Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.698857\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43091 | −1.71891 | −0.859456 | − | 0.511210i | \(-0.829197\pi\) | ||||
−0.859456 | + | 0.511210i | \(0.829197\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.90931 | 1.95466 | ||||||||
\(5\) | −1.43091 | −0.639921 | −0.319961 | − | 0.947431i | \(-0.603670\pi\) | ||||
−0.319961 | + | 0.947431i | \(0.603670\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.64136 | −1.64097 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.47841 | 1.09997 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.30114 | 0.638222 | 0.319111 | − | 0.947717i | \(-0.396616\pi\) | ||||
0.319111 | + | 0.947717i | \(0.396616\pi\) | |||||||
\(14\) | 2.43091 | 0.649687 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.46410 | 0.866025 | ||||||||
\(17\) | −1.14407 | −0.277477 | −0.138739 | − | 0.990329i | \(-0.544305\pi\) | ||||
−0.138739 | + | 0.990329i | \(0.544305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.47841 | 1.25683 | 0.628416 | − | 0.777877i | \(-0.283704\pi\) | ||||
0.628416 | + | 0.777877i | \(0.283704\pi\) | |||||||
\(20\) | −5.59387 | −1.25083 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00588 | −0.626770 | −0.313385 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313385 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.95250 | −0.590501 | ||||||||
\(26\) | −5.59387 | −1.09705 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.90931 | −0.738791 | ||||||||
\(29\) | 3.16727 | 0.588147 | 0.294073 | − | 0.955783i | \(-0.404989\pi\) | ||||
0.294073 | + | 0.955783i | \(0.404989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.99589 | −1.25650 | −0.628249 | − | 0.778012i | \(-0.716228\pi\) | ||||
−0.628249 | + | 0.778012i | \(0.716228\pi\) | |||||||
\(32\) | 0.861816 | 0.152349 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.78112 | 0.476959 | ||||||||
\(35\) | 1.43091 | 0.241868 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.16884 | −1.34295 | −0.671475 | − | 0.741027i | \(-0.734339\pi\) | ||||
−0.671475 | + | 0.741027i | \(0.734339\pi\) | |||||||
\(38\) | −13.3175 | −2.16038 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.64136 | 1.05009 | ||||||||
\(41\) | −5.59387 | −0.873615 | −0.436808 | − | 0.899555i | \(-0.643891\pi\) | ||||
−0.436808 | + | 0.899555i | \(0.643891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5939 | 1.61555 | 0.807775 | − | 0.589491i | \(-0.200672\pi\) | ||||
0.807775 | + | 0.589491i | \(0.200672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.30703 | 1.07736 | ||||||||
\(47\) | 12.9384 | 1.88726 | 0.943629 | − | 0.331004i | \(-0.107387\pi\) | ||||
0.943629 | + | 0.331004i | \(0.107387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.17726 | 1.01502 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.99589 | 1.24751 | ||||||||
\(53\) | −9.28273 | −1.27508 | −0.637540 | − | 0.770417i | \(-0.720048\pi\) | ||||
−0.637540 | + | 0.770417i | \(0.720048\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.64136 | 0.620228 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.69933 | −1.01097 | ||||||||
\(59\) | 6.89501 | 0.897654 | 0.448827 | − | 0.893619i | \(-0.351842\pi\) | ||||
0.448827 | + | 0.893619i | \(0.351842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.50160 | −1.08852 | −0.544259 | − | 0.838917i | \(-0.683189\pi\) | ||||
−0.544259 | + | 0.838917i | \(0.683189\pi\) | |||||||
\(62\) | 17.0064 | 2.15981 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.02320 | −1.12790 | ||||||||
\(65\) | −3.29272 | −0.408412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.61405 | 0.930205 | 0.465102 | − | 0.885257i | \(-0.346018\pi\) | ||||
0.465102 | + | 0.885257i | \(0.346018\pi\) | |||||||
\(68\) | −4.47252 | −0.542373 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.47841 | −0.415749 | ||||||||
\(71\) | 1.92362 | 0.228291 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.83704 | 0.566133 | 0.283066 | − | 0.959100i | \(-0.408648\pi\) | ||||
0.283066 | + | 0.959100i | \(0.408648\pi\) | |||||||
\(74\) | 19.8577 | 2.30841 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 21.4168 | 2.45668 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5348 | 1.52278 | 0.761392 | − | 0.648292i | \(-0.224516\pi\) | ||||
0.761392 | + | 0.648292i | \(0.224516\pi\) | |||||||
\(80\) | −4.95681 | −0.554188 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.5982 | 1.50167 | ||||||||
\(83\) | −9.40661 | −1.03251 | −0.516255 | − | 0.856435i | \(-0.672674\pi\) | ||||
−0.516255 | + | 0.856435i | \(0.672674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.63706 | 0.177564 | ||||||||
\(86\) | −25.7527 | −2.77699 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.35911 | 0.462065 | 0.231032 | − | 0.972946i | \(-0.425790\pi\) | ||||
0.231032 | + | 0.972946i | \(0.425790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.30114 | −0.241225 | ||||||||
\(92\) | −11.7509 | −1.22512 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.4520 | −3.24403 | ||||||||
\(95\) | −7.83909 | −0.804274 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.56067 | −0.666135 | −0.333068 | − | 0.942903i | \(-0.608084\pi\) | ||||
−0.333068 | + | 0.942903i | \(0.608084\pi\) | |||||||
\(98\) | −2.43091 | −0.245559 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.5423 | −1.15423 | ||||||||
\(101\) | −10.1239 | −1.00736 | −0.503682 | − | 0.863889i | \(-0.668022\pi\) | ||||
−0.503682 | + | 0.863889i | \(0.668022\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00158 | −0.492820 | −0.246410 | − | 0.969166i | \(-0.579251\pi\) | ||||
−0.246410 | + | 0.969166i | \(0.579251\pi\) | |||||||
\(104\) | −10.6804 | −1.04730 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.5655 | 2.19175 | ||||||||
\(107\) | 17.6186 | 1.70326 | 0.851629 | − | 0.524145i | \(-0.175615\pi\) | ||||
0.851629 | + | 0.524145i | \(0.175615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5813 | −1.20507 | −0.602537 | − | 0.798091i | \(-0.705843\pi\) | ||||
−0.602537 | + | 0.798091i | \(0.705843\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | −3.20457 | −0.301461 | −0.150730 | − | 0.988575i | \(-0.548163\pi\) | ||||
−0.150730 | + | 0.988575i | \(0.548163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.30114 | 0.401084 | ||||||||
\(116\) | 12.3818 | 1.14962 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.7611 | −1.54299 | ||||||||
\(119\) | 1.14407 | 0.104877 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 20.6666 | 1.87107 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.3491 | −2.45602 | ||||||||
\(125\) | 11.3793 | 1.01780 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.77524 | 0.423734 | 0.211867 | − | 0.977298i | \(-0.432046\pi\) | ||||
0.211867 | + | 0.977298i | \(0.432046\pi\) | |||||||
\(128\) | 20.2109 | 1.78641 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.00431 | 0.702024 | ||||||||
\(131\) | 16.5713 | 1.44784 | 0.723922 | − | 0.689882i | \(-0.242337\pi\) | ||||
0.723922 | + | 0.689882i | \(0.242337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.47841 | −0.475038 | ||||||||
\(134\) | −18.5091 | −1.59894 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.31004 | 0.455332 | ||||||||
\(137\) | −9.64725 | −0.824220 | −0.412110 | − | 0.911134i | \(-0.635208\pi\) | ||||
−0.412110 | + | 0.911134i | \(0.635208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.9647 | −1.77821 | −0.889103 | − | 0.457707i | \(-0.848671\pi\) | ||||
−0.889103 | + | 0.457707i | \(0.848671\pi\) | |||||||
\(140\) | 5.59387 | 0.472768 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.67613 | −0.392412 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.53207 | −0.376368 | ||||||||
\(146\) | −11.7584 | −0.973132 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −31.9346 | −2.62500 | ||||||||
\(149\) | −12.3823 | −1.01440 | −0.507199 | − | 0.861829i | \(-0.669319\pi\) | ||||
−0.507199 | + | 0.861829i | \(0.669319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6952 | −1.60277 | −0.801387 | − | 0.598146i | \(-0.795904\pi\) | ||||
−0.801387 | + | 0.598146i | \(0.795904\pi\) | |||||||
\(152\) | −25.4273 | −2.06242 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0105 | 0.804060 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.54001 | −0.122906 | −0.0614531 | − | 0.998110i | \(-0.519573\pi\) | ||||
−0.0614531 | + | 0.998110i | \(0.519573\pi\) | |||||||
\(158\) | −32.9018 | −2.61753 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.23318 | −0.0974913 | ||||||||
\(161\) | 3.00588 | 0.236897 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.7343 | 1.93734 | 0.968670 | − | 0.248352i | \(-0.0798890\pi\) | ||||
0.968670 | + | 0.248352i | \(0.0798890\pi\) | |||||||
\(164\) | −21.8682 | −1.70762 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.8666 | 1.77479 | ||||||||
\(167\) | 12.2020 | 0.944222 | 0.472111 | − | 0.881539i | \(-0.343492\pi\) | ||||
0.472111 | + | 0.881539i | \(0.343492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.70474 | −0.592672 | ||||||||
\(170\) | −3.97953 | −0.305216 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 41.4147 | 3.15784 | ||||||||
\(173\) | 12.3486 | 0.938850 | 0.469425 | − | 0.882972i | \(-0.344461\pi\) | ||||
0.469425 | + | 0.882972i | \(0.344461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.95250 | 0.223188 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.5966 | −0.794249 | ||||||||
\(179\) | −17.7036 | −1.32323 | −0.661616 | − | 0.749843i | \(-0.730129\pi\) | ||||
−0.661616 | + | 0.749843i | \(0.730129\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.64677 | −0.419721 | −0.209861 | − | 0.977731i | \(-0.567301\pi\) | ||||
−0.209861 | + | 0.977731i | \(0.567301\pi\) | |||||||
\(182\) | 5.59387 | 0.414645 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.9514 | 1.02851 | ||||||||
\(185\) | 11.6889 | 0.859382 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 50.5802 | 3.68894 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.0561 | 1.38248 | ||||||||
\(191\) | 6.86229 | 0.496538 | 0.248269 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248269 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.803848 | 0.0578622 | 0.0289311 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289311 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(194\) | 15.9484 | 1.14503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.90931 | 0.279237 | ||||||||
\(197\) | 16.4482 | 1.17189 | 0.585944 | − | 0.810352i | \(-0.300724\pi\) | ||||
0.585944 | + | 0.810352i | \(0.300724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.65156 | −0.258852 | −0.129426 | − | 0.991589i | \(-0.541313\pi\) | ||||
−0.129426 | + | 0.991589i | \(0.541313\pi\) | |||||||
\(200\) | 13.7036 | 0.968994 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.6102 | 1.73157 | ||||||||
\(203\) | −3.16727 | −0.222298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00431 | 0.559045 | ||||||||
\(206\) | 12.1584 | 0.847114 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.97139 | 0.552717 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2468 | 1.25616 | 0.628081 | − | 0.778148i | \(-0.283841\pi\) | ||||
0.628081 | + | 0.778148i | \(0.283841\pi\) | |||||||
\(212\) | −36.2891 | −2.49234 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −42.8293 | −2.92775 | ||||||||
\(215\) | −15.1588 | −1.03382 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.99589 | 0.474912 | ||||||||
\(218\) | 30.5841 | 2.07141 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.63266 | −0.177092 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.3164 | −1.62835 | −0.814173 | − | 0.580622i | \(-0.802809\pi\) | ||||
−0.814173 | + | 0.580622i | \(0.802809\pi\) | |||||||
\(224\) | −0.861816 | −0.0575825 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.79002 | 0.518184 | ||||||||
\(227\) | −9.08069 | −0.602707 | −0.301353 | − | 0.953513i | \(-0.597438\pi\) | ||||
−0.301353 | + | 0.953513i | \(0.597438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23318 | 0.0814907 | 0.0407454 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407454 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(230\) | −10.4557 | −0.689427 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.7004 | −0.965131 | ||||||||
\(233\) | 9.13996 | 0.598778 | 0.299389 | − | 0.954131i | \(-0.403217\pi\) | ||||
0.299389 | + | 0.954131i | \(0.403217\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5137 | −1.20770 | ||||||||
\(236\) | 26.9547 | 1.75460 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.78112 | −0.180274 | ||||||||
\(239\) | −25.7745 | −1.66721 | −0.833606 | − | 0.552359i | \(-0.813728\pi\) | ||||
−0.833606 | + | 0.552359i | \(0.813728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.70617 | 0.238736 | 0.119368 | − | 0.992850i | \(-0.461913\pi\) | ||||
0.119368 | + | 0.992850i | \(0.461913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −33.2354 | −2.12768 | ||||||||
\(245\) | −1.43091 | −0.0914173 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6066 | 0.802138 | ||||||||
\(248\) | 32.4705 | 2.06188 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −27.6620 | −1.74950 | ||||||||
\(251\) | 17.7354 | 1.11945 | 0.559724 | − | 0.828679i | \(-0.310907\pi\) | ||||
0.559724 | + | 0.828679i | \(0.310907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.6082 | −0.728361 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.0845 | −1.94278 | ||||||||
\(257\) | −8.43426 | −0.526114 | −0.263057 | − | 0.964780i | \(-0.584731\pi\) | ||||
−0.263057 | + | 0.964780i | \(0.584731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.16884 | 0.507587 | ||||||||
\(260\) | −12.8723 | −0.798305 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −40.2834 | −2.48872 | ||||||||
\(263\) | 3.09226 | 0.190677 | 0.0953386 | − | 0.995445i | \(-0.469607\pi\) | ||||
0.0953386 | + | 0.995445i | \(0.469607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.2827 | 0.815951 | ||||||||
\(266\) | 13.3175 | 0.816548 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 29.7657 | 1.81823 | ||||||||
\(269\) | 12.7468 | 0.777188 | 0.388594 | − | 0.921409i | \(-0.372961\pi\) | ||||
0.388594 | + | 0.921409i | \(0.372961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.6995 | 1.37890 | 0.689449 | − | 0.724334i | \(-0.257853\pi\) | ||||
0.689449 | + | 0.724334i | \(0.257853\pi\) | |||||||
\(272\) | −3.96317 | −0.240302 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.4516 | 1.41676 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.43679 | 0.386749 | 0.193375 | − | 0.981125i | \(-0.438057\pi\) | ||||
0.193375 | + | 0.981125i | \(0.438057\pi\) | |||||||
\(278\) | 50.9634 | 3.05658 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.64136 | −0.396897 | ||||||||
\(281\) | 1.70455 | 0.101685 | 0.0508423 | − | 0.998707i | \(-0.483809\pi\) | ||||
0.0508423 | + | 0.998707i | \(0.483809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.00861477 | −0.000512095 0 | −0.000256048 | − | 1.00000i | \(-0.500082\pi\) | ||||
−0.000256048 | 1.00000i | \(0.500082\pi\) | ||||||||
\(284\) | 7.52002 | 0.446231 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.59387 | 0.330195 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6911 | −0.923006 | ||||||||
\(290\) | 11.0170 | 0.646943 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.9095 | 1.10660 | ||||||||
\(293\) | −2.99130 | −0.174754 | −0.0873768 | − | 0.996175i | \(-0.527848\pi\) | ||||
−0.0873768 | + | 0.996175i | \(0.527848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.86612 | −0.574428 | ||||||||
\(296\) | 37.9146 | 2.20374 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.1003 | 1.74366 | ||||||||
\(299\) | −6.91697 | −0.400019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5939 | −0.610620 | ||||||||
\(302\) | 47.8773 | 2.75503 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.9778 | 1.08845 | ||||||||
\(305\) | 12.1650 | 0.696566 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.6115 | 0.948069 | 0.474035 | − | 0.880506i | \(-0.342797\pi\) | ||||
0.474035 | + | 0.880506i | \(0.342797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.3345 | −1.38211 | ||||||||
\(311\) | −18.0280 | −1.02227 | −0.511136 | − | 0.859500i | \(-0.670775\pi\) | ||||
−0.511136 | + | 0.859500i | \(0.670775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.1350 | 1.81638 | 0.908189 | − | 0.418559i | \(-0.137465\pi\) | ||||
0.908189 | + | 0.418559i | \(0.137465\pi\) | |||||||
\(314\) | 3.74362 | 0.211265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 52.9118 | 2.97652 | ||||||||
\(317\) | 25.9290 | 1.45632 | 0.728159 | − | 0.685408i | \(-0.240376\pi\) | ||||
0.728159 | + | 0.685408i | \(0.240376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.9114 | 0.721767 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.30703 | −0.407205 | ||||||||
\(323\) | −6.26767 | −0.348742 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.79413 | −0.376871 | ||||||||
\(326\) | −60.1268 | −3.33012 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 25.9632 | 1.43358 | ||||||||
\(329\) | −12.9384 | −0.713317 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6498 | −0.585365 | −0.292683 | − | 0.956210i | \(-0.594548\pi\) | ||||
−0.292683 | + | 0.956210i | \(0.594548\pi\) | |||||||
\(332\) | −36.7734 | −2.01820 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −29.6620 | −1.62303 | ||||||||
\(335\) | −10.8950 | −0.595258 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5148 | 0.790669 | 0.395334 | − | 0.918537i | \(-0.370629\pi\) | ||||
0.395334 | + | 0.918537i | \(0.370629\pi\) | |||||||
\(338\) | 18.7295 | 1.01875 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.39977 | 0.347076 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −49.1700 | −2.65107 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.0184 | −1.61380 | ||||||||
\(347\) | −14.7064 | −0.789479 | −0.394740 | − | 0.918793i | \(-0.629165\pi\) | ||||
−0.394740 | + | 0.918793i | \(0.629165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.89548 | −0.101463 | −0.0507315 | − | 0.998712i | \(-0.516155\pi\) | ||||
−0.0507315 | + | 0.998712i | \(0.516155\pi\) | |||||||
\(350\) | −7.17726 | −0.383641 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1014 | −1.22956 | −0.614780 | − | 0.788698i | \(-0.710755\pi\) | ||||
−0.614780 | + | 0.788698i | \(0.710755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.75252 | −0.146088 | ||||||||
\(356\) | 17.0411 | 0.903178 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 43.0359 | 2.27452 | ||||||||
\(359\) | 4.19869 | 0.221598 | 0.110799 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110799 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0129 | 0.579627 | ||||||||
\(362\) | 13.7268 | 0.721464 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.99589 | −0.471513 | ||||||||
\(365\) | −6.92136 | −0.362281 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.95073 | −0.154027 | −0.0770134 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770134 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(368\) | −10.4127 | −0.542799 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.4145 | −1.47720 | ||||||||
\(371\) | 9.28273 | 0.481935 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6666 | −1.12185 | −0.560927 | − | 0.827865i | \(-0.689555\pi\) | ||||
−0.560927 | + | 0.827865i | \(0.689555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −60.0518 | −3.09693 | ||||||||
\(377\) | 7.28833 | 0.375368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.3165 | 1.50589 | 0.752945 | − | 0.658084i | \(-0.228633\pi\) | ||||
0.752945 | + | 0.658084i | \(0.228633\pi\) | |||||||
\(380\) | −30.6455 | −1.57208 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.6816 | −0.853505 | ||||||||
\(383\) | −37.2326 | −1.90249 | −0.951247 | − | 0.308429i | \(-0.900197\pi\) | ||||
−0.951247 | + | 0.308429i | \(0.900197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.95408 | −0.0994600 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.6477 | −1.30207 | ||||||||
\(389\) | 29.3869 | 1.48997 | 0.744987 | − | 0.667079i | \(-0.232455\pi\) | ||||
0.744987 | + | 0.667079i | \(0.232455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43894 | 0.173915 | ||||||||
\(392\) | −4.64136 | −0.234424 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.9841 | −2.01437 | ||||||||
\(395\) | −19.3670 | −0.974462 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.5537 | −0.931183 | −0.465591 | − | 0.885000i | \(-0.654158\pi\) | ||||
−0.465591 | + | 0.885000i | \(0.654158\pi\) | |||||||
\(398\) | 8.87659 | 0.444943 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.2278 | −0.511388 | ||||||||
\(401\) | −3.09911 | −0.154762 | −0.0773810 | − | 0.997002i | \(-0.524656\pi\) | ||||
−0.0773810 | + | 0.997002i | \(0.524656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0985 | −0.801925 | ||||||||
\(404\) | −39.5774 | −1.96905 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.69933 | 0.382111 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5912 | 0.672041 | 0.336020 | − | 0.941855i | \(-0.390919\pi\) | ||||
0.336020 | + | 0.941855i | \(0.390919\pi\) | |||||||
\(410\) | −19.4577 | −0.960949 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −19.5527 | −0.963294 | ||||||||
\(413\) | −6.89501 | −0.339281 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4600 | 0.660725 | ||||||||
\(416\) | 1.98316 | 0.0972325 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.38136 | 0.0674838 | 0.0337419 | − | 0.999431i | \(-0.489258\pi\) | ||||
0.0337419 | + | 0.999431i | \(0.489258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1477 | 1.37184 | 0.685919 | − | 0.727678i | \(-0.259401\pi\) | ||||
0.685919 | + | 0.727678i | \(0.259401\pi\) | |||||||
\(422\) | −44.3563 | −2.15923 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 43.0845 | 2.09237 | ||||||||
\(425\) | 3.37786 | 0.163851 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.50160 | 0.411421 | ||||||||
\(428\) | 68.8768 | 3.32928 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 36.8498 | 1.77705 | ||||||||
\(431\) | −10.7754 | −0.519034 | −0.259517 | − | 0.965738i | \(-0.583563\pi\) | ||||
−0.259517 | + | 0.965738i | \(0.583563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7516 | −0.708917 | −0.354459 | − | 0.935072i | \(-0.615335\pi\) | ||||
−0.354459 | + | 0.935072i | \(0.615335\pi\) | |||||||
\(434\) | −17.0064 | −0.816331 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −49.1844 | −2.35550 | ||||||||
\(437\) | −16.4675 | −0.787745 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.56545 | 0.217897 | 0.108949 | − | 0.994047i | \(-0.465252\pi\) | ||||
0.108949 | + | 0.994047i | \(0.465252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.39977 | 0.304406 | ||||||||
\(443\) | −19.1300 | −0.908896 | −0.454448 | − | 0.890773i | \(-0.650163\pi\) | ||||
−0.454448 | + | 0.890773i | \(0.650163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.23749 | −0.295685 | ||||||||
\(446\) | 59.1109 | 2.79898 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.02320 | 0.426306 | ||||||||
\(449\) | 27.4346 | 1.29472 | 0.647359 | − | 0.762185i | \(-0.275873\pi\) | ||||
0.647359 | + | 0.762185i | \(0.275873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.5277 | −0.589252 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.0743 | 1.03600 | ||||||||
\(455\) | 3.29272 | 0.154365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.58244 | −0.261135 | −0.130568 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130568 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(458\) | −2.99774 | −0.140075 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.8145 | 0.783981 | ||||||||
\(461\) | 31.2918 | 1.45740 | 0.728701 | − | 0.684832i | \(-0.240124\pi\) | ||||
0.728701 | + | 0.684832i | \(0.240124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5780 | 0.956340 | 0.478170 | − | 0.878267i | \(-0.341300\pi\) | ||||
0.478170 | + | 0.878267i | \(0.341300\pi\) | |||||||
\(464\) | 10.9717 | 0.509350 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.2184 | −1.02925 | ||||||||
\(467\) | 40.8220 | 1.88902 | 0.944508 | − | 0.328489i | \(-0.106539\pi\) | ||||
0.944508 | + | 0.328489i | \(0.106539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.61405 | −0.351584 | ||||||||
\(470\) | 45.0050 | 2.07592 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.0022 | −1.47302 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.1750 | −0.742160 | ||||||||
\(476\) | 4.47252 | 0.204998 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 62.6554 | 2.86579 | ||||||||
\(479\) | −26.5969 | −1.21525 | −0.607623 | − | 0.794226i | \(-0.707877\pi\) | ||||
−0.607623 | + | 0.794226i | \(0.707877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.7977 | −0.857100 | ||||||||
\(482\) | −9.00937 | −0.410366 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.38772 | 0.426274 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6150 | 1.07010 | 0.535049 | − | 0.844821i | \(-0.320293\pi\) | ||||
0.535049 | + | 0.844821i | \(0.320293\pi\) | |||||||
\(488\) | 39.4590 | 1.78623 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.47841 | 0.157138 | ||||||||
\(491\) | −40.8045 | −1.84148 | −0.920741 | − | 0.390174i | \(-0.872415\pi\) | ||||
−0.920741 | + | 0.390174i | \(0.872415\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.62357 | −0.163197 | ||||||||
\(494\) | −30.6455 | −1.37880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.2345 | −1.08816 | ||||||||
\(497\) | −1.92362 | −0.0862860 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.57197 | 0.428500 | 0.214250 | − | 0.976779i | \(-0.431269\pi\) | ||||
0.214250 | + | 0.976779i | \(0.431269\pi\) | |||||||
\(500\) | 44.4852 | 1.98944 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −43.1131 | −1.92423 | ||||||||
\(503\) | −20.1131 | −0.896797 | −0.448399 | − | 0.893834i | \(-0.648005\pi\) | ||||
−0.448399 | + | 0.893834i | \(0.648005\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4863 | 0.644634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.6679 | 0.828255 | ||||||||
\(509\) | −6.27889 | −0.278307 | −0.139154 | − | 0.990271i | \(-0.544438\pi\) | ||||
−0.139154 | + | 0.990271i | \(0.544438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.83704 | −0.213978 | ||||||||
\(512\) | 35.1417 | 1.55306 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.5029 | 0.904344 | ||||||||
\(515\) | 7.15680 | 0.315366 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.8577 | −0.872497 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.2827 | 0.670192 | ||||||||
\(521\) | 23.5173 | 1.03031 | 0.515156 | − | 0.857097i | \(-0.327734\pi\) | ||||
0.515156 | + | 0.857097i | \(0.327734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.38211 | −0.322797 | −0.161399 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161399 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(524\) | 64.7825 | 2.83004 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.51701 | −0.327757 | ||||||||
\(527\) | 8.00377 | 0.348650 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.9647 | −0.607159 | ||||||||
\(530\) | −32.2891 | −1.40255 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.4168 | −0.928536 | ||||||||
\(533\) | −12.8723 | −0.557561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.2107 | −1.08995 | ||||||||
\(536\) | −35.3396 | −1.52644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.9864 | −1.33592 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5161 | 0.452123 | 0.226061 | − | 0.974113i | \(-0.427415\pi\) | ||||
0.226061 | + | 0.974113i | \(0.427415\pi\) | |||||||
\(542\) | −55.1805 | −2.37020 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.985976 | −0.0422734 | ||||||||
\(545\) | 18.0027 | 0.771152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.42803 | 0.403114 | 0.201557 | − | 0.979477i | \(-0.435400\pi\) | ||||
0.201557 | + | 0.979477i | \(0.435400\pi\) | |||||||
\(548\) | −37.7141 | −1.61107 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.3516 | 0.739202 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.5348 | −0.575558 | ||||||||
\(554\) | −15.6472 | −0.664788 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −81.9578 | −3.47578 | ||||||||
\(557\) | −2.83580 | −0.120157 | −0.0600784 | − | 0.998194i | \(-0.519135\pi\) | ||||
−0.0600784 | + | 0.998194i | \(0.519135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.3780 | 1.03108 | ||||||||
\(560\) | 4.95681 | 0.209463 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.14359 | −0.174787 | ||||||||
\(563\) | 13.8127 | 0.582138 | 0.291069 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291069 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.58545 | 0.192911 | ||||||||
\(566\) | 0.0209417 | 0.000880246 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.92820 | −0.374619 | ||||||||
\(569\) | 20.9491 | 0.878230 | 0.439115 | − | 0.898431i | \(-0.355292\pi\) | ||||
0.439115 | + | 0.898431i | \(0.355292\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.2109 | 1.26429 | 0.632144 | − | 0.774851i | \(-0.282175\pi\) | ||||
0.632144 | + | 0.774851i | \(0.282175\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.5982 | −0.567577 | ||||||||
\(575\) | 8.87488 | 0.370108 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.1976 | 1.83997 | 0.919985 | − | 0.391955i | \(-0.128201\pi\) | ||||
0.919985 | + | 0.391955i | \(0.128201\pi\) | |||||||
\(578\) | 38.1436 | 1.58657 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.7173 | −0.735669 | ||||||||
\(581\) | 9.40661 | 0.390252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −22.4505 | −0.929007 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.27158 | 0.300386 | ||||||||
\(587\) | 7.43693 | 0.306955 | 0.153477 | − | 0.988152i | \(-0.450953\pi\) | ||||
0.153477 | + | 0.988152i | \(0.450953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.3263 | −1.57921 | ||||||||
\(590\) | 23.9836 | 0.987391 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.2977 | −1.16303 | ||||||||
\(593\) | 30.7149 | 1.26131 | 0.630656 | − | 0.776063i | \(-0.282786\pi\) | ||||
0.630656 | + | 0.776063i | \(0.282786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.63706 | −0.0671128 | ||||||||
\(596\) | −48.4063 | −1.98280 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.8145 | 0.687597 | ||||||||
\(599\) | −11.3859 | −0.465217 | −0.232609 | − | 0.972570i | \(-0.574726\pi\) | ||||
−0.232609 | + | 0.972570i | \(0.574726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.93519 | 0.201311 | 0.100655 | − | 0.994921i | \(-0.467906\pi\) | ||||
0.100655 | + | 0.994921i | \(0.467906\pi\) | |||||||
\(602\) | 25.7527 | 1.04960 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −76.9948 | −3.13287 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.24652 | −0.0911836 | −0.0455918 | − | 0.998960i | \(-0.514517\pi\) | ||||
−0.0455918 | + | 0.998960i | \(0.514517\pi\) | |||||||
\(608\) | 4.72138 | 0.191477 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.5720 | −1.19734 | ||||||||
\(611\) | 29.7731 | 1.20449 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.3261 | 1.06330 | 0.531651 | − | 0.846964i | \(-0.321572\pi\) | ||||
0.531651 | + | 0.846964i | \(0.321572\pi\) | |||||||
\(614\) | −40.3811 | −1.62965 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.08323 | −0.244901 | −0.122451 | − | 0.992475i | \(-0.539075\pi\) | ||||
−0.122451 | + | 0.992475i | \(0.539075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6732 | −0.710345 | −0.355172 | − | 0.934801i | \(-0.615578\pi\) | ||||
−0.355172 | + | 0.934801i | \(0.615578\pi\) | |||||||
\(620\) | 39.1341 | 1.57166 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 43.8244 | 1.75720 | ||||||||
\(623\) | −4.35911 | −0.174644 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.52021 | −0.0608085 | ||||||||
\(626\) | −78.1173 | −3.12219 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.02038 | −0.240239 | ||||||||
\(629\) | 9.34571 | 0.372638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2270 | −0.606178 | −0.303089 | − | 0.952962i | \(-0.598018\pi\) | ||||
−0.303089 | + | 0.952962i | \(0.598018\pi\) | |||||||
\(632\) | −62.8199 | −2.49884 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −63.0310 | −2.50328 | ||||||||
\(635\) | −6.83293 | −0.271157 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.30114 | 0.0911746 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.9200 | −1.14316 | ||||||||
\(641\) | −40.3827 | −1.59502 | −0.797510 | − | 0.603305i | \(-0.793850\pi\) | ||||
−0.797510 | + | 0.603305i | \(0.793850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.813217 | −0.0320701 | −0.0160351 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160351 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(644\) | 11.7509 | 0.463052 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.2361 | 0.599457 | ||||||||
\(647\) | −30.9476 | −1.21667 | −0.608337 | − | 0.793679i | \(-0.708163\pi\) | ||||
−0.608337 | + | 0.793679i | \(0.708163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 16.5159 | 0.647807 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 96.6941 | 3.78683 | ||||||||
\(653\) | −7.68593 | −0.300774 | −0.150387 | − | 0.988627i | \(-0.548052\pi\) | ||||
−0.150387 | + | 0.988627i | \(0.548052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.7121 | −0.926507 | ||||||||
\(656\) | −19.3777 | −0.756573 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 31.4520 | 1.22613 | ||||||||
\(659\) | −8.17999 | −0.318647 | −0.159324 | − | 0.987226i | \(-0.550931\pi\) | ||||
−0.159324 | + | 0.987226i | \(0.550931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5381 | 1.18780 | 0.593898 | − | 0.804540i | \(-0.297588\pi\) | ||||
0.593898 | + | 0.804540i | \(0.297588\pi\) | |||||||
\(662\) | 25.8886 | 1.00619 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 43.6595 | 1.69432 | ||||||||
\(665\) | 7.83909 | 0.303987 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.52043 | −0.368633 | ||||||||
\(668\) | 47.7016 | 1.84563 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.4848 | 1.02320 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.4546 | 1.32813 | 0.664063 | − | 0.747676i | \(-0.268831\pi\) | ||||
0.664063 | + | 0.747676i | \(0.268831\pi\) | |||||||
\(674\) | −35.2840 | −1.35909 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.1202 | −1.15847 | ||||||||
\(677\) | 40.6807 | 1.56349 | 0.781744 | − | 0.623600i | \(-0.214331\pi\) | ||||
0.781744 | + | 0.623600i | \(0.214331\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.56067 | 0.251776 | ||||||||
\(680\) | −7.59817 | −0.291377 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.4349 | 1.47067 | 0.735336 | − | 0.677703i | \(-0.237024\pi\) | ||||
0.735336 | + | 0.677703i | \(0.237024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8043 | 0.527436 | ||||||||
\(686\) | 2.43091 | 0.0928125 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.6982 | 1.39911 | ||||||||
\(689\) | −21.3609 | −0.813785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.8850 | −0.528211 | −0.264105 | − | 0.964494i | \(-0.585077\pi\) | ||||
−0.264105 | + | 0.964494i | \(0.585077\pi\) | |||||||
\(692\) | 48.2747 | 1.83513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.7498 | 1.35704 | ||||||||
\(695\) | 29.9986 | 1.13791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.39977 | 0.242408 | ||||||||
\(698\) | 4.60775 | 0.174406 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.5423 | 0.436256 | ||||||||
\(701\) | −44.2982 | −1.67312 | −0.836560 | − | 0.547876i | \(-0.815437\pi\) | ||||
−0.836560 | + | 0.547876i | \(0.815437\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.7522 | −1.68786 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 56.1573 | 2.11351 | ||||||||
\(707\) | 10.1239 | 0.380748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.8278 | 1.53332 | 0.766660 | − | 0.642053i | \(-0.221917\pi\) | ||||
0.766660 | + | 0.642053i | \(0.221917\pi\) | |||||||
\(710\) | 6.69112 | 0.251113 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.2322 | −0.758234 | ||||||||
\(713\) | 21.0288 | 0.787536 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −69.2091 | −2.58646 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.2066 | −0.380908 | ||||||||
\(719\) | 30.4882 | 1.13702 | 0.568510 | − | 0.822676i | \(-0.307520\pi\) | ||||
0.568510 | + | 0.822676i | \(0.307520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.00158 | 0.186268 | ||||||||
\(722\) | −26.7714 | −0.996328 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.0750 | −0.820411 | ||||||||
\(725\) | −9.35136 | −0.347301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4661 | 0.981572 | 0.490786 | − | 0.871280i | \(-0.336710\pi\) | ||||
0.490786 | + | 0.871280i | \(0.336710\pi\) | |||||||
\(728\) | 10.6804 | 0.395843 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.8252 | 0.622728 | ||||||||
\(731\) | −12.1201 | −0.448278 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.68895 | 0.0623826 | 0.0311913 | − | 0.999513i | \(-0.490070\pi\) | ||||
0.0311913 | + | 0.999513i | \(0.490070\pi\) | |||||||
\(734\) | 7.17295 | 0.264759 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.59052 | −0.0954878 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5644 | 1.60254 | 0.801270 | − | 0.598302i | \(-0.204158\pi\) | ||||
0.801270 | + | 0.598302i | \(0.204158\pi\) | |||||||
\(740\) | 45.6954 | 1.67980 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.5655 | −0.828404 | ||||||||
\(743\) | 9.89726 | 0.363095 | 0.181548 | − | 0.983382i | \(-0.441889\pi\) | ||||
0.181548 | + | 0.983382i | \(0.441889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7179 | 0.649135 | ||||||||
\(746\) | 52.6695 | 1.92837 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.6186 | −0.643771 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8450 | −0.979589 | −0.489795 | − | 0.871838i | \(-0.662928\pi\) | ||||
−0.489795 | + | 0.871838i | \(0.662928\pi\) | |||||||
\(752\) | 44.8199 | 1.63441 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.7173 | −0.645225 | ||||||||
\(755\) | 28.1820 | 1.02565 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.5277 | 0.782437 | 0.391218 | − | 0.920298i | \(-0.372054\pi\) | ||||
0.391218 | + | 0.920298i | \(0.372054\pi\) | |||||||
\(758\) | −71.2658 | −2.58849 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.3841 | 1.31979 | ||||||||
\(761\) | 29.3264 | 1.06308 | 0.531540 | − | 0.847033i | \(-0.321613\pi\) | ||||
0.531540 | + | 0.847033i | \(0.321613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.5813 | 0.455475 | ||||||||
\(764\) | 26.8268 | 0.970561 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 90.5089 | 3.27022 | ||||||||
\(767\) | 15.8664 | 0.572903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.6982 | −1.10701 | −0.553503 | − | 0.832847i | \(-0.686709\pi\) | ||||
−0.553503 | + | 0.832847i | \(0.686709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.14249 | 0.113101 | ||||||||
\(773\) | 23.7252 | 0.853336 | 0.426668 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426668 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.6554 | 0.741963 | ||||||||
\(776\) | 30.4505 | 1.09311 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −71.4368 | −2.56113 | ||||||||
\(779\) | −30.6455 | −1.09799 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.35974 | −0.298944 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.46410 | 0.123718 | ||||||||
\(785\) | 2.20361 | 0.0786503 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87454 | 0.0668202 | 0.0334101 | − | 0.999442i | \(-0.489363\pi\) | ||||
0.0334101 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(788\) | 64.3012 | 2.29064 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 47.0795 | 1.67501 | ||||||||
\(791\) | 3.20457 | 0.113941 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5634 | −0.694717 | ||||||||
\(794\) | 45.1023 | 1.60062 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.2751 | −0.505966 | ||||||||
\(797\) | 9.58066 | 0.339365 | 0.169682 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169682 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.8024 | −0.523672 | ||||||||
\(800\) | −2.54451 | −0.0899621 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.53364 | 0.266022 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.30114 | −0.151595 | ||||||||
\(806\) | 39.1341 | 1.37844 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 46.9886 | 1.65305 | ||||||||
\(809\) | 38.1237 | 1.34036 | 0.670179 | − | 0.742199i | \(-0.266217\pi\) | ||||
0.670179 | + | 0.742199i | \(0.266217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.4724 | 1.38606 | 0.693032 | − | 0.720907i | \(-0.256274\pi\) | ||||
0.693032 | + | 0.720907i | \(0.256274\pi\) | |||||||
\(812\) | −12.3818 | −0.434517 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.3925 | −1.23975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.0375 | 2.03047 | ||||||||
\(818\) | −33.0389 | −1.15518 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 31.2913 | 1.09274 | ||||||||
\(821\) | −28.2469 | −0.985822 | −0.492911 | − | 0.870080i | \(-0.664067\pi\) | ||||
−0.492911 | + | 0.870080i | \(0.664067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.4954 | 1.30701 | 0.653503 | − | 0.756924i | \(-0.273299\pi\) | ||||
0.653503 | + | 0.756924i | \(0.273299\pi\) | |||||||
\(824\) | 23.2141 | 0.808703 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.7611 | 0.583194 | ||||||||
\(827\) | −19.9210 | −0.692722 | −0.346361 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346361 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.7189 | 1.72681 | 0.863404 | − | 0.504513i | \(-0.168328\pi\) | ||||
0.863404 | + | 0.504513i | \(0.168328\pi\) | |||||||
\(830\) | −32.7200 | −1.13573 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.7637 | −0.719851 | ||||||||
\(833\) | −1.14407 | −0.0396396 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4600 | −0.604228 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.35796 | −0.115999 | ||||||||
\(839\) | −2.57431 | −0.0888749 | −0.0444375 | − | 0.999012i | \(-0.514150\pi\) | ||||
−0.0444375 | + | 0.999012i | \(0.514150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9684 | −0.654084 | ||||||||
\(842\) | −68.4246 | −2.35807 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 71.3325 | 2.45536 | ||||||||
\(845\) | 11.0248 | 0.379264 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −32.1563 | −1.10425 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.21128 | −0.281645 | ||||||||
\(851\) | 24.5546 | 0.841721 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3968 | 1.38316 | 0.691580 | − | 0.722300i | \(-0.256915\pi\) | ||||
0.691580 | + | 0.722300i | \(0.256915\pi\) | |||||||
\(854\) | −20.6666 | −0.707197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −81.7745 | −2.79500 | ||||||||
\(857\) | 3.24467 | 0.110836 | 0.0554179 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554179 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.75730 | 0.230556 | 0.115278 | − | 0.993333i | \(-0.463224\pi\) | ||||
0.115278 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(860\) | −59.2607 | −2.02077 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.1941 | 0.892174 | ||||||||
\(863\) | −13.7259 | −0.467234 | −0.233617 | − | 0.972329i | \(-0.575056\pi\) | ||||
−0.233617 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.6698 | −0.600790 | ||||||||
\(866\) | 35.8598 | 1.21857 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 27.3491 | 0.928289 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5210 | 0.593677 | ||||||||
\(872\) | 58.3946 | 1.97749 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 40.0309 | 1.35406 | ||||||||
\(875\) | −11.3793 | −0.384691 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.63610 | −0.325388 | −0.162694 | − | 0.986677i | \(-0.552018\pi\) | ||||
−0.162694 | + | 0.986677i | \(0.552018\pi\) | |||||||
\(878\) | −11.0982 | −0.374546 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.2777 | −0.817937 | −0.408968 | − | 0.912549i | \(-0.634111\pi\) | ||||
−0.408968 | + | 0.912549i | \(0.634111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8564 | −0.432653 | −0.216326 | − | 0.976321i | \(-0.569407\pi\) | ||||
−0.216326 | + | 0.976321i | \(0.569407\pi\) | |||||||
\(884\) | −10.2919 | −0.346154 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.5034 | 1.56231 | ||||||||
\(887\) | 47.1594 | 1.58346 | 0.791729 | − | 0.610873i | \(-0.209181\pi\) | ||||
0.791729 | + | 0.610873i | \(0.209181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.77524 | −0.160156 | ||||||||
\(890\) | 15.1628 | 0.508257 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −95.0604 | −3.18286 | ||||||||
\(893\) | 70.8818 | 2.37197 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.3323 | 0.846765 | ||||||||
\(896\) | −20.2109 | −0.675200 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −66.6910 | −2.22551 | ||||||||
\(899\) | −22.1578 | −0.739005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6201 | 0.353806 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.8736 | 0.494688 | ||||||||
\(905\) | 8.08001 | 0.268589 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.99890 | −0.165986 | −0.0829928 | − | 0.996550i | \(-0.526448\pi\) | ||||
−0.0829928 | + | 0.996550i | \(0.526448\pi\) | |||||||
\(908\) | −35.4993 | −1.17808 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00431 | −0.265340 | ||||||||
\(911\) | −24.2373 | −0.803017 | −0.401509 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401509 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.5704 | 0.448869 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.82088 | 0.159286 | ||||||||
\(917\) | −16.5713 | −0.547234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.5240 | 1.23780 | 0.618901 | − | 0.785469i | \(-0.287578\pi\) | ||||
0.618901 | + | 0.785469i | \(0.287578\pi\) | |||||||
\(920\) | −19.9632 | −0.658166 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −76.0674 | −2.50515 | ||||||||
\(923\) | 4.42652 | 0.145701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1185 | 0.793012 | ||||||||
\(926\) | −50.0232 | −1.64386 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.72960 | 0.0896035 | ||||||||
\(929\) | 20.8638 | 0.684519 | 0.342259 | − | 0.939606i | \(-0.388808\pi\) | ||||
0.342259 | + | 0.939606i | \(0.388808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.47841 | 0.179547 | ||||||||
\(932\) | 35.7309 | 1.17041 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −99.2345 | −3.24705 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.463822 | −0.0151524 | −0.00757620 | − | 0.999971i | \(-0.502412\pi\) | ||||
−0.00757620 | + | 0.999971i | \(0.502412\pi\) | |||||||
\(938\) | 18.5091 | 0.604342 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −72.3757 | −2.36063 | ||||||||
\(941\) | −23.6522 | −0.771039 | −0.385519 | − | 0.922700i | \(-0.625978\pi\) | ||||
−0.385519 | + | 0.922700i | \(0.625978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.8145 | 0.547556 | ||||||||
\(944\) | 23.8850 | 0.777391 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.3269 | 0.920499 | 0.460250 | − | 0.887789i | \(-0.347760\pi\) | ||||
0.460250 | + | 0.887789i | \(0.347760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1307 | 0.361319 | ||||||||
\(950\) | 39.3199 | 1.27571 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.31004 | −0.172099 | ||||||||
\(953\) | 48.2418 | 1.56270 | 0.781352 | − | 0.624090i | \(-0.214530\pi\) | ||||
0.781352 | + | 0.624090i | \(0.214530\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.81931 | −0.317745 | ||||||||
\(956\) | −100.760 | −3.25883 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64.6547 | 2.08890 | ||||||||
\(959\) | 9.64725 | 0.311526 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.9424 | 0.578789 | ||||||||
\(962\) | 45.6954 | 1.47328 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.4886 | 0.466646 | ||||||||
\(965\) | −1.15023 | −0.0370273 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1632 | 1.13077 | 0.565387 | − | 0.824826i | \(-0.308727\pi\) | ||||
0.565387 | + | 0.824826i | \(0.308727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.8207 | −0.732728 | ||||||||
\(971\) | 54.0629 | 1.73496 | 0.867480 | − | 0.497471i | \(-0.165738\pi\) | ||||
0.867480 | + | 0.497471i | \(0.165738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9647 | 0.672099 | ||||||||
\(974\) | −57.4059 | −1.83940 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.4504 | −0.942685 | ||||||||
\(977\) | 42.2318 | 1.35111 | 0.675557 | − | 0.737307i | \(-0.263903\pi\) | ||||
0.675557 | + | 0.737307i | \(0.263903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.59387 | −0.178690 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 99.1920 | 3.16534 | ||||||||
\(983\) | 0.876060 | 0.0279420 | 0.0139710 | − | 0.999902i | \(-0.495553\pi\) | ||||
0.0139710 | + | 0.999902i | \(0.495553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.5359 | −0.749916 | ||||||||
\(986\) | 8.80856 | 0.280522 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 49.2831 | 1.56790 | ||||||||
\(989\) | −31.8439 | −1.01258 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.7171 | −1.32519 | −0.662594 | − | 0.748979i | \(-0.730544\pi\) | ||||
−0.662594 | + | 0.748979i | \(0.730544\pi\) | |||||||
\(992\) | −6.02917 | −0.191426 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.67613 | 0.148318 | ||||||||
\(995\) | 5.22504 | 0.165645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.75731 | 0.245676 | 0.122838 | − | 0.992427i | \(-0.460800\pi\) | ||||
0.122838 | + | 0.992427i | \(0.460800\pi\) | |||||||
\(998\) | −23.2686 | −0.736554 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.cg.1.1 | 4 | ||
3.2 | odd | 2 | 2541.2.a.bp.1.4 | yes | 4 | ||
11.10 | odd | 2 | 7623.2.a.cn.1.4 | 4 | |||
33.32 | even | 2 | 2541.2.a.bl.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bl.1.1 | ✓ | 4 | 33.32 | even | 2 | ||
2541.2.a.bp.1.4 | yes | 4 | 3.2 | odd | 2 | ||
7623.2.a.cg.1.1 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.cn.1.4 | 4 | 11.10 | odd | 2 |