Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Character | \(\chi\) | \(=\) | 108.65 |
Dual form | 108.5.k.a.5.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.53499 | + | 7.09676i | −0.614998 | + | 0.788528i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −14.0519 | + | 38.6073i | −0.562077 | + | 1.54429i | 0.254509 | + | 0.967070i | \(0.418086\pi\) |
−0.816586 | + | 0.577223i | \(0.804136\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.57324 | + | 31.6074i | −0.113740 | + | 0.645050i | 0.873627 | + | 0.486596i | \(0.161762\pi\) |
−0.987367 | + | 0.158453i | \(0.949349\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.7279 | − | 78.5609i | −0.243554 | − | 0.969887i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.11688 | − | 11.3110i | −0.0340238 | − | 0.0934797i | 0.921518 | − | 0.388337i | \(-0.126950\pi\) |
−0.955541 | + | 0.294857i | \(0.904728\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 91.3096 | − | 76.6178i | 0.540293 | − | 0.453360i | −0.331345 | − | 0.943510i | \(-0.607502\pi\) |
0.871638 | + | 0.490150i | \(0.163058\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −196.210 | − | 313.414i | −0.872043 | − | 1.39295i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −175.368 | + | 101.249i | −0.606810 | + | 0.350342i | −0.771716 | − | 0.635967i | \(-0.780601\pi\) |
0.164906 | + | 0.986309i | \(0.447268\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.3348 | − | 170.321i | 0.272395 | − | 0.471803i | −0.697079 | − | 0.716994i | \(-0.745517\pi\) |
0.969475 | + | 0.245191i | \(0.0788508\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −193.462 | − | 214.499i | −0.438690 | − | 0.486391i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −707.360 | + | 124.727i | −1.33716 | + | 0.235778i | −0.796081 | − | 0.605191i | \(-0.793097\pi\) |
−0.541084 | + | 0.840969i | \(0.681986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −814.293 | − | 683.273i | −1.30287 | − | 1.09324i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 666.721 | + | 294.829i | 0.914569 | + | 0.404430i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 523.078 | − | 623.381i | 0.621972 | − | 0.741237i | −0.359436 | − | 0.933170i | \(-0.617031\pi\) |
0.981408 | + | 0.191932i | \(0.0614754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.4024 | + | 161.078i | 0.0295550 | + | 0.167615i | 0.996013 | − | 0.0892109i | \(-0.0284345\pi\) |
−0.966458 | + | 0.256826i | \(0.917323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 103.059 | + | 33.3899i | 0.0946360 | + | 0.0306611i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1141.96 | − | 659.313i | −0.932216 | − | 0.538215i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −941.906 | − | 1631.43i | −0.688025 | − | 1.19169i | −0.972476 | − | 0.233004i | \(-0.925145\pi\) |
0.284451 | − | 0.958691i | \(-0.408189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 38.3409 | + | 1072.08i | 0.0252077 | + | 0.704852i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1759.69 | + | 2097.12i | 1.04681 | + | 1.24754i | 0.968079 | + | 0.250646i | \(0.0806429\pi\) |
0.0787328 | + | 0.996896i | \(0.474913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3246.83 | + | 1181.75i | −1.75599 | + | 0.639129i | −0.999883 | − | 0.0153148i | \(-0.995125\pi\) |
−0.756110 | + | 0.654444i | \(0.772903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3310.24 | + | 342.290i | 1.63469 | + | 0.169032i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 89.3900 | + | 15.7619i | 0.0404663 | + | 0.00713530i | 0.193845 | − | 0.981032i | \(-0.437904\pi\) |
−0.153378 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1288.23 | + | 468.879i | 0.536540 | + | 0.195285i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 252.122 | − | 1804.96i | 0.0969326 | − | 0.693947i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 844.122i | 0.300506i | 0.988648 | + | 0.150253i | \(0.0480088\pi\) | ||||
−0.988648 | + | 0.150253i | \(0.951991\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 494.540 | 0.163484 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 664.444 | + | 1640.58i | 0.204507 | + | 0.504950i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1831.29 | + | 5031.42i | −0.526081 | + | 1.44540i | 0.337568 | + | 0.941301i | \(0.390396\pi\) |
−0.863649 | + | 0.504094i | \(0.831826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 860.325 | − | 4879.15i | 0.231208 | − | 1.31125i | −0.619246 | − | 0.785197i | \(-0.712562\pi\) |
0.850454 | − | 0.526049i | \(-0.176327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2593.06 | − | 185.709i | 0.653327 | − | 0.0467898i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1674.94 | + | 4601.85i | 0.396435 | + | 1.08919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 561.501 | − | 471.156i | 0.125084 | − | 0.104958i | −0.578100 | − | 0.815966i | \(-0.696206\pi\) |
0.703184 | + | 0.711008i | \(0.251761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3030.07 | − | 5710.32i | 0.636436 | − | 1.19940i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3351.53 | + | 1935.01i | −0.664855 | + | 0.383854i | −0.794124 | − | 0.607756i | \(-0.792070\pi\) |
0.129270 | + | 0.991609i | \(0.458737\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1199.32 | − | 2077.29i | 0.225056 | − | 0.389808i | −0.731280 | − | 0.682077i | \(-0.761077\pi\) |
0.956336 | + | 0.292269i | \(0.0944103\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9356.12 | − | 1996.93i | 1.66331 | − | 0.355010i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 380.457 | − | 67.0849i | 0.0641689 | − | 0.0113147i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3238.29 | + | 2717.25i | 0.518874 | + | 0.435387i | 0.864239 | − | 0.503082i | \(-0.167801\pi\) |
−0.345365 | + | 0.938468i | \(0.612245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5782.62 | + | 3099.68i | −0.881363 | + | 0.472440i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6782.64 | + | 8083.24i | −0.984561 | + | 1.17335i | 0.000298097 | 1.00000i | \(0.499905\pi\) | |
−0.984859 | + | 0.173355i | \(0.944539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1444.69 | − | 8193.24i | −0.199957 | − | 1.13401i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1528.75 | + | 7162.56i | 0.201975 | + | 0.946302i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4410.52 | + | 2546.41i | 0.556813 | + | 0.321476i | 0.751865 | − | 0.659317i | \(-0.229154\pi\) |
−0.195052 | + | 0.980793i | \(0.562488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1912.80 | + | 3313.07i | 0.230987 | + | 0.400081i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1300.34 | − | 689.999i | −0.150345 | − | 0.0797778i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5193.84 | + | 6189.78i | 0.575495 | + | 0.685848i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14646.8 | + | 5331.01i | −1.55668 | + | 0.566586i | −0.969973 | − | 0.243212i | \(-0.921799\pi\) |
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −807.388 | + | 546.569i | −0.0823781 | + | 0.0557666i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13396.2 | − | 2362.10i | −1.31322 | − | 0.231556i | −0.527191 | − | 0.849747i | \(-0.676755\pi\) |
−0.786028 | + | 0.618191i | \(0.787866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13783.3 | − | 5016.70i | −1.29921 | − | 0.472872i | −0.402468 | − | 0.915434i | \(-0.631848\pi\) |
−0.896738 | + | 0.442562i | \(0.854070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10999.7 | − | 4454.95i | 0.997709 | − | 0.404077i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8097.26i | − | 0.707246i | −0.935388 | − | 0.353623i | \(-0.884950\pi\) | ||
0.935388 | − | 0.353623i | \(-0.115050\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13401.0 | −1.12793 | −0.563966 | − | 0.825798i | \(-0.690725\pi\) | ||||
−0.563966 | + | 0.825798i | \(0.690725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16791.3 | + | 2345.46i | 1.36282 | + | 0.190363i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7402.08 | − | 20337.0i | 0.579691 | − | 1.59269i | −0.209012 | − | 0.977913i | \(-0.567025\pi\) |
0.788703 | − | 0.614775i | \(-0.210753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5124.40 | − | 29061.9i | 0.387479 | − | 2.19750i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7820.51 | − | 5661.85i | −0.571299 | − | 0.413606i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2222.85 | − | 6107.22i | −0.156970 | − | 0.431270i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11104.7 | − | 9317.92i | 0.758464 | − | 0.636427i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24622.6 | + | 880.579i | −1.62751 | + | 0.0582047i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15583.8 | − | 8997.30i | 0.997361 | − | 0.575827i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14330.6 | + | 24821.3i | −0.888497 | + | 1.53892i | −0.0468449 | + | 0.998902i | \(0.514917\pi\) |
−0.841652 | + | 0.540020i | \(0.818417\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9584.57 | − | 29582.9i | 0.575961 | − | 1.77771i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7511.50 | + | 1324.48i | −0.437707 | + | 0.0771796i | −0.388160 | − | 0.921592i | \(-0.626889\pi\) |
−0.0495477 | + | 0.998772i | \(0.515778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4835.36 | + | 4057.35i | 0.273354 | + | 0.229371i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20751.3 | + | 21597.4i | −1.13862 | + | 1.18504i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18103.1 | + | 21574.5i | −0.964524 | + | 1.14947i | 0.0241978 | + | 0.999707i | \(0.492297\pi\) |
−0.988721 | + | 0.149767i | \(0.952148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2705.80 | − | 15345.3i | −0.140044 | − | 0.794231i | −0.971213 | − | 0.238211i | \(-0.923439\pi\) |
0.831169 | − | 0.556020i | \(-0.187672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −606.630 | + | 547.137i | −0.0305131 | + | 0.0275206i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1242.54 | − | 717.380i | −0.0607628 | − | 0.0350814i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16716.8 | + | 28954.4i | 0.795092 | + | 1.37714i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10457.9 | + | 6547.04i | −0.483959 | + | 0.302978i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8817.28 | + | 10508.0i | 0.397157 | + | 0.473313i | 0.927151 | − | 0.374688i | \(-0.122250\pi\) |
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14397.6 | + | 5240.31i | −0.631447 | + | 0.229828i | −0.637861 | − | 0.770152i | \(-0.720181\pi\) |
0.00641405 | + | 0.999979i | \(0.497958\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11413.8 | + | 11779.6i | 0.487583 | + | 0.503210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6617.89 | − | 1166.91i | −0.275459 | − | 0.0485708i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 41354.0 | + | 15051.6i | 1.67771 | + | 0.610638i | 0.992994 | − | 0.118168i | \(-0.0377022\pi\) |
0.684720 | + | 0.728806i | \(0.259924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5990.53 | − | 4672.20i | −0.236958 | − | 0.184811i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23053.0i | − | 0.889355i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 46133.7 | 1.73637 | 0.868186 | − | 0.496239i | \(-0.165286\pi\) | ||||
0.868186 | + | 0.496239i | \(0.165286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2737.27 | + | 3509.63i | −0.100542 | + | 0.128912i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10403.4 | + | 28583.1i | −0.373029 | + | 1.02489i | 0.601155 | + | 0.799132i | \(0.294707\pi\) |
−0.974184 | + | 0.225756i | \(0.927515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2492.42 | + | 14135.2i | −0.0872665 | + | 0.494913i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15320.5 | − | 4365.20i | −0.523939 | − | 0.149283i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4830.95 | − | 13272.9i | −0.161414 | − | 0.443480i | 0.832449 | − | 0.554102i | \(-0.186938\pi\) |
−0.993863 | + | 0.110621i | \(0.964716\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26134.7 | − | 21929.7i | 0.853379 | − | 0.716070i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25570.6 | − | 40845.0i | −0.816196 | − | 1.30375i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6081.38 | − | 3511.09i | 0.189800 | − | 0.109581i | −0.402089 | − | 0.915601i | \(-0.631716\pi\) |
0.591889 | + | 0.806020i | \(0.298382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5455.83 | + | 9449.78i | −0.166534 | + | 0.288446i | −0.937199 | − | 0.348795i | \(-0.886591\pi\) |
0.770665 | + | 0.637241i | \(0.219924\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29864.2 | + | 33111.5i | 0.891762 | + | 0.988728i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 76220.7 | − | 13439.8i | 2.22705 | − | 0.392689i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1867.20 | + | 1566.77i | 0.0533959 | + | 0.0448044i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13034.6 | + | 19430.2i | −0.364900 | + | 0.543943i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 30575.4 | − | 36438.4i | 0.838119 | − | 0.998832i | −0.161809 | − | 0.986822i | \(-0.551733\pi\) |
0.999928 | − | 0.0120095i | \(-0.00382285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7552.68 | + | 42833.4i | 0.202762 | + | 1.14992i | 0.900923 | + | 0.433979i | \(0.142891\pi\) |
−0.698161 | + | 0.715941i | \(0.745998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −41928.9 | − | 13584.6i | −1.10267 | − | 0.357253i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11406.4 | − | 6585.49i | −0.293911 | − | 0.169690i | 0.345793 | − | 0.938311i | \(-0.387610\pi\) |
−0.639704 | + | 0.768621i | \(0.720943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17462.9 | + | 30246.6i | 0.440971 | + | 0.763785i | 0.997762 | − | 0.0668682i | \(-0.0213007\pi\) |
−0.556790 | + | 0.830653i | \(0.687967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 235.774 | + | 6592.68i | 0.00583585 | + | 0.163181i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16788.2 | + | 20007.4i | 0.407392 | + | 0.485511i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −105691. | + | 38468.4i | −2.51496 | + | 0.915370i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23753.3 | + | 53110.2i | 0.554350 | + | 1.23947i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2331.34 | − | 411.078i | −0.0533719 | − | 0.00941091i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 51237.9 | + | 18649.1i | 1.15087 | + | 0.418883i | 0.845828 | − | 0.533456i | \(-0.179107\pi\) |
0.305043 | + | 0.952339i | \(0.401329\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4818.40 | − | 34495.2i | 0.106205 | − | 0.760326i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 141957.i | − | 3.07101i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5249.55 | −0.111481 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8103.76 | + | 20009.0i | 0.168966 | + | 0.417194i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8255.32 | + | 22681.3i | −0.169024 | + | 0.464391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5832.28 | − | 33076.5i | 0.117281 | − | 0.665135i | −0.868314 | − | 0.496015i | \(-0.834796\pi\) |
0.985595 | − | 0.169120i | \(-0.0540927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −37614.2 | + | 77451.1i | −0.742997 | + | 1.52990i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2193.22 | + | 6025.83i | 0.0425629 | + | 0.116941i | 0.959153 | − | 0.282887i | \(-0.0912922\pi\) |
−0.916590 | + | 0.399828i | \(0.869070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13000.1 | − | 10908.4i | 0.247900 | − | 0.208013i | −0.510367 | − | 0.859956i | \(-0.670491\pi\) |
0.758267 | + | 0.651944i | \(0.226046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1629.74 | + | 3071.33i | −0.0305418 | + | 0.0575575i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18170.9 | − | 10491.0i | 0.334706 | − | 0.193243i | −0.323222 | − | 0.946323i | \(-0.604766\pi\) |
0.657929 | + | 0.753080i | \(0.271433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1864.63 | + | 3229.63i | −0.0337642 | + | 0.0584812i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −37207.5 | + | 7941.43i | −0.662421 | + | 0.141385i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17008.7 | − | 2999.10i | 0.297767 | − | 0.0525043i | −0.0227689 | − | 0.999741i | \(-0.507248\pi\) |
0.320536 | + | 0.947236i | \(0.396137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27227.2 | − | 22846.4i | −0.468780 | − | 0.393353i | 0.377569 | − | 0.925981i | \(-0.376760\pi\) |
−0.846349 | + | 0.532628i | \(0.821205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10009.1 | − | 58194.5i | 0.169504 | − | 0.985529i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36204.3 | + | 43146.6i | −0.603154 | + | 0.718811i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4070.71 | − | 23086.1i | −0.0667230 | − | 0.378405i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19822.9 | − | 92875.4i | −0.319720 | − | 1.49797i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −54334.9 | − | 31370.3i | −0.862445 | − | 0.497933i | 0.00238560 | − | 0.999997i | \(-0.499241\pi\) |
−0.864830 | + | 0.502065i | \(0.832574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4322.91 | + | 7487.50i | 0.0675359 | + | 0.116976i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 66141.7 | + | 35096.8i | 1.01717 | + | 0.539744i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 43512.8 | + | 51856.5i | 0.658796 | + | 0.785122i | 0.987212 | − | 0.159411i | \(-0.0509594\pi\) |
−0.328417 | + | 0.944533i | \(0.606515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 56814.8 | − | 20678.9i | 0.846958 | − | 0.308267i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −59292.5 | − | 28795.5i | −0.870400 | − | 0.422711i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −121068. | − | 21347.5i | −1.75032 | − | 0.308628i | −0.795530 | − | 0.605914i | \(-0.792808\pi\) |
−0.954789 | + | 0.297285i | \(0.903919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32589.3 | − | 11861.5i | −0.464070 | − | 0.168908i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −42483.4 | + | 17206.0i | −0.595932 | + | 0.241356i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 39540.0i | − | 0.546427i | −0.961953 | − | 0.273213i | \(-0.911913\pi\) | ||
0.961953 | − | 0.273213i | \(-0.0880865\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27986.9 | 0.381080 | 0.190540 | − | 0.981679i | \(-0.438976\pi\) | ||||
0.190540 | + | 0.981679i | \(0.438976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34099.4 | − | 4763.11i | −0.457532 | − | 0.0639095i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4376.18 | + | 12023.5i | −0.0578668 | + | 0.158988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17151.2 | + | 97269.1i | −0.223529 | + | 1.26770i | 0.641948 | + | 0.766748i | \(0.278126\pi\) |
−0.865477 | + | 0.500948i | \(0.832985\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12094.1 | − | 5409.04i | 0.155369 | − | 0.0694883i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6829.25 | + | 18763.2i | 0.0864890 | + | 0.237626i | 0.975396 | − | 0.220462i | \(-0.0707565\pi\) |
−0.888907 | + | 0.458088i | \(0.848534\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 77950.3 | − | 65408.0i | 0.973296 | − | 0.816692i | −0.00976888 | − | 0.999952i | \(-0.503110\pi\) |
0.983064 | + | 0.183260i | \(0.0586651\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −72675.2 | + | 2599.09i | −0.894739 | + | 0.0319986i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −76091.7 | + | 43931.5i | −0.923790 | + | 0.533350i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21257.9 | + | 36819.7i | −0.254521 | + | 0.440843i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 43237.1 | − | 133452.i | 0.510588 | − | 1.57594i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24682.6 | − | 4352.21i | 0.287512 | − | 0.0506961i | −0.0280322 | − | 0.999607i | \(-0.508924\pi\) |
0.315544 | + | 0.948911i | \(0.397813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −168517. | − | 141402.i | −1.93642 | − | 1.62485i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 590.016 | − | 8755.09i | 0.00668884 | − | 0.0992539i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −55032.5 | + | 65585.1i | −0.615569 | + | 0.733606i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19256.7 | − | 109210.i | −0.212544 | − | 1.20540i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 90910.8 | − | 81995.0i | 0.990216 | − | 0.893104i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 176282. | + | 101776.i | 1.89499 | + | 1.09407i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 35159.3 | + | 60897.6i | 0.373046 | + | 0.646135i | 0.990033 | − | 0.140839i | \(-0.0449799\pi\) |
−0.616986 | + | 0.786974i | \(0.711647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 111893. | − | 70049.2i | 1.17188 | − | 0.733645i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −49685.8 | − | 59213.2i | −0.513702 | − | 0.612207i | 0.445377 | − | 0.895343i | \(-0.353070\pi\) |
−0.959080 | + | 0.283136i | \(0.908625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 143003. | − | 52048.7i | 1.45967 | − | 0.531277i | 0.514397 | − | 0.857552i | \(-0.328016\pi\) |
0.945275 | + | 0.326275i | \(0.105794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −29267.7 | + | 102721.i | −0.294963 | + | 1.03523i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12789.7 | + | 2255.17i | 0.127275 | + | 0.0224419i | 0.236923 | − | 0.971529i | \(-0.423861\pi\) |
−0.109648 | + | 0.993970i | \(0.534972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9204.54 | − | 3350.18i | −0.0904525 | − | 0.0329220i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 57464.3 | + | 44818.2i | 0.557684 | + | 0.434955i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39825.1i | 0.381726i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −126704. | −1.19956 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 74174.1 | − | 95103.3i | 0.693676 | − | 0.889406i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −996.384 | + | 2737.54i | −0.00920524 | + | 0.0252912i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5541.63 | + | 31428.2i | −0.0505803 | + | 0.286855i | −0.999598 | − | 0.0283690i | \(-0.990969\pi\) |
0.949017 | + | 0.315224i | \(0.102080\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −109585. | + | 106182.i | −0.988238 | + | 0.957549i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10299.9 | + | 28298.7i | 0.0917789 | + | 0.252161i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −82087.2 | + | 68879.3i | −0.722796 | + | 0.606498i | −0.928157 | − | 0.372188i | \(-0.878608\pi\) |
0.205361 | + | 0.978686i | \(0.434163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 103357. | + | 165096.i | 0.899371 | + | 1.43660i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1705.03 | − | 984.399i | 0.0146630 | − | 0.00846569i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60529.8 | + | 104841.i | −0.514494 | + | 0.891131i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 177882. | + | 197224.i | 1.49449 | + | 1.65700i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −52650.6 | + | 9283.71i | −0.437264 | + | 0.0771015i | −0.387947 | − | 0.921682i | \(-0.626816\pi\) |
−0.0493173 | + | 0.998783i | \(0.515705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −67043.3 | − | 56256.0i | −0.550433 | − | 0.461868i | 0.324654 | − | 0.945833i | \(-0.394752\pi\) |
−0.875088 | + | 0.483964i | \(0.839196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 83467.2 | − | 24162.0i | 0.677488 | − | 0.196118i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −77840.5 | + | 92766.7i | −0.624678 | + | 0.744462i | −0.981867 | − | 0.189570i | \(-0.939291\pi\) |
0.357189 | + | 0.934032i | \(0.383735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27610.0 | − | 156584.i | −0.219084 | − | 1.24249i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 55644.9 | + | 18028.4i | 0.436605 | + | 0.141456i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 192373. | + | 111067.i | 1.49264 | + | 0.861777i | 0.999964 | − | 0.00843513i | \(-0.00268502\pi\) |
0.492677 | + | 0.870212i | \(0.336018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45821.0 | + | 79364.4i | 0.351601 | + | 0.608991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4662.85 | + | 130382.i | 0.0353865 | + | 0.989471i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63345.7 | + | 75492.5i | 0.475479 | + | 0.566654i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29765.6 | − | 10833.8i | 0.220995 | − | 0.0804356i | −0.229150 | − | 0.973391i | \(-0.573595\pi\) |
0.450145 | + | 0.892956i | \(0.351372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 130036. | − | 179614.i | 0.955019 | − | 1.31913i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26680.5 | − | 4704.50i | −0.193841 | − | 0.0341795i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −136230. | − | 49583.8i | −0.979167 | − | 0.356387i | −0.197650 | − | 0.980273i | \(-0.563331\pi\) |
−0.781516 | + | 0.623885i | \(0.785553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22404.3 | + | 160394.i | −0.159320 | + | 1.14058i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 96997.8i | − | 0.682463i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23022.1 | 0.160275 | 0.0801375 | − | 0.996784i | \(-0.474464\pi\) | ||||
0.0801375 | + | 0.996784i | \(0.474464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −96831.0 | − | 239086.i | −0.667060 | − | 1.64704i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3524.06 | + | 9682.28i | −0.0240240 | + | 0.0660055i | −0.951125 | − | 0.308806i | \(-0.900070\pi\) |
0.927101 | + | 0.374812i | \(0.122293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2756.19 | + | 15631.1i | −0.0185946 | + | 0.105455i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 156892. | + | 231760.i | 1.04756 | + | 1.54745i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7973.83 | + | 21907.9i | 0.0526948 | + | 0.144778i | 0.963248 | − | 0.268615i | \(-0.0865659\pi\) |
−0.910553 | + | 0.413393i | \(0.864344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 111420. | − | 93492.4i | 0.728802 | − | 0.611537i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32176.5 | − | 60638.2i | 0.208331 | − | 0.392610i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −150410. | + | 86839.2i | −0.964012 | + | 0.556573i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 73141.1 | − | 126684.i | 0.464067 | − | 0.803787i | −0.535092 | − | 0.844794i | \(-0.679723\pi\) |
0.999159 | + | 0.0410065i | \(0.0130564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −55557.7 | + | 11858.0i | −0.348978 | + | 0.0744845i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8594.38 | − | 1515.42i | 0.0534473 | − | 0.00942420i | −0.146861 | − | 0.989157i | \(-0.546917\pi\) |
0.200308 | + | 0.979733i | \(0.435806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14934.8 | + | 12531.8i | 0.0919582 | + | 0.0771621i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −38413.4 | − | 266808.i | −0.234192 | − | 1.62663i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14575.5 | + | 17370.3i | −0.0879900 | + | 0.104862i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36219.7 | + | 205412.i | 0.216520 | + | 1.22795i | 0.878249 | + | 0.478204i | \(0.158712\pi\) |
−0.661729 | + | 0.749743i | \(0.730177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −52908.2 | − | 247888.i | −0.313213 | − | 1.46748i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −148824. | − | 85923.6i | −0.872515 | − | 0.503747i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −216763. | − | 375445.i | −1.25860 | − | 2.17997i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 123879. | + | 65733.9i | 0.712401 | + | 0.378022i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38386.2 | − | 45746.9i | −0.218649 | − | 0.260576i | 0.645559 | − | 0.763710i | \(-0.276624\pi\) |
−0.864208 | + | 0.503135i | \(0.832180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 98284.1 | − | 35772.5i | 0.554523 | − | 0.201830i | −0.0495322 | − | 0.998773i | \(-0.515773\pi\) |
0.604055 | + | 0.796943i | \(0.293551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −525.209 | − | 7333.50i | −0.00293529 | − | 0.0409856i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 211982. | + | 37378.1i | 1.17360 | + | 0.206937i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 149422. | + | 54385.3i | 0.819521 | + | 0.298281i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11968.5 | − | 4847.31i | 0.0650317 | − | 0.0263382i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 92728.7i | 0.499183i | 0.968351 | + | 0.249591i | \(0.0802963\pi\) | ||||
−0.968351 | + | 0.249591i | \(0.919704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 48094.2 | 0.256517 | 0.128259 | − | 0.991741i | \(-0.459061\pi\) | ||||
0.128259 | + | 0.991741i | \(0.459061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −298009. | − | 41626.9i | −1.57489 | − | 0.219986i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −48314.5 | + | 132743.i | −0.252997 | + | 0.695103i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4555.68 | + | 25836.5i | −0.0236387 | + | 0.134062i | −0.994343 | − | 0.106215i | \(-0.966127\pi\) |
0.970705 | + | 0.240276i | \(0.0772381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11421.4 | − | 110455.i | 0.0587276 | − | 0.567946i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11637.5 | − | 31973.7i | −0.0592995 | − | 0.162924i | 0.906505 | − | 0.422195i | \(-0.138740\pi\) |
−0.965805 | + | 0.259271i | \(0.916518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −160287. | + | 134496.i | −0.809426 | + | 0.679189i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −123376. | + | 4412.32i | −0.617472 | + | 0.0220827i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −324556. | + | 187382.i | −1.60989 | + | 0.929472i | −0.620500 | + | 0.784206i | \(0.713070\pi\) |
−0.989393 | + | 0.145266i | \(0.953596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16476.1 | − | 28537.5i | 0.0810033 | − | 0.140302i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 42501.4 | − | 131181.i | 0.207113 | − | 0.639258i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −154787. | + | 27293.2i | −0.747675 | + | 0.131835i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 51282.0 | + | 43030.7i | 0.245546 | + | 0.206038i | 0.757252 | − | 0.653123i | \(-0.226542\pi\) |
−0.511706 | + | 0.859161i | \(0.670986\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −146773. | + | 15801.0i | −0.696658 | + | 0.0749998i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 170802. | − | 203553.i | 0.803693 | − | 0.957804i | −0.196048 | − | 0.980594i | \(-0.562811\pi\) |
0.999740 | + | 0.0227907i | \(0.00725514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39061.0 | + | 221526.i | 0.182214 | + | 1.03339i | 0.929483 | + | 0.368865i | \(0.120253\pi\) |
−0.747269 | + | 0.664521i | \(0.768635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 44911.2 | − | 40506.7i | 0.207706 | − | 0.187336i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 187102. | + | 108023.i | 0.857916 | + | 0.495318i | 0.863314 | − | 0.504667i | \(-0.168385\pi\) |
−0.00539770 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11762.6 | + | 20373.5i | 0.0534760 | + | 0.0926231i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −335711. | + | 210169.i | −1.51330 | + | 0.947384i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26733.7 | + | 31859.9i | 0.119491 | + | 0.142404i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −196449. | + | 71501.5i | −0.870687 | + | 0.316904i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66314.9 | − | 16652.7i | 0.291457 | − | 0.0731895i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23419.4 | − | 4129.47i | −0.102071 | − | 0.0179980i | 0.122379 | − | 0.992483i | \(-0.460948\pi\) |
−0.224451 | + | 0.974485i | \(0.572059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −211002. | − | 76798.3i | −0.912002 | − | 0.331942i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 163601. | + | 127598.i | 0.701281 | + | 0.546952i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 640386.i | − | 2.72244i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 211780. | 0.892951 | 0.446476 | − | 0.894796i | \(-0.352679\pi\) | ||||
0.446476 | + | 0.894796i | \(0.352679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −255349. | + | 327399.i | −1.06787 | + | 1.36918i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 104745. | − | 287783.i | 0.434479 | − | 1.19372i | −0.508556 | − | 0.861029i | \(-0.669821\pi\) |
0.943035 | − | 0.332692i | \(-0.107957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28614.7 | + | 162282.i | −0.117732 | + | 0.667693i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9756.22 | − | 38851.5i | −0.0398172 | − | 0.158561i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42481.7 | − | 116718.i | −0.171985 | − | 0.472524i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −172810. | + | 145005.i | −0.694015 | + | 0.582348i | −0.920064 | − | 0.391768i | \(-0.871863\pi\) |
0.226049 | + | 0.974116i | \(0.427419\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −145265. | − | 232037.i | −0.578741 | − | 0.924448i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −173648. | + | 100256.i | −0.686333 | + | 0.396254i | −0.802237 | − | 0.597006i | \(-0.796357\pi\) |
0.115904 | + | 0.993260i | \(0.463023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 279436. | − | 483998.i | 1.09572 | − | 1.89784i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −86518.6 | − | 95926.2i | −0.336584 | − | 0.373183i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −208089. | + | 36691.7i | −0.803181 | + | 0.141622i | −0.560145 | − | 0.828395i | \(-0.689255\pi\) |
−0.243036 | + | 0.970017i | \(0.578143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 58973.6 | + | 49484.7i | 0.225848 | + | 0.189509i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 115777. | − | 84564.5i | 0.439936 | − | 0.321331i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 387363. | − | 461641.i | 1.46051 | − | 1.74057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −189.725 | − | 1075.98i | −0.000709812 | − | 0.00402555i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 120934. | + | 39181.4i | 0.448966 | + | 0.145460i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 162900. | + | 94050.5i | 0.600131 | + | 0.346486i | 0.769093 | − | 0.639137i | \(-0.220708\pi\) |
−0.168962 | + | 0.985623i | \(0.554041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −140142. | − | 242732.i | −0.512346 | − | 0.887410i | −0.999898 | − | 0.0143156i | \(-0.995443\pi\) |
0.487551 | − | 0.873094i | \(-0.337890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10974.0 | + | 306852.i | 0.0398149 | + | 1.11330i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21289.8 | − | 25372.2i | −0.0766568 | − | 0.0913560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 221837. | − | 80742.0i | 0.792725 | − | 0.288528i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 431400. | + | 44608.3i | 1.53000 | + | 0.158207i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 321353. | + | 56663.2i | 1.13117 | + | 0.199456i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 312614. | + | 113782.i | 1.09220 | + | 0.397527i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8743.03 | + | 62591.9i | −0.0303189 | + | 0.217055i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 16501.6i | − | 0.0568000i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −438601. | −1.49856 | −0.749281 | − | 0.662252i | \(-0.769601\pi\) | ||||
−0.749281 | + | 0.662252i | \(0.769601\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36864.8 | − | 91023.1i | −0.125030 | − | 0.308711i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 188309. | − | 517375.i | 0.633984 | − | 1.74186i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22416.7 | + | 127132.i | −0.0749200 | + | 0.424892i | 0.924160 | + | 0.382006i | \(0.124767\pi\) |
−0.999080 | + | 0.0428866i | \(0.986345\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −400282. | + | 28667.3i | −1.32807 | + | 0.0951135i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54737.9 | − | 150391.i | −0.180295 | − | 0.495358i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −103933. | + | 87210.1i | −0.339862 | + | 0.285178i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −326502. | + | 615309.i | −1.05999 | + | 1.99759i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −365276. | + | 210892.i | −1.17737 | + | 0.679752i | −0.955404 | − | 0.295303i | \(-0.904579\pi\) |
−0.221962 | + | 0.975055i | \(0.571246\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −205924. | + | 356670.i | −0.658996 | + | 1.14141i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21453.9 | + | 4579.03i | −0.0681679 | + | 0.0145495i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −270231. | + | 47648.9i | −0.852546 | + | 0.150327i | −0.582811 | − | 0.812608i | \(-0.698047\pi\) |
−0.269735 | + | 0.962935i | \(0.586936\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 681145. | + | 571549.i | 2.13375 | + | 1.79043i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −65744.9 | − | 200049.i | −0.204501 | − | 0.622258i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 100787. | − | 120113.i | 0.311300 | − | 0.370993i | −0.587597 | − | 0.809154i | \(-0.699926\pi\) |
0.898896 | + | 0.438162i | \(0.144370\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 60411.6 | + | 342611.i | 0.185288 | + | 1.05082i | 0.925584 | + | 0.378541i | \(0.123574\pi\) |
−0.740296 | + | 0.672281i | \(0.765315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 89359.7 | + | 418672.i | 0.272165 | + | 1.27516i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 661220. | + | 381756.i | 1.99991 | + | 1.15465i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 288340. | + | 499420.i | 0.866071 | + | 1.50008i | 0.865980 | + | 0.500079i | \(0.166696\pi\) |
9.13367e−5 | 1.00000i | \(0.499971\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −345782. | − | 183483.i | −1.03144 | − | 0.547315i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −217689. | − | 259432.i | −0.644888 | − | 0.768548i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9547.90 | − | 3475.15i | 0.0280912 | − | 0.0102244i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 328482. | − | 222369.i | 0.959843 | − | 0.649775i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 318374. | + | 56137.9i | 0.923978 | + | 0.162922i | 0.615344 | − | 0.788259i | \(-0.289017\pi\) |
0.308634 | + | 0.951181i | \(0.400128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30227.8 | + | 11002.0i | 0.0871318 | + | 0.0317134i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 109870. | − | 44497.9i | 0.314560 | − | 0.127398i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 101060.i | 0.287388i | 0.989622 | + | 0.143694i | \(0.0458982\pi\) | ||||
−0.989622 | + | 0.143694i | \(0.954102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 267019. | 0.754237 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −311310. | − | 43484.7i | −0.873463 | − | 0.122008i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −150516. | + | 413539.i | −0.419497 | + | 1.15256i | 0.532494 | + | 0.846434i | \(0.321255\pi\) |
−0.951991 | + | 0.306125i | \(0.900967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 119609. | − | 678335.i | 0.331142 | − | 1.87800i | −0.131289 | − | 0.991344i | \(-0.541912\pi\) |
0.462431 | − | 0.886655i | \(-0.346977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48091.6 | − | 34817.1i | −0.132262 | − | 0.0957543i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 203698. | + | 559656.i | 0.556515 | + | 1.52901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −109880. | + | 92199.9i | −0.298222 | + | 0.250238i | −0.779604 | − | 0.626273i | \(-0.784580\pi\) |
0.481382 | + | 0.876511i | \(0.340135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −234910. | + | 8401.11i | −0.633384 | + | 0.0226518i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9369.80 | − | 5409.66i | 0.0250985 | − | 0.0144906i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 172287. | − | 298409.i | 0.458491 | − | 0.794130i | −0.540390 | − | 0.841414i | \(-0.681723\pi\) |
0.998881 | + | 0.0472845i | \(0.0150567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 311998. | − | 962987.i | 0.824900 | − | 2.54607i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 678405. | − | 119621.i | 1.78204 | − | 0.314223i | 0.817065 | − | 0.576546i | \(-0.195600\pi\) |
0.964980 | + | 0.262324i | \(0.0844888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 499982. | + | 419535.i | 1.30489 | + | 1.09493i | 0.989278 | + | 0.146042i | \(0.0466534\pi\) |
0.315610 | + | 0.948889i | \(0.397791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −508385. | − | 125393.i | −1.31828 | − | 0.325154i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −105066. | + | 125213.i | −0.270700 | + | 0.322608i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13014.0 | + | 73805.8i | 0.0333157 | + | 0.188943i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15821.2 | − | 14269.6i | 0.0402444 | − | 0.0362976i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 330361. | + | 190734.i | 0.835001 | + | 0.482088i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45688.2 | + | 79134.3i | 0.114748 | + | 0.198749i | 0.917679 | − | 0.397323i | \(-0.130061\pi\) |
−0.802931 | + | 0.596072i | \(0.796727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −415949. | + | 260401.i | −1.03808 | + | 0.649882i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −756911. | − | 902052.i | −1.87714 | − | 2.23709i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 153553. | − | 55888.6i | 0.378424 | − | 0.137735i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 218135. | + | 225126.i | 0.534223 | + | 0.551345i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −736459. | − | 129858.i | −1.79239 | − | 0.316047i | −0.824206 | − | 0.566290i | \(-0.808378\pi\) |
−0.968183 | + | 0.250243i | \(0.919489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −378214. | − | 137659.i | −0.914779 | − | 0.332952i | −0.158620 | − | 0.987340i | \(-0.550704\pi\) |
−0.756159 | + | 0.654387i | \(0.772927\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.00744e6 | + | 785732.i | 2.42158 | + | 1.88867i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 363926.i | 0.869371i | 0.900582 | + | 0.434685i | \(0.143140\pi\) | ||||
−0.900582 | + | 0.434685i | \(0.856860\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 64449.8 | 0.153014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29056.2 | − | 37254.8i | 0.0685609 | − | 0.0879063i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25486.2 | + | 70022.7i | −0.0597693 | + | 0.164215i | −0.965983 | − | 0.258605i | \(-0.916737\pi\) |
0.906214 | + | 0.422819i | \(0.138960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54416.3 | − | 308610.i | 0.126837 | − | 0.719330i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −186853. | − | 53239.3i | −0.432883 | − | 0.123339i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −201632. | − | 553979.i | −0.464289 | − | 1.27562i | −0.922230 | − | 0.386642i | \(-0.873635\pi\) |
0.457941 | − | 0.888983i | \(-0.348587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −101124. | + | 84853.5i | −0.231448 | + | 0.194208i | −0.751135 | − | 0.660149i | \(-0.770493\pi\) |
0.519687 | + | 0.854357i | \(0.326049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −115271. | − | 184127.i | −0.262236 | − | 0.418880i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −224590. | + | 129667.i | −0.507863 | + | 0.293215i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −292253. | + | 506196.i | −0.656911 | + | 1.13780i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 202454. | + | 224468.i | 0.452350 | + | 0.501536i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58730.1 | + | 10355.7i | −0.130441 | + | 0.0230003i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 338696. | + | 284200.i | 0.747791 | + | 0.627471i | 0.934918 | − | 0.354865i | \(-0.115473\pi\) |
−0.187127 | + | 0.982336i | \(0.559918\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −341457. | − | 695629.i | −0.749426 | − | 1.52676i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −158293. | + | 188647.i | −0.345370 | + | 0.411596i | −0.910568 | − | 0.413359i | \(-0.864355\pi\) |
0.565198 | + | 0.824955i | \(0.308800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −86869.1 | − | 492659.i | −0.188420 | − | 1.06858i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54903.3 | − | 17788.1i | −0.118387 | − | 0.0383562i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 385117. | + | 222347.i | 0.825565 | + | 0.476640i | 0.852332 | − | 0.523002i | \(-0.175188\pi\) |
−0.0267669 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −578550. | − | 1.00208e6i | −1.23299 | − | 2.13560i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5458.75 | + | 152636.i | 0.0115659 | + | 0.323404i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 64674.8 | + | 77076.4i | 0.136237 | + | 0.162361i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −260760. | + | 94909.0i | −0.546117 | + | 0.198770i | −0.600320 | − | 0.799760i | \(-0.704960\pi\) |
0.0542035 | + | 0.998530i | \(0.482738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12775.9 | − | 28565.6i | −0.0266026 | − | 0.0594809i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 630465. | + | 111168.i | 1.30524 | + | 0.230149i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −520924. | − | 189601.i | −1.07228 | − | 0.390279i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26123.7 | + | 187021.i | −0.0534664 | + | 0.382769i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 589634.i | − | 1.19990i | −0.800036 | − | 0.599952i | \(-0.795186\pi\) | ||
0.800036 | − | 0.599952i | \(-0.204814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −370489. | −0.749660 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12599.2 | − | 31108.7i | −0.0253492 | − | 0.0625899i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 149320. | − | 410253.i | 0.298730 | − | 0.820755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17459.5 | − | 99017.7i | 0.0347327 | − | 0.196979i | −0.962504 | − | 0.271267i | \(-0.912557\pi\) |
0.997237 | + | 0.0742880i | \(0.0236684\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 149585. | − | 308008.i | 0.295902 | − | 0.609289i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40181.4 | − | 110397.i | −0.0790398 | − | 0.217160i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 45156.2 | − | 37890.5i | 0.0883294 | − | 0.0741172i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −72859.2 | + | 137307.i | −0.141725 | + | 0.267088i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −706697. | + | 408012.i | −1.36702 | + | 0.789250i | −0.990547 | − | 0.137176i | \(-0.956197\pi\) |
−0.376475 | + | 0.926427i | \(0.622864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 235383. | − | 407695.i | 0.452797 | − | 0.784268i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 312837. | − | 66770.7i | 0.598470 | − | 0.127735i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −851878. | + | 150209.i | −1.62069 | + | 0.285772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −295988. | − | 248363.i | −0.560022 | − | 0.469914i | 0.318296 | − | 0.947991i | \(-0.396889\pi\) |
−0.878318 | + | 0.478077i | \(0.841334\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 357592. | + | 393138.i | 0.672873 | + | 0.739758i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 449740. | − | 535979.i | 0.841640 | − | 1.00303i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21566.7 | − | 122311.i | −0.0401399 | − | 0.227645i | 0.958138 | − | 0.286307i | \(-0.0924277\pi\) |
−0.998278 | + | 0.0586621i | \(0.981317\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −105811. | − | 495749.i | −0.195864 | − | 0.917672i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7640.90 | − | 4411.47i | −0.0140673 | − | 0.00812173i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42912.2 | + | 74326.1i | 0.0785763 | + | 0.136098i | 0.902636 | − | 0.430405i | \(-0.141629\pi\) |
−0.824060 | + | 0.566503i | \(0.808296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 186368. | + | 98892.5i | 0.339418 | + | 0.180106i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 146820. | + | 174974.i | 0.265956 | + | 0.316953i | 0.882450 | − | 0.470405i | \(-0.155892\pi\) |
−0.616495 | + | 0.787359i | \(0.711448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −529587. | + | 192754.i | −0.954167 | + | 0.347288i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 768834. | + | 373385.i | 1.37782 | + | 0.669138i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 255934. | + | 45128.0i | 0.456209 | + | 0.0804419i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −518723. | − | 188800.i | −0.919719 | − | 0.334750i | −0.161592 | − | 0.986858i | \(-0.551663\pi\) |
−0.758127 | + | 0.652107i | \(0.773885\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 523370. | − | 211967.i | 0.923036 | − | 0.373834i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 629490.i | − | 1.10432i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −291561. | −0.508788 | −0.254394 | − | 0.967101i | \(-0.581876\pi\) | ||||
−0.254394 | + | 0.967101i | \(0.581876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −77064.2 | − | 10764.6i | −0.133773 | − | 0.0186858i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40839.4 | − | 112205.i | 0.0705197 | − | 0.193751i | −0.899426 | − | 0.437073i | \(-0.856015\pi\) |
0.969946 | + | 0.243322i | \(0.0782372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 74686.8 | − | 423570.i | 0.128291 | − | 0.727572i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −615167. | + | 275131.i | −1.05116 | + | 0.470129i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 218283. | + | 599726.i | 0.371046 | + | 1.01944i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −625266. | + | 524661.i | −1.05733 | + | 0.887209i | −0.993846 | − | 0.110774i | \(-0.964667\pi\) |
−0.0634883 | + | 0.997983i | \(0.520223\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −608856. | + | 21774.6i | −1.02425 | + | 0.0366303i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −893014. | + | 515582.i | −1.49451 | + | 0.862856i | −0.999980 | − | 0.00630343i | \(-0.997994\pi\) |
−0.494531 | + | 0.869160i | \(0.664660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 86932.2 | − | 150571.i | 0.144736 | − | 0.250691i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −167716. | + | 517658.i | −0.277800 | + | 0.857434i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 530221. | − | 93492.4i | 0.873740 | − | 0.154064i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35684.8 | + | 29943.1i | 0.0585034 | + | 0.0490902i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 532538. | − | 261402.i | 0.868615 | − | 0.426369i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.16221e6 | + | 1.38506e6i | −1.88601 | + | 2.24766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35062.6 | + | 198850.i | 0.0566103 | + | 0.321053i | 0.999942 | − | 0.0107993i | \(-0.00343760\pi\) |
−0.943331 | + | 0.331852i | \(0.892326\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 821607. | − | 741031.i | 1.31981 | − | 1.19037i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 601548. | + | 347304.i | 0.961429 | + | 0.555081i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −295274. | − | 511429.i | −0.469546 | − | 0.813278i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 264560. | − | 165625.i | 0.418591 | − | 0.262054i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 400366. | + | 477137.i | 0.630290 | + | 0.751150i | 0.982803 | − | 0.184657i | \(-0.0591173\pi\) |
−0.352513 | + | 0.935807i | \(0.614673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17272.0 | + | 6286.50i | −0.0270551 | + | 0.00984726i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 113038. | − | 396729.i | 0.176182 | − | 0.618343i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28433.7 | − | 5013.64i | −0.0440964 | − | 0.00777538i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 890014. | + | 323938.i | 1.37342 | + | 0.499886i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 280606. | + | 218853.i | 0.430873 | + | 0.336052i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32342.0i | − | 0.0494163i | −0.999695 | − | 0.0247081i | \(-0.992134\pi\) | ||
0.999695 | − | 0.0247081i | \(-0.00786564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 411096. | 0.625032 | 0.312516 | − | 0.949913i | \(-0.398828\pi\) | ||||
0.312516 | + | 0.949913i | \(0.398828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −154907. | + | 198616.i | −0.234364 | + | 0.300493i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −648267. | + | 1.78110e6i | −0.975975 | + | 2.68147i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −118000. | + | 669210.i | −0.176782 | + | 1.00258i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 222542. | − | 215631.i | 0.331776 | − | 0.321473i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −111388. | − | 306037.i | −0.165255 | − | 0.454033i | 0.829231 | − | 0.558906i | \(-0.188779\pi\) |
−0.994486 | + | 0.104873i | \(0.966557\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 540305. | − | 453370.i | 0.797700 | − | 0.669349i | −0.149939 | − | 0.988695i | \(-0.547908\pi\) |
0.947638 | + | 0.319346i | \(0.103463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −61105.4 | − | 97606.3i | −0.0897784 | − | 0.143407i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29454.2 | − | 17005.4i | 0.0430662 | − | 0.0248643i | −0.478312 | − | 0.878190i | \(-0.658751\pi\) |
0.521379 | + | 0.853326i | \(0.325418\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 517682. | − | 896652.i | 0.753276 | − | 1.30471i | −0.192951 | − | 0.981208i | \(-0.561806\pi\) |
0.946227 | − | 0.323504i | \(-0.104861\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −595363. | − | 660101.i | −0.862145 | − | 0.955890i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −273388. | + | 48205.8i | −0.393995 | + | 0.0694719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −957330. | − | 803295.i | −1.37306 | − | 1.15213i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28554.0 | + | 115768.i | −0.0407583 | + | 0.165248i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 696381. | − | 829915.i | 0.989289 | − | 1.17899i | 0.00544039 | − | 0.999985i | \(-0.498268\pi\) |
0.983848 | − | 0.179003i | \(-0.0572873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7825.75 | + | 44382.1i | 0.0110646 | + | 0.0627502i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −170958. | − | 55388.6i | −0.240566 | − | 0.0779409i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −510700. | − | 294853.i | −0.715240 | − | 0.412944i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 232627. | + | 402921.i | 0.324259 | + | 0.561634i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32731.3 | + | 915227.i | 0.0454096 | + | 1.26974i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 869749. | + | 1.03653e6i | 1.20098 | + | 1.43127i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 227061. | − | 82643.5i | 0.312065 | − | 0.113582i | −0.181240 | − | 0.983439i | \(-0.558011\pi\) |
0.493305 | + | 0.869857i | \(0.335789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 383811. | − | 530144.i | 0.525031 | − | 0.725206i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −526074. | − | 92761.0i | −0.716284 | − | 0.126300i | −0.196384 | − | 0.980527i | \(-0.562920\pi\) |
−0.519900 | + | 0.854227i | \(0.674031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 932319. | + | 339336.i | 1.26351 | + | 0.459879i | 0.884945 | − | 0.465696i | \(-0.154196\pi\) |
0.378563 | + | 0.925575i | \(0.376418\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 109395. | − | 783164.i | 0.147567 | − | 1.05644i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 628886.i | − | 0.844404i | −0.906502 | − | 0.422202i | \(-0.861257\pi\) | ||
0.906502 | − | 0.422202i | \(-0.138743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 580316. | 0.775590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −143638. | − | 354658.i | −0.191088 | − | 0.471815i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17403.3 | − | 47815.0i | 0.0230457 | − | 0.0633177i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15171.5 | − | 86042.0i | 0.0199983 | − | 0.113416i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 707759. | + | 1.04550e6i | 0.928661 | + | 1.37181i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 197529. | + | 542707.i | 0.257997 | + | 0.708842i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 627237. | − | 526315.i | 0.815516 | − | 0.684300i | −0.136401 | − | 0.990654i | \(-0.543554\pi\) |
0.951918 | + | 0.306354i | \(0.0991092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −105731. | + | 199256.i | −0.136844 | + | 0.257889i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −524079. | + | 302577.i | −0.675220 | + | 0.389838i | −0.798051 | − | 0.602589i | \(-0.794136\pi\) |
0.122832 | + | 0.992427i | \(0.460802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −406102. | + | 703389.i | −0.520851 | + | 0.902140i | 0.478855 | + | 0.877894i | \(0.341052\pi\) |
−0.999706 | + | 0.0242463i | \(0.992281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.93624e6 | − | 413262.i | 2.47213 | − | 0.527642i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 82766.8 | − | 14594.0i | 0.105198 | − | 0.0185493i | −0.120801 | − | 0.992677i | \(-0.538546\pi\) |
0.225999 | + | 0.974127i | \(0.427435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −704669. | − | 591287.i | −0.891624 | − | 0.748161i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58867.0 | + | 52646.5i | 0.0741509 | + | 0.0663153i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11474.7 | − | 13675.0i | 0.0143893 | − | 0.0171485i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50098.6 | + | 284123.i | 0.0625432 | + | 0.354700i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −160838. | − | 753565.i | −0.199896 | − | 0.936560i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 115269. | + | 66550.8i | 0.142625 | + | 0.0823444i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −85466.3 | − | 148032.i | −0.105280 | − | 0.182350i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 881623. | + | 467817.i | 1.08120 | + | 0.573720i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −288166. | − | 343423.i | −0.351840 | − | 0.419307i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 60016.5 | − | 21844.2i | 0.0729552 | − | 0.0265535i | −0.305285 | − | 0.952261i | \(-0.598752\pi\) |
0.378240 | + | 0.925708i | \(0.376529\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 78708.8 | + | 1.09901e6i | 0.0952567 | + | 1.33007i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 811994. | + | 143176.i | 0.978399 | + | 0.172518i | 0.639908 | − | 0.768451i | \(-0.278972\pi\) |
0.338491 | + | 0.940970i | \(0.390083\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 119353. | + | 43441.0i | 0.143183 | + | 0.0521145i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.69800e6 | + | 687698.i | −2.02813 | + | 0.821401i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 244801.i | − | 0.291121i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.09322e6 | −1.29442 | −0.647211 | − | 0.762311i | \(-0.724065\pi\) | ||||
−0.647211 | + | 0.762311i | \(0.724065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −626782. | − | 87550.8i | −0.738919 | − | 0.103214i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −157771. | + | 433472.i | −0.185192 | + | 0.508812i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −347724. | + | 1.97204e6i | −0.406397 | + | 2.30479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −122202. | + | 1.18180e6i | −0.142206 | + | 1.37525i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 62157.0 | + | 170775.i | 0.0720209 | + | 0.197876i | 0.970480 | − | 0.241181i | \(-0.0775348\pi\) |
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 206538. | − | 173306.i | 0.238287 | − | 0.199947i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 695232. | − | 24863.6i | 0.798668 | − | 0.0285628i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −86726.5 | + | 50071.5i | −0.0992038 | + | 0.0572753i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −288933. | + | 500447.i | −0.329093 | + | 0.570006i | −0.982332 | − | 0.187146i | \(-0.940076\pi\) |
0.653239 | + | 0.757152i | \(0.273410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −422140. | + | 1.30294e6i | −0.478769 | + | 1.47773i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.47102e6 | − | 259381.i | 1.66127 | − | 0.292927i | 0.737351 | − | 0.675510i | \(-0.236077\pi\) |
0.923921 | + | 0.382583i | \(0.124965\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.50630e6 | − | 1.26394e6i | −1.69390 | − | 1.42135i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −566986. | − | 776262.i | −0.634905 | − | 0.869250i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9993.66 | + | 11910.0i | −0.0111436 | + | 0.0132804i | −0.771587 | − | 0.636123i | \(-0.780537\pi\) |
0.760444 | + | 0.649404i | \(0.224981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49647.6 | − | 281566.i | −0.0551272 | − | 0.312642i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −86795.1 | + | 78283.0i | −0.0959698 | + | 0.0865579i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 927031. | + | 535222.i | 1.02072 | + | 0.589316i | 0.914314 | − | 0.405007i | \(-0.132731\pi\) |
0.106411 | + | 0.994322i | \(0.466064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 977145. | + | 1.69247e6i | 1.07140 | + | 1.85572i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 74722.4 | − | 46779.2i | 0.0815881 | − | 0.0510774i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −581021. | − | 692434.i | −0.631763 | − | 0.752906i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 842687. | − | 306713.i | 0.912471 | − | 0.332112i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −636128. | + | 159742.i | −0.685949 | + | 0.172253i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.75981e6 | − | 310302.i | −1.88978 | − | 0.333220i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.17361e6 | − | 427160.i | −1.25508 | − | 0.456812i | −0.372966 | − | 0.927845i | \(-0.621659\pi\) |
−0.882116 | + | 0.471033i | \(0.843881\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −282629. | − | 220431.i | −0.301002 | − | 0.234761i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 579172.i | − | 0.614284i | −0.951664 | − | 0.307142i | \(-0.900627\pi\) | ||
0.951664 | − | 0.307142i | \(-0.0993727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 500107. | 0.528247 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 701303. | − | 899185.i | 0.737728 | − | 0.945888i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 450926. | − | 1.23891e6i | 0.472407 | − | 1.29793i | −0.443405 | − | 0.896321i | \(-0.646230\pi\) |
0.915812 | − | 0.401607i | \(-0.131548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10645.0 | − | 60370.8i | 0.0111066 | − | 0.0629886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 264372. | + | 1.05279e6i | 0.274712 | + | 1.09397i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −439089. | − | 1.20639e6i | −0.454408 | − | 1.24848i | −0.929592 | − | 0.368589i | \(-0.879841\pi\) |
0.475185 | − | 0.879886i | \(-0.342381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 414530. | − | 347832.i | 0.427252 | − | 0.358507i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13912.7 | − | 22223.4i | −0.0142816 | − | 0.0228126i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.14928e6 | − | 1.24089e6i | 2.19736 | − | 1.26865i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −656993. | + | 1.13795e6i | −0.668981 | + | 1.15871i | 0.309209 | + | 0.950994i | \(0.399936\pi\) |
−0.978190 | + | 0.207714i | \(0.933398\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −192365. | − | 213282.i | −0.195087 | − | 0.216300i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.41313e6 | + | 249173.i | −1.42737 | + | 0.251683i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 553254. | + | 464235.i | 0.556589 | + | 0.467033i | 0.877165 | − | 0.480189i | \(-0.159432\pi\) |
−0.320576 | + | 0.947223i | \(0.603877\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −146995. | − | 1.36541e6i | −0.147290 | − | 1.36814i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.5.k.a.65.4 | yes | 72 | |
3.2 | odd | 2 | 324.5.k.a.197.12 | 72 | |||
27.5 | odd | 18 | inner | 108.5.k.a.5.4 | ✓ | 72 | |
27.22 | even | 9 | 324.5.k.a.125.12 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.4 | ✓ | 72 | 27.5 | odd | 18 | inner | |
108.5.k.a.65.4 | yes | 72 | 1.1 | even | 1 | trivial | |
324.5.k.a.125.12 | 72 | 27.22 | even | 9 | |||
324.5.k.a.197.12 | 72 | 3.2 | odd | 2 |