | + | 1.02360i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2419.72 | + | 1675.99i | −0.719299 | + | 0.498212i | ||||
\(59\) | −1864.25 | + | 1076.32i | −0.535549 | + | 0.309200i | −0.743273 | − | 0.668988i | \(-0.766728\pi\) |
0.207724 | + | 0.978188i | \(0.433394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.1660 | − | 57.4451i | 0.00891319 | − | 0.0154381i | −0.861534 | − | 0.507699i | \(-0.830496\pi\) |
0.870448 | + | 0.492261i | \(0.163829\pi\) | |||||||
\(62\) | 2335.80 | − | 192.360i | 0.607648 | − | 0.0500416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3608.23 | + | 1938.53i | −0.880915 | + | 0.473275i | ||||
\(65\) | −345.759 | + | 598.872i | −0.0818365 | + | 0.141745i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3554.82 | + | 2052.38i | −0.791897 | + | 0.457202i | −0.840630 | − | 0.541610i | \(-0.817815\pi\) |
0.0487331 | + | 0.998812i | \(0.484482\pi\) | |||||||
\(68\) | 1246.26 | + | 1516.38i | 0.269521 | + | 0.327937i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −504.545 | + | 1067.75i | −0.102968 | + | 0.217908i | ||||
\(71\) | 5031.65i | 0.998145i | 0.866560 | + | 0.499072i | \(0.166326\pi\) | ||||
−0.866560 | + | 0.499072i | \(0.833674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2705.16 | 0.507631 | 0.253815 | − | 0.967253i | \(-0.418314\pi\) | ||||
0.253815 | + | 0.967253i | \(0.418314\pi\) | |||||||
\(74\) | −8279.36 | − | 3912.25i | −1.51194 | − | 0.714435i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7337.76 | − | 6030.67i | 1.27039 | − | 1.04409i | ||||
\(77\) | −2781.03 | − | 4816.88i | −0.469055 | − | 0.812427i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1196.02 | + | 690.524i | 0.191639 | + | 0.110643i | 0.592750 | − | 0.805387i | \(-0.298042\pi\) |
−0.401110 | + | 0.916030i | \(0.631376\pi\) | |||||||
\(80\) | −1371.84 | + | 467.852i | −0.214350 | + | 0.0731019i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 941.652 | + | 11434.4i | 0.140043 | + | 1.70053i | ||||
\(83\) | 2605.31 | + | 1504.18i | 0.378184 | + | 0.218345i | 0.677028 | − | 0.735957i | \(-0.263268\pi\) |
−0.298844 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 347.282 | + | 601.509i | 0.0480667 | + | 0.0832539i | ||||
\(86\) | −5112.05 | − | 7380.57i | −0.691191 | − | 0.997914i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1867.48 | − | 6566.08i | 0.241152 | − | 0.847893i | ||||
\(89\) | −3186.35 | −0.402267 | −0.201133 | − | 0.979564i | \(-0.564462\pi\) | ||||
−0.201133 | + | 0.979564i | \(0.564462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6368.92i | − | 0.769100i | ||||||
\(92\) | 8192.07 | + | 3076.64i | 0.967872 | + | 0.363497i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2402.50 | + | 3468.64i | 0.271899 | + | 0.392558i | ||||
\(95\) | 2910.71 | − | 1680.50i | 0.322516 | − | 0.186205i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2407.03 | − | 4169.10i | 0.255822 | − | 0.443097i | −0.709296 | − | 0.704910i | \(-0.750987\pi\) |
0.965118 | + | 0.261814i | \(0.0843206\pi\) | |||||||
\(98\) | −104.455 | − | 1268.38i | −0.0108762 | − | 0.132068i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9359.28 | − | 1552.05i | 0.935928 | − | 0.155205i | ||||
\(101\) | −3510.47 | + | 6080.30i | −0.344130 | + | 0.596050i | −0.985195 | − | 0.171436i | \(-0.945159\pi\) |
0.641066 | + | 0.767486i | \(0.278493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1858.85 | − | 1073.21i | 0.175214 | − | 0.101160i | −0.409828 | − | 0.912163i | \(-0.634411\pi\) |
0.585042 | + | 0.811003i | \(0.301078\pi\) | |||||||
\(104\) | 5611.20 | − | 5442.10i | 0.518787 | − | 0.503153i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17188.1 | − | 8121.90i | −1.52973 | − | 0.722846i | ||||
\(107\) | − | 13846.7i | − | 1.20943i | −0.796443 | − | 0.604713i | \(-0.793288\pi\) | ||
0.796443 | − | 0.604713i | \(-0.206712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19384.9 | −1.63159 | −0.815793 | − | 0.578344i | \(-0.803699\pi\) | ||||
−0.815793 | + | 0.578344i | \(0.803699\pi\) | |||||||
\(110\) | 1032.05 | − | 2184.08i | 0.0852930 | − | 0.180503i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8787.53 | − | 10049.0i | 0.700536 | − | 0.801102i | ||||
\(113\) | 6817.20 | + | 11807.7i | 0.533887 | + | 0.924719i | 0.999216 | + | 0.0395818i | \(0.0126026\pi\) |
−0.465329 | + | 0.885138i | \(0.654064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2681.71 | + | 1548.29i | 0.202776 | + | 0.117073i | ||||
\(116\) | 11615.2 | − | 1926.16i | 0.863201 | − | 0.143145i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8581.54 | − | 706.715i | 0.616313 | − | 0.0507551i | ||||
\(119\) | −5539.93 | − | 3198.48i | −0.391211 | − | 0.225866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1631.91 | − | 2826.55i | −0.111462 | − | 0.193057i | ||||
\(122\) | −218.117 | + | 151.076i | −0.0146545 | + | 0.0101502i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8776.30 | − | 3296.05i | −0.570779 | − | 0.214363i | ||||
\(125\) | 6895.78 | 0.441330 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15689.6i | − | 0.972754i | −0.873749 | − | 0.486377i | \(-0.838318\pi\) | ||
0.873749 | − | 0.486377i | \(-0.161682\pi\) | |||||||
\(128\) | 16362.2 | − | 844.606i | 0.998670 | − | 0.0515506i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2273.89 | − | 1574.98i | 0.134550 | − | 0.0931941i | ||||
\(131\) | 7250.25 | − | 4185.93i | 0.422484 | − | 0.243921i | −0.273656 | − | 0.961828i | \(-0.588233\pi\) |
0.696140 | + | 0.717907i | \(0.254899\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15477.5 | + | 26807.7i | −0.874977 | + | 1.51550i | ||||
\(134\) | 16363.6 | − | 1347.59i | 0.911319 | − | 0.0750497i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1915.80 | − | 7613.87i | −0.103579 | − | 0.411650i | ||||
\(137\) | −14965.1 | + | 25920.4i | −0.797333 | + | 1.38102i | 0.124014 | + | 0.992280i | \(0.460423\pi\) |
−0.921347 | + | 0.388741i | \(0.872910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20651.8 | + | 11923.3i | −1.06888 | + | 0.617118i | −0.927875 | − | 0.372891i | \(-0.878367\pi\) |
−0.141005 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(140\) | 3649.44 | − | 2999.36i | 0.186196 | − | 0.153028i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8598.76 | − | 18197.3i | 0.426441 | − | 0.902464i | ||||
\(143\) | 13027.6i | 0.637078i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4166.34 | 0.198161 | ||||||||
\(146\) | −9783.40 | − | 4622.95i | −0.458970 | − | 0.216877i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23257.0 | + | 28297.8i | 1.06177 | + | 1.29190i | ||||
\(149\) | 2636.98 | + | 4567.39i | 0.118778 | + | 0.205729i | 0.919284 | − | 0.393596i | \(-0.128769\pi\) |
−0.800506 | + | 0.599325i | \(0.795436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 28946.1 | + | 16712.0i | 1.26951 | + | 0.732951i | 0.974895 | − | 0.222665i | \(-0.0714756\pi\) |
0.294614 | + | 0.955616i | \(0.404809\pi\) | |||||||
\(152\) | −36843.5 | + | 9270.55i | −1.59468 | + | 0.401253i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1826.02 | + | 22173.2i | 0.0769954 | + | 0.934945i | ||||
\(155\) | −2872.96 | − | 1658.71i | −0.119582 | − | 0.0690408i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8500.73 | − | 14723.7i | −0.344871 | − | 0.597334i | 0.640459 | − | 0.767992i | \(-0.278744\pi\) |
−0.985330 | + | 0.170658i | \(0.945411\pi\) | |||||||
\(158\) | −3145.43 | − | 4541.25i | −0.125999 | − | 0.181912i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5760.88 | + | 652.373i | 0.225034 | + | 0.0254833i | ||||
\(161\) | −28519.6 | −1.10025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 30843.8i | − | 1.16089i | −0.814298 | − | 0.580447i | \(-0.802878\pi\) | ||
0.814298 | − | 0.580447i | \(-0.197122\pi\) | |||||||
\(164\) | 16135.0 | − | 42962.3i | 0.599904 | − | 1.59735i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6851.74 | − | 9892.27i | −0.248648 | − | 0.358988i | ||||
\(167\) | −13682.1 | + | 7899.35i | −0.490591 | + | 0.283243i | −0.724819 | − | 0.688939i | \(-0.758077\pi\) |
0.234229 | + | 0.972181i | \(0.424743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6821.76 | − | 11815.6i | 0.238849 | − | 0.413698i | ||||
\(170\) | −228.025 | − | 2768.88i | −0.00789015 | − | 0.0958090i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5875.12 | + | 35428.5i | 0.198591 | + | 1.19756i | ||||
\(173\) | 23531.4 | − | 40757.6i | 0.786241 | − | 1.36181i | −0.142015 | − | 0.989865i | \(-0.545358\pi\) |
0.928255 | − | 0.371944i | \(-0.121309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26777.0 | + | 15459.7i | −0.874352 | + | 0.504807i | ||||
\(176\) | −17974.9 | + | 20555.3i | −0.580284 | + | 0.663586i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11523.7 | + | 5445.28i | 0.363706 | + | 0.171862i | ||||
\(179\) | 2545.69i | 0.0794511i | 0.999211 | + | 0.0397256i | \(0.0126484\pi\) | ||||
−0.999211 | + | 0.0397256i | \(0.987352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5676.58 | 0.173272 | 0.0866362 | − | 0.996240i | \(-0.472388\pi\) | ||||
0.0866362 | + | 0.996240i | \(0.472388\pi\) | |||||||
\(182\) | −10884.1 | + | 23033.6i | −0.328586 | + | 0.695375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24369.4 | − | 25126.6i | −0.719795 | − | 0.742160i | ||||
\(185\) | 6480.77 | + | 11225.0i | 0.189358 | + | 0.327977i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11331.9 | + | 6542.49i | 0.324056 | + | 0.187094i | ||||
\(188\) | −2761.12 | − | 16650.3i | −0.0781214 | − | 0.471092i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13398.6 | + | 1103.41i | −0.371153 | + | 0.0305655i | ||||
\(191\) | 28127.2 | + | 16239.2i | 0.771009 | + | 0.445142i | 0.833234 | − | 0.552920i | \(-0.186487\pi\) |
−0.0622257 | + | 0.998062i | \(0.519820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −393.717 | − | 681.937i | −0.0105699 | − | 0.0183075i | 0.860692 | − | 0.509126i | \(-0.170031\pi\) |
−0.871262 | + | 0.490818i | \(0.836698\pi\) | |||||||
\(194\) | −15829.9 | + | 10964.3i | −0.420605 | + | 0.291326i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1789.81 | + | 4765.68i | −0.0465903 | + | 0.124055i | ||||
\(197\) | −24825.9 | −0.639694 | −0.319847 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319847 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12008.5i | 0.303237i | 0.988439 | + | 0.151619i | \(0.0484485\pi\) | ||||
−0.988439 | + | 0.151619i | \(0.951551\pi\) | |||||||
\(200\) | −36500.8 | − | 10381.3i | −0.912520 | − | 0.259533i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 23086.7 | − | 15990.7i | 0.565794 | − | 0.391889i | ||||
\(203\) | −33231.3 | + | 19186.1i | −0.806409 | + | 0.465580i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8119.80 | − | 14063.9i | 0.193213 | − | 0.334656i | ||||
\(206\) | −8556.69 | + | 704.668i | −0.201638 | + | 0.0166054i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −29593.5 | + | 10092.5i | −0.684020 | + | 0.233278i | ||||
\(209\) | 31659.1 | − | 54835.2i | 0.724780 | − | 1.25536i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25764.7 | + | 14875.2i | −0.578708 | + | 0.334117i | −0.760620 | − | 0.649198i | \(-0.775105\pi\) |
0.181912 | + | 0.983315i | \(0.441771\pi\) | |||||||
\(212\) | 48282.1 | + | 58746.7i | 1.07427 | + | 1.30711i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23663.2 | + | 50077.6i | −0.516708 | + | 1.09349i | ||||
\(215\) | 12708.1i | 0.274917i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30553.5 | 0.648846 | ||||||||
\(218\) | 70106.6 | + | 33127.5i | 1.47518 | + | 0.697069i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7464.92 | + | 6135.18i | −0.154234 | + | 0.126760i | ||||
\(221\) | 7491.58 | + | 12975.8i | 0.153387 | + | 0.265674i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 45854.8 | + | 26474.3i | 0.922093 | + | 0.532371i | 0.884302 | − | 0.466915i | \(-0.154635\pi\) |
0.0377910 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(224\) | −48953.8 | + | 21325.6i | −0.975642 | + | 0.425016i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4476.18 | − | 54353.6i | −0.0876376 | − | 1.06417i | ||||
\(227\) | −32593.5 | − | 18817.9i | −0.632528 | − | 0.365190i | 0.149203 | − | 0.988807i | \(-0.452329\pi\) |
−0.781730 | + | 0.623616i | \(0.785663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28619.2 | + | 49569.9i | 0.545741 | + | 0.945251i | 0.998560 | + | 0.0536486i | \(0.0170851\pi\) |
−0.452819 | + | 0.891603i | \(0.649582\pi\) | |||||||
\(230\) | −7052.66 | − | 10182.4i | −0.133321 | − | 0.192483i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −45298.9 | − | 12883.6i | −0.841612 | − | 0.239366i | ||||
\(233\) | 36468.7 | 0.671751 | 0.335876 | − | 0.941906i | \(-0.390968\pi\) | ||||
0.335876 | + | 0.941906i | \(0.390968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5972.39i | − | 0.108147i | ||||||
\(236\) | −32243.4 | − | 12109.4i | −0.578918 | − | 0.217420i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14569.5 | + | 21034.9i | 0.257212 | + | 0.371353i | ||||
\(239\) | 45342.6 | − | 26178.6i | 0.793799 | − | 0.458300i | −0.0474993 | − | 0.998871i | \(-0.515125\pi\) |
0.841298 | + | 0.540571i | \(0.181792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6755.56 | − | 11701.0i | 0.116313 | − | 0.201460i | −0.801991 | − | 0.597336i | \(-0.796226\pi\) |
0.918304 | + | 0.395877i | \(0.129559\pi\) | |||||||
\(242\) | 1071.51 | + | 13011.2i | 0.0182964 | + | 0.222171i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1047.01 | − | 173.627i | 0.0175862 | − | 0.00291633i | ||||
\(245\) | −900.705 | + | 1560.07i | −0.0150055 | + | 0.0259903i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62789.9 | − | 36251.8i | 1.02919 | − | 0.594204i | ||||
\(248\) | 26107.3 | + | 26918.5i | 0.424482 | + | 0.437671i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24939.0 | − | 11784.4i | −0.399024 | − | 0.188551i | ||||
\(251\) | − | 111309.i | − | 1.76678i | −0.468635 | − | 0.883392i | \(-0.655254\pi\) | ||
0.468635 | − | 0.883392i | \(-0.344746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58336.8 | 0.911385 | ||||||||
\(254\) | −26812.4 | + | 56742.3i | −0.415594 | + | 0.879507i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −60618.4 | − | 24907.4i | −0.924963 | − | 0.380057i | ||||
\(257\) | −36956.5 | − | 64010.6i | −0.559532 | − | 0.969138i | −0.997535 | − | 0.0701645i | \(-0.977648\pi\) |
0.438003 | − | 0.898973i | \(-0.355686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −103383. | − | 59688.2i | −1.54117 | − | 0.889793i | ||||
\(260\) | −10915.2 | + | 1810.08i | −0.161468 | + | 0.0267763i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −33374.5 | + | 2748.48i | −0.486197 | + | 0.0400397i | ||||
\(263\) | 6380.84 | + | 3683.98i | 0.0922500 | + | 0.0532606i | 0.545415 | − | 0.838166i | \(-0.316372\pi\) |
−0.453165 | + | 0.891426i | \(0.649705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13454.2 | + | 23303.3i | 0.191587 | + | 0.331838i | ||||
\(266\) | 101788. | − | 70502.0i | 1.43858 | − | 0.996410i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −61483.1 | − | 23090.8i | −0.856024 | − | 0.321491i | ||||
\(269\) | 38604.8 | 0.533502 | 0.266751 | − | 0.963765i | \(-0.414050\pi\) | ||||
0.266751 | + | 0.963765i | \(0.414050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12540.3i | 0.170753i | 0.996349 | + | 0.0853767i | \(0.0272094\pi\) | ||||
−0.996349 | + | 0.0853767i | \(0.972791\pi\) | |||||||
\(272\) | −6083.01 | + | 30810.0i | −0.0822206 | + | 0.416442i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 98418.7 | − | 68168.3i | 1.31092 | − | 0.907990i | ||||
\(275\) | 54772.4 | − | 31622.8i | 0.724263 | − | 0.418153i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 46052.4 | − | 79765.0i | 0.600195 | − | 1.03957i | −0.392596 | − | 0.919711i | \(-0.628423\pi\) |
0.992791 | − | 0.119857i | \(-0.0382436\pi\) | |||||||
\(278\) | 95064.9 | − | 7828.87i | 1.23007 | − | 0.101300i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18324.1 | + | 4610.71i | −0.233726 | + | 0.0588101i | ||||
\(281\) | 11148.0 | − | 19308.8i | 0.141183 | − | 0.244537i | −0.786759 | − | 0.617260i | \(-0.788243\pi\) |
0.927942 | + | 0.372723i | \(0.121576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21648.6 | − | 12498.8i | 0.270307 | − | 0.156062i | −0.358720 | − | 0.933445i | \(-0.616787\pi\) |
0.629027 | + | 0.777383i | \(0.283453\pi\) | |||||||
\(284\) | −62196.0 | + | 51116.9i | −0.771126 | + | 0.633764i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22263.4 | − | 47115.2i | 0.272182 | − | 0.576009i | ||||
\(287\) | 149568.i | 1.81582i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68471.9 | −0.819816 | ||||||||
\(290\) | −15067.8 | − | 7120.01i | −0.179166 | − | 0.0846612i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27482.0 | + | 33438.4i | 0.322316 | + | 0.392175i | ||||
\(293\) | −11748.6 | − | 20349.1i | −0.136852 | − | 0.237034i | 0.789452 | − | 0.613813i | \(-0.210365\pi\) |
−0.926303 | + | 0.376779i | \(0.877032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10555.0 | − | 6093.95i | −0.121287 | − | 0.0700253i | ||||
\(296\) | −35751.5 | − | 142086.i | −0.408048 | − | 1.62169i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1731.44 | − | 21024.7i | −0.0194974 | − | 0.236754i | ||||
\(299\) | 57850.1 | + | 33399.7i | 0.647085 | + | 0.373595i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −58521.0 | − | 101361.i | −0.645920 | − | 1.11877i | ||||
\(302\) | −76125.6 | − | 109907.i | −0.834673 | − | 1.20507i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 149090. | + | 29435.7i | 1.61325 | + | 0.318513i | ||||
\(305\) | 375.559 | 0.00403719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32060.0i | 0.340163i | 0.985430 | + | 0.170082i | \(0.0544031\pi\) | ||||
−0.985430 | + | 0.170082i | \(0.945597\pi\) | |||||||
\(308\) | 31288.6 | − | 83311.2i | 0.329826 | − | 0.878217i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7555.63 | + | 10908.5i | 0.0786226 | + | 0.113512i | ||||
\(311\) | −61441.4 | + | 35473.2i | −0.635244 | + | 0.366758i | −0.782780 | − | 0.622298i | \(-0.786199\pi\) |
0.147536 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −59259.6 | + | 102641.i | −0.604882 | + | 1.04769i | 0.387189 | + | 0.922001i | \(0.373446\pi\) |
−0.992070 | + | 0.125685i | \(0.959887\pi\) | |||||||
\(314\) | 5581.58 | + | 67776.4i | 0.0566106 | + | 0.687415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3614.95 | + | 21799.1i | 0.0362016 | + | 0.218305i | ||||
\(317\) | −67390.6 | + | 116724.i | −0.670626 | + | 1.16156i | 0.307100 | + | 0.951677i | \(0.400641\pi\) |
−0.977727 | + | 0.209882i | \(0.932692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 67974.6 | − | 39245.2i | 0.667983 | − | 0.385660i | ||||
\(320\) | −19719.7 | − | 12204.3i | −0.192576 | − | 0.119183i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 103143. | + | 48738.2i | 0.994782 | + | 0.470065i | ||||
\(323\) | − | 72822.8i | − | 0.698011i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 72420.4 | 0.685637 | ||||||||
\(326\) | −52710.0 | + | 111548.i | −0.495973 | + | 1.04961i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −131773. | + | 127802.i | −1.22484 | + | 1.18793i | ||||
\(329\) | 27503.0 | + | 47636.7i | 0.254091 | + | 0.440098i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −133143. | − | 76870.2i | −1.21524 | − | 0.701620i | −0.251345 | − | 0.967898i | \(-0.580873\pi\) |
−0.963896 | + | 0.266278i | \(0.914206\pi\) | |||||||
\(332\) | 7874.49 | + | 47485.2i | 0.0714408 | + | 0.430806i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62981.6 | − | 5186.72i | 0.564574 | − | 0.0464943i | ||||
\(335\) | −20126.8 | − | 11620.2i | −0.179343 | − | 0.103544i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11471.8 | + | 19869.8i | 0.101012 | + | 0.174958i | 0.912102 | − | 0.409964i | \(-0.134459\pi\) |
−0.811090 | + | 0.584922i | \(0.801125\pi\) | |||||||
\(338\) | −44863.5 | + | 31074.1i | −0.392699 | + | 0.271997i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3907.17 | + | 10403.5i | −0.0337990 | + | 0.0899958i | ||||
\(341\) | −62497.2 | −0.537467 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 108611.i | 0.923175i | ||||||||
\(344\) | 39297.3 | − | 138170.i | 0.332082 | − | 1.16760i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −154755. | + | 107189.i | −1.29268 | + | 0.895358i | ||||
\(347\) | 6260.87 | − | 3614.72i | 0.0519967 | − | 0.0300203i | −0.473776 | − | 0.880645i | \(-0.657109\pi\) |
0.525773 | + | 0.850625i | \(0.323776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −55282.6 | + | 95752.3i | −0.453877 | + | 0.786137i | −0.998623 | − | 0.0524636i | \(-0.983293\pi\) |
0.544746 | + | 0.838601i | \(0.316626\pi\) | |||||||
\(350\) | 123260. | − | 10150.9i | 1.00621 | − | 0.0828641i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 100135. | − | 43621.5i | 0.808165 | − | 0.352059i | ||||
\(353\) | −30801.7 | + | 53350.1i | −0.247187 | + | 0.428140i | −0.962744 | − | 0.270414i | \(-0.912840\pi\) |
0.715557 | + | 0.698554i | \(0.246173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24671.6 | + | 14244.1i | −0.195767 | + | 0.113026i | ||||
\(356\) | −32370.4 | − | 39386.4i | −0.255416 | − | 0.310775i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4350.43 | − | 9206.66i | 0.0339442 | − | 0.0718350i | ||||
\(359\) | 84462.7i | 0.655354i | 0.944790 | + | 0.327677i | \(0.106266\pi\) | ||||
−0.944790 | + | 0.327677i | \(0.893734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −222069. | −1.70401 | ||||||||
\(362\) | −20529.7 | − | 9700.91i | −0.156663 | − | 0.0740279i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 78725.9 | − | 64702.3i | 0.594176 | − | 0.488334i | ||||
\(365\) | 7658.07 | + | 13264.2i | 0.0574823 | + | 0.0995622i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 161018. | + | 92963.9i | 1.19548 | + | 0.690212i | 0.959545 | − | 0.281556i | \(-0.0908507\pi\) |
0.235937 | + | 0.971768i | \(0.424184\pi\) | |||||||
\(368\) | 45193.7 | + | 132518.i | 0.333720 | + | 0.978538i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4255.27 | − | 51671.2i | −0.0310831 | − | 0.377438i | ||||
\(371\) | −214625. | − | 123914.i | −1.55931 | − | 0.900268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 42545.6 | + | 73691.2i | 0.305800 | + | 0.529661i | 0.977439 | − | 0.211217i | \(-0.0677428\pi\) |
−0.671639 | + | 0.740878i | \(0.734409\pi\) | |||||||
\(374\) | −29801.9 | − | 43026.9i | −0.213060 | − | 0.307607i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18468.5 | + | 64935.4i | −0.130634 | + | 0.459310i | ||||
\(377\) | 89876.5 | 0.632359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 146982.i | 1.02326i | 0.859206 | + | 0.511630i | \(0.170958\pi\) | ||||
−0.859206 | + | 0.511630i | \(0.829042\pi\) | |||||||
\(380\) | 50342.6 | + | 18906.8i | 0.348633 | + | 0.130934i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −73971.9 | − | 106798.i | −0.506921 | − | 0.731872i | ||||
\(383\) | −161253. | + | 93099.7i | −1.09929 | + | 0.634674i | −0.936034 | − | 0.351910i | \(-0.885532\pi\) |
−0.163254 | + | 0.986584i | \(0.552199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15745.7 | − | 27272.3i | 0.106228 | − | 0.183993i | ||||
\(386\) | 258.515 | + | 3139.11i | 0.00173504 | + | 0.0210684i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 75987.2 | − | 12601.0i | 0.504751 | − | 0.0837030i | ||||
\(389\) | −128002. | + | 221706.i | −0.845897 | + | 1.46514i | 0.0389437 | + | 0.999241i | \(0.487601\pi\) |
−0.884840 | + | 0.465894i | \(0.845733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 58104.8 | − | 33546.8i | 0.380066 | − | 0.219431i | ||||
\(392\) | 14617.2 | − | 14176.7i | 0.0951245 | − | 0.0922579i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 89784.4 | + | 42425.9i | 0.578374 | + | 0.273299i | ||||
\(395\) | 7819.24i | 0.0501153i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260735. | −1.65432 | −0.827159 | − | 0.561968i | \(-0.810044\pi\) | ||||
−0.827159 | + | 0.561968i | \(0.810044\pi\) | |||||||
\(398\) | 20521.7 | − | 43429.5i | 0.129553 | − | 0.274169i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 114267. | + | 99922.3i | 0.714166 | + | 0.624514i | ||||
\(401\) | 26507.0 | + | 45911.4i | 0.164843 | + | 0.285517i | 0.936600 | − | 0.350401i | \(-0.113955\pi\) |
−0.771756 | + | 0.635918i | \(0.780621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −61975.7 | − | 35781.7i | −0.381603 | − | 0.220318i | ||||
\(404\) | −110821. | + | 18377.6i | −0.678986 | + | 0.112597i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 152971. | − | 12597.6i | 0.928019 | − | 0.0764251i | ||||
\(407\) | 211470. | + | 122092.i | 1.27661 | + | 0.737053i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −73697.8 | − | 127648.i | −0.440563 | − | 0.763078i | 0.557168 | − | 0.830400i | \(-0.311888\pi\) |
−0.997731 | + | 0.0673220i | \(0.978555\pi\) | |||||||
\(410\) | −53400.1 | + | 36986.8i | −0.317668 | + | 0.220028i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 32150.1 | + | 12074.4i | 0.189403 | + | 0.0711328i | ||||
\(413\) | 112251. | 0.658099 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17032.8i | 0.0988983i | ||||||||
\(416\) | 124274. | + | 14073.0i | 0.718115 | + | 0.0813206i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −208207. | + | 144212.i | −1.19163 | + | 0.825368i | ||||
\(419\) | 201431. | − | 116296.i | 1.14736 | − | 0.662426i | 0.199115 | − | 0.979976i | \(-0.436193\pi\) |
0.948242 | + | 0.317550i | \(0.102860\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34900.8 | − | 60449.9i | 0.196911 | − | 0.341060i | −0.750614 | − | 0.660741i | \(-0.770242\pi\) |
0.947525 | + | 0.319680i | \(0.103576\pi\) | |||||||
\(422\) | 118600. | − | 9767.08i | 0.665980 | − | 0.0548454i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −74220.8 | − | 294972.i | −0.412852 | − | 1.64078i | ||||
\(425\) | 36369.7 | − | 62994.1i | 0.201355 | − | 0.348756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2995.51 | + | 1729.46i | −0.0164292 | + | 0.00948539i | ||||
\(428\) | 171159. | − | 140670.i | 0.934354 | − | 0.767916i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21717.3 | − | 45959.5i | 0.117454 | − | 0.248564i | ||||
\(431\) | − | 147873.i | − | 0.796037i | −0.917377 | − | 0.398019i | \(-0.869698\pi\) | ||
0.917377 | − | 0.398019i | \(-0.130302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 294850. | 1.57262 | 0.786312 | − | 0.617830i | \(-0.211988\pi\) | ||||
0.786312 | + | 0.617830i | \(0.211988\pi\) | |||||||
\(434\) | −110499. | − | 52214.0i | −0.586649 | − | 0.277209i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −196932. | − | 239615.i | −1.03596 | − | 1.26050i | ||||
\(437\) | −162333. | − | 281169.i | −0.850050 | − | 1.47233i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −62468.0 | − | 36065.9i | −0.324137 | − | 0.187140i | 0.329098 | − | 0.944296i | \(-0.393255\pi\) |
−0.653235 | + | 0.757155i | \(0.726589\pi\) | |||||||
\(440\) | 37482.0 | − | 9431.20i | 0.193605 | − | 0.0487149i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4918.98 | − | 59730.5i | −0.0251785 | − | 0.305739i | ||||
\(443\) | −165331. | − | 95453.7i | −0.842453 | − | 0.486391i | 0.0156440 | − | 0.999878i | \(-0.495020\pi\) |
−0.858097 | + | 0.513487i | \(0.828353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9020.28 | − | 15623.6i | −0.0455512 | − | 0.0788970i | ||||
\(446\) | −120594. | − | 174109.i | −0.606255 | − | 0.875288i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 213489. | + | 6533.50i | 1.06370 | + | 0.0325529i | ||||
\(449\) | −192859. | −0.956639 | −0.478319 | − | 0.878186i | \(-0.658754\pi\) | ||||
−0.478319 | + | 0.878186i | \(0.658754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 305940.i | − | 1.50412i | ||||||
\(452\) | −76698.5 | + | 204223.i | −0.375414 | + | 0.999603i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 85718.0 | + | 123756.i | 0.415873 | + | 0.600421i | ||||
\(455\) | 31228.6 | − | 18029.8i | 0.150844 | − | 0.0870901i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2962.66 | − | 5131.48i | 0.0141857 | − | 0.0245703i | −0.858845 | − | 0.512235i | \(-0.828818\pi\) |
0.873031 | + | 0.487665i | \(0.162151\pi\) | |||||||
\(458\) | −18791.4 | − | 228181.i | −0.0895834 | − | 1.08780i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8105.41 | + | 48877.7i | 0.0383053 | + | 0.230991i | ||||
\(461\) | 63341.9 | − | 109711.i | 0.298050 | − | 0.516238i | −0.677640 | − | 0.735394i | \(-0.736997\pi\) |
0.975690 | + | 0.219156i | \(0.0703304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 204011. | − | 117786.i | 0.951682 | − | 0.549454i | 0.0580790 | − | 0.998312i | \(-0.481502\pi\) |
0.893603 | + | 0.448858i | \(0.148169\pi\) | |||||||
\(464\) | 141809. | + | 124007.i | 0.658671 | + | 0.575985i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −131891. | − | 62322.7i | −0.607358 | − | 0.286995i | ||||
\(467\) | − | 97776.2i | − | 0.448332i | −0.974551 | − | 0.224166i | \(-0.928034\pi\) | ||
0.974551 | − | 0.224166i | \(-0.0719658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 214045. | 0.973105 | ||||||||
\(470\) | −10206.4 | + | 21599.5i | −0.0462039 | + | 0.0977798i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 95916.2 | + | 98896.5i | 0.430534 | + | 0.443912i | ||||
\(473\) | 119705. | + | 207334.i | 0.535043 | + | 0.926721i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −304829. | − | 175993.i | −1.35104 | − | 0.780024i | ||||
\(476\) | −16744.3 | − | 100972.i | −0.0739015 | − | 0.445645i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −208722. | + | 17188.8i | −0.913508 | + | 0.0752300i | ||||
\(479\) | 349162. | + | 201589.i | 1.52179 | + | 0.878608i | 0.999669 | + | 0.0257398i | \(0.00819415\pi\) |
0.522126 | + | 0.852869i | \(0.325139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 139803. | + | 242147.i | 0.604266 | + | 1.04662i | ||||
\(482\) | −44428.1 | + | 30772.5i | −0.191233 | + | 0.132455i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18360.2 | − | 48887.1i | 0.0783766 | − | 0.208691i | ||||
\(485\) | 27256.3 | 0.115873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 195207.i | 0.823071i | 0.911394 | + | 0.411536i | \(0.135007\pi\) | ||||
−0.911394 | + | 0.411536i | \(0.864993\pi\) | |||||||
\(488\) | −4083.30 | − | 1161.35i | −0.0171464 | − | 0.00487665i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5923.51 | − | 4102.83i | 0.0246710 | − | 0.0170880i | ||||
\(491\) | 65937.1 | − | 38068.8i | 0.273506 | − | 0.157909i | −0.356974 | − | 0.934114i | \(-0.616191\pi\) |
0.630480 | + | 0.776206i | \(0.282858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45136.2 | − | 78178.1i | 0.185708 | − | 0.321656i | ||||
\(494\) | −289036. | + | 23802.9i | −1.18440 | + | 0.0975386i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48416.8 | − | 141968.i | −0.196803 | − | 0.577069i | ||||
\(497\) | 131189. | − | 227226.i | 0.531111 | − | 0.919912i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12618.3 | + | 7285.17i | −0.0506757 | + | 0.0292576i | −0.525124 | − | 0.851026i | \(-0.675981\pi\) |
0.474448 | + | 0.880283i | \(0.342648\pi\) | |||||||
\(500\) | 70054.7 | + | 85238.4i | 0.280219 | + | 0.340953i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −190220. | + | 402557.i | −0.754830 | + | 1.59742i | ||||
\(503\) | 280154.i | 1.10729i | 0.832753 | + | 0.553645i | \(0.186764\pi\) | ||||
−0.832753 | + | 0.553645i | \(0.813236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39751.2 | −0.155872 | ||||||||
\(506\) | −210979. | − | 99693.9i | −0.824020 | − | 0.389375i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 193938. | − | 159391.i | 0.751511 | − | 0.617643i | ||||
\(509\) | 101505. | + | 175811.i | 0.391787 | + | 0.678595i | 0.992685 | − | 0.120731i | \(-0.0385238\pi\) |
−0.600899 | + | 0.799325i | \(0.705190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −122164. | − | 70531.3i | −0.467843 | − | 0.270110i | ||||
\(512\) | 176665. | + | 193672.i | 0.673924 | + | 0.738801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24265.7 | + | 294655.i | 0.0918472 | + | 1.11529i | ||||
\(515\) | 10524.5 | + | 6076.30i | 0.0396813 | + | 0.0229100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56257.4 | − | 97440.7i | −0.210474 | − | 0.364552i | ||||
\(518\) | 271888. | + | 392541.i | 1.01328 | + | 1.46294i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 42568.9 | + | 12107.2i | 0.157429 | + | 0.0447750i | ||||
\(521\) | 30822.1 | 0.113550 | 0.0567749 | − | 0.998387i | \(-0.481918\pi\) | ||||
0.0567749 | + | 0.998387i | \(0.481918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 94412.3i | 0.345164i | 0.984995 | + | 0.172582i | \(0.0552109\pi\) | ||||
−0.984995 | + | 0.172582i | \(0.944789\pi\) | |||||||
\(524\) | 125398. | + | 47094.8i | 0.456697 | + | 0.171518i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16781.0 | − | 24227.8i | −0.0606523 | − | 0.0875674i | ||||
\(527\) | −62248.6 | + | 35939.3i | −0.224134 | + | 0.129404i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9641.45 | − | 16699.5i | 0.0344533 | − | 0.0596749i | ||||
\(530\) | −8834.03 | − | 107270.i | −0.0314490 | − | 0.381881i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −488606. | + | 81025.8i | −1.72638 | + | 0.286286i | ||||
\(533\) | 175161. | − | 303387.i | 0.616570 | − | 1.06793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 67894.3 | − | 39198.8i | 0.237206 | − | 0.136951i | ||||
\(536\) | 182897. | + | 188580.i | 0.636615 | + | 0.656396i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −139617. | − | 65973.1i | −0.482361 | − | 0.227930i | ||||
\(539\) | 33937.0i | 0.116814i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 166561. | 0.569087 | 0.284544 | − | 0.958663i | \(-0.408158\pi\) | ||||
0.284544 | + | 0.958663i | \(0.408158\pi\) | |||||||
\(542\) | 21430.6 | − | 45352.8i | 0.0729517 | − | 0.154385i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 74651.9 | − | 101031.i | 0.252257 | − | 0.341395i | ||||
\(545\) | −54876.8 | − | 95049.4i | −0.184755 | − | 0.320005i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 256245. | + | 147943.i | 0.856410 | + | 0.494448i | 0.862808 | − | 0.505531i | \(-0.168703\pi\) |
−0.00639865 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(548\) | −472433. | + | 78343.7i | −1.57318 | + | 0.260881i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −252129. | + | 20763.6i | −0.833485 | + | 0.0686399i | ||||
\(551\) | −378304. | − | 218414.i | −1.24606 | − | 0.719411i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36007.8 | − | 62367.3i | −0.117746 | − | 0.203942i | ||||
\(554\) | −302865. | + | 209775.i | −0.986800 | + | 0.683492i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −357187. | − | 134146.i | −1.15544 | − | 0.433939i | ||||
\(557\) | 30600.2 | 0.0986312 | 0.0493156 | − | 0.998783i | \(-0.484296\pi\) | ||||
0.0493156 | + | 0.998783i | \(0.484296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 274139.i | 0.877298i | ||||||||
\(560\) | 74149.8 | + | 14639.8i | 0.236447 | + | 0.0466832i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −73314.9 | + | 50780.5i | −0.232124 | + | 0.160777i | ||||
\(563\) | −210267. | + | 121398.i | −0.663369 | + | 0.382996i | −0.793559 | − | 0.608493i | \(-0.791774\pi\) |
0.130191 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38597.8 | + | 66853.3i | −0.120911 | + | 0.209424i | ||||
\(566\) | −99653.3 | + | 8206.73i | −0.311070 | + | 0.0256175i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 312291. | − | 78578.6i | 0.967973 | − | 0.243561i | ||||
\(569\) | 148459. | − | 257138.i | 0.458545 | − | 0.794223i | −0.540339 | − | 0.841447i | \(-0.681704\pi\) |
0.998884 | + | 0.0472242i | \(0.0150375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −228446. | + | 131893.i | −0.700665 | + | 0.404529i | −0.807595 | − | 0.589737i | \(-0.799231\pi\) |
0.106930 | + | 0.994267i | \(0.465898\pi\) | |||||||
\(572\) | −161034. | + | 132349.i | −0.492181 | + | 0.404508i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 255601. | − | 540921.i | 0.775781 | − | 1.64176i | ||||
\(575\) | − | 324294.i | − | 0.980852i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 350367. | 1.05238 | 0.526188 | − | 0.850368i | \(-0.323621\pi\) | ||||
0.526188 | + | 0.850368i | \(0.323621\pi\) | |||||||
\(578\) | 247633. | + | 117014.i | 0.741229 | + | 0.350253i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 42326.2 | + | 51499.9i | 0.125821 | + | 0.153091i | ||||
\(581\) | −78436.3 | − | 135856.i | −0.232362 | − | 0.402463i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 439015. | + | 253466.i | 1.29164 | + | 0.745730i | ||||
\(584\) | −42246.2 | − | 167897.i | −0.123869 | − | 0.492286i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7714.12 | + | 93671.5i | 0.0224642 | + | 0.272780i | ||||
\(587\) | −5965.76 | − | 3444.33i | −0.0173137 | − | 0.00999606i | 0.491318 | − | 0.870980i | \(-0.336515\pi\) |
−0.508632 | + | 0.860984i | \(0.669849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 173910. | + | 301221.i | 0.501296 | + | 0.868270i | ||||
\(590\) | 27758.8 | + | 40077.0i | 0.0797437 | + | 0.115131i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −113517. | + | 574959.i | −0.323906 | + | 1.64056i | ||||
\(593\) | −544416. | −1.54818 | −0.774090 | − | 0.633076i | \(-0.781792\pi\) | ||||
−0.774090 | + | 0.633076i | \(0.781792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 36218.4i | − | 0.102305i | ||||||
\(596\) | −29668.0 | + | 78996.0i | −0.0835209 | + | 0.222389i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −152140. | − | 219654.i | −0.425444 | − | 0.614239i | ||||
\(599\) | −122771. | + | 70881.9i | −0.342170 | + | 0.197552i | −0.661231 | − | 0.750182i | \(-0.729966\pi\) |
0.319061 | + | 0.947734i | \(0.396633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 265380. | − | 459652.i | 0.734715 | − | 1.27256i | −0.220133 | − | 0.975470i | \(-0.570649\pi\) |
0.954848 | − | 0.297094i | \(-0.0960176\pi\) | |||||||
\(602\) | 38424.9 | + | 466588.i | 0.106028 | + | 1.28748i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 87488.8 | + | 527580.i | 0.239816 | + | 1.44615i | ||||
\(605\) | 9239.58 | − | 16003.4i | 0.0252430 | − | 0.0437222i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35215.7 | + | 20331.8i | −0.0955782 | + | 0.0551821i | −0.547027 | − | 0.837115i | \(-0.684241\pi\) |
0.451449 | + | 0.892297i | \(0.350907\pi\) | |||||||
\(608\) | −488889. | − | 361241.i | −1.32252 | − | 0.977214i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1358.23 | − | 641.807i | −0.00365019 | − | 0.00172482i | ||||
\(611\) | − | 128837.i | − | 0.345110i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −498556. | −1.32676 | −0.663382 | − | 0.748281i | \(-0.730879\pi\) | ||||
−0.663382 | + | 0.748281i | \(0.730879\pi\) | |||||||
\(614\) | 54788.5 | − | 115947.i | 0.145329 | − | 0.307555i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −255531. | + | 247830.i | −0.673413 | + | 0.653120i | ||||
\(617\) | −45030.4 | − | 77995.0i | −0.118287 | − | 0.204879i | 0.800802 | − | 0.598929i | \(-0.204407\pi\) |
−0.919089 | + | 0.394050i | \(0.871074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 149379. | + | 86244.1i | 0.389860 | + | 0.225086i | 0.682099 | − | 0.731259i | \(-0.261067\pi\) |
−0.292240 | + | 0.956345i | \(0.594400\pi\) | |||||||
\(620\) | −8683.45 | − | 52363.5i | −0.0225896 | − | 0.136221i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 282828. | − | 23291.7i | 0.731042 | − | 0.0602034i | ||||
\(623\) | 143894. | + | 83077.2i | 0.370738 | + | 0.214045i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −165774. | − | 287128.i | −0.424380 | − | 0.735049i | ||||
\(626\) | 389723. | − | 269936.i | 0.994505 | − | 0.688830i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 95639.3 | − | 254656.i | 0.242503 | − | 0.645706i | ||||
\(629\) | 280838. | 0.709831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 210621.i | − | 0.528985i | −0.964388 | − | 0.264492i | \(-0.914796\pi\) | ||
0.964388 | − | 0.264492i | \(-0.0852044\pi\) | |||||||
\(632\) | 24179.5 | − | 85015.4i | 0.0605359 | − | 0.212845i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 443196. | − | 306973.i | 1.10260 | − | 0.763699i | ||||
\(635\) | 76930.2 | − | 44415.7i | 0.190787 | − | 0.110151i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19430.1 | + | 33653.9i | −0.0478846 | + | 0.0829385i | ||||
\(638\) | −312902. | + | 25768.4i | −0.768718 | + | 0.0633061i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50461.3 | + | 77837.5i | 0.123196 | + | 0.190033i | ||||
\(641\) | −232262. | + | 402289.i | −0.565278 | + | 0.979089i | 0.431746 | + | 0.901995i | \(0.357898\pi\) |
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −361978. | + | 208988.i | −0.875509 | + | 0.505476i | −0.869175 | − | 0.494504i | \(-0.835350\pi\) |
−0.00633423 | + | 0.999980i | \(0.502016\pi\) | |||||||
\(644\) | −289733. | − | 352530.i | −0.698596 | − | 0.850010i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −124450. | + | 263368.i | −0.298214 | + | 0.631101i | ||||
\(647\) | 825841.i | 1.97282i | 0.164299 | + | 0.986411i | \(0.447464\pi\) | ||||
−0.164299 | + | 0.986411i | \(0.552536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −229610. | −0.545131 | ||||||||
\(650\) | −261913. | − | 123762.i | −0.619913 | − | 0.292928i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 381258. | − | 313344.i | 0.896859 | − | 0.737100i | ||||
\(653\) | 164273. | + | 284529.i | 0.385247 | + | 0.667267i | 0.991803 | − | 0.127773i | \(-0.0407830\pi\) |
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41049.6 | + | 23700.0i | 0.0956811 | + | 0.0552415i | ||||
\(656\) | 694972. | − | 237013.i | 1.61495 | − | 0.550762i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18058.5 | − | 219282.i | −0.0417090 | − | 0.506467i | ||||
\(659\) | 144939. | + | 83680.3i | 0.333744 | + | 0.192687i | 0.657502 | − | 0.753453i | \(-0.271613\pi\) |
−0.323758 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 152616. | + | 264339.i | 0.349300 | + | 0.605005i | 0.986125 | − | 0.166003i | \(-0.0530862\pi\) |
−0.636826 | + | 0.771008i | \(0.719753\pi\) | |||||||
\(662\) | 350154. | + | 505539.i | 0.798994 | + | 1.15356i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 52670.6 | − | 185190.i | 0.119463 | − | 0.420032i | ||||
\(665\) | −175261. | −0.396317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 402461.i | − | 0.904633i | ||||||
\(668\) | −236641. | − | 88873.4i | −0.530318 | − | 0.199168i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 52931.6 | + | 76420.5i | 0.117914 | + | 0.170240i | ||||
\(671\) | 6127.32 | − | 3537.61i | 0.0136090 | − | 0.00785715i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −403032. | + | 698073.i | −0.889836 | + | 1.54124i | −0.0497671 | + | 0.998761i | \(0.515848\pi\) |
−0.840069 | + | 0.542480i | \(0.817485\pi\) | |||||||
\(674\) | −7532.41 | − | 91465.0i | −0.0165811 | − | 0.201342i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 215355. | − | 35712.5i | 0.471262 | − | 0.0781496i | ||||
\(677\) | −183117. | + | 317169.i | −0.399533 | + | 0.692011i | −0.993668 | − | 0.112354i | \(-0.964161\pi\) |
0.594136 | + | 0.804365i | \(0.297494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −217400. | + | 125516.i | −0.471542 | + | 0.272245i | ||||
\(680\) | 31909.5 | − | 30947.9i | 0.0690084 | − | 0.0669288i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 226025. | + | 106804.i | 0.485946 | + | 0.229624i | ||||
\(683\) | − | 398332.i | − | 0.853894i | −0.904277 | − | 0.426947i | \(-0.859589\pi\) | ||
0.904277 | − | 0.426947i | \(-0.140411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −169460. | −0.361148 | ||||||||
\(686\) | 185609. | − | 392797.i | 0.394412 | − | 0.834680i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −378244. | + | 432543.i | −0.799089 | + | 0.913802i | ||||
\(689\) | 290235. | + | 502701.i | 0.611379 | + | 1.05894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −304679. | − | 175906.i | −0.638096 | − | 0.368405i | 0.145785 | − | 0.989316i | \(-0.453429\pi\) |
−0.783881 | + | 0.620912i | \(0.786763\pi\) | |||||||
\(692\) | 742860. | − | 123189.i | 1.55130 | − | 0.257252i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28820.2 | + | 2373.42i | −0.0598381 | + | 0.00492784i | ||||
\(695\) | −116927. | − | 67507.8i | −0.242072 | − | 0.139760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −175932. | − | 304723.i | −0.362143 | − | 0.627249i | ||||
\(698\) | 363568. | − | 251820.i | 0.746233 | − | 0.516868i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −463127. | − | 173933.i | −0.945156 | − | 0.354965i | ||||
\(701\) | 620142. | 1.26199 | 0.630994 | − | 0.775788i | \(-0.282647\pi\) | ||||
0.630994 | + | 0.775788i | \(0.282647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.35898e6i | − | 2.74980i | ||||||
\(704\) | −436691. | − | 13364.3i | −0.881107 | − | 0.0269650i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 202568. | − | 140306.i | 0.406408 | − | 0.281493i | ||||
\(707\) | 317061. | − | 183055.i | 0.634314 | − | 0.366222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −157448. | + | 272708.i | −0.313217 | + | 0.542508i | −0.979057 | − | 0.203587i | \(-0.934740\pi\) |
0.665840 | + | 0.746095i | \(0.268073\pi\) | |||||||
\(710\) | 113569. | − | 9352.70i | 0.225290 | − | 0.0185533i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 49760.9 | + | 197762.i | 0.0981585 | + | 0.390107i | ||||
\(713\) | −160228. | + | 277523.i | −0.315181 | + | 0.545909i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −63878.0 | + | 36880.0i | −0.124951 | + | 0.0721404i | ||||
\(716\) | −31467.2 | + | 25861.9i | −0.0613807 | + | 0.0504469i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 144341. | − | 305465.i | 0.279990 | − | 0.592533i | ||||
\(719\) | − | 361941.i | − | 0.700132i | −0.936725 | − | 0.350066i | \(-0.886159\pi\) | ||
0.936725 | − | 0.350066i | \(-0.113841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −111926. | −0.215308 | ||||||||
\(722\) | 803126. | + | 379501.i | 1.54067 | + | 0.728013i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 57668.8 | + | 70167.9i | 0.110018 | + | 0.133863i | ||||
\(725\) | −218164. | − | 377870.i | −0.415056 | − | 0.718897i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 267542. | + | 154465.i | 0.506200 | + | 0.292255i | 0.731270 | − | 0.682088i | \(-0.238928\pi\) |
−0.225070 | + | 0.974343i | \(0.572261\pi\) | |||||||
\(728\) | −395289. | + | 99462.6i | −0.745852 | + | 0.187671i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5028.29 | − | 61057.9i | −0.00943572 | − | 0.114577i | ||||
\(731\) | 238457. | + | 137673.i | 0.446247 | + | 0.257641i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −441272. | − | 764305.i | −0.821293 | − | 1.42252i | −0.904719 | − | 0.426008i | \(-0.859920\pi\) |
0.0834259 | − | 0.996514i | \(-0.473414\pi\) | |||||||
\(734\) | −423464. | − | 611380.i | −0.786002 | − | 1.13480i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 63018.1 | − | 556492.i | 0.116335 | − | 1.02731i | ||||
\(737\) | −437829. | −0.806065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 396910.i | − | 0.726781i | −0.931637 | − | 0.363390i | \(-0.881619\pi\) | ||
0.931637 | − | 0.363390i | \(-0.118381\pi\) | |||||||
\(740\) | −72913.3 | + | 194144.i | −0.133151 | + | 0.354537i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 564444. | + | 814923.i | 1.02521 | + | 1.48016i | ||||
\(743\) | 831366. | − | 479989.i | 1.50596 | − | 0.869469i | 0.505988 | − | 0.862541i | \(-0.331128\pi\) |
0.999976 | − | 0.00692819i | \(-0.00220533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14930.1 | + | 25859.7i | −0.0268999 | + | 0.0465920i | ||||
\(746\) | −27935.5 | − | 339217.i | −0.0501971 | − | 0.609536i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34250.5 | + | 206539.i | 0.0612158 | + | 0.369147i | ||||
\(749\) | −361023. | + | 625310.i | −0.643534 | + | 1.11463i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −572212. | + | 330367.i | −1.01456 | + | 0.585756i | −0.912523 | − | 0.409025i | \(-0.865869\pi\) |
−0.102036 | + | 0.994781i | \(0.532536\pi\) | |||||||
\(752\) | 177763. | − | 203282.i | 0.314344 | − | 0.359470i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −325044. | − | 153593.i | −0.571742 | − | 0.270165i | ||||
\(755\) | 189241.i | 0.331987i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 326842. | 0.570356 | 0.285178 | − | 0.958475i | \(-0.407947\pi\) | ||||
0.285178 | + | 0.958475i | \(0.407947\pi\) | |||||||
\(758\) | 251183. | − | 531570.i | 0.437171 | − | 0.925171i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −149757. | − | 154410.i | −0.259274 | − | 0.267330i | ||||
\(761\) | 164813. | + | 285464.i | 0.284591 | + | 0.492927i | 0.972510 | − | 0.232861i | \(-0.0748088\pi\) |
−0.687919 | + | 0.725788i | \(0.741475\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 875410. | + | 505418.i | 1.50370 | + | 0.868164i | ||||
\(764\) | 85013.7 | + | 512654.i | 0.145647 | + | 0.878290i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 742285. | − | 61129.3i | 1.26507 | − | 0.104182i | ||||
\(767\) | −227694. | − | 131459.i | −0.387044 | − | 0.223460i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 299738. | + | 519162.i | 0.506862 | + | 0.877910i | 0.999968 | + | 0.00794129i | \(0.00252782\pi\) |
−0.493107 | + | 0.869969i | \(0.664139\pi\) | |||||||
\(770\) | −103552. | + | 71723.7i | −0.174653 | + | 0.120971i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4429.60 | − | 11794.6i | 0.00743241 | − | 0.0197901i | ||||
\(773\) | 58555.0 | 0.0979952 | 0.0489976 | − | 0.998799i | \(-0.484397\pi\) | ||||
0.0489976 | + | 0.998799i | \(0.484397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 347422.i | 0.578433i | ||||||||
\(776\) | −296347. | − | 84285.0i | −0.492127 | − | 0.139967i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 841808. | − | 583066.i | 1.39077 | − | 0.963294i | ||||
\(779\) | −1.47456e6 | + | 851336.i | −2.42989 | + | 1.40290i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −268347. | + | 464791.i | −0.439942 | + | 0.762002i | ||||
\(782\) | −267469. | + | 22026.9i | −0.437381 | + | 0.0360196i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −77091.2 | + | 26291.1i | −0.125422 | + | 0.0427737i | ||||
\(785\) | 48129.6 | − | 83362.8i | 0.0781039 | − | 0.135280i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 553254. | − | 319421.i | 0.893254 | − | 0.515720i | 0.0182482 | − | 0.999833i | \(-0.494191\pi\) |
0.875005 | + | 0.484113i | \(0.160858\pi\) | |||||||
\(788\) | −252208. | − | 306872.i | −0.406169 | − | 0.494202i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13362.6 | − | 28278.8i | 0.0214110 | − | 0.0453113i | ||||
\(791\) | − | 710975.i | − | 1.13632i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8101.59 | 0.0128832 | ||||||||
\(794\) | 942966. | + | 445580.i | 1.49574 | + | 0.706781i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −148436. | + | 121995.i | −0.234269 | + | 0.192538i | ||||
\(797\) | −587628. | − | 1.01780e6i | −0.925095 | − | 1.60231i | −0.791409 | − | 0.611287i | \(-0.790652\pi\) |
−0.133686 | − | 0.991024i | \(-0.542681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −112067. | − | 64702.1i | −0.175544 | − | 0.101350i | ||||
\(800\) | −242492. | − | 556649.i | −0.378893 | − | 0.869765i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17404.5 | − | 211340.i | −0.0270591 | − | 0.328574i | ||||
\(803\) | 249886. | + | 144272.i | 0.387535 | + | 0.223743i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −80736.4 | − | 139840.i | −0.124588 | − | 0.215793i | ||||
\(806\) | 162991. | + | 235319.i | 0.250895 | + | 0.362233i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 432199. | + | 122923.i | 0.662005 | + | 0.188283i | ||||
\(809\) | 215543. | 0.329334 | 0.164667 | − | 0.986349i | \(-0.447345\pi\) | ||||
0.164667 | + | 0.986349i | \(0.447345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.05773e6i | 1.60817i | 0.594512 | + | 0.804087i | \(0.297345\pi\) | ||||
−0.594512 | + | 0.804087i | \(0.702655\pi\) | |||||||
\(812\) | −574758. | − | 215858.i | −0.871712 | − | 0.327382i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −556146. | − | 802942.i | −0.839345 | − | 1.21181i | ||||
\(815\) | 151236. | − | 87315.9i | 0.227687 | − | 0.131455i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 666201. | − | 1.15389e6i | 0.998070 | − | 1.72871i | ||||
\(818\) | 48390.0 | + | 587594.i | 0.0723185 | + | 0.878153i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 256333. | − | 42507.8i | 0.381221 | − | 0.0632180i | ||||
\(821\) | −37925.7 | + | 65689.3i | −0.0562662 | + | 0.0974559i | −0.892787 | − | 0.450480i | \(-0.851253\pi\) |
0.836520 | + | 0.547936i | \(0.184586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −569508. | + | 328806.i | −0.840815 | + | 0.485445i | −0.857541 | − | 0.514416i | \(-0.828009\pi\) |
0.0167265 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(824\) | −95638.4 | − | 98610.1i | −0.140857 | − | 0.145234i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −405964. | − | 191830.i | −0.595014 | − | 0.281162i | ||||
\(827\) | 669017.i | 0.978196i | 0.872229 | + | 0.489098i | \(0.162674\pi\) | ||||
−0.872229 | + | 0.489098i | \(0.837326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −637042. | −0.926955 | −0.463478 | − | 0.886109i | \(-0.653399\pi\) | ||||
−0.463478 | + | 0.886109i | \(0.653399\pi\) | |||||||
\(830\) | 29107.9 | − | 61600.1i | 0.0422527 | − | 0.0894180i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −425395. | − | 263273.i | −0.614534 | − | 0.380328i | ||||
\(833\) | 19515.6 | + | 33802.1i | 0.0281250 | + | 0.0487139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −77465.4 | − | 44724.7i | −0.111105 | − | 0.0641467i | ||||
\(836\) | 999443. | − | 165738.i | 1.43003 | − | 0.237143i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −927231. | + | 76360.1i | −1.32038 | + | 0.108737i | ||||
\(839\) | −872716. | − | 503863.i | −1.23979 | − | 0.715795i | −0.270741 | − | 0.962652i | \(-0.587269\pi\) |
−0.969052 | + | 0.246858i | \(0.920602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82891.1 | + | 143572.i | 0.117197 | + | 0.202991i | ||||
\(842\) | −229526. | + | 158978.i | −0.323748 | + | 0.224240i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −445617. | − | 167357.i | −0.625572 | − | 0.234941i | ||||
\(845\) | 77247.2 | 0.108186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 170194.i | 0.237234i | ||||||||
\(848\) | −235664. | + | 1.19362e6i | −0.327720 | + | 1.65988i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −239186. | + | 165669.i | −0.331054 | + | 0.229299i | ||||
\(851\) | 1.08432e6 | − | 626031.i | 1.49726 | − | 0.864444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 96790.1 | − | 167645.i | 0.133025 | − | 0.230406i | −0.791816 | − | 0.610759i | \(-0.790864\pi\) |
0.924841 | + | 0.380353i | \(0.124198\pi\) | |||||||
\(854\) | 13789.0 | − | 1135.56i | 0.0189068 | − | 0.00155703i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −859402. | + | 216242.i | −1.17287 | + | 0.295116i | ||||
\(857\) | 461864. | − | 799972.i | 0.628858 | − | 1.08921i | −0.358923 | − | 0.933367i | \(-0.616856\pi\) |
0.987781 | − | 0.155847i | \(-0.0498107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 628431. | − | 362825.i | 0.851670 | − | 0.491712i | −0.00954418 | − | 0.999954i | \(-0.503038\pi\) |
0.861214 | + | 0.508243i | \(0.169705\pi\) | |||||||
\(860\) | −157084. | + | 129102.i | −0.212390 | + | 0.174557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −252705. | + | 534791.i | −0.340094 | + | 0.719730i | ||||
\(863\) | 444700.i | 0.597097i | 0.954394 | + | 0.298549i | \(0.0965025\pi\) | ||||
−0.954394 | + | 0.298549i | \(0.903497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 266461. | 0.356124 | ||||||||
\(866\) | −1.06634e6 | − | 503879.i | −1.42187 | − | 0.671878i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 310396. | + | 377671.i | 0.411980 | + | 0.501272i | ||||
\(869\) | 73653.9 | + | 127572.i | 0.0975341 | + | 0.168934i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −434176. | − | 250672.i | −0.572308 | − | 0.330422i | ||||
\(872\) | 302731. | + | 1.20313e6i | 0.398129 | + | 1.58227i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 106588. | + | 1.29428e6i | 0.139536 | + | 1.69436i | ||||
\(875\) | −311409. | − | 179792.i | −0.406739 | − | 0.234831i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 288301. | + | 499353.i | 0.374841 | + | 0.649244i | 0.990303 | − | 0.138922i | \(-0.0443638\pi\) |
−0.615462 | + | 0.788167i | \(0.711031\pi\) | |||||||
\(878\) | 164285. | + | 237188.i | 0.213113 | + | 0.307684i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −151673. | − | 29945.8i | −0.195859 | − | 0.0386696i | ||||
\(881\) | 1.16458e6 | 1.50044 | 0.750219 | − | 0.661190i | \(-0.229948\pi\) | ||||
0.750219 | + | 0.661190i | \(0.229948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12142.2i | 0.0155731i | 0.999970 | + | 0.00778655i | \(0.00247856\pi\) | ||||
−0.999970 | + | 0.00778655i | \(0.997521\pi\) | |||||||
\(884\) | −84285.7 | + | 224425.i | −0.107857 | + | 0.287189i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 434805. | + | 627754.i | 0.553894 | + | 0.799691i | ||||
\(887\) | −1.12130e6 | + | 647385.i | −1.42520 | + | 0.822840i | −0.996737 | − | 0.0807193i | \(-0.974278\pi\) |
−0.428464 | + | 0.903559i | \(0.640945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −409071. | + | 708532.i | −0.517601 | + | 0.896511i | ||||
\(890\) | 5922.72 | + | 71918.8i | 0.00747723 | + | 0.0907951i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 138595. | + | 835763.i | 0.174188 | + | 1.05040i | ||||
\(893\) | −313094. | + | 542294.i | −0.392619 | + | 0.680036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12482.2 | + | 7206.63i | −0.0155828 | + | 0.00899676i | ||||
\(896\) | −760930. | − | 388467.i | −0.947826 | − | 0.483881i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 697488. | + | 329584.i | 0.864937 | + | 0.408709i | ||||
\(899\) | 431164.i | 0.533485i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 583026. | 0.718188 | ||||||||
\(902\) | −522832. | + | 1.10645e6i | −0.642613 | + | 1.35994i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 626389. | − | 607512.i | 0.766491 | − | 0.743393i | ||||
\(905\) | 16069.9 | + | 27833.8i | 0.0196207 | + | 0.0339841i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 593065. | + | 342406.i | 0.720921 | + | 0.416224i | 0.815091 | − | 0.579332i | \(-0.196687\pi\) |
−0.0941708 | + | 0.995556i | \(0.530020\pi\) | |||||||
\(908\) | −98513.1 | − | 594059.i | −0.119487 | − | 0.720540i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −143752. | + | 11838.4i | −0.173593 | + | 0.0142958i | ||||
\(911\) | 621519. | + | 358834.i | 0.748890 | + | 0.432372i | 0.825293 | − | 0.564705i | \(-0.191010\pi\) |
−0.0764028 | + | 0.997077i | \(0.524343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 160441. | + | 277893.i | 0.192475 | + | 0.333377i | ||||
\(914\) | −19484.0 | + | 13495.3i | −0.0233231 | + | 0.0161544i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −321987. | + | 857345.i | −0.383749 | + | 1.02180i | ||||
\(917\) | −436556. | −0.519160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 441444.i | 0.522691i | 0.965245 | + | 0.261345i | \(0.0841661\pi\) | ||||
−0.965245 | + | 0.261345i | \(0.915834\pi\) | |||||||
\(920\) | 54215.1 | − | 190621.i | 0.0640538 | − | 0.225214i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −416570. | + | 288531.i | −0.490034 | + | 0.339415i | ||||
\(923\) | −532217. | + | 307275.i | −0.624720 | + | 0.360682i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 678710. | − | 1.17556e6i | 0.793232 | − | 1.37392i | ||||
\(926\) | −939108. | + | 77338.2i | −1.09520 | + | 0.0901929i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −300941. | − | 690823.i | −0.349451 | − | 0.802179i | ||||
\(929\) | 633285. | − | 1.09688e6i | 0.733783 | − | 1.27095i | −0.221472 | − | 0.975167i | \(-0.571086\pi\) |
0.955255 | − | 0.295783i | \(-0.0955804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 163568. | − | 94436.2i | 0.188712 | − | 0.108953i | ||||
\(932\) | 370488. | + | 450788.i | 0.426523 | + | 0.518968i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −167093. | + | 353614.i | −0.191543 | + | 0.405355i | ||||
\(935\) | 74084.8i | 0.0847434i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 377258. | 0.429694 | 0.214847 | − | 0.976648i | \(-0.431075\pi\) | ||||
0.214847 | + | 0.976648i | \(0.431075\pi\) | |||||||
\(938\) | −774108. | − | 365790.i | −0.879825 | − | 0.415744i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 73824.5 | − | 60674.0i | 0.0835497 | − | 0.0686668i | ||||
\(941\) | −645770. | − | 1.11851e6i | −0.729288 | − | 1.26316i | −0.957185 | − | 0.289478i | \(-0.906518\pi\) |
0.227897 | − | 0.973685i | \(-0.426815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.35855e6 | − | 784359.i | −1.52775 | − | 0.882046i | ||||
\(944\) | −177879. | − | 521580.i | −0.199610 | − | 0.585298i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −78598.0 | − | 954405.i | −0.0878273 | − | 1.06647i | ||||
\(947\) | 1.02088e6 | + | 589403.i | 1.13834 | + | 0.657222i | 0.946019 | − | 0.324110i | \(-0.105065\pi\) |
0.192322 | + | 0.981332i | \(0.438398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 165200. | + | 286136.i | 0.183434 | + | 0.317716i | ||||
\(950\) | 801672. | + | 1.15742e6i | 0.888279 | + | 1.28246i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −111999. | + | 393788.i | −0.123577 | + | 0.434499i | ||||
\(953\) | −613396. | −0.675391 | −0.337695 | − | 0.941255i | \(-0.609647\pi\) | ||||
−0.337695 | + | 0.941255i | \(0.609647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 183887.i | 0.201625i | ||||||||
\(956\) | 784231. | + | 294528.i | 0.858081 | + | 0.322263i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −918265. | − | 1.32575e6i | −1.00055 | − | 1.44455i | ||||
\(959\) | 1.35163e6 | − | 780367.i | 1.46968 | − | 0.848519i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −290105. | + | 502477.i | −0.314130 | + | 0.544089i | ||||
\(962\) | −91795.0 | − | 1.11465e6i | −0.0991903 | − | 1.20445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 213265. | − | 35365.9i | 0.229491 | − | 0.0380567i | ||||
\(965\) | 2229.15 | − | 3861.01i | 0.00239379 | − | 0.00414616i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41063.4 | − | 23708.0i | 0.0439139 | − | 0.0253537i | −0.477882 | − | 0.878424i | \(-0.658595\pi\) |
0.521796 | + | 0.853070i | \(0.325262\pi\) | |||||||
\(968\) | −149946. | + | 145427.i | −0.160023 | + | 0.155201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −98574.2 | − | 46579.3i | −0.104766 | − | 0.0495051i | ||||
\(971\) | 746340.i | 0.791586i | 0.918340 | + | 0.395793i | \(0.129530\pi\) | ||||
−0.918340 | + | 0.395793i | \(0.870470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.24350e6 | 1.31347 | ||||||||
\(974\) | 333596. | − | 705978.i | 0.351644 | − | 0.744172i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12782.9 | + | 11178.2i | 0.0134193 | + | 0.0117347i | ||||
\(977\) | −143356. | − | 248299.i | −0.150185 | − | 0.260128i | 0.781111 | − | 0.624393i | \(-0.214654\pi\) |
−0.931295 | + | 0.364265i | \(0.881320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −294335. | − | 169934.i | −0.307098 | − | 0.177303i | ||||
\(980\) | −28434.2 | + | 4715.26i | −0.0296067 | + | 0.00490969i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −303523. | + | 24996.0i | −0.314752 | + | 0.0259208i | ||||
\(983\) | −504643. | − | 291356.i | −0.522249 | − | 0.301521i | 0.215605 | − | 0.976481i | \(-0.430828\pi\) |
−0.737854 | + | 0.674960i | \(0.764161\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70279.8 | − | 121728.i | −0.0724366 | − | 0.125464i | ||||
\(986\) | −296839. | + | 205601.i | −0.305329 | + | 0.211481i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.08599e6 | + | 407859.i | 1.11253 | + | 0.417826i | ||||
\(989\) | 1.22758e6 | 1.25504 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 918794.i | − | 0.935558i | −0.883845 | − | 0.467779i | \(-0.845054\pi\) | ||
0.883845 | − | 0.467779i | \(-0.154946\pi\) | |||||||
\(992\) | −67512.3 | + | 596178.i | −0.0686056 | + | 0.605833i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −862770. | + | 597585.i | −0.873217 | + | 0.604821i | ||||
\(995\) | −58881.0 | + | 33995.0i | −0.0594742 | + | 0.0343375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 697626. | − | 1.20832e6i | 0.701830 | − | 1.21561i | −0.265993 | − | 0.963975i | \(-0.585700\pi\) |
0.967823 | − | 0.251631i | \(-0.0809668\pi\) | |||||||
\(998\) | 58084.7 | − | 4783.45i | 0.0583178 | − | 0.00480264i | ||||
\(999\) | 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.19.4 | 44 | ||
3.2 | odd | 2 | 36.5.f.a.7.19 | yes | 44 | ||
4.3 | odd | 2 | inner | 108.5.f.a.19.19 | 44 | ||
9.2 | odd | 6 | 324.5.d.f.163.11 | 22 | |||
9.4 | even | 3 | inner | 108.5.f.a.91.19 | 44 | ||
9.5 | odd | 6 | 36.5.f.a.31.4 | yes | 44 | ||
9.7 | even | 3 | 324.5.d.e.163.12 | 22 | |||
12.11 | even | 2 | 36.5.f.a.7.4 | ✓ | 44 | ||
36.7 | odd | 6 | 324.5.d.e.163.11 | 22 | |||
36.11 | even | 6 | 324.5.d.f.163.12 | 22 | |||
36.23 | even | 6 | 36.5.f.a.31.19 | yes | 44 | ||
36.31 | odd | 6 | inner | 108.5.f.a.91.4 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.4 | ✓ | 44 | 12.11 | even | 2 | ||
36.5.f.a.7.19 | yes | 44 | 3.2 | odd | 2 | ||
36.5.f.a.31.4 | yes | 44 | 9.5 | odd | 6 | ||
36.5.f.a.31.19 | yes | 44 | 36.23 | even | 6 | ||
108.5.f.a.19.4 | 44 | 1.1 | even | 1 | trivial | ||
108.5.f.a.19.19 | 44 | 4.3 | odd | 2 | inner | ||
108.5.f.a.91.4 | 44 | 36.31 | odd | 6 | inner | ||
108.5.f.a.91.19 | 44 | 9.4 | even | 3 | inner | ||
324.5.d.e.163.11 | 22 | 36.7 | odd | 6 | |||
324.5.d.e.163.12 | 22 | 9.7 | even | 3 | |||
324.5.d.f.163.11 | 22 | 9.2 | odd | 6 | |||
324.5.d.f.163.12 | 22 | 36.11 | even | 6 |