Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8450,2,Mod(1,8450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8450.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: | \(67.4735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 650) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.30278 | 0.940104 | ||||||||
\(7\) | 0.697224 | 0.263526 | 0.131763 | − | 0.991281i | \(-0.457936\pi\) | ||||
0.131763 | + | 0.991281i | \(0.457936\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.697224 | 0.210221 | 0.105111 | − | 0.994461i | \(-0.466480\pi\) | ||||
0.105111 | + | 0.994461i | \(0.466480\pi\) | |||||||
\(12\) | 2.30278 | 0.664754 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.697224 | 0.186341 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.90833 | −0.705373 | −0.352686 | − | 0.935742i | \(-0.614732\pi\) | ||||
−0.352686 | + | 0.935742i | \(0.614732\pi\) | |||||||
\(18\) | 2.30278 | 0.542769 | ||||||||
\(19\) | 0.394449 | 0.0904927 | 0.0452464 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452464 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.60555 | 0.350360 | ||||||||
\(22\) | 0.697224 | 0.148649 | ||||||||
\(23\) | 5.60555 | 1.16884 | 0.584419 | − | 0.811452i | \(-0.301322\pi\) | ||||
0.584419 | + | 0.811452i | \(0.301322\pi\) | |||||||
\(24\) | 2.30278 | 0.470052 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | 0.697224 | 0.131763 | ||||||||
\(29\) | 3.30278 | 0.613310 | 0.306655 | − | 0.951821i | \(-0.400790\pi\) | ||||
0.306655 | + | 0.951821i | \(0.400790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.60555 | 1.54560 | 0.772801 | − | 0.634648i | \(-0.218855\pi\) | ||||
0.772801 | + | 0.634648i | \(0.218855\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.60555 | 0.279491 | ||||||||
\(34\) | −2.90833 | −0.498774 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.30278 | 0.383796 | ||||||||
\(37\) | −3.69722 | −0.607820 | −0.303910 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303910 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(38\) | 0.394449 | 0.0639880 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | −0.0780869 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780869 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(42\) | 1.60555 | 0.247742 | ||||||||
\(43\) | −8.51388 | −1.29835 | −0.649177 | − | 0.760637i | \(-0.724887\pi\) | ||||
−0.649177 | + | 0.760637i | \(0.724887\pi\) | |||||||
\(44\) | 0.697224 | 0.105111 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.60555 | 0.826493 | ||||||||
\(47\) | 10.3028 | 1.50281 | 0.751407 | − | 0.659839i | \(-0.229375\pi\) | ||||
0.751407 | + | 0.659839i | \(0.229375\pi\) | |||||||
\(48\) | 2.30278 | 0.332377 | ||||||||
\(49\) | −6.51388 | −0.930554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.69722 | −0.937799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2111 | 1.67732 | 0.838662 | − | 0.544652i | \(-0.183338\pi\) | ||||
0.838662 | + | 0.544652i | \(0.183338\pi\) | |||||||
\(54\) | −1.60555 | −0.218488 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.697224 | 0.0931705 | ||||||||
\(57\) | 0.908327 | 0.120311 | ||||||||
\(58\) | 3.30278 | 0.433676 | ||||||||
\(59\) | 10.2111 | 1.32937 | 0.664686 | − | 0.747123i | \(-0.268565\pi\) | ||||
0.664686 | + | 0.747123i | \(0.268565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.21110 | 0.539176 | 0.269588 | − | 0.962976i | \(-0.413112\pi\) | ||||
0.269588 | + | 0.962976i | \(0.413112\pi\) | |||||||
\(62\) | 8.60555 | 1.09291 | ||||||||
\(63\) | 1.60555 | 0.202280 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.60555 | 0.197630 | ||||||||
\(67\) | 5.60555 | 0.684827 | 0.342414 | − | 0.939549i | \(-0.388756\pi\) | ||||
0.342414 | + | 0.939549i | \(0.388756\pi\) | |||||||
\(68\) | −2.90833 | −0.352686 | ||||||||
\(69\) | 12.9083 | 1.55398 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6056 | 1.25865 | 0.629324 | − | 0.777143i | \(-0.283332\pi\) | ||||
0.629324 | + | 0.777143i | \(0.283332\pi\) | |||||||
\(72\) | 2.30278 | 0.271385 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | −3.69722 | −0.429794 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.394449 | 0.0452464 | ||||||||
\(77\) | 0.486122 | 0.0553987 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.30278 | 1.04664 | 0.523322 | − | 0.852135i | \(-0.324692\pi\) | ||||
0.523322 | + | 0.852135i | \(0.324692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 16.8167 | 1.84587 | 0.922934 | − | 0.384959i | \(-0.125784\pi\) | ||||
0.922934 | + | 0.384959i | \(0.125784\pi\) | |||||||
\(84\) | 1.60555 | 0.175180 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.51388 | −0.918075 | ||||||||
\(87\) | 7.60555 | 0.815401 | ||||||||
\(88\) | 0.697224 | 0.0743244 | ||||||||
\(89\) | −0.0916731 | −0.00971733 | −0.00485866 | − | 0.999988i | \(-0.501547\pi\) | ||||
−0.00485866 | + | 0.999988i | \(0.501547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.60555 | 0.584419 | ||||||||
\(93\) | 19.8167 | 2.05489 | ||||||||
\(94\) | 10.3028 | 1.06265 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.30278 | 0.235026 | ||||||||
\(97\) | −11.6972 | −1.18767 | −0.593837 | − | 0.804586i | \(-0.702387\pi\) | ||||
−0.593837 | + | 0.804586i | \(0.702387\pi\) | |||||||
\(98\) | −6.51388 | −0.658001 | ||||||||
\(99\) | 1.60555 | 0.161364 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.21110 | −0.618028 | −0.309014 | − | 0.951058i | \(-0.599999\pi\) | ||||
−0.309014 | + | 0.951058i | \(0.599999\pi\) | |||||||
\(102\) | −6.69722 | −0.663124 | ||||||||
\(103\) | −6.39445 | −0.630064 | −0.315032 | − | 0.949081i | \(-0.602015\pi\) | ||||
−0.315032 | + | 0.949081i | \(0.602015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2111 | 1.18605 | ||||||||
\(107\) | −13.8167 | −1.33571 | −0.667853 | − | 0.744293i | \(-0.732787\pi\) | ||||
−0.667853 | + | 0.744293i | \(0.732787\pi\) | |||||||
\(108\) | −1.60555 | −0.154494 | ||||||||
\(109\) | −11.6056 | −1.11161 | −0.555805 | − | 0.831313i | \(-0.687590\pi\) | ||||
−0.555805 | + | 0.831313i | \(0.687590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.51388 | −0.808102 | ||||||||
\(112\) | 0.697224 | 0.0658815 | ||||||||
\(113\) | 10.5139 | 0.989062 | 0.494531 | − | 0.869160i | \(-0.335340\pi\) | ||||
0.494531 | + | 0.869160i | \(0.335340\pi\) | |||||||
\(114\) | 0.908327 | 0.0850726 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30278 | 0.306655 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.2111 | 0.940008 | ||||||||
\(119\) | −2.02776 | −0.185884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5139 | −0.955807 | ||||||||
\(122\) | 4.21110 | 0.381255 | ||||||||
\(123\) | −2.30278 | −0.207634 | ||||||||
\(124\) | 8.60555 | 0.772801 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.60555 | 0.143034 | ||||||||
\(127\) | −4.90833 | −0.435544 | −0.217772 | − | 0.976000i | \(-0.569879\pi\) | ||||
−0.217772 | + | 0.976000i | \(0.569879\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −19.6056 | −1.72617 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81665 | 0.770315 | 0.385157 | − | 0.922851i | \(-0.374147\pi\) | ||||
0.385157 | + | 0.922851i | \(0.374147\pi\) | |||||||
\(132\) | 1.60555 | 0.139745 | ||||||||
\(133\) | 0.275019 | 0.0238472 | ||||||||
\(134\) | 5.60555 | 0.484246 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.90833 | −0.249387 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 12.9083 | 1.09883 | ||||||||
\(139\) | −9.81665 | −0.832638 | −0.416319 | − | 0.909219i | \(-0.636680\pi\) | ||||
−0.416319 | + | 0.909219i | \(0.636680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.7250 | 1.99800 | ||||||||
\(142\) | 10.6056 | 0.889998 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.30278 | 0.191898 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | −15.0000 | −1.23718 | ||||||||
\(148\) | −3.69722 | −0.303910 | ||||||||
\(149\) | 8.30278 | 0.680190 | 0.340095 | − | 0.940391i | \(-0.389541\pi\) | ||||
0.340095 | + | 0.940391i | \(0.389541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1194 | 0.986265 | 0.493133 | − | 0.869954i | \(-0.335852\pi\) | ||||
0.493133 | + | 0.869954i | \(0.335852\pi\) | |||||||
\(152\) | 0.394449 | 0.0319940 | ||||||||
\(153\) | −6.69722 | −0.541438 | ||||||||
\(154\) | 0.486122 | 0.0391728 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.4222 | 1.94910 | 0.974552 | − | 0.224161i | \(-0.0719642\pi\) | ||||
0.974552 | + | 0.224161i | \(0.0719642\pi\) | |||||||
\(158\) | 9.30278 | 0.740089 | ||||||||
\(159\) | 28.1194 | 2.23002 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.90833 | 0.308019 | ||||||||
\(162\) | −10.6056 | −0.833251 | ||||||||
\(163\) | −1.90833 | −0.149472 | −0.0747358 | − | 0.997203i | \(-0.523811\pi\) | ||||
−0.0747358 | + | 0.997203i | \(0.523811\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.8167 | 1.30523 | ||||||||
\(167\) | −3.60555 | −0.279006 | −0.139503 | − | 0.990222i | \(-0.544550\pi\) | ||||
−0.139503 | + | 0.990222i | \(0.544550\pi\) | |||||||
\(168\) | 1.60555 | 0.123871 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.908327 | 0.0694615 | ||||||||
\(172\) | −8.51388 | −0.649177 | ||||||||
\(173\) | −6.48612 | −0.493131 | −0.246565 | − | 0.969126i | \(-0.579302\pi\) | ||||
−0.246565 | + | 0.969126i | \(0.579302\pi\) | |||||||
\(174\) | 7.60555 | 0.576575 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.697224 | 0.0525553 | ||||||||
\(177\) | 23.5139 | 1.76741 | ||||||||
\(178\) | −0.0916731 | −0.00687119 | ||||||||
\(179\) | 7.21110 | 0.538983 | 0.269492 | − | 0.963003i | \(-0.413144\pi\) | ||||
0.269492 | + | 0.963003i | \(0.413144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9083 | −1.33112 | −0.665558 | − | 0.746346i | \(-0.731806\pi\) | ||||
−0.665558 | + | 0.746346i | \(0.731806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.69722 | 0.716839 | ||||||||
\(184\) | 5.60555 | 0.413247 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 19.8167 | 1.45303 | ||||||||
\(187\) | −2.02776 | −0.148284 | ||||||||
\(188\) | 10.3028 | 0.751407 | ||||||||
\(189\) | −1.11943 | −0.0814265 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8167 | −0.782666 | −0.391333 | − | 0.920249i | \(-0.627986\pi\) | ||||
−0.391333 | + | 0.920249i | \(0.627986\pi\) | |||||||
\(192\) | 2.30278 | 0.166189 | ||||||||
\(193\) | 17.5139 | 1.26068 | 0.630338 | − | 0.776321i | \(-0.282916\pi\) | ||||
0.630338 | + | 0.776321i | \(0.282916\pi\) | |||||||
\(194\) | −11.6972 | −0.839812 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.51388 | −0.465277 | ||||||||
\(197\) | −22.3028 | −1.58901 | −0.794503 | − | 0.607260i | \(-0.792269\pi\) | ||||
−0.794503 | + | 0.607260i | \(0.792269\pi\) | |||||||
\(198\) | 1.60555 | 0.114102 | ||||||||
\(199\) | 3.90833 | 0.277054 | 0.138527 | − | 0.990359i | \(-0.455763\pi\) | ||||
0.138527 | + | 0.990359i | \(0.455763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.9083 | 0.910483 | ||||||||
\(202\) | −6.21110 | −0.437012 | ||||||||
\(203\) | 2.30278 | 0.161623 | ||||||||
\(204\) | −6.69722 | −0.468899 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.39445 | −0.445522 | ||||||||
\(207\) | 12.9083 | 0.897191 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.275019 | 0.0190235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.81665 | −0.469278 | −0.234639 | − | 0.972083i | \(-0.575391\pi\) | ||||
−0.234639 | + | 0.972083i | \(0.575391\pi\) | |||||||
\(212\) | 12.2111 | 0.838662 | ||||||||
\(213\) | 24.4222 | 1.67338 | ||||||||
\(214\) | −13.8167 | −0.944487 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.60555 | −0.109244 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −11.6056 | −0.786027 | ||||||||
\(219\) | −18.4222 | −1.24486 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.51388 | −0.571414 | ||||||||
\(223\) | 26.8167 | 1.79578 | 0.897888 | − | 0.440224i | \(-0.145101\pi\) | ||||
0.897888 | + | 0.440224i | \(0.145101\pi\) | |||||||
\(224\) | 0.697224 | 0.0465853 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5139 | 0.699373 | ||||||||
\(227\) | −19.0000 | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(228\) | 0.908327 | 0.0601554 | ||||||||
\(229\) | −7.51388 | −0.496531 | −0.248266 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248266 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.11943 | 0.0736531 | ||||||||
\(232\) | 3.30278 | 0.216838 | ||||||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.2111 | 0.664686 | ||||||||
\(237\) | 21.4222 | 1.39152 | ||||||||
\(238\) | −2.02776 | −0.131440 | ||||||||
\(239\) | 0.577795 | 0.0373744 | 0.0186872 | − | 0.999825i | \(-0.494051\pi\) | ||||
0.0186872 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | −0.322078 | −0.161039 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161039 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(242\) | −10.5139 | −0.675858 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | 4.21110 | 0.269588 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.30278 | −0.146820 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.60555 | 0.546453 | ||||||||
\(249\) | 38.7250 | 2.45410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3305 | −1.09389 | −0.546947 | − | 0.837167i | \(-0.684210\pi\) | ||||
−0.546947 | + | 0.837167i | \(0.684210\pi\) | |||||||
\(252\) | 1.60555 | 0.101140 | ||||||||
\(253\) | 3.90833 | 0.245714 | ||||||||
\(254\) | −4.90833 | −0.307976 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.60555 | 0.349665 | 0.174832 | − | 0.984598i | \(-0.444062\pi\) | ||||
0.174832 | + | 0.984598i | \(0.444062\pi\) | |||||||
\(258\) | −19.6056 | −1.22059 | ||||||||
\(259\) | −2.57779 | −0.160176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.60555 | 0.470772 | ||||||||
\(262\) | 8.81665 | 0.544695 | ||||||||
\(263\) | 18.7250 | 1.15463 | 0.577316 | − | 0.816521i | \(-0.304100\pi\) | ||||
0.577316 | + | 0.816521i | \(0.304100\pi\) | |||||||
\(264\) | 1.60555 | 0.0988149 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.275019 | 0.0168625 | ||||||||
\(267\) | −0.211103 | −0.0129193 | ||||||||
\(268\) | 5.60555 | 0.342414 | ||||||||
\(269\) | −28.8167 | −1.75698 | −0.878491 | − | 0.477759i | \(-0.841449\pi\) | ||||
−0.878491 | + | 0.477759i | \(0.841449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.42221 | −0.147138 | −0.0735692 | − | 0.997290i | \(-0.523439\pi\) | ||||
−0.0735692 | + | 0.997290i | \(0.523439\pi\) | |||||||
\(272\) | −2.90833 | −0.176343 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.9083 | 0.776990 | ||||||||
\(277\) | −32.1194 | −1.92987 | −0.964935 | − | 0.262490i | \(-0.915456\pi\) | ||||
−0.964935 | + | 0.262490i | \(0.915456\pi\) | |||||||
\(278\) | −9.81665 | −0.588764 | ||||||||
\(279\) | 19.8167 | 1.18639 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3028 | −0.793577 | −0.396789 | − | 0.917910i | \(-0.629875\pi\) | ||||
−0.396789 | + | 0.917910i | \(0.629875\pi\) | |||||||
\(282\) | 23.7250 | 1.41280 | ||||||||
\(283\) | 22.5139 | 1.33831 | 0.669156 | − | 0.743122i | \(-0.266656\pi\) | ||||
0.669156 | + | 0.743122i | \(0.266656\pi\) | |||||||
\(284\) | 10.6056 | 0.629324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.697224 | −0.0411559 | ||||||||
\(288\) | 2.30278 | 0.135692 | ||||||||
\(289\) | −8.54163 | −0.502449 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.9361 | −1.57902 | ||||||||
\(292\) | −8.00000 | −0.468165 | ||||||||
\(293\) | −2.51388 | −0.146862 | −0.0734312 | − | 0.997300i | \(-0.523395\pi\) | ||||
−0.0734312 | + | 0.997300i | \(0.523395\pi\) | |||||||
\(294\) | −15.0000 | −0.874818 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.69722 | −0.214897 | ||||||||
\(297\) | −1.11943 | −0.0649559 | ||||||||
\(298\) | 8.30278 | 0.480967 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.93608 | −0.342150 | ||||||||
\(302\) | 12.1194 | 0.697395 | ||||||||
\(303\) | −14.3028 | −0.821673 | ||||||||
\(304\) | 0.394449 | 0.0226232 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.69722 | −0.382855 | ||||||||
\(307\) | −11.2111 | −0.639851 | −0.319926 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319926 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(308\) | 0.486122 | 0.0276994 | ||||||||
\(309\) | −14.7250 | −0.837675 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.90833 | −0.561850 | −0.280925 | − | 0.959730i | \(-0.590641\pi\) | ||||
−0.280925 | + | 0.959730i | \(0.590641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.9083 | −0.899192 | −0.449596 | − | 0.893232i | \(-0.648432\pi\) | ||||
−0.449596 | + | 0.893232i | \(0.648432\pi\) | |||||||
\(314\) | 24.4222 | 1.37822 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.30278 | 0.523322 | ||||||||
\(317\) | −11.4861 | −0.645125 | −0.322562 | − | 0.946548i | \(-0.604544\pi\) | ||||
−0.322562 | + | 0.946548i | \(0.604544\pi\) | |||||||
\(318\) | 28.1194 | 1.57686 | ||||||||
\(319\) | 2.30278 | 0.128931 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.8167 | −1.77583 | ||||||||
\(322\) | 3.90833 | 0.217803 | ||||||||
\(323\) | −1.14719 | −0.0638311 | ||||||||
\(324\) | −10.6056 | −0.589197 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.90833 | −0.105692 | ||||||||
\(327\) | −26.7250 | −1.47789 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 7.18335 | 0.396031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9083 | 1.14923 | 0.574613 | − | 0.818425i | \(-0.305153\pi\) | ||||
0.574613 | + | 0.818425i | \(0.305153\pi\) | |||||||
\(332\) | 16.8167 | 0.922934 | ||||||||
\(333\) | −8.51388 | −0.466558 | ||||||||
\(334\) | −3.60555 | −0.197287 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.60555 | 0.0875900 | ||||||||
\(337\) | 14.0278 | 0.764141 | 0.382070 | − | 0.924133i | \(-0.375211\pi\) | ||||
0.382070 | + | 0.924133i | \(0.375211\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.2111 | 1.31497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0.908327 | 0.0491167 | ||||||||
\(343\) | −9.42221 | −0.508751 | ||||||||
\(344\) | −8.51388 | −0.459038 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.48612 | −0.348696 | ||||||||
\(347\) | −2.21110 | −0.118698 | −0.0593491 | − | 0.998237i | \(-0.518903\pi\) | ||||
−0.0593491 | + | 0.998237i | \(0.518903\pi\) | |||||||
\(348\) | 7.60555 | 0.407700 | ||||||||
\(349\) | 33.7250 | 1.80526 | 0.902628 | − | 0.430421i | \(-0.141635\pi\) | ||||
0.902628 | + | 0.430421i | \(0.141635\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.697224 | 0.0371622 | ||||||||
\(353\) | −20.5139 | −1.09184 | −0.545922 | − | 0.837836i | \(-0.683820\pi\) | ||||
−0.545922 | + | 0.837836i | \(0.683820\pi\) | |||||||
\(354\) | 23.5139 | 1.24975 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0916731 | −0.00485866 | ||||||||
\(357\) | −4.66947 | −0.247134 | ||||||||
\(358\) | 7.21110 | 0.381119 | ||||||||
\(359\) | 22.9361 | 1.21052 | 0.605260 | − | 0.796028i | \(-0.293069\pi\) | ||||
0.605260 | + | 0.796028i | \(0.293069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8444 | −0.991811 | ||||||||
\(362\) | −17.9083 | −0.941241 | ||||||||
\(363\) | −24.2111 | −1.27075 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.69722 | 0.506882 | ||||||||
\(367\) | −25.8167 | −1.34762 | −0.673809 | − | 0.738905i | \(-0.735343\pi\) | ||||
−0.673809 | + | 0.738905i | \(0.735343\pi\) | |||||||
\(368\) | 5.60555 | 0.292210 | ||||||||
\(369\) | −2.30278 | −0.119878 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.51388 | 0.442019 | ||||||||
\(372\) | 19.8167 | 1.02745 | ||||||||
\(373\) | −15.2111 | −0.787601 | −0.393801 | − | 0.919196i | \(-0.628840\pi\) | ||||
−0.393801 | + | 0.919196i | \(0.628840\pi\) | |||||||
\(374\) | −2.02776 | −0.104853 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3028 | 0.531325 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.11943 | −0.0575772 | ||||||||
\(379\) | 34.8167 | 1.78841 | 0.894206 | − | 0.447656i | \(-0.147741\pi\) | ||||
0.894206 | + | 0.447656i | \(0.147741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3028 | −0.579059 | ||||||||
\(382\) | −10.8167 | −0.553428 | ||||||||
\(383\) | −11.6056 | −0.593016 | −0.296508 | − | 0.955030i | \(-0.595822\pi\) | ||||
−0.296508 | + | 0.955030i | \(0.595822\pi\) | |||||||
\(384\) | 2.30278 | 0.117513 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.5139 | 0.891433 | ||||||||
\(387\) | −19.6056 | −0.996606 | ||||||||
\(388\) | −11.6972 | −0.593837 | ||||||||
\(389\) | −9.21110 | −0.467021 | −0.233511 | − | 0.972354i | \(-0.575021\pi\) | ||||
−0.233511 | + | 0.972354i | \(0.575021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3028 | −0.824467 | ||||||||
\(392\) | −6.51388 | −0.329001 | ||||||||
\(393\) | 20.3028 | 1.02414 | ||||||||
\(394\) | −22.3028 | −1.12360 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.60555 | 0.0806820 | ||||||||
\(397\) | 10.3305 | 0.518475 | 0.259237 | − | 0.965814i | \(-0.416529\pi\) | ||||
0.259237 | + | 0.965814i | \(0.416529\pi\) | |||||||
\(398\) | 3.90833 | 0.195907 | ||||||||
\(399\) | 0.633308 | 0.0317050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7250 | −0.735330 | −0.367665 | − | 0.929958i | \(-0.619843\pi\) | ||||
−0.367665 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(402\) | 12.9083 | 0.643809 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.21110 | −0.309014 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.30278 | 0.114285 | ||||||||
\(407\) | −2.57779 | −0.127777 | ||||||||
\(408\) | −6.69722 | −0.331562 | ||||||||
\(409\) | 34.2111 | 1.69163 | 0.845815 | − | 0.533476i | \(-0.179115\pi\) | ||||
0.845815 | + | 0.533476i | \(0.179115\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.39445 | −0.315032 | ||||||||
\(413\) | 7.11943 | 0.350324 | ||||||||
\(414\) | 12.9083 | 0.634410 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.6056 | −1.10700 | ||||||||
\(418\) | 0.275019 | 0.0134516 | ||||||||
\(419\) | 17.3028 | 0.845296 | 0.422648 | − | 0.906294i | \(-0.361101\pi\) | ||||
0.422648 | + | 0.906294i | \(0.361101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9083 | 1.45764 | 0.728821 | − | 0.684704i | \(-0.240068\pi\) | ||||
0.728821 | + | 0.684704i | \(0.240068\pi\) | |||||||
\(422\) | −6.81665 | −0.331830 | ||||||||
\(423\) | 23.7250 | 1.15355 | ||||||||
\(424\) | 12.2111 | 0.593024 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 24.4222 | 1.18326 | ||||||||
\(427\) | 2.93608 | 0.142087 | ||||||||
\(428\) | −13.8167 | −0.667853 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.908327 | −0.0437526 | −0.0218763 | − | 0.999761i | \(-0.506964\pi\) | ||||
−0.0218763 | + | 0.999761i | \(0.506964\pi\) | |||||||
\(432\) | −1.60555 | −0.0772471 | ||||||||
\(433\) | 36.8167 | 1.76930 | 0.884648 | − | 0.466260i | \(-0.154399\pi\) | ||||
0.884648 | + | 0.466260i | \(0.154399\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.6056 | −0.555805 | ||||||||
\(437\) | 2.21110 | 0.105771 | ||||||||
\(438\) | −18.4222 | −0.880247 | ||||||||
\(439\) | 11.0278 | 0.526326 | 0.263163 | − | 0.964751i | \(-0.415234\pi\) | ||||
0.263163 | + | 0.964751i | \(0.415234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.88057 | 0.374417 | 0.187209 | − | 0.982320i | \(-0.440056\pi\) | ||||
0.187209 | + | 0.982320i | \(0.440056\pi\) | |||||||
\(444\) | −8.51388 | −0.404051 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.8167 | 1.26981 | ||||||||
\(447\) | 19.1194 | 0.904318 | ||||||||
\(448\) | 0.697224 | 0.0329408 | ||||||||
\(449\) | −36.9083 | −1.74181 | −0.870906 | − | 0.491450i | \(-0.836467\pi\) | ||||
−0.870906 | + | 0.491450i | \(0.836467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.697224 | −0.0328310 | ||||||||
\(452\) | 10.5139 | 0.494531 | ||||||||
\(453\) | 27.9083 | 1.31125 | ||||||||
\(454\) | −19.0000 | −0.891714 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.908327 | 0.0425363 | ||||||||
\(457\) | −10.5139 | −0.491818 | −0.245909 | − | 0.969293i | \(-0.579087\pi\) | ||||
−0.245909 | + | 0.969293i | \(0.579087\pi\) | |||||||
\(458\) | −7.51388 | −0.351100 | ||||||||
\(459\) | 4.66947 | 0.217952 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.48612 | −0.395238 | −0.197619 | − | 0.980279i | \(-0.563321\pi\) | ||||
−0.197619 | + | 0.980279i | \(0.563321\pi\) | |||||||
\(462\) | 1.11943 | 0.0520806 | ||||||||
\(463\) | −10.4861 | −0.487331 | −0.243666 | − | 0.969859i | \(-0.578350\pi\) | ||||
−0.243666 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(464\) | 3.30278 | 0.153328 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.0000 | −0.972806 | ||||||||
\(467\) | 16.4861 | 0.762887 | 0.381443 | − | 0.924392i | \(-0.375427\pi\) | ||||
0.381443 | + | 0.924392i | \(0.375427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.90833 | 0.180470 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 56.2389 | 2.59135 | ||||||||
\(472\) | 10.2111 | 0.470004 | ||||||||
\(473\) | −5.93608 | −0.272941 | ||||||||
\(474\) | 21.4222 | 0.983954 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.02776 | −0.0929421 | ||||||||
\(477\) | 28.1194 | 1.28750 | ||||||||
\(478\) | 0.577795 | 0.0264277 | ||||||||
\(479\) | −31.7250 | −1.44955 | −0.724776 | − | 0.688985i | \(-0.758057\pi\) | ||||
−0.724776 | + | 0.688985i | \(0.758057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.00000 | −0.227744 | ||||||||
\(483\) | 9.00000 | 0.409514 | ||||||||
\(484\) | −10.5139 | −0.477904 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.6056 | −0.889326 | ||||||||
\(487\) | 0.302776 | 0.0137201 | 0.00686004 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686004 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(488\) | 4.21110 | 0.190628 | ||||||||
\(489\) | −4.39445 | −0.198724 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.4222 | −1.68884 | −0.844420 | − | 0.535681i | \(-0.820055\pi\) | ||||
−0.844420 | + | 0.535681i | \(0.820055\pi\) | |||||||
\(492\) | −2.30278 | −0.103817 | ||||||||
\(493\) | −9.60555 | −0.432612 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.60555 | 0.386401 | ||||||||
\(497\) | 7.39445 | 0.331686 | ||||||||
\(498\) | 38.7250 | 1.73531 | ||||||||
\(499\) | 28.6333 | 1.28180 | 0.640901 | − | 0.767623i | \(-0.278561\pi\) | ||||
0.640901 | + | 0.767623i | \(0.278561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.30278 | −0.370941 | ||||||||
\(502\) | −17.3305 | −0.773499 | ||||||||
\(503\) | −24.6056 | −1.09711 | −0.548554 | − | 0.836115i | \(-0.684821\pi\) | ||||
−0.548554 | + | 0.836115i | \(0.684821\pi\) | |||||||
\(504\) | 1.60555 | 0.0715169 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.90833 | 0.173746 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.90833 | −0.217772 | ||||||||
\(509\) | 4.18335 | 0.185424 | 0.0927118 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927118 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.57779 | −0.246747 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.633308 | −0.0279612 | ||||||||
\(514\) | 5.60555 | 0.247250 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19.6056 | −0.863086 | ||||||||
\(517\) | 7.18335 | 0.315923 | ||||||||
\(518\) | −2.57779 | −0.113262 | ||||||||
\(519\) | −14.9361 | −0.655621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8444 | −1.00083 | −0.500416 | − | 0.865785i | \(-0.666820\pi\) | ||||
−0.500416 | + | 0.865785i | \(0.666820\pi\) | |||||||
\(522\) | 7.60555 | 0.332886 | ||||||||
\(523\) | 23.2111 | 1.01495 | 0.507475 | − | 0.861666i | \(-0.330579\pi\) | ||||
0.507475 | + | 0.861666i | \(0.330579\pi\) | |||||||
\(524\) | 8.81665 | 0.385157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7250 | 0.816448 | ||||||||
\(527\) | −25.0278 | −1.09023 | ||||||||
\(528\) | 1.60555 | 0.0698727 | ||||||||
\(529\) | 8.42221 | 0.366183 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.5139 | 1.02042 | ||||||||
\(532\) | 0.275019 | 0.0119236 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.211103 | −0.00913530 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.60555 | 0.242123 | ||||||||
\(537\) | 16.6056 | 0.716582 | ||||||||
\(538\) | −28.8167 | −1.24237 | ||||||||
\(539\) | −4.54163 | −0.195622 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8167 | −0.765998 | −0.382999 | − | 0.923749i | \(-0.625109\pi\) | ||||
−0.382999 | + | 0.923749i | \(0.625109\pi\) | |||||||
\(542\) | −2.42221 | −0.104043 | ||||||||
\(543\) | −41.2389 | −1.76973 | ||||||||
\(544\) | −2.90833 | −0.124693 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6056 | −0.923787 | −0.461893 | − | 0.886935i | \(-0.652830\pi\) | ||||
−0.461893 | + | 0.886935i | \(0.652830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.69722 | 0.413867 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.30278 | 0.0555001 | ||||||||
\(552\) | 12.9083 | 0.549415 | ||||||||
\(553\) | 6.48612 | 0.275818 | ||||||||
\(554\) | −32.1194 | −1.36462 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.81665 | −0.416319 | ||||||||
\(557\) | 9.81665 | 0.415945 | 0.207972 | − | 0.978135i | \(-0.433314\pi\) | ||||
0.207972 | + | 0.978135i | \(0.433314\pi\) | |||||||
\(558\) | 19.8167 | 0.838906 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.66947 | −0.197145 | ||||||||
\(562\) | −13.3028 | −0.561144 | ||||||||
\(563\) | 20.7250 | 0.873454 | 0.436727 | − | 0.899594i | \(-0.356138\pi\) | ||||
0.436727 | + | 0.899594i | \(0.356138\pi\) | |||||||
\(564\) | 23.7250 | 0.999002 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.5139 | 0.946329 | ||||||||
\(567\) | −7.39445 | −0.310538 | ||||||||
\(568\) | 10.6056 | 0.444999 | ||||||||
\(569\) | 28.1472 | 1.17999 | 0.589996 | − | 0.807406i | \(-0.299129\pi\) | ||||
0.589996 | + | 0.807406i | \(0.299129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5139 | 0.565538 | 0.282769 | − | 0.959188i | \(-0.408747\pi\) | ||||
0.282769 | + | 0.959188i | \(0.408747\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.9083 | −1.04056 | ||||||||
\(574\) | −0.697224 | −0.0291016 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.30278 | 0.0959490 | ||||||||
\(577\) | −23.6056 | −0.982712 | −0.491356 | − | 0.870959i | \(-0.663499\pi\) | ||||
−0.491356 | + | 0.870959i | \(0.663499\pi\) | |||||||
\(578\) | −8.54163 | −0.355285 | ||||||||
\(579\) | 40.3305 | 1.67608 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.7250 | 0.486434 | ||||||||
\(582\) | −26.9361 | −1.11654 | ||||||||
\(583\) | 8.51388 | 0.352609 | ||||||||
\(584\) | −8.00000 | −0.331042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.51388 | −0.103847 | ||||||||
\(587\) | −14.4861 | −0.597906 | −0.298953 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298953 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(588\) | −15.0000 | −0.618590 | ||||||||
\(589\) | 3.39445 | 0.139866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −51.3583 | −2.11260 | ||||||||
\(592\) | −3.69722 | −0.151955 | ||||||||
\(593\) | −42.6611 | −1.75188 | −0.875940 | − | 0.482420i | \(-0.839758\pi\) | ||||
−0.875940 | + | 0.482420i | \(0.839758\pi\) | |||||||
\(594\) | −1.11943 | −0.0459307 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.30278 | 0.340095 | ||||||||
\(597\) | 9.00000 | 0.368345 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.6611 | 1.53879 | 0.769395 | − | 0.638774i | \(-0.220558\pi\) | ||||
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.39445 | −0.342417 | −0.171208 | − | 0.985235i | \(-0.554767\pi\) | ||||
−0.171208 | + | 0.985235i | \(0.554767\pi\) | |||||||
\(602\) | −5.93608 | −0.241937 | ||||||||
\(603\) | 12.9083 | 0.525668 | ||||||||
\(604\) | 12.1194 | 0.493133 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.3028 | −0.581011 | ||||||||
\(607\) | −31.0555 | −1.26050 | −0.630252 | − | 0.776390i | \(-0.717049\pi\) | ||||
−0.630252 | + | 0.776390i | \(0.717049\pi\) | |||||||
\(608\) | 0.394449 | 0.0159970 | ||||||||
\(609\) | 5.30278 | 0.214879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.69722 | −0.270719 | ||||||||
\(613\) | −21.4500 | −0.866356 | −0.433178 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433178 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(614\) | −11.2111 | −0.452443 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.486122 | 0.0195864 | ||||||||
\(617\) | −23.0555 | −0.928180 | −0.464090 | − | 0.885788i | \(-0.653619\pi\) | ||||
−0.464090 | + | 0.885788i | \(0.653619\pi\) | |||||||
\(618\) | −14.7250 | −0.592326 | ||||||||
\(619\) | −7.33053 | −0.294639 | −0.147319 | − | 0.989089i | \(-0.547065\pi\) | ||||
−0.147319 | + | 0.989089i | \(0.547065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.00000 | −0.361158 | ||||||||
\(622\) | −9.90833 | −0.397288 | ||||||||
\(623\) | −0.0639167 | −0.00256077 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.9083 | −0.635825 | ||||||||
\(627\) | 0.633308 | 0.0252919 | ||||||||
\(628\) | 24.4222 | 0.974552 | ||||||||
\(629\) | 10.7527 | 0.428740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09167 | 0.202696 | 0.101348 | − | 0.994851i | \(-0.467684\pi\) | ||||
0.101348 | + | 0.994851i | \(0.467684\pi\) | |||||||
\(632\) | 9.30278 | 0.370045 | ||||||||
\(633\) | −15.6972 | −0.623909 | ||||||||
\(634\) | −11.4861 | −0.456172 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28.1194 | 1.11501 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.30278 | 0.0911678 | ||||||||
\(639\) | 24.4222 | 0.966128 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.1749 | 1.86330 | 0.931649 | − | 0.363359i | \(-0.118370\pi\) | ||||
0.931649 | + | 0.363359i | \(0.118370\pi\) | |||||||
\(642\) | −31.8167 | −1.25570 | ||||||||
\(643\) | −35.4222 | −1.39692 | −0.698458 | − | 0.715651i | \(-0.746130\pi\) | ||||
−0.698458 | + | 0.715651i | \(0.746130\pi\) | |||||||
\(644\) | 3.90833 | 0.154010 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.14719 | −0.0451354 | ||||||||
\(647\) | −16.3028 | −0.640928 | −0.320464 | − | 0.947261i | \(-0.603839\pi\) | ||||
−0.320464 | + | 0.947261i | \(0.603839\pi\) | |||||||
\(648\) | −10.6056 | −0.416625 | ||||||||
\(649\) | 7.11943 | 0.279462 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.8167 | 0.541517 | ||||||||
\(652\) | −1.90833 | −0.0747358 | ||||||||
\(653\) | 8.21110 | 0.321325 | 0.160663 | − | 0.987009i | \(-0.448637\pi\) | ||||
0.160663 | + | 0.987009i | \(0.448637\pi\) | |||||||
\(654\) | −26.7250 | −1.04503 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −18.4222 | −0.718719 | ||||||||
\(658\) | 7.18335 | 0.280036 | ||||||||
\(659\) | −9.21110 | −0.358814 | −0.179407 | − | 0.983775i | \(-0.557418\pi\) | ||||
−0.179407 | + | 0.983775i | \(0.557418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3028 | 1.10085 | 0.550425 | − | 0.834884i | \(-0.314466\pi\) | ||||
0.550425 | + | 0.834884i | \(0.314466\pi\) | |||||||
\(662\) | 20.9083 | 0.812625 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.8167 | 0.652613 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.51388 | −0.329906 | ||||||||
\(667\) | 18.5139 | 0.716860 | ||||||||
\(668\) | −3.60555 | −0.139503 | ||||||||
\(669\) | 61.7527 | 2.38750 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.93608 | 0.113346 | ||||||||
\(672\) | 1.60555 | 0.0619355 | ||||||||
\(673\) | −15.0278 | −0.579277 | −0.289639 | − | 0.957136i | \(-0.593535\pi\) | ||||
−0.289639 | + | 0.957136i | \(0.593535\pi\) | |||||||
\(674\) | 14.0278 | 0.540329 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.42221 | −0.285259 | −0.142629 | − | 0.989776i | \(-0.545556\pi\) | ||||
−0.142629 | + | 0.989776i | \(0.545556\pi\) | |||||||
\(678\) | 24.2111 | 0.929822 | ||||||||
\(679\) | −8.15559 | −0.312983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −43.7527 | −1.67661 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | 16.6333 | 0.636456 | 0.318228 | − | 0.948014i | \(-0.396912\pi\) | ||||
0.318228 | + | 0.948014i | \(0.396912\pi\) | |||||||
\(684\) | 0.908327 | 0.0347307 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.42221 | −0.359741 | ||||||||
\(687\) | −17.3028 | −0.660142 | ||||||||
\(688\) | −8.51388 | −0.324589 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.3944 | 0.889967 | 0.444983 | − | 0.895539i | \(-0.353210\pi\) | ||||
0.444983 | + | 0.895539i | \(0.353210\pi\) | |||||||
\(692\) | −6.48612 | −0.246565 | ||||||||
\(693\) | 1.11943 | 0.0425236 | ||||||||
\(694\) | −2.21110 | −0.0839323 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.60555 | 0.288288 | ||||||||
\(697\) | 2.90833 | 0.110161 | ||||||||
\(698\) | 33.7250 | 1.27651 | ||||||||
\(699\) | −48.3583 | −1.82908 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.09167 | −0.116771 | −0.0583854 | − | 0.998294i | \(-0.518595\pi\) | ||||
−0.0583854 | + | 0.998294i | \(0.518595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45837 | −0.0550033 | ||||||||
\(704\) | 0.697224 | 0.0262776 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.5139 | −0.772050 | ||||||||
\(707\) | −4.33053 | −0.162866 | ||||||||
\(708\) | 23.5139 | 0.883706 | ||||||||
\(709\) | −6.54163 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.4222 | 0.803395 | ||||||||
\(712\) | −0.0916731 | −0.00343559 | ||||||||
\(713\) | 48.2389 | 1.80656 | ||||||||
\(714\) | −4.66947 | −0.174750 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.21110 | 0.269492 | ||||||||
\(717\) | 1.33053 | 0.0496896 | ||||||||
\(718\) | 22.9361 | 0.855967 | ||||||||
\(719\) | −7.93608 | −0.295966 | −0.147983 | − | 0.988990i | \(-0.547278\pi\) | ||||
−0.147983 | + | 0.988990i | \(0.547278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.45837 | −0.166038 | ||||||||
\(722\) | −18.8444 | −0.701316 | ||||||||
\(723\) | −11.5139 | −0.428206 | ||||||||
\(724\) | −17.9083 | −0.665558 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24.2111 | −0.898558 | ||||||||
\(727\) | −42.0555 | −1.55975 | −0.779876 | − | 0.625934i | \(-0.784718\pi\) | ||||
−0.779876 | + | 0.625934i | \(0.784718\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.7611 | 0.915824 | ||||||||
\(732\) | 9.69722 | 0.358420 | ||||||||
\(733\) | −41.5416 | −1.53438 | −0.767188 | − | 0.641423i | \(-0.778344\pi\) | ||||
−0.767188 | + | 0.641423i | \(0.778344\pi\) | |||||||
\(734\) | −25.8167 | −0.952910 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.60555 | 0.206623 | ||||||||
\(737\) | 3.90833 | 0.143965 | ||||||||
\(738\) | −2.30278 | −0.0847663 | ||||||||
\(739\) | 14.7250 | 0.541667 | 0.270834 | − | 0.962626i | \(-0.412701\pi\) | ||||
0.270834 | + | 0.962626i | \(0.412701\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.51388 | 0.312554 | ||||||||
\(743\) | −35.2111 | −1.29177 | −0.645885 | − | 0.763435i | \(-0.723511\pi\) | ||||
−0.645885 | + | 0.763435i | \(0.723511\pi\) | |||||||
\(744\) | 19.8167 | 0.726514 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.2111 | −0.556918 | ||||||||
\(747\) | 38.7250 | 1.41687 | ||||||||
\(748\) | −2.02776 | −0.0741421 | ||||||||
\(749\) | −9.63331 | −0.351993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.6333 | 1.19081 | 0.595403 | − | 0.803427i | \(-0.296992\pi\) | ||||
0.595403 | + | 0.803427i | \(0.296992\pi\) | |||||||
\(752\) | 10.3028 | 0.375704 | ||||||||
\(753\) | −39.9083 | −1.45434 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.11943 | −0.0407133 | ||||||||
\(757\) | −9.78890 | −0.355784 | −0.177892 | − | 0.984050i | \(-0.556928\pi\) | ||||
−0.177892 | + | 0.984050i | \(0.556928\pi\) | |||||||
\(758\) | 34.8167 | 1.26460 | ||||||||
\(759\) | 9.00000 | 0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.6056 | 0.710701 | 0.355350 | − | 0.934733i | \(-0.384362\pi\) | ||||
0.355350 | + | 0.934733i | \(0.384362\pi\) | |||||||
\(762\) | −11.3028 | −0.409456 | ||||||||
\(763\) | −8.09167 | −0.292938 | ||||||||
\(764\) | −10.8167 | −0.391333 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.6056 | −0.419326 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.30278 | 0.0830943 | ||||||||
\(769\) | −21.4500 | −0.773505 | −0.386753 | − | 0.922183i | \(-0.626403\pi\) | ||||
−0.386753 | + | 0.922183i | \(0.626403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.9083 | 0.464882 | ||||||||
\(772\) | 17.5139 | 0.630338 | ||||||||
\(773\) | 40.8444 | 1.46907 | 0.734536 | − | 0.678570i | \(-0.237400\pi\) | ||||
0.734536 | + | 0.678570i | \(0.237400\pi\) | |||||||
\(774\) | −19.6056 | −0.704707 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.6972 | −0.419906 | ||||||||
\(777\) | −5.93608 | −0.212956 | ||||||||
\(778\) | −9.21110 | −0.330234 | ||||||||
\(779\) | −0.394449 | −0.0141326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.39445 | 0.264594 | ||||||||
\(782\) | −16.3028 | −0.582986 | ||||||||
\(783\) | −5.30278 | −0.189506 | ||||||||
\(784\) | −6.51388 | −0.232639 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.3028 | 0.724176 | ||||||||
\(787\) | −18.3028 | −0.652423 | −0.326212 | − | 0.945297i | \(-0.605772\pi\) | ||||
−0.326212 | + | 0.945297i | \(0.605772\pi\) | |||||||
\(788\) | −22.3028 | −0.794503 | ||||||||
\(789\) | 43.1194 | 1.53509 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.33053 | 0.260644 | ||||||||
\(792\) | 1.60555 | 0.0570508 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 10.3305 | 0.366617 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.90833 | 0.138527 | ||||||||
\(797\) | 1.00000 | 0.0354218 | 0.0177109 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177109 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(798\) | 0.633308 | 0.0224188 | ||||||||
\(799\) | −29.9638 | −1.06004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.211103 | −0.00745894 | ||||||||
\(802\) | −14.7250 | −0.519957 | ||||||||
\(803\) | −5.57779 | −0.196836 | ||||||||
\(804\) | 12.9083 | 0.455242 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −66.3583 | −2.33592 | ||||||||
\(808\) | −6.21110 | −0.218506 | ||||||||
\(809\) | −13.6333 | −0.479322 | −0.239661 | − | 0.970857i | \(-0.577036\pi\) | ||||
−0.239661 | + | 0.970857i | \(0.577036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6972 | 0.761893 | 0.380946 | − | 0.924597i | \(-0.375598\pi\) | ||||
0.380946 | + | 0.924597i | \(0.375598\pi\) | |||||||
\(812\) | 2.30278 | 0.0808116 | ||||||||
\(813\) | −5.57779 | −0.195622 | ||||||||
\(814\) | −2.57779 | −0.0903517 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.69722 | −0.234450 | ||||||||
\(817\) | −3.35829 | −0.117492 | ||||||||
\(818\) | 34.2111 | 1.19616 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.4222 | −1.37584 | −0.687922 | − | 0.725784i | \(-0.741477\pi\) | ||||
−0.687922 | + | 0.725784i | \(0.741477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.1833 | −0.424685 | −0.212342 | − | 0.977195i | \(-0.568109\pi\) | ||||
−0.212342 | + | 0.977195i | \(0.568109\pi\) | |||||||
\(824\) | −6.39445 | −0.222761 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.11943 | 0.247717 | ||||||||
\(827\) | −50.4500 | −1.75432 | −0.877159 | − | 0.480201i | \(-0.840564\pi\) | ||||
−0.877159 | + | 0.480201i | \(0.840564\pi\) | |||||||
\(828\) | 12.9083 | 0.448595 | ||||||||
\(829\) | 38.9083 | 1.35134 | 0.675671 | − | 0.737203i | \(-0.263854\pi\) | ||||
0.675671 | + | 0.737203i | \(0.263854\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −73.9638 | −2.56578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.9445 | 0.656388 | ||||||||
\(834\) | −22.6056 | −0.782766 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.275019 | 0.00951174 | ||||||||
\(837\) | −13.8167 | −0.477573 | ||||||||
\(838\) | 17.3028 | 0.597714 | ||||||||
\(839\) | −12.9361 | −0.446603 | −0.223302 | − | 0.974749i | \(-0.571683\pi\) | ||||
−0.223302 | + | 0.974749i | \(0.571683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.0917 | −0.623851 | ||||||||
\(842\) | 29.9083 | 1.03071 | ||||||||
\(843\) | −30.6333 | −1.05507 | ||||||||
\(844\) | −6.81665 | −0.234639 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23.7250 | 0.815682 | ||||||||
\(847\) | −7.33053 | −0.251880 | ||||||||
\(848\) | 12.2111 | 0.419331 | ||||||||
\(849\) | 51.8444 | 1.77930 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.7250 | −0.710443 | ||||||||
\(852\) | 24.4222 | 0.836691 | ||||||||
\(853\) | −8.27502 | −0.283331 | −0.141666 | − | 0.989915i | \(-0.545246\pi\) | ||||
−0.141666 | + | 0.989915i | \(0.545246\pi\) | |||||||
\(854\) | 2.93608 | 0.100471 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.8167 | −0.472244 | ||||||||
\(857\) | −20.5778 | −0.702924 | −0.351462 | − | 0.936202i | \(-0.614315\pi\) | ||||
−0.351462 | + | 0.936202i | \(0.614315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.1194 | 0.515868 | 0.257934 | − | 0.966163i | \(-0.416958\pi\) | ||||
0.257934 | + | 0.966163i | \(0.416958\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.60555 | −0.0547170 | ||||||||
\(862\) | −0.908327 | −0.0309377 | ||||||||
\(863\) | −4.02776 | −0.137106 | −0.0685532 | − | 0.997647i | \(-0.521838\pi\) | ||||
−0.0685532 | + | 0.997647i | \(0.521838\pi\) | |||||||
\(864\) | −1.60555 | −0.0546220 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.8167 | 1.25108 | ||||||||
\(867\) | −19.6695 | −0.668010 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | 6.48612 | 0.220027 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.6056 | −0.393014 | ||||||||
\(873\) | −26.9361 | −0.911648 | ||||||||
\(874\) | 2.21110 | 0.0747917 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.4222 | −0.622429 | ||||||||
\(877\) | −47.4777 | −1.60321 | −0.801604 | − | 0.597855i | \(-0.796020\pi\) | ||||
−0.801604 | + | 0.597855i | \(0.796020\pi\) | |||||||
\(878\) | 11.0278 | 0.372169 | ||||||||
\(879\) | −5.78890 | −0.195255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.5694 | 1.09729 | 0.548645 | − | 0.836055i | \(-0.315144\pi\) | ||||
0.548645 | + | 0.836055i | \(0.315144\pi\) | |||||||
\(882\) | −15.0000 | −0.505076 | ||||||||
\(883\) | −2.11943 | −0.0713245 | −0.0356622 | − | 0.999364i | \(-0.511354\pi\) | ||||
−0.0356622 | + | 0.999364i | \(0.511354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.88057 | 0.264753 | ||||||||
\(887\) | −38.4222 | −1.29009 | −0.645046 | − | 0.764144i | \(-0.723162\pi\) | ||||
−0.645046 | + | 0.764144i | \(0.723162\pi\) | |||||||
\(888\) | −8.51388 | −0.285707 | ||||||||
\(889\) | −3.42221 | −0.114777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.39445 | −0.247723 | ||||||||
\(892\) | 26.8167 | 0.897888 | ||||||||
\(893\) | 4.06392 | 0.135994 | ||||||||
\(894\) | 19.1194 | 0.639449 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.697224 | 0.0232926 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.9083 | −1.23165 | ||||||||
\(899\) | 28.4222 | 0.947934 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.5139 | −1.18314 | ||||||||
\(902\) | −0.697224 | −0.0232150 | ||||||||
\(903\) | −13.6695 | −0.454891 | ||||||||
\(904\) | 10.5139 | 0.349686 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.9083 | 0.927192 | ||||||||
\(907\) | 45.6611 | 1.51615 | 0.758075 | − | 0.652167i | \(-0.226140\pi\) | ||||
0.758075 | + | 0.652167i | \(0.226140\pi\) | |||||||
\(908\) | −19.0000 | −0.630537 | ||||||||
\(909\) | −14.3028 | −0.474393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.57779 | 0.284195 | 0.142098 | − | 0.989853i | \(-0.454615\pi\) | ||||
0.142098 | + | 0.989853i | \(0.454615\pi\) | |||||||
\(912\) | 0.908327 | 0.0300777 | ||||||||
\(913\) | 11.7250 | 0.388040 | ||||||||
\(914\) | −10.5139 | −0.347768 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.51388 | −0.248266 | ||||||||
\(917\) | 6.14719 | 0.202998 | ||||||||
\(918\) | 4.66947 | 0.154115 | ||||||||
\(919\) | 28.2389 | 0.931514 | 0.465757 | − | 0.884913i | \(-0.345782\pi\) | ||||
0.465757 | + | 0.884913i | \(0.345782\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.8167 | −0.850688 | ||||||||
\(922\) | −8.48612 | −0.279476 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.11943 | 0.0368265 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.4861 | −0.344595 | ||||||||
\(927\) | −14.7250 | −0.483632 | ||||||||
\(928\) | 3.30278 | 0.108419 | ||||||||
\(929\) | 40.6611 | 1.33405 | 0.667023 | − | 0.745037i | \(-0.267568\pi\) | ||||
0.667023 | + | 0.745037i | \(0.267568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.56939 | −0.0842084 | ||||||||
\(932\) | −21.0000 | −0.687878 | ||||||||
\(933\) | −22.8167 | −0.746984 | ||||||||
\(934\) | 16.4861 | 0.539442 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.3305 | 1.25220 | 0.626102 | − | 0.779741i | \(-0.284649\pi\) | ||||
0.626102 | + | 0.779741i | \(0.284649\pi\) | |||||||
\(938\) | 3.90833 | 0.127611 | ||||||||
\(939\) | −36.6333 | −1.19548 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.5694 | 1.38772 | 0.693861 | − | 0.720109i | \(-0.255908\pi\) | ||||
0.693861 | + | 0.720109i | \(0.255908\pi\) | |||||||
\(942\) | 56.2389 | 1.83236 | ||||||||
\(943\) | −5.60555 | −0.182542 | ||||||||
\(944\) | 10.2111 | 0.332343 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.93608 | −0.192999 | ||||||||
\(947\) | 51.3305 | 1.66802 | 0.834009 | − | 0.551751i | \(-0.186040\pi\) | ||||
0.834009 | + | 0.551751i | \(0.186040\pi\) | |||||||
\(948\) | 21.4222 | 0.695761 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.4500 | −0.857699 | ||||||||
\(952\) | −2.02776 | −0.0657200 | ||||||||
\(953\) | −57.4777 | −1.86189 | −0.930943 | − | 0.365165i | \(-0.881013\pi\) | ||||
−0.930943 | + | 0.365165i | \(0.881013\pi\) | |||||||
\(954\) | 28.1194 | 0.910400 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.577795 | 0.0186872 | ||||||||
\(957\) | 5.30278 | 0.171414 | ||||||||
\(958\) | −31.7250 | −1.02499 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.0555 | 1.38889 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.8167 | −1.02528 | ||||||||
\(964\) | −5.00000 | −0.161039 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | 0.289570 | ||||||||
\(967\) | 41.0278 | 1.31936 | 0.659682 | − | 0.751545i | \(-0.270691\pi\) | ||||
0.659682 | + | 0.751545i | \(0.270691\pi\) | |||||||
\(968\) | −10.5139 | −0.337929 | ||||||||
\(969\) | −2.64171 | −0.0848640 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4500 | −0.592087 | −0.296044 | − | 0.955174i | \(-0.595667\pi\) | ||||
−0.296044 | + | 0.955174i | \(0.595667\pi\) | |||||||
\(972\) | −19.6056 | −0.628848 | ||||||||
\(973\) | −6.84441 | −0.219422 | ||||||||
\(974\) | 0.302776 | 0.00970156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.21110 | 0.134794 | ||||||||
\(977\) | 16.8167 | 0.538012 | 0.269006 | − | 0.963138i | \(-0.413305\pi\) | ||||
0.269006 | + | 0.963138i | \(0.413305\pi\) | |||||||
\(978\) | −4.39445 | −0.140519 | ||||||||
\(979\) | −0.0639167 | −0.00204279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.7250 | −0.853263 | ||||||||
\(982\) | −37.4222 | −1.19419 | ||||||||
\(983\) | 28.9638 | 0.923803 | 0.461902 | − | 0.886931i | \(-0.347167\pi\) | ||||
0.461902 | + | 0.886931i | \(0.347167\pi\) | |||||||
\(984\) | −2.30278 | −0.0734098 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.60555 | −0.305903 | ||||||||
\(987\) | 16.5416 | 0.526526 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.7250 | −1.51757 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84441 | 0.0903557 | 0.0451778 | − | 0.998979i | \(-0.485615\pi\) | ||||
0.0451778 | + | 0.998979i | \(0.485615\pi\) | |||||||
\(992\) | 8.60555 | 0.273227 | ||||||||
\(993\) | 48.1472 | 1.52790 | ||||||||
\(994\) | 7.39445 | 0.234538 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.7250 | 1.22705 | ||||||||
\(997\) | 1.09167 | 0.0345736 | 0.0172868 | − | 0.999851i | \(-0.494497\pi\) | ||||
0.0172868 | + | 0.999851i | \(0.494497\pi\) | |||||||
\(998\) | 28.6333 | 0.906372 | ||||||||
\(999\) | 5.93608 | 0.187809 |
(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 | 8450.2.a.bl.1.2 | 2 | ||
5.4 | even | 2 | 8450.2.a.ba.1.1 | 2 | |||
13.4 | even | 6 | 650.2.e.g.601.1 | yes | 4 | ||
13.10 | even | 6 | 650.2.e.g.451.1 | yes | 4 | ||
13.12 | even | 2 | 8450.2.a.bd.1.2 | 2 | |||
65.4 | even | 6 | 650.2.e.e.601.2 | yes | 4 | ||
65.17 | odd | 12 | 650.2.o.h.549.1 | 8 | |||
65.23 | odd | 12 | 650.2.o.h.399.1 | 8 | |||
65.43 | odd | 12 | 650.2.o.h.549.4 | 8 | |||
65.49 | even | 6 | 650.2.e.e.451.2 | ✓ | 4 | ||
65.62 | odd | 12 | 650.2.o.h.399.4 | 8 | |||
65.64 | even | 2 | 8450.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
650.2.e.e.451.2 | ✓ | 4 | 65.49 | even | 6 | ||
650.2.e.e.601.2 | yes | 4 | 65.4 | even | 6 | ||
650.2.e.g.451.1 | yes | 4 | 13.10 | even | 6 | ||
650.2.e.g.601.1 | yes | 4 | 13.4 | even | 6 | ||
650.2.o.h.399.1 | 8 | 65.23 | odd | 12 | |||
650.2.o.h.399.4 | 8 | 65.62 | odd | 12 | |||
650.2.o.h.549.1 | 8 | 65.17 | odd | 12 | |||
650.2.o.h.549.4 | 8 | 65.43 | odd | 12 | |||
8450.2.a.ba.1.1 | 2 | 5.4 | even | 2 | |||
8450.2.a.bd.1.2 | 2 | 13.12 | even | 2 | |||
8450.2.a.bi.1.1 | 2 | 65.64 | even | 2 | |||
8450.2.a.bl.1.2 | 2 | 1.1 | even | 1 | trivial |