Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1672,2,Mod(1,1672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1672 = 2^{3} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1672.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: | \(13.3509872180\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13676.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 6x^{2} + 7x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.18363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1672.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.18363 | −1.26072 | −0.630359 | − | 0.776304i | \(-0.717092\pi\) | ||||
−0.630359 | + | 0.776304i | \(0.717092\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.493910 | 0.220883 | 0.110442 | − | 0.993883i | \(-0.464774\pi\) | ||||
0.110442 | + | 0.993883i | \(0.464774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.18363 | 0.447370 | 0.223685 | − | 0.974662i | \(-0.428191\pi\) | ||||
0.223685 | + | 0.974662i | \(0.428191\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.76823 | 0.589411 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.80419 | −0.500392 | −0.250196 | − | 0.968195i | \(-0.580495\pi\) | ||||
−0.250196 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.07852 | −0.278471 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.21401 | −1.50712 | −0.753559 | − | 0.657380i | \(-0.771665\pi\) | ||||
−0.753559 | + | 0.657380i | \(0.771665\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.58461 | −0.564007 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.62940 | 0.965297 | 0.482648 | − | 0.875814i | \(-0.339675\pi\) | ||||
0.482648 | + | 0.875814i | \(0.339675\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75605 | −0.951211 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.68972 | 0.517637 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.44577 | 0.825559 | 0.412780 | − | 0.910831i | \(-0.364558\pi\) | ||||
0.412780 | + | 0.910831i | \(0.364558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.457953 | 0.0822508 | 0.0411254 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411254 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18363 | −0.380121 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.584606 | 0.0988164 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58461 | −0.589306 | −0.294653 | − | 0.955604i | \(-0.595204\pi\) | ||||
−0.294653 | + | 0.955604i | \(0.595204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.93968 | 0.630854 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.33688 | −0.208785 | −0.104393 | − | 0.994536i | \(-0.533290\pi\) | ||||
−0.104393 | + | 0.994536i | \(0.533290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75605 | −0.420294 | −0.210147 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210147 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.873348 | 0.130191 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.97564 | 0.579906 | 0.289953 | − | 0.957041i | \(-0.406360\pi\) | ||||
0.289953 | + | 0.957041i | \(0.406360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.59902 | −0.799860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.5691 | 1.90005 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.98782 | −0.959851 | −0.479925 | − | 0.877309i | \(-0.659336\pi\) | ||||
−0.479925 | + | 0.877309i | \(0.659336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.493910 | 0.0665988 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18363 | −0.289229 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.415394 | 0.0540798 | 0.0270399 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270399 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.75048 | 0.992347 | 0.496173 | − | 0.868223i | \(-0.334738\pi\) | ||||
0.496173 | + | 0.868223i | \(0.334738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.09293 | 0.263685 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.891107 | −0.110528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.28874 | 0.401784 | 0.200892 | − | 0.979613i | \(-0.435616\pi\) | ||||
0.200892 | + | 0.979613i | \(0.435616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.1089 | −1.21697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.9911 | −1.89779 | −0.948896 | − | 0.315589i | \(-0.897798\pi\) | ||||
−0.948896 | + | 0.315589i | \(0.897798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.391619 | −0.0458355 | −0.0229178 | − | 0.999737i | \(-0.507296\pi\) | ||||
−0.0229178 | + | 0.999737i | \(0.507296\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.3855 | 1.19921 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.18363 | 0.134887 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14107 | −0.128380 | −0.0641902 | − | 0.997938i | \(-0.520446\pi\) | ||||
−0.0641902 | + | 0.997938i | \(0.520446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1781 | −1.24201 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.3617 | −1.68616 | −0.843082 | − | 0.537786i | \(-0.819261\pi\) | ||||
−0.843082 | + | 0.537786i | \(0.819261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.06916 | −0.332897 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.70792 | −1.04080 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4762 | −1.32247 | −0.661235 | − | 0.750179i | \(-0.729967\pi\) | ||||
−0.661235 | + | 0.750179i | \(0.729967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13549 | −0.223860 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.493910 | 0.0506741 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.06032 | −0.310728 | −0.155364 | − | 0.987857i | \(-0.549655\pi\) | ||||
−0.155364 | + | 0.987857i | \(0.549655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.76823 | 0.177714 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.68972 | 0.367141 | 0.183570 | − | 0.983007i | \(-0.441234\pi\) | ||||
0.183570 | + | 0.983007i | \(0.441234\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.19522 | −0.314835 | −0.157417 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157417 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.27656 | −0.124580 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.7831 | −1.91250 | −0.956252 | − | 0.292545i | \(-0.905498\pi\) | ||||
−0.956252 | + | 0.292545i | \(0.905498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7345 | −1.02818 | −0.514090 | − | 0.857736i | \(-0.671870\pi\) | ||||
−0.514090 | + | 0.857736i | \(0.671870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.82745 | 0.742948 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.89111 | −0.366045 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.28651 | 0.213218 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.19023 | −0.294937 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.35508 | −0.674239 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.91925 | 0.263220 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.81861 | −0.430989 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1177 | −1.43022 | −0.715109 | − | 0.699013i | \(-0.753623\pi\) | ||||
−0.715109 | + | 0.699013i | \(0.753623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.01820 | 0.529873 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5425 | 1.09584 | 0.547921 | − | 0.836530i | \(-0.315419\pi\) | ||||
0.547921 | + | 0.836530i | \(0.315419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.18363 | 0.102634 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.32848 | 0.114337 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.0868 | −1.45982 | −0.729911 | − | 0.683543i | \(-0.760438\pi\) | ||||
−0.729911 | + | 0.683543i | \(0.760438\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.7411 | 1.58960 | 0.794800 | − | 0.606871i | \(-0.207576\pi\) | ||||
0.794800 | + | 0.606871i | \(0.207576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.68132 | −0.731099 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.80419 | −0.150874 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.19581 | 0.182352 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.2262 | 1.00840 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.30753 | −0.434809 | −0.217405 | − | 0.976082i | \(-0.569759\pi\) | ||||
−0.217405 | + | 0.976082i | \(0.569759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.11395 | −0.497546 | −0.248773 | − | 0.968562i | \(-0.580027\pi\) | ||||
−0.248773 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.9878 | −0.888313 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.226188 | 0.0181678 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6686 | 1.01107 | 0.505533 | − | 0.862807i | \(-0.331296\pi\) | ||||
0.505533 | + | 0.862807i | \(0.331296\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2588 | 1.21010 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.47949 | 0.431844 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.673759 | −0.0527729 | −0.0263864 | − | 0.999652i | \(-0.508400\pi\) | ||||
−0.0263864 | + | 0.999652i | \(0.508400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.07852 | −0.0839623 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.58126 | −0.664038 | −0.332019 | − | 0.943273i | \(-0.607730\pi\) | ||||
−0.332019 | + | 0.943273i | \(0.607730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.74490 | −0.749607 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.76823 | 0.135220 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.78867 | 0.212019 | 0.106009 | − | 0.994365i | \(-0.466193\pi\) | ||||
0.106009 | + | 0.994365i | \(0.466193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.62940 | −0.425543 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.907067 | −0.0681794 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0906960 | 0.00677893 | 0.00338947 | − | 0.999994i | \(-0.498921\pi\) | ||||
0.00338947 | + | 0.999994i | \(0.498921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3799 | 1.51482 | 0.757412 | − | 0.652937i | \(-0.226463\pi\) | ||||
0.757412 | + | 0.652937i | \(0.226463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.9242 | −1.25107 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.77047 | −0.130168 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.21401 | −0.454413 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.18363 | 0.231575 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8594 | 1.14754 | 0.573772 | − | 0.819015i | \(-0.305480\pi\) | ||||
0.573772 | + | 0.819015i | \(0.305480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8700 | −1.21433 | −0.607165 | − | 0.794576i | \(-0.707693\pi\) | ||||
−0.607165 | + | 0.794576i | \(0.707693\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.94585 | 0.139345 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1775 | 0.796361 | 0.398181 | − | 0.917307i | \(-0.369642\pi\) | ||||
0.398181 | + | 0.917307i | \(0.369642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6494 | 1.03847 | 0.519234 | − | 0.854632i | \(-0.326217\pi\) | ||||
0.519234 | + | 0.854632i | \(0.326217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.18139 | −0.506536 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.26214 | 0.369330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.660298 | −0.0461172 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.18587 | 0.568957 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.6830 | −1.07966 | −0.539832 | − | 0.841773i | \(-0.681512\pi\) | ||||
−0.539832 | + | 0.841773i | \(0.681512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.9186 | 2.39258 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.36124 | −0.0928359 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.542047 | 0.0367965 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.855151 | 0.0577857 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2113 | 0.754150 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.98070 | −0.668357 | −0.334178 | − | 0.942510i | \(-0.608459\pi\) | ||||
−0.334178 | + | 0.942510i | \(0.608459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.40982 | −0.560654 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.62434 | −0.174184 | −0.0870918 | − | 0.996200i | \(-0.527757\pi\) | ||||
−0.0870918 | + | 0.996200i | \(0.527757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5347 | −0.762232 | −0.381116 | − | 0.924527i | \(-0.624460\pi\) | ||||
−0.381116 | + | 0.924527i | \(0.624460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.58461 | −0.170055 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.53269 | 0.100410 | 0.0502049 | − | 0.998739i | \(-0.484013\pi\) | ||||
0.0502049 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.96361 | 0.128092 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.49167 | 0.161852 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.2560 | 0.728089 | 0.364044 | − | 0.931382i | \(-0.381396\pi\) | ||||
0.364044 | + | 0.931382i | \(0.381396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.48507 | −0.288909 | −0.144454 | − | 0.989511i | \(-0.546143\pi\) | ||||
−0.144454 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.3396 | 1.04818 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.76541 | −0.176676 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.80419 | −0.114798 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 33.5442 | 2.12578 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6902 | −0.927234 | −0.463617 | − | 0.886036i | \(-0.653449\pi\) | ||||
−0.463617 | + | 0.886036i | \(0.653449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.62940 | 0.291048 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.70190 | 0.419689 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3429 | 0.894685 | 0.447343 | − | 0.894363i | \(-0.352370\pi\) | ||||
0.447343 | + | 0.894363i | \(0.352370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.24284 | −0.263637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.86117 | 0.486594 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0747 | −0.744560 | −0.372280 | − | 0.928120i | \(-0.621424\pi\) | ||||
−0.372280 | + | 0.928120i | \(0.621424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.45135 | −0.212015 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.2433 | 1.66726 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.9568 | −1.64358 | −0.821792 | − | 0.569788i | \(-0.807025\pi\) | ||||
−0.821792 | + | 0.569788i | \(0.807025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2284 | 1.10730 | 0.553649 | − | 0.832750i | \(-0.313235\pi\) | ||||
0.553649 | + | 0.832750i | \(0.313235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.66312 | 0.282225 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.75605 | −0.286801 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1382 | 1.02973 | 0.514866 | − | 0.857270i | \(-0.327842\pi\) | ||||
0.514866 | + | 0.857270i | \(0.327842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.809769 | 0.0484796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.08229 | −0.482149 | −0.241075 | − | 0.970507i | \(-0.577500\pi\) | ||||
−0.241075 | + | 0.970507i | \(0.577500\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1471 | 1.19762 | 0.598810 | − | 0.800891i | \(-0.295640\pi\) | ||||
0.598810 | + | 0.800891i | \(0.295640\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.07852 | −0.0638857 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.58237 | −0.0934043 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.6139 | 1.27140 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.68260 | 0.391741 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.84521 | 0.166219 | 0.0831094 | − | 0.996540i | \(-0.473515\pi\) | ||||
0.0831094 | + | 0.996540i | \(0.473515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.205167 | 0.0119453 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.68972 | 0.156073 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.35232 | −0.483027 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.26214 | −0.188027 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.05698 | −0.462861 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.82803 | 0.219193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.97288 | −0.512109 | −0.256055 | − | 0.966662i | \(-0.582423\pi\) | ||||
−0.256055 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.97718 | 0.396918 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.63274 | −0.432813 | −0.216407 | − | 0.976303i | \(-0.569434\pi\) | ||||
−0.216407 | + | 0.976303i | \(0.569434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0956 | −1.24892 | −0.624459 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624459 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.03372 | 0.0582435 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.8798 | 1.28506 | 0.642529 | − | 0.766261i | \(-0.277885\pi\) | ||||
0.642529 | + | 0.766261i | \(0.277885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.44577 | 0.248915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 43.1989 | 2.41113 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.21401 | −0.345757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.58083 | 0.475979 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.4402 | 1.29625 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.70568 | 0.259433 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6714 | 1.63089 | 0.815443 | − | 0.578837i | \(-0.196493\pi\) | ||||
0.815443 | + | 0.578837i | \(0.196493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.33842 | −0.347343 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.62434 | 0.0887472 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.81637 | 0.480258 | 0.240129 | − | 0.970741i | \(-0.422810\pi\) | ||||
0.240129 | + | 0.970741i | \(0.422810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.49673 | 0.461479 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.457953 | 0.0247996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.9126 | −0.805203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.99288 | −0.268808 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.96070 | 0.534719 | 0.267359 | − | 0.963597i | \(-0.413849\pi\) | ||||
0.267359 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.31578 | −0.0704320 | −0.0352160 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352160 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.85277 | −0.259021 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.76324 | −0.147073 | −0.0735363 | − | 0.997293i | \(-0.523428\pi\) | ||||
−0.0735363 | + | 0.997293i | \(0.523428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.89815 | −0.419190 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0608 | 0.850025 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2892 | 0.859710 | 0.429855 | − | 0.902898i | \(-0.358565\pi\) | ||||
0.429855 | + | 0.902898i | \(0.358565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.18363 | −0.114611 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.193424 | −0.0101243 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0873 | 1.67494 | 0.837471 | − | 0.546482i | \(-0.184033\pi\) | ||||
0.837471 | + | 0.546482i | \(0.184033\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.36392 | −0.123061 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.27098 | −0.429408 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.8345 | −1.59655 | −0.798275 | − | 0.602294i | \(-0.794254\pi\) | ||||
−0.798275 | + | 0.602294i | \(0.794254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.5221 | 0.543356 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.02102 | −0.413104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2112 | 0.986812 | 0.493406 | − | 0.869799i | \(-0.335752\pi\) | ||||
0.493406 | + | 0.869799i | \(0.335752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.1951 | 1.80310 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.1803 | −1.84873 | −0.924363 | − | 0.381514i | \(-0.875403\pi\) | ||||
−0.924363 | + | 0.381514i | \(0.875403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.584606 | 0.0297943 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.87335 | −0.247726 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.0481 | −0.813669 | −0.406834 | − | 0.913502i | \(-0.633367\pi\) | ||||
−0.406834 | + | 0.913502i | \(0.633367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.7671 | −1.45482 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.3881 | −1.38155 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.563585 | −0.0283571 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4584 | 1.57885 | 0.789426 | − | 0.613846i | \(-0.210378\pi\) | ||||
0.789426 | + | 0.613846i | \(0.210378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.58461 | −0.129392 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.8262 | −0.990072 | −0.495036 | − | 0.868873i | \(-0.664845\pi\) | ||||
−0.495036 | + | 0.868873i | \(0.664845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.826235 | −0.0411577 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.52095 | −0.274338 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.58461 | −0.177682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3540 | 1.69869 | 0.849347 | − | 0.527834i | \(-0.176996\pi\) | ||||
0.849347 | + | 0.527834i | \(0.176996\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 37.3112 | 1.84042 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.491673 | 0.0241936 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.58728 | −0.372445 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −40.9236 | −2.00404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.78324 | 0.331383 | 0.165691 | − | 0.986178i | \(-0.447014\pi\) | ||||
0.165691 | + | 0.986178i | \(0.447014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.08409 | −0.345258 | −0.172629 | − | 0.984987i | \(-0.555226\pi\) | ||||
−0.172629 | + | 0.984987i | \(0.555226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.02986 | 0.341803 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.5541 | 1.43359 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.17368 | 0.443946 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.93968 | 0.190210 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.6139 | 0.896599 | 0.448299 | − | 0.893883i | \(-0.352030\pi\) | ||||
0.448299 | + | 0.893883i | \(0.352030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.88751 | 0.475163 | 0.237582 | − | 0.971368i | \(-0.423645\pi\) | ||||
0.237582 | + | 0.971368i | \(0.423645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.79483 | −0.229895 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.62940 | 0.221454 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.49270 | 0.0712425 | 0.0356213 | − | 0.999365i | \(-0.488659\pi\) | ||||
0.0356213 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.90038 | −0.471447 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0276 | −0.761492 | −0.380746 | − | 0.924680i | \(-0.624333\pi\) | ||||
−0.380746 | + | 0.924680i | \(0.624333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.16209 | −0.292111 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5897 | 0.548172 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.40975 | 0.302495 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33688 | −0.0629512 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.3506 | 0.627266 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.05474 | −0.0494470 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.9906 | 1.16901 | 0.584505 | − | 0.811390i | \(-0.301289\pi\) | ||||
0.584505 | + | 0.811390i | \(0.301289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.7139 | −0.780140 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.8318 | −1.20311 | −0.601554 | − | 0.798832i | \(-0.705451\pi\) | ||||
−0.601554 | + | 0.798832i | \(0.705451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5762 | −0.677414 | −0.338707 | − | 0.940892i | \(-0.609989\pi\) | ||||
−0.338707 | + | 0.940892i | \(0.609989\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.493910 | −0.0229045 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.9445 | −0.830372 | −0.415186 | − | 0.909737i | \(-0.636283\pi\) | ||||
−0.415186 | + | 0.909737i | \(0.636283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.89265 | 0.179746 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.6636 | −1.27467 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.75605 | −0.126723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.75605 | −0.218223 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3561 | −0.565747 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.82187 | 0.0832433 | 0.0416217 | − | 0.999133i | \(-0.486748\pi\) | ||||
0.0416217 | + | 0.999133i | \(0.486748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.46731 | 0.294884 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.9652 | −0.544434 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.51152 | −0.0686346 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.2489 | −1.09882 | −0.549410 | − | 0.835553i | \(-0.685148\pi\) | ||||
−0.549410 | + | 0.835553i | \(0.685148\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.47124 | 0.0665317 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.86495 | 0.264681 | 0.132341 | − | 0.991204i | \(-0.457751\pi\) | ||||
0.132341 | + | 0.991204i | \(0.457751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.6261 | −1.24422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.873348 | 0.0392541 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.9275 | −0.849014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.5830 | 1.41385 | 0.706924 | − | 0.707289i | \(-0.250082\pi\) | ||||
0.706924 | + | 0.707289i | \(0.250082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.7383 | 0.837165 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.5160 | 1.09311 | 0.546556 | − | 0.837422i | \(-0.315938\pi\) | ||||
0.546556 | + | 0.837422i | \(0.315938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.82239 | 0.0810952 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.2792 | 0.945044 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.3423 | −0.990305 | −0.495153 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495153 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.463532 | −0.0205054 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.68972 | 0.118754 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.57815 | −0.0695417 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.97564 | 0.174848 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.08942 | −0.267296 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.5779 | 1.20821 | 0.604105 | − | 0.796904i | \(-0.293531\pi\) | ||||
0.604105 | + | 0.796904i | \(0.293531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.7289 | 0.906410 | 0.453205 | − | 0.891406i | \(-0.350281\pi\) | ||||
0.453205 | + | 0.891406i | \(0.350281\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.2925 | 0.536490 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.84572 | −0.123962 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.56865 | −0.0682020 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.734515 | 0.0318752 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.41199 | 0.104475 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.77106 | −0.422440 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.198046 | −0.00854633 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.59902 | −0.241167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.19735 | −0.223452 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −44.5021 | −1.90977 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.30188 | −0.227108 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.0887 | 1.92786 | 0.963928 | − | 0.266164i | \(-0.0857562\pi\) | ||||
0.963928 | + | 0.266164i | \(0.0857562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.7047 | 0.584900 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.44577 | 0.189396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.35060 | −0.0574335 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.86605 | 0.164105 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.0905 | −1.86817 | −0.934087 | − | 0.357047i | \(-0.883784\pi\) | ||||
−0.934087 | + | 0.357047i | \(0.883784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.97245 | 0.210312 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5691 | 0.572887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.2372 | −1.06362 | −0.531810 | − | 0.846864i | \(-0.678488\pi\) | ||||
−0.531810 | + | 0.846864i | \(0.678488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.92185 | −0.0808530 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.2307 | −0.555636 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.44258 | −0.144320 | −0.0721602 | − | 0.997393i | \(-0.522989\pi\) | ||||
−0.0721602 | + | 0.997393i | \(0.522989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.16389 | 0.0905559 | 0.0452780 | − | 0.998974i | \(-0.485583\pi\) | ||||
0.0452780 | + | 0.998974i | \(0.485583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.6310 | −1.44673 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.0177 | −0.918201 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1000 | −0.795142 | −0.397571 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397571 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.8378 | 1.53093 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.1825 | −0.754338 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.98782 | −0.289406 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.57569 | −0.0651466 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.78221 | 0.321206 | 0.160603 | − | 0.987019i | \(-0.448656\pi\) | ||||
0.160603 | + | 0.987019i | \(0.448656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.457953 | 0.0188696 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.4074 | −1.00399 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.6214 | −1.66812 | −0.834061 | − | 0.551672i | \(-0.813990\pi\) | ||||
−0.834061 | + | 0.551672i | \(0.813990\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.63274 | −0.148928 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.9888 | −1.30922 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.6299 | 0.720339 | 0.360169 | − | 0.932887i | \(-0.382719\pi\) | ||||
0.360169 | + | 0.932887i | \(0.382719\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5751 | −0.512949 | −0.256475 | − | 0.966551i | \(-0.582561\pi\) | ||||
−0.256475 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.81527 | 0.236816 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.493910 | 0.0200803 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4661 | 0.952461 | 0.476230 | − | 0.879321i | \(-0.342003\pi\) | ||||
0.476230 | + | 0.879321i | \(0.342003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.4906 | −0.465621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.17281 | −0.290181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.8159 | −0.759965 | −0.379983 | − | 0.924994i | \(-0.624070\pi\) | ||||
−0.379983 | + | 0.924994i | \(0.624070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.44184 | 0.0581408 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.65094 | 0.0664643 | 0.0332322 | − | 0.999448i | \(-0.489420\pi\) | ||||
0.0332322 | + | 0.999448i | \(0.489420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.4799 | −0.823158 | −0.411579 | − | 0.911374i | \(-0.635023\pi\) | ||||
−0.411579 | + | 0.911374i | \(0.635023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.4518 | 0.499673 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.7671 | −0.591633 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.4003 | 0.856012 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.18363 | −0.0872057 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.2748 | 0.888153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8892 | −1.07044 | −0.535222 | − | 0.844712i | \(-0.679772\pi\) | ||||
−0.535222 | + | 0.844712i | \(0.679772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.2459 | 1.36115 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.96070 | −0.315911 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.1017 | 0.400244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.2760 | −1.11858 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0171 | 0.474647 | 0.237323 | − | 0.971431i | \(-0.423730\pi\) | ||||
0.237323 | + | 0.971431i | \(0.423730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.84527 | −0.112207 | −0.0561033 | − | 0.998425i | \(-0.517868\pi\) | ||||
−0.0561033 | + | 0.998425i | \(0.517868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.97245 | 0.117040 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.2975 | −0.758664 | −0.379332 | − | 0.925261i | \(-0.623846\pi\) | ||||
−0.379332 | + | 0.925261i | \(0.623846\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.415394 | 0.0163057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.18363 | −0.0463901 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.7017 | 1.35798 | 0.678991 | − | 0.734147i | \(-0.262418\pi\) | ||||
0.678991 | + | 0.734147i | \(0.262418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.19485 | 0.242053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.692474 | −0.0270160 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.36057 | 0.169864 | 0.0849319 | − | 0.996387i | \(-0.472933\pi\) | ||||
0.0849319 | + | 0.996387i | \(0.472933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.43307 | 0.172427 | 0.0862133 | − | 0.996277i | \(-0.472523\pi\) | ||||
0.0862133 | + | 0.996277i | \(0.472523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.4812 | −0.950771 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.584606 | 0.0226700 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.5813 | 0.796910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.7941 | 0.842610 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.75048 | 0.299204 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9264 | 0.845200 | 0.422600 | − | 0.906316i | \(-0.361117\pi\) | ||||
0.422600 | + | 0.906316i | \(0.361117\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.7924 | −0.492382 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.2924 | 1.35640 | 0.678198 | − | 0.734879i | \(-0.262761\pi\) | ||||
0.678198 | + | 0.734879i | \(0.262761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.62228 | −0.139010 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.73059 | 0.219597 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.1138 | −1.57318 | −0.786588 | − | 0.617478i | \(-0.788154\pi\) | ||||
−0.786588 | + | 0.617478i | \(0.788154\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.43932 | −0.322450 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.1874 | 0.960961 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.6074 | 0.480302 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6912 | 0.825171 | 0.412586 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412586 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.09293 | 0.0795039 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.25642 | 0.351116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.30738 | 0.314664 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.34682 | −0.126588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6458 | −0.628703 | −0.314352 | − | 0.949307i | \(-0.601787\pi\) | ||||
−0.314352 | + | 0.949307i | \(0.601787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58461 | −0.135196 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.28779 | −0.161487 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.36726 | 0.164248 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1731 | −0.870282 | −0.435141 | − | 0.900362i | \(-0.643302\pi\) | ||||
−0.435141 | + | 0.900362i | \(0.643302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.01768 | −0.0756689 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.12005 | 0.0793965 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.891107 | −0.0333255 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5789 | −0.917915 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.3892 | −1.02144 | −0.510722 | − | 0.859746i | \(-0.670622\pi\) | ||||
−0.510722 | + | 0.859746i | \(0.670622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.78196 | −0.140847 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.79373 | 0.364233 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.1443 | −0.785281 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.97898 | −0.110484 | −0.0552421 | − | 0.998473i | \(-0.517593\pi\) | ||||
−0.0552421 | + | 0.998473i | \(0.517593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.14537 | −0.0794581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.1261 | 0.633433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.6851 | 0.468535 | 0.234267 | − | 0.972172i | \(-0.424731\pi\) | ||||
0.234267 | + | 0.972172i | \(0.424731\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.03863 | 0.222738 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.28874 | 0.121142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.6272 | 0.685211 | 0.342606 | − | 0.939479i | \(-0.388691\pi\) | ||||
0.342606 | + | 0.939479i | \(0.388691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.93968 | 0.144728 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.8878 | −1.50003 | −0.750013 | − | 0.661423i | \(-0.769953\pi\) | ||||
−0.750013 | + | 0.661423i | \(0.769953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.62144 | −0.0960420 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.1630 | −0.993844 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.4158 | −0.855596 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2482 | 0.556416 | 0.278208 | − | 0.960521i | \(-0.410260\pi\) | ||||
0.278208 | + | 0.960521i | \(0.410260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.0778 | 1.16898 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.01974 | −0.109900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.09565 | 0.0398220 | 0.0199110 | − | 0.999802i | \(-0.493662\pi\) | ||||
0.0199110 | + | 0.999802i | \(0.493662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.1089 | −0.366930 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.6858 | 1.72861 | 0.864304 | − | 0.502970i | \(-0.167759\pi\) | ||||
0.864304 | + | 0.502970i | \(0.167759\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.7057 | −0.459976 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.42699 | −0.196213 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.749451 | −0.0270611 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.70913 | −0.277998 | −0.138999 | − | 0.990293i | \(-0.544389\pi\) | ||||
−0.138999 | + | 0.990293i | \(0.544389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3196 | −1.12795 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.5085 | 0.629737 | 0.314869 | − | 0.949135i | \(-0.398040\pi\) | ||||
0.314869 | + | 0.949135i | \(0.398040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.17805 | −0.0782379 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.26479 | 0.332373 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.33688 | −0.0478987 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.9911 | −0.572206 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.9579 | 0.427340 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.25715 | 0.223327 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.47468 | 0.195151 | 0.0975756 | − | 0.995228i | \(-0.468891\pi\) | ||||
0.0975756 | + | 0.995228i | \(0.468891\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.3667 | 0.938681 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.60563 | −0.163757 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.9833 | −0.496563 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.53647 | 0.267291 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0404 | −1.17035 | −0.585176 | − | 0.810906i | \(-0.698975\pi\) | ||||
−0.585176 | + | 0.810906i | \(0.698975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.7046 | −0.873987 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0608 | −0.779478 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.391619 | −0.0138199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.70637 | 0.0953871 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 58.8636 | 2.07210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.1534 | −0.497608 | −0.248804 | − | 0.968554i | \(-0.580038\pi\) | ||||
−0.248804 | + | 0.968554i | \(0.580038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2514 | 1.51876 | 0.759381 | − | 0.650646i | \(-0.225502\pi\) | ||||
0.759381 | + | 0.650646i | \(0.225502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.8041 | −1.39599 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.332776 | −0.0116566 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.75605 | −0.0964221 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.77605 | −0.131946 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.1419 | 1.64527 | 0.822633 | − | 0.568573i | \(-0.192504\pi\) | ||||
0.822633 | + | 0.568573i | \(0.192504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.3098 | −1.02168 | −0.510838 | − | 0.859677i | \(-0.670665\pi\) | ||||
−0.510838 | + | 0.859677i | \(0.670665\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.3855 | 0.361575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8963 | 0.413677 | 0.206838 | − | 0.978375i | \(-0.433683\pi\) | ||||
0.206838 | + | 0.978375i | \(0.433683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.91532 | 0.309642 | 0.154821 | − | 0.987943i | \(-0.450520\pi\) | ||||
0.154821 | + | 0.987943i | \(0.450520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.4234 | −1.29820 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.7924 | 1.20548 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.23837 | −0.146675 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.23177 | 0.0425761 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.2566 | −1.63148 | −0.815739 | − | 0.578420i | \(-0.803669\pi\) | ||||
−0.815739 | + | 0.578420i | \(0.803669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.23511 | −0.318452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.6487 | 0.607855 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.81310 | −0.165576 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18363 | 0.0406700 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.9938 | −1.50986 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.5946 | −0.568855 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.04189 | −0.241110 | −0.120555 | − | 0.992707i | \(-0.538467\pi\) | ||||
−0.120555 | + | 0.992707i | \(0.538467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.873348 | 0.0298679 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.1303 | 1.74658 | 0.873288 | − | 0.487204i | \(-0.161983\pi\) | ||||
0.873288 | + | 0.487204i | \(0.161983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.52646 | 0.325038 | 0.162519 | − | 0.986705i | \(-0.448038\pi\) | ||||
0.162519 | + | 0.986705i | \(0.448038\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.45531 | 0.117757 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.2935 | 1.20140 | 0.600702 | − | 0.799473i | \(-0.294888\pi\) | ||||
0.600702 | + | 0.799473i | \(0.294888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.37735 | 0.0468313 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.1967 | −1.60288 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.14107 | −0.0387081 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.93352 | −0.201050 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.41136 | −0.183147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.70344 | −0.192812 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.5103 | −0.760119 | −0.380060 | − | 0.924962i | \(-0.624097\pi\) | ||||
−0.380060 | + | 0.924962i | \(0.624097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.21287 | −0.209555 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.4317 | −1.16003 | −0.580017 | − | 0.814604i | \(-0.696954\pi\) | ||||
−0.580017 | + | 0.814604i | \(0.696954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3992 | 0.484571 | 0.242285 | − | 0.970205i | \(-0.422103\pi\) | ||||
0.242285 | + | 0.970205i | \(0.422103\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.448009 | −0.0150597 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.3560 | −1.45575 | −0.727875 | − | 0.685710i | \(-0.759492\pi\) | ||||
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.0774 | −0.639836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1781 | −0.374479 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.97564 | 0.133040 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0447956 | 0.00149735 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.2384 | 0.608961 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.03596 | 0.0679029 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4224 | 1.44661 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.12331 | 0.237049 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0658 | 0.334599 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.306501 | 0.0101772 | 0.00508861 | − | 0.999987i | \(-0.498380\pi\) | ||||
0.00508861 | + | 0.999987i | \(0.498380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.52429 | 0.216397 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0563 | −0.399442 | −0.199721 | − | 0.979853i | \(-0.564004\pi\) | ||||
−0.199721 | + | 0.979853i | \(0.564004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3617 | −0.508397 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.35900 | −0.276340 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8456 | 0.490246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0917 | −0.332895 | −0.166448 | − | 0.986050i | \(-0.553230\pi\) | ||||
−0.166448 | + | 0.986050i | \(0.553230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5934 | 0.645626 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.8510 | 0.949641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.0486 | 0.560554 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.64990 | −0.185567 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.6178 | 1.59510 | 0.797550 | − | 0.603253i | \(-0.206129\pi\) | ||||
0.797550 | + | 0.603253i | \(0.206129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.59902 | −0.183501 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.6671 | 0.545656 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.06916 | −0.100372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.8047 | 0.450980 | 0.225490 | − | 0.974245i | \(-0.427602\pi\) | ||||
0.225490 | + | 0.974245i | \(0.427602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.2486 | 1.57453 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.4773 | 1.09133 | 0.545664 | − | 0.838004i | \(-0.316277\pi\) | ||||
0.545664 | + | 0.838004i | \(0.316277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.18895 | −0.201540 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.57242 | 0.0511510 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.9114 | −0.842007 | −0.421004 | − | 0.907059i | \(-0.638322\pi\) | ||||
−0.421004 | + | 0.907059i | \(0.638322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.706555 | 0.0229358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.9610 | −1.62010 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.8963 | 0.838865 | 0.419433 | − | 0.907787i | \(-0.362229\pi\) | ||||
0.419433 | + | 0.907787i | \(0.362229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.83309 | 0.253473 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.70792 | −0.313812 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.2244 | −0.653080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7903 | −0.993235 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.9811 | −1.12725 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.33226 | −0.268225 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.73280 | −0.0557230 | −0.0278615 | − | 0.999612i | \(-0.508870\pi\) | ||||
−0.0278615 | + | 0.999612i | \(0.508870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.5691 | 0.435902 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0088 | −0.481654 | −0.240827 | − | 0.970568i | \(-0.577419\pi\) | ||||
−0.240827 | + | 0.970568i | \(0.577419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.1825 | 0.711139 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.7373 | −0.600075 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.33234 | −0.298568 | −0.149284 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149284 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4762 | −0.398739 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.9811 | −0.606021 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.83086 | −0.154080 | −0.0770402 | − | 0.997028i | \(-0.524547\pi\) | ||||
−0.0770402 | + | 0.997028i | \(0.524547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.52066 | 0.175903 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.2755 | −0.327071 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7589 | −0.405709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.0069 | 1.11203 | 0.556015 | − | 0.831172i | \(-0.312330\pi\) | ||||
0.556015 | + | 0.831172i | \(0.312330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −64.7913 | −2.05609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.23548 | 0.229380 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.1287 | −0.700824 | −0.350412 | − | 0.936596i | \(-0.613958\pi\) | ||||
−0.350412 | + | 0.936596i | \(0.613958\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.64158 | −0.305046 |
(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 | 1672.2.a.f.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 3344.2.a.s.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.f.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3344.2.a.s.1.4 | 4 | 4.3 | odd | 2 |