Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.57500224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 7x^{4} + 12x^{3} + 11x^{2} - 18x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.64887\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −0.648873 | −0.374627 | −0.187314 | − | 0.982300i | \(-0.559978\pi\) | ||||
−0.187314 | + | 0.982300i | \(0.559978\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.55597 | 0.695850 | 0.347925 | − | 0.937522i | \(-0.386886\pi\) | ||||
0.347925 | + | 0.937522i | \(0.386886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00900 | 1.13729 | 0.568647 | − | 0.822582i | \(-0.307467\pi\) | ||||
0.568647 | + | 0.822582i | \(0.307467\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.57896 | −0.859655 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.37832 | −0.659627 | −0.329813 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329813 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00963 | −0.260684 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.984536 | −0.238785 | −0.119393 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119393 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.95246 | −0.426061 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.60342 | −0.751366 | −0.375683 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375683 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.57896 | −0.515793 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.62004 | 0.696677 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.28857 | 1.35345 | 0.676727 | − | 0.736234i | \(-0.263398\pi\) | ||||
0.676727 | + | 0.736234i | \(0.263398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1972 | 1.83148 | 0.915738 | − | 0.401777i | \(-0.131607\pi\) | ||||
0.915738 | + | 0.401777i | \(0.131607\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.648873 | 0.112954 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.68190 | 0.791386 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.17499 | −1.01516 | −0.507581 | − | 0.861604i | \(-0.669460\pi\) | ||||
−0.507581 | + | 0.861604i | \(0.669460\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.54323 | 0.247114 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.843023 | 0.131658 | 0.0658291 | − | 0.997831i | \(-0.479031\pi\) | ||||
0.0658291 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.86165 | 1.50389 | 0.751943 | − | 0.659228i | \(-0.229117\pi\) | ||||
0.751943 | + | 0.659228i | \(0.229117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.01278 | −0.598191 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.7074 | 1.99943 | 0.999717 | − | 0.0237903i | \(-0.00757340\pi\) | ||||
0.999717 | + | 0.0237903i | \(0.00757340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.05406 | 0.293437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.638839 | 0.0894554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.54950 | 0.350201 | 0.175100 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175100 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.55597 | −0.209807 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.648873 | −0.0859453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.68822 | −1.26130 | −0.630649 | − | 0.776068i | \(-0.717211\pi\) | ||||
−0.630649 | + | 0.776068i | \(0.717211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0762 | 1.67423 | 0.837116 | − | 0.547026i | \(-0.184240\pi\) | ||||
0.837116 | + | 0.547026i | \(0.184240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.76009 | −0.977680 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.70059 | −0.459001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0084 | 1.34489 | 0.672443 | − | 0.740149i | \(-0.265245\pi\) | ||||
0.672443 | + | 0.740149i | \(0.265245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.33817 | 0.281482 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.22930 | 1.09532 | 0.547658 | − | 0.836702i | \(-0.315519\pi\) | ||||
0.547658 | + | 0.836702i | \(0.315519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.67776 | −0.430449 | −0.215225 | − | 0.976565i | \(-0.569048\pi\) | ||||
−0.215225 | + | 0.976565i | \(0.569048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.67342 | 0.193230 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00900 | −0.342907 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.14246 | 0.466064 | 0.233032 | − | 0.972469i | \(-0.425135\pi\) | ||||
0.233032 | + | 0.972469i | \(0.425135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.38794 | 0.598660 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.87924 | −0.535566 | −0.267783 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267783 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.53191 | −0.166159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.72936 | −0.507040 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9154 | −1.26303 | −0.631514 | − | 0.775365i | \(-0.717566\pi\) | ||||
−0.631514 | + | 0.775365i | \(0.717566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.15635 | −0.750190 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.61670 | −0.686120 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55597 | 0.159639 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.28693 | −0.942945 | −0.471472 | − | 0.881881i | \(-0.656277\pi\) | ||||
−0.471472 | + | 0.881881i | \(0.656277\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.57896 | 0.259196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1668 | 1.60865 | 0.804327 | − | 0.594187i | \(-0.202526\pi\) | ||||
0.804327 | + | 0.594187i | \(0.202526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.19210 | −0.117461 | −0.0587306 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587306 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.03796 | −0.296475 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.77337 | −0.654807 | −0.327403 | − | 0.944885i | \(-0.606174\pi\) | ||||
−0.327403 | + | 0.944885i | \(0.606174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.54415 | 0.531034 | 0.265517 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265517 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00679 | 0.380308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.98597 | 0.845329 | 0.422664 | − | 0.906286i | \(-0.361095\pi\) | ||||
0.422664 | + | 0.906286i | \(0.361095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.60681 | −0.522838 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.13360 | 0.567051 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.96247 | −0.271569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.547015 | −0.0493227 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7926 | −1.05476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4102 | −1.72238 | −0.861188 | − | 0.508287i | \(-0.830279\pi\) | ||||
−0.861188 | + | 0.508287i | \(0.830279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.39896 | −0.563397 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9306 | 1.21713 | 0.608563 | − | 0.793506i | \(-0.291746\pi\) | ||||
0.608563 | + | 0.793506i | \(0.291746\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00900 | 0.260913 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.63267 | 0.484783 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.92919 | −0.250258 | −0.125129 | − | 0.992140i | \(-0.539934\pi\) | ||||
−0.125129 | + | 0.992140i | \(0.539934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.20274 | 0.271653 | 0.135826 | − | 0.990733i | \(-0.456631\pi\) | ||||
0.135826 | + | 0.990733i | \(0.456631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.89438 | −0.749042 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.37832 | 0.198885 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.3408 | 0.941801 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.33283 | −0.109930 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.34696 | −0.192270 | −0.0961350 | − | 0.995368i | \(-0.530648\pi\) | ||||
−0.0961350 | + | 0.995368i | \(0.530648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5033 | 1.01751 | 0.508754 | − | 0.860912i | \(-0.330106\pi\) | ||||
0.508754 | + | 0.860912i | \(0.330106\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.53908 | 0.205273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.8666 | 1.27443 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3829 | 1.46712 | 0.733558 | − | 0.679627i | \(-0.237858\pi\) | ||||
0.733558 | + | 0.679627i | \(0.237858\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.65430 | −0.131195 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8427 | −0.854524 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3211 | 0.808410 | 0.404205 | − | 0.914668i | \(-0.367548\pi\) | ||||
0.404205 | + | 0.914668i | \(0.367548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00963 | 0.0785993 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.89364 | 0.223916 | 0.111958 | − | 0.993713i | \(-0.464288\pi\) | ||||
0.111958 | + | 0.993713i | \(0.464288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.34360 | −0.564892 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.57896 | −0.197218 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.2755 | 1.92166 | 0.960829 | − | 0.277142i | \(-0.0893872\pi\) | ||||
0.960829 | + | 0.277142i | \(0.0893872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.76009 | −0.586608 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.28643 | 0.472517 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2398 | −0.840103 | −0.420052 | − | 0.907500i | \(-0.637988\pi\) | ||||
−0.420052 | + | 0.907500i | \(0.637988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8790 | −1.03162 | −0.515810 | − | 0.856703i | \(-0.672509\pi\) | ||||
−0.515810 | + | 0.856703i | \(0.672509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.48477 | −0.627212 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.60809 | −0.706401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.984536 | 0.0719964 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.8927 | 0.792326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.4623 | −0.829386 | −0.414693 | − | 0.909961i | \(-0.636111\pi\) | ||||
−0.414693 | + | 0.909961i | \(0.636111\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.77127 | −0.559388 | −0.279694 | − | 0.960089i | \(-0.590233\pi\) | ||||
−0.279694 | + | 0.960089i | \(0.590233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.40121 | 0.171954 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.8954 | −1.55998 | −0.779992 | − | 0.625789i | \(-0.784777\pi\) | ||||
−0.779992 | + | 0.625789i | \(0.784777\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.30406 | 0.375995 | 0.187998 | − | 0.982169i | \(-0.439800\pi\) | ||||
0.187998 | + | 0.982169i | \(0.439800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.14303 | −0.503831 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.9313 | 1.53927 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.31172 | 0.0916143 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.29310 | 0.645915 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0516 | 1.44925 | 0.724624 | − | 0.689144i | \(-0.242013\pi\) | ||||
0.724624 | + | 0.689144i | \(0.242013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.98865 | −0.410335 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.3444 | 1.04648 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.6834 | 2.08293 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.38640 | 0.161258 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.34154 | 0.157509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2686 | 1.35729 | 0.678645 | − | 0.734467i | \(-0.262568\pi\) | ||||
0.678645 | + | 0.734467i | \(0.262568\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65105 | 0.443404 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4348 | −1.28993 | −0.644966 | − | 0.764211i | \(-0.723129\pi\) | ||||
−0.644966 | + | 0.764211i | \(0.723129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3074 | 1.47412 | 0.737058 | − | 0.675829i | \(-0.236214\pi\) | ||||
0.737058 | + | 0.675829i | \(0.236214\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.95246 | 0.128462 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.60970 | 0.105455 | 0.0527274 | − | 0.998609i | \(-0.483209\pi\) | ||||
0.0527274 | + | 0.998609i | \(0.483209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3283 | 1.39131 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.68793 | −0.174600 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.8702 | −1.60872 | −0.804360 | − | 0.594142i | \(-0.797492\pi\) | ||||
−0.804360 | + | 0.594142i | \(0.797492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.62638 | −0.555674 | −0.277837 | − | 0.960628i | \(-0.589618\pi\) | ||||
−0.277837 | + | 0.960628i | \(0.589618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3562 | −0.920951 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.19605 | 0.204188 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.37832 | −0.151329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.16601 | 0.200638 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2395 | −1.08815 | −0.544073 | − | 0.839038i | \(-0.683119\pi\) | ||||
−0.544073 | + | 0.839038i | \(0.683119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.60342 | 0.226545 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.994013 | 0.0622475 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.30942 | 0.455949 | 0.227975 | − | 0.973667i | \(-0.426790\pi\) | ||||
0.227975 | + | 0.973667i | \(0.426790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.5805 | −1.15454 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.7970 | −1.16350 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.9406 | 1.04460 | 0.522302 | − | 0.852761i | \(-0.325073\pi\) | ||||
0.522302 | + | 0.852761i | \(0.325073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.96694 | 0.243687 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.73157 | 0.473164 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.0938 | 1.52999 | 0.764997 | − | 0.644034i | \(-0.222740\pi\) | ||||
0.764997 | + | 0.644034i | \(0.222740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.38851 | −0.509565 | −0.254783 | − | 0.966998i | \(-0.582004\pi\) | ||||
−0.254783 | + | 0.966998i | \(0.582004\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.64357 | 0.281041 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.57896 | 0.155517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.197132 | −0.0118445 | −0.00592226 | − | 0.999982i | \(-0.501885\pi\) | ||||
−0.00592226 | + | 0.999982i | \(0.501885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.2983 | −1.57444 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3356 | 1.03416 | 0.517078 | − | 0.855939i | \(-0.327020\pi\) | ||||
0.517078 | + | 0.855939i | \(0.327020\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.1466 | 1.37592 | 0.687962 | − | 0.725747i | \(-0.258506\pi\) | ||||
0.687962 | + | 0.725747i | \(0.258506\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00963 | −0.0598051 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.53665 | 0.149734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0307 | −0.942982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.02604 | 0.353253 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.8615 | −1.27716 | −0.638582 | − | 0.769554i | \(-0.720479\pi\) | ||||
−0.638582 | + | 0.769554i | \(0.720479\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0746 | −0.877675 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.62004 | −0.210056 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.57009 | 0.495621 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.6737 | 1.71036 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4902 | −0.602645 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.3461 | 1.16501 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.95976 | 0.568434 | 0.284217 | − | 0.958760i | \(-0.408266\pi\) | ||||
0.284217 | + | 0.958760i | \(0.408266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.773522 | 0.0440041 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9164 | 1.41288 | 0.706440 | − | 0.707773i | \(-0.250300\pi\) | ||||
0.706440 | + | 0.707773i | \(0.250300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.2798 | 1.76804 | 0.884019 | − | 0.467451i | \(-0.154828\pi\) | ||||
0.884019 | + | 0.467451i | \(0.154828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0745 | −0.680319 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4148 | −1.09044 | −0.545222 | − | 0.838292i | \(-0.683555\pi\) | ||||
−0.545222 | + | 0.838292i | \(0.683555\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.28857 | −0.408082 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.39506 | 0.245308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.984536 | −0.0547811 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.13360 | 0.340231 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.59745 | −0.198940 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.2456 | 2.27394 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3051 | 0.786278 | 0.393139 | − | 0.919479i | \(-0.371389\pi\) | ||||
0.393139 | + | 0.919479i | \(0.371389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9251 | 0.872689 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.1287 | 0.935839 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1133 | 0.986694 | 0.493347 | − | 0.869833i | \(-0.335773\pi\) | ||||
0.493347 | + | 0.869833i | \(0.335773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.83075 | −0.316683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.1972 | −0.552211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.8823 | −0.803569 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.63811 | 0.195869 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.68351 | 0.305107 | 0.152553 | − | 0.988295i | \(-0.451250\pi\) | ||||
0.152553 | + | 0.988295i | \(0.451250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.0341 | 1.87533 | 0.937666 | − | 0.347537i | \(-0.112982\pi\) | ||||
0.937666 | + | 0.347537i | \(0.112982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.60961 | −0.459547 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.60545 | 0.191899 | 0.0959494 | − | 0.995386i | \(-0.469411\pi\) | ||||
0.0959494 | + | 0.995386i | \(0.469411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3605 | 0.762176 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.92227 | 0.101737 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6880 | 0.827982 | 0.413991 | − | 0.910281i | \(-0.364134\pi\) | ||||
0.413991 | + | 0.910281i | \(0.364134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.648873 | −0.0340570 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.72248 | −0.299528 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.2412 | −1.47418 | −0.737088 | − | 0.675796i | \(-0.763800\pi\) | ||||
−0.737088 | + | 0.675796i | \(0.763800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.17413 | −0.113180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.67144 | 0.398281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6776 | −0.863531 | −0.431766 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431766 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.65192 | 0.395143 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.3345 | −0.892775 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5322 | −1.31150 | −0.655751 | − | 0.754977i | \(-0.727648\pi\) | ||||
−0.655751 | + | 0.754977i | \(0.727648\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.5947 | 0.645249 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.8917 | −1.22081 | −0.610403 | − | 0.792091i | \(-0.708993\pi\) | ||||
−0.610403 | + | 0.792091i | \(0.708993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.68190 | −0.238612 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.4328 | −1.29282 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6454 | −0.793255 | −0.396628 | − | 0.917980i | \(-0.629820\pi\) | ||||
−0.396628 | + | 0.917980i | \(0.629820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.54770 | 0.179415 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.03921 | −0.455968 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.44554 | 0.324310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3915 | 0.521534 | 0.260767 | − | 0.965402i | \(-0.416025\pi\) | ||||
0.260767 | + | 0.965402i | \(0.416025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.95246 | −0.0977451 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4409 | 0.721144 | 0.360572 | − | 0.932731i | \(-0.382582\pi\) | ||||
0.360572 | + | 0.932731i | \(0.382582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.2522 | −1.20809 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.38347 | 0.416578 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.17499 | 0.306083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5325 | −0.866925 | −0.433462 | − | 0.901172i | \(-0.642708\pi\) | ||||
−0.433462 | + | 0.901172i | \(0.642708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.90067 | 0.0937534 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.1518 | −1.43447 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.59194 | −0.372674 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.07817 | −0.101768 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9059 | −0.532787 | −0.266394 | − | 0.963864i | \(-0.585832\pi\) | ||||
−0.266394 | + | 0.963864i | \(0.585832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00303 | −0.195096 | −0.0975480 | − | 0.995231i | \(-0.531100\pi\) | ||||
−0.0975480 | + | 0.995231i | \(0.531100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −35.3510 | −1.71882 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.53908 | 0.123164 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.3461 | 1.90409 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.54323 | −0.0745077 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1424 | −1.74092 | −0.870459 | − | 0.492241i | \(-0.836178\pi\) | ||||
−0.870459 | + | 0.492241i | \(0.836178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.449187 | −0.0215866 | −0.0107933 | − | 0.999942i | \(-0.503436\pi\) | ||||
−0.0107933 | + | 0.999942i | \(0.503436\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.35873 | −0.352824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.60342 | −0.172375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6963 | −1.17869 | −0.589344 | − | 0.807882i | \(-0.700614\pi\) | ||||
−0.589344 | + | 0.807882i | \(0.700614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.29735 | −0.252255 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.3811 | 1.77603 | 0.888014 | − | 0.459817i | \(-0.152085\pi\) | ||||
0.888014 | + | 0.459817i | \(0.152085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.5399 | −0.878878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.52288 | 0.0720296 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5090 | −0.590337 | −0.295168 | − | 0.955445i | \(-0.595376\pi\) | ||||
−0.295168 | + | 0.955445i | \(0.595376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.843023 | −0.0396964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.11308 | −0.381186 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.1351 | −0.522020 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.0973 | −1.54823 | −0.774114 | − | 0.633047i | \(-0.781804\pi\) | ||||
−0.774114 | + | 0.633047i | \(0.781804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.56406 | −0.166356 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.5472 | −0.956978 | −0.478489 | − | 0.878093i | \(-0.658815\pi\) | ||||
−0.478489 | + | 0.878093i | \(0.658815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.1889 | −1.96068 | −0.980342 | − | 0.197305i | \(-0.936781\pi\) | ||||
−0.980342 | + | 0.197305i | \(0.936781\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.2954 | −0.477437 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.0985 | 1.39279 | 0.696397 | − | 0.717657i | \(-0.254785\pi\) | ||||
0.696397 | + | 0.717657i | \(0.254785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.1241 | 1.52953 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9282 | −0.549621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.86165 | −0.453439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.57896 | −0.118331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.57507 | −0.301052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.08471 | −0.415091 | −0.207545 | − | 0.978225i | \(-0.566547\pi\) | ||||
−0.207545 | + | 0.978225i | \(0.566547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6861 | 0.669629 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.03553 | 0.320128 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.4502 | −0.656148 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.1126 | −1.13796 | −0.568980 | − | 0.822351i | \(-0.692662\pi\) | ||||
−0.568980 | + | 0.822351i | \(0.692662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.69708 | −0.302852 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.7076 | 0.618616 | 0.309308 | − | 0.950962i | \(-0.399903\pi\) | ||||
0.309308 | + | 0.950962i | \(0.399903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.17586 | −0.323185 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.01278 | 0.180361 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7709 | 1.24570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.34793 | 0.328938 | 0.164469 | − | 0.986382i | \(-0.447409\pi\) | ||||
0.164469 | + | 0.986382i | \(0.447409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.87760 | −0.0838852 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8783 | 0.752565 | 0.376282 | − | 0.926505i | \(-0.377202\pi\) | ||||
0.376282 | + | 0.926505i | \(0.377202\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.1550 | 1.11938 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.76506 | 0.211624 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4487 | −1.34961 | −0.674807 | − | 0.737995i | \(-0.735773\pi\) | ||||
−0.674807 | + | 0.737995i | \(0.735773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0664 | −0.489547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.62004 | 0.159829 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.85487 | −0.0817353 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7074 | −0.602852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.4006 | −0.719905 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.59750 | −0.332852 | −0.166426 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166426 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2619 | 0.579904 | 0.289952 | − | 0.957041i | \(-0.406361\pi\) | ||||
0.289952 | + | 0.957041i | \(0.406361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.03532 | 0.219759 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0395 | −0.437329 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0153 | −0.435449 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.9856 | 1.08428 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00498 | −0.0868452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.5392 | −0.455647 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.29321 | 0.314725 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.05406 | −0.0884747 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.5111 | 1.48375 | 0.741874 | − | 0.670540i | \(-0.233937\pi\) | ||||
0.741874 | + | 0.670540i | \(0.233937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.00573 | 0.386473 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.62652 | 0.369520 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4643 | −1.34532 | −0.672659 | − | 0.739952i | \(-0.734848\pi\) | ||||
−0.672659 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.7230 | −1.43926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.28857 | 0.310504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.4647 | 0.530051 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.23443 | 0.264637 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.7346 | 0.497209 | 0.248604 | − | 0.968605i | \(-0.420028\pi\) | ||||
0.248604 | + | 0.968605i | \(0.420028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.4541 | −0.992004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.638839 | −0.0269718 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.8769 | 1.80705 | 0.903523 | − | 0.428540i | \(-0.140972\pi\) | ||||
0.903523 | + | 0.428540i | \(0.140972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.9819 | 0.588222 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.2123 | 0.680853 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.6183 | −1.40935 | −0.704677 | − | 0.709528i | \(-0.748908\pi\) | ||||
−0.704677 | + | 0.709528i | \(0.748908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.83048 | −0.118452 | −0.0592260 | − | 0.998245i | \(-0.518863\pi\) | ||||
−0.0592260 | + | 0.998245i | \(0.518863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.43761 | 0.310711 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.29310 | 0.387549 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6118 | −0.691558 | −0.345779 | − | 0.938316i | \(-0.612385\pi\) | ||||
−0.345779 | + | 0.938316i | \(0.612385\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.04257 | 0.209562 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6816 | −0.609096 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.54950 | −0.105590 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.54368 | 0.394583 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.95793 | −0.122087 | −0.0610433 | − | 0.998135i | \(-0.519443\pi\) | ||||
−0.0610433 | + | 0.998135i | \(0.519443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.1972 | 0.420169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2074 | 0.584412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.7969 | −1.14148 | −0.570740 | − | 0.821130i | \(-0.693344\pi\) | ||||
−0.570740 | + | 0.821130i | \(0.693344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.60950 | −0.188971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.44166 | −0.140858 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7222 | −0.764967 | −0.382484 | − | 0.923962i | \(-0.624931\pi\) | ||||
−0.382484 | + | 0.923962i | \(0.624931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0097 | 1.06096 | 0.530480 | − | 0.847698i | \(-0.322012\pi\) | ||||
0.530480 | + | 0.847698i | \(0.322012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.3902 | −1.15614 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.55597 | 0.0632591 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.46452 | 0.221798 | 0.110899 | − | 0.993832i | \(-0.464627\pi\) | ||||
0.110899 | + | 0.993832i | \(0.464627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.2306 | −0.576654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.6006 | −1.31888 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.86368 | −0.317611 | −0.158806 | − | 0.987310i | \(-0.550764\pi\) | ||||
−0.158806 | + | 0.987310i | \(0.550764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.851138 | −0.0343212 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7961 | −0.756703 | −0.378351 | − | 0.925662i | \(-0.623509\pi\) | ||||
−0.378351 | + | 0.925662i | \(0.623509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.67151 | 0.388731 | 0.194365 | − | 0.980929i | \(-0.437735\pi\) | ||||
0.194365 | + | 0.980929i | \(0.437735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.0445 | −0.523459 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.8533 | −1.43643 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.45413 | −0.218165 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.648873 | 0.0259135 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.07951 | 0.242406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.9683 | 1.75035 | 0.875175 | − | 0.483806i | \(-0.160746\pi\) | ||||
0.875175 | + | 0.483806i | \(0.160746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.6598 | −0.542928 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.2016 | −1.19852 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.88521 | −0.193559 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.8020 | −0.941594 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5103 | −0.454629 | −0.227314 | − | 0.973821i | \(-0.572995\pi\) | ||||
−0.227314 | + | 0.973821i | \(0.572995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9328 | 0.707199 | 0.353599 | − | 0.935397i | \(-0.384958\pi\) | ||||
0.353599 | + | 0.935397i | \(0.384958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.95657 | −0.392040 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.27370 | 0.246645 | 0.123322 | − | 0.992367i | \(-0.460645\pi\) | ||||
0.123322 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.68822 | 0.380296 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.9096 | −0.780320 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.0285 | 1.64470 | 0.822351 | − | 0.568981i | \(-0.192662\pi\) | ||||
0.822351 | + | 0.568981i | \(0.192662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.6756 | 0.846937 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.48481 | 0.370038 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.5487 | −1.61851 | −0.809254 | − | 0.587458i | \(-0.800129\pi\) | ||||
−0.809254 | + | 0.587458i | \(0.800129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.4271 | −0.405567 | −0.202783 | − | 0.979224i | \(-0.564999\pi\) | ||||
−0.202783 | + | 0.979224i | \(0.564999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.51936 | −0.0590072 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.68190 | 0.181556 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.2638 | −1.01694 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1518 | −0.508477 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0762 | −0.504800 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.99864 | 0.115589 | 0.0577945 | − | 0.998329i | \(-0.481593\pi\) | ||||
0.0577945 | + | 0.998329i | \(0.481593\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.33595 | −0.359341 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.4801 | −1.59421 | −0.797104 | − | 0.603842i | \(-0.793636\pi\) | ||||
−0.797104 | + | 0.603842i | \(0.793636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.9443 | −1.07241 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.6107 | 0.483244 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.0700 | −1.03580 | −0.517902 | − | 0.855440i | \(-0.673287\pi\) | ||||
−0.517902 | + | 0.855440i | \(0.673287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.55773 | −0.174142 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4747 | −0.552244 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.06353 | −0.231002 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3633 | 0.622491 | 0.311245 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311245 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.76009 | 0.294782 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.98336 | 0.189030 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.829987 | −0.0314380 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.04449 | −0.0395062 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.61332 | −0.0987039 | −0.0493520 | − | 0.998781i | \(-0.515716\pi\) | ||||
−0.0493520 | + | 0.998781i | \(0.515716\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.17499 | −0.232894 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8394 | −0.521221 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.6458 | 1.82951 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.0692 | 1.27950 | 0.639748 | − | 0.768585i | \(-0.279039\pi\) | ||||
0.639748 | + | 0.768585i | \(0.279039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6833 | −0.400654 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.7449 | −1.37611 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.70059 | 0.138394 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.1376 | 0.602670 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.55433 | 0.132554 | 0.0662771 | − | 0.997801i | \(-0.478888\pi\) | ||||
0.0662771 | + | 0.997801i | \(0.478888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.58703 | −0.133588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.59743 | 0.208171 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.7970 | −0.698102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4519 | 0.795605 | 0.397803 | − | 0.917471i | \(-0.369773\pi\) | ||||
0.397803 | + | 0.917471i | \(0.369773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.84847 | −0.253647 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.70915 | −0.359106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0026 | −0.406392 | −0.203196 | − | 0.979138i | \(-0.565133\pi\) | ||||
−0.203196 | + | 0.979138i | \(0.565133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.07383 | −0.0764945 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0084 | −0.405498 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2742 | 0.488300 | 0.244150 | − | 0.969738i | \(-0.421491\pi\) | ||||
0.244150 | + | 0.969738i | \(0.421491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.54323 | 0.0566919 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.6244 | −0.683264 | −0.341632 | − | 0.939834i | \(-0.610980\pi\) | ||||
−0.341632 | + | 0.939834i | \(0.610980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.65179 | −0.133791 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.5834 | 0.460402 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.3811 | −0.744708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.9807 | 1.60488 | 0.802440 | − | 0.596733i | \(-0.203535\pi\) | ||||
0.802440 | + | 0.596733i | \(0.203535\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.1862 | 0.407649 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.4548 | 0.708032 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.80658 | 0.102007 | 0.0510035 | − | 0.998698i | \(-0.483758\pi\) | ||||
0.0510035 | + | 0.998698i | \(0.483758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.33817 | −0.0848700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.6635 | −1.40155 | −0.700776 | − | 0.713381i | \(-0.747163\pi\) | ||||
−0.700776 | + | 0.713381i | \(0.747163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6823 | 0.603941 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.95073 | 0.142839 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.0417 | 0.831987 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.0719 | −1.76958 | −0.884789 | − | 0.465991i | \(-0.845698\pi\) | ||||
−0.884789 | + | 0.465991i | \(0.845698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.74289 | −0.170811 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.3520 | 0.480237 | 0.240118 | − | 0.970744i | \(-0.422814\pi\) | ||||
0.240118 | + | 0.970744i | \(0.422814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.2983 | −0.944662 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.0564 | 0.432521 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.843023 | 0.0302044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.22930 | −0.330250 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.3849 | 0.942920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.6032 | 1.02089 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.302278 | 0.0107750 | 0.00538752 | − | 0.999985i | \(-0.498285\pi\) | ||||
0.00538752 | + | 0.999985i | \(0.498285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.9923 | −0.391337 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.0387 | 0.961387 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0993 | −1.10437 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.57404 | −0.0912919 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.7238 | 1.58420 | 0.792099 | − | 0.610393i | \(-0.208988\pi\) | ||||
0.792099 | + | 0.610393i | \(0.208988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4955 | −0.477435 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.7293 | 1.08577 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.67776 | 0.129785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.8709 | −0.594620 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.2827 | −0.573177 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.2857 | 0.396785 | 0.198392 | − | 0.980123i | \(-0.436428\pi\) | ||||
0.198392 | + | 0.980123i | \(0.436428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0389 | −0.773889 | −0.386944 | − | 0.922103i | \(-0.626469\pi\) | ||||
−0.386944 | + | 0.922103i | \(0.626469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.44308 | 0.190897 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0593 | 0.562532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.86165 | 0.345015 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.4560 | 0.644904 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.0370 | −1.85100 | −0.925501 | − | 0.378744i | \(-0.876356\pi\) | ||||
−0.925501 | + | 0.378744i | \(0.876356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.62045 | 0.0913431 | 0.0456715 | − | 0.998957i | \(-0.485457\pi\) | ||||
0.0456715 | + | 0.998957i | \(0.485457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.67342 | −0.0582610 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8370 | 0.898440 | 0.449220 | − | 0.893421i | \(-0.351702\pi\) | ||||
0.449220 | + | 0.893421i | \(0.351702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1565 | −0.700065 | −0.350033 | − | 0.936738i | \(-0.613830\pi\) | ||||
−0.350033 | + | 0.936738i | \(0.613830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.127914 | 0.00443728 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.02230 | −0.0700685 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.50241 | 0.155812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.9143 | 1.27595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.8056 | 0.476623 | 0.238312 | − | 0.971189i | \(-0.423406\pi\) | ||||
0.238312 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1233 | 0.831838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.2486 | −0.387422 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4264 | −0.393080 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00900 | 0.103390 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.0192 | −0.515458 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.2511 | 0.762759 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.63274 | 0.0901432 | 0.0450716 | − | 0.998984i | \(-0.485648\pi\) | ||||
0.0450716 | + | 0.998984i | \(0.485648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.01278 | −0.137234 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.6437 | −0.773494 | −0.386747 | − | 0.922186i | \(-0.626401\pi\) | ||||
−0.386747 | + | 0.922186i | \(0.626401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8614 | 0.711783 | 0.355892 | − | 0.934527i | \(-0.384177\pi\) | ||||
0.355892 | + | 0.934527i | \(0.384177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.64597 | −0.0560944 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.2239 | −0.450148 | −0.225074 | − | 0.974342i | \(-0.572262\pi\) | ||||
−0.225074 | + | 0.974342i | \(0.572262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.3278 | 1.33719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4019 | 0.353266 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.14246 | −0.140523 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.1814 | −0.887123 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.9507 | 0.810607 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.4840 | −1.19958 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.6565 | −0.798824 | −0.399412 | − | 0.916772i | \(-0.630786\pi\) | ||||
−0.399412 | + | 0.916772i | \(0.630786\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.1854 | 0.478460 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.2543 | −0.918222 | −0.459111 | − | 0.888379i | \(-0.651832\pi\) | ||||
−0.459111 | + | 0.888379i | \(0.651832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0737 | 1.21398 | 0.606989 | − | 0.794710i | \(-0.292377\pi\) | ||||
0.606989 | + | 0.794710i | \(0.292377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.78148 | 0.328801 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0861 | 0.372234 | 0.186117 | − | 0.982528i | \(-0.440410\pi\) | ||||
0.186117 | + | 0.982528i | \(0.440410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.4052 | −1.95885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.38794 | −0.180503 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.7074 | 0.458702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.4888 | −0.584586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.56090 | −0.185673 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 74.3232 | 2.47882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.51008 | −0.0836228 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.2544 | −0.640748 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.5953 | −0.717853 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.1209 | 1.43181 | 0.715903 | − | 0.698199i | \(-0.246015\pi\) | ||||
0.715903 | + | 0.698199i | \(0.246015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.6935 | −1.38289 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.8066 | 0.391171 | 0.195586 | − | 0.980687i | \(-0.437339\pi\) | ||||
0.195586 | + | 0.980687i | \(0.437339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.87924 | 0.161479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.2020 | −0.436446 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41.9172 | 1.38423 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.44474 | −0.212592 | −0.106296 | − | 0.994335i | \(-0.533899\pi\) | ||||
−0.106296 | + | 0.994335i | \(0.533899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.46262 | −0.212951 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.9502 | −0.722500 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.9251 | 0.523614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.07438 | 0.100976 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.63030 | 0.250342 | 0.125171 | − | 0.992135i | \(-0.460052\pi\) | ||||
0.125171 | + | 0.992135i | \(0.460052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.05406 | 0.0673192 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.1676 | −0.529303 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.53191 | 0.0500987 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9049 | −0.846276 | −0.423138 | − | 0.906065i | \(-0.639071\pi\) | ||||
−0.423138 | + | 0.906065i | \(0.639071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.2966 | −0.662355 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.05992 | 0.0345524 | 0.0172762 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172762 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.03777 | −0.0989234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.9487 | 0.551340 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5255 | −0.731980 | −0.365990 | − | 0.930619i | \(-0.619270\pi\) | ||||
−0.365990 | + | 0.930619i | \(0.619270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.74688 | 0.283936 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5977 | 0.408510 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0244 | −0.583867 | −0.291934 | − | 0.956439i | \(-0.594299\pi\) | ||||
−0.291934 | + | 0.956439i | \(0.594299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8350 | −0.577129 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.72936 | 0.152878 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.81393 | −0.284617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.9833 | 2.35430 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.4683 | 0.562908 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.0918 | −0.389250 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.5167 | 1.56019 | 0.780095 | − | 0.625661i | \(-0.215170\pi\) | ||||
0.780095 | + | 0.625661i | \(0.215170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.638839 | 0.0205225 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.89132 | 0.317428 | 0.158714 | − | 0.987325i | \(-0.449265\pi\) | ||||
0.158714 | + | 0.987325i | \(0.449265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.63703 | 0.308949 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.97993 | −0.127460 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.7584 | −0.568140 | −0.284070 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284070 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9154 | 0.380817 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2982 | −0.456505 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.9045 | −0.890015 | −0.445007 | − | 0.895527i | \(-0.646799\pi\) | ||||
−0.445007 | + | 0.895527i | \(0.646799\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.0686 | −1.08552 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.7632 | −0.851881 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.5357 | −1.12997 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0158 | −1.01701 | −0.508507 | − | 0.861058i | \(-0.669802\pi\) | ||||
−0.508507 | + | 0.861058i | \(0.669802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.28218 | −0.294561 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.25295 | 0.261636 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.5713 | −0.524818 | −0.262409 | − | 0.964957i | \(-0.584517\pi\) | ||||
−0.262409 | + | 0.964957i | \(0.584517\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.3537 | −0.707241 |
(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 | 3344.2.a.y.1.2 | 6 | ||
4.3 | odd | 2 | 1672.2.a.h.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.h.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.y.1.2 | 6 | 1.1 | even | 1 | trivial |