Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, 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("1764.325");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.z (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: | \(48.0655186332\) |
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: | \(\Z[a_1, \ldots, a_{25}]\) |
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 | 901.1 | ||
Root | \(0.662827 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.901 |
Dual form | 1764.3.z.k.325.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.33820 | − | 4.23671i | −1.46764 | − | 0.847343i | −0.468297 | − | 0.883571i | \(-0.655132\pi\) |
−0.999344 | + | 0.0362281i | \(0.988466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.94975 | + | 3.37706i | 0.177250 | + | 0.307006i | 0.940938 | − | 0.338580i | \(-0.109947\pi\) |
−0.763688 | + | 0.645586i | \(0.776613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.1886i | 1.47604i | 0.674777 | + | 0.738022i | \(0.264240\pi\) | ||||
−0.674777 | + | 0.738022i | \(0.735760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.5897 | − | 6.69133i | 0.681748 | − | 0.393607i | −0.118765 | − | 0.992922i | \(-0.537894\pi\) |
0.800513 | + | 0.599315i | \(0.204560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.80462 | − | 3.35130i | −0.305506 | − | 0.176384i | 0.339408 | − | 0.940639i | \(-0.389773\pi\) |
−0.644914 | + | 0.764255i | \(0.723107\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.0000 | − | 22.5167i | 0.565217 | − | 0.978985i | −0.431812 | − | 0.901964i | \(-0.642126\pi\) |
0.997029 | − | 0.0770216i | \(-0.0245410\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.3995 | + | 40.5291i | 0.935980 | + | 1.62116i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.7990 | 0.406862 | 0.203431 | − | 0.979089i | \(-0.434791\pi\) | ||||
0.203431 | + | 0.979089i | \(0.434791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.6825 | + | 18.2919i | −1.02202 | + | 0.590061i | −0.914687 | − | 0.404163i | \(-0.867563\pi\) |
−0.107328 | + | 0.994224i | \(0.534230\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.0000 | − | 27.7128i | 0.432432 | − | 0.748995i | −0.564650 | − | 0.825331i | \(-0.690989\pi\) |
0.997082 | + | 0.0763357i | \(0.0243221\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | \(-0.126512\pi\) | ||||
0.922052 | + | 0.387066i | \(0.126512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3858 | − | 7.15093i | −0.263527 | − | 0.152148i | 0.362415 | − | 0.932017i | \(-0.381952\pi\) |
−0.625943 | + | 0.779869i | \(0.715286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.89949 | − | 11.9503i | −0.130179 | − | 0.225477i | 0.793566 | − | 0.608484i | \(-0.208222\pi\) |
−0.923746 | + | 0.383007i | \(0.874889\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 33.0421i | − | 0.600765i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.31869 | + | 4.22545i | −0.124046 | + | 0.0716178i | −0.560739 | − | 0.827993i | \(-0.689483\pi\) |
0.436693 | + | 0.899610i | \(0.356150\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −27.4114 | − | 15.8260i | −0.449368 | − | 0.259443i | 0.258195 | − | 0.966093i | \(-0.416872\pi\) |
−0.707563 | + | 0.706650i | \(0.750206\pi\) | |||||||
\(62\) | 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 | \(-0.0913850\pi\) |
−0.724765 | + | 0.688996i | \(0.758052\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.626632\pi\) |
0.604686 | + | 0.796464i | \(0.293299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39.8995 | + | 69.1080i | −0.505057 | + | 0.874784i | 0.494926 | + | 0.868935i | \(0.335195\pi\) |
−0.999983 | + | 0.00584908i | \(0.998138\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −100.852 | − | 58.2269i | −1.13317 | − | 0.654235i | −0.188439 | − | 0.982085i | \(-0.560343\pi\) |
−0.944730 | + | 0.327850i | \(0.893676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −78.3906 | + | 45.2588i | −0.776145 | + | 0.448107i | −0.835062 | − | 0.550156i | \(-0.814568\pi\) |
0.0589176 | + | 0.998263i | \(0.481235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3468 | + | 7.12840i | 0.119871 | + | 0.0692078i | 0.558737 | − | 0.829345i | \(-0.311286\pi\) |
−0.438865 | + | 0.898553i | \(0.644620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −24.7990 | + | 42.9531i | −0.231766 | + | 0.401431i | −0.958328 | − | 0.285670i | \(-0.907784\pi\) |
0.726562 | + | 0.687101i | \(0.241117\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −73.5980 | − | 127.475i | −0.675211 | − | 1.16950i | −0.976407 | − | 0.215937i | \(-0.930719\pi\) |
0.301196 | − | 0.953562i | \(-0.402614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −74.3015 | −0.657536 | −0.328768 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328768 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −190.793 | + | 110.155i | −1.65907 | + | 0.957866i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 52.8970 | − | 91.6202i | 0.437165 | − | 0.757192i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 184.712i | − | 1.47770i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −76.9949 | −0.606259 | −0.303130 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303130 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −134.398 | − | 77.5946i | −1.02594 | − | 0.592325i | −0.110119 | − | 0.993918i | \(-0.535123\pi\) |
−0.915818 | + | 0.401593i | \(0.868457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −65.0503 | − | 112.670i | −0.474819 | − | 0.822411i | 0.524765 | − | 0.851247i | \(-0.324153\pi\) |
−0.999584 | + | 0.0288360i | \(0.990820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 200.740i | − | 1.44417i | −0.691804 | − | 0.722086i | \(-0.743184\pi\) | ||
0.691804 | − | 0.722086i | \(-0.256816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | −0.428274 | − | 0.903649i | \(-0.640878\pi\) |
0.996720 | − | 0.0809286i | \(-0.0257886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10051 | + | 1.90613i | 0.00728811 | + | 0.0126234i | 0.869646 | − | 0.493675i | \(-0.164347\pi\) |
−0.862358 | + | 0.506298i | \(0.831013\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 309.990 | 1.99993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 139.504 | − | 80.5426i | 0.888560 | − | 0.513010i | 0.0150888 | − | 0.999886i | \(-0.495197\pi\) |
0.873471 | + | 0.486876i | \(0.161864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111.146 | − | 192.510i | 0.681876 | − | 1.18104i | −0.292532 | − | 0.956256i | \(-0.594498\pi\) |
0.974408 | − | 0.224787i | \(-0.0721688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 240.608 | + | 138.915i | 1.39080 | + | 0.802976i | 0.993403 | − | 0.114673i | \(-0.0365819\pi\) |
0.397392 | + | 0.917649i | \(0.369915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.196 | + | 294.788i | 0.950815 | + | 1.64686i | 0.743666 | + | 0.668551i | \(0.233085\pi\) |
0.207149 | + | 0.978309i | \(0.433581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 184.174i | 1.01753i | 0.860904 | + | 0.508767i | \(0.169899\pi\) | ||||
−0.860904 | + | 0.508767i | \(0.830101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | −0.391652 | − | 0.920113i | \(-0.628096\pi\) |
0.992668 | − | 0.120876i | \(-0.0385703\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7487 | + | 35.9379i | 0.107506 | + | 0.186207i | 0.914759 | − | 0.403999i | \(-0.132380\pi\) |
−0.807253 | + | 0.590205i | \(0.799047\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −253.598 | −1.28730 | −0.643650 | − | 0.765320i | \(-0.722581\pi\) | ||||
−0.643650 | + | 0.765320i | \(0.722581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 97.2990 | − | 56.1756i | 0.488940 | − | 0.282289i | −0.235195 | − | 0.971948i | \(-0.575573\pi\) |
0.724135 | + | 0.689659i | \(0.242239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 88.7990 | − | 153.804i | 0.433166 | − | 0.750265i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 26.1367i | − | 0.125056i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 353.789 | 1.67672 | 0.838362 | − | 0.545113i | \(-0.183513\pi\) | ||||
0.838362 | + | 0.545113i | \(0.183513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −581.894 | − | 335.956i | −2.70648 | − | 1.56259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −195.589 | + | 112.923i | −0.861626 | + | 0.497460i | −0.864557 | − | 0.502535i | \(-0.832401\pi\) |
0.00293018 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −223.680 | − | 129.141i | −0.976767 | − | 0.563937i | −0.0754744 | − | 0.997148i | \(-0.524047\pi\) |
−0.901292 | + | 0.433211i | \(0.857380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.8492 | − | 49.9684i | 0.123816 | − | 0.214456i | −0.797453 | − | 0.603381i | \(-0.793820\pi\) |
0.921270 | + | 0.388924i | \(0.127153\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 60.5929 | + | 104.950i | 0.257842 | + | 0.446596i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | \(-0.579282\pi\) |
0.716048 | + | 0.698051i | \(0.245949\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 64.3066 | − | 111.382i | 0.260350 | − | 0.450940i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.52272 | + | 2.61119i | 0.0175981 | + | 0.0101603i | 0.508773 | − | 0.860901i | \(-0.330099\pi\) |
−0.491175 | + | 0.871061i | \(0.663432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −66.7035 | − | 115.534i | −0.253626 | − | 0.439292i | 0.710896 | − | 0.703297i | \(-0.248290\pi\) |
−0.964521 | + | 0.264005i | \(0.914956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 116.925i | 0.441225i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.57252 | − | 2.06260i | 0.0132808 | − | 0.00766765i | −0.493345 | − | 0.869834i | \(-0.664226\pi\) |
0.506626 | + | 0.862166i | \(0.330893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −273.455 | − | 157.879i | −1.00906 | − | 0.582580i | −0.0981429 | − | 0.995172i | \(-0.531290\pi\) |
−0.910916 | + | 0.412592i | \(0.864624\pi\) | |||||||
\(272\) | 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 | 0.999398 | − | 0.0346877i | \(-0.0110436\pi\) |
−0.529740 | + | 0.848160i | \(0.677710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 372.894 | 1.32703 | 0.663513 | − | 0.748165i | \(-0.269065\pi\) | ||||
0.663513 | + | 0.748165i | \(0.269065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 69.2476 | − | 39.9801i | 0.244691 | − | 0.141273i | −0.372640 | − | 0.927976i | \(-0.621547\pi\) |
0.617331 | + | 0.786704i | \(0.288214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −54.9523 | + | 95.1801i | −0.190146 | + | 0.329343i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 432.062 | + | 249.451i | 1.44502 | + | 0.834285i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 366.290 | − | 211.477i | 1.17778 | − | 0.679992i | 0.222280 | − | 0.974983i | \(-0.428650\pi\) |
0.955500 | + | 0.294991i | \(0.0953166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 75.9634 | + | 43.8575i | 0.242695 | + | 0.140120i | 0.616415 | − | 0.787422i | \(-0.288585\pi\) |
−0.373720 | + | 0.927542i | \(0.621918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 215.693 | − | 373.592i | 0.680421 | − | 1.17852i | −0.294432 | − | 0.955673i | \(-0.595130\pi\) |
0.974853 | − | 0.222851i | \(-0.0715364\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.0051 | + | 39.8459i | 0.0721161 | + | 0.124909i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −89.6985 | −0.277704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −777.696 | + | 449.003i | −2.39291 | + | 1.38155i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 170.744 | − | 295.737i | 0.515842 | − | 0.893464i | −0.483989 | − | 0.875074i | \(-0.660813\pi\) |
0.999831 | − | 0.0183904i | \(-0.00585416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −123.546 | − | 71.3291i | −0.362304 | − | 0.209176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −304.241 | − | 526.961i | −0.876776 | − | 1.51862i | −0.854859 | − | 0.518860i | \(-0.826357\pi\) |
−0.0219166 | − | 0.999760i | \(-0.506977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 93.1627i | 0.266942i | 0.991053 | + | 0.133471i | \(0.0426123\pi\) | ||||
−0.991053 | + | 0.133471i | \(0.957388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −80.0022 | + | 46.1893i | −0.226635 | + | 0.130848i | −0.609019 | − | 0.793156i | \(-0.708437\pi\) |
0.382384 | + | 0.924004i | \(0.375103\pi\) | |||||||
\(354\) | 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 | −0.994057 | − | 0.108861i | \(-0.965280\pi\) |
0.591305 | + | 0.806448i | \(0.298613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.038 | − | 273.729i | −0.437777 | − | 0.758253i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −155.186 | −0.425167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 458.968 | − | 264.986i | 1.25060 | − | 0.722032i | 0.279368 | − | 0.960184i | \(-0.409875\pi\) |
0.971228 | + | 0.238153i | \(0.0765419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −232.899 | + | 403.394i | −0.624395 | + | 1.08148i | 0.364262 | + | 0.931297i | \(0.381321\pi\) |
−0.988657 | + | 0.150188i | \(0.952012\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 226.406i | 0.600546i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 91.8793 | 0.242426 | 0.121213 | − | 0.992627i | \(-0.461322\pi\) | ||||
0.121213 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −269.572 | − | 155.638i | −0.703844 | − | 0.406364i | 0.104934 | − | 0.994479i | \(-0.466537\pi\) |
−0.808777 | + | 0.588115i | \(0.799870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −271.296 | − | 469.899i | −0.697420 | − | 1.20797i | −0.969358 | − | 0.245652i | \(-0.920998\pi\) |
0.271938 | − | 0.962315i | \(-0.412336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 347.949i | − | 0.889895i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | \(-0.267202\pi\) |
−0.310616 | + | 0.950535i | \(0.600535\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −71.7035 | + | 124.194i | −0.178812 | + | 0.309711i | −0.941474 | − | 0.337086i | \(-0.890559\pi\) |
0.762662 | + | 0.646797i | \(0.223892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −350.995 | − | 607.941i | −0.870955 | − | 1.50854i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 124.784 | 0.306594 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −251.150 | + | 145.001i | −0.614058 | + | 0.354526i | −0.774552 | − | 0.632510i | \(-0.782025\pi\) |
0.160494 | + | 0.987037i | \(0.448691\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −598.990 | + | 1037.48i | −1.44335 | + | 2.49995i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 542.387 | + | 313.147i | 1.27621 | + | 0.736817i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2965 | − | 24.7622i | −0.0331705 | − | 0.0574529i | 0.848964 | − | 0.528451i | \(-0.177227\pi\) |
−0.882134 | + | 0.470998i | \(0.843894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 243.736i | − | 0.562900i | −0.959576 | − | 0.281450i | \(-0.909185\pi\) | ||
0.959576 | − | 0.281450i | \(-0.0908153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(-0.523948\pi\) |
−0.901157 | + | 0.433492i | \(0.857281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.6985 | − | 68.7598i | 0.0896128 | − | 0.155214i | −0.817735 | − | 0.575595i | \(-0.804770\pi\) |
0.907348 | + | 0.420381i | \(0.138104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 493.382 | + | 854.562i | 1.10872 | + | 1.92036i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −804.362 | −1.79145 | −0.895726 | − | 0.444607i | \(-0.853343\pi\) | ||||
−0.895726 | + | 0.444607i | \(0.853343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −70.7812 | + | 40.8655i | −0.156943 | + | 0.0906109i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −268.739 | + | 465.469i | −0.588050 | + | 1.01853i | 0.406438 | + | 0.913678i | \(0.366771\pi\) |
−0.994488 | + | 0.104853i | \(0.966563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | \(-0.684424\pi\) | ||||
−0.547511 | + | 0.836799i | \(0.684424\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 178.234 | + | 102.903i | 0.381657 | + | 0.220350i | 0.678539 | − | 0.734564i | \(-0.262613\pi\) |
−0.296882 | + | 0.954914i | \(0.595947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 154.608 | + | 267.789i | 0.326867 | + | 0.566150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 313.675i | − | 0.660368i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 429.577 | − | 248.016i | 0.896820 | − | 0.517779i | 0.0206527 | − | 0.999787i | \(-0.493426\pi\) |
0.876167 | + | 0.482008i | \(0.160092\pi\) | |||||||
\(480\) | 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 | \(-0.328216\pi\) |
−0.999871 | + | 0.0160761i | \(0.994883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 223.497 | − | 387.109i | 0.447891 | − | 0.775770i | −0.550358 | − | 0.834929i | \(-0.685509\pi\) |
0.998249 | + | 0.0591594i | \(0.0188420\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 421.228 | + | 243.196i | 0.827559 | + | 0.477792i | 0.853016 | − | 0.521884i | \(-0.174771\pi\) |
−0.0254569 | + | 0.999676i | \(0.508104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −60.4020 | − | 104.619i | −0.117285 | − | 0.203144i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 55.7701i | − | 0.107872i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −89.0106 | + | 51.3903i | −0.170846 | + | 0.0986378i | −0.582985 | − | 0.812483i | \(-0.698115\pi\) |
0.412139 | + | 0.911121i | \(0.364782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −447.960 | − | 258.630i | −0.856520 | − | 0.494512i | 0.00632508 | − | 0.999980i | \(-0.497987\pi\) |
−0.862846 | + | 0.505468i | \(0.831320\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −402.181 | −0.754561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 363.960 | − | 210.132i | 0.680299 | − | 0.392771i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 225.201 | − | 390.060i | 0.416268 | − | 0.720997i | −0.579293 | − | 0.815120i | \(-0.696671\pi\) |
0.995561 | + | 0.0941223i | \(0.0300045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1247.25i | 2.28854i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 195.095 | 0.356664 | 0.178332 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178332 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −68.4886 | − | 39.5419i | −0.124299 | − | 0.0717639i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −344.980 | − | 597.523i | −0.619353 | − | 1.07275i | −0.989604 | − | 0.143820i | \(-0.954062\pi\) |
0.370251 | − | 0.928932i | \(-0.379272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1521.59i | 2.72198i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 724.755 | − | 418.438i | 1.28731 | − | 0.743229i | 0.309136 | − | 0.951018i | \(-0.399960\pi\) |
0.978174 | + | 0.207789i | \(0.0666268\pi\) | |||||||
\(564\) | 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 | \(-0.831146\pi\) |
0.869440 | + | 0.494038i | \(0.164480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.854293 | − | 1.47968i | −0.00149613 | − | 0.00259138i | 0.865276 | − | 0.501295i | \(-0.167143\pi\) |
−0.866773 | + | 0.498704i | \(0.833810\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1216.77 | 2.11613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −187.824 | + | 108.440i | −0.325518 | + | 0.187938i | −0.653849 | − | 0.756625i | \(-0.726847\pi\) |
0.328332 | + | 0.944563i | \(0.393514\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.9045 | − | 46.6000i | 0.0461484 | − | 0.0799315i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 563.586 | + | 325.387i | 0.950398 | + | 0.548713i | 0.893205 | − | 0.449650i | \(-0.148451\pi\) |
0.0571937 | + | 0.998363i | \(0.481785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8944 | − | 29.2620i | −0.0282044 | − | 0.0488515i | 0.851579 | − | 0.524227i | \(-0.175646\pi\) |
−0.879783 | + | 0.475375i | \(0.842312\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 415.133i | 0.690737i | 0.938467 | + | 0.345368i | \(0.112246\pi\) | ||||
−0.938467 | + | 0.345368i | \(0.887754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | \(-0.450101\pi\) |
−0.777346 | + | 0.629074i | \(0.783434\pi\) | |||||||
\(608\) | 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 | 0.639155 | − | 0.769078i | \(-0.279284\pi\) |
−0.985618 | + | 0.168986i | \(0.945951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 726.563 | 1.17757 | 0.588787 | − | 0.808289i | \(-0.299606\pi\) | ||||
0.588787 | + | 0.808289i | \(0.299606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 613.943 | − | 354.460i | 0.991830 | − | 0.572633i | 0.0860094 | − | 0.996294i | \(-0.472588\pi\) |
0.905821 | + | 0.423661i | \(0.139255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −197.585 | + | 342.228i | −0.316137 | + | 0.547565i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 428.245i | − | 0.680835i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 207.176 | 0.328329 | 0.164165 | − | 0.986433i | \(-0.447507\pi\) | ||||
0.164165 | + | 0.986433i | \(0.447507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 565.005 | + | 326.206i | 0.889771 | + | 0.513710i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 456.291 | + | 790.320i | 0.711843 | + | 1.23295i | 0.964165 | + | 0.265305i | \(0.0854726\pi\) |
−0.252321 | + | 0.967643i | \(0.581194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 656.917i | 1.02164i | 0.859686 | + | 0.510822i | \(0.170659\pi\) | ||||
−0.859686 | + | 0.510822i | \(0.829341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.0014 | − | 19.0534i | 0.0510068 | − | 0.0294488i | −0.474280 | − | 0.880374i | \(-0.657291\pi\) |
0.525287 | + | 0.850925i | \(0.323958\pi\) | |||||||
\(648\) | 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 | \(-0.926439\pi\) |
0.685067 | + | 0.728480i | \(0.259773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 657.492 | + | 1138.81i | 1.00381 | + | 1.73864i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | 0.528716 | − | 0.848799i | \(-0.322674\pi\) |
0.999439 | − | 0.0334815i | \(-0.0106595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 153.387 | − | 265.674i | 0.229965 | − | 0.398312i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −486.263 | − | 280.744i | −0.718261 | − | 0.414688i | 0.0958511 | − | 0.995396i | \(-0.469443\pi\) |
−0.814112 | + | 0.580707i | \(0.802776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 176.080 | + | 304.980i | 0.257804 | + | 0.446530i | 0.965653 | − | 0.259834i | \(-0.0836677\pi\) |
−0.707849 | + | 0.706364i | \(0.750334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1102.40i | 1.60934i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | \(-0.0595293\pi\) |
0.330263 | + | 0.943889i | \(0.392863\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −809.990 | −1.15548 | −0.577739 | − | 0.816222i | \(-0.696065\pi\) | ||||
−0.577739 | + | 0.816222i | \(0.696065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −185.748 | + | 107.241i | −0.264221 | + | 0.152548i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 229.980 | − | 398.337i | 0.324372 | − | 0.561829i | −0.657013 | − | 0.753879i | \(-0.728180\pi\) |
0.981385 | + | 0.192050i | \(0.0615137\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 951.178i | 1.33405i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 634.030 | 0.886756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 74.5098 | + | 43.0183i | 0.103630 | + | 0.0598307i | 0.550919 | − | 0.834559i | \(-0.314277\pi\) |
−0.447289 | + | 0.894389i | \(0.647611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | \(-0.218014\pi\) |
−0.160614 | + | 0.987017i | \(0.551347\pi\) | |||||||
\(734\) | 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 | −0.927678 | − | 0.373382i | \(-0.878198\pi\) |
0.140481 | − | 0.990083i | \(-0.455135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.69343 | + | 2.93311i | −0.00225491 | + | 0.00390561i | −0.867151 | − | 0.498046i | \(-0.834051\pi\) |
0.864896 | + | 0.501952i | \(0.167384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −529.962 | − | 305.974i | −0.696403 | − | 0.402068i | 0.109604 | − | 0.993975i | \(-0.465042\pi\) |
−0.806006 | + | 0.591907i | \(0.798375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −411.367 | + | 237.503i | −0.532169 | + | 0.307248i | −0.741899 | − | 0.670511i | \(-0.766075\pi\) |
0.209730 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1364.94 | −1.73878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1277.76 | − | 737.717i | 1.62359 | − | 0.937378i | 0.637637 | − | 0.770337i | \(-0.279912\pi\) |
0.985950 | − | 0.167041i | \(-0.0534212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 303.678 | − | 525.986i | 0.382949 | − | 0.663287i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 61.8489 | + | 35.7085i | 0.0770223 | + | 0.0444688i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −367.945 | − | 637.299i | −0.454814 | − | 0.787761i | 0.543863 | − | 0.839174i | \(-0.316961\pi\) |
−0.998678 | + | 0.0514125i | \(0.983628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1129.32i | − | 1.39251i | −0.717796 | − | 0.696253i | \(-0.754849\pi\) | ||
0.717796 | − | 0.696253i | \(-0.245151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | −0.0403194 | + | 0.999187i | \(0.512838\pi\) |
−0.845162 | + | 0.534511i | \(0.820496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 292.482 | + | 506.594i | 0.355386 | + | 0.615546i | 0.987184 | − | 0.159587i | \(-0.0510162\pi\) |
−0.631798 | + | 0.775133i | \(0.717683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | \(-0.588398\pi\) |
0.695767 | + | 0.718268i | \(0.255065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −877.357 | + | 1519.63i | −1.05073 | + | 1.81991i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1461.78 | + | 843.958i | 1.72991 | + | 0.998767i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 813.631 | − | 469.750i | 0.949395 | − | 0.548133i | 0.0565020 | − | 0.998402i | \(-0.482005\pi\) |
0.892893 | + | 0.450269i | \(0.148672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 805.866 | + | 465.267i | 0.938144 | + | 0.541638i | 0.889378 | − | 0.457172i | \(-0.151138\pi\) |
0.0487662 | + | 0.998810i | \(0.484471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 586.080 | − | 1015.12i | 0.679120 | − | 1.17627i | −0.296127 | − | 0.955149i | \(-0.595695\pi\) |
0.975246 | − | 0.221121i | \(-0.0709716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1177.09 | − | 2038.77i | −1.36079 | − | 2.35696i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −311.176 | −0.358085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −521.748 | + | 301.231i | −0.599022 | + | 0.345845i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 250.704 | − | 434.231i | 0.285865 | − | 0.495133i | −0.686954 | − | 0.726701i | \(-0.741052\pi\) |
0.972819 | + | 0.231569i | \(0.0743858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | \(-0.481384\pi\) | ||||
0.0584520 | + | 0.998290i | \(0.481384\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 467.667 | + | 270.007i | 0.527245 | + | 0.304405i | 0.739894 | − | 0.672723i | \(-0.234876\pi\) |
−0.212649 | + | 0.977129i | \(0.568209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.9298 | + | 83.0168i | 0.0536728 | + | 0.0929640i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2884.29i | − | 3.22267i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | \(-0.0362927\pi\) |
−0.595281 | + | 0.803517i | \(0.702959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −538.492 | + | 932.696i | −0.585955 | + | 1.01490i | 0.408801 | + | 0.912624i | \(0.365947\pi\) |
−0.994756 | + | 0.102280i | \(0.967386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1834.39i | − | 1.98742i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1497.57 | 1.61899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1084.29 | − | 626.015i | −1.16716 | − | 0.673859i | −0.214150 | − | 0.976801i | \(-0.568698\pi\) |
−0.953009 | + | 0.302942i | \(0.902031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 613.422 | − | 354.159i | 0.651883 | − | 0.376365i | −0.137294 | − | 0.990530i | \(-0.543841\pi\) |
0.789177 | + | 0.614165i | \(0.210507\pi\) | |||||||
\(942\) | 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 | −0.709847 | − | 0.704356i | \(-0.751236\pi\) |
0.964914 | + | 0.262568i | \(0.0845694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 175.714 | + | 304.345i | 0.185157 | + | 0.320701i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −67.5778 | −0.0709106 | −0.0354553 | − | 0.999371i | \(-0.511288\pi\) | ||||
−0.0354553 | + | 0.999371i | \(0.511288\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1684.76 | + | 972.698i | −1.76415 | + | 1.01853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 188.686 | − | 326.813i | 0.196343 | − | 0.340076i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 351.626i | − | 0.364379i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −806.382 | −0.833901 | −0.416950 | − | 0.908929i | \(-0.636901\pi\) | ||||
−0.416950 | + | 0.908929i | \(0.636901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −598.531 | − | 345.562i | −0.616407 | − | 0.355883i | 0.159062 | − | 0.987269i | \(-0.449153\pi\) |
−0.775469 | + | 0.631386i | \(0.782486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 179.824 | + | 311.464i | 0.184057 | + | 0.318797i | 0.943258 | − | 0.332059i | \(-0.107743\pi\) |
−0.759201 | + | 0.650856i | \(0.774410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 454.111i | − | 0.463852i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −339.267 | + | 195.876i | −0.345134 | + | 0.199263i | −0.662540 | − | 0.749027i | \(-0.730522\pi\) |
0.317406 | + | 0.948290i | \(0.397188\pi\) | |||||||
\(984\) | 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 | −0.964447 | − | 0.264276i | \(-0.914867\pi\) |
0.253354 | − | 0.967374i | \(-0.418466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −952.000 | −0.956784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −398.864 | + | 230.284i | −0.400064 | + | 0.230977i | −0.686512 | − | 0.727119i | \(-0.740859\pi\) |
0.286448 | + | 0.958096i | \(0.407526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.3.z.k.901.1 | 8 | ||
3.2 | odd | 2 | 196.3.h.c.117.1 | 8 | |||
7.2 | even | 3 | 1764.3.d.e.685.4 | 4 | |||
7.3 | odd | 6 | inner | 1764.3.z.k.325.1 | 8 | ||
7.4 | even | 3 | inner | 1764.3.z.k.325.4 | 8 | ||
7.5 | odd | 6 | 1764.3.d.e.685.1 | 4 | |||
7.6 | odd | 2 | inner | 1764.3.z.k.901.4 | 8 | ||
12.11 | even | 2 | 784.3.s.g.705.4 | 8 | |||
21.2 | odd | 6 | 196.3.b.b.97.1 | ✓ | 4 | ||
21.5 | even | 6 | 196.3.b.b.97.4 | yes | 4 | ||
21.11 | odd | 6 | 196.3.h.c.129.4 | 8 | |||
21.17 | even | 6 | 196.3.h.c.129.1 | 8 | |||
21.20 | even | 2 | 196.3.h.c.117.4 | 8 | |||
84.11 | even | 6 | 784.3.s.g.129.1 | 8 | |||
84.23 | even | 6 | 784.3.c.d.97.4 | 4 | |||
84.47 | odd | 6 | 784.3.c.d.97.1 | 4 | |||
84.59 | odd | 6 | 784.3.s.g.129.4 | 8 | |||
84.83 | odd | 2 | 784.3.s.g.705.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.3.b.b.97.1 | ✓ | 4 | 21.2 | odd | 6 | ||
196.3.b.b.97.4 | yes | 4 | 21.5 | even | 6 | ||
196.3.h.c.117.1 | 8 | 3.2 | odd | 2 | |||
196.3.h.c.117.4 | 8 | 21.20 | even | 2 | |||
196.3.h.c.129.1 | 8 | 21.17 | even | 6 | |||
196.3.h.c.129.4 | 8 | 21.11 | odd | 6 | |||
784.3.c.d.97.1 | 4 | 84.47 | odd | 6 | |||
784.3.c.d.97.4 | 4 | 84.23 | even | 6 | |||
784.3.s.g.129.1 | 8 | 84.11 | even | 6 | |||
784.3.s.g.129.4 | 8 | 84.59 | odd | 6 | |||
784.3.s.g.705.1 | 8 | 84.83 | odd | 2 | |||
784.3.s.g.705.4 | 8 | 12.11 | even | 2 | |||
1764.3.d.e.685.1 | 4 | 7.5 | odd | 6 | |||
1764.3.d.e.685.4 | 4 | 7.2 | even | 3 | |||
1764.3.z.k.325.1 | 8 | 7.3 | odd | 6 | inner | ||
1764.3.z.k.325.4 | 8 | 7.4 | even | 3 | inner | ||
1764.3.z.k.901.1 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.z.k.901.4 | 8 | 7.6 | odd | 2 | inner |