Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.41421 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.24264 | 0.543920 | 0.271960 | − | 0.962309i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962309i | \(0.412328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.17157 | −0.588946 | −0.294473 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294473 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.58579 | 0.823632 | 0.411816 | − | 0.911267i | \(-0.364895\pi\) | ||||
0.411816 | + | 0.911267i | \(0.364895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41421 | 0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.82843 | −0.464991 | −0.232495 | − | 0.972598i | \(-0.574689\pi\) | ||||
−0.232495 | + | 0.972598i | \(0.574689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.82843 | −0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264 | 0.662589 | 0.331295 | − | 0.943527i | \(-0.392515\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.24264 | 1.20231 | 0.601156 | − | 0.799131i | \(-0.294707\pi\) | ||||
0.601156 | + | 0.799131i | \(0.294707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.17157 | 0.444109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.48528 | −0.616101 | −0.308050 | − | 0.951370i | \(-0.599677\pi\) | ||||
−0.308050 | + | 0.951370i | \(0.599677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.58579 | −0.597019 | −0.298509 | − | 0.954407i | \(-0.596489\pi\) | ||||
−0.298509 | + | 0.954407i | \(0.596489\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2426 | −1.56751 | −0.783755 | − | 0.621070i | \(-0.786698\pi\) | ||||
−0.783755 | + | 0.621070i | \(0.786698\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.41421 | −0.423481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.31371 | −1.13785 | −0.568925 | − | 0.822389i | \(-0.692641\pi\) | ||||
−0.568925 | + | 0.822389i | \(0.692641\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843 | 0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48528 | 0.532305 | 0.266152 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2426 | −1.19881 | −0.599405 | − | 0.800446i | \(-0.704596\pi\) | ||||
−0.599405 | + | 0.800446i | \(0.704596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.41421 | 0.163299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.17157 | −0.806865 | −0.403432 | − | 0.915009i | \(-0.632183\pi\) | ||||
−0.403432 | + | 0.915009i | \(0.632183\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.6569 | −1.93809 | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||||
−0.969046 | + | 0.246881i | \(0.920594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24264 | 0.243249 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.48528 | −0.480873 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.17157 | −0.336186 | −0.168093 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168093 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.41421 | 0.357907 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.48528 | 0.672492 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65685 | −0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.31371 | −0.945664 | −0.472832 | − | 0.881153i | \(-0.656768\pi\) | ||||
−0.472832 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421 | 0.140720 | 0.0703598 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703598 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4142 | 1.32174 | 0.660871 | − | 0.750500i | \(-0.270187\pi\) | ||||
0.660871 | + | 0.750500i | \(0.270187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41421 | −0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3137 | 1.09374 | 0.546869 | − | 0.837218i | \(-0.315820\pi\) | ||||
0.546869 | + | 0.837218i | \(0.315820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8284 | −1.22874 | −0.614370 | − | 0.789018i | \(-0.710590\pi\) | ||||
−0.614370 | + | 0.789018i | \(0.710590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.31371 | −0.876160 | −0.438080 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438080 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.41421 | 0.315644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.24264 | −0.205583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | 0.541002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82843 | 0.249029 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.31371 | 0.639002 | 0.319501 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319501 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.65685 | 0.490511 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.51472 | −0.300283 | −0.150141 | − | 0.988665i | \(-0.547973\pi\) | ||||
−0.150141 | + | 0.988665i | \(0.547973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.48528 | −0.719712 | −0.359856 | − | 0.933008i | \(-0.617174\pi\) | ||||
−0.359856 | + | 0.933008i | \(0.617174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6569 | 0.981684 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41421 | −0.285511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.17157 | −0.263385 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.41421 | 0.116642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8284 | −1.04396 | −0.521981 | − | 0.852957i | \(-0.674807\pi\) | ||||
−0.521981 | + | 0.852957i | \(0.674807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.24264 | −0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.58579 | 0.368339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1421 | −1.28828 | −0.644141 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644141 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.34315 | −0.503044 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.31371 | 0.102898 | 0.0514488 | − | 0.998676i | \(-0.483616\pi\) | ||||
0.0514488 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.41421 | 0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.1421 | 1.71341 | 0.856705 | − | 0.515807i | \(-0.172508\pi\) | ||||
0.856705 | + | 0.515807i | \(0.172508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.65685 | 0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.58579 | −0.652765 | −0.326383 | − | 0.945238i | \(-0.605830\pi\) | ||||
−0.326383 | + | 0.945238i | \(0.605830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.48528 | −0.487464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.3137 | −0.845626 | −0.422813 | − | 0.906217i | \(-0.638957\pi\) | ||||
−0.422813 | + | 0.906217i | \(0.638957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.3137 | −1.27987 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | −0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24264 | 0.163998 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.65685 | 0.411476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.65685 | −0.119886 | −0.0599429 | − | 0.998202i | \(-0.519092\pi\) | ||||
−0.0599429 | + | 0.998202i | \(0.519092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.4853 | −0.898710 | −0.449355 | − | 0.893353i | \(-0.648346\pi\) | ||||
−0.449355 | + | 0.893353i | \(0.648346\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.82843 | −0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.8284 | −1.34147 | −0.670735 | − | 0.741697i | \(-0.734021\pi\) | ||||
−0.670735 | + | 0.741697i | \(0.734021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5563 | 1.52809 | 0.764045 | − | 0.645164i | \(-0.223211\pi\) | ||||
0.764045 | + | 0.645164i | \(0.223211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.1716 | −0.929051 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.17157 | 0.222601 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.24264 | 0.296319 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | −0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.686292 | 0.0472463 | 0.0236231 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236231 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.34315 | 0.434625 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.58579 | −0.311303 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.4853 | −0.978825 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.65685 | −0.515056 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.24264 | −0.284108 | −0.142054 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142054 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9706 | 1.39187 | 0.695933 | − | 0.718107i | \(-0.254991\pi\) | ||||
0.695933 | + | 0.718107i | \(0.254991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.828427 | 0.0547440 | 0.0273720 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273720 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41421 | −0.0930484 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.24264 | 0.537691 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.1421 | −0.658803 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.65685 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.7279 | −1.85053 | −0.925264 | − | 0.379324i | \(-0.876157\pi\) | ||||
−0.925264 | + | 0.379324i | \(0.876157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.3137 | 1.22890 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.9706 | −1.58245 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.07107 | −0.320083 | −0.160041 | − | 0.987110i | \(-0.551163\pi\) | ||||
−0.160041 | + | 0.987110i | \(0.551163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.17157 | 0.198612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.828427 | 0.0516759 | 0.0258379 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258379 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.82843 | 0.175750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.17157 | 0.196315 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.65685 | 0.595467 | 0.297734 | − | 0.954649i | \(-0.403769\pi\) | ||||
0.297734 | + | 0.954649i | \(0.403769\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.48528 | −0.275529 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.48528 | −0.274495 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3137 | 0.811751 | 0.405876 | − | 0.913928i | \(-0.366967\pi\) | ||||
0.405876 | + | 0.913928i | \(0.366967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17157 | −0.0711680 | −0.0355840 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355840 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843 | 0.292230 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.79899 | 0.468596 | 0.234298 | − | 0.972165i | \(-0.424721\pi\) | ||||
0.234298 | + | 0.972165i | \(0.424721\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.58579 | −0.274544 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.48528 | 0.148259 | 0.0741297 | − | 0.997249i | \(-0.476382\pi\) | ||||
0.0741297 | + | 0.997249i | \(0.476382\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.24264 | −0.250435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1716 | −0.772131 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8995 | 0.928858 | 0.464429 | − | 0.885610i | \(-0.346260\pi\) | ||||
0.464429 | + | 0.885610i | \(0.346260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.58579 | −0.266995 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.82843 | −0.394898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.2426 | −0.701012 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1716 | 0.751741 | 0.375871 | − | 0.926672i | \(-0.377344\pi\) | ||||
0.375871 | + | 0.926672i | \(0.377344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9706 | 1.07920 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.2132 | 1.76994 | 0.884969 | − | 0.465650i | \(-0.154179\pi\) | ||||
0.884969 | + | 0.465650i | \(0.154179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.31371 | −0.526442 | −0.263221 | − | 0.964736i | \(-0.584785\pi\) | ||||
−0.263221 | + | 0.964736i | \(0.584785\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.9706 | 0.840831 | 0.420415 | − | 0.907332i | \(-0.361884\pi\) | ||||
0.420415 | + | 0.907332i | \(0.361884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.17157 | −0.177574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0000 | 0.893033 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.6863 | −0.705884 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.41421 | −0.189386 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1421 | −1.00326 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.24264 | −0.454431 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.686292 | −0.0377220 | −0.0188610 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188610 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.82843 | 0.154997 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.31371 | −0.508862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6274 | 1.23259 | 0.616297 | − | 0.787514i | \(-0.288632\pi\) | ||||
0.616297 | + | 0.787514i | \(0.288632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.1716 | −0.715382 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.58579 | 0.248334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.82843 | 0.152277 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00000 | 0.107366 | 0.0536828 | − | 0.998558i | \(-0.482904\pi\) | ||||
0.0536828 | + | 0.998558i | \(0.482904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.3848 | 0.984115 | 0.492057 | − | 0.870563i | \(-0.336245\pi\) | ||||
0.492057 | + | 0.870563i | \(0.336245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3137 | 1.03089 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.6274 | −1.73658 | −0.868291 | − | 0.496055i | \(-0.834781\pi\) | ||||
−0.868291 | + | 0.496055i | \(0.834781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.48528 | 0.238054 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.17157 | −0.167857 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1421 | −0.640837 | −0.320419 | − | 0.947276i | \(-0.603824\pi\) | ||||
−0.320419 | + | 0.947276i | \(0.603824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421 | 0.0742270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2426 | −0.536124 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.27208 | 0.379599 | 0.189800 | − | 0.981823i | \(-0.439216\pi\) | ||||
0.189800 | + | 0.981823i | \(0.439216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.24264 | −0.220863 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.48528 | 0.232864 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8284 | −1.18201 | −0.591006 | − | 0.806667i | \(-0.701269\pi\) | ||||
−0.591006 | + | 0.806667i | \(0.701269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41421 | 0.0730297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8284 | 0.557692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.85786 | −0.506364 | −0.253182 | − | 0.967419i | \(-0.581477\pi\) | ||||
−0.253182 | + | 0.967419i | \(0.581477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6569 | −0.699662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.72792 | −0.241586 | −0.120793 | − | 0.992678i | \(-0.538544\pi\) | ||||
−0.120793 | + | 0.992678i | \(0.538544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2843 | 1.53547 | 0.767737 | − | 0.640765i | \(-0.221383\pi\) | ||||
0.767737 | + | 0.640765i | \(0.221383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.48528 | 0.226830 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3431 | 0.521743 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.17157 | −0.360841 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.85786 | −0.193621 | −0.0968103 | − | 0.995303i | \(-0.530864\pi\) | ||||
−0.0968103 | + | 0.995303i | \(0.530864\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.3137 | 1.06436 | 0.532178 | − | 0.846633i | \(-0.321374\pi\) | ||||
0.532178 | + | 0.846633i | \(0.321374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6569 | −0.779923 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.00000 | −0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.82843 | −0.140200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7574 | −0.581364 | −0.290682 | − | 0.956820i | \(-0.593882\pi\) | ||||
−0.290682 | + | 0.956820i | \(0.593882\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.97056 | −0.245180 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.58579 | 0.225652 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6569 | −0.866741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.3848 | −1.58210 | −0.791050 | − | 0.611752i | \(-0.790465\pi\) | ||||
−0.791050 | + | 0.611752i | \(0.790465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.6274 | 1.68764 | 0.843819 | − | 0.536629i | \(-0.180302\pi\) | ||||
0.843819 | + | 0.536629i | \(0.180302\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.24264 | −0.400771 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.24264 | 0.108784 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2426 | 0.592463 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.82843 | −0.233119 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.14214 | −0.392193 | −0.196096 | − | 0.980585i | \(-0.562827\pi\) | ||||
−0.196096 | + | 0.980585i | \(0.562827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.4558 | 1.31944 | 0.659722 | − | 0.751510i | \(-0.270674\pi\) | ||||
0.659722 | + | 0.751510i | \(0.270674\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.48528 | −0.215053 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.3137 | −0.541208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.7990 | −1.70859 | −0.854296 | − | 0.519786i | \(-0.826012\pi\) | ||||
−0.854296 | + | 0.519786i | \(0.826012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1127 | 1.38319 | 0.691593 | − | 0.722287i | \(-0.256909\pi\) | ||||
0.691593 | + | 0.722287i | \(0.256909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.17157 | −0.150347 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.48528 | 0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3431 | 0.865667 | 0.432833 | − | 0.901474i | \(-0.357514\pi\) | ||||
0.432833 | + | 0.901474i | \(0.357514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.24264 | 0.199778 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1421 | −0.852392 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.41421 | 0.160061 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.51472 | −0.164412 | −0.0822058 | − | 0.996615i | \(-0.526196\pi\) | ||||
−0.0822058 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6863 | −0.592145 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.27208 | 0.338694 | 0.169347 | − | 0.985556i | \(-0.445834\pi\) | ||||
0.169347 | + | 0.985556i | \(0.445834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000 | 1.02243 | 0.511213 | − | 0.859454i | \(-0.329196\pi\) | ||||
0.511213 | + | 0.859454i | \(0.329196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.48528 | 0.300748 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.8701 | 0.688104 | 0.344052 | − | 0.938951i | \(-0.388200\pi\) | ||||
0.344052 | + | 0.938951i | \(0.388200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.31371 | 0.430067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.8284 | −1.05188 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65685 | −0.259554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.48528 | 0.205367 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | 0.365529 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.65685 | 0.440315 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.82843 | −0.128698 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.31371 | −0.422914 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.2843 | 1.37231 | 0.686156 | − | 0.727455i | \(-0.259297\pi\) | ||||
0.686156 | + | 0.727455i | \(0.259297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.85786 | 0.0840155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4853 | −1.55630 | −0.778149 | − | 0.628079i | \(-0.783841\pi\) | ||||
−0.778149 | + | 0.628079i | \(0.783841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.11270 | −0.320340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.48528 | −0.201192 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.201010 | −0.00899845 | −0.00449922 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449922 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.3137 | 1.39899 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6569 | −0.787280 | −0.393640 | − | 0.919265i | \(-0.628784\pi\) | ||||
−0.393640 | + | 0.919265i | \(0.628784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.41421 | 0.0629317 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.89949 | −0.0843595 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.4853 | −0.819346 | −0.409673 | − | 0.912233i | \(-0.634357\pi\) | ||||
−0.409673 | + | 0.912233i | \(0.634357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2426 | 0.453108 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.0000 | 1.41283 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.4142 | 0.591101 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.24264 | 0.362511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.1421 | −0.532981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3137 | 1.63474 | 0.817372 | − | 0.576111i | \(-0.195430\pi\) | ||||
0.817372 | + | 0.576111i | \(0.195430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.7696 | −1.78273 | −0.891364 | − | 0.453288i | \(-0.850251\pi\) | ||||
−0.891364 | + | 0.453288i | \(0.850251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.41421 | −0.0617213 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2843 | 0.447990 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.58579 | 0.199006 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4853 | −0.627427 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3137 | 0.489134 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0000 | −0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.31371 | 0.0564807 | 0.0282404 | − | 0.999601i | \(-0.491010\pi\) | ||||
0.0282404 | + | 0.999601i | \(0.491010\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.48528 | −0.364138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8284 | −0.549509 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3137 | 0.654767 | 0.327383 | − | 0.944892i | \(-0.393833\pi\) | ||||
0.327383 | + | 0.944892i | \(0.393833\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.2426 | 0.522503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9411 | 0.764318 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.17157 | 0.304966 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | −0.169791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.79899 | 0.160968 | 0.0804842 | − | 0.996756i | \(-0.474353\pi\) | ||||
0.0804842 | + | 0.996756i | \(0.474353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.82843 | −0.288812 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.17157 | 0.133904 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5147 | 0.822447 | 0.411224 | − | 0.911534i | \(-0.365102\pi\) | ||||
0.411224 | + | 0.911534i | \(0.365102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.31371 | −0.391831 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00000 | 0.209980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.8284 | 1.87931 | 0.939653 | − | 0.342130i | \(-0.111148\pi\) | ||||
0.939653 | + | 0.342130i | \(0.111148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6274 | 1.11432 | 0.557161 | − | 0.830404i | \(-0.311890\pi\) | ||||
0.557161 | + | 0.830404i | \(0.311890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.34315 | −0.0978863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.627417 | 0.0261197 | 0.0130599 | − | 0.999915i | \(-0.495843\pi\) | ||||
0.0130599 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.6569 | −0.733794 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.6569 | 0.732530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.48528 | −0.185761 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.41421 | 0.141160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.0416 | −1.48760 | −0.743799 | − | 0.668404i | \(-0.766978\pi\) | ||||
−0.743799 | + | 0.668404i | \(0.766978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.9411 | −1.06889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.6274 | −1.09531 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.8995 | 0.652914 | 0.326457 | − | 0.945212i | \(-0.394145\pi\) | ||||
0.326457 | + | 0.945212i | \(0.394145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.24264 | −0.0919393 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.4853 | 1.24768 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7990 | −1.13584 | −0.567918 | − | 0.823085i | \(-0.692251\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.0416 | −1.63333 | −0.816666 | − | 0.577110i | \(-0.804180\pi\) | ||||
−0.816666 | + | 0.577110i | \(0.804180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.31371 | 0.379284 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1421 | 1.22343 | 0.611716 | − | 0.791078i | \(-0.290480\pi\) | ||||
0.611716 | + | 0.791078i | \(0.290480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.48528 | 0.181753 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.1421 | −1.13851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.31371 | −0.133839 | −0.0669197 | − | 0.997758i | \(-0.521317\pi\) | ||||
−0.0669197 | + | 0.997758i | \(0.521317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.51472 | −0.141497 | −0.0707486 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707486 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.9289 | −1.08237 | −0.541183 | − | 0.840905i | \(-0.682023\pi\) | ||||
−0.541183 | + | 0.840905i | \(0.682023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.3137 | −0.454003 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.17157 | 0.127066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.34315 | −0.252918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6863 | 0.505033 | 0.252517 | − | 0.967593i | \(-0.418742\pi\) | ||||
0.252517 | + | 0.967593i | \(0.418742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.970563 | 0.0385764 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.65685 | −0.383221 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.41421 | −0.135276 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.48528 | −0.177435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.68629 | −0.343088 | −0.171544 | − | 0.985176i | \(-0.554876\pi\) | ||||
−0.171544 | + | 0.985176i | \(0.554876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.8995 | −1.49461 | −0.747305 | − | 0.664481i | \(-0.768653\pi\) | ||||
−0.747305 | + | 0.664481i | \(0.768653\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.82843 | 0.111369 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.8701 | −0.584602 | −0.292301 | − | 0.956326i | \(-0.594421\pi\) | ||||
−0.292301 | + | 0.956326i | \(0.594421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.58579 | −0.180008 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.48528 | −0.254178 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.31371 | −0.207941 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.31371 | 0.285770 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2426 | 0.399603 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.4853 | −1.03172 | −0.515860 | − | 0.856673i | \(-0.672528\pi\) | ||||
−0.515860 | + | 0.856673i | \(0.672528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.51472 | −0.370080 | −0.185040 | − | 0.982731i | \(-0.559241\pi\) | ||||
−0.185040 | + | 0.982731i | \(0.559241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.8284 | −0.420541 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.65685 | 0.219363 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.34315 | −0.245608 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.2426 | −0.472622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6863 | 0.489021 | 0.244510 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244510 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.3848 | −1.39838 | −0.699190 | − | 0.714936i | \(-0.746456\pi\) | ||||
−0.699190 | + | 0.714936i | \(0.746456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.31371 | 0.357427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.6569 | 1.13645 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.4558 | −1.50974 | −0.754868 | − | 0.655877i | \(-0.772299\pi\) | ||||
−0.754868 | + | 0.655877i | \(0.772299\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.51472 | −0.134290 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.17157 | 0.0446983 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.3137 | 0.583406 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.2426 | 0.541816 | 0.270908 | − | 0.962605i | \(-0.412676\pi\) | ||||
0.270908 | + | 0.962605i | \(0.412676\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.48528 | −0.321865 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.51472 | 0.360396 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685 | 0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.4558 | 1.03699 | 0.518496 | − | 0.855080i | \(-0.326492\pi\) | ||||
0.518496 | + | 0.855080i | \(0.326492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | 0.603451 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.6569 | 0.439023 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.41421 | −0.0531870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.3137 | 0.950676 | 0.475338 | − | 0.879803i | \(-0.342326\pi\) | ||||
0.475338 | + | 0.879803i | \(0.342326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.17157 | 0.268955 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.17157 | 0.343478 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.41421 | −0.127684 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.384776 | 0.0143497 | 0.00717487 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717487 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4142 | −0.499571 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −40.6274 | −1.51095 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.17157 | −0.117789 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.10051 | 0.0779034 | 0.0389517 | − | 0.999241i | \(-0.487598\pi\) | ||||
0.0389517 | + | 0.999241i | \(0.487598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.48528 | 0.165894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.786797 | −0.0290610 | −0.0145305 | − | 0.999894i | \(-0.504625\pi\) | ||||
−0.0145305 | + | 0.999894i | \(0.504625\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.31371 | −0.343075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.65685 | −0.355233 | −0.177617 | − | 0.984100i | \(-0.556839\pi\) | ||||
−0.177617 | + | 0.984100i | \(0.556839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.3137 | 1.00339 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.9706 | 0.475844 | 0.237922 | − | 0.971284i | \(-0.423534\pi\) | ||||
0.237922 | + | 0.971284i | \(0.423534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.6569 | 0.646031 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.45584 | 0.345049 | 0.172524 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.17157 | −0.261347 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.8284 | −0.466874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3431 | 1.32091 | 0.660457 | − | 0.750864i | \(-0.270363\pi\) | ||||
0.660457 | + | 0.750864i | \(0.270363\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.82843 | 0.102665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3848 | −0.376448 | −0.188224 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188224 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8284 | 0.464420 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.24264 | −0.0810828 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.6569 | 0.565336 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.2426 | −0.874212 | −0.437106 | − | 0.899410i | \(-0.643997\pi\) | ||||
−0.437106 | + | 0.899410i | \(0.643997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.17157 | 0.0421932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.9706 | 0.826194 | 0.413097 | − | 0.910687i | \(-0.364447\pi\) | ||||
0.413097 | + | 0.910687i | \(0.364447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.58579 | 0.164726 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0000 | −0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.48528 | 0.160496 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.9411 | 0.641164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.1421 | −0.576138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.8284 | 1.52667 | 0.763334 | − | 0.646004i | \(-0.223561\pi\) | ||||
0.763334 | + | 0.646004i | \(0.223561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.6569 | 0.486197 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.31371 | 0.331157 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.7990 | 1.48433 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.34315 | −0.224968 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.45584 | −0.122412 | −0.0612061 | − | 0.998125i | \(-0.519495\pi\) | ||||
−0.0612061 | + | 0.998125i | \(0.519495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.4853 | 0.653962 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.17157 | 0.112062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.2426 | −0.361455 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.00000 | −0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.8284 | 0.662792 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.6274 | −1.70965 | −0.854824 | − | 0.518917i | \(-0.826335\pi\) | ||||
−0.854824 | + | 0.518917i | \(0.826335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1421 | 0.777516 | 0.388758 | − | 0.921340i | \(-0.372904\pi\) | ||||
0.388758 | + | 0.921340i | \(0.372904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.65685 | −0.0581084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.31371 | 0.0460172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.3137 | −0.395817 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.41421 | −0.119302 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.5980 | −1.59138 | −0.795690 | − | 0.605704i | \(-0.792892\pi\) | ||||
−0.795690 | + | 0.605704i | \(0.792892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.8284 | −0.865465 | −0.432732 | − | 0.901522i | \(-0.642450\pi\) | ||||
−0.432732 | + | 0.901522i | \(0.642450\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.41421 | 0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.9706 | −1.49423 | −0.747116 | − | 0.664693i | \(-0.768562\pi\) | ||||
−0.747116 | + | 0.664693i | \(0.768562\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.343146 | 0.0119179 | 0.00595897 | − | 0.999982i | \(-0.498103\pi\) | ||||
0.00595897 | + | 0.999982i | \(0.498103\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0294 | 0.382607 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.24264 | 0.0777029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.1421 | 0.766260 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.9411 | −0.896656 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.0122 | 1.76114 | 0.880568 | − | 0.473919i | \(-0.157161\pi\) | ||||
0.880568 | + | 0.473919i | \(0.157161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.51472 | 0.121053 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.34315 | −0.0462056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.65685 | 0.194143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.65685 | −0.193914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.9289 | 1.19594 | 0.597972 | − | 0.801517i | \(-0.295973\pi\) | ||||
0.597972 | + | 0.801517i | \(0.295973\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.65685 | 0.193460 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.5858 | −1.52302 | −0.761511 | − | 0.648152i | \(-0.775542\pi\) | ||||
−0.761511 | + | 0.648152i | \(0.775542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.5563 | 1.69084 | 0.845420 | − | 0.534101i | \(-0.179350\pi\) | ||||
0.845420 | + | 0.534101i | \(0.179350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | −0.204479 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.4558 | −1.61542 | −0.807708 | − | 0.589583i | \(-0.799292\pi\) | ||||
−0.807708 | + | 0.589583i | \(0.799292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.58579 | −0.291925 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9289 | −0.574937 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.17157 | −0.243279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.7990 | 1.07747 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.31371 | 0.315221 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.68629 | −0.158245 | −0.0791224 | − | 0.996865i | \(-0.525212\pi\) | ||||
−0.0791224 | + | 0.996865i | \(0.525212\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.4853 | 0.758410 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3137 | 0.987604 | 0.493802 | − | 0.869574i | \(-0.335607\pi\) | ||||
0.493802 | + | 0.869574i | \(0.335607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.4558 | 1.32779 | 0.663897 | − | 0.747824i | \(-0.268901\pi\) | ||||
0.663897 | + | 0.747824i | \(0.268901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.48528 | −0.218000 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.79899 | −0.261864 | −0.130932 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130932 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.65685 | 0.323880 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.00000 | −0.167506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.6274 | −1.56033 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.3137 | −0.378176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.65685 | −0.322433 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.5442 | −0.485075 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0589 | −0.335110 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.82843 | −0.0941242 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.00000 | −0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.9411 | −0.927770 | −0.463885 | − | 0.885895i | \(-0.653545\pi\) | ||||
−0.463885 | + | 0.885895i | \(0.653545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.41421 | −0.0469065 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.8579 | −0.724183 | −0.362092 | − | 0.932142i | \(-0.617937\pi\) | ||||
−0.362092 | + | 0.932142i | \(0.617937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.6569 | −0.584357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.3137 | −0.572374 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.31371 | −0.241520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.970563 | 0.0320159 | 0.0160080 | − | 0.999872i | \(-0.494904\pi\) | ||||
0.0160080 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6274 | 0.613794 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.3137 | −0.504057 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.82843 | −0.0929981 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.4142 | −0.440581 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65685 | −0.185396 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.1421 | 1.44515 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.24264 | 0.0733422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.55635 | 0.312192 | 0.156096 | − | 0.987742i | \(-0.450109\pi\) | ||||
0.156096 | + | 0.987742i | \(0.450109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.1716 | −0.429838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.0122 | 1.46736 | 0.733678 | − | 0.679498i | \(-0.237802\pi\) | ||||
0.733678 | + | 0.679498i | \(0.237802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.48528 | 0.276319 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.65685 | 0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.5147 | −0.699134 | −0.349567 | − | 0.936911i | \(-0.613671\pi\) | ||||
−0.349567 | + | 0.936911i | \(0.613671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.9706 | 1.13519 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.1716 | 0.686535 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.5147 | 0.761716 | 0.380858 | − | 0.924633i | \(-0.375629\pi\) | ||||
0.380858 | + | 0.924633i | \(0.375629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.65685 | −0.0536145 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.48528 | −0.144989 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.51472 | 0.113496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.3137 | −0.364579 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4853 | −0.401915 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.9411 | −0.576352 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0416 | 0.322251 | 0.161126 | − | 0.986934i | \(-0.448488\pi\) | ||||
0.161126 | + | 0.986934i | \(0.448488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.48528 | 0.272026 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.82843 | −0.154633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.2843 | −0.840908 | −0.420454 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420454 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.17157 | −0.101364 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8284 | 0.409580 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.2426 | 1.53870 | 0.769351 | − | 0.638827i | \(-0.220580\pi\) | ||||
0.769351 | + | 0.638827i | \(0.220580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.8284 | −0.599924 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.6569 | −0.371042 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | 0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.7696 | −1.04096 | −0.520480 | − | 0.853874i | \(-0.674247\pi\) | ||||
−0.520480 | + | 0.853874i | \(0.674247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.970563 | −0.0307999 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.5563 | 0.683382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.8406 | −1.19842 | −0.599212 | − | 0.800590i | \(-0.704519\pi\) | ||||
−0.599212 | + | 0.800590i | \(0.704519\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 6160.2.a.bb.1.2 | 2 | ||
4.3 | odd | 2 | 3080.2.a.i.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.i.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
6160.2.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial |