Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8112,2,Mod(1,8112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8112.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: | \(64.7746461197\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27700337.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 19x^{4} + 17x^{3} + 103x^{2} - 71x - 127 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4056) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.12925\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8112.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.88227 | −0.841776 | −0.420888 | − | 0.907113i | \(-0.638281\pi\) | ||||
−0.420888 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.29156 | 0.488164 | 0.244082 | − | 0.969755i | \(-0.421513\pi\) | ||||
0.244082 | + | 0.969755i | \(0.421513\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.19367 | 1.26444 | 0.632219 | − | 0.774790i | \(-0.282144\pi\) | ||||
0.632219 | + | 0.774790i | \(0.282144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.88227 | 0.486000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.68421 | −0.408480 | −0.204240 | − | 0.978921i | \(-0.565472\pi\) | ||||
−0.204240 | + | 0.978921i | \(0.565472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.19025 | 0.273061 | 0.136531 | − | 0.990636i | \(-0.456405\pi\) | ||||
0.136531 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.29156 | −0.281841 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.01499 | −0.628670 | −0.314335 | − | 0.949312i | \(-0.601781\pi\) | ||||
−0.314335 | + | 0.949312i | \(0.601781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.45707 | −0.291413 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.15000 | 0.584941 | 0.292471 | − | 0.956275i | \(-0.405523\pi\) | ||||
0.292471 | + | 0.956275i | \(0.405523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.47463 | −0.264851 | −0.132425 | − | 0.991193i | \(-0.542277\pi\) | ||||
−0.132425 | + | 0.991193i | \(0.542277\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.19367 | −0.730024 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.43106 | −0.410924 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.15343 | −1.34041 | −0.670207 | − | 0.742174i | \(-0.733795\pi\) | ||||
−0.670207 | + | 0.742174i | \(0.733795\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0181 | 1.56457 | 0.782285 | − | 0.622921i | \(-0.214054\pi\) | ||||
0.782285 | + | 0.622921i | \(0.214054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7587 | −1.64069 | −0.820345 | − | 0.571869i | \(-0.806218\pi\) | ||||
−0.820345 | + | 0.571869i | \(0.806218\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.88227 | −0.280592 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.31909 | −0.775869 | −0.387934 | − | 0.921687i | \(-0.626811\pi\) | ||||
−0.387934 | + | 0.921687i | \(0.626811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.33187 | −0.761696 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.68421 | 0.235836 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.29590 | 1.13953 | 0.569765 | − | 0.821808i | \(-0.307034\pi\) | ||||
0.569765 | + | 0.821808i | \(0.307034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.89361 | −1.06437 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19025 | −0.157652 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.03369 | −0.394953 | −0.197477 | − | 0.980308i | \(-0.563275\pi\) | ||||
−0.197477 | + | 0.980308i | \(0.563275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.84487 | 1.00443 | 0.502216 | − | 0.864742i | \(-0.332518\pi\) | ||||
0.502216 | + | 0.864742i | \(0.332518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.29156 | 0.162721 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.50497 | 0.550370 | 0.275185 | − | 0.961391i | \(-0.411261\pi\) | ||||
0.275185 | + | 0.961391i | \(0.411261\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.01499 | 0.362963 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.85816 | −0.457880 | −0.228940 | − | 0.973441i | \(-0.573526\pi\) | ||||
−0.228940 | + | 0.973441i | \(0.573526\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.76494 | −0.206571 | −0.103285 | − | 0.994652i | \(-0.532936\pi\) | ||||
−0.103285 | + | 0.994652i | \(0.532936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.45707 | 0.168248 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.41637 | 0.617253 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6593 | 1.42428 | 0.712140 | − | 0.702037i | \(-0.247726\pi\) | ||||
0.712140 | + | 0.702037i | \(0.247726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6280 | −1.71540 | −0.857701 | − | 0.514149i | \(-0.828108\pi\) | ||||
−0.857701 | + | 0.514149i | \(0.828108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17013 | 0.343849 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.15000 | −0.337716 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6679 | −1.13080 | −0.565398 | − | 0.824818i | \(-0.691278\pi\) | ||||
−0.565398 | + | 0.824818i | \(0.691278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.47463 | 0.152912 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.24036 | −0.229856 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.38541 | 0.242201 | 0.121101 | − | 0.992640i | \(-0.461358\pi\) | ||||
0.121101 | + | 0.992640i | \(0.461358\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.19367 | 0.421479 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.880061 | −0.0875693 | −0.0437847 | − | 0.999041i | \(-0.513942\pi\) | ||||
−0.0437847 | + | 0.999041i | \(0.513942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.21107 | −0.513462 | −0.256731 | − | 0.966483i | \(-0.582645\pi\) | ||||
−0.256731 | + | 0.966483i | \(0.582645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.43106 | 0.237247 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.9637 | −1.92996 | −0.964981 | − | 0.262319i | \(-0.915513\pi\) | ||||
−0.964981 | + | 0.262319i | \(0.915513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.5577 | 1.77751 | 0.888753 | − | 0.458386i | \(-0.151572\pi\) | ||||
0.888753 | + | 0.458386i | \(0.151572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.15343 | 0.773889 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.98409 | 0.939224 | 0.469612 | − | 0.882873i | \(-0.344394\pi\) | ||||
0.469612 | + | 0.882873i | \(0.344394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.67503 | 0.529199 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.17525 | −0.199405 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.58685 | 0.598805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.0181 | −0.903305 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1539 | 1.08708 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7930 | 1.31267 | 0.656335 | − | 0.754469i | \(-0.272106\pi\) | ||||
0.656335 | + | 0.754469i | \(0.272106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7587 | 0.947252 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.834088 | 0.0728746 | 0.0364373 | − | 0.999336i | \(-0.488399\pi\) | ||||
0.0364373 | + | 0.999336i | \(0.488399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.53727 | 0.133299 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.88227 | 0.162000 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.20377 | −0.530024 | −0.265012 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265012 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1616 | 1.71008 | 0.855042 | − | 0.518559i | \(-0.173531\pi\) | ||||
0.855042 | + | 0.518559i | \(0.173531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.31909 | 0.447948 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.92915 | −0.492389 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.33187 | 0.439766 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2561 | −1.33175 | −0.665876 | − | 0.746063i | \(-0.731942\pi\) | ||||
−0.665876 | + | 0.746063i | \(0.731942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.0930 | −1.47239 | −0.736195 | − | 0.676769i | \(-0.763379\pi\) | ||||
−0.736195 | + | 0.676769i | \(0.763379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.68421 | −0.136160 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.77564 | 0.222945 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0559 | 1.20159 | 0.600795 | − | 0.799403i | \(-0.294851\pi\) | ||||
0.600795 | + | 0.799403i | \(0.294851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.29590 | −0.657907 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.89404 | −0.306894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.31660 | 0.573080 | 0.286540 | − | 0.958068i | \(-0.407495\pi\) | ||||
0.286540 | + | 0.958068i | \(0.407495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.89361 | 0.614517 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.9586 | −0.925385 | −0.462693 | − | 0.886519i | \(-0.653117\pi\) | ||||
−0.462693 | + | 0.886519i | \(0.653117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.19025 | 0.0910204 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6231 | −1.26383 | −0.631915 | − | 0.775038i | \(-0.717731\pi\) | ||||
−0.631915 | + | 0.775038i | \(0.717731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.88189 | −0.142257 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.03369 | 0.228026 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.89790 | −0.141856 | −0.0709278 | − | 0.997481i | \(-0.522596\pi\) | ||||
−0.0709278 | + | 0.997481i | \(0.522596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3850 | 1.21789 | 0.608944 | − | 0.793213i | \(-0.291594\pi\) | ||||
0.608944 | + | 0.793213i | \(0.291594\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.84487 | −0.579909 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.3469 | 1.12833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.06300 | −0.516498 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.29156 | −0.0939471 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5859 | −0.983042 | −0.491521 | − | 0.870866i | \(-0.663559\pi\) | ||||
−0.491521 | + | 0.870866i | \(0.663559\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8588 | −1.78938 | −0.894689 | − | 0.446689i | \(-0.852603\pi\) | ||||
−0.894689 | + | 0.446689i | \(0.852603\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.47333 | −0.318711 | −0.159356 | − | 0.987221i | \(-0.550942\pi\) | ||||
−0.159356 | + | 0.987221i | \(0.550942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.49522 | 0.318658 | 0.159329 | − | 0.987226i | \(-0.449067\pi\) | ||||
0.159329 | + | 0.987226i | \(0.449067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50497 | −0.317756 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.06842 | 0.285547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.8568 | −1.31702 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.01499 | −0.209557 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.99150 | 0.345269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.7861 | −1.49982 | −0.749908 | − | 0.661542i | \(-0.769902\pi\) | ||||
−0.749908 | + | 0.661542i | \(0.769902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.85816 | 0.264357 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.2508 | 1.38109 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.90457 | −0.129291 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.76494 | 0.119264 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0555395 | 0.00371920 | 0.00185960 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00185960 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.45707 | −0.0971378 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.24936 | −0.348412 | −0.174206 | − | 0.984709i | \(-0.555736\pi\) | ||||
−0.174206 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6951 | 1.43365 | 0.716826 | − | 0.697252i | \(-0.245594\pi\) | ||||
0.716826 | + | 0.697252i | \(0.245594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.41637 | −0.356371 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.34933 | 0.612495 | 0.306248 | − | 0.951952i | \(-0.400926\pi\) | ||||
0.306248 | + | 0.951952i | \(0.400926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0119 | 0.653107 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6593 | −0.822309 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7781 | −0.955913 | −0.477957 | − | 0.878383i | \(-0.658622\pi\) | ||||
−0.477957 | + | 0.878383i | \(0.658622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7668 | 1.08004 | 0.540022 | − | 0.841651i | \(-0.318416\pi\) | ||||
0.540022 | + | 0.841651i | \(0.318416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.0360 | 0.641178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.6280 | 0.990387 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.44048 | −0.0909222 | −0.0454611 | − | 0.998966i | \(-0.514476\pi\) | ||||
−0.0454611 | + | 0.998966i | \(0.514476\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.6439 | −0.794914 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.17013 | −0.198521 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.0265 | −1.31160 | −0.655799 | − | 0.754935i | \(-0.727668\pi\) | ||||
−0.655799 | + | 0.754935i | \(0.727668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5306 | −0.654342 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.15000 | 0.194980 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.6833 | −0.658760 | −0.329380 | − | 0.944197i | \(-0.606840\pi\) | ||||
−0.329380 | + | 0.944197i | \(0.606840\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.6151 | −0.959228 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.6679 | 0.652866 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3247 | 1.11728 | 0.558638 | − | 0.829412i | \(-0.311324\pi\) | ||||
0.558638 | + | 0.829412i | \(0.311324\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.64076 | −0.221161 | −0.110580 | − | 0.993867i | \(-0.535271\pi\) | ||||
−0.110580 | + | 0.993867i | \(0.535271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.11045 | −0.368474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3601 | 1.34349 | 0.671744 | − | 0.740783i | \(-0.265546\pi\) | ||||
0.671744 | + | 0.740783i | \(0.265546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.47463 | −0.0882836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.39777 | −0.143039 | −0.0715195 | − | 0.997439i | \(-0.522785\pi\) | ||||
−0.0715195 | + | 0.997439i | \(0.522785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.64168 | 0.0975879 | 0.0487939 | − | 0.998809i | \(-0.484462\pi\) | ||||
0.0487939 | + | 0.998809i | \(0.484462\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.24036 | 0.132708 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.9390 | 0.763766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1635 | −0.833144 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.38541 | −0.139835 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.35348 | −0.0790709 | −0.0395355 | − | 0.999218i | \(-0.512588\pi\) | ||||
−0.0395355 | + | 0.999218i | \(0.512588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.71022 | 0.332462 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.19367 | −0.243341 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8955 | −0.800925 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.880061 | 0.0505582 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.7661 | −0.845507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9864 | −1.36898 | −0.684489 | − | 0.729023i | \(-0.739975\pi\) | ||||
−0.684489 | + | 0.729023i | \(0.739975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.21107 | 0.296447 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.23414 | −0.353506 | −0.176753 | − | 0.984255i | \(-0.556559\pi\) | ||||
−0.176753 | + | 0.984255i | \(0.556559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.7120 | −1.62290 | −0.811450 | − | 0.584422i | \(-0.801321\pi\) | ||||
−0.811450 | + | 0.584422i | \(0.801321\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.43106 | −0.136975 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8082 | −0.775545 | −0.387772 | − | 0.921755i | \(-0.626755\pi\) | ||||
−0.387772 | + | 0.921755i | \(0.626755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.2101 | 0.739622 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.9637 | 1.11426 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00462 | −0.111540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5577 | −1.02624 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.86992 | −0.378751 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.06203 | 0.388165 | 0.194082 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.15343 | −0.446805 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.47956 | −0.463288 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9635 | −0.869585 | −0.434792 | − | 0.900531i | \(-0.643178\pi\) | ||||
−0.434792 | + | 0.900531i | \(0.643178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.98409 | −0.542261 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.18410 | −0.334888 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9274 | −0.859996 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.67503 | −0.305533 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.1822 | −0.922388 | −0.461194 | − | 0.887299i | \(-0.652579\pi\) | ||||
−0.461194 | + | 0.887299i | \(0.652579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.2999 | −1.51486 | −0.757429 | − | 0.652918i | \(-0.773545\pi\) | ||||
−0.757429 | + | 0.652918i | \(0.773545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.313161 | −0.0166679 | −0.00833393 | − | 0.999965i | \(-0.502653\pi\) | ||||
−0.00833393 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.26210 | 0.385432 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.17525 | 0.115127 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.3342 | 0.650977 | 0.325488 | − | 0.945546i | \(-0.394471\pi\) | ||||
0.325488 | + | 0.945546i | \(0.394471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5833 | −0.925438 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.58685 | −0.345720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.32209 | 0.173886 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.08368 | 0.474164 | 0.237082 | − | 0.971490i | \(-0.423809\pi\) | ||||
0.237082 | + | 0.971490i | \(0.423809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0181 | 0.521523 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.7146 | 0.556277 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5431 | −0.856569 | −0.428285 | − | 0.903644i | \(-0.640882\pi\) | ||||
−0.428285 | + | 0.903644i | \(0.640882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1539 | −0.627626 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4212 | 0.535299 | 0.267650 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267650 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.7930 | −0.757871 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.5767 | −0.795931 | −0.397965 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397965 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1951 | −0.519589 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.7587 | −0.546896 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0121 | 0.659742 | 0.329871 | − | 0.944026i | \(-0.392995\pi\) | ||||
0.329871 | + | 0.944026i | \(0.392995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.07787 | 0.256799 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.834088 | −0.0420742 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.8282 | −1.19892 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.9449 | 1.70364 | 0.851822 | − | 0.523831i | \(-0.175498\pi\) | ||||
0.851822 | + | 0.523831i | \(0.175498\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.53727 | −0.0769600 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.0787 | −1.85162 | −0.925811 | − | 0.377988i | \(-0.876616\pi\) | ||||
−0.925811 | + | 0.377988i | \(0.876616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.88227 | −0.0935307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.1928 | −1.69487 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.0280 | −1.53424 | −0.767118 | − | 0.641505i | \(-0.778310\pi\) | ||||
−0.767118 | + | 0.641505i | \(0.778310\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.20377 | 0.306009 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.91819 | −0.192802 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.4162 | 1.44398 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.1616 | −0.987317 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.5226 | 1.34457 | 0.672284 | − | 0.740293i | \(-0.265313\pi\) | ||||
0.672284 | + | 0.740293i | \(0.265313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2919 | 0.501599 | 0.250799 | − | 0.968039i | \(-0.419307\pi\) | ||||
0.250799 | + | 0.968039i | \(0.419307\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.31909 | −0.258623 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.45400 | 0.119036 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.1321 | 0.490327 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.9340 | −1.49004 | −0.745020 | − | 0.667043i | \(-0.767560\pi\) | ||||
−0.745020 | + | 0.667043i | \(0.767560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.59342 | 0.461030 | 0.230515 | − | 0.973069i | \(-0.425959\pi\) | ||||
0.230515 | + | 0.973069i | \(0.425959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.92915 | 0.284281 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.58859 | −0.171665 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.3735 | −0.876918 | −0.438459 | − | 0.898751i | \(-0.644476\pi\) | ||||
−0.438459 | + | 0.898751i | \(0.644476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.33187 | −0.253899 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7144 | 0.794125 | 0.397062 | − | 0.917792i | \(-0.370030\pi\) | ||||
0.397062 | + | 0.917792i | \(0.370030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.0799 | 0.951878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.2561 | 0.768887 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.4482 | −1.53132 | −0.765662 | − | 0.643243i | \(-0.777588\pi\) | ||||
−0.765662 | + | 0.643243i | \(0.777588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.0127 | 1.97830 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0930 | 0.850085 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5767 | 0.775427 | 0.387713 | − | 0.921780i | \(-0.373265\pi\) | ||||
0.387713 | + | 0.921780i | \(0.373265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.68421 | 0.0786120 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.43380 | 0.113353 | 0.0566767 | − | 0.998393i | \(-0.481950\pi\) | ||||
0.0566767 | + | 0.998393i | \(0.481950\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.9325 | −1.43755 | −0.718777 | − | 0.695240i | \(-0.755298\pi\) | ||||
−0.718777 | + | 0.695240i | \(0.755298\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.77564 | −0.128717 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.4582 | −0.900417 | −0.450208 | − | 0.892924i | \(-0.648650\pi\) | ||||
−0.450208 | + | 0.892924i | \(0.648650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.81844 | 0.268670 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0559 | −0.693738 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −45.1185 | −2.07455 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.73427 | −0.0795737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.29590 | 0.379843 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0622 | −0.962356 | −0.481178 | − | 0.876623i | \(-0.659791\pi\) | ||||
−0.481178 | + | 0.876623i | \(0.659791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.89404 | 0.177185 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.48997 | −0.203879 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.6092 | −1.70424 | −0.852118 | − | 0.523349i | \(-0.824682\pi\) | ||||
−0.852118 | + | 0.523349i | \(0.824682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.31660 | −0.330868 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.5335 | −1.64873 | −0.824367 | − | 0.566056i | \(-0.808469\pi\) | ||||
−0.824367 | + | 0.566056i | \(0.808469\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.30526 | −0.238937 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.89361 | −0.354791 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.98305 | −0.223520 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4840 | 1.00652 | 0.503262 | − | 0.864134i | \(-0.332133\pi\) | ||||
0.503262 | + | 0.864134i | \(0.332133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.9586 | 0.534271 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.21863 | 0.0989237 | 0.0494619 | − | 0.998776i | \(-0.484249\pi\) | ||||
0.0494619 | + | 0.998776i | \(0.484249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.65651 | 0.0737137 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.2456 | −1.25196 | −0.625982 | − | 0.779837i | \(-0.715302\pi\) | ||||
−0.625982 | + | 0.779837i | \(0.715302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.27953 | −0.100840 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.19025 | −0.0525507 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.80863 | 0.432220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.3065 | −0.981038 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6231 | 0.729673 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.1688 | 1.23410 | 0.617050 | − | 0.786924i | \(-0.288328\pi\) | ||||
0.617050 | + | 0.786924i | \(0.288328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.70961 | −0.205937 | −0.102968 | − | 0.994685i | \(-0.532834\pi\) | ||||
−0.102968 | + | 0.994685i | \(0.532834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.88189 | 0.0821323 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.48358 | 0.108186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.9098 | −0.604774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.03369 | −0.131651 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.5770 | 1.62460 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.89790 | 0.0819004 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.3601 | −0.963118 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.17651 | 0.136569 | 0.0682844 | − | 0.997666i | \(-0.478247\pi\) | ||||
0.0682844 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.3850 | −0.703148 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.9306 | −1.49626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4331 | 1.08744 | 0.543721 | − | 0.839266i | \(-0.317015\pi\) | ||||
0.543721 | + | 0.839266i | \(0.317015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.84487 | 0.334811 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.74928 | 0.159725 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.3502 | 0.695282 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3469 | −0.651441 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.1670 | 0.854505 | 0.427252 | − | 0.904132i | \(-0.359482\pi\) | ||||
0.427252 | + | 0.904132i | \(0.359482\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.06300 | 0.298200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2498 | 0.769136 | 0.384568 | − | 0.923097i | \(-0.374350\pi\) | ||||
0.384568 | + | 0.923097i | \(0.374350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.7927 | −0.790616 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.29156 | 0.0542404 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.4857 | 1.15226 | 0.576129 | − | 0.817359i | \(-0.304562\pi\) | ||||
0.576129 | + | 0.817359i | \(0.304562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0250476 | 0.00104821 | 0.000524106 | − | 1.00000i | \(-0.499833\pi\) | ||||
0.000524106 | 1.00000i | \(0.499833\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5859 | 0.567559 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.39305 | 0.183203 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.0269 | −0.875362 | −0.437681 | − | 0.899130i | \(-0.644200\pi\) | ||||
−0.437681 | + | 0.899130i | \(0.644200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.8588 | 1.03310 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.1846 | −0.837397 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.7902 | 1.44086 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.4551 | −1.21574 | −0.607872 | − | 0.794035i | \(-0.707976\pi\) | ||||
−0.607872 | + | 0.794035i | \(0.707976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.75517 | −0.0723206 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.47333 | 0.184008 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.93477 | 0.161582 | 0.0807909 | − | 0.996731i | \(-0.474255\pi\) | ||||
0.0807909 | + | 0.996731i | \(0.474255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.09441 | 0.167854 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.49522 | −0.183977 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.1931 | −1.43795 | −0.718975 | − | 0.695036i | \(-0.755388\pi\) | ||||
−0.718975 | + | 0.695036i | \(0.755388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9780 | −0.610967 | −0.305484 | − | 0.952197i | \(-0.598818\pi\) | ||||
−0.305484 | + | 0.952197i | \(0.598818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.50497 | 0.183457 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.3982 | −0.504059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6169 | 0.999170 | 0.499585 | − | 0.866265i | \(-0.333486\pi\) | ||||
0.499585 | + | 0.866265i | \(0.333486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.06842 | −0.164861 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.1429 | −1.45980 | −0.729900 | − | 0.683554i | \(-0.760433\pi\) | ||||
−0.729900 | + | 0.683554i | \(0.760433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.8568 | 0.760380 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0808 | 0.486356 | 0.243178 | − | 0.969982i | \(-0.421810\pi\) | ||||
0.243178 | + | 0.969982i | \(0.421810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.1257 | 0.929500 | 0.464750 | − | 0.885442i | \(-0.346144\pi\) | ||||
0.464750 | + | 0.885442i | \(0.346144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.01499 | 0.120988 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.7782 | −0.552014 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5916 | −0.623665 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.99150 | −0.199341 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.7320 | 0.547533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.7565 | −1.74192 | −0.870960 | − | 0.491354i | \(-0.836502\pi\) | ||||
−0.870960 | + | 0.491354i | \(0.836502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.7861 | 0.865920 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.8445 | −1.10497 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.85816 | −0.152627 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.76562 | −0.306724 | −0.153362 | − | 0.988170i | \(-0.549010\pi\) | ||||
−0.153362 | + | 0.988170i | \(0.549010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.44419 | −0.372442 | −0.186221 | − | 0.982508i | \(-0.559624\pi\) | ||||
−0.186221 | + | 0.982508i | \(0.559624\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.2508 | −0.797374 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.8606 | 1.64571 | 0.822856 | − | 0.568250i | \(-0.192379\pi\) | ||||
0.822856 | + | 0.568250i | \(0.192379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.7223 | −0.499394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.90457 | 0.0746460 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.8823 | −1.71725 | −0.858624 | − | 0.512605i | \(-0.828680\pi\) | ||||
−0.858624 | + | 0.512605i | \(0.828680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.56998 | −0.0613441 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.76494 | −0.0688569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.3533 | 1.06553 | 0.532767 | − | 0.846262i | \(-0.321152\pi\) | ||||
0.532767 | + | 0.846262i | \(0.321152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.8238 | 1.82123 | 0.910617 | − | 0.413251i | \(-0.135607\pi\) | ||||
0.910617 | + | 0.413251i | \(0.135607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.89356 | −0.112208 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.49724 | −0.367735 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.0555395 | −0.00214728 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.8988 | 1.27004 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.2574 | 1.39762 | 0.698811 | − | 0.715307i | \(-0.253713\pi\) | ||||
0.698811 | + | 0.715307i | \(0.253713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.45707 | 0.0560825 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 51.1630 | 1.96636 | 0.983178 | − | 0.182652i | \(-0.0584682\pi\) | ||||
0.983178 | + | 0.182652i | \(0.0584682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.08089 | 0.118234 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.24936 | 0.201156 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.8240 | −1.17945 | −0.589724 | − | 0.807605i | \(-0.700763\pi\) | ||||
−0.589724 | + | 0.807605i | \(0.700763\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.6772 | 0.446161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.6951 | −0.827720 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.12305 | 0.156848 | 0.0784241 | − | 0.996920i | \(-0.475011\pi\) | ||||
0.0784241 | + | 0.996920i | \(0.475011\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.41637 | 0.205751 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.9495 | −1.43951 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.8726 | −0.639095 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.34933 | −0.353624 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.97922 | 0.263602 | 0.131801 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131801 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.70459 | −0.366015 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.0119 | −0.377072 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.13665 | −0.0427482 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.1455 | 0.869247 | 0.434623 | − | 0.900612i | \(-0.356882\pi\) | ||||
0.434623 | + | 0.900612i | \(0.356882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6593 | 0.474760 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.44599 | 0.166504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.7781 | 0.551897 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8249 | −0.813930 | −0.406965 | − | 0.913444i | \(-0.633413\pi\) | ||||
−0.406965 | + | 0.913444i | \(0.633413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.73041 | −0.250653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.7668 | −0.623563 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.58976 | −0.170460 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.0916 | 1.59818 | 0.799090 | − | 0.601211i | \(-0.205315\pi\) | ||||
0.799090 | + | 0.601211i | \(0.205315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.1199 | 0.670189 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5077 | 0.868277 | 0.434138 | − | 0.900846i | \(-0.357053\pi\) | ||||
0.434138 | + | 0.900846i | \(0.357053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.0360 | −0.370184 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.8923 | 0.695909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9187 | −0.879862 | −0.439931 | − | 0.898032i | \(-0.644997\pi\) | ||||
−0.439931 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.613067 | −0.0224912 | −0.0112456 | − | 0.999937i | \(-0.503580\pi\) | ||||
−0.0112456 | + | 0.999937i | \(0.503580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.5983 | 1.12104 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.6280 | −0.571800 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.7843 | −0.942137 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.945022 | −0.0344843 | −0.0172422 | − | 0.999851i | \(-0.505489\pi\) | ||||
−0.0172422 | + | 0.999851i | \(0.505489\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.44048 | 0.0524939 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.0559 | 1.23942 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.8014 | −0.537966 | −0.268983 | − | 0.963145i | \(-0.586688\pi\) | ||||
−0.268983 | + | 0.963145i | \(0.586688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.6439 | 0.458944 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.6688 | 0.422994 | 0.211497 | − | 0.977379i | \(-0.432166\pi\) | ||||
0.211497 | + | 0.977379i | \(0.432166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.9684 | 0.867714 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.17013 | 0.114616 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.64412 | −0.0953494 | −0.0476747 | − | 0.998863i | \(-0.515181\pi\) | ||||
−0.0476747 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.0265 | 0.757252 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.0776248 | 0.00279197 | 0.00139599 | − | 0.999999i | \(-0.499556\pi\) | ||||
0.00139599 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.14863 | 0.0771811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5306 | 0.377784 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.9240 | 0.427223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.1799 | −0.578961 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.15000 | −0.112572 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.3392 | −1.01147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.3434 | −0.867749 | −0.433874 | − | 0.900973i | \(-0.642854\pi\) | ||||
−0.433874 | + | 0.900973i | \(0.642854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.6833 | 0.380335 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8950 | 0.458495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.6151 | 0.553811 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.4833 | −1.64652 | −0.823261 | − | 0.567663i | \(-0.807848\pi\) | ||||
−0.823261 | + | 0.567663i | \(0.807848\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.95844 | 0.316927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6679 | −0.376932 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.40158 | −0.261196 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.32964 | 0.258336 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3247 | −0.645060 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.4581 | 0.613796 | 0.306898 | − | 0.951742i | \(-0.400709\pi\) | ||||
0.306898 | + | 0.951742i | \(0.400709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3281 | −0.468012 | −0.234006 | − | 0.972235i | \(-0.575183\pi\) | ||||
−0.234006 | + | 0.972235i | \(0.575183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.64076 | 0.127687 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.7718 | −0.482405 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.8055 | −0.448009 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.0294 | −0.384928 | −0.192464 | − | 0.981304i | \(-0.561648\pi\) | ||||
−0.192464 | + | 0.981304i | \(0.561648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1161 | 0.422340 | 0.211170 | − | 0.977449i | \(-0.432273\pi\) | ||||
0.211170 | + | 0.977449i | \(0.432273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.11045 | 0.212739 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6413 | 0.822087 | 0.411044 | − | 0.911616i | \(-0.365164\pi\) | ||||
0.411044 | + | 0.911616i | \(0.365164\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.4519 | −1.50915 | −0.754574 | − | 0.656215i | \(-0.772157\pi\) | ||||
−0.754574 | + | 0.656215i | \(0.772157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.3601 | −0.775663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.97997 | 0.311138 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.5093 | 0.778967 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.47463 | 0.0509706 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.2176 | −0.594416 | −0.297208 | − | 0.954813i | \(-0.596055\pi\) | ||||
−0.297208 | + | 0.954813i | \(0.596055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0775 | −0.657844 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.39777 | 0.0825836 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.50731 | 0.292315 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.64168 | −0.0563424 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5825 | 0.842678 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.5329 | −0.668793 | −0.334397 | − | 0.942432i | \(-0.608533\pi\) | ||||
−0.334397 | + | 0.942432i | \(0.608533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.24036 | −0.0766188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.9607 | −0.681843 | −0.340922 | − | 0.940092i | \(-0.610739\pi\) | ||||
−0.340922 | + | 0.940092i | \(0.610739\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0681 | −1.23063 | −0.615315 | − | 0.788282i | \(-0.710971\pi\) | ||||
−0.615315 | + | 0.788282i | \(0.710971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.9390 | −0.440960 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.06724 | −0.104410 | −0.0522051 | − | 0.998636i | \(-0.516625\pi\) | ||||
−0.0522051 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.2891 | 1.06386 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.1635 | 0.481016 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.0888 | 1.80091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.38541 | 0.0807337 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.6975 | 0.530673 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.5958 | 0.898075 | 0.449038 | − | 0.893513i | \(-0.351767\pi\) | ||||
0.449038 | + | 0.893513i | \(0.351767\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.35348 | 0.0456516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.4634 | 1.90230 | 0.951151 | − | 0.308727i | \(-0.0999030\pi\) | ||||
0.951151 | + | 0.308727i | \(0.0999030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.6728 | −0.998568 | −0.499284 | − | 0.866438i | \(-0.666404\pi\) | ||||
−0.499284 | + | 0.866438i | \(0.666404\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.71022 | −0.191947 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.4301 | 1.42466 | 0.712332 | − | 0.701843i | \(-0.247639\pi\) | ||||
0.712332 | + | 0.701843i | \(0.247639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1061 | 0.640798 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.19367 | 0.140493 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.33103 | −0.211860 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.57236 | 0.119411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.64508 | −0.154922 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.9720 | −0.465475 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.8955 | 0.462414 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.8410 | −1.02519 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1465 | 0.370114 | 0.185057 | − | 0.982728i | \(-0.440753\pi\) | ||||
0.185057 | + | 0.982728i | \(0.440753\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.880061 | −0.0291898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.4798 | 1.47368 | 0.736841 | − | 0.676066i | \(-0.236317\pi\) | ||||
0.736841 | + | 0.676066i | \(0.236317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −65.5389 | −2.16902 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.7661 | 0.488154 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.07727 | 0.0355747 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.2712 | 1.03154 | 0.515771 | − | 0.856726i | \(-0.327505\pi\) | ||||
0.515771 | + | 0.856726i | \(0.327505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.9864 | 0.790380 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.8801 | 0.390615 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.21107 | −0.171154 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.2303 | −0.630927 | −0.315464 | − | 0.948938i | \(-0.602160\pi\) | ||||
−0.315464 | + | 0.948938i | \(0.602160\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.34625 | −0.207990 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.23414 | 0.204097 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.2945 | 0.434775 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.1991 | −1.31325 | −0.656624 | − | 0.754218i | \(-0.728016\pi\) | ||||
−0.656624 | + | 0.754218i | \(0.728016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.7120 | 0.936982 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.3886 | −1.87082 | −0.935408 | − | 0.353570i | \(-0.884968\pi\) | ||||
−0.935408 | + | 0.353570i | \(0.884968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.2046 | −0.983597 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43106 | 0.0790824 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.1040 | −0.393328 | −0.196664 | − | 0.980471i | \(-0.563011\pi\) | ||||
−0.196664 | + | 0.980471i | \(0.563011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.8082 | 0.447761 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.5095 | 0.761547 | 0.380773 | − | 0.924668i | \(-0.375658\pi\) | ||||
0.380773 | + | 0.924668i | \(0.375658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.5723 | 0.827501 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.2101 | −0.427021 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.01254 | −0.258738 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8255 | −0.929854 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.9637 | −0.643321 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.7910 | 1.50626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.1235 | 1.45107 | 0.725537 | − | 0.688183i | \(-0.241591\pi\) | ||||
0.725537 | + | 0.688183i | \(0.241591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00462 | 0.0643977 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.7833 | −1.27671 | −0.638353 | − | 0.769744i | \(-0.720384\pi\) | ||||
−0.638353 | + | 0.769744i | \(0.720384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.0399 | 0.834801 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.4379 | −0.333937 | −0.166968 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166968 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.7377 | −1.42982 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.5577 | 0.592502 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.56154 | −0.0498052 | −0.0249026 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249026 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.42000 | 0.268283 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.86992 | 0.218672 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.4375 | 1.03145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.79782 | 0.120642 | 0.0603209 | − | 0.998179i | \(-0.480788\pi\) | ||||
0.0603209 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.06203 | −0.224107 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.46121 | −0.268238 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.2540 | −0.609780 | −0.304890 | − | 0.952388i | \(-0.598620\pi\) | ||||
−0.304890 | + | 0.952388i | \(0.598620\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.15343 | 0.257963 |
(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 | 8112.2.a.ct.1.3 | 6 | ||
4.3 | odd | 2 | 4056.2.a.bh.1.3 | ✓ | 6 | ||
13.12 | even | 2 | 8112.2.a.cu.1.4 | 6 | |||
52.31 | even | 4 | 4056.2.c.r.337.8 | 12 | |||
52.47 | even | 4 | 4056.2.c.r.337.5 | 12 | |||
52.51 | odd | 2 | 4056.2.a.bi.1.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.bh.1.3 | ✓ | 6 | 4.3 | odd | 2 | ||
4056.2.a.bi.1.4 | yes | 6 | 52.51 | odd | 2 | ||
4056.2.c.r.337.5 | 12 | 52.47 | even | 4 | |||
4056.2.c.r.337.8 | 12 | 52.31 | even | 4 | |||
8112.2.a.ct.1.3 | 6 | 1.1 | even | 1 | trivial | ||
8112.2.a.cu.1.4 | 6 | 13.12 | even | 2 |