Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.40622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −3.40622 | −1.96658 | −0.983291 | − | 0.182040i | \(-0.941730\pi\) | ||||
−0.983291 | + | 0.182040i | \(0.941730\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.33790 | 0.883645 | 0.441822 | − | 0.897103i | \(-0.354332\pi\) | ||||
0.441822 | + | 0.897103i | \(0.354332\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.60234 | 2.86745 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.16565 | −1.85901 | −0.929507 | − | 0.368806i | \(-0.879767\pi\) | ||||
−0.929507 | + | 0.368806i | \(0.879767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.40622 | −0.879482 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.07520 | 0.745844 | 0.372922 | − | 0.927863i | \(-0.378356\pi\) | ||||
0.372922 | + | 0.927863i | \(0.378356\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0902681 | −0.0207089 | −0.0103545 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103545 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.96342 | −1.73776 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.81954 | 1.00494 | 0.502472 | − | 0.864594i | \(-0.332424\pi\) | ||||
0.502472 | + | 0.864594i | \(0.332424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.0828 | −3.67249 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.63201 | 1.04584 | 0.522919 | − | 0.852382i | \(-0.324843\pi\) | ||||
0.522919 | + | 0.852382i | \(0.324843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34078 | 1.49805 | 0.749024 | − | 0.662543i | \(-0.230523\pi\) | ||||
0.749024 | + | 0.662543i | \(0.230523\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 21.0016 | 3.65590 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.33790 | 0.395178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.794425 | 0.130603 | 0.0653014 | − | 0.997866i | \(-0.479199\pi\) | ||||
0.0653014 | + | 0.997866i | \(0.479199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.95907 | −0.618302 | −0.309151 | − | 0.951013i | \(-0.600045\pi\) | ||||
−0.309151 | + | 0.951013i | \(0.600045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.75108 | −1.33453 | −0.667264 | − | 0.744822i | \(-0.732535\pi\) | ||||
−0.667264 | + | 0.744822i | \(0.732535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.60234 | 1.28236 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.67871 | −0.536595 | −0.268298 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268298 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.53420 | −0.219172 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.4748 | −1.46676 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.08456 | 1.11050 | 0.555250 | − | 0.831683i | \(-0.312623\pi\) | ||||
0.555250 | + | 0.831683i | \(0.312623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.16565 | −0.831376 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.307473 | 0.0407258 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.379577 | 0.0494167 | 0.0247084 | − | 0.999695i | \(-0.492134\pi\) | ||||
0.0247084 | + | 0.999695i | \(0.492134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.96367 | −0.635533 | −0.317766 | − | 0.948169i | \(-0.602933\pi\) | ||||
−0.317766 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.1114 | 2.53380 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.376774 | 0.0460302 | 0.0230151 | − | 0.999735i | \(-0.492673\pi\) | ||||
0.0230151 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.4164 | −1.97630 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.04130 | −1.07300 | −0.536502 | − | 0.843899i | \(-0.680255\pi\) | ||||
−0.536502 | + | 0.843899i | \(0.680255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.48133 | 0.641541 | 0.320770 | − | 0.947157i | \(-0.396058\pi\) | ||||
0.320770 | + | 0.947157i | \(0.396058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.40622 | −0.393316 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.4147 | −1.64271 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.79283 | −0.539235 | −0.269617 | − | 0.962967i | \(-0.586897\pi\) | ||||
−0.269617 | + | 0.962967i | \(0.586897\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 39.1932 | 4.35480 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.6189 | 1.27534 | 0.637670 | − | 0.770310i | \(-0.279898\pi\) | ||||
0.637670 | + | 0.770310i | \(0.279898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.07520 | 0.333552 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.1839 | −2.05673 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7118 | −1.24145 | −0.620724 | − | 0.784029i | \(-0.713161\pi\) | ||||
−0.620724 | + | 0.784029i | \(0.713161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.4105 | −2.94603 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0902681 | −0.00926131 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.43658 | 0.247397 | 0.123698 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123698 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −53.0390 | −5.33062 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.52834 | −0.550090 | −0.275045 | − | 0.961431i | \(-0.588693\pi\) | ||||
−0.275045 | + | 0.961431i | \(0.588693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.46999 | 0.834573 | 0.417287 | − | 0.908775i | \(-0.362981\pi\) | ||||
0.417287 | + | 0.908775i | \(0.362981\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.96342 | −0.777150 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3891 | 1.10103 | 0.550514 | − | 0.834826i | \(-0.314432\pi\) | ||||
0.550514 | + | 0.834826i | \(0.314432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.04624 | −0.866473 | −0.433236 | − | 0.901280i | \(-0.642628\pi\) | ||||
−0.433236 | + | 0.901280i | \(0.642628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.70599 | −0.256841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.99157 | −0.281423 | −0.140712 | − | 0.990051i | \(-0.544939\pi\) | ||||
−0.140712 | + | 0.990051i | \(0.544939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.81954 | 0.449425 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.18951 | 0.659061 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.0152 | 2.45593 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4855 | 1.21594 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6776 | 0.947482 | 0.473741 | − | 0.880664i | \(-0.342903\pi\) | ||||
0.473741 | + | 0.880664i | \(0.342903\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 29.8081 | 2.62446 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.6072 | −1.80046 | −0.900231 | − | 0.435412i | \(-0.856603\pi\) | ||||
−0.900231 | + | 0.435412i | \(0.856603\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.211038 | −0.0182993 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.0828 | −1.64239 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0850150 | −0.00726332 | −0.00363166 | − | 0.999993i | \(-0.501156\pi\) | ||||
−0.00363166 | + | 0.999993i | \(0.501156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0101 | 0.933864 | 0.466932 | − | 0.884293i | \(-0.345359\pi\) | ||||
0.466932 | + | 0.884293i | \(0.345359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5305 | 1.05526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.63201 | 0.467713 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.22584 | 0.431020 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.41512 | 0.361701 | 0.180850 | − | 0.983511i | \(-0.442115\pi\) | ||||
0.180850 | + | 0.983511i | \(0.442115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7555 | 1.28216 | 0.641081 | − | 0.767473i | \(-0.278486\pi\) | ||||
0.641081 | + | 0.767473i | \(0.278486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.4539 | 2.13867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.34078 | 0.669947 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.40120 | 0.271445 | 0.135722 | − | 0.990747i | \(-0.456664\pi\) | ||||
0.135722 | + | 0.990747i | \(0.456664\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.5378 | −2.18389 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2676 | 0.888013 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4332 | 1.13050 | 0.565249 | − | 0.824920i | \(-0.308780\pi\) | ||||
0.565249 | + | 0.824920i | \(0.308780\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.0016 | 1.63497 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9815 | −1.46883 | −0.734417 | − | 0.678698i | \(-0.762544\pi\) | ||||
−0.734417 | + | 0.678698i | \(0.762544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.776517 | −0.0593817 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0970 | 0.843691 | 0.421845 | − | 0.906668i | \(-0.361383\pi\) | ||||
0.421845 | + | 0.906668i | \(0.361383\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.33790 | 0.176729 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.29292 | −0.0971821 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.27165 | 0.394021 | 0.197011 | − | 0.980401i | \(-0.436877\pi\) | ||||
0.197011 | + | 0.980401i | \(0.436877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1744 | 1.20223 | 0.601117 | − | 0.799161i | \(-0.294723\pi\) | ||||
0.601117 | + | 0.799161i | \(0.294723\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9074 | 1.24983 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.794425 | 0.0584073 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.9606 | −1.38653 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −44.6138 | −3.24517 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.75365 | −0.488677 | −0.244338 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244338 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.481519 | 0.0346605 | 0.0173302 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173302 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8881 | 1.55946 | 0.779732 | − | 0.626113i | \(-0.215355\pi\) | ||||
0.779732 | + | 0.626113i | \(0.215355\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5567 | 1.66989 | 0.834947 | − | 0.550331i | \(-0.185498\pi\) | ||||
0.834947 | + | 0.550331i | \(0.185498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28337 | −0.0905223 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.1671 | 0.924149 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.95907 | −0.276513 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.4593 | 2.88162 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.556561 | 0.0384981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0661 | −0.761824 | −0.380912 | − | 0.924611i | \(-0.624390\pi\) | ||||
−0.380912 | + | 0.924611i | \(0.624390\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.7967 | 2.11015 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.75108 | −0.596819 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.4999 | 1.32374 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.6706 | −1.26164 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.3465 | 1.63036 | 0.815182 | − | 0.579205i | \(-0.196637\pi\) | ||||
0.815182 | + | 0.579205i | \(0.196637\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.60234 | 0.573489 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.100791 | 0.00668971 | 0.00334485 | − | 0.999994i | \(-0.498935\pi\) | ||||
0.00334485 | + | 0.999994i | \(0.498935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.60506 | −0.370393 | −0.185196 | − | 0.982702i | \(-0.559292\pi\) | ||||
−0.185196 | + | 0.982702i | \(0.559292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 49.0996 | 3.23052 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2785 | 0.869902 | 0.434951 | − | 0.900454i | \(-0.356766\pi\) | ||||
0.434951 | + | 0.900454i | \(0.356766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.67871 | −0.239973 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.3254 | 1.06045 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9817 | −0.839715 | −0.419858 | − | 0.907590i | \(-0.637920\pi\) | ||||
−0.419858 | + | 0.907590i | \(0.637920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.49222 | 0.0961223 | 0.0480612 | − | 0.998844i | \(-0.484696\pi\) | ||||
0.0480612 | + | 0.998844i | \(0.484696\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −76.2524 | −4.89159 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.53420 | −0.0980167 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.5765 | −2.50806 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.2640 | −0.710975 | −0.355487 | − | 0.934681i | \(-0.615685\pi\) | ||||
−0.355487 | + | 0.934681i | \(0.615685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.7156 | −1.86820 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.4748 | −0.655957 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0148 | 0.936600 | 0.468300 | − | 0.883569i | \(-0.344867\pi\) | ||||
0.468300 | + | 0.883569i | \(0.344867\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85729 | 0.115406 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 48.4484 | 2.99888 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4305 | 0.704837 | 0.352418 | − | 0.935843i | \(-0.385359\pi\) | ||||
0.352418 | + | 0.935843i | \(0.385359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.08456 | 0.496631 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.8930 | 2.44141 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.3906 | 1.54809 | 0.774047 | − | 0.633129i | \(-0.218230\pi\) | ||||
0.774047 | + | 0.633129i | \(0.218230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6327 | 0.645892 | 0.322946 | − | 0.946417i | \(-0.395327\pi\) | ||||
0.322946 | + | 0.946417i | \(0.395327\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.16565 | −0.371803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.9901 | 1.56159 | 0.780797 | − | 0.624785i | \(-0.214813\pi\) | ||||
0.780797 | + | 0.624785i | \(0.214813\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 71.7502 | 4.29557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.65920 | −0.456909 | −0.228455 | − | 0.973555i | \(-0.573367\pi\) | ||||
−0.228455 | + | 0.973555i | \(0.573367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.5025 | 1.15930 | 0.579651 | − | 0.814865i | \(-0.303189\pi\) | ||||
0.579651 | + | 0.814865i | \(0.303189\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.307473 | 0.0182131 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.25592 | −0.546360 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.54317 | −0.443716 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.29952 | −0.486526 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7879 | −0.747078 | −0.373539 | − | 0.927614i | \(-0.621856\pi\) | ||||
−0.373539 | + | 0.927614i | \(0.621856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.379577 | 0.0220998 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 117.658 | 6.82720 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.4592 | −1.17925 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.8307 | 1.08180 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.96367 | −0.284219 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.5882 | 1.85990 | 0.929952 | − | 0.367680i | \(-0.119848\pi\) | ||||
0.929952 | + | 0.367680i | \(0.119848\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.8507 | −1.64126 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.51961 | 0.256284 | 0.128142 | − | 0.991756i | \(-0.459099\pi\) | ||||
0.128142 | + | 0.991756i | \(0.459099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.40976 | −0.136208 | −0.0681038 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681038 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.1114 | 1.13315 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6751 | 0.655739 | 0.327870 | − | 0.944723i | \(-0.393669\pi\) | ||||
0.327870 | + | 0.944723i | \(0.393669\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.7250 | −1.94423 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.7939 | −2.16526 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.277592 | −0.0154456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.8135 | 1.70399 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.60048 | −0.474160 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3827 | 1.23026 | 0.615131 | − | 0.788425i | \(-0.289103\pi\) | ||||
0.615131 | + | 0.788425i | \(0.289103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.83392 | 0.374496 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.376774 | 0.0205854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6686 | 0.690102 | 0.345051 | − | 0.938584i | \(-0.387862\pi\) | ||||
0.345051 | + | 0.938584i | \(0.387862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1900 | 0.553442 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.4263 | −2.78489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9522 | −1.07731 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.4164 | −0.883830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.56502 | 0.406111 | 0.203056 | − | 0.979167i | \(-0.434913\pi\) | ||||
0.203056 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.3617 | −0.982879 | −0.491439 | − | 0.870912i | \(-0.663529\pi\) | ||||
−0.491439 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.27380 | −0.0677976 | −0.0338988 | − | 0.999425i | \(-0.510792\pi\) | ||||
−0.0338988 | + | 0.999425i | \(0.510792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.04130 | −0.479862 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.4891 | −1.29610 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.0008 | −0.580598 | −0.290299 | − | 0.956936i | \(-0.593755\pi\) | ||||
−0.290299 | + | 0.956936i | \(0.593755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9919 | −0.999571 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −92.0198 | −4.82979 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.48133 | 0.286906 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.95825 | 0.311018 | 0.155509 | − | 0.987834i | \(-0.450298\pi\) | ||||
0.155509 | + | 0.987834i | \(0.450298\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −34.0572 | −1.77295 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9009 | 0.981288 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.7186 | −1.12455 | −0.562274 | − | 0.826951i | \(-0.690073\pi\) | ||||
−0.562274 | + | 0.826951i | \(0.690073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.40622 | −0.175896 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.5331 | 1.51701 | 0.758507 | − | 0.651665i | \(-0.225929\pi\) | ||||
0.758507 | + | 0.651665i | \(0.225929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.3702 | −1.86330 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.8889 | −1.37396 | −0.686980 | − | 0.726676i | \(-0.741064\pi\) | ||||
−0.686980 | + | 0.726676i | \(0.741064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.4147 | −0.734641 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75.2798 | −3.82669 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.11775 | −0.158076 | −0.0790380 | − | 0.996872i | \(-0.525185\pi\) | ||||
−0.0790380 | + | 0.996872i | \(0.525185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8210 | 0.749532 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 70.1928 | 3.54076 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.79283 | −0.241153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.2851 | −1.06827 | −0.534133 | − | 0.845400i | \(-0.679362\pi\) | ||||
−0.534133 | + | 0.845400i | \(0.679362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.718842 | 0.0359871 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.30134 | 0.364611 | 0.182306 | − | 0.983242i | \(-0.441644\pi\) | ||||
0.182306 | + | 0.983242i | \(0.441644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 39.1932 | 1.94753 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.89815 | −0.242792 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.26732 | −0.211005 | −0.105503 | − | 0.994419i | \(-0.533645\pi\) | ||||
−0.105503 | + | 0.994419i | \(0.533645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.289580 | 0.0142839 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.887415 | 0.0436668 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.6189 | 0.570349 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.5028 | −1.83652 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.14300 | −0.397811 | −0.198906 | − | 0.980019i | \(-0.563739\pi\) | ||||
−0.198906 | + | 0.980019i | \(0.563739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.36448 | 0.358923 | 0.179461 | − | 0.983765i | \(-0.442564\pi\) | ||||
0.179461 | + | 0.983765i | \(0.442564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.6455 | −1.53866 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.07520 | 0.149169 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.6046 | −0.561585 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.1661 | −0.971369 | −0.485684 | − | 0.874134i | \(-0.661430\pi\) | ||||
−0.485684 | + | 0.874134i | \(0.661430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0657 | 0.531783 | 0.265892 | − | 0.964003i | \(-0.414334\pi\) | ||||
0.265892 | + | 0.964003i | \(0.414334\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.1839 | −0.919796 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.435051 | −0.0208113 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5470 | 1.64884 | 0.824419 | − | 0.565980i | \(-0.191502\pi\) | ||||
0.824419 | + | 0.565980i | \(0.191502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.1977 | −0.628464 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.22275 | −0.0580947 | −0.0290473 | − | 0.999578i | \(-0.509247\pi\) | ||||
−0.0290473 | + | 0.999578i | \(0.509247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7118 | −0.555193 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0389 | −0.711315 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2491 | 0.861228 | 0.430614 | − | 0.902536i | \(-0.358297\pi\) | ||||
0.430614 | + | 0.902536i | \(0.358297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.4102 | 1.14943 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −53.6666 | −2.52148 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2180 | −1.08609 | −0.543046 | − | 0.839703i | \(-0.682729\pi\) | ||||
−0.543046 | + | 0.839703i | \(0.682729\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −58.6833 | −2.73910 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6014 | 1.37868 | 0.689338 | − | 0.724440i | \(-0.257901\pi\) | ||||
0.689338 | + | 0.724440i | \(0.257901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4362 | −1.41449 | −0.707244 | − | 0.706969i | \(-0.750062\pi\) | ||||
−0.707244 | + | 0.706969i | \(0.750062\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.4105 | −1.31751 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.6000 | 0.721880 | 0.360940 | − | 0.932589i | \(-0.382456\pi\) | ||||
0.360940 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.880861 | 0.0406744 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5852 | −0.533819 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.9561 | 2.48090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0902681 | −0.00414178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 69.5462 | 3.18430 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.5259 | −1.89737 | −0.948684 | − | 0.316227i | \(-0.897584\pi\) | ||||
−0.948684 | + | 0.316227i | \(0.897584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38.3800 | −1.74635 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.43658 | 0.110639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.84163 | −0.445967 | −0.222983 | − | 0.974822i | \(-0.571580\pi\) | ||||
−0.222983 | + | 0.974822i | \(0.571580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −49.1628 | −2.22322 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1322 | 1.31472 | 0.657359 | − | 0.753577i | \(-0.271673\pi\) | ||||
0.657359 | + | 0.753577i | \(0.271673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3195 | 0.780032 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −53.0390 | −2.38393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.1377 | −0.948155 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.1347 | 1.48331 | 0.741656 | − | 0.670781i | \(-0.234041\pi\) | ||||
0.741656 | + | 0.670781i | \(0.234041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 64.6553 | 2.88858 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.3323 | 1.08492 | 0.542462 | − | 0.840080i | \(-0.317492\pi\) | ||||
0.542462 | + | 0.840080i | \(0.317492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.52834 | −0.246008 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9484 | −0.751223 | −0.375611 | − | 0.926777i | \(-0.622567\pi\) | ||||
−0.375611 | + | 0.926777i | \(0.622567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8148 | 0.566894 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.72257 | 0.0760532 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.46999 | 0.373232 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.6817 | 0.997538 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.7989 | −1.65919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.0211 | −0.701896 | −0.350948 | − | 0.936395i | \(-0.614141\pi\) | ||||
−0.350948 | + | 0.936395i | \(0.614141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.05699 | −0.221127 | −0.110563 | − | 0.993869i | \(-0.535266\pi\) | ||||
−0.110563 | + | 0.993869i | \(0.535266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.96342 | −0.347552 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.6495 | 1.11731 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.227981 | 0.00991221 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.26525 | 0.141700 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3891 | 0.492395 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.9564 | −0.774876 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.45936 | 0.407444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.1770 | 1.89932 | 0.949659 | − | 0.313286i | \(-0.101430\pi\) | ||||
0.949659 | + | 0.313286i | \(0.101430\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −55.0936 | −2.36429 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.04624 | −0.387498 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3624 | 0.699605 | 0.349803 | − | 0.936823i | \(-0.386249\pi\) | ||||
0.349803 | + | 0.936823i | \(0.386249\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −42.6992 | −1.82236 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.508391 | −0.0216582 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.2052 | −0.476492 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.70599 | −0.114863 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.8749 | −1.26584 | −0.632919 | − | 0.774218i | \(-0.718143\pi\) | ||||
−0.632919 | + | 0.774218i | \(0.718143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.5839 | 2.72673 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9922 | 0.716135 | 0.358067 | − | 0.933696i | \(-0.383436\pi\) | ||||
0.358067 | + | 0.933696i | \(0.383436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.99157 | −0.125856 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 91.6300 | 3.84810 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.8326 | 0.705660 | 0.352830 | − | 0.935687i | \(-0.385219\pi\) | ||||
0.352830 | + | 0.935687i | \(0.385219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09953 | 0.0460138 | 0.0230069 | − | 0.999735i | \(-0.492676\pi\) | ||||
0.0230069 | + | 0.999735i | \(0.492676\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.0044 | 0.961023 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.81954 | 0.200989 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1153 | 0.879042 | 0.439521 | − | 0.898232i | \(-0.355148\pi\) | ||||
0.439521 | + | 0.898232i | \(0.355148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.64016 | −0.0681627 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1639 | 1.12695 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.8466 | −2.06443 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.2938 | −1.33291 | −0.666453 | − | 0.745547i | \(-0.732188\pi\) | ||||
−0.666453 | + | 0.745547i | \(0.732188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.752906 | −0.0310229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −74.5558 | −3.06681 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5827 | 0.516711 | 0.258356 | − | 0.966050i | \(-0.416819\pi\) | ||||
0.258356 | + | 0.966050i | \(0.416819\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.18951 | 0.294741 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −80.2395 | −3.28398 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.46110 | 0.386570 | 0.193285 | − | 0.981143i | \(-0.438086\pi\) | ||||
0.193285 | + | 0.981143i | \(0.438086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.02016 | 0.327149 | 0.163574 | − | 0.986531i | \(-0.447698\pi\) | ||||
0.163574 | + | 0.986531i | \(0.447698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.24114 | 0.131989 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.0152 | 1.09833 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.5832 | −1.07898 | −0.539490 | − | 0.841992i | \(-0.681383\pi\) | ||||
−0.539490 | + | 0.841992i | \(0.681383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −44.8500 | −1.81742 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.8547 | 1.81166 | 0.905831 | − | 0.423639i | \(-0.139247\pi\) | ||||
0.905831 | + | 0.423639i | \(0.139247\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.4855 | 0.543786 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9169 | −0.842082 | −0.421041 | − | 0.907042i | \(-0.638335\pi\) | ||||
−0.421041 | + | 0.907042i | \(0.638335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.55179 | 0.383919 | 0.191959 | − | 0.981403i | \(-0.438516\pi\) | ||||
0.191959 | + | 0.981403i | \(0.438516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −91.9704 | −3.69064 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.3811 | −1.09700 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.89577 | −0.0757098 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.44301 | 0.0974093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.38539 | −0.174580 | −0.0872899 | − | 0.996183i | \(-0.527821\pi\) | ||||
−0.0872899 | + | 0.996183i | \(0.527821\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.6937 | 1.49819 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.6776 | 0.423727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −77.7763 | −3.07678 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1325 | −0.755690 | −0.377845 | − | 0.925869i | \(-0.623335\pi\) | ||||
−0.377845 | + | 0.925869i | \(0.623335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.7043 | −0.698190 | −0.349095 | − | 0.937087i | \(-0.613511\pi\) | ||||
−0.349095 | + | 0.937087i | \(0.613511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.8081 | 1.17369 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0594 | −1.18176 | −0.590879 | − | 0.806761i | \(-0.701219\pi\) | ||||
−0.590879 | + | 0.806761i | \(0.701219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.34034 | −0.0918663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66.4211 | −2.60325 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.3677 | −0.757915 | −0.378958 | − | 0.925414i | \(-0.623717\pi\) | ||||
−0.378958 | + | 0.925414i | \(0.623717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6072 | −0.805191 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 47.1522 | 1.83958 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.47410 | 0.330104 | 0.165052 | − | 0.986285i | \(-0.447221\pi\) | ||||
0.165052 | + | 0.986285i | \(0.447221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9713 | −0.582318 | −0.291159 | − | 0.956675i | \(-0.594041\pi\) | ||||
−0.291159 | + | 0.956675i | \(0.594041\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.211038 | −0.00818371 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.1437 | 1.05101 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −82.9296 | −3.20625 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.6043 | 1.18146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3418 | 1.36233 | 0.681163 | − | 0.732132i | \(-0.261475\pi\) | ||||
0.681163 | + | 0.732132i | \(0.261475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.0828 | −0.734497 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.1737 | −1.19810 | −0.599051 | − | 0.800711i | \(-0.704455\pi\) | ||||
−0.599051 | + | 0.800711i | \(0.704455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.69648 | 0.218611 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.343315 | −0.0131559 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.5452 | 1.85753 | 0.928766 | − | 0.370667i | \(-0.120871\pi\) | ||||
0.928766 | + | 0.370667i | \(0.120871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0850150 | −0.00324826 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.0921 | 0.728408 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9719 | −0.683684 | −0.341842 | − | 0.939757i | \(-0.611051\pi\) | ||||
−0.341842 | + | 0.939757i | \(0.611051\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −124.000 | −4.71037 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.0101 | 0.417637 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1749 | −0.461157 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.2294 | −1.71073 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0567 | 0.493147 | 0.246573 | − | 0.969124i | \(-0.420695\pi\) | ||||
0.246573 | + | 0.969124i | \(0.420695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0717113 | −0.00270464 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.5305 | 0.471926 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.9247 | −0.486084 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9427 | −0.561186 | −0.280593 | − | 0.959827i | \(-0.590531\pi\) | ||||
−0.280593 | + | 0.959827i | \(0.590531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.2295 | −1.54623 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.1987 | 1.50545 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.2185 | 1.65137 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7997 | 0.402761 | 0.201381 | − | 0.979513i | \(-0.435457\pi\) | ||||
0.201381 | + | 0.979513i | \(0.435457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8020 | 0.737466 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.08283 | −0.189032 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.63201 | 0.209168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1935 | −0.934376 | −0.467188 | − | 0.884158i | \(-0.654733\pi\) | ||||
−0.467188 | + | 0.884158i | \(0.654733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 142.153 | 5.26491 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.9113 | −0.995350 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.1714 | −1.18828 | −0.594139 | − | 0.804363i | \(-0.702507\pi\) | ||||
−0.594139 | + | 0.804363i | \(0.702507\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.22584 | 0.192758 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.32306 | −0.0855708 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.1036 | 1.62238 | 0.811188 | − | 0.584785i | \(-0.198821\pi\) | ||||
0.811188 | + | 0.584785i | \(0.198821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4544 | −1.63087 | −0.815437 | − | 0.578846i | \(-0.803503\pi\) | ||||
−0.815437 | + | 0.578846i | \(0.803503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.41512 | 0.161758 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 99.9497 | 3.65697 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.6267 | 0.972918 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.6126 | 1.37250 | 0.686252 | − | 0.727364i | \(-0.259255\pi\) | ||||
0.686252 | + | 0.727364i | \(0.259255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.3675 | 1.39819 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.7555 | 0.573400 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.3294 | 1.28407 | 0.642034 | − | 0.766676i | \(-0.278091\pi\) | ||||
0.642034 | + | 0.766676i | \(0.278091\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 101.218 | 3.67398 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3170 | 0.990240 | 0.495120 | − | 0.868825i | \(-0.335124\pi\) | ||||
0.495120 | + | 0.868825i | \(0.335124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.1492 | −0.765654 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.4539 | 0.956442 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.1958 | −0.836460 | −0.418230 | − | 0.908341i | \(-0.637349\pi\) | ||||
−0.418230 | + | 0.908341i | \(0.637349\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.1439 | −1.84190 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.52005 | 0.234510 | 0.117255 | − | 0.993102i | \(-0.462591\pi\) | ||||
0.117255 | + | 0.993102i | \(0.462591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.34078 | 0.299610 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.32634 | −0.226956 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.357377 | 0.0128044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.7455 | 1.99473 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −107.475 | −3.84083 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.40120 | 0.121394 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.7311 | −1.45191 | −0.725954 | − | 0.687744i | \(-0.758601\pi\) | ||||
−0.725954 | + | 0.687744i | \(0.758601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.9349 | −1.38612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.99401 | −0.248678 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.5378 | −0.976665 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.48208 | 0.158763 | 0.0793816 | − | 0.996844i | \(-0.474705\pi\) | ||||
0.0793816 | + | 0.996844i | \(0.474705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3128 | −0.400217 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −100.749 | −3.55979 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.7959 | −1.19263 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.2676 | 0.397132 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −86.4860 | −3.04445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.7884 | 1.15278 | 0.576390 | − | 0.817175i | \(-0.304461\pi\) | ||||
0.576390 | + | 0.817175i | \(0.304461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.5808 | −1.03872 | −0.519361 | − | 0.854555i | \(-0.673830\pi\) | ||||
−0.519361 | + | 0.854555i | \(0.673830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.2174 | −1.27020 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.4332 | 0.505574 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.789943 | 0.0276366 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.1035 | 1.64392 | 0.821962 | − | 0.569543i | \(-0.192880\pi\) | ||||
0.821962 | + | 0.569543i | \(0.192880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4099 | −0.572012 | −0.286006 | − | 0.958228i | \(-0.592328\pi\) | ||||
−0.286006 | + | 0.958228i | \(0.592328\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.0016 | 0.731180 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.42042 | −0.258033 | −0.129017 | − | 0.991642i | \(-0.541182\pi\) | ||||
−0.129017 | + | 0.991642i | \(0.541182\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.0555 | −1.66904 | −0.834518 | − | 0.550980i | \(-0.814254\pi\) | ||||
−0.834518 | + | 0.550980i | \(0.814254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −88.5280 | −3.07100 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.71798 | −0.163468 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9815 | −0.656883 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −159.165 | −5.50156 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5460 | 0.433136 | 0.216568 | − | 0.976268i | \(-0.430514\pi\) | ||||
0.216568 | + | 0.976268i | \(0.430514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.71952 | 0.0937766 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.0889 | 0.898550 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 63.1590 | 2.17017 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −66.4298 | −2.27986 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.82877 | 0.131248 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.26494 | 0.282986 | 0.141493 | − | 0.989939i | \(-0.454810\pi\) | ||||
0.141493 | + | 0.989939i | \(0.454810\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.776517 | −0.0265563 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0212 | 0.513115 | 0.256558 | − | 0.966529i | \(-0.417412\pi\) | ||||
0.256558 | + | 0.966529i | \(0.417412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3863 | 0.763810 | 0.381905 | − | 0.924202i | \(-0.375268\pi\) | ||||
0.381905 | + | 0.924202i | \(0.375268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.5277 | 1.07446 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.17657 | 0.142172 | 0.0710860 | − | 0.997470i | \(-0.477354\pi\) | ||||
0.0710860 | + | 0.997470i | \(0.477354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0970 | 0.377310 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.6937 | 0.872604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.5509 | 1.00244 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.9603 | 0.709397 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.33790 | 0.0790356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.2315 | −1.32475 | −0.662377 | − | 0.749171i | \(-0.730452\pi\) | ||||
−0.662377 | + | 0.749171i | \(0.730452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43.5585 | 1.46919 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.53832 | 0.287663 | 0.143832 | − | 0.989602i | \(-0.454058\pi\) | ||||
0.143832 | + | 0.989602i | \(0.454058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.7515 | 1.50601 | 0.753004 | − | 0.658016i | \(-0.228604\pi\) | ||||
0.753004 | + | 0.658016i | \(0.228604\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.29292 | −0.0434611 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.1035 | 1.24581 | 0.622906 | − | 0.782296i | \(-0.285952\pi\) | ||||
0.622906 | + | 0.782296i | \(0.285952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.9632 | 0.837237 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −241.652 | −8.09563 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.332070 | 0.0111123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.27165 | 0.176212 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.9753 | 1.56671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.8616 | 0.828260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 69.6885 | 2.31909 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.1744 | 0.537655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.6342 | −1.24962 | −0.624812 | − | 0.780776i | \(-0.714824\pi\) | ||||
−0.624812 | + | 0.780776i | \(0.714824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.5566 | −1.57735 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.8183 | 1.31924 | 0.659619 | − | 0.751600i | \(-0.270718\pi\) | ||||
0.659619 | + | 0.751600i | \(0.270718\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.6380 | −2.37087 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.9074 | 0.558940 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.1777 | −1.59097 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.1947 | −1.12798 | −0.563989 | − | 0.825782i | \(-0.690734\pi\) | ||||
−0.563989 | + | 0.825782i | \(0.690734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −111.002 | −3.65766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.794425 | 0.0261205 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 72.8617 | 2.39309 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.5866 | −1.00351 | −0.501757 | − | 0.865009i | \(-0.667313\pi\) | ||||
−0.501757 | + | 0.865009i | \(0.667313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.138490 | 0.00453881 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.3948 | −0.504003 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.9606 | −0.620077 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.0385 | −1.27533 | −0.637666 | − | 0.770313i | \(-0.720100\pi\) | ||||
−0.637666 | + | 0.770313i | \(0.720100\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.20816 | 0.267863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.92575 | −0.225773 | −0.112886 | − | 0.993608i | \(-0.536010\pi\) | ||||
−0.112886 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0809 | −0.621359 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44.6138 | −1.45129 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.2145 | 0.494405 | 0.247202 | − | 0.968964i | \(-0.420489\pi\) | ||||
0.247202 | + | 0.968964i | \(0.420489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.7680 | −1.28957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.06168 | −0.163964 | −0.0819819 | − | 0.996634i | \(-0.526125\pi\) | ||||
−0.0819819 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.75365 | −0.218543 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 118.281 | 3.82348 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.198757 | −0.00641820 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.5686 | 1.24415 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 97.9732 | 3.15714 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.481519 | 0.0155006 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.3231 | 1.55397 | 0.776983 | − | 0.629522i | \(-0.216749\pi\) | ||||
0.776983 | + | 0.629522i | \(0.216749\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.945539 | 0.0303751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.8463 | 1.47128 | 0.735638 | − | 0.677374i | \(-0.236882\pi\) | ||||
0.735638 | + | 0.677374i | \(0.236882\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.7405 | 0.825204 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.2717 | 1.38438 | 0.692192 | − | 0.721714i | \(-0.256645\pi\) | ||||
0.692192 | + | 0.721714i | \(0.256645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.2108 | 2.30787 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −77.8188 | −2.48456 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.695243 | 0.0221748 | 0.0110874 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110874 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8881 | 0.697414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.2951 | 0.932474 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.1762 | −1.34113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.1973 | 0.673355 | 0.336677 | − | 0.941620i | \(-0.390697\pi\) | ||||
0.336677 | + | 0.941620i | \(0.390697\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −76.2403 | −2.41941 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.5567 | 0.746799 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.7860 | −1.16503 | −0.582513 | − | 0.812822i | \(-0.697930\pi\) | ||||
−0.582513 | + | 0.812822i | \(0.697930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.1599 | −0.479637 |
(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 | 3380.2.a.s.1.1 | yes | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.1 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.2 | 18 | |||
13.12 | even | 2 | 3380.2.a.r.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.1 | ✓ | 9 | 13.12 | even | 2 | ||
3380.2.a.s.1.1 | yes | 9 | 1.1 | even | 1 | trivial | |
3380.2.f.j.3041.1 | 18 | 13.5 | odd | 4 | |||
3380.2.f.j.3041.2 | 18 | 13.8 | odd | 4 |