Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 117x^{6} + 333x^{4} + 396x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(-2.61696i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.w.4049.10 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.61696i | − 1.51090i | −0.655204 | − | 0.755452i | \(-0.727417\pi\) | ||||
0.655204 | − | 0.755452i | \(-0.272583\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.83744i | 1.45041i | 0.688531 | + | 0.725207i | \(0.258256\pi\) | ||||
−0.688531 | + | 0.725207i | \(0.741744\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.84849 | −1.28283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.508005 | −0.153169 | −0.0765847 | − | 0.997063i | \(-0.524402\pi\) | ||||
−0.0765847 | + | 0.997063i | \(0.524402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.01106i | − 0.280417i | −0.990122 | − | 0.140208i | \(-0.955223\pi\) | ||||
0.990122 | − | 0.140208i | \(-0.0447772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.44705i | 0.350961i | 0.984483 | + | 0.175481i | \(0.0561479\pi\) | ||||
−0.984483 | + | 0.175481i | \(0.943852\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.508005 | 0.116544 | 0.0582722 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582722 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.0424 | 2.19144 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.22047i | 0.427330i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.51040 | −1.39465 | −0.697323 | − | 0.716757i | \(-0.745626\pi\) | ||||
−0.697323 | + | 0.716757i | \(0.745626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.439038 | −0.0788536 | −0.0394268 | − | 0.999222i | \(-0.512553\pi\) | ||||
−0.0394268 | + | 0.999222i | \(0.512553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.32943i | 0.231424i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.02642i | − 1.15514i | −0.816343 | − | 0.577568i | \(-0.804002\pi\) | ||||
0.816343 | − | 0.577568i | \(-0.195998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.64590 | −0.423683 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.47041 | 0.854335 | 0.427167 | − | 0.904173i | \(-0.359512\pi\) | ||||
0.427167 | + | 0.904173i | \(0.359512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 6.72592i | − 1.02569i | −0.858480 | − | 0.512847i | \(-0.828591\pi\) | ||||
0.858480 | − | 0.512847i | \(-0.171409\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.64098i | − 0.385227i | −0.981275 | − | 0.192614i | \(-0.938304\pi\) | ||||
0.981275 | − | 0.192614i | \(-0.0616964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.72592 | −1.10370 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.78688 | 0.530269 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.77648i | − 0.656100i | −0.944660 | − | 0.328050i | \(-0.893609\pi\) | ||||
0.944660 | − | 0.328050i | \(-0.106391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.32943i | − 0.176087i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.85345 | −0.501676 | −0.250838 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250838 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.05844 | −1.15981 | −0.579907 | − | 0.814683i | \(-0.696911\pi\) | ||||
−0.579907 | + | 0.814683i | \(0.696911\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 14.7683i | − 1.86064i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.45696i | 0.422335i | 0.977450 | + | 0.211167i | \(0.0677265\pi\) | ||||
−0.977450 | + | 0.211167i | \(0.932273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.61696 | 0.315045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.73649 | −0.324762 | −0.162381 | − | 0.986728i | \(-0.551917\pi\) | ||||
−0.162381 | + | 0.986728i | \(0.551917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.21300i | 1.07830i | 0.842210 | + | 0.539150i | \(0.181254\pi\) | ||||
−0.842210 | + | 0.539150i | \(0.818746\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.94944i | − 0.222159i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5504 | −1.18702 | −0.593508 | − | 0.804828i | \(-0.702258\pi\) | ||||
−0.593508 | + | 0.804828i | \(0.702258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.73458 | −0.637176 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.40211i | 0.153901i | 0.997035 | + | 0.0769505i | \(0.0245183\pi\) | ||||
−0.997035 | + | 0.0769505i | \(0.975482\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.6544i | 2.10718i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.77086 | −0.717710 | −0.358855 | − | 0.933393i | \(-0.616833\pi\) | ||||
−0.358855 | + | 0.933393i | \(0.616833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.87986 | 0.406720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.14895i | 0.119140i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.313420i | − 0.0318230i | −0.999873 | − | 0.0159115i | \(-0.994935\pi\) | ||||
0.999873 | − | 0.0159115i | \(-0.00506500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95506 | 0.196490 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.83182 | −0.480784 | −0.240392 | − | 0.970676i | \(-0.577276\pi\) | ||||
−0.240392 | + | 0.970676i | \(0.577276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.07746i | − 0.795896i | −0.917408 | − | 0.397948i | \(-0.869722\pi\) | ||||
0.917408 | − | 0.397948i | \(-0.130278\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.1587i | − 1.07876i | −0.842064 | − | 0.539378i | \(-0.818659\pi\) | ||||
0.842064 | − | 0.539378i | \(-0.181341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6015 | −1.68592 | −0.842958 | − | 0.537979i | \(-0.819188\pi\) | ||||
−0.842958 | + | 0.537979i | \(0.819188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.3879 | −1.74530 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.06454i | 0.382360i | 0.981555 | + | 0.191180i | \(0.0612314\pi\) | ||||
−0.981555 | + | 0.191180i | \(0.938769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.89104i | 0.359727i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.55296 | −0.509039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7419 | −0.976539 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 14.3159i | − 1.29082i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.75246i | 0.421713i | 0.977517 | + | 0.210856i | \(0.0676252\pi\) | ||||
−0.977517 | + | 0.210856i | \(0.932375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.6015 | −1.54972 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.96851 | 0.171989 | 0.0859946 | − | 0.996296i | \(-0.472593\pi\) | ||||
0.0859946 | + | 0.996296i | \(0.472593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.94944i | 0.169038i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 5.64285i | − 0.482101i | −0.970513 | − | 0.241051i | \(-0.922508\pi\) | ||||
0.970513 | − | 0.241051i | \(-0.0774920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.59724 | 0.644390 | 0.322195 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322195 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.91136 | −0.582041 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.513622i | 0.0429512i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.2184i | 1.66759i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.7709 | −0.882384 | −0.441192 | − | 0.897413i | \(-0.645444\pi\) | ||||
−0.441192 | + | 0.897413i | \(0.645444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5333 | −1.34546 | −0.672729 | − | 0.739889i | \(-0.734878\pi\) | ||||
−0.672729 | + | 0.739889i | \(0.734878\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 5.56896i | − 0.450224i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 11.5436i | − 0.921281i | −0.887587 | − | 0.460640i | \(-0.847620\pi\) | ||||
0.887587 | − | 0.460640i | \(-0.152380\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4999 | −0.991304 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.83744 | −0.302432 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.32143i | − 0.260155i | −0.991504 | − | 0.130077i | \(-0.958477\pi\) | ||||
0.991504 | − | 0.130077i | \(-0.0415226\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6742i | 0.980755i | 0.871510 | + | 0.490378i | \(0.163141\pi\) | ||||
−0.871510 | + | 0.490378i | \(0.836859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9778 | 0.921367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.95506 | −0.149507 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 17.5733i | − 1.33607i | −0.744130 | − | 0.668035i | \(-0.767136\pi\) | ||||
0.744130 | − | 0.668035i | \(-0.232864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0843i | 0.757984i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8952 | 1.11332 | 0.556659 | − | 0.830741i | \(-0.312083\pi\) | ||||
0.556659 | + | 0.830741i | \(0.312083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.2868 | −1.73089 | −0.865446 | − | 0.501003i | \(-0.832965\pi\) | ||||
−0.865446 | + | 0.501003i | \(0.832965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.7056i | 1.75237i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.735109i | − 0.0537565i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.52093 | −0.619806 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.92360 | 0.500974 | 0.250487 | − | 0.968120i | \(-0.419409\pi\) | ||||
0.250487 | + | 0.968120i | \(0.419409\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.74318i | 0.557366i | 0.960383 | + | 0.278683i | \(0.0898979\pi\) | ||||
−0.960383 | + | 0.278683i | \(0.910102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.8908i | − 1.70215i | −0.525045 | − | 0.851074i | \(-0.675952\pi\) | ||||
0.525045 | − | 0.851074i | \(-0.324048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9444 | 1.69737 | 0.848687 | − | 0.528896i | \(-0.177394\pi\) | ||||
0.848687 | + | 0.528896i | \(0.177394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.04673 | 0.638107 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 28.8207i | − 2.02282i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.84849i | − 0.267489i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.258070 | −0.0178510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4709 | 0.996220 | 0.498110 | − | 0.867114i | \(-0.334027\pi\) | ||||
0.498110 | + | 0.867114i | \(0.334027\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.16129i | 0.490684i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.68478i | − 0.114370i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.1101 | 1.62921 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46305 | 0.0984153 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.74755i | 0.317919i | 0.987285 | + | 0.158960i | \(0.0508140\pi\) | ||||
−0.987285 | + | 0.158960i | \(0.949186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.98399i | 0.596288i | 0.954521 | + | 0.298144i | \(0.0963676\pi\) | ||||
−0.954521 | + | 0.298144i | \(0.903632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7290 | −1.36981 | −0.684906 | − | 0.728631i | \(-0.740157\pi\) | ||||
−0.684906 | + | 0.728631i | \(0.740157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.10161 | −0.335661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 26.0634i | − 1.70747i | −0.520707 | − | 0.853735i | \(-0.674332\pi\) | ||||
0.520707 | − | 0.853735i | \(-0.325668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.6101i | 1.79347i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.94209 | 0.190308 | 0.0951540 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951540 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9413 | −1.60661 | −0.803306 | − | 0.595567i | \(-0.796927\pi\) | ||||
−0.803306 | + | 0.595567i | \(0.796927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6686i | 1.39004i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.513622i | − 0.0326810i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.66926 | 0.232530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1908 | 1.33755 | 0.668774 | − | 0.743465i | \(-0.266819\pi\) | ||||
0.668774 | + | 0.743465i | \(0.266819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.508005i | − 0.0319380i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.2110i | 1.63500i | 0.575929 | + | 0.817500i | \(0.304640\pi\) | ||||
−0.575929 | + | 0.817500i | \(0.695360\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.9634 | 1.67543 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.9037 | 1.78910 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.65276i | 0.348564i | 0.984696 | + | 0.174282i | \(0.0557605\pi\) | ||||
−0.984696 | + | 0.174282i | \(0.944240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7191i | 1.08439i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.65772 | −0.588841 | −0.294421 | − | 0.955676i | \(-0.595127\pi\) | ||||
−0.294421 | + | 0.955676i | \(0.595127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.39040 | 0.509680 | 0.254840 | − | 0.966983i | \(-0.417977\pi\) | ||||
0.254840 | + | 0.966983i | \(0.417977\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 10.1535i | − 0.614515i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3317i | 1.82246i | 0.411900 | + | 0.911229i | \(0.364865\pi\) | ||||
−0.411900 | + | 0.911229i | \(0.635135\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.68964 | 0.101156 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3132 | −1.51006 | −0.755028 | − | 0.655692i | \(-0.772377\pi\) | ||||
−0.755028 | + | 0.655692i | \(0.772377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9629i | 0.770566i | 0.922798 | + | 0.385283i | \(0.125896\pi\) | ||||
−0.922798 | + | 0.385283i | \(0.874104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.9924i | 1.23914i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9060 | 0.876826 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.820209 | −0.0480815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 25.9469i | − 1.51584i | −0.652350 | − | 0.757918i | \(-0.726217\pi\) | ||||
0.652350 | − | 0.757918i | \(-0.273783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1.12801i | − 0.0654539i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.01106 | 0.0584709 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8103 | 1.48768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.6447i | 0.726419i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0640i | 0.688531i | 0.938872 | + | 0.344266i | \(0.111872\pi\) | ||||
−0.938872 | + | 0.344266i | \(0.888128\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.1384 | −1.20252 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8125 | −1.80392 | −0.901959 | − | 0.431821i | \(-0.857871\pi\) | ||||
−0.901959 | + | 0.431821i | \(0.857871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30122i | 0.243119i | 0.992584 | + | 0.121560i | \(0.0387895\pi\) | ||||
−0.992584 | + | 0.121560i | \(0.961210\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6.28317i | − 0.352898i | −0.984310 | − | 0.176449i | \(-0.943539\pi\) | ||||
0.984310 | − | 0.176449i | \(-0.0564611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.81532 | 0.213617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.2020 | −1.62990 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.735109i | 0.0409026i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.0624i | 2.54726i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.1346 | 0.558739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00053 | −0.439749 | −0.219874 | − | 0.975528i | \(-0.570565\pi\) | ||||
−0.219874 | + | 0.975528i | \(0.570565\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.0411i | 1.48184i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1436i | 0.552554i | 0.961078 | + | 0.276277i | \(0.0891008\pi\) | ||||
−0.961078 | + | 0.276277i | \(0.910899\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6367 | 0.577709 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.223034 | 0.0120780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.78567i | − 0.150412i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 18.8747i | − 1.01325i | −0.862167 | − | 0.506625i | \(-0.830893\pi\) | ||||
0.862167 | − | 0.506625i | \(-0.169107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.26611 | −0.496004 | −0.248002 | − | 0.968760i | \(-0.579774\pi\) | ||||
−0.248002 | + | 0.968760i | \(0.579774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.24502 | 0.119831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.04442i | − 0.428161i | −0.976816 | − | 0.214081i | \(-0.931324\pi\) | ||||
0.976816 | − | 0.214081i | \(-0.0686755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5319i | 0.769109i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5443 | −1.08429 | −0.542144 | − | 0.840285i | \(-0.682387\pi\) | ||||
−0.542144 | + | 0.840285i | \(0.682387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7419 | −0.986417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.1112i | 1.47546i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.64032i | − 0.451021i | −0.974241 | − | 0.225511i | \(-0.927595\pi\) | ||||
0.974241 | − | 0.225511i | \(-0.0724050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.0528 | −1.09597 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.3294 | 0.951617 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0442i | 0.986073i | 0.870009 | + | 0.493037i | \(0.164113\pi\) | ||||
−0.870009 | + | 0.493037i | \(0.835887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.59344i | 0.391082i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.926121 | −0.0475717 | −0.0237858 | − | 0.999717i | \(-0.507572\pi\) | ||||
−0.0237858 | + | 0.999717i | \(0.507572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4370 | 0.637167 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.38526i | 0.479564i | 0.970827 | + | 0.239782i | \(0.0770760\pi\) | ||||
−0.970827 | + | 0.239782i | \(0.922924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.8847i | 1.31579i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.22865 | −0.112997 | −0.0564985 | − | 0.998403i | \(-0.517994\pi\) | ||||
−0.0564985 | + | 0.998403i | \(0.517994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44705 | −0.0731805 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.15151i | − 0.259859i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0448i | 0.654701i | 0.944903 | + | 0.327350i | \(0.106156\pi\) | ||||
−0.944903 | + | 0.327350i | \(0.893844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.10161 | 0.255400 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.22221 | −0.110972 | −0.0554859 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554859 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.443893i | 0.0221119i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.56946i | 0.176931i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5232 | 0.965362 | 0.482681 | − | 0.875796i | \(-0.339663\pi\) | ||||
0.482681 | + | 0.875796i | \(0.339663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7671 | −0.728409 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 14.7874i | − 0.727638i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 19.8817i | − 0.973611i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.9180 | 1.21732 | 0.608662 | − | 0.793430i | \(-0.291707\pi\) | ||||
0.608662 | + | 0.793430i | \(0.291707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.10721 | 0.297647 | 0.148824 | − | 0.988864i | \(-0.452451\pi\) | ||||
0.148824 | + | 0.988864i | \(0.452451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.1638i | 0.494181i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 34.7612i | − 1.68221i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.34413 | 0.0648952 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.44095 | 0.213913 | 0.106956 | − | 0.994264i | \(-0.465889\pi\) | ||||
0.106956 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.25554i | − 0.156451i | −0.996936 | − | 0.0782257i | \(-0.975075\pi\) | ||||
0.996936 | − | 0.0782257i | \(-0.0249255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.508005i | 0.0243012i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9611 | 1.28678 | 0.643392 | − | 0.765537i | \(-0.277527\pi\) | ||||
0.643392 | + | 0.765537i | \(0.277527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.7331 | 1.41586 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0072i | 0.760526i | 0.924878 | + | 0.380263i | \(0.124167\pi\) | ||||
−0.924878 | + | 0.380263i | \(0.875833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.1869i | 1.33320i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.4278 | 1.76633 | 0.883163 | − | 0.469066i | \(-0.155409\pi\) | ||||
0.883163 | + | 0.469066i | \(0.155409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.77900 | −0.130858 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.2670i | 2.03286i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 8.75949i | − 0.409752i | −0.978788 | − | 0.204876i | \(-0.934321\pi\) | ||||
0.978788 | − | 0.204876i | \(-0.0656790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.21314 | −0.149976 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4459 | 0.533089 | 0.266545 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266545 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.23570i | − 0.382745i | −0.981517 | − | 0.191373i | \(-0.938706\pi\) | ||||
0.981517 | − | 0.191373i | \(-0.0612939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 28.9436i | − 1.33935i | −0.742654 | − | 0.669675i | \(-0.766433\pi\) | ||||
0.742654 | − | 0.669675i | \(-0.233567\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2659 | −0.612561 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.2092 | −1.39197 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.41680i | 0.157105i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.3823i | 0.841666i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1031 | −1.42114 | −0.710569 | − | 0.703627i | \(-0.751563\pi\) | ||||
−0.710569 | + | 0.703627i | \(0.751563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.10410 | −0.323919 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0424i | 0.456946i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.90588i | 0.0863635i | 0.999067 | + | 0.0431817i | \(0.0137494\pi\) | ||||
−0.999067 | + | 0.0431817i | \(0.986251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.69206 | −0.393069 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.2222 | −1.22852 | −0.614259 | − | 0.789104i | \(-0.710545\pi\) | ||||
−0.614259 | + | 0.789104i | \(0.710545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 10.8679i | − 0.489467i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 10.5011i | − 0.471039i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.38913 | 0.420315 | 0.210158 | − | 0.977668i | \(-0.432602\pi\) | ||||
0.210158 | + | 0.977668i | \(0.432602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.1678 | 1.48183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 29.5613i | − 1.31807i | −0.752110 | − | 0.659037i | \(-0.770964\pi\) | ||||
0.752110 | − | 0.659037i | \(-0.229036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 31.3454i | − 1.39210i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.448890 | −0.0198967 | −0.00994835 | − | 0.999951i | \(-0.503167\pi\) | ||||
−0.00994835 | + | 0.999951i | \(0.503167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.3543 | −1.56398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.12801i | 0.0498030i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.34163i | 0.0590050i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.9886 | −2.01867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8712 | 1.17725 | 0.588623 | − | 0.808407i | \(-0.299670\pi\) | ||||
0.588623 | + | 0.808407i | \(0.299670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.90473i | − 0.127015i | −0.997981 | − | 0.0635075i | \(-0.979771\pi\) | ||||
0.997981 | − | 0.0635075i | \(-0.0202287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 0.635311i | − 0.0276746i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8300 | 0.643566 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.53089i | − 0.239570i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 38.9801i | − 1.68212i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.92481 | 0.169053 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0386 | 1.46343 | 0.731716 | − | 0.681610i | \(-0.238720\pi\) | ||||
0.731716 | + | 0.681610i | \(0.238720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.9406i | 2.61521i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 23.8364i | − 1.01917i | −0.860420 | − | 0.509586i | \(-0.829798\pi\) | ||||
0.860420 | − | 0.509586i | \(-0.170202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.8613 | 1.48785 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.81532 | −0.162538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 40.4866i | − 1.72167i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.4201i | 1.71265i | 0.516435 | + | 0.856326i | \(0.327259\pi\) | ||||
−0.516435 | + | 0.856326i | \(0.672741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.80028 | −0.287621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.92375 | −0.0812209 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.54758i | 0.275948i | 0.990436 | + | 0.137974i | \(0.0440590\pi\) | ||||
−0.990436 | + | 0.137974i | \(0.955941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 22.0061i | − 0.924169i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.4590 | −0.857686 | −0.428843 | − | 0.903379i | \(-0.641079\pi\) | ||||
−0.428843 | + | 0.903379i | \(0.641079\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.71300 | 0.197233 | 0.0986164 | − | 0.995126i | \(-0.468558\pi\) | ||||
0.0986164 | + | 0.995126i | \(0.468558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 18.1188i | − 0.756924i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 25.9331i | − 1.07961i | −0.841790 | − | 0.539805i | \(-0.818498\pi\) | ||||
0.841790 | − | 0.539805i | \(-0.181502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.2636 | 0.842127 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.38049 | −0.223220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.42648i | 0.100494i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4711i | 0.432189i | 0.976372 | + | 0.216095i | \(0.0693320\pi\) | ||||
−0.976372 | + | 0.216095i | \(0.930668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.223034 | −0.00918995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.5213 | −2.57178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 20.8158i | − 0.854803i | −0.904062 | − | 0.427401i | \(-0.859429\pi\) | ||||
0.904062 | − | 0.427401i | \(-0.140571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 62.6616i | − 2.56457i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7951 | 0.604511 | 0.302256 | − | 0.953227i | \(-0.402260\pi\) | ||||
0.302256 | + | 0.953227i | \(0.402260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.8995 | −1.38279 | −0.691394 | − | 0.722477i | \(-0.743003\pi\) | ||||
−0.691394 | + | 0.722477i | \(0.743003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13.3041i | − 0.541784i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9350i | 1.33679i | 0.743807 | + | 0.668394i | \(0.233018\pi\) | ||||
−0.743807 | + | 0.668394i | \(0.766982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −75.4227 | −3.05628 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.67018 | −0.108024 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.8664i | 1.00434i | 0.864768 | + | 0.502172i | \(0.167465\pi\) | ||||
−0.864768 | + | 0.502172i | \(0.832535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 20.1280i | − 0.810324i | −0.914245 | − | 0.405162i | \(-0.867215\pi\) | ||||
0.914245 | − | 0.405162i | \(-0.132785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3719 | 0.617847 | 0.308924 | − | 0.951087i | \(-0.400031\pi\) | ||||
0.308924 | + | 0.951087i | \(0.400031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.22047 | −0.0891046 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 25.9828i | − 1.04098i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.675358i | 0.0269712i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1676 | 0.405408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.7115 | −1.02356 | −0.511779 | − | 0.859117i | \(-0.671013\pi\) | ||||
−0.511779 | + | 0.859117i | \(0.671013\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 37.8699i | − 1.50519i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.81134i | 0.309497i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5314 | 0.416614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.95684 | 0.116788 | 0.0583941 | − | 0.998294i | \(-0.481402\pi\) | ||||
0.0583941 | + | 0.998294i | \(0.481402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7764i | 0.661596i | 0.943702 | + | 0.330798i | \(0.107318\pi\) | ||||
−0.943702 | + | 0.330798i | \(0.892682\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1.99247i | − 0.0783322i | −0.999233 | − | 0.0391661i | \(-0.987530\pi\) | ||||
0.999233 | − | 0.0391661i | \(-0.0124702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.95757 | 0.0768414 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.40901 | −0.172803 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 46.4989i | − 1.81964i | −0.414999 | − | 0.909822i | \(-0.636218\pi\) | ||||
0.414999 | − | 0.909822i | \(-0.363782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 35.4562i | − 1.38328i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1468 | 1.44703 | 0.723517 | − | 0.690307i | \(-0.242524\pi\) | ||||
0.723517 | + | 0.690307i | \(0.242524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.01756 | −0.272952 | −0.136476 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136476 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.82874i | − 0.148696i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.51040i | − 0.290804i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.4242 | 0.480346 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.60174 | 0.177648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.81155i | 0.262566i | 0.991345 | + | 0.131283i | \(0.0419096\pi\) | ||||
−0.991345 | + | 0.131283i | \(0.958090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.522812i | 0.0200933i | 0.999950 | + | 0.0100466i | \(0.00319800\pi\) | ||||
−0.999950 | + | 0.0100466i | \(0.996802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.20273 | 0.0461566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5108 | 0.900934 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 2.93412i | − 0.112271i | −0.998423 | − | 0.0561355i | \(-0.982122\pi\) | ||||
0.998423 | − | 0.0561355i | \(-0.0178779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.2471i | 2.06965i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.82929 | −0.183981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.8456 | −1.21146 | −0.605731 | − | 0.795669i | \(-0.707119\pi\) | ||||
−0.605731 | + | 0.795669i | \(0.707119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50240i | 0.284993i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.91596i | 0.299838i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −68.2070 | −2.57982 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2070 | 0.423283 | 0.211642 | − | 0.977347i | \(-0.432119\pi\) | ||||
0.211642 | + | 0.977347i | \(0.432119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.56946i | − 0.134625i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.5418i | − 0.697336i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.7300 | −0.891198 | −0.445599 | − | 0.895233i | \(-0.647009\pi\) | ||||
−0.445599 | + | 0.895233i | \(0.647009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.6033 | 1.52274 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 0.439038i | − 0.0164421i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7.69934i | − 0.287537i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8687 | 1.03933 | 0.519664 | − | 0.854371i | \(-0.326057\pi\) | ||||
0.519664 | + | 0.854371i | \(0.326057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.9968 | 1.15438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 65.2705i | 2.42744i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 47.5773i | − 1.76455i | −0.470739 | − | 0.882273i | \(-0.656013\pi\) | ||||
0.470739 | − | 0.882273i | \(-0.343987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.5022 | 1.46304 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.73274 | 0.359978 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15.4086i | − 0.569129i | −0.958657 | − | 0.284565i | \(-0.908151\pi\) | ||||
0.958657 | − | 0.284565i | \(-0.0918490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.75615i | − 0.0646888i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.0212 | −1.95042 | −0.975208 | − | 0.221292i | \(-0.928973\pi\) | ||||
−0.975208 | + | 0.221292i | \(0.928973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.34413 | −0.0493778 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 15.6611i | − 0.574551i | −0.957848 | − | 0.287275i | \(-0.907250\pi\) | ||||
0.957848 | − | 0.287275i | \(-0.0927495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.39599i | − 0.197429i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.8209 | 1.56464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.6216 | 1.26336 | 0.631679 | − | 0.775230i | \(-0.282366\pi\) | ||||
0.631679 | + | 0.775230i | \(0.282366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 55.4554i | − 2.02091i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 38.4389i | − 1.39709i | −0.715568 | − | 0.698543i | \(-0.753832\pi\) | ||||
0.715568 | − | 0.698543i | \(-0.246168\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.32943 | −0.0482553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0932 | 1.52588 | 0.762939 | − | 0.646470i | \(-0.223755\pi\) | ||||
0.762939 | + | 0.646470i | \(0.223755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 67.5446i | − 2.44528i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.89605i | 0.140678i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.2859 | −1.23638 | −0.618191 | − | 0.786028i | \(-0.712134\pi\) | ||||
−0.618191 | + | 0.786028i | \(0.712134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 68.5933 | 2.47033 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7422i | 0.458304i | 0.973391 | + | 0.229152i | \(0.0735953\pi\) | ||||
−0.973391 | + | 0.229152i | \(0.926405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 70.5623i | − 2.53141i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.77900 | 0.0995679 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.39015 | 0.0497436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 16.6766i | − 0.595975i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5534i | 1.01782i | 0.860820 | + | 0.508910i | \(0.169951\pi\) | ||||
−0.860820 | + | 0.508910i | \(0.830049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7931 | 0.526647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5974 | −0.554580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.15859i | 0.325231i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 8.39925i | − 0.297517i | −0.988874 | − | 0.148758i | \(-0.952472\pi\) | ||||
0.988874 | − | 0.148758i | \(-0.0475276\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.82164 | 0.135200 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.0576 | 0.920701 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.68026i | − 0.165163i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2739i | 0.889683i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8816 | 1.01542 | 0.507712 | − | 0.861527i | \(-0.330491\pi\) | ||||
0.507712 | + | 0.861527i | \(0.330491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.5292 | −1.63386 | −0.816931 | − | 0.576736i | \(-0.804326\pi\) | ||||
−0.816931 | + | 0.576736i | \(0.804326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 21.9574i | − 0.770078i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.41680i | − 0.119539i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.9316 | −0.521753 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.99065 | −0.104374 | −0.0521872 | − | 0.998637i | \(-0.516619\pi\) | ||||
−0.0521872 | + | 0.998637i | \(0.516619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 5.14357i | − 0.179294i | −0.995974 | − | 0.0896468i | \(-0.971426\pi\) | ||||
0.995974 | − | 0.0896468i | \(-0.0285738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 53.4288i | − 1.85790i | −0.370205 | − | 0.928950i | \(-0.620713\pi\) | ||||
0.370205 | − | 0.928950i | \(-0.379287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.5290 | −0.400420 | −0.200210 | − | 0.979753i | \(-0.564162\pi\) | ||||
−0.200210 | + | 0.979753i | \(0.564162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 79.3770 | 2.75356 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 11.1798i | − 0.387357i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.974874i | − 0.0336966i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0983 | −0.417678 | −0.208839 | − | 0.977950i | \(-0.566968\pi\) | ||||
−0.208839 | + | 0.977950i | \(0.566968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4061 | 0.945038 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 66.2436i | 2.28155i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 41.2215i | − 1.41639i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.9235 | 1.16425 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.02642 | 0.240862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.10103i | − 0.106177i | −0.998590 | − | 0.0530886i | \(-0.983093\pi\) | ||||
0.998590 | − | 0.0530886i | \(-0.0169066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.39457i | 0.150116i | 0.997179 | + | 0.0750578i | \(0.0239141\pi\) | ||||
−0.997179 | + | 0.0750578i | \(0.976086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0453 | 0.991014 | 0.495507 | − | 0.868604i | \(-0.334982\pi\) | ||||
0.495507 | + | 0.868604i | \(0.334982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 54.9362 | 1.87222 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.1020i | 1.36509i | 0.730845 | + | 0.682543i | \(0.239126\pi\) | ||||
−0.730845 | + | 0.682543i | \(0.760874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 39.0086i | − 1.32480i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.35968 | 0.181815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.49518 | 0.118430 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.20620i | 0.0408235i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.7503i | 1.27474i | 0.770559 | + | 0.637368i | \(0.219977\pi\) | ||||
−0.770559 | + | 0.637368i | \(0.780023\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −67.9021 | −2.29028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.1541 | −0.982227 | −0.491113 | − | 0.871096i | \(-0.663410\pi\) | ||||
−0.491113 | + | 0.871096i | \(0.663410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3971i | 1.46043i | 0.683218 | + | 0.730214i | \(0.260580\pi\) | ||||
−0.683218 | + | 0.730214i | \(0.739420\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 25.4091i | − 0.853155i | −0.904451 | − | 0.426578i | \(-0.859719\pi\) | ||||
0.904451 | − | 0.426578i | \(-0.140281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.2373 | −0.611658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.91320 | 0.0975958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.34163i | − 0.0448961i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.64590i | − 0.0883439i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.29735 | 0.109973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.91181 | 0.230266 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 67.5446i | − 2.24774i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00778i | 0.0666672i | 0.999444 | + | 0.0333336i | \(0.0106124\pi\) | ||||
−0.999444 | + | 0.0333336i | \(0.989388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.5952 | 0.616765 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.45792 | −0.280223 | −0.140112 | − | 0.990136i | \(-0.544746\pi\) | ||||
−0.140112 | + | 0.990136i | \(0.544746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 0.712277i | − 0.0235729i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.55402i | 0.249456i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.840028 | −0.0277100 | −0.0138550 | − | 0.999904i | \(-0.504410\pi\) | ||||
−0.0138550 | + | 0.999904i | \(0.504410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5711 | 1.04030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.76675i | 0.0910686i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.0861i | 1.02100i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.7877 | −0.517979 | −0.258989 | − | 0.965880i | \(-0.583389\pi\) | ||||
−0.258989 | + | 0.965880i | \(0.583389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.92481 | −0.128630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 83.2520i | 2.72555i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.6568i | 1.03418i | 0.855930 | + | 0.517091i | \(0.172985\pi\) | ||||
−0.855930 | + | 0.517091i | \(0.827015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2561 | 0.367330 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.3932 | −1.25158 | −0.625792 | − | 0.779990i | \(-0.715224\pi\) | ||||
−0.625792 | + | 0.779990i | \(0.715224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.47041i | 0.178141i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 34.3783i | − 1.11714i | −0.829456 | − | 0.558572i | \(-0.811349\pi\) | ||||
0.829456 | − | 0.558572i | \(-0.188651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.31486 | 0.302373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.4428 | −0.533195 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 48.3782i | − 1.56712i | −0.621314 | − | 0.783562i | \(-0.713401\pi\) | ||||
0.621314 | − | 0.783562i | \(-0.286599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.98456i | − 0.322755i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.6541 | 0.699247 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8072 | −0.993782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.9443i | 1.38386i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 51.3705i | − 1.65196i | −0.563697 | − | 0.825982i | \(-0.690621\pi\) | ||||
0.563697 | − | 0.825982i | \(-0.309379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.92375 | 0.0617999 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.4587 | 1.61930 | 0.809649 | − | 0.586914i | \(-0.199657\pi\) | ||||
0.809649 | + | 0.586914i | \(0.199657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1539i | 0.934633i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1406i | 1.02827i | 0.857710 | + | 0.514134i | \(0.171887\pi\) | ||||
−0.857710 | + | 0.514134i | \(0.828113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.43964 | 0.109931 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 67.7392 | 2.16275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 24.1306i | − 0.769647i | −0.922990 | − | 0.384824i | \(-0.874262\pi\) | ||||
0.922990 | − | 0.384824i | \(-0.125738\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 26.5219i | − 0.844201i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.72592 | 0.213872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1267 | 1.27467 | 0.637333 | − | 0.770588i | \(-0.280038\pi\) | ||||
0.637333 | + | 0.770588i | \(0.280038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.9371i | 0.664418i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 48.9890i | − 1.55150i | −0.631042 | − | 0.775749i | \(-0.717372\pi\) | ||||
0.631042 | − | 0.775749i | \(-0.282628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.6020 | 0.493625 |
(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 | 4600.2.e.w.4049.1 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bd.1.1 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bf.1.5 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.w.4049.10 | 10 | ||
20.3 | even | 4 | 9200.2.a.ct.1.1 | 5 | |||
20.7 | even | 4 | 9200.2.a.cv.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.1 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bf.1.5 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.w.4049.1 | 10 | 1.1 | even | 1 | trivial | ||
4600.2.e.w.4049.10 | 10 | 5.4 | even | 2 | inner | ||
9200.2.a.ct.1.1 | 5 | 20.3 | even | 4 | |||
9200.2.a.cv.1.5 | 5 | 20.7 | even | 4 |