Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.697224 | 0.263526 | 0.131763 | − | 0.991281i | \(-0.457936\pi\) | ||||
0.131763 | + | 0.991281i | \(0.457936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.90833 | −1.67552 | −0.837758 | − | 0.546042i | \(-0.816134\pi\) | ||||
−0.837758 | + | 0.546042i | \(0.816134\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | \(0.775471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.908327 | 0.168672 | 0.0843360 | − | 0.996437i | \(-0.473123\pi\) | ||||
0.0843360 | + | 0.996437i | \(0.473123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2111 | −1.83397 | −0.916984 | − | 0.398924i | \(-0.869384\pi\) | ||||
−0.916984 | + | 0.398924i | \(0.869384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.30278 | 0.400862 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.39445 | −0.393645 | −0.196822 | − | 0.980439i | \(-0.563062\pi\) | ||||
−0.196822 | + | 0.980439i | \(0.563062\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.5139 | −1.84370 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.60555 | −0.875440 | −0.437720 | − | 0.899111i | \(-0.644214\pi\) | ||||
−0.437720 | + | 0.899111i | \(0.644214\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.21110 | 1.09968 | 0.549841 | − | 0.835269i | \(-0.314688\pi\) | ||||
0.549841 | + | 0.835269i | \(0.314688\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.51388 | −0.930554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.9083 | −2.22761 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.30278 | 0.178950 | 0.0894750 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894750 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.30278 | 0.305010 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2111 | 1.85013 | 0.925064 | − | 0.379811i | \(-0.124011\pi\) | ||||
0.925064 | + | 0.379811i | \(0.124011\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.90833 | −1.01256 | −0.506279 | − | 0.862370i | \(-0.668979\pi\) | ||||
−0.506279 | + | 0.862370i | \(0.668979\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.60555 | 0.202280 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.8167 | −2.02449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.60555 | 0.309222 | 0.154611 | − | 0.987975i | \(-0.450588\pi\) | ||||
0.154611 | + | 0.987975i | \(0.450588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.90833 | 0.925600 | 0.462800 | − | 0.886463i | \(-0.346845\pi\) | ||||
0.462800 | + | 0.886463i | \(0.346845\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.697224 | 0.0794561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.51388 | −0.385698 | −0.192849 | − | 0.981228i | \(-0.561773\pi\) | ||||
−0.192849 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.5139 | −2.43828 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3028 | −1.55376 | −0.776881 | − | 0.629648i | \(-0.783199\pi\) | ||||
−0.776881 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.30278 | 0.231438 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.513878 | −0.0511328 | −0.0255664 | − | 0.999673i | \(-0.508139\pi\) | ||||
−0.0255664 | + | 0.999673i | \(0.508139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.90833 | 0.286566 | 0.143283 | − | 0.989682i | \(-0.454234\pi\) | ||||
0.143283 | + | 0.989682i | \(0.454234\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5139 | 1.10283 | 0.551415 | − | 0.834231i | \(-0.314088\pi\) | ||||
0.551415 | + | 0.834231i | \(0.314088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.51388 | −0.523354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.8167 | 1.01755 | 0.508773 | − | 0.860901i | \(-0.330099\pi\) | ||||
0.508773 | + | 0.860901i | \(0.330099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.5139 | −1.06446 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.81665 | −0.441542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.9083 | −1.16390 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.11943 | 0.720483 | 0.360241 | − | 0.932859i | \(-0.382694\pi\) | ||||
0.360241 | + | 0.932859i | \(0.382694\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9083 | 1.10283 | 0.551416 | − | 0.834230i | \(-0.314088\pi\) | ||||
0.551416 | + | 0.834230i | \(0.314088\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.0000 | −1.23718 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.2111 | 1.40999 | 0.704994 | − | 0.709213i | \(-0.250950\pi\) | ||||
0.704994 | + | 0.709213i | \(0.250950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.816654 | −0.0664583 | −0.0332292 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332292 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.9083 | −1.28611 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2111 | −1.53321 | −0.766606 | − | 0.642117i | \(-0.778056\pi\) | ||||
−0.766606 | + | 0.642117i | \(0.778056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.09167 | −0.401280 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.30278 | 0.728650 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4222 | 1.03864 | 0.519321 | − | 0.854579i | \(-0.326185\pi\) | ||||
0.519321 | + | 0.854579i | \(0.326185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.30278 | 0.176098 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.81665 | 0.366203 | 0.183102 | − | 0.983094i | \(-0.441386\pi\) | ||||
0.183102 | + | 0.983094i | \(0.441386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.7250 | 2.45976 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5139 | −0.935331 | −0.467666 | − | 0.883905i | \(-0.654905\pi\) | ||||
−0.467666 | + | 0.883905i | \(0.654905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9083 | −1.47977 | −0.739887 | − | 0.672731i | \(-0.765121\pi\) | ||||
−0.739887 | + | 0.672731i | \(0.765121\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.2111 | −1.34620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.90833 | −0.505187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.11943 | −0.0814265 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3028 | −0.745483 | −0.372741 | − | 0.927935i | \(-0.621582\pi\) | ||||
−0.372741 | + | 0.927935i | \(0.621582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2111 | −0.950956 | −0.475478 | − | 0.879728i | \(-0.657725\pi\) | ||||
−0.475478 | + | 0.879728i | \(0.657725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −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 | \(-0.426162\pi\) | ||||
0.229894 | + | 0.973216i | \(0.426162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.21110 | −0.649701 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.633308 | 0.0444495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.8167 | −1.16884 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2389 | 1.73751 | 0.868757 | − | 0.495238i | \(-0.164919\pi\) | ||||
0.868757 | + | 0.495238i | \(0.164919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.11943 | −0.483298 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.2111 | 1.23059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.5416 | 2.32352 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.6333 | −1.51564 | −0.757819 | − | 0.652465i | \(-0.773735\pi\) | ||||
−0.757819 | + | 0.652465i | \(0.773735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.69722 | 0.112649 | 0.0563244 | − | 0.998413i | \(-0.482062\pi\) | ||||
0.0563244 | + | 0.998413i | \(0.482062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7250 | −1.23738 | −0.618691 | − | 0.785635i | \(-0.712337\pi\) | ||||
−0.618691 | + | 0.785635i | \(0.712337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.60555 | 0.105638 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.9083 | −1.04219 | −0.521095 | − | 0.853499i | \(-0.674476\pi\) | ||||
−0.521095 | + | 0.853499i | \(0.674476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.1194 | 1.63168 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(-0.250267\pi\) | ||||
0.706514 | + | 0.707699i | \(0.250267\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | −0.318142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.09167 | −0.512789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.90833 | −0.436050 | −0.218025 | − | 0.975943i | \(-0.569961\pi\) | ||||
−0.218025 | + | 0.975943i | \(0.569961\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.30278 | −0.459122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.66947 | −0.103736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.09167 | 0.129471 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.8167 | −1.40694 | −0.703468 | − | 0.710727i | \(-0.748366\pi\) | ||||
−0.703468 | + | 0.710727i | \(0.748366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.90833 | 0.239186 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(0.497959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.02776 | −0.485862 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3944 | −0.864879 | −0.432439 | − | 0.901663i | \(-0.642347\pi\) | ||||
−0.432439 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.5139 | −1.40774 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.18335 | −0.0705925 | −0.0352963 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352963 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.30278 | 0.374661 | 0.187331 | − | 0.982297i | \(-0.440016\pi\) | ||||
0.187331 | + | 0.982297i | \(0.440016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.90833 | −0.230701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.7250 | 1.80735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.2389 | −2.06574 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.788897 | −0.0460879 | −0.0230439 | − | 0.999734i | \(-0.507336\pi\) | ||||
−0.0230439 | + | 0.999734i | \(0.507336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.60555 | −0.0931635 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.5139 | 2.11165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.02776 | 0.289795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.18335 | −0.0679815 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9083 | −0.965009 | −0.482505 | − | 0.875893i | \(-0.660273\pi\) | ||||
−0.482505 | + | 0.875893i | \(0.660273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.69722 | 0.380992 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.81665 | −0.273127 | −0.136564 | − | 0.990631i | \(-0.543606\pi\) | ||||
−0.136564 | + | 0.990631i | \(0.543606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.183346 | −0.0103633 | −0.00518167 | − | 0.999987i | \(-0.501649\pi\) | ||||
−0.00518167 | + | 0.999987i | \(0.501649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.908327 | 0.0510167 | 0.0255084 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255084 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.908327 | 0.0508565 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.90833 | −0.385585 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.90833 | −0.384390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.5139 | 1.46622 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.09167 | −0.115318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6056 | 1.18755 | 0.593774 | − | 0.804632i | \(-0.297637\pi\) | ||||
0.593774 | + | 0.804632i | \(0.297637\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.51388 | −0.302159 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.8444 | 1.68020 | 0.840101 | − | 0.542430i | \(-0.182496\pi\) | ||||
0.840101 | + | 0.542430i | \(0.182496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.9083 | 1.35283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2111 | −0.552962 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.42221 | −0.508751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5139 | −0.671780 | −0.335890 | − | 0.941901i | \(-0.609037\pi\) | ||||
−0.335890 | + | 0.941901i | \(0.609037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.18335 | −0.277458 | −0.138729 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138729 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.02776 | 0.428490 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.6333 | −0.991751 | −0.495875 | − | 0.868394i | \(-0.665153\pi\) | ||||
−0.495875 | + | 0.868394i | \(0.665153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.0917 | −0.587034 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.30278 | 0.120864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.6972 | −1.08039 | −0.540193 | − | 0.841541i | \(-0.681649\pi\) | ||||
−0.540193 | + | 0.841541i | \(0.681649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.9083 | −0.671981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.908327 | 0.0471580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.4222 | −1.41987 | −0.709934 | − | 0.704268i | \(-0.751275\pi\) | ||||
−0.709934 | + | 0.704268i | \(0.751275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.54163 | −0.233906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.18335 | −0.163518 | −0.0817588 | − | 0.996652i | \(-0.526054\pi\) | ||||
−0.0817588 | + | 0.996652i | \(0.526054\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6972 | 0.957888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6333 | 1.10541 | 0.552705 | − | 0.833377i | \(-0.313596\pi\) | ||||
0.552705 | + | 0.833377i | \(0.313596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.6056 | 0.844108 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.8167 | 1.15095 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.6972 | −1.08895 | −0.544476 | − | 0.838776i | \(-0.683272\pi\) | ||||
−0.544476 | + | 0.838776i | \(0.683272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.60555 | 0.0803781 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7889 | −0.638647 | −0.319324 | − | 0.947646i | \(-0.603456\pi\) | ||||
−0.319324 | + | 0.947646i | \(0.603456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 51.0555 | 2.54326 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.39445 | −0.118688 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.21110 | −0.307119 | −0.153560 | − | 0.988139i | \(-0.549074\pi\) | ||||
−0.153560 | + | 0.988139i | \(0.549074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.7250 | 1.46623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.90833 | 0.487557 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3028 | 0.700410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.39445 | −0.312389 | −0.156195 | − | 0.987726i | \(-0.549923\pi\) | ||||
−0.156195 | + | 0.987726i | \(0.549923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.697224 | 0.0339806 | 0.0169903 | − | 0.999856i | \(-0.494592\pi\) | ||||
0.0169903 | + | 0.999856i | \(0.494592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.90833 | −0.335894 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.51388 | −0.266835 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.5139 | −0.555895 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | −0.240285 | −0.120142 | − | 0.992757i | \(-0.538335\pi\) | ||||
−0.120142 | + | 0.992757i | \(0.538335\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.30278 | −0.349339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.60555 | −0.408862 | −0.204431 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204431 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.6333 | 1.87459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4861 | 1.10838 | 0.554189 | − | 0.832391i | \(-0.313028\pi\) | ||||
0.554189 | + | 0.832391i | \(0.313028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.60555 | −0.263955 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.88057 | −0.0883569 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6972 | 0.968175 | 0.484088 | − | 0.875020i | \(-0.339152\pi\) | ||||
0.484088 | + | 0.875020i | \(0.339152\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.0917 | 0.517715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.2111 | 1.50022 | 0.750110 | − | 0.661313i | \(-0.230000\pi\) | ||||
0.750110 | + | 0.661313i | \(0.230000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7889 | 0.547877 | 0.273938 | − | 0.961747i | \(-0.411674\pi\) | ||||
0.273938 | + | 0.961747i | \(0.411674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.6333 | −0.862247 | −0.431123 | − | 0.902293i | \(-0.641883\pi\) | ||||
−0.431123 | + | 0.902293i | \(0.641883\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.78890 | −0.128779 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.2389 | −2.03842 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.21110 | 0.331567 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.7250 | −0.533505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.21110 | 0.190823 | 0.0954116 | − | 0.995438i | \(-0.469583\pi\) | ||||
0.0954116 | + | 0.995438i | \(0.469583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.4222 | 0.968746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.78890 | 0.441767 | 0.220883 | − | 0.975300i | \(-0.429106\pi\) | ||||
0.220883 | + | 0.975300i | \(0.429106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.27502 | −0.282613 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.81665 | 0.0814881 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.48612 | 0.156060 | 0.0780301 | − | 0.996951i | \(-0.475137\pi\) | ||||
0.0780301 | + | 0.996951i | \(0.475137\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.9083 | 1.38088 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.39445 | 0.418878 | 0.209439 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209439 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.6333 | 1.22724 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.60555 | −0.0708868 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | −0.131940 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0917 | 0.486870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4500 | −1.81596 | −0.907978 | − | 0.419018i | \(-0.862374\pi\) | ||||
−0.907978 | + | 0.419018i | \(0.862374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4222 | −1.41772 | −0.708862 | − | 0.705347i | \(-0.750791\pi\) | ||||
−0.708862 | + | 0.705347i | \(0.750791\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 70.5416 | 3.07284 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.3305 | 1.31872 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.7250 | 1.42014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.0278 | 1.21402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.8167 | −1.24353 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.51388 | −0.280573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7250 | 1.10600 | 0.553002 | − | 0.833180i | \(-0.313482\pi\) | ||||
0.553002 | + | 0.833180i | \(0.313482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −45.8444 | −1.96737 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.11943 | −0.304405 | −0.152202 | − | 0.988349i | \(-0.548637\pi\) | ||||
−0.152202 | + | 0.988349i | \(0.548637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.2111 | −0.777231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.908327 | 0.0386960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.60555 | 0.323421 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.4222 | −0.822945 | −0.411473 | − | 0.911422i | \(-0.634985\pi\) | ||||
−0.411473 | + | 0.911422i | \(0.634985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.0555 | −1.52499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.9083 | −0.671650 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.09167 | 0.341023 | 0.170512 | − | 0.985356i | \(-0.445458\pi\) | ||||
0.170512 | + | 0.985356i | \(0.445458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.39445 | −0.310538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.1472 | −1.93459 | −0.967295 | − | 0.253653i | \(-0.918368\pi\) | ||||
−0.967295 | + | 0.253653i | \(0.918368\pi\) | |||||||
\(570\) | 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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.3583 | −1.84666 | −0.923330 | − | 0.384008i | \(-0.874544\pi\) | ||||
−0.923330 | + | 0.384008i | \(0.874544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.4222 | −1.26430 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44996 | −0.101642 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.30278 | 0.0539555 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5416 | 0.682746 | 0.341373 | − | 0.939928i | \(-0.389108\pi\) | ||||
0.341373 | + | 0.939928i | \(0.389108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2111 | −0.420741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.6333 | −1.26009 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.39445 | 0.262589 | 0.131294 | − | 0.991343i | \(-0.458087\pi\) | ||||
0.131294 | + | 0.991343i | \(0.458087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9361 | 0.611293 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.9083 | 1.01773 | 0.508863 | − | 0.860847i | \(-0.330066\pi\) | ||||
0.508863 | + | 0.860847i | \(0.330066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.90833 | −0.0778423 | −0.0389211 | − | 0.999242i | \(-0.512392\pi\) | ||||
−0.0389211 | + | 0.999242i | \(0.512392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.21110 | −0.375105 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.21110 | 0.292690 | 0.146345 | − | 0.989234i | \(-0.453249\pi\) | ||||
0.146345 | + | 0.989234i | \(0.453249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.45837 | 0.0590959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8806 | 0.641410 | 0.320705 | − | 0.947179i | \(-0.396080\pi\) | ||||
0.320705 | + | 0.947179i | \(0.396080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.39445 | −0.136655 | −0.0683277 | − | 0.997663i | \(-0.521766\pi\) | ||||
−0.0683277 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.4222 | 0.459097 | 0.229549 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229549 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7250 | 0.470507 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.18335 | 0.0474098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.30278 | 0.0919640 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.5416 | 0.659558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.93608 | −0.276121 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.1194 | 2.31004 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 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 | \(0.315086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.2389 | −1.30675 | −0.653377 | − | 0.757033i | \(-0.726648\pi\) | ||||
−0.653377 | + | 0.757033i | \(0.726648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2111 | 0.557835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3944 | −0.642549 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.11943 | −0.239472 | −0.119736 | − | 0.992806i | \(-0.538205\pi\) | ||||
−0.119736 | + | 0.992806i | \(0.538205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.2111 | 0.710483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.554850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 79.5416 | 3.08914 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.63331 | −0.256843 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.1194 | −2.01505 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.90833 | −0.305298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0278 | −1.15748 | −0.578742 | − | 0.815510i | \(-0.696456\pi\) | ||||
−0.578742 | + | 0.815510i | \(0.696456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.2389 | −0.931575 | −0.465788 | − | 0.884897i | \(-0.654229\pi\) | ||||
−0.465788 | + | 0.884897i | \(0.654229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −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 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.1194 | −1.64511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.51388 | −0.248159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.5416 | −1.04773 | −0.523867 | − | 0.851800i | \(-0.675511\pi\) | ||||
−0.523867 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.60555 | 0.0609898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.7250 | 1.46681 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.6333 | −1.38560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2111 | −1.55652 | −0.778261 | − | 0.627941i | \(-0.783898\pi\) | ||||
−0.778261 | + | 0.627941i | \(0.783898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.39445 | −0.0903083 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.358288 | −0.0134748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 74.5694 | 2.79265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48.6333 | −1.81624 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.18335 | −0.267894 | −0.133947 | − | 0.990989i | \(-0.542765\pi\) | ||||
−0.133947 | + | 0.990989i | \(0.542765\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.02776 | 0.0755176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.5139 | 1.87863 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3305 | −1.45869 | −0.729344 | − | 0.684147i | \(-0.760175\pi\) | ||||
−0.729344 | + | 0.684147i | \(0.760175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.8167 | −1.84254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6056 | −0.724148 | −0.362074 | − | 0.932149i | \(-0.617931\pi\) | ||||
−0.362074 | + | 0.932149i | \(0.617931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.6972 | 1.49304 | 0.746518 | − | 0.665365i | \(-0.231724\pi\) | ||||
0.746518 | + | 0.665365i | \(0.231724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.09167 | −0.296059 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09167 | −0.0764281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.3305 | 1.65413 | 0.827067 | − | 0.562103i | \(-0.190008\pi\) | ||||
0.827067 | + | 0.562103i | \(0.190008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.9083 | −0.579732 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.0555 | −1.78295 | −0.891476 | − | 0.453067i | \(-0.850330\pi\) | ||||
−0.891476 | + | 0.453067i | \(0.850330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.8167 | −0.610406 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5778 | −0.492195 | −0.246097 | − | 0.969245i | \(-0.579148\pi\) | ||||
−0.246097 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.02776 | 0.290624 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −71.0555 | −2.56567 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.18335 | −0.186916 | −0.0934581 | − | 0.995623i | \(-0.529792\pi\) | ||||
−0.0934581 | + | 0.995623i | \(0.529792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.4500 | 1.49278 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.11943 | −0.112198 | −0.0560990 | − | 0.998425i | \(-0.517866\pi\) | ||||
−0.0560990 | + | 0.998425i | \(0.517866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.84441 | −0.137917 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.60555 | −0.200840 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.60555 | 0.0932340 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.45837 | −0.0521177 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2111 | 0.363986 | 0.181993 | − | 0.983300i | \(-0.441745\pi\) | ||||
0.181993 | + | 0.983300i | \(0.441745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −52.5416 | −1.87053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.54163 | 0.268150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.5416 | 1.40416 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.51388 | −0.124468 | −0.0622340 | − | 0.998062i | \(-0.519822\pi\) | ||||
−0.0622340 | + | 0.998062i | \(0.519822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.7250 | 0.733197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.90833 | 0.138094 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.90833 | 0.279079 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0917 | 0.707260 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.6333 | 1.39343 | 0.696716 | − | 0.717347i | \(-0.254644\pi\) | ||||
0.696716 | + | 0.717347i | \(0.254644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.8722 | −1.36499 | −0.682493 | − | 0.730892i | \(-0.739104\pi\) | ||||
−0.682493 | + | 0.730892i | \(0.739104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.486122 | 0.0170490 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.21110 | 0.252285 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.02776 | −0.280513 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | 0.418803 | 0.209401 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209401 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.4222 | 0.642158 | 0.321079 | − | 0.947052i | \(-0.395955\pi\) | ||||
0.321079 | + | 0.947052i | \(0.395955\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.8167 | 0.480452 | 0.240226 | − | 0.970717i | \(-0.422778\pi\) | ||||
0.240226 | + | 0.970717i | \(0.422778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 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 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.0000 | 1.55916 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.3944 | 0.566675 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.11943 | 0.314838 | 0.157419 | − | 0.987532i | \(-0.449683\pi\) | ||||
0.157419 | + | 0.987532i | \(0.449683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1749 | −0.971550 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.72498 | −0.0938533 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.697224 | 0.0239569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.5139 | 0.498115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.4861 | 0.599417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7250 | 0.435695 | 0.217848 | − | 0.975983i | \(-0.430096\pi\) | ||||
0.217848 | + | 0.975983i | \(0.430096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 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 | \(-0.749583\pi\) | ||||
−0.706180 | + | 0.708032i | \(0.749583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | −0.306719 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.3944 | −0.421912 | −0.210956 | − | 0.977496i | \(-0.567658\pi\) | ||||
−0.210956 | + | 0.977496i | \(0.567658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 70.7527 | 2.40289 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9083 | 0.370040 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.2389 | −1.19265 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | −0.675352 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.81665 | −0.0612742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5416 | 0.658374 | 0.329187 | − | 0.944265i | \(-0.393225\pi\) | ||||
0.329187 | + | 0.944265i | \(0.393225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.4500 | 1.76508 | 0.882541 | − | 0.470236i | \(-0.155831\pi\) | ||||
0.882541 | + | 0.470236i | \(0.155831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.23886 | −0.108750 | −0.0543751 | − | 0.998521i | \(-0.517317\pi\) | ||||
−0.0543751 | + | 0.998521i | \(0.517317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.66106 | 0.189866 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.6056 | −0.355299 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.00000 | −0.100391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 84.0833 | 2.80746 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.27502 | −0.309339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5778 | 0.385285 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.18335 | −0.0392491 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.7889 | 0.821293 | 0.410646 | − | 0.911795i | \(-0.365303\pi\) | ||||
0.410646 | + | 0.911795i | \(0.365303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.51388 | −0.116292 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.90833 | 0.228133 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.0278 | −0.428814 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.69722 | 0.219966 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.0917 | −0.363125 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.21110 | 0.300914 | 0.150457 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150457 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.422205 | −0.0137781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.6056 | 1.94309 | 0.971543 | − | 0.236864i | \(-0.0761197\pi\) | ||||
0.971543 | + | 0.236864i | \(0.0761197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.9361 | 1.33306 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.63331 | 0.215554 | 0.107777 | − | 0.994175i | \(-0.465627\pi\) | ||||
0.107777 | + | 0.994175i | \(0.465627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.5416 | −1.28358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.09167 | 0.0678271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.2666 | −1.20718 | −0.603592 | − | 0.797293i | \(-0.706264\pi\) | ||||
−0.603592 | + | 0.797293i | \(0.706264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.09167 | 0.0676142 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.2666 | 2.36344 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.90833 | −0.222618 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9083 | 0.479419 | 0.239710 | − | 0.970845i | \(-0.422948\pi\) | ||||
0.239710 | + | 0.970845i | \(0.422948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.9083 | −0.511049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.3583 | −1.45562 | −0.727808 | − | 0.685781i | \(-0.759461\pi\) | ||||
−0.727808 | + | 0.685781i | \(0.759461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.33053 | 0.138830 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.0278 | 1.66452 | 0.832258 | − | 0.554389i | \(-0.187048\pi\) | ||||
0.832258 | + | 0.554389i | \(0.187048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.69722 | 0.0542435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.5139 | 0.846523 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.84441 | 0.282093 | 0.141046 | − | 0.990003i | \(-0.454953\pi\) | ||||
0.141046 | + | 0.990003i | \(0.454953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.81665 | −0.153316 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.6611 | −1.67452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.9083 | 0.537111 | 0.268555 | − | 0.963264i | \(-0.413454\pi\) | ||||
0.268555 | + | 0.963264i | \(0.413454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.7527 | 1.57886 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.7250 | −1.47979 | −0.739897 | − | 0.672720i | \(-0.765126\pi\) | ||||
−0.739897 | + | 0.672720i | \(0.765126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4400.2.a.bs.1.2 | 2 | ||
4.3 | odd | 2 | 275.2.a.e.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 4400.2.b.y.4049.1 | 4 | |||
5.3 | odd | 4 | 4400.2.b.y.4049.4 | 4 | |||
5.4 | even | 2 | 4400.2.a.bh.1.1 | 2 | |||
12.11 | even | 2 | 2475.2.a.t.1.1 | 2 | |||
20.3 | even | 4 | 275.2.b.c.199.2 | 4 | |||
20.7 | even | 4 | 275.2.b.c.199.3 | 4 | |||
20.19 | odd | 2 | 275.2.a.f.1.1 | yes | 2 | ||
44.43 | even | 2 | 3025.2.a.n.1.1 | 2 | |||
60.23 | odd | 4 | 2475.2.c.k.199.3 | 4 | |||
60.47 | odd | 4 | 2475.2.c.k.199.2 | 4 | |||
60.59 | even | 2 | 2475.2.a.o.1.2 | 2 | |||
220.219 | even | 2 | 3025.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.e.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
275.2.a.f.1.1 | yes | 2 | 20.19 | odd | 2 | ||
275.2.b.c.199.2 | 4 | 20.3 | even | 4 | |||
275.2.b.c.199.3 | 4 | 20.7 | even | 4 | |||
2475.2.a.o.1.2 | 2 | 60.59 | even | 2 | |||
2475.2.a.t.1.1 | 2 | 12.11 | even | 2 | |||
2475.2.c.k.199.2 | 4 | 60.47 | odd | 4 | |||
2475.2.c.k.199.3 | 4 | 60.23 | odd | 4 | |||
3025.2.a.h.1.2 | 2 | 220.219 | even | 2 | |||
3025.2.a.n.1.1 | 2 | 44.43 | even | 2 | |||
4400.2.a.bh.1.1 | 2 | 5.4 | even | 2 | |||
4400.2.a.bs.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.b.y.4049.1 | 4 | 5.2 | odd | 4 | |||
4400.2.b.y.4049.4 | 4 | 5.3 | odd | 4 |