Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-3.91663 - 2.26127i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.a.593.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.632851 | − | 1.09613i | −0.0566040 | − | 0.0980409i | 0.836335 | − | 0.548219i | \(-0.184694\pi\) |
−0.892939 | + | 0.450178i | \(0.851361\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.4032 | + | 12.7810i | −0.723705 | + | 0.690109i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36.0248 | − | 20.7989i | −0.987443 | − | 0.570101i | −0.0829344 | − | 0.996555i | \(-0.526429\pi\) |
−0.904509 | + | 0.426454i | \(0.859763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 85.7355i | 1.82914i | 0.404433 | + | 0.914568i | \(0.367469\pi\) | ||||
−0.404433 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 38.8929 | − | 67.3645i | 0.554878 | − | 0.961076i | −0.443035 | − | 0.896504i | \(-0.646098\pi\) |
0.997913 | − | 0.0645722i | \(-0.0205683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.1638 | + | 24.3433i | −0.509107 | + | 0.293933i | −0.732466 | − | 0.680803i | \(-0.761631\pi\) |
0.223360 | + | 0.974736i | \(0.428298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −78.7639 | + | 45.4743i | −0.714061 | + | 0.412263i | −0.812563 | − | 0.582874i | \(-0.801928\pi\) |
0.0985019 | + | 0.995137i | \(0.468595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.6990 | − | 106.866i | 0.493592 | − | 0.854926i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 151.196i | 0.968151i | 0.875026 | + | 0.484075i | \(0.160844\pi\) | ||||
−0.875026 | + | 0.484075i | \(0.839156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −76.3661 | − | 44.0900i | −0.442444 | − | 0.255445i | 0.262190 | − | 0.965016i | \(-0.415555\pi\) |
−0.704634 | + | 0.709571i | \(0.748889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.4919 | + | 6.60319i | 0.108624 | + | 0.0318898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −45.2914 | − | 78.4470i | −0.201239 | − | 0.348557i | 0.747689 | − | 0.664050i | \(-0.231164\pi\) |
−0.948928 | + | 0.315493i | \(0.897830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 383.530 | 1.46091 | 0.730455 | − | 0.682961i | \(-0.239308\pi\) | ||||
0.730455 | + | 0.682961i | \(0.239308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 227.894 | 0.808222 | 0.404111 | − | 0.914710i | \(-0.367581\pi\) | ||||
0.404111 | + | 0.914710i | \(0.367581\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −69.5529 | − | 120.469i | −0.215858 | − | 0.373877i | 0.737680 | − | 0.675151i | \(-0.235922\pi\) |
−0.953538 | + | 0.301274i | \(0.902588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.2918 | − | 342.613i | 0.0474981 | − | 0.998871i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −289.749 | − | 167.287i | −0.750945 | − | 0.433558i | 0.0750904 | − | 0.997177i | \(-0.476075\pi\) |
−0.826035 | + | 0.563619i | \(0.809409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 52.6505i | 0.129080i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 440.050 | − | 762.189i | 0.971010 | − | 1.68184i | 0.278493 | − | 0.960438i | \(-0.410165\pi\) |
0.692518 | − | 0.721401i | \(-0.256501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3944 | − | 6.57854i | 0.0239164 | − | 0.0138081i | −0.487994 | − | 0.872847i | \(-0.662271\pi\) |
0.511911 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 93.9774 | − | 54.2579i | 0.179330 | − | 0.103536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −221.212 | + | 383.151i | −0.403364 | + | 0.698647i | −0.994130 | − | 0.108197i | \(-0.965492\pi\) |
0.590766 | + | 0.806843i | \(0.298826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 341.552i | 0.570912i | 0.958392 | + | 0.285456i | \(0.0921450\pi\) | ||||
−0.958392 | + | 0.285456i | \(0.907855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −798.218 | − | 460.851i | −1.27979 | − | 0.738885i | −0.302977 | − | 0.952998i | \(-0.597981\pi\) |
−0.976809 | + | 0.214113i | \(0.931314\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 748.678 | − | 181.661i | 1.10805 | − | 0.268859i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −206.564 | − | 357.780i | −0.294181 | − | 0.509537i | 0.680613 | − | 0.732643i | \(-0.261714\pi\) |
−0.974794 | + | 0.223107i | \(0.928380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 954.307 | 1.26203 | 0.631017 | − | 0.775769i | \(-0.282638\pi\) | ||||
0.631017 | + | 0.775769i | \(0.282638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −98.4538 | −0.125633 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8490 | − | 25.7193i | −0.0176853 | − | 0.0306319i | 0.857047 | − | 0.515238i | \(-0.172296\pi\) |
−0.874733 | + | 0.484606i | \(0.838963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1095.79 | − | 1149.13i | −1.26230 | − | 1.32375i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 53.3668 | + | 30.8113i | 0.0576349 | + | 0.0332755i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1199.63i | 1.25572i | 0.778328 | + | 0.627858i | \(0.216068\pi\) | ||||
−0.778328 | + | 0.627858i | \(0.783932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 327.422 | − | 567.111i | 0.322571 | − | 0.558710i | −0.658447 | − | 0.752628i | \(-0.728786\pi\) |
0.981018 | + | 0.193918i | \(0.0621195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1186.01 | − | 684.744i | 1.13457 | − | 0.655047i | 0.189493 | − | 0.981882i | \(-0.439316\pi\) |
0.945081 | + | 0.326836i | \(0.105982\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 371.311 | − | 214.377i | 0.335477 | − | 0.193688i | −0.322793 | − | 0.946470i | \(-0.604622\pi\) |
0.658270 | + | 0.752782i | \(0.271289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 334.261 | − | 578.957i | 0.293728 | − | 0.508752i | −0.680960 | − | 0.732321i | \(-0.738437\pi\) |
0.974688 | + | 0.223568i | \(0.0717706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 914.837i | − | 0.761598i | −0.924658 | − | 0.380799i | \(-0.875649\pi\) | ||
0.924658 | − | 0.380799i | \(-0.124351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 99.6917 | + | 57.5570i | 0.0808374 | + | 0.0466715i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 339.696 | + | 1399.99i | 0.261680 | + | 1.07846i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 199.690 | + | 345.873i | 0.150030 | + | 0.259859i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −314.398 | −0.224965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1260.95 | −0.881034 | −0.440517 | − | 0.897744i | \(-0.645205\pi\) | ||||
−0.440517 | + | 0.897744i | \(0.645205\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −683.600 | − | 1184.03i | −0.455926 | − | 0.789688i | 0.542814 | − | 0.839853i | \(-0.317359\pi\) |
−0.998741 | + | 0.0501648i | \(0.984025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 253.998 | − | 865.173i | 0.165597 | − | 0.564060i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −953.631 | − | 550.579i | −0.594702 | − | 0.343351i | 0.172252 | − | 0.985053i | \(-0.444896\pi\) |
−0.766955 | + | 0.641701i | \(0.778229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2306.56i | − | 1.40748i | −0.710458 | − | 0.703739i | \(-0.751512\pi\) | ||
0.710458 | − | 0.703739i | \(-0.248488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1783.21 | − | 3088.60i | 1.04279 | − | 1.80617i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 165.730 | − | 95.6845i | 0.0949184 | − | 0.0548012i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1520.57 | − | 877.901i | 0.836040 | − | 0.482688i | −0.0198764 | − | 0.999802i | \(-0.506327\pi\) |
0.855916 | + | 0.517115i | \(0.172994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −262.491 | + | 454.647i | −0.141465 | + | 0.245024i | −0.928048 | − | 0.372460i | \(-0.878515\pi\) |
0.786584 | + | 0.617484i | \(0.211848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 111.610i | 0.0578368i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1141.44 | − | 659.009i | −0.580233 | − | 0.334998i | 0.180993 | − | 0.983484i | \(-0.442069\pi\) |
−0.761226 | + | 0.648487i | \(0.775402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 474.481 | − | 1616.18i | 0.232263 | − | 0.791137i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −223.916 | − | 387.834i | −0.107598 | − | 0.186365i | 0.807199 | − | 0.590280i | \(-0.200983\pi\) |
−0.914797 | + | 0.403915i | \(0.867649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −811.124 | −0.375848 | −0.187924 | − | 0.982184i | \(-0.560176\pi\) | ||||
−0.187924 | + | 0.982184i | \(0.560176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5153.58 | −2.34574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1121.24 | + | 1942.04i | 0.492751 | + | 0.853470i | 0.999965 | − | 0.00834994i | \(-0.00265790\pi\) |
−0.507214 | + | 0.861820i | \(0.669325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 538.888 | + | 2220.92i | 0.232778 | + | 0.959347i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2531.77 | + | 1461.72i | 1.05717 | + | 0.610357i | 0.924648 | − | 0.380824i | \(-0.124359\pi\) |
0.132521 | + | 0.991180i | \(0.457693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 282.859i | − | 0.116159i | −0.998312 | − | 0.0580794i | \(-0.981502\pi\) | ||
0.998312 | − | 0.0580794i | \(-0.0184977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −57.3255 | + | 99.2906i | −0.0227819 | + | 0.0394594i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2802.22 | + | 1617.86i | −1.09582 | + | 0.632672i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3998.63 | − | 2308.61i | 1.51482 | − | 0.874582i | 0.514971 | − | 0.857208i | \(-0.327803\pi\) |
0.999849 | − | 0.0173741i | \(-0.00553064\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2077.73 | − | 3598.73i | 0.774912 | − | 1.34219i | −0.159933 | − | 0.987128i | \(-0.551128\pi\) |
0.934844 | − | 0.355058i | \(-0.115539\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1626.36i | − | 0.588190i | −0.955776 | − | 0.294095i | \(-0.904982\pi\) | ||
0.955776 | − | 0.294095i | \(-0.0950183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −150.861 | − | 87.0995i | −0.0537399 | − | 0.0310267i | 0.472889 | − | 0.881122i | \(-0.343211\pi\) |
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1932.44 | − | 2026.51i | −0.668130 | − | 0.700656i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −242.718 | − | 420.399i | −0.0826933 | − | 0.143229i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2025.25 | 0.670286 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2942.35 | 0.959999 | 0.479999 | − | 0.877269i | \(-0.340637\pi\) | ||||
0.479999 | + | 0.877269i | \(0.340637\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −144.223 | − | 249.802i | −0.0457486 | − | 0.0792389i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1587.06 | − | 385.088i | 0.496484 | − | 0.120468i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5775.53 | + | 3334.51i | 1.75794 | + | 1.01495i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3374.75i | − | 1.01341i | −0.862120 | − | 0.506704i | \(-0.830864\pi\) | ||
0.862120 | − | 0.506704i | \(-0.169136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1515.43 | + | 2624.79i | −0.443094 | + | 0.767461i | −0.997917 | − | 0.0645069i | \(-0.979453\pi\) |
0.554823 | + | 0.831968i | \(0.312786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 960.030 | − | 554.274i | 0.277033 | − | 0.159945i | −0.355046 | − | 0.934849i | \(-0.615535\pi\) |
0.632080 | + | 0.774904i | \(0.282202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2684.57 | − | 1549.94i | 0.754815 | − | 0.435793i | −0.0726160 | − | 0.997360i | \(-0.523135\pi\) |
0.827431 | + | 0.561567i | \(0.189801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −88.0333 | + | 152.478i | −0.0244368 | + | 0.0423259i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1735.25i | − | 0.469640i | −0.972039 | − | 0.234820i | \(-0.924550\pi\) | ||
0.972039 | − | 0.234820i | \(-0.0754501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1039.26 | − | 600.019i | −0.277779 | − | 0.160376i | 0.354638 | − | 0.935004i | \(-0.384604\pi\) |
−0.632418 | + | 0.774628i | \(0.717937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −385.859 | + | 198.965i | −0.100619 | + | 0.0518833i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2087.08 | − | 3614.93i | −0.537643 | − | 0.931225i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3712.56 | 0.933603 | 0.466802 | − | 0.884362i | \(-0.345406\pi\) | ||||
0.466802 | + | 0.884362i | \(0.345406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3783.27 | 0.940126 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −389.574 | − | 674.762i | −0.0945563 | − | 0.163776i | 0.814867 | − | 0.579648i | \(-0.196810\pi\) |
−0.909423 | + | 0.415872i | \(0.863477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1609.68 | + | 472.572i | 0.386180 | + | 0.113375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1702.07 | − | 982.690i | −0.399065 | − | 0.230400i | 0.287015 | − | 0.957926i | \(-0.407337\pi\) |
−0.686080 | + | 0.727526i | \(0.740670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 423.470i | 0.0981644i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1236.41 | + | 2141.53i | −0.280243 | + | 0.485395i | −0.971444 | − | 0.237267i | \(-0.923748\pi\) |
0.691201 | + | 0.722662i | \(0.257082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4095.79 | + | 2364.71i | −0.918088 | + | 0.530058i | −0.883025 | − | 0.469327i | \(-0.844497\pi\) |
−0.0350633 | + | 0.999385i | \(0.511163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4445.39 | + | 2566.54i | −0.974788 | + | 0.562794i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −586.579 | + | 1015.98i | −0.127235 | + | 0.220378i | −0.922604 | − | 0.385747i | \(-0.873944\pi\) |
0.795369 | + | 0.606125i | \(0.207277\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8195.18i | − | 1.73980i | −0.493229 | − | 0.869899i | \(-0.664184\pi\) | ||
0.493229 | − | 0.869899i | \(-0.335816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2242.44 | − | 1294.67i | −0.471021 | − | 0.271944i | 0.245646 | − | 0.969360i | \(-0.421000\pi\) |
−0.716667 | + | 0.697415i | \(0.754333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5140.53 | + | 4901.90i | −1.05727 | + | 1.00819i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −568.820 | − | 985.225i | −0.115779 | − | 0.200534i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8871.16 | −1.76880 | −0.884400 | − | 0.466729i | \(-0.845432\pi\) | ||||
−0.884400 | + | 0.466729i | \(0.845432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1113.94 | −0.219852 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3898.77 | − | 6752.86i | −0.754085 | − | 1.30611i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3054.51 | + | 2912.72i | −0.584915 | + | 0.557762i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4219 | − | 8.32647i | −0.00270752 | − | 0.00156319i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2707.52i | 0.503344i | 0.967813 | + | 0.251672i | \(0.0809804\pi\) | ||||
−0.967813 | + | 0.251672i | \(0.919020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1080.55 | − | 1871.56i | 0.197017 | − | 0.341243i | −0.750543 | − | 0.660822i | \(-0.770208\pi\) |
0.947560 | + | 0.319579i | \(0.103541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7300.25 | + | 4214.80i | −1.31832 | + | 0.761133i | −0.983459 | − | 0.181133i | \(-0.942023\pi\) |
−0.334863 | + | 0.942267i | \(0.608690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8310.07 | + | 4797.82i | −1.47237 | + | 0.850071i | −0.999517 | − | 0.0310734i | \(-0.990107\pi\) |
−0.472848 | + | 0.881144i | \(0.656774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3144.71 | − | 5446.80i | 0.551943 | − | 0.955994i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3787.12i | 0.652387i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9162.20 | + | 5289.80i | 1.56378 | + | 0.902847i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2471.95 | + | 725.717i | 0.414234 | + | 0.121611i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4271.96 | + | 7399.25i | 0.709390 | + | 1.22870i | 0.965084 | + | 0.261941i | \(0.0843626\pi\) |
−0.255694 | + | 0.966758i | \(0.582304\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 559.978 | 0.0913280 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 598.875 | 0.0968036 | 0.0484018 | − | 0.998828i | \(-0.484587\pi\) | ||||
0.0484018 | + | 0.998828i | \(0.484587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1834.05 | + | 3176.66i | 0.291259 | + | 0.504475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4160.57 | + | 4800.34i | 0.654956 | + | 0.755667i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6149.62 | + | 3550.49i | 0.951381 | + | 0.549280i | 0.893510 | − | 0.449044i | \(-0.148235\pi\) |
0.0578712 | + | 0.998324i | \(0.481569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3620.71i | − | 0.555336i | −0.960677 | − | 0.277668i | \(-0.910438\pi\) | ||
0.960677 | − | 0.277668i | \(-0.0895616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1164.89 | − | 2017.64i | 0.175639 | − | 0.304216i | −0.764743 | − | 0.644335i | \(-0.777134\pi\) |
0.940382 | + | 0.340119i | \(0.110467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 374.386 | − | 216.152i | 0.0559727 | − | 0.0323159i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1522.43 | − | 878.975i | 0.223818 | − | 0.129222i | −0.383899 | − | 0.923375i | \(-0.625419\pi\) |
0.607717 | + | 0.794154i | \(0.292086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2244.31 | + | 3887.26i | −0.327207 | + | 0.566739i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1166.60i | 0.167295i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1458.89 | − | 842.290i | −0.207503 | − | 0.119802i | 0.392648 | − | 0.919689i | \(-0.371559\pi\) |
−0.600150 | + | 0.799887i | \(0.704893\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6021.65 | − | 1461.11i | 0.842665 | − | 0.204466i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 148.646 | + | 257.462i | 0.0206343 | + | 0.0357397i | 0.876158 | − | 0.482024i | \(-0.160098\pi\) |
−0.855524 | + | 0.517763i | \(0.826765\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12962.9 | −1.77088 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7402.78 | 1.00331 | 0.501656 | − | 0.865067i | \(-0.332724\pi\) | ||||
0.501656 | + | 0.865067i | \(0.332724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6263.77 | + | 10849.2i | 0.835676 | + | 1.44743i | 0.893479 | + | 0.449105i | \(0.148257\pi\) |
−0.0578031 | + | 0.998328i | \(0.518410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −672.926 | − | 705.685i | −0.0890792 | − | 0.0934157i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6904.14 | + | 3986.11i | 0.899881 | + | 0.519547i | 0.877162 | − | 0.480195i | \(-0.159434\pi\) |
0.0227196 | + | 0.999742i | \(0.492767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7074.52i | 0.915023i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −261.449 | + | 452.843i | −0.0333036 | + | 0.0576836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10832.5 | − | 6254.16i | 1.36944 | − | 0.790648i | 0.378586 | − | 0.925566i | \(-0.376410\pi\) |
0.990857 | + | 0.134918i | \(0.0430770\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6943.55 | + | 4008.86i | −0.864699 | + | 0.499234i | −0.865583 | − | 0.500765i | \(-0.833052\pi\) |
0.000883860 | 1.00000i | \(0.499719\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3780.08 | − | 6547.29i | 0.467243 | − | 0.809289i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3768.05i | 0.458907i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7566.04 | − | 4368.26i | −0.914711 | − | 0.528109i | −0.0327670 | − | 0.999463i | \(-0.510432\pi\) |
−0.881944 | + | 0.471354i | \(0.843765\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3843.46 | + | 15840.1i | 0.457928 | + | 1.88726i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −603.935 | − | 1046.05i | −0.0714361 | − | 0.123731i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3926.67 | −0.457829 | −0.228914 | − | 0.973447i | \(-0.573518\pi\) | ||||
−0.228914 | + | 0.973447i | \(0.573518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1443.44 | 0.167100 | 0.0835499 | − | 0.996504i | \(-0.473374\pi\) | ||||
0.0835499 | + | 0.996504i | \(0.473374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4799.31 | − | 8312.65i | −0.547766 | − | 0.948759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −68.6406 | + | 233.805i | −0.00777928 | + | 0.0264979i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12820.5 | − | 7401.92i | −1.43281 | − | 0.827234i | −0.435477 | − | 0.900200i | \(-0.643420\pi\) |
−0.997334 | + | 0.0729655i | \(0.976754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15872.1i | 1.76158i | 0.473508 | + | 0.880790i | \(0.342988\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2213.99 | − | 3834.74i | 0.242356 | − | 0.419772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2626.58 | − | 1516.45i | 0.285557 | − | 0.164867i | −0.350379 | − | 0.936608i | \(-0.613947\pi\) |
0.635937 | + | 0.771741i | \(0.280614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11126.8 | + | 6424.08i | −1.19334 | + | 0.688978i | −0.959064 | − | 0.283191i | \(-0.908607\pi\) |
−0.234281 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.7945 | + | 32.5530i | −0.00200212 | + | 0.00346777i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 107.668i | − | 0.0113166i | −0.999984 | − | 0.00565831i | \(-0.998199\pi\) | ||
0.999984 | − | 0.00565831i | \(-0.00180111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13816.6 | − | 7977.01i | −1.44257 | − | 0.832866i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −566.128 | + | 1928.35i | −0.0583308 | + | 0.198687i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4888.53 | + | 8467.18i | 0.500385 | + | 0.866691i | 1.00000 | 0.000444115i | \(0.000141366\pi\) | |
−0.499615 | + | 0.866247i | \(0.666525\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −638.874 | −0.0645452 | −0.0322726 | − | 0.999479i | \(-0.510274\pi\) | ||||
−0.0322726 | + | 0.999479i | \(0.510274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5602.26 | 0.562331 | 0.281165 | − | 0.959659i | \(-0.409279\pi\) | ||||
0.281165 | + | 0.959659i | \(0.409279\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2759.44 | − | 4779.49i | −0.273430 | − | 0.473594i | 0.696308 | − | 0.717743i | \(-0.254825\pi\) |
−0.969738 | + | 0.244149i | \(0.921491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1932.10 | − | 7962.76i | −0.190226 | − | 0.783979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8209.84 | − | 4739.95i | −0.798074 | − | 0.460768i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6007.82i | 0.580332i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2734.40 | + | 4736.11i | −0.260830 | + | 0.451771i | −0.966463 | − | 0.256807i | \(-0.917330\pi\) |
0.705632 | + | 0.708578i | \(0.250663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6725.70 | − | 3883.08i | 0.637558 | − | 0.368094i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1314.96 | − | 759.190i | 0.123112 | − | 0.0710785i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5866.72 | + | 10161.5i | −0.545886 | + | 0.945502i | 0.452665 | + | 0.891681i | \(0.350473\pi\) |
−0.998551 | + | 0.0538213i | \(0.982860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3514.92i | 0.323068i | 0.986867 | + | 0.161534i | \(0.0516441\pi\) | ||||
−0.986867 | + | 0.161534i | \(0.948356\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10185.2 | + | 5880.45i | 0.930467 | + | 0.537205i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4365.38 | − | 4577.89i | −0.393992 | − | 0.413172i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4944.49 | + | 8564.11i | 0.443579 | + | 0.768301i | 0.997952 | − | 0.0639672i | \(-0.0203753\pi\) |
−0.554373 | + | 0.832268i | \(0.687042\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10172.2 | −0.901698 | −0.450849 | − | 0.892600i | \(-0.648879\pi\) | ||||
−0.450849 | + | 0.892600i | \(0.648879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −828.838 | −0.0730353 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2149.56 | + | 3723.15i | 0.187186 | + | 0.324216i | 0.944311 | − | 0.329054i | \(-0.106730\pi\) |
−0.757125 | + | 0.653270i | \(0.773397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16588.8 | − | 4025.14i | 1.43610 | − | 0.348458i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1501.14 | − | 866.682i | −0.128443 | − | 0.0741565i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5786.50i | 0.492243i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5496.48 | − | 9520.18i | 0.462198 | − | 0.800550i | −0.536872 | − | 0.843664i | \(-0.680394\pi\) |
0.999070 | + | 0.0431133i | \(0.0137276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7386.80 | + | 4264.77i | −0.617595 | + | 0.356569i | −0.775932 | − | 0.630817i | \(-0.782720\pi\) |
0.158337 | + | 0.987385i | \(0.449387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5940.20 | + | 3429.58i | −0.491004 | + | 0.283481i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1947.67 | + | 3373.46i | −0.160078 | + | 0.277263i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32882.2i | 2.67220i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −469.970 | − | 271.337i | −0.0379786 | − | 0.0219270i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7712.89 | + | 12003.7i | −0.616359 | + | 0.959250i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4352.93 | + | 7539.49i | 0.345928 | + | 0.599165i | 0.985522 | − | 0.169548i | \(-0.0542308\pi\) |
−0.639594 | + | 0.768713i | \(0.720897\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −846.150 | −0.0665047 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17183.8 | −1.34319 | −0.671596 | − | 0.740917i | \(-0.734391\pi\) | ||||
−0.671596 | + | 0.740917i | \(0.734391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3680.60 | − | 6374.99i | −0.284571 | − | 0.492892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7341.41 | + | 2155.30i | 0.564536 | + | 0.165737i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8989.79 | + | 5190.26i | 0.683859 | + | 0.394826i | 0.801307 | − | 0.598253i | \(-0.204138\pi\) |
−0.117448 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19538.6i | 1.47835i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9248.22 | − | 16018.4i | 0.692302 | − | 1.19910i | −0.278780 | − | 0.960355i | \(-0.589930\pi\) |
0.971082 | − | 0.238747i | \(-0.0767366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1002.78 | + | 578.956i | −0.0746678 | + | 0.0431095i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3493.45 | − | 2016.94i | 0.257386 | − | 0.148602i | −0.365755 | − | 0.930711i | \(-0.619189\pi\) |
0.623142 | + | 0.782109i | \(0.285856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6430.01 | − | 11137.1i | 0.471257 | − | 0.816241i | −0.528203 | − | 0.849118i | \(-0.677134\pi\) |
0.999459 | + | 0.0328777i | \(0.0104672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11222.9i | 0.813959i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17669.2 | − | 10201.3i | −1.27483 | − | 0.736026i | −0.298940 | − | 0.954272i | \(-0.596633\pi\) |
−0.975894 | + | 0.218246i | \(0.929967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12790.8 | + | 12197.0i | −0.913340 | + | 0.870941i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6958.76 | + | 12052.9i | 0.494344 | + | 0.856228i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16279.7 | −1.14470 | −0.572348 | − | 0.820011i | \(-0.693967\pi\) | ||||
−0.572348 | + | 0.820011i | \(0.693967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4293.17 | 0.300335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1342.16 | − | 2324.68i | −0.0929440 | − | 0.160984i | 0.815805 | − | 0.578328i | \(-0.196294\pi\) |
−0.908749 | + | 0.417344i | \(0.862961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1319.60 | − | 1258.34i | 0.0909213 | − | 0.0867006i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12224.6 | + | 7057.90i | 0.833865 | + | 0.481432i | 0.855174 | − | 0.518341i | \(-0.173450\pi\) |
−0.0213091 | + | 0.999773i | \(0.506783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11096.1i | − | 0.753109i | −0.926394 | − | 0.376555i | \(-0.877109\pi\) | ||
0.926394 | − | 0.376555i | \(-0.122891\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 252.748 | − | 437.772i | 0.0169846 | − | 0.0294181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9592.70 | − | 5538.35i | 0.641442 | − | 0.370337i | −0.143728 | − | 0.989617i | \(-0.545909\pi\) |
0.785170 | + | 0.619280i | \(0.212576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10328.5 | − | 5963.15i | 0.683872 | − | 0.394834i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3801.34 | − | 6584.11i | 0.250464 | − | 0.433817i | −0.713189 | − | 0.700971i | \(-0.752750\pi\) |
0.963654 | + | 0.267154i | \(0.0860834\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11325.9i | − | 0.738998i | −0.929231 | − | 0.369499i | \(-0.879529\pi\) | ||
0.929231 | − | 0.369499i | \(-0.120471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16595.2 | + | 9581.22i | 1.07757 | + | 0.622136i | 0.930240 | − | 0.366952i | \(-0.119599\pi\) |
0.147330 | + | 0.989087i | \(0.452932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 527.743 | + | 154.935i | 0.0339383 | + | 0.00996365i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7513.41 | − | 13013.6i | −0.480858 | − | 0.832871i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7046.06 | −0.446653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10140.7 | −0.639768 | −0.319884 | − | 0.947457i | \(-0.603644\pi\) | ||||
−0.319884 | + | 0.947457i | \(0.603644\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 797.995 | + | 1382.17i | 0.0498700 | + | 0.0863774i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29374.1 | + | 1396.79i | 1.82707 | + | 0.0868804i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2950.66 | + | 1703.56i | 0.181816 | + | 0.104972i | 0.588146 | − | 0.808755i | \(-0.299858\pi\) |
−0.406330 | + | 0.913727i | \(0.633192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 659.110i | 0.0404242i | 0.999796 | + | 0.0202121i | \(0.00643415\pi\) | ||||
−0.999796 | + | 0.0202121i | \(0.993566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3303.47 | − | 5721.78i | 0.200731 | − | 0.347676i | −0.748033 | − | 0.663661i | \(-0.769002\pi\) |
0.948764 | + | 0.315985i | \(0.102335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31705.4 | + | 18305.1i | −1.91764 | + | 1.10715i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22417.1 | + | 12942.5i | −1.34342 | + | 0.775622i | −0.987307 | − | 0.158823i | \(-0.949230\pi\) |
−0.356109 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −865.234 | + | 1498.63i | −0.0516145 | + | 0.0893989i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7468.86i | − | 0.441495i | −0.975331 | − | 0.220748i | \(-0.929150\pi\) | ||
0.975331 | − | 0.220748i | \(-0.0708497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5501.96 | − | 3176.56i | −0.323754 | − | 0.186919i | 0.329311 | − | 0.944222i | \(-0.393184\pi\) |
−0.653065 | + | 0.757302i | \(0.726517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1109.09 | + | 269.111i | −0.0646744 | + | 0.0156927i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6875.53 | − | 11908.8i | −0.399133 | − | 0.691319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −547.306 | −0.0314881 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20238.2 | −1.15918 | −0.579589 | − | 0.814909i | \(-0.696787\pi\) | ||||
−0.579589 | + | 0.814909i | \(0.696787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5658.37 | − | 9800.59i | −0.321224 | − | 0.556377i | 0.659516 | − | 0.751690i | \(-0.270761\pi\) |
−0.980741 | + | 0.195313i | \(0.937428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15332.5 | − | 16078.9i | −0.866581 | − | 0.908768i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14869.4 | + | 8584.87i | 0.833035 | + | 0.480953i | 0.854891 | − | 0.518808i | \(-0.173624\pi\) |
−0.0218557 | + | 0.999761i | \(0.506957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1393.74i | 0.0777402i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14342.4 | − | 24841.8i | 0.793037 | − | 1.37358i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7238.59 | − | 4179.20i | 0.398508 | − | 0.230079i | −0.287332 | − | 0.957831i | \(-0.592768\pi\) |
0.685840 | + | 0.727752i | \(0.259435\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2528.29 | + | 1459.71i | −0.137990 | + | 0.0796688i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14916.6 | − | 25836.3i | 0.810627 | − | 1.40405i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19235.8i | − | 1.03641i | −0.855256 | − | 0.518206i | \(-0.826600\pi\) | ||
0.855256 | − | 0.518206i | \(-0.173400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3819.31 | + | 2205.08i | 0.204905 | + | 0.118302i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2859.75 | + | 11785.9i | 0.152124 | + | 0.626951i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5160.17 | + | 8937.67i | 0.273334 | + | 0.473429i | 0.969714 | − | 0.244245i | \(-0.0785401\pi\) |
−0.696379 | + | 0.717674i | \(0.745207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8019.85 | 0.421242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4514.02 | −0.236105 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11679.8 | − | 20229.9i | −0.605815 | − | 1.04930i | −0.991922 | − | 0.126849i | \(-0.959514\pi\) |
0.386107 | − | 0.922454i | \(-0.373820\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7144.63 | + | 24336.2i | −0.369043 | + | 1.25704i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16157.7 | + | 9328.63i | 0.827698 | + | 0.477871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22260.4i | − | 1.13561i | −0.823162 | − | 0.567807i | \(-0.807792\pi\) | ||
0.823162 | − | 0.567807i | \(-0.192208\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8863.48 | − | 15352.0i | 0.448464 | − | 0.776763i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9047.84 | − | 5223.77i | 0.455920 | − | 0.263226i | −0.254407 | − | 0.967097i | \(-0.581880\pi\) |
0.710327 | + | 0.703872i | \(0.248547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15938.2 | − | 9201.95i | 0.796598 | − | 0.459916i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6595.44 | − | 11423.6i | 0.328304 | − | 0.568640i | −0.653871 | − | 0.756606i | \(-0.726856\pi\) |
0.982176 | + | 0.187966i | \(0.0601895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 35382.2i | − | 1.74703i | −0.486795 | − | 0.873517i | \(-0.661834\pi\) | ||
0.486795 | − | 0.873517i | \(-0.338166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1924.59 | − | 1111.16i | −0.0946463 | − | 0.0546441i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2236.81 | + | 7619.07i | −0.109121 | + | 0.371688i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14692.3 | − | 25447.8i | −0.713888 | − | 1.23649i | −0.963387 | − | 0.268116i | \(-0.913599\pi\) |
0.249498 | − | 0.968375i | \(-0.419734\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 664.470 | 0.0320299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11329.1 | 0.543939 | 0.271969 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271969 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12696.5 | − | 21990.9i | −0.604792 | − | 1.04753i | −0.992084 | − | 0.125574i | \(-0.959923\pi\) |
0.387292 | − | 0.921957i | \(-0.373411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2919.48 | + | 12032.1i | 0.138522 | + | 0.570891i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65346.7 | + | 37727.9i | 3.07631 | + | 1.77611i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18120.8i | 0.849744i | 0.905253 | + | 0.424872i | \(0.139681\pi\) | ||||
−0.905253 | + | 0.424872i | \(0.860319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8673.05 | + | 15022.2i | −0.403555 | + | 0.698978i | −0.994152 | − | 0.107989i | \(-0.965559\pi\) |
0.590597 | + | 0.806967i | \(0.298892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9423.42 | + | 5440.61i | −0.436773 | + | 0.252171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16171.1 | + | 9336.37i | −0.743759 | + | 0.429410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7103.91 | − | 12304.3i | 0.325477 | − | 0.563743i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1668.22i | 0.0758488i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1801.52 | − | 1040.11i | −0.0815977 | − | 0.0471104i | 0.458646 | − | 0.888619i | \(-0.348335\pi\) |
−0.540244 | + | 0.841509i | \(0.681668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11692.5 | + | 12261.7i | 0.525586 | + | 0.551172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 564.014 | + | 976.901i | 0.0252569 | + | 0.0437463i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39737.3 | 1.76608 | 0.883041 | − | 0.469297i | \(-0.155493\pi\) | ||||
0.883041 | + | 0.469297i | \(0.155493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10820.5 | −0.479099 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19170.4 | + | 33204.1i | 0.842477 | + | 1.45921i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2071.82 | + | 502.711i | −0.0907108 | + | 0.0220102i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9713.37 | + | 5608.02i | 0.422131 | + | 0.243717i | 0.695989 | − | 0.718053i | \(-0.254966\pi\) |
−0.273858 | + | 0.961770i | \(0.588300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14792.0i | 0.640465i | 0.947339 | + | 0.320232i | \(0.103761\pi\) | ||||
−0.947339 | + | 0.320232i | \(0.896239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −283.411 | + | 490.882i | −0.0121809 | + | 0.0210980i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9608.88 | + | 5547.69i | −0.411471 | + | 0.237563i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28632.7 | − | 16531.1i | 1.21716 | − | 0.702726i | 0.252849 | − | 0.967506i | \(-0.418632\pi\) |
0.964309 | + | 0.264779i | \(0.0852992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10045.4 | − | 17399.1i | 0.425467 | − | 0.736930i | −0.570997 | − | 0.820952i | \(-0.693443\pi\) |
0.996464 | + | 0.0840220i | \(0.0267766\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36882.5i | − | 1.55082i | −0.631458 | − | 0.775410i | \(-0.717543\pi\) | ||
0.631458 | − | 0.775410i | \(-0.282457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32697.0 | − | 18877.6i | −1.36986 | − | 0.790888i | −0.378949 | − | 0.925418i | \(-0.623714\pi\) |
−0.990910 | + | 0.134530i | \(0.957048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22446.3 | − | 14422.7i | −0.933636 | − | 0.599901i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 513.321 | + | 889.098i | 0.0212745 | + | 0.0368485i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44250.4 | −1.82085 | −0.910426 | − | 0.413672i | \(-0.864246\pi\) | ||||
−0.910426 | + | 0.413672i | \(0.864246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1528.81 | 0.0626844 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3261.45 | + | 5649.00i | 0.132778 | + | 0.229978i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7097.08 | − | 2083.57i | −0.287909 | − | 0.0845245i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7134.65 | + | 4119.19i | 0.287394 | + | 0.165927i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14952.2i | 0.600179i | 0.953911 | + | 0.300089i | \(0.0970165\pi\) | ||||
−0.953911 | + | 0.300089i | \(0.902983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1224.76 | − | 2121.35i | 0.0488181 | − | 0.0845555i | −0.840584 | − | 0.541682i | \(-0.817788\pi\) |
0.889402 | + | 0.457126i | \(0.151121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5751.97 | − | 3320.90i | 0.228469 | − | 0.131906i | −0.381397 | − | 0.924411i | \(-0.624557\pi\) |
0.609865 | + | 0.792505i | \(0.291223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16339.2 | − | 9433.46i | 0.644489 | − | 0.372096i | −0.141853 | − | 0.989888i | \(-0.545306\pi\) |
0.786342 | + | 0.617792i | \(0.211973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1419.15 | − | 2458.04i | 0.0557833 | − | 0.0966196i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17185.3i | 0.670851i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32849.6 | − | 18965.8i | −1.27792 | − | 0.737807i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4213.94 | − | 4018.32i | 0.162808 | − | 0.155250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5989.84 | − | 10374.7i | −0.230630 | − | 0.399463i | 0.727364 | − | 0.686252i | \(-0.240745\pi\) |
−0.957994 | + | 0.286789i | \(0.907412\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34504.0 | −1.31949 | −0.659743 | − | 0.751491i | \(-0.729335\pi\) | ||||
−0.659743 | + | 0.751491i | \(0.729335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8148.85 | 0.310567 | 0.155283 | − | 0.987870i | \(-0.450371\pi\) | ||||
0.155283 | + | 0.987870i | \(0.450371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17477.6 | − | 30272.1i | −0.661602 | − | 1.14593i | −0.980195 | − | 0.198036i | \(-0.936544\pi\) |
0.318593 | − | 0.947892i | \(-0.396790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16900.8 | − | 16116.2i | 0.637609 | − | 0.608010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5865.22 | + | 3386.29i | 0.219790 | + | 0.126896i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3700.20i | − | 0.138194i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6666.22 | − | 11546.2i | 0.247309 | − | 0.428352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22538.4 | + | 13012.5i | −0.833365 | + | 0.481144i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −310.051 | + | 179.008i | −0.0113883 | + | 0.00657505i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12494.5 | + | 21641.1i | −0.457412 | + | 0.792261i | −0.998823 | − | 0.0484970i | \(-0.984557\pi\) |
0.541411 | + | 0.840758i | \(0.317890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41609.1i | − | 1.51325i | −0.653849 | − | 0.756625i | \(-0.726847\pi\) | ||
0.653849 | − | 0.756625i | \(-0.273153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34378.7 | − | 19848.5i | −1.24619 | − | 0.719486i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24295.5 | + | 7132.70i | 0.874927 | + | 0.256862i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25496.0 | + | 44160.4i | 0.915164 | + | 1.58511i | 0.806661 | + | 0.591014i | \(0.201272\pi\) |
0.108502 | + | 0.994096i | \(0.465395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29283.1 | −1.04428 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11177.7 | −0.397321 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23746.5 | − | 41130.2i | −0.838642 | − | 1.45257i | −0.891031 | − | 0.453943i | \(-0.850017\pi\) |
0.0523888 | − | 0.998627i | \(-0.483316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7653.39 | + | 14842.4i | 0.269420 | + | 0.522493i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3546.78 | + | 2047.73i | 0.124056 | + | 0.0716235i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6811.98i | − | 0.237500i | −0.992924 | − | 0.118750i | \(-0.962111\pi\) | ||
0.992924 | − | 0.118750i | \(-0.0378887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16271.0 | − | 28182.2i | 0.563677 | − | 0.976318i | −0.433494 | − | 0.901156i | \(-0.642720\pi\) |
0.997171 | − | 0.0751612i | \(-0.0239471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30208.3 | + | 17440.8i | −1.04318 | + | 0.602280i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10119.9 | − | 5842.70i | 0.347256 | − | 0.200488i | −0.316220 | − | 0.948686i | \(-0.602414\pi\) |
0.663476 | + | 0.748198i | \(0.269080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39511.3 | − | 68435.7i | 1.35152 | − | 2.34090i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46457.5i | − | 1.57912i | −0.613671 | − | 0.789562i | \(-0.710308\pi\) | ||
0.613671 | − | 0.789562i | \(-0.289692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5061.08 | − | 2922.01i | −0.171490 | − | 0.0990096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19818.7 | − | 4808.84i | 0.667339 | − | 0.161924i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11007.6 | − | 19065.8i | −0.369496 | − | 0.639986i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5259.57 | −0.175452 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27949.1 | 0.929455 | 0.464728 | − | 0.885454i | \(-0.346152\pi\) | ||||
0.464728 | + | 0.885454i | \(0.346152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1609.85 | + | 2788.33i | 0.0532053 | + | 0.0921544i | 0.891401 | − | 0.453215i | \(-0.149723\pi\) |
−0.838196 | + | 0.545369i | \(0.816390\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29480.1 | + | 30915.2i | 0.971314 | + | 1.01860i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33258.6 | + | 19201.9i | 1.08909 | + | 0.628785i | 0.933333 | − | 0.359011i | \(-0.116886\pi\) |
0.155754 | + | 0.987796i | \(0.450219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1235.38i | 0.0403297i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13709.1 | − | 23744.8i | 0.444814 | − | 0.770440i | −0.553226 | − | 0.833031i | \(-0.686603\pi\) |
0.998039 | + | 0.0625917i | \(0.0199366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1782.71 | + | 1029.25i | −0.0576667 | + | 0.0332939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17949.8 | + | 10363.3i | −0.577120 | + | 0.333200i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21857.9 | − | 37859.1i | 0.700646 | − | 1.21355i | −0.267594 | − | 0.963532i | \(-0.586229\pi\) |
0.968240 | − | 0.250023i | \(-0.0804381\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 220.484i | 0.00702495i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21930.8 | − | 12661.7i | −0.696644 | − | 0.402208i | 0.109452 | − | 0.993992i | \(-0.465090\pi\) |
−0.806096 | + | 0.591784i | \(0.798424\pi\) | |||||||
\(998\) | 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 | 1008.4.bt.a.17.4 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.a.17.5 | 16 | ||
4.3 | odd | 2 | 63.4.p.a.17.2 | ✓ | 16 | ||
7.5 | odd | 6 | inner | 1008.4.bt.a.593.5 | 16 | ||
12.11 | even | 2 | 63.4.p.a.17.7 | yes | 16 | ||
21.5 | even | 6 | inner | 1008.4.bt.a.593.4 | 16 | ||
28.3 | even | 6 | 441.4.c.a.440.3 | 16 | |||
28.11 | odd | 6 | 441.4.c.a.440.4 | 16 | |||
28.19 | even | 6 | 63.4.p.a.26.7 | yes | 16 | ||
28.23 | odd | 6 | 441.4.p.c.215.7 | 16 | |||
28.27 | even | 2 | 441.4.p.c.80.2 | 16 | |||
84.11 | even | 6 | 441.4.c.a.440.13 | 16 | |||
84.23 | even | 6 | 441.4.p.c.215.2 | 16 | |||
84.47 | odd | 6 | 63.4.p.a.26.2 | yes | 16 | ||
84.59 | odd | 6 | 441.4.c.a.440.14 | 16 | |||
84.83 | odd | 2 | 441.4.p.c.80.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.2 | ✓ | 16 | 4.3 | odd | 2 | ||
63.4.p.a.17.7 | yes | 16 | 12.11 | even | 2 | ||
63.4.p.a.26.2 | yes | 16 | 84.47 | odd | 6 | ||
63.4.p.a.26.7 | yes | 16 | 28.19 | even | 6 | ||
441.4.c.a.440.3 | 16 | 28.3 | even | 6 | |||
441.4.c.a.440.4 | 16 | 28.11 | odd | 6 | |||
441.4.c.a.440.13 | 16 | 84.11 | even | 6 | |||
441.4.c.a.440.14 | 16 | 84.59 | odd | 6 | |||
441.4.p.c.80.2 | 16 | 28.27 | even | 2 | |||
441.4.p.c.80.7 | 16 | 84.83 | odd | 2 | |||
441.4.p.c.215.2 | 16 | 84.23 | even | 6 | |||
441.4.p.c.215.7 | 16 | 28.23 | odd | 6 | |||
1008.4.bt.a.17.4 | 16 | 1.1 | even | 1 | trivial | ||
1008.4.bt.a.17.5 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.a.593.4 | 16 | 21.5 | even | 6 | inner | ||
1008.4.bt.a.593.5 | 16 | 7.5 | odd | 6 | inner |