Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 93x^{6} - 119x^{5} - 174x^{4} + 107x^{3} + 51x^{2} - 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.672934\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | −0.672934 | −0.388519 | −0.194259 | − | 0.980950i | \(-0.562230\pi\) | ||||
−0.194259 | + | 0.980950i | \(0.562230\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.538228 | 0.240703 | 0.120351 | − | 0.992731i | \(-0.461598\pi\) | ||||
0.120351 | + | 0.992731i | \(0.461598\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.54716 | −0.849053 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.362192 | −0.0935176 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70606 | −0.413779 | −0.206890 | − | 0.978364i | \(-0.566334\pi\) | ||||
−0.206890 | + | 0.978364i | \(0.566334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.21645 | 0.967320 | 0.483660 | − | 0.875256i | \(-0.339307\pi\) | ||||
0.483660 | + | 0.875256i | \(0.339307\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.672934 | 0.146846 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.56036 | 0.742387 | 0.371194 | − | 0.928555i | \(-0.378949\pi\) | ||||
0.371194 | + | 0.928555i | \(0.378949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71031 | −0.942062 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.73287 | 0.718392 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.32798 | 1.73216 | 0.866081 | − | 0.499903i | \(-0.166631\pi\) | ||||
0.866081 | + | 0.499903i | \(0.166631\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.69704 | −1.02322 | −0.511609 | − | 0.859218i | \(-0.670951\pi\) | ||||
−0.511609 | + | 0.859218i | \(0.670951\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.672934 | 0.117143 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.538228 | −0.0909772 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.10326 | −1.33217 | −0.666084 | − | 0.745877i | \(-0.732031\pi\) | ||||
−0.666084 | + | 0.745877i | \(0.732031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.672934 | 0.107756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.73633 | −1.05204 | −0.526019 | − | 0.850473i | \(-0.676316\pi\) | ||||
−0.526019 | + | 0.850473i | \(0.676316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5566 | −1.91486 | −0.957432 | − | 0.288660i | \(-0.906790\pi\) | ||||
−0.957432 | + | 0.288660i | \(0.906790\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.37095 | −0.204370 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2622 | 1.78863 | 0.894313 | − | 0.447441i | \(-0.147665\pi\) | ||||
0.894313 | + | 0.447441i | \(0.147665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.14806 | 0.160761 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.52462 | 1.03359 | 0.516793 | − | 0.856110i | \(-0.327126\pi\) | ||||
0.516793 | + | 0.856110i | \(0.327126\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.538228 | −0.0725747 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.83739 | −0.375822 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63094 | 0.212330 | 0.106165 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106165 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.27727 | 1.05980 | 0.529898 | − | 0.848061i | \(-0.322230\pi\) | ||||
0.529898 | + | 0.848061i | \(0.322230\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.54716 | 0.320912 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.538228 | −0.0667590 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.26536 | −1.00977 | −0.504887 | − | 0.863185i | \(-0.668466\pi\) | ||||
−0.504887 | + | 0.863185i | \(0.668466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.39589 | −0.288431 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.58999 | 1.13812 | 0.569061 | − | 0.822295i | \(-0.307307\pi\) | ||||
0.569061 | + | 0.822295i | \(0.307307\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50579 | 0.878486 | 0.439243 | − | 0.898368i | \(-0.355247\pi\) | ||||
0.439243 | + | 0.898368i | \(0.355247\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.16973 | 0.366009 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6682 | 1.42529 | 0.712644 | − | 0.701526i | \(-0.247498\pi\) | ||||
0.712644 | + | 0.701526i | \(0.247498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.12950 | 0.569945 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4121 | −1.14288 | −0.571438 | − | 0.820645i | \(-0.693614\pi\) | ||||
−0.571438 | + | 0.820645i | \(0.693614\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.918247 | −0.0995979 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.27712 | −0.672977 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0335338 | 0.00355458 | 0.00177729 | − | 0.999998i | \(-0.499434\pi\) | ||||
0.00177729 | + | 0.999998i | \(0.499434\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.83373 | 0.397540 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.26941 | 0.232837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7427 | 1.29382 | 0.646910 | − | 0.762566i | \(-0.276061\pi\) | ||||
0.646910 | + | 0.762566i | \(0.276061\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.54716 | 0.255999 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1490 | 1.10936 | 0.554681 | − | 0.832063i | \(-0.312840\pi\) | ||||
0.554681 | + | 0.832063i | \(0.312840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.61935 | 0.553691 | 0.276846 | − | 0.960914i | \(-0.410711\pi\) | ||||
0.276846 | + | 0.960914i | \(0.410711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.362192 | 0.0353463 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.13010 | 0.689292 | 0.344646 | − | 0.938733i | \(-0.387999\pi\) | ||||
0.344646 | + | 0.938733i | \(0.387999\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3848 | 1.47360 | 0.736798 | − | 0.676112i | \(-0.236337\pi\) | ||||
0.736798 | + | 0.676112i | \(0.236337\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.45296 | 0.517572 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5604 | 1.18158 | 0.590789 | − | 0.806826i | \(-0.298816\pi\) | ||||
0.590789 | + | 0.806826i | \(0.298816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.91629 | 0.178695 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.54716 | 0.235485 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.70606 | 0.156394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.53311 | 0.408736 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.22636 | −0.467460 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4061 | −1.54455 | −0.772273 | − | 0.635291i | \(-0.780880\pi\) | ||||
−0.772273 | + | 0.635291i | \(0.780880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.44976 | 0.743960 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.8268 | −1.38280 | −0.691398 | − | 0.722474i | \(-0.743005\pi\) | ||||
−0.691398 | + | 0.722474i | \(0.743005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.21645 | −0.365612 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00914 | 0.172919 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.89307 | −0.503479 | −0.251739 | − | 0.967795i | \(-0.581003\pi\) | ||||
−0.251739 | + | 0.967795i | \(0.581003\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8018 | −1.00102 | −0.500509 | − | 0.865731i | \(-0.666854\pi\) | ||||
−0.500509 | + | 0.865731i | \(0.666854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.25165 | −0.694915 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.02058 | 0.416937 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.672934 | −0.0555027 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.5371 | −1.68246 | −0.841231 | − | 0.540676i | \(-0.818168\pi\) | ||||
−0.841231 | + | 0.540676i | \(0.818168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.85237 | 0.639017 | 0.319508 | − | 0.947583i | \(-0.396482\pi\) | ||||
0.319508 | + | 0.947583i | \(0.396482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.34560 | 0.351321 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.06631 | −0.246292 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0690 | −0.963215 | −0.481607 | − | 0.876387i | \(-0.659947\pi\) | ||||
−0.481607 | + | 0.876387i | \(0.659947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.06357 | −0.401567 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.56036 | −0.280596 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3458 | 1.59361 | 0.796804 | − | 0.604237i | \(-0.206522\pi\) | ||||
0.796804 | + | 0.604237i | \(0.206522\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.362192 | 0.0281966 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.151712 | −0.0117398 | −0.00586990 | − | 0.999983i | \(-0.501868\pi\) | ||||
−0.00586990 | + | 0.999983i | \(0.501868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.7400 | −0.821306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.52069 | 0.723845 | 0.361922 | − | 0.932208i | \(-0.382121\pi\) | ||||
0.361922 | + | 0.932208i | \(0.382121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.71031 | 0.356066 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.09751 | −0.0824943 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.92886 | 0.144170 | 0.0720850 | − | 0.997398i | \(-0.477035\pi\) | ||||
0.0720850 | + | 0.997398i | \(0.477035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7724 | 1.61833 | 0.809166 | − | 0.587580i | \(-0.199919\pi\) | ||||
0.809166 | + | 0.587580i | \(0.199919\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.57005 | −0.411750 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.36140 | −0.320657 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.70606 | 0.124759 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.73287 | −0.271526 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.82575 | −0.204464 | −0.102232 | − | 0.994761i | \(-0.532598\pi\) | ||||
−0.102232 | + | 0.994761i | \(0.532598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.2031 | 1.38227 | 0.691134 | − | 0.722727i | \(-0.257111\pi\) | ||||
0.691134 | + | 0.722727i | \(0.257111\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.362192 | 0.0259371 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8466 | 1.12903 | 0.564513 | − | 0.825424i | \(-0.309064\pi\) | ||||
0.564513 | + | 0.825424i | \(0.309064\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.57704 | 0.537122 | 0.268561 | − | 0.963263i | \(-0.413452\pi\) | ||||
0.268561 | + | 0.963263i | \(0.413452\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.56204 | 0.392316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.32798 | −0.654696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.62568 | −0.253229 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.06882 | −0.630326 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.21645 | −0.291658 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.62864 | 0.456334 | 0.228167 | − | 0.973622i | \(-0.426727\pi\) | ||||
0.228167 | + | 0.973622i | \(0.426727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.45343 | −0.442182 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.75831 | −0.460913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.69704 | 0.386740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.05090 | −0.341308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.70606 | 0.114762 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.9808 | −0.802291 | −0.401146 | − | 0.916014i | \(-0.631388\pi\) | ||||
−0.401146 | + | 0.916014i | \(0.631388\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.9979 | 0.799861 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1516 | −1.07202 | −0.536011 | − | 0.844211i | \(-0.680069\pi\) | ||||
−0.536011 | + | 0.844211i | \(0.680069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4721 | 1.68324 | 0.841621 | − | 0.540068i | \(-0.181602\pi\) | ||||
0.841621 | + | 0.540068i | \(0.181602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.672934 | −0.0442758 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.2582 | 1.32716 | 0.663579 | − | 0.748106i | \(-0.269037\pi\) | ||||
0.663579 | + | 0.748106i | \(0.269037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.59986 | 0.430528 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.52488 | −0.553751 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9477 | 0.772831 | 0.386415 | − | 0.922325i | \(-0.373713\pi\) | ||||
0.386415 | + | 0.922325i | \(0.373713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.9032 | 1.73299 | 0.866493 | − | 0.499189i | \(-0.166369\pi\) | ||||
0.866493 | + | 0.499189i | \(0.166369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6504 | −0.939826 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.538228 | 0.0343861 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.21645 | −0.268286 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.00666 | 0.444029 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.52645 | 0.0963490 | 0.0481745 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481745 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.56036 | −0.223838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.617919 | 0.0386956 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.33923 | 0.582565 | 0.291283 | − | 0.956637i | \(-0.405918\pi\) | ||||
0.291283 | + | 0.956637i | \(0.405918\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.10326 | 0.503512 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.7599 | −1.47070 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5211 | −0.648758 | −0.324379 | − | 0.945927i | \(-0.605155\pi\) | ||||
−0.324379 | + | 0.945927i | \(0.605155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.04996 | 0.248787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0225661 | −0.00138102 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1026 | 0.737908 | 0.368954 | − | 0.929448i | \(-0.379716\pi\) | ||||
0.368954 | + | 0.929448i | \(0.379716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7953 | 0.716515 | 0.358258 | − | 0.933623i | \(-0.383371\pi\) | ||||
0.358258 | + | 0.933623i | \(0.383371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.672934 | −0.0407278 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.71031 | 0.284042 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.83652 | −0.470851 | −0.235425 | − | 0.971892i | \(-0.575648\pi\) | ||||
−0.235425 | + | 0.971892i | \(0.575648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5113 | 0.868767 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.38147 | −0.0824113 | −0.0412057 | − | 0.999151i | \(-0.513120\pi\) | ||||
−0.0412057 | + | 0.999151i | \(0.513120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4298 | 1.27387 | 0.636934 | − | 0.770918i | \(-0.280202\pi\) | ||||
0.636934 | + | 0.770918i | \(0.280202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.52716 | −0.0904614 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.73633 | 0.397633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0894 | −0.828787 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.57497 | −0.502673 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.4337 | −0.960066 | −0.480033 | − | 0.877250i | \(-0.659375\pi\) | ||||
−0.480033 | + | 0.877250i | \(0.659375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.877818 | 0.0511085 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.73287 | −0.216603 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.56036 | −0.205901 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5566 | 0.723750 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.50251 | −0.431008 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.45506 | 0.255096 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4134 | 1.45042 | 0.725209 | − | 0.688529i | \(-0.241743\pi\) | ||||
0.725209 | + | 0.688529i | \(0.241743\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.78145 | −0.215119 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.2211 | −1.26004 | −0.630021 | − | 0.776578i | \(-0.716954\pi\) | ||||
−0.630021 | + | 0.776578i | \(0.716954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4758 | −0.987793 | −0.493896 | − | 0.869521i | \(-0.664428\pi\) | ||||
−0.493896 | + | 0.869521i | \(0.664428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.37095 | 0.0772445 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.35194 | 0.300595 | 0.150297 | − | 0.988641i | \(-0.451977\pi\) | ||||
0.150297 | + | 0.988641i | \(0.451977\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.32798 | −0.522267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.79808 | −0.267803 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.19349 | −0.400257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.71031 | 0.261281 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.3530 | −0.572520 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.2622 | −0.676037 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.5298 | −1.84297 | −0.921483 | − | 0.388419i | \(-0.873021\pi\) | ||||
−0.921483 | + | 0.388419i | \(0.873021\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.6403 | 1.13108 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.44865 | −0.243056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.5363 | 1.39105 | 0.695527 | − | 0.718500i | \(-0.255171\pi\) | ||||
0.695527 | + | 0.718500i | \(0.255171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.45229 | −0.459065 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.69704 | 0.308512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.28954 | −0.0694262 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.2720 | 1.03458 | 0.517288 | − | 0.855811i | \(-0.326942\pi\) | ||||
0.517288 | + | 0.855811i | \(0.326942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0534 | −0.698731 | −0.349365 | − | 0.936987i | \(-0.613603\pi\) | ||||
−0.349365 | + | 0.936987i | \(0.613603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.73287 | −0.199246 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3319 | 0.922485 | 0.461243 | − | 0.887274i | \(-0.347404\pi\) | ||||
0.461243 | + | 0.887274i | \(0.347404\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16160 | 0.273949 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.14806 | −0.0607619 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.598945 | 0.0316111 | 0.0158056 | − | 0.999875i | \(-0.494969\pi\) | ||||
0.0158056 | + | 0.999875i | \(0.494969\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.22156 | −0.0642927 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.672934 | −0.0353199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.03983 | 0.211454 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.57145 | 0.343027 | 0.171513 | − | 0.985182i | \(-0.445134\pi\) | ||||
0.171513 | + | 0.985182i | \(0.445134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.1585 | 0.893237 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.52462 | −0.390659 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7645 | 0.816253 | 0.408126 | − | 0.912925i | \(-0.366182\pi\) | ||||
0.408126 | + | 0.912925i | \(0.366182\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.51700 | 0.181617 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.32798 | −0.480416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.9448 | 0.613565 | 0.306783 | − | 0.951780i | \(-0.400747\pi\) | ||||
0.306783 | + | 0.951780i | \(0.400747\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7132 | 0.600084 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.4537 | 0.942942 | 0.471471 | − | 0.881882i | \(-0.343723\pi\) | ||||
0.471471 | + | 0.881882i | \(0.343723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.538228 | 0.0274306 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.9837 | 1.62582 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.4060 | 1.44024 | 0.720122 | − | 0.693848i | \(-0.244086\pi\) | ||||
0.720122 | + | 0.693848i | \(0.244086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.07418 | −0.307184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.6504 | 0.537242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.81840 | 0.343071 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.07267 | −0.104024 | −0.0520122 | − | 0.998646i | \(-0.516563\pi\) | ||||
−0.0520122 | + | 0.998646i | \(0.516563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.83739 | 0.142047 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.8582 | 0.692045 | 0.346022 | − | 0.938226i | \(-0.387532\pi\) | ||||
0.346022 | + | 0.938226i | \(0.387532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.69704 | 0.283790 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.76084 | 0.137187 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.10326 | 0.401664 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5491 | −0.917192 | −0.458596 | − | 0.888645i | \(-0.651647\pi\) | ||||
−0.458596 | + | 0.888645i | \(0.651647\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.96565 | 0.195611 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.63094 | −0.0802533 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.60408 | −0.275094 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.94185 | 0.388914 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.4582 | −0.999450 | −0.499725 | − | 0.866184i | \(-0.666566\pi\) | ||||
−0.499725 | + | 0.866184i | \(0.666566\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.02752 | −0.245026 | −0.122513 | − | 0.992467i | \(-0.539095\pi\) | ||||
−0.122513 | + | 0.992467i | \(0.539095\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.2338 | −1.51864 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.03605 | 0.389806 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.27727 | −0.400565 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.672934 | −0.0324896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.12654 | 0.198769 | 0.0993843 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993843 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.7599 | −1.67045 | −0.835227 | − | 0.549905i | \(-0.814664\pi\) | ||||
−0.835227 | + | 0.549905i | \(0.814664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.37852 | −0.161988 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.0121 | 0.718126 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.778157 | −0.0371394 | −0.0185697 | − | 0.999828i | \(-0.505911\pi\) | ||||
−0.0185697 | + | 0.999828i | \(0.505911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.54716 | −0.121293 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6935 | 1.64834 | 0.824169 | − | 0.566343i | \(-0.191642\pi\) | ||||
0.824169 | + | 0.566343i | \(0.191642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0180489 | 0.000855598 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8201 | 0.653668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4109 | −0.916056 | −0.458028 | − | 0.888938i | \(-0.651444\pi\) | ||||
−0.458028 | + | 0.888938i | \(0.651444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.73633 | 0.317201 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.28413 | −0.248270 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.538228 | 0.0252325 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2186 | −0.524783 | −0.262391 | − | 0.964962i | \(-0.584511\pi\) | ||||
−0.262391 | + | 0.964962i | \(0.584511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.36849 | −0.297255 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.58868 | −0.260291 | −0.130145 | − | 0.991495i | \(-0.541544\pi\) | ||||
−0.130145 | + | 0.991495i | \(0.541544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4767 | −1.04458 | −0.522290 | − | 0.852768i | \(-0.674922\pi\) | ||||
−0.522290 | + | 0.852768i | \(0.674922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.06342 | 0.0956889 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.2930 | −0.615129 | −0.307564 | − | 0.951527i | \(-0.599514\pi\) | ||||
−0.307564 | + | 0.951527i | \(0.599514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.26536 | 0.381659 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.12167 | 0.374227 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.5566 | 0.577353 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8608 | −0.911275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.1664 | −0.877569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4999 | 0.525445 | 0.262723 | − | 0.964871i | \(-0.415380\pi\) | ||||
0.262723 | + | 0.964871i | \(0.415380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.10326 | 0.369477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.39589 | 0.109017 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.85846 | 0.311426 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4335 | −0.744671 | −0.372335 | − | 0.928098i | \(-0.621443\pi\) | ||||
−0.372335 | + | 0.928098i | \(0.621443\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.6914 | −0.619147 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4190 | −1.14714 | −0.573572 | − | 0.819155i | \(-0.694443\pi\) | ||||
−0.573572 | + | 0.819155i | \(0.694443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.9141 | −0.716733 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.37095 | 0.0616198 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.58999 | −0.430170 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0845 | 0.451446 | 0.225723 | − | 0.974191i | \(-0.427526\pi\) | ||||
0.225723 | + | 0.974191i | \(0.427526\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.102092 | 0.00456113 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.2866 | −1.08289 | −0.541443 | − | 0.840738i | \(-0.682122\pi\) | ||||
−0.541443 | + | 0.840738i | \(0.682122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00068 | 0.267027 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.672934 | −0.0298860 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3881 | 0.460444 | 0.230222 | − | 0.973138i | \(-0.426055\pi\) | ||||
0.230222 | + | 0.973138i | \(0.426055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.50579 | −0.332036 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.7395 | 0.694914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.02449 | 0.133275 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.2622 | −0.539291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.40680 | −0.281227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4927 | −1.81783 | −0.908915 | − | 0.416981i | \(-0.863088\pi\) | ||||
−0.908915 | + | 0.416981i | \(0.863088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.19012 | 0.0957674 | 0.0478837 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478837 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.16973 | −0.138338 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.71947 | 0.423387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.3238 | −0.448861 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.15427 | −0.180280 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.73633 | 0.291783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.83762 | 0.165915 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.29800 | −0.0560127 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0027 | 1.71985 | 0.859925 | − | 0.510420i | \(-0.170510\pi\) | ||||
0.859925 | + | 0.510420i | \(0.170510\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.6514 | −0.628752 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.28053 | 0.354699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.70909 | 0.329617 | 0.164809 | − | 0.986326i | \(-0.447299\pi\) | ||||
0.164809 | + | 0.986326i | \(0.447299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.0835 | −0.899823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.3310 | 1.67556 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6682 | −0.538708 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.93493 | 0.124581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.8851 | 1.64761 | 0.823807 | − | 0.566871i | \(-0.191846\pi\) | ||||
0.823807 | + | 0.566871i | \(0.191846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5566 | 0.531087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.14806 | −0.0484712 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.3929 | −1.70236 | −0.851179 | − | 0.524875i | \(-0.824112\pi\) | ||||
−0.851179 | + | 0.524875i | \(0.824112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.76034 | 0.284409 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.12950 | −0.215419 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.1163 | 0.424099 | 0.212049 | − | 0.977259i | \(-0.431986\pi\) | ||||
0.212049 | + | 0.977259i | \(0.431986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.2032 | 1.76615 | 0.883074 | − | 0.469234i | \(-0.155470\pi\) | ||||
0.883074 | + | 0.469234i | \(0.155470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.90154 | 0.0794382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7704 | −0.699375 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0021 | −1.41553 | −0.707764 | − | 0.706449i | \(-0.750296\pi\) | ||||
−0.707764 | + | 0.706449i | \(0.750296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9224 | −0.537037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.4121 | 0.431967 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.52462 | −0.311638 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.37095 | 0.0566819 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.7956 | −0.486857 | −0.243428 | − | 0.969919i | \(-0.578272\pi\) | ||||
−0.243428 | + | 0.969919i | \(0.578272\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0213 | −0.989780 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.6637 | −0.438647 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.8832 | −1.88420 | −0.942099 | − | 0.335334i | \(-0.891151\pi\) | ||||
−0.942099 | + | 0.335334i | \(0.891151\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.918247 | 0.0376445 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.09885 | −0.208682 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.7991 | 1.42185 | 0.710927 | − | 0.703266i | \(-0.248276\pi\) | ||||
0.710927 | + | 0.703266i | \(0.248276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8665 | 1.46302 | 0.731512 | − | 0.681828i | \(-0.238815\pi\) | ||||
0.731512 | + | 0.681828i | \(0.238815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.0532 | 0.857352 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.538228 | 0.0218821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5866 | 0.510874 | 0.255437 | − | 0.966826i | \(-0.417781\pi\) | ||||
0.255437 | + | 0.966826i | \(0.417781\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.27712 | 0.254362 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2622 | −0.496076 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3997 | −1.14705 | −0.573527 | − | 0.819186i | \(-0.694425\pi\) | ||||
−0.573527 | + | 0.819186i | \(0.694425\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.43985 | 0.0983841 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.3564 | −1.06107 | −0.530534 | − | 0.847663i | \(-0.678009\pi\) | ||||
−0.530534 | + | 0.847663i | \(0.678009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1729 | 0.449076 | 0.224538 | − | 0.974465i | \(-0.427913\pi\) | ||||
0.224538 | + | 0.974465i | \(0.427913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.2904 | 0.533325 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0335338 | −0.00134351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.7386 | 0.829543 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83739 | 0.113314 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8246 | 0.551223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.1256 | −1.35852 | −0.679259 | − | 0.733898i | \(-0.737699\pi\) | ||||
−0.679259 | + | 0.733898i | \(0.737699\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.46063 | −0.177294 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.36847 | −0.371776 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.4272 | −0.966327 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.35218 | 0.211398 | 0.105699 | − | 0.994398i | \(-0.466292\pi\) | ||||
0.105699 | + | 0.994398i | \(0.466292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.1919 | −1.93994 | −0.969970 | − | 0.243226i | \(-0.921794\pi\) | ||||
−0.969970 | + | 0.243226i | \(0.921794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.54790 | 0.179073 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2193 | −0.401763 | −0.200881 | − | 0.979616i | \(-0.564381\pi\) | ||||
−0.200881 | + | 0.979616i | \(0.564381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.63094 | −0.0640200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.83373 | −0.150256 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.76322 | −0.0690003 | −0.0345001 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345001 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.51844 | −0.332843 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.1184 | −0.745881 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.27817 | −0.127699 | −0.0638496 | − | 0.997960i | \(-0.520338\pi\) | ||||
−0.0638496 | + | 0.997960i | \(0.520338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2156 | 0.669608 | 0.334804 | − | 0.942288i | \(-0.391330\pi\) | ||||
0.334804 | + | 0.942288i | \(0.391330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.14806 | −0.0445870 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.26941 | −0.0880040 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.2110 | 1.28594 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.06226 | 0.311705 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.27727 | −0.319540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5166 | 0.443931 | 0.221966 | − | 0.975054i | \(-0.428753\pi\) | ||||
0.221966 | + | 0.975054i | \(0.428753\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.5830 | −0.676769 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.99010 | 0.307084 | 0.153542 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153542 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.7427 | −0.489018 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8690 | 0.416500 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.67293 | 0.102277 | 0.0511384 | − | 0.998692i | \(-0.483715\pi\) | ||||
0.0511384 | + | 0.998692i | \(0.483715\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.17182 | −0.121189 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.1410 | −0.653971 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.52462 | −0.286665 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7347 | 0.864867 | 0.432434 | − | 0.901666i | \(-0.357655\pi\) | ||||
0.432434 | + | 0.901666i | \(0.357655\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.54716 | −0.0967586 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.35208 | −0.240948 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4926 | 0.435312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.6324 | −0.515625 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0708 | 0.493678 | 0.246839 | − | 0.969056i | \(-0.420608\pi\) | ||||
0.246839 | + | 0.969056i | \(0.420608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.1670 | −1.28863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.44127 | −0.167268 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.1490 | −0.419300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2329 | 0.910086 | 0.455043 | − | 0.890470i | \(-0.349624\pi\) | ||||
0.455043 | + | 0.890470i | \(0.349624\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.2680 | −1.21015 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.2835 | −0.759625 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.538228 | 0.0201286 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.03999 | −0.300259 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5402 | −1.51189 | −0.755947 | − | 0.654632i | \(-0.772823\pi\) | ||||
−0.755947 | + | 0.654632i | \(0.772823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.61935 | −0.209276 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.1041 | −0.673297 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −43.9377 | −1.63180 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.38603 | 0.311021 | 0.155510 | − | 0.987834i | \(-0.450298\pi\) | ||||
0.155510 | + | 0.987834i | \(0.450298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.52974 | −0.204805 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4222 | 0.792330 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.7946 | −0.878873 | −0.439437 | − | 0.898274i | \(-0.644822\pi\) | ||||
−0.439437 | + | 0.898274i | \(0.644822\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.362192 | −0.0133597 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.26536 | 0.304458 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3233 | 1.00510 | 0.502552 | − | 0.864547i | \(-0.332395\pi\) | ||||
0.502552 | + | 0.864547i | \(0.332395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.83739 | 0.104234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.2512 | −1.18318 | −0.591592 | − | 0.806238i | \(-0.701500\pi\) | ||||
−0.591592 | + | 0.806238i | \(0.701500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0536 | −0.404973 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.5213 | 0.970363 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.13010 | −0.260528 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.78681 | −0.138183 | −0.0690913 | − | 0.997610i | \(-0.522010\pi\) | ||||
−0.0690913 | + | 0.997610i | \(0.522010\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.02720 | −0.0374334 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.22637 | 0.153813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6522 | 0.750619 | 0.375309 | − | 0.926900i | \(-0.377536\pi\) | ||||
0.375309 | + | 0.926900i | \(0.377536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.39589 | 0.0869653 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1253 | 0.765790 | 0.382895 | − | 0.923792i | \(-0.374927\pi\) | ||||
0.382895 | + | 0.923792i | \(0.374927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3848 | −0.556967 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.33892 | 0.0845639 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.63094 | −0.0588898 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.64664 | −0.275745 | −0.137872 | − | 0.990450i | \(-0.544026\pi\) | ||||
−0.137872 | + | 0.990450i | \(0.544026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.28468 | −0.226337 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.0537 | −0.613379 | −0.306689 | − | 0.951810i | \(-0.599221\pi\) | ||||
−0.306689 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.8348 | 0.963936 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.45296 | −0.195624 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.4034 | −1.01766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.58999 | −0.343157 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.8202 | 1.24437 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.49590 | −0.231849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.1001 | −0.573905 | −0.286953 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286953 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.08000 | 0.252055 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5604 | −0.446595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.27727 | −0.293934 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.72536 | −0.0966584 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.1516 | 1.42224 | 0.711122 | − | 0.703069i | \(-0.248187\pi\) | ||||
0.711122 | + | 0.703069i | \(0.248187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.9200 | −0.740096 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0854161 | −0.00301803 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.50579 | −0.264873 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.91629 | −0.0675403 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.14424 | −0.286691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0345 | −1.26690 | −0.633452 | − | 0.773782i | \(-0.718363\pi\) | ||||
−0.633452 | + | 0.773782i | \(0.718363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.0083 | −1.47511 | −0.737555 | − | 0.675287i | \(-0.764020\pi\) | ||||
−0.737555 | + | 0.675287i | \(0.764020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.93748 | −0.278380 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.9507 | 0.383586 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −52.9442 | −1.85228 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.54716 | −0.0890050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.2213 | −0.566126 | −0.283063 | − | 0.959101i | \(-0.591350\pi\) | ||||
−0.283063 | + | 0.959101i | \(0.591350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.3340 | −0.987661 | −0.493830 | − | 0.869558i | \(-0.664404\pi\) | ||||
−0.493830 | + | 0.869558i | \(0.664404\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.16973 | −0.110356 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0942 | 1.08125 | 0.540625 | − | 0.841264i | \(-0.318188\pi\) | ||||
0.540625 | + | 0.841264i | \(0.318188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2909 | 0.426882 | 0.213441 | − | 0.976956i | \(-0.431533\pi\) | ||||
0.213441 | + | 0.976956i | \(0.431533\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.27346 | 0.182934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.70606 | −0.0591113 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.0816555 | −0.00282581 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.2663 | −0.735072 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.0450 | −1.69322 | −0.846611 | − | 0.532213i | \(-0.821361\pi\) | ||||
−0.846611 | + | 0.532213i | \(0.821361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.0112 | 2.00039 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.929635 | 0.0320183 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.538228 | 0.0185156 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.4208 | −0.494921 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.8506 | −0.988984 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.8025 | −0.575305 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.78055 | −0.197691 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.6045 | 0.737995 | 0.368998 | − | 0.929430i | \(-0.379701\pi\) | ||||
0.368998 | + | 0.929430i | \(0.379701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.06380 | −0.241014 | −0.120507 | − | 0.992712i | \(-0.538452\pi\) | ||||
−0.120507 | + | 0.992712i | \(0.538452\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.53311 | −0.154488 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.6779 | −1.38469 | −0.692345 | − | 0.721567i | \(-0.743422\pi\) | ||||
−0.692345 | + | 0.721567i | \(0.743422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.12430 | 0.174232 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.48122 | 0.321999 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.6682 | −0.429740 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.26536 | 0.280061 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.4576 | −1.09852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.22636 | 0.176683 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.7205 | 1.88155 | 0.940775 | − | 0.339033i | \(-0.110100\pi\) | ||||
0.940775 | + | 0.339033i | \(0.110100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.0588 | 0.373004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.3931 | 0.585989 | 0.292994 | − | 0.956114i | \(-0.405348\pi\) | ||||
0.292994 | + | 0.956114i | \(0.405348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.4938 | 0.622367 | 0.311183 | − | 0.950350i | \(-0.399275\pi\) | ||||
0.311183 | + | 0.950350i | \(0.399275\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.590713 | −0.0198566 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.90249 | 0.198186 | 0.0990931 | − | 0.995078i | \(-0.468406\pi\) | ||||
0.0990931 | + | 0.995078i | \(0.468406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.4061 | 0.583783 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.12950 | −0.171845 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.7030 | 1.73017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.03817 | 0.0347021 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.39589 | 0.0799964 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.1419 | −1.77238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8374 | −0.427676 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.44976 | −0.281190 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7185 | 0.389537 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0760 | 0.733022 | 0.366511 | − | 0.930414i | \(-0.380552\pi\) | ||||
0.366511 | + | 0.930414i | \(0.380552\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.3982 | −0.941908 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2537 | 0.339720 | 0.169860 | − | 0.985468i | \(-0.445668\pi\) | ||||
0.169860 | + | 0.985468i | \(0.445668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4121 | 0.344590 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.99796 | −0.0991095 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.8268 | 0.522648 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.10317 | −0.201325 | −0.100663 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100663 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1015 | −0.563514 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.58999 | −0.315658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.1689 | 1.25498 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.3134 | −0.470113 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.8438 | 1.63532 | 0.817660 | − | 0.575701i | \(-0.195271\pi\) | ||||
0.817660 | + | 0.575701i | \(0.195271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.21645 | 0.138189 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.9533 | 0.489550 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.918247 | 0.0300299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.75458 | 0.0899881 | 0.0449941 | − | 0.998987i | \(-0.485673\pi\) | ||||
0.0449941 | + | 0.998987i | \(0.485673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.7601 | 0.383776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.1728 | −1.83118 | −0.915591 | − | 0.402111i | \(-0.868276\pi\) | ||||
−0.915591 | + | 0.402111i | \(0.868276\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.9838 | −0.781020 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.00914 | −0.0653572 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.86955 | −0.255726 | −0.127863 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127863 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.50579 | −0.243648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.60150 | −0.116787 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.62240 | −0.182127 | −0.0910637 | − | 0.995845i | \(-0.529027\pi\) | ||||
−0.0910637 | + | 0.995845i | \(0.529027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.52090 | −0.0492152 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.27712 | 0.202910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.89307 | 0.190297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.45629 | 0.0469769 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.1615 | −0.585246 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3356 | 0.332716 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0719 | 1.61020 | 0.805102 | − | 0.593137i | \(-0.202111\pi\) | ||||
0.805102 | + | 0.593137i | \(0.202111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.84075 | 0.155507 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.6410 | 1.24005 | 0.620024 | − | 0.784582i | \(-0.287123\pi\) | ||||
0.620024 | + | 0.784582i | \(0.287123\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8018 | 0.378349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.16973 | −0.101513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.1764 | −0.325573 | −0.162786 | − | 0.986661i | \(-0.552048\pi\) | ||||
−0.162786 | + | 0.986661i | \(0.552048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0335338 | −0.00107175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.1876 | −1.25116 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.8713 | 0.346741 | 0.173371 | − | 0.984857i | \(-0.444534\pi\) | ||||
0.173371 | + | 0.984857i | \(0.444534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.52910 | 0.271760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.25165 | 0.262653 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.7061 | −1.42157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8489 | 0.789353 | 0.394676 | − | 0.918820i | \(-0.370857\pi\) | ||||
0.394676 | + | 0.918820i | \(0.370857\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.5634 | 0.716026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.07818 | 0.129287 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.4611 | −0.616340 | −0.308170 | − | 0.951331i | \(-0.599717\pi\) | ||||
−0.308170 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.2484 | −0.957018 |
(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 | 4004.2.a.j.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.j.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial |