Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.743347\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.743347 | 0.525626 | 0.262813 | − | 0.964847i | \(-0.415350\pi\) | ||||
0.262813 | + | 0.964847i | \(0.415350\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.44743 | −0.723717 | ||||||||
\(5\) | 3.36180 | 1.50344 | 0.751721 | − | 0.659482i | \(-0.229224\pi\) | ||||
0.751721 | + | 0.659482i | \(0.229224\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.98340 | −1.12762 | −0.563809 | − | 0.825905i | \(-0.690665\pi\) | ||||
−0.563809 | + | 0.825905i | \(0.690665\pi\) | |||||||
\(8\) | −2.56264 | −0.906031 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.49898 | 0.790248 | ||||||||
\(11\) | −1.73328 | −0.522605 | −0.261302 | − | 0.965257i | \(-0.584152\pi\) | ||||
−0.261302 | + | 0.965257i | \(0.584152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.418547 | 0.116084 | 0.0580420 | − | 0.998314i | \(-0.481514\pi\) | ||||
0.0580420 | + | 0.998314i | \(0.481514\pi\) | |||||||
\(14\) | −2.21770 | −0.592706 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.989937 | 0.247484 | ||||||||
\(17\) | −3.04186 | −0.737758 | −0.368879 | − | 0.929477i | \(-0.620258\pi\) | ||||
−0.368879 | + | 0.929477i | \(0.620258\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.79263 | 1.55834 | 0.779168 | − | 0.626815i | \(-0.215642\pi\) | ||||
0.779168 | + | 0.626815i | \(0.215642\pi\) | |||||||
\(20\) | −4.86598 | −1.08807 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.28843 | −0.274695 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.30168 | 1.26034 | ||||||||
\(26\) | 0.311125 | 0.0610167 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.31828 | 0.816077 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26899 | −0.227918 | −0.113959 | − | 0.993485i | \(-0.536353\pi\) | ||||
−0.113959 | + | 0.993485i | \(0.536353\pi\) | |||||||
\(32\) | 5.86115 | 1.03611 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.26116 | −0.387785 | ||||||||
\(35\) | −10.0296 | −1.69531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.40619 | −1.38197 | −0.690985 | − | 0.722869i | \(-0.742823\pi\) | ||||
−0.690985 | + | 0.722869i | \(0.742823\pi\) | |||||||
\(38\) | 5.04928 | 0.819102 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.61508 | −1.36216 | ||||||||
\(41\) | 5.67691 | 0.886584 | 0.443292 | − | 0.896377i | \(-0.353811\pi\) | ||||
0.443292 | + | 0.896377i | \(0.353811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38122 | 0.363133 | 0.181566 | − | 0.983379i | \(-0.441883\pi\) | ||||
0.181566 | + | 0.983379i | \(0.441883\pi\) | |||||||
\(44\) | 2.50882 | 0.378218 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.743347 | −0.109601 | ||||||||
\(47\) | 1.01953 | 0.148713 | 0.0743566 | − | 0.997232i | \(-0.476310\pi\) | ||||
0.0743566 | + | 0.997232i | \(0.476310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.90067 | 0.271525 | ||||||||
\(50\) | 4.68433 | 0.662465 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.605819 | −0.0840120 | ||||||||
\(53\) | −1.08924 | −0.149619 | −0.0748095 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748095 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.82695 | −0.785706 | ||||||||
\(56\) | 7.64538 | 1.02166 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.743347 | 0.0976063 | ||||||||
\(59\) | 0.434930 | 0.0566231 | 0.0283115 | − | 0.999599i | \(-0.490987\pi\) | ||||
0.0283115 | + | 0.999599i | \(0.490987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8388 | −1.51580 | −0.757901 | − | 0.652369i | \(-0.773775\pi\) | ||||
−0.757901 | + | 0.652369i | \(0.773775\pi\) | |||||||
\(62\) | −0.943302 | −0.119800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.37699 | 0.297124 | ||||||||
\(65\) | 1.40707 | 0.174525 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.29594 | −0.524833 | −0.262416 | − | 0.964955i | \(-0.584519\pi\) | ||||
−0.262416 | + | 0.964955i | \(0.584519\pi\) | |||||||
\(68\) | 4.40289 | 0.533929 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.45546 | −0.891098 | ||||||||
\(71\) | 7.01482 | 0.832506 | 0.416253 | − | 0.909249i | \(-0.363343\pi\) | ||||
0.416253 | + | 0.909249i | \(0.363343\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.28137 | −1.08630 | −0.543151 | − | 0.839635i | \(-0.682769\pi\) | ||||
−0.543151 | + | 0.839635i | \(0.682769\pi\) | |||||||
\(74\) | −6.24872 | −0.726399 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.83189 | −1.12780 | ||||||||
\(77\) | 5.17108 | 0.589299 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.43604 | 0.274076 | 0.137038 | − | 0.990566i | \(-0.456242\pi\) | ||||
0.137038 | + | 0.990566i | \(0.456242\pi\) | |||||||
\(80\) | 3.32797 | 0.372078 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.21991 | 0.466011 | ||||||||
\(83\) | −15.3185 | −1.68142 | −0.840712 | − | 0.541482i | \(-0.817864\pi\) | ||||
−0.840712 | + | 0.541482i | \(0.817864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.2261 | −1.10918 | ||||||||
\(86\) | 1.77007 | 0.190872 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.44179 | 0.473496 | ||||||||
\(89\) | −11.8322 | −1.25421 | −0.627105 | − | 0.778935i | \(-0.715760\pi\) | ||||
−0.627105 | + | 0.778935i | \(0.715760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.24869 | −0.130898 | ||||||||
\(92\) | 1.44743 | 0.150906 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.757862 | 0.0781675 | ||||||||
\(95\) | 22.8354 | 2.34287 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.37241 | 0.443951 | 0.221975 | − | 0.975052i | \(-0.428750\pi\) | ||||
0.221975 | + | 0.975052i | \(0.428750\pi\) | |||||||
\(98\) | 1.41286 | 0.142720 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.12126 | −0.912126 | ||||||||
\(101\) | 7.23477 | 0.719886 | 0.359943 | − | 0.932974i | \(-0.382796\pi\) | ||||
0.359943 | + | 0.932974i | \(0.382796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9998 | −1.77358 | −0.886788 | − | 0.462176i | \(-0.847069\pi\) | ||||
−0.886788 | + | 0.462176i | \(0.847069\pi\) | |||||||
\(104\) | −1.07258 | −0.105176 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.809686 | −0.0786437 | ||||||||
\(107\) | 5.18130 | 0.500895 | 0.250447 | − | 0.968130i | \(-0.419422\pi\) | ||||
0.250447 | + | 0.968130i | \(0.419422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3146 | −1.08375 | −0.541873 | − | 0.840460i | \(-0.682285\pi\) | ||||
−0.541873 | + | 0.840460i | \(0.682285\pi\) | |||||||
\(110\) | −4.33145 | −0.412987 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.95338 | −0.279068 | ||||||||
\(113\) | −6.08524 | −0.572451 | −0.286226 | − | 0.958162i | \(-0.592401\pi\) | ||||
−0.286226 | + | 0.958162i | \(0.592401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.36180 | −0.313489 | ||||||||
\(116\) | −1.44743 | −0.134391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.323304 | 0.0297625 | ||||||||
\(119\) | 9.07507 | 0.831910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.99572 | −0.726884 | ||||||||
\(122\) | −8.80034 | −0.796745 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.83678 | 0.164948 | ||||||||
\(125\) | 4.37597 | 0.391399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.68174 | −0.237966 | −0.118983 | − | 0.992896i | \(-0.537963\pi\) | ||||
−0.118983 | + | 0.992896i | \(0.537963\pi\) | |||||||
\(128\) | −9.95537 | −0.879938 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.04594 | 0.0917350 | ||||||||
\(131\) | −5.26968 | −0.460414 | −0.230207 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230207 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.2651 | −1.75721 | ||||||||
\(134\) | −3.19338 | −0.275866 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.79518 | 0.668432 | ||||||||
\(137\) | −11.0969 | −0.948071 | −0.474036 | − | 0.880506i | \(-0.657203\pi\) | ||||
−0.474036 | + | 0.880506i | \(0.657203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7752 | −1.16840 | −0.584200 | − | 0.811610i | \(-0.698592\pi\) | ||||
−0.584200 | + | 0.811610i | \(0.698592\pi\) | |||||||
\(140\) | 14.5172 | 1.22692 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.21445 | 0.437587 | ||||||||
\(143\) | −0.725460 | −0.0606660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.36180 | 0.279182 | ||||||||
\(146\) | −6.89928 | −0.570989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.1674 | 1.00016 | ||||||||
\(149\) | −2.15134 | −0.176244 | −0.0881222 | − | 0.996110i | \(-0.528087\pi\) | ||||
−0.0881222 | + | 0.996110i | \(0.528087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3565 | 1.49383 | 0.746915 | − | 0.664920i | \(-0.231534\pi\) | ||||
0.746915 | + | 0.664920i | \(0.231534\pi\) | |||||||
\(152\) | −17.4071 | −1.41190 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.84391 | 0.309751 | ||||||||
\(155\) | −4.26610 | −0.342661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.545808 | −0.0435602 | −0.0217801 | − | 0.999763i | \(-0.506933\pi\) | ||||
−0.0217801 | + | 0.999763i | \(0.506933\pi\) | |||||||
\(158\) | 1.81082 | 0.144061 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 19.7040 | 1.55774 | ||||||||
\(161\) | 2.98340 | 0.235125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.544969 | −0.0426853 | −0.0213426 | − | 0.999772i | \(-0.506794\pi\) | ||||
−0.0213426 | + | 0.999772i | \(0.506794\pi\) | |||||||
\(164\) | −8.21695 | −0.641636 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.3870 | −0.883800 | ||||||||
\(167\) | −13.5418 | −1.04790 | −0.523950 | − | 0.851749i | \(-0.675542\pi\) | ||||
−0.523950 | + | 0.851749i | \(0.675542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8248 | −0.986525 | ||||||||
\(170\) | −7.60154 | −0.583012 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.44666 | −0.262806 | ||||||||
\(173\) | 2.48390 | 0.188847 | 0.0944236 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944236 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.8004 | −1.42118 | ||||||||
\(176\) | −1.71584 | −0.129337 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.79543 | −0.659245 | ||||||||
\(179\) | 8.19708 | 0.612679 | 0.306339 | − | 0.951922i | \(-0.400896\pi\) | ||||
0.306339 | + | 0.951922i | \(0.400896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.21935 | −0.610940 | −0.305470 | − | 0.952202i | \(-0.598814\pi\) | ||||
−0.305470 | + | 0.952202i | \(0.598814\pi\) | |||||||
\(182\) | −0.928211 | −0.0688036 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.56264 | 0.188920 | ||||||||
\(185\) | −28.2599 | −2.07771 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.27240 | 0.385556 | ||||||||
\(188\) | −1.47570 | −0.107626 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.9747 | 1.23147 | ||||||||
\(191\) | 14.0910 | 1.01959 | 0.509794 | − | 0.860296i | \(-0.329722\pi\) | ||||
0.509794 | + | 0.860296i | \(0.329722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.272693 | 0.0196289 | 0.00981444 | − | 0.999952i | \(-0.496876\pi\) | ||||
0.00981444 | + | 0.999952i | \(0.496876\pi\) | |||||||
\(194\) | 3.25022 | 0.233352 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.75110 | −0.196507 | ||||||||
\(197\) | −23.5938 | −1.68099 | −0.840495 | − | 0.541819i | \(-0.817736\pi\) | ||||
−0.840495 | + | 0.541819i | \(0.817736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.51044 | 0.248848 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(200\) | −16.1489 | −1.14190 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.37795 | 0.378391 | ||||||||
\(203\) | −2.98340 | −0.209394 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.0846 | 1.33293 | ||||||||
\(206\) | −13.3801 | −0.932238 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.414335 | 0.0287290 | ||||||||
\(209\) | −11.7736 | −0.814394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.138150 | −0.00951064 | −0.00475532 | − | 0.999989i | \(-0.501514\pi\) | ||||
−0.00475532 | + | 0.999989i | \(0.501514\pi\) | |||||||
\(212\) | 1.57661 | 0.108282 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.85150 | 0.263283 | ||||||||
\(215\) | 8.00518 | 0.545949 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.78591 | 0.257004 | ||||||||
\(218\) | −8.41070 | −0.569645 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.43413 | 0.568629 | ||||||||
\(221\) | −1.27316 | −0.0856419 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.7576 | 1.32306 | 0.661532 | − | 0.749917i | \(-0.269907\pi\) | ||||
0.661532 | + | 0.749917i | \(0.269907\pi\) | |||||||
\(224\) | −17.4862 | −1.16834 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.52345 | −0.300895 | ||||||||
\(227\) | 21.2886 | 1.41297 | 0.706486 | − | 0.707727i | \(-0.250279\pi\) | ||||
0.706486 | + | 0.707727i | \(0.250279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.98323 | −0.659711 | −0.329855 | − | 0.944031i | \(-0.607000\pi\) | ||||
−0.329855 | + | 0.944031i | \(0.607000\pi\) | |||||||
\(230\) | −2.49898 | −0.164778 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.56264 | −0.168246 | ||||||||
\(233\) | 11.7610 | 0.770490 | 0.385245 | − | 0.922814i | \(-0.374117\pi\) | ||||
0.385245 | + | 0.922814i | \(0.374117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.42744 | 0.223581 | ||||||||
\(236\) | −0.629533 | −0.0409791 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.74593 | 0.437274 | ||||||||
\(239\) | 14.7029 | 0.951053 | 0.475527 | − | 0.879701i | \(-0.342258\pi\) | ||||
0.475527 | + | 0.879701i | \(0.342258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.48179 | −0.417529 | −0.208764 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208764 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(242\) | −5.94360 | −0.382069 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.1359 | 1.09701 | ||||||||
\(245\) | 6.38967 | 0.408221 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.84303 | 0.180898 | ||||||||
\(248\) | 3.25197 | 0.206501 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.25286 | 0.205729 | ||||||||
\(251\) | −5.51951 | −0.348389 | −0.174194 | − | 0.984711i | \(-0.555732\pi\) | ||||
−0.174194 | + | 0.984711i | \(0.555732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.73328 | 0.108971 | ||||||||
\(254\) | −1.99347 | −0.125081 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.1543 | −0.759643 | ||||||||
\(257\) | 20.9651 | 1.30776 | 0.653882 | − | 0.756597i | \(-0.273139\pi\) | ||||
0.653882 | + | 0.756597i | \(0.273139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.0790 | 1.55833 | ||||||||
\(260\) | −2.03664 | −0.126307 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.91720 | −0.242005 | ||||||||
\(263\) | −4.37099 | −0.269527 | −0.134763 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134763 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.66181 | −0.224943 | ||||||||
\(266\) | −15.0640 | −0.923635 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.21809 | 0.379831 | ||||||||
\(269\) | 18.5392 | 1.13035 | 0.565177 | − | 0.824970i | \(-0.308808\pi\) | ||||
0.565177 | + | 0.824970i | \(0.308808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8222 | −1.08262 | −0.541311 | − | 0.840822i | \(-0.682072\pi\) | ||||
−0.541311 | + | 0.840822i | \(0.682072\pi\) | |||||||
\(272\) | −3.01125 | −0.182584 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.24884 | −0.498331 | ||||||||
\(275\) | −10.9226 | −0.658657 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.652922 | 0.0392303 | 0.0196152 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196152 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(278\) | −10.2398 | −0.614142 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.7022 | 1.53600 | ||||||||
\(281\) | 24.5072 | 1.46198 | 0.730988 | − | 0.682390i | \(-0.239060\pi\) | ||||
0.730988 | + | 0.682390i | \(0.239060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.4332 | −1.74962 | −0.874810 | − | 0.484466i | \(-0.839014\pi\) | ||||
−0.874810 | + | 0.484466i | \(0.839014\pi\) | |||||||
\(284\) | −10.1535 | −0.602499 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.539269 | −0.0318876 | ||||||||
\(287\) | −16.9365 | −0.999729 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.74711 | −0.455713 | ||||||||
\(290\) | 2.49898 | 0.146745 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.4342 | 0.786176 | ||||||||
\(293\) | −10.4542 | −0.610739 | −0.305369 | − | 0.952234i | \(-0.598780\pi\) | ||||
−0.305369 | + | 0.952234i | \(0.598780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.46215 | 0.0851294 | ||||||||
\(296\) | 21.5421 | 1.25211 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.59919 | −0.0926387 | ||||||||
\(299\) | −0.418547 | −0.0242052 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.10413 | −0.409476 | ||||||||
\(302\) | 13.6452 | 0.785195 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.72428 | 0.385664 | ||||||||
\(305\) | −39.7996 | −2.27892 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.3141 | −1.67304 | −0.836522 | − | 0.547933i | \(-0.815415\pi\) | ||||
−0.836522 | + | 0.547933i | \(0.815415\pi\) | |||||||
\(308\) | −7.48480 | −0.426486 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.17119 | −0.180112 | ||||||||
\(311\) | 14.2023 | 0.805338 | 0.402669 | − | 0.915346i | \(-0.368083\pi\) | ||||
0.402669 | + | 0.915346i | \(0.368083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3008 | −1.03443 | −0.517213 | − | 0.855857i | \(-0.673030\pi\) | ||||
−0.517213 | + | 0.855857i | \(0.673030\pi\) | |||||||
\(314\) | −0.405725 | −0.0228964 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.52600 | −0.198353 | ||||||||
\(317\) | −1.64584 | −0.0924397 | −0.0462198 | − | 0.998931i | \(-0.514717\pi\) | ||||
−0.0462198 | + | 0.998931i | \(0.514717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.73328 | −0.0970453 | ||||||||
\(320\) | 7.99097 | 0.446709 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.21770 | 0.123588 | ||||||||
\(323\) | −20.6622 | −1.14968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.63754 | 0.146305 | ||||||||
\(326\) | −0.405101 | −0.0224365 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.5479 | −0.803272 | ||||||||
\(329\) | −3.04165 | −0.167692 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4258 | −0.792914 | −0.396457 | − | 0.918053i | \(-0.629760\pi\) | ||||
−0.396457 | + | 0.918053i | \(0.629760\pi\) | |||||||
\(332\) | 22.1725 | 1.21688 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.0663 | −0.550803 | ||||||||
\(335\) | −14.4421 | −0.789055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.79363 | −0.424546 | −0.212273 | − | 0.977210i | \(-0.568087\pi\) | ||||
−0.212273 | + | 0.977210i | \(0.568087\pi\) | |||||||
\(338\) | −9.53329 | −0.518543 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.8016 | 0.802730 | ||||||||
\(341\) | 2.19953 | 0.119111 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2133 | 0.821443 | ||||||||
\(344\) | −6.10222 | −0.329009 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.84640 | 0.0992630 | ||||||||
\(347\) | 27.5605 | 1.47953 | 0.739764 | − | 0.672867i | \(-0.234937\pi\) | ||||
0.739764 | + | 0.672867i | \(0.234937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.9855 | −1.60509 | −0.802543 | − | 0.596594i | \(-0.796520\pi\) | ||||
−0.802543 | + | 0.596594i | \(0.796520\pi\) | |||||||
\(350\) | −13.9752 | −0.747008 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.1590 | −0.541479 | ||||||||
\(353\) | 29.6920 | 1.58034 | 0.790172 | − | 0.612885i | \(-0.209991\pi\) | ||||
0.790172 | + | 0.612885i | \(0.209991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.5824 | 1.25162 | ||||||||
\(356\) | 17.1263 | 0.907694 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.09328 | 0.322040 | ||||||||
\(359\) | −2.09906 | −0.110784 | −0.0553921 | − | 0.998465i | \(-0.517641\pi\) | ||||
−0.0553921 | + | 0.998465i | \(0.517641\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.1398 | 1.42841 | ||||||||
\(362\) | −6.10983 | −0.321126 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.80740 | 0.0947335 | ||||||||
\(365\) | −31.2021 | −1.63319 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.4918 | 1.01746 | 0.508732 | − | 0.860925i | \(-0.330114\pi\) | ||||
0.508732 | + | 0.860925i | \(0.330114\pi\) | |||||||
\(368\) | −0.989937 | −0.0516041 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.0069 | −1.09210 | ||||||||
\(371\) | 3.24965 | 0.168713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.4309 | −1.73099 | −0.865494 | − | 0.500919i | \(-0.832995\pi\) | ||||
−0.865494 | + | 0.500919i | \(0.832995\pi\) | |||||||
\(374\) | 3.91923 | 0.202658 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.61268 | −0.134739 | ||||||||
\(377\) | 0.418547 | 0.0215562 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.4822 | 1.20620 | 0.603100 | − | 0.797665i | \(-0.293932\pi\) | ||||
0.603100 | + | 0.797665i | \(0.293932\pi\) | |||||||
\(380\) | −33.0528 | −1.69557 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.4745 | 0.535922 | ||||||||
\(383\) | −22.0092 | −1.12462 | −0.562310 | − | 0.826927i | \(-0.690087\pi\) | ||||
−0.562310 | + | 0.826927i | \(0.690087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.3841 | 0.885977 | ||||||||
\(386\) | 0.202706 | 0.0103174 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.32877 | −0.321295 | ||||||||
\(389\) | −14.7724 | −0.748991 | −0.374496 | − | 0.927229i | \(-0.622184\pi\) | ||||
−0.374496 | + | 0.927229i | \(0.622184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.04186 | 0.153833 | ||||||||
\(392\) | −4.87074 | −0.246010 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.5384 | −0.883572 | ||||||||
\(395\) | 8.18946 | 0.412056 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7744 | 1.09283 | 0.546413 | − | 0.837516i | \(-0.315993\pi\) | ||||
0.546413 | + | 0.837516i | \(0.315993\pi\) | |||||||
\(398\) | 2.60947 | 0.130801 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.23826 | 0.311913 | ||||||||
\(401\) | 2.37651 | 0.118677 | 0.0593387 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593387 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.531133 | −0.0264576 | ||||||||
\(404\) | −10.4719 | −0.520994 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.21770 | −0.110063 | ||||||||
\(407\) | 14.5703 | 0.722224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.143213 | 0.00708141 | 0.00354071 | − | 0.999994i | \(-0.498873\pi\) | ||||
0.00354071 | + | 0.999994i | \(0.498873\pi\) | |||||||
\(410\) | 14.1865 | 0.700621 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.0536 | 1.28357 | ||||||||
\(413\) | −1.29757 | −0.0638492 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −51.4977 | −2.52792 | ||||||||
\(416\) | 2.45316 | 0.120276 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.75185 | −0.428067 | ||||||||
\(419\) | 1.85725 | 0.0907324 | 0.0453662 | − | 0.998970i | \(-0.485555\pi\) | ||||
0.0453662 | + | 0.998970i | \(0.485555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.7959 | 0.818584 | 0.409292 | − | 0.912403i | \(-0.365776\pi\) | ||||
0.409292 | + | 0.912403i | \(0.365776\pi\) | |||||||
\(422\) | −0.102693 | −0.00499904 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.79134 | 0.135559 | ||||||||
\(425\) | −19.1688 | −0.929823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.3199 | 1.70925 | ||||||||
\(428\) | −7.49959 | −0.362506 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.95063 | 0.286965 | ||||||||
\(431\) | −15.4833 | −0.745803 | −0.372901 | − | 0.927871i | \(-0.621637\pi\) | ||||
−0.372901 | + | 0.927871i | \(0.621637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.8387 | −0.520873 | −0.260436 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260436 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(434\) | 2.81425 | 0.135088 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.3772 | 0.784326 | ||||||||
\(437\) | −6.79263 | −0.324936 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0587 | 0.623260 | 0.311630 | − | 0.950204i | \(-0.399125\pi\) | ||||
0.311630 | + | 0.950204i | \(0.399125\pi\) | |||||||
\(440\) | 14.9324 | 0.711873 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.946399 | −0.0450156 | ||||||||
\(443\) | 13.9516 | 0.662861 | 0.331431 | − | 0.943480i | \(-0.392469\pi\) | ||||
0.331431 | + | 0.943480i | \(0.392469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.7774 | −1.88563 | ||||||||
\(446\) | 14.6867 | 0.695437 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.09153 | −0.335043 | ||||||||
\(449\) | −0.108496 | −0.00512024 | −0.00256012 | − | 0.999997i | \(-0.500815\pi\) | ||||
−0.00256012 | + | 0.999997i | \(0.500815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.83969 | −0.463333 | ||||||||
\(452\) | 8.80799 | 0.414293 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.8248 | 0.742695 | ||||||||
\(455\) | −4.19785 | −0.196798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6297 | 1.33924 | 0.669621 | − | 0.742703i | \(-0.266457\pi\) | ||||
0.669621 | + | 0.742703i | \(0.266457\pi\) | |||||||
\(458\) | −7.42101 | −0.346761 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.86598 | 0.226878 | ||||||||
\(461\) | −27.3672 | −1.27462 | −0.637310 | − | 0.770608i | \(-0.719953\pi\) | ||||
−0.637310 | + | 0.770608i | \(0.719953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.24333 | −0.429574 | −0.214787 | − | 0.976661i | \(-0.568906\pi\) | ||||
−0.214787 | + | 0.976661i | \(0.568906\pi\) | |||||||
\(464\) | 0.989937 | 0.0459567 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.74253 | 0.404990 | ||||||||
\(467\) | −27.1433 | −1.25604 | −0.628022 | − | 0.778196i | \(-0.716135\pi\) | ||||
−0.628022 | + | 0.778196i | \(0.716135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8165 | 0.591811 | ||||||||
\(470\) | 2.54778 | 0.117520 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.11457 | −0.0513022 | ||||||||
\(473\) | −4.12733 | −0.189775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.8050 | 1.96403 | ||||||||
\(476\) | −13.1356 | −0.602068 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.9294 | 0.499898 | ||||||||
\(479\) | 15.3490 | 0.701315 | 0.350657 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350657 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.51838 | −0.160424 | ||||||||
\(482\) | −4.81822 | −0.219464 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5733 | 0.526059 | ||||||||
\(485\) | 14.6991 | 0.667454 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.2996 | −1.05581 | −0.527904 | − | 0.849304i | \(-0.677022\pi\) | ||||
−0.527904 | + | 0.849304i | \(0.677022\pi\) | |||||||
\(488\) | 30.3386 | 1.37336 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.74974 | 0.214572 | ||||||||
\(491\) | 31.9633 | 1.44248 | 0.721242 | − | 0.692683i | \(-0.243571\pi\) | ||||
0.721242 | + | 0.692683i | \(0.243571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.04186 | −0.136998 | ||||||||
\(494\) | 2.11336 | 0.0950846 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.25622 | −0.0564061 | ||||||||
\(497\) | −20.9280 | −0.938750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4662 | 0.916194 | 0.458097 | − | 0.888902i | \(-0.348531\pi\) | ||||
0.458097 | + | 0.888902i | \(0.348531\pi\) | |||||||
\(500\) | −6.33393 | −0.283262 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.10292 | −0.183122 | ||||||||
\(503\) | 0.0476041 | 0.00212256 | 0.00106128 | − | 0.999999i | \(-0.499662\pi\) | ||||
0.00106128 | + | 0.999999i | \(0.499662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.3218 | 1.08231 | ||||||||
\(506\) | 1.28843 | 0.0572778 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.88165 | 0.172220 | ||||||||
\(509\) | −11.6626 | −0.516935 | −0.258467 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258467 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6900 | 1.22494 | ||||||||
\(512\) | 10.8759 | 0.480651 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.5843 | 0.687395 | ||||||||
\(515\) | −60.5118 | −2.66647 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.76713 | −0.0777182 | ||||||||
\(518\) | 18.6424 | 0.819101 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.60581 | −0.158125 | ||||||||
\(521\) | 20.4685 | 0.896743 | 0.448371 | − | 0.893847i | \(-0.352004\pi\) | ||||
0.448371 | + | 0.893847i | \(0.352004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5007 | −0.721523 | −0.360762 | − | 0.932658i | \(-0.617483\pi\) | ||||
−0.360762 | + | 0.932658i | \(0.617483\pi\) | |||||||
\(524\) | 7.62752 | 0.333210 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.24916 | −0.141670 | ||||||||
\(527\) | 3.86009 | 0.168148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.72200 | −0.118236 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 29.3325 | 1.27172 | ||||||||
\(533\) | 2.37605 | 0.102918 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.4185 | 0.753066 | ||||||||
\(536\) | 11.0090 | 0.475514 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.7811 | 0.594144 | ||||||||
\(539\) | −3.29441 | −0.141900 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.89169 | −0.339290 | −0.169645 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169645 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(542\) | −13.2481 | −0.569055 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.8288 | −0.764402 | ||||||||
\(545\) | −38.0375 | −1.62935 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.3963 | −1.47068 | −0.735340 | − | 0.677698i | \(-0.762978\pi\) | ||||
−0.735340 | + | 0.677698i | \(0.762978\pi\) | |||||||
\(548\) | 16.0620 | 0.686136 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.11928 | −0.346207 | ||||||||
\(551\) | 6.79263 | 0.289376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.26767 | −0.309053 | ||||||||
\(554\) | 0.485348 | 0.0206205 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.9388 | 0.845592 | ||||||||
\(557\) | −44.5893 | −1.88931 | −0.944655 | − | 0.328066i | \(-0.893603\pi\) | ||||
−0.944655 | + | 0.328066i | \(0.893603\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.996652 | 0.0421539 | ||||||||
\(560\) | −9.92866 | −0.419562 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.2173 | 0.768452 | ||||||||
\(563\) | 1.52081 | 0.0640943 | 0.0320472 | − | 0.999486i | \(-0.489797\pi\) | ||||
0.0320472 | + | 0.999486i | \(0.489797\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.4573 | −0.860647 | ||||||||
\(566\) | −21.8791 | −0.919646 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.9765 | −0.754276 | ||||||||
\(569\) | −2.96412 | −0.124262 | −0.0621311 | − | 0.998068i | \(-0.519790\pi\) | ||||
−0.0621311 | + | 0.998068i | \(0.519790\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2318 | 0.930371 | 0.465185 | − | 0.885213i | \(-0.345988\pi\) | ||||
0.465185 | + | 0.885213i | \(0.345988\pi\) | |||||||
\(572\) | 1.05006 | 0.0439051 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.5897 | −0.525483 | ||||||||
\(575\) | −6.30168 | −0.262798 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.31813 | 0.0548745 | 0.0274373 | − | 0.999624i | \(-0.491265\pi\) | ||||
0.0274373 | + | 0.999624i | \(0.491265\pi\) | |||||||
\(578\) | −5.75880 | −0.239534 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.86598 | −0.202049 | ||||||||
\(581\) | 45.7012 | 1.89601 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.88797 | 0.0781917 | ||||||||
\(584\) | 23.7848 | 0.984223 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.77107 | −0.321020 | ||||||||
\(587\) | −9.07620 | −0.374615 | −0.187307 | − | 0.982301i | \(-0.559976\pi\) | ||||
−0.187307 | + | 0.982301i | \(0.559976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.61980 | −0.355173 | ||||||||
\(590\) | 1.08688 | 0.0447462 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.32160 | −0.342016 | ||||||||
\(593\) | 40.3794 | 1.65818 | 0.829092 | − | 0.559112i | \(-0.188858\pi\) | ||||
0.829092 | + | 0.559112i | \(0.188858\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.5085 | 1.25073 | ||||||||
\(596\) | 3.11392 | 0.127551 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.311125 | −0.0127229 | ||||||||
\(599\) | −13.4887 | −0.551132 | −0.275566 | − | 0.961282i | \(-0.588865\pi\) | ||||
−0.275566 | + | 0.961282i | \(0.588865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.4881 | −0.468608 | −0.234304 | − | 0.972163i | \(-0.575281\pi\) | ||||
−0.234304 | + | 0.972163i | \(0.575281\pi\) | |||||||
\(602\) | −5.28084 | −0.215231 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.5698 | −1.08111 | ||||||||
\(605\) | −26.8800 | −1.09283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.94753 | −0.160225 | −0.0801126 | − | 0.996786i | \(-0.525528\pi\) | ||||
−0.0801126 | + | 0.996786i | \(0.525528\pi\) | |||||||
\(608\) | 39.8126 | 1.61462 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.5849 | −1.19786 | ||||||||
\(611\) | 0.426719 | 0.0172632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.36193 | 0.176177 | 0.0880884 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880884 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(614\) | −21.7906 | −0.879396 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.2516 | −0.533923 | ||||||||
\(617\) | −20.0408 | −0.806813 | −0.403407 | − | 0.915021i | \(-0.632174\pi\) | ||||
−0.403407 | + | 0.915021i | \(0.632174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.6150 | 1.27071 | 0.635357 | − | 0.772219i | \(-0.280853\pi\) | ||||
0.635357 | + | 0.772219i | \(0.280853\pi\) | |||||||
\(620\) | 6.17490 | 0.247990 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.5572 | 0.423306 | ||||||||
\(623\) | 35.3002 | 1.41427 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.7973 | −0.671891 | ||||||||
\(626\) | −13.6039 | −0.543721 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.790021 | 0.0315253 | ||||||||
\(629\) | 25.5704 | 1.01956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0088 | 0.677110 | 0.338555 | − | 0.940947i | \(-0.390062\pi\) | ||||
0.338555 | + | 0.940947i | \(0.390062\pi\) | |||||||
\(632\) | −6.24269 | −0.248321 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.22343 | −0.0485887 | ||||||||
\(635\) | −9.01548 | −0.357768 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.795520 | 0.0315196 | ||||||||
\(638\) | −1.28843 | −0.0510095 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −33.4679 | −1.32294 | ||||||||
\(641\) | −17.9247 | −0.707982 | −0.353991 | − | 0.935249i | \(-0.615176\pi\) | ||||
−0.353991 | + | 0.935249i | \(0.615176\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9092 | 0.785143 | 0.392571 | − | 0.919722i | \(-0.371586\pi\) | ||||
0.392571 | + | 0.919722i | \(0.371586\pi\) | |||||||
\(644\) | −4.31828 | −0.170164 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.3592 | −0.604299 | ||||||||
\(647\) | −43.0673 | −1.69315 | −0.846574 | − | 0.532270i | \(-0.821339\pi\) | ||||
−0.846574 | + | 0.532270i | \(0.821339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.753857 | −0.0295915 | ||||||||
\(650\) | 1.96061 | 0.0769015 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.788807 | 0.0308921 | ||||||||
\(653\) | −1.82134 | −0.0712744 | −0.0356372 | − | 0.999365i | \(-0.511346\pi\) | ||||
−0.0356372 | + | 0.999365i | \(0.511346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.7156 | −0.692205 | ||||||||
\(656\) | 5.61978 | 0.219416 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.26100 | −0.0881431 | ||||||||
\(659\) | −26.8403 | −1.04555 | −0.522774 | − | 0.852471i | \(-0.675103\pi\) | ||||
−0.522774 | + | 0.852471i | \(0.675103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.26124 | 0.165743 | 0.0828715 | − | 0.996560i | \(-0.473591\pi\) | ||||
0.0828715 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(662\) | −10.7234 | −0.416776 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 39.2558 | 1.52342 | ||||||||
\(665\) | −68.1272 | −2.64186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 19.6009 | 0.758383 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.7355 | −0.414748 | ||||||||
\(671\) | 20.5200 | 0.792166 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.95990 | 0.306832 | 0.153416 | − | 0.988162i | \(-0.450973\pi\) | ||||
0.153416 | + | 0.988162i | \(0.450973\pi\) | |||||||
\(674\) | −5.79337 | −0.223152 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5631 | 0.713965 | ||||||||
\(677\) | −45.3855 | −1.74431 | −0.872154 | − | 0.489232i | \(-0.837277\pi\) | ||||
−0.872154 | + | 0.489232i | \(0.837277\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0446 | −0.500607 | ||||||||
\(680\) | 26.2058 | 1.00495 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.63501 | 0.0626078 | ||||||||
\(683\) | −10.6867 | −0.408914 | −0.204457 | − | 0.978876i | \(-0.565543\pi\) | ||||
−0.204457 | + | 0.978876i | \(0.565543\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.3055 | −1.42537 | ||||||||
\(686\) | 11.3088 | 0.431772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.35726 | 0.0898697 | ||||||||
\(689\) | −0.455899 | −0.0173684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.8789 | −1.09861 | −0.549303 | − | 0.835623i | \(-0.685107\pi\) | ||||
−0.549303 | + | 0.835623i | \(0.685107\pi\) | |||||||
\(692\) | −3.59528 | −0.136672 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.4871 | 0.777678 | ||||||||
\(695\) | −46.3096 | −1.75662 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.2683 | −0.654085 | ||||||||
\(698\) | −22.2896 | −0.843675 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.2124 | 1.02853 | ||||||||
\(701\) | 39.1416 | 1.47836 | 0.739179 | − | 0.673510i | \(-0.235214\pi\) | ||||
0.739179 | + | 0.673510i | \(0.235214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.1002 | −2.15357 | ||||||||
\(704\) | −4.12001 | −0.155279 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0714 | 0.830670 | ||||||||
\(707\) | −21.5842 | −0.811758 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0885 | −1.43045 | −0.715223 | − | 0.698897i | \(-0.753675\pi\) | ||||
−0.715223 | + | 0.698897i | \(0.753675\pi\) | |||||||
\(710\) | 17.5299 | 0.657886 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.3217 | 1.13635 | ||||||||
\(713\) | 1.26899 | 0.0475242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.43885 | −0.0912078 | ||||||||
\(716\) | −11.8647 | −0.443406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.56033 | −0.0582311 | ||||||||
\(719\) | −9.52549 | −0.355241 | −0.177620 | − | 0.984099i | \(-0.556840\pi\) | ||||
−0.177620 | + | 0.984099i | \(0.556840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.7007 | 1.99992 | ||||||||
\(722\) | 20.1743 | 0.750810 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.8970 | 0.442148 | ||||||||
\(725\) | 6.30168 | 0.234038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.13864 | −0.227669 | −0.113835 | − | 0.993500i | \(-0.536313\pi\) | ||||
−0.113835 | + | 0.993500i | \(0.536313\pi\) | |||||||
\(728\) | 3.19995 | 0.118598 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23.1940 | −0.858448 | ||||||||
\(731\) | −7.24333 | −0.267904 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.0637 | 1.36898 | 0.684489 | − | 0.729023i | \(-0.260025\pi\) | ||||
0.684489 | + | 0.729023i | \(0.260025\pi\) | |||||||
\(734\) | 14.4892 | 0.534806 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.86115 | −0.216045 | ||||||||
\(737\) | 7.44609 | 0.274280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6507 | 1.01715 | 0.508573 | − | 0.861019i | \(-0.330173\pi\) | ||||
0.508573 | + | 0.861019i | \(0.330173\pi\) | |||||||
\(740\) | 40.9044 | 1.50367 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.41562 | 0.0886801 | ||||||||
\(743\) | 23.5165 | 0.862738 | 0.431369 | − | 0.902176i | \(-0.358031\pi\) | ||||
0.431369 | + | 0.902176i | \(0.358031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.23236 | −0.264973 | ||||||||
\(746\) | −24.8508 | −0.909852 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.63146 | −0.279034 | ||||||||
\(749\) | −15.4579 | −0.564819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.7925 | −1.45205 | −0.726025 | − | 0.687669i | \(-0.758634\pi\) | ||||
−0.726025 | + | 0.687669i | \(0.758634\pi\) | |||||||
\(752\) | 1.00927 | 0.0368042 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.311125 | 0.0113305 | ||||||||
\(755\) | 61.7108 | 2.24588 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1170 | 0.694818 | 0.347409 | − | 0.937714i | \(-0.387062\pi\) | ||||
0.347409 | + | 0.937714i | \(0.387062\pi\) | |||||||
\(758\) | 17.4554 | 0.634010 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −58.5190 | −2.12271 | ||||||||
\(761\) | 23.8344 | 0.863996 | 0.431998 | − | 0.901874i | \(-0.357809\pi\) | ||||
0.431998 | + | 0.901874i | \(0.357809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.7561 | 1.22205 | ||||||||
\(764\) | −20.3958 | −0.737894 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.3605 | −0.591129 | ||||||||
\(767\) | 0.182038 | 0.00657303 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.2669 | 1.30782 | 0.653909 | − | 0.756573i | \(-0.273128\pi\) | ||||
0.653909 | + | 0.756573i | \(0.273128\pi\) | |||||||
\(770\) | 12.9224 | 0.465692 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.394706 | −0.0142058 | ||||||||
\(773\) | −31.7295 | −1.14123 | −0.570616 | − | 0.821217i | \(-0.693296\pi\) | ||||
−0.570616 | + | 0.821217i | \(0.693296\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.99678 | −0.287253 | ||||||||
\(776\) | −11.2049 | −0.402233 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.9810 | −0.393689 | ||||||||
\(779\) | 38.5611 | 1.38160 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1587 | −0.435072 | ||||||||
\(782\) | 2.26116 | 0.0808587 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.88155 | 0.0671981 | ||||||||
\(785\) | −1.83489 | −0.0654902 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.23836 | −0.151081 | −0.0755405 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755405 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(788\) | 34.1505 | 1.21656 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.08761 | 0.216588 | ||||||||
\(791\) | 18.1547 | 0.645507 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.95509 | −0.175960 | ||||||||
\(794\) | 16.1859 | 0.574418 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.08113 | −0.180096 | ||||||||
\(797\) | 24.4161 | 0.864863 | 0.432432 | − | 0.901667i | \(-0.357656\pi\) | ||||
0.432432 | + | 0.901667i | \(0.357656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.10125 | −0.109714 | ||||||||
\(800\) | 36.9351 | 1.30585 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.76657 | 0.0623799 | ||||||||
\(803\) | 16.0873 | 0.567707 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0296 | 0.353496 | ||||||||
\(806\) | −0.394816 | −0.0139068 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.5401 | −0.652239 | ||||||||
\(809\) | −27.0005 | −0.949287 | −0.474644 | − | 0.880178i | \(-0.657423\pi\) | ||||
−0.474644 | + | 0.880178i | \(0.657423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8385 | 0.942428 | 0.471214 | − | 0.882019i | \(-0.343816\pi\) | ||||
0.471214 | + | 0.882019i | \(0.343816\pi\) | |||||||
\(812\) | 4.31828 | 0.151542 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8308 | 0.379620 | ||||||||
\(815\) | −1.83207 | −0.0641748 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.1748 | 0.565883 | ||||||||
\(818\) | 0.106457 | 0.00372217 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.6237 | −0.964662 | ||||||||
\(821\) | 53.0026 | 1.84980 | 0.924901 | − | 0.380208i | \(-0.124148\pi\) | ||||
0.924901 | + | 0.380208i | \(0.124148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.65489 | −0.197117 | −0.0985585 | − | 0.995131i | \(-0.531423\pi\) | ||||
−0.0985585 | + | 0.995131i | \(0.531423\pi\) | |||||||
\(824\) | 46.1271 | 1.60691 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.964545 | −0.0335608 | ||||||||
\(827\) | 39.2613 | 1.36525 | 0.682624 | − | 0.730770i | \(-0.260839\pi\) | ||||
0.682624 | + | 0.730770i | \(0.260839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.1229 | 1.04621 | 0.523106 | − | 0.852268i | \(-0.324773\pi\) | ||||
0.523106 | + | 0.852268i | \(0.324773\pi\) | |||||||
\(830\) | −38.2807 | −1.32874 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.994883 | 0.0344914 | ||||||||
\(833\) | −5.78157 | −0.200320 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.5249 | −1.57546 | ||||||||
\(836\) | 17.0415 | 0.589391 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.38058 | 0.0476913 | ||||||||
\(839\) | −2.39338 | −0.0826286 | −0.0413143 | − | 0.999146i | \(-0.513155\pi\) | ||||
−0.0413143 | + | 0.999146i | \(0.513155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 12.4852 | 0.430269 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.199963 | 0.00688301 | ||||||||
\(845\) | −43.1144 | −1.48318 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.8544 | 0.819648 | ||||||||
\(848\) | −1.07828 | −0.0370284 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.2491 | −0.488739 | ||||||||
\(851\) | 8.40619 | 0.288161 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.8704 | 0.714588 | 0.357294 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357294 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(854\) | 26.2549 | 0.898425 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.2778 | −0.453826 | ||||||||
\(857\) | −45.3139 | −1.54789 | −0.773946 | − | 0.633251i | \(-0.781720\pi\) | ||||
−0.773946 | + | 0.633251i | \(0.781720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.5885 | −1.21427 | −0.607133 | − | 0.794600i | \(-0.707680\pi\) | ||||
−0.607133 | + | 0.794600i | \(0.707680\pi\) | |||||||
\(860\) | −11.5870 | −0.395113 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.5094 | −0.392013 | ||||||||
\(863\) | 20.3394 | 0.692362 | 0.346181 | − | 0.938168i | \(-0.387478\pi\) | ||||
0.346181 | + | 0.938168i | \(0.387478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.35036 | 0.283921 | ||||||||
\(866\) | −8.05689 | −0.273784 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.47986 | −0.185999 | ||||||||
\(869\) | −4.22235 | −0.143233 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.79805 | −0.0609246 | ||||||||
\(872\) | 28.9954 | 0.981907 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.04928 | −0.170795 | ||||||||
\(875\) | −13.0553 | −0.441348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.6368 | −1.60858 | −0.804290 | − | 0.594238i | \(-0.797454\pi\) | ||||
−0.804290 | + | 0.594238i | \(0.797454\pi\) | |||||||
\(878\) | 9.70718 | 0.327601 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.76832 | −0.194450 | ||||||||
\(881\) | −22.4664 | −0.756911 | −0.378455 | − | 0.925620i | \(-0.623545\pi\) | ||||
−0.378455 | + | 0.925620i | \(0.623545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.1244 | 1.58586 | 0.792931 | − | 0.609311i | \(-0.208554\pi\) | ||||
0.792931 | + | 0.609311i | \(0.208554\pi\) | |||||||
\(884\) | 1.84281 | 0.0619805 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.3709 | 0.348417 | ||||||||
\(887\) | −24.4228 | −0.820036 | −0.410018 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410018 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00071 | 0.268335 | ||||||||
\(890\) | −29.5684 | −0.991136 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.5978 | −0.957524 | ||||||||
\(893\) | 6.92526 | 0.231745 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.5569 | 0.921126 | ||||||||
\(896\) | 29.7008 | 0.992235 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0806501 | −0.00269133 | ||||||||
\(899\) | −1.26899 | −0.0423233 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.31332 | 0.110383 | ||||||||
\(902\) | −7.31431 | −0.243540 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.5943 | 0.518658 | ||||||||
\(905\) | −27.6318 | −0.918512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.1574 | −1.26700 | −0.633498 | − | 0.773744i | \(-0.718381\pi\) | ||||
−0.633498 | + | 0.773744i | \(0.718381\pi\) | |||||||
\(908\) | −30.8138 | −1.02259 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.12046 | −0.103442 | ||||||||
\(911\) | 21.7734 | 0.721386 | 0.360693 | − | 0.932685i | \(-0.382540\pi\) | ||||
0.360693 | + | 0.932685i | \(0.382540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.5513 | 0.878721 | ||||||||
\(914\) | 21.2818 | 0.703940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.4501 | 0.477444 | ||||||||
\(917\) | 15.7216 | 0.519171 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5974 | 0.613472 | 0.306736 | − | 0.951795i | \(-0.400763\pi\) | ||||
0.306736 | + | 0.951795i | \(0.400763\pi\) | |||||||
\(920\) | 8.61508 | 0.284031 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.3434 | −0.669973 | ||||||||
\(923\) | 2.93603 | 0.0966406 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.9731 | −1.74174 | ||||||||
\(926\) | −6.87100 | −0.225795 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.86115 | 0.192402 | ||||||||
\(929\) | 8.38393 | 0.275068 | 0.137534 | − | 0.990497i | \(-0.456082\pi\) | ||||
0.137534 | + | 0.990497i | \(0.456082\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.9106 | 0.423127 | ||||||||
\(932\) | −17.0233 | −0.557617 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.1769 | −0.660209 | ||||||||
\(935\) | 17.7247 | 0.579661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.3141 | 1.51301 | 0.756507 | − | 0.653985i | \(-0.226904\pi\) | ||||
0.756507 | + | 0.653985i | \(0.226904\pi\) | |||||||
\(938\) | 9.52711 | 0.311071 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.96099 | −0.161810 | ||||||||
\(941\) | −38.1202 | −1.24268 | −0.621342 | − | 0.783540i | \(-0.713412\pi\) | ||||
−0.621342 | + | 0.783540i | \(0.713412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.67691 | −0.184865 | ||||||||
\(944\) | 0.430553 | 0.0140133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.06804 | −0.0997507 | ||||||||
\(947\) | 25.5915 | 0.831612 | 0.415806 | − | 0.909453i | \(-0.363500\pi\) | ||||
0.415806 | + | 0.909453i | \(0.363500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.88469 | −0.126102 | ||||||||
\(950\) | 31.8189 | 1.03234 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.2561 | −0.753736 | ||||||||
\(953\) | 9.53149 | 0.308755 | 0.154378 | − | 0.988012i | \(-0.450663\pi\) | ||||
0.154378 | + | 0.988012i | \(0.450663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.3710 | 1.53289 | ||||||||
\(956\) | −21.2815 | −0.688294 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.4097 | 0.368629 | ||||||||
\(959\) | 33.1064 | 1.06906 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3897 | −0.948053 | ||||||||
\(962\) | −2.61538 | −0.0843232 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.38197 | 0.302173 | ||||||||
\(965\) | 0.916739 | 0.0295109 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.4719 | 1.84817 | 0.924086 | − | 0.382184i | \(-0.124828\pi\) | ||||
0.924086 | + | 0.382184i | \(0.124828\pi\) | |||||||
\(968\) | 20.4902 | 0.658579 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.9266 | 0.350831 | ||||||||
\(971\) | −2.22999 | −0.0715636 | −0.0357818 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357818 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.0970 | 1.31751 | ||||||||
\(974\) | −17.3197 | −0.554960 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.7197 | −0.375137 | ||||||||
\(977\) | −16.0703 | −0.514133 | −0.257067 | − | 0.966394i | \(-0.582756\pi\) | ||||
−0.257067 | + | 0.966394i | \(0.582756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.5086 | 0.655456 | ||||||||
\(980\) | −9.24863 | −0.295437 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.7598 | 0.758207 | ||||||||
\(983\) | 43.1593 | 1.37657 | 0.688284 | − | 0.725441i | \(-0.258364\pi\) | ||||
0.688284 | + | 0.725441i | \(0.258364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −79.3176 | −2.52727 | ||||||||
\(986\) | −2.26116 | −0.0720098 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.11510 | −0.130919 | ||||||||
\(989\) | −2.38122 | −0.0757184 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.6889 | 0.911334 | 0.455667 | − | 0.890150i | \(-0.349401\pi\) | ||||
0.455667 | + | 0.890150i | \(0.349401\pi\) | |||||||
\(992\) | −7.43776 | −0.236149 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.5568 | −0.493431 | ||||||||
\(995\) | 11.8014 | 0.374129 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.9493 | 1.64525 | 0.822625 | − | 0.568584i | \(-0.192509\pi\) | ||||
0.822625 | + | 0.568584i | \(0.192509\pi\) | |||||||
\(998\) | 15.2135 | 0.481575 | ||||||||
\(999\) | 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 | 6003.2.a.j.1.4 | 7 | ||
3.2 | odd | 2 | 2001.2.a.i.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.i.1.4 | ✓ | 7 | 3.2 | odd | 2 | ||
6003.2.a.j.1.4 | 7 | 1.1 | even | 1 | trivial |