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: | \( x^{10} + 28x^{8} + 260x^{6} + 897x^{4} + 1056x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.6 | ||
Root | \(0.568386i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.u.4049.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.568386i | 0.328158i | 0.986447 | + | 0.164079i | \(0.0524652\pi\) | ||||
−0.986447 | + | 0.164079i | \(0.947535\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73770i | 1.79068i | 0.445381 | + | 0.895341i | \(0.353068\pi\) | ||||
−0.445381 | + | 0.895341i | \(0.646932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.67694 | 0.892312 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.360532 | −0.108704 | −0.0543522 | − | 0.998522i | \(-0.517309\pi\) | ||||
−0.0543522 | + | 0.998522i | \(0.517309\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.26123i | − 1.45920i | −0.683873 | − | 0.729601i | \(-0.739706\pi\) | ||||
0.683873 | − | 0.729601i | \(-0.260294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.370852i | 0.0899449i | 0.998988 | + | 0.0449724i | \(0.0143200\pi\) | ||||
−0.998988 | + | 0.0449724i | \(0.985680\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.60586 | 1.05666 | 0.528328 | − | 0.849040i | \(-0.322819\pi\) | ||||
0.528328 | + | 0.849040i | \(0.322819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.69284 | −0.587626 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.22669i | 0.620977i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.939238 | −0.174412 | −0.0872061 | − | 0.996190i | \(-0.527794\pi\) | ||||
−0.0872061 | + | 0.996190i | \(0.527794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.66662 | 1.73618 | 0.868088 | − | 0.496411i | \(-0.165349\pi\) | ||||
0.868088 | + | 0.496411i | \(0.165349\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.204921i | − 0.0356722i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.26862i | 0.537357i | 0.963230 | + | 0.268679i | \(0.0865869\pi\) | ||||
−0.963230 | + | 0.268679i | \(0.913413\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.99041 | 0.478849 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.29977 | 0.827685 | 0.413843 | − | 0.910348i | \(-0.364186\pi\) | ||||
0.413843 | + | 0.910348i | \(0.364186\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.25491i | − 0.183048i | −0.995803 | − | 0.0915240i | \(-0.970826\pi\) | ||||
0.995803 | − | 0.0915240i | \(-0.0291738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.4458 | −2.20654 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.210787 | −0.0295161 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.9278i | − 1.50106i | −0.660839 | − | 0.750528i | \(-0.729799\pi\) | ||||
0.660839 | − | 0.750528i | \(-0.270201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.61790i | 0.346750i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.66955 | 1.25887 | 0.629434 | − | 0.777054i | \(-0.283287\pi\) | ||||
0.629434 | + | 0.777054i | \(0.283287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.71441 | 1.24380 | 0.621901 | − | 0.783096i | \(-0.286361\pi\) | ||||
0.621901 | + | 0.783096i | \(0.286361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.6825i | 1.59785i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.07001i | − 0.863739i | −0.901936 | − | 0.431870i | \(-0.857854\pi\) | ||||
0.901936 | − | 0.431870i | \(-0.142146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.568386 | −0.0684257 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3747 | 1.34993 | 0.674965 | − | 0.737850i | \(-0.264159\pi\) | ||||
0.674965 | + | 0.737850i | \(0.264159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.745086i | − 0.0872057i | −0.999049 | − | 0.0436029i | \(-0.986116\pi\) | ||||
0.999049 | − | 0.0436029i | \(-0.0138836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.70809i | − 0.194655i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.415709 | −0.0467709 | −0.0233854 | − | 0.999727i | \(-0.507444\pi\) | ||||
−0.0233854 | + | 0.999727i | \(0.507444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.19680 | 0.688534 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.26862i | 1.01736i | 0.860955 | + | 0.508681i | \(0.169867\pi\) | ||||
−0.860955 | + | 0.508681i | \(0.830133\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 0.533850i | − 0.0572347i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6122 | −1.33689 | −0.668444 | − | 0.743763i | \(-0.733039\pi\) | ||||
−0.668444 | + | 0.743763i | \(0.733039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.9261 | 2.61297 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.49437i | 0.569740i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0404i | 1.42559i | 0.701374 | + | 0.712793i | \(0.252570\pi\) | ||||
−0.701374 | + | 0.712793i | \(0.747430\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.965121 | −0.0969983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7440 | −1.26808 | −0.634038 | − | 0.773302i | \(-0.718604\pi\) | ||||
−0.634038 | + | 0.773302i | \(0.718604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.31347i | 0.326486i | 0.986586 | + | 0.163243i | \(0.0521955\pi\) | ||||
−0.986586 | + | 0.163243i | \(0.947805\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.13184i | − 0.786135i | −0.919510 | − | 0.393067i | \(-0.871414\pi\) | ||||
0.919510 | − | 0.393067i | \(-0.128586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.79508 | 0.555068 | 0.277534 | − | 0.960716i | \(-0.410483\pi\) | ||||
0.277534 | + | 0.960716i | \(0.410483\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.85784 | −0.176338 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.60724i | 0.715629i | 0.933793 | + | 0.357815i | \(0.116478\pi\) | ||||
−0.933793 | + | 0.357815i | \(0.883522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 14.0840i | − 1.30206i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.75699 | −0.161063 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8700 | −0.988183 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.01232i | 0.271611i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.13077i | − 0.366547i | −0.983062 | − | 0.183273i | \(-0.941331\pi\) | ||||
0.983062 | − | 0.183273i | \(-0.0586693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7582 | −1.55154 | −0.775770 | − | 0.631016i | \(-0.782638\pi\) | ||||
−0.775770 | + | 0.631016i | \(0.782638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.8212i | 1.89213i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.86954i | 0.586905i | 0.955974 | + | 0.293452i | \(0.0948042\pi\) | ||||
−0.955974 | + | 0.293452i | \(0.905196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.6635 | −1.75266 | −0.876330 | − | 0.481712i | \(-0.840015\pi\) | ||||
−0.876330 | + | 0.481712i | \(0.840015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.713276 | 0.0600686 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.89684i | 0.158622i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 8.77917i | − 0.724094i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4763 | 1.34979 | 0.674896 | − | 0.737912i | \(-0.264188\pi\) | ||||
0.674896 | + | 0.737912i | \(0.264188\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.89224 | −0.723640 | −0.361820 | − | 0.932248i | \(-0.617844\pi\) | ||||
−0.361820 | + | 0.932248i | \(0.617844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.992748i | 0.0802589i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.62249i | − 0.528532i | −0.964450 | − | 0.264266i | \(-0.914870\pi\) | ||||
0.964450 | − | 0.264266i | \(-0.0851297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.21124 | 0.492583 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.73770 | −0.373383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0779i | 1.25932i | 0.776872 | + | 0.629658i | \(0.216805\pi\) | ||||
−0.776872 | + | 0.629658i | \(0.783195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8763i | 1.07378i | 0.843651 | + | 0.536891i | \(0.180402\pi\) | ||||
−0.843651 | + | 0.536891i | \(0.819598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.6805 | −1.12927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.3296 | 0.942867 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.05518i | 0.156252i | 0.996943 | + | 0.0781261i | \(0.0248937\pi\) | ||||
−0.996943 | + | 0.0781261i | \(0.975106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.49604i | 0.413108i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.6478 | −1.31906 | −0.659531 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659531 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.85477 | 0.212193 | 0.106097 | − | 0.994356i | \(-0.466165\pi\) | ||||
0.106097 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.52153i | 0.408164i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.133704i | − 0.00977741i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.2871 | −1.11197 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.13677 | 0.0822540 | 0.0411270 | − | 0.999154i | \(-0.486905\pi\) | ||||
0.0411270 | + | 0.999154i | \(0.486905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.4694i | 1.90531i | 0.304055 | + | 0.952654i | \(0.401659\pi\) | ||||
−0.304055 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.44424i | 0.387886i | 0.981013 | + | 0.193943i | \(0.0621277\pi\) | ||||
−0.981013 | + | 0.193943i | \(0.937872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6122 | 1.31938 | 0.659691 | − | 0.751537i | \(-0.270687\pi\) | ||||
0.659691 | + | 0.751537i | \(0.270687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.01850 | 0.283443 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.44983i | − 0.312317i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.67694i | 0.186060i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.66056 | −0.114863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.10003 | 0.419944 | 0.209972 | − | 0.977707i | \(-0.432663\pi\) | ||||
0.209972 | + | 0.977707i | \(0.432663\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.46523i | 0.442990i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 45.7975i | 3.10894i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.423497 | 0.0286173 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.95114 | 0.131248 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4136i | 1.09913i | 0.835450 | + | 0.549567i | \(0.185207\pi\) | ||||
−0.835450 | + | 0.549567i | \(0.814793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.21171i | 0.0804240i | 0.999191 | + | 0.0402120i | \(0.0128033\pi\) | ||||
−0.999191 | + | 0.0402120i | \(0.987197\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.8293 | 1.50860 | 0.754300 | − | 0.656529i | \(-0.227976\pi\) | ||||
0.754300 | + | 0.656529i | \(0.227976\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.970856 | 0.0638776 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 21.9420i | − 1.43747i | −0.695284 | − | 0.718735i | \(-0.744722\pi\) | ||||
0.695284 | − | 0.718735i | \(-0.255278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.236283i | − 0.0153482i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.58274 | 0.555172 | 0.277586 | − | 0.960701i | \(-0.410466\pi\) | ||||
0.277586 | + | 0.960701i | \(0.410466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3857 | 0.991079 | 0.495540 | − | 0.868585i | \(-0.334970\pi\) | ||||
0.495540 | + | 0.868585i | \(0.334970\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.2023i | 0.846925i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 24.2325i | − 1.54187i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.26815 | −0.333856 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.85477 | −0.558908 | −0.279454 | − | 0.960159i | \(-0.590153\pi\) | ||||
−0.279454 | + | 0.960159i | \(0.590153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.360532i | − 0.0226664i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.6008i | − 1.40980i | −0.709308 | − | 0.704899i | \(-0.750992\pi\) | ||||
0.709308 | − | 0.704899i | \(-0.249008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.4857 | −0.962236 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.51428 | −0.155630 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.73590i | 0.477016i | 0.971141 | + | 0.238508i | \(0.0766583\pi\) | ||||
−0.971141 | + | 0.238508i | \(0.923342\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.16858i | − 0.438710i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.87154 | 0.236052 | 0.118026 | − | 0.993011i | \(-0.462343\pi\) | ||||
0.118026 | + | 0.993011i | \(0.462343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.24705 | 0.257990 | 0.128995 | − | 0.991645i | \(-0.458825\pi\) | ||||
0.128995 | + | 0.991645i | \(0.458825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1677i | 0.857466i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7.26754i | − 0.436664i | −0.975875 | − | 0.218332i | \(-0.929938\pi\) | ||||
0.975875 | − | 0.218332i | \(-0.0700616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.8769 | 1.54921 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0131 | −0.776297 | −0.388148 | − | 0.921597i | \(-0.626885\pi\) | ||||
−0.388148 | + | 0.921597i | \(0.626885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.8342i | − 1.06013i | −0.847956 | − | 0.530067i | \(-0.822167\pi\) | ||||
0.847956 | − | 0.530067i | \(-0.177833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.1087i | 1.48212i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8625 | 0.991910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.98037 | −0.467818 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.32291i | − 0.427809i | −0.976855 | − | 0.213905i | \(-0.931382\pi\) | ||||
0.976855 | − | 0.213905i | \(-0.0686182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1.16333i | − 0.0675030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.26123 | 0.304265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 7.24352i | − 0.416129i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 29.1127i | − 1.66155i | −0.556608 | − | 0.830775i | \(-0.687897\pi\) | ||||
0.556608 | − | 0.830775i | \(-0.312103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.88333 | −0.107139 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.458912 | 0.0260225 | 0.0130113 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130113 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.8279i | 1.00769i | 0.863794 | + | 0.503846i | \(0.168082\pi\) | ||||
−0.863794 | + | 0.503846i | \(0.831918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8799i | 1.34123i | 0.741807 | + | 0.670614i | \(0.233969\pi\) | ||||
−0.741807 | + | 0.670614i | \(0.766031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.338625 | 0.0189594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.62203 | 0.257976 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.70809i | 0.0950407i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.29384i | 0.182150i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.94540 | 0.327781 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0214 | 1.65013 | 0.825063 | − | 0.565041i | \(-0.191140\pi\) | ||||
0.825063 | + | 0.565041i | \(0.191140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.74988i | 0.479490i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.9440i | 0.650631i | 0.945605 | + | 0.325316i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325316i | \(0.894529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.32385 | −0.234839 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.48512 | −0.188730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 40.0136i | − 2.16053i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 0.873132i | − 0.0468722i | −0.999725 | − | 0.0234361i | \(-0.992539\pi\) | ||||
0.999725 | − | 0.0234361i | \(-0.00746062\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.8868 | 1.01099 | 0.505493 | − | 0.862831i | \(-0.331311\pi\) | ||||
0.505493 | + | 0.862831i | \(0.331311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.9764 | 0.906131 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.43875i | 0.289475i | 0.989470 | + | 0.144738i | \(0.0462338\pi\) | ||||
−0.989470 | + | 0.144738i | \(0.953766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.998646i | − 0.0528540i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4229 | 1.23622 | 0.618108 | − | 0.786093i | \(-0.287899\pi\) | ||||
0.618108 | + | 0.786093i | \(0.287899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.21390 | 0.116521 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6.17837i | − 0.324280i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2014i | 1.41990i | 0.704252 | + | 0.709951i | \(0.251283\pi\) | ||||
−0.704252 | + | 0.709951i | \(0.748717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.1872 | 0.738554 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 51.7728 | 2.68791 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.0431i | − 1.03779i | −0.854837 | − | 0.518897i | \(-0.826343\pi\) | ||||
0.854837 | − | 0.518897i | \(-0.173657\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.94155i | 0.254503i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8364 | 0.659362 | 0.329681 | − | 0.944092i | \(-0.393059\pi\) | ||||
0.329681 | + | 0.944092i | \(0.393059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.34787 | 0.120285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.5405i | 1.56055i | 0.625439 | + | 0.780273i | \(0.284920\pi\) | ||||
−0.625439 | + | 0.780273i | \(0.715080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.3392 | −1.63966 | −0.819831 | − | 0.572605i | \(-0.805933\pi\) | ||||
−0.819831 | + | 0.572605i | \(0.805933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.370852 | −0.0187548 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 10.0935i | − 0.509150i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.9147i | 1.45119i | 0.688123 | + | 0.725594i | \(0.258435\pi\) | ||||
−0.688123 | + | 0.725594i | \(0.741565\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.4028 | −0.620919 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2862 | 1.21279 | 0.606397 | − | 0.795162i | \(-0.292614\pi\) | ||||
0.606397 | + | 0.795162i | \(0.292614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 50.8583i | − 2.53343i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.17844i | − 0.0584131i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8371 | −1.57424 | −0.787122 | − | 0.616797i | \(-0.788430\pi\) | ||||
−0.787122 | + | 0.616797i | \(0.788430\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.90455 | −0.192597 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.8114i | 2.25423i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 11.7449i | − 0.575149i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.4880 | 1.04976 | 0.524879 | − | 0.851177i | \(-0.324110\pi\) | ||||
0.524879 | + | 0.851177i | \(0.324110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2930 | −0.647859 | −0.323930 | − | 0.946081i | \(-0.605004\pi\) | ||||
−0.323930 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3.35933i | − 0.163336i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.0239i | 2.22725i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.07814 | −0.0520530 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.534460 | −0.0257440 | −0.0128720 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128720 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 16.3377i | − 0.785140i | −0.919722 | − | 0.392570i | \(-0.871586\pi\) | ||||
0.919722 | − | 0.392570i | \(-0.128414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.60586i | 0.220328i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.7573 | −1.37251 | −0.686255 | − | 0.727361i | \(-0.740746\pi\) | ||||
−0.686255 | + | 0.727361i | \(0.740746\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.3474 | −1.96892 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6542i | 0.743751i | 0.928283 | + | 0.371876i | \(0.121285\pi\) | ||||
−0.928283 | + | 0.371876i | \(0.878715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.36491i | 0.442945i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4302 | −1.81363 | −0.906817 | − | 0.421525i | \(-0.861495\pi\) | ||||
−0.906817 | + | 0.421525i | \(0.861495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.91074 | −0.0899730 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 5.05422i | − 0.237468i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 37.2199i | − 1.74107i | −0.492104 | − | 0.870536i | \(-0.663772\pi\) | ||||
0.492104 | − | 0.870536i | \(-0.336228\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.19663 | −0.0558537 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.25491 | −0.151596 | −0.0757982 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757982 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 29.9534i | − 1.39205i | −0.718016 | − | 0.696027i | \(-0.754950\pi\) | ||||
0.718016 | − | 0.696027i | \(-0.245050\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 39.3302i | − 1.81999i | −0.414623 | − | 0.909993i | \(-0.636087\pi\) | ||||
0.414623 | − | 0.909993i | \(-0.363913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.4956 | 1.54668 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.76413 | 0.173442 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 29.2532i | − 1.33941i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.18660 | −0.374055 | −0.187028 | − | 0.982355i | \(-0.559885\pi\) | ||||
−0.187028 | + | 0.982355i | \(0.559885\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.1969 | 0.784113 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.69284i | − 0.122529i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 31.9963i | − 1.44989i | −0.688806 | − | 0.724946i | \(-0.741865\pi\) | ||||
0.688806 | − | 0.724946i | \(-0.258135\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.13844 | −0.413255 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.12584 | −0.321585 | −0.160792 | − | 0.986988i | \(-0.551405\pi\) | ||||
−0.160792 | + | 0.986988i | \(0.551405\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.348319i | − 0.0156875i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 53.8899i | 2.41729i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.4219 | −1.04851 | −0.524254 | − | 0.851562i | \(-0.675656\pi\) | ||||
−0.524254 | + | 0.851562i | \(0.675656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.88711 | −0.352370 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.94170i | 0.175752i | 0.996131 | + | 0.0878758i | \(0.0280079\pi\) | ||||
−0.996131 | + | 0.0878758i | \(0.971992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 8.34421i | − 0.370579i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.5237 | −1.70753 | −0.853766 | − | 0.520656i | \(-0.825687\pi\) | ||||
−0.853766 | + | 0.520656i | \(0.825687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52999 | 0.156158 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.8617i | 0.656159i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.452436i | 0.0198981i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.16813 | −0.0512754 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.2428 | −1.71926 | −0.859630 | − | 0.510917i | \(-0.829306\pi\) | ||||
−0.859630 | + | 0.510917i | \(0.829306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.0190i | 1.70618i | 0.521763 | + | 0.853090i | \(0.325274\pi\) | ||||
−0.521763 | + | 0.853090i | \(0.674726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.58489i | 0.156160i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.8848 | 1.12330 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 27.8833i | − 1.20776i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 10.0308i | − 0.432860i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.56870 | 0.239861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.54061 | 0.109230 | 0.0546148 | − | 0.998508i | \(-0.482607\pi\) | ||||
0.0546148 | + | 0.998508i | \(0.482607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.62261i | 0.0696329i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.78776i | 0.290224i | 0.989415 | + | 0.145112i | \(0.0463542\pi\) | ||||
−0.989415 | + | 0.145112i | \(0.953646\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.0049 | 1.10986 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.32600 | −0.184294 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.96950i | − 0.0837517i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 24.7086i | − 1.04694i | −0.852045 | − | 0.523468i | \(-0.824638\pi\) | ||||
0.852045 | − | 0.523468i | \(-0.175362\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0759955 | 0.00320853 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.1423i | 1.18606i | 0.805181 | + | 0.593029i | \(0.202068\pi\) | ||||
−0.805181 | + | 0.593029i | \(0.797932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.3586i | 1.23294i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.1938 | −1.72694 | −0.863468 | − | 0.504404i | \(-0.831712\pi\) | ||||
−0.863468 | + | 0.504404i | \(0.831712\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4687 | 1.35877 | 0.679387 | − | 0.733780i | \(-0.262246\pi\) | ||||
0.679387 | + | 0.733780i | \(0.262246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.646126i | 0.0269923i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.61770i | 0.275498i | 0.990467 | + | 0.137749i | \(0.0439868\pi\) | ||||
−0.990467 | + | 0.137749i | \(0.956013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.0448 | −0.625242 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.9119 | −1.82177 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.93984i | 0.163171i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 8.18008i | − 0.337628i | −0.985648 | − | 0.168814i | \(-0.946006\pi\) | ||||
0.985648 | − | 0.168814i | \(-0.0539937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.5230 | 1.83454 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.09443 | −0.127288 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.7489i | − 1.22164i | −0.791768 | − | 0.610821i | \(-0.790839\pi\) | ||||
0.791768 | − | 0.610821i | \(-0.209161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.5789i | 0.432966i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.4069 | −1.61012 | −0.805061 | − | 0.593192i | \(-0.797868\pi\) | ||||
−0.805061 | + | 0.593192i | \(0.797868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.3183 | −1.39987 | −0.699937 | − | 0.714205i | \(-0.746788\pi\) | ||||
−0.699937 | + | 0.714205i | \(0.746788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.9260i | − 0.770725i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 11.7570i | − 0.477200i | −0.971118 | − | 0.238600i | \(-0.923312\pi\) | ||||
0.971118 | − | 0.238600i | \(-0.0766885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.52922 | 0.102489 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.60239 | −0.267104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.86862i | − 0.237031i | −0.992952 | − | 0.118516i | \(-0.962186\pi\) | ||||
0.992952 | − | 0.118516i | \(-0.0378136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.45842i | − 0.340523i | −0.985399 | − | 0.170262i | \(-0.945539\pi\) | ||||
0.985399 | − | 0.170262i | \(-0.0544613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.851047 | −0.0342065 | −0.0171032 | − | 0.999854i | \(-0.505444\pi\) | ||||
−0.0171032 | + | 0.999854i | \(0.505444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.22669 | −0.129483 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 59.7527i | − 2.39394i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.943838i | − 0.0376933i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.21217 | −0.0483325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7131 | 0.784768 | 0.392384 | − | 0.919802i | \(-0.371650\pi\) | ||||
0.392384 | + | 0.919802i | \(0.371650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.46717i | 0.137808i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 81.2638i | 3.21979i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.4494 | 1.20456 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.3593 | −1.35711 | −0.678555 | − | 0.734550i | \(-0.737393\pi\) | ||||
−0.678555 | + | 0.734550i | \(0.737393\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2817i | 0.957578i | 0.877930 | + | 0.478789i | \(0.158924\pi\) | ||||
−0.877930 | + | 0.478789i | \(0.841076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 30.1465i | − 1.18518i | −0.805504 | − | 0.592590i | \(-0.798105\pi\) | ||||
0.805504 | − | 0.592590i | \(-0.201895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.48618 | −0.136845 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.0307 | −1.02022 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.17298i | 0.280700i | 0.990102 | + | 0.140350i | \(0.0448228\pi\) | ||||
−0.990102 | + | 0.140350i | \(0.955177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 1.99455i | − 0.0778148i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.8521 | 0.500645 | 0.250323 | − | 0.968162i | \(-0.419463\pi\) | ||||
0.250323 | + | 0.968162i | \(0.419463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.72426 | 0.144857 | 0.0724285 | − | 0.997374i | \(-0.476925\pi\) | ||||
0.0724285 | + | 0.997374i | \(0.476925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.10900i | 0.0430700i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.939238i | − 0.0363675i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.32924 | −0.360689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.50235 | −0.135207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 13.5204i | − 0.521175i | −0.965450 | − | 0.260587i | \(-0.916084\pi\) | ||||
0.965450 | − | 0.260587i | \(-0.0839162\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 17.8534i | − 0.686161i | −0.939306 | − | 0.343081i | \(-0.888530\pi\) | ||||
0.939306 | − | 0.343081i | \(-0.111470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −66.5192 | −2.55277 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.688719 | −0.0263918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 15.8200i | − 0.605337i | −0.953096 | − | 0.302669i | \(-0.902122\pi\) | ||||
0.953096 | − | 0.302669i | \(-0.0978776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.9758i | 0.495059i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.4939 | −2.19034 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.45476 | 0.359676 | 0.179838 | − | 0.983696i | \(-0.442443\pi\) | ||||
0.179838 | + | 0.983696i | \(0.442443\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4.57245i | − 0.173693i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.96543i | 0.0744460i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.4715 | 0.471717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.0096 | 1.09568 | 0.547838 | − | 0.836584i | \(-0.315451\pi\) | ||||
0.547838 | + | 0.836584i | \(0.315451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0548i | 0.567801i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 60.3773i | − 2.27072i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.22423 | 0.308868 | 0.154434 | − | 0.988003i | \(-0.450645\pi\) | ||||
0.154434 | + | 0.988003i | \(0.450645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.11283 | −0.0417342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.66662i | 0.362018i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.87831i | 0.182184i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5468 | 0.467917 | 0.233958 | − | 0.972247i | \(-0.424832\pi\) | ||||
0.233958 | + | 0.972247i | \(0.424832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6982 | −0.584633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.74501i | 0.325230i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 29.1952i | − 1.08279i | −0.840768 | − | 0.541395i | \(-0.817896\pi\) | ||||
0.840768 | − | 0.541395i | \(-0.182104\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.0864 | 0.410609 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.0414i | 1.33122i | 0.746299 | + | 0.665611i | \(0.231829\pi\) | ||||
−0.746299 | + | 0.665611i | \(0.768171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.54896i | 0.0938923i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.728002 | −0.0267800 | −0.0133900 | − | 0.999910i | \(-0.504262\pi\) | ||||
−0.0133900 | + | 0.999910i | \(0.504262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7734 | 0.505978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.8880i | 1.20655i | 0.797535 | + | 0.603273i | \(0.206137\pi\) | ||||
−0.797535 | + | 0.603273i | \(0.793863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.8115i | 0.907805i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.5262 | 1.40772 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3337 | 0.523044 | 0.261522 | − | 0.965197i | \(-0.415776\pi\) | ||||
0.261522 | + | 0.965197i | \(0.415776\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 5.03293i | − 0.183410i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.0587519i | − 0.00213537i | −0.999999 | − | 0.00106769i | \(-0.999660\pi\) | ||||
0.999999 | − | 0.00106769i | \(-0.000339855\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.204921 | 0.00743817 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.7135 | 1.65711 | 0.828556 | − | 0.559906i | \(-0.189163\pi\) | ||||
0.828556 | + | 0.559906i | \(0.189163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.4553i | 0.993950i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 50.8737i | − 1.83694i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.3949 | 1.42061 | 0.710307 | − | 0.703892i | \(-0.248556\pi\) | ||||
0.710307 | + | 0.703892i | \(0.248556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8460 | 0.462636 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 21.1799i | − 0.761788i | −0.924619 | − | 0.380894i | \(-0.875616\pi\) | ||||
0.924619 | − | 0.380894i | \(-0.124384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 8.80187i | − 0.315765i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.4100 | 0.874578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.10094 | −0.146743 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.03063i | − 0.108306i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5154i | 0.766941i | 0.923553 | + | 0.383470i | \(0.125271\pi\) | ||||
−0.923553 | + | 0.383470i | \(0.874729\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.39698 | −0.156537 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0408 | −1.28146 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 51.1097i | − 1.81496i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 54.7227i | − 1.93838i | −0.246320 | − | 0.969189i | \(-0.579221\pi\) | ||||
0.246320 | − | 0.969189i | \(-0.420779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.465388 | 0.0164642 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.7620 | −1.19292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.268627i | 0.00947965i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.20053i | 0.0774623i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.5554 | 1.53133 | 0.765663 | − | 0.643242i | \(-0.222411\pi\) | ||||
0.765663 | + | 0.643242i | \(0.222411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1837 | −0.462944 | −0.231472 | − | 0.972842i | \(-0.574354\pi\) | ||||
−0.231472 | + | 0.972842i | \(0.574354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.41397i | 0.0846615i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 66.7256 | 2.33158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.63328 | −0.126803 | −0.0634013 | − | 0.997988i | \(-0.520195\pi\) | ||||
−0.0634013 | + | 0.997988i | \(0.520195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.5044i | 1.37704i | 0.725220 | + | 0.688518i | \(0.241738\pi\) | ||||
−0.725220 | + | 0.688518i | \(0.758262\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.3819i | 1.68240i | 0.540721 | + | 0.841202i | \(0.318152\pi\) | ||||
−0.540721 | + | 0.841202i | \(0.681848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.5864 | 1.54855 | 0.774275 | − | 0.632850i | \(-0.218115\pi\) | ||||
0.774275 | + | 0.632850i | \(0.218115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.13077 | 0.143295 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.72810i | − 0.198467i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.1912i | 1.07813i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.2324 | 1.00921 | 0.504606 | − | 0.863350i | \(-0.331638\pi\) | ||||
0.504606 | + | 0.863350i | \(0.331638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1178 | −0.969580 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7.39647i | − 0.254748i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 51.4989i | − 1.76952i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.1367 | 0.347891 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.26862 | −0.112047 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 50.5599i | − 1.73114i | −0.500790 | − | 0.865569i | \(-0.666957\pi\) | ||||
0.500790 | − | 0.865569i | \(-0.333043\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.9568i | − 0.750030i | −0.927019 | − | 0.375015i | \(-0.877638\pi\) | ||||
0.927019 | − | 0.375015i | \(-0.122362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7671 | −0.469726 | −0.234863 | − | 0.972029i | \(-0.575464\pi\) | ||||
−0.234863 | + | 0.972029i | \(0.575464\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.2714 | −0.486370 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5748i | 0.904618i | 0.891861 | + | 0.452309i | \(0.149400\pi\) | ||||
−0.891861 | + | 0.452309i | \(0.850600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.58439i | 0.325503i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.149876 | 0.00508420 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.1969 | −1.26037 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.5853i | 1.27207i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.9414i | 1.55133i | 0.631145 | + | 0.775665i | \(0.282585\pi\) | ||||
−0.631145 | + | 0.775665i | \(0.717415\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.16224 | 0.140389 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.9054 | −0.805392 | −0.402696 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402696 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52.4002i | − 1.76341i | −0.471804 | − | 0.881703i | \(-0.656397\pi\) | ||||
0.471804 | − | 0.881703i | \(-0.343603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 32.7608i | − 1.10000i | −0.835165 | − | 0.550000i | \(-0.814628\pi\) | ||||
0.835165 | − | 0.550000i | \(-0.185372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.5703 | 0.656368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.23415 | −0.0748467 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.77995i | − 0.193419i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.99041i | 0.0998469i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.07926 | −0.302810 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.05262 | 0.135012 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.9426i | 0.695388i | 0.937608 | + | 0.347694i | \(0.113035\pi\) | ||||
−0.937608 | + | 0.347694i | \(0.886965\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.1149 | −1.13152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6418 | 1.34652 | 0.673262 | − | 0.739404i | \(-0.264893\pi\) | ||||
0.673262 | + | 0.739404i | \(0.264893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3.34163i | − 0.110592i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 84.1330i | − 2.77831i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.3241 | 1.66004 | 0.830019 | − | 0.557735i | \(-0.188330\pi\) | ||||
0.830019 | + | 0.557735i | \(0.188330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.5473 | 0.545251 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 59.8449i | − 1.96982i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.86996i | 0.291328i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.1954 | −0.793825 | −0.396912 | − | 0.917856i | \(-0.629918\pi\) | ||||
−0.396912 | + | 0.917856i | \(0.629918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.1411 | −2.33155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.260839i | 0.00853949i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 37.2988i | − 1.21850i | −0.792978 | − | 0.609250i | \(-0.791471\pi\) | ||||
0.792978 | − | 0.609250i | \(-0.208529\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.1331 | −0.330682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6467 | 0.542667 | 0.271334 | − | 0.962485i | \(-0.412535\pi\) | ||||
0.271334 | + | 0.962485i | \(0.412535\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.29977i | 0.172584i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 30.1868i | − 0.980938i | −0.871459 | − | 0.490469i | \(-0.836825\pi\) | ||||
0.871459 | − | 0.490469i | \(-0.163175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.92007 | −0.127251 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.5730 | −0.440134 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 34.6992i | − 1.12402i | −0.827132 | − | 0.562008i | \(-0.810029\pi\) | ||||
0.827132 | − | 0.562008i | \(-0.189971\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.192470i | 0.00622167i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.5458 | −1.05096 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.4435 | 2.01431 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 21.7684i | − 0.701478i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 11.4788i | − 0.369133i | −0.982820 | − | 0.184566i | \(-0.940912\pi\) | ||||
0.982820 | − | 0.184566i | \(-0.0590881\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.970856 | −0.0311884 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.8441 | −1.50330 | −0.751650 | − | 0.659563i | \(-0.770742\pi\) | ||||
−0.751650 | + | 0.659563i | \(0.770742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 97.8977i | − 3.13846i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.3737i | 1.25968i | 0.776727 | + | 0.629838i | \(0.216879\pi\) | ||||
−0.776727 | + | 0.629838i | \(0.783121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.54709 | 0.145326 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5131 | 0.495294 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 42.3505i | − 1.35077i | −0.737465 | − | 0.675385i | \(-0.763977\pi\) | ||||
0.737465 | − | 0.675385i | \(-0.236023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.37929i | 0.107564i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00104 | −0.0635652 | −0.0317826 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317826 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0638i | 0.541502i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.97936i | 0.0626869i | 0.999509 | + | 0.0313435i | \(0.00997857\pi\) | ||||
−0.999509 | + | 0.0313435i | \(0.990021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.5468 | −0.333687 |
(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.u.4049.6 | 10 | ||
5.2 | odd | 4 | 4600.2.a.be.1.3 | 5 | |||
5.3 | odd | 4 | 920.2.a.j.1.3 | ✓ | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.u.4049.5 | 10 | ||
15.8 | even | 4 | 8280.2.a.bs.1.5 | 5 | |||
20.3 | even | 4 | 1840.2.a.v.1.3 | 5 | |||
20.7 | even | 4 | 9200.2.a.cu.1.3 | 5 | |||
40.3 | even | 4 | 7360.2.a.cp.1.3 | 5 | |||
40.13 | odd | 4 | 7360.2.a.co.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.j.1.3 | ✓ | 5 | 5.3 | odd | 4 | ||
1840.2.a.v.1.3 | 5 | 20.3 | even | 4 | |||
4600.2.a.be.1.3 | 5 | 5.2 | odd | 4 | |||
4600.2.e.u.4049.5 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.u.4049.6 | 10 | 1.1 | even | 1 | trivial | ||
7360.2.a.co.1.3 | 5 | 40.13 | odd | 4 | |||
7360.2.a.cp.1.3 | 5 | 40.3 | even | 4 | |||
8280.2.a.bs.1.5 | 5 | 15.8 | even | 4 | |||
9200.2.a.cu.1.3 | 5 | 20.7 | even | 4 |