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 | 1.7 | ||
Root | \(1.19920\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19920 | 0.847964 | 0.423982 | − | 0.905671i | \(-0.360632\pi\) | ||||
0.423982 | + | 0.905671i | \(0.360632\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.561916 | −0.280958 | ||||||||
\(5\) | −0.572653 | −0.256098 | −0.128049 | − | 0.991768i | \(-0.540872\pi\) | ||||
−0.128049 | + | 0.991768i | \(0.540872\pi\) | |||||||
\(6\) | −1.19920 | −0.489572 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.07225 | −1.08621 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.686727 | −0.217162 | ||||||||
\(11\) | 2.52510 | 0.761347 | 0.380674 | − | 0.924709i | \(-0.375692\pi\) | ||||
0.380674 | + | 0.924709i | \(0.375692\pi\) | |||||||
\(12\) | 0.561916 | 0.162211 | ||||||||
\(13\) | −5.05314 | −1.40149 | −0.700744 | − | 0.713413i | \(-0.747149\pi\) | ||||
−0.700744 | + | 0.713413i | \(0.747149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.572653 | 0.147858 | ||||||||
\(16\) | −2.56042 | −0.640105 | ||||||||
\(17\) | −2.25223 | −0.546247 | −0.273123 | − | 0.961979i | \(-0.588057\pi\) | ||||
−0.273123 | + | 0.961979i | \(0.588057\pi\) | |||||||
\(18\) | 1.19920 | 0.282655 | ||||||||
\(19\) | 2.39935 | 0.550448 | 0.275224 | − | 0.961380i | \(-0.411248\pi\) | ||||
0.275224 | + | 0.961380i | \(0.411248\pi\) | |||||||
\(20\) | 0.321783 | 0.0719528 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.02811 | 0.645595 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.07225 | 0.627121 | ||||||||
\(25\) | −4.67207 | −0.934414 | ||||||||
\(26\) | −6.05973 | −1.18841 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.796522 | 0.147910 | 0.0739552 | − | 0.997262i | \(-0.476438\pi\) | ||||
0.0739552 | + | 0.997262i | \(0.476438\pi\) | |||||||
\(30\) | 0.686727 | 0.125379 | ||||||||
\(31\) | −3.45731 | −0.620952 | −0.310476 | − | 0.950581i | \(-0.600488\pi\) | ||||
−0.310476 | + | 0.950581i | \(0.600488\pi\) | |||||||
\(32\) | 3.07405 | 0.543420 | ||||||||
\(33\) | −2.52510 | −0.439564 | ||||||||
\(34\) | −2.70088 | −0.463197 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.561916 | −0.0936526 | ||||||||
\(37\) | 8.80485 | 1.44751 | 0.723754 | − | 0.690058i | \(-0.242415\pi\) | ||||
0.723754 | + | 0.690058i | \(0.242415\pi\) | |||||||
\(38\) | 2.87730 | 0.466760 | ||||||||
\(39\) | 5.05314 | 0.809150 | ||||||||
\(40\) | 1.75934 | 0.278175 | ||||||||
\(41\) | 10.9790 | 1.71464 | 0.857319 | − | 0.514785i | \(-0.172128\pi\) | ||||
0.857319 | + | 0.514785i | \(0.172128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90984 | −0.291248 | −0.145624 | − | 0.989340i | \(-0.546519\pi\) | ||||
−0.145624 | + | 0.989340i | \(0.546519\pi\) | |||||||
\(44\) | −1.41890 | −0.213906 | ||||||||
\(45\) | −0.572653 | −0.0853661 | ||||||||
\(46\) | 1.19920 | 0.176813 | ||||||||
\(47\) | −1.93652 | −0.282470 | −0.141235 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141235 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(48\) | 2.56042 | 0.369565 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.60275 | −0.792349 | ||||||||
\(51\) | 2.25223 | 0.315376 | ||||||||
\(52\) | 2.83944 | 0.393759 | ||||||||
\(53\) | 9.57060 | 1.31462 | 0.657312 | − | 0.753619i | \(-0.271693\pi\) | ||||
0.657312 | + | 0.753619i | \(0.271693\pi\) | |||||||
\(54\) | −1.19920 | −0.163191 | ||||||||
\(55\) | −1.44601 | −0.194980 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.39935 | −0.317801 | ||||||||
\(58\) | 0.955190 | 0.125423 | ||||||||
\(59\) | −4.40927 | −0.574038 | −0.287019 | − | 0.957925i | \(-0.592664\pi\) | ||||
−0.287019 | + | 0.957925i | \(0.592664\pi\) | |||||||
\(60\) | −0.321783 | −0.0415420 | ||||||||
\(61\) | 2.12670 | 0.272296 | 0.136148 | − | 0.990689i | \(-0.456528\pi\) | ||||
0.136148 | + | 0.990689i | \(0.456528\pi\) | |||||||
\(62\) | −4.14602 | −0.526545 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.80724 | 1.10091 | ||||||||
\(65\) | 2.89370 | 0.358919 | ||||||||
\(66\) | −3.02811 | −0.372734 | ||||||||
\(67\) | 4.01556 | 0.490579 | 0.245289 | − | 0.969450i | \(-0.421117\pi\) | ||||
0.245289 | + | 0.969450i | \(0.421117\pi\) | |||||||
\(68\) | 1.26557 | 0.153472 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.424132 | 0.0503353 | 0.0251676 | − | 0.999683i | \(-0.491988\pi\) | ||||
0.0251676 | + | 0.999683i | \(0.491988\pi\) | |||||||
\(72\) | −3.07225 | −0.362069 | ||||||||
\(73\) | −14.0009 | −1.63868 | −0.819341 | − | 0.573306i | \(-0.805661\pi\) | ||||
−0.819341 | + | 0.573306i | \(0.805661\pi\) | |||||||
\(74\) | 10.5588 | 1.22743 | ||||||||
\(75\) | 4.67207 | 0.539484 | ||||||||
\(76\) | −1.34823 | −0.154653 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.05973 | 0.686129 | ||||||||
\(79\) | 4.97332 | 0.559542 | 0.279771 | − | 0.960067i | \(-0.409741\pi\) | ||||
0.279771 | + | 0.960067i | \(0.409741\pi\) | |||||||
\(80\) | 1.46623 | 0.163930 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.1661 | 1.45395 | ||||||||
\(83\) | −10.1555 | −1.11471 | −0.557355 | − | 0.830275i | \(-0.688184\pi\) | ||||
−0.557355 | + | 0.830275i | \(0.688184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.28975 | 0.139893 | ||||||||
\(86\) | −2.29028 | −0.246967 | ||||||||
\(87\) | −0.796522 | −0.0853961 | ||||||||
\(88\) | −7.75776 | −0.826980 | ||||||||
\(89\) | 3.82713 | 0.405675 | 0.202838 | − | 0.979212i | \(-0.434984\pi\) | ||||
0.202838 | + | 0.979212i | \(0.434984\pi\) | |||||||
\(90\) | −0.686727 | −0.0723874 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.561916 | −0.0585838 | ||||||||
\(93\) | 3.45731 | 0.358507 | ||||||||
\(94\) | −2.32227 | −0.239524 | ||||||||
\(95\) | −1.37399 | −0.140969 | ||||||||
\(96\) | −3.07405 | −0.313744 | ||||||||
\(97\) | 15.4364 | 1.56733 | 0.783665 | − | 0.621184i | \(-0.213348\pi\) | ||||
0.783665 | + | 0.621184i | \(0.213348\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.52510 | 0.253782 | ||||||||
\(100\) | 2.62531 | 0.262531 | ||||||||
\(101\) | −6.89184 | −0.685763 | −0.342882 | − | 0.939379i | \(-0.611403\pi\) | ||||
−0.342882 | + | 0.939379i | \(0.611403\pi\) | |||||||
\(102\) | 2.70088 | 0.267427 | ||||||||
\(103\) | 10.7593 | 1.06014 | 0.530071 | − | 0.847953i | \(-0.322165\pi\) | ||||
0.530071 | + | 0.847953i | \(0.322165\pi\) | |||||||
\(104\) | 15.5245 | 1.52230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.4771 | 1.11475 | ||||||||
\(107\) | 8.73468 | 0.844414 | 0.422207 | − | 0.906500i | \(-0.361256\pi\) | ||||
0.422207 | + | 0.906500i | \(0.361256\pi\) | |||||||
\(108\) | 0.561916 | 0.0540704 | ||||||||
\(109\) | −2.99347 | −0.286722 | −0.143361 | − | 0.989670i | \(-0.545791\pi\) | ||||
−0.143361 | + | 0.989670i | \(0.545791\pi\) | |||||||
\(110\) | −1.73406 | −0.165336 | ||||||||
\(111\) | −8.80485 | −0.835720 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.3312 | 1.53631 | 0.768156 | − | 0.640263i | \(-0.221175\pi\) | ||||
0.768156 | + | 0.640263i | \(0.221175\pi\) | |||||||
\(114\) | −2.87730 | −0.269484 | ||||||||
\(115\) | −0.572653 | −0.0534002 | ||||||||
\(116\) | −0.447578 | −0.0415566 | ||||||||
\(117\) | −5.05314 | −0.467163 | ||||||||
\(118\) | −5.28761 | −0.486764 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.75934 | −0.160605 | ||||||||
\(121\) | −4.62385 | −0.420350 | ||||||||
\(122\) | 2.55034 | 0.230897 | ||||||||
\(123\) | −10.9790 | −0.989947 | ||||||||
\(124\) | 1.94272 | 0.174461 | ||||||||
\(125\) | 5.53874 | 0.495400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.5959 | 1.65012 | 0.825061 | − | 0.565044i | \(-0.191141\pi\) | ||||
0.825061 | + | 0.565044i | \(0.191141\pi\) | |||||||
\(128\) | 4.41356 | 0.390107 | ||||||||
\(129\) | 1.90984 | 0.168152 | ||||||||
\(130\) | 3.47013 | 0.304350 | ||||||||
\(131\) | 17.9120 | 1.56498 | 0.782490 | − | 0.622663i | \(-0.213949\pi\) | ||||
0.782490 | + | 0.622663i | \(0.213949\pi\) | |||||||
\(132\) | 1.41890 | 0.123499 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.81547 | 0.415993 | ||||||||
\(135\) | 0.572653 | 0.0492862 | ||||||||
\(136\) | 6.91943 | 0.593336 | ||||||||
\(137\) | 16.1522 | 1.37998 | 0.689989 | − | 0.723820i | \(-0.257615\pi\) | ||||
0.689989 | + | 0.723820i | \(0.257615\pi\) | |||||||
\(138\) | −1.19920 | −0.102083 | ||||||||
\(139\) | −1.14087 | −0.0967677 | −0.0483839 | − | 0.998829i | \(-0.515407\pi\) | ||||
−0.0483839 | + | 0.998829i | \(0.515407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.93652 | 0.163084 | ||||||||
\(142\) | 0.508620 | 0.0426825 | ||||||||
\(143\) | −12.7597 | −1.06702 | ||||||||
\(144\) | −2.56042 | −0.213368 | ||||||||
\(145\) | −0.456131 | −0.0378796 | ||||||||
\(146\) | −16.7899 | −1.38954 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.94758 | −0.406689 | ||||||||
\(149\) | 8.02342 | 0.657304 | 0.328652 | − | 0.944451i | \(-0.393406\pi\) | ||||
0.328652 | + | 0.944451i | \(0.393406\pi\) | |||||||
\(150\) | 5.60275 | 0.457463 | ||||||||
\(151\) | 20.2695 | 1.64951 | 0.824753 | − | 0.565494i | \(-0.191314\pi\) | ||||
0.824753 | + | 0.565494i | \(0.191314\pi\) | |||||||
\(152\) | −7.37140 | −0.597899 | ||||||||
\(153\) | −2.25223 | −0.182082 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.97984 | 0.159025 | ||||||||
\(156\) | −2.83944 | −0.227337 | ||||||||
\(157\) | −6.64919 | −0.530663 | −0.265331 | − | 0.964157i | \(-0.585481\pi\) | ||||
−0.265331 | + | 0.964157i | \(0.585481\pi\) | |||||||
\(158\) | 5.96401 | 0.474471 | ||||||||
\(159\) | −9.57060 | −0.758998 | ||||||||
\(160\) | −1.76036 | −0.139169 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.19920 | 0.0942182 | ||||||||
\(163\) | 3.74710 | 0.293496 | 0.146748 | − | 0.989174i | \(-0.453119\pi\) | ||||
0.146748 | + | 0.989174i | \(0.453119\pi\) | |||||||
\(164\) | −6.16930 | −0.481741 | ||||||||
\(165\) | 1.44601 | 0.112572 | ||||||||
\(166\) | −12.1785 | −0.945233 | ||||||||
\(167\) | −2.97131 | −0.229927 | −0.114964 | − | 0.993370i | \(-0.536675\pi\) | ||||
−0.114964 | + | 0.993370i | \(0.536675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5342 | 0.964170 | ||||||||
\(170\) | 1.54667 | 0.118624 | ||||||||
\(171\) | 2.39935 | 0.183483 | ||||||||
\(172\) | 1.07317 | 0.0818283 | ||||||||
\(173\) | 11.5181 | 0.875701 | 0.437851 | − | 0.899048i | \(-0.355740\pi\) | ||||
0.437851 | + | 0.899048i | \(0.355740\pi\) | |||||||
\(174\) | −0.955190 | −0.0724128 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.46532 | −0.487342 | ||||||||
\(177\) | 4.40927 | 0.331421 | ||||||||
\(178\) | 4.58950 | 0.343998 | ||||||||
\(179\) | −11.9135 | −0.890455 | −0.445228 | − | 0.895417i | \(-0.646877\pi\) | ||||
−0.445228 | + | 0.895417i | \(0.646877\pi\) | |||||||
\(180\) | 0.321783 | 0.0239843 | ||||||||
\(181\) | 25.9847 | 1.93143 | 0.965713 | − | 0.259612i | \(-0.0835947\pi\) | ||||
0.965713 | + | 0.259612i | \(0.0835947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.12670 | −0.157210 | ||||||||
\(184\) | −3.07225 | −0.226490 | ||||||||
\(185\) | −5.04213 | −0.370705 | ||||||||
\(186\) | 4.14602 | 0.304001 | ||||||||
\(187\) | −5.68712 | −0.415884 | ||||||||
\(188\) | 1.08816 | 0.0793621 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.64770 | −0.119536 | ||||||||
\(191\) | −18.0234 | −1.30412 | −0.652062 | − | 0.758165i | \(-0.726096\pi\) | ||||
−0.652062 | + | 0.758165i | \(0.726096\pi\) | |||||||
\(192\) | −8.80724 | −0.635608 | ||||||||
\(193\) | −4.68289 | −0.337082 | −0.168541 | − | 0.985695i | \(-0.553906\pi\) | ||||
−0.168541 | + | 0.985695i | \(0.553906\pi\) | |||||||
\(194\) | 18.5114 | 1.32904 | ||||||||
\(195\) | −2.89370 | −0.207222 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4797 | −1.60161 | −0.800804 | − | 0.598926i | \(-0.795594\pi\) | ||||
−0.800804 | + | 0.598926i | \(0.795594\pi\) | |||||||
\(198\) | 3.02811 | 0.215198 | ||||||||
\(199\) | 2.73372 | 0.193788 | 0.0968941 | − | 0.995295i | \(-0.469109\pi\) | ||||
0.0968941 | + | 0.995295i | \(0.469109\pi\) | |||||||
\(200\) | 14.3538 | 1.01497 | ||||||||
\(201\) | −4.01556 | −0.283236 | ||||||||
\(202\) | −8.26470 | −0.581502 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.26557 | −0.0886073 | ||||||||
\(205\) | −6.28719 | −0.439116 | ||||||||
\(206\) | 12.9025 | 0.898961 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 12.9382 | 0.897100 | ||||||||
\(209\) | 6.05860 | 0.419082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.94428 | −0.271536 | −0.135768 | − | 0.990741i | \(-0.543350\pi\) | ||||
−0.135768 | + | 0.990741i | \(0.543350\pi\) | |||||||
\(212\) | −5.37787 | −0.369354 | ||||||||
\(213\) | −0.424132 | −0.0290611 | ||||||||
\(214\) | 10.4746 | 0.716032 | ||||||||
\(215\) | 1.09368 | 0.0745881 | ||||||||
\(216\) | 3.07225 | 0.209040 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.58977 | −0.243130 | ||||||||
\(219\) | 14.0009 | 0.946094 | ||||||||
\(220\) | 0.812535 | 0.0547811 | ||||||||
\(221\) | 11.3808 | 0.765559 | ||||||||
\(222\) | −10.5588 | −0.708660 | ||||||||
\(223\) | −17.8955 | −1.19837 | −0.599187 | − | 0.800609i | \(-0.704509\pi\) | ||||
−0.599187 | + | 0.800609i | \(0.704509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.67207 | −0.311471 | ||||||||
\(226\) | 19.5844 | 1.30274 | ||||||||
\(227\) | 18.1777 | 1.20649 | 0.603247 | − | 0.797554i | \(-0.293873\pi\) | ||||
0.603247 | + | 0.797554i | \(0.293873\pi\) | |||||||
\(228\) | 1.34823 | 0.0892887 | ||||||||
\(229\) | 7.17469 | 0.474117 | 0.237059 | − | 0.971495i | \(-0.423817\pi\) | ||||
0.237059 | + | 0.971495i | \(0.423817\pi\) | |||||||
\(230\) | −0.686727 | −0.0452814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.44712 | −0.160661 | ||||||||
\(233\) | −14.3870 | −0.942525 | −0.471262 | − | 0.881993i | \(-0.656201\pi\) | ||||
−0.471262 | + | 0.881993i | \(0.656201\pi\) | |||||||
\(234\) | −6.05973 | −0.396137 | ||||||||
\(235\) | 1.10895 | 0.0723401 | ||||||||
\(236\) | 2.47764 | 0.161281 | ||||||||
\(237\) | −4.97332 | −0.323052 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.51078 | −0.0977241 | −0.0488620 | − | 0.998806i | \(-0.515559\pi\) | ||||
−0.0488620 | + | 0.998806i | \(0.515559\pi\) | |||||||
\(240\) | −1.46623 | −0.0946449 | ||||||||
\(241\) | 30.7830 | 1.98291 | 0.991453 | − | 0.130464i | \(-0.0416467\pi\) | ||||
0.991453 | + | 0.130464i | \(0.0416467\pi\) | |||||||
\(242\) | −5.54493 | −0.356442 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.19503 | −0.0765037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.1661 | −0.839439 | ||||||||
\(247\) | −12.1242 | −0.771446 | ||||||||
\(248\) | 10.6217 | 0.674481 | ||||||||
\(249\) | 10.1555 | 0.643578 | ||||||||
\(250\) | 6.64207 | 0.420081 | ||||||||
\(251\) | 12.8572 | 0.811540 | 0.405770 | − | 0.913975i | \(-0.367003\pi\) | ||||
0.405770 | + | 0.913975i | \(0.367003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.52510 | 0.158752 | ||||||||
\(254\) | 22.3003 | 1.39924 | ||||||||
\(255\) | −1.28975 | −0.0807672 | ||||||||
\(256\) | −12.3217 | −0.770108 | ||||||||
\(257\) | 4.16813 | 0.260001 | 0.130000 | − | 0.991514i | \(-0.458502\pi\) | ||||
0.130000 | + | 0.991514i | \(0.458502\pi\) | |||||||
\(258\) | 2.29028 | 0.142587 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.62601 | −0.100841 | ||||||||
\(261\) | 0.796522 | 0.0493035 | ||||||||
\(262\) | 21.4801 | 1.32705 | ||||||||
\(263\) | 9.13504 | 0.563291 | 0.281645 | − | 0.959519i | \(-0.409120\pi\) | ||||
0.281645 | + | 0.959519i | \(0.409120\pi\) | |||||||
\(264\) | 7.75776 | 0.477457 | ||||||||
\(265\) | −5.48064 | −0.336673 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.82713 | −0.234217 | ||||||||
\(268\) | −2.25641 | −0.137832 | ||||||||
\(269\) | −9.03201 | −0.550691 | −0.275346 | − | 0.961345i | \(-0.588792\pi\) | ||||
−0.275346 | + | 0.961345i | \(0.588792\pi\) | |||||||
\(270\) | 0.686727 | 0.0417929 | ||||||||
\(271\) | 7.05301 | 0.428440 | 0.214220 | − | 0.976785i | \(-0.431279\pi\) | ||||
0.214220 | + | 0.976785i | \(0.431279\pi\) | |||||||
\(272\) | 5.76666 | 0.349655 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.3698 | 1.17017 | ||||||||
\(275\) | −11.7975 | −0.711413 | ||||||||
\(276\) | 0.561916 | 0.0338233 | ||||||||
\(277\) | 11.3120 | 0.679671 | 0.339835 | − | 0.940485i | \(-0.389629\pi\) | ||||
0.339835 | + | 0.940485i | \(0.389629\pi\) | |||||||
\(278\) | −1.36814 | −0.0820555 | ||||||||
\(279\) | −3.45731 | −0.206984 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.3499 | −1.33329 | −0.666643 | − | 0.745377i | \(-0.732269\pi\) | ||||
−0.666643 | + | 0.745377i | \(0.732269\pi\) | |||||||
\(282\) | 2.32227 | 0.138289 | ||||||||
\(283\) | −18.4769 | −1.09834 | −0.549168 | − | 0.835712i | \(-0.685055\pi\) | ||||
−0.549168 | + | 0.835712i | \(0.685055\pi\) | |||||||
\(284\) | −0.238327 | −0.0141421 | ||||||||
\(285\) | 1.37399 | 0.0813884 | ||||||||
\(286\) | −15.3014 | −0.904794 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.07405 | 0.181140 | ||||||||
\(289\) | −11.9274 | −0.701614 | ||||||||
\(290\) | −0.546993 | −0.0321205 | ||||||||
\(291\) | −15.4364 | −0.904898 | ||||||||
\(292\) | 7.86733 | 0.460401 | ||||||||
\(293\) | 0.717401 | 0.0419110 | 0.0209555 | − | 0.999780i | \(-0.493329\pi\) | ||||
0.0209555 | + | 0.999780i | \(0.493329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.52498 | 0.147010 | ||||||||
\(296\) | −27.0507 | −1.57229 | ||||||||
\(297\) | −2.52510 | −0.146521 | ||||||||
\(298\) | 9.62170 | 0.557370 | ||||||||
\(299\) | −5.05314 | −0.292231 | ||||||||
\(300\) | −2.62531 | −0.151572 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.3072 | 1.39872 | ||||||||
\(303\) | 6.89184 | 0.395926 | ||||||||
\(304\) | −6.14333 | −0.352344 | ||||||||
\(305\) | −1.21786 | −0.0697346 | ||||||||
\(306\) | −2.70088 | −0.154399 | ||||||||
\(307\) | −8.27982 | −0.472555 | −0.236277 | − | 0.971686i | \(-0.575927\pi\) | ||||
−0.236277 | + | 0.971686i | \(0.575927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7593 | −0.612073 | ||||||||
\(310\) | 2.37423 | 0.134847 | ||||||||
\(311\) | −8.94613 | −0.507288 | −0.253644 | − | 0.967298i | \(-0.581629\pi\) | ||||
−0.253644 | + | 0.967298i | \(0.581629\pi\) | |||||||
\(312\) | −15.5245 | −0.878903 | ||||||||
\(313\) | −4.93844 | −0.279137 | −0.139569 | − | 0.990212i | \(-0.544572\pi\) | ||||
−0.139569 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(314\) | −7.97371 | −0.449983 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.79458 | −0.157208 | ||||||||
\(317\) | −15.7414 | −0.884124 | −0.442062 | − | 0.896985i | \(-0.645753\pi\) | ||||
−0.442062 | + | 0.896985i | \(0.645753\pi\) | |||||||
\(318\) | −11.4771 | −0.643603 | ||||||||
\(319\) | 2.01130 | 0.112611 | ||||||||
\(320\) | −5.04350 | −0.281940 | ||||||||
\(321\) | −8.73468 | −0.487522 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.40389 | −0.300680 | ||||||||
\(324\) | −0.561916 | −0.0312175 | ||||||||
\(325\) | 23.6086 | 1.30957 | ||||||||
\(326\) | 4.49353 | 0.248874 | ||||||||
\(327\) | 2.99347 | 0.165539 | ||||||||
\(328\) | −33.7304 | −1.86245 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.73406 | 0.0954567 | ||||||||
\(331\) | −27.3344 | −1.50244 | −0.751218 | − | 0.660054i | \(-0.770533\pi\) | ||||
−0.751218 | + | 0.660054i | \(0.770533\pi\) | |||||||
\(332\) | 5.70653 | 0.313186 | ||||||||
\(333\) | 8.80485 | 0.482503 | ||||||||
\(334\) | −3.56320 | −0.194970 | ||||||||
\(335\) | −2.29952 | −0.125636 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.73803 | 0.530465 | 0.265232 | − | 0.964185i | \(-0.414551\pi\) | ||||
0.265232 | + | 0.964185i | \(0.414551\pi\) | |||||||
\(338\) | 15.0310 | 0.817581 | ||||||||
\(339\) | −16.3312 | −0.886990 | ||||||||
\(340\) | −0.724730 | −0.0393040 | ||||||||
\(341\) | −8.73008 | −0.472760 | ||||||||
\(342\) | 2.87730 | 0.155587 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.86751 | 0.316355 | ||||||||
\(345\) | 0.572653 | 0.0308306 | ||||||||
\(346\) | 13.8125 | 0.742563 | ||||||||
\(347\) | −28.9292 | −1.55300 | −0.776502 | − | 0.630115i | \(-0.783008\pi\) | ||||
−0.776502 | + | 0.630115i | \(0.783008\pi\) | |||||||
\(348\) | 0.447578 | 0.0239927 | ||||||||
\(349\) | 19.9972 | 1.07042 | 0.535212 | − | 0.844718i | \(-0.320232\pi\) | ||||
0.535212 | + | 0.844718i | \(0.320232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.05314 | 0.269717 | ||||||||
\(352\) | 7.76229 | 0.413731 | ||||||||
\(353\) | −24.5968 | −1.30915 | −0.654577 | − | 0.755995i | \(-0.727153\pi\) | ||||
−0.654577 | + | 0.755995i | \(0.727153\pi\) | |||||||
\(354\) | 5.28761 | 0.281033 | ||||||||
\(355\) | −0.242881 | −0.0128908 | ||||||||
\(356\) | −2.15052 | −0.113978 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2867 | −0.755074 | ||||||||
\(359\) | 20.3150 | 1.07218 | 0.536091 | − | 0.844160i | \(-0.319900\pi\) | ||||
0.536091 | + | 0.844160i | \(0.319900\pi\) | |||||||
\(360\) | 1.75934 | 0.0927252 | ||||||||
\(361\) | −13.2431 | −0.697007 | ||||||||
\(362\) | 31.1609 | 1.63778 | ||||||||
\(363\) | 4.62385 | 0.242689 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.01767 | 0.419664 | ||||||||
\(366\) | −2.55034 | −0.133309 | ||||||||
\(367\) | −3.48022 | −0.181666 | −0.0908330 | − | 0.995866i | \(-0.528953\pi\) | ||||
−0.0908330 | + | 0.995866i | \(0.528953\pi\) | |||||||
\(368\) | −2.56042 | −0.133471 | ||||||||
\(369\) | 10.9790 | 0.571546 | ||||||||
\(370\) | −6.04653 | −0.314344 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.94272 | −0.100725 | ||||||||
\(373\) | −30.1089 | −1.55898 | −0.779490 | − | 0.626415i | \(-0.784521\pi\) | ||||
−0.779490 | + | 0.626415i | \(0.784521\pi\) | |||||||
\(374\) | −6.82000 | −0.352654 | ||||||||
\(375\) | −5.53874 | −0.286019 | ||||||||
\(376\) | 5.94947 | 0.306820 | ||||||||
\(377\) | −4.02494 | −0.207295 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.6106 | −1.36689 | −0.683446 | − | 0.730001i | \(-0.739520\pi\) | ||||
−0.683446 | + | 0.730001i | \(0.739520\pi\) | |||||||
\(380\) | 0.772069 | 0.0396063 | ||||||||
\(381\) | −18.5959 | −0.952698 | ||||||||
\(382\) | −21.6136 | −1.10585 | ||||||||
\(383\) | −22.0176 | −1.12505 | −0.562524 | − | 0.826781i | \(-0.690169\pi\) | ||||
−0.562524 | + | 0.826781i | \(0.690169\pi\) | |||||||
\(384\) | −4.41356 | −0.225229 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.61573 | −0.285833 | ||||||||
\(387\) | −1.90984 | −0.0970826 | ||||||||
\(388\) | −8.67396 | −0.440354 | ||||||||
\(389\) | 18.3864 | 0.932227 | 0.466113 | − | 0.884725i | \(-0.345654\pi\) | ||||
0.466113 | + | 0.884725i | \(0.345654\pi\) | |||||||
\(390\) | −3.47013 | −0.175717 | ||||||||
\(391\) | −2.25223 | −0.113900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.9120 | −0.903542 | ||||||||
\(394\) | −26.9576 | −1.35811 | ||||||||
\(395\) | −2.84799 | −0.143298 | ||||||||
\(396\) | −1.41890 | −0.0713022 | ||||||||
\(397\) | 10.0731 | 0.505557 | 0.252778 | − | 0.967524i | \(-0.418656\pi\) | ||||
0.252778 | + | 0.967524i | \(0.418656\pi\) | |||||||
\(398\) | 3.27828 | 0.164325 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.9625 | 0.598123 | ||||||||
\(401\) | −10.8915 | −0.543896 | −0.271948 | − | 0.962312i | \(-0.587668\pi\) | ||||
−0.271948 | + | 0.962312i | \(0.587668\pi\) | |||||||
\(402\) | −4.81547 | −0.240174 | ||||||||
\(403\) | 17.4703 | 0.870257 | ||||||||
\(404\) | 3.87263 | 0.192671 | ||||||||
\(405\) | −0.572653 | −0.0284554 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.2332 | 1.10206 | ||||||||
\(408\) | −6.91943 | −0.342563 | ||||||||
\(409\) | −12.5106 | −0.618608 | −0.309304 | − | 0.950963i | \(-0.600096\pi\) | ||||
−0.309304 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(410\) | −7.53960 | −0.372354 | ||||||||
\(411\) | −16.1522 | −0.796731 | ||||||||
\(412\) | −6.04580 | −0.297855 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.19920 | 0.0589375 | ||||||||
\(415\) | 5.81557 | 0.285475 | ||||||||
\(416\) | −15.5336 | −0.761597 | ||||||||
\(417\) | 1.14087 | 0.0558689 | ||||||||
\(418\) | 7.26548 | 0.355366 | ||||||||
\(419\) | 32.3891 | 1.58231 | 0.791157 | − | 0.611613i | \(-0.209479\pi\) | ||||
0.791157 | + | 0.611613i | \(0.209479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.76745 | −0.134877 | −0.0674387 | − | 0.997723i | \(-0.521483\pi\) | ||||
−0.0674387 | + | 0.997723i | \(0.521483\pi\) | |||||||
\(422\) | −4.72999 | −0.230252 | ||||||||
\(423\) | −1.93652 | −0.0941566 | ||||||||
\(424\) | −29.4033 | −1.42795 | ||||||||
\(425\) | 10.5226 | 0.510420 | ||||||||
\(426\) | −0.508620 | −0.0246427 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.90815 | −0.237245 | ||||||||
\(429\) | 12.7597 | 0.616044 | ||||||||
\(430\) | 1.31154 | 0.0632480 | ||||||||
\(431\) | 37.9249 | 1.82678 | 0.913389 | − | 0.407088i | \(-0.133456\pi\) | ||||
0.913389 | + | 0.407088i | \(0.133456\pi\) | |||||||
\(432\) | 2.56042 | 0.123188 | ||||||||
\(433\) | 17.8080 | 0.855798 | 0.427899 | − | 0.903827i | \(-0.359254\pi\) | ||||
0.427899 | + | 0.903827i | \(0.359254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.456131 | 0.0218698 | ||||||||
\(436\) | 1.68208 | 0.0805568 | ||||||||
\(437\) | 2.39935 | 0.114776 | ||||||||
\(438\) | 16.7899 | 0.802253 | ||||||||
\(439\) | 39.0320 | 1.86290 | 0.931448 | − | 0.363874i | \(-0.118546\pi\) | ||||
0.931448 | + | 0.363874i | \(0.118546\pi\) | |||||||
\(440\) | 4.44251 | 0.211788 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.6479 | 0.649166 | ||||||||
\(443\) | 19.9008 | 0.945513 | 0.472757 | − | 0.881193i | \(-0.343259\pi\) | ||||
0.472757 | + | 0.881193i | \(0.343259\pi\) | |||||||
\(444\) | 4.94758 | 0.234802 | ||||||||
\(445\) | −2.19162 | −0.103893 | ||||||||
\(446\) | −21.4603 | −1.01618 | ||||||||
\(447\) | −8.02342 | −0.379495 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.7323 | 1.49754 | 0.748769 | − | 0.662831i | \(-0.230645\pi\) | ||||
0.748769 | + | 0.662831i | \(0.230645\pi\) | |||||||
\(450\) | −5.60275 | −0.264116 | ||||||||
\(451\) | 27.7232 | 1.30544 | ||||||||
\(452\) | −9.17677 | −0.431639 | ||||||||
\(453\) | −20.2695 | −0.952342 | ||||||||
\(454\) | 21.7987 | 1.02306 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.37140 | 0.345197 | ||||||||
\(457\) | −6.27845 | −0.293694 | −0.146847 | − | 0.989159i | \(-0.546912\pi\) | ||||
−0.146847 | + | 0.989159i | \(0.546912\pi\) | |||||||
\(458\) | 8.60390 | 0.402034 | ||||||||
\(459\) | 2.25223 | 0.105125 | ||||||||
\(460\) | 0.321783 | 0.0150032 | ||||||||
\(461\) | −20.4402 | −0.951996 | −0.475998 | − | 0.879446i | \(-0.657913\pi\) | ||||
−0.475998 | + | 0.879446i | \(0.657913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.31436 | −0.386401 | −0.193201 | − | 0.981159i | \(-0.561887\pi\) | ||||
−0.193201 | + | 0.981159i | \(0.561887\pi\) | |||||||
\(464\) | −2.03943 | −0.0946782 | ||||||||
\(465\) | −1.97984 | −0.0918130 | ||||||||
\(466\) | −17.2529 | −0.799226 | ||||||||
\(467\) | 3.47840 | 0.160961 | 0.0804807 | − | 0.996756i | \(-0.474354\pi\) | ||||
0.0804807 | + | 0.996756i | \(0.474354\pi\) | |||||||
\(468\) | 2.83944 | 0.131253 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.32986 | 0.0613417 | ||||||||
\(471\) | 6.64919 | 0.306378 | ||||||||
\(472\) | 13.5464 | 0.623524 | ||||||||
\(473\) | −4.82254 | −0.221741 | ||||||||
\(474\) | −5.96401 | −0.273936 | ||||||||
\(475\) | −11.2099 | −0.514346 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.57060 | 0.438208 | ||||||||
\(478\) | −1.81173 | −0.0828665 | ||||||||
\(479\) | 20.7534 | 0.948249 | 0.474124 | − | 0.880458i | \(-0.342765\pi\) | ||||
0.474124 | + | 0.880458i | \(0.342765\pi\) | |||||||
\(480\) | 1.76036 | 0.0803492 | ||||||||
\(481\) | −44.4921 | −2.02867 | ||||||||
\(482\) | 36.9150 | 1.68143 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.59822 | 0.118101 | ||||||||
\(485\) | −8.83971 | −0.401391 | ||||||||
\(486\) | −1.19920 | −0.0543969 | ||||||||
\(487\) | −26.2962 | −1.19159 | −0.595796 | − | 0.803135i | \(-0.703163\pi\) | ||||
−0.595796 | + | 0.803135i | \(0.703163\pi\) | |||||||
\(488\) | −6.53376 | −0.295769 | ||||||||
\(489\) | −3.74710 | −0.169450 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.35237 | −0.241549 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(492\) | 6.16930 | 0.278133 | ||||||||
\(493\) | −1.79395 | −0.0807956 | ||||||||
\(494\) | −14.5394 | −0.654158 | ||||||||
\(495\) | −1.44601 | −0.0649933 | ||||||||
\(496\) | 8.85217 | 0.397474 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.1785 | 0.545730 | ||||||||
\(499\) | 38.8594 | 1.73959 | 0.869794 | − | 0.493416i | \(-0.164252\pi\) | ||||
0.869794 | + | 0.493416i | \(0.164252\pi\) | |||||||
\(500\) | −3.11231 | −0.139187 | ||||||||
\(501\) | 2.97131 | 0.132749 | ||||||||
\(502\) | 15.4184 | 0.688156 | ||||||||
\(503\) | −22.5980 | −1.00760 | −0.503798 | − | 0.863822i | \(-0.668064\pi\) | ||||
−0.503798 | + | 0.863822i | \(0.668064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.94663 | 0.175623 | ||||||||
\(506\) | 3.02811 | 0.134616 | ||||||||
\(507\) | −12.5342 | −0.556664 | ||||||||
\(508\) | −10.4493 | −0.463615 | ||||||||
\(509\) | −41.6437 | −1.84583 | −0.922913 | − | 0.385010i | \(-0.874198\pi\) | ||||
−0.922913 | + | 0.385010i | \(0.874198\pi\) | |||||||
\(510\) | −1.54667 | −0.0684877 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −23.6034 | −1.04313 | ||||||||
\(513\) | −2.39935 | −0.105934 | ||||||||
\(514\) | 4.99843 | 0.220471 | ||||||||
\(515\) | −6.16133 | −0.271500 | ||||||||
\(516\) | −1.07317 | −0.0472436 | ||||||||
\(517\) | −4.88990 | −0.215058 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.5181 | −0.505586 | ||||||||
\(520\) | −8.89017 | −0.389860 | ||||||||
\(521\) | 17.4077 | 0.762646 | 0.381323 | − | 0.924442i | \(-0.375469\pi\) | ||||
0.381323 | + | 0.924442i | \(0.375469\pi\) | |||||||
\(522\) | 0.955190 | 0.0418076 | ||||||||
\(523\) | 18.4315 | 0.805955 | 0.402977 | − | 0.915210i | \(-0.367975\pi\) | ||||
0.402977 | + | 0.915210i | \(0.367975\pi\) | |||||||
\(524\) | −10.0650 | −0.439694 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9548 | 0.477650 | ||||||||
\(527\) | 7.78668 | 0.339193 | ||||||||
\(528\) | 6.46532 | 0.281367 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.57239 | −0.285486 | ||||||||
\(531\) | −4.40927 | −0.191346 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −55.4786 | −2.40305 | ||||||||
\(534\) | −4.58950 | −0.198607 | ||||||||
\(535\) | −5.00195 | −0.216253 | ||||||||
\(536\) | −12.3368 | −0.532869 | ||||||||
\(537\) | 11.9135 | 0.514105 | ||||||||
\(538\) | −10.8312 | −0.466966 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.321783 | −0.0138473 | ||||||||
\(541\) | −16.8540 | −0.724611 | −0.362305 | − | 0.932059i | \(-0.618010\pi\) | ||||
−0.362305 | + | 0.932059i | \(0.618010\pi\) | |||||||
\(542\) | 8.45798 | 0.363302 | ||||||||
\(543\) | −25.9847 | −1.11511 | ||||||||
\(544\) | −6.92347 | −0.296841 | ||||||||
\(545\) | 1.71422 | 0.0734291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9994 | 1.49647 | 0.748233 | − | 0.663436i | \(-0.230903\pi\) | ||||
0.748233 | + | 0.663436i | \(0.230903\pi\) | |||||||
\(548\) | −9.07619 | −0.387716 | ||||||||
\(549\) | 2.12670 | 0.0907654 | ||||||||
\(550\) | −14.1475 | −0.603253 | ||||||||
\(551\) | 1.91113 | 0.0814170 | ||||||||
\(552\) | 3.07225 | 0.130764 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.5653 | 0.576336 | ||||||||
\(555\) | 5.04213 | 0.214026 | ||||||||
\(556\) | 0.641075 | 0.0271876 | ||||||||
\(557\) | −25.4013 | −1.07629 | −0.538143 | − | 0.842853i | \(-0.680874\pi\) | ||||
−0.538143 | + | 0.842853i | \(0.680874\pi\) | |||||||
\(558\) | −4.14602 | −0.175515 | ||||||||
\(559\) | 9.65068 | 0.408180 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.68712 | 0.240110 | ||||||||
\(562\) | −26.8021 | −1.13058 | ||||||||
\(563\) | −10.4735 | −0.441404 | −0.220702 | − | 0.975341i | \(-0.570835\pi\) | ||||
−0.220702 | + | 0.975341i | \(0.570835\pi\) | |||||||
\(564\) | −1.08816 | −0.0458197 | ||||||||
\(565\) | −9.35213 | −0.393447 | ||||||||
\(566\) | −22.1575 | −0.931350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.30304 | −0.0546744 | ||||||||
\(569\) | 24.0842 | 1.00966 | 0.504830 | − | 0.863219i | \(-0.331555\pi\) | ||||
0.504830 | + | 0.863219i | \(0.331555\pi\) | |||||||
\(570\) | 1.64770 | 0.0690144 | ||||||||
\(571\) | 25.7969 | 1.07957 | 0.539783 | − | 0.841804i | \(-0.318506\pi\) | ||||
0.539783 | + | 0.841804i | \(0.318506\pi\) | |||||||
\(572\) | 7.16987 | 0.299787 | ||||||||
\(573\) | 18.0234 | 0.752937 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.67207 | −0.194839 | ||||||||
\(576\) | 8.80724 | 0.366968 | ||||||||
\(577\) | 11.5859 | 0.482326 | 0.241163 | − | 0.970485i | \(-0.422471\pi\) | ||||
0.241163 | + | 0.970485i | \(0.422471\pi\) | |||||||
\(578\) | −14.3034 | −0.594943 | ||||||||
\(579\) | 4.68289 | 0.194614 | ||||||||
\(580\) | 0.256307 | 0.0106426 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.5114 | −0.767321 | ||||||||
\(583\) | 24.1668 | 1.00089 | ||||||||
\(584\) | 43.0143 | 1.77995 | ||||||||
\(585\) | 2.89370 | 0.119640 | ||||||||
\(586\) | 0.860308 | 0.0355390 | ||||||||
\(587\) | −8.06567 | −0.332906 | −0.166453 | − | 0.986049i | \(-0.553231\pi\) | ||||
−0.166453 | + | 0.986049i | \(0.553231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.29529 | −0.341802 | ||||||||
\(590\) | 3.02797 | 0.124659 | ||||||||
\(591\) | 22.4797 | 0.924689 | ||||||||
\(592\) | −22.5441 | −0.926558 | ||||||||
\(593\) | −24.5938 | −1.00995 | −0.504973 | − | 0.863135i | \(-0.668498\pi\) | ||||
−0.504973 | + | 0.863135i | \(0.668498\pi\) | |||||||
\(594\) | −3.02811 | −0.124245 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.50849 | −0.184675 | ||||||||
\(597\) | −2.73372 | −0.111884 | ||||||||
\(598\) | −6.05973 | −0.247801 | ||||||||
\(599\) | −17.4274 | −0.712064 | −0.356032 | − | 0.934474i | \(-0.615871\pi\) | ||||
−0.356032 | + | 0.934474i | \(0.615871\pi\) | |||||||
\(600\) | −14.3538 | −0.585990 | ||||||||
\(601\) | 46.7989 | 1.90897 | 0.954484 | − | 0.298263i | \(-0.0964071\pi\) | ||||
0.954484 | + | 0.298263i | \(0.0964071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.01556 | 0.163526 | ||||||||
\(604\) | −11.3897 | −0.463441 | ||||||||
\(605\) | 2.64787 | 0.107651 | ||||||||
\(606\) | 8.26470 | 0.335731 | ||||||||
\(607\) | −17.9031 | −0.726665 | −0.363333 | − | 0.931659i | \(-0.618361\pi\) | ||||
−0.363333 | + | 0.931659i | \(0.618361\pi\) | |||||||
\(608\) | 7.37570 | 0.299124 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.46046 | −0.0591324 | ||||||||
\(611\) | 9.78548 | 0.395878 | ||||||||
\(612\) | 1.26557 | 0.0511574 | ||||||||
\(613\) | −34.8986 | −1.40954 | −0.704770 | − | 0.709436i | \(-0.748950\pi\) | ||||
−0.704770 | + | 0.709436i | \(0.748950\pi\) | |||||||
\(614\) | −9.92918 | −0.400709 | ||||||||
\(615\) | 6.28719 | 0.253524 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.6661 | −1.91896 | −0.959482 | − | 0.281771i | \(-0.909078\pi\) | ||||
−0.959482 | + | 0.281771i | \(0.909078\pi\) | |||||||
\(618\) | −12.9025 | −0.519015 | ||||||||
\(619\) | 39.4321 | 1.58491 | 0.792455 | − | 0.609930i | \(-0.208803\pi\) | ||||
0.792455 | + | 0.609930i | \(0.208803\pi\) | |||||||
\(620\) | −1.11250 | −0.0446793 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −10.7282 | −0.430162 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12.9382 | −0.517941 | ||||||||
\(625\) | 20.1886 | 0.807542 | ||||||||
\(626\) | −5.92219 | −0.236698 | ||||||||
\(627\) | −6.05860 | −0.241957 | ||||||||
\(628\) | 3.73628 | 0.149094 | ||||||||
\(629\) | −19.8306 | −0.790697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.93619 | −0.276125 | −0.138063 | − | 0.990423i | \(-0.544088\pi\) | ||||
−0.138063 | + | 0.990423i | \(0.544088\pi\) | |||||||
\(632\) | −15.2793 | −0.607777 | ||||||||
\(633\) | 3.94428 | 0.156771 | ||||||||
\(634\) | −18.8771 | −0.749705 | ||||||||
\(635\) | −10.6490 | −0.422593 | ||||||||
\(636\) | 5.37787 | 0.213247 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.41195 | 0.0954902 | ||||||||
\(639\) | 0.424132 | 0.0167784 | ||||||||
\(640\) | −2.52744 | −0.0999059 | ||||||||
\(641\) | 25.6360 | 1.01256 | 0.506281 | − | 0.862368i | \(-0.331020\pi\) | ||||
0.506281 | + | 0.862368i | \(0.331020\pi\) | |||||||
\(642\) | −10.4746 | −0.413401 | ||||||||
\(643\) | 14.2975 | 0.563840 | 0.281920 | − | 0.959438i | \(-0.409029\pi\) | ||||
0.281920 | + | 0.959438i | \(0.409029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.09368 | −0.0430635 | ||||||||
\(646\) | −6.48035 | −0.254966 | ||||||||
\(647\) | −33.3271 | −1.31022 | −0.655111 | − | 0.755533i | \(-0.727378\pi\) | ||||
−0.655111 | + | 0.755533i | \(0.727378\pi\) | |||||||
\(648\) | −3.07225 | −0.120690 | ||||||||
\(649\) | −11.1339 | −0.437043 | ||||||||
\(650\) | 28.3115 | 1.11047 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.10556 | −0.0824599 | ||||||||
\(653\) | 0.716990 | 0.0280580 | 0.0140290 | − | 0.999902i | \(-0.495534\pi\) | ||||
0.0140290 | + | 0.999902i | \(0.495534\pi\) | |||||||
\(654\) | 3.58977 | 0.140371 | ||||||||
\(655\) | −10.2574 | −0.400789 | ||||||||
\(656\) | −28.1110 | −1.09755 | ||||||||
\(657\) | −14.0009 | −0.546228 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.0825 | −0.860214 | −0.430107 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430107 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(660\) | −0.812535 | −0.0316279 | ||||||||
\(661\) | −20.7710 | −0.807898 | −0.403949 | − | 0.914782i | \(-0.632363\pi\) | ||||
−0.403949 | + | 0.914782i | \(0.632363\pi\) | |||||||
\(662\) | −32.7795 | −1.27401 | ||||||||
\(663\) | −11.3808 | −0.441995 | ||||||||
\(664\) | 31.2002 | 1.21080 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.5588 | 0.409145 | ||||||||
\(667\) | 0.796522 | 0.0308415 | ||||||||
\(668\) | 1.66963 | 0.0645998 | ||||||||
\(669\) | 17.8955 | 0.691881 | ||||||||
\(670\) | −2.75759 | −0.106535 | ||||||||
\(671\) | 5.37014 | 0.207312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5462 | 0.406525 | 0.203262 | − | 0.979124i | \(-0.434846\pi\) | ||||
0.203262 | + | 0.979124i | \(0.434846\pi\) | |||||||
\(674\) | 11.6779 | 0.449815 | ||||||||
\(675\) | 4.67207 | 0.179828 | ||||||||
\(676\) | −7.04317 | −0.270891 | ||||||||
\(677\) | −14.0346 | −0.539393 | −0.269696 | − | 0.962945i | \(-0.586923\pi\) | ||||
−0.269696 | + | 0.962945i | \(0.586923\pi\) | |||||||
\(678\) | −19.5844 | −0.752135 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.96244 | −0.151952 | ||||||||
\(681\) | −18.1777 | −0.696570 | ||||||||
\(682\) | −10.4691 | −0.400883 | ||||||||
\(683\) | 43.3231 | 1.65771 | 0.828856 | − | 0.559462i | \(-0.188992\pi\) | ||||
0.828856 | + | 0.559462i | \(0.188992\pi\) | |||||||
\(684\) | −1.34823 | −0.0515509 | ||||||||
\(685\) | −9.24963 | −0.353410 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.17469 | −0.273732 | ||||||||
\(688\) | 4.88999 | 0.186429 | ||||||||
\(689\) | −48.3616 | −1.84243 | ||||||||
\(690\) | 0.686727 | 0.0261432 | ||||||||
\(691\) | 37.9027 | 1.44189 | 0.720944 | − | 0.692993i | \(-0.243708\pi\) | ||||
0.720944 | + | 0.692993i | \(0.243708\pi\) | |||||||
\(692\) | −6.47217 | −0.246035 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.6920 | −1.31689 | ||||||||
\(695\) | 0.653326 | 0.0247821 | ||||||||
\(696\) | 2.44712 | 0.0927577 | ||||||||
\(697\) | −24.7274 | −0.936616 | ||||||||
\(698\) | 23.9806 | 0.907681 | ||||||||
\(699\) | 14.3870 | 0.544167 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.9525 | −0.678058 | −0.339029 | − | 0.940776i | \(-0.610099\pi\) | ||||
−0.339029 | + | 0.940776i | \(0.610099\pi\) | |||||||
\(702\) | 6.05973 | 0.228710 | ||||||||
\(703\) | 21.1259 | 0.796778 | ||||||||
\(704\) | 22.2392 | 0.838171 | ||||||||
\(705\) | −1.10895 | −0.0417656 | ||||||||
\(706\) | −29.4965 | −1.11011 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.47764 | −0.0931154 | ||||||||
\(709\) | 31.9105 | 1.19843 | 0.599213 | − | 0.800590i | \(-0.295480\pi\) | ||||
0.599213 | + | 0.800590i | \(0.295480\pi\) | |||||||
\(710\) | −0.291263 | −0.0109309 | ||||||||
\(711\) | 4.97332 | 0.186514 | ||||||||
\(712\) | −11.7579 | −0.440646 | ||||||||
\(713\) | −3.45731 | −0.129477 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.30688 | 0.273262 | ||||||||
\(716\) | 6.69437 | 0.250180 | ||||||||
\(717\) | 1.51078 | 0.0564210 | ||||||||
\(718\) | 24.3617 | 0.909172 | ||||||||
\(719\) | 10.3283 | 0.385182 | 0.192591 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192591 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(720\) | 1.46623 | 0.0546433 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.8812 | −0.591037 | ||||||||
\(723\) | −30.7830 | −1.14483 | ||||||||
\(724\) | −14.6012 | −0.542649 | ||||||||
\(725\) | −3.72141 | −0.138210 | ||||||||
\(726\) | 5.54493 | 0.205792 | ||||||||
\(727\) | 32.5415 | 1.20690 | 0.603448 | − | 0.797402i | \(-0.293793\pi\) | ||||
0.603448 | + | 0.797402i | \(0.293793\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.61480 | 0.355860 | ||||||||
\(731\) | 4.30140 | 0.159093 | ||||||||
\(732\) | 1.19503 | 0.0441694 | ||||||||
\(733\) | 30.9326 | 1.14252 | 0.571262 | − | 0.820768i | \(-0.306454\pi\) | ||||
0.571262 | + | 0.820768i | \(0.306454\pi\) | |||||||
\(734\) | −4.17349 | −0.154046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.07405 | 0.113311 | ||||||||
\(737\) | 10.1397 | 0.373501 | ||||||||
\(738\) | 13.1661 | 0.484650 | ||||||||
\(739\) | 31.6017 | 1.16249 | 0.581244 | − | 0.813730i | \(-0.302566\pi\) | ||||
0.581244 | + | 0.813730i | \(0.302566\pi\) | |||||||
\(740\) | 2.83325 | 0.104152 | ||||||||
\(741\) | 12.1242 | 0.445395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6217 | −0.389674 | −0.194837 | − | 0.980836i | \(-0.562418\pi\) | ||||
−0.194837 | + | 0.980836i | \(0.562418\pi\) | |||||||
\(744\) | −10.6217 | −0.389412 | ||||||||
\(745\) | −4.59464 | −0.168335 | ||||||||
\(746\) | −36.1066 | −1.32196 | ||||||||
\(747\) | −10.1555 | −0.371570 | ||||||||
\(748\) | 3.19568 | 0.116846 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.64207 | −0.242534 | ||||||||
\(751\) | −0.0261115 | −0.000952821 0 | −0.000476410 | − | 1.00000i | \(-0.500152\pi\) | ||||
−0.000476410 | 1.00000i | \(0.500152\pi\) | ||||||||
\(752\) | 4.95829 | 0.180810 | ||||||||
\(753\) | −12.8572 | −0.468543 | ||||||||
\(754\) | −4.82671 | −0.175778 | ||||||||
\(755\) | −11.6074 | −0.422436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50079 | 0.0545471 | 0.0272735 | − | 0.999628i | \(-0.491317\pi\) | ||||
0.0272735 | + | 0.999628i | \(0.491317\pi\) | |||||||
\(758\) | −31.9114 | −1.15907 | ||||||||
\(759\) | −2.52510 | −0.0916554 | ||||||||
\(760\) | 4.22126 | 0.153121 | ||||||||
\(761\) | −37.4931 | −1.35912 | −0.679562 | − | 0.733618i | \(-0.737830\pi\) | ||||
−0.679562 | + | 0.733618i | \(0.737830\pi\) | |||||||
\(762\) | −22.3003 | −0.807853 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.1276 | 0.366404 | ||||||||
\(765\) | 1.28975 | 0.0466310 | ||||||||
\(766\) | −26.4036 | −0.953999 | ||||||||
\(767\) | 22.2807 | 0.804508 | ||||||||
\(768\) | 12.3217 | 0.444622 | ||||||||
\(769\) | 32.9794 | 1.18927 | 0.594633 | − | 0.803997i | \(-0.297297\pi\) | ||||
0.594633 | + | 0.803997i | \(0.297297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.16813 | −0.150112 | ||||||||
\(772\) | 2.63139 | 0.0947057 | ||||||||
\(773\) | −42.7241 | −1.53668 | −0.768340 | − | 0.640042i | \(-0.778917\pi\) | ||||
−0.768340 | + | 0.640042i | \(0.778917\pi\) | |||||||
\(774\) | −2.29028 | −0.0823225 | ||||||||
\(775\) | 16.1528 | 0.580226 | ||||||||
\(776\) | −47.4245 | −1.70244 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.0490 | 0.790494 | ||||||||
\(779\) | 26.3425 | 0.943819 | ||||||||
\(780\) | 1.62601 | 0.0582206 | ||||||||
\(781\) | 1.07098 | 0.0383226 | ||||||||
\(782\) | −2.70088 | −0.0965833 | ||||||||
\(783\) | −0.796522 | −0.0284654 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.80768 | 0.135902 | ||||||||
\(786\) | −21.4801 | −0.766171 | ||||||||
\(787\) | 11.7935 | 0.420394 | 0.210197 | − | 0.977659i | \(-0.432589\pi\) | ||||
0.210197 | + | 0.977659i | \(0.432589\pi\) | |||||||
\(788\) | 12.6317 | 0.449985 | ||||||||
\(789\) | −9.13504 | −0.325216 | ||||||||
\(790\) | −3.41531 | −0.121511 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.75776 | −0.275660 | ||||||||
\(793\) | −10.7465 | −0.381620 | ||||||||
\(794\) | 12.0797 | 0.428694 | ||||||||
\(795\) | 5.48064 | 0.194378 | ||||||||
\(796\) | −1.53612 | −0.0544463 | ||||||||
\(797\) | −30.7118 | −1.08787 | −0.543934 | − | 0.839128i | \(-0.683066\pi\) | ||||
−0.543934 | + | 0.839128i | \(0.683066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.36148 | 0.154298 | ||||||||
\(800\) | −14.3622 | −0.507779 | ||||||||
\(801\) | 3.82713 | 0.135225 | ||||||||
\(802\) | −13.0611 | −0.461204 | ||||||||
\(803\) | −35.3537 | −1.24761 | ||||||||
\(804\) | 2.25641 | 0.0795773 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.9504 | 0.737946 | ||||||||
\(807\) | 9.03201 | 0.317942 | ||||||||
\(808\) | 21.1735 | 0.744880 | ||||||||
\(809\) | −41.2129 | −1.44897 | −0.724484 | − | 0.689291i | \(-0.757922\pi\) | ||||
−0.724484 | + | 0.689291i | \(0.757922\pi\) | |||||||
\(810\) | −0.686727 | −0.0241291 | ||||||||
\(811\) | 37.4927 | 1.31655 | 0.658273 | − | 0.752779i | \(-0.271287\pi\) | ||||
0.658273 | + | 0.752779i | \(0.271287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.05301 | −0.247360 | ||||||||
\(814\) | 26.6620 | 0.934504 | ||||||||
\(815\) | −2.14579 | −0.0751638 | ||||||||
\(816\) | −5.76666 | −0.201874 | ||||||||
\(817\) | −4.58237 | −0.160317 | ||||||||
\(818\) | −15.0027 | −0.524557 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.53287 | 0.123373 | ||||||||
\(821\) | 30.8579 | 1.07695 | 0.538473 | − | 0.842643i | \(-0.319001\pi\) | ||||
0.538473 | + | 0.842643i | \(0.319001\pi\) | |||||||
\(822\) | −19.3698 | −0.675599 | ||||||||
\(823\) | −7.20897 | −0.251289 | −0.125644 | − | 0.992075i | \(-0.540100\pi\) | ||||
−0.125644 | + | 0.992075i | \(0.540100\pi\) | |||||||
\(824\) | −33.0552 | −1.15153 | ||||||||
\(825\) | 11.7975 | 0.410735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.7245 | 1.72909 | 0.864546 | − | 0.502554i | \(-0.167606\pi\) | ||||
0.864546 | + | 0.502554i | \(0.167606\pi\) | |||||||
\(828\) | −0.561916 | −0.0195279 | ||||||||
\(829\) | 22.3658 | 0.776796 | 0.388398 | − | 0.921492i | \(-0.373029\pi\) | ||||
0.388398 | + | 0.921492i | \(0.373029\pi\) | |||||||
\(830\) | 6.97404 | 0.242073 | ||||||||
\(831\) | −11.3120 | −0.392408 | ||||||||
\(832\) | −44.5042 | −1.54291 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.36814 | 0.0473748 | ||||||||
\(835\) | 1.70153 | 0.0588840 | ||||||||
\(836\) | −3.40442 | −0.117744 | ||||||||
\(837\) | 3.45731 | 0.119502 | ||||||||
\(838\) | 38.8411 | 1.34174 | ||||||||
\(839\) | 25.3478 | 0.875102 | 0.437551 | − | 0.899194i | \(-0.355846\pi\) | ||||
0.437551 | + | 0.899194i | \(0.355846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3656 | −0.978123 | ||||||||
\(842\) | −3.31873 | −0.114371 | ||||||||
\(843\) | 22.3499 | 0.769773 | ||||||||
\(844\) | 2.21635 | 0.0762901 | ||||||||
\(845\) | −7.17776 | −0.246922 | ||||||||
\(846\) | −2.32227 | −0.0798414 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.5048 | −0.841497 | ||||||||
\(849\) | 18.4769 | 0.634125 | ||||||||
\(850\) | 12.6187 | 0.432818 | ||||||||
\(851\) | 8.80485 | 0.301826 | ||||||||
\(852\) | 0.238327 | 0.00816494 | ||||||||
\(853\) | 7.98030 | 0.273240 | 0.136620 | − | 0.990624i | \(-0.456376\pi\) | ||||
0.136620 | + | 0.990624i | \(0.456376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.37399 | −0.0469896 | ||||||||
\(856\) | −26.8352 | −0.917207 | ||||||||
\(857\) | 18.6632 | 0.637522 | 0.318761 | − | 0.947835i | \(-0.396733\pi\) | ||||
0.318761 | + | 0.947835i | \(0.396733\pi\) | |||||||
\(858\) | 15.3014 | 0.522383 | ||||||||
\(859\) | 6.59371 | 0.224975 | 0.112487 | − | 0.993653i | \(-0.464118\pi\) | ||||
0.112487 | + | 0.993653i | \(0.464118\pi\) | |||||||
\(860\) | −0.614554 | −0.0209561 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.4796 | 1.54904 | ||||||||
\(863\) | −6.50683 | −0.221495 | −0.110748 | − | 0.993849i | \(-0.535325\pi\) | ||||
−0.110748 | + | 0.993849i | \(0.535325\pi\) | |||||||
\(864\) | −3.07405 | −0.104581 | ||||||||
\(865\) | −6.59585 | −0.224266 | ||||||||
\(866\) | 21.3554 | 0.725685 | ||||||||
\(867\) | 11.9274 | 0.405077 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5581 | 0.426006 | ||||||||
\(870\) | 0.546993 | 0.0185448 | ||||||||
\(871\) | −20.2912 | −0.687541 | ||||||||
\(872\) | 9.19669 | 0.311439 | ||||||||
\(873\) | 15.4364 | 0.522443 | ||||||||
\(874\) | 2.87730 | 0.0973261 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.86733 | −0.265812 | ||||||||
\(877\) | 28.9978 | 0.979186 | 0.489593 | − | 0.871951i | \(-0.337145\pi\) | ||||
0.489593 | + | 0.871951i | \(0.337145\pi\) | |||||||
\(878\) | 46.8072 | 1.57967 | ||||||||
\(879\) | −0.717401 | −0.0241973 | ||||||||
\(880\) | 3.70239 | 0.124808 | ||||||||
\(881\) | −0.393718 | −0.0132647 | −0.00663235 | − | 0.999978i | \(-0.502111\pi\) | ||||
−0.00663235 | + | 0.999978i | \(0.502111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.9604 | 1.91687 | 0.958435 | − | 0.285310i | \(-0.0920964\pi\) | ||||
0.958435 | + | 0.285310i | \(0.0920964\pi\) | |||||||
\(884\) | −6.39508 | −0.215090 | ||||||||
\(885\) | −2.52498 | −0.0848764 | ||||||||
\(886\) | 23.8650 | 0.801761 | ||||||||
\(887\) | 9.84441 | 0.330543 | 0.165271 | − | 0.986248i | \(-0.447150\pi\) | ||||
0.165271 | + | 0.986248i | \(0.447150\pi\) | |||||||
\(888\) | 27.0507 | 0.907763 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.62819 | −0.0880972 | ||||||||
\(891\) | 2.52510 | 0.0845941 | ||||||||
\(892\) | 10.0558 | 0.336692 | ||||||||
\(893\) | −4.64637 | −0.155485 | ||||||||
\(894\) | −9.62170 | −0.321798 | ||||||||
\(895\) | 6.82229 | 0.228044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.05314 | 0.168719 | ||||||||
\(898\) | 38.0534 | 1.26986 | ||||||||
\(899\) | −2.75383 | −0.0918453 | ||||||||
\(900\) | 2.62531 | 0.0875103 | ||||||||
\(901\) | −21.5552 | −0.718109 | ||||||||
\(902\) | 33.2457 | 1.10696 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.1736 | −1.66875 | ||||||||
\(905\) | −14.8802 | −0.494635 | ||||||||
\(906\) | −24.3072 | −0.807551 | ||||||||
\(907\) | −22.2794 | −0.739774 | −0.369887 | − | 0.929077i | \(-0.620604\pi\) | ||||
−0.369887 | + | 0.929077i | \(0.620604\pi\) | |||||||
\(908\) | −10.2143 | −0.338974 | ||||||||
\(909\) | −6.89184 | −0.228588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.74501 | 0.190341 | 0.0951703 | − | 0.995461i | \(-0.469660\pi\) | ||||
0.0951703 | + | 0.995461i | \(0.469660\pi\) | |||||||
\(912\) | 6.14333 | 0.203426 | ||||||||
\(913\) | −25.6436 | −0.848681 | ||||||||
\(914\) | −7.52913 | −0.249041 | ||||||||
\(915\) | 1.21786 | 0.0402613 | ||||||||
\(916\) | −4.03157 | −0.133207 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.70088 | 0.0891424 | ||||||||
\(919\) | 20.0743 | 0.662192 | 0.331096 | − | 0.943597i | \(-0.392582\pi\) | ||||
0.331096 | + | 0.943597i | \(0.392582\pi\) | |||||||
\(920\) | 1.75934 | 0.0580036 | ||||||||
\(921\) | 8.27982 | 0.272829 | ||||||||
\(922\) | −24.5120 | −0.807258 | ||||||||
\(923\) | −2.14320 | −0.0705443 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.1369 | −1.35257 | ||||||||
\(926\) | −9.97059 | −0.327654 | ||||||||
\(927\) | 10.7593 | 0.353380 | ||||||||
\(928\) | 2.44855 | 0.0803775 | ||||||||
\(929\) | −37.1362 | −1.21840 | −0.609199 | − | 0.793017i | \(-0.708509\pi\) | ||||
−0.609199 | + | 0.793017i | \(0.708509\pi\) | |||||||
\(930\) | −2.37423 | −0.0778541 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.08429 | 0.264810 | ||||||||
\(933\) | 8.94613 | 0.292883 | ||||||||
\(934\) | 4.17131 | 0.136489 | ||||||||
\(935\) | 3.25675 | 0.106507 | ||||||||
\(936\) | 15.5245 | 0.507435 | ||||||||
\(937\) | −7.45112 | −0.243418 | −0.121709 | − | 0.992566i | \(-0.538837\pi\) | ||||
−0.121709 | + | 0.992566i | \(0.538837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.93844 | 0.161160 | ||||||||
\(940\) | −0.623138 | −0.0203245 | ||||||||
\(941\) | 21.3759 | 0.696835 | 0.348417 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348417 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(942\) | 7.97371 | 0.259798 | ||||||||
\(943\) | 10.9790 | 0.357527 | ||||||||
\(944\) | 11.2896 | 0.367445 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.78320 | −0.188028 | ||||||||
\(947\) | −8.80385 | −0.286087 | −0.143043 | − | 0.989716i | \(-0.545689\pi\) | ||||
−0.143043 | + | 0.989716i | \(0.545689\pi\) | |||||||
\(948\) | 2.79458 | 0.0907639 | ||||||||
\(949\) | 70.7485 | 2.29659 | ||||||||
\(950\) | −13.4429 | −0.436146 | ||||||||
\(951\) | 15.7414 | 0.510449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2400 | 1.46547 | 0.732734 | − | 0.680515i | \(-0.238244\pi\) | ||||
0.732734 | + | 0.680515i | \(0.238244\pi\) | |||||||
\(954\) | 11.4771 | 0.371584 | ||||||||
\(955\) | 10.3211 | 0.333984 | ||||||||
\(956\) | 0.848930 | 0.0274563 | ||||||||
\(957\) | −2.01130 | −0.0650161 | ||||||||
\(958\) | 24.8876 | 0.804081 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.04350 | 0.162778 | ||||||||
\(961\) | −19.0470 | −0.614419 | ||||||||
\(962\) | −53.3550 | −1.72024 | ||||||||
\(963\) | 8.73468 | 0.281471 | ||||||||
\(964\) | −17.2974 | −0.557113 | ||||||||
\(965\) | 2.68167 | 0.0863261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.60142 | −0.180130 | −0.0900648 | − | 0.995936i | \(-0.528707\pi\) | ||||
−0.0900648 | + | 0.995936i | \(0.528707\pi\) | |||||||
\(968\) | 14.2056 | 0.456587 | ||||||||
\(969\) | 5.40389 | 0.173598 | ||||||||
\(970\) | −10.6006 | −0.340365 | ||||||||
\(971\) | 12.4528 | 0.399628 | 0.199814 | − | 0.979834i | \(-0.435966\pi\) | ||||
0.199814 | + | 0.979834i | \(0.435966\pi\) | |||||||
\(972\) | 0.561916 | 0.0180235 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.5344 | −1.01043 | ||||||||
\(975\) | −23.6086 | −0.756081 | ||||||||
\(976\) | −5.44524 | −0.174298 | ||||||||
\(977\) | −40.1908 | −1.28582 | −0.642909 | − | 0.765942i | \(-0.722273\pi\) | ||||
−0.642909 | + | 0.765942i | \(0.722273\pi\) | |||||||
\(978\) | −4.49353 | −0.143687 | ||||||||
\(979\) | 9.66390 | 0.308860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.99347 | −0.0955740 | ||||||||
\(982\) | −6.41857 | −0.204825 | ||||||||
\(983\) | 46.5198 | 1.48375 | 0.741875 | − | 0.670538i | \(-0.233937\pi\) | ||||
0.741875 | + | 0.670538i | \(0.233937\pi\) | |||||||
\(984\) | 33.7304 | 1.07529 | ||||||||
\(985\) | 12.8731 | 0.410169 | ||||||||
\(986\) | −2.15131 | −0.0685117 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.81279 | 0.216744 | ||||||||
\(989\) | −1.90984 | −0.0607294 | ||||||||
\(990\) | −1.73406 | −0.0551119 | ||||||||
\(991\) | −14.5301 | −0.461565 | −0.230782 | − | 0.973005i | \(-0.574129\pi\) | ||||
−0.230782 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(992\) | −10.6279 | −0.337438 | ||||||||
\(993\) | 27.3344 | 0.867432 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.56547 | −0.0496288 | ||||||||
\(996\) | −5.70653 | −0.180818 | ||||||||
\(997\) | −4.08275 | −0.129302 | −0.0646510 | − | 0.997908i | \(-0.520593\pi\) | ||||
−0.0646510 | + | 0.997908i | \(0.520593\pi\) | |||||||
\(998\) | 46.6003 | 1.47511 | ||||||||
\(999\) | −8.80485 | −0.278573 |
(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.bi.1.7 | 10 | ||
7.2 | even | 3 | 483.2.i.h.277.4 | ✓ | 20 | ||
7.4 | even | 3 | 483.2.i.h.415.4 | yes | 20 | ||
7.6 | odd | 2 | 3381.2.a.bj.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.4 | ✓ | 20 | 7.2 | even | 3 | ||
483.2.i.h.415.4 | yes | 20 | 7.4 | even | 3 | ||
3381.2.a.bi.1.7 | 10 | 1.1 | even | 1 | trivial | ||
3381.2.a.bj.1.7 | 10 | 7.6 | odd | 2 |