Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.31792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.31792 | 1.63902 | 0.819509 | − | 0.573066i | \(-0.194246\pi\) | ||||
0.819509 | + | 0.573066i | \(0.194246\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.37276 | 1.68638 | ||||||||
\(5\) | 2.47951 | 1.10887 | 0.554436 | − | 0.832226i | \(-0.312934\pi\) | ||||
0.554436 | + | 0.832226i | \(0.312934\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26859 | 1.23541 | 0.617705 | − | 0.786410i | \(-0.288062\pi\) | ||||
0.617705 | + | 0.786410i | \(0.288062\pi\) | |||||||
\(8\) | 3.18195 | 1.12499 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.74732 | 1.81746 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.05111 | 1.67827 | 0.839137 | − | 0.543920i | \(-0.183060\pi\) | ||||
0.839137 | + | 0.543920i | \(0.183060\pi\) | |||||||
\(14\) | 7.57633 | 2.02486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.629993 | 0.157498 | ||||||||
\(17\) | 6.63735 | 1.60979 | 0.804897 | − | 0.593414i | \(-0.202220\pi\) | ||||
0.804897 | + | 0.593414i | \(0.202220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.68664 | −1.07519 | −0.537595 | − | 0.843203i | \(-0.680667\pi\) | ||||
−0.537595 | + | 0.843203i | \(0.680667\pi\) | |||||||
\(20\) | 8.36281 | 1.86998 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.31792 | −0.494183 | ||||||||
\(23\) | 6.72397 | 1.40204 | 0.701022 | − | 0.713139i | \(-0.252727\pi\) | ||||
0.701022 | + | 0.713139i | \(0.252727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14799 | 0.229598 | ||||||||
\(26\) | 14.0260 | 2.75072 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.0242 | 2.08337 | ||||||||
\(29\) | 6.44005 | 1.19589 | 0.597944 | − | 0.801538i | \(-0.295985\pi\) | ||||
0.597944 | + | 0.801538i | \(0.295985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.17187 | −1.10850 | −0.554250 | − | 0.832350i | \(-0.686995\pi\) | ||||
−0.554250 | + | 0.832350i | \(0.686995\pi\) | |||||||
\(32\) | −4.90363 | −0.866847 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.3849 | 2.63848 | ||||||||
\(35\) | 8.10451 | 1.36991 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.59063 | −1.08349 | −0.541747 | − | 0.840542i | \(-0.682237\pi\) | ||||
−0.541747 | + | 0.840542i | \(0.682237\pi\) | |||||||
\(38\) | −10.8633 | −1.76225 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.88969 | 1.24747 | ||||||||
\(41\) | −8.91287 | −1.39196 | −0.695978 | − | 0.718063i | \(-0.745029\pi\) | ||||
−0.695978 | + | 0.718063i | \(0.745029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.98140 | −1.36965 | −0.684825 | − | 0.728707i | \(-0.740122\pi\) | ||||
−0.684825 | + | 0.728707i | \(0.740122\pi\) | |||||||
\(44\) | −3.37276 | −0.508463 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.5856 | 2.29798 | ||||||||
\(47\) | −10.7447 | −1.56728 | −0.783639 | − | 0.621217i | \(-0.786639\pi\) | ||||
−0.783639 | + | 0.621217i | \(0.786639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.68368 | 0.526240 | ||||||||
\(50\) | 2.66095 | 0.376315 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.4089 | 2.83021 | ||||||||
\(53\) | −11.7082 | −1.60825 | −0.804125 | − | 0.594460i | \(-0.797366\pi\) | ||||
−0.804125 | + | 0.594460i | \(0.797366\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.47951 | −0.334338 | ||||||||
\(56\) | 10.4005 | 1.38982 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.9275 | 1.96008 | ||||||||
\(59\) | −3.81524 | −0.496702 | −0.248351 | − | 0.968670i | \(-0.579889\pi\) | ||||
−0.248351 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −14.3059 | −1.81685 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6262 | −1.57828 | ||||||||
\(65\) | 15.0038 | 1.86099 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.27788 | 0.400456 | 0.200228 | − | 0.979749i | \(-0.435832\pi\) | ||||
0.200228 | + | 0.979749i | \(0.435832\pi\) | |||||||
\(68\) | 22.3862 | 2.71473 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 18.7856 | 2.24531 | ||||||||
\(71\) | 13.3606 | 1.58561 | 0.792804 | − | 0.609476i | \(-0.208620\pi\) | ||||
0.792804 | + | 0.609476i | \(0.208620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.29610 | −0.736903 | −0.368451 | − | 0.929647i | \(-0.620112\pi\) | ||||
−0.368451 | + | 0.929647i | \(0.620112\pi\) | |||||||
\(74\) | −15.2766 | −1.77587 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.8069 | −1.81318 | ||||||||
\(77\) | −3.26859 | −0.372490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.89560 | −0.663307 | −0.331653 | − | 0.943401i | \(-0.607606\pi\) | ||||
−0.331653 | + | 0.943401i | \(0.607606\pi\) | |||||||
\(80\) | 1.56208 | 0.174645 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −20.6593 | −2.28144 | ||||||||
\(83\) | 6.77257 | 0.743386 | 0.371693 | − | 0.928356i | \(-0.378777\pi\) | ||||
0.371693 | + | 0.928356i | \(0.378777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.4574 | 1.78506 | ||||||||
\(86\) | −20.8182 | −2.24488 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.18195 | −0.339197 | ||||||||
\(89\) | 2.86664 | 0.303863 | 0.151932 | − | 0.988391i | \(-0.451451\pi\) | ||||
0.151932 | + | 0.988391i | \(0.451451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.7786 | 2.07336 | ||||||||
\(92\) | 22.6783 | 2.36438 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.9054 | −2.56880 | ||||||||
\(95\) | −11.6206 | −1.19225 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.49974 | 0.863018 | 0.431509 | − | 0.902109i | \(-0.357981\pi\) | ||||
0.431509 | + | 0.902109i | \(0.357981\pi\) | |||||||
\(98\) | 8.53848 | 0.862517 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.87189 | 0.387189 | ||||||||
\(101\) | 4.21053 | 0.418964 | 0.209482 | − | 0.977813i | \(-0.432822\pi\) | ||||
0.209482 | + | 0.977813i | \(0.432822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1476 | −1.78813 | −0.894067 | − | 0.447934i | \(-0.852160\pi\) | ||||
−0.894067 | + | 0.447934i | \(0.852160\pi\) | |||||||
\(104\) | 19.2543 | 1.88804 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.1388 | −2.63595 | ||||||||
\(107\) | 6.78421 | 0.655854 | 0.327927 | − | 0.944703i | \(-0.393650\pi\) | ||||
0.327927 | + | 0.944703i | \(0.393650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.58488 | −0.151804 | −0.0759021 | − | 0.997115i | \(-0.524184\pi\) | ||||
−0.0759021 | + | 0.997115i | \(0.524184\pi\) | |||||||
\(110\) | −5.74732 | −0.547985 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.05919 | 0.194575 | ||||||||
\(113\) | −0.642108 | −0.0604045 | −0.0302022 | − | 0.999544i | \(-0.509615\pi\) | ||||
−0.0302022 | + | 0.999544i | \(0.509615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.6722 | 1.55469 | ||||||||
\(116\) | 21.7207 | 2.01672 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.84342 | −0.814103 | ||||||||
\(119\) | 21.6948 | 1.98876 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.31792 | −0.209855 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.8162 | −1.86935 | ||||||||
\(125\) | −9.55111 | −0.854278 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6746 | 1.03595 | 0.517975 | − | 0.855396i | \(-0.326686\pi\) | ||||
0.517975 | + | 0.855396i | \(0.326686\pi\) | |||||||
\(128\) | −19.4593 | −1.71998 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 34.7776 | 3.05020 | ||||||||
\(131\) | 6.62541 | 0.578865 | 0.289432 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289432 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3187 | −1.32830 | ||||||||
\(134\) | 7.59786 | 0.656355 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.1197 | 1.81100 | ||||||||
\(137\) | 6.72646 | 0.574681 | 0.287340 | − | 0.957829i | \(-0.407229\pi\) | ||||
0.287340 | + | 0.957829i | \(0.407229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.5108 | 1.48525 | 0.742625 | − | 0.669707i | \(-0.233580\pi\) | ||||
0.742625 | + | 0.669707i | \(0.233580\pi\) | |||||||
\(140\) | 27.3346 | 2.31019 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 30.9688 | 2.59884 | ||||||||
\(143\) | −6.05111 | −0.506019 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9682 | 1.32609 | ||||||||
\(146\) | −14.5939 | −1.20780 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22.2286 | −1.82718 | ||||||||
\(149\) | 21.6874 | 1.77670 | 0.888352 | − | 0.459163i | \(-0.151851\pi\) | ||||
0.888352 | + | 0.459163i | \(0.151851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.3753 | −1.00709 | −0.503544 | − | 0.863970i | \(-0.667971\pi\) | ||||
−0.503544 | + | 0.863970i | \(0.667971\pi\) | |||||||
\(152\) | −14.9127 | −1.20958 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.57633 | −0.610518 | ||||||||
\(155\) | −15.3032 | −1.22919 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.60694 | 0.527292 | 0.263646 | − | 0.964620i | \(-0.415075\pi\) | ||||
0.263646 | + | 0.964620i | \(0.415075\pi\) | |||||||
\(158\) | −13.6655 | −1.08717 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.1586 | −0.961223 | ||||||||
\(161\) | 21.9779 | 1.73210 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.97660 | −0.703102 | −0.351551 | − | 0.936169i | \(-0.614346\pi\) | ||||
−0.351551 | + | 0.936169i | \(0.614346\pi\) | |||||||
\(164\) | −30.0610 | −2.34737 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.6983 | 1.21842 | ||||||||
\(167\) | 6.34806 | 0.491228 | 0.245614 | − | 0.969368i | \(-0.421010\pi\) | ||||
0.245614 | + | 0.969368i | \(0.421010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.6159 | 1.81661 | ||||||||
\(170\) | 38.1470 | 2.92574 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −30.2921 | −2.30975 | ||||||||
\(173\) | 10.8803 | 0.827215 | 0.413607 | − | 0.910455i | \(-0.364269\pi\) | ||||
0.413607 | + | 0.910455i | \(0.364269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.75230 | 0.283648 | ||||||||
\(176\) | −0.629993 | −0.0474875 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.64465 | 0.498038 | ||||||||
\(179\) | −21.7370 | −1.62470 | −0.812351 | − | 0.583168i | \(-0.801813\pi\) | ||||
−0.812351 | + | 0.583168i | \(0.801813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.85061 | −0.211884 | −0.105942 | − | 0.994372i | \(-0.533786\pi\) | ||||
−0.105942 | + | 0.994372i | \(0.533786\pi\) | |||||||
\(182\) | 45.8452 | 3.39827 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21.3953 | 1.57729 | ||||||||
\(185\) | −16.3416 | −1.20146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.63735 | −0.485371 | ||||||||
\(188\) | −36.2393 | −2.64303 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.9356 | −1.95412 | ||||||||
\(191\) | −16.8513 | −1.21932 | −0.609659 | − | 0.792664i | \(-0.708693\pi\) | ||||
−0.609659 | + | 0.792664i | \(0.708693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0491126 | −0.00353520 | −0.00176760 | − | 0.999998i | \(-0.500563\pi\) | ||||
−0.00176760 | + | 0.999998i | \(0.500563\pi\) | |||||||
\(194\) | 19.7017 | 1.41450 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4242 | 0.887440 | ||||||||
\(197\) | −6.18214 | −0.440459 | −0.220230 | − | 0.975448i | \(-0.570681\pi\) | ||||
−0.220230 | + | 0.975448i | \(0.570681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69298 | −0.545341 | −0.272670 | − | 0.962108i | \(-0.587907\pi\) | ||||
−0.272670 | + | 0.962108i | \(0.587907\pi\) | |||||||
\(200\) | 3.65284 | 0.258295 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.75968 | 0.686689 | ||||||||
\(203\) | 21.0499 | 1.47741 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0996 | −1.54350 | ||||||||
\(206\) | −42.0647 | −2.93078 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.81215 | 0.264325 | ||||||||
\(209\) | 4.68664 | 0.324182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7265 | −1.77108 | −0.885541 | − | 0.464561i | \(-0.846212\pi\) | ||||
−0.885541 | + | 0.464561i | \(0.846212\pi\) | |||||||
\(212\) | −39.4891 | −2.71212 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7253 | 1.07496 | ||||||||
\(215\) | −22.2695 | −1.51877 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1733 | −1.36945 | ||||||||
\(218\) | −3.67363 | −0.248810 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.36281 | −0.563820 | ||||||||
\(221\) | 40.1633 | 2.70168 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4211 | 0.898741 | 0.449371 | − | 0.893345i | \(-0.351648\pi\) | ||||
0.449371 | + | 0.893345i | \(0.351648\pi\) | |||||||
\(224\) | −16.0280 | −1.07091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.48836 | −0.0990040 | ||||||||
\(227\) | 22.1736 | 1.47171 | 0.735856 | − | 0.677138i | \(-0.236780\pi\) | ||||
0.735856 | + | 0.677138i | \(0.236780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.20706 | 0.542338 | 0.271169 | − | 0.962532i | \(-0.412590\pi\) | ||||
0.271169 | + | 0.962532i | \(0.412590\pi\) | |||||||
\(230\) | 38.6448 | 2.54816 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.4919 | 1.34536 | ||||||||
\(233\) | 15.5362 | 1.01781 | 0.508906 | − | 0.860822i | \(-0.330050\pi\) | ||||
0.508906 | + | 0.860822i | \(0.330050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.6417 | −1.73791 | ||||||||
\(236\) | −12.8679 | −0.837628 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 50.2868 | 3.25961 | ||||||||
\(239\) | −7.51917 | −0.486375 | −0.243187 | − | 0.969979i | \(-0.578193\pi\) | ||||
−0.243187 | + | 0.969979i | \(0.578193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5840 | −1.00385 | −0.501927 | − | 0.864910i | \(-0.667376\pi\) | ||||
−0.501927 | + | 0.864910i | \(0.667376\pi\) | |||||||
\(242\) | 2.31792 | 0.149002 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.37276 | −0.215919 | ||||||||
\(245\) | 9.13373 | 0.583533 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.3594 | −1.80446 | ||||||||
\(248\) | −19.6386 | −1.24705 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −22.1387 | −1.40018 | ||||||||
\(251\) | −29.0362 | −1.83275 | −0.916373 | − | 0.400326i | \(-0.868897\pi\) | ||||
−0.916373 | + | 0.400326i | \(0.868897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.72397 | −0.422732 | ||||||||
\(254\) | 27.0607 | 1.69794 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.8527 | −1.24080 | ||||||||
\(257\) | −7.42017 | −0.462858 | −0.231429 | − | 0.972852i | \(-0.574340\pi\) | ||||
−0.231429 | + | 0.972852i | \(0.574340\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.5421 | −1.33856 | ||||||||
\(260\) | 50.6042 | 3.13834 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.3572 | 0.948770 | ||||||||
\(263\) | −5.43921 | −0.335396 | −0.167698 | − | 0.985838i | \(-0.553633\pi\) | ||||
−0.167698 | + | 0.985838i | \(0.553633\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.0307 | −1.78334 | ||||||||
\(266\) | −35.5076 | −2.17711 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.0555 | 0.675322 | ||||||||
\(269\) | 10.2198 | 0.623113 | 0.311557 | − | 0.950228i | \(-0.399150\pi\) | ||||
0.311557 | + | 0.950228i | \(0.399150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.36832 | 0.447593 | 0.223797 | − | 0.974636i | \(-0.428155\pi\) | ||||
0.223797 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(272\) | 4.18148 | 0.253540 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.5914 | 0.941912 | ||||||||
\(275\) | −1.14799 | −0.0692263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2638 | −1.15745 | −0.578725 | − | 0.815523i | \(-0.696450\pi\) | ||||
−0.578725 | + | 0.815523i | \(0.696450\pi\) | |||||||
\(278\) | 40.5888 | 2.43435 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.7882 | 1.54114 | ||||||||
\(281\) | −1.00514 | −0.0599619 | −0.0299809 | − | 0.999550i | \(-0.509545\pi\) | ||||
−0.0299809 | + | 0.999550i | \(0.509545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9883 | 0.890965 | 0.445482 | − | 0.895291i | \(-0.353032\pi\) | ||||
0.445482 | + | 0.895291i | \(0.353032\pi\) | |||||||
\(284\) | 45.0620 | 2.67394 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.0260 | −0.829374 | ||||||||
\(287\) | −29.1325 | −1.71964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.0544 | 1.59144 | ||||||||
\(290\) | 37.0130 | 2.17348 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −21.2352 | −1.24270 | ||||||||
\(293\) | 32.8105 | 1.91681 | 0.958404 | − | 0.285416i | \(-0.0921318\pi\) | ||||
0.958404 | + | 0.285416i | \(0.0921318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.45993 | −0.550779 | ||||||||
\(296\) | −20.9711 | −1.21892 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 50.2698 | 2.91205 | ||||||||
\(299\) | 40.6875 | 2.35302 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.3565 | −1.69208 | ||||||||
\(302\) | −28.6850 | −1.65063 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.95255 | −0.169340 | ||||||||
\(305\) | −2.47951 | −0.141977 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.14961 | 0.408050 | 0.204025 | − | 0.978966i | \(-0.434598\pi\) | ||||
0.204025 | + | 0.978966i | \(0.434598\pi\) | |||||||
\(308\) | −11.0242 | −0.628160 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.4717 | −2.01466 | ||||||||
\(311\) | 18.8314 | 1.06783 | 0.533916 | − | 0.845538i | \(-0.320720\pi\) | ||||
0.533916 | + | 0.845538i | \(0.320720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.7753 | 1.34386 | 0.671928 | − | 0.740616i | \(-0.265466\pi\) | ||||
0.671928 | + | 0.740616i | \(0.265466\pi\) | |||||||
\(314\) | 15.3144 | 0.864240 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8845 | −1.11859 | ||||||||
\(317\) | 15.5940 | 0.875848 | 0.437924 | − | 0.899012i | \(-0.355714\pi\) | ||||
0.437924 | + | 0.899012i | \(0.355714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.44005 | −0.360573 | ||||||||
\(320\) | −31.3069 | −1.75011 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 50.9431 | 2.83895 | ||||||||
\(323\) | −31.1069 | −1.73083 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.94660 | 0.385328 | ||||||||
\(326\) | −20.8071 | −1.15240 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −28.3603 | −1.56594 | ||||||||
\(329\) | −35.1200 | −1.93623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3454 | −1.00835 | −0.504177 | − | 0.863600i | \(-0.668204\pi\) | ||||
−0.504177 | + | 0.863600i | \(0.668204\pi\) | |||||||
\(332\) | 22.8422 | 1.25363 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7143 | 0.805131 | ||||||||
\(335\) | 8.12754 | 0.444055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.343178 | −0.0186941 | −0.00934704 | − | 0.999956i | \(-0.502975\pi\) | ||||
−0.00934704 | + | 0.999956i | \(0.502975\pi\) | |||||||
\(338\) | 54.7397 | 2.97745 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 55.5069 | 3.01028 | ||||||||
\(341\) | 6.17187 | 0.334226 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.8397 | −0.585288 | ||||||||
\(344\) | −28.5784 | −1.54084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.2197 | 1.35582 | ||||||||
\(347\) | 2.46579 | 0.132370 | 0.0661852 | − | 0.997807i | \(-0.478917\pi\) | ||||
0.0661852 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.2419 | 1.40470 | 0.702348 | − | 0.711834i | \(-0.252135\pi\) | ||||
0.702348 | + | 0.711834i | \(0.252135\pi\) | |||||||
\(350\) | 8.69755 | 0.464904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.90363 | 0.261364 | ||||||||
\(353\) | 8.93973 | 0.475814 | 0.237907 | − | 0.971288i | \(-0.423539\pi\) | ||||
0.237907 | + | 0.971288i | \(0.423539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.1277 | 1.75824 | ||||||||
\(356\) | 9.66849 | 0.512429 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −50.3848 | −2.66292 | ||||||||
\(359\) | −24.1204 | −1.27303 | −0.636513 | − | 0.771266i | \(-0.719624\pi\) | ||||
−0.636513 | + | 0.771266i | \(0.719624\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.96461 | 0.156032 | ||||||||
\(362\) | −6.60750 | −0.347282 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 66.7084 | 3.49647 | ||||||||
\(365\) | −15.6113 | −0.817131 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.09954 | 0.213994 | 0.106997 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106997 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(368\) | 4.23605 | 0.220819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −37.8785 | −1.96921 | ||||||||
\(371\) | −38.2694 | −1.98685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.36673 | 0.226101 | 0.113050 | − | 0.993589i | \(-0.463938\pi\) | ||||
0.113050 | + | 0.993589i | \(0.463938\pi\) | |||||||
\(374\) | −15.3849 | −0.795532 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −34.1891 | −1.76317 | ||||||||
\(377\) | 38.9694 | 2.00703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.3572 | 1.97028 | 0.985139 | − | 0.171761i | \(-0.0549457\pi\) | ||||
0.985139 | + | 0.171761i | \(0.0549457\pi\) | |||||||
\(380\) | −39.1935 | −2.01058 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −39.0600 | −1.99848 | ||||||||
\(383\) | −3.77120 | −0.192699 | −0.0963497 | − | 0.995348i | \(-0.530717\pi\) | ||||
−0.0963497 | + | 0.995348i | \(0.530717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.10451 | −0.413044 | ||||||||
\(386\) | −0.113839 | −0.00579426 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.6676 | 1.45538 | ||||||||
\(389\) | −33.2927 | −1.68800 | −0.844002 | − | 0.536339i | \(-0.819807\pi\) | ||||
−0.844002 | + | 0.536339i | \(0.819807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.6294 | 2.25700 | ||||||||
\(392\) | 11.7213 | 0.592014 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.3297 | −0.721921 | ||||||||
\(395\) | −14.6182 | −0.735523 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5260 | −0.979980 | −0.489990 | − | 0.871728i | \(-0.663000\pi\) | ||||
−0.489990 | + | 0.871728i | \(0.663000\pi\) | |||||||
\(398\) | −17.8317 | −0.893823 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.723225 | 0.0361612 | ||||||||
\(401\) | 38.0053 | 1.89789 | 0.948946 | − | 0.315438i | \(-0.102152\pi\) | ||||
0.948946 | + | 0.315438i | \(0.102152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.3466 | −1.86037 | ||||||||
\(404\) | 14.2011 | 0.706532 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.7920 | 2.42150 | ||||||||
\(407\) | 6.59063 | 0.326686 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.79051 | −0.137982 | −0.0689909 | − | 0.997617i | \(-0.521978\pi\) | ||||
−0.0689909 | + | 0.997617i | \(0.521978\pi\) | |||||||
\(410\) | −51.2251 | −2.52983 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −61.2074 | −3.01547 | ||||||||
\(413\) | −12.4704 | −0.613630 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7927 | 0.824320 | ||||||||
\(416\) | −29.6724 | −1.45481 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.8633 | 0.531340 | ||||||||
\(419\) | 1.30588 | 0.0637964 | 0.0318982 | − | 0.999491i | \(-0.489845\pi\) | ||||
0.0318982 | + | 0.999491i | \(0.489845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.6901 | −0.910897 | −0.455449 | − | 0.890262i | \(-0.650521\pi\) | ||||
−0.455449 | + | 0.890262i | \(0.650521\pi\) | |||||||
\(422\) | −59.6319 | −2.90284 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −37.2550 | −1.80927 | ||||||||
\(425\) | 7.61961 | 0.369605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.26859 | −0.158178 | ||||||||
\(428\) | 22.8815 | 1.10602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −51.6190 | −2.48929 | ||||||||
\(431\) | 4.71349 | 0.227041 | 0.113520 | − | 0.993536i | \(-0.463787\pi\) | ||||
0.113520 | + | 0.993536i | \(0.463787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.0077 | −1.29791 | −0.648953 | − | 0.760829i | \(-0.724793\pi\) | ||||
−0.648953 | + | 0.760829i | \(0.724793\pi\) | |||||||
\(434\) | −46.7602 | −2.24456 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.34543 | −0.255999 | ||||||||
\(437\) | −31.5128 | −1.50746 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0507 | 1.33879 | 0.669394 | − | 0.742907i | \(-0.266554\pi\) | ||||
0.669394 | + | 0.742907i | \(0.266554\pi\) | |||||||
\(440\) | −7.88969 | −0.376126 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 93.0954 | 4.42810 | ||||||||
\(443\) | −12.6047 | −0.598866 | −0.299433 | − | 0.954117i | \(-0.596798\pi\) | ||||
−0.299433 | + | 0.954117i | \(0.596798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.10788 | 0.336946 | ||||||||
\(446\) | 31.1090 | 1.47305 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −41.2699 | −1.94982 | ||||||||
\(449\) | −9.95289 | −0.469706 | −0.234853 | − | 0.972031i | \(-0.575461\pi\) | ||||
−0.234853 | + | 0.972031i | \(0.575461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.91287 | 0.419691 | ||||||||
\(452\) | −2.16568 | −0.101865 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 51.3966 | 2.41216 | ||||||||
\(455\) | 49.0413 | 2.29909 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4066 | 1.46914 | 0.734569 | − | 0.678534i | \(-0.237384\pi\) | ||||
0.734569 | + | 0.678534i | \(0.237384\pi\) | |||||||
\(458\) | 19.0233 | 0.888902 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 56.2313 | 2.62180 | ||||||||
\(461\) | −29.2165 | −1.36075 | −0.680373 | − | 0.732866i | \(-0.738182\pi\) | ||||
−0.680373 | + | 0.732866i | \(0.738182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.3649 | −1.22528 | −0.612640 | − | 0.790362i | \(-0.709892\pi\) | ||||
−0.612640 | + | 0.790362i | \(0.709892\pi\) | |||||||
\(464\) | 4.05718 | 0.188350 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.0117 | 1.66821 | ||||||||
\(467\) | 14.1452 | 0.654563 | 0.327281 | − | 0.944927i | \(-0.393868\pi\) | ||||
0.327281 | + | 0.944927i | \(0.393868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7140 | 0.494728 | ||||||||
\(470\) | −61.7533 | −2.84847 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.1399 | −0.558784 | ||||||||
\(473\) | 8.98140 | 0.412965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.38021 | −0.246861 | ||||||||
\(476\) | 73.1713 | 3.35380 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.4289 | −0.797177 | ||||||||
\(479\) | −3.16963 | −0.144824 | −0.0724121 | − | 0.997375i | \(-0.523070\pi\) | ||||
−0.0724121 | + | 0.997375i | \(0.523070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.8806 | −1.81840 | ||||||||
\(482\) | −36.1225 | −1.64534 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.37276 | 0.153307 | ||||||||
\(485\) | 21.0752 | 0.956976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.73207 | −0.0784876 | −0.0392438 | − | 0.999230i | \(-0.512495\pi\) | ||||
−0.0392438 | + | 0.999230i | \(0.512495\pi\) | |||||||
\(488\) | −3.18195 | −0.144040 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 21.1713 | 0.956421 | ||||||||
\(491\) | 33.0415 | 1.49114 | 0.745572 | − | 0.666425i | \(-0.232176\pi\) | ||||
0.745572 | + | 0.666425i | \(0.232176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.7449 | 1.92513 | ||||||||
\(494\) | −65.7348 | −2.95755 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.88823 | −0.174587 | ||||||||
\(497\) | 43.6702 | 1.95888 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.4982 | −0.649027 | −0.324514 | − | 0.945881i | \(-0.605201\pi\) | ||||
−0.324514 | + | 0.945881i | \(0.605201\pi\) | |||||||
\(500\) | −32.2136 | −1.44064 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −67.3035 | −3.00390 | ||||||||
\(503\) | 38.2279 | 1.70450 | 0.852250 | − | 0.523136i | \(-0.175238\pi\) | ||||
0.852250 | + | 0.523136i | \(0.175238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4401 | 0.464577 | ||||||||
\(506\) | −15.5856 | −0.692866 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 39.3755 | 1.74701 | ||||||||
\(509\) | 0.825848 | 0.0366051 | 0.0183025 | − | 0.999832i | \(-0.494174\pi\) | ||||
0.0183025 | + | 0.999832i | \(0.494174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.5794 | −0.910378 | ||||||||
\(512\) | −7.09846 | −0.313711 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.1994 | −0.758632 | ||||||||
\(515\) | −44.9972 | −1.98281 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7447 | 0.472552 | ||||||||
\(518\) | −49.9329 | −2.19392 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 47.7414 | 2.09360 | ||||||||
\(521\) | −12.2959 | −0.538695 | −0.269348 | − | 0.963043i | \(-0.586808\pi\) | ||||
−0.269348 | + | 0.963043i | \(0.586808\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6237 | −1.03299 | −0.516496 | − | 0.856290i | \(-0.672764\pi\) | ||||
−0.516496 | + | 0.856290i | \(0.672764\pi\) | |||||||
\(524\) | 22.3459 | 0.976186 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.6077 | −0.549721 | ||||||||
\(527\) | −40.9649 | −1.78446 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2118 | 0.965730 | ||||||||
\(530\) | −67.2910 | −2.92293 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −51.6663 | −2.24002 | ||||||||
\(533\) | −53.9327 | −2.33608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8215 | 0.727259 | ||||||||
\(536\) | 10.4300 | 0.450509 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.6887 | 1.02129 | ||||||||
\(539\) | −3.68368 | −0.158667 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5431 | 0.453283 | 0.226642 | − | 0.973978i | \(-0.427225\pi\) | ||||
0.226642 | + | 0.973978i | \(0.427225\pi\) | |||||||
\(542\) | 17.0792 | 0.733614 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.5471 | −1.39545 | ||||||||
\(545\) | −3.92974 | −0.168331 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.08152 | −0.388298 | −0.194149 | − | 0.980972i | \(-0.562194\pi\) | ||||
−0.194149 | + | 0.980972i | \(0.562194\pi\) | |||||||
\(548\) | 22.6868 | 0.969130 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.66095 | −0.113463 | ||||||||
\(551\) | −30.1822 | −1.28580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.2703 | −0.819457 | ||||||||
\(554\) | −44.6520 | −1.89708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 59.0599 | 2.50470 | ||||||||
\(557\) | −5.77966 | −0.244892 | −0.122446 | − | 0.992475i | \(-0.539074\pi\) | ||||
−0.122446 | + | 0.992475i | \(0.539074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −54.3474 | −2.29865 | ||||||||
\(560\) | 5.10578 | 0.215759 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.32985 | −0.0982786 | ||||||||
\(563\) | 15.7767 | 0.664909 | 0.332455 | − | 0.943119i | \(-0.392123\pi\) | ||||
0.332455 | + | 0.943119i | \(0.392123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.59212 | −0.0669808 | ||||||||
\(566\) | 34.7418 | 1.46031 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.5127 | 1.78379 | ||||||||
\(569\) | 21.8817 | 0.917329 | 0.458665 | − | 0.888609i | \(-0.348328\pi\) | ||||
0.458665 | + | 0.888609i | \(0.348328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.534112 | 0.0223519 | 0.0111759 | − | 0.999938i | \(-0.496443\pi\) | ||||
0.0111759 | + | 0.999938i | \(0.496443\pi\) | |||||||
\(572\) | −20.4089 | −0.853340 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −67.5269 | −2.81852 | ||||||||
\(575\) | 7.71904 | 0.321906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.32355 | −0.346514 | −0.173257 | − | 0.984877i | \(-0.555429\pi\) | ||||
−0.173257 | + | 0.984877i | \(0.555429\pi\) | |||||||
\(578\) | 62.7101 | 2.60839 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 53.8569 | 2.23629 | ||||||||
\(581\) | 22.1367 | 0.918387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7082 | 0.484906 | ||||||||
\(584\) | −20.0339 | −0.829008 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 76.0521 | 3.14168 | ||||||||
\(587\) | 19.5104 | 0.805281 | 0.402641 | − | 0.915358i | \(-0.368092\pi\) | ||||
0.402641 | + | 0.915358i | \(0.368092\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.9253 | 1.19185 | ||||||||
\(590\) | −21.9274 | −0.902736 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.15205 | −0.170648 | ||||||||
\(593\) | 20.9055 | 0.858486 | 0.429243 | − | 0.903189i | \(-0.358780\pi\) | ||||
0.429243 | + | 0.903189i | \(0.358780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 53.7925 | 2.20528 | ||||||||
\(596\) | 73.1465 | 2.99620 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 94.3103 | 3.85664 | ||||||||
\(599\) | −17.3363 | −0.708341 | −0.354170 | − | 0.935181i | \(-0.615237\pi\) | ||||
−0.354170 | + | 0.935181i | \(0.615237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.8920 | 0.444293 | 0.222147 | − | 0.975013i | \(-0.428694\pi\) | ||||
0.222147 | + | 0.975013i | \(0.428694\pi\) | |||||||
\(602\) | −68.0461 | −2.77335 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −41.7389 | −1.69833 | ||||||||
\(605\) | 2.47951 | 0.100807 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.3377 | 1.39372 | 0.696862 | − | 0.717205i | \(-0.254579\pi\) | ||||
0.696862 | + | 0.717205i | \(0.254579\pi\) | |||||||
\(608\) | 22.9816 | 0.932025 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.74732 | −0.232702 | ||||||||
\(611\) | −65.0174 | −2.63032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.44572 | −0.300730 | −0.150365 | − | 0.988631i | \(-0.548045\pi\) | ||||
−0.150365 | + | 0.988631i | \(0.548045\pi\) | |||||||
\(614\) | 16.5722 | 0.668801 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.4005 | −0.419048 | ||||||||
\(617\) | 23.0634 | 0.928497 | 0.464249 | − | 0.885705i | \(-0.346324\pi\) | ||||
0.464249 | + | 0.885705i | \(0.346324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8519 | −0.677334 | −0.338667 | − | 0.940906i | \(-0.609976\pi\) | ||||
−0.338667 | + | 0.940906i | \(0.609976\pi\) | |||||||
\(620\) | −51.6142 | −2.07287 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 43.6497 | 1.75020 | ||||||||
\(623\) | 9.36987 | 0.375396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4221 | −1.17688 | ||||||||
\(626\) | 55.1092 | 2.20261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.2836 | 0.889214 | ||||||||
\(629\) | −43.7444 | −1.74420 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.8979 | 1.23002 | 0.615012 | − | 0.788518i | \(-0.289151\pi\) | ||||
0.615012 | + | 0.788518i | \(0.289151\pi\) | |||||||
\(632\) | −18.7595 | −0.746213 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.1458 | 1.43553 | ||||||||
\(635\) | 28.9473 | 1.14874 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.2903 | 0.883175 | ||||||||
\(638\) | −14.9275 | −0.590986 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −48.2496 | −1.90723 | ||||||||
\(641\) | −7.28363 | −0.287686 | −0.143843 | − | 0.989601i | \(-0.545946\pi\) | ||||
−0.143843 | + | 0.989601i | \(0.545946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.6899 | −1.48634 | −0.743172 | − | 0.669101i | \(-0.766679\pi\) | ||||
−0.743172 | + | 0.669101i | \(0.766679\pi\) | |||||||
\(644\) | 74.1262 | 2.92098 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −72.1033 | −2.83687 | ||||||||
\(647\) | −49.6098 | −1.95036 | −0.975181 | − | 0.221409i | \(-0.928934\pi\) | ||||
−0.975181 | + | 0.221409i | \(0.928934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.81524 | 0.149761 | ||||||||
\(650\) | 16.1017 | 0.631560 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.2759 | −1.18570 | ||||||||
\(653\) | 23.6399 | 0.925101 | 0.462551 | − | 0.886593i | \(-0.346934\pi\) | ||||
0.462551 | + | 0.886593i | \(0.346934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.4278 | 0.641887 | ||||||||
\(656\) | −5.61504 | −0.219231 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −81.4055 | −3.17352 | ||||||||
\(659\) | −28.7430 | −1.11967 | −0.559834 | − | 0.828605i | \(-0.689135\pi\) | ||||
−0.559834 | + | 0.828605i | \(0.689135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.89740 | 0.229382 | 0.114691 | − | 0.993401i | \(-0.463412\pi\) | ||||
0.114691 | + | 0.993401i | \(0.463412\pi\) | |||||||
\(662\) | −42.5232 | −1.65271 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.5500 | 0.836301 | ||||||||
\(665\) | −37.9829 | −1.47292 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.3027 | 1.67669 | ||||||||
\(668\) | 21.4105 | 0.828397 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.8390 | 0.727814 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.9587 | 0.923539 | 0.461769 | − | 0.887000i | \(-0.347215\pi\) | ||||
0.461769 | + | 0.887000i | \(0.347215\pi\) | |||||||
\(674\) | −0.795459 | −0.0306400 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 79.6507 | 3.06349 | ||||||||
\(677\) | −10.7860 | −0.414539 | −0.207270 | − | 0.978284i | \(-0.566458\pi\) | ||||
−0.207270 | + | 0.978284i | \(0.566458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7822 | 1.06618 | ||||||||
\(680\) | 52.3667 | 2.00817 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.3059 | 0.547802 | ||||||||
\(683\) | −28.2231 | −1.07993 | −0.539964 | − | 0.841688i | \(-0.681562\pi\) | ||||
−0.539964 | + | 0.841688i | \(0.681562\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6784 | 0.637247 | ||||||||
\(686\) | −25.1256 | −0.959298 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.65822 | −0.215718 | ||||||||
\(689\) | −70.8478 | −2.69909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.63955 | −0.366706 | −0.183353 | − | 0.983047i | \(-0.558695\pi\) | ||||
−0.183353 | + | 0.983047i | \(0.558695\pi\) | |||||||
\(692\) | 36.6967 | 1.39500 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.71550 | 0.216958 | ||||||||
\(695\) | 43.4184 | 1.64695 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.1578 | −2.24076 | ||||||||
\(698\) | 60.8266 | 2.30232 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.6556 | 0.478338 | ||||||||
\(701\) | 5.33675 | 0.201566 | 0.100783 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100783 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.8879 | 1.16496 | ||||||||
\(704\) | 12.6262 | 0.475868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.7216 | 0.779867 | ||||||||
\(707\) | 13.7625 | 0.517592 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.2039 | 1.54744 | 0.773722 | − | 0.633525i | \(-0.218393\pi\) | ||||
0.773722 | + | 0.633525i | \(0.218393\pi\) | |||||||
\(710\) | 76.7875 | 2.88178 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.12151 | 0.341843 | ||||||||
\(713\) | −41.4995 | −1.55417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0038 | −0.561110 | ||||||||
\(716\) | −73.3138 | −2.73987 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −55.9092 | −2.08651 | ||||||||
\(719\) | −13.1824 | −0.491620 | −0.245810 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245810 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.3170 | −2.20908 | ||||||||
\(722\) | 6.87173 | 0.255739 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.61444 | −0.357318 | ||||||||
\(725\) | 7.39310 | 0.274573 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.00135 | −0.333842 | −0.166921 | − | 0.985970i | \(-0.553382\pi\) | ||||
−0.166921 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(728\) | 62.9345 | 2.33251 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.1857 | −1.33929 | ||||||||
\(731\) | −59.6127 | −2.20486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6369 | −1.09467 | −0.547333 | − | 0.836915i | \(-0.684357\pi\) | ||||
−0.547333 | + | 0.836915i | \(0.684357\pi\) | |||||||
\(734\) | 9.50240 | 0.350740 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.9719 | −1.21536 | ||||||||
\(737\) | −3.27788 | −0.120742 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8776 | −0.878350 | −0.439175 | − | 0.898401i | \(-0.644729\pi\) | ||||
−0.439175 | + | 0.898401i | \(0.644729\pi\) | |||||||
\(740\) | −55.1162 | −2.02611 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −88.7055 | −3.25648 | ||||||||
\(743\) | 46.5931 | 1.70933 | 0.854667 | − | 0.519177i | \(-0.173762\pi\) | ||||
0.854667 | + | 0.519177i | \(0.173762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.7743 | 1.97014 | ||||||||
\(746\) | 10.1217 | 0.370583 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.3862 | −0.818520 | ||||||||
\(749\) | 22.1748 | 0.810250 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2932 | −0.412095 | −0.206047 | − | 0.978542i | \(-0.566060\pi\) | ||||
−0.206047 | + | 0.978542i | \(0.566060\pi\) | |||||||
\(752\) | −6.76909 | −0.246843 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 90.3280 | 3.28955 | ||||||||
\(755\) | −30.6847 | −1.11673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.6228 | 0.894931 | 0.447466 | − | 0.894301i | \(-0.352327\pi\) | ||||
0.447466 | + | 0.894301i | \(0.352327\pi\) | |||||||
\(758\) | 88.9090 | 3.22932 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.9762 | −1.34127 | ||||||||
\(761\) | −37.1943 | −1.34829 | −0.674146 | − | 0.738598i | \(-0.735488\pi\) | ||||
−0.674146 | + | 0.738598i | \(0.735488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.18033 | −0.187540 | ||||||||
\(764\) | −56.8354 | −2.05623 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.74135 | −0.315838 | ||||||||
\(767\) | −23.0864 | −0.833602 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.5613 | −1.06601 | −0.533004 | − | 0.846113i | \(-0.678937\pi\) | ||||
−0.533004 | + | 0.846113i | \(0.678937\pi\) | |||||||
\(770\) | −18.7856 | −0.676987 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.165645 | −0.00596170 | ||||||||
\(773\) | −9.44618 | −0.339755 | −0.169878 | − | 0.985465i | \(-0.554337\pi\) | ||||
−0.169878 | + | 0.985465i | \(0.554337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.08524 | −0.254509 | ||||||||
\(776\) | 27.0458 | 0.970886 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −77.1698 | −2.76667 | ||||||||
\(779\) | 41.7714 | 1.49662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3606 | −0.478079 | ||||||||
\(782\) | 103.447 | 3.69927 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.32069 | 0.0828818 | ||||||||
\(785\) | 16.3820 | 0.584699 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3687 | 0.690421 | 0.345211 | − | 0.938525i | \(-0.387807\pi\) | ||||
0.345211 | + | 0.938525i | \(0.387807\pi\) | |||||||
\(788\) | −20.8509 | −0.742782 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.8839 | −1.20554 | ||||||||
\(791\) | −2.09879 | −0.0746243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.05111 | −0.214881 | ||||||||
\(794\) | −45.2596 | −1.60620 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.9466 | −0.919652 | ||||||||
\(797\) | −6.30009 | −0.223161 | −0.111580 | − | 0.993755i | \(-0.535591\pi\) | ||||
−0.111580 | + | 0.993755i | \(0.535591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −71.3164 | −2.52299 | ||||||||
\(800\) | −5.62931 | −0.199026 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 88.0932 | 3.11068 | ||||||||
\(803\) | 6.29610 | 0.222185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.4945 | 1.92068 | ||||||||
\(806\) | −86.5666 | −3.04918 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.3977 | 0.471330 | ||||||||
\(809\) | −5.41537 | −0.190394 | −0.0951971 | − | 0.995458i | \(-0.530348\pi\) | ||||
−0.0951971 | + | 0.995458i | \(0.530348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.7092 | −1.04323 | −0.521616 | − | 0.853180i | \(-0.674671\pi\) | ||||
−0.521616 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(812\) | 70.9962 | 2.49148 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.2766 | 0.535444 | ||||||||
\(815\) | −22.2576 | −0.779650 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.0926 | 1.47263 | ||||||||
\(818\) | −6.46818 | −0.226155 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −74.5366 | −2.60293 | ||||||||
\(821\) | 22.5460 | 0.786862 | 0.393431 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393431 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8510 | 0.935967 | 0.467984 | − | 0.883737i | \(-0.344981\pi\) | ||||
0.467984 | + | 0.883737i | \(0.344981\pi\) | |||||||
\(824\) | −57.7447 | −2.01163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.9055 | −1.00575 | ||||||||
\(827\) | 24.0270 | 0.835502 | 0.417751 | − | 0.908562i | \(-0.362818\pi\) | ||||
0.417751 | + | 0.908562i | \(0.362818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.6281 | 1.34161 | 0.670805 | − | 0.741634i | \(-0.265949\pi\) | ||||
0.670805 | + | 0.741634i | \(0.265949\pi\) | |||||||
\(830\) | 38.9241 | 1.35108 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −76.4025 | −2.64878 | ||||||||
\(833\) | 24.4499 | 0.847138 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.7401 | 0.544709 | ||||||||
\(836\) | 15.8069 | 0.546694 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.02693 | 0.104563 | ||||||||
\(839\) | −49.6307 | −1.71344 | −0.856720 | − | 0.515781i | \(-0.827502\pi\) | ||||
−0.856720 | + | 0.515781i | \(0.827502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4742 | 0.430146 | ||||||||
\(842\) | −43.3221 | −1.49298 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −86.7692 | −2.98672 | ||||||||
\(845\) | 58.5559 | 2.01438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.26859 | 0.112310 | ||||||||
\(848\) | −7.37610 | −0.253296 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.6616 | 0.605790 | ||||||||
\(851\) | −44.3152 | −1.51911 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.49047 | 0.0510326 | 0.0255163 | − | 0.999674i | \(-0.491877\pi\) | ||||
0.0255163 | + | 0.999674i | \(0.491877\pi\) | |||||||
\(854\) | −7.57633 | −0.259257 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.5870 | 0.737830 | ||||||||
\(857\) | −5.29697 | −0.180941 | −0.0904705 | − | 0.995899i | \(-0.528837\pi\) | ||||
−0.0904705 | + | 0.995899i | \(0.528837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.5876 | −1.58955 | −0.794774 | − | 0.606905i | \(-0.792411\pi\) | ||||
−0.794774 | + | 0.606905i | \(0.792411\pi\) | |||||||
\(860\) | −75.1097 | −2.56122 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.9255 | 0.372124 | ||||||||
\(863\) | 56.2138 | 1.91354 | 0.956770 | − | 0.290847i | \(-0.0939369\pi\) | ||||
0.956770 | + | 0.290847i | \(0.0939369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.9779 | 0.917276 | ||||||||
\(866\) | −62.6017 | −2.12729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −68.0397 | −2.30942 | ||||||||
\(869\) | 5.89560 | 0.199995 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.8348 | 0.672076 | ||||||||
\(872\) | −5.04302 | −0.170778 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −73.0443 | −2.47076 | ||||||||
\(875\) | −31.2187 | −1.05538 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3453 | 0.484408 | 0.242204 | − | 0.970225i | \(-0.422130\pi\) | ||||
0.242204 | + | 0.970225i | \(0.422130\pi\) | |||||||
\(878\) | 65.0194 | 2.19430 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.56208 | −0.0526576 | ||||||||
\(881\) | −23.0396 | −0.776225 | −0.388112 | − | 0.921612i | \(-0.626873\pi\) | ||||
−0.388112 | + | 0.921612i | \(0.626873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.9199 | −0.670358 | −0.335179 | − | 0.942155i | \(-0.608797\pi\) | ||||
−0.335179 | + | 0.942155i | \(0.608797\pi\) | |||||||
\(884\) | 135.461 | 4.55605 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.2167 | −0.981553 | ||||||||
\(887\) | 7.91120 | 0.265632 | 0.132816 | − | 0.991141i | \(-0.457598\pi\) | ||||
0.132816 | + | 0.991141i | \(0.457598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.1594 | 1.27982 | ||||||||
\(890\) | 16.4755 | 0.552260 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.2661 | 1.51562 | ||||||||
\(893\) | 50.3566 | 1.68512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53.8973 | −1.80159 | ||||||||
\(896\) | −63.6045 | −2.12488 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.0700 | −0.769857 | ||||||||
\(899\) | −39.7471 | −1.32564 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.7117 | −2.58895 | ||||||||
\(902\) | 20.6593 | 0.687880 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.04316 | −0.0679544 | ||||||||
\(905\) | −7.06814 | −0.234953 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.9038 | −0.494872 | −0.247436 | − | 0.968904i | \(-0.579588\pi\) | ||||
−0.247436 | + | 0.968904i | \(0.579588\pi\) | |||||||
\(908\) | 74.7862 | 2.48187 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 113.674 | 3.76825 | ||||||||
\(911\) | 52.3222 | 1.73351 | 0.866756 | − | 0.498732i | \(-0.166201\pi\) | ||||
0.866756 | + | 0.498732i | \(0.166201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.77257 | −0.224139 | ||||||||
\(914\) | 72.7980 | 2.40794 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.6805 | 0.914588 | ||||||||
\(917\) | 21.6557 | 0.715136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.3325 | 0.703693 | 0.351846 | − | 0.936058i | \(-0.385554\pi\) | ||||
0.351846 | + | 0.936058i | \(0.385554\pi\) | |||||||
\(920\) | 53.0501 | 1.74901 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −67.7215 | −2.23029 | ||||||||
\(923\) | 80.8462 | 2.66109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.56598 | −0.248768 | ||||||||
\(926\) | −61.1117 | −2.00826 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −31.5796 | −1.03665 | ||||||||
\(929\) | −22.5813 | −0.740867 | −0.370433 | − | 0.928859i | \(-0.620791\pi\) | ||||
−0.370433 | + | 0.928859i | \(0.620791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.2641 | −0.565807 | ||||||||
\(932\) | 52.3999 | 1.71642 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.7875 | 1.07284 | ||||||||
\(935\) | −16.4574 | −0.538215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.3641 | −1.12263 | −0.561314 | − | 0.827603i | \(-0.689704\pi\) | ||||
−0.561314 | + | 0.827603i | \(0.689704\pi\) | |||||||
\(938\) | 24.8343 | 0.810868 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −89.8559 | −2.93078 | ||||||||
\(941\) | 6.54597 | 0.213393 | 0.106696 | − | 0.994292i | \(-0.465973\pi\) | ||||
0.106696 | + | 0.994292i | \(0.465973\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.9299 | −1.95158 | ||||||||
\(944\) | −2.40357 | −0.0782296 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.8182 | 0.676858 | ||||||||
\(947\) | 54.5844 | 1.77375 | 0.886877 | − | 0.462005i | \(-0.152870\pi\) | ||||
0.886877 | + | 0.462005i | \(0.152870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.0984 | −1.23673 | ||||||||
\(950\) | −12.4709 | −0.404610 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69.0317 | 2.23733 | ||||||||
\(953\) | −22.4941 | −0.728654 | −0.364327 | − | 0.931271i | \(-0.618701\pi\) | ||||
−0.364327 | + | 0.931271i | \(0.618701\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.7830 | −1.35207 | ||||||||
\(956\) | −25.3604 | −0.820213 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.34696 | −0.237369 | ||||||||
\(959\) | 21.9860 | 0.709967 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.09198 | 0.228774 | ||||||||
\(962\) | −92.4402 | −2.98039 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −52.5612 | −1.69288 | ||||||||
\(965\) | −0.121775 | −0.00392009 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2301 | 0.393294 | 0.196647 | − | 0.980474i | \(-0.436995\pi\) | ||||
0.196647 | + | 0.980474i | \(0.436995\pi\) | |||||||
\(968\) | 3.18195 | 0.102272 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.8507 | 1.56850 | ||||||||
\(971\) | −43.7846 | −1.40511 | −0.702557 | − | 0.711627i | \(-0.747959\pi\) | ||||
−0.702557 | + | 0.711627i | \(0.747959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.2358 | 1.83489 | ||||||||
\(974\) | −4.01480 | −0.128643 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.629993 | −0.0201656 | ||||||||
\(977\) | −31.3439 | −1.00278 | −0.501390 | − | 0.865221i | \(-0.667178\pi\) | ||||
−0.501390 | + | 0.865221i | \(0.667178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.86664 | −0.0916183 | ||||||||
\(980\) | 30.8059 | 0.984058 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 76.5877 | 2.44401 | ||||||||
\(983\) | 44.4268 | 1.41699 | 0.708497 | − | 0.705713i | \(-0.249373\pi\) | ||||
0.708497 | + | 0.705713i | \(0.249373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.3287 | −0.488413 | ||||||||
\(986\) | 99.0792 | 3.15533 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −95.6493 | −3.04301 | ||||||||
\(989\) | −60.3907 | −1.92031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.16593 | 0.259399 | 0.129700 | − | 0.991553i | \(-0.458599\pi\) | ||||
0.129700 | + | 0.991553i | \(0.458599\pi\) | |||||||
\(992\) | 30.2646 | 0.960901 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 101.224 | 3.21064 | ||||||||
\(995\) | −19.0748 | −0.604713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9667 | −0.378989 | −0.189494 | − | 0.981882i | \(-0.560685\pi\) | ||||
−0.189494 | + | 0.981882i | \(0.560685\pi\) | |||||||
\(998\) | −33.6056 | −1.06377 | ||||||||
\(999\) | 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 | 6039.2.a.f.1.10 | 12 | ||
3.2 | odd | 2 | 2013.2.a.c.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.c.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
6039.2.a.f.1.10 | 12 | 1.1 | even | 1 | trivial |