Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.11942\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.11942 | −0.947832 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.802640 | −0.303369 | −0.151685 | − | 0.988429i | \(-0.548470\pi\) | ||||
−0.151685 | + | 0.988429i | \(0.548470\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.53063 | −0.461503 | −0.230752 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230752 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.15404 | 1.70682 | 0.853412 | − | 0.521236i | \(-0.174529\pi\) | ||||
0.853412 | + | 0.521236i | \(0.174529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.11942 | 0.547231 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.02477 | 0.491079 | 0.245539 | − | 0.969387i | \(-0.421035\pi\) | ||||
0.245539 | + | 0.969387i | \(0.421035\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.09372 | −1.85683 | −0.928414 | − | 0.371548i | \(-0.878827\pi\) | ||||
−0.928414 | + | 0.371548i | \(0.878827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.802640 | 0.175150 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.69737 | −0.353927 | −0.176963 | − | 0.984217i | \(-0.556627\pi\) | ||||
−0.176963 | + | 0.984217i | \(0.556627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.508068 | −0.101614 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.39635 | 1.55916 | 0.779582 | − | 0.626301i | \(-0.215432\pi\) | ||||
0.779582 | + | 0.626301i | \(0.215432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.83232 | 0.329095 | 0.164548 | − | 0.986369i | \(-0.447384\pi\) | ||||
0.164548 | + | 0.986369i | \(0.447384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.53063 | 0.266449 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.70113 | 0.287543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.93315 | −1.63300 | −0.816500 | − | 0.577345i | \(-0.804089\pi\) | ||||
−0.816500 | + | 0.577345i | \(0.804089\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.15404 | −0.985436 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.89174 | −0.451614 | −0.225807 | − | 0.974172i | \(-0.572502\pi\) | ||||
−0.225807 | + | 0.974172i | \(0.572502\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.94539 | 0.449168 | 0.224584 | − | 0.974455i | \(-0.427898\pi\) | ||||
0.224584 | + | 0.974455i | \(0.427898\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.11942 | −0.315944 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.81191 | −1.13948 | −0.569742 | − | 0.821823i | \(-0.692957\pi\) | ||||
−0.569742 | + | 0.821823i | \(0.692957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35577 | −0.907967 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.02477 | −0.283524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.25602 | 1.27141 | 0.635706 | − | 0.771931i | \(-0.280709\pi\) | ||||
0.635706 | + | 0.771931i | \(0.280709\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24405 | 0.437428 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.09372 | 1.07204 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.76308 | 0.750289 | 0.375144 | − | 0.926966i | \(-0.377593\pi\) | ||||
0.375144 | + | 0.926966i | \(0.377593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0936477 | −0.0119904 | −0.00599518 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599518 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.802640 | −0.101123 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.0430 | −1.61778 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.66806 | −1.05897 | −0.529486 | − | 0.848319i | \(-0.677615\pi\) | ||||
−0.529486 | + | 0.848319i | \(0.677615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.69737 | 0.204340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00704 | −0.950261 | −0.475130 | − | 0.879915i | \(-0.657599\pi\) | ||||
−0.475130 | + | 0.879915i | \(0.657599\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.52554 | 0.178552 | 0.0892758 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892758 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.508068 | 0.0586667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.22855 | 0.140006 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5706 | 1.75183 | 0.875917 | − | 0.482461i | \(-0.160257\pi\) | ||||
0.875917 | + | 0.482461i | \(0.160257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.8255 | 1.51755 | 0.758775 | − | 0.651352i | \(-0.225798\pi\) | ||||
0.758775 | + | 0.651352i | \(0.225798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.29133 | −0.465460 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.39635 | −0.900183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9663 | 1.26842 | 0.634211 | − | 0.773160i | \(-0.281325\pi\) | ||||
0.634211 | + | 0.773160i | \(0.281325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.93948 | −0.517798 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.83232 | −0.190003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.1540 | 1.75996 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7852 | −1.39968 | −0.699840 | − | 0.714300i | \(-0.746745\pi\) | ||||
−0.699840 | + | 0.714300i | \(0.746745\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.53063 | −0.153834 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2301 | 1.31644 | 0.658220 | − | 0.752825i | \(-0.271309\pi\) | ||||
0.658220 | + | 0.752825i | \(0.271309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.58267 | −0.944209 | −0.472104 | − | 0.881543i | \(-0.656505\pi\) | ||||
−0.472104 | + | 0.881543i | \(0.656505\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.70113 | −0.166013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.19020 | 0.308408 | 0.154204 | − | 0.988039i | \(-0.450719\pi\) | ||||
0.154204 | + | 0.988039i | \(0.450719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5473 | −1.29760 | −0.648800 | − | 0.760959i | \(-0.724729\pi\) | ||||
−0.648800 | + | 0.760959i | \(0.724729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.93315 | 0.942813 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.42224 | 0.604154 | 0.302077 | − | 0.953284i | \(-0.402320\pi\) | ||||
0.302077 | + | 0.953284i | \(0.402320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.59744 | 0.335463 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.15404 | 0.568942 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62516 | −0.148978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.65716 | −0.787015 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.89174 | 0.260740 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6739 | 1.04415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.93176 | 0.615094 | 0.307547 | − | 0.951533i | \(-0.400492\pi\) | ||||
0.307547 | + | 0.951533i | \(0.400492\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.94539 | −0.259327 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.62848 | −0.491762 | −0.245881 | − | 0.969300i | \(-0.579077\pi\) | ||||
−0.245881 | + | 0.969300i | \(0.579077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.49634 | 0.563304 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.11942 | 0.182410 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.30884 | 0.111822 | 0.0559109 | − | 0.998436i | \(-0.482194\pi\) | ||||
0.0559109 | + | 0.998436i | \(0.482194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9293 | 1.43593 | 0.717963 | − | 0.696082i | \(-0.245075\pi\) | ||||
0.717963 | + | 0.696082i | \(0.245075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.81191 | 0.657882 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.41959 | −0.787705 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.7954 | −1.47783 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.35577 | 0.524215 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.9654 | 1.96332 | 0.981660 | − | 0.190642i | \(-0.0610570\pi\) | ||||
0.981660 | + | 0.190642i | \(0.0610570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.74051 | 0.385777 | 0.192888 | − | 0.981221i | \(-0.438214\pi\) | ||||
0.192888 | + | 0.981221i | \(0.438214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.02477 | 0.163693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.88346 | −0.311927 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2918 | 0.980991 | 0.490495 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490495 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.25602 | −0.734050 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.36238 | 0.107371 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4990 | 1.13565 | 0.567823 | − | 0.823151i | \(-0.307786\pi\) | ||||
0.567823 | + | 0.823151i | \(0.307786\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.24405 | −0.252549 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.8723 | 1.91325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.09372 | −0.618943 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.2287 | −1.08179 | −0.540893 | − | 0.841091i | \(-0.681914\pi\) | ||||
−0.540893 | + | 0.841091i | \(0.681914\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.407796 | 0.0308265 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.76308 | −0.433180 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.46854 | 0.408738 | 0.204369 | − | 0.978894i | \(-0.434486\pi\) | ||||
0.204369 | + | 0.978894i | \(0.434486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.71174 | 0.647538 | 0.323769 | − | 0.946136i | \(-0.395050\pi\) | ||||
0.323769 | + | 0.946136i | \(0.395050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0936477 | 0.00692263 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.0525 | 1.54781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.09918 | −0.226634 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.802640 | 0.0583834 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.84326 | −0.495161 | −0.247580 | − | 0.968867i | \(-0.579635\pi\) | ||||
−0.247580 | + | 0.968867i | \(0.579635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6905 | 0.841499 | 0.420750 | − | 0.907177i | \(-0.361767\pi\) | ||||
0.420750 | + | 0.907177i | \(0.361767\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.0430 | 0.934028 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4537 | 1.45727 | 0.728633 | − | 0.684904i | \(-0.240156\pi\) | ||||
0.728633 | + | 0.684904i | \(0.240156\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5826 | 1.38817 | 0.694086 | − | 0.719892i | \(-0.255809\pi\) | ||||
0.694086 | + | 0.719892i | \(0.255809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.66806 | 0.611398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.73924 | −0.473002 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.12881 | 0.428055 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.69737 | −0.117976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.3885 | 0.856932 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0070 | −0.826598 | −0.413299 | − | 0.910595i | \(-0.635624\pi\) | ||||
−0.413299 | + | 0.910595i | \(0.635624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00704 | 0.548633 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.24252 | −0.425736 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.47070 | −0.0998373 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.52554 | −0.103087 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.4605 | 0.838185 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.0988 | 1.34591 | 0.672957 | − | 0.739681i | \(-0.265024\pi\) | ||||
0.672957 | + | 0.739681i | \(0.265024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.508068 | −0.0338712 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.1963 | 0.942242 | 0.471121 | − | 0.882068i | \(-0.343849\pi\) | ||||
0.471121 | + | 0.882068i | \(0.343849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7750 | 1.30677 | 0.653386 | − | 0.757025i | \(-0.273348\pi\) | ||||
0.653386 | + | 0.757025i | \(0.273348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.22855 | −0.0808324 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.37536 | 0.614200 | 0.307100 | − | 0.951677i | \(-0.400641\pi\) | ||||
0.307100 | + | 0.951677i | \(0.400641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.5567 | 1.08004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.5706 | −1.01142 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0467 | −0.714551 | −0.357276 | − | 0.933999i | \(-0.616294\pi\) | ||||
−0.357276 | + | 0.933999i | \(0.616294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.14465 | 0.202565 | 0.101282 | − | 0.994858i | \(-0.467705\pi\) | ||||
0.101282 | + | 0.994858i | \(0.467705\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.4705 | 0.860601 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −49.8091 | −3.16928 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.8255 | −0.876158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.4249 | 1.22609 | 0.613044 | − | 0.790049i | \(-0.289945\pi\) | ||||
0.613044 | + | 0.790049i | \(0.289945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.59806 | 0.163338 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.29133 | 0.268734 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.3783 | 1.52068 | 0.760338 | − | 0.649528i | \(-0.225033\pi\) | ||||
0.760338 | + | 0.649528i | \(0.225033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.97274 | 0.495402 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.39635 | 0.519721 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.1381 | −1.18010 | −0.590051 | − | 0.807366i | \(-0.700893\pi\) | ||||
−0.590051 | + | 0.807366i | \(0.700893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.6174 | −1.20509 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9663 | −0.732324 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.8583 | −1.94244 | −0.971218 | − | 0.238192i | \(-0.923445\pi\) | ||||
−0.971218 | + | 0.238192i | \(0.923445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.6866 | −1.68184 | −0.840922 | − | 0.541157i | \(-0.817986\pi\) | ||||
−0.840922 | + | 0.541157i | \(0.817986\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.93948 | 0.298951 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.777666 | 0.0468951 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.5531 | 0.994582 | 0.497291 | − | 0.867584i | \(-0.334328\pi\) | ||||
0.497291 | + | 0.867584i | \(0.334328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.83232 | 0.109698 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1221 | −0.961766 | −0.480883 | − | 0.876785i | \(-0.659684\pi\) | ||||
−0.480883 | + | 0.876785i | \(0.659684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.4620 | −0.919118 | −0.459559 | − | 0.888147i | \(-0.651992\pi\) | ||||
−0.459559 | + | 0.888147i | \(0.651992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.1540 | −1.01611 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.32103 | 0.137006 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9003 | −0.758842 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7852 | 0.808105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.3824 | −0.781806 | −0.390903 | − | 0.920432i | \(-0.627837\pi\) | ||||
−0.390903 | + | 0.920432i | \(0.627837\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2144 | −0.711148 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.53063 | 0.0888164 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4457 | −0.604091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.36409 | −0.136264 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.2301 | −0.760048 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.198479 | 0.0113648 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3905 | −0.593018 | −0.296509 | − | 0.955030i | \(-0.595822\pi\) | ||||
−0.296509 | + | 0.955030i | \(0.595822\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.58267 | 0.545139 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.04038 | 0.285814 | 0.142907 | − | 0.989736i | \(-0.454355\pi\) | ||||
0.142907 | + | 0.989736i | \(0.454355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.2609 | 0.693025 | 0.346513 | − | 0.938045i | \(-0.387366\pi\) | ||||
0.346513 | + | 0.938045i | \(0.387366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.70113 | 0.0958477 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.7166 | −0.882731 | −0.441365 | − | 0.897327i | \(-0.645506\pi\) | ||||
−0.441365 | + | 0.897327i | \(0.645506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8517 | −0.719559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.19020 | −0.178059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.3879 | −0.911848 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.12668 | −0.173437 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.5473 | 0.749169 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.27015 | 0.345685 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.2687 | −1.00414 | −0.502069 | − | 0.864827i | \(-0.667428\pi\) | ||||
−0.502069 | + | 0.864827i | \(0.667428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.93315 | −0.544334 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.3712 | 1.00373 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6321 | 1.12390 | 0.561951 | − | 0.827171i | \(-0.310051\pi\) | ||||
0.561951 | + | 0.827171i | \(0.310051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.42224 | −0.348808 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.80462 | −0.151878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.7199 | 0.578819 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.59744 | −0.193680 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.45323 | 0.400110 | 0.200055 | − | 0.979785i | \(-0.435888\pi\) | ||||
0.200055 | + | 0.979785i | \(0.435888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.1869 | 1.08058 | 0.540289 | − | 0.841480i | \(-0.318315\pi\) | ||||
0.540289 | + | 0.841480i | \(0.318315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.15404 | −0.328479 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.40011 | 0.287419 | 0.143709 | − | 0.989620i | \(-0.454097\pi\) | ||||
0.143709 | + | 0.989620i | \(0.454097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9703 | 0.900688 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.62516 | 0.0860126 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1097 | 0.744680 | 0.372340 | − | 0.928096i | \(-0.378555\pi\) | ||||
0.372340 | + | 0.928096i | \(0.378555\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.5084 | 2.44781 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.65716 | 0.454383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.23327 | −0.169237 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.40423 | 0.438697 | 0.219349 | − | 0.975647i | \(-0.429607\pi\) | ||||
0.219349 | + | 0.975647i | \(0.429607\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.89174 | −0.150538 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.42925 | −0.385707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3605 | −1.20956 | −0.604780 | − | 0.796393i | \(-0.706739\pi\) | ||||
−0.604780 | + | 0.796393i | \(0.706739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.6739 | −0.602837 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.6715 | 2.66122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8583 | 1.84192 | 0.920959 | − | 0.389659i | \(-0.127407\pi\) | ||||
0.920959 | + | 0.389659i | \(0.127407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.93176 | −0.355125 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.69504 | −0.0866123 | −0.0433061 | − | 0.999062i | \(-0.513789\pi\) | ||||
−0.0433061 | + | 0.999062i | \(0.513789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.60380 | −0.132702 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.94539 | 0.149723 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.2244 | 0.721203 | 0.360602 | − | 0.932720i | \(-0.382571\pi\) | ||||
0.360602 | + | 0.932720i | \(0.382571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.43679 | −0.173806 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.62848 | 0.283919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.0007 | −1.66045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0556 | −0.655240 | −0.327620 | − | 0.944810i | \(-0.606247\pi\) | ||||
−0.327620 | + | 0.944810i | \(0.606247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.49634 | −0.325224 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.8074 | 1.63832 | 0.819162 | − | 0.573563i | \(-0.194439\pi\) | ||||
0.819162 | + | 0.573563i | \(0.194439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2762 | 0.561708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.11942 | −0.105315 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.2040 | 0.753635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4482 | −0.763865 | −0.381932 | − | 0.924190i | \(-0.624741\pi\) | ||||
−0.381932 | + | 0.924190i | \(0.624741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.30884 | −0.0645603 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.62567 | −0.227615 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.3021 | −1.43838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.9293 | −0.829032 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.69199 | −0.0826592 | −0.0413296 | − | 0.999146i | \(-0.513159\pi\) | ||||
−0.0413296 | + | 0.999146i | \(0.513159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1615 | 1.37251 | 0.686254 | − | 0.727362i | \(-0.259254\pi\) | ||||
0.686254 | + | 0.727362i | \(0.259254\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.81191 | −0.379828 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.02872 | −0.0499003 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0751653 | 0.00363750 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.41959 | 0.454782 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.1892 | −0.731636 | −0.365818 | − | 0.930686i | \(-0.619211\pi\) | ||||
−0.365818 | + | 0.930686i | \(0.619211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.76398 | −0.421170 | −0.210585 | − | 0.977576i | \(-0.567537\pi\) | ||||
−0.210585 | + | 0.977576i | \(0.567537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.7954 | 0.853223 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.7381 | 0.657181 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.6631 | −1.55892 | −0.779462 | − | 0.626450i | \(-0.784507\pi\) | ||||
−0.779462 | + | 0.626450i | \(0.784507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.35577 | −0.302656 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5636 | 0.501894 | 0.250947 | − | 0.968001i | \(-0.419258\pi\) | ||||
0.250947 | + | 0.968001i | \(0.419258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.3615 | −1.20225 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.9654 | −1.13352 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.46969 | 0.210938 | 0.105469 | − | 0.994423i | \(-0.466366\pi\) | ||||
0.105469 | + | 0.994423i | \(0.466366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.42620 | 0.208421 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.74051 | −0.222728 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4688 | 0.490786 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9914 | 1.07549 | 0.537745 | − | 0.843107i | \(-0.319276\pi\) | ||||
0.537745 | + | 0.843107i | \(0.319276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.02477 | −0.0945081 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.77260 | 0.362006 | 0.181003 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181003 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.5847 | −0.863705 | −0.431853 | − | 0.901944i | \(-0.642140\pi\) | ||||
−0.431853 | + | 0.901944i | \(0.642140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.88346 | 0.180091 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.4040 | 0.759088 | 0.379544 | − | 0.925174i | \(-0.376081\pi\) | ||||
0.379544 | + | 0.925174i | \(0.376081\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95733 | 0.321260 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.2918 | −0.566375 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.50832 | −0.207293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.11217 | 0.188679 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.25602 | 0.423804 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.17459 | 0.190742 | 0.0953709 | − | 0.995442i | \(-0.469596\pi\) | ||||
0.0953709 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −61.1291 | −2.78725 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.36238 | −0.0619904 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.2167 | 1.32666 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.01182 | −0.363050 | −0.181525 | − | 0.983386i | \(-0.558103\pi\) | ||||
−0.181525 | + | 0.983386i | \(0.558103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.4990 | −0.655666 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5821 | 0.883730 | 0.441865 | − | 0.897082i | \(-0.354317\pi\) | ||||
0.441865 | + | 0.897082i | \(0.354317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0007 | 0.765672 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.24405 | 0.145809 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.42677 | 0.288280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.25191 | 0.0560432 | 0.0280216 | − | 0.999607i | \(-0.491079\pi\) | ||||
0.0280216 | + | 0.999607i | \(0.491079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5341 | −0.915572 | −0.457786 | − | 0.889062i | \(-0.651357\pi\) | ||||
−0.457786 | + | 0.889062i | \(0.651357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0400 | −1.24777 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.8723 | −1.10462 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.7060 | −0.962102 | −0.481051 | − | 0.876693i | \(-0.659745\pi\) | ||||
−0.481051 | + | 0.876693i | \(0.659745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.22446 | −0.0541670 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.09372 | 0.357347 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3097 | 0.894952 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9572 | 0.525876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2287 | 0.624570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.3324 | 1.37270 | 0.686350 | − | 0.727272i | \(-0.259212\pi\) | ||||
0.686350 | + | 0.727272i | \(0.259212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8582 | 0.605979 | 0.302989 | − | 0.952994i | \(-0.402015\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402015\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.407796 | −0.0177977 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.71003 | 0.161612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1189 | −0.874736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.76308 | 0.250096 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.7959 | −0.770826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.76136 | −0.292319 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.46854 | −0.235985 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.72835 | 0.419030 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.41986 | 0.361998 | 0.180999 | − | 0.983483i | \(-0.442067\pi\) | ||||
0.180999 | + | 0.983483i | \(0.442067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.71174 | −0.373856 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.7125 | 1.22991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.8513 | −1.40462 | −0.702310 | − | 0.711871i | \(-0.747848\pi\) | ||||
−0.702310 | + | 0.711871i | \(0.747848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0936477 | −0.00399679 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −67.9577 | −2.89510 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.4976 | −0.531453 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.0525 | −0.893629 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.3326 | −1.75132 | −0.875659 | − | 0.482929i | \(-0.839573\pi\) | ||||
−0.875659 | + | 0.482929i | \(0.839573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.1261 | 0.766651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.09918 | 0.130847 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.5494 | 1.24536 | 0.622680 | − | 0.782477i | \(-0.286044\pi\) | ||||
0.622680 | + | 0.782477i | \(0.286044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6114 | −0.572637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.802640 | −0.0337077 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3368 | 1.18794 | 0.593971 | − | 0.804487i | \(-0.297559\pi\) | ||||
0.593971 | + | 0.804487i | \(0.297559\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1544 | 1.09453 | 0.547265 | − | 0.836960i | \(-0.315669\pi\) | ||||
0.547265 | + | 0.836960i | \(0.315669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.84326 | 0.285881 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.862382 | 0.0359638 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.89822 | 0.328807 | 0.164404 | − | 0.986393i | \(-0.447430\pi\) | ||||
0.164404 | + | 0.986393i | \(0.447430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6905 | −0.485840 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.0969 | −0.460378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.1676 | −0.586761 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.0430 | −0.539261 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.8279 | 1.47878 | 0.739388 | − | 0.673280i | \(-0.235115\pi\) | ||||
0.739388 | + | 0.673280i | \(0.235115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8303 | −0.611073 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.4537 | −0.841353 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5505 | −0.884974 | −0.442487 | − | 0.896775i | \(-0.645904\pi\) | ||||
−0.442487 | + | 0.896775i | \(0.645904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.44439 | 0.141206 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5826 | −0.801462 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3883 | −0.669608 | −0.334804 | − | 0.942288i | \(-0.608670\pi\) | ||||
−0.334804 | + | 0.942288i | \(0.608670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5147 | −0.714439 | −0.357220 | − | 0.934020i | \(-0.616275\pi\) | ||||
−0.357220 | + | 0.934020i | \(0.616275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.66806 | −0.352991 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.3481 | 0.745958 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.07723 | 0.246667 | 0.123334 | − | 0.992365i | \(-0.460641\pi\) | ||||
0.123334 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.73924 | 0.273088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0749 | −1.94490 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.9440 | −0.765140 | −0.382570 | − | 0.923927i | \(-0.624961\pi\) | ||||
−0.382570 | + | 0.923927i | \(0.624961\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.12881 | −0.247137 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.1057 | −0.970458 | −0.485229 | − | 0.874387i | \(-0.661264\pi\) | ||||
−0.485229 | + | 0.874387i | \(0.661264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4384 | 0.419555 | 0.209777 | − | 0.977749i | \(-0.432726\pi\) | ||||
0.209777 | + | 0.977749i | \(0.432726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.69737 | 0.0681133 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.60460 | −0.384800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.2015 | −0.888061 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.3885 | −0.494750 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.1123 | −0.801932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.14705 | −0.284519 | −0.142260 | − | 0.989829i | \(-0.545437\pi\) | ||||
−0.142260 | + | 0.989829i | \(0.545437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0070 | 0.477237 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6913 | −0.583006 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.1137 | −1.54974 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00704 | −0.316754 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.9265 | −1.65600 | −0.827998 | − | 0.560731i | \(-0.810520\pi\) | ||||
−0.827998 | + | 0.560731i | \(0.810520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0956 | 1.62065 | 0.810327 | − | 0.585978i | \(-0.199289\pi\) | ||||
0.810327 | + | 0.585978i | \(0.199289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.24252 | 0.245799 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.0967 | 1.73362 | 0.866810 | − | 0.498638i | \(-0.166166\pi\) | ||||
0.866810 | + | 0.498638i | \(0.166166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.82116 | −0.346261 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.47070 | 0.0576411 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0236 | −0.705318 | −0.352659 | − | 0.935752i | \(-0.614722\pi\) | ||||
−0.352659 | + | 0.935752i | \(0.614722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.9291 | 0.466108 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.52554 | 0.0595172 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.10967 | −0.121135 | −0.0605677 | − | 0.998164i | \(-0.519291\pi\) | ||||
−0.0605677 | + | 0.998164i | \(0.519291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.6200 | 1.93000 | 0.964998 | − | 0.262259i | \(-0.0844674\pi\) | ||||
0.964998 | + | 0.262259i | \(0.0844674\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.4605 | −0.483926 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.7685 | −0.533918 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2517 | −0.551830 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.0988 | −0.777064 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.143340 | 0.00553359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6182 | 0.602039 | 0.301019 | − | 0.953618i | \(-0.402673\pi\) | ||||
0.301019 | + | 0.953618i | \(0.402673\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.508068 | 0.0195556 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.8253 | 1.91494 | 0.957471 | − | 0.288529i | \(-0.0931663\pi\) | ||||
0.957471 | + | 0.288529i | \(0.0931663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0646 | 0.424620 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.1963 | −0.544004 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.6091 | 0.444210 | 0.222105 | − | 0.975023i | \(-0.428707\pi\) | ||||
0.222105 | + | 0.975023i | \(0.428707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.77398 | −0.105988 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.7750 | −0.754465 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.9620 | 2.17008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2300 | −0.693501 | −0.346751 | − | 0.937957i | \(-0.612715\pi\) | ||||
−0.346751 | + | 0.937957i | \(0.612715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.22855 | 0.0466686 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.8803 | −1.36102 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.85511 | −0.221778 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.37536 | −0.354609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9534 | 0.866937 | 0.433468 | − | 0.901169i | \(-0.357290\pi\) | ||||
0.433468 | + | 0.901169i | \(0.357290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.3962 | 3.03220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.5567 | −0.623562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6190 | −0.399368 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.5154 | −1.63425 | −0.817127 | − | 0.576458i | \(-0.804434\pi\) | ||||
−0.817127 | + | 0.576458i | \(0.804434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5706 | 0.583945 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.11014 | −0.116476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.9640 | 0.746613 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.0467 | 0.412546 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.0902 | 1.86805 | 0.934026 | − | 0.357206i | \(-0.116271\pi\) | ||||
0.934026 | + | 0.357206i | \(0.116271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.69143 | 0.286444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.14465 | −0.116951 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.26592 | −0.158432 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.8400 | −0.958354 | −0.479177 | − | 0.877718i | \(-0.659065\pi\) | ||||
−0.479177 | + | 0.877718i | \(0.659065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.96374 | 0.220577 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2488 | 0.452420 | 0.226210 | − | 0.974079i | \(-0.427366\pi\) | ||||
0.226210 | + | 0.974079i | \(0.427366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.4705 | −0.496868 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2676 | 0.488719 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.4080 | −1.74393 | −0.871966 | − | 0.489567i | \(-0.837155\pi\) | ||||
−0.871966 | + | 0.489567i | \(0.837155\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 49.8091 | 1.82978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.720168 | 0.0264204 | 0.0132102 | − | 0.999913i | \(-0.495795\pi\) | ||||
0.0132102 | + | 0.999913i | \(0.495795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.7926 | −1.86090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.8255 | 0.505850 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.56058 | −0.0935614 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7424 | 0.610940 | 0.305470 | − | 0.952202i | \(-0.401186\pi\) | ||||
0.305470 | + | 0.952202i | \(0.401186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.4249 | −0.707882 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0471 | −0.365652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0703 | −1.31100 | −0.655498 | − | 0.755197i | \(-0.727541\pi\) | ||||
−0.655498 | + | 0.755197i | \(0.727541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.59806 | −0.0943035 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3511 | −0.375226 | −0.187613 | − | 0.982243i | \(-0.560075\pi\) | ||||
−0.187613 | + | 0.982243i | \(0.560075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8736 | 0.393652 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.29133 | −0.155153 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.4662 | 1.28061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.2909 | −0.984134 | −0.492067 | − | 0.870557i | \(-0.663758\pi\) | ||||
−0.492067 | + | 0.870557i | \(0.663758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.3783 | −0.877962 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.8338 | 1.61256 | 0.806279 | − | 0.591535i | \(-0.201478\pi\) | ||||
0.806279 | + | 0.591535i | \(0.201478\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.930946 | −0.0334406 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.97274 | −0.286021 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.4050 | 0.838570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.2558 | 0.438548 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.39635 | −0.300061 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.0514 | −0.929815 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.8489 | −0.778830 | −0.389415 | − | 0.921062i | \(-0.627323\pi\) | ||||
−0.389415 | + | 0.921062i | \(0.627323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.1381 | 0.681333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.15475 | −0.183282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.576312 | −0.0204654 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.6174 | 0.695756 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.1416 | 0.678030 | 0.339015 | − | 0.940781i | \(-0.389906\pi\) | ||||
0.339015 | + | 0.940781i | \(0.389906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.8173 | −0.559577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.9663 | 0.422807 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.33505 | −0.0824021 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.88745 | −0.101769 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.8583 | 1.12147 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.0992 | −1.65592 | −0.827960 | − | 0.560787i | \(-0.810499\pi\) | ||||
−0.827960 | + | 0.560787i | \(0.810499\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1864 | 1.09510 | 0.547552 | − | 0.836772i | \(-0.315560\pi\) | ||||
0.547552 | + | 0.836772i | \(0.315560\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.6866 | 0.971013 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.7294 | −1.07640 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.8392 | −0.834028 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.93948 | −0.172599 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0414 | −0.908851 | −0.454425 | − | 0.890785i | \(-0.650155\pi\) | ||||
−0.454425 | + | 0.890785i | \(0.650155\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8099 | −1.14368 | −0.571841 | − | 0.820364i | \(-0.693771\pi\) | ||||
−0.571841 | + | 0.820364i | \(0.693771\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.777666 | −0.0270749 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.60622 | −0.264494 | −0.132247 | − | 0.991217i | \(-0.542219\pi\) | ||||
−0.132247 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5841 | 0.714917 | 0.357458 | − | 0.933929i | \(-0.383643\pi\) | ||||
0.357458 | + | 0.933929i | \(0.383643\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.5531 | −0.574222 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.8690 | −0.445883 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.11942 | −0.0733455 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.83232 | −0.0633344 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.8511 | −1.79010 | −0.895050 | − | 0.445966i | \(-0.852860\pi\) | ||||
−0.895050 | + | 0.445966i | \(0.852860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.4987 | 1.43099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.1221 | 0.555276 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −52.7147 | −1.81344 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.94858 | 0.238756 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.4620 | 0.530653 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.8603 | 0.577963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.0857 | −1.33827 | −0.669135 | − | 0.743141i | \(-0.733335\pi\) | ||||
−0.669135 | + | 0.743141i | \(0.733335\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.1540 | 0.586654 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.2522 | −0.965077 | −0.482538 | − | 0.875875i | \(-0.660285\pi\) | ||||
−0.482538 | + | 0.875875i | \(0.660285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.1161 | −1.74406 | −0.872030 | − | 0.489453i | \(-0.837196\pi\) | ||||
−0.872030 | + | 0.489453i | \(0.837196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.32103 | −0.0791004 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.24574 | −0.178567 | −0.0892835 | − | 0.996006i | \(-0.528458\pi\) | ||||
−0.0892835 | + | 0.996006i | \(0.528458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.1565 | 1.02535 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.9003 | 0.438118 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.8330 | −0.808478 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.3437 | −1.80748 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.7852 | −0.466560 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.36993 | −0.316762 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.27093 | −0.110451 | −0.0552257 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552257 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.3824 | 0.451376 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.23440 | 0.243733 | 0.121867 | − | 0.992546i | \(-0.461112\pi\) | ||||
0.121867 | + | 0.992546i | \(0.461112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.28825 | 0.177964 | 0.0889820 | − | 0.996033i | \(-0.471639\pi\) | ||||
0.0889820 | + | 0.996033i | \(0.471639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.2144 | 0.410582 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.41900 | −0.148376 | −0.0741878 | − | 0.997244i | \(-0.523636\pi\) | ||||
−0.0741878 | + | 0.997244i | \(0.523636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.56370 | −0.186601 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.53063 | −0.0512781 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 63.2275 | 2.11583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5901 | −0.387415 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.4457 | 0.348772 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.3848 | 0.513113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7413 | 0.624363 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.36409 | 0.0786719 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.4638 | −0.613758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.3464 | 0.908022 | 0.454011 | − | 0.890996i | \(-0.349993\pi\) | ||||
0.454011 | + | 0.890996i | \(0.349993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.2301 | 0.438814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3819 | 0.708415 | 0.354207 | − | 0.935167i | \(-0.384751\pi\) | ||||
0.354207 | + | 0.935167i | \(0.384751\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.1618 | −0.700355 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.198479 | −0.00656150 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.51764 | 0.149186 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.1624 | 1.65471 | 0.827353 | − | 0.561682i | \(-0.189846\pi\) | ||||
0.827353 | + | 0.561682i | \(0.189846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3905 | 0.342379 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.2757 | −1.62193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.04672 | 0.165935 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.58267 | −0.314736 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.5655 | −1.52777 | −0.763883 | − | 0.645355i | \(-0.776709\pi\) | ||||
−0.763883 | + | 0.645355i | \(0.776709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.4418 | 1.68594 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.04038 | −0.165015 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.56845 | 0.214811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1861 | 0.757457 | 0.378728 | − | 0.925508i | \(-0.376361\pi\) | ||||
0.378728 | + | 0.925508i | \(0.376361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.2609 | −0.400118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.8102 | −0.939186 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.90837 | 0.159838 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70113 | −0.0553377 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.1110 | 0.880989 | 0.440495 | − | 0.897755i | \(-0.354803\pi\) | ||||
0.440495 | + | 0.897755i | \(0.354803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.38827 | 0.304756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.7166 | 0.509645 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.3342 | 1.76006 | 0.880028 | − | 0.474922i | \(-0.157524\pi\) | ||||
0.880028 | + | 0.474922i | \(0.157524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.5037 | 0.469329 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.8517 | 0.415438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.05053 | −0.0339233 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6426 | −0.891696 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.19020 | 0.102803 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.7770 | −0.797600 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.3646 | 1.07293 | 0.536466 | − | 0.843922i | \(-0.319759\pi\) | ||||
0.536466 | + | 0.843922i | \(0.319759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.3879 | 0.526456 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.5247 | 1.81396 | 0.906982 | − | 0.421170i | \(-0.138380\pi\) | ||||
0.906982 | + | 0.421170i | \(0.138380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.5881 | −0.435616 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.12668 | 0.100134 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7001 | 0.502292 | 0.251146 | − | 0.967949i | \(-0.419193\pi\) | ||||
0.251146 | + | 0.967949i | \(0.419193\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.3160 | −0.585381 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5473 | −0.432533 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.5877 | 0.529066 | 0.264533 | − | 0.964377i | \(-0.414782\pi\) | ||||
0.264533 | + | 0.964377i | \(0.414782\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.3500 | −1.38124 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.27015 | −0.199581 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.99943 | −0.158973 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.8301 | −1.10641 | −0.553207 | − | 0.833044i | \(-0.686596\pi\) | ||||
−0.553207 | + | 0.833044i | \(0.686596\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.2687 | 0.579740 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.5037 | −1.31576 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.7106 | −1.44767 | −0.723834 | − | 0.689974i | \(-0.757622\pi\) | ||||
−0.723834 | + | 0.689974i | \(0.757622\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.93315 | 0.314271 |
(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 | 4008.2.a.k.1.2 | ✓ | 11 | |
4.3 | odd | 2 | 8016.2.a.be.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.2 | ✓ | 11 | 1.1 | even | 1 | trivial | |
8016.2.a.be.1.2 | 11 | 4.3 | odd | 2 |