Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5148,2,Mod(1,5148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5148.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: | \(41.1069869606\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 572) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5148.1 |
$q$-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 | ||||||||
\(5\) | −3.58774 | −1.60449 | −0.802243 | − | 0.596997i | \(-0.796360\pi\) | ||||
−0.802243 | + | 0.596997i | \(0.796360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.75698 | −1.79797 | −0.898985 | − | 0.437980i | \(-0.855694\pi\) | ||||
−0.898985 | + | 0.437980i | \(0.855694\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.22982 | 1.51095 | 0.755476 | − | 0.655176i | \(-0.227406\pi\) | ||||
0.755476 | + | 0.655176i | \(0.227406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.34472 | 1.22616 | 0.613082 | − | 0.790019i | \(-0.289930\pi\) | ||||
0.613082 | + | 0.790019i | \(0.289930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.83076 | 1.00728 | 0.503642 | − | 0.863913i | \(-0.331993\pi\) | ||||
0.503642 | + | 0.863913i | \(0.331993\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.87189 | 1.57438 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28415 | 0.981242 | 0.490621 | − | 0.871373i | \(-0.336770\pi\) | ||||
0.490621 | + | 0.871373i | \(0.336770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.35793 | −1.32152 | −0.660761 | − | 0.750596i | \(-0.729766\pi\) | ||||
−0.660761 | + | 0.750596i | \(0.729766\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.0668 | 2.88482 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.58774 | −1.24742 | −0.623709 | − | 0.781657i | \(-0.714375\pi\) | ||||
−0.623709 | + | 0.781657i | \(0.714375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.98680 | 1.09115 | 0.545577 | − | 0.838061i | \(-0.316310\pi\) | ||||
0.545577 | + | 0.838061i | \(0.316310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.66152 | −1.16837 | −0.584185 | − | 0.811620i | \(-0.698586\pi\) | ||||
−0.584185 | + | 0.811620i | \(0.698586\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.17548 | 0.754922 | 0.377461 | − | 0.926026i | \(-0.376797\pi\) | ||||
0.377461 | + | 0.926026i | \(0.376797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.6289 | 2.23270 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.169240 | −0.0232469 | −0.0116234 | − | 0.999932i | \(-0.503700\pi\) | ||||
−0.0116234 | + | 0.999932i | \(0.503700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.58774 | 0.483771 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.21037 | −0.157577 | −0.0787883 | − | 0.996891i | \(-0.525105\pi\) | ||||
−0.0787883 | + | 0.996891i | \(0.525105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1212 | −1.29588 | −0.647940 | − | 0.761691i | \(-0.724369\pi\) | ||||
−0.647940 | + | 0.761691i | \(0.724369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.58774 | 0.445005 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9930 | 1.58735 | 0.793676 | − | 0.608340i | \(-0.208164\pi\) | ||||
0.793676 | + | 0.608340i | \(0.208164\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.24926 | −1.09769 | −0.548843 | − | 0.835926i | \(-0.684931\pi\) | ||||
−0.548843 | + | 0.835926i | \(0.684931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.49228 | 0.642823 | 0.321411 | − | 0.946940i | \(-0.395843\pi\) | ||||
0.321411 | + | 0.946940i | \(0.395843\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.75698 | 0.542108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.74378 | −0.871243 | −0.435622 | − | 0.900130i | \(-0.643471\pi\) | ||||
−0.435622 | + | 0.900130i | \(0.643471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.47283 | −0.381193 | −0.190597 | − | 0.981668i | \(-0.561042\pi\) | ||||
−0.190597 | + | 0.981668i | \(0.561042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.3510 | −2.42430 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.04737 | 0.429021 | 0.214510 | − | 0.976722i | \(-0.431184\pi\) | ||||
0.214510 | + | 0.976722i | \(0.431184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.75698 | 0.498667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.1755 | −1.96736 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.58774 | 0.364280 | 0.182140 | − | 0.983273i | \(-0.441698\pi\) | ||||
0.182140 | + | 0.983273i | \(0.441698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7981 | −1.07445 | −0.537226 | − | 0.843438i | \(-0.680528\pi\) | ||||
−0.537226 | + | 0.843438i | \(0.680528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1623 | 1.00132 | 0.500660 | − | 0.865644i | \(-0.333091\pi\) | ||||
0.500660 | + | 0.865644i | \(0.333091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.17548 | −0.113638 | −0.0568191 | − | 0.998384i | \(-0.518096\pi\) | ||||
−0.0568191 | + | 0.998384i | \(0.518096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.29039 | 0.219380 | 0.109690 | − | 0.993966i | \(-0.465014\pi\) | ||||
0.109690 | + | 0.993966i | \(0.465014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5940 | 0.996598 | 0.498299 | − | 0.867005i | \(-0.333958\pi\) | ||||
0.498299 | + | 0.867005i | \(0.333958\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.3315 | −1.61617 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −29.6351 | −2.71665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3036 | −0.921581 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.85244 | −0.164378 | −0.0821888 | − | 0.996617i | \(-0.526191\pi\) | ||||
−0.0821888 | + | 0.996617i | \(0.526191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.14756 | −0.362374 | −0.181187 | − | 0.983449i | \(-0.557994\pi\) | ||||
−0.181187 | + | 0.983449i | \(0.557994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.4247 | −2.20460 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23.3315 | −1.99335 | −0.996673 | − | 0.0815031i | \(-0.974028\pi\) | ||||
−0.996673 | + | 0.0815031i | \(0.974028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.4053 | −1.13702 | −0.568511 | − | 0.822675i | \(-0.692480\pi\) | ||||
−0.568511 | + | 0.822675i | \(0.692480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.9582 | −1.57439 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47283 | 0.448352 | 0.224176 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224176 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.89134 | 0.153915 | 0.0769574 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769574 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.3983 | 2.12037 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1538 | 0.810362 | 0.405181 | − | 0.914237i | \(-0.367209\pi\) | ||||
0.405181 | + | 0.914237i | \(0.367209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.9798 | −1.81106 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.2298 | −1.74117 | −0.870587 | − | 0.492015i | \(-0.836261\pi\) | ||||
−0.870587 | + | 0.492015i | \(0.836261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.9798 | −1.31394 | −0.656970 | − | 0.753917i | \(-0.728162\pi\) | ||||
−0.656970 | + | 0.753917i | \(0.728162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.74378 | −0.588748 | −0.294374 | − | 0.955690i | \(-0.595111\pi\) | ||||
−0.294374 | + | 0.955690i | \(0.595111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37.4464 | −2.83068 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.4402 | 0.855079 | 0.427540 | − | 0.903997i | \(-0.359380\pi\) | ||||
0.427540 | + | 0.903997i | \(0.359380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4464 | −0.776477 | −0.388238 | − | 0.921559i | \(-0.626916\pi\) | ||||
−0.388238 | + | 0.921559i | \(0.626916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.2229 | 2.00146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.22982 | −0.455569 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.18869 | 0.375440 | 0.187720 | − | 0.982223i | \(-0.439890\pi\) | ||||
0.187720 | + | 0.982223i | \(0.439890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.188687 | −0.0135820 | −0.00679098 | − | 0.999977i | \(-0.502162\pi\) | ||||
−0.00679098 | + | 0.999977i | \(0.502162\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.31680 | 0.450053 | 0.225027 | − | 0.974353i | \(-0.427753\pi\) | ||||
0.225027 | + | 0.974353i | \(0.427753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4534 | 0.953685 | 0.476843 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476843 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.1366 | −1.76424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.0668 | −1.75074 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.34472 | −0.369702 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.06682 | 0.486500 | 0.243250 | − | 0.969964i | \(-0.421786\pi\) | ||||
0.243250 | + | 0.969964i | \(0.421786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.4876 | 1.87464 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.0015 | 2.37606 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.22982 | −0.419063 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2772 | −1.09000 | −0.545001 | − | 0.838436i | \(-0.683471\pi\) | ||||
−0.545001 | + | 0.838436i | \(0.683471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.9519 | −1.19151 | −0.595755 | − | 0.803166i | \(-0.703147\pi\) | ||||
−0.595755 | + | 0.803166i | \(0.703147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6157 | 1.09799 | 0.548997 | − | 0.835824i | \(-0.315010\pi\) | ||||
0.548997 | + | 0.835824i | \(0.315010\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.377373 | −0.0247225 | −0.0123613 | − | 0.999924i | \(-0.503935\pi\) | ||||
−0.0123613 | + | 0.999924i | \(0.503935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5683 | −1.21126 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6678 | 1.07815 | 0.539074 | − | 0.842258i | \(-0.318774\pi\) | ||||
0.539074 | + | 0.842258i | \(0.318774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.3921 | −1.44240 | −0.721201 | − | 0.692726i | \(-0.756409\pi\) | ||||
−0.721201 | + | 0.692726i | \(0.756409\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −56.0723 | −3.58233 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.34472 | −0.340077 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7111 | 1.24416 | 0.622078 | − | 0.782956i | \(-0.286289\pi\) | ||||
0.622078 | + | 0.782956i | \(0.286289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.83076 | −0.303707 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.5676 | −1.47011 | −0.735053 | − | 0.678010i | \(-0.762843\pi\) | ||||
−0.735053 | + | 0.678010i | \(0.762843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.0947 | 2.24282 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.66152 | 0.595755 | 0.297877 | − | 0.954604i | \(-0.403721\pi\) | ||||
0.297877 | + | 0.954604i | \(0.403721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.607188 | 0.0372993 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.70265 | 0.225754 | 0.112877 | − | 0.993609i | \(-0.463993\pi\) | ||||
0.112877 | + | 0.993609i | \(0.463993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.26247 | −0.441163 | −0.220582 | − | 0.975369i | \(-0.570796\pi\) | ||||
−0.220582 | + | 0.975369i | \(0.570796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.87189 | −0.474693 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2423 | 1.09607 | 0.548037 | − | 0.836454i | \(-0.315375\pi\) | ||||
0.548037 | + | 0.836454i | \(0.315375\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.46587 | 0.326067 | 0.163033 | − | 0.986621i | \(-0.447872\pi\) | ||||
0.163033 | + | 0.986621i | \(0.447872\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0000 | −0.594438 | −0.297219 | − | 0.954809i | \(-0.596059\pi\) | ||||
−0.297219 | + | 0.954809i | \(0.596059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.2361 | −1.96186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.8106 | 1.28298 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.10866 | 0.240031 | 0.120015 | − | 0.992772i | \(-0.461706\pi\) | ||||
0.120015 | + | 0.992772i | \(0.461706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.34249 | 0.252829 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.83076 | −0.279370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.4457 | 2.10070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.3121 | 2.07922 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.7827 | −0.672473 | −0.336236 | − | 0.941778i | \(-0.609154\pi\) | ||||
−0.336236 | + | 0.941778i | \(0.609154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.45339 | −0.0824140 | −0.0412070 | − | 0.999151i | \(-0.513120\pi\) | ||||
−0.0412070 | + | 0.999151i | \(0.513120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.3183 | −1.71369 | −0.856846 | − | 0.515572i | \(-0.827579\pi\) | ||||
−0.856846 | + | 0.515572i | \(0.827579\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2772 | 1.13888 | 0.569440 | − | 0.822033i | \(-0.307160\pi\) | ||||
0.569440 | + | 0.822033i | \(0.307160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.28415 | −0.295855 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.2966 | 1.85267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.87189 | −0.436654 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.6197 | −1.35733 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9651 | −0.767592 | −0.383796 | − | 0.923418i | \(-0.625383\pi\) | ||||
−0.383796 | + | 0.923418i | \(0.625383\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −46.6157 | −2.54689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.12115 | −0.224493 | −0.112247 | − | 0.993680i | \(-0.535805\pi\) | ||||
−0.112247 | + | 0.993680i | \(0.535805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.35793 | 0.398454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −41.0474 | −2.21635 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.4442 | −1.15118 | −0.575592 | − | 0.817737i | \(-0.695228\pi\) | ||||
−0.575592 | + | 0.817737i | \(0.695228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.29735 | 0.122974 | 0.0614872 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614872 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6421 | −0.566420 | −0.283210 | − | 0.959058i | \(-0.591399\pi\) | ||||
−0.283210 | + | 0.959058i | \(0.591399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.1840 | 1.76122 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1623 | 0.853012 | 0.426506 | − | 0.904485i | \(-0.359744\pi\) | ||||
0.426506 | + | 0.904485i | \(0.359744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.56606 | 0.503477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.7049 | −1.03140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.5676 | 1.17802 | 0.589009 | − | 0.808126i | \(-0.299518\pi\) | ||||
0.589009 | + | 0.808126i | \(0.299518\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.805070 | 0.0417972 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.43171 | −0.384799 | −0.192400 | − | 0.981317i | \(-0.561627\pi\) | ||||
−0.192400 | + | 0.981317i | \(0.561627\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.28415 | −0.272147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.68097 | −0.137712 | −0.0688560 | − | 0.997627i | \(-0.521935\pi\) | ||||
−0.0688560 | + | 0.997627i | \(0.521935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5768 | −0.744838 | −0.372419 | − | 0.928065i | \(-0.621472\pi\) | ||||
−0.372419 | + | 0.928065i | \(0.621472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.0668 | −0.869806 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.39058 | −0.222611 | −0.111306 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111306 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.0947 | 1.52196 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.7827 | 1.39790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4721 | −0.625958 | −0.312979 | − | 0.949760i | \(-0.601327\pi\) | ||||
−0.312979 | + | 0.949760i | \(0.601327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.3664 | −1.06699 | −0.533494 | − | 0.845804i | \(-0.679121\pi\) | ||||
−0.533494 | + | 0.845804i | \(0.679121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.35793 | 0.366524 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.58774 | 0.376110 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.2423 | 1.49539 | 0.747693 | − | 0.664045i | \(-0.231162\pi\) | ||||
0.747693 | + | 0.664045i | \(0.231162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.75770 | 0.283318 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.4596 | 0.611619 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.9714 | −1.56190 | −0.780952 | − | 0.624592i | \(-0.785265\pi\) | ||||
−0.780952 | + | 0.624592i | \(0.785265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.26871 | −0.208044 | −0.104022 | − | 0.994575i | \(-0.533171\pi\) | ||||
−0.104022 | + | 0.994575i | \(0.533171\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 49.0404 | 2.37881 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.1461 | 2.32995 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5008 | 1.08382 | 0.541912 | − | 0.840435i | \(-0.317701\pi\) | ||||
0.541912 | + | 0.840435i | \(0.317701\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7291 | 0.611719 | 0.305860 | − | 0.952077i | \(-0.401056\pi\) | ||||
0.305860 | + | 0.952077i | \(0.401056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.8191 | 1.23509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9193 | 0.902967 | 0.451484 | − | 0.892279i | \(-0.350895\pi\) | ||||
0.451484 | + | 0.892279i | \(0.350895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.25150 | 0.154483 | 0.0772416 | − | 0.997012i | \(-0.475389\pi\) | ||||
0.0772416 | + | 0.997012i | \(0.475389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5209 | −0.688358 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.8844 | −1.45752 | −0.728762 | − | 0.684767i | \(-0.759904\pi\) | ||||
−0.728762 | + | 0.684767i | \(0.759904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.98680 | −0.328995 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.0668 | −0.800105 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.87412 | 0.0876678 | 0.0438339 | − | 0.999039i | \(-0.486043\pi\) | ||||
0.0438339 | + | 0.999039i | \(0.486043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.48131 | −0.301865 | −0.150932 | − | 0.988544i | \(-0.548228\pi\) | ||||
−0.150932 | + | 0.988544i | \(0.548228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.9541 | −1.62446 | −0.812228 | − | 0.583339i | \(-0.801746\pi\) | ||||
−0.812228 | + | 0.583339i | \(0.801746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.58774 | −0.351119 | −0.175559 | − | 0.984469i | \(-0.556173\pi\) | ||||
−0.175559 | + | 0.984469i | \(0.556173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −61.8076 | −2.85401 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.66152 | 0.352277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.0731 | 1.93044 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.2702 | 1.42877 | 0.714387 | − | 0.699751i | \(-0.246706\pi\) | ||||
0.714387 | + | 0.699751i | \(0.246706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.58774 | 0.345971 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.8719 | −0.584482 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.4916 | −1.88016 | −0.940081 | − | 0.340951i | \(-0.889251\pi\) | ||||
−0.940081 | + | 0.340951i | \(0.889251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.25774 | 0.0567610 | 0.0283805 | − | 0.999597i | \(-0.490965\pi\) | ||||
0.0283805 | + | 0.999597i | \(0.490965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.9193 | 1.48261 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.9986 | 1.97361 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7049 | −0.703047 | −0.351524 | − | 0.936179i | \(-0.614336\pi\) | ||||
−0.351524 | + | 0.936179i | \(0.614336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.7283 | 1.10258 | 0.551291 | − | 0.834313i | \(-0.314135\pi\) | ||||
0.551291 | + | 0.834313i | \(0.314135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.7408 | 1.72394 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8455 | 1.10126 | 0.550628 | − | 0.834751i | \(-0.314388\pi\) | ||||
0.550628 | + | 0.834751i | \(0.314388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.1267 | −1.15578 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.4596 | −1.60660 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.17548 | −0.227617 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.62887 | 0.246605 | 0.123303 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123303 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.95664 | 0.260466 | 0.130233 | − | 0.991483i | \(-0.458428\pi\) | ||||
0.130233 | + | 0.991483i | \(0.458428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −45.8385 | −1.99676 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.336245 | 0.0146193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.98680 | −0.302632 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.21733 | 0.182331 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.6289 | −0.673183 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1468 | 0.995160 | 0.497580 | − | 0.867418i | \(-0.334222\pi\) | ||||
0.497580 | + | 0.867418i | \(0.334222\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.21733 | −0.351992 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5529 | −1.09256 | −0.546281 | − | 0.837602i | \(-0.683957\pi\) | ||||
−0.546281 | + | 0.837602i | \(0.683957\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.2423 | 1.20316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.8370 | 1.56647 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.6483 | 1.72232 | 0.861162 | − | 0.508330i | \(-0.169737\pi\) | ||||
0.861162 | + | 0.508330i | \(0.169737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.66152 | 0.324048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.0404 | −1.64536 | −0.822679 | − | 0.568507i | \(-0.807521\pi\) | ||||
−0.822679 | + | 0.568507i | \(0.807521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.0085 | −1.59903 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.9317 | 0.625971 | 0.312986 | − | 0.949758i | \(-0.398671\pi\) | ||||
0.312986 | + | 0.949758i | \(0.398671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3664 | 0.643064 | 0.321532 | − | 0.946899i | \(-0.395802\pi\) | ||||
0.321532 | + | 0.946899i | \(0.395802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.0272 | 1.58584 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.15604 | −0.339540 | −0.169770 | − | 0.985484i | \(-0.554303\pi\) | ||||
−0.169770 | + | 0.985484i | \(0.554303\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5202 | 0.685374 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.169240 | 0.00700919 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.16004 | −0.336801 | −0.168401 | − | 0.985719i | \(-0.553860\pi\) | ||||
−0.168401 | + | 0.985719i | \(0.553860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.3261 | −1.62040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4031 | 1.53596 | 0.767980 | − | 0.640474i | \(-0.221262\pi\) | ||||
0.767980 | + | 0.640474i | \(0.221262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 106.323 | 4.35882 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.22357 | −0.295147 | −0.147574 | − | 0.989051i | \(-0.547146\pi\) | ||||
−0.147574 | + | 0.989051i | \(0.547146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8106 | 1.33837 | 0.669186 | − | 0.743095i | \(-0.266643\pi\) | ||||
0.669186 | + | 0.743095i | \(0.266643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58774 | −0.145862 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7981 | 0.600637 | 0.300318 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300318 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.17548 | −0.209378 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.8976 | −1.40950 | −0.704750 | − | 0.709456i | \(-0.748941\pi\) | ||||
−0.704750 | + | 0.709456i | \(0.748941\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.3121 | −0.978767 | −0.489384 | − | 0.872069i | \(-0.662778\pi\) | ||||
−0.489384 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.3983 | −1.94529 | −0.972647 | − | 0.232289i | \(-0.925378\pi\) | ||||
−0.972647 | + | 0.232289i | \(0.925378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.2533 | −0.771366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.39281 | −0.0957125 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47.2702 | −1.88479 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6266 | 0.462849 | 0.231425 | − | 0.972853i | \(-0.425661\pi\) | ||||
0.231425 | + | 0.972853i | \(0.425661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.64608 | 0.263742 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6289 | −0.619238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.8851 | 0.785414 | 0.392707 | − | 0.919664i | \(-0.371539\pi\) | ||||
0.392707 | + | 0.919664i | \(0.371539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1406 | 0.439342 | 0.219671 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219671 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.55357 | −0.218334 | −0.109167 | − | 0.994023i | \(-0.534818\pi\) | ||||
−0.109167 | + | 0.994023i | \(0.534818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.21037 | 0.0475111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.0753 | 1.29434 | 0.647168 | − | 0.762347i | \(-0.275953\pi\) | ||||
0.647168 | + | 0.762347i | \(0.275953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8804 | 0.581424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.5404 | −1.22864 | −0.614319 | − | 0.789058i | \(-0.710569\pi\) | ||||
−0.614319 | + | 0.789058i | \(0.710569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6825 | 0.532187 | 0.266093 | − | 0.963947i | \(-0.414267\pi\) | ||||
0.266093 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 91.2174 | 3.53726 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.5264 | 0.988388 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1212 | 0.390723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.9986 | −1.92730 | −0.963652 | − | 0.267162i | \(-0.913914\pi\) | ||||
−0.963652 | + | 0.267162i | \(0.913914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.4487 | −0.978071 | −0.489036 | − | 0.872264i | \(-0.662651\pi\) | ||||
−0.489036 | + | 0.872264i | \(0.662651\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.0668 | −0.654964 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.7019 | −0.945193 | −0.472597 | − | 0.881279i | \(-0.656683\pi\) | ||||
−0.472597 | + | 0.881279i | \(0.656683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 83.7075 | 3.19830 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.169240 | 0.00644752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3470 | 0.697951 | 0.348976 | − | 0.937132i | \(-0.386530\pi\) | ||||
0.348976 | + | 0.937132i | \(0.386530\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.0947 | 1.82434 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.5264 | 1.64868 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.7563 | −0.444028 | −0.222014 | − | 0.975043i | \(-0.571263\pi\) | ||||
−0.222014 | + | 0.975043i | \(0.571263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.5544 | −1.52954 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 51.3664 | 1.93183 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.7478 | −0.741644 | −0.370822 | − | 0.928704i | \(-0.620924\pi\) | ||||
−0.370822 | + | 0.928704i | \(0.620924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.5444 | −1.33115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58774 | −0.134174 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.3594 | −1.20680 | −0.603402 | − | 0.797437i | \(-0.706188\pi\) | ||||
−0.603402 | + | 0.797437i | \(0.706188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.3418 | −1.80034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.5962 | 1.54484 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.10242 | −0.226326 | −0.113163 | − | 0.993576i | \(-0.536098\pi\) | ||||
−0.113163 | + | 0.993576i | \(0.536098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.7299 | −1.76535 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.4744 | −1.42108 | −0.710541 | − | 0.703656i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703656i | \(0.751550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.9930 | −0.478605 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.3487 | −1.26354 | −0.631769 | − | 0.775157i | \(-0.717671\pi\) | ||||
−0.631769 | + | 0.775157i | \(0.717671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.7967 | −1.34994 | −0.674970 | − | 0.737846i | \(-0.735843\pi\) | ||||
−0.674970 | + | 0.737846i | \(0.735843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6351 | −0.719375 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.59175 | 0.204318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.45891 | −0.308670 | −0.154335 | − | 0.988019i | \(-0.549324\pi\) | ||||
−0.154335 | + | 0.988019i | \(0.549324\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.78562 | −0.246954 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0257 | −1.12765 | −0.563824 | − | 0.825895i | \(-0.690670\pi\) | ||||
−0.563824 | + | 0.825895i | \(0.690670\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.7959 | 1.04385 | 0.521925 | − | 0.852991i | \(-0.325214\pi\) | ||||
0.521925 | + | 0.852991i | \(0.325214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8953 | −0.394438 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.21037 | 0.0437039 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.7849 | −0.929827 | −0.464914 | − | 0.885356i | \(-0.653915\pi\) | ||||
−0.464914 | + | 0.885356i | \(0.653915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3246 | −0.659089 | −0.329544 | − | 0.944140i | \(-0.606895\pi\) | ||||
−0.329544 | + | 0.944140i | \(0.606895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −57.9208 | −2.08058 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.3425 | 1.33793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.24926 | 0.330965 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.4292 | −1.30021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.3921 | 1.43982 | 0.719911 | − | 0.694066i | \(-0.244182\pi\) | ||||
0.719911 | + | 0.694066i | \(0.244182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.3954 | −1.79185 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.1212 | 0.359413 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.5209 | 0.443514 | 0.221757 | − | 0.975102i | \(-0.428821\pi\) | ||||
0.221757 | + | 0.975102i | \(0.428821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.2423 | 1.14065 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.49228 | −0.193818 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 82.4457 | 2.90583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.4736 | −1.66908 | −0.834542 | − | 0.550944i | \(-0.814268\pi\) | ||||
−0.834542 | + | 0.550944i | \(0.814268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.6080 | −1.49617 | −0.748084 | − | 0.663604i | \(-0.769026\pi\) | ||||
−0.748084 | + | 0.663604i | \(0.769026\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 79.7548 | 2.79369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.9487 | −1.43261 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.4487 | −1.23717 | −0.618583 | − | 0.785719i | \(-0.712293\pi\) | ||||
−0.618583 | + | 0.785719i | \(0.712293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8991 | 0.519350 | 0.259675 | − | 0.965696i | \(-0.416385\pi\) | ||||
0.259675 | + | 0.965696i | \(0.416385\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.53413 | 0.0881202 | 0.0440601 | − | 0.999029i | \(-0.485971\pi\) | ||||
0.0440601 | + | 0.999029i | \(0.485971\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9644 | 1.14490 | 0.572450 | − | 0.819939i | \(-0.305993\pi\) | ||||
0.572450 | + | 0.819939i | \(0.305993\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 97.3650 | 3.37350 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60.9193 | 2.10820 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.3425 | 1.18563 | 0.592817 | − | 0.805337i | \(-0.298016\pi\) | ||||
0.592817 | + | 0.805337i | \(0.298016\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.07779 | −0.0371651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.58774 | −0.123422 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.75698 | −0.163452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.6546 | −1.25650 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.8044 | 0.883524 | 0.441762 | − | 0.897132i | \(-0.354354\pi\) | ||||
0.441762 | + | 0.897132i | \(0.354354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.1212 | −1.37051 | −0.685256 | − | 0.728302i | \(-0.740310\pi\) | ||||
−0.685256 | + | 0.728302i | \(0.740310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6204 | −0.498841 | −0.249421 | − | 0.968395i | \(-0.580240\pi\) | ||||
−0.249421 | + | 0.968395i | \(0.580240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.2577 | −0.995945 | −0.497973 | − | 0.867193i | \(-0.665922\pi\) | ||||
−0.497973 | + | 0.867193i | \(0.665922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.7827 | 0.944639 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.74378 | 0.262690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9930 | −0.440252 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 49.0140 | 1.65698 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.4813 | −0.759140 | −0.379570 | − | 0.925163i | \(-0.623928\pi\) | ||||
−0.379570 | + | 0.925163i | \(0.623928\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.9170 | 1.95127 | 0.975637 | − | 0.219391i | \(-0.0704069\pi\) | ||||
0.975637 | + | 0.219391i | \(0.0704069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.7236 | −1.90890 | −0.954451 | − | 0.298368i | \(-0.903558\pi\) | ||||
−0.954451 | + | 0.298368i | \(0.903558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.8385 | −1.53911 | −0.769553 | − | 0.638582i | \(-0.779521\pi\) | ||||
−0.769553 | + | 0.638582i | \(0.779521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.81203 | 0.295546 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.6615 | 0.925657 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.0444 | −1.37196 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.8804 | −1.29673 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.05433 | −0.0351249 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.4791 | 1.24585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.4075 | −0.976461 | −0.488231 | − | 0.872715i | \(-0.662357\pi\) | ||||
−0.488231 | + | 0.872715i | \(0.662357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4868 | −1.54018 | −0.770089 | − | 0.637937i | \(-0.779788\pi\) | ||||
−0.770089 | + | 0.637937i | \(0.779788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.47283 | 0.114934 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.7299 | 0.651537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.2841 | −0.636125 | −0.318063 | − | 0.948070i | \(-0.603032\pi\) | ||||
−0.318063 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.24926 | 0.304443 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.7299 | −1.96391 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.7672 | −0.943822 | −0.471911 | − | 0.881646i | \(-0.656436\pi\) | ||||
−0.471911 | + | 0.881646i | \(0.656436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 83.5320 | 2.73765 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.3510 | 0.730955 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1645 | 0.397397 | 0.198699 | − | 0.980061i | \(-0.436328\pi\) | ||||
0.198699 | + | 0.980061i | \(0.436328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.75297 | 0.187542 | 0.0937708 | − | 0.995594i | \(-0.470108\pi\) | ||||
0.0937708 | + | 0.995594i | \(0.470108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.7515 | 1.09910 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.6157 | 0.864893 | 0.432446 | − | 0.901660i | \(-0.357650\pi\) | ||||
0.432446 | + | 0.901660i | \(0.357650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.49228 | −0.178287 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0389 | 0.584337 | 0.292169 | − | 0.956367i | \(-0.405623\pi\) | ||||
0.292169 | + | 0.956367i | \(0.405623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.6157 | −0.602389 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 110.988 | 3.58398 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.1391 | 0.746422 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.676959 | 0.0217921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.5048 | −1.78491 | −0.892456 | − | 0.451133i | \(-0.851020\pi\) | ||||
−0.892456 | + | 0.451133i | \(0.851020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.3782 | −1.19952 | −0.599761 | − | 0.800179i | \(-0.704738\pi\) | ||||
−0.599761 | + | 0.800179i | \(0.704738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 63.7688 | 2.04433 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1421 | 1.02832 | 0.514159 | − | 0.857695i | \(-0.328104\pi\) | ||||
0.514159 | + | 0.857695i | \(0.328104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.04737 | −0.129355 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.5349 | 1.06960 | 0.534799 | − | 0.844979i | \(-0.320387\pi\) | ||||
0.534799 | + | 0.844979i | \(0.320387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6630 | −0.722104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.0110 | −1.17688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.3697 | −1.12356 | −0.561778 | − | 0.827288i | \(-0.689882\pi\) | ||||
−0.561778 | + | 0.827288i | \(0.689882\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.2673 | −1.53018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.58078 | −0.208415 | −0.104208 | − | 0.994556i | \(-0.533231\pi\) | ||||
−0.104208 | + | 0.994556i | \(0.533231\pi\) | |||||||
\(998\) | 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 | 5148.2.a.o.1.1 | 3 | ||
3.2 | odd | 2 | 572.2.a.e.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 2288.2.a.w.1.3 | 3 | |||
24.5 | odd | 2 | 9152.2.a.cc.1.3 | 3 | |||
24.11 | even | 2 | 9152.2.a.bv.1.1 | 3 | |||
33.32 | even | 2 | 6292.2.a.p.1.1 | 3 | |||
39.38 | odd | 2 | 7436.2.a.l.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.a.e.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
2288.2.a.w.1.3 | 3 | 12.11 | even | 2 | |||
5148.2.a.o.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6292.2.a.p.1.1 | 3 | 33.32 | even | 2 | |||
7436.2.a.l.1.1 | 3 | 39.38 | odd | 2 | |||
9152.2.a.bv.1.1 | 3 | 24.11 | even | 2 | |||
9152.2.a.cc.1.3 | 3 | 24.5 | odd | 2 |