Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.81775 | −1.62683 | −0.813413 | − | 0.581687i | \(-0.802393\pi\) | ||||
−0.813413 | + | 0.581687i | \(0.802393\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.243389 | −0.108847 | −0.0544235 | − | 0.998518i | \(-0.517332\pi\) | ||||
−0.0544235 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.929492 | 0.351315 | 0.175658 | − | 0.984451i | \(-0.443795\pi\) | ||||
0.175658 | + | 0.984451i | \(0.443795\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.93969 | 1.64656 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.38796 | 1.32302 | 0.661510 | − | 0.749936i | \(-0.269916\pi\) | ||||
0.661510 | + | 0.749936i | \(0.269916\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.17004 | −0.324512 | −0.162256 | − | 0.986749i | \(-0.551877\pi\) | ||||
−0.162256 | + | 0.986749i | \(0.551877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.685809 | 0.177075 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.41492 | 1.55585 | 0.777923 | − | 0.628360i | \(-0.216273\pi\) | ||||
0.777923 | + | 0.628360i | \(0.216273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.61907 | −0.571528 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.17766 | −1.28813 | −0.644066 | − | 0.764970i | \(-0.722754\pi\) | ||||
−0.644066 | + | 0.764970i | \(0.722754\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94076 | −0.988152 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.46555 | −1.05184 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16503 | −0.959122 | −0.479561 | − | 0.877508i | \(-0.659204\pi\) | ||||
−0.479561 | + | 0.877508i | \(0.659204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.29647 | −1.49009 | −0.745045 | − | 0.667015i | \(-0.767572\pi\) | ||||
−0.745045 | + | 0.667015i | \(0.767572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.3642 | −2.15232 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.226229 | −0.0382396 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.1767 | −1.83744 | −0.918718 | − | 0.394914i | \(-0.870775\pi\) | ||||
−0.918718 | + | 0.394914i | \(0.870775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.29689 | 0.527925 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.11040 | 0.485763 | 0.242881 | − | 0.970056i | \(-0.421907\pi\) | ||||
0.242881 | + | 0.970056i | \(0.421907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.53876 | 0.844653 | 0.422326 | − | 0.906444i | \(-0.361214\pi\) | ||||
0.422326 | + | 0.906444i | \(0.361214\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.20227 | −0.179223 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.81464 | 1.28575 | 0.642874 | − | 0.765972i | \(-0.277742\pi\) | ||||
0.642874 | + | 0.765972i | \(0.277742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.13604 | −0.876578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.0756 | −2.53109 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.2900 | 1.41344 | 0.706720 | − | 0.707494i | \(-0.250174\pi\) | ||||
0.706720 | + | 0.707494i | \(0.250174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.06798 | −0.144007 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.81775 | −0.373219 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0099 | −1.43336 | −0.716682 | − | 0.697400i | \(-0.754340\pi\) | ||||
−0.716682 | + | 0.697400i | \(0.754340\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.358578 | 0.0459113 | 0.0229556 | − | 0.999736i | \(-0.492692\pi\) | ||||
0.0229556 | + | 0.999736i | \(0.492692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.59140 | 0.578462 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.284776 | 0.0353222 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8751 | 1.45077 | 0.725385 | − | 0.688344i | \(-0.241662\pi\) | ||||
0.725385 | + | 0.688344i | \(0.241662\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.4071 | 2.09557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.27001 | 0.862792 | 0.431396 | − | 0.902163i | \(-0.358021\pi\) | ||||
0.431396 | + | 0.902163i | \(0.358021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0340 | −1.64255 | −0.821276 | − | 0.570530i | \(-0.806738\pi\) | ||||
−0.821276 | + | 0.570530i | \(0.806738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.9218 | 1.60755 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.07858 | 0.464797 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.581451 | 0.0646056 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.31006 | 0.692619 | 0.346309 | − | 0.938120i | \(-0.387435\pi\) | ||||
0.346309 | + | 0.938120i | \(0.387435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.56132 | −0.169349 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.5537 | 1.56033 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.87396 | 0.622639 | 0.311319 | − | 0.950305i | \(-0.399229\pi\) | ||||
0.311319 | + | 0.950305i | \(0.399229\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.08755 | −0.114006 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.3773 | 2.42412 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.243389 | −0.0249712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4974 | −1.06585 | −0.532926 | − | 0.846162i | \(-0.678908\pi\) | ||||
−0.532926 | + | 0.846162i | \(0.678908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.6752 | 2.17844 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.14271 | 0.113704 | 0.0568519 | − | 0.998383i | \(-0.481894\pi\) | ||||
0.0568519 | + | 0.998383i | \(0.481894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.8972 | −1.46787 | −0.733934 | − | 0.679221i | \(-0.762318\pi\) | ||||
−0.733934 | + | 0.679221i | \(0.762318\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.637454 | 0.0622092 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8657 | −1.24378 | −0.621888 | − | 0.783106i | \(-0.713634\pi\) | ||||
−0.621888 | + | 0.783106i | \(0.713634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.90646 | 0.182606 | 0.0913030 | − | 0.995823i | \(-0.470897\pi\) | ||||
0.0913030 | + | 0.995823i | \(0.470897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.4931 | 2.98919 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3402 | 0.972723 | 0.486362 | − | 0.873758i | \(-0.338324\pi\) | ||||
0.486362 | + | 0.873758i | \(0.338324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50358 | 0.140209 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.77966 | −0.534329 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.96262 | 0.546592 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.25422 | 0.750384 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.76431 | −0.790251 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.41948 | 0.216404 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.81705 | 0.604915 | 0.302458 | − | 0.953163i | \(-0.402193\pi\) | ||||
0.302458 | + | 0.953163i | \(0.402193\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.6068 | −1.37410 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.88813 | 0.776559 | 0.388280 | − | 0.921542i | \(-0.373069\pi\) | ||||
0.388280 | + | 0.921542i | \(0.373069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.929492 | 0.0805972 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.33026 | 0.114490 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.19350 | −0.272839 | −0.136420 | − | 0.990651i | \(-0.543560\pi\) | ||||
−0.136420 | + | 0.990651i | \(0.543560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6744 | 0.905392 | 0.452696 | − | 0.891665i | \(-0.350462\pi\) | ||||
0.452696 | + | 0.891665i | \(0.350462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.8374 | −2.09169 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.13411 | −0.429336 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.25711 | 0.104398 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.2898 | 1.42604 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.99354 | −0.572933 | −0.286467 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286467 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.9826 | 1.70754 | 0.853771 | − | 0.520648i | \(-0.174310\pi\) | ||||
0.853771 | + | 0.520648i | \(0.174310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.6877 | 2.56180 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.01927 | 0.162192 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.91794 | 0.631921 | 0.315960 | − | 0.948772i | \(-0.397673\pi\) | ||||
0.315960 | + | 0.948772i | \(0.397673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.9946 | −2.29942 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.74209 | −0.452540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.71896 | 0.526270 | 0.263135 | − | 0.964759i | \(-0.415244\pi\) | ||||
0.263135 | + | 0.964759i | \(0.415244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00931 | 0.234274 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.9171 | −0.844790 | −0.422395 | − | 0.906412i | \(-0.638810\pi\) | ||||
−0.422395 | + | 0.906412i | \(0.638810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6310 | −0.894692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.93969 | 0.377747 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2211 | −1.84149 | −0.920747 | − | 0.390159i | \(-0.872420\pi\) | ||||
−0.920747 | + | 0.390159i | \(0.872420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.59240 | −0.347153 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 31.0230 | 2.33183 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.3740 | −1.59757 | −0.798783 | − | 0.601619i | \(-0.794522\pi\) | ||||
−0.798783 | + | 0.601619i | \(0.794522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2771 | −1.20987 | −0.604933 | − | 0.796277i | \(-0.706800\pi\) | ||||
−0.604933 | + | 0.796277i | \(0.706800\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.01038 | −0.0746896 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.72029 | 0.200000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.1484 | 2.05842 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.08018 | −0.369529 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.8455 | −1.43597 | −0.717984 | − | 0.696060i | \(-0.754935\pi\) | ||||
−0.717984 | + | 0.696060i | \(0.754935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.2372 | −1.31274 | −0.656371 | − | 0.754438i | \(-0.727910\pi\) | ||||
−0.656371 | + | 0.754438i | \(0.727910\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.802427 | −0.0574630 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7045 | −0.762666 | −0.381333 | − | 0.924438i | \(-0.624535\pi\) | ||||
−0.381333 | + | 0.924438i | \(0.624535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.75540 | −0.549766 | −0.274883 | − | 0.961478i | \(-0.588639\pi\) | ||||
−0.274883 | + | 0.961478i | \(0.588639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.4609 | −2.36015 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.80086 | −0.336954 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.757038 | −0.0528738 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30.5157 | −2.12099 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.38796 | 0.303522 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.6690 | −1.83597 | −0.917985 | − | 0.396615i | \(-0.870185\pi\) | ||||
−0.917985 | + | 0.396615i | \(0.870185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.4850 | −1.40361 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.34808 | −0.0919380 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.71150 | −0.523491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.5442 | 2.67215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.50574 | −0.504891 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3667 | 0.828135 | 0.414067 | − | 0.910246i | \(-0.364108\pi\) | ||||
0.414067 | + | 0.910246i | \(0.364108\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.4058 | −1.62705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9197 | 1.12300 | 0.561499 | − | 0.827477i | \(-0.310225\pi\) | ||||
0.561499 | + | 0.827477i | \(0.310225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3415 | 1.07988 | 0.539939 | − | 0.841704i | \(-0.318447\pi\) | ||||
0.539939 | + | 0.841704i | \(0.318447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.4924 | −0.756144 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.98952 | −0.588923 | −0.294461 | − | 0.955663i | \(-0.595140\pi\) | ||||
−0.294461 | + | 0.955663i | \(0.595140\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.14539 | −0.139950 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.81775 | 0.183032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1449 | 1.23838 | 0.619191 | − | 0.785240i | \(-0.287461\pi\) | ||||
0.619191 | + | 0.785240i | \(0.287461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0048 | −0.644466 | −0.322233 | − | 0.946660i | \(-0.604433\pi\) | ||||
−0.322233 | + | 0.946660i | \(0.604433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7583 | 0.946743 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.49345 | 0.0954129 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17004 | −0.0744482 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.7801 | −1.12677 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.33666 | 0.273727 | 0.136864 | − | 0.990590i | \(-0.456298\pi\) | ||||
0.136864 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.1074 | −1.70422 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.39941 | 0.275502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.4324 | 1.77356 | 0.886782 | − | 0.462187i | \(-0.152935\pi\) | ||||
0.886782 | + | 0.462187i | \(0.152935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3886 | −0.645519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.5136 | −1.57926 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.4259 | −1.07453 | −0.537263 | − | 0.843415i | \(-0.680542\pi\) | ||||
−0.537263 | + | 0.843415i | \(0.680542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.50447 | −0.153849 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.5513 | −1.01292 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.8170 | −1.57409 | −0.787045 | − | 0.616895i | \(-0.788390\pi\) | ||||
−0.787045 | + | 0.616895i | \(0.788390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2688 | −1.41348 | −0.706739 | − | 0.707475i | \(-0.749834\pi\) | ||||
−0.706739 | + | 0.707475i | \(0.749834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.06443 | 0.185468 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.6799 | −1.30735 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.8827 | 0.713962 | 0.356981 | − | 0.934112i | \(-0.383806\pi\) | ||||
0.356981 | + | 0.934112i | \(0.383806\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −40.9820 | −2.45353 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6975 | −0.638157 | −0.319079 | − | 0.947728i | \(-0.603373\pi\) | ||||
−0.319079 | + | 0.947728i | \(0.603373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.06296 | 0.538737 | 0.269368 | − | 0.963037i | \(-0.413185\pi\) | ||||
0.269368 | + | 0.963037i | \(0.413185\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.685809 | 0.0406238 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.89109 | 0.170656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.1512 | 1.42066 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.5791 | 1.73396 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.2216 | 1.64872 | 0.824361 | − | 0.566064i | \(-0.191535\pi\) | ||||
0.824361 | + | 0.566064i | \(0.191535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.67969 | 0.156017 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.9826 | −1.39161 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.22814 | 0.418014 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.14823 | 0.296739 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.21986 | −0.184976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0872742 | −0.00499731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.9355 | 1.76558 | 0.882791 | − | 0.469765i | \(-0.155661\pi\) | ||||
0.882791 | + | 0.469765i | \(0.155661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 41.9766 | 2.38796 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.88612 | −0.220361 | −0.110181 | − | 0.993912i | \(-0.535143\pi\) | ||||
−0.110181 | + | 0.993912i | \(0.535143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.03801 | −0.284765 | −0.142383 | − | 0.989812i | \(-0.545476\pi\) | ||||
−0.142383 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.11750 | −0.0629639 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8736 | 0.835386 | 0.417693 | − | 0.908588i | \(-0.362839\pi\) | ||||
0.417693 | + | 0.908588i | \(0.362839\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.6640 | −1.26894 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.2523 | 2.02341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.41492 | 0.356936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.78091 | 0.320667 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.37193 | −0.297068 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.19314 | 0.451703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.8329 | 1.58480 | 0.792399 | − | 0.610003i | \(-0.208832\pi\) | ||||
0.792399 | + | 0.610003i | \(0.208832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −55.2094 | −3.02545 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.89026 | −0.157912 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1520 | −1.64249 | −0.821243 | − | 0.570579i | \(-0.806719\pi\) | ||||
−0.821243 | + | 0.570579i | \(0.806719\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.1360 | −1.58245 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.4046 | −1.97142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.2099 | −0.659270 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.23670 | −0.228096 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0836 | 0.756045 | 0.378023 | − | 0.925796i | \(-0.376604\pi\) | ||||
0.378023 | + | 0.925796i | \(0.376604\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.47266 | −0.132358 | −0.0661792 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661792 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.39493 | 0.341336 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.95360 | 0.476552 | 0.238276 | − | 0.971197i | \(-0.423418\pi\) | ||||
0.238276 | + | 0.971197i | \(0.423418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.76944 | −0.0939123 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.8011 | −0.889210 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.84896 | 0.414252 | 0.207126 | − | 0.978314i | \(-0.433589\pi\) | ||||
0.207126 | + | 0.978314i | \(0.433589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.2583 | −1.22074 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.41572 | 0.178787 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8354 | −1.40079 | −0.700397 | − | 0.713753i | \(-0.746994\pi\) | ||||
−0.700397 | + | 0.713753i | \(0.746994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.3644 | 0.799839 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.56447 | 0.496563 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.5460 | −1.01205 | −0.506027 | − | 0.862517i | \(-0.668887\pi\) | ||||
−0.506027 | + | 0.862517i | \(0.668887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.81747 | −0.352052 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.04332 | 0.311247 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31232 | 0.426975 | 0.213488 | − | 0.976946i | \(-0.431518\pi\) | ||||
0.213488 | + | 0.976946i | \(0.431518\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.2087 | −0.984092 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.08070 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533246\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.992682 | −0.0505918 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.3597 | 1.39077 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.2795 | −0.926808 | −0.463404 | − | 0.886147i | \(-0.653372\pi\) | ||||
−0.463404 | + | 0.886147i | \(0.653372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.6292 | −2.00413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.0445 | −1.26333 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.243389 | 0.0122462 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.50119 | 0.276097 | 0.138048 | − | 0.990426i | \(-0.455917\pi\) | ||||
0.138048 | + | 0.990426i | \(0.455917\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.61907 | −0.131118 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.46487 | −0.222965 | −0.111482 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111482 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.70724 | 0.483552 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.141519 | −0.00703213 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.0429 | −2.43097 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5789 | 0.671432 | 0.335716 | − | 0.941963i | \(-0.391022\pi\) | ||||
0.335716 | + | 0.941963i | \(0.391022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.99847 | 0.443862 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2336 | −0.503562 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.53580 | −0.0753895 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0778 | −1.47292 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.8314 | 1.50621 | 0.753106 | − | 0.657899i | \(-0.228555\pi\) | ||||
0.753106 | + | 0.657899i | \(0.228555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4084 | −0.799697 | −0.399849 | − | 0.916581i | \(-0.630937\pi\) | ||||
−0.399849 | + | 0.916581i | \(0.630937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 43.5416 | 2.11706 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.6946 | −1.53741 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.333296 | 0.0161293 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.4666 | 0.698455 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.2586 | −1.93919 | −0.969594 | − | 0.244718i | \(-0.921305\pi\) | ||||
−0.969594 | + | 0.244718i | \(0.921305\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.477039 | 0.0229250 | 0.0114625 | − | 0.999934i | \(-0.496351\pi\) | ||||
0.0114625 | + | 0.999934i | \(0.496351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.54223 | −0.169837 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.17766 | −0.295518 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8587 | −1.28190 | −0.640948 | − | 0.767584i | \(-0.721459\pi\) | ||||
−0.640948 | + | 0.767584i | \(0.721459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.3101 | −1.44334 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0326 | −1.14182 | −0.570912 | − | 0.821011i | \(-0.693410\pi\) | ||||
−0.570912 | + | 0.821011i | \(0.693410\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.42966 | −0.0677724 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.7060 | 0.932063 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.9547 | −1.93277 | −0.966386 | − | 0.257097i | \(-0.917234\pi\) | ||||
−0.966386 | + | 0.257097i | \(0.917234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.6483 | 0.642674 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −59.1237 | −2.77787 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.264698 | 0.0124092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.32008 | 0.108529 | 0.0542644 | − | 0.998527i | \(-0.482719\pi\) | ||||
0.0542644 | + | 0.998527i | \(0.482719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.0610 | −1.63651 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.92454 | 0.229359 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1476 | −0.611021 | −0.305511 | − | 0.952189i | \(-0.598827\pi\) | ||||
−0.305511 | + | 0.952189i | \(0.598827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.68979 | −0.263858 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5271 | −0.764784 | −0.382392 | − | 0.924000i | \(-0.624900\pi\) | ||||
−0.382392 | + | 0.924000i | \(0.624900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0378 | 0.509677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.3107 | −1.02802 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.3039 | 1.11749 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.94076 | −0.226698 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 50.8294 | 2.32732 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.2636 | 0.925869 | 0.462934 | − | 0.886393i | \(-0.346797\pi\) | ||||
0.462934 | + | 0.886393i | \(0.346797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0772 | 0.596270 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.1797 | 0.736204 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.55496 | 0.116015 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7595 | 1.25791 | 0.628953 | − | 0.777444i | \(-0.283484\pi\) | ||||
0.628953 | + | 0.777444i | \(0.283484\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.9323 | −0.856149 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9007 | −0.943235 | −0.471617 | − | 0.881803i | \(-0.656330\pi\) | ||||
−0.471617 | + | 0.881803i | \(0.656330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.1333 | −1.49225 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.27550 | −0.237116 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.75742 | 0.303112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9602 | 0.848775 | 0.424387 | − | 0.905481i | \(-0.360490\pi\) | ||||
0.424387 | + | 0.905481i | \(0.360490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.7616 | 1.37433 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.88996 | 0.440972 | 0.220486 | − | 0.975390i | \(-0.429236\pi\) | ||||
0.220486 | + | 0.975390i | \(0.429236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.278123 | −0.0123763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.7732 | 1.45551 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.67539 | −0.251557 | −0.125779 | − | 0.992058i | \(-0.540143\pi\) | ||||
−0.125779 | + | 0.992058i | \(0.540143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0445 | −0.577054 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.46555 | −0.241310 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.62583 | 0.159773 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.6783 | 1.70107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 68.2488 | 2.99579 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6584 | −1.38698 | −0.693490 | − | 0.720466i | \(-0.743928\pi\) | ||||
−0.693490 | + | 0.720466i | \(0.743928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.52863 | −0.0668423 | −0.0334212 | − | 0.999441i | \(-0.510640\pi\) | ||||
−0.0334212 | + | 0.999441i | \(0.510640\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.9402 | 0.564757 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −53.2211 | −2.31835 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1635 | 0.659282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −54.3854 | −2.36012 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.63931 | −0.157636 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.13138 | 0.135381 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 60.2264 | 2.59896 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.9247 | −1.15973 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.5133 | −1.22588 | −0.612942 | − | 0.790128i | \(-0.710014\pi\) | ||||
−0.612942 | + | 0.790128i | \(0.710014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.8646 | 1.96824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.464013 | −0.0198761 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.90948 | −0.252671 | −0.126336 | − | 0.991988i | \(-0.540322\pi\) | ||||
−0.126336 | + | 0.991988i | \(0.540322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.77127 | 0.0755958 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.16503 | −0.220038 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.929492 | −0.0395260 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.66508 | −0.325364 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.9039 | −0.970467 | −0.485234 | − | 0.874385i | \(-0.661265\pi\) | ||||
−0.485234 | + | 0.874385i | \(0.661265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.48060 | −0.274100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −79.3151 | −3.34869 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6582 | −0.491333 | −0.245667 | − | 0.969354i | \(-0.579007\pi\) | ||||
−0.245667 | + | 0.969354i | \(0.579007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.51669 | −0.105878 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.540454 | 0.0226969 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.57711 | 0.0661160 | 0.0330580 | − | 0.999453i | \(-0.489475\pi\) | ||||
0.0330580 | + | 0.999453i | \(0.489475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3873 | 1.27167 | 0.635834 | − | 0.771826i | \(-0.280656\pi\) | ||||
0.635834 | + | 0.771826i | \(0.280656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.9195 | 2.33607 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.5224 | 1.27287 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.6605 | −1.02663 | −0.513315 | − | 0.858200i | \(-0.671583\pi\) | ||||
−0.513315 | + | 0.858200i | \(0.671583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.3878 | 2.13560 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.86515 | 0.243327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.1521 | 1.87001 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.40671 | 0.0581602 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.9821 | −1.11367 | −0.556835 | − | 0.830623i | \(-0.687985\pi\) | ||||
−0.556835 | + | 0.830623i | \(0.687985\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.29647 | −0.341850 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.1626 | 1.24073 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.7153 | −0.645351 | −0.322676 | − | 0.946510i | \(-0.604582\pi\) | ||||
−0.322676 | + | 0.946510i | \(0.604582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.45124 | −0.0594949 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.8527 | 0.894373 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.2265 | 0.703856 | 0.351928 | − | 0.936027i | \(-0.385526\pi\) | ||||
0.351928 | + | 0.936027i | \(0.385526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.2061 | −1.47688 | −0.738438 | − | 0.674321i | \(-0.764436\pi\) | ||||
−0.738438 | + | 0.674321i | \(0.764436\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 58.6591 | 2.38878 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00899 | −0.0816770 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7548 | 0.436525 | 0.218263 | − | 0.975890i | \(-0.429961\pi\) | ||||
0.218263 | + | 0.975890i | \(0.429961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.5276 | 0.548166 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.3135 | −0.417241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.77027 | −0.233059 | −0.116530 | − | 0.993187i | \(-0.537177\pi\) | ||||
−0.116530 | + | 0.993187i | \(0.537177\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.13314 | 0.0860165 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.48806 | −0.0599069 | −0.0299535 | − | 0.999551i | \(-0.509536\pi\) | ||||
−0.0299535 | + | 0.999551i | \(0.509536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.1127 | −1.53188 | −0.765940 | − | 0.642913i | \(-0.777726\pi\) | ||||
−0.765940 | + | 0.642913i | \(0.777726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.7643 | 1.35491 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.45980 | 0.218742 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1149 | 0.964597 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.3642 | −0.493777 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −71.6975 | −2.85877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.2918 | 0.489329 | 0.244664 | − | 0.969608i | \(-0.421322\pi\) | ||||
0.244664 | + | 0.969608i | \(0.421322\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 75.1465 | 2.98680 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.65920 | −0.0658432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.17945 | 0.284460 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.9116 | 1.42064 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1875 | −1.42932 | −0.714659 | − | 0.699473i | \(-0.753418\pi\) | ||||
−0.714659 | + | 0.699473i | \(0.753418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.1619 | −0.755672 | −0.377836 | − | 0.925872i | \(-0.623332\pi\) | ||||
−0.377836 | + | 0.925872i | \(0.623332\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.79853 | 0.149567 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.0331 | 1.61318 | 0.806589 | − | 0.591113i | \(-0.201311\pi\) | ||||
0.806589 | + | 0.591113i | \(0.201311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.3109 | −1.89637 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.7290 | 0.851628 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.30259 | 0.364038 | 0.182019 | − | 0.983295i | \(-0.441737\pi\) | ||||
0.182019 | + | 0.983295i | \(0.441737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.16328 | −0.0845262 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −69.3235 | −2.70457 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.9866 | 0.466931 | 0.233466 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233466 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0263 | −0.584455 | −0.292228 | − | 0.956349i | \(-0.594396\pi\) | ||||
−0.292228 | + | 0.956349i | \(0.594396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.1493 | 0.821369 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.226229 | −0.00877277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.9078 | 1.23548 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.8462 | −1.34723 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.57343 | 0.0607416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.447914 | −0.0172658 | −0.00863291 | − | 0.999963i | \(-0.502748\pi\) | ||||
−0.00863291 | + | 0.999963i | \(0.502748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.0040 | 1.03938 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.7839 | −0.606624 | −0.303312 | − | 0.952891i | \(-0.598092\pi\) | ||||
−0.303312 | + | 0.952891i | \(0.598092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.75728 | −0.374450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.6753 | −1.82692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.9490 | 1.60513 | 0.802566 | − | 0.596563i | \(-0.203467\pi\) | ||||
0.802566 | + | 0.596563i | \(0.203467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.777264 | 0.0296977 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.0462 | −1.75677 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0398 | −0.458678 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9636 | 0.493160 | 0.246580 | − | 0.969122i | \(-0.420693\pi\) | ||||
0.246580 | + | 0.969122i | \(0.420693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20.1469 | 0.765318 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.59804 | −0.0985492 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.9529 | 0.755772 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.3302 | 0.958075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.7159 | −1.57559 | −0.787795 | − | 0.615938i | \(-0.788777\pi\) | ||||
−0.787795 | + | 0.615938i | \(0.788777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.1767 | −0.421537 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.04516 | 0.227674 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.06214 | 0.0399458 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.9243 | −0.673160 | −0.336580 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336580 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.93969 | −0.185253 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.2528 | 1.91943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.24959 | 0.0467320 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −53.9455 | −2.01463 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7196 | −0.959180 | −0.479590 | − | 0.877493i | \(-0.659215\pi\) | ||||
−0.479590 | + | 0.877493i | \(0.659215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8469 | −0.515684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.1910 | 1.04843 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.5192 | 0.947759 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.8235 | −1.47697 | −0.738485 | − | 0.674270i | \(-0.764459\pi\) | ||||
−0.738485 | + | 0.674270i | \(0.764459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.3294 | −1.60479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.5307 | 1.31415 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.2629 | 1.19166 | 0.595829 | − | 0.803111i | \(-0.296823\pi\) | ||||
0.595829 | + | 0.803111i | \(0.296823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.20816 | −0.155220 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.1073 | 1.91940 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.8038 | −1.90563 | −0.952816 | − | 0.303548i | \(-0.901829\pi\) | ||||
−0.952816 | + | 0.303548i | \(0.901829\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.29689 | 0.121114 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.9802 | −0.549570 | −0.274785 | − | 0.961506i | \(-0.588607\pi\) | ||||
−0.274785 | + | 0.961506i | \(0.588607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.70215 | 0.0623621 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.1697 | 1.14044 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.9586 | −0.436957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6191 | −0.460477 | −0.230238 | − | 0.973134i | \(-0.573951\pi\) | ||||
−0.230238 | + | 0.973134i | \(0.573951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.2196 | −0.445307 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.10695 | −0.185861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.6477 | −0.386997 | −0.193499 | − | 0.981101i | \(-0.561984\pi\) | ||||
−0.193499 | + | 0.981101i | \(0.561984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 76.3816 | 2.77248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.9322 | 0.976293 | 0.488146 | − | 0.872762i | \(-0.337673\pi\) | ||||
0.488146 | + | 0.872762i | \(0.337673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.77204 | 0.0641523 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.71245 | −0.278844 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.8821 | 0.465144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.3676 | 0.770536 | 0.385268 | − | 0.922805i | \(-0.374109\pi\) | ||||
0.385268 | + | 0.922805i | \(0.374109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −80.1153 | −2.88528 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.1433 | −0.364829 | −0.182415 | − | 0.983222i | \(-0.558391\pi\) | ||||
−0.182415 | + | 0.983222i | \(0.558391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.9909 | 1.47244 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.2726 | 1.05015 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.11040 | 0.111442 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.9005 | 1.14149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.2297 | 1.00885 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.92714 | −0.0687827 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.2597 | 1.00735 | 0.503675 | − | 0.863893i | \(-0.331981\pi\) | ||||
0.503675 | + | 0.863893i | \(0.331981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.1017 | 1.74807 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.61113 | 0.341732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.419553 | −0.0148988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.05697 | 0.250285 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.3864 | 1.89104 | 0.945522 | − | 0.325557i | \(-0.105552\pi\) | ||||
0.945522 | + | 0.325557i | \(0.105552\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.5452 | 2.00043 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.0155 | 1.02521 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61.5806 | −2.17313 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39756 | 0.0492576 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.7457 | 2.56077 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.13616 | −0.0399453 | −0.0199726 | − | 0.999801i | \(-0.506358\pi\) | ||||
−0.0199726 | + | 0.999801i | \(0.506358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5890 | −1.39016 | −0.695078 | − | 0.718934i | \(-0.744630\pi\) | ||||
−0.695078 | + | 0.718934i | \(0.744630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.5655 | 2.29948 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.63532 | −0.0572829 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.53876 | 0.193777 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.37215 | −0.187718 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1082 | −0.387677 | −0.193839 | − | 0.981033i | \(-0.562094\pi\) | ||||
−0.193839 | + | 0.981033i | \(0.562094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.81783 | −0.307370 | −0.153685 | − | 0.988120i | \(-0.549114\pi\) | ||||
−0.153685 | + | 0.988120i | \(0.549114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 61.0884 | 2.12682 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.3086 | 1.67985 | 0.839927 | − | 0.542699i | \(-0.182598\pi\) | ||||
0.839927 | + | 0.542699i | \(0.182598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9899 | −0.729008 | −0.364504 | − | 0.931202i | \(-0.618761\pi\) | ||||
−0.364504 | + | 0.931202i | \(0.618761\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.4824 | −1.16149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.3622 | −1.36382 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.65710 | 0.0919528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.3447 | 1.56734 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.6224 | −0.435774 | −0.217887 | − | 0.975974i | \(-0.569916\pi\) | ||||
−0.217887 | + | 0.975974i | \(0.569916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.32244 | −0.0800841 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.1427 | 1.03817 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.83086 | 0.0973846 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.67224 | 0.263621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.5371 | −0.876431 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.0458 | 2.36686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2597 | 0.967592 | 0.483796 | − | 0.875181i | \(-0.339258\pi\) | ||||
0.483796 | + | 0.875181i | \(0.339258\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.20227 | −0.0411167 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.10377 | 0.242660 | 0.121330 | − | 0.992612i | \(-0.461284\pi\) | ||||
0.121330 | + | 0.992612i | \(0.461284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.6812 | 0.876232 | 0.438116 | − | 0.898918i | \(-0.355646\pi\) | ||||
0.438116 | + | 0.898918i | \(0.355646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.14636 | −0.277627 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.1636 | −1.77567 | −0.887835 | − | 0.460161i | \(-0.847792\pi\) | ||||
−0.887835 | + | 0.460161i | \(0.847792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.89515 | 0.200441 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −68.0518 | −2.31116 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.38796 | −0.148851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8944 | −0.470792 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −51.8540 | −1.75499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.24888 | 0.0760262 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2518 | −0.852692 | −0.426346 | − | 0.904560i | \(-0.640199\pi\) | ||||
−0.426346 | + | 0.904560i | \(0.640199\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −79.5212 | −2.68218 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.7053 | −1.80938 | −0.904689 | − | 0.426072i | \(-0.859897\pi\) | ||||
−0.904689 | + | 0.426072i | \(0.859897\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.33046 | −0.246690 | −0.123345 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123345 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.55067 | −0.253813 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.5751 | 1.56384 | 0.781920 | − | 0.623379i | \(-0.214241\pi\) | ||||
0.781920 | + | 0.623379i | \(0.214241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.33639 | 0.212516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.55138 | 0.0854746 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.81464 | 0.294971 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.20220 | 0.173890 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.3671 | −0.680036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.8515 | 1.42918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.0095 | 2.19909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.5064 | −0.482743 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.96167 | 0.131690 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.2496 | 1.73492 | 0.867460 | − | 0.497508i | \(-0.165751\pi\) | ||||
0.867460 | + | 0.497508i | \(0.165751\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.64462 | 0.187220 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.5725 | −1.31109 | −0.655547 | − | 0.755154i | \(-0.727562\pi\) | ||||
−0.655547 | + | 0.755154i | \(0.727562\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.6883 | 0.916349 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.245916 | 0.00812975 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.26145 | 0.272817 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.1585 | −0.664968 | −0.332484 | − | 0.943109i | \(-0.607887\pi\) | ||||
−0.332484 | + | 0.943109i | \(0.607887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −87.1684 | −2.87230 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.50624 | −0.279986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.2214 | 1.81567 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −73.5876 | −2.41694 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.9692 | 0.392696 | 0.196348 | − | 0.980534i | \(-0.437092\pi\) | ||||
0.196348 | + | 0.980534i | \(0.437092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.13604 | −0.201101 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9501 | 0.358490 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.85103 | −0.224053 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.8914 | 0.486480 | 0.243240 | − | 0.969966i | \(-0.421790\pi\) | ||||
0.243240 | + | 0.969966i | \(0.421790\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1958 | 0.463263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8992 | −0.453103 | −0.226551 | − | 0.973999i | \(-0.572745\pi\) | ||||
−0.226551 | + | 0.973999i | \(0.572745\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.2150 | −0.625726 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.23646 | 0.0402221 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.8171 | −1.45636 | −0.728180 | − | 0.685386i | \(-0.759633\pi\) | ||||
−0.728180 | + | 0.685386i | \(0.759633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.4204 | 0.533028 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.9101 | −1.35903 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.2210 | 1.10853 | 0.554264 | − | 0.832341i | \(-0.313000\pi\) | ||||
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.83018 | 0.156301 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 63.8613 | 2.06434 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.96833 | −0.0958525 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8313 | 1.22037 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −63.5526 | −2.04796 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.43874 | 0.142888 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2353 | 1.55114 | 0.775571 | − | 0.631260i | \(-0.217462\pi\) | ||||
0.775571 | + | 0.631260i | \(0.217462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.0756 | −0.580672 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.7510 | 1.14730 | 0.573652 | − | 0.819099i | \(-0.305526\pi\) | ||||
0.573652 | + | 0.819099i | \(0.305526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.92179 | 0.318078 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.2891 | −0.521670 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.06258 | −0.0659876 | −0.0329938 | − | 0.999456i | \(-0.510504\pi\) | ||||
−0.0329938 | + | 0.999456i | \(0.510504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.7747 | 0.823764 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.41733 | 0.300672 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.1827 | −0.739413 | −0.369707 | − | 0.929149i | \(-0.620542\pi\) | ||||
−0.369707 | + | 0.929149i | \(0.620542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.60537 | 0.0830140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.0862 | −0.734841 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.2166 | −1.08802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.8141 | −0.407053 | −0.203526 | − | 0.979069i | \(-0.565240\pi\) | ||||
−0.203526 | + | 0.979069i | \(0.565240\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −81.2437 | −2.57819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.88758 | 0.0598404 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.1866 | 0.956019 | 0.478010 | − | 0.878355i | \(-0.341358\pi\) | ||||
0.478010 | + | 0.878355i | \(0.341358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 61.0867 | 1.93270 |
(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 | 6004.2.a.g.1.2 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.2 | ✓ | 27 | 1.1 | even | 1 | trivial |