Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 66x^{7} - 125x^{6} - 115x^{5} + 227x^{4} + 40x^{3} - 129x^{2} + 26x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.0512060\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0512060 | 0.0362081 | 0.0181041 | − | 0.999836i | \(-0.494237\pi\) | ||||
0.0181041 | + | 0.999836i | \(0.494237\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99738 | −0.998689 | ||||||||
\(5\) | −3.74211 | −1.67352 | −0.836761 | − | 0.547569i | \(-0.815553\pi\) | ||||
−0.836761 | + | 0.547569i | \(0.815553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.65643 | −1.75997 | −0.879983 | − | 0.475005i | \(-0.842446\pi\) | ||||
−0.879983 | + | 0.475005i | \(0.842446\pi\) | |||||||
\(8\) | −0.204690 | −0.0723688 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.191618 | −0.0605951 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.845440 | −0.234483 | −0.117241 | − | 0.993103i | \(-0.537405\pi\) | ||||
−0.117241 | + | 0.993103i | \(0.537405\pi\) | |||||||
\(14\) | −0.238437 | −0.0637251 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.98427 | 0.996069 | ||||||||
\(17\) | −1.99161 | −0.483035 | −0.241518 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241518 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.676988 | −0.155312 | −0.0776559 | − | 0.996980i | \(-0.524744\pi\) | ||||
−0.0776559 | + | 0.996980i | \(0.524744\pi\) | |||||||
\(20\) | 7.47440 | 1.67133 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0512060 | −0.0109172 | ||||||||
\(23\) | 3.54686 | 0.739570 | 0.369785 | − | 0.929117i | \(-0.379431\pi\) | ||||
0.369785 | + | 0.929117i | \(0.379431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.00337 | 1.80067 | ||||||||
\(26\) | −0.0432916 | −0.00849019 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.30066 | 1.75766 | ||||||||
\(29\) | 0.677171 | 0.125748 | 0.0628738 | − | 0.998021i | \(-0.479973\pi\) | ||||
0.0628738 | + | 0.998021i | \(0.479973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.69354 | 1.38180 | 0.690900 | − | 0.722950i | \(-0.257214\pi\) | ||||
0.690900 | + | 0.722950i | \(0.257214\pi\) | |||||||
\(32\) | 0.613399 | 0.108435 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.101982 | −0.0174898 | ||||||||
\(35\) | 17.4249 | 2.94534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.80691 | −0.954650 | −0.477325 | − | 0.878727i | \(-0.658394\pi\) | ||||
−0.477325 | + | 0.878727i | \(0.658394\pi\) | |||||||
\(38\) | −0.0346659 | −0.00562355 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.765971 | 0.121111 | ||||||||
\(41\) | 3.31122 | 0.517126 | 0.258563 | − | 0.965994i | \(-0.416751\pi\) | ||||
0.258563 | + | 0.965994i | \(0.416751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.83130 | −1.34676 | −0.673380 | − | 0.739297i | \(-0.735158\pi\) | ||||
−0.673380 | + | 0.739297i | \(0.735158\pi\) | |||||||
\(44\) | 1.99738 | 0.301116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.181620 | 0.0267785 | ||||||||
\(47\) | 5.37613 | 0.784189 | 0.392095 | − | 0.919925i | \(-0.371751\pi\) | ||||
0.392095 | + | 0.919925i | \(0.371751\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.6824 | 2.09748 | ||||||||
\(50\) | 0.461027 | 0.0651990 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.68866 | 0.234175 | ||||||||
\(53\) | 7.32872 | 1.00668 | 0.503339 | − | 0.864089i | \(-0.332105\pi\) | ||||
0.503339 | + | 0.864089i | \(0.332105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.74211 | 0.504586 | ||||||||
\(56\) | 0.953125 | 0.127367 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0346752 | 0.00455308 | ||||||||
\(59\) | −0.636788 | −0.0829027 | −0.0414513 | − | 0.999141i | \(-0.513198\pi\) | ||||
−0.0414513 | + | 0.999141i | \(0.513198\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 0.393955 | 0.0500324 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.93714 | −0.992142 | ||||||||
\(65\) | 3.16373 | 0.392412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.23733 | −0.762012 | −0.381006 | − | 0.924573i | \(-0.624422\pi\) | ||||
−0.381006 | + | 0.924573i | \(0.624422\pi\) | |||||||
\(68\) | 3.97799 | 0.482402 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.892259 | 0.106645 | ||||||||
\(71\) | 2.06467 | 0.245032 | 0.122516 | − | 0.992467i | \(-0.460904\pi\) | ||||
0.122516 | + | 0.992467i | \(0.460904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.66830 | 0.897506 | 0.448753 | − | 0.893656i | \(-0.351868\pi\) | ||||
0.448753 | + | 0.893656i | \(0.351868\pi\) | |||||||
\(74\) | −0.297349 | −0.0345661 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.35220 | 0.155108 | ||||||||
\(77\) | 4.65643 | 0.530650 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.09202 | 0.235371 | 0.117685 | − | 0.993051i | \(-0.462453\pi\) | ||||
0.117685 | + | 0.993051i | \(0.462453\pi\) | |||||||
\(80\) | −14.9096 | −1.66694 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.169554 | 0.0187242 | ||||||||
\(83\) | 3.47537 | 0.381471 | 0.190736 | − | 0.981641i | \(-0.438913\pi\) | ||||
0.190736 | + | 0.981641i | \(0.438913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.45280 | 0.808370 | ||||||||
\(86\) | −0.452216 | −0.0487637 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.204690 | 0.0218200 | ||||||||
\(89\) | −8.92973 | −0.946550 | −0.473275 | − | 0.880915i | \(-0.656928\pi\) | ||||
−0.473275 | + | 0.880915i | \(0.656928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.93673 | 0.412682 | ||||||||
\(92\) | −7.08441 | −0.738601 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.275290 | 0.0283940 | ||||||||
\(95\) | 2.53336 | 0.259918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.1658 | −1.64138 | −0.820692 | − | 0.571371i | \(-0.806412\pi\) | ||||
−0.820692 | + | 0.571371i | \(0.806412\pi\) | |||||||
\(98\) | 0.751826 | 0.0759459 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.9831 | −1.79831 | ||||||||
\(101\) | 1.26799 | 0.126170 | 0.0630851 | − | 0.998008i | \(-0.479906\pi\) | ||||
0.0630851 | + | 0.998008i | \(0.479906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.31535 | −0.129605 | −0.0648026 | − | 0.997898i | \(-0.520642\pi\) | ||||
−0.0648026 | + | 0.997898i | \(0.520642\pi\) | |||||||
\(104\) | 0.173053 | 0.0169692 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.375275 | 0.0364499 | ||||||||
\(107\) | 20.2934 | 1.96183 | 0.980916 | − | 0.194430i | \(-0.0622856\pi\) | ||||
0.980916 | + | 0.194430i | \(0.0622856\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.2096 | −1.64838 | −0.824189 | − | 0.566315i | \(-0.808369\pi\) | ||||
−0.824189 | + | 0.566315i | \(0.808369\pi\) | |||||||
\(110\) | 0.191618 | 0.0182701 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.5525 | −1.75305 | ||||||||
\(113\) | 10.5949 | 0.996680 | 0.498340 | − | 0.866982i | \(-0.333943\pi\) | ||||
0.498340 | + | 0.866982i | \(0.333943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.2727 | −1.23769 | ||||||||
\(116\) | −1.35257 | −0.125583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0326074 | −0.00300175 | ||||||||
\(119\) | 9.27378 | 0.850126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.0512060 | 0.00463598 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.3669 | −1.37999 | ||||||||
\(125\) | −14.9810 | −1.33994 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.743672 | 0.0659902 | 0.0329951 | − | 0.999456i | \(-0.489495\pi\) | ||||
0.0329951 | + | 0.999456i | \(0.489495\pi\) | |||||||
\(128\) | −1.63323 | −0.144358 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.162002 | 0.0142085 | ||||||||
\(131\) | 9.42555 | 0.823514 | 0.411757 | − | 0.911294i | \(-0.364915\pi\) | ||||
0.411757 | + | 0.911294i | \(0.364915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.15235 | 0.273343 | ||||||||
\(134\) | −0.319389 | −0.0275910 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.407662 | 0.0349567 | ||||||||
\(137\) | −14.3819 | −1.22873 | −0.614364 | − | 0.789022i | \(-0.710588\pi\) | ||||
−0.614364 | + | 0.789022i | \(0.710588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0951 | −1.28035 | −0.640177 | − | 0.768227i | \(-0.721139\pi\) | ||||
−0.640177 | + | 0.768227i | \(0.721139\pi\) | |||||||
\(140\) | −34.8041 | −2.94148 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.105724 | 0.00887215 | ||||||||
\(143\) | 0.845440 | 0.0706992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.53405 | −0.210441 | ||||||||
\(146\) | 0.392663 | 0.0324970 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.5986 | 0.953398 | ||||||||
\(149\) | 16.2231 | 1.32905 | 0.664523 | − | 0.747268i | \(-0.268635\pi\) | ||||
0.664523 | + | 0.747268i | \(0.268635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.18378 | −0.747366 | −0.373683 | − | 0.927557i | \(-0.621905\pi\) | ||||
−0.373683 | + | 0.927557i | \(0.621905\pi\) | |||||||
\(152\) | 0.138573 | 0.0112397 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.238437 | 0.0192138 | ||||||||
\(155\) | −28.7900 | −2.31247 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2002 | 1.77177 | 0.885886 | − | 0.463904i | \(-0.153552\pi\) | ||||
0.885886 | + | 0.463904i | \(0.153552\pi\) | |||||||
\(158\) | 0.107124 | 0.00852234 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.29540 | −0.181468 | ||||||||
\(161\) | −16.5157 | −1.30162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.88448 | −0.539234 | −0.269617 | − | 0.962968i | \(-0.586897\pi\) | ||||
−0.269617 | + | 0.962968i | \(0.586897\pi\) | |||||||
\(164\) | −6.61376 | −0.516448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.177960 | 0.0138124 | ||||||||
\(167\) | −11.1697 | −0.864340 | −0.432170 | − | 0.901792i | \(-0.642252\pi\) | ||||
−0.432170 | + | 0.901792i | \(0.642252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2852 | −0.945018 | ||||||||
\(170\) | 0.381629 | 0.0292696 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.6394 | 1.34499 | ||||||||
\(173\) | 17.3542 | 1.31942 | 0.659708 | − | 0.751522i | \(-0.270680\pi\) | ||||
0.659708 | + | 0.751522i | \(0.270680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −41.9236 | −3.16913 | ||||||||
\(176\) | −3.98427 | −0.300326 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.457256 | −0.0342728 | ||||||||
\(179\) | 10.7455 | 0.803160 | 0.401580 | − | 0.915824i | \(-0.368461\pi\) | ||||
0.401580 | + | 0.915824i | \(0.368461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.08954 | 0.452632 | 0.226316 | − | 0.974054i | \(-0.427332\pi\) | ||||
0.226316 | + | 0.974054i | \(0.427332\pi\) | |||||||
\(182\) | 0.201585 | 0.0149424 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.726005 | −0.0535218 | ||||||||
\(185\) | 21.7301 | 1.59763 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.99161 | 0.145641 | ||||||||
\(188\) | −10.7382 | −0.783161 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.129723 | 0.00941113 | ||||||||
\(191\) | −26.7454 | −1.93523 | −0.967616 | − | 0.252426i | \(-0.918772\pi\) | ||||
−0.967616 | + | 0.252426i | \(0.918772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0367 | 1.37029 | 0.685147 | − | 0.728405i | \(-0.259738\pi\) | ||||
0.685147 | + | 0.728405i | \(0.259738\pi\) | |||||||
\(194\) | −0.827784 | −0.0594314 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.3262 | −2.09473 | ||||||||
\(197\) | 25.4318 | 1.81194 | 0.905970 | − | 0.423341i | \(-0.139143\pi\) | ||||
0.905970 | + | 0.423341i | \(0.139143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.4140 | −1.94333 | −0.971663 | − | 0.236371i | \(-0.924042\pi\) | ||||
−0.971663 | + | 0.236371i | \(0.924042\pi\) | |||||||
\(200\) | −1.84290 | −0.130313 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0649290 | 0.00456839 | ||||||||
\(203\) | −3.15320 | −0.221311 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.3909 | −0.865421 | ||||||||
\(206\) | −0.0673538 | −0.00469276 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.36846 | −0.233561 | ||||||||
\(209\) | 0.676988 | 0.0468283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3356 | 1.05575 | 0.527874 | − | 0.849323i | \(-0.322989\pi\) | ||||
0.527874 | + | 0.849323i | \(0.322989\pi\) | |||||||
\(212\) | −14.6382 | −1.00536 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.03914 | 0.0710343 | ||||||||
\(215\) | 33.0477 | 2.25383 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −35.8244 | −2.43192 | ||||||||
\(218\) | −0.881234 | −0.0596847 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.47440 | −0.503924 | ||||||||
\(221\) | 1.68378 | 0.113264 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8414 | 1.39564 | 0.697821 | − | 0.716272i | \(-0.254153\pi\) | ||||
0.697821 | + | 0.716272i | \(0.254153\pi\) | |||||||
\(224\) | −2.85625 | −0.190841 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.542520 | 0.0360879 | ||||||||
\(227\) | 12.4259 | 0.824735 | 0.412368 | − | 0.911018i | \(-0.364702\pi\) | ||||
0.412368 | + | 0.911018i | \(0.364702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.52577 | −0.497317 | −0.248658 | − | 0.968591i | \(-0.579990\pi\) | ||||
−0.248658 | + | 0.968591i | \(0.579990\pi\) | |||||||
\(230\) | −0.679643 | −0.0448143 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.138610 | −0.00910020 | ||||||||
\(233\) | −3.98849 | −0.261295 | −0.130647 | − | 0.991429i | \(-0.541706\pi\) | ||||
−0.130647 | + | 0.991429i | \(0.541706\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.1181 | −1.31236 | ||||||||
\(236\) | 1.27191 | 0.0827940 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.474873 | 0.0307815 | ||||||||
\(239\) | 7.60269 | 0.491777 | 0.245889 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245889 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.67663 | 0.172417 | 0.0862083 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862083 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(242\) | 0.0512060 | 0.00329165 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.99738 | −0.127869 | ||||||||
\(245\) | −54.9430 | −3.51018 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.572353 | 0.0364179 | ||||||||
\(248\) | −1.57479 | −0.0999992 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.767119 | −0.0485169 | ||||||||
\(251\) | −0.514360 | −0.0324661 | −0.0162331 | − | 0.999868i | \(-0.505167\pi\) | ||||
−0.0162331 | + | 0.999868i | \(0.505167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.54686 | −0.222989 | ||||||||
\(254\) | 0.0380805 | 0.00238938 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.7906 | 0.986915 | ||||||||
\(257\) | 6.99608 | 0.436404 | 0.218202 | − | 0.975904i | \(-0.429981\pi\) | ||||
0.218202 | + | 0.975904i | \(0.429981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.0395 | 1.68015 | ||||||||
\(260\) | −6.31916 | −0.391898 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.482645 | 0.0298179 | ||||||||
\(263\) | 15.1643 | 0.935072 | 0.467536 | − | 0.883974i | \(-0.345142\pi\) | ||||
0.467536 | + | 0.883974i | \(0.345142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.4249 | −1.68470 | ||||||||
\(266\) | 0.161419 | 0.00989726 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4583 | 0.761013 | ||||||||
\(269\) | −26.7507 | −1.63102 | −0.815509 | − | 0.578745i | \(-0.803543\pi\) | ||||
−0.815509 | + | 0.578745i | \(0.803543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00706 | 0.182666 | 0.0913331 | − | 0.995820i | \(-0.470887\pi\) | ||||
0.0913331 | + | 0.995820i | \(0.470887\pi\) | |||||||
\(272\) | −7.93511 | −0.481136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.736440 | −0.0444900 | ||||||||
\(275\) | −9.00337 | −0.542924 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.761643 | 0.0457627 | 0.0228813 | − | 0.999738i | \(-0.492716\pi\) | ||||
0.0228813 | + | 0.999738i | \(0.492716\pi\) | |||||||
\(278\) | −0.772963 | −0.0463592 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.56670 | −0.213151 | ||||||||
\(281\) | −19.2471 | −1.14819 | −0.574094 | − | 0.818789i | \(-0.694646\pi\) | ||||
−0.574094 | + | 0.818789i | \(0.694646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5209 | −1.21984 | −0.609921 | − | 0.792463i | \(-0.708799\pi\) | ||||
−0.609921 | + | 0.792463i | \(0.708799\pi\) | |||||||
\(284\) | −4.12394 | −0.244711 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0432916 | 0.00255989 | ||||||||
\(287\) | −15.4185 | −0.910124 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0335 | −0.766677 | ||||||||
\(290\) | −0.129758 | −0.00761968 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.3165 | −0.896330 | ||||||||
\(293\) | 11.1033 | 0.648660 | 0.324330 | − | 0.945944i | \(-0.394861\pi\) | ||||
0.324330 | + | 0.945944i | \(0.394861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.38293 | 0.138739 | ||||||||
\(296\) | 1.18862 | 0.0690869 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.830720 | 0.0481223 | ||||||||
\(299\) | −2.99865 | −0.173417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.1223 | 2.37025 | ||||||||
\(302\) | −0.470265 | −0.0270607 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.69731 | −0.154701 | ||||||||
\(305\) | −3.74211 | −0.214272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7237 | 1.35398 | 0.676991 | − | 0.735991i | \(-0.263284\pi\) | ||||
0.676991 | + | 0.735991i | \(0.263284\pi\) | |||||||
\(308\) | −9.30066 | −0.529954 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.47422 | −0.0837303 | ||||||||
\(311\) | −8.52580 | −0.483454 | −0.241727 | − | 0.970344i | \(-0.577714\pi\) | ||||
−0.241727 | + | 0.970344i | \(0.577714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.02754 | 0.114603 | 0.0573016 | − | 0.998357i | \(-0.481750\pi\) | ||||
0.0573016 | + | 0.998357i | \(0.481750\pi\) | |||||||
\(314\) | 1.13679 | 0.0641525 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.17856 | −0.235062 | ||||||||
\(317\) | −31.9495 | −1.79446 | −0.897231 | − | 0.441561i | \(-0.854425\pi\) | ||||
−0.897231 | + | 0.441561i | \(0.854425\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.677171 | −0.0379143 | ||||||||
\(320\) | 29.7016 | 1.66037 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.845703 | −0.0471292 | ||||||||
\(323\) | 1.34829 | 0.0750211 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.61181 | −0.422227 | ||||||||
\(326\) | −0.352527 | −0.0195247 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.677773 | −0.0374238 | ||||||||
\(329\) | −25.0336 | −1.38015 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3691 | −1.00966 | −0.504828 | − | 0.863220i | \(-0.668444\pi\) | ||||
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(332\) | −6.94163 | −0.380971 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.571958 | −0.0312961 | ||||||||
\(335\) | 23.3408 | 1.27524 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.49840 | −0.462937 | −0.231469 | − | 0.972842i | \(-0.574353\pi\) | ||||
−0.231469 | + | 0.972842i | \(0.574353\pi\) | |||||||
\(338\) | −0.629078 | −0.0342173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.8861 | −0.807310 | ||||||||
\(341\) | −7.69354 | −0.416628 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35.7724 | −1.93153 | ||||||||
\(344\) | 1.80768 | 0.0974634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.888640 | 0.0477736 | ||||||||
\(347\) | 17.1538 | 0.920865 | 0.460433 | − | 0.887695i | \(-0.347694\pi\) | ||||
0.460433 | + | 0.887695i | \(0.347694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.06840 | −0.431892 | −0.215946 | − | 0.976405i | \(-0.569283\pi\) | ||||
−0.215946 | + | 0.976405i | \(0.569283\pi\) | |||||||
\(350\) | −2.14674 | −0.114748 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.613399 | −0.0326943 | ||||||||
\(353\) | −17.6885 | −0.941462 | −0.470731 | − | 0.882277i | \(-0.656010\pi\) | ||||
−0.470731 | + | 0.882277i | \(0.656010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.72624 | −0.410066 | ||||||||
\(356\) | 17.8361 | 0.945309 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.550237 | 0.0290809 | ||||||||
\(359\) | −19.1909 | −1.01286 | −0.506428 | − | 0.862282i | \(-0.669034\pi\) | ||||
−0.506428 | + | 0.862282i | \(0.669034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5417 | −0.975878 | ||||||||
\(362\) | 0.311821 | 0.0163890 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.86315 | −0.412141 | ||||||||
\(365\) | −28.6956 | −1.50200 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.55481 | 0.342158 | 0.171079 | − | 0.985257i | \(-0.445275\pi\) | ||||
0.171079 | + | 0.985257i | \(0.445275\pi\) | |||||||
\(368\) | 14.1316 | 0.736663 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.11271 | 0.0578471 | ||||||||
\(371\) | −34.1257 | −1.77172 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.5579 | 1.84112 | 0.920559 | − | 0.390602i | \(-0.127733\pi\) | ||||
0.920559 | + | 0.390602i | \(0.127733\pi\) | |||||||
\(374\) | 0.101982 | 0.00527338 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.10044 | −0.0567508 | ||||||||
\(377\) | −0.572507 | −0.0294856 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.4271 | 1.46020 | 0.730102 | − | 0.683338i | \(-0.239473\pi\) | ||||
0.730102 | + | 0.683338i | \(0.239473\pi\) | |||||||
\(380\) | −5.06008 | −0.259577 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.36953 | −0.0700712 | ||||||||
\(383\) | −21.6032 | −1.10387 | −0.551936 | − | 0.833887i | \(-0.686111\pi\) | ||||
−0.551936 | + | 0.833887i | \(0.686111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.4249 | −0.888054 | ||||||||
\(386\) | 0.974795 | 0.0496158 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 32.2891 | 1.63923 | ||||||||
\(389\) | 20.4103 | 1.03485 | 0.517423 | − | 0.855730i | \(-0.326891\pi\) | ||||
0.517423 | + | 0.855730i | \(0.326891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.06394 | −0.357239 | ||||||||
\(392\) | −3.00533 | −0.151792 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.30226 | 0.0656070 | ||||||||
\(395\) | −7.82857 | −0.393898 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7419 | 0.890439 | 0.445220 | − | 0.895421i | \(-0.353126\pi\) | ||||
0.445220 | + | 0.895421i | \(0.353126\pi\) | |||||||
\(398\) | −1.40376 | −0.0703642 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 35.8719 | 1.79359 | ||||||||
\(401\) | −9.35139 | −0.466986 | −0.233493 | − | 0.972358i | \(-0.575016\pi\) | ||||
−0.233493 | + | 0.972358i | \(0.575016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.50442 | −0.324008 | ||||||||
\(404\) | −2.53267 | −0.126005 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.161463 | −0.00801327 | ||||||||
\(407\) | 5.80691 | 0.287838 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.73559 | 0.382500 | 0.191250 | − | 0.981541i | \(-0.438746\pi\) | ||||
0.191250 | + | 0.981541i | \(0.438746\pi\) | |||||||
\(410\) | −0.634491 | −0.0313353 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.62725 | 0.129435 | ||||||||
\(413\) | 2.96516 | 0.145906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.0052 | −0.638401 | ||||||||
\(416\) | −0.518592 | −0.0254260 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0346659 | 0.00169556 | ||||||||
\(419\) | −28.4807 | −1.39137 | −0.695686 | − | 0.718346i | \(-0.744899\pi\) | ||||
−0.695686 | + | 0.718346i | \(0.744899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6217 | 0.761357 | 0.380679 | − | 0.924707i | \(-0.375690\pi\) | ||||
0.380679 | + | 0.924707i | \(0.375690\pi\) | |||||||
\(422\) | 0.785277 | 0.0382267 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.50012 | −0.0728520 | ||||||||
\(425\) | −17.9312 | −0.869789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.65643 | −0.225341 | ||||||||
\(428\) | −40.5335 | −1.95926 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.69224 | 0.0816070 | ||||||||
\(431\) | 16.7493 | 0.806783 | 0.403392 | − | 0.915027i | \(-0.367831\pi\) | ||||
0.403392 | + | 0.915027i | \(0.367831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.73632 | −0.371784 | −0.185892 | − | 0.982570i | \(-0.559517\pi\) | ||||
−0.185892 | + | 0.982570i | \(0.559517\pi\) | |||||||
\(434\) | −1.83443 | −0.0880553 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 34.3740 | 1.64622 | ||||||||
\(437\) | −2.40118 | −0.114864 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.8535 | 1.52028 | 0.760142 | − | 0.649757i | \(-0.225130\pi\) | ||||
0.760142 | + | 0.649757i | \(0.225130\pi\) | |||||||
\(440\) | −0.765971 | −0.0365163 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0862199 | 0.00410106 | ||||||||
\(443\) | 5.53681 | 0.263062 | 0.131531 | − | 0.991312i | \(-0.458011\pi\) | ||||
0.131531 | + | 0.991312i | \(0.458011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.4160 | 1.58407 | ||||||||
\(446\) | 1.06720 | 0.0505336 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36.9588 | 1.74614 | ||||||||
\(449\) | 22.8076 | 1.07636 | 0.538179 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538179 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.31122 | −0.155919 | ||||||||
\(452\) | −21.1619 | −0.995373 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.636280 | 0.0298621 | ||||||||
\(455\) | −14.7317 | −0.690632 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1371 | −1.17587 | −0.587933 | − | 0.808910i | \(-0.700058\pi\) | ||||
−0.587933 | + | 0.808910i | \(0.700058\pi\) | |||||||
\(458\) | −0.385365 | −0.0180069 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26.5106 | 1.23606 | ||||||||
\(461\) | 1.84514 | 0.0859366 | 0.0429683 | − | 0.999076i | \(-0.486319\pi\) | ||||
0.0429683 | + | 0.999076i | \(0.486319\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.1385 | 1.26123 | 0.630617 | − | 0.776094i | \(-0.282802\pi\) | ||||
0.630617 | + | 0.776094i | \(0.282802\pi\) | |||||||
\(464\) | 2.69804 | 0.125253 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.204235 | −0.00946099 | ||||||||
\(467\) | 40.1833 | 1.85946 | 0.929732 | − | 0.368238i | \(-0.120039\pi\) | ||||
0.929732 | + | 0.368238i | \(0.120039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.0437 | 1.34111 | ||||||||
\(470\) | −1.03017 | −0.0475180 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.130344 | 0.00599957 | ||||||||
\(473\) | 8.83130 | 0.406063 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.09518 | −0.279666 | ||||||||
\(476\) | −18.5232 | −0.849011 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.389304 | 0.0178063 | ||||||||
\(479\) | −35.3352 | −1.61451 | −0.807253 | − | 0.590206i | \(-0.799046\pi\) | ||||
−0.807253 | + | 0.590206i | \(0.799046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.90939 | 0.223849 | ||||||||
\(482\) | 0.137059 | 0.00624289 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.99738 | −0.0907899 | ||||||||
\(485\) | 60.4940 | 2.74689 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.3147 | −1.05649 | −0.528244 | − | 0.849092i | \(-0.677149\pi\) | ||||
−0.528244 | + | 0.849092i | \(0.677149\pi\) | |||||||
\(488\) | −0.204690 | −0.00926587 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.81341 | −0.127097 | ||||||||
\(491\) | 21.8539 | 0.986253 | 0.493127 | − | 0.869957i | \(-0.335854\pi\) | ||||
0.493127 | + | 0.869957i | \(0.335854\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.34866 | −0.0607405 | ||||||||
\(494\) | 0.0293079 | 0.00131863 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.6532 | 1.37637 | ||||||||
\(497\) | −9.61402 | −0.431248 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.66654 | 0.164137 | 0.0820685 | − | 0.996627i | \(-0.473847\pi\) | ||||
0.0820685 | + | 0.996627i | \(0.473847\pi\) | |||||||
\(500\) | 29.9228 | 1.33819 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.0263384 | −0.00117554 | ||||||||
\(503\) | −1.25493 | −0.0559546 | −0.0279773 | − | 0.999609i | \(-0.508907\pi\) | ||||
−0.0279773 | + | 0.999609i | \(0.508907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.74497 | −0.211149 | ||||||||
\(506\) | −0.181620 | −0.00807401 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.48539 | −0.0659037 | ||||||||
\(509\) | −6.93766 | −0.307507 | −0.153753 | − | 0.988109i | \(-0.549136\pi\) | ||||
−0.153753 | + | 0.988109i | \(0.549136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.7069 | −1.57958 | ||||||||
\(512\) | 4.07503 | 0.180093 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.358242 | 0.0158014 | ||||||||
\(515\) | 4.92218 | 0.216897 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.37613 | −0.236442 | ||||||||
\(518\) | 1.38458 | 0.0608352 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.647583 | −0.0283984 | ||||||||
\(521\) | 18.4786 | 0.809561 | 0.404781 | − | 0.914414i | \(-0.367348\pi\) | ||||
0.404781 | + | 0.914414i | \(0.367348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.3942 | 0.541961 | 0.270980 | − | 0.962585i | \(-0.412652\pi\) | ||||
0.270980 | + | 0.962585i | \(0.412652\pi\) | |||||||
\(524\) | −18.8264 | −0.822434 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.776505 | 0.0338572 | ||||||||
\(527\) | −15.3225 | −0.667458 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.4198 | −0.453036 | ||||||||
\(530\) | −1.40432 | −0.0609997 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.29644 | −0.272985 | ||||||||
\(533\) | −2.79944 | −0.121257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −75.9399 | −3.28317 | ||||||||
\(536\) | 1.27672 | 0.0551459 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.36980 | −0.0590561 | ||||||||
\(539\) | −14.6824 | −0.632414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.95379 | 0.384953 | 0.192477 | − | 0.981302i | \(-0.438348\pi\) | ||||
0.192477 | + | 0.981302i | \(0.438348\pi\) | |||||||
\(542\) | 0.153980 | 0.00661400 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.22165 | −0.0523777 | ||||||||
\(545\) | 64.4001 | 2.75860 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.30109 | 0.0556308 | 0.0278154 | − | 0.999613i | \(-0.491145\pi\) | ||||
0.0278154 | + | 0.999613i | \(0.491145\pi\) | |||||||
\(548\) | 28.7261 | 1.22712 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.461027 | −0.0196582 | ||||||||
\(551\) | −0.458437 | −0.0195301 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.74136 | −0.414245 | ||||||||
\(554\) | 0.0390007 | 0.00165698 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.1507 | 1.27868 | ||||||||
\(557\) | 7.18106 | 0.304271 | 0.152136 | − | 0.988360i | \(-0.451385\pi\) | ||||
0.152136 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.46633 | 0.315792 | ||||||||
\(560\) | 69.4255 | 2.93376 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.985570 | −0.0415738 | ||||||||
\(563\) | −39.3214 | −1.65720 | −0.828599 | − | 0.559842i | \(-0.810862\pi\) | ||||
−0.828599 | + | 0.559842i | \(0.810862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.6471 | −1.66797 | ||||||||
\(566\) | −1.05079 | −0.0441682 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.422618 | −0.0177327 | ||||||||
\(569\) | −31.0189 | −1.30038 | −0.650189 | − | 0.759772i | \(-0.725310\pi\) | ||||
−0.650189 | + | 0.759772i | \(0.725310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.12927 | −0.172805 | −0.0864023 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864023 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(572\) | −1.68866 | −0.0706065 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.789519 | −0.0329539 | ||||||||
\(575\) | 31.9336 | 1.33173 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.2320 | −0.509226 | −0.254613 | − | 0.967043i | \(-0.581948\pi\) | ||||
−0.254613 | + | 0.967043i | \(0.581948\pi\) | |||||||
\(578\) | −0.667394 | −0.0277599 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.06145 | 0.210165 | ||||||||
\(581\) | −16.1828 | −0.671377 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.32872 | −0.303525 | ||||||||
\(584\) | −1.56962 | −0.0649515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.568554 | 0.0234868 | ||||||||
\(587\) | −10.0217 | −0.413642 | −0.206821 | − | 0.978379i | \(-0.566312\pi\) | ||||
−0.206821 | + | 0.978379i | \(0.566312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.20843 | −0.214610 | ||||||||
\(590\) | 0.122020 | 0.00502350 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.1363 | −0.950897 | ||||||||
\(593\) | 7.55520 | 0.310255 | 0.155127 | − | 0.987894i | \(-0.450421\pi\) | ||||
0.155127 | + | 0.987894i | \(0.450421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.7035 | −1.42270 | ||||||||
\(596\) | −32.4036 | −1.32730 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.153549 | −0.00627909 | ||||||||
\(599\) | 35.1654 | 1.43682 | 0.718410 | − | 0.695620i | \(-0.244870\pi\) | ||||
0.718410 | + | 0.695620i | \(0.244870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4203 | 0.669799 | 0.334899 | − | 0.942254i | \(-0.391298\pi\) | ||||
0.334899 | + | 0.942254i | \(0.391298\pi\) | |||||||
\(602\) | 2.10571 | 0.0858224 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.3435 | 0.746386 | ||||||||
\(605\) | −3.74211 | −0.152138 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2135 | 0.861029 | 0.430515 | − | 0.902584i | \(-0.358332\pi\) | ||||
0.430515 | + | 0.902584i | \(0.358332\pi\) | |||||||
\(608\) | −0.415264 | −0.0168412 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.191618 | −0.00775841 | ||||||||
\(611\) | −4.54520 | −0.183879 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.39536 | 0.137137 | 0.0685686 | − | 0.997646i | \(-0.478157\pi\) | ||||
0.0685686 | + | 0.997646i | \(0.478157\pi\) | |||||||
\(614\) | 1.21480 | 0.0490252 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.953125 | −0.0384025 | ||||||||
\(617\) | −12.9192 | −0.520109 | −0.260055 | − | 0.965594i | \(-0.583741\pi\) | ||||
−0.260055 | + | 0.965594i | \(0.583741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.8280 | −1.72140 | −0.860700 | − | 0.509112i | \(-0.829974\pi\) | ||||
−0.860700 | + | 0.509112i | \(0.829974\pi\) | |||||||
\(620\) | 57.5046 | 2.30944 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.436573 | −0.0175050 | ||||||||
\(623\) | 41.5807 | 1.66590 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0438 | 0.441752 | ||||||||
\(626\) | 0.103822 | 0.00414957 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −44.3423 | −1.76945 | ||||||||
\(629\) | 11.5651 | 0.461130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.0931 | −1.39703 | −0.698516 | − | 0.715594i | \(-0.746156\pi\) | ||||
−0.698516 | + | 0.715594i | \(0.746156\pi\) | |||||||
\(632\) | −0.428216 | −0.0170335 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.63601 | −0.0649741 | ||||||||
\(635\) | −2.78290 | −0.110436 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.4131 | −0.491823 | ||||||||
\(638\) | −0.0346752 | −0.00137281 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.11171 | 0.241587 | ||||||||
\(641\) | 13.2012 | 0.521418 | 0.260709 | − | 0.965417i | \(-0.416044\pi\) | ||||
0.260709 | + | 0.965417i | \(0.416044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.7731 | 1.52906 | 0.764532 | − | 0.644586i | \(-0.222970\pi\) | ||||
0.764532 | + | 0.644586i | \(0.222970\pi\) | |||||||
\(644\) | 32.9881 | 1.29991 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0690408 | 0.00271637 | ||||||||
\(647\) | −8.06386 | −0.317023 | −0.158512 | − | 0.987357i | \(-0.550670\pi\) | ||||
−0.158512 | + | 0.987357i | \(0.550670\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.636788 | 0.0249961 | ||||||||
\(650\) | −0.389770 | −0.0152881 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7509 | 0.538527 | ||||||||
\(653\) | −20.3231 | −0.795304 | −0.397652 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397652 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.2714 | −1.37817 | ||||||||
\(656\) | 13.1928 | 0.515093 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.28187 | −0.0499725 | ||||||||
\(659\) | 12.8616 | 0.501015 | 0.250508 | − | 0.968115i | \(-0.419403\pi\) | ||||
0.250508 | + | 0.968115i | \(0.419403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.50897 | 0.369856 | 0.184928 | − | 0.982752i | \(-0.440795\pi\) | ||||
0.184928 | + | 0.982752i | \(0.440795\pi\) | |||||||
\(662\) | −0.940609 | −0.0365578 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.711373 | −0.0276066 | ||||||||
\(665\) | −11.7964 | −0.457446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.40183 | 0.0929991 | ||||||||
\(668\) | 22.3102 | 0.863207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.19519 | 0.0461742 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0528 | −0.541695 | −0.270848 | − | 0.962622i | \(-0.587304\pi\) | ||||
−0.270848 | + | 0.962622i | \(0.587304\pi\) | |||||||
\(674\) | −0.435169 | −0.0167621 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.5383 | 0.943779 | ||||||||
\(677\) | 21.7382 | 0.835467 | 0.417733 | − | 0.908570i | \(-0.362825\pi\) | ||||
0.417733 | + | 0.908570i | \(0.362825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 75.2747 | 2.88878 | ||||||||
\(680\) | −1.52551 | −0.0585008 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.393955 | −0.0150853 | ||||||||
\(683\) | 31.1910 | 1.19349 | 0.596745 | − | 0.802431i | \(-0.296461\pi\) | ||||
0.596745 | + | 0.802431i | \(0.296461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.8186 | 2.05630 | ||||||||
\(686\) | −1.83176 | −0.0699371 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −35.1863 | −1.34147 | ||||||||
\(689\) | −6.19600 | −0.236049 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4676 | −0.816666 | −0.408333 | − | 0.912833i | \(-0.633890\pi\) | ||||
−0.408333 | + | 0.912833i | \(0.633890\pi\) | |||||||
\(692\) | −34.6629 | −1.31769 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.878379 | 0.0333428 | ||||||||
\(695\) | 56.4877 | 2.14270 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.59465 | −0.249790 | ||||||||
\(698\) | −0.413151 | −0.0156380 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 83.7372 | 3.16497 | ||||||||
\(701\) | −21.0539 | −0.795195 | −0.397597 | − | 0.917560i | \(-0.630156\pi\) | ||||
−0.397597 | + | 0.917560i | \(0.630156\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.93121 | 0.148268 | ||||||||
\(704\) | 7.93714 | 0.299142 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.905756 | −0.0340886 | ||||||||
\(707\) | −5.90433 | −0.222055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1132 | −1.16848 | −0.584241 | − | 0.811581i | \(-0.698608\pi\) | ||||
−0.584241 | + | 0.811581i | \(0.698608\pi\) | |||||||
\(710\) | −0.395630 | −0.0148477 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.82783 | 0.0685007 | ||||||||
\(713\) | 27.2879 | 1.02194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.16373 | −0.118317 | ||||||||
\(716\) | −21.4629 | −0.802107 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.982689 | −0.0366736 | ||||||||
\(719\) | 5.72958 | 0.213677 | 0.106839 | − | 0.994276i | \(-0.465927\pi\) | ||||
0.106839 | + | 0.994276i | \(0.465927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.12484 | 0.228101 | ||||||||
\(722\) | −0.949446 | −0.0353347 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.1631 | −0.452039 | ||||||||
\(725\) | 6.09682 | 0.226430 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.70140 | 0.248541 | 0.124271 | − | 0.992248i | \(-0.460341\pi\) | ||||
0.124271 | + | 0.992248i | \(0.460341\pi\) | |||||||
\(728\) | −0.805810 | −0.0298653 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.46939 | −0.0543845 | ||||||||
\(731\) | 17.5885 | 0.650533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5158 | 0.905513 | 0.452756 | − | 0.891634i | \(-0.350441\pi\) | ||||
0.452756 | + | 0.891634i | \(0.350441\pi\) | |||||||
\(734\) | 0.335646 | 0.0123889 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.17564 | 0.0801950 | ||||||||
\(737\) | 6.23733 | 0.229755 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1631 | −0.778497 | −0.389249 | − | 0.921133i | \(-0.627265\pi\) | ||||
−0.389249 | + | 0.921133i | \(0.627265\pi\) | |||||||
\(740\) | −43.4032 | −1.59553 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.74744 | −0.0641506 | ||||||||
\(743\) | 48.0278 | 1.76197 | 0.880985 | − | 0.473144i | \(-0.156881\pi\) | ||||
0.880985 | + | 0.473144i | \(0.156881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −60.7085 | −2.22419 | ||||||||
\(746\) | 1.82078 | 0.0666635 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.97799 | −0.145450 | ||||||||
\(749\) | −94.4947 | −3.45276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.94046 | 0.180280 | 0.0901400 | − | 0.995929i | \(-0.471269\pi\) | ||||
0.0901400 | + | 0.995929i | \(0.471269\pi\) | |||||||
\(752\) | 21.4200 | 0.781106 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0293158 | −0.00106762 | ||||||||
\(755\) | 34.3667 | 1.25073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6690 | 1.29641 | 0.648207 | − | 0.761464i | \(-0.275519\pi\) | ||||
0.648207 | + | 0.761464i | \(0.275519\pi\) | |||||||
\(758\) | 1.45564 | 0.0528712 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.518554 | −0.0188099 | ||||||||
\(761\) | −25.9419 | −0.940393 | −0.470197 | − | 0.882562i | \(-0.655817\pi\) | ||||
−0.470197 | + | 0.882562i | \(0.655817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 80.1352 | 2.90109 | ||||||||
\(764\) | 53.4208 | 1.93270 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.10621 | −0.0399691 | ||||||||
\(767\) | 0.538366 | 0.0194393 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.2246 | −1.91933 | −0.959664 | − | 0.281150i | \(-0.909284\pi\) | ||||
−0.959664 | + | 0.281150i | \(0.909284\pi\) | |||||||
\(770\) | −0.892259 | −0.0321548 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38.0235 | −1.36850 | ||||||||
\(773\) | 20.0661 | 0.721729 | 0.360865 | − | 0.932618i | \(-0.382482\pi\) | ||||
0.360865 | + | 0.932618i | \(0.382482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 69.2677 | 2.48817 | ||||||||
\(776\) | 3.30897 | 0.118785 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.04513 | 0.0374698 | ||||||||
\(779\) | −2.24166 | −0.0803157 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.06467 | −0.0738799 | ||||||||
\(782\) | −0.361716 | −0.0129349 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 58.4986 | 2.08924 | ||||||||
\(785\) | −83.0756 | −2.96510 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9934 | −0.748336 | −0.374168 | − | 0.927361i | \(-0.622072\pi\) | ||||
−0.374168 | + | 0.927361i | \(0.622072\pi\) | |||||||
\(788\) | −50.7969 | −1.80957 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.400870 | −0.0142623 | ||||||||
\(791\) | −49.3342 | −1.75412 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.845440 | −0.0300225 | ||||||||
\(794\) | 0.908491 | 0.0322411 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 54.7561 | 1.94078 | ||||||||
\(797\) | −15.0047 | −0.531494 | −0.265747 | − | 0.964043i | \(-0.585619\pi\) | ||||
−0.265747 | + | 0.964043i | \(0.585619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7071 | −0.378791 | ||||||||
\(800\) | 5.52265 | 0.195255 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.478847 | −0.0169087 | ||||||||
\(803\) | −7.66830 | −0.270608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 61.8035 | 2.17829 | ||||||||
\(806\) | −0.333066 | −0.0117317 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.259546 | −0.00913079 | ||||||||
\(809\) | 11.9417 | 0.419848 | 0.209924 | − | 0.977718i | \(-0.432678\pi\) | ||||
0.209924 | + | 0.977718i | \(0.432678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.6992 | 1.00777 | 0.503883 | − | 0.863772i | \(-0.331904\pi\) | ||||
0.503883 | + | 0.863772i | \(0.331904\pi\) | |||||||
\(812\) | 6.29814 | 0.221021 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.297349 | 0.0104221 | ||||||||
\(815\) | 25.7625 | 0.902420 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.97868 | 0.209168 | ||||||||
\(818\) | 0.396109 | 0.0138496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.7494 | 0.864287 | ||||||||
\(821\) | 16.2117 | 0.565791 | 0.282896 | − | 0.959151i | \(-0.408705\pi\) | ||||
0.282896 | + | 0.959151i | \(0.408705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.55261 | 0.332983 | 0.166491 | − | 0.986043i | \(-0.446756\pi\) | ||||
0.166491 | + | 0.986043i | \(0.446756\pi\) | |||||||
\(824\) | 0.269239 | 0.00937937 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.151834 | 0.00528298 | ||||||||
\(827\) | −44.0421 | −1.53149 | −0.765747 | − | 0.643142i | \(-0.777631\pi\) | ||||
−0.765747 | + | 0.643142i | \(0.777631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.8291 | −1.27913 | −0.639564 | − | 0.768738i | \(-0.720885\pi\) | ||||
−0.639564 | + | 0.768738i | \(0.720885\pi\) | |||||||
\(830\) | −0.665945 | −0.0231153 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.71037 | 0.232640 | ||||||||
\(833\) | −29.2415 | −1.01316 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.7983 | 1.44649 | ||||||||
\(836\) | −1.35220 | −0.0467669 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.45838 | −0.0503790 | ||||||||
\(839\) | 0.737017 | 0.0254447 | 0.0127223 | − | 0.999919i | \(-0.495950\pi\) | ||||
0.0127223 | + | 0.999919i | \(0.495950\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5414 | −0.984188 | ||||||||
\(842\) | 0.799927 | 0.0275673 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.6311 | −1.05436 | ||||||||
\(845\) | 45.9727 | 1.58151 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.65643 | −0.159997 | ||||||||
\(848\) | 29.1996 | 1.00272 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.918184 | −0.0314934 | ||||||||
\(851\) | −20.5963 | −0.706031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.92173 | −0.202756 | −0.101378 | − | 0.994848i | \(-0.532325\pi\) | ||||
−0.101378 | + | 0.994848i | \(0.532325\pi\) | |||||||
\(854\) | −0.238437 | −0.00815916 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.15384 | −0.141975 | ||||||||
\(857\) | −27.3082 | −0.932831 | −0.466415 | − | 0.884566i | \(-0.654455\pi\) | ||||
−0.466415 | + | 0.884566i | \(0.654455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.24564 | −0.315457 | −0.157729 | − | 0.987483i | \(-0.550417\pi\) | ||||
−0.157729 | + | 0.987483i | \(0.550417\pi\) | |||||||
\(860\) | −66.0087 | −2.25088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.857663 | 0.0292121 | ||||||||
\(863\) | 14.7556 | 0.502288 | 0.251144 | − | 0.967950i | \(-0.419193\pi\) | ||||
0.251144 | + | 0.967950i | \(0.419193\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −64.9413 | −2.20807 | ||||||||
\(866\) | −0.396146 | −0.0134616 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 71.5549 | 2.42873 | ||||||||
\(869\) | −2.09202 | −0.0709670 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.27329 | 0.178679 | ||||||||
\(872\) | 3.52263 | 0.119291 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.122955 | −0.00415901 | ||||||||
\(875\) | 69.7582 | 2.35826 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.2504 | −1.76437 | −0.882185 | − | 0.470903i | \(-0.843928\pi\) | ||||
−0.882185 | + | 0.470903i | \(0.843928\pi\) | |||||||
\(878\) | 1.63109 | 0.0550466 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.9096 | 0.502602 | ||||||||
\(881\) | −26.3428 | −0.887510 | −0.443755 | − | 0.896148i | \(-0.646354\pi\) | ||||
−0.443755 | + | 0.896148i | \(0.646354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.2865 | 1.52401 | 0.762006 | − | 0.647570i | \(-0.224215\pi\) | ||||
0.762006 | + | 0.647570i | \(0.224215\pi\) | |||||||
\(884\) | −3.36315 | −0.113115 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.283518 | 0.00952498 | ||||||||
\(887\) | 10.1077 | 0.339384 | 0.169692 | − | 0.985497i | \(-0.445723\pi\) | ||||
0.169692 | + | 0.985497i | \(0.445723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.46286 | −0.116141 | ||||||||
\(890\) | 1.71110 | 0.0573563 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.6281 | −1.39381 | ||||||||
\(893\) | −3.63958 | −0.121794 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.2110 | −1.34411 | ||||||||
\(896\) | 7.60501 | 0.254066 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.16789 | 0.0389729 | ||||||||
\(899\) | 5.20984 | 0.173758 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.5959 | −0.486261 | ||||||||
\(902\) | −0.169554 | −0.00564555 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.16866 | −0.0721285 | ||||||||
\(905\) | −22.7877 | −0.757490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.5028 | −0.979625 | −0.489813 | − | 0.871828i | \(-0.662935\pi\) | ||||
−0.489813 | + | 0.871828i | \(0.662935\pi\) | |||||||
\(908\) | −24.8192 | −0.823654 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.754351 | −0.0250065 | ||||||||
\(911\) | −54.3951 | −1.80219 | −0.901095 | − | 0.433623i | \(-0.857235\pi\) | ||||
−0.901095 | + | 0.433623i | \(0.857235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.47537 | −0.115018 | ||||||||
\(914\) | −1.28717 | −0.0425759 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.0318 | 0.496665 | ||||||||
\(917\) | −43.8894 | −1.44936 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.6870 | −1.37513 | −0.687563 | − | 0.726125i | \(-0.741319\pi\) | ||||
−0.687563 | + | 0.726125i | \(0.741319\pi\) | |||||||
\(920\) | 2.71679 | 0.0895699 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0944822 | 0.00311161 | ||||||||
\(923\) | −1.74556 | −0.0574558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.2817 | −1.71901 | ||||||||
\(926\) | 1.38966 | 0.0456669 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.415376 | 0.0136354 | ||||||||
\(929\) | −12.8663 | −0.422130 | −0.211065 | − | 0.977472i | \(-0.567693\pi\) | ||||
−0.211065 | + | 0.977472i | \(0.567693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.93979 | −0.325764 | ||||||||
\(932\) | 7.96652 | 0.260952 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.05763 | 0.0673277 | ||||||||
\(935\) | −7.45280 | −0.243733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.3290 | −1.41550 | −0.707748 | − | 0.706465i | \(-0.750289\pi\) | ||||
−0.707748 | + | 0.706465i | \(0.750289\pi\) | |||||||
\(938\) | 1.48721 | 0.0485593 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 40.1834 | 1.31064 | ||||||||
\(941\) | 53.7199 | 1.75122 | 0.875609 | − | 0.483020i | \(-0.160460\pi\) | ||||
0.875609 | + | 0.483020i | \(0.160460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7444 | 0.382451 | ||||||||
\(944\) | −2.53714 | −0.0825768 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.452216 | 0.0147028 | ||||||||
\(947\) | −6.94150 | −0.225568 | −0.112784 | − | 0.993620i | \(-0.535977\pi\) | ||||
−0.112784 | + | 0.993620i | \(0.535977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.48309 | −0.210450 | ||||||||
\(950\) | −0.312110 | −0.0101262 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.89825 | −0.0615226 | ||||||||
\(953\) | 45.7414 | 1.48171 | 0.740855 | − | 0.671665i | \(-0.234421\pi\) | ||||
0.740855 | + | 0.671665i | \(0.234421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 100.084 | 3.23865 | ||||||||
\(956\) | −15.1854 | −0.491132 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.80937 | −0.0584582 | ||||||||
\(959\) | 66.9684 | 2.16252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.1905 | 0.909371 | ||||||||
\(962\) | 0.251390 | 0.00810515 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.34624 | −0.172191 | ||||||||
\(965\) | −71.2375 | −2.29322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3862 | 1.29873 | 0.649366 | − | 0.760476i | \(-0.275034\pi\) | ||||
0.649366 | + | 0.760476i | \(0.275034\pi\) | |||||||
\(968\) | −0.204690 | −0.00657898 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.09766 | 0.0994598 | ||||||||
\(971\) | 17.8315 | 0.572240 | 0.286120 | − | 0.958194i | \(-0.407634\pi\) | ||||
0.286120 | + | 0.958194i | \(0.407634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.2896 | 2.25338 | ||||||||
\(974\) | −1.19385 | −0.0382535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.98427 | 0.127534 | ||||||||
\(977\) | 14.1563 | 0.452899 | 0.226449 | − | 0.974023i | \(-0.427288\pi\) | ||||
0.226449 | + | 0.974023i | \(0.427288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.92973 | 0.285396 | ||||||||
\(980\) | 109.742 | 3.50558 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.11905 | 0.0357104 | ||||||||
\(983\) | −35.7906 | −1.14154 | −0.570772 | − | 0.821109i | \(-0.693356\pi\) | ||||
−0.570772 | + | 0.821109i | \(0.693356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −95.1685 | −3.03232 | ||||||||
\(986\) | −0.0690594 | −0.00219930 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.14321 | −0.0363702 | ||||||||
\(989\) | −31.3233 | −0.996024 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.02047 | −0.286545 | −0.143272 | − | 0.989683i | \(-0.545762\pi\) | ||||
−0.143272 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(992\) | 4.71920 | 0.149835 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.492296 | −0.0156147 | ||||||||
\(995\) | 102.586 | 3.25220 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.2128 | 1.55858 | 0.779292 | − | 0.626661i | \(-0.215579\pi\) | ||||
0.779292 | + | 0.626661i | \(0.215579\pi\) | |||||||
\(998\) | 0.187749 | 0.00594309 | ||||||||
\(999\) | 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 | 6039.2.a.c.1.5 | 11 | ||
3.2 | odd | 2 | 2013.2.a.b.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.b.1.7 | ✓ | 11 | 3.2 | odd | 2 | ||
6039.2.a.c.1.5 | 11 | 1.1 | even | 1 | trivial |