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 | 129.1 | ||
Root | \(-0.662827 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.129 |
Dual form | 784.3.s.g.705.1 |
$q$-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 | −0.309495 | − | 0.950901i | \(-0.600160\pi\) |
−0.978252 | + | 0.207420i | \(0.933493\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.33820 | + | 4.23671i | −1.46764 | + | 0.847343i | −0.999344 | − | 0.0362281i | \(-0.988466\pi\) |
−0.468297 | + | 0.883571i | \(0.655132\pi\) | |||||||
\(6\) | 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 | \(0.264240\pi\) | ||||
−0.674777 | + | 0.738022i | \(0.735760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37.7990 | 2.51993 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.5897 | + | 6.69133i | 0.681748 | + | 0.393607i | 0.800513 | − | 0.599315i | \(-0.204560\pi\) |
−0.118765 | + | 0.992922i | \(0.537894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.80462 | + | 3.35130i | −0.305506 | + | 0.176384i | −0.644914 | − | 0.764255i | \(-0.723107\pi\) |
0.339408 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(20\) | 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 | −0.107328 | − | 0.994224i | \(-0.534230\pi\) |
−0.914687 | + | 0.404163i | \(0.867563\pi\) | |||||||
\(32\) | 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 | \(-0.917726\pi\) | ||
0.966782 | − | 0.255602i | \(-0.0822738\pi\) | |||||||
\(42\) | 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 | −0.362415 | − | 0.932017i | \(-0.618048\pi\) |
0.625943 | + | 0.779869i | \(0.284714\pi\) | |||||||
\(48\) | 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 | 0.560739 | − | 0.827993i | \(-0.310517\pi\) |
−0.436693 | + | 0.899610i | \(0.643850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.4114 | − | 15.8260i | 0.449368 | − | 0.259443i | −0.258195 | − | 0.966093i | \(-0.583128\pi\) |
0.707563 | + | 0.706650i | \(0.249794\pi\) | |||||||
\(62\) | 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 | 0.387415 | − | 0.921905i | \(-0.373368\pi\) |
−0.604686 | + | 0.796464i | \(0.706701\pi\) | |||||||
\(74\) | 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 | \(-0.675577\pi\) | ||
0.524044 | − | 0.851691i | \(-0.324423\pi\) | |||||||
\(84\) | 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 | −0.944730 | − | 0.327850i | \(-0.893676\pi\) |
−0.188439 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(90\) | 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 | \(-0.749612\pi\) | ||
0.706245 | − | 0.707967i | \(-0.250388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 42.5025 | 0.429318 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −78.3906 | − | 45.2588i | −0.776145 | − | 0.448107i | 0.0589176 | − | 0.998263i | \(-0.481235\pi\) |
−0.835062 | + | 0.550156i | \(0.814568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3468 | − | 7.12840i | 0.119871 | − | 0.0692078i | −0.438865 | − | 0.898553i | \(-0.644620\pi\) |
0.558737 | + | 0.829345i | \(0.311286\pi\) | |||||||
\(104\) | 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 | 0.110119 | − | 0.993918i | \(-0.464877\pi\) |
0.915818 | + | 0.401593i | \(0.131543\pi\) | |||||||
\(132\) | 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 | \(0.256816\pi\) | ||||
−0.691804 | + | 0.722086i | \(0.743184\pi\) | |||||||
\(140\) | 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 | −0.0150888 | − | 0.999886i | \(-0.504803\pi\) |
−0.873471 | + | 0.486876i | \(0.838136\pi\) | |||||||
\(158\) | 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 | \(-0.787127\pi\) | ||
0.784592 | − | 0.620013i | \(-0.212873\pi\) | |||||||
\(168\) | 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 | 0.397392 | − | 0.917649i | \(-0.369915\pi\) |
0.993403 | + | 0.114673i | \(0.0365819\pi\) | |||||||
\(174\) | 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 | \(0.169899\pi\) | ||||
−0.860904 | + | 0.508767i | \(0.830101\pi\) | |||||||
\(182\) | 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 | 0.724135 | − | 0.689659i | \(-0.242239\pi\) |
−0.235195 | + | 0.971948i | \(0.575573\pi\) | |||||||
\(200\) | 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 | \(-0.908347\pi\) | ||
0.958832 | − | 0.283976i | \(-0.0916534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 510.085 | 2.26705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 195.589 | + | 112.923i | 0.861626 | + | 0.497460i | 0.864557 | − | 0.502535i | \(-0.167599\pi\) |
−0.00293018 | + | 0.999996i | \(0.500933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 223.680 | − | 129.141i | 0.976767 | − | 0.563937i | 0.0754744 | − | 0.997148i | \(-0.475953\pi\) |
0.901292 | + | 0.433211i | \(0.142620\pi\) | |||||||
\(230\) | 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 | 0.246506 | − | 0.969141i | \(-0.420718\pi\) |
−0.716048 | + | 0.698051i | \(0.754051\pi\) | |||||||
\(242\) | 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 | \(0.0964911\pi\) | ||||
−0.954405 | + | 0.298514i | \(0.903509\pi\) | |||||||
\(252\) | 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 | −0.491175 | − | 0.871061i | \(-0.663432\pi\) |
0.508773 | + | 0.860901i | \(0.330099\pi\) | |||||||
\(258\) | 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 | 0.506626 | − | 0.862166i | \(-0.330893\pi\) |
−0.493345 | + | 0.869834i | \(0.664226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −273.455 | + | 157.879i | −1.00906 | + | 0.582580i | −0.910916 | − | 0.412592i | \(-0.864624\pi\) |
−0.0981429 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(272\) | 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 | 0.617331 | − | 0.786704i | \(-0.288214\pi\) |
−0.372640 | + | 0.927976i | \(0.621547\pi\) | |||||||
\(284\) | 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 | \(-0.938765\pi\) | ||
0.981553 | − | 0.191191i | \(-0.0612351\pi\) | |||||||
\(294\) | 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 | \(0.0765160\pi\) | ||||
−0.971247 | + | 0.238074i | \(0.923484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −63.5980 | −0.205819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −366.290 | − | 211.477i | −1.17778 | − | 0.679992i | −0.222280 | − | 0.974983i | \(-0.571350\pi\) |
−0.955500 | + | 0.294991i | \(0.904683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −75.9634 | + | 43.8575i | −0.242695 | + | 0.140120i | −0.616415 | − | 0.787422i | \(-0.711415\pi\) |
0.373720 | + | 0.927542i | \(0.378082\pi\) | |||||||
\(314\) | 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 | \(0.0426123\pi\) | ||||
−0.991053 | + | 0.133471i | \(0.957388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 162.593 | 0.463228 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −80.0022 | − | 46.1893i | −0.226635 | − | 0.130848i | 0.382384 | − | 0.924004i | \(-0.375103\pi\) |
−0.609019 | + | 0.793156i | \(0.708437\pi\) | |||||||
\(354\) | 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 | 0.971228 | − | 0.238153i | \(-0.0765419\pi\) |
0.279368 | + | 0.960184i | \(0.409875\pi\) | |||||||
\(368\) | 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 | −0.104934 | − | 0.994479i | \(-0.533463\pi\) |
0.808777 | + | 0.588115i | \(0.200130\pi\) | |||||||
\(384\) | 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 | −0.667880 | − | 0.744269i | \(-0.732798\pi\) |
0.310616 | + | 0.950535i | \(0.399465\pi\) | |||||||
\(398\) | 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 | 0.774552 | − | 0.632510i | \(-0.217975\pi\) |
−0.160494 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(410\) | 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 | \(-0.866948\pi\) | ||
0.913904 | − | 0.405930i | \(-0.133052\pi\) | |||||||
\(420\) | 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 | \(-0.909185\pi\) | ||
0.959576 | − | 0.281450i | \(-0.0908153\pi\) | |||||||
\(434\) | 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 | −0.901157 | − | 0.433492i | \(-0.857281\pi\) |
−0.0751637 | + | 0.997171i | \(0.523948\pi\) | |||||||
\(440\) | 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 | \(-0.807473\pi\) | ||
0.822593 | − | 0.568631i | \(-0.192527\pi\) | |||||||
\(462\) | 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 | −0.678539 | − | 0.734564i | \(-0.737387\pi\) |
0.296882 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(468\) | 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 | −0.0206527 | − | 0.999787i | \(-0.506574\pi\) |
−0.876167 | + | 0.482008i | \(0.839908\pi\) | |||||||
\(480\) | 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 | \(0.227925\pi\) | ||||
−0.754406 | + | 0.656408i | \(0.772075\pi\) | |||||||
\(504\) | 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 | −0.0254569 | − | 0.999676i | \(-0.508104\pi\) |
0.853016 | + | 0.521884i | \(0.174771\pi\) | |||||||
\(510\) | 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 | 0.412139 | − | 0.911121i | \(-0.364782\pi\) |
−0.582985 | + | 0.812483i | \(0.698115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −447.960 | + | 258.630i | −0.856520 | + | 0.494512i | −0.862846 | − | 0.505468i | \(-0.831320\pi\) |
0.00632508 | + | 0.999980i | \(0.497987\pi\) | |||||||
\(524\) | 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 | −0.309136 | − | 0.951018i | \(-0.600040\pi\) |
−0.978174 | + | 0.207789i | \(0.933373\pi\) | |||||||
\(564\) | 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 | 0.653849 | − | 0.756625i | \(-0.273153\pi\) |
−0.328332 | + | 0.944563i | \(0.606486\pi\) | |||||||
\(578\) | 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 | \(-0.986168\pi\) | ||
0.999056 | − | 0.0434398i | \(-0.0138317\pi\) | |||||||
\(588\) | 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 | 0.0571937 | − | 0.998363i | \(-0.481785\pi\) |
0.893205 | + | 0.449650i | \(0.148451\pi\) | |||||||
\(594\) | 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 | \(0.112246\pi\) | ||||
−0.938467 | + | 0.345368i | \(0.887754\pi\) | |||||||
\(602\) | 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 | −0.777346 | − | 0.629074i | \(-0.783434\pi\) |
0.156121 | + | 0.987738i | \(0.450101\pi\) | |||||||
\(608\) | 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 | 0.905821 | − | 0.423661i | \(-0.139255\pi\) |
0.0860094 | + | 0.996294i | \(0.472588\pi\) | |||||||
\(620\) | 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 | \(-0.829341\pi\) | ||
0.859686 | − | 0.510822i | \(-0.170659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2997.33 | −4.64702 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.0014 | − | 19.0534i | −0.0510068 | − | 0.0294488i | 0.474280 | − | 0.880374i | \(-0.342709\pi\) |
−0.525287 | + | 0.850925i | \(0.676042\pi\) | |||||||
\(648\) | 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 | \(-0.989341\pi\) |
−0.528716 | − | 0.848799i | \(-0.677326\pi\) | |||||||
\(662\) | 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 | −0.814112 | − | 0.580707i | \(-0.802776\pi\) |
0.0958511 | + | 0.995396i | \(0.469443\pi\) | |||||||
\(678\) | 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 | 0.330263 | − | 0.943889i | \(-0.392863\pi\) |
0.982563 | + | 0.185929i | \(0.0595293\pi\) | |||||||
\(692\) | 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 | −0.550919 | − | 0.834559i | \(-0.685723\pi\) |
0.447289 | + | 0.894389i | \(0.352389\pi\) | |||||||
\(720\) | 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 | \(0.0171744\pi\) | ||||
−0.998545 | + | 0.0539288i | \(0.982826\pi\) | |||||||
\(728\) | 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 | −0.774475 | − | 0.632604i | \(-0.781986\pi\) |
0.160614 | + | 0.987017i | \(0.448653\pi\) | |||||||
\(734\) | 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 | −0.806006 | − | 0.591907i | \(-0.798375\pi\) |
0.109604 | + | 0.993975i | \(0.465042\pi\) | |||||||
\(762\) | 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 | \(-0.863773\pi\) | ||
0.909810 | − | 0.415026i | \(-0.136227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.2965 | −0.0302159 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −411.367 | − | 237.503i | −0.532169 | − | 0.307248i | 0.209730 | − | 0.977759i | \(-0.432741\pi\) |
−0.741899 | + | 0.670511i | \(0.766075\pi\) | |||||||
\(774\) | 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 | \(0.0534212\pi\) |
0.637637 | + | 0.770337i | \(0.279912\pi\) | |||||||
\(788\) | 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 | \(-0.933444\pi\) | ||
0.978220 | − | 0.207572i | \(-0.0665560\pi\) | |||||||
\(798\) | 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 | \(0.245151\pi\) | ||||
−0.717796 | + | 0.696253i | \(0.754849\pi\) | |||||||
\(812\) | 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 | 0.274155 | − | 0.961685i | \(-0.411602\pi\) |
−0.695767 | + | 0.718268i | \(0.744935\pi\) | |||||||
\(830\) | 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 | \(0.0364109\pi\) | ||||
−0.993465 | + | 0.114139i | \(0.963589\pi\) | |||||||
\(840\) | 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 | \(0.0413308\pi\) | ||||
−0.991582 | + | 0.129480i | \(0.958669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 619.025 | 0.724006 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 813.631 | + | 469.750i | 0.949395 | + | 0.548133i | 0.892893 | − | 0.450269i | \(-0.148672\pi\) |
0.0565020 | + | 0.998402i | \(0.482005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 805.866 | − | 465.267i | 0.938144 | − | 0.541638i | 0.0487662 | − | 0.998810i | \(-0.484471\pi\) |
0.889378 | + | 0.457172i | \(0.151138\pi\) | |||||||
\(860\) | 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 | \(0.200327\pi\) | ||||
−0.808412 | + | 0.588616i | \(0.799673\pi\) | |||||||
\(882\) | 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 | −0.739894 | − | 0.672723i | \(-0.765124\pi\) |
0.212649 | + | 0.977129i | \(0.431791\pi\) | |||||||
\(888\) | 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 | −0.953009 | − | 0.302942i | \(-0.902031\pi\) |
−0.214150 | + | 0.976801i | \(0.568698\pi\) | |||||||
\(930\) | 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 | \(0.151239\pi\) | ||||
−0.889232 | + | 0.457456i | \(0.848761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 391.286 | 0.416705 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 613.422 | + | 354.159i | 0.651883 | + | 0.376365i | 0.789177 | − | 0.614165i | \(-0.210507\pi\) |
−0.137294 | + | 0.990530i | \(0.543841\pi\) | |||||||
\(942\) | 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 | −0.159062 | − | 0.987269i | \(-0.550847\pi\) |
0.775469 | + | 0.631386i | \(0.217514\pi\) | |||||||
\(972\) | 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 | 0.662540 | − | 0.749027i | \(-0.269478\pi\) |
−0.317406 | + | 0.948290i | \(0.602812\pi\) | |||||||
\(984\) | 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 | 0.686512 | − | 0.727119i | \(-0.259141\pi\) |
−0.286448 | + | 0.958096i | \(0.592474\pi\) | |||||||
\(998\) | 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.129.1 | 8 | ||
4.3 | odd | 2 | 196.3.h.c.129.4 | 8 | |||
7.2 | even | 3 | inner | 784.3.s.g.705.4 | 8 | ||
7.3 | odd | 6 | 784.3.c.d.97.1 | 4 | |||
7.4 | even | 3 | 784.3.c.d.97.4 | 4 | |||
7.5 | odd | 6 | inner | 784.3.s.g.705.1 | 8 | ||
7.6 | odd | 2 | inner | 784.3.s.g.129.4 | 8 | ||
12.11 | even | 2 | 1764.3.z.k.325.4 | 8 | |||
28.3 | even | 6 | 196.3.b.b.97.4 | yes | 4 | ||
28.11 | odd | 6 | 196.3.b.b.97.1 | ✓ | 4 | ||
28.19 | even | 6 | 196.3.h.c.117.4 | 8 | |||
28.23 | odd | 6 | 196.3.h.c.117.1 | 8 | |||
28.27 | even | 2 | 196.3.h.c.129.1 | 8 | |||
84.11 | even | 6 | 1764.3.d.e.685.4 | 4 | |||
84.23 | even | 6 | 1764.3.z.k.901.1 | 8 | |||
84.47 | odd | 6 | 1764.3.z.k.901.4 | 8 | |||
84.59 | odd | 6 | 1764.3.d.e.685.1 | 4 | |||
84.83 | odd | 2 | 1764.3.z.k.325.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.3.b.b.97.1 | ✓ | 4 | 28.11 | odd | 6 | ||
196.3.b.b.97.4 | yes | 4 | 28.3 | even | 6 | ||
196.3.h.c.117.1 | 8 | 28.23 | odd | 6 | |||
196.3.h.c.117.4 | 8 | 28.19 | even | 6 | |||
196.3.h.c.129.1 | 8 | 28.27 | even | 2 | |||
196.3.h.c.129.4 | 8 | 4.3 | odd | 2 | |||
784.3.c.d.97.1 | 4 | 7.3 | odd | 6 | |||
784.3.c.d.97.4 | 4 | 7.4 | even | 3 | |||
784.3.s.g.129.1 | 8 | 1.1 | even | 1 | trivial | ||
784.3.s.g.129.4 | 8 | 7.6 | odd | 2 | inner | ||
784.3.s.g.705.1 | 8 | 7.5 | odd | 6 | inner | ||
784.3.s.g.705.4 | 8 | 7.2 | even | 3 | inner | ||
1764.3.d.e.685.1 | 4 | 84.59 | odd | 6 | |||
1764.3.d.e.685.4 | 4 | 84.11 | even | 6 | |||
1764.3.z.k.325.1 | 8 | 84.83 | odd | 2 | |||
1764.3.z.k.325.4 | 8 | 12.11 | even | 2 | |||
1764.3.z.k.901.1 | 8 | 84.23 | even | 6 | |||
1764.3.z.k.901.4 | 8 | 84.47 | odd | 6 |