Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2550,2,Mod(1,2550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2550.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: | \(20.3618525154\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 510) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.44949 | 0.925820 | 0.462910 | − | 0.886405i | \(-0.346805\pi\) | ||||
0.462910 | + | 0.886405i | \(0.346805\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89898 | −1.47710 | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.89898 | 1.58273 | 0.791367 | − | 0.611341i | \(-0.209370\pi\) | ||||
0.791367 | + | 0.611341i | \(0.209370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.44949 | −0.534522 | ||||||||
\(22\) | −4.89898 | −1.04447 | ||||||||
\(23\) | −6.44949 | −1.34481 | −0.672406 | − | 0.740183i | \(-0.734739\pi\) | ||||
−0.672406 | + | 0.740183i | \(0.734739\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.44949 | 0.462910 | ||||||||
\(29\) | −9.34847 | −1.73597 | −0.867984 | − | 0.496593i | \(-0.834584\pi\) | ||||
−0.867984 | + | 0.496593i | \(0.834584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.44949 | −1.15836 | −0.579181 | − | 0.815199i | \(-0.696628\pi\) | ||||
−0.579181 | + | 0.815199i | \(0.696628\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.89898 | 0.852803 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.449490 | 0.0738957 | 0.0369478 | − | 0.999317i | \(-0.488236\pi\) | ||||
0.0369478 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(38\) | 6.89898 | 1.11916 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.10102 | −0.171951 | −0.0859753 | − | 0.996297i | \(-0.527401\pi\) | ||||
−0.0859753 | + | 0.996297i | \(0.527401\pi\) | |||||||
\(42\) | −2.44949 | −0.377964 | ||||||||
\(43\) | 2.89898 | 0.442090 | 0.221045 | − | 0.975264i | \(-0.429053\pi\) | ||||
0.221045 | + | 0.975264i | \(0.429053\pi\) | |||||||
\(44\) | −4.89898 | −0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.44949 | −0.950925 | ||||||||
\(47\) | −4.89898 | −0.714590 | −0.357295 | − | 0.933992i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933992i | \(0.616301\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −6.00000 | −0.832050 | ||||||||
\(53\) | 1.10102 | 0.151237 | 0.0756184 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756184 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.44949 | 0.327327 | ||||||||
\(57\) | −6.89898 | −0.913792 | ||||||||
\(58\) | −9.34847 | −1.22751 | ||||||||
\(59\) | 5.79796 | 0.754830 | 0.377415 | − | 0.926044i | \(-0.376813\pi\) | ||||
0.377415 | + | 0.926044i | \(0.376813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3485 | 1.70910 | 0.854548 | − | 0.519372i | \(-0.173834\pi\) | ||||
0.854548 | + | 0.519372i | \(0.173834\pi\) | |||||||
\(62\) | −6.44949 | −0.819086 | ||||||||
\(63\) | 2.44949 | 0.308607 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.89898 | 0.603023 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 6.44949 | 0.776427 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.44949 | 0.290701 | 0.145350 | − | 0.989380i | \(-0.453569\pi\) | ||||
0.145350 | + | 0.989380i | \(0.453569\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −14.8990 | −1.74379 | −0.871897 | − | 0.489690i | \(-0.837110\pi\) | ||||
−0.871897 | + | 0.489690i | \(0.837110\pi\) | |||||||
\(74\) | 0.449490 | 0.0522521 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.89898 | 0.791367 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −1.55051 | −0.174446 | −0.0872230 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872230 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.10102 | −0.121587 | ||||||||
\(83\) | −2.89898 | −0.318204 | −0.159102 | − | 0.987262i | \(-0.550860\pi\) | ||||
−0.159102 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(84\) | −2.44949 | −0.267261 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.89898 | 0.312605 | ||||||||
\(87\) | 9.34847 | 1.00226 | ||||||||
\(88\) | −4.89898 | −0.522233 | ||||||||
\(89\) | −1.79796 | −0.190583 | −0.0952916 | − | 0.995449i | \(-0.530378\pi\) | ||||
−0.0952916 | + | 0.995449i | \(0.530378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.6969 | −1.54066 | ||||||||
\(92\) | −6.44949 | −0.672406 | ||||||||
\(93\) | 6.44949 | 0.668781 | ||||||||
\(94\) | −4.89898 | −0.505291 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 3.79796 | 0.385624 | 0.192812 | − | 0.981236i | \(-0.438239\pi\) | ||||
0.192812 | + | 0.981236i | \(0.438239\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −4.89898 | −0.492366 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.79796 | 0.377911 | 0.188956 | − | 0.981986i | \(-0.439490\pi\) | ||||
0.188956 | + | 0.981986i | \(0.439490\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −16.8990 | −1.66511 | −0.832553 | − | 0.553945i | \(-0.813122\pi\) | ||||
−0.832553 | + | 0.553945i | \(0.813122\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.10102 | 0.106941 | ||||||||
\(107\) | −3.10102 | −0.299787 | −0.149893 | − | 0.988702i | \(-0.547893\pi\) | ||||
−0.149893 | + | 0.988702i | \(0.547893\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.2474 | 1.74779 | 0.873894 | − | 0.486116i | \(-0.161587\pi\) | ||||
0.873894 | + | 0.486116i | \(0.161587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.449490 | −0.0426637 | ||||||||
\(112\) | 2.44949 | 0.231455 | ||||||||
\(113\) | −16.6969 | −1.57072 | −0.785358 | − | 0.619042i | \(-0.787521\pi\) | ||||
−0.785358 | + | 0.619042i | \(0.787521\pi\) | |||||||
\(114\) | −6.89898 | −0.646149 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.34847 | −0.867984 | ||||||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | 5.79796 | 0.533745 | ||||||||
\(119\) | −2.44949 | −0.224544 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 13.3485 | 1.20851 | ||||||||
\(123\) | 1.10102 | 0.0992757 | ||||||||
\(124\) | −6.44949 | −0.579181 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.44949 | 0.218218 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.89898 | −0.255241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.89898 | 0.428026 | 0.214013 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214013 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(132\) | 4.89898 | 0.426401 | ||||||||
\(133\) | 16.8990 | 1.46533 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | 6.44949 | 0.549017 | ||||||||
\(139\) | −16.8990 | −1.43335 | −0.716676 | − | 0.697406i | \(-0.754338\pi\) | ||||
−0.716676 | + | 0.697406i | \(0.754338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.89898 | 0.412568 | ||||||||
\(142\) | 2.44949 | 0.205557 | ||||||||
\(143\) | 29.3939 | 2.45804 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.8990 | −1.23305 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0.449490 | 0.0369478 | ||||||||
\(149\) | 12.6969 | 1.04017 | 0.520087 | − | 0.854113i | \(-0.325900\pi\) | ||||
0.520087 | + | 0.854113i | \(0.325900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7980 | 1.12286 | 0.561431 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561431 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(152\) | 6.89898 | 0.559581 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | −16.6969 | −1.33256 | −0.666280 | − | 0.745701i | \(-0.732115\pi\) | ||||
−0.666280 | + | 0.745701i | \(0.732115\pi\) | |||||||
\(158\) | −1.55051 | −0.123352 | ||||||||
\(159\) | −1.10102 | −0.0873166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.7980 | −1.24505 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.79796 | −0.454131 | −0.227066 | − | 0.973879i | \(-0.572913\pi\) | ||||
−0.227066 | + | 0.973879i | \(0.572913\pi\) | |||||||
\(164\) | −1.10102 | −0.0859753 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.89898 | −0.225004 | ||||||||
\(167\) | −4.65153 | −0.359946 | −0.179973 | − | 0.983672i | \(-0.557601\pi\) | ||||
−0.179973 | + | 0.983672i | \(0.557601\pi\) | |||||||
\(168\) | −2.44949 | −0.188982 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.89898 | 0.527578 | ||||||||
\(172\) | 2.89898 | 0.221045 | ||||||||
\(173\) | 13.3485 | 1.01487 | 0.507433 | − | 0.861691i | \(-0.330595\pi\) | ||||
0.507433 | + | 0.861691i | \(0.330595\pi\) | |||||||
\(174\) | 9.34847 | 0.708706 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.89898 | −0.369274 | ||||||||
\(177\) | −5.79796 | −0.435801 | ||||||||
\(178\) | −1.79796 | −0.134763 | ||||||||
\(179\) | −20.6969 | −1.54696 | −0.773481 | − | 0.633820i | \(-0.781486\pi\) | ||||
−0.773481 | + | 0.633820i | \(0.781486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.44949 | 0.330728 | 0.165364 | − | 0.986233i | \(-0.447120\pi\) | ||||
0.165364 | + | 0.986233i | \(0.447120\pi\) | |||||||
\(182\) | −14.6969 | −1.08941 | ||||||||
\(183\) | −13.3485 | −0.986747 | ||||||||
\(184\) | −6.44949 | −0.475463 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.44949 | 0.472900 | ||||||||
\(187\) | 4.89898 | 0.358249 | ||||||||
\(188\) | −4.89898 | −0.357295 | ||||||||
\(189\) | −2.44949 | −0.178174 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8990 | −1.22277 | −0.611384 | − | 0.791334i | \(-0.709387\pi\) | ||||
−0.611384 | + | 0.791334i | \(0.709387\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 3.79796 | 0.272678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −19.1464 | −1.36413 | −0.682063 | − | 0.731293i | \(-0.738917\pi\) | ||||
−0.682063 | + | 0.731293i | \(0.738917\pi\) | |||||||
\(198\) | −4.89898 | −0.348155 | ||||||||
\(199\) | −18.0454 | −1.27921 | −0.639603 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639603 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 3.79796 | 0.267223 | ||||||||
\(203\) | −22.8990 | −1.60719 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.8990 | −1.17741 | ||||||||
\(207\) | −6.44949 | −0.448271 | ||||||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | −33.7980 | −2.33785 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.10102 | −0.213483 | −0.106742 | − | 0.994287i | \(-0.534042\pi\) | ||||
−0.106742 | + | 0.994287i | \(0.534042\pi\) | |||||||
\(212\) | 1.10102 | 0.0756184 | ||||||||
\(213\) | −2.44949 | −0.167836 | ||||||||
\(214\) | −3.10102 | −0.211981 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −15.7980 | −1.07244 | ||||||||
\(218\) | 18.2474 | 1.23587 | ||||||||
\(219\) | 14.8990 | 1.00678 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | −0.449490 | −0.0301678 | ||||||||
\(223\) | −4.89898 | −0.328060 | −0.164030 | − | 0.986455i | \(-0.552449\pi\) | ||||
−0.164030 | + | 0.986455i | \(0.552449\pi\) | |||||||
\(224\) | 2.44949 | 0.163663 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.6969 | −1.11066 | ||||||||
\(227\) | 19.5959 | 1.30063 | 0.650313 | − | 0.759666i | \(-0.274638\pi\) | ||||
0.650313 | + | 0.759666i | \(0.274638\pi\) | |||||||
\(228\) | −6.89898 | −0.456896 | ||||||||
\(229\) | 18.0000 | 1.18947 | 0.594737 | − | 0.803921i | \(-0.297256\pi\) | ||||
0.594737 | + | 0.803921i | \(0.297256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | 0.789542 | ||||||||
\(232\) | −9.34847 | −0.613757 | ||||||||
\(233\) | 1.10102 | 0.0721303 | 0.0360651 | − | 0.999349i | \(-0.488518\pi\) | ||||
0.0360651 | + | 0.999349i | \(0.488518\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.79796 | 0.377415 | ||||||||
\(237\) | 1.55051 | 0.100716 | ||||||||
\(238\) | −2.44949 | −0.158777 | ||||||||
\(239\) | 8.89898 | 0.575627 | 0.287814 | − | 0.957686i | \(-0.407072\pi\) | ||||
0.287814 | + | 0.957686i | \(0.407072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.89898 | −0.444402 | −0.222201 | − | 0.975001i | \(-0.571324\pi\) | ||||
−0.222201 | + | 0.975001i | \(0.571324\pi\) | |||||||
\(242\) | 13.0000 | 0.835672 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.3485 | 0.854548 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.10102 | 0.0701985 | ||||||||
\(247\) | −41.3939 | −2.63383 | ||||||||
\(248\) | −6.44949 | −0.409543 | ||||||||
\(249\) | 2.89898 | 0.183715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.6969 | −1.30638 | −0.653190 | − | 0.757194i | \(-0.726570\pi\) | ||||
−0.653190 | + | 0.757194i | \(0.726570\pi\) | |||||||
\(252\) | 2.44949 | 0.154303 | ||||||||
\(253\) | 31.5959 | 1.98642 | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.0000 | 1.24757 | 0.623783 | − | 0.781598i | \(-0.285595\pi\) | ||||
0.623783 | + | 0.781598i | \(0.285595\pi\) | |||||||
\(258\) | −2.89898 | −0.180483 | ||||||||
\(259\) | 1.10102 | 0.0684141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.34847 | −0.578656 | ||||||||
\(262\) | 4.89898 | 0.302660 | ||||||||
\(263\) | 26.6969 | 1.64620 | 0.823102 | − | 0.567894i | \(-0.192242\pi\) | ||||
0.823102 | + | 0.567894i | \(0.192242\pi\) | |||||||
\(264\) | 4.89898 | 0.301511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.8990 | 1.03614 | ||||||||
\(267\) | 1.79796 | 0.110033 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 23.5505 | 1.43590 | 0.717950 | − | 0.696095i | \(-0.245081\pi\) | ||||
0.717950 | + | 0.696095i | \(0.245081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.59592 | −0.461419 | −0.230710 | − | 0.973023i | \(-0.574105\pi\) | ||||
−0.230710 | + | 0.973023i | \(0.574105\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 14.6969 | 0.889499 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.44949 | 0.388214 | ||||||||
\(277\) | 28.4495 | 1.70936 | 0.854682 | − | 0.519152i | \(-0.173752\pi\) | ||||
0.854682 | + | 0.519152i | \(0.173752\pi\) | |||||||
\(278\) | −16.8990 | −1.01353 | ||||||||
\(279\) | −6.44949 | −0.386121 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.79796 | 0.584497 | 0.292249 | − | 0.956342i | \(-0.405597\pi\) | ||||
0.292249 | + | 0.956342i | \(0.405597\pi\) | |||||||
\(282\) | 4.89898 | 0.291730 | ||||||||
\(283\) | 6.69694 | 0.398092 | 0.199046 | − | 0.979990i | \(-0.436216\pi\) | ||||
0.199046 | + | 0.979990i | \(0.436216\pi\) | |||||||
\(284\) | 2.44949 | 0.145350 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.3939 | 1.73810 | ||||||||
\(287\) | −2.69694 | −0.159195 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.79796 | −0.222640 | ||||||||
\(292\) | −14.8990 | −0.871897 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.449490 | 0.0261261 | ||||||||
\(297\) | 4.89898 | 0.284268 | ||||||||
\(298\) | 12.6969 | 0.735514 | ||||||||
\(299\) | 38.6969 | 2.23790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.10102 | 0.409296 | ||||||||
\(302\) | 13.7980 | 0.793983 | ||||||||
\(303\) | −3.79796 | −0.218187 | ||||||||
\(304\) | 6.89898 | 0.395684 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −10.8990 | −0.622038 | −0.311019 | − | 0.950404i | \(-0.600670\pi\) | ||||
−0.311019 | + | 0.950404i | \(0.600670\pi\) | |||||||
\(308\) | −12.0000 | −0.683763 | ||||||||
\(309\) | 16.8990 | 0.961349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.3485 | −1.32397 | −0.661985 | − | 0.749517i | \(-0.730286\pi\) | ||||
−0.661985 | + | 0.749517i | \(0.730286\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | −16.6969 | −0.942263 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.55051 | −0.0872230 | ||||||||
\(317\) | 8.44949 | 0.474571 | 0.237285 | − | 0.971440i | \(-0.423742\pi\) | ||||
0.237285 | + | 0.971440i | \(0.423742\pi\) | |||||||
\(318\) | −1.10102 | −0.0617422 | ||||||||
\(319\) | 45.7980 | 2.56419 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.10102 | 0.173082 | ||||||||
\(322\) | −15.7980 | −0.880386 | ||||||||
\(323\) | −6.89898 | −0.383869 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.79796 | −0.321119 | ||||||||
\(327\) | −18.2474 | −1.00909 | ||||||||
\(328\) | −1.10102 | −0.0607937 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.3939 | 1.83549 | 0.917747 | − | 0.397166i | \(-0.130006\pi\) | ||||
0.917747 | + | 0.397166i | \(0.130006\pi\) | |||||||
\(332\) | −2.89898 | −0.159102 | ||||||||
\(333\) | 0.449490 | 0.0246319 | ||||||||
\(334\) | −4.65153 | −0.254520 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.44949 | −0.133631 | ||||||||
\(337\) | −2.89898 | −0.157917 | −0.0789587 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789587 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(338\) | 23.0000 | 1.25104 | ||||||||
\(339\) | 16.6969 | 0.906853 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.5959 | 1.71101 | ||||||||
\(342\) | 6.89898 | 0.373054 | ||||||||
\(343\) | −19.5959 | −1.05808 | ||||||||
\(344\) | 2.89898 | 0.156302 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3485 | 0.717618 | ||||||||
\(347\) | 13.7980 | 0.740713 | 0.370357 | − | 0.928890i | \(-0.379235\pi\) | ||||
0.370357 | + | 0.928890i | \(0.379235\pi\) | |||||||
\(348\) | 9.34847 | 0.501131 | ||||||||
\(349\) | 7.30306 | 0.390924 | 0.195462 | − | 0.980711i | \(-0.437379\pi\) | ||||
0.195462 | + | 0.980711i | \(0.437379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | −4.89898 | −0.261116 | ||||||||
\(353\) | −10.0000 | −0.532246 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(354\) | −5.79796 | −0.308158 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.79796 | −0.0952916 | ||||||||
\(357\) | 2.44949 | 0.129641 | ||||||||
\(358\) | −20.6969 | −1.09387 | ||||||||
\(359\) | −6.20204 | −0.327331 | −0.163666 | − | 0.986516i | \(-0.552332\pi\) | ||||
−0.163666 | + | 0.986516i | \(0.552332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | 4.44949 | 0.233860 | ||||||||
\(363\) | −13.0000 | −0.682323 | ||||||||
\(364\) | −14.6969 | −0.770329 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.3485 | −0.697736 | ||||||||
\(367\) | 14.0454 | 0.733164 | 0.366582 | − | 0.930386i | \(-0.380528\pi\) | ||||
0.366582 | + | 0.930386i | \(0.380528\pi\) | |||||||
\(368\) | −6.44949 | −0.336203 | ||||||||
\(369\) | −1.10102 | −0.0573168 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.69694 | 0.140018 | ||||||||
\(372\) | 6.44949 | 0.334390 | ||||||||
\(373\) | 11.7980 | 0.610875 | 0.305438 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305438 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(374\) | 4.89898 | 0.253320 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.89898 | −0.252646 | ||||||||
\(377\) | 56.0908 | 2.88882 | ||||||||
\(378\) | −2.44949 | −0.125988 | ||||||||
\(379\) | −10.2020 | −0.524044 | −0.262022 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | −16.8990 | −0.864627 | ||||||||
\(383\) | −16.8990 | −0.863498 | −0.431749 | − | 0.901994i | \(-0.642103\pi\) | ||||
−0.431749 | + | 0.901994i | \(0.642103\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 2.89898 | 0.147363 | ||||||||
\(388\) | 3.79796 | 0.192812 | ||||||||
\(389\) | 3.30306 | 0.167472 | 0.0837359 | − | 0.996488i | \(-0.473315\pi\) | ||||
0.0837359 | + | 0.996488i | \(0.473315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.44949 | 0.326165 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −4.89898 | −0.247121 | ||||||||
\(394\) | −19.1464 | −0.964583 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.89898 | −0.246183 | ||||||||
\(397\) | 36.0454 | 1.80907 | 0.904534 | − | 0.426402i | \(-0.140219\pi\) | ||||
0.904534 | + | 0.426402i | \(0.140219\pi\) | |||||||
\(398\) | −18.0454 | −0.904535 | ||||||||
\(399\) | −16.8990 | −0.846007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.696938 | −0.0348034 | −0.0174017 | − | 0.999849i | \(-0.505539\pi\) | ||||
−0.0174017 | + | 0.999849i | \(0.505539\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | 38.6969 | 1.92763 | ||||||||
\(404\) | 3.79796 | 0.188956 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.8990 | −1.13646 | ||||||||
\(407\) | −2.20204 | −0.109151 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 15.5959 | 0.771169 | 0.385584 | − | 0.922673i | \(-0.374000\pi\) | ||||
0.385584 | + | 0.922673i | \(0.374000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | −16.8990 | −0.832553 | ||||||||
\(413\) | 14.2020 | 0.698837 | ||||||||
\(414\) | −6.44949 | −0.316975 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | 16.8990 | 0.827547 | ||||||||
\(418\) | −33.7980 | −1.65311 | ||||||||
\(419\) | 7.59592 | 0.371085 | 0.185542 | − | 0.982636i | \(-0.440596\pi\) | ||||
0.185542 | + | 0.982636i | \(0.440596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.696938 | −0.0339667 | −0.0169834 | − | 0.999856i | \(-0.505406\pi\) | ||||
−0.0169834 | + | 0.999856i | \(0.505406\pi\) | |||||||
\(422\) | −3.10102 | −0.150955 | ||||||||
\(423\) | −4.89898 | −0.238197 | ||||||||
\(424\) | 1.10102 | 0.0534703 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.44949 | −0.118678 | ||||||||
\(427\) | 32.6969 | 1.58232 | ||||||||
\(428\) | −3.10102 | −0.149893 | ||||||||
\(429\) | −29.3939 | −1.41915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.1464 | 1.21126 | 0.605630 | − | 0.795746i | \(-0.292921\pi\) | ||||
0.605630 | + | 0.795746i | \(0.292921\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 10.0000 | 0.480569 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(434\) | −15.7980 | −0.758326 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.2474 | 0.873894 | ||||||||
\(437\) | −44.4949 | −2.12848 | ||||||||
\(438\) | 14.8990 | 0.711901 | ||||||||
\(439\) | −27.3485 | −1.30527 | −0.652636 | − | 0.757672i | \(-0.726337\pi\) | ||||
−0.652636 | + | 0.757672i | \(0.726337\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | 10.2020 | 0.484714 | 0.242357 | − | 0.970187i | \(-0.422080\pi\) | ||||
0.242357 | + | 0.970187i | \(0.422080\pi\) | |||||||
\(444\) | −0.449490 | −0.0213318 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.89898 | −0.231973 | ||||||||
\(447\) | −12.6969 | −0.600545 | ||||||||
\(448\) | 2.44949 | 0.115728 | ||||||||
\(449\) | −32.6969 | −1.54306 | −0.771532 | − | 0.636191i | \(-0.780509\pi\) | ||||
−0.771532 | + | 0.636191i | \(0.780509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.39388 | 0.253988 | ||||||||
\(452\) | −16.6969 | −0.785358 | ||||||||
\(453\) | −13.7980 | −0.648285 | ||||||||
\(454\) | 19.5959 | 0.919682 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.89898 | −0.323074 | ||||||||
\(457\) | −1.59592 | −0.0746539 | −0.0373269 | − | 0.999303i | \(-0.511884\pi\) | ||||
−0.0373269 | + | 0.999303i | \(0.511884\pi\) | |||||||
\(458\) | 18.0000 | 0.841085 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.5959 | −1.00582 | −0.502911 | − | 0.864338i | \(-0.667738\pi\) | ||||
−0.502911 | + | 0.864338i | \(0.667738\pi\) | |||||||
\(462\) | 12.0000 | 0.558291 | ||||||||
\(463\) | 5.30306 | 0.246454 | 0.123227 | − | 0.992378i | \(-0.460676\pi\) | ||||
0.123227 | + | 0.992378i | \(0.460676\pi\) | |||||||
\(464\) | −9.34847 | −0.433992 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.10102 | 0.0510038 | ||||||||
\(467\) | 0.404082 | 0.0186987 | 0.00934934 | − | 0.999956i | \(-0.497024\pi\) | ||||
0.00934934 | + | 0.999956i | \(0.497024\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | −9.79796 | −0.452428 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.6969 | 0.769354 | ||||||||
\(472\) | 5.79796 | 0.266873 | ||||||||
\(473\) | −14.2020 | −0.653011 | ||||||||
\(474\) | 1.55051 | 0.0712173 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.44949 | −0.112272 | ||||||||
\(477\) | 1.10102 | 0.0504123 | ||||||||
\(478\) | 8.89898 | 0.407030 | ||||||||
\(479\) | 15.3485 | 0.701289 | 0.350645 | − | 0.936509i | \(-0.385962\pi\) | ||||
0.350645 | + | 0.936509i | \(0.385962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69694 | −0.122970 | ||||||||
\(482\) | −6.89898 | −0.314240 | ||||||||
\(483\) | 15.7980 | 0.718832 | ||||||||
\(484\) | 13.0000 | 0.590909 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 15.3485 | 0.695506 | 0.347753 | − | 0.937586i | \(-0.386945\pi\) | ||||
0.347753 | + | 0.937586i | \(0.386945\pi\) | |||||||
\(488\) | 13.3485 | 0.604257 | ||||||||
\(489\) | 5.79796 | 0.262193 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8990 | −0.672382 | −0.336191 | − | 0.941794i | \(-0.609139\pi\) | ||||
−0.336191 | + | 0.941794i | \(0.609139\pi\) | |||||||
\(492\) | 1.10102 | 0.0496378 | ||||||||
\(493\) | 9.34847 | 0.421034 | ||||||||
\(494\) | −41.3939 | −1.86240 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.44949 | −0.289591 | ||||||||
\(497\) | 6.00000 | 0.269137 | ||||||||
\(498\) | 2.89898 | 0.129906 | ||||||||
\(499\) | 0.898979 | 0.0402438 | 0.0201219 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201219 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.65153 | 0.207815 | ||||||||
\(502\) | −20.6969 | −0.923750 | ||||||||
\(503\) | −33.5505 | −1.49594 | −0.747972 | − | 0.663731i | \(-0.768972\pi\) | ||||
−0.747972 | + | 0.663731i | \(0.768972\pi\) | |||||||
\(504\) | 2.44949 | 0.109109 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.5959 | 1.40461 | ||||||||
\(507\) | −23.0000 | −1.02147 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | −10.8990 | −0.483089 | −0.241544 | − | 0.970390i | \(-0.577654\pi\) | ||||
−0.241544 | + | 0.970390i | \(0.577654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.4949 | −1.61444 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.89898 | −0.304597 | ||||||||
\(514\) | 20.0000 | 0.882162 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.89898 | −0.127620 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | 1.10102 | 0.0483761 | ||||||||
\(519\) | −13.3485 | −0.585933 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.6969 | −0.731506 | −0.365753 | − | 0.930712i | \(-0.619189\pi\) | ||||
−0.365753 | + | 0.930712i | \(0.619189\pi\) | |||||||
\(522\) | −9.34847 | −0.409171 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 4.89898 | 0.214013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.6969 | 1.16404 | ||||||||
\(527\) | 6.44949 | 0.280944 | ||||||||
\(528\) | 4.89898 | 0.213201 | ||||||||
\(529\) | 18.5959 | 0.808518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.79796 | 0.251610 | ||||||||
\(532\) | 16.8990 | 0.732664 | ||||||||
\(533\) | 6.60612 | 0.286143 | ||||||||
\(534\) | 1.79796 | 0.0778053 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | 20.6969 | 0.893139 | ||||||||
\(538\) | 23.5505 | 1.01533 | ||||||||
\(539\) | 4.89898 | 0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1464 | 1.33909 | 0.669545 | − | 0.742772i | \(-0.266489\pi\) | ||||
0.669545 | + | 0.742772i | \(0.266489\pi\) | |||||||
\(542\) | −7.59592 | −0.326273 | ||||||||
\(543\) | −4.44949 | −0.190946 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.6969 | 0.628971 | ||||||||
\(547\) | −18.6969 | −0.799423 | −0.399712 | − | 0.916641i | \(-0.630890\pi\) | ||||
−0.399712 | + | 0.916641i | \(0.630890\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 13.3485 | 0.569699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −64.4949 | −2.74758 | ||||||||
\(552\) | 6.44949 | 0.274509 | ||||||||
\(553\) | −3.79796 | −0.161506 | ||||||||
\(554\) | 28.4495 | 1.20870 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8990 | −0.716676 | ||||||||
\(557\) | 2.89898 | 0.122834 | 0.0614169 | − | 0.998112i | \(-0.480438\pi\) | ||||
0.0614169 | + | 0.998112i | \(0.480438\pi\) | |||||||
\(558\) | −6.44949 | −0.273029 | ||||||||
\(559\) | −17.3939 | −0.735683 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.89898 | −0.206835 | ||||||||
\(562\) | 9.79796 | 0.413302 | ||||||||
\(563\) | −6.89898 | −0.290757 | −0.145379 | − | 0.989376i | \(-0.546440\pi\) | ||||
−0.145379 | + | 0.989376i | \(0.546440\pi\) | |||||||
\(564\) | 4.89898 | 0.206284 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.69694 | 0.281493 | ||||||||
\(567\) | 2.44949 | 0.102869 | ||||||||
\(568\) | 2.44949 | 0.102778 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3939 | −0.895306 | −0.447653 | − | 0.894207i | \(-0.647740\pi\) | ||||
−0.447653 | + | 0.894207i | \(0.647740\pi\) | |||||||
\(572\) | 29.3939 | 1.22902 | ||||||||
\(573\) | 16.8990 | 0.705965 | ||||||||
\(574\) | −2.69694 | −0.112568 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.2020 | 0.424717 | 0.212358 | − | 0.977192i | \(-0.431886\pi\) | ||||
0.212358 | + | 0.977192i | \(0.431886\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.10102 | −0.294600 | ||||||||
\(582\) | −3.79796 | −0.157430 | ||||||||
\(583\) | −5.39388 | −0.223392 | ||||||||
\(584\) | −14.8990 | −0.616524 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0000 | 0.413096 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −44.4949 | −1.83338 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.1464 | 0.787579 | ||||||||
\(592\) | 0.449490 | 0.0184739 | ||||||||
\(593\) | −1.79796 | −0.0738333 | −0.0369167 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369167 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(594\) | 4.89898 | 0.201008 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.6969 | 0.520087 | ||||||||
\(597\) | 18.0454 | 0.738549 | ||||||||
\(598\) | 38.6969 | 1.58244 | ||||||||
\(599\) | 13.7980 | 0.563769 | 0.281885 | − | 0.959448i | \(-0.409040\pi\) | ||||
0.281885 | + | 0.959448i | \(0.409040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.202041 | 0.00824143 | 0.00412071 | − | 0.999992i | \(-0.498688\pi\) | ||||
0.00412071 | + | 0.999992i | \(0.498688\pi\) | |||||||
\(602\) | 7.10102 | 0.289416 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 13.7980 | 0.561431 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.79796 | −0.154282 | ||||||||
\(607\) | 26.4495 | 1.07355 | 0.536776 | − | 0.843725i | \(-0.319642\pi\) | ||||
0.536776 | + | 0.843725i | \(0.319642\pi\) | |||||||
\(608\) | 6.89898 | 0.279791 | ||||||||
\(609\) | 22.8990 | 0.927913 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3939 | 1.18915 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 48.2929 | 1.95053 | 0.975265 | − | 0.221039i | \(-0.0709447\pi\) | ||||
0.975265 | + | 0.221039i | \(0.0709447\pi\) | |||||||
\(614\) | −10.8990 | −0.439847 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | −0.483494 | ||||||||
\(617\) | 26.4949 | 1.06664 | 0.533322 | − | 0.845912i | \(-0.320943\pi\) | ||||
0.533322 | + | 0.845912i | \(0.320943\pi\) | |||||||
\(618\) | 16.8990 | 0.679777 | ||||||||
\(619\) | −16.0000 | −0.643094 | −0.321547 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321547 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.44949 | 0.258809 | ||||||||
\(622\) | −23.3485 | −0.936188 | ||||||||
\(623\) | −4.40408 | −0.176446 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.00000 | −0.0799361 | ||||||||
\(627\) | 33.7980 | 1.34976 | ||||||||
\(628\) | −16.6969 | −0.666280 | ||||||||
\(629\) | −0.449490 | −0.0179223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4949 | 0.975126 | 0.487563 | − | 0.873088i | \(-0.337886\pi\) | ||||
0.487563 | + | 0.873088i | \(0.337886\pi\) | |||||||
\(632\) | −1.55051 | −0.0616760 | ||||||||
\(633\) | 3.10102 | 0.123255 | ||||||||
\(634\) | 8.44949 | 0.335572 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.10102 | −0.0436583 | ||||||||
\(637\) | 6.00000 | 0.237729 | ||||||||
\(638\) | 45.7980 | 1.81316 | ||||||||
\(639\) | 2.44949 | 0.0969003 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.69694 | 0.343508 | 0.171754 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171754 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(642\) | 3.10102 | 0.122388 | ||||||||
\(643\) | 8.00000 | 0.315489 | 0.157745 | − | 0.987480i | \(-0.449578\pi\) | ||||
0.157745 | + | 0.987480i | \(0.449578\pi\) | |||||||
\(644\) | −15.7980 | −0.622527 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.89898 | −0.271437 | ||||||||
\(647\) | −30.2929 | −1.19094 | −0.595468 | − | 0.803379i | \(-0.703033\pi\) | ||||
−0.595468 | + | 0.803379i | \(0.703033\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −28.4041 | −1.11496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.7980 | 0.619171 | ||||||||
\(652\) | −5.79796 | −0.227066 | ||||||||
\(653\) | −20.4495 | −0.800250 | −0.400125 | − | 0.916460i | \(-0.631033\pi\) | ||||
−0.400125 | + | 0.916460i | \(0.631033\pi\) | |||||||
\(654\) | −18.2474 | −0.713532 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.10102 | −0.0429876 | ||||||||
\(657\) | −14.8990 | −0.581265 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −15.5959 | −0.607531 | −0.303765 | − | 0.952747i | \(-0.598244\pi\) | ||||
−0.303765 | + | 0.952747i | \(0.598244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.4949 | −1.80844 | −0.904221 | − | 0.427065i | \(-0.859548\pi\) | ||||
−0.904221 | + | 0.427065i | \(0.859548\pi\) | |||||||
\(662\) | 33.3939 | 1.29789 | ||||||||
\(663\) | −6.00000 | −0.233021 | ||||||||
\(664\) | −2.89898 | −0.112502 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.449490 | 0.0174174 | ||||||||
\(667\) | 60.2929 | 2.33455 | ||||||||
\(668\) | −4.65153 | −0.179973 | ||||||||
\(669\) | 4.89898 | 0.189405 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.3939 | −2.52450 | ||||||||
\(672\) | −2.44949 | −0.0944911 | ||||||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −2.89898 | −0.111665 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | −47.6413 | −1.83100 | −0.915502 | − | 0.402312i | \(-0.868207\pi\) | ||||
−0.915502 | + | 0.402312i | \(0.868207\pi\) | |||||||
\(678\) | 16.6969 | 0.641242 | ||||||||
\(679\) | 9.30306 | 0.357019 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.5959 | −0.750917 | ||||||||
\(682\) | 31.5959 | 1.20987 | ||||||||
\(683\) | 9.79796 | 0.374908 | 0.187454 | − | 0.982273i | \(-0.439976\pi\) | ||||
0.187454 | + | 0.982273i | \(0.439976\pi\) | |||||||
\(684\) | 6.89898 | 0.263789 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.5959 | −0.748176 | ||||||||
\(687\) | −18.0000 | −0.686743 | ||||||||
\(688\) | 2.89898 | 0.110523 | ||||||||
\(689\) | −6.60612 | −0.251673 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.2929 | −1.91323 | −0.956615 | − | 0.291354i | \(-0.905894\pi\) | ||||
−0.956615 | + | 0.291354i | \(0.905894\pi\) | |||||||
\(692\) | 13.3485 | 0.507433 | ||||||||
\(693\) | −12.0000 | −0.455842 | ||||||||
\(694\) | 13.7980 | 0.523763 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.34847 | 0.354353 | ||||||||
\(697\) | 1.10102 | 0.0417041 | ||||||||
\(698\) | 7.30306 | 0.276425 | ||||||||
\(699\) | −1.10102 | −0.0416444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 6.00000 | 0.226455 | ||||||||
\(703\) | 3.10102 | 0.116957 | ||||||||
\(704\) | −4.89898 | −0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.0000 | −0.376355 | ||||||||
\(707\) | 9.30306 | 0.349878 | ||||||||
\(708\) | −5.79796 | −0.217901 | ||||||||
\(709\) | −24.4495 | −0.918220 | −0.459110 | − | 0.888379i | \(-0.651832\pi\) | ||||
−0.459110 | + | 0.888379i | \(0.651832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.55051 | −0.0581487 | ||||||||
\(712\) | −1.79796 | −0.0673814 | ||||||||
\(713\) | 41.5959 | 1.55778 | ||||||||
\(714\) | 2.44949 | 0.0916698 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.6969 | −0.773481 | ||||||||
\(717\) | −8.89898 | −0.332338 | ||||||||
\(718\) | −6.20204 | −0.231458 | ||||||||
\(719\) | 12.2474 | 0.456753 | 0.228376 | − | 0.973573i | \(-0.426658\pi\) | ||||
0.228376 | + | 0.973573i | \(0.426658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.3939 | −1.54159 | ||||||||
\(722\) | 28.5959 | 1.06423 | ||||||||
\(723\) | 6.89898 | 0.256576 | ||||||||
\(724\) | 4.44949 | 0.165364 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.0000 | −0.482475 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | −14.6969 | −0.544705 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.89898 | −0.107223 | ||||||||
\(732\) | −13.3485 | −0.493374 | ||||||||
\(733\) | −19.7980 | −0.731254 | −0.365627 | − | 0.930761i | \(-0.619145\pi\) | ||||
−0.365627 | + | 0.930761i | \(0.619145\pi\) | |||||||
\(734\) | 14.0454 | 0.518425 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.44949 | −0.237731 | ||||||||
\(737\) | 19.5959 | 0.721825 | ||||||||
\(738\) | −1.10102 | −0.0405291 | ||||||||
\(739\) | −17.1010 | −0.629071 | −0.314536 | − | 0.949246i | \(-0.601849\pi\) | ||||
−0.314536 | + | 0.949246i | \(0.601849\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 41.3939 | 1.52064 | ||||||||
\(742\) | 2.69694 | 0.0990077 | ||||||||
\(743\) | −14.4495 | −0.530100 | −0.265050 | − | 0.964235i | \(-0.585389\pi\) | ||||
−0.265050 | + | 0.964235i | \(0.585389\pi\) | |||||||
\(744\) | 6.44949 | 0.236450 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.7980 | 0.431954 | ||||||||
\(747\) | −2.89898 | −0.106068 | ||||||||
\(748\) | 4.89898 | 0.179124 | ||||||||
\(749\) | −7.59592 | −0.277549 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.24745 | 0.300954 | 0.150477 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150477 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(752\) | −4.89898 | −0.178647 | ||||||||
\(753\) | 20.6969 | 0.754238 | ||||||||
\(754\) | 56.0908 | 2.04271 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.44949 | −0.0890871 | ||||||||
\(757\) | −5.50510 | −0.200086 | −0.100043 | − | 0.994983i | \(-0.531898\pi\) | ||||
−0.100043 | + | 0.994983i | \(0.531898\pi\) | |||||||
\(758\) | −10.2020 | −0.370555 | ||||||||
\(759\) | −31.5959 | −1.14686 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.59592 | 0.347852 | 0.173926 | − | 0.984759i | \(-0.444355\pi\) | ||||
0.173926 | + | 0.984759i | \(0.444355\pi\) | |||||||
\(762\) | −8.00000 | −0.289809 | ||||||||
\(763\) | 44.6969 | 1.61814 | ||||||||
\(764\) | −16.8990 | −0.611384 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.8990 | −0.610585 | ||||||||
\(767\) | −34.7878 | −1.25611 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 27.3939 | 0.987848 | 0.493924 | − | 0.869505i | \(-0.335562\pi\) | ||||
0.493924 | + | 0.869505i | \(0.335562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0000 | −0.720282 | ||||||||
\(772\) | −14.0000 | −0.503871 | ||||||||
\(773\) | −42.0000 | −1.51064 | −0.755318 | − | 0.655359i | \(-0.772517\pi\) | ||||
−0.755318 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(774\) | 2.89898 | 0.104202 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.79796 | 0.136339 | ||||||||
\(777\) | −1.10102 | −0.0394989 | ||||||||
\(778\) | 3.30306 | 0.118420 | ||||||||
\(779\) | −7.59592 | −0.272152 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 6.44949 | 0.230633 | ||||||||
\(783\) | 9.34847 | 0.334087 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.89898 | −0.174741 | ||||||||
\(787\) | 17.3031 | 0.616788 | 0.308394 | − | 0.951259i | \(-0.400209\pi\) | ||||
0.308394 | + | 0.951259i | \(0.400209\pi\) | |||||||
\(788\) | −19.1464 | −0.682063 | ||||||||
\(789\) | −26.6969 | −0.950436 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.8990 | −1.45420 | ||||||||
\(792\) | −4.89898 | −0.174078 | ||||||||
\(793\) | −80.0908 | −2.84411 | ||||||||
\(794\) | 36.0454 | 1.27920 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0454 | −0.639603 | ||||||||
\(797\) | 22.8990 | 0.811123 | 0.405562 | − | 0.914068i | \(-0.367076\pi\) | ||||
0.405562 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(798\) | −16.8990 | −0.598217 | ||||||||
\(799\) | 4.89898 | 0.173313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.79796 | −0.0635278 | ||||||||
\(802\) | −0.696938 | −0.0246098 | ||||||||
\(803\) | 72.9898 | 2.57575 | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.6969 | 1.36304 | ||||||||
\(807\) | −23.5505 | −0.829017 | ||||||||
\(808\) | 3.79796 | 0.133612 | ||||||||
\(809\) | 42.0908 | 1.47983 | 0.739917 | − | 0.672698i | \(-0.234865\pi\) | ||||
0.739917 | + | 0.672698i | \(0.234865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.79796 | 0.0631349 | 0.0315674 | − | 0.999502i | \(-0.489950\pi\) | ||||
0.0315674 | + | 0.999502i | \(0.489950\pi\) | |||||||
\(812\) | −22.8990 | −0.803597 | ||||||||
\(813\) | 7.59592 | 0.266400 | ||||||||
\(814\) | −2.20204 | −0.0771815 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 20.0000 | 0.699711 | ||||||||
\(818\) | 15.5959 | 0.545298 | ||||||||
\(819\) | −14.6969 | −0.513553 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.6413 | 1.24389 | 0.621945 | − | 0.783061i | \(-0.286343\pi\) | ||||
0.621945 | + | 0.783061i | \(0.286343\pi\) | |||||||
\(822\) | 12.0000 | 0.418548 | ||||||||
\(823\) | 26.4495 | 0.921971 | 0.460986 | − | 0.887408i | \(-0.347496\pi\) | ||||
0.460986 | + | 0.887408i | \(0.347496\pi\) | |||||||
\(824\) | −16.8990 | −0.588704 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.2020 | 0.494152 | ||||||||
\(827\) | −16.4949 | −0.573584 | −0.286792 | − | 0.957993i | \(-0.592589\pi\) | ||||
−0.286792 | + | 0.957993i | \(0.592589\pi\) | |||||||
\(828\) | −6.44949 | −0.224135 | ||||||||
\(829\) | 8.20204 | 0.284869 | 0.142434 | − | 0.989804i | \(-0.454507\pi\) | ||||
0.142434 | + | 0.989804i | \(0.454507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.4495 | −0.986902 | ||||||||
\(832\) | −6.00000 | −0.208013 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 16.8990 | 0.585164 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −33.7980 | −1.16893 | ||||||||
\(837\) | 6.44949 | 0.222927 | ||||||||
\(838\) | 7.59592 | 0.262397 | ||||||||
\(839\) | −39.3485 | −1.35846 | −0.679230 | − | 0.733925i | \(-0.737686\pi\) | ||||
−0.679230 | + | 0.733925i | \(0.737686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.3939 | 2.01358 | ||||||||
\(842\) | −0.696938 | −0.0240181 | ||||||||
\(843\) | −9.79796 | −0.337460 | ||||||||
\(844\) | −3.10102 | −0.106742 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.89898 | −0.168430 | ||||||||
\(847\) | 31.8434 | 1.09415 | ||||||||
\(848\) | 1.10102 | 0.0378092 | ||||||||
\(849\) | −6.69694 | −0.229838 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.89898 | −0.0993757 | ||||||||
\(852\) | −2.44949 | −0.0839181 | ||||||||
\(853\) | −10.6515 | −0.364701 | −0.182351 | − | 0.983234i | \(-0.558371\pi\) | ||||
−0.182351 | + | 0.983234i | \(0.558371\pi\) | |||||||
\(854\) | 32.6969 | 1.11887 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.10102 | −0.105991 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | −29.3939 | −1.00349 | ||||||||
\(859\) | −26.2020 | −0.894002 | −0.447001 | − | 0.894533i | \(-0.647508\pi\) | ||||
−0.447001 | + | 0.894533i | \(0.647508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.69694 | 0.0919114 | ||||||||
\(862\) | 25.1464 | 0.856491 | ||||||||
\(863\) | −23.5959 | −0.803214 | −0.401607 | − | 0.915812i | \(-0.631548\pi\) | ||||
−0.401607 | + | 0.915812i | \(0.631548\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.0000 | 0.339814 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −15.7980 | −0.536218 | ||||||||
\(869\) | 7.59592 | 0.257674 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 18.2474 | 0.617937 | ||||||||
\(873\) | 3.79796 | 0.128541 | ||||||||
\(874\) | −44.4949 | −1.50506 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.8990 | 0.503390 | ||||||||
\(877\) | −18.6515 | −0.629817 | −0.314909 | − | 0.949122i | \(-0.601974\pi\) | ||||
−0.314909 | + | 0.949122i | \(0.601974\pi\) | |||||||
\(878\) | −27.3485 | −0.922966 | ||||||||
\(879\) | −10.0000 | −0.337292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.1918 | −1.25302 | −0.626512 | − | 0.779411i | \(-0.715518\pi\) | ||||
−0.626512 | + | 0.779411i | \(0.715518\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 10.2020 | 0.343326 | 0.171663 | − | 0.985156i | \(-0.445086\pi\) | ||||
0.171663 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(884\) | 6.00000 | 0.201802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.2020 | 0.342744 | ||||||||
\(887\) | −40.2474 | −1.35138 | −0.675689 | − | 0.737187i | \(-0.736154\pi\) | ||||
−0.675689 | + | 0.737187i | \(0.736154\pi\) | |||||||
\(888\) | −0.449490 | −0.0150839 | ||||||||
\(889\) | 19.5959 | 0.657226 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.89898 | −0.164122 | ||||||||
\(892\) | −4.89898 | −0.164030 | ||||||||
\(893\) | −33.7980 | −1.13101 | ||||||||
\(894\) | −12.6969 | −0.424649 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.44949 | 0.0818317 | ||||||||
\(897\) | −38.6969 | −1.29205 | ||||||||
\(898\) | −32.6969 | −1.09111 | ||||||||
\(899\) | 60.2929 | 2.01088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.10102 | −0.0366803 | ||||||||
\(902\) | 5.39388 | 0.179596 | ||||||||
\(903\) | −7.10102 | −0.236307 | ||||||||
\(904\) | −16.6969 | −0.555332 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.7980 | −0.458406 | ||||||||
\(907\) | −50.6969 | −1.68336 | −0.841682 | − | 0.539973i | \(-0.818434\pi\) | ||||
−0.841682 | + | 0.539973i | \(0.818434\pi\) | |||||||
\(908\) | 19.5959 | 0.650313 | ||||||||
\(909\) | 3.79796 | 0.125970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6515 | −1.08179 | −0.540897 | − | 0.841089i | \(-0.681915\pi\) | ||||
−0.540897 | + | 0.841089i | \(0.681915\pi\) | |||||||
\(912\) | −6.89898 | −0.228448 | ||||||||
\(913\) | 14.2020 | 0.470019 | ||||||||
\(914\) | −1.59592 | −0.0527883 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.0000 | 0.594737 | ||||||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −24.0000 | −0.791687 | −0.395843 | − | 0.918318i | \(-0.629548\pi\) | ||||
−0.395843 | + | 0.918318i | \(0.629548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.8990 | 0.359134 | ||||||||
\(922\) | −21.5959 | −0.711224 | ||||||||
\(923\) | −14.6969 | −0.483756 | ||||||||
\(924\) | 12.0000 | 0.394771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.30306 | 0.174269 | ||||||||
\(927\) | −16.8990 | −0.555035 | ||||||||
\(928\) | −9.34847 | −0.306879 | ||||||||
\(929\) | −36.6969 | −1.20399 | −0.601994 | − | 0.798501i | \(-0.705627\pi\) | ||||
−0.601994 | + | 0.798501i | \(0.705627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.89898 | −0.226105 | ||||||||
\(932\) | 1.10102 | 0.0360651 | ||||||||
\(933\) | 23.3485 | 0.764395 | ||||||||
\(934\) | 0.404082 | 0.0132220 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | −9.79796 | −0.319915 | ||||||||
\(939\) | 2.00000 | 0.0652675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.75255 | 0.317924 | 0.158962 | − | 0.987285i | \(-0.449185\pi\) | ||||
0.158962 | + | 0.987285i | \(0.449185\pi\) | |||||||
\(942\) | 16.6969 | 0.544016 | ||||||||
\(943\) | 7.10102 | 0.231241 | ||||||||
\(944\) | 5.79796 | 0.188707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.2020 | −0.461748 | ||||||||
\(947\) | −31.1010 | −1.01065 | −0.505324 | − | 0.862930i | \(-0.668627\pi\) | ||||
−0.505324 | + | 0.862930i | \(0.668627\pi\) | |||||||
\(948\) | 1.55051 | 0.0503582 | ||||||||
\(949\) | 89.3939 | 2.90185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.44949 | −0.273993 | ||||||||
\(952\) | −2.44949 | −0.0793884 | ||||||||
\(953\) | 33.5959 | 1.08828 | 0.544139 | − | 0.838995i | \(-0.316856\pi\) | ||||
0.544139 | + | 0.838995i | \(0.316856\pi\) | |||||||
\(954\) | 1.10102 | 0.0356469 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.89898 | 0.287814 | ||||||||
\(957\) | −45.7980 | −1.48044 | ||||||||
\(958\) | 15.3485 | 0.495887 | ||||||||
\(959\) | −29.3939 | −0.949178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5959 | 0.341804 | ||||||||
\(962\) | −2.69694 | −0.0869528 | ||||||||
\(963\) | −3.10102 | −0.0999290 | ||||||||
\(964\) | −6.89898 | −0.222201 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.7980 | 0.508291 | ||||||||
\(967\) | 42.6969 | 1.37304 | 0.686520 | − | 0.727110i | \(-0.259137\pi\) | ||||
0.686520 | + | 0.727110i | \(0.259137\pi\) | |||||||
\(968\) | 13.0000 | 0.417836 | ||||||||
\(969\) | 6.89898 | 0.221627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.0000 | −1.41203 | −0.706014 | − | 0.708198i | \(-0.749508\pi\) | ||||
−0.706014 | + | 0.708198i | \(0.749508\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −41.3939 | −1.32703 | ||||||||
\(974\) | 15.3485 | 0.491797 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.3485 | 0.427274 | ||||||||
\(977\) | −0.404082 | −0.0129277 | −0.00646387 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646387 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(978\) | 5.79796 | 0.185398 | ||||||||
\(979\) | 8.80816 | 0.281510 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2474 | 0.582596 | ||||||||
\(982\) | −14.8990 | −0.475446 | ||||||||
\(983\) | −18.8536 | −0.601336 | −0.300668 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300668 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(984\) | 1.10102 | 0.0350993 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.34847 | 0.297716 | ||||||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | −41.3939 | −1.31691 | ||||||||
\(989\) | −18.6969 | −0.594528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.2474 | 1.02437 | 0.512187 | − | 0.858874i | \(-0.328835\pi\) | ||||
0.512187 | + | 0.858874i | \(0.328835\pi\) | |||||||
\(992\) | −6.44949 | −0.204772 | ||||||||
\(993\) | −33.3939 | −1.05972 | ||||||||
\(994\) | 6.00000 | 0.190308 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.89898 | 0.0918577 | ||||||||
\(997\) | −46.7423 | −1.48034 | −0.740172 | − | 0.672417i | \(-0.765256\pi\) | ||||
−0.740172 | + | 0.672417i | \(0.765256\pi\) | |||||||
\(998\) | 0.898979 | 0.0284567 | ||||||||
\(999\) | −0.449490 | −0.0142212 |
(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 | 2550.2.a.bj.1.2 | 2 | ||
3.2 | odd | 2 | 7650.2.a.ct.1.2 | 2 | |||
5.2 | odd | 4 | 510.2.d.c.409.3 | yes | 4 | ||
5.3 | odd | 4 | 510.2.d.c.409.1 | ✓ | 4 | ||
5.4 | even | 2 | 2550.2.a.bi.1.1 | 2 | |||
15.2 | even | 4 | 1530.2.d.e.919.2 | 4 | |||
15.8 | even | 4 | 1530.2.d.e.919.4 | 4 | |||
15.14 | odd | 2 | 7650.2.a.dg.1.1 | 2 | |||
20.3 | even | 4 | 4080.2.m.o.2449.3 | 4 | |||
20.7 | even | 4 | 4080.2.m.o.2449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
510.2.d.c.409.1 | ✓ | 4 | 5.3 | odd | 4 | ||
510.2.d.c.409.3 | yes | 4 | 5.2 | odd | 4 | ||
1530.2.d.e.919.2 | 4 | 15.2 | even | 4 | |||
1530.2.d.e.919.4 | 4 | 15.8 | even | 4 | |||
2550.2.a.bi.1.1 | 2 | 5.4 | even | 2 | |||
2550.2.a.bj.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4080.2.m.o.2449.1 | 4 | 20.7 | even | 4 | |||
4080.2.m.o.2449.3 | 4 | 20.3 | even | 4 | |||
7650.2.a.ct.1.2 | 2 | 3.2 | odd | 2 | |||
7650.2.a.dg.1.1 | 2 | 15.14 | odd | 2 |