Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 14 x^{10} + 13 x^{9} + 70 x^{8} - 61 x^{7} - 152 x^{6} + 127 x^{5} + 138 x^{4} + \cdots + 1 \) |
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 | 1.8 | ||
Root | \(-0.679772\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.679772 | 0.480672 | 0.240336 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240336 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.53791 | −0.768955 | ||||||||
\(5\) | −3.36496 | −1.50486 | −0.752428 | − | 0.658674i | \(-0.771118\pi\) | ||||
−0.752428 | + | 0.658674i | \(0.771118\pi\) | |||||||
\(6\) | −0.679772 | −0.277516 | ||||||||
\(7\) | 0.0622521 | 0.0235291 | 0.0117645 | − | 0.999931i | \(-0.496255\pi\) | ||||
0.0117645 | + | 0.999931i | \(0.496255\pi\) | |||||||
\(8\) | −2.40497 | −0.850286 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.28741 | −0.723342 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.53791 | 0.443956 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.0423172 | 0.0113098 | ||||||||
\(15\) | 3.36496 | 0.868829 | ||||||||
\(16\) | 1.44099 | 0.360246 | ||||||||
\(17\) | −2.45300 | −0.594941 | −0.297470 | − | 0.954731i | \(-0.596143\pi\) | ||||
−0.297470 | + | 0.954731i | \(0.596143\pi\) | |||||||
\(18\) | 0.679772 | 0.160224 | ||||||||
\(19\) | −0.283042 | −0.0649343 | −0.0324671 | − | 0.999473i | \(-0.510336\pi\) | ||||
−0.0324671 | + | 0.999473i | \(0.510336\pi\) | |||||||
\(20\) | 5.17501 | 1.15717 | ||||||||
\(21\) | −0.0622521 | −0.0135845 | ||||||||
\(22\) | −0.679772 | −0.144928 | ||||||||
\(23\) | 1.33715 | 0.278814 | 0.139407 | − | 0.990235i | \(-0.455480\pi\) | ||||
0.139407 | + | 0.990235i | \(0.455480\pi\) | |||||||
\(24\) | 2.40497 | 0.490913 | ||||||||
\(25\) | 6.32297 | 1.26459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0957381 | −0.0180928 | ||||||||
\(29\) | 2.25549 | 0.418834 | 0.209417 | − | 0.977826i | \(-0.432843\pi\) | ||||
0.209417 | + | 0.977826i | \(0.432843\pi\) | |||||||
\(30\) | 2.28741 | 0.417622 | ||||||||
\(31\) | 6.67832 | 1.19946 | 0.599731 | − | 0.800202i | \(-0.295274\pi\) | ||||
0.599731 | + | 0.800202i | \(0.295274\pi\) | |||||||
\(32\) | 5.78949 | 1.02345 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −1.66748 | −0.285971 | ||||||||
\(35\) | −0.209476 | −0.0354079 | ||||||||
\(36\) | −1.53791 | −0.256318 | ||||||||
\(37\) | 3.56253 | 0.585677 | 0.292838 | − | 0.956162i | \(-0.405400\pi\) | ||||
0.292838 | + | 0.956162i | \(0.405400\pi\) | |||||||
\(38\) | −0.192404 | −0.0312121 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.09264 | 1.27956 | ||||||||
\(41\) | 10.0209 | 1.56501 | 0.782503 | − | 0.622647i | \(-0.213943\pi\) | ||||
0.782503 | + | 0.622647i | \(0.213943\pi\) | |||||||
\(42\) | −0.0423172 | −0.00652969 | ||||||||
\(43\) | −8.65994 | −1.32063 | −0.660314 | − | 0.750989i | \(-0.729577\pi\) | ||||
−0.660314 | + | 0.750989i | \(0.729577\pi\) | |||||||
\(44\) | 1.53791 | 0.231849 | ||||||||
\(45\) | −3.36496 | −0.501619 | ||||||||
\(46\) | 0.908955 | 0.134018 | ||||||||
\(47\) | −4.79855 | −0.699940 | −0.349970 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349970 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(48\) | −1.44099 | −0.207988 | ||||||||
\(49\) | −6.99612 | −0.999446 | ||||||||
\(50\) | 4.29818 | 0.607854 | ||||||||
\(51\) | 2.45300 | 0.343489 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.34343 | 0.596616 | 0.298308 | − | 0.954470i | \(-0.403578\pi\) | ||||
0.298308 | + | 0.954470i | \(0.403578\pi\) | |||||||
\(54\) | −0.679772 | −0.0925053 | ||||||||
\(55\) | 3.36496 | 0.453731 | ||||||||
\(56\) | −0.149715 | −0.0200065 | ||||||||
\(57\) | 0.283042 | 0.0374898 | ||||||||
\(58\) | 1.53322 | 0.201322 | ||||||||
\(59\) | 13.7575 | 1.79108 | 0.895539 | − | 0.444983i | \(-0.146790\pi\) | ||||
0.895539 | + | 0.444983i | \(0.146790\pi\) | |||||||
\(60\) | −5.17501 | −0.668091 | ||||||||
\(61\) | 2.03838 | 0.260987 | 0.130494 | − | 0.991449i | \(-0.458344\pi\) | ||||
0.130494 | + | 0.991449i | \(0.458344\pi\) | |||||||
\(62\) | 4.53974 | 0.576547 | ||||||||
\(63\) | 0.0622521 | 0.00784303 | ||||||||
\(64\) | 1.05356 | 0.131695 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.679772 | 0.0836742 | ||||||||
\(67\) | −2.33966 | −0.285835 | −0.142918 | − | 0.989735i | \(-0.545648\pi\) | ||||
−0.142918 | + | 0.989735i | \(0.545648\pi\) | |||||||
\(68\) | 3.77250 | 0.457483 | ||||||||
\(69\) | −1.33715 | −0.160974 | ||||||||
\(70\) | −0.142396 | −0.0170196 | ||||||||
\(71\) | 8.74173 | 1.03745 | 0.518726 | − | 0.854940i | \(-0.326406\pi\) | ||||
0.518726 | + | 0.854940i | \(0.326406\pi\) | |||||||
\(72\) | −2.40497 | −0.283429 | ||||||||
\(73\) | −13.1075 | −1.53411 | −0.767057 | − | 0.641579i | \(-0.778279\pi\) | ||||
−0.767057 | + | 0.641579i | \(0.778279\pi\) | |||||||
\(74\) | 2.42171 | 0.281518 | ||||||||
\(75\) | −6.32297 | −0.730114 | ||||||||
\(76\) | 0.435293 | 0.0499315 | ||||||||
\(77\) | −0.0622521 | −0.00709428 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.65672 | 0.186396 | 0.0931979 | − | 0.995648i | \(-0.470291\pi\) | ||||
0.0931979 | + | 0.995648i | \(0.470291\pi\) | |||||||
\(80\) | −4.84886 | −0.542119 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.81195 | 0.752254 | ||||||||
\(83\) | 5.86499 | 0.643767 | 0.321883 | − | 0.946779i | \(-0.395684\pi\) | ||||
0.321883 | + | 0.946779i | \(0.395684\pi\) | |||||||
\(84\) | 0.0957381 | 0.0104459 | ||||||||
\(85\) | 8.25426 | 0.895301 | ||||||||
\(86\) | −5.88679 | −0.634789 | ||||||||
\(87\) | −2.25549 | −0.241814 | ||||||||
\(88\) | 2.40497 | 0.256371 | ||||||||
\(89\) | 7.18799 | 0.761925 | 0.380963 | − | 0.924590i | \(-0.375593\pi\) | ||||
0.380963 | + | 0.924590i | \(0.375593\pi\) | |||||||
\(90\) | −2.28741 | −0.241114 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.05641 | −0.214396 | ||||||||
\(93\) | −6.67832 | −0.692510 | ||||||||
\(94\) | −3.26192 | −0.336441 | ||||||||
\(95\) | 0.952425 | 0.0977168 | ||||||||
\(96\) | −5.78949 | −0.590887 | ||||||||
\(97\) | −8.30250 | −0.842991 | −0.421495 | − | 0.906831i | \(-0.638495\pi\) | ||||
−0.421495 | + | 0.906831i | \(0.638495\pi\) | |||||||
\(98\) | −4.75577 | −0.480405 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −9.72416 | −0.972416 | ||||||||
\(101\) | −1.60575 | −0.159778 | −0.0798890 | − | 0.996804i | \(-0.525457\pi\) | ||||
−0.0798890 | + | 0.996804i | \(0.525457\pi\) | |||||||
\(102\) | 1.66748 | 0.165106 | ||||||||
\(103\) | −7.09787 | −0.699374 | −0.349687 | − | 0.936867i | \(-0.613712\pi\) | ||||
−0.349687 | + | 0.936867i | \(0.613712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.209476 | 0.0204428 | ||||||||
\(106\) | 2.95254 | 0.286776 | ||||||||
\(107\) | −8.02814 | −0.776110 | −0.388055 | − | 0.921636i | \(-0.626853\pi\) | ||||
−0.388055 | + | 0.921636i | \(0.626853\pi\) | |||||||
\(108\) | 1.53791 | 0.147985 | ||||||||
\(109\) | −0.0538086 | −0.00515393 | −0.00257696 | − | 0.999997i | \(-0.500820\pi\) | ||||
−0.00257696 | + | 0.999997i | \(0.500820\pi\) | |||||||
\(110\) | 2.28741 | 0.218096 | ||||||||
\(111\) | −3.56253 | −0.338141 | ||||||||
\(112\) | 0.0897044 | 0.00847627 | ||||||||
\(113\) | −3.42218 | −0.321931 | −0.160966 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160966 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(114\) | 0.192404 | 0.0180203 | ||||||||
\(115\) | −4.49945 | −0.419576 | ||||||||
\(116\) | −3.46874 | −0.322065 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.35199 | 0.860920 | ||||||||
\(119\) | −0.152705 | −0.0139984 | ||||||||
\(120\) | −8.09264 | −0.738754 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.38563 | 0.125449 | ||||||||
\(123\) | −10.0209 | −0.903556 | ||||||||
\(124\) | −10.2707 | −0.922332 | ||||||||
\(125\) | −4.45174 | −0.398176 | ||||||||
\(126\) | 0.0423172 | 0.00376992 | ||||||||
\(127\) | −13.5267 | −1.20030 | −0.600150 | − | 0.799888i | \(-0.704892\pi\) | ||||
−0.600150 | + | 0.799888i | \(0.704892\pi\) | |||||||
\(128\) | −10.8628 | −0.960144 | ||||||||
\(129\) | 8.65994 | 0.762465 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4271 | −1.60999 | −0.804993 | − | 0.593284i | \(-0.797831\pi\) | ||||
−0.804993 | + | 0.593284i | \(0.797831\pi\) | |||||||
\(132\) | −1.53791 | −0.133858 | ||||||||
\(133\) | −0.0176200 | −0.00152784 | ||||||||
\(134\) | −1.59044 | −0.137393 | ||||||||
\(135\) | 3.36496 | 0.289610 | ||||||||
\(136\) | 5.89941 | 0.505870 | ||||||||
\(137\) | 16.5528 | 1.41420 | 0.707102 | − | 0.707112i | \(-0.250002\pi\) | ||||
0.707102 | + | 0.707112i | \(0.250002\pi\) | |||||||
\(138\) | −0.908955 | −0.0773754 | ||||||||
\(139\) | 16.7090 | 1.41724 | 0.708619 | − | 0.705591i | \(-0.249318\pi\) | ||||
0.708619 | + | 0.705591i | \(0.249318\pi\) | |||||||
\(140\) | 0.322155 | 0.0272271 | ||||||||
\(141\) | 4.79855 | 0.404111 | ||||||||
\(142\) | 5.94239 | 0.498674 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.44099 | 0.120082 | ||||||||
\(145\) | −7.58964 | −0.630286 | ||||||||
\(146\) | −8.91009 | −0.737405 | ||||||||
\(147\) | 6.99612 | 0.577031 | ||||||||
\(148\) | −5.47885 | −0.450359 | ||||||||
\(149\) | −6.37375 | −0.522158 | −0.261079 | − | 0.965317i | \(-0.584078\pi\) | ||||
−0.261079 | + | 0.965317i | \(0.584078\pi\) | |||||||
\(150\) | −4.29818 | −0.350945 | ||||||||
\(151\) | −20.4640 | −1.66534 | −0.832670 | − | 0.553770i | \(-0.813189\pi\) | ||||
−0.832670 | + | 0.553770i | \(0.813189\pi\) | |||||||
\(152\) | 0.680708 | 0.0552127 | ||||||||
\(153\) | −2.45300 | −0.198314 | ||||||||
\(154\) | −0.0423172 | −0.00341002 | ||||||||
\(155\) | −22.4723 | −1.80502 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.501348 | 0.0400119 | 0.0200060 | − | 0.999800i | \(-0.493631\pi\) | ||||
0.0200060 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(158\) | 1.12619 | 0.0895952 | ||||||||
\(159\) | −4.34343 | −0.344456 | ||||||||
\(160\) | −19.4814 | −1.54014 | ||||||||
\(161\) | 0.0832402 | 0.00656025 | ||||||||
\(162\) | 0.679772 | 0.0534080 | ||||||||
\(163\) | 9.68039 | 0.758227 | 0.379113 | − | 0.925350i | \(-0.376229\pi\) | ||||
0.379113 | + | 0.925350i | \(0.376229\pi\) | |||||||
\(164\) | −15.4113 | −1.20342 | ||||||||
\(165\) | −3.36496 | −0.261962 | ||||||||
\(166\) | 3.98686 | 0.309440 | ||||||||
\(167\) | 3.66836 | 0.283866 | 0.141933 | − | 0.989876i | \(-0.454668\pi\) | ||||
0.141933 | + | 0.989876i | \(0.454668\pi\) | |||||||
\(168\) | 0.149715 | 0.0115507 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.61102 | 0.430346 | ||||||||
\(171\) | −0.283042 | −0.0216448 | ||||||||
\(172\) | 13.3182 | 1.01550 | ||||||||
\(173\) | 13.6952 | 1.04123 | 0.520615 | − | 0.853792i | \(-0.325703\pi\) | ||||
0.520615 | + | 0.853792i | \(0.325703\pi\) | |||||||
\(174\) | −1.53322 | −0.116233 | ||||||||
\(175\) | 0.393618 | 0.0297547 | ||||||||
\(176\) | −1.44099 | −0.108618 | ||||||||
\(177\) | −13.7575 | −1.03408 | ||||||||
\(178\) | 4.88619 | 0.366236 | ||||||||
\(179\) | 18.7715 | 1.40305 | 0.701524 | − | 0.712646i | \(-0.252503\pi\) | ||||
0.701524 | + | 0.712646i | \(0.252503\pi\) | |||||||
\(180\) | 5.17501 | 0.385722 | ||||||||
\(181\) | −4.63979 | −0.344873 | −0.172436 | − | 0.985021i | \(-0.555164\pi\) | ||||
−0.172436 | + | 0.985021i | \(0.555164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.03838 | −0.150681 | ||||||||
\(184\) | −3.21580 | −0.237072 | ||||||||
\(185\) | −11.9878 | −0.881360 | ||||||||
\(186\) | −4.53974 | −0.332870 | ||||||||
\(187\) | 2.45300 | 0.179381 | ||||||||
\(188\) | 7.37974 | 0.538223 | ||||||||
\(189\) | −0.0622521 | −0.00452817 | ||||||||
\(190\) | 0.647432 | 0.0469697 | ||||||||
\(191\) | 26.3850 | 1.90915 | 0.954576 | − | 0.297968i | \(-0.0963089\pi\) | ||||
0.954576 | + | 0.297968i | \(0.0963089\pi\) | |||||||
\(192\) | −1.05356 | −0.0760343 | ||||||||
\(193\) | −16.8077 | −1.20985 | −0.604923 | − | 0.796284i | \(-0.706796\pi\) | ||||
−0.604923 | + | 0.796284i | \(0.706796\pi\) | |||||||
\(194\) | −5.64381 | −0.405202 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.7594 | 0.768529 | ||||||||
\(197\) | −21.1316 | −1.50556 | −0.752781 | − | 0.658271i | \(-0.771288\pi\) | ||||
−0.752781 | + | 0.658271i | \(0.771288\pi\) | |||||||
\(198\) | −0.679772 | −0.0483093 | ||||||||
\(199\) | −21.7455 | −1.54150 | −0.770750 | − | 0.637138i | \(-0.780118\pi\) | ||||
−0.770750 | + | 0.637138i | \(0.780118\pi\) | |||||||
\(200\) | −15.2066 | −1.07527 | ||||||||
\(201\) | 2.33966 | 0.165027 | ||||||||
\(202\) | −1.09154 | −0.0768007 | ||||||||
\(203\) | 0.140409 | 0.00985479 | ||||||||
\(204\) | −3.77250 | −0.264128 | ||||||||
\(205\) | −33.7200 | −2.35511 | ||||||||
\(206\) | −4.82494 | −0.336169 | ||||||||
\(207\) | 1.33715 | 0.0929381 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.283042 | 0.0195784 | ||||||||
\(210\) | 0.142396 | 0.00982625 | ||||||||
\(211\) | 3.29543 | 0.226867 | 0.113433 | − | 0.993546i | \(-0.463815\pi\) | ||||
0.113433 | + | 0.993546i | \(0.463815\pi\) | |||||||
\(212\) | −6.67980 | −0.458771 | ||||||||
\(213\) | −8.74173 | −0.598974 | ||||||||
\(214\) | −5.45731 | −0.373054 | ||||||||
\(215\) | 29.1404 | 1.98736 | ||||||||
\(216\) | 2.40497 | 0.163638 | ||||||||
\(217\) | 0.415740 | 0.0282222 | ||||||||
\(218\) | −0.0365776 | −0.00247735 | ||||||||
\(219\) | 13.1075 | 0.885721 | ||||||||
\(220\) | −5.17501 | −0.348899 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.42171 | −0.162535 | ||||||||
\(223\) | −21.5223 | −1.44124 | −0.720619 | − | 0.693332i | \(-0.756142\pi\) | ||||
−0.720619 | + | 0.693332i | \(0.756142\pi\) | |||||||
\(224\) | 0.360408 | 0.0240808 | ||||||||
\(225\) | 6.32297 | 0.421531 | ||||||||
\(226\) | −2.32630 | −0.154743 | ||||||||
\(227\) | −8.47294 | −0.562369 | −0.281184 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281184 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(228\) | −0.435293 | −0.0288280 | ||||||||
\(229\) | 14.9492 | 0.987870 | 0.493935 | − | 0.869499i | \(-0.335558\pi\) | ||||
0.493935 | + | 0.869499i | \(0.335558\pi\) | |||||||
\(230\) | −3.05860 | −0.201678 | ||||||||
\(231\) | 0.0622521 | 0.00409589 | ||||||||
\(232\) | −5.42440 | −0.356129 | ||||||||
\(233\) | −27.6123 | −1.80894 | −0.904470 | − | 0.426538i | \(-0.859733\pi\) | ||||
−0.904470 | + | 0.426538i | \(0.859733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1469 | 1.05331 | ||||||||
\(236\) | −21.1578 | −1.37726 | ||||||||
\(237\) | −1.65672 | −0.107616 | ||||||||
\(238\) | −0.103804 | −0.00672864 | ||||||||
\(239\) | 3.17249 | 0.205211 | 0.102606 | − | 0.994722i | \(-0.467282\pi\) | ||||
0.102606 | + | 0.994722i | \(0.467282\pi\) | |||||||
\(240\) | 4.84886 | 0.312993 | ||||||||
\(241\) | −3.37747 | −0.217562 | −0.108781 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108781 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(242\) | 0.679772 | 0.0436974 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.13484 | −0.200687 | ||||||||
\(245\) | 23.5417 | 1.50402 | ||||||||
\(246\) | −6.81195 | −0.434314 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.0612 | −1.01989 | ||||||||
\(249\) | −5.86499 | −0.371679 | ||||||||
\(250\) | −3.02617 | −0.191392 | ||||||||
\(251\) | −11.8347 | −0.747000 | −0.373500 | − | 0.927630i | \(-0.621842\pi\) | ||||
−0.373500 | + | 0.927630i | \(0.621842\pi\) | |||||||
\(252\) | −0.0957381 | −0.00603093 | ||||||||
\(253\) | −1.33715 | −0.0840657 | ||||||||
\(254\) | −9.19506 | −0.576950 | ||||||||
\(255\) | −8.25426 | −0.516902 | ||||||||
\(256\) | −9.49135 | −0.593209 | ||||||||
\(257\) | 4.07570 | 0.254235 | 0.127118 | − | 0.991888i | \(-0.459427\pi\) | ||||
0.127118 | + | 0.991888i | \(0.459427\pi\) | |||||||
\(258\) | 5.88679 | 0.366495 | ||||||||
\(259\) | 0.221775 | 0.0137804 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.25549 | 0.139611 | ||||||||
\(262\) | −12.5263 | −0.773874 | ||||||||
\(263\) | −25.1902 | −1.55330 | −0.776648 | − | 0.629934i | \(-0.783082\pi\) | ||||
−0.776648 | + | 0.629934i | \(0.783082\pi\) | |||||||
\(264\) | −2.40497 | −0.148016 | ||||||||
\(265\) | −14.6155 | −0.897821 | ||||||||
\(266\) | −0.0119776 | −0.000734391 0 | ||||||||
\(267\) | −7.18799 | −0.439898 | ||||||||
\(268\) | 3.59819 | 0.219795 | ||||||||
\(269\) | 23.4644 | 1.43065 | 0.715325 | − | 0.698792i | \(-0.246279\pi\) | ||||
0.715325 | + | 0.698792i | \(0.246279\pi\) | |||||||
\(270\) | 2.28741 | 0.139207 | ||||||||
\(271\) | −8.84070 | −0.537034 | −0.268517 | − | 0.963275i | \(-0.586534\pi\) | ||||
−0.268517 | + | 0.963275i | \(0.586534\pi\) | |||||||
\(272\) | −3.53474 | −0.214325 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2522 | 0.679768 | ||||||||
\(275\) | −6.32297 | −0.381289 | ||||||||
\(276\) | 2.05641 | 0.123781 | ||||||||
\(277\) | 3.88461 | 0.233404 | 0.116702 | − | 0.993167i | \(-0.462768\pi\) | ||||
0.116702 | + | 0.993167i | \(0.462768\pi\) | |||||||
\(278\) | 11.3583 | 0.681226 | ||||||||
\(279\) | 6.67832 | 0.399821 | ||||||||
\(280\) | 0.503784 | 0.0301068 | ||||||||
\(281\) | 15.4133 | 0.919480 | 0.459740 | − | 0.888054i | \(-0.347943\pi\) | ||||
0.459740 | + | 0.888054i | \(0.347943\pi\) | |||||||
\(282\) | 3.26192 | 0.194245 | ||||||||
\(283\) | −16.1099 | −0.957632 | −0.478816 | − | 0.877915i | \(-0.658934\pi\) | ||||
−0.478816 | + | 0.877915i | \(0.658934\pi\) | |||||||
\(284\) | −13.4440 | −0.797754 | ||||||||
\(285\) | −0.952425 | −0.0564168 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.623823 | 0.0368231 | ||||||||
\(288\) | 5.78949 | 0.341149 | ||||||||
\(289\) | −10.9828 | −0.646045 | ||||||||
\(290\) | −5.15923 | −0.302960 | ||||||||
\(291\) | 8.30250 | 0.486701 | ||||||||
\(292\) | 20.1581 | 1.17966 | ||||||||
\(293\) | −4.23935 | −0.247666 | −0.123833 | − | 0.992303i | \(-0.539519\pi\) | ||||
−0.123833 | + | 0.992303i | \(0.539519\pi\) | |||||||
\(294\) | 4.75577 | 0.277362 | ||||||||
\(295\) | −46.2936 | −2.69532 | ||||||||
\(296\) | −8.56779 | −0.497993 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −4.33270 | −0.250987 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9.72416 | 0.561424 | ||||||||
\(301\) | −0.539099 | −0.0310732 | ||||||||
\(302\) | −13.9109 | −0.800481 | ||||||||
\(303\) | 1.60575 | 0.0922479 | ||||||||
\(304\) | −0.407859 | −0.0233923 | ||||||||
\(305\) | −6.85906 | −0.392749 | ||||||||
\(306\) | −1.66748 | −0.0953237 | ||||||||
\(307\) | 27.1091 | 1.54720 | 0.773598 | − | 0.633677i | \(-0.218455\pi\) | ||||
0.773598 | + | 0.633677i | \(0.218455\pi\) | |||||||
\(308\) | 0.0957381 | 0.00545518 | ||||||||
\(309\) | 7.09787 | 0.403784 | ||||||||
\(310\) | −15.2761 | −0.867621 | ||||||||
\(311\) | −2.84322 | −0.161224 | −0.0806122 | − | 0.996746i | \(-0.525688\pi\) | ||||
−0.0806122 | + | 0.996746i | \(0.525688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.2591 | −1.54077 | −0.770387 | − | 0.637577i | \(-0.779937\pi\) | ||||
−0.770387 | + | 0.637577i | \(0.779937\pi\) | |||||||
\(314\) | 0.340802 | 0.0192326 | ||||||||
\(315\) | −0.209476 | −0.0118026 | ||||||||
\(316\) | −2.54789 | −0.143330 | ||||||||
\(317\) | −10.6977 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(318\) | −2.95254 | −0.165570 | ||||||||
\(319\) | −2.25549 | −0.126283 | ||||||||
\(320\) | −3.54520 | −0.198182 | ||||||||
\(321\) | 8.02814 | 0.448087 | ||||||||
\(322\) | 0.0565844 | 0.00315332 | ||||||||
\(323\) | 0.694303 | 0.0386321 | ||||||||
\(324\) | −1.53791 | −0.0854394 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.58046 | 0.364458 | ||||||||
\(327\) | 0.0538086 | 0.00297562 | ||||||||
\(328\) | −24.1001 | −1.33070 | ||||||||
\(329\) | −0.298720 | −0.0164690 | ||||||||
\(330\) | −2.28741 | −0.125918 | ||||||||
\(331\) | 25.9797 | 1.42797 | 0.713987 | − | 0.700159i | \(-0.246888\pi\) | ||||
0.713987 | + | 0.700159i | \(0.246888\pi\) | |||||||
\(332\) | −9.01983 | −0.495027 | ||||||||
\(333\) | 3.56253 | 0.195226 | ||||||||
\(334\) | 2.49365 | 0.136446 | ||||||||
\(335\) | 7.87288 | 0.430141 | ||||||||
\(336\) | −0.0897044 | −0.00489377 | ||||||||
\(337\) | −21.6922 | −1.18165 | −0.590825 | − | 0.806800i | \(-0.701198\pi\) | ||||
−0.590825 | + | 0.806800i | \(0.701198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.42218 | 0.185867 | ||||||||
\(340\) | −12.6943 | −0.688446 | ||||||||
\(341\) | −6.67832 | −0.361652 | ||||||||
\(342\) | −0.192404 | −0.0104040 | ||||||||
\(343\) | −0.871288 | −0.0470451 | ||||||||
\(344\) | 20.8269 | 1.12291 | ||||||||
\(345\) | 4.49945 | 0.242242 | ||||||||
\(346\) | 9.30965 | 0.500490 | ||||||||
\(347\) | 2.68078 | 0.143912 | 0.0719560 | − | 0.997408i | \(-0.477076\pi\) | ||||
0.0719560 | + | 0.997408i | \(0.477076\pi\) | |||||||
\(348\) | 3.46874 | 0.185944 | ||||||||
\(349\) | 21.6257 | 1.15760 | 0.578799 | − | 0.815471i | \(-0.303522\pi\) | ||||
0.578799 | + | 0.815471i | \(0.303522\pi\) | |||||||
\(350\) | 0.267571 | 0.0143023 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.78949 | −0.308581 | ||||||||
\(353\) | 8.84205 | 0.470615 | 0.235307 | − | 0.971921i | \(-0.424390\pi\) | ||||
0.235307 | + | 0.971921i | \(0.424390\pi\) | |||||||
\(354\) | −9.35199 | −0.497052 | ||||||||
\(355\) | −29.4156 | −1.56122 | ||||||||
\(356\) | −11.0545 | −0.585886 | ||||||||
\(357\) | 0.152705 | 0.00808198 | ||||||||
\(358\) | 12.7603 | 0.674405 | ||||||||
\(359\) | −33.6139 | −1.77408 | −0.887038 | − | 0.461697i | \(-0.847241\pi\) | ||||
−0.887038 | + | 0.461697i | \(0.847241\pi\) | |||||||
\(360\) | 8.09264 | 0.426520 | ||||||||
\(361\) | −18.9199 | −0.995784 | ||||||||
\(362\) | −3.15400 | −0.165771 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.1061 | 2.30862 | ||||||||
\(366\) | −1.38563 | −0.0724281 | ||||||||
\(367\) | 16.4407 | 0.858200 | 0.429100 | − | 0.903257i | \(-0.358831\pi\) | ||||
0.429100 | + | 0.903257i | \(0.358831\pi\) | |||||||
\(368\) | 1.92681 | 0.100442 | ||||||||
\(369\) | 10.0209 | 0.521668 | ||||||||
\(370\) | −8.14897 | −0.423645 | ||||||||
\(371\) | 0.270388 | 0.0140378 | ||||||||
\(372\) | 10.2707 | 0.532509 | ||||||||
\(373\) | 0.748625 | 0.0387623 | 0.0193812 | − | 0.999812i | \(-0.493830\pi\) | ||||
0.0193812 | + | 0.999812i | \(0.493830\pi\) | |||||||
\(374\) | 1.66748 | 0.0862235 | ||||||||
\(375\) | 4.45174 | 0.229887 | ||||||||
\(376\) | 11.5404 | 0.595150 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.0423172 | −0.00217656 | ||||||||
\(379\) | 22.4141 | 1.15134 | 0.575669 | − | 0.817683i | \(-0.304742\pi\) | ||||
0.575669 | + | 0.817683i | \(0.304742\pi\) | |||||||
\(380\) | −1.46474 | −0.0751398 | ||||||||
\(381\) | 13.5267 | 0.692993 | ||||||||
\(382\) | 17.9358 | 0.917675 | ||||||||
\(383\) | 22.5514 | 1.15232 | 0.576161 | − | 0.817336i | \(-0.304550\pi\) | ||||
0.576161 | + | 0.817336i | \(0.304550\pi\) | |||||||
\(384\) | 10.8628 | 0.554340 | ||||||||
\(385\) | 0.209476 | 0.0106759 | ||||||||
\(386\) | −11.4254 | −0.581539 | ||||||||
\(387\) | −8.65994 | −0.440210 | ||||||||
\(388\) | 12.7685 | 0.648222 | ||||||||
\(389\) | −7.51672 | −0.381113 | −0.190556 | − | 0.981676i | \(-0.561029\pi\) | ||||
−0.190556 | + | 0.981676i | \(0.561029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.28003 | −0.165878 | ||||||||
\(392\) | 16.8255 | 0.849816 | ||||||||
\(393\) | 18.4271 | 0.929526 | ||||||||
\(394\) | −14.3647 | −0.723681 | ||||||||
\(395\) | −5.57481 | −0.280499 | ||||||||
\(396\) | 1.53791 | 0.0772829 | ||||||||
\(397\) | 18.0969 | 0.908259 | 0.454129 | − | 0.890936i | \(-0.349950\pi\) | ||||
0.454129 | + | 0.890936i | \(0.349950\pi\) | |||||||
\(398\) | −14.7820 | −0.740955 | ||||||||
\(399\) | 0.0176200 | 0.000882101 0 | ||||||||
\(400\) | 9.11131 | 0.455565 | ||||||||
\(401\) | 5.52026 | 0.275669 | 0.137834 | − | 0.990455i | \(-0.455986\pi\) | ||||
0.137834 | + | 0.990455i | \(0.455986\pi\) | |||||||
\(402\) | 1.59044 | 0.0793239 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.46950 | 0.122862 | ||||||||
\(405\) | −3.36496 | −0.167206 | ||||||||
\(406\) | 0.0954462 | 0.00473692 | ||||||||
\(407\) | −3.56253 | −0.176588 | ||||||||
\(408\) | −5.89941 | −0.292064 | ||||||||
\(409\) | −27.6153 | −1.36549 | −0.682744 | − | 0.730657i | \(-0.739214\pi\) | ||||
−0.682744 | + | 0.730657i | \(0.739214\pi\) | |||||||
\(410\) | −22.9219 | −1.13203 | ||||||||
\(411\) | −16.5528 | −0.816491 | ||||||||
\(412\) | 10.9159 | 0.537787 | ||||||||
\(413\) | 0.856435 | 0.0421424 | ||||||||
\(414\) | 0.908955 | 0.0446727 | ||||||||
\(415\) | −19.7355 | −0.968776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.7090 | −0.818243 | ||||||||
\(418\) | 0.192404 | 0.00941079 | ||||||||
\(419\) | −11.0744 | −0.541018 | −0.270509 | − | 0.962717i | \(-0.587192\pi\) | ||||
−0.270509 | + | 0.962717i | \(0.587192\pi\) | |||||||
\(420\) | −0.322155 | −0.0157196 | ||||||||
\(421\) | 29.2020 | 1.42322 | 0.711610 | − | 0.702575i | \(-0.247967\pi\) | ||||
0.711610 | + | 0.702575i | \(0.247967\pi\) | |||||||
\(422\) | 2.24014 | 0.109048 | ||||||||
\(423\) | −4.79855 | −0.233313 | ||||||||
\(424\) | −10.4458 | −0.507294 | ||||||||
\(425\) | −15.5103 | −0.752359 | ||||||||
\(426\) | −5.94239 | −0.287910 | ||||||||
\(427\) | 0.126893 | 0.00614079 | ||||||||
\(428\) | 12.3466 | 0.596793 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.8088 | 0.955266 | ||||||||
\(431\) | 7.61037 | 0.366578 | 0.183289 | − | 0.983059i | \(-0.441326\pi\) | ||||
0.183289 | + | 0.983059i | \(0.441326\pi\) | |||||||
\(432\) | −1.44099 | −0.0693295 | ||||||||
\(433\) | 10.3182 | 0.495860 | 0.247930 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247930 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(434\) | 0.282608 | 0.0135656 | ||||||||
\(435\) | 7.58964 | 0.363896 | ||||||||
\(436\) | 0.0827527 | 0.00396314 | ||||||||
\(437\) | −0.378469 | −0.0181046 | ||||||||
\(438\) | 8.91009 | 0.425741 | ||||||||
\(439\) | −10.7735 | −0.514190 | −0.257095 | − | 0.966386i | \(-0.582765\pi\) | ||||
−0.257095 | + | 0.966386i | \(0.582765\pi\) | |||||||
\(440\) | −8.09264 | −0.385802 | ||||||||
\(441\) | −6.99612 | −0.333149 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.4493 | −0.876551 | −0.438275 | − | 0.898841i | \(-0.644411\pi\) | ||||
−0.438275 | + | 0.898841i | \(0.644411\pi\) | |||||||
\(444\) | 5.47885 | 0.260015 | ||||||||
\(445\) | −24.1873 | −1.14659 | ||||||||
\(446\) | −14.6302 | −0.692762 | ||||||||
\(447\) | 6.37375 | 0.301468 | ||||||||
\(448\) | 0.0655864 | 0.00309867 | ||||||||
\(449\) | −35.4123 | −1.67121 | −0.835605 | − | 0.549331i | \(-0.814882\pi\) | ||||
−0.835605 | + | 0.549331i | \(0.814882\pi\) | |||||||
\(450\) | 4.29818 | 0.202618 | ||||||||
\(451\) | −10.0209 | −0.471867 | ||||||||
\(452\) | 5.26300 | 0.247551 | ||||||||
\(453\) | 20.4640 | 0.961484 | ||||||||
\(454\) | −5.75967 | −0.270315 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.680708 | −0.0318771 | ||||||||
\(457\) | 21.1979 | 0.991595 | 0.495798 | − | 0.868438i | \(-0.334876\pi\) | ||||
0.495798 | + | 0.868438i | \(0.334876\pi\) | |||||||
\(458\) | 10.1620 | 0.474841 | ||||||||
\(459\) | 2.45300 | 0.114496 | ||||||||
\(460\) | 6.91974 | 0.322635 | ||||||||
\(461\) | −34.3108 | −1.59801 | −0.799006 | − | 0.601323i | \(-0.794641\pi\) | ||||
−0.799006 | + | 0.601323i | \(0.794641\pi\) | |||||||
\(462\) | 0.0423172 | 0.00196878 | ||||||||
\(463\) | −17.7724 | −0.825951 | −0.412976 | − | 0.910742i | \(-0.635511\pi\) | ||||
−0.412976 | + | 0.910742i | \(0.635511\pi\) | |||||||
\(464\) | 3.25013 | 0.150884 | ||||||||
\(465\) | 22.4723 | 1.04213 | ||||||||
\(466\) | −18.7701 | −0.869506 | ||||||||
\(467\) | −8.01133 | −0.370720 | −0.185360 | − | 0.982671i | \(-0.559345\pi\) | ||||
−0.185360 | + | 0.982671i | \(0.559345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.145649 | −0.00672544 | ||||||||
\(470\) | 10.9762 | 0.506296 | ||||||||
\(471\) | −0.501348 | −0.0231009 | ||||||||
\(472\) | −33.0865 | −1.52293 | ||||||||
\(473\) | 8.65994 | 0.398185 | ||||||||
\(474\) | −1.12619 | −0.0517278 | ||||||||
\(475\) | −1.78967 | −0.0821155 | ||||||||
\(476\) | 0.234846 | 0.0107641 | ||||||||
\(477\) | 4.34343 | 0.198872 | ||||||||
\(478\) | 2.15657 | 0.0986392 | ||||||||
\(479\) | 11.4168 | 0.521646 | 0.260823 | − | 0.965387i | \(-0.416006\pi\) | ||||
0.260823 | + | 0.965387i | \(0.416006\pi\) | |||||||
\(480\) | 19.4814 | 0.889200 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.29591 | −0.104576 | ||||||||
\(483\) | −0.0832402 | −0.00378756 | ||||||||
\(484\) | −1.53791 | −0.0699050 | ||||||||
\(485\) | 27.9376 | 1.26858 | ||||||||
\(486\) | −0.679772 | −0.0308351 | ||||||||
\(487\) | 30.6526 | 1.38900 | 0.694501 | − | 0.719492i | \(-0.255625\pi\) | ||||
0.694501 | + | 0.719492i | \(0.255625\pi\) | |||||||
\(488\) | −4.90224 | −0.221914 | ||||||||
\(489\) | −9.68039 | −0.437762 | ||||||||
\(490\) | 16.0030 | 0.722941 | ||||||||
\(491\) | −28.7518 | −1.29755 | −0.648775 | − | 0.760980i | \(-0.724718\pi\) | ||||
−0.648775 | + | 0.760980i | \(0.724718\pi\) | |||||||
\(492\) | 15.4113 | 0.694794 | ||||||||
\(493\) | −5.53273 | −0.249182 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.36496 | 0.151244 | ||||||||
\(496\) | 9.62337 | 0.432102 | ||||||||
\(497\) | 0.544191 | 0.0244103 | ||||||||
\(498\) | −3.98686 | −0.178655 | ||||||||
\(499\) | 0.548949 | 0.0245743 | 0.0122872 | − | 0.999925i | \(-0.496089\pi\) | ||||
0.0122872 | + | 0.999925i | \(0.496089\pi\) | |||||||
\(500\) | 6.84638 | 0.306179 | ||||||||
\(501\) | −3.66836 | −0.163890 | ||||||||
\(502\) | −8.04490 | −0.359061 | ||||||||
\(503\) | 15.8593 | 0.707131 | 0.353566 | − | 0.935410i | \(-0.384969\pi\) | ||||
0.353566 | + | 0.935410i | \(0.384969\pi\) | |||||||
\(504\) | −0.149715 | −0.00666882 | ||||||||
\(505\) | 5.40328 | 0.240443 | ||||||||
\(506\) | −0.908955 | −0.0404080 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.8028 | 0.922976 | ||||||||
\(509\) | −38.1514 | −1.69103 | −0.845514 | − | 0.533953i | \(-0.820706\pi\) | ||||
−0.845514 | + | 0.533953i | \(0.820706\pi\) | |||||||
\(510\) | −5.61102 | −0.248460 | ||||||||
\(511\) | −0.815967 | −0.0360963 | ||||||||
\(512\) | 15.2736 | 0.675005 | ||||||||
\(513\) | 0.283042 | 0.0124966 | ||||||||
\(514\) | 2.77055 | 0.122204 | ||||||||
\(515\) | 23.8841 | 1.05246 | ||||||||
\(516\) | −13.3182 | −0.586301 | ||||||||
\(517\) | 4.79855 | 0.211040 | ||||||||
\(518\) | 0.150757 | 0.00662386 | ||||||||
\(519\) | −13.6952 | −0.601154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4297 | 0.851232 | 0.425616 | − | 0.904904i | \(-0.360057\pi\) | ||||
0.425616 | + | 0.904904i | \(0.360057\pi\) | |||||||
\(522\) | 1.53322 | 0.0671073 | ||||||||
\(523\) | 21.4060 | 0.936020 | 0.468010 | − | 0.883723i | \(-0.344971\pi\) | ||||
0.468010 | + | 0.883723i | \(0.344971\pi\) | |||||||
\(524\) | 28.3393 | 1.23801 | ||||||||
\(525\) | −0.393618 | −0.0171789 | ||||||||
\(526\) | −17.1236 | −0.746626 | ||||||||
\(527\) | −16.3820 | −0.713609 | ||||||||
\(528\) | 1.44099 | 0.0627108 | ||||||||
\(529\) | −21.2120 | −0.922263 | ||||||||
\(530\) | −9.93519 | −0.431557 | ||||||||
\(531\) | 13.7575 | 0.597026 | ||||||||
\(532\) | 0.0270979 | 0.00117484 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.88619 | −0.211446 | ||||||||
\(535\) | 27.0144 | 1.16793 | ||||||||
\(536\) | 5.62683 | 0.243042 | ||||||||
\(537\) | −18.7715 | −0.810050 | ||||||||
\(538\) | 15.9505 | 0.687673 | ||||||||
\(539\) | 6.99612 | 0.301344 | ||||||||
\(540\) | −5.17501 | −0.222697 | ||||||||
\(541\) | 3.71159 | 0.159574 | 0.0797868 | − | 0.996812i | \(-0.474576\pi\) | ||||
0.0797868 | + | 0.996812i | \(0.474576\pi\) | |||||||
\(542\) | −6.00966 | −0.258137 | ||||||||
\(543\) | 4.63979 | 0.199112 | ||||||||
\(544\) | −14.2016 | −0.608890 | ||||||||
\(545\) | 0.181064 | 0.00775592 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.5420 | −1.73345 | −0.866725 | − | 0.498786i | \(-0.833779\pi\) | ||||
−0.866725 | + | 0.498786i | \(0.833779\pi\) | |||||||
\(548\) | −25.4568 | −1.08746 | ||||||||
\(549\) | 2.03838 | 0.0869958 | ||||||||
\(550\) | −4.29818 | −0.183275 | ||||||||
\(551\) | −0.638399 | −0.0271967 | ||||||||
\(552\) | 3.21580 | 0.136874 | ||||||||
\(553\) | 0.103134 | 0.00438572 | ||||||||
\(554\) | 2.64065 | 0.112191 | ||||||||
\(555\) | 11.9878 | 0.508853 | ||||||||
\(556\) | −25.6969 | −1.08979 | ||||||||
\(557\) | 16.3173 | 0.691386 | 0.345693 | − | 0.938348i | \(-0.387644\pi\) | ||||
0.345693 | + | 0.938348i | \(0.387644\pi\) | |||||||
\(558\) | 4.53974 | 0.192182 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.301852 | −0.0127556 | ||||||||
\(561\) | −2.45300 | −0.103566 | ||||||||
\(562\) | 10.4775 | 0.441968 | ||||||||
\(563\) | 16.0740 | 0.677439 | 0.338719 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338719 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(564\) | −7.37974 | −0.310743 | ||||||||
\(565\) | 11.5155 | 0.484460 | ||||||||
\(566\) | −10.9510 | −0.460307 | ||||||||
\(567\) | 0.0622521 | 0.00261434 | ||||||||
\(568\) | −21.0236 | −0.882132 | ||||||||
\(569\) | −0.916789 | −0.0384338 | −0.0192169 | − | 0.999815i | \(-0.506117\pi\) | ||||
−0.0192169 | + | 0.999815i | \(0.506117\pi\) | |||||||
\(570\) | −0.647432 | −0.0271180 | ||||||||
\(571\) | 0.906071 | 0.0379179 | 0.0189590 | − | 0.999820i | \(-0.493965\pi\) | ||||
0.0189590 | + | 0.999820i | \(0.493965\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.3850 | −1.10225 | ||||||||
\(574\) | 0.424058 | 0.0176998 | ||||||||
\(575\) | 8.45474 | 0.352587 | ||||||||
\(576\) | 1.05356 | 0.0438984 | ||||||||
\(577\) | 0.545156 | 0.0226952 | 0.0113476 | − | 0.999936i | \(-0.496388\pi\) | ||||
0.0113476 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(578\) | −7.46578 | −0.310536 | ||||||||
\(579\) | 16.8077 | 0.698505 | ||||||||
\(580\) | 11.6722 | 0.484661 | ||||||||
\(581\) | 0.365108 | 0.0151472 | ||||||||
\(582\) | 5.64381 | 0.233943 | ||||||||
\(583\) | −4.34343 | −0.179886 | ||||||||
\(584\) | 31.5231 | 1.30444 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.88180 | −0.119046 | ||||||||
\(587\) | 39.0656 | 1.61241 | 0.806206 | − | 0.591635i | \(-0.201517\pi\) | ||||
0.806206 | + | 0.591635i | \(0.201517\pi\) | |||||||
\(588\) | −10.7594 | −0.443711 | ||||||||
\(589\) | −1.89025 | −0.0778862 | ||||||||
\(590\) | −31.4691 | −1.29556 | ||||||||
\(591\) | 21.1316 | 0.869236 | ||||||||
\(592\) | 5.13356 | 0.210988 | ||||||||
\(593\) | 8.21394 | 0.337306 | 0.168653 | − | 0.985675i | \(-0.446058\pi\) | ||||
0.168653 | + | 0.985675i | \(0.446058\pi\) | |||||||
\(594\) | 0.679772 | 0.0278914 | ||||||||
\(595\) | 0.513845 | 0.0210656 | ||||||||
\(596\) | 9.80226 | 0.401516 | ||||||||
\(597\) | 21.7455 | 0.889985 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.01963 | −0.164237 | −0.0821187 | − | 0.996623i | \(-0.526169\pi\) | ||||
−0.0821187 | + | 0.996623i | \(0.526169\pi\) | |||||||
\(600\) | 15.2066 | 0.620806 | ||||||||
\(601\) | 41.4912 | 1.69246 | 0.846230 | − | 0.532817i | \(-0.178867\pi\) | ||||
0.846230 | + | 0.532817i | \(0.178867\pi\) | |||||||
\(602\) | −0.366465 | −0.0149360 | ||||||||
\(603\) | −2.33966 | −0.0952785 | ||||||||
\(604\) | 31.4718 | 1.28057 | ||||||||
\(605\) | −3.36496 | −0.136805 | ||||||||
\(606\) | 1.09154 | 0.0443409 | ||||||||
\(607\) | 15.9867 | 0.648881 | 0.324441 | − | 0.945906i | \(-0.394824\pi\) | ||||
0.324441 | + | 0.945906i | \(0.394824\pi\) | |||||||
\(608\) | −1.63867 | −0.0664568 | ||||||||
\(609\) | −0.140409 | −0.00568966 | ||||||||
\(610\) | −4.66260 | −0.188783 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.77250 | 0.152494 | ||||||||
\(613\) | 46.0791 | 1.86112 | 0.930559 | − | 0.366142i | \(-0.119321\pi\) | ||||
0.930559 | + | 0.366142i | \(0.119321\pi\) | |||||||
\(614\) | 18.4280 | 0.743693 | ||||||||
\(615\) | 33.7200 | 1.35972 | ||||||||
\(616\) | 0.149715 | 0.00603217 | ||||||||
\(617\) | 4.06514 | 0.163656 | 0.0818282 | − | 0.996646i | \(-0.473924\pi\) | ||||
0.0818282 | + | 0.996646i | \(0.473924\pi\) | |||||||
\(618\) | 4.82494 | 0.194087 | ||||||||
\(619\) | −22.4783 | −0.903478 | −0.451739 | − | 0.892150i | \(-0.649196\pi\) | ||||
−0.451739 | + | 0.892150i | \(0.649196\pi\) | |||||||
\(620\) | 34.5604 | 1.38798 | ||||||||
\(621\) | −1.33715 | −0.0536579 | ||||||||
\(622\) | −1.93274 | −0.0774960 | ||||||||
\(623\) | 0.447467 | 0.0179274 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.6349 | −0.665396 | ||||||||
\(626\) | −18.5300 | −0.740606 | ||||||||
\(627\) | −0.283042 | −0.0113036 | ||||||||
\(628\) | −0.771028 | −0.0307674 | ||||||||
\(629\) | −8.73891 | −0.348443 | ||||||||
\(630\) | −0.142396 | −0.00567319 | ||||||||
\(631\) | 44.5257 | 1.77254 | 0.886270 | − | 0.463168i | \(-0.153287\pi\) | ||||
0.886270 | + | 0.463168i | \(0.153287\pi\) | |||||||
\(632\) | −3.98437 | −0.158490 | ||||||||
\(633\) | −3.29543 | −0.130981 | ||||||||
\(634\) | −7.27199 | −0.288808 | ||||||||
\(635\) | 45.5168 | 1.80628 | ||||||||
\(636\) | 6.67980 | 0.264871 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.53322 | −0.0607008 | ||||||||
\(639\) | 8.74173 | 0.345818 | ||||||||
\(640\) | 36.5529 | 1.44488 | ||||||||
\(641\) | 21.9038 | 0.865147 | 0.432573 | − | 0.901599i | \(-0.357606\pi\) | ||||
0.432573 | + | 0.901599i | \(0.357606\pi\) | |||||||
\(642\) | 5.45731 | 0.215383 | ||||||||
\(643\) | −38.3705 | −1.51319 | −0.756593 | − | 0.653886i | \(-0.773138\pi\) | ||||
−0.756593 | + | 0.653886i | \(0.773138\pi\) | |||||||
\(644\) | −0.128016 | −0.00504453 | ||||||||
\(645\) | −29.1404 | −1.14740 | ||||||||
\(646\) | 0.471968 | 0.0185693 | ||||||||
\(647\) | −9.35693 | −0.367859 | −0.183929 | − | 0.982939i | \(-0.558882\pi\) | ||||
−0.183929 | + | 0.982939i | \(0.558882\pi\) | |||||||
\(648\) | −2.40497 | −0.0944763 | ||||||||
\(649\) | −13.7575 | −0.540030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.415740 | −0.0162941 | ||||||||
\(652\) | −14.8876 | −0.583042 | ||||||||
\(653\) | −42.1669 | −1.65012 | −0.825059 | − | 0.565047i | \(-0.808858\pi\) | ||||
−0.825059 | + | 0.565047i | \(0.808858\pi\) | |||||||
\(654\) | 0.0365776 | 0.00143030 | ||||||||
\(655\) | 62.0066 | 2.42280 | ||||||||
\(656\) | 14.4400 | 0.563788 | ||||||||
\(657\) | −13.1075 | −0.511371 | ||||||||
\(658\) | −0.203061 | −0.00791616 | ||||||||
\(659\) | −22.1040 | −0.861048 | −0.430524 | − | 0.902579i | \(-0.641671\pi\) | ||||
−0.430524 | + | 0.902579i | \(0.641671\pi\) | |||||||
\(660\) | 5.17501 | 0.201437 | ||||||||
\(661\) | −39.4885 | −1.53592 | −0.767962 | − | 0.640496i | \(-0.778729\pi\) | ||||
−0.767962 | + | 0.640496i | \(0.778729\pi\) | |||||||
\(662\) | 17.6603 | 0.686386 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.1051 | −0.547386 | ||||||||
\(665\) | 0.0592905 | 0.00229919 | ||||||||
\(666\) | 2.42171 | 0.0938394 | ||||||||
\(667\) | 3.01592 | 0.116777 | ||||||||
\(668\) | −5.64160 | −0.218280 | ||||||||
\(669\) | 21.5223 | 0.832099 | ||||||||
\(670\) | 5.35176 | 0.206757 | ||||||||
\(671\) | −2.03838 | −0.0786906 | ||||||||
\(672\) | −0.360408 | −0.0139030 | ||||||||
\(673\) | −22.9059 | −0.882959 | −0.441479 | − | 0.897271i | \(-0.645546\pi\) | ||||
−0.441479 | + | 0.897271i | \(0.645546\pi\) | |||||||
\(674\) | −14.7458 | −0.567986 | ||||||||
\(675\) | −6.32297 | −0.243371 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1550 | −0.467155 | −0.233578 | − | 0.972338i | \(-0.575043\pi\) | ||||
−0.233578 | + | 0.972338i | \(0.575043\pi\) | |||||||
\(678\) | 2.32630 | 0.0893410 | ||||||||
\(679\) | −0.516848 | −0.0198348 | ||||||||
\(680\) | −19.8513 | −0.761262 | ||||||||
\(681\) | 8.47294 | 0.324684 | ||||||||
\(682\) | −4.53974 | −0.173836 | ||||||||
\(683\) | 17.5269 | 0.670650 | 0.335325 | − | 0.942103i | \(-0.391154\pi\) | ||||
0.335325 | + | 0.942103i | \(0.391154\pi\) | |||||||
\(684\) | 0.435293 | 0.0166438 | ||||||||
\(685\) | −55.6997 | −2.12817 | ||||||||
\(686\) | −0.592277 | −0.0226133 | ||||||||
\(687\) | −14.9492 | −0.570347 | ||||||||
\(688\) | −12.4789 | −0.475752 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.05860 | 0.116439 | ||||||||
\(691\) | 34.0368 | 1.29482 | 0.647411 | − | 0.762141i | \(-0.275852\pi\) | ||||
0.647411 | + | 0.762141i | \(0.275852\pi\) | |||||||
\(692\) | −21.0620 | −0.800659 | ||||||||
\(693\) | −0.0622521 | −0.00236476 | ||||||||
\(694\) | 1.82232 | 0.0691744 | ||||||||
\(695\) | −56.2251 | −2.13274 | ||||||||
\(696\) | 5.42440 | 0.205611 | ||||||||
\(697\) | −24.5814 | −0.931086 | ||||||||
\(698\) | 14.7006 | 0.556424 | ||||||||
\(699\) | 27.6123 | 1.04439 | ||||||||
\(700\) | −0.605349 | −0.0228800 | ||||||||
\(701\) | 39.7219 | 1.50027 | 0.750137 | − | 0.661283i | \(-0.229988\pi\) | ||||
0.750137 | + | 0.661283i | \(0.229988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00835 | −0.0380305 | ||||||||
\(704\) | −1.05356 | −0.0397076 | ||||||||
\(705\) | −16.1469 | −0.608129 | ||||||||
\(706\) | 6.01058 | 0.226211 | ||||||||
\(707\) | −0.0999612 | −0.00375943 | ||||||||
\(708\) | 21.1578 | 0.795160 | ||||||||
\(709\) | −22.0079 | −0.826524 | −0.413262 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413262 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(710\) | −19.9959 | −0.750433 | ||||||||
\(711\) | 1.65672 | 0.0621319 | ||||||||
\(712\) | −17.2869 | −0.647855 | ||||||||
\(713\) | 8.92990 | 0.334427 | ||||||||
\(714\) | 0.103804 | 0.00388478 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.8689 | −1.07888 | ||||||||
\(717\) | −3.17249 | −0.118479 | ||||||||
\(718\) | −22.8498 | −0.852748 | ||||||||
\(719\) | 5.74870 | 0.214390 | 0.107195 | − | 0.994238i | \(-0.465813\pi\) | ||||
0.107195 | + | 0.994238i | \(0.465813\pi\) | |||||||
\(720\) | −4.84886 | −0.180706 | ||||||||
\(721\) | −0.441857 | −0.0164556 | ||||||||
\(722\) | −12.8612 | −0.478645 | ||||||||
\(723\) | 3.37747 | 0.125610 | ||||||||
\(724\) | 7.13558 | 0.265192 | ||||||||
\(725\) | 14.2614 | 0.529655 | ||||||||
\(726\) | −0.679772 | −0.0252287 | ||||||||
\(727\) | 21.1337 | 0.783805 | 0.391903 | − | 0.920007i | \(-0.371817\pi\) | ||||
0.391903 | + | 0.920007i | \(0.371817\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 29.9821 | 1.10969 | ||||||||
\(731\) | 21.2429 | 0.785696 | ||||||||
\(732\) | 3.13484 | 0.115867 | ||||||||
\(733\) | −36.7004 | −1.35556 | −0.677780 | − | 0.735265i | \(-0.737058\pi\) | ||||
−0.677780 | + | 0.735265i | \(0.737058\pi\) | |||||||
\(734\) | 11.1760 | 0.412512 | ||||||||
\(735\) | −23.5417 | −0.868348 | ||||||||
\(736\) | 7.74139 | 0.285352 | ||||||||
\(737\) | 2.33966 | 0.0861826 | ||||||||
\(738\) | 6.81195 | 0.250751 | ||||||||
\(739\) | −29.1613 | −1.07272 | −0.536358 | − | 0.843990i | \(-0.680200\pi\) | ||||
−0.536358 | + | 0.843990i | \(0.680200\pi\) | |||||||
\(740\) | 18.4361 | 0.677726 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.183802 | 0.00674758 | ||||||||
\(743\) | −13.3594 | −0.490109 | −0.245054 | − | 0.969509i | \(-0.578806\pi\) | ||||
−0.245054 | + | 0.969509i | \(0.578806\pi\) | |||||||
\(744\) | 16.0612 | 0.588832 | ||||||||
\(745\) | 21.4474 | 0.785773 | ||||||||
\(746\) | 0.508895 | 0.0186320 | ||||||||
\(747\) | 5.86499 | 0.214589 | ||||||||
\(748\) | −3.77250 | −0.137936 | ||||||||
\(749\) | −0.499768 | −0.0182611 | ||||||||
\(750\) | 3.02617 | 0.110500 | ||||||||
\(751\) | −6.99106 | −0.255107 | −0.127554 | − | 0.991832i | \(-0.540713\pi\) | ||||
−0.127554 | + | 0.991832i | \(0.540713\pi\) | |||||||
\(752\) | −6.91464 | −0.252151 | ||||||||
\(753\) | 11.8347 | 0.431280 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 68.8607 | 2.50610 | ||||||||
\(756\) | 0.0957381 | 0.00348196 | ||||||||
\(757\) | 3.67122 | 0.133433 | 0.0667164 | − | 0.997772i | \(-0.478748\pi\) | ||||
0.0667164 | + | 0.997772i | \(0.478748\pi\) | |||||||
\(758\) | 15.2365 | 0.553415 | ||||||||
\(759\) | 1.33715 | 0.0485354 | ||||||||
\(760\) | −2.29056 | −0.0830872 | ||||||||
\(761\) | −12.5202 | −0.453857 | −0.226928 | − | 0.973911i | \(-0.572868\pi\) | ||||
−0.226928 | + | 0.973911i | \(0.572868\pi\) | |||||||
\(762\) | 9.19506 | 0.333102 | ||||||||
\(763\) | −0.00334970 | −0.000121267 0 | ||||||||
\(764\) | −40.5777 | −1.46805 | ||||||||
\(765\) | 8.25426 | 0.298434 | ||||||||
\(766\) | 15.3298 | 0.553889 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9.49135 | 0.342490 | ||||||||
\(769\) | −45.6176 | −1.64501 | −0.822507 | − | 0.568755i | \(-0.807425\pi\) | ||||
−0.822507 | + | 0.568755i | \(0.807425\pi\) | |||||||
\(770\) | 0.142396 | 0.00513159 | ||||||||
\(771\) | −4.07570 | −0.146783 | ||||||||
\(772\) | 25.8488 | 0.930317 | ||||||||
\(773\) | 4.28007 | 0.153944 | 0.0769718 | − | 0.997033i | \(-0.475475\pi\) | ||||
0.0769718 | + | 0.997033i | \(0.475475\pi\) | |||||||
\(774\) | −5.88679 | −0.211596 | ||||||||
\(775\) | 42.2268 | 1.51683 | ||||||||
\(776\) | 19.9673 | 0.716783 | ||||||||
\(777\) | −0.221775 | −0.00795614 | ||||||||
\(778\) | −5.10966 | −0.183190 | ||||||||
\(779\) | −2.83634 | −0.101622 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.74173 | −0.312804 | ||||||||
\(782\) | −2.22967 | −0.0797329 | ||||||||
\(783\) | −2.25549 | −0.0806047 | ||||||||
\(784\) | −10.0813 | −0.360047 | ||||||||
\(785\) | −1.68702 | −0.0602122 | ||||||||
\(786\) | 12.5263 | 0.446797 | ||||||||
\(787\) | 14.3385 | 0.511113 | 0.255557 | − | 0.966794i | \(-0.417741\pi\) | ||||
0.255557 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(788\) | 32.4984 | 1.15771 | ||||||||
\(789\) | 25.1902 | 0.896796 | ||||||||
\(790\) | −3.78960 | −0.134828 | ||||||||
\(791\) | −0.213038 | −0.00757475 | ||||||||
\(792\) | 2.40497 | 0.0854570 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.3018 | 0.436574 | ||||||||
\(795\) | 14.6155 | 0.518357 | ||||||||
\(796\) | 33.4427 | 1.18534 | ||||||||
\(797\) | 22.2788 | 0.789157 | 0.394578 | − | 0.918862i | \(-0.370891\pi\) | ||||
0.394578 | + | 0.918862i | \(0.370891\pi\) | |||||||
\(798\) | 0.0119776 | 0.000424001 0 | ||||||||
\(799\) | 11.7709 | 0.416423 | ||||||||
\(800\) | 36.6068 | 1.29424 | ||||||||
\(801\) | 7.18799 | 0.253975 | ||||||||
\(802\) | 3.75252 | 0.132506 | ||||||||
\(803\) | 13.1075 | 0.462553 | ||||||||
\(804\) | −3.59819 | −0.126898 | ||||||||
\(805\) | −0.280100 | −0.00987223 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.4644 | −0.825986 | ||||||||
\(808\) | 3.86178 | 0.135857 | ||||||||
\(809\) | 18.7900 | 0.660622 | 0.330311 | − | 0.943872i | \(-0.392846\pi\) | ||||
0.330311 | + | 0.943872i | \(0.392846\pi\) | |||||||
\(810\) | −2.28741 | −0.0803713 | ||||||||
\(811\) | 37.7256 | 1.32472 | 0.662362 | − | 0.749184i | \(-0.269554\pi\) | ||||
0.662362 | + | 0.749184i | \(0.269554\pi\) | |||||||
\(812\) | −0.215936 | −0.00757789 | ||||||||
\(813\) | 8.84070 | 0.310057 | ||||||||
\(814\) | −2.42171 | −0.0848809 | ||||||||
\(815\) | −32.5741 | −1.14102 | ||||||||
\(816\) | 3.53474 | 0.123741 | ||||||||
\(817\) | 2.45113 | 0.0857541 | ||||||||
\(818\) | −18.7721 | −0.656352 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51.8584 | 1.81097 | ||||||||
\(821\) | 37.1959 | 1.29815 | 0.649073 | − | 0.760726i | \(-0.275157\pi\) | ||||
0.649073 | + | 0.760726i | \(0.275157\pi\) | |||||||
\(822\) | −11.2522 | −0.392464 | ||||||||
\(823\) | 48.8280 | 1.70204 | 0.851018 | − | 0.525137i | \(-0.175986\pi\) | ||||
0.851018 | + | 0.525137i | \(0.175986\pi\) | |||||||
\(824\) | 17.0702 | 0.594668 | ||||||||
\(825\) | 6.32297 | 0.220138 | ||||||||
\(826\) | 0.582181 | 0.0202567 | ||||||||
\(827\) | 18.9284 | 0.658204 | 0.329102 | − | 0.944294i | \(-0.393254\pi\) | ||||
0.329102 | + | 0.944294i | \(0.393254\pi\) | |||||||
\(828\) | −2.05641 | −0.0714652 | ||||||||
\(829\) | 42.2999 | 1.46914 | 0.734568 | − | 0.678535i | \(-0.237385\pi\) | ||||
0.734568 | + | 0.678535i | \(0.237385\pi\) | |||||||
\(830\) | −13.4156 | −0.465663 | ||||||||
\(831\) | −3.88461 | −0.134756 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.1615 | 0.594611 | ||||||||
\(834\) | −11.3583 | −0.393306 | ||||||||
\(835\) | −12.3439 | −0.427178 | ||||||||
\(836\) | −0.435293 | −0.0150549 | ||||||||
\(837\) | −6.67832 | −0.230837 | ||||||||
\(838\) | −7.52805 | −0.260052 | ||||||||
\(839\) | −40.3172 | −1.39191 | −0.695953 | − | 0.718088i | \(-0.745018\pi\) | ||||
−0.695953 | + | 0.718088i | \(0.745018\pi\) | |||||||
\(840\) | −0.503784 | −0.0173822 | ||||||||
\(841\) | −23.9128 | −0.824578 | ||||||||
\(842\) | 19.8507 | 0.684101 | ||||||||
\(843\) | −15.4133 | −0.530862 | ||||||||
\(844\) | −5.06807 | −0.174450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.26192 | −0.112147 | ||||||||
\(847\) | 0.0622521 | 0.00213901 | ||||||||
\(848\) | 6.25882 | 0.214929 | ||||||||
\(849\) | 16.1099 | 0.552889 | ||||||||
\(850\) | −10.5435 | −0.361637 | ||||||||
\(851\) | 4.76363 | 0.163295 | ||||||||
\(852\) | 13.4440 | 0.460584 | ||||||||
\(853\) | 24.6591 | 0.844313 | 0.422157 | − | 0.906523i | \(-0.361273\pi\) | ||||
0.422157 | + | 0.906523i | \(0.361273\pi\) | |||||||
\(854\) | 0.0862585 | 0.00295170 | ||||||||
\(855\) | 0.952425 | 0.0325723 | ||||||||
\(856\) | 19.3075 | 0.659915 | ||||||||
\(857\) | 42.7014 | 1.45865 | 0.729326 | − | 0.684166i | \(-0.239834\pi\) | ||||
0.729326 | + | 0.684166i | \(0.239834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.44298 | 0.0492339 | 0.0246170 | − | 0.999697i | \(-0.492163\pi\) | ||||
0.0246170 | + | 0.999697i | \(0.492163\pi\) | |||||||
\(860\) | −44.8153 | −1.52819 | ||||||||
\(861\) | −0.623823 | −0.0212598 | ||||||||
\(862\) | 5.17332 | 0.176204 | ||||||||
\(863\) | −42.5985 | −1.45007 | −0.725034 | − | 0.688713i | \(-0.758176\pi\) | ||||
−0.725034 | + | 0.688713i | \(0.758176\pi\) | |||||||
\(864\) | −5.78949 | −0.196962 | ||||||||
\(865\) | −46.0840 | −1.56690 | ||||||||
\(866\) | 7.01401 | 0.238346 | ||||||||
\(867\) | 10.9828 | 0.372995 | ||||||||
\(868\) | −0.639370 | −0.0217016 | ||||||||
\(869\) | −1.65672 | −0.0562005 | ||||||||
\(870\) | 5.15923 | 0.174914 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.129408 | 0.00438231 | ||||||||
\(873\) | −8.30250 | −0.280997 | ||||||||
\(874\) | −0.257272 | −0.00870237 | ||||||||
\(875\) | −0.277130 | −0.00936872 | ||||||||
\(876\) | −20.1581 | −0.681079 | ||||||||
\(877\) | −58.0496 | −1.96020 | −0.980098 | − | 0.198515i | \(-0.936388\pi\) | ||||
−0.980098 | + | 0.198515i | \(0.936388\pi\) | |||||||
\(878\) | −7.32351 | −0.247157 | ||||||||
\(879\) | 4.23935 | 0.142990 | ||||||||
\(880\) | 4.84886 | 0.163455 | ||||||||
\(881\) | −23.0071 | −0.775128 | −0.387564 | − | 0.921843i | \(-0.626683\pi\) | ||||
−0.387564 | + | 0.921843i | \(0.626683\pi\) | |||||||
\(882\) | −4.75577 | −0.160135 | ||||||||
\(883\) | −32.9518 | −1.10892 | −0.554459 | − | 0.832211i | \(-0.687075\pi\) | ||||
−0.554459 | + | 0.832211i | \(0.687075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 46.2936 | 1.55614 | ||||||||
\(886\) | −12.5413 | −0.421333 | ||||||||
\(887\) | −2.90304 | −0.0974746 | −0.0487373 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487373 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(888\) | 8.56779 | 0.287516 | ||||||||
\(889\) | −0.842064 | −0.0282419 | ||||||||
\(890\) | −16.4419 | −0.551132 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 33.0993 | 1.10825 | ||||||||
\(893\) | 1.35819 | 0.0454501 | ||||||||
\(894\) | 4.33270 | 0.144907 | ||||||||
\(895\) | −63.1654 | −2.11139 | ||||||||
\(896\) | −0.676232 | −0.0225913 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0723 | −0.803303 | ||||||||
\(899\) | 15.0629 | 0.502376 | ||||||||
\(900\) | −9.72416 | −0.324139 | ||||||||
\(901\) | −10.6544 | −0.354951 | ||||||||
\(902\) | −6.81195 | −0.226813 | ||||||||
\(903\) | 0.539099 | 0.0179401 | ||||||||
\(904\) | 8.23024 | 0.273734 | ||||||||
\(905\) | 15.6127 | 0.518984 | ||||||||
\(906\) | 13.9109 | 0.462158 | ||||||||
\(907\) | 23.3724 | 0.776068 | 0.388034 | − | 0.921645i | \(-0.373154\pi\) | ||||
0.388034 | + | 0.921645i | \(0.373154\pi\) | |||||||
\(908\) | 13.0306 | 0.432436 | ||||||||
\(909\) | −1.60575 | −0.0532593 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1517 | −0.435734 | −0.217867 | − | 0.975978i | \(-0.569910\pi\) | ||||
−0.217867 | + | 0.975978i | \(0.569910\pi\) | |||||||
\(912\) | 0.407859 | 0.0135056 | ||||||||
\(913\) | −5.86499 | −0.194103 | ||||||||
\(914\) | 14.4097 | 0.476632 | ||||||||
\(915\) | 6.85906 | 0.226753 | ||||||||
\(916\) | −22.9905 | −0.759627 | ||||||||
\(917\) | −1.14713 | −0.0378815 | ||||||||
\(918\) | 1.66748 | 0.0550352 | ||||||||
\(919\) | 19.4954 | 0.643095 | 0.321547 | − | 0.946893i | \(-0.395797\pi\) | ||||
0.321547 | + | 0.946893i | \(0.395797\pi\) | |||||||
\(920\) | 10.8211 | 0.356759 | ||||||||
\(921\) | −27.1091 | −0.893274 | ||||||||
\(922\) | −23.3235 | −0.768119 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.0957381 | −0.00314955 | ||||||||
\(925\) | 22.5258 | 0.740643 | ||||||||
\(926\) | −12.0812 | −0.397011 | ||||||||
\(927\) | −7.09787 | −0.233125 | ||||||||
\(928\) | 13.0581 | 0.428655 | ||||||||
\(929\) | −9.95694 | −0.326677 | −0.163338 | − | 0.986570i | \(-0.552226\pi\) | ||||
−0.163338 | + | 0.986570i | \(0.552226\pi\) | |||||||
\(930\) | 15.2761 | 0.500921 | ||||||||
\(931\) | 1.98020 | 0.0648983 | ||||||||
\(932\) | 42.4652 | 1.39099 | ||||||||
\(933\) | 2.84322 | 0.0930829 | ||||||||
\(934\) | −5.44588 | −0.178195 | ||||||||
\(935\) | −8.25426 | −0.269943 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3817 | 0.959858 | 0.479929 | − | 0.877307i | \(-0.340662\pi\) | ||||
0.479929 | + | 0.877307i | \(0.340662\pi\) | |||||||
\(938\) | −0.0990081 | −0.00323273 | ||||||||
\(939\) | 27.2591 | 0.889566 | ||||||||
\(940\) | −24.8325 | −0.809948 | ||||||||
\(941\) | 29.1121 | 0.949027 | 0.474514 | − | 0.880248i | \(-0.342624\pi\) | ||||
0.474514 | + | 0.880248i | \(0.342624\pi\) | |||||||
\(942\) | −0.340802 | −0.0111039 | ||||||||
\(943\) | 13.3994 | 0.436346 | ||||||||
\(944\) | 19.8244 | 0.645229 | ||||||||
\(945\) | 0.209476 | 0.00681425 | ||||||||
\(946\) | 5.88679 | 0.191396 | ||||||||
\(947\) | −20.7275 | −0.673552 | −0.336776 | − | 0.941585i | \(-0.609337\pi\) | ||||
−0.336776 | + | 0.941585i | \(0.609337\pi\) | |||||||
\(948\) | 2.54789 | 0.0827516 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.21657 | −0.0394706 | ||||||||
\(951\) | 10.6977 | 0.346896 | ||||||||
\(952\) | 0.367250 | 0.0119027 | ||||||||
\(953\) | 36.6806 | 1.18820 | 0.594100 | − | 0.804391i | \(-0.297508\pi\) | ||||
0.594100 | + | 0.804391i | \(0.297508\pi\) | |||||||
\(954\) | 2.95254 | 0.0955921 | ||||||||
\(955\) | −88.7845 | −2.87300 | ||||||||
\(956\) | −4.87900 | −0.157798 | ||||||||
\(957\) | 2.25549 | 0.0729097 | ||||||||
\(958\) | 7.76081 | 0.250741 | ||||||||
\(959\) | 1.03045 | 0.0332749 | ||||||||
\(960\) | 3.54520 | 0.114421 | ||||||||
\(961\) | 13.6000 | 0.438710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.02814 | −0.258703 | ||||||||
\(964\) | 5.19425 | 0.167295 | ||||||||
\(965\) | 56.5574 | 1.82065 | ||||||||
\(966\) | −0.0565844 | −0.00182057 | ||||||||
\(967\) | −29.5774 | −0.951144 | −0.475572 | − | 0.879677i | \(-0.657759\pi\) | ||||
−0.475572 | + | 0.879677i | \(0.657759\pi\) | |||||||
\(968\) | −2.40497 | −0.0772988 | ||||||||
\(969\) | −0.694303 | −0.0223042 | ||||||||
\(970\) | 18.9912 | 0.609770 | ||||||||
\(971\) | −20.2417 | −0.649586 | −0.324793 | − | 0.945785i | \(-0.605295\pi\) | ||||
−0.324793 | + | 0.945785i | \(0.605295\pi\) | |||||||
\(972\) | 1.53791 | 0.0493285 | ||||||||
\(973\) | 1.04017 | 0.0333463 | ||||||||
\(974\) | 20.8368 | 0.667653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.93727 | 0.0940197 | ||||||||
\(977\) | −42.2256 | −1.35092 | −0.675459 | − | 0.737398i | \(-0.736054\pi\) | ||||
−0.675459 | + | 0.737398i | \(0.736054\pi\) | |||||||
\(978\) | −6.58046 | −0.210420 | ||||||||
\(979\) | −7.18799 | −0.229729 | ||||||||
\(980\) | −36.2050 | −1.15653 | ||||||||
\(981\) | −0.0538086 | −0.00171798 | ||||||||
\(982\) | −19.5447 | −0.623695 | ||||||||
\(983\) | 2.26617 | 0.0722796 | 0.0361398 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361398 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(984\) | 24.1001 | 0.768282 | ||||||||
\(985\) | 71.1069 | 2.26565 | ||||||||
\(986\) | −3.76100 | −0.119775 | ||||||||
\(987\) | 0.298720 | 0.00950836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5796 | −0.368210 | ||||||||
\(990\) | 2.28741 | 0.0726986 | ||||||||
\(991\) | −36.1269 | −1.14761 | −0.573804 | − | 0.818993i | \(-0.694533\pi\) | ||||
−0.573804 | + | 0.818993i | \(0.694533\pi\) | |||||||
\(992\) | 38.6641 | 1.22759 | ||||||||
\(993\) | −25.9797 | −0.824441 | ||||||||
\(994\) | 0.369926 | 0.0117333 | ||||||||
\(995\) | 73.1729 | 2.31974 | ||||||||
\(996\) | 9.01983 | 0.285804 | ||||||||
\(997\) | −17.0560 | −0.540168 | −0.270084 | − | 0.962837i | \(-0.587051\pi\) | ||||
−0.270084 | + | 0.962837i | \(0.587051\pi\) | |||||||
\(998\) | 0.373160 | 0.0118122 | ||||||||
\(999\) | −3.56253 | −0.112714 |
(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 | 5577.2.a.ba.1.8 | ✓ | 12 | |
13.12 | even | 2 | 5577.2.a.bc.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5577.2.a.ba.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
5577.2.a.bc.1.5 | yes | 12 | 13.12 | even | 2 |