Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,6,Mod(17,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.l (of order \(10\), degree \(4\), 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: | \(31.7559963230\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 35.3 | ||
Character | \(\chi\) | \(=\) | 198.35 |
Dual form | 198.6.l.b.17.3 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23607 | + | 3.80423i | −0.218508 | + | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −12.9443 | − | 9.40456i | −0.404508 | − | 0.293893i | ||||
\(5\) | −55.4865 | + | 18.0286i | −0.992572 | + | 0.322506i | −0.759894 | − | 0.650047i | \(-0.774749\pi\) |
−0.232679 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 111.028 | − | 152.817i | 0.856424 | − | 1.17877i | −0.125986 | − | 0.992032i | \(-0.540209\pi\) |
0.982410 | − | 0.186735i | \(-0.0597906\pi\) | |||||||
\(8\) | 51.7771 | − | 37.6183i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 233.368i | − | 0.737974i | ||||||
\(11\) | −373.403 | − | 147.042i | −0.930457 | − | 0.366402i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 538.953 | + | 175.116i | 0.884489 | + | 0.287388i | 0.715820 | − | 0.698285i | \(-0.246053\pi\) |
0.168669 | + | 0.985673i | \(0.446053\pi\) | |||||||
\(14\) | 444.114 | + | 611.270i | 0.605583 | + | 0.833514i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 79.1084 | + | 243.470i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 78.2115 | + | 240.710i | 0.0656369 | + | 0.202010i | 0.978496 | − | 0.206264i | \(-0.0661307\pi\) |
−0.912859 | + | 0.408274i | \(0.866131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 675.162 | + | 929.281i | 0.429066 | + | 0.590558i | 0.967739 | − | 0.251957i | \(-0.0810740\pi\) |
−0.538673 | + | 0.842515i | \(0.681074\pi\) | |||||||
\(20\) | 887.784 | + | 288.458i | 0.496286 | + | 0.161253i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1020.93 | − | 1238.76i | 0.449717 | − | 0.545669i | ||||
\(23\) | 516.449i | 0.203567i | 0.994807 | + | 0.101784i | \(0.0324549\pi\) | ||||
−0.994807 | + | 0.101784i | \(0.967545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 225.539 | − | 163.863i | 0.0721724 | − | 0.0524363i | ||||
\(26\) | −1332.36 | + | 1833.84i | −0.386536 | + | 0.532021i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2874.36 | + | 933.937i | −0.692862 | + | 0.225124i | ||||
\(29\) | −2508.18 | − | 1822.30i | −0.553814 | − | 0.402370i | 0.275376 | − | 0.961337i | \(-0.411198\pi\) |
−0.829190 | + | 0.558967i | \(0.811198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −433.171 | + | 1333.16i | −0.0809572 | + | 0.249161i | −0.983340 | − | 0.181774i | \(-0.941816\pi\) |
0.902383 | + | 0.430935i | \(0.141816\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1012.39 | −0.150193 | ||||||||
\(35\) | −3405.48 | + | 10481.0i | −0.469903 | + | 1.44621i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1261.05 | − | 916.206i | −0.151436 | − | 0.110024i | 0.509487 | − | 0.860478i | \(-0.329835\pi\) |
−0.660923 | + | 0.750454i | \(0.729835\pi\) | |||||||
\(38\) | −4369.74 | + | 1419.81i | −0.490904 | + | 0.159504i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2194.72 | + | 3020.78i | −0.216885 | + | 0.298517i | ||||
\(41\) | −16182.7 | + | 11757.4i | −1.50346 | + | 1.09232i | −0.534476 | + | 0.845183i | \(0.679491\pi\) |
−0.968980 | + | 0.247141i | \(0.920509\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7770.64i | − | 0.640893i | −0.947267 | − | 0.320447i | \(-0.896167\pi\) | ||
0.947267 | − | 0.320447i | \(-0.103833\pi\) | |||||||
\(44\) | 3450.57 | + | 5415.04i | 0.268695 | + | 0.421667i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1964.69 | − | 638.366i | −0.136899 | − | 0.0444810i | ||||
\(47\) | 10311.3 | + | 14192.3i | 0.680876 | + | 0.937146i | 0.999944 | − | 0.0105861i | \(-0.00336974\pi\) |
−0.319068 | + | 0.947732i | \(0.603370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5832.23 | − | 17949.8i | −0.347012 | − | 1.06799i | ||||
\(50\) | 344.593 | + | 1060.55i | 0.0194931 | + | 0.0599936i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5329.46 | − | 7335.37i | −0.273322 | − | 0.376196i | ||||
\(53\) | 19423.3 | + | 6311.00i | 0.949801 | + | 0.308609i | 0.742635 | − | 0.669697i | \(-0.233576\pi\) |
0.207166 | + | 0.978306i | \(0.433576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23369.8 | + | 1426.86i | 1.04171 | + | 0.0636027i | ||||
\(56\) | − | 12089.1i | − | 0.515140i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10032.7 | − | 7289.21i | 0.391606 | − | 0.284518i | ||||
\(59\) | −13162.0 | + | 18115.9i | −0.492257 | + | 0.677533i | −0.980802 | − | 0.195005i | \(-0.937528\pi\) |
0.488545 | + | 0.872538i | \(0.337528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −45868.3 | + | 14903.5i | −1.57829 | + | 0.512819i | −0.961616 | − | 0.274397i | \(-0.911522\pi\) |
−0.616677 | + | 0.787216i | \(0.711522\pi\) | |||||||
\(62\) | −4536.23 | − | 3295.76i | −0.149870 | − | 0.108887i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1265.73 | − | 3895.53i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −33061.7 | −0.970603 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18877.8 | −0.513764 | −0.256882 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256882 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(68\) | 1251.38 | − | 3851.36i | 0.0328185 | − | 0.101005i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −35662.7 | − | 25910.4i | −0.869899 | − | 0.632019i | ||||
\(71\) | −15687.4 | + | 5097.13i | −0.369321 | + | 0.120000i | −0.487797 | − | 0.872957i | \(-0.662199\pi\) |
0.118476 | + | 0.992957i | \(0.462199\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42570.9 | + | 58593.8i | −0.934987 | + | 1.28690i | 0.0228956 | + | 0.999738i | \(0.492711\pi\) |
−0.957882 | + | 0.287161i | \(0.907289\pi\) | |||||||
\(74\) | 5044.20 | − | 3664.83i | 0.107081 | − | 0.0777990i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 18378.5i | − | 0.364985i | ||||||
\(77\) | −63928.9 | + | 40736.7i | −1.22877 | + | 0.782996i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −43389.7 | − | 14098.2i | −0.782202 | − | 0.254153i | −0.109422 | − | 0.993995i | \(-0.534900\pi\) |
−0.672780 | + | 0.739843i | \(0.734900\pi\) | |||||||
\(80\) | −8778.89 | − | 12083.1i | −0.153361 | − | 0.211083i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24724.9 | − | 76095.5i | −0.406070 | − | 1.24975i | ||||
\(83\) | 663.433 | + | 2041.84i | 0.0105707 | + | 0.0325331i | 0.956203 | − | 0.292705i | \(-0.0945555\pi\) |
−0.945632 | + | 0.325238i | \(0.894555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8679.36 | − | 11946.1i | −0.130299 | − | 0.179341i | ||||
\(86\) | 29561.3 | + | 9605.04i | 0.431000 | + | 0.140040i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24865.2 | + | 6433.39i | −0.342282 | + | 0.0885591i | ||||
\(89\) | − | 30448.3i | − | 0.407463i | −0.979027 | − | 0.203731i | \(-0.934693\pi\) | ||
0.979027 | − | 0.203731i | \(-0.0653069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 86599.9 | − | 62918.5i | 1.09626 | − | 0.796480i | ||||
\(92\) | 4856.97 | − | 6685.05i | 0.0598269 | − | 0.0823446i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −66736.0 | + | 21683.9i | −0.779006 | + | 0.253114i | ||||
\(95\) | −54216.0 | − | 39390.3i | −0.616338 | − | 0.447796i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11667.3 | + | 35908.1i | −0.125904 | + | 0.387493i | −0.994065 | − | 0.108790i | \(-0.965302\pi\) |
0.868161 | + | 0.496283i | \(0.165302\pi\) | |||||||
\(98\) | 75494.0 | 0.794049 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4460.50 | −0.0446050 | ||||||||
\(101\) | −62850.9 | + | 193435.i | −0.613067 | + | 1.88683i | −0.186197 | + | 0.982512i | \(0.559616\pi\) |
−0.426870 | + | 0.904313i | \(0.640384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 169553. | + | 123188.i | 1.57476 | + | 1.14413i | 0.922414 | + | 0.386203i | \(0.126213\pi\) |
0.652342 | + | 0.757925i | \(0.273787\pi\) | |||||||
\(104\) | 34493.0 | − | 11207.4i | 0.312714 | − | 0.101607i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48016.9 | + | 66089.7i | −0.415078 | + | 0.571306i | ||||
\(107\) | 145332. | − | 105590.i | 1.22716 | − | 0.891583i | 0.230485 | − | 0.973076i | \(-0.425969\pi\) |
0.996674 | + | 0.0814930i | \(0.0259688\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 36243.5i | − | 0.292189i | −0.989271 | − | 0.146094i | \(-0.953330\pi\) | ||
0.989271 | − | 0.146094i | \(-0.0466703\pi\) | |||||||
\(110\) | −34314.7 | + | 87140.2i | −0.270395 | + | 0.686652i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 45989.8 | + | 14943.0i | 0.346431 | + | 0.112562i | ||||
\(113\) | 41565.7 | + | 57210.3i | 0.306224 | + | 0.421481i | 0.934199 | − | 0.356752i | \(-0.116116\pi\) |
−0.627975 | + | 0.778234i | \(0.716116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9310.87 | − | 28655.9i | −0.0656517 | − | 0.202055i | ||||
\(116\) | 15328.6 | + | 47176.7i | 0.105769 | + | 0.325524i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −52648.0 | − | 72463.7i | −0.348078 | − | 0.479088i | ||||
\(119\) | 45468.4 | + | 14773.6i | 0.294336 | + | 0.0956354i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117809. | + | 109811.i | 0.731499 | + | 0.681843i | ||||
\(122\) | − | 192915.i | − | 1.17346i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18144.9 | − | 13183.0i | 0.105974 | − | 0.0769948i | ||||
\(125\) | 97604.0 | − | 134340.i | 0.558718 | − | 0.769010i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 273479. | − | 88858.6i | 1.50458 | − | 0.488867i | 0.563228 | − | 0.826302i | \(-0.309559\pi\) |
0.941349 | + | 0.337435i | \(0.109559\pi\) | |||||||
\(128\) | 13254.9 | + | 9630.27i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 40866.5 | − | 125774.i | 0.212085 | − | 0.652729i | ||||
\(131\) | −202835. | −1.03268 | −0.516339 | − | 0.856384i | \(-0.672706\pi\) | ||||
−0.516339 | + | 0.856384i | \(0.672706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 216972. | 1.06359 | ||||||||
\(134\) | 23334.2 | − | 71815.3i | 0.112262 | − | 0.345506i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13104.7 | + | 9521.10i | 0.0607545 | + | 0.0441407i | ||||
\(137\) | −43749.9 | + | 14215.2i | −0.199148 | + | 0.0647071i | −0.406893 | − | 0.913476i | \(-0.633388\pi\) |
0.207745 | + | 0.978183i | \(0.433388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −222219. | + | 305858.i | −0.975537 | + | 1.34271i | −0.0363368 | + | 0.999340i | \(0.511569\pi\) |
−0.939200 | + | 0.343371i | \(0.888431\pi\) | |||||||
\(140\) | 142651. | − | 103642.i | 0.615111 | − | 0.446905i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 65978.7i | − | 0.274589i | ||||||
\(143\) | −175497. | − | 144637.i | −0.717679 | − | 0.591481i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 172024. | + | 55893.9i | 0.679467 | + | 0.220772i | ||||
\(146\) | −170284. | − | 234375.i | −0.661135 | − | 0.909975i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7706.85 | + | 23719.2i | 0.0289216 | + | 0.0890116i | ||||
\(149\) | 25864.5 | + | 79602.6i | 0.0954416 | + | 0.293739i | 0.987369 | − | 0.158441i | \(-0.0506466\pi\) |
−0.891927 | + | 0.452180i | \(0.850647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 301263. | + | 414653.i | 1.07523 | + | 1.47993i | 0.864662 | + | 0.502355i | \(0.167533\pi\) |
0.210573 | + | 0.977578i | \(0.432467\pi\) | |||||||
\(152\) | 69915.8 | + | 22717.0i | 0.245452 | + | 0.0797522i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −75951.3 | − | 293553.i | −0.258068 | − | 0.997436i | ||||
\(155\) | − | 81782.0i | − | 0.273419i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −876.256 | + | 636.637i | −0.00283715 | + | 0.00206131i | −0.589203 | − | 0.807985i | \(-0.700558\pi\) |
0.586366 | + | 0.810046i | \(0.300558\pi\) | |||||||
\(158\) | 107265. | − | 147638.i | 0.341835 | − | 0.470495i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 56818.2 | − | 18461.3i | 0.175464 | − | 0.0570116i | ||||
\(161\) | 78922.4 | + | 57340.5i | 0.239958 | + | 0.174340i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −173173. | + | 532970.i | −0.510517 | + | 1.57121i | 0.280777 | + | 0.959773i | \(0.409408\pi\) |
−0.791294 | + | 0.611436i | \(0.790592\pi\) | |||||||
\(164\) | 320046. | 0.929187 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8587.66 | −0.0241882 | ||||||||
\(167\) | 41984.4 | − | 129215.i | 0.116492 | − | 0.358526i | −0.875763 | − | 0.482741i | \(-0.839641\pi\) |
0.992255 | + | 0.124215i | \(0.0396412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −40578.1 | − | 29481.7i | −0.109289 | − | 0.0794028i | ||||
\(170\) | 56174.0 | − | 18252.0i | 0.149078 | − | 0.0484383i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −73079.5 | + | 100585.i | −0.188354 | + | 0.259247i | ||||
\(173\) | 530956. | − | 385762.i | 1.34879 | − | 0.979951i | 0.349716 | − | 0.936856i | \(-0.386278\pi\) |
0.999071 | − | 0.0430957i | \(-0.0137220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 52659.8i | − | 0.129982i | ||||||
\(176\) | 6260.97 | − | 102545.i | 0.0152356 | − | 0.249535i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 115832. | + | 37636.2i | 0.274018 | + | 0.0890339i | ||||
\(179\) | 117587. | + | 161845.i | 0.274302 | + | 0.377544i | 0.923836 | − | 0.382788i | \(-0.125036\pi\) |
−0.649534 | + | 0.760332i | \(0.725036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −134581. | − | 414199.i | −0.305344 | − | 0.939751i | −0.979549 | − | 0.201207i | \(-0.935514\pi\) |
0.674205 | − | 0.738544i | \(-0.264486\pi\) | |||||||
\(182\) | 132313. | + | 407217.i | 0.296090 | + | 0.911271i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19427.9 | + | 26740.2i | 0.0423040 | + | 0.0582264i | ||||
\(185\) | 86489.2 | + | 28102.0i | 0.185794 | + | 0.0603682i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6189.99 | − | 101382.i | 0.0129445 | − | 0.212011i | ||||
\(188\) | − | 280682.i | − | 0.579188i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 216864. | − | 157561.i | 0.435817 | − | 0.316639i | ||||
\(191\) | 12671.1 | − | 17440.3i | 0.0251322 | − | 0.0345915i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.821398 | + | 0.570355i | \(0.193194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 121739. | − | 39555.5i | 0.235254 | − | 0.0764387i | −0.189017 | − | 0.981974i | \(-0.560530\pi\) |
0.424271 | + | 0.905535i | \(0.360530\pi\) | |||||||
\(194\) | −122181. | − | 88769.8i | −0.233077 | − | 0.169341i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −93315.7 | + | 287196.i | −0.173506 | + | 0.533996i | ||||
\(197\) | −282934. | −0.519421 | −0.259710 | − | 0.965687i | \(-0.583627\pi\) | ||||
−0.259710 | + | 0.965687i | \(0.583627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −240937. | −0.431291 | −0.215646 | − | 0.976472i | \(-0.569186\pi\) | ||||
−0.215646 | + | 0.976472i | \(0.569186\pi\) | |||||||
\(200\) | 5513.48 | − | 16968.7i | 0.00974655 | − | 0.0299968i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −658183. | − | 478198.i | −1.13493 | − | 0.824573i | ||||
\(203\) | −556959. | + | 180967.i | −0.948600 | + | 0.308219i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 685950. | − | 944129.i | 1.14001 | − | 1.56908i | ||||
\(206\) | −678213. | + | 492751.i | −1.11352 | + | 0.809020i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 145072.i | 0.232502i | ||||||||
\(209\) | −115465. | − | 446273.i | −0.182845 | − | 0.706700i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −976788. | − | 317378.i | −1.51041 | − | 0.490761i | −0.567374 | − | 0.823460i | \(-0.692041\pi\) |
−0.943033 | + | 0.332699i | \(0.892041\pi\) | |||||||
\(212\) | −192068. | − | 264359.i | −0.293505 | − | 0.403974i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 222047. | + | 683390.i | 0.331444 | + | 1.02008i | ||||
\(215\) | 140094. | + | 431165.i | 0.206692 | + | 0.636133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 155636. | + | 214215.i | 0.224368 | + | 0.308817i | ||||
\(218\) | 137878. | + | 44799.4i | 0.196496 | + | 0.0638456i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −289086. | − | 238252.i | −0.402689 | − | 0.331879i | ||||
\(221\) | 143428.i | 0.197539i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 39541.2 | − | 28728.3i | 0.0532461 | − | 0.0386855i | −0.560844 | − | 0.827922i | \(-0.689523\pi\) |
0.614090 | + | 0.789236i | \(0.289523\pi\) | |||||||
\(224\) | −113693. | + | 156485.i | −0.151396 | + | 0.208379i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −269019. | + | 87409.6i | −0.350358 | + | 0.113838i | ||||
\(227\) | 183811. | + | 133546.i | 0.236759 | + | 0.172015i | 0.699838 | − | 0.714301i | \(-0.253255\pi\) |
−0.463079 | + | 0.886317i | \(0.653255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −290053. | + | 892692.i | −0.365501 | + | 1.12490i | 0.584165 | + | 0.811635i | \(0.301422\pi\) |
−0.949667 | + | 0.313262i | \(0.898578\pi\) | |||||||
\(230\) | 120522. | 0.150227 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −198418. | −0.242026 | ||||||||
\(233\) | 370625. | − | 1.14067e6i | 0.447244 | − | 1.37648i | −0.432759 | − | 0.901510i | \(-0.642460\pi\) |
0.880004 | − | 0.474967i | \(-0.157540\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −828004. | − | 601580.i | −0.978054 | − | 0.710598i | ||||
\(236\) | 340745. | − | 110715.i | 0.398244 | − | 0.129397i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −112404. | + | 154711.i | −0.128629 | + | 0.177043i | ||||
\(239\) | −341192. | + | 247891.i | −0.386371 | + | 0.280715i | −0.763967 | − | 0.645256i | \(-0.776751\pi\) |
0.377596 | + | 0.925970i | \(0.376751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 541841.i | − | 0.600938i | −0.953792 | − | 0.300469i | \(-0.902857\pi\) | ||
0.953792 | − | 0.300469i | \(-0.0971431\pi\) | |||||||
\(242\) | −563367. | + | 312436.i | −0.618377 | + | 0.342944i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 733892. | + | 238456.i | 0.789147 | + | 0.256409i | ||||
\(245\) | 647220. | + | 890822.i | 0.688869 | + | 0.948147i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 201148. | + | 619070.i | 0.209785 | + | 0.645651i | ||||
\(248\) | 27723.0 | + | 85322.5i | 0.0286227 | + | 0.0880915i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 390416. | + | 537362.i | 0.395073 | + | 0.543772i | ||||
\(251\) | −1.22984e6 | − | 399598.i | −1.23215 | − | 0.400349i | −0.380656 | − | 0.924717i | \(-0.624302\pi\) |
−0.851492 | + | 0.524367i | \(0.824302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 75939.4 | − | 192843.i | 0.0745874 | − | 0.189410i | ||||
\(254\) | 1.15021e6i | 1.11865i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −53019.7 | + | 38521.1i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −59958.0 | + | 82525.2i | −0.0566258 | + | 0.0779388i | −0.836391 | − | 0.548134i | \(-0.815339\pi\) |
0.779765 | + | 0.626072i | \(0.215339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −280025. | + | 90985.5i | −0.259386 | + | 0.0842797i | ||||
\(260\) | 427960. | + | 310931.i | 0.392617 | + | 0.285253i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 250718. | − | 771631.i | 0.225649 | − | 0.694475i | ||||
\(263\) | 770186. | 0.686603 | 0.343302 | − | 0.939225i | \(-0.388455\pi\) | ||||
0.343302 | + | 0.939225i | \(0.388455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.19151e6 | −1.04227 | ||||||||
\(266\) | −268193. | + | 825412.i | −0.232404 | + | 0.715265i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 244359. | + | 177537.i | 0.207822 | + | 0.150992i | ||||
\(269\) | −2.07807e6 | + | 675207.i | −1.75098 | + | 0.568927i | −0.996203 | − | 0.0870589i | \(-0.972253\pi\) |
−0.754773 | + | 0.655986i | \(0.772253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 857133. | − | 1.17974e6i | 0.708965 | − | 0.975807i | −0.290854 | − | 0.956768i | \(-0.593939\pi\) |
0.999819 | − | 0.0190392i | \(-0.00606074\pi\) | |||||||
\(272\) | −52418.7 | + | 38084.4i | −0.0429599 | + | 0.0312122i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 184005.i | − | 0.148066i | ||||||
\(275\) | −108312. | + | 28023.6i | −0.0863661 | + | 0.0223456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.11502e6 | − | 687211.i | −1.65621 | − | 0.538134i | −0.676135 | − | 0.736777i | \(-0.736347\pi\) |
−0.980072 | + | 0.198643i | \(0.936347\pi\) | |||||||
\(278\) | −888875. | − | 1.22343e6i | −0.689809 | − | 0.949440i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 217951. | + | 670784.i | 0.166136 | + | 0.511314i | ||||
\(281\) | 567917. | + | 1.74787e6i | 0.429061 | + | 1.32051i | 0.899051 | + | 0.437843i | \(0.144257\pi\) |
−0.469990 | + | 0.882672i | \(0.655743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 352515. | + | 485196.i | 0.261645 | + | 0.360123i | 0.919547 | − | 0.392980i | \(-0.128556\pi\) |
−0.657902 | + | 0.753103i | \(0.728556\pi\) | |||||||
\(284\) | 250998. | + | 81554.1i | 0.184660 | + | 0.0599998i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 767160. | − | 488849.i | 0.554588 | − | 0.353395i | ||||
\(287\) | 3.77840e6i | 2.70772i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.09686e6 | − | 796918.i | 0.772517 | − | 0.561267i | ||||
\(290\) | −425266. | + | 585329.i | −0.296938 | + | 0.408700i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.10210e6 | − | 358093.i | 0.756420 | − | 0.245776i | ||||
\(293\) | −946891. | − | 687957.i | −0.644364 | − | 0.468158i | 0.216983 | − | 0.976175i | \(-0.430378\pi\) |
−0.861347 | + | 0.508018i | \(0.830378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 403707. | − | 1.24248e6i | 0.270092 | − | 0.831257i | ||||
\(296\) | −99759.6 | −0.0661798 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −334797. | −0.218394 | ||||||||
\(299\) | −90438.6 | + | 278341.i | −0.0585027 | + | 0.180053i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.18749e6 | − | 862762.i | −0.755464 | − | 0.548876i | ||||
\(302\) | −1.94981e6 | + | 633533.i | −1.23020 | + | 0.399716i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −172841. | + | 237896.i | −0.107266 | + | 0.147640i | ||||
\(305\) | 2.27638e6 | − | 1.65389e6i | 1.40118 | − | 1.01802i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.09919e6i | 0.665622i | 0.942994 | + | 0.332811i | \(0.107997\pi\) | ||||
−0.942994 | + | 0.332811i | \(0.892003\pi\) | |||||||
\(308\) | 1.21062e6 | + | 73915.8i | 0.727164 | + | 0.0443977i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 311117. | + | 101088.i | 0.183874 | + | 0.0597442i | ||||
\(311\) | −508841. | − | 700360.i | −0.298319 | − | 0.410601i | 0.633375 | − | 0.773845i | \(-0.281669\pi\) |
−0.931694 | + | 0.363244i | \(0.881669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −84692.7 | − | 260657.i | −0.0488636 | − | 0.150387i | 0.923648 | − | 0.383243i | \(-0.125193\pi\) |
−0.972511 | + | 0.232856i | \(0.925193\pi\) | |||||||
\(314\) | −1338.80 | − | 4120.40i | −0.000766287 | − | 0.00235839i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 429061. | + | 590552.i | 0.241714 | + | 0.332690i | ||||
\(317\) | 966118. | + | 313911.i | 0.539985 | + | 0.175452i | 0.566296 | − | 0.824202i | \(-0.308376\pi\) |
−0.0263107 | + | 0.999654i | \(0.508376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 668609. | + | 1.04926e6i | 0.367871 | + | 0.577306i | ||||
\(320\) | 238969.i | 0.130457i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −315690. | + | 229362.i | −0.169676 | + | 0.123277i | ||||
\(323\) | −170882. | + | 235199.i | −0.0911360 | + | 0.125438i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 150250. | − | 48819.1i | 0.0789052 | − | 0.0256379i | ||||
\(326\) | −1.81349e6 | − | 1.31758e6i | −0.945084 | − | 0.686644i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −395599. | + | 1.21753e6i | −0.203035 | + | 0.624877i | ||||
\(329\) | 3.31367e6 | 1.68780 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.58179e6 | −1.29524 | −0.647622 | − | 0.761962i | \(-0.724236\pi\) | ||||
−0.647622 | + | 0.761962i | \(0.724236\pi\) | |||||||
\(332\) | 10614.9 | − | 32669.4i | 0.00528533 | − | 0.0162666i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 439666. | + | 319436.i | 0.215654 | + | 0.156682i | ||||
\(335\) | 1.04746e6 | − | 340341.i | 0.509948 | − | 0.165692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −650722. | + | 895642.i | −0.312119 | + | 0.429595i | −0.936041 | − | 0.351892i | \(-0.885539\pi\) |
0.623921 | + | 0.781487i | \(0.285539\pi\) | |||||||
\(338\) | 162312. | − | 117927.i | 0.0772787 | − | 0.0561462i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 236259.i | 0.110839i | ||||||||
\(341\) | 357778. | − | 434113.i | 0.166620 | − | 0.202170i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −371240. | − | 120623.i | −0.170381 | − | 0.0553600i | ||||
\(344\) | −292318. | − | 402341.i | −0.133186 | − | 0.183315i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 811229. | + | 2.49671e6i | 0.364295 | + | 1.12118i | ||||
\(347\) | −969210. | − | 2.98292e6i | −0.432110 | − | 1.32990i | −0.896019 | − | 0.444015i | \(-0.853554\pi\) |
0.463909 | − | 0.885883i | \(-0.346446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.18158e6 | − | 3.00268e6i | −0.958754 | − | 1.31961i | −0.947527 | − | 0.319675i | \(-0.896426\pi\) |
−0.0112267 | − | 0.999937i | \(-0.503574\pi\) | |||||||
\(350\) | 200330. | + | 65091.1i | 0.0874128 | + | 0.0284021i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 382365. | + | 150571.i | 0.164483 | + | 0.0647714i | ||||
\(353\) | − | 2.17924e6i | − | 0.930826i | −0.885094 | − | 0.465413i | \(-0.845906\pi\) | ||
0.885094 | − | 0.465413i | \(-0.154094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 778542. | − | 565644.i | 0.327877 | − | 0.238217i | ||||
\(356\) | −286353. | + | 394131.i | −0.119750 | + | 0.164822i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −761042. | + | 247277.i | −0.313835 | + | 0.101971i | ||||
\(359\) | −3.01659e6 | − | 2.19168e6i | −1.23532 | − | 0.897514i | −0.238045 | − | 0.971254i | \(-0.576507\pi\) |
−0.997278 | + | 0.0737399i | \(0.976507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 357438. | − | 1.10008e6i | 0.144355 | − | 0.444280i | ||||
\(362\) | 1.74206e6 | 0.698701 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.71269e6 | −0.677526 | ||||||||
\(365\) | 1.30574e6 | − | 4.01866e6i | 0.513009 | − | 1.57888i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.74019e6 | + | 2.71741e6i | 1.44954 | + | 1.05315i | 0.985940 | + | 0.167102i | \(0.0534410\pi\) |
0.463596 | + | 0.886047i | \(0.346559\pi\) | |||||||
\(368\) | −125740. | + | 40855.4i | −0.0484009 | + | 0.0157264i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −213813. | + | 294288.i | −0.0811951 | + | 0.111755i | ||||
\(371\) | 3.12097e6 | − | 2.26751e6i | 1.17721 | − | 0.855294i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 206140.i | 0.0767167i | 0.999264 | + | 0.0383584i | \(0.0122128\pi\) | ||||
−0.999264 | + | 0.0383584i | \(0.987787\pi\) | |||||||
\(374\) | 378030. | + | 148864.i | 0.139748 | + | 0.0550312i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.06778e6 | + | 346942.i | 0.389503 | + | 0.126557i | ||||
\(377\) | −1.03268e6 | − | 1.42136e6i | −0.374206 | − | 0.515051i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 740397. | + | 2.27871e6i | 0.264769 | + | 0.814875i | 0.991747 | + | 0.128214i | \(0.0409243\pi\) |
−0.726978 | + | 0.686661i | \(0.759076\pi\) | |||||||
\(380\) | 331339. | + | 1.01976e6i | 0.117710 | + | 0.362274i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 50684.3 | + | 69761.0i | 0.0177711 | + | 0.0244599i | ||||
\(383\) | −2.13590e6 | − | 693995.i | −0.744017 | − | 0.241746i | −0.0876124 | − | 0.996155i | \(-0.527924\pi\) |
−0.656405 | + | 0.754409i | \(0.727924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.81276e6 | − | 3.41289e6i | 0.967121 | − | 1.17347i | ||||
\(386\) | 512017.i | 0.174910i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 488725. | − | 355079.i | 0.164811 | − | 0.119742i | ||||
\(389\) | −2.31995e6 | + | 3.19314e6i | −0.777328 | + | 1.06990i | 0.218243 | + | 0.975894i | \(0.429967\pi\) |
−0.995572 | + | 0.0940063i | \(0.970033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −124314. | + | 40392.2i | −0.0411225 | + | 0.0133615i | ||||
\(392\) | −977214. | − | 709988.i | −0.321199 | − | 0.233365i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 349725. | − | 1.07634e6i | 0.113498 | − | 0.349310i | ||||
\(395\) | 2.66171e6 | 0.858358 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2153.12 | −0.000685635 | −0.000342817 | − | 1.00000i | \(-0.500109\pi\) | ||||
−0.000342817 | 1.00000i | \(0.500109\pi\) | ||||||||
\(398\) | 297814. | − | 916579.i | 0.0942406 | − | 0.290043i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 57737.9 | + | 41949.1i | 0.0180431 | + | 0.0131091i | ||||
\(401\) | 2.30183e6 | − | 747910.i | 0.714846 | − | 0.232267i | 0.0710587 | − | 0.997472i | \(-0.477362\pi\) |
0.643787 | + | 0.765205i | \(0.277362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −466917. | + | 642657.i | −0.143211 | + | 0.197114i | ||||
\(404\) | 2.63273e6 | − | 1.91279e6i | 0.802515 | − | 0.583061i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 2.34249e6i | − | 0.705280i | ||||||
\(407\) | 336159. | + | 527541.i | 0.100591 | + | 0.157859i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.51774e6 | − | 493144.i | −0.448631 | − | 0.145769i | 0.0759831 | − | 0.997109i | \(-0.475790\pi\) |
−0.524614 | + | 0.851340i | \(0.675790\pi\) | |||||||
\(410\) | 2.74380e6 | + | 3.77651e6i | 0.806107 | + | 1.10951i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.03622e6 | − | 3.18915e6i | −0.300752 | − | 0.925618i | ||||
\(413\) | 1.30708e6 | + | 4.02277e6i | 0.377073 | + | 1.16051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73623.1 | − | 101334.i | −0.0209843 | − | 0.0288824i | ||||
\(416\) | −551888. | − | 179319.i | −0.156357 | − | 0.0508035i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.84045e6 | + | 112370.i | 0.515208 | + | 0.0314565i | ||||
\(419\) | − | 2.54567e6i | − | 0.708380i | −0.935173 | − | 0.354190i | \(-0.884757\pi\) | ||
0.935173 | − | 0.354190i | \(-0.115243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.76812e6 | − | 3.46424e6i | 1.31112 | − | 0.952583i | 0.311120 | − | 0.950371i | \(-0.399296\pi\) |
0.999998 | − | 0.00221240i | \(-0.000704230\pi\) | |||||||
\(422\) | 2.41475e6 | − | 3.32362e6i | 0.660072 | − | 0.908511i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.24309e6 | − | 403904.i | 0.335805 | − | 0.109110i | ||||
\(425\) | 57083.4 | + | 41473.5i | 0.0153298 | + | 0.0111378i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.81516e6 | + | 8.66419e6i | −0.747195 | + | 2.29963i | ||||
\(428\) | −2.87424e6 | −0.758426 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.81342e6 | −0.472962 | ||||||||
\(431\) | 718274. | − | 2.21062e6i | 0.186250 | − | 0.573220i | −0.813717 | − | 0.581261i | \(-0.802560\pi\) |
0.999968 | + | 0.00804113i | \(0.00255960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.71187e6 | + | 1.24375e6i | 0.438785 | + | 0.318796i | 0.785152 | − | 0.619303i | \(-0.212585\pi\) |
−0.346367 | + | 0.938099i | \(0.612585\pi\) | |||||||
\(434\) | −1.00730e6 | + | 327292.i | −0.256705 | + | 0.0834085i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −340854. | + | 469145.i | −0.0858721 | + | 0.118193i | ||||
\(437\) | −479926. | + | 348686.i | −0.120218 | + | 0.0873437i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.50383e6i | 1.85832i | 0.369672 | + | 0.929162i | \(0.379470\pi\) | ||||
−0.369672 | + | 0.929162i | \(0.620530\pi\) | |||||||
\(440\) | 1.26370e6 | − | 805251.i | 0.311179 | − | 0.198290i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −545631. | − | 177286.i | −0.132844 | − | 0.0431638i | ||||
\(443\) | −2.45763e6 | − | 3.38263e6i | −0.594985 | − | 0.818927i | 0.400252 | − | 0.916405i | \(-0.368922\pi\) |
−0.995238 | + | 0.0974778i | \(0.968922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 548942. | + | 1.68947e6i | 0.131409 | + | 0.404436i | ||||
\(446\) | 60413.5 | + | 185934.i | 0.0143813 | + | 0.0442610i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −454772. | − | 625940.i | −0.107053 | − | 0.147346i | ||||
\(449\) | 7.19958e6 | + | 2.33929e6i | 1.68536 | + | 0.547605i | 0.985938 | − | 0.167109i | \(-0.0534432\pi\) |
0.699417 | + | 0.714714i | \(0.253443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.77149e6 | − | 2.01072e6i | 1.79913 | − | 0.465491i | ||||
\(452\) | − | 1.13145e6i | − | 0.260490i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −735243. | + | 534186.i | −0.167414 | + | 0.121633i | ||||
\(455\) | −3.67079e6 | + | 5.05241e6i | −0.831248 | + | 1.14412i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.45041e6 | − | 796186.i | 0.548843 | − | 0.178330i | −0.0214519 | − | 0.999770i | \(-0.506829\pi\) |
0.570295 | + | 0.821440i | \(0.306829\pi\) | |||||||
\(458\) | −3.03748e6 | − | 2.20686e6i | −0.676627 | − | 0.491598i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −148974. | + | 458495.i | −0.0328258 | + | 0.101028i | ||||
\(461\) | −67882.5 | −0.0148767 | −0.00743833 | − | 0.999972i | \(-0.502368\pi\) | ||||
−0.00743833 | + | 0.999972i | \(0.502368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.38848e6 | −1.81857 | −0.909287 | − | 0.416170i | \(-0.863372\pi\) | ||||
−0.909287 | + | 0.416170i | \(0.863372\pi\) | |||||||
\(464\) | 245258. | − | 754828.i | 0.0528846 | − | 0.162762i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.88123e6 | + | 2.81988e6i | 0.827952 | + | 0.601542i | ||||
\(467\) | −5.43283e6 | + | 1.76523e6i | −1.15275 | + | 0.374550i | −0.822177 | − | 0.569232i | \(-0.807241\pi\) |
−0.330569 | + | 0.943782i | \(0.607241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.09597e6 | + | 2.88485e6i | −0.440000 | + | 0.605608i | ||||
\(470\) | 3.31202e6 | − | 2.40632e6i | 0.691589 | − | 0.502469i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.43312e6i | 0.296093i | ||||||||
\(473\) | −1.14261e6 | + | 2.90158e6i | −0.234825 | + | 0.596323i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 304550. | + | 98954.4i | 0.0619334 | + | 0.0201234i | ||||
\(476\) | −449617. | − | 618844.i | −0.0909547 | − | 0.125188i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −521295. | − | 1.60438e6i | −0.104355 | − | 0.321172i | ||||
\(479\) | 1.34790e6 | + | 4.14840e6i | 0.268422 | + | 0.826117i | 0.990885 | + | 0.134708i | \(0.0430097\pi\) |
−0.722464 | + | 0.691409i | \(0.756990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −519204. | − | 714622.i | −0.102323 | − | 0.140836i | ||||
\(482\) | 2.06129e6 | + | 669752.i | 0.404130 | + | 0.131310i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −492217. | − | 2.52937e6i | −0.0955088 | − | 0.490793i | ||||
\(485\) | − | 2.20276e6i | − | 0.425219i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.53017e6 | − | 4.01790e6i | 1.05661 | − | 0.767674i | 0.0831544 | − | 0.996537i | \(-0.473501\pi\) |
0.973459 | + | 0.228862i | \(0.0735005\pi\) | |||||||
\(488\) | −1.81428e6 | + | 2.49714e6i | −0.344870 | + | 0.474673i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.18889e6 | + | 1.36105e6i | −0.788151 | + | 0.256086i | ||||
\(491\) | 620372. | + | 450727.i | 0.116131 | + | 0.0843742i | 0.644335 | − | 0.764743i | \(-0.277134\pi\) |
−0.528204 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 242478. | − | 746270.i | 0.0449319 | − | 0.138286i | ||||
\(494\) | −2.60372e6 | −0.480039 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −358853. | −0.0654957 | ||||||||
\(497\) | −962812. | + | 2.96323e6i | −0.174844 | + | 0.538114i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.31398e6 | − | 2.40775e6i | −0.595797 | − | 0.432872i | 0.248587 | − | 0.968609i | \(-0.420034\pi\) |
−0.844385 | + | 0.535738i | \(0.820034\pi\) | |||||||
\(500\) | −2.52683e6 | + | 821016.i | −0.452012 | + | 0.146868i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.04032e6 | − | 4.18464e6i | 0.538469 | − | 0.741138i | ||||
\(503\) | −2.14161e6 | + | 1.55597e6i | −0.377416 | + | 0.274209i | −0.760279 | − | 0.649596i | \(-0.774938\pi\) |
0.382863 | + | 0.923805i | \(0.374938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.18661e7i | − | 2.07053i | ||||||
\(506\) | 639754. | + | 527258.i | 0.111080 | + | 0.0915476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.37566e6 | − | 1.42174e6i | −0.752288 | − | 0.244433i | ||||
\(509\) | 3.87733e6 | + | 5.33669e6i | 0.663344 | + | 0.913015i | 0.999586 | − | 0.0287609i | \(-0.00915614\pi\) |
−0.336242 | + | 0.941775i | \(0.609156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.22758e6 | + | 1.30111e7i | 0.716208 | + | 2.20426i | ||||
\(512\) | −81007.0 | − | 249314.i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −239832. | − | 330101.i | −0.0400405 | − | 0.0551110i | ||||
\(515\) | −1.16288e7 | − | 3.77843e6i | −1.93205 | − | 0.627760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.76341e6 | − | 6.81562e6i | −0.290153 | − | 1.12145i | ||||
\(518\) | − | 1.17774e6i | − | 0.192853i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.71184e6 | + | 1.24372e6i | −0.277622 | + | 0.201704i | ||||
\(521\) | 459391. | − | 632298.i | 0.0741461 | − | 0.102053i | −0.770333 | − | 0.637642i | \(-0.779910\pi\) |
0.844479 | + | 0.535588i | \(0.179910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.92221e6 | − | 1.92424e6i | 0.946738 | − | 0.307614i | 0.205348 | − | 0.978689i | \(-0.434167\pi\) |
0.741389 | + | 0.671075i | \(0.234167\pi\) | |||||||
\(524\) | 2.62555e6 | + | 1.90758e6i | 0.417727 | + | 0.303497i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −952002. | + | 2.92996e6i | −0.150028 | + | 0.461740i | ||||
\(527\) | −354785. | −0.0556466 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.16962e6 | 0.958560 | ||||||||
\(530\) | 1.47278e6 | − | 4.53276e6i | 0.227745 | − | 0.700928i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.80855e6 | − | 2.04053e6i | −0.430232 | − | 0.312582i | ||||
\(533\) | −1.07806e7 | + | 3.50283e6i | −1.64371 | + | 0.534074i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.16030e6 | + | 8.47893e6i | −0.930503 | + | 1.28073i | ||||
\(536\) | −977436. | + | 710149.i | −0.146952 | + | 0.106767i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 8.74007e6i | − | 1.30184i | ||||||
\(539\) | −461587. | + | 7.56007e6i | −0.0684356 | + | 1.12087i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.58684e6 | − | 1.49035e6i | −0.673783 | − | 0.218925i | −0.0479117 | − | 0.998852i | \(-0.515257\pi\) |
−0.625872 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(542\) | 3.42853e6 | + | 4.71897e6i | 0.501314 | + | 0.690000i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −80088.6 | − | 246487.i | −0.0116031 | − | 0.0357106i | ||||
\(545\) | 653421. | + | 2.01102e6i | 0.0942327 | + | 0.290018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.42586e6 | + | 6.09167e6i | 0.632454 | + | 0.870498i | 0.998185 | − | 0.0602224i | \(-0.0191810\pi\) |
−0.365731 | + | 0.930721i | \(0.619181\pi\) | |||||||
\(548\) | 699998. | + | 227443.i | 0.0995739 | + | 0.0323535i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 27272.5 | − | 446681.i | 0.00384431 | − | 0.0629637i | ||||
\(551\) | − | 3.56115e6i | − | 0.499703i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.97193e6 | + | 5.06541e6i | −0.969483 | + | 0.704371i | ||||
\(554\) | 5.22861e6 | − | 7.19657e6i | 0.723789 | − | 0.996210i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.75292e6 | − | 1.86924e6i | 0.789226 | − | 0.256435i | ||||
\(557\) | 6.35081e6 | + | 4.61413e6i | 0.867344 | + | 0.630162i | 0.929873 | − | 0.367881i | \(-0.119917\pi\) |
−0.0625291 | + | 0.998043i | \(0.519917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.36077e6 | − | 4.18801e6i | 0.184185 | − | 0.566863i | ||||
\(560\) | −2.82122e6 | −0.380160 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.35128e6 | −0.981798 | ||||||||
\(563\) | −1.16535e6 | + | 3.58658e6i | −0.154948 | + | 0.476880i | −0.998156 | − | 0.0607076i | \(-0.980664\pi\) |
0.843208 | + | 0.537588i | \(0.180664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.33776e6 | − | 2.42502e6i | −0.439880 | − | 0.319591i | ||||
\(566\) | −2.28153e6 | + | 741313.i | −0.299354 | + | 0.0972659i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −620501. | + | 854046.i | −0.0806996 | + | 0.111073i | ||||
\(569\) | 4.91058e6 | − | 3.56774e6i | 0.635846 | − | 0.461969i | −0.222575 | − | 0.974916i | \(-0.571446\pi\) |
0.858421 | + | 0.512946i | \(0.171446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 588638.i | 0.0755541i | 0.999286 | + | 0.0377771i | \(0.0120277\pi\) | ||||
−0.999286 | + | 0.0377771i | \(0.987972\pi\) | |||||||
\(572\) | 911432. | + | 3.52270e6i | 0.116475 | + | 0.450179i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.43739e7 | − | 4.67036e6i | −1.82094 | − | 0.591658i | ||||
\(575\) | 84627.1 | + | 116479.i | 0.0106743 | + | 0.0146919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.10273e6 | + | 6.47154e6i | 0.262933 | + | 0.809223i | 0.992162 | + | 0.124955i | \(0.0398785\pi\) |
−0.729230 | + | 0.684269i | \(0.760121\pi\) | |||||||
\(578\) | 1.67586e6 | + | 5.15776e6i | 0.208650 | + | 0.642158i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.70107e6 | − | 2.34132e6i | −0.209967 | − | 0.288995i | ||||
\(581\) | 385688. | + | 125318.i | 0.0474019 | + | 0.0154018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.32473e6 | − | 5.21257e6i | −0.770673 | − | 0.635156i | ||||
\(584\) | 4.63526e6i | 0.562395i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.78757e6 | − | 2.75183e6i | 0.455634 | − | 0.331038i | ||||
\(587\) | −689901. | + | 949568.i | −0.0826403 | + | 0.113745i | −0.848336 | − | 0.529459i | \(-0.822395\pi\) |
0.765695 | + | 0.643203i | \(0.222395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.53134e6 | + | 497564.i | −0.181880 | + | 0.0590963i | ||||
\(590\) | 4.22767e6 | + | 3.07159e6i | 0.500002 | + | 0.363272i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 123310. | − | 379508.i | 0.0144608 | − | 0.0445058i | ||||
\(593\) | 5.48179e6 | 0.640156 | 0.320078 | − | 0.947391i | \(-0.396291\pi\) | ||||
0.320078 | + | 0.947391i | \(0.396291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.78923e6 | −0.322992 | ||||||||
\(596\) | 413831. | − | 1.27364e6i | 0.0477208 | − | 0.146869i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −947085. | − | 688098.i | −0.108302 | − | 0.0786859i | ||||
\(599\) | −1.56358e7 | + | 5.08037e6i | −1.78054 | + | 0.578533i | −0.998974 | − | 0.0452862i | \(-0.985580\pi\) |
−0.781568 | + | 0.623820i | \(0.785580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −411630. | + | 566560.i | −0.0464859 | + | 0.0639823i | −0.831627 | − | 0.555334i | \(-0.812590\pi\) |
0.785141 | + | 0.619317i | \(0.212590\pi\) | |||||||
\(602\) | 4.74996e6 | − | 3.45105e6i | 0.534193 | − | 0.388114i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.20062e6i | − | 0.914649i | ||||||
\(605\) | −8.51654e6 | − | 3.96912e6i | −0.945964 | − | 0.440865i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10827e7 | − | 3.60098e6i | −1.22088 | − | 0.396687i | −0.373477 | − | 0.927640i | \(-0.621834\pi\) |
−0.847402 | + | 0.530952i | \(0.821834\pi\) | |||||||
\(608\) | −691366. | − | 951583.i | −0.0758488 | − | 0.104397i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.47800e6 | + | 1.07042e7i | 0.378447 | + | 1.16474i | ||||
\(611\) | 3.07200e6 | + | 9.45464e6i | 0.332903 | + | 1.02457i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.71868e6 | − | 7.87109e6i | −0.614674 | − | 0.846026i | 0.382278 | − | 0.924047i | \(-0.375140\pi\) |
−0.996952 | + | 0.0780214i | \(0.975140\pi\) | |||||||
\(614\) | −4.18157e6 | − | 1.35868e6i | −0.447629 | − | 0.145444i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.77761e6 | + | 4.51412e6i | −0.188749 | + | 0.479315i | ||||
\(617\) | − | 1.66441e7i | − | 1.76014i | −0.474840 | − | 0.880072i | \(-0.657494\pi\) | ||
0.474840 | − | 0.880072i | \(-0.342506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −981939. | + | 713420.i | −0.103005 | + | 0.0748374i | −0.638095 | − | 0.769957i | \(-0.720277\pi\) |
0.535091 | + | 0.844795i | \(0.320277\pi\) | |||||||
\(620\) | −769124. | + | 1.05861e6i | −0.0803558 | + | 0.110600i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.29329e6 | − | 1.07005e6i | 0.341314 | − | 0.110900i | ||||
\(623\) | −4.65303e6 | − | 3.38063e6i | −0.480304 | − | 0.348961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.26294e6 | + | 1.00423e7i | −0.334125 | + | 1.02833i | ||||
\(626\) | 1.09629e6 | 0.111812 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17329.8 | 0.00175345 | ||||||||
\(629\) | 121912. | − | 375206.i | 0.0122862 | − | 0.0378131i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.01882e6 | − | 2.19330e6i | −0.301831 | − | 0.219293i | 0.426552 | − | 0.904463i | \(-0.359728\pi\) |
−0.728383 | + | 0.685170i | \(0.759728\pi\) | |||||||
\(632\) | −2.77694e6 | + | 902282.i | −0.276550 | + | 0.0898566i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.38837e6 | + | 3.28732e6i | −0.235982 | + | 0.324802i | ||||
\(635\) | −1.35724e7 | + | 9.86091e6i | −1.33574 | + | 0.970471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.06954e7i | − | 1.04435i | ||||||
\(638\) | −4.81807e6 | + | 1.24658e6i | −0.468620 | + | 0.121247i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −909090. | − | 295381.i | −0.0877318 | − | 0.0285058i | ||||
\(641\) | −5.51918e6 | − | 7.59650e6i | −0.530554 | − | 0.730245i | 0.456661 | − | 0.889641i | \(-0.349045\pi\) |
−0.987215 | + | 0.159396i | \(0.949045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.28509e6 | + | 1.62658e7i | 0.504109 | + | 1.55149i | 0.802263 | + | 0.596971i | \(0.203629\pi\) |
−0.298153 | + | 0.954518i | \(0.596371\pi\) | |||||||
\(644\) | −482331. | − | 1.48446e6i | −0.0458279 | − | 0.141044i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −683528. | − | 940795.i | −0.0644429 | − | 0.0886980i | ||||
\(647\) | −1.67935e6 | − | 545655.i | −0.157718 | − | 0.0512457i | 0.229094 | − | 0.973404i | \(-0.426424\pi\) |
−0.386812 | + | 0.922159i | \(0.626424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.57852e6 | − | 4.82918e6i | 0.706273 | − | 0.450051i | ||||
\(650\) | 631928.i | 0.0586657i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.25395e6 | − | 5.27030e6i | 0.668275 | − | 0.485530i | ||||
\(653\) | 1.11034e7 | − | 1.52825e7i | 1.01899 | − | 1.40253i | 0.106089 | − | 0.994357i | \(-0.466167\pi\) |
0.912906 | − | 0.408169i | \(-0.133833\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.12546e7 | − | 3.65685e6i | 1.02501 | − | 0.333045i | ||||
\(656\) | −4.14276e6 | − | 3.00989e6i | −0.375864 | − | 0.273081i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.09592e6 | + | 1.26060e7i | −0.368797 | + | 1.13504i | ||||
\(659\) | 1.72599e7 | 1.54820 | 0.774098 | − | 0.633066i | \(-0.218204\pi\) | ||||
0.774098 | + | 0.633066i | \(0.218204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.66702e7 | 1.48402 | 0.742008 | − | 0.670391i | \(-0.233874\pi\) | ||||
0.742008 | + | 0.670391i | \(0.233874\pi\) | |||||||
\(662\) | 3.19127e6 | − | 9.82173e6i | 0.283021 | − | 0.871050i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 111161. | + | 80763.2i | 0.00978435 | + | 0.00710875i | ||||
\(665\) | −1.20390e7 | + | 3.91172e6i | −1.05569 | + | 0.343015i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 941125. | − | 1.29535e6i | 0.0819092 | − | 0.112738i | ||||
\(668\) | −1.75867e6 | + | 1.27775e6i | −0.152490 | + | 0.110791i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.40546e6i | 0.379144i | ||||||||
\(671\) | 1.93188e7 | + | 1.17953e6i | 1.65643 | + | 0.101135i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.47284e7 | − | 4.78555e6i | −1.25348 | − | 0.407281i | −0.394314 | − | 0.918976i | \(-0.629018\pi\) |
−0.859167 | + | 0.511695i | \(0.829018\pi\) | |||||||
\(674\) | −2.60289e6 | − | 3.58257e6i | −0.220702 | − | 0.303770i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 247991. | + | 763238.i | 0.0208723 | + | 0.0642382i | ||||
\(677\) | 2.92375e6 | + | 8.99838e6i | 0.245171 | + | 0.754558i | 0.995608 | + | 0.0936167i | \(0.0298428\pi\) |
−0.750438 | + | 0.660941i | \(0.770157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.19199e6 | + | 5.76979e6i | 0.348936 | + | 0.480270i | ||||
\(680\) | −898784. | − | 292033.i | −0.0745389 | − | 0.0242192i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.20923e6 | + | 1.89766e6i | 0.0995513 | + | 0.156228i | ||||
\(683\) | 1.91424e6i | 0.157016i | 0.996913 | + | 0.0785080i | \(0.0250156\pi\) | ||||
−0.996913 | + | 0.0785080i | \(0.974984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.17125e6 | − | 1.57750e6i | 0.176800 | − | 0.128453i | ||||
\(686\) | 917757. | − | 1.26318e6i | 0.0744590 | − | 0.102484i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.89192e6 | − | 614722.i | 0.152381 | − | 0.0495117i | ||||
\(689\) | 9.36306e6 | + | 6.80266e6i | 0.751398 | + | 0.545922i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.64900e6 | − | 8.15279e6i | 0.211051 | − | 0.649548i | −0.788359 | − | 0.615215i | \(-0.789069\pi\) |
0.999410 | − | 0.0343332i | \(-0.0109307\pi\) | |||||||
\(692\) | −1.05008e7 | −0.833596 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.25457e7 | 0.988774 | ||||||||
\(695\) | 6.81593e6 | − | 2.09773e7i | 0.535258 | − | 1.64735i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.09580e6 | − | 2.97577e6i | −0.319342 | − | 0.232016i | ||||
\(698\) | 1.41195e7 | − | 4.58769e6i | 1.09693 | − | 0.356415i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −495242. | + | 681642.i | −0.0382008 | + | 0.0525789i | ||||
\(701\) | 1.38189e7 | − | 1.00400e7i | 1.06213 | − | 0.771684i | 0.0876502 | − | 0.996151i | \(-0.472064\pi\) |
0.974482 | + | 0.224467i | \(0.0720642\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.79046e6i | − | 0.136639i | ||||||
\(704\) | −1.04543e6 | + | 1.26849e6i | −0.0794995 | + | 0.0964615i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.29033e6 | + | 2.69369e6i | 0.625979 | + | 0.203393i | ||||
\(707\) | 2.25820e7 | + | 3.10815e7i | 1.69908 | + | 2.33859i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.59771e6 | + | 1.41503e7i | 0.343499 | + | 1.05718i | 0.962382 | + | 0.271699i | \(0.0875855\pi\) |
−0.618883 | + | 0.785483i | \(0.712414\pi\) | |||||||
\(710\) | 1.18951e6 | + | 3.66092e6i | 0.0885566 | + | 0.272549i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.14541e6 | − | 1.57652e6i | −0.0846763 | − | 0.116547i | ||||
\(713\) | −688510. | − | 223711.i | −0.0507209 | − | 0.0164802i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.23453e7 | + | 4.86144e6i | 0.903104 | + | 0.355631i | ||||
\(716\) | − | 3.20083e6i | − | 0.233335i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.20664e7 | − | 8.76673e6i | 0.873505 | − | 0.634638i | ||||
\(719\) | −98679.2 | + | 135820.i | −0.00711874 | + | 0.00979811i | −0.812562 | − | 0.582875i | \(-0.801928\pi\) |
0.805443 | + | 0.592674i | \(0.201928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.76505e7 | − | 1.22334e7i | 2.69732 | − | 0.876412i | ||||
\(722\) | 3.74314e6 | + | 2.71955e6i | 0.267235 | + | 0.194157i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.15330e6 | + | 6.62719e6i | −0.152672 | + | 0.469875i | ||||
\(725\) | −864301. | −0.0610689 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.61449e7 | −1.13292 | −0.566460 | − | 0.824090i | \(-0.691687\pi\) | ||||
−0.566460 | + | 0.824090i | \(0.691687\pi\) | |||||||
\(728\) | 2.11701e6 | − | 6.51547e6i | 0.148045 | − | 0.455636i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.36739e7 | + | 9.93467e6i | 0.949697 | + | 0.689995i | ||||
\(731\) | 1.87047e6 | − | 607753.i | 0.129467 | − | 0.0420663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.19223e7 | + | 1.64096e7i | −0.819596 | + | 1.12808i | 0.170175 | + | 0.985414i | \(0.445567\pi\) |
−0.989771 | + | 0.142664i | \(0.954433\pi\) | |||||||
\(734\) | −1.49608e7 | + | 1.08696e7i | −1.02498 | + | 0.744689i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 528843.i | − | 0.0359859i | ||||||
\(737\) | 7.04902e6 | + | 2.77582e6i | 0.478035 | + | 0.188244i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.63455e6 | + | 2.48062e6i | 0.514248 | + | 0.167089i | 0.554633 | − | 0.832095i | \(-0.312859\pi\) |
−0.0403854 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(740\) | −855252. | − | 1.17715e6i | −0.0574136 | − | 0.0790230i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.76841e6 | + | 1.46757e7i | 0.317954 | + | 0.978561i | ||||
\(743\) | −7.78217e6 | − | 2.39511e7i | −0.517165 | − | 1.59167i | −0.779309 | − | 0.626640i | \(-0.784430\pi\) |
0.262144 | − | 0.965029i | \(-0.415570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.87025e6 | − | 3.95057e6i | −0.189465 | − | 0.260777i | ||||
\(746\) | −784203. | − | 254803.i | −0.0515919 | − | 0.0167632i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.03358e6 | + | 1.25411e6i | −0.0675446 | + | 0.0819559i | ||||
\(749\) | − | 3.39327e7i | − | 2.21011i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.45895e6 | + | 4.69270e6i | −0.417890 | + | 0.303615i | −0.776788 | − | 0.629762i | \(-0.783152\pi\) |
0.358898 | + | 0.933377i | \(0.383152\pi\) | |||||||
\(752\) | −2.63969e6 | + | 3.63322e6i | −0.170219 | + | 0.234286i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.68363e6 | − | 2.17164e6i | 0.428138 | − | 0.139110i | ||||
\(755\) | −2.41916e7 | − | 1.75763e7i | −1.54454 | − | 1.12217i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.17328e6 | + | 9.76634e6i | −0.201265 | + | 0.619430i | 0.798581 | + | 0.601887i | \(0.205584\pi\) |
−0.999846 | + | 0.0175429i | \(0.994416\pi\) | |||||||
\(758\) | −9.58390e6 | −0.605856 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.28894e6 | −0.269349 | ||||||||
\(761\) | −1.61270e6 | + | 4.96338e6i | −0.100947 | + | 0.310682i | −0.988758 | − | 0.149526i | \(-0.952225\pi\) |
0.887811 | + | 0.460208i | \(0.152225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.53863e6 | − | 4.02405e6i | −0.344422 | − | 0.250238i | ||||
\(764\) | −328036. | + | 106585.i | −0.0203324 | + | 0.00660639i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.28022e6 | − | 7.26761e6i | 0.325148 | − | 0.447527i | ||||
\(767\) | −1.02661e7 | + | 7.45875e6i | −0.630110 | + | 0.457802i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.93201e7i | − | 1.17813i | −0.808084 | − | 0.589067i | \(-0.799496\pi\) | ||
0.808084 | − | 0.589067i | \(-0.200504\pi\) | |||||||
\(770\) | 9.50664e6 | + | 1.49189e7i | 0.577830 | + | 0.906799i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.94783e6 | − | 632887.i | −0.117627 | − | 0.0382193i | ||||
\(773\) | 7.69397e6 | + | 1.05898e7i | 0.463129 | + | 0.637442i | 0.975154 | − | 0.221528i | \(-0.0711045\pi\) |
−0.512025 | + | 0.858971i | \(0.671104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 120760. | + | 371661.i | 0.00722219 | + | 0.0222276i | ||||
\(776\) | 746705. | + | 2.29812e6i | 0.0445138 | + | 0.136999i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.27980e6 | − | 1.27725e7i | −0.549654 | − | 0.756534i | ||||
\(779\) | −2.18519e7 | − | 7.10010e6i | −1.29016 | − | 0.419199i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.60720e6 | + | 403409.i | 0.387605 | + | 0.0236656i | ||||
\(782\) | − | 522848.i | − | 0.0305744i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.90886e6 | − | 2.83995e6i | 0.227122 | − | 0.165014i | ||||
\(785\) | 37142.7 | − | 51122.5i | 0.00215129 | − | 0.00296100i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.92301e6 | − | 1.27466e6i | 0.225778 | − | 0.0733598i | −0.193943 | − | 0.981013i | \(-0.562128\pi\) |
0.419721 | + | 0.907653i | \(0.362128\pi\) | |||||||
\(788\) | 3.66237e6 | + | 2.66087e6i | 0.210110 | + | 0.152654i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.29006e6 | + | 1.01258e7i | −0.187558 | + | 0.577244i | ||||
\(791\) | 1.33577e7 | 0.759086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.73307e7 | −1.54336 | ||||||||
\(794\) | 2661.41 | − | 8190.97i | 0.000149817 | − | 0.000461088i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.11875e6 | + | 2.26591e6i | 0.174461 | + | 0.126753i | ||||
\(797\) | 1.61686e6 | − | 525350.i | 0.0901628 | − | 0.0292957i | −0.263588 | − | 0.964635i | \(-0.584906\pi\) |
0.353751 | + | 0.935340i | \(0.384906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.60976e6 | + | 3.59203e6i | −0.144622 | + | 0.199055i | ||||
\(800\) | −230952. | + | 167796.i | −0.0127584 | + | 0.00926952i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.68115e6i | 0.531485i | ||||||||
\(803\) | 2.45118e7 | − | 1.56194e7i | 1.34149 | − | 0.854822i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.41290e6 | − | 1.75876e6i | −0.294401 | − | 0.0956568i | ||||
\(806\) | −1.86767e6 | − | 2.57063e6i | −0.101266 | − | 0.139380i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.02246e6 | + | 1.23798e7i | 0.216752 | + | 0.667094i | ||||
\(809\) | 4.00196e6 | + | 1.23168e7i | 0.214982 | + | 0.661646i | 0.999155 | + | 0.0411038i | \(0.0130874\pi\) |
−0.784173 | + | 0.620542i | \(0.786913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.11470e7 | − | 1.53425e7i | −0.595120 | − | 0.819113i | 0.400130 | − | 0.916458i | \(-0.368965\pi\) |
−0.995251 | + | 0.0973453i | \(0.968965\pi\) | |||||||
\(812\) | 8.91134e6 | + | 2.89547e6i | 0.474300 | + | 0.154109i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.42240e6 | + | 626750.i | −0.128140 | + | 0.0331538i | ||||
\(815\) | − | 3.26947e7i | − | 1.72418i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.22110e6 | − | 5.24644e6i | 0.378485 | − | 0.274985i | ||||
\(818\) | 3.75206e6 | − | 5.16427e6i | 0.196059 | − | 0.269852i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.77582e7 | + | 5.77000e6i | −0.922285 | + | 0.299669i | ||||
\(821\) | −1.54271e7 | − | 1.12084e7i | −0.798777 | − | 0.580345i | 0.111778 | − | 0.993733i | \(-0.464345\pi\) |
−0.910555 | + | 0.413388i | \(0.864345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.90658e6 | + | 1.20232e7i | −0.201047 | + | 0.618758i | 0.798806 | + | 0.601589i | \(0.205465\pi\) |
−0.999853 | + | 0.0171693i | \(0.994535\pi\) | |||||||
\(824\) | 1.34131e7 | 0.688194 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.69191e7 | −0.862836 | ||||||||
\(827\) | −1.50970e6 | + | 4.64637e6i | −0.0767584 | + | 0.236238i | −0.982072 | − | 0.188505i | \(-0.939636\pi\) |
0.905314 | + | 0.424743i | \(0.139636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.17488e6 | + | 3.03323e6i | 0.210988 | + | 0.153292i | 0.688261 | − | 0.725464i | \(-0.258375\pi\) |
−0.477273 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(830\) | 476499. | − | 154824.i | 0.0240086 | − | 0.00780086i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.36434e6 | − | 1.87785e6i | 0.0683305 | − | 0.0940489i | ||||
\(833\) | 3.86454e6 | − | 2.80776e6i | 0.192968 | − | 0.140200i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.92659e6i | 0.393432i | ||||||||
\(836\) | −2.70240e6 | + | 6.86257e6i | −0.133731 | + | 0.339603i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.68429e6 | + | 3.14662e6i | 0.476384 | + | 0.154787i | ||||
\(839\) | 6.23850e6 | + | 8.58656e6i | 0.305968 | + | 0.421128i | 0.934118 | − | 0.356963i | \(-0.116188\pi\) |
−0.628151 | + | 0.778092i | \(0.716188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.36810e6 | − | 1.03659e7i | −0.164208 | − | 0.505380i | ||||
\(842\) | 7.28504e6 | + | 2.24210e7i | 0.354121 | + | 1.08987i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.65901e6 | + | 1.32945e7i | 0.466742 | + | 0.642415i | ||||
\(845\) | 2.78305e6 | + | 904267.i | 0.134085 | + | 0.0435667i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.98612e7 | − | 5.81102e6i | 1.43021 | − | 0.278320i | ||||
\(848\) | 5.22824e6i | 0.249670i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −228333. | + | 165894.i | −0.0108398 | + | 0.00787559i | ||||
\(851\) | 473173. | − | 651267.i | 0.0223973 | − | 0.0308273i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.83550e7 | − | 5.96392e6i | 0.863740 | − | 0.280646i | 0.156550 | − | 0.987670i | \(-0.449963\pi\) |
0.707190 | + | 0.707024i | \(0.249963\pi\) | |||||||
\(854\) | −2.94808e7 | − | 2.14190e7i | −1.38323 | − | 1.00498i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.55275e6 | − | 1.09342e7i | 0.165722 | − | 0.510040i | ||||
\(857\) | 1.48801e7 | 0.692074 | 0.346037 | − | 0.938221i | \(-0.387527\pi\) | ||||
0.346037 | + | 0.938221i | \(0.387527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.59749e7 | −1.20108 | −0.600538 | − | 0.799596i | \(-0.705047\pi\) | ||||
−0.600538 | + | 0.799596i | \(0.705047\pi\) | |||||||
\(860\) | 2.24151e6 | − | 6.89865e6i | 0.103346 | − | 0.318066i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.52187e6 | + | 5.46496e6i | 0.344792 | + | 0.250506i | ||||
\(863\) | 1.80833e7 | − | 5.87561e6i | 0.826514 | − | 0.268551i | 0.134938 | − | 0.990854i | \(-0.456917\pi\) |
0.691576 | + | 0.722304i | \(0.256917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.25061e7 | + | 3.09770e7i | −1.02273 | + | 1.40766i | ||||
\(866\) | −6.84749e6 | + | 4.97499e6i | −0.310268 | + | 0.225423i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 4.23655e6i | − | 0.190859i | ||||||
\(869\) | 1.41288e7 | + | 1.16444e7i | 0.634683 | + | 0.523079i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.01742e7 | − | 3.30581e6i | −0.454419 | − | 0.147650i | ||||
\(872\) | −1.36342e6 | − | 1.87658e6i | −0.0607207 | − | 0.0835749i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −733261. | − | 2.25675e6i | −0.0324698 | − | 0.0999319i | ||||
\(875\) | −9.69275e6 | − | 2.98312e7i | −0.427983 | − | 1.31720i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.41157e7 | − | 3.31924e7i | −1.05877 | − | 1.45727i | −0.880952 | − | 0.473206i | \(-0.843097\pi\) |
−0.177816 | − | 0.984064i | \(-0.556903\pi\) | |||||||
\(878\) | −2.85463e7 | − | 9.27524e6i | −1.24972 | − | 0.406059i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50135e6 | + | 5.80273e6i | 0.0653543 | + | 0.252595i | ||||
\(881\) | 2.64642e7i | 1.14873i | 0.818599 | + | 0.574365i | \(0.194751\pi\) | ||||
−0.818599 | + | 0.574365i | \(0.805249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.21978e6 | − | 3.79239e6i | 0.225295 | − | 0.163686i | −0.469412 | − | 0.882979i | \(-0.655534\pi\) |
0.694707 | + | 0.719293i | \(0.255534\pi\) | |||||||
\(884\) | 1.34887e6 | − | 1.85657e6i | 0.0580551 | − | 0.0799060i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.59061e7 | − | 5.16820e6i | 0.680736 | − | 0.221185i | ||||
\(887\) | 4.70117e6 | + | 3.41560e6i | 0.200631 | + | 0.145767i | 0.683564 | − | 0.729890i | \(-0.260429\pi\) |
−0.482934 | + | 0.875657i | \(0.660429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.67848e7 | − | 5.16582e7i | 0.712296 | − | 2.19222i | ||||
\(890\) | −7.10565e6 | −0.300697 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −782009. | −0.0329079 | ||||||||
\(893\) | −6.22681e6 | + | 1.91642e7i | −0.261299 | + | 0.804194i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.44236e6 | − | 6.86028e6i | −0.394024 | − | 0.286275i | ||||
\(896\) | 2.94335e6 | − | 956352.i | 0.122482 | − | 0.0397968i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.77983e7 | + | 2.44973e7i | −0.736527 | + | 1.01374i | ||||
\(899\) | 3.51590e6 | − | 2.55445e6i | 0.145090 | − | 0.105414i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.16897e6i | 0.212125i | ||||||||
\(902\) | −1.95684e6 | + | 3.20499e7i | −0.0800826 | + | 1.31163i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.30430e6 | + | 1.39855e6i | 0.175179 | + | 0.0569191i | ||||
\(905\) | 1.49349e7 | + | 2.05561e7i | 0.606151 | + | 0.834295i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.17657e6 | − | 1.59318e7i | −0.208941 | − | 0.643055i | −0.999528 | − | 0.0307054i | \(-0.990225\pi\) |
0.790587 | − | 0.612349i | \(-0.209775\pi\) | |||||||
\(908\) | −1.12335e6 | − | 3.45732e6i | −0.0452169 | − | 0.139163i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.46831e7 | − | 2.02096e7i | −0.587781 | − | 0.809012i | ||||
\(911\) | −2.60012e7 | − | 8.44829e6i | −1.03800 | − | 0.337266i | −0.260050 | − | 0.965595i | \(-0.583739\pi\) |
−0.777948 | + | 0.628329i | \(0.783739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52506.9 | − | 859980.i | 0.00208468 | − | 0.0341438i | ||||
\(914\) | 1.03061e7i | 0.408063i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.21499e7 | − | 8.82742e6i | 0.478447 | − | 0.347612i | ||||
\(917\) | −2.25205e7 | + | 3.09968e7i | −0.884411 | + | 1.21729i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.22800e7 | + | 3.99001e6i | −0.479633 | + | 0.155842i | −0.538848 | − | 0.842403i | \(-0.681140\pi\) |
0.0592147 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(920\) | −1.56008e6 | − | 1.13346e6i | −0.0607681 | − | 0.0441506i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 83907.3 | − | 258240.i | 0.00325067 | − | 0.0100045i | ||||
\(923\) | −9.34734e6 | −0.361147 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −434548. | −0.0166987 | ||||||||
\(926\) | 1.03687e7 | − | 3.19117e7i | 0.397373 | − | 1.22299i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.56838e6 | + | 1.86604e6i | 0.0979015 | + | 0.0711296i | ||||
\(929\) | −3.63192e7 | + | 1.18008e7i | −1.38069 | + | 0.448614i | −0.902897 | − | 0.429856i | \(-0.858564\pi\) |
−0.477796 | + | 0.878471i | \(0.658564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.27427e7 | − | 1.75388e7i | 0.481821 | − | 0.663170i | ||||
\(932\) | −1.55249e7 | + | 1.12795e7i | −0.585450 | + | 0.425355i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2.28497e7i | − | 0.857063i | ||||||
\(935\) | 1.48432e6 | + | 5.73694e6i | 0.0555265 | + | 0.214611i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.81317e7 | − | 1.56389e7i | −1.79094 | − | 0.581913i | −0.791377 | − | 0.611328i | \(-0.790636\pi\) |
−0.999567 | + | 0.0294146i | \(0.990636\pi\) | |||||||
\(938\) | −8.38388e6 | − | 1.15394e7i | −0.311127 | − | 0.428230i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.06031e6 | + | 1.55740e7i | 0.186792 | + | 0.574886i | ||||
\(941\) | −1.03874e7 | − | 3.19691e7i | −0.382413 | − | 1.17695i | −0.938340 | − | 0.345715i | \(-0.887637\pi\) |
0.555927 | − | 0.831231i | \(-0.312363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.07209e6 | − | 8.35752e6i | −0.222361 | − | 0.306054i | ||||
\(944\) | −5.45192e6 | − | 1.77144e6i | −0.199122 | − | 0.0646987i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.62593e6 | − | 7.93328e6i | −0.349715 | − | 0.288221i | ||||
\(947\) | 3.65340e7i | 1.32380i | 0.749593 | + | 0.661899i | \(0.230249\pi\) | ||||
−0.749593 | + | 0.661899i | \(0.769751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.32044e7 | + | 2.41244e7i | −1.19682 | + | 0.869544i | ||||
\(950\) | −752890. | + | 1.03626e6i | −0.0270659 | + | 0.0372530i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.90998e6 | − | 945510.i | 0.104063 | − | 0.0338122i | ||||
\(953\) | 2.61597e7 | + | 1.90061e7i | 0.933041 | + | 0.677894i | 0.946736 | − | 0.322012i | \(-0.104359\pi\) |
−0.0136944 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −388650. | + | 1.19614e6i | −0.0137895 | + | 0.0424399i | ||||
\(956\) | 6.74779e6 | 0.238790 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.74475e7 | −0.614215 | ||||||||
\(959\) | −2.68515e6 | + | 8.26404e6i | −0.0942805 | + | 0.290166i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.15718e7 | + | 1.56728e7i | 0.753490 | + | 0.547443i | ||||
\(962\) | 3.36036e6 | − | 1.09185e6i | 0.117071 | − | 0.0380385i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.09578e6 | + | 7.01374e6i | −0.176611 | + | 0.243084i | ||||
\(965\) | −6.04175e6 | + | 4.38959e6i | −0.208855 | + | 0.151742i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.12957e7i | 0.388462i | 0.980956 | + | 0.194231i | \(0.0622212\pi\) | ||||
−0.980956 | + | 0.194231i | \(0.937779\pi\) | |||||||
\(968\) | 1.02307e7 | + | 1.25396e6i | 0.350927 | + | 0.0430127i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.37980e6 | + | 2.72276e6i | 0.285959 | + | 0.0929138i | ||||
\(971\) | 1.63135e7 | + | 2.24536e7i | 0.555264 | + | 0.764255i | 0.990715 | − | 0.135958i | \(-0.0434111\pi\) |
−0.435451 | + | 0.900212i | \(0.643411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.20678e7 | + | 6.79178e7i | 0.747270 | + | 2.29986i | ||||
\(974\) | 8.44935e6 | + | 2.60044e7i | 0.285381 | + | 0.878314i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.25713e6 | − | 9.98858e6i | −0.243860 | − | 0.335644i | ||||
\(977\) | −3.73267e7 | − | 1.21282e7i | −1.25107 | − | 0.406499i | −0.392769 | − | 0.919637i | \(-0.628483\pi\) |
−0.858306 | + | 0.513138i | \(0.828483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.47716e6 | + | 1.13695e7i | −0.149295 | + | 0.379126i | ||||
\(980\) | − | 1.76179e7i | − | 0.585987i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.48149e6 | + | 1.80291e6i | −0.0821171 | + | 0.0596616i | ||||
\(983\) | −2.41892e7 | + | 3.32936e7i | −0.798433 | + | 1.09895i | 0.194573 | + | 0.980888i | \(0.437668\pi\) |
−0.993006 | + | 0.118061i | \(0.962332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.56990e7 | − | 5.10091e6i | 0.515563 | − | 0.167516i | ||||
\(986\) | 2.53926e6 | + | 1.84488e6i | 0.0831793 | + | 0.0604333i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.21837e6 | − | 9.90512e6i | 0.104892 | − | 0.322825i | ||||
\(989\) | 4.01314e6 | 0.130465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.06389e7 | 0.344122 | 0.172061 | − | 0.985086i | \(-0.444957\pi\) | ||||
0.172061 | + | 0.985086i | \(0.444957\pi\) | |||||||
\(992\) | 443567. | − | 1.36516e6i | 0.0143113 | − | 0.0440458i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.00827e7 | − | 7.32551e6i | −0.323676 | − | 0.235164i | ||||
\(995\) | 1.33687e7 | − | 4.34377e6i | 0.428088 | − | 0.139094i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.86643e7 | + | 3.94530e7i | −0.913278 | + | 1.25702i | 0.0527575 | + | 0.998607i | \(0.483199\pi\) |
−0.966035 | + | 0.258411i | \(0.916801\pi\) | |||||||
\(998\) | 1.32559e7 | − | 9.63099e6i | 0.421292 | − | 0.306087i | ||||
\(999\) | 0 | 0 |
(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 | 198.6.l.b.35.3 | yes | 40 | |
3.2 | odd | 2 | 198.6.l.a.35.8 | yes | 40 | ||
11.6 | odd | 10 | 198.6.l.a.17.8 | ✓ | 40 | ||
33.17 | even | 10 | inner | 198.6.l.b.17.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
198.6.l.a.17.8 | ✓ | 40 | 11.6 | odd | 10 | ||
198.6.l.a.35.8 | yes | 40 | 3.2 | odd | 2 | ||
198.6.l.b.17.3 | yes | 40 | 33.17 | even | 10 | inner | |
198.6.l.b.35.3 | yes | 40 | 1.1 | even | 1 | trivial |