Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (of order \(2\), degree \(1\), 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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 264 x^{18} + 28274 x^{16} - 1545308 x^{14} + 45358441 x^{12} - 637328868 x^{10} + \cdots + 194396337216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.6 | ||
Root | \(-5.08927 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.q.721.5 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −5.08927 | −1.01785 | −0.508927 | − | 0.860810i | \(-0.669958\pi\) | ||||
−0.508927 | + | 0.860810i | \(0.669958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.6968 | 1.67098 | 0.835488 | − | 0.549509i | \(-0.185185\pi\) | ||||
0.835488 | + | 0.549509i | \(0.185185\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.6358 | 1.33053 | 0.665266 | − | 0.746607i | \(-0.268318\pi\) | ||||
0.665266 | + | 0.746607i | \(0.268318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.9834i | 1.30642i | 0.757179 | + | 0.653208i | \(0.226577\pi\) | ||||
−0.757179 | + | 0.653208i | \(0.773423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.79536 | 0.517374 | 0.258687 | − | 0.965961i | \(-0.416710\pi\) | ||||
0.258687 | + | 0.965961i | \(0.416710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.9638 | − | 14.7603i | 0.629673 | − | 0.776861i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.84997 | 0.297825 | 0.148912 | − | 0.988850i | \(-0.452423\pi\) | ||||
0.148912 | + | 0.988850i | \(0.452423\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.900640 | 0.0360256 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 45.8127i | 1.57975i | 0.613270 | + | 0.789873i | \(0.289854\pi\) | ||||
−0.613270 | + | 0.789873i | \(0.710146\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 50.1201i | 1.61678i | 0.588648 | + | 0.808389i | \(0.299660\pi\) | ||||
−0.588648 | + | 0.808389i | \(0.700340\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −59.5283 | −1.70081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.1916i | 0.951124i | 0.879682 | + | 0.475562i | \(0.157755\pi\) | ||||
−0.879682 | + | 0.475562i | \(0.842245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 60.4216i | − | 1.47370i | −0.676057 | − | 0.736849i | \(-0.736313\pi\) | ||
0.676057 | − | 0.736849i | \(-0.263687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 75.0196 | 1.74464 | 0.872321 | − | 0.488933i | \(-0.162614\pi\) | ||||
0.872321 | + | 0.488933i | \(0.162614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −52.6783 | −1.12082 | −0.560408 | − | 0.828217i | \(-0.689356\pi\) | ||||
−0.560408 | + | 0.828217i | \(0.689356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 87.8158 | 1.79216 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 93.2242i | − | 1.75895i | −0.475947 | − | 0.879474i | \(-0.657895\pi\) | ||
0.475947 | − | 0.879474i | \(-0.342105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −74.4857 | −1.35429 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.0988i | − | 0.222014i | −0.993820 | − | 0.111007i | \(-0.964592\pi\) | ||
0.993820 | − | 0.111007i | \(-0.0354077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.36673 | −0.0224055 | −0.0112027 | − | 0.999937i | \(-0.503566\pi\) | ||||
−0.0112027 | + | 0.999937i | \(0.503566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 86.4331i | − | 1.32974i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69.4258i | 1.03621i | 0.855318 | + | 0.518103i | \(0.173362\pi\) | ||||
−0.855318 | + | 0.518103i | \(0.826638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58.7253i | 0.827116i | 0.910478 | + | 0.413558i | \(0.135714\pi\) | ||||
−0.910478 | + | 0.413558i | \(0.864286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.4946 | −0.568419 | −0.284210 | − | 0.958762i | \(-0.591731\pi\) | ||||
−0.284210 | + | 0.958762i | \(0.591731\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 171.193 | 2.22329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 90.3616i | − | 1.14382i | −0.820317 | − | 0.571909i | \(-0.806203\pi\) | ||
0.820317 | − | 0.571909i | \(-0.193797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −155.789 | −1.87698 | −0.938491 | − | 0.345304i | \(-0.887776\pi\) | ||||
−0.938491 | + | 0.345304i | \(0.887776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44.7620 | −0.526611 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 73.4230i | − | 0.824978i | −0.910963 | − | 0.412489i | \(-0.864660\pi\) | ||
0.910963 | − | 0.412489i | \(-0.135340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 198.652i | 2.18299i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −60.8869 | + | 75.1194i | −0.640915 | + | 0.790730i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36.7235i | 0.378592i | 0.981920 | + | 0.189296i | \(0.0606206\pi\) | ||||
−0.981920 | + | 0.189296i | \(0.939379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −102.594 | −1.01578 | −0.507892 | − | 0.861421i | \(-0.669575\pi\) | ||||
−0.507892 | + | 0.861421i | \(0.669575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 64.2479i | − | 0.623766i | −0.950121 | − | 0.311883i | \(-0.899040\pi\) | ||
0.950121 | − | 0.311883i | \(-0.100960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19.9788i | − | 0.186718i | −0.995633 | − | 0.0933588i | \(-0.970240\pi\) | ||
0.995633 | − | 0.0933588i | \(-0.0297604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 144.748i | 1.32796i | 0.747749 | + | 0.663981i | \(0.231134\pi\) | ||||
−0.747749 | + | 0.663981i | \(0.768866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 127.440i | 1.12779i | 0.825846 | + | 0.563895i | \(0.190698\pi\) | ||||
−0.825846 | + | 0.563895i | \(0.809302\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.8613 | −0.303142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 102.878 | 0.864520 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 93.2079 | 0.770313 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 122.648 | 0.981185 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 34.1643i | 0.269010i | 0.990913 | + | 0.134505i | \(0.0429445\pi\) | ||||
−0.990913 | + | 0.134505i | \(0.957056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −33.9589 | −0.259228 | −0.129614 | − | 0.991565i | \(-0.541374\pi\) | ||||
−0.129614 | + | 0.991565i | \(0.541374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 139.938 | − | 172.649i | 1.05217 | − | 1.29811i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −110.031 | −0.803148 | −0.401574 | − | 0.915827i | \(-0.631537\pi\) | ||||
−0.401574 | + | 0.915827i | \(0.631537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3672 | 0.117750 | 0.0588748 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588748 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 248.566i | 1.73823i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 233.153i | − | 1.60795i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 249.958 | 1.67757 | 0.838784 | − | 0.544465i | \(-0.183267\pi\) | ||||
0.838784 | + | 0.544465i | \(0.183267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 153.037i | − | 1.01349i | −0.862097 | − | 0.506743i | \(-0.830849\pi\) | ||
0.862097 | − | 0.506743i | \(-0.169151\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 255.075i | − | 1.64564i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 80.1194 | 0.510315 | 0.255157 | − | 0.966900i | \(-0.417873\pi\) | ||||
0.255157 | + | 0.966900i | \(0.417873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 80.1229 | 0.497658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 209.684 | 1.28640 | 0.643202 | − | 0.765696i | \(-0.277605\pi\) | ||||
0.643202 | + | 0.765696i | \(0.277605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 26.1320i | − | 0.156479i | −0.996935 | − | 0.0782395i | \(-0.975070\pi\) | ||
0.996935 | − | 0.0782395i | \(-0.0249299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.436 | −0.706722 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 148.817i | 0.860216i | 0.902777 | + | 0.430108i | \(0.141525\pi\) | ||||
−0.902777 | + | 0.430108i | \(0.858475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.5346 | 0.0601979 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 346.022i | 1.93308i | 0.256512 | + | 0.966541i | \(0.417427\pi\) | ||||
−0.256512 | + | 0.966541i | \(0.582573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 283.289i | 1.56514i | 0.622566 | + | 0.782568i | \(0.286090\pi\) | ||||
−0.622566 | + | 0.782568i | \(0.713910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 179.099i | − | 0.968105i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 128.728 | 0.688383 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 315.646 | 1.65260 | 0.826300 | − | 0.563231i | \(-0.190442\pi\) | ||||
0.826300 | + | 0.563231i | \(0.190442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 47.4748i | 0.245983i | 0.992408 | + | 0.122992i | \(0.0392489\pi\) | ||||
−0.992408 | + | 0.122992i | \(0.960751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 197.715 | 1.00363 | 0.501816 | − | 0.864974i | \(-0.332665\pi\) | ||||
0.501816 | + | 0.864974i | \(0.332665\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 107.198 | 0.538684 | 0.269342 | − | 0.963045i | \(-0.413194\pi\) | ||||
0.269342 | + | 0.963045i | \(0.413194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 535.863i | 2.63972i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 307.502i | 1.50001i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 175.100 | − | 216.030i | 0.837799 | − | 1.03364i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 377.831i | 1.79067i | 0.445394 | + | 0.895335i | \(0.353064\pi\) | ||||
−0.445394 | + | 0.895335i | \(0.646936\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −381.795 | −1.77579 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 586.247i | 2.70160i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 149.375i | 0.675906i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.5498i | 0.132510i | 0.997803 | + | 0.0662551i | \(0.0211051\pi\) | ||||
−0.997803 | + | 0.0662551i | \(0.978895\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 234.224i | − | 1.03182i | −0.856642 | − | 0.515911i | \(-0.827454\pi\) | ||
0.856642 | − | 0.515911i | \(-0.172546\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 68.7496 | 0.300216 | 0.150108 | − | 0.988670i | \(-0.452038\pi\) | ||||
0.150108 | + | 0.988670i | \(0.452038\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 190.805 | 0.818904 | 0.409452 | − | 0.912332i | \(-0.365720\pi\) | ||||
0.409452 | + | 0.912332i | \(0.365720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 268.094 | 1.14083 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −413.869 | −1.73167 | −0.865835 | − | 0.500330i | \(-0.833212\pi\) | ||||
−0.865835 | + | 0.500330i | \(0.833212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 271.817i | − | 1.12787i | −0.825819 | − | 0.563935i | \(-0.809287\pi\) | ||
0.825819 | − | 0.563935i | \(-0.190713\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −446.918 | −1.82416 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 250.681 | + | 203.186i | 1.01490 | + | 0.822614i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 218.692 | 0.871283 | 0.435641 | − | 0.900120i | \(-0.356522\pi\) | ||||
0.435641 | + | 0.900120i | \(0.356522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 100.255 | 0.396265 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 115.480i | 0.449339i | 0.974435 | + | 0.224669i | \(0.0721302\pi\) | ||||
−0.974435 | + | 0.224669i | \(0.927870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 411.630i | 1.58931i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −101.290 | −0.385134 | −0.192567 | − | 0.981284i | \(-0.561681\pi\) | ||||
−0.192567 | + | 0.981284i | \(0.561681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 474.443i | 1.79035i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 223.290i | 0.830075i | 0.909804 | + | 0.415037i | \(0.136232\pi\) | ||||
−0.909804 | + | 0.415037i | \(0.863768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −486.033 | −1.79348 | −0.896741 | − | 0.442556i | \(-0.854072\pi\) | ||||
−0.896741 | + | 0.442556i | \(0.854072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1816 | 0.0479332 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0729 | 0.0580250 | 0.0290125 | − | 0.999579i | \(-0.490764\pi\) | ||||
0.0290125 | + | 0.999579i | \(0.490764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 165.956i | − | 0.590589i | −0.955406 | − | 0.295295i | \(-0.904582\pi\) | ||
0.955406 | − | 0.295295i | \(-0.0954178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 154.300 | 0.545230 | 0.272615 | − | 0.962123i | \(-0.412111\pi\) | ||||
0.272615 | + | 0.962123i | \(0.412111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 706.741i | − | 2.46251i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −211.642 | −0.732324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 448.580i | − | 1.53099i | −0.643441 | − | 0.765496i | \(-0.722494\pi\) | ||
0.643441 | − | 0.765496i | \(-0.277506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 66.6635i | 0.225978i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 116.336i | 0.389083i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 877.492 | 2.91525 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.95568 | 0.0228055 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 164.603i | 0.536166i | 0.963396 | + | 0.268083i | \(0.0863901\pi\) | ||||
−0.963396 | + | 0.268083i | \(0.913610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 290.496 | 0.934072 | 0.467036 | − | 0.884238i | \(-0.345322\pi\) | ||||
0.467036 | + | 0.884238i | \(0.345322\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 568.470 | 1.81620 | 0.908100 | − | 0.418754i | \(-0.137533\pi\) | ||||
0.908100 | + | 0.418754i | \(0.137533\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 150.231i | − | 0.473915i | −0.971520 | − | 0.236957i | \(-0.923850\pi\) | ||
0.971520 | − | 0.236957i | \(-0.0761502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 670.507i | 2.10190i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 105.226 | − | 129.823i | 0.325777 | − | 0.401928i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.2959i | 0.0470644i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −616.169 | −1.87285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.4836i | − | 0.0407360i | −0.999793 | − | 0.0203680i | \(-0.993516\pi\) | ||
0.999793 | − | 0.0203680i | \(-0.00648378\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 353.327i | − | 1.05471i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 209.994i | − | 0.623129i | −0.950225 | − | 0.311565i | \(-0.899147\pi\) | ||
0.950225 | − | 0.311565i | \(-0.100853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 733.550i | 2.15117i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 454.022 | 1.32368 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 195.718 | 0.564028 | 0.282014 | − | 0.959410i | \(-0.408998\pi\) | ||||
0.282014 | + | 0.959410i | \(0.408998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 283.953 | 0.813618 | 0.406809 | − | 0.913513i | \(-0.366641\pi\) | ||||
0.406809 | + | 0.913513i | \(0.366641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −395.888 | −1.12150 | −0.560748 | − | 0.827986i | \(-0.689486\pi\) | ||||
−0.560748 | + | 0.827986i | \(0.689486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 298.869i | − | 0.841883i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 442.196 | 1.23174 | 0.615872 | − | 0.787846i | \(-0.288804\pi\) | ||||
0.615872 | + | 0.787846i | \(0.288804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −74.7358 | − | 353.179i | −0.207025 | − | 0.978336i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 211.177 | 0.578567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.85524 | −0.0105048 | −0.00525238 | − | 0.999986i | \(-0.501672\pi\) | ||||
−0.00525238 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1090.43i | − | 2.93916i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 547.618i | 1.46814i | 0.679072 | + | 0.734072i | \(0.262382\pi\) | ||||
−0.679072 | + | 0.734072i | \(0.737618\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −778.055 | −2.06381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 495.686i | − | 1.30788i | −0.756548 | − | 0.653939i | \(-0.773115\pi\) | ||
0.756548 | − | 0.653939i | \(-0.226885\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 334.651i | 0.873763i | 0.899519 | + | 0.436881i | \(0.143917\pi\) | ||||
−0.899519 | + | 0.436881i | \(0.856083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −871.247 | −2.26298 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −348.223 | −0.895175 | −0.447588 | − | 0.894240i | \(-0.647717\pi\) | ||||
−0.447588 | + | 0.894240i | \(0.647717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 60.2480 | 0.154087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 459.874i | 1.16424i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 55.7961 | 0.140544 | 0.0702721 | − | 0.997528i | \(-0.477613\pi\) | ||||
0.0702721 | + | 0.997528i | \(0.477613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 422.248i | 1.05299i | 0.850179 | + | 0.526494i | \(0.176494\pi\) | ||||
−0.850179 | + | 0.526494i | \(0.823506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −851.210 | −2.11218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 515.059i | 1.26550i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.23852i | 0.00791814i | 0.999992 | + | 0.00395907i | \(0.00126021\pi\) | ||||
−0.999992 | + | 0.00395907i | \(0.998740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 153.215i | − | 0.370981i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 792.854 | 1.91049 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 427.843 | 1.02110 | 0.510552 | − | 0.859847i | \(-0.329441\pi\) | ||||
0.510552 | + | 0.859847i | \(0.329441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 592.172i | − | 1.40658i | −0.710901 | − | 0.703292i | \(-0.751713\pi\) | ||
0.710901 | − | 0.703292i | \(-0.248287\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.92146 | 0.0186387 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.9865 | −0.0374390 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 411.855i | − | 0.955579i | −0.878474 | − | 0.477790i | \(-0.841438\pi\) | ||
0.878474 | − | 0.477790i | \(-0.158562\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 607.670i | − | 1.40340i | −0.712475 | − | 0.701698i | \(-0.752426\pi\) | ||
0.712475 | − | 0.701698i | \(-0.247574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 81.9515 | − | 101.108i | 0.187532 | − | 0.231368i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.58398i | − | 0.0149977i | −0.999972 | − | 0.00749884i | \(-0.997613\pi\) | ||
0.999972 | − | 0.00749884i | \(-0.00238698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −270.742 | −0.611156 | −0.305578 | − | 0.952167i | \(-0.598850\pi\) | ||||
−0.305578 | + | 0.952167i | \(0.598850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 373.669i | 0.839706i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 229.268i | 0.510620i | 0.966859 | + | 0.255310i | \(0.0821775\pi\) | ||||
−0.966859 | + | 0.255310i | \(0.917822\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 884.321i | − | 1.96080i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1010.99i | − | 2.22196i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6628 | 0.0561548 | 0.0280774 | − | 0.999606i | \(-0.491062\pi\) | ||||
0.0280774 | + | 0.999606i | \(0.491062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −546.064 | −1.18452 | −0.592260 | − | 0.805747i | \(-0.701764\pi\) | ||||
−0.592260 | + | 0.805747i | \(0.701764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 218.764 | 0.472492 | 0.236246 | − | 0.971693i | \(-0.424083\pi\) | ||||
0.236246 | + | 0.971693i | \(0.424083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8980 | 0.0426082 | 0.0213041 | − | 0.999773i | \(-0.493218\pi\) | ||||
0.0213041 | + | 0.999773i | \(0.493218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 812.062i | 1.73148i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1097.98 | 2.32130 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.7751 | − | 13.2938i | 0.0226843 | − | 0.0279869i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −95.8635 | −0.200133 | −0.100066 | − | 0.994981i | \(-0.531905\pi\) | ||||
−0.100066 | + | 0.994981i | \(0.531905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −597.673 | −1.24256 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 186.895i | − | 0.385352i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 305.504i | 0.627318i | 0.949536 | + | 0.313659i | \(0.101555\pi\) | ||||
−0.949536 | + | 0.313659i | \(0.898445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −379.267 | −0.772438 | −0.386219 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386219 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 402.939i | 0.817321i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 686.899i | 1.38209i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −189.530 | −0.379819 | −0.189910 | − | 0.981802i | \(-0.560820\pi\) | ||||
−0.189910 | + | 0.981802i | \(0.560820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.3009 | −0.0602403 | −0.0301201 | − | 0.999546i | \(-0.509589\pi\) | ||||
−0.0301201 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 522.129 | 1.03392 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 481.358i | 0.945693i | 0.881145 | + | 0.472846i | \(0.156773\pi\) | ||||
−0.881145 | + | 0.472846i | \(0.843227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −485.355 | −0.949814 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 326.975i | 0.634902i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −770.992 | −1.49128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 311.850i | − | 0.598561i | −0.954165 | − | 0.299281i | \(-0.903253\pi\) | ||
0.954165 | − | 0.299281i | \(-0.0967467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 22.6368i | − | 0.0432826i | −0.999766 | − | 0.0216413i | \(-0.993111\pi\) | ||
0.999766 | − | 0.0216413i | \(-0.00688918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 440.825i | 0.836480i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −482.078 | −0.911300 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1026.16 | 1.92526 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 101.677i | 0.190051i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1285.26 | 2.38452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −767.716 | −1.41907 | −0.709534 | − | 0.704671i | \(-0.751095\pi\) | ||||
−0.709534 | + | 0.704671i | \(0.751095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 736.661i | − | 1.35167i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 237.682i | − | 0.434519i | −0.976114 | − | 0.217260i | \(-0.930288\pi\) | ||
0.976114 | − | 0.217260i | \(-0.0697118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 676.211 | + | 548.093i | 1.22724 | + | 0.994724i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1056.94i | − | 1.91129i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −227.023 | −0.407581 | −0.203790 | − | 0.979015i | \(-0.565326\pi\) | ||||
−0.203790 | + | 0.979015i | \(0.565326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1274.09i | 2.27923i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 99.7946i | 0.177255i | 0.996065 | + | 0.0886275i | \(0.0282481\pi\) | ||||
−0.996065 | + | 0.0886275i | \(0.971752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 648.578i | − | 1.14793i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 635.343i | 1.11660i | 0.829641 | + | 0.558298i | \(0.188545\pi\) | ||||
−0.829641 | + | 0.558298i | \(0.811455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −587.396 | −1.02871 | −0.514357 | − | 0.857576i | \(-0.671969\pi\) | ||||
−0.514357 | + | 0.857576i | \(0.671969\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.16936 | 0.0107293 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 889.609 | 1.54178 | 0.770892 | − | 0.636966i | \(-0.219811\pi\) | ||||
0.770892 | + | 0.636966i | \(0.219811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1822.24 | −3.13639 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1364.41i | − | 2.34033i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −400.577 | −0.682414 | −0.341207 | − | 0.939988i | \(-0.610836\pi\) | ||||
−0.341207 | + | 0.939988i | \(0.610836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 739.791 | + | 599.626i | 1.25601 | + | 1.01804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −402.176 | −0.678205 | −0.339103 | − | 0.940749i | \(-0.610123\pi\) | ||||
−0.339103 | + | 0.940749i | \(0.610123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −523.573 | −0.879955 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 479.823i | 0.801039i | 0.916288 | + | 0.400520i | \(0.131170\pi\) | ||||
−0.916288 | + | 0.400520i | \(0.868830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 207.462i | − | 0.345195i | −0.984992 | − | 0.172597i | \(-0.944784\pi\) | ||
0.984992 | − | 0.172597i | \(-0.0552160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −474.360 | −0.784066 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 96.0000i | − | 0.158155i | −0.996868 | − | 0.0790774i | \(-0.974803\pi\) | ||
0.996868 | − | 0.0790774i | \(-0.0251974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 894.657i | − | 1.46425i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 208.034 | 0.339370 | 0.169685 | − | 0.985498i | \(-0.445725\pi\) | ||||
0.169685 | + | 0.985498i | \(0.445725\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 67.9068 | 0.110060 | 0.0550298 | − | 0.998485i | \(-0.482475\pi\) | ||||
0.0550298 | + | 0.998485i | \(0.482475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 485.579 | 0.784458 | 0.392229 | − | 0.919868i | \(-0.371704\pi\) | ||||
0.392229 | + | 0.919868i | \(0.371704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 858.816i | − | 1.37852i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −646.705 | −1.03473 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 309.523i | 0.492087i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −378.427 | −0.599726 | −0.299863 | − | 0.953982i | \(-0.596941\pi\) | ||||
−0.299863 | + | 0.953982i | \(0.596941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 173.871i | − | 0.273813i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1491.41i | 2.34130i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 152.435i | − | 0.237808i | −0.992906 | − | 0.118904i | \(-0.962062\pi\) | ||
0.992906 | − | 0.118904i | \(-0.0379380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 214.750 | 0.333981 | 0.166991 | − | 0.985958i | \(-0.446595\pi\) | ||||
0.166991 | + | 0.985958i | \(0.446595\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 93.1807 | 0.144020 | 0.0720098 | − | 0.997404i | \(-0.477059\pi\) | ||||
0.0720098 | + | 0.997404i | \(0.477059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 191.713i | − | 0.295397i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 995.847 | 1.52503 | 0.762517 | − | 0.646968i | \(-0.223963\pi\) | ||||
0.762517 | + | 0.646968i | \(0.223963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 172.826 | 0.263857 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 26.3579i | − | 0.0399968i | −0.999800 | − | 0.0199984i | \(-0.993634\pi\) | ||
0.999800 | − | 0.0199984i | \(-0.00636612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 808.835i | − | 1.22365i | −0.790992 | − | 0.611827i | \(-0.790435\pi\) | ||
0.790992 | − | 0.611827i | \(-0.209565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −712.183 | + | 878.658i | −1.07095 | + | 1.32129i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 313.815i | 0.470488i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.0033 | −0.0298112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 450.410i | − | 0.669257i | −0.942350 | − | 0.334629i | \(-0.891389\pi\) | ||
0.942350 | − | 0.334629i | \(-0.108611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 743.973i | − | 1.09893i | −0.835518 | − | 0.549463i | \(-0.814832\pi\) | ||
0.835518 | − | 0.549463i | \(-0.185168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 429.548i | 0.632619i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 158.596i | − | 0.232205i | −0.993237 | − | 0.116102i | \(-0.962960\pi\) | ||
0.993237 | − | 0.116102i | \(-0.0370400\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 559.979 | 0.817487 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1583.26 | 2.29792 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1120.91 | 1.62216 | 0.811080 | − | 0.584936i | \(-0.198880\pi\) | ||||
0.811080 | + | 0.584936i | \(0.198880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −83.2971 | −0.119852 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 531.430i | − | 0.762454i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −272.473 | −0.388691 | −0.194346 | − | 0.980933i | \(-0.562258\pi\) | ||||
−0.194346 | + | 0.980933i | \(0.562258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 519.440 | + | 421.025i | 0.738891 | + | 0.598897i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1200.03 | −1.69735 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.34415 | −0.00612716 | −0.00306358 | − | 0.999995i | \(-0.500975\pi\) | ||||
−0.00306358 | + | 0.999995i | \(0.500975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 343.321i | 0.481517i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1265.02i | − | 1.76926i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 969.937 | 1.34901 | 0.674504 | − | 0.738271i | \(-0.264358\pi\) | ||||
0.674504 | + | 0.738271i | \(0.264358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 751.497i | − | 1.04230i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.2607i | 0.0569113i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −213.362 | −0.293482 | −0.146741 | − | 0.989175i | \(-0.546878\pi\) | ||||
−0.146741 | + | 0.989175i | \(0.546878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 659.825 | 0.902633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1281.86 | 1.74879 | 0.874393 | − | 0.485219i | \(-0.161260\pi\) | ||||
0.874393 | + | 0.485219i | \(0.161260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1016.11i | 1.37870i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1339.79 | −1.81298 | −0.906491 | − | 0.422226i | \(-0.861249\pi\) | ||||
−0.906491 | + | 0.422226i | \(0.861249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 650.113i | 0.874984i | 0.899222 | + | 0.437492i | \(0.144133\pi\) | ||||
−0.899222 | + | 0.437492i | \(0.855867\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1272.10 | −1.70752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 233.688i | − | 0.312000i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1408.26i | − | 1.87518i | −0.347745 | − | 0.937589i | \(-0.613052\pi\) | ||
0.347745 | − | 0.937589i | \(-0.386948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 778.844i | 1.03158i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 881.249 | 1.16413 | 0.582067 | − | 0.813141i | \(-0.302244\pi\) | ||||
0.582067 | + | 0.813141i | \(0.302244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 218.184 | 0.286707 | 0.143353 | − | 0.989672i | \(-0.454211\pi\) | ||||
0.143353 | + | 0.989672i | \(0.454211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1693.09i | 2.21899i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 222.463 | 0.290043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −624.448 | −0.812026 | −0.406013 | − | 0.913867i | \(-0.633081\pi\) | ||||
−0.406013 | + | 0.913867i | \(0.633081\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 425.151i | − | 0.550002i | −0.961444 | − | 0.275001i | \(-0.911322\pi\) | ||
0.961444 | − | 0.275001i | \(-0.0886781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.1402i | 0.0582454i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −891.844 | − | 722.871i | −1.14486 | − | 0.927947i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 859.494i | 1.10050i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −407.749 | −0.519426 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 757.949i | − | 0.963086i | −0.876422 | − | 0.481543i | \(-0.840076\pi\) | ||
0.876422 | − | 0.481543i | \(-0.159924\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1490.65i | 1.88451i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 23.2118i | − | 0.0292709i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1466.54i | − | 1.84008i | −0.391828 | − | 0.920038i | \(-0.628157\pi\) | ||
0.391828 | − | 0.920038i | \(-0.371843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −463.325 | −0.579881 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −607.308 | −0.756299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −407.767 | −0.506543 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1576.10 | 1.94821 | 0.974104 | − | 0.226098i | \(-0.0725971\pi\) | ||||
0.974104 | + | 0.226098i | \(0.0725971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 163.777i | 0.201945i | 0.994889 | + | 0.100973i | \(0.0321954\pi\) | ||||
−0.994889 | + | 0.100973i | \(0.967805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1067.14 | −1.30937 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 897.518 | − | 1107.32i | 1.09855 | − | 1.35534i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 603.584 | 0.735181 | 0.367591 | − | 0.929988i | \(-0.380183\pi\) | ||||
0.367591 | + | 0.929988i | \(0.380183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −790.775 | −0.960844 | −0.480422 | − | 0.877037i | \(-0.659516\pi\) | ||||
−0.480422 | + | 0.877037i | \(0.659516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 290.501i | 0.351271i | 0.984455 | + | 0.175635i | \(0.0561980\pi\) | ||||
−0.984455 | + | 0.175635i | \(0.943802\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 915.557i | 1.10441i | 0.833708 | + | 0.552206i | \(0.186214\pi\) | ||||
−0.833708 | + | 0.552206i | \(0.813786\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 772.372 | 0.927217 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 132.993i | 0.159273i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 818.866i | 0.976002i | 0.872843 | + | 0.488001i | \(0.162274\pi\) | ||||
−0.872843 | + | 0.488001i | \(0.837726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1257.80 | −1.49560 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 607.841 | 0.719339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1090.24 | 1.28717 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 241.061i | 0.283268i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1063.70 | −1.24701 | −0.623505 | − | 0.781819i | \(-0.714292\pi\) | ||||
−0.623505 | + | 0.781819i | \(0.714292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1028.97i | − | 1.20067i | −0.799749 | − | 0.600335i | \(-0.795034\pi\) | ||
0.799749 | − | 0.600335i | \(-0.204966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −481.326 | −0.560333 | −0.280166 | − | 0.959951i | \(-0.590390\pi\) | ||||
−0.280166 | + | 0.959951i | \(0.590390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 693.908i | 0.804065i | 0.915625 | + | 0.402033i | \(0.131696\pi\) | ||||
−0.915625 | + | 0.402033i | \(0.868304\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 757.371i | − | 0.875574i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1322.52i | − | 1.52189i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1179.09 | −1.35372 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1434.59 | 1.63954 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 942.448i | − | 1.07463i | −0.843383 | − | 0.537313i | \(-0.819439\pi\) | ||
0.843383 | − | 0.537313i | \(-0.180561\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 84.6900 | 0.0961294 | 0.0480647 | − | 0.998844i | \(-0.484695\pi\) | ||||
0.0480647 | + | 0.998844i | \(0.484695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −784.001 | −0.887883 | −0.443941 | − | 0.896056i | \(-0.646420\pi\) | ||||
−0.443941 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 239.164i | 0.269632i | 0.990871 | + | 0.134816i | \(0.0430444\pi\) | ||||
−0.990871 | + | 0.134816i | \(0.956956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 399.614i | 0.449509i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −630.232 | + | 777.550i | −0.705747 | + | 0.870717i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1761.00i | − | 1.96759i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2296.14 | −2.55410 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 819.941i | − | 0.910034i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1441.74i | − | 1.59308i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 699.827i | 0.771584i | 0.922586 | + | 0.385792i | \(0.126072\pi\) | ||||
−0.922586 | + | 0.385792i | \(0.873928\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 539.505i | − | 0.592212i | −0.955155 | − | 0.296106i | \(-0.904312\pi\) | ||
0.955155 | − | 0.296106i | \(-0.0956881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2280.11 | −2.49738 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −397.212 | −0.433164 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −337.584 | −0.367338 | −0.183669 | − | 0.982988i | \(-0.558798\pi\) | ||||
−0.183669 | + | 0.982988i | \(0.558798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −997.355 | −1.08056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.6950i | 0.0342648i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 998.673 | 1.07500 | 0.537499 | − | 0.843264i | \(-0.319369\pi\) | ||||
0.537499 | + | 0.843264i | \(0.319369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1050.61 | − | 1296.19i | 1.12847 | − | 1.39226i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −655.129 | −0.700673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.98538 | 0.00638781 | 0.00319390 | − | 0.999995i | \(-0.498983\pi\) | ||||
0.00319390 | + | 0.999995i | \(0.498983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1196.81i | 1.27185i | 0.771752 | + | 0.635924i | \(0.219381\pi\) | ||||
−0.771752 | + | 0.635924i | \(0.780619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 413.886i | − | 0.438904i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 343.433 | 0.362654 | 0.181327 | − | 0.983423i | \(-0.441961\pi\) | ||||
0.181327 | + | 0.983423i | \(0.441961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 704.719i | − | 0.742591i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1342.45i | − | 1.40865i | −0.709876 | − | 0.704327i | \(-0.751249\pi\) | ||
0.709876 | − | 0.704327i | \(-0.248751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1606.41 | −1.68210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1287.02 | −1.34204 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1551.03 | −1.61397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 241.612i | − | 0.250375i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −334.092 | −0.345494 | −0.172747 | − | 0.984966i | \(-0.555264\pi\) | ||||
−0.172747 | + | 0.984966i | \(0.555264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1197.90i | 1.23367i | 0.787091 | + | 0.616836i | \(0.211586\pi\) | ||||
−0.787091 | + | 0.616836i | \(0.788414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 191.444 | 0.196757 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 798.084i | − | 0.816872i | −0.912787 | − | 0.408436i | \(-0.866074\pi\) | ||
0.912787 | − | 0.408436i | \(-0.133926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1074.61i | − | 1.09766i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 142.172i | − | 0.144631i | −0.997382 | − | 0.0723154i | \(-0.976961\pi\) | ||
0.997382 | − | 0.0723154i | \(-0.0230388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1006.23 | −1.02155 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 513.882 | 0.519598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 982.532i | − | 0.991455i | −0.868478 | − | 0.495727i | \(-0.834902\pi\) | ||
0.868478 | − | 0.495727i | \(-0.165098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −545.560 | −0.548302 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 808.860 | 0.811293 | 0.405647 | − | 0.914030i | \(-0.367046\pi\) | ||||
0.405647 | + | 0.914030i | \(0.367046\pi\) | |||||||
\(998\) | 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 | 2736.3.o.q.721.6 | 20 | ||
3.2 | odd | 2 | inner | 2736.3.o.q.721.16 | 20 | ||
4.3 | odd | 2 | 1368.3.o.d.721.6 | yes | 20 | ||
12.11 | even | 2 | 1368.3.o.d.721.16 | yes | 20 | ||
19.18 | odd | 2 | inner | 2736.3.o.q.721.5 | 20 | ||
57.56 | even | 2 | inner | 2736.3.o.q.721.15 | 20 | ||
76.75 | even | 2 | 1368.3.o.d.721.5 | ✓ | 20 | ||
228.227 | odd | 2 | 1368.3.o.d.721.15 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.3.o.d.721.5 | ✓ | 20 | 76.75 | even | 2 | ||
1368.3.o.d.721.6 | yes | 20 | 4.3 | odd | 2 | ||
1368.3.o.d.721.15 | yes | 20 | 228.227 | odd | 2 | ||
1368.3.o.d.721.16 | yes | 20 | 12.11 | even | 2 | ||
2736.3.o.q.721.5 | 20 | 19.18 | odd | 2 | inner | ||
2736.3.o.q.721.6 | 20 | 1.1 | even | 1 | trivial | ||
2736.3.o.q.721.15 | 20 | 57.56 | even | 2 | inner | ||
2736.3.o.q.721.16 | 20 | 3.2 | odd | 2 | inner |