Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, 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("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.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: | \(24.1547466114\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30278 | 0.921201 | 0.460601 | − | 0.887607i | \(-0.347634\pi\) | ||||
0.460601 | + | 0.887607i | \(0.347634\pi\) | |||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | −0.302776 | −0.151388 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | −0.697224 | −0.263526 | −0.131763 | − | 0.991281i | \(-0.542064\pi\) | ||||
−0.131763 | + | 0.991281i | \(0.542064\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.697224 | −0.201271 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −0.908327 | −0.242761 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.30278 | −0.825694 | ||||||||
\(17\) | −6.90833 | −1.67552 | −0.837758 | − | 0.546042i | \(-0.816134\pi\) | ||||
−0.837758 | + | 0.546042i | \(0.816134\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.60555 | −0.350360 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.30278 | −1.52273 | −0.761367 | − | 0.648321i | \(-0.775471\pi\) | ||||
−0.761367 | + | 0.648321i | \(0.775471\pi\) | |||||||
\(24\) | −6.90833 | −1.41016 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.51388 | −1.27748 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | 0.211103 | 0.0398946 | ||||||||
\(29\) | −0.908327 | −0.168672 | −0.0843360 | − | 0.996437i | \(-0.526877\pi\) | ||||
−0.0843360 | + | 0.996437i | \(0.526877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2111 | 1.83397 | 0.916984 | − | 0.398924i | \(-0.130616\pi\) | ||||
0.916984 | + | 0.398924i | \(0.130616\pi\) | |||||||
\(32\) | 1.69722 | 0.300030 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.00000 | −1.54349 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.697224 | −0.116204 | ||||||||
\(37\) | 2.39445 | 0.393645 | 0.196822 | − | 0.980439i | \(-0.436938\pi\) | ||||
0.196822 | + | 0.980439i | \(0.436938\pi\) | |||||||
\(38\) | 1.30278 | 0.211338 | ||||||||
\(39\) | −11.5139 | −1.84370 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.60555 | 0.875440 | 0.437720 | − | 0.899111i | \(-0.355786\pi\) | ||||
0.437720 | + | 0.899111i | \(0.355786\pi\) | |||||||
\(42\) | −2.09167 | −0.322752 | ||||||||
\(43\) | −7.21110 | −1.09968 | −0.549841 | − | 0.835269i | \(-0.685312\pi\) | ||||
−0.549841 | + | 0.835269i | \(0.685312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.51388 | −1.40274 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | −7.60555 | −1.09777 | ||||||||
\(49\) | −6.51388 | −0.930554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.9083 | −2.22761 | ||||||||
\(52\) | 1.51388 | 0.209937 | ||||||||
\(53\) | −1.30278 | −0.178950 | −0.0894750 | − | 0.995989i | \(-0.528519\pi\) | ||||
−0.0894750 | + | 0.995989i | \(0.528519\pi\) | |||||||
\(54\) | −2.09167 | −0.284641 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09167 | 0.279512 | ||||||||
\(57\) | 2.30278 | 0.305010 | ||||||||
\(58\) | −1.18335 | −0.155381 | ||||||||
\(59\) | −14.2111 | −1.85013 | −0.925064 | − | 0.379811i | \(-0.875989\pi\) | ||||
−0.925064 | + | 0.379811i | \(0.875989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.90833 | 1.01256 | 0.506279 | − | 0.862370i | \(-0.331021\pi\) | ||||
0.506279 | + | 0.862370i | \(0.331021\pi\) | |||||||
\(62\) | 13.3028 | 1.68945 | ||||||||
\(63\) | −1.60555 | −0.202280 | ||||||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 2.09167 | 0.253653 | ||||||||
\(69\) | −16.8167 | −2.02449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.60555 | −0.309222 | −0.154611 | − | 0.987975i | \(-0.549412\pi\) | ||||
−0.154611 | + | 0.987975i | \(0.549412\pi\) | |||||||
\(72\) | −6.90833 | −0.814154 | ||||||||
\(73\) | 7.90833 | 0.925600 | 0.462800 | − | 0.886463i | \(-0.346845\pi\) | ||||
0.462800 | + | 0.886463i | \(0.346845\pi\) | |||||||
\(74\) | 3.11943 | 0.362626 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.302776 | −0.0347307 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −15.0000 | −1.69842 | ||||||||
\(79\) | 10.9083 | 1.22728 | 0.613641 | − | 0.789585i | \(-0.289704\pi\) | ||||
0.613641 | + | 0.789585i | \(0.289704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | 7.30278 | 0.806457 | ||||||||
\(83\) | 3.51388 | 0.385698 | 0.192849 | − | 0.981228i | \(-0.438227\pi\) | ||||
0.192849 | + | 0.981228i | \(0.438227\pi\) | |||||||
\(84\) | 0.486122 | 0.0530402 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.39445 | −1.01303 | ||||||||
\(87\) | −2.09167 | −0.224251 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.69722 | 0.179905 | 0.0899527 | − | 0.995946i | \(-0.471328\pi\) | ||||
0.0899527 | + | 0.995946i | \(0.471328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.48612 | 0.365445 | ||||||||
\(92\) | 2.21110 | 0.230523 | ||||||||
\(93\) | 23.5139 | 2.43828 | ||||||||
\(94\) | −3.90833 | −0.403113 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.90833 | 0.398892 | ||||||||
\(97\) | 15.3028 | 1.55376 | 0.776881 | − | 0.629648i | \(-0.216801\pi\) | ||||
0.776881 | + | 0.629648i | \(0.216801\pi\) | |||||||
\(98\) | −8.48612 | −0.857228 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.513878 | 0.0511328 | 0.0255664 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255664 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(102\) | −20.7250 | −2.05208 | ||||||||
\(103\) | 2.90833 | 0.286566 | 0.143283 | − | 0.989682i | \(-0.454234\pi\) | ||||
0.143283 | + | 0.989682i | \(0.454234\pi\) | |||||||
\(104\) | 15.0000 | 1.47087 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.69722 | −0.164849 | ||||||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 0.486122 | 0.0467771 | ||||||||
\(109\) | −11.5139 | −1.10283 | −0.551415 | − | 0.834231i | \(-0.685912\pi\) | ||||
−0.551415 | + | 0.834231i | \(0.685912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.51388 | 0.523354 | ||||||||
\(112\) | 2.30278 | 0.217592 | ||||||||
\(113\) | −10.8167 | −1.01755 | −0.508773 | − | 0.860901i | \(-0.669901\pi\) | ||||
−0.508773 | + | 0.860901i | \(0.669901\pi\) | |||||||
\(114\) | 3.00000 | 0.280976 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.275019 | 0.0255349 | ||||||||
\(117\) | −11.5139 | −1.06446 | ||||||||
\(118\) | −18.5139 | −1.70434 | ||||||||
\(119\) | 4.81665 | 0.441542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.3028 | 0.932769 | ||||||||
\(123\) | 12.9083 | 1.16390 | ||||||||
\(124\) | −3.09167 | −0.277640 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.09167 | −0.186341 | ||||||||
\(127\) | −8.11943 | −0.720483 | −0.360241 | − | 0.932859i | \(-0.617306\pi\) | ||||
−0.360241 | + | 0.932859i | \(0.617306\pi\) | |||||||
\(128\) | 8.09167 | 0.715210 | ||||||||
\(129\) | −16.6056 | −1.46204 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.90833 | 0.865695 | 0.432847 | − | 0.901467i | \(-0.357509\pi\) | ||||
0.432847 | + | 0.901467i | \(0.357509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.697224 | −0.0604570 | ||||||||
\(134\) | −5.21110 | −0.450171 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.7250 | 1.77715 | ||||||||
\(137\) | −12.9083 | −1.10283 | −0.551416 | − | 0.834230i | \(-0.685912\pi\) | ||||
−0.551416 | + | 0.834230i | \(0.685912\pi\) | |||||||
\(138\) | −21.9083 | −1.86496 | ||||||||
\(139\) | 6.21110 | 0.526819 | 0.263409 | − | 0.964684i | \(-0.415153\pi\) | ||||
0.263409 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.90833 | −0.581786 | ||||||||
\(142\) | −3.39445 | −0.284856 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.60555 | −0.633796 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.3028 | 0.852664 | ||||||||
\(147\) | −15.0000 | −1.23718 | ||||||||
\(148\) | −0.724981 | −0.0595930 | ||||||||
\(149\) | −17.2111 | −1.40999 | −0.704994 | − | 0.709213i | \(-0.749050\pi\) | ||||
−0.704994 | + | 0.709213i | \(0.749050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.816654 | −0.0664583 | −0.0332292 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332292 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | −15.9083 | −1.28611 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.48612 | 0.279113 | ||||||||
\(157\) | 19.2111 | 1.53321 | 0.766606 | − | 0.642117i | \(-0.221944\pi\) | ||||
0.766606 | + | 0.642117i | \(0.221944\pi\) | |||||||
\(158\) | 14.2111 | 1.13057 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.09167 | 0.401280 | ||||||||
\(162\) | −13.8167 | −1.08554 | ||||||||
\(163\) | 9.30278 | 0.728650 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(164\) | −1.69722 | −0.132531 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.57779 | 0.355306 | ||||||||
\(167\) | −13.4222 | −1.03864 | −0.519321 | − | 0.854579i | \(-0.673815\pi\) | ||||
−0.519321 | + | 0.854579i | \(0.673815\pi\) | |||||||
\(168\) | 4.81665 | 0.371613 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.30278 | 0.176098 | ||||||||
\(172\) | 2.18335 | 0.166479 | ||||||||
\(173\) | 4.81665 | 0.366203 | 0.183102 | − | 0.983094i | \(-0.441386\pi\) | ||||
0.183102 | + | 0.983094i | \(0.441386\pi\) | |||||||
\(174\) | −2.72498 | −0.206580 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.7250 | −2.45976 | ||||||||
\(178\) | 2.21110 | 0.165729 | ||||||||
\(179\) | 12.5139 | 0.935331 | 0.467666 | − | 0.883905i | \(-0.345095\pi\) | ||||
0.467666 | + | 0.883905i | \(0.345095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9083 | −1.47977 | −0.739887 | − | 0.672731i | \(-0.765121\pi\) | ||||
−0.739887 | + | 0.672731i | \(0.765121\pi\) | |||||||
\(182\) | 4.54163 | 0.336648 | ||||||||
\(183\) | 18.2111 | 1.34620 | ||||||||
\(184\) | 21.9083 | 1.61510 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 30.6333 | 2.24614 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.908327 | 0.0662465 | ||||||||
\(189\) | 1.11943 | 0.0814265 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3028 | 0.745483 | 0.372741 | − | 0.927935i | \(-0.378418\pi\) | ||||
0.372741 | + | 0.927935i | \(0.378418\pi\) | |||||||
\(192\) | 20.3028 | 1.46523 | ||||||||
\(193\) | −13.2111 | −0.950956 | −0.475478 | − | 0.879728i | \(-0.657725\pi\) | ||||
−0.475478 | + | 0.879728i | \(0.657725\pi\) | |||||||
\(194\) | 19.9361 | 1.43133 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.97224 | 0.140875 | ||||||||
\(197\) | −13.3028 | −0.947784 | −0.473892 | − | 0.880583i | \(-0.657151\pi\) | ||||
−0.473892 | + | 0.880583i | \(0.657151\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.48612 | −0.459789 | −0.229894 | − | 0.973216i | \(-0.573838\pi\) | ||||
−0.229894 | + | 0.973216i | \(0.573838\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.21110 | −0.649701 | ||||||||
\(202\) | 0.669468 | 0.0471036 | ||||||||
\(203\) | 0.633308 | 0.0444495 | ||||||||
\(204\) | 4.81665 | 0.337233 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.78890 | 0.263985 | ||||||||
\(207\) | −16.8167 | −1.16884 | ||||||||
\(208\) | 16.5139 | 1.14503 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2389 | 1.73751 | 0.868757 | − | 0.495238i | \(-0.164919\pi\) | ||||
0.868757 | + | 0.495238i | \(0.164919\pi\) | |||||||
\(212\) | 0.394449 | 0.0270908 | ||||||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 3.90833 | 0.267168 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.81665 | 0.327732 | ||||||||
\(217\) | −7.11943 | −0.483298 | ||||||||
\(218\) | −15.0000 | −1.01593 | ||||||||
\(219\) | 18.2111 | 1.23059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.5416 | 2.32352 | ||||||||
\(222\) | 7.18335 | 0.482115 | ||||||||
\(223\) | −22.6333 | −1.51564 | −0.757819 | − | 0.652465i | \(-0.773735\pi\) | ||||
−0.757819 | + | 0.652465i | \(0.773735\pi\) | |||||||
\(224\) | −1.18335 | −0.0790656 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0917 | −0.937364 | ||||||||
\(227\) | −1.69722 | −0.112649 | −0.0563244 | − | 0.998413i | \(-0.517938\pi\) | ||||
−0.0563244 | + | 0.998413i | \(0.517938\pi\) | |||||||
\(228\) | −0.697224 | −0.0461748 | ||||||||
\(229\) | −18.7250 | −1.23738 | −0.618691 | − | 0.785635i | \(-0.712337\pi\) | ||||
−0.618691 | + | 0.785635i | \(0.712337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.72498 | 0.178904 | ||||||||
\(233\) | −15.9083 | −1.04219 | −0.521095 | − | 0.853499i | \(-0.674476\pi\) | ||||
−0.521095 | + | 0.853499i | \(0.674476\pi\) | |||||||
\(234\) | −15.0000 | −0.980581 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.30278 | 0.280087 | ||||||||
\(237\) | 25.1194 | 1.63168 | ||||||||
\(238\) | 6.27502 | 0.406749 | ||||||||
\(239\) | −21.1194 | −1.36610 | −0.683051 | − | 0.730371i | \(-0.739347\pi\) | ||||
−0.683051 | + | 0.730371i | \(0.739347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9361 | −1.41303 | −0.706514 | − | 0.707699i | \(-0.749733\pi\) | ||||
−0.706514 | + | 0.707699i | \(0.749733\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | −2.39445 | −0.153289 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 16.8167 | 1.07219 | ||||||||
\(247\) | −5.00000 | −0.318142 | ||||||||
\(248\) | −30.6333 | −1.94522 | ||||||||
\(249\) | 8.09167 | 0.512789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.90833 | 0.436050 | 0.218025 | − | 0.975943i | \(-0.430039\pi\) | ||||
0.218025 | + | 0.975943i | \(0.430039\pi\) | |||||||
\(252\) | 0.486122 | 0.0306228 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.5778 | −0.663710 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.09167 | −0.443230 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | −21.6333 | −1.34683 | ||||||||
\(259\) | −1.66947 | −0.103736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.09167 | −0.129471 | ||||||||
\(262\) | 12.9083 | 0.797479 | ||||||||
\(263\) | 22.8167 | 1.40694 | 0.703468 | − | 0.710727i | \(-0.251634\pi\) | ||||
0.703468 | + | 0.710727i | \(0.251634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.908327 | −0.0556931 | ||||||||
\(267\) | 3.90833 | 0.239186 | ||||||||
\(268\) | 1.21110 | 0.0739799 | ||||||||
\(269\) | 8.72498 | 0.531971 | 0.265986 | − | 0.963977i | \(-0.414303\pi\) | ||||
0.265986 | + | 0.963977i | \(0.414303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.211103 | 0.0128236 | 0.00641178 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641178 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(272\) | 22.8167 | 1.38346 | ||||||||
\(273\) | 8.02776 | 0.485862 | ||||||||
\(274\) | −16.8167 | −1.01593 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.09167 | 0.306483 | ||||||||
\(277\) | −14.3944 | −0.864879 | −0.432439 | − | 0.901663i | \(-0.642347\pi\) | ||||
−0.432439 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(278\) | 8.09167 | 0.485306 | ||||||||
\(279\) | 23.5139 | 1.40774 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.18335 | 0.0705925 | 0.0352963 | − | 0.999377i | \(-0.488763\pi\) | ||||
0.0352963 | + | 0.999377i | \(0.488763\pi\) | |||||||
\(282\) | −9.00000 | −0.535942 | ||||||||
\(283\) | −6.30278 | −0.374661 | −0.187331 | − | 0.982297i | \(-0.559984\pi\) | ||||
−0.187331 | + | 0.982297i | \(0.559984\pi\) | |||||||
\(284\) | 0.788897 | 0.0468125 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.90833 | −0.230701 | ||||||||
\(288\) | 3.90833 | 0.230300 | ||||||||
\(289\) | 30.7250 | 1.80735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.2389 | 2.06574 | ||||||||
\(292\) | −2.39445 | −0.140125 | ||||||||
\(293\) | −0.788897 | −0.0460879 | −0.0230439 | − | 0.999734i | \(-0.507336\pi\) | ||||
−0.0230439 | + | 0.999734i | \(0.507336\pi\) | |||||||
\(294\) | −19.5416 | −1.13969 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.18335 | −0.417524 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.4222 | −1.29888 | ||||||||
\(299\) | 36.5139 | 2.11165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.02776 | 0.289795 | ||||||||
\(302\) | −1.06392 | −0.0612215 | ||||||||
\(303\) | 1.18335 | 0.0679815 | ||||||||
\(304\) | −3.30278 | −0.189427 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −20.7250 | −1.18477 | ||||||||
\(307\) | 16.9083 | 0.965009 | 0.482505 | − | 0.875893i | \(-0.339727\pi\) | ||||
0.482505 | + | 0.875893i | \(0.339727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.69722 | 0.380992 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.81665 | 0.273127 | 0.136564 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136564 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(312\) | 34.5416 | 1.95553 | ||||||||
\(313\) | 0.183346 | 0.0103633 | 0.00518167 | − | 0.999987i | \(-0.498351\pi\) | ||||
0.00518167 | + | 0.999987i | \(0.498351\pi\) | |||||||
\(314\) | 25.0278 | 1.41240 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.30278 | −0.185796 | ||||||||
\(317\) | −0.908327 | −0.0510167 | −0.0255084 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255084 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(318\) | −3.90833 | −0.219168 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.90833 | 0.385585 | ||||||||
\(322\) | 6.63331 | 0.369660 | ||||||||
\(323\) | −6.90833 | −0.384390 | ||||||||
\(324\) | 3.21110 | 0.178395 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.1194 | 0.671233 | ||||||||
\(327\) | −26.5139 | −1.46622 | ||||||||
\(328\) | −16.8167 | −0.928544 | ||||||||
\(329\) | 2.09167 | 0.115318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.6056 | −1.18755 | −0.593774 | − | 0.804632i | \(-0.702363\pi\) | ||||
−0.593774 | + | 0.804632i | \(0.702363\pi\) | |||||||
\(332\) | −1.06392 | −0.0583900 | ||||||||
\(333\) | 5.51388 | 0.302159 | ||||||||
\(334\) | −17.4861 | −0.956798 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.30278 | 0.289290 | ||||||||
\(337\) | 30.8444 | 1.68020 | 0.840101 | − | 0.542430i | \(-0.182496\pi\) | ||||
0.840101 | + | 0.542430i | \(0.182496\pi\) | |||||||
\(338\) | 15.6333 | 0.850340 | ||||||||
\(339\) | −24.9083 | −1.35283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | 9.42221 | 0.508751 | ||||||||
\(344\) | 21.6333 | 1.16639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.27502 | 0.337347 | ||||||||
\(347\) | 12.5139 | 0.671780 | 0.335890 | − | 0.941901i | \(-0.390963\pi\) | ||||
0.335890 | + | 0.941901i | \(0.390963\pi\) | |||||||
\(348\) | 0.633308 | 0.0339489 | ||||||||
\(349\) | 5.18335 | 0.277458 | 0.138729 | − | 0.990330i | \(-0.455698\pi\) | ||||
0.138729 | + | 0.990330i | \(0.455698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.02776 | 0.428490 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.6333 | 0.991751 | 0.495875 | − | 0.868394i | \(-0.334847\pi\) | ||||
0.495875 | + | 0.868394i | \(0.334847\pi\) | |||||||
\(354\) | −42.6333 | −2.26593 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.513878 | −0.0272355 | ||||||||
\(357\) | 11.0917 | 0.587034 | ||||||||
\(358\) | 16.3028 | 0.861628 | ||||||||
\(359\) | −0.788897 | −0.0416364 | −0.0208182 | − | 0.999783i | \(-0.506627\pi\) | ||||
−0.0208182 | + | 0.999783i | \(0.506627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −25.9361 | −1.36317 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.05551 | −0.0553239 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 23.7250 | 1.24012 | ||||||||
\(367\) | −20.6972 | −1.08039 | −0.540193 | − | 0.841541i | \(-0.681649\pi\) | ||||
−0.540193 | + | 0.841541i | \(0.681649\pi\) | |||||||
\(368\) | 24.1194 | 1.25731 | ||||||||
\(369\) | 12.9083 | 0.671981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.908327 | 0.0471580 | ||||||||
\(372\) | −7.11943 | −0.369125 | ||||||||
\(373\) | −27.4222 | −1.41987 | −0.709934 | − | 0.704268i | \(-0.751275\pi\) | ||||
−0.709934 | + | 0.704268i | \(0.751275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.00000 | 0.464140 | ||||||||
\(377\) | 4.54163 | 0.233906 | ||||||||
\(378\) | 1.45837 | 0.0750102 | ||||||||
\(379\) | 3.18335 | 0.163518 | 0.0817588 | − | 0.996652i | \(-0.473946\pi\) | ||||
0.0817588 | + | 0.996652i | \(0.473946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.6972 | −0.957888 | ||||||||
\(382\) | 13.4222 | 0.686740 | ||||||||
\(383\) | 21.6333 | 1.10541 | 0.552705 | − | 0.833377i | \(-0.313596\pi\) | ||||
0.552705 | + | 0.833377i | \(0.313596\pi\) | |||||||
\(384\) | 18.6333 | 0.950877 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.2111 | −0.876022 | ||||||||
\(387\) | −16.6056 | −0.844108 | ||||||||
\(388\) | −4.63331 | −0.235221 | ||||||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.4500 | 2.55136 | ||||||||
\(392\) | 19.5416 | 0.987002 | ||||||||
\(393\) | 22.8167 | 1.15095 | ||||||||
\(394\) | −17.3305 | −0.873100 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6972 | 1.08895 | 0.544476 | − | 0.838776i | \(-0.316728\pi\) | ||||
0.544476 | + | 0.838776i | \(0.316728\pi\) | |||||||
\(398\) | −8.44996 | −0.423558 | ||||||||
\(399\) | −1.60555 | −0.0803781 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7889 | −0.638647 | −0.319324 | − | 0.947646i | \(-0.603456\pi\) | ||||
−0.319324 | + | 0.947646i | \(0.603456\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | −51.0555 | −2.54326 | ||||||||
\(404\) | −0.155590 | −0.00774088 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.825058 | 0.0409469 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 47.7250 | 2.36274 | ||||||||
\(409\) | 6.21110 | 0.307119 | 0.153560 | − | 0.988139i | \(-0.450926\pi\) | ||||
0.153560 | + | 0.988139i | \(0.450926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.7250 | −1.46623 | ||||||||
\(412\) | −0.880571 | −0.0433826 | ||||||||
\(413\) | 9.90833 | 0.487557 | ||||||||
\(414\) | −21.9083 | −1.07674 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.48612 | −0.416066 | ||||||||
\(417\) | 14.3028 | 0.700410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.39445 | 0.312389 | 0.156195 | − | 0.987726i | \(-0.450077\pi\) | ||||
0.156195 | + | 0.987726i | \(0.450077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.697224 | 0.0339806 | 0.0169903 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169903 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(422\) | 32.8806 | 1.60060 | ||||||||
\(423\) | −6.90833 | −0.335894 | ||||||||
\(424\) | 3.90833 | 0.189805 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.81665 | −0.378718 | ||||||||
\(427\) | −5.51388 | −0.266835 | ||||||||
\(428\) | −0.908327 | −0.0439056 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 5.30278 | 0.255130 | ||||||||
\(433\) | 5.00000 | 0.240285 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(434\) | −9.27502 | −0.445215 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.48612 | 0.166955 | ||||||||
\(437\) | −7.30278 | −0.349339 | ||||||||
\(438\) | 23.7250 | 1.13362 | ||||||||
\(439\) | −24.3028 | −1.15991 | −0.579954 | − | 0.814649i | \(-0.696930\pi\) | ||||
−0.579954 | + | 0.814649i | \(0.696930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 45.0000 | 2.14043 | ||||||||
\(443\) | −8.60555 | −0.408862 | −0.204431 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204431 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(444\) | −1.66947 | −0.0792294 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −29.4861 | −1.39621 | ||||||||
\(447\) | −39.6333 | −1.87459 | ||||||||
\(448\) | −6.14719 | −0.290427 | ||||||||
\(449\) | 23.4861 | 1.10838 | 0.554189 | − | 0.832391i | \(-0.313028\pi\) | ||||
0.554189 | + | 0.832391i | \(0.313028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.27502 | 0.154044 | ||||||||
\(453\) | −1.88057 | −0.0883569 | ||||||||
\(454\) | −2.21110 | −0.103772 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.90833 | −0.323512 | ||||||||
\(457\) | 20.6972 | 0.968175 | 0.484088 | − | 0.875020i | \(-0.339152\pi\) | ||||
0.484088 | + | 0.875020i | \(0.339152\pi\) | |||||||
\(458\) | −24.3944 | −1.13988 | ||||||||
\(459\) | 11.0917 | 0.517715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.2111 | −1.50022 | −0.750110 | − | 0.661313i | \(-0.770000\pi\) | ||||
−0.750110 | + | 0.661313i | \(0.770000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7889 | 0.547877 | 0.273938 | − | 0.961747i | \(-0.411674\pi\) | ||||
0.273938 | + | 0.961747i | \(0.411674\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7250 | −0.960066 | ||||||||
\(467\) | −18.6333 | −0.862247 | −0.431123 | − | 0.902293i | \(-0.641883\pi\) | ||||
−0.431123 | + | 0.902293i | \(0.641883\pi\) | |||||||
\(468\) | 3.48612 | 0.161146 | ||||||||
\(469\) | 2.78890 | 0.128779 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.2389 | 2.03842 | ||||||||
\(472\) | 42.6333 | 1.96236 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 32.7250 | 1.50311 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.45837 | −0.0668441 | ||||||||
\(477\) | −3.00000 | −0.137361 | ||||||||
\(478\) | −27.5139 | −1.25846 | ||||||||
\(479\) | 34.8167 | 1.59081 | 0.795407 | − | 0.606076i | \(-0.207257\pi\) | ||||
0.795407 | + | 0.606076i | \(0.207257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9722 | −0.545887 | ||||||||
\(482\) | −28.5778 | −1.30168 | ||||||||
\(483\) | 11.7250 | 0.533505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −25.5416 | −1.15859 | ||||||||
\(487\) | 4.21110 | 0.190823 | 0.0954116 | − | 0.995438i | \(-0.469583\pi\) | ||||
0.0954116 | + | 0.995438i | \(0.469583\pi\) | |||||||
\(488\) | −23.7250 | −1.07398 | ||||||||
\(489\) | 21.4222 | 0.968746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.78890 | 0.441767 | 0.220883 | − | 0.975300i | \(-0.429106\pi\) | ||||
0.220883 | + | 0.975300i | \(0.429106\pi\) | |||||||
\(492\) | −3.90833 | −0.176201 | ||||||||
\(493\) | 6.27502 | 0.282613 | ||||||||
\(494\) | −6.51388 | −0.293073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.7250 | −1.51430 | ||||||||
\(497\) | 1.81665 | 0.0814881 | ||||||||
\(498\) | 10.5416 | 0.472382 | ||||||||
\(499\) | −3.48612 | −0.156060 | −0.0780301 | − | 0.996951i | \(-0.524863\pi\) | ||||
−0.0780301 | + | 0.996951i | \(0.524863\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.9083 | −1.38088 | ||||||||
\(502\) | 9.00000 | 0.401690 | ||||||||
\(503\) | −9.39445 | −0.418878 | −0.209439 | − | 0.977822i | \(-0.567164\pi\) | ||||
−0.209439 | + | 0.977822i | \(0.567164\pi\) | |||||||
\(504\) | 4.81665 | 0.214551 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.6333 | 1.22724 | ||||||||
\(508\) | 2.45837 | 0.109072 | ||||||||
\(509\) | −22.6972 | −1.00604 | −0.503018 | − | 0.864276i | \(-0.667777\pi\) | ||||
−0.503018 | + | 0.864276i | \(0.667777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.51388 | −0.243920 | ||||||||
\(512\) | −25.4222 | −1.12351 | ||||||||
\(513\) | −1.60555 | −0.0708868 | ||||||||
\(514\) | −23.4500 | −1.03433 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.02776 | 0.221335 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.17494 | −0.0955615 | ||||||||
\(519\) | 11.0917 | 0.486870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4500 | −1.81596 | −0.907978 | − | 0.419018i | \(-0.862374\pi\) | ||||
−0.907978 | + | 0.419018i | \(0.862374\pi\) | |||||||
\(522\) | −2.72498 | −0.119269 | ||||||||
\(523\) | 32.4222 | 1.41772 | 0.708862 | − | 0.705347i | \(-0.249209\pi\) | ||||
0.708862 | + | 0.705347i | \(0.249209\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.7250 | 1.29607 | ||||||||
\(527\) | −70.5416 | −3.07284 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.3305 | 1.31872 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.7250 | −1.42014 | ||||||||
\(532\) | 0.211103 | 0.00915246 | ||||||||
\(533\) | −28.0278 | −1.21402 | ||||||||
\(534\) | 5.09167 | 0.220338 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 28.8167 | 1.24353 | ||||||||
\(538\) | 11.3667 | 0.490053 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7250 | −1.10600 | −0.553002 | − | 0.833180i | \(-0.686518\pi\) | ||||
−0.553002 | + | 0.833180i | \(0.686518\pi\) | |||||||
\(542\) | 0.275019 | 0.0118131 | ||||||||
\(543\) | −45.8444 | −1.96737 | ||||||||
\(544\) | −11.7250 | −0.502704 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.4584 | 0.447577 | ||||||||
\(547\) | 7.11943 | 0.304405 | 0.152202 | − | 0.988349i | \(-0.451363\pi\) | ||||
0.152202 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(548\) | 3.90833 | 0.166955 | ||||||||
\(549\) | 18.2111 | 0.777231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.908327 | −0.0386960 | ||||||||
\(552\) | 50.4500 | 2.14729 | ||||||||
\(553\) | −7.60555 | −0.323421 | ||||||||
\(554\) | −18.7527 | −0.796727 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.88057 | −0.0797540 | ||||||||
\(557\) | −19.4222 | −0.822945 | −0.411473 | − | 0.911422i | \(-0.634985\pi\) | ||||
−0.411473 | + | 0.911422i | \(0.634985\pi\) | |||||||
\(558\) | 30.6333 | 1.29681 | ||||||||
\(559\) | 36.0555 | 1.52499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.54163 | 0.0650299 | ||||||||
\(563\) | −8.09167 | −0.341023 | −0.170512 | − | 0.985356i | \(-0.554542\pi\) | ||||
−0.170512 | + | 0.985356i | \(0.554542\pi\) | |||||||
\(564\) | 2.09167 | 0.0880753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.21110 | −0.345138 | ||||||||
\(567\) | 7.39445 | 0.310538 | ||||||||
\(568\) | 7.81665 | 0.327980 | ||||||||
\(569\) | 46.1472 | 1.93459 | 0.967295 | − | 0.253653i | \(-0.0816321\pi\) | ||||
0.967295 | + | 0.253653i | \(0.0816321\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3305 | −0.934504 | −0.467252 | − | 0.884124i | \(-0.654756\pi\) | ||||
−0.467252 | + | 0.884124i | \(0.654756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7250 | 0.991125 | ||||||||
\(574\) | −5.09167 | −0.212522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.3028 | 0.845949 | ||||||||
\(577\) | 44.3583 | 1.84666 | 0.923330 | − | 0.384008i | \(-0.125456\pi\) | ||||
0.923330 | + | 0.384008i | \(0.125456\pi\) | |||||||
\(578\) | 40.0278 | 1.66494 | ||||||||
\(579\) | −30.4222 | −1.26430 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44996 | −0.101642 | ||||||||
\(582\) | 45.9083 | 1.90296 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −23.7250 | −0.981747 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.02776 | −0.0424562 | ||||||||
\(587\) | 16.5416 | 0.682746 | 0.341373 | − | 0.939928i | \(-0.389108\pi\) | ||||
0.341373 | + | 0.939928i | \(0.389108\pi\) | |||||||
\(588\) | 4.54163 | 0.187294 | ||||||||
\(589\) | 10.2111 | 0.420741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.6333 | −1.26009 | ||||||||
\(592\) | −7.90833 | −0.325030 | ||||||||
\(593\) | 6.39445 | 0.262589 | 0.131294 | − | 0.991343i | \(-0.458087\pi\) | ||||
0.131294 | + | 0.991343i | \(0.458087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.21110 | 0.213455 | ||||||||
\(597\) | −14.9361 | −0.611293 | ||||||||
\(598\) | 47.5694 | 1.94526 | ||||||||
\(599\) | −24.9083 | −1.01773 | −0.508863 | − | 0.860847i | \(-0.669934\pi\) | ||||
−0.508863 | + | 0.860847i | \(0.669934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.90833 | 0.0778423 | 0.0389211 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389211 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(602\) | 6.55004 | 0.266960 | ||||||||
\(603\) | −9.21110 | −0.375105 | ||||||||
\(604\) | 0.247263 | 0.0100610 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.54163 | 0.0626246 | ||||||||
\(607\) | −7.21110 | −0.292690 | −0.146345 | − | 0.989234i | \(-0.546751\pi\) | ||||
−0.146345 | + | 0.989234i | \(0.546751\pi\) | |||||||
\(608\) | 1.69722 | 0.0688315 | ||||||||
\(609\) | 1.45837 | 0.0590959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 4.81665 | 0.194702 | ||||||||
\(613\) | 15.8806 | 0.641410 | 0.320705 | − | 0.947179i | \(-0.396080\pi\) | ||||
0.320705 | + | 0.947179i | \(0.396080\pi\) | |||||||
\(614\) | 22.0278 | 0.888968 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.39445 | 0.136655 | 0.0683277 | − | 0.997663i | \(-0.478234\pi\) | ||||
0.0683277 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(618\) | 8.72498 | 0.350970 | ||||||||
\(619\) | −11.4222 | −0.459097 | −0.229549 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229549 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7250 | 0.470507 | ||||||||
\(622\) | 6.27502 | 0.251605 | ||||||||
\(623\) | −1.18335 | −0.0474098 | ||||||||
\(624\) | 38.0278 | 1.52233 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.238859 | 0.00954672 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.81665 | −0.232110 | ||||||||
\(629\) | −16.5416 | −0.659558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.93608 | 0.276121 | 0.138061 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138061 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(632\) | −32.7250 | −1.30173 | ||||||||
\(633\) | 58.1194 | 2.31004 | ||||||||
\(634\) | −1.18335 | −0.0469967 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.908327 | 0.0360175 | ||||||||
\(637\) | 32.5694 | 1.29045 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7889 | 1.09760 | 0.548798 | − | 0.835955i | \(-0.315086\pi\) | ||||
0.548798 | + | 0.835955i | \(0.315086\pi\) | |||||||
\(642\) | 9.00000 | 0.355202 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | −1.54163 | −0.0607489 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.00000 | −0.354100 | ||||||||
\(647\) | −33.2389 | −1.30675 | −0.653377 | − | 0.757033i | \(-0.726648\pi\) | ||||
−0.653377 | + | 0.757033i | \(0.726648\pi\) | |||||||
\(648\) | 31.8167 | 1.24988 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3944 | −0.642549 | ||||||||
\(652\) | −2.81665 | −0.110309 | ||||||||
\(653\) | 6.11943 | 0.239472 | 0.119736 | − | 0.992806i | \(-0.461795\pi\) | ||||
0.119736 | + | 0.992806i | \(0.461795\pi\) | |||||||
\(654\) | −34.5416 | −1.35068 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.5139 | −0.722846 | ||||||||
\(657\) | 18.2111 | 0.710483 | ||||||||
\(658\) | 2.72498 | 0.106231 | ||||||||
\(659\) | 30.9083 | 1.20402 | 0.602009 | − | 0.798489i | \(-0.294367\pi\) | ||||
0.602009 | + | 0.798489i | \(0.294367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.81665 | −0.342928 | −0.171464 | − | 0.985190i | \(-0.554850\pi\) | ||||
−0.171464 | + | 0.985190i | \(0.554850\pi\) | |||||||
\(662\) | −28.1472 | −1.09397 | ||||||||
\(663\) | 79.5416 | 3.08914 | ||||||||
\(664\) | −10.5416 | −0.409095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.18335 | 0.278349 | ||||||||
\(667\) | 6.63331 | 0.256843 | ||||||||
\(668\) | 4.06392 | 0.157238 | ||||||||
\(669\) | −52.1194 | −2.01505 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.72498 | −0.105118 | ||||||||
\(673\) | −30.0278 | −1.15748 | −0.578742 | − | 0.815510i | \(-0.696456\pi\) | ||||
−0.578742 | + | 0.815510i | \(0.696456\pi\) | |||||||
\(674\) | 40.1833 | 1.54780 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.63331 | −0.139743 | ||||||||
\(677\) | −24.2389 | −0.931575 | −0.465788 | − | 0.884897i | \(-0.654229\pi\) | ||||
−0.465788 | + | 0.884897i | \(0.654229\pi\) | |||||||
\(678\) | −32.4500 | −1.24623 | ||||||||
\(679\) | −10.6695 | −0.409457 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.90833 | −0.149767 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.8444 | 1.83072 | 0.915358 | − | 0.402642i | \(-0.131908\pi\) | ||||
0.915358 | + | 0.402642i | \(0.131908\pi\) | |||||||
\(684\) | −0.697224 | −0.0266590 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.2750 | 0.468662 | ||||||||
\(687\) | −43.1194 | −1.64511 | ||||||||
\(688\) | 23.8167 | 0.908001 | ||||||||
\(689\) | 6.51388 | 0.248159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.5416 | 1.04773 | 0.523867 | − | 0.851800i | \(-0.324489\pi\) | ||||
0.523867 | + | 0.851800i | \(0.324489\pi\) | |||||||
\(692\) | −1.45837 | −0.0554387 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3028 | 0.618845 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.27502 | 0.237854 | ||||||||
\(697\) | −38.7250 | −1.46681 | ||||||||
\(698\) | 6.75274 | 0.255595 | ||||||||
\(699\) | −36.6333 | −1.38560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.2111 | 1.55652 | 0.778261 | − | 0.627941i | \(-0.216102\pi\) | ||||
0.778261 | + | 0.627941i | \(0.216102\pi\) | |||||||
\(702\) | 10.4584 | 0.394726 | ||||||||
\(703\) | 2.39445 | 0.0903083 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.2750 | 0.913602 | ||||||||
\(707\) | −0.358288 | −0.0134748 | ||||||||
\(708\) | 9.90833 | 0.372378 | ||||||||
\(709\) | −31.6333 | −1.18801 | −0.594007 | − | 0.804460i | \(-0.702455\pi\) | ||||
−0.594007 | + | 0.804460i | \(0.702455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.1194 | 0.942052 | ||||||||
\(712\) | −5.09167 | −0.190819 | ||||||||
\(713\) | −74.5694 | −2.79265 | ||||||||
\(714\) | 14.4500 | 0.540776 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.78890 | −0.141598 | ||||||||
\(717\) | −48.6333 | −1.81624 | ||||||||
\(718\) | −1.02776 | −0.0383555 | ||||||||
\(719\) | 7.18335 | 0.267894 | 0.133947 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133947 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.02776 | −0.0755176 | ||||||||
\(722\) | −23.4500 | −0.872717 | ||||||||
\(723\) | −50.5139 | −1.87863 | ||||||||
\(724\) | 6.02776 | 0.224020 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3305 | −1.45869 | −0.729344 | − | 0.684147i | \(-0.760175\pi\) | ||||
−0.729344 | + | 0.684147i | \(0.760175\pi\) | |||||||
\(728\) | −10.4584 | −0.387613 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.8167 | 1.84254 | ||||||||
\(732\) | −5.51388 | −0.203799 | ||||||||
\(733\) | −19.6056 | −0.724148 | −0.362074 | − | 0.932149i | \(-0.617931\pi\) | ||||
−0.362074 | + | 0.932149i | \(0.617931\pi\) | |||||||
\(734\) | −26.9638 | −0.995253 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.3944 | −0.456865 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.8167 | 0.619030 | ||||||||
\(739\) | −35.1194 | −1.29189 | −0.645945 | − | 0.763384i | \(-0.723536\pi\) | ||||
−0.645945 | + | 0.763384i | \(0.723536\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.5139 | −0.422973 | ||||||||
\(742\) | 1.18335 | 0.0434420 | ||||||||
\(743\) | −40.6972 | −1.49304 | −0.746518 | − | 0.665365i | \(-0.768276\pi\) | ||||
−0.746518 | + | 0.665365i | \(0.768276\pi\) | |||||||
\(744\) | −70.5416 | −2.58618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.7250 | −1.30798 | ||||||||
\(747\) | 8.09167 | 0.296059 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09167 | −0.0764281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.3305 | −1.65413 | −0.827067 | − | 0.562103i | \(-0.809992\pi\) | ||||
−0.827067 | + | 0.562103i | \(0.809992\pi\) | |||||||
\(752\) | 9.90833 | 0.361320 | ||||||||
\(753\) | 15.9083 | 0.579732 | ||||||||
\(754\) | 5.91673 | 0.215475 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.338936 | −0.0123270 | ||||||||
\(757\) | 49.0555 | 1.78295 | 0.891476 | − | 0.453067i | \(-0.149670\pi\) | ||||
0.891476 | + | 0.453067i | \(0.149670\pi\) | |||||||
\(758\) | 4.14719 | 0.150633 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5778 | 0.492195 | 0.246097 | − | 0.969245i | \(-0.420852\pi\) | ||||
0.246097 | + | 0.969245i | \(0.420852\pi\) | |||||||
\(762\) | −24.3583 | −0.882408 | ||||||||
\(763\) | 8.02776 | 0.290624 | ||||||||
\(764\) | −3.11943 | −0.112857 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.1833 | 1.01831 | ||||||||
\(767\) | 71.0555 | 2.56567 | ||||||||
\(768\) | −16.3305 | −0.589277 | ||||||||
\(769\) | 5.18335 | 0.186916 | 0.0934581 | − | 0.995623i | \(-0.470208\pi\) | ||||
0.0934581 | + | 0.995623i | \(0.470208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.4500 | −1.49278 | ||||||||
\(772\) | 4.00000 | 0.143963 | ||||||||
\(773\) | 3.11943 | 0.112198 | 0.0560990 | − | 0.998425i | \(-0.482134\pi\) | ||||
0.0560990 | + | 0.998425i | \(0.482134\pi\) | |||||||
\(774\) | −21.6333 | −0.777593 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −45.9083 | −1.64801 | ||||||||
\(777\) | −3.84441 | −0.137917 | ||||||||
\(778\) | 15.6333 | 0.560481 | ||||||||
\(779\) | 5.60555 | 0.200840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 65.7250 | 2.35032 | ||||||||
\(783\) | 1.45837 | 0.0521177 | ||||||||
\(784\) | 21.5139 | 0.768353 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 29.7250 | 1.06025 | ||||||||
\(787\) | −10.2111 | −0.363986 | −0.181993 | − | 0.983300i | \(-0.558255\pi\) | ||||
−0.181993 | + | 0.983300i | \(0.558255\pi\) | |||||||
\(788\) | 4.02776 | 0.143483 | ||||||||
\(789\) | 52.5416 | 1.87053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.54163 | 0.268150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.5416 | −1.40416 | ||||||||
\(794\) | 28.2666 | 1.00314 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.96384 | 0.0696065 | ||||||||
\(797\) | 3.51388 | 0.124468 | 0.0622340 | − | 0.998062i | \(-0.480178\pi\) | ||||
0.0622340 | + | 0.998062i | \(0.480178\pi\) | |||||||
\(798\) | −2.09167 | −0.0740444 | ||||||||
\(799\) | 20.7250 | 0.733197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.90833 | 0.138094 | ||||||||
\(802\) | −16.6611 | −0.588323 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.78890 | 0.0983568 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −66.5139 | −2.34285 | ||||||||
\(807\) | 20.0917 | 0.707260 | ||||||||
\(808\) | −1.54163 | −0.0542345 | ||||||||
\(809\) | −39.6333 | −1.39343 | −0.696716 | − | 0.717347i | \(-0.745356\pi\) | ||||
−0.696716 | + | 0.717347i | \(0.745356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.8722 | −1.36499 | −0.682493 | − | 0.730892i | \(-0.739104\pi\) | ||||
−0.682493 | + | 0.730892i | \(0.739104\pi\) | |||||||
\(812\) | −0.191750 | −0.00672911 | ||||||||
\(813\) | 0.486122 | 0.0170490 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 52.5416 | 1.83933 | ||||||||
\(817\) | −7.21110 | −0.252285 | ||||||||
\(818\) | 8.09167 | 0.282919 | ||||||||
\(819\) | 8.02776 | 0.280513 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | −0.418803 | −0.209401 | − | 0.977830i | \(-0.567152\pi\) | ||||
−0.209401 | + | 0.977830i | \(0.567152\pi\) | |||||||
\(822\) | −38.7250 | −1.35069 | ||||||||
\(823\) | 18.4222 | 0.642158 | 0.321079 | − | 0.947052i | \(-0.395955\pi\) | ||||
0.321079 | + | 0.947052i | \(0.395955\pi\) | |||||||
\(824\) | −8.72498 | −0.303949 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9083 | 0.449138 | ||||||||
\(827\) | −13.8167 | −0.480452 | −0.240226 | − | 0.970717i | \(-0.577222\pi\) | ||||
−0.240226 | + | 0.970717i | \(0.577222\pi\) | |||||||
\(828\) | 5.09167 | 0.176948 | ||||||||
\(829\) | 29.7527 | 1.03336 | 0.516678 | − | 0.856180i | \(-0.327169\pi\) | ||||
0.516678 | + | 0.856180i | \(0.327169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.1472 | −1.14986 | ||||||||
\(832\) | −44.0833 | −1.52831 | ||||||||
\(833\) | 45.0000 | 1.55916 | ||||||||
\(834\) | 18.6333 | 0.645219 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.3944 | −0.566675 | ||||||||
\(838\) | 8.33053 | 0.287773 | ||||||||
\(839\) | −9.11943 | −0.314838 | −0.157419 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157419 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1749 | −0.971550 | ||||||||
\(842\) | 0.908327 | 0.0313030 | ||||||||
\(843\) | 2.72498 | 0.0938533 | ||||||||
\(844\) | −7.64171 | −0.263039 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.30278 | 0.147758 | ||||||||
\(849\) | −14.5139 | −0.498115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.4861 | −0.599417 | ||||||||
\(852\) | 1.81665 | 0.0622375 | ||||||||
\(853\) | 12.7250 | 0.435695 | 0.217848 | − | 0.975983i | \(-0.430096\pi\) | ||||
0.217848 | + | 0.975983i | \(0.430096\pi\) | |||||||
\(854\) | −7.18335 | −0.245809 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.00000 | −0.307614 | ||||||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3944 | 1.41236 | 0.706180 | − | 0.708032i | \(-0.250417\pi\) | ||||
0.706180 | + | 0.708032i | \(0.250417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | −0.306719 | ||||||||
\(862\) | −42.9916 | −1.46430 | ||||||||
\(863\) | −12.3944 | −0.421912 | −0.210956 | − | 0.977496i | \(-0.567658\pi\) | ||||
−0.210956 | + | 0.977496i | \(0.567658\pi\) | |||||||
\(864\) | −2.72498 | −0.0927057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.51388 | 0.221351 | ||||||||
\(867\) | 70.7527 | 2.40289 | ||||||||
\(868\) | 2.15559 | 0.0731655 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 34.5416 | 1.16973 | ||||||||
\(873\) | 35.2389 | 1.19265 | ||||||||
\(874\) | −9.51388 | −0.321812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.51388 | −0.186297 | ||||||||
\(877\) | −20.0000 | −0.675352 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(878\) | −31.6611 | −1.06851 | ||||||||
\(879\) | −1.81665 | −0.0612742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5416 | 0.658374 | 0.329187 | − | 0.944265i | \(-0.393225\pi\) | ||||
0.329187 | + | 0.944265i | \(0.393225\pi\) | |||||||
\(882\) | −19.5416 | −0.658001 | ||||||||
\(883\) | 52.4500 | 1.76508 | 0.882541 | − | 0.470236i | \(-0.155831\pi\) | ||||
0.882541 | + | 0.470236i | \(0.155831\pi\) | |||||||
\(884\) | −10.4584 | −0.351753 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.2111 | −0.376644 | ||||||||
\(887\) | 3.23886 | 0.108750 | 0.0543751 | − | 0.998521i | \(-0.482683\pi\) | ||||
0.0543751 | + | 0.998521i | \(0.482683\pi\) | |||||||
\(888\) | −16.5416 | −0.555101 | ||||||||
\(889\) | 5.66106 | 0.189866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.85281 | 0.229449 | ||||||||
\(893\) | −3.00000 | −0.100391 | ||||||||
\(894\) | −51.6333 | −1.72688 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.64171 | −0.188476 | ||||||||
\(897\) | 84.0833 | 2.80746 | ||||||||
\(898\) | 30.5971 | 1.02104 | ||||||||
\(899\) | −9.27502 | −0.309339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | 0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5778 | 0.385285 | ||||||||
\(904\) | 32.4500 | 1.07927 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.44996 | −0.0813945 | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 0.513878 | 0.0170536 | ||||||||
\(909\) | 1.18335 | 0.0392491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7889 | −0.821293 | −0.410646 | − | 0.911795i | \(-0.634697\pi\) | ||||
−0.410646 | + | 0.911795i | \(0.634697\pi\) | |||||||
\(912\) | −7.60555 | −0.251845 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.9638 | 0.891885 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.66947 | 0.187324 | ||||||||
\(917\) | −6.90833 | −0.228133 | ||||||||
\(918\) | 14.4500 | 0.476920 | ||||||||
\(919\) | −26.7889 | −0.883684 | −0.441842 | − | 0.897093i | \(-0.645675\pi\) | ||||
−0.441842 | + | 0.897093i | \(0.645675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.9361 | 1.28299 | ||||||||
\(922\) | −41.9638 | −1.38201 | ||||||||
\(923\) | 13.0278 | 0.428814 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.3583 | 0.504705 | ||||||||
\(927\) | 6.69722 | 0.219966 | ||||||||
\(928\) | −1.54163 | −0.0506066 | ||||||||
\(929\) | 53.6056 | 1.75874 | 0.879371 | − | 0.476138i | \(-0.157964\pi\) | ||||
0.879371 | + | 0.476138i | \(0.157964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.51388 | −0.213484 | ||||||||
\(932\) | 4.81665 | 0.157775 | ||||||||
\(933\) | 11.0917 | 0.363125 | ||||||||
\(934\) | −24.2750 | −0.794303 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 34.5416 | 1.12903 | ||||||||
\(937\) | 9.21110 | 0.300914 | 0.150457 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150457 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(938\) | 3.63331 | 0.118632 | ||||||||
\(939\) | 0.422205 | 0.0137781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.6056 | −1.94309 | −0.971543 | − | 0.236864i | \(-0.923880\pi\) | ||||
−0.971543 | + | 0.236864i | \(0.923880\pi\) | |||||||
\(942\) | 57.6333 | 1.87779 | ||||||||
\(943\) | −40.9361 | −1.33306 | ||||||||
\(944\) | 46.9361 | 1.52764 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.63331 | 0.215554 | 0.107777 | − | 0.994175i | \(-0.465627\pi\) | ||||
0.107777 | + | 0.994175i | \(0.465627\pi\) | |||||||
\(948\) | −7.60555 | −0.247017 | ||||||||
\(949\) | −39.5416 | −1.28358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.09167 | −0.0678271 | ||||||||
\(952\) | −14.4500 | −0.468326 | ||||||||
\(953\) | −37.2666 | −1.20718 | −0.603592 | − | 0.797293i | \(-0.706264\pi\) | ||||
−0.603592 | + | 0.797293i | \(0.706264\pi\) | |||||||
\(954\) | −3.90833 | −0.126537 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.39445 | 0.206811 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45.3583 | 1.46546 | ||||||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.2666 | 2.36344 | ||||||||
\(962\) | −15.5971 | −0.502872 | ||||||||
\(963\) | 6.90833 | 0.222618 | ||||||||
\(964\) | 6.64171 | 0.213915 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.2750 | 0.491466 | ||||||||
\(967\) | −14.9083 | −0.479419 | −0.239710 | − | 0.970845i | \(-0.577052\pi\) | ||||
−0.239710 | + | 0.970845i | \(0.577052\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.9083 | −0.511049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3583 | 1.45562 | 0.727808 | − | 0.685781i | \(-0.240539\pi\) | ||||
0.727808 | + | 0.685781i | \(0.240539\pi\) | |||||||
\(972\) | 5.93608 | 0.190400 | ||||||||
\(973\) | −4.33053 | −0.138830 | ||||||||
\(974\) | 5.48612 | 0.175787 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.1194 | −0.836063 | ||||||||
\(977\) | −52.0278 | −1.66452 | −0.832258 | − | 0.554389i | \(-0.812952\pi\) | ||||
−0.832258 | + | 0.554389i | \(0.812952\pi\) | |||||||
\(978\) | 27.9083 | 0.892410 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5139 | −0.846523 | ||||||||
\(982\) | 12.7527 | 0.406956 | ||||||||
\(983\) | 8.84441 | 0.282093 | 0.141046 | − | 0.990003i | \(-0.454953\pi\) | ||||
0.141046 | + | 0.990003i | \(0.454953\pi\) | |||||||
\(984\) | −38.7250 | −1.23451 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.17494 | 0.260343 | ||||||||
\(987\) | 4.81665 | 0.153316 | ||||||||
\(988\) | 1.51388 | 0.0481629 | ||||||||
\(989\) | 52.6611 | 1.67452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9083 | −0.537111 | −0.268555 | − | 0.963264i | \(-0.586546\pi\) | ||||
−0.268555 | + | 0.963264i | \(0.586546\pi\) | |||||||
\(992\) | 17.3305 | 0.550245 | ||||||||
\(993\) | −49.7527 | −1.57886 | ||||||||
\(994\) | 2.36669 | 0.0750669 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.44996 | −0.0776300 | ||||||||
\(997\) | −46.7250 | −1.47979 | −0.739897 | − | 0.672720i | \(-0.765126\pi\) | ||||
−0.739897 | + | 0.672720i | \(0.765126\pi\) | |||||||
\(998\) | −4.54163 | −0.143763 | ||||||||
\(999\) | −3.84441 | −0.121632 |
(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 | 3025.2.a.h.1.2 | 2 | ||
5.4 | even | 2 | 3025.2.a.n.1.1 | 2 | |||
11.10 | odd | 2 | 275.2.a.f.1.1 | yes | 2 | ||
33.32 | even | 2 | 2475.2.a.o.1.2 | 2 | |||
44.43 | even | 2 | 4400.2.a.bh.1.1 | 2 | |||
55.32 | even | 4 | 275.2.b.c.199.2 | 4 | |||
55.43 | even | 4 | 275.2.b.c.199.3 | 4 | |||
55.54 | odd | 2 | 275.2.a.e.1.2 | ✓ | 2 | ||
165.32 | odd | 4 | 2475.2.c.k.199.3 | 4 | |||
165.98 | odd | 4 | 2475.2.c.k.199.2 | 4 | |||
165.164 | even | 2 | 2475.2.a.t.1.1 | 2 | |||
220.43 | odd | 4 | 4400.2.b.y.4049.1 | 4 | |||
220.87 | odd | 4 | 4400.2.b.y.4049.4 | 4 | |||
220.219 | even | 2 | 4400.2.a.bs.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.e.1.2 | ✓ | 2 | 55.54 | odd | 2 | ||
275.2.a.f.1.1 | yes | 2 | 11.10 | odd | 2 | ||
275.2.b.c.199.2 | 4 | 55.32 | even | 4 | |||
275.2.b.c.199.3 | 4 | 55.43 | even | 4 | |||
2475.2.a.o.1.2 | 2 | 33.32 | even | 2 | |||
2475.2.a.t.1.1 | 2 | 165.164 | even | 2 | |||
2475.2.c.k.199.2 | 4 | 165.98 | odd | 4 | |||
2475.2.c.k.199.3 | 4 | 165.32 | odd | 4 | |||
3025.2.a.h.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3025.2.a.n.1.1 | 2 | 5.4 | even | 2 | |||
4400.2.a.bh.1.1 | 2 | 44.43 | even | 2 | |||
4400.2.a.bs.1.2 | 2 | 220.219 | even | 2 | |||
4400.2.b.y.4049.1 | 4 | 220.43 | odd | 4 | |||
4400.2.b.y.4049.4 | 4 | 220.87 | odd | 4 |