Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9360,2,Mod(1,9360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9360.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: | \(74.7399762919\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9360.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.73205 | 0.986701 | 0.493350 | − | 0.869831i | \(-0.335772\pi\) | ||||
0.493350 | + | 0.869831i | \(0.335772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.46410 | 1.75744 | 0.878720 | − | 0.477338i | \(-0.158398\pi\) | ||||
0.878720 | + | 0.477338i | \(0.158398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.196152 | 0.0352300 | 0.0176150 | − | 0.999845i | \(-0.494393\pi\) | ||||
0.0176150 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1962 | −1.55490 | −0.777449 | − | 0.628946i | \(-0.783487\pi\) | ||||
−0.777449 | + | 0.628946i | \(0.783487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.26795 | −0.170970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.1244 | −1.96902 | −0.984512 | − | 0.175319i | \(-0.943904\pi\) | ||||
−0.984512 | + | 0.175319i | \(0.943904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3923 | 1.58667 | 0.793336 | − | 0.608784i | \(-0.208342\pi\) | ||||
0.793336 | + | 0.608784i | \(0.208342\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3923 | 1.75830 | 0.879150 | − | 0.476545i | \(-0.158111\pi\) | ||||
0.879150 | + | 0.476545i | \(0.158111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26795 | 0.150478 | 0.0752389 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752389 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.53590 | 0.288992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3923 | −1.39424 | −0.697122 | − | 0.716953i | \(-0.745536\pi\) | ||||
−0.697122 | + | 0.716953i | \(0.745536\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.19615 | −0.430516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9282 | −1.28640 | −0.643202 | − | 0.765696i | \(-0.722395\pi\) | ||||
−0.643202 | + | 0.765696i | \(0.722395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1962 | −1.00466 | −0.502328 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502328 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.339746 | 0.0328445 | 0.0164222 | − | 0.999865i | \(-0.494772\pi\) | ||||
0.0164222 | + | 0.999865i | \(0.494772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.4641 | −1.45474 | −0.727370 | − | 0.686245i | \(-0.759258\pi\) | ||||
−0.727370 | + | 0.686245i | \(0.759258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.73205 | 0.441266 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.80385 | −0.515008 | −0.257504 | − | 0.966277i | \(-0.582900\pi\) | ||||
−0.257504 | + | 0.966277i | \(0.582900\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.39230 | 0.727705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9282 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.39230 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26795 | −0.106031 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.46410 | 0.785951 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.8564 | −1.62670 | −0.813350 | − | 0.581775i | \(-0.802359\pi\) | ||||
−0.813350 | + | 0.581775i | \(0.802359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1962 | 0.992509 | 0.496254 | − | 0.868177i | \(-0.334708\pi\) | ||||
0.496254 | + | 0.868177i | \(0.334708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.196152 | 0.0157553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.39230 | −0.500684 | −0.250342 | − | 0.968157i | \(-0.580543\pi\) | ||||
−0.250342 | + | 0.968157i | \(0.580543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9282 | 1.00041 | 0.500207 | − | 0.865906i | \(-0.333257\pi\) | ||||
0.500207 | + | 0.865906i | \(0.333257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.4641 | −1.17571 | −0.587857 | − | 0.808965i | \(-0.700028\pi\) | ||||
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.07180 | −0.379084 | −0.189542 | − | 0.981873i | \(-0.560700\pi\) | ||||
−0.189542 | + | 0.981873i | \(0.560700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3923 | −1.51575 | −0.757874 | − | 0.652401i | \(-0.773762\pi\) | ||||
−0.757874 | + | 0.652401i | \(0.773762\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.39230 | 0.321197 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.928203 | −0.0661317 | −0.0330659 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330659 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.9282 | −1.32850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.32051 | 0.368027 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.1962 | −0.695372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.392305 | −0.0266314 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | −0.233021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | −0.133930 | −0.0669650 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669650 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.46410 | 0.229920 | 0.114960 | − | 0.993370i | \(-0.463326\pi\) | ||||
0.114960 | + | 0.993370i | \(0.463326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3923 | −0.951070 | −0.475535 | − | 0.879697i | \(-0.657746\pi\) | ||||
−0.475535 | + | 0.879697i | \(0.657746\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.80385 | −0.246050 | −0.123025 | − | 0.992404i | \(-0.539260\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3923 | 1.18475 | 0.592376 | − | 0.805661i | \(-0.298190\pi\) | ||||
0.592376 | + | 0.805661i | \(0.298190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.19615 | −0.266995 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.5359 | −0.917498 | −0.458749 | − | 0.888566i | \(-0.651702\pi\) | ||||
−0.458749 | + | 0.888566i | \(0.651702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.85641 | 0.490069 | 0.245035 | − | 0.969514i | \(-0.421201\pi\) | ||||
0.245035 | + | 0.969514i | \(0.421201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.73205 | 0.291791 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3923 | 0.638394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.85641 | −0.479014 | −0.239507 | − | 0.970895i | \(-0.576986\pi\) | ||||
−0.239507 | + | 0.970895i | \(0.576986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9808 | 1.27449 | 0.637245 | − | 0.770661i | \(-0.280074\pi\) | ||||
0.637245 | + | 0.770661i | \(0.280074\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.26795 | −0.0764602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.60770 | −0.336934 | −0.168467 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168467 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.60770 | −0.0959071 | −0.0479535 | − | 0.998850i | \(-0.515270\pi\) | ||||
−0.0479535 | + | 0.998850i | \(0.515270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.41154 | −0.0839075 | −0.0419538 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419538 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9282 | 1.10580 | 0.552899 | − | 0.833248i | \(-0.313522\pi\) | ||||
0.552899 | + | 0.833248i | \(0.313522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.1244 | −0.880574 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.73205 | 0.273662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3923 | 1.17539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.3923 | 0.709581 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.7846 | −1.30039 | −0.650193 | − | 0.759769i | \(-0.725312\pi\) | ||||
−0.650193 | + | 0.759769i | \(0.725312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.39230 | 0.249065 | 0.124532 | − | 0.992216i | \(-0.460257\pi\) | ||||
0.124532 | + | 0.992216i | \(0.460257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39230 | 0.361314 | 0.180657 | − | 0.983546i | \(-0.442178\pi\) | ||||
0.180657 | + | 0.983546i | \(0.442178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.0000 | −1.34797 | −0.673987 | − | 0.738743i | \(-0.735420\pi\) | ||||
−0.673987 | + | 0.738743i | \(0.735420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5359 | 0.808799 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.5885 | 1.57136 | 0.785682 | − | 0.618631i | \(-0.212312\pi\) | ||||
0.785682 | + | 0.618631i | \(0.212312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.3923 | 0.786336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.60770 | −0.305471 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.248711 | −0.0134685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6603 | 0.625955 | 0.312978 | − | 0.949761i | \(-0.398674\pi\) | ||||
0.312978 | + | 0.949761i | \(0.398674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.39230 | 0.342172 | 0.171086 | − | 0.985256i | \(-0.445272\pi\) | ||||
0.171086 | + | 0.985256i | \(0.445272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.7128 | −1.47500 | −0.737502 | − | 0.675345i | \(-0.763995\pi\) | ||||
−0.737502 | + | 0.675345i | \(0.763995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26795 | 0.0672958 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.19615 | 0.432576 | 0.216288 | − | 0.976330i | \(-0.430605\pi\) | ||||
0.216288 | + | 0.976330i | \(0.430605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.1962 | −1.15863 | −0.579315 | − | 0.815104i | \(-0.696680\pi\) | ||||
−0.579315 | + | 0.815104i | \(0.696680\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.7846 | −1.07908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.46410 | 0.487426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.9808 | 1.69411 | 0.847054 | − | 0.531507i | \(-0.178374\pi\) | ||||
0.847054 | + | 0.531507i | \(0.178374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.928203 | −0.0474290 | −0.0237145 | − | 0.999719i | \(-0.507549\pi\) | ||||
−0.0237145 | + | 0.999719i | \(0.507549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.53590 | 0.129241 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3923 | −0.828994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.3923 | −0.623525 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7846 | −0.641641 | −0.320821 | − | 0.947140i | \(-0.603959\pi\) | ||||
−0.320821 | + | 0.947140i | \(0.603959\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.0718 | 1.15215 | 0.576075 | − | 0.817397i | \(-0.304584\pi\) | ||||
0.576075 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.196152 | 0.00977105 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.07180 | 0.251400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.3923 | −1.89838 | −0.949189 | − | 0.314708i | \(-0.898094\pi\) | ||||
−0.949189 | + | 0.314708i | \(0.898094\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.2487 | 1.48844 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.46410 | −0.462352 | −0.231176 | − | 0.972912i | \(-0.574257\pi\) | ||||
−0.231176 | + | 0.972912i | \(0.574257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7846 | 0.525610 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.7846 | −1.19941 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5167 | 0.940084 | 0.470042 | − | 0.882644i | \(-0.344239\pi\) | ||||
0.470042 | + | 0.882644i | \(0.344239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.78461 | −0.326048 | −0.163024 | − | 0.986622i | \(-0.552125\pi\) | ||||
−0.163024 | + | 0.986622i | \(0.552125\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.8564 | −0.949861 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0000 | −1.52728 | −0.763638 | − | 0.645644i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645644i | \(0.776589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9808 | 1.66199 | 0.830993 | − | 0.556283i | \(-0.187773\pi\) | ||||
0.830993 | + | 0.556283i | \(0.187773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.928203 | −0.0440011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.4641 | −1.29611 | −0.648056 | − | 0.761593i | \(-0.724418\pi\) | ||||
−0.648056 | + | 0.761593i | \(0.724418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.39230 | −0.206826 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.7846 | −1.44004 | −0.720022 | − | 0.693952i | \(-0.755868\pi\) | ||||
−0.720022 | + | 0.693952i | \(0.755868\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.46410 | −0.161339 | −0.0806696 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806696 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.3923 | −0.854763 | −0.427381 | − | 0.904071i | \(-0.640564\pi\) | ||||
−0.427381 | + | 0.904071i | \(0.640564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.1962 | 1.76751 | 0.883754 | − | 0.467953i | \(-0.155008\pi\) | ||||
0.883754 | + | 0.467953i | \(0.155008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.7846 | −1.32915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9282 | 0.594439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.19615 | −0.192533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.3397 | 0.837964 | 0.418982 | − | 0.907994i | \(-0.362387\pi\) | ||||
0.418982 | + | 0.907994i | \(0.362387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.60770 | 0.254109 | 0.127054 | − | 0.991896i | \(-0.459448\pi\) | ||||
0.127054 | + | 0.991896i | \(0.459448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.46410 | −0.427109 | −0.213554 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213554 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.7846 | −1.47654 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.53590 | −0.113751 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9808 | −0.581099 | −0.290549 | − | 0.956860i | \(-0.593838\pi\) | ||||
−0.290549 | + | 0.956860i | \(0.593838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.5167 | −1.13773 | −0.568866 | − | 0.822430i | \(-0.692618\pi\) | ||||
−0.568866 | + | 0.822430i | \(0.692618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9282 | −0.575297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.5359 | −1.44213 | −0.721064 | − | 0.692868i | \(-0.756347\pi\) | ||||
−0.721064 | + | 0.692868i | \(0.756347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.1962 | −0.449296 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.60770 | −0.334586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.60770 | 0.333299 | 0.166650 | − | 0.986016i | \(-0.446705\pi\) | ||||
0.166650 | + | 0.986016i | \(0.446705\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8038 | 0.603600 | 0.301800 | − | 0.953371i | \(-0.402412\pi\) | ||||
0.301800 | + | 0.953371i | \(0.402412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.679492 | −0.0295991 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.46410 | 0.150047 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.339746 | 0.0146885 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.80385 | 0.163843 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.60770 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.80385 | 0.0771270 | 0.0385635 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385635 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.7128 | −1.69182 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.7846 | 1.05395 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.8564 | 1.09557 | 0.547786 | − | 0.836619i | \(-0.315471\pi\) | ||||
0.547786 | + | 0.836619i | \(0.315471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1962 | −0.431251 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0526 | 0.676535 | 0.338267 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338267 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.4641 | −0.650580 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.46410 | 0.396756 | 0.198378 | − | 0.980126i | \(-0.436433\pi\) | ||||
0.198378 | + | 0.980126i | \(0.436433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6077 | −0.653162 | −0.326581 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326581 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.73205 | 0.197340 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1769 | −0.545732 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.4641 | −0.638272 | −0.319136 | − | 0.947709i | \(-0.603393\pi\) | ||||
−0.319136 | + | 0.947709i | \(0.603393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.823085 | −0.0339146 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7846 | 0.607131 | 0.303566 | − | 0.952811i | \(-0.401823\pi\) | ||||
0.303566 | + | 0.952811i | \(0.401823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.92820 | 0.284029 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3923 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.5692 | −1.61406 | −0.807031 | − | 0.590509i | \(-0.798927\pi\) | ||||
−0.807031 | + | 0.590509i | \(0.798927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.39230 | −0.381851 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.9808 | 1.09512 | 0.547558 | − | 0.836768i | \(-0.315558\pi\) | ||||
0.547558 | + | 0.836768i | \(0.315558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0000 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.7128 | 0.874125 | 0.437062 | − | 0.899431i | \(-0.356019\pi\) | ||||
0.437062 | + | 0.899431i | \(0.356019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.9808 | 1.80793 | 0.903965 | − | 0.427607i | \(-0.140643\pi\) | ||||
0.903965 | + | 0.427607i | \(0.140643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.85641 | 0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1962 | −0.644759 | −0.322379 | − | 0.946611i | \(-0.604483\pi\) | ||||
−0.322379 | + | 0.946611i | \(0.604483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.80385 | −0.230319 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | −0.118864 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.928203 | 0.0366618 | 0.0183309 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183309 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.7846 | −1.37177 | −0.685886 | − | 0.727709i | \(-0.740585\pi\) | ||||
−0.685886 | + | 0.727709i | \(0.740585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0526 | −0.631091 | −0.315546 | − | 0.948910i | \(-0.602188\pi\) | ||||
−0.315546 | + | 0.948910i | \(0.602188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.1769 | 0.752760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.8564 | 0.777041 | 0.388521 | − | 0.921440i | \(-0.372986\pi\) | ||||
0.388521 | + | 0.921440i | \(0.372986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5359 | −0.566238 | −0.283119 | − | 0.959085i | \(-0.591369\pi\) | ||||
−0.283119 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7846 | −1.19738 | −0.598691 | − | 0.800980i | \(-0.704312\pi\) | ||||
−0.598691 | + | 0.800980i | \(0.704312\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.39230 | 0.325440 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.7846 | 1.73407 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7128 | −0.606586 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.39230 | 0.246405 | 0.123203 | − | 0.992382i | \(-0.460683\pi\) | ||||
0.123203 | + | 0.992382i | \(0.460683\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.3923 | 0.399409 | 0.199704 | − | 0.979856i | \(-0.436002\pi\) | ||||
0.199704 | + | 0.979856i | \(0.436002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.4641 | 1.51005 | 0.755026 | − | 0.655695i | \(-0.227624\pi\) | ||||
0.755026 | + | 0.655695i | \(0.227624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9282 | 0.493961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.3923 | 0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.7654 | −1.74100 | −0.870498 | − | 0.492171i | \(-0.836203\pi\) | ||||
−0.870498 | + | 0.492171i | \(0.836203\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.39230 | 0.318338 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | −0.454532 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7846 | 0.633044 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.8564 | 0.972430 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.60770 | 0.360825 | 0.180412 | − | 0.983591i | \(-0.442257\pi\) | ||||
0.180412 | + | 0.983591i | \(0.442257\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.928203 | 0.0347615 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.26795 | −0.0474186 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.85641 | 0.0692323 | 0.0346161 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346161 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.3923 | 0.759449 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.46410 | 0.351488 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4115 | −0.497407 | −0.248703 | − | 0.968580i | \(-0.580004\pi\) | ||||
−0.248703 | + | 0.968580i | \(0.580004\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3205 | 1.30638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.0000 | 1.40356 | 0.701781 | − | 0.712393i | \(-0.252388\pi\) | ||||
0.701781 | + | 0.712393i | \(0.252388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.2487 | −0.672200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.80385 | 0.287069 | 0.143535 | − | 0.989645i | \(-0.454153\pi\) | ||||
0.143535 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.8564 | −1.60894 | −0.804468 | − | 0.593996i | \(-0.797549\pi\) | ||||
−0.804468 | + | 0.593996i | \(0.797549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.8564 | −0.727482 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.679492 | −0.0248281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.6077 | −0.569533 | −0.284766 | − | 0.958597i | \(-0.591916\pi\) | ||||
−0.284766 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1962 | 0.443863 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3923 | 0.668480 | 0.334240 | − | 0.942488i | \(-0.391520\pi\) | ||||
0.334240 | + | 0.942488i | \(0.391520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.85641 | −0.284795 | −0.142397 | − | 0.989810i | \(-0.545481\pi\) | ||||
−0.142397 | + | 0.989810i | \(0.545481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.1244 | −0.546109 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.78461 | −0.244659 | −0.122330 | − | 0.992490i | \(-0.539037\pi\) | ||||
−0.122330 | + | 0.992490i | \(0.539037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.92820 | 0.249190 | 0.124595 | − | 0.992208i | \(-0.460237\pi\) | ||||
0.124595 | + | 0.992208i | \(0.460237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.196152 | 0.00704600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.5359 | −0.520803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60770 | −0.0575279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0000 | −0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.5692 | 1.83824 | 0.919122 | − | 0.393973i | \(-0.128900\pi\) | ||||
0.919122 | + | 0.393973i | \(0.128900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.9282 | 1.09968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3923 | 0.440064 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.6410 | −1.01452 | −0.507258 | − | 0.861794i | \(-0.669341\pi\) | ||||
−0.507258 | + | 0.861794i | \(0.669341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7846 | −0.735307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.07180 | 0.178980 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.46410 | −0.333566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.46410 | 0.332740 | 0.166370 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166370 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.1962 | −0.990101 | −0.495050 | − | 0.868864i | \(-0.664850\pi\) | ||||
−0.495050 | + | 0.868864i | \(0.664850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.39230 | −0.223913 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.7846 | 1.49684 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6410 | 1.41838 | 0.709191 | − | 0.705017i | \(-0.249061\pi\) | ||||
0.709191 | + | 0.705017i | \(0.249061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.5885 | 1.62397 | 0.811986 | − | 0.583677i | \(-0.198387\pi\) | ||||
0.811986 | + | 0.583677i | \(0.198387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000 | 0.625921 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3923 | −0.708254 | −0.354127 | − | 0.935197i | \(-0.615222\pi\) | ||||
−0.354127 | + | 0.935197i | \(0.615222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3923 | 0.360072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.9282 | 0.447399 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.6603 | 0.609700 | 0.304850 | − | 0.952400i | \(-0.401394\pi\) | ||||
0.304850 | + | 0.952400i | \(0.401394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60.5692 | 2.08859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.7846 | 0.645447 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.9282 | −0.648850 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.00000 | 0.273915 | 0.136957 | − | 0.990577i | \(-0.456268\pi\) | ||||
0.136957 | + | 0.990577i | \(0.456268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.5692 | −1.62493 | −0.812467 | − | 0.583007i | \(-0.801876\pi\) | ||||
−0.812467 | + | 0.583007i | \(0.801876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.1769 | −1.54142 | −0.770708 | − | 0.637188i | \(-0.780097\pi\) | ||||
−0.770708 | + | 0.637188i | \(0.780097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.78461 | 0.0947892 | 0.0473946 | − | 0.998876i | \(-0.484908\pi\) | ||||
0.0473946 | + | 0.998876i | \(0.484908\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.4641 | −0.525795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.7128 | 0.533021 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3923 | 0.487665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000 | 0.0675352 | 0.0337676 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337676 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6795 | 0.427183 | 0.213591 | − | 0.976923i | \(-0.431484\pi\) | ||||
0.213591 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.1962 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9090 | 0.601324 | 0.300662 | − | 0.953731i | \(-0.402792\pi\) | ||||
0.300662 | + | 0.953731i | \(0.402792\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6077 | 0.389310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.1769 | −0.842513 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.07180 | −0.169531 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.85641 | 0.0619146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.3923 | −0.677863 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7654 | −1.32039 | −0.660194 | − | 0.751095i | \(-0.729526\pi\) | ||||
−0.660194 | + | 0.751095i | \(0.729526\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.60770 | 0.251778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.1769 | 1.75414 | 0.877072 | − | 0.480358i | \(-0.159493\pi\) | ||||
0.877072 | + | 0.480358i | \(0.159493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.26795 | 0.0417351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.4641 | −1.68848 | −0.844241 | − | 0.535963i | \(-0.819948\pi\) | ||||
−0.844241 | + | 0.535963i | \(0.819948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5885 | 0.412570 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.39230 | 0.143644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.78461 | −0.221644 | −0.110822 | − | 0.993840i | \(-0.535348\pi\) | ||||
−0.110822 | + | 0.993840i | \(0.535348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1769 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.3923 | 0.533807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.6410 | −0.930708 | −0.465354 | − | 0.885125i | \(-0.654073\pi\) | ||||
−0.465354 | + | 0.885125i | \(0.654073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.9282 | 0.418786 | 0.209393 | − | 0.977832i | \(-0.432851\pi\) | ||||
0.209393 | + | 0.977832i | \(0.432851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.9282 | −0.612502 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.8564 | −0.834947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | −0.321911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6077 | 0.952119 | 0.476060 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476060 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.07180 | 0.162762 | 0.0813809 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813809 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7846 | −0.538090 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.7128 | −1.27053 | −0.635263 | − | 0.772296i | \(-0.719108\pi\) | ||||
−0.635263 | + | 0.772296i | \(0.719108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.17691 | 0.0376144 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.6077 | −0.434018 | −0.217009 | − | 0.976170i | \(-0.569630\pi\) | ||||
−0.217009 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.928203 | −0.0295750 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.2487 | −1.53422 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0000 | −0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.3923 | 1.72262 | 0.861311 | − | 0.508078i | \(-0.169644\pi\) | ||||
0.861311 | + | 0.508078i | \(0.169644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9360.2.a.cm.1.2 | 2 | ||
3.2 | odd | 2 | 1040.2.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 585.2.a.k.1.1 | 2 | |||
12.11 | even | 2 | 65.2.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 5200.2.a.ca.1.1 | 2 | |||
20.3 | even | 4 | 2925.2.c.v.2224.3 | 4 | |||
20.7 | even | 4 | 2925.2.c.v.2224.2 | 4 | |||
20.19 | odd | 2 | 2925.2.a.z.1.2 | 2 | |||
24.5 | odd | 2 | 4160.2.a.bj.1.1 | 2 | |||
24.11 | even | 2 | 4160.2.a.y.1.2 | 2 | |||
52.51 | odd | 2 | 7605.2.a.be.1.2 | 2 | |||
60.23 | odd | 4 | 325.2.b.e.274.2 | 4 | |||
60.47 | odd | 4 | 325.2.b.e.274.3 | 4 | |||
60.59 | even | 2 | 325.2.a.g.1.1 | 2 | |||
84.83 | odd | 2 | 3185.2.a.k.1.2 | 2 | |||
132.131 | odd | 2 | 7865.2.a.h.1.1 | 2 | |||
156.11 | odd | 12 | 845.2.m.a.316.2 | 4 | |||
156.23 | even | 6 | 845.2.e.f.191.2 | 4 | |||
156.35 | even | 6 | 845.2.e.e.146.1 | 4 | |||
156.47 | odd | 4 | 845.2.c.e.506.3 | 4 | |||
156.59 | odd | 12 | 845.2.m.c.361.2 | 4 | |||
156.71 | odd | 12 | 845.2.m.a.361.2 | 4 | |||
156.83 | odd | 4 | 845.2.c.e.506.1 | 4 | |||
156.95 | even | 6 | 845.2.e.f.146.2 | 4 | |||
156.107 | even | 6 | 845.2.e.e.191.1 | 4 | |||
156.119 | odd | 12 | 845.2.m.c.316.2 | 4 | |||
156.155 | even | 2 | 845.2.a.d.1.1 | 2 | |||
780.779 | even | 2 | 4225.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.c.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
325.2.a.g.1.1 | 2 | 60.59 | even | 2 | |||
325.2.b.e.274.2 | 4 | 60.23 | odd | 4 | |||
325.2.b.e.274.3 | 4 | 60.47 | odd | 4 | |||
585.2.a.k.1.1 | 2 | 4.3 | odd | 2 | |||
845.2.a.d.1.1 | 2 | 156.155 | even | 2 | |||
845.2.c.e.506.1 | 4 | 156.83 | odd | 4 | |||
845.2.c.e.506.3 | 4 | 156.47 | odd | 4 | |||
845.2.e.e.146.1 | 4 | 156.35 | even | 6 | |||
845.2.e.e.191.1 | 4 | 156.107 | even | 6 | |||
845.2.e.f.146.2 | 4 | 156.95 | even | 6 | |||
845.2.e.f.191.2 | 4 | 156.23 | even | 6 | |||
845.2.m.a.316.2 | 4 | 156.11 | odd | 12 | |||
845.2.m.a.361.2 | 4 | 156.71 | odd | 12 | |||
845.2.m.c.316.2 | 4 | 156.119 | odd | 12 | |||
845.2.m.c.361.2 | 4 | 156.59 | odd | 12 | |||
1040.2.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
2925.2.a.z.1.2 | 2 | 20.19 | odd | 2 | |||
2925.2.c.v.2224.2 | 4 | 20.7 | even | 4 | |||
2925.2.c.v.2224.3 | 4 | 20.3 | even | 4 | |||
3185.2.a.k.1.2 | 2 | 84.83 | odd | 2 | |||
4160.2.a.y.1.2 | 2 | 24.11 | even | 2 | |||
4160.2.a.bj.1.1 | 2 | 24.5 | odd | 2 | |||
4225.2.a.w.1.2 | 2 | 780.779 | even | 2 | |||
5200.2.a.ca.1.1 | 2 | 15.14 | odd | 2 | |||
7605.2.a.be.1.2 | 2 | 52.51 | odd | 2 | |||
7865.2.a.h.1.1 | 2 | 132.131 | odd | 2 | |||
9360.2.a.cm.1.2 | 2 | 1.1 | even | 1 | trivial |