Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(1,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.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: | \(10.9235349965\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.59774\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59774 | −0.714529 | −0.357264 | − | 0.934003i | \(-0.616291\pi\) | ||||
−0.357264 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.94370 | 1.86854 | 0.934271 | − | 0.356563i | \(-0.116052\pi\) | ||||
0.934271 | + | 0.356563i | \(0.116052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59774 | −1.68778 | −0.843890 | − | 0.536516i | \(-0.819740\pi\) | ||||
−0.843890 | + | 0.536516i | \(0.819740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.49646 | −0.969742 | −0.484871 | − | 0.874586i | \(-0.661134\pi\) | ||||
−0.484871 | + | 0.874586i | \(0.661134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.09419 | −1.72059 | −0.860297 | − | 0.509793i | \(-0.829722\pi\) | ||||
−0.860297 | + | 0.509793i | \(0.829722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.19547 | 0.666302 | 0.333151 | − | 0.942874i | \(-0.391888\pi\) | ||||
0.333151 | + | 0.942874i | \(0.391888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44724 | −0.489448 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.69193 | 0.871269 | 0.435634 | − | 0.900124i | \(-0.356524\pi\) | ||||
0.435634 | + | 0.900124i | \(0.356524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.89872 | −1.33513 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50354 | −0.390988 | −0.195494 | − | 0.980705i | \(-0.562631\pi\) | ||||
−0.195494 | + | 0.980705i | \(0.562631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.94370 | −1.36390 | −0.681951 | − | 0.731398i | \(-0.738868\pi\) | ||||
−0.681951 | + | 0.731398i | \(0.738868\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.28966 | 0.917441 | 0.458721 | − | 0.888580i | \(-0.348308\pi\) | ||||
0.458721 | + | 0.888580i | \(0.348308\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.4402 | 2.49145 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.69901 | −0.782820 | −0.391410 | − | 0.920216i | \(-0.628013\pi\) | ||||
−0.391410 | + | 0.920216i | \(0.628013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.94370 | 1.20597 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.99291 | 0.910400 | 0.455200 | − | 0.890389i | \(-0.349568\pi\) | ||||
0.455200 | + | 0.890389i | \(0.349568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.44724 | −0.441374 | −0.220687 | − | 0.975345i | \(-0.570830\pi\) | ||||
−0.220687 | + | 0.975345i | \(0.570830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.58641 | 0.692909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3839 | −1.63510 | −0.817549 | − | 0.575859i | \(-0.804668\pi\) | ||||
−0.817549 | + | 0.575859i | \(0.804668\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3839 | −1.58837 | −0.794186 | − | 0.607675i | \(-0.792102\pi\) | ||||
−0.794186 | + | 0.607675i | \(0.792102\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44015 | −0.285599 | −0.142799 | − | 0.989752i | \(-0.545610\pi\) | ||||
−0.142799 | + | 0.989752i | \(0.545610\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.6735 | −3.15369 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.49646 | −1.06843 | −0.534217 | − | 0.845347i | \(-0.679394\pi\) | ||||
−0.534217 | + | 0.845347i | \(0.679394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.691927 | 0.0759488 | 0.0379744 | − | 0.999279i | \(-0.487909\pi\) | ||||
0.0379744 | + | 0.999279i | \(0.487909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.3346 | 1.22941 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.69193 | −0.921342 | −0.460671 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460671 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.2854 | −1.81200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59774 | 0.163924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.3909 | 1.66425 | 0.832124 | − | 0.554590i | \(-0.187125\pi\) | ||||
0.832124 | + | 0.554590i | \(0.187125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.49646 | −0.546918 | −0.273459 | − | 0.961884i | \(-0.588168\pi\) | ||||
−0.273459 | + | 0.961884i | \(0.588168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.992912 | 0.0978346 | 0.0489173 | − | 0.998803i | \(-0.484423\pi\) | ||||
0.0489173 | + | 0.998803i | \(0.484423\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.5793 | −1.98948 | −0.994739 | − | 0.102440i | \(-0.967335\pi\) | ||||
−0.994739 | + | 0.102440i | \(0.967335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3909 | −0.995272 | −0.497636 | − | 0.867386i | \(-0.665798\pi\) | ||||
−0.497636 | + | 0.867386i | \(0.665798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.0829 | 1.79517 | 0.897583 | − | 0.440846i | \(-0.145322\pi\) | ||||
0.897583 | + | 0.440846i | \(0.145322\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.10552 | −0.476092 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −35.0715 | −3.21500 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.3346 | 1.84860 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8987 | 1.06425 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3839 | 1.36510 | 0.682548 | − | 0.730841i | \(-0.260872\pi\) | ||||
0.682548 | + | 0.730841i | \(0.260872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.98159 | −0.609984 | −0.304992 | − | 0.952355i | \(-0.598654\pi\) | ||||
−0.304992 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.94370 | −0.428673 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.48513 | 0.468626 | 0.234313 | − | 0.972161i | \(-0.424716\pi\) | ||||
0.234313 | + | 0.972161i | \(0.424716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.943698 | 0.0800435 | 0.0400217 | − | 0.999199i | \(-0.487257\pi\) | ||||
0.0400217 | + | 0.999199i | \(0.487257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.5722 | 1.63671 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.49646 | −0.622547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.79321 | 0.392675 | 0.196337 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196337 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.49646 | −0.772811 | −0.386405 | − | 0.922329i | \(-0.626283\pi\) | ||||
−0.386405 | + | 0.922329i | \(0.626283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.58641 | 0.769999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.7974 | 1.24501 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.99291 | −0.234423 | −0.117211 | − | 0.993107i | \(-0.537396\pi\) | ||||
−0.117211 | + | 0.993107i | \(0.537396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1955 | 1.17586 | 0.587930 | − | 0.808912i | \(-0.299943\pi\) | ||||
0.587930 | + | 0.808912i | \(0.299943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.774794 | −0.0595995 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.0829 | 1.14673 | 0.573365 | − | 0.819300i | \(-0.305638\pi\) | ||||
0.573365 | + | 0.819300i | \(0.305638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0984 | −0.914555 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.57932 | 0.641249 | 0.320624 | − | 0.947206i | \(-0.396107\pi\) | ||||
0.320624 | + | 0.947206i | \(0.396107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8803 | 0.957386 | 0.478693 | − | 0.877982i | \(-0.341111\pi\) | ||||
0.478693 | + | 0.877982i | \(0.341111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.39094 | −0.469871 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.7114 | 2.90399 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.28966 | −0.455104 | −0.227552 | − | 0.973766i | \(-0.573072\pi\) | ||||
−0.227552 | + | 0.973766i | \(0.573072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.49646 | 0.683570 | 0.341785 | − | 0.939778i | \(-0.388969\pi\) | ||||
0.341785 | + | 0.939778i | \(0.388969\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.4965 | −1.53156 | −0.765780 | − | 0.643103i | \(-0.777647\pi\) | ||||
−0.765780 | + | 0.643103i | \(0.777647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.94370 | −0.634002 | −0.317001 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317001 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.1955 | 1.62800 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.59774 | 0.387203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.39094 | −0.164599 | −0.0822996 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822996 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.2897 | 0.974547 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.6622 | −2.01360 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.8045 | 1.66853 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.89448 | −0.327759 | −0.163879 | − | 0.986480i | \(-0.552401\pi\) | ||||
−0.163879 | + | 0.986480i | \(0.552401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1955 | 1.00856 | 0.504279 | − | 0.863541i | \(-0.331758\pi\) | ||||
0.504279 | + | 0.863541i | \(0.331758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.44015 | 0.425577 | 0.212789 | − | 0.977098i | \(-0.431745\pi\) | ||||
0.212789 | + | 0.977098i | \(0.431745\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.89163 | −0.451486 | −0.225743 | − | 0.974187i | \(-0.572481\pi\) | ||||
−0.225743 | + | 0.974187i | \(0.572481\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0492 | −0.655538 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.89163 | −0.187044 | −0.0935221 | − | 0.995617i | \(-0.529813\pi\) | ||||
−0.0935221 | + | 0.995617i | \(0.529813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.89448 | 0.315281 | 0.157641 | − | 0.987497i | \(-0.449611\pi\) | ||||
0.157641 | + | 0.987497i | \(0.449611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −27.8647 | −1.78021 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.49646 | 0.222474 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.5906 | 1.55215 | 0.776074 | − | 0.630642i | \(-0.217208\pi\) | ||||
0.776074 | + | 0.630642i | \(0.217208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8874 | −1.12457 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.50354 | 0.156167 | 0.0780834 | − | 0.996947i | \(-0.475120\pi\) | ||||
0.0780834 | + | 0.996947i | \(0.475120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.7748 | 1.22875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9058 | −0.795806 | −0.397903 | − | 0.917427i | \(-0.630262\pi\) | ||||
−0.397903 | + | 0.917427i | \(0.630262\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.10552 | 0.559347 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.691927 | 0.0421875 | 0.0210938 | − | 0.999778i | \(-0.493285\pi\) | ||||
0.0210938 | + | 0.999778i | \(0.493285\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7819 | −1.01943 | −0.509713 | − | 0.860344i | \(-0.670249\pi\) | ||||
−0.509713 | + | 0.860344i | \(0.670249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.6990 | 0.826082 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3346 | −1.76255 | −0.881274 | − | 0.472606i | \(-0.843313\pi\) | ||||
−0.881274 | + | 0.472606i | \(0.843313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.4667 | −1.93680 | −0.968401 | − | 0.249398i | \(-0.919767\pi\) | ||||
−0.968401 | + | 0.249398i | \(0.919767\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9508 | −1.06706 | −0.533532 | − | 0.845780i | \(-0.679136\pi\) | ||||
−0.533532 | + | 0.845780i | \(0.679136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.3768 | −0.730577 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.3276 | 1.96044 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.8803 | 1.33668 | 0.668341 | − | 0.743855i | \(-0.267005\pi\) | ||||
0.668341 | + | 0.743855i | \(0.267005\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.1728 | −0.650507 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.1728 | −0.646141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −44.2149 | −2.54851 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.50778 | 0.315375 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.39094 | −0.136458 | −0.0682291 | − | 0.997670i | \(-0.521735\pi\) | ||||
−0.0682291 | + | 0.997670i | \(0.521735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.89872 | 0.447895 | 0.223948 | − | 0.974601i | \(-0.428106\pi\) | ||||
0.223948 | + | 0.974601i | \(0.428106\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.7819 | 1.28771 | 0.643854 | − | 0.765148i | \(-0.277334\pi\) | ||||
0.643854 | + | 0.765148i | \(0.277334\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.49646 | 0.533374 | 0.266687 | − | 0.963783i | \(-0.414071\pi\) | ||||
0.266687 | + | 0.963783i | \(0.414071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.2642 | −1.47051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.09419 | 0.394731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.55668 | 0.474639 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.0942 | 1.71428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.39803 | 0.186773 | 0.0933863 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933863 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.3839 | 1.16832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.39094 | −0.457084 | −0.228542 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228542 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.5864 | 1.81881 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 51.6130 | 2.78684 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.9887 | −1.07305 | −0.536524 | − | 0.843885i | \(-0.680263\pi\) | ||||
−0.536524 | + | 0.843885i | \(0.680263\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4331 | −1.14729 | −0.573643 | − | 0.819106i | \(-0.694470\pi\) | ||||
−0.573643 | + | 0.819106i | \(0.694470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.7748 | −1.26540 | −0.632702 | − | 0.774395i | \(-0.718054\pi\) | ||||
−0.632702 | + | 0.774395i | \(0.718054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.3839 | 1.13494 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.8690 | 1.84031 | 0.920157 | − | 0.391549i | \(-0.128061\pi\) | ||||
0.920157 | + | 0.391549i | \(0.128061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.89872 | 0.204068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00709 | 0.261368 | 0.130684 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130684 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.1742 | −1.46273 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7819 | 1.28316 | 0.641579 | − | 0.767057i | \(-0.278280\pi\) | ||||
0.641579 | + | 0.767057i | \(0.278280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.4051 | −0.844906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.8874 | 0.713348 | 0.356674 | − | 0.934229i | \(-0.383911\pi\) | ||||
0.356674 | + | 0.934229i | \(0.383911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.7974 | −0.807212 | −0.403606 | − | 0.914933i | \(-0.632243\pi\) | ||||
−0.403606 | + | 0.914933i | \(0.632243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 44.2149 | 2.25340 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9958 | 0.658911 | 0.329456 | − | 0.944171i | \(-0.393135\pi\) | ||||
0.329456 | + | 0.944171i | \(0.393135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.6693 | −1.14643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.1728 | 0.763428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4472 | −0.775275 | −0.387637 | − | 0.921812i | \(-0.626709\pi\) | ||||
−0.387637 | + | 0.921812i | \(0.626709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.8945 | 1.44292 | 0.721461 | − | 0.692455i | \(-0.243471\pi\) | ||||
0.721461 | + | 0.692455i | \(0.243471\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9787 | 1.04503 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.3909 | −1.10988 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.7677 | 1.42247 | 0.711236 | − | 0.702954i | \(-0.248136\pi\) | ||||
0.711236 | + | 0.702954i | \(0.248136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.5709 | 1.70112 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.10552 | −0.0542676 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.08287 | 0.346021 | 0.173010 | − | 0.984920i | \(-0.444651\pi\) | ||||
0.173010 | + | 0.984920i | \(0.444651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6622 | 1.05575 | 0.527875 | − | 0.849322i | \(-0.322989\pi\) | ||||
0.527875 | + | 0.849322i | \(0.322989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.3612 | 0.842142 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.0421 | −0.824726 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8045 | 0.809446 | 0.404723 | − | 0.914439i | \(-0.367368\pi\) | ||||
0.404723 | + | 0.914439i | \(0.367368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.3839 | 0.547073 | 0.273537 | − | 0.961862i | \(-0.411807\pi\) | ||||
0.273537 | + | 0.961862i | \(0.411807\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.19547 | −0.152860 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.1586 | −1.67803 | −0.839015 | − | 0.544108i | \(-0.816868\pi\) | ||||
−0.839015 | + | 0.544108i | \(0.816868\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.3796 | −0.873242 | −0.436621 | − | 0.899646i | \(-0.643825\pi\) | ||||
−0.436621 | + | 0.899646i | \(0.643825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8874 | 0.658326 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8874 | −0.938544 | −0.469272 | − | 0.883054i | \(-0.655484\pi\) | ||||
−0.469272 | + | 0.883054i | \(0.655484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0142 | 0.659902 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.6175 | 1.29473 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.1094 | −1.73591 | −0.867953 | − | 0.496646i | \(-0.834565\pi\) | ||||
−0.867953 | + | 0.496646i | \(0.834565\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.2068 | −0.521952 | −0.260976 | − | 0.965345i | \(-0.584044\pi\) | ||||
−0.260976 | + | 0.965345i | \(0.584044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0633891 | −0.00294594 | −0.00147297 | − | 0.999999i | \(-0.500469\pi\) | ||||
−0.00147297 | + | 0.999999i | \(0.500469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.7493 | 1.93193 | 0.965963 | − | 0.258678i | \(-0.0832870\pi\) | ||||
0.965963 | + | 0.258678i | \(0.0832870\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −66.1657 | −3.05525 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.0645 | 2.30197 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.44724 | 0.112287 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.79744 | −0.356274 | −0.178137 | − | 0.984006i | \(-0.557007\pi\) | ||||
−0.178137 | + | 0.984006i | \(0.557007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.9858 | −0.637699 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.1884 | −1.18915 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5035 | 0.475961 | 0.237981 | − | 0.971270i | \(-0.423515\pi\) | ||||
0.237981 | + | 0.971270i | \(0.423515\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.31516 | −0.194740 | −0.0973702 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973702 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.2854 | −1.49910 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −66.1657 | −2.96794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.8382 | 0.529950 | 0.264975 | − | 0.964255i | \(-0.414636\pi\) | ||||
0.264975 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5722 | −0.694332 | −0.347166 | − | 0.937804i | \(-0.612856\pi\) | ||||
−0.347166 | + | 0.937804i | \(0.612856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.78188 | 0.390789 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.6848 | −0.695218 | −0.347609 | − | 0.937640i | \(-0.613006\pi\) | ||||
−0.347609 | + | 0.937640i | \(0.613006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0634 | −0.533653 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.58641 | −0.0699056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.2079 | −1.54844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.2783 | −1.32652 | −0.663259 | − | 0.748390i | \(-0.730827\pi\) | ||||
−0.663259 | + | 0.748390i | \(0.730827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.880309 | −0.0384932 | −0.0192466 | − | 0.999815i | \(-0.506127\pi\) | ||||
−0.0192466 | + | 0.999815i | \(0.506127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.5651 | 1.85417 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.7890 | −0.556042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.75353 | 0.379158 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.8803 | 1.42154 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −97.6254 | −4.20502 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.43307 | 0.405559 | 0.202780 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202780 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.6020 | 0.711150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.4894 | 0.961576 | 0.480788 | − | 0.876837i | \(-0.340351\pi\) | ||||
0.480788 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.69193 | −0.199883 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46.9476 | −1.99642 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.98159 | 0.126334 | 0.0631670 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631670 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.2713 | 1.32263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.3980 | 0.817529 | 0.408765 | − | 0.912640i | \(-0.365960\pi\) | ||||
0.408765 | + | 0.912640i | \(0.365960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.4894 | −1.28270 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.3081 | 0.474059 | 0.237030 | − | 0.971502i | \(-0.423826\pi\) | ||||
0.237030 | + | 0.971502i | \(0.423826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9929 | 0.460039 | 0.230020 | − | 0.973186i | \(-0.426121\pi\) | ||||
0.230020 | + | 0.973186i | \(0.426121\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.82009 | −0.326120 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.1023 | 1.83600 | 0.918002 | − | 0.396575i | \(-0.129801\pi\) | ||||
0.918002 | + | 0.396575i | \(0.129801\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.42068 | 0.141914 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.9016 | 1.32123 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.40226 | −0.0991521 | −0.0495760 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495760 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.7677 | −1.09922 | −0.549609 | − | 0.835422i | \(-0.685223\pi\) | ||||
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 56.0350 | 2.29721 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.60197 | −0.351467 | −0.175734 | − | 0.984438i | \(-0.556230\pi\) | ||||
−0.175734 | + | 0.984438i | \(0.556230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4965 | 1.20319 | 0.601593 | − | 0.798803i | \(-0.294533\pi\) | ||||
0.601593 | + | 0.798803i | \(0.294533\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.4894 | −1.32088 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.6161 | −0.512074 | −0.256037 | − | 0.966667i | \(-0.582417\pi\) | ||||
−0.256037 | + | 0.966667i | \(0.582417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.9915 | −0.889682 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3346 | −0.700139 | −0.350070 | − | 0.936724i | \(-0.613842\pi\) | ||||
−0.350070 | + | 0.936724i | \(0.613842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.6664 | −0.912516 | −0.456258 | − | 0.889848i | \(-0.650811\pi\) | ||||
−0.456258 | + | 0.889848i | \(0.650811\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.9703 | −1.72157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.77479 | −0.270992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.3768 | −1.13146 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.95787 | 0.117751 | 0.0588755 | − | 0.998265i | \(-0.481248\pi\) | ||||
0.0588755 | + | 0.998265i | \(0.481248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.5793 | −0.975401 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −60.9787 | −2.41607 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3081 | −0.446642 | −0.223321 | − | 0.974745i | \(-0.571690\pi\) | ||||
−0.223321 | + | 0.974745i | \(0.571690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.7256 | −0.856773 | −0.428387 | − | 0.903596i | \(-0.640918\pi\) | ||||
−0.428387 | + | 0.903596i | \(0.640918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.0942 | −1.06518 | −0.532591 | − | 0.846373i | \(-0.678782\pi\) | ||||
−0.532591 | + | 0.846373i | \(0.678782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.1445 | −1.53655 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.1912 | −1.25974 | −0.629870 | − | 0.776700i | \(-0.716892\pi\) | ||||
−0.629870 | + | 0.776700i | \(0.716892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1547 | 0.435851 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9703 | 0.427341 | 0.213670 | − | 0.976906i | \(-0.431458\pi\) | ||||
0.213670 | + | 0.976906i | \(0.431458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9929 | 0.427575 | 0.213787 | − | 0.976880i | \(-0.431420\pi\) | ||||
0.213787 | + | 0.976880i | \(0.431420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.89872 | 0.306299 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9929 | 0.580528 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.2967 | 0.744943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.2783 | −0.396201 | −0.198100 | − | 0.980182i | \(-0.563477\pi\) | ||||
−0.198100 | + | 0.980182i | \(0.563477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.4667 | 1.40153 | 0.700765 | − | 0.713392i | \(-0.252842\pi\) | ||||
0.700765 | + | 0.713392i | \(0.252842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 81.0319 | 3.10972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.5651 | −1.16954 | −0.584771 | − | 0.811198i | \(-0.698816\pi\) | ||||
−0.584771 | + | 0.811198i | \(0.698816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.76379 | −0.334847 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.9264 | 0.759134 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.82401 | −0.373723 | −0.186861 | − | 0.982386i | \(-0.559832\pi\) | ||||
−0.186861 | + | 0.982386i | \(0.559832\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.50778 | −0.0571934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.7606 | 0.672731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0531 | 1.28617 | 0.643085 | − | 0.765795i | \(-0.277654\pi\) | ||||
0.643085 | + | 0.765795i | \(0.277654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.1728 | −1.02194 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.76771 | 0.329278 | 0.164639 | − | 0.986354i | \(-0.447354\pi\) | ||||
0.164639 | + | 0.986354i | \(0.447354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.1728 | −0.718028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.2713 | −1.16948 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1013 | −0.898826 | −0.449413 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449413 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.90866 | 0.182808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.4823 | −0.426441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.8240 | −1.40281 | −0.701407 | − | 0.712761i | \(-0.747445\pi\) | ||||
−0.701407 | + | 0.712761i | \(0.747445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.4483 | 2.34672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.00000 | −0.221615 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 74.9193 | 2.75969 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0421 | −0.479762 | −0.239881 | − | 0.970802i | \(-0.577108\pi\) | ||||
−0.239881 | + | 0.970802i | \(0.577108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.7890 | −0.505868 | −0.252934 | − | 0.967484i | \(-0.581396\pi\) | ||||
−0.252934 | + | 0.967484i | \(0.581396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.65827 | −0.280577 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −101.738 | −3.71742 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.8874 | 0.725701 | 0.362851 | − | 0.931847i | \(-0.381803\pi\) | ||||
0.362851 | + | 0.931847i | \(0.381803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.1728 | 0.552196 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4543 | −0.888808 | −0.444404 | − | 0.895827i | \(-0.646584\pi\) | ||||
−0.444404 | + | 0.895827i | \(0.646584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.4696 | 1.53952 | 0.769760 | − | 0.638333i | \(-0.220376\pi\) | ||||
0.769760 | + | 0.638333i | \(0.220376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.3697 | −1.85971 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.4504 | −0.882853 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.54567 | 0.272104 | 0.136052 | − | 0.990702i | \(-0.456559\pi\) | ||||
0.136052 | + | 0.990702i | \(0.456559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5035 | 0.809396 | 0.404698 | − | 0.914450i | \(-0.367377\pi\) | ||||
0.404698 | + | 0.914450i | \(0.367377\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6835 | 0.527445 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.50354 | 0.0896988 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 74.9193 | 2.68082 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.19547 | −0.114051 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.7819 | 0.883379 | 0.441689 | − | 0.897168i | \(-0.354379\pi\) | ||||
0.441689 | + | 0.897168i | \(0.354379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 94.3399 | 3.35434 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0531 | 0.428019 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.11260 | 0.287363 | 0.143682 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143682 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.6201 | −1.57854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6593 | 0.482028 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.2401 | −0.889598 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.6948 | −0.657273 | −0.328637 | − | 0.944456i | \(-0.606589\pi\) | ||||
−0.328637 | + | 0.944456i | \(0.606589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.0460 | −1.09017 | −0.545087 | − | 0.838379i | \(-0.683503\pi\) | ||||
−0.545087 | + | 0.838379i | \(0.683503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.78188 | 0.167502 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.94370 | 0.312900 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.5977 | 0.614165 | 0.307083 | − | 0.951683i | \(-0.400647\pi\) | ||||
0.307083 | + | 0.951683i | \(0.400647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.7327 | 0.513549 | 0.256774 | − | 0.966471i | \(-0.417340\pi\) | ||||
0.256774 | + | 0.966471i | \(0.417340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.5638 | −1.58441 | −0.792204 | − | 0.610257i | \(-0.791066\pi\) | ||||
−0.792204 | + | 0.610257i | \(0.791066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.7890 | −0.895688 | −0.447844 | − | 0.894112i | \(-0.647808\pi\) | ||||
−0.447844 | + | 0.894112i | \(0.647808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −123.724 | −4.28678 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.2783 | −0.840187 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.97026 | 0.102545 | 0.0512725 | − | 0.998685i | \(-0.483672\pi\) | ||||
0.0512725 | + | 0.998685i | \(0.483672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.98582 | −0.240891 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.23792 | 0.0425856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 100.528 | 3.45419 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7819 | 0.438157 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.5567 | 1.86798 | 0.933992 | − | 0.357293i | \(-0.116300\pi\) | ||||
0.933992 | + | 0.357293i | \(0.116300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.27125 | 0.316700 | 0.158350 | − | 0.987383i | \(-0.449383\pi\) | ||||
0.158350 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.85236 | −0.199680 | −0.0998399 | − | 0.995004i | \(-0.531833\pi\) | ||||
−0.0998399 | + | 0.995004i | \(0.531833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.5496 | −1.61861 | −0.809303 | − | 0.587391i | \(-0.800155\pi\) | ||||
−0.809303 | + | 0.587391i | \(0.800155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.0984 | −0.819371 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.1586 | 1.80328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.7961 | 1.58562 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 58.8237 | 1.98860 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.6622 | 1.13669 | 0.568346 | − | 0.822790i | \(-0.307584\pi\) | ||||
0.568346 | + | 0.822790i | \(0.307584\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.6664 | −1.03318 | −0.516589 | − | 0.856233i | \(-0.672799\pi\) | ||||
−0.516589 | + | 0.856233i | \(0.672799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.6059 | −1.02997 | −0.514985 | − | 0.857199i | \(-0.672203\pi\) | ||||
−0.514985 | + | 0.857199i | \(0.672203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.7606 | −1.13357 | −0.566785 | − | 0.823866i | \(-0.691813\pi\) | ||||
−0.566785 | + | 0.823866i | \(0.691813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 76.0531 | 2.55074 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.28966 | −0.210476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.7075 | −0.458191 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.1516 | −0.938907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.4299 | 1.34692 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5793 | −0.684080 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.87322 | −0.261426 | −0.130713 | − | 0.991420i | \(-0.541727\pi\) | ||||
−0.130713 | + | 0.991420i | \(0.541727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.02974 | 0.166643 | 0.0833213 | − | 0.996523i | \(-0.473447\pi\) | ||||
0.0833213 | + | 0.996523i | \(0.473447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.87322 | −0.128185 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.5149 | −1.13978 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.7890 | −1.11460 | −0.557298 | − | 0.830313i | \(-0.688162\pi\) | ||||
−0.557298 | + | 0.830313i | \(0.688162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.7961 | 1.54031 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.78897 | −0.321859 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.38385 | −0.0454028 | −0.0227014 | − | 0.999742i | \(-0.507227\pi\) | ||||
−0.0227014 | + | 0.999742i | \(0.507227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.4402 | −0.571578 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.4483 | −2.07498 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.2362 | −1.08578 | −0.542890 | − | 0.839804i | \(-0.682670\pi\) | ||||
−0.542890 | + | 0.839804i | \(0.682670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.4880 | −1.02648 | −0.513239 | − | 0.858245i | \(-0.671555\pi\) | ||||
−0.513239 | + | 0.858245i | \(0.671555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.6778 | −1.51682 | −0.758412 | − | 0.651776i | \(-0.774024\pi\) | ||||
−0.758412 | + | 0.651776i | \(0.774024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.53189 | 0.276957 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.4894 | −1.44115 | −0.720576 | − | 0.693376i | \(-0.756123\pi\) | ||||
−0.720576 | + | 0.693376i | \(0.756123\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0492 | 0.325185 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.1168 | 0.875648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.1728 | −0.488430 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9858 | −0.707016 | −0.353508 | − | 0.935431i | \(-0.615011\pi\) | ||||
−0.353508 | + | 0.935431i | \(0.615011\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0000 | 1.28366 | 0.641831 | − | 0.766846i | \(-0.278175\pi\) | ||||
0.641831 | + | 0.766846i | \(0.278175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.66536 | 0.149565 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.69901 | 0.182328 | 0.0911638 | − | 0.995836i | \(-0.470941\pi\) | ||||
0.0911638 | + | 0.995836i | \(0.470941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.6551 | 1.55502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.1586 | −1.56792 | −0.783959 | − | 0.620813i | \(-0.786803\pi\) | ||||
−0.783959 | + | 0.620813i | \(0.786803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.3456 | 1.09434 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.5793 | −0.908770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.90866 | −0.0923966 | −0.0461983 | − | 0.998932i | \(-0.514711\pi\) | ||||
−0.0461983 | + | 0.998932i | \(0.514711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2897 | 0.453013 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.0882 | −1.83967 | −0.919835 | − | 0.392305i | \(-0.871678\pi\) | ||||
−0.919835 | + | 0.392305i | \(0.871678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1368.2.a.o.1.1 | yes | 3 | |
3.2 | odd | 2 | 1368.2.a.m.1.3 | ✓ | 3 | ||
4.3 | odd | 2 | 2736.2.a.be.1.1 | 3 | |||
12.11 | even | 2 | 2736.2.a.bc.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.a.m.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1368.2.a.o.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
2736.2.a.bc.1.3 | 3 | 12.11 | even | 2 | |||
2736.2.a.be.1.1 | 3 | 4.3 | odd | 2 |