Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, 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("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.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: | \(60.4387692899\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 31x^{14} + 397x^{12} - 2723x^{10} + 10845x^{8} - 25387x^{6} + 33562x^{4} - 22454x^{2} + 5821 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.64329\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64329 | −1.16198 | −0.580990 | − | 0.813911i | \(-0.697334\pi\) | ||||
−0.580990 | + | 0.813911i | \(0.697334\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.700392 | 0.350196 | ||||||||
\(5\) | 1.62862 | 0.728339 | 0.364169 | − | 0.931333i | \(-0.381353\pi\) | ||||
0.364169 | + | 0.931333i | \(0.381353\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.373038 | 0.140995 | 0.0704975 | − | 0.997512i | \(-0.477541\pi\) | ||||
0.0704975 | + | 0.997512i | \(0.477541\pi\) | |||||||
\(8\) | 2.13563 | 0.755059 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.67628 | −0.846315 | ||||||||
\(11\) | 2.25630 | 0.680299 | 0.340149 | − | 0.940371i | \(-0.389522\pi\) | ||||
0.340149 | + | 0.940371i | \(0.389522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.41272 | 1.50122 | 0.750609 | − | 0.660747i | \(-0.229760\pi\) | ||||
0.750609 | + | 0.660747i | \(0.229760\pi\) | |||||||
\(14\) | −0.613008 | −0.163833 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.91024 | −1.22756 | ||||||||
\(17\) | 2.79201 | 0.677162 | 0.338581 | − | 0.940937i | \(-0.390053\pi\) | ||||
0.338581 | + | 0.940937i | \(0.390053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.62779 | 0.602857 | 0.301429 | − | 0.953489i | \(-0.402536\pi\) | ||||
0.301429 | + | 0.953489i | \(0.402536\pi\) | |||||||
\(20\) | 1.14067 | 0.255061 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.70774 | −0.790493 | ||||||||
\(23\) | −3.35111 | −0.698754 | −0.349377 | − | 0.936982i | \(-0.613607\pi\) | ||||
−0.349377 | + | 0.936982i | \(0.613607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.34761 | −0.469522 | ||||||||
\(26\) | −8.89465 | −1.74438 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.261273 | 0.0493759 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.01079 | 0.540755 | 0.270377 | − | 0.962754i | \(-0.412852\pi\) | ||||
0.270377 | + | 0.962754i | \(0.412852\pi\) | |||||||
\(32\) | 3.79767 | 0.671339 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.58807 | −0.786848 | ||||||||
\(35\) | 0.607535 | 0.102692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.20826 | 1.02063 | 0.510316 | − | 0.859987i | \(-0.329528\pi\) | ||||
0.510316 | + | 0.859987i | \(0.329528\pi\) | |||||||
\(38\) | −4.31822 | −0.700508 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.47812 | 0.549939 | ||||||||
\(41\) | −4.29911 | −0.671409 | −0.335704 | − | 0.941967i | \(-0.608974\pi\) | ||||
−0.335704 | + | 0.941967i | \(0.608974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.708513 | −0.108047 | −0.0540236 | − | 0.998540i | \(-0.517205\pi\) | ||||
−0.0540236 | + | 0.998540i | \(0.517205\pi\) | |||||||
\(44\) | 1.58029 | 0.238238 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.50683 | 0.811938 | ||||||||
\(47\) | 10.7372 | 1.56618 | 0.783088 | − | 0.621911i | \(-0.213643\pi\) | ||||
0.783088 | + | 0.621911i | \(0.213643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.86084 | −0.980120 | ||||||||
\(50\) | 3.85780 | 0.545575 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.79102 | 0.525720 | ||||||||
\(53\) | 13.8501 | 1.90246 | 0.951230 | − | 0.308482i | \(-0.0998211\pi\) | ||||
0.951230 | + | 0.308482i | \(0.0998211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.67464 | 0.495488 | ||||||||
\(56\) | 0.796670 | 0.106460 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.48056 | 0.322942 | 0.161471 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161471 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.78277 | 0.228260 | 0.114130 | − | 0.993466i | \(-0.463592\pi\) | ||||
0.114130 | + | 0.993466i | \(0.463592\pi\) | |||||||
\(62\) | −4.94760 | −0.628346 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.57981 | 0.447477 | ||||||||
\(65\) | 8.81523 | 1.09340 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.94023 | −0.481375 | −0.240688 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240688 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(68\) | 1.95550 | 0.237139 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.998354 | −0.119326 | ||||||||
\(71\) | −14.7180 | −1.74670 | −0.873350 | − | 0.487092i | \(-0.838057\pi\) | ||||
−0.873350 | + | 0.487092i | \(0.838057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3319 | 1.56038 | 0.780191 | − | 0.625541i | \(-0.215122\pi\) | ||||
0.780191 | + | 0.625541i | \(0.215122\pi\) | |||||||
\(74\) | −10.2020 | −1.18595 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.84049 | 0.211118 | ||||||||
\(77\) | 0.841683 | 0.0959187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.49825 | 0.393584 | 0.196792 | − | 0.980445i | \(-0.436948\pi\) | ||||
0.196792 | + | 0.980445i | \(0.436948\pi\) | |||||||
\(80\) | −7.99688 | −0.894079 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.06468 | 0.780163 | ||||||||
\(83\) | 12.4465 | 1.36618 | 0.683089 | − | 0.730335i | \(-0.260636\pi\) | ||||
0.683089 | + | 0.730335i | \(0.260636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.54711 | 0.493203 | ||||||||
\(86\) | 1.16429 | 0.125549 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.81861 | 0.513665 | ||||||||
\(89\) | −2.54336 | −0.269595 | −0.134798 | − | 0.990873i | \(-0.543038\pi\) | ||||
−0.134798 | + | 0.990873i | \(0.543038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.01915 | 0.211664 | ||||||||
\(92\) | −2.34709 | −0.244701 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.6442 | −1.81986 | ||||||||
\(95\) | 4.27967 | 0.439085 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1555 | 1.23420 | 0.617100 | − | 0.786884i | \(-0.288307\pi\) | ||||
0.617100 | + | 0.786884i | \(0.288307\pi\) | |||||||
\(98\) | 11.2743 | 1.13888 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.64425 | −0.164425 | ||||||||
\(101\) | −0.0790358 | −0.00786435 | −0.00393218 | − | 0.999992i | \(-0.501252\pi\) | ||||
−0.00393218 | + | 0.999992i | \(0.501252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0482 | 1.67981 | 0.839907 | − | 0.542731i | \(-0.182610\pi\) | ||||
0.839907 | + | 0.542731i | \(0.182610\pi\) | |||||||
\(104\) | 11.5596 | 1.13351 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.7597 | −2.21062 | ||||||||
\(107\) | −16.3525 | −1.58086 | −0.790429 | − | 0.612554i | \(-0.790142\pi\) | ||||
−0.790429 | + | 0.612554i | \(0.790142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.68290 | 0.256975 | 0.128487 | − | 0.991711i | \(-0.458988\pi\) | ||||
0.128487 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(110\) | −6.03848 | −0.575747 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.83170 | −0.173080 | ||||||||
\(113\) | −13.8065 | −1.29881 | −0.649403 | − | 0.760444i | \(-0.724981\pi\) | ||||
−0.649403 | + | 0.760444i | \(0.724981\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.45766 | −0.508930 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.07628 | −0.375252 | ||||||||
\(119\) | 1.04153 | 0.0954765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.90913 | −0.537194 | ||||||||
\(122\) | −2.92960 | −0.265234 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.10874 | 0.189370 | ||||||||
\(125\) | −11.9664 | −1.07031 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9165 | 1.58984 | 0.794918 | − | 0.606717i | \(-0.207514\pi\) | ||||
0.794918 | + | 0.606717i | \(0.207514\pi\) | |||||||
\(128\) | −13.4780 | −1.19130 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.4860 | −1.27050 | ||||||||
\(131\) | −10.5180 | −0.918961 | −0.459481 | − | 0.888188i | \(-0.651964\pi\) | ||||
−0.459481 | + | 0.888188i | \(0.651964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.980267 | 0.0849999 | ||||||||
\(134\) | 6.47492 | 0.559348 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.96270 | 0.511297 | ||||||||
\(137\) | −19.3331 | −1.65174 | −0.825868 | − | 0.563864i | \(-0.809314\pi\) | ||||
−0.825868 | + | 0.563864i | \(0.809314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.9103 | 1.09504 | 0.547520 | − | 0.836792i | \(-0.315572\pi\) | ||||
0.547520 | + | 0.836792i | \(0.315572\pi\) | |||||||
\(140\) | 0.425513 | 0.0359624 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 24.1858 | 2.02963 | ||||||||
\(143\) | 12.2127 | 1.02128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.9082 | −1.81313 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.34822 | 0.357421 | ||||||||
\(149\) | −20.6557 | −1.69218 | −0.846091 | − | 0.533038i | \(-0.821050\pi\) | ||||
−0.846091 | + | 0.533038i | \(0.821050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.84913 | 0.801511 | 0.400756 | − | 0.916185i | \(-0.368748\pi\) | ||||
0.400756 | + | 0.916185i | \(0.368748\pi\) | |||||||
\(152\) | 5.61199 | 0.455193 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.38313 | −0.111456 | ||||||||
\(155\) | 4.90343 | 0.393853 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.01656 | −0.559983 | −0.279991 | − | 0.960003i | \(-0.590332\pi\) | ||||
−0.279991 | + | 0.960003i | \(0.590332\pi\) | |||||||
\(158\) | −5.74863 | −0.457337 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.18494 | 0.488962 | ||||||||
\(161\) | −1.25009 | −0.0985208 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3424 | 0.966728 | 0.483364 | − | 0.875419i | \(-0.339415\pi\) | ||||
0.483364 | + | 0.875419i | \(0.339415\pi\) | |||||||
\(164\) | −3.01107 | −0.235125 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.4531 | −1.58747 | ||||||||
\(167\) | −10.0491 | −0.777626 | −0.388813 | − | 0.921317i | \(-0.627115\pi\) | ||||
−0.388813 | + | 0.921317i | \(0.627115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.2975 | 1.25365 | ||||||||
\(170\) | −7.47221 | −0.573092 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.496237 | −0.0378377 | ||||||||
\(173\) | −13.6711 | −1.03940 | −0.519699 | − | 0.854349i | \(-0.673956\pi\) | ||||
−0.519699 | + | 0.854349i | \(0.673956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.875748 | −0.0662003 | ||||||||
\(176\) | −11.0789 | −0.835106 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.17947 | 0.313264 | ||||||||
\(179\) | −1.14662 | −0.0857021 | −0.0428511 | − | 0.999081i | \(-0.513644\pi\) | ||||
−0.0428511 | + | 0.999081i | \(0.513644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1064 | −0.751203 | −0.375602 | − | 0.926781i | \(-0.622564\pi\) | ||||
−0.375602 | + | 0.926781i | \(0.622564\pi\) | |||||||
\(182\) | −3.31804 | −0.245949 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.15672 | −0.527600 | ||||||||
\(185\) | 10.1109 | 0.743366 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.29960 | 0.460672 | ||||||||
\(188\) | 7.52022 | 0.548469 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.03272 | −0.510207 | ||||||||
\(191\) | 21.3388 | 1.54402 | 0.772011 | − | 0.635609i | \(-0.219251\pi\) | ||||
0.772011 | + | 0.635609i | \(0.219251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.89472 | −0.352330 | −0.176165 | − | 0.984361i | \(-0.556369\pi\) | ||||
−0.176165 | + | 0.984361i | \(0.556369\pi\) | |||||||
\(194\) | −19.9749 | −1.43412 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.80528 | −0.343234 | ||||||||
\(197\) | −4.46002 | −0.317763 | −0.158882 | − | 0.987298i | \(-0.550789\pi\) | ||||
−0.158882 | + | 0.987298i | \(0.550789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.2018 | −0.794073 | −0.397036 | − | 0.917803i | \(-0.629961\pi\) | ||||
−0.397036 | + | 0.917803i | \(0.629961\pi\) | |||||||
\(200\) | −5.01363 | −0.354517 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.129878 | 0.00913822 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00160 | −0.489013 | ||||||||
\(206\) | −28.0152 | −1.95191 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −26.5777 | −1.84283 | ||||||||
\(209\) | 5.92908 | 0.410123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.16651 | 0.217992 | 0.108996 | − | 0.994042i | \(-0.465236\pi\) | ||||
0.108996 | + | 0.994042i | \(0.465236\pi\) | |||||||
\(212\) | 9.70051 | 0.666234 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.8719 | 1.83692 | ||||||||
\(215\) | −1.15389 | −0.0786950 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.12314 | 0.0762437 | ||||||||
\(218\) | −4.40877 | −0.298599 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.57369 | 0.173518 | ||||||||
\(221\) | 15.1124 | 1.01657 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1423 | −1.14794 | −0.573968 | − | 0.818878i | \(-0.694597\pi\) | ||||
−0.573968 | + | 0.818878i | \(0.694597\pi\) | |||||||
\(224\) | 1.41667 | 0.0946555 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.6880 | 1.50919 | ||||||||
\(227\) | 10.7698 | 0.714816 | 0.357408 | − | 0.933948i | \(-0.383661\pi\) | ||||
0.357408 | + | 0.933948i | \(0.383661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.98851 | −0.263568 | −0.131784 | − | 0.991278i | \(-0.542071\pi\) | ||||
−0.131784 | + | 0.991278i | \(0.542071\pi\) | |||||||
\(230\) | 8.96850 | 0.591366 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5903 | 1.67647 | 0.838237 | − | 0.545306i | \(-0.183587\pi\) | ||||
0.838237 | + | 0.545306i | \(0.183587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.4867 | 1.14071 | ||||||||
\(236\) | 1.73737 | 0.113093 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.71153 | −0.110942 | ||||||||
\(239\) | 13.7321 | 0.888254 | 0.444127 | − | 0.895964i | \(-0.353514\pi\) | ||||
0.444127 | + | 0.895964i | \(0.353514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5978 | 1.06916 | 0.534581 | − | 0.845117i | \(-0.320470\pi\) | ||||
0.534581 | + | 0.845117i | \(0.320470\pi\) | |||||||
\(242\) | 9.71040 | 0.624208 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.24864 | 0.0799358 | ||||||||
\(245\) | −11.1737 | −0.713860 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2235 | 0.905020 | ||||||||
\(248\) | 6.42994 | 0.408302 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.6643 | 1.24368 | ||||||||
\(251\) | 17.5574 | 1.10821 | 0.554106 | − | 0.832446i | \(-0.313060\pi\) | ||||
0.554106 | + | 0.832446i | \(0.313060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.56108 | −0.475361 | ||||||||
\(254\) | −29.4420 | −1.84736 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.9886 | 0.936787 | ||||||||
\(257\) | 5.75740 | 0.359137 | 0.179568 | − | 0.983745i | \(-0.442530\pi\) | ||||
0.179568 | + | 0.983745i | \(0.442530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31592 | 0.143904 | ||||||||
\(260\) | 6.17412 | 0.382903 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.2841 | 1.06781 | ||||||||
\(263\) | 5.22043 | 0.321905 | 0.160953 | − | 0.986962i | \(-0.448543\pi\) | ||||
0.160953 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.5565 | 1.38564 | ||||||||
\(266\) | −1.61086 | −0.0987681 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.75970 | −0.168576 | ||||||||
\(269\) | −18.9198 | −1.15356 | −0.576779 | − | 0.816900i | \(-0.695691\pi\) | ||||
−0.576779 | + | 0.816900i | \(0.695691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0038 | −1.33663 | −0.668317 | − | 0.743877i | \(-0.732985\pi\) | ||||
−0.668317 | + | 0.743877i | \(0.732985\pi\) | |||||||
\(272\) | −13.7094 | −0.831256 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 31.7698 | 1.91928 | ||||||||
\(275\) | −5.29691 | −0.319415 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.2254 | −0.794636 | −0.397318 | − | 0.917681i | \(-0.630059\pi\) | ||||
−0.397318 | + | 0.917681i | \(0.630059\pi\) | |||||||
\(278\) | −21.2154 | −1.27241 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.29747 | 0.0775386 | ||||||||
\(281\) | −15.0461 | −0.897575 | −0.448788 | − | 0.893638i | \(-0.648144\pi\) | ||||
−0.448788 | + | 0.893638i | \(0.648144\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.7504 | −1.82792 | −0.913960 | − | 0.405804i | \(-0.866991\pi\) | ||||
−0.913960 | + | 0.405804i | \(0.866991\pi\) | |||||||
\(284\) | −10.3083 | −0.611688 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.0690 | −1.18670 | ||||||||
\(287\) | −1.60373 | −0.0946653 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.20468 | −0.541452 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.33757 | 0.546440 | ||||||||
\(293\) | 4.27848 | 0.249952 | 0.124976 | − | 0.992160i | \(-0.460115\pi\) | ||||
0.124976 | + | 0.992160i | \(0.460115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.03988 | 0.235211 | ||||||||
\(296\) | 13.2585 | 0.770637 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 33.9433 | 1.96628 | ||||||||
\(299\) | −18.1386 | −1.04898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.264302 | −0.0152341 | ||||||||
\(302\) | −16.1850 | −0.931339 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.9031 | −0.740043 | ||||||||
\(305\) | 2.90345 | 0.166251 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9080 | 1.47865 | 0.739324 | − | 0.673350i | \(-0.235145\pi\) | ||||
0.739324 | + | 0.673350i | \(0.235145\pi\) | |||||||
\(308\) | 0.589508 | 0.0335904 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.05774 | −0.457649 | ||||||||
\(311\) | −27.7460 | −1.57333 | −0.786665 | − | 0.617379i | \(-0.788194\pi\) | ||||
−0.786665 | + | 0.617379i | \(0.788194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4201 | 1.49335 | 0.746676 | − | 0.665188i | \(-0.231649\pi\) | ||||
0.746676 | + | 0.665188i | \(0.231649\pi\) | |||||||
\(314\) | 11.5302 | 0.650688 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.45015 | 0.137832 | ||||||||
\(317\) | 6.19862 | 0.348149 | 0.174075 | − | 0.984732i | \(-0.444307\pi\) | ||||
0.174075 | + | 0.984732i | \(0.444307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.83014 | 0.325915 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.05425 | 0.114479 | ||||||||
\(323\) | 7.33683 | 0.408232 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7070 | −0.704855 | ||||||||
\(326\) | −20.2820 | −1.12332 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.18131 | −0.506953 | ||||||||
\(329\) | 4.00537 | 0.220823 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.6349 | 1.46399 | 0.731993 | − | 0.681312i | \(-0.238590\pi\) | ||||
0.731993 | + | 0.681312i | \(0.238590\pi\) | |||||||
\(332\) | 8.71741 | 0.478430 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5136 | 0.903585 | ||||||||
\(335\) | −6.41711 | −0.350604 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1020 | −0.877134 | −0.438567 | − | 0.898698i | \(-0.644514\pi\) | ||||
−0.438567 | + | 0.898698i | \(0.644514\pi\) | |||||||
\(338\) | −26.7815 | −1.45672 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.18476 | 0.172718 | ||||||||
\(341\) | 6.79324 | 0.367875 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.17062 | −0.279187 | ||||||||
\(344\) | −1.51312 | −0.0815820 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.4656 | 1.20776 | ||||||||
\(347\) | −11.9111 | −0.639422 | −0.319711 | − | 0.947515i | \(-0.603586\pi\) | ||||
−0.319711 | + | 0.947515i | \(0.603586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.50331 | 0.401643 | 0.200822 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200822 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(350\) | 1.43911 | 0.0769234 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.56866 | 0.456711 | ||||||||
\(353\) | 20.3746 | 1.08443 | 0.542216 | − | 0.840239i | \(-0.317585\pi\) | ||||
0.542216 | + | 0.840239i | \(0.317585\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.9699 | −1.27219 | ||||||||
\(356\) | −1.78135 | −0.0944113 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.88422 | 0.0995841 | ||||||||
\(359\) | −19.1003 | −1.00808 | −0.504038 | − | 0.863681i | \(-0.668153\pi\) | ||||
−0.504038 | + | 0.863681i | \(0.668153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0947 | −0.636563 | ||||||||
\(362\) | 16.6077 | 0.872883 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.41420 | 0.0741240 | ||||||||
\(365\) | 21.7126 | 1.13649 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.3448 | −1.63619 | −0.818093 | − | 0.575086i | \(-0.804968\pi\) | ||||
−0.818093 | + | 0.575086i | \(0.804968\pi\) | |||||||
\(368\) | 16.4547 | 0.857761 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.6151 | −0.863776 | ||||||||
\(371\) | 5.16662 | 0.268237 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0294 | −0.571083 | −0.285541 | − | 0.958366i | \(-0.592173\pi\) | ||||
−0.285541 | + | 0.958366i | \(0.592173\pi\) | |||||||
\(374\) | −10.3521 | −0.535292 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.9306 | 1.18256 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6969 | 1.21723 | 0.608614 | − | 0.793466i | \(-0.291726\pi\) | ||||
0.608614 | + | 0.793466i | \(0.291726\pi\) | |||||||
\(380\) | 2.99744 | 0.153766 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −35.0658 | −1.79412 | ||||||||
\(383\) | −24.9756 | −1.27619 | −0.638097 | − | 0.769956i | \(-0.720278\pi\) | ||||
−0.638097 | + | 0.769956i | \(0.720278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.37078 | 0.0698613 | ||||||||
\(386\) | 8.04343 | 0.409400 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.51359 | 0.432212 | ||||||||
\(389\) | 15.4660 | 0.784155 | 0.392078 | − | 0.919932i | \(-0.371756\pi\) | ||||
0.392078 | + | 0.919932i | \(0.371756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.35632 | −0.473170 | ||||||||
\(392\) | −14.6522 | −0.740049 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.32909 | 0.369234 | ||||||||
\(395\) | 5.69731 | 0.286663 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.26306 | −0.414711 | −0.207356 | − | 0.978266i | \(-0.566486\pi\) | ||||
−0.207356 | + | 0.978266i | \(0.566486\pi\) | |||||||
\(398\) | 18.4077 | 0.922696 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.5273 | 0.576366 | ||||||||
\(401\) | −24.7673 | −1.23682 | −0.618409 | − | 0.785857i | \(-0.712222\pi\) | ||||
−0.618409 | + | 0.785857i | \(0.712222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2966 | 0.811791 | ||||||||
\(404\) | −0.0553560 | −0.00275407 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.0077 | 0.694335 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.10464 | −0.252408 | −0.126204 | − | 0.992004i | \(-0.540279\pi\) | ||||
−0.126204 | + | 0.992004i | \(0.540279\pi\) | |||||||
\(410\) | 11.5056 | 0.568223 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.9405 | 0.588264 | ||||||||
\(413\) | 0.925343 | 0.0455332 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.2705 | 0.995040 | ||||||||
\(416\) | 20.5557 | 1.00783 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.74318 | −0.476555 | ||||||||
\(419\) | 24.8882 | 1.21587 | 0.607935 | − | 0.793987i | \(-0.291998\pi\) | ||||
0.607935 | + | 0.793987i | \(0.291998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.2350 | 1.66851 | 0.834257 | − | 0.551376i | \(-0.185897\pi\) | ||||
0.834257 | + | 0.551376i | \(0.185897\pi\) | |||||||
\(422\) | −5.20349 | −0.253302 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.5787 | 1.43647 | ||||||||
\(425\) | −6.55456 | −0.317943 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.665040 | 0.0321836 | ||||||||
\(428\) | −11.4532 | −0.553610 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.89618 | 0.0914419 | ||||||||
\(431\) | 8.32784 | 0.401138 | 0.200569 | − | 0.979680i | \(-0.435721\pi\) | ||||
0.200569 | + | 0.979680i | \(0.435721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.43346 | −0.165002 | −0.0825008 | − | 0.996591i | \(-0.526291\pi\) | ||||
−0.0825008 | + | 0.996591i | \(0.526291\pi\) | |||||||
\(434\) | −1.84564 | −0.0885936 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.87908 | 0.0899916 | ||||||||
\(437\) | −8.80602 | −0.421249 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8754 | −1.09179 | −0.545893 | − | 0.837855i | \(-0.683809\pi\) | ||||
−0.545893 | + | 0.837855i | \(0.683809\pi\) | |||||||
\(440\) | 7.84766 | 0.374123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.8340 | −1.18123 | ||||||||
\(443\) | 32.8455 | 1.56054 | 0.780268 | − | 0.625446i | \(-0.215083\pi\) | ||||
0.780268 | + | 0.625446i | \(0.215083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.14215 | −0.196357 | ||||||||
\(446\) | 28.1698 | 1.33388 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.33541 | 0.0630920 | ||||||||
\(449\) | −26.3567 | −1.24385 | −0.621924 | − | 0.783078i | \(-0.713649\pi\) | ||||
−0.621924 | + | 0.783078i | \(0.713649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.70007 | −0.456758 | ||||||||
\(452\) | −9.66996 | −0.454837 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.6978 | −0.830601 | ||||||||
\(455\) | 3.28842 | 0.154163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5928 | 0.729402 | 0.364701 | − | 0.931125i | \(-0.381171\pi\) | ||||
0.364701 | + | 0.931125i | \(0.381171\pi\) | |||||||
\(458\) | 6.55426 | 0.306261 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.82250 | −0.178225 | ||||||||
\(461\) | 28.3944 | 1.32246 | 0.661229 | − | 0.750184i | \(-0.270035\pi\) | ||||
0.661229 | + | 0.750184i | \(0.270035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.69723 | 0.171825 | 0.0859125 | − | 0.996303i | \(-0.472619\pi\) | ||||
0.0859125 | + | 0.996303i | \(0.472619\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42.0522 | −1.94803 | ||||||||
\(467\) | −0.293937 | −0.0136018 | −0.00680089 | − | 0.999977i | \(-0.502165\pi\) | ||||
−0.00680089 | + | 0.999977i | \(0.502165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.46985 | −0.0678715 | ||||||||
\(470\) | −28.7357 | −1.32548 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.29756 | 0.243840 | ||||||||
\(473\) | −1.59861 | −0.0735044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.16904 | −0.283055 | ||||||||
\(476\) | 0.729476 | 0.0334355 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.5657 | −1.03213 | ||||||||
\(479\) | −18.3071 | −0.836472 | −0.418236 | − | 0.908339i | \(-0.637351\pi\) | ||||
−0.418236 | + | 0.908339i | \(0.637351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.6036 | 1.53219 | ||||||||
\(482\) | −27.2750 | −1.24234 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.13871 | −0.188123 | ||||||||
\(485\) | 19.7966 | 0.898917 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.78702 | 0.262235 | 0.131118 | − | 0.991367i | \(-0.458143\pi\) | ||||
0.131118 | + | 0.991367i | \(0.458143\pi\) | |||||||
\(488\) | 3.80733 | 0.172350 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.3616 | 0.829490 | ||||||||
\(491\) | −21.7469 | −0.981423 | −0.490712 | − | 0.871322i | \(-0.663263\pi\) | ||||
−0.490712 | + | 0.871322i | \(0.663263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −23.3733 | −1.05161 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.7837 | −0.663808 | ||||||||
\(497\) | −5.49036 | −0.246276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3340 | 0.865510 | 0.432755 | − | 0.901512i | \(-0.357542\pi\) | ||||
0.432755 | + | 0.901512i | \(0.357542\pi\) | |||||||
\(500\) | −8.38120 | −0.374818 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.8518 | −1.28772 | ||||||||
\(503\) | −38.2983 | −1.70764 | −0.853819 | − | 0.520569i | \(-0.825720\pi\) | ||||
−0.853819 | + | 0.520569i | \(0.825720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.128719 | −0.00572791 | ||||||||
\(506\) | 12.4250 | 0.552360 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.5486 | 0.556754 | ||||||||
\(509\) | 30.3390 | 1.34475 | 0.672376 | − | 0.740210i | \(-0.265274\pi\) | ||||
0.672376 | + | 0.740210i | \(0.265274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.97331 | 0.220006 | ||||||||
\(512\) | 2.32544 | 0.102771 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.46107 | −0.417310 | ||||||||
\(515\) | 27.7650 | 1.22347 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.2262 | 1.06547 | ||||||||
\(518\) | −3.80572 | −0.167214 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.8261 | 0.825578 | ||||||||
\(521\) | 1.15099 | 0.0504259 | 0.0252129 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252129 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.09010 | −0.310028 | −0.155014 | − | 0.987912i | \(-0.549542\pi\) | ||||
−0.155014 | + | 0.987912i | \(0.549542\pi\) | |||||||
\(524\) | −7.36672 | −0.321817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.57866 | −0.374047 | ||||||||
\(527\) | 8.40617 | 0.366179 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7701 | −0.511743 | ||||||||
\(530\) | −37.0668 | −1.61008 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.686571 | 0.0297666 | ||||||||
\(533\) | −23.2699 | −1.00793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6320 | −1.15140 | ||||||||
\(536\) | −8.41486 | −0.363467 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.0906 | 1.34041 | ||||||||
\(539\) | −15.4801 | −0.666775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9272 | −1.02871 | −0.514355 | − | 0.857578i | \(-0.671968\pi\) | ||||
−0.514355 | + | 0.857578i | \(0.671968\pi\) | |||||||
\(542\) | 36.1585 | 1.55314 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.6031 | 0.454605 | ||||||||
\(545\) | 4.36941 | 0.187165 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.76378 | −0.0754138 | −0.0377069 | − | 0.999289i | \(-0.512005\pi\) | ||||
−0.0377069 | + | 0.999289i | \(0.512005\pi\) | |||||||
\(548\) | −13.5407 | −0.578431 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.70434 | 0.371154 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.30498 | 0.0554934 | ||||||||
\(554\) | 21.7331 | 0.923351 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.04230 | 0.383479 | ||||||||
\(557\) | 40.1163 | 1.69978 | 0.849891 | − | 0.526958i | \(-0.176668\pi\) | ||||
0.849891 | + | 0.526958i | \(0.176668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.83498 | −0.162202 | ||||||||
\(560\) | −2.98314 | −0.126061 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.7251 | 1.04296 | ||||||||
\(563\) | 16.9855 | 0.715854 | 0.357927 | − | 0.933750i | \(-0.383484\pi\) | ||||
0.357927 | + | 0.933750i | \(0.383484\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.4855 | −0.945971 | ||||||||
\(566\) | 50.5317 | 2.12401 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.4321 | −1.31886 | ||||||||
\(569\) | −29.7390 | −1.24672 | −0.623361 | − | 0.781934i | \(-0.714233\pi\) | ||||
−0.623361 | + | 0.781934i | \(0.714233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0295 | 1.08930 | 0.544650 | − | 0.838664i | \(-0.316663\pi\) | ||||
0.544650 | + | 0.838664i | \(0.316663\pi\) | |||||||
\(572\) | 8.55367 | 0.357647 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.63539 | 0.109999 | ||||||||
\(575\) | 7.86710 | 0.328081 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.64937 | 0.151925 | 0.0759626 | − | 0.997111i | \(-0.475797\pi\) | ||||
0.0759626 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(578\) | 15.1259 | 0.629156 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.64300 | 0.192624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.2500 | 1.29424 | ||||||||
\(584\) | 28.4720 | 1.17818 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.03077 | −0.290439 | ||||||||
\(587\) | 2.47754 | 0.102259 | 0.0511296 | − | 0.998692i | \(-0.483718\pi\) | ||||
0.0511296 | + | 0.998692i | \(0.483718\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.91175 | 0.325998 | ||||||||
\(590\) | −6.63868 | −0.273310 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.4840 | −1.25289 | ||||||||
\(593\) | −15.8763 | −0.651962 | −0.325981 | − | 0.945376i | \(-0.605695\pi\) | ||||
−0.325981 | + | 0.945376i | \(0.605695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.69624 | 0.0695392 | ||||||||
\(596\) | −14.4671 | −0.592596 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.8069 | 1.21889 | ||||||||
\(599\) | −1.44578 | −0.0590732 | −0.0295366 | − | 0.999564i | \(-0.509403\pi\) | ||||
−0.0295366 | + | 0.999564i | \(0.509403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.5274 | −0.918912 | −0.459456 | − | 0.888201i | \(-0.651956\pi\) | ||||
−0.459456 | + | 0.888201i | \(0.651956\pi\) | |||||||
\(602\) | 0.434324 | 0.0177017 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.89825 | 0.280686 | ||||||||
\(605\) | −9.62370 | −0.391259 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.6228 | −0.958818 | −0.479409 | − | 0.877592i | \(-0.659149\pi\) | ||||
−0.479409 | + | 0.877592i | \(0.659149\pi\) | |||||||
\(608\) | 9.97949 | 0.404722 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.77119 | −0.193180 | ||||||||
\(611\) | 58.1172 | 2.35117 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.8449 | 0.963085 | 0.481542 | − | 0.876423i | \(-0.340077\pi\) | ||||
0.481542 | + | 0.876423i | \(0.340077\pi\) | |||||||
\(614\) | −42.5743 | −1.71816 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.79752 | 0.0724243 | ||||||||
\(617\) | 18.4046 | 0.740943 | 0.370471 | − | 0.928844i | \(-0.379196\pi\) | ||||
0.370471 | + | 0.928844i | \(0.379196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9332 | 1.08254 | 0.541268 | − | 0.840850i | \(-0.317945\pi\) | ||||
0.541268 | + | 0.840850i | \(0.317945\pi\) | |||||||
\(620\) | 3.43432 | 0.137926 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.5946 | 1.82818 | ||||||||
\(623\) | −0.948769 | −0.0380116 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.75066 | −0.310026 | ||||||||
\(626\) | −43.4158 | −1.73524 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.91435 | −0.196104 | ||||||||
\(629\) | 17.3335 | 0.691133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3093 | −1.48526 | −0.742630 | − | 0.669702i | \(-0.766422\pi\) | ||||
−0.742630 | + | 0.669702i | \(0.766422\pi\) | |||||||
\(632\) | 7.47097 | 0.297179 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.1861 | −0.404542 | ||||||||
\(635\) | 29.1791 | 1.15794 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.1358 | −1.47137 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.9505 | −0.867668 | ||||||||
\(641\) | −1.52697 | −0.0603117 | −0.0301558 | − | 0.999545i | \(-0.509600\pi\) | ||||
−0.0301558 | + | 0.999545i | \(0.509600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4450 | 1.04289 | 0.521444 | − | 0.853286i | \(-0.325394\pi\) | ||||
0.521444 | + | 0.853286i | \(0.325394\pi\) | |||||||
\(644\) | −0.875552 | −0.0345016 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0565 | −0.474357 | ||||||||
\(647\) | 15.0249 | 0.590692 | 0.295346 | − | 0.955390i | \(-0.404565\pi\) | ||||
0.295346 | + | 0.955390i | \(0.404565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.59688 | 0.219697 | ||||||||
\(650\) | 20.8812 | 0.819027 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.64449 | 0.338544 | ||||||||
\(653\) | 22.6351 | 0.885780 | 0.442890 | − | 0.896576i | \(-0.353953\pi\) | ||||
0.442890 | + | 0.896576i | \(0.353953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1298 | −0.669315 | ||||||||
\(656\) | 21.1097 | 0.824194 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.58197 | −0.256592 | ||||||||
\(659\) | 19.2087 | 0.748264 | 0.374132 | − | 0.927375i | \(-0.377941\pi\) | ||||
0.374132 | + | 0.927375i | \(0.377941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9135 | 1.12460 | 0.562301 | − | 0.826932i | \(-0.309916\pi\) | ||||
0.562301 | + | 0.826932i | \(0.309916\pi\) | |||||||
\(662\) | −43.7688 | −1.70112 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.5810 | 1.03154 | ||||||||
\(665\) | 1.59648 | 0.0619087 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −7.03834 | −0.272322 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.5452 | 0.407395 | ||||||||
\(671\) | 4.02245 | 0.155285 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.85259 | −0.341242 | −0.170621 | − | 0.985337i | \(-0.554577\pi\) | ||||
−0.170621 | + | 0.985337i | \(0.554577\pi\) | |||||||
\(674\) | 26.4603 | 1.01921 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.4146 | 0.439025 | ||||||||
\(677\) | −34.0025 | −1.30682 | −0.653412 | − | 0.757003i | \(-0.726663\pi\) | ||||
−0.653412 | + | 0.757003i | \(0.726663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.53445 | 0.174016 | ||||||||
\(680\) | 9.71094 | 0.372398 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.1632 | −0.427463 | ||||||||
\(683\) | 6.78343 | 0.259561 | 0.129780 | − | 0.991543i | \(-0.458573\pi\) | ||||
0.129780 | + | 0.991543i | \(0.458573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.4861 | −1.20302 | ||||||||
\(686\) | 8.49681 | 0.324410 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.47896 | 0.132634 | ||||||||
\(689\) | 74.9668 | 2.85601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.9928 | 1.40727 | 0.703637 | − | 0.710560i | \(-0.251558\pi\) | ||||
0.703637 | + | 0.710560i | \(0.251558\pi\) | |||||||
\(692\) | −9.57516 | −0.363993 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.5734 | 0.742995 | ||||||||
\(695\) | 21.0260 | 0.797561 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0032 | −0.454653 | ||||||||
\(698\) | −12.3301 | −0.466701 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.613367 | −0.0231831 | ||||||||
\(701\) | −2.60481 | −0.0983823 | −0.0491912 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491912 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3140 | 0.615296 | ||||||||
\(704\) | 8.07711 | 0.304418 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.4814 | −1.26009 | ||||||||
\(707\) | −0.0294833 | −0.00110883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0044 | −0.375723 | −0.187862 | − | 0.982195i | \(-0.560156\pi\) | ||||
−0.187862 | + | 0.982195i | \(0.560156\pi\) | |||||||
\(710\) | 39.3894 | 1.47826 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.43167 | −0.203560 | ||||||||
\(713\) | −10.0895 | −0.377854 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.8898 | 0.743835 | ||||||||
\(716\) | −0.803081 | −0.0300125 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.3873 | 1.17136 | ||||||||
\(719\) | 39.6266 | 1.47782 | 0.738912 | − | 0.673802i | \(-0.235340\pi\) | ||||
0.738912 | + | 0.673802i | \(0.235340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.35964 | 0.236845 | ||||||||
\(722\) | 19.8751 | 0.739673 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.07845 | −0.263068 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.0756 | 1.48632 | 0.743160 | − | 0.669114i | \(-0.233326\pi\) | ||||
0.743160 | + | 0.669114i | \(0.233326\pi\) | |||||||
\(728\) | 4.31215 | 0.159819 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −35.6800 | −1.32057 | ||||||||
\(731\) | −1.97818 | −0.0731655 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.62875 | 0.318710 | 0.159355 | − | 0.987221i | \(-0.449059\pi\) | ||||
0.159355 | + | 0.987221i | \(0.449059\pi\) | |||||||
\(734\) | 51.5085 | 1.90121 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.7264 | −0.469101 | ||||||||
\(737\) | −8.89032 | −0.327479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.4519 | 1.89269 | 0.946345 | − | 0.323159i | \(-0.104745\pi\) | ||||
0.946345 | + | 0.323159i | \(0.104745\pi\) | |||||||
\(740\) | 7.08158 | 0.260324 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.49024 | −0.311686 | ||||||||
\(743\) | −33.8098 | −1.24036 | −0.620181 | − | 0.784459i | \(-0.712941\pi\) | ||||
−0.620181 | + | 0.784459i | \(0.712941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.6402 | −1.23248 | ||||||||
\(746\) | 18.1245 | 0.663586 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.41219 | 0.161326 | ||||||||
\(749\) | −6.10011 | −0.222893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8360 | −0.468392 | −0.234196 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234196 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(752\) | −52.7220 | −1.92257 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0404 | 0.583772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.712810 | 0.0259075 | 0.0129538 | − | 0.999916i | \(-0.495877\pi\) | ||||
0.0129538 | + | 0.999916i | \(0.495877\pi\) | |||||||
\(758\) | −38.9408 | −1.41439 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.13978 | 0.331535 | ||||||||
\(761\) | −28.8108 | −1.04439 | −0.522196 | − | 0.852826i | \(-0.674887\pi\) | ||||
−0.522196 | + | 0.852826i | \(0.674887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00082 | 0.0362322 | ||||||||
\(764\) | 14.9455 | 0.540710 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.0421 | 1.48291 | ||||||||
\(767\) | 13.4266 | 0.484806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.12281 | −0.292916 | −0.146458 | − | 0.989217i | \(-0.546787\pi\) | ||||
−0.146458 | + | 0.989217i | \(0.546787\pi\) | |||||||
\(770\) | −2.25258 | −0.0811774 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.42822 | −0.123384 | ||||||||
\(773\) | 32.2194 | 1.15885 | 0.579425 | − | 0.815025i | \(-0.303277\pi\) | ||||
0.579425 | + | 0.815025i | \(0.303277\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.06818 | −0.253896 | ||||||||
\(776\) | 25.9596 | 0.931894 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.4150 | −0.911172 | ||||||||
\(779\) | −11.2972 | −0.404764 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.2081 | −1.18828 | ||||||||
\(782\) | 15.3751 | 0.549813 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.6884 | 1.20316 | ||||||||
\(785\) | −11.4273 | −0.407857 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.6267 | 0.770909 | 0.385454 | − | 0.922727i | \(-0.374045\pi\) | ||||
0.385454 | + | 0.922727i | \(0.374045\pi\) | |||||||
\(788\) | −3.12376 | −0.111279 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.36231 | −0.333096 | ||||||||
\(791\) | −5.15035 | −0.183125 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.64963 | 0.342668 | ||||||||
\(794\) | 13.5786 | 0.481886 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.84564 | −0.278081 | ||||||||
\(797\) | −29.1287 | −1.03179 | −0.515896 | − | 0.856651i | \(-0.672541\pi\) | ||||
−0.515896 | + | 0.856651i | \(0.672541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.9783 | 1.06056 | ||||||||
\(800\) | −8.91545 | −0.315209 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.6997 | 1.43716 | ||||||||
\(803\) | 30.0807 | 1.06153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.03591 | −0.0717565 | ||||||||
\(806\) | −26.7800 | −0.943284 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.168791 | −0.00593805 | ||||||||
\(809\) | 42.9069 | 1.50853 | 0.754263 | − | 0.656572i | \(-0.227994\pi\) | ||||
0.754263 | + | 0.656572i | \(0.227994\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.3136 | −0.783535 | −0.391768 | − | 0.920064i | \(-0.628136\pi\) | ||||
−0.391768 | + | 0.920064i | \(0.628136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.0186 | −0.806803 | ||||||||
\(815\) | 20.1010 | 0.704106 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.86183 | −0.0651371 | ||||||||
\(818\) | 8.38839 | 0.293293 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.90387 | −0.171250 | ||||||||
\(821\) | −4.25873 | −0.148631 | −0.0743153 | − | 0.997235i | \(-0.523677\pi\) | ||||
−0.0743153 | + | 0.997235i | \(0.523677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.5344 | 1.58723 | 0.793615 | − | 0.608420i | \(-0.208196\pi\) | ||||
0.793615 | + | 0.608420i | \(0.208196\pi\) | |||||||
\(824\) | 36.4087 | 1.26836 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.52060 | −0.0529086 | ||||||||
\(827\) | 6.33221 | 0.220193 | 0.110096 | − | 0.993921i | \(-0.464884\pi\) | ||||
0.110096 | + | 0.993921i | \(0.464884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3857 | 0.985877 | 0.492938 | − | 0.870064i | \(-0.335923\pi\) | ||||
0.492938 | + | 0.870064i | \(0.335923\pi\) | |||||||
\(830\) | −33.3103 | −1.15622 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.3765 | 0.671760 | ||||||||
\(833\) | −19.1555 | −0.663700 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3662 | −0.566375 | ||||||||
\(836\) | 4.15268 | 0.143623 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.8985 | −1.41282 | ||||||||
\(839\) | −32.5963 | −1.12535 | −0.562675 | − | 0.826678i | \(-0.690228\pi\) | ||||
−0.562675 | + | 0.826678i | \(0.690228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −56.2580 | −1.93878 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.21780 | 0.0763399 | ||||||||
\(845\) | 26.5424 | 0.913085 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.20433 | −0.0757417 | ||||||||
\(848\) | −68.0073 | −2.33538 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.7710 | 0.369443 | ||||||||
\(851\) | −20.8045 | −0.713171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.5977 | −0.636773 | −0.318387 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318387 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(854\) | −1.09285 | −0.0373966 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34.9229 | −1.19364 | ||||||||
\(857\) | 26.3931 | 0.901570 | 0.450785 | − | 0.892633i | \(-0.351144\pi\) | ||||
0.450785 | + | 0.892633i | \(0.351144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5273 | −0.700381 | −0.350190 | − | 0.936679i | \(-0.613883\pi\) | ||||
−0.350190 | + | 0.936679i | \(0.613883\pi\) | |||||||
\(860\) | −0.808179 | −0.0275587 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.6850 | −0.466114 | ||||||||
\(863\) | 12.5561 | 0.427413 | 0.213707 | − | 0.976898i | \(-0.431446\pi\) | ||||
0.213707 | + | 0.976898i | \(0.431446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.2650 | −0.757034 | ||||||||
\(866\) | 5.64216 | 0.191729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.786638 | 0.0267002 | ||||||||
\(869\) | 7.89309 | 0.267755 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.3273 | −0.722649 | ||||||||
\(872\) | 5.72967 | 0.194031 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.4708 | 0.489483 | ||||||||
\(875\) | −4.46393 | −0.150908 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8685 | 0.805983 | 0.402991 | − | 0.915204i | \(-0.367970\pi\) | ||||
0.402991 | + | 0.915204i | \(0.367970\pi\) | |||||||
\(878\) | 37.5909 | 1.26863 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.0433 | −0.608241 | ||||||||
\(881\) | −40.6117 | −1.36824 | −0.684121 | − | 0.729368i | \(-0.739814\pi\) | ||||
−0.684121 | + | 0.729368i | \(0.739814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2345 | 0.950168 | 0.475084 | − | 0.879941i | \(-0.342418\pi\) | ||||
0.475084 | + | 0.879941i | \(0.342418\pi\) | |||||||
\(884\) | 10.5846 | 0.355998 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53.9745 | −1.81331 | ||||||||
\(887\) | 37.5966 | 1.26237 | 0.631185 | − | 0.775632i | \(-0.282569\pi\) | ||||
0.631185 | + | 0.775632i | \(0.282569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.68354 | 0.224159 | ||||||||
\(890\) | 6.80674 | 0.228163 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.0064 | −0.402003 | ||||||||
\(893\) | 28.2151 | 0.944181 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.86740 | −0.0624202 | ||||||||
\(896\) | −5.02780 | −0.167967 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43.3116 | 1.44533 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.6697 | 1.28827 | ||||||||
\(902\) | 15.9400 | 0.530744 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.4856 | −0.980675 | ||||||||
\(905\) | −16.4595 | −0.547131 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5124 | 0.913533 | 0.456766 | − | 0.889587i | \(-0.349008\pi\) | ||||
0.456766 | + | 0.889587i | \(0.349008\pi\) | |||||||
\(908\) | 7.54307 | 0.250326 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.40381 | −0.179135 | ||||||||
\(911\) | 30.2567 | 1.00245 | 0.501224 | − | 0.865318i | \(-0.332883\pi\) | ||||
0.501224 | + | 0.865318i | \(0.332883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.0829 | 0.929409 | ||||||||
\(914\) | −25.6235 | −0.847551 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.79352 | −0.0923005 | ||||||||
\(917\) | −3.92361 | −0.129569 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.33000 | −0.274781 | −0.137391 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137391 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(920\) | −11.6555 | −0.384272 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −46.6601 | −1.53667 | ||||||||
\(923\) | −79.6642 | −2.62218 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.5746 | −0.479210 | ||||||||
\(926\) | −6.07561 | −0.199657 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.2153 | −1.02414 | −0.512070 | − | 0.858944i | \(-0.671121\pi\) | ||||
−0.512070 | + | 0.858944i | \(0.671121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0289 | −0.590873 | ||||||||
\(932\) | 17.9232 | 0.587095 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.483022 | 0.0158050 | ||||||||
\(935\) | 10.2596 | 0.335526 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.5237 | −0.474469 | −0.237234 | − | 0.971452i | \(-0.576241\pi\) | ||||
−0.237234 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(938\) | 2.41539 | 0.0788653 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.2476 | 0.399471 | ||||||||
\(941\) | 14.9109 | 0.486080 | 0.243040 | − | 0.970016i | \(-0.421855\pi\) | ||||
0.243040 | + | 0.970016i | \(0.421855\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4068 | 0.469149 | ||||||||
\(944\) | −12.1801 | −0.396430 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.62698 | 0.0854105 | ||||||||
\(947\) | 28.7646 | 0.934722 | 0.467361 | − | 0.884066i | \(-0.345205\pi\) | ||||
0.467361 | + | 0.884066i | \(0.345205\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.1619 | 2.34247 | ||||||||
\(950\) | 10.1375 | 0.328904 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.22431 | 0.0720904 | ||||||||
\(953\) | −30.4381 | −0.985987 | −0.492994 | − | 0.870033i | \(-0.664097\pi\) | ||||
−0.492994 | + | 0.870033i | \(0.664097\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.7527 | 1.12457 | ||||||||
\(956\) | 9.61784 | 0.311063 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.0838 | 0.971963 | ||||||||
\(959\) | −7.21197 | −0.232887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9351 | −0.707584 | ||||||||
\(962\) | −55.2203 | −1.78037 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.6250 | 0.374416 | ||||||||
\(965\) | −7.97161 | −0.256615 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.9553 | 1.70293 | 0.851464 | − | 0.524412i | \(-0.175715\pi\) | ||||
0.851464 | + | 0.524412i | \(0.175715\pi\) | |||||||
\(968\) | −12.6197 | −0.405613 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −32.5315 | −1.04452 | ||||||||
\(971\) | −11.4036 | −0.365958 | −0.182979 | − | 0.983117i | \(-0.558574\pi\) | ||||
−0.182979 | + | 0.983117i | \(0.558574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.81604 | 0.154395 | ||||||||
\(974\) | −9.50974 | −0.304712 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.75382 | −0.280203 | ||||||||
\(977\) | 21.5535 | 0.689559 | 0.344780 | − | 0.938684i | \(-0.387954\pi\) | ||||
0.344780 | + | 0.938684i | \(0.387954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.73857 | −0.183405 | ||||||||
\(980\) | −7.82595 | −0.249991 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.7364 | 1.14039 | ||||||||
\(983\) | 13.8780 | 0.442639 | 0.221319 | − | 0.975201i | \(-0.428964\pi\) | ||||
0.221319 | + | 0.975201i | \(0.428964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.26366 | −0.231439 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.96203 | 0.316935 | ||||||||
\(989\) | 2.37430 | 0.0754984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8339 | 0.534746 | 0.267373 | − | 0.963593i | \(-0.413844\pi\) | ||||
0.267373 | + | 0.963593i | \(0.413844\pi\) | |||||||
\(992\) | 11.4340 | 0.363030 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.02223 | 0.286168 | ||||||||
\(995\) | −18.2434 | −0.578354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.3768 | −1.27875 | −0.639373 | − | 0.768897i | \(-0.720806\pi\) | ||||
−0.639373 | + | 0.768897i | \(0.720806\pi\) | |||||||
\(998\) | −31.7713 | −1.00570 | ||||||||
\(999\) | 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 | 7569.2.a.bv.1.6 | yes | 16 | |
3.2 | odd | 2 | inner | 7569.2.a.bv.1.11 | yes | 16 | |
29.28 | even | 2 | 7569.2.a.bu.1.11 | yes | 16 | ||
87.86 | odd | 2 | 7569.2.a.bu.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7569.2.a.bu.1.6 | ✓ | 16 | 87.86 | odd | 2 | ||
7569.2.a.bu.1.11 | yes | 16 | 29.28 | even | 2 | ||
7569.2.a.bv.1.6 | yes | 16 | 1.1 | even | 1 | trivial | |
7569.2.a.bv.1.11 | yes | 16 | 3.2 | odd | 2 | inner |