Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.12 | ||
Character | \(\chi\) | \(=\) | 108.5 |
Dual form | 108.5.k.a.65.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 8.73547 | + | 2.16600i | 0.970608 | + | 0.240667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.54164 | + | 26.2154i | 0.381666 | + | 1.04862i | 0.970655 | + | 0.240477i | \(0.0773037\pi\) |
−0.588989 | + | 0.808141i | \(0.700474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.541932 | − | 3.07345i | −0.0110598 | − | 0.0627235i | 0.978778 | − | 0.204922i | \(-0.0656940\pi\) |
−0.989838 | + | 0.142198i | \(0.954583\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 71.6168 | + | 37.8421i | 0.884159 | + | 0.467187i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44.3351 | + | 121.810i | −0.366406 | + | 1.00669i | 0.610312 | + | 0.792161i | \(0.291044\pi\) |
−0.976717 | + | 0.214530i | \(0.931178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.3898 | − | 25.5001i | −0.179821 | − | 0.150888i | 0.548434 | − | 0.836194i | \(-0.315224\pi\) |
−0.728256 | + | 0.685306i | \(0.759669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.5679 | + | 249.671i | 0.118080 | + | 1.10965i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −72.0247 | − | 41.5835i | −0.249220 | − | 0.143887i | 0.370187 | − | 0.928957i | \(-0.379294\pi\) |
−0.619407 | + | 0.785070i | \(0.712627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.6516 | + | 56.5542i | 0.0904476 | + | 0.156660i | 0.907700 | − | 0.419621i | \(-0.137837\pi\) |
−0.817252 | + | 0.576281i | \(0.804504\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.92308 | − | 28.0219i | 0.00436072 | − | 0.0635417i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 346.437 | + | 61.0862i | 0.654890 | + | 0.115475i | 0.491214 | − | 0.871039i | \(-0.336553\pi\) |
0.163677 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.428 | + | 98.5341i | −0.187885 | + | 0.157655i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 543.640 | + | 485.691i | 0.745735 | + | 0.666243i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 421.220 | + | 501.991i | 0.500856 | + | 0.596897i | 0.955944 | − | 0.293549i | \(-0.0948365\pi\) |
−0.455088 | + | 0.890447i | \(0.650392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.7225 | + | 106.181i | −0.0194823 | + | 0.110490i | −0.992998 | − | 0.118130i | \(-0.962310\pi\) |
0.973516 | + | 0.228620i | \(0.0734212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −651.128 | + | 968.034i | −0.597914 | + | 0.888920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 75.4009 | − | 43.5328i | 0.0615518 | − | 0.0355369i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −745.268 | + | 1290.84i | −0.544389 | + | 0.942909i | 0.454256 | + | 0.890871i | \(0.349905\pi\) |
−0.998645 | + | 0.0520382i | \(0.983428\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −210.236 | − | 288.580i | −0.138222 | − | 0.189730i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1342.26 | − | 1599.64i | 0.798486 | − | 0.951599i | −0.201123 | − | 0.979566i | \(-0.564459\pi\) |
0.999609 | + | 0.0279673i | \(0.00890341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1405.92 | − | 511.712i | −0.760366 | − | 0.276750i | −0.0674048 | − | 0.997726i | \(-0.521472\pi\) |
−0.692961 | + | 0.720975i | \(0.743694\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −308.706 | + | 2238.54i | −0.152447 | + | 1.10545i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2360.91 | − | 416.292i | 1.06877 | − | 0.188453i | 0.388524 | − | 0.921439i | \(-0.372985\pi\) |
0.680244 | + | 0.732986i | \(0.261874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2247.05 | − | 817.859i | 0.935881 | − | 0.340633i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −539.100 | − | 519.257i | −0.207266 | − | 0.199637i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2343.67i | − | 0.834344i | −0.908828 | − | 0.417172i | \(-0.863021\pi\) | ||
0.908828 | − | 0.417172i | \(-0.136979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3616.32 | −1.19548 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 162.730 | + | 564.751i | 0.0500863 | + | 0.173823i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −978.002 | − | 2687.04i | −0.280954 | − | 0.771916i | −0.997249 | − | 0.0741183i | \(-0.976386\pi\) |
0.716295 | − | 0.697797i | \(-0.245836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1139.50 | − | 6462.44i | −0.306236 | − | 1.73675i | −0.617630 | − | 0.786469i | \(-0.711907\pi\) |
0.311394 | − | 0.950281i | \(-0.399204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 77.4945 | − | 240.619i | 0.0195249 | − | 0.0606245i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 378.527 | − | 1040.00i | 0.0895923 | − | 0.246153i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6613.79 | − | 5549.63i | −1.47333 | − | 1.23627i | −0.912971 | − | 0.408024i | \(-0.866218\pi\) |
−0.560361 | − | 0.828249i | \(-0.689337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2893.98 | + | 1284.00i | 0.607851 | + | 0.269691i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −426.072 | − | 245.993i | −0.0845214 | − | 0.0487985i | 0.457144 | − | 0.889393i | \(-0.348873\pi\) |
−0.541665 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2004.31 | − | 3471.57i | −0.376114 | − | 0.651449i | 0.614379 | − | 0.789011i | \(-0.289407\pi\) |
−0.990493 | + | 0.137562i | \(0.956073\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1239.22 | + | 606.391i | −0.220305 | + | 0.107803i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 398.403 | + | 70.2491i | 0.0671956 | + | 0.0118484i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5374.08 | + | 4509.39i | −0.861093 | + | 0.722543i | −0.962203 | − | 0.272332i | \(-0.912205\pi\) |
0.101110 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3696.94 | + | 5420.27i | 0.563473 | + | 0.826135i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1605.97 | + | 1913.93i | 0.233122 | + | 0.277823i | 0.869905 | − | 0.493219i | \(-0.164180\pi\) |
−0.636784 | + | 0.771043i | \(0.719735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 402.895 | − | 2284.93i | 0.0557641 | − | 0.316254i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2592.24 | + | 5297.49i | 0.342481 | + | 0.699893i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12923.1 | − | 7461.14i | 1.63150 | − | 0.941945i | 0.647864 | − | 0.761756i | \(-0.275662\pi\) |
0.983632 | − | 0.180189i | \(-0.0576710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61.9041 | + | 107.221i | −0.00747543 | + | 0.0129478i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −393.538 | + | 886.984i | −0.0455009 | + | 0.102553i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1171.04 | + | 1395.60i | −0.129756 | + | 0.154637i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15873.9 | + | 5777.63i | 1.68710 | + | 0.614054i | 0.994255 | − | 0.107034i | \(-0.0341352\pi\) |
0.692844 | + | 0.721088i | \(0.256357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7784.68 | + | 7045.89i | −0.794274 | + | 0.718895i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3976.62 | − | 701.186i | 0.389827 | − | 0.0687370i | 0.0247004 | − | 0.999695i | \(-0.492137\pi\) |
0.365127 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12081.1 | + | 4397.16i | −1.13876 | + | 0.414475i | −0.841465 | − | 0.540311i | \(-0.818307\pi\) |
−0.297295 | + | 0.954786i | \(0.596084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 752.955 | − | 216.960i | 0.0682952 | − | 0.0196789i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6203.55i | − | 0.541842i | −0.962602 | − | 0.270921i | \(-0.912672\pi\) | ||
0.962602 | − | 0.270921i | \(-0.0873283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6362.04 | −0.535480 | −0.267740 | − | 0.963491i | \(-0.586277\pi\) | ||||
−0.267740 | + | 0.963491i | \(0.586277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9306.24 | + | 9661.86i | −0.755315 | + | 0.784178i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2688.37 | + | 7386.23i | 0.210539 | + | 0.578450i | 0.999345 | − | 0.0361920i | \(-0.0115228\pi\) |
−0.788806 | + | 0.614642i | \(0.789301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1704.18 | + | 9664.86i | 0.128860 | + | 0.730802i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1211.45 | − | 2976.25i | −0.0884977 | − | 0.217419i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −88.7723 | + | 243.900i | −0.00626879 | + | 0.0172233i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1656.33 | − | 1389.83i | −0.113130 | − | 0.0949271i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15190.1 | − | 11066.3i | 1.00404 | − | 0.731460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11396.6 | + | 6579.83i | 0.729382 | + | 0.421109i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2979.36 | + | 5160.40i | 0.184721 | + | 0.319946i | 0.943482 | − | 0.331423i | \(-0.107529\pi\) |
−0.758762 | + | 0.651368i | \(0.774195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11173.0 | − | 7515.26i | −0.671412 | − | 0.451611i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22916.5 | − | 4040.80i | −1.33538 | − | 0.235464i | −0.540048 | − | 0.841634i | \(-0.681594\pi\) |
−0.795335 | + | 0.606171i | \(0.792705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 156.122 | − | 131.002i | 0.00882592 | − | 0.00740583i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7545.39 | + | 18886.1i | −0.414013 | + | 1.03627i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8869.93 | + | 10570.8i | 0.472584 | + | 0.563204i | 0.948700 | − | 0.316179i | \(-0.102400\pi\) |
−0.476115 | + | 0.879383i | \(0.657956\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3753.73 | − | 21288.5i | 0.194283 | − | 1.10183i | −0.719154 | − | 0.694850i | \(-0.755471\pi\) |
0.913437 | − | 0.406981i | \(-0.133418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21525.3 | + | 1477.23i | 1.08271 | + | 0.0743038i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4453.49 | − | 2571.23i | 0.217785 | − | 0.125738i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9140.77 | + | 15832.3i | −0.434757 | + | 0.753022i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21400.5 | − | 2277.26i | 0.990352 | − | 0.105385i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22455.8 | + | 26761.7i | −1.01148 | + | 1.20543i | −0.0329171 | + | 0.999458i | \(0.510480\pi\) |
−0.978558 | + | 0.205971i | \(0.933965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 39773.2 | + | 14476.3i | 1.74436 | + | 0.634896i | 0.999478 | − | 0.0322972i | \(-0.0102823\pi\) |
0.744885 | + | 0.667193i | \(0.232505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3584.57 | − | 5703.65i | −0.153128 | − | 0.243652i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2962.21 | + | 522.318i | −0.123297 | + | 0.0217406i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15090.4 | − | 5492.45i | 0.612211 | − | 0.222826i | −0.0172596 | − | 0.999851i | \(-0.505494\pi\) |
0.629470 | + | 0.777025i | \(0.283272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5076.40 | − | 20473.1i | 0.200799 | − | 0.809820i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1097.86i | − | 0.0423541i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10729.0 | −0.403815 | −0.201908 | − | 0.979405i | \(-0.564714\pi\) | ||||
−0.201908 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −31590.3 | − | 7832.97i | −1.16034 | − | 0.287712i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9638.45 | − | 26481.4i | −0.345600 | − | 0.949529i | −0.983738 | − | 0.179607i | \(-0.942517\pi\) |
0.638138 | − | 0.769922i | \(-0.279705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4686.28 | − | 26577.2i | −0.164080 | − | 0.930542i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 198.271 | + | 5285.84i | 0.00678060 | + | 0.180768i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12892.4 | + | 35421.5i | −0.430765 | + | 1.18352i | 0.514579 | + | 0.857443i | \(0.327948\pi\) |
−0.945344 | + | 0.326074i | \(0.894274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 366.478 | + | 307.511i | 0.0119666 | + | 0.0100412i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2723.17 | − | 25590.9i | −0.0869216 | − | 0.816844i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −47834.6 | − | 27617.3i | −1.49292 | − | 0.861938i | −0.492953 | − | 0.870056i | \(-0.664082\pi\) |
−0.999967 | + | 0.00811870i | \(0.997416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5248.19 | + | 9090.13i | 0.160196 | + | 0.277468i | 0.934939 | − | 0.354809i | \(-0.115454\pi\) |
−0.774743 | + | 0.632277i | \(0.782121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4043.59 | − | 58920.7i | 0.120744 | − | 1.75940i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40951.1 | − | 7220.78i | −1.19653 | − | 0.210980i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8258.49 | − | 6929.70i | 0.236166 | − | 0.198167i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1198.13 | − | 1934.06i | 0.0335414 | − | 0.0541436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25833.2 | + | 30786.8i | 0.708127 | + | 0.843913i | 0.993420 | − | 0.114527i | \(-0.0365353\pi\) |
−0.285293 | + | 0.958440i | \(0.592091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8845.50 | − | 50165.3i | 0.237469 | − | 1.34676i | −0.599881 | − | 0.800089i | \(-0.704785\pi\) |
0.837350 | − | 0.546667i | \(-0.184104\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5559.25 | − | 8264.95i | 0.146200 | − | 0.217356i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24425.4 | − | 14102.0i | 0.629376 | − | 0.363370i | −0.151135 | − | 0.988513i | \(-0.548293\pi\) |
0.780510 | + | 0.625143i | \(0.214959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25117.8 | + | 43505.4i | −0.634273 | + | 1.09859i | 0.352396 | + | 0.935851i | \(0.385367\pi\) |
−0.986669 | + | 0.162742i | \(0.947966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45754.0 | − | 62804.1i | −1.13250 | − | 1.55452i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1314.57 | − | 1566.64i | 0.0319001 | − | 0.0380170i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54742.5 | + | 19924.6i | 1.30262 | + | 0.474114i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22499.1 | + | 17484.7i | 0.525079 | + | 0.408054i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8336.46 | + | 1469.94i | −0.190849 | + | 0.0336518i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17352.0 | − | 6315.62i | 0.389749 | − | 0.141857i | −0.139710 | − | 0.990192i | \(-0.544617\pi\) |
0.529459 | + | 0.848335i | \(0.322395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3189.12 | − | 3071.74i | −0.0702929 | − | 0.0677057i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 41739.3i | − | 0.902959i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 336.487 | 0.00714577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9989.17 | − | 34667.2i | −0.208277 | − | 0.722820i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1128.44 | + | 3100.35i | 0.0231043 | + | 0.0634785i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11371.6 | + | 64491.7i | 0.228672 | + | 1.29686i | 0.855540 | + | 0.517737i | \(0.173226\pi\) |
−0.626868 | + | 0.779126i | \(0.715663\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12138.6 | + | 2612.96i | −0.239775 | + | 0.0516140i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21863.2 | + | 60068.6i | −0.424289 | + | 1.16572i | 0.524941 | + | 0.851139i | \(0.324088\pi\) |
−0.949229 | + | 0.314585i | \(0.898135\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1269.42 | + | 1065.17i | 0.0242067 | + | 0.0203118i | 0.654811 | − | 0.755793i | \(-0.272748\pi\) |
−0.630604 | + | 0.776105i | \(0.717193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3328.07 | + | 1476.60i | 0.0623690 | + | 0.0276719i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18385.1 | − | 10614.6i | −0.338652 | − | 0.195521i | 0.321024 | − | 0.947071i | \(-0.395973\pi\) |
−0.659676 | + | 0.751550i | \(0.729306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33440.2 | + | 57920.1i | 0.605526 | + | 1.04880i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −56712.5 | + | 27751.3i | −1.00968 | + | 0.494069i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18699.3 | − | 3297.20i | −0.327363 | − | 0.0577230i | 0.00755117 | − | 0.999971i | \(-0.497596\pi\) |
−0.334915 | + | 0.942248i | \(0.608707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25092.7 | − | 21055.3i | 0.432030 | − | 0.362516i | −0.400687 | − | 0.916215i | \(-0.631228\pi\) |
0.832717 | + | 0.553699i | \(0.186784\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20554.2 | + | 55356.2i | 0.348088 | + | 0.937462i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 42881.1 | + | 51103.7i | 0.714387 | + | 0.851373i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 449.862 | − | 2551.29i | 0.00737369 | − | 0.0418183i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9883.37 | + | 20197.6i | 0.159407 | + | 0.325762i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27978.7 | − | 16153.5i | 0.444099 | − | 0.256401i | −0.261236 | − | 0.965275i | \(-0.584130\pi\) |
0.705335 | + | 0.708874i | \(0.250797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22800.2 | + | 39491.1i | −0.356203 | + | 0.616962i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8468.66 | − | 19087.3i | 0.130237 | − | 0.293538i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −45702.6 | + | 54466.3i | −0.691950 | + | 0.824634i | −0.991590 | − | 0.129418i | \(-0.958689\pi\) |
0.299640 | + | 0.954052i | \(0.403134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4371.23 | + | 1591.00i | 0.0651634 | + | 0.0237175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11170.1 | + | 51890.9i | 0.163974 | + | 0.761745i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 45451.4 | − | 8014.31i | 0.657107 | − | 0.115866i | 0.164854 | − | 0.986318i | \(-0.447285\pi\) |
0.492253 | + | 0.870452i | \(0.336174\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 61440.4 | − | 22362.5i | 0.874907 | − | 0.318440i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 129050. | − | 37185.1i | 1.81024 | − | 0.521611i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 62867.5i | 0.868804i | 0.900719 | + | 0.434402i | \(0.143040\pi\) | ||||
−0.900719 | + | 0.434402i | \(0.856960\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89938.3 | −1.22463 | −0.612317 | − | 0.790612i | \(-0.709762\pi\) | ||||
−0.612317 | + | 0.790612i | \(0.709762\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −773.002 | + | 802.541i | −0.0103718 | + | 0.0107682i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6796.21 | − | 18672.4i | −0.0898672 | − | 0.246908i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2359.61 | + | 13382.0i | 0.0307525 | + | 0.174406i | 0.996316 | − | 0.0857630i | \(-0.0273328\pi\) |
−0.965563 | + | 0.260169i | \(0.916222\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5358.95 | + | 6895.82i | −0.0688448 | + | 0.0885885i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12110.1 | + | 33272.1i | −0.153368 | + | 0.421374i | −0.992453 | − | 0.122626i | \(-0.960869\pi\) |
0.839085 | + | 0.544000i | \(0.183091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −87306.7 | − | 73259.0i | −1.09012 | − | 0.914720i | −0.0933993 | − | 0.995629i | \(-0.529773\pi\) |
−0.996722 | + | 0.0809087i | \(0.974218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13252.5 | + | 9654.70i | −0.163158 | + | 0.118864i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5643.82 | − | 3258.46i | −0.0685187 | − | 0.0395593i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38302.1 | − | 66341.2i | −0.458593 | − | 0.794306i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 126152. | + | 84853.3i | 1.48973 | + | 1.00204i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −70486.8 | − | 12428.7i | −0.821056 | − | 0.144774i | −0.252687 | − | 0.967548i | \(-0.581314\pi\) |
−0.568369 | + | 0.822774i | \(0.692425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 61110.1 | − | 51277.5i | 0.702214 | − | 0.589227i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −83264.2 | + | 44687.5i | −0.943943 | + | 0.506609i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8970.46 | − | 10690.6i | −0.100340 | − | 0.119580i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −810.809 | + | 4598.33i | −0.00894923 | + | 0.0507536i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36256.5 | + | 2488.20i | 0.394912 | + | 0.0271019i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 158543. | − | 91534.9i | 1.70431 | − | 0.983982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8937.59 | + | 15480.4i | −0.0948296 | + | 0.164250i | −0.909537 | − | 0.415622i | \(-0.863564\pi\) |
0.814708 | + | 0.579872i | \(0.196897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −115058. | + | 12243.5i | −1.20504 | + | 0.128230i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3233.99 | + | 3854.12i | −0.0334363 | + | 0.0398478i | −0.782503 | − | 0.622646i | \(-0.786058\pi\) |
0.749067 | + | 0.662494i | \(0.230502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −47171.3 | − | 17169.0i | −0.481493 | − | 0.175249i | 0.0898588 | − | 0.995955i | \(-0.471358\pi\) |
−0.571351 | + | 0.820706i | \(0.693581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7047.35 | − | 264.346i | 0.0710239 | − | 0.00266410i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 43193.0 | − | 7616.09i | 0.429828 | − | 0.0757903i | 0.0454512 | − | 0.998967i | \(-0.485527\pi\) |
0.384377 | + | 0.923176i | \(0.374416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −79822.1 | + | 29052.9i | −0.784408 | + | 0.285501i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13436.9 | − | 54190.9i | 0.130404 | − | 0.525916i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5431.07i | − | 0.0520571i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6081.26 | 0.0575740 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −55575.4 | − | 13780.2i | −0.519741 | − | 0.128873i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2558.90 | − | 7030.53i | −0.0236408 | − | 0.0649526i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24127.4 | + | 136833.i | 0.220219 | + | 1.24892i | 0.871618 | + | 0.490186i | \(0.163071\pi\) |
−0.651399 | + | 0.758735i | \(0.725818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −102222. | + | 64243.5i | −0.921841 | + | 0.579350i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 82379.5 | − | 226336.i | 0.734057 | − | 2.01680i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −103874. | − | 87160.2i | −0.914629 | − | 0.767465i | 0.0583648 | − | 0.998295i | \(-0.481411\pi\) |
−0.972994 | + | 0.230830i | \(0.925856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7485.54 | + | 70345.2i | 0.0651364 | + | 0.612118i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12103.8 | − | 6988.11i | −0.104091 | − | 0.0600967i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7478.00 | − | 12952.3i | −0.0635619 | − | 0.110092i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6047.36 | + | 88118.3i | −0.0508075 | + | 0.740334i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23696.0 | + | 4178.25i | 0.196796 | + | 0.0347005i | 0.271177 | − | 0.962529i | \(-0.412587\pi\) |
−0.0743812 | + | 0.997230i | \(0.523698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 39974.2 | − | 33542.4i | 0.328193 | − | 0.275387i | −0.463770 | − | 0.885956i | \(-0.653504\pi\) |
0.791963 | + | 0.610569i | \(0.209059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4135.97 | − | 28623.0i | −0.0335709 | − | 0.232327i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6742.14 | + | 8034.97i | 0.0541064 | + | 0.0644814i | 0.792419 | − | 0.609977i | \(-0.208821\pi\) |
−0.738313 | + | 0.674459i | \(0.764377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2383.39 | − | 13516.8i | 0.0189120 | − | 0.107255i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1303.76 | + | 1938.30i | −0.0102296 | + | 0.0152084i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 193420. | − | 111671.i | 1.50077 | − | 0.866467i | 0.500766 | − | 0.865583i | \(-0.333052\pi\) |
1.00000 | 0.000884863i | \(-0.000281661\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 63028.2 | − | 109168.i | 0.483638 | − | 0.837686i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11458.5 | − | 15728.4i | −0.0869587 | − | 0.119364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 71884.3 | − | 85668.4i | 0.539571 | − | 0.643035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −114748. | − | 41764.8i | −0.851946 | − | 0.310083i | −0.121113 | − | 0.992639i | \(-0.538646\pi\) |
−0.730834 | + | 0.682556i | \(0.760868\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 156662. | − | 63767.2i | 1.15056 | − | 0.468322i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7203.16 | + | 1270.11i | −0.0523329 | + | 0.00922771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85335.1 | + | 31059.4i | −0.613352 | + | 0.223242i | −0.629969 | − | 0.776620i | \(-0.716933\pi\) |
0.0166172 | + | 0.999862i | \(0.494710\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 85302.7 | + | 82163.0i | 0.606597 | + | 0.584270i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25996.6i | − | 0.182908i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −122906. | −0.855645 | −0.427823 | − | 0.903863i | \(-0.640719\pi\) | ||||
−0.427823 | + | 0.903863i | \(0.640719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14848.7 | + | 51531.9i | 0.102291 | + | 0.354998i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1901.62 | − | 5224.66i | −0.0129636 | − | 0.0356173i | 0.933042 | − | 0.359767i | \(-0.117144\pi\) |
−0.946006 | + | 0.324150i | \(0.894922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1959.80 | + | 11114.6i | 0.0132218 | + | 0.0749846i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −81323.0 | − | 89850.0i | −0.542990 | − | 0.599924i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −45262.3 | + | 124357.i | −0.299114 | + | 0.821810i | 0.695534 | + | 0.718493i | \(0.255168\pi\) |
−0.994649 | + | 0.103317i | \(0.967054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22411.8 | − | 18805.8i | −0.146597 | − | 0.123009i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −191434. | − | 84935.5i | −1.23946 | − | 0.549926i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −169493. | − | 97856.9i | −1.08632 | − | 0.627187i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −101449. | − | 175715.i | −0.643676 | − | 1.11488i | −0.984605 | − | 0.174791i | \(-0.944075\pi\) |
0.340929 | − | 0.940089i | \(-0.389258\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1647.55 | − | 806.200i | 0.0103488 | − | 0.00506404i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 168219. | + | 29661.5i | 1.04613 | + | 0.184461i | 0.670195 | − | 0.742185i | \(-0.266211\pi\) |
0.375935 | + | 0.926646i | \(0.377322\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3276.59 | − | 2749.39i | 0.0201749 | − | 0.0169288i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −106820. | + | 148635.i | −0.651241 | + | 0.906174i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −124196. | − | 148011.i | −0.749751 | − | 0.893519i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12770.1 | − | 72422.8i | 0.0763391 | − | 0.432941i | −0.922552 | − | 0.385872i | \(-0.873901\pi\) |
0.998892 | − | 0.0470691i | \(-0.0149881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54586.7 | + | 111553.i | 0.323149 | + | 0.660386i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7728.47 | + | 4462.04i | −0.0453099 | + | 0.0261597i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34850.8 | + | 60363.3i | −0.202356 | + | 0.350491i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 78901.6 | − | 177834.i | 0.453747 | − | 1.02269i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14771.8 | + | 17604.3i | −0.0841404 | + | 0.100275i | −0.806472 | − | 0.591272i | \(-0.798626\pi\) |
0.722332 | + | 0.691547i | \(0.243070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −143751. | − | 52321.0i | −0.811046 | − | 0.295197i | −0.0969904 | − | 0.995285i | \(-0.530922\pi\) |
−0.714056 | + | 0.700089i | \(0.753144\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 184834. | + | 59528.3i | 1.03300 | + | 0.332692i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12555.1 | − | 2213.81i | 0.0695094 | − | 0.0122564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19244.5 | + | 7004.42i | −0.105548 | + | 0.0384164i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44472.6 | − | 12814.6i | 0.241645 | − | 0.0696289i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 350782.i | 1.88835i | 0.329444 | + | 0.944175i | \(0.393139\pi\) | ||||
−0.329444 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 262879. | 1.40210 | 0.701051 | − | 0.713111i | \(-0.252715\pi\) | ||||
0.701051 | + | 0.713111i | \(0.252715\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −114142. | + | 118503.i | −0.603206 | + | 0.626257i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7857.04 | + | 21587.0i | 0.0411430 | + | 0.113039i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29423.4 | − | 166868.i | −0.152674 | − | 0.865855i | −0.960882 | − | 0.276958i | \(-0.910674\pi\) |
0.808208 | − | 0.588897i | \(-0.200438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 191876. | + | 26460.7i | 0.986606 | + | 0.136058i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15829.7 | − | 43491.8i | 0.0806614 | − | 0.221615i | −0.892806 | − | 0.450442i | \(-0.851267\pi\) |
0.973467 | + | 0.228826i | \(0.0734888\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 318905. | + | 267593.i | 1.61043 | + | 1.35131i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −254128. | + | 185137.i | −1.27185 | + | 0.926570i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −63267.2 | − | 36527.3i | −0.313824 | − | 0.181186i | 0.334813 | − | 0.942285i | \(-0.391327\pi\) |
−0.648636 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 135342. | + | 234420.i | 0.665396 | + | 1.15250i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 316082. | + | 212606.i | 1.54029 | + | 1.03605i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3401.51 | − | 599.778i | −0.0164304 | − | 0.00289713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −98911.9 | + | 82997.0i | −0.473605 | + | 0.397402i | −0.848108 | − | 0.529824i | \(-0.822258\pi\) |
0.374503 | + | 0.927226i | \(0.377813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18958.8 | − | 57588.2i | −0.0899882 | − | 0.273343i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 228366. | + | 272156.i | 1.07456 | + | 1.28061i | 0.957796 | + | 0.287450i | \(0.0928074\pi\) |
0.116763 | + | 0.993160i | \(0.462748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5698.10 | + | 32315.6i | −0.0265808 | + | 0.150747i | −0.995210 | − | 0.0977652i | \(-0.968831\pi\) |
0.968629 | + | 0.248512i | \(0.0799417\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27007.7 | − | 1853.48i | −0.124905 | − | 0.00857198i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −154413. | + | 89150.2i | −0.708026 | + | 0.408779i | −0.810330 | − | 0.585974i | \(-0.800712\pi\) |
0.102304 | + | 0.994753i | \(0.467379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13472.3 | + | 23334.7i | −0.0612485 | + | 0.106086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 143718. | − | 15293.3i | 0.647843 | − | 0.0689380i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 124663. | − | 148567.i | 0.557204 | − | 0.664050i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9406.74 | − | 3423.77i | −0.0416919 | − | 0.0151746i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 88689.5 | − | 167846.i | 0.389794 | − | 0.737692i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −100124. | + | 17654.6i | −0.436383 | + | 0.0769462i | −0.387524 | − | 0.921860i | \(-0.626670\pi\) |
−0.0488591 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55565.2 | − | 20224.1i | 0.240167 | − | 0.0874135i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2377.97 | − | 9590.34i | 0.0101933 | − | 0.0411093i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 471270.i | 2.00348i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −126703. | −0.534229 | −0.267115 | − | 0.963665i | \(-0.586070\pi\) | ||||
−0.267115 | + | 0.963665i | \(0.586070\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −93722.6 | − | 23239.0i | −0.391946 | − | 0.0971851i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38725.2 | + | 106397.i | 0.160632 | + | 0.441332i | 0.993732 | − | 0.111790i | \(-0.0356585\pi\) |
−0.833100 | + | 0.553122i | \(0.813436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9463.74 | − | 53671.5i | −0.0389376 | − | 0.220826i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −258990. | − | 136849.i | −1.05699 | − | 0.558512i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −525.145 | + | 1442.82i | −0.00212602 | + | 0.00584118i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 293152. | + | 245983.i | 1.17731 | + | 0.987881i | 0.999993 | + | 0.00372771i | \(0.00118657\pi\) |
0.177318 | + | 0.984154i | \(0.443258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26837.5 | − | 252204.i | −0.106922 | − | 1.00479i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −357988. | − | 206684.i | −1.41492 | − | 0.816905i | −0.419074 | − | 0.907952i | \(-0.637645\pi\) |
−0.995847 | + | 0.0910468i | \(0.970979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 56325.4 | + | 97558.5i | 0.220862 | + | 0.382545i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16629.5 | − | 242315.i | 0.0646940 | − | 0.942680i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40339.3 | + | 7112.92i | 0.155702 | + | 0.0274544i | 0.250956 | − | 0.967999i | \(-0.419255\pi\) |
−0.0952539 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9583.50 | + | 8041.51i | −0.0367014 | + | 0.0307961i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9717.16 | + | 46603.8i | −0.0369237 | + | 0.177087i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −230547. | − | 274755.i | −0.869251 | − | 1.03593i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −53962.7 | + | 306038.i | −0.201889 | + | 1.14497i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −189344. | + | 281498.i | −0.702937 | + | 1.04506i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 171490. | − | 99009.5i | 0.631775 | − | 0.364755i | −0.149664 | − | 0.988737i | \(-0.547819\pi\) |
0.781439 | + | 0.623982i | \(0.214486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 54197.2 | − | 93872.3i | 0.198141 | − | 0.343190i | −0.749785 | − | 0.661682i | \(-0.769843\pi\) |
0.947926 | + | 0.318492i | \(0.103176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2535.29 | + | 3480.05i | 0.00919831 | + | 0.0126260i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5763.84 | − | 6869.08i | 0.0207535 | − | 0.0247330i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −146677. | − | 53386.2i | −0.524146 | − | 0.190773i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31641.9 | − | 229447.i | 0.112221 | − | 0.813754i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −81581.8 | + | 14385.1i | −0.287170 | + | 0.0506358i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 162629. | − | 59192.0i | 0.568185 | − | 0.206803i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −358039. | − | 344860.i | −1.24160 | − | 1.19590i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 309972.i | 1.06695i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 570303. | 1.94855 | 0.974274 | − | 0.225368i | \(-0.0723584\pi\) | ||||
0.974274 | + | 0.225368i | \(0.0723584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26156.1 | + | 90774.2i | 0.0887103 | + | 0.307867i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −60704.3 | − | 166784.i | −0.204374 | − | 0.561514i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30332.4 | − | 172024.i | −0.101375 | − | 0.574929i | −0.992606 | − | 0.121379i | \(-0.961268\pi\) |
0.891231 | − | 0.453550i | \(-0.149843\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 162945. | − | 505941.i | 0.540626 | − | 1.67863i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14636.2 | + | 40212.6i | −0.0482086 | + | 0.132452i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16771.8 | + | 14073.2i | 0.0548440 | + | 0.0460196i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −342087. | − | 151777.i | −1.11058 | − | 0.492743i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −381382. | − | 220191.i | −1.22928 | − | 0.709723i | −0.262398 | − | 0.964960i | \(-0.584513\pi\) |
−0.966879 | + | 0.255237i | \(0.917847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29676.9 | + | 51401.8i | 0.0949717 | + | 0.164496i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 87151.5 | − | 42646.2i | 0.276917 | − | 0.135505i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 438021. | + | 77234.9i | 1.38190 | + | 0.243667i | 0.814687 | − | 0.579901i | \(-0.196909\pi\) |
0.567218 | + | 0.823568i | \(0.308020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −167982. | + | 140953.i | −0.526217 | + | 0.441549i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14655.4 | − | 14299.8i | 0.0455861 | − | 0.0444799i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −388030. | − | 462436.i | −1.19851 | − | 1.42833i | −0.876374 | − | 0.481632i | \(-0.840044\pi\) |
−0.322134 | − | 0.946694i | \(-0.604400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31098.8 | + | 176370.i | −0.0953831 | + | 0.540944i | 0.899246 | + | 0.437443i | \(0.144116\pi\) |
−0.994629 | + | 0.103502i | \(0.966995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 158981. | + | 324892.i | 0.484212 | + | 0.989532i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46700.6 | + | 26962.6i | −0.141249 | + | 0.0815504i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 283964. | − | 491839.i | 0.852925 | − | 1.47731i | −0.0256315 | − | 0.999671i | \(-0.508160\pi\) |
0.878557 | − | 0.477638i | \(-0.158507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 185928. | − | 419058.i | 0.554610 | − | 1.25002i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5012.03 | − | 5973.10i | 0.0148478 | − | 0.0176949i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 285482. | + | 103907.i | 0.839926 | + | 0.305708i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 66464.6 | − | 60156.9i | 0.194213 | − | 0.175782i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −295856. | + | 52167.4i | −0.858626 | + | 0.151399i | −0.585592 | − | 0.810606i | \(-0.699138\pi\) |
−0.273033 | + | 0.962005i | \(0.588027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6616.28 | + | 2408.13i | −0.0190714 | + | 0.00694143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 243913. | − | 70282.3i | 0.698328 | − | 0.201220i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 452524.i | 1.28686i | 0.765503 | + | 0.643432i | \(0.222490\pi\) | ||||
−0.765503 | + | 0.643432i | \(0.777510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7240.97 | −0.0204533 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −313649. | + | 325635.i | −0.880026 | + | 0.913654i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 222816. | + | 612183.i | 0.621003 | + | 1.70619i | 0.704520 | + | 0.709684i | \(0.251162\pi\) |
−0.0835172 | + | 0.996506i | \(0.526615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22312.8 | + | 126542.i | 0.0617739 | + | 0.350337i | 0.999991 | + | 0.00428948i | \(0.00136539\pi\) |
−0.938217 | + | 0.346048i | \(0.887524\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −263649. | − | 647727.i | −0.725089 | − | 1.78138i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20630.8 | − | 56682.7i | 0.0563645 | − | 0.154860i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −304661. | − | 255641.i | −0.826875 | − | 0.693831i | 0.127696 | − | 0.991813i | \(-0.459242\pi\) |
−0.954571 | + | 0.297983i | \(0.903686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14876.8 | − | 10838.0i | 0.0401119 | − | 0.0292223i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −82363.0 | − | 47552.3i | −0.220623 | − | 0.127376i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −267072. | − | 462583.i | −0.710736 | − | 1.23103i | −0.964581 | − | 0.263785i | \(-0.915029\pi\) |
0.253846 | − | 0.967245i | \(-0.418304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 435045. | + | 292624.i | 1.15023 | + | 0.773676i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −528258. | − | 93146.1i | −1.38764 | − | 0.244678i | −0.570582 | − | 0.821240i | \(-0.693283\pi\) |
−0.817053 | + | 0.576563i | \(0.804394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −71460.3 | + | 59962.3i | −0.186502 | + | 0.156494i | −0.731258 | − | 0.682101i | \(-0.761067\pi\) |
0.544756 | + | 0.838594i | \(0.316622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 158668. | + | 201470.i | 0.411440 | + | 0.522430i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29934.9 | − | 35675.0i | −0.0771262 | − | 0.0919154i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −80387.6 | + | 455901.i | −0.205792 | + | 1.16711i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −76006.8 | − | 5216.17i | −0.193338 | − | 0.0132684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 107355. | − | 61981.7i | 0.271346 | − | 0.156661i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 257879. | − | 446660.i | 0.647676 | − | 1.12181i | −0.336001 | − | 0.941862i | \(-0.609074\pi\) |
0.983677 | − | 0.179946i | \(-0.0575923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 165258. | − | 17585.3i | 0.412434 | − | 0.0438877i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −106854. | + | 127344.i | −0.264999 | + | 0.315814i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −89142.9 | − | 32445.4i | −0.219689 | − | 0.0799602i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21205.1 | − | 33740.7i | −0.0519323 | − | 0.0826329i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −323390. | + | 57022.3i | −0.787064 | + | 0.138781i | −0.552713 | − | 0.833371i | \(-0.686408\pi\) |
−0.234351 | + | 0.972152i | \(0.575296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −122155. | + | 44460.8i | −0.295454 | + | 0.107536i | −0.485494 | − | 0.874240i | \(-0.661360\pi\) |
0.190040 | + | 0.981776i | \(0.439138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 90407.4 | − | 364612.i | 0.217313 | − | 0.876419i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 667031.i | 1.59345i | 0.604345 | + | 0.796723i | \(0.293435\pi\) | ||||
−0.604345 | + | 0.796723i | \(0.706565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 370667. | 0.880024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2939.37 | + | 728.833i | 0.00693574 | + | 0.00171975i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −129771. | − | 356543.i | −0.304335 | − | 0.836153i | −0.993734 | − | 0.111771i | \(-0.964348\pi\) |
0.689399 | − | 0.724382i | \(-0.257875\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −112730. | − | 639322.i | −0.262758 | − | 1.49017i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12170.9 | − | 324470.i | −0.0281962 | − | 0.751700i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 228126. | − | 626770.i | 0.525295 | − | 1.44324i | −0.339257 | − | 0.940694i | \(-0.610176\pi\) |
0.864552 | − | 0.502543i | \(-0.167602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 254247. | + | 213339.i | 0.581906 | + | 0.488277i | 0.885572 | − | 0.464501i | \(-0.153766\pi\) |
−0.303666 | + | 0.952778i | \(0.598211\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3142.04 | + | 29527.2i | 0.00714800 | + | 0.0671731i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4923.92 | + | 2842.83i | 0.0111344 | + | 0.00642846i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 115262. | + | 199639.i | 0.259079 | + | 0.448738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40352.8 | + | 587996.i | −0.0901617 | + | 1.31378i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 837708. | + | 147711.i | 1.86058 | + | 0.328070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −558140. | + | 468335.i | −1.23229 | + | 1.03401i | −0.234203 | + | 0.972188i | \(0.575248\pi\) |
−0.998087 | + | 0.0618264i | \(0.980307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −111696. | − | 3466.81i | −0.245149 | − | 0.00760891i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −148547. | − | 177031.i | −0.324105 | − | 0.386254i | 0.579248 | − | 0.815152i | \(-0.303346\pi\) |
−0.903353 | + | 0.428898i | \(0.858902\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9154.69 | − | 51918.8i | 0.0198566 | − | 0.112612i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −321094. | + | 477372.i | −0.692369 | + | 1.02935i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 192239. | − | 110989.i | 0.412098 | − | 0.237925i | −0.279593 | − | 0.960119i | \(-0.590199\pi\) |
0.691691 | + | 0.722194i | \(0.256866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −192484. | + | 333392.i | −0.410216 | + | 0.710516i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8781.82 | + | 12054.3i | 0.0186068 | + | 0.0255405i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59763.8 | + | 71223.8i | −0.125893 | + | 0.150033i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 660421. | + | 240374.i | 1.38314 | + | 0.503420i | 0.923127 | − | 0.384494i | \(-0.125624\pi\) |
0.460008 | + | 0.887915i | \(0.347846\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25874.0 | + | 20107.4i | 0.0538761 | + | 0.0418688i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 593903. | − | 104721.i | 1.22955 | − | 0.216803i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −163194. | + | 59397.8i | −0.335922 | + | 0.122266i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −137611. | − | 132546.i | −0.281643 | − | 0.271277i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16939.1i | − | 0.0344710i | −0.999851 | − | 0.0172355i | \(-0.994514\pi\) | ||
0.999851 | − | 0.0172355i | \(-0.00548649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −97336.8 | −0.196955 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 166660. | + | 578391.i | 0.335316 | + | 1.16371i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4310.12 | − | 11842.0i | −0.00862285 | − | 0.0236911i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30941.8 | − | 175479.i | −0.0615535 | − | 0.349087i | −0.999993 | − | 0.00364447i | \(-0.998840\pi\) |
0.938440 | − | 0.345443i | \(-0.112271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −555520. | + | 119582.i | −1.09891 | + | 0.236551i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12972.3 | + | 35641.2i | −0.0255176 | + | 0.0701089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 109899. | + | 92216.5i | 0.214973 | + | 0.180383i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −156206. | − | 69305.4i | −0.303849 | − | 0.134812i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −187920. | − | 108496.i | −0.363509 | − | 0.209872i | 0.307110 | − | 0.951674i | \(-0.400638\pi\) |
−0.670619 | + | 0.741802i | \(0.733971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20061.6 | + | 34747.7i | 0.0385918 | + | 0.0668430i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 264803. | − | 129577.i | 0.506578 | − | 0.247886i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −98926.4 | − | 17443.4i | −0.188207 | − | 0.0331860i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −113085. | + | 94889.8i | −0.213962 | + | 0.179536i | −0.743470 | − | 0.668770i | \(-0.766821\pi\) |
0.529507 | + | 0.848305i | \(0.322377\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 59649.0 | + | 528083.i | 0.112240 | + | 0.993681i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 79981.9 | + | 95318.7i | 0.149678 | + | 0.178379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −124786. | + | 707699.i | −0.232252 | + | 1.31717i | 0.616073 | + | 0.787689i | \(0.288723\pi\) |
−0.848325 | + | 0.529476i | \(0.822388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 263895. | + | 539295.i | 0.488492 | + | 0.998279i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 969221. | − | 559580.i | 1.78438 | − | 1.03021i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34667.1 | + | 60045.2i | −0.0634788 | + | 0.109948i | −0.896018 | − | 0.444017i | \(-0.853553\pi\) |
0.832539 | + | 0.553966i | \(0.186886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9455.86 | − | 21312.3i | 0.0172213 | − | 0.0388145i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 349329. | − | 416315.i | 0.632787 | − | 0.754126i | −0.350425 | − | 0.936591i | \(-0.613963\pi\) |
0.983212 | + | 0.182464i | \(0.0584074\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −915835. | − | 333337.i | −1.65008 | − | 0.600580i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42587.8 | + | 197843.i | 0.0763210 | + | 0.354551i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19066.3 | + | 3361.91i | −0.0339862 | + | 0.00599269i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 133159. | − | 48466.0i | 0.236097 | − | 0.0859324i | −0.221262 | − | 0.975214i | \(-0.571018\pi\) |
0.457359 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 279396. | − | 80506.5i | 0.492754 | − | 0.141985i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.18080e6i | 2.07149i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −497775. | −0.868643 | −0.434322 | − | 0.900758i | \(-0.643012\pi\) | ||||
−0.434322 | + | 0.900758i | \(0.643012\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −284708. | + | 295588.i | −0.494216 | + | 0.513101i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 130892. | + | 359622.i | 0.226018 | + | 0.620979i | 0.999924 | − | 0.0123215i | \(-0.00392215\pi\) |
−0.773906 | + | 0.633300i | \(0.781700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3447.80 | + | 19553.4i | 0.00592233 | + | 0.0335872i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 115321. | − | 148393.i | 0.197054 | − | 0.253566i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38798.4 | + | 106598.i | −0.0659513 | + | 0.181200i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16103.1 | + | 13512.1i | 0.0272305 | + | 0.0228491i | 0.656301 | − | 0.754499i | \(-0.272120\pi\) |
−0.629071 | + | 0.777348i | \(0.716564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −517208. | + | 376796.i | −0.870075 | + | 0.633867i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −337649. | − | 194942.i | −0.565076 | − | 0.326247i | 0.190104 | − | 0.981764i | \(-0.439117\pi\) |
−0.755180 | + | 0.655517i | \(0.772451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8263.86 | − | 14313.4i | −0.0137588 | − | 0.0238309i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34738.6 | + | 23366.2i | 0.0575401 | + | 0.0387031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 134293. | + | 23679.5i | 0.221299 | + | 0.0390209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48854.3 | − | 40993.6i | 0.0800941 | − | 0.0672069i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14820.1 | + | 477485.i | −0.0241729 | + | 0.778819i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 287974. | + | 343194.i | 0.467319 | + | 0.556930i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 160183. | − | 908442.i | 0.258622 | − | 1.46672i | −0.527978 | − | 0.849258i | \(-0.677050\pi\) |
0.786600 | − | 0.617463i | \(-0.211839\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 414398. | + | 28439.2i | 0.665678 | + | 0.0456840i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21244.3 | − | 12265.4i | 0.0339539 | − | 0.0196033i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −130164. | + | 225450.i | −0.206987 | + | 0.358512i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 585148. | − | 62266.5i | 0.925830 | − | 0.0985190i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 591632. | − | 705079.i | 0.931397 | − | 1.11000i | −0.0623181 | − | 0.998056i | \(-0.519849\pi\) |
0.993715 | − | 0.111939i | \(-0.0357062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −187354. | − | 68191.5i | −0.293475 | − | 0.106816i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.20786e6 | − | 45306.6i | 1.88257 | − | 0.0706149i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 511732. | − | 90232.2i | 0.793618 | − | 0.139936i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28780.9 | − | 10475.4i | 0.0444133 | − | 0.0161651i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −136171. | + | 549177.i | −0.209093 | + | 0.843268i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 497784.i | − | 0.760578i | −0.924868 | − | 0.380289i | \(-0.875824\pi\) | ||
0.924868 | − | 0.380289i | \(-0.124176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 275127. | 0.418304 | 0.209152 | − | 0.977883i | \(-0.432930\pi\) | ||||
0.209152 | + | 0.977883i | \(0.432930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −785654. | − | 194807.i | −1.18864 | − | 0.294729i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −102372. | − | 281265.i | −0.154122 | − | 0.423448i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16965.9 | − | 96218.7i | −0.0254176 | − | 0.144150i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8490.85 | + | 5336.25i | −0.0126585 | + | 0.00795551i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23033.1 | − | 63282.9i | 0.0341717 | − | 0.0938859i | −0.921434 | − | 0.388536i | \(-0.872981\pi\) |
0.955605 | + | 0.294650i | \(0.0952031\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −972832. | − | 816303.i | −1.43628 | − | 1.20518i | −0.941883 | − | 0.335942i | \(-0.890945\pi\) |
−0.494394 | − | 0.869238i | \(-0.664610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18923.5 | − | 177833.i | −0.0278031 | − | 0.261279i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.12901e6 | − | 651837.i | −1.65078 | − | 0.953077i | −0.976753 | − | 0.214369i | \(-0.931231\pi\) |
−0.674025 | − | 0.738708i | \(-0.735436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −442947. | − | 767206.i | −0.644529 | − | 1.11636i | −0.984410 | − | 0.175888i | \(-0.943720\pi\) |
0.339881 | − | 0.940468i | \(-0.389613\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8373.20 | + | 122009.i | −0.0121252 | + | 0.176681i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −195853. | − | 34534.1i | −0.282253 | − | 0.0497689i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 602255. | − | 505352.i | 0.863789 | − | 0.724805i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −61749.3 | + | 48630.7i | −0.0881417 | + | 0.0694160i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 137520. | + | 163890.i | 0.195362 | + | 0.232824i | 0.854829 | − | 0.518910i | \(-0.173662\pi\) |
−0.659466 | + | 0.751734i | \(0.729218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48249.9 | − | 273639.i | 0.0682188 | − | 0.386888i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −177855. | + | 264417.i | −0.250271 | + | 0.372078i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 652018. | − | 376443.i | 0.913159 | − | 0.527213i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3373.95 | + | 5843.85i | −0.00470296 | + | 0.00814577i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −603986. | − | 829059.i | −0.837937 | − | 1.15019i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −337041. | + | 401670.i | −0.465397 | + | 0.554639i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −998450. | − | 363406.i | −1.37223 | − | 0.499452i | −0.452419 | − | 0.891805i | \(-0.649439\pi\) |
−0.919815 | + | 0.392353i | \(0.871661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −136679. | + | 55633.3i | −0.186969 | + | 0.0761032i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −730137. | + | 128743.i | −0.994129 | + | 0.175292i | −0.646971 | − | 0.762515i | \(-0.723965\pi\) |
−0.347158 | + | 0.937806i | \(0.612853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −317020. | + | 115386.i | −0.429636 | + | 0.156375i | −0.547781 | − | 0.836622i | \(-0.684527\pi\) |
0.118145 | + | 0.992996i | \(0.462305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42243.6 | − | 40688.7i | −0.0569842 | − | 0.0548868i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 783845.i | − | 1.05247i | −0.850340 | − | 0.526234i | \(-0.823604\pi\) | ||
0.850340 | − | 0.526234i | \(-0.176396\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.05160e6 | −1.40546 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −190892. | − | 662484.i | −0.253950 | − | 0.881328i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −311027. | − | 854539.i | −0.411868 | − | 1.13160i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59475.9 | + | 337304.i | 0.0783979 | + | 0.444617i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 918202. | + | 1.01448e6i | 1.20479 | + | 1.33111i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14046.6 | − | 38592.7i | 0.0183466 | − | 0.0504068i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 544116. | + | 456568.i | 0.707444 | + | 0.593616i | 0.923881 | − | 0.382680i | \(-0.124999\pi\) |
−0.216436 | + | 0.976297i | \(0.569443\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −588815. | − | 261246.i | −0.762081 | − | 0.338120i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54907.6 | + | 31700.9i | 0.0707425 | + | 0.0408432i | 0.534954 | − | 0.844881i | \(-0.320329\pi\) |
−0.464212 | + | 0.885724i | \(0.653662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 87691.3 | + | 151886.i | 0.112470 | + | 0.194803i | 0.916765 | − | 0.399426i | \(-0.130791\pi\) |
−0.804296 | + | 0.594229i | \(0.797457\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 644893. | − | 315568.i | 0.823382 | − | 0.402909i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 914676. | + | 161282.i | 1.16257 | + | 0.204993i | 0.721458 | − | 0.692458i | \(-0.243472\pi\) |
0.441114 | + | 0.897451i | \(0.354583\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14245.6 | − | 11953.5i | 0.0180251 | − | 0.0151249i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −824145. | + | 210015.i | −1.03812 | + | 0.264543i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 100630. | + | 119927.i | 0.126190 | + | 0.150388i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 267580. | − | 1.51752e6i | 0.334047 | − | 1.89447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −55205.3 | − | 112817.i | −0.0686114 | − | 0.140214i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61188.0 | + | 35326.9i | −0.0757088 | + | 0.0437105i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −97458.0 | + | 168802.i | −0.120052 | + | 0.207935i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17042.8 | + | 38412.3i | −0.0209009 | + | 0.0471081i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −188225. | + | 224318.i | −0.229816 | + | 0.273885i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 763552. | + | 277910.i | 0.928163 | + | 0.337824i | 0.761481 | − | 0.648187i | \(-0.224472\pi\) |
0.166682 | + | 0.986011i | \(0.446695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 311328. | + | 100267.i | 0.376782 | + | 0.121348i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 529460. | − | 93358.1i | 0.637964 | − | 0.112490i | 0.154695 | − | 0.987962i | \(-0.450560\pi\) |
0.483269 | + | 0.875472i | \(0.339449\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −304336. | + | 110769.i | −0.365100 | + | 0.132885i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.58321e6 | − | 456195.i | 1.89102 | − | 0.544889i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 72622.6i | 0.0863640i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −214963. | −0.254526 | −0.127263 | − | 0.991869i | \(-0.540619\pi\) | ||||
−0.127263 | + | 0.991869i | \(0.540619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −111605. | + | 115869.i | −0.131572 | + | 0.136600i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6675.42 | + | 18340.6i | 0.00783566 | + | 0.0215283i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39676.4 | − | 225016.i | −0.0463712 | − | 0.262984i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.03161e6 | − | 142264.i | −1.20048 | − | 0.165552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −418240. | + | 1.14911e6i | −0.484612 | + | 1.33146i | 0.420887 | + | 0.907113i | \(0.361719\pi\) |
−0.905499 | + | 0.424348i | \(0.860503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 119623. | + | 100376.i | 0.138012 | + | 0.115806i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36598.5 | + | 26662.7i | −0.0420436 | + | 0.0306296i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 260464. | + | 150379.i | 0.297938 | + | 0.172014i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 701240. | + | 1.21458e6i | 0.798707 | + | 1.38340i | 0.920458 | + | 0.390841i | \(0.127816\pi\) |
−0.121751 | + | 0.992561i | \(0.538851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −374876. | − | 252152.i | −0.425164 | − | 0.285977i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.59805e6 | − | 281779.i | −1.80472 | − | 0.318222i | −0.832811 | − | 0.553558i | \(-0.813270\pi\) |
−0.971914 | + | 0.235336i | \(0.924381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 562723. | − | 472180.i | 0.632807 | − | 0.530988i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 62134.5 | + | 12955.4i | 0.0695775 | + | 0.0145073i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 358034. | + | 426688.i | 0.399231 | + | 0.475785i | 0.927785 | − | 0.373115i | \(-0.121710\pi\) |
−0.528554 | + | 0.848899i | \(0.677266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27614.7 | + | 156611.i | −0.0306625 | + | 0.173896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 393807. | + | 27026.1i | 0.435435 | + | 0.0298829i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.07755e6 | − | 622122.i | 1.18645 | − | 0.684998i | 0.228954 | − | 0.973437i | \(-0.426470\pi\) |
0.957498 | + | 0.288439i | \(0.0931362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −560598. | + | 970985.i | −0.614674 | + | 1.06465i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −760212. | + | 80895.4i | −0.830063 | + | 0.0883283i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27681.9 | − | 32990.0i | 0.0300994 | − | 0.0358711i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 856902. | + | 311887.i | 0.927864 | + | 0.337715i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 234756. | − | 444279.i | 0.253142 | − | 0.479075i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.39951e6 | − | 246771.i | 1.50287 | − | 0.264996i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42404.6 | − | 15434.0i | 0.0453482 | − | 0.0165054i | −0.319246 | − | 0.947672i | \(-0.603430\pi\) |
0.364595 | + | 0.931166i | \(0.381208\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11763.7 | − | 47442.9i | 0.0125284 | − | 0.0505270i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 699818.i | 0.742244i | 0.928584 | + | 0.371122i | \(0.121027\pi\) | ||||
−0.928584 | + | 0.371122i | \(0.878973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67463.4 | −0.0712594 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 53122.6 | + | 13172.0i | 0.0558818 | + | 0.0138562i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 164161. | + | 451029.i | 0.171981 | + | 0.472514i | 0.995499 | − | 0.0947767i | \(-0.0302137\pi\) |
−0.823517 | + | 0.567291i | \(0.807991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 335893. | + | 1.90495e6i | 0.350458 | + | 1.98755i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −455629. | − | 240753.i | −0.473449 | − | 0.250169i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 182645. | − | 501813.i | 0.189017 | − | 0.519320i | −0.808597 | − | 0.588363i | \(-0.799773\pi\) |
0.997614 | + | 0.0690436i | \(0.0219948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 602750. | + | 505767.i | 0.621247 | + | 0.521288i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7125.06 | − | 66957.6i | −0.00731399 | − | 0.0687330i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −455803. | − | 263158.i | −0.465998 | − | 0.269044i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15806.5 | − | 27377.7i | −0.0160949 | − | 0.0278772i | 0.857866 | − | 0.513874i | \(-0.171790\pi\) |
−0.873961 | + | 0.485997i | \(0.838457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −85617.3 | + | 1.24756e6i | −0.0868287 | + | 1.26521i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.38018e6 | − | 243363.i | −1.39408 | − | 0.245815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 333671. | − | 279983.i | 0.335682 | − | 0.281670i | −0.459328 | − | 0.888267i | \(-0.651910\pi\) |
0.795010 | + | 0.606596i | \(0.207465\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.03211e6 | + | 339784.i | −1.03418 | + | 0.340465i |
(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.k.a.5.12 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.125.3 | 72 | |||
27.11 | odd | 18 | inner | 108.5.k.a.65.12 | yes | 72 | |
27.16 | even | 9 | 324.5.k.a.197.3 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.12 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.65.12 | yes | 72 | 27.11 | odd | 18 | inner | |
324.5.k.a.125.3 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.197.3 | 72 | 27.16 | even | 9 |