Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(3497,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.3497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.c (of order \(2\), degree \(1\), 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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3497.12 | ||
Character | \(\chi\) | \(=\) | 4028.3497 |
Dual form | 4028.2.c.a.3497.71 |
$q$-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 \(\left(\mathbb{Z}/4028\mathbb{Z}\right)^\times\).
\(n\) | \(2015\) | \(2281\) | \(2757\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.46723i | − | 1.42446i | −0.701947 | − | 0.712229i | \(-0.747686\pi\) | ||
0.701947 | − | 0.712229i | \(-0.252314\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.35102i | − | 1.94584i | −0.231151 | − | 0.972918i | \(-0.574249\pi\) | ||
0.231151 | − | 0.972918i | \(-0.425751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12403 | 0.424844 | 0.212422 | − | 0.977178i | \(-0.431865\pi\) | ||||
0.212422 | + | 0.977178i | \(0.431865\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.08725 | −1.02908 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.799448 | −0.241043 | −0.120521 | − | 0.992711i | \(-0.538457\pi\) | ||||
−0.120521 | + | 0.992711i | \(0.538457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.10995 | 1.97195 | 0.985973 | − | 0.166906i | \(-0.0533776\pi\) | ||||
0.985973 | + | 0.166906i | \(0.0533776\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.7350 | −2.77176 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.99464 | 1.45391 | 0.726957 | − | 0.686683i | \(-0.240934\pi\) | ||||
0.726957 | + | 0.686683i | \(0.240934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.77325i | − | 0.605173i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.333262i | 0.0694900i | 0.999396 | + | 0.0347450i | \(0.0110619\pi\) | ||||
−0.999396 | + | 0.0347450i | \(0.988938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.9314 | −2.78628 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.215258i | 0.0414264i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.55636 | −1.21748 | −0.608742 | − | 0.793368i | \(-0.708326\pi\) | ||||
−0.608742 | + | 0.793368i | \(0.708326\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.36396i | − | 0.604185i | −0.953279 | − | 0.302092i | \(-0.902315\pi\) | ||
0.953279 | − | 0.302092i | \(-0.0976851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97243i | 0.343355i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.89068i | − | 0.826677i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2091 | −1.67837 | −0.839186 | − | 0.543845i | \(-0.816968\pi\) | ||||
−0.839186 | + | 0.543845i | \(0.816968\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 17.5419i | − | 2.80895i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.96823i | 0.775908i | 0.921679 | + | 0.387954i | \(0.126818\pi\) | ||||
−0.921679 | + | 0.387954i | \(0.873182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.65351 | 1.01465 | 0.507325 | − | 0.861755i | \(-0.330634\pi\) | ||||
0.507325 | + | 0.861755i | \(0.330634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.4327i | 2.00243i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65151 | −0.824358 | −0.412179 | − | 0.911103i | \(-0.635232\pi\) | ||||
−0.412179 | + | 0.911103i | \(0.635232\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.73655 | −0.819508 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 14.7902i | − | 2.07104i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.17877 | + | 6.54946i | −0.436638 | + | 0.899637i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.47842i | 0.469030i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.46723 | −0.326793 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.81155 | 1.14717 | 0.573583 | − | 0.819147i | \(-0.305553\pi\) | ||||
0.573583 | + | 0.819147i | \(0.305553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.2919i | − | 1.57382i | −0.617068 | − | 0.786910i | \(-0.711680\pi\) | ||
0.617068 | − | 0.786910i | \(-0.288320\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.47016 | −0.437199 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 30.9356i | − | 3.83708i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.5470i | − | 1.28852i | −0.764807 | − | 0.644259i | \(-0.777166\pi\) | ||
0.764807 | − | 0.644259i | \(-0.222834\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.822236 | 0.0989856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.10535i | 0.961928i | 0.876740 | + | 0.480964i | \(0.159713\pi\) | ||||
−0.876740 | + | 0.480964i | \(0.840287\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.90391i | 1.15917i | 0.814913 | + | 0.579583i | \(0.196784\pi\) | ||||
−0.814913 | + | 0.579583i | \(0.803216\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 34.3720i | 3.96894i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.898605 | −0.102406 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.69444i | − | 0.415657i | −0.978165 | − | 0.207828i | \(-0.933360\pi\) | ||
0.978165 | − | 0.207828i | \(-0.0666396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.73065 | −0.970072 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.54897i | − | 0.828608i | −0.910139 | − | 0.414304i | \(-0.864025\pi\) | ||
0.910139 | − | 0.414304i | \(-0.135975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 26.0828i | − | 2.82908i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.1761i | 1.73426i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.95256 | −0.418970 | −0.209485 | − | 0.977812i | \(-0.567179\pi\) | ||||
−0.209485 | + | 0.977812i | \(0.567179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.99181 | 0.837769 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.29967 | −0.860636 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.35102 | −0.446405 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.60480 | −0.366012 | −0.183006 | − | 0.983112i | \(-0.558583\pi\) | ||||
−0.183006 | + | 0.983112i | \(0.558583\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.46809 | 0.248053 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.00383i | − | 0.597403i | −0.954347 | − | 0.298702i | \(-0.903446\pi\) | ||
0.954347 | − | 0.298702i | \(-0.0965535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.32269i | − | 0.918591i | −0.888283 | − | 0.459296i | \(-0.848102\pi\) | ||
0.888283 | − | 0.459296i | \(-0.151898\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0665 | −1.17757 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7521 | 1.52281 | 0.761406 | − | 0.648276i | \(-0.224510\pi\) | ||||
0.761406 | + | 0.648276i | \(0.224510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.31508i | − | 0.317527i | −0.987317 | − | 0.158764i | \(-0.949249\pi\) | ||
0.987317 | − | 0.158764i | \(-0.0507508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.1883i | 2.39077i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.01932 | −0.378106 | −0.189053 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189053 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45003 | 0.135216 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −21.9502 | −2.02929 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.73817 | 0.617687 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3609 | −0.941898 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2578 | 1.10525 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 38.8607i | 3.47580i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8113i | 1.04808i | 0.851693 | + | 0.524042i | \(0.175576\pi\) | ||||
−0.851693 | + | 0.524042i | \(0.824424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 16.4158i | − | 1.44533i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.8521 | −1.99660 | −0.998298 | − | 0.0583252i | \(-0.981424\pi\) | ||||
−0.998298 | + | 0.0583252i | \(0.981424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.12403i | − | 0.0974659i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.936593 | 0.0806091 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.67465i | − | 0.313946i | −0.987603 | − | 0.156973i | \(-0.949826\pi\) | ||
0.987603 | − | 0.156973i | \(-0.0501736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.6803i | − | 1.24517i | −0.782554 | − | 0.622583i | \(-0.786083\pi\) | ||
0.782554 | − | 0.622583i | \(-0.213917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.9436i | 1.17426i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.68404 | −0.475323 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.5268i | 2.36903i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.1534i | 1.16735i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5594 | 1.43852 | 0.719259 | − | 0.694742i | \(-0.244481\pi\) | ||||
0.719259 | + | 0.694742i | \(0.244481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16.5791i | − | 1.34918i | −0.738191 | − | 0.674592i | \(-0.764320\pi\) | ||
0.738191 | − | 0.674592i | \(-0.235680\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.5069 | −1.49620 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6367 | −1.17564 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0601i | 1.12212i | 0.827775 | + | 0.561060i | \(0.189606\pi\) | ||||
−0.827775 | + | 0.561060i | \(0.810394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.1591 | + | 7.84278i | 1.28150 | + | 0.621973i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.374597i | 0.0295224i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5711 | 0.984644 | 0.492322 | − | 0.870413i | \(-0.336148\pi\) | ||||
0.492322 | + | 0.870413i | \(0.336148\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.58207 | 0.668113 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5056i | 1.12248i | 0.827654 | + | 0.561239i | \(0.189675\pi\) | ||||
−0.827654 | + | 0.561239i | \(0.810325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.5514 | 2.88857 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.08725i | 0.236088i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9586i | 0.833164i | 0.909098 | + | 0.416582i | \(0.136772\pi\) | ||||
−0.909098 | + | 0.416582i | \(0.863228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6593 | −1.18373 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 21.7402i | − | 1.63409i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.07052i | − | 0.378988i | −0.981882 | − | 0.189494i | \(-0.939315\pi\) | ||
0.981882 | − | 0.189494i | \(-0.0606848\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.195193i | 0.0145086i | 0.999974 | + | 0.00725430i | \(0.00230914\pi\) | ||||
−0.999974 | + | 0.00725430i | \(0.997691\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.3271 | −2.24184 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 44.4202i | 3.26584i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.79241 | −0.350455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.241957i | 0.0175998i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.2536i | − | 1.53786i | −0.639334 | − | 0.768929i | \(-0.720790\pi\) | ||
0.639334 | − | 0.768929i | \(-0.279210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.31833i | 0.0948951i | 0.998874 | + | 0.0474476i | \(0.0151087\pi\) | ||||
−0.998874 | + | 0.0474476i | \(0.984891\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −76.3253 | −5.46577 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.8466 | 1.20027 | 0.600134 | − | 0.799900i | \(-0.295114\pi\) | ||||
0.600134 | + | 0.799900i | \(0.295114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4864 | 1.16869 | 0.584347 | − | 0.811504i | \(-0.301351\pi\) | ||||
0.584347 | + | 0.811504i | \(0.301351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.0219 | −1.83544 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.36955 | −0.517241 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.6169 | 1.50979 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.02886i | − | 0.0715109i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.799448i | 0.0552990i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.04700 | 0.416292 | 0.208146 | − | 0.978098i | \(-0.433257\pi\) | ||||
0.208146 | + | 0.978098i | \(0.433257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.9978 | 1.37023 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 28.9495i | − | 1.97434i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.78119i | − | 0.256684i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.4353 | 1.65118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.6216 | 2.86704 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9707 | 0.935546 | 0.467773 | − | 0.883849i | \(-0.345056\pi\) | ||||
0.467773 | + | 0.883849i | \(0.345056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 43.0096 | 2.86731 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.90088 | 0.590772 | 0.295386 | − | 0.955378i | \(-0.404552\pi\) | ||||
0.295386 | + | 0.955378i | \(0.404552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.25597 | 0.0829965 | 0.0414983 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414983 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.21707i | 0.145872i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8034i | 1.29736i | 0.761059 | + | 0.648682i | \(0.224680\pi\) | ||||
−0.761059 | + | 0.648682i | \(0.775320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.5898i | 1.60406i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.11505 | −0.592086 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6074i | 1.07424i | 0.843505 | + | 0.537121i | \(0.180488\pi\) | ||||
−0.843505 | + | 0.537121i | \(0.819512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2728 | −1.11264 | −0.556319 | − | 0.830969i | \(-0.687787\pi\) | ||||
−0.556319 | + | 0.830969i | \(0.687787\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1863i | 1.42325i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.9599i | 1.59463i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.10995i | − | 0.452395i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.6251 | −1.18032 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1738i | 1.33648i | 0.743946 | + | 0.668240i | \(0.232952\pi\) | ||||
−0.743946 | + | 0.668240i | \(0.767048\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.266426i | − | 0.0167501i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −64.3524 | −4.02991 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.43990i | 0.276954i | 0.990366 | + | 0.138477i | \(0.0442206\pi\) | ||||
−0.990366 | + | 0.138477i | \(0.955779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4754 | −0.713046 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.2411 | 1.25289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.5056i | 1.63441i | 0.576349 | + | 0.817204i | \(0.304477\pi\) | ||||
−0.576349 | + | 0.817204i | \(0.695523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.4968 | + | 13.8309i | 1.75055 | + | 0.849626i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.75189i | 0.596806i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.32516 | 0.202738 | 0.101369 | − | 0.994849i | \(-0.467678\pi\) | ||||
0.101369 | + | 0.994849i | \(0.467678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7057 | 1.44002 | 0.720009 | − | 0.693965i | \(-0.244138\pi\) | ||||
0.720009 | + | 0.693965i | \(0.244138\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 19.7177i | − | 1.19337i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1374 | 0.671612 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.21164i | − | 0.313137i | −0.987667 | − | 0.156568i | \(-0.949957\pi\) | ||
0.987667 | − | 0.156568i | \(-0.0500432\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3854i | 0.621756i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.63957 | 0.575049 | 0.287524 | − | 0.957773i | \(-0.407168\pi\) | ||||
0.287524 | + | 0.957773i | \(0.407168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 27.0307i | − | 1.60681i | −0.595433 | − | 0.803405i | \(-0.703019\pi\) | ||
0.595433 | − | 0.803405i | \(-0.296981\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7350i | 0.635886i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.58445i | 0.329640i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.9357 | 1.11387 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.89390i | 0.521369i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1003 | −0.823746 | −0.411873 | − | 0.911241i | \(-0.635125\pi\) | ||||
−0.411873 | + | 0.911241i | \(0.635125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 38.3393i | − | 2.23220i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.172088i | − | 0.00998554i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.36948i | 0.137031i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.47875 | 0.431068 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.8129 | −0.850976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −53.4824 | −3.06239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5676 | 1.34507 | 0.672536 | − | 0.740064i | \(-0.265205\pi\) | ||||
0.672536 | + | 0.740064i | \(0.265205\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.0013 | −1.30850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0856000 | 0.00485393 | 0.00242696 | − | 0.999997i | \(-0.499227\pi\) | ||||
0.00242696 | + | 0.999997i | \(0.499227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 28.0803i | − | 1.58719i | −0.608444 | − | 0.793597i | \(-0.708206\pi\) | ||
0.608444 | − | 0.793597i | \(-0.291794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.0987i | 0.850718i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.85550 | −0.497374 | −0.248687 | − | 0.968584i | \(-0.579999\pi\) | ||||
−0.248687 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.24147 | 0.293466 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.8641i | − | 2.16918i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.99464i | − | 0.333551i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −99.0515 | −5.49439 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.17908 | −0.452304 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.35248 | −0.350223 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.89230 | −0.433800 | −0.216900 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216900 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.5181 | 1.72718 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −45.8901 | −2.50725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.33311i | − | 0.236040i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) | ||
0.993011 | − | 0.118020i | \(-0.0376546\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.91660i | 0.538596i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.68931i | 0.145634i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3163 | −0.773007 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 3.57757i | − | 0.192610i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3427 | 0.823638 | 0.411819 | − | 0.911266i | \(-0.364894\pi\) | ||||
0.411819 | + | 0.911266i | \(0.364894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.05386i | − | 0.163469i | −0.996654 | − | 0.0817347i | \(-0.973954\pi\) | ||
0.996654 | − | 0.0817347i | \(-0.0260460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.53047i | 0.0816907i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.0742i | − | 0.589421i | −0.955587 | − | 0.294711i | \(-0.904777\pi\) | ||
0.955587 | − | 0.294711i | \(-0.0952232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.2666 | 1.87175 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 16.6246i | − | 0.879869i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.90570i | − | 0.311691i | −0.987781 | − | 0.155845i | \(-0.950190\pi\) | ||
0.987781 | − | 0.155845i | \(-0.0498102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.5627i | 1.34170i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.0921 | 2.25555 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.2944 | −1.26816 | −0.634080 | − | 0.773268i | \(-0.718621\pi\) | ||||
−0.634080 | + | 0.773268i | \(0.718621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 15.3382i | − | 0.798473i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.57304 | + | 7.36180i | −0.185503 | + | 0.382205i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9477i | 0.981076i | 0.871420 | + | 0.490538i | \(0.163200\pi\) | ||||
−0.871420 | + | 0.490538i | \(0.836800\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 95.8784 | 4.95114 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.6154 | −2.40081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.5267i | − | 0.746187i | −0.927794 | − | 0.373094i | \(-0.878297\pi\) | ||
0.927794 | − | 0.373094i | \(-0.121703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.1413 | 1.49295 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.1599i | 0.876828i | 0.898773 | + | 0.438414i | \(0.144460\pi\) | ||||
−0.898773 | + | 0.438414i | \(0.855540\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.90985i | 0.199264i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.5410 | −1.04416 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.2500i | 0.570398i | 0.958468 | + | 0.285199i | \(0.0920597\pi\) | ||||
−0.958468 | + | 0.285199i | \(0.907940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.99779i | 0.101033i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 56.3814i | 2.84407i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0746 | −0.808800 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.1600i | − | 0.560102i | −0.959985 | − | 0.280051i | \(-0.909649\pi\) | ||
0.959985 | − | 0.280051i | \(-0.0903514\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.77325 | −0.138836 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.9036i | − | 0.993940i | −0.867768 | − | 0.496970i | \(-0.834446\pi\) | ||
0.867768 | − | 0.496970i | \(-0.165554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 23.9176i | − | 1.19142i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 37.9872i | 1.88760i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.16168 | 0.404559 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.9676 | 1.18512 | 0.592560 | − | 0.805526i | \(-0.298117\pi\) | ||||
0.592560 | + | 0.805526i | \(0.298117\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.06622 | −0.447204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.90446 | 0.487367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.8457 | −1.61233 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.2197 | −1.77369 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.48249i | − | 0.414397i | −0.978299 | − | 0.207198i | \(-0.933565\pi\) | ||
0.978299 | − | 0.207198i | \(-0.0664345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.117834i | 0.00574287i | 0.999996 | + | 0.00287143i | \(0.000914007\pi\) | ||||
−0.999996 | + | 0.00287143i | \(0.999086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.4476 | 0.848332 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −83.5137 | −4.05101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.8165i | − | 0.668628i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.0239i | 0.677078i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.88258 | −0.138849 | −0.0694246 | − | 0.997587i | \(-0.522116\pi\) | ||||
−0.0694246 | + | 0.997587i | \(0.522116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4341 | 1.03006 | 0.515030 | − | 0.857172i | \(-0.327781\pi\) | ||||
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 70.3824 | 3.37458 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.333262 | 0.0159421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5508 | 1.50584 | 0.752918 | − | 0.658114i | \(-0.228646\pi\) | ||||
0.752918 | + | 0.658114i | \(0.228646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.7102 | 0.843341 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5530i | 0.691436i | 0.938339 | + | 0.345718i | \(0.112365\pi\) | ||||
−0.938339 | + | 0.345718i | \(0.887635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.1977i | 0.815248i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 43.3230i | − | 2.04911i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.98908 | 0.329835 | 0.164917 | − | 0.986307i | \(-0.447264\pi\) | ||||
0.164917 | + | 0.986307i | \(0.447264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.97185i | − | 0.187027i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −40.9044 | −1.92186 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 34.7725i | − | 1.63016i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 37.5696i | − | 1.75743i | −0.477343 | − | 0.878717i | \(-0.658400\pi\) | ||
0.477343 | − | 0.878717i | \(-0.341600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.29040i | 0.0602305i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1987 | 0.847599 | 0.423799 | − | 0.905756i | \(-0.360696\pi\) | ||||
0.423799 | + | 0.905756i | \(0.360696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.9973i | − | 1.11525i | −0.830094 | − | 0.557624i | \(-0.811713\pi\) | ||
0.830094 | − | 0.557624i | \(-0.188287\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.1121i | 1.67466i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9992 | 1.01800 | 0.509001 | − | 0.860766i | \(-0.330015\pi\) | ||||
0.509001 | + | 0.860766i | \(0.330015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.8551i | − | 0.547419i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.6896 | 1.59841 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.31913 | −0.244574 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.9314i | 0.639216i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.81365 | − | 20.2198i | 0.449336 | − | 0.925801i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 6.19442i | − | 0.283030i | −0.989936 | − | 0.141515i | \(-0.954803\pi\) | ||
0.989936 | − | 0.141515i | \(-0.0451974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −72.5865 | −3.30966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.924219 | 0.0420534 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.6846i | 0.712200i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.5011 | −1.29151 | −0.645755 | − | 0.763545i | \(-0.723457\pi\) | ||||
−0.645755 | + | 0.763545i | \(0.723457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 31.0158i | − | 1.40258i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.3098i | − | 1.18734i | −0.804708 | − | 0.593671i | \(-0.797678\pi\) | ||
0.804708 | − | 0.593671i | \(-0.202322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.3030 | −1.77012 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 10.7387i | − | 0.482670i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.11067i | 0.408669i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.5145i | 1.90321i | 0.307321 | + | 0.951606i | \(0.400568\pi\) | ||||
−0.307321 | + | 0.951606i | \(0.599432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.7888 | 1.59892 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.8489i | − | 0.617493i | −0.951144 | − | 0.308746i | \(-0.900091\pi\) | ||
0.951144 | − | 0.308746i | \(-0.0999094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.1228 | −1.16245 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 92.6481i | − | 4.11465i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.7897i | − | 0.788515i | −0.919000 | − | 0.394257i | \(-0.871002\pi\) | ||
0.919000 | − | 0.394257i | \(-0.128998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.1323i | 0.492464i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.215258 | 0.00950388 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.5632 | −1.78743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.51809 | 0.198705 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0373 | 1.18681 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.3978 | 1.72605 | 0.863024 | − | 0.505163i | \(-0.168568\pi\) | ||||
0.863024 | + | 0.505163i | \(0.168568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.8615 | −1.34948 | −0.674739 | − | 0.738057i | \(-0.735744\pi\) | ||||
−0.674739 | + | 0.738057i | \(0.735744\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 38.6352i | 1.68618i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20.1657i | − | 0.878433i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8889 | 0.995171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.2034 | −1.18053 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.3239i | 1.53005i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 68.5377i | − | 2.96314i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.5102 | −0.539853 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.58608 | 0.197536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4291 | −0.792331 | −0.396165 | − | 0.918179i | \(-0.629659\pi\) | ||||
−0.396165 | + | 0.918179i | \(0.629659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.481588 | 0.0206669 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4240 | −0.617856 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.08161 | −0.174517 | −0.0872585 | − | 0.996186i | \(-0.527811\pi\) | ||||
−0.0872585 | + | 0.996186i | \(0.527811\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.9482i | 1.61959i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55636i | 0.279310i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.15267i | − | 0.176589i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 109.595 | 4.65205 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5063i | 0.995995i | 0.867178 | + | 0.497998i | \(0.165931\pi\) | ||||
−0.867178 | + | 0.497998i | \(0.834069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.3061 | 2.00084 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.8240i | 0.499209i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 34.0375i | − | 1.43451i | −0.696811 | − | 0.717255i | \(-0.745398\pi\) | ||
0.696811 | − | 0.717255i | \(-0.254602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.4881i | 0.735732i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.81352 | −0.412129 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.8506i | − | 0.496803i | −0.968657 | − | 0.248402i | \(-0.920095\pi\) | ||
0.968657 | − | 0.248402i | \(-0.0799053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.7548i | − | 0.491921i | −0.969280 | − | 0.245961i | \(-0.920897\pi\) | ||
0.969280 | − | 0.245961i | \(-0.0791034\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.4377 | −2.19061 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.64281i | − | 0.193618i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.13371 | 0.130458 | 0.0652291 | − | 0.997870i | \(-0.479222\pi\) | ||||
0.0652291 | + | 0.997870i | \(0.479222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.25262 | 0.135174 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.48528i | − | 0.352029i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.54126 | − | 5.23595i | 0.105248 | − | 0.216851i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 95.5057i | 3.94867i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5255 | 0.805902 | 0.402951 | − | 0.915222i | \(-0.367985\pi\) | ||||
0.402951 | + | 0.915222i | \(0.367985\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.36396 | −0.138609 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 41.5644i | − | 1.70973i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3680 | −0.877478 | −0.438739 | − | 0.898614i | \(-0.644575\pi\) | ||||
−0.438739 | + | 0.898614i | \(0.644575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 29.3179i | − | 1.20192i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 40.6759i | − | 1.66475i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.6978 | 0.968266 | 0.484133 | − | 0.874995i | \(-0.339135\pi\) | ||||
0.484133 | + | 0.874995i | \(0.339135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.7233i | 1.70193i | 0.525224 | + | 0.850964i | \(0.323981\pi\) | ||||
−0.525224 | + | 0.850964i | \(0.676019\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.5611i | 1.32599i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 45.0804i | 1.83278i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.78387 | 0.112994 | 0.0564969 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564969 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.1824i | 0.736788i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.1820 | −1.62559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 41.8172i | − | 1.68898i | −0.535571 | − | 0.844490i | \(-0.679904\pi\) | ||
0.535571 | − | 0.844490i | \(-0.320096\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 53.3339i | − | 2.15063i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.8234i | − | 1.16038i | −0.814479 | − | 0.580192i | \(-0.802977\pi\) | ||
0.814479 | − | 0.580192i | \(-0.197023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.62025 | 0.185704 | 0.0928518 | − | 0.995680i | \(-0.470402\pi\) | ||||
0.0928518 | + | 0.995680i | \(0.470402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0717374 | −0.00287872 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.44280 | −0.177997 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 99.4266 | 3.97707 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.97243 | 0.0787711 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −61.2001 | −2.44021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.2552i | − | 0.726729i | −0.931647 | − | 0.363365i | \(-0.881628\pi\) | ||
0.931647 | − | 0.363365i | \(-0.118372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 14.9194i | − | 0.592991i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.3912 | 2.03940 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40.7866 | −1.61602 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 25.0232i | − | 0.989903i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1655i | 0.638500i | 0.947670 | + | 0.319250i | \(0.103431\pi\) | ||||
−0.947670 | + | 0.319250i | \(0.896569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9130 | 0.982474 | 0.491237 | − | 0.871026i | \(-0.336545\pi\) | ||||
0.491237 | + | 0.871026i | \(0.336545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −71.4253 | −2.81237 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8797 | 1.44989 | 0.724945 | − | 0.688807i | \(-0.241865\pi\) | ||||
0.724945 | + | 0.688807i | \(0.241865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.04438 | −0.276516 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.32909 | −0.365636 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.2267 | −0.674132 | −0.337066 | − | 0.941481i | \(-0.609435\pi\) | ||||
−0.337066 | + | 0.941481i | \(0.609435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 99.4299i | 3.88505i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 30.5758i | − | 1.19288i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.64099i | − | 0.219742i | −0.993946 | − | 0.109871i | \(-0.964956\pi\) | ||
0.993946 | − | 0.109871i | \(-0.0350438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1239 | 1.09389 | 0.546947 | − | 0.837167i | \(-0.315790\pi\) | ||||
0.546947 | + | 0.837167i | \(0.315790\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 105.158i | − | 4.08398i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.89068 | −0.189653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.18499i | − | 0.0846030i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 34.4690i | − | 1.33265i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.82675i | 0.379358i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.2664 | −0.434287 | −0.217143 | − | 0.976140i | \(-0.569674\pi\) | ||||
−0.217143 | + | 0.976140i | \(0.569674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.99884i | − | 0.115426i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.72673i | − | 0.104797i | −0.998626 | − | 0.0523983i | \(-0.983313\pi\) | ||
0.998626 | − | 0.0523983i | \(-0.0166865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.05191 | −0.155498 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 21.9606i | − | 0.841530i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.20070 | 0.160735 | 0.0803676 | − | 0.996765i | \(-0.474391\pi\) | ||||
0.0803676 | + | 0.996765i | \(0.474391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9885 | −0.610888 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.09876i | − | 0.118225i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6009 | + | 46.5663i | −0.861026 | + | 1.77404i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3582i | 0.698380i | 0.937052 | + | 0.349190i | \(0.113543\pi\) | ||||
−0.937052 | + | 0.349190i | \(0.886457\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.77421 | 0.105384 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −63.8743 | −2.42289 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.7828i | 1.12810i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.8597 | 1.84804 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.0729i | − | 0.833681i | −0.908980 | − | 0.416841i | \(-0.863137\pi\) | ||
0.908980 | − | 0.416841i | \(-0.136863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2091i | 0.385045i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 60.6689 | 2.28492 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 6.74849i | − | 0.253803i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.9825i | − | 0.412456i | −0.978504 | − | 0.206228i | \(-0.933881\pi\) | ||
0.978504 | − | 0.206228i | \(-0.0661189\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.4056i | 0.427745i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.12108 | 0.0419848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.7314i | 0.924901i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.9743 | 1.53021 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.53125i | 0.318162i | 0.987266 | + | 0.159081i | \(0.0508531\pi\) | ||||
−0.987266 | + | 0.159081i | \(0.949147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.4790i | − | 0.390258i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.6160i | 1.58491i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 91.3392 | 3.39225 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.9667 | 0.517997 | 0.258999 | − | 0.965878i | \(-0.416607\pi\) | ||||
0.258999 | + | 0.965878i | \(0.416607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5469 | 1.05729 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.8854 | 1.47521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.3695 | −1.63883 | −0.819413 | − | 0.573204i | \(-0.805700\pi\) | ||||
−0.819413 | + | 0.573204i | \(0.805700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 61.5819 | 2.27148 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.43176i | 0.310588i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.29746i | 0.268441i | 0.990951 | + | 0.134221i | \(0.0428531\pi\) | ||||
−0.990951 | + | 0.134221i | \(0.957147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.5419 | −0.644418 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.4881 | 1.55874 | 0.779369 | − | 0.626565i | \(-0.215540\pi\) | ||||
0.779369 | + | 0.626565i | \(0.215540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 76.4011i | − | 2.79912i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.3055i | 0.852705i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7058 | 0.646957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3091 | −1.25196 | −0.625979 | − | 0.779840i | \(-0.715300\pi\) | ||||
−0.625979 | + | 0.779840i | \(0.715300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 52.2408 | 1.90376 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.1358 | −2.62529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5103 | −0.818150 | −0.409075 | − | 0.912501i | \(-0.634149\pi\) | ||||
−0.409075 | + | 0.912501i | \(0.634149\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.657335 | −0.0238598 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.3050i | − | 0.699806i | −0.936786 | − | 0.349903i | \(-0.886215\pi\) | ||
0.936786 | − | 0.349903i | \(-0.113785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.72625i | − | 0.134899i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 80.5241i | 2.91135i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 62.6497 | 2.26215 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.48851i | − | 0.233982i | −0.993133 | − | 0.116991i | \(-0.962675\pi\) | ||
0.993133 | − | 0.116991i | \(-0.0373248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9543 | 0.394509 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.2672i | 1.34041i | 0.742176 | + | 0.670205i | \(0.233794\pi\) | ||||
−0.742176 | + | 0.670205i | \(0.766206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.8646i | 1.68343i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.3125i | 1.01570i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.96823 | 0.178005 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.47981i | − | 0.231866i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.41131i | − | 0.0504361i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 61.1759 | 2.18346 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.8874i | 1.42183i | 0.703276 | + | 0.710917i | \(0.251720\pi\) | ||||
−0.703276 | + | 0.710917i | \(0.748280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 65.3956 | 2.32815 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.51784 | −0.160636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 87.3950i | − | 3.10349i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.1241 | − | 70.3084i | 1.21026 | − | 2.49358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.4702i | 1.11473i | 0.830267 | + | 0.557365i | \(0.188188\pi\) | ||||
−0.830267 | + | 0.557365i | \(0.811812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.8788 | −1.19855 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2025 | 0.431155 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 7.91766i | − | 0.279408i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.62988 | 0.0574458 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.20395i | − | 0.288793i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.1518i | 1.69293i | 0.532446 | + | 0.846464i | \(0.321273\pi\) | ||||
−0.532446 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.7113 | −1.14865 | −0.574324 | − | 0.818628i | \(-0.694735\pi\) | ||||
−0.574324 | + | 0.818628i | \(0.694735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 58.4875i | − | 2.05125i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 54.6971i | − | 1.91596i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.65351i | − | 0.232777i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.6727 | −0.862133 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1657i | 0.389684i | 0.980835 | + | 0.194842i | \(0.0624195\pi\) | ||||
−0.980835 | + | 0.194842i | \(0.937581\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0893 | 0.386547 | 0.193274 | − | 0.981145i | \(-0.438089\pi\) | ||||
0.193274 | + | 0.981145i | \(0.438089\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 27.4786i | − | 0.956683i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.7674i | − | 0.722155i | −0.932536 | − | 0.361077i | \(-0.882409\pi\) | ||
0.932536 | − | 0.361077i | \(-0.117591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.2672i | − | 0.912299i | −0.889903 | − | 0.456150i | \(-0.849228\pi\) | ||
0.889903 | − | 0.456150i | \(-0.150772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.8583 | −0.446051 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.3886 | −1.19149 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.1143 | 2.18416 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.724119 | 0.0250292 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.86134 | 0.0642606 | 0.0321303 | − | 0.999484i | \(-0.489771\pi\) | ||||
0.0321303 | + | 0.999484i | \(0.489771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.9858 | 0.482269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 23.7831i | − | 0.819133i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 163.387i | − | 5.62068i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.6460 | −0.400160 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −66.6911 | −2.28883 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.40232i | − | 0.116630i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.6400i | 1.93932i | 0.244466 | + | 0.969658i | \(0.421387\pi\) | ||||
−0.244466 | + | 0.969658i | \(0.578613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.4327 | 0.459388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.63673 | 0.158388 | 0.0791939 | − | 0.996859i | \(-0.474765\pi\) | ||||
0.0791939 | + | 0.996859i | \(0.474765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8934 | −0.746993 | −0.373497 | − | 0.927632i | \(-0.621841\pi\) | ||||
−0.373497 | + | 0.927632i | \(0.621841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.7781 | 0.469558 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.9550 | 1.56433 | 0.782164 | − | 0.623073i | \(-0.214116\pi\) | ||||
0.782164 | + | 0.623073i | \(0.214116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.6809 | 1.62120 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 46.7189i | − | 1.58666i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.95351i | 0.100191i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 74.9885i | − | 2.54089i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.1289 | 0.376657 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.6806i | 1.47667i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.07009 | 0.272508 | 0.136254 | − | 0.990674i | \(-0.456494\pi\) | ||||
0.136254 | + | 0.990674i | \(0.456494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.7887i | 1.17339i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3542i | 0.348842i | 0.984671 | + | 0.174421i | \(0.0558054\pi\) | ||||
−0.984671 | + | 0.174421i | \(0.944195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8133i | 0.666769i | 0.942791 | + | 0.333385i | \(0.108191\pi\) | ||||
−0.942791 | + | 0.333385i | \(0.891809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −94.5920 | −3.17967 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 56.7227i | − | 1.90456i | −0.305222 | − | 0.952281i | \(-0.598731\pi\) | ||
0.305222 | − | 0.952281i | \(-0.401269\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.2763i | 0.445272i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.97970 | 0.233829 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.65151i | 0.189121i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.0619 | −0.737449 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.84606 | 0.195194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.0553i | 0.735586i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.0556 | + | 39.2617i | −0.634834 | + | 1.30800i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 18.4518i | − | 0.614038i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.849290 | 0.0282314 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.25269 | −0.108004 | −0.0540020 | − | 0.998541i | \(-0.517198\pi\) | ||||
−0.0540020 | + | 0.998541i | \(0.517198\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.5353i | 0.614777i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.6023 | −1.57713 | −0.788567 | − | 0.614949i | \(-0.789177\pi\) | ||||
−0.788567 | + | 0.614949i | \(0.789177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.03501i | 0.199730i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 131.954i | 4.36225i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.6864 | −0.848241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.1078i | − | 1.15810i | −0.815293 | − | 0.579049i | \(-0.803424\pi\) | ||
0.815293 | − | 0.579049i | \(-0.196576\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 58.1467i | − | 1.91600i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.6287i | 1.89687i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 142.227 | 4.67641 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.7814i | 0.945306i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.66566 | 0.0874575 | 0.0437288 | − | 0.999043i | \(-0.486076\pi\) | ||||
0.0437288 | + | 0.999043i | \(0.486076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.73655i | 0.188008i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 0.211195i | − | 0.00691422i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.8519i | 0.681929i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.5138 | −0.474145 | −0.237073 | − | 0.971492i | \(-0.576188\pi\) | ||||
−0.237073 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −69.2807 | −2.26089 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.71991 | 0.186464 | 0.0932319 | − | 0.995644i | \(-0.470280\pi\) | ||||
0.0932319 | + | 0.995644i | \(0.470280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.65573 | −0.0539178 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.05276 | 0.0342463 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.6649 | −0.639024 | −0.319512 | − | 0.947582i | \(-0.603519\pi\) | ||||
−0.319512 | + | 0.947582i | \(0.603519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 70.4163i | 2.28581i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.8486i | 0.708489i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.5107 | 1.57141 | 0.785707 | − | 0.618598i | \(-0.212299\pi\) | ||||
0.785707 | + | 0.618598i | \(0.212299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −92.4749 | −2.99242 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 12.9319i | − | 0.418030i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 4.13042i | − | 0.133378i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.6838 | 0.634961 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −48.6306 | −1.56710 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.73606 | 0.184650 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.8192 | 1.05540 | 0.527698 | − | 0.849432i | \(-0.323055\pi\) | ||||
0.527698 | + | 0.849432i | \(0.323055\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.7902 | −0.475129 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.21415 | −0.167330 | −0.0836651 | − | 0.996494i | \(-0.526663\pi\) | ||||
−0.0836651 | + | 0.996494i | \(0.526663\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16.5011i | − | 0.529001i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 244.383i | 7.82653i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.2134i | 1.03060i | 0.857010 | + | 0.515300i | \(0.172319\pi\) | ||||
−0.857010 | + | 0.515300i | \(0.827681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.15987 | 0.100990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.2345i | 0.326762i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.0382 | −0.352063 | −0.176032 | − | 0.984385i | \(-0.556326\pi\) | ||||
−0.176032 | + | 0.984385i | \(0.556326\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 73.2997i | − | 2.33552i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.6730i | 0.498879i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.21736i | 0.0705080i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.3737 | −1.85430 | −0.927151 | − | 0.374687i | \(-0.877750\pi\) | ||||
−0.927151 | + | 0.374687i | \(0.877750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.4721i | 0.617930i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 71.7329i | − | 2.27409i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.4790 | 0.680247 | 0.340123 | − | 0.940381i | \(-0.389531\pi\) | ||||
0.340123 | + | 0.940381i | \(0.389531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 2.19760i | − | 0.0695290i |
(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 | 4028.2.c.a.3497.12 | ✓ | 82 | |
53.52 | even | 2 | inner | 4028.2.c.a.3497.71 | yes | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.c.a.3497.12 | ✓ | 82 | 1.1 | even | 1 | trivial | |
4028.2.c.a.3497.71 | yes | 82 | 53.52 | even | 2 | inner |