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: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
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 | 593.5 | ||
Root | \(3.91663 - 2.26127i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.a.17.5 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | \(-0.815306\pi\) |
0.892939 | + | 0.450178i | \(0.148639\pi\) | |||||||
\(6\) | 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 | \(-0.473571\pi\) |
0.904509 | + | 0.426454i | \(0.140237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 85.7355i | − | 1.82914i | −0.404433 | − | 0.914568i | \(-0.632531\pi\) | ||
0.404433 | − | 0.914568i | \(-0.367469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −38.8929 | − | 67.3645i | −0.554878 | − | 0.961076i | −0.997913 | − | 0.0645722i | \(-0.979432\pi\) |
0.443035 | − | 0.896504i | \(-0.353902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.1638 | − | 24.3433i | −0.509107 | − | 0.293933i | 0.223360 | − | 0.974736i | \(-0.428298\pi\) |
−0.732466 | + | 0.680803i | \(0.761631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 78.7639 | + | 45.4743i | 0.714061 | + | 0.412263i | 0.812563 | − | 0.582874i | \(-0.198072\pi\) |
−0.0985019 | + | 0.995137i | \(0.531405\pi\) | |||||||
\(24\) | 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 | −0.704634 | − | 0.709571i | \(-0.748889\pi\) |
0.262190 | + | 0.965016i | \(0.415555\pi\) | |||||||
\(32\) | 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 | −0.948928 | − | 0.315493i | \(-0.897830\pi\) |
0.747689 | + | 0.664050i | \(0.231164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −383.530 | −1.46091 | −0.730455 | − | 0.682961i | \(-0.760692\pi\) | ||||
−0.730455 | + | 0.682961i | \(0.760692\pi\) | |||||||
\(42\) | 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 | \(-0.764078\pi\) |
0.953538 | + | 0.301274i | \(0.0974118\pi\) | |||||||
\(48\) | 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 | \(-0.523925\pi\) |
0.826035 | + | 0.563619i | \(0.190591\pi\) | |||||||
\(54\) | 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 | −0.692518 | − | 0.721401i | \(-0.743499\pi\) |
−0.278493 | − | 0.960438i | \(-0.589835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3944 | + | 6.57854i | 0.0239164 | + | 0.0138081i | 0.511911 | − | 0.859039i | \(-0.328938\pi\) |
−0.487994 | + | 0.872847i | \(0.662271\pi\) | |||||||
\(62\) | 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 | 0.590766 | − | 0.806843i | \(-0.298826\pi\) |
−0.994130 | + | 0.108197i | \(0.965492\pi\) | |||||||
\(68\) | 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 | −0.976809 | − | 0.214113i | \(-0.931314\pi\) |
−0.302977 | + | 0.952998i | \(0.597981\pi\) | |||||||
\(74\) | 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 | −0.974794 | − | 0.223107i | \(-0.928380\pi\) |
0.680613 | + | 0.732643i | \(0.261714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −954.307 | −1.26203 | −0.631017 | − | 0.775769i | \(-0.717362\pi\) | ||||
−0.631017 | + | 0.775769i | \(0.717362\pi\) | |||||||
\(84\) | 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 | \(-0.827704\pi\) |
0.874733 | + | 0.484606i | \(0.161037\pi\) | |||||||
\(90\) | 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 | \(-0.783932\pi\) | ||
0.778328 | − | 0.627858i | \(-0.216068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −327.422 | − | 567.111i | −0.322571 | − | 0.558710i | 0.658447 | − | 0.752628i | \(-0.271214\pi\) |
−0.981018 | + | 0.193918i | \(0.937881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1186.01 | + | 684.744i | 1.13457 | + | 0.655047i | 0.945081 | − | 0.326836i | \(-0.105982\pi\) |
0.189493 | + | 0.981882i | \(0.439316\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −371.311 | − | 214.377i | −0.335477 | − | 0.193688i | 0.322793 | − | 0.946470i | \(-0.395378\pi\) |
−0.658270 | + | 0.752782i | \(0.728711\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 334.261 | + | 578.957i | 0.293728 | + | 0.508752i | 0.974688 | − | 0.223568i | \(-0.0717706\pi\) |
−0.680960 | + | 0.732321i | \(0.738437\pi\) | |||||||
\(110\) | 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 | \(-0.682641\pi\) |
0.998741 | + | 0.0501648i | \(0.0159747\pi\) | |||||||
\(132\) | 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 | \(-0.555104\pi\) |
0.766955 | + | 0.641701i | \(0.221771\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2306.56i | 1.40748i | 0.710458 | + | 0.703739i | \(0.248488\pi\) | ||||
−0.710458 | + | 0.703739i | \(0.751512\pi\) | |||||||
\(140\) | 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 | \(-0.493673\pi\) |
−0.855916 | + | 0.517115i | \(0.827006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −262.491 | − | 454.647i | −0.141465 | − | 0.245024i | 0.786584 | − | 0.617484i | \(-0.211848\pi\) |
−0.928048 | + | 0.372460i | \(0.878515\pi\) | |||||||
\(152\) | 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 | −0.761226 | − | 0.648487i | \(-0.775402\pi\) |
0.180993 | + | 0.983484i | \(0.442069\pi\) | |||||||
\(158\) | 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 | −0.914797 | − | 0.403915i | \(-0.867649\pi\) |
0.807199 | + | 0.590280i | \(0.200983\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 811.124 | 0.375848 | 0.187924 | − | 0.982184i | \(-0.439824\pi\) | ||||
0.187924 | + | 0.982184i | \(0.439824\pi\) | |||||||
\(168\) | 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 | \(-0.997342\pi\) |
0.507214 | + | 0.861820i | \(0.330675\pi\) | |||||||
\(174\) | 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 | \(-0.875641\pi\) |
−0.132521 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 282.859i | 0.116159i | 0.998312 | + | 0.0580794i | \(0.0184977\pi\) | ||||
−0.998312 | + | 0.0580794i | \(0.981502\pi\) | |||||||
\(182\) | 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 | −0.999849 | − | 0.0173741i | \(-0.994469\pi\) |
−0.514971 | − | 0.857208i | \(-0.672197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2077.73 | + | 3598.73i | 0.774912 | + | 1.34219i | 0.934844 | + | 0.355058i | \(0.115539\pi\) |
−0.159933 | + | 0.987128i | \(0.551128\pi\) | |||||||
\(194\) | 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 | −0.526629 | − | 0.850095i | \(-0.676544\pi\) |
0.472889 | + | 0.881122i | \(0.343211\pi\) | |||||||
\(200\) | 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 | \(0.169136\pi\) | ||||
−0.862120 | + | 0.506704i | \(0.830864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1515.43 | + | 2624.79i | 0.443094 | + | 0.767461i | 0.997917 | − | 0.0645069i | \(-0.0205475\pi\) |
−0.554823 | + | 0.831968i | \(0.687214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 960.030 | + | 554.274i | 0.277033 | + | 0.159945i | 0.632080 | − | 0.774904i | \(-0.282202\pi\) |
−0.355046 | + | 0.934849i | \(0.615535\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2684.57 | − | 1549.94i | −0.754815 | − | 0.435793i | 0.0726160 | − | 0.997360i | \(-0.476865\pi\) |
−0.827431 | + | 0.561567i | \(0.810199\pi\) | |||||||
\(234\) | 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 | −0.632418 | − | 0.774628i | \(-0.717937\pi\) |
0.354638 | + | 0.935004i | \(0.384604\pi\) | |||||||
\(242\) | 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 | \(-0.654594\pi\) | ||||
−0.466802 | + | 0.884362i | \(0.654594\pi\) | |||||||
\(252\) | 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 | \(-0.803190\pi\) |
0.909423 | + | 0.415872i | \(0.136523\pi\) | |||||||
\(258\) | 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 | \(-0.592663\pi\) |
0.686080 | + | 0.727526i | \(0.259330\pi\) | |||||||
\(264\) | 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 | \(-0.0762516\pi\) |
−0.691201 | + | 0.722662i | \(0.742918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4095.79 | − | 2364.71i | −0.918088 | − | 0.530058i | −0.0350633 | − | 0.999385i | \(-0.511163\pi\) |
−0.883025 | + | 0.469327i | \(0.844497\pi\) | |||||||
\(272\) | 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 | 0.795369 | − | 0.606125i | \(-0.207277\pi\) |
−0.922604 | + | 0.385747i | \(0.873944\pi\) | |||||||
\(278\) | 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 | −0.716667 | − | 0.697415i | \(-0.754333\pi\) |
0.245646 | + | 0.969360i | \(0.421000\pi\) | |||||||
\(284\) | 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 | \(-0.154568\pi\) | ||||
0.884400 | + | 0.466729i | \(0.154568\pi\) | |||||||
\(294\) | 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 | \(-0.919020\pi\) | ||
0.967813 | − | 0.251672i | \(-0.0809804\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1080.55 | − | 1871.56i | −0.197017 | − | 0.341243i | 0.750543 | − | 0.660822i | \(-0.229792\pi\) |
−0.947560 | + | 0.319579i | \(0.896459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7300.25 | − | 4214.80i | −1.31832 | − | 0.761133i | −0.334863 | − | 0.942267i | \(-0.608690\pi\) |
−0.983459 | + | 0.181133i | \(0.942023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8310.07 | + | 4797.82i | 1.47237 | + | 0.850071i | 0.999517 | − | 0.0310734i | \(-0.00989256\pi\) |
0.472848 | + | 0.881144i | \(0.343226\pi\) | |||||||
\(318\) | 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 | −0.255694 | − | 0.966758i | \(-0.582304\pi\) |
0.965084 | − | 0.261941i | \(-0.0843626\pi\) | |||||||
\(332\) | 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 | \(-0.851765\pi\) |
−0.0578712 | + | 0.998324i | \(0.518431\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3620.71i | 0.555336i | 0.960677 | + | 0.277668i | \(0.0895616\pi\) | ||||
−0.960677 | + | 0.277668i | \(0.910438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1164.89 | − | 2017.64i | −0.175639 | − | 0.304216i | 0.764743 | − | 0.644335i | \(-0.222866\pi\) |
−0.940382 | + | 0.340119i | \(0.889533\pi\) | |||||||
\(354\) | 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 | \(-0.374581\pi\) |
−0.607717 | + | 0.794154i | \(0.707914\pi\) | |||||||
\(360\) | 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 | −0.600150 | − | 0.799887i | \(-0.704893\pi\) |
0.392648 | + | 0.919689i | \(0.371559\pi\) | |||||||
\(368\) | 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 | −0.855524 | − | 0.517763i | \(-0.826765\pi\) |
0.876158 | + | 0.482024i | \(0.160098\pi\) | |||||||
\(374\) | 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 | 0.0578031 | + | 0.998328i | \(0.481590\pi\) |
−0.893479 | + | 0.449105i | \(0.851743\pi\) | |||||||
\(384\) | 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 | \(-0.840566\pi\) |
−0.0227196 | + | 0.999742i | \(0.507233\pi\) | |||||||
\(390\) | 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 | 0.990857 | − | 0.134918i | \(-0.0430770\pi\) |
0.378586 | + | 0.925566i | \(0.376410\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6943.55 | + | 4008.86i | 0.864699 | + | 0.499234i | 0.865583 | − | 0.500765i | \(-0.166948\pi\) |
−0.000883860 | 1.00000i | \(0.500281\pi\) | ||||||||
\(402\) | 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 | −0.881944 | − | 0.471354i | \(-0.843765\pi\) |
−0.0327670 | + | 0.999463i | \(0.510432\pi\) | |||||||
\(410\) | 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 | \(-0.426482\pi\) | ||||
0.228914 | + | 0.973447i | \(0.426482\pi\) | |||||||
\(420\) | 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 | \(-0.356580\pi\) |
0.997334 | + | 0.0729655i | \(0.0232463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15872.1i | − | 1.76158i | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||
0.473508 | − | 0.880790i | \(-0.342988\pi\) | |||||||
\(434\) | 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 | 0.635937 | − | 0.771741i | \(-0.280614\pi\) |
−0.350379 | + | 0.936608i | \(0.613947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11126.8 | + | 6424.08i | 1.19334 | + | 0.688978i | 0.959064 | − | 0.283191i | \(-0.0913930\pi\) |
0.234281 | + | 0.972169i | \(0.424726\pi\) | |||||||
\(444\) | 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 | −0.499615 | − | 0.866247i | \(-0.666525\pi\) |
1.00000 | 0.000444115i | \(-0.000141366\pi\) | ||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 638.874 | 0.0645452 | 0.0322726 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322726 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(462\) | 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 | \(-0.745175\pi\) |
0.969738 | + | 0.244149i | \(0.0785086\pi\) | |||||||
\(468\) | 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 | \(-0.0826703\pi\) |
−0.705632 | + | 0.708578i | \(0.749337\pi\) | |||||||
\(480\) | 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 | −0.998551 | − | 0.0538213i | \(-0.982860\pi\) |
0.452665 | − | 0.891681i | \(-0.350473\pi\) | |||||||
\(488\) | 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 | −0.554373 | − | 0.832268i | \(-0.687042\pi\) |
0.997952 | + | 0.0639672i | \(0.0203753\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10172.2 | 0.901698 | 0.450849 | − | 0.892600i | \(-0.351121\pi\) | ||||
0.450849 | + | 0.892600i | \(0.351121\pi\) | |||||||
\(504\) | 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 | \(-0.893270\pi\) |
0.757125 | + | 0.653270i | \(0.226603\pi\) | |||||||
\(510\) | 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 | \(-0.319606\pi\) |
−0.999070 | + | 0.0431133i | \(0.986272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7386.80 | − | 4264.77i | −0.617595 | − | 0.356569i | 0.158337 | − | 0.987385i | \(-0.449387\pi\) |
−0.775932 | + | 0.630817i | \(0.782720\pi\) | |||||||
\(524\) | 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 | −0.639594 | − | 0.768713i | \(-0.720897\pi\) |
0.985522 | + | 0.169548i | \(0.0542308\pi\) | |||||||
\(542\) | 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 | \(-0.795862\pi\) |
0.117448 | + | 0.993079i | \(0.462529\pi\) | |||||||
\(558\) | 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 | −0.971082 | − | 0.238747i | \(-0.923263\pi\) |
0.278780 | − | 0.960355i | \(-0.410070\pi\) | |||||||
\(564\) | 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 | \(-0.380811\pi\) |
−0.623142 | + | 0.782109i | \(0.714144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6430.01 | + | 11137.1i | 0.471257 | + | 0.816241i | 0.999459 | − | 0.0328777i | \(-0.0104672\pi\) |
−0.528203 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(572\) | 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 | −0.975894 | − | 0.218246i | \(-0.929967\pi\) |
−0.298940 | + | 0.954272i | \(0.596633\pi\) | |||||||
\(578\) | 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 | \(-0.306033\pi\) | ||||
0.572348 | + | 0.820011i | \(0.306033\pi\) | |||||||
\(588\) | 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 | \(-0.803706\pi\) |
0.908749 | + | 0.417344i | \(0.137039\pi\) | |||||||
\(594\) | 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 | \(-0.826550\pi\) |
0.0213091 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11096.1i | 0.753109i | 0.926394 | + | 0.376555i | \(0.122891\pi\) | ||||
−0.926394 | + | 0.376555i | \(0.877109\pi\) | |||||||
\(602\) | 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 | 0.785170 | − | 0.619280i | \(-0.212576\pi\) |
−0.143728 | + | 0.989617i | \(0.545909\pi\) | |||||||
\(608\) | 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 | 0.963654 | − | 0.267154i | \(-0.0860834\pi\) |
−0.713189 | + | 0.700971i | \(0.752750\pi\) | |||||||
\(614\) | 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 | 0.147330 | − | 0.989087i | \(-0.452932\pi\) |
0.930240 | + | 0.366952i | \(0.119599\pi\) | |||||||
\(620\) | 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 | \(-0.700142\pi\) |
0.406330 | + | 0.913727i | \(0.366808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 659.110i | − | 0.0404242i | −0.999796 | − | 0.0202121i | \(-0.993566\pi\) | ||
0.999796 | − | 0.0202121i | \(-0.00643415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3303.47 | − | 5721.78i | −0.200731 | − | 0.347676i | 0.748033 | − | 0.663661i | \(-0.230998\pi\) |
−0.948764 | + | 0.315985i | \(0.897665\pi\) | |||||||
\(648\) | 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 | \(-0.0507698\pi\) |
0.356109 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(654\) | 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 | −0.653065 | − | 0.757302i | \(-0.726517\pi\) |
0.329311 | + | 0.944222i | \(0.393184\pi\) | |||||||
\(662\) | 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 | \(-0.729239\pi\) |
0.980741 | + | 0.195313i | \(0.0625723\pi\) | |||||||
\(678\) | 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 | \(-0.826376\pi\) |
0.0218557 | + | 0.999761i | \(0.493043\pi\) | |||||||
\(684\) | 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 | 0.685840 | − | 0.727752i | \(-0.259435\pi\) |
−0.287332 | + | 0.957831i | \(0.592768\pi\) | |||||||
\(692\) | 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 | −0.696379 | − | 0.717674i | \(-0.745207\pi\) |
0.969714 | + | 0.244245i | \(0.0785401\pi\) | |||||||
\(710\) | 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 | −0.386107 | − | 0.922454i | \(-0.626180\pi\) |
0.991922 | − | 0.126849i | \(-0.0404864\pi\) | |||||||
\(720\) | 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 | \(0.192208\pi\) | ||||
−0.823162 | + | 0.567807i | \(0.807792\pi\) | |||||||
\(728\) | 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 | 0.710327 | − | 0.703872i | \(-0.248547\pi\) |
−0.254407 | + | 0.967097i | \(0.581880\pi\) | |||||||
\(734\) | 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 | 0.982176 | − | 0.187966i | \(-0.0601895\pi\) |
−0.653871 | + | 0.756606i | \(0.726856\pi\) | |||||||
\(740\) | 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 | 0.249498 | + | 0.968375i | \(0.419734\pi\) |
−0.963387 | + | 0.268116i | \(0.913599\pi\) | |||||||
\(752\) | 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 | −0.387292 | − | 0.921957i | \(-0.626589\pi\) |
0.992084 | − | 0.125574i | \(-0.0400772\pi\) | |||||||
\(762\) | 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 | \(-0.860319\pi\) | ||
0.905253 | − | 0.424872i | \(-0.139681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8673.05 | + | 15022.2i | 0.403555 | + | 0.698978i | 0.994152 | − | 0.107989i | \(-0.0344410\pi\) |
−0.590597 | + | 0.806967i | \(0.701108\pi\) | |||||||
\(774\) | 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 | −0.540244 | − | 0.841509i | \(-0.681668\pi\) |
0.458646 | + | 0.888619i | \(0.348335\pi\) | |||||||
\(788\) | 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 | \(-0.844507\pi\) | ||||
−0.883041 | + | 0.469297i | \(0.844507\pi\) | |||||||
\(798\) | 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 | \(-0.745034\pi\) |
0.273858 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14792.0i | − | 0.640465i | −0.947339 | − | 0.320232i | \(-0.896239\pi\) | ||
0.947339 | − | 0.320232i | \(-0.103761\pi\) | |||||||
\(812\) | 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 | \(-0.581368\pi\) |
−0.964309 | + | 0.264779i | \(0.914701\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10045.4 | + | 17399.1i | 0.425467 | + | 0.736930i | 0.996464 | − | 0.0840220i | \(-0.0267766\pi\) |
−0.570997 | + | 0.820952i | \(0.693443\pi\) | |||||||
\(824\) | 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 | −0.990910 | − | 0.134530i | \(-0.957048\pi\) |
−0.378949 | + | 0.925418i | \(0.623714\pi\) | |||||||
\(830\) | 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 | \(-0.135754\pi\) | ||||
0.910426 | + | 0.413672i | \(0.135754\pi\) | |||||||
\(840\) | 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 | \(-0.902983\pi\) | ||
0.953911 | − | 0.300089i | \(-0.0970165\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1224.76 | − | 2121.35i | −0.0488181 | − | 0.0845555i | 0.840584 | − | 0.541682i | \(-0.182212\pi\) |
−0.889402 | + | 0.457126i | \(0.848879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5751.97 | + | 3320.90i | 0.228469 | + | 0.131906i | 0.609865 | − | 0.792505i | \(-0.291223\pi\) |
−0.381397 | + | 0.924411i | \(0.624557\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16339.2 | − | 9433.46i | −0.644489 | − | 0.372096i | 0.141853 | − | 0.989888i | \(-0.454694\pi\) |
−0.786342 | + | 0.617792i | \(0.788027\pi\) | |||||||
\(864\) | 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 | −0.957994 | − | 0.286789i | \(-0.907412\pi\) |
0.727364 | + | 0.686252i | \(0.240745\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34504.0 | 1.31949 | 0.659743 | − | 0.751491i | \(-0.270665\pi\) | ||||
0.659743 | + | 0.751491i | \(0.270665\pi\) | |||||||
\(882\) | 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 | −0.318593 | − | 0.947892i | \(-0.603210\pi\) |
0.980195 | − | 0.198036i | \(-0.0634563\pi\) | |||||||
\(888\) | 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 | 0.541411 | − | 0.840758i | \(-0.317890\pi\) |
−0.998823 | + | 0.0484970i | \(0.984557\pi\) | |||||||
\(908\) | 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 | 0.108502 | − | 0.994096i | \(-0.465395\pi\) |
0.806661 | − | 0.591014i | \(-0.201272\pi\) | |||||||
\(920\) | 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 | −0.0523888 | − | 0.998627i | \(-0.516684\pi\) |
0.891031 | − | 0.453943i | \(-0.149983\pi\) | |||||||
\(930\) | 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 | \(0.0378887\pi\) | ||||
−0.992924 | + | 0.118750i | \(0.962111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16271.0 | − | 28182.2i | −0.563677 | − | 0.976318i | −0.997171 | − | 0.0751612i | \(-0.976053\pi\) |
0.433494 | − | 0.901156i | \(-0.357280\pi\) | |||||||
\(942\) | 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 | \(-0.397586\pi\) |
−0.663476 | + | 0.748198i | \(0.730920\pi\) | |||||||
\(948\) | 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 | \(-0.850277\pi\) |
0.838196 | + | 0.545369i | \(0.183610\pi\) | |||||||
\(972\) | 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 | \(-0.883114\pi\) |
−0.155754 | + | 0.987796i | \(0.549781\pi\) | |||||||
\(978\) | 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 | \(-0.313397\pi\) |
−0.998039 | + | 0.0625917i | \(0.980063\pi\) | |||||||
\(984\) | 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 | 0.968240 | + | 0.250023i | \(0.0804381\pi\) |
−0.267594 | + | 0.963532i | \(0.586229\pi\) | |||||||
\(992\) | 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 | −0.806096 | − | 0.591784i | \(-0.798424\pi\) |
0.109452 | + | 0.993992i | \(0.465090\pi\) | |||||||
\(998\) | 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.593.5 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.a.593.4 | 16 | ||
4.3 | odd | 2 | 63.4.p.a.26.7 | yes | 16 | ||
7.3 | odd | 6 | inner | 1008.4.bt.a.17.4 | 16 | ||
12.11 | even | 2 | 63.4.p.a.26.2 | yes | 16 | ||
21.17 | even | 6 | inner | 1008.4.bt.a.17.5 | 16 | ||
28.3 | even | 6 | 63.4.p.a.17.2 | ✓ | 16 | ||
28.11 | odd | 6 | 441.4.p.c.80.2 | 16 | |||
28.19 | even | 6 | 441.4.c.a.440.4 | 16 | |||
28.23 | odd | 6 | 441.4.c.a.440.3 | 16 | |||
28.27 | even | 2 | 441.4.p.c.215.7 | 16 | |||
84.11 | even | 6 | 441.4.p.c.80.7 | 16 | |||
84.23 | even | 6 | 441.4.c.a.440.14 | 16 | |||
84.47 | odd | 6 | 441.4.c.a.440.13 | 16 | |||
84.59 | odd | 6 | 63.4.p.a.17.7 | yes | 16 | ||
84.83 | odd | 2 | 441.4.p.c.215.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.2 | ✓ | 16 | 28.3 | even | 6 | ||
63.4.p.a.17.7 | yes | 16 | 84.59 | odd | 6 | ||
63.4.p.a.26.2 | yes | 16 | 12.11 | even | 2 | ||
63.4.p.a.26.7 | yes | 16 | 4.3 | odd | 2 | ||
441.4.c.a.440.3 | 16 | 28.23 | odd | 6 | |||
441.4.c.a.440.4 | 16 | 28.19 | even | 6 | |||
441.4.c.a.440.13 | 16 | 84.47 | odd | 6 | |||
441.4.c.a.440.14 | 16 | 84.23 | even | 6 | |||
441.4.p.c.80.2 | 16 | 28.11 | odd | 6 | |||
441.4.p.c.80.7 | 16 | 84.11 | even | 6 | |||
441.4.p.c.215.2 | 16 | 84.83 | odd | 2 | |||
441.4.p.c.215.7 | 16 | 28.27 | even | 2 | |||
1008.4.bt.a.17.4 | 16 | 7.3 | odd | 6 | inner | ||
1008.4.bt.a.17.5 | 16 | 21.17 | even | 6 | inner | ||
1008.4.bt.a.593.4 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.a.593.5 | 16 | 1.1 | even | 1 | trivial |