Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,4,Mod(56,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.56");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.l (of order \(6\), degree \(2\), 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: | \(10.0893266110\) |
Analytic rank: | \(0\) |
Dimension: | \(116\) |
Relative dimension: | \(58\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.52 | ||
Character | \(\chi\) | \(=\) | 171.113 |
Dual form | 171.4.l.a.56.52 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33859 | + | 4.05055i | 0.826815 | + | 1.43209i | 0.900524 | + | 0.434806i | \(0.143183\pi\) |
−0.0737095 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(3\) | 0.999995 | − | 5.09902i | 0.192449 | − | 0.981307i | ||||
\(4\) | −6.93796 | + | 12.0169i | −0.867246 | + | 1.50211i | ||||
\(5\) | −12.0396 | − | 6.95107i | −1.07686 | − | 0.621723i | −0.146809 | − | 0.989165i | \(-0.546900\pi\) |
−0.930046 | + | 0.367442i | \(0.880234\pi\) | |||||||
\(6\) | 22.9924 | − | 7.87397i | 1.56444 | − | 0.535756i | ||||
\(7\) | −3.03908 | − | 5.26384i | −0.164095 | − | 0.284221i | 0.772239 | − | 0.635333i | \(-0.219137\pi\) |
−0.936333 | + | 0.351112i | \(0.885804\pi\) | |||||||
\(8\) | −27.4827 | −1.21458 | ||||||||
\(9\) | −25.0000 | − | 10.1980i | −0.925927 | − | 0.377703i | ||||
\(10\) | − | 65.0227i | − | 2.05620i | ||||||
\(11\) | −47.9412 | + | 27.6789i | −1.31407 | + | 0.758681i | −0.982768 | − | 0.184842i | \(-0.940823\pi\) |
−0.331306 | + | 0.943523i | \(0.607489\pi\) | |||||||
\(12\) | 54.3365 | + | 47.3937i | 1.30713 | + | 1.14011i | ||||
\(13\) | −62.8599 | − | 36.2922i | −1.34109 | − | 0.774280i | −0.354124 | − | 0.935199i | \(-0.615221\pi\) |
−0.986968 | + | 0.160919i | \(0.948554\pi\) | |||||||
\(14\) | 14.2143 | − | 24.6199i | 0.271352 | − | 0.469996i | ||||
\(15\) | −47.4832 | + | 54.4392i | −0.817340 | + | 0.937075i | ||||
\(16\) | −8.76699 | − | 15.1849i | −0.136984 | − | 0.237264i | ||||
\(17\) | − | 94.7080i | − | 1.35118i | −0.737277 | − | 0.675590i | \(-0.763889\pi\) | ||
0.737277 | − | 0.675590i | \(-0.236111\pi\) | |||||||
\(18\) | −17.1572 | − | 125.113i | −0.224666 | − | 1.63830i | ||||
\(19\) | 73.8113 | + | 37.5618i | 0.891236 | + | 0.453541i | ||||
\(20\) | 167.061 | − | 96.4525i | 1.86780 | − | 1.07837i | ||||
\(21\) | −29.8795 | + | 10.2325i | −0.310488 | + | 0.106329i | ||||
\(22\) | −224.229 | − | 129.459i | −2.17299 | − | 1.25458i | ||||
\(23\) | 81.2476 | + | 46.9083i | 0.736578 | + | 0.425264i | 0.820824 | − | 0.571181i | \(-0.193515\pi\) |
−0.0842456 | + | 0.996445i | \(0.526848\pi\) | |||||||
\(24\) | −27.4826 | + | 140.135i | −0.233744 | + | 1.19187i | ||||
\(25\) | 34.1347 | + | 59.1231i | 0.273078 | + | 0.472985i | ||||
\(26\) | − | 339.489i | − | 2.56074i | ||||||
\(27\) | −76.9997 | + | 117.278i | −0.548837 | + | 0.835930i | ||||
\(28\) | 84.3401 | 0.569242 | ||||||||
\(29\) | −95.7201 | − | 165.792i | −0.612923 | − | 1.06161i | −0.990745 | − | 0.135736i | \(-0.956660\pi\) |
0.377822 | − | 0.925878i | \(-0.376673\pi\) | |||||||
\(30\) | −331.552 | − | 65.0224i | −2.01776 | − | 0.395714i | ||||
\(31\) | 99.3033 | + | 57.3328i | 0.575336 | + | 0.332170i | 0.759278 | − | 0.650767i | \(-0.225552\pi\) |
−0.183942 | + | 0.982937i | \(0.558886\pi\) | |||||||
\(32\) | −68.9262 | + | 119.384i | −0.380767 | + | 0.659508i | ||||
\(33\) | 93.1941 | + | 272.132i | 0.491607 | + | 1.43552i | ||||
\(34\) | 383.619 | − | 221.483i | 1.93501 | − | 1.11718i | ||||
\(35\) | 84.4994i | 0.408086i | ||||||||
\(36\) | 295.998 | − | 229.670i | 1.37036 | − | 1.06329i | ||||
\(37\) | − | 119.548i | − | 0.531177i | −0.964087 | − | 0.265588i | \(-0.914434\pi\) | ||
0.964087 | − | 0.265588i | \(-0.0855662\pi\) | |||||||
\(38\) | 20.4680 | + | 386.818i | 0.0873776 | + | 1.65132i | ||||
\(39\) | −247.914 | + | 284.232i | −1.01790 | + | 1.16701i | ||||
\(40\) | 330.881 | + | 191.034i | 1.30792 | + | 0.755130i | ||||
\(41\) | −125.956 | + | 218.162i | −0.479781 | + | 0.831006i | −0.999731 | − | 0.0231912i | \(-0.992617\pi\) |
0.519950 | + | 0.854197i | \(0.325951\pi\) | |||||||
\(42\) | −111.323 | − | 97.0987i | −0.408988 | − | 0.356730i | ||||
\(43\) | 110.035 | + | 190.587i | 0.390238 | + | 0.675912i | 0.992481 | − | 0.122401i | \(-0.0390594\pi\) |
−0.602243 | + | 0.798313i | \(0.705726\pi\) | |||||||
\(44\) | − | 768.140i | − | 2.63185i | ||||||
\(45\) | 230.103 | + | 296.557i | 0.762262 | + | 0.982401i | ||||
\(46\) | 438.797i | 1.40646i | ||||||||
\(47\) | −73.9759 | + | 42.7100i | −0.229585 | + | 0.132551i | −0.610381 | − | 0.792108i | \(-0.708983\pi\) |
0.380796 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(48\) | −86.1949 | + | 29.5183i | −0.259191 | + | 0.0887624i | ||||
\(49\) | 153.028 | − | 265.052i | 0.446146 | − | 0.772747i | ||||
\(50\) | −159.654 | + | 276.529i | −0.451570 | + | 0.782142i | ||||
\(51\) | −482.918 | − | 94.7075i | −1.32592 | − | 0.260033i | ||||
\(52\) | 872.239 | − | 503.587i | 2.32611 | − | 1.34298i | ||||
\(53\) | −460.643 | −1.19385 | −0.596927 | − | 0.802296i | \(-0.703612\pi\) | ||||
−0.596927 | + | 0.802296i | \(0.703612\pi\) | |||||||
\(54\) | −655.109 | − | 37.6270i | −1.65091 | − | 0.0948221i | ||||
\(55\) | 769.591 | 1.88676 | ||||||||
\(56\) | 83.5222 | + | 144.665i | 0.199306 | + | 0.345208i | ||||
\(57\) | 265.339 | − | 338.804i | 0.616580 | − | 0.787292i | ||||
\(58\) | 447.699 | − | 775.438i | 1.01355 | − | 1.75552i | ||||
\(59\) | 364.768 | − | 631.797i | 0.804894 | − | 1.39412i | −0.111469 | − | 0.993768i | \(-0.535555\pi\) |
0.916363 | − | 0.400349i | \(-0.131111\pi\) | |||||||
\(60\) | −324.754 | − | 948.298i | −0.698759 | − | 2.04041i | ||||
\(61\) | −66.4453 | − | 115.087i | −0.139466 | − | 0.241563i | 0.787828 | − | 0.615895i | \(-0.211205\pi\) |
−0.927295 | + | 0.374332i | \(0.877872\pi\) | |||||||
\(62\) | 536.311i | 1.09857i | ||||||||
\(63\) | 22.2964 | + | 162.589i | 0.0445887 | + | 0.325147i | ||||
\(64\) | −785.031 | −1.53326 | ||||||||
\(65\) | 504.539 | + | 873.887i | 0.962774 | + | 1.66757i | ||||
\(66\) | −884.341 | + | 1013.89i | −1.64932 | + | 1.89093i | ||||
\(67\) | −56.4927 | − | 32.6161i | −0.103010 | − | 0.0594730i | 0.447610 | − | 0.894229i | \(-0.352275\pi\) |
−0.550620 | + | 0.834756i | \(0.685609\pi\) | |||||||
\(68\) | 1138.10 | + | 657.081i | 2.02963 | + | 1.17180i | ||||
\(69\) | 320.434 | − | 367.375i | 0.559068 | − | 0.640968i | ||||
\(70\) | −342.269 | + | 197.609i | −0.584414 | + | 0.337411i | ||||
\(71\) | −943.829 | −1.57763 | −0.788817 | − | 0.614629i | \(-0.789306\pi\) | ||||
−0.788817 | + | 0.614629i | \(0.789306\pi\) | |||||||
\(72\) | 687.069 | + | 280.269i | 1.12461 | + | 0.458750i | ||||
\(73\) | 30.1146 | 0.0482828 | 0.0241414 | − | 0.999709i | \(-0.492315\pi\) | ||||
0.0241414 | + | 0.999709i | \(0.492315\pi\) | |||||||
\(74\) | 484.234 | − | 279.573i | 0.760690 | − | 0.439185i | ||||
\(75\) | 335.604 | − | 114.931i | 0.516697 | − | 0.176948i | ||||
\(76\) | −963.477 | + | 626.381i | −1.45419 | + | 0.945406i | ||||
\(77\) | 291.394 | + | 168.237i | 0.431266 | + | 0.248991i | ||||
\(78\) | −1731.06 | − | 339.488i | −2.51288 | − | 0.492813i | ||||
\(79\) | 597.192 | − | 344.789i | 0.850498 | − | 0.491035i | −0.0103206 | − | 0.999947i | \(-0.503285\pi\) |
0.860819 | + | 0.508911i | \(0.169952\pi\) | |||||||
\(80\) | 243.760i | 0.340665i | ||||||||
\(81\) | 521.002 | + | 509.900i | 0.714680 | + | 0.699451i | ||||
\(82\) | −1178.24 | −1.58676 | ||||||||
\(83\) | −1196.61 | + | 690.862i | −1.58247 | + | 0.913638i | −0.587970 | + | 0.808883i | \(0.700073\pi\) |
−0.994498 | + | 0.104756i | \(0.966594\pi\) | |||||||
\(84\) | 84.3397 | − | 430.052i | 0.109550 | − | 0.558601i | ||||
\(85\) | −658.322 | + | 1140.25i | −0.840059 | + | 1.45503i | ||||
\(86\) | −514.654 | + | 891.407i | −0.645309 | + | 1.11771i | ||||
\(87\) | −941.097 | + | 322.288i | −1.15973 | + | 0.397159i | ||||
\(88\) | 1317.55 | − | 760.691i | 1.59604 | − | 0.921476i | ||||
\(89\) | −618.214 | −0.736298 | −0.368149 | − | 0.929767i | \(-0.620008\pi\) | ||||
−0.368149 | + | 0.929767i | \(0.620008\pi\) | |||||||
\(90\) | −663.101 | + | 1625.57i | −0.776633 | + | 1.90389i | ||||
\(91\) | 441.179i | 0.508221i | ||||||||
\(92\) | −1127.39 | + | 650.897i | −1.27759 | + | 0.737616i | ||||
\(93\) | 391.644 | − | 449.017i | 0.436684 | − | 0.500655i | ||||
\(94\) | −345.998 | − | 199.762i | −0.379649 | − | 0.219190i | ||||
\(95\) | −627.564 | − | 965.297i | −0.677755 | − | 1.04250i | ||||
\(96\) | 539.814 | + | 470.839i | 0.573901 | + | 0.500571i | ||||
\(97\) | −359.859 | + | 207.765i | −0.376682 | + | 0.217478i | −0.676374 | − | 0.736559i | \(-0.736450\pi\) |
0.299692 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(98\) | 1431.48 | 1.47552 | ||||||||
\(99\) | 1480.80 | − | 203.068i | 1.50329 | − | 0.206153i | ||||
\(100\) | −947.302 | −0.947302 | ||||||||
\(101\) | 1493.00 | − | 861.982i | 1.47088 | − | 0.849212i | 0.471413 | − | 0.881912i | \(-0.343744\pi\) |
0.999465 | + | 0.0327005i | \(0.0104107\pi\) | |||||||
\(102\) | −745.728 | − | 2177.56i | −0.723902 | − | 2.11383i | ||||
\(103\) | −328.361 | − | 189.579i | −0.314120 | − | 0.181357i | 0.334649 | − | 0.942343i | \(-0.391382\pi\) |
−0.648769 | + | 0.760986i | \(0.724716\pi\) | |||||||
\(104\) | 1727.56 | + | 997.407i | 1.62886 | + | 0.940422i | ||||
\(105\) | 430.864 | + | 84.4990i | 0.400457 | + | 0.0785358i | ||||
\(106\) | −1077.25 | − | 1865.86i | −0.987096 | − | 1.70970i | ||||
\(107\) | −289.640 | −0.261688 | −0.130844 | − | 0.991403i | \(-0.541769\pi\) | ||||
−0.130844 | + | 0.991403i | \(0.541769\pi\) | |||||||
\(108\) | −875.094 | − | 1738.97i | −0.779685 | − | 1.54937i | ||||
\(109\) | − | 1277.62i | − | 1.12269i | −0.827581 | − | 0.561347i | \(-0.810283\pi\) | ||
0.827581 | − | 0.561347i | \(-0.189717\pi\) | |||||||
\(110\) | 1799.75 | + | 3117.27i | 1.56000 | + | 2.70200i | ||||
\(111\) | −609.577 | − | 119.547i | −0.521247 | − | 0.102225i | ||||
\(112\) | −53.2871 | + | 92.2960i | −0.0449568 | + | 0.0778674i | ||||
\(113\) | 90.4256 | − | 156.622i | 0.0752790 | − | 0.130387i | −0.825929 | − | 0.563775i | \(-0.809349\pi\) |
0.901208 | + | 0.433388i | \(0.142682\pi\) | |||||||
\(114\) | 1992.86 | + | 282.449i | 1.63727 | + | 0.232051i | ||||
\(115\) | −652.126 | − | 1129.52i | −0.528792 | − | 0.915895i | ||||
\(116\) | 2656.41 | 2.12622 | ||||||||
\(117\) | 1201.39 | + | 1548.35i | 0.949304 | + | 1.22346i | ||||
\(118\) | 3412.16 | 2.66199 | ||||||||
\(119\) | −498.528 | + | 287.825i | −0.384033 | + | 0.221722i | ||||
\(120\) | 1304.97 | − | 1496.14i | 0.992722 | − | 1.13815i | ||||
\(121\) | 866.739 | − | 1501.24i | 0.651194 | − | 1.12790i | ||||
\(122\) | 310.776 | − | 538.280i | 0.230626 | − | 0.399456i | ||||
\(123\) | 986.459 | + | 860.414i | 0.723138 | + | 0.630739i | ||||
\(124\) | −1377.93 | + | 795.546i | −0.997915 | + | 0.576146i | ||||
\(125\) | 788.676i | 0.564330i | ||||||||
\(126\) | −606.431 | + | 470.540i | −0.428771 | + | 0.332691i | ||||
\(127\) | − | 249.495i | − | 0.174324i | −0.996194 | − | 0.0871619i | \(-0.972220\pi\) | ||
0.996194 | − | 0.0871619i | \(-0.0277797\pi\) | |||||||
\(128\) | −1284.45 | − | 2224.74i | −0.886958 | − | 1.53626i | ||||
\(129\) | 1081.84 | − | 370.487i | 0.738378 | − | 0.252865i | ||||
\(130\) | −2359.81 | + | 4087.32i | −1.59207 | + | 2.75755i | ||||
\(131\) | 874.228 | + | 504.736i | 0.583066 | + | 0.336633i | 0.762351 | − | 0.647164i | \(-0.224045\pi\) |
−0.179285 | + | 0.983797i | \(0.557378\pi\) | |||||||
\(132\) | −3916.76 | − | 768.136i | −2.58265 | − | 0.506498i | ||||
\(133\) | −26.5989 | − | 502.684i | −0.0173415 | − | 0.327731i | ||||
\(134\) | − | 305.102i | − | 0.196693i | ||||||
\(135\) | 1742.25 | − | 876.747i | 1.11073 | − | 0.558951i | ||||
\(136\) | 2602.83i | 1.64111i | ||||||||
\(137\) | −154.197 | + | 89.0254i | −0.0961599 | + | 0.0555179i | −0.547309 | − | 0.836931i | \(-0.684348\pi\) |
0.451149 | + | 0.892449i | \(0.351014\pi\) | |||||||
\(138\) | 2237.43 | + | 438.795i | 1.38017 | + | 0.270672i | ||||
\(139\) | 833.977 | − | 1444.49i | 0.508899 | − | 0.881440i | −0.491047 | − | 0.871133i | \(-0.663386\pi\) |
0.999947 | − | 0.0103068i | \(-0.00328082\pi\) | |||||||
\(140\) | −1015.42 | − | 586.254i | −0.612991 | − | 0.353911i | ||||
\(141\) | 143.804 | + | 419.914i | 0.0858897 | + | 0.250803i | ||||
\(142\) | −2207.23 | − | 3823.03i | −1.30441 | − | 2.25931i | ||||
\(143\) | 4018.10 | 2.34973 | ||||||||
\(144\) | 64.3197 | + | 469.028i | 0.0372221 | + | 0.271428i | ||||
\(145\) | 2661.43i | 1.52427i | ||||||||
\(146\) | 70.4256 | + | 121.981i | 0.0399210 | + | 0.0691451i | ||||
\(147\) | −1198.48 | − | 1045.34i | −0.672442 | − | 0.586520i | ||||
\(148\) | 1436.59 | + | 829.418i | 0.797888 | + | 0.460661i | ||||
\(149\) | −2502.98 | − | 1445.10i | −1.37619 | − | 0.794544i | −0.384492 | − | 0.923128i | \(-0.625623\pi\) |
−0.991699 | + | 0.128584i | \(0.958957\pi\) | |||||||
\(150\) | 1250.37 | + | 1090.61i | 0.680617 | + | 0.593651i | ||||
\(151\) | 249.924 | − | 144.294i | 0.134692 | − | 0.0777647i | −0.431140 | − | 0.902285i | \(-0.641888\pi\) |
0.565832 | + | 0.824520i | \(0.308555\pi\) | |||||||
\(152\) | −2028.54 | − | 1032.30i | −1.08247 | − | 0.550860i | ||||
\(153\) | −965.831 | + | 2367.70i | −0.510345 | + | 1.25109i | ||||
\(154\) | 1573.74i | 0.823479i | ||||||||
\(155\) | −797.049 | − | 1380.53i | −0.413035 | − | 0.715398i | ||||
\(156\) | −1695.57 | − | 4951.15i | −0.870218 | − | 2.54108i | ||||
\(157\) | 861.947 | − | 1492.94i | 0.438158 | − | 0.758913i | −0.559389 | − | 0.828905i | \(-0.688964\pi\) |
0.997548 | + | 0.0699926i | \(0.0222976\pi\) | |||||||
\(158\) | 2793.17 | + | 1612.64i | 1.40641 | + | 0.811991i | ||||
\(159\) | −460.641 | + | 2348.83i | −0.229756 | + | 1.17154i | ||||
\(160\) | 1659.69 | − | 958.222i | 0.820062 | − | 0.473463i | ||||
\(161\) | − | 570.233i | − | 0.279134i | ||||||
\(162\) | −846.967 | + | 3302.79i | −0.410766 | + | 1.60180i | ||||
\(163\) | 669.137 | 0.321539 | 0.160769 | − | 0.986992i | \(-0.448602\pi\) | ||||
0.160769 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(164\) | −1747.76 | − | 3027.21i | −0.832177 | − | 1.44137i | ||||
\(165\) | 769.587 | − | 3924.16i | 0.363105 | − | 1.85149i | ||||
\(166\) | −5596.74 | − | 3231.28i | −2.61682 | − | 1.51082i | ||||
\(167\) | 35.4557 | − | 61.4111i | 0.0164290 | − | 0.0284559i | −0.857694 | − | 0.514160i | \(-0.828104\pi\) |
0.874123 | + | 0.485705i | \(0.161437\pi\) | |||||||
\(168\) | 821.170 | − | 281.217i | 0.377111 | − | 0.129145i | ||||
\(169\) | 1535.74 | + | 2659.98i | 0.699018 | + | 1.21073i | ||||
\(170\) | −6158.17 | −2.77829 | ||||||||
\(171\) | −1462.23 | − | 1691.77i | −0.653915 | − | 0.756568i | ||||
\(172\) | −3053.69 | −1.35373 | ||||||||
\(173\) | 997.168 | + | 1727.15i | 0.438227 | + | 0.759032i | 0.997553 | − | 0.0699163i | \(-0.0222732\pi\) |
−0.559326 | + | 0.828948i | \(0.688940\pi\) | |||||||
\(174\) | −3506.28 | − | 3058.26i | −1.52764 | − | 1.33245i | ||||
\(175\) | 207.476 | − | 359.359i | 0.0896213 | − | 0.155229i | ||||
\(176\) | 840.600 | + | 485.321i | 0.360015 | + | 0.207855i | ||||
\(177\) | −2856.78 | − | 2491.75i | −1.21316 | − | 1.05814i | ||||
\(178\) | −1445.75 | − | 2504.10i | −0.608782 | − | 1.05444i | ||||
\(179\) | −2894.05 | −1.20844 | −0.604222 | − | 0.796816i | \(-0.706516\pi\) | ||||
−0.604222 | + | 0.796816i | \(0.706516\pi\) | |||||||
\(180\) | −5160.14 | + | 707.632i | −2.13675 | + | 0.293021i | ||||
\(181\) | 1057.22i | 0.434159i | 0.976154 | + | 0.217079i | \(0.0696530\pi\) | ||||
−0.976154 | + | 0.217079i | \(0.930347\pi\) | |||||||
\(182\) | −1787.02 | + | 1031.73i | −0.727816 | + | 0.420205i | ||||
\(183\) | −653.274 | + | 223.720i | −0.263888 | + | 0.0903708i | ||||
\(184\) | −2232.91 | − | 1289.17i | −0.894631 | − | 0.516515i | ||||
\(185\) | −830.985 | + | 1439.31i | −0.330245 | + | 0.572000i | ||||
\(186\) | 2734.66 | + | 536.308i | 1.07804 | + | 0.211419i | ||||
\(187\) | 2621.41 | + | 4540.42i | 1.02511 | + | 1.77555i | ||||
\(188\) | − | 1185.28i | − | 0.459817i | ||||||
\(189\) | 851.339 | + | 48.8977i | 0.327650 | + | 0.0188190i | ||||
\(190\) | 2442.37 | − | 4799.41i | 0.932570 | − | 1.83256i | ||||
\(191\) | 526.299 | − | 303.859i | 0.199380 | − | 0.115112i | −0.396986 | − | 0.917825i | \(-0.629944\pi\) |
0.596366 | + | 0.802712i | \(0.296611\pi\) | |||||||
\(192\) | −785.027 | + | 4002.89i | −0.295075 | + | 1.50460i | ||||
\(193\) | 509.975 | + | 294.434i | 0.190201 | + | 0.109813i | 0.592077 | − | 0.805882i | \(-0.298308\pi\) |
−0.401876 | + | 0.915694i | \(0.631642\pi\) | |||||||
\(194\) | −1683.12 | − | 971.752i | −0.622893 | − | 0.359627i | ||||
\(195\) | 4960.50 | − | 1698.77i | 1.82169 | − | 0.623854i | ||||
\(196\) | 2123.41 | + | 3677.85i | 0.773836 | + | 1.34032i | ||||
\(197\) | 2523.22i | 0.912546i | 0.889840 | + | 0.456273i | \(0.150816\pi\) | ||||
−0.889840 | + | 0.456273i | \(0.849184\pi\) | |||||||
\(198\) | 4285.52 | + | 5523.16i | 1.53817 | + | 1.98239i | ||||
\(199\) | 5115.89 | 1.82239 | 0.911196 | − | 0.411974i | \(-0.135161\pi\) | ||||
0.911196 | + | 0.411974i | \(0.135161\pi\) | |||||||
\(200\) | −938.115 | − | 1624.86i | −0.331674 | − | 0.574476i | ||||
\(201\) | −222.803 | + | 255.442i | −0.0781855 | + | 0.0896391i | ||||
\(202\) | 6983.00 | + | 4031.64i | 2.43229 | + | 1.40428i | ||||
\(203\) | −581.802 | + | 1007.71i | −0.201155 | + | 0.348411i | ||||
\(204\) | 4488.56 | − | 5146.10i | 1.54050 | − | 1.76617i | ||||
\(205\) | 3032.92 | − | 1751.06i | 1.03331 | − | 0.596582i | ||||
\(206\) | − | 1773.39i | − | 0.599795i | ||||||
\(207\) | −1552.82 | − | 2001.27i | −0.521394 | − | 0.671971i | ||||
\(208\) | 1272.69i | 0.424256i | ||||||||
\(209\) | −4578.27 | + | 242.254i | −1.51524 | + | 0.0801773i | ||||
\(210\) | 665.345 | + | 1942.84i | 0.218634 | + | 0.638424i | ||||
\(211\) | −1635.10 | − | 944.027i | −0.533484 | − | 0.308007i | 0.208950 | − | 0.977926i | \(-0.432995\pi\) |
−0.742434 | + | 0.669919i | \(0.766329\pi\) | |||||||
\(212\) | 3195.93 | − | 5535.51i | 1.03536 | − | 1.79330i | ||||
\(213\) | −943.825 | + | 4812.61i | −0.303614 | + | 1.54814i | ||||
\(214\) | −677.348 | − | 1173.20i | −0.216367 | − | 0.374759i | ||||
\(215\) | − | 3059.45i | − | 0.970479i | ||||||
\(216\) | 2116.16 | − | 3223.11i | 0.666604 | − | 1.01530i | ||||
\(217\) | − | 696.956i | − | 0.218030i | ||||||
\(218\) | 5175.05 | − | 2987.82i | 1.60779 | − | 0.928260i | ||||
\(219\) | 30.1144 | − | 153.555i | 0.00929199 | − | 0.0473803i | ||||
\(220\) | −5339.39 | + | 9248.10i | −1.63628 | + | 2.83412i | ||||
\(221\) | −3437.16 | + | 5953.33i | −1.04619 | + | 1.81206i | ||||
\(222\) | −941.315 | − | 2748.69i | −0.284581 | − | 0.830992i | ||||
\(223\) | −3501.86 | + | 2021.80i | −1.05158 | + | 0.607128i | −0.923090 | − | 0.384583i | \(-0.874345\pi\) |
−0.128486 | + | 0.991711i | \(0.541012\pi\) | |||||||
\(224\) | 837.889 | 0.249928 | ||||||||
\(225\) | −250.432 | − | 1826.18i | −0.0742021 | − | 0.541092i | ||||
\(226\) | 845.872 | 0.248967 | ||||||||
\(227\) | −646.769 | − | 1120.24i | −0.189108 | − | 0.327545i | 0.755845 | − | 0.654751i | \(-0.227226\pi\) |
−0.944953 | + | 0.327206i | \(0.893893\pi\) | |||||||
\(228\) | 2230.46 | + | 5539.17i | 0.647875 | + | 1.60895i | ||||
\(229\) | 2123.23 | − | 3677.54i | 0.612694 | − | 1.06122i | −0.378091 | − | 0.925769i | \(-0.623419\pi\) |
0.990784 | − | 0.135448i | \(-0.0432474\pi\) | |||||||
\(230\) | 3050.11 | − | 5282.94i | 0.874426 | − | 1.51455i | ||||
\(231\) | 1149.23 | − | 1317.59i | 0.327334 | − | 0.375286i | ||||
\(232\) | 2630.65 | + | 4556.42i | 0.744442 | + | 1.28941i | ||||
\(233\) | − | 986.111i | − | 0.277263i | −0.990344 | − | 0.138631i | \(-0.955730\pi\) | ||
0.990344 | − | 0.138631i | \(-0.0442703\pi\) | |||||||
\(234\) | −3462.11 | + | 8487.24i | −0.967201 | + | 2.37106i | ||||
\(235\) | 1187.52 | 0.329640 | ||||||||
\(236\) | 5061.49 | + | 8766.77i | 1.39608 | + | 2.41808i | ||||
\(237\) | −1160.90 | − | 3389.88i | −0.318179 | − | 0.929099i | ||||
\(238\) | −2331.70 | − | 1346.21i | −0.635049 | − | 0.366646i | ||||
\(239\) | −427.600 | − | 246.875i | −0.115729 | − | 0.0668159i | 0.441018 | − | 0.897498i | \(-0.354617\pi\) |
−0.556747 | + | 0.830682i | \(0.687951\pi\) | |||||||
\(240\) | 1242.94 | + | 243.759i | 0.334297 | + | 0.0655606i | ||||
\(241\) | −2148.00 | + | 1240.15i | −0.574127 | + | 0.331473i | −0.758796 | − | 0.651328i | \(-0.774212\pi\) |
0.184669 | + | 0.982801i | \(0.440879\pi\) | |||||||
\(242\) | 8107.78 | 2.15367 | ||||||||
\(243\) | 3120.99 | − | 2146.70i | 0.823916 | − | 0.566712i | ||||
\(244\) | 1843.98 | 0.483807 | ||||||||
\(245\) | −3684.79 | + | 2127.42i | −0.960869 | + | 0.554758i | ||||
\(246\) | −1178.23 | + | 6007.85i | −0.305371 | + | 1.55710i | ||||
\(247\) | −3276.57 | − | 5039.90i | −0.844061 | − | 1.29831i | ||||
\(248\) | −2729.13 | − | 1575.66i | −0.698789 | − | 0.403446i | ||||
\(249\) | 2326.12 | + | 6792.39i | 0.592015 | + | 1.72872i | ||||
\(250\) | −3194.57 | + | 1844.39i | −0.808169 | + | 0.466597i | ||||
\(251\) | − | 4964.68i | − | 1.24848i | −0.781234 | − | 0.624238i | \(-0.785409\pi\) | ||
0.781234 | − | 0.624238i | \(-0.214591\pi\) | |||||||
\(252\) | −2108.50 | − | 860.099i | −0.527076 | − | 0.215005i | ||||
\(253\) | −5193.48 | −1.29056 | ||||||||
\(254\) | 1010.59 | − | 583.466i | 0.249646 | − | 0.144133i | ||||
\(255\) | 5155.82 | + | 4497.04i | 1.26616 | + | 1.10437i | ||||
\(256\) | 2867.48 | − | 4966.62i | 0.700069 | − | 1.21255i | ||||
\(257\) | 3049.56 | − | 5282.00i | 0.740181 | − | 1.28203i | −0.212232 | − | 0.977219i | \(-0.568073\pi\) |
0.952413 | − | 0.304812i | \(-0.0985936\pi\) | |||||||
\(258\) | 4030.65 | + | 3515.64i | 0.972626 | + | 0.848348i | ||||
\(259\) | −629.280 | + | 363.315i | −0.150971 | + | 0.0871634i | ||||
\(260\) | −14001.9 | −3.33985 | ||||||||
\(261\) | 702.258 | + | 5120.96i | 0.166547 | + | 1.21448i | ||||
\(262\) | 4721.47i | 1.11333i | ||||||||
\(263\) | 2088.69 | − | 1205.91i | 0.489712 | − | 0.282735i | −0.234743 | − | 0.972057i | \(-0.575425\pi\) |
0.724455 | + | 0.689322i | \(0.242092\pi\) | |||||||
\(264\) | −2561.23 | − | 7478.93i | −0.597094 | − | 1.74355i | ||||
\(265\) | 5545.96 | + | 3201.96i | 1.28561 | + | 0.742246i | ||||
\(266\) | 1973.94 | − | 1283.31i | 0.455001 | − | 0.295808i | ||||
\(267\) | −618.211 | + | 3152.28i | −0.141700 | + | 0.722534i | ||||
\(268\) | 783.889 | − | 452.579i | 0.178670 | − | 0.103155i | ||||
\(269\) | −7731.22 | −1.75234 | −0.876172 | − | 0.481998i | \(-0.839911\pi\) | ||||
−0.876172 | + | 0.481998i | \(0.839911\pi\) | |||||||
\(270\) | 7625.71 | + | 5006.72i | 1.71884 | + | 1.12852i | ||||
\(271\) | −4493.26 | −1.00718 | −0.503590 | − | 0.863943i | \(-0.667988\pi\) | ||||
−0.503590 | + | 0.863943i | \(0.667988\pi\) | |||||||
\(272\) | −1438.13 | + | 830.304i | −0.320586 | + | 0.185090i | ||||
\(273\) | 2249.58 | + | 441.177i | 0.498721 | + | 0.0978067i | ||||
\(274\) | −721.204 | − | 416.387i | −0.159013 | − | 0.0918061i | ||||
\(275\) | −3272.92 | − | 1889.62i | −0.717689 | − | 0.414358i | ||||
\(276\) | 2191.56 | + | 6399.46i | 0.477957 | + | 1.39566i | ||||
\(277\) | −1131.45 | − | 1959.72i | −0.245422 | − | 0.425084i | 0.716828 | − | 0.697250i | \(-0.245593\pi\) |
−0.962250 | + | 0.272166i | \(0.912260\pi\) | |||||||
\(278\) | 7801.31 | 1.68306 | ||||||||
\(279\) | −1897.91 | − | 2446.02i | −0.407257 | − | 0.524871i | ||||
\(280\) | − | 2322.27i | − | 0.495651i | ||||||
\(281\) | 584.925 | + | 1013.12i | 0.124177 | + | 0.215081i | 0.921411 | − | 0.388590i | \(-0.127038\pi\) |
−0.797234 | + | 0.603670i | \(0.793704\pi\) | |||||||
\(282\) | −1364.59 | + | 1564.49i | −0.288156 | + | 0.330369i | ||||
\(283\) | −2578.51 | + | 4466.11i | −0.541613 | + | 0.938101i | 0.457199 | + | 0.889364i | \(0.348853\pi\) |
−0.998812 | + | 0.0487363i | \(0.984481\pi\) | |||||||
\(284\) | 6548.26 | − | 11341.9i | 1.36820 | − | 2.36978i | ||||
\(285\) | −5549.63 | + | 2234.67i | −1.15344 | + | 0.464458i | ||||
\(286\) | 9396.68 | + | 16275.5i | 1.94279 | + | 3.36501i | ||||
\(287\) | 1531.16 | 0.314919 | ||||||||
\(288\) | 2940.63 | − | 2281.69i | 0.601661 | − | 0.466839i | ||||
\(289\) | −4056.60 | −0.825688 | ||||||||
\(290\) | −10780.2 | + | 6223.98i | −2.18289 | + | 1.26029i | ||||
\(291\) | 699.540 | + | 2042.69i | 0.140920 | + | 0.411494i | ||||
\(292\) | −208.934 | + | 361.884i | −0.0418731 | + | 0.0725263i | ||||
\(293\) | −1713.30 | + | 2967.53i | −0.341611 | + | 0.591688i | −0.984732 | − | 0.174076i | \(-0.944306\pi\) |
0.643121 | + | 0.765765i | \(0.277639\pi\) | |||||||
\(294\) | 1431.47 | − | 7299.13i | 0.283963 | − | 1.44794i | ||||
\(295\) | −8783.33 | + | 5071.06i | −1.73351 | + | 1.00084i | ||||
\(296\) | 3285.50i | 0.645155i | ||||||||
\(297\) | 445.344 | − | 7753.70i | 0.0870083 | − | 1.51487i | ||||
\(298\) | − | 13517.9i | − | 2.62776i | ||||||
\(299\) | −3404.81 | − | 5897.30i | −0.658546 | − | 1.14064i | ||||
\(300\) | −947.298 | + | 4830.31i | −0.182308 | + | 0.929594i | ||||
\(301\) | 668.812 | − | 1158.42i | 0.128072 | − | 0.221827i | ||||
\(302\) | 1168.94 | + | 674.887i | 0.222731 | + | 0.128594i | ||||
\(303\) | −2902.27 | − | 8474.80i | −0.550268 | − | 1.60681i | ||||
\(304\) | −76.7314 | − | 1450.12i | −0.0144765 | − | 0.273586i | ||||
\(305\) | 1847.46i | 0.346838i | ||||||||
\(306\) | −11849.2 | + | 1624.93i | −2.21363 | + | 0.303565i | ||||
\(307\) | − | 1856.14i | − | 0.345066i | −0.985004 | − | 0.172533i | \(-0.944805\pi\) | ||
0.985004 | − | 0.172533i | \(-0.0551952\pi\) | |||||||
\(308\) | −4043.37 | + | 2334.44i | −0.748026 | + | 0.431873i | ||||
\(309\) | −1295.03 | + | 1484.74i | −0.238419 | + | 0.273346i | ||||
\(310\) | 3727.93 | − | 6456.97i | 0.683008 | − | 1.18300i | ||||
\(311\) | 6845.02 | + | 3951.98i | 1.24806 | + | 0.720566i | 0.970722 | − | 0.240207i | \(-0.0772155\pi\) |
0.277335 | + | 0.960773i | \(0.410549\pi\) | |||||||
\(312\) | 6813.35 | − | 7811.46i | 1.23631 | − | 1.41743i | ||||
\(313\) | 4007.03 | + | 6940.37i | 0.723612 | + | 1.25333i | 0.959543 | + | 0.281562i | \(0.0908527\pi\) |
−0.235931 | + | 0.971770i | \(0.575814\pi\) | |||||||
\(314\) | 8062.95 | 1.44910 | ||||||||
\(315\) | 861.724 | − | 2112.49i | 0.154135 | − | 0.377858i | ||||
\(316\) | 9568.54i | 1.70339i | ||||||||
\(317\) | −3855.13 | − | 6677.27i | −0.683046 | − | 1.18307i | −0.974047 | − | 0.226347i | \(-0.927322\pi\) |
0.291001 | − | 0.956723i | \(-0.406012\pi\) | |||||||
\(318\) | −10591.3 | + | 3627.09i | −1.86771 | + | 0.639614i | ||||
\(319\) | 9177.87 | + | 5298.85i | 1.61085 | + | 0.930027i | ||||
\(320\) | 9451.46 | + | 5456.81i | 1.65110 | + | 0.953265i | ||||
\(321\) | −289.639 | + | 1476.88i | −0.0503616 | + | 0.256796i | ||||
\(322\) | 2309.75 | − | 1333.54i | 0.399744 | − | 0.230792i | ||||
\(323\) | 3557.41 | − | 6990.52i | 0.612815 | − | 1.20422i | ||||
\(324\) | −9742.11 | + | 2723.16i | −1.67046 | + | 0.466935i | ||||
\(325\) | − | 4955.29i | − | 0.845754i | ||||||
\(326\) | 1564.83 | + | 2710.37i | 0.265853 | + | 0.460471i | ||||
\(327\) | −6514.60 | − | 1277.61i | −1.10171 | − | 0.216061i | ||||
\(328\) | 3461.62 | − | 5995.70i | 0.582731 | − | 1.00932i | ||||
\(329\) | 449.637 | + | 259.598i | 0.0753474 | + | 0.0435019i | ||||
\(330\) | 17694.7 | − | 6059.73i | 2.95171 | − | 1.01084i | ||||
\(331\) | −8296.74 | + | 4790.12i | −1.37773 | + | 0.795435i | −0.991886 | − | 0.127128i | \(-0.959424\pi\) |
−0.385847 | + | 0.922563i | \(0.626091\pi\) | |||||||
\(332\) | − | 19172.7i | − | 3.16940i | ||||||
\(333\) | −1219.15 | + | 2988.70i | −0.200627 | + | 0.491831i | ||||
\(334\) | 331.665 | 0.0543350 | ||||||||
\(335\) | 453.434 | + | 785.370i | 0.0739514 | + | 0.128088i | ||||
\(336\) | 417.332 | + | 364.008i | 0.0677600 | + | 0.0591019i | ||||
\(337\) | −2992.66 | − | 1727.81i | −0.483741 | − | 0.279288i | 0.238233 | − | 0.971208i | \(-0.423432\pi\) |
−0.721974 | + | 0.691920i | \(0.756765\pi\) | |||||||
\(338\) | −7182.93 | + | 12441.2i | −1.15592 | + | 2.00211i | ||||
\(339\) | −708.192 | − | 617.703i | −0.113462 | − | 0.0989646i | ||||
\(340\) | −9134.83 | − | 15822.0i | −1.45708 | − | 2.52373i | ||||
\(341\) | −6347.63 | −1.00805 | ||||||||
\(342\) | 3433.06 | − | 9879.19i | 0.542804 | − | 1.56200i | ||||
\(343\) | −3945.06 | −0.621030 | ||||||||
\(344\) | −3024.07 | − | 5237.85i | −0.473974 | − | 0.820947i | ||||
\(345\) | −6411.55 | + | 2195.69i | −1.00054 | + | 0.342644i | ||||
\(346\) | −4663.93 | + | 8078.16i | −0.724665 | + | 1.25516i | ||||
\(347\) | 8714.12 | + | 5031.10i | 1.34812 | + | 0.778339i | 0.987984 | − | 0.154559i | \(-0.0493958\pi\) |
0.360139 | + | 0.932898i | \(0.382729\pi\) | |||||||
\(348\) | 2656.40 | − | 13545.1i | 0.409189 | − | 2.08647i | ||||
\(349\) | −3578.54 | − | 6198.21i | −0.548868 | − | 0.950667i | −0.998352 | − | 0.0573789i | \(-0.981726\pi\) |
0.449485 | − | 0.893288i | \(-0.351608\pi\) | |||||||
\(350\) | 1940.80 | 0.296401 | ||||||||
\(351\) | 9096.45 | − | 4577.57i | 1.38328 | − | 0.696105i | ||||
\(352\) | − | 7631.20i | − | 1.15552i | ||||||
\(353\) | −10161.4 | + | 5866.69i | −1.53212 | + | 0.884567i | −0.532851 | + | 0.846209i | \(0.678879\pi\) |
−0.999264 | + | 0.0383580i | \(0.987787\pi\) | |||||||
\(354\) | 3412.15 | − | 17398.7i | 0.512298 | − | 2.61223i | ||||
\(355\) | 11363.3 | + | 6560.62i | 1.69888 | + | 0.980850i | ||||
\(356\) | 4289.14 | − | 7429.01i | 0.638551 | − | 1.10600i | ||||
\(357\) | 969.101 | + | 2829.83i | 0.143670 | + | 0.419525i | ||||
\(358\) | −6767.99 | − | 11722.5i | −0.999160 | − | 1.73060i | ||||
\(359\) | 1419.99i | 0.208758i | 0.994538 | + | 0.104379i | \(0.0332855\pi\) | ||||
−0.994538 | + | 0.104379i | \(0.966715\pi\) | |||||||
\(360\) | −6323.87 | − | 8150.19i | −0.925825 | − | 1.19320i | ||||
\(361\) | 4037.22 | + | 5544.98i | 0.588601 | + | 0.808423i | ||||
\(362\) | −4282.33 | + | 2472.40i | −0.621752 | + | 0.358969i | ||||
\(363\) | −6788.10 | − | 5920.75i | −0.981496 | − | 0.856085i | ||||
\(364\) | −5301.61 | − | 3060.88i | −0.763406 | − | 0.440752i | ||||
\(365\) | −362.568 | − | 209.329i | −0.0519936 | − | 0.0300185i | ||||
\(366\) | −2433.93 | − | 2122.93i | −0.347605 | − | 0.303190i | ||||
\(367\) | 397.894 | + | 689.173i | 0.0565938 | + | 0.0980233i | 0.892934 | − | 0.450187i | \(-0.148643\pi\) |
−0.836341 | + | 0.548210i | \(0.815309\pi\) | |||||||
\(368\) | − | 1644.98i | − | 0.233018i | ||||||
\(369\) | 5373.72 | − | 4169.56i | 0.758116 | − | 0.588235i | ||||
\(370\) | −7773.32 | −1.09220 | ||||||||
\(371\) | 1399.93 | + | 2424.75i | 0.195905 | + | 0.339318i | ||||
\(372\) | 2678.59 | + | 7821.62i | 0.373329 | + | 1.09014i | ||||
\(373\) | 2209.70 | + | 1275.77i | 0.306739 | + | 0.177096i | 0.645466 | − | 0.763789i | \(-0.276663\pi\) |
−0.338727 | + | 0.940885i | \(0.609996\pi\) | |||||||
\(374\) | −12260.8 | + | 21236.3i | −1.69516 | + | 2.93610i | ||||
\(375\) | 4021.47 | + | 788.672i | 0.553781 | + | 0.108605i | ||||
\(376\) | 2033.06 | − | 1173.79i | 0.278849 | − | 0.160993i | ||||
\(377\) | 13895.6i | 1.89830i | ||||||||
\(378\) | 1792.87 | + | 3562.74i | 0.243955 | + | 0.484782i | ||||
\(379\) | 4983.14i | 0.675374i | 0.941258 | + | 0.337687i | \(0.109645\pi\) | ||||
−0.941258 | + | 0.337687i | \(0.890355\pi\) | |||||||
\(380\) | 15953.9 | − | 844.182i | 2.15373 | − | 0.113962i | ||||
\(381\) | −1272.18 | − | 249.494i | −0.171065 | − | 0.0335485i | ||||
\(382\) | 2461.59 | + | 1421.20i | 0.329701 | + | 0.190353i | ||||
\(383\) | 2833.62 | − | 4907.97i | 0.378045 | − | 0.654793i | −0.612733 | − | 0.790290i | \(-0.709930\pi\) |
0.990778 | + | 0.135497i | \(0.0432631\pi\) | |||||||
\(384\) | −12628.4 | + | 4324.72i | −1.67823 | + | 0.574727i | ||||
\(385\) | −2338.85 | − | 4051.00i | −0.309607 | − | 0.536255i | ||||
\(386\) | 2754.24i | 0.363179i | ||||||||
\(387\) | −807.283 | − | 5886.81i | −0.106038 | − | 0.773239i | ||||
\(388\) | − | 5765.86i | − | 0.754426i | ||||||
\(389\) | −3422.21 | + | 1975.81i | −0.446049 | + | 0.257526i | −0.706160 | − | 0.708052i | \(-0.749574\pi\) |
0.260111 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(390\) | 18481.5 | + | 16120.0i | 2.39961 | + | 2.09300i | ||||
\(391\) | 4442.59 | − | 7694.80i | 0.574608 | − | 0.995250i | ||||
\(392\) | −4205.63 | + | 7284.36i | −0.541878 | + | 0.938560i | ||||
\(393\) | 3447.88 | − | 3952.97i | 0.442551 | − | 0.507382i | ||||
\(394\) | −10220.4 | + | 5900.76i | −1.30684 | + | 0.754507i | ||||
\(395\) | −9586.61 | −1.22115 | ||||||||
\(396\) | −7833.48 | + | 19203.5i | −0.994059 | + | 2.43690i | ||||
\(397\) | −15579.7 | −1.96958 | −0.984788 | − | 0.173761i | \(-0.944408\pi\) | ||||
−0.984788 | + | 0.173761i | \(0.944408\pi\) | |||||||
\(398\) | 11963.9 | + | 20722.2i | 1.50678 | + | 2.60982i | ||||
\(399\) | −2589.80 | − | 367.053i | −0.324942 | − | 0.0460542i | ||||
\(400\) | 598.518 | − | 1036.66i | 0.0748147 | − | 0.129583i | ||||
\(401\) | 6622.95 | − | 11471.3i | 0.824774 | − | 1.42855i | −0.0773184 | − | 0.997006i | \(-0.524636\pi\) |
0.902092 | − | 0.431544i | \(-0.142031\pi\) | |||||||
\(402\) | −1555.72 | − | 305.101i | −0.193016 | − | 0.0378533i | ||||
\(403\) | −4161.46 | − | 7207.86i | −0.514385 | − | 0.890941i | ||||
\(404\) | 23921.6i | 2.94590i | ||||||||
\(405\) | −2728.31 | − | 9760.52i | −0.334742 | − | 1.19754i | ||||
\(406\) | −5442.37 | −0.665272 | ||||||||
\(407\) | 3308.95 | + | 5731.27i | 0.402994 | + | 0.698006i | ||||
\(408\) | 13271.9 | + | 2602.82i | 1.61043 | + | 0.315830i | ||||
\(409\) | 6493.14 | + | 3748.82i | 0.785001 | + | 0.453220i | 0.838200 | − | 0.545364i | \(-0.183608\pi\) |
−0.0531989 | + | 0.998584i | \(0.516942\pi\) | |||||||
\(410\) | 14185.5 | + | 8190.00i | 1.70871 | + | 0.986525i | ||||
\(411\) | 299.747 | + | 875.276i | 0.0359742 | + | 0.105047i | ||||
\(412\) | 4556.31 | − | 2630.59i | 0.544838 | − | 0.314562i | ||||
\(413\) | −4434.23 | −0.528316 | ||||||||
\(414\) | 4474.84 | − | 10969.9i | 0.531224 | − | 1.30228i | ||||
\(415\) | 19208.9 | 2.27212 | ||||||||
\(416\) | 8665.38 | − | 5002.96i | 1.02129 | − | 0.589640i | ||||
\(417\) | −6531.51 | − | 5696.95i | −0.767026 | − | 0.669019i | ||||
\(418\) | −11687.9 | − | 17978.0i | −1.36765 | − | 2.10366i | ||||
\(419\) | −182.782 | − | 105.529i | −0.0213114 | − | 0.0123042i | 0.489306 | − | 0.872112i | \(-0.337250\pi\) |
−0.510618 | + | 0.859808i | \(0.670583\pi\) | |||||||
\(420\) | −4004.74 | + | 4591.40i | −0.465265 | + | 0.533423i | ||||
\(421\) | 9322.88 | − | 5382.57i | 1.07926 | − | 0.623112i | 0.148565 | − | 0.988903i | \(-0.452535\pi\) |
0.930697 | + | 0.365790i | \(0.119201\pi\) | |||||||
\(422\) | − | 8830.75i | − | 1.01866i | ||||||
\(423\) | 2284.96 | − | 313.345i | 0.262644 | − | 0.0360174i | ||||
\(424\) | 12659.7 | 1.45003 | ||||||||
\(425\) | 5599.43 | − | 3232.83i | 0.639088 | − | 0.368977i | ||||
\(426\) | −21700.9 | + | 7431.68i | −2.46810 | + | 0.845226i | ||||
\(427\) | −403.865 | + | 699.515i | −0.0457714 | + | 0.0792785i | ||||
\(428\) | 2009.51 | − | 3480.58i | 0.226947 | − | 0.393085i | ||||
\(429\) | 4018.08 | − | 20488.4i | 0.452203 | − | 2.30580i | ||||
\(430\) | 12392.5 | − | 7154.79i | 1.38981 | − | 0.802407i | ||||
\(431\) | 12464.4 | 1.39302 | 0.696508 | − | 0.717549i | \(-0.254736\pi\) | ||||
0.696508 | + | 0.717549i | \(0.254736\pi\) | |||||||
\(432\) | 2455.90 | + | 141.058i | 0.273518 | + | 0.0157098i | ||||
\(433\) | 1352.78i | 0.150139i | 0.997178 | + | 0.0750696i | \(0.0239179\pi\) | ||||
−0.997178 | + | 0.0750696i | \(0.976082\pi\) | |||||||
\(434\) | 2823.05 | − | 1629.89i | 0.312237 | − | 0.180270i | ||||
\(435\) | 13570.7 | + | 2661.42i | 1.49578 | + | 0.293345i | ||||
\(436\) | 15353.0 | + | 8864.07i | 1.68641 | + | 0.973651i | ||||
\(437\) | 4235.03 | + | 6514.18i | 0.463590 | + | 0.713078i | ||||
\(438\) | 692.407 | − | 237.121i | 0.0755354 | − | 0.0258678i | ||||
\(439\) | −1267.90 | + | 732.023i | −0.137844 | + | 0.0795843i | −0.567336 | − | 0.823486i | \(-0.692026\pi\) |
0.429492 | + | 0.903071i | \(0.358693\pi\) | |||||||
\(440\) | −21150.5 | −2.29161 | ||||||||
\(441\) | −6528.70 | + | 5065.73i | −0.704967 | + | 0.546996i | ||||
\(442\) | −32152.3 | −3.46003 | ||||||||
\(443\) | −10278.5 | + | 5934.29i | −1.10236 | + | 0.636449i | −0.936840 | − | 0.349758i | \(-0.886264\pi\) |
−0.165521 | + | 0.986206i | \(0.552931\pi\) | |||||||
\(444\) | 5665.81 | − | 6495.81i | 0.605602 | − | 0.694319i | ||||
\(445\) | 7443.05 | + | 4297.25i | 0.792886 | + | 0.457773i | ||||
\(446\) | −16378.8 | − | 9456.29i | −1.73892 | − | 1.00396i | ||||
\(447\) | −9871.56 | + | 11317.7i | −1.04454 | + | 1.19756i | ||||
\(448\) | 2385.77 | + | 4132.28i | 0.251601 | + | 0.435785i | ||||
\(449\) | −13726.2 | −1.44272 | −0.721358 | − | 0.692562i | \(-0.756482\pi\) | ||||
−0.721358 | + | 0.692562i | \(0.756482\pi\) | |||||||
\(450\) | 6811.39 | − | 5285.08i | 0.713538 | − | 0.553646i | ||||
\(451\) | − | 13945.3i | − | 1.45600i | ||||||
\(452\) | 1254.74 | + | 2173.27i | 0.130571 | + | 0.226155i | ||||
\(453\) | −485.834 | − | 1418.66i | −0.0503896 | − | 0.147140i | ||||
\(454\) | 3025.05 | − | 5239.54i | 0.312715 | − | 0.541638i | ||||
\(455\) | 3066.67 | − | 5311.62i | 0.315972 | − | 0.547280i | ||||
\(456\) | −7292.25 | + | 9311.25i | −0.748884 | + | 0.956226i | ||||
\(457\) | 9366.19 | + | 16222.7i | 0.958713 | + | 1.66054i | 0.725633 | + | 0.688082i | \(0.241547\pi\) |
0.233080 | + | 0.972457i | \(0.425119\pi\) | |||||||
\(458\) | 19861.4 | 2.02634 | ||||||||
\(459\) | 11107.1 | + | 7292.48i | 1.12949 | + | 0.741577i | ||||
\(460\) | 18097.7 | 1.83437 | ||||||||
\(461\) | 5223.23 | − | 3015.64i | 0.527701 | − | 0.304668i | −0.212379 | − | 0.977187i | \(-0.568121\pi\) |
0.740080 | + | 0.672519i | \(0.234788\pi\) | |||||||
\(462\) | 8024.54 | + | 1573.73i | 0.808085 | + | 0.158478i | ||||
\(463\) | −125.524 | + | 217.414i | −0.0125996 | + | 0.0218231i | −0.872256 | − | 0.489049i | \(-0.837344\pi\) |
0.859657 | + | 0.510872i | \(0.170677\pi\) | |||||||
\(464\) | −1678.35 | + | 2906.99i | −0.167922 | + | 0.290849i | ||||
\(465\) | −7836.39 | + | 2683.65i | −0.781514 | + | 0.267637i | ||||
\(466\) | 3994.29 | − | 2306.10i | 0.397064 | − | 0.229245i | ||||
\(467\) | − | 1838.85i | − | 0.182210i | −0.995841 | − | 0.0911049i | \(-0.970960\pi\) | ||
0.995841 | − | 0.0911049i | \(-0.0290399\pi\) | |||||||
\(468\) | −26941.6 | + | 3694.61i | −2.66106 | + | 0.364922i | ||||
\(469\) | 396.492i | 0.0390368i | ||||||||
\(470\) | 2777.12 | + | 4810.11i | 0.272551 | + | 0.472072i | ||||
\(471\) | −6750.57 | − | 5888.01i | −0.660403 | − | 0.576020i | ||||
\(472\) | −10024.8 | + | 17363.5i | −0.977605 | + | 1.69326i | ||||
\(473\) | −10550.5 | − | 6091.31i | −1.02560 | − | 0.592132i | ||||
\(474\) | 11016.0 | − | 12629.8i | 1.06747 | − | 1.22385i | ||||
\(475\) | 298.758 | + | 5646.12i | 0.0288588 | + | 0.545393i | ||||
\(476\) | − | 7987.68i | − | 0.769149i | ||||||
\(477\) | 11516.1 | + | 4697.64i | 1.10542 | + | 0.450922i | ||||
\(478\) | − | 2309.35i | − | 0.220978i | ||||||
\(479\) | 13867.8 | − | 8006.60i | 1.32283 | − | 0.763739i | 0.338655 | − | 0.940911i | \(-0.390028\pi\) |
0.984180 | + | 0.177171i | \(0.0566947\pi\) | |||||||
\(480\) | −3226.31 | − | 9421.00i | −0.306792 | − | 0.895850i | ||||
\(481\) | −4338.65 | + | 7514.76i | −0.411279 | + | 0.712357i | ||||
\(482\) | −10046.6 | − | 5800.38i | −0.949394 | − | 0.548133i | ||||
\(483\) | −2907.63 | − | 570.230i | −0.273916 | − | 0.0537192i | ||||
\(484\) | 12026.8 | + | 20831.1i | 1.12949 | + | 1.95633i | ||||
\(485\) | 5776.75 | 0.540843 | ||||||||
\(486\) | 15994.0 | + | 7621.48i | 1.49281 | + | 0.711352i | ||||
\(487\) | 9570.79i | 0.890542i | 0.895396 | + | 0.445271i | \(0.146893\pi\) | ||||
−0.895396 | + | 0.445271i | \(0.853107\pi\) | |||||||
\(488\) | 1826.10 | + | 3162.90i | 0.169393 | + | 0.293397i | ||||
\(489\) | 669.134 | − | 3411.94i | 0.0618799 | − | 0.315528i | ||||
\(490\) | −17234.4 | − | 9950.29i | −1.58892 | − | 0.917364i | ||||
\(491\) | 1457.55 | + | 841.518i | 0.133968 | + | 0.0773466i | 0.565486 | − | 0.824758i | \(-0.308689\pi\) |
−0.431518 | + | 0.902104i | \(0.642022\pi\) | |||||||
\(492\) | −17183.5 | + | 5884.66i | −1.57458 | + | 0.539230i | ||||
\(493\) | −15701.8 | + | 9065.46i | −1.43443 | + | 0.828170i | ||||
\(494\) | 12751.8 | − | 25058.1i | 1.16140 | − | 2.28223i | ||||
\(495\) | −19239.8 | − | 7848.28i | −1.74700 | − | 0.712634i | ||||
\(496\) | − | 2010.54i | − | 0.182008i | ||||||
\(497\) | 2868.37 | + | 4968.17i | 0.258881 | + | 0.448396i | ||||
\(498\) | −22073.1 | + | 25306.6i | −1.98618 | + | 2.27714i | ||||
\(499\) | −5764.82 | + | 9984.97i | −0.517172 | + | 0.895769i | 0.482629 | + | 0.875825i | \(0.339682\pi\) |
−0.999801 | + | 0.0199436i | \(0.993651\pi\) | |||||||
\(500\) | −9477.44 | − | 5471.80i | −0.847688 | − | 0.489413i | ||||
\(501\) | −277.681 | − | 242.200i | −0.0247622 | − | 0.0215982i | ||||
\(502\) | 20109.7 | − | 11610.3i | 1.78792 | − | 1.03226i | ||||
\(503\) | 10110.3i | 0.896211i | 0.893981 | + | 0.448105i | \(0.147901\pi\) | ||||
−0.893981 | + | 0.448105i | \(0.852099\pi\) | |||||||
\(504\) | −612.767 | − | 4468.38i | −0.0541564 | − | 0.394915i | ||||
\(505\) | −23966.8 | −2.11190 | ||||||||
\(506\) | −12145.4 | − | 21036.4i | −1.06705 | − | 1.84819i | ||||
\(507\) | 15099.0 | − | 5170.81i | 1.32263 | − | 0.452946i | ||||
\(508\) | 2998.16 | + | 1730.99i | 0.261854 | + | 0.151182i | ||||
\(509\) | 3677.75 | − | 6370.05i | 0.320262 | − | 0.554710i | −0.660280 | − | 0.751020i | \(-0.729562\pi\) |
0.980542 | + | 0.196309i | \(0.0628957\pi\) | |||||||
\(510\) | −6158.14 | + | 31400.6i | −0.534680 | + | 2.72636i | ||||
\(511\) | −91.5206 | − | 158.518i | −0.00792296 | − | 0.0137230i | ||||
\(512\) | 6272.15 | 0.541392 | ||||||||
\(513\) | −10088.6 | + | 5764.17i | −0.868271 | + | 0.496090i | ||||
\(514\) | 28526.7 | 2.44797 | ||||||||
\(515\) | 2635.56 | + | 4564.92i | 0.225508 | + | 0.390591i | ||||
\(516\) | −3053.67 | + | 15570.8i | −0.260524 | + | 1.32842i | ||||
\(517\) | 2364.33 | − | 4095.14i | 0.201128 | − | 0.348364i | ||||
\(518\) | −2943.25 | − | 1699.29i | −0.249651 | − | 0.144136i | ||||
\(519\) | 9803.92 | − | 3357.44i | 0.829180 | − | 0.283960i | ||||
\(520\) | −13866.1 | − | 24016.8i | −1.16936 | − | 2.02540i | ||||
\(521\) | 12968.3 | 1.09050 | 0.545249 | − | 0.838274i | \(-0.316435\pi\) | ||||
0.545249 | + | 0.838274i | \(0.316435\pi\) | |||||||
\(522\) | −19100.4 | + | 14820.3i | −1.60154 | + | 1.24266i | ||||
\(523\) | − | 15373.2i | − | 1.28532i | −0.766151 | − | 0.642661i | \(-0.777830\pi\) | ||
0.766151 | − | 0.642661i | \(-0.222170\pi\) | |||||||
\(524\) | −12130.7 | + | 7003.68i | −1.01132 | + | 0.583887i | ||||
\(525\) | −1624.91 | − | 1417.28i | −0.135079 | − | 0.117820i | ||||
\(526\) | 9769.16 | + | 5640.23i | 0.809802 | + | 0.467539i | ||||
\(527\) | 5429.87 | − | 9404.82i | 0.448822 | − | 0.777382i | ||||
\(528\) | 3315.26 | − | 3800.92i | 0.273254 | − | 0.313284i | ||||
\(529\) | −1682.72 | − | 2914.55i | −0.138302 | − | 0.239545i | ||||
\(530\) | 29952.3i | 2.45480i | ||||||||
\(531\) | −15562.3 | + | 12075.0i | −1.27184 | + | 0.986839i | ||||
\(532\) | 6225.25 | + | 3167.97i | 0.507329 | + | 0.258174i | ||||
\(533\) | 15835.2 | − | 9142.44i | 1.28686 | − | 0.742970i | ||||
\(534\) | −14214.2 | + | 4867.79i | −1.15189 | + | 0.394476i | ||||
\(535\) | 3487.15 | + | 2013.31i | 0.281800 | + | 0.162697i | ||||
\(536\) | 1552.57 | + | 896.379i | 0.125114 | + | 0.0722345i | ||||
\(537\) | −2894.04 | + | 14756.8i | −0.232564 | + | 1.18586i | ||||
\(538\) | −18080.1 | − | 31315.7i | −1.44886 | − | 2.50951i | ||||
\(539\) | 16942.6i | 1.35393i | ||||||||
\(540\) | −1551.89 | + | 27019.3i | −0.123672 | + | 2.15320i | ||||
\(541\) | 16796.8 | 1.33484 | 0.667421 | − | 0.744680i | \(-0.267398\pi\) | ||||
0.667421 | + | 0.744680i | \(0.267398\pi\) | |||||||
\(542\) | −10507.9 | − | 18200.2i | −0.832752 | − | 1.44237i | ||||
\(543\) | 5390.80 | + | 1057.22i | 0.426043 | + | 0.0835535i | ||||
\(544\) | 11306.6 | + | 6527.86i | 0.891114 | + | 0.514485i | ||||
\(545\) | −8880.81 | + | 15382.0i | −0.698004 | + | 1.20898i | ||||
\(546\) | 3473.83 | + | 10143.8i | 0.272282 | + | 0.795079i | ||||
\(547\) | −8175.46 | + | 4720.10i | −0.639044 | + | 0.368952i | −0.784246 | − | 0.620450i | \(-0.786950\pi\) |
0.145202 | + | 0.989402i | \(0.453617\pi\) | |||||||
\(548\) | − | 2470.62i | − | 0.192591i | ||||||
\(549\) | 487.482 | + | 3554.78i | 0.0378965 | + | 0.276347i | ||||
\(550\) | − | 17676.2i | − | 1.37039i | ||||||
\(551\) | −837.772 | − | 15832.8i | −0.0647736 | − | 1.22413i | ||||
\(552\) | −8806.39 | + | 10096.5i | −0.679031 | + | 0.778504i | ||||
\(553\) | −3629.83 | − | 2095.68i | −0.279125 | − | 0.161153i | ||||
\(554\) | 5291.96 | − | 9165.95i | 0.405837 | − | 0.702931i | ||||
\(555\) | 6508.08 | + | 5676.51i | 0.497753 | + | 0.434152i | ||||
\(556\) | 11572.2 | + | 20043.7i | 0.882682 | + | 1.52885i | ||||
\(557\) | − | 13649.4i | − | 1.03832i | −0.854678 | − | 0.519159i | \(-0.826245\pi\) | ||
0.854678 | − | 0.519159i | \(-0.173755\pi\) | |||||||
\(558\) | 5469.29 | − | 13407.8i | 0.414935 | − | 1.01720i | ||||
\(559\) | − | 15973.7i | − | 1.20861i | ||||||
\(560\) | 1283.11 | − | 740.805i | 0.0968239 | − | 0.0559013i | ||||
\(561\) | 25773.1 | − | 8826.23i | 1.93964 | − | 0.664249i | ||||
\(562\) | −2735.80 | + | 4738.54i | −0.205343 | + | 0.355664i | ||||
\(563\) | −7951.58 | + | 13772.5i | −0.595238 | + | 1.03098i | 0.398275 | + | 0.917266i | \(0.369609\pi\) |
−0.993513 | + | 0.113717i | \(0.963724\pi\) | |||||||
\(564\) | −6043.78 | − | 1185.28i | −0.451222 | − | 0.0884914i | ||||
\(565\) | −2177.38 | + | 1257.11i | −0.162129 | + | 0.0936053i | ||||
\(566\) | −24120.2 | −1.79125 | ||||||||
\(567\) | 1100.67 | − | 4292.10i | 0.0815231 | − | 0.317903i | ||||
\(568\) | 25939.0 | 1.91616 | ||||||||
\(569\) | 1165.84 | + | 2019.29i | 0.0858956 | + | 0.148775i | 0.905772 | − | 0.423764i | \(-0.139292\pi\) |
−0.819877 | + | 0.572540i | \(0.805958\pi\) | |||||||
\(570\) | −22029.9 | − | 17253.1i | −1.61883 | − | 1.26781i | ||||
\(571\) | −9904.65 | + | 17155.4i | −0.725914 | + | 1.25732i | 0.232683 | + | 0.972553i | \(0.425250\pi\) |
−0.958597 | + | 0.284767i | \(0.908084\pi\) | |||||||
\(572\) | −27877.5 | + | 48285.2i | −2.03779 | + | 3.52955i | ||||
\(573\) | −1023.09 | − | 2987.47i | −0.0745900 | − | 0.217807i | ||||
\(574\) | 3580.75 | + | 6202.05i | 0.260379 | + | 0.450990i | ||||
\(575\) | 6404.81i | 0.464520i | ||||||||
\(576\) | 19625.8 | + | 8005.74i | 1.41969 | + | 0.579119i | ||||
\(577\) | −3148.14 | −0.227138 | −0.113569 | − | 0.993530i | \(-0.536228\pi\) | ||||
−0.113569 | + | 0.993530i | \(0.536228\pi\) | |||||||
\(578\) | −9486.71 | − | 16431.5i | −0.682691 | − | 1.18246i | ||||
\(579\) | 2011.30 | − | 2305.94i | 0.144364 | − | 0.165512i | ||||
\(580\) | −31982.1 | − | 18464.9i | −2.28963 | − | 1.32192i | ||||
\(581\) | 7273.18 | + | 4199.17i | 0.519350 | + | 0.299847i | ||||
\(582\) | −6638.10 | + | 7610.54i | −0.472780 | + | 0.542039i | ||||
\(583\) | 22083.8 | − | 12750.1i | 1.56881 | − | 0.905754i | ||||
\(584\) | −827.631 | −0.0586432 | ||||||||
\(585\) | −3701.59 | − | 26992.5i | −0.261610 | − | 1.90769i | ||||
\(586\) | −16026.8 | −1.12980 | ||||||||
\(587\) | 10095.0 | − | 5828.34i | 0.709821 | − | 0.409815i | −0.101174 | − | 0.994869i | \(-0.532260\pi\) |
0.810995 | + | 0.585054i | \(0.198927\pi\) | |||||||
\(588\) | 20876.8 | − | 7149.46i | 1.46419 | − | 0.501427i | ||||
\(589\) | 5176.18 | + | 7961.82i | 0.362107 | + | 0.556980i | ||||
\(590\) | −41081.1 | − | 23718.2i | −2.86658 | − | 1.65502i | ||||
\(591\) | 12865.9 | + | 2523.20i | 0.895488 | + | 0.175619i | ||||
\(592\) | −1815.32 | + | 1048.07i | −0.126029 | + | 0.0727628i | ||||
\(593\) | − | 21221.1i | − | 1.46956i | −0.678307 | − | 0.734779i | \(-0.737286\pi\) | ||
0.678307 | − | 0.734779i | \(-0.262714\pi\) | |||||||
\(594\) | 32448.2 | − | 16328.8i | 2.24136 | − | 1.12791i | ||||
\(595\) | 8002.77 | 0.551397 | ||||||||
\(596\) | 34731.2 | − | 20052.1i | 2.38699 | − | 1.37813i | ||||
\(597\) | 5115.86 | − | 26086.0i | 0.350718 | − | 1.78833i | ||||
\(598\) | 15924.9 | − | 27582.7i | 1.08899 | − | 1.88619i | ||||
\(599\) | 7895.64 | − | 13675.7i | 0.538576 | − | 0.932842i | −0.460405 | − | 0.887709i | \(-0.652296\pi\) |
0.998981 | − | 0.0451324i | \(-0.0143710\pi\) | |||||||
\(600\) | −9223.32 | + | 3158.61i | −0.627568 | + | 0.214916i | ||||
\(601\) | 7260.17 | − | 4191.66i | 0.492760 | − | 0.284495i | −0.232959 | − | 0.972487i | \(-0.574841\pi\) |
0.725719 | + | 0.687992i | \(0.241507\pi\) | |||||||
\(602\) | 6256.30 | 0.423568 | ||||||||
\(603\) | 1079.70 | + | 1391.52i | 0.0729168 | + | 0.0939749i | ||||
\(604\) | 4004.42i | 0.269764i | ||||||||
\(605\) | −20870.4 | + | 12049.5i | −1.40248 | + | 0.809724i | ||||
\(606\) | 27540.4 | − | 31574.8i | 1.84612 | − | 2.11657i | ||||
\(607\) | 6897.14 | + | 3982.06i | 0.461196 | + | 0.266272i | 0.712547 | − | 0.701624i | \(-0.247541\pi\) |
−0.251351 | + | 0.967896i | \(0.580875\pi\) | |||||||
\(608\) | −9571.80 | + | 6222.87i | −0.638467 | + | 0.415083i | ||||
\(609\) | 4556.54 | + | 3974.33i | 0.303186 | + | 0.264446i | ||||
\(610\) | −7483.25 | + | 4320.45i | −0.496701 | + | 0.286771i | ||||
\(611\) | 6200.15 | 0.410526 | ||||||||
\(612\) | −21751.5 | − | 28033.3i | −1.43669 | − | 1.85160i | ||||
\(613\) | −7491.18 | −0.493582 | −0.246791 | − | 0.969069i | \(-0.579376\pi\) | ||||
−0.246791 | + | 0.969069i | \(0.579376\pi\) | |||||||
\(614\) | 7518.37 | − | 4340.73i | 0.494164 | − | 0.285306i | ||||
\(615\) | −5895.78 | − | 17216.0i | −0.386570 | − | 1.12881i | ||||
\(616\) | −8008.31 | − | 4623.60i | −0.523805 | − | 0.302419i | ||||
\(617\) | 20996.2 | + | 12122.2i | 1.36998 | + | 0.790957i | 0.990925 | − | 0.134418i | \(-0.0429164\pi\) |
0.379053 | + | 0.925375i | \(0.376250\pi\) | |||||||
\(618\) | −9042.54 | − | 1773.38i | −0.588583 | − | 0.115430i | ||||
\(619\) | 10184.0 | + | 17639.2i | 0.661277 | + | 1.14536i | 0.980280 | + | 0.197611i | \(0.0633183\pi\) |
−0.319004 | + | 0.947753i | \(0.603348\pi\) | |||||||
\(620\) | 22119.6 | 1.43281 | ||||||||
\(621\) | −11757.3 | + | 5916.61i | −0.759752 | + | 0.382327i | ||||
\(622\) | 36968.1i | 2.38310i | ||||||||
\(623\) | 1878.80 | + | 3254.18i | 0.120823 | + | 0.209271i | ||||
\(624\) | 6489.48 | + | 1272.69i | 0.416326 | + | 0.0816477i | ||||
\(625\) | 9748.98 | − | 16885.7i | 0.623935 | − | 1.08069i | ||||
\(626\) | −18741.5 | + | 32461.3i | −1.19659 | + | 2.07255i | ||||
\(627\) | −3342.99 | + | 23587.0i | −0.212929 | + | 1.50235i | ||||
\(628\) | 11960.3 | + | 20715.9i | 0.759982 | + | 1.31633i | ||||
\(629\) | −11322.1 | −0.717715 | ||||||||
\(630\) | 10571.9 | − | 1449.77i | 0.668566 | − | 0.0916832i | ||||
\(631\) | 4862.83 | 0.306793 | 0.153396 | − | 0.988165i | \(-0.450979\pi\) | ||||
0.153396 | + | 0.988165i | \(0.450979\pi\) | |||||||
\(632\) | −16412.5 | + | 9475.74i | −1.03300 | + | 0.596400i | ||||
\(633\) | −6448.71 | + | 7393.40i | −0.404918 | + | 0.464236i | ||||
\(634\) | 18031.1 | − | 31230.8i | 1.12950 | − | 1.95636i | ||||
\(635\) | −1734.26 | + | 3003.82i | −0.108381 | + | 0.187721i | ||||
\(636\) | −25029.8 | − | 21831.6i | −1.56053 | − | 1.36113i | ||||
\(637\) | −19238.6 | + | 11107.4i | −1.19664 | + | 0.690883i | ||||
\(638\) | 49567.2i | 3.07584i | ||||||||
\(639\) | 23595.8 | + | 9625.16i | 1.46077 | + | 0.595877i | ||||
\(640\) | 35713.3i | 2.20577i | ||||||||
\(641\) | 7820.49 | + | 13545.5i | 0.481889 | + | 0.834656i | 0.999784 | − | 0.0207884i | \(-0.00661764\pi\) |
−0.517895 | + | 0.855444i | \(0.673284\pi\) | |||||||
\(642\) | −6659.53 | + | 2280.62i | −0.409393 | + | 0.140201i | ||||
\(643\) | −8099.85 | + | 14029.3i | −0.496776 | + | 0.860441i | −0.999993 | − | 0.00371920i | \(-0.998816\pi\) |
0.503217 | + | 0.864160i | \(0.332149\pi\) | |||||||
\(644\) | 6852.43 | + | 3956.25i | 0.419291 | + | 0.242078i | ||||
\(645\) | −15600.2 | − | 3059.44i | −0.952338 | − | 0.186768i | ||||
\(646\) | 36634.7 | − | 1938.48i | 2.23123 | − | 0.118063i | ||||
\(647\) | − | 24275.2i | − | 1.47505i | −0.675319 | − | 0.737526i | \(-0.735994\pi\) | ||
0.675319 | − | 0.737526i | \(-0.264006\pi\) | |||||||
\(648\) | −14318.6 | − | 14013.4i | −0.868034 | − | 0.849537i | ||||
\(649\) | 40385.5i | 2.44263i | ||||||||
\(650\) | 20071.7 | − | 11588.4i | 1.21119 | − | 0.699282i | ||||
\(651\) | −3553.79 | − | 696.952i | −0.213954 | − | 0.0419596i | ||||
\(652\) | −4642.45 | + | 8040.96i | −0.278853 | + | 0.482988i | ||||
\(653\) | −5751.21 | − | 3320.46i | −0.344659 | − | 0.198989i | 0.317671 | − | 0.948201i | \(-0.397099\pi\) |
−0.662330 | + | 0.749212i | \(0.730432\pi\) | |||||||
\(654\) | −10059.9 | − | 29375.5i | −0.601489 | − | 1.75638i | ||||
\(655\) | −7016.90 | − | 12153.6i | −0.418585 | − | 0.725010i | ||||
\(656\) | 4417.02 | 0.262890 | ||||||||
\(657\) | −752.865 | − | 307.108i | −0.0447064 | − | 0.0182366i | ||||
\(658\) | 2428.37i | 0.143872i | ||||||||
\(659\) | −9694.33 | − | 16791.1i | −0.573046 | − | 0.992545i | −0.996251 | − | 0.0865113i | \(-0.972428\pi\) |
0.423204 | − | 0.906034i | \(-0.360905\pi\) | |||||||
\(660\) | 41816.9 | + | 36473.7i | 2.46624 | + | 2.15112i | ||||
\(661\) | −14607.1 | − | 8433.44i | −0.859534 | − | 0.496252i | 0.00432229 | − | 0.999991i | \(-0.498624\pi\) |
−0.863856 | + | 0.503739i | \(0.831958\pi\) | |||||||
\(662\) | −38805.3 | − | 22404.2i | −2.27826 | − | 1.31535i | ||||
\(663\) | 26919.0 | + | 23479.4i | 1.57684 | + | 1.37536i | ||||
\(664\) | 32886.1 | − | 18986.8i | 1.92203 | − | 1.10968i | ||||
\(665\) | −3173.95 | + | 6237.01i | −0.185084 | + | 0.363701i | ||||
\(666\) | −14956.9 | + | 2051.11i | −0.870225 | + | 0.119338i | ||||
\(667\) | − | 17960.3i | − | 1.04262i | ||||||
\(668\) | 491.981 | + | 852.136i | 0.0284960 | + | 0.0493565i | ||||
\(669\) | 6807.35 | + | 19877.8i | 0.393404 | + | 1.14876i | ||||
\(670\) | −2120.79 | + | 3673.31i | −0.122288 | + | 0.211809i | ||||
\(671\) | 6370.94 | + | 3678.26i | 0.366539 | + | 0.211621i | ||||
\(672\) | 837.884 | − | 4272.41i | 0.0480984 | − | 0.245256i | ||||
\(673\) | −5860.90 | + | 3383.79i | −0.335693 | + | 0.193812i | −0.658366 | − | 0.752698i | \(-0.728752\pi\) |
0.322673 | + | 0.946510i | \(0.395419\pi\) | |||||||
\(674\) | − | 16162.6i | − | 0.923678i | ||||||
\(675\) | −9562.18 | − | 549.216i | −0.545257 | − | 0.0313175i | ||||
\(676\) | −42619.7 | −2.42488 | ||||||||
\(677\) | −1008.53 | − | 1746.83i | −0.0572542 | − | 0.0991672i | 0.835978 | − | 0.548763i | \(-0.184901\pi\) |
−0.893232 | + | 0.449596i | \(0.851568\pi\) | |||||||
\(678\) | 845.868 | − | 4313.12i | 0.0479135 | − | 0.244313i | ||||
\(679\) | 2187.28 | + | 1262.83i | 0.123623 | + | 0.0713739i | ||||
\(680\) | 18092.5 | − | 31337.1i | 1.02032 | − | 1.76724i | ||||
\(681\) | −6358.88 | + | 2177.66i | −0.357816 | + | 0.122537i | ||||
\(682\) | −14844.5 | − | 25711.4i | −0.833467 | − | 1.44361i | ||||
\(683\) | 3569.02 | 0.199949 | 0.0999743 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999743 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(684\) | 30474.8 | − | 5834.00i | 1.70356 | − | 0.326124i | ||||
\(685\) | 2475.29 | 0.138067 | ||||||||
\(686\) | −9225.87 | − | 15979.7i | −0.513477 | − | 0.889369i | ||||
\(687\) | −16628.6 | − | 14503.9i | −0.923467 | − | 0.805471i | ||||
\(688\) | 1929.36 | − | 3341.74i | 0.106913 | − | 0.185179i | ||||
\(689\) | 28956.0 | + | 16717.7i | 1.60107 | + | 0.924376i | ||||
\(690\) | −23887.7 | − | 20835.5i | −1.31796 | − | 1.14955i | ||||
\(691\) | −8360.32 | − | 14480.5i | −0.460263 | − | 0.797199i | 0.538711 | − | 0.842491i | \(-0.318912\pi\) |
−0.998974 | + | 0.0452919i | \(0.985578\pi\) | |||||||
\(692\) | −27673.3 | −1.52020 | ||||||||
\(693\) | −5569.19 | − | 7177.55i | −0.305275 | − | 0.393438i | ||||
\(694\) | 47062.6i | 2.57417i | ||||||||
\(695\) | −20081.5 | + | 11594.1i | −1.09602 | + | 0.632788i | ||||
\(696\) | 25863.9 | − | 8857.34i | 1.40858 | − | 0.482380i | ||||
\(697\) | 20661.7 | + | 11929.0i | 1.12284 | + | 0.648271i | ||||
\(698\) | 16737.4 | − | 28990.1i | 0.907624 | − | 1.57205i | ||||
\(699\) | −5028.20 | − | 986.106i | −0.272080 | − | 0.0533590i | ||||
\(700\) | 2878.93 | + | 4986.45i | 0.155447 | + | 0.269243i | ||||
\(701\) | 5700.03i | 0.307115i | 0.988140 | + | 0.153557i | \(0.0490730\pi\) | ||||
−0.988140 | + | 0.153557i | \(0.950927\pi\) | |||||||
\(702\) | 39814.5 | + | 26140.6i | 2.14060 | + | 1.40543i | ||||
\(703\) | 4490.43 | − | 8823.98i | 0.240910 | − | 0.473404i | ||||
\(704\) | 37635.3 | − | 21728.8i | 2.01482 | − | 1.16326i | ||||
\(705\) | 1187.52 | − | 6055.19i | 0.0634389 | − | 0.323478i | ||||
\(706\) | −47526.6 | − | 27439.5i | −2.53355 | − | 1.46275i | ||||
\(707\) | −9074.67 | − | 5239.26i | −0.482727 | − | 0.278703i | ||||
\(708\) | 49763.4 | − | 17041.9i | 2.64156 | − | 0.904626i | ||||
\(709\) | −6075.74 | − | 10523.5i | −0.321833 | − | 0.557430i | 0.659034 | − | 0.752114i | \(-0.270965\pi\) |
−0.980866 | + | 0.194683i | \(0.937632\pi\) | |||||||
\(710\) | 61370.3i | 3.24393i | ||||||||
\(711\) | −18446.0 | + | 2529.57i | −0.972965 | + | 0.133427i | ||||
\(712\) | 16990.2 | 0.894290 | ||||||||
\(713\) | 5378.77 | + | 9316.31i | 0.282520 | + | 0.489339i | ||||
\(714\) | −9196.02 | + | 10543.2i | −0.482006 | + | 0.552617i | ||||
\(715\) | −48376.4 | − | 27930.1i | −2.53031 | − | 1.46088i | ||||
\(716\) | 20078.8 | − | 34777.6i | 1.04802 | − | 1.81522i | ||||
\(717\) | −1686.42 | + | 1933.47i | −0.0878388 | + | 0.100707i | ||||
\(718\) | −5751.73 | + | 3320.76i | −0.298959 | + | 0.172604i | ||||
\(719\) | − | 1863.41i | − | 0.0966529i | −0.998832 | − | 0.0483264i | \(-0.984611\pi\) | ||
0.998832 | − | 0.0483264i | \(-0.0153888\pi\) | |||||||
\(720\) | 2485.86 | − | 6094.00i | 0.128670 | − | 0.315430i | ||||
\(721\) | 2304.58i | 0.119039i | ||||||||
\(722\) | −13018.8 | + | 29320.3i | −0.671067 | + | 1.51134i | ||||
\(723\) | 4175.55 | + | 12192.8i | 0.214786 | + | 0.627187i | ||||
\(724\) | −12704.5 | − | 7334.97i | −0.652156 | − | 0.376522i | ||||
\(725\) | 6534.76 | − | 11318.5i | 0.334752 | − | 0.579807i | ||||
\(726\) | 8107.74 | − | 41341.7i | 0.414472 | − | 2.11341i | ||||
\(727\) | −18227.9 | − | 31571.6i | −0.929896 | − | 1.61063i | −0.783491 | − | 0.621403i | \(-0.786563\pi\) |
−0.146406 | − | 0.989225i | \(-0.546770\pi\) | |||||||
\(728\) | − | 12124.8i | − | 0.617273i | ||||||
\(729\) | −7825.10 | − | 18060.7i | −0.397556 | − | 0.917578i | ||||
\(730\) | − | 1958.13i | − | 0.0992790i | ||||||
\(731\) | 18050.1 | − | 10421.2i | 0.913279 | − | 0.527282i | ||||
\(732\) | 1843.97 | − | 9402.50i | 0.0931082 | − | 0.474763i | ||||
\(733\) | 6230.32 | − | 10791.2i | 0.313946 | − | 0.543770i | −0.665267 | − | 0.746605i | \(-0.731682\pi\) |
0.979213 | + | 0.202836i | \(0.0650157\pi\) | |||||||
\(734\) | −1861.02 | + | 3223.38i | −0.0935851 | + | 0.162094i | ||||
\(735\) | 7162.96 | + | 20916.2i | 0.359469 | + | 1.04967i | ||||
\(736\) | −11200.2 | + | 6466.43i | −0.560930 | + | 0.323853i | ||||
\(737\) | 3611.11 | 0.180484 | ||||||||
\(738\) | 29455.9 | + | 12015.6i | 1.46922 | + | 0.599325i | ||||
\(739\) | −7037.01 | −0.350285 | −0.175143 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175143 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(740\) | −11530.7 | − | 19971.7i | −0.572806 | − | 0.992130i | ||||
\(741\) | −28975.1 | + | 11667.4i | −1.43647 | + | 0.578425i | ||||
\(742\) | −6547.72 | + | 11341.0i | −0.323955 | + | 0.561106i | ||||
\(743\) | 12280.1 | − | 21269.8i | 0.606344 | − | 1.05022i | −0.385494 | − | 0.922711i | \(-0.625969\pi\) |
0.991838 | − | 0.127508i | \(-0.0406979\pi\) | |||||||
\(744\) | −10763.4 | + | 12340.2i | −0.530386 | + | 0.608084i | ||||
\(745\) | 20090.0 | + | 34796.8i | 0.987972 | + | 1.71122i | ||||
\(746\) | 11934.0i | 0.585702i | ||||||||
\(747\) | 36960.6 | − | 5068.57i | 1.81033 | − | 0.248259i | ||||
\(748\) | −72749.0 | −3.55611 | ||||||||
\(749\) | 880.239 | + | 1524.62i | 0.0429416 | + | 0.0743770i | ||||
\(750\) | 6210.01 | + | 18133.6i | 0.302343 | + | 0.882858i | ||||
\(751\) | 632.174 | + | 364.986i | 0.0307168 | + | 0.0177344i | 0.515280 | − | 0.857022i | \(-0.327688\pi\) |
−0.484563 | + | 0.874756i | \(0.661021\pi\) | |||||||
\(752\) | 1297.09 | + | 748.876i | 0.0628990 | + | 0.0363148i | ||||
\(753\) | −25315.0 | − | 4964.65i | −1.22514 | − | 0.240268i | ||||
\(754\) | −56284.6 | + | 32496.0i | −2.71852 | + | 1.56954i | ||||
\(755\) | −4011.99 | −0.193392 | ||||||||
\(756\) | −6494.16 | + | 9891.21i | −0.312421 | + | 0.475846i | ||||
\(757\) | 25210.2 | 1.21041 | 0.605204 | − | 0.796071i | \(-0.293092\pi\) | ||||
0.605204 | + | 0.796071i | \(0.293092\pi\) | |||||||
\(758\) | −20184.5 | + | 11653.5i | −0.967193 | + | 0.558409i | ||||
\(759\) | −5193.45 | + | 26481.7i | −0.248367 | + | 1.26643i | ||||
\(760\) | 17247.2 | + | 26529.0i | 0.823185 | + | 1.26619i | ||||
\(761\) | −4150.32 | − | 2396.19i | −0.197699 | − | 0.114142i | 0.397883 | − | 0.917436i | \(-0.369745\pi\) |
−0.595582 | + | 0.803295i | \(0.703078\pi\) | |||||||
\(762\) | −1964.52 | − | 5736.49i | −0.0933949 | − | 0.272718i | ||||
\(763\) | −6725.17 | + | 3882.78i | −0.319093 | + | 0.184228i | ||||
\(764\) | 8432.65i | 0.399323i | ||||||||
\(765\) | 28086.3 | − | 21792.6i | 1.32740 | − | 1.02995i | ||||
\(766\) | 26506.7 | 1.25029 | ||||||||
\(767\) | −45858.5 | + | 26476.4i | −2.15887 | + | 1.24643i | ||||
\(768\) | −22457.4 | − | 19587.9i | −1.05516 | − | 0.920337i | ||||
\(769\) | −50.4656 | + | 87.4091i | −0.00236650 | + | 0.00409890i | −0.867206 | − | 0.497949i | \(-0.834087\pi\) |
0.864840 | + | 0.502048i | \(0.167420\pi\) | |||||||
\(770\) | 10939.2 | − | 18947.2i | 0.511975 | − | 0.886767i | ||||
\(771\) | −23883.5 | − | 20831.8i | −1.11562 | − | 0.973071i | ||||
\(772\) | −7076.37 | + | 4085.55i | −0.329902 | + | 0.190469i | ||||
\(773\) | 28747.4 | 1.33761 | 0.668804 | − | 0.743439i | \(-0.266807\pi\) | ||||
0.668804 | + | 0.743439i | \(0.266807\pi\) | |||||||
\(774\) | 21956.9 | − | 17036.8i | 1.01967 | − | 0.791180i | ||||
\(775\) | 7828.16i | 0.362833i | ||||||||
\(776\) | 9889.92 | − | 5709.95i | 0.457509 | − | 0.264143i | ||||
\(777\) | 1223.27 | + | 3572.03i | 0.0564797 | + | 0.164924i | ||||
\(778\) | −16006.3 | − | 9241.22i | −0.737600 | − | 0.425853i | ||||
\(779\) | −17491.6 | + | 11371.7i | −0.804493 | + | 0.523021i | ||||
\(780\) | −14001.8 | + | 71395.9i | −0.642751 | + | 3.27741i | ||||
\(781\) | 45248.3 | − | 26124.1i | 2.07313 | − | 1.19692i | ||||
\(782\) | 41557.5 | 1.90038 | ||||||||
\(783\) | 26814.1 | + | 1540.10i | 1.22383 | + | 0.0702922i | ||||
\(784\) | −5366.38 | −0.244460 | ||||||||
\(785\) | −20755.0 | + | 11982.9i | −0.943666 | + | 0.544826i | ||||
\(786\) | 24074.9 | + | 4721.45i | 1.09252 | + | 0.214260i | ||||
\(787\) | −32542.4 | − | 18788.4i | −1.47397 | − | 0.850995i | −0.474397 | − | 0.880311i | \(-0.657334\pi\) |
−0.999570 | + | 0.0293159i | \(0.990667\pi\) | |||||||
\(788\) | −30321.2 | − | 17506.0i | −1.37075 | − | 0.791402i | ||||
\(789\) | −4060.26 | − | 11856.2i | −0.183205 | − | 0.534969i | ||||
\(790\) | −22419.1 | − | 38831.0i | −1.00967 | − | 1.74879i | ||||
\(791\) | −1099.24 | −0.0494116 | ||||||||
\(792\) | −40696.4 | + | 5580.87i | −1.82586 | + | 0.250388i | ||||
\(793\) | 9645.78i | 0.431944i | ||||||||
\(794\) | −36434.4 | − | 63106.2i | −1.62847 | − | 2.82060i | ||||
\(795\) | 21872.8 | − | 25077.0i | 0.975785 | − | 1.11873i | ||||
\(796\) | −35493.9 | + | 61477.2i | −1.58046 | + | 2.73744i | ||||
\(797\) | −7447.36 | + | 12899.2i | −0.330990 | + | 0.573291i | −0.982706 | − | 0.185172i | \(-0.940716\pi\) |
0.651716 | + | 0.758463i | \(0.274049\pi\) | |||||||
\(798\) | −4569.69 | − | 11348.5i | −0.202713 | − | 0.503423i | ||||
\(799\) | 4044.98 | + | 7006.11i | 0.179100 | + | 0.310211i | ||||
\(800\) | −9411.11 | −0.415916 | ||||||||
\(801\) | 15455.4 | + | 6304.54i | 0.681758 | + | 0.278102i | ||||
\(802\) | 61953.3 | 2.72774 | ||||||||
\(803\) | −1443.73 | + | 833.538i | −0.0634472 | + | 0.0366313i | ||||
\(804\) | −1523.82 | − | 4449.64i | −0.0668421 | − | 0.195183i | ||||
\(805\) | −3963.73 | + | 6865.37i | −0.173544 | + | 0.300587i | ||||
\(806\) | 19463.9 | − | 33712.4i | 0.850603 | − | 1.47329i | ||||
\(807\) | −7731.18 | + | 39421.6i | −0.337237 | + | 1.71959i | ||||
\(808\) | −41031.6 | + | 23689.6i | −1.78649 | + | 1.03143i | ||||
\(809\) | 12307.4i | 0.534864i | 0.963577 | + | 0.267432i | \(0.0861752\pi\) | ||||
−0.963577 | + | 0.267432i | \(0.913825\pi\) | |||||||
\(810\) | 33155.1 | − | 33876.9i | 1.43821 | − | 1.46952i | ||||
\(811\) | − | 23809.2i | − | 1.03089i | −0.856921 | − | 0.515447i | \(-0.827626\pi\) | ||
0.856921 | − | 0.515447i | \(-0.172374\pi\) | |||||||
\(812\) | −8073.04 | − | 13982.9i | −0.348902 | − | 0.604316i | ||||
\(813\) | −4493.24 | + | 22911.2i | −0.193831 | + | 0.988353i | ||||
\(814\) | −15476.5 | + | 26806.1i | −0.666402 | + | 1.15424i | ||||
\(815\) | −8056.14 | − | 4651.22i | −0.346251 | − | 0.199908i | ||||
\(816\) | 2795.61 | + | 8163.35i | 0.119934 | + | 0.350214i | ||||
\(817\) | 963.063 | + | 18200.6i | 0.0412403 | + | 0.779386i | ||||
\(818\) | 35067.7i | 1.49892i | ||||||||
\(819\) | 4499.14 | − | 11029.5i | 0.191957 | − | 0.470575i | ||||
\(820\) | 48595.1i | 2.06953i | ||||||||
\(821\) | −23315.1 | + | 13461.0i | −0.991112 | + | 0.572219i | −0.905607 | − | 0.424119i | \(-0.860584\pi\) |
−0.0855055 | + | 0.996338i | \(0.527251\pi\) | |||||||
\(822\) | −2844.37 | + | 3261.05i | −0.120692 | + | 0.138372i | ||||
\(823\) | −5285.61 | + | 9154.94i | −0.223870 | + | 0.387754i | −0.955980 | − | 0.293433i | \(-0.905202\pi\) |
0.732110 | + | 0.681186i | \(0.238536\pi\) | |||||||
\(824\) | 9024.25 | + | 5210.15i | 0.381523 | + | 0.220272i | ||||
\(825\) | −12908.1 | + | 14799.1i | −0.544731 | + | 0.624531i | ||||
\(826\) | −10369.8 | − | 17961.1i | −0.436819 | − | 0.756593i | ||||
\(827\) | −23804.1 | −1.00090 | −0.500452 | − | 0.865764i | \(-0.666833\pi\) | ||||
−0.500452 | + | 0.865764i | \(0.666833\pi\) | |||||||
\(828\) | 34822.5 | − | 4775.36i | 1.46155 | − | 0.200429i | ||||
\(829\) | − | 37975.0i | − | 1.59098i | −0.605964 | − | 0.795492i | \(-0.707212\pi\) | ||
0.605964 | − | 0.795492i | \(-0.292788\pi\) | |||||||
\(830\) | 44921.7 | + | 77806.7i | 1.87862 | + | 3.25387i | ||||
\(831\) | −11124.1 | + | 3809.55i | −0.464369 | + | 0.159027i | ||||
\(832\) | 49346.9 | + | 28490.5i | 2.05625 | + | 1.18717i | ||||
\(833\) | −25102.6 | − | 14493.0i | −1.04412 | − | 0.602823i | ||||
\(834\) | 7801.27 | − | 39779.0i | 0.323904 | − | 1.65160i | ||||
\(835\) | −853.745 | + | 492.910i | −0.0353833 | + | 0.0204286i | ||||
\(836\) | 28852.7 | − | 56697.4i | 1.19365 | − | 2.34560i | ||||
\(837\) | −14370.2 | + | 7231.46i | −0.593436 | + | 0.298633i | ||||
\(838\) | − | 987.158i | − | 0.0406931i | ||||||
\(839\) | 21230.4 | + | 36772.1i | 0.873604 | + | 1.51313i | 0.858242 | + | 0.513245i | \(0.171557\pi\) |
0.0153625 | + | 0.999882i | \(0.495110\pi\) | |||||||
\(840\) | −11841.3 | − | 2322.26i | −0.486386 | − | 0.0953877i | ||||
\(841\) | −6130.18 | + | 10617.8i | −0.251350 | + | 0.435351i | ||||
\(842\) | 43604.7 | + | 25175.2i | 1.78470 | + | 1.03040i | ||||
\(843\) | 5750.84 | − | 1969.43i | 0.234958 | − | 0.0804636i | ||||
\(844\) | 22688.6 | − | 13099.3i | 0.925323 | − | 0.534236i | ||||
\(845\) | − | 42700.2i | − | 1.73838i | ||||||
\(846\) | 6612.79 | + | 8522.54i | 0.268738 | + | 0.346349i | ||||
\(847\) | −10536.4 | −0.427430 | ||||||||
\(848\) | 4038.45 | + | 6994.81i | 0.163539 | + | 0.283258i | ||||
\(849\) | 20194.3 | + | 17614.0i | 0.816332 | + | 0.712025i | ||||
\(850\) | 26189.5 | + | 15120.5i | 1.05681 | + | 0.610152i | ||||
\(851\) | 5607.79 | − | 9712.98i | 0.225890 | − | 0.391253i | ||||
\(852\) | −51284.4 | − | 44731.5i | −2.06218 | − | 1.79868i | ||||
\(853\) | −2706.70 | − | 4688.14i | −0.108647 | − | 0.188181i | 0.806576 | − | 0.591131i | \(-0.201318\pi\) |
−0.915222 | + | 0.402949i | \(0.867985\pi\) | |||||||
\(854\) | −3777.89 | −0.151378 | ||||||||
\(855\) | 5845.02 | + | 30532.3i | 0.233796 | + | 1.22127i | ||||
\(856\) | 7960.10 | 0.317840 | ||||||||
\(857\) | 19215.9 | + | 33282.9i | 0.765931 | + | 1.32663i | 0.939753 | + | 0.341855i | \(0.111055\pi\) |
−0.173821 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(858\) | 92385.9 | − | 31638.4i | 3.67599 | − | 1.25888i | ||||
\(859\) | 12111.8 | − | 20978.3i | 0.481082 | − | 0.833259i | −0.518682 | − | 0.854967i | \(-0.673577\pi\) |
0.999764 | + | 0.0217082i | \(0.00691048\pi\) | |||||||
\(860\) | 36765.2 | + | 21226.4i | 1.45777 | + | 0.841644i | ||||
\(861\) | 1531.15 | − | 7807.43i | 0.0606058 | − | 0.309032i | ||||
\(862\) | 29149.1 | + | 50487.8i | 1.15177 | + | 1.99492i | ||||
\(863\) | −22200.0 | −0.875664 | −0.437832 | − | 0.899057i | \(-0.644253\pi\) | ||||
−0.437832 | + | 0.899057i | \(0.644253\pi\) | |||||||
\(864\) | −8693.75 | − | 17276.0i | −0.342323 | − | 0.680257i | ||||
\(865\) | − | 27725.5i | − | 1.08982i | ||||||
\(866\) | −5479.49 | + | 3163.58i | −0.215012 | + | 0.124137i | ||||
\(867\) | −4056.58 | + | 20684.7i | −0.158903 | + | 0.810253i | ||||
\(868\) | 8375.25 | + | 4835.45i | 0.327505 | + | 0.189085i | ||||
\(869\) | −19086.7 | + | 33059.2i | −0.745079 | + | 1.29051i | ||||
\(870\) | 20956.0 | + | 61192.6i | 0.816638 | + | 2.38463i | ||||
\(871\) | 2367.42 | + | 4100.49i | 0.0920974 | + | 0.159517i | ||||
\(872\) | 35112.4i | 1.36360i | ||||||||
\(873\) | 11115.3 | − | 1524.28i | 0.430922 | − | 0.0590942i | ||||
\(874\) | −16482.0 | + | 32388.2i | −0.637886 | + | 1.25348i | ||||
\(875\) | 4151.46 | − | 2396.85i | 0.160394 | − | 0.0926037i | ||||
\(876\) | 1636.32 | + | 1427.24i | 0.0631121 | + | 0.0550480i | ||||
\(877\) | 14935.9 | + | 8623.22i | 0.575083 | + | 0.332024i | 0.759177 | − | 0.650884i | \(-0.225602\pi\) |
−0.184094 | + | 0.982909i | \(0.558935\pi\) | |||||||
\(878\) | −5930.19 | − | 3423.79i | −0.227943 | − | 0.131603i | ||||
\(879\) | 13418.2 | + | 11703.7i | 0.514885 | + | 0.449096i | ||||
\(880\) | −6746.99 | − | 11686.1i | −0.258456 | − | 0.447659i | ||||
\(881\) | 4543.30i | 0.173743i | 0.996220 | + | 0.0868716i | \(0.0276870\pi\) | ||||
−0.996220 | + | 0.0868716i | \(0.972313\pi\) | |||||||
\(882\) | −35786.9 | − | 14598.2i | −1.36622 | − | 0.557309i | ||||
\(883\) | −11541.7 | −0.439873 | −0.219936 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219936 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(884\) | −47693.8 | − | 82608.0i | −1.81461 | − | 3.14300i | ||||
\(885\) | 17074.1 | + | 49857.4i | 0.648521 | + | 1.89371i | ||||
\(886\) | −48074.3 | − | 27755.7i | −1.82290 | − | 1.05245i | ||||
\(887\) | 13178.3 | − | 22825.5i | 0.498854 | − | 0.864041i | −0.501145 | − | 0.865364i | \(-0.667088\pi\) |
0.999999 | + | 0.00132221i | \(0.000420872\pi\) | |||||||
\(888\) | 16752.8 | + | 3285.48i | 0.633095 | + | 0.124159i | ||||
\(889\) | −1313.30 | + | 758.235i | −0.0495464 | + | 0.0286056i | ||||
\(890\) | 40197.9i | 1.51397i | ||||||||
\(891\) | −39090.9 | − | 10024.5i | −1.46980 | − | 0.376916i | ||||
\(892\) | − | 56108.6i | − | 2.10612i | ||||||
\(893\) | −7064.52 | + | 373.811i | −0.264732 | + | 0.0140080i | ||||
\(894\) | −68928.3 | − | 13517.9i | −2.57864 | − | 0.505711i | ||||
\(895\) | 34843.2 | + | 20116.8i | 1.30132 | + | 0.751317i | ||||
\(896\) | −7807.11 | + | 13522.3i | −0.291090 | + | 0.504184i | ||||
\(897\) | −33475.3 | + | 11463.9i | −1.24605 | + | 0.426721i | ||||
\(898\) | −32099.9 | − | 55598.7i | −1.19286 | − | 2.06609i | ||||
\(899\) | − | 21951.6i | − | 0.814380i | ||||||
\(900\) | 23682.6 | + | 9660.58i | 0.877132 | + | 0.357799i | ||||
\(901\) | 43626.6i | 1.61311i | ||||||||
\(902\) | 56486.1 | − | 32612.2i | 2.08512 | − | 1.20385i | ||||
\(903\) | −5237.98 | − | 4568.70i | −0.193033 | − | 0.168369i | ||||
\(904\) | −2485.14 | + | 4304.39i | −0.0914321 | + | 0.158365i | ||||
\(905\) | 7348.83 | − | 12728.5i | 0.269926 | − | 0.467526i | ||||
\(906\) | 4610.20 | − | 5285.56i | 0.169055 | − | 0.193820i | ||||
\(907\) | −5451.08 | + | 3147.18i | −0.199559 | + | 0.115216i | −0.596450 | − | 0.802650i | \(-0.703423\pi\) |
0.396891 | + | 0.917866i | \(0.370089\pi\) | |||||||
\(908\) | 17949.0 | 0.656013 | ||||||||
\(909\) | −46115.4 | + | 6324.00i | −1.68268 | + | 0.230752i | ||||
\(910\) | 28686.6 | 1.04500 | ||||||||
\(911\) | −8578.74 | − | 14858.8i | −0.311994 | − | 0.540389i | 0.666800 | − | 0.745237i | \(-0.267664\pi\) |
−0.978794 | + | 0.204847i | \(0.934330\pi\) | |||||||
\(912\) | −7470.92 | − | 1058.86i | −0.271257 | − | 0.0384455i | ||||
\(913\) | 38244.6 | − | 66241.5i | 1.38632 | − | 2.40118i | ||||
\(914\) | −43807.3 | + | 75876.4i | −1.58536 | + | 2.74592i | ||||
\(915\) | 9420.26 | + | 1847.46i | 0.340354 | + | 0.0667486i | ||||
\(916\) | 29461.8 | + | 51029.3i | 1.06271 | + | 1.84067i | ||||
\(917\) | − | 6135.72i | − | 0.220959i | ||||||
\(918\) | −3563.58 | + | 62044.1i | −0.128122 | + | 2.23068i | ||||
\(919\) | 9028.79 | 0.324083 | 0.162041 | − | 0.986784i | \(-0.448192\pi\) | ||||
0.162041 | + | 0.986784i | \(0.448192\pi\) | |||||||
\(920\) | 17922.2 | + | 31042.2i | 0.642258 | + | 1.11242i | ||||
\(921\) | −9464.48 | − | 1856.13i | −0.338616 | − | 0.0664077i | ||||
\(922\) | 24430.0 | + | 14104.6i | 0.872622 | + | 0.503809i | ||||
\(923\) | 59329.0 | + | 34253.6i | 2.11575 | + | 1.22153i | ||||
\(924\) | 7860.00 | + | 22951.6i | 0.279843 | + | 0.817157i | ||||
\(925\) | 7068.04 | − | 4080.73i | 0.251238 | − | 0.145053i | ||||
\(926\) | −1174.20 | −0.0416701 | ||||||||
\(927\) | 6275.70 | + | 8088.10i | 0.222353 | + | 0.286568i | ||||
\(928\) | 26390.5 | 0.933524 | ||||||||
\(929\) | 42263.1 | − | 24400.6i | 1.49258 | − | 0.861742i | 0.492617 | − | 0.870246i | \(-0.336040\pi\) |
0.999964 | + | 0.00850449i | \(0.00270710\pi\) | |||||||
\(930\) | −29196.3 | − | 25465.7i | −1.02945 | − | 0.897908i | ||||
\(931\) | 21251.0 | − | 13815.8i | 0.748093 | − | 0.486354i | ||||
\(932\) | 11850.0 | + | 6841.60i | 0.416480 | + | 0.240455i | ||||
\(933\) | 26996.2 | − | 30951.0i | 0.947284 | − | 1.08605i | ||||
\(934\) | 7448.37 | − | 4300.32i | 0.260940 | − | 0.150654i | ||||
\(935\) | − | 72886.4i | − | 2.54935i | ||||||
\(936\) | −33017.5 | − | 42552.9i | −1.15300 | − | 1.48599i | ||||
\(937\) | −20991.0 | −0.731854 | −0.365927 | − | 0.930644i | \(-0.619248\pi\) | ||||
−0.365927 | + | 0.930644i | \(0.619248\pi\) | |||||||
\(938\) | −1606.01 | + | 927.229i | −0.0559041 | + | 0.0322762i | ||||
\(939\) | 39396.1 | − | 13491.6i | 1.36916 | − | 0.468882i | ||||
\(940\) | −8238.98 | + | 14270.3i | −0.285879 | + | 0.495156i | ||||
\(941\) | −11951.0 | + | 20699.8i | −0.414019 | + | 0.717102i | −0.995325 | − | 0.0965833i | \(-0.969209\pi\) |
0.581306 | + | 0.813685i | \(0.302542\pi\) | |||||||
\(942\) | 8062.91 | − | 41113.1i | 0.278879 | − | 1.42202i | ||||
\(943\) | −20467.3 | + | 11816.8i | −0.706793 | + | 0.408067i | ||||
\(944\) | −12791.7 | −0.441031 | ||||||||
\(945\) | −9909.89 | − | 6506.42i | −0.341131 | − | 0.223972i | ||||
\(946\) | − | 56980.2i | − | 1.95834i | ||||||
\(947\) | 8420.25 | − | 4861.44i | 0.288935 | − | 0.166817i | −0.348526 | − | 0.937299i | \(-0.613318\pi\) |
0.637461 | + | 0.770482i | \(0.279985\pi\) | |||||||
\(948\) | 48790.2 | + | 9568.49i | 1.67155 | + | 0.327817i | ||||
\(949\) | −1893.00 | − | 1092.92i | −0.0647517 | − | 0.0373844i | ||||
\(950\) | −22171.2 | + | 14414.1i | −0.757188 | + | 0.492267i | ||||
\(951\) | −37902.7 | + | 12980.1i | −1.29241 | + | 0.442597i | ||||
\(952\) | 13700.9 | − | 7910.22i | 0.466438 | − | 0.269298i | ||||
\(953\) | 5578.49 | 0.189617 | 0.0948084 | − | 0.995496i | \(-0.469776\pi\) | ||||
0.0948084 | + | 0.995496i | \(0.469776\pi\) | |||||||
\(954\) | 7903.36 | + | 57632.3i | 0.268219 | + | 1.95589i | ||||
\(955\) | −8448.58 | −0.286272 | ||||||||
\(956\) | 5933.34 | − | 3425.62i | 0.200730 | − | 0.115892i | ||||
\(957\) | 36196.8 | − | 41499.3i | 1.22265 | − | 1.40176i | ||||
\(958\) | 64862.3 | + | 37448.3i | 2.18748 | + | 1.26294i | ||||
\(959\) | 937.231 | + | 541.111i | 0.0315587 | + | 0.0182204i | ||||
\(960\) | 37275.8 | − | 42736.4i | 1.25320 | − | 1.43678i | ||||
\(961\) | −8321.40 | − | 14413.1i | −0.279326 | − | 0.483807i | ||||
\(962\) | −40585.2 | −1.36021 | ||||||||
\(963\) | 7241.01 | + | 2953.75i | 0.242304 | + | 0.0988403i | ||||
\(964\) | − | 34416.4i | − | 1.14987i | ||||||
\(965\) | −4093.26 | − | 7089.74i | −0.136546 | − | 0.236505i | ||||
\(966\) | −4489.99 | − | 13111.0i | −0.149548 | − | 0.436687i | ||||
\(967\) | 714.230 | − | 1237.08i | 0.0237519 | − | 0.0411395i | −0.853905 | − | 0.520429i | \(-0.825772\pi\) |
0.877657 | + | 0.479289i | \(0.159105\pi\) | |||||||
\(968\) | −23820.4 | + | 41258.1i | −0.790925 | + | 1.36992i | ||||
\(969\) | −32087.4 | − | 25129.8i | −1.06377 | − | 0.833111i | ||||
\(970\) | 13509.4 | + | 23399.0i | 0.447177 | + | 0.774533i | ||||
\(971\) | 26230.6 | 0.866920 | 0.433460 | − | 0.901173i | \(-0.357292\pi\) | ||||
0.433460 | + | 0.901173i | \(0.357292\pi\) | |||||||
\(972\) | 4143.40 | + | 52398.4i | 0.136728 | + | 1.72909i | ||||
\(973\) | −10138.1 | −0.334031 | ||||||||
\(974\) | −38767.0 | + | 22382.1i | −1.27533 | + | 0.736313i | ||||
\(975\) | −25267.1 | − | 4955.27i | −0.829945 | − | 0.162765i | ||||
\(976\) | −1165.05 | + | 2017.93i | −0.0382094 | + | 0.0661806i | ||||
\(977\) | −20334.6 | + | 35220.5i | −0.665875 | + | 1.15333i | 0.313172 | + | 0.949697i | \(0.398608\pi\) |
−0.979047 | + | 0.203634i | \(0.934725\pi\) | |||||||
\(978\) | 15385.1 | − | 5268.76i | 0.503027 | − | 0.172266i | ||||
\(979\) | 29637.9 | − | 17111.5i | 0.967550 | − | 0.558615i | ||||
\(980\) | − | 59039.8i | − | 1.92444i | ||||||
\(981\) | −13029.1 | + | 31940.5i | −0.424045 | + | 1.03953i | ||||
\(982\) | 7871.85i | 0.255805i | ||||||||
\(983\) | −19160.0 | − | 33186.1i | −0.621678 | − | 1.07678i | −0.989173 | − | 0.146752i | \(-0.953118\pi\) |
0.367496 | − | 0.930025i | \(-0.380215\pi\) | |||||||
\(984\) | −27110.6 | − | 23646.5i | −0.878307 | − | 0.766081i | ||||
\(985\) | 17539.0 | − | 30378.5i | 0.567351 | − | 0.982680i | ||||
\(986\) | −73440.2 | − | 42400.7i | −2.37202 | − | 1.36949i | ||||
\(987\) | 1773.33 | − | 2033.11i | 0.0571892 | − | 0.0655671i | ||||
\(988\) | 83296.8 | − | 4407.55i | 2.68221 | − | 0.141926i | ||||
\(989\) | 20646.3i | 0.663816i | ||||||||
\(990\) | −13204.0 | − | 96285.6i | −0.423891 | − | 3.09107i | ||||
\(991\) | − | 32865.0i | − | 1.05347i | −0.850029 | − | 0.526736i | \(-0.823416\pi\) | ||
0.850029 | − | 0.526736i | \(-0.176584\pi\) | |||||||
\(992\) | −13689.2 | + | 7903.47i | −0.438138 | + | 0.252959i | ||||
\(993\) | 16128.2 | + | 47095.3i | 0.515422 | + | 1.50506i | ||||
\(994\) | −13415.9 | + | 23237.0i | −0.428094 | + | 0.741481i | ||||
\(995\) | −61593.3 | − | 35560.9i | −1.96245 | − | 1.13302i | ||||
\(996\) | −97762.1 | − | 19172.6i | −3.11015 | − | 0.609947i | ||||
\(997\) | 3063.06 | + | 5305.37i | 0.0972999 | + | 0.168528i | 0.910566 | − | 0.413363i | \(-0.135646\pi\) |
−0.813266 | + | 0.581892i | \(0.802313\pi\) | |||||||
\(998\) | −53926.1 | −1.71042 | ||||||||
\(999\) | 14020.3 | + | 9205.14i | 0.444026 | + | 0.291529i |
(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 | 171.4.l.a.113.52 | yes | 116 | |
9.2 | odd | 6 | inner | 171.4.l.a.56.7 | ✓ | 116 | |
19.18 | odd | 2 | inner | 171.4.l.a.113.7 | yes | 116 | |
171.56 | even | 6 | inner | 171.4.l.a.56.52 | yes | 116 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.4.l.a.56.7 | ✓ | 116 | 9.2 | odd | 6 | inner | |
171.4.l.a.56.52 | yes | 116 | 171.56 | even | 6 | inner | |
171.4.l.a.113.7 | yes | 116 | 19.18 | odd | 2 | inner | |
171.4.l.a.113.52 | yes | 116 | 1.1 | even | 1 | trivial |