Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,3,Mod(129,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.s (of order \(6\), degree \(2\), not 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: | \(21.3624527258\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 7^{4} \) |
Twist minimal: | no (minimal twist has level 196) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.4 | ||
Root | \(0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.129 |
Dual form | 784.3.s.g.705.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 3.86324 | + | 2.23044i | 1.28775 | + | 0.743481i | 0.978252 | − | 0.207420i | \(-0.0665068\pi\) |
0.309495 | + | 0.950901i | \(0.399840\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.33820 | − | 4.23671i | 1.46764 | − | 0.847343i | 0.468297 | − | 0.883571i | \(-0.344868\pi\) |
0.999344 | + | 0.0362281i | \(0.0115343\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.44975 | + | 9.43924i | 0.605527 | + | 1.04880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.94975 | − | 3.37706i | 0.177250 | − | 0.307006i | −0.763688 | − | 0.645586i | \(-0.776613\pi\) |
0.940938 | + | 0.338580i | \(0.109947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 19.1886i | − | 1.47604i | −0.674777 | − | 0.738022i | \(-0.735760\pi\) | ||
0.674777 | − | 0.738022i | \(-0.264240\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37.7990 | 2.51993 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.5897 | − | 6.69133i | −0.681748 | − | 0.393607i | 0.118765 | − | 0.992922i | \(-0.462106\pi\) |
−0.800513 | + | 0.599315i | \(0.795440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.80462 | − | 3.35130i | 0.305506 | − | 0.176384i | −0.339408 | − | 0.940639i | \(-0.610227\pi\) |
0.644914 | + | 0.764255i | \(0.276893\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.0000 | + | 22.5167i | 0.565217 | + | 0.978985i | 0.997029 | + | 0.0770216i | \(0.0245410\pi\) |
−0.431812 | + | 0.901964i | \(0.642126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.3995 | − | 40.5291i | 0.935980 | − | 1.62116i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.47343i | 0.313831i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.7990 | −0.406862 | −0.203431 | − | 0.979089i | \(-0.565209\pi\) | ||||
−0.203431 | + | 0.979089i | \(0.565209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.6825 | + | 18.2919i | 1.02202 | + | 0.590061i | 0.914687 | − | 0.404163i | \(-0.132437\pi\) |
0.107328 | + | 0.994224i | \(0.465770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.0647 | − | 8.69760i | 0.456506 | − | 0.263564i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.0000 | + | 27.7128i | 0.432432 | + | 0.748995i | 0.997082 | − | 0.0763357i | \(-0.0243221\pi\) |
−0.564650 | + | 0.825331i | \(0.690989\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 42.7990 | − | 74.1300i | 1.09741 | − | 1.90077i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.9594i | 0.511205i | 0.966782 | + | 0.255602i | \(0.0822738\pi\) | ||||
−0.966782 | + | 0.255602i | \(0.917726\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −79.2965 | −1.84410 | −0.922052 | − | 0.387066i | \(-0.873488\pi\) | ||||
−0.922052 | + | 0.387066i | \(0.873488\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 79.9827 | + | 46.1780i | 1.77739 | + | 1.02618i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3858 | + | 7.15093i | −0.263527 | + | 0.152148i | −0.625943 | − | 0.779869i | \(-0.715286\pi\) |
0.362415 | + | 0.932017i | \(0.381952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −29.8492 | − | 51.7004i | −0.585279 | − | 1.01373i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.89949 | − | 11.9503i | 0.130179 | − | 0.225477i | −0.793566 | − | 0.608484i | \(-0.791778\pi\) |
0.923746 | + | 0.383007i | \(0.125111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 33.0421i | − | 0.600765i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 29.8995 | 0.524553 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.31869 | − | 4.22545i | −0.124046 | − | 0.0716178i | 0.436693 | − | 0.899610i | \(-0.356150\pi\) |
−0.560739 | + | 0.827993i | \(0.689483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.4114 | + | 15.8260i | −0.449368 | + | 0.259443i | −0.707563 | − | 0.706650i | \(-0.750206\pi\) |
0.258195 | + | 0.966093i | \(0.416872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −81.2965 | − | 140.810i | −1.25071 | − | 2.16630i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.6985 | + | 27.1906i | −0.234306 | + | 0.405829i | −0.959071 | − | 0.283167i | \(-0.908615\pi\) |
0.724765 | + | 0.688996i | \(0.241948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 115.983i | 1.68091i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −95.5980 | −1.34645 | −0.673225 | − | 0.739438i | \(-0.735092\pi\) | ||||
−0.673225 | + | 0.739438i | \(0.735092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.8607 | + | 9.15721i | 0.217270 | + | 0.125441i | 0.604686 | − | 0.796464i | \(-0.293299\pi\) |
−0.387415 | + | 0.921905i | \(0.626632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 180.796 | − | 104.382i | 2.41061 | − | 1.39177i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39.8995 | + | 69.1080i | 0.505057 | + | 0.874784i | 0.999983 | + | 0.00584908i | \(0.00186183\pi\) |
−0.494926 | + | 0.868935i | \(0.664805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.1482 | − | 52.2183i | 0.372200 | − | 0.644670i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 141.381i | 1.70338i | 0.524044 | + | 0.851691i | \(0.324423\pi\) | ||||
−0.524044 | + | 0.851691i | \(0.675577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −113.397 | −1.33408 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −45.5823 | − | 26.3170i | −0.523935 | − | 0.302494i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 100.852 | − | 58.2269i | 1.13317 | − | 0.654235i | 0.188439 | − | 0.982085i | \(-0.439657\pi\) |
0.944730 | + | 0.327850i | \(0.106324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 81.5980 | + | 141.332i | 0.877398 | + | 1.51970i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.3970 | − | 49.1850i | 0.298915 | − | 0.517737i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 137.346i | 1.41593i | 0.706245 | + | 0.707967i | \(0.250388\pi\) | ||||
−0.706245 | + | 0.707967i | \(0.749612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42.5025 | 0.429318 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 78.3906 | + | 45.2588i | 0.776145 | + | 0.448107i | 0.835062 | − | 0.550156i | \(-0.185432\pi\) |
−0.0589176 | + | 0.998263i | \(0.518765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3468 | + | 7.12840i | −0.119871 | + | 0.0692078i | −0.558737 | − | 0.829345i | \(-0.688714\pi\) |
0.438865 | + | 0.898553i | \(0.355380\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −24.7990 | − | 42.9531i | −0.231766 | − | 0.401431i | 0.726562 | − | 0.687101i | \(-0.241117\pi\) |
−0.958328 | + | 0.285670i | \(0.907784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −73.5980 | + | 127.475i | −0.675211 | + | 1.16950i | 0.301196 | + | 0.953562i | \(0.402614\pi\) |
−0.976407 | + | 0.215937i | \(0.930719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 142.748i | 1.28602i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 74.3015 | 0.657536 | 0.328768 | − | 0.944411i | \(-0.393367\pi\) | ||||
0.328768 | + | 0.944411i | \(0.393367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 190.793 | + | 110.155i | 1.65907 | + | 0.957866i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 181.125 | − | 104.573i | 1.54808 | − | 0.893785i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 52.8970 | + | 91.6202i | 0.437165 | + | 0.757192i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −46.7487 | + | 80.9712i | −0.380071 | + | 0.658302i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 184.712i | − | 1.47770i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 76.9949 | 0.606259 | 0.303130 | − | 0.952949i | \(-0.401968\pi\) | ||||
0.303130 | + | 0.952949i | \(0.401968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −306.341 | − | 176.866i | −2.37474 | − | 1.37106i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −134.398 | + | 77.5946i | −1.02594 | + | 0.592325i | −0.915818 | − | 0.401593i | \(-0.868457\pi\) |
−0.110119 | + | 0.993918i | \(0.535123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.8995 | + | 62.1797i | 0.265922 | + | 0.460591i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 65.0503 | − | 112.670i | 0.474819 | − | 0.822411i | −0.524765 | − | 0.851247i | \(-0.675847\pi\) |
0.999584 | + | 0.0288360i | \(0.00918006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 200.740i | − | 1.44417i | −0.691804 | − | 0.722086i | \(-0.743184\pi\) | ||
0.691804 | − | 0.722086i | \(-0.256816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −63.7990 | −0.452475 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −64.8010 | − | 37.4129i | −0.453154 | − | 0.261628i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −86.5834 | + | 49.9889i | −0.597127 | + | 0.344751i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −84.6985 | − | 146.702i | −0.568446 | − | 0.984578i | −0.996720 | − | 0.0809286i | \(-0.974211\pi\) |
0.428274 | − | 0.903649i | \(-0.359122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.10051 | + | 1.90613i | −0.00728811 | + | 0.0126234i | −0.869646 | − | 0.493675i | \(-0.835653\pi\) |
0.862358 | + | 0.506298i | \(0.168987\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 145.864i | − | 0.953361i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 309.990 | 1.99993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 139.504 | + | 80.5426i | 0.888560 | + | 0.513010i | 0.873471 | − | 0.486876i | \(-0.161864\pi\) |
0.0150888 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 53.3088 | − | 30.7779i | 0.335276 | − | 0.193571i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −111.146 | − | 192.510i | −0.681876 | − | 1.18104i | −0.974408 | − | 0.224787i | \(-0.927831\pi\) |
0.292532 | − | 0.956256i | \(-0.405502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 73.6985 | − | 127.650i | 0.446657 | − | 0.773633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 207.084i | 1.24003i | 0.784592 | + | 0.620013i | \(0.212873\pi\) | ||||
−0.784592 | + | 0.620013i | \(0.787127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −199.201 | −1.17870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 63.2674 | + | 36.5274i | 0.369985 | + | 0.213611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −240.608 | + | 138.915i | −1.39080 | + | 0.802976i | −0.993403 | − | 0.114673i | \(-0.963418\pi\) |
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.8492 | − | 32.6478i | −0.106493 | − | 0.184451i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.196 | − | 294.788i | 0.950815 | − | 1.64686i | 0.207149 | − | 0.978309i | \(-0.433581\pi\) |
0.743666 | − | 0.668551i | \(-0.233085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 184.174i | − | 1.01753i | −0.860904 | − | 0.508767i | \(-0.830101\pi\) | ||
0.860904 | − | 0.508767i | \(-0.169899\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −141.196 | −0.771563 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 234.823 | + | 135.575i | 1.26931 | + | 0.732837i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45.1941 | + | 26.0928i | −0.241679 | + | 0.139534i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 114.794 | + | 198.829i | 0.601015 | + | 1.04099i | 0.992668 | + | 0.120876i | \(0.0385703\pi\) |
−0.391652 | + | 0.920113i | \(0.628096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7487 | − | 35.9379i | 0.107506 | − | 0.186207i | −0.807253 | − | 0.590205i | \(-0.799047\pi\) |
0.914759 | + | 0.403999i | \(0.132380\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 725.308i | − | 3.71953i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 253.598 | 1.28730 | 0.643650 | − | 0.765320i | \(-0.277419\pi\) | ||||
0.643650 | + | 0.765320i | \(0.277419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −97.2990 | − | 56.1756i | −0.488940 | − | 0.282289i | 0.235195 | − | 0.971948i | \(-0.424427\pi\) |
−0.724135 | + | 0.689659i | \(0.757761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −121.294 | + | 70.0291i | −0.603453 | + | 0.348404i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 88.7990 | + | 153.804i | 0.433166 | + | 0.750265i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −141.693 | + | 245.420i | −0.684509 | + | 1.18560i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 26.1367i | − | 0.125056i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −353.789 | −1.67672 | −0.838362 | − | 0.545113i | \(-0.816487\pi\) | ||||
−0.838362 | + | 0.545113i | \(0.816487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −369.318 | − | 213.226i | −1.73389 | − | 1.00106i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −581.894 | + | 335.956i | −2.70648 | + | 1.56259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 40.8492 | + | 70.7530i | 0.186526 | + | 0.323073i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −128.397 | + | 222.390i | −0.580982 | + | 1.00629i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 126.653i | 0.567951i | 0.958832 | + | 0.283976i | \(0.0916534\pi\) | ||||
−0.958832 | + | 0.283976i | \(0.908347\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 510.085 | 2.26705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −195.589 | − | 112.923i | −0.861626 | − | 0.497460i | 0.00293018 | − | 0.999996i | \(-0.499067\pi\) |
−0.864557 | + | 0.502535i | \(0.832401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −223.680 | + | 129.141i | −0.976767 | + | 0.563937i | −0.901292 | − | 0.433211i | \(-0.857380\pi\) |
−0.0754744 | + | 0.997148i | \(0.524047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.8492 | − | 49.9684i | −0.123816 | − | 0.214456i | 0.797453 | − | 0.603381i | \(-0.206180\pi\) |
−0.921270 | + | 0.388924i | \(0.872847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −60.5929 | + | 104.950i | −0.257842 | + | 0.446596i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 355.974i | 1.50200i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −82.6030 | −0.345619 | −0.172810 | − | 0.984955i | \(-0.555285\pi\) | ||||
−0.172810 | + | 0.984955i | \(0.555285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 113.160 | + | 65.3328i | 0.469543 | + | 0.271091i | 0.716048 | − | 0.698051i | \(-0.245949\pi\) |
−0.246506 | + | 0.969141i | \(0.579282\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 298.984 | − | 172.618i | 1.23038 | − | 0.710363i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −64.3066 | − | 111.382i | −0.260350 | − | 0.450940i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −315.342 | + | 546.188i | −1.26643 | + | 2.19353i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 149.854i | − | 0.597029i | −0.954405 | − | 0.298514i | \(-0.903509\pi\) | ||
0.954405 | − | 0.298514i | \(-0.0964911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 101.387 | 0.400739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −438.080 | − | 252.925i | −1.71796 | − | 0.991864i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.52272 | + | 2.61119i | −0.0175981 | + | 0.0101603i | −0.508773 | − | 0.860901i | \(-0.669901\pi\) |
0.491175 | + | 0.871061i | \(0.336568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −64.3015 | − | 111.373i | −0.246366 | − | 0.426718i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −66.7035 | + | 115.534i | −0.253626 | + | 0.439292i | −0.964521 | − | 0.264005i | \(-0.914956\pi\) |
0.710896 | + | 0.703297i | \(0.248290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 116.925i | − | 0.441225i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 519.487 | 1.94565 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.57252 | − | 2.06260i | −0.0132808 | − | 0.00766765i | 0.493345 | − | 0.869834i | \(-0.335774\pi\) |
−0.506626 | + | 0.862166i | \(0.669107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 273.455 | − | 157.879i | 1.00906 | − | 0.582580i | 0.0981429 | − | 0.995172i | \(-0.468710\pi\) |
0.910916 | + | 0.412592i | \(0.135376\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −91.2462 | − | 158.043i | −0.331804 | − | 0.574702i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 130.095 | − | 225.332i | 0.469659 | − | 0.813473i | −0.529740 | − | 0.848160i | \(-0.677710\pi\) |
0.999398 | + | 0.0346877i | \(0.0110436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 398.745i | 1.42919i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −372.894 | −1.32703 | −0.663513 | − | 0.748165i | \(-0.730935\pi\) | ||||
−0.663513 | + | 0.748165i | \(0.730935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −69.2476 | − | 39.9801i | −0.244691 | − | 0.141273i | 0.372640 | − | 0.927976i | \(-0.378453\pi\) |
−0.617331 | + | 0.786704i | \(0.711786\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 219.409 | − | 126.676i | 0.769855 | − | 0.444476i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −54.9523 | − | 95.1801i | −0.190146 | − | 0.329343i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −306.342 | + | 530.599i | −1.05272 | + | 1.82337i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 112.038i | 0.382382i | 0.981553 | + | 0.191191i | \(0.0612351\pi\) | ||||
−0.981553 | + | 0.191191i | \(0.938765\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −71.6081 | −0.242739 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.6153 | + | 16.5210i | 0.0963478 | + | 0.0556264i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 432.062 | − | 249.451i | 1.44502 | − | 0.834285i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 201.894 | + | 349.691i | 0.666318 | + | 1.15410i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −134.101 | + | 232.269i | −0.439674 | + | 0.761537i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 146.177i | − | 0.476148i | −0.971247 | − | 0.238074i | \(-0.923484\pi\) | ||
0.971247 | − | 0.238074i | \(-0.0765160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −63.5980 | −0.205819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 366.290 | + | 211.477i | 1.17778 | + | 0.679992i | 0.955500 | − | 0.294991i | \(-0.0953166\pi\) |
0.222280 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75.9634 | − | 43.8575i | 0.242695 | − | 0.140120i | −0.373720 | − | 0.927542i | \(-0.621918\pi\) |
0.616415 | + | 0.787422i | \(0.288585\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −215.693 | − | 373.592i | −0.680421 | − | 1.17852i | −0.974853 | − | 0.222851i | \(-0.928464\pi\) |
0.294432 | − | 0.955673i | \(-0.404870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.0051 | + | 39.8459i | −0.0721161 | + | 0.124909i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 221.251i | − | 0.689255i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −89.6985 | −0.277704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −777.696 | − | 449.003i | −2.39291 | − | 1.38155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −568.653 | + | 328.312i | −1.73900 | + | 1.00401i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −170.744 | − | 295.737i | −0.515842 | − | 0.893464i | −0.999831 | − | 0.0183904i | \(-0.994146\pi\) |
0.483989 | − | 0.875074i | \(-0.339187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −174.392 | + | 302.056i | −0.523699 | + | 0.907074i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 266.040i | 0.794149i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −391.377 | −1.16136 | −0.580678 | − | 0.814134i | \(-0.697212\pi\) | ||||
−0.580678 | + | 0.814134i | \(0.697212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 287.045 | + | 165.725i | 0.846739 | + | 0.488865i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 123.546 | − | 71.3291i | 0.362304 | − | 0.209176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 491.387 | + | 851.107i | 1.42431 | + | 2.46698i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −304.241 | + | 526.961i | −0.876776 | + | 1.51862i | −0.0219166 | + | 0.999760i | \(0.506977\pi\) |
−0.854859 | + | 0.518860i | \(0.826357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 93.1627i | − | 0.266942i | −0.991053 | − | 0.133471i | \(-0.957388\pi\) | ||
0.991053 | − | 0.133471i | \(-0.0426123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 162.593 | 0.463228 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 80.0022 | + | 46.1893i | 0.226635 | + | 0.130848i | 0.609019 | − | 0.793156i | \(-0.291563\pi\) |
−0.382384 | + | 0.924004i | \(0.624897\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −701.518 | + | 405.021i | −1.97611 | + | 1.14091i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −144.588 | − | 250.434i | −0.402752 | − | 0.697586i | 0.591305 | − | 0.806448i | \(-0.298613\pi\) |
−0.994057 | + | 0.108861i | \(0.965280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.038 | + | 273.729i | −0.437777 | + | 0.758253i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 471.935i | 1.30010i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 155.186 | 0.425167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −458.968 | − | 264.986i | −1.25060 | − | 0.722032i | −0.279368 | − | 0.960184i | \(-0.590125\pi\) |
−0.971228 | + | 0.238153i | \(0.923458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −197.841 | + | 114.223i | −0.536154 | + | 0.309549i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −232.899 | − | 403.394i | −0.624395 | − | 1.08148i | −0.988657 | − | 0.150188i | \(-0.952012\pi\) |
0.364262 | − | 0.931297i | \(-0.381321\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 411.990 | − | 713.587i | 1.09864 | − | 1.90290i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 226.406i | 0.600546i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −91.8793 | −0.242426 | −0.121213 | − | 0.992627i | \(-0.538678\pi\) | ||||
−0.121213 | + | 0.992627i | \(0.538678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 297.450 | + | 171.733i | 0.780709 | + | 0.450742i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −269.572 | + | 155.638i | −0.703844 | + | 0.406364i | −0.808777 | − | 0.588115i | \(-0.799870\pi\) |
0.104934 | + | 0.994479i | \(0.466537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −432.146 | − | 748.498i | −1.11666 | − | 1.93410i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 271.296 | − | 469.899i | 0.697420 | − | 1.20797i | −0.271938 | − | 0.962315i | \(-0.587664\pi\) |
0.969358 | − | 0.245652i | \(-0.0790022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 347.949i | − | 0.889895i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −692.281 | −1.76153 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 585.581 | + | 338.086i | 1.48248 | + | 0.855913i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 141.834 | − | 81.8877i | 0.357263 | − | 0.206266i | −0.310616 | − | 0.950535i | \(-0.600535\pi\) |
0.667880 | + | 0.744269i | \(0.267202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 71.7035 | + | 124.194i | 0.178812 | + | 0.309711i | 0.941474 | − | 0.337086i | \(-0.109441\pi\) |
−0.762662 | + | 0.646797i | \(0.776108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 350.995 | − | 607.941i | 0.870955 | − | 1.50854i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 510.918i | − | 1.26153i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 124.784 | 0.306594 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −251.150 | − | 145.001i | −0.614058 | − | 0.354526i | 0.160494 | − | 0.987037i | \(-0.448691\pi\) |
−0.774552 | + | 0.632510i | \(0.782025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 502.609 | − | 290.182i | 1.22289 | − | 0.706038i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 598.990 | + | 1037.48i | 1.44335 | + | 2.49995i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 447.739 | − | 775.506i | 1.07371 | − | 1.85973i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 340.170i | 0.811860i | 0.913904 | + | 0.405930i | \(0.133052\pi\) | ||||
−0.913904 | + | 0.405930i | \(0.866948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.18081 | −0.0146813 | −0.00734063 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734063 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −134.999 | − | 77.9416i | −0.319146 | − | 0.184259i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −542.387 | + | 313.147i | −1.27621 | + | 0.736817i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −166.894 | − | 289.070i | −0.389031 | − | 0.673822i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2965 | + | 24.7622i | −0.0331705 | + | 0.0574529i | −0.882134 | − | 0.470998i | \(-0.843894\pi\) |
0.848964 | + | 0.528451i | \(0.177227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 243.736i | 0.562900i | 0.959576 | + | 0.281450i | \(0.0908153\pi\) | ||||
−0.959576 | + | 0.281450i | \(0.909185\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −445.990 | −1.02526 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 150.920 | + | 87.1337i | 0.345355 | + | 0.199391i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 428.605 | − | 247.455i | 0.976321 | − | 0.563679i | 0.0751637 | − | 0.997171i | \(-0.476052\pi\) |
0.901157 | + | 0.433492i | \(0.142719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.6985 | + | 68.7598i | 0.0896128 | + | 0.155214i | 0.907348 | − | 0.420381i | \(-0.138104\pi\) |
−0.817735 | + | 0.575595i | \(0.804770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 493.382 | − | 854.562i | 1.10872 | − | 1.92036i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 755.660i | − | 1.69052i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 804.362 | 1.79145 | 0.895726 | − | 0.444607i | \(-0.146657\pi\) | ||||
0.895726 | + | 0.444607i | \(0.146657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 70.7812 | + | 40.8655i | 0.156943 | + | 0.0906109i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.50303 | + | 4.90923i | −0.0187705 | + | 0.0108371i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −268.739 | − | 465.469i | −0.588050 | − | 1.01853i | −0.994488 | − | 0.104853i | \(-0.966563\pi\) |
0.406438 | − | 0.913678i | \(-0.366771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 56.6985 | − | 98.2047i | 0.123526 | − | 0.213953i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 524.278i | 1.13726i | 0.822593 | + | 0.568631i | \(0.192527\pi\) | ||||
−0.822593 | + | 0.568631i | \(0.807473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 506.995 | 1.09502 | 0.547511 | − | 0.836799i | \(-0.315576\pi\) | ||||
0.547511 | + | 0.836799i | \(0.315576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1197.57 | + | 691.415i | 2.57541 | + | 1.48691i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 178.234 | − | 102.903i | 0.381657 | − | 0.220350i | −0.296882 | − | 0.954914i | \(-0.595947\pi\) |
0.678539 | + | 0.734564i | \(0.262613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 359.291 | + | 622.311i | 0.762827 | + | 1.32125i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −154.608 | + | 267.789i | −0.326867 | + | 0.566150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 313.675i | − | 0.660368i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 150.402 | 0.315308 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 429.577 | + | 248.016i | 0.896820 | + | 0.517779i | 0.876167 | − | 0.482008i | \(-0.160092\pi\) |
0.0206527 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 531.769 | − | 307.017i | 1.10555 | − | 0.638289i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 581.894 | + | 1007.87i | 1.19978 | + | 2.07808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 236.688 | − | 409.956i | 0.486013 | − | 0.841799i | −0.513858 | − | 0.857875i | \(-0.671784\pi\) |
0.999871 | + | 0.0160761i | \(0.00511739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 991.616i | − | 2.02785i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 143.417 | 0.292092 | 0.146046 | − | 0.989278i | \(-0.453345\pi\) | ||||
0.146046 | + | 0.989278i | \(0.453345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 136.747 | + | 78.9509i | 0.277377 | + | 0.160144i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 311.892 | − | 180.071i | 0.630085 | − | 0.363780i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −223.497 | − | 387.109i | −0.447891 | − | 0.775770i | 0.550358 | − | 0.834929i | \(-0.314491\pi\) |
−0.998249 | + | 0.0591594i | \(0.981158\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −461.889 | + | 800.016i | −0.921935 | + | 1.59684i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 660.346i | − | 1.31282i | −0.754406 | − | 0.656408i | \(-0.772075\pi\) | ||
0.754406 | − | 0.656408i | \(-0.227925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 766.995 | 1.51880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −769.561 | − | 444.306i | −1.51787 | − | 0.876344i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −421.228 | + | 243.196i | −0.827559 | + | 0.477792i | −0.853016 | − | 0.521884i | \(-0.825229\pi\) |
0.0254569 | + | 0.999676i | \(0.491896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.3970 | + | 49.1850i | 0.0553547 | + | 0.0958772i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −60.4020 | + | 104.619i | −0.117285 | + | 0.203144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.7701i | 0.107872i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1239.37 | −2.38799 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 89.0106 | + | 51.3903i | 0.170846 | + | 0.0986378i | 0.582985 | − | 0.812483i | \(-0.301885\pi\) |
−0.412139 | + | 0.911121i | \(0.635218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 447.960 | − | 258.630i | 0.856520 | − | 0.494512i | −0.00632508 | − | 0.999980i | \(-0.502013\pi\) |
0.862846 | + | 0.505468i | \(0.168680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −244.794 | − | 423.996i | −0.464505 | − | 0.804546i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −73.5000 | + | 127.306i | −0.138941 | + | 0.240654i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 92.1105i | − | 0.173466i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 402.181 | 0.754561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −363.960 | − | 210.132i | −0.680299 | − | 0.392771i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1315.02 | − | 759.225i | 2.44882 | − | 1.41383i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 225.201 | + | 390.060i | 0.416268 | + | 0.720997i | 0.995561 | − | 0.0941223i | \(-0.0300045\pi\) |
−0.579293 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 410.789 | − | 711.507i | 0.756517 | − | 1.31033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1247.25i | 2.28854i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −195.095 | −0.356664 | −0.178332 | − | 0.983970i | \(-0.557070\pi\) | ||||
−0.178332 | + | 0.983970i | \(0.557070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −298.771 | − | 172.495i | −0.544209 | − | 0.314199i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −68.4886 | + | 39.5419i | −0.124299 | + | 0.0717639i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 604.784 | + | 1047.52i | 1.08970 | + | 1.88742i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 344.980 | − | 597.523i | 0.619353 | − | 1.07275i | −0.370251 | − | 0.928932i | \(-0.620728\pi\) |
0.989604 | − | 0.143820i | \(-0.0459385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1521.59i | 2.72198i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −232.794 | −0.414962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 724.755 | + | 418.438i | 1.28731 | + | 0.743229i | 0.978174 | − | 0.207789i | \(-0.0666268\pi\) |
0.309136 | + | 0.951018i | \(0.399960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 545.240 | − | 314.794i | 0.965026 | − | 0.557158i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.90960 | − | 6.77162i | −0.00687100 | − | 0.0119009i | 0.862569 | − | 0.505939i | \(-0.168854\pi\) |
−0.869440 | + | 0.494038i | \(0.835520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.854293 | − | 1.47968i | 0.00149613 | − | 0.00259138i | −0.865276 | − | 0.501295i | \(-0.832857\pi\) |
0.866773 | + | 0.498704i | \(0.166190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1024.17i | 1.78737i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1216.77 | 2.11613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −187.824 | − | 108.440i | −0.325518 | − | 0.187938i | 0.328332 | − | 0.944563i | \(-0.393514\pi\) |
−0.653849 | + | 0.756625i | \(0.726847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 160.315 | − | 92.5577i | 0.276882 | − | 0.159858i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.9045 | − | 46.6000i | −0.0461484 | − | 0.0799315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 886.090 | − | 1534.75i | 1.51468 | − | 2.62351i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 50.9983i | 0.0868795i | 0.999056 | + | 0.0434398i | \(0.0138317\pi\) | ||||
−0.999056 | + | 0.0434398i | \(0.986168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 245.206 | 0.416309 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 979.710 | + | 565.636i | 1.65772 | + | 0.957082i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −563.586 | + | 325.387i | −0.950398 | + | 0.548713i | −0.893205 | − | 0.449650i | \(-0.851549\pi\) |
−0.0571937 | + | 0.998363i | \(0.518215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −250.593 | − | 434.040i | −0.419754 | − | 0.727035i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8944 | + | 29.2620i | −0.0282044 | + | 0.0488515i | −0.879783 | − | 0.475375i | \(-0.842312\pi\) |
0.851579 | + | 0.524227i | \(0.175646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 415.133i | − | 0.690737i | −0.938467 | − | 0.345368i | \(-0.887754\pi\) | ||
0.938467 | − | 0.345368i | \(-0.112246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −342.211 | −0.567514 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 776.338 | + | 448.219i | 1.28320 | + | 0.740857i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 377.083 | − | 217.709i | 0.621225 | − | 0.358664i | −0.156121 | − | 0.987738i | \(-0.549899\pi\) |
0.777346 | + | 0.629074i | \(0.216566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 137.216 | + | 237.665i | 0.224576 | + | 0.388978i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −212.382 | + | 367.856i | −0.346463 | + | 0.600092i | −0.985618 | − | 0.168986i | \(-0.945951\pi\) |
0.639155 | + | 0.769078i | \(0.279284\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 792.244i | 1.28820i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −726.563 | −1.17757 | −0.588787 | − | 0.808289i | \(-0.700394\pi\) | ||||
−0.588787 | + | 0.808289i | \(0.700394\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −613.943 | − | 354.460i | −0.991830 | − | 0.572633i | −0.0860094 | − | 0.996294i | \(-0.527412\pi\) |
−0.905821 | + | 0.423661i | \(0.860745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −190.793 | + | 110.155i | −0.307236 | + | 0.177383i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −197.585 | − | 342.228i | −0.316137 | − | 0.547565i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 58.2965 | − | 100.972i | 0.0929768 | − | 0.161041i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 428.245i | − | 0.680835i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −207.176 | −0.328329 | −0.164165 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164165 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1366.77 | − | 789.106i | −2.15920 | − | 1.24661i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 565.005 | − | 326.206i | 0.889771 | − | 0.513710i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −520.985 | − | 902.372i | −0.815313 | − | 1.41216i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −456.291 | + | 790.320i | −0.711843 | + | 1.23295i | 0.252321 | + | 0.967643i | \(0.418806\pi\) |
−0.964165 | + | 0.265305i | \(0.914527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 656.917i | 1.02164i | 0.859686 | + | 0.510822i | \(0.170659\pi\) | ||||
−0.859686 | + | 0.510822i | \(0.829341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2997.33 | −4.64702 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.0014 | + | 19.0534i | 0.0510068 | + | 0.0294488i | 0.525287 | − | 0.850925i | \(-0.323958\pi\) |
−0.474280 | + | 0.880374i | \(0.657291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.5392 | + | 16.4771i | −0.0439741 | + | 0.0253885i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 188.291 | + | 326.130i | 0.288348 | + | 0.499434i | 0.973416 | − | 0.229046i | \(-0.0735606\pi\) |
−0.685067 | + | 0.728480i | \(0.740227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −657.492 | + | 1138.81i | −1.00381 | + | 1.73864i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 199.618i | 0.303832i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 954.291 | 1.44809 | 0.724045 | − | 0.689753i | \(-0.242281\pi\) | ||||
0.724045 | + | 0.689753i | \(0.242281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1010.11 | + | 583.187i | 1.52815 | + | 0.882281i | 0.999439 | + | 0.0334815i | \(0.0106595\pi\) |
0.528716 | + | 0.848799i | \(0.322674\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −992.057 | + | 572.764i | −1.49631 | + | 0.863898i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −153.387 | − | 265.674i | −0.229965 | − | 0.398312i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −282.492 | + | 489.291i | −0.422261 | + | 0.731377i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 123.427i | 0.183945i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −774.101 | −1.15022 | −0.575112 | − | 0.818075i | \(-0.695041\pi\) | ||||
−0.575112 | + | 0.818075i | \(0.695041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 343.421 | + | 198.274i | 0.508771 | + | 0.293739i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 486.263 | − | 280.744i | 0.718261 | − | 0.414688i | −0.0958511 | − | 0.995396i | \(-0.530557\pi\) |
0.814112 | + | 0.580707i | \(0.197224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −503.739 | − | 872.501i | −0.739704 | − | 1.28121i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 176.080 | − | 304.980i | 0.257804 | − | 0.446530i | −0.707849 | − | 0.706364i | \(-0.750334\pi\) |
0.965653 | + | 0.259834i | \(0.0836677\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1102.40i | − | 1.60934i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1152.17 | −1.67710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −229.309 | − | 132.391i | −0.332814 | − | 0.192150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −907.163 | + | 523.751i | −1.31283 | + | 0.757961i | −0.982563 | − | 0.185929i | \(-0.940471\pi\) |
−0.330263 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −850.477 | − | 1473.07i | −1.22371 | − | 2.11952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 140.246 | − | 242.914i | 0.201214 | − | 0.348513i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 257.386i | − | 0.368221i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 809.990 | 1.15548 | 0.577739 | − | 0.816222i | \(-0.303935\pi\) | ||||
0.577739 | + | 0.816222i | \(0.303935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 185.748 | + | 107.241i | 0.264221 | + | 0.152548i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −468.170 | + | 270.298i | −0.664071 | + | 0.383402i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 229.980 | + | 398.337i | 0.324372 | + | 0.561829i | 0.981385 | − | 0.192050i | \(-0.0615137\pi\) |
−0.657013 | + | 0.753879i | \(0.728180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −434.884 | + | 753.242i | −0.611652 | + | 1.05941i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 951.178i | 1.33405i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −634.030 | −0.886756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −319.115 | − | 184.241i | −0.445070 | − | 0.256961i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 74.5098 | − | 43.0183i | 0.103630 | − | 0.0598307i | −0.447289 | − | 0.894389i | \(-0.647611\pi\) |
0.550919 | + | 0.834559i | \(0.314277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 291.442 | + | 504.793i | 0.403101 | + | 0.698192i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −276.090 | + | 478.203i | −0.380814 | + | 0.659590i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 78.4124i | − | 0.107858i | −0.998545 | − | 0.0539288i | \(-0.982826\pi\) | ||
0.998545 | − | 0.0539288i | \(-0.0171744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 997.392 | 1.36816 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 919.024 | + | 530.599i | 1.25721 | + | 0.725853i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 449.960 | − | 259.785i | 0.613861 | − | 0.354413i | −0.160614 | − | 0.987017i | \(-0.551347\pi\) |
0.774475 | + | 0.632604i | \(0.218014\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 61.2162 | + | 106.030i | 0.0830613 | + | 0.143866i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 581.739 | − | 1007.60i | 0.787197 | − | 1.36347i | −0.140481 | − | 0.990083i | \(-0.544865\pi\) |
0.927678 | − | 0.373382i | \(-0.121802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 573.728i | − | 0.774262i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 66.8040 | 0.0899112 | 0.0449556 | − | 0.998989i | \(-0.485685\pi\) | ||||
0.0449556 | + | 0.998989i | \(0.485685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1243.07 | − | 717.687i | −1.66855 | − | 0.963338i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1334.53 | + | 770.489i | −1.78652 | + | 1.03145i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.69343 | + | 2.93311i | 0.00225491 | + | 0.00390561i | 0.867151 | − | 0.498046i | \(-0.165949\pi\) |
−0.864896 | + | 0.501952i | \(0.832616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 334.241 | − | 578.923i | 0.443879 | − | 0.768822i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.6501i | 0.0247021i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −700.402 | −0.925234 | −0.462617 | − | 0.886558i | \(-0.653089\pi\) | ||||
−0.462617 | + | 0.886558i | \(0.653089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 391.682 | + | 226.138i | 0.516050 | + | 0.297941i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 529.962 | − | 305.974i | 0.696403 | − | 0.402068i | −0.109604 | − | 0.993975i | \(-0.534958\pi\) |
0.806006 | + | 0.591907i | \(0.201625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −617.985 | − | 1070.38i | −0.807823 | − | 1.39919i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −81.0803 | + | 140.435i | −0.105711 | + | 0.183097i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 638.310i | 0.830052i | 0.909810 | + | 0.415026i | \(0.136227\pi\) | ||||
−0.909810 | + | 0.415026i | \(0.863773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.2965 | −0.0302159 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 411.367 | + | 237.503i | 0.532169 | + | 0.307248i | 0.741899 | − | 0.670511i | \(-0.233925\pi\) |
−0.209730 | + | 0.977759i | \(0.567259\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1482.71 | − | 856.042i | 1.91317 | − | 1.10457i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 70.2412 | + | 121.661i | 0.0901684 | + | 0.156176i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −186.392 | + | 322.840i | −0.238658 | + | 0.413368i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 99.9779i | − | 0.127686i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1364.94 | 1.73878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1277.76 | − | 737.717i | −1.62359 | − | 0.937378i | −0.985950 | − | 0.167041i | \(-0.946579\pi\) |
−0.637637 | − | 0.770337i | \(-0.720088\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −515.383 | + | 297.557i | −0.653211 | + | 0.377132i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 303.678 | + | 525.986i | 0.382949 | + | 0.663287i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 260.794 | − | 451.708i | 0.328043 | − | 0.568187i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 330.869i | 0.415143i | 0.978220 | + | 0.207572i | \(0.0665560\pi\) | ||||
−0.978220 | + | 0.207572i | \(0.933444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 191.397 | 0.239546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1099.24 | + | 634.644i | 1.37233 | + | 0.792315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 61.8489 | − | 35.7085i | 0.0770223 | − | 0.0444688i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.20101 | − | 15.9366i | −0.0114015 | − | 0.0197480i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 367.945 | − | 637.299i | 0.454814 | − | 0.787761i | −0.543863 | − | 0.839174i | \(-0.683039\pi\) |
0.998678 | + | 0.0514125i | \(0.0163723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1129.32i | − | 1.39251i | −0.717796 | − | 0.696253i | \(-0.754849\pi\) | ||
0.717796 | − | 0.696253i | \(-0.245151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1408.56 | 1.73255 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1631.22 | − | 941.785i | −2.00150 | − | 1.15556i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −460.285 | + | 265.746i | −0.563385 | + | 0.325270i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 726.980 | + | 1259.17i | 0.885481 | + | 1.53370i | 0.845162 | + | 0.534511i | \(0.179504\pi\) |
0.0403194 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −292.482 | + | 506.594i | −0.355386 | + | 0.615546i | −0.987184 | − | 0.159587i | \(-0.948984\pi\) |
0.631798 | + | 0.775133i | \(0.282317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 814.078i | − | 0.986761i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1453.16 | 1.75714 | 0.878570 | − | 0.477613i | \(-0.158498\pi\) | ||||
0.878570 | + | 0.477613i | \(0.158498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 349.516 | + | 201.793i | 0.421611 | + | 0.243417i | 0.695767 | − | 0.718268i | \(-0.255065\pi\) |
−0.274155 | + | 0.961685i | \(0.588398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1005.18 | − | 580.341i | 1.20960 | − | 0.698364i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 877.357 | + | 1519.63i | 1.05073 | + | 1.81991i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −154.995 | + | 268.459i | −0.185179 | + | 0.320740i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 191.525i | − | 0.228278i | −0.993465 | − | 0.114139i | \(-0.963589\pi\) | ||
0.993465 | − | 0.114139i | \(-0.0364109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −701.784 | −0.834464 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1440.58 | − | 831.720i | −1.70887 | − | 0.986619i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1461.78 | + | 843.958i | −1.72991 | + | 0.998767i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −178.347 | − | 308.906i | −0.210067 | − | 0.363846i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −416.000 | + | 720.533i | −0.488837 | + | 0.846690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 220.893i | − | 0.258960i | −0.991582 | − | 0.129480i | \(-0.958669\pi\) | ||
0.991582 | − | 0.129480i | \(-0.0413308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 619.025 | 0.724006 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −813.631 | − | 469.750i | −0.949395 | − | 0.548133i | −0.0565020 | − | 0.998402i | \(-0.517995\pi\) |
−0.892893 | + | 0.450269i | \(0.851328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −805.866 | + | 465.267i | −0.938144 | + | 0.541638i | −0.889378 | − | 0.457172i | \(-0.848862\pi\) |
−0.0487662 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 586.080 | + | 1015.12i | 0.679120 | + | 1.17627i | 0.975246 | + | 0.221121i | \(0.0709716\pi\) |
−0.296127 | + | 0.955149i | \(0.595695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1177.09 | + | 2038.77i | −1.36079 | + | 2.35696i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 490.272i | − | 0.565480i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 311.176 | 0.358085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 521.748 | + | 301.231i | 0.599022 | + | 0.345845i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1296.44 | + | 748.499i | −1.48504 | + | 0.857388i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 250.704 | + | 434.231i | 0.285865 | + | 0.495133i | 0.972819 | − | 0.231569i | \(-0.0743858\pi\) |
−0.686954 | + | 0.726701i | \(0.741052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −249.894 | + | 432.830i | −0.284294 | + | 0.492412i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1037.14i | − | 1.17723i | −0.808412 | − | 0.588616i | \(-0.799673\pi\) | ||
0.808412 | − | 0.588616i | \(-0.200327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −103.226 | −0.116904 | −0.0584520 | − | 0.998290i | \(-0.518616\pi\) | ||||
−0.0584520 | + | 0.998290i | \(0.518616\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −276.639 | − | 159.718i | −0.312587 | − | 0.180472i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 467.667 | − | 270.007i | 0.527245 | − | 0.304405i | −0.212649 | − | 0.977129i | \(-0.568209\pi\) |
0.739894 | + | 0.672723i | \(0.234876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −117.563 | − | 203.625i | −0.131945 | − | 0.228535i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.9298 | + | 83.0168i | −0.0536728 | + | 0.0929640i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2884.29i | − | 3.22267i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2225.55 | 2.48110 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −373.821 | − | 215.826i | −0.415819 | − | 0.240073i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −159.926 | + | 92.3336i | −0.177499 | + | 0.102479i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −780.291 | − | 1351.50i | −0.862200 | − | 1.49337i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −361.191 | + | 625.601i | −0.398226 | + | 0.689748i | −0.993507 | − | 0.113770i | \(-0.963707\pi\) |
0.595281 | + | 0.803517i | \(0.297041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 986.597i | 1.08537i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1292.59 | −1.41887 | −0.709436 | − | 0.704770i | \(-0.751050\pi\) | ||||
−0.709436 | + | 0.704770i | \(0.751050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 477.452 | + | 275.657i | 0.522948 | + | 0.301924i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1036.12 | + | 598.207i | −1.13238 | + | 0.653778i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 538.492 | + | 932.696i | 0.585955 | + | 1.01490i | 0.994756 | + | 0.102280i | \(0.0326137\pi\) |
−0.408801 | + | 0.912624i | \(0.634053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 326.040 | − | 564.718i | 0.354007 | − | 0.613158i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1834.39i | 1.98742i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1497.57 | 1.61899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −134.573 | − | 77.6960i | −0.145171 | − | 0.0838145i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1084.29 | − | 626.015i | 1.16716 | − | 0.673859i | 0.214150 | − | 0.976801i | \(-0.431302\pi\) |
0.953009 | + | 0.302942i | \(0.0979687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 943.377 | + | 1633.98i | 1.01112 | + | 1.75131i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −221.095 | + | 382.949i | −0.236466 | + | 0.409571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 857.272i | − | 0.914911i | −0.889232 | − | 0.457456i | \(-0.848761\pi\) | ||
0.889232 | − | 0.457456i | \(-0.151239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 391.286 | 0.416705 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −613.422 | − | 354.159i | −0.651883 | − | 0.376365i | 0.137294 | − | 0.990530i | \(-0.456159\pi\) |
−0.789177 | + | 0.614165i | \(0.789493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −471.936 | + | 272.472i | −0.500462 | + | 0.288942i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 241.548 | + | 418.373i | 0.255066 | + | 0.441788i | 0.964914 | − | 0.262568i | \(-0.0845694\pi\) |
−0.709847 | + | 0.704356i | \(0.751236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 175.714 | − | 304.345i | 0.185157 | − | 0.320701i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1924.37i | − | 2.02352i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 67.5778 | 0.0709106 | 0.0354553 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354553 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1684.76 | + | 972.698i | 1.76415 | + | 1.01853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −177.748 | + | 102.623i | −0.185735 | + | 0.107234i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 188.686 | + | 326.813i | 0.196343 | + | 0.340076i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 270.296 | − | 468.167i | 0.280682 | − | 0.486155i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 351.626i | − | 0.364379i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 806.382 | 0.833901 | 0.416950 | − | 0.908929i | \(-0.363099\pi\) | ||||
0.416950 | + | 0.908929i | \(0.363099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −346.527 | − | 200.067i | −0.357613 | − | 0.206468i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −598.531 | + | 345.562i | −0.616407 | + | 0.355883i | −0.775469 | − | 0.631386i | \(-0.782486\pi\) |
0.159062 | + | 0.987269i | \(0.449153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2002.95 | − | 3469.21i | −2.05431 | − | 3.55816i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −179.824 | + | 311.464i | −0.184057 | + | 0.318797i | −0.943258 | − | 0.332059i | \(-0.892257\pi\) |
0.759201 | + | 0.650856i | \(0.225590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 454.111i | − | 0.463852i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1604.36 | −1.63543 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −339.267 | − | 195.876i | −0.345134 | − | 0.199263i | 0.317406 | − | 0.948290i | \(-0.397188\pi\) |
−0.662540 | + | 0.749027i | \(0.730522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1860.95 | − | 1074.42i | 1.88929 | − | 1.09078i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1030.85 | − | 1785.49i | −1.04232 | − | 1.80535i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 704.693 | − | 1220.56i | 0.711093 | − | 1.23165i | −0.253354 | − | 0.967374i | \(-0.581534\pi\) |
0.964447 | − | 0.264276i | \(-0.0851330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1523.34i | − | 1.53407i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −952.000 | −0.956784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −398.864 | − | 230.284i | −0.400064 | − | 0.230977i | 0.286448 | − | 0.958096i | \(-0.407526\pi\) |
−0.686512 | + | 0.727119i | \(0.740859\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −234.823 | + | 135.575i | −0.235058 | + | 0.135711i |
(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 | 784.3.s.g.129.4 | 8 | ||
4.3 | odd | 2 | 196.3.h.c.129.1 | 8 | |||
7.2 | even | 3 | inner | 784.3.s.g.705.1 | 8 | ||
7.3 | odd | 6 | 784.3.c.d.97.4 | 4 | |||
7.4 | even | 3 | 784.3.c.d.97.1 | 4 | |||
7.5 | odd | 6 | inner | 784.3.s.g.705.4 | 8 | ||
7.6 | odd | 2 | inner | 784.3.s.g.129.1 | 8 | ||
12.11 | even | 2 | 1764.3.z.k.325.1 | 8 | |||
28.3 | even | 6 | 196.3.b.b.97.1 | ✓ | 4 | ||
28.11 | odd | 6 | 196.3.b.b.97.4 | yes | 4 | ||
28.19 | even | 6 | 196.3.h.c.117.1 | 8 | |||
28.23 | odd | 6 | 196.3.h.c.117.4 | 8 | |||
28.27 | even | 2 | 196.3.h.c.129.4 | 8 | |||
84.11 | even | 6 | 1764.3.d.e.685.1 | 4 | |||
84.23 | even | 6 | 1764.3.z.k.901.4 | 8 | |||
84.47 | odd | 6 | 1764.3.z.k.901.1 | 8 | |||
84.59 | odd | 6 | 1764.3.d.e.685.4 | 4 | |||
84.83 | odd | 2 | 1764.3.z.k.325.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.3.b.b.97.1 | ✓ | 4 | 28.3 | even | 6 | ||
196.3.b.b.97.4 | yes | 4 | 28.11 | odd | 6 | ||
196.3.h.c.117.1 | 8 | 28.19 | even | 6 | |||
196.3.h.c.117.4 | 8 | 28.23 | odd | 6 | |||
196.3.h.c.129.1 | 8 | 4.3 | odd | 2 | |||
196.3.h.c.129.4 | 8 | 28.27 | even | 2 | |||
784.3.c.d.97.1 | 4 | 7.4 | even | 3 | |||
784.3.c.d.97.4 | 4 | 7.3 | odd | 6 | |||
784.3.s.g.129.1 | 8 | 7.6 | odd | 2 | inner | ||
784.3.s.g.129.4 | 8 | 1.1 | even | 1 | trivial | ||
784.3.s.g.705.1 | 8 | 7.2 | even | 3 | inner | ||
784.3.s.g.705.4 | 8 | 7.5 | odd | 6 | inner | ||
1764.3.d.e.685.1 | 4 | 84.11 | even | 6 | |||
1764.3.d.e.685.4 | 4 | 84.59 | odd | 6 | |||
1764.3.z.k.325.1 | 8 | 12.11 | even | 2 | |||
1764.3.z.k.325.4 | 8 | 84.83 | odd | 2 | |||
1764.3.z.k.901.1 | 8 | 84.47 | odd | 6 | |||
1764.3.z.k.901.4 | 8 | 84.23 | even | 6 |