Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.27502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27502 | 1.60868 | 0.804342 | − | 0.594167i | \(-0.202518\pi\) | ||||
0.804342 | + | 0.594167i | \(0.202518\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.17573 | 1.58786 | ||||||||
\(5\) | 1.23869 | 0.553961 | 0.276980 | − | 0.960876i | \(-0.410666\pi\) | ||||
0.276980 | + | 0.960876i | \(0.410666\pi\) | |||||||
\(6\) | 2.27502 | 0.928774 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.67481 | 0.945688 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.81806 | 0.891148 | ||||||||
\(11\) | 6.12669 | 1.84727 | 0.923633 | − | 0.383277i | \(-0.125205\pi\) | ||||
0.923633 | + | 0.383277i | \(0.125205\pi\) | |||||||
\(12\) | 3.17573 | 0.916754 | ||||||||
\(13\) | −0.910400 | −0.252500 | −0.126250 | − | 0.991998i | \(-0.540294\pi\) | ||||
−0.126250 | + | 0.991998i | \(0.540294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23869 | 0.319829 | ||||||||
\(16\) | −0.266205 | −0.0665513 | ||||||||
\(17\) | −4.90873 | −1.19054 | −0.595271 | − | 0.803525i | \(-0.702955\pi\) | ||||
−0.595271 | + | 0.803525i | \(0.702955\pi\) | |||||||
\(18\) | 2.27502 | 0.536228 | ||||||||
\(19\) | 6.90370 | 1.58382 | 0.791909 | − | 0.610639i | \(-0.209087\pi\) | ||||
0.791909 | + | 0.610639i | \(0.209087\pi\) | |||||||
\(20\) | 3.93376 | 0.879614 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.9384 | 2.97167 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.67481 | 0.545993 | ||||||||
\(25\) | −3.46564 | −0.693128 | ||||||||
\(26\) | −2.07118 | −0.406192 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.36004 | 0.623944 | 0.311972 | − | 0.950091i | \(-0.399010\pi\) | ||||
0.311972 | + | 0.950091i | \(0.399010\pi\) | |||||||
\(30\) | 2.81806 | 0.514504 | ||||||||
\(31\) | −5.43735 | −0.976577 | −0.488289 | − | 0.872682i | \(-0.662379\pi\) | ||||
−0.488289 | + | 0.872682i | \(0.662379\pi\) | |||||||
\(32\) | −5.95524 | −1.05275 | ||||||||
\(33\) | 6.12669 | 1.06652 | ||||||||
\(34\) | −11.1675 | −1.91521 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.17573 | 0.529288 | ||||||||
\(37\) | 6.54665 | 1.07626 | 0.538132 | − | 0.842861i | \(-0.319130\pi\) | ||||
0.538132 | + | 0.842861i | \(0.319130\pi\) | |||||||
\(38\) | 15.7061 | 2.54786 | ||||||||
\(39\) | −0.910400 | −0.145781 | ||||||||
\(40\) | 3.31327 | 0.523874 | ||||||||
\(41\) | 2.52207 | 0.393882 | 0.196941 | − | 0.980415i | \(-0.436899\pi\) | ||||
0.196941 | + | 0.980415i | \(0.436899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.231369 | −0.0352834 | −0.0176417 | − | 0.999844i | \(-0.505616\pi\) | ||||
−0.0176417 | + | 0.999844i | \(0.505616\pi\) | |||||||
\(44\) | 19.4567 | 2.93321 | ||||||||
\(45\) | 1.23869 | 0.184654 | ||||||||
\(46\) | 2.27502 | 0.335434 | ||||||||
\(47\) | −13.3578 | −1.94843 | −0.974217 | − | 0.225614i | \(-0.927561\pi\) | ||||
−0.974217 | + | 0.225614i | \(0.927561\pi\) | |||||||
\(48\) | −0.266205 | −0.0384234 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.88440 | −1.11502 | ||||||||
\(51\) | −4.90873 | −0.687360 | ||||||||
\(52\) | −2.89118 | −0.400935 | ||||||||
\(53\) | 4.22681 | 0.580597 | 0.290298 | − | 0.956936i | \(-0.406245\pi\) | ||||
0.290298 | + | 0.956936i | \(0.406245\pi\) | |||||||
\(54\) | 2.27502 | 0.309591 | ||||||||
\(55\) | 7.58909 | 1.02331 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.90370 | 0.914418 | ||||||||
\(58\) | 7.64417 | 1.00373 | ||||||||
\(59\) | 0.754201 | 0.0981886 | 0.0490943 | − | 0.998794i | \(-0.484367\pi\) | ||||
0.0490943 | + | 0.998794i | \(0.484367\pi\) | |||||||
\(60\) | 3.93376 | 0.507846 | ||||||||
\(61\) | −3.57664 | −0.457942 | −0.228971 | − | 0.973433i | \(-0.573536\pi\) | ||||
−0.228971 | + | 0.973433i | \(0.573536\pi\) | |||||||
\(62\) | −12.3701 | −1.57100 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0159 | −1.62699 | ||||||||
\(65\) | −1.12771 | −0.139875 | ||||||||
\(66\) | 13.9384 | 1.71569 | ||||||||
\(67\) | −4.49406 | −0.549036 | −0.274518 | − | 0.961582i | \(-0.588518\pi\) | ||||
−0.274518 | + | 0.961582i | \(0.588518\pi\) | |||||||
\(68\) | −15.5888 | −1.89042 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.8575 | 1.88194 | 0.940968 | − | 0.338495i | \(-0.109918\pi\) | ||||
0.940968 | + | 0.338495i | \(0.109918\pi\) | |||||||
\(72\) | 2.67481 | 0.315229 | ||||||||
\(73\) | 4.27776 | 0.500674 | 0.250337 | − | 0.968159i | \(-0.419459\pi\) | ||||
0.250337 | + | 0.968159i | \(0.419459\pi\) | |||||||
\(74\) | 14.8938 | 1.73137 | ||||||||
\(75\) | −3.46564 | −0.400177 | ||||||||
\(76\) | 21.9243 | 2.51489 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.07118 | −0.234515 | ||||||||
\(79\) | −0.222015 | −0.0249787 | −0.0124893 | − | 0.999922i | \(-0.503976\pi\) | ||||
−0.0124893 | + | 0.999922i | \(0.503976\pi\) | |||||||
\(80\) | −0.329747 | −0.0368668 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.73777 | 0.633631 | ||||||||
\(83\) | −15.5197 | −1.70351 | −0.851753 | − | 0.523944i | \(-0.824460\pi\) | ||||
−0.851753 | + | 0.523944i | \(0.824460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.08041 | −0.659513 | ||||||||
\(86\) | −0.526369 | −0.0567598 | ||||||||
\(87\) | 3.36004 | 0.360234 | ||||||||
\(88\) | 16.3877 | 1.74694 | ||||||||
\(89\) | −0.559363 | −0.0592924 | −0.0296462 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296462 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(90\) | 2.81806 | 0.297049 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.17573 | 0.331093 | ||||||||
\(93\) | −5.43735 | −0.563827 | ||||||||
\(94\) | −30.3893 | −3.13441 | ||||||||
\(95\) | 8.55157 | 0.877373 | ||||||||
\(96\) | −5.95524 | −0.607804 | ||||||||
\(97\) | −17.6476 | −1.79185 | −0.895923 | − | 0.444209i | \(-0.853485\pi\) | ||||
−0.895923 | + | 0.444209i | \(0.853485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.12669 | 0.615756 | ||||||||
\(100\) | −11.0059 | −1.10059 | ||||||||
\(101\) | 8.13075 | 0.809040 | 0.404520 | − | 0.914529i | \(-0.367439\pi\) | ||||
0.404520 | + | 0.914529i | \(0.367439\pi\) | |||||||
\(102\) | −11.1675 | −1.10574 | ||||||||
\(103\) | 14.2795 | 1.40700 | 0.703500 | − | 0.710695i | \(-0.251619\pi\) | ||||
0.703500 | + | 0.710695i | \(0.251619\pi\) | |||||||
\(104\) | −2.43515 | −0.238786 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.61609 | 0.933997 | ||||||||
\(107\) | −6.55764 | −0.633951 | −0.316975 | − | 0.948434i | \(-0.602667\pi\) | ||||
−0.316975 | + | 0.948434i | \(0.602667\pi\) | |||||||
\(108\) | 3.17573 | 0.305585 | ||||||||
\(109\) | 18.2358 | 1.74668 | 0.873338 | − | 0.487114i | \(-0.161950\pi\) | ||||
0.873338 | + | 0.487114i | \(0.161950\pi\) | |||||||
\(110\) | 17.2654 | 1.64619 | ||||||||
\(111\) | 6.54665 | 0.621381 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5945 | −1.74922 | −0.874610 | − | 0.484828i | \(-0.838882\pi\) | ||||
−0.874610 | + | 0.484828i | \(0.838882\pi\) | |||||||
\(114\) | 15.7061 | 1.47101 | ||||||||
\(115\) | 1.23869 | 0.115509 | ||||||||
\(116\) | 10.6706 | 0.990738 | ||||||||
\(117\) | −0.910400 | −0.0841665 | ||||||||
\(118\) | 1.71582 | 0.157954 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.31327 | 0.302459 | ||||||||
\(121\) | 26.5363 | 2.41239 | ||||||||
\(122\) | −8.13695 | −0.736685 | ||||||||
\(123\) | 2.52207 | 0.227408 | ||||||||
\(124\) | −17.2676 | −1.55067 | ||||||||
\(125\) | −10.4863 | −0.937926 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.19807 | −0.372518 | −0.186259 | − | 0.982501i | \(-0.559636\pi\) | ||||
−0.186259 | + | 0.982501i | \(0.559636\pi\) | |||||||
\(128\) | −17.7010 | −1.56456 | ||||||||
\(129\) | −0.231369 | −0.0203709 | ||||||||
\(130\) | −2.56556 | −0.225014 | ||||||||
\(131\) | −3.83542 | −0.335102 | −0.167551 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167551 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(132\) | 19.4567 | 1.69349 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.2241 | −0.883226 | ||||||||
\(135\) | 1.23869 | 0.106610 | ||||||||
\(136\) | −13.1299 | −1.12588 | ||||||||
\(137\) | 7.25647 | 0.619962 | 0.309981 | − | 0.950743i | \(-0.399677\pi\) | ||||
0.309981 | + | 0.950743i | \(0.399677\pi\) | |||||||
\(138\) | 2.27502 | 0.193663 | ||||||||
\(139\) | −3.52170 | −0.298707 | −0.149353 | − | 0.988784i | \(-0.547719\pi\) | ||||
−0.149353 | + | 0.988784i | \(0.547719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.3578 | −1.12493 | ||||||||
\(142\) | 36.0761 | 3.02744 | ||||||||
\(143\) | −5.57774 | −0.466434 | ||||||||
\(144\) | −0.266205 | −0.0221838 | ||||||||
\(145\) | 4.16206 | 0.345640 | ||||||||
\(146\) | 9.73201 | 0.805427 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.7904 | 1.70896 | ||||||||
\(149\) | −10.9243 | −0.894951 | −0.447475 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447475 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(150\) | −7.88440 | −0.643759 | ||||||||
\(151\) | −15.8535 | −1.29014 | −0.645071 | − | 0.764122i | \(-0.723172\pi\) | ||||
−0.645071 | + | 0.764122i | \(0.723172\pi\) | |||||||
\(152\) | 18.4661 | 1.49780 | ||||||||
\(153\) | −4.90873 | −0.396847 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.73521 | −0.540985 | ||||||||
\(156\) | −2.89118 | −0.231480 | ||||||||
\(157\) | 9.19996 | 0.734237 | 0.367118 | − | 0.930174i | \(-0.380344\pi\) | ||||
0.367118 | + | 0.930174i | \(0.380344\pi\) | |||||||
\(158\) | −0.505090 | −0.0401828 | ||||||||
\(159\) | 4.22681 | 0.335208 | ||||||||
\(160\) | −7.37672 | −0.583181 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.27502 | 0.178743 | ||||||||
\(163\) | −1.64877 | −0.129142 | −0.0645709 | − | 0.997913i | \(-0.520568\pi\) | ||||
−0.0645709 | + | 0.997913i | \(0.520568\pi\) | |||||||
\(164\) | 8.00942 | 0.625431 | ||||||||
\(165\) | 7.58909 | 0.590810 | ||||||||
\(166\) | −35.3076 | −2.74040 | ||||||||
\(167\) | −5.46655 | −0.423015 | −0.211507 | − | 0.977376i | \(-0.567837\pi\) | ||||
−0.211507 | + | 0.977376i | \(0.567837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1712 | −0.936244 | ||||||||
\(170\) | −13.8331 | −1.06095 | ||||||||
\(171\) | 6.90370 | 0.527939 | ||||||||
\(172\) | −0.734764 | −0.0560252 | ||||||||
\(173\) | 0.509172 | 0.0387117 | 0.0193558 | − | 0.999813i | \(-0.493838\pi\) | ||||
0.0193558 | + | 0.999813i | \(0.493838\pi\) | |||||||
\(174\) | 7.64417 | 0.579503 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.63096 | −0.122938 | ||||||||
\(177\) | 0.754201 | 0.0566892 | ||||||||
\(178\) | −1.27256 | −0.0953827 | ||||||||
\(179\) | 8.35087 | 0.624173 | 0.312087 | − | 0.950054i | \(-0.398972\pi\) | ||||
0.312087 | + | 0.950054i | \(0.398972\pi\) | |||||||
\(180\) | 3.93376 | 0.293205 | ||||||||
\(181\) | 2.42861 | 0.180517 | 0.0902584 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902584 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.57664 | −0.264393 | ||||||||
\(184\) | 2.67481 | 0.197190 | ||||||||
\(185\) | 8.10930 | 0.596208 | ||||||||
\(186\) | −12.3701 | −0.907020 | ||||||||
\(187\) | −30.0743 | −2.19925 | ||||||||
\(188\) | −42.4207 | −3.09385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.4550 | 1.41142 | ||||||||
\(191\) | −14.2931 | −1.03421 | −0.517107 | − | 0.855921i | \(-0.672991\pi\) | ||||
−0.517107 | + | 0.855921i | \(0.672991\pi\) | |||||||
\(192\) | −13.0159 | −0.939342 | ||||||||
\(193\) | 2.09005 | 0.150445 | 0.0752225 | − | 0.997167i | \(-0.476033\pi\) | ||||
0.0752225 | + | 0.997167i | \(0.476033\pi\) | |||||||
\(194\) | −40.1488 | −2.88251 | ||||||||
\(195\) | −1.12771 | −0.0807568 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8863 | 0.775614 | 0.387807 | − | 0.921741i | \(-0.373233\pi\) | ||||
0.387807 | + | 0.921741i | \(0.373233\pi\) | |||||||
\(198\) | 13.9384 | 0.990556 | ||||||||
\(199\) | −3.44053 | −0.243893 | −0.121946 | − | 0.992537i | \(-0.538914\pi\) | ||||
−0.121946 | + | 0.992537i | \(0.538914\pi\) | |||||||
\(200\) | −9.26992 | −0.655482 | ||||||||
\(201\) | −4.49406 | −0.316986 | ||||||||
\(202\) | 18.4976 | 1.30149 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −15.5888 | −1.09143 | ||||||||
\(205\) | 3.12408 | 0.218195 | ||||||||
\(206\) | 32.4862 | 2.26342 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0.242353 | 0.0168042 | ||||||||
\(209\) | 42.2968 | 2.92573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6690 | 0.803324 | 0.401662 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401662 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(212\) | 13.4232 | 0.921909 | ||||||||
\(213\) | 15.8575 | 1.08654 | ||||||||
\(214\) | −14.9188 | −1.01983 | ||||||||
\(215\) | −0.286595 | −0.0195456 | ||||||||
\(216\) | 2.67481 | 0.181998 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 41.4869 | 2.80985 | ||||||||
\(219\) | 4.27776 | 0.289065 | ||||||||
\(220\) | 24.1009 | 1.62488 | ||||||||
\(221\) | 4.46891 | 0.300611 | ||||||||
\(222\) | 14.8938 | 0.999605 | ||||||||
\(223\) | −2.48168 | −0.166185 | −0.0830926 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830926 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.46564 | −0.231043 | ||||||||
\(226\) | −42.3028 | −2.81394 | ||||||||
\(227\) | 22.0495 | 1.46348 | 0.731738 | − | 0.681586i | \(-0.238710\pi\) | ||||
0.731738 | + | 0.681586i | \(0.238710\pi\) | |||||||
\(228\) | 21.9243 | 1.45197 | ||||||||
\(229\) | −14.7467 | −0.974488 | −0.487244 | − | 0.873266i | \(-0.661998\pi\) | ||||
−0.487244 | + | 0.873266i | \(0.661998\pi\) | |||||||
\(230\) | 2.81806 | 0.185817 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.98747 | 0.590056 | ||||||||
\(233\) | −3.41615 | −0.223799 | −0.111900 | − | 0.993720i | \(-0.535694\pi\) | ||||
−0.111900 | + | 0.993720i | \(0.535694\pi\) | |||||||
\(234\) | −2.07118 | −0.135397 | ||||||||
\(235\) | −16.5462 | −1.07936 | ||||||||
\(236\) | 2.39514 | 0.155910 | ||||||||
\(237\) | −0.222015 | −0.0144215 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8751 | −0.703453 | −0.351727 | − | 0.936103i | \(-0.614405\pi\) | ||||
−0.351727 | + | 0.936103i | \(0.614405\pi\) | |||||||
\(240\) | −0.329747 | −0.0212851 | ||||||||
\(241\) | 21.3965 | 1.37827 | 0.689134 | − | 0.724634i | \(-0.257991\pi\) | ||||
0.689134 | + | 0.724634i | \(0.257991\pi\) | |||||||
\(242\) | 60.3708 | 3.88078 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.3585 | −0.727150 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.73777 | 0.365827 | ||||||||
\(247\) | −6.28513 | −0.399913 | ||||||||
\(248\) | −14.5439 | −0.923537 | ||||||||
\(249\) | −15.5197 | −0.983520 | ||||||||
\(250\) | −23.8566 | −1.50883 | ||||||||
\(251\) | −4.68560 | −0.295752 | −0.147876 | − | 0.989006i | \(-0.547244\pi\) | ||||
−0.147876 | + | 0.989006i | \(0.547244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.12669 | 0.385182 | ||||||||
\(254\) | −9.55070 | −0.599264 | ||||||||
\(255\) | −6.08041 | −0.380770 | ||||||||
\(256\) | −14.2383 | −0.889897 | ||||||||
\(257\) | 27.0174 | 1.68530 | 0.842650 | − | 0.538462i | \(-0.180994\pi\) | ||||
0.842650 | + | 0.538462i | \(0.180994\pi\) | |||||||
\(258\) | −0.526369 | −0.0327703 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.58129 | −0.222102 | ||||||||
\(261\) | 3.36004 | 0.207981 | ||||||||
\(262\) | −8.72566 | −0.539073 | ||||||||
\(263\) | −20.0063 | −1.23364 | −0.616822 | − | 0.787103i | \(-0.711580\pi\) | ||||
−0.616822 | + | 0.787103i | \(0.711580\pi\) | |||||||
\(264\) | 16.3877 | 1.00859 | ||||||||
\(265\) | 5.23572 | 0.321628 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.559363 | −0.0342325 | ||||||||
\(268\) | −14.2719 | −0.871795 | ||||||||
\(269\) | 6.28072 | 0.382942 | 0.191471 | − | 0.981498i | \(-0.438674\pi\) | ||||
0.191471 | + | 0.981498i | \(0.438674\pi\) | |||||||
\(270\) | 2.81806 | 0.171501 | ||||||||
\(271\) | −25.4203 | −1.54417 | −0.772085 | − | 0.635519i | \(-0.780786\pi\) | ||||
−0.772085 | + | 0.635519i | \(0.780786\pi\) | |||||||
\(272\) | 1.30673 | 0.0792321 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5086 | 0.997323 | ||||||||
\(275\) | −21.2329 | −1.28039 | ||||||||
\(276\) | 3.17573 | 0.191156 | ||||||||
\(277\) | −15.1411 | −0.909739 | −0.454869 | − | 0.890558i | \(-0.650314\pi\) | ||||
−0.454869 | + | 0.890558i | \(0.650314\pi\) | |||||||
\(278\) | −8.01195 | −0.480525 | ||||||||
\(279\) | −5.43735 | −0.325526 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.3149 | −1.62947 | −0.814736 | − | 0.579833i | \(-0.803118\pi\) | ||||
−0.814736 | + | 0.579833i | \(0.803118\pi\) | |||||||
\(282\) | −30.3893 | −1.80965 | ||||||||
\(283\) | −8.54261 | −0.507805 | −0.253903 | − | 0.967230i | \(-0.581714\pi\) | ||||
−0.253903 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(284\) | 50.3590 | 2.98826 | ||||||||
\(285\) | 8.55157 | 0.506551 | ||||||||
\(286\) | −12.6895 | −0.750345 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.95524 | −0.350916 | ||||||||
\(289\) | 7.09562 | 0.417390 | ||||||||
\(290\) | 9.46879 | 0.556026 | ||||||||
\(291\) | −17.6476 | −1.03452 | ||||||||
\(292\) | 13.5850 | 0.795003 | ||||||||
\(293\) | −13.6153 | −0.795413 | −0.397707 | − | 0.917513i | \(-0.630194\pi\) | ||||
−0.397707 | + | 0.917513i | \(0.630194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.934224 | 0.0543926 | ||||||||
\(296\) | 17.5110 | 1.01781 | ||||||||
\(297\) | 6.12669 | 0.355507 | ||||||||
\(298\) | −24.8530 | −1.43969 | ||||||||
\(299\) | −0.910400 | −0.0526498 | ||||||||
\(300\) | −11.0059 | −0.635427 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −36.0672 | −2.07543 | ||||||||
\(303\) | 8.13075 | 0.467100 | ||||||||
\(304\) | −1.83780 | −0.105405 | ||||||||
\(305\) | −4.43037 | −0.253682 | ||||||||
\(306\) | −11.1675 | −0.638402 | ||||||||
\(307\) | 1.94494 | 0.111003 | 0.0555017 | − | 0.998459i | \(-0.482324\pi\) | ||||
0.0555017 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2795 | 0.812332 | ||||||||
\(310\) | −15.3228 | −0.870275 | ||||||||
\(311\) | 14.2020 | 0.805319 | 0.402660 | − | 0.915350i | \(-0.368086\pi\) | ||||
0.402660 | + | 0.915350i | \(0.368086\pi\) | |||||||
\(312\) | −2.43515 | −0.137863 | ||||||||
\(313\) | 4.20457 | 0.237656 | 0.118828 | − | 0.992915i | \(-0.462086\pi\) | ||||
0.118828 | + | 0.992915i | \(0.462086\pi\) | |||||||
\(314\) | 20.9301 | 1.18115 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.705061 | −0.0396628 | ||||||||
\(317\) | 0.738433 | 0.0414745 | 0.0207373 | − | 0.999785i | \(-0.493399\pi\) | ||||
0.0207373 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(318\) | 9.61609 | 0.539243 | ||||||||
\(319\) | 20.5859 | 1.15259 | ||||||||
\(320\) | −16.1227 | −0.901287 | ||||||||
\(321\) | −6.55764 | −0.366012 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.8884 | −1.88560 | ||||||||
\(324\) | 3.17573 | 0.176429 | ||||||||
\(325\) | 3.15512 | 0.175014 | ||||||||
\(326\) | −3.75100 | −0.207748 | ||||||||
\(327\) | 18.2358 | 1.00844 | ||||||||
\(328\) | 6.74607 | 0.372489 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 17.2654 | 0.950427 | ||||||||
\(331\) | −20.5989 | −1.13222 | −0.566108 | − | 0.824331i | \(-0.691552\pi\) | ||||
−0.566108 | + | 0.824331i | \(0.691552\pi\) | |||||||
\(332\) | −49.2863 | −2.70494 | ||||||||
\(333\) | 6.54665 | 0.358754 | ||||||||
\(334\) | −12.4365 | −0.680497 | ||||||||
\(335\) | −5.56676 | −0.304145 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.9032 | −1.51999 | −0.759993 | − | 0.649932i | \(-0.774797\pi\) | ||||
−0.759993 | + | 0.649932i | \(0.774797\pi\) | |||||||
\(338\) | −27.6897 | −1.50612 | ||||||||
\(339\) | −18.5945 | −1.00991 | ||||||||
\(340\) | −19.3097 | −1.04722 | ||||||||
\(341\) | −33.3130 | −1.80400 | ||||||||
\(342\) | 15.7061 | 0.849287 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.618867 | −0.0333671 | ||||||||
\(345\) | 1.23869 | 0.0666890 | ||||||||
\(346\) | 1.15838 | 0.0622748 | ||||||||
\(347\) | −2.08533 | −0.111946 | −0.0559732 | − | 0.998432i | \(-0.517826\pi\) | ||||
−0.0559732 | + | 0.998432i | \(0.517826\pi\) | |||||||
\(348\) | 10.6706 | 0.572003 | ||||||||
\(349\) | 4.04322 | 0.216429 | 0.108214 | − | 0.994128i | \(-0.465487\pi\) | ||||
0.108214 | + | 0.994128i | \(0.465487\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.910400 | −0.0485936 | ||||||||
\(352\) | −36.4859 | −1.94471 | ||||||||
\(353\) | 4.50793 | 0.239933 | 0.119966 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119966 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(354\) | 1.71582 | 0.0911950 | ||||||||
\(355\) | 19.6426 | 1.04252 | ||||||||
\(356\) | −1.77639 | −0.0941483 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.9984 | 1.00410 | ||||||||
\(359\) | −20.8138 | −1.09851 | −0.549254 | − | 0.835656i | \(-0.685088\pi\) | ||||
−0.549254 | + | 0.835656i | \(0.685088\pi\) | |||||||
\(360\) | 3.31327 | 0.174625 | ||||||||
\(361\) | 28.6611 | 1.50848 | ||||||||
\(362\) | 5.52513 | 0.290394 | ||||||||
\(363\) | 26.5363 | 1.39280 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.29884 | 0.277354 | ||||||||
\(366\) | −8.13695 | −0.425325 | ||||||||
\(367\) | −8.57218 | −0.447464 | −0.223732 | − | 0.974651i | \(-0.571824\pi\) | ||||
−0.223732 | + | 0.974651i | \(0.571824\pi\) | |||||||
\(368\) | −0.266205 | −0.0138769 | ||||||||
\(369\) | 2.52207 | 0.131294 | ||||||||
\(370\) | 18.4488 | 0.959109 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17.2676 | −0.895281 | ||||||||
\(373\) | −1.45507 | −0.0753407 | −0.0376703 | − | 0.999290i | \(-0.511994\pi\) | ||||
−0.0376703 | + | 0.999290i | \(0.511994\pi\) | |||||||
\(374\) | −68.4196 | −3.53790 | ||||||||
\(375\) | −10.4863 | −0.541512 | ||||||||
\(376\) | −35.7295 | −1.84261 | ||||||||
\(377\) | −3.05898 | −0.157546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.61370 | −0.134257 | −0.0671283 | − | 0.997744i | \(-0.521384\pi\) | ||||
−0.0671283 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(380\) | 27.1575 | 1.39315 | ||||||||
\(381\) | −4.19807 | −0.215074 | ||||||||
\(382\) | −32.5172 | −1.66372 | ||||||||
\(383\) | 11.3203 | 0.578438 | 0.289219 | − | 0.957263i | \(-0.406604\pi\) | ||||
0.289219 | + | 0.957263i | \(0.406604\pi\) | |||||||
\(384\) | −17.7010 | −0.903300 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.75491 | 0.242018 | ||||||||
\(387\) | −0.231369 | −0.0117611 | ||||||||
\(388\) | −56.0441 | −2.84521 | ||||||||
\(389\) | −30.9710 | −1.57029 | −0.785147 | − | 0.619310i | \(-0.787412\pi\) | ||||
−0.785147 | + | 0.619310i | \(0.787412\pi\) | |||||||
\(390\) | −2.56556 | −0.129912 | ||||||||
\(391\) | −4.90873 | −0.248245 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.83542 | −0.193471 | ||||||||
\(394\) | 24.7665 | 1.24772 | ||||||||
\(395\) | −0.275009 | −0.0138372 | ||||||||
\(396\) | 19.4567 | 0.977736 | ||||||||
\(397\) | −25.0396 | −1.25670 | −0.628350 | − | 0.777931i | \(-0.716269\pi\) | ||||
−0.628350 | + | 0.777931i | \(0.716269\pi\) | |||||||
\(398\) | −7.82728 | −0.392346 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.922571 | 0.0461285 | ||||||||
\(401\) | 34.9745 | 1.74654 | 0.873272 | − | 0.487234i | \(-0.161994\pi\) | ||||
0.873272 | + | 0.487234i | \(0.161994\pi\) | |||||||
\(402\) | −10.2241 | −0.509931 | ||||||||
\(403\) | 4.95017 | 0.246585 | ||||||||
\(404\) | 25.8211 | 1.28465 | ||||||||
\(405\) | 1.23869 | 0.0615512 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.1093 | 1.98815 | ||||||||
\(408\) | −13.1299 | −0.650028 | ||||||||
\(409\) | 24.1704 | 1.19515 | 0.597576 | − | 0.801812i | \(-0.296131\pi\) | ||||
0.597576 | + | 0.801812i | \(0.296131\pi\) | |||||||
\(410\) | 7.10735 | 0.351007 | ||||||||
\(411\) | 7.25647 | 0.357935 | ||||||||
\(412\) | 45.3478 | 2.23413 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.27502 | 0.111811 | ||||||||
\(415\) | −19.2241 | −0.943675 | ||||||||
\(416\) | 5.42165 | 0.265818 | ||||||||
\(417\) | −3.52170 | −0.172458 | ||||||||
\(418\) | 96.2263 | 4.70658 | ||||||||
\(419\) | 19.9385 | 0.974059 | 0.487029 | − | 0.873386i | \(-0.338080\pi\) | ||||
0.487029 | + | 0.873386i | \(0.338080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.1003 | −1.75942 | −0.879711 | − | 0.475508i | \(-0.842264\pi\) | ||||
−0.879711 | + | 0.475508i | \(0.842264\pi\) | |||||||
\(422\) | 26.5471 | 1.29229 | ||||||||
\(423\) | −13.3578 | −0.649478 | ||||||||
\(424\) | 11.3059 | 0.549063 | ||||||||
\(425\) | 17.0119 | 0.825197 | ||||||||
\(426\) | 36.0761 | 1.74789 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.8253 | −1.00663 | ||||||||
\(429\) | −5.57774 | −0.269296 | ||||||||
\(430\) | −0.652010 | −0.0314427 | ||||||||
\(431\) | 10.8677 | 0.523479 | 0.261739 | − | 0.965139i | \(-0.415704\pi\) | ||||
0.261739 | + | 0.965139i | \(0.415704\pi\) | |||||||
\(432\) | −0.266205 | −0.0128078 | ||||||||
\(433\) | 26.1898 | 1.25860 | 0.629301 | − | 0.777161i | \(-0.283341\pi\) | ||||
0.629301 | + | 0.777161i | \(0.283341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.16206 | 0.199556 | ||||||||
\(436\) | 57.9121 | 2.77349 | ||||||||
\(437\) | 6.90370 | 0.330249 | ||||||||
\(438\) | 9.73201 | 0.465013 | ||||||||
\(439\) | 31.4062 | 1.49894 | 0.749468 | − | 0.662041i | \(-0.230310\pi\) | ||||
0.749468 | + | 0.662041i | \(0.230310\pi\) | |||||||
\(440\) | 20.2994 | 0.967735 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.1669 | 0.483589 | ||||||||
\(443\) | −9.07886 | −0.431350 | −0.215675 | − | 0.976465i | \(-0.569195\pi\) | ||||
−0.215675 | + | 0.976465i | \(0.569195\pi\) | |||||||
\(444\) | 20.7904 | 0.986668 | ||||||||
\(445\) | −0.692880 | −0.0328457 | ||||||||
\(446\) | −5.64587 | −0.267340 | ||||||||
\(447\) | −10.9243 | −0.516700 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.9369 | 1.12965 | 0.564825 | − | 0.825211i | \(-0.308944\pi\) | ||||
0.564825 | + | 0.825211i | \(0.308944\pi\) | |||||||
\(450\) | −7.88440 | −0.371674 | ||||||||
\(451\) | 15.4520 | 0.727604 | ||||||||
\(452\) | −59.0510 | −2.77752 | ||||||||
\(453\) | −15.8535 | −0.744864 | ||||||||
\(454\) | 50.1631 | 2.35427 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.4661 | 0.864754 | ||||||||
\(457\) | −4.81036 | −0.225019 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(458\) | −33.5490 | −1.56764 | ||||||||
\(459\) | −4.90873 | −0.229120 | ||||||||
\(460\) | 3.93376 | 0.183412 | ||||||||
\(461\) | −23.4694 | −1.09308 | −0.546540 | − | 0.837433i | \(-0.684055\pi\) | ||||
−0.546540 | + | 0.837433i | \(0.684055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4343 | 1.08908 | 0.544542 | − | 0.838733i | \(-0.316703\pi\) | ||||
0.544542 | + | 0.838733i | \(0.316703\pi\) | |||||||
\(464\) | −0.894460 | −0.0415243 | ||||||||
\(465\) | −6.73521 | −0.312338 | ||||||||
\(466\) | −7.77182 | −0.360022 | ||||||||
\(467\) | −13.4506 | −0.622417 | −0.311209 | − | 0.950342i | \(-0.600734\pi\) | ||||
−0.311209 | + | 0.950342i | \(0.600734\pi\) | |||||||
\(468\) | −2.89118 | −0.133645 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −37.6430 | −1.73634 | ||||||||
\(471\) | 9.19996 | 0.423912 | ||||||||
\(472\) | 2.01734 | 0.0928557 | ||||||||
\(473\) | −1.41752 | −0.0651778 | ||||||||
\(474\) | −0.505090 | −0.0231996 | ||||||||
\(475\) | −23.9257 | −1.09779 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.22681 | 0.193532 | ||||||||
\(478\) | −24.7411 | −1.13163 | ||||||||
\(479\) | −6.76164 | −0.308947 | −0.154474 | − | 0.987997i | \(-0.549368\pi\) | ||||
−0.154474 | + | 0.987997i | \(0.549368\pi\) | |||||||
\(480\) | −7.37672 | −0.336700 | ||||||||
\(481\) | −5.96007 | −0.271756 | ||||||||
\(482\) | 48.6774 | 2.21720 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 84.2722 | 3.83055 | ||||||||
\(485\) | −21.8600 | −0.992612 | ||||||||
\(486\) | 2.27502 | 0.103197 | ||||||||
\(487\) | 19.8666 | 0.900241 | 0.450121 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450121 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(488\) | −9.56684 | −0.433071 | ||||||||
\(489\) | −1.64877 | −0.0745601 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.20340 | 0.189697 | 0.0948483 | − | 0.995492i | \(-0.469763\pi\) | ||||
0.0948483 | + | 0.995492i | \(0.469763\pi\) | |||||||
\(492\) | 8.00942 | 0.361093 | ||||||||
\(493\) | −16.4935 | −0.742831 | ||||||||
\(494\) | −14.2988 | −0.643334 | ||||||||
\(495\) | 7.58909 | 0.341104 | ||||||||
\(496\) | 1.44745 | 0.0649925 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −35.3076 | −1.58217 | ||||||||
\(499\) | 6.94840 | 0.311053 | 0.155527 | − | 0.987832i | \(-0.450293\pi\) | ||||
0.155527 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(500\) | −33.3017 | −1.48930 | ||||||||
\(501\) | −5.46655 | −0.244228 | ||||||||
\(502\) | −10.6598 | −0.475772 | ||||||||
\(503\) | −5.90346 | −0.263222 | −0.131611 | − | 0.991301i | \(-0.542015\pi\) | ||||
−0.131611 | + | 0.991301i | \(0.542015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0715 | 0.448176 | ||||||||
\(506\) | 13.9384 | 0.619636 | ||||||||
\(507\) | −12.1712 | −0.540541 | ||||||||
\(508\) | −13.3319 | −0.591508 | ||||||||
\(509\) | 26.6647 | 1.18189 | 0.590947 | − | 0.806711i | \(-0.298754\pi\) | ||||
0.590947 | + | 0.806711i | \(0.298754\pi\) | |||||||
\(510\) | −13.8331 | −0.612539 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.00941 | 0.132998 | ||||||||
\(513\) | 6.90370 | 0.304806 | ||||||||
\(514\) | 61.4652 | 2.71111 | ||||||||
\(515\) | 17.6879 | 0.779423 | ||||||||
\(516\) | −0.734764 | −0.0323462 | ||||||||
\(517\) | −81.8390 | −3.59928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.509172 | 0.0223502 | ||||||||
\(520\) | −3.01640 | −0.132278 | ||||||||
\(521\) | −5.31311 | −0.232771 | −0.116386 | − | 0.993204i | \(-0.537131\pi\) | ||||
−0.116386 | + | 0.993204i | \(0.537131\pi\) | |||||||
\(522\) | 7.64417 | 0.334576 | ||||||||
\(523\) | −17.0386 | −0.745047 | −0.372524 | − | 0.928023i | \(-0.621507\pi\) | ||||
−0.372524 | + | 0.928023i | \(0.621507\pi\) | |||||||
\(524\) | −12.1802 | −0.532096 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.5149 | −1.98454 | ||||||||
\(527\) | 26.6905 | 1.16266 | ||||||||
\(528\) | −1.63096 | −0.0709783 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 11.9114 | 0.517398 | ||||||||
\(531\) | 0.754201 | 0.0327295 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.29610 | −0.0994550 | ||||||||
\(534\) | −1.27256 | −0.0550692 | ||||||||
\(535\) | −8.12290 | −0.351184 | ||||||||
\(536\) | −12.0207 | −0.519217 | ||||||||
\(537\) | 8.35087 | 0.360367 | ||||||||
\(538\) | 14.2888 | 0.616033 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.93376 | 0.169282 | ||||||||
\(541\) | 38.7960 | 1.66797 | 0.833986 | − | 0.551786i | \(-0.186053\pi\) | ||||
0.833986 | + | 0.551786i | \(0.186053\pi\) | |||||||
\(542\) | −57.8317 | −2.48408 | ||||||||
\(543\) | 2.42861 | 0.104221 | ||||||||
\(544\) | 29.2327 | 1.25334 | ||||||||
\(545\) | 22.5886 | 0.967590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.7356 | 1.27140 | 0.635701 | − | 0.771935i | \(-0.280711\pi\) | ||||
0.635701 | + | 0.771935i | \(0.280711\pi\) | |||||||
\(548\) | 23.0446 | 0.984415 | ||||||||
\(549\) | −3.57664 | −0.152647 | ||||||||
\(550\) | −48.3053 | −2.05975 | ||||||||
\(551\) | 23.1967 | 0.988214 | ||||||||
\(552\) | 2.67481 | 0.113847 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −34.4463 | −1.46348 | ||||||||
\(555\) | 8.10930 | 0.344221 | ||||||||
\(556\) | −11.1840 | −0.474306 | ||||||||
\(557\) | −33.5645 | −1.42217 | −0.711086 | − | 0.703105i | \(-0.751796\pi\) | ||||
−0.711086 | + | 0.703105i | \(0.751796\pi\) | |||||||
\(558\) | −12.3701 | −0.523668 | ||||||||
\(559\) | 0.210638 | 0.00890904 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.0743 | −1.26974 | ||||||||
\(562\) | −62.1421 | −2.62130 | ||||||||
\(563\) | 30.5532 | 1.28766 | 0.643831 | − | 0.765167i | \(-0.277344\pi\) | ||||
0.643831 | + | 0.765167i | \(0.277344\pi\) | |||||||
\(564\) | −42.4207 | −1.78623 | ||||||||
\(565\) | −23.0328 | −0.968999 | ||||||||
\(566\) | −19.4346 | −0.816898 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.4157 | 1.77972 | ||||||||
\(569\) | 42.1160 | 1.76559 | 0.882797 | − | 0.469754i | \(-0.155657\pi\) | ||||
0.882797 | + | 0.469754i | \(0.155657\pi\) | |||||||
\(570\) | 19.4550 | 0.814881 | ||||||||
\(571\) | 6.51703 | 0.272729 | 0.136365 | − | 0.990659i | \(-0.456458\pi\) | ||||
0.136365 | + | 0.990659i | \(0.456458\pi\) | |||||||
\(572\) | −17.7134 | −0.740634 | ||||||||
\(573\) | −14.2931 | −0.597104 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.46564 | −0.144527 | ||||||||
\(576\) | −13.0159 | −0.542329 | ||||||||
\(577\) | −41.5356 | −1.72915 | −0.864575 | − | 0.502503i | \(-0.832412\pi\) | ||||
−0.864575 | + | 0.502503i | \(0.832412\pi\) | |||||||
\(578\) | 16.1427 | 0.671448 | ||||||||
\(579\) | 2.09005 | 0.0868594 | ||||||||
\(580\) | 13.2176 | 0.548830 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −40.1488 | −1.66422 | ||||||||
\(583\) | 25.8963 | 1.07252 | ||||||||
\(584\) | 11.4422 | 0.473482 | ||||||||
\(585\) | −1.12771 | −0.0466249 | ||||||||
\(586\) | −30.9751 | −1.27957 | ||||||||
\(587\) | −12.6109 | −0.520506 | −0.260253 | − | 0.965540i | \(-0.583806\pi\) | ||||
−0.260253 | + | 0.965540i | \(0.583806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.5379 | −1.54672 | ||||||||
\(590\) | 2.12538 | 0.0875005 | ||||||||
\(591\) | 10.8863 | 0.447801 | ||||||||
\(592\) | −1.74275 | −0.0716267 | ||||||||
\(593\) | −10.3859 | −0.426498 | −0.213249 | − | 0.976998i | \(-0.568404\pi\) | ||||
−0.213249 | + | 0.976998i | \(0.568404\pi\) | |||||||
\(594\) | 13.9384 | 0.571898 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.6925 | −1.42106 | ||||||||
\(597\) | −3.44053 | −0.140812 | ||||||||
\(598\) | −2.07118 | −0.0846969 | ||||||||
\(599\) | 28.0358 | 1.14551 | 0.572757 | − | 0.819725i | \(-0.305874\pi\) | ||||
0.572757 | + | 0.819725i | \(0.305874\pi\) | |||||||
\(600\) | −9.26992 | −0.378443 | ||||||||
\(601\) | −3.81190 | −0.155491 | −0.0777454 | − | 0.996973i | \(-0.524772\pi\) | ||||
−0.0777454 | + | 0.996973i | \(0.524772\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.49406 | −0.183012 | ||||||||
\(604\) | −50.3465 | −2.04857 | ||||||||
\(605\) | 32.8704 | 1.33637 | ||||||||
\(606\) | 18.4976 | 0.751416 | ||||||||
\(607\) | −0.159930 | −0.00649136 | −0.00324568 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324568 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(608\) | −41.1132 | −1.66736 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0792 | −0.408094 | ||||||||
\(611\) | 12.1609 | 0.491979 | ||||||||
\(612\) | −15.5888 | −0.630140 | ||||||||
\(613\) | −16.5339 | −0.667797 | −0.333899 | − | 0.942609i | \(-0.608364\pi\) | ||||
−0.333899 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(614\) | 4.42477 | 0.178569 | ||||||||
\(615\) | 3.12408 | 0.125975 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.8727 | 1.44418 | 0.722091 | − | 0.691798i | \(-0.243181\pi\) | ||||
0.722091 | + | 0.691798i | \(0.243181\pi\) | |||||||
\(618\) | 32.4862 | 1.30679 | ||||||||
\(619\) | 36.6950 | 1.47490 | 0.737448 | − | 0.675404i | \(-0.236031\pi\) | ||||
0.737448 | + | 0.675404i | \(0.236031\pi\) | |||||||
\(620\) | −21.3892 | −0.859011 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 32.3098 | 1.29550 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.242353 | 0.00970189 | ||||||||
\(625\) | 4.33883 | 0.173553 | ||||||||
\(626\) | 9.56548 | 0.382314 | ||||||||
\(627\) | 42.2968 | 1.68917 | ||||||||
\(628\) | 29.2166 | 1.16587 | ||||||||
\(629\) | −32.1358 | −1.28134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3865 | 0.493098 | 0.246549 | − | 0.969130i | \(-0.420703\pi\) | ||||
0.246549 | + | 0.969130i | \(0.420703\pi\) | |||||||
\(632\) | −0.593849 | −0.0236220 | ||||||||
\(633\) | 11.6690 | 0.463799 | ||||||||
\(634\) | 1.67995 | 0.0667194 | ||||||||
\(635\) | −5.20012 | −0.206360 | ||||||||
\(636\) | 13.4232 | 0.532264 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 46.8335 | 1.85415 | ||||||||
\(639\) | 15.8575 | 0.627312 | ||||||||
\(640\) | −21.9261 | −0.866705 | ||||||||
\(641\) | 27.0383 | 1.06795 | 0.533974 | − | 0.845501i | \(-0.320698\pi\) | ||||
0.533974 | + | 0.845501i | \(0.320698\pi\) | |||||||
\(642\) | −14.9188 | −0.588797 | ||||||||
\(643\) | 27.4371 | 1.08201 | 0.541006 | − | 0.841019i | \(-0.318044\pi\) | ||||
0.541006 | + | 0.841019i | \(0.318044\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.286595 | −0.0112847 | ||||||||
\(646\) | −77.0969 | −3.03334 | ||||||||
\(647\) | −0.875536 | −0.0344209 | −0.0172104 | − | 0.999852i | \(-0.505479\pi\) | ||||
−0.0172104 | + | 0.999852i | \(0.505479\pi\) | |||||||
\(648\) | 2.67481 | 0.105076 | ||||||||
\(649\) | 4.62075 | 0.181380 | ||||||||
\(650\) | 7.17796 | 0.281543 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.23606 | −0.205060 | ||||||||
\(653\) | −15.5487 | −0.608466 | −0.304233 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304233 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(654\) | 41.4869 | 1.62227 | ||||||||
\(655\) | −4.75091 | −0.185633 | ||||||||
\(656\) | −0.671389 | −0.0262133 | ||||||||
\(657\) | 4.27776 | 0.166891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.1989 | 0.825794 | 0.412897 | − | 0.910778i | \(-0.364517\pi\) | ||||
0.412897 | + | 0.910778i | \(0.364517\pi\) | |||||||
\(660\) | 24.1009 | 0.938126 | ||||||||
\(661\) | 8.65093 | 0.336482 | 0.168241 | − | 0.985746i | \(-0.446191\pi\) | ||||
0.168241 | + | 0.985746i | \(0.446191\pi\) | |||||||
\(662\) | −46.8629 | −1.82138 | ||||||||
\(663\) | 4.46891 | 0.173558 | ||||||||
\(664\) | −41.5122 | −1.61099 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.8938 | 0.577122 | ||||||||
\(667\) | 3.36004 | 0.130101 | ||||||||
\(668\) | −17.3603 | −0.671690 | ||||||||
\(669\) | −2.48168 | −0.0959471 | ||||||||
\(670\) | −12.6645 | −0.489273 | ||||||||
\(671\) | −21.9130 | −0.845942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.05137 | −0.348905 | −0.174452 | − | 0.984666i | \(-0.555816\pi\) | ||||
−0.174452 | + | 0.984666i | \(0.555816\pi\) | |||||||
\(674\) | −63.4805 | −2.44518 | ||||||||
\(675\) | −3.46564 | −0.133392 | ||||||||
\(676\) | −38.6523 | −1.48663 | ||||||||
\(677\) | 16.8996 | 0.649503 | 0.324751 | − | 0.945799i | \(-0.394719\pi\) | ||||
0.324751 | + | 0.945799i | \(0.394719\pi\) | |||||||
\(678\) | −42.3028 | −1.62463 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.2639 | −0.623694 | ||||||||
\(681\) | 22.0495 | 0.844938 | ||||||||
\(682\) | −75.7878 | −2.90206 | ||||||||
\(683\) | 22.7419 | 0.870194 | 0.435097 | − | 0.900384i | \(-0.356714\pi\) | ||||
0.435097 | + | 0.900384i | \(0.356714\pi\) | |||||||
\(684\) | 21.9243 | 0.838296 | ||||||||
\(685\) | 8.98854 | 0.343434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7467 | −0.562621 | ||||||||
\(688\) | 0.0615915 | 0.00234815 | ||||||||
\(689\) | −3.84809 | −0.146600 | ||||||||
\(690\) | 2.81806 | 0.107282 | ||||||||
\(691\) | −35.1619 | −1.33762 | −0.668810 | − | 0.743433i | \(-0.733196\pi\) | ||||
−0.668810 | + | 0.743433i | \(0.733196\pi\) | |||||||
\(692\) | 1.61699 | 0.0614689 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.74418 | −0.180086 | ||||||||
\(695\) | −4.36231 | −0.165472 | ||||||||
\(696\) | 8.98747 | 0.340669 | ||||||||
\(697\) | −12.3802 | −0.468933 | ||||||||
\(698\) | 9.19842 | 0.348165 | ||||||||
\(699\) | −3.41615 | −0.129211 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.0402 | −1.32345 | −0.661725 | − | 0.749746i | \(-0.730175\pi\) | ||||
−0.661725 | + | 0.749746i | \(0.730175\pi\) | |||||||
\(702\) | −2.07118 | −0.0781717 | ||||||||
\(703\) | 45.1961 | 1.70460 | ||||||||
\(704\) | −79.7444 | −3.00548 | ||||||||
\(705\) | −16.5462 | −0.623166 | ||||||||
\(706\) | 10.2556 | 0.385976 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.39514 | 0.0900147 | ||||||||
\(709\) | −49.6644 | −1.86519 | −0.932593 | − | 0.360930i | \(-0.882459\pi\) | ||||
−0.932593 | + | 0.360930i | \(0.882459\pi\) | |||||||
\(710\) | 44.6873 | 1.67708 | ||||||||
\(711\) | −0.222015 | −0.00832623 | ||||||||
\(712\) | −1.49619 | −0.0560721 | ||||||||
\(713\) | −5.43735 | −0.203630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.90911 | −0.258386 | ||||||||
\(716\) | 26.5201 | 0.991103 | ||||||||
\(717\) | −10.8751 | −0.406139 | ||||||||
\(718\) | −47.3518 | −1.76715 | ||||||||
\(719\) | −3.54087 | −0.132052 | −0.0660261 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660261 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(720\) | −0.329747 | −0.0122889 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 65.2046 | 2.42667 | ||||||||
\(723\) | 21.3965 | 0.795743 | ||||||||
\(724\) | 7.71259 | 0.286636 | ||||||||
\(725\) | −11.6447 | −0.432473 | ||||||||
\(726\) | 60.3708 | 2.24057 | ||||||||
\(727\) | −7.64097 | −0.283388 | −0.141694 | − | 0.989911i | \(-0.545255\pi\) | ||||
−0.141694 | + | 0.989911i | \(0.545255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.0550 | 0.446175 | ||||||||
\(731\) | 1.13573 | 0.0420063 | ||||||||
\(732\) | −11.3585 | −0.419820 | ||||||||
\(733\) | −20.1456 | −0.744094 | −0.372047 | − | 0.928214i | \(-0.621344\pi\) | ||||
−0.372047 | + | 0.928214i | \(0.621344\pi\) | |||||||
\(734\) | −19.5019 | −0.719829 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.95524 | −0.219513 | ||||||||
\(737\) | −27.5337 | −1.01422 | ||||||||
\(738\) | 5.73777 | 0.211210 | ||||||||
\(739\) | 38.9079 | 1.43125 | 0.715626 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715626 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(740\) | 25.7529 | 0.946697 | ||||||||
\(741\) | −6.28513 | −0.230890 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.5828 | −0.461617 | −0.230809 | − | 0.972999i | \(-0.574137\pi\) | ||||
−0.230809 | + | 0.972999i | \(0.574137\pi\) | |||||||
\(744\) | −14.5439 | −0.533205 | ||||||||
\(745\) | −13.5318 | −0.495768 | ||||||||
\(746\) | −3.31032 | −0.121199 | ||||||||
\(747\) | −15.5197 | −0.567835 | ||||||||
\(748\) | −95.5077 | −3.49211 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −23.8566 | −0.871122 | ||||||||
\(751\) | −23.2255 | −0.847511 | −0.423756 | − | 0.905777i | \(-0.639288\pi\) | ||||
−0.423756 | + | 0.905777i | \(0.639288\pi\) | |||||||
\(752\) | 3.55591 | 0.129671 | ||||||||
\(753\) | −4.68560 | −0.170753 | ||||||||
\(754\) | −6.95925 | −0.253441 | ||||||||
\(755\) | −19.6377 | −0.714688 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.3210 | −1.13838 | −0.569191 | − | 0.822205i | \(-0.692744\pi\) | ||||
−0.569191 | + | 0.822205i | \(0.692744\pi\) | |||||||
\(758\) | −5.94622 | −0.215976 | ||||||||
\(759\) | 6.12669 | 0.222385 | ||||||||
\(760\) | 22.8738 | 0.829721 | ||||||||
\(761\) | 25.8770 | 0.938040 | 0.469020 | − | 0.883188i | \(-0.344607\pi\) | ||||
0.469020 | + | 0.883188i | \(0.344607\pi\) | |||||||
\(762\) | −9.55070 | −0.345985 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −45.3911 | −1.64219 | ||||||||
\(765\) | −6.08041 | −0.219838 | ||||||||
\(766\) | 25.7538 | 0.930524 | ||||||||
\(767\) | −0.686624 | −0.0247926 | ||||||||
\(768\) | −14.2383 | −0.513782 | ||||||||
\(769\) | −2.66864 | −0.0962338 | −0.0481169 | − | 0.998842i | \(-0.515322\pi\) | ||||
−0.0481169 | + | 0.998842i | \(0.515322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.0174 | 0.973008 | ||||||||
\(772\) | 6.63742 | 0.238886 | ||||||||
\(773\) | 5.78286 | 0.207995 | 0.103998 | − | 0.994578i | \(-0.466837\pi\) | ||||
0.103998 | + | 0.994578i | \(0.466837\pi\) | |||||||
\(774\) | −0.526369 | −0.0189199 | ||||||||
\(775\) | 18.8439 | 0.676893 | ||||||||
\(776\) | −47.2041 | −1.69453 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −70.4598 | −2.52611 | ||||||||
\(779\) | 17.4116 | 0.623837 | ||||||||
\(780\) | −3.58129 | −0.128231 | ||||||||
\(781\) | 97.1539 | 3.47644 | ||||||||
\(782\) | −11.1675 | −0.399348 | ||||||||
\(783\) | 3.36004 | 0.120078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.3959 | 0.406738 | ||||||||
\(786\) | −8.72566 | −0.311234 | ||||||||
\(787\) | 7.55455 | 0.269291 | 0.134645 | − | 0.990894i | \(-0.457010\pi\) | ||||
0.134645 | + | 0.990894i | \(0.457010\pi\) | |||||||
\(788\) | 34.5718 | 1.23157 | ||||||||
\(789\) | −20.0063 | −0.712244 | ||||||||
\(790\) | −0.625652 | −0.0222597 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.3877 | 0.582313 | ||||||||
\(793\) | 3.25618 | 0.115630 | ||||||||
\(794\) | −56.9656 | −2.02163 | ||||||||
\(795\) | 5.23572 | 0.185692 | ||||||||
\(796\) | −10.9262 | −0.387269 | ||||||||
\(797\) | 17.6173 | 0.624035 | 0.312018 | − | 0.950076i | \(-0.398995\pi\) | ||||
0.312018 | + | 0.950076i | \(0.398995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.5698 | 2.31969 | ||||||||
\(800\) | 20.6387 | 0.729689 | ||||||||
\(801\) | −0.559363 | −0.0197641 | ||||||||
\(802\) | 79.5678 | 2.80964 | ||||||||
\(803\) | 26.2085 | 0.924879 | ||||||||
\(804\) | −14.2719 | −0.503331 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.2617 | 0.396678 | ||||||||
\(807\) | 6.28072 | 0.221092 | ||||||||
\(808\) | 21.7482 | 0.765099 | ||||||||
\(809\) | 23.2841 | 0.818624 | 0.409312 | − | 0.912394i | \(-0.365769\pi\) | ||||
0.409312 | + | 0.912394i | \(0.365769\pi\) | |||||||
\(810\) | 2.81806 | 0.0990164 | ||||||||
\(811\) | −35.2946 | −1.23936 | −0.619680 | − | 0.784855i | \(-0.712738\pi\) | ||||
−0.619680 | + | 0.784855i | \(0.712738\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.4203 | −0.891527 | ||||||||
\(814\) | 91.2496 | 3.19830 | ||||||||
\(815\) | −2.04232 | −0.0715395 | ||||||||
\(816\) | 1.30673 | 0.0457447 | ||||||||
\(817\) | −1.59730 | −0.0558824 | ||||||||
\(818\) | 54.9883 | 1.92262 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.92122 | 0.346464 | ||||||||
\(821\) | 1.86839 | 0.0652072 | 0.0326036 | − | 0.999468i | \(-0.489620\pi\) | ||||
0.0326036 | + | 0.999468i | \(0.489620\pi\) | |||||||
\(822\) | 16.5086 | 0.575804 | ||||||||
\(823\) | −19.4504 | −0.677997 | −0.338999 | − | 0.940787i | \(-0.610088\pi\) | ||||
−0.338999 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(824\) | 38.1949 | 1.33058 | ||||||||
\(825\) | −21.2329 | −0.739234 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1883 | 0.389055 | 0.194527 | − | 0.980897i | \(-0.437683\pi\) | ||||
0.194527 | + | 0.980897i | \(0.437683\pi\) | |||||||
\(828\) | 3.17573 | 0.110364 | ||||||||
\(829\) | −0.598968 | −0.0208030 | −0.0104015 | − | 0.999946i | \(-0.503311\pi\) | ||||
−0.0104015 | + | 0.999946i | \(0.503311\pi\) | |||||||
\(830\) | −43.7353 | −1.51808 | ||||||||
\(831\) | −15.1411 | −0.525238 | ||||||||
\(832\) | 11.8497 | 0.410814 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.01195 | −0.277431 | ||||||||
\(835\) | −6.77139 | −0.234333 | ||||||||
\(836\) | 134.323 | 4.64567 | ||||||||
\(837\) | −5.43735 | −0.187942 | ||||||||
\(838\) | 45.3605 | 1.56695 | ||||||||
\(839\) | 43.0684 | 1.48689 | 0.743443 | − | 0.668799i | \(-0.233191\pi\) | ||||
0.743443 | + | 0.668799i | \(0.233191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.7101 | −0.610694 | ||||||||
\(842\) | −82.1291 | −2.83036 | ||||||||
\(843\) | −27.3149 | −0.940776 | ||||||||
\(844\) | 37.0574 | 1.27557 | ||||||||
\(845\) | −15.0764 | −0.518642 | ||||||||
\(846\) | −30.3893 | −1.04480 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.12520 | −0.0386395 | ||||||||
\(849\) | −8.54261 | −0.293182 | ||||||||
\(850\) | 38.7024 | 1.32748 | ||||||||
\(851\) | 6.54665 | 0.224416 | ||||||||
\(852\) | 50.3590 | 1.72527 | ||||||||
\(853\) | −32.0125 | −1.09609 | −0.548043 | − | 0.836450i | \(-0.684627\pi\) | ||||
−0.548043 | + | 0.836450i | \(0.684627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.55157 | 0.292458 | ||||||||
\(856\) | −17.5404 | −0.599520 | ||||||||
\(857\) | 45.7684 | 1.56342 | 0.781710 | − | 0.623642i | \(-0.214348\pi\) | ||||
0.781710 | + | 0.623642i | \(0.214348\pi\) | |||||||
\(858\) | −12.6895 | −0.433212 | ||||||||
\(859\) | 43.2491 | 1.47564 | 0.737820 | − | 0.674998i | \(-0.235855\pi\) | ||||
0.737820 | + | 0.674998i | \(0.235855\pi\) | |||||||
\(860\) | −0.910147 | −0.0310358 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.7243 | 0.842112 | ||||||||
\(863\) | −36.0384 | −1.22676 | −0.613380 | − | 0.789788i | \(-0.710191\pi\) | ||||
−0.613380 | + | 0.789788i | \(0.710191\pi\) | |||||||
\(864\) | −5.95524 | −0.202601 | ||||||||
\(865\) | 0.630709 | 0.0214447 | ||||||||
\(866\) | 59.5825 | 2.02469 | ||||||||
\(867\) | 7.09562 | 0.240980 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.36022 | −0.0461423 | ||||||||
\(870\) | 9.46879 | 0.321022 | ||||||||
\(871\) | 4.09139 | 0.138631 | ||||||||
\(872\) | 48.7774 | 1.65181 | ||||||||
\(873\) | −17.6476 | −0.597282 | ||||||||
\(874\) | 15.7061 | 0.531266 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5850 | 0.458995 | ||||||||
\(877\) | 26.9432 | 0.909806 | 0.454903 | − | 0.890541i | \(-0.349674\pi\) | ||||
0.454903 | + | 0.890541i | \(0.349674\pi\) | |||||||
\(878\) | 71.4498 | 2.41131 | ||||||||
\(879\) | −13.6153 | −0.459232 | ||||||||
\(880\) | −2.02026 | −0.0681028 | ||||||||
\(881\) | 36.5231 | 1.23050 | 0.615248 | − | 0.788334i | \(-0.289056\pi\) | ||||
0.615248 | + | 0.788334i | \(0.289056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.7823 | −1.84357 | −0.921785 | − | 0.387702i | \(-0.873269\pi\) | ||||
−0.921785 | + | 0.387702i | \(0.873269\pi\) | |||||||
\(884\) | 14.1920 | 0.477330 | ||||||||
\(885\) | 0.934224 | 0.0314036 | ||||||||
\(886\) | −20.6546 | −0.693906 | ||||||||
\(887\) | 13.7438 | 0.461470 | 0.230735 | − | 0.973017i | \(-0.425887\pi\) | ||||
0.230735 | + | 0.973017i | \(0.425887\pi\) | |||||||
\(888\) | 17.5110 | 0.587632 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.57632 | −0.0528383 | ||||||||
\(891\) | 6.12669 | 0.205252 | ||||||||
\(892\) | −7.88113 | −0.263880 | ||||||||
\(893\) | −92.2182 | −3.08596 | ||||||||
\(894\) | −24.8530 | −0.831207 | ||||||||
\(895\) | 10.3442 | 0.345767 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.910400 | −0.0303974 | ||||||||
\(898\) | 54.4569 | 1.81725 | ||||||||
\(899\) | −18.2697 | −0.609330 | ||||||||
\(900\) | −11.0059 | −0.366864 | ||||||||
\(901\) | −20.7483 | −0.691225 | ||||||||
\(902\) | 35.1536 | 1.17049 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.7366 | −1.65422 | ||||||||
\(905\) | 3.00830 | 0.0999992 | ||||||||
\(906\) | −36.0672 | −1.19825 | ||||||||
\(907\) | −21.9841 | −0.729970 | −0.364985 | − | 0.931013i | \(-0.618926\pi\) | ||||
−0.364985 | + | 0.931013i | \(0.618926\pi\) | |||||||
\(908\) | 70.0232 | 2.32380 | ||||||||
\(909\) | 8.13075 | 0.269680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.3602 | −0.575170 | −0.287585 | − | 0.957755i | \(-0.592852\pi\) | ||||
−0.287585 | + | 0.957755i | \(0.592852\pi\) | |||||||
\(912\) | −1.83780 | −0.0608557 | ||||||||
\(913\) | −95.0843 | −3.14683 | ||||||||
\(914\) | −10.9437 | −0.361984 | ||||||||
\(915\) | −4.43037 | −0.146463 | ||||||||
\(916\) | −46.8315 | −1.54735 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.1675 | −0.368581 | ||||||||
\(919\) | 5.14845 | 0.169832 | 0.0849159 | − | 0.996388i | \(-0.472938\pi\) | ||||
0.0849159 | + | 0.996388i | \(0.472938\pi\) | |||||||
\(920\) | 3.31327 | 0.109235 | ||||||||
\(921\) | 1.94494 | 0.0640878 | ||||||||
\(922\) | −53.3935 | −1.75842 | ||||||||
\(923\) | −14.4367 | −0.475188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6883 | −0.745988 | ||||||||
\(926\) | 53.3136 | 1.75199 | ||||||||
\(927\) | 14.2795 | 0.469000 | ||||||||
\(928\) | −20.0099 | −0.656856 | ||||||||
\(929\) | −12.4649 | −0.408961 | −0.204480 | − | 0.978871i | \(-0.565550\pi\) | ||||
−0.204480 | + | 0.978871i | \(0.565550\pi\) | |||||||
\(930\) | −15.3228 | −0.502453 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.8488 | −0.355363 | ||||||||
\(933\) | 14.2020 | 0.464951 | ||||||||
\(934\) | −30.6003 | −1.00127 | ||||||||
\(935\) | −37.2528 | −1.21830 | ||||||||
\(936\) | −2.43515 | −0.0795953 | ||||||||
\(937\) | 1.66532 | 0.0544038 | 0.0272019 | − | 0.999630i | \(-0.491340\pi\) | ||||
0.0272019 | + | 0.999630i | \(0.491340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.20457 | 0.137211 | ||||||||
\(940\) | −52.5463 | −1.71387 | ||||||||
\(941\) | 34.1661 | 1.11378 | 0.556892 | − | 0.830585i | \(-0.311994\pi\) | ||||
0.556892 | + | 0.830585i | \(0.311994\pi\) | |||||||
\(942\) | 20.9301 | 0.681940 | ||||||||
\(943\) | 2.52207 | 0.0821300 | ||||||||
\(944\) | −0.200772 | −0.00653457 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.22490 | −0.104851 | ||||||||
\(947\) | 52.3162 | 1.70005 | 0.850024 | − | 0.526744i | \(-0.176587\pi\) | ||||
0.850024 | + | 0.526744i | \(0.176587\pi\) | |||||||
\(948\) | −0.705061 | −0.0228993 | ||||||||
\(949\) | −3.89448 | −0.126420 | ||||||||
\(950\) | −54.4316 | −1.76599 | ||||||||
\(951\) | 0.738433 | 0.0239453 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.3873 | −1.14631 | −0.573154 | − | 0.819448i | \(-0.694280\pi\) | ||||
−0.573154 | + | 0.819448i | \(0.694280\pi\) | |||||||
\(954\) | 9.61609 | 0.311332 | ||||||||
\(955\) | −17.7048 | −0.572914 | ||||||||
\(956\) | −34.5364 | −1.11699 | ||||||||
\(957\) | 20.5859 | 0.665449 | ||||||||
\(958\) | −15.3829 | −0.496998 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.1227 | −0.520358 | ||||||||
\(961\) | −1.43520 | −0.0462967 | ||||||||
\(962\) | −13.5593 | −0.437170 | ||||||||
\(963\) | −6.55764 | −0.211317 | ||||||||
\(964\) | 67.9494 | 2.18850 | ||||||||
\(965\) | 2.58893 | 0.0833406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.97543 | −0.0635254 | −0.0317627 | − | 0.999495i | \(-0.510112\pi\) | ||||
−0.0317627 | + | 0.999495i | \(0.510112\pi\) | |||||||
\(968\) | 70.9796 | 2.28137 | ||||||||
\(969\) | −33.8884 | −1.08865 | ||||||||
\(970\) | −49.7320 | −1.59680 | ||||||||
\(971\) | 28.7536 | 0.922746 | 0.461373 | − | 0.887206i | \(-0.347357\pi\) | ||||
0.461373 | + | 0.887206i | \(0.347357\pi\) | |||||||
\(972\) | 3.17573 | 0.101862 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 45.1969 | 1.44820 | ||||||||
\(975\) | 3.15512 | 0.101045 | ||||||||
\(976\) | 0.952121 | 0.0304767 | ||||||||
\(977\) | −10.7374 | −0.343520 | −0.171760 | − | 0.985139i | \(-0.554945\pi\) | ||||
−0.171760 | + | 0.985139i | \(0.554945\pi\) | |||||||
\(978\) | −3.75100 | −0.119944 | ||||||||
\(979\) | −3.42705 | −0.109529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2358 | 0.582226 | ||||||||
\(982\) | 9.56282 | 0.305162 | ||||||||
\(983\) | 46.2766 | 1.47599 | 0.737997 | − | 0.674804i | \(-0.235772\pi\) | ||||
0.737997 | + | 0.674804i | \(0.235772\pi\) | |||||||
\(984\) | 6.74607 | 0.215057 | ||||||||
\(985\) | 13.4848 | 0.429660 | ||||||||
\(986\) | −37.5232 | −1.19498 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.9599 | −0.635008 | ||||||||
\(989\) | −0.231369 | −0.00735709 | ||||||||
\(990\) | 17.2654 | 0.548729 | ||||||||
\(991\) | −42.9752 | −1.36515 | −0.682576 | − | 0.730814i | \(-0.739141\pi\) | ||||
−0.682576 | + | 0.730814i | \(0.739141\pi\) | |||||||
\(992\) | 32.3807 | 1.02809 | ||||||||
\(993\) | −20.5989 | −0.653686 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.26176 | −0.135107 | ||||||||
\(996\) | −49.2863 | −1.56170 | ||||||||
\(997\) | 12.0816 | 0.382628 | 0.191314 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191314 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(998\) | 15.8078 | 0.500386 | ||||||||
\(999\) | 6.54665 | 0.207127 |
(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 | 3381.2.a.bj.1.8 | 10 | ||
7.3 | odd | 6 | 483.2.i.h.415.3 | yes | 20 | ||
7.5 | odd | 6 | 483.2.i.h.277.3 | ✓ | 20 | ||
7.6 | odd | 2 | 3381.2.a.bi.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.3 | ✓ | 20 | 7.5 | odd | 6 | ||
483.2.i.h.415.3 | yes | 20 | 7.3 | odd | 6 | ||
3381.2.a.bi.1.8 | 10 | 7.6 | odd | 2 | |||
3381.2.a.bj.1.8 | 10 | 1.1 | even | 1 | trivial |