Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(1025,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(33.1336001462\) |
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: | \( x^{8} + 34x^{6} + 345x^{4} + 1064x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.6 | ||
Root | \(2.27869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.m.1025.3 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.27869i | 0.759563i | 0.925076 | + | 0.379781i | \(0.124001\pi\) | ||||
−0.925076 | + | 0.379781i | \(0.875999\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.29008 | −1.25802 | −0.629008 | − | 0.777399i | \(-0.716539\pi\) | ||||
−0.629008 | + | 0.777399i | \(0.716539\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03740 | −0.148200 | −0.0741000 | − | 0.997251i | \(-0.523608\pi\) | ||||
−0.0741000 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.80758 | 0.423064 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.67493 | 0.424993 | 0.212497 | − | 0.977162i | \(-0.431841\pi\) | ||||
0.212497 | + | 0.977162i | \(0.431841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.2282i | 1.01755i | 0.860899 | + | 0.508776i | \(0.169902\pi\) | ||||
−0.860899 | + | 0.508776i | \(0.830098\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 14.3331i | − | 0.955543i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.09766 | 0.535156 | 0.267578 | − | 0.963536i | \(-0.413777\pi\) | ||||
0.267578 | + | 0.963536i | \(0.413777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.7726 | + | 11.9487i | −0.777505 | + | 0.628877i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.36391i | − | 0.112567i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.2925 | −0.708369 | −0.354185 | − | 0.935176i | \(-0.615242\pi\) | ||||
−0.354185 | + | 0.935176i | \(0.615242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.5651 | 0.582605 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.1845i | 1.08091i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 12.4187i | − | 0.428230i | −0.976808 | − | 0.214115i | \(-0.931313\pi\) | ||
0.976808 | − | 0.214115i | \(-0.0686867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.6747i | 1.02177i | 0.859650 | + | 0.510883i | \(0.170681\pi\) | ||||
−0.859650 | + | 0.510883i | \(0.829319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.6527i | 0.322809i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.52533 | 0.186438 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 57.9305i | − | 1.56569i | −0.622217 | − | 0.782845i | \(-0.713768\pi\) | ||
0.622217 | − | 0.782845i | \(-0.286232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −30.1429 | −0.772895 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.8737i | 0.826188i | 0.910688 | + | 0.413094i | \(0.135552\pi\) | ||||
−0.910688 | + | 0.413094i | \(0.864448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.3008 | 0.727926 | 0.363963 | − | 0.931413i | \(-0.381423\pi\) | ||||
0.363963 | + | 0.931413i | \(0.381423\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23.9500 | −0.532222 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.7654 | 0.314157 | 0.157079 | − | 0.987586i | \(-0.449792\pi\) | ||||
0.157079 | + | 0.987586i | \(0.449792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.9238 | −0.978037 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.7307i | 0.406485i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.57547i | 0.0485938i | 0.999705 | + | 0.0242969i | \(0.00773471\pi\) | ||||
−0.999705 | + | 0.0242969i | \(0.992265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −29.4057 | −0.534649 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.2273 | − | 33.6621i | −0.477672 | − | 0.590564i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 43.3981i | − | 0.735561i | −0.929913 | − | 0.367780i | \(-0.880118\pi\) | ||
0.929913 | − | 0.367780i | \(-0.119882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50.5698 | −0.829014 | −0.414507 | − | 0.910046i | \(-0.636046\pi\) | ||||
−0.414507 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.94998 | −0.0626981 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 83.2063i | − | 1.28010i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 83.1046i | − | 1.24037i | −0.784457 | − | 0.620184i | \(-0.787058\pi\) | ||
0.784457 | − | 0.620184i | \(-0.212942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 37.1255i | − | 0.538051i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.54578i | − | 0.120363i | −0.998187 | − | 0.0601815i | \(-0.980832\pi\) | ||
0.998187 | − | 0.0601815i | \(-0.0191680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −145.369 | −1.99135 | −0.995677 | − | 0.0928852i | \(-0.970391\pi\) | ||||
−0.995677 | + | 0.0928852i | \(0.970391\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 33.1894i | 0.442525i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.84977 | −0.0629840 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 100.604i | 1.27347i | 0.771081 | + | 0.636737i | \(0.219716\pi\) | ||||
−0.771081 | + | 0.636737i | \(0.780284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −32.2341 | −0.397952 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −139.547 | −1.68129 | −0.840646 | − | 0.541585i | \(-0.817824\pi\) | ||||
−0.840646 | + | 0.541585i | \(0.817824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −57.2250 | −0.673236 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.2983 | 0.325268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 109.901i | − | 1.23484i | −0.786635 | − | 0.617419i | \(-0.788178\pi\) | ||
0.786635 | − | 0.617419i | \(-0.211822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.7229i | − | 0.150801i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −72.1769 | −0.776095 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 92.9208 | − | 75.1581i | 0.978114 | − | 0.791138i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 81.1313i | − | 0.836405i | −0.908354 | − | 0.418202i | \(-0.862660\pi\) | ||
0.908354 | − | 0.418202i | \(-0.137340\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.8001 | 0.179799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −64.4920 | −0.638534 | −0.319267 | − | 0.947665i | \(-0.603437\pi\) | ||||
−0.319267 | + | 0.947665i | \(0.603437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 78.1486i | − | 0.758724i | −0.925248 | − | 0.379362i | \(-0.876143\pi\) | ||
0.925248 | − | 0.379362i | \(-0.123857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.8692i | 0.141611i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 82.2978i | 0.769138i | 0.923096 | + | 0.384569i | \(0.125650\pi\) | ||||
−0.923096 | + | 0.384569i | \(0.874350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 136.311i | − | 1.25056i | −0.780399 | − | 0.625282i | \(-0.784984\pi\) | ||
0.780399 | − | 0.625282i | \(-0.215016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 132.006 | 1.18924 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 175.141i | − | 1.54992i | −0.632010 | − | 0.774960i | \(-0.717770\pi\) | ||
0.632010 | − | 0.774960i | \(-0.282230\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 102.481 | 0.891140 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 50.3673i | 0.430490i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.43791 | −0.0793102 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −99.1451 | −0.819381 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −77.1876 | −0.627541 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 65.6362 | 0.525089 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 108.592i | 0.855056i | 0.904002 | + | 0.427528i | \(0.140616\pi\) | ||||
−0.904002 | + | 0.427528i | \(0.859384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 71.3248i | 0.552905i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.84988 | −0.0751900 | −0.0375950 | − | 0.999293i | \(-0.511970\pi\) | ||||
−0.0375950 | + | 0.999293i | \(0.511970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.3251 | − | 12.3955i | 0.115226 | − | 0.0931996i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 183.573i | − | 1.35980i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −89.7964 | −0.655448 | −0.327724 | − | 0.944773i | \(-0.606282\pi\) | ||||
−0.327724 | + | 0.944773i | \(0.606282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.1860 | 0.166806 | 0.0834030 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834030 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.6457i | 0.238622i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 61.8407i | 0.432453i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 78.1145i | 0.538721i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 109.203i | − | 0.742880i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 110.326 | 0.740443 | 0.370221 | − | 0.928944i | \(-0.379282\pi\) | ||||
0.370221 | + | 0.928944i | \(0.379282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 115.413i | − | 0.764326i | −0.924095 | − | 0.382163i | \(-0.875179\pi\) | ||
0.924095 | − | 0.382163i | \(-0.124821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.6401 | 0.226406 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 199.237i | − | 1.28540i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −171.069 | −1.08961 | −0.544805 | − | 0.838563i | \(-0.683396\pi\) | ||||
−0.544805 | + | 0.838563i | \(0.683396\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.86870 | −0.0369101 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.9018 | 0.104980 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 196.012 | 1.20253 | 0.601263 | − | 0.799051i | \(-0.294665\pi\) | ||||
0.601263 | + | 0.799051i | \(0.294665\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 67.0064i | − | 0.406099i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 235.541i | 1.41043i | 0.708996 | + | 0.705213i | \(0.249149\pi\) | ||||
−0.708996 | + | 0.705213i | \(0.750851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.98462 | −0.0354119 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −56.2478 | + | 45.4955i | −0.328934 | + | 0.266055i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 336.786i | 1.94674i | 0.229237 | + | 0.973371i | \(0.426377\pi\) | ||||
−0.229237 | + | 0.973371i | \(0.573623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.1099 | −0.0863421 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 98.8907 | 0.558705 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 39.3051i | − | 0.219582i | −0.993955 | − | 0.109791i | \(-0.964982\pi\) | ||
0.993955 | − | 0.109791i | \(-0.0350181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 331.772i | − | 1.83300i | −0.400038 | − | 0.916498i | \(-0.631003\pi\) | ||
0.400038 | − | 0.916498i | \(-0.368997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 115.233i | − | 0.629688i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 364.388i | 1.96966i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.5309 | 0.227438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 30.2760i | − | 0.160190i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1093 | 0.115755 | 0.0578777 | − | 0.998324i | \(-0.481567\pi\) | ||||
0.0578777 | + | 0.998324i | \(0.481567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 50.1326i | − | 0.259754i | −0.991530 | − | 0.129877i | \(-0.958542\pi\) | ||
0.991530 | − | 0.129877i | \(-0.0414583\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 189.601 | 0.972314 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 43.8312 | 0.222493 | 0.111247 | − | 0.993793i | \(-0.464516\pi\) | ||||
0.111247 | + | 0.993793i | \(0.464516\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −376.691 | −1.89292 | −0.946461 | − | 0.322818i | \(-0.895370\pi\) | ||||
−0.946461 | + | 0.322818i | \(0.895370\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 189.370 | 0.942137 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8831i | 0.0634637i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 213.068i | − | 1.03936i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −62.0349 | −0.299686 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −69.0608 | + | 55.8591i | −0.330434 | + | 0.267269i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 299.111i | 1.41759i | 0.705416 | + | 0.708794i | \(0.250760\pi\) | ||||
−0.705416 | + | 0.708794i | \(0.749240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.4732 | 0.0914233 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −196.885 | −0.915743 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 32.8594i | − | 0.151426i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 331.250i | − | 1.51256i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 120.345i | 0.544550i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 96.3080i | 0.431874i | 0.976407 | + | 0.215937i | \(0.0692807\pi\) | ||||
−0.976407 | + | 0.215937i | \(0.930719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 55.4579 | 0.246480 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 425.697i | 1.87532i | 0.347556 | + | 0.937659i | \(0.387012\pi\) | ||||
−0.347556 | + | 0.937659i | \(0.612988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −210.329 | −0.918466 | −0.459233 | − | 0.888316i | \(-0.651876\pi\) | ||||
−0.459233 | + | 0.888316i | \(0.651876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.0511i | − | 0.0478403i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.2820 | −0.0999226 | −0.0499613 | − | 0.998751i | \(-0.515910\pi\) | ||||
−0.0499613 | + | 0.998751i | \(0.515910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −92.8755 | −0.395215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −229.246 | −0.967283 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 182.968 | 0.765558 | 0.382779 | − | 0.923840i | \(-0.374967\pi\) | ||||
0.382779 | + | 0.923840i | \(0.374967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 64.3761i | − | 0.267121i | −0.991041 | − | 0.133560i | \(-0.957359\pi\) | ||
0.991041 | − | 0.133560i | \(-0.0426410\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 189.209i | 0.778637i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 301.445 | 1.23039 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −158.059 | − | 195.414i | −0.639915 | − | 0.791151i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 317.985i | − | 1.27705i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −396.215 | −1.57855 | −0.789273 | − | 0.614043i | \(-0.789542\pi\) | ||||
−0.789273 | + | 0.614043i | \(0.789542\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −76.1662 | −0.301052 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 130.398i | − | 0.511365i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 53.3251i | − | 0.207491i | −0.994604 | − | 0.103745i | \(-0.966917\pi\) | ||
0.994604 | − | 0.103745i | \(-0.0330827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 60.0971i | 0.232035i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 47.2851i | − | 0.181169i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 457.541 | 1.73970 | 0.869850 | − | 0.493316i | \(-0.164215\pi\) | ||||
0.869850 | + | 0.493316i | \(0.164215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.1999i | − | 0.0611319i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 250.429 | 0.937937 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 354.156i | − | 1.31657i | −0.752770 | − | 0.658283i | \(-0.771283\pi\) | ||
0.752770 | − | 0.658283i | \(-0.228717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 178.839 | 0.659922 | 0.329961 | − | 0.943994i | \(-0.392964\pi\) | ||||
0.329961 | + | 0.943994i | \(0.392964\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 31.2702 | 0.114543 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 68.0909 | 0.247603 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −249.791 | −0.901772 | −0.450886 | − | 0.892581i | \(-0.648892\pi\) | ||||
−0.450886 | + | 0.892581i | \(0.648892\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 120.604i | 0.432272i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 62.6513i | 0.222958i | 0.993767 | + | 0.111479i | \(0.0355588\pi\) | ||||
−0.993767 | + | 0.111479i | \(0.964441\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −517.713 | −1.82938 | −0.914688 | − | 0.404160i | \(-0.867564\pi\) | ||||
−0.914688 | + | 0.404160i | \(0.867564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 171.262 | + | 211.738i | 0.600919 | + | 0.742939i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 35.1405i | − | 0.122441i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −206.233 | −0.713608 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 184.873 | 0.635302 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 416.666i | 1.42207i | 0.703158 | + | 0.711034i | \(0.251773\pi\) | ||||
−0.703158 | + | 0.711034i | \(0.748227\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 272.978i | 0.925348i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 136.435i | 0.459378i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 215.520i | − | 0.720802i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.4714 | −0.107879 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 146.957i | − | 0.485007i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 318.088 | 1.04291 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 163.173i | − | 0.531508i | −0.964041 | − | 0.265754i | \(-0.914379\pi\) | ||
0.964041 | − | 0.265754i | \(-0.0856209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 178.076 | 0.576299 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −439.856 | −1.41433 | −0.707163 | − | 0.707050i | \(-0.750025\pi\) | ||||
−0.707163 | + | 0.707050i | \(0.750025\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 98.4282 | 0.314467 | 0.157234 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157234 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.8457 | 0.0788752 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 392.584i | 1.23843i | 0.785220 | + | 0.619217i | \(0.212550\pi\) | ||||
−0.785220 | + | 0.619217i | \(0.787450\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 58.0564i | − | 0.181995i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −187.531 | −0.584209 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −134.396 | + | 108.705i | −0.416087 | + | 0.336548i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 192.670i | 0.592831i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 310.611 | 0.949882 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3176 | −0.0465581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 482.498i | 1.45770i | 0.684675 | + | 0.728849i | \(0.259944\pi\) | ||||
−0.684675 | + | 0.728849i | \(0.740056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 220.575i | − | 0.662387i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 522.735i | 1.56040i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 158.934i | 0.471614i | 0.971800 | + | 0.235807i | \(0.0757733\pi\) | ||||
−0.971800 | + | 0.235807i | \(0.924227\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 399.092 | 1.17726 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 148.077i | 0.434244i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 100.549 | 0.293145 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 233.523i | 0.676877i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −421.620 | −1.21504 | −0.607522 | − | 0.794303i | \(-0.707836\pi\) | ||||
−0.607522 | + | 0.794303i | \(0.707836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 276.480 | 0.792206 | 0.396103 | − | 0.918206i | \(-0.370362\pi\) | ||||
0.396103 | + | 0.918206i | \(0.370362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −386.057 | −1.09988 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 116.083 | 0.328846 | 0.164423 | − | 0.986390i | \(-0.447424\pi\) | ||||
0.164423 | + | 0.986390i | \(0.447424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 53.7537i | 0.151419i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 21.5061i | − | 0.0602410i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 102.430 | 0.285319 | 0.142660 | − | 0.989772i | \(-0.454435\pi\) | ||||
0.142660 | + | 0.989772i | \(0.454435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 75.4586 | − | 353.025i | 0.209027 | − | 0.977910i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 225.921i | − | 0.622371i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 914.382 | 2.50516 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −244.921 | −0.667360 | −0.333680 | − | 0.942686i | \(-0.608290\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 128.977i | 0.349530i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.67180i | − | 0.00720160i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 205.089i | 0.549837i | 0.961468 | + | 0.274918i | \(0.0886509\pi\) | ||||
−0.961468 | + | 0.274918i | \(0.911349\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 149.564i | 0.398838i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 164.276 | 0.435746 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 488.205i | − | 1.28814i | −0.764966 | − | 0.644070i | \(-0.777244\pi\) | ||
0.764966 | − | 0.644070i | \(-0.222756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −247.448 | −0.649469 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 539.079i | 1.40752i | 0.710439 | + | 0.703759i | \(0.248496\pi\) | ||||
−0.710439 | + | 0.703759i | \(0.751504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.5054 | 0.0792349 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 119.180 | 0.307959 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 195.648 | 0.502951 | 0.251475 | − | 0.967864i | \(-0.419084\pi\) | ||||
0.251475 | + | 0.967864i | \(0.419084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −148.224 | −0.379088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 22.4448i | − | 0.0571115i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 632.810i | − | 1.60205i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 575.496 | 1.44961 | 0.724806 | − | 0.688953i | \(-0.241929\pi\) | ||||
0.724806 | + | 0.688953i | \(0.241929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.2456 | + | 34.9211i | 0.0707909 | + | 0.0875215i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 548.087i | 1.36680i | 0.730044 | + | 0.683400i | \(0.239499\pi\) | ||||
−0.730044 | + | 0.683400i | \(0.760501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −418.999 | −1.03970 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 202.755 | 0.500631 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 270.821i | − | 0.665407i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 480.592i | 1.17504i | 0.809209 | + | 0.587520i | \(0.199896\pi\) | ||||
−0.809209 | + | 0.587520i | \(0.800104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 204.618i | − | 0.497854i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.0212i | 0.109010i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 877.763 | 2.11509 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 52.8338i | 0.126700i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 636.344 | 1.51872 | 0.759360 | − | 0.650670i | \(-0.225512\pi\) | ||||
0.759360 | + | 0.650670i | \(0.225512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 39.9171i | − | 0.0948150i | −0.998876 | − | 0.0474075i | \(-0.984904\pi\) | ||
0.998876 | − | 0.0474075i | \(-0.0150959\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 56.2204 | 0.132909 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 132.509 | 0.311785 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.4611 | 0.122860 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −140.916 | −0.328475 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 763.895i | − | 1.77238i | −0.463323 | − | 0.886189i | \(-0.653343\pi\) | ||
0.463323 | − | 0.886189i | \(-0.346657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 470.042i | − | 1.08555i | −0.839879 | − | 0.542774i | \(-0.817374\pi\) | ||
0.839879 | − | 0.542774i | \(-0.182626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −177.999 | −0.409192 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 240.682 | − | 194.674i | 0.550760 | − | 0.445477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 173.834i | − | 0.395977i | −0.980204 | − | 0.197988i | \(-0.936559\pi\) | ||
0.980204 | − | 0.197988i | \(-0.0634408\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −182.474 | −0.413772 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −494.990 | −1.11736 | −0.558680 | − | 0.829384i | \(-0.688692\pi\) | ||||
−0.558680 | + | 0.829384i | \(0.688692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 691.283i | 1.55345i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 251.398i | 0.562413i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 517.523i | 1.15261i | 0.817234 | + | 0.576306i | \(0.195506\pi\) | ||||
−0.817234 | + | 0.576306i | \(0.804494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 158.357i | 0.351124i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 262.991 | 0.580554 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 86.3182i | 0.189710i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 354.686 | 0.776119 | 0.388059 | − | 0.921634i | \(-0.373146\pi\) | ||||
0.388059 | + | 0.921634i | \(0.373146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 265.511i | 0.578454i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 176.578 | 0.383033 | 0.191516 | − | 0.981489i | \(-0.438659\pi\) | ||||
0.191516 | + | 0.981489i | \(0.438659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.7054 | 0.0792773 | 0.0396387 | − | 0.999214i | \(-0.487379\pi\) | ||||
0.0396387 | + | 0.999214i | \(0.487379\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 453.998 | 0.976341 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 781.984 | 1.67448 | 0.837242 | − | 0.546832i | \(-0.184166\pi\) | ||||
0.837242 | + | 0.546832i | \(0.184166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 86.2127i | 0.183822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 389.812i | − | 0.827627i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 146.329 | 0.309364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −215.165 | + | 174.034i | −0.452978 | + | 0.366387i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.80632i | 0.0205583i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 357.010 | 0.745324 | 0.372662 | − | 0.927967i | \(-0.378445\pi\) | ||||
0.372662 | + | 0.927967i | \(0.378445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 766.315 | 1.59317 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.5140i | 0.0797391i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 510.322i | 1.05221i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 752.081i | − | 1.54431i | −0.635432 | − | 0.772157i | \(-0.719178\pi\) | ||
0.635432 | − | 0.772157i | \(-0.280822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 446.650i | 0.913394i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 481.529 | 0.980711 | 0.490356 | − | 0.871523i | \(-0.336867\pi\) | ||||
0.490356 | + | 0.871523i | \(0.336867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 112.981i | − | 0.229170i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −111.964 | −0.226191 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.86539i | 0.0178378i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 322.939 | 0.647172 | 0.323586 | − | 0.946199i | \(-0.395112\pi\) | ||||
0.323586 | + | 0.946199i | \(0.395112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −536.725 | −1.07131 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −614.923 | −1.22251 | −0.611256 | − | 0.791433i | \(-0.709335\pi\) | ||||
−0.611256 | + | 0.791433i | \(0.709335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 405.660 | 0.803287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 13.6371i | − | 0.0268976i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 408.948i | − | 0.803434i | −0.915764 | − | 0.401717i | \(-0.868414\pi\) | ||
0.915764 | − | 0.401717i | \(-0.131586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 150.806 | 0.295118 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −348.716 | − | 431.130i | −0.679758 | − | 0.840410i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 491.561i | 0.954487i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.0271 | 0.133515 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −767.431 | −1.47867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1101i | 0.0328408i | 0.999865 | + | 0.0164204i | \(0.00522701\pi\) | ||||
−0.999865 | + | 0.0164204i | \(0.994773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 306.964i | 0.586929i | 0.955970 | + | 0.293465i | \(0.0948083\pi\) | ||||
−0.955970 | + | 0.293465i | \(0.905192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 34.4307i | − | 0.0655822i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 288.166i | 0.546805i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −263.555 | −0.498213 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 165.242i | − | 0.311189i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −448.087 | −0.840689 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 517.660i | − | 0.967588i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 89.5641 | 0.166786 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −224.040 | −0.415659 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −727.145 | −1.34408 | −0.672038 | − | 0.740517i | \(-0.734581\pi\) | ||||
−0.672038 | + | 0.740517i | \(0.734581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 756.006 | 1.39228 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 857.410i | 1.57323i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 153.277i | 0.280213i | 0.990136 | + | 0.140107i | \(0.0447445\pi\) | ||||
−0.990136 | + | 0.140107i | \(0.955255\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −192.549 | −0.350726 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 148.387 | + | 183.456i | 0.269304 | + | 0.332951i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 104.367i | − | 0.188729i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −830.326 | −1.49608 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −294.840 | −0.529335 | −0.264668 | − | 0.964340i | \(-0.585262\pi\) | ||||
−0.264668 | + | 0.964340i | \(0.585262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 414.053i | 0.740702i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 96.9147i | 0.172753i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 181.727i | − | 0.322783i | −0.986890 | − | 0.161391i | \(-0.948402\pi\) | ||
0.986890 | − | 0.161391i | \(-0.0515982\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1101.65i | 1.94983i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.4397 | 0.0589765 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 940.429i | − | 1.65278i | −0.563102 | − | 0.826388i | \(-0.690392\pi\) | ||
0.563102 | − | 0.826388i | \(-0.309608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 546.519 | 0.957125 | 0.478563 | − | 0.878053i | \(-0.341158\pi\) | ||||
0.478563 | + | 0.878053i | \(0.341158\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.3802i | 0.0879235i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −237.302 | −0.412700 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6269 | 0.0236168 | 0.0118084 | − | 0.999930i | \(-0.496241\pi\) | ||||
0.0118084 | + | 0.999930i | \(0.496241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 114.237 | 0.197300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 144.766 | 0.249167 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0402i | 0.0206521i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 316.815i | − | 0.541563i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −147.276 | −0.250896 | −0.125448 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125448 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −378.471 | − | 467.918i | −0.642565 | − | 0.794427i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 99.8776i | 0.168998i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −218.789 | −0.368953 | −0.184477 | − | 0.982837i | \(-0.559059\pi\) | ||||
−0.184477 | + | 0.982837i | \(0.559059\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 59.3652 | 0.0997735 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 858.363i | − | 1.43779i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 547.699i | − | 0.914356i | −0.889375 | − | 0.457178i | \(-0.848860\pi\) | ||
0.889375 | − | 0.457178i | \(-0.151140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 245.418i | − | 0.408349i | −0.978934 | − | 0.204175i | \(-0.934549\pi\) | ||
0.978934 | − | 0.204175i | \(-0.0654511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 316.427i | − | 0.524755i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 623.631 | 1.03079 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 333.015i | 0.548625i | 0.961641 | + | 0.274312i | \(0.0884502\pi\) | ||||
−0.961641 | + | 0.274312i | \(0.911550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.3566 | −0.0482046 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 195.319i | 0.319671i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −131.044 | −0.213776 | −0.106888 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106888 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 485.516 | 0.789457 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1029.88 | 1.66917 | 0.834583 | − | 0.550882i | \(-0.185709\pi\) | ||||
0.834583 | + | 0.550882i | \(0.185709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 841.181 | 1.35893 | 0.679467 | − | 0.733706i | \(-0.262211\pi\) | ||||
0.679467 | + | 0.733706i | \(0.262211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 475.488i | − | 0.765681i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 114.011i | 0.183003i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −776.985 | −1.24318 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −127.286 | − | 157.368i | −0.203007 | − | 0.250986i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 527.032i | − | 0.837889i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −999.068 | −1.58331 | −0.791655 | − | 0.610969i | \(-0.790780\pi\) | ||||
−0.791655 | + | 0.610969i | \(0.790780\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −681.581 | −1.07675 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 683.054i | − | 1.07567i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 633.944i | − | 0.995203i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 32.5387i | − | 0.0509213i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 176.109i | − | 0.274741i | −0.990520 | − | 0.137371i | \(-0.956135\pi\) | ||
0.990520 | − | 0.137371i | \(-0.0438651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −155.981 | −0.242583 | −0.121292 | − | 0.992617i | \(-0.538704\pi\) | ||||
−0.121292 | + | 0.992617i | \(0.538704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 448.639i | − | 0.695564i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −595.470 | −0.920356 | −0.460178 | − | 0.887827i | \(-0.652214\pi\) | ||||
−0.460178 | + | 0.887827i | \(0.652214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 202.883i | − | 0.312608i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 74.8762 | 0.115017 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 608.312 | 0.931565 | 0.465782 | − | 0.884899i | \(-0.345773\pi\) | ||||
0.465782 | + | 0.884899i | \(0.345773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 61.9566 | 0.0945902 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −553.503 | −0.842471 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 210.781i | − | 0.319849i | −0.987129 | − | 0.159925i | \(-0.948875\pi\) | ||
0.987129 | − | 0.159925i | \(-0.0511251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 475.867i | − | 0.719920i | −0.932968 | − | 0.359960i | \(-0.882790\pi\) | ||
0.932968 | − | 0.359960i | \(-0.117210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −274.230 | −0.413620 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −96.3960 | + | 77.9690i | −0.144956 | + | 0.117247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 202.331i | 0.303345i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −219.456 | −0.328036 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −236.410 | −0.352325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 860.374i | 1.27842i | 0.769034 | + | 0.639208i | \(0.220738\pi\) | ||||
−0.769034 | + | 0.639208i | \(0.779262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 425.076i | 0.629742i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 805.478i | 1.18978i | 0.803809 | + | 0.594888i | \(0.202803\pi\) | ||||
−0.803809 | + | 0.594888i | \(0.797197\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 84.1655i | 0.123955i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −970.032 | −1.42442 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 678.667i | 0.993656i | 0.867849 | + | 0.496828i | \(0.165502\pi\) | ||||
−0.867849 | + | 0.496828i | \(0.834498\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 564.827 | 0.824564 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 479.274i | − | 0.697633i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.0688 | −0.0494468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −636.921 | −0.921738 | −0.460869 | − | 0.887468i | \(-0.652462\pi\) | ||||
−0.460869 | + | 0.887468i | \(0.652462\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.4659 | −0.0266463 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −145.842 | −0.209845 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 308.171i | 0.442140i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 53.0524i | − | 0.0758975i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1039.31 | −1.48261 | −0.741306 | − | 0.671167i | \(-0.765793\pi\) | ||||
−0.741306 | + | 0.671167i | \(0.765793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 692.192 | + | 855.783i | 0.984626 | + | 1.21733i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 211.634i | − | 0.300191i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 66.9039 | 0.0946307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1068.61 | −1.50721 | −0.753606 | − | 0.657326i | \(-0.771687\pi\) | ||||
−0.753606 | + | 0.657326i | \(0.771687\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 383.059i | 0.538761i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 516.060i | − | 0.723787i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 388.983i | − | 0.544033i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 416.928i | 0.581489i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1046.98 | 1.45616 | 0.728078 | − | 0.685494i | \(-0.240414\pi\) | ||||
0.728078 | + | 0.685494i | \(0.240414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 81.0713i | 0.112443i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 146.693 | 0.202895 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 180.880i | − | 0.249489i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −610.242 | −0.839398 | −0.419699 | − | 0.907663i | \(-0.637864\pi\) | ||||
−0.419699 | + | 0.907663i | \(0.637864\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −721.255 | −0.989376 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 284.764 | 0.389554 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 111.114 | 0.151588 | 0.0757941 | − | 0.997123i | \(-0.475851\pi\) | ||||
0.0757941 | + | 0.997123i | \(0.475851\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 686.899i | 0.934556i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 388.508i | − | 0.527148i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1056.20 | −1.42923 | −0.714613 | − | 0.699520i | \(-0.753397\pi\) | ||||
−0.714613 | + | 0.699520i | \(0.753397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 445.288 | − | 360.167i | 0.600929 | − | 0.486056i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 760.688i | 1.02381i | 0.859043 | + | 0.511903i | \(0.171059\pi\) | ||||
−0.859043 | + | 0.511903i | \(0.828941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −693.959 | −0.931489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −531.337 | −0.711294 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 85.3757i | − | 0.113986i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.7326i | 0.0142910i | 0.999974 | + | 0.00714551i | \(0.00227451\pi\) | ||||
−0.999974 | + | 0.00714551i | \(0.997725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 902.850i | − | 1.19900i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 725.959i | 0.961535i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 592.194 | 0.782291 | 0.391146 | − | 0.920329i | \(-0.372079\pi\) | ||||
0.391146 | + | 0.920329i | \(0.372079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 173.559i | − | 0.228668i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 488.932 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 141.409i | 0.185333i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −217.889 | −0.284822 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 574.078 | 0.748471 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −785.922 | −1.02201 | −0.511003 | − | 0.859579i | \(-0.670726\pi\) | ||||
−0.511003 | + | 0.859579i | \(0.670726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 121.511 | 0.157602 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 225.009i | − | 0.291085i | −0.989352 | − | 0.145543i | \(-0.953507\pi\) | ||
0.989352 | − | 0.145543i | \(-0.0464928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 461.347i | 0.595286i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −136.943 | −0.176245 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −404.745 | − | 500.402i | −0.519571 | − | 0.642365i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.9509i | − | 0.0511535i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 362.433 | 0.462877 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1076.04 | 1.37075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 447.434i | − | 0.568531i | −0.958746 | − | 0.284266i | \(-0.908250\pi\) | ||
0.958746 | − | 0.284266i | \(-0.0917498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1042.59i | 1.32141i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 181.691i | 0.229698i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 668.947i | − | 0.843564i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.9146 | 0.0464335 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 81.7849i | 0.102616i | 0.998683 | + | 0.0513080i | \(0.0163390\pi\) | ||||
−0.998683 | + | 0.0513080i | \(0.983661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 134.331 | 0.168123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 418.455i | − | 0.522416i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −679.588 | −0.846312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −106.314 | −0.132067 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 807.012 | 1.00001 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −277.637 | −0.343185 | −0.171593 | − | 0.985168i | \(-0.554891\pi\) | ||||
−0.171593 | + | 0.985168i | \(0.554891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.8435i | 0.0269340i | 0.999909 | + | 0.0134670i | \(0.00428681\pi\) | ||||
−0.999909 | + | 0.0134670i | \(0.995713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 407.518i | 0.501253i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1232.93 | −1.51280 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −462.394 | + | 374.003i | −0.565966 | + | 0.457776i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 52.2510i | − | 0.0637986i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −445.574 | −0.542720 | −0.271360 | − | 0.962478i | \(-0.587473\pi\) | ||||
−0.271360 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −652.986 | −0.793422 | −0.396711 | − | 0.917944i | \(-0.629848\pi\) | ||||
−0.396711 | + | 0.917944i | \(0.629848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 155.158i | 0.188070i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1085.77i | 1.31290i | 0.754370 | + | 0.656450i | \(0.227943\pi\) | ||||
−0.754370 | + | 0.656450i | \(0.772057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 578.238i | 0.697512i | 0.937214 | + | 0.348756i | \(0.113396\pi\) | ||||
−0.937214 | + | 0.348756i | \(0.886604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 569.196i | − | 0.684953i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −435.994 | −0.523403 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1481.57i | − | 1.77434i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −924.411 | −1.10443 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1128.80i | − | 1.34541i | −0.739911 | − | 0.672704i | \(-0.765133\pi\) | ||
0.739911 | − | 0.672704i | \(-0.234867\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 686.777 | 0.816619 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −142.763 | −0.169351 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.6437 | 0.0445488 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 102.853 | 0.121432 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1179.71i | − | 1.38953i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 943.832i | 1.10909i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 838.329 | 0.982800 | 0.491400 | − | 0.870934i | \(-0.336485\pi\) | ||||
0.491400 | + | 0.870934i | \(0.336485\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 353.803 | − | 286.170i | 0.413805 | − | 0.334702i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 971.203i | 1.13326i | 0.823973 | + | 0.566630i | \(0.191753\pi\) | ||||
−0.823973 | + | 0.566630i | \(0.808247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −154.488 | −0.179846 | −0.0899232 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899232 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 80.0744 | 0.0930016 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 198.110i | 0.229559i | 0.993391 | + | 0.114780i | \(0.0366162\pi\) | ||||
−0.993391 | + | 0.114780i | \(0.963384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 2118.41i | − | 2.44903i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 469.940i | − | 0.542030i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 470.318i | 0.541217i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1099.32 | 1.26214 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 308.914i | − | 0.353853i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −68.0909 | −0.0778182 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 173.558i | − | 0.197900i | −0.995092 | − | 0.0989498i | \(-0.968452\pi\) | ||
0.995092 | − | 0.0989498i | \(-0.0315483\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −949.451 | −1.08015 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 561.120 | 0.636913 | 0.318456 | − | 0.947938i | \(-0.396836\pi\) | ||||
0.318456 | + | 0.947938i | \(0.396836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 449.856 | 0.509463 | 0.254732 | − | 0.967012i | \(-0.418013\pi\) | ||||
0.254732 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −622.031 | −0.702860 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 532.156i | − | 0.599950i | −0.953947 | − | 0.299975i | \(-0.903022\pi\) | ||
0.953947 | − | 0.299975i | \(-0.0969784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 112.653i | − | 0.126719i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −150.692 | −0.169127 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −218.123 | + | 176.427i | −0.244259 | + | 0.197566i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 247.232i | 0.276237i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 491.103 | 0.547495 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 393.358 | 0.437551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4308i | 0.0260053i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 73.9923i | − | 0.0819406i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2086.88i | 2.30594i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 586.664i | 0.646818i | 0.946259 | + | 0.323409i | \(0.104829\pi\) | ||||
−0.946259 | + | 0.323409i | \(0.895171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −245.558 | −0.270141 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.8590i | 0.0470461i | 0.999723 | + | 0.0235230i | \(0.00748830\pi\) | ||||
−0.999723 | + | 0.0235230i | \(0.992512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −652.373 | −0.714538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 724.824i | 0.792158i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2183 | 0.0111431 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 949.641 | 1.03334 | 0.516671 | − | 0.856184i | \(-0.327171\pi\) | ||||
0.516671 | + | 0.856184i | \(0.327171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 371.820 | 0.403714 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 113.045 | 0.122476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 843.766i | − | 0.912179i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 297.557i | − | 0.320989i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 475.866 | 0.512235 | 0.256117 | − | 0.966646i | \(-0.417557\pi\) | ||||
0.256117 | + | 0.966646i | \(0.417557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 707.959 | − | 572.626i | 0.760428 | − | 0.615065i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1002.29i | − | 1.07427i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −267.523 | −0.286121 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −398.277 | −0.425056 | −0.212528 | − | 0.977155i | \(-0.568170\pi\) | ||||
−0.212528 | + | 0.977155i | \(0.568170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 224.287i | 0.238857i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 913.121i | − | 0.970373i | −0.874411 | − | 0.485187i | \(-0.838752\pi\) | ||
0.874411 | − | 0.485187i | \(-0.161248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 551.887i | − | 0.585246i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 190.438i | 0.201522i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 287.682 | 0.303782 | 0.151891 | − | 0.988397i | \(-0.451464\pi\) | ||||
0.151891 | + | 0.988397i | \(0.451464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1922.96i | − | 2.02631i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −894.576 | −0.940669 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 821.664i | − | 0.862187i | −0.902307 | − | 0.431093i | \(-0.858128\pi\) | ||
0.902307 | − | 0.431093i | \(-0.141872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −139.069 | −0.145622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 132.292 | 0.138237 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 93.1547 | 0.0971374 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.2888 | −0.0440050 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 313.355i | 0.325395i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 315.338i | 0.326775i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −239.162 | −0.247324 | −0.123662 | − | 0.992324i | \(-0.539464\pi\) | ||||
−0.123662 | + | 0.992324i | \(0.539464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −247.705 | − | 306.247i | −0.255629 | − | 0.316044i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1935.48i | − | 1.99328i | −0.0819035 | − | 0.996640i | \(-0.526100\pi\) | ||
0.0819035 | − | 0.996640i | \(-0.473900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0532 | −0.0247206 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −439.035 | −0.450293 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1095.11i | 1.12089i | 0.828193 | + | 0.560444i | \(0.189369\pi\) | ||||
−0.828193 | + | 0.560444i | \(0.810631\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 513.777i | − | 0.524798i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 519.017i | − | 0.529069i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 219.814i | − | 0.223615i | −0.993730 | − | 0.111807i | \(-0.964336\pi\) | ||
0.993730 | − | 0.111807i | \(-0.0356640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −275.702 | −0.279900 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 34.9041i | − | 0.0353638i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −509.968 | −0.515640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 887.026i | 0.895082i | 0.894263 | + | 0.447541i | \(0.147700\pi\) | ||||
−0.894263 | + | 0.447541i | \(0.852300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1099.46 | −1.10721 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2369.42 | 2.38133 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 227.450 | 0.228135 | 0.114067 | − | 0.993473i | \(-0.463612\pi\) | ||||
0.114067 | + | 0.993473i | \(0.463612\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1690.67 | 1.69236 |
(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 | 1216.3.e.m.1025.6 | 8 | ||
4.3 | odd | 2 | 1216.3.e.n.1025.3 | 8 | |||
8.3 | odd | 2 | 304.3.e.g.113.6 | 8 | |||
8.5 | even | 2 | 152.3.e.b.113.3 | ✓ | 8 | ||
19.18 | odd | 2 | inner | 1216.3.e.m.1025.3 | 8 | ||
24.5 | odd | 2 | 1368.3.o.b.721.1 | 8 | |||
24.11 | even | 2 | 2736.3.o.p.721.1 | 8 | |||
76.75 | even | 2 | 1216.3.e.n.1025.6 | 8 | |||
152.37 | odd | 2 | 152.3.e.b.113.6 | yes | 8 | ||
152.75 | even | 2 | 304.3.e.g.113.3 | 8 | |||
456.227 | odd | 2 | 2736.3.o.p.721.2 | 8 | |||
456.341 | even | 2 | 1368.3.o.b.721.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.3.e.b.113.3 | ✓ | 8 | 8.5 | even | 2 | ||
152.3.e.b.113.6 | yes | 8 | 152.37 | odd | 2 | ||
304.3.e.g.113.3 | 8 | 152.75 | even | 2 | |||
304.3.e.g.113.6 | 8 | 8.3 | odd | 2 | |||
1216.3.e.m.1025.3 | 8 | 19.18 | odd | 2 | inner | ||
1216.3.e.m.1025.6 | 8 | 1.1 | even | 1 | trivial | ||
1216.3.e.n.1025.3 | 8 | 4.3 | odd | 2 | |||
1216.3.e.n.1025.6 | 8 | 76.75 | even | 2 | |||
1368.3.o.b.721.1 | 8 | 24.5 | odd | 2 | |||
1368.3.o.b.721.2 | 8 | 456.341 | even | 2 | |||
2736.3.o.p.721.1 | 8 | 24.11 | even | 2 | |||
2736.3.o.p.721.2 | 8 | 456.227 | odd | 2 |