Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, 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("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.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: | \(3.48774738381\) |
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 | 15.1 | ||
Character | \(\chi\) | \(=\) | 128.15 |
Dual form | 128.3.h.a.111.1 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −4.35131 | + | 1.80237i | −1.45044 | + | 0.600791i | −0.962304 | − | 0.271977i | \(-0.912322\pi\) |
−0.488135 | + | 0.872768i | \(0.662322\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.81639 | − | 1.16659i | −0.563278 | − | 0.233318i | 0.0828294 | − | 0.996564i | \(-0.473604\pi\) |
−0.646108 | + | 0.763246i | \(0.723604\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.23443 | − | 6.23443i | 0.890633 | − | 0.890633i | −0.103950 | − | 0.994583i | \(-0.533148\pi\) |
0.994583 | + | 0.103950i | \(0.0331481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.32143 | − | 9.32143i | 1.03571 | − | 1.03571i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.06262 | + | 3.33965i | 0.732965 | + | 0.303604i | 0.717770 | − | 0.696280i | \(-0.245163\pi\) |
0.0151955 | + | 0.999885i | \(0.495163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.3208 | − | 5.51766i | 1.02468 | − | 0.424436i | 0.193889 | − | 0.981023i | \(-0.437890\pi\) |
0.830789 | + | 0.556588i | \(0.187890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.3576 | 0.957176 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.56488i | − | 0.268522i | −0.990946 | − | 0.134261i | \(-0.957134\pi\) | ||
0.990946 | − | 0.134261i | \(-0.0428661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.4421 | − | 32.4522i | −0.707481 | − | 1.70801i | −0.706201 | − | 0.708011i | \(-0.749593\pi\) |
−0.00128016 | − | 0.999999i | \(-0.500407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.8912 | + | 38.3647i | −0.756724 | + | 1.82689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.75277 | + | 6.75277i | 0.293599 | + | 0.293599i | 0.838500 | − | 0.544901i | \(-0.183433\pi\) |
−0.544901 | + | 0.838500i | \(0.683433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.1065 | − | 11.1065i | −0.444261 | − | 0.444261i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.53841 | + | 18.1993i | −0.279200 | + | 0.674050i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.266504 | − | 0.643399i | −0.00918981 | − | 0.0221862i | 0.919218 | − | 0.393749i | \(-0.128822\pi\) |
−0.928408 | + | 0.371563i | \(0.878822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.326715i | 0.0105392i | 0.999986 | + | 0.00526959i | \(0.00167737\pi\) | ||||
−0.999986 | + | 0.00526959i | \(0.998323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −41.1023 | −1.24552 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.8316 | + | 10.2856i | −0.709475 | + | 0.293874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 31.5133 | + | 13.0532i | 0.851710 | + | 0.352790i | 0.765460 | − | 0.643484i | \(-0.222512\pi\) |
0.0862502 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −48.0182 | + | 48.0182i | −1.23124 | + | 1.23124i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.7509 | − | 15.7509i | 0.384169 | − | 0.384169i | −0.488433 | − | 0.872601i | \(-0.662431\pi\) |
0.872601 | + | 0.488433i | \(0.162431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.83274 | − | 2.00179i | −0.112389 | − | 0.0465531i | 0.325780 | − | 0.945446i | \(-0.394373\pi\) |
−0.438170 | + | 0.898892i | \(0.644373\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −37.1271 | + | 15.3785i | −0.825046 | + | 0.341745i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 49.7096 | 1.05765 | 0.528825 | − | 0.848731i | \(-0.322633\pi\) | ||||
0.528825 | + | 0.848731i | \(0.322633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 28.7362i | − | 0.586454i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.22762 | + | 19.8632i | 0.161326 | + | 0.389475i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.45882 | − | 10.7645i | 0.0841286 | − | 0.203105i | −0.876217 | − | 0.481917i | \(-0.839941\pi\) |
0.960346 | + | 0.278812i | \(0.0899407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.8115 | − | 18.8115i | −0.342027 | − | 0.342027i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 116.982 | + | 116.982i | 2.05232 | + | 2.05232i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1268 | + | 31.6909i | −0.222488 | + | 0.537134i | −0.995227 | − | 0.0975907i | \(-0.968886\pi\) |
0.772739 | + | 0.634724i | \(0.218886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.4023 | − | 85.4687i | −0.580366 | − | 1.40113i | −0.892482 | − | 0.451083i | \(-0.851038\pi\) |
0.312116 | − | 0.950044i | \(-0.398962\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 116.228i | − | 1.84488i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −43.9535 | −0.676207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41.3348 | − | 17.1214i | 0.616938 | − | 0.255544i | −0.0522539 | − | 0.998634i | \(-0.516641\pi\) |
0.669192 | + | 0.743090i | \(0.266641\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −41.5545 | − | 17.2124i | −0.602239 | − | 0.249455i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −37.6381 | + | 37.6381i | −0.530114 | + | 0.530114i | −0.920606 | − | 0.390492i | \(-0.872305\pi\) |
0.390492 | + | 0.920606i | \(0.372305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52.2302 | + | 52.2302i | −0.715482 | + | 0.715482i | −0.967677 | − | 0.252195i | \(-0.918848\pi\) |
0.252195 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 68.3461 | + | 28.3099i | 0.911282 | + | 0.377465i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 71.0866 | − | 29.4450i | 0.923203 | − | 0.382403i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26.9061 | −0.340583 | −0.170292 | − | 0.985394i | \(-0.554471\pi\) | ||||
−0.170292 | + | 0.985394i | \(0.554471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.8643i | 0.319313i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6315 | − | 25.6667i | −0.128090 | − | 0.309237i | 0.846804 | − | 0.531905i | \(-0.178524\pi\) |
−0.974894 | + | 0.222667i | \(0.928524\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.32533 | + | 12.8565i | −0.0626510 | + | 0.151253i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.31929 | + | 2.31929i | 0.0266585 | + | 0.0266585i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −103.292 | − | 103.292i | −1.16058 | − | 1.16058i | −0.984348 | − | 0.176234i | \(-0.943609\pi\) |
−0.176234 | − | 0.984348i | \(-0.556391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48.6482 | − | 117.447i | 0.534596 | − | 1.29063i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.588862 | − | 1.42164i | −0.00633185 | − | 0.0152864i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107.080i | 1.12715i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 77.9778 | 0.803895 | 0.401948 | − | 0.915663i | \(-0.368333\pi\) | ||||
0.401948 | + | 0.915663i | \(0.368333\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 106.285 | − | 44.0249i | 1.07359 | − | 0.444696i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 104.064 | + | 43.1046i | 1.03033 | + | 0.426778i | 0.832833 | − | 0.553525i | \(-0.186718\pi\) |
0.197500 | + | 0.980303i | \(0.436718\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.6571 | − | 76.6571i | 0.744243 | − | 0.744243i | −0.229148 | − | 0.973392i | \(-0.573594\pi\) |
0.973392 | + | 0.229148i | \(0.0735940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 89.5117 | − | 89.5117i | 0.852492 | − | 0.852492i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 40.9728 | + | 16.9715i | 0.382923 | + | 0.158612i | 0.565837 | − | 0.824517i | \(-0.308553\pi\) |
−0.182914 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 102.183 | − | 42.3255i | 0.937456 | − | 0.388307i | 0.138954 | − | 0.990299i | \(-0.455626\pi\) |
0.798502 | + | 0.601992i | \(0.205626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −160.651 | −1.44731 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 123.602i | 1.09383i | 0.837190 | + | 0.546913i | \(0.184197\pi\) | ||||
−0.837190 | + | 0.546913i | \(0.815803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.1408 | − | 26.8962i | −0.0968761 | − | 0.233880i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 72.7365 | − | 175.602i | 0.621680 | − | 1.50087i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.4594 | − | 28.4594i | −0.239155 | − | 0.239155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −31.7073 | − | 31.7073i | −0.262044 | − | 0.262044i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40.1481 | + | 96.9262i | −0.326408 | + | 0.788018i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 47.4883 | + | 114.647i | 0.379906 | + | 0.917175i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 133.213i | 1.04892i | 0.851434 | + | 0.524462i | \(0.175734\pi\) | ||||
−0.851434 | + | 0.524462i | \(0.824266\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.6367 | 0.190982 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −228.056 | + | 94.4640i | −1.74089 | + | 0.721100i | −0.742185 | + | 0.670195i | \(0.766210\pi\) |
−0.998704 | + | 0.0509041i | \(0.983790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −286.125 | − | 118.517i | −2.15132 | − | 0.891104i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 42.4622 | − | 42.4622i | 0.314535 | − | 0.314535i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −111.817 | + | 111.817i | −0.816180 | + | 0.816180i | −0.985552 | − | 0.169372i | \(-0.945826\pi\) |
0.169372 | + | 0.985552i | \(0.445826\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −31.7750 | − | 13.1616i | −0.228597 | − | 0.0946880i | 0.265445 | − | 0.964126i | \(-0.414481\pi\) |
−0.494042 | + | 0.869438i | \(0.664481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −216.302 | + | 89.5952i | −1.53406 | + | 0.635427i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 125.828 | 0.879914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.12296i | 0.0146411i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 51.7934 | + | 125.040i | 0.352336 | + | 0.850615i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −108.344 | + | 261.565i | −0.727140 | + | 1.75547i | −0.0752422 | + | 0.997165i | \(0.523973\pi\) |
−0.651898 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −51.5292 | − | 51.5292i | −0.341253 | − | 0.341253i | 0.515585 | − | 0.856838i | \(-0.327575\pi\) |
−0.856838 | + | 0.515585i | \(0.827575\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −42.5512 | − | 42.5512i | −0.278112 | − | 0.278112i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.381142 | − | 0.920157i | 0.00245898 | − | 0.00593650i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 39.3450 | + | 94.9872i | 0.250605 | + | 0.605014i | 0.998253 | − | 0.0590811i | \(-0.0188171\pi\) |
−0.747648 | + | 0.664095i | \(0.768817\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 54.8764i | 0.345134i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 84.1994 | 0.522978 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.97467 | − | 2.06057i | 0.0305194 | − | 0.0126416i | −0.367372 | − | 0.930074i | \(-0.619742\pi\) |
0.397891 | + | 0.917433i | \(0.369742\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 115.760 | + | 47.9494i | 0.701577 | + | 0.290603i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 165.012 | − | 165.012i | 0.988097 | − | 0.988097i | −0.0118333 | − | 0.999930i | \(-0.503767\pi\) |
0.999930 | + | 0.0118333i | \(0.00376674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.4985 | − | 27.4985i | 0.162713 | − | 0.162713i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −427.801 | − | 177.201i | −2.50176 | − | 1.03626i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −115.760 | + | 47.9493i | −0.669132 | + | 0.277163i | −0.691275 | − | 0.722591i | \(-0.742951\pi\) |
0.0221438 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −138.486 | −0.791348 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 161.556i | − | 0.912748i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 44.8368 | + | 108.246i | 0.250485 | + | 0.604724i | 0.998243 | − | 0.0592467i | \(-0.0188699\pi\) |
−0.747758 | + | 0.663971i | \(0.768870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 80.3652 | − | 194.019i | 0.444007 | − | 1.07193i | −0.530524 | − | 0.847670i | \(-0.678005\pi\) |
0.974530 | − | 0.224256i | \(-0.0719953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 308.093 | + | 308.093i | 1.68357 | + | 1.68357i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −73.5260 | − | 73.5260i | −0.397438 | − | 0.397438i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2451 | − | 36.8049i | 0.0815245 | − | 0.196818i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 66.4648 | + | 160.460i | 0.351666 | + | 0.848996i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 338.117i | − | 1.77025i | −0.465357 | − | 0.885123i | \(-0.654074\pi\) | ||
0.465357 | − | 0.885123i | \(-0.345926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 234.508 | 1.21507 | 0.607533 | − | 0.794295i | \(-0.292159\pi\) | ||||
0.607533 | + | 0.794295i | \(0.292159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 191.255 | − | 79.2206i | 0.980797 | − | 0.406259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 237.007 | + | 98.1713i | 1.20308 | + | 0.498332i | 0.891993 | − | 0.452050i | \(-0.149307\pi\) |
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −39.2172 | + | 39.2172i | −0.197071 | + | 0.197071i | −0.798743 | − | 0.601672i | \(-0.794501\pi\) |
0.601672 | + | 0.798743i | \(0.294501\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −149.002 | + | 149.002i | −0.741302 | + | 0.741302i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.67273 | − | 2.34972i | −0.0279445 | − | 0.0115750i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −62.7356 | + | 25.9859i | −0.306027 | + | 0.126761i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 125.891 | 0.608169 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 306.542i | − | 1.46671i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 79.9026 | + | 192.902i | 0.378685 | + | 0.914227i | 0.992213 | + | 0.124554i | \(0.0397499\pi\) |
−0.613528 | + | 0.789673i | \(0.710250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 95.9373 | − | 231.613i | 0.450410 | − | 1.08739i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.2756 | + | 11.2756i | 0.0524448 | + | 0.0524448i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.03688 | + | 2.03688i | 0.00938655 | + | 0.00938655i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 133.132 | − | 321.408i | 0.607907 | − | 1.46762i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.1875 | − | 60.8079i | −0.113970 | − | 0.275149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 344.421i | 1.54449i | 0.635326 | + | 0.772244i | \(0.280866\pi\) | ||||
−0.635326 | + | 0.772244i | \(0.719134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −207.058 | −0.920256 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −68.2639 | + | 28.2758i | −0.300722 | + | 0.124563i | −0.527942 | − | 0.849280i | \(-0.677036\pi\) |
0.227220 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −41.8202 | − | 17.3225i | −0.182621 | − | 0.0756440i | 0.289499 | − | 0.957178i | \(-0.406511\pi\) |
−0.472120 | + | 0.881534i | \(0.656511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −256.249 | + | 256.249i | −1.10930 | + | 1.10930i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 203.044 | − | 203.044i | 0.871432 | − | 0.871432i | −0.121197 | − | 0.992629i | \(-0.538673\pi\) |
0.992629 | + | 0.121197i | \(0.0386731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −140.002 | − | 57.9906i | −0.595752 | − | 0.246768i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 117.077 | − | 48.4948i | 0.493995 | − | 0.204619i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −87.6710 | −0.366824 | −0.183412 | − | 0.983036i | \(-0.558714\pi\) | ||||
−0.183412 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.4754i | − | 0.0642135i | −0.999484 | − | 0.0321067i | \(-0.989778\pi\) | ||
0.999484 | − | 0.0321067i | \(-0.0102216\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −114.463 | − | 276.338i | −0.471041 | − | 1.13719i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −33.5233 | + | 80.9325i | −0.136830 | + | 0.330337i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −358.121 | − | 358.121i | −1.44988 | − | 1.44988i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 92.5220 | + | 92.5220i | 0.371574 | + | 0.371574i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −95.9530 | + | 231.651i | −0.382283 | + | 0.922913i | 0.609241 | + | 0.792985i | \(0.291474\pi\) |
−0.991524 | + | 0.129927i | \(0.958526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.8932 | + | 76.9969i | 0.126060 | + | 0.304336i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 65.5409i | − | 0.257023i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −131.142 | −0.510282 | −0.255141 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255141 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 277.847 | − | 115.088i | 1.07277 | − | 0.444355i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.48160 | − | 3.51319i | −0.0324965 | − | 0.0134605i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 281.350 | − | 281.350i | 1.06977 | − | 1.06977i | 0.0723955 | − | 0.997376i | \(-0.476936\pi\) |
0.997376 | − | 0.0723955i | \(-0.0230644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.1156 | + | 25.1156i | −0.0947757 | + | 0.0947757i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 635.626 | + | 263.285i | 2.38062 | + | 0.986085i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 133.290 | − | 55.2107i | 0.495503 | − | 0.205244i | −0.120915 | − | 0.992663i | \(-0.538583\pi\) |
0.616419 | + | 0.787419i | \(0.288583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 368.673 | 1.36042 | 0.680208 | − | 0.733019i | \(-0.261889\pi\) | ||||
0.680208 | + | 0.733019i | \(0.261889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 598.732i | 2.19316i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −52.4559 | − | 126.640i | −0.190749 | − | 0.460508i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6001 | − | 52.1472i | 0.0779786 | − | 0.188257i | −0.880083 | − | 0.474821i | \(-0.842513\pi\) |
0.958061 | + | 0.286564i | \(0.0925130\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.04545 | + | 3.04545i | 0.0109156 | + | 0.0109156i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 85.0605 | + | 85.0605i | 0.302706 | + | 0.302706i | 0.842072 | − | 0.539365i | \(-0.181336\pi\) |
−0.539365 | + | 0.842072i | \(0.681336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.0948 | + | 65.4127i | −0.0957414 | + | 0.231140i | −0.964493 | − | 0.264107i | \(-0.914923\pi\) |
0.868752 | + | 0.495248i | \(0.164923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −192.997 | − | 465.937i | −0.677184 | − | 1.63487i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 196.396i | − | 0.684306i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 268.162 | 0.927896 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −339.306 | + | 140.545i | −1.16600 | + | 0.482973i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −321.033 | − | 132.976i | −1.09568 | − | 0.453844i | −0.239694 | − | 0.970849i | \(-0.577047\pi\) |
−0.855983 | + | 0.517005i | \(0.827047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 73.9404 | − | 73.9404i | 0.250645 | − | 0.250645i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −121.559 | + | 121.559i | −0.409289 | + | 0.409289i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 127.212 | + | 52.6929i | 0.425458 | + | 0.176231i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.6094 | + | 17.6494i | −0.141559 | + | 0.0586358i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −530.504 | −1.75084 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 282.013i | 0.924634i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 92.6973 | + | 223.791i | 0.301946 | + | 0.728961i | 0.999918 | + | 0.0128360i | \(0.00408593\pi\) |
−0.697972 | + | 0.716125i | \(0.745914\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −195.394 | + | 471.724i | −0.632344 | + | 1.52661i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 44.5768 | + | 44.5768i | 0.143334 | + | 0.143334i | 0.775133 | − | 0.631799i | \(-0.217683\pi\) |
−0.631799 | + | 0.775133i | \(0.717683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.9303 | − | 27.9303i | −0.0892343 | − | 0.0892343i | 0.661081 | − | 0.750315i | \(-0.270098\pi\) |
−0.750315 | + | 0.661081i | \(0.770098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −135.590 | + | 327.342i | −0.430443 | + | 1.03918i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −125.850 | − | 303.829i | −0.397003 | − | 0.958450i | −0.988373 | − | 0.152049i | \(-0.951413\pi\) |
0.591370 | − | 0.806400i | \(-0.298587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.07751i | − | 0.0190518i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −208.874 | −0.650699 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −148.140 | + | 61.3618i | −0.458639 | + | 0.189975i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −209.230 | − | 86.6660i | −0.643785 | − | 0.266665i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −368.343 | + | 368.343i | −1.12643 | + | 1.12643i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 309.911 | − | 309.911i | 0.941978 | − | 0.941978i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 169.515 | + | 70.2155i | 0.512131 | + | 0.212131i | 0.623756 | − | 0.781619i | \(-0.285606\pi\) |
−0.111626 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 415.423 | − | 172.074i | 1.24752 | − | 0.516739i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −136.389 | −0.407131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 67.3116i | 0.199738i | 0.995001 | + | 0.0998689i | \(0.0318423\pi\) | ||||
−0.995001 | + | 0.0998689i | \(0.968158\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −222.778 | − | 537.833i | −0.657161 | − | 1.58653i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.09111 | + | 2.63418i | −0.00319974 | + | 0.00772486i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 126.333 | + | 126.333i | 0.368318 | + | 0.368318i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 96.9538 | + | 96.9538i | 0.281026 | + | 0.281026i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 107.157 | − | 258.699i | 0.308809 | − | 0.745530i | −0.690935 | − | 0.722916i | \(-0.742801\pi\) |
0.999744 | − | 0.0226140i | \(-0.00719886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 165.558 | + | 399.692i | 0.474378 | + | 1.14525i | 0.962209 | + | 0.272311i | \(0.0877881\pi\) |
−0.487831 | + | 0.872938i | \(0.662212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 284.024i | 0.809187i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −574.524 | −1.62755 | −0.813773 | − | 0.581183i | \(-0.802590\pi\) | ||||
−0.813773 | + | 0.581183i | \(0.802590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 149.912 | − | 62.0955i | 0.422287 | − | 0.174917i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 175.130 | + | 72.5414i | 0.490562 | + | 0.203197i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −499.243 | + | 499.243i | −1.39065 | + | 1.39065i | −0.566782 | + | 0.823868i | \(0.691812\pi\) |
−0.823868 | + | 0.566782i | \(0.808188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −617.189 | + | 617.189i | −1.70966 | + | 1.70966i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 195.117 | + | 80.8201i | 0.537512 | + | 0.222645i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 208.032 | − | 86.1696i | 0.569950 | − | 0.236081i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −295.566 | −0.805357 | −0.402679 | − | 0.915341i | \(-0.631921\pi\) | ||||
−0.402679 | + | 0.915341i | \(0.631921\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 293.642i | − | 0.795778i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −39.3126 | − | 94.9090i | −0.105964 | − | 0.255819i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −133.878 | + | 323.209i | −0.358921 | + | 0.866512i | 0.636531 | + | 0.771251i | \(0.280369\pi\) |
−0.995452 | + | 0.0952612i | \(0.969631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −413.273 | − | 413.273i | −1.10206 | − | 1.10206i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.10011 | − | 7.10011i | −0.0188332 | − | 0.0188332i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −170.642 | + | 411.967i | −0.450244 | + | 1.08698i | 0.521986 | + | 0.852954i | \(0.325191\pi\) |
−0.972229 | + | 0.234030i | \(0.924809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −240.100 | − | 579.654i | −0.630185 | − | 1.52140i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 254.902i | − | 0.665540i | −0.943008 | − | 0.332770i | \(-0.892017\pi\) | ||
0.943008 | − | 0.332770i | \(-0.107983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −234.558 | −0.609242 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −63.7075 | + | 26.3885i | −0.164619 | + | 0.0681874i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 687.246 | + | 284.667i | 1.76670 | + | 0.731791i | 0.995453 | + | 0.0952550i | \(0.0303666\pi\) |
0.771247 | + | 0.636536i | \(0.219633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.8256 | − | 30.8256i | 0.0788379 | − | 0.0788379i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 822.086 | − | 822.086i | 2.09182 | − | 2.09182i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 75.7781 | + | 31.3883i | 0.191843 | + | 0.0794640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −56.8981 | + | 23.5679i | −0.143320 | + | 0.0593651i | −0.453191 | − | 0.891414i | \(-0.649714\pi\) |
0.309871 | + | 0.950779i | \(0.399714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1458.63 | 3.65572 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 704.010i | − | 1.75564i | −0.478994 | − | 0.877818i | \(-0.658999\pi\) | ||
0.478994 | − | 0.877818i | \(-0.341001\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.80270 | + | 4.35211i | 0.00447321 | + | 0.0107993i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.1730 | − | 72.8441i | 0.0745013 | − | 0.179862i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 210.486 | + | 210.486i | 0.517166 | + | 0.517166i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 528.488 | + | 528.488i | 1.29215 | + | 1.29215i | 0.933457 | + | 0.358690i | \(0.116776\pi\) |
0.358690 | + | 0.933457i | \(0.383224\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 285.014 | − | 688.085i | 0.693465 | − | 1.67417i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 115.737 | + | 279.413i | 0.280234 | + | 0.676544i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 84.6901i | 0.204072i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 161.985 | 0.388453 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 153.485 | − | 63.5754i | 0.366312 | − | 0.151731i | −0.191932 | − | 0.981408i | \(-0.561475\pi\) |
0.558244 | + | 0.829677i | \(0.311475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −240.175 | − | 99.4838i | −0.570487 | − | 0.236304i | 0.0787437 | − | 0.996895i | \(-0.474909\pi\) |
−0.649231 | + | 0.760591i | \(0.724909\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 463.364 | − | 463.364i | 1.09542 | − | 1.09542i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −50.7000 | + | 50.7000i | −0.119294 | + | 0.119294i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −753.562 | − | 312.136i | −1.76478 | − | 0.730997i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −547.516 | + | 226.789i | −1.27626 | + | 0.528645i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 607.318 | 1.40909 | 0.704546 | − | 0.709659i | \(-0.251151\pi\) | ||||
0.704546 | + | 0.709659i | \(0.251151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 233.380i | − | 0.538984i | −0.963003 | − | 0.269492i | \(-0.913144\pi\) | ||
0.963003 | − | 0.269492i | \(-0.0868557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.82637 | − | 9.23768i | −0.00879626 | − | 0.0212361i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 128.371 | − | 309.914i | 0.293754 | − | 0.709185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 496.850 | + | 496.850i | 1.13178 | + | 1.13178i | 0.989882 | + | 0.141896i | \(0.0453200\pi\) |
0.141896 | + | 0.989882i | \(0.454680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −267.863 | − | 267.863i | −0.607399 | − | 0.607399i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −59.8483 | + | 144.487i | −0.135098 | + | 0.326155i | −0.976922 | − | 0.213597i | \(-0.931482\pi\) |
0.841824 | + | 0.539752i | \(0.181482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 170.411 | + | 411.409i | 0.382947 | + | 0.924515i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1333.43i | − | 2.98306i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.4530 | −0.0344165 | −0.0172082 | − | 0.999852i | \(-0.505478\pi\) | ||||
−0.0172082 | + | 0.999852i | \(0.505478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 179.596 | − | 74.3911i | 0.398217 | − | 0.164947i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 317.095 | + | 131.345i | 0.699989 | + | 0.289945i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −274.025 | + | 274.025i | −0.602253 | + | 0.602253i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −93.8365 | + | 93.8365i | −0.205332 | + | 0.205332i | −0.802280 | − | 0.596948i | \(-0.796380\pi\) |
0.596948 | + | 0.802280i | \(0.296380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 83.0778 | + | 34.4120i | 0.180997 | + | 0.0749716i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −574.348 | + | 237.903i | −1.24588 | + | 0.516058i | −0.905546 | − | 0.424248i | \(-0.860538\pi\) |
−0.340329 | + | 0.940306i | \(0.610538\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −568.089 | −1.22697 | −0.613487 | − | 0.789705i | \(-0.710234\pi\) | ||||
−0.613487 | + | 0.789705i | \(0.710234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.69085i | 0.0100879i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 156.459 | + | 377.726i | 0.335030 | + | 0.808835i | 0.998178 | + | 0.0603459i | \(0.0192204\pi\) |
−0.663147 | + | 0.748489i | \(0.730780\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 150.957 | − | 364.442i | 0.321869 | − | 0.777061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −342.405 | − | 342.405i | −0.726974 | − | 0.726974i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.2793 | − | 32.2793i | −0.0682437 | − | 0.0682437i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −211.136 | + | 509.727i | −0.444497 | + | 1.07311i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −58.7783 | − | 141.903i | −0.123225 | − | 0.297492i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 327.880i | 0.684509i | 0.939607 | + | 0.342254i | \(0.111190\pi\) | ||||
−0.939607 | + | 0.342254i | \(0.888810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 491.806 | 1.02247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −366.378 | + | 151.759i | −0.758547 | + | 0.314200i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −219.616 | − | 90.9680i | −0.452817 | − | 0.187563i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 147.493 | − | 147.493i | 0.302861 | − | 0.302861i | −0.539271 | − | 0.842132i | \(-0.681300\pi\) |
0.842132 | + | 0.539271i | \(0.181300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.9324 | + | 17.9324i | −0.0366716 | + | 0.0366716i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −598.802 | − | 248.032i | −1.21956 | − | 0.505157i | −0.322288 | − | 0.946642i | \(-0.604452\pi\) |
−0.897269 | + | 0.441485i | \(0.854452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93704 | + | 1.21656i | −0.00595748 | + | 0.00246767i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −350.700 | −0.708485 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 469.304i | 0.944274i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −58.1446 | − | 140.373i | −0.116522 | − | 0.281309i | 0.854849 | − | 0.518877i | \(-0.173650\pi\) |
−0.971371 | + | 0.237568i | \(0.923650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −420.606 | + | 1015.43i | −0.839533 | + | 2.02681i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 256.204 | + | 256.204i | 0.509351 | + | 0.509351i | 0.914327 | − | 0.404976i | \(-0.132720\pi\) |
−0.404976 | + | 0.914327i | \(0.632720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −242.799 | − | 242.799i | −0.480789 | − | 0.480789i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −70.0921 | + | 169.217i | −0.138249 | + | 0.333762i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −229.271 | − | 553.510i | −0.450435 | − | 1.08745i | −0.972157 | − | 0.234331i | \(-0.924710\pi\) |
0.521722 | − | 0.853115i | \(-0.325290\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 651.251i | 1.27446i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 691.941 | 1.34881 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −305.324 | + | 126.469i | −0.592861 | + | 0.245571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 400.789 | + | 166.012i | 0.775221 | + | 0.321107i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 417.285 | − | 417.285i | 0.804017 | − | 0.804017i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 80.7376 | − | 80.7376i | 0.154967 | − | 0.154967i | −0.625365 | − | 0.780332i | \(-0.715050\pi\) |
0.780332 | + | 0.625365i | \(0.215050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −123.197 | − | 51.0300i | −0.235559 | − | 0.0975717i | 0.261781 | − | 0.965127i | \(-0.415690\pi\) |
−0.497341 | + | 0.867555i | \(0.665690\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 602.595 | − | 249.603i | 1.14780 | − | 0.475435i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.49141 | 0.00283001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 437.800i | − | 0.827599i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 173.044 | + | 417.765i | 0.325883 | + | 0.786751i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 122.907 | − | 296.723i | 0.230594 | − | 0.556704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −95.5966 | − | 95.5966i | −0.178685 | − | 0.178685i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −390.198 | − | 390.198i | −0.726626 | − | 0.726626i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 95.9689 | − | 231.689i | 0.178050 | − | 0.429850i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 184.993 | + | 446.613i | 0.341947 | + | 0.825532i | 0.997519 | + | 0.0703996i | \(0.0224275\pi\) |
−0.655572 | + | 0.755132i | \(0.727573\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 989.085i | 1.82152i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −337.163 | −0.618648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 570.529 | − | 236.321i | 1.04302 | − | 0.432031i | 0.205622 | − | 0.978632i | \(-0.434078\pi\) |
0.837394 | + | 0.546600i | \(0.184078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1126.69 | − | 466.691i | −2.05226 | − | 0.850074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.2973 | + | 17.2973i | −0.0313926 | + | 0.0313926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −167.744 | + | 167.744i | −0.303335 | + | 0.303335i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 452.456 | + | 187.413i | 0.815236 | + | 0.337682i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 340.362 | − | 140.983i | 0.611063 | − | 0.253111i | −0.0556199 | − | 0.998452i | \(-0.517714\pi\) |
0.666683 | + | 0.745341i | \(0.267714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −75.4212 | −0.134922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 187.627i | 0.334451i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −241.885 | − | 583.963i | −0.429637 | − | 1.03723i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) |
0.549766 | − | 0.835319i | \(-0.314717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 144.193 | − | 348.113i | 0.255209 | − | 0.616128i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 161.249 | + | 161.249i | 0.284390 | + | 0.284390i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 88.6373 | + | 88.6373i | 0.155777 | + | 0.155777i | 0.780693 | − | 0.624915i | \(-0.214866\pi\) |
−0.624915 | + | 0.780693i | \(0.714866\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 160.453 | − | 387.367i | 0.281003 | − | 0.678401i | −0.718857 | − | 0.695158i | \(-0.755334\pi\) |
0.999860 | + | 0.0167573i | \(0.00533426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 609.413 | + | 1471.25i | 1.06355 | + | 2.56763i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 150.000i | − | 0.260869i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −501.285 | −0.868778 | −0.434389 | − | 0.900725i | \(-0.643036\pi\) | ||||
−0.434389 | + | 0.900725i | \(0.643036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1020.42 | + | 422.670i | −1.76238 | + | 0.730000i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −226.299 | − | 93.7360i | −0.389498 | − | 0.161336i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 71.8995 | − | 71.8995i | 0.123327 | − | 0.123327i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −409.709 | + | 409.709i | −0.700358 | + | 0.700358i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 805.600 | + | 333.691i | 1.37240 | + | 0.568468i | 0.942439 | − | 0.334378i | \(-0.108526\pi\) |
0.429964 | + | 0.902846i | \(0.358526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.6026 | − | 4.39175i | 0.0180010 | − | 0.00745628i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1208.23 | −2.04438 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1035.33i | 1.74591i | 0.487798 | + | 0.872957i | \(0.337800\pi\) | ||||
−0.487798 | + | 0.872957i | \(0.662200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46.9525 | + | 113.353i | 0.0789117 | + | 0.190510i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 99.9623 | − | 241.330i | 0.167441 | − | 0.404238i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −361.938 | − | 361.938i | −0.604237 | − | 0.604237i | 0.337197 | − | 0.941434i | \(-0.390521\pi\) |
−0.941434 | + | 0.337197i | \(0.890521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −221.839 | − | 221.839i | −0.369116 | − | 0.369116i | 0.498039 | − | 0.867155i | \(-0.334054\pi\) |
−0.867155 | + | 0.498039i | \(0.834054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 225.703 | − | 544.896i | 0.374301 | − | 0.903642i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 52.3109 | + | 126.290i | 0.0864642 | + | 0.208743i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 465.834i | 0.767437i | 0.923450 | + | 0.383719i | \(0.125357\pi\) | ||||
−0.923450 | + | 0.383719i | \(0.874643\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.9189 | 0.0474859 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 662.172 | − | 274.281i | 1.08375 | − | 0.448905i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 292.579 | + | 121.190i | 0.477290 | + | 0.197700i | 0.608341 | − | 0.793676i | \(-0.291835\pi\) |
−0.131051 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 226.146 | − | 226.146i | 0.367717 | − | 0.367717i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −226.657 | + | 226.657i | −0.367354 | + | 0.367354i | −0.866511 | − | 0.499158i | \(-0.833643\pi\) |
0.499158 | + | 0.866511i | \(0.333643\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −756.530 | − | 313.365i | −1.22218 | − | 0.506244i | −0.324078 | − | 0.946030i | \(-0.605054\pi\) |
−0.898102 | + | 0.439787i | \(0.855054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −173.801 | + | 71.9908i | −0.279873 | + | 0.115927i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1287.93 | −2.06730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.3854i | 0.0230167i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 552.503 | + | 1333.86i | 0.881185 | + | 2.12737i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 59.5864 | − | 143.854i | 0.0947320 | − | 0.228703i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −338.810 | − | 338.810i | −0.536941 | − | 0.536941i | 0.385688 | − | 0.922629i | \(-0.373964\pi\) |
−0.922629 | + | 0.385688i | \(0.873964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −695.363 | − | 695.363i | −1.09852 | − | 1.09852i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 155.405 | − | 375.181i | 0.244733 | − | 0.590837i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −158.557 | − | 382.790i | −0.248912 | − | 0.600927i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 701.682i | 1.09809i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 729.839 | 1.13859 | 0.569297 | − | 0.822132i | \(-0.307215\pi\) | ||||
0.569297 | + | 0.822132i | \(0.307215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 370.578 | − | 153.498i | 0.576327 | − | 0.238722i | −0.0754293 | − | 0.997151i | \(-0.524033\pi\) |
0.651756 | + | 0.758429i | \(0.274033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −69.3867 | − | 28.7409i | −0.107576 | − | 0.0445595i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 179.567 | − | 179.567i | 0.277538 | − | 0.277538i | −0.554587 | − | 0.832126i | \(-0.687124\pi\) |
0.832126 | + | 0.554587i | \(0.187124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −211.673 | + | 211.673i | −0.326152 | + | 0.326152i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5343 | − | 5.19189i | −0.0192540 | − | 0.00797525i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −964.894 | + | 399.672i | −1.47763 | + | 0.612056i | −0.968585 | − | 0.248683i | \(-0.920002\pi\) |
−0.509048 | + | 0.860738i | \(0.670002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 752.497 | 1.14885 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 973.720i | 1.48207i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −233.939 | − | 564.778i | −0.354990 | − | 0.857023i | −0.995989 | − | 0.0894804i | \(-0.971479\pi\) |
0.640998 | − | 0.767542i | \(-0.278521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 281.181 | − | 678.831i | 0.425387 | − | 1.02698i | −0.555345 | − | 0.831620i | \(-0.687414\pi\) |
0.980732 | − | 0.195356i | \(-0.0625862\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 219.197 | + | 219.197i | 0.330614 | + | 0.330614i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 667.580 | + | 667.580i | 1.00388 | + | 1.00388i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.54508 | − | 6.14437i | 0.00381571 | − | 0.00921195i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −620.775 | − | 1498.68i | −0.927915 | − | 2.24018i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 807.333i | − | 1.20318i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 705.345 | 1.04806 | 0.524031 | − | 0.851699i | \(-0.324428\pi\) | ||||
0.524031 | + | 0.851699i | \(0.324428\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 285.857 | − | 118.406i | 0.423492 | − | 0.175416i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.4550 | − | 4.33061i | −0.0154432 | − | 0.00639676i | 0.374948 | − | 0.927046i | \(-0.377660\pi\) |
−0.390392 | + | 0.920649i | \(0.627660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 486.147 | − | 486.147i | 0.715976 | − | 0.715976i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 246.074 | − | 246.074i | 0.361342 | − | 0.361342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 307.101 | + | 127.205i | 0.449635 | + | 0.186245i | 0.595998 | − | 0.802986i | \(-0.296757\pi\) |
−0.146363 | + | 0.989231i | \(0.546757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 445.364 | − | 184.476i | 0.650166 | − | 0.269308i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 213.194 | 0.310327 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 167.995i | − | 0.243824i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 243.176 | + | 587.078i | 0.351919 | + | 0.849607i | 0.996383 | + | 0.0849727i | \(0.0270803\pi\) |
−0.644465 | + | 0.764634i | \(0.722920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 388.159 | − | 937.099i | 0.560114 | − | 1.35224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 74.1366 | + | 74.1366i | 0.106671 | + | 0.106671i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −71.9010 | − | 71.9010i | −0.103158 | − | 0.103158i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −517.546 | + | 1249.47i | −0.740410 | + | 1.78751i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 65.7383 | + | 158.706i | 0.0937779 | + | 0.226400i | 0.963807 | − | 0.266600i | \(-0.0859003\pi\) |
−0.870029 | + | 0.493000i | \(0.835900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1198.14i | − | 1.70432i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 713.712 | 1.01236 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 917.510 | − | 380.045i | 1.29775 | − | 0.537546i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1029.00 | − | 426.228i | −1.45135 | − | 0.601167i | −0.488827 | − | 0.872381i | \(-0.662575\pi\) |
−0.962519 | + | 0.271214i | \(0.912575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −250.803 | + | 250.803i | −0.352747 | + | 0.352747i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.20623 | + | 2.20623i | −0.00309429 | + | 0.00309429i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −354.380 | − | 146.789i | −0.495637 | − | 0.205299i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 381.484 | − | 158.016i | 0.532056 | − | 0.220385i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 439.735 | 0.611592 | 0.305796 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305796 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 955.826i | − | 1.32570i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.8925 | + | 67.3385i | 0.0385789 | + | 0.0931377i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.18599 | + | 10.1059i | −0.00577378 | + | 0.0139391i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −137.308 | − | 137.308i | −0.188869 | − | 0.188869i | 0.606338 | − | 0.795207i | \(-0.292638\pi\) |
−0.795207 | + | 0.606338i | \(0.792638\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 831.529 | + | 831.529i | 1.14064 | + | 1.14064i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.13791 | + | 22.0609i | −0.0125006 | + | 0.0301790i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 57.7693 | + | 139.467i | 0.0788121 | + | 0.190269i | 0.958374 | − | 0.285514i | \(-0.0921645\pi\) |
−0.879562 | + | 0.475784i | \(0.842164\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 412.584i | − | 0.561339i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 390.447 | 0.529778 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −536.590 | + | 222.263i | −0.726103 | + | 0.300762i | −0.714950 | − | 0.699176i | \(-0.753550\pi\) |
−0.0111538 | + | 0.999938i | \(0.503550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2203.76 | + | 912.828i | 2.97404 | + | 1.23189i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −907.324 | + | 907.324i | −1.22116 | + | 1.22116i | −0.253944 | + | 0.967219i | \(0.581728\pi\) |
−0.967219 | + | 0.253944i | \(0.918272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 610.278 | − | 610.278i | 0.819165 | − | 0.819165i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −338.351 | − | 140.150i | −0.452947 | − | 0.187617i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 361.249 | − | 149.634i | 0.482309 | − | 0.199779i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 662.862 | 0.882639 | 0.441320 | − | 0.897350i | \(-0.354511\pi\) | ||||
0.441320 | + | 0.897350i | \(0.354511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1180.93i | − | 1.56830i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 85.0132 | + | 205.240i | 0.112600 | + | 0.271841i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 76.1190 | − | 183.767i | 0.100553 | − | 0.242757i | −0.865595 | − | 0.500745i | \(-0.833059\pi\) |
0.966148 | + | 0.257988i | \(0.0830594\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −277.554 | − | 277.554i | −0.365684 | − | 0.365684i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 435.811 | + | 435.811i | 0.572683 | + | 0.572683i | 0.932877 | − | 0.360195i | \(-0.117290\pi\) |
−0.360195 | + | 0.932877i | \(0.617290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 373.176 | − | 900.926i | 0.489090 | − | 1.18077i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 70.2012 | + | 169.481i | 0.0917662 | + | 0.221543i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 494.578i | 0.644821i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1422.48 | −1.84978 | −0.924889 | − | 0.380237i | \(-0.875843\pi\) | ||||
−0.924889 | + | 0.380237i | \(0.875843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 570.642 | − | 236.368i | 0.740132 | − | 0.306573i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.439715 | − | 0.182136i | −0.000568842 | − | 0.000235622i | 0.382399 | − | 0.923997i | \(-0.375098\pi\) |
−0.382968 | + | 0.923762i | \(0.625098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.62867 | − | 3.62867i | 0.00468215 | − | 0.00468215i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1001.57 | + | 1001.57i | −1.28902 | + | 1.28902i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −722.878 | − | 299.426i | −0.927956 | − | 0.384372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −429.160 | + | 177.764i | −0.549500 | + | 0.227610i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.7184 | 0.0175204 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 313.420i | − | 0.399262i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0303 | − | 55.6002i | −0.0292635 | − | 0.0706482i | 0.908572 | − | 0.417728i | \(-0.137173\pi\) |
−0.937836 | + | 0.347079i | \(0.887173\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −717.144 | + | 1731.34i | −0.908928 | + | 2.19435i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 770.590 | + | 770.590i | 0.974197 | + | 0.974197i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −943.175 | − | 943.175i | −1.18938 | − | 1.18938i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 64.0181 | − | 154.553i | 0.0805259 | − | 0.194407i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.3444 | + | 119.128i | 0.0619127 | + | 0.149470i | 0.951808 | − | 0.306694i | \(-0.0992229\pi\) |
−0.889895 | + | 0.456165i | \(0.849223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 226.918i | − | 0.284003i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1925.65 | −2.40406 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −595.542 | + | 246.682i | −0.741647 | + | 0.307200i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −237.138 | − | 98.2260i | −0.294582 | − | 0.122020i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −480.478 | + | 480.478i | −0.595388 | + | 0.595388i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.6470 | − | 29.6470i | 0.0366465 | − | 0.0366465i | −0.688546 | − | 0.725193i | \(-0.741751\pi\) |
0.725193 | + | 0.688546i | \(0.241751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 755.209 | + | 312.818i | 0.931207 | + | 0.385719i | 0.796136 | − | 0.605117i | \(-0.206874\pi\) |
0.135071 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1604.21 | + | 664.486i | −1.97320 | + | 0.817326i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4144 | −0.0201404 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 183.741i | 0.224897i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −641.305 | − | 1548.25i | −0.783034 | − | 1.89041i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 120.712 | − | 291.425i | 0.147031 | − | 0.354964i | −0.833156 | − | 0.553038i | \(-0.813469\pi\) |
0.980187 | + | 0.198074i | \(0.0634685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −173.105 | − | 173.105i | −0.210334 | − | 0.210334i | 0.594076 | − | 0.804409i | \(-0.297518\pi\) |
−0.804409 | + | 0.594076i | \(0.797518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 456.504 | + | 456.504i | 0.553338 | + | 0.553338i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 59.9551 | − | 144.744i | 0.0724971 | − | 0.175023i | −0.883477 | − | 0.468475i | \(-0.844804\pi\) |
0.955974 | + | 0.293451i | \(0.0948038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 259.829 | + | 627.283i | 0.313425 | + | 0.756674i | 0.999573 | + | 0.0292124i | \(0.00929993\pi\) |
−0.686149 | + | 0.727461i | \(0.740700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 265.840i | 0.319904i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −131.178 | −0.157476 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −657.240 | + | 272.238i | −0.787114 | + | 0.326033i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.94599 | − | 2.46291i | −0.00710394 | − | 0.00294255i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −182.343 | + | 182.343i | −0.217333 | + | 0.217333i | −0.807374 | − | 0.590040i | \(-0.799112\pi\) |
0.590040 | + | 0.807374i | \(0.299112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 594.334 | − | 594.334i | 0.706699 | − | 0.706699i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −523.436 | − | 216.814i | −0.620920 | − | 0.257194i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −109.526 | + | 45.3671i | −0.129617 | + | 0.0536889i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −395.354 | −0.466770 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 333.466i | − | 0.392775i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 124.657 | + | 300.947i | 0.146482 | + | 0.353640i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −300.757 | + | 726.092i | −0.352588 | + | 0.851222i | 0.643712 | + | 0.765268i | \(0.277394\pi\) |
−0.996299 | + | 0.0859535i | \(0.972606\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 998.134 | + | 998.134i | 1.16741 | + | 1.16741i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −545.430 | − | 545.430i | −0.636441 | − | 0.636441i | 0.313235 | − | 0.949676i | \(-0.398587\pi\) |
−0.949676 | + | 0.313235i | \(0.898587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −230.652 | + | 556.843i | −0.268512 | + | 0.648246i | −0.999414 | − | 0.0342370i | \(-0.989100\pi\) |
0.730901 | + | 0.682483i | \(0.239100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 353.979 | + | 854.580i | 0.411125 | + | 0.992544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 980.846i | 1.13655i | 0.822837 | + | 0.568277i | \(0.192390\pi\) | ||||
−0.822837 | + | 0.568277i | \(0.807610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 381.962 | 0.441574 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1166.86 | + | 483.328i | −1.34586 | + | 0.557472i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −216.933 | − | 89.8568i | −0.249636 | − | 0.103403i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 456.143 | − | 456.143i | 0.523701 | − | 0.523701i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 726.865 | − | 726.865i | 0.832606 | − | 0.832606i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1010.82 | + | 418.696i | 1.15522 | + | 0.478509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1395.56 | − | 578.059i | 1.59129 | − | 0.659132i | 0.601137 | − | 0.799146i | \(-0.294715\pi\) |
0.990150 | + | 0.140014i | \(0.0447146\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1636.59 | 1.86188 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1513.62i | 1.71807i | 0.511914 | + | 0.859037i | \(0.328937\pi\) | ||||
−0.511914 | + | 0.859037i | \(0.671063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 91.3318 | + | 220.494i | 0.103434 | + | 0.249711i | 0.967121 | − | 0.254317i | \(-0.0818508\pi\) |
−0.863687 | + | 0.504028i | \(0.831851\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −188.470 | + | 455.006i | −0.212960 | + | 0.514131i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −892.828 | − | 892.828i | −1.00657 | − | 1.00657i | −0.999978 | − | 0.00659168i | \(-0.997902\pi\) |
−0.00659168 | − | 0.999978i | \(-0.502098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 830.510 | + | 830.510i | 0.934207 | + | 0.934207i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −86.3777 | + | 208.534i | −0.0969447 | + | 0.234045i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −668.203 | − | 1613.19i | −0.748268 | − | 1.80648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 357.168i | − | 0.399071i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −648.512 | −0.722978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.210208 | − | 0.0870710i | 0.000233824 | − | 9.68531e-5i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.1388 | − | 20.3540i | −0.0545381 | − | 0.0225904i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 153.596 | − | 153.596i | 0.170095 | − | 0.170095i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −452.680 | + | 452.680i | −0.500199 | + | 0.500199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 469.078 | + | 194.298i | 0.517175 | + | 0.214221i | 0.625976 | − | 0.779843i | \(-0.284701\pi\) |
−0.108800 | + | 0.994064i | \(0.534701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1371.82 | − | 568.226i | 1.50915 | − | 0.625111i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −469.566 | −0.515441 | −0.257720 | − | 0.966220i | \(-0.582971\pi\) | ||||
−0.257720 | + | 0.966220i | \(0.582971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 242.446i | − | 0.265549i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −508.293 | − | 1227.13i | −0.555512 | − | 1.34112i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −832.872 | + | 2010.73i | −0.908257 | + | 2.19273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −737.868 | − | 737.868i | −0.802903 | − | 0.802903i | 0.180645 | − | 0.983548i | \(-0.442181\pi\) |
−0.983548 | + | 0.180645i | \(0.942181\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −806.710 | − | 806.710i | −0.875907 | − | 0.875907i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −293.696 | + | 709.045i | −0.318197 | + | 0.768196i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −205.027 | − | 494.979i | −0.221651 | − | 0.535113i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1429.11i | − | 1.54165i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 796.539 | 0.857416 | 0.428708 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428708 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −932.554 | + | 386.277i | −1.00167 | + | 0.414905i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −274.312 | − | 113.624i | −0.294011 | − | 0.121783i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −85.8723 | + | 85.8723i | −0.0918420 | + | 0.0918420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 764.262 | − | 764.262i | 0.815648 | − | 0.815648i | −0.169826 | − | 0.985474i | \(-0.554321\pi\) |
0.985474 | + | 0.169826i | \(0.0543206\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 171.875 | + | 71.1927i | 0.183040 | + | 0.0758176i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 113.549 | − | 47.0336i | 0.120669 | − | 0.0499826i | −0.321532 | − | 0.946899i | \(-0.604198\pi\) |
0.442201 | + | 0.896916i | \(0.354198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 212.725 | 0.225583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 529.456i | − | 0.560271i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −396.726 | − | 957.782i | −0.418930 | − | 1.01139i | −0.982658 | − | 0.185425i | \(-0.940634\pi\) |
0.563729 | − | 0.825960i | \(-0.309366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −407.560 | + | 983.937i | −0.429463 | + | 1.03681i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1095.23 | + | 1095.23i | 1.15166 | + | 1.15166i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 391.136 | + | 391.136i | 0.410426 | + | 0.410426i | 0.881887 | − | 0.471461i | \(-0.156273\pi\) |
−0.471461 | + | 0.881887i | \(0.656273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −394.443 | + | 952.270i | −0.413030 | + | 0.997142i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.9539 | + | 26.4452i | 0.0114461 | + | 0.0276334i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1394.23i | 1.45383i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 960.893 | 0.999889 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 540.123 | − | 223.726i | 0.560875 | − | 0.232322i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −660.465 | − | 273.574i | −0.684420 | − | 0.283496i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8939 | − | 22.8939i | 0.0236752 | − | 0.0236752i | −0.695170 | − | 0.718845i | \(-0.744671\pi\) |
0.718845 | + | 0.695170i | \(0.244671\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 534.009 | − | 534.009i | 0.551093 | − | 0.551093i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 619.006 | + | 256.401i | 0.637493 | + | 0.264058i | 0.677933 | − | 0.735124i | \(-0.262876\pi\) |
−0.0404399 | + | 0.999182i | \(0.512876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −280.154 | + | 116.044i | −0.287928 | + | 0.119264i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1066.63 | 1.09398 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 430.856i | − | 0.440999i | −0.975387 | − | 0.220500i | \(-0.929231\pi\) | ||
0.975387 | − | 0.220500i | \(-0.0707688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −487.844 | − | 1177.76i | −0.498309 | − | 1.20302i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 557.955 | − | 1347.02i | 0.568762 | − | 1.37311i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −154.209 | − | 154.209i | −0.156876 | − | 0.156876i | 0.624305 | − | 0.781181i | \(-0.285382\pi\) |
−0.781181 | + | 0.624305i | \(0.785382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −552.978 | − | 552.978i | −0.561399 | − | 0.561399i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −789.945 | + | 1907.09i | −0.800349 | + | 1.93221i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.1168 | − | 46.1520i | −0.0193294 | − | 0.0466653i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 966.543i | − | 0.975320i | −0.873033 | − | 0.487660i | \(-0.837850\pi\) | ||
0.873033 | − | 0.487660i | \(-0.162150\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −864.169 | −0.870260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 156.201 | − | 64.7007i | 0.156986 | − | 0.0650258i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 732.694 | + | 303.492i | 0.734899 | + | 0.304405i | 0.718564 | − | 0.695461i | \(-0.244800\pi\) |
0.0163357 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −475.120 | + | 475.120i | −0.475596 | + | 0.475596i |
(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 | 128.3.h.a.15.1 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.27.4 | yes | 28 | ||
8.3 | odd | 2 | 256.3.h.b.31.1 | 28 | |||
8.5 | even | 2 | 256.3.h.a.31.7 | 28 | |||
12.11 | even | 2 | 288.3.u.a.91.4 | 28 | |||
32.3 | odd | 8 | 256.3.h.a.223.7 | 28 | |||
32.13 | even | 8 | 32.3.h.a.19.4 | ✓ | 28 | ||
32.19 | odd | 8 | inner | 128.3.h.a.111.1 | 28 | ||
32.29 | even | 8 | 256.3.h.b.223.1 | 28 | |||
96.77 | odd | 8 | 288.3.u.a.19.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.4 | ✓ | 28 | 32.13 | even | 8 | ||
32.3.h.a.27.4 | yes | 28 | 4.3 | odd | 2 | ||
128.3.h.a.15.1 | 28 | 1.1 | even | 1 | trivial | ||
128.3.h.a.111.1 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.a.31.7 | 28 | 8.5 | even | 2 | |||
256.3.h.a.223.7 | 28 | 32.3 | odd | 8 | |||
256.3.h.b.31.1 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.223.1 | 28 | 32.29 | even | 8 | |||
288.3.u.a.19.4 | 28 | 96.77 | odd | 8 | |||
288.3.u.a.91.4 | 28 | 12.11 | even | 2 |