Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(441,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, 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("572.441");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.f (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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 21x^{6} + 136x^{4} + 309x^{2} + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 441.7 | ||
Root | \(-2.51091i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.441 |
Dual form | 572.2.f.c.441.8 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.51091 | 1.44968 | 0.724838 | − | 0.688919i | \(-0.241914\pi\) | ||||
0.724838 | + | 0.688919i | \(0.241914\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.81560i | − | 1.70639i | −0.521593 | − | 0.853195i | \(-0.674662\pi\) | ||
0.521593 | − | 0.853195i | \(-0.325338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.51091i | − | 0.571072i | −0.958368 | − | 0.285536i | \(-0.907828\pi\) | ||
0.958368 | − | 0.285536i | \(-0.0921716\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.30469 | 1.10156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24595 | + | 1.56965i | −0.900265 | + | 0.435343i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.58065i | − | 2.47371i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.13930 | 1.24646 | 0.623232 | − | 0.782037i | \(-0.285819\pi\) | ||||
0.623232 | + | 0.782037i | \(0.285819\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83462i | 0.420890i | 0.977606 | + | 0.210445i | \(0.0674913\pi\) | ||||
−0.977606 | + | 0.210445i | \(0.932509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.79377i | − | 0.827869i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.32652 | −1.11066 | −0.555328 | − | 0.831632i | \(-0.687407\pi\) | ||||
−0.555328 | + | 0.831632i | \(0.687407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.55882 | −1.91176 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.765046 | 0.147233 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.51373 | 1.76665 | 0.883327 | − | 0.468756i | \(-0.155298\pi\) | ||||
0.883327 | + | 0.468756i | \(0.155298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.81560i | − | 1.76293i | −0.472245 | − | 0.881467i | \(-0.656556\pi\) | ||
0.472245 | − | 0.881467i | \(-0.343444\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.51091i | 0.437094i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.76505 | −0.974471 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.20623i | 0.527100i | 0.964646 | + | 0.263550i | \(0.0848934\pi\) | ||||
−0.964646 | + | 0.263550i | \(0.915107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.15030 | + | 3.94126i | −1.30509 | + | 0.631107i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.74603i | 1.05355i | 0.850004 | + | 0.526777i | \(0.176600\pi\) | ||||
−0.850004 | + | 0.526777i | \(0.823400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.51373 | 1.14583 | 0.572916 | − | 0.819614i | \(-0.305812\pi\) | ||||
0.572916 | + | 0.819614i | \(0.305812\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 12.6094i | − | 1.87969i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.02183i | 1.31597i | 0.753032 | + | 0.657984i | \(0.228591\pi\) | ||||
−0.753032 | + | 0.657984i | \(0.771409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.71714 | 0.673877 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9044 | 1.80697 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06973 | −0.146939 | −0.0734697 | − | 0.997297i | \(-0.523407\pi\) | ||||
−0.0734697 | + | 0.997297i | \(0.523407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.81560 | 0.514496 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.60656i | 0.610154i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.19003i | 1.06625i | 0.846036 | + | 0.533125i | \(0.178983\pi\) | ||||
−0.846036 | + | 0.533125i | \(0.821017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.51373 | 0.705961 | 0.352980 | − | 0.935631i | \(-0.385168\pi\) | ||||
0.352980 | + | 0.935631i | \(0.385168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 4.99310i | − | 0.629071i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.98917 | + | 12.3853i | 0.742865 | + | 1.53620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.46301i | − | 0.545243i | −0.962121 | − | 0.272622i | \(-0.912109\pi\) | ||
0.962121 | − | 0.272622i | \(-0.0878907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.3744 | −1.61009 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.58065i | 0.424945i | 0.977167 | + | 0.212472i | \(0.0681516\pi\) | ||||
−0.977167 | + | 0.212472i | \(0.931848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.71714i | 1.13731i | 0.822578 | + | 0.568653i | \(0.192535\pi\) | ||||
−0.822578 | + | 0.568653i | \(0.807465\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −24.0014 | −2.77144 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.51091 | 0.172185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.25695 | −0.478944 | −0.239472 | − | 0.970903i | \(-0.576974\pi\) | ||||
−0.239472 | + | 0.970903i | \(0.576974\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.99310 | −0.888122 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.98099i | 0.546734i | 0.961910 | + | 0.273367i | \(0.0881374\pi\) | ||||
−0.961910 | + | 0.273367i | \(0.911863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 19.6095i | − | 2.12695i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.8882 | 2.56108 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 17.8593i | − | 1.89308i | −0.322590 | − | 0.946539i | \(-0.604554\pi\) | ||
0.322590 | − | 0.946539i | \(-0.395446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.37161 | + | 4.90435i | 0.248612 | + | 0.514116i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 24.6461i | − | 2.55568i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.00017 | 0.718202 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.18440i | − | 0.424861i | −0.977176 | − | 0.212431i | \(-0.931862\pi\) | ||
0.977176 | − | 0.212431i | \(-0.0681379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.30469i | 0.332134i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.60673 | 0.552447 | 0.276224 | − | 0.961093i | \(-0.410917\pi\) | ||||
0.276224 | + | 0.961093i | \(0.410917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.4755 | −1.41267 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.88252 | −0.568685 | −0.284342 | − | 0.958723i | \(-0.591775\pi\) | ||||
−0.284342 | + | 0.958723i | \(0.591775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.18721i | − | 0.305280i | −0.988282 | − | 0.152640i | \(-0.951223\pi\) | ||
0.988282 | − | 0.152640i | \(-0.0487774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.05056i | 0.764125i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.90154 | 0.743314 | 0.371657 | − | 0.928370i | \(-0.378790\pi\) | ||||
0.371657 | + | 0.928370i | \(0.378790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.3239i | 1.89521i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7269 | + | 5.18721i | −0.991698 | + | 0.479558i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.76505i | − | 0.711821i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.9387i | 1.52731i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17.3946i | 1.55582i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9838 | −1.15213 | −0.576063 | − | 0.817405i | \(-0.695412\pi\) | ||||
−0.576063 | + | 0.817405i | \(0.695412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.8663 | 1.66109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4125 | −0.909740 | −0.454870 | − | 0.890558i | \(-0.650314\pi\) | ||||
−0.454870 | + | 0.890558i | \(0.650314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.77195 | 0.240358 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.91911i | − | 0.251237i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6983i | 1.42663i | 0.700843 | + | 0.713316i | \(0.252807\pi\) | ||||
−0.700843 | + | 0.713316i | \(0.747193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7650 | −1.16754 | −0.583768 | − | 0.811921i | \(-0.698422\pi\) | ||||
−0.583768 | + | 0.811921i | \(0.698422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.6530i | 1.90773i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.56965 | − | 3.24595i | −0.131261 | − | 0.271440i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 36.3006i | − | 3.01460i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8443 | 0.976904 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.1639i | − | 0.832663i | −0.909213 | − | 0.416331i | \(-0.863316\pi\) | ||
0.909213 | − | 0.416331i | \(-0.136684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6532i | 1.76211i | 0.473012 | + | 0.881056i | \(0.343167\pi\) | ||||
−0.473012 | + | 0.881056i | \(0.656833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.9838 | 1.37306 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.4524 | −3.00825 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0916 | −0.885203 | −0.442602 | − | 0.896718i | \(-0.645944\pi\) | ||||
−0.442602 | + | 0.896718i | \(0.645944\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.68601 | −0.213015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.04791i | 0.634264i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.27861i | − | 0.648431i | −0.945983 | − | 0.324215i | \(-0.894900\pi\) | ||
0.945983 | − | 0.324215i | \(-0.105100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.58065 | 0.745852 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.4660i | 1.73847i | 0.494399 | + | 0.869235i | \(0.335388\pi\) | ||||
−0.494399 | + | 0.869235i | \(0.664612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.07238 | − | 10.1900i | 0.620953 | − | 0.783848i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.06283i | 0.463637i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.18296 | −0.546110 | −0.273055 | − | 0.961998i | \(-0.588034\pi\) | ||||
−0.273055 | + | 0.961998i | \(0.588034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.4426i | 1.09175i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.5644i | 1.54572i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9114 | 0.890301 | 0.445151 | − | 0.895456i | \(-0.353150\pi\) | ||||
0.445151 | + | 0.895456i | \(0.353150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.02448 | 0.670784 | 0.335392 | − | 0.942079i | \(-0.391131\pi\) | ||||
0.335392 | + | 0.942079i | \(0.391131\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8445 | 1.02341 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.2337 | 0.899438 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.13930i | 0.375823i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.15592i | − | 0.0840808i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7677 | −0.851481 | −0.425740 | − | 0.904845i | \(-0.639986\pi\) | ||||
−0.425740 | + | 0.904845i | \(0.639986\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.5384i | − | 1.33442i | −0.744869 | − | 0.667211i | \(-0.767488\pi\) | ||
0.744869 | − | 0.667211i | \(-0.232512\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.0383 | + | 31.0983i | 1.07691 | + | 2.22700i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.46036i | − | 0.317787i | −0.987296 | − | 0.158894i | \(-0.949207\pi\) | ||
0.987296 | − | 0.158894i | \(-0.0507927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.23070 | 0.441683 | 0.220841 | − | 0.975310i | \(-0.429120\pi\) | ||||
0.220841 | + | 0.975310i | \(0.429120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.2062i | − | 0.790426i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 14.3744i | − | 1.00889i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.7402 | 1.79777 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.6025 | −1.22346 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.83462 | −0.126903 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9098 | −1.09528 | −0.547638 | − | 0.836715i | \(-0.684473\pi\) | ||||
−0.547638 | + | 0.836715i | \(0.684473\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.99070i | 0.616033i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 28.6694i | − | 1.95524i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.8305 | −1.00676 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.3989i | 1.64872i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.6819 | + | 8.06692i | −1.12215 | + | 0.542640i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3292i | − | 0.691692i | −0.938291 | − | 0.345846i | \(-0.887592\pi\) | ||
0.938291 | − | 0.345846i | \(-0.112408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.5889 | −2.10593 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.53418i | − | 0.433689i | −0.976206 | − | 0.216844i | \(-0.930424\pi\) | ||
0.976206 | − | 0.216844i | \(-0.0695764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.1957i | − | 1.46673i | −0.679835 | − | 0.733365i | \(-0.737949\pi\) | ||
0.679835 | − | 0.733365i | \(-0.262051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.79377 | 0.249612 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.30044 | −0.347243 | −0.173622 | − | 0.984812i | \(-0.555547\pi\) | ||||
−0.173622 | + | 0.984812i | \(0.555547\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.4237 | 2.24556 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.6888 | −0.694314 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.59950i | 0.297517i | 0.988874 | + | 0.148758i | \(0.0475277\pi\) | ||||
−0.988874 | + | 0.148758i | \(0.952472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.27580i | 0.275428i | 0.990472 | + | 0.137714i | \(0.0439755\pi\) | ||||
−0.990472 | + | 0.137714i | \(0.956024\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3651 | −1.43472 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 17.9987i | − | 1.14990i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.87971 | − | 5.95507i | −0.183232 | − | 0.378912i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.5068i | 0.792588i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6791 | −1.17902 | −0.589508 | − | 0.807763i | \(-0.700678\pi\) | ||||
−0.589508 | + | 0.807763i | \(0.700678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.32652i | − | 0.334875i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 49.2379i | − | 3.08340i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1259 | 0.881151 | 0.440575 | − | 0.897716i | \(-0.354774\pi\) | ||||
0.440575 | + | 0.897716i | \(0.354774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.84433 | 0.301012 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.4399 | 1.94608 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.8087 | 1.22146 | 0.610728 | − | 0.791840i | \(-0.290877\pi\) | ||||
0.610728 | + | 0.791840i | \(0.290877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.08168i | 0.250736i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 44.8431i | − | 2.74435i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8910 | −1.57860 | −0.789300 | − | 0.614008i | \(-0.789556\pi\) | ||||
−0.789300 | + | 0.614008i | \(0.789556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.46566i | 0.514252i | 0.966378 | + | 0.257126i | \(0.0827755\pi\) | ||||
−0.966378 | + | 0.257126i | \(0.917224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.95491 | + | 12.3144i | 0.360407 | + | 0.745302i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 9.55882i | − | 0.576419i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.1613 | 1.63196 | 0.815982 | − | 0.578077i | \(-0.196197\pi\) | ||||
0.815982 | + | 0.578077i | \(0.196197\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 32.4375i | − | 1.94198i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.0373i | 1.73222i | 0.499852 | + | 0.866111i | \(0.333388\pi\) | ||||
−0.499852 | + | 0.866111i | \(0.666612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.92618 | 0.114499 | 0.0572497 | − | 0.998360i | \(-0.481767\pi\) | ||||
0.0572497 | + | 0.998360i | \(0.481767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.5768 | 1.04116 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1927 | 0.601655 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.41245 | 0.553674 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.5067i | − | 0.615911i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 29.9318i | − | 1.74863i | −0.485355 | − | 0.874317i | \(-0.661309\pi\) | ||
0.485355 | − | 0.874317i | \(-0.338691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.2499 | 1.81944 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.765046i | 0.0443925i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.2896 | − | 8.36078i | 0.999884 | − | 0.483516i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 11.3526i | − | 0.654353i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.0655 | −0.865489 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 21.0382i | − | 1.20464i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.748847i | − | 0.0427389i | −0.999772 | − | 0.0213695i | \(-0.993197\pi\) | ||
0.999772 | − | 0.0213695i | \(-0.00680263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0780 | 0.800870 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5453 | −0.881491 | −0.440746 | − | 0.897632i | \(-0.645286\pi\) | ||||
−0.440746 | + | 0.897632i | \(0.645286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.3159 | −1.82661 | −0.913303 | − | 0.407282i | \(-0.866477\pi\) | ||||
−0.913303 | + | 0.407282i | \(0.866477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.0517 | −1.07344 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.6243i | 1.77620i | 0.459652 | + | 0.888099i | \(0.347974\pi\) | ||||
−0.459652 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.51373i | 0.532666i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.7705 | −0.824409 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.42865i | 0.524624i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.0275 | − | 15.0040i | 1.72109 | − | 0.832274i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.00281i | − | 0.442557i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6312 | 0.751513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 25.4905i | − | 1.40108i | −0.713612 | − | 0.700541i | \(-0.752942\pi\) | ||
0.713612 | − | 0.700541i | \(-0.247058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.5956i | 0.580634i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.0291 | −0.930397 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8445 | −0.863105 | −0.431552 | − | 0.902088i | \(-0.642034\pi\) | ||||
−0.431552 | + | 0.902088i | \(0.642034\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.8401 | 1.07757 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.81560 | 0.531545 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.7036i | − | 0.955904i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 51.0315i | 2.74744i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.48627 | 0.133470 | 0.0667350 | − | 0.997771i | \(-0.478742\pi\) | ||||
0.0667350 | + | 0.997771i | \(0.478742\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.8908i | − | 1.33237i | −0.745785 | − | 0.666187i | \(-0.767925\pi\) | ||
0.745785 | − | 0.666187i | \(-0.232075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.48330 | + | 1.20086i | −0.132549 | + | 0.0640970i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.99310i | − | 0.318981i | −0.987200 | − | 0.159490i | \(-0.949015\pi\) | ||
0.987200 | − | 0.159490i | \(-0.0509851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6623 | 0.725121 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 19.4974i | − | 1.03191i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.9345i | − | 1.31599i | −0.753022 | − | 0.657995i | \(-0.771405\pi\) | ||
0.753022 | − | 0.657995i | \(-0.228595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.6342 | 0.822852 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.51091 | −0.131789 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.0767 | 1.94069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3718 | 0.541402 | 0.270701 | − | 0.962663i | \(-0.412744\pi\) | ||||
0.270701 | + | 0.962663i | \(0.412744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.2935i | 1.16056i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.61628i | 0.0839129i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.93164 | 0.462463 | 0.231231 | − | 0.972899i | \(-0.425725\pi\) | ||||
0.231231 | + | 0.972899i | \(0.425725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 43.6765i | 2.25544i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.8811 | + | 14.9332i | −1.59046 | + | 0.769101i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.3675i | − | 1.35441i | −0.735795 | − | 0.677204i | \(-0.763191\pi\) | ||
0.735795 | − | 0.677204i | \(-0.236809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.6012 | −1.67021 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8212i | 1.11501i | 0.830173 | + | 0.557506i | \(0.188242\pi\) | ||||
−0.830173 | + | 0.557506i | \(0.811758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 5.76505i | − | 0.293814i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.8305 | 1.26221 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.53274 | 0.381925 | 0.190963 | − | 0.981597i | \(-0.438839\pi\) | ||||
0.190963 | + | 0.981597i | \(0.438839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.3746 | −1.38439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.1448 | −1.31883 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.2428i | 0.817265i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.748847i | 0.0375835i | 0.999823 | + | 0.0187918i | \(0.00598196\pi\) | ||||
−0.999823 | + | 0.0187918i | \(0.994018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.96012 | 0.348442 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.47024i | 0.323108i | 0.986864 | + | 0.161554i | \(0.0516506\pi\) | ||||
−0.986864 | + | 0.161554i | \(0.948349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4071 | + | 31.8610i | 0.767481 | + | 1.58711i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.4985i | 1.51548i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.20623 | −0.158927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.98380i | 0.147539i | 0.997275 | + | 0.0737697i | \(0.0235030\pi\) | ||||
−0.997275 | + | 0.0737697i | \(0.976497\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.9280i | 2.06815i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.3744 | 0.608906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.0055 | 0.932941 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.5628 | −1.69255 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6339 | 0.519498 | 0.259749 | − | 0.965676i | \(-0.416360\pi\) | ||||
0.259749 | + | 0.965676i | \(0.416360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.78125i | 0.233024i | 0.993189 | + | 0.116512i | \(0.0371713\pi\) | ||||
−0.993189 | + | 0.116512i | \(0.962829\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.8143i | 1.44962i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −49.1257 | −2.38295 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.33077i | − | 0.403154i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.94126 | − | 8.15030i | −0.190286 | − | 0.393500i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3251i | 1.36437i | 0.731179 | + | 0.682186i | \(0.238970\pi\) | ||||
−0.731179 | + | 0.682186i | \(0.761030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.74620 | 0.228088 | 0.114044 | − | 0.993476i | \(-0.463620\pi\) | ||||
0.114044 | + | 0.993476i | \(0.463620\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 91.1477i | − | 4.37020i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.77211i | − | 0.467464i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.3386 | −0.875255 | −0.437628 | − | 0.899156i | \(-0.644181\pi\) | ||||
−0.437628 | + | 0.899156i | \(0.644181\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.5887 | 0.742318 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.98805 | 0.0944552 | 0.0472276 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472276 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −68.1438 | −3.23033 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 25.5208i | − | 1.20709i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.23368i | − | 0.105414i | −0.998610 | − | 0.0527070i | \(-0.983215\pi\) | ||
0.998610 | − | 0.0527070i | \(-0.0167849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.74603 | −0.317658 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 54.3693i | 2.55449i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18.7131 | − | 9.04912i | 0.877281 | − | 0.424229i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.37017i | 0.110872i | 0.998462 | + | 0.0554360i | \(0.0176549\pi\) | ||||
−0.998462 | + | 0.0554360i | \(0.982345\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.93181 | 0.183521 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.1816i | − | 0.613928i | −0.951721 | − | 0.306964i | \(-0.900687\pi\) | ||
0.951721 | − | 0.306964i | \(-0.0993130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.3675i | − | 1.13245i | −0.824249 | − | 0.566227i | \(-0.808402\pi\) | ||
0.824249 | − | 0.566227i | \(-0.191598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −94.0398 | −4.36099 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.3239 | 0.847927 | 0.423964 | − | 0.905679i | \(-0.360638\pi\) | ||||
0.423964 | + | 0.905679i | \(0.360638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.74322 | −0.311373 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.8500 | −1.28326 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.51373i | 0.345482i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 17.5368i | − | 0.804642i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.53514 | −0.161863 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8249i | 0.768749i | 0.923177 | + | 0.384375i | \(0.125583\pi\) | ||||
−0.923177 | + | 0.384375i | \(0.874417\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.03266 | − | 10.4072i | −0.229469 | − | 0.474530i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.2076i | 0.919478i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.9660 | −0.724979 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8811i | 0.674326i | 0.941446 | + | 0.337163i | \(0.109467\pi\) | ||||
−0.941446 | + | 0.337163i | \(0.890533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 20.7869i | − | 0.940015i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.3582 | 1.77621 | 0.888106 | − | 0.459639i | \(-0.152021\pi\) | ||||
0.888106 | + | 0.459639i | \(0.152021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.8939 | 2.20207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.6094 | 0.566749 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.41005 | 0.242674 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3223i | 0.641153i | 0.947223 | + | 0.320576i | \(0.103877\pi\) | ||||
−0.947223 | + | 0.320576i | \(0.896123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.4102i | 2.52022i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0578 | 1.07268 | 0.536342 | − | 0.844001i | \(-0.319806\pi\) | ||||
0.536342 | + | 0.844001i | \(0.319806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.8936i | 1.01875i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2691 | − | 25.5863i | 0.900181 | − | 1.13633i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.755747i | 0.0334979i | 0.999860 | + | 0.0167490i | \(0.00533161\pi\) | ||||
−0.999860 | + | 0.0167490i | \(0.994668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6818 | 0.649483 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.40357i | 0.0619690i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 21.3930i | − | 0.942690i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.02183 | −0.396780 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0358 | −0.791683 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2307 | 0.579648 | 0.289824 | − | 0.957080i | \(-0.406403\pi\) | ||||
0.289824 | + | 0.957080i | \(0.406403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.0167 | −1.79354 | −0.896768 | − | 0.442501i | \(-0.854091\pi\) | ||||
−0.896768 | + | 0.442501i | \(0.854091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 36.2640i | 1.58269i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 50.4454i | − | 2.19743i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.37177 | 0.233555 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0655i | 1.17454i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.5889 | − | 21.8973i | −0.458657 | − | 0.948477i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.4454i | 0.970398i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.9085 | 1.29065 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.71714i | 0.203182i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.4783i | − | 0.450499i | −0.974301 | − | 0.225250i | \(-0.927680\pi\) | ||
0.974301 | − | 0.225250i | \(-0.0723198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.6597 | 0.972420 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.1611 | −0.520926 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6150 | −0.453865 | −0.226932 | − | 0.973911i | \(-0.572870\pi\) | ||||
−0.226932 | + | 0.973911i | \(0.572870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.2212 | 0.777660 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4540i | 0.743567i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.43188i | 0.273511i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.7177 | 1.30389 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6122i | 0.619138i | 0.950877 | + | 0.309569i | \(0.100185\pi\) | ||||
−0.950877 | + | 0.309569i | \(0.899815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.3892 | + | 11.7939i | −1.03155 | + | 0.498831i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9044i | 0.544822i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.5577 | −1.75145 | −0.875724 | − | 0.482811i | \(-0.839616\pi\) | ||||
−0.875724 | + | 0.482811i | \(0.839616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 30.1491i | − | 1.26838i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.0769i | 0.507181i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6530 | 1.36889 | 0.684443 | − | 0.729066i | \(-0.260045\pi\) | ||||
0.684443 | + | 0.729066i | \(0.260045\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.69106 | −0.112617 | −0.0563087 | − | 0.998413i | \(-0.517933\pi\) | ||||
−0.0563087 | + | 0.998413i | \(0.517933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.5477 | −1.23437 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 50.9152 | 2.12331 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7036i | 1.19495i | 0.801889 | + | 0.597473i | \(0.203828\pi\) | ||||
−0.801889 | + | 0.597473i | \(0.796172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 46.5482i | − | 1.93448i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.52584 | 0.312225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.06973i | − | 0.0443039i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7923 | + | 40.9294i | 0.818312 | + | 1.69222i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.28711i | 0.176948i | 0.996078 | + | 0.0884740i | \(0.0281990\pi\) | ||||
−0.996078 | + | 0.0884740i | \(0.971801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0079 | 0.742001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 11.1996i | − | 0.460689i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.02448i | − | 0.0831353i | −0.999136 | − | 0.0415676i | \(-0.986765\pi\) | ||
0.999136 | − | 0.0415676i | \(-0.0132352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.6283 | −1.21464 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.6448 | 0.640297 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.0916 | −0.412330 | −0.206165 | − | 0.978517i | \(-0.566098\pi\) | ||||
−0.206165 | + | 0.978517i | \(0.566098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.94014 | 0.201513 | 0.100756 | − | 0.994911i | \(-0.467874\pi\) | ||||
0.100756 | + | 0.994911i | \(0.467874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 14.7488i | − | 0.600619i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.81560i | 0.155126i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9697 | −0.932310 | −0.466155 | − | 0.884703i | \(-0.654361\pi\) | ||||
−0.466155 | + | 0.884703i | \(0.654361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 36.0929i | − | 1.46256i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.1611 | − | 29.2844i | −0.572898 | − | 1.18472i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.8459i | 1.20546i | 0.797944 | + | 0.602732i | \(0.205921\pi\) | ||||
−0.797944 | + | 0.602732i | \(0.794079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 64.6314 | 2.60619 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.5083i | 0.503564i | 0.967784 | + | 0.251782i | \(0.0810166\pi\) | ||||
−0.967784 | + | 0.251782i | \(0.918983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 15.1597i | − | 0.609320i | −0.952461 | − | 0.304660i | \(-0.901457\pi\) | ||
0.952461 | − | 0.304660i | \(-0.0985428\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.07503 | −0.163525 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.9838 | −1.08108 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5770 | 0.743078 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.60656 | −0.183968 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.4778i | 0.657012i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.94382i | − | 0.236620i | −0.992977 | − | 0.118310i | \(-0.962252\pi\) | ||
0.992977 | − | 0.118310i | \(-0.0377476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.9482 | −1.58780 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.5410i | 1.96598i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.3116 | + | 7.40427i | −0.606668 | + | 0.293368i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8329i | 0.468103i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.0592 | 1.62174 | 0.810870 | − | 0.585227i | \(-0.198994\pi\) | ||||
0.810870 | + | 0.585227i | \(0.198994\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.46863i | 0.0973534i | 0.998815 | + | 0.0486767i | \(0.0155004\pi\) | ||||
−0.998815 | + | 0.0486767i | \(0.984500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 71.9864i | − | 2.83446i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.97552 | −0.116980 | −0.0584900 | − | 0.998288i | \(-0.518629\pi\) | ||||
−0.0584900 | + | 0.998288i | \(0.518629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.19003 | −0.321487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.2382 | −1.45948 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.2915 | 1.18540 | 0.592698 | − | 0.805425i | \(-0.298063\pi\) | ||||
0.592698 | + | 0.805425i | \(0.298063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.7298i | 1.55237i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.1121i | 1.25281i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.07095 | 0.314399 | 0.157200 | − | 0.987567i | \(-0.449753\pi\) | ||||
0.157200 | + | 0.987567i | \(0.449753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 34.8952i | − | 1.35727i | −0.734477 | − | 0.678633i | \(-0.762573\pi\) | ||
0.734477 | − | 0.678633i | \(-0.237427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −41.8869 | + | 20.2553i | −1.62675 | + | 0.786652i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 10.5766i | − | 0.410145i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.6750 | −1.96214 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 25.9356i | − | 1.00273i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.51373i | 0.212855i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9424 | 0.421798 | 0.210899 | − | 0.977508i | \(-0.432361\pi\) | ||||
0.210899 | + | 0.977508i | \(0.432361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.31294 | −0.281475 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.79250 | 0.337923 | 0.168962 | − | 0.985623i | \(-0.445959\pi\) | ||||
0.168962 | + | 0.985623i | \(0.445959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.32226 | −0.242626 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 16.4068i | − | 0.628708i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.4917i | − | 0.975414i | −0.873007 | − | 0.487707i | \(-0.837833\pi\) | ||
0.873007 | − | 0.487707i | \(-0.162167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.7140 | 2.43439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 55.7314i | − | 2.12628i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.47231 | − | 1.67911i | 0.132284 | − | 0.0639691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.3675i | − | 0.850901i | −0.904982 | − | 0.425450i | \(-0.860116\pi\) | ||
0.904982 | − | 0.425450i | \(-0.139884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.99310 | 0.189672 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 52.5219i | 1.99227i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.6699i | 1.31322i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.3089 | −0.503390 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.8362 | −1.76898 | −0.884489 | − | 0.466562i | \(-0.845493\pi\) | ||||
−0.884489 | + | 0.466562i | \(0.845493\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.88219 | −0.221851 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 86.4350 | 3.25533 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.06548i | 0.340943i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.4168i | − | 1.81833i | −0.416435 | − | 0.909166i | \(-0.636721\pi\) | ||
0.416435 | − | 0.909166i | \(-0.363279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.0679 | −0.527587 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.2830i | 1.95801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.3853 | + | 5.98917i | −0.463182 | + | 0.223982i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.5489i | 0.431303i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.9114 | −0.891745 | −0.445873 | − | 0.895096i | \(-0.647107\pi\) | ||||
−0.445873 | + | 0.895096i | \(0.647107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.47128i | − | 0.315487i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.7362i | 0.399282i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −90.9400 | −3.37743 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.51781 | 0.130469 | 0.0652343 | − | 0.997870i | \(-0.479221\pi\) | ||||
0.0652343 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.1776 | −1.19176 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.6153 | 1.42824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5709i | 1.01836i | 0.860661 | + | 0.509178i | \(0.170050\pi\) | ||||
−0.860661 | + | 0.509178i | \(0.829950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 45.1933i | − | 1.66698i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.46301 | 0.164397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.19428i | − | 0.0439322i | −0.999759 | − | 0.0219661i | \(-0.993007\pi\) | ||
0.999759 | − | 0.0219661i | \(-0.00699259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.23070 | − | 14.9527i | −0.265626 | − | 0.549300i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.6391i | 1.16072i | 0.814358 | + | 0.580362i | \(0.197089\pi\) | ||||
−0.814358 | + | 0.580362i | \(0.802911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.7816 | −1.42085 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.4606i | 0.602262i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.88799i | 0.324760i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.2294 | −1.54097 | −0.770487 | − | 0.637456i | \(-0.779987\pi\) | ||||
−0.770487 | + | 0.637456i | \(0.779987\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.9016 | −1.70919 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 82.6200 | 3.00685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.39360 | −0.0869970 | −0.0434985 | − | 0.999053i | \(-0.513850\pi\) | ||||
−0.0434985 | + | 0.999053i | \(0.513850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 13.3744i | − | 0.485461i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 20.5604i | − | 0.745313i | −0.927969 | − | 0.372656i | \(-0.878447\pi\) | ||
0.927969 | − | 0.372656i | \(-0.121553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.81560 | −0.174337 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 64.8034i | − | 2.34297i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.8555 | − | 26.5844i | −0.464185 | − | 0.959908i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.5003i | − | 1.74897i | −0.485055 | − | 0.874484i | \(-0.661200\pi\) | ||
0.485055 | − | 0.874484i | \(-0.338800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.4690 | 1.27738 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.13384i | − | 0.0767490i | −0.999263 | − | 0.0383745i | \(-0.987782\pi\) | ||
0.999263 | − | 0.0383745i | \(-0.0122180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 93.8256i | 3.37031i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.1637 | 0.436370 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.3764 | −0.443430 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.58065 | −0.128126 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.27844 | 0.260110 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.3210i | 1.51050i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.3609i | 1.22483i | 0.790535 | + | 0.612416i | \(0.209802\pi\) | ||||
−0.790535 | + | 0.612416i | \(0.790198\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.7379 | 1.77072 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.9385i | − | 0.424486i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.8973 | + | 8.65464i | −0.635551 | + | 0.307335i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2488i | 0.363486i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.4715 | −0.583451 | −0.291725 | − | 0.956502i | \(-0.594229\pi\) | ||||
−0.291725 | + | 0.956502i | \(0.594229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.3659i | 1.64031i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 59.0193i | − | 2.08534i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.71714 | −0.342910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.7076 | 1.08230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −65.0100 | −2.28846 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.7978 | 0.449947 | 0.224973 | − | 0.974365i | \(-0.427770\pi\) | ||||
0.224973 | + | 0.974365i | \(0.427770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.5928i | − | 1.84678i | −0.383861 | − | 0.923391i | \(-0.625406\pi\) | ||
0.383861 | − | 0.923391i | \(-0.374594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.2565i | 0.745499i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.5879 | −1.10648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.7848i | 0.482269i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.83743 | + | 16.2074i | 0.273862 | + | 0.566331i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 44.5792i | − | 1.55583i | −0.628372 | − | 0.777913i | \(-0.716279\pi\) | ||
0.628372 | − | 0.777913i | \(-0.283721\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3864 | −0.919771 | −0.459886 | − | 0.887978i | \(-0.652110\pi\) | ||||
−0.459886 | + | 0.887978i | \(0.652110\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 24.0014i | − | 0.835621i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.9688i | − | 1.21598i | −0.793943 | − | 0.607992i | \(-0.791975\pi\) | ||
0.793943 | − | 0.607992i | \(-0.208025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.4300 | 1.61258 | 0.806291 | − | 0.591519i | \(-0.201472\pi\) | ||||
0.806291 | + | 0.591519i | \(0.201472\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 68.1997 | 2.36582 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.2428 | 0.839964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 85.7213 | 2.96651 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.50939i | − | 0.259563i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.4274i | 1.56833i | 0.620554 | + | 0.784164i | \(0.286908\pi\) | ||||
−0.620554 | + | 0.784164i | \(0.713092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.5110 | 2.12107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 72.9102i | 2.51116i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.8811 | − | 30.8010i | −1.33755 | − | 1.05959i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.51091i | 0.0519156i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.83647 | 0.165987 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 17.0780i | − | 0.585427i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.7143i | 1.08588i | 0.839773 | + | 0.542938i | \(0.182688\pi\) | ||||
−0.839773 | + | 0.542938i | \(0.817312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.1334 | 0.791144 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.27331 | 0.282611 | 0.141305 | − | 0.989966i | \(-0.454870\pi\) | ||||
0.141305 | + | 0.989966i | \(0.454870\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2598 | 0.930091 | 0.465046 | − | 0.885287i | \(-0.346038\pi\) | ||||
0.465046 | + | 0.885287i | \(0.346038\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.5929 | 0.872205 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 30.0929i | − | 1.02438i | −0.858873 | − | 0.512188i | \(-0.828835\pi\) | ||
0.858873 | − | 0.512188i | \(-0.171165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.4073i | 0.931877i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.6339 | 0.802648 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.25695i | − | 0.144407i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00537 | + | 14.4867i | 0.237368 | + | 0.490863i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.8281i | − | 0.468011i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.2818 | 0.888488 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4876i | 0.894424i | 0.894428 | + | 0.447212i | \(0.147583\pi\) | ||||
−0.894428 | + | 0.447212i | \(0.852417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 75.1562i | − | 2.53496i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7155 | 0.596852 | 0.298426 | − | 0.954433i | \(-0.403538\pi\) | ||||
0.298426 | + | 0.954433i | \(0.403538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.585366 | −0.0196991 | −0.00984956 | − | 0.999951i | \(-0.503135\pi\) | ||||
−0.00984956 | + | 0.999951i | \(0.503135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 78.4658 | 2.63760 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.2865 | −1.28553 | −0.642767 | − | 0.766062i | \(-0.722214\pi\) | ||||
−0.642767 | + | 0.766062i | \(0.722214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.6174i | 0.657947i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 7.99310i | − | 0.267779i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.5516 | −0.553878 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 45.4492i | − | 1.51920i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.4127 | − | 20.9932i | 1.44951 | − | 0.700942i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 93.3830i | − | 3.11450i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.49769 | −0.183155 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 28.5054i | − | 0.948600i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 34.4338i | − | 1.14462i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.98115 | 0.331419 | 0.165709 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165709 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.8281 | −0.657658 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1696 | −0.336933 | −0.168467 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168467 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.98099 | −0.164847 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 52.8251i | − | 1.74634i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.7323i | 0.519527i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.37989 | 0.0455182 | 0.0227591 | − | 0.999741i | \(-0.492755\pi\) | ||||
0.0227591 | + | 0.999741i | \(0.492755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.88029i | − | 0.0619576i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.62037 | − | 11.6226i | −0.184997 | − | 0.382563i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 30.6477i | − | 1.00769i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.5285 | 0.608555 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.0767i | − | 1.41330i | −0.707562 | − | 0.706651i | \(-0.750205\pi\) | ||
0.707562 | − | 0.706651i | \(-0.249795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.65414i | 0.283628i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.0328 | −1.27788 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.6095 | 0.641301 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.2704 | −1.70760 | −0.853800 | − | 0.520601i | \(-0.825708\pi\) | ||||
−0.853800 | + | 0.520601i | \(0.825708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −81.1426 | −2.64799 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11.7969i | − | 0.384569i | −0.981339 | − | 0.192284i | \(-0.938410\pi\) | ||
0.981339 | − | 0.192284i | \(-0.0615896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 35.9329i | − | 1.17013i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.41053 | −0.143474 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.2915i | − | 1.30930i | −0.755934 | − | 0.654648i | \(-0.772817\pi\) | ||
0.755934 | − | 0.654648i | \(-0.227183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2525 | − | 31.5413i | −0.495118 | − | 1.02388i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.4059i | 2.57491i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.5685 | 1.89722 | 0.948609 | − | 0.316449i | \(-0.102491\pi\) | ||||
0.948609 | + | 0.316449i | \(0.102491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.9008i | 1.45296i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.8882i | 0.772194i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.2297 | 0.814709 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −65.3460 | −2.10794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.4399 | −0.626442 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −70.7350 | −2.27704 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.77699i | − | 0.0893021i | −0.999003 | − | 0.0446511i | \(-0.985782\pi\) | ||
0.999003 | − | 0.0446511i | \(-0.0142176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.6745i | 0.760535i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.6039 | 1.55977 | 0.779886 | − | 0.625922i | \(-0.215277\pi\) | ||||
0.779886 | + | 0.625922i | \(0.215277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.7978i | 0.666747i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 77.9073 | − | 37.6738i | 2.49503 | − | 1.20653i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7201i | 0.758874i | 0.925218 | + | 0.379437i | \(0.123882\pi\) | ||||
−0.925218 | + | 0.379437i | \(0.876118\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.8593 | 0.570784 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.5327i | − | 0.336285i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5123i | 0.718031i | 0.933332 | + | 0.359015i | \(0.116887\pi\) | ||||
−0.933332 | + | 0.359015i | \(0.883113\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.0190 | −0.542269 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.2268 | 1.08945 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.0220 | −1.27263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.7939 | −1.74058 | −0.870292 | − | 0.492535i | \(-0.836070\pi\) | ||||
−0.870292 | + | 0.492535i | \(0.836070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 64.0044i | − | 2.03112i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 23.7739i | − | 0.753683i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.229656 | 0.00727328 | 0.00363664 | − | 0.999993i | \(-0.498842\pi\) | ||||
0.00363664 | + | 0.999993i | \(0.498842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.45291i | 0.0776067i |
(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 | 572.2.f.c.441.7 | ✓ | 8 | |
3.2 | odd | 2 | 5148.2.e.c.1585.7 | 8 | |||
4.3 | odd | 2 | 2288.2.j.i.1585.1 | 8 | |||
13.5 | odd | 4 | 7436.2.a.o.1.4 | 4 | |||
13.8 | odd | 4 | 7436.2.a.p.1.4 | 4 | |||
13.12 | even | 2 | inner | 572.2.f.c.441.8 | yes | 8 | |
39.38 | odd | 2 | 5148.2.e.c.1585.2 | 8 | |||
52.51 | odd | 2 | 2288.2.j.i.1585.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.f.c.441.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
572.2.f.c.441.8 | yes | 8 | 13.12 | even | 2 | inner | |
2288.2.j.i.1585.1 | 8 | 4.3 | odd | 2 | |||
2288.2.j.i.1585.2 | 8 | 52.51 | odd | 2 | |||
5148.2.e.c.1585.2 | 8 | 39.38 | odd | 2 | |||
5148.2.e.c.1585.7 | 8 | 3.2 | odd | 2 | |||
7436.2.a.o.1.4 | 4 | 13.5 | odd | 4 | |||
7436.2.a.p.1.4 | 4 | 13.8 | odd | 4 |