Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(19,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bi (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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.19 |
Dual form | 315.3.bi.a.199.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −0.750000 | − | 0.433013i | 0.0756939 | − | 0.997131i | \(-0.475883\pi\) |
−0.825694 | + | 0.564118i | \(0.809216\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.29150 | − | 4.58258i | 0.755929 | − | 0.654654i | ||||
\(8\) | 8.66025i | 1.08253i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.50000 | + | 4.33013i | −0.750000 | + | 0.433013i | ||||
\(11\) | −9.26013 | − | 16.0390i | −0.841830 | − | 1.45809i | −0.888346 | − | 0.459175i | \(-0.848145\pi\) |
0.0465160 | − | 0.998918i | \(-0.485188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5203 | 1.42464 | 0.712318 | − | 0.701857i | \(-0.247646\pi\) | ||||
0.712318 | + | 0.701857i | \(0.247646\pi\) | |||||||
\(14\) | −11.9059 | + | 2.29129i | −0.850420 | + | 0.163663i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.50000 | − | 9.52628i | 0.343750 | − | 0.595392i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.0588235 | − | 0.101885i | 0.835114 | − | 0.550077i | \(-0.185402\pi\) |
−0.893938 | + | 0.448192i | \(0.852068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.5000 | + | 11.2583i | 1.02632 | + | 0.592544i | 0.915927 | − | 0.401345i | \(-0.131457\pi\) |
0.110389 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(20\) | −5.00000 | −0.250000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 32.0780i | 1.45809i | ||||||||
\(23\) | 4.50000 | + | 2.59808i | 0.195652 | + | 0.112960i | 0.594626 | − | 0.804003i | \(-0.297300\pi\) |
−0.398974 | + | 0.916962i | \(0.630634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(26\) | −27.7804 | − | 16.0390i | −1.06848 | − | 0.616885i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.61438 | − | 2.29129i | −0.236228 | − | 0.0818317i | ||||
\(29\) | −37.0405 | −1.27726 | −0.638630 | − | 0.769514i | \(-0.720498\pi\) | ||||
−0.638630 | + | 0.769514i | \(0.720498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.0000 | + | 19.0526i | −1.06452 | + | 0.614599i | −0.926678 | − | 0.375856i | \(-0.877349\pi\) |
−0.137838 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(32\) | 13.5000 | − | 7.79423i | 0.421875 | − | 0.243570i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410i | 0.101885i | ||||||||
\(35\) | −6.61438 | − | 34.3693i | −0.188982 | − | 0.981981i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.7804 | − | 16.0390i | −0.750821 | − | 0.433487i | 0.0751693 | − | 0.997171i | \(-0.476050\pi\) |
−0.825991 | + | 0.563684i | \(0.809384\pi\) | |||||||
\(38\) | −19.5000 | − | 33.7750i | −0.513158 | − | 0.888816i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 37.5000 | + | 21.6506i | 0.937500 | + | 0.541266i | ||||
\(41\) | − | 32.0780i | − | 0.782391i | −0.920308 | − | 0.391195i | \(-0.872062\pi\) | ||
0.920308 | − | 0.391195i | \(-0.127938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 64.1561i | − | 1.49200i | −0.665945 | − | 0.746001i | \(-0.731972\pi\) | ||
0.665945 | − | 0.746001i | \(-0.268028\pi\) | |||||||
\(44\) | −9.26013 | + | 16.0390i | −0.210457 | + | 0.364523i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50000 | − | 7.79423i | −0.0978261 | − | 0.169440i | ||||
\(47\) | −20.5000 | + | 35.5070i | −0.436170 | + | 0.755469i | −0.997390 | − | 0.0721976i | \(-0.976999\pi\) |
0.561220 | + | 0.827667i | \(0.310332\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | − | 48.4974i | 0.142857 | − | 0.989743i | ||||
\(50\) | 43.3013i | 0.866025i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.26013 | − | 16.0390i | −0.178079 | − | 0.308443i | ||||
\(53\) | 19.5000 | − | 11.2583i | 0.367925 | − | 0.212421i | −0.304627 | − | 0.952472i | \(-0.598532\pi\) |
0.672551 | + | 0.740050i | \(0.265198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −92.6013 | −1.68366 | ||||||||
\(56\) | 39.6863 | + | 45.8258i | 0.708683 | + | 0.818317i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 55.5608 | + | 32.0780i | 0.957944 | + | 0.553069i | ||||
\(59\) | −55.5608 | + | 32.0780i | −0.941708 | + | 0.543695i | −0.890495 | − | 0.454992i | \(-0.849642\pi\) |
−0.0512127 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.0000 | + | 27.7128i | 0.786885 | + | 0.454308i | 0.838865 | − | 0.544340i | \(-0.183220\pi\) |
−0.0519796 | + | 0.998648i | \(0.516553\pi\) | |||||||
\(62\) | 66.0000 | 1.06452 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −71.0000 | −1.10938 | ||||||||
\(65\) | 46.3006 | − | 80.1951i | 0.712318 | − | 1.23377i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55.5608 | + | 32.0780i | −0.829265 | + | 0.478777i | −0.853601 | − | 0.520927i | \(-0.825586\pi\) |
0.0243357 | + | 0.999704i | \(0.492253\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.0147059 | + | 0.0254713i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −19.8431 | + | 57.2822i | −0.283473 | + | 0.818317i | ||||
\(71\) | 74.0810 | 1.04339 | 0.521697 | − | 0.853131i | \(-0.325299\pi\) | ||||
0.521697 | + | 0.853131i | \(0.325299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.5203 | + | 32.0780i | 0.253702 | + | 0.439425i | 0.964542 | − | 0.263929i | \(-0.0850184\pi\) |
−0.710840 | + | 0.703354i | \(0.751685\pi\) | |||||||
\(74\) | 27.7804 | + | 48.1170i | 0.375411 | + | 0.650230i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 22.5167i | − | 0.296272i | ||||||
\(77\) | −122.500 | − | 42.4352i | −1.59091 | − | 0.551107i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −52.0000 | + | 90.0666i | −0.658228 | + | 1.14008i | 0.322846 | + | 0.946451i | \(0.395360\pi\) |
−0.981074 | + | 0.193633i | \(0.937973\pi\) | |||||||
\(80\) | −27.5000 | − | 47.6314i | −0.343750 | − | 0.595392i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −27.7804 | + | 48.1170i | −0.338785 | + | 0.586793i | ||||
\(83\) | 32.0000 | 0.385542 | 0.192771 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192771 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0000 | −0.117647 | ||||||||
\(86\) | −55.5608 | + | 96.2341i | −0.646056 | + | 1.11900i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 138.902 | − | 80.1951i | 1.57843 | − | 0.911308i | ||||
\(89\) | 55.5608 | + | 32.0780i | 0.624278 | + | 0.360427i | 0.778533 | − | 0.627604i | \(-0.215964\pi\) |
−0.154254 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 98.0000 | − | 84.8705i | 1.07692 | − | 0.932643i | ||||
\(92\) | − | 5.19615i | − | 0.0564799i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 61.5000 | − | 35.5070i | 0.654255 | − | 0.377734i | ||||
\(95\) | 97.5000 | − | 56.2917i | 1.02632 | − | 0.592544i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 74.0810 | 0.763722 | 0.381861 | − | 0.924220i | \(-0.375283\pi\) | ||||
0.381861 | + | 0.924220i | \(0.375283\pi\) | |||||||
\(98\) | −52.5000 | + | 66.6840i | −0.535714 | + | 0.680449i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.5000 | + | 21.6506i | −0.125000 | + | 0.216506i | ||||
\(101\) | 166.682 | − | 96.2341i | 1.65032 | − | 0.952813i | 0.673381 | − | 0.739296i | \(-0.264841\pi\) |
0.976939 | − | 0.213517i | \(-0.0684918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.0810 | − | 128.312i | 0.719233 | − | 1.24575i | −0.242071 | − | 0.970259i | \(-0.577827\pi\) |
0.961304 | − | 0.275490i | \(-0.0888401\pi\) | |||||||
\(104\) | 160.390i | 1.54221i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −39.0000 | −0.367925 | ||||||||
\(107\) | 96.0000 | + | 55.4256i | 0.897196 | + | 0.517997i | 0.876289 | − | 0.481785i | \(-0.160011\pi\) |
0.0209068 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −28.0000 | − | 48.4974i | −0.256881 | − | 0.444930i | 0.708524 | − | 0.705687i | \(-0.249361\pi\) |
−0.965405 | + | 0.260756i | \(0.916028\pi\) | |||||||
\(110\) | 138.902 | + | 80.1951i | 1.26274 | + | 0.729046i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.5516 | − | 75.6125i | −0.129925 | − | 0.675112i | ||||
\(113\) | 162.813i | 1.44082i | 0.693548 | + | 0.720411i | \(0.256047\pi\) | ||||
−0.693548 | + | 0.720411i | \(0.743953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.5000 | − | 12.9904i | 0.195652 | − | 0.112960i | ||||
\(116\) | 18.5203 | + | 32.0780i | 0.159657 | + | 0.276535i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 111.122 | 0.941708 | ||||||||
\(119\) | −13.2288 | − | 4.58258i | −0.111166 | − | 0.0385090i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −111.000 | + | 192.258i | −0.917355 | + | 1.58891i | ||||
\(122\) | −48.0000 | − | 83.1384i | −0.393443 | − | 0.681463i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 33.0000 | + | 19.0526i | 0.266129 | + | 0.153650i | ||||
\(125\) | −125.000 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 96.2341i | 0.757749i | 0.925448 | + | 0.378874i | \(0.123689\pi\) | ||||
−0.925448 | + | 0.378874i | \(0.876311\pi\) | |||||||
\(128\) | 52.5000 | + | 30.3109i | 0.410156 | + | 0.236804i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −138.902 | + | 80.1951i | −1.06848 | + | 0.616885i | ||||
\(131\) | −83.3412 | − | 48.1170i | −0.636192 | − | 0.367306i | 0.146954 | − | 0.989143i | \(-0.453053\pi\) |
−0.783146 | + | 0.621838i | \(0.786386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 154.776 | − | 29.7867i | 1.16373 | − | 0.223960i | ||||
\(134\) | 111.122 | 0.829265 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0000 | − | 8.66025i | 0.110294 | − | 0.0636783i | ||||
\(137\) | 144.000 | − | 83.1384i | 1.05109 | − | 0.606850i | 0.128139 | − | 0.991756i | \(-0.459100\pi\) |
0.922956 | + | 0.384906i | \(0.125766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 117.779i | − | 0.847334i | −0.905818 | − | 0.423667i | \(-0.860743\pi\) | ||
0.905818 | − | 0.423667i | \(-0.139257\pi\) | |||||||
\(140\) | −26.4575 | + | 22.9129i | −0.188982 | + | 0.163663i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −111.122 | − | 64.1561i | −0.782546 | − | 0.451803i | ||||
\(143\) | −171.500 | − | 297.047i | −1.19930 | − | 2.07725i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −92.6013 | + | 160.390i | −0.638630 | + | 1.10614i | ||||
\(146\) | − | 64.1561i | − | 0.439425i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.0780i | 0.216743i | ||||||||
\(149\) | 18.5203 | − | 32.0780i | 0.124297 | − | 0.215289i | −0.797161 | − | 0.603767i | \(-0.793666\pi\) |
0.921458 | + | 0.388478i | \(0.126999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −85.0000 | − | 147.224i | −0.562914 | − | 0.974995i | −0.997240 | − | 0.0742400i | \(-0.976347\pi\) |
0.434326 | − | 0.900756i | \(-0.356986\pi\) | |||||||
\(152\) | −97.5000 | + | 168.875i | −0.641447 | + | 1.11102i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 147.000 | + | 169.741i | 0.954545 | + | 1.10221i | ||||
\(155\) | 190.526i | 1.22920i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.26013 | − | 16.0390i | −0.0589817 | − | 0.102159i | 0.835027 | − | 0.550209i | \(-0.185452\pi\) |
−0.894009 | + | 0.448050i | \(0.852119\pi\) | |||||||
\(158\) | 156.000 | − | 90.0666i | 0.987342 | − | 0.570042i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 77.9423i | − | 0.487139i | ||||||
\(161\) | 35.7176 | − | 6.87386i | 0.221849 | − | 0.0426948i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 55.5608 | + | 32.0780i | 0.340864 | + | 0.196798i | 0.660654 | − | 0.750691i | \(-0.270279\pi\) |
−0.319790 | + | 0.947488i | \(0.603612\pi\) | |||||||
\(164\) | −27.7804 | + | 16.0390i | −0.169393 | + | 0.0977989i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −48.0000 | − | 27.7128i | −0.289157 | − | 0.166945i | ||||
\(167\) | 89.0000 | 0.532934 | 0.266467 | − | 0.963844i | \(-0.414144\pi\) | ||||
0.266467 | + | 0.963844i | \(0.414144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 174.000 | 1.02959 | ||||||||
\(170\) | 15.0000 | + | 8.66025i | 0.0882353 | + | 0.0509427i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −55.5608 | + | 32.0780i | −0.323028 | + | 0.186500i | ||||
\(173\) | 48.5000 | − | 84.0045i | 0.280347 | − | 0.485575i | −0.691123 | − | 0.722737i | \(-0.742884\pi\) |
0.971470 | + | 0.237162i | \(0.0762172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −165.359 | − | 57.2822i | −0.944911 | − | 0.327327i | ||||
\(176\) | −203.723 | −1.15752 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −55.5608 | − | 96.2341i | −0.312139 | − | 0.540641i | ||||
\(179\) | −64.8209 | − | 112.273i | −0.362128 | − | 0.627224i | 0.626183 | − | 0.779676i | \(-0.284616\pi\) |
−0.988311 | + | 0.152452i | \(0.951283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 103.923i | 0.574160i | 0.957907 | + | 0.287080i | \(0.0926846\pi\) | ||||
−0.957907 | + | 0.287080i | \(0.907315\pi\) | |||||||
\(182\) | −220.500 | + | 42.4352i | −1.21154 | + | 0.233161i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.5000 | + | 38.9711i | −0.122283 | + | 0.211800i | ||||
\(185\) | −138.902 | + | 80.1951i | −0.750821 | + | 0.433487i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.5203 | + | 32.0780i | −0.0990388 | + | 0.171540i | ||||
\(188\) | 41.0000 | 0.218085 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −195.000 | −1.02632 | ||||||||
\(191\) | 18.5203 | − | 32.0780i | 0.0969647 | − | 0.167948i | −0.813462 | − | 0.581618i | \(-0.802420\pi\) |
0.910427 | + | 0.413670i | \(0.135753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111.122 | − | 64.1561i | 0.575759 | − | 0.332415i | −0.183687 | − | 0.982985i | \(-0.558803\pi\) |
0.759446 | + | 0.650570i | \(0.225470\pi\) | |||||||
\(194\) | −111.122 | − | 64.1561i | −0.572792 | − | 0.330701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −45.5000 | + | 18.1865i | −0.232143 | + | 0.0927884i | ||||
\(197\) | 77.9423i | 0.395646i | 0.980238 | + | 0.197823i | \(0.0633871\pi\) | ||||
−0.980238 | + | 0.197823i | \(0.936613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −165.000 | + | 95.2628i | −0.829146 | + | 0.478708i | −0.853560 | − | 0.520994i | \(-0.825561\pi\) |
0.0244144 | + | 0.999702i | \(0.492228\pi\) | |||||||
\(200\) | 187.500 | − | 108.253i | 0.937500 | − | 0.541266i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −333.365 | −1.65032 | ||||||||
\(203\) | −196.000 | + | 169.741i | −0.965517 | + | 0.836162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −138.902 | − | 80.1951i | −0.677570 | − | 0.391195i | ||||
\(206\) | −222.243 | + | 128.312i | −1.07885 | + | 0.622874i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 101.861 | − | 176.429i | 0.489718 | − | 0.848217i | ||||
\(209\) | − | 417.014i | − | 1.99528i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 287.000 | 1.36019 | 0.680095 | − | 0.733124i | \(-0.261939\pi\) | ||||
0.680095 | + | 0.733124i | \(0.261939\pi\) | |||||||
\(212\) | −19.5000 | − | 11.2583i | −0.0919811 | − | 0.0531053i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −96.0000 | − | 166.277i | −0.448598 | − | 0.776995i | ||||
\(215\) | −277.804 | − | 160.390i | −1.29211 | − | 0.746001i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −87.3098 | + | 252.042i | −0.402349 | + | 1.16148i | ||||
\(218\) | 96.9948i | 0.444930i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 46.3006 | + | 80.1951i | 0.210457 | + | 0.364523i | ||||
\(221\) | −18.5203 | − | 32.0780i | −0.0838021 | − | 0.145149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 74.0810 | 0.332202 | 0.166101 | − | 0.986109i | \(-0.446882\pi\) | ||||
0.166101 | + | 0.986109i | \(0.446882\pi\) | |||||||
\(224\) | 35.7176 | − | 103.108i | 0.159454 | − | 0.460303i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 141.000 | − | 244.219i | 0.623894 | − | 1.08062i | ||||
\(227\) | −67.0000 | − | 116.047i | −0.295154 | − | 0.511222i | 0.679867 | − | 0.733336i | \(-0.262038\pi\) |
−0.975021 | + | 0.222114i | \(0.928704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.0000 | − | 15.5885i | −0.117904 | − | 0.0680719i | 0.439888 | − | 0.898053i | \(-0.355018\pi\) |
−0.557792 | + | 0.829981i | \(0.688351\pi\) | |||||||
\(230\) | −45.0000 | −0.195652 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 320.780i | − | 1.38267i | ||||||
\(233\) | 321.000 | + | 185.329i | 1.37768 | + | 0.795405i | 0.991880 | − | 0.127176i | \(-0.0405914\pi\) |
0.385802 | + | 0.922581i | \(0.373925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 102.500 | + | 177.535i | 0.436170 | + | 0.755469i | ||||
\(236\) | 55.5608 | + | 32.0780i | 0.235427 | + | 0.135924i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.8745 | + | 18.3303i | 0.0666996 | + | 0.0770181i | ||||
\(239\) | −259.284 | −1.08487 | −0.542434 | − | 0.840098i | \(-0.682497\pi\) | ||||
−0.542434 | + | 0.840098i | \(0.682497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5000 | + | 7.79423i | −0.0560166 | + | 0.0323412i | −0.527747 | − | 0.849402i | \(-0.676963\pi\) |
0.471730 | + | 0.881743i | \(0.343630\pi\) | |||||||
\(242\) | 333.000 | − | 192.258i | 1.37603 | − | 0.794453i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 55.4256i | − | 0.227154i | ||||||
\(245\) | −192.500 | − | 151.554i | −0.785714 | − | 0.618590i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 361.145 | + | 208.507i | 1.46213 | + | 0.844159i | ||||
\(248\) | −165.000 | − | 285.788i | −0.665323 | − | 1.15237i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 187.500 | + | 108.253i | 0.750000 | + | 0.433013i | ||||
\(251\) | 288.702i | 1.15021i | 0.818080 | + | 0.575104i | \(0.195038\pi\) | ||||
−0.818080 | + | 0.575104i | \(0.804962\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 96.2341i | − | 0.380372i | ||||||
\(254\) | 83.3412 | − | 144.351i | 0.328115 | − | 0.568312i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 89.5000 | + | 155.019i | 0.349609 | + | 0.605541i | ||||
\(257\) | −28.0000 | + | 48.4974i | −0.108949 | + | 0.188706i | −0.915345 | − | 0.402671i | \(-0.868082\pi\) |
0.806396 | + | 0.591377i | \(0.201415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −220.500 | + | 42.4352i | −0.851351 | + | 0.163843i | ||||
\(260\) | −92.6013 | −0.356159 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 83.3412 | + | 144.351i | 0.318096 | + | 0.550959i | ||||
\(263\) | −270.000 | + | 155.885i | −1.02662 | + | 0.592717i | −0.916013 | − | 0.401148i | \(-0.868611\pi\) |
−0.110603 | + | 0.993865i | \(0.535278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 112.583i | − | 0.424843i | ||||||
\(266\) | −257.961 | − | 89.3602i | −0.969777 | − | 0.335941i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 55.5608 | + | 32.0780i | 0.207316 | + | 0.119694i | ||||
\(269\) | 388.925 | − | 224.546i | 1.44582 | − | 0.834744i | 0.447591 | − | 0.894238i | \(-0.352282\pi\) |
0.998229 | + | 0.0594942i | \(0.0189488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −219.000 | − | 126.440i | −0.808118 | − | 0.466567i | 0.0381838 | − | 0.999271i | \(-0.487843\pi\) |
−0.846302 | + | 0.532704i | \(0.821176\pi\) | |||||||
\(272\) | −22.0000 | −0.0808824 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −288.000 | −1.05109 | ||||||||
\(275\) | −231.503 | + | 400.975i | −0.841830 | + | 1.45809i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 166.682 | − | 96.2341i | 0.601741 | − | 0.347415i | −0.167985 | − | 0.985790i | \(-0.553726\pi\) |
0.769726 | + | 0.638374i | \(0.220393\pi\) | |||||||
\(278\) | −102.000 | + | 176.669i | −0.366906 | + | 0.635501i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 297.647 | − | 57.2822i | 1.06303 | − | 0.204579i | ||||
\(281\) | 240.763 | 0.856809 | 0.428405 | − | 0.903587i | \(-0.359076\pi\) | ||||
0.428405 | + | 0.903587i | \(0.359076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74.0810 | + | 128.312i | 0.261770 | + | 0.453400i | 0.966712 | − | 0.255865i | \(-0.0823603\pi\) |
−0.704942 | + | 0.709265i | \(0.749027\pi\) | |||||||
\(284\) | −37.0405 | − | 64.1561i | −0.130424 | − | 0.225902i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 594.093i | 2.07725i | ||||||||
\(287\) | −147.000 | − | 169.741i | −0.512195 | − | 0.591432i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 142.500 | − | 246.817i | 0.493080 | − | 0.854039i | ||||
\(290\) | 277.804 | − | 160.390i | 0.957944 | − | 0.553069i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.5203 | − | 32.0780i | 0.0634255 | − | 0.109856i | ||||
\(293\) | 455.000 | 1.55290 | 0.776451 | − | 0.630178i | \(-0.217018\pi\) | ||||
0.776451 | + | 0.630178i | \(0.217018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 320.780i | 1.08739i | ||||||||
\(296\) | 138.902 | − | 240.585i | 0.469263 | − | 0.812788i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −55.5608 | + | 32.0780i | −0.186446 | + | 0.107644i | ||||
\(299\) | 83.3412 | + | 48.1170i | 0.278733 | + | 0.160927i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −294.000 | − | 339.482i | −0.976744 | − | 1.12785i | ||||
\(302\) | 294.449i | 0.974995i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 214.500 | − | 123.842i | 0.705592 | − | 0.407374i | ||||
\(305\) | 240.000 | − | 138.564i | 0.786885 | − | 0.454308i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 74.0810 | 0.241306 | 0.120653 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120653 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(308\) | 24.5000 | + | 127.306i | 0.0795455 | + | 0.413330i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 165.000 | − | 285.788i | 0.532258 | − | 0.921898i | ||||
\(311\) | −388.925 | + | 224.546i | −1.25056 | + | 0.722014i | −0.971222 | − | 0.238178i | \(-0.923450\pi\) |
−0.279343 | + | 0.960191i | \(0.590117\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −148.162 | + | 256.624i | −0.473361 | + | 0.819886i | −0.999535 | − | 0.0304913i | \(-0.990293\pi\) |
0.526174 | + | 0.850377i | \(0.323626\pi\) | |||||||
\(314\) | 32.0780i | 0.102159i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 104.000 | 0.329114 | ||||||||
\(317\) | 174.000 | + | 100.459i | 0.548896 | + | 0.316905i | 0.748677 | − | 0.662935i | \(-0.230690\pi\) |
−0.199781 | + | 0.979841i | \(0.564023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 343.000 | + | 594.093i | 1.07524 | + | 1.86236i | ||||
\(320\) | −177.500 | + | 307.439i | −0.554688 | + | 0.960747i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −59.5294 | − | 20.6216i | −0.184874 | − | 0.0640422i | ||||
\(323\) | − | 45.0333i | − | 0.139422i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −231.503 | − | 400.975i | −0.712318 | − | 1.23377i | ||||
\(326\) | −55.5608 | − | 96.2341i | −0.170432 | − | 0.295197i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 277.804 | 0.846963 | ||||||||
\(329\) | 54.2379 | + | 281.828i | 0.164857 | + | 0.856621i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 87.5000 | − | 151.554i | 0.264350 | − | 0.457868i | −0.703043 | − | 0.711148i | \(-0.748176\pi\) |
0.967393 | + | 0.253279i | \(0.0815091\pi\) | |||||||
\(332\) | −16.0000 | − | 27.7128i | −0.0481928 | − | 0.0834723i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −133.500 | − | 77.0763i | −0.399701 | − | 0.230767i | ||||
\(335\) | 320.780i | 0.957553i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 64.1561i | 0.190374i | 0.995459 | + | 0.0951870i | \(0.0303449\pi\) | ||||
−0.995459 | + | 0.0951870i | \(0.969655\pi\) | |||||||
\(338\) | −261.000 | − | 150.688i | −0.772189 | − | 0.445824i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.00000 | + | 8.66025i | 0.0147059 | + | 0.0254713i | ||||
\(341\) | 611.169 | + | 352.858i | 1.79228 | + | 1.03478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −185.203 | − | 288.702i | −0.539949 | − | 0.841698i | ||||
\(344\) | 555.608 | 1.61514 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −145.500 | + | 84.0045i | −0.420520 | + | 0.242787i | ||||
\(347\) | 75.0000 | − | 43.3013i | 0.216138 | − | 0.124788i | −0.388023 | − | 0.921650i | \(-0.626842\pi\) |
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.92820i | − | 0.0198516i | −0.999951 | − | 0.00992579i | \(-0.996840\pi\) | ||
0.999951 | − | 0.00992579i | \(-0.00315953\pi\) | |||||||
\(350\) | 198.431 | + | 229.129i | 0.566947 | + | 0.654654i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −250.023 | − | 144.351i | −0.710294 | − | 0.410088i | ||||
\(353\) | −259.000 | − | 448.601i | −0.733711 | − | 1.27082i | −0.955287 | − | 0.295682i | \(-0.904453\pi\) |
0.221576 | − | 0.975143i | \(-0.428880\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 185.203 | − | 320.780i | 0.521697 | − | 0.903606i | ||||
\(356\) | − | 64.1561i | − | 0.180214i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 224.546i | 0.627224i | ||||||||
\(359\) | −92.6013 | + | 160.390i | −0.257942 | + | 0.446769i | −0.965691 | − | 0.259696i | \(-0.916378\pi\) |
0.707748 | + | 0.706465i | \(0.249711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 73.0000 | + | 126.440i | 0.202216 | + | 0.350249i | ||||
\(362\) | 90.0000 | − | 155.885i | 0.248619 | − | 0.430620i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −122.500 | − | 42.4352i | −0.336538 | − | 0.116580i | ||||
\(365\) | 185.203 | 0.507404 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.26013 | − | 16.0390i | −0.0252320 | − | 0.0437030i | 0.853134 | − | 0.521692i | \(-0.174699\pi\) |
−0.878366 | + | 0.477989i | \(0.841366\pi\) | |||||||
\(368\) | 49.5000 | − | 28.5788i | 0.134511 | − | 0.0776599i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 277.804 | 0.750821 | ||||||||
\(371\) | 51.5922 | − | 148.934i | 0.139062 | − | 0.401439i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −500.047 | − | 288.702i | −1.34061 | − | 0.774001i | −0.353712 | − | 0.935354i | \(-0.615081\pi\) |
−0.986897 | + | 0.161354i | \(0.948414\pi\) | |||||||
\(374\) | 55.5608 | − | 32.0780i | 0.148558 | − | 0.0857701i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −307.500 | − | 177.535i | −0.817819 | − | 0.472168i | ||||
\(377\) | −686.000 | −1.81963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −67.0000 | −0.176781 | −0.0883905 | − | 0.996086i | \(-0.528172\pi\) | ||||
−0.0883905 | + | 0.996086i | \(0.528172\pi\) | |||||||
\(380\) | −97.5000 | − | 56.2917i | −0.256579 | − | 0.148136i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −55.5608 | + | 32.0780i | −0.145447 | + | 0.0839739i | ||||
\(383\) | 273.500 | − | 473.716i | 0.714099 | − | 1.23686i | −0.249207 | − | 0.968450i | \(-0.580170\pi\) |
0.963306 | − | 0.268406i | \(-0.0864968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −490.000 | + | 424.352i | −1.27273 | + | 1.10221i | ||||
\(386\) | −222.243 | −0.575759 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −37.0405 | − | 64.1561i | −0.0954653 | − | 0.165351i | ||||
\(389\) | 240.763 | + | 417.014i | 0.618929 | + | 1.07202i | 0.989682 | + | 0.143285i | \(0.0457665\pi\) |
−0.370753 | + | 0.928732i | \(0.620900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3923i | − | 0.0265788i | ||||||
\(392\) | 420.000 | + | 60.6218i | 1.07143 | + | 0.154647i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 67.5000 | − | 116.913i | 0.171320 | − | 0.296735i | ||||
\(395\) | 260.000 | + | 450.333i | 0.658228 | + | 1.14008i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 74.0810 | − | 128.312i | 0.186602 | − | 0.323204i | −0.757513 | − | 0.652820i | \(-0.773586\pi\) |
0.944115 | + | 0.329616i | \(0.106919\pi\) | |||||||
\(398\) | 330.000 | 0.829146 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −275.000 | −0.687500 | ||||||||
\(401\) | 157.422 | − | 272.663i | 0.392574 | − | 0.679958i | −0.600214 | − | 0.799839i | \(-0.704918\pi\) |
0.992788 | + | 0.119881i | \(0.0382513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −611.169 | + | 352.858i | −1.51655 | + | 0.875579i | ||||
\(404\) | −166.682 | − | 96.2341i | −0.412580 | − | 0.238203i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 441.000 | − | 84.8705i | 1.08621 | − | 0.209041i | ||||
\(407\) | 594.093i | 1.45969i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 444.000 | − | 256.344i | 1.08557 | − | 0.626757i | 0.153180 | − | 0.988198i | \(-0.451049\pi\) |
0.932395 | + | 0.361442i | \(0.117715\pi\) | |||||||
\(410\) | 138.902 | + | 240.585i | 0.338785 | + | 0.586793i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −148.162 | −0.359617 | ||||||||
\(413\) | −147.000 | + | 424.352i | −0.355932 | + | 1.02749i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 80.0000 | − | 138.564i | 0.192771 | − | 0.333889i | ||||
\(416\) | 250.023 | − | 144.351i | 0.601018 | − | 0.346998i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −361.145 | + | 625.522i | −0.863983 | + | 1.49646i | ||||
\(419\) | 352.858i | 0.842144i | 0.907027 | + | 0.421072i | \(0.138346\pi\) | ||||
−0.907027 | + | 0.421072i | \(0.861654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 752.000 | 1.78622 | 0.893112 | − | 0.449835i | \(-0.148517\pi\) | ||||
0.893112 | + | 0.449835i | \(0.148517\pi\) | |||||||
\(422\) | −430.500 | − | 248.549i | −1.02014 | − | 0.588979i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 97.5000 | + | 168.875i | 0.229953 | + | 0.398290i | ||||
\(425\) | −25.0000 | + | 43.3013i | −0.0588235 | + | 0.101885i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 380.988 | − | 73.3212i | 0.892244 | − | 0.171712i | ||||
\(428\) | − | 110.851i | − | 0.258998i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 277.804 | + | 481.170i | 0.646056 | + | 1.11900i | ||||
\(431\) | 351.885 | + | 609.483i | 0.816438 | + | 1.41411i | 0.908290 | + | 0.418340i | \(0.137388\pi\) |
−0.0918522 | + | 0.995773i | \(0.529279\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −703.770 | −1.62533 | −0.812667 | − | 0.582728i | \(-0.801985\pi\) | ||||
−0.812667 | + | 0.582728i | \(0.801985\pi\) | |||||||
\(434\) | 349.239 | − | 302.450i | 0.804699 | − | 0.696889i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.0000 | + | 48.4974i | −0.0642202 | + | 0.111233i | ||||
\(437\) | 58.5000 | + | 101.325i | 0.133867 | + | 0.231865i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −132.000 | − | 76.2102i | −0.300683 | − | 0.173600i | 0.342066 | − | 0.939676i | \(-0.388873\pi\) |
−0.642750 | + | 0.766076i | \(0.722207\pi\) | |||||||
\(440\) | − | 801.951i | − | 1.82262i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 64.1561i | 0.145149i | ||||||||
\(443\) | 390.000 | + | 225.167i | 0.880361 | + | 0.508277i | 0.870777 | − | 0.491677i | \(-0.163616\pi\) |
0.00958369 | + | 0.999954i | \(0.496949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 277.804 | − | 160.390i | 0.624278 | − | 0.360427i | ||||
\(446\) | −111.122 | − | 64.1561i | −0.249151 | − | 0.143848i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −375.697 | + | 325.363i | −0.838609 | + | 0.726256i | ||||
\(449\) | −203.723 | −0.453726 | −0.226863 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226863 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −514.500 | + | 297.047i | −1.14080 | + | 0.658640i | ||||
\(452\) | 141.000 | − | 81.4064i | 0.311947 | − | 0.180103i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 232.095i | 0.511222i | ||||||||
\(455\) | −122.500 | − | 636.529i | −0.269231 | − | 1.39896i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 277.804 | + | 160.390i | 0.607886 | + | 0.350963i | 0.772138 | − | 0.635455i | \(-0.219188\pi\) |
−0.164252 | + | 0.986418i | \(0.552521\pi\) | |||||||
\(458\) | 27.0000 | + | 46.7654i | 0.0589520 | + | 0.102108i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.5000 | − | 12.9904i | −0.0489130 | − | 0.0282400i | ||||
\(461\) | 128.312i | 0.278334i | 0.990269 | + | 0.139167i | \(0.0444425\pi\) | ||||
−0.990269 | + | 0.139167i | \(0.955557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 224.546i | − | 0.484981i | −0.970154 | − | 0.242491i | \(-0.922036\pi\) | ||
0.970154 | − | 0.242491i | \(-0.0779643\pi\) | |||||||
\(464\) | −203.723 | + | 352.858i | −0.439058 | + | 0.760471i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −321.000 | − | 555.988i | −0.688841 | − | 1.19311i | ||||
\(467\) | 170.000 | − | 294.449i | 0.364026 | − | 0.630511i | −0.624594 | − | 0.780950i | \(-0.714735\pi\) |
0.988619 | + | 0.150439i | \(0.0480687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −147.000 | + | 424.352i | −0.313433 | + | 0.904803i | ||||
\(470\) | − | 355.070i | − | 0.755469i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −277.804 | − | 481.170i | −0.588568 | − | 1.01943i | ||||
\(473\) | −1029.00 | + | 594.093i | −2.17548 | + | 1.25601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 562.917i | − | 1.18509i | ||||||
\(476\) | 2.64575 | + | 13.7477i | 0.00555830 | + | 0.0288818i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 388.925 | + | 224.546i | 0.813652 | + | 0.469762i | ||||
\(479\) | −666.729 | + | 384.936i | −1.39192 | + | 0.803625i | −0.993528 | − | 0.113590i | \(-0.963765\pi\) |
−0.398392 | + | 0.917215i | \(0.630431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −514.500 | − | 297.047i | −1.06965 | − | 0.617561i | ||||
\(482\) | 27.0000 | 0.0560166 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 222.000 | 0.458678 | ||||||||
\(485\) | 185.203 | − | 320.780i | 0.381861 | − | 0.661403i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 388.925 | − | 224.546i | 0.798615 | − | 0.461081i | −0.0443717 | − | 0.999015i | \(-0.514129\pi\) |
0.842987 | + | 0.537935i | \(0.180795\pi\) | |||||||
\(488\) | −240.000 | + | 415.692i | −0.491803 | + | 0.851828i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 157.500 | + | 394.042i | 0.321429 | + | 0.804166i | ||||
\(491\) | −148.162 | −0.301756 | −0.150878 | − | 0.988552i | \(-0.548210\pi\) | ||||
−0.150878 | + | 0.988552i | \(0.548210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.0405 | + | 64.1561i | 0.0751329 | + | 0.130134i | ||||
\(494\) | −361.145 | − | 625.522i | −0.731063 | − | 1.26624i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 419.156i | 0.845073i | ||||||||
\(497\) | 392.000 | − | 339.482i | 0.788732 | − | 0.683062i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −109.000 | + | 188.794i | −0.218437 | + | 0.378344i | −0.954330 | − | 0.298754i | \(-0.903429\pi\) |
0.735893 | + | 0.677097i | \(0.236762\pi\) | |||||||
\(500\) | 62.5000 | + | 108.253i | 0.125000 | + | 0.216506i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 250.023 | − | 433.053i | 0.498055 | − | 0.862656i | ||||
\(503\) | 290.000 | 0.576541 | 0.288270 | − | 0.957549i | \(-0.406920\pi\) | ||||
0.288270 | + | 0.957549i | \(0.406920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 962.341i | − | 1.90563i | ||||||
\(506\) | −83.3412 | + | 144.351i | −0.164706 | + | 0.285279i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 83.3412 | − | 48.1170i | 0.164057 | − | 0.0947186i | ||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 245.000 | + | 84.8705i | 0.479452 | + | 0.166087i | ||||
\(512\) | − | 552.524i | − | 1.07915i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 84.0000 | − | 48.4974i | 0.163424 | − | 0.0943530i | ||||
\(515\) | −370.405 | − | 641.561i | −0.719233 | − | 1.24575i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 759.331 | 1.46872 | ||||||||
\(518\) | 367.500 | + | 127.306i | 0.709459 | + | 0.245764i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 694.510 | + | 400.975i | 1.33560 | + | 0.771106i | ||||
\(521\) | 305.584 | − | 176.429i | 0.586534 | − | 0.338636i | −0.177192 | − | 0.984176i | \(-0.556701\pi\) |
0.763726 | + | 0.645541i | \(0.223368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 185.203 | − | 320.780i | 0.354116 | − | 0.613347i | −0.632850 | − | 0.774274i | \(-0.718115\pi\) |
0.986966 | + | 0.160927i | \(0.0514485\pi\) | |||||||
\(524\) | 96.2341i | 0.183653i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 540.000 | 1.02662 | ||||||||
\(527\) | 66.0000 | + | 38.1051i | 0.125237 | + | 0.0723057i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −251.000 | − | 434.745i | −0.474480 | − | 0.821824i | ||||
\(530\) | −97.5000 | + | 168.875i | −0.183962 | + | 0.318632i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −103.184 | − | 119.147i | −0.193955 | − | 0.223960i | ||||
\(533\) | − | 594.093i | − | 1.11462i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 480.000 | − | 277.128i | 0.897196 | − | 0.517997i | ||||
\(536\) | −277.804 | − | 481.170i | −0.518291 | − | 0.897706i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −777.851 | −1.44582 | ||||||||
\(539\) | −842.672 | + | 336.819i | −1.56340 | + | 0.624897i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −235.000 | + | 407.032i | −0.434381 | + | 0.752370i | −0.997245 | − | 0.0741799i | \(-0.976366\pi\) |
0.562864 | + | 0.826549i | \(0.309699\pi\) | |||||||
\(542\) | 219.000 | + | 379.319i | 0.404059 | + | 0.699851i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.0000 | − | 15.5885i | −0.0496324 | − | 0.0286553i | ||||
\(545\) | −280.000 | −0.513761 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 128.312i | 0.234574i | 0.993098 | + | 0.117287i | \(0.0374198\pi\) | ||||
−0.993098 | + | 0.117287i | \(0.962580\pi\) | |||||||
\(548\) | −144.000 | − | 83.1384i | −0.262774 | − | 0.151712i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 694.510 | − | 400.975i | 1.26274 | − | 0.729046i | ||||
\(551\) | −722.290 | − | 417.014i | −1.31087 | − | 0.756832i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 137.579 | + | 714.882i | 0.248787 | + | 1.29273i | ||||
\(554\) | −333.365 | −0.601741 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −102.000 | + | 58.8897i | −0.183453 | + | 0.105917i | ||||
\(557\) | −223.500 | + | 129.038i | −0.401257 | + | 0.231666i | −0.687026 | − | 0.726633i | \(-0.741084\pi\) |
0.285769 | + | 0.958298i | \(0.407751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1188.19i | − | 2.12556i | ||||||
\(560\) | −363.791 | − | 126.021i | −0.649626 | − | 0.225037i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −361.145 | − | 208.507i | −0.642607 | − | 0.371009i | ||||
\(563\) | 113.000 | + | 195.722i | 0.200710 | + | 0.347641i | 0.948758 | − | 0.316005i | \(-0.102342\pi\) |
−0.748047 | + | 0.663646i | \(0.769008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 705.000 | + | 407.032i | 1.24779 | + | 0.720411i | ||||
\(566\) | − | 256.624i | − | 0.453400i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 641.561i | 1.12951i | ||||||||
\(569\) | 46.3006 | − | 80.1951i | 0.0813720 | − | 0.140940i | −0.822468 | − | 0.568812i | \(-0.807403\pi\) |
0.903839 | + | 0.427872i | \(0.140736\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 203.000 | + | 351.606i | 0.355517 | + | 0.615773i | 0.987206 | − | 0.159449i | \(-0.0509716\pi\) |
−0.631690 | + | 0.775221i | \(0.717638\pi\) | |||||||
\(572\) | −171.500 | + | 297.047i | −0.299825 | + | 0.519312i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 73.5000 | + | 381.917i | 0.128049 | + | 0.665361i | ||||
\(575\) | − | 129.904i | − | 0.225920i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 518.567 | + | 898.185i | 0.898730 | + | 1.55665i | 0.829119 | + | 0.559072i | \(0.188842\pi\) |
0.0696109 | + | 0.997574i | \(0.477824\pi\) | |||||||
\(578\) | −427.500 | + | 246.817i | −0.739619 | + | 0.427019i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 185.203 | 0.319315 | ||||||||
\(581\) | 169.328 | − | 146.642i | 0.291442 | − | 0.252397i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −361.145 | − | 208.507i | −0.619460 | − | 0.357645i | ||||
\(584\) | −277.804 | + | 160.390i | −0.475692 | + | 0.274641i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −682.500 | − | 394.042i | −1.16468 | − | 0.672426i | ||||
\(587\) | −556.000 | −0.947189 | −0.473595 | − | 0.880743i | \(-0.657044\pi\) | ||||
−0.473595 | + | 0.880743i | \(0.657044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −858.000 | −1.45671 | ||||||||
\(590\) | 277.804 | − | 481.170i | 0.470854 | − | 0.815543i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −305.584 | + | 176.429i | −0.516190 | + | 0.298022i | ||||
\(593\) | 446.000 | − | 772.495i | 0.752108 | − | 1.30269i | −0.194691 | − | 0.980865i | \(-0.562371\pi\) |
0.946799 | − | 0.321825i | \(-0.104296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −52.9150 | + | 45.8258i | −0.0889328 | + | 0.0770181i | ||||
\(596\) | −37.0405 | −0.0621485 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −83.3412 | − | 144.351i | −0.139366 | − | 0.241390i | ||||
\(599\) | 74.0810 | + | 128.312i | 0.123675 | + | 0.214211i | 0.921214 | − | 0.389056i | \(-0.127199\pi\) |
−0.797540 | + | 0.603267i | \(0.793865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 658.179i | 1.09514i | 0.836760 | + | 0.547570i | \(0.184447\pi\) | ||||
−0.836760 | + | 0.547570i | \(0.815553\pi\) | |||||||
\(602\) | 147.000 | + | 763.834i | 0.244186 | + | 1.26883i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −85.0000 | + | 147.224i | −0.140728 | + | 0.243749i | ||||
\(605\) | 555.000 | + | 961.288i | 0.917355 | + | 1.58891i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −342.625 | + | 593.444i | −0.564456 | + | 0.977666i | 0.432644 | + | 0.901565i | \(0.357581\pi\) |
−0.997100 | + | 0.0761017i | \(0.975753\pi\) | |||||||
\(608\) | 351.000 | 0.577303 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −480.000 | −0.786885 | ||||||||
\(611\) | −379.665 | + | 657.600i | −0.621383 | + | 1.07627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −694.510 | + | 400.975i | −1.13297 | + | 0.654120i | −0.944680 | − | 0.327994i | \(-0.893627\pi\) |
−0.188289 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(614\) | −111.122 | − | 64.1561i | −0.180980 | − | 0.104489i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 367.500 | − | 1060.88i | 0.596591 | − | 1.72221i | ||||
\(617\) | − | 263.272i | − | 0.426696i | −0.976976 | − | 0.213348i | \(-0.931563\pi\) | ||
0.976976 | − | 0.213348i | \(-0.0684369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −580.500 | + | 335.152i | −0.937803 | + | 0.541441i | −0.889271 | − | 0.457381i | \(-0.848788\pi\) |
−0.0485320 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(620\) | 165.000 | − | 95.2628i | 0.266129 | − | 0.153650i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 777.851 | 1.25056 | ||||||||
\(623\) | 441.000 | − | 84.8705i | 0.707865 | − | 0.136229i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.500000 | + | 0.866025i | ||||
\(626\) | 444.486 | − | 256.624i | 0.710042 | − | 0.409943i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.26013 | + | 16.0390i | −0.0147454 | + | 0.0255398i | ||||
\(629\) | 64.1561i | 0.101997i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 662.000 | 1.04913 | 0.524564 | − | 0.851371i | \(-0.324228\pi\) | ||||
0.524564 | + | 0.851371i | \(0.324228\pi\) | |||||||
\(632\) | −780.000 | − | 450.333i | −1.23418 | − | 0.712553i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −174.000 | − | 301.377i | −0.274448 | − | 0.475358i | ||||
\(635\) | 416.706 | + | 240.585i | 0.656230 | + | 0.378874i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 129.642 | − | 898.185i | 0.203519 | − | 1.41002i | ||||
\(638\) | − | 1188.19i | − | 1.86236i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 262.500 | − | 151.554i | 0.410156 | − | 0.236804i | ||||
\(641\) | −453.746 | − | 785.912i | −0.707873 | − | 1.22607i | −0.965645 | − | 0.259866i | \(-0.916322\pi\) |
0.257772 | − | 0.966206i | \(-0.417012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −481.527 | −0.748875 | −0.374438 | − | 0.927252i | \(-0.622164\pi\) | ||||
−0.374438 | + | 0.927252i | \(0.622164\pi\) | |||||||
\(644\) | −23.8118 | − | 27.4955i | −0.0369748 | − | 0.0426948i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.0000 | + | 67.5500i | −0.0603715 | + | 0.104567i | ||||
\(647\) | 504.500 | + | 873.820i | 0.779753 | + | 1.35057i | 0.932084 | + | 0.362242i | \(0.117989\pi\) |
−0.152331 | + | 0.988329i | \(0.548678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1029.00 | + | 594.093i | 1.58552 | + | 0.915398i | ||||
\(650\) | 801.951i | 1.23377i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 64.1561i | − | 0.0983989i | ||||||
\(653\) | −211.500 | − | 122.110i | −0.323890 | − | 0.186998i | 0.329235 | − | 0.944248i | \(-0.393209\pi\) |
−0.653125 | + | 0.757250i | \(0.726542\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −416.706 | + | 240.585i | −0.636192 | + | 0.367306i | ||||
\(656\) | −305.584 | − | 176.429i | −0.465830 | − | 0.268947i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 162.714 | − | 469.714i | 0.247285 | − | 0.713851i | ||||
\(659\) | −592.648 | −0.899315 | −0.449657 | − | 0.893201i | \(-0.648454\pi\) | ||||
−0.449657 | + | 0.893201i | \(0.648454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 516.000 | − | 297.913i | 0.780635 | − | 0.450700i | −0.0560200 | − | 0.998430i | \(-0.517841\pi\) |
0.836655 | + | 0.547730i | \(0.184508\pi\) | |||||||
\(662\) | −262.500 | + | 151.554i | −0.396526 | + | 0.228934i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 277.128i | 0.417362i | ||||||||
\(665\) | 257.961 | − | 744.669i | 0.387911 | − | 1.11980i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −166.682 | − | 96.2341i | −0.249899 | − | 0.144279i | ||||
\(668\) | −44.5000 | − | 77.0763i | −0.0666168 | − | 0.115384i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 277.804 | − | 481.170i | 0.414633 | − | 0.718165i | ||||
\(671\) | − | 1026.50i | − | 1.52980i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 513.248i | 0.762628i | 0.924446 | + | 0.381314i | \(0.124528\pi\) | ||||
−0.924446 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(674\) | 55.5608 | − | 96.2341i | 0.0824344 | − | 0.142781i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −87.0000 | − | 150.688i | −0.128698 | − | 0.222912i | ||||
\(677\) | 339.500 | − | 588.031i | 0.501477 | − | 0.868584i | −0.498521 | − | 0.866877i | \(-0.666123\pi\) |
0.999999 | − | 0.00170645i | \(-0.000543182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 392.000 | − | 339.482i | 0.577320 | − | 0.499973i | ||||
\(680\) | − | 86.6025i | − | 0.127357i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −611.169 | − | 1058.57i | −0.896142 | − | 1.55216i | ||||
\(683\) | −1101.00 | + | 635.663i | −1.61201 | + | 0.930692i | −0.623101 | + | 0.782141i | \(0.714127\pi\) |
−0.988905 | + | 0.148551i | \(0.952539\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 831.384i | − | 1.21370i | ||||||
\(686\) | 27.7804 | + | 593.444i | 0.0404962 | + | 0.865078i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −611.169 | − | 352.858i | −0.888326 | − | 0.512875i | ||||
\(689\) | 361.145 | − | 208.507i | 0.524158 | − | 0.302623i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | + | 6.92820i | 0.0173661 | + | 0.0100263i | 0.508658 | − | 0.860969i | \(-0.330142\pi\) |
−0.491292 | + | 0.870995i | \(0.663475\pi\) | |||||||
\(692\) | −97.0000 | −0.140173 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −150.000 | −0.216138 | ||||||||
\(695\) | −510.000 | − | 294.449i | −0.733813 | − | 0.423667i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.5608 | + | 32.0780i | −0.0797142 | + | 0.0460230i | ||||
\(698\) | −6.00000 | + | 10.3923i | −0.00859599 | + | 0.0148887i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 33.0719 | + | 171.847i | 0.0472456 | + | 0.245495i | ||||
\(701\) | 740.810 | 1.05679 | 0.528395 | − | 0.848998i | \(-0.322794\pi\) | ||||
0.528395 | + | 0.848998i | \(0.322794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −361.145 | − | 625.522i | −0.513720 | − | 0.889789i | ||||
\(704\) | 657.469 | + | 1138.77i | 0.933905 | + | 1.61757i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 897.202i | 1.27082i | ||||||||
\(707\) | 441.000 | − | 1273.06i | 0.623762 | − | 1.80065i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −73.0000 | + | 126.440i | −0.102962 | + | 0.178335i | −0.912904 | − | 0.408175i | \(-0.866165\pi\) |
0.809942 | + | 0.586510i | \(0.199499\pi\) | |||||||
\(710\) | −555.608 | + | 320.780i | −0.782546 | + | 0.451803i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −277.804 | + | 481.170i | −0.390174 | + | 0.675801i | ||||
\(713\) | −198.000 | −0.277700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1715.00 | −2.39860 | ||||||||
\(716\) | −64.8209 | + | 112.273i | −0.0905320 | + | 0.156806i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 277.804 | − | 160.390i | 0.386913 | − | 0.223385i | ||||
\(719\) | 555.608 | + | 320.780i | 0.772751 | + | 0.446148i | 0.833855 | − | 0.551984i | \(-0.186129\pi\) |
−0.0611043 | + | 0.998131i | \(0.519462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −196.000 | − | 1018.45i | −0.271845 | − | 1.41255i | ||||
\(722\) | − | 252.879i | − | 0.350249i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 90.0000 | − | 51.9615i | 0.124309 | − | 0.0717701i | ||||
\(725\) | 463.006 | + | 801.951i | 0.638630 | + | 1.10614i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 240.763 | 0.331174 | 0.165587 | − | 0.986195i | \(-0.447048\pi\) | ||||
0.165587 | + | 0.986195i | \(0.447048\pi\) | |||||||
\(728\) | 735.000 | + | 848.705i | 1.00962 | + | 1.16580i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −277.804 | − | 160.390i | −0.380553 | − | 0.219713i | ||||
\(731\) | −111.122 | + | 64.1561i | −0.152013 | + | 0.0877648i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −342.625 | + | 593.444i | −0.467428 | + | 0.809609i | −0.999307 | − | 0.0372109i | \(-0.988153\pi\) |
0.531879 | + | 0.846820i | \(0.321486\pi\) | |||||||
\(734\) | 32.0780i | 0.0437030i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 81.0000 | 0.110054 | ||||||||
\(737\) | 1029.00 | + | 594.093i | 1.39620 | + | 0.806097i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 126.500 | + | 219.104i | 0.171177 | + | 0.296488i | 0.938832 | − | 0.344376i | \(-0.111910\pi\) |
−0.767654 | + | 0.640864i | \(0.778576\pi\) | |||||||
\(740\) | 138.902 | + | 80.1951i | 0.187705 | + | 0.108372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −206.369 | + | 178.720i | −0.278125 | + | 0.240863i | ||||
\(743\) | 718.801i | 0.967431i | 0.875225 | + | 0.483715i | \(0.160713\pi\) | ||||
−0.875225 | + | 0.483715i | \(0.839287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −92.6013 | − | 160.390i | −0.124297 | − | 0.215289i | ||||
\(746\) | 500.047 | + | 866.107i | 0.670304 | + | 1.16100i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 37.0405 | 0.0495194 | ||||||||
\(749\) | 761.976 | − | 146.642i | 1.01732 | − | 0.195784i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −310.000 | + | 536.936i | −0.412783 | + | 0.714961i | −0.995193 | − | 0.0979342i | \(-0.968777\pi\) |
0.582410 | + | 0.812895i | \(0.302110\pi\) | |||||||
\(752\) | 225.500 | + | 390.577i | 0.299867 | + | 0.519385i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1029.00 | + | 594.093i | 1.36472 | + | 0.787922i | ||||
\(755\) | −850.000 | −1.12583 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 962.341i | 1.27126i | 0.771995 | + | 0.635628i | \(0.219259\pi\) | ||||
−0.771995 | + | 0.635628i | \(0.780741\pi\) | |||||||
\(758\) | 100.500 | + | 58.0237i | 0.132586 | + | 0.0765484i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 487.500 | + | 844.375i | 0.641447 | + | 1.11102i | ||||
\(761\) | −416.706 | − | 240.585i | −0.547577 | − | 0.316144i | 0.200567 | − | 0.979680i | \(-0.435721\pi\) |
−0.748144 | + | 0.663536i | \(0.769055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −370.405 | − | 128.312i | −0.485459 | − | 0.168168i | ||||
\(764\) | −37.0405 | −0.0484824 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −820.500 | + | 473.716i | −1.07115 | + | 0.618428i | ||||
\(767\) | −1029.00 | + | 594.093i | −1.34159 | + | 0.774568i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 299.645i | − | 0.389655i | −0.980838 | − | 0.194828i | \(-0.937585\pi\) | ||
0.980838 | − | 0.194828i | \(-0.0624147\pi\) | |||||||
\(770\) | 1102.50 | − | 212.176i | 1.43182 | − | 0.275554i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −111.122 | − | 64.1561i | −0.143940 | − | 0.0831037i | ||||
\(773\) | 219.500 | + | 380.185i | 0.283959 | + | 0.491831i | 0.972356 | − | 0.233503i | \(-0.0750188\pi\) |
−0.688398 | + | 0.725334i | \(0.741686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 825.000 | + | 476.314i | 1.06452 | + | 0.614599i | ||||
\(776\) | 641.561i | 0.826753i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 834.029i | − | 1.07202i | ||||||
\(779\) | 361.145 | − | 625.522i | 0.463601 | − | 0.802980i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −686.000 | − | 1188.19i | −0.878361 | − | 1.52137i | ||||
\(782\) | −9.00000 | + | 15.5885i | −0.0115090 | + | 0.0199341i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −423.500 | − | 333.420i | −0.540179 | − | 0.425280i | ||||
\(785\) | −92.6013 | −0.117963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 407.446 | + | 705.717i | 0.517720 | + | 0.896717i | 0.999788 | + | 0.0205837i | \(0.00655246\pi\) |
−0.482068 | + | 0.876134i | \(0.660114\pi\) | |||||||
\(788\) | 67.5000 | − | 38.9711i | 0.0856599 | − | 0.0494558i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 900.666i | − | 1.14008i | ||||||
\(791\) | 746.102 | + | 861.524i | 0.943239 | + | 1.08916i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 888.972 | + | 513.248i | 1.12102 | + | 0.647224i | ||||
\(794\) | −222.243 | + | 128.312i | −0.279903 | + | 0.161602i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 165.000 | + | 95.2628i | 0.207286 | + | 0.119677i | ||||
\(797\) | −46.0000 | −0.0577164 | −0.0288582 | − | 0.999584i | \(-0.509187\pi\) | ||||
−0.0288582 | + | 0.999584i | \(0.509187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.0000 | 0.102628 | ||||||||
\(800\) | −337.500 | − | 194.856i | −0.421875 | − | 0.243570i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −472.267 | + | 272.663i | −0.588861 | + | 0.339979i | ||||
\(803\) | 343.000 | − | 594.093i | 0.427148 | − | 0.739842i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 59.5294 | − | 171.847i | 0.0739496 | − | 0.213474i | ||||
\(806\) | 1222.34 | 1.51655 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 833.412 | + | 1443.51i | 1.03145 | + | 1.78652i | ||||
\(809\) | −398.186 | − | 689.678i | −0.492195 | − | 0.852506i | 0.507765 | − | 0.861496i | \(-0.330472\pi\) |
−0.999960 | + | 0.00898937i | \(0.997139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1148.35i | 1.41597i | 0.706229 | + | 0.707984i | \(0.250395\pi\) | ||||
−0.706229 | + | 0.707984i | \(0.749605\pi\) | |||||||
\(812\) | 245.000 | + | 84.8705i | 0.301724 | + | 0.104520i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 514.500 | − | 891.140i | 0.632064 | − | 1.09477i | ||||
\(815\) | 277.804 | − | 160.390i | 0.340864 | − | 0.196798i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 722.290 | − | 1251.04i | 0.884076 | − | 1.53126i | ||||
\(818\) | −888.000 | −1.08557 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 160.390i | 0.195598i | ||||||||
\(821\) | −203.723 | + | 352.858i | −0.248140 | + | 0.429791i | −0.963010 | − | 0.269467i | \(-0.913153\pi\) |
0.714870 | + | 0.699258i | \(0.246486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 944.533 | − | 545.327i | 1.14767 | − | 0.662608i | 0.199352 | − | 0.979928i | \(-0.436116\pi\) |
0.948319 | + | 0.317320i | \(0.102783\pi\) | |||||||
\(824\) | 1111.22 | + | 641.561i | 1.34856 | + | 0.778593i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 588.000 | − | 509.223i | 0.711864 | − | 0.616493i | ||||
\(827\) | − | 1423.75i | − | 1.72158i | −0.508961 | − | 0.860789i | \(-0.669970\pi\) | ||
0.508961 | − | 0.860789i | \(-0.330030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −201.000 | + | 116.047i | −0.242461 | + | 0.139985i | −0.616307 | − | 0.787506i | \(-0.711372\pi\) |
0.373846 | + | 0.927491i | \(0.378039\pi\) | |||||||
\(830\) | −240.000 | + | 138.564i | −0.289157 | + | 0.166945i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1314.94 | −1.58045 | ||||||||
\(833\) | −91.0000 | + | 36.3731i | −0.109244 | + | 0.0436651i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 222.500 | − | 385.381i | 0.266467 | − | 0.461534i | ||||
\(836\) | −361.145 | + | 208.507i | −0.431992 | + | 0.249411i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 305.584 | − | 529.287i | 0.364659 | − | 0.631608i | ||||
\(839\) | − | 641.561i | − | 0.764673i | −0.924023 | − | 0.382336i | \(-0.875120\pi\) | ||
0.924023 | − | 0.382336i | \(-0.124880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 531.000 | 0.631391 | ||||||||
\(842\) | −1128.00 | − | 651.251i | −1.33967 | − | 0.773457i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −143.500 | − | 248.549i | −0.170024 | − | 0.294490i | ||||
\(845\) | 435.000 | − | 753.442i | 0.514793 | − | 0.891647i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 293.678 | + | 1526.00i | 0.346728 | + | 1.80165i | ||||
\(848\) | − | 247.683i | − | 0.292079i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 75.0000 | − | 43.3013i | 0.0882353 | − | 0.0509427i | ||||
\(851\) | −83.3412 | − | 144.351i | −0.0979332 | − | 0.169625i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1463.10 | 1.71524 | 0.857620 | − | 0.514283i | \(-0.171942\pi\) | ||||
0.857620 | + | 0.514283i | \(0.171942\pi\) | |||||||
\(854\) | −634.980 | − | 219.964i | −0.743537 | − | 0.257569i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −480.000 | + | 831.384i | −0.560748 | + | 0.971243i | ||||
\(857\) | 365.000 | + | 632.199i | 0.425904 | + | 0.737688i | 0.996504 | − | 0.0835401i | \(-0.0266227\pi\) |
−0.570600 | + | 0.821228i | \(0.693289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 594.000 | + | 342.946i | 0.691502 | + | 0.399239i | 0.804174 | − | 0.594393i | \(-0.202608\pi\) |
−0.112673 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(860\) | 320.780i | 0.373000i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1218.97i | − | 1.41411i | ||||||
\(863\) | 208.500 | + | 120.378i | 0.241599 | + | 0.139487i | 0.615911 | − | 0.787815i | \(-0.288788\pi\) |
−0.374312 | + | 0.927303i | \(0.622121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −242.500 | − | 420.022i | −0.280347 | − | 0.485575i | ||||
\(866\) | 1055.65 | + | 609.483i | 1.21900 | + | 0.703790i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 261.929 | − | 50.4083i | 0.301762 | − | 0.0580741i | ||||
\(869\) | 1926.11 | 2.21646 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1029.00 | + | 594.093i | −1.18140 | + | 0.682082i | ||||
\(872\) | 420.000 | − | 242.487i | 0.481651 | − | 0.278082i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 202.650i | − | 0.231865i | ||||||
\(875\) | −661.438 | + | 572.822i | −0.755929 | + | 0.654654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 916.753 | + | 529.287i | 1.04533 | + | 0.603521i | 0.921338 | − | 0.388763i | \(-0.127097\pi\) |
0.123990 | + | 0.992283i | \(0.460431\pi\) | |||||||
\(878\) | 132.000 | + | 228.631i | 0.150342 | + | 0.260399i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −509.307 | + | 882.146i | −0.578758 | + | 1.00244i | ||||
\(881\) | 866.107i | 0.983095i | 0.870851 | + | 0.491548i | \(0.163569\pi\) | ||||
−0.870851 | + | 0.491548i | \(0.836431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 962.341i | − | 1.08985i | −0.838484 | − | 0.544927i | \(-0.816557\pi\) | ||
0.838484 | − | 0.544927i | \(-0.183443\pi\) | |||||||
\(884\) | −18.5203 | + | 32.0780i | −0.0209505 | + | 0.0362874i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −390.000 | − | 675.500i | −0.440181 | − | 0.762415i | ||||
\(887\) | −535.000 | + | 926.647i | −0.603157 | + | 1.04470i | 0.389183 | + | 0.921160i | \(0.372757\pi\) |
−0.992340 | + | 0.123538i | \(0.960576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 441.000 | + | 509.223i | 0.496063 | + | 0.572804i | ||||
\(890\) | −555.608 | −0.624278 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.0405 | − | 64.1561i | −0.0415252 | − | 0.0719238i | ||||
\(893\) | −799.500 | + | 461.592i | −0.895297 | + | 0.516900i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −648.209 | −0.724256 | ||||||||
\(896\) | 416.706 | − | 80.1951i | 0.465073 | − | 0.0895034i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 305.584 | + | 176.429i | 0.340294 | + | 0.196469i | ||||
\(899\) | 1222.34 | − | 705.717i | 1.35966 | − | 0.785002i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.0000 | − | 22.5167i | −0.0432852 | − | 0.0249907i | ||||
\(902\) | 1029.00 | 1.14080 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1410.00 | −1.55973 | ||||||||
\(905\) | 450.000 | + | 259.808i | 0.497238 | + | 0.287080i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1166.78 | − | 673.639i | 1.28641 | − | 0.742711i | 0.308400 | − | 0.951257i | \(-0.400206\pi\) |
0.978013 | + | 0.208546i | \(0.0668731\pi\) | |||||||
\(908\) | −67.0000 | + | 116.047i | −0.0737885 | + | 0.127806i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −367.500 | + | 1060.88i | −0.403846 | + | 1.16580i | ||||
\(911\) | −1592.74 | −1.74834 | −0.874172 | − | 0.485616i | \(-0.838596\pi\) | ||||
−0.874172 | + | 0.485616i | \(0.838596\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −296.324 | − | 513.248i | −0.324561 | − | 0.562156i | ||||
\(914\) | −277.804 | − | 481.170i | −0.303943 | − | 0.526445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.1769i | 0.0340359i | ||||||||
\(917\) | −661.500 | + | 127.306i | −0.721374 | + | 0.138828i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −175.000 | + | 303.109i | −0.190424 | + | 0.329825i | −0.945391 | − | 0.325939i | \(-0.894320\pi\) |
0.754967 | + | 0.655763i | \(0.227653\pi\) | |||||||
\(920\) | 112.500 | + | 194.856i | 0.122283 | + | 0.211800i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 111.122 | − | 192.468i | 0.120522 | − | 0.208751i | ||||
\(923\) | 1372.00 | 1.48646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 801.951i | 0.866974i | ||||||||
\(926\) | −194.463 | + | 336.819i | −0.210003 | + | 0.363736i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −500.047 | + | 288.702i | −0.538844 | + | 0.311102i | ||||
\(929\) | −1305.68 | − | 753.834i | −1.40547 | − | 0.811446i | −0.410520 | − | 0.911852i | \(-0.634653\pi\) |
−0.994947 | + | 0.100405i | \(0.967986\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 682.500 | − | 866.891i | 0.733083 | − | 0.931140i | ||||
\(932\) | − | 370.659i | − | 0.397703i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −510.000 | + | 294.449i | −0.546039 | + | 0.315256i | ||||
\(935\) | 92.6013 | + | 160.390i | 0.0990388 | + | 0.171540i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1592.74 | −1.69983 | −0.849916 | − | 0.526918i | \(-0.823347\pi\) | ||||
−0.849916 | + | 0.526918i | \(0.823347\pi\) | |||||||
\(938\) | 588.000 | − | 509.223i | 0.626866 | − | 0.542882i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 102.500 | − | 177.535i | 0.109043 | − | 0.188867i | ||||
\(941\) | 611.169 | − | 352.858i | 0.649488 | − | 0.374982i | −0.138772 | − | 0.990324i | \(-0.544315\pi\) |
0.788260 | + | 0.615342i | \(0.210982\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 83.3412 | − | 144.351i | 0.0883788 | − | 0.153076i | ||||
\(944\) | 705.717i | 0.747581i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2058.00 | 2.17548 | ||||||||
\(947\) | −51.0000 | − | 29.4449i | −0.0538543 | − | 0.0310928i | 0.472831 | − | 0.881153i | \(-0.343232\pi\) |
−0.526685 | + | 0.850060i | \(0.676565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 343.000 | + | 594.093i | 0.361433 | + | 0.626020i | ||||
\(950\) | −487.500 | + | 844.375i | −0.513158 | + | 0.888816i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39.6863 | − | 114.564i | 0.0416873 | − | 0.120341i | ||||
\(953\) | − | 696.284i | − | 0.730624i | −0.930885 | − | 0.365312i | \(-0.880962\pi\) | ||
0.930885 | − | 0.365312i | \(-0.119038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −92.6013 | − | 160.390i | −0.0969647 | − | 0.167948i | ||||
\(956\) | 129.642 | + | 224.546i | 0.135609 | + | 0.234881i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1333.46 | 1.39192 | ||||||||
\(959\) | 380.988 | − | 1099.82i | 0.397277 | − | 1.14684i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 245.500 | − | 425.218i | 0.255463 | − | 0.442475i | ||||
\(962\) | 514.500 | + | 891.140i | 0.534823 | + | 0.926341i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.5000 | + | 7.79423i | 0.0140041 | + | 0.00808530i | ||||
\(965\) | − | 641.561i | − | 0.664830i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 320.780i | − | 0.331727i | −0.986149 | − | 0.165864i | \(-0.946959\pi\) | ||
0.986149 | − | 0.165864i | \(-0.0530412\pi\) | |||||||
\(968\) | −1665.00 | − | 961.288i | −1.72004 | − | 0.993066i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −555.608 | + | 320.780i | −0.572792 | + | 0.330701i | ||||
\(971\) | −194.463 | − | 112.273i | −0.200271 | − | 0.115626i | 0.396511 | − | 0.918030i | \(-0.370221\pi\) |
−0.596782 | + | 0.802404i | \(0.703554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −539.733 | − | 623.230i | −0.554710 | − | 0.640524i | ||||
\(974\) | −777.851 | −0.798615 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 528.000 | − | 304.841i | 0.540984 | − | 0.312337i | ||||
\(977\) | −789.000 | + | 455.529i | −0.807574 | + | 0.466253i | −0.846113 | − | 0.533004i | \(-0.821063\pi\) |
0.0385386 | + | 0.999257i | \(0.487730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1188.19i | − | 1.21367i | ||||||
\(980\) | −35.0000 | + | 242.487i | −0.0357143 | + | 0.247436i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 222.243 | + | 128.312i | 0.226317 | + | 0.130664i | ||||
\(983\) | −143.500 | − | 248.549i | −0.145982 | − | 0.252848i | 0.783757 | − | 0.621067i | \(-0.213301\pi\) |
−0.929739 | + | 0.368220i | \(0.879967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 337.500 | + | 194.856i | 0.342640 | + | 0.197823i | ||||
\(986\) | − | 128.312i | − | 0.130134i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 417.014i | − | 0.422079i | ||||||
\(989\) | 166.682 | − | 288.702i | 0.168536 | − | 0.291913i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −550.000 | − | 952.628i | −0.554995 | − | 0.961279i | −0.997904 | − | 0.0647129i | \(-0.979387\pi\) |
0.442909 | − | 0.896567i | \(-0.353946\pi\) | |||||||
\(992\) | −297.000 | + | 514.419i | −0.299395 | + | 0.518568i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −882.000 | + | 169.741i | −0.887324 | + | 0.170766i | ||||
\(995\) | 952.628i | 0.957415i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −370.405 | − | 641.561i | −0.371520 | − | 0.643491i | 0.618280 | − | 0.785958i | \(-0.287830\pi\) |
−0.989800 | + | 0.142467i | \(0.954497\pi\) | |||||||
\(998\) | 327.000 | − | 188.794i | 0.327655 | − | 0.189172i | ||||
\(999\) | 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 | 315.3.bi.a.19.2 | yes | 4 | |
3.2 | odd | 2 | 315.3.bi.b.19.2 | yes | 4 | ||
5.4 | even | 2 | 315.3.bi.b.19.1 | yes | 4 | ||
7.3 | odd | 6 | 315.3.bi.b.199.1 | yes | 4 | ||
15.14 | odd | 2 | inner | 315.3.bi.a.19.1 | ✓ | 4 | |
21.17 | even | 6 | inner | 315.3.bi.a.199.1 | yes | 4 | |
35.24 | odd | 6 | inner | 315.3.bi.a.199.2 | yes | 4 | |
105.59 | even | 6 | 315.3.bi.b.199.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.3.bi.a.19.1 | ✓ | 4 | 15.14 | odd | 2 | inner | |
315.3.bi.a.19.2 | yes | 4 | 1.1 | even | 1 | trivial | |
315.3.bi.a.199.1 | yes | 4 | 21.17 | even | 6 | inner | |
315.3.bi.a.199.2 | yes | 4 | 35.24 | odd | 6 | inner | |
315.3.bi.b.19.1 | yes | 4 | 5.4 | even | 2 | ||
315.3.bi.b.19.2 | yes | 4 | 3.2 | odd | 2 | ||
315.3.bi.b.199.1 | yes | 4 | 7.3 | odd | 6 | ||
315.3.bi.b.199.2 | yes | 4 | 105.59 | even | 6 |