Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), degree \(4\), 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: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 159.1 | ||
Character | \(\chi\) | \(=\) | 256.159 |
Dual form | 256.3.h.b.95.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.10187 | − | 5.07436i | −0.700624 | − | 1.69145i | −0.722197 | − | 0.691688i | \(-0.756867\pi\) |
0.0215732 | − | 0.999767i | \(-0.493133\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.74699 | + | 4.21761i | −0.349399 | + | 0.843523i | 0.647293 | + | 0.762242i | \(0.275901\pi\) |
−0.996691 | + | 0.0812812i | \(0.974099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.392379 | + | 0.392379i | −0.0560541 | + | 0.0560541i | −0.734578 | − | 0.678524i | \(-0.762620\pi\) |
0.678524 | + | 0.734578i | \(0.262620\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.9674 | + | 14.9674i | −1.66304 | + | 1.66304i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.90924 | + | 7.02353i | −0.264477 | + | 0.638503i | −0.999205 | − | 0.0398581i | \(-0.987309\pi\) |
0.734729 | + | 0.678361i | \(0.237309\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50555 | + | 10.8774i | 0.346581 | + | 0.836720i | 0.997019 | + | 0.0771604i | \(0.0245853\pi\) |
−0.650438 | + | 0.759559i | \(0.725415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0737 | 1.67158 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 10.5402i | − | 0.620012i | −0.950735 | − | 0.310006i | \(-0.899669\pi\) | ||
0.950735 | − | 0.310006i | \(-0.100331\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.88707 | − | 0.781651i | 0.0993196 | − | 0.0411395i | −0.332470 | − | 0.943114i | \(-0.607882\pi\) |
0.431790 | + | 0.901974i | \(0.357882\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.81580 | + | 1.16634i | 0.134086 | + | 0.0555401i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.445453 | − | 0.445453i | −0.0193675 | − | 0.0193675i | 0.697357 | − | 0.716724i | \(-0.254359\pi\) |
−0.716724 | + | 0.697357i | \(0.754359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.94139 | + | 2.94139i | 0.117656 | + | 0.117656i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 61.7400 | + | 25.5735i | 2.28667 | + | 0.947168i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.741814 | + | 0.307270i | −0.0255798 | + | 0.0105955i | −0.395437 | − | 0.918493i | \(-0.629407\pi\) |
0.369857 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.6947i | 1.53854i | 0.638924 | + | 0.769270i | \(0.279380\pi\) | ||||
−0.638924 | + | 0.769270i | \(0.720620\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 41.7548 | 1.26530 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.969419 | − | 2.34038i | −0.0276977 | − | 0.0668681i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.5080 | + | 35.0255i | −0.392109 | + | 0.946635i | 0.597371 | + | 0.801965i | \(0.296212\pi\) |
−0.989480 | + | 0.144670i | \(0.953788\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45.7256 | − | 45.7256i | 1.17245 | − | 1.17245i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3365 | + | 11.3365i | −0.276501 | + | 0.276501i | −0.831711 | − | 0.555209i | \(-0.812638\pi\) |
0.555209 | + | 0.831711i | \(0.312638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14.6421 | − | 35.3493i | 0.340515 | − | 0.822076i | −0.657149 | − | 0.753761i | \(-0.728238\pi\) |
0.997664 | − | 0.0683149i | \(-0.0217622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36.9787 | − | 89.2744i | −0.821748 | − | 1.98388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −80.5164 | −1.71312 | −0.856558 | − | 0.516051i | \(-0.827402\pi\) | ||||
−0.856558 | + | 0.516051i | \(0.827402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6921i | 0.993716i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −53.4849 | + | 22.1542i | −1.04872 | + | 0.434395i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 66.6128 | + | 27.5919i | 1.25685 | + | 0.520602i | 0.908940 | − | 0.416927i | \(-0.136893\pi\) |
0.347905 | + | 0.937530i | \(0.386893\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.5401 | − | 24.5401i | −0.446184 | − | 0.446184i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.93277 | − | 7.93277i | −0.139171 | − | 0.139171i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −65.0706 | − | 26.9531i | −1.10289 | − | 0.456833i | −0.244408 | − | 0.969673i | \(-0.578594\pi\) |
−0.858484 | + | 0.512840i | \(0.828594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −87.4322 | + | 36.2156i | −1.43331 | + | 0.593698i | −0.958168 | − | 0.286208i | \(-0.907605\pi\) |
−0.475147 | + | 0.879906i | \(0.657605\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 11.7457i | − | 0.186440i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −53.7476 | −0.826887 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.12379 | + | 17.1984i | 0.106325 | + | 0.256692i | 0.968084 | − | 0.250627i | \(-0.0806367\pi\) |
−0.861759 | + | 0.507319i | \(0.830637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.32411 | + | 3.19668i | −0.0191900 | + | 0.0463287i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8103 | + | 14.8103i | −0.208596 | + | 0.208596i | −0.803671 | − | 0.595074i | \(-0.797123\pi\) |
0.595074 | + | 0.803671i | \(0.297123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.6720 | − | 18.6720i | 0.255781 | − | 0.255781i | −0.567555 | − | 0.823336i | \(-0.692110\pi\) |
0.823336 | + | 0.567555i | \(0.192110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.74326 | − | 21.1081i | 0.116577 | − | 0.281441i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.61436 | − | 3.89741i | −0.0209657 | − | 0.0506157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −36.2398 | −0.458732 | −0.229366 | − | 0.973340i | \(-0.573665\pi\) | ||||
−0.229366 | + | 0.973340i | \(0.573665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 176.540i | − | 2.17951i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −27.0868 | + | 11.2197i | −0.326347 | + | 0.135177i | −0.539841 | − | 0.841767i | \(-0.681516\pi\) |
0.213494 | + | 0.976944i | \(0.431516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44.4545 | + | 18.4137i | 0.522994 | + | 0.216631i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.11840 | + | 3.11840i | 0.0358436 | + | 0.0358436i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −56.4944 | − | 56.4944i | −0.634769 | − | 0.634769i | 0.314491 | − | 0.949260i | \(-0.398166\pi\) |
−0.949260 | + | 0.314491i | \(0.898166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.03592 | − | 2.50016i | −0.0663288 | − | 0.0274743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 242.020 | − | 100.248i | 2.60237 | − | 1.07794i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.32448i | 0.0981525i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 158.579 | 1.63484 | 0.817419 | − | 0.576043i | \(-0.195404\pi\) | ||||
0.817419 | + | 0.576043i | \(0.195404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −61.5800 | − | 148.667i | −0.622021 | − | 1.50169i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 53.8420 | − | 129.986i | 0.533089 | − | 1.28699i | −0.396379 | − | 0.918087i | \(-0.629733\pi\) |
0.929468 | − | 0.368903i | \(-0.120267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.94607 | − | 9.94607i | 0.0965638 | − | 0.0965638i | −0.657175 | − | 0.753738i | \(-0.728249\pi\) |
0.753738 | + | 0.657175i | \(0.228249\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.83837 | + | 9.83837i | −0.0936987 | + | 0.0936987i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −68.8129 | + | 166.129i | −0.643111 | + | 1.55261i | 0.179350 | + | 0.983785i | \(0.442601\pi\) |
−0.822461 | + | 0.568822i | \(0.807399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.61301 | − | 8.72257i | −0.0331469 | − | 0.0800236i | 0.906439 | − | 0.422336i | \(-0.138790\pi\) |
−0.939586 | + | 0.342313i | \(0.888790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 208.226 | 1.87591 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 85.8345i | 0.759598i | 0.925069 | + | 0.379799i | \(0.124007\pi\) | ||||
−0.925069 | + | 0.379799i | \(0.875993\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.65695 | − | 1.10055i | 0.0231039 | − | 0.00956997i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −230.241 | − | 95.3691i | −1.96788 | − | 0.815121i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.13575 | + | 4.13575i | 0.0347542 | + | 0.0347542i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 44.6936 | + | 44.6936i | 0.369369 | + | 0.369369i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 81.3537 | + | 33.6978i | 0.661412 | + | 0.273966i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −122.985 | + | 50.9419i | −0.983877 | + | 0.407535i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2873i | 0.136120i | 0.997681 | + | 0.0680601i | \(0.0216810\pi\) | ||||
−0.997681 | + | 0.0680601i | \(0.978319\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −210.151 | −1.62908 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 40.2223 | + | 97.1053i | 0.307041 | + | 0.741262i | 0.999798 | + | 0.0200911i | \(0.00639562\pi\) |
−0.692758 | + | 0.721171i | \(0.743604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.433744 | + | 1.04715i | −0.00326123 | + | 0.00787331i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −215.719 | + | 215.719i | −1.59792 | + | 1.59792i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 25.5351 | − | 25.5351i | 0.186387 | − | 0.186387i | −0.607745 | − | 0.794132i | \(-0.707926\pi\) |
0.794132 | + | 0.607745i | \(0.207926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 52.2202 | − | 126.071i | 0.375685 | − | 0.906984i | −0.617079 | − | 0.786901i | \(-0.711684\pi\) |
0.992764 | − | 0.120083i | \(-0.0383160\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 169.235 | + | 408.570i | 1.20025 | + | 2.89766i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −89.5052 | −0.625910 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.66548i | − | 0.0252792i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 247.081 | − | 102.344i | 1.68083 | − | 0.696221i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −151.298 | − | 62.6697i | −1.01542 | − | 0.420602i | −0.187993 | − | 0.982170i | \(-0.560198\pi\) |
−0.827430 | + | 0.561569i | \(0.810198\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −123.292 | − | 123.292i | −0.816505 | − | 0.816505i | 0.169095 | − | 0.985600i | \(-0.445916\pi\) |
−0.985600 | + | 0.169095i | \(0.945916\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 157.759 | + | 157.759i | 1.03111 | + | 1.03111i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −201.158 | − | 83.3223i | −1.29779 | − | 0.537563i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −107.069 | + | 44.3494i | −0.681968 | + | 0.282480i | −0.696649 | − | 0.717412i | \(-0.745327\pi\) |
0.0146813 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 396.012i | − | 2.49064i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.349573 | 0.00217126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 48.6441 | + | 117.437i | 0.298430 | + | 0.720474i | 0.999969 | + | 0.00784306i | \(0.00249655\pi\) |
−0.701539 | + | 0.712631i | \(0.747503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −72.9453 | + | 176.106i | −0.442093 | + | 1.06731i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 88.6392 | − | 88.6392i | 0.530774 | − | 0.530774i | −0.390029 | − | 0.920803i | \(-0.627535\pi\) |
0.920803 | + | 0.390029i | \(0.127535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.4841 | − | 21.4841i | 0.127125 | − | 0.127125i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.5452 | + | 39.9437i | −0.0967558 | + | 0.233589i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −87.2836 | − | 210.721i | −0.504530 | − | 1.21804i | −0.946993 | − | 0.321255i | \(-0.895895\pi\) |
0.442463 | − | 0.896787i | \(-0.354105\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.30827 | −0.0131901 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 386.844i | 2.18556i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.53118 | − | 2.29109i | 0.0309005 | − | 0.0127994i | −0.367180 | − | 0.930150i | \(-0.619677\pi\) |
0.398080 | + | 0.917351i | \(0.369677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 273.836 | + | 113.427i | 1.51291 | + | 0.626666i | 0.976155 | − | 0.217075i | \(-0.0696516\pi\) |
0.536751 | + | 0.843741i | \(0.319652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 367.542 | + | 367.542i | 2.00843 | + | 2.00843i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −122.379 | − | 122.379i | −0.661506 | − | 0.661506i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 74.0295 | + | 30.6640i | 0.395880 | + | 0.163979i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.2600 | + | 14.1909i | −0.181270 | + | 0.0750843i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 140.503i | 0.735620i | 0.929901 | + | 0.367810i | \(0.119892\pi\) | ||||
−0.929901 | + | 0.367810i | \(0.880108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −159.719 | −0.827560 | −0.413780 | − | 0.910377i | \(-0.635792\pi\) | ||||
−0.413780 | + | 0.910377i | \(0.635792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 112.971 | + | 272.735i | 0.579336 | + | 1.39864i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.3511 | − | 56.3745i | 0.118533 | − | 0.286165i | −0.853466 | − | 0.521149i | \(-0.825504\pi\) |
0.971999 | + | 0.234984i | \(0.0755037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 138.741 | − | 138.741i | 0.697191 | − | 0.697191i | −0.266613 | − | 0.963804i | \(-0.585904\pi\) |
0.963804 | + | 0.266613i | \(0.0859044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 72.2974 | − | 72.2974i | 0.359689 | − | 0.359689i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.170506 | − | 0.411638i | 0.000839931 | − | 0.00202777i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.0083 | − | 67.6180i | −0.136626 | − | 0.329844i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.3345 | 0.0644180 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.5279i | 0.0742963i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 194.276 | − | 80.4718i | 0.920740 | − | 0.381383i | 0.128582 | − | 0.991699i | \(-0.458957\pi\) |
0.792158 | + | 0.610316i | \(0.208957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 106.283 | + | 44.0237i | 0.498979 | + | 0.206684i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.510 | + | 123.510i | 0.574464 | + | 0.574464i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.7144 | − | 18.7144i | −0.0862414 | − | 0.0862414i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −133.995 | − | 55.5025i | −0.611849 | − | 0.253436i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 114.650 | − | 47.4894i | 0.518776 | − | 0.214884i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 285.957i | 1.28232i | 0.767408 | + | 0.641160i | \(0.221546\pi\) | ||||
−0.767408 | + | 0.641160i | \(0.778454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −88.0496 | −0.391332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.02885 | − | 19.3834i | −0.0353694 | − | 0.0853893i | 0.905208 | − | 0.424969i | \(-0.139715\pi\) |
−0.940577 | + | 0.339580i | \(0.889715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 66.9028 | − | 161.518i | 0.292152 | − | 0.705317i | −0.707848 | − | 0.706365i | \(-0.750334\pi\) |
0.999999 | + | 0.00104819i | \(0.000333649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.3837 | + | 16.3837i | −0.0709251 | + | 0.0709251i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 282.286 | − | 282.286i | 1.21153 | − | 1.21153i | 0.241001 | − | 0.970525i | \(-0.422524\pi\) |
0.970525 | − | 0.241001i | \(-0.0774758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 140.662 | − | 339.587i | 0.598560 | − | 1.44505i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 76.1714 | + | 183.894i | 0.321398 | + | 0.775925i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1618 | 0.0550704 | 0.0275352 | − | 0.999621i | \(-0.491234\pi\) | ||||
0.0275352 | + | 0.999621i | \(0.491234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 231.745i | − | 0.961599i | −0.876830 | − | 0.480800i | \(-0.840346\pi\) | ||
0.876830 | − | 0.480800i | \(-0.159654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −340.169 | + | 140.903i | −1.39987 | + | 0.579847i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −205.364 | − | 85.0647i | −0.838222 | − | 0.347203i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.0046 | + | 17.0046i | 0.0688445 | + | 0.0688445i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 113.866 | + | 113.866i | 0.457293 | + | 0.457293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −131.701 | − | 54.5521i | −0.524703 | − | 0.217339i | 0.104578 | − | 0.994517i | \(-0.466651\pi\) |
−0.629281 | + | 0.777177i | \(0.716651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.42459 | − | 1.83272i | 0.0174885 | − | 0.00724397i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 264.282i | − | 1.03640i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −70.0955 | −0.272745 | −0.136373 | − | 0.990658i | \(-0.543544\pi\) | ||||
−0.136373 | + | 0.990658i | \(0.543544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.05061 | − | 19.4359i | −0.0310834 | − | 0.0750420i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.50399 | − | 15.7020i | 0.0249195 | − | 0.0601610i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −245.883 | + | 245.883i | −0.934916 | + | 0.934916i | −0.998008 | − | 0.0630921i | \(-0.979904\pi\) |
0.0630921 | + | 0.998008i | \(0.479904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −232.744 | + | 232.744i | −0.878280 | + | 0.878280i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −167.929 | + | 405.417i | −0.628949 | + | 1.51842i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.33716 | − | 17.7135i | −0.0272757 | − | 0.0658493i | 0.909655 | − | 0.415365i | \(-0.136346\pi\) |
−0.936931 | + | 0.349516i | \(0.886346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 327.600 | 1.20886 | 0.604429 | − | 0.796659i | \(-0.293401\pi\) | ||||
0.604429 | + | 0.796659i | \(0.293401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 35.8835i | 0.131441i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.2161 | + | 12.1017i | −0.106240 | + | 0.0440063i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.9345 | + | 13.2277i | 0.115287 | + | 0.0477535i | 0.439581 | − | 0.898203i | \(-0.355127\pi\) |
−0.324294 | + | 0.945956i | \(0.605127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −713.864 | − | 713.864i | −2.55865 | − | 2.55865i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −263.413 | − | 263.413i | −0.937413 | − | 0.937413i | 0.0607409 | − | 0.998154i | \(-0.480654\pi\) |
−0.998154 | + | 0.0607409i | \(0.980654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 268.113 | + | 111.056i | 0.947397 | + | 0.392425i | 0.802252 | − | 0.596986i | \(-0.203635\pi\) |
0.145145 | + | 0.989410i | \(0.453635\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 47.3158 | − | 19.5989i | 0.166020 | − | 0.0687679i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.89644i | − | 0.0309980i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 177.904 | 0.615585 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −333.313 | − | 804.689i | −1.14541 | − | 2.76526i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −44.7772 | + | 108.102i | −0.152823 | + | 0.368948i | −0.981687 | − | 0.190503i | \(-0.938988\pi\) |
0.828863 | + | 0.559451i | \(0.188988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 227.356 | − | 227.356i | 0.770698 | − | 0.770698i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −359.233 | + | 359.233i | −1.20954 | + | 1.20954i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.83834 | − | 6.85237i | 0.00949279 | − | 0.0229176i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.12503 | + | 19.6155i | 0.0269934 | + | 0.0651679i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −772.765 | −2.55038 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 432.024i | − | 1.41647i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −430.497 | + | 178.318i | −1.40227 | + | 0.580839i | −0.950340 | − | 0.311215i | \(-0.899264\pi\) |
−0.451930 | + | 0.892054i | \(0.649264\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −71.3754 | − | 29.5646i | −0.230988 | − | 0.0956784i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −61.3250 | − | 61.3250i | −0.197187 | − | 0.197187i | 0.601606 | − | 0.798793i | \(-0.294528\pi\) |
−0.798793 | + | 0.601606i | \(0.794528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 129.308 | + | 129.308i | 0.413124 | + | 0.413124i | 0.882826 | − | 0.469701i | \(-0.155638\pi\) |
−0.469701 | + | 0.882826i | \(0.655638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 49.5390 | + | 20.5197i | 0.157267 | + | 0.0651420i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 286.711 | − | 118.760i | 0.904452 | − | 0.374636i | 0.118522 | − | 0.992951i | \(-0.462184\pi\) |
0.785930 | + | 0.618315i | \(0.212184\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.10408i | − | 0.0191350i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 987.635 | 3.07674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.23877 | − | 19.8901i | −0.0255070 | − | 0.0615794i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.7420 | + | 45.2471i | −0.0576676 | + | 0.139222i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.6674 | + | 36.6674i | −0.112133 | + | 0.112133i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.5929 | − | 31.5929i | 0.0960271 | − | 0.0960271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −123.164 | + | 297.345i | −0.372098 | + | 0.898324i | 0.621297 | + | 0.783575i | \(0.286606\pi\) |
−0.993395 | + | 0.114748i | \(0.963394\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −307.092 | − | 741.386i | −0.922198 | − | 2.22638i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −84.9812 | −0.253675 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 263.653i | − | 0.782354i | −0.920315 | − | 0.391177i | \(-0.872068\pi\) | ||
0.920315 | − | 0.391177i | \(-0.127932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 435.556 | − | 180.413i | 1.28483 | − | 0.532192i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −334.985 | − | 138.755i | −0.982362 | − | 0.406908i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38.3323 | − | 38.3323i | −0.111756 | − | 0.111756i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1691 | − | 11.1691i | −0.0323743 | − | 0.0323743i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 388.417 | + | 160.888i | 1.11936 | + | 0.463653i | 0.864151 | − | 0.503233i | \(-0.167856\pi\) |
0.255208 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −448.277 | + | 185.683i | −1.28446 | + | 0.532042i | −0.917330 | − | 0.398127i | \(-0.869660\pi\) |
−0.367132 | + | 0.930169i | \(0.619660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 786.791i | 2.24157i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −106.951 | −0.302976 | −0.151488 | − | 0.988459i | \(-0.548407\pi\) | ||||
−0.151488 | + | 0.988459i | \(0.548407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.5908 | − | 88.3379i | −0.103073 | − | 0.248839i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.2935 | − | 29.6791i | 0.0344356 | − | 0.0831348i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −208.761 | + | 208.761i | −0.581508 | + | 0.581508i | −0.935317 | − | 0.353810i | \(-0.884886\pi\) |
0.353810 | + | 0.935317i | \(0.384886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −252.315 | + | 252.315i | −0.698935 | + | 0.698935i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 132.852 | − | 320.732i | 0.365982 | − | 0.883559i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.1315 | + | 111.371i | 0.126388 | + | 0.305127i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 711.002 | 1.93734 | 0.968668 | − | 0.248361i | \(-0.0798919\pi\) | ||||
0.968668 | + | 0.248361i | \(0.0798919\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 339.356i | − | 0.919665i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.9639 | + | 15.3110i | −0.0996332 | + | 0.0412694i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 587.430 | + | 243.321i | 1.57488 | + | 0.652336i | 0.987592 | − | 0.157043i | \(-0.0501961\pi\) |
0.587287 | + | 0.809379i | \(0.300196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 516.995 | + | 516.995i | 1.37865 | + | 1.37865i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.68456 | − | 6.68456i | −0.0177309 | − | 0.0177309i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.5203 | + | 14.2988i | 0.0910825 | + | 0.0377276i | 0.427759 | − | 0.903893i | \(-0.359303\pi\) |
−0.336677 | + | 0.941620i | \(0.609303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 87.7220 | − | 36.3356i | 0.230241 | − | 0.0953691i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 347.623i | − | 0.907631i | −0.891096 | − | 0.453815i | \(-0.850063\pi\) | ||
0.891096 | − | 0.453815i | \(-0.149937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.2580 | 0.0500209 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 309.931 | + | 748.239i | 0.800855 | + | 1.93343i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 60.7529 | − | 146.670i | 0.156177 | − | 0.377045i | −0.826352 | − | 0.563154i | \(-0.809588\pi\) |
0.982529 | + | 0.186109i | \(0.0595878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.69517 | + | 4.69517i | −0.0120081 | + | 0.0120081i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 408.205 | − | 408.205i | 1.03869 | − | 1.03869i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 63.3107 | − | 152.846i | 0.160280 | − | 0.386951i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −179.460 | − | 433.255i | −0.452041 | − | 1.09132i | −0.971545 | − | 0.236855i | \(-0.923883\pi\) |
0.519505 | − | 0.854468i | \(-0.326117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.22529 | 0.0156022 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 680.550i | 1.69713i | 0.529089 | + | 0.848566i | \(0.322534\pi\) | ||||
−0.529089 | + | 0.848566i | \(0.677466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −518.792 | + | 214.891i | −1.28733 | + | 0.533228i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 744.578 | + | 308.414i | 1.83847 | + | 0.761517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −203.795 | − | 203.795i | −0.500725 | − | 0.500725i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 239.915 | + | 239.915i | 0.586589 | + | 0.586589i | 0.936706 | − | 0.350117i | \(-0.113858\pi\) |
−0.350117 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −183.246 | − | 75.9028i | −0.445853 | − | 0.184678i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.1082 | − | 14.9565i | 0.0874289 | − | 0.0362143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 133.843i | − | 0.322512i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −749.489 | −1.79734 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.5102 | − | 80.9009i | −0.0799767 | − | 0.193081i | 0.878833 | − | 0.477129i | \(-0.158322\pi\) |
−0.958810 | + | 0.284048i | \(0.908322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.2975 | + | 90.0441i | −0.0885926 | + | 0.213882i | −0.961966 | − | 0.273170i | \(-0.911928\pi\) |
0.873373 | + | 0.487052i | \(0.161928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1205.12 | − | 1205.12i | 2.84898 | − | 2.84898i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.0028 | − | 31.0028i | 0.0729479 | − | 0.0729479i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0963 | − | 48.5167i | 0.0470639 | − | 0.113622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 188.128 | + | 454.182i | 0.438527 | + | 1.05870i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −509.094 | −1.18119 | −0.590596 | − | 0.806967i | \(-0.701107\pi\) | ||||
−0.590596 | + | 0.806967i | \(0.701107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 66.0083i | − | 0.152444i | −0.997091 | − | 0.0762220i | \(-0.975714\pi\) | ||
0.997091 | − | 0.0762220i | \(-0.0242858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.6000 | + | 7.70438i | −0.0427586 | + | 0.0177112i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.18879 | − | 0.492414i | −0.00272035 | − | 0.00112681i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.8501 | − | 39.8501i | −0.0907747 | − | 0.0907747i | 0.660261 | − | 0.751036i | \(-0.270446\pi\) |
−0.751036 | + | 0.660261i | \(0.770446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −728.792 | − | 728.792i | −1.65259 | − | 1.65259i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 193.778 | + | 80.2656i | 0.437423 | + | 0.181187i | 0.590517 | − | 0.807025i | \(-0.298924\pi\) |
−0.153094 | + | 0.988212i | \(0.548924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 336.967 | − | 139.576i | 0.757229 | − | 0.313655i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 899.465i | 2.01223i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 124.217 | 0.276652 | 0.138326 | − | 0.990387i | \(-0.455828\pi\) | ||||
0.138326 | + | 0.990387i | \(0.455828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −46.6418 | − | 112.603i | −0.103419 | − | 0.249675i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −366.485 | + | 884.774i | −0.809019 | + | 1.95314i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.0894 | − | 21.0894i | 0.0463504 | − | 0.0463504i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −573.100 | + | 573.100i | −1.25405 | + | 1.25405i | −0.300159 | + | 0.953889i | \(0.597040\pi\) |
−0.953889 | + | 0.300159i | \(0.902960\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 269.550 | − | 650.752i | 0.587256 | − | 1.41776i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 86.0707 | + | 207.793i | 0.186704 | + | 0.450744i | 0.989321 | − | 0.145750i | \(-0.0465596\pi\) |
−0.802617 | + | 0.596495i | \(0.796560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −555.587 | −1.19997 | −0.599986 | − | 0.800010i | \(-0.704827\pi\) | ||||
−0.599986 | + | 0.800010i | \(0.704827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1195.88i | 2.57179i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 319.806 | − | 132.468i | 0.684809 | − | 0.283657i | −0.0130269 | − | 0.999915i | \(-0.504147\pi\) |
0.697835 | + | 0.716258i | \(0.254147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.54349 | − | 3.95304i | −0.0203486 | − | 0.00842866i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 450.090 | + | 450.090i | 0.955606 | + | 0.955606i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 205.679 | + | 205.679i | 0.434839 | + | 0.434839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.84975 | + | 3.25147i | 0.0165258 | + | 0.00684521i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1410.00 | + | 584.039i | −2.95597 | + | 1.22440i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 239.576i | − | 0.500159i | −0.968225 | − | 0.250079i | \(-0.919543\pi\) | ||
0.968225 | − | 0.250079i | \(-0.0804567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −446.351 | −0.927965 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.734757 | − | 1.77386i | −0.00152124 | − | 0.00367259i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −277.037 | + | 668.826i | −0.571210 | + | 1.37902i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −269.525 | + | 269.525i | −0.553439 | + | 0.553439i | −0.927432 | − | 0.373992i | \(-0.877989\pi\) |
0.373992 | + | 0.927432i | \(0.377989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 493.676 | − | 493.676i | 1.00956 | − | 1.00956i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −285.394 | + | 689.002i | −0.581250 | + | 1.40326i | 0.310430 | + | 0.950596i | \(0.399527\pi\) |
−0.891680 | + | 0.452666i | \(0.850473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.23869 | + | 7.81888i | 0.00656934 | + | 0.0158598i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 734.601 | 1.48404 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.6225i | − | 0.0233854i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −581.267 | + | 240.769i | −1.16486 | + | 0.482503i | −0.879492 | − | 0.475914i | \(-0.842117\pi\) |
−0.285373 | + | 0.958417i | \(0.592117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −636.096 | − | 263.479i | −1.26965 | − | 0.525907i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 204.189 | + | 204.189i | 0.405942 | + | 0.405942i | 0.880321 | − | 0.474379i | \(-0.157327\pi\) |
−0.474379 | + | 0.880321i | \(0.657327\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 454.169 | + | 454.169i | 0.899345 | + | 0.899345i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −154.175 | − | 63.8615i | −0.304093 | − | 0.125960i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 397.562 | − | 164.676i | 0.781066 | − | 0.323528i | 0.0437202 | − | 0.999044i | \(-0.486079\pi\) |
0.737345 | + | 0.675516i | \(0.236079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6530i | 0.0286751i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 136.497 | 0.266077 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.5730 | + | 59.3244i | 0.0477145 | + | 0.115193i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 234.242 | − | 565.510i | 0.453079 | − | 1.09383i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −885.818 | + | 885.818i | −1.70678 | + | 1.70678i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −333.835 | + | 333.835i | −0.640759 | + | 0.640759i | −0.950742 | − | 0.309983i | \(-0.899676\pi\) |
0.309983 | + | 0.950742i | \(0.399676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 211.672 | − | 511.022i | 0.404727 | − | 0.977097i | −0.581775 | − | 0.813350i | \(-0.697642\pi\) |
0.986502 | − | 0.163748i | \(-0.0523583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.85170 | + | 11.7130i | 0.00924132 | + | 0.0223105i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 502.712 | 0.953913 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 528.603i | − | 0.999250i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1377.35 | − | 570.518i | 2.59388 | − | 1.07442i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −174.389 | − | 72.2343i | −0.327184 | − | 0.135524i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −580.452 | − | 580.452i | −1.08496 | − | 1.08496i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.2517 | − | 23.2517i | −0.0432992 | − | 0.0432992i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −341.990 | − | 141.657i | −0.634490 | − | 0.262815i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 529.582 | − | 219.360i | 0.978896 | − | 0.405472i | 0.164879 | − | 0.986314i | \(-0.447277\pi\) |
0.814016 | + | 0.580842i | \(0.197277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1627.95i | − | 2.99807i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 43.1003 | 0.0790832 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 68.4960 | + | 165.364i | 0.125221 | + | 0.302311i | 0.974041 | − | 0.226371i | \(-0.0726863\pi\) |
−0.848820 | + | 0.528682i | \(0.822686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 766.577 | − | 1850.68i | 1.39632 | − | 3.37100i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.15968 | + | 1.15968i | −0.00210468 | + | 0.00210468i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.2197 | − | 14.2197i | 0.0257138 | − | 0.0257138i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −363.770 | + | 878.217i | −0.655441 | + | 1.58237i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 308.610 | + | 745.049i | 0.554057 | + | 1.33761i | 0.914408 | + | 0.404794i | \(0.132657\pi\) |
−0.360351 | + | 0.932817i | \(0.617343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 450.477 | 0.805863 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 440.104i | − | 0.784500i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 347.195 | − | 143.813i | 0.616687 | − | 0.255440i | −0.0523978 | − | 0.998626i | \(-0.516686\pi\) |
0.669085 | + | 0.743186i | \(0.266686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −362.017 | − | 149.952i | −0.640738 | − | 0.265402i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 69.2706 | + | 69.2706i | 0.122170 | + | 0.122170i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 717.322 | + | 717.322i | 1.26067 | + | 1.26067i | 0.950768 | + | 0.309903i | \(0.100297\pi\) |
0.309903 | + | 0.950768i | \(0.399703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 327.041 | + | 135.465i | 0.572751 | + | 0.237241i | 0.650210 | − | 0.759754i | \(-0.274681\pi\) |
−0.0774591 | + | 0.996996i | \(0.524681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 712.966 | − | 295.320i | 1.24427 | − | 0.515393i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.62050i | − | 0.00455740i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 531.710 | 0.921507 | 0.460754 | − | 0.887528i | \(-0.347579\pi\) | ||||
0.460754 | + | 0.887528i | \(0.347579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 335.709 | + | 810.473i | 0.579808 | + | 1.39978i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.22591 | − | 15.0307i | 0.0107158 | − | 0.0258703i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −387.585 | + | 387.585i | −0.664812 | + | 0.664812i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 804.460 | − | 804.460i | 1.37515 | − | 1.37515i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −105.581 | + | 254.894i | −0.179865 | + | 0.434232i | −0.987938 | − | 0.154850i | \(-0.950510\pi\) |
0.808073 | + | 0.589082i | \(0.200510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.2806 | + | 90.0034i | 0.0632948 | + | 0.152807i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −335.145 | −0.567082 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 405.861i | − | 0.684419i | −0.939624 | − | 0.342210i | \(-0.888825\pi\) | ||
0.939624 | − | 0.342210i | \(-0.111175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.6681 | + | 10.2179i | −0.0414590 | + | 0.0171729i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −995.638 | − | 412.407i | −1.66774 | − | 0.690799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 561.484 | + | 561.484i | 0.937370 | + | 0.937370i | 0.998151 | − | 0.0607815i | \(-0.0193593\pi\) |
−0.0607815 | + | 0.998151i | \(0.519359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −358.762 | − | 358.762i | −0.596941 | − | 0.596941i | 0.342556 | − | 0.939497i | \(-0.388707\pi\) |
−0.939497 | + | 0.342556i | \(0.888707\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −364.038 | − | 150.790i | −0.603712 | − | 0.250066i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −266.580 | + | 110.421i | −0.440628 | + | 0.182514i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 571.923i | 0.942213i | 0.882076 | + | 0.471107i | \(0.156145\pi\) | ||||
−0.882076 | + | 0.471107i | \(0.843855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.44718 | −0.00401836 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −362.771 | − | 875.806i | −0.593733 | − | 1.43340i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −401.254 | + | 968.712i | −0.654574 | + | 1.58028i | 0.151494 | + | 0.988458i | \(0.451591\pi\) |
−0.806068 | + | 0.591823i | \(0.798409\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −284.249 | + | 284.249i | −0.462193 | + | 0.462193i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −151.870 | + | 151.870i | −0.246143 | + | 0.246143i | −0.819386 | − | 0.573242i | \(-0.805685\pi\) |
0.573242 | + | 0.819386i | \(0.305685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −146.518 | + | 353.725i | −0.236701 | + | 0.571446i | −0.996938 | − | 0.0781999i | \(-0.975083\pi\) |
0.760237 | + | 0.649646i | \(0.225083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.1105 | − | 38.8941i | −0.0259428 | − | 0.0626314i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.3344 | 0.0711628 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 503.703i | − | 0.805924i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 78.7944 | − | 32.6377i | 0.125669 | − | 0.0520537i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 369.176 | + | 152.918i | 0.586925 | + | 0.243112i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −682.535 | − | 682.535i | −1.08167 | − | 1.08167i | −0.996354 | − | 0.0853189i | \(-0.972809\pi\) |
−0.0853189 | − | 0.996354i | \(-0.527191\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −816.687 | − | 816.687i | −1.29018 | − | 1.29018i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −72.9111 | − | 30.2007i | −0.114821 | − | 0.0475602i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −529.641 | + | 219.385i | −0.831462 | + | 0.344403i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 443.344i | − | 0.693808i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.9310 | 0.0607348 | 0.0303674 | − | 0.999539i | \(-0.490332\pi\) | ||||
0.0303674 | + | 0.999539i | \(0.490332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −318.631 | − | 769.243i | −0.495538 | − | 1.19633i | −0.951864 | − | 0.306522i | \(-0.900835\pi\) |
0.456326 | − | 0.889813i | \(-0.349165\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 367.132 | − | 886.335i | 0.569197 | − | 1.37416i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −157.445 | + | 157.445i | −0.243346 | + | 0.243346i | −0.818233 | − | 0.574887i | \(-0.805046\pi\) |
0.574887 | + | 0.818233i | \(0.305046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 378.612 | − | 378.612i | 0.583378 | − | 0.583378i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −55.6284 | + | 134.299i | −0.0854507 | + | 0.206296i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6861 | + | 37.8696i | 0.0240216 | + | 0.0579933i | 0.935435 | − | 0.353498i | \(-0.115008\pi\) |
−0.911414 | + | 0.411492i | \(0.865008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −479.821 | −0.732551 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 558.942i | 0.850748i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −187.169 | + | 77.5281i | −0.284020 | + | 0.117645i | −0.520146 | − | 0.854078i | \(-0.674122\pi\) |
0.236125 | + | 0.971723i | \(0.424122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.1818 | − | 12.5017i | −0.0456608 | − | 0.0189133i | 0.359736 | − | 0.933054i | \(-0.382867\pi\) |
−0.405397 | + | 0.914141i | \(0.632867\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −481.957 | − | 481.957i | −0.726934 | − | 0.726934i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.65873 | − | 3.65873i | −0.00550184 | − | 0.00550184i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.467318 | + | 0.193569i | 0.000700627 | + | 0.000290209i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1451.05 | − | 601.045i | 2.16899 | − | 0.898423i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 719.443i | − | 1.07219i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −327.878 | −0.487189 | −0.243595 | − | 0.969877i | \(-0.578327\pi\) | ||||
−0.243595 | + | 0.969877i | \(0.578327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 106.380 | + | 256.823i | 0.157599 | + | 0.380479i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −117.661 | + | 284.058i | −0.173797 | + | 0.419583i | −0.986643 | − | 0.162895i | \(-0.947917\pi\) |
0.812846 | + | 0.582478i | \(0.197917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −62.2231 | + | 62.2231i | −0.0916393 | + | 0.0916393i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −81.4826 | + | 81.4826i | −0.119651 | + | 0.119651i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 324.811 | − | 784.162i | 0.475564 | − | 1.14811i | −0.486104 | − | 0.873901i | \(-0.661583\pi\) |
0.961669 | − | 0.274213i | \(-0.0884175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.0875 | + | 152.307i | 0.0920985 | + | 0.222345i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −960.220 | −1.39770 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 848.888i | 1.23206i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −826.286 | + | 342.259i | −1.19578 | + | 0.495309i | −0.889634 | − | 0.456674i | \(-0.849041\pi\) |
−0.306149 | + | 0.951984i | \(0.599041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 82.4966 | + | 34.1712i | 0.119043 | + | 0.0493091i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 440.490 | + | 440.490i | 0.633798 | + | 0.633798i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 119.490 | + | 119.490i | 0.171434 | + | 0.171434i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2025.75 | − | 839.092i | −2.89807 | − | 1.20042i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −430.597 | + | 178.359i | −0.614260 | + | 0.254435i | −0.668049 | − | 0.744117i | \(-0.732870\pi\) |
0.0537885 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 77.4359i | 0.110151i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2018.84 | −2.86361 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.8773 | + | 72.1301i | 0.0422592 | + | 0.102023i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 77.1066 | − | 186.152i | 0.108754 | − | 0.262555i | −0.860128 | − | 0.510078i | \(-0.829616\pi\) |
0.968882 | + | 0.247523i | \(0.0796165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 542.414 | − | 542.414i | 0.762889 | − | 0.762889i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.2458 | − | 21.2458i | 0.0297977 | − | 0.0297977i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 156.365 | − | 377.498i | 0.218692 | − | 0.527970i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.6645 | − | 66.7879i | −0.0385836 | − | 0.0931491i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 809.898 | 1.12642 | 0.563212 | − | 0.826313i | \(-0.309566\pi\) | ||||
0.563212 | + | 0.826313i | \(0.309566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.80525i | 0.0108256i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1175.96 | + | 487.099i | −1.62650 | + | 0.673719i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.08576 | − | 1.27817i | −0.00425623 | − | 0.00176299i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 542.456 | + | 542.456i | 0.746156 | + | 0.746156i | 0.973755 | − | 0.227599i | \(-0.0730875\pi\) |
−0.227599 | + | 0.973755i | \(0.573087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 306.489 | + | 306.489i | 0.420424 | + | 0.420424i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −372.588 | − | 154.331i | −0.509697 | − | 0.211123i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −562.276 | + | 232.903i | −0.767089 | + | 0.317739i | −0.731693 | − | 0.681635i | \(-0.761269\pi\) |
−0.0353965 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1220.89i | 1.66107i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −141.518 | −0.192019 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 305.819 | + | 738.312i | 0.413828 | + | 0.999070i | 0.984100 | + | 0.177614i | \(0.0568378\pi\) |
−0.570272 | + | 0.821456i | \(0.693162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.5461 | − | 122.029i | 0.0682133 | − | 0.164681i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 581.334 | − | 581.334i | 0.782414 | − | 0.782414i | −0.197823 | − | 0.980238i | \(-0.563387\pi\) |
0.980238 | + | 0.197823i | \(0.0633873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 528.633 | − | 528.633i | 0.709574 | − | 0.709574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 237.488 | − | 573.348i | 0.317923 | − | 0.767534i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38.1847 | − | 92.1861i | −0.0509810 | − | 0.123079i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −187.901 | −0.250201 | −0.125100 | − | 0.992144i | \(-0.539925\pi\) | ||||
−0.125100 | + | 0.992144i | \(0.539925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 782.958i | 1.03978i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 735.390 | − | 304.608i | 0.974026 | − | 0.403455i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 168.645 | + | 69.8549i | 0.222780 | + | 0.0922786i | 0.491282 | − | 0.871001i | \(-0.336528\pi\) |
−0.268502 | + | 0.963279i | \(0.586528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.5998 | − | 18.5998i | −0.0245057 | − | 0.0245057i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 391.406 | + | 391.406i | 0.514331 | + | 0.514331i | 0.915850 | − | 0.401520i | \(-0.131518\pi\) |
−0.401520 | + | 0.915850i | \(0.631518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.84022 | + | 2.00488i | 0.00634367 | + | 0.00262763i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −940.971 | + | 389.763i | −1.23003 | + | 0.509494i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 829.235i | − | 1.08114i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 184.433 | 0.239835 | 0.119918 | − | 0.992784i | \(-0.461737\pi\) | ||||
0.119918 | + | 0.992784i | \(0.461737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 147.332 | + | 355.690i | 0.191092 | + | 0.461336i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 140.532 | − | 339.275i | 0.181801 | − | 0.438907i | −0.806537 | − | 0.591184i | \(-0.798661\pi\) |
0.988338 | + | 0.152277i | \(0.0486607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −140.289 | + | 140.289i | −0.181018 | + | 0.181018i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −81.7035 | + | 81.7035i | −0.105152 | + | 0.105152i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.5317 | + | 30.2541i | −0.0160869 | + | 0.0388371i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.9340 | − | 147.108i | −0.0780206 | − | 0.188358i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −53.6576 | −0.0685282 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 529.054i | − | 0.673954i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 926.743 | − | 383.870i | 1.17756 | − | 0.487763i | 0.293878 | − | 0.955843i | \(-0.405054\pi\) |
0.883686 | + | 0.468080i | \(0.155054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1764.51 | + | 730.885i | 2.23639 | + | 0.926344i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.6796 | − | 33.6796i | −0.0425785 | − | 0.0425785i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −787.860 | − | 787.860i | −0.993518 | − | 0.993518i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1670.23 | + | 691.831i | 2.10091 | + | 0.870227i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 871.860 | − | 361.136i | 1.09393 | − | 0.453119i | 0.238553 | − | 0.971130i | \(-0.423327\pi\) |
0.855374 | + | 0.518010i | \(0.173327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 848.660i | 1.06215i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1691.14 | 2.11129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 76.8221 | + | 185.465i | 0.0956689 | + | 0.230965i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.610701 | + | 1.47436i | −0.000758635 | + | 0.00183151i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −74.4628 | + | 74.4628i | −0.0922711 | + | 0.0922711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 744.003 | − | 744.003i | 0.919658 | − | 0.919658i | −0.0773465 | − | 0.997004i | \(-0.524645\pi\) |
0.997004 | + | 0.0773465i | \(0.0246448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 307.315 | − | 741.925i | 0.378934 | − | 0.914827i | −0.613233 | − | 0.789902i | \(-0.710131\pi\) |
0.992166 | − | 0.124924i | \(-0.0398688\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −688.574 | − | 1662.36i | −0.846954 | − | 2.04473i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −580.286 | −0.712007 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 78.1517i | − | 0.0956569i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 127.763 | − | 52.9210i | 0.155998 | − | 0.0646166i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 948.269 | + | 392.786i | 1.15502 | + | 0.478424i | 0.876213 | − | 0.481924i | \(-0.160062\pi\) |
0.278804 | + | 0.960348i | \(0.410062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 492.275 | + | 492.275i | 0.598147 | + | 0.598147i | 0.939819 | − | 0.341672i | \(-0.110993\pi\) |
−0.341672 | + | 0.939819i | \(0.610993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 122.817 | + | 122.817i | 0.148869 | + | 0.148869i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1350.77 | + | 559.506i | 1.63333 | + | 0.676549i | 0.995600 | − | 0.0937082i | \(-0.0298721\pi\) |
0.637734 | + | 0.770257i | \(0.279872\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −441.547 | + | 182.895i | −0.532627 | + | 0.220621i | −0.632753 | − | 0.774354i | \(-0.718075\pi\) |
0.100127 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 189.850i | − | 0.228460i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 513.225 | 0.616116 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 218.994 | + | 528.698i | 0.262268 | + | 0.633171i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1219.72 | + | 2944.67i | −1.45726 | + | 3.51813i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 849.569 | − | 849.569i | 1.01260 | − | 1.01260i | 0.0126775 | − | 0.999920i | \(-0.495965\pi\) |
0.999920 | − | 0.0126775i | \(-0.00403549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −594.221 | + | 594.221i | −0.706565 | + | 0.706565i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −782.994 | + | 1890.31i | −0.928818 | + | 2.24236i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 53.0792 | + | 128.144i | 0.0628156 | + | 0.151650i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0736 | −0.0414093 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1593.93i | − | 1.87742i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.0649 | − | 9.13957i | 0.0259282 | − | 0.0107398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −773.493 | − | 320.391i | −0.906791 | − | 0.375605i | −0.119964 | − | 0.992778i | \(-0.538278\pi\) |
−0.786827 | + | 0.617173i | \(0.788278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −139.563 | − | 139.563i | −0.163231 | − | 0.163231i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −259.040 | − | 259.040i | −0.302264 | − | 0.302264i | 0.539635 | − | 0.841899i | \(-0.318562\pi\) |
−0.841899 | + | 0.539635i | \(0.818562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 762.123 | + | 315.682i | 0.887221 | + | 0.367499i | 0.779293 | − | 0.626660i | \(-0.215578\pi\) |
0.107928 | + | 0.994159i | \(0.465578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −45.1438 | + | 18.6992i | −0.0524318 | + | 0.0217180i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1078.25i | 1.24942i | 0.780855 | + | 0.624712i | \(0.214784\pi\) | ||||
−0.780855 | + | 0.624712i | \(0.785216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1041.22 | 1.20373 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −373.931 | − | 902.750i | −0.431293 | − | 1.04123i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 105.430 | − | 254.532i | 0.121324 | − | 0.292902i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −154.976 | + | 154.976i | −0.177929 | + | 0.177929i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2373.51 | + | 2373.51i | −2.71880 | + | 2.71880i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.2680 | − | 68.2450i | 0.0323063 | − | 0.0779943i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −387.984 | − | 936.676i | −0.442399 | − | 1.06805i | −0.975105 | − | 0.221745i | \(-0.928825\pi\) |
0.532706 | − | 0.846301i | \(-0.321175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 642.663 | 0.731130 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1281.50i | 1.45460i | 0.686318 | + | 0.727301i | \(0.259226\pi\) | ||||
−0.686318 | + | 0.727301i | \(0.740774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1014.19 | − | 420.092i | 1.14857 | − | 0.475755i | 0.274519 | − | 0.961582i | \(-0.411481\pi\) |
0.874055 | + | 0.485826i | \(0.161481\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1631.56 | − | 675.814i | −1.84357 | − | 0.763632i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.0987 | − | 57.0987i | −0.0643728 | − | 0.0643728i | 0.674187 | − | 0.738560i | \(-0.264494\pi\) |
−0.738560 | + | 0.674187i | \(0.764494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.78316 | − | 6.78316i | −0.00763010 | − | 0.00763010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1239.94 | + | 513.598i | 1.39162 | + | 0.576429i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −151.940 | + | 62.9358i | −0.170146 | + | 0.0704768i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.3309i | 0.0305373i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.7372 | −0.0454150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.6551 | − | 35.3806i | −0.0163016 | − | 0.0393555i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 290.825 | − | 702.113i | 0.322780 | − | 0.779260i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 82.4587 | − | 82.4587i | 0.0913164 | − | 0.0913164i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −956.779 | + | 956.779i | −1.05721 | + | 1.05721i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −312.323 | + | 754.015i | −0.344348 | + | 0.831329i | 0.652918 | + | 0.757429i | \(0.273545\pi\) |
−0.997266 | + | 0.0739002i | \(0.976455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1139.67 | + | 2751.42i | 1.25377 | + | 3.02686i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1374.15 | 1.50840 | 0.754201 | − | 0.656644i | \(-0.228024\pi\) | ||||
0.754201 | + | 0.656644i | \(0.228024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 222.886i | − | 0.244125i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2192.25 | + | 908.058i | −2.39590 | + | 0.992413i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −53.8844 | − | 22.3196i | −0.0587616 | − | 0.0243399i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −317.523 | − | 317.523i | −0.345510 | − | 0.345510i | 0.512924 | − | 0.858434i | \(-0.328562\pi\) |
−0.858434 | + | 0.512924i | \(0.828562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1809.70 | + | 1809.70i | 1.96493 | + | 1.96493i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −227.826 | − | 94.3687i | −0.246832 | − | 0.102241i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −145.697 | + | 60.3498i | −0.157511 | + | 0.0652430i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 297.733i | 0.321179i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.9926 | −0.0505841 | −0.0252920 | − | 0.999680i | \(-0.508052\pi\) | ||||
−0.0252920 | + | 0.999680i | \(0.508052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.0602 | + | 91.8855i | 0.0408810 | + | 0.0986955i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −182.288 | + | 440.083i | −0.195379 | + | 0.471686i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −258.658 | + | 258.658i | −0.276640 | + | 0.276640i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 381.311 | − | 381.311i | 0.406949 | − | 0.406949i | −0.473724 | − | 0.880673i | \(-0.657091\pi\) |
0.880673 | + | 0.473724i | \(0.157091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 384.367 | − | 927.944i | 0.409337 | − | 0.988226i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −319.284 | − | 770.819i | −0.339303 | − | 0.819149i | −0.997783 | − | 0.0665513i | \(-0.978800\pi\) |
0.658480 | − | 0.752598i | \(-0.271200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0998 | 0.0107103 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 169.287i | − | 0.179139i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.3711 | − | 19.2075i | 0.0489663 | − | 0.0202825i | −0.358066 | − | 0.933696i | \(-0.616564\pi\) |
0.407032 | + | 0.913414i | \(0.366564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 287.230 | + | 118.975i | 0.302666 | + | 0.125368i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1205.26 | − | 1205.26i | −1.26736 | − | 1.26736i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −456.351 | − | 456.351i | −0.478858 | − | 0.478858i | 0.425909 | − | 0.904766i | \(-0.359955\pi\) |
−0.904766 | + | 0.425909i | \(0.859955\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −592.589 | − | 245.459i | −0.620512 | − | 0.257025i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.9743 | + | 12.8300i | −0.0323661 | + | 0.0134065i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0388i | 0.0208955i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1313.79 | −1.36710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1456.56 | − | 3516.46i | −1.51253 | − | 3.65157i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 279.028 | − | 673.634i | 0.289148 | − | 0.698066i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 476.069 | − | 476.069i | 0.492316 | − | 0.492316i | −0.416719 | − | 0.909035i | \(-0.636820\pi\) |
0.909035 | + | 0.416719i | \(0.136820\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −83.6130 | + | 83.6130i | −0.0862879 | + | 0.0862879i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 502.303 | − | 1212.67i | 0.517305 | − | 1.24888i | −0.422248 | − | 0.906480i | \(-0.638759\pi\) |
0.939553 | − | 0.342404i | \(-0.111241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9774 | + | 69.9576i | 0.0297815 | + | 0.0718988i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 268.993 | 0.275891 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.17535i | − | 0.00120302i | −1.00000 | 0.000601512i | \(-0.999809\pi\) | |||
1.00000 | 0.000601512i | \(-0.000191467\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 561.146 | − | 232.434i | 0.573183 | − | 0.237420i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 184.631 | + | 76.4767i | 0.188207 | + | 0.0779579i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1006.98 | − | 1006.98i | −1.02439 | − | 1.02439i | −0.999695 | − | 0.0246998i | \(-0.992137\pi\) |
−0.0246998 | − | 0.999695i | \(-0.507863\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 196.972 | + | 196.972i | 0.199971 | + | 0.199971i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −226.718 | − | 93.9098i | −0.229704 | − | 0.0951467i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.2688 | + | 9.22405i | −0.0225165 | + | 0.00932665i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1294.48i | − | 1.30624i | −0.757256 | − | 0.653118i | \(-0.773461\pi\) | ||
0.757256 | − | 0.653118i | \(-0.226539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1767.71 | 1.78017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 342.777 | + | 827.536i | 0.344499 | + | 0.831694i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −82.2498 | + | 198.568i | −0.0824973 | + | 0.199166i | −0.959746 | − | 0.280871i | \(-0.909377\pi\) |
0.877248 | + | 0.480037i | \(0.159377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1791.45 | + | 1791.45i | −1.79325 | + | 1.79325i |
(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 | 256.3.h.b.159.1 | 28 | ||
4.3 | odd | 2 | 256.3.h.a.159.7 | 28 | |||
8.3 | odd | 2 | 128.3.h.a.79.1 | 28 | |||
8.5 | even | 2 | 32.3.h.a.11.2 | yes | 28 | ||
24.5 | odd | 2 | 288.3.u.a.235.6 | 28 | |||
32.3 | odd | 8 | inner | 256.3.h.b.95.1 | 28 | ||
32.13 | even | 8 | 128.3.h.a.47.1 | 28 | |||
32.19 | odd | 8 | 32.3.h.a.3.2 | ✓ | 28 | ||
32.29 | even | 8 | 256.3.h.a.95.7 | 28 | |||
96.83 | even | 8 | 288.3.u.a.163.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.2 | ✓ | 28 | 32.19 | odd | 8 | ||
32.3.h.a.11.2 | yes | 28 | 8.5 | even | 2 | ||
128.3.h.a.47.1 | 28 | 32.13 | even | 8 | |||
128.3.h.a.79.1 | 28 | 8.3 | odd | 2 | |||
256.3.h.a.95.7 | 28 | 32.29 | even | 8 | |||
256.3.h.a.159.7 | 28 | 4.3 | odd | 2 | |||
256.3.h.b.95.1 | 28 | 32.3 | odd | 8 | inner | ||
256.3.h.b.159.1 | 28 | 1.1 | even | 1 | trivial | ||
288.3.u.a.163.6 | 28 | 96.83 | even | 8 | |||
288.3.u.a.235.6 | 28 | 24.5 | odd | 2 |