Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.3 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.3 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.88193 | + | 0.833354i | −0.960643 | + | 0.277785i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 7.26979i | − | 1.45396i | −0.686660 | − | 0.726979i | \(-0.740924\pi\) | ||
0.686660 | − | 0.726979i | \(-0.259076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.75776 | − | 6.50863i | 0.536823 | − | 0.929804i | −0.462250 | − | 0.886750i | \(-0.652958\pi\) |
0.999073 | − | 0.0430544i | \(-0.0137089\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.61104 | − | 4.80334i | 0.845671 | − | 0.533704i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.6898 | − | 8.48117i | −1.33544 | − | 0.771015i | −0.349310 | − | 0.937007i | \(-0.613584\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.1476 | − | 17.5762i | 0.780585 | − | 1.35201i | −0.151016 | − | 0.988531i | \(-0.548255\pi\) |
0.931601 | − | 0.363482i | \(-0.118412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.05831 | + | 20.9510i | 0.403887 | + | 1.39673i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.9313 | + | 7.46590i | 0.760666 | + | 0.439170i | 0.829535 | − | 0.558455i | \(-0.188606\pi\) |
−0.0688691 | + | 0.997626i | \(0.521939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.9208 | − | 6.31229i | −0.943200 | − | 0.332226i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.40560 | + | 21.8890i | −0.257410 | + | 1.04233i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.8029 | + | 16.6293i | 1.25230 | + | 0.723015i | 0.971565 | − | 0.236771i | \(-0.0760891\pi\) |
0.280733 | + | 0.959786i | \(0.409422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −27.8498 | −1.11399 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.9316 | + | 20.1856i | −0.664133 | + | 0.747614i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.3086i | 1.04512i | 0.852601 | + | 0.522562i | \(0.175024\pi\) | ||||
−0.852601 | + | 0.522562i | \(0.824976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.8575 | − | 41.3223i | −0.769596 | − | 1.33298i | −0.937782 | − | 0.347224i | \(-0.887124\pi\) |
0.168187 | − | 0.985755i | \(-0.446209\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.4028 | + | 12.2003i | 1.49706 | + | 0.369706i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −47.3163 | − | 27.3181i | −1.35190 | − | 0.780517i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.1099 | 0.678647 | 0.339324 | − | 0.940670i | \(-0.389802\pi\) | ||||
0.339324 | + | 0.940670i | \(0.389802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.5975 | + | 59.1098i | −0.374295 | + | 1.51564i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.04512i | − | 0.123052i | −0.998105 | − | 0.0615258i | \(-0.980403\pi\) | ||
0.998105 | − | 0.0615258i | \(-0.0195967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.8411 | − | 43.0261i | −0.577701 | − | 1.00061i | −0.995742 | − | 0.0921791i | \(-0.970617\pi\) |
0.418042 | − | 0.908428i | \(-0.362717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −34.9192 | − | 55.3306i | −0.775983 | − | 1.22957i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 62.4682i | 1.32911i | 0.747239 | + | 0.664555i | \(0.231379\pi\) | ||||
−0.747239 | + | 0.664555i | \(0.768621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.74149 | − | 6.48044i | −0.0763569 | − | 0.132254i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −43.4889 | − | 10.7398i | −0.852723 | − | 0.210585i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 47.5227 | − | 27.4372i | 0.896654 | − | 0.517684i | 0.0205412 | − | 0.999789i | \(-0.493461\pi\) |
0.876113 | + | 0.482105i | \(0.160128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −61.6563 | + | 106.792i | −1.12102 | + | 1.94167i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 56.9069 | + | 3.25720i | 0.998366 | + | 0.0571438i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 73.6284i | − | 1.24794i | −0.781449 | − | 0.623969i | \(-0.785519\pi\) | ||
0.781449 | − | 0.623969i | \(-0.214481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.3512 | −1.56314 | −0.781568 | − | 0.623821i | \(-0.785580\pi\) | ||||
−0.781568 | + | 0.623821i | \(0.785580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.66269 | − | 67.5872i | −0.0422650 | − | 1.07281i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −127.775 | − | 73.7709i | −1.96577 | − | 1.13494i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.588665 | − | 1.01960i | 0.00878605 | − | 0.0152179i | −0.861599 | − | 0.507590i | \(-0.830537\pi\) |
0.870385 | + | 0.492372i | \(0.163870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −96.8660 | − | 23.9216i | −1.40385 | − | 0.346690i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3658 | − | 7.13938i | −0.174166 | − | 0.100555i | 0.410383 | − | 0.911913i | \(-0.365395\pi\) |
−0.584549 | + | 0.811359i | \(0.698728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −59.5390 | + | 103.125i | −0.815603 | + | 1.41267i | 0.0932911 | + | 0.995639i | \(0.470261\pi\) |
−0.908894 | + | 0.417027i | \(0.863072\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 80.2611 | − | 23.2087i | 1.07015 | − | 0.309450i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −110.401 | + | 63.7403i | −1.43379 | + | 0.827796i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0750630 | + | 0.130013i | 0.000950165 | + | 0.00164573i | 0.866500 | − | 0.499177i | \(-0.166364\pi\) |
−0.865550 | + | 0.500823i | \(0.833031\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34.8559 | − | 73.1168i | 0.430319 | − | 0.902677i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −41.9662 | − | 24.2292i | −0.505617 | − | 0.291918i | 0.225413 | − | 0.974263i | \(-0.427627\pi\) |
−0.731030 | + | 0.682345i | \(0.760960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.2755 | − | 94.0079i | 0.638535 | − | 1.10598i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −25.2578 | − | 87.3472i | −0.290320 | − | 1.00399i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 67.4096 | − | 38.9190i | 0.757412 | − | 0.437292i | −0.0709540 | − | 0.997480i | \(-0.522604\pi\) |
0.828366 | + | 0.560188i | \(0.189271\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −76.2645 | − | 132.094i | −0.838071 | − | 1.45158i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 103.192 | + | 99.2064i | 1.10959 | + | 1.06674i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −45.8890 | + | 130.280i | −0.483042 | + | 1.37137i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47.2818 | − | 81.8945i | −0.487441 | − | 0.844273i | 0.512455 | − | 0.858714i | \(-0.328736\pi\) |
−0.999896 | + | 0.0144414i | \(0.995403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −152.543 | + | 6.00963i | −1.54083 | + | 0.0607034i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 84.7721i | 0.839328i | 0.907680 | + | 0.419664i | \(0.137852\pi\) | ||||
−0.907680 | + | 0.419664i | \(0.862148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.50170 | − | 6.06512i | −0.0339971 | − | 0.0588846i | 0.848526 | − | 0.529153i | \(-0.177490\pi\) |
−0.882523 | + | 0.470269i | \(0.844157\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 159.128 | + | 39.2976i | 1.51550 | + | 0.374262i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 97.9295i | 0.915229i | 0.889151 | + | 0.457614i | \(0.151296\pi\) | ||||
−0.889151 | + | 0.457614i | \(0.848704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75.3829 | − | 130.567i | 0.691587 | − | 1.19786i | −0.279731 | − | 0.960078i | \(-0.590245\pi\) |
0.971318 | − | 0.237785i | \(-0.0764213\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −72.3651 | + | 20.9255i | −0.651938 | + | 0.188518i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 39.6676 | − | 22.9021i | 0.351041 | − | 0.202674i | −0.314103 | − | 0.949389i | \(-0.601704\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 120.892 | − | 209.391i | 1.05123 | − | 1.82079i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.19045 | − | 182.515i | −0.0614568 | − | 1.55996i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 97.1855 | − | 56.1101i | 0.816685 | − | 0.471513i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 83.3603 | + | 144.384i | 0.688928 | + | 1.19326i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.20437 | + | 14.5397i | 0.0341819 | + | 0.118209i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.7173i | 0.165739i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0912 | − | 24.4067i | −0.110955 | − | 0.192179i | 0.805201 | − | 0.593002i | \(-0.202058\pi\) |
−0.916155 | + | 0.400823i | \(0.868724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 107.446 | + | 103.297i | 0.832918 | + | 0.800750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 252.087i | 1.92433i | 0.272466 | + | 0.962166i | \(0.412161\pi\) | ||||
−0.272466 | + | 0.962166i | \(0.587839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −108.426 | + | 92.9197i | −0.815236 | + | 0.698645i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 146.745 | + | 130.359i | 1.08700 | + | 0.965622i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 86.3432i | − | 0.630242i | −0.949051 | − | 0.315121i | \(-0.897955\pi\) | ||
0.949051 | − | 0.315121i | \(-0.102045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.7671 | + | 143.357i | −0.595447 | + | 1.03134i | 0.398037 | + | 0.917369i | \(0.369692\pi\) |
−0.993484 | + | 0.113974i | \(0.963642\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −52.0582 | − | 180.029i | −0.369207 | − | 1.27680i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −298.133 | + | 172.127i | −2.08484 | + | 1.20369i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 220.337 | 1.51957 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.1832 | + | 15.5582i | 0.110090 | + | 0.105838i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 196.064i | 1.31587i | 0.753076 | + | 0.657934i | \(0.228569\pi\) | ||||
−0.753076 | + | 0.657934i | \(0.771431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.412875 | − | 0.715121i | 0.00273427 | − | 0.00473590i | −0.864655 | − | 0.502366i | \(-0.832463\pi\) |
0.867389 | + | 0.497630i | \(0.165796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 134.282 | − | 5.29023i | 0.877660 | − | 0.0345767i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −300.405 | + | 173.439i | −1.93809 | + | 1.11896i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −128.511 | −0.818541 | −0.409271 | − | 0.912413i | \(-0.634217\pi\) | ||||
−0.409271 | + | 0.912413i | \(0.634217\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −114.092 | + | 118.675i | −0.717560 | + | 0.746386i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 216.468 | − | 124.978i | 1.34452 | − | 0.776261i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 236.259 | 1.44944 | 0.724722 | − | 0.689041i | \(-0.241968\pi\) | ||||
0.724722 | + | 0.689041i | \(0.241968\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 88.6936 | − | 359.148i | 0.537537 | − | 2.17665i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 144.149 | + | 83.2244i | 0.863167 | + | 0.498350i | 0.865072 | − | 0.501648i | \(-0.167273\pi\) |
−0.00190452 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −121.448 | − | 210.354i | −0.718626 | − | 1.24470i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −166.716 | + | 38.0366i | −0.974947 | + | 0.222436i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −58.6776 | + | 33.8776i | −0.339177 | + | 0.195824i | −0.659908 | − | 0.751346i | \(-0.729405\pi\) |
0.320731 | + | 0.947170i | \(0.396071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −104.653 | + | 181.264i | −0.598016 | + | 1.03579i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 61.3585 | + | 212.192i | 0.346658 | + | 1.19882i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 60.5311i | − | 0.338163i | −0.985602 | − | 0.169081i | \(-0.945920\pi\) | ||
0.985602 | − | 0.169081i | \(-0.0540801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 83.4816 | + | 144.594i | 0.461224 | + | 0.798864i | 0.999022 | − | 0.0442096i | \(-0.0140769\pi\) |
−0.537798 | + | 0.843074i | \(0.680744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 274.796 | − | 79.4614i | 1.50162 | − | 0.434215i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 182.544i | − | 0.986724i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −126.639 | − | 219.345i | −0.677214 | − | 1.17297i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 63.9978 | + | 192.563i | 0.338613 | + | 1.01885i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 133.030 | + | 76.8050i | 0.696493 | + | 0.402120i | 0.806040 | − | 0.591861i | \(-0.201607\pi\) |
−0.109547 | + | 0.993982i | \(0.534940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 238.302 | 1.23473 | 0.617364 | − | 0.786678i | \(-0.288201\pi\) | ||||
0.617364 | + | 0.786678i | \(0.288201\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 429.716 | + | 106.121i | 2.20367 | + | 0.544209i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 109.602i | − | 0.556357i | −0.960529 | − | 0.278178i | \(-0.910269\pi\) | ||
0.960529 | − | 0.278178i | \(-0.0897306\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −126.692 | − | 219.437i | −0.636643 | − | 1.10270i | −0.986165 | − | 0.165770i | \(-0.946989\pi\) |
0.349522 | − | 0.936928i | \(-0.386344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.846806 | + | 3.42898i | −0.00421296 | + | 0.0170596i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 197.267 | + | 113.892i | 0.971760 | + | 0.561046i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −36.6769 | −0.178912 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 299.096 | − | 11.7833i | 1.44491 | − | 0.0569242i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 209.718 | + | 244.716i | 1.00343 | + | 1.17089i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 394.462 | 1.86949 | 0.934745 | − | 0.355320i | \(-0.115628\pi\) | ||||
0.934745 | + | 0.355320i | \(0.115628\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.5869 | + | 10.2701i | 0.195244 | + | 0.0482165i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −312.791 | + | 180.590i | −1.45484 | + | 0.839952i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −358.602 | −1.65255 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 85.6479 | − | 346.815i | 0.391086 | − | 1.58363i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 262.444 | − | 151.522i | 1.18753 | − | 0.685620i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 97.6081 | + | 169.062i | 0.437705 | + | 0.758127i | 0.997512 | − | 0.0704962i | \(-0.0224583\pi\) |
−0.559807 | + | 0.828623i | \(0.689125\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −211.966 | + | 133.772i | −0.942070 | + | 0.594542i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −253.263 | − | 146.222i | −1.11570 | − | 0.644148i | −0.175398 | − | 0.984498i | \(-0.556121\pi\) |
−0.940299 | + | 0.340349i | \(0.889455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −70.4763 | − | 122.069i | −0.307757 | − | 0.533050i | 0.670114 | − | 0.742258i | \(-0.266245\pi\) |
−0.977871 | + | 0.209207i | \(0.932912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 265.051 | − | 275.699i | 1.14741 | − | 1.19350i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −198.955 | − | 114.867i | −0.853885 | − | 0.492991i | 0.00807462 | − | 0.999967i | \(-0.497430\pi\) |
−0.861960 | + | 0.506977i | \(0.830763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 454.130 | 1.93247 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.324673 | − | 0.312134i | −0.00136993 | − | 0.00131702i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −203.641 | + | 117.572i | −0.852053 | + | 0.491933i | −0.861343 | − | 0.508024i | \(-0.830376\pi\) |
0.00929033 | + | 0.999957i | \(0.497043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 69.1883 | 0.287089 | 0.143544 | − | 0.989644i | \(-0.454150\pi\) | ||||
0.143544 | + | 0.989644i | \(0.454150\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −39.5200 | + | 239.765i | −0.162634 | + | 0.986687i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −47.1114 | + | 27.1998i | −0.192292 | + | 0.111020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −292.799 | + | 250.924i | −1.18542 | + | 1.01589i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 141.135 | + | 34.8542i | 0.566808 | + | 0.139977i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6371 | + | 10.7602i | −0.0742515 | + | 0.0428692i | −0.536666 | − | 0.843795i | \(-0.680317\pi\) |
0.462415 | + | 0.886664i | \(0.346983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −282.072 | − | 488.564i | −1.11491 | − | 1.93108i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −78.0762 | + | 316.155i | −0.306181 | + | 1.23982i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −252.333 | − | 145.684i | −0.981839 | − | 0.566865i | −0.0790144 | − | 0.996873i | \(-0.525177\pi\) |
−0.902825 | + | 0.430008i | \(0.858511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 94.3571 | − | 163.431i | 0.364313 | − | 0.631009i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 145.582 | + | 230.680i | 0.557787 | + | 0.883831i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −140.817 | + | 81.3007i | −0.535426 | + | 0.309128i | −0.743223 | − | 0.669044i | \(-0.766704\pi\) |
0.207797 | + | 0.978172i | \(0.433371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −199.463 | − | 345.480i | −0.752690 | − | 1.30370i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −161.837 | + | 168.338i | −0.606129 | + | 0.630479i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.2134 | + | 16.8664i | 0.108600 | + | 0.0627003i | 0.553316 | − | 0.832971i | \(-0.313362\pi\) |
−0.444716 | + | 0.895672i | \(0.646695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −88.5330 | + | 153.344i | −0.326690 | + | 0.565844i | −0.981853 | − | 0.189644i | \(-0.939267\pi\) |
0.655163 | + | 0.755488i | \(0.272600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 329.870 | + | 317.130i | 1.20831 | + | 1.16165i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 409.108 | + | 236.199i | 1.48767 | + | 0.858904i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 88.8575 | − | 153.906i | 0.320785 | − | 0.555616i | −0.659865 | − | 0.751384i | \(-0.729387\pi\) |
0.980650 | + | 0.195768i | \(0.0627199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −380.065 | − | 199.911i | −1.36224 | − | 0.716525i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 336.283i | − | 1.19674i | −0.801221 | − | 0.598369i | \(-0.795816\pi\) | ||
0.801221 | − | 0.598369i | \(-0.204184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.1149 | 0.109947 | 0.0549733 | − | 0.998488i | \(-0.482493\pi\) | ||||
0.0549733 | + | 0.998488i | \(0.482493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.6791 | − | 413.701i | 0.0830846 | − | 1.45158i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32.8368 | − | 18.9583i | −0.114414 | − | 0.0660569i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.0207 | − | 57.1936i | −0.114259 | − | 0.197902i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 204.510 | + | 196.612i | 0.702783 | + | 0.675641i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 180.338 | − | 104.118i | 0.615487 | − | 0.355351i | −0.159623 | − | 0.987178i | \(-0.551028\pi\) |
0.775110 | + | 0.631827i | \(0.217695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −535.263 | −1.81445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 434.609 | − | 144.441i | 1.46333 | − | 0.486335i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 584.560 | − | 337.496i | 1.95505 | − | 1.12875i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −373.388 | −1.24049 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −70.6452 | − | 244.307i | −0.233153 | − | 0.806295i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 693.183i | 2.27273i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 251.455 | − | 435.532i | 0.819071 | − | 1.41867i | −0.0872974 | − | 0.996182i | \(-0.527823\pi\) |
0.906368 | − | 0.422489i | \(-0.138844\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.1460 | + | 14.5611i | 0.0490163 | + | 0.0471233i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 241.751 | − | 139.575i | 0.777334 | − | 0.448794i | −0.0581507 | − | 0.998308i | \(-0.518520\pi\) |
0.835485 | + | 0.549514i | \(0.185187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −113.259 | −0.361850 | −0.180925 | − | 0.983497i | \(-0.557909\pi\) | ||||
−0.180925 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −491.345 | + | 19.3572i | −1.55982 | + | 0.0614515i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 109.393i | − | 0.345089i | −0.985002 | − | 0.172544i | \(-0.944801\pi\) | ||
0.985002 | − | 0.172544i | \(-0.0551988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 257.052 | − | 445.227i | 0.805806 | − | 1.39570i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −81.6100 | − | 282.226i | −0.254237 | − | 0.879209i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −184.613 | − | 215.421i | −0.571556 | − | 0.666938i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −282.609 | + | 489.492i | −0.869565 | + | 1.50613i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −108.440 | + | 439.106i | −0.331620 | + | 1.34283i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 406.582 | + | 234.740i | 1.23581 | + | 0.713497i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −50.5317 | + | 87.5235i | −0.152664 | + | 0.264422i | −0.932206 | − | 0.361928i | \(-0.882119\pi\) |
0.779542 | + | 0.626350i | \(0.215452\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 191.113 | − | 120.612i | 0.573912 | − | 0.362197i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.41226 | − | 4.27947i | −0.0221262 | − | 0.0127745i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −560.509 | −1.66323 | −0.831616 | − | 0.555351i | \(-0.812584\pi\) | ||||
−0.831616 | + | 0.555351i | \(0.812584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −95.2337 | + | 99.0595i | −0.280925 | + | 0.292211i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 809.357i | 2.37348i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 312.022 | 0.909685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −173.905 | + | 704.195i | −0.504072 | + | 2.04114i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 106.009i | 0.305501i | 0.988265 | + | 0.152751i | \(0.0488132\pi\) | ||||
−0.988265 | + | 0.152751i | \(0.951187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 120.332 | − | 208.421i | 0.344791 | − | 0.597196i | −0.640525 | − | 0.767938i | \(-0.721283\pi\) |
0.985316 | + | 0.170742i | \(0.0546164\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 172.822 | + | 520.004i | 0.492371 | + | 1.48149i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −438.326 | − | 253.068i | −1.24172 | − | 0.716906i | −0.272274 | − | 0.962220i | \(-0.587776\pi\) |
−0.969444 | + | 0.245314i | \(0.921109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −51.9018 | + | 89.8965i | −0.146202 | + | 0.253229i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −233.322 | + | 242.695i | −0.653564 | + | 0.679819i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −481.722 | − | 278.122i | −1.34184 | − | 0.774714i | −0.354766 | − | 0.934955i | \(-0.615439\pi\) |
−0.987078 | + | 0.160242i | \(0.948773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 281.310 | + | 226.243i | 0.779252 | + | 0.626711i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −360.562 | − | 346.637i | −0.993284 | − | 0.954922i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 749.694 | + | 432.836i | 2.05396 | + | 1.18585i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 608.527 | 1.65811 | 0.829056 | − | 0.559165i | \(-0.188878\pi\) | ||||
0.829056 | + | 0.559165i | \(0.188878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.2334 | − | 38.3986i | −0.0656732 | − | 0.104061i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 412.410i | − | 1.11162i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 61.6756 | + | 106.825i | 0.165350 | + | 0.286395i | 0.936780 | − | 0.349920i | \(-0.113791\pi\) |
−0.771429 | + | 0.636315i | \(0.780458\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.2649 | − | 59.7059i | −0.0460397 | − | 0.159216i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 532.709 | + | 307.560i | 1.41302 | + | 0.815808i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −358.690 | −0.946412 | −0.473206 | − | 0.880952i | \(-0.656903\pi\) | ||||
−0.473206 | + | 0.880952i | \(0.656903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 60.9495 | + | 58.5955i | 0.159972 | + | 0.153794i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 366.840i | − | 0.957806i | −0.877868 | − | 0.478903i | \(-0.841035\pi\) | ||
0.877868 | − | 0.478903i | \(-0.158965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 463.379 | + | 802.595i | 1.20358 | + | 2.08466i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −395.736 | − | 208.153i | −1.02257 | − | 0.537863i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 190.120i | 0.488740i | 0.969682 | + | 0.244370i | \(0.0785812\pi\) | ||||
−0.969682 | + | 0.244370i | \(0.921419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 248.306 | + | 430.078i | 0.635054 | + | 1.09995i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −210.078 | − | 726.498i | −0.534550 | − | 1.84860i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.945166 | − | 0.545692i | 0.00239283 | − | 0.00138150i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 115.434 | − | 199.937i | 0.290765 | − | 0.503619i | −0.683226 | − | 0.730207i | \(-0.739424\pi\) |
0.973991 | + | 0.226588i | \(0.0727570\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 235.042 | − | 358.146i | 0.589078 | − | 0.897608i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 439.408i | 1.09578i | 0.836551 | + | 0.547890i | \(0.184569\pi\) | ||||
−0.836551 | + | 0.547890i | \(0.815431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −968.385 | −2.40294 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −531.544 | − | 253.395i | −1.31245 | − | 0.625666i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −368.860 | − | 212.962i | −0.906291 | − | 0.523247i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 131.307 | − | 227.431i | 0.321045 | − | 0.556065i | −0.659659 | − | 0.751565i | \(-0.729299\pi\) |
0.980704 | + | 0.195499i | \(0.0626328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 71.9545 | + | 248.835i | 0.175072 | + | 0.605438i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −479.220 | − | 276.678i | −1.16034 | − | 0.669922i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −176.141 | + | 305.086i | −0.424437 | + | 0.735146i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 119.062 | − | 482.119i | 0.285520 | − | 1.15616i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 490.534 | − | 283.210i | 1.17072 | − | 0.675918i | 0.216874 | − | 0.976200i | \(-0.430414\pi\) |
0.953851 | + | 0.300281i | \(0.0970806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 239.616 | + | 415.027i | 0.569158 | + | 0.985811i | 0.996649 | + | 0.0817918i | \(0.0260642\pi\) |
−0.427491 | + | 0.904020i | \(0.640602\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 300.056 | + | 475.448i | 0.709352 | + | 1.12399i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −360.134 | − | 207.924i | −0.847375 | − | 0.489232i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −358.307 | + | 620.606i | −0.839126 | + | 1.45341i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 715.755 | − | 744.508i | 1.66843 | − | 1.73545i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 480.030 | − | 277.145i | 1.11376 | − | 0.643029i | 0.173958 | − | 0.984753i | \(-0.444344\pi\) |
0.939800 | + | 0.341724i | \(0.111011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −116.826 | − | 202.348i | −0.269805 | − | 0.467316i | 0.699006 | − | 0.715116i | \(-0.253626\pi\) |
−0.968811 | + | 0.247799i | \(0.920293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −634.996 | + | 183.619i | −1.45976 | + | 0.422112i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −411.201 | − | 479.823i | −0.940964 | − | 1.09799i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −100.290 | − | 173.707i | −0.228451 | − | 0.395688i | 0.728898 | − | 0.684622i | \(-0.240033\pi\) |
−0.957349 | + | 0.288934i | \(0.906699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −59.6044 | − | 31.3513i | −0.135157 | − | 0.0710914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 296.907i | − | 0.670219i | −0.942179 | − | 0.335110i | \(-0.891227\pi\) | ||
0.942179 | − | 0.335110i | \(-0.108773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −282.933 | − | 490.054i | −0.635804 | − | 1.10124i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −163.391 | − | 565.043i | −0.365528 | − | 1.26408i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 392.134i | 0.873349i | 0.899620 | + | 0.436675i | \(0.143844\pi\) | ||||
−0.899620 | + | 0.436675i | \(0.856156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.7885 | + | 74.1118i | −0.0948747 | + | 0.164328i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.593928 | + | 2.40500i | −0.00131110 | + | 0.00530905i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −960.295 | + | 554.426i | −2.11054 | + | 1.21852i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 101.699 | − | 176.148i | 0.222537 | − | 0.385445i | −0.733041 | − | 0.680184i | \(-0.761900\pi\) |
0.955578 | + | 0.294740i | \(0.0952330\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −382.583 | + | 127.151i | −0.833513 | + | 0.277017i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −121.048 | + | 69.8873i | −0.262578 | + | 0.151599i | −0.625510 | − | 0.780216i | \(-0.715109\pi\) |
0.362932 | + | 0.931816i | \(0.381776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 94.0240 | + | 162.854i | 0.203076 | + | 0.351737i | 0.949518 | − | 0.313713i | \(-0.101573\pi\) |
−0.746442 | + | 0.665450i | \(0.768240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 721.209 | − | 750.182i | 1.55099 | − | 1.61329i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 370.749i | − | 0.793896i | −0.917841 | − | 0.396948i | \(-0.870069\pi\) | ||
0.917841 | − | 0.396948i | \(-0.129931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.42412 | − | 7.66281i | −0.00943310 | − | 0.0163386i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 370.360 | − | 107.095i | 0.786326 | − | 0.227378i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 842.727i | 1.78166i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 499.090 | + | 175.796i | 1.05072 | + | 0.370097i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 229.907 | − | 437.093i | 0.481985 | − | 0.916338i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 330.120i | − | 0.689185i | −0.938752 | − | 0.344592i | \(-0.888017\pi\) | ||
0.938752 | − | 0.344592i | \(-0.111983\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 254.806 | − | 441.337i | 0.529742 | − | 0.917540i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −519.696 | + | 540.573i | −1.07597 | + | 1.11920i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −595.355 | + | 343.729i | −1.22754 | + | 0.708719i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 709.032 | 1.45592 | 0.727959 | − | 0.685621i | \(-0.240469\pi\) | ||||
0.727959 | + | 0.685621i | \(0.240469\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −680.883 | + | 196.888i | −1.39240 | + | 0.402634i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 363.330i | − | 0.739980i | −0.929036 | − | 0.369990i | \(-0.879361\pi\) | ||
0.929036 | − | 0.369990i | \(-0.120639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −226.281 | + | 391.930i | −0.458988 | + | 0.794990i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43.6887 | + | 1108.95i | 0.0882601 | + | 2.24031i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −92.9351 | + | 53.6561i | −0.186992 | + | 0.107960i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −743.071 | −1.48912 | −0.744560 | − | 0.667556i | \(-0.767341\pi\) | ||||
−0.744560 | + | 0.667556i | \(0.767341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −484.782 | − | 119.720i | −0.967630 | − | 0.238962i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −319.580 | + | 184.509i | −0.635348 | + | 0.366818i | −0.782820 | − | 0.622248i | \(-0.786220\pi\) |
0.147473 | + | 0.989066i | \(0.452886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 616.275 | 1.22035 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 525.303 | + | 505.016i | 1.03610 | + | 0.996086i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −106.451 | − | 61.4595i | −0.209137 | − | 0.120746i | 0.391773 | − | 0.920062i | \(-0.371862\pi\) |
−0.600910 | + | 0.799316i | \(0.705195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 447.466 | + | 775.035i | 0.875668 | + | 1.51670i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 448.766 | − | 248.552i | 0.874787 | − | 0.484507i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −44.0921 | + | 25.4566i | −0.0856157 | + | 0.0494303i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 529.803 | − | 917.646i | 1.02476 | − | 1.77494i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 140.873 | − | 146.532i | 0.271431 | − | 0.282335i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 883.174i | − | 1.69515i | −0.530674 | − | 0.847576i | \(-0.678061\pi\) | ||
0.530674 | − | 0.847576i | \(-0.321939\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 82.8317 | + | 143.469i | 0.158378 | + | 0.274319i | 0.934284 | − | 0.356530i | \(-0.116040\pi\) |
−0.775906 | + | 0.630849i | \(0.782707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 150.545 | − | 609.603i | 0.286752 | − | 1.16115i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 712.470i | − | 1.35193i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 288.570 | + | 499.818i | 0.545501 | + | 0.944835i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −353.662 | − | 560.389i | −0.666030 | − | 1.05535i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −88.6738 | − | 51.1959i | −0.166367 | − | 0.0960523i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 711.926 | 1.33070 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.4439 | + | 174.446i | 0.0939364 | + | 0.324854i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 126.929i | 0.235489i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −239.705 | − | 415.182i | −0.443079 | − | 0.767435i | 0.554838 | − | 0.831959i | \(-0.312780\pi\) |
−0.997916 | + | 0.0645241i | \(0.979447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −361.087 | − | 347.141i | −0.664985 | − | 0.639302i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −949.195 | − | 548.018i | −1.74164 | − | 1.00554i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 323.732 | 0.591831 | 0.295916 | − | 0.955214i | \(-0.404375\pi\) | ||||
0.295916 | + | 0.955214i | \(0.404375\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −725.722 | + | 458.004i | −1.32190 | + | 0.834252i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 191.317 | − | 543.154i | 0.347217 | − | 0.985761i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.12827 | 0.00204028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 152.124 | + | 526.079i | 0.274097 | + | 0.947890i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −139.331 | + | 80.4425i | −0.250145 | + | 0.144421i | −0.619830 | − | 0.784736i | \(-0.712799\pi\) |
0.369686 | + | 0.929157i | \(0.379465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1008.31 | −1.80378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 547.757 | + | 526.602i | 0.976394 | + | 0.938685i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −351.195 | + | 202.763i | −0.623793 | + | 0.360147i | −0.778344 | − | 0.627838i | \(-0.783940\pi\) |
0.154551 | + | 0.987985i | \(0.450607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −166.493 | − | 288.375i | −0.294679 | − | 0.510398i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −344.910 | − | 501.619i | −0.608307 | − | 0.884690i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 937.203 | + | 541.095i | 1.64711 | + | 0.950957i | 0.978214 | + | 0.207597i | \(0.0665644\pi\) |
0.668892 | + | 0.743360i | \(0.266769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −275.915 | − | 477.899i | −0.483214 | − | 0.836951i | 0.516600 | − | 0.856227i | \(-0.327197\pi\) |
−0.999814 | + | 0.0192758i | \(0.993864\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −447.389 | − | 110.485i | −0.780784 | − | 0.192819i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −802.154 | − | 463.124i | −1.39505 | − | 0.805432i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.66081 | −0.0132770 | −0.00663848 | − | 0.999978i | \(-0.502113\pi\) | ||||
−0.00663848 | + | 0.999978i | \(0.502113\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −686.771 | + | 198.590i | −1.18613 | + | 0.342988i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −315.398 | + | 182.095i | −0.542854 | + | 0.313417i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −930.799 | −1.59657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1326.85 | + | 52.2730i | −2.26811 | + | 0.0893556i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −686.241 | + | 396.201i | −1.16906 | + | 0.674960i | −0.953459 | − | 0.301521i | \(-0.902506\pi\) |
−0.215605 | + | 0.976481i | \(0.569172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 166.706 | + | 891.125i | 0.283033 | + | 1.51295i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 91.3376 | + | 315.866i | 0.154547 | + | 0.534460i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −541.981 | + | 312.913i | −0.913965 | + | 0.527678i | −0.881705 | − | 0.471802i | \(-0.843604\pi\) |
−0.0322602 | + | 0.999480i | \(0.510271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −407.908 | − | 706.518i | −0.685560 | − | 1.18742i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 547.986 | + | 526.822i | 0.917899 | + | 0.882450i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −150.471 | − | 86.8742i | −0.251203 | − | 0.145032i | 0.369112 | − | 0.929385i | \(-0.379662\pi\) |
−0.620315 | + | 0.784353i | \(0.712995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −138.816 | + | 240.436i | −0.230975 | + | 0.400060i | −0.958095 | − | 0.286450i | \(-0.907525\pi\) |
0.727120 | + | 0.686510i | \(0.240858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.417120 | − | 10.5878i | −0.000691741 | − | 0.0175585i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1049.64 | − | 606.012i | 1.73495 | − | 1.00167i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 236.591 | + | 409.787i | 0.389770 | + | 0.675102i | 0.992418 | − | 0.122905i | \(-0.0392211\pi\) |
−0.602648 | + | 0.798007i | \(0.705888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −663.423 | − | 163.836i | −1.08937 | − | 0.269025i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1097.95 | + | 633.903i | 1.79697 | + | 1.03748i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 412.386 | − | 714.274i | 0.672735 | − | 1.16521i | −0.304391 | − | 0.952547i | \(-0.598453\pi\) |
0.977126 | − | 0.212663i | \(-0.0682137\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 105.700 | − | 30.5649i | 0.171870 | − | 0.0496990i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 449.661 | + | 259.612i | 0.728786 | + | 0.420765i | 0.817978 | − | 0.575250i | \(-0.195095\pi\) |
−0.0891918 | + | 0.996014i | \(0.528428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 515.153 | − | 892.272i | 0.832235 | − | 1.44147i | −0.0640275 | − | 0.997948i | \(-0.520395\pi\) |
0.896262 | − | 0.443525i | \(-0.146272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −852.154 | + | 283.212i | −1.37223 | + | 0.456058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 584.992i | − | 0.938992i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −545.634 | −0.873015 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −808.326 | − | 530.484i | −1.28920 | − | 0.846067i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 324.705 | + | 187.468i | 0.516224 | + | 0.298042i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 282.848 | + | 489.908i | 0.448254 | + | 0.776399i | 0.998273 | − | 0.0587536i | \(-0.0187126\pi\) |
−0.550018 | + | 0.835153i | \(0.685379\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1136.81 | + | 328.727i | −1.79591 | + | 0.519316i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −177.432 | + | 102.440i | −0.279420 | + | 0.161323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −151.868 | −0.238412 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −128.409 | + | 5.05886i | −0.200953 | + | 0.00791684i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 427.649 | − | 246.903i | 0.667159 | − | 0.385184i | −0.127840 | − | 0.991795i | \(-0.540805\pi\) |
0.794999 | + | 0.606610i | \(0.207471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 921.506 | 1.43314 | 0.716568 | − | 0.697518i | \(-0.245712\pi\) | ||||
0.716568 | + | 0.697518i | \(0.245712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 750.945 | − | 781.112i | 1.16426 | − | 1.21103i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 838.370i | − | 1.29578i | −0.761734 | − | 0.647890i | \(-0.775652\pi\) | ||
0.761734 | − | 0.647890i | \(-0.224348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −624.454 | + | 1081.59i | −0.962179 | + | 1.66654i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1033.47 | − | 298.843i | 1.58751 | − | 0.459052i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 671.238 | − | 387.539i | 1.02793 | − | 0.593475i | 0.111539 | − | 0.993760i | \(-0.464422\pi\) |
0.916391 | + | 0.400285i | \(0.131089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1832.62 | 2.79789 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.1885 | + | 1070.87i | 0.0642139 | + | 1.62994i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 82.4435i | − | 0.125104i | −0.998042 | − | 0.0625520i | \(-0.980076\pi\) | ||
0.998042 | − | 0.0625520i | \(-0.0199239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −434.594 | + | 752.739i | −0.657479 | + | 1.13879i | 0.323787 | + | 0.946130i | \(0.395044\pi\) |
−0.981266 | + | 0.192657i | \(0.938289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −630.073 | + | 655.384i | −0.950336 | + | 0.988513i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 675.507 | + | 788.236i | 1.01580 | + | 1.18532i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −504.012 | + | 872.974i | −0.755640 | + | 1.30881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −422.189 | − | 405.883i | −0.631074 | − | 0.606702i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1400.69 | + | 808.690i | 2.08747 | + | 1.20520i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −379.173 | + | 656.747i | −0.563407 | + | 0.975850i | 0.433789 | + | 0.901015i | \(0.357176\pi\) |
−0.997196 | + | 0.0748351i | \(0.976157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 499.391 | − | 562.164i | 0.739839 | − | 0.832836i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 910.405 | + | 525.622i | 1.34476 | + | 0.776400i | 0.987502 | − | 0.157605i | \(-0.0503773\pi\) |
0.357261 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −710.694 | −1.04668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 851.742 | + | 210.342i | 1.25072 | + | 0.308873i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 834.766i | − | 1.22221i | −0.791551 | − | 0.611103i | \(-0.790726\pi\) | ||
0.791551 | − | 0.611103i | \(-0.209274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −627.697 | −0.916345 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 304.834 | + | 293.061i | 0.443718 | + | 0.426581i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1113.69i | − | 1.61638i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2273 | − | 71.4077i | 0.0596632 | − | 0.103340i | −0.834651 | − | 0.550779i | \(-0.814331\pi\) |
0.894314 | + | 0.447439i | \(0.147664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −534.104 | + | 1015.43i | −0.770713 | + | 1.46526i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1042.17 | + | 601.699i | 1.49953 | + | 0.865754i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.6663 | − | 65.2400i | 0.0540407 | − | 0.0936012i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 669.100 | + | 165.238i | 0.957225 | + | 0.236392i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.1386 | − | 25.4834i | −0.0629652 | − | 0.0363530i | 0.468187 | − | 0.883629i | \(-0.344907\pi\) |
−0.531152 | + | 0.847276i | \(0.678241\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −449.990 | − | 158.501i | −0.640100 | − | 0.225464i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1308.77 | + | 378.452i | −1.85641 | + | 0.536811i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 551.750 | + | 318.553i | 0.780410 | + | 0.450570i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −210.795 | −0.297313 | −0.148657 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148657 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.19580 | + | 0.628981i | 0.00168186 | + | 0.000884642i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1586.94i | − | 2.22572i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1251.33 | + | 2167.36i | 1.75011 | + | 3.03127i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 488.899 | − | 508.539i | 0.681867 | − | 0.709259i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 399.243 | + | 230.503i | 0.555276 | + | 0.320589i | 0.751247 | − | 0.660021i | \(-0.229453\pi\) |
−0.195971 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.6341 | −0.0730015 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −199.396 | + | 57.6584i | −0.275790 | + | 0.0797488i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 844.088i | − | 1.16426i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −267.029 | − | 462.507i | −0.367302 | − | 0.636186i | 0.621841 | − | 0.783144i | \(-0.286385\pi\) |
−0.989143 | + | 0.146958i | \(0.953052\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −85.9153 | − | 723.920i | −0.117854 | − | 0.993031i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 741.845i | − | 1.01484i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 262.174 | + | 454.098i | 0.357672 | + | 0.619506i | 0.987571 | − | 0.157171i | \(-0.0502372\pi\) |
−0.629899 | + | 0.776677i | \(0.716904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 113.105 | − | 117.648i | 0.153884 | − | 0.160066i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.2948 | + | 9.98514i | −0.0234664 | + | 0.0135484i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8402 | + | 29.1681i | −0.0227878 | + | 0.0394696i | −0.877194 | − | 0.480135i | \(-0.840588\pi\) |
0.854407 | + | 0.519605i | \(0.173921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 634.717 | − | 967.152i | 0.856569 | − | 1.30520i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7053i | 0.0171000i | 0.999963 | + | 0.00855001i | \(0.00272159\pi\) | ||||
−0.999963 | + | 0.00855001i | \(0.997278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1425.35 | 1.91321 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −435.788 | + | 17.1685i | −0.583384 | + | 0.0229832i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 637.387 | + | 367.995i | 0.850983 | + | 0.491316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 734.945 | − | 1272.96i | 0.978622 | − | 1.69502i | 0.311197 | − | 0.950345i | \(-0.399270\pi\) |
0.667424 | − | 0.744678i | \(-0.267397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.7439 | − | 46.5414i | 0.0594209 | − | 0.0618079i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.19877 | − | 3.00151i | −0.00688579 | − | 0.00397551i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −141.145 | + | 244.470i | −0.186453 | + | 0.322945i | −0.944065 | − | 0.329759i | \(-0.893032\pi\) |
0.757612 | + | 0.652705i | \(0.226366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1220.06 | + | 1172.94i | 1.60746 | + | 1.54538i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 917.495 | − | 529.716i | 1.20564 | − | 0.696079i | 0.243839 | − | 0.969816i | \(-0.421593\pi\) |
0.961805 | + | 0.273737i | \(0.0882597\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −566.542 | − | 981.279i | −0.742519 | − | 1.28608i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.4588 | − | 976.201i | −0.0502730 | − | 1.27608i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1294.10 | − | 747.152i | −1.68723 | − | 0.974122i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 548.055 | − | 949.259i | 0.712685 | − | 1.23441i | −0.251160 | − | 0.967946i | \(-0.580812\pi\) |
0.963845 | − | 0.266462i | \(-0.0858546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 848.612 | + | 209.570i | 1.10066 | + | 0.271815i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −428.849 | + | 247.596i | −0.554786 | + | 0.320306i | −0.751050 | − | 0.660245i | \(-0.770452\pi\) |
0.196264 | + | 0.980551i | \(0.437119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 664.425 | + | 1150.82i | 0.857323 | + | 1.48493i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −135.734 | + | 549.630i | −0.174690 | + | 0.707375i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.8462 | + | 90.4125i | −0.0408809 | + | 0.116062i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 121.101 | + | 209.752i | 0.155058 | + | 0.268569i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −611.797 | − | 543.482i | −0.781349 | − | 0.694102i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 934.247i | 1.19012i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −134.383 | − | 232.757i | −0.170753 | − | 0.295753i | 0.767930 | − | 0.640533i | \(-0.221287\pi\) |
−0.938683 | + | 0.344781i | \(0.887953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 338.072 | − | 351.654i | 0.428482 | − | 0.445695i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 344.242i | − | 0.435199i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −967.587 | + | 1675.91i | −1.22016 | + | 2.11338i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 862.745 | + | 829.425i | 1.08521 | + | 1.04330i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1058.28 | − | 610.999i | 1.32783 | − | 0.766624i | 0.342868 | − | 0.939384i | \(-0.388602\pi\) |
0.984964 | + | 0.172760i | \(0.0552684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −466.381 | + | 807.796i | −0.583706 | + | 1.01101i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 326.117 | − | 620.005i | 0.407137 | − | 0.774039i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1749.23 | − | 1009.92i | 2.17837 | − | 1.25768i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −908.564 | − | 1573.68i | −1.12865 | − | 1.95488i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −98.2467 | − | 24.2626i | −0.121743 | − | 0.0300652i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1065.41i | 1.31695i | 0.752605 | + | 0.658473i | \(0.228797\pi\) | ||||
−0.752605 | + | 0.658473i | \(0.771203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 270.922 | + | 469.251i | 0.334059 | + | 0.578608i | 0.983304 | − | 0.181972i | \(-0.0582481\pi\) |
−0.649244 | + | 0.760580i | \(0.724915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 127.356 | − | 515.705i | 0.156650 | − | 0.634323i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1717.56i | − | 2.10743i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 173.580 | + | 927.866i | 0.212460 | + | 1.13570i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1214.94 | − | 639.048i | −1.48345 | − | 0.780279i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 340.662i | 0.414936i | 0.978242 | + | 0.207468i | \(0.0665222\pi\) | ||||
−0.978242 | + | 0.207468i | \(0.933478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 532.112 | − | 921.644i | 0.646551 | − | 1.11986i | −0.337390 | − | 0.941365i | \(-0.609544\pi\) |
0.983941 | − | 0.178494i | \(-0.0571227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1375.86 | − | 339.776i | −1.66771 | − | 0.411850i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −885.426 | + | 511.201i | −1.07065 | + | 0.618139i | −0.928358 | − | 0.371686i | \(-0.878780\pi\) |
−0.142289 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −671.808 | −0.810384 | −0.405192 | − | 0.914232i | \(-0.632795\pi\) | ||||
−0.405192 | + | 0.914232i | \(0.632795\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −127.823 | + | 517.595i | −0.153818 | + | 0.622858i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 111.734i | − | 0.134135i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 605.024 | − | 1047.93i | 0.724579 | − | 1.25501i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1261.92 | + | 259.399i | 1.50767 | + | 0.309915i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −824.312 | + | 475.917i | −0.982493 | + | 0.567243i | −0.903022 | − | 0.429595i | \(-0.858657\pi\) |
−0.0794712 | + | 0.996837i | \(0.525323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.6109 | −0.0922840 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 280.243 | + | 969.145i | 0.332436 | + | 1.14964i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1529.23 | + | 882.899i | −1.80974 | + | 1.04485i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1252.99 | 1.47933 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −89.6710 | + | 25.9297i | −0.105620 | + | 0.0305415i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 723.238 | + | 417.562i | 0.849869 | + | 0.490672i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.4431 | − | 31.9445i | −0.0216215 | − | 0.0374495i | 0.855012 | − | 0.518608i | \(-0.173550\pi\) |
−0.876634 | + | 0.481158i | \(0.840216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 276.518 | + | 1211.99i | 0.323413 | + | 1.41753i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −393.745 | + | 227.329i | −0.459446 | + | 0.265261i | −0.711811 | − | 0.702371i | \(-0.752125\pi\) |
0.252365 | + | 0.967632i | \(0.418792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −261.644 | + | 453.180i | −0.304591 | + | 0.527567i | −0.977170 | − | 0.212458i | \(-0.931853\pi\) |
0.672579 | + | 0.740025i | \(0.265187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 110.432 | + | 27.2719i | 0.128261 | + | 0.0316747i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 537.201i | 0.622481i | 0.950331 | + | 0.311240i | \(0.100744\pi\) | ||||
−0.950331 | + | 0.311240i | \(0.899256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 246.283 | + | 426.574i | 0.284720 | + | 0.493149i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 142.826 | + | 137.310i | 0.164736 | + | 0.158374i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.54649i | − | 0.00293037i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9471 | − | 20.6930i | −0.0137165 | − | 0.0237577i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −753.231 | − | 396.192i | −0.862807 | − | 0.453828i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 134.841 | + | 77.8507i | 0.154104 | + | 0.0889722i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 731.890 | 0.834539 | 0.417269 | − | 0.908783i | \(-0.362987\pi\) | ||||
0.417269 | + | 0.908783i | \(0.362987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −432.953 | + | 450.346i | −0.492552 | + | 0.512339i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 520.652i | 0.590979i | 0.955346 | + | 0.295489i | \(0.0954827\pi\) | ||||
−0.955346 | + | 0.295489i | \(0.904517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −492.648 | − | 853.291i | −0.557925 | − | 0.966354i | −0.997670 | − | 0.0682312i | \(-0.978264\pi\) |
0.439745 | − | 0.898123i | \(-0.355069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1542.59 | − | 446.063i | 1.74304 | − | 0.504027i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 742.547 | + | 428.710i | 0.837144 | + | 0.483325i | 0.856292 | − | 0.516491i | \(-0.172762\pi\) |
−0.0191484 | + | 0.999817i | \(0.506096\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −211.806 | −0.238252 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1132.14 | + | 778.454i | −1.27064 | + | 0.873685i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 394.317 | − | 1119.48i | 0.441565 | − | 1.25362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −440.048 | −0.491674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1403.41 | + | 1459.79i | −1.56456 | + | 1.62741i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1252.42 | − | 723.086i | 1.39313 | − | 0.804323i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 819.374 | 0.909406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1076.08 | − | 311.164i | 1.19167 | − | 0.344590i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1051.17 | − | 606.894i | 1.16151 | − | 0.670601i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 620.439 | + | 1074.63i | 0.684057 | + | 1.18482i | 0.973732 | + | 0.227696i | \(0.0731192\pi\) |
−0.289676 | + | 0.957125i | \(0.593547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 407.189 | + | 645.204i | 0.447953 | + | 0.709795i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −692.109 | − | 399.589i | −0.759725 | − | 0.438627i | 0.0694723 | − | 0.997584i | \(-0.477868\pi\) |
−0.829197 | + | 0.558957i | \(0.811202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 410.984 | + | 711.845i | 0.450147 | + | 0.779677i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −577.667 | − | 1997.71i | −0.631330 | − | 2.18328i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1640.74 | + | 947.283i | 1.78925 | + | 1.03302i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1507.71 | 1.64060 | 0.820299 | − | 0.571934i | \(-0.193807\pi\) | ||||
0.820299 | + | 0.571934i | \(0.193807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −361.722 | + | 1464.72i | −0.392749 | + | 1.59036i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −250.966 | + | 144.895i | −0.271902 | + | 0.156983i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −699.307 | −0.756007 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55.7844 | − | 29.3420i | −0.0601773 | − | 0.0316527i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −871.341 | + | 503.069i | −0.937934 | + | 0.541516i | −0.889312 | − | 0.457301i | \(-0.848816\pi\) |
−0.0486219 | + | 0.998817i | \(0.515483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.1440 | + | 139.752i | 0.0280816 | + | 0.150110i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −580.394 | + | 603.709i | −0.622072 | + | 0.647062i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1594.59 | + | 920.639i | −1.70545 | + | 0.984640i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −622.963 | − | 1079.00i | −0.664848 | − | 1.15155i | −0.979326 | − | 0.202286i | \(-0.935163\pi\) |
0.314478 | − | 0.949265i | \(-0.398170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 326.405 | − | 94.3849i | 0.347609 | − | 0.100516i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −952.114 | − | 549.703i | −1.01181 | − | 0.584169i | −0.100090 | − | 0.994978i | \(-0.531913\pi\) |
−0.911721 | + | 0.410809i | \(0.865246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 83.8970 | − | 145.314i | 0.0889682 | − | 0.154097i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1399.89 | − | 465.250i | 1.48136 | − | 0.492328i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 533.426 | − | 307.974i | 0.563280 | − | 0.325210i | −0.191181 | − | 0.981555i | \(-0.561232\pi\) |
0.754461 | + | 0.656345i | \(0.227898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1208.36 | + | 2092.94i | 1.27329 | + | 2.20541i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 91.1632 | + | 315.263i | 0.0958604 | + | 0.331507i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 447.017 | + | 258.085i | 0.469063 | + | 0.270814i | 0.715847 | − | 0.698257i | \(-0.246041\pi\) |
−0.246784 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 558.356 | − | 967.101i | 0.584666 | − | 1.01267i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −369.774 | + | 1497.33i | −0.386389 | + | 1.56461i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −561.976 | − | 324.457i | −0.586002 | − | 0.338328i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −657.858 | + | 1139.44i | −0.684555 | + | 1.18568i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 470.389 | + | 745.345i | 0.488462 | + | 0.773983i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1732.41i | − | 1.79524i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 864.526 | 0.894029 | 0.447014 | − | 0.894527i | \(-0.352487\pi\) | ||||
0.447014 | + | 0.894527i | \(0.352487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 711.563 | + | 466.981i | 0.734327 | + | 0.481920i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1640.42 | − | 947.099i | −1.68942 | − | 0.975386i | −0.954962 | − | 0.296729i | \(-0.904104\pi\) |
−0.734456 | − | 0.678657i | \(-0.762562\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 622.037 | + | 1077.40i | 0.639298 | + | 1.10730i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 406.537 | − | 1646.20i | 0.416962 | − | 1.68841i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1561.64 | + | 901.613i | −1.59840 | + | 0.922838i | −0.606608 | + | 0.795001i | \(0.707470\pi\) |
−0.991795 | + | 0.127837i | \(0.959197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1320.31 | −1.34863 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −53.4153 | − | 1355.84i | −0.0544498 | − | 1.38210i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −345.988 | + | 199.756i | −0.351972 | + | 0.203211i | −0.665553 | − | 0.746350i | \(-0.731804\pi\) |
0.313582 | + | 0.949561i | \(0.398471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −796.785 | −0.808919 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1367.36 | − | 337.678i | −1.38537 | − | 0.342126i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1652.37i | − | 1.67074i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 479.340 | − | 830.240i | 0.483693 | − | 0.837780i | −0.516132 | − | 0.856509i | \(-0.672629\pi\) |
0.999825 | + | 0.0187287i | \(0.00596188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 72.6908 | − | 294.348i | 0.0732032 | − | 0.296423i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1595.26 | + | 921.023i | −1.60328 | + | 0.925651i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1169.13 | −1.17265 | −0.586326 | − | 0.810075i | \(-0.699426\pi\) | ||||
−0.586326 | + | 0.810075i | \(0.699426\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −450.262 | + | 506.859i | −0.450712 | + | 0.507366i |
(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 | 684.3.m.a.353.3 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.38 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.3 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.23 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.23 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.3 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.3 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.3 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.3 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.3 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.23 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.23 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.3 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.38 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.3 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.3 | 80 | 57.26 | odd | 6 |