Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9421813736\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 15x^{6} + 56x^{5} + 87x^{4} - 248x^{3} - 241x^{2} + 340x + 248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.94482\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.94482 | −0.869752 | −0.434876 | − | 0.900490i | \(-0.643208\pi\) | ||||
−0.434876 | + | 0.900490i | \(0.643208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.969069 | −0.366274 | −0.183137 | − | 0.983087i | \(-0.558625\pi\) | ||||
−0.183137 | + | 0.983087i | \(0.558625\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.202183 | 0.0609604 | 0.0304802 | − | 0.999535i | \(-0.490296\pi\) | ||||
0.0304802 | + | 0.999535i | \(0.490296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.56979 | −1.54478 | −0.772391 | − | 0.635147i | \(-0.780939\pi\) | ||||
−0.772391 | + | 0.635147i | \(0.780939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.01217 | 0.730558 | 0.365279 | − | 0.930898i | \(-0.380974\pi\) | ||||
0.365279 | + | 0.930898i | \(0.380974\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.09105 | 1.27007 | 0.635036 | − | 0.772483i | \(-0.280985\pi\) | ||||
0.635036 | + | 0.772483i | \(0.280985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.21766 | −0.243531 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.46811 | −1.20110 | −0.600549 | − | 0.799588i | \(-0.705051\pi\) | ||||
−0.600549 | + | 0.799588i | \(0.705051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83369 | −1.04776 | −0.523881 | − | 0.851791i | \(-0.675516\pi\) | ||||
−0.523881 | + | 0.851791i | \(0.675516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.88467 | 0.318567 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.65467 | 1.42282 | 0.711410 | − | 0.702777i | \(-0.248057\pi\) | ||||
0.711410 | + | 0.702777i | \(0.248057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.53148 | −1.17622 | −0.588110 | − | 0.808781i | \(-0.700128\pi\) | ||||
−0.588110 | + | 0.808781i | \(0.700128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.75737 | 0.420495 | 0.210247 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210247 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.83447 | 0.869752 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.67933 | −0.828416 | −0.414208 | − | 0.910182i | \(-0.635941\pi\) | ||||
−0.414208 | + | 0.910182i | \(0.635941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.06091 | −0.865844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1865 | −1.67395 | −0.836975 | − | 0.547241i | \(-0.815678\pi\) | ||||
−0.836975 | + | 0.547241i | \(0.815678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.393210 | −0.0530204 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5931 | −1.37910 | −0.689551 | − | 0.724237i | \(-0.742192\pi\) | ||||
−0.689551 | + | 0.724237i | \(0.742192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.88233 | 0.241007 | 0.120504 | − | 0.992713i | \(-0.461549\pi\) | ||||
0.120504 | + | 0.992713i | \(0.461549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.90721 | 0.366274 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.8323 | 1.34358 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.95699 | 1.09427 | 0.547135 | − | 0.837044i | \(-0.315718\pi\) | ||||
0.547135 | + | 0.837044i | \(0.315718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.27497 | 0.626024 | 0.313012 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313012 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.05092 | −1.05933 | −0.529665 | − | 0.848207i | \(-0.677682\pi\) | ||||
−0.529665 | + | 0.848207i | \(0.677682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.195929 | −0.0223282 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.23359 | 0.464697 | 0.232348 | − | 0.972633i | \(-0.425359\pi\) | ||||
0.232348 | + | 0.972633i | \(0.425359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.85814 | −0.635404 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.91293 | −0.838768 | −0.419384 | − | 0.907809i | \(-0.637754\pi\) | ||||
−0.419384 | + | 0.907809i | \(0.637754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.39751 | 0.565813 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.94482 | −0.199535 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3246 | −1.25138 | −0.625689 | − | 0.780073i | \(-0.715182\pi\) | ||||
−0.625689 | + | 0.780073i | \(0.715182\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.606548 | −0.0609604 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.68432 | 0.665115 | 0.332557 | − | 0.943083i | \(-0.392089\pi\) | ||||
0.332557 | + | 0.943083i | \(0.392089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1474 | 1.49251 | 0.746257 | − | 0.665658i | \(-0.231849\pi\) | ||||
0.746257 | + | 0.665658i | \(0.231849\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2790 | 1.28373 | 0.641866 | − | 0.766817i | \(-0.278161\pi\) | ||||
0.641866 | + | 0.766817i | \(0.278161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.19533 | 0.306057 | 0.153029 | − | 0.988222i | \(-0.451097\pi\) | ||||
0.153029 | + | 0.988222i | \(0.451097\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.6953 | 1.85277 | 0.926387 | − | 0.376573i | \(-0.122898\pi\) | ||||
0.926387 | + | 0.376573i | \(0.122898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.8460 | −1.10465 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7094 | 1.54478 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.91900 | −0.267584 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9591 | −0.996284 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0923 | 1.08156 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7327 | 1.83973 | 0.919863 | − | 0.392240i | \(-0.128300\pi\) | ||||
0.919863 | + | 0.392240i | \(0.128300\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.19154 | 0.366217 | 0.183108 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183108 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.969069 | −0.0840289 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.02851 | 0.515051 | 0.257525 | − | 0.966272i | \(-0.417093\pi\) | ||||
0.257525 | + | 0.966272i | \(0.417093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.9788 | −1.35531 | −0.677654 | − | 0.735381i | \(-0.737003\pi\) | ||||
−0.677654 | + | 0.735381i | \(0.737003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.12612 | −0.0941705 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5793 | 1.04466 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.01337 | 0.574558 | 0.287279 | − | 0.957847i | \(-0.407249\pi\) | ||||
0.287279 | + | 0.957847i | \(0.407249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7433 | 1.19979 | 0.599895 | − | 0.800079i | \(-0.295209\pi\) | ||||
0.599895 | + | 0.800079i | \(0.295209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.03650 | −0.730558 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.3455 | 0.911293 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.06136 | −0.563557 | −0.281779 | − | 0.959479i | \(-0.590924\pi\) | ||||
−0.281779 | + | 0.959479i | \(0.590924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.90265 | −0.465194 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3905 | 0.970497 | 0.485248 | − | 0.874376i | \(-0.338729\pi\) | ||||
0.485248 | + | 0.874376i | \(0.338729\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8319 | 1.84417 | 0.922084 | − | 0.386990i | \(-0.126485\pi\) | ||||
0.922084 | + | 0.386990i | \(0.126485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.0226 | 1.38635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0368 | −0.763084 | −0.381542 | − | 0.924352i | \(-0.624607\pi\) | ||||
−0.381542 | + | 0.924352i | \(0.624607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.17999 | 0.0891991 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.48749 | −0.410155 | −0.205077 | − | 0.978746i | \(-0.565745\pi\) | ||||
−0.205077 | + | 0.978746i | \(0.565745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2243 | 0.908625 | 0.454312 | − | 0.890842i | \(-0.349885\pi\) | ||||
0.454312 | + | 0.890842i | \(0.349885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.8318 | −1.23750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.609008 | 0.0445351 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.55204 | 0.546447 | 0.273223 | − | 0.961951i | \(-0.411910\pi\) | ||||
0.273223 | + | 0.961951i | \(0.411910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6413 | 1.34183 | 0.670914 | − | 0.741535i | \(-0.265902\pi\) | ||||
0.670914 | + | 0.741535i | \(0.265902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1324 | −1.00689 | −0.503445 | − | 0.864027i | \(-0.667934\pi\) | ||||
−0.503445 | + | 0.864027i | \(0.667934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9218 | −0.916001 | −0.458000 | − | 0.888952i | \(-0.651434\pi\) | ||||
−0.458000 | + | 0.888952i | \(0.651434\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.26804 | 0.439931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.6474 | 1.02302 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.2732 | −1.27007 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.202183 | 0.0139853 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4115 | 0.854444 | 0.427222 | − | 0.904147i | \(-0.359492\pi\) | ||||
0.427222 | + | 0.904147i | \(0.359492\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.36260 | −0.365726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.65325 | 0.383768 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.7771 | −1.12855 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.3449 | 1.56329 | 0.781645 | − | 0.623723i | \(-0.214381\pi\) | ||||
0.781645 | + | 0.623723i | \(0.214381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.65297 | 0.243531 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.73366 | −0.646046 | −0.323023 | − | 0.946391i | \(-0.604699\pi\) | ||||
−0.323023 | + | 0.946391i | \(0.604699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9689 | 1.12133 | 0.560667 | − | 0.828041i | \(-0.310545\pi\) | ||||
0.560667 | + | 0.828041i | \(0.310545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.09564 | −0.530363 | −0.265181 | − | 0.964199i | \(-0.585432\pi\) | ||||
−0.265181 | + | 0.964199i | \(0.585432\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0453 | 0.720517 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.56166 | 0.618492 | 0.309246 | − | 0.950982i | \(-0.399923\pi\) | ||||
0.309246 | + | 0.950982i | \(0.399923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8100 | 0.889582 | 0.444791 | − | 0.895634i | \(-0.353278\pi\) | ||||
0.444791 | + | 0.895634i | \(0.353278\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7874 | 0.753069 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.56979 | −0.354397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.14231 | 0.261461 | 0.130730 | − | 0.991418i | \(-0.458268\pi\) | ||||
0.130730 | + | 0.991418i | \(0.458268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.23150 | 0.0774240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.39737 | −0.274301 | −0.137150 | − | 0.990550i | \(-0.543794\pi\) | ||||
−0.137150 | + | 0.990550i | \(0.543794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.38698 | −0.521141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.4043 | 1.20110 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0955 | −0.745842 | −0.372921 | − | 0.927863i | \(-0.621644\pi\) | ||||
−0.372921 | + | 0.927863i | \(0.621644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.7007 | 1.45592 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.368422 | −0.0224631 | −0.0112315 | − | 0.999937i | \(-0.503575\pi\) | ||||
−0.0112315 | + | 0.999937i | \(0.503575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3494 | −1.11465 | −0.557324 | − | 0.830295i | \(-0.688172\pi\) | ||||
−0.557324 | + | 0.830295i | \(0.688172\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.246189 | −0.0148458 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.7165 | 1.96574 | 0.982871 | − | 0.184293i | \(-0.0589995\pi\) | ||||
0.982871 | + | 0.184293i | \(0.0589995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.5011 | 1.04776 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.9586 | −0.832703 | −0.416351 | − | 0.909204i | \(-0.636691\pi\) | ||||
−0.416351 | + | 0.909204i | \(0.636691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.7577 | −1.35281 | −0.676404 | − | 0.736531i | \(-0.736463\pi\) | ||||
−0.676404 | + | 0.736531i | \(0.736463\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.29852 | 0.430818 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.92685 | −0.466285 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6839 | 1.14995 | 0.574973 | − | 0.818172i | \(-0.305012\pi\) | ||||
0.574973 | + | 0.818172i | \(0.305012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.6017 | 1.19948 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.9259 | −1.96198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.67208 | −0.154016 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.66079 | −0.209616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1331 | −1.14906 | −0.574528 | − | 0.818485i | \(-0.694815\pi\) | ||||
−0.574528 | + | 0.818485i | \(0.694815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7448 | −0.722689 | −0.361344 | − | 0.932432i | \(-0.617682\pi\) | ||||
−0.361344 | + | 0.932432i | \(0.617682\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0674 | −0.625568 | −0.312784 | − | 0.949824i | \(-0.601262\pi\) | ||||
−0.312784 | + | 0.949824i | \(0.601262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.65401 | −0.318567 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.62769 | −0.372248 | −0.186124 | − | 0.982526i | \(-0.559593\pi\) | ||||
−0.186124 | + | 0.982526i | \(0.559593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.30774 | −0.0732194 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.01217 | 0.167601 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.78209 | 0.376203 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.50367 | 0.303427 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.2445 | −1.00281 | −0.501405 | − | 0.865213i | \(-0.667183\pi\) | ||||
−0.501405 | + | 0.865213i | \(0.667183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.9640 | −1.42282 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.4198 | −0.951744 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.8573 | −1.68091 | −0.840453 | − | 0.541884i | \(-0.817711\pi\) | ||||
−0.840453 | + | 0.541884i | \(0.817711\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17947 | −0.0638720 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6569 | 0.683409 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.7593 | −0.631273 | −0.315637 | − | 0.948880i | \(-0.602218\pi\) | ||||
−0.315637 | + | 0.948880i | \(0.602218\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3591 | −1.08980 | −0.544898 | − | 0.838503i | \(-0.683431\pi\) | ||||
−0.544898 | + | 0.838503i | \(0.683431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8354 | 1.32186 | 0.660929 | − | 0.750449i | \(-0.270163\pi\) | ||||
0.660929 | + | 0.750449i | \(0.270163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2589 | −0.544486 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1124 | 1.21983 | 0.609913 | − | 0.792469i | \(-0.291205\pi\) | ||||
0.609913 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.6024 | 0.921354 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.8920 | 1.35155 | 0.675775 | − | 0.737108i | \(-0.263809\pi\) | ||||
0.675775 | + | 0.737108i | \(0.263809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.5944 | 1.17622 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.8096 | 0.613124 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.1282 | −1.71531 | −0.857656 | − | 0.514224i | \(-0.828080\pi\) | ||||
−0.857656 | + | 0.514224i | \(0.828080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.0260 | 1.85544 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.51614 | −0.231978 | −0.115989 | − | 0.993250i | \(-0.537004\pi\) | ||||
−0.115989 | + | 0.993250i | \(0.537004\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.7382 | −1.11077 | −0.555385 | − | 0.831593i | \(-0.687429\pi\) | ||||
−0.555385 | + | 0.831593i | \(0.687429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.381047 | 0.0194200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.27211 | −0.420495 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5420 | 0.990820 | 0.495410 | − | 0.868659i | \(-0.335018\pi\) | ||||
0.495410 | + | 0.868659i | \(0.335018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.3473 | 0.927861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.94482 | −0.0978548 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.5986 | −0.682496 | −0.341248 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341248 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.7974 | 1.78763 | 0.893817 | − | 0.448431i | \(-0.148017\pi\) | ||||
0.893817 | + | 0.448431i | \(0.148017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.4925 | 1.61856 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.5034 | −0.869752 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.74983 | 0.0867356 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.401479 | 0.0198519 | 0.00992594 | − | 0.999951i | \(-0.496840\pi\) | ||||
0.00992594 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.2654 | 0.505129 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.23359 | −0.404171 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.924684 | 0.0451738 | 0.0225869 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225869 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3875 | −0.944888 | −0.472444 | − | 0.881361i | \(-0.656628\pi\) | ||||
−0.472444 | + | 0.881361i | \(0.656628\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.0380 | 0.828416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.66778 | −0.177914 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.82410 | −0.0882745 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7203 | 0.516380 | 0.258190 | − | 0.966094i | \(-0.416874\pi\) | ||||
0.258190 | + | 0.966094i | \(0.416874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.5768 | 1.61360 | 0.806800 | − | 0.590825i | \(-0.201198\pi\) | ||||
0.806800 | + | 0.590825i | \(0.201198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.09105 | 0.291374 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9305 | 1.09441 | 0.547206 | − | 0.836998i | \(-0.315691\pi\) | ||||
0.547206 | + | 0.836998i | \(0.315691\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.1827 | 0.865844 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.7061 | 1.07880 | 0.539399 | − | 0.842050i | \(-0.318651\pi\) | ||||
0.539399 | + | 0.842050i | \(0.318651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.3893 | 0.729521 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.4201 | 0.633335 | 0.316668 | − | 0.948537i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948537i | \(0.397436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52274 | −0.0717028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.4972 | −0.492117 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.34889 | −0.250210 | −0.125105 | − | 0.992143i | \(-0.539927\pi\) | ||||
−0.125105 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0556 | 0.794360 | 0.397180 | − | 0.917741i | \(-0.369989\pi\) | ||||
0.397180 | + | 0.917741i | \(0.369989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2936 | −0.803703 | −0.401852 | − | 0.915705i | \(-0.631633\pi\) | ||||
−0.401852 | + | 0.915705i | \(0.631633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0380 | 0.834701 | 0.417350 | − | 0.908746i | \(-0.362959\pi\) | ||||
0.417350 | + | 0.908746i | \(0.362959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.67994 | −0.400802 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.557492 | 0.0256335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.21766 | −0.0558699 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.5596 | 1.67395 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.2513 | −0.605468 | −0.302734 | − | 0.953075i | \(-0.597899\pi\) | ||||
−0.302734 | + | 0.953075i | \(0.597899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.2047 | −2.19795 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.9693 | 1.08839 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8466 | 1.57905 | 0.789525 | − | 0.613719i | \(-0.210327\pi\) | ||||
0.789525 | + | 0.613719i | \(0.210327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.28039 | 0.148042 | 0.0740210 | − | 0.997257i | \(-0.476417\pi\) | ||||
0.0740210 | + | 0.997257i | \(0.476417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.4830 | −0.877471 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.17963 | 0.0530204 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.11181 | −0.229296 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.4043 | −1.09248 | −0.546242 | − | 0.837627i | \(-0.683942\pi\) | ||||
−0.546242 | + | 0.837627i | \(0.683942\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.92788 | −0.219723 | −0.109862 | − | 0.993947i | \(-0.535041\pi\) | ||||
−0.109862 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9998 | −0.578485 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.19457 | −0.0972728 | −0.0486364 | − | 0.998817i | \(-0.515488\pi\) | ||||
−0.0486364 | + | 0.998817i | \(0.515488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.77096 | 0.388004 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.4590 | −1.29812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.14826 | −0.0505006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.2667 | 0.975524 | 0.487762 | − | 0.872977i | \(-0.337813\pi\) | ||||
0.487762 | + | 0.872977i | \(0.337813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2664 | 0.623826 | 0.311913 | − | 0.950111i | \(-0.399030\pi\) | ||||
0.311913 | + | 0.950111i | \(0.399030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.5721 | −0.765451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.1009 | 0.613082 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.7793 | 1.37910 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.9488 | 1.81700 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.8254 | −1.11653 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22541 | −0.0527822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0710 | −1.24986 | −0.624931 | − | 0.780680i | \(-0.714873\pi\) | ||||
−0.624931 | + | 0.780680i | \(0.714873\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.21436 | −0.266194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.2386 | −1.67772 | −0.838862 | − | 0.544345i | \(-0.816778\pi\) | ||||
−0.838862 | + | 0.544345i | \(0.816778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.64698 | −0.241007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.46811 | −0.275551 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.969069 | −0.0412090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.35817 | 0.227033 | 0.113517 | − | 0.993536i | \(-0.463789\pi\) | ||||
0.113517 | + | 0.993536i | \(0.463789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.3580 | −0.649573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.4894 | −1.11640 | −0.558198 | − | 0.829708i | \(-0.688507\pi\) | ||||
−0.558198 | + | 0.829708i | \(0.688507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.3038 | −1.61145 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.72162 | −0.366274 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.4626 | 1.61243 | 0.806217 | − | 0.591620i | \(-0.201511\pi\) | ||||
0.806217 | + | 0.591620i | \(0.201511\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.4314 | −0.562088 | −0.281044 | − | 0.959695i | \(-0.590681\pi\) | ||||
−0.281044 | + | 0.959695i | \(0.590681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.41681 | −0.309302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0959 | 1.08639 | 0.543194 | − | 0.839607i | \(-0.317215\pi\) | ||||
0.543194 | + | 0.839607i | \(0.317215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.10264 | −0.170206 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.46391 | −0.102045 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −32.4968 | −1.34358 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.5272 | 1.21872 | 0.609360 | − | 0.792894i | \(-0.291427\pi\) | ||||
0.609360 | + | 0.792894i | \(0.291427\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.83369 | −0.240373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.9870 | −0.902898 | −0.451449 | − | 0.892297i | \(-0.649093\pi\) | ||||
−0.451449 | + | 0.892297i | \(0.649093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.67694 | 0.232732 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.5233 | −1.61488 | −0.807440 | − | 0.589950i | \(-0.799148\pi\) | ||||
−0.807440 | + | 0.589950i | \(0.799148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.24732 | −0.132461 | −0.0662305 | − | 0.997804i | \(-0.521097\pi\) | ||||
−0.0662305 | + | 0.997804i | \(0.521097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.8710 | −1.09427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3136 | 0.866520 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.4957 | −0.547773 | −0.273887 | − | 0.961762i | \(-0.588309\pi\) | ||||
−0.273887 | + | 0.961762i | \(0.588309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.6327 | 1.27972 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3846 | 0.500209 | 0.250104 | − | 0.968219i | \(-0.419535\pi\) | ||||
0.250104 | + | 0.968219i | \(0.419535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.3042 | −1.66285 | −0.831423 | − | 0.555640i | \(-0.812473\pi\) | ||||
−0.831423 | + | 0.555640i | \(0.812473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6149 | −1.02955 | −0.514775 | − | 0.857326i | \(-0.672124\pi\) | ||||
−0.514775 | + | 0.857326i | \(0.672124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.66817 | 0.307219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4290 | −0.697161 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.0693 | 1.03945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7156 | 1.34220 | 0.671099 | − | 0.741368i | \(-0.265823\pi\) | ||||
0.671099 | + | 0.741368i | \(0.265823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.3214 | −1.60011 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.7580 | 1.33754 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.8249 | −0.626024 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.97060 | −0.0778342 | −0.0389171 | − | 0.999242i | \(-0.512391\pi\) | ||||
−0.0389171 | + | 0.999242i | \(0.512391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.2746 | −1.43053 | −0.715266 | − | 0.698853i | \(-0.753694\pi\) | ||||
−0.715266 | + | 0.698853i | \(0.753694\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.81188 | −0.267803 | −0.133901 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133901 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.14174 | −0.0840706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3988 | 1.38526 | 0.692631 | − | 0.721292i | \(-0.256452\pi\) | ||||
0.692631 | + | 0.721292i | \(0.256452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.15182 | −0.318518 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.1527 | 1.05933 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4679 | −0.446725 | −0.223362 | − | 0.974735i | \(-0.571703\pi\) | ||||
−0.223362 | + | 0.974735i | \(0.571703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6931 | −1.19382 | −0.596911 | − | 0.802308i | \(-0.703605\pi\) | ||||
−0.596911 | + | 0.802308i | \(0.703605\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.88467 | 0.0730843 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.3976 | −1.52548 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.380574 | 0.0146919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2566 | −1.01212 | −0.506059 | − | 0.862499i | \(-0.668898\pi\) | ||||
−0.506059 | + | 0.862499i | \(0.668898\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.0683 | 0.925021 | 0.462510 | − | 0.886614i | \(-0.346949\pi\) | ||||
0.462510 | + | 0.886614i | \(0.346949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9434 | 0.458347 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2822 | −0.737813 | −0.368907 | − | 0.929466i | \(-0.620268\pi\) | ||||
−0.368907 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.7244 | −0.447966 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 67.8765 | 2.58589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.9343 | 0.796378 | 0.398189 | − | 0.917303i | \(-0.369639\pi\) | ||||
0.398189 | + | 0.917303i | \(0.369639\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.587787 | 0.0223282 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.0761 | 1.17878 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.6861 | −0.859297 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8817 | −0.750922 | −0.375461 | − | 0.926838i | \(-0.622516\pi\) | ||||
−0.375461 | + | 0.926838i | \(0.622516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.65467 | 0.326417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.47756 | −0.243614 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8869 | −0.897090 | −0.448545 | − | 0.893760i | \(-0.648058\pi\) | ||||
−0.448545 | + | 0.893760i | \(0.648058\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.00000 | −0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.5333 | −1.33073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.19010 | 0.0819050 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9661 | 0.707316 | 0.353658 | − | 0.935375i | \(-0.384938\pi\) | ||||
0.353658 | + | 0.935375i | \(0.384938\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.6788 | −0.546669 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.87594 | 0.292505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.3342 | 0.828328 | 0.414164 | − | 0.910202i | \(-0.364074\pi\) | ||||
0.414164 | + | 0.910202i | \(0.364074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.30565 | 0.307196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.6152 | 1.64790 | 0.823949 | − | 0.566663i | \(-0.191766\pi\) | ||||
0.823949 | + | 0.566663i | \(0.191766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.81095 | 0.0667071 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.1349 | −0.593531 | −0.296766 | − | 0.954950i | \(-0.595908\pi\) | ||||
−0.296766 | + | 0.954950i | \(0.595908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.1469 | 1.65628 | 0.828139 | − | 0.560523i | \(-0.189400\pi\) | ||||
0.828139 | + | 0.560523i | \(0.189400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6398 | −0.499723 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.7008 | −0.464697 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.8683 | −0.470197 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9280 | 0.690694 | 0.345347 | − | 0.938475i | \(-0.387761\pi\) | ||||
0.345347 | + | 0.938475i | \(0.387761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.6731 | −1.04352 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.8498 | −1.63010 | −0.815048 | − | 0.579394i | \(-0.803289\pi\) | ||||
−0.815048 | + | 0.579394i | \(0.803289\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.18519 | 0.0792129 | 0.0396065 | − | 0.999215i | \(-0.487390\pi\) | ||||
0.0396065 | + | 0.999215i | \(0.487390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.09650 | −0.112101 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.5744 | 0.635404 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 59.0013 | 2.13041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.1606 | 0.727009 | 0.363504 | − | 0.931593i | \(-0.381580\pi\) | ||||
0.363504 | + | 0.931593i | \(0.381580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.4852 | −0.592933 | −0.296466 | − | 0.955043i | \(-0.595808\pi\) | ||||
−0.296466 | + | 0.955043i | \(0.595808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.10343 | 0.255163 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.53148 | −0.269843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06651 | 0.0381626 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7331 | 0.490155 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5662 | −0.875691 | −0.437846 | − | 0.899050i | \(-0.644258\pi\) | ||||
−0.437846 | + | 0.899050i | \(0.644258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.0861 | −0.678622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4842 | −0.372303 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6913 | −0.768347 | −0.384173 | − | 0.923261i | \(-0.625513\pi\) | ||||
−0.384173 | + | 0.923261i | \(0.625513\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.1071 | −0.605206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.7388 | 0.838768 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.82994 | −0.0645771 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.4796 | 0.404603 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.94747 | 0.138786 | 0.0693928 | − | 0.997589i | \(-0.477894\pi\) | ||||
0.0693928 | + | 0.997589i | \(0.477894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.2087 | 1.58749 | 0.793747 | − | 0.608248i | \(-0.208128\pi\) | ||||
0.793747 | + | 0.608248i | \(0.208128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.0973 | −0.844092 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.75737 | 0.0964681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.1925 | −0.565813 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.2213 | 1.75273 | 0.876367 | − | 0.481643i | \(-0.159960\pi\) | ||||
0.876367 | + | 0.481643i | \(0.159960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1103 | −1.01472 | −0.507361 | − | 0.861733i | \(-0.669379\pi\) | ||||
−0.507361 | + | 0.861733i | \(0.669379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.2082 | 0.494068 | 0.247034 | − | 0.969007i | \(-0.420544\pi\) | ||||
0.247034 | + | 0.969007i | \(0.420544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.9336 | 1.35222 | 0.676109 | − | 0.736801i | \(-0.263665\pi\) | ||||
0.676109 | + | 0.736801i | \(0.263665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.2565 | −0.632549 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46.3489 | −1.60397 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.01237 | −0.311141 | −0.155571 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155571 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8365 | 0.442637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.0508 | −1.20578 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6201 | 0.364912 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52.7161 | 1.80708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0696 | −0.652931 | −0.326465 | − | 0.945209i | \(-0.605858\pi\) | ||||
−0.326465 | + | 0.945209i | \(0.605858\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.83447 | 0.199535 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.43388 | −0.253937 | −0.126968 | − | 0.991907i | \(-0.540525\pi\) | ||||
−0.126968 | + | 0.991907i | \(0.540525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.5873 | −0.941267 | −0.470634 | − | 0.882329i | \(-0.655975\pi\) | ||||
−0.470634 | + | 0.882329i | \(0.655975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.59800 | −0.156518 | −0.0782588 | − | 0.996933i | \(-0.524936\pi\) | ||||
−0.0782588 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.5198 | 0.663694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.202183 | 0.00685858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.8886 | −1.69041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.9739 | 1.25138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7182 | −0.396148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.4654 | 1.43396 | 0.716978 | − | 0.697096i | \(-0.245525\pi\) | ||||
0.716978 | + | 0.697096i | \(0.245525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.8572 | −1.51128 | −0.755640 | − | 0.654988i | \(-0.772674\pi\) | ||||
−0.755640 | + | 0.654988i | \(0.772674\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.7323 | −1.87554 | −0.937770 | − | 0.347256i | \(-0.887113\pi\) | ||||
−0.937770 | + | 0.347256i | \(0.887113\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.9354 | 1.77740 | 0.888699 | − | 0.458492i | \(-0.151610\pi\) | ||||
0.888699 | + | 0.458492i | \(0.151610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0914 | −0.673843 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.81964 | 0.0609604 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.67933 | −0.190052 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6722 | 0.356733 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.7330 | 1.25847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.7079 | −1.22292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.7741 | −0.790278 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.64552 | −0.220661 | −0.110330 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110330 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.0530 | −0.665115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.9453 | 0.760213 | 0.380107 | − | 0.924943i | \(-0.375887\pi\) | ||||
0.380107 | + | 0.924943i | \(0.375887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.855958 | 0.0283281 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.06189 | −0.134136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1037 | −1.25693 | −0.628463 | − | 0.777839i | \(-0.716316\pi\) | ||||
−0.628463 | + | 0.777839i | \(0.716316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.3805 | −0.967071 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5384 | −0.346501 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.4421 | −1.49251 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.0523 | 1.15003 | 0.575014 | − | 0.818143i | \(-0.304996\pi\) | ||||
0.575014 | + | 0.818143i | \(0.304996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.06091 | −0.198638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.18441 | −0.0387345 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.5571 | 0.834914 | 0.417457 | − | 0.908697i | \(-0.362921\pi\) | ||||
0.417457 | + | 0.908697i | \(0.362921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6856 | 1.06552 | 0.532760 | − | 0.846266i | \(-0.321155\pi\) | ||||
0.532760 | + | 0.846266i | \(0.321155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.8746 | −1.49388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.6671 | 0.346635 | 0.173318 | − | 0.984866i | \(-0.444551\pi\) | ||||
0.173318 | + | 0.984866i | \(0.444551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.4117 | 1.63643 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.5537 | 1.54041 | 0.770207 | − | 0.637794i | \(-0.220153\pi\) | ||||
0.770207 | + | 0.637794i | \(0.220153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.6874 | −0.475273 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.84204 | −0.188649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03196 | 0.0978053 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.8371 | −1.28373 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.2540 | −1.16706 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9357 | 0.448141 | 0.224071 | − | 0.974573i | \(-0.428065\pi\) | ||||
0.224071 | + | 0.974573i | \(0.428065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.2793 | 0.458245 | 0.229122 | − | 0.973398i | \(-0.426414\pi\) | ||||
0.229122 | + | 0.973398i | \(0.426414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.4846 | 0.496413 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.0764 | 1.05821 | 0.529104 | − | 0.848557i | \(-0.322528\pi\) | ||||
0.529104 | + | 0.848557i | \(0.322528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.59986 | −0.0511316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.58600 | −0.306057 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.6310 | −1.10456 | −0.552279 | − | 0.833660i | \(-0.686242\pi\) | ||||
−0.552279 | + | 0.833660i | \(0.686242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.4850 | 0.875745 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7953 | 0.534059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.1870 | 0.673026 | 0.336513 | − | 0.941679i | \(-0.390752\pi\) | ||||
0.336513 | + | 0.941679i | \(0.390752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1306 | 0.796694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2962 | 0.547777 | 0.273889 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273889 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6004.2.a.d.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.d.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial |