Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3645,2,Mod(1,3645)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3645, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3645.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3645 = 3^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3645.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: | \(29.1054715368\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 3 x^{14} - 15 x^{13} + 47 x^{12} + 84 x^{11} - 279 x^{10} - 219 x^{9} + 783 x^{8} + 279 x^{7} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.694378\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3645.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.694378 | −0.491000 | −0.245500 | − | 0.969397i | \(-0.578952\pi\) | ||||
−0.245500 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.51784 | −0.758919 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.291597 | −0.110213 | −0.0551066 | − | 0.998480i | \(-0.517550\pi\) | ||||
−0.0551066 | + | 0.998480i | \(0.517550\pi\) | |||||||
\(8\) | 2.44271 | 0.863629 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.694378 | 0.219582 | ||||||||
\(11\) | 1.78834 | 0.539203 | 0.269602 | − | 0.962972i | \(-0.413108\pi\) | ||||
0.269602 | + | 0.962972i | \(0.413108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.19103 | 0.607682 | 0.303841 | − | 0.952723i | \(-0.401731\pi\) | ||||
0.303841 | + | 0.952723i | \(0.401731\pi\) | |||||||
\(14\) | 0.202478 | 0.0541146 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.33951 | 0.334878 | ||||||||
\(17\) | −5.46565 | −1.32562 | −0.662808 | − | 0.748790i | \(-0.730635\pi\) | ||||
−0.662808 | + | 0.748790i | \(0.730635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.84486 | −1.57032 | −0.785159 | − | 0.619295i | \(-0.787419\pi\) | ||||
−0.785159 | + | 0.619295i | \(0.787419\pi\) | |||||||
\(20\) | 1.51784 | 0.339399 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.24178 | −0.264749 | ||||||||
\(23\) | 5.34257 | 1.11400 | 0.557001 | − | 0.830512i | \(-0.311952\pi\) | ||||
0.557001 | + | 0.830512i | \(0.311952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.52140 | −0.298372 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.442597 | 0.0836429 | ||||||||
\(29\) | −2.95275 | −0.548312 | −0.274156 | − | 0.961685i | \(-0.588398\pi\) | ||||
−0.274156 | + | 0.961685i | \(0.588398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.22487 | 1.11802 | 0.559010 | − | 0.829161i | \(-0.311181\pi\) | ||||
0.559010 | + | 0.829161i | \(0.311181\pi\) | |||||||
\(32\) | −5.81555 | −1.02805 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.79523 | 0.650877 | ||||||||
\(35\) | 0.291597 | 0.0492888 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.54729 | −1.40517 | −0.702583 | − | 0.711602i | \(-0.747970\pi\) | ||||
−0.702583 | + | 0.711602i | \(0.747970\pi\) | |||||||
\(38\) | 4.75292 | 0.771025 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.44271 | −0.386226 | ||||||||
\(41\) | 4.55506 | 0.711381 | 0.355690 | − | 0.934604i | \(-0.384246\pi\) | ||||
0.355690 | + | 0.934604i | \(0.384246\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.37931 | 1.43033 | 0.715166 | − | 0.698955i | \(-0.246351\pi\) | ||||
0.715166 | + | 0.698955i | \(0.246351\pi\) | |||||||
\(44\) | −2.71440 | −0.409212 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.70976 | −0.546975 | ||||||||
\(47\) | 5.46220 | 0.796744 | 0.398372 | − | 0.917224i | \(-0.369575\pi\) | ||||
0.398372 | + | 0.917224i | \(0.369575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91497 | −0.987853 | ||||||||
\(50\) | −0.694378 | −0.0981999 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.32563 | −0.461182 | ||||||||
\(53\) | −2.24096 | −0.307820 | −0.153910 | − | 0.988085i | \(-0.549187\pi\) | ||||
−0.153910 | + | 0.988085i | \(0.549187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.78834 | −0.241139 | ||||||||
\(56\) | −0.712286 | −0.0951833 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.05033 | 0.269221 | ||||||||
\(59\) | 10.4333 | 1.35831 | 0.679153 | − | 0.733997i | \(-0.262347\pi\) | ||||
0.679153 | + | 0.733997i | \(0.262347\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.296654 | 0.0379827 | 0.0189913 | − | 0.999820i | \(-0.493955\pi\) | ||||
0.0189913 | + | 0.999820i | \(0.493955\pi\) | |||||||
\(62\) | −4.32241 | −0.548947 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.35917 | 0.169896 | ||||||||
\(65\) | −2.19103 | −0.271764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.45758 | −0.544580 | −0.272290 | − | 0.962215i | \(-0.587781\pi\) | ||||
−0.272290 | + | 0.962215i | \(0.587781\pi\) | |||||||
\(68\) | 8.29598 | 1.00604 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.202478 | −0.0242008 | ||||||||
\(71\) | 9.49280 | 1.12659 | 0.563294 | − | 0.826256i | \(-0.309534\pi\) | ||||
0.563294 | + | 0.826256i | \(0.309534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4842 | −1.22709 | −0.613544 | − | 0.789661i | \(-0.710257\pi\) | ||||
−0.613544 | + | 0.789661i | \(0.710257\pi\) | |||||||
\(74\) | 5.93505 | 0.689936 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3894 | 1.19174 | ||||||||
\(77\) | −0.521473 | −0.0594273 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.12060 | −0.801131 | −0.400565 | − | 0.916268i | \(-0.631186\pi\) | ||||
−0.400565 | + | 0.916268i | \(0.631186\pi\) | |||||||
\(80\) | −1.33951 | −0.149762 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.16293 | −0.349288 | ||||||||
\(83\) | −6.21102 | −0.681748 | −0.340874 | − | 0.940109i | \(-0.610723\pi\) | ||||
−0.340874 | + | 0.940109i | \(0.610723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.46565 | 0.592833 | ||||||||
\(86\) | −6.51279 | −0.702292 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.36839 | 0.465671 | ||||||||
\(89\) | 12.3795 | 1.31223 | 0.656113 | − | 0.754662i | \(-0.272199\pi\) | ||||
0.656113 | + | 0.754662i | \(0.272199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.638896 | −0.0669745 | ||||||||
\(92\) | −8.10916 | −0.845438 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.79283 | −0.391201 | ||||||||
\(95\) | 6.84486 | 0.702267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0798 | 1.42958 | 0.714792 | − | 0.699337i | \(-0.246521\pi\) | ||||
0.714792 | + | 0.699337i | \(0.246521\pi\) | |||||||
\(98\) | 4.80161 | 0.485035 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.51784 | −0.151784 | ||||||||
\(101\) | −12.6104 | −1.25478 | −0.627389 | − | 0.778706i | \(-0.715876\pi\) | ||||
−0.627389 | + | 0.778706i | \(0.715876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.89515 | −0.580867 | −0.290433 | − | 0.956895i | \(-0.593799\pi\) | ||||
−0.290433 | + | 0.956895i | \(0.593799\pi\) | |||||||
\(104\) | 5.35205 | 0.524811 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.55608 | 0.151140 | ||||||||
\(107\) | 6.13206 | 0.592808 | 0.296404 | − | 0.955063i | \(-0.404212\pi\) | ||||
0.296404 | + | 0.955063i | \(0.404212\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00653 | −0.479538 | −0.239769 | − | 0.970830i | \(-0.577072\pi\) | ||||
−0.239769 | + | 0.970830i | \(0.577072\pi\) | |||||||
\(110\) | 1.24178 | 0.118399 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.390597 | −0.0369080 | ||||||||
\(113\) | 2.24677 | 0.211358 | 0.105679 | − | 0.994400i | \(-0.466298\pi\) | ||||
0.105679 | + | 0.994400i | \(0.466298\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.34257 | −0.498197 | ||||||||
\(116\) | 4.48180 | 0.416125 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.24469 | −0.666928 | ||||||||
\(119\) | 1.59377 | 0.146100 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.80186 | −0.709260 | ||||||||
\(122\) | −0.205990 | −0.0186495 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.44835 | −0.848487 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.01072 | 0.355894 | 0.177947 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177947 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(128\) | 10.6873 | 0.944635 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.52140 | 0.133436 | ||||||||
\(131\) | −14.2980 | −1.24922 | −0.624610 | − | 0.780937i | \(-0.714742\pi\) | ||||
−0.624610 | + | 0.780937i | \(0.714742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.99594 | 0.173070 | ||||||||
\(134\) | 3.09524 | 0.267388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.3510 | −1.14484 | ||||||||
\(137\) | 1.49411 | 0.127650 | 0.0638250 | − | 0.997961i | \(-0.479670\pi\) | ||||
0.0638250 | + | 0.997961i | \(0.479670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.34934 | −0.368906 | −0.184453 | − | 0.982841i | \(-0.559051\pi\) | ||||
−0.184453 | + | 0.982841i | \(0.559051\pi\) | |||||||
\(140\) | −0.442597 | −0.0374062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.59160 | −0.553155 | ||||||||
\(143\) | 3.91829 | 0.327664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.95275 | 0.245213 | ||||||||
\(146\) | 7.28003 | 0.602499 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.9734 | 1.06641 | ||||||||
\(149\) | −11.8839 | −0.973566 | −0.486783 | − | 0.873523i | \(-0.661830\pi\) | ||||
−0.486783 | + | 0.873523i | \(0.661830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.7802 | −1.77245 | −0.886225 | − | 0.463254i | \(-0.846682\pi\) | ||||
−0.886225 | + | 0.463254i | \(0.846682\pi\) | |||||||
\(152\) | −16.7200 | −1.35617 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.362099 | 0.0291788 | ||||||||
\(155\) | −6.22487 | −0.499993 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.8666 | −1.02687 | −0.513435 | − | 0.858129i | \(-0.671627\pi\) | ||||
−0.513435 | + | 0.858129i | \(0.671627\pi\) | |||||||
\(158\) | 4.94439 | 0.393355 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.81555 | 0.459760 | ||||||||
\(161\) | −1.55788 | −0.122778 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1843 | −1.26765 | −0.633826 | − | 0.773476i | \(-0.718516\pi\) | ||||
−0.633826 | + | 0.773476i | \(0.718516\pi\) | |||||||
\(164\) | −6.91385 | −0.539881 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.31280 | 0.334738 | ||||||||
\(167\) | 16.4702 | 1.27450 | 0.637250 | − | 0.770658i | \(-0.280072\pi\) | ||||
0.637250 | + | 0.770658i | \(0.280072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.19940 | −0.630723 | ||||||||
\(170\) | −3.79523 | −0.291081 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.2363 | −1.08551 | ||||||||
\(173\) | −10.2644 | −0.780389 | −0.390195 | − | 0.920732i | \(-0.627592\pi\) | ||||
−0.390195 | + | 0.920732i | \(0.627592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.291597 | −0.0220426 | ||||||||
\(176\) | 2.39550 | 0.180567 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.59607 | −0.644303 | ||||||||
\(179\) | 6.81389 | 0.509294 | 0.254647 | − | 0.967034i | \(-0.418041\pi\) | ||||
0.254647 | + | 0.967034i | \(0.418041\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.9084 | −1.92575 | −0.962876 | − | 0.269943i | \(-0.912995\pi\) | ||||
−0.962876 | + | 0.269943i | \(0.912995\pi\) | |||||||
\(182\) | 0.443636 | 0.0328845 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.0504 | 0.962085 | ||||||||
\(185\) | 8.54729 | 0.628409 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.77442 | −0.714776 | ||||||||
\(188\) | −8.29074 | −0.604665 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.75292 | −0.344813 | ||||||||
\(191\) | 19.5004 | 1.41100 | 0.705500 | − | 0.708710i | \(-0.250722\pi\) | ||||
0.705500 | + | 0.708710i | \(0.250722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1259 | −1.23275 | −0.616374 | − | 0.787454i | \(-0.711399\pi\) | ||||
−0.616374 | + | 0.787454i | \(0.711399\pi\) | |||||||
\(194\) | −9.77669 | −0.701925 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4958 | 0.749701 | ||||||||
\(197\) | −19.5552 | −1.39325 | −0.696624 | − | 0.717436i | \(-0.745316\pi\) | ||||
−0.696624 | + | 0.717436i | \(0.745316\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3564 | −1.51391 | −0.756956 | − | 0.653466i | \(-0.773314\pi\) | ||||
−0.756956 | + | 0.653466i | \(0.773314\pi\) | |||||||
\(200\) | 2.44271 | 0.172726 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.75636 | 0.616095 | ||||||||
\(203\) | 0.861012 | 0.0604312 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55506 | −0.318139 | ||||||||
\(206\) | 4.09347 | 0.285205 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.93491 | 0.203499 | ||||||||
\(209\) | −12.2409 | −0.846720 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.84964 | 0.127335 | 0.0636673 | − | 0.997971i | \(-0.479720\pi\) | ||||
0.0636673 | + | 0.997971i | \(0.479720\pi\) | |||||||
\(212\) | 3.40142 | 0.233611 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.25797 | −0.291069 | ||||||||
\(215\) | −9.37931 | −0.639664 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.81515 | −0.123220 | ||||||||
\(218\) | 3.47642 | 0.235453 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.71440 | 0.183005 | ||||||||
\(221\) | −11.9754 | −0.805552 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.66619 | −0.178542 | −0.0892708 | − | 0.996007i | \(-0.528454\pi\) | ||||
−0.0892708 | + | 0.996007i | \(0.528454\pi\) | |||||||
\(224\) | 1.69579 | 0.113305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.56011 | −0.103777 | ||||||||
\(227\) | −4.48110 | −0.297421 | −0.148711 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148711 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.3717 | 1.61053 | 0.805265 | − | 0.592915i | \(-0.202023\pi\) | ||||
0.805265 | + | 0.592915i | \(0.202023\pi\) | |||||||
\(230\) | 3.70976 | 0.244615 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.21272 | −0.473538 | ||||||||
\(233\) | −4.80472 | −0.314767 | −0.157384 | − | 0.987538i | \(-0.550306\pi\) | ||||
−0.157384 | + | 0.987538i | \(0.550306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.46220 | −0.356315 | ||||||||
\(236\) | −15.8361 | −1.03084 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.10668 | −0.0717352 | ||||||||
\(239\) | −16.5595 | −1.07115 | −0.535573 | − | 0.844489i | \(-0.679904\pi\) | ||||
−0.535573 | + | 0.844489i | \(0.679904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.9515 | 1.80052 | 0.900258 | − | 0.435356i | \(-0.143378\pi\) | ||||
0.900258 | + | 0.435356i | \(0.143378\pi\) | |||||||
\(242\) | 5.41744 | 0.348246 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.450273 | −0.0288258 | ||||||||
\(245\) | 6.91497 | 0.441781 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9973 | −0.954253 | ||||||||
\(248\) | 15.2056 | 0.965554 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.694378 | 0.0439163 | ||||||||
\(251\) | −23.1222 | −1.45946 | −0.729730 | − | 0.683736i | \(-0.760354\pi\) | ||||
−0.729730 | + | 0.683736i | \(0.760354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.55431 | 0.600674 | ||||||||
\(254\) | −2.78496 | −0.174744 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1394 | −0.633711 | ||||||||
\(257\) | −27.8963 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.49236 | 0.154868 | ||||||||
\(260\) | 3.32563 | 0.206247 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.92820 | 0.613367 | ||||||||
\(263\) | −15.4147 | −0.950514 | −0.475257 | − | 0.879847i | \(-0.657645\pi\) | ||||
−0.475257 | + | 0.879847i | \(0.657645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.24096 | 0.137661 | ||||||||
\(266\) | −1.38594 | −0.0849771 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.76588 | 0.413292 | ||||||||
\(269\) | 16.5120 | 1.00675 | 0.503377 | − | 0.864067i | \(-0.332091\pi\) | ||||
0.503377 | + | 0.864067i | \(0.332091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.72926 | −0.165791 | −0.0828953 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828953 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(272\) | −7.32131 | −0.443920 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.03747 | −0.0626761 | ||||||||
\(275\) | 1.78834 | 0.107841 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.58747 | 0.576055 | 0.288028 | − | 0.957622i | \(-0.407001\pi\) | ||||
0.288028 | + | 0.957622i | \(0.407001\pi\) | |||||||
\(278\) | 3.02009 | 0.181133 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.712286 | 0.0425672 | ||||||||
\(281\) | 3.21598 | 0.191849 | 0.0959245 | − | 0.995389i | \(-0.469419\pi\) | ||||
0.0959245 | + | 0.995389i | \(0.469419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3104 | −1.50455 | −0.752273 | − | 0.658852i | \(-0.771042\pi\) | ||||
−0.752273 | + | 0.658852i | \(0.771042\pi\) | |||||||
\(284\) | −14.4085 | −0.854990 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.72078 | −0.160883 | ||||||||
\(287\) | −1.32824 | −0.0784035 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8734 | 0.757256 | ||||||||
\(290\) | −2.05033 | −0.120399 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.9134 | 0.931260 | ||||||||
\(293\) | 23.8942 | 1.39591 | 0.697957 | − | 0.716140i | \(-0.254093\pi\) | ||||
0.697957 | + | 0.716140i | \(0.254093\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.4333 | −0.607453 | ||||||||
\(296\) | −20.8785 | −1.21354 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.25191 | 0.478020 | ||||||||
\(299\) | 11.7057 | 0.676959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.73497 | −0.157641 | ||||||||
\(302\) | 15.1237 | 0.870273 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.16877 | −0.525865 | ||||||||
\(305\) | −0.296654 | −0.0169864 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0776 | −0.917597 | −0.458799 | − | 0.888540i | \(-0.651720\pi\) | ||||
−0.458799 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(308\) | 0.791511 | 0.0451005 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.32241 | 0.245497 | ||||||||
\(311\) | −17.3187 | −0.982053 | −0.491027 | − | 0.871145i | \(-0.663378\pi\) | ||||
−0.491027 | + | 0.871145i | \(0.663378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4037 | 0.757621 | 0.378811 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378811 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(314\) | 8.93431 | 0.504192 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8079 | 0.607994 | ||||||||
\(317\) | 21.4215 | 1.20315 | 0.601576 | − | 0.798815i | \(-0.294540\pi\) | ||||
0.601576 | + | 0.798815i | \(0.294540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.28051 | −0.295652 | ||||||||
\(320\) | −1.35917 | −0.0759797 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.08175 | 0.0602838 | ||||||||
\(323\) | 37.4116 | 2.08164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.19103 | 0.121536 | ||||||||
\(326\) | 11.2380 | 0.622416 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.1267 | 0.614369 | ||||||||
\(329\) | −1.59276 | −0.0878117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.04681 | −0.442293 | −0.221146 | − | 0.975241i | \(-0.570980\pi\) | ||||
−0.221146 | + | 0.975241i | \(0.570980\pi\) | |||||||
\(332\) | 9.42732 | 0.517392 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.4365 | −0.625779 | ||||||||
\(335\) | 4.45758 | 0.243543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6757 | 1.12628 | 0.563139 | − | 0.826362i | \(-0.309594\pi\) | ||||
0.563139 | + | 0.826362i | \(0.309594\pi\) | |||||||
\(338\) | 5.69348 | 0.309685 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.29598 | −0.449913 | ||||||||
\(341\) | 11.1322 | 0.602840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.05756 | 0.219088 | ||||||||
\(344\) | 22.9109 | 1.23528 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.12739 | 0.383171 | ||||||||
\(347\) | −9.17856 | −0.492731 | −0.246366 | − | 0.969177i | \(-0.579236\pi\) | ||||
−0.246366 | + | 0.969177i | \(0.579236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.3345 | −1.08848 | −0.544240 | − | 0.838930i | \(-0.683182\pi\) | ||||
−0.544240 | + | 0.838930i | \(0.683182\pi\) | |||||||
\(350\) | 0.202478 | 0.0108229 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.4002 | −0.554330 | ||||||||
\(353\) | 5.72152 | 0.304526 | 0.152263 | − | 0.988340i | \(-0.451344\pi\) | ||||
0.152263 | + | 0.988340i | \(0.451344\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.49280 | −0.503826 | ||||||||
\(356\) | −18.7901 | −0.995874 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.73141 | −0.250063 | ||||||||
\(359\) | −32.4662 | −1.71350 | −0.856749 | − | 0.515733i | \(-0.827520\pi\) | ||||
−0.856749 | + | 0.515733i | \(0.827520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.8520 | 1.46590 | ||||||||
\(362\) | 17.9902 | 0.945544 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.969742 | 0.0508283 | ||||||||
\(365\) | 10.4842 | 0.548770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.18664 | 0.218541 | 0.109271 | − | 0.994012i | \(-0.465149\pi\) | ||||
0.109271 | + | 0.994012i | \(0.465149\pi\) | |||||||
\(368\) | 7.15644 | 0.373055 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.93505 | −0.308549 | ||||||||
\(371\) | 0.653458 | 0.0339258 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.90859 | 0.357713 | 0.178857 | − | 0.983875i | \(-0.442760\pi\) | ||||
0.178857 | + | 0.983875i | \(0.442760\pi\) | |||||||
\(374\) | 6.78714 | 0.350955 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.3426 | 0.688091 | ||||||||
\(377\) | −6.46956 | −0.333199 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.83488 | −0.505184 | −0.252592 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252592 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(380\) | −10.3894 | −0.532964 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.5407 | −0.692800 | ||||||||
\(383\) | 29.9760 | 1.53170 | 0.765851 | − | 0.643018i | \(-0.222318\pi\) | ||||
0.765851 | + | 0.643018i | \(0.222318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.521473 | 0.0265767 | ||||||||
\(386\) | 11.8918 | 0.605279 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.3708 | −1.08494 | ||||||||
\(389\) | −11.9460 | −0.605685 | −0.302843 | − | 0.953041i | \(-0.597936\pi\) | ||||
−0.302843 | + | 0.953041i | \(0.597936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.2006 | −1.47674 | ||||||||
\(392\) | −16.8913 | −0.853138 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.5787 | 0.684085 | ||||||||
\(395\) | 7.12060 | 0.358277 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9255 | −0.598526 | −0.299263 | − | 0.954171i | \(-0.596741\pi\) | ||||
−0.299263 | + | 0.954171i | \(0.596741\pi\) | |||||||
\(398\) | 14.8294 | 0.743330 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.33951 | 0.0669756 | ||||||||
\(401\) | −34.9016 | −1.74290 | −0.871452 | − | 0.490481i | \(-0.836821\pi\) | ||||
−0.871452 | + | 0.490481i | \(0.836821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6389 | 0.679400 | ||||||||
\(404\) | 19.1405 | 0.952275 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.597868 | −0.0296717 | ||||||||
\(407\) | −15.2854 | −0.757670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.4755 | −0.567427 | −0.283713 | − | 0.958909i | \(-0.591566\pi\) | ||||
−0.283713 | + | 0.958909i | \(0.591566\pi\) | |||||||
\(410\) | 3.16293 | 0.156206 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.94789 | 0.440831 | ||||||||
\(413\) | −3.04233 | −0.149703 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.21102 | 0.304887 | ||||||||
\(416\) | −12.7420 | −0.624730 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.49981 | 0.415739 | ||||||||
\(419\) | 30.9446 | 1.51174 | 0.755872 | − | 0.654719i | \(-0.227213\pi\) | ||||
0.755872 | + | 0.654719i | \(0.227213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.46162 | 0.461131 | 0.230566 | − | 0.973057i | \(-0.425942\pi\) | ||||
0.230566 | + | 0.973057i | \(0.425942\pi\) | |||||||
\(422\) | −1.28435 | −0.0625213 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.47403 | −0.265842 | ||||||||
\(425\) | −5.46565 | −0.265123 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0865033 | −0.00418619 | ||||||||
\(428\) | −9.30747 | −0.449894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.51279 | 0.314075 | ||||||||
\(431\) | −2.72680 | −0.131345 | −0.0656727 | − | 0.997841i | \(-0.520919\pi\) | ||||
−0.0656727 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.8159 | −0.904237 | −0.452118 | − | 0.891958i | \(-0.649332\pi\) | ||||
−0.452118 | + | 0.891958i | \(0.649332\pi\) | |||||||
\(434\) | 1.26040 | 0.0605012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.59910 | 0.363931 | ||||||||
\(437\) | −36.5691 | −1.74934 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.2550 | −0.680356 | −0.340178 | − | 0.940361i | \(-0.610487\pi\) | ||||
−0.340178 | + | 0.940361i | \(0.610487\pi\) | |||||||
\(440\) | −4.36839 | −0.208255 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.31545 | 0.395526 | ||||||||
\(443\) | −4.24329 | −0.201605 | −0.100802 | − | 0.994906i | \(-0.532141\pi\) | ||||
−0.100802 | + | 0.994906i | \(0.532141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.3795 | −0.586846 | ||||||||
\(446\) | 1.85135 | 0.0876638 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.396328 | −0.0187248 | ||||||||
\(449\) | −1.09920 | −0.0518742 | −0.0259371 | − | 0.999664i | \(-0.508257\pi\) | ||||
−0.0259371 | + | 0.999664i | \(0.508257\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.14597 | 0.383579 | ||||||||
\(452\) | −3.41023 | −0.160404 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.11158 | 0.146034 | ||||||||
\(455\) | 0.638896 | 0.0299519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.53135 | −0.165189 | −0.0825947 | − | 0.996583i | \(-0.526321\pi\) | ||||
−0.0825947 | + | 0.996583i | \(0.526321\pi\) | |||||||
\(458\) | −16.9232 | −0.790770 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.10916 | 0.378092 | ||||||||
\(461\) | −21.4747 | −1.00017 | −0.500087 | − | 0.865975i | \(-0.666699\pi\) | ||||
−0.500087 | + | 0.865975i | \(0.666699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4028 | 1.08762 | 0.543810 | − | 0.839208i | \(-0.316981\pi\) | ||||
0.543810 | + | 0.839208i | \(0.316981\pi\) | |||||||
\(464\) | −3.95525 | −0.183618 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.33629 | 0.154551 | ||||||||
\(467\) | 29.7095 | 1.37479 | 0.687396 | − | 0.726283i | \(-0.258754\pi\) | ||||
0.687396 | + | 0.726283i | \(0.258754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.29981 | 0.0600198 | ||||||||
\(470\) | 3.79283 | 0.174950 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.4857 | 1.17307 | ||||||||
\(473\) | 16.7733 | 0.771239 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.84486 | −0.314064 | ||||||||
\(476\) | −2.41908 | −0.110878 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.4986 | 0.525932 | ||||||||
\(479\) | −10.7927 | −0.493131 | −0.246566 | − | 0.969126i | \(-0.579302\pi\) | ||||
−0.246566 | + | 0.969126i | \(0.579302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.7273 | −0.853893 | ||||||||
\(482\) | −19.4089 | −0.884053 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.8420 | 0.538271 | ||||||||
\(485\) | −14.0798 | −0.639329 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.9786 | 1.26783 | 0.633916 | − | 0.773402i | \(-0.281446\pi\) | ||||
0.633916 | + | 0.773402i | \(0.281446\pi\) | |||||||
\(488\) | 0.724640 | 0.0328029 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.80161 | −0.216914 | ||||||||
\(491\) | −32.9123 | −1.48531 | −0.742655 | − | 0.669674i | \(-0.766434\pi\) | ||||
−0.742655 | + | 0.669674i | \(0.766434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1387 | 0.726851 | ||||||||
\(494\) | 10.4138 | 0.468538 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.33829 | 0.374400 | ||||||||
\(497\) | −2.76807 | −0.124165 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7063 | −0.703112 | −0.351556 | − | 0.936167i | \(-0.614347\pi\) | ||||
−0.351556 | + | 0.936167i | \(0.614347\pi\) | |||||||
\(500\) | 1.51784 | 0.0678798 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.0555 | 0.716594 | ||||||||
\(503\) | −19.0851 | −0.850964 | −0.425482 | − | 0.904967i | \(-0.639896\pi\) | ||||
−0.425482 | + | 0.904967i | \(0.639896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6104 | 0.561154 | ||||||||
\(506\) | −6.63430 | −0.294931 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.08763 | −0.270095 | ||||||||
\(509\) | 13.7678 | 0.610245 | 0.305122 | − | 0.952313i | \(-0.401303\pi\) | ||||
0.305122 | + | 0.952313i | \(0.401303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.05717 | 0.135241 | ||||||||
\(512\) | −14.3341 | −0.633483 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.3706 | 0.854401 | ||||||||
\(515\) | 5.89515 | 0.259772 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.76825 | 0.429607 | ||||||||
\(518\) | −1.73064 | −0.0760400 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.35205 | −0.234703 | ||||||||
\(521\) | 15.6068 | 0.683748 | 0.341874 | − | 0.939746i | \(-0.388938\pi\) | ||||
0.341874 | + | 0.939746i | \(0.388938\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5475 | 0.636117 | 0.318058 | − | 0.948071i | \(-0.396969\pi\) | ||||
0.318058 | + | 0.948071i | \(0.396969\pi\) | |||||||
\(524\) | 21.7020 | 0.948057 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.7037 | 0.466702 | ||||||||
\(527\) | −34.0230 | −1.48206 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.54305 | 0.241002 | ||||||||
\(530\) | −1.55608 | −0.0675917 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.02951 | −0.131346 | ||||||||
\(533\) | 9.98026 | 0.432293 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.13206 | −0.265112 | ||||||||
\(536\) | −10.8886 | −0.470315 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.4656 | −0.494316 | ||||||||
\(539\) | −12.3663 | −0.532654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.02903 | −0.0442416 | −0.0221208 | − | 0.999755i | \(-0.507042\pi\) | ||||
−0.0221208 | + | 0.999755i | \(0.507042\pi\) | |||||||
\(542\) | 1.89514 | 0.0814032 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 31.7858 | 1.36280 | ||||||||
\(545\) | 5.00653 | 0.214456 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.3080 | 1.16761 | 0.583803 | − | 0.811896i | \(-0.301564\pi\) | ||||
0.583803 | + | 0.811896i | \(0.301564\pi\) | |||||||
\(548\) | −2.26781 | −0.0968761 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.24178 | −0.0529497 | ||||||||
\(551\) | 20.2112 | 0.861024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.07634 | 0.0882951 | ||||||||
\(554\) | −6.65733 | −0.282843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.60159 | 0.279970 | ||||||||
\(557\) | −14.3369 | −0.607476 | −0.303738 | − | 0.952756i | \(-0.598235\pi\) | ||||
−0.303738 | + | 0.952756i | \(0.598235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.5503 | 0.869186 | ||||||||
\(560\) | 0.390597 | 0.0165057 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.23310 | −0.0941978 | ||||||||
\(563\) | 29.0423 | 1.22399 | 0.611994 | − | 0.790863i | \(-0.290368\pi\) | ||||
0.611994 | + | 0.790863i | \(0.290368\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.24677 | −0.0945221 | ||||||||
\(566\) | 17.5750 | 0.738731 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.1882 | 0.972954 | ||||||||
\(569\) | −3.69642 | −0.154962 | −0.0774810 | − | 0.996994i | \(-0.524688\pi\) | ||||
−0.0774810 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.33907 | 0.223433 | 0.111717 | − | 0.993740i | \(-0.464365\pi\) | ||||
0.111717 | + | 0.993740i | \(0.464365\pi\) | |||||||
\(572\) | −5.94734 | −0.248671 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.922301 | 0.0384961 | ||||||||
\(575\) | 5.34257 | 0.222801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4615 | 0.893455 | 0.446727 | − | 0.894670i | \(-0.352589\pi\) | ||||
0.446727 | + | 0.894670i | \(0.352589\pi\) | |||||||
\(578\) | −8.93898 | −0.371812 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.48180 | −0.186097 | ||||||||
\(581\) | 1.81111 | 0.0751376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00760 | −0.165978 | ||||||||
\(584\) | −25.6100 | −1.05975 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.5916 | −0.685393 | ||||||||
\(587\) | −6.08738 | −0.251253 | −0.125627 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125627 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.6083 | −1.75565 | ||||||||
\(590\) | 7.24469 | 0.298259 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.4492 | −0.470559 | ||||||||
\(593\) | 0.198543 | 0.00815319 | 0.00407660 | − | 0.999992i | \(-0.498702\pi\) | ||||
0.00407660 | + | 0.999992i | \(0.498702\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.59377 | −0.0653380 | ||||||||
\(596\) | 18.0378 | 0.738858 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.12820 | −0.332387 | ||||||||
\(599\) | −8.54109 | −0.348979 | −0.174490 | − | 0.984659i | \(-0.555828\pi\) | ||||
−0.174490 | + | 0.984659i | \(0.555828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3212 | 0.543383 | 0.271691 | − | 0.962384i | \(-0.412417\pi\) | ||||
0.271691 | + | 0.962384i | \(0.412417\pi\) | |||||||
\(602\) | 1.89911 | 0.0774018 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 33.0589 | 1.34515 | ||||||||
\(605\) | 7.80186 | 0.317191 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.25384 | −0.0508917 | −0.0254458 | − | 0.999676i | \(-0.508101\pi\) | ||||
−0.0254458 | + | 0.999676i | \(0.508101\pi\) | |||||||
\(608\) | 39.8066 | 1.61437 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.205990 | 0.00834030 | ||||||||
\(611\) | 11.9678 | 0.484167 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7765 | −0.596818 | −0.298409 | − | 0.954438i | \(-0.596456\pi\) | ||||
−0.298409 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(614\) | 11.1639 | 0.450540 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.27381 | −0.0513231 | ||||||||
\(617\) | 2.12796 | 0.0856684 | 0.0428342 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428342 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7002 | −0.711430 | −0.355715 | − | 0.934594i | \(-0.615763\pi\) | ||||
−0.355715 | + | 0.934594i | \(0.615763\pi\) | |||||||
\(620\) | 9.44835 | 0.379455 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0257 | 0.482188 | ||||||||
\(623\) | −3.60983 | −0.144625 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.30723 | −0.371992 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.5295 | 0.779311 | ||||||||
\(629\) | 46.7165 | 1.86271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0809 | 0.480933 | 0.240466 | − | 0.970657i | \(-0.422700\pi\) | ||||
0.240466 | + | 0.970657i | \(0.422700\pi\) | |||||||
\(632\) | −17.3936 | −0.691879 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.8746 | −0.590747 | ||||||||
\(635\) | −4.01072 | −0.159161 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.1509 | −0.600300 | ||||||||
\(638\) | 3.66667 | 0.145165 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.6873 | −0.422454 | ||||||||
\(641\) | 14.1528 | 0.559004 | 0.279502 | − | 0.960145i | \(-0.409831\pi\) | ||||
0.279502 | + | 0.960145i | \(0.409831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5908 | 0.930329 | 0.465164 | − | 0.885224i | \(-0.345995\pi\) | ||||
0.465164 | + | 0.885224i | \(0.345995\pi\) | |||||||
\(644\) | 2.36460 | 0.0931784 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.9778 | −1.02208 | ||||||||
\(647\) | 0.0994615 | 0.00391023 | 0.00195512 | − | 0.999998i | \(-0.499378\pi\) | ||||
0.00195512 | + | 0.999998i | \(0.499378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6583 | 0.732403 | ||||||||
\(650\) | −1.52140 | −0.0596743 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.5652 | 0.962046 | ||||||||
\(653\) | 16.4226 | 0.642666 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2980 | 0.558668 | ||||||||
\(656\) | 6.10156 | 0.238226 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.10598 | 0.0431155 | ||||||||
\(659\) | −37.9333 | −1.47767 | −0.738836 | − | 0.673885i | \(-0.764624\pi\) | ||||
−0.738836 | + | 0.673885i | \(0.764624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0649 | −0.508166 | −0.254083 | − | 0.967182i | \(-0.581774\pi\) | ||||
−0.254083 | + | 0.967182i | \(0.581774\pi\) | |||||||
\(662\) | 5.58753 | 0.217165 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.1717 | −0.588777 | ||||||||
\(665\) | −1.99594 | −0.0773991 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.7753 | −0.610821 | ||||||||
\(668\) | −24.9990 | −0.967242 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.09524 | −0.119580 | ||||||||
\(671\) | 0.530517 | 0.0204804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.04776 | 0.156030 | 0.0780148 | − | 0.996952i | \(-0.475142\pi\) | ||||
0.0780148 | + | 0.996952i | \(0.475142\pi\) | |||||||
\(674\) | −14.3568 | −0.553002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.4454 | 0.478668 | ||||||||
\(677\) | −14.9229 | −0.573535 | −0.286768 | − | 0.958000i | \(-0.592581\pi\) | ||||
−0.286768 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.10561 | −0.157559 | ||||||||
\(680\) | 13.3510 | 0.511988 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.72992 | −0.295994 | ||||||||
\(683\) | −23.3698 | −0.894220 | −0.447110 | − | 0.894479i | \(-0.647547\pi\) | ||||
−0.447110 | + | 0.894479i | \(0.647547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.49411 | −0.0570868 | ||||||||
\(686\) | −2.81748 | −0.107572 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.5637 | 0.478987 | ||||||||
\(689\) | −4.91002 | −0.187057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5671 | 0.478077 | 0.239038 | − | 0.971010i | \(-0.423168\pi\) | ||||
0.239038 | + | 0.971010i | \(0.423168\pi\) | |||||||
\(692\) | 15.5797 | 0.592252 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.37340 | 0.241931 | ||||||||
\(695\) | 4.34934 | 0.164980 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.8964 | −0.943017 | ||||||||
\(698\) | 14.1198 | 0.534443 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.442597 | 0.0167286 | ||||||||
\(701\) | −38.3903 | −1.44998 | −0.724991 | − | 0.688758i | \(-0.758156\pi\) | ||||
−0.724991 | + | 0.688758i | \(0.758156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.5049 | 2.20656 | ||||||||
\(704\) | 2.43065 | 0.0916084 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.97290 | −0.149522 | ||||||||
\(707\) | 3.67714 | 0.138293 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.80062 | −0.292959 | −0.146479 | − | 0.989214i | \(-0.546794\pi\) | ||||
−0.146479 | + | 0.989214i | \(0.546794\pi\) | |||||||
\(710\) | 6.59160 | 0.247378 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.2396 | 1.13328 | ||||||||
\(713\) | 33.2568 | 1.24548 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.91829 | −0.146536 | ||||||||
\(716\) | −10.3424 | −0.386513 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.5438 | 0.841327 | ||||||||
\(719\) | −29.6952 | −1.10744 | −0.553722 | − | 0.832702i | \(-0.686793\pi\) | ||||
−0.553722 | + | 0.832702i | \(0.686793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.71901 | 0.0640192 | ||||||||
\(722\) | −19.3399 | −0.719755 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 39.3247 | 1.46149 | ||||||||
\(725\) | −2.95275 | −0.109662 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.771126 | 0.0285995 | 0.0142997 | − | 0.999898i | \(-0.495448\pi\) | ||||
0.0142997 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(728\) | −1.56064 | −0.0578411 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.28003 | −0.269446 | ||||||||
\(731\) | −51.2640 | −1.89607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.04505 | −0.0755358 | −0.0377679 | − | 0.999287i | \(-0.512025\pi\) | ||||
−0.0377679 | + | 0.999287i | \(0.512025\pi\) | |||||||
\(734\) | −2.90711 | −0.107304 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.0700 | −1.14525 | ||||||||
\(737\) | −7.97164 | −0.293639 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.56527 | −0.315079 | −0.157539 | − | 0.987513i | \(-0.550356\pi\) | ||||
−0.157539 | + | 0.987513i | \(0.550356\pi\) | |||||||
\(740\) | −12.9734 | −0.476912 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.453747 | −0.0166576 | ||||||||
\(743\) | 33.5742 | 1.23172 | 0.615860 | − | 0.787856i | \(-0.288809\pi\) | ||||
0.615860 | + | 0.787856i | \(0.288809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8839 | 0.435392 | ||||||||
\(746\) | −4.79717 | −0.175637 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.8360 | 0.542458 | ||||||||
\(749\) | −1.78809 | −0.0653353 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4434 | −0.855463 | −0.427731 | − | 0.903906i | \(-0.640687\pi\) | ||||
−0.427731 | + | 0.903906i | \(0.640687\pi\) | |||||||
\(752\) | 7.31669 | 0.266812 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.49232 | 0.163601 | ||||||||
\(755\) | 21.7802 | 0.792664 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.94896 | 0.107182 | 0.0535909 | − | 0.998563i | \(-0.482933\pi\) | ||||
0.0535909 | + | 0.998563i | \(0.482933\pi\) | |||||||
\(758\) | 6.82913 | 0.248045 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.7200 | 0.606498 | ||||||||
\(761\) | −29.7536 | −1.07857 | −0.539284 | − | 0.842124i | \(-0.681305\pi\) | ||||
−0.539284 | + | 0.842124i | \(0.681305\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.45989 | 0.0528515 | ||||||||
\(764\) | −29.5985 | −1.07084 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.8147 | −0.752065 | ||||||||
\(767\) | 22.8598 | 0.825418 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.98003 | −0.287767 | −0.143884 | − | 0.989595i | \(-0.545959\pi\) | ||||
−0.143884 | + | 0.989595i | \(0.545959\pi\) | |||||||
\(770\) | −0.362099 | −0.0130491 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.9943 | 0.935556 | ||||||||
\(773\) | 0.375937 | 0.0135215 | 0.00676076 | − | 0.999977i | \(-0.497848\pi\) | ||||
0.00676076 | + | 0.999977i | \(0.497848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.22487 | 0.223604 | ||||||||
\(776\) | 34.3928 | 1.23463 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.29503 | 0.297391 | ||||||||
\(779\) | −31.1787 | −1.11709 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9763 | 0.607460 | ||||||||
\(782\) | 20.2763 | 0.725078 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.26269 | −0.330810 | ||||||||
\(785\) | 12.8666 | 0.459230 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.90797 | −0.210596 | −0.105298 | − | 0.994441i | \(-0.533580\pi\) | ||||
−0.105298 | + | 0.994441i | \(0.533580\pi\) | |||||||
\(788\) | 29.6816 | 1.05736 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.94439 | −0.175914 | ||||||||
\(791\) | −0.655149 | −0.0232944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.649977 | 0.0230814 | ||||||||
\(794\) | 8.28083 | 0.293876 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.4155 | 1.14894 | ||||||||
\(797\) | 51.5520 | 1.82607 | 0.913033 | − | 0.407886i | \(-0.133734\pi\) | ||||
0.913033 | + | 0.407886i | \(0.133734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.8545 | −1.05618 | ||||||||
\(800\) | −5.81555 | −0.205611 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.2349 | 0.855765 | ||||||||
\(803\) | −18.7493 | −0.661649 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.55788 | 0.0549079 | ||||||||
\(806\) | −9.47053 | −0.333585 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −30.8035 | −1.08366 | ||||||||
\(809\) | −37.4718 | −1.31744 | −0.658719 | − | 0.752389i | \(-0.728901\pi\) | ||||
−0.658719 | + | 0.752389i | \(0.728901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.5789 | 0.968426 | 0.484213 | − | 0.874950i | \(-0.339106\pi\) | ||||
0.484213 | + | 0.874950i | \(0.339106\pi\) | |||||||
\(812\) | −1.30688 | −0.0458624 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.6139 | 0.372016 | ||||||||
\(815\) | 16.1843 | 0.566911 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.2000 | −2.24607 | ||||||||
\(818\) | 7.96834 | 0.278606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.91385 | 0.241442 | ||||||||
\(821\) | −44.5274 | −1.55402 | −0.777008 | − | 0.629491i | \(-0.783263\pi\) | ||||
−0.777008 | + | 0.629491i | \(0.783263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.2956 | −0.881748 | −0.440874 | − | 0.897569i | \(-0.645331\pi\) | ||||
−0.440874 | + | 0.897569i | \(0.645331\pi\) | |||||||
\(824\) | −14.4002 | −0.501653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.11253 | 0.0735042 | ||||||||
\(827\) | 18.9379 | 0.658534 | 0.329267 | − | 0.944237i | \(-0.393198\pi\) | ||||
0.329267 | + | 0.944237i | \(0.393198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.45210 | 0.119896 | 0.0599482 | − | 0.998201i | \(-0.480906\pi\) | ||||
0.0599482 | + | 0.998201i | \(0.480906\pi\) | |||||||
\(830\) | −4.31280 | −0.149699 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.97797 | 0.103243 | ||||||||
\(833\) | 37.7948 | 1.30951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.4702 | −0.569973 | ||||||||
\(836\) | 18.5797 | 0.642593 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.4873 | −0.742266 | ||||||||
\(839\) | −19.1777 | −0.662088 | −0.331044 | − | 0.943615i | \(-0.607401\pi\) | ||||
−0.331044 | + | 0.943615i | \(0.607401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2813 | −0.699354 | ||||||||
\(842\) | −6.56994 | −0.226415 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.80746 | −0.0966367 | ||||||||
\(845\) | 8.19940 | 0.282068 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27500 | 0.0781698 | ||||||||
\(848\) | −3.00180 | −0.103082 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.79523 | 0.130175 | ||||||||
\(851\) | −45.6645 | −1.56536 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.84922 | −0.200273 | −0.100137 | − | 0.994974i | \(-0.531928\pi\) | ||||
−0.100137 | + | 0.994974i | \(0.531928\pi\) | |||||||
\(854\) | 0.0600660 | 0.00205542 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.9788 | 0.511966 | ||||||||
\(857\) | 49.4113 | 1.68786 | 0.843930 | − | 0.536454i | \(-0.180236\pi\) | ||||
0.843930 | + | 0.536454i | \(0.180236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.77965 | 0.265438 | 0.132719 | − | 0.991154i | \(-0.457629\pi\) | ||||
0.132719 | + | 0.991154i | \(0.457629\pi\) | |||||||
\(860\) | 14.2363 | 0.485453 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.89343 | 0.0644905 | ||||||||
\(863\) | −11.8283 | −0.402639 | −0.201320 | − | 0.979526i | \(-0.564523\pi\) | ||||
−0.201320 | + | 0.979526i | \(0.564523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2644 | 0.349001 | ||||||||
\(866\) | 13.0654 | 0.443980 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.75511 | 0.0935144 | ||||||||
\(869\) | −12.7340 | −0.431972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.76667 | −0.330931 | ||||||||
\(872\) | −12.2295 | −0.414143 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.3928 | 0.858924 | ||||||||
\(875\) | 0.291597 | 0.00985777 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.5832 | −1.60677 | −0.803386 | − | 0.595459i | \(-0.796970\pi\) | ||||
−0.803386 | + | 0.595459i | \(0.796970\pi\) | |||||||
\(878\) | 9.89839 | 0.334054 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.39550 | −0.0807522 | ||||||||
\(881\) | −25.7202 | −0.866535 | −0.433268 | − | 0.901265i | \(-0.642639\pi\) | ||||
−0.433268 | + | 0.901265i | \(0.642639\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.9567 | 1.51291 | 0.756456 | − | 0.654044i | \(-0.226929\pi\) | ||||
0.756456 | + | 0.654044i | \(0.226929\pi\) | |||||||
\(884\) | 18.1767 | 0.611349 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.94645 | 0.0989879 | ||||||||
\(887\) | −14.6098 | −0.490548 | −0.245274 | − | 0.969454i | \(-0.578878\pi\) | ||||
−0.245274 | + | 0.969454i | \(0.578878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16951 | −0.0392242 | ||||||||
\(890\) | 8.59607 | 0.288141 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.04685 | 0.135499 | ||||||||
\(893\) | −37.3880 | −1.25114 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.81389 | −0.227763 | ||||||||
\(896\) | −3.11639 | −0.104111 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.763258 | 0.0254702 | ||||||||
\(899\) | −18.3805 | −0.613023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2483 | 0.408051 | ||||||||
\(902\) | −5.65639 | −0.188337 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.48820 | 0.182535 | ||||||||
\(905\) | 25.9084 | 0.861223 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.3136 | −1.07296 | −0.536479 | − | 0.843914i | \(-0.680246\pi\) | ||||
−0.536479 | + | 0.843914i | \(0.680246\pi\) | |||||||
\(908\) | 6.80159 | 0.225719 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.443636 | −0.0147064 | ||||||||
\(911\) | −10.8366 | −0.359033 | −0.179517 | − | 0.983755i | \(-0.557453\pi\) | ||||
−0.179517 | + | 0.983755i | \(0.557453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1074 | −0.367601 | ||||||||
\(914\) | 2.45209 | 0.0811080 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.9924 | −1.22226 | ||||||||
\(917\) | 4.16924 | 0.137681 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.87445 | −0.259754 | −0.129877 | − | 0.991530i | \(-0.541458\pi\) | ||||
−0.129877 | + | 0.991530i | \(0.541458\pi\) | |||||||
\(920\) | −13.0504 | −0.430257 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.9115 | 0.491085 | ||||||||
\(923\) | 20.7990 | 0.684607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.54729 | −0.281033 | ||||||||
\(926\) | −16.2504 | −0.534021 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.1719 | 0.563694 | ||||||||
\(929\) | 32.3988 | 1.06297 | 0.531485 | − | 0.847068i | \(-0.321634\pi\) | ||||
0.531485 | + | 0.847068i | \(0.321634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.3320 | 1.55124 | ||||||||
\(932\) | 7.29279 | 0.238883 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.6296 | −0.675022 | ||||||||
\(935\) | 9.77442 | 0.319658 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.9943 | 1.99260 | 0.996298 | − | 0.0859685i | \(-0.0273984\pi\) | ||||
0.996298 | + | 0.0859685i | \(0.0273984\pi\) | |||||||
\(938\) | −0.902563 | −0.0294697 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.29074 | 0.270414 | ||||||||
\(941\) | 15.3190 | 0.499387 | 0.249693 | − | 0.968325i | \(-0.419670\pi\) | ||||
0.249693 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.3357 | 0.792480 | ||||||||
\(944\) | 13.9756 | 0.454867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.6470 | −0.378678 | ||||||||
\(947\) | 55.4559 | 1.80207 | 0.901037 | − | 0.433742i | \(-0.142807\pi\) | ||||
0.901037 | + | 0.433742i | \(0.142807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.9713 | −0.745679 | ||||||||
\(950\) | 4.75292 | 0.154205 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.89311 | 0.126176 | ||||||||
\(953\) | 2.86574 | 0.0928304 | 0.0464152 | − | 0.998922i | \(-0.485220\pi\) | ||||
0.0464152 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5004 | −0.631018 | ||||||||
\(956\) | 25.1347 | 0.812914 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.49422 | 0.242127 | ||||||||
\(959\) | −0.435676 | −0.0140687 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.74898 | 0.249967 | ||||||||
\(962\) | 13.0039 | 0.419261 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −42.4259 | −1.36645 | ||||||||
\(965\) | 17.1259 | 0.551301 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2225 | 1.48642 | 0.743208 | − | 0.669061i | \(-0.233303\pi\) | ||||
0.743208 | + | 0.669061i | \(0.233303\pi\) | |||||||
\(968\) | −19.0577 | −0.612537 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.77669 | 0.313910 | ||||||||
\(971\) | 35.1848 | 1.12914 | 0.564568 | − | 0.825387i | \(-0.309043\pi\) | ||||
0.564568 | + | 0.825387i | \(0.309043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.26825 | 0.0406583 | ||||||||
\(974\) | −19.4277 | −0.622505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.397372 | 0.0127196 | ||||||||
\(977\) | −25.8171 | −0.825962 | −0.412981 | − | 0.910740i | \(-0.635512\pi\) | ||||
−0.412981 | + | 0.910740i | \(0.635512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.1387 | 0.707557 | ||||||||
\(980\) | −10.4958 | −0.335276 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.8536 | 0.729287 | ||||||||
\(983\) | 10.6669 | 0.340221 | 0.170111 | − | 0.985425i | \(-0.445588\pi\) | ||||
0.170111 | + | 0.985425i | \(0.445588\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.5552 | 0.623080 | ||||||||
\(986\) | −11.2064 | −0.356883 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 22.7634 | 0.724201 | ||||||||
\(989\) | 50.1096 | 1.59339 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.3676 | 1.88587 | 0.942937 | − | 0.332972i | \(-0.108051\pi\) | ||||
0.942937 | + | 0.332972i | \(0.108051\pi\) | |||||||
\(992\) | −36.2010 | −1.14938 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.92209 | 0.0609649 | ||||||||
\(995\) | 21.3564 | 0.677042 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8247 | 0.881216 | 0.440608 | − | 0.897699i | \(-0.354763\pi\) | ||||
0.440608 | + | 0.897699i | \(0.354763\pi\) | |||||||
\(998\) | 10.9061 | 0.345228 | ||||||||
\(999\) | 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 | 3645.2.a.h.1.6 | 15 | ||
3.2 | odd | 2 | 3645.2.a.g.1.10 | 15 | |||
27.4 | even | 9 | 135.2.k.a.16.2 | ✓ | 30 | ||
27.7 | even | 9 | 135.2.k.a.76.2 | yes | 30 | ||
27.20 | odd | 18 | 405.2.k.a.361.4 | 30 | |||
27.23 | odd | 18 | 405.2.k.a.46.4 | 30 | |||
135.4 | even | 18 | 675.2.l.d.151.4 | 30 | |||
135.7 | odd | 36 | 675.2.u.c.49.4 | 60 | |||
135.34 | even | 18 | 675.2.l.d.76.4 | 30 | |||
135.58 | odd | 36 | 675.2.u.c.124.4 | 60 | |||
135.88 | odd | 36 | 675.2.u.c.49.7 | 60 | |||
135.112 | odd | 36 | 675.2.u.c.124.7 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.k.a.16.2 | ✓ | 30 | 27.4 | even | 9 | ||
135.2.k.a.76.2 | yes | 30 | 27.7 | even | 9 | ||
405.2.k.a.46.4 | 30 | 27.23 | odd | 18 | |||
405.2.k.a.361.4 | 30 | 27.20 | odd | 18 | |||
675.2.l.d.76.4 | 30 | 135.34 | even | 18 | |||
675.2.l.d.151.4 | 30 | 135.4 | even | 18 | |||
675.2.u.c.49.4 | 60 | 135.7 | odd | 36 | |||
675.2.u.c.49.7 | 60 | 135.88 | odd | 36 | |||
675.2.u.c.124.4 | 60 | 135.58 | odd | 36 | |||
675.2.u.c.124.7 | 60 | 135.112 | odd | 36 | |||
3645.2.a.g.1.10 | 15 | 3.2 | odd | 2 | |||
3645.2.a.h.1.6 | 15 | 1.1 | even | 1 | trivial |