Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3328,2,Mod(1,3328)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3328, 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("3328.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3328 = 2^{8} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3328.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: | \(26.5742137927\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1664) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3328.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.82843 | −1.71212 | −0.856062 | − | 0.516873i | \(-0.827096\pi\) | ||||
−0.856062 | + | 0.516873i | \(0.827096\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.82843 | −1.44701 | −0.723505 | − | 0.690319i | \(-0.757470\pi\) | ||||
−0.723505 | + | 0.690319i | \(0.757470\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.82843 | 0.988496 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.65685 | 1.61452 | 0.807262 | − | 0.590193i | \(-0.200948\pi\) | ||||
0.807262 | + | 0.590193i | \(0.200948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.82843 | 0.835431 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.17157 | 0.661319 | 0.330659 | − | 0.943750i | \(-0.392729\pi\) | ||||
0.330659 | + | 0.943750i | \(0.392729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.65685 | 1.93137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.17157 | −0.588946 | −0.294473 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294473 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.82843 | −0.840521 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.6569 | 2.47746 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.82843 | −0.629390 | −0.314695 | − | 0.949193i | \(-0.601902\pi\) | ||||
−0.314695 | + | 0.949193i | \(0.601902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | −0.457496 | −0.228748 | − | 0.973486i | \(-0.573463\pi\) | ||||
−0.228748 | + | 0.973486i | \(0.573463\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.65685 | 1.14142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4853 | 1.67530 | 0.837650 | − | 0.546207i | \(-0.183929\pi\) | ||||
0.837650 | + | 0.546207i | \(0.183929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.65685 | 1.09384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.65685 | −0.932146 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.17157 | −0.435649 | −0.217825 | − | 0.975988i | \(-0.569896\pi\) | ||||
−0.217825 | + | 0.975988i | \(0.569896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.4853 | −2.49255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17157 | −0.673281 | −0.336641 | − | 0.941633i | \(-0.609291\pi\) | ||||
−0.336641 | + | 0.941633i | \(0.609291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8284 | −1.38644 | −0.693219 | − | 0.720727i | \(-0.743808\pi\) | ||||
−0.693219 | + | 0.720727i | \(0.743808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.65685 | 0.964673 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.82843 | −0.474858 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.65685 | 0.446756 | 0.223378 | − | 0.974732i | \(-0.428292\pi\) | ||||
0.223378 | + | 0.974732i | \(0.428292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.17157 | −0.381813 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1716 | 1.20714 | 0.603572 | − | 0.797309i | \(-0.293744\pi\) | ||||
0.603572 | + | 0.797309i | \(0.293744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.17157 | 0.605287 | 0.302643 | − | 0.953104i | \(-0.402131\pi\) | ||||
0.302643 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.65685 | −1.11508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.4853 | −2.10659 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.65685 | 0.861463 | 0.430732 | − | 0.902480i | \(-0.358256\pi\) | ||||
0.430732 | + | 0.902480i | \(0.358256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.4853 | −2.76427 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.17157 | 0.340028 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.6569 | −1.87162 | −0.935811 | − | 0.352501i | \(-0.885331\pi\) | ||||
−0.935811 | + | 0.352501i | \(0.885331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.82843 | −0.401328 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.3137 | 1.57115 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4853 | −1.47076 | −0.735379 | − | 0.677656i | \(-0.762996\pi\) | ||||
−0.735379 | + | 0.677656i | \(0.762996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.65685 | −0.970550 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.6569 | −1.43036 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3137 | −1.48043 | −0.740216 | − | 0.672369i | \(-0.765277\pi\) | ||||
−0.740216 | + | 0.672369i | \(0.765277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.82843 | −0.366697 | −0.183348 | − | 0.983048i | \(-0.558694\pi\) | ||||
−0.183348 | + | 0.983048i | \(0.558694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.82843 | 0.363378 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.65685 | −0.344008 | −0.172004 | − | 0.985096i | \(-0.555024\pi\) | ||||
−0.172004 | + | 0.985096i | \(0.555024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1421 | −1.13226 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.4853 | −2.33623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.82843 | −0.255031 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −17.8284 | −1.59462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.4853 | −1.64030 | −0.820152 | − | 0.572146i | \(-0.806111\pi\) | ||||
−0.820152 | + | 0.572146i | \(0.806111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | 0.264135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.65685 | 0.232130 | 0.116065 | − | 0.993242i | \(-0.462972\pi\) | ||||
0.116065 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.3137 | 1.32787 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.1421 | −1.64749 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.1421 | −1.72086 | −0.860429 | − | 0.509570i | \(-0.829805\pi\) | ||||
−0.860429 | + | 0.509570i | \(0.829805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6569 | 1.58245 | 0.791227 | − | 0.611523i | \(-0.209443\pi\) | ||||
0.791227 | + | 0.611523i | \(0.209443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4853 | −0.967235 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.82843 | 0.403773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.1421 | 1.00835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.65685 | −0.631527 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.31371 | 0.107623 | 0.0538116 | − | 0.998551i | \(-0.482863\pi\) | ||||
0.0538116 | + | 0.998551i | \(0.482863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.51472 | −0.204645 | −0.102322 | − | 0.994751i | \(-0.532627\pi\) | ||||
−0.102322 | + | 0.994751i | \(0.532627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.3137 | −1.07635 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.48528 | 0.357964 | 0.178982 | − | 0.983852i | \(-0.442720\pi\) | ||||
0.178982 | + | 0.983852i | \(0.442720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.17157 | 0.251522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.1421 | −0.956934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8284 | −1.00480 | −0.502400 | − | 0.864635i | \(-0.667549\pi\) | ||||
−0.502400 | + | 0.864635i | \(0.667549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.4853 | 1.43908 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.6569 | −1.67586 | −0.837929 | − | 0.545779i | \(-0.816234\pi\) | ||||
−0.837929 | + | 0.545779i | \(0.816234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9706 | 1.74642 | 0.873210 | − | 0.487345i | \(-0.162034\pi\) | ||||
0.873210 | + | 0.487345i | \(0.162034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −36.9706 | −2.79471 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.17157 | 0.388719 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.31371 | 0.621396 | 0.310698 | − | 0.950509i | \(-0.399437\pi\) | ||||
0.310698 | + | 0.950509i | \(0.399437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.9706 | −1.70739 | −0.853694 | − | 0.520775i | \(-0.825643\pi\) | ||||
−0.853694 | + | 0.520775i | \(0.825643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8284 | 0.800460 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.6569 | 1.07759 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.1421 | 2.35047 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.1421 | −1.39239 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.17157 | −0.229487 | −0.114743 | − | 0.993395i | \(-0.536605\pi\) | ||||
−0.114743 | + | 0.993395i | \(0.536605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.82843 | 0.274159 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.8284 | −1.27022 | −0.635111 | − | 0.772421i | \(-0.719046\pi\) | ||||
−0.635111 | + | 0.772421i | \(0.719046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.9706 | 1.62834 | 0.814170 | − | 0.580627i | \(-0.197192\pi\) | ||||
0.814170 | + | 0.580627i | \(0.197192\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.65685 | −0.257935 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1421 | 0.852211 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.8284 | −0.756290 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.34315 | −0.440879 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.3137 | −1.33596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.34315 | −0.0924660 | −0.0462330 | − | 0.998931i | \(-0.514722\pi\) | ||||
−0.0462330 | + | 0.998931i | \(0.514722\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.1716 | −0.696945 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.4853 | 0.783290 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.17157 | −0.349463 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.65685 | 0.447788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1716 | 0.681139 | 0.340569 | − | 0.940219i | \(-0.389380\pi\) | ||||
0.340569 | + | 0.940219i | \(0.389380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.3137 | −1.28758 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.17157 | 0.608739 | 0.304369 | − | 0.952554i | \(-0.401554\pi\) | ||||
0.304369 | + | 0.952554i | \(0.401554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1716 | 0.672156 | 0.336078 | − | 0.941834i | \(-0.390899\pi\) | ||||
0.336078 | + | 0.941834i | \(0.390899\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.4853 | 1.21624 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3137 | 1.33080 | 0.665398 | − | 0.746489i | \(-0.268262\pi\) | ||||
0.665398 | + | 0.746489i | \(0.268262\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −43.9706 | −2.86832 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.65685 | −0.497366 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.1421 | −1.23820 | −0.619101 | − | 0.785311i | \(-0.712503\pi\) | ||||
−0.619101 | + | 0.785311i | \(0.712503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.31371 | 0.213455 | 0.106727 | − | 0.994288i | \(-0.465963\pi\) | ||||
0.106727 | + | 0.994288i | \(0.465963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.3137 | −1.87278 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | −0.254514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.6274 | 1.68071 | 0.840354 | − | 0.542038i | \(-0.182347\pi\) | ||||
0.840354 | + | 0.542038i | \(0.182347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137 | 0.962765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25.4853 | 1.59595 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.34315 | −0.0837831 | −0.0418916 | − | 0.999122i | \(-0.513338\pi\) | ||||
−0.0418916 | + | 0.999122i | \(0.513338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.6569 | 0.910733 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.34315 | 0.392631 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.1421 | −1.61199 | −0.805997 | − | 0.591920i | \(-0.798370\pi\) | ||||
−0.805997 | + | 0.591920i | \(0.798370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1421 | 0.745885 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.6569 | 1.08058 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990 | 1.20717 | 0.603583 | − | 0.797300i | \(-0.293739\pi\) | ||||
0.603583 | + | 0.797300i | \(0.293739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.51472 | 0.152758 | 0.0763791 | − | 0.997079i | \(-0.475664\pi\) | ||||
0.0763791 | + | 0.997079i | \(0.475664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.82843 | 0.231707 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 46.6274 | 2.81174 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.48528 | 0.269494 | 0.134747 | − | 0.990880i | \(-0.456978\pi\) | ||||
0.134747 | + | 0.990880i | \(0.456978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.97056 | −0.296519 | −0.148259 | − | 0.988948i | \(-0.547367\pi\) | ||||
−0.148259 | + | 0.988948i | \(0.547367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6274 | −0.869510 | −0.434755 | − | 0.900549i | \(-0.643165\pi\) | ||||
−0.434755 | + | 0.900549i | \(0.643165\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.3137 | −0.907106 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8284 | −0.639182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.3137 | 1.60669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.4853 | 0.849142 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7990 | −0.747725 | −0.373862 | − | 0.927484i | \(-0.621967\pi\) | ||||
−0.373862 | + | 0.927484i | \(0.621967\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.7990 | 1.15274 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.1421 | 1.40087 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.17157 | 0.183417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4853 | 0.662001 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.4558 | 2.37375 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1716 | 0.751741 | 0.375871 | − | 0.926672i | \(-0.377344\pi\) | ||||
0.375871 | + | 0.926672i | \(0.377344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0000 | −0.796432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2843 | 1.37703 | 0.688517 | − | 0.725220i | \(-0.258262\pi\) | ||||
0.688517 | + | 0.725220i | \(0.258262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9706 | 1.12880 | 0.564401 | − | 0.825500i | \(-0.309107\pi\) | ||||
0.564401 | + | 0.825500i | \(0.309107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −29.3137 | −1.65164 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.3137 | −1.64642 | −0.823211 | − | 0.567736i | \(-0.807820\pi\) | ||||
−0.823211 | + | 0.567736i | \(0.807820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.3137 | −0.857403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3137 | 0.854728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.6274 | −1.48159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.65685 | 0.535666 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.82843 | 0.211713 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −43.9706 | −2.42418 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9706 | 0.602997 | 0.301498 | − | 0.953467i | \(-0.402513\pi\) | ||||
0.301498 | + | 0.953467i | \(0.402513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65685 | 0.419593 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.0000 | −0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.97056 | −0.107343 | −0.0536717 | − | 0.998559i | \(-0.517092\pi\) | ||||
−0.0536717 | + | 0.998559i | \(0.517092\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.65685 | 0.198613 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.51472 | −0.135782 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.1421 | 0.653711 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0000 | −0.805242 | −0.402621 | − | 0.915367i | \(-0.631901\pi\) | ||||
−0.402621 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4853 | −1.36420 | −0.682098 | − | 0.731261i | \(-0.738932\pi\) | ||||
−0.682098 | + | 0.731261i | \(0.738932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.3137 | −0.921516 | −0.460758 | − | 0.887526i | \(-0.652422\pi\) | ||||
−0.460758 | + | 0.887526i | \(0.652422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −38.9411 | −2.06678 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.4853 | 1.34882 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.6569 | 1.14301 | 0.571503 | − | 0.820600i | \(-0.306361\pi\) | ||||
0.571503 | + | 0.820600i | \(0.306361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3137 | −0.646302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.7990 | −1.03633 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.9411 | −1.66731 | −0.833657 | − | 0.552283i | \(-0.813757\pi\) | ||||
−0.833657 | + | 0.552283i | \(0.813757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.65685 | −0.294484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.1421 | 0.630388 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.97056 | 0.464478 | 0.232239 | − | 0.972659i | \(-0.425395\pi\) | ||||
0.232239 | + | 0.972659i | \(0.425395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.8284 | 0.920656 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.17157 | −0.163344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.4558 | −1.20485 | −0.602423 | − | 0.798177i | \(-0.705798\pi\) | ||||
−0.602423 | + | 0.798177i | \(0.705798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.4853 | 0.947030 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8284 | −0.910990 | −0.455495 | − | 0.890238i | \(-0.650538\pi\) | ||||
−0.455495 | + | 0.890238i | \(0.650538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 70.7696 | 3.60675 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.00000 | 0.304997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1421 | −1.32546 | −0.662729 | − | 0.748859i | \(-0.730602\pi\) | ||||
−0.662729 | + | 0.748859i | \(0.730602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.1127 | 1.06772 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.65685 | −0.134021 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.3137 | −1.47493 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.31371 | −0.0659331 | −0.0329666 | − | 0.999456i | \(-0.510495\pi\) | ||||
−0.0329666 | + | 0.999456i | \(0.510495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.3137 | −0.766644 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1716 | −0.557882 | −0.278941 | − | 0.960308i | \(-0.589983\pi\) | ||||
−0.278941 | + | 0.960308i | \(0.589983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.82843 | −0.190236 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.4853 | −0.916281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.51472 | −0.0748980 | −0.0374490 | − | 0.999299i | \(-0.511923\pi\) | ||||
−0.0374490 | + | 0.999299i | \(0.511923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1421 | 0.993538 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.7990 | 0.974245 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.9706 | −1.12758 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.6569 | −0.913630 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.3431 | −0.944975 | −0.472487 | − | 0.881338i | \(-0.656644\pi\) | ||||
−0.472487 | + | 0.881338i | \(0.656644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.85786 | 0.431706 | 0.215853 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215853 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.9706 | −1.11687 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 64.2843 | 3.11825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.4558 | 2.00619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.82843 | −0.233119 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.8284 | 0.858765 | 0.429383 | − | 0.903123i | \(-0.358731\pi\) | ||||
0.429383 | + | 0.903123i | \(0.358731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.1421 | −0.582171 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6863 | −0.606868 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.48528 | 0.214071 | 0.107035 | − | 0.994255i | \(-0.465864\pi\) | ||||
0.107035 | + | 0.994255i | \(0.465864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.3137 | −0.729224 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.313708 | −0.0149047 | −0.00745237 | − | 0.999972i | \(-0.502372\pi\) | ||||
−0.00745237 | + | 0.999972i | \(0.502372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 67.5980 | 3.20445 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.31371 | −0.0621363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1421 | 0.573023 | 0.286511 | − | 0.958077i | \(-0.407504\pi\) | ||||
0.286511 | + | 0.958077i | \(0.407504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.6569 | 0.643076 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.51472 | 0.118152 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.6569 | 0.687124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.9706 | −0.980962 | −0.490481 | − | 0.871452i | \(-0.663179\pi\) | ||||
−0.490481 | + | 0.871452i | \(0.663179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 33.2843 | 1.55358 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4853 | 0.534923 | 0.267461 | − | 0.963569i | \(-0.413815\pi\) | ||||
0.267461 | + | 0.963569i | \(0.413815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.3431 | −1.40411 | −0.702057 | − | 0.712121i | \(-0.747735\pi\) | ||||
−0.702057 | + | 0.712121i | \(0.747735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.48528 | −0.206671 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.4853 | −0.666034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.6274 | −1.77235 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.34315 | 0.290433 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.1421 | −0.874627 | −0.437313 | − | 0.899309i | \(-0.644070\pi\) | ||||
−0.437313 | + | 0.899309i | \(0.644070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.82843 | −0.174561 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.1421 | 0.552486 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 55.4558 | 2.51812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.97056 | 0.406495 | 0.203247 | − | 0.979127i | \(-0.434850\pi\) | ||||
0.203247 | + | 0.979127i | \(0.434850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.8284 | 0.580122 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6863 | 0.798171 | 0.399086 | − | 0.916914i | \(-0.369328\pi\) | ||||
0.399086 | + | 0.916914i | \(0.369328\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.1127 | −0.950868 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.9706 | 1.66170 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −38.9411 | −1.74675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1421 | −0.812154 | −0.406077 | − | 0.913839i | \(-0.633103\pi\) | ||||
−0.406077 | + | 0.913839i | \(0.633103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6569 | 0.967557 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3137 | −0.682805 | −0.341402 | − | 0.939917i | \(-0.610902\pi\) | ||||
−0.341402 | + | 0.939917i | \(0.610902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.2843 | −1.69692 | −0.848460 | − | 0.529259i | \(-0.822470\pi\) | ||||
−0.848460 | + | 0.529259i | \(0.822470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.7990 | −0.875856 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | −0.883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −53.5980 | −2.36181 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.4558 | 2.43895 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.9706 | −1.00830 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.3137 | 0.627095 | 0.313547 | − | 0.949573i | \(-0.398483\pi\) | ||||
0.313547 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.65685 | 0.422265 | 0.211132 | − | 0.977457i | \(-0.432285\pi\) | ||||
0.211132 | + | 0.977457i | \(0.432285\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 36.9706 | 1.61353 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9411 | −0.562658 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3431 | 0.448854 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.82843 | 0.122513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 58.6274 | 2.53468 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.31371 | −0.358763 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.9706 | 1.59243 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5147 | 0.710023 | 0.355012 | − | 0.934862i | \(-0.384477\pi\) | ||||
0.355012 | + | 0.934862i | \(0.384477\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.9706 | 0.985761 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.6569 | 0.627831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.62742 | 0.240611 | 0.120305 | − | 0.992737i | \(-0.461613\pi\) | ||||
0.120305 | + | 0.992737i | \(0.461613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.6569 | 0.924292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6863 | 0.540454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.3137 | −1.24655 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.6569 | −0.622149 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.14214 | −0.217879 | −0.108940 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108940 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.1421 | −1.35704 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.5980 | −1.62671 | −0.813355 | − | 0.581767i | \(-0.802362\pi\) | ||||
−0.813355 | + | 0.581767i | \(0.802362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.82843 | −0.160779 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.97056 | −0.0826103 | −0.0413051 | − | 0.999147i | \(-0.513152\pi\) | ||||
−0.0413051 | + | 0.999147i | \(0.513152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.6569 | −0.948160 | −0.474080 | − | 0.880482i | \(-0.657219\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.17157 | 0.132494 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.6274 | 1.27725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4558 | 1.39279 | 0.696393 | − | 0.717661i | \(-0.254787\pi\) | ||||
0.696393 | + | 0.717661i | \(0.254787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9706 | −0.952980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.3137 | −0.634229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.65685 | 0.316572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1127 | −1.03651 | −0.518256 | − | 0.855226i | \(-0.673419\pi\) | ||||
−0.518256 | + | 0.855226i | \(0.673419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.8284 | 0.733363 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.14214 | −0.334357 | −0.167179 | − | 0.985927i | \(-0.553466\pi\) | ||||
−0.167179 | + | 0.985927i | \(0.553466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 97.5685 | 3.99992 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.9706 | −0.940123 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.85786 | 0.0759103 | 0.0379551 | − | 0.999279i | \(-0.487916\pi\) | ||||
0.0379551 | + | 0.999279i | \(0.487916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.68629 | 0.0687853 | 0.0343926 | − | 0.999408i | \(-0.489050\pi\) | ||||
0.0343926 | + | 0.999408i | \(0.489050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.31371 | −0.297837 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −47.1421 | −1.91660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.8284 | 0.439512 | 0.219756 | − | 0.975555i | \(-0.429474\pi\) | ||||
0.219756 | + | 0.975555i | \(0.429474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.1421 | −0.492024 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4853 | 0.464645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0000 | 1.69636 | 0.848182 | − | 0.529705i | \(-0.177697\pi\) | ||||
0.848182 | + | 0.529705i | \(0.177697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.8284 | 0.436644 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.686292 | −0.0276291 | −0.0138145 | − | 0.999905i | \(-0.504397\pi\) | ||||
−0.0138145 | + | 0.999905i | \(0.504397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.1421 | 0.729194 | 0.364597 | − | 0.931165i | \(-0.381207\pi\) | ||||
0.364597 | + | 0.931165i | \(0.381207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.8579 | 0.636354 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 67.5980 | 2.70826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.3137 | 0.771315 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.4853 | −1.01616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7990 | 0.509520 | 0.254760 | − | 0.967004i | \(-0.418004\pi\) | ||||
0.254760 | + | 0.967004i | \(0.418004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.34315 | 0.0533853 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 70.7696 | 2.80840 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.65685 | 0.303376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.3431 | −0.804762 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.9706 | −0.907283 | −0.453641 | − | 0.891184i | \(-0.649875\pi\) | ||||
−0.453641 | + | 0.891184i | \(0.649875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −48.6274 | −1.91768 | −0.958839 | − | 0.283950i | \(-0.908355\pi\) | ||||
−0.958839 | + | 0.283950i | \(0.908355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.4853 | −0.452233 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.1716 | −0.675084 | −0.337542 | − | 0.941310i | \(-0.609596\pi\) | ||||
−0.337542 | + | 0.941310i | \(0.609596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.9706 | −0.980180 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3137 | −0.599272 | −0.299636 | − | 0.954054i | \(-0.596865\pi\) | ||||
−0.299636 | + | 0.954054i | \(0.596865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1716 | −0.397436 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3431 | −0.403525 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.97056 | −0.193626 | −0.0968128 | − | 0.995303i | \(-0.530865\pi\) | ||||
−0.0968128 | + | 0.995303i | \(0.530865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.31371 | −0.0510973 | −0.0255487 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255487 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.65685 | −0.258531 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −58.6274 | −2.27347 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0589 | −0.389481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1716 | −0.393256 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.2843 | −2.01841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.3137 | 0.474659 | 0.237329 | − | 0.971429i | \(-0.423728\pi\) | ||||
0.237329 | + | 0.971429i | \(0.423728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 48.2843 | 1.85846 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3137 | 1.12662 | 0.563309 | − | 0.826247i | \(-0.309528\pi\) | ||||
0.563309 | + | 0.826247i | \(0.309528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.4558 | 2.12820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.17157 | −0.351455 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.6569 | −1.51743 | −0.758714 | − | 0.651424i | \(-0.774172\pi\) | ||||
−0.758714 | + | 0.651424i | \(0.774172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 77.1127 | 2.94632 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.1716 | −0.388070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.17157 | −0.120827 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.02944 | −0.267412 | −0.133706 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133706 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 36.9706 | 1.40440 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −71.4264 | −2.70936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.8284 | 0.713178 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3137 | −0.768335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1421 | 0.458602 | 0.229301 | − | 0.973356i | \(-0.426356\pi\) | ||||
0.229301 | + | 0.973356i | \(0.426356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3137 | 0.577567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.9706 | 1.65603 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.65685 | −0.287559 | −0.143780 | − | 0.989610i | \(-0.545926\pi\) | ||||
−0.143780 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.3137 | −0.574309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.4853 | −0.691310 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.1421 | 0.714876 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.9706 | 0.856657 | 0.428329 | − | 0.903623i | \(-0.359103\pi\) | ||||
0.428329 | + | 0.903623i | \(0.359103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.5980 | −1.99609 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.31371 | −0.123238 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.6274 | −1.13747 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.4853 | 0.685581 | 0.342791 | − | 0.939412i | \(-0.388628\pi\) | ||||
0.342791 | + | 0.939412i | \(0.388628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.9706 | −0.738638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.7696 | −1.32118 | −0.660589 | − | 0.750747i | \(-0.729694\pi\) | ||||
−0.660589 | + | 0.750747i | \(0.729694\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.3137 | 1.08125 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.6569 | 0.650399 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5147 | 1.15929 | 0.579644 | − | 0.814870i | \(-0.303192\pi\) | ||||
0.579644 | + | 0.814870i | \(0.303192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.7990 | −1.49677 | −0.748385 | − | 0.663265i | \(-0.769170\pi\) | ||||
−0.748385 | + | 0.663265i | \(0.769170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.02944 | −0.184264 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 58.6274 | 2.14220 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5147 | 0.858064 | 0.429032 | − | 0.903289i | \(-0.358855\pi\) | ||||
0.429032 | + | 0.903289i | \(0.358855\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.6274 | −0.970357 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.62742 | 0.350378 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.1716 | −1.13295 | −0.566475 | − | 0.824079i | \(-0.691693\pi\) | ||||
−0.566475 | + | 0.824079i | \(0.691693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.3137 | −0.555852 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.1716 | −1.20247 | −0.601234 | − | 0.799073i | \(-0.705324\pi\) | ||||
−0.601234 | + | 0.799073i | \(0.705324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6569 | 0.530614 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 50.9706 | 1.84284 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.17157 | −0.186735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6569 | −0.492479 | −0.246239 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246239 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.34315 | 0.0483722 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.7990 | 0.963893 | 0.481946 | − | 0.876201i | \(-0.339930\pi\) | ||||
0.481946 | + | 0.876201i | \(0.339930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6569 | −0.525812 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3137 | −0.405356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.1127 | 1.75739 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.8579 | −0.566714 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.1716 | −0.612880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5147 | −0.410455 | −0.205228 | − | 0.978714i | \(-0.565793\pi\) | ||||
−0.205228 | + | 0.978714i | \(0.565793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.1421 | 0.930685 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.8284 | −0.384529 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.1421 | −0.430637 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.3431 | −1.21650 | −0.608248 | − | 0.793747i | \(-0.708128\pi\) | ||||
−0.608248 | + | 0.793747i | \(0.708128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.4558 | 2.70481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.3137 | 1.24775 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.9706 | 0.881192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.4853 | 1.63839 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.7990 | −0.696957 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.0000 | 0.949269 | 0.474635 | − | 0.880183i | \(-0.342580\pi\) | ||||
0.474635 | + | 0.880183i | \(0.342580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.9706 | 1.01729 | 0.508647 | − | 0.860975i | \(-0.330146\pi\) | ||||
0.508647 | + | 0.860975i | \(0.330146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.51472 | −0.0881950 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.1127 | 1.72034 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.65685 | 0.267552 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4853 | 0.400839 | 0.200420 | − | 0.979710i | \(-0.435769\pi\) | ||||
0.200420 | + | 0.979710i | \(0.435769\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7696 | −1.00284 | −0.501422 | − | 0.865203i | \(-0.667189\pi\) | ||||
−0.501422 | + | 0.865203i | \(0.667189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −46.6274 | −1.62336 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.6274 | 1.06502 | 0.532510 | − | 0.846424i | \(-0.321249\pi\) | ||||
0.532510 | + | 0.846424i | \(0.321249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.9706 | 0.797801 | 0.398900 | − | 0.916994i | \(-0.369392\pi\) | ||||
0.398900 | + | 0.916994i | \(0.369392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.48528 | −0.155593 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50.9706 | 1.76603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 82.9117 | 2.86928 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.6863 | 0.437979 | 0.218990 | − | 0.975727i | \(-0.429724\pi\) | ||||
0.218990 | + | 0.975727i | \(0.429724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.97056 | 0.171195 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.82843 | −0.131702 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.1421 | −1.61982 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.6274 | 0.502012 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.1421 | −0.416227 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7696 | −1.22473 | −0.612363 | − | 0.790577i | \(-0.709781\pi\) | ||||
−0.612363 | + | 0.790577i | \(0.709781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.6274 | −1.04744 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.3137 | 1.41125 | 0.705625 | − | 0.708586i | \(-0.250666\pi\) | ||||
0.705625 | + | 0.708586i | \(0.250666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.97056 | −0.169593 | −0.0847967 | − | 0.996398i | \(-0.527024\pi\) | ||||
−0.0847967 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8284 | 0.369032 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1127 | 0.480402 | 0.240201 | − | 0.970723i | \(-0.422787\pi\) | ||||
0.240201 | + | 0.970723i | \(0.422787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −87.9411 | −2.99009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.3137 | −0.927622 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.9706 | 1.25414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.65685 | 0.123908 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.9706 | 0.980505 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 68.2548 | 2.30743 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.5147 | 0.557662 | 0.278831 | − | 0.960340i | \(-0.410053\pi\) | ||||
0.278831 | + | 0.960340i | \(0.410053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.7990 | 0.431699 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3137 | 1.35820 | 0.679102 | − | 0.734044i | \(-0.262370\pi\) | ||||
0.679102 | + | 0.734044i | \(0.262370\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.97056 | −0.0663147 | −0.0331574 | − | 0.999450i | \(-0.510556\pi\) | ||||
−0.0331574 | + | 0.999450i | \(0.510556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.7990 | −0.665536 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.1421 | 0.877767 | 0.438884 | − | 0.898544i | \(-0.355374\pi\) | ||||
0.438884 | + | 0.898544i | \(0.355374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.7696 | 2.37353 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82843 | 0.161758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.9411 | −1.53736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.8284 | −1.06391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.17157 | −0.105896 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.1127 | −0.703366 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4853 | −0.382206 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 87.9411 | 2.92326 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.9411 | −0.828156 | −0.414078 | − | 0.910241i | \(-0.635896\pi\) | ||||
−0.414078 | + | 0.910241i | \(0.635896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.4558 | −1.83733 | −0.918667 | − | 0.395033i | \(-0.870733\pi\) | ||||
−0.918667 | + | 0.395033i | \(0.870733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.9706 | 0.958786 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.4558 | −1.37049 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.1716 | −0.335895 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3137 | −0.505153 | −0.252576 | − | 0.967577i | \(-0.581278\pi\) | ||||
−0.252576 | + | 0.967577i | \(0.581278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.1716 | −0.434018 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.1716 | 0.334801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.9706 | −1.21558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.0000 | −0.919641 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.6863 | −0.941167 | −0.470583 | − | 0.882356i | \(-0.655956\pi\) | ||||
−0.470583 | + | 0.882356i | \(0.655956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.6274 | −1.00377 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2843 | −0.795031 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −123.054 | −4.02429 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.6569 | −0.511487 | −0.255744 | − | 0.966745i | \(-0.582320\pi\) | ||||
−0.255744 | + | 0.966745i | \(0.582320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.9706 | −0.651715 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.7990 | 1.33001 | 0.665005 | − | 0.746839i | \(-0.268430\pi\) | ||||
0.665005 | + | 0.746839i | \(0.268430\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.97056 | 0.292122 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 73.2843 | 2.38394 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.1127 | −1.20600 | −0.603000 | − | 0.797741i | \(-0.706028\pi\) | ||||
−0.603000 | + | 0.797741i | \(0.706028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.17157 | 0.167876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.3137 | 0.950562 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.68629 | −0.184197 | −0.0920985 | − | 0.995750i | \(-0.529357\pi\) | ||||
−0.0920985 | + | 0.995750i | \(0.529357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1421 | 0.392910 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.3137 | 0.495022 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77.1127 | 2.49010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6274 | 0.986955 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.9706 | 0.739449 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.2010 | −0.488832 | −0.244416 | − | 0.969671i | \(-0.578596\pi\) | ||||
−0.244416 | + | 0.969671i | \(0.578596\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.6274 | 0.855396 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.5980 | −1.17449 | −0.587243 | − | 0.809411i | \(-0.699787\pi\) | ||||
−0.587243 | + | 0.809411i | \(0.699787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −71.4264 | −2.28983 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.65685 | −0.309267 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.28427 | 0.0730803 | 0.0365402 | − | 0.999332i | \(-0.488366\pi\) | ||||
0.0365402 | + | 0.999332i | \(0.488366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −85.2548 | −2.72476 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65685 | 0.244465 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.7696 | −0.694341 | −0.347170 | − | 0.937802i | \(-0.612857\pi\) | ||||
−0.347170 | + | 0.937802i | \(0.612857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.2548 | 2.17478 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 43.9706 | 1.39960 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.51472 | −0.302550 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0294 | −0.604490 | −0.302245 | − | 0.953230i | \(-0.597736\pi\) | ||||
−0.302245 | + | 0.953230i | \(0.597736\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9706 | −0.348140 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −87.9411 | −2.78792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.4558 | −0.869535 | −0.434768 | − | 0.900543i | \(-0.643170\pi\) | ||||
−0.434768 | + | 0.900543i | \(0.643170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.1421 | −0.605630 |
(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 | 3328.2.a.o.1.1 | 2 | ||
4.3 | odd | 2 | 3328.2.a.z.1.1 | 2 | |||
8.3 | odd | 2 | 3328.2.a.r.1.2 | 2 | |||
8.5 | even | 2 | 3328.2.a.ba.1.2 | 2 | |||
16.3 | odd | 4 | 1664.2.b.e.833.4 | yes | 4 | ||
16.5 | even | 4 | 1664.2.b.i.833.3 | yes | 4 | ||
16.11 | odd | 4 | 1664.2.b.e.833.1 | ✓ | 4 | ||
16.13 | even | 4 | 1664.2.b.i.833.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1664.2.b.e.833.1 | ✓ | 4 | 16.11 | odd | 4 | ||
1664.2.b.e.833.4 | yes | 4 | 16.3 | odd | 4 | ||
1664.2.b.i.833.2 | yes | 4 | 16.13 | even | 4 | ||
1664.2.b.i.833.3 | yes | 4 | 16.5 | even | 4 | ||
3328.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3328.2.a.r.1.2 | 2 | 8.3 | odd | 2 | |||
3328.2.a.z.1.1 | 2 | 4.3 | odd | 2 | |||
3328.2.a.ba.1.2 | 2 | 8.5 | even | 2 |