Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,4,Mod(145,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.145");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.i (of order \(3\), 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: | \(25.4888251225\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} - 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(-2.31174 + 1.91203i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.145 |
Dual form | 432.4.i.b.289.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 5.43521 | − | 9.41407i | 0.486140 | − | 0.842020i | −0.513733 | − | 0.857950i | \(-0.671738\pi\) |
0.999873 | + | 0.0159306i | \(0.00507109\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.4352 | + | 21.5384i | 0.671438 | + | 1.16297i | 0.977496 | + | 0.210953i | \(0.0676565\pi\) |
−0.306058 | + | 0.952013i | \(0.599010\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.3704 | + | 37.0147i | 0.585766 | + | 1.01458i | 0.994779 | + | 0.102048i | \(0.0325396\pi\) |
−0.409013 | + | 0.912528i | \(0.634127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.56479 | + | 13.1026i | −0.161392 | + | 0.279539i | −0.935368 | − | 0.353676i | \(-0.884932\pi\) |
0.773976 | + | 0.633215i | \(0.218265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.8704 | 0.197887 | 0.0989433 | − | 0.995093i | \(-0.468454\pi\) | ||||
0.0989433 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −143.352 | −1.73091 | −0.865454 | − | 0.500989i | \(-0.832970\pi\) | ||||
−0.865454 | + | 0.500989i | \(0.832970\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.56479 | + | 16.5667i | −0.0867129 | + | 0.150191i | −0.906120 | − | 0.423021i | \(-0.860970\pi\) |
0.819407 | + | 0.573212i | \(0.194303\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.41692 | + | 5.91828i | 0.0273353 | + | 0.0473462i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.046 | + | 195.802i | 0.723869 | + | 1.25378i | 0.959438 | + | 0.281920i | \(0.0909714\pi\) |
−0.235569 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.6944 | − | 51.4321i | 0.172041 | − | 0.297983i | −0.767092 | − | 0.641537i | \(-0.778297\pi\) |
0.939133 | + | 0.343553i | \(0.111631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 270.352 | 1.30565 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −84.1860 | −0.374056 | −0.187028 | − | 0.982355i | \(-0.559886\pi\) | ||||
−0.187028 | + | 0.982355i | \(0.559886\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 101.630 | − | 176.028i | 0.387119 | − | 0.670510i | −0.604942 | − | 0.796270i | \(-0.706804\pi\) |
0.992061 | + | 0.125760i | \(0.0401370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 162.945 | + | 282.229i | 0.577881 | + | 1.00092i | 0.995722 | + | 0.0923995i | \(0.0294537\pi\) |
−0.417841 | + | 0.908520i | \(0.637213\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.47180 | − | 9.47744i | −0.0169818 | − | 0.0294133i | 0.857410 | − | 0.514635i | \(-0.172072\pi\) |
−0.874391 | + | 0.485221i | \(0.838739\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −137.769 | + | 238.623i | −0.401659 | + | 0.695694i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 140.186 | 0.363321 | 0.181661 | − | 0.983361i | \(-0.441853\pi\) | ||||
0.181661 | + | 0.983361i | \(0.441853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 464.611 | 1.13906 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −57.3704 | + | 99.3685i | −0.126593 | + | 0.219266i | −0.922355 | − | 0.386345i | \(-0.873738\pi\) |
0.795761 | + | 0.605610i | \(0.207071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 377.528 | + | 653.898i | 0.792419 | + | 1.37251i | 0.924465 | + | 0.381266i | \(0.124512\pi\) |
−0.132047 | + | 0.991243i | \(0.542155\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 82.2325 | + | 142.431i | 0.156918 | + | 0.271790i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −383.723 | + | 664.627i | −0.699689 | + | 1.21190i | 0.268885 | + | 0.963172i | \(0.413345\pi\) |
−0.968574 | + | 0.248725i | \(0.919989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 335.854 | 0.561387 | 0.280694 | − | 0.959797i | \(-0.409436\pi\) | ||||
0.280694 | + | 0.959797i | \(0.409436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 167.279 | 0.268199 | 0.134099 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134099 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −531.492 | + | 920.570i | −0.786612 | + | 1.36245i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6578 | − | 21.9239i | −0.0180267 | − | 0.0312232i | 0.856871 | − | 0.515530i | \(-0.172405\pi\) |
−0.874898 | + | 0.484307i | \(0.839072\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −143.861 | − | 249.174i | −0.190250 | − | 0.329523i | 0.755083 | − | 0.655629i | \(-0.227597\pi\) |
−0.945333 | + | 0.326107i | \(0.894263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 75.3887 | − | 130.577i | 0.0962006 | − | 0.166624i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 860.817 | 1.02524 | 0.512620 | − | 0.858615i | \(-0.328675\pi\) | ||||
0.512620 | + | 0.858615i | \(0.328675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −376.279 | −0.433459 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −779.149 | + | 1349.53i | −0.841464 | + | 1.45746i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 201.075 | + | 348.272i | 0.210475 | + | 0.364553i | 0.951863 | − | 0.306523i | \(-0.0991657\pi\) |
−0.741389 | + | 0.671076i | \(0.765832\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −665.714 | − | 1153.05i | −0.655852 | − | 1.13597i | −0.981680 | − | 0.190540i | \(-0.938976\pi\) |
0.325828 | − | 0.945429i | \(-0.394357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −259.252 | + | 449.038i | −0.248009 | + | 0.429563i | −0.962973 | − | 0.269597i | \(-0.913109\pi\) |
0.714965 | + | 0.699161i | \(0.246443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1471.87 | 1.32982 | 0.664912 | − | 0.746922i | \(-0.268469\pi\) | ||||
0.664912 | + | 0.746922i | \(0.268469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −643.668 | −0.565616 | −0.282808 | − | 0.959176i | \(-0.591266\pi\) | ||||
−0.282808 | + | 0.959176i | \(0.591266\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 511.864 | − | 886.574i | 0.426125 | − | 0.738069i | −0.570400 | − | 0.821367i | \(-0.693212\pi\) |
0.996525 | + | 0.0832976i | \(0.0265452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 103.973 | + | 180.087i | 0.0843092 | + | 0.146028i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 172.482 | + | 298.747i | 0.132869 | + | 0.230135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −247.890 | + | 429.358i | −0.186244 | + | 0.322583i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1433.09 | 1.02544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 31.4481 | 0.0219730 | 0.0109865 | − | 0.999940i | \(-0.496503\pi\) | ||||
0.0109865 | + | 0.999940i | \(0.496503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 968.678 | − | 1677.80i | 0.646059 | − | 1.11901i | −0.337997 | − | 0.941147i | \(-0.609749\pi\) |
0.984056 | − | 0.177860i | \(-0.0569174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1782.61 | − | 3087.58i | −1.16220 | − | 2.01299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 579.297 | + | 1003.37i | 0.361261 | + | 0.625722i | 0.988169 | − | 0.153372i | \(-0.0490131\pi\) |
−0.626908 | + | 0.779093i | \(0.715680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1155.80 | − | 2001.90i | 0.705277 | − | 1.22158i | −0.261314 | − | 0.965254i | \(-0.584156\pi\) |
0.966591 | − | 0.256323i | \(-0.0825109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −646.651 | −0.378151 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2457.73 | 1.40761 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1475.11 | + | 2554.96i | −0.811043 | + | 1.40477i | 0.101092 | + | 0.994877i | \(0.467766\pi\) |
−0.912135 | + | 0.409890i | \(0.865567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −863.199 | − | 1495.10i | −0.465206 | − | 0.805761i | 0.534005 | − | 0.845482i | \(-0.320686\pi\) |
−0.999211 | + | 0.0397208i | \(0.987353\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −322.790 | − | 559.089i | −0.167272 | − | 0.289723i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −641.694 | + | 1111.45i | −0.326196 | + | 0.564988i | −0.981754 | − | 0.190157i | \(-0.939100\pi\) |
0.655558 | + | 0.755145i | \(0.272434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −475.761 | −0.232889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1033.93 | −0.496831 | −0.248415 | − | 0.968654i | \(-0.579910\pi\) | ||||
−0.248415 | + | 0.968654i | \(0.579910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 141.309 | − | 244.754i | 0.0654778 | − | 0.113411i | −0.831428 | − | 0.555632i | \(-0.812476\pi\) |
0.896906 | + | 0.442222i | \(0.145810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 984.048 | + | 1704.42i | 0.447905 | + | 0.775795i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1766.36 | − | 3059.43i | −0.776266 | − | 1.34453i | −0.934080 | − | 0.357063i | \(-0.883778\pi\) |
0.157814 | − | 0.987469i | \(-0.449555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −84.9802 | + | 147.190i | −0.0367080 | + | 0.0635801i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4052.74 | −1.69227 | −0.846135 | − | 0.532969i | \(-0.821076\pi\) | ||||
−0.846135 | + | 0.532969i | \(0.821076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2830.97 | −1.16257 | −0.581283 | − | 0.813702i | \(-0.697449\pi\) | ||||
−0.581283 | + | 0.813702i | \(0.697449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −457.569 | + | 792.532i | −0.181844 | + | 0.314963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 296.417 | + | 513.409i | 0.115915 | + | 0.200771i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2254.62 | − | 3905.12i | −0.854129 | − | 1.47940i | −0.877451 | − | 0.479667i | \(-0.840757\pi\) |
0.0233215 | − | 0.999728i | \(-0.492576\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1610.56 | − | 2789.58i | 0.600678 | − | 1.04040i | −0.392041 | − | 0.919948i | \(-0.628231\pi\) |
0.992719 | − | 0.120457i | \(-0.0384359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3784.20 | −1.36859 | −0.684297 | − | 0.729204i | \(-0.739891\pi\) | ||||
−0.684297 | + | 0.729204i | \(0.739891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2926.27 | 1.04240 | 0.521200 | − | 0.853435i | \(-0.325485\pi\) | ||||
0.521200 | + | 0.853435i | \(0.325485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2811.51 | + | 4869.69i | −0.972067 | + | 1.68367i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1104.76 | − | 1913.49i | −0.376388 | − | 0.651923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3063.50 | − | 5306.13i | −1.01391 | − | 1.75614i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 156.737 | − | 271.476i | 0.0511385 | − | 0.0885744i | −0.839323 | − | 0.543633i | \(-0.817048\pi\) |
0.890462 | + | 0.455059i | \(0.150382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3542.57 | 1.12373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1477.02 | 0.462059 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −104.927 | + | 181.739i | −0.0319373 | + | 0.0553170i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −355.193 | − | 615.212i | −0.106661 | − | 0.184743i | 0.807754 | − | 0.589519i | \(-0.200683\pi\) |
−0.914416 | + | 0.404776i | \(0.867349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.3308 | − | 28.2858i | −0.00477496 | − | 0.00827046i | 0.863628 | − | 0.504130i | \(-0.168187\pi\) |
−0.868403 | + | 0.495859i | \(0.834853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2751.92 | − | 4766.47i | 0.794114 | − | 1.37545i | −0.129286 | − | 0.991607i | \(-0.541268\pi\) |
0.923400 | − | 0.383839i | \(-0.125398\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6788.81 | 1.90880 | 0.954399 | − | 0.298534i | \(-0.0964977\pi\) | ||||
0.954399 | + | 0.298534i | \(0.0964977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −118.962 | −0.0330221 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 214.694 | − | 371.862i | 0.0581064 | − | 0.100643i | −0.835509 | − | 0.549477i | \(-0.814827\pi\) |
0.893615 | + | 0.448834i | \(0.148160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2421.82 | + | 4194.72i | 0.647317 | + | 1.12119i | 0.983761 | + | 0.179483i | \(0.0574424\pi\) |
−0.336444 | + | 0.941703i | \(0.609224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1497.61 | + | 2593.93i | 0.390525 | + | 0.676410i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1084.43 | − | 1878.28i | 0.279354 | − | 0.483856i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2400.87 | 0.603752 | 0.301876 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301876 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −817.614 | −0.203174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1490.50 | − | 2581.62i | 0.361769 | − | 0.626602i | −0.626483 | − | 0.779435i | \(-0.715506\pi\) |
0.988252 | + | 0.152833i | \(0.0488396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1046.87 | − | 1813.23i | −0.251156 | − | 0.435015i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2780.41 | − | 4815.81i | −0.651891 | − | 1.12911i | −0.982664 | − | 0.185398i | \(-0.940643\pi\) |
0.330773 | − | 0.943710i | \(-0.392691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 761.941 | − | 1319.72i | 0.176625 | − | 0.305924i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6288.50 | −1.42534 | −0.712671 | − | 0.701499i | \(-0.752515\pi\) | ||||
−0.712671 | + | 0.701499i | \(0.752515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6854.90 | −1.53655 | −0.768275 | − | 0.640119i | \(-0.778885\pi\) | ||||
−0.768275 | + | 0.640119i | \(0.778885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −146.042 | + | 252.952i | −0.0320242 | + | 0.0554676i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −449.086 | − | 777.840i | −0.0974114 | − | 0.168722i | 0.813201 | − | 0.581983i | \(-0.197723\pi\) |
−0.910612 | + | 0.413261i | \(0.864390\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 119.385 | + | 206.781i | 0.0253448 | + | 0.0438986i | 0.878420 | − | 0.477890i | \(-0.158598\pi\) |
−0.853075 | + | 0.521789i | \(0.825265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1035.58 | − | 1793.68i | 0.217523 | − | 0.376760i | −0.736527 | − | 0.676408i | \(-0.763536\pi\) |
0.954050 | + | 0.299647i | \(0.0968690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5055.14 | 1.03971 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4720.61 | −0.960841 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3288.88 | + | 5696.51i | −0.655763 | + | 1.13581i | 0.325939 | + | 0.945391i | \(0.394319\pi\) |
−0.981702 | + | 0.190423i | \(0.939014\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 623.641 | + | 1080.18i | 0.123084 | + | 0.213188i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −144.711 | − | 250.647i | −0.0279895 | − | 0.0484792i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4052.51 | + | 7019.16i | −0.776023 | + | 1.34411i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8207.78 | 1.54091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5237.30 | 0.973644 | 0.486822 | − | 0.873501i | \(-0.338156\pi\) | ||||
0.486822 | + | 0.873501i | \(0.338156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2852.49 | + | 4940.67i | −0.520097 | + | 0.900834i | 0.479630 | + | 0.877471i | \(0.340771\pi\) |
−0.999727 | + | 0.0233635i | \(0.992562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2538.74 | − | 4397.23i | −0.458460 | − | 0.794076i | 0.540420 | − | 0.841396i | \(-0.318265\pi\) |
−0.998880 | + | 0.0473193i | \(0.984932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1434.46 | + | 2484.55i | 0.254155 | + | 0.440209i | 0.964666 | − | 0.263477i | \(-0.0848694\pi\) |
−0.710511 | + | 0.703686i | \(0.751536\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4831.70 | + | 8368.76i | −0.848036 | + | 1.46884i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1988.36 | −0.342523 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −103.393 | −0.0176468 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 136.086 | − | 235.708i | 0.0228045 | − | 0.0394985i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1015.67 | + | 1759.20i | 0.168660 | + | 0.292128i | 0.937949 | − | 0.346773i | \(-0.112723\pi\) |
−0.769289 | + | 0.638901i | \(0.779389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4171.23 | + | 7224.78i | 0.680294 | + | 1.17830i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4899.14 | + | 8485.56i | −0.791909 | + | 1.37163i | 0.132875 | + | 0.991133i | \(0.457579\pi\) |
−0.924784 | + | 0.380493i | \(0.875754\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2538.32 | 0.403103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1677.81 | 0.264120 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2278.28 | − | 3946.10i | 0.352463 | − | 0.610483i | −0.634218 | − | 0.773154i | \(-0.718678\pi\) |
0.986680 | + | 0.162671i | \(0.0520111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1674.44 | − | 2900.22i | −0.256822 | − | 0.444829i | 0.708567 | − | 0.705644i | \(-0.249342\pi\) |
−0.965389 | + | 0.260815i | \(0.916009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 931.134 | + | 1612.77i | 0.140395 | + | 0.243170i | 0.927645 | − | 0.373463i | \(-0.121830\pi\) |
−0.787251 | + | 0.616633i | \(0.788496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1825.44 | − | 3161.75i | 0.272913 | − | 0.472699i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6179.46 | 0.908466 | 0.454233 | − | 0.890883i | \(-0.349913\pi\) | ||||
0.454233 | + | 0.890883i | \(0.349913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13690.8 | 1.99604 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 909.197 | − | 1574.77i | 0.130382 | − | 0.225829i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3436.98 | + | 5953.02i | 0.488852 | + | 0.846717i | 0.999918 | − | 0.0128251i | \(-0.00408245\pi\) |
−0.511066 | + | 0.859542i | \(0.670749\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1743.24 | + | 3019.38i | 0.243948 | + | 0.422530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −635.013 | + | 1099.87i | −0.0881494 | + | 0.152679i | −0.906729 | − | 0.421714i | \(-0.861429\pi\) |
0.818580 | + | 0.574393i | \(0.194762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3420.69 | −0.467306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2490.54 | −0.337548 | −0.168774 | − | 0.985655i | \(-0.553981\pi\) | ||||
−0.168774 | + | 0.985655i | \(0.553981\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −156.213 | + | 270.568i | −0.0208410 | + | 0.0360976i | −0.876258 | − | 0.481843i | \(-0.839968\pi\) |
0.855417 | + | 0.517940i | \(0.173301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5777.54 | + | 10007.0i | 0.764807 | + | 1.32468i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4821.58 | + | 8351.23i | 0.628442 | + | 1.08849i | 0.987864 | + | 0.155319i | \(0.0496404\pi\) |
−0.359422 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −132.668 | + | 229.787i | −0.0171593 | + | 0.0297208i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −275.191 | −0.0350540 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2260.32 | −0.285749 | −0.142874 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142874 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5084.64 | − | 8806.85i | 0.633204 | − | 1.09674i | −0.353689 | − | 0.935363i | \(-0.615073\pi\) |
0.986893 | − | 0.161378i | \(-0.0515938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 449.263 | + | 778.146i | 0.0555320 | + | 0.0961842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1799.09 | − | 3116.12i | −0.219110 | − | 0.379509i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 474.916 | − | 822.579i | 0.0574159 | − | 0.0994472i | −0.835889 | − | 0.548899i | \(-0.815047\pi\) |
0.893305 | + | 0.449452i | \(0.148381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2853.65 | −0.339998 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3127.65 | −0.369953 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5899.63 | − | 10218.5i | 0.687866 | − | 1.19142i | −0.284660 | − | 0.958628i | \(-0.591881\pi\) |
0.972527 | − | 0.232791i | \(-0.0747859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3206.46 | + | 5553.76i | 0.371196 | + | 0.642930i | 0.989750 | − | 0.142812i | \(-0.0456145\pi\) |
−0.618554 | + | 0.785742i | \(0.712281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 47.3941 | + | 82.0890i | 0.00540930 | + | 0.00936918i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9389.29 | + | 16262.7i | −1.06412 | + | 1.84311i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12042.7 | −1.34589 | −0.672945 | − | 0.739693i | \(-0.734971\pi\) | ||||
−0.672945 | + | 0.739693i | \(0.734971\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7279.83 | 0.807959 | 0.403980 | − | 0.914768i | \(-0.367627\pi\) | ||||
0.403980 | + | 0.914768i | \(0.367627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1371.13 | − | 2374.87i | 0.150092 | − | 0.259967i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1799.35 | − | 3116.57i | −0.195623 | − | 0.338828i | 0.751482 | − | 0.659754i | \(-0.229339\pi\) |
−0.947104 | + | 0.320926i | \(0.896006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7393.18 | + | 12805.4i | 0.792913 | + | 1.37337i | 0.924156 | + | 0.382016i | \(0.124770\pi\) |
−0.131243 | + | 0.991350i | \(0.541897\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4678.72 | − | 8103.79i | 0.498411 | − | 0.863273i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −114.489 | −0.0120336 | −0.00601681 | − | 0.999982i | \(-0.501915\pi\) | ||||
−0.00601681 | + | 0.999982i | \(0.501915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8687.47 | 0.907044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2045.16 | + | 3542.31i | −0.210722 | + | 0.364981i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3155.57 | − | 5465.60i | −0.323001 | − | 0.559453i | 0.658105 | − | 0.752926i | \(-0.271358\pi\) |
−0.981106 | + | 0.193473i | \(0.938025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6872.41 | − | 11903.4i | −0.694317 | − | 1.20259i | −0.970411 | − | 0.241461i | \(-0.922373\pi\) |
0.276094 | − | 0.961131i | \(-0.410960\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7824.30 | − | 13552.1i | 0.785369 | − | 1.36030i | −0.143409 | − | 0.989664i | \(-0.545806\pi\) |
0.928778 | − | 0.370636i | \(-0.120860\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7395.79 | −0.732840 | −0.366420 | − | 0.930450i | \(-0.619417\pi\) | ||||
−0.366420 | + | 0.930450i | \(0.619417\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19086.7 | −1.87919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6964.41 | + | 12062.7i | −0.677006 | + | 1.17261i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −489.822 | − | 848.397i | −0.0473149 | − | 0.0819519i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3130.53 | + | 5422.24i | 0.298617 | + | 0.517221i | 0.975820 | − | 0.218576i | \(-0.0701412\pi\) |
−0.677202 | + | 0.735797i | \(0.736808\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 636.849 | − | 1103.05i | 0.0603697 | − | 0.104563i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4371.54 | 0.409281 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10314.7 | 0.959763 | 0.479881 | − | 0.877333i | \(-0.340680\pi\) | ||||
0.479881 | + | 0.877333i | \(0.340680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1380.45 | − | 2391.01i | 0.126881 | − | 0.219765i | −0.795585 | − | 0.605841i | \(-0.792837\pi\) |
0.922467 | + | 0.386076i | \(0.126170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1568.00 | + | 2715.86i | 0.143244 | + | 0.248106i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4176.41 | + | 7233.76i | 0.376937 | + | 0.652874i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4793.00 | + | 8301.71i | −0.429988 | + | 0.744761i | −0.996872 | − | 0.0790369i | \(-0.974816\pi\) |
0.566884 | + | 0.823798i | \(0.308149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8829.60 | 0.782689 | 0.391344 | − | 0.920244i | \(-0.372010\pi\) | ||||
0.391344 | + | 0.920244i | \(0.372010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14473.2 | −1.27534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2370.87 | − | 4106.47i | 0.206458 | − | 0.357595i | −0.744138 | − | 0.668025i | \(-0.767140\pi\) |
0.950596 | + | 0.310430i | \(0.100473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2080.15 | + | 3602.92i | 0.180079 | + | 0.311906i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2818.18 | + | 4881.24i | 0.241134 | + | 0.417656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 233.870 | − | 405.074i | 0.0198947 | − | 0.0344587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2753.22 | 0.231518 | 0.115759 | − | 0.993277i | \(-0.463070\pi\) | ||||
0.115759 | + | 0.993277i | \(0.463070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17115.3 | −1.43098 | −0.715489 | − | 0.698624i | \(-0.753796\pi\) | ||||
−0.715489 | + | 0.698624i | \(0.753796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 411.873 | − | 713.386i | 0.0340446 | − | 0.0589669i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5900.53 | + | 10220.0i | 0.484962 | + | 0.839978i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1537.61 | + | 2663.22i | 0.124956 | + | 0.216430i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7999.93 | − | 13856.3i | 0.646481 | − | 1.11974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11776.7 | −0.941113 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17880.1 | 1.42093 | 0.710467 | − | 0.703731i | \(-0.248484\pi\) | ||||
0.710467 | + | 0.703731i | \(0.248484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3498.47 | + | 6059.53i | −0.274969 | + | 0.476260i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6534.73 | − | 11318.5i | −0.510795 | − | 0.884723i | −0.999922 | − | 0.0125101i | \(-0.996018\pi\) |
0.489127 | − | 0.872213i | \(-0.337316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16205.5 | − | 28068.7i | −1.25295 | − | 2.17017i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 314.804 | − | 545.257i | 0.0242077 | − | 0.0419289i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9507.62 | −0.723251 | −0.361626 | − | 0.932323i | \(-0.617778\pi\) | ||||
−0.361626 | + | 0.932323i | \(0.617778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4930.58 | −0.373061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10222.3 | − | 17705.6i | 0.765221 | − | 1.32540i | −0.174909 | − | 0.984585i | \(-0.555963\pi\) |
0.940130 | − | 0.340817i | \(-0.110704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5564.17 | − | 9637.43i | −0.414313 | − | 0.717610i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1323.03 | + | 2291.56i | 0.0974770 | + | 0.168835i | 0.910640 | − | 0.413201i | \(-0.135589\pi\) |
−0.813163 | + | 0.582036i | \(0.802256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 878.514 | − | 1521.63i | 0.0643864 | − | 0.111521i | −0.832035 | − | 0.554723i | \(-0.812824\pi\) |
0.896422 | + | 0.443202i | \(0.146158\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −130.728 | −0.00948130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7515.43 | −0.542238 | −0.271119 | − | 0.962546i | \(-0.587394\pi\) | ||||
−0.271119 | + | 0.962546i | \(0.587394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3577.87 | − | 6197.06i | 0.255482 | − | 0.442508i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2995.83 | + | 5188.94i | 0.212821 | + | 0.368617i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2476.24 | + | 4288.98i | 0.174115 | + | 0.301576i | 0.939855 | − | 0.341575i | \(-0.110960\pi\) |
−0.765740 | + | 0.643151i | \(0.777627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4256.75 | + | 7372.91i | −0.297787 | + | 0.515782i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17115.3 | −1.18523 | −0.592613 | − | 0.805487i | \(-0.701904\pi\) | ||||
−0.592613 | + | 0.805487i | \(0.701904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3749.90 | 0.258371 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4207.06 | + | 7286.85i | −0.286972 | + | 0.497049i | −0.973085 | − | 0.230445i | \(-0.925982\pi\) |
0.686114 | + | 0.727494i | \(0.259315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14047.1 | − | 24330.3i | −0.953399 | − | 1.65134i | −0.737990 | − | 0.674812i | \(-0.764225\pi\) |
−0.215409 | − | 0.976524i | \(-0.569108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2694.67 | + | 4667.31i | 0.181081 | + | 0.313642i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 715.423 | − | 1239.15i | 0.0478388 | − | 0.0828592i | −0.841114 | − | 0.540857i | \(-0.818100\pi\) |
0.888953 | + | 0.457998i | \(0.151433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 165.572 | 0.0109629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14438.1 | 0.951306 | 0.475653 | − | 0.879633i | \(-0.342212\pi\) | ||||
0.475653 | + | 0.879633i | \(0.342212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12722.5 | − | 22036.0i | 0.830125 | − | 1.43782i | −0.0678130 | − | 0.997698i | \(-0.521602\pi\) |
0.897938 | − | 0.440121i | \(-0.145065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1739.73 | − | 3013.30i | −0.112966 | − | 0.195662i | 0.803999 | − | 0.594631i | \(-0.202702\pi\) |
−0.916965 | + | 0.398968i | \(0.869368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10704.4 | + | 18540.6i | 0.688386 | + | 1.19232i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7362.03 | − | 12751.4i | 0.471170 | − | 0.816091i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1167.70 | −0.0740208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11151.7 | −0.703552 | −0.351776 | − | 0.936084i | \(-0.614422\pi\) | ||||
−0.351776 | + | 0.936084i | \(0.614422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 170.927 | − | 296.055i | 0.0106820 | − | 0.0185017i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2084.39 | − | 3610.26i | −0.129649 | − | 0.224559i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −546.388 | − | 946.373i | −0.0336678 | − | 0.0583143i | 0.848701 | − | 0.528874i | \(-0.177385\pi\) |
−0.882368 | + | 0.470559i | \(0.844052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15847.0 | − | 27447.8i | 0.971922 | − | 1.68342i | 0.282181 | − | 0.959361i | \(-0.408942\pi\) |
0.689741 | − | 0.724056i | \(-0.257724\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13719.9 | −0.833672 | −0.416836 | − | 0.908982i | \(-0.636861\pi\) | ||||
−0.416836 | + | 0.908982i | \(0.636861\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4904.12 | −0.296616 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6642.59 | − | 11505.3i | 0.398078 | − | 0.689491i | −0.595411 | − | 0.803421i | \(-0.703011\pi\) |
0.993489 | + | 0.113930i | \(0.0363441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10529.9 | − | 18238.4i | −0.628151 | − | 1.08799i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1296.99 | + | 2246.45i | 0.0766670 | + | 0.132791i | 0.901810 | − | 0.432133i | \(-0.142239\pi\) |
−0.825143 | + | 0.564924i | \(0.808905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7937.67 | − | 13748.4i | 0.467079 | − | 0.809005i | −0.532213 | − | 0.846610i | \(-0.678640\pi\) |
0.999293 | + | 0.0376052i | \(0.0119729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38755.6 | −2.25996 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4325.06 | −0.251075 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16135.9 | + | 27948.2i | −0.928344 | + | 1.60794i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10717.3 | − | 18563.0i | −0.613853 | − | 1.06323i | −0.990585 | − | 0.136903i | \(-0.956285\pi\) |
0.376731 | − | 0.926323i | \(-0.377048\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10166.5 | − | 17608.9i | −0.577150 | − | 0.999653i | −0.995804 | − | 0.0915074i | \(-0.970832\pi\) |
0.418655 | − | 0.908146i | \(-0.362502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5000.81 | + | 8661.66i | −0.282642 | + | 0.489549i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27149.0 | −1.52097 | −0.760487 | − | 0.649353i | \(-0.775040\pi\) | ||||
−0.760487 | + | 0.649353i | \(0.775040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12594.4 | 0.702493 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1060.48 | + | 1836.80i | −0.0586371 | + | 0.101562i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11355.1 | + | 19667.6i | 0.625134 | + | 1.08276i | 0.988515 | + | 0.151123i | \(0.0482891\pi\) |
−0.363381 | + | 0.931641i | \(0.618378\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12564.0 | − | 21761.5i | −0.685728 | − | 1.18771i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1409.65 | − | 2441.58i | 0.0766056 | − | 0.132685i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20079.5 | 1.08187 | 0.540936 | − | 0.841064i | \(-0.318070\pi\) | ||||
0.540936 | + | 0.841064i | \(0.318070\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12068.2 | 0.647457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16556.6 | − | 28676.9i | 0.880728 | − | 1.52547i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14491.8 | + | 25100.6i | 0.767634 | + | 1.32958i | 0.938843 | + | 0.344346i | \(0.111899\pi\) |
−0.171209 | + | 0.985235i | \(0.554767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 568.040 | + | 983.875i | 0.0298363 | + | 0.0516780i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3514.69 | + | 6087.61i | −0.183835 | + | 0.318411i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14496.2 | 0.751901 | 0.375951 | − | 0.926640i | \(-0.377316\pi\) | ||||
0.375951 | + | 0.926640i | \(0.377316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12895.4 | −0.666090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −772.541 | + | 1338.08i | −0.0395744 | + | 0.0685449i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2500.25 | + | 4330.56i | 0.127550 | + | 0.220924i | 0.922727 | − | 0.385454i | \(-0.125955\pi\) |
−0.795177 | + | 0.606378i | \(0.792622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2260.12 | + | 3914.64i | 0.114355 | + | 0.198069i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8757.79 | + | 15168.9i | −0.441305 | + | 0.764362i | −0.997787 | − | 0.0664977i | \(-0.978817\pi\) |
0.556482 | + | 0.830860i | \(0.312151\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32801.3 | −1.63942 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20169.2 | 1.00397 | 0.501985 | − | 0.864876i | \(-0.332603\pi\) | ||||
0.501985 | + | 0.864876i | \(0.332603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18351.3 | − | 31785.4i | 0.906116 | − | 1.56944i | 0.0867044 | − | 0.996234i | \(-0.472366\pi\) |
0.819412 | − | 0.573205i | \(-0.194300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16035.0 | + | 27773.5i | 0.788561 | + | 1.36583i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18303.0 | + | 31701.8i | 0.892894 | + | 1.54654i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16660.0 | + | 28856.0i | −0.809499 | + | 1.40209i | 0.103713 | + | 0.994607i | \(0.466928\pi\) |
−0.913212 | + | 0.407485i | \(0.866406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18766.7 | −0.904622 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26515.6 | 1.27309 | 0.636543 | − | 0.771241i | \(-0.280364\pi\) | ||||
0.636543 | + | 0.771241i | \(0.280364\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2842.17 | + | 4922.79i | −0.135386 | + | 0.234495i | −0.925745 | − | 0.378149i | \(-0.876561\pi\) |
0.790359 | + | 0.612644i | \(0.209894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8004.14 | − | 13863.6i | −0.379777 | − | 0.657792i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −867.990 | − | 1503.40i | −0.0408622 | − | 0.0707754i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 199.189 | − | 345.005i | 0.00934060 | − | 0.0161784i | −0.861317 | − | 0.508067i | \(-0.830360\pi\) |
0.870658 | + | 0.491889i | \(0.163693\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8437.17 | 0.392579 | 0.196290 | − | 0.980546i | \(-0.437111\pi\) | ||||
0.196290 | + | 0.980546i | \(0.437111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 405.853 | 0.0188112 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14568.8 | + | 25233.9i | −0.670067 | + | 1.16059i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7177.34 | + | 12431.5i | 0.328842 | + | 0.569570i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6975.49 | + | 12081.9i | 0.317154 | + | 0.549327i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8138.94 | − | 14097.1i | 0.368643 | − | 0.638508i | −0.620711 | − | 0.784040i | \(-0.713156\pi\) |
0.989354 | + | 0.145531i | \(0.0464892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25460.5 | 1.14447 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11423.7 | −0.511560 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2556.06 | − | 4427.22i | 0.113601 | − | 0.196763i | −0.803619 | − | 0.595145i | \(-0.797095\pi\) |
0.917220 | + | 0.398382i | \(0.130428\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.8963 | − | 131.456i | −0.00336047 | − | 0.00582051i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3574.82 | + | 6191.77i | 0.157102 | + | 0.272108i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2585.86 | + | 4478.84i | −0.113217 | + | 0.196097i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13141.2 | 0.571100 | 0.285550 | − | 0.958364i | \(-0.407824\pi\) | ||||
0.285550 | + | 0.958364i | \(0.407824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18614.2 | 0.805957 | 0.402979 | − | 0.915209i | \(-0.367975\pi\) | ||||
0.402979 | + | 0.915209i | \(0.367975\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5619.61 | + | 9733.45i | −0.241529 | + | 0.418341i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23358.5 | − | 40458.2i | −1.00026 | − | 1.73250i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5660.01 | − | 9803.43i | −0.240604 | − | 0.416738i | 0.720283 | − | 0.693681i | \(-0.244012\pi\) |
−0.960886 | + | 0.276943i | \(0.910679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5433.29 | − | 9410.73i | 0.230125 | − | 0.398587i | −0.727720 | − | 0.685874i | \(-0.759420\pi\) |
0.957845 | + | 0.287287i | \(0.0927533\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13059.3 | −0.549114 | −0.274557 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274557 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21203.7 | −0.888341 | −0.444171 | − | 0.895942i | \(-0.646502\pi\) | ||||
−0.444171 | + | 0.895942i | \(0.646502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1910.92 | + | 3309.80i | −0.0794829 | + | 0.137669i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1536.09 | − | 2660.58i | −0.0636628 | − | 0.110267i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7240.28 | + | 12540.5i | 0.297929 | + | 0.516028i | 0.975662 | − | 0.219280i | \(-0.0703708\pi\) |
−0.677733 | + | 0.735308i | \(0.737038\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13364.5 | + | 23148.0i | −0.547973 | + | 0.949117i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21394.0 | 0.870979 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12330.3 | −0.500204 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 805.221 | − | 1394.68i | 0.0324355 | − | 0.0561799i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3233.61 | + | 5600.78i | 0.129797 | + | 0.224815i | 0.923598 | − | 0.383363i | \(-0.125234\pi\) |
−0.793801 | + | 0.608178i | \(0.791901\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1947.32 | + | 3372.85i | 0.0776186 | + | 0.134439i | 0.902222 | − | 0.431272i | \(-0.141935\pi\) |
−0.824603 | + | 0.565711i | \(0.808602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18826.9 | + | 32609.1i | −0.747805 | + | 1.29524i | 0.201067 | + | 0.979577i | \(0.435559\pi\) |
−0.948873 | + | 0.315659i | \(0.897774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47067.5 | 1.85654 | 0.928271 | − | 0.371905i | \(-0.121295\pi\) | ||||
0.928271 | + | 0.371905i | \(0.121295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38402.2 | −1.50950 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 541.004 | − | 937.046i | 0.0211189 | − | 0.0365790i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5805.56 | − | 10055.5i | −0.225848 | − | 0.391181i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17820.8 | + | 30866.5i | 0.688517 | + | 1.19255i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3721.77 | − | 6446.29i | 0.143301 | − | 0.248205i | −0.785437 | − | 0.618942i | \(-0.787562\pi\) |
0.928738 | + | 0.370737i | \(0.120895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13781.9 | 0.527040 | 0.263520 | − | 0.964654i | \(-0.415116\pi\) | ||||
0.263520 | + | 0.964654i | \(0.415116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12230.3 | −0.466119 | −0.233060 | − | 0.972462i | \(-0.574874\pi\) | ||||
−0.233060 | + | 0.972462i | \(0.574874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 837.437 | − | 1450.48i | 0.0317005 | − | 0.0549069i | −0.849740 | − | 0.527202i | \(-0.823241\pi\) |
0.881440 | + | 0.472295i | \(0.156574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 391.064 | + | 677.343i | 0.0147535 | + | 0.0255538i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 784.395 | + | 1358.61i | 0.0293939 | + | 0.0509118i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22027.5 | + | 38152.8i | −0.822680 | + | 1.42492i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13427.4 | 0.498140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1944.44 | 0.0718964 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15386.9 | + | 26650.9i | −0.565170 | + | 0.978903i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8544.04 | + | 14798.7i | 0.312790 | + | 0.541768i | 0.978965 | − | 0.204027i | \(-0.0654031\pi\) |
−0.666175 | + | 0.745795i | \(0.732070\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10644.2 | − | 18436.3i | −0.387111 | − | 0.670496i | 0.604949 | − | 0.796264i | \(-0.293194\pi\) |
−0.992060 | + | 0.125769i | \(0.959860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6148.72 | − | 10649.9i | 0.222884 | − | 0.386046i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 48182.8 | 1.73516 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10413.4 | 0.373784 | 0.186892 | − | 0.982380i | \(-0.440159\pi\) | ||||
0.186892 | + | 0.982380i | \(0.440159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2540.66 | + | 4400.55i | −0.0906033 | + | 0.156930i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −287.657 | − | 498.236i | −0.0102250 | − | 0.0177102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3411.72 | − | 5909.26i | −0.120490 | − | 0.208694i | 0.799471 | − | 0.600704i | \(-0.205113\pi\) |
−0.919961 | + | 0.392010i | \(0.871780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19749.5 | − | 34207.1i | 0.695234 | − | 1.20418i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6444.36 | 0.225404 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41049.8 | 1.43120 | 0.715602 | − | 0.698508i | \(-0.246152\pi\) | ||||
0.715602 | + | 0.698508i | \(0.246152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1208.06 | − | 2092.42i | 0.0418508 | − | 0.0724878i | −0.844341 | − | 0.535806i | \(-0.820008\pi\) |
0.886192 | + | 0.463318i | \(0.153341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1944.13 | + | 3367.33i | 0.0671364 | + | 0.116284i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1197.04 | + | 2073.33i | 0.0410755 | + | 0.0711448i | 0.885832 | − | 0.464006i | \(-0.153588\pi\) |
−0.844757 | + | 0.535150i | \(0.820255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1265.43 | + | 2191.79i | −0.0432851 | + | 0.0749720i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50651.3 | 1.72168 | 0.860838 | − | 0.508879i | \(-0.169940\pi\) | ||||
0.860838 | + | 0.508879i | \(0.169940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49017.4 | −1.66091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14407.4 | + | 24954.3i | −0.485128 | + | 0.840267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13132.0 | + | 22745.3i | 0.440804 | + | 0.763495i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17507.5 | − | 30323.9i | −0.584027 | − | 1.01156i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12517.5 | − | 21680.9i | 0.416271 | − | 0.721003i | −0.579290 | − | 0.815122i | \(-0.696670\pi\) |
0.995561 | + | 0.0941189i | \(0.0300034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49553.7 | 1.63775 | 0.818875 | − | 0.573972i | \(-0.194598\pi\) | ||||
0.818875 | + | 0.573972i | \(0.194598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57490.4 | 1.89420 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17588.1 | + | 30463.5i | −0.575939 | + | 0.997556i | 0.419999 | + | 0.907524i | \(0.362030\pi\) |
−0.995939 | + | 0.0900320i | \(0.971303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18396.0 | + | 31862.9i | 0.600551 | + | 1.04019i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16674.6 | − | 28881.3i | −0.541036 | − | 0.937102i | −0.998845 | − | 0.0480511i | \(-0.984699\pi\) |
0.457809 | − | 0.889051i | \(-0.348634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20567.9 | + | 35624.7i | −0.665328 | + | 1.15238i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6234.14 | −0.200439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23066.3 | −0.739378 | −0.369689 | − | 0.929156i | \(-0.620536\pi\) | ||||
−0.369689 | + | 0.929156i | \(0.620536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15904.9 | − | 27548.1i | 0.506752 | − | 0.877721i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27884.9 | + | 48298.1i | 0.885782 | + | 1.53422i | 0.844815 | + | 0.535059i | \(0.179711\pi\) |
0.0409671 | + | 0.999160i | \(0.486956\pi\) | |||||||
\(998\) | 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 | 432.4.i.b.145.2 | 4 | ||
3.2 | odd | 2 | 144.4.i.b.49.1 | 4 | |||
4.3 | odd | 2 | 54.4.c.b.37.2 | 4 | |||
9.2 | odd | 6 | 144.4.i.b.97.1 | 4 | |||
9.4 | even | 3 | 1296.4.a.r.1.1 | 2 | |||
9.5 | odd | 6 | 1296.4.a.l.1.2 | 2 | |||
9.7 | even | 3 | inner | 432.4.i.b.289.2 | 4 | ||
12.11 | even | 2 | 18.4.c.b.13.2 | yes | 4 | ||
36.7 | odd | 6 | 54.4.c.b.19.2 | 4 | |||
36.11 | even | 6 | 18.4.c.b.7.2 | ✓ | 4 | ||
36.23 | even | 6 | 162.4.a.f.1.2 | 2 | |||
36.31 | odd | 6 | 162.4.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.4.c.b.7.2 | ✓ | 4 | 36.11 | even | 6 | ||
18.4.c.b.13.2 | yes | 4 | 12.11 | even | 2 | ||
54.4.c.b.19.2 | 4 | 36.7 | odd | 6 | |||
54.4.c.b.37.2 | 4 | 4.3 | odd | 2 | |||
144.4.i.b.49.1 | 4 | 3.2 | odd | 2 | |||
144.4.i.b.97.1 | 4 | 9.2 | odd | 6 | |||
162.4.a.f.1.2 | 2 | 36.23 | even | 6 | |||
162.4.a.g.1.1 | 2 | 36.31 | odd | 6 | |||
432.4.i.b.145.2 | 4 | 1.1 | even | 1 | trivial | ||
432.4.i.b.289.2 | 4 | 9.7 | even | 3 | inner | ||
1296.4.a.l.1.2 | 2 | 9.5 | odd | 6 | |||
1296.4.a.r.1.1 | 2 | 9.4 | even | 3 |